LMFDB - Embedded newform 48.7.l.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	48.19
Dual form			48.7.l.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.47563 + 2.84868i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(47.7700 - 42.5914i) q^{4} +(-55.7840 + 55.7840i) q^{5} +(51.0014 - 113.802i) q^{6} +496.753 q^{7} +(-235.781 + 454.479i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(-7.47563 + 2.84868i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(47.7700 - 42.5914i) q^{4} +(-55.7840 + 55.7840i) q^{5} +(51.0014 - 113.802i) q^{6} +496.753 q^{7} +(-235.781 + 454.479i) q^{8} -243.000i q^{9} +(258.109 - 575.931i) q^{10} +(694.522 + 694.522i) q^{11} +(-57.0825 + 996.027i) q^{12} +(214.555 + 214.555i) q^{13} +(-3713.54 + 1415.09i) q^{14} -1229.78i q^{15} +(467.948 - 4069.18i) q^{16} -4131.33 q^{17} +(692.230 + 1816.58i) q^{18} +(-7221.52 + 7221.52i) q^{19} +(-288.885 + 5040.72i) q^{20} +(-5475.56 + 5475.56i) q^{21} +(-7170.46 - 3213.52i) q^{22} -20205.1 q^{23} +(-2410.64 - 7608.54i) q^{24} +9401.30i q^{25} +(-2215.13 - 992.733i) q^{26} +(2678.52 + 2678.52i) q^{27} +(23729.9 - 21157.4i) q^{28} +(25794.6 + 25794.6i) q^{29} +(3503.25 + 9193.38i) q^{30} -35543.8i q^{31} +(8093.60 + 31752.7i) q^{32} -15311.0 q^{33} +(30884.3 - 11768.8i) q^{34} +(-27710.9 + 27710.9i) q^{35} +(-10349.7 - 11608.1i) q^{36} +(-12024.7 + 12024.7i) q^{37} +(33413.6 - 74557.2i) q^{38} -4729.95 q^{39} +(-12199.8 - 38505.5i) q^{40} +5598.69i q^{41} +(25335.1 - 56531.4i) q^{42} +(-12263.5 - 12263.5i) q^{43} +(62758.0 + 3596.67i) q^{44} +(13555.5 + 13555.5i) q^{45} +(151046. - 57557.9i) q^{46} +126271. i q^{47} +(39695.3 + 50011.4i) q^{48} +129115. q^{49} +(-26781.3 - 70280.6i) q^{50} +(45538.4 - 45538.4i) q^{51} +(19387.5 + 1111.10i) q^{52} +(-69107.7 + 69107.7i) q^{53} +(-27653.8 - 12393.4i) q^{54} -77486.4 q^{55} +(-117125. + 225764. i) q^{56} -159201. i q^{57} +(-266311. - 119350. i) q^{58} +(-101232. - 101232. i) q^{59} +(-52378.0 - 58746.6i) q^{60} +(123707. + 123707. i) q^{61} +(101253. + 265712. i) q^{62} -120711. i q^{63} +(-150958. - 214315. i) q^{64} -23937.4 q^{65} +(114460. - 43616.3i) q^{66} +(-394365. + 394365. i) q^{67} +(-197354. + 175959. i) q^{68} +(222715. - 222715. i) q^{69} +(128217. - 286095. i) q^{70} -264238. q^{71} +(110438. + 57294.9i) q^{72} +230983. i q^{73} +(55637.8 - 124147. i) q^{74} +(-103628. - 103628. i) q^{75} +(-37397.6 + 652547. i) q^{76} +(345006. + 345006. i) q^{77} +(35359.3 - 13474.1i) q^{78} -278466. i q^{79} +(200891. + 253099. i) q^{80} -59049.0 q^{81} +(-15948.9 - 41853.7i) q^{82} +(605066. - 605066. i) q^{83} +(-28355.9 + 494779. i) q^{84} +(230462. - 230462. i) q^{85} +(126612. + 56742.5i) q^{86} -568652. q^{87} +(-479401. + 151890. i) q^{88} -526452. i q^{89} +(-139951. - 62720.6i) q^{90} +(106581. + 106581. i) q^{91} +(-965197. + 860562. i) q^{92} +(391789. + 391789. i) q^{93} +(-359705. - 943952. i) q^{94} -805690. i q^{95} +(-439214. - 260788. i) q^{96} +840241. q^{97} +(-965212. + 367806. i) q^{98} +(168769. - 168769. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−7.47563	+	2.84868i	−0.934453	+	0.356085i
$2$	−7.47563	+	2.84868i	−0.934453	+	0.356085i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$4$	47.7700	−	42.5914i	0.746406	−	0.665490i
$5$	−55.7840	+	55.7840i	−0.446272	+	0.446272i	−0.894113	−	0.447841i	$-0.852193\pi$
$5$	−55.7840	+	55.7840i	−0.446272	+	0.446272i	0.447841	+	0.894113i	$0.352193\pi$
$6$	51.0014	−	113.802i	0.236118	−	0.526860i
$7$	496.753			1.44826			0.724130	−	0.689664i	$-0.242242\pi$
$7$	496.753			1.44826			0.724130	+	0.689664i	$0.242242\pi$
$8$	−235.781	+	454.479i	−0.460511	+	0.887654i
$9$		−	243.000i		−	0.333333i
$10$	258.109	−	575.931i	0.258109	−	0.575931i
$11$	694.522	+	694.522i	0.521805	+	0.521805i	0.918116	−	0.396311i	$-0.129710\pi$
$11$	694.522	+	694.522i	0.521805	+	0.521805i	−0.396311	+	0.918116i	$0.629710\pi$
$12$	−57.0825	+	996.027i	−0.0330339	+	0.576404i
$13$	214.555	+	214.555i	0.0976581	+	0.0976581i	0.754248	−	0.656590i	$-0.228002\pi$
$13$	214.555	+	214.555i	0.0976581	+	0.0976581i	−0.656590	+	0.754248i	$0.728002\pi$
$14$	−3713.54	+	1415.09i	−1.35333	+	0.515704i
$15$		−	1229.78i		−	0.364379i
$16$	467.948	−	4069.18i	0.114245	−	0.993453i
$17$	−4131.33			−0.840897			−0.420449	−	0.907316i	$-0.638127\pi$
$17$	−4131.33			−0.840897			−0.420449	+	0.907316i	$0.638127\pi$
$18$	692.230	+	1816.58i	0.118695	+	0.311484i
$19$	−7221.52	+	7221.52i	−1.05285	+	1.05285i	−0.0543305	+	0.998523i	$0.517302\pi$
$19$	−7221.52	+	7221.52i	−1.05285	+	1.05285i	−0.998523	+	0.0543305i	$0.982698\pi$
$20$	−288.885	+	5040.72i	−0.0361106	+	0.630090i
$21$	−5475.56	+	5475.56i	−0.591249	+	0.591249i
$22$	−7170.46	−	3213.52i	−0.673409	−	0.301795i
$23$	−20205.1			−1.66065			−0.830323	−	0.557283i	$-0.811844\pi$
$23$	−20205.1			−1.66065			−0.830323	+	0.557283i	$0.811844\pi$
$24$	−2410.64	−	7608.54i	−0.174381	−	0.550386i
$25$			9401.30i			0.601683i
$26$	−2215.13	−	992.733i	−0.126032	−	0.0564823i
$27$	2678.52	+	2678.52i	0.136083	+	0.136083i
$28$	23729.9	−	21157.4i	1.08099	−	0.963803i
$29$	25794.6	+	25794.6i	1.05763	+	1.05763i	0.998234	+	0.0593977i	$0.0189180\pi$
$29$	25794.6	+	25794.6i	1.05763	+	1.05763i	0.0593977	+	0.998234i	$0.481082\pi$
$30$	3503.25	+	9193.38i	0.129750	+	0.340496i
$31$		−	35543.8i		−	1.19311i	−0.802574	−	0.596553i	$-0.796537\pi$
$31$		−	35543.8i		−	1.19311i	0.802574	−	0.596553i	$-0.203463\pi$
$32$	8093.60	+	31752.7i	0.246997	+	0.969016i
$33$	−15311.0			−0.426052
$34$	30884.3	−	11768.8i	0.785779	−	0.299431i
$35$	−27710.9	+	27710.9i	−0.646317	+	0.646317i
$36$	−10349.7	−	11608.1i	−0.221830	−	0.248802i
$37$	−12024.7	+	12024.7i	−0.237394	+	0.237394i	−0.815770	−	0.578376i	$-0.803687\pi$
$37$	−12024.7	+	12024.7i	−0.237394	+	0.237394i	0.578376	+	0.815770i	$0.303687\pi$
$38$	33413.6	−	74557.2i	0.608937	−	1.35875i
$39$	−4729.95			−0.0797375
$40$	−12199.8	−	38505.5i	−0.190622	−	0.601648i
$41$			5598.69i			0.0812335i	0.999175	+	0.0406167i	$0.0129323\pi$
$41$			5598.69i			0.0812335i	−0.999175	+	0.0406167i	$0.987068\pi$
$42$	25335.1	−	56531.4i	0.341960	−	0.763030i
$43$	−12263.5	−	12263.5i	−0.154244	−	0.154244i	0.625766	−	0.780010i	$-0.284786\pi$
$43$	−12263.5	−	12263.5i	−0.154244	−	0.154244i	−0.780010	+	0.625766i	$0.784786\pi$
$44$	62758.0	+	3596.67i	0.736735	+	0.0422224i
$45$	13555.5	+	13555.5i	0.148757	+	0.148757i
$46$	151046.	−	57557.9i	1.55180	−	0.591332i
$47$			126271.i			1.21621i	0.793857	+	0.608105i	$0.208070\pi$
$47$			126271.i			1.21621i	−0.793857	+	0.608105i	$0.791930\pi$
$48$	39695.3	+	50011.4i	0.358935	+	0.452216i
$49$	129115.			1.09746
$50$	−26781.3	−	70280.6i	−0.214250	−	0.562245i
$51$	45538.4	−	45538.4i	0.343295	−	0.343295i
$52$	19387.5	+	1111.10i	0.137883	+	0.00790211i
$53$	−69107.7	+	69107.7i	−0.464193	+	0.464193i	−0.900027	−	0.435834i	$-0.856454\pi$
$53$	−69107.7	+	69107.7i	−0.464193	+	0.464193i	0.435834	+	0.900027i	$0.356454\pi$
$54$	−27653.8	−	12393.4i	−0.175620	−	0.0787059i
$55$	−77486.4			−0.465734
$56$	−117125.	+	225764.i	−0.666939	+	1.28555i
$57$		−	159201.i		−	0.859651i
$58$	−266311.	−	119350.i	−1.36492	−	0.611701i
$59$	−101232.	−	101232.i	−0.492903	−	0.492903i	0.416316	−	0.909220i	$-0.363321\pi$
$59$	−101232.	−	101232.i	−0.492903	−	0.492903i	−0.909220	+	0.416316i	$0.863321\pi$
$60$	−52378.0	−	58746.6i	−0.242491	−	0.271975i
$61$	123707.	+	123707.i	0.545011	+	0.545011i	0.924994	−	0.379982i	$-0.124070\pi$
$61$	123707.	+	123707.i	0.545011	+	0.545011i	−0.379982	+	0.924994i	$0.624070\pi$
$62$	101253.	+	265712.i	0.424847	+	1.11490i
$63$		−	120711.i		−	0.482753i
$64$	−150958.	−	214315.i	−0.575860	−	0.817549i
$65$	−23937.4			−0.0871641
$66$	114460.	−	43616.3i	0.398126	−	0.151711i
$67$	−394365.	+	394365.i	−1.31121	+	1.31121i	−0.390694	+	0.920521i	$0.627765\pi$
$67$	−394365.	+	394365.i	−1.31121	+	1.31121i	−0.920521	+	0.390694i	$0.872235\pi$
$68$	−197354.	+	175959.i	−0.627651	+	0.559609i
$69$	222715.	−	222715.i	0.677956	−	0.677956i
$70$	128217.	−	286095.i	0.373809	−	0.834098i
$71$	−264238.			−0.738280			−0.369140	−	0.929374i	$-0.620348\pi$
$71$	−264238.			−0.738280			−0.369140	+	0.929374i	$0.620348\pi$
$72$	110438.	+	57294.9i	0.295885	+	0.153504i
$73$			230983.i			0.593761i	0.954915	+	0.296880i	$0.0959462\pi$
$73$			230983.i			0.593761i	−0.954915	+	0.296880i	$0.904054\pi$
$74$	55637.8	−	124147.i	0.137301	−	0.306367i
$75$	−103628.	−	103628.i	−0.245636	−	0.245636i
$76$	−37397.6	+	652547.i	−0.0851928	+	1.48652i
$77$	345006.	+	345006.i	0.755709	+	0.755709i
$78$	35359.3	−	13474.1i	0.0745110	−	0.0283933i
$79$		−	278466.i		−	0.564795i	−0.959297	−	0.282398i	$-0.908870\pi$
$79$		−	278466.i		−	0.564795i	0.959297	−	0.282398i	$-0.0911298\pi$
$80$	200891.	+	253099.i	0.392365	+	0.494334i
$81$	−59049.0			−0.111111
$82$	−15948.9	−	41853.7i	−0.0289261	−	0.0759089i
$83$	605066.	−	605066.i	1.05820	−	1.05820i	0.0600039	−	0.998198i	$-0.480889\pi$
$83$	605066.	−	605066.i	1.05820	−	1.05820i	0.998198	−	0.0600039i	$-0.0191113\pi$
$84$	−28355.9	+	494779.i	−0.0478416	+	0.834783i
$85$	230462.	−	230462.i	0.375269	−	0.375269i
$86$	126612.	+	56742.5i	0.199058	+	0.0892098i
$87$	−568652.			−0.863553
$88$	−479401.	+	151890.i	−0.703479	+	0.222885i
$89$		−	526452.i		−	0.746773i	−0.927676	−	0.373386i	$-0.878197\pi$
$89$		−	526452.i		−	0.746773i	0.927676	−	0.373386i	$-0.121803\pi$
$90$	−139951.	−	62720.6i	−0.191977	−	0.0860365i
$91$	106581.	+	106581.i	0.141434	+	0.141434i
$92$	−965197.	+	860562.i	−1.23952	+	1.10514i
$93$	391789.	+	391789.i	0.487083	+	0.487083i
$94$	−359705.	−	943952.i	−0.433075	−	1.13649i
$95$		−	805690.i		−	0.939718i
$96$	−439214.	−	260788.i	−0.496435	−	0.294763i
$97$	840241.			0.920637			0.460319	−	0.887754i	$-0.347735\pi$
$97$	840241.			0.920637			0.460319	+	0.887754i	$0.347735\pi$
$98$	−965212.	+	367806.i	−1.02552	+	0.390788i
$99$	168769.	−	168769.i	0.173935	−	0.173935i
$100$	400414.	+	449100.i	0.400414	+	0.449100i
$101$	−222739.	+	222739.i	−0.216188	+	0.216188i	−0.806890	−	0.590702i	$-0.798851\pi$
$101$	−222739.	+	222739.i	−0.216188	+	0.216188i	0.590702	+	0.806890i	$0.298851\pi$
$102$	−210704.	+	470153.i	−0.198551	+	0.443035i
$103$	−660421.			−0.604379			−0.302189	−	0.953248i	$-0.597717\pi$
$103$	−660421.			−0.604379			−0.302189	+	0.953248i	$0.597717\pi$
$104$	−148099.	+	46922.6i	−0.131659	+	0.0417140i
$105$		−	610897.i		−	0.527716i
$106$	319758.	−	713490.i	0.268475	−	0.599060i
$107$	−79564.2	−	79564.2i	−0.0649481	−	0.0649481i	0.673887	−	0.738835i	$-0.264624\pi$
$107$	−79564.2	−	79564.2i	−0.0649481	−	0.0649481i	−0.738835	+	0.673887i	$0.764624\pi$
$108$	242035.	+	13871.1i	0.192135	+	0.0110113i
$109$	1.17937e6	+	1.17937e6i	0.910694	+	0.910694i	0.996327	−	0.0856332i	$-0.0272913\pi$
$109$	1.17937e6	+	1.17937e6i	0.910694	+	0.910694i	−0.0856332	+	0.996327i	$0.527291\pi$
$110$	579260.	−	220734.i	0.435206	−	0.165841i
$111$		−	265090.i		−	0.193832i
$112$	232455.	−	2.02138e6i	0.165457	−	1.43878i
$113$	2.00498e6			1.38955			0.694777	−	0.719226i	$-0.255503\pi$
$113$	2.00498e6			1.38955			0.694777	+	0.719226i	$0.255503\pi$
$114$	453514.	+	1.19013e6i	0.306109	+	0.803304i
$115$	1.12712e6	−	1.12712e6i	0.741099	−	0.741099i
$116$	2.33084e6	+	133581.i	1.49327	+	0.0855795i
$117$	52136.8	−	52136.8i	0.0325527	−	0.0325527i
$118$	1.04515e6	+	468395.i	0.636111	+	0.285080i
$119$	−2.05225e6			−1.21784
$120$	558909.	+	289959.i	0.323443	+	0.167801i
$121$		−	806839.i		−	0.455439i
$122$	−1.27719e6	−	572387.i	−0.703358	−	0.315217i
$123$	−61712.7	−	61712.7i	−0.0331634	−	0.0331634i
$124$	−1.51386e6	−	1.69793e6i	−0.794000	−	0.890542i
$125$	−1.39607e6	−	1.39607e6i	−0.714786	−	0.714786i
$126$	343867.	+	902390.i	0.171901	+	0.451110i
$127$			3.68727e6i			1.80009i	0.435800	+	0.900043i	$0.356465\pi$
$127$			3.68727e6i			1.80009i	−0.435800	+	0.900043i	$0.643535\pi$
$128$	1.73902e6	+	1.17211e6i	0.829231	+	0.558906i
$129$	270353.			0.125940
$130$	178947.	−	68190.2i	0.0814508	−	0.0310378i
$131$	1.70561e6	−	1.70561e6i	0.758691	−	0.758691i	−0.217393	−	0.976084i	$-0.569755\pi$
$131$	1.70561e6	−	1.70561e6i	0.758691	−	0.758691i	0.976084	+	0.217393i	$0.0697554\pi$
$132$	−731408.	+	652118.i	−0.318008	+	0.283533i
$133$	−3.58731e6	+	3.58731e6i	−1.52481	+	1.52481i
$134$	1.82470e6	−	4.07155e6i	0.758365	−	1.69217i
$135$	−298837.			−0.121460
$136$	974091.	−	1.87760e6i	0.387242	−	0.746426i
$137$		−	2.48475e6i		−	0.966318i	−0.875533	−	0.483159i	$-0.839489\pi$
$137$		−	2.48475e6i		−	0.966318i	0.875533	−	0.483159i	$-0.160511\pi$
$138$	−1.03049e6	+	2.29937e6i	−0.392108	+	0.874928i
$139$	3.44106e6	+	3.44106e6i	1.28129	+	1.28129i	0.939933	+	0.341359i	$0.110887\pi$
$139$	3.44106e6	+	3.44106e6i	1.28129	+	1.28129i	0.341359	+	0.939933i	$0.389113\pi$
$140$	−143504.	+	2.50399e6i	−0.0522975	+	0.912533i
$141$	−1.39184e6	−	1.39184e6i	−0.496516	−	0.496516i
$142$	1.97535e6	−	752731.i	0.689888	−	0.262891i
$143$			298026.i			0.101917i
$144$	−988811.	−	113711.i	−0.331151	−	0.0380817i
$145$	−2.87785e6			−0.943983
$146$	−657997.	−	1.72674e6i	−0.211429	−	0.554842i
$147$	−1.42319e6	+	1.42319e6i	−0.448034	+	0.448034i
$148$	−62271.7	+	1.08657e6i	−0.0192090	+	0.335176i
$149$	−2.43736e6	+	2.43736e6i	−0.736819	+	0.736819i	−0.971961	−	0.235142i	$-0.924444\pi$
$149$	−2.43736e6	+	2.43736e6i	−0.736819	+	0.736819i	0.235142	+	0.971961i	$0.424444\pi$
$150$	1.06988e6	+	479480.i	0.317003	+	0.142068i
$151$	−6.62460e6			−1.92411			−0.962053	−	0.272863i	$-0.912029\pi$
$151$	−6.62460e6			−1.92411			−0.962053	+	0.272863i	$0.912029\pi$
$152$	−1.57933e6	−	4.98473e6i	−0.449719	−	1.41942i
$153$			1.00391e6i			0.280299i
$154$	−3.56195e6	−	1.59632e6i	−0.975271	−	0.437078i
$155$	1.98278e6	+	1.98278e6i	0.532449	+	0.532449i
$156$	−225950.	+	201455.i	−0.0595166	+	0.0530645i
$157$	3.45318e6	+	3.45318e6i	0.892320	+	0.892320i	0.994741	−	0.102421i	$-0.0326588\pi$
$157$	3.45318e6	+	3.45318e6i	0.892320	+	0.892320i	−0.102421	+	0.994741i	$0.532659\pi$
$158$	793262.	+	2.08171e6i	0.201115	+	0.527775i
$159$		−	1.52351e6i		−	0.379012i
$160$	−2.22279e6	−	1.31980e6i	−0.542672	−	0.322217i
$161$	−1.00369e7			−2.40505
$162$	441428.	−	168212.i	0.103828	−	0.0395650i
$163$	−1.39390e6	+	1.39390e6i	−0.321860	+	0.321860i	−0.849480	−	0.527620i	$-0.823084\pi$
$163$	−1.39390e6	+	1.39390e6i	−0.321860	+	0.321860i	0.527620	+	0.849480i	$0.323084\pi$
$164$	238456.	+	267450.i	0.0540601	+	0.0606332i
$165$	854110.	−	854110.i	0.190135	−	0.190135i
$166$	−2.79961e6	+	6.24689e6i	−0.612030	+	1.36565i
$167$	6.08424e6			1.30634			0.653171	−	0.757211i	$-0.273438\pi$
$167$	6.08424e6			1.30634			0.653171	+	0.757211i	$0.273438\pi$
$168$	−1.19749e6	−	3.77956e6i	−0.252548	−	0.797102i
$169$		−	4.73474e6i		−	0.980926i
$170$	−1.06633e6	+	2.37936e6i	−0.217043	+	0.484299i
$171$	1.75483e6	+	1.75483e6i	0.350951	+	0.350951i
$172$	−1.10815e6	−	63508.1i	−0.217777	−	0.0124808i
$173$	1.58288e6	+	1.58288e6i	0.305710	+	0.305710i	0.843243	−	0.537533i	$-0.180644\pi$
$173$	1.58288e6	+	1.58288e6i	0.305710	+	0.305710i	−0.537533	+	0.843243i	$0.680644\pi$
$174$	4.25103e6	−	1.61991e6i	0.806950	−	0.307499i
$175$			4.67012e6i			0.871393i
$176$	3.15114e6	−	2.50114e6i	0.578002	−	0.458775i
$177$	2.23170e6			0.402454
$178$	1.49969e6	+	3.93556e6i	0.265915	+	0.697824i
$179$	5.83249e6	−	5.83249e6i	1.01694	−	1.01694i	0.0170847	−	0.999854i	$-0.494561\pi$
$179$	5.83249e6	−	5.83249e6i	1.01694	−	1.01694i	0.999854	−	0.0170847i	$-0.00543851\pi$
$180$	1.22489e6	+	70199.0i	0.210030	+	0.0120369i
$181$	1.51655e6	−	1.51655e6i	0.255754	−	0.255754i	−0.567571	−	0.823325i	$-0.692117\pi$
$181$	1.51655e6	−	1.51655e6i	0.255754	−	0.255754i	0.823325	+	0.567571i	$0.192117\pi$
$182$	−1.10037e6	−	493143.i	−0.182526	−	0.0818010i
$183$	−2.72718e6			−0.445000
$184$	4.76398e6	−	9.18278e6i	0.764745	−	1.47408i
$185$		−	1.34157e6i		−	0.211885i
$186$	−4.04495e6	−	1.81279e6i	−0.628600	−	0.281713i
$187$	−2.86930e6	−	2.86930e6i	−0.438784	−	0.438784i
$188$	5.37804e6	+	6.03195e6i	0.809376	+	0.907787i
$189$	1.33056e6	+	1.33056e6i	0.197083	+	0.197083i
$190$	2.29516e6	+	6.02304e6i	0.334620	+	0.878122i
$191$		−	8.72584e6i		−	1.25230i	−0.779704	−	0.626148i	$-0.784631\pi$
$191$		−	8.72584e6i		−	1.25230i	0.779704	−	0.626148i	$-0.215369\pi$
$192$	4.02630e6	+	698368.i	0.568857	+	0.0986690i
$193$	3.56415e6			0.495774			0.247887	−	0.968789i	$-0.420264\pi$
$193$	3.56415e6			0.495774			0.247887	+	0.968789i	$0.420264\pi$
$194$	−6.28133e6	+	2.39358e6i	−0.860293	+	0.327825i
$195$	263855.	−	263855.i	0.0355846	−	0.0355846i
$196$	6.16780e6	−	5.49917e6i	0.819148	−	0.730346i
$197$	−5.20680e6	+	5.20680e6i	−0.681039	+	0.681039i	−0.960234	−	0.279195i	$-0.909932\pi$
$197$	−5.20680e6	+	5.20680e6i	−0.681039	+	0.681039i	0.279195	+	0.960234i	$0.409932\pi$
$198$	−780884.	+	1.74242e6i	−0.100598	+	0.224470i
$199$	6.78464e6			0.860929			0.430464	−	0.902608i	$-0.358350\pi$
$199$	6.78464e6			0.860929			0.430464	+	0.902608i	$0.358350\pi$
$200$	−4.27269e6	−	2.21665e6i	−0.534086	−	0.277081i
$201$		−	8.69393e6i		−	1.07060i
$202$	1.03060e6	−	2.29963e6i	0.125036	−	0.279000i
$203$	1.28135e7	+	1.28135e7i	1.53173	+	1.53173i
$204$	235827.	−	4.11491e6i	0.0277781	−	0.484697i
$205$	−312317.	−	312317.i	−0.0362522	−	0.0362522i
$206$	4.93706e6	−	1.88133e6i	0.564764	−	0.215210i
$207$			4.90983e6i			0.553549i
$208$	973463.	−	772662.i	0.108176	−	0.0858617i
$209$	−1.00310e7			−1.09877
$210$	1.74025e6	+	4.56684e6i	0.187912	+	0.493126i
$211$	6.46771e6	−	6.46771e6i	0.688499	−	0.688499i	−0.273401	−	0.961900i	$-0.588149\pi$
$211$	6.46771e6	−	6.46771e6i	0.688499	−	0.688499i	0.961900	+	0.273401i	$0.0881487\pi$
$212$	−357883.	+	6.24467e6i	−0.0375607	+	0.655393i
$213$	2.91262e6	−	2.91262e6i	0.301401	−	0.301401i
$214$	821445.	+	368139.i	0.0838180	+	0.0375639i
$215$	1.36821e6			0.137670
$216$	−1.84887e6	+	585785.i	−0.183462	+	0.0581269i
$217$		−	1.76565e7i		−	1.72793i
$218$	−1.21762e7	−	5.45690e6i	−1.17529	−	0.526716i
$219$	−2.54606e6	−	2.54606e6i	−0.242402	−	0.242402i
$220$	−3.70153e6	+	3.30025e6i	−0.347627	+	0.309941i
$221$	−886396.	−	886396.i	−0.0821204	−	0.0821204i
$222$	755158.	+	1.98172e6i	0.0690206	+	0.181127i
$223$		−	9.39293e6i		−	0.847006i	−0.905895	−	0.423503i	$-0.860800\pi$
$223$		−	9.39293e6i		−	0.847006i	0.905895	−	0.423503i	$-0.139200\pi$
$224$	4.02052e6	+	1.57733e7i	0.357716	+	1.40339i
$225$	2.28452e6			0.200561
$226$	−1.49885e7	+	5.71156e6i	−1.29847	+	0.494799i
$227$	1.85693e6	−	1.85693e6i	0.158751	−	0.158751i	−0.623262	−	0.782013i	$-0.714193\pi$
$227$	1.85693e6	−	1.85693e6i	0.158751	−	0.158751i	0.782013	+	0.623262i	$0.214193\pi$
$228$	−6.78061e6	−	7.60505e6i	−0.572090	−	0.641649i
$229$	−2.24949e6	+	2.24949e6i	−0.187317	+	0.187317i	−0.794535	−	0.607218i	$-0.792285\pi$
$229$	−2.24949e6	+	2.24949e6i	−0.187317	+	0.187317i	0.607218	+	0.794535i	$0.292285\pi$
$230$	−5.21512e6	+	1.16367e7i	−0.428628	+	0.956417i
$231$	−7.60580e6			−0.617034
$232$	−1.78050e7	+	5.64121e6i	−1.42586	+	0.451761i
$233$			1.06680e7i			0.843363i	0.906744	+	0.421681i	$0.138560\pi$
$233$			1.06680e7i			0.843363i	−0.906744	+	0.421681i	$0.861440\pi$
$234$	−241234.	+	538277.i	−0.0188274	+	0.0420105i
$235$	−7.04387e6	−	7.04387e6i	−0.542760	−	0.542760i
$236$	−9.14747e6	−	524243.i	−0.695929	−	0.0398838i
$237$	3.06945e6	+	3.06945e6i	0.230577	+	0.230577i
$238$	1.53419e7	−	5.84621e6i	1.13801	−	0.433654i
$239$			3.18359e6i			0.233198i	0.993179	+	0.116599i	$0.0371992\pi$
$239$			3.18359e6i			0.233198i	−0.993179	+	0.116599i	$0.962801\pi$
$240$	−5.00420e6	−	575474.i	−0.361994	−	0.0416286i
$241$	2.52000e7			1.80032			0.900158	−	0.435564i	$-0.143451\pi$
$241$	2.52000e7			1.80032			0.900158	+	0.435564i	$0.143451\pi$
$242$	2.29843e6	+	6.03163e6i	0.162175	+	0.425587i
$243$	650880.	−	650880.i	0.0453609	−	0.0453609i
$244$	1.11784e7	+	640634.i	0.769500	+	0.0441002i
$245$	−7.20252e6	+	7.20252e6i	−0.489763	+	0.489763i
$246$	637142.	+	285541.i	0.0427987	+	0.0191807i
$247$	−3.09882e6			−0.205639
$248$	1.61539e7	+	8.38057e6i	1.05907	+	0.549438i
$249$			1.33389e7i			0.864018i
$250$	1.44134e7	+	6.45952e6i	0.922459	+	0.413409i
$251$	−903606.	−	903606.i	−0.0571423	−	0.0571423i	0.677958	−	0.735100i	$-0.262865\pi$
$251$	−903606.	−	903606.i	−0.0571423	−	0.0571423i	−0.735100	+	0.677958i	$0.762865\pi$
$252$	−5.14125e6	−	5.76636e6i	−0.321268	−	0.360330i
$253$	−1.40329e7	−	1.40329e7i	−0.866533	−	0.866533i
$254$	−1.05039e7	−	2.75646e7i	−0.640984	−	1.68210i
$255$			5.08063e6i			0.306406i
$256$	−1.63393e7	−	3.80833e6i	−0.973896	−	0.226994i
$257$	−909145.			−0.0535591			−0.0267796	−	0.999641i	$-0.508525\pi$
$257$	−909145.			−0.0535591			−0.0267796	+	0.999641i	$0.508525\pi$
$258$	−2.02106e6	+	770151.i	−0.117685	+	0.0448453i
$259$	−5.97332e6	+	5.97332e6i	−0.343809	+	0.343809i
$260$	−1.14349e6	+	1.01953e6i	−0.0650598	+	0.0580068i
$261$	6.26809e6	−	6.26809e6i	0.352544	−	0.352544i
$262$	−7.89174e6	+	1.76092e7i	−0.438803	+	0.979120i
$263$	−1.10225e7			−0.605915			−0.302957	−	0.953004i	$-0.597974\pi$
$263$	−1.10225e7			−0.605915			−0.302957	+	0.953004i	$0.597974\pi$
$264$	3.61006e6	−	6.95854e6i	0.196201	−	0.378187i
$265$		−	7.71021e6i		−	0.414313i
$266$	1.65983e7	−	3.70365e7i	0.881899	−	1.96782i
$267$	5.80292e6	+	5.80292e6i	0.304869	+	0.304869i
$268$	−2.04227e6	+	3.56354e7i	−0.106098	+	1.85130i
$269$	1.78576e7	+	1.78576e7i	0.917416	+	0.917416i	0.996841	−	0.0794249i	$-0.0253084\pi$
$269$	1.78576e7	+	1.78576e7i	0.917416	+	0.917416i	−0.0794249	+	0.996841i	$0.525308\pi$
$270$	2.23399e6	−	851291.i	0.113499	−	0.0432501i
$271$		−	2.40422e6i		−	0.120800i	−0.998174	−	0.0604000i	$-0.980762\pi$
$271$		−	2.40422e6i		−	0.120800i	0.998174	−	0.0604000i	$-0.0192376\pi$
$272$	−1.93325e6	+	1.68111e7i	−0.0960685	+	0.835392i
$273$	−2.34962e6			−0.115481
$274$	7.07825e6	+	1.85750e7i	0.344092	+	0.902980i
$275$	−6.52941e6	+	6.52941e6i	−0.313961	+	0.313961i
$276$	1.15336e6	−	2.01248e7i	0.0548576	−	0.957204i
$277$	6.70939e6	−	6.70939e6i	0.315678	−	0.315678i	−0.531427	−	0.847104i	$-0.678344\pi$
$277$	6.70939e6	−	6.70939e6i	0.315678	−	0.315678i	0.847104	+	0.531427i	$0.178344\pi$
$278$	−3.55266e7	−	1.59216e7i	−1.65356	−	0.741058i
$279$	−8.63715e6			−0.397702
$280$	−6.06029e6	−	1.91277e7i	−0.276070	−	0.871342i
$281$			1.26165e7i			0.568616i	0.958733	+	0.284308i	$0.0917638\pi$
$281$			1.26165e7i			0.568616i	−0.958733	+	0.284308i	$0.908236\pi$
$282$	1.43698e7	+	6.43998e6i	0.640773	+	0.287169i
$283$	−1.79614e7	−	1.79614e7i	−0.792464	−	0.792464i	0.189430	−	0.981894i	$-0.439336\pi$
$283$	−1.79614e7	−	1.79614e7i	−0.792464	−	0.792464i	−0.981894	+	0.189430i	$0.939336\pi$
$284$	−1.26227e7	+	1.12543e7i	−0.551057	+	0.491318i
$285$	8.88089e6	+	8.88089e6i	0.383638	+	0.383638i
$286$	−848982.	−	2.22793e6i	−0.0362911	−	0.0952366i
$287$			2.78117e6i			0.117647i
$288$	7.71591e6	−	1.96674e6i	0.323005	−	0.0823324i
$289$	−7.06970e6			−0.292892
$290$	2.15137e7	−	8.19808e6i	0.882108	−	0.336138i
$291$	−9.26173e6	+	9.26173e6i	−0.375849	+	0.375849i
$292$	9.83788e6	+	1.10341e7i	0.395142	+	0.443187i
$293$	1.10111e7	−	1.10111e7i	0.437752	−	0.437752i	−0.453503	−	0.891255i	$-0.649826\pi$
$293$	1.10111e7	−	1.10111e7i	0.437752	−	0.437752i	0.891255	+	0.453503i	$0.149826\pi$
$294$	6.58503e6	−	1.46935e7i	0.259129	−	0.578206i
$295$	1.12942e7			0.439938
$296$	−2.62978e6	−	8.30020e6i	−0.101401	−	0.320047i
$297$			3.72058e6i			0.142017i
$298$	1.12775e7	−	2.51641e7i	0.426153	−	0.950894i
$299$	−4.33510e6	−	4.33510e6i	−0.162175	−	0.162175i
$300$	−9.36394e6	−	536650.i	−0.346813	−	0.0198759i
$301$	−6.09192e6	−	6.09192e6i	−0.223385	−	0.223385i
$302$	4.95231e7	−	1.88714e7i	1.79799	−	0.685146i
$303$		−	4.91037e6i		−	0.176517i
$304$	2.60064e7	+	3.27650e7i	0.925677	+	1.16624i
$305$	−1.38018e7			−0.486446
$306$	−2.85983e6	−	7.50488e6i	−0.0998104	−	0.261926i
$307$	−3.55938e7	+	3.55938e7i	−1.23015	+	1.23015i	−0.266250	+	0.963904i	$0.585785\pi$
$307$	−3.55938e7	+	3.55938e7i	−1.23015	+	1.23015i	−0.963904	+	0.266250i	$0.914215\pi$
$308$	3.11752e7	+	1.78666e6i	1.06698	+	0.0611490i
$309$	7.27962e6	−	7.27962e6i	0.246737	−	0.246737i
$310$	−2.04708e7	−	9.17419e6i	−0.687147	−	0.307952i
$311$	1.92583e7			0.640230			0.320115	−	0.947379i	$-0.396278\pi$
$311$	1.92583e7			0.640230			0.320115	+	0.947379i	$0.396278\pi$
$312$	1.11523e6	−	2.14966e6i	0.0367200	−	0.0707793i
$313$			4.68811e7i			1.52885i	0.644714	+	0.764424i	$0.276977\pi$
$313$			4.68811e7i			1.52885i	−0.644714	+	0.764424i	$0.723023\pi$
$314$	−3.56517e7	−	1.59777e7i	−1.15157	−	0.516090i
$315$	6.73374e6	+	6.73374e6i	0.215439	+	0.215439i
$316$	−1.18603e7	−	1.33023e7i	−0.375866	−	0.421567i
$317$	−3.62609e7	−	3.62609e7i	−1.13831	−	1.13831i	−0.988753	−	0.149556i	$-0.952216\pi$
$317$	−3.62609e7	−	3.62609e7i	−1.13831	−	1.13831i	−0.149556	−	0.988753i	$-0.547784\pi$
$318$	4.33999e6	+	1.13892e7i	0.134961	+	0.354169i
$319$			3.58298e7i			1.10376i
$320$	2.03764e7	+	3.53432e6i	0.621839	+	0.107859i
$321$	1.75403e6			0.0530299
$322$	7.50324e7	−	2.85920e7i	2.24740	−	0.856402i
$323$	2.98345e7	−	2.98345e7i	0.885342	−	0.885342i
$324$	−2.82077e6	+	2.51498e6i	−0.0829341	+	0.0739434i
$325$	−2.01709e6	+	2.01709e6i	−0.0587592	+	0.0587592i
$326$	6.44948e6	−	1.43910e7i	0.186154	−	0.415373i
$327$	−2.59998e7			−0.743578
$328$	−2.54449e6	−	1.32007e6i	−0.0721072	−	0.0374089i
$329$			6.27253e7i			1.76139i
$330$	−3.95192e6	+	8.81809e6i	−0.109968	+	0.245376i
$331$	−4.94385e7	−	4.94385e7i	−1.36327	−	1.36327i	−0.869717	−	0.493550i	$-0.835699\pi$
$331$	−4.94385e7	−	4.94385e7i	−1.36327	−	1.36327i	−0.493550	−	0.869717i	$-0.664301\pi$
$332$	3.13341e6	−	5.46746e7i	0.0856256	−	1.49407i
$333$	2.92201e6	+	2.92201e6i	0.0791314	+	0.0791314i
$334$	−4.54835e7	+	1.73321e7i	−1.22072	+	0.465169i
$335$		−	4.39985e7i		−	1.17032i
$336$	1.97188e7	+	2.48433e7i	0.519831	+	0.654926i
$337$	6.97311e7			1.82195			0.910976	−	0.412460i	$-0.135330\pi$
$337$	6.97311e7			1.82195			0.910976	+	0.412460i	$0.135330\pi$
$338$	1.34878e7	+	3.53952e7i	0.349293	+	0.916629i
$339$	−2.21003e7	+	2.21003e7i	−0.567283	+	0.567283i
$340$	1.19348e6	−	2.08249e7i	0.0303653	−	0.529841i
$341$	2.46860e7	−	2.46860e7i	0.622568	−	0.622568i
$342$	−1.81174e7	−	8.11950e6i	−0.452916	−	0.202979i
$343$	5.69554e6			0.141141
$344$	8.46500e6	−	2.68199e6i	0.207946	−	0.0658843i
$345$			2.48478e7i			0.605105i
$346$	−1.63421e7	−	7.32389e6i	−0.394530	−	0.176813i
$347$	−2.21474e7	−	2.21474e7i	−0.530070	−	0.530070i	0.390523	−	0.920593i	$-0.372294\pi$
$347$	−2.21474e7	−	2.21474e7i	−0.530070	−	0.530070i	−0.920593	+	0.390523i	$0.872294\pi$
$348$	−2.71645e7	+	2.42197e7i	−0.644562	+	0.574686i
$349$	3.60324e7	+	3.60324e7i	0.847651	+	0.847651i	0.989840	−	0.142188i	$-0.0454138\pi$
$349$	3.60324e7	+	3.60324e7i	0.847651	+	0.847651i	−0.142188	+	0.989840i	$0.545414\pi$
$350$	−1.33037e7	−	3.49121e7i	−0.310290	−	0.814276i
$351$			1.14938e6i			0.0265792i
$352$	−1.64318e7	+	2.76742e7i	−0.376753	+	0.634522i
$353$	2.11146e7			0.480020			0.240010	−	0.970770i	$-0.422849\pi$
$353$	2.11146e7			0.480020			0.240010	+	0.970770i	$0.422849\pi$
$354$	−1.66834e7	+	6.35741e6i	−0.376075	+	0.143308i
$355$	1.47403e7	−	1.47403e7i	0.329473	−	0.329473i
$356$	−2.24223e7	−	2.51486e7i	−0.496970	−	0.557396i
$357$	2.26213e7	−	2.26213e7i	0.497180	−	0.497180i
$358$	−2.69866e7	+	6.02164e7i	−0.588165	+	1.31240i
$359$	4.86766e7			1.05205			0.526025	−	0.850469i	$-0.323682\pi$
$359$	4.86766e7			1.05205			0.526025	+	0.850469i	$0.323682\pi$
$360$	−9.35683e6	+	2.96455e6i	−0.200549	+	0.0635407i
$361$		−	5.72549e7i		−	1.21700i
$362$	−7.01701e6	+	1.56574e7i	−0.147920	+	0.330060i
$363$	8.89354e6	+	8.89354e6i	0.185932	+	0.185932i
$364$	9.63078e6	+	551942.i	0.199691	+	0.0114443i
$365$	−1.28851e7	−	1.28851e7i	−0.264979	−	0.264979i
$366$	2.03874e7	−	7.76886e6i	0.415832	−	0.158458i
$367$			7.99759e6i			0.161793i	0.996722	+	0.0808967i	$0.0257784\pi$
$367$			7.99759e6i			0.161793i	−0.996722	+	0.0808967i	$0.974222\pi$
$368$	−9.45493e6	+	8.22181e7i	−0.189721	+	1.64977i
$369$	1.36048e6			0.0270778
$370$	3.82172e6	+	1.00291e7i	0.0754490	+	0.197996i
$371$	−3.43295e7	+	3.43295e7i	−0.672272	+	0.672272i
$372$	3.54026e7	+	2.02893e6i	0.687711	+	0.0394129i
$373$	−2.69021e7	+	2.69021e7i	−0.518394	+	0.518394i	−0.917085	−	0.398692i	$-0.869464\pi$
$373$	−2.69021e7	+	2.69021e7i	−0.518394	+	0.518394i	0.398692	+	0.917085i	$0.369464\pi$
$374$	2.96235e7	+	1.32761e7i	0.566268	+	0.253779i
$375$	3.07768e7			0.583620
$376$	−5.73873e7	−	2.97723e7i	−1.07957	−	0.560078i
$377$			1.10687e7i			0.206573i
$378$	−1.37371e7	−	6.15643e6i	−0.254343	−	0.113987i
$379$	−3.06914e7	−	3.06914e7i	−0.563765	−	0.563765i	0.366610	−	0.930375i	$-0.380519\pi$
$379$	−3.06914e7	−	3.06914e7i	−0.563765	−	0.563765i	−0.930375	+	0.366610i	$0.880519\pi$
$380$	−3.43155e7	−	3.84878e7i	−0.625373	−	0.701411i
$381$	−4.06437e7	−	4.06437e7i	−0.734882	−	0.734882i
$382$	2.48571e7	+	6.52311e7i	0.445924	+	1.17021i
$383$			4.04427e7i			0.719853i	0.932981	+	0.359926i	$0.117198\pi$
$383$			4.04427e7i			0.719853i	−0.932981	+	0.359926i	$0.882802\pi$
$384$	−3.20886e7	+	6.24892e6i	−0.566705	+	0.110360i
$385$	−3.84916e7			−0.674503
$386$	−2.66442e7	+	1.01531e7i	−0.463278	+	0.176538i
$387$	−2.98003e6	+	2.98003e6i	−0.0514147	+	0.0514147i
$388$	4.01383e7	−	3.57870e7i	0.687170	−	0.612675i
$389$	−1.80046e7	+	1.80046e7i	−0.305869	+	0.305869i	−0.843305	−	0.537436i	$-0.819393\pi$
$389$	−1.80046e7	+	1.80046e7i	−0.305869	+	0.305869i	0.537436	+	0.843305i	$0.319393\pi$
$390$	−1.22084e6	+	2.72412e6i	−0.0205810	+	0.0459233i
$391$	8.34738e7			1.39643
$392$	−3.04428e7	+	5.86798e7i	−0.505390	+	0.974161i
$393$			3.76008e7i			0.619468i
$394$	2.40916e7	−	5.37566e7i	0.393891	−	0.878907i
$395$	1.55339e7	+	1.55339e7i	0.252052	+	0.252052i
$396$	873992.	−	1.52502e7i	0.0140741	−	0.245578i
$397$	−2.46768e7	−	2.46768e7i	−0.394383	−	0.394383i	0.481863	−	0.876246i	$-0.339960\pi$
$397$	−2.46768e7	−	2.46768e7i	−0.394383	−	0.394383i	−0.876246	+	0.481863i	$0.839960\pi$
$398$	−5.07194e7	+	1.93273e7i	−0.804498	+	0.306564i
$399$		−	7.90838e7i		−	1.24500i
$400$	3.82556e7	+	4.39932e6i	0.597744	+	0.0687394i
$401$	−6.93037e7			−1.07479			−0.537394	−	0.843331i	$-0.680591\pi$
$401$	−6.93037e7			−1.07479			−0.537394	+	0.843331i	$0.680591\pi$
$402$	2.47663e7	+	6.49926e7i	0.381226	+	1.00043i
$403$	7.62609e6	−	7.62609e6i	0.116516	−	0.116516i
$404$	−1.15348e6	+	2.01270e7i	−0.0174931	+	0.305236i
$405$	3.29399e6	−	3.29399e6i	0.0495858	−	0.0495858i
$406$	−1.32291e8	−	5.92875e7i	−1.97675	−	0.885901i
$407$	−1.67029e7			−0.247747
$408$	9.95913e6	+	3.14334e7i	0.146636	+	0.462818i
$409$		−	7.56422e7i		−	1.10559i	−0.833317	−	0.552795i	$-0.813561\pi$
$409$		−	7.56422e7i		−	1.10559i	0.833317	−	0.552795i	$-0.186439\pi$
$410$	3.22446e6	+	1.44508e6i	0.0467849	+	0.0209671i
$411$	2.73886e7	+	2.73886e7i	0.394498	+	0.394498i
$412$	−3.15483e7	+	2.81282e7i	−0.451112	+	0.402208i
$413$	−5.02873e7	−	5.02873e7i	−0.713852	−	0.713852i
$414$	−1.39866e7	−	3.67041e7i	−0.197111	−	0.517265i
$415$			6.75060e7i			0.944491i
$416$	−5.07618e6	+	8.54922e6i	−0.0705110	+	0.118753i
$417$	−7.58596e7			−1.04617
$418$	7.49881e7	−	2.85752e7i	1.02675	−	0.391255i
$419$	−2.91448e7	+	2.91448e7i	−0.396204	+	0.396204i	−0.876892	−	0.480688i	$-0.840387\pi$
$419$	−2.91448e7	+	2.91448e7i	−0.396204	+	0.396204i	0.480688	+	0.876892i	$0.340387\pi$
$420$	−2.60190e7	−	2.91826e7i	−0.351190	−	0.393891i
$421$	−2.16659e6	+	2.16659e6i	−0.0290355	+	0.0290355i	−0.721476	−	0.692440i	$-0.756536\pi$
$421$	−2.16659e6	+	2.16659e6i	−0.0290355	+	0.0290355i	0.692440	+	0.721476i	$0.256536\pi$
$422$	−2.99257e7	+	6.67747e7i	−0.398206	+	0.888534i
$423$	3.06837e7			0.405403
$424$	−1.51137e7	−	4.77023e7i	−0.198277	−	0.625809i
$425$		−	3.88398e7i		−	0.505954i
$426$	−1.34765e7	+	3.00708e7i	−0.174321	+	0.388970i
$427$	6.14519e7	+	6.14519e7i	0.789318	+	0.789318i
$428$	−7.18953e6	−	412034.i	−0.0917000	−	0.00525535i
$429$	−3.28505e6	−	3.28505e6i	−0.0416074	−	0.0416074i
$430$	−1.02282e7	+	3.89760e6i	−0.128646	+	0.0490221i
$431$		−	1.18801e8i		−	1.48385i	−0.670485	−	0.741923i	$-0.733914\pi$
$431$		−	1.18801e8i		−	1.48385i	0.670485	−	0.741923i	$-0.266086\pi$
$432$	1.21528e7	−	9.64596e6i	0.150739	−	0.119645i
$433$	−2.58626e7			−0.318572			−0.159286	−	0.987232i	$-0.550919\pi$
$433$	−2.58626e7			−0.318572			−0.159286	+	0.987232i	$0.550919\pi$
$434$	5.02978e7	+	1.31993e8i	0.615289	+	1.61467i
$435$	3.17217e7	−	3.17217e7i	0.385379	−	0.385379i
$436$	1.06570e8	+	6.10755e6i	1.28581	+	0.0736898i
$437$	1.45911e8	−	1.45911e8i	1.74842	−	1.74842i
$438$	2.62863e7	+	1.17805e7i	0.312829	+	0.140197i
$439$	1.54103e8			1.82145			0.910725	−	0.413013i	$-0.135523\pi$
$439$	1.54103e8			1.82145			0.910725	+	0.413013i	$0.135523\pi$
$440$	1.82699e7	−	3.52159e7i	0.214475	−	0.413410i
$441$		−	3.13748e7i		−	0.365818i
$442$	9.15143e6	+	4.10131e6i	0.105980	+	0.0474958i
$443$	8.89562e7	+	8.89562e7i	1.02321	+	1.02321i	0.999724	+	0.0234864i	$0.00747663\pi$
$443$	8.89562e7	+	8.89562e7i	1.02321	+	1.02321i	0.0234864	+	0.999724i	$0.492523\pi$
$444$	−1.12906e7	−	1.26634e7i	−0.128993	−	0.144677i
$445$	2.93676e7	+	2.93676e7i	0.333264	+	0.333264i
$446$	2.67575e7	+	7.02180e7i	0.301606	+	0.791488i
$447$		−	5.37326e7i		−	0.601610i
$448$	−7.49889e7	−	1.06462e8i	−0.833994	−	1.18402i
$449$	1.15494e8			1.27591			0.637956	−	0.770073i	$-0.279780\pi$
$449$	1.15494e8			1.27591			0.637956	+	0.770073i	$0.279780\pi$
$450$	−1.70782e7	+	6.50786e6i	−0.187415	+	0.0714168i
$451$	−3.88842e6	+	3.88842e6i	−0.0423880	+	0.0423880i
$452$	9.57780e7	−	8.53949e7i	1.03717	−	0.924734i
$453$	7.30210e7	−	7.30210e7i	0.785513	−	0.785513i
$454$	−8.59191e6	+	1.91715e7i	−0.0918168	+	0.204875i
$455$	−1.18910e7			−0.126236
$456$	7.23537e7	+	3.75367e7i	0.763073	+	0.395879i
$457$			1.19475e8i			1.25178i	0.779913	+	0.625888i	$0.215263\pi$
$457$			1.19475e8i			1.25178i	−0.779913	+	0.625888i	$0.784737\pi$
$458$	1.04082e7	−	2.32244e7i	0.108338	−	0.241740i
$459$	−1.10658e7	−	1.10658e7i	−0.114432	−	0.114432i
$460$	5.83694e6	−	1.01848e8i	0.0599669	−	1.04636i
$461$	4.11301e7	+	4.11301e7i	0.419814	+	0.419814i	0.885140	−	0.465326i	$-0.154063\pi$
$461$	4.11301e7	+	4.11301e7i	0.419814	+	0.419814i	−0.465326	+	0.885140i	$0.654063\pi$
$462$	5.68581e7	−	2.16665e7i	0.576589	−	0.219717i
$463$			7.63639e7i			0.769388i	0.923044	+	0.384694i	$0.125693\pi$
$463$			7.63639e7i			0.769388i	−0.923044	+	0.384694i	$0.874307\pi$
$464$	1.17033e8	−	9.28923e7i	1.17154	−	0.929878i
$465$	−4.37111e7			−0.434743
$466$	−3.03897e7	−	7.97498e7i	−0.300309	−	0.788083i
$467$	−5.02857e7	+	5.02857e7i	−0.493734	+	0.493734i	−0.909481	−	0.415746i	$-0.863520\pi$
$467$	−5.02857e7	+	5.02857e7i	−0.493734	+	0.493734i	0.415746	+	0.909481i	$0.363520\pi$
$468$	269997.	−	4.71115e6i	0.00263404	−	0.0459610i
$469$	−1.95902e8	+	1.95902e8i	−1.89898	+	1.89898i
$470$	7.27231e7	+	3.25916e7i	0.700453	+	0.313915i
$471$	−7.61269e7			−0.728577
$472$	6.98765e7	−	2.21392e7i	0.664515	−	0.210540i
$473$		−	1.70345e7i		−	0.160971i
$474$	−3.16900e7	−	1.42022e7i	−0.297568	−	0.133358i
$475$	−6.78917e7	−	6.78917e7i	−0.633484	−	0.633484i
$476$	−9.80360e7	+	8.74081e7i	−0.909002	+	0.810459i
$477$	1.67932e7	+	1.67932e7i	0.154731	+	0.154731i
$478$	−9.06905e6	−	2.37994e7i	−0.0830382	−	0.217912i
$479$			7.03911e7i			0.640489i	0.947335	+	0.320244i	$0.103765\pi$
$479$			7.03911e7i			0.640489i	−0.947335	+	0.320244i	$0.896235\pi$
$480$	3.90489e7	−	9.95335e6i	0.353090	−	0.0900006i
$481$	−5.15993e6			−0.0463669
$482$	−1.88385e8	+	7.17867e7i	−1.68231	+	0.641066i
$483$	1.10634e8	−	1.10634e8i	0.981856	−	0.981856i
$484$	−3.43644e7	−	3.85427e7i	−0.303091	−	0.339943i
$485$	−4.68720e7	+	4.68720e7i	−0.410854	+	0.410854i
$486$	−3.01158e6	+	6.71988e6i	−0.0262353	+	0.0585400i
$487$	6.50586e7			0.563272			0.281636	−	0.959521i	$-0.409123\pi$
$487$	6.50586e7			0.563272			0.281636	+	0.959521i	$0.409123\pi$
$488$	−8.53902e7	+	2.70545e7i	−0.734765	+	0.232798i
$489$		−	3.07290e7i		−	0.262798i
$490$	3.33257e7	−	7.43611e7i	0.283264	−	0.632059i
$491$	−7.38935e7	−	7.38935e7i	−0.624254	−	0.624254i	0.322362	−	0.946616i	$-0.395523\pi$
$491$	−7.38935e7	−	7.38935e7i	−0.624254	−	0.624254i	−0.946616	+	0.322362i	$0.895523\pi$
$492$	−5.57645e6	−	319588.i	−0.0468233	−	0.00268346i
$493$	−1.06566e8	−	1.06566e8i	−0.889360	−	0.889360i
$494$	2.31657e7	−	8.82757e6i	0.192160	−	0.0732251i
$495$			1.88292e7i			0.155245i
$496$	−1.44634e8	−	1.66327e7i	−1.18529	−	0.136307i
$497$	−1.31261e8			−1.06922
$498$	−3.79984e7	−	9.97169e7i	−0.307664	−	0.807385i
$499$	−1.88982e7	+	1.88982e7i	−0.152097	+	0.152097i	−0.779054	−	0.626957i	$-0.784300\pi$
$499$	−1.88982e7	+	1.88982e7i	−0.152097	+	0.152097i	0.626957	+	0.779054i	$0.284300\pi$
$500$	−1.26150e8	−	7.22971e6i	−1.00920	−	0.0578377i
$501$	−6.70647e7	+	6.70647e7i	−0.533312	+	0.533312i
$502$	9.32911e6	+	4.18093e6i	0.0737444	+	0.0330493i
$503$	−1.97908e8			−1.55511			−0.777554	−	0.628817i	$-0.783540\pi$
$503$	−1.97908e8			−1.55511			−0.777554	+	0.628817i	$0.783540\pi$
$504$	5.48606e7	+	2.84614e7i	0.428518	+	0.222313i
$505$		−	2.48505e7i		−	0.192958i
$506$	1.44880e8	+	6.49293e7i	1.11829	+	0.501175i
$507$	5.21897e7	+	5.21897e7i	0.400461	+	0.400461i
$508$	1.57046e8	+	1.76141e8i	1.19794	+	1.34360i
$509$	3.61874e7	+	3.61874e7i	0.274412	+	0.274412i	0.830874	−	0.556461i	$-0.187841\pi$
$509$	3.61874e7	+	3.61874e7i	0.274412	+	0.274412i	−0.556461	+	0.830874i	$0.687841\pi$
$510$	−1.44731e7	−	3.79809e7i	−0.109107	−	0.286322i
$511$			1.14741e8i			0.859919i
$512$	1.32995e8	−	1.80757e7i	0.990890	−	0.134674i
$513$	−3.86859e7			−0.286550
$514$	6.79643e6	−	2.58986e6i	0.0500485	−	0.0190716i
$515$	3.68409e7	−	3.68409e7i	0.269717	−	0.269717i
$516$	1.29148e7	−	1.15147e7i	0.0940022	−	0.0838117i
$517$	−8.76977e7	+	8.76977e7i	−0.634624	+	0.634624i
$518$	2.76382e7	−	6.16704e7i	0.198848	−	0.443698i
$519$	−3.48952e7			−0.249611
$520$	5.64400e6	−	1.08791e7i	0.0401400	−	0.0773715i
$521$			1.38334e8i			0.978175i	0.872235	+	0.489087i	$0.162670\pi$
$521$			1.38334e8i			0.978175i	−0.872235	+	0.489087i	$0.837330\pi$
$522$	−2.90021e7	+	6.47137e7i	−0.203900	+	0.454972i
$523$	−8.07473e7	−	8.07473e7i	−0.564446	−	0.564446i	0.366121	−	0.930567i	$-0.380686\pi$
$523$	−8.07473e7	−	8.07473e7i	−0.564446	−	0.564446i	−0.930567	+	0.366121i	$0.880686\pi$
$524$	8.83270e6	−	1.54121e8i	0.0613903	−	1.07119i
$525$	−5.14774e7	−	5.14774e7i	−0.355745	−	0.355745i
$526$	8.23998e7	−	3.13995e7i	0.566199	−	0.215757i
$527$			1.46843e8i			1.00328i
$528$	−7.16477e6	+	6.23033e7i	−0.0486744	+	0.423262i
$529$	2.60209e8			1.75774
$530$	2.19639e7	+	5.76386e7i	0.147531	+	0.387156i
$531$	−2.45994e7	+	2.45994e7i	−0.164301	+	0.164301i
$532$	−1.85774e7	+	3.24155e8i	−0.123381	+	2.15287i
$533$	−1.20123e6	+	1.20123e6i	−0.00793311	+	0.00793311i
$534$	−5.99111e7	−	2.68498e7i	−0.393445	−	0.176326i
$535$	8.87681e6			0.0579690
$536$	−8.62466e7	−	2.72214e8i	−0.560077	−	1.76773i
$537$			1.28580e8i			0.830327i
$538$	−1.84367e8	−	8.26261e7i	−1.18396	−	0.530604i
$539$	8.96729e7	+	8.96729e7i	0.572658	+	0.572658i
$540$	−1.42754e7	+	1.27279e7i	−0.0906584	+	0.0808303i
$541$	−4.12188e7	−	4.12188e7i	−0.260318	−	0.260318i	0.564865	−	0.825183i	$-0.308928\pi$
$541$	−4.12188e7	−	4.12188e7i	−0.260318	−	0.260318i	−0.825183	+	0.564865i	$0.808928\pi$
$542$	6.84887e6	+	1.79731e7i	0.0430151	+	0.112882i
$543$			3.34330e7i			0.208822i
$544$	−3.34373e7	−	1.31181e8i	−0.207699	−	0.814843i
$545$	−1.31580e8			−0.812834
$546$	1.75648e7	−	6.69331e6i	0.107911	−	0.0411209i
$547$	3.64952e7	−	3.64952e7i	0.222984	−	0.222984i	−0.586770	−	0.809754i	$-0.699601\pi$
$547$	3.64952e7	−	3.64952e7i	0.222984	−	0.222984i	0.809754	+	0.586770i	$0.199601\pi$
$548$	−1.05829e8	−	1.18696e8i	−0.643076	−	0.721266i
$549$	3.00609e7	−	3.00609e7i	0.181670	−	0.181670i
$550$	3.02112e7	−	6.74117e7i	0.181585	−	0.405179i
$551$	−3.72552e8			−2.22706
$552$	4.87071e7	+	1.53731e8i	0.289584	+	0.913996i
$553$		−	1.38329e8i		−	0.817970i
$554$	−3.10440e7	+	6.92699e7i	−0.182578	+	0.407394i
$555$	1.47878e7	+	1.47878e7i	0.0865016	+	0.0865016i
$556$	3.10939e8	+	1.78200e7i	1.80905	+	0.103677i
$557$	1.55783e8	+	1.55783e8i	0.901477	+	0.901477i	0.995564	−	0.0940866i	$-0.0299931\pi$
$557$	1.55783e8	+	1.55783e8i	0.901477	+	0.901477i	−0.0940866	+	0.995564i	$0.529993\pi$
$558$	6.45681e7	−	2.46045e7i	0.371634	−	0.141616i
$559$		−	5.26238e6i		−	0.0301264i
$560$	9.97933e7	+	1.25728e8i	0.568247	+	0.715924i
$561$	6.32549e7			0.358266
$562$	−3.59403e7	−	9.43160e7i	−0.202476	−	0.531345i
$563$	5.52051e7	−	5.52051e7i	0.309353	−	0.309353i	−0.535306	−	0.844658i	$-0.679804\pi$
$563$	5.52051e7	−	5.52051e7i	0.309353	−	0.309353i	0.844658	+	0.535306i	$0.179804\pi$
$564$	−1.25769e8	−	7.20784e6i	−0.701029	−	0.0401761i
$565$	−1.11846e8	+	1.11846e8i	−0.620118	+	0.620118i
$566$	1.85439e8	+	8.31062e7i	1.02271	+	0.458336i
$567$	−2.93328e7			−0.160918
$568$	6.23025e7	−	1.20091e8i	0.339986	−	0.655337i
$569$		−	3.17482e8i		−	1.72338i	−0.507433	−	0.861691i	$-0.669405\pi$
$569$		−	3.17482e8i		−	1.72338i	0.507433	−	0.861691i	$-0.330595\pi$
$570$	−9.16890e7	−	4.10914e7i	−0.495100	−	0.221884i
$571$	−5.83480e7	−	5.83480e7i	−0.313413	−	0.313413i	0.532817	−	0.846230i	$-0.321133\pi$
$571$	−5.83480e7	−	5.83480e7i	−0.313413	−	0.313413i	−0.846230	+	0.532817i	$0.821133\pi$
$572$	1.26933e7	+	1.42367e7i	0.0678247	+	0.0760714i
$573$	9.61823e7	+	9.61823e7i	0.511248	+	0.511248i
$574$	−7.92266e6	−	2.07910e7i	−0.0418924	−	0.109936i
$575$		−	1.89954e8i		−	0.999182i
$576$	−5.20787e7	+	3.66828e7i	−0.272516	+	0.191953i
$577$	1.26597e8			0.659015			0.329507	−	0.944153i	$-0.393117\pi$
$577$	1.26597e8			0.659015			0.329507	+	0.944153i	$0.393117\pi$
$578$	5.28504e7	−	2.01393e7i	0.273694	−	0.104294i
$579$	−3.92865e7	+	3.92865e7i	−0.202399	+	0.202399i
$580$	−1.37475e8	+	1.22572e8i	−0.704595	+	0.628211i
$581$	3.00568e8	−	3.00568e8i	1.53255	−	1.53255i
$582$	4.28535e7	−	9.56209e7i	0.217379	−	0.485047i
$583$	−9.59937e7			−0.484437
$584$	−1.04977e8	−	5.44615e7i	−0.527054	−	0.273433i
$585$			5.81680e6i			0.0290547i
$586$	−5.09478e7	+	1.13682e8i	−0.253182	+	0.564936i
$587$	1.49945e8	+	1.49945e8i	0.741342	+	0.741342i	0.972836	−	0.231494i	$-0.0743614\pi$
$587$	1.49945e8	+	1.49945e8i	0.741342	+	0.741342i	−0.231494	+	0.972836i	$0.574361\pi$
$588$	−7.37018e6	+	1.28602e8i	−0.0362532	+	0.632578i
$589$	2.56680e8	+	2.56680e8i	1.25617	+	1.25617i
$590$	−8.44316e7	+	3.21737e7i	−0.411101	+	0.156655i
$591$		−	1.14786e8i		−	0.556066i
$592$	4.33039e7	+	5.45578e7i	0.208719	+	0.262961i
$593$	2.26564e8			1.08649			0.543245	−	0.839574i	$-0.317195\pi$
$593$	2.26564e8			1.08649			0.543245	+	0.839574i	$0.317195\pi$
$594$	−1.05987e7	−	2.78137e7i	−0.0505703	−	0.132709i
$595$	1.14483e8	−	1.14483e8i	0.543486	−	0.543486i
$596$	−1.26222e7	+	2.20243e8i	−0.0596205	+	1.04031i
$597$	−7.47850e7	+	7.47850e7i	−0.351473	+	0.351473i
$598$	4.47569e7	+	2.00582e7i	0.209294	+	0.0937971i
$599$	−1.65861e7			−0.0771727			−0.0385864	−	0.999255i	$-0.512285\pi$
$599$	−1.65861e7			−0.0771727			−0.0385864	+	0.999255i	$0.512285\pi$
$600$	7.15301e7	−	2.26631e7i	0.331158	−	0.104922i
$601$		−	3.72359e8i		−	1.71529i	−0.514238	−	0.857647i	$-0.671925\pi$
$601$		−	3.72359e8i		−	1.71529i	0.514238	−	0.857647i	$-0.328075\pi$
$602$	6.28949e7	+	2.81870e7i	0.288288	+	0.129199i
$603$	9.58307e7	+	9.58307e7i	0.437072	+	0.437072i
$604$	−3.16457e8	+	2.82151e8i	−1.43616	+	1.28047i
$605$	4.50087e7	+	4.50087e7i	0.203250	+	0.203250i
$606$	1.39881e7	+	3.67081e7i	0.0628551	+	0.164947i
$607$		−	2.68278e8i		−	1.19955i	−0.800168	−	0.599776i	$-0.795256\pi$
$607$		−	2.68278e8i		−	1.19955i	0.800168	−	0.599776i	$-0.204744\pi$
$608$	−2.87751e8	−	1.70855e8i	−1.28028	−	0.760180i
$609$	−2.82480e8			−1.25065
$610$	1.03177e8	−	3.93168e7i	0.454562	−	0.173216i
$611$	−2.70920e7	+	2.70920e7i	−0.118773	+	0.118773i
$612$	4.27580e7	+	4.79569e7i	0.186536	+	0.209217i
$613$	−1.58322e7	+	1.58322e7i	−0.0687322	+	0.0687322i	−0.740637	−	0.671905i	$-0.765476\pi$
$613$	−1.58322e7	+	1.58322e7i	−0.0687322	+	0.0687322i	0.671905	+	0.740637i	$0.265476\pi$
$614$	1.64691e8	−	3.67482e8i	0.711482	−	1.58756i
$615$	6.88516e6			0.0295998
$616$	−2.38144e8	+	7.54519e7i	−1.01882	+	0.322796i
$617$			1.28338e7i			0.0546387i	0.999627	+	0.0273193i	$0.00869710\pi$
$617$			1.28338e7i			0.0546387i	−0.999627	+	0.0273193i	$0.991303\pi$
$618$	−3.36824e7	+	7.51571e7i	−0.142705	+	0.318423i
$619$	1.76902e8	+	1.76902e8i	0.745864	+	0.745864i	0.973700	−	0.227835i	$-0.0731648\pi$
$619$	1.76902e8	+	1.76902e8i	0.745864	+	0.745864i	−0.227835	+	0.973700i	$0.573165\pi$
$620$	1.79166e8	+	1.02681e7i	0.751764	+	0.0430837i
$621$	−5.41196e7	−	5.41196e7i	−0.225985	−	0.225985i
$622$	−1.43968e8	+	5.48607e7i	−0.598265	+	0.227976i
$623$		−	2.61516e8i		−	1.08152i
$624$	−2.21337e6	+	1.92470e7i	−0.00910962	+	0.0792154i
$625$	8.86098e6			0.0362946
$626$	−1.33549e8	−	3.50465e8i	−0.544400	−	1.42864i
$627$	1.10569e8	−	1.10569e8i	0.448570	−	0.448570i
$628$	3.12035e8	+	1.78828e7i	1.25986	+	0.0722031i
$629$	4.96781e7	−	4.96781e7i	0.199624	−	0.199624i
$630$	−6.95212e7	−	3.11566e7i	−0.278033	−	0.124603i
$631$	−2.96825e8			−1.18144			−0.590721	−	0.806876i	$-0.701157\pi$
$631$	−2.96825e8			−1.18144			−0.590721	+	0.806876i	$0.701157\pi$
$632$	1.26557e8	+	6.56572e7i	0.501343	+	0.260094i
$633$			1.42583e8i			0.562157i
$634$	3.74368e8	+	1.67777e8i	1.46903	+	0.658362i
$635$	−2.05690e8	−	2.05690e8i	−0.803328	−	0.803328i
$636$	−6.48883e7	−	7.27780e7i	−0.252229	−	0.282897i
$637$	2.77021e7	+	2.77021e7i	0.107175	+	0.107175i
$638$	−1.02068e8	−	2.67850e8i	−0.393031	−	1.03141i
$639$			6.42099e7i			0.246093i
$640$	−1.62395e8	+	3.16247e7i	−0.619486	+	0.120639i
$641$	4.80696e8			1.82514			0.912571	−	0.408918i	$-0.134094\pi$
$641$	4.80696e8			1.82514			0.912571	+	0.408918i	$0.134094\pi$
$642$	−1.31124e7	+	4.99666e6i	−0.0495540	+	0.0188832i
$643$	1.10391e8	−	1.10391e8i	0.415242	−	0.415242i	−0.468318	−	0.883560i	$-0.655140\pi$
$643$	1.10391e8	−	1.10391e8i	0.415242	−	0.415242i	0.883560	+	0.468318i	$0.155140\pi$
$644$	−4.79464e8	+	4.27487e8i	−1.79514	+	1.60053i
$645$	−1.50814e7	+	1.50814e7i	−0.0562034	+	0.0562034i
$646$	−1.38042e8	+	3.08020e8i	−0.512053	+	1.14257i
$647$	−1.38174e6			−0.00510170			−0.00255085	−	0.999997i	$-0.500812\pi$
$647$	−1.38174e6			−0.00510170			−0.00255085	+	0.999997i	$0.500812\pi$
$648$	1.39227e7	−	2.68365e7i	0.0511679	−	0.0986282i
$649$		−	1.40616e8i		−	0.514399i
$650$	9.33298e6	−	2.08251e7i	0.0339844	−	0.0758310i
$651$	1.94622e8	+	1.94622e8i	0.705423	+	0.705423i
$652$	−7.21847e6	+	1.25954e8i	−0.0260437	+	0.454434i
$653$	9.70802e7	+	9.70802e7i	0.348651	+	0.348651i	0.859607	−	0.510956i	$-0.170708\pi$
$653$	9.70802e7	+	9.70802e7i	0.348651	+	0.348651i	−0.510956	+	0.859607i	$0.670708\pi$
$654$	1.94365e8	−	7.40652e7i	0.694839	−	0.264777i
$655$			1.90291e8i			0.677165i
$656$	2.27821e7	+	2.61990e6i	0.0807016	+	0.00928054i
$657$	5.61289e7			0.197920
$658$	−1.78684e8	−	4.68911e8i	−0.627204	−	1.64593i
$659$	−1.68632e8	+	1.68632e8i	−0.589229	+	0.589229i	−0.937423	−	0.348194i	$-0.886795\pi$
$659$	−1.68632e8	+	1.68632e8i	−0.589229	+	0.589229i	0.348194	+	0.937423i	$0.386795\pi$
$660$	4.42312e6	−	7.71786e7i	0.0153850	−	0.268451i
$661$	−3.28246e7	+	3.28246e7i	−0.113657	+	0.113657i	−0.761648	−	0.647991i	$-0.775609\pi$
$661$	−3.28246e7	+	3.28246e7i	−0.113657	+	0.113657i	0.647991	+	0.761648i	$0.275609\pi$
$662$	5.10418e8	+	2.28749e8i	1.75935	+	0.788470i
$663$	1.95410e7			0.0670510
$664$	1.32326e8	+	4.17653e8i	0.452004	+	1.42663i
$665$		−	4.00229e8i		−	1.36095i
$666$	−3.01677e7	−	1.35200e7i	−0.102122	−	0.0457671i
$667$	−5.21182e8	−	5.21182e8i	−1.75635	−	1.75635i
$668$	2.90644e8	−	2.59136e8i	0.975062	−	0.869358i
$669$	1.03535e8	+	1.03535e8i	0.345789	+	0.345789i
$670$	1.25338e8	+	3.28916e8i	0.416732	+	1.09361i
$671$			1.71835e8i			0.568779i
$672$	−2.18181e8	−	1.29547e8i	−0.718967	−	0.426893i
$673$	−2.71251e8			−0.889870			−0.444935	−	0.895563i	$-0.646773\pi$
$673$	−2.71251e8			−0.889870			−0.444935	+	0.895563i	$0.646773\pi$
$674$	−5.21284e8	+	1.98642e8i	−1.70253	+	0.648770i
$675$	−2.51815e7	+	2.51815e7i	−0.0818787	+	0.0818787i
$676$	−2.01659e8	−	2.26179e8i	−0.652797	−	0.732169i
$677$	−2.72402e8	+	2.72402e8i	−0.877897	+	0.877897i	−0.993317	−	0.115420i	$-0.963179\pi$
$677$	−2.72402e8	+	2.72402e8i	−0.877897	+	0.877897i	0.115420	+	0.993317i	$0.463179\pi$
$678$	1.02257e8	−	2.28171e8i	0.328098	−	0.732100i
$679$	4.17392e8			1.33332
$680$	5.04014e7	+	1.59079e8i	0.160294	+	0.505924i
$681$			4.09367e7i			0.129620i
$682$	−1.14221e8	+	2.54866e8i	−0.360074	+	0.803449i
$683$	1.80546e8	+	1.80546e8i	0.566664	+	0.566664i	0.931192	−	0.364528i	$-0.118770\pi$
$683$	1.80546e8	+	1.80546e8i	0.566664	+	0.566664i	−0.364528	+	0.931192i	$0.618770\pi$
$684$	1.58569e8	+	9.08762e6i	0.495507	+	0.0283976i
$685$	1.38609e8	+	1.38609e8i	0.431241	+	0.431241i
$686$	−4.25777e7	+	1.62248e7i	−0.131889	+	0.0502582i
$687$		−	4.95908e7i		−	0.152944i
$688$	−5.56410e7	+	4.41637e7i	−0.170856	+	0.135613i
$689$	−2.96548e7			−0.0906645
$690$	−7.07835e7	−	1.85753e8i	−0.215469	−	0.565443i
$691$	2.41248e8	−	2.41248e8i	0.731189	−	0.731189i	−0.239666	−	0.970855i	$-0.577038\pi$
$691$	2.41248e8	−	2.41248e8i	0.731189	−	0.731189i	0.970855	+	0.239666i	$0.0770380\pi$
$692$	1.43031e8	+	8.19714e6i	0.431630	+	0.0247368i
$693$	8.38365e7	−	8.38365e7i	0.251903	−	0.251903i
$694$	2.28656e8	+	1.02475e8i	0.684076	+	0.306576i
$695$	−3.83912e8			−1.14361
$696$	1.34078e8	−	2.58440e8i	0.397675	−	0.766536i
$697$		−	2.31300e7i		−	0.0683090i
$698$	−3.72010e8	−	1.66720e8i	−1.09393	−	0.490254i
$699$	−1.17590e8	−	1.17590e8i	−0.344301	−	0.344301i
$700$	1.98907e8	+	2.23092e8i	0.579904	+	0.650413i
$701$	−7.64461e7	−	7.64461e7i	−0.221922	−	0.221922i	0.587385	−	0.809308i	$-0.300157\pi$
$701$	−7.64461e7	−	7.64461e7i	−0.221922	−	0.221922i	−0.809308	+	0.587385i	$0.800157\pi$
$702$	−3.27421e6	−	8.59232e6i	−0.00946445	−	0.0248370i
$703$		−	1.73674e8i		−	0.499883i
$704$	4.40030e7	−	2.53691e8i	0.126114	−	0.727087i
$705$	1.55285e8			0.443162
$706$	−1.57845e8	+	6.01489e7i	−0.448557	+	0.170928i
$707$	−1.10646e8	+	1.10646e8i	−0.313097	+	0.313097i
$708$	1.06608e8	−	9.50512e7i	0.300394	−	0.267829i
$709$	9.09088e7	−	9.09088e7i	0.255074	−	0.255074i	−0.567973	−	0.823047i	$-0.692272\pi$
$709$	9.09088e7	−	9.09088e7i	0.255074	−	0.255074i	0.823047	+	0.567973i	$0.192272\pi$
$710$	−6.82024e7	+	1.52183e8i	−0.190557	+	0.425198i
$711$	−6.76673e7			−0.188265
$712$	2.39261e8	+	1.24128e8i	0.662876	+	0.343897i
$713$			7.18165e8i			1.98133i
$714$	−1.04668e8	+	2.33550e8i	−0.287553	+	0.641630i
$715$	−1.66251e7	−	1.66251e7i	−0.0454826	−	0.0454826i
$716$	3.02043e7	−	5.27032e8i	0.0822867	−	1.43581i
$717$	−3.50918e7	−	3.50918e7i	−0.0952025	−	0.0952025i
$718$	−3.63888e8	+	1.38664e8i	−0.983093	+	0.374620i
$719$			4.32498e8i			1.16358i	0.813338	+	0.581791i	$0.197648\pi$
$719$			4.32498e8i			1.16358i	−0.813338	+	0.581791i	$0.802352\pi$
$720$	6.15031e7	−	4.88165e7i	0.164778	−	0.130788i
$721$	−3.28066e8			−0.875297
$722$	1.63101e8	+	4.28016e8i	0.433356	+	1.13723i
$723$	−2.77772e8	+	2.77772e8i	−0.734976	+	0.734976i
$724$	7.85367e6	−	1.37038e8i	0.0206946	−	0.361098i
$725$	−2.42503e8	+	2.42503e8i	−0.636359	+	0.636359i
$726$	−9.18197e7	−	4.11499e7i	−0.239953	−	0.107537i
$727$	−4.23063e8			−1.10104			−0.550518	−	0.834823i	$-0.685570\pi$
$727$	−4.23063e8			−1.10104			−0.550518	+	0.834823i	$0.685570\pi$
$728$	−7.35685e7	+	2.33089e7i	−0.190677	+	0.0604127i
$729$			1.43489e7i			0.0370370i
$730$	1.33030e8	+	5.96189e7i	0.341965	+	0.153255i
$731$	5.06645e7	+	5.06645e7i	0.129703	+	0.129703i
$732$	−1.30277e8	+	1.16154e8i	−0.332151	+	0.296143i
$733$	−2.01686e8	−	2.01686e8i	−0.512111	−	0.512111i	0.403062	−	0.915173i	$-0.367946\pi$
$733$	−2.01686e8	−	2.01686e8i	−0.512111	−	0.512111i	−0.915173	+	0.403062i	$0.867946\pi$
$734$	−2.27826e7	−	5.97870e7i	−0.0576123	−	0.151188i
$735$		−	1.58783e8i		−	0.399890i
$736$	−1.63532e8	−	6.41566e8i	−0.410175	−	1.60919i
$737$	−5.47790e8			−1.36840
$738$	−1.01705e7	+	3.87558e6i	−0.0253030	+	0.00964202i
$739$	−2.56114e8	+	2.56114e8i	−0.634601	+	0.634601i	−0.949219	−	0.314617i	$-0.898124\pi$
$739$	−2.56114e8	+	2.56114e8i	−0.634601	+	0.634601i	0.314617	+	0.949219i	$0.398124\pi$
$740$	−5.71395e7	−	6.40870e7i	−0.141007	−	0.158152i
$741$	3.41574e7	−	3.41574e7i	0.0839519	−	0.0839519i
$742$	1.58841e8	−	3.54428e8i	0.388821	−	0.867594i
$743$	4.27129e8			1.04134			0.520670	−	0.853758i	$-0.325682\pi$
$743$	4.27129e8			1.04134			0.520670	+	0.853758i	$0.325682\pi$
$744$	−2.70436e8	+	8.56832e7i	−0.656669	+	0.208054i
$745$		−	2.71931e8i		−	0.657643i
$746$	1.24475e8	−	2.77746e8i	0.299822	−	0.669007i
$747$	−1.47031e8	−	1.47031e8i	−0.352734	−	0.352734i
$748$	−2.59274e8	−	1.48590e7i	−0.619518	−	0.0355047i
$749$	−3.95238e7	−	3.95238e7i	−0.0940617	−	0.0940617i
$750$	−2.30076e8	+	8.76735e7i	−0.545366	+	0.207819i
$751$			5.54989e8i			1.31028i	0.755507	+	0.655140i	$0.227391\pi$
$751$			5.54989e8i			1.31028i	−0.755507	+	0.655140i	$0.772609\pi$
$752$	5.13818e8	+	5.90881e7i	1.20825	+	0.138946i
$753$	1.99204e7			0.0466565
$754$	−3.15312e7	−	8.27455e7i	−0.0735575	−	0.193032i
$755$	3.69547e8	−	3.69547e8i	0.858674	−	0.858674i
$756$	1.20231e8	+	6.89049e6i	0.278261	+	0.0159472i
$757$	−1.31247e8	+	1.31247e8i	−0.302553	+	0.302553i	−0.842012	−	0.539459i	$-0.818629\pi$
$757$	−1.31247e8	+	1.31247e8i	−0.302553	+	0.302553i	0.539459	+	0.842012i	$0.318629\pi$
$758$	3.16867e8	+	1.42007e8i	0.727561	+	0.326064i
$759$	3.09360e8			0.707521
$760$	3.66169e8	+	1.89967e8i	0.834144	+	0.432750i
$761$			4.29874e8i			0.975411i	0.873008	+	0.487705i	$0.162166\pi$
$761$			4.29874e8i			0.975411i	−0.873008	+	0.487705i	$0.837834\pi$
$762$	4.19618e8	+	1.88056e8i	0.948394	+	0.425032i
$763$	5.85858e8	+	5.85858e8i	1.31892	+	1.31892i
$764$	−3.71645e8	−	4.16833e8i	−0.833391	−	0.934722i
$765$	−5.60022e7	−	5.60022e7i	−0.125090	−	0.125090i
$766$	−1.15208e8	−	3.02335e8i	−0.256329	−	0.672669i
$767$		−	4.34396e7i		−	0.0962720i
$768$	2.22081e8	−	1.38125e8i	0.490261	−	0.304921i
$769$	1.99225e8			0.438091			0.219045	−	0.975715i	$-0.429706\pi$
$769$	1.99225e8			0.438091			0.219045	+	0.975715i	$0.429706\pi$
$770$	2.87749e8	−	1.09650e8i	0.630292	−	0.240181i
$771$	1.00212e7	−	1.00212e7i	0.0218654	−	0.0218654i
$772$	1.70259e8	−	1.51802e8i	0.370049	−	0.329933i
$773$	1.29385e8	−	1.29385e8i	0.280121	−	0.280121i	−0.553036	−	0.833157i	$-0.686531\pi$
$773$	1.29385e8	−	1.29385e8i	0.280121	−	0.280121i	0.833157	+	0.553036i	$0.186531\pi$
$774$	1.37884e7	−	3.07667e7i	0.0297366	−	0.0663527i
$775$	3.34158e8			0.717871
$776$	−1.98113e8	+	3.81872e8i	−0.423963	+	0.817207i
$777$		−	1.31684e8i		−	0.280718i
$778$	8.33065e7	−	1.85885e8i	0.176905	−	0.394736i
$779$	−4.04311e7	−	4.04311e7i	−0.0855270	−	0.0855270i
$780$	1.36641e6	−	2.38423e7i	0.00287937	−	0.0502418i
$781$	−1.83519e8	−	1.83519e8i	−0.385238	−	0.385238i
$782$	−6.24019e8	+	2.37790e8i	−1.30490	+	0.497249i
$783$			1.38182e8i			0.287851i
$784$	6.04189e7	−	5.25391e8i	0.125379	−	1.09027i
$785$	−3.85265e8			−0.796435
$786$	−1.07113e8	−	2.81089e8i	−0.220584	−	0.578864i
$787$	−2.68473e7	+	2.68473e7i	−0.0550778	+	0.0550778i	−0.734109	−	0.679031i	$-0.762400\pi$
$787$	−2.68473e7	+	2.68473e7i	−0.0550778	+	0.0550778i	0.679031	+	0.734109i	$0.262400\pi$
$788$	−2.69641e7	+	4.70493e8i	−0.0551070	+	0.961557i
$789$	1.21497e8	−	1.21497e8i	0.247364	−	0.247364i
$790$	−1.60377e8	−	7.18747e7i	−0.325283	−	0.145779i
$791$	9.95981e8			2.01243
$792$	3.69093e7	+	1.16494e8i	0.0742952	+	0.234493i
$793$			5.30840e7i			0.106450i
$794$	2.54771e8	+	1.14178e8i	0.508966	+	0.228098i
$795$	8.49873e7	+	8.49873e7i	0.169143	+	0.169143i
$796$	3.24102e8	−	2.88967e8i	0.642603	−	0.572940i
$797$	−5.83661e8	−	5.83661e8i	−1.15288	−	1.15288i	−0.985972	−	0.166913i	$-0.946620\pi$
$797$	−5.83661e8	−	5.83661e8i	−1.15288	−	1.15288i	−0.166913	−	0.985972i	$-0.553380\pi$
$798$	2.25285e8	+	5.91201e8i	0.443326	+	1.16339i
$799$		−	5.21665e8i		−	1.02271i
$800$	−2.98517e8	+	7.60903e7i	−0.583041	+	0.148614i
$801$	−1.27928e8			−0.248924
$802$	5.18089e8	−	1.97424e8i	1.00434	−	0.382717i
$803$	−1.60423e8	+	1.60423e8i	−0.309827	+	0.309827i
$804$	−3.70287e8	−	4.15309e8i	−0.712475	−	0.799104i
$805$	5.59900e8	−	5.59900e8i	1.07330	−	1.07330i
$806$	−3.52855e7	+	7.87342e7i	−0.0673894	+	0.150369i
$807$	−3.93678e8			−0.749067
$808$	−4.87125e7	−	1.53748e8i	−0.0923435	−	0.291458i
$809$			2.19319e8i			0.414219i	0.978318	+	0.207110i	$0.0664057\pi$
$809$			2.19319e8i			0.414219i	−0.978318	+	0.207110i	$0.933594\pi$
$810$	−1.52411e7	+	3.40082e7i	−0.0286788	+	0.0639923i
$811$	5.12226e6	+	5.12226e6i	0.00960282	+	0.00960282i	0.711892	−	0.702289i	$-0.247839\pi$
$811$	5.12226e6	+	5.12226e6i	0.00960282	+	0.00960282i	−0.702289	+	0.711892i	$0.747839\pi$
$812$	1.15785e9	+	6.63566e7i	2.16264	+	0.123941i
$813$	2.65010e7	+	2.65010e7i	0.0493164	+	0.0493164i
$814$	1.24865e8	−	4.75812e7i	0.231508	−	0.0882191i
$815$		−	1.55514e8i		−	0.287274i
$816$	−1.63994e8	−	2.06614e8i	−0.301827	−	0.380267i
$817$	1.77122e8			0.324793
$818$	2.15481e8	+	5.65473e8i	0.393685	+	1.03312i
$819$	2.58991e7	−	2.58991e7i	0.0471447	−	0.0471447i
$820$	−2.82214e7	−	1.61738e6i	−0.0511844	−	0.00293339i
$821$	−6.18920e8	+	6.18920e8i	−1.11842	+	1.11842i	−0.126447	+	0.991973i	$0.540357\pi$
$821$	−6.18920e8	+	6.18920e8i	−1.11842	+	1.11842i	−0.991973	+	0.126447i	$0.959643\pi$
$822$	−2.82769e8	−	1.26726e8i	−0.509115	−	0.228165i
$823$	4.08281e8			0.732420			0.366210	−	0.930532i	$-0.380655\pi$
$823$	4.08281e8			0.732420			0.366210	+	0.930532i	$0.380655\pi$
$824$	1.55715e8	−	3.00147e8i	0.278323	−	0.536479i
$825$		−	1.43943e8i		−	0.256348i
$826$	5.19182e8	+	2.32677e8i	0.921254	+	0.412869i
$827$	2.35915e8	+	2.35915e8i	0.417099	+	0.417099i	0.884203	−	0.467103i	$-0.154702\pi$
$827$	2.35915e8	+	2.35915e8i	0.417099	+	0.417099i	−0.467103	+	0.884203i	$0.654702\pi$
$828$	2.09117e8	+	2.34543e8i	0.368381	+	0.413172i
$829$	−1.79611e8	−	1.79611e8i	−0.315260	−	0.315260i	0.531683	−	0.846943i	$-0.321560\pi$
$829$	−1.79611e8	−	1.79611e8i	−0.315260	−	0.315260i	−0.846943	+	0.531683i	$0.821560\pi$
$830$	−1.92303e8	−	5.04650e8i	−0.336320	−	0.882583i
$831$			1.47911e8i			0.257750i
$832$	1.35936e7	−	7.83712e7i	0.0236029	−	0.136078i
$833$	−5.33415e8			−0.922847
$834$	5.67098e8	−	2.16100e8i	0.977598	−	0.372526i
$835$	−3.39403e8	+	3.39403e8i	−0.582983	+	0.582983i
$836$	−4.79182e8	+	4.27235e8i	−0.820128	+	0.731220i
$837$	9.52047e7	−	9.52047e7i	0.162361	−	0.162361i
$838$	1.34851e8	−	3.00900e8i	0.229152	−	0.511317i
$839$	1.16608e7			0.0197444			0.00987221	−	0.999951i	$-0.496858\pi$
$839$	1.16608e7			0.0197444			0.00987221	+	0.999951i	$0.496858\pi$
$840$	2.77640e8	+	1.44038e8i	0.468429	+	0.243019i
$841$			7.35898e8i			1.23717i
$842$	1.00247e7	−	2.23685e7i	0.0167932	−	0.0374715i
$843$	−1.39068e8	−	1.39068e8i	−0.232136	−	0.232136i
$844$	3.34939e7	−	5.84431e8i	0.0557107	−	0.972089i
$845$	2.64123e8	+	2.64123e8i	0.437760	+	0.437760i
$846$	−2.29380e8	+	8.74083e7i	−0.378831	+	0.144358i
$847$		−	4.00800e8i		−	0.659594i
$848$	2.48873e8	+	3.13551e8i	0.408122	+	0.514186i
$849$	3.95965e8			0.647044
$850$	1.10642e8	+	2.90352e8i	0.180163	+	0.472790i
$851$	2.42961e8	−	2.42961e8i	0.394228	−	0.394228i
$852$	1.50834e7	−	2.63189e8i	0.0243882	−	0.425548i
$853$	9.74736e7	−	9.74736e7i	0.157051	−	0.157051i	−0.624208	−	0.781258i	$-0.714578\pi$
$853$	9.74736e7	−	9.74736e7i	0.157051	−	0.157051i	0.781258	+	0.624208i	$0.214578\pi$
$854$	−6.34449e8	−	2.84335e8i	−1.01865	−	0.456516i
$855$	−1.95783e8			−0.313239
$856$	5.49200e7	−	1.74005e7i	0.0875607	−	0.0277421i
$857$		−	9.03691e8i		−	1.43575i	−0.696174	−	0.717873i	$-0.745116\pi$
$857$		−	9.03691e8i		−	1.43575i	0.696174	−	0.717873i	$-0.254884\pi$
$858$	3.39159e7	+	1.51998e7i	0.0536960	+	0.0240644i
$859$	1.52064e8	+	1.52064e8i	0.239909	+	0.239909i	0.816812	−	0.576903i	$-0.195739\pi$
$859$	1.52064e8	+	1.52064e8i	0.239909	+	0.239909i	−0.576903	+	0.816812i	$0.695739\pi$
$860$	6.53595e7	−	5.82740e7i	0.102757	−	0.0916178i
$861$	−3.06560e7	−	3.06560e7i	−0.0480293	−	0.0480293i
$862$	3.38427e8	+	8.88113e8i	0.528376	+	1.38659i
$863$			3.80994e8i			0.592770i	0.955069	+	0.296385i	$0.0957811\pi$
$863$			3.80994e8i			0.592770i	−0.955069	+	0.296385i	$0.904219\pi$
$864$	−6.33714e7	+	1.06729e8i	−0.0982544	+	0.165478i
$865$	−1.76598e8			−0.272859
$866$	1.93339e8	−	7.36742e7i	0.297691	−	0.113439i
$867$	7.79272e7	−	7.79272e7i	0.119573	−	0.119573i
$868$	−7.52015e8	−	8.43451e8i	−1.14992	−	1.28974i
$869$	1.93401e8	−	1.93401e8i	0.294713	−	0.294713i
$870$	−1.46774e8	+	3.27504e8i	−0.222891	+	0.497347i
$871$	−1.69226e8			−0.256101
$872$	−8.14076e8	+	2.57926e8i	−1.22777	+	0.388997i
$873$		−	2.04179e8i		−	0.306879i
$874$	−6.75124e8	+	1.50643e9i	−1.01123	+	2.25640i
$875$	−6.93500e8	−	6.93500e8i	−1.03520	−	1.03520i
$876$	−2.30065e8	−	1.31851e7i	−0.342246	−	0.0196142i
$877$	−5.62865e8	−	5.62865e8i	−0.834460	−	0.834460i	0.153663	−	0.988123i	$-0.450893\pi$
$877$	−5.62865e8	−	5.62865e8i	−0.834460	−	0.834460i	−0.988123	+	0.153663i	$0.950893\pi$
$878$	−1.15202e9	+	4.38990e8i	−1.70206	+	0.648592i
$879$			2.42744e8i			0.357423i
$880$	−3.62596e7	+	3.15306e8i	−0.0532078	+	0.462684i
$881$	1.19313e9			1.74486			0.872428	−	0.488743i	$-0.162544\pi$
$881$	1.19313e9			1.74486			0.872428	+	0.488743i	$0.162544\pi$
$882$	8.93769e7	+	2.34547e8i	0.130263	+	0.341840i
$883$	−3.93429e8	+	3.93429e8i	−0.571458	+	0.571458i	−0.932536	−	0.361078i	$-0.882409\pi$
$883$	−3.93429e8	+	3.93429e8i	−0.571458	+	0.571458i	0.361078	+	0.932536i	$0.382409\pi$
$884$	−8.00960e7	−	4.59032e6i	−0.115946	−	0.00664486i
$885$	−1.24493e8	+	1.24493e8i	−0.179604	+	0.179604i
$886$	−9.18411e8	−	4.11595e8i	−1.32049	−	0.591792i
$887$	6.77947e8			0.971460			0.485730	−	0.874109i	$-0.338554\pi$
$887$	6.77947e8			0.971460			0.485730	+	0.874109i	$0.338554\pi$
$888$	1.20478e8	+	6.25033e7i	0.172055	+	0.0892615i
$889$			1.83166e9i			2.60699i
$890$	−3.03200e8	−	1.35882e8i	−0.430090	−	0.192749i
$891$	−4.10108e7	−	4.10108e7i	−0.0579783	−	0.0579783i
$892$	−4.00058e8	−	4.48700e8i	−0.563674	−	0.632211i
$893$	−9.11866e8	−	9.11866e8i	−1.28049	−	1.28049i
$894$	1.53067e8	+	4.01685e8i	0.214225	+	0.562177i
$895$			6.50719e8i			0.907662i
$896$	8.63865e8	+	5.82249e8i	1.20094	+	0.809441i
$897$	9.55689e7			0.132416
$898$	−8.63391e8	+	3.29006e8i	−1.19228	+	0.454334i
$899$	9.16838e8	−	9.16838e8i	1.26187	−	1.26187i
$900$	1.09131e8	−	9.73007e7i	0.149700	−	0.133471i
$901$	2.85507e8	−	2.85507e8i	0.390339	−	0.390339i
$902$	1.79915e7	−	4.01452e7i	0.0245159	−	0.0547034i
$903$	1.34299e8			0.182393
$904$	−4.72738e8	+	9.11222e8i	−0.639904	+	1.23344i
$905$			1.69199e8i			0.228271i
$906$	−3.37864e8	+	7.53892e8i	−0.454316	+	1.01373i
$907$	−4.68493e8	−	4.68493e8i	−0.627887	−	0.627887i	0.319649	−	0.947536i	$-0.396435\pi$
$907$	−4.68493e8	−	4.68493e8i	−0.627887	−	0.627887i	−0.947536	+	0.319649i	$0.896435\pi$
$908$	9.61635e6	−	1.67795e8i	0.0128455	−	0.224141i
$909$	5.41256e7	+	5.41256e7i	0.0720628	+	0.0720628i
$910$	8.88926e7	−	3.38737e7i	0.117962	−	0.0449509i
$911$		−	3.97237e8i		−	0.525406i	−0.964877	−	0.262703i	$-0.915386\pi$
$911$		−	3.97237e8i		−	0.525406i	0.964877	−	0.262703i	$-0.0846139\pi$
$912$	−6.47819e8	−	7.44980e7i	−0.854023	−	0.0982110i
$913$	8.40464e8			1.10435
$914$	−3.40345e8	−	8.93147e8i	−0.445739	−	1.16973i
$915$	1.52133e8	−	1.52133e8i	0.198591	−	0.198591i
$916$	−1.16493e7	+	2.03267e8i	−0.0151570	+	0.264472i
$917$	8.47265e8	−	8.47265e8i	1.09878	−	1.09878i
$918$	1.14247e8	+	5.12010e7i	0.147678	+	0.0661836i
$919$	5.37068e8			0.691963			0.345982	−	0.938241i	$-0.387546\pi$
$919$	5.37068e8			0.691963			0.345982	+	0.938241i	$0.387546\pi$
$920$	2.46498e8	+	7.78006e8i	0.316556	+	0.999124i
$921$		−	7.84680e8i		−	1.00442i
$922$	−4.24640e8	−	1.90307e8i	−0.541786	−	0.242807i
$923$	−5.66936e7	−	5.66936e7i	−0.0720989	−	0.0720989i
$924$	−3.63329e8	+	3.23941e8i	−0.460558	+	0.410630i
$925$	−1.13048e8	−	1.13048e8i	−0.142836	−	0.142836i
$926$	−2.17537e8	−	5.70868e8i	−0.273968	−	0.718957i
$927$			1.60482e8i			0.201460i
$928$	−6.10277e8	+	1.02782e9i	−0.763631	+	1.28609i
$929$	−1.33360e9			−1.66333			−0.831667	−	0.555275i	$-0.812613\pi$
$929$	−1.33360e9			−1.66333			−0.831667	+	0.555275i	$0.812613\pi$
$930$	3.26768e8	−	1.24519e8i	0.406247	−	0.154806i
$931$	−9.32403e8	+	9.32403e8i	−1.15546	+	1.15546i
$932$	4.54364e8	+	5.09610e8i	0.561250	+	0.629491i
$933$	−2.12278e8	+	2.12278e8i	−0.261373	+	0.261373i
$934$	2.32669e8	−	5.19165e8i	0.285560	−	0.637184i
$935$	3.20122e8			0.391634
$936$	1.14022e7	+	3.59880e7i	0.0139047	+	0.0438864i
$937$			6.89471e8i			0.838102i	0.907963	+	0.419051i	$0.137637\pi$
$937$			6.89471e8i			0.838102i	−0.907963	+	0.419051i	$0.862363\pi$
$938$	9.06427e8	−	2.02255e9i	1.09831	−	2.45071i
$939$	−5.16756e8	−	5.16756e8i	−0.624150	−	0.624150i
$940$	−6.36494e8	−	3.64776e7i	−0.766321	−	0.0439180i
$941$	5.75999e8	+	5.75999e8i	0.691278	+	0.691278i	0.962513	−	0.271235i	$-0.0874322\pi$
$941$	5.75999e8	+	5.75999e8i	0.691278	+	0.691278i	−0.271235	+	0.962513i	$0.587432\pi$
$942$	5.69096e8	−	2.16861e8i	0.680821	−	0.259435i
$943$		−	1.13122e8i		−	0.134900i
$944$	−4.59303e8	+	3.64560e8i	−0.545988	+	0.433364i
$945$	−1.48448e8			−0.175905
$946$	4.85260e7	+	1.27344e8i	0.0573193	+	0.150420i
$947$	−3.25772e8	+	3.25772e8i	−0.383587	+	0.383587i	−0.872393	−	0.488806i	$-0.837433\pi$
$947$	−3.25772e8	+	3.25772e8i	−0.383587	+	0.383587i	0.488806	+	0.872393i	$0.337433\pi$
$948$	2.77360e8	+	1.58956e7i	0.325551	+	0.0186574i
$949$	−4.95585e7	+	4.95585e7i	−0.0579855	+	0.0579855i
$950$	7.00935e8	+	3.14131e8i	0.817536	+	0.366387i
$951$	7.99385e8			0.929426
$952$	4.83882e8	−	9.32704e8i	0.560827	−	1.08102i
$953$			7.99405e7i			0.0923609i	0.998933	+	0.0461804i	$0.0147049\pi$
$953$			7.99405e7i			0.0923609i	−0.998933	+	0.0461804i	$0.985295\pi$
$954$	−1.73378e8	−	7.77011e7i	−0.199687	−	0.0894916i
$955$	4.86762e8	+	4.86762e8i	0.558864	+	0.558864i
$956$	1.35594e8	+	1.52080e8i	0.155191	+	0.174060i
$957$	−3.94942e8	−	3.94942e8i	−0.450606	−	0.450606i
$958$	−2.00522e8	−	5.26218e8i	−0.228069	−	0.598507i
$959$		−	1.23430e9i		−	1.39948i
$960$	−2.63561e8	+	1.85645e8i	−0.297898	+	0.209831i
$961$	−3.75859e8			−0.423501
$962$	3.85737e7	−	1.46990e7i	0.0433277	−	0.0165106i
$963$	−1.93341e7	+	1.93341e7i	−0.0216494	+	0.0216494i
$964$	1.20380e9	−	1.07330e9i	1.34377	−	1.19809i
$965$	−1.98822e8	+	1.98822e8i	−0.221250	+	0.221250i
$966$	−5.11898e8	+	1.14222e9i	−0.567874	+	1.26712i
$967$	−1.19083e9			−1.31696			−0.658479	−	0.752599i	$-0.728800\pi$
$967$	−1.19083e9			−1.31696			−0.658479	+	0.752599i	$0.728800\pi$
$968$	3.66691e8	+	1.90238e8i	0.404273	+	0.209735i
$969$			6.57713e8i			0.722878i
$970$	2.16874e8	−	4.83921e8i	0.237625	−	0.530224i
$971$	−7.36800e8	−	7.36800e8i	−0.804808	−	0.804808i	0.179035	−	0.983843i	$-0.442702\pi$
$971$	−7.36800e8	−	7.36800e8i	−0.804808	−	0.804808i	−0.983843	+	0.179035i	$0.942702\pi$
$972$	3.37067e6	−	5.88144e7i	0.00367043	−	0.0640449i
$973$	1.70936e9	+	1.70936e9i	1.85564	+	1.85564i
$974$	−4.86354e8	+	1.85331e8i	−0.526351	+	0.200573i
$975$		−	4.44676e7i		−	0.0479767i
$976$	5.61276e8	−	4.45499e8i	0.603708	−	0.479178i
$977$	7.27724e8			0.780338			0.390169	−	0.920743i	$-0.372417\pi$
$977$	7.27724e8			0.780338			0.390169	+	0.920743i	$0.372417\pi$
$978$	8.75372e7	+	2.29719e8i	0.0935785	+	0.245572i
$979$	3.65632e8	−	3.65632e8i	0.389670	−	0.389670i
$980$	−3.72992e7	+	6.50830e8i	−0.0396298	+	0.691495i
$981$	2.86588e8	−	2.86588e8i	0.303565	−	0.303565i
$982$	7.62899e8	+	3.41901e8i	0.805625	+	0.361049i
$983$	4.20246e8			0.442428			0.221214	−	0.975225i	$-0.428998\pi$
$983$	4.20246e8			0.442428			0.221214	+	0.975225i	$0.428998\pi$
$984$	4.25979e7	−	1.34964e7i	0.0447098	−	0.0141655i
$985$		−	5.80912e8i		−	0.607857i
$986$	1.10022e9	+	4.93075e8i	1.14775	+	0.514377i
$987$	−6.91402e8	−	6.91402e8i	−0.719083	−	0.719083i
$988$	−1.48031e8	+	1.31983e8i	−0.153490	+	0.136851i
$989$	2.47785e8	+	2.47785e8i	0.256145	+	0.256145i
$990$	−5.36384e7	−	1.40760e8i	−0.0552803	−	0.145069i
$991$			2.01934e8i			0.207486i	0.994604	+	0.103743i	$0.0330820\pi$
$991$			2.01934e8i			0.207486i	−0.994604	+	0.103743i	$0.966918\pi$
$992$	1.12861e9	−	2.87677e8i	1.15614	−	0.294694i
$993$	1.08989e9			1.11310
$994$	9.81260e8	−	3.73922e8i	0.999137	−	0.380734i
$995$	−3.78474e8	+	3.78474e8i	−0.384208	+	0.384208i
$996$	5.68123e8	+	6.37201e8i	0.574996	+	0.644909i
$997$	1.25907e9	−	1.25907e9i	1.27047	−	1.27047i	0.324626	−	0.945842i	$-0.394761\pi$
$997$	1.25907e9	−	1.25907e9i	1.27047	−	1.27047i	0.945842	−	0.324626i	$-0.105239\pi$
$998$	8.74410e7	−	1.95111e8i	0.0879678	−	0.196286i
$999$	−6.44169e7			−0.0646105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.3	✓	48
4.3	odd	2		192.7.l.a.175.19		48
8.3	odd	2		384.7.l.a.223.6		48
8.5	even	2		384.7.l.b.223.19		48
16.3	odd	4		384.7.l.b.31.19		48
16.5	even	4		192.7.l.a.79.19		48
16.11	odd	4	inner	48.7.l.a.43.3	yes	48
16.13	even	4		384.7.l.a.31.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.3	✓	48	1.1	even	1	trivial
48.7.l.a.43.3	yes	48	16.11	odd	4	inner
192.7.l.a.79.19		48	16.5	even	4
192.7.l.a.175.19		48	4.3	odd	2
384.7.l.a.31.6		48	16.13	even	4
384.7.l.a.223.6		48	8.3	odd	2
384.7.l.b.31.19		48	16.3	odd	4
384.7.l.b.223.19		48	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.47563 + 2.84868i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(47.7700 - 42.5914i) q^{4} +(-55.7840 + 55.7840i) q^{5} +(51.0014 - 113.802i) q^{6} +496.753 q^{7} +(-235.781 + 454.479i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(-7.47563 + 2.84868i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(47.7700 - 42.5914i) q^{4} +(-55.7840 + 55.7840i) q^{5} +(51.0014 - 113.802i) q^{6} +496.753 q^{7} +(-235.781 + 454.479i) q^{8} -243.000i q^{9} +(258.109 - 575.931i) q^{10} +(694.522 + 694.522i) q^{11} +(-57.0825 + 996.027i) q^{12} +(214.555 + 214.555i) q^{13} +(-3713.54 + 1415.09i) q^{14} -1229.78i q^{15} +(467.948 - 4069.18i) q^{16} -4131.33 q^{17} +(692.230 + 1816.58i) q^{18} +(-7221.52 + 7221.52i) q^{19} +(-288.885 + 5040.72i) q^{20} +(-5475.56 + 5475.56i) q^{21} +(-7170.46 - 3213.52i) q^{22} -20205.1 q^{23} +(-2410.64 - 7608.54i) q^{24} +9401.30i q^{25} +(-2215.13 - 992.733i) q^{26} +(2678.52 + 2678.52i) q^{27} +(23729.9 - 21157.4i) q^{28} +(25794.6 + 25794.6i) q^{29} +(3503.25 + 9193.38i) q^{30} -35543.8i q^{31} +(8093.60 + 31752.7i) q^{32} -15311.0 q^{33} +(30884.3 - 11768.8i) q^{34} +(-27710.9 + 27710.9i) q^{35} +(-10349.7 - 11608.1i) q^{36} +(-12024.7 + 12024.7i) q^{37} +(33413.6 - 74557.2i) q^{38} -4729.95 q^{39} +(-12199.8 - 38505.5i) q^{40} +5598.69i q^{41} +(25335.1 - 56531.4i) q^{42} +(-12263.5 - 12263.5i) q^{43} +(62758.0 + 3596.67i) q^{44} +(13555.5 + 13555.5i) q^{45} +(151046. - 57557.9i) q^{46} +126271. i q^{47} +(39695.3 + 50011.4i) q^{48} +129115. q^{49} +(-26781.3 - 70280.6i) q^{50} +(45538.4 - 45538.4i) q^{51} +(19387.5 + 1111.10i) q^{52} +(-69107.7 + 69107.7i) q^{53} +(-27653.8 - 12393.4i) q^{54} -77486.4 q^{55} +(-117125. + 225764. i) q^{56} -159201. i q^{57} +(-266311. - 119350. i) q^{58} +(-101232. - 101232. i) q^{59} +(-52378.0 - 58746.6i) q^{60} +(123707. + 123707. i) q^{61} +(101253. + 265712. i) q^{62} -120711. i q^{63} +(-150958. - 214315. i) q^{64} -23937.4 q^{65} +(114460. - 43616.3i) q^{66} +(-394365. + 394365. i) q^{67} +(-197354. + 175959. i) q^{68} +(222715. - 222715. i) q^{69} +(128217. - 286095. i) q^{70} -264238. q^{71} +(110438. + 57294.9i) q^{72} +230983. i q^{73} +(55637.8 - 124147. i) q^{74} +(-103628. - 103628. i) q^{75} +(-37397.6 + 652547. i) q^{76} +(345006. + 345006. i) q^{77} +(35359.3 - 13474.1i) q^{78} -278466. i q^{79} +(200891. + 253099. i) q^{80} -59049.0 q^{81} +(-15948.9 - 41853.7i) q^{82} +(605066. - 605066. i) q^{83} +(-28355.9 + 494779. i) q^{84} +(230462. - 230462. i) q^{85} +(126612. + 56742.5i) q^{86} -568652. q^{87} +(-479401. + 151890. i) q^{88} -526452. i q^{89} +(-139951. - 62720.6i) q^{90} +(106581. + 106581. i) q^{91} +(-965197. + 860562. i) q^{92} +(391789. + 391789. i) q^{93} +(-359705. - 943952. i) q^{94} -805690. i q^{95} +(-439214. - 260788. i) q^{96} +840241. q^{97} +(-965212. + 367806. i) q^{98} +(168769. - 168769. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

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