LMFDB - Embedded newform 62.7.f.a.15.13

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)

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);

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")

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			15.13
Character	$\chi$	$=$	62.15
Dual form			62.7.f.a.29.13

$q$-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} +(0.519266 - 0.714708i) q^{3} +(9.88854 - 30.4338i) q^{4} -131.510 q^{5} -4.99742i q^{6} +(-80.4012 + 247.449i) q^{7} +(-55.9381 - 172.160i) q^{8} +(225.032 + 692.578i) q^{9} +(-601.854 + 437.272i) q^{10} +(1620.86 + 526.649i) q^{11} +(-16.6165 - 22.8707i) q^{12} +(-1241.32 + 1708.54i) q^{13} +(454.818 + 1399.79i) q^{14} +(-68.2886 + 93.9911i) q^{15} +(-828.433 - 601.892i) q^{16} +(5956.07 - 1935.24i) q^{17} +(3332.69 + 2421.34i) q^{18} +(-10156.5 + 7379.16i) q^{19} +(-1300.44 + 4002.35i) q^{20} +(135.105 + 185.955i) q^{21} +(9168.97 - 2979.18i) q^{22} +(-996.325 + 323.726i) q^{23} +(-152.091 - 49.4172i) q^{24} +1669.85 q^{25} +11946.5i q^{26} +(1224.34 + 397.812i) q^{27} +(6735.78 + 4893.83i) q^{28} +(12895.5 + 17749.1i) q^{29} +657.210i q^{30} +(-1896.62 + 29730.6i) q^{31} -5792.62 q^{32} +(1218.06 - 884.970i) q^{33} +(20823.2 - 28660.7i) q^{34} +(10573.6 - 32542.1i) q^{35} +23303.0 q^{36} -83566.2i q^{37} +(-21945.5 + 67541.3i) q^{38} +(576.527 + 1774.37i) q^{39} +(7356.41 + 22640.7i) q^{40} +(-109070. + 79243.8i) q^{41} +(1236.61 + 401.799i) q^{42} +(22107.7 + 30428.7i) q^{43} +(32055.9 - 44121.1i) q^{44} +(-29594.0 - 91080.8i) q^{45} +(-3483.28 + 4794.32i) q^{46} +(-17721.0 - 12875.1i) q^{47} +(-860.354 + 279.546i) q^{48} +(40413.1 + 29361.9i) q^{49} +(7642.04 - 5552.27i) q^{50} +(1709.65 - 5261.76i) q^{51} +(39722.4 + 54673.2i) q^{52} +(-43773.3 + 14222.8i) q^{53} +(6925.92 - 2250.37i) q^{54} +(-213159. - 69259.6i) q^{55} +47098.3 q^{56} +11090.7i q^{57} +(118032. + 38351.0i) q^{58} +(-199967. - 145284. i) q^{59} +(2185.23 + 3007.72i) q^{60} -419634. i q^{61} +(90174.7 + 142368. i) q^{62} -189471. q^{63} +(-26509.9 + 19260.5i) q^{64} +(163246. - 224689. i) q^{65} +(2631.89 - 8100.12i) q^{66} +78380.7 q^{67} -200403. i q^{68} +(-285.988 + 880.181i) q^{69} +(-59813.0 - 184086. i) q^{70} +(-123227. - 379255. i) q^{71} +(106646. - 77482.9i) q^{72} +(407779. + 132495. i) q^{73} +(-277859. - 382440. i) q^{74} +(867.094 - 1193.45i) q^{75} +(124143. + 382071. i) q^{76} +(-260638. + 358738. i) q^{77} +(8538.28 + 6203.42i) q^{78} +(517310. - 168084. i) q^{79} +(108947. + 79154.8i) q^{80} +(-428564. + 311370. i) q^{81} +(-235670. + 725317. i) q^{82} +(634601. + 873453. i) q^{83} +(6995.32 - 2272.92i) q^{84} +(-783282. + 254504. i) q^{85} +(202352. + 65748.1i) q^{86} +19381.6 q^{87} -308506. i q^{88} +(321953. + 104609. i) q^{89} +(-438282. - 318430. i) q^{90} +(-322972. - 444533. i) q^{91} +33523.1i q^{92} +(20263.8 + 16793.6i) q^{93} -123910. q^{94} +(1.33569e6 - 970432. i) q^{95} +(-3007.91 + 4140.03i) q^{96} +(-433583. + 1.33443e6i) q^{97} +282579. q^{98} +1.24108e6i 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
$3$	0.519266	−	0.714708i	0.0192321	−	0.0264707i	−0.799293	−	0.600942i	$-0.794792\pi$
$3$	0.519266	−	0.714708i	0.0192321	−	0.0264707i	0.818525	+	0.574471i	$0.194792\pi$
$4$	9.88854	−	30.4338i	0.154508	−	0.475528i
$5$	−131.510			−1.05208			−0.526040	−	0.850460i	$-0.676324\pi$
$5$	−131.510			−1.05208			−0.526040	+	0.850460i	$0.676324\pi$
$6$		−	4.99742i		−	0.0231362i
$7$	−80.4012	+	247.449i	−0.234406	+	0.721427i	0.762794	+	0.646642i	$0.223827\pi$
$7$	−80.4012	+	247.449i	−0.234406	+	0.721427i	−0.997200	+	0.0747853i	$0.976173\pi$
$8$	−55.9381	−	172.160i	−0.109254	−	0.336249i
$9$	225.032	+	692.578i	0.308686	+	0.950038i
$10$	−601.854	+	437.272i	−0.601854	+	0.437272i
$11$	1620.86	+	526.649i	1.21778	+	0.395679i	0.846271	−	0.532752i	$-0.178842\pi$
$11$	1620.86	+	526.649i	1.21778	+	0.395679i	0.371504	+	0.928431i	$0.378842\pi$
$12$	−16.6165	−	22.8707i	−0.00961603	−	0.0132353i
$13$	−1241.32	+	1708.54i	−0.565009	+	0.777668i	−0.991953	−	0.126610i	$-0.959590\pi$
$13$	−1241.32	+	1708.54i	−0.565009	+	0.777668i	0.426944	+	0.904278i	$0.359590\pi$
$14$	454.818	+	1399.79i	0.165750	+	0.510126i
$15$	−68.2886	+	93.9911i	−0.0202336	+	0.0278492i
$16$	−828.433	−	601.892i	−0.202254	−	0.146946i
$17$	5956.07	−	1935.24i	1.21231	−	0.393903i	0.368033	−	0.929813i	$-0.380031\pi$
$17$	5956.07	−	1935.24i	1.21231	−	0.393903i	0.844275	+	0.535910i	$0.180031\pi$
$18$	3332.69	+	2421.34i	0.571449	+	0.415182i
$19$	−10156.5	+	7379.16i	−1.48076	+	1.07584i	−0.503451	+	0.864024i	$0.667936\pi$
$19$	−10156.5	+	7379.16i	−1.48076	+	1.07584i	−0.977310	+	0.211812i	$0.932064\pi$
$20$	−1300.44	+	4002.35i	−0.162555	+	0.500293i
$21$	135.105	+	185.955i	0.0145885	+	0.0200794i
$22$	9168.97	−	2979.18i	0.861097	−	0.279788i
$23$	−996.325	+	323.726i	−0.0818875	+	0.0266069i	−0.349674	−	0.936871i	$-0.613708\pi$
$23$	−996.325	+	323.726i	−0.0818875	+	0.0266069i	0.267787	+	0.963478i	$0.413708\pi$
$24$	−152.091	−	49.4172i	−0.0110019	−	0.00357474i
$25$	1669.85			0.106870
$26$			11946.5i			0.679707i
$27$	1224.34	+	397.812i	0.0622029	+	0.0202110i
$28$	6735.78	+	4893.83i	0.306841	+	0.222933i
$29$	12895.5	+	17749.1i	0.528742	+	0.727751i	0.986938	−	0.161100i	$-0.0515042\pi$
$29$	12895.5	+	17749.1i	0.528742	+	0.727751i	−0.458196	+	0.888851i	$0.651504\pi$
$30$			657.210i			0.0243411i
$31$	−1896.62	+	29730.6i	−0.0636642	+	0.997971i
$31$	−1896.62	+	29730.6i	−0.0636642	+	0.997971i
$32$	−5792.62			−0.176777
$33$	1218.06	−	884.970i	0.0338942	−	0.0246256i
$34$	20823.2	−	28660.7i	0.529798	−	0.729205i
$35$	10573.6	−	32542.1i	0.246613	−	0.758998i
$36$	23303.0			0.499465
$37$		−	83566.2i		−	1.64978i	−0.565295	−	0.824889i	$-0.691238\pi$
$37$		−	83566.2i		−	1.64978i	0.565295	−	0.824889i	$-0.308762\pi$
$38$	−21945.5	+	67541.3i	−0.399940	+	1.23089i
$39$	576.527	+	1774.37i	0.00971910	+	0.0299123i
$40$	7356.41	+	22640.7i	0.114944	+	0.353761i
$41$	−109070.	+	79243.8i	−1.58253	+	1.14978i	−0.668814	+	0.743430i	$0.733198\pi$
$41$	−109070.	+	79243.8i	−1.58253	+	1.14978i	−0.913719	+	0.406347i	$0.866802\pi$
$42$	1236.61	+	401.799i	0.0166911	+	0.00542326i
$43$	22107.7	+	30428.7i	0.278060	+	0.382717i	0.925090	−	0.379747i	$-0.123989\pi$
$43$	22107.7	+	30428.7i	0.278060	+	0.382717i	−0.647030	+	0.762465i	$0.723989\pi$
$44$	32055.9	−	44121.1i	0.376313	−	0.517951i
$45$	−29594.0	−	91080.8i	−0.324762	−	0.999515i
$46$	−3483.28	+	4794.32i	−0.0357861	+	0.0492554i
$47$	−17721.0	−	12875.1i	−0.170685	−	0.124010i	0.499163	−	0.866508i	$-0.333641\pi$
$47$	−17721.0	−	12875.1i	−0.170685	−	0.124010i	−0.669848	+	0.742498i	$0.733641\pi$
$48$	−860.354	+	279.546i	−0.00777953	+	0.00252772i
$49$	40413.1	+	29361.9i	0.343506	+	0.249572i
$50$	7642.04	−	5552.27i	0.0611363	−	0.0444181i
$51$	1709.65	−	5261.76i	0.0128883	−	0.0396662i
$52$	39722.4	+	54673.2i	0.282504	+	0.388834i
$53$	−43773.3	+	14222.8i	−0.294023	+	0.0955339i	−0.452314	−	0.891859i	$-0.649401\pi$
$53$	−43773.3	+	14222.8i	−0.294023	+	0.0955339i	0.158291	+	0.987392i	$0.449401\pi$
$54$	6925.92	−	2250.37i	0.0439841	−	0.0142913i
$55$	−213159.	−	69259.6i	−1.28120	−	0.416286i
$56$	47098.3			0.268189
$57$			11090.7i			0.0598873i
$58$	118032.	+	38351.0i	0.604946	+	0.196559i
$59$	−199967.	−	145284.i	−0.973647	−	0.707396i	−0.0173670	−	0.999849i	$-0.505528\pi$
$59$	−199967.	−	145284.i	−0.973647	−	0.707396i	−0.956280	+	0.292453i	$0.905528\pi$
$60$	2185.23	+	3007.72i	0.0101168	+	0.0139246i
$61$		−	419634.i		−	1.84876i	−0.381469	−	0.924382i	$-0.624582\pi$
$61$		−	419634.i		−	1.84876i	0.381469	−	0.924382i	$-0.375418\pi$
$62$	90174.7	+	142368.i	0.378364	+	0.597361i
$63$	−189471.			−0.757741
$64$	−26509.9	+	19260.5i	−0.101127	+	0.0734732i
$65$	163246.	−	224689.i	0.594434	−	0.818168i
$66$	2631.89	−	8100.12i	0.00915452	−	0.0281747i
$67$	78380.7			0.260606			0.130303	−	0.991474i	$-0.458405\pi$
$67$	78380.7			0.260606			0.130303	+	0.991474i	$0.458405\pi$
$68$		−	200403.i		−	0.637348i
$69$	−285.988	+	880.181i	−0.000870564	+	0.00267932i
$70$	−59813.0	−	184086.i	−0.174382	−	0.536693i
$71$	−123227.	−	379255.i	−0.344296	−	1.05963i	−0.961959	−	0.273192i	$-0.911921\pi$
$71$	−123227.	−	379255.i	−0.344296	−	1.05963i	0.617663	−	0.786443i	$-0.288079\pi$
$72$	106646.	−	77482.9i	0.285724	−	0.207591i
$73$	407779.	+	132495.i	1.04823	+	0.340590i	0.781973	−	0.623312i	$-0.214213\pi$
$73$	407779.	+	132495.i	1.04823	+	0.340590i	0.266256	+	0.963902i	$0.414213\pi$
$74$	−277859.	−	382440.i	−0.685692	−	0.943774i
$75$	867.094	−	1193.45i	0.00205533	−	0.00282893i
$76$	124143.	+	382071.i	0.282800	+	0.870370i
$77$	−260638.	+	358738.i	−0.570908	+	0.785787i
$78$	8538.28	+	6203.42i	0.0179923	+	0.0130722i
$79$	517310.	−	168084.i	1.04923	−	0.340915i	0.266863	−	0.963735i	$-0.414013\pi$
$79$	517310.	−	168084.i	1.04923	−	0.340915i	0.782365	+	0.622820i	$0.214013\pi$
$80$	108947.	+	79154.8i	0.212787	+	0.154599i
$81$	−428564.	+	311370.i	−0.806420	+	0.585898i
$82$	−235670.	+	725317.i	−0.427427	+	1.31549i
$83$	634601.	+	873453.i	1.10986	+	1.52758i	0.821629	+	0.570022i	$0.193065\pi$
$83$	634601.	+	873453.i	1.10986	+	1.52758i	0.288226	+	0.957562i	$0.406935\pi$
$84$	6995.32	−	2272.92i	0.0118024	−	0.00383483i
$85$	−783282.	+	254504.i	−1.27544	+	0.414417i
$86$	202352.	+	65748.1i	0.318135	+	0.103368i
$87$	19381.6			0.0294329
$88$		−	308506.i		−	0.452706i
$89$	321953.	+	104609.i	0.456691	+	0.148388i	0.528324	−	0.849043i	$-0.322821\pi$
$89$	321953.	+	104609.i	0.456691	+	0.148388i	−0.0716323	+	0.997431i	$0.522821\pi$
$90$	−438282.	−	318430.i	−0.601209	−	0.436804i
$91$	−322972.	−	444533.i	−0.428589	−	0.589903i
$92$			33523.1i			0.0430508i
$93$	20263.8	+	16793.6i	0.0251926	+	0.0208783i
$94$	−123910.			−0.149184
$95$	1.33569e6	−	970432.i	1.55788	−	1.13186i
$96$	−3007.91	+	4140.03i	−0.00339978	+	0.00467940i
$97$	−433583.	+	1.33443e6i	−0.475069	+	1.46211i	0.370796	+	0.928714i	$0.379085\pi$
$97$	−433583.	+	1.33443e6i	−0.475069	+	1.46211i	−0.845865	+	0.533397i	$0.820915\pi$
$98$	282579.			0.300235
$99$			1.24108e6i			1.27907i
$100$	16512.4	−	50819.8i	0.0165124	−	0.0508198i
$101$	435719.	+	1.34100e6i	0.422904	+	1.30157i	0.904987	+	0.425440i	$0.139881\pi$
$101$	435719.	+	1.34100e6i	0.422904	+	1.30157i	−0.482082	+	0.876126i	$0.660119\pi$
$102$	−9671.23	−	29765.0i	−0.00911342	−	0.0280482i
$103$	533357.	−	387507.i	0.488098	−	0.354624i	−0.316355	−	0.948641i	$-0.602459\pi$
$103$	533357.	−	387507.i	0.488098	−	0.354624i	0.804452	+	0.594017i	$0.202459\pi$
$104$	363578.	+	118134.i	0.323220	+	0.105020i
$105$	−17767.6	−	24455.0i	−0.0153483	−	0.0211251i
$106$	−153037.	+	210637.i	−0.128493	+	0.176855i
$107$	158359.	+	487380.i	0.129268	+	0.397847i	0.994655	−	0.103258i	$-0.0329268\pi$
$107$	158359.	+	487380.i	0.129268	+	0.397847i	−0.865386	+	0.501106i	$0.832927\pi$
$108$	24213.9	−	33327.6i	0.0192218	−	0.0264565i
$109$	−229978.	−	167089.i	−0.177585	−	0.129023i	0.495442	−	0.868641i	$-0.335006\pi$
$109$	−229978.	−	167089.i	−0.177585	−	0.129023i	−0.673027	+	0.739618i	$0.735006\pi$
$110$	−1.20581e6	+	391791.i	−0.905943	+	0.294359i
$111$	−59725.4	−	43393.0i	−0.0436707	−	0.0317286i
$112$	215545.	−	156603.i	0.153421	−	0.111467i
$113$	154521.	−	475568.i	0.107091	−	0.329592i	−0.883125	−	0.469139i	$-0.844564\pi$
$113$	154521.	−	475568.i	0.107091	−	0.329592i	0.990216	+	0.139546i	$0.0445645\pi$
$114$	36876.8	+	50756.5i	0.0248908	+	0.0342592i
$115$	131027.	−	42573.1i	0.0861521	−	0.0279925i
$116$	667691.	−	216946.i	0.427761	−	0.138988i
$117$	−1.46263e6	−	475238.i	−0.913225	−	0.296725i
$118$	−1.39822e6			−0.850998
$119$			1.62942e6i			0.966925i
$120$	20001.4	+	6498.85i	0.0115749	+	0.00376091i
$121$	916603.	+	665951.i	0.517399	+	0.375912i
$122$	−1.39529e6	−	1.92045e6i	−0.768396	−	1.05761i
$123$			119102.i			0.0640033i
$124$	886060.	+	351713.i	0.464727	+	0.184469i
$125$	1.83524e6			0.939643
$126$	−867112.	+	629994.i	−0.433475	+	0.314938i
$127$	1.84662e6	−	2.54166e6i	0.901503	−	1.24081i	−0.0684825	−	0.997652i	$-0.521816\pi$
$127$	1.84662e6	−	2.54166e6i	0.901503	−	1.24081i	0.969986	−	0.243161i	$-0.0781843\pi$
$128$	−57280.6	+	176291.i	−0.0273135	+	0.0840623i
$129$	33227.4			0.0154785
$130$		−	1.57109e6i		−	0.715105i
$131$	284117.	−	874423.i	0.126382	−	0.388963i	−0.867769	−	0.496968i	$-0.834447\pi$
$131$	284117.	−	874423.i	0.126382	−	0.388963i	0.994150	+	0.108006i	$0.0344465\pi$
$132$	−14888.2	−	45821.2i	−0.00647322	−	0.0199225i
$133$	−1.00937e6	−	3.10652e6i	−0.429038	−	1.32044i
$134$	358709.	−	260617.i	0.149083	−	0.108315i
$135$	−161013.	−	52316.3i	−0.0654424	−	0.0212635i
$136$	−666342.	−	917141.i	−0.264899	−	0.364602i
$137$	356727.	−	490993.i	0.138731	−	0.190947i	−0.733998	−	0.679152i	$-0.762348\pi$
$137$	356727.	−	490993.i	0.138731	−	0.190947i	0.872729	+	0.488204i	$0.162348\pi$
$138$	1617.79	+	4979.05i	0.000615582	+	0.00189457i
$139$	1.12410e6	−	1.54719e6i	0.418562	−	0.576101i	−0.546719	−	0.837316i	$-0.684123\pi$
$139$	1.12410e6	−	1.54719e6i	0.418562	−	0.576101i	0.965281	+	0.261215i	$0.0841233\pi$
$140$	−885821.	−	643587.i	−0.322821	−	0.234543i
$141$	−18403.8	+	5979.77i	−0.00656524	+	0.00213318i
$142$	−1.82498e6	−	1.32592e6i	−0.637371	−	0.463077i
$143$	−2.91181e6	+	2.11555e6i	−0.995761	+	0.723463i
$144$	230433.	−	709200.i	0.0771715	−	0.237510i
$145$	−1.69588e6	−	2.33418e6i	−0.556278	−	0.765652i
$146$	2.30675e6	−	749508.i	0.741210	−	0.240834i
$147$	41970.3	−	13637.0i	0.0132127	−	0.00429305i
$148$	−2.54324e6	−	826348.i	−0.784516	−	0.254905i
$149$	−3.81418e6			−1.15303			−0.576517	−	0.817085i	$-0.695588\pi$
$149$	−3.81418e6			−1.15303			−0.576517	+	0.817085i	$0.695588\pi$
$150$		−	8344.93i		−	0.00247257i
$151$	2.74058e6	+	890467.i	0.795996	+	0.258635i	0.678655	−	0.734457i	$-0.262563\pi$
$151$	2.74058e6	+	890467.i	0.795996	+	0.258635i	0.117341	+	0.993092i	$0.462563\pi$
$152$	1.83853e6	+	1.33577e6i	0.523528	+	0.380365i
$153$	2.68062e6	+	3.68955e6i	0.748446	+	1.03015i
$154$			2.50839e6i			0.686803i
$155$	249424.	−	3.90986e6i	0.0669798	−	1.04994i
$156$	59701.8			0.0157258
$157$	−2.60325e6	+	1.89137e6i	−0.672694	+	0.488741i	−0.870926	−	0.491414i	$-0.836480\pi$
$157$	−2.60325e6	+	1.89137e6i	−0.672694	+	0.488741i	0.198232	+	0.980155i	$0.436480\pi$
$158$	1.80858e6	−	2.48930e6i	0.458530	−	0.631112i
$159$	−12564.8	+	38670.5i	−0.00312582	+	0.00962030i
$160$	761787.			0.185983
$161$		−	272568.i		−	0.0653126i
$162$	−926010.	+	2.84997e6i	−0.217806	+	0.670339i
$163$	196626.	+	605153.i	0.0454023	+	0.139734i	0.971188	−	0.238315i	$-0.0765951\pi$
$163$	196626.	+	605153.i	0.0454023	+	0.139734i	−0.925786	+	0.378049i	$0.876595\pi$
$164$	1.33315e6	+	4.10301e6i	0.302237	+	0.930189i
$165$	−160187.	+	116382.i	−0.0356594	+	0.0259081i
$166$	5.80849e6	+	1.88729e6i	1.26981	+	0.412587i
$167$	172153.	+	236949.i	0.0369629	+	0.0508750i	0.827098	−	0.562057i	$-0.189990\pi$
$167$	172153.	+	236949.i	0.0369629	+	0.0508750i	−0.790136	+	0.612932i	$0.789990\pi$
$168$	24456.5	−	33661.5i	0.00515783	−	0.00709914i
$169$	113356.	+	348873.i	0.0234846	+	0.0722782i
$170$	−2.73845e6	+	3.76916e6i	−0.557389	+	0.767181i
$171$	−7.39619e6	−	5.37365e6i	−1.47918	−	1.07468i
$172$	1.14467e6	−	371927.i	0.224956	−	0.0730925i
$173$	158946.	+	115481.i	0.0306982	+	0.0223035i	0.603029	−	0.797720i	$-0.293960\pi$
$173$	158946.	+	115481.i	0.0306982	+	0.0223035i	−0.572330	+	0.820023i	$0.693960\pi$
$174$	88699.8	−	64444.2i	0.0168374	−	0.0122331i
$175$	−134258.	+	413203.i	−0.0250510	+	0.0770991i
$176$	−1.02579e6	−	1.41188e6i	−0.188157	−	0.258975i
$177$	−207672.	+	67476.6i	−0.0374505	+	0.0121684i
$178$	1.82124e6	−	591758.i	0.322930	−	0.104926i
$179$	−4.71529e6	−	1.53209e6i	−0.822146	−	0.267131i	−0.132412	−	0.991195i	$-0.542272\pi$
$179$	−4.71529e6	−	1.53209e6i	−0.822146	−	0.267131i	−0.689734	+	0.724063i	$0.742272\pi$
$180$	−3.06458e6			−0.525476
$181$		−	874364.i		−	0.147454i	−0.997278	−	0.0737270i	$-0.976511\pi$
$181$		−	874364.i		−	0.147454i	0.997278	−	0.0737270i	$-0.0234893\pi$
$182$	−2.95616e6	−	960515.i	−0.490359	−	0.159327i
$183$	−299916.	−	217902.i	−0.0489380	−	0.0355555i
$184$	111465.	+	153418.i	0.0178931	+	0.0246277i
$185$			1.09898e7i			1.73570i
$186$	148576.	+	9478.21i	0.0230893	+	0.00147295i
$187$	1.06731e7			1.63218
$188$	−567072.	+	412002.i	−0.0853424	+	0.0620049i
$189$	−196877.	+	270978.i	−0.0291615	+	0.0401373i
$190$	2.88605e6	−	8.88235e6i	0.420768	−	1.29499i
$191$	8.85612e6			1.27099			0.635497	−	0.772103i	$-0.280795\pi$
$191$	8.85612e6			1.27099			0.635497	+	0.772103i	$0.280795\pi$
$192$			28948.2i			0.00408994i
$193$	−3.59914e6	+	1.10770e7i	−0.500641	+	1.54081i	0.307336	+	0.951601i	$0.400562\pi$
$193$	−3.59914e6	+	1.10770e7i	−0.500641	+	1.54081i	−0.807977	+	0.589214i	$0.799438\pi$
$194$	2.45271e6	+	7.54868e6i	0.335924	+	1.03387i
$195$	−75819.0	−	233347.i	−0.0102253	−	0.0314701i
$196$	1.29322e6	−	939580.i	0.171753	−	0.124786i
$197$	−6.47281e6	−	2.10314e6i	−0.846631	−	0.275087i	−0.146596	−	0.989196i	$-0.546832\pi$
$197$	−6.47281e6	−	2.10314e6i	−0.846631	−	0.275087i	−0.700034	+	0.714109i	$0.746832\pi$
$198$	4.12663e6	+	5.67981e6i	0.531618	+	0.731709i
$199$	4.61408e6	−	6.35074e6i	0.585499	−	0.805870i	−0.408786	−	0.912630i	$-0.634048\pi$
$199$	4.61408e6	−	6.35074e6i	0.585499	−	0.805870i	0.994285	+	0.106760i	$0.0340478\pi$
$200$	−93408.0	−	287480.i	−0.0116760	−	0.0359350i
$201$	40700.4	−	56019.3i	0.00501199	−	0.00689842i
$202$	6.45292e6	+	4.68832e6i	0.782893	+	0.568805i
$203$	−5.42882e6	+	1.76393e6i	−0.648960	+	0.210860i
$204$	−143229.	−	104062.i	−0.0168710	−	0.0122575i
$205$	1.43437e7	−	1.04213e7i	1.66495	−	1.20966i
$206$	1.15244e6	−	3.54684e6i	0.131831	−	0.405733i
$207$	−448410.	−	617184.i	−0.0505551	−	0.0695831i
$208$	2.05671e6	−	668265.i	0.228551	−	0.0742607i
$209$	−2.03486e7	+	6.61165e6i	−2.22892	+	0.724220i
$210$	−162626.	−	52840.5i	−0.0175603	−	0.00570570i
$211$	1.13137e7			1.20437			0.602183	−	0.798358i	$-0.294298\pi$
$211$	1.13137e7			1.20437			0.602183	+	0.798358i	$0.294298\pi$
$212$			1.47283e6i			0.154577i
$213$	−335044.	−	108862.i	−0.0346708	−	0.0112652i
$214$	2.34528e6	+	1.70394e6i	0.239306	+	0.173866i
$215$	−2.90739e6	−	4.00167e6i	−0.292541	−	0.402649i
$216$		−	233035.i		−	0.0231238i
$217$	−7.20432e6	−	2.85969e6i	−0.705040	−	0.279859i
$218$	−1.60807e6			−0.155215
$219$	306441.	−	222643.i	0.0291753	−	0.0211971i
$220$	−4.21566e6	+	5.80236e6i	−0.395911	+	0.544925i
$221$	−4.08698e6	+	1.25784e7i	−0.378639	+	1.16533i
$222$	−417615.			−0.0381696
$223$			9.26699e6i			0.835649i	0.908528	+	0.417824i	$0.137207\pi$
$223$			9.26699e6i			0.835649i	−0.908528	+	0.417824i	$0.862793\pi$
$224$	465734.	−	1.43338e6i	0.0414375	−	0.127531i
$225$	375769.	+	1.15650e6i	0.0329894	+	0.101531i
$226$	−874104.	−	2.69022e6i	−0.0757248	−	0.233057i
$227$	1.05825e7	−	7.68862e6i	0.904711	−	0.657311i	−0.0349605	−	0.999389i	$-0.511131\pi$
$227$	1.05825e7	−	7.68862e6i	0.904711	−	0.657311i	0.939672	+	0.342078i	$0.111131\pi$
$228$	337532.	+	109671.i	0.0284781	+	0.00925309i
$229$	−1.00165e7	−	1.37865e7i	−0.834081	−	1.14801i	−0.987150	−	0.159799i	$-0.948915\pi$
$229$	−1.00165e7	−	1.37865e7i	−0.834081	−	1.14801i	0.153068	−	0.988216i	$-0.451085\pi$
$230$	458086.	−	630501.i	0.0376498	−	0.0518206i
$231$	121052.	+	372560.i	0.00982057	+	0.0302246i
$232$	2.33433e6	−	3.21293e6i	0.186939	−	0.257299i
$233$	−1.25743e6	−	913574.i	−0.0994065	−	0.0722231i	0.536972	−	0.843600i	$-0.319568\pi$
$233$	−1.25743e6	−	913574.i	−0.0994065	−	0.0722231i	−0.636378	+	0.771377i	$0.719568\pi$
$234$	−8.27390e6	+	2.68835e6i	−0.645747	+	0.209816i
$235$	2.33049e6	+	1.69320e6i	0.179574	+	0.130468i
$236$	−6.39893e6	+	4.64910e6i	−0.486823	+	0.353698i
$237$	148490.	−	457006.i	0.0111546	−	0.0343303i
$238$	5.41785e6	+	7.45704e6i	0.401880	+	0.553141i
$239$	5.15169e6	−	1.67389e6i	0.377360	−	0.122612i	−0.114195	−	0.993458i	$-0.536429\pi$
$239$	5.15169e6	−	1.67389e6i	0.377360	−	0.122612i	0.491555	+	0.870847i	$0.336429\pi$
$240$	113145.	−	36763.1i	0.00818468	−	0.00265936i
$241$	−5.74377e6	−	1.86626e6i	−0.410342	−	0.133328i	0.0965698	−	0.995326i	$-0.469213\pi$
$241$	−5.74377e6	−	1.86626e6i	−0.410342	−	0.133328i	−0.506912	+	0.861998i	$0.669213\pi$
$242$	6.40913e6			0.452223
$243$			1.40646e6i			0.0980185i
$244$	−1.27711e7	−	4.14957e6i	−0.879139	−	0.285650i
$245$	−5.31473e6	−	3.86138e6i	−0.361396	−	0.262569i
$246$	396015.	+	545067.i	0.0266015	+	0.0366138i
$247$		−	2.65127e7i		−	1.75940i
$248$	5.22450e6	−	1.33655e6i	0.342523	−	0.0876253i
$249$	953790.			0.0617810
$250$	8.39896e6	−	6.10220e6i	0.537534	−	0.390541i
$251$	−8.43423e6	+	1.16087e7i	−0.533365	+	0.734113i	−0.987639	−	0.156749i	$-0.949899\pi$
$251$	−8.43423e6	+	1.16087e7i	−0.533365	+	0.734113i	0.454274	+	0.890862i	$0.349899\pi$
$252$	−1.87359e6	+	5.76632e6i	−0.117077	+	0.360327i
$253$	−1.78539e6			−0.110248
$254$		−	1.77719e7i		−	1.08451i
$255$	−224836.	+	691973.i	−0.0135595	+	0.0417319i
$256$	324028.	+	997255.i	0.0193136	+	0.0594410i
$257$	−341858.	−	1.05213e6i	−0.0201394	−	0.0619828i	0.940482	−	0.339844i	$-0.110374\pi$
$257$	−341858.	−	1.05213e6i	−0.0201394	−	0.0619828i	−0.960621	+	0.277862i	$0.910374\pi$
$258$	152065.	−	110482.i	0.00885463	−	0.00643326i
$259$	2.06784e7	+	6.71882e6i	1.19019	+	0.386717i
$260$	−5.22388e6	−	7.19006e6i	−0.297217	−	0.409084i
$261$	−9.39075e6	+	1.29253e7i	−0.528176	+	0.726972i
$262$	−1.60721e6	−	4.94648e6i	−0.0893653	−	0.275038i
$263$	860543.	−	1.18444e6i	0.0473048	−	0.0651095i	−0.784709	−	0.619864i	$-0.787188\pi$
$263$	860543.	−	1.18444e6i	0.0473048	−	0.0651095i	0.832014	+	0.554754i	$0.187188\pi$
$264$	−220492.	−	160197.i	−0.0119834	−	0.00870647i
$265$	5.75662e6	−	1.87044e6i	0.309335	−	0.100509i
$266$	−1.49486e7	−	1.08608e7i	−0.794248	−	0.577055i
$267$	241944.	−	175783.i	0.0127110	−	0.00923512i
$268$	775071.	−	2.38542e6i	0.0402659	−	0.123926i
$269$	1.45187e7	+	1.99833e7i	0.745885	+	1.02662i	0.998258	+	0.0589924i	$0.0187888\pi$
$269$	1.45187e7	+	1.99833e7i	0.745885	+	1.02662i	−0.252374	+	0.967630i	$0.581211\pi$
$270$	−910826.	+	295945.i	−0.0462748	+	0.0150356i
$271$	−4.26035e6	+	1.38427e6i	−0.214061	+	0.0695526i	−0.414084	−	0.910238i	$-0.635898\pi$
$271$	−4.26035e6	+	1.38427e6i	−0.214061	+	0.0695526i	0.200023	+	0.979791i	$0.435898\pi$
$272$	−6.09902e6	−	1.98169e6i	−0.303077	−	0.0984757i
$273$	−485420.			−0.0238578
$274$		−	3.43315e6i		−	0.166894i
$275$	2.70659e6	+	879424.i	0.130144	+	0.0422863i
$276$	23959.2	+	17407.4i	0.00113958	+	0.000827956i
$277$	4.52736e6	+	6.23138e6i	0.213013	+	0.293187i	0.902131	−	0.431462i	$-0.142002\pi$
$277$	4.52736e6	+	6.23138e6i	0.213013	+	0.293187i	−0.689118	+	0.724649i	$0.742002\pi$
$278$		−	1.08183e7i		−	0.503531i
$279$	−2.10175e7	+	5.37678e6i	−0.967763	+	0.247577i
$280$	−6.19389e6			−0.282156
$281$	1.67542e7	−	1.21726e7i	0.755100	−	0.548612i	−0.142304	−	0.989823i	$-0.545451\pi$
$281$	1.67542e7	−	1.21726e7i	0.755100	−	0.548612i	0.897403	+	0.441211i	$0.145451\pi$
$282$	−64342.1	+	88559.3i	−0.00286912	+	0.00394900i
$283$	1.35125e7	−	4.15872e7i	0.596178	−	1.83485i	0.0474049	−	0.998876i	$-0.484905\pi$
$283$	1.35125e7	−	4.15872e7i	0.596178	−	1.83485i	0.548773	−	0.835971i	$-0.315095\pi$
$284$	−1.27607e7			−0.557083
$285$		−	1.45854e6i		−	0.0630061i
$286$	−6.29163e6	+	1.93636e7i	−0.268946	+	0.827730i
$287$	−1.08395e7	−	3.33605e7i	−0.458525	−	1.41120i
$288$	−1.30353e6	−	4.01184e6i	−0.0545685	−	0.167945i
$289$	1.22019e7	−	8.86520e6i	0.505515	−	0.367278i
$290$	−1.55224e7	−	5.04353e6i	−0.636451	−	0.206795i
$291$	728583.	+	1.00281e6i	0.0295665	+	0.0406948i
$292$	8.06468e6	−	1.11001e7i	0.323921	−	0.445839i
$293$	−1.94615e6	−	5.98963e6i	−0.0773702	−	0.238121i	0.904890	−	0.425646i	$-0.139953\pi$
$293$	−1.94615e6	−	5.98963e6i	−0.0773702	−	0.238121i	−0.982260	+	0.187526i	$0.939953\pi$
$294$	146734.	−	201962.i	0.00577414	−	0.00794743i
$295$	2.62976e7	+	1.91063e7i	1.02435	+	0.744236i
$296$	−1.43867e7	+	4.67453e6i	−0.554736	+	0.180245i
$297$	1.77498e6	+	1.28960e6i	0.0677522	+	0.0492248i
$298$	−1.74555e7	+	1.26822e7i	−0.659606	+	0.479232i
$299$	683665.	−	2.10411e6i	0.0255758	−	0.0787144i
$300$	−27747.0	−	38190.5i	−0.00102767	−	0.00141446i
$301$	−9.30706e6	+	3.02405e6i	−0.341282	+	0.110889i
$302$	1.55030e7	−	5.03724e6i	0.562854	−	0.182882i
$303$	1.18468e6	+	384926.i	0.0425866	+	0.0138372i
$304$	1.28555e7			0.457580
$305$			5.51860e7i			1.94504i
$306$	2.45356e7	+	7.97211e6i	0.856314	+	0.278233i
$307$	7.67283e6	+	5.57464e6i	0.265180	+	0.192664i	0.712427	−	0.701746i	$-0.247596\pi$
$307$	7.67283e6	+	5.57464e6i	0.265180	+	0.192664i	−0.447248	+	0.894410i	$0.647596\pi$
$308$	8.34042e6	+	1.14796e7i	0.285454	+	0.392893i
$309$		−	582414.i		−	0.0197404i
$310$	−1.18589e7	−	1.87228e7i	−0.398069	−	0.628471i
$311$	−1.37910e7			−0.458473			−0.229236	−	0.973371i	$-0.573623\pi$
$311$	−1.37910e7			−0.458473			−0.229236	+	0.973371i	$0.573623\pi$
$312$	273225.	−	198509.i	0.00899614	−	0.00653608i
$313$	4.49543e6	−	6.18742e6i	0.146601	−	0.201779i	−0.729401	−	0.684087i	$-0.760201\pi$
$313$	4.49543e6	−	6.18742e6i	0.146601	−	0.201779i	0.876002	+	0.482307i	$0.160201\pi$
$314$	−5.62492e6	+	1.73117e7i	−0.181688	+	0.559180i
$315$	2.49173e7			0.797204
$316$		−	1.74058e7i		−	0.551612i
$317$	−4.03873e6	+	1.24299e7i	−0.126785	+	0.390203i	−0.994222	−	0.107343i	$-0.965766\pi$
$317$	−4.03873e6	+	1.24299e7i	−0.126785	+	0.390203i	0.867437	+	0.497547i	$0.165766\pi$
$318$	71077.3	+	218753.i	0.00221029	+	0.00680258i
$319$	1.15542e7	+	3.55602e7i	0.355933	+	1.09545i
$320$	3.48631e6	−	2.53295e6i	0.106394	−	0.0772996i
$321$	430565.	+	139899.i	0.0130174	+	0.00422960i
$322$	−906293.	−	1.24741e6i	−0.0271457	−	0.0373628i
$323$	−4.62126e7	+	6.36062e7i	−1.37136	+	1.88752i
$324$	5.23831e6	+	1.61218e7i	0.154012	+	0.474002i
$325$	−2.07282e6	+	2.85299e6i	−0.0603826	+	0.0831095i
$326$	2.91200e6	+	2.11569e6i	0.0840501	+	0.0610660i
$327$	−238839.	+	77603.6i	−0.00683066	+	0.00221942i
$328$	1.97437e7	+	1.43447e7i	0.559510	+	0.406508i
$329$	4.61072e6	−	3.34988e6i	0.129474	−	0.0940680i
$330$	−346119.	+	1.06525e6i	−0.00963128	+	0.0296420i
$331$	−1.69022e7	−	2.32639e7i	−0.466080	−	0.641504i	0.509676	−	0.860366i	$-0.329765\pi$
$331$	−1.69022e7	−	2.32639e7i	−0.466080	−	0.641504i	−0.975756	+	0.218863i	$0.929765\pi$
$332$	3.28578e7	−	1.06761e7i	0.897892	−	0.291743i
$333$	5.78761e7	−	1.88051e7i	1.56735	−	0.509263i
$334$	1.57572e6	+	511981.i	0.0422901	+	0.0137409i
$335$	−1.03078e7			−0.274178
$336$		−	235370.i		−	0.00620488i
$337$	2.21624e7	+	7.20100e6i	0.579065	+	0.188150i	0.583882	−	0.811839i	$-0.301533\pi$
$337$	2.21624e7	+	7.20100e6i	0.579065	+	0.188150i	−0.00481682	+	0.999988i	$0.501533\pi$
$338$	1.67878e6	+	1.21970e6i	0.0434754	+	0.0315867i
$339$	−259654.	−	357383.i	−0.00666494	−	0.00917351i
$340$			2.63549e7i			0.670541i
$341$	−1.87317e7	+	4.71902e7i	−0.472405	+	1.19011i
$342$	−5.17161e7			−1.29285
$343$	−3.52791e7	+	2.56318e7i	−0.874250	+	0.635180i
$344$	4.00193e6	−	5.50818e6i	0.0983092	−	0.135311i
$345$	37610.3	−	115752.i	0.000915902	−	0.00281886i
$346$	1.11139e6			0.0268312
$347$		−	1.78386e7i		−	0.426945i	−0.976949	−	0.213472i	$-0.931523\pi$
$347$		−	1.78386e7i		−	0.426945i	0.976949	−	0.213472i	$-0.0684773\pi$
$348$	191656.	−	589857.i	0.00454763	−	0.0139962i
$349$	−1.42203e7	−	4.37657e7i	−0.334529	−	1.02957i	−0.966954	−	0.254952i	$-0.917940\pi$
$349$	−1.42203e7	−	4.37657e7i	−0.334529	−	1.02957i	0.632425	−	0.774621i	$-0.282060\pi$
$350$	759476.	+	2.33743e6i	0.0177137	+	0.0545173i
$351$	−2.19948e6	+	1.59802e6i	−0.0508626	+	0.0369539i
$352$	−9.38902e6	−	3.05068e6i	−0.215274	−	0.0699469i
$353$	2.47871e7	+	3.41165e7i	0.563510	+	0.775605i	0.991768	−	0.128052i	$-0.0408723\pi$
$353$	2.47871e7	+	3.41165e7i	0.563510	+	0.775605i	−0.428257	+	0.903657i	$0.640872\pi$
$354$	−726046.	+	999317.i	−0.0163665	+	0.0225265i
$355$	1.62056e7	+	4.98758e7i	0.362227	+	1.11482i
$356$	6.36730e6	−	8.76383e6i	0.141125	−	0.194242i
$357$	1.16456e6	+	846103.i	0.0255951	+	0.0185960i
$358$	−2.66737e7	+	8.66680e6i	−0.581345	+	0.188890i
$359$	3.83738e7	+	2.78802e7i	0.829376	+	0.602577i	0.919383	−	0.393364i	$-0.128689\pi$
$359$	3.83738e7	+	2.78802e7i	0.829376	+	0.602577i	−0.0900067	+	0.995941i	$0.528689\pi$
$360$	−1.40250e7	+	1.01898e7i	−0.300605	+	0.218402i
$361$	3.41654e7	−	1.05150e8i	0.726214	−	2.23506i
$362$	−2.90727e6	−	4.00152e6i	−0.0612858	−	0.0843527i
$363$	951921.	−	309298.i	0.0199013	−	0.00646632i
$364$	−1.67226e7	+	5.43349e6i	−0.346736	+	0.112661i
$365$	−5.36270e7	−	1.74245e7i	−1.10282	−	0.358328i
$366$	−2.09709e6			−0.0427734
$367$			4.07495e7i			0.824373i	0.911099	+	0.412187i	$0.135235\pi$
$367$			4.07495e7i			0.824373i	−0.911099	+	0.412187i	$0.864765\pi$
$368$	1.02024e6	+	331495.i	0.0204719	+	0.00665171i
$369$	−7.94267e7	−	5.77069e7i	−1.58084	−	1.14855i
$370$	3.65412e7	+	5.02946e7i	0.721402	+	0.992925i
$371$		−	1.19752e7i		−	0.234510i
$372$	711473.	−	450641.i	0.0138207	−	0.00875391i
$373$	1.05022e7			0.202373			0.101186	−	0.994867i	$-0.467736\pi$
$373$	1.05022e7			0.202373			0.101186	+	0.994867i	$0.467736\pi$
$374$	4.88456e7	−	3.54884e7i	0.933706	−	0.678377i
$375$	952977.	−	1.31166e6i	0.0180713	−	0.0248730i
$376$	−1.22529e6	+	3.77105e6i	−0.0230502	+	0.0709412i
$377$	−4.63325e7			−0.864693
$378$			1.89475e6i			0.0350813i
$379$	2.68614e7	−	8.26708e7i	0.493413	−	1.51857i	−0.326002	−	0.945369i	$-0.605702\pi$
$379$	2.68614e7	−	8.26708e7i	0.493413	−	1.51857i	0.819415	−	0.573201i	$-0.194298\pi$
$380$	−1.63260e7	−	5.02462e7i	−0.297528	−	0.915698i
$381$	−857656.	−	2.63959e6i	−0.0155074	−	0.0477268i
$382$	4.05300e7	−	2.94468e7i	0.727087	−	0.528259i
$383$	1.11258e7	+	3.61499e6i	0.198032	+	0.0643444i	0.406354	−	0.913716i	$-0.366800\pi$
$383$	1.11258e7	+	3.61499e6i	0.198032	+	0.0643444i	−0.208322	+	0.978060i	$0.566800\pi$
$384$	96253.1	+	132481.i	0.00169989	+	0.00233970i
$385$	3.42765e7	−	4.71775e7i	0.600640	−	0.826710i
$386$	2.03598e7	+	6.26610e7i	0.354007	+	1.08952i
$387$	−1.60993e7	+	2.21588e7i	−0.277763	+	0.382308i
$388$	3.63243e7	+	2.63911e7i	0.621873	+	0.451817i
$389$	−1.43146e7	+	4.65111e6i	−0.243182	+	0.0790147i	−0.428072	−	0.903745i	$-0.640807\pi$
$389$	−1.43146e7	+	4.65111e6i	−0.243182	+	0.0790147i	0.184890	+	0.982759i	$0.440807\pi$
$390$	−1.12287e6	−	815811.i	−0.0189293	−	0.0137529i
$391$	−5.30769e6	+	3.85626e6i	−0.0887923	+	0.0645114i
$392$	2.79430e6	−	8.59996e6i	0.0463889	−	0.142770i
$393$	−477425.	−	657119.i	−0.00786552	−	0.0108260i
$394$	−3.66157e7	+	1.18972e7i	−0.598658	+	0.194516i
$395$	−6.80314e7	+	2.21048e7i	−1.10387	+	0.358669i
$396$	3.77709e7	+	1.22725e7i	0.608236	+	0.197628i
$397$	−9.31034e7			−1.48797			−0.743985	−	0.668196i	$-0.767067\pi$
$397$	−9.31034e7			−1.48797			−0.743985	+	0.668196i	$0.767067\pi$
$398$		−	4.44060e7i		−	0.704356i
$399$	−2.74439e6	−	891706.i	−0.0432043	−	0.0140379i
$400$	−1.38336e6	−	1.00507e6i	−0.0216150	−	0.0157042i
$401$	2.94892e7	+	4.05884e7i	0.457330	+	0.629461i	0.973952	−	0.226752i	$-0.0728108\pi$
$401$	2.94892e7	+	4.05884e7i	0.457330	+	0.629461i	−0.516622	+	0.856213i	$0.672811\pi$
$402$		−	391701.i		−	0.00602944i
$403$	−4.84414e7	−	4.01457e7i	−0.740119	−	0.613372i
$404$	4.51205e7			0.684274
$405$	5.63605e7	−	4.09483e7i	0.848417	−	0.616411i
$406$	−1.89799e7	+	2.61235e7i	−0.283606	+	0.390350i
$407$	4.40101e7	−	1.35449e8i	0.652783	−	2.00906i
$408$	−1.00150e6			−0.0147458
$409$			2.37865e7i			0.347665i	0.984775	+	0.173832i	$0.0556151\pi$
$409$			2.37865e7i			0.347665i	−0.984775	+	0.173832i	$0.944385\pi$
$410$	3.09929e7	−	9.53864e7i	0.449687	−	1.38400i
$411$	−165680.	−	509911.i	−0.00238641	−	0.00734462i
$412$	−6.51918e6	−	2.00640e7i	−0.0932184	−	0.286897i
$413$	5.20281e7	−	3.78006e7i	0.738563	−	0.536597i
$414$	−4.10429e6	−	1.33357e6i	−0.0578412	−	0.0187937i
$415$	−8.34563e7	−	1.14868e8i	−1.16766	−	1.60714i
$416$	7.19052e6	−	9.89690e6i	0.0998804	−	0.137474i
$417$	−522082.	−	1.60680e6i	−0.00719997	−	0.0221592i
$418$	−7.11412e7	+	9.79174e7i	−0.974074	+	1.34070i
$419$	−1.13850e8	−	8.27166e7i	−1.54771	−	1.12448i	−0.945259	−	0.326322i	$-0.894191\pi$
$419$	−1.13850e8	−	8.27166e7i	−1.54771	−	1.12448i	−0.602452	−	0.798155i	$-0.705809\pi$
$420$	−919953.	+	298911.i	−0.0124170	+	0.00403454i
$421$	−1.50193e7	−	1.09122e7i	−0.201281	−	0.146239i	0.482579	−	0.875853i	$-0.339700\pi$
$421$	−1.50193e7	−	1.09122e7i	−0.201281	−	0.146239i	−0.683860	+	0.729613i	$0.739700\pi$
$422$	5.17772e7	−	3.76183e7i	0.688972	−	0.500567i
$423$	4.92919e6	−	1.51705e7i	0.0651260	−	0.200437i
$424$	4.89718e6	+	6.74039e6i	0.0642464	+	0.0884275i
$425$	9.94573e6	−	3.23156e6i	0.129560	−	0.0420965i
$426$	−1.89530e6	+	615819.i	−0.0245159	+	0.00796571i
$427$	1.03838e8	+	3.37391e7i	1.33375	+	0.433361i
$428$	1.63988e7			0.209161
$429$			3.17963e6i			0.0402721i
$430$	−2.66113e7	−	8.64652e6i	−0.334703	−	0.108752i
$431$	5.58432e7	+	4.05725e7i	0.697491	+	0.506757i	0.879114	−	0.476611i	$-0.158135\pi$
$431$	5.58432e7	+	4.05725e7i	0.697491	+	0.506757i	−0.181623	+	0.983368i	$0.558135\pi$
$432$	−774845.	−	1.06648e6i	−0.00961088	−	0.0132282i
$433$			8.40737e7i			1.03561i	0.855499	+	0.517805i	$0.173251\pi$
$433$			8.40737e7i			1.03561i	−0.855499	+	0.517805i	$0.826749\pi$
$434$	−4.24790e7	+	1.08671e7i	−0.519643	+	0.132937i
$435$	−2.54887e6			−0.0309657
$436$	−7.35930e6	+	5.34684e6i	−0.0887926	+	0.0645116i
$437$	7.73039e6	−	1.06400e7i	0.0926312	−	0.127496i
$438$	662136.	−	2.03784e6i	0.00787997	−	0.0242521i
$439$	−1.00136e8			−1.18358			−0.591789	−	0.806093i	$-0.701578\pi$
$439$	−1.00136e8			−1.18358			−0.591789	+	0.806093i	$0.701578\pi$
$440$			4.05716e7i			0.476282i
$441$	−1.12411e7	+	3.45966e7i	−0.131067	+	0.403383i
$442$	2.31194e7	+	7.11543e7i	0.267738	+	0.824014i
$443$	4.52912e7	+	1.39392e8i	0.520958	+	1.60334i	0.772173	+	0.635412i	$0.219170\pi$
$443$	4.52912e7	+	1.39392e8i	0.520958	+	1.60334i	−0.251215	+	0.967931i	$0.580830\pi$
$444$	−1.91121e6	+	1.38858e6i	−0.0218353	+	0.0158643i
$445$	−4.23400e7	−	1.37571e7i	−0.480475	−	0.156116i
$446$	3.08129e7	+	4.24103e7i	0.347318	+	0.478043i
$447$	−1.98057e6	+	2.72602e6i	−0.0221752	+	0.0305216i
$448$	−2.63459e6	−	8.10842e6i	−0.0293007	−	0.0901784i
$449$	4.04219e7	−	5.56360e7i	0.446558	−	0.614634i	−0.525096	−	0.851043i	$-0.675970\pi$
$449$	4.04219e7	−	5.56360e7i	0.446558	−	0.614634i	0.971654	+	0.236409i	$0.0759705\pi$
$450$	5.56508e6	+	4.04327e6i	0.0610709	+	0.0443706i
$451$	−2.18520e8	+	7.10016e7i	−2.38211	+	0.773995i
$452$	−1.29453e7	−	9.40534e6i	−0.140184	−	0.101850i
$453$	2.05951e6	−	1.49632e6i	0.0221549	−	0.0160965i
$454$	2.28658e7	−	7.03738e7i	0.244354	−	0.752045i
$455$	4.24741e7	+	5.84605e7i	0.450910	+	0.620624i
$456$	1.90937e6	−	620392.i	0.0201371	−	0.00654292i
$457$	−3.09734e7	+	1.00639e7i	−0.324519	+	0.105443i	−0.466746	−	0.884391i	$-0.654574\pi$
$457$	−3.09734e7	+	1.00639e7i	−0.324519	+	0.105443i	0.142227	+	0.989834i	$0.454574\pi$
$458$	−9.16806e7	−	2.97888e7i	−0.954292	−	0.310068i
$459$	8.06212e6			0.0833703
$460$		−	4.40862e6i		−	0.0452928i
$461$	1.75043e8	+	5.68750e7i	1.78666	+	0.580522i	0.999351	−	0.0360316i	$-0.0114717\pi$
$461$	1.75043e8	+	5.68750e7i	1.78666	+	0.580522i	0.787313	+	0.616554i	$0.211472\pi$
$462$	1.79276e6	+	1.30252e6i	0.0181801	+	0.0132086i
$463$	8.67863e7	+	1.19451e8i	0.874396	+	1.20350i	0.977942	+	0.208879i	$0.0669814\pi$
$463$	8.67863e7	+	1.19451e8i	0.874396	+	1.20350i	−0.103545	+	0.994625i	$0.533019\pi$
$464$		−	2.24657e7i		−	0.224887i
$465$	−2.66489e6	−	2.20852e6i	−0.0265046	−	0.0219656i
$466$	−8.79225e6			−0.0868845
$467$	4.37965e7	−	3.18200e7i	0.430020	−	0.312428i	−0.351637	−	0.936137i	$-0.614375\pi$
$467$	4.37965e7	−	3.18200e7i	0.430020	−	0.312428i	0.781657	+	0.623708i	$0.214375\pi$
$468$	−2.89266e7	+	3.98141e7i	−0.282202	+	0.388418i
$469$	−6.30190e6	+	1.93953e7i	−0.0610876	+	0.188008i
$470$	1.62954e7			0.156953
$471$			2.84269e6i			0.0272062i
$472$	−1.38263e7	+	4.25531e7i	−0.131486	+	0.404674i
$473$	1.98083e7	+	6.09637e7i	0.187182	+	0.576087i
$474$	−839988.	−	2.58522e6i	−0.00788748	−	0.0242752i
$475$	−1.69599e7	+	1.23221e7i	−0.158249	+	0.114975i
$476$	4.95895e7	+	1.61126e7i	0.459800	+	0.149398i
$477$	−1.97008e7	−	2.71158e7i	−0.181522	−	0.249843i
$478$	1.80110e7	−	2.47900e7i	0.164912	−	0.226982i
$479$	1.19283e7	+	3.67116e7i	0.108536	+	0.334039i	0.990544	−	0.137195i	$-0.0438087\pi$
$479$	1.19283e7	+	3.67116e7i	0.108536	+	0.334039i	−0.882008	+	0.471234i	$0.843809\pi$
$480$	395570.	−	544455.i	0.00357684	−	0.00492309i
$481$	1.42776e8	+	1.03733e8i	1.28298	+	0.932139i
$482$	−3.24917e7	+	1.05572e7i	−0.290155	+	0.0942772i
$483$	−194807.	−	141535.i	−0.00172887	−	0.00125610i
$484$	2.93313e7	−	2.13104e7i	0.258699	−	0.187956i
$485$	5.70204e7	−	1.75491e8i	0.499810	−	1.53826i
$486$	4.67650e6	+	6.43665e6i	0.0407391	+	0.0560726i
$487$	3.70789e7	−	1.20477e7i	0.321026	−	0.104308i	−0.144071	−	0.989567i	$-0.546019\pi$
$487$	3.70789e7	−	1.20477e7i	0.321026	−	0.104308i	0.465097	+	0.885260i	$0.346019\pi$
$488$	−7.22440e7	+	2.34735e7i	−0.621645	+	0.201985i
$489$	534609.	+	173705.i	0.00457203	+	0.00148554i
$490$	−3.71619e7			−0.315871
$491$			3.20184e7i			0.270492i	0.990812	+	0.135246i	$0.0431825\pi$
$491$			3.20184e7i			0.270492i	−0.990812	+	0.135246i	$0.956817\pi$
$492$	3.62471e6	+	1.17774e6i	0.0304354	+	0.00988905i
$493$	1.11155e8	+	8.07591e7i	0.927662	+	0.673986i
$494$	−8.81553e7	−	1.21335e8i	−0.731253	−	1.00648i
$495$		−	1.63215e8i		−	1.34569i
$496$	1.94658e7	−	2.34882e7i	0.159525	−	0.192489i
$497$	1.03754e8			0.845154
$498$	4.36501e6	−	3.17137e6i	0.0353425	−	0.0256778i
$499$	−1.12940e8	+	1.55448e8i	−0.908962	+	1.25108i	0.0585580	+	0.998284i	$0.481350\pi$
$499$	−1.12940e8	+	1.55448e8i	−0.908962	+	1.25108i	−0.967520	+	0.252795i	$0.918650\pi$
$500$	1.81479e7	−	5.58534e7i	0.145183	−	0.446827i
$501$	258742.			0.00205757
$502$			8.11711e7i			0.641639i
$503$	−6.51708e7	+	2.00575e8i	−0.512093	+	1.57606i	0.276417	+	0.961038i	$0.410853\pi$
$503$	−6.51708e7	+	2.00575e8i	−0.512093	+	1.57606i	−0.788510	+	0.615022i	$0.789147\pi$
$504$	1.05986e7	+	3.26192e7i	0.0827863	+	0.254790i
$505$	−5.73013e7	−	1.76355e8i	−0.444929	−	1.36935i
$506$	−8.17083e6	+	5.93646e6i	−0.0630688	+	0.0458222i
$507$	308204.	+	100142.i	0.00236491	+	0.000768405i
$508$	−5.90920e7	−	8.13331e7i	−0.450752	−	0.620407i
$509$	5.60568e7	−	7.71555e7i	0.425084	−	0.585078i	−0.541732	−	0.840551i	$-0.682231\pi$
$509$	5.60568e7	−	7.71555e7i	0.425084	−	0.585078i	0.966816	+	0.255473i	$0.0822313\pi$
$510$	1.27186e6	+	3.91439e6i	0.00958804	+	0.0295089i
$511$	−6.55719e7	+	9.02520e7i	−0.491422	+	0.676385i
$512$	4.79880e6	+	3.48653e6i	0.0357538	+	0.0259767i
$513$	−1.53706e7	+	4.99421e6i	−0.113851	+	0.0369926i
$514$	−5.06287e6	−	3.67839e6i	−0.0372827	−	0.0270875i
$515$	−7.01418e7	+	5.09610e7i	−0.513517	+	0.373092i
$516$	328571.	−	1.01124e6i	0.00239155	−	0.00736044i
$517$	−2.19426e7	−	3.02014e7i	−0.158788	−	0.218553i
$518$	1.16975e8	−	3.80074e7i	0.841594	−	0.273451i
$519$	165071.	−	53634.8i	0.00118078	−	0.000383658i
$520$	−4.78141e7	−	1.55358e7i	−0.340053	−	0.110490i
$521$	−5.22172e6			−0.0369233			−0.0184616	−	0.999830i	$-0.505877\pi$
$521$	−5.22172e6			−0.0369233			−0.0184616	+	0.999830i	$0.505877\pi$
$522$			9.03767e7i			0.635397i
$523$	1.97190e8	+	6.40710e7i	1.37842	+	0.447875i	0.902149	−	0.431425i	$-0.141989\pi$
$523$	1.97190e8	+	6.40710e7i	1.37842	+	0.447875i	0.476269	+	0.879300i	$0.341989\pi$
$524$	−2.38025e7	−	1.72935e7i	−0.165436	−	0.120196i
$525$	225604.	+	310517.i	0.00155908	+	0.00214589i
$526$		−	8.28188e6i		−	0.0569078i
$527$	4.62395e7	+	1.80748e8i	0.315923	+	1.23493i
$528$	−1.54174e6			−0.0104739
$529$	−1.18876e8	+	8.63682e7i	−0.803019	+	0.583428i
$530$	2.01259e7	−	2.77009e7i	0.135185	−	0.186066i
$531$	5.56217e7	−	1.71186e8i	0.371502	−	1.14337i
$532$	−1.04525e8			−0.694198
$533$		−	2.84717e8i		−	1.88032i
$534$	522775.	−	1.60894e6i	0.00343314	−	0.0105661i
$535$	−2.08258e7	−	6.40953e7i	−0.136001	−	0.418567i
$536$	−4.38446e6	−	1.34940e7i	−0.0284723	−	0.0876286i
$537$	−3.54348e6	+	2.57449e6i	−0.0228827	+	0.0166253i
$538$	1.32890e8	+	4.31785e7i	0.853384	+	0.277281i
$539$	5.00406e7	+	6.88750e7i	0.319563	+	0.439841i
$540$	−3.18437e6	+	4.38290e6i	−0.0202228	+	0.0278343i
$541$	1.04054e7	+	3.20247e7i	0.0657157	+	0.202252i	0.978523	−	0.206139i	$-0.0660899\pi$
$541$	1.04054e7	+	3.20247e7i	0.0657157	+	0.202252i	−0.912807	+	0.408391i	$0.866090\pi$
$542$	−1.48947e7	+	2.05008e7i	−0.0935481	+	0.128758i
$543$	−624915.	−	454027.i	−0.00390320	−	0.00283584i
$544$	−3.45012e7	+	1.12101e7i	−0.214308	+	0.0696328i
$545$	3.02444e7	+	2.19738e7i	0.186834	+	0.135743i
$546$	−2.22152e6	+	1.61403e6i	−0.0136481	+	0.00991593i
$547$	−1.22988e7	+	3.78517e7i	−0.0751449	+	0.231272i	−0.981573	−	0.191088i	$-0.938798\pi$
$547$	−1.22988e7	+	3.78517e7i	−0.0751449	+	0.231272i	0.906428	+	0.422360i	$0.138798\pi$
$548$	−1.14153e7	−	1.57118e7i	−0.0693656	−	0.0954736i
$549$	2.90629e8	−	9.44312e7i	1.75640	−	0.570688i
$550$	1.53108e7	−	4.97477e6i	0.0920257	−	0.0299010i
$551$	−2.61947e8	−	8.51118e7i	−1.56588	−	0.508786i
$552$	167529.			0.000996032
$553$			1.41522e8i			0.836854i
$554$	4.14389e7	+	1.34643e7i	0.243713	+	0.0791872i
$555$	7.85448e6	+	5.70661e6i	0.0459450	+	0.0333810i
$556$	−3.59711e7	−	4.95100e7i	−0.209281	−	0.288051i
$557$		−	1.47354e7i		−	0.0852701i	−0.999091	−	0.0426351i	$-0.986425\pi$
$557$		−	1.47354e7i		−	0.0852701i	0.999091	−	0.0426351i	$-0.0135753\pi$
$558$	−7.83087e7	+	9.44904e7i	−0.450721	+	0.543857i
$559$	−7.94314e7			−0.454733
$560$	−2.83463e7	+	2.05948e7i	−0.161411	+	0.117272i
$561$	5.54220e6	−	7.62818e6i	0.0313902	−	0.0432049i
$562$	3.62012e7	−	1.11416e8i	0.203945	−	0.627679i
$563$	6.76595e7			0.379143			0.189572	−	0.981867i	$-0.439290\pi$
$563$	6.76595e7			0.379143			0.189572	+	0.981867i	$0.439290\pi$
$564$			619230.i			0.00345155i
$565$	−2.03211e7	+	6.25418e7i	−0.112668	+	0.346757i
$566$	−7.64382e7	−	2.35252e8i	−0.421561	−	1.29743i
$567$	−4.25913e7	−	1.31083e8i	−0.233653	−	0.719111i
$568$	−5.83993e7	+	4.24296e7i	−0.318686	+	0.231539i
$569$	−1.61677e7	−	5.25322e6i	−0.0877632	−	0.0285160i	0.264806	−	0.964302i	$-0.414692\pi$
$569$	−1.61677e7	−	5.25322e6i	−0.0877632	−	0.0285160i	−0.352569	+	0.935786i	$0.614692\pi$
$570$	−4.84966e6	−	6.67498e6i	−0.0261871	−	0.0360434i
$571$	7.89584e7	−	1.08677e8i	0.424121	−	0.583753i	−0.542470	−	0.840075i	$-0.682511\pi$
$571$	7.89584e7	−	1.08677e8i	0.424121	−	0.583753i	0.966591	+	0.256322i	$0.0825108\pi$
$572$	3.55908e7	+	1.09537e8i	0.190173	+	0.585294i
$573$	4.59868e6	−	6.32954e6i	0.0244438	−	0.0336441i
$574$	−1.60531e8	−	1.16633e8i	−0.848836	−	0.616715i
$575$	−1.66371e6	+	540572.i	−0.00875133	+	0.00284348i
$576$	−1.93050e7	−	1.40259e7i	−0.101019	−	0.0733945i
$577$	5.98317e7	−	4.34703e7i	0.311461	−	0.226290i	−0.421062	−	0.907032i	$-0.638343\pi$
$577$	5.98317e7	−	4.34703e7i	0.311461	−	0.226290i	0.732523	+	0.680742i	$0.238343\pi$
$578$	2.63650e7	−	8.11430e7i	0.136535	−	0.420211i
$579$	6.04792e6	+	8.32424e6i	0.0311580	+	0.0428854i
$580$	−8.78080e7	+	2.85305e7i	−0.450039	+	0.146226i
$581$	−2.67158e8	+	8.68050e7i	−1.36220	+	0.442605i
$582$	6.66871e6	+	2.16679e6i	0.0338277	+	0.0109913i
$583$	−7.84407e7			−0.395855
$584$		−	7.76147e7i		−	0.389677i
$585$	1.92351e8	+	6.24985e7i	0.960785	+	0.312178i
$586$	−2.88222e7	−	2.09405e7i	−0.143230	−	0.104063i
$587$	−9.89552e7	−	1.36200e8i	−0.489243	−	0.673385i	0.491005	−	0.871157i	$-0.336630\pi$
$587$	−9.89552e7	−	1.36200e8i	−0.489243	−	0.673385i	−0.980248	+	0.197772i	$0.936630\pi$
$588$		−	1.41217e6i		−	0.00694631i
$589$	−2.00123e8	−	3.15955e8i	−0.979382	−	1.54625i
$590$	1.83879e8			0.895318
$591$	−4.86424e6	+	3.53408e6i	−0.0235642	+	0.0171204i
$592$	−5.02978e7	+	6.92290e7i	−0.242429	+	0.333674i
$593$	−8.35674e7	+	2.57194e8i	−0.400749	+	1.23338i	0.523643	+	0.851938i	$0.324573\pi$
$593$	−8.35674e7	+	2.57194e8i	−0.400749	+	1.23338i	−0.924393	+	0.381442i	$0.875427\pi$
$594$	1.24111e7			0.0592176
$595$		−	2.14285e8i		−	1.01728i
$596$	−3.77166e7	+	1.16080e8i	−0.178153	+	0.548300i
$597$	−2.14299e6	−	6.59544e6i	−0.0100716	−	0.0309971i
$598$	−3.86740e6	−	1.19026e7i	−0.0180849	−	0.0556595i
$599$	1.31530e8	−	9.55621e7i	0.611990	−	0.444637i	−0.238124	−	0.971235i	$-0.576533\pi$
$599$	1.31530e8	−	9.55621e7i	0.611990	−	0.444637i	0.850115	+	0.526598i	$0.176533\pi$
$600$	−253968.	−	82519.2i	−0.00117578	−	0.000382033i
$601$	1.52187e8	+	2.09467e8i	0.701056	+	0.964921i	0.999943	+	0.0106327i	$0.00338457\pi$
$601$	1.52187e8	+	2.09467e8i	0.701056	+	0.964921i	−0.298887	+	0.954288i	$0.596615\pi$
$602$	−3.25387e7	+	4.47856e7i	−0.149146	+	0.205281i
$603$	1.76382e7	+	5.42847e7i	0.0804455	+	0.247586i
$604$	5.42006e7	−	7.46008e7i	0.245976	−	0.338557i
$605$	−1.20542e8	−	8.75792e7i	−0.544344	−	0.395489i
$606$	6.70156e6	−	2.17747e6i	0.0301133	−	0.00978440i
$607$	1.97843e8	+	1.43741e8i	0.884616	+	0.642711i	0.934469	−	0.356045i	$-0.115875\pi$
$607$	1.97843e8	+	1.43741e8i	0.884616	+	0.642711i	−0.0498525	+	0.998757i	$0.515875\pi$
$608$	5.88330e7	−	4.27447e7i	0.261764	−	0.190183i
$609$	−1.55831e6	+	4.79597e6i	−0.00689923	+	0.0212337i
$610$	1.83494e8	+	2.52558e8i	0.808413	+	1.11269i
$611$	4.39950e7	−	1.42949e7i	0.192877	−	0.0626695i
$612$	1.38794e8	−	4.50971e7i	0.605505	−	0.196741i
$613$	−4.12120e8	−	1.33906e8i	−1.78913	−	0.581325i	−0.789653	−	0.613554i	$-0.789739\pi$
$613$	−4.12120e8	−	1.33906e8i	−1.78913	−	0.581325i	−0.999481	+	0.0322290i	$0.989739\pi$
$614$	5.36504e7			0.231776
$615$		−	1.56630e7i		−	0.0673365i
$616$	7.63397e7	+	2.48043e7i	0.326594	+	0.106117i
$617$	2.70520e8	+	1.96545e8i	1.15171	+	0.836769i	0.988708	−	0.149856i	$-0.0478810\pi$
$617$	2.70520e8	+	1.96545e8i	1.15171	+	0.836769i	0.163006	+	0.986625i	$0.447881\pi$
$618$	−1.93654e6	−	2.66541e6i	−0.00820465	−	0.0112927i
$619$		−	2.18188e8i		−	0.919938i	−0.887935	−	0.459969i	$-0.847860\pi$
$619$		−	2.18188e8i		−	0.919938i	0.887935	−	0.459969i	$-0.152140\pi$
$620$	−1.16526e8	−	4.62538e7i	−0.488929	−	0.194076i
$621$	−1.34862e6			−0.00563139
$622$	−6.31142e7	+	4.58552e7i	−0.262275	+	0.190554i
$623$	−5.17709e7	+	7.12565e7i	−0.214102	+	0.294686i
$624$	590364.	−	1.81695e6i	0.00242978	−	0.00747808i
$625$	−2.67444e8			−1.09545
$626$		−	4.32641e7i		−	0.176362i
$627$	−5.84091e6	+	1.79765e7i	−0.0236962	+	0.0729293i
$628$	3.18193e7	+	9.79299e7i	0.128473	+	0.395400i
$629$	−1.61721e8	−	4.97726e8i	−0.649852	−	2.00004i
$630$	1.14034e8	−	8.28504e7i	0.456049	−	0.331339i
$631$	−7.64876e7	−	2.48523e7i	−0.304441	−	0.0989189i	0.152813	−	0.988255i	$-0.451167\pi$
$631$	−7.64876e7	−	2.48523e7i	−0.304441	−	0.0989189i	−0.457254	+	0.889336i	$0.651167\pi$
$632$	−5.78747e7	−	7.96577e7i	−0.229265	−	0.315556i
$633$	5.87483e6	−	8.08602e6i	0.0231625	−	0.0318804i
$634$	2.28465e7	+	7.03143e7i	0.0896504	+	0.275916i
$635$	−2.42849e8	+	3.34253e8i	−0.948453	+	1.30543i
$636$	1.05264e6	+	764790.i	0.00409176	+	0.00297283i
$637$	−1.00332e8	+	3.25997e7i	−0.388168	+	0.126123i
$638$	1.71116e8	+	1.24323e8i	0.658914	+	0.478729i
$639$	2.34933e8	−	1.70689e8i	0.900414	−	0.654189i
$640$	7.53296e6	−	2.31841e7i	0.0287360	−	0.0884402i
$641$	2.03145e8	+	2.79606e8i	0.771317	+	1.06163i	0.996187	+	0.0872384i	$0.0278042\pi$
$641$	2.03145e8	+	2.79606e8i	0.771317	+	1.06163i	−0.224870	+	0.974389i	$0.572196\pi$
$642$	2.43564e6	−	791389.i	0.00920468	−	0.00299078i
$643$	3.02977e8	−	9.84433e7i	1.13967	−	0.370300i	0.322424	−	0.946595i	$-0.395502\pi$
$643$	3.02977e8	−	9.84433e7i	1.13967	−	0.370300i	0.817241	+	0.576296i	$0.195502\pi$
$644$	−8.29528e6	−	2.69530e6i	−0.0310580	−	0.0100914i
$645$	−4.36973e6			−0.0162846
$646$			4.44751e8i			1.64975i
$647$	−3.81448e8	−	1.23940e8i	−1.40839	−	0.457613i	−0.496494	−	0.868040i	$-0.665380\pi$
$647$	−3.81448e8	−	1.23940e8i	−1.40839	−	0.457613i	−0.911893	+	0.410427i	$0.865380\pi$
$648$	7.75784e7	+	5.63640e7i	0.285112	+	0.207146i
$649$	−2.47604e8	−	3.40798e8i	−0.905782	−	1.24670i
$650$			1.99489e7i			0.0726404i
$651$	−5.78480e6	+	3.66405e6i	−0.0209674	+	0.0132806i
$652$	2.03614e7			0.0734625
$653$	−1.45576e8	+	1.05767e8i	−0.522819	+	0.379850i	−0.817665	−	0.575695i	$-0.804732\pi$
$653$	−1.45576e8	+	1.05767e8i	−0.522819	+	0.379850i	0.294846	+	0.955545i	$0.404732\pi$
$654$	−835013.	+	1.14930e6i	−0.00298511	+	0.00410865i
$655$	−3.73642e7	+	1.14995e8i	−0.132963	+	0.409219i
$656$	1.38053e8			0.489029
$657$			3.12235e8i			1.10099i
$658$	9.96250e6	−	3.06614e7i	0.0349696	−	0.107625i
$659$	4.84071e7	+	1.48982e8i	0.169143	+	0.520567i	0.999318	−	0.0369355i	$-0.0117596\pi$
$659$	4.84071e7	+	1.48982e8i	0.169143	+	0.520567i	−0.830175	+	0.557503i	$0.811760\pi$
$660$	1.95795e6	+	6.02594e6i	0.00681034	+	0.0209601i
$661$	2.77905e8	−	2.01910e8i	0.962259	−	0.699122i	0.00858443	−	0.999963i	$-0.497267\pi$
$661$	2.77905e8	−	2.01910e8i	0.962259	−	0.699122i	0.953674	+	0.300841i	$0.0972675\pi$
$662$	−1.54706e8	−	5.02670e7i	−0.533252	−	0.173264i
$663$	6.86767e6	+	9.45254e6i	0.0235651	+	0.0324346i
$664$	1.14875e8	−	1.58112e8i	0.392393	−	0.540083i
$665$	1.32742e8	+	4.08539e8i	0.451382	+	1.38921i
$666$	2.02342e8	−	2.78500e8i	0.684958	−	0.942763i
$667$	−1.85939e7	−	1.35093e7i	−0.0626605	−	0.0455255i
$668$	8.91359e6	−	2.89620e6i	0.0299036	−	0.00971626i
$669$	6.62319e6	+	4.81203e6i	0.0221202	+	0.0160713i
$670$	−4.71737e7	+	3.42737e7i	−0.156847	+	0.113956i
$671$	2.21000e8	−	6.80168e8i	0.731517	−	2.25138i
$672$	−782609.	−	1.07717e6i	−0.00257891	−	0.00354957i
$673$	4.77260e8	−	1.55071e8i	1.56571	−	0.508729i	0.607381	−	0.794411i	$-0.292220\pi$
$673$	4.77260e8	−	1.55071e8i	1.56571	−	0.508729i	0.958324	+	0.285682i	$0.0922202\pi$
$674$	1.25369e8	−	4.07350e7i	0.409461	−	0.133042i
$675$	2.04446e6	+	664286.i	0.00664764	+	0.00215995i
$676$	1.17385e7			0.0379989
$677$			2.53433e7i			0.0816764i	0.999166	+	0.0408382i	$0.0130028\pi$
$677$			2.53433e7i			0.0816764i	−0.999166	+	0.0408382i	$0.986997\pi$
$678$	−2.37661e6	−	772208.i	−0.00762551	−	0.00247768i
$679$	−2.95343e8	−	2.14580e8i	−0.943448	−	0.685455i
$680$	8.76305e7	+	1.20613e8i	0.278695	+	0.383590i
$681$		−	1.15558e7i		−	0.0365898i
$682$	7.11826e7	+	2.78249e8i	0.224399	+	0.877163i
$683$	2.10099e8			0.659419			0.329709	−	0.944082i	$-0.393049\pi$
$683$	2.10099e8			0.659419			0.329709	+	0.944082i	$0.393049\pi$
$684$	−2.36678e8	+	1.71957e8i	−0.739588	+	0.537342i
$685$	−4.69131e7	+	6.45704e7i	−0.145956	+	0.200892i
$686$	−7.62286e7	+	2.34607e8i	−0.236127	+	0.726724i
$687$	−1.50545e7			−0.0464298
$688$		−	3.85146e7i		−	0.118266i
$689$	3.00366e7	−	9.24433e7i	0.0918319	−	0.282630i
$690$	−212756.	−	654795.i	−0.000647641	−	0.00199323i
$691$	3.96940e7	+	1.22166e8i	0.120307	+	0.370267i	0.993017	−	0.117972i	$-0.0376394\pi$
$691$	3.96940e7	+	1.22166e8i	0.120307	+	0.370267i	−0.872710	+	0.488239i	$0.837639\pi$
$692$	5.08629e6	−	3.69540e6i	0.0153491	−	0.0111518i
$693$	−3.07106e8	−	9.97847e7i	−0.922759	−	0.299823i
$694$	−5.93135e7	−	8.16381e7i	−0.177450	−	0.244239i
$695$	−1.47830e8	+	2.03471e8i	−0.440360	+	0.606104i
$696$	−1.08417e6	−	3.33673e6i	−0.00321566	−	0.00989678i
$697$	−4.96271e8	+	6.83058e8i	−1.46562	+	2.01725i
$698$	−2.10601e8	−	1.53010e8i	−0.619289	−	0.449940i
$699$	−1.30588e6	+	424305.i	−0.00382358	+	0.00124236i
$700$	1.12477e7	+	8.17195e6i	0.0327922	+	0.0238249i
$701$	−2.63883e8	+	1.91722e8i	−0.766051	+	0.556568i	−0.900760	−	0.434317i	$-0.856990\pi$
$701$	−2.63883e8	+	1.91722e8i	−0.766051	+	0.556568i	0.134710	+	0.990885i	$0.456990\pi$
$702$	−4.75248e6	+	1.46266e7i	−0.0137375	+	0.0422798i
$703$	6.16648e8	+	8.48743e8i	1.77489	+	2.44293i
$704$	−5.31123e7	+	1.72572e7i	−0.152222	+	0.0494599i
$705$	2.42028e6	−	786398.i	0.00690715	−	0.00224427i
$706$	2.26876e8	+	7.37165e7i	0.644725	+	0.209484i
$707$	−3.66863e8			−1.03812
$708$			6.98748e6i			0.0196889i
$709$	1.68542e8	+	5.47626e7i	0.472900	+	0.153655i	0.535764	−	0.844368i	$-0.320024\pi$
$709$	1.68542e8	+	5.47626e7i	0.472900	+	0.153655i	−0.0628643	+	0.998022i	$0.520024\pi$
$710$	2.40003e8	+	1.74372e8i	0.670565	+	0.487194i
$711$	2.32823e8	+	3.20453e8i	0.647764	+	0.891571i
$712$		−	6.12790e7i		−	0.169774i
$713$	−7.73489e6	−	3.02353e7i	−0.0213396	−	0.0834153i
$714$	8.14291e6			0.0223710
$715$	3.82932e8	−	2.78216e8i	1.04762	−	0.761140i
$716$	−9.32546e7	+	1.28354e8i	−0.254057	+	0.349680i
$717$	1.47876e6	−	4.55114e6i	0.00401180	−	0.0123470i
$718$	2.68319e8			0.724901
$719$		−	2.42666e8i		−	0.652864i	−0.945221	−	0.326432i	$-0.894154\pi$
$719$		−	2.42666e8i		−	0.652864i	0.945221	−	0.326432i	$-0.105846\pi$
$720$	−3.03042e7	+	9.32668e7i	−0.0811906	+	0.249879i
$721$	5.30058e7	+	1.63135e8i	0.141422	+	0.435253i
$722$	−1.93268e8	−	5.94819e8i	−0.513511	−	1.58042i
$723$	−4.31637e6	+	3.13603e6i	−0.0114210	+	0.00829784i
$724$	−2.66102e7	−	8.64618e6i	−0.0701185	−	0.0227829i
$725$	2.15335e7	+	2.96383e7i	0.0565068	+	0.0777749i
$726$	3.32804e6	−	4.58065e6i	0.00869718	−	0.0119706i
$727$	−1.84402e7	−	5.67530e7i	−0.0479912	−	0.147702i	0.924189	−	0.381935i	$-0.124742\pi$
$727$	−1.84402e7	−	5.67530e7i	−0.0479912	−	0.147702i	−0.972180	+	0.234233i	$0.924742\pi$
$728$	−5.84643e7	+	8.04691e7i	−0.151529	+	0.208562i
$729$	−3.11418e8	−	2.26259e8i	−0.803825	−	0.584013i
$730$	−3.03360e8	+	9.85677e7i	−0.779812	+	0.253376i
$731$	1.90562e8	+	1.38452e8i	0.487848	+	0.354443i
$732$	−9.59731e6	+	6.97285e6i	−0.0244690	+	0.0177778i
$733$	−9.45613e7	+	2.91030e8i	−0.240105	+	0.738968i	0.756298	+	0.654227i	$0.227006\pi$
$733$	−9.45613e7	+	2.91030e8i	−0.240105	+	0.738968i	−0.996403	+	0.0847403i	$0.972994\pi$
$734$	1.35493e8	+	1.86490e8i	0.342632	+	0.471592i
$735$	−5.51951e6	+	1.79340e6i	−0.0139008	+	0.00451663i
$736$	5.77133e6	−	1.87522e6i	0.0144758	−	0.00470347i
$737$	1.27044e8	+	4.12791e7i	0.317360	+	0.103116i
$738$	−5.55372e8			−1.38170
$739$		−	4.95897e8i		−	1.22873i	−0.789020	−	0.614367i	$-0.789411\pi$
$739$		−	4.95897e8i		−	1.22873i	0.789020	−	0.614367i	$-0.210589\pi$
$740$	3.34461e8	+	1.08673e8i	0.825372	+	0.268180i
$741$	−1.89489e7	−	1.37672e7i	−0.0465724	−	0.0338368i
$742$	−3.98177e7	−	5.48044e7i	−0.0974686	−	0.134154i
$743$			3.00047e8i			0.731513i	0.930710	+	0.365757i	$0.119190\pi$
$743$			3.00047e8i			0.731513i	−0.930710	+	0.365757i	$0.880810\pi$
$744$	1.75766e6	−	4.42801e6i	0.00426792	−	0.0107520i
$745$	5.01602e8			1.21308
$746$	4.80630e7	−	3.49198e7i	0.115770	−	0.0841116i
$747$	−4.62129e8	+	6.36066e8i	−1.10867	+	1.52595i
$748$	1.05542e8	−	3.24825e8i	0.252185	−	0.776147i
$749$	−1.33334e8			−0.317319
$750$		−	9.17147e6i		−	0.0217398i
$751$	1.71631e8	−	5.28227e8i	0.405207	−	1.24710i	−0.515516	−	0.856880i	$-0.672400\pi$
$751$	1.71631e8	−	5.28227e8i	0.405207	−	1.24710i	0.920723	−	0.390218i	$-0.127600\pi$
$752$	6.93128e6	+	2.13323e7i	0.0162989	+	0.0501630i
$753$	3.91724e6	+	1.20560e7i	0.00917477	+	0.0282370i
$754$	−2.12040e8	+	1.54056e8i	−0.494657	+	0.359389i
$755$	−3.60413e8	−	1.17105e8i	−0.837451	−	0.272104i
$756$	6.30006e6	+	8.67129e6i	0.0145807	+	0.0200687i
$757$	4.51482e7	−	6.21411e7i	0.104076	−	0.143249i	−0.753802	−	0.657102i	$-0.771782\pi$
$757$	4.51482e7	−	6.21411e7i	0.104076	−	0.143249i	0.857878	+	0.513853i	$0.171782\pi$
$758$	−1.51951e8	−	4.67657e8i	−0.348896	−	1.07379i
$759$	−927093.	+	1.27603e6i	−0.00212030	+	0.00291835i
$760$	−2.41785e8	−	1.75667e8i	−0.550793	−	0.400175i
$761$	−4.56587e8	+	1.48354e8i	−1.03602	+	0.336625i	−0.777169	−	0.629291i	$-0.783345\pi$
$761$	−4.56587e8	+	1.48354e8i	−1.03602	+	0.336625i	−0.258855	+	0.965916i	$0.583345\pi$
$762$	−1.27017e7	−	9.22836e6i	−0.0287077	−	0.0208574i
$763$	5.98366e7	−	4.34738e7i	0.134708	−	0.0978710i
$764$	8.75742e7	−	2.69526e8i	0.196379	−	0.604394i
$765$	−3.52527e8	−	4.85212e8i	−0.787424	−	1.08380i
$766$	6.29370e7	−	2.04495e7i	0.140030	−	0.0454984i
$767$	4.96447e8	−	1.61305e8i	1.10024	−	0.357489i
$768$	881003.	+	286255.i	0.00194488	+	0.000631931i
$769$	−2.50494e8			−0.550831			−0.275416	−	0.961325i	$-0.588815\pi$
$769$	−2.50494e8			−0.550831			−0.275416	+	0.961325i	$0.588815\pi$
$770$		−	3.29877e8i		−	0.722571i
$771$	−929483.	−	302007.i	−0.00202805	−	0.000658953i
$772$	3.01525e8	+	2.19071e8i	0.655348	+	0.476138i
$773$	−2.21944e8	−	3.05480e8i	−0.480513	−	0.661370i	0.498090	−	0.867125i	$-0.334035\pi$
$773$	−2.21944e8	−	3.05480e8i	−0.480513	−	0.661370i	−0.978603	+	0.205755i	$0.934035\pi$
$774$			1.54940e8i			0.334149i
$775$	−3.16707e6	+	4.96455e7i	−0.00680381	+	0.106653i
$776$	2.53989e8			0.543537
$777$	1.55396e7	−	1.12902e7i	0.0331266	−	0.0240678i
$778$	−5.00458e7	+	6.88822e7i	−0.106274	+	0.146274i
$779$	5.23019e8	−	1.60969e9i	1.10638	−	3.40509i
$780$	−7.85138e6			−0.0165448
$781$		−	6.79617e8i		−	1.42663i
$782$	−1.14685e7	+	3.52963e7i	−0.0239820	+	0.0738090i
$783$	8.72765e6	+	2.68610e7i	0.0181808	+	0.0559546i
$784$	−1.58069e7	−	4.86487e7i	−0.0328019	−	0.100954i
$785$	3.42354e8	−	2.48734e8i	0.707727	−	0.514194i
$786$	−4.36986e6	−	1.41985e6i	−0.00899912	−	0.00292399i
$787$	−1.95173e8	−	2.68632e8i	−0.400400	−	0.551104i	0.560444	−	0.828192i	$-0.310630\pi$
$787$	−1.95173e8	−	2.68632e8i	−0.400400	−	0.551104i	−0.960844	+	0.277088i	$0.910630\pi$
$788$	−1.28013e8	+	1.76195e8i	−0.261623	+	0.360094i
$789$	−399675.	−	1.23007e6i	−0.000813722	−	0.00250438i
$790$	−2.37847e8	+	3.27368e8i	−0.482409	+	0.663979i
$791$	1.05255e8	+	7.64724e7i	0.212674	+	0.154517i
$792$	2.13665e8	−	6.94239e7i	0.430088	−	0.139744i
$793$	7.16960e8	+	5.20902e8i	1.43772	+	1.04457i
$794$	−4.26087e8	+	3.09570e8i	−0.851210	+	0.618440i
$795$	1.65240e6	−	5.08555e6i	0.00328861	−	0.0101213i
$796$	−1.47651e8	−	2.03224e8i	−0.292749	−	0.402935i
$797$	1.40332e7	−	4.55967e6i	0.0277193	−	0.00900655i	−0.295125	−	0.955459i	$-0.595361\pi$
$797$	1.40332e7	−	4.55967e6i	0.0277193	−	0.00900655i	0.322844	+	0.946452i	$0.395361\pi$
$798$	−1.55246e7	+	5.04425e6i	−0.0305501	+	0.00992631i
$799$	−1.30464e8	−	4.23903e7i	−0.255770	−	0.0831048i
$800$	−9.67279e6			−0.0188922
$801$			2.46518e8i			0.479680i
$802$	2.69914e8	+	8.77004e7i	0.523242	+	0.170012i
$803$	5.91174e8	+	4.29513e8i	1.14174	+	0.829526i
$804$	−1.30241e6	−	1.79262e6i	−0.00250600	−	0.00344921i
$805$			3.58454e7i			0.0687141i
$806$	−3.55177e8	−	2.26580e7i	−0.678328	−	0.0432730i
$807$	2.18213e7			0.0415203
$808$	2.06494e8	−	1.50026e8i	0.391447	−	0.284403i
$809$	−2.22987e8	+	3.06916e8i	−0.421148	+	0.579660i	−0.965893	−	0.258941i	$-0.916626\pi$
$809$	−2.22987e8	+	3.06916e8i	−0.421148	+	0.579660i	0.544745	+	0.838602i	$0.316626\pi$
$810$	1.21780e8	−	3.74799e8i	0.229150	−	0.705250i
$811$	−3.85992e8			−0.723628			−0.361814	−	0.932250i	$-0.617843\pi$
$811$	−3.85992e8			−0.723628			−0.361814	+	0.932250i	$0.617843\pi$
$812$			1.82662e8i			0.341178i
$813$	−1.22290e6	+	3.76371e6i	−0.00227573	+	0.00700398i
$814$	−2.48958e8	−	7.66215e8i	−0.461587	−	1.42062i
$815$	−2.58583e7	−	7.95835e7i	−0.0477668	−	0.147011i
$816$	−4.58334e6	+	3.32999e6i	−0.00843551	+	0.00612876i
$817$	−4.49076e8	−	1.45914e8i	−0.823482	−	0.267566i
$818$	7.90905e7	+	1.08859e8i	0.144499	+	0.198886i
$819$	2.35195e8	−	3.23718e8i	0.428130	−	0.589271i
$820$	−1.75322e8	−	5.39587e8i	−0.317977	−	0.978633i
$821$	−3.84165e8	+	5.28758e8i	−0.694206	+	0.955493i	0.305788	+	0.952100i	$0.401080\pi$
$821$	−3.84165e8	+	5.28758e8i	−0.694206	+	0.955493i	−0.999994	+	0.00339338i	$0.998920\pi$
$822$	−2.45370e6	−	1.78272e6i	−0.00441780	−	0.00320972i
$823$	−3.50197e7	+	1.13786e7i	−0.0628222	+	0.0204122i	−0.340260	−	0.940332i	$-0.610515\pi$
$823$	−3.50197e7	+	1.13786e7i	−0.0628222	+	0.0204122i	0.277437	+	0.960744i	$0.410515\pi$
$824$	−9.65480e7	−	7.01462e7i	−0.172569	−	0.125378i
$825$	2.03397e6	−	1.47777e6i	0.00362228	−	0.00263174i
$826$	1.12418e8	−	3.45988e8i	0.199479	−	0.613933i
$827$	4.75850e8	+	6.54951e8i	0.841305	+	1.15796i	0.985712	+	0.168439i	$0.0538726\pi$
$827$	4.75850e8	+	6.54951e8i	0.841305	+	1.15796i	−0.144407	+	0.989518i	$0.546127\pi$
$828$	−2.32174e7	+	7.54379e6i	−0.0408999	+	0.0132892i
$829$	6.58468e8	−	2.13949e8i	1.15577	−	0.375532i	0.332455	−	0.943119i	$-0.392123\pi$
$829$	6.58468e8	−	2.13949e8i	1.15577	−	0.375532i	0.823313	+	0.567587i	$0.192123\pi$
$830$	−7.63874e8	−	2.48198e8i	−1.33594	−	0.434074i
$831$	6.80452e6			0.0118575
$832$		−	6.92017e7i		−	0.120156i
$833$	2.97526e8	+	9.66720e7i	0.514742	+	0.167250i
$834$	−7.73195e6	−	5.61759e6i	−0.0133288	−	0.00968394i
$835$	−2.26398e7	−	3.11611e7i	−0.0388879	−	0.0535245i
$836$			6.84664e8i			1.17181i
$837$	−1.41493e7	+	3.56458e7i	−0.0241301	+	0.0607900i
$838$	−7.96066e8			−1.35275
$839$	−8.37385e8	+	6.08396e8i	−1.41788	+	1.03015i	−0.425763	+	0.904835i	$0.639994\pi$
$839$	−8.37385e8	+	6.08396e8i	−1.41788	+	1.03015i	−0.992117	+	0.125315i	$0.960006\pi$
$840$	−3.21628e6	+	4.42682e6i	−0.00542644	+	0.00746886i
$841$	3.50729e7	−	1.07943e8i	0.0589636	−	0.181471i
$842$	−1.05019e8			−0.175926
$843$		−	1.82952e7i		−	0.0305389i
$844$	1.11876e8	−	3.44320e8i	0.186085	−	0.572710i
$845$	−1.49074e7	−	4.58802e7i	−0.0247077	−	0.0760424i
$846$	−2.78837e7	−	8.58172e7i	−0.0460510	−	0.141731i
$847$	−2.38485e8	+	1.73270e8i	−0.392474	+	0.285149i
$848$	4.48238e7	+	1.45641e7i	0.0735057	+	0.0238835i
$849$	−2.27061e7	−	3.12523e7i	−0.0371039	−	0.0510691i
$850$	3.47715e7	−	4.78589e7i	0.0566196	−	0.0779303i
$851$	2.70525e7	+	8.32590e7i	0.0438954	+	0.135096i
$852$	−6.62620e6	+	9.12018e6i	−0.0107139	+	0.0147464i
$853$	2.54247e8	+	1.84721e8i	0.409646	+	0.297625i	0.773459	−	0.633847i	$-0.218525\pi$
$853$	2.54247e8	+	1.84721e8i	0.409646	+	0.297625i	−0.363812	+	0.931472i	$0.618525\pi$
$854$	5.87398e8	−	1.90857e8i	0.943102	−	0.306432i
$855$	9.72672e8	+	7.06688e8i	1.55621	+	1.13065i
$856$	7.50489e7	−	5.45262e7i	0.119653	−	0.0869329i
$857$	−1.80684e8	+	5.56089e8i	−0.287063	+	0.883490i	0.698709	+	0.715406i	$0.253758\pi$
$857$	−1.80684e8	+	5.56089e8i	−0.287063	+	0.883490i	−0.985773	+	0.168084i	$0.946242\pi$
$858$	1.05723e7	+	1.45515e7i	0.0167382	+	0.0230381i
$859$	5.68713e7	−	1.84786e7i	0.0897250	−	0.0291534i	−0.263810	−	0.964575i	$-0.584979\pi$
$859$	5.68713e7	−	1.84786e7i	0.0897250	−	0.0291534i	0.353536	+	0.935421i	$0.384979\pi$
$860$	−1.50536e8	+	4.89121e7i	−0.236671	+	0.0768991i
$861$	−2.94716e7	−	9.57591e6i	−0.0461737	−	0.0150027i
$862$	3.90470e8			0.609630
$863$		−	1.15744e9i		−	1.80080i	−0.435063	−	0.900400i	$-0.643274\pi$
$863$		−	1.15744e9i		−	1.80080i	0.435063	−	0.900400i	$-0.356726\pi$
$864$	−7.09214e6	−	2.30438e6i	−0.0109960	−	0.00357283i
$865$	−2.09030e7	−	1.51869e7i	−0.0322969	−	0.0234651i
$866$	2.79546e8	+	3.84763e8i	0.430428	+	0.592433i
$867$		−	1.33242e7i		−	0.0204448i
$868$	−1.58272e8	+	1.90977e8i	−0.242016	+	0.292026i
$869$	9.27009e8			1.41262
$870$	−1.16649e7	+	8.47505e6i	−0.0177143	+	0.0128702i
$871$	−9.72959e7	+	1.33916e8i	−0.147245	+	0.202665i
$872$	−1.59014e7	+	4.89396e7i	−0.0239821	+	0.0738092i
$873$	−1.02177e9			−1.53571
$874$		−	7.43974e7i		−	0.111435i
$875$	−1.47556e8	+	4.54129e8i	−0.220258	+	0.677884i
$876$	−3.74561e6	−	1.15278e7i	−0.00557198	−	0.0171488i
$877$	−3.33351e8	−	1.02595e9i	−0.494200	−	1.52099i	−0.818200	−	0.574934i	$-0.805028\pi$
$877$	−3.33351e8	−	1.02595e9i	−0.494200	−	1.52099i	0.324000	−	0.946057i	$-0.394972\pi$
$878$	−4.58272e8	+	3.32954e8i	−0.677079	+	0.491927i
$879$	−5.29141e6	−	1.71928e6i	−0.00779121	−	0.00253152i
$880$	1.34901e8	+	1.85676e8i	0.197956	+	0.272463i
$881$	−4.10625e8	+	5.65177e8i	−0.600507	+	0.826527i	−0.995755	−	0.0920478i	$-0.970659\pi$
$881$	−4.10625e8	+	5.65177e8i	−0.600507	+	0.826527i	0.395248	+	0.918575i	$0.370659\pi$
$882$	6.35894e7	+	1.95708e8i	0.0926785	+	0.285235i
$883$	3.50776e8	−	4.82801e8i	0.509504	−	0.701272i	−0.474332	−	0.880346i	$-0.657310\pi$
$883$	3.50776e8	−	4.82801e8i	0.509504	−	0.701272i	0.983836	+	0.179074i	$0.0573103\pi$
$884$	3.42395e8	+	2.48765e8i	0.495645	+	0.360107i
$885$	2.73109e7	−	8.87384e6i	0.0394009	−	0.0128021i
$886$	6.70755e8	+	4.87332e8i	0.964413	+	0.700687i
$887$	8.09156e8	−	5.87886e8i	1.15947	−	0.842408i	0.169763	−	0.985485i	$-0.445700\pi$
$887$	8.09156e8	−	5.87886e8i	1.15947	−	0.842408i	0.989712	+	0.143077i	$0.0456997\pi$
$888$	−4.12961e6	+	1.27096e7i	−0.00589753	+	0.0181507i
$889$	4.80462e8	+	6.61299e8i	0.683838	+	0.941223i
$890$	−2.39511e8	+	7.78220e7i	−0.339747	+	0.110391i
$891$	−8.58626e8	+	2.78984e8i	−1.21387	+	0.394409i
$892$	2.82030e8	+	9.16370e7i	0.397375	+	0.129115i
$893$	2.74991e8			0.386158
$894$			1.90610e7i			0.0266768i
$895$	6.20107e8	+	2.01485e8i	0.864962	+	0.281043i
$896$	−3.90178e7	−	2.83481e7i	−0.0542424	−	0.0394094i
$897$	−1.14882e6	−	1.58121e6i	−0.00159175	−	0.00219085i
$898$		−	3.89021e8i		−	0.537210i
$899$	−5.52149e8	+	3.49727e8i	−0.759937	+	0.481338i
$900$	3.89125e7			0.0533779
$901$	−2.33192e8	+	1.69424e8i	−0.318815	+	0.231633i
$902$	−7.63975e8	+	1.05152e9i	−1.04102	+	1.43284i
$903$	−2.67153e6	+	8.22211e6i	−0.00362824	+	0.0111666i
$904$	−9.05171e7			−0.122525
$905$			1.14987e8i			0.155133i
$906$	4.45004e6	−	1.36958e7i	0.00598383	−	0.0184163i
$907$	2.51216e8	+	7.73164e8i	0.336687	+	1.03622i	0.965885	+	0.258971i	$0.0833832\pi$
$907$	2.51216e8	+	7.73164e8i	0.336687	+	1.03622i	−0.629199	+	0.777245i	$0.716617\pi$
$908$	−1.29349e8	−	3.98095e8i	−0.172784	−	0.531776i
$909$	−8.30699e8	+	6.03538e8i	−1.10599	+	0.803551i
$910$	3.88764e8	+	1.26317e8i	0.515896	+	0.167625i
$911$	−3.57531e8	−	4.92099e8i	−0.472888	−	0.650875i	0.504231	−	0.863569i	$-0.331776\pi$
$911$	−3.57531e8	−	4.92099e8i	−0.472888	−	0.650875i	−0.977119	+	0.212694i	$0.931776\pi$
$912$	6.67541e6	−	9.18791e6i	0.00880021	−	0.0121125i
$913$	5.68595e8	+	1.74996e9i	0.747121	+	2.29940i
$914$	−1.08287e8	+	1.49044e8i	−0.141820	+	0.195199i
$915$	3.94419e7	+	2.86562e7i	0.0514866	+	0.0374072i
$916$	−5.18624e8	+	1.68511e8i	−0.674786	+	0.219251i
$917$	1.93532e8	+	1.40609e8i	0.250984	+	0.182350i
$918$	3.68962e7	−	2.68067e7i	0.0476929	−	0.0346509i
$919$	1.49754e8	−	4.60897e8i	0.192945	−	0.593823i	−0.807050	−	0.590484i	$-0.798937\pi$
$919$	1.49754e8	−	4.60897e8i	0.192945	−	0.593823i	0.999994	−	0.00333945i	$-0.00106298\pi$
$920$	−1.46587e7	−	2.01760e7i	−0.0188249	−	0.0259103i
$921$	7.96848e6	−	2.58911e6i	0.0101999	−	0.00331415i
$922$	9.90195e8	−	3.21734e8i	1.26336	−	0.410491i
$923$	8.00936e8	+	2.60240e8i	1.01857	+	0.330955i
$924$	1.25355e7			0.0158900
$925$		−	1.39543e8i		−	0.176312i
$926$	7.94354e8	+	2.58101e8i	1.00042	+	0.325055i
$927$	3.88401e8	+	2.82190e8i	0.487575	+	0.354244i
$928$	−7.46987e7	−	1.02814e8i	−0.0934693	−	0.128649i
$929$		−	6.66852e8i		−	0.831730i	−0.909426	−	0.415865i	$-0.863479\pi$
$929$		−	6.66852e8i		−	0.831730i	0.909426	−	0.415865i	$-0.136521\pi$
$930$	−1.95392e7	−	1.24648e6i	−0.0242917	−	0.00154966i
$931$	−6.27124e8			−0.777149
$932$	−4.02376e7	+	2.92344e7i	−0.0497033	+	0.0361115i
$933$	−7.16117e6	+	9.85651e6i	−0.00881738	+	0.0121361i
$934$	9.46323e7	−	2.91248e8i	0.116145	−	0.357456i
$935$	−1.40362e9			−1.71718
$936$			2.78390e8i			0.339489i
$937$	4.22986e8	−	1.30182e9i	0.514171	−	1.58245i	−0.270616	−	0.962688i	$-0.587227\pi$
$937$	4.22986e8	−	1.30182e9i	0.514171	−	1.58245i	0.784786	−	0.619767i	$-0.212773\pi$
$938$	3.56489e7	+	1.09716e8i	0.0431955	+	0.132942i
$939$	−2.08788e6	−	6.42583e6i	−0.00252179	−	0.00776127i
$940$	7.45756e7	−	5.41824e7i	0.0897870	−	0.0652340i
$941$	−1.03054e8	−	3.34841e7i	−0.123678	−	0.0401856i	0.246524	−	0.969137i	$-0.420712\pi$
$941$	−1.03054e8	−	3.34841e7i	−0.123678	−	0.0401856i	−0.370202	+	0.928951i	$0.620712\pi$
$942$	9.45200e6	+	1.30096e7i	0.0113076	+	0.0155636i
$943$	8.30156e7	−	1.14261e8i	0.0989976	−	0.136259i
$944$	7.82136e7	+	2.40717e8i	0.0929750	+	0.286148i
$945$	2.58913e7	−	3.56363e7i	0.0306802	−	0.0422276i
$946$	2.93358e8	+	2.13137e8i	0.346517	+	0.251759i
$947$	9.84368e8	−	3.19841e8i	1.15906	−	0.376603i	0.334514	−	0.942391i	$-0.391428\pi$
$947$	9.84368e8	−	3.19841e8i	1.15906	−	0.376603i	0.824551	+	0.565788i	$0.191428\pi$
$948$	−1.24401e7	−	9.03825e6i	−0.0146015	−	0.0106086i
$949$	−7.32560e8	+	5.32236e8i	−0.857125	+	0.622738i
$950$	−3.66456e7	+	1.12784e8i	−0.0427417	+	0.131545i
$951$	6.78660e6	+	9.34095e6i	0.00789061	+	0.0108605i
$952$	2.80521e8	−	9.11467e7i	0.325128	−	0.105640i
$953$	−5.81692e8	+	1.89003e8i	−0.672069	+	0.218369i	−0.625120	−	0.780529i	$-0.714950\pi$
$953$	−5.81692e8	+	1.89003e8i	−0.672069	+	0.218369i	−0.0469494	+	0.998897i	$0.514950\pi$
$954$	−1.80321e8	−	5.85898e7i	−0.207683	−	0.0674803i
$955$	−1.16467e9			−1.33719
$956$		−	1.73338e8i		−	0.198390i
$957$	3.14149e7	+	1.02073e7i	0.0358426	+	0.0116460i
$958$	1.76657e8	+	1.28349e8i	0.200925	+	0.145980i
$959$	9.28146e7	+	1.27748e8i	0.105235	+	0.144844i
$960$		−	3.80697e6i		−	0.00430294i
$961$	−8.80309e8	−	1.12775e8i	−0.991894	−	0.127070i
$962$	9.98325e8			1.12136
$963$	−3.01913e8	+	2.19353e8i	−0.338067	+	0.245620i
$964$	−1.13595e8	+	1.56350e8i	−0.126803	+	0.174529i
$965$	4.73322e8	−	1.45674e9i	0.526714	−	1.62106i
$966$	−1.36214e6			−0.00151109
$967$		−	1.72435e9i		−	1.90698i	−0.301427	−	0.953489i	$-0.597463\pi$
$967$		−	1.72435e9i		−	1.90698i	0.301427	−	0.953489i	$-0.402537\pi$
$968$	6.33769e7	−	1.95054e8i	0.0698723	−	0.215045i
$969$	2.14632e7	+	6.60570e7i	0.0235898	+	0.0726018i
$970$	−3.22556e8	−	9.92725e8i	−0.353419	−	1.08771i
$971$	1.15817e9	−	8.41463e8i	1.26508	−	0.919131i	0.266080	−	0.963951i	$-0.414271\pi$
$971$	1.15817e9	−	8.41463e8i	1.26508	−	0.919131i	0.998995	+	0.0448199i	$0.0142714\pi$
$972$	4.28039e7	+	1.39078e7i	0.0466106	+	0.0151447i
$973$	2.92472e8	+	4.02553e8i	0.317502	+	0.437003i
$974$	1.29633e8	−	1.78424e8i	0.140293	−	0.193097i
$975$	962713.	+	2.96292e6i	0.00103868	+	0.00319674i
$976$	−2.52574e8	+	3.47639e8i	−0.271669	+	0.373920i
$977$	−6.63966e8	−	4.82399e8i	−0.711970	−	0.517277i	0.171838	−	0.985125i	$-0.445029\pi$
$977$	−6.63966e8	−	4.82399e8i	−0.711970	−	0.517277i	−0.883809	+	0.467848i	$0.845029\pi$
$978$	3.02420e6	−	982623.i	0.00323292	−	0.00105044i
$979$	4.66749e8	+	3.39113e8i	0.497434	+	0.361407i
$980$	−1.70071e8	+	1.23564e8i	−0.180698	+	0.131285i
$981$	6.39696e7	−	1.96878e8i	0.0677589	−	0.208540i
$982$	1.06462e8	+	1.46532e8i	0.112424	+	0.154738i
$983$	−5.20515e8	+	1.69126e8i	−0.547990	+	0.178053i	−0.569910	−	0.821707i	$-0.693022\pi$
$983$	−5.20515e8	+	1.69126e8i	−0.547990	+	0.178053i	0.0219200	+	0.999760i	$0.493022\pi$
$984$	2.05045e7	−	6.66231e6i	0.0215211	−	0.00699261i
$985$	8.51238e8	+	2.76584e8i	0.890722	+	0.289413i
$986$	7.77227e8			0.810806
$987$		−	5.03480e6i		−	0.00523637i
$988$	−8.06884e8	−	2.62172e8i	−0.836643	−	0.271842i
$989$	−3.18770e7	−	2.31600e7i	−0.0329526	−	0.0239414i
$990$	−5.42692e8	−	7.46951e8i	−0.559304	−	0.769816i
$991$		−	1.81193e8i		−	0.186175i	−0.995658	−	0.0930875i	$-0.970326\pi$
$991$		−	1.81193e8i		−	0.186175i	0.995658	−	0.0930875i	$-0.0296736\pi$
$992$	1.09864e7	−	1.72218e8i	0.0112544	−	0.176418i
$993$	−2.54037e7			−0.0259447
$994$	4.74830e8	−	3.44984e8i	0.483480	−	0.351269i
$995$	−6.06797e8	+	8.35185e8i	−0.615991	+	0.847839i
$996$	9.43160e6	−	2.90275e7i	0.00954569	−	0.0293786i
$997$	−1.48857e9			−1.50205			−0.751024	−	0.660275i	$-0.770440\pi$
$997$	−1.48857e9			−1.50205			−0.751024	+	0.660275i	$0.770440\pi$
$998$			1.08694e9i			1.09348i
$999$	3.32437e7	−	1.02313e8i	0.0333436	−	0.102621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.15.13	✓	64
31.29	odd	10	inner	62.7.f.a.29.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.15.13	✓	64	1.1	even	1	trivial
62.7.f.a.29.13	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} +(0.519266 - 0.714708i) q^{3} +(9.88854 - 30.4338i) q^{4} -131.510 q^{5} -4.99742i q^{6} +(-80.4012 + 247.449i) q^{7} +(-55.9381 - 172.160i) q^{8} +(225.032 + 692.578i) q^{9} +(-601.854 + 437.272i) q^{10} +(1620.86 + 526.649i) q^{11} +(-16.6165 - 22.8707i) q^{12} +(-1241.32 + 1708.54i) q^{13} +(454.818 + 1399.79i) q^{14} +(-68.2886 + 93.9911i) q^{15} +(-828.433 - 601.892i) q^{16} +(5956.07 - 1935.24i) q^{17} +(3332.69 + 2421.34i) q^{18} +(-10156.5 + 7379.16i) q^{19} +(-1300.44 + 4002.35i) q^{20} +(135.105 + 185.955i) q^{21} +(9168.97 - 2979.18i) q^{22} +(-996.325 + 323.726i) q^{23} +(-152.091 - 49.4172i) q^{24} +1669.85 q^{25} +11946.5i q^{26} +(1224.34 + 397.812i) q^{27} +(6735.78 + 4893.83i) q^{28} +(12895.5 + 17749.1i) q^{29} +657.210i q^{30} +(-1896.62 + 29730.6i) q^{31} -5792.62 q^{32} +(1218.06 - 884.970i) q^{33} +(20823.2 - 28660.7i) q^{34} +(10573.6 - 32542.1i) q^{35} +23303.0 q^{36} -83566.2i q^{37} +(-21945.5 + 67541.3i) q^{38} +(576.527 + 1774.37i) q^{39} +(7356.41 + 22640.7i) q^{40} +(-109070. + 79243.8i) q^{41} +(1236.61 + 401.799i) q^{42} +(22107.7 + 30428.7i) q^{43} +(32055.9 - 44121.1i) q^{44} +(-29594.0 - 91080.8i) q^{45} +(-3483.28 + 4794.32i) q^{46} +(-17721.0 - 12875.1i) q^{47} +(-860.354 + 279.546i) q^{48} +(40413.1 + 29361.9i) q^{49} +(7642.04 - 5552.27i) q^{50} +(1709.65 - 5261.76i) q^{51} +(39722.4 + 54673.2i) q^{52} +(-43773.3 + 14222.8i) q^{53} +(6925.92 - 2250.37i) q^{54} +(-213159. - 69259.6i) q^{55} +47098.3 q^{56} +11090.7i q^{57} +(118032. + 38351.0i) q^{58} +(-199967. - 145284. i) q^{59} +(2185.23 + 3007.72i) q^{60} -419634. i q^{61} +(90174.7 + 142368. i) q^{62} -189471. q^{63} +(-26509.9 + 19260.5i) q^{64} +(163246. - 224689. i) q^{65} +(2631.89 - 8100.12i) q^{66} +78380.7 q^{67} -200403. i q^{68} +(-285.988 + 880.181i) q^{69} +(-59813.0 - 184086. i) q^{70} +(-123227. - 379255. i) q^{71} +(106646. - 77482.9i) q^{72} +(407779. + 132495. i) q^{73} +(-277859. - 382440. i) q^{74} +(867.094 - 1193.45i) q^{75} +(124143. + 382071. i) q^{76} +(-260638. + 358738. i) q^{77} +(8538.28 + 6203.42i) q^{78} +(517310. - 168084. i) q^{79} +(108947. + 79154.8i) q^{80} +(-428564. + 311370. i) q^{81} +(-235670. + 725317. i) q^{82} +(634601. + 873453. i) q^{83} +(6995.32 - 2272.92i) q^{84} +(-783282. + 254504. i) q^{85} +(202352. + 65748.1i) q^{86} +19381.6 q^{87} -308506. i q^{88} +(321953. + 104609. i) q^{89} +(-438282. - 318430. i) q^{90} +(-322972. - 444533. i) q^{91} +33523.1i q^{92} +(20263.8 + 16793.6i) q^{93} -123910. q^{94} +(1.33569e6 - 970432. i) q^{95} +(-3007.91 + 4140.03i) q^{96} +(-433583. + 1.33443e6i) q^{97} +282579. q^{98} +1.24108e6i 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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