LMFDB - Embedded newform 210.8.i.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,8,Mod(121,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("210.121");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	210.i (of order $3$, 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:	$65.6008553517$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5593x^{2} + 5592x + 31270464 $ x^4 - x^3 + 5593x^2 + 5592x + 31270464
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$-37.1407 + 64.3295i$ of defining polynomial
Character	$\chi$	$=$	210.151
Dual form			210.8.i.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(62.5000 + 108.253i) q^{5} +216.000 q^{6} +(-804.454 - 419.996i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})$	\(q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(62.5000 + 108.253i) q^{5} +216.000 q^{6} +(-804.454 - 419.996i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(500.000 - 866.025i) q^{10} +(-1248.71 + 2162.82i) q^{11} +(-864.000 - 1496.49i) q^{12} +6889.83 q^{13} +(308.000 + 7253.41i) q^{14} -3375.00 q^{15} +(-2048.00 - 3547.24i) q^{16} +(1956.85 - 3389.37i) q^{17} +(-2916.00 + 5050.66i) q^{18} +(-21717.2 - 37615.2i) q^{19} -8000.00 q^{20} +(20680.8 - 13140.4i) q^{21} +19979.3 q^{22} +(17705.2 + 30666.3i) q^{23} +(-6912.00 + 11971.9i) q^{24} +(-7812.50 + 13531.6i) q^{25} +(-27559.3 - 47734.1i) q^{26} +19683.0 q^{27} +(49021.1 - 31147.5i) q^{28} +165644. q^{29} +(13500.0 + 23382.7i) q^{30} +(96362.4 - 166905. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-33715.1 - 58396.2i) q^{33} -31309.7 q^{34} +(-4812.50 - 113334. i) q^{35} +46656.0 q^{36} +(-46542.1 - 80613.3i) q^{37} +(-173737. + 300922. i) q^{38} +(-93012.7 + 161103. i) q^{39} +(32000.0 + 55425.6i) q^{40} -318203. q^{41} +(-173762. - 90719.1i) q^{42} -216188. q^{43} +(-79917.2 - 138421. i) q^{44} +(45562.5 - 78916.6i) q^{45} +(141642. - 245331. i) q^{46} +(-497242. - 861249. i) q^{47} +110592. q^{48} +(470750. + 675735. i) q^{49} +125000. q^{50} +(52835.0 + 91513.0i) q^{51} +(-220474. + 381873. i) q^{52} +(-687312. + 1.19046e6i) q^{53} +(-78732.0 - 136368. i) q^{54} -312177. q^{55} +(-411881. - 215038. i) q^{56} +1.17273e6 q^{57} +(-662578. - 1.14762e6i) q^{58} +(-907332. + 1.57155e6i) q^{59} +(108000. - 187061. i) q^{60} +(1.15535e6 + 2.00113e6i) q^{61} -1.54180e6 q^{62} +(28066.5 + 660967. i) q^{63} +262144. q^{64} +(430614. + 745846. i) q^{65} +(-269721. + 467170. i) q^{66} +(854623. - 1.48025e6i) q^{67} +(125239. + 216920. i) q^{68} -956081. q^{69} +(-765954. + 486680. i) q^{70} -1.24555e6 q^{71} +(-186624. - 323242. i) q^{72} +(-2.05615e6 + 3.56136e6i) q^{73} +(-372337. + 644907. i) q^{74} +(-210938. - 365354. i) q^{75} +2.77980e6 q^{76} +(1.91290e6 - 1.21544e6i) q^{77} +1.48820e6 q^{78} +(2.30583e6 + 3.99382e6i) q^{79} +(256000. - 443405. i) q^{80} +(-265720. + 460241. i) q^{81} +(1.27281e6 + 2.20458e6i) q^{82} +8.47496e6 q^{83} +(66528.0 + 1.56674e6i) q^{84} +489213. q^{85} +(864751. + 1.49779e6i) q^{86} +(-2.23620e6 + 3.87321e6i) q^{87} +(-639338. + 1.10737e6i) q^{88} +(2.76891e6 + 4.79589e6i) q^{89} -729000. q^{90} +(-5.54255e6 - 2.89370e6i) q^{91} -2.26627e6 q^{92} +(2.60179e6 + 4.50643e6i) q^{93} +(-3.97794e6 + 6.88999e6i) q^{94} +(2.71465e6 - 4.70191e6i) q^{95} +(-442368. - 766204. i) q^{96} +884161. q^{97} +(2.79863e6 - 5.96439e6i) q^{98} +1.82061e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 250 q^{5} + 864 q^{6} - 77 q^{7} + 2048 q^{8} - 1458 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 - 54 * q^3 - 128 * q^4 + 250 * q^5 + 864 * q^6 - 77 * q^7 + 2048 * q^8 - 1458 * q^9	\( 4 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 250 q^{5} + 864 q^{6} - 77 q^{7} + 2048 q^{8} - 1458 q^{9} + 2000 q^{10} + 5325 q^{11} - 3456 q^{12} - 13720 q^{13} + 1232 q^{14} - 13500 q^{15} - 8192 q^{16} - 21786 q^{17} - 11664 q^{18} - 44692 q^{19} - 32000 q^{20} - 2079 q^{21} - 85200 q^{22} + 46143 q^{23} - 27648 q^{24} - 31250 q^{25} + 54880 q^{26} + 78732 q^{27} - 4928 q^{28} + 481308 q^{29} + 54000 q^{30} + 341927 q^{31} - 65536 q^{32} + 143775 q^{33} + 348576 q^{34} - 19250 q^{35} + 186624 q^{36} - 258856 q^{37} - 357536 q^{38} + 185220 q^{39} + 128000 q^{40} - 641958 q^{41} - 16632 q^{42} - 1980190 q^{43} + 340800 q^{44} + 182250 q^{45} + 369144 q^{46} - 1722897 q^{47} + 442368 q^{48} + 1641157 q^{49} + 500000 q^{50} - 588222 q^{51} + 439040 q^{52} - 2994681 q^{53} - 314928 q^{54} + 1331250 q^{55} - 39424 q^{56} + 2413368 q^{57} - 1925232 q^{58} + 858450 q^{59} + 432000 q^{60} + 3920558 q^{61} - 5470832 q^{62} + 112266 q^{63} + 1048576 q^{64} - 857500 q^{65} + 1150200 q^{66} + 4109921 q^{67} - 1394304 q^{68} - 2491722 q^{69} + 77000 q^{70} - 12572220 q^{71} - 746496 q^{72} - 4115065 q^{73} - 2070848 q^{74} - 843750 q^{75} + 5720576 q^{76} + 16411353 q^{77} - 2963520 q^{78} + 1753115 q^{79} + 1024000 q^{80} - 1062882 q^{81} + 2567832 q^{82} + 31085664 q^{83} + 266112 q^{84} - 5446500 q^{85} + 7920760 q^{86} - 6497658 q^{87} + 2726400 q^{88} + 5883408 q^{89} - 2916000 q^{90} - 32148571 q^{91} - 5906304 q^{92} + 9232029 q^{93} - 13783176 q^{94} + 5586500 q^{95} - 1769472 q^{96} - 21519892 q^{97} + 13129256 q^{98} - 7763850 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 54 * q^3 - 128 * q^4 + 250 * q^5 + 864 * q^6 - 77 * q^7 + 2048 * q^8 - 1458 * q^9 + 2000 * q^10 + 5325 * q^11 - 3456 * q^12 - 13720 * q^13 + 1232 * q^14 - 13500 * q^15 - 8192 * q^16 - 21786 * q^17 - 11664 * q^18 - 44692 * q^19 - 32000 * q^20 - 2079 * q^21 - 85200 * q^22 + 46143 * q^23 - 27648 * q^24 - 31250 * q^25 + 54880 * q^26 + 78732 * q^27 - 4928 * q^28 + 481308 * q^29 + 54000 * q^30 + 341927 * q^31 - 65536 * q^32 + 143775 * q^33 + 348576 * q^34 - 19250 * q^35 + 186624 * q^36 - 258856 * q^37 - 357536 * q^38 + 185220 * q^39 + 128000 * q^40 - 641958 * q^41 - 16632 * q^42 - 1980190 * q^43 + 340800 * q^44 + 182250 * q^45 + 369144 * q^46 - 1722897 * q^47 + 442368 * q^48 + 1641157 * q^49 + 500000 * q^50 - 588222 * q^51 + 439040 * q^52 - 2994681 * q^53 - 314928 * q^54 + 1331250 * q^55 - 39424 * q^56 + 2413368 * q^57 - 1925232 * q^58 + 858450 * q^59 + 432000 * q^60 + 3920558 * q^61 - 5470832 * q^62 + 112266 * q^63 + 1048576 * q^64 - 857500 * q^65 + 1150200 * q^66 + 4109921 * q^67 - 1394304 * q^68 - 2491722 * q^69 + 77000 * q^70 - 12572220 * q^71 - 746496 * q^72 - 4115065 * q^73 - 2070848 * q^74 - 843750 * q^75 + 5720576 * q^76 + 16411353 * q^77 - 2963520 * q^78 + 1753115 * q^79 + 1024000 * q^80 - 1062882 * q^81 + 2567832 * q^82 + 31085664 * q^83 + 266112 * q^84 - 5446500 * q^85 + 7920760 * q^86 - 6497658 * q^87 + 2726400 * q^88 + 5883408 * q^89 - 2916000 * q^90 - 32148571 * q^91 - 5906304 * q^92 + 9232029 * q^93 - 13783176 * q^94 + 5586500 * q^95 - 1769472 * q^96 - 21519892 * q^97 + 13129256 * q^98 - 7763850 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	62.5000	+	108.253i	0.223607	+	0.387298i
$5$	62.5000	+	108.253i	0.223607	+	0.387298i
$6$	216.000			0.408248
$7$	−804.454	−	419.996i	−0.886458	−	0.462809i
$7$	−804.454	−	419.996i	−0.886458	−	0.462809i
$8$	512.000			0.353553
$9$	−364.500	−	631.333i	−0.166667	−	0.288675i
$10$	500.000	−	866.025i	0.158114	−	0.273861i
$11$	−1248.71	+	2162.82i	−0.282869	+	0.489944i	−0.972090	−	0.234607i	$-0.924620\pi$
$11$	−1248.71	+	2162.82i	−0.282869	+	0.489944i	0.689221	+	0.724551i	$0.257953\pi$
$12$	−864.000	−	1496.49i	−0.144338	−	0.250000i
$13$	6889.83			0.869774			0.434887	−	0.900485i	$-0.356788\pi$
$13$	6889.83			0.869774			0.434887	+	0.900485i	$0.356788\pi$
$14$	308.000	+	7253.41i	0.0299987	+	0.706470i
$15$	−3375.00			−0.258199
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	1956.85	−	3389.37i	0.0966022	−	0.167320i	−0.813674	−	0.581322i	$-0.802536\pi$
$17$	1956.85	−	3389.37i	0.0966022	−	0.167320i	0.910276	+	0.414002i	$0.135869\pi$
$18$	−2916.00	+	5050.66i	−0.117851	+	0.204124i
$19$	−21717.2	−	37615.2i	−0.726383	−	1.25813i	−0.958402	−	0.285421i	$-0.907867\pi$
$19$	−21717.2	−	37615.2i	−0.726383	−	1.25813i	0.232019	−	0.972711i	$-0.425467\pi$
$20$	−8000.00			−0.223607
$21$	20680.8	−	13140.4i	0.487303	−	0.309628i
$22$	19979.3			0.400038
$23$	17705.2	+	30666.3i	0.303427	+	0.525550i	0.976910	−	0.213652i	$-0.0685359\pi$
$23$	17705.2	+	30666.3i	0.303427	+	0.525550i	−0.673483	+	0.739203i	$0.735203\pi$
$24$	−6912.00	+	11971.9i	−0.102062	+	0.176777i
$25$	−7812.50	+	13531.6i	−0.100000	+	0.173205i
$26$	−27559.3	−	47734.1i	−0.307512	−	0.532626i
$27$	19683.0			0.192450
$28$	49021.1	−	31147.5i	0.422017	−	0.268145i
$29$	165644.			1.26120			0.630600	−	0.776108i	$-0.282809\pi$
$29$	165644.			1.26120			0.630600	+	0.776108i	$0.282809\pi$
$30$	13500.0	+	23382.7i	0.0912871	+	0.158114i
$31$	96362.4	−	166905.i	0.580954	−	1.00624i	−0.414412	−	0.910089i	$-0.636013\pi$
$31$	96362.4	−	166905.i	0.580954	−	1.00624i	0.995367	−	0.0961529i	$-0.0306538\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$	−33715.1	−	58396.2i	−0.163315	−	0.282869i
$34$	−31309.7			−0.136616
$35$	−4812.50	−	113334.i	−0.0189729	−	0.446811i
$36$	46656.0			0.166667
$37$	−46542.1	−	80613.3i	−0.151057	−	0.261638i	0.780559	−	0.625082i	$-0.214934\pi$
$37$	−46542.1	−	80613.3i	−0.151057	−	0.261638i	−0.931616	+	0.363444i	$0.881601\pi$
$38$	−173737.	+	300922.i	−0.513630	+	0.889634i
$39$	−93012.7	+	161103.i	−0.251082	+	0.434887i
$40$	32000.0	+	55425.6i	0.0790569	+	0.136931i
$41$	−318203.			−0.721043			−0.360522	−	0.932751i	$-0.617401\pi$
$41$	−318203.			−0.721043			−0.360522	+	0.932751i	$0.617401\pi$
$42$	−173762.	−	90719.1i	−0.361895	−	0.188941i
$43$	−216188.			−0.414660			−0.207330	−	0.978271i	$-0.566477\pi$
$43$	−216188.			−0.414660			−0.207330	+	0.978271i	$0.566477\pi$
$44$	−79917.2	−	138421.i	−0.141435	−	0.244972i
$45$	45562.5	−	78916.6i	0.0745356	−	0.129099i
$46$	141642.	−	245331.i	0.214555	−	0.371620i
$47$	−497242.	−	861249.i	−0.698595	−	1.21000i	−0.968954	−	0.247242i	$-0.920476\pi$
$47$	−497242.	−	861249.i	−0.698595	−	1.21000i	0.270359	−	0.962760i	$-0.412858\pi$
$48$	110592.			0.144338
$49$	470750.	+	675735.i	0.571616	+	0.820522i
$50$	125000.			0.141421
$51$	52835.0	+	91513.0i	0.0557733	+	0.0966022i
$52$	−220474.	+	381873.i	−0.217444	+	0.376623i
$53$	−687312.	+	1.19046e6i	−0.634145	+	1.09837i	0.352551	+	0.935793i	$0.385314\pi$
$53$	−687312.	+	1.19046e6i	−0.634145	+	1.09837i	−0.986696	+	0.162578i	$0.948019\pi$
$54$	−78732.0	−	136368.i	−0.0680414	−	0.117851i
$55$	−312177.			−0.253006
$56$	−411881.	−	215038.i	−0.313410	−	0.163628i
$57$	1.17273e6			0.838755
$58$	−662578.	−	1.14762e6i	−0.445902	−	0.772324i
$59$	−907332.	+	1.57155e6i	−0.575154	+	0.996196i	0.420871	+	0.907121i	$0.361725\pi$
$59$	−907332.	+	1.57155e6i	−0.575154	+	0.996196i	−0.996025	+	0.0890755i	$0.971609\pi$
$60$	108000.	−	187061.i	0.0645497	−	0.111803i
$61$	1.15535e6	+	2.00113e6i	0.651718	+	1.12881i	0.982706	+	0.185174i	$0.0592849\pi$
$61$	1.15535e6	+	2.00113e6i	0.651718	+	1.12881i	−0.330987	+	0.943635i	$0.607382\pi$
$62$	−1.54180e6			−0.821593
$63$	28066.5	+	660967.i	0.0141415	+	0.333033i
$64$	262144.			0.125000
$65$	430614.	+	745846.i	0.194487	+	0.336862i
$66$	−269721.	+	467170.i	−0.115481	+	0.200019i
$67$	854623.	−	1.48025e6i	0.347147	−	0.601275i	−0.638595	−	0.769543i	$-0.720484\pi$
$67$	854623.	−	1.48025e6i	0.347147	−	0.601275i	0.985741	+	0.168268i	$0.0538173\pi$
$68$	125239.	+	216920.i	0.0483011	+	0.0836600i
$69$	−956081.			−0.350367
$70$	−765954.	+	486680.i	−0.266907	+	0.169590i
$71$	−1.24555e6			−0.413008			−0.206504	−	0.978446i	$-0.566209\pi$
$71$	−1.24555e6			−0.413008			−0.206504	+	0.978446i	$0.566209\pi$
$72$	−186624.	−	323242.i	−0.0589256	−	0.102062i
$73$	−2.05615e6	+	3.56136e6i	−0.618621	+	1.07148i	0.371116	+	0.928586i	$0.378975\pi$
$73$	−2.05615e6	+	3.56136e6i	−0.618621	+	1.07148i	−0.989738	+	0.142897i	$0.954358\pi$
$74$	−372337.	+	644907.i	−0.106813	+	0.185006i
$75$	−210938.	−	365354.i	−0.0577350	−	0.100000i
$76$	2.77980e6			0.726383
$77$	1.91290e6	−	1.21544e6i	0.477502	−	0.303400i
$78$	1.48820e6			0.355084
$79$	2.30583e6	+	3.99382e6i	0.526178	+	0.911367i	0.999535	+	0.0304962i	$0.00970874\pi$
$79$	2.30583e6	+	3.99382e6i	0.526178	+	0.911367i	−0.473357	+	0.880871i	$0.656958\pi$
$80$	256000.	−	443405.i	0.0559017	−	0.0968246i
$81$	−265720.	+	460241.i	−0.0555556	+	0.0962250i
$82$	1.27281e6	+	2.20458e6i	0.254927	+	0.441547i
$83$	8.47496e6			1.62691			0.813456	−	0.581626i	$-0.197583\pi$
$83$	8.47496e6			1.62691			0.813456	+	0.581626i	$0.197583\pi$
$84$	66528.0	+	1.56674e6i	0.0122469	+	0.288415i
$85$	489213.			0.0864036
$86$	864751.	+	1.49779e6i	0.146604	+	0.253926i
$87$	−2.23620e6	+	3.87321e6i	−0.364077	+	0.630600i
$88$	−639338.	+	1.10737e6i	−0.100009	+	0.173221i
$89$	2.76891e6	+	4.79589e6i	0.416335	+	0.721114i	0.995568	−	0.0940486i	$-0.0299809\pi$
$89$	2.76891e6	+	4.79589e6i	0.416335	+	0.721114i	−0.579232	+	0.815163i	$0.696648\pi$
$90$	−729000.			−0.105409
$91$	−5.54255e6	−	2.89370e6i	−0.771018	−	0.402539i
$92$	−2.26627e6			−0.303427
$93$	2.60179e6	+	4.50643e6i	0.335414	+	0.580954i
$94$	−3.97794e6	+	6.88999e6i	−0.493981	+	0.855601i
$95$	2.71465e6	−	4.70191e6i	0.324848	−	0.562654i
$96$	−442368.	−	766204.i	−0.0510310	−	0.0883883i
$97$	884161.			0.0983627			0.0491814	−	0.998790i	$-0.484339\pi$
$97$	884161.			0.0983627			0.0491814	+	0.998790i	$0.484339\pi$
$98$	2.79863e6	−	5.96439e6i	0.300368	−	0.640140i
$99$	1.82061e6			0.188580
$100$	−500000.	−	866025.i	−0.0500000	−	0.0866025i
$101$	2.22033e6	−	3.84572e6i	0.214434	−	0.371410i	−0.738664	−	0.674074i	$-0.764543\pi$
$101$	2.22033e6	−	3.84572e6i	0.214434	−	0.371410i	0.953097	+	0.302664i	$0.0978761\pi$
$102$	422680.	−	732104.i	0.0394377	−	0.0683081i
$103$	−1.99433e6	−	3.45429e6i	−0.179832	−	0.311478i	0.761991	−	0.647588i	$-0.224222\pi$
$103$	−1.99433e6	−	3.45429e6i	−0.179832	−	0.311478i	−0.941823	+	0.336109i	$0.890889\pi$
$104$	3.52759e6			0.307512
$105$	2.71503e6	+	1.41749e6i	0.228882	+	0.119497i
$106$	1.09970e7			0.896816
$107$	5.51236e6	+	9.54768e6i	0.435005	+	0.753450i	0.997296	−	0.0734889i	$-0.0234134\pi$
$107$	5.51236e6	+	9.54768e6i	0.435005	+	0.753450i	−0.562291	+	0.826939i	$0.690080\pi$
$108$	−629856.	+	1.09094e6i	−0.0481125	+	0.0833333i
$109$	−6.38569e6	+	1.10603e7i	−0.472297	+	0.818042i	−0.999497	−	0.0316990i	$-0.989908\pi$
$109$	−6.38569e6	+	1.10603e7i	−0.472297	+	0.818042i	0.527201	+	0.849741i	$0.323242\pi$
$110$	1.24871e6	+	2.16282e6i	0.0894512	+	0.154934i
$111$	2.51328e6			0.174425
$112$	157696.	+	3.71374e6i	0.0106061	+	0.249775i
$113$	1.75250e7			1.14257			0.571286	−	0.820751i	$-0.306445\pi$
$113$	1.75250e7			1.14257			0.571286	+	0.820751i	$0.306445\pi$
$114$	−4.69091e6	−	8.12489e6i	−0.296545	−	0.513630i
$115$	−2.21315e6	+	3.83329e6i	−0.135697	+	0.235033i
$116$	−5.30062e6	+	9.18095e6i	−0.315300	+	0.546116i
$117$	−2.51134e6	−	4.34977e6i	−0.144962	−	0.251082i
$118$	1.45173e7			0.813391
$119$	−2.99772e6	+	1.90472e6i	−0.163071	+	0.103614i
$120$	−1.72800e6			−0.0912871
$121$	6.62505e6	+	1.14749e7i	0.339970	+	0.588845i
$122$	9.24282e6	−	1.60090e7i	0.460834	−	0.798189i
$123$	4.29575e6	−	7.44045e6i	0.208147	−	0.360522i
$124$	6.16720e6	+	1.06819e7i	0.290477	+	0.503121i
$125$	−1.95312e6			−0.0894427
$126$	4.46704e6	−	2.83832e6i	0.198941	−	0.126405i
$127$	−1.87961e7			−0.814243			−0.407122	−	0.913374i	$-0.633467\pi$
$127$	−1.87961e7			−0.814243			−0.407122	+	0.913374i	$0.633467\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$	2.91854e6	−	5.05505e6i	0.119702	−	0.207330i
$130$	3.44491e6	−	5.96676e6i	0.137523	−	0.238197i
$131$	2.09798e7	+	3.63381e7i	0.815366	+	1.41226i	0.909065	+	0.416655i	$0.136798\pi$
$131$	2.09798e7	+	3.63381e7i	0.815366	+	1.41226i	−0.0936988	+	0.995601i	$0.529869\pi$
$132$	4.31553e6			0.163315
$133$	1.67222e6	+	3.93809e7i	0.0616330	+	1.45146i
$134$	−1.36740e7			−0.490939
$135$	1.23019e6	+	2.13075e6i	0.0430331	+	0.0745356i
$136$	1.00191e6	−	1.73536e6i	0.0341540	−	0.0591565i
$137$	7.84653e6	−	1.35906e7i	0.260709	−	0.451561i	−0.705722	−	0.708489i	$-0.749377\pi$
$137$	7.84653e6	−	1.35906e7i	0.260709	−	0.451561i	0.966430	+	0.256928i	$0.0827105\pi$
$138$	3.82433e6	+	6.62393e6i	0.123873	+	0.214555i
$139$	4.57791e7			1.44582			0.722912	−	0.690940i	$-0.242803\pi$
$139$	4.57791e7			1.44582			0.722912	+	0.690940i	$0.242803\pi$
$140$	6.43563e6	+	3.35997e6i	0.198218	+	0.103487i
$141$	2.68511e7			0.806668
$142$	4.98221e6	+	8.62944e6i	0.146020	+	0.252914i
$143$	−8.60337e6	+	1.49015e7i	−0.246033	+	0.426141i
$144$	−1.49299e6	+	2.58594e6i	−0.0416667	+	0.0721688i
$145$	1.03528e7	+	1.79315e7i	0.282013	+	0.488461i
$146$	3.28984e7			0.874862
$147$	−2.21556e7	+	1.88498e6i	−0.575272	+	0.0489436i
$148$	5.95739e6			0.151057
$149$	8.63132e6	+	1.49499e7i	0.213759	+	0.370242i	0.952888	−	0.303322i	$-0.0980958\pi$
$149$	8.63132e6	+	1.49499e7i	0.213759	+	0.370242i	−0.739129	+	0.673564i	$0.764762\pi$
$150$	−1.68750e6	+	2.92284e6i	−0.0408248	+	0.0707107i
$151$	−2.21494e7	+	3.83638e7i	−0.523531	+	0.906781i	0.476094	+	0.879394i	$0.342052\pi$
$151$	−2.21494e7	+	3.83638e7i	−0.523531	+	0.906781i	−0.999625	+	0.0273873i	$0.991281\pi$
$152$	−1.11192e7	−	1.92590e7i	−0.256815	−	0.444817i
$153$	−2.85309e6			−0.0644015
$154$	−1.60724e7	−	8.39122e6i	−0.354617	−	0.185141i
$155$	2.40906e7			0.519621
$156$	−5.95281e6	−	1.03106e7i	−0.125541	−	0.217444i
$157$	−3.48279e7	+	6.03236e7i	−0.718254	+	1.24405i	0.243437	+	0.969917i	$0.421725\pi$
$157$	−3.48279e7	+	6.03236e7i	−0.718254	+	1.24405i	−0.961691	+	0.274136i	$0.911608\pi$
$158$	1.84466e7	−	3.19505e7i	0.372064	−	0.644434i
$159$	−1.85574e7	−	3.21424e7i	−0.366124	−	0.634145i
$160$	−4.09600e6			−0.0790569
$161$	−1.36330e6	−	3.21058e7i	−0.0257455	−	0.606307i
$162$	4.25153e6			0.0785674
$163$	−1.72197e7	−	2.98253e7i	−0.311436	−	0.539422i	0.667238	−	0.744845i	$-0.267476\pi$
$163$	−1.72197e7	−	2.98253e7i	−0.311436	−	0.539422i	−0.978673	+	0.205423i	$0.934143\pi$
$164$	1.01825e7	−	1.76366e7i	0.180261	−	0.312221i
$165$	4.21438e6	−	7.29953e6i	0.0730366	−	0.126503i
$166$	−3.38998e7	−	5.87162e7i	−0.575201	−	0.996277i
$167$	−8.20344e7			−1.36298			−0.681488	−	0.731829i	$-0.738667\pi$
$167$	−8.20344e7			−1.36298			−0.681488	+	0.731829i	$0.738667\pi$
$168$	1.05886e7	−	6.72786e6i	0.172288	−	0.109470i
$169$	−1.52788e7			−0.243493
$170$	−1.95685e6	−	3.38937e6i	−0.0305483	−	0.0529112i
$171$	−1.58318e7	+	2.74215e7i	−0.242128	+	0.419377i
$172$	6.91801e6	−	1.19823e7i	0.103665	−	0.179553i
$173$	3.64959e7	+	6.32127e7i	0.535899	+	0.928204i	0.999119	+	0.0419606i	$0.0133604\pi$
$173$	3.64959e7	+	6.32127e7i	0.535899	+	0.928204i	−0.463221	+	0.886243i	$0.653306\pi$
$174$	3.57792e7			0.514883
$175$	1.19680e7	−	7.60437e6i	0.168807	−	0.107258i
$176$	1.02294e7			0.141435
$177$	−2.44980e7	−	4.24317e7i	−0.332065	−	0.575154i
$178$	2.21513e7	−	3.83671e7i	0.294394	−	0.509905i
$179$	−2.89204e7	+	5.00916e7i	−0.376894	+	0.652799i	−0.990609	−	0.136729i	$-0.956341\pi$
$179$	−2.89204e7	+	5.00916e7i	−0.376894	+	0.652799i	0.613715	+	0.789528i	$0.289674\pi$
$180$	2.91600e6	+	5.05066e6i	0.0372678	+	0.0645497i
$181$	−1.14259e8			−1.43224			−0.716118	−	0.697979i	$-0.754083\pi$
$181$	−1.14259e8			−1.43224			−0.716118	+	0.697979i	$0.754083\pi$
$182$	2.12207e6	+	4.99747e7i	0.0260921	+	0.614470i
$183$	−6.23890e7			−0.752540
$184$	9.06507e6	+	1.57012e7i	0.107278	+	0.185810i
$185$	5.81777e6	−	1.00767e7i	0.0675546	−	0.117008i
$186$	2.08143e7	−	3.60514e7i	0.237174	−	0.410797i
$187$	4.88707e6	+	8.46466e6i	0.0546516	+	0.0946594i
$188$	6.36470e7			0.698595
$189$	−1.58341e7	−	8.26678e6i	−0.170599	−	0.0890676i
$190$	−4.34343e7			−0.459405
$191$	−3.10268e7	−	5.37399e7i	−0.322196	−	0.558059i	0.658745	−	0.752366i	$-0.271088\pi$
$191$	−3.10268e7	−	5.37399e7i	−0.322196	−	0.558059i	−0.980941	+	0.194307i	$0.937754\pi$
$192$	−3.53894e6	+	6.12963e6i	−0.0360844	+	0.0625000i
$193$	−2.15489e6	+	3.73238e6i	−0.0215762	+	0.0373711i	−0.876612	−	0.481198i	$-0.840202\pi$
$193$	−2.15489e6	+	3.73238e6i	−0.0215762	+	0.0373711i	0.855036	+	0.518569i	$0.173535\pi$
$194$	−3.53665e6	−	6.12565e6i	−0.0347765	−	0.0602346i
$195$	−2.32532e7			−0.224575
$196$	−5.25170e7	+	4.46810e6i	−0.498200	+	0.0423864i
$197$	6.03060e7			0.561990			0.280995	−	0.959709i	$-0.409336\pi$
$197$	6.03060e7			0.561990			0.280995	+	0.959709i	$0.409336\pi$
$198$	−7.28246e6	−	1.26136e7i	−0.0666730	−	0.115481i
$199$	−7.98002e7	+	1.38218e8i	−0.717825	+	1.24331i	0.244035	+	0.969766i	$0.421529\pi$
$199$	−7.98002e7	+	1.38218e8i	−0.717825	+	1.24331i	−0.961860	+	0.273542i	$0.911805\pi$
$200$	−4.00000e6	+	6.92820e6i	−0.0353553	+	0.0612372i
$201$	2.30748e7	+	3.99668e7i	0.200425	+	0.347147i
$202$	−3.55253e7			−0.303255
$203$	−1.33253e8	−	6.95700e7i	−1.11800	−	0.583695i
$204$	−6.76289e6			−0.0557733
$205$	−1.98877e7	−	3.44465e7i	−0.161230	−	0.279259i
$206$	−1.59547e7	+	2.76343e7i	−0.127161	+	0.220249i
$207$	1.29071e7	−	2.23558e7i	0.101142	−	0.175183i
$208$	−1.41104e7	−	2.44399e7i	−0.108722	−	0.188312i
$209$	1.08473e8			0.821886
$210$	−1.03950e6	−	2.44802e7i	−0.00774563	−	0.182410i
$211$	−1.25755e8			−0.921584			−0.460792	−	0.887508i	$-0.652435\pi$
$211$	−1.25755e8			−0.921584			−0.460792	+	0.887508i	$0.652435\pi$
$212$	−4.39880e7	−	7.61894e7i	−0.317072	−	0.549186i
$213$	1.68150e7	−	2.91244e7i	0.119225	−	0.206504i
$214$	4.40988e7	−	7.63814e7i	0.307595	−	0.532770i
$215$	−1.35117e7	−	2.34030e7i	−0.0927207	−	0.160597i
$216$	1.00777e7			0.0680414
$217$	−1.47618e8	+	9.37953e7i	−0.980689	+	0.623120i
$218$	1.02171e8			0.667928
$219$	−5.55160e7	−	9.61566e7i	−0.357161	−	0.618621i
$220$	9.98965e6	−	1.73026e7i	0.0632515	−	0.109555i
$221$	1.34824e7	−	2.33522e7i	0.0840221	−	0.145531i
$222$	−1.00531e7	−	1.74125e7i	−0.0616687	−	0.106813i
$223$	2.16513e8			1.30743			0.653714	−	0.756742i	$-0.273210\pi$
$223$	2.16513e8			1.30743			0.653714	+	0.756742i	$0.273210\pi$
$224$	2.50988e7	−	1.59475e7i	0.149205	−	0.0948037i
$225$	1.13906e7			0.0666667
$226$	−7.01000e7	−	1.21417e8i	−0.403960	−	0.699679i
$227$	9.36602e7	−	1.62224e8i	0.531452	−	0.920503i	−0.467874	−	0.883795i	$-0.654980\pi$
$227$	9.36602e7	−	1.62224e8i	0.531452	−	0.920503i	0.999326	−	0.0367073i	$-0.0116869\pi$
$228$	−3.75273e7	+	6.49991e7i	−0.209689	+	0.363191i
$229$	−5.75986e7	−	9.97637e7i	−0.316948	−	0.548970i	0.662902	−	0.748706i	$-0.269325\pi$
$229$	−5.75986e7	−	9.97637e7i	−0.316948	−	0.548970i	−0.979850	+	0.199737i	$0.935991\pi$
$230$	3.54104e7			0.191904
$231$	2.59606e6	+	6.11373e7i	0.0138571	+	0.326335i
$232$	8.48100e7			0.445902
$233$	3.07487e7	+	5.32583e7i	0.159250	+	0.275830i	0.934599	−	0.355704i	$-0.115759\pi$
$233$	3.07487e7	+	5.32583e7i	0.159250	+	0.275830i	−0.775348	+	0.631534i	$0.782426\pi$
$234$	−2.00907e7	+	3.47982e7i	−0.102504	+	0.177542i
$235$	6.21553e7	−	1.07656e8i	0.312421	−	0.541129i
$236$	−5.80693e7	−	1.00579e8i	−0.287577	−	0.498098i
$237$	−1.24515e8			−0.607578
$238$	2.51872e7	+	1.31499e7i	0.121104	+	0.0632272i
$239$	2.06640e8			0.979089			0.489544	−	0.871978i	$-0.337163\pi$
$239$	2.06640e8			0.979089			0.489544	+	0.871978i	$0.337163\pi$
$240$	6.91200e6	+	1.19719e7i	0.0322749	+	0.0559017i
$241$	−5.00082e7	+	8.66167e7i	−0.230134	+	0.398604i	−0.957847	−	0.287277i	$-0.907250\pi$
$241$	−5.00082e7	+	8.66167e7i	−0.230134	+	0.398604i	0.727713	+	0.685882i	$0.240583\pi$
$242$	5.30004e7	−	9.17994e7i	0.240395	−	0.416376i
$243$	−7.17445e6	−	1.24265e7i	−0.0320750	−	0.0555556i
$244$	−1.47885e8			−0.651718
$245$	−4.37286e7	+	9.31936e7i	−0.189970	+	0.404860i
$246$	−6.87319e7			−0.294365
$247$	−1.49628e8	−	2.59162e8i	−0.631789	−	1.09429i
$248$	4.93376e7	−	8.54552e7i	0.205398	−	0.355760i
$249$	−1.14412e8	+	1.98167e8i	−0.469649	+	0.813456i
$250$	7.81250e6	+	1.35316e7i	0.0316228	+	0.0547723i
$251$	3.66655e8			1.46352			0.731762	−	0.681561i	$-0.238698\pi$
$251$	3.66655e8			1.46352			0.731762	+	0.681561i	$0.238698\pi$
$252$	−3.75326e7	−	1.95953e7i	−0.147743	−	0.0771348i
$253$	−8.84344e7			−0.343320
$254$	7.51843e7	+	1.30223e8i	0.287878	+	0.498620i
$255$	−6.60438e6	+	1.14391e7i	−0.0249426	+	0.0432018i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−2.40119e8	−	4.15899e8i	−0.882390	−	1.52835i	−0.848676	−	0.528914i	$-0.822600\pi$
$257$	−2.40119e8	−	4.15899e8i	−0.882390	−	1.52835i	−0.0337148	−	0.999431i	$-0.510734\pi$
$258$	−4.66966e7			−0.169284
$259$	3.58374e6	+	8.43972e7i	0.0128170	+	0.301842i
$260$	−5.51186e7			−0.194487
$261$	−6.03774e7	−	1.04577e8i	−0.210200	−	0.364077i
$262$	1.67839e8	−	2.90705e8i	0.576551	−	0.998615i
$263$	3.89974e6	−	6.75455e6i	0.0132188	−	0.0228956i	−0.859340	−	0.511404i	$-0.829126\pi$
$263$	3.89974e6	−	6.75455e6i	0.0132188	−	0.0228956i	0.872559	+	0.488509i	$0.162459\pi$
$264$	−1.72621e7	−	2.98989e7i	−0.0577405	−	0.100009i
$265$	−1.71828e8			−0.567196
$266$	2.66150e8	−	1.69109e8i	0.867042	−	0.550910i
$267$	−1.49521e8			−0.480743
$268$	5.46959e7	+	9.47360e7i	0.173573	+	0.300638i
$269$	−1.46701e8	+	2.54094e8i	−0.459516	+	0.795905i	−0.998935	−	0.0461326i	$-0.985310\pi$
$269$	−1.46701e8	+	2.54094e8i	−0.459516	+	0.795905i	0.539420	+	0.842037i	$0.318644\pi$
$270$	9.84150e6	−	1.70460e7i	0.0304290	−	0.0527046i
$271$	−2.85290e7	−	4.94136e7i	−0.0870751	−	0.150818i	0.819198	−	0.573510i	$-0.194419\pi$
$271$	−2.85290e7	−	4.94136e7i	−0.0870751	−	0.150818i	−0.906274	+	0.422692i	$0.861085\pi$
$272$	−1.60305e7			−0.0483011
$273$	1.42487e8	−	9.05348e7i	0.423844	−	0.269306i
$274$	−1.25544e8			−0.368698
$275$	−1.95110e7	−	3.37941e7i	−0.0565739	−	0.0979888i
$276$	3.05946e7	−	5.29914e7i	0.0875917	−	0.151713i
$277$	6.39770e7	−	1.10811e8i	0.180861	−	0.313260i	−0.761313	−	0.648384i	$-0.775445\pi$
$277$	6.39770e7	−	1.10811e8i	0.180861	−	0.313260i	0.942174	+	0.335124i	$0.108778\pi$
$278$	−1.83117e8	−	3.17167e8i	−0.511176	−	0.885383i
$279$	−1.40496e8			−0.387303
$280$	−2.46400e6	−	5.80272e7i	−0.00670792	−	0.157972i
$281$	−1.10566e8			−0.297269			−0.148634	−	0.988892i	$-0.547488\pi$
$281$	−1.10566e8			−0.297269			−0.148634	+	0.988892i	$0.547488\pi$
$282$	−1.07404e8	−	1.86030e8i	−0.285200	−	0.493981i
$283$	−3.95056e7	+	6.84257e7i	−0.103611	+	0.179460i	−0.913170	−	0.407579i	$-0.866373\pi$
$283$	−3.95056e7	+	6.84257e7i	−0.103611	+	0.179460i	0.809559	+	0.587039i	$0.199706\pi$
$284$	3.98577e7	−	6.90356e7i	0.103252	−	0.178838i
$285$	7.32954e7	+	1.26951e8i	0.187551	+	0.324848i
$286$	1.37654e8			0.347943
$287$	2.55980e8	+	1.33644e8i	0.639174	+	0.333705i
$288$	2.38879e7			0.0589256
$289$	1.97511e8	+	3.42099e8i	0.481336	+	0.833698i
$290$	8.28222e7	−	1.43452e8i	0.199413	−	0.345394i
$291$	−1.19362e7	+	2.06741e7i	−0.0283949	+	0.0491814i
$292$	−1.31594e8	−	2.27927e8i	−0.309311	−	0.535742i
$293$	6.45874e8			1.50007			0.750034	−	0.661399i	$-0.230037\pi$
$293$	6.45874e8			1.50007			0.750034	+	0.661399i	$0.230037\pi$
$294$	1.01682e8	+	1.45959e8i	0.233361	+	0.334977i
$295$	−2.26833e8			−0.514433
$296$	−2.38296e7	−	4.12740e7i	−0.0534066	−	0.0925030i
$297$	−2.45783e7	+	4.25708e7i	−0.0544382	+	0.0942898i
$298$	6.90506e7	−	1.19599e8i	0.151151	−	0.261801i
$299$	1.21986e8	+	2.11286e8i	0.263913	+	0.457110i
$300$	2.70000e7			0.0577350
$301$	1.73913e8	+	9.07980e7i	0.367578	+	0.191908i
$302$	3.54390e8			0.740384
$303$	5.99489e7	+	1.03835e8i	0.123803	+	0.214434i
$304$	−8.89535e7	+	1.54072e8i	−0.181596	+	0.314533i
$305$	−1.44419e8	+	2.50141e8i	−0.291457	+	0.504819i
$306$	1.14124e7	+	1.97668e7i	0.0227694	+	0.0394377i
$307$	9.83921e8			1.94078			0.970389	−	0.241546i	$-0.0776544\pi$
$307$	9.83921e8			1.94078			0.970389	+	0.241546i	$0.0776544\pi$
$308$	6.15363e6	+	1.44918e8i	0.0120006	+	0.282615i
$309$	1.07694e8			0.207652
$310$	−9.63624e7	−	1.66905e8i	−0.183714	−	0.318202i
$311$	−4.47174e6	+	7.74527e6i	−0.00842975	+	0.0146008i	−0.870210	−	0.492682i	$-0.836017\pi$
$311$	−4.47174e6	+	7.74527e6i	−0.00842975	+	0.0146008i	0.861780	+	0.507283i	$0.169350\pi$
$312$	−4.76225e7	+	8.24846e7i	−0.0887710	+	0.153756i
$313$	1.87669e7	+	3.25052e7i	0.0345930	+	0.0599168i	0.882804	−	0.469742i	$-0.155653\pi$
$313$	1.87669e7	+	3.25052e7i	0.0345930	+	0.0599168i	−0.848211	+	0.529659i	$0.822320\pi$
$314$	5.57246e8			1.01576
$315$	−6.97976e7	+	4.43487e7i	−0.125821	+	0.0799455i
$316$	−2.95146e8			−0.526178
$317$	−2.43981e8	−	4.22587e8i	−0.430178	−	0.745090i	0.566711	−	0.823917i	$-0.308216\pi$
$317$	−2.43981e8	−	4.22587e8i	−0.430178	−	0.745090i	−0.996888	+	0.0788272i	$0.974882\pi$
$318$	−1.48459e8	+	2.57139e8i	−0.258889	+	0.448408i
$319$	−2.06841e8	+	3.58260e8i	−0.356755	+	0.617918i
$320$	1.63840e7	+	2.83779e7i	0.0279508	+	0.0484123i
$321$	−2.97667e8			−0.502300
$322$	−2.16982e8	+	1.37868e8i	−0.362183	+	0.230128i
$323$	−1.69989e8			−0.280681
$324$	−1.70061e7	−	2.94555e7i	−0.0277778	−	0.0481125i
$325$	−5.38268e7	+	9.32307e7i	−0.0869774	+	0.150649i
$326$	−1.37757e8	+	2.38603e8i	−0.220218	+	0.381429i
$327$	−1.72414e8	−	2.98629e8i	−0.272681	−	0.472297i
$328$	−1.62920e8			−0.254927
$329$	3.82877e7	+	9.01675e8i	0.0592752	+	1.39593i
$330$	−6.74302e7			−0.103289
$331$	−1.33164e8	−	2.30648e8i	−0.201832	−	0.349583i	0.747287	−	0.664502i	$-0.231356\pi$
$331$	−1.33164e8	−	2.30648e8i	−0.201832	−	0.349583i	−0.949119	+	0.314918i	$0.898023\pi$
$332$	−2.71199e8	+	4.69730e8i	−0.406728	+	0.704474i
$333$	−3.39292e7	+	5.87671e7i	−0.0503523	+	0.0872127i
$334$	3.28138e8	+	5.68351e8i	0.481885	+	0.834649i
$335$	2.13656e8			0.310497
$336$	−8.89662e7	−	4.64482e7i	−0.127949	−	0.0668007i
$337$	−6.07348e8			−0.864437			−0.432218	−	0.901769i	$-0.642269\pi$
$337$	−6.07348e8			−0.864437			−0.432218	+	0.901769i	$0.642269\pi$
$338$	6.11153e7	+	1.05855e8i	0.0860877	+	0.149108i
$339$	−2.36587e8	+	4.09781e8i	−0.329832	+	0.571286i
$340$	−1.56548e7	+	2.71150e7i	−0.0216009	+	0.0374139i
$341$	2.40657e8	+	4.16830e8i	0.328668	+	0.569270i
$342$	2.53309e8			0.342420
$343$	−9.48910e7	−	7.41311e8i	−0.126968	−	0.991907i
$344$	−1.10688e8			−0.146604
$345$	−5.97551e7	−	1.03499e8i	−0.0783444	−	0.135697i
$346$	2.91967e8	−	5.05702e8i	0.378938	−	0.656339i
$347$	2.25113e8	−	3.89908e8i	0.289233	−	0.500967i	−0.684394	−	0.729113i	$-0.739933\pi$
$347$	2.25113e8	−	3.89908e8i	0.289233	−	0.500967i	0.973627	+	0.228146i	$0.0732663\pi$
$348$	−1.43117e8	−	2.47886e8i	−0.182039	−	0.315300i
$349$	−8.84767e7			−0.111414			−0.0557070	−	0.998447i	$-0.517741\pi$
$349$	−8.84767e7			−0.111414			−0.0557070	+	0.998447i	$0.517741\pi$
$350$	−1.00557e8	−	5.24995e7i	−0.125364	−	0.0654511i
$351$	1.35612e8			0.167388
$352$	−4.09176e7	−	7.08714e7i	−0.0500047	−	0.0866107i
$353$	2.71756e8	−	4.70695e8i	0.328827	−	0.569545i	−0.653452	−	0.756968i	$-0.726680\pi$
$353$	2.71756e8	−	4.70695e8i	0.328827	−	0.569545i	0.982279	+	0.187423i	$0.0600134\pi$
$354$	−1.95984e8	+	3.39454e8i	−0.234806	+	0.406695i
$355$	−7.78471e7	−	1.34835e8i	−0.0923513	−	0.159957i
$356$	−3.54420e8			−0.416335
$357$	−4.06830e6	−	9.58085e7i	−0.00473232	−	0.111446i
$358$	4.62727e8			0.533008
$359$	−1.66818e8	−	2.88938e8i	−0.190289	−	0.329590i	0.755057	−	0.655659i	$-0.227609\pi$
$359$	−1.66818e8	−	2.88938e8i	−0.190289	−	0.329590i	−0.945346	+	0.326069i	$0.894276\pi$
$360$	2.33280e7	−	4.04053e7i	0.0263523	−	0.0456435i
$361$	−4.96335e8	+	8.59678e8i	−0.555264	+	0.961746i
$362$	4.57035e8	+	7.91609e8i	0.506372	+	0.877062i
$363$	−3.57753e8			−0.392563
$364$	3.37747e8	−	2.14601e8i	0.367059	−	0.233226i
$365$	−5.14037e8			−0.553312
$366$	2.49556e8	+	4.32244e8i	0.266063	+	0.460834i
$367$	−8.16968e8	+	1.41503e9i	−0.862728	+	1.49429i	0.00655730	+	0.999979i	$0.497913\pi$
$367$	−8.16968e8	+	1.41503e9i	−0.862728	+	1.49429i	−0.869285	+	0.494310i	$0.835421\pi$
$368$	7.25205e7	−	1.25609e8i	0.0758567	−	0.131388i
$369$	1.15985e8	+	2.00892e8i	0.120174	+	0.208147i
$370$	−9.30843e7			−0.0955367
$371$	1.05290e9	−	6.69002e8i	1.07048	−	0.680172i
$372$	−3.33029e8			−0.335414
$373$	−6.28249e8	−	1.08816e9i	−0.626831	−	1.08570i	−0.988184	−	0.153274i	$-0.951018\pi$
$373$	−6.28249e8	−	1.08816e9i	−0.626831	−	1.08570i	0.361352	−	0.932429i	$-0.382315\pi$
$374$	3.90966e7	−	6.77172e7i	0.0386445	−	0.0669343i
$375$	2.63672e7	−	4.56693e7i	0.0258199	−	0.0447214i
$376$	−2.54588e8	−	4.40959e8i	−0.246991	−	0.427800i
$377$	1.14126e9			1.09696
$378$	6.06236e6	+	1.42769e8i	0.00577325	+	0.135960i
$379$	2.84767e8			0.268690			0.134345	−	0.990935i	$-0.457107\pi$
$379$	2.84767e8			0.268690			0.134345	+	0.990935i	$0.457107\pi$
$380$	1.73737e8	+	3.00922e8i	0.162424	+	0.281327i
$381$	2.53747e8	−	4.39503e8i	0.235052	−	0.407122i
$382$	−2.48214e8	+	4.29919e8i	−0.227827	+	0.394607i
$383$	8.92229e8	+	1.54539e9i	0.811486	+	1.40553i	0.911824	+	0.410581i	$0.134674\pi$
$383$	8.92229e8	+	1.54539e9i	0.811486	+	1.40553i	−0.100339	+	0.994953i	$0.531993\pi$
$384$	5.66231e7			0.0510310
$385$	2.51132e8	+	1.31113e8i	0.224279	+	0.117094i
$386$	3.44783e7			0.0305134
$387$	7.88005e7	+	1.36486e8i	0.0691099	+	0.119702i
$388$	−2.82932e7	+	4.90052e7i	−0.0245907	+	0.0425923i
$389$	−5.47901e8	+	9.48992e8i	−0.471931	+	0.817408i	−0.999484	−	0.0321137i	$-0.989776\pi$
$389$	−5.47901e8	+	9.48992e8i	−0.471931	+	0.817408i	0.527553	+	0.849522i	$0.323109\pi$
$390$	9.30127e7	+	1.61103e8i	0.0793992	+	0.137523i
$391$	1.38586e8			0.117247
$392$	2.41024e8	+	3.45976e8i	0.202097	+	0.290098i
$393$	−1.13291e9			−0.941504
$394$	−2.41224e8	−	4.17812e8i	−0.198693	−	0.344147i
$395$	−2.88229e8	+	4.99227e8i	−0.235314	+	0.407576i
$396$	−5.82597e7	+	1.00909e8i	−0.0471449	+	0.0816574i
$397$	−2.91991e8	−	5.05742e8i	−0.234208	−	0.405660i	0.724834	−	0.688923i	$-0.241916\pi$
$397$	−2.91991e8	−	5.05742e8i	−0.234208	−	0.405660i	−0.959042	+	0.283263i	$0.908583\pi$
$398$	1.27680e9			1.01516
$399$	−9.43405e8	−	4.92541e8i	−0.743521	−	0.388183i
$400$	6.40000e7			0.0500000
$401$	7.06847e8	+	1.22429e9i	0.547419	+	0.948158i	0.998450	+	0.0556498i	$0.0177230\pi$
$401$	7.06847e8	+	1.22429e9i	0.547419	+	0.948158i	−0.451031	+	0.892508i	$0.648944\pi$
$402$	1.84599e8	−	3.19734e8i	0.141722	−	0.245470i
$403$	6.63920e8	−	1.14994e9i	0.505299	−	0.875203i
$404$	1.42101e8	+	2.46126e8i	0.107217	+	0.185705i
$405$	−6.64301e7			−0.0496904
$406$	5.10185e7	+	1.20149e9i	0.0378344	+	0.891000i
$407$	2.32470e8			0.170917
$408$	2.70515e7	+	4.68546e7i	0.0197188	+	0.0341540i
$409$	−1.02297e9	+	1.77184e9i	−0.739322	+	1.28054i	0.213480	+	0.976948i	$0.431520\pi$
$409$	−1.02297e9	+	1.77184e9i	−0.739322	+	1.28054i	−0.952801	+	0.303595i	$0.901813\pi$
$410$	−1.59102e8	+	2.75572e8i	−0.114007	+	0.197466i
$411$	2.11856e8	+	3.66946e8i	0.150520	+	0.260709i
$412$	2.55275e8			0.179832
$413$	1.38995e9	−	8.83160e8i	0.970899	−	0.616899i
$414$	−2.06514e8			−0.143037
$415$	5.29685e8	+	9.17441e8i	0.363789	+	0.630101i
$416$	−1.12883e8	+	1.95519e8i	−0.0768779	+	0.133156i
$417$	−6.18018e8	+	1.07044e9i	−0.417374	+	0.722912i
$418$	−4.33894e8	−	7.51526e8i	−0.290581	−	0.503300i
$419$	3.07289e8			0.204079			0.102039	−	0.994780i	$-0.467463\pi$
$419$	3.07289e8			0.204079			0.102039	+	0.994780i	$0.467463\pi$
$420$	−1.65446e8	+	1.05123e8i	−0.108964	+	0.0692348i
$421$	2.70391e9			1.76606			0.883030	−	0.469316i	$-0.155499\pi$
$421$	2.70391e9			1.76606			0.883030	+	0.469316i	$0.155499\pi$
$422$	5.03018e8	+	8.71253e8i	0.325829	+	0.564353i
$423$	−3.62490e8	+	6.27850e8i	−0.232865	+	0.403334i
$424$	−3.51904e8	+	6.09515e8i	−0.224204	+	0.388333i
$425$	3.05758e7	+	5.29589e7i	0.0193204	+	0.0334640i
$426$	−2.69039e8			−0.168610
$427$	−8.89621e7	−	2.09506e9i	−0.0552978	−	1.30226i
$428$	−7.05581e8			−0.435005
$429$	−2.32291e8	−	4.02340e8i	−0.142047	−	0.246033i
$430$	−1.08094e8	+	1.87224e8i	−0.0655634	+	0.113559i
$431$	8.89431e8	−	1.54054e9i	0.535109	−	0.926835i	−0.464049	−	0.885809i	$-0.653604\pi$
$431$	8.89431e8	−	1.54054e9i	0.535109	−	0.926835i	0.999158	−	0.0410261i	$-0.0130627\pi$
$432$	−4.03108e7	−	6.98203e7i	−0.0240563	−	0.0416667i
$433$	8.71941e8			0.516154			0.258077	−	0.966124i	$-0.416911\pi$
$433$	8.71941e8			0.516154			0.258077	+	0.966124i	$0.416911\pi$
$434$	1.24031e9	+	6.47549e8i	0.728308	+	0.380241i
$435$	−5.59050e8			−0.325640
$436$	−4.08684e8	−	7.07861e8i	−0.236148	−	0.409021i
$437$	7.69014e8	−	1.33197e9i	0.440808	−	0.763502i
$438$	−4.44128e8	+	7.69253e8i	−0.252551	+	0.437431i
$439$	−1.95426e8	−	3.38487e8i	−0.110244	−	0.190948i	0.805625	−	0.592426i	$-0.201830\pi$
$439$	−1.95426e8	−	3.38487e8i	−0.110244	−	0.190948i	−0.915869	+	0.401478i	$0.868497\pi$
$440$	−1.59834e8			−0.0894512
$441$	2.55025e8	−	5.43505e8i	0.141595	−	0.301765i
$442$	−2.15718e8			−0.118825
$443$	−8.23764e8	−	1.42680e9i	−0.450184	−	0.779741i	0.548213	−	0.836338i	$-0.315308\pi$
$443$	−8.23764e8	−	1.42680e9i	−0.450184	−	0.779741i	−0.998397	+	0.0565975i	$0.981975\pi$
$444$	−8.04248e7	+	1.39300e8i	−0.0436063	+	0.0755284i
$445$	−3.46113e8	+	5.99486e8i	−0.186191	+	0.322492i
$446$	−8.66053e8	−	1.50005e9i	−0.462245	−	0.800633i
$447$	−4.66091e8			−0.246828
$448$	−2.10883e8	−	1.10099e8i	−0.110807	−	0.0578511i
$449$	3.50220e8			0.182591			0.0912954	−	0.995824i	$-0.470899\pi$
$449$	3.50220e8			0.182591			0.0912954	+	0.995824i	$0.470899\pi$
$450$	−4.55625e7	−	7.89166e7i	−0.0235702	−	0.0408248i
$451$	3.97343e8	−	6.88218e8i	0.203961	−	0.353271i
$452$	−5.60800e8	+	9.71334e8i	−0.285643	+	0.494748i
$453$	−5.98033e8	−	1.03582e9i	−0.302260	−	0.523531i
$454$	−1.49856e9			−0.751587
$455$	−3.31573e7	−	7.80855e8i	−0.0165021	−	0.388625i
$456$	6.00436e8			0.296545
$457$	9.83159e8	+	1.70288e9i	0.481856	+	0.834599i	0.999783	−	0.0208259i	$-0.00662955\pi$
$457$	9.83159e8	+	1.70288e9i	0.481856	+	0.834599i	−0.517927	+	0.855425i	$0.673296\pi$
$458$	−4.60789e8	+	7.98109e8i	−0.224116	+	0.388180i
$459$	3.85167e7	−	6.67130e7i	0.0185911	−	0.0322007i
$460$	−1.41642e8	−	2.45331e8i	−0.0678483	−	0.117517i
$461$	3.47902e9			1.65388			0.826940	−	0.562291i	$-0.190080\pi$
$461$	3.47902e9			1.65388			0.826940	+	0.562291i	$0.190080\pi$
$462$	4.13187e8	−	2.62535e8i	0.194940	−	0.123863i
$463$	4.54976e8			0.213037			0.106519	−	0.994311i	$-0.466030\pi$
$463$	4.54976e8			0.213037			0.106519	+	0.994311i	$0.466030\pi$
$464$	−3.39240e8	−	5.87581e8i	−0.157650	−	0.273058i
$465$	−3.25223e8	+	5.63303e8i	−0.150002	+	0.259811i
$466$	2.45989e8	−	4.26066e8i	0.112607	−	0.195041i
$467$	−4.40916e8	−	7.63689e8i	−0.200330	−	0.346982i	0.748304	−	0.663355i	$-0.230868\pi$
$467$	−4.40916e8	−	7.63689e8i	−0.200330	−	0.346982i	−0.948635	+	0.316373i	$0.897535\pi$
$468$	3.21452e8			0.144962
$469$	−1.30920e9	+	8.31856e8i	−0.586007	+	0.372343i
$470$	−9.94485e8			−0.441830
$471$	−9.40352e8	−	1.62874e9i	−0.414684	−	0.718254i
$472$	−4.64554e8	+	8.04631e8i	−0.203348	+	0.352209i
$473$	2.69955e8	−	4.67576e8i	0.117295	−	0.203160i
$474$	4.98059e8	+	8.62664e8i	0.214811	+	0.372064i
$475$	6.78662e8			0.290553
$476$	−9.64337e6	−	2.27102e8i	−0.00409831	−	0.0965152i
$477$	1.00210e9			0.422763
$478$	−8.26561e8	−	1.43164e9i	−0.346160	−	0.599567i
$479$	1.67711e8	−	2.90485e8i	0.0697249	−	0.120767i	−0.829055	−	0.559167i	$-0.811121\pi$
$479$	1.67711e8	−	2.90485e8i	0.0697249	−	0.120767i	0.898780	+	0.438400i	$0.144455\pi$
$480$	5.52960e7	−	9.57755e7i	0.0228218	−	0.0395285i
$481$	−3.20667e8	−	5.55412e8i	−0.131385	−	0.227566i
$482$	8.00131e8			0.325459
$483$	7.69124e8	+	4.01550e8i	0.310586	+	0.162153i
$484$	−8.48006e8			−0.339970
$485$	5.52601e7	+	9.57133e7i	0.0219946	+	0.0380957i
$486$	−5.73956e7	+	9.94121e7i	−0.0226805	+	0.0392837i
$487$	2.06768e8	−	3.58133e8i	0.0811208	−	0.140505i	−0.822611	−	0.568605i	$-0.807483\pi$
$487$	2.06768e8	−	3.58133e8i	0.0811208	−	0.140505i	0.903732	+	0.428099i	$0.140817\pi$
$488$	5.91540e8	+	1.02458e9i	0.230417	+	0.399094i
$489$	9.29862e8			0.359615
$490$	8.20578e8	−	6.98140e7i	0.315089	−	0.0268075i
$491$	−3.14575e9			−1.19933			−0.599666	−	0.800251i	$-0.704700\pi$
$491$	−3.14575e9			−1.19933			−0.599666	+	0.800251i	$0.704700\pi$
$492$	2.74928e8	+	4.76189e8i	0.104074	+	0.180261i
$493$	3.24142e8	−	5.61430e8i	0.121835	−	0.211024i
$494$	−1.19702e9	+	2.07330e9i	−0.446742	+	0.773780i
$495$	1.13788e8	+	1.97087e8i	0.0421677	+	0.0730366i
$496$	−7.89401e8			−0.290477
$497$	1.00199e9	+	5.23127e8i	0.366114	+	0.191144i
$498$	1.83059e9			0.664184
$499$	8.70891e8	+	1.50843e9i	0.313770	+	0.543466i	0.979175	−	0.203017i	$-0.0650745\pi$
$499$	8.70891e8	+	1.50843e9i	0.313770	+	0.543466i	−0.665405	+	0.746482i	$0.731741\pi$
$500$	6.25000e7	−	1.08253e8i	0.0223607	−	0.0387298i
$501$	1.10746e9	−	1.91818e9i	0.393457	−	0.681488i
$502$	−1.46662e9	−	2.54026e9i	−0.517434	−	0.896221i
$503$	−1.92201e9			−0.673393			−0.336696	−	0.941613i	$-0.609310\pi$
$503$	−1.92201e9			−0.673393			−0.336696	+	0.941613i	$0.609310\pi$
$504$	1.43700e7	+	3.38415e8i	0.00499979	+	0.117745i
$505$	5.55082e8			0.191795
$506$	3.53738e8	+	6.12692e8i	0.121382	+	0.210240i
$507$	2.06264e8	−	3.57260e8i	0.0702903	−	0.121746i
$508$	6.01474e8	−	1.04178e9i	0.203561	−	0.352578i
$509$	3.88901e8	+	6.73596e8i	0.130715	+	0.226406i	0.923953	−	0.382507i	$-0.124939\pi$
$509$	3.88901e8	+	6.73596e8i	0.130715	+	0.226406i	−0.793237	+	0.608913i	$0.791606\pi$
$510$	1.05670e8			0.0352741
$511$	3.14983e9	−	2.00137e9i	1.04427	−	0.663521i
$512$	1.34218e8			0.0441942
$513$	−4.27459e8	−	7.40381e8i	−0.139792	−	0.242128i
$514$	−1.92095e9	+	3.32719e9i	−0.623944	+	1.08070i
$515$	2.49292e8	−	4.31786e8i	0.0804234	−	0.139297i
$516$	1.86786e8	+	3.23523e8i	0.0598510	+	0.103665i
$517$	2.48364e9			0.790445
$518$	5.70386e8	−	3.62418e8i	0.180308	−	0.114566i
$519$	−1.97078e9			−0.618802
$520$	2.20474e8	+	3.81873e8i	0.0687617	+	0.119099i
$521$	−1.08188e9	+	1.87387e9i	−0.335155	+	0.580506i	−0.983515	−	0.180828i	$-0.942122\pi$
$521$	−1.08188e9	+	1.87387e9i	−0.335155	+	0.580506i	0.648359	+	0.761334i	$0.275455\pi$
$522$	−4.83019e8	+	8.36614e8i	−0.148634	+	0.257441i
$523$	−2.30865e8	−	3.99870e8i	−0.0705670	−	0.122226i	0.828583	−	0.559866i	$-0.189148\pi$
$523$	−2.30865e8	−	3.99870e8i	−0.0705670	−	0.122226i	−0.899150	+	0.437641i	$0.855814\pi$
$524$	−2.68542e9			−0.815366
$525$	1.62422e7	+	3.82504e8i	0.00489877	+	0.115366i
$526$	−6.23958e7			−0.0186941
$527$	−3.77134e8	−	6.53216e8i	−0.112243	−	0.194410i
$528$	−1.38097e8	+	2.39191e8i	−0.0408287	+	0.0707174i
$529$	1.07546e9	−	1.86276e9i	0.315865	−	0.547093i
$530$	6.87312e8	+	1.19046e9i	0.200534	+	0.347335i
$531$	1.32289e9			0.383436
$532$	−2.23622e9	−	1.16750e9i	−0.643908	−	0.336177i
$533$	−2.19237e9			−0.627145
$534$	5.98084e8	+	1.03591e9i	0.169968	+	0.294394i
$535$	−6.89044e8	+	1.19346e9i	−0.194540	+	0.336953i
$536$	4.37567e8	−	7.57888e8i	0.122735	−	0.212583i
$537$	−7.80851e8	−	1.35247e9i	−0.217600	−	0.376894i
$538$	2.34722e9			0.649853
$539$	−2.04932e9	+	1.74354e8i	−0.563702	+	0.0479592i
$540$	−1.57464e8			−0.0430331
$541$	3.26677e9	+	5.65821e9i	0.887009	+	1.53635i	0.843393	+	0.537297i	$0.180554\pi$
$541$	3.26677e9	+	5.65821e9i	0.887009	+	1.53635i	0.0436159	+	0.999048i	$0.486112\pi$
$542$	−2.28232e8	+	3.95309e8i	−0.0615714	+	0.106645i
$543$	1.54249e9	−	2.67168e9i	0.413451	−	0.716118i
$544$	6.41222e7	+	1.11063e8i	0.0170770	+	0.0295783i
$545$	−1.59642e9			−0.422435
$546$	−1.19719e9	−	6.25039e8i	−0.314767	−	0.164336i
$547$	−7.45082e9			−1.94647			−0.973237	−	0.229804i	$-0.926192\pi$
$547$	−7.45082e9			−1.94647			−0.973237	+	0.229804i	$0.926192\pi$
$548$	5.02178e8	+	8.69797e8i	0.130354	+	0.225780i
$549$	8.42252e8	−	1.45882e9i	0.217239	−	0.376270i
$550$	−1.56088e8	+	2.70353e8i	−0.0400038	+	0.0692886i
$551$	−3.59733e9	−	6.23076e9i	−0.916114	−	1.58676i
$552$	−4.89514e8			−0.123873
$553$	−1.77549e8	−	4.18128e9i	−0.0446458	−	1.05141i
$554$	−1.02363e9			−0.255776
$555$	1.57080e8	+	2.72070e8i	0.0390027	+	0.0675546i
$556$	−1.46493e9	+	2.53734e9i	−0.361456	+	0.626061i
$557$	3.24626e9	−	5.62269e9i	0.795958	−	1.37864i	−0.126272	−	0.991996i	$-0.540301\pi$
$557$	3.24626e9	−	5.62269e9i	0.795958	−	1.37864i	0.922229	−	0.386644i	$-0.126366\pi$
$558$	5.61986e8	+	9.73388e8i	0.136932	+	0.237174i
$559$	−1.48950e9			−0.360660
$560$	−3.92169e8	+	2.49180e8i	−0.0943658	+	0.0599591i
$561$	−2.63902e8			−0.0631063
$562$	4.42263e8	+	7.66023e8i	0.105100	+	0.182039i
$563$	3.79713e9	−	6.57681e9i	0.896759	−	1.55323i	0.0651459	−	0.997876i	$-0.479249\pi$
$563$	3.79713e9	−	6.57681e9i	0.896759	−	1.55323i	0.831613	−	0.555356i	$-0.187418\pi$
$564$	−8.59235e8	+	1.48824e9i	−0.201667	+	0.349298i
$565$	1.09531e9	+	1.89714e9i	0.255487	+	0.442516i
$566$	6.32089e8			0.146528
$567$	4.07059e8	−	2.58642e8i	0.0937815	−	0.0595878i
$568$	−6.37723e8			−0.146020
$569$	9.16096e8	+	1.58672e9i	0.208472	+	0.361084i	0.951233	−	0.308472i	$-0.0998176\pi$
$569$	9.16096e8	+	1.58672e9i	0.208472	+	0.361084i	−0.742761	+	0.669556i	$0.766484\pi$
$570$	5.86364e8	−	1.01561e9i	0.132619	−	0.229702i
$571$	−1.23186e9	+	2.13365e9i	−0.276909	+	0.479620i	−0.970615	−	0.240638i	$-0.922643\pi$
$571$	−1.23186e9	+	2.13365e9i	−0.276909	+	0.479620i	0.693706	+	0.720258i	$0.255977\pi$
$572$	−5.50616e8	−	9.53694e8i	−0.123016	−	0.213070i
$573$	1.67545e9			0.372039
$574$	−9.80066e7	−	2.30806e9i	−0.0216304	−	0.509395i
$575$	−5.53288e8			−0.121371
$576$	−9.55515e7	−	1.65500e8i	−0.0208333	−	0.0360844i
$577$	−1.15039e9	+	1.99254e9i	−0.249305	+	0.431809i	−0.963333	−	0.268308i	$-0.913536\pi$
$577$	−1.15039e9	+	1.99254e9i	−0.249305	+	0.431809i	0.714028	+	0.700117i	$0.246869\pi$
$578$	1.58009e9	−	2.73679e9i	0.340356	−	0.589514i
$579$	−5.81821e7	−	1.00774e8i	−0.0124570	−	0.0215762i
$580$	−1.32516e9			−0.282013
$581$	−6.81772e9	−	3.55945e9i	−1.44219	−	0.752950i
$582$	1.90979e8			0.0401564
$583$	−1.71650e9	−	2.97307e9i	−0.358760	−	0.621391i
$584$	−1.05275e9	+	1.82341e9i	−0.218716	+	0.378827i
$585$	3.13918e8	−	5.43721e8i	0.0648291	−	0.112287i
$586$	−2.58349e9	−	4.47474e9i	−0.530354	−	0.918600i
$587$	7.56546e9			1.54384			0.771919	−	0.635721i	$-0.219297\pi$
$587$	7.56546e9			1.54384			0.771919	+	0.635721i	$0.219297\pi$
$588$	6.04504e8	−	1.28831e9i	0.122625	−	0.261336i
$589$	−8.37088e9			−1.68798
$590$	9.07332e8	+	1.57155e9i	0.181880	+	0.315025i
$591$	−8.14130e8	+	1.41012e9i	−0.162232	+	0.280995i
$592$	−1.90637e8	+	3.30192e8i	−0.0377642	+	0.0654095i
$593$	−4.53870e9	−	7.86127e9i	−0.893800	−	1.54811i	−0.835283	−	0.549821i	$-0.814696\pi$
$593$	−4.53870e9	−	7.86127e9i	−0.893800	−	1.54811i	−0.0585175	−	0.998286i	$-0.518637\pi$
$594$	3.93253e8			0.0769873
$595$	−3.93550e8	−	2.05468e8i	−0.0765932	−	0.0399884i
$596$	−1.10481e9			−0.213759
$597$	−2.15461e9	−	3.73189e9i	−0.414436	−	0.717825i
$598$	9.75887e8	−	1.69029e9i	0.186614	−	0.323226i
$599$	−4.03758e9	+	6.99329e9i	−0.767586	+	1.32950i	0.171282	+	0.985222i	$0.445209\pi$
$599$	−4.03758e9	+	6.99329e9i	−0.767586	+	1.32950i	−0.938868	+	0.344277i	$0.888124\pi$
$600$	−1.08000e8	−	1.87061e8i	−0.0204124	−	0.0353553i
$601$	1.56774e9			0.294587			0.147293	−	0.989093i	$-0.452944\pi$
$601$	1.56774e9			0.294587			0.147293	+	0.989093i	$0.452944\pi$
$602$	−6.65859e7	−	1.56810e9i	−0.0124393	−	0.292945i
$603$	−1.24604e9			−0.231431
$604$	−1.41756e9	−	2.45529e9i	−0.261765	−	0.453391i
$605$	−8.28131e8	+	1.43437e9i	−0.152039	+	0.263339i
$606$	4.79591e8	−	8.30676e8i	0.0875421	−	0.151627i
$607$	4.35680e9	+	7.54620e9i	0.790692	+	1.36952i	0.925539	+	0.378652i	$0.123612\pi$
$607$	4.35680e9	+	7.54620e9i	0.790692	+	1.36952i	−0.134847	+	0.990866i	$0.543054\pi$
$608$	1.42326e9			0.256815
$609$	3.42565e9	−	2.17663e9i	0.614587	−	0.390502i
$610$	2.31070e9			0.412183
$611$	−3.42591e9	−	5.93385e9i	−0.607620	−	1.05243i
$612$	9.12990e7	−	1.58134e8i	0.0161004	−	0.0278867i
$613$	−1.33420e9	+	2.31090e9i	−0.233943	+	0.405201i	−0.958965	−	0.283525i	$-0.908496\pi$
$613$	−1.33420e9	+	2.31090e9i	−0.233943	+	0.405201i	0.725022	+	0.688725i	$0.241829\pi$
$614$	−3.93569e9	−	6.81681e9i	−0.686169	−	1.18848i
$615$	1.07394e9			0.186173
$616$	9.79407e8	−	6.22306e8i	0.168823	−	0.107268i
$617$	−7.81236e9			−1.33901			−0.669506	−	0.742807i	$-0.733494\pi$
$617$	−7.81236e9			−1.33901			−0.669506	+	0.742807i	$0.733494\pi$
$618$	−4.30776e8	−	7.46126e8i	−0.0734162	−	0.127161i
$619$	−2.12502e9	+	3.68064e9i	−0.360119	+	0.623744i	−0.987980	−	0.154581i	$-0.950597\pi$
$619$	−2.12502e9	+	3.68064e9i	−0.360119	+	0.623744i	0.627861	+	0.778325i	$0.283930\pi$
$620$	−7.70899e8	+	1.33524e9i	−0.129905	+	0.225003i
$621$	3.48492e8	+	6.03605e8i	0.0583945	+	0.101142i
$622$	7.15478e7			0.0119215
$623$	−2.13206e8	−	5.02100e9i	−0.0353257	−	0.831921i
$624$	7.61960e8			0.125541
$625$	−1.22070e8	−	2.11432e8i	−0.0200000	−	0.0346410i
$626$	1.50135e8	−	2.60042e8i	0.0244609	−	0.0423675i
$627$	−1.46439e9	+	2.53640e9i	−0.237258	+	0.410943i
$628$	−2.22898e9	−	3.86071e9i	−0.359127	−	0.622026i
$629$	−3.64305e8			−0.0583697
$630$	5.86447e8	+	3.06177e8i	0.0934409	+	0.0487844i
$631$	7.48122e9			1.18541			0.592707	−	0.805419i	$-0.298059\pi$
$631$	7.48122e9			1.18541			0.592707	+	0.805419i	$0.298059\pi$
$632$	1.18059e9	+	2.04483e9i	0.186032	+	0.322217i
$633$	1.69769e9	−	2.94048e9i	0.266038	−	0.460792i
$634$	−1.95185e9	+	3.38069e9i	−0.304182	+	0.526858i
$635$	−1.17475e9	−	2.03473e9i	−0.182070	−	0.315355i
$636$	2.37535e9			0.366124
$637$	3.24339e9	+	4.65570e9i	0.497176	+	0.713669i
$638$	3.30946e9			0.504528
$639$	4.54004e8	+	7.86358e8i	0.0688346	+	0.119225i
$640$	1.31072e8	−	2.27023e8i	0.0197642	−	0.0342327i
$641$	−8.13131e8	+	1.40838e9i	−0.121943	+	0.211212i	−0.920534	−	0.390663i	$-0.872246\pi$
$641$	−8.13131e8	+	1.40838e9i	−0.121943	+	0.211212i	0.798591	+	0.601874i	$0.205579\pi$
$642$	1.19067e9	+	2.06230e9i	0.177590	+	0.307595i
$643$	6.53453e8			0.0969340			0.0484670	−	0.998825i	$-0.484566\pi$
$643$	6.53453e8			0.0969340			0.0484670	+	0.998825i	$0.484566\pi$
$644$	1.82311e9	+	9.51823e8i	0.268975	+	0.140429i
$645$	7.29634e8			0.107065
$646$	6.79957e8	+	1.17772e9i	0.0992356	+	0.171881i
$647$	3.65625e7	−	6.33282e7i	0.00530727	−	0.00919247i	−0.863360	−	0.504589i	$-0.831644\pi$
$647$	3.65625e7	−	6.33282e7i	0.00530727	−	0.00919247i	0.868667	+	0.495397i	$0.164977\pi$
$648$	−1.36049e8	+	2.35644e8i	−0.0196419	+	0.0340207i
$649$	−2.26598e9	−	3.92480e9i	−0.325387	−	0.563587i
$650$	8.61228e8			0.123005
$651$	−2.00338e8	−	4.71795e9i	−0.0284596	−	0.670224i
$652$	2.20412e9			0.311436
$653$	4.53040e9	+	7.84689e9i	0.636708	+	1.10281i	0.986150	+	0.165853i	$0.0530378\pi$
$653$	4.53040e9	+	7.84689e9i	0.636708	+	1.10281i	−0.349442	+	0.936958i	$0.613629\pi$
$654$	−1.37931e9	+	2.38903e9i	−0.192814	+	0.333964i
$655$	−2.62248e9	+	4.54227e9i	−0.364643	+	0.631580i
$656$	6.51680e8	+	1.12874e9i	0.0901304	+	0.156110i
$657$	2.99787e9			0.412414
$658$	6.09384e9	−	3.87196e9i	0.833873	−	0.529835i
$659$	−1.54691e9			−0.210556			−0.105278	−	0.994443i	$-0.533573\pi$
$659$	−1.54691e9			−0.210556			−0.105278	+	0.994443i	$0.533573\pi$
$660$	2.69721e8	+	4.67170e8i	0.0365183	+	0.0632515i
$661$	1.52525e9	−	2.64181e9i	0.205417	−	0.355792i	−0.744849	−	0.667233i	$-0.767478\pi$
$661$	1.52525e9	−	2.64181e9i	0.205417	−	0.355792i	0.950265	+	0.311441i	$0.100812\pi$
$662$	−1.06532e9	+	1.84518e9i	−0.142717	+	0.247193i
$663$	3.64024e8	+	6.30509e8i	0.0485102	+	0.0840221i
$664$	4.33918e9			0.575201
$665$	−4.15859e9	+	2.64233e9i	−0.548366	+	0.348426i
$666$	5.42867e8			0.0712089
$667$	2.93277e9	+	5.07971e9i	0.382682	+	0.662824i
$668$	2.62510e9	−	4.54681e9i	0.340744	−	0.590186i
$669$	−2.92293e9	+	5.06266e9i	−0.377422	+	0.653714i
$670$	−8.54623e8	−	1.48025e9i	−0.109777	−	0.190140i
$671$	−5.77078e9			−0.737405
$672$	3.40623e7	+	8.02169e8i	0.00432994	+	0.101970i
$673$	1.31871e10			1.66761			0.833806	−	0.552057i	$-0.186157\pi$
$673$	1.31871e10			1.66761			0.833806	+	0.552057i	$0.186157\pi$
$674$	2.42939e9	+	4.20783e9i	0.305625	+	0.529357i
$675$	−1.53773e8	+	2.66343e8i	−0.0192450	+	0.0333333i
$676$	4.88922e8	−	8.46838e8i	0.0608732	−	0.105435i
$677$	3.61123e9	+	6.25483e9i	0.447295	+	0.774738i	0.998209	−	0.0598242i	$-0.0190540\pi$
$677$	3.61123e9	+	6.25483e9i	0.447295	+	0.774738i	−0.550914	+	0.834562i	$0.685721\pi$
$678$	3.78540e9			0.466453
$679$	−7.11267e8	−	3.71344e8i	−0.0871944	−	0.0455232i
$680$	2.50477e8			0.0305483
$681$	2.52882e9	+	4.38005e9i	0.306834	+	0.531452i
$682$	1.92525e9	−	3.33464e9i	0.232404	−	0.402535i
$683$	−3.40841e9	+	5.90354e9i	−0.409336	+	0.708990i	−0.994815	−	0.101697i	$-0.967573\pi$
$683$	−3.40841e9	+	5.90354e9i	−0.409336	+	0.708990i	0.585480	+	0.810687i	$0.300906\pi$
$684$	−1.01324e9	−	1.75498e9i	−0.121064	−	0.209689i
$685$	1.96163e9			0.233185
$686$	−4.75639e9	+	3.62267e9i	−0.562526	+	0.428444i
$687$	3.11032e9			0.365980
$688$	4.42753e8	+	7.66870e8i	0.0518324	+	0.0897764i
$689$	−4.73546e9	+	8.20206e9i	−0.551563	+	0.955335i
$690$	−4.78041e8	+	8.27991e8i	−0.0553979	+	0.0959519i
$691$	−8.22343e9	−	1.42434e10i	−0.948156	−	1.64225i	−0.749306	−	0.662224i	$-0.769613\pi$
$691$	−8.22343e9	−	1.42434e10i	−0.948156	−	1.64225i	−0.198850	−	0.980030i	$-0.563721\pi$
$692$	−4.67147e9			−0.535899
$693$	−1.46460e9	−	7.64650e8i	−0.167168	−	0.0872764i
$694$	−3.60182e9			−0.409038
$695$	2.86120e9	+	4.95574e9i	0.323296	+	0.559966i
$696$	−1.14493e9	+	1.98309e9i	−0.128721	+	0.222951i
$697$	−6.22677e8	+	1.07851e9i	−0.0696544	+	0.120645i
$698$	3.53907e8	+	6.12985e8i	0.0393908	+	0.0682269i
$699$	−1.66043e9			−0.183887
$700$	3.85000e7	+	9.06676e8i	0.00424246	+	0.0999100i
$701$	−2.23041e9			−0.244552			−0.122276	−	0.992496i	$-0.539019\pi$
$701$	−2.23041e9			−0.244552			−0.122276	+	0.992496i	$0.539019\pi$
$702$	−5.42450e8	−	9.39551e8i	−0.0591806	−	0.102504i
$703$	−2.02153e9	+	3.50139e9i	−0.219450	+	0.380099i
$704$	−3.27341e8	+	5.66971e8i	−0.0353587	+	0.0612430i
$705$	1.67819e9	+	2.90671e9i	0.180376	+	0.312421i
$706$	−4.34809e9			−0.465032
$707$	−3.40134e9	+	2.16118e9i	−0.361978	+	0.229997i
$708$	3.13574e9			0.332065
$709$	6.44749e9	+	1.11674e10i	0.679405	+	1.17676i	0.975160	+	0.221500i	$0.0710954\pi$
$709$	6.44749e9	+	1.11674e10i	0.679405	+	1.17676i	−0.295755	+	0.955264i	$0.595571\pi$
$710$	−6.22777e8	+	1.07868e9i	−0.0653022	+	0.113107i
$711$	1.68095e9	−	2.91149e9i	0.175393	−	0.303789i
$712$	1.41768e9	+	2.45549e9i	0.147197	+	0.254952i
$713$	6.82447e9			0.705108
$714$	−6.47508e8	+	4.11420e8i	−0.0665735	+	0.0423001i
$715$	−2.15084e9			−0.220058
$716$	−1.85091e9	−	3.20586e9i	−0.188447	−	0.326399i
$717$	−2.78964e9	+	4.83180e9i	−0.282639	+	0.489544i
$718$	−1.33455e9	+	2.31150e9i	−0.134554	+	0.233055i
$719$	−2.07539e9	−	3.59468e9i	−0.208232	−	0.360669i	0.742925	−	0.669374i	$-0.233438\pi$
$719$	−2.07539e9	−	3.59468e9i	−0.208232	−	0.360669i	−0.951158	+	0.308705i	$0.900104\pi$
$720$	−3.73248e8			−0.0372678
$721$	1.53564e8	+	3.61643e9i	0.0152586	+	0.359340i
$722$	7.94136e9			0.785262
$723$	−1.35022e9	−	2.33865e9i	−0.132868	−	0.230134i
$724$	3.65628e9	−	6.33287e9i	0.358059	−	0.620177i
$725$	−1.29410e9	+	2.24144e9i	−0.126120	+	0.218446i
$726$	1.43101e9	+	2.47858e9i	0.138792	+	0.240395i
$727$	1.16247e10			1.12205			0.561026	−	0.827798i	$-0.310407\pi$
$727$	1.16247e10			1.12205			0.561026	+	0.827798i	$0.310407\pi$
$728$	−2.83779e9	−	1.48157e9i	−0.272596	−	0.142319i
$729$	3.87420e8			0.0370370
$730$	2.05615e9	+	3.56136e9i	0.195625	+	0.338833i
$731$	−4.23048e8	+	7.32741e8i	−0.0400570	+	0.0693808i
$732$	1.99645e9	−	3.45795e9i	0.188135	−	0.325859i
$733$	5.05569e8	+	8.75672e8i	0.0474151	+	0.0821254i	0.888759	−	0.458375i	$-0.151568\pi$
$733$	5.05569e8	+	8.75672e8i	0.0474151	+	0.0821254i	−0.841344	+	0.540500i	$0.818235\pi$
$734$	1.30715e10			1.22008
$735$	−1.58878e9	−	2.28060e9i	−0.147590	−	0.211858i
$736$	−1.16033e9			−0.107278
$737$	2.13435e9	+	3.69680e9i	0.196394	+	0.340165i
$738$	9.27881e8	−	1.60714e9i	0.0849758	−	0.147182i
$739$	−6.53735e9	+	1.13230e10i	−0.595862	+	1.03206i	0.397562	+	0.917575i	$0.369856\pi$
$739$	−6.53735e9	+	1.13230e10i	−0.595862	+	1.03206i	−0.993425	+	0.114489i	$0.963477\pi$
$740$	3.72337e8	+	6.44907e8i	0.0337773	+	0.0585040i
$741$	8.07989e9			0.729527
$742$	−8.84658e9	−	4.61869e9i	−0.794990	−	0.415055i
$743$	−1.82088e10			−1.62863			−0.814314	−	0.580425i	$-0.802886\pi$
$743$	−1.82088e10			−1.62863			−0.814314	+	0.580425i	$0.802886\pi$
$744$	1.33211e9	+	2.30729e9i	0.118587	+	0.205398i
$745$	−1.07891e9	+	1.86874e9i	−0.0955961	+	0.165577i
$746$	−5.02599e9	+	8.70527e9i	−0.443237	+	0.767709i
$747$	−3.08912e9	−	5.35052e9i	−0.271152	−	0.469649i
$748$	−6.25545e8			−0.0546516
$749$	−4.24451e8	−	9.99584e9i	−0.0369098	−	0.869226i
$750$	−4.21875e8			−0.0365148
$751$	7.91951e9	+	1.37170e10i	0.682274	+	1.18173i	0.974285	+	0.225318i	$0.0723421\pi$
$751$	7.91951e9	+	1.37170e10i	0.682274	+	1.18173i	−0.292012	+	0.956415i	$0.594325\pi$
$752$	−2.03670e9	+	3.52768e9i	−0.174649	+	0.302501i
$753$	−4.94984e9	+	8.57338e9i	−0.422483	+	0.731762i
$754$	−4.56505e9	−	7.90689e9i	−0.387834	−	0.671748i
$755$	−5.53734e9			−0.468260
$756$	9.64882e8	−	6.13076e8i	0.0812172	−	0.0516046i
$757$	1.15099e10			0.964352			0.482176	−	0.876074i	$-0.339847\pi$
$757$	1.15099e10			0.964352			0.482176	+	0.876074i	$0.339847\pi$
$758$	−1.13907e9	−	1.97292e9i	−0.0949964	−	0.164539i
$759$	1.19387e9	−	2.06783e9i	0.0991081	−	0.171660i
$760$	1.38990e9	−	2.40738e9i	0.114851	−	0.198928i
$761$	9.12229e9	+	1.58003e10i	0.750339	+	1.29963i	0.947658	+	0.319286i	$0.103443\pi$
$761$	9.12229e9	+	1.58003e10i	0.750339	+	1.29963i	−0.197320	+	0.980339i	$0.563224\pi$
$762$	−4.05995e9			−0.332413
$763$	9.78229e9	−	6.21557e9i	0.797268	−	0.506576i
$764$	3.97143e9			0.322196
$765$	−1.78318e8	−	3.08856e8i	−0.0144006	−	0.0249426i
$766$	7.13783e9	−	1.23631e10i	0.573807	−	0.993863i
$767$	−6.25136e9	+	1.08277e10i	−0.500254	+	0.866466i
$768$	−2.26492e8	−	3.92296e8i	−0.0180422	−	0.0312500i
$769$	1.48792e10			1.17988			0.589940	−	0.807447i	$-0.299151\pi$
$769$	1.48792e10			1.17988			0.589940	+	0.807447i	$0.299151\pi$
$770$	−9.61504e7	−	2.26434e9i	−0.00758986	−	0.178741i
$771$	1.29664e10			1.01890
$772$	−1.37913e8	−	2.38873e8i	−0.0107881	−	0.0186855i
$773$	2.26257e9	−	3.91888e9i	0.176187	−	0.305164i	−0.764385	−	0.644761i	$-0.776957\pi$
$773$	2.26257e9	−	3.91888e9i	0.176187	−	0.305164i	0.940571	+	0.339596i	$0.110290\pi$
$774$	6.30404e8	−	1.09189e9i	0.0488681	−	0.0846420i
$775$	1.50566e9	+	2.60788e9i	0.116191	+	0.201248i
$776$	4.52691e8			0.0347765
$777$	−2.02181e9	−	1.05557e9i	−0.154621	−	0.0807256i
$778$	8.76641e9			0.667411
$779$	6.91048e9	+	1.19693e10i	0.523753	+	0.907168i
$780$	7.44101e8	−	1.28882e9i	0.0561437	−	0.0972437i
$781$	1.55533e9	−	2.69391e9i	0.116827	−	0.202351i
$782$	−5.54344e8	−	9.60152e8i	−0.0414530	−	0.0717987i
$783$	3.26038e9			0.242718
$784$	1.43290e9	−	3.05377e9i	0.106196	−	0.226324i
$785$	−8.70696e9			−0.642426
$786$	4.53164e9	+	7.84904e9i	0.332872	+	0.576551i
$787$	−1.87857e9	+	3.25378e9i	−0.137378	+	0.237945i	−0.926503	−	0.376287i	$-0.877201\pi$
$787$	−1.87857e9	+	3.25378e9i	−0.137378	+	0.237945i	0.789125	+	0.614232i	$0.210534\pi$
$788$	−1.92979e9	+	3.34250e9i	−0.140497	+	0.243349i
$789$	1.05293e8	+	1.82373e8i	0.00763185	+	0.0132188i
$790$	4.61166e9			0.332784
$791$	−1.40981e10	−	7.36042e9i	−1.01284	−	0.528792i
$792$	9.32154e8			0.0666730
$793$	7.96018e9	+	1.37874e10i	0.566848	+	0.981809i
$794$	−2.33592e9	+	4.04594e9i	−0.165610	+	0.286845i
$795$	2.31968e9	−	4.01780e9i	0.163736	−	0.283598i
$796$	−5.10722e9	−	8.84596e9i	−0.358912	−	0.621654i
$797$	1.04418e10			0.730588			0.365294	−	0.930892i	$-0.380968\pi$
$797$	1.04418e10			0.730588			0.365294	+	0.930892i	$0.380968\pi$
$798$	3.61200e8	+	8.50627e9i	0.0251616	+	0.592555i
$799$	−3.89212e9			−0.269943
$800$	−2.56000e8	−	4.43405e8i	−0.0176777	−	0.0306186i
$801$	2.01853e9	−	3.49620e9i	0.138778	−	0.240371i
$802$	5.65478e9	−	9.79436e9i	0.387084	−	0.670449i
$803$	−5.13506e9	−	8.89418e9i	−0.349978	−	0.606180i
$804$	−2.95358e9			−0.200425
$805$	3.39035e9	−	2.15419e9i	0.229065	−	0.145546i
$806$	−1.06227e10			−0.714601
$807$	−3.96093e9	−	6.86053e9i	−0.265302	−	0.459516i
$808$	1.13681e9	−	1.96901e9i	0.0758137	−	0.131313i
$809$	−1.29712e10	+	2.24668e10i	−0.861313	+	1.49184i	0.00934827	+	0.999956i	$0.497024\pi$
$809$	−1.29712e10	+	2.24668e10i	−0.861313	+	1.49184i	−0.870662	+	0.491882i	$0.836309\pi$
$810$	2.65721e8	+	4.60241e8i	0.0175682	+	0.0304290i
$811$	1.26120e10			0.830256			0.415128	−	0.909763i	$-0.363737\pi$
$811$	1.26120e10			0.830256			0.415128	+	0.909763i	$0.363737\pi$
$812$	8.12007e9	−	5.15941e9i	0.532248	−	0.338185i
$813$	1.54057e9			0.100546
$814$	−9.29879e8	−	1.61060e9i	−0.0604284	−	0.104665i
$815$	2.15246e9	−	3.72817e9i	0.139278	−	0.241237i
$816$	2.16412e8	−	3.74837e8i	0.0139433	−	0.0241506i
$817$	4.69499e9	+	8.13196e9i	0.301202	+	0.521697i
$818$	1.63676e10			1.04556
$819$	1.93373e8	+	4.55394e9i	0.0122999	+	0.289664i
$820$	2.54563e9			0.161230
$821$	4.72942e9	+	8.19160e9i	0.298268	+	0.516616i	0.975740	−	0.218933i	$-0.0702577\pi$
$821$	4.72942e9	+	8.19160e9i	0.298268	+	0.516616i	−0.677472	+	0.735549i	$0.736924\pi$
$822$	1.69485e9	−	2.93557e9i	0.106434	−	0.184349i
$823$	−6.48480e8	+	1.12320e9i	−0.0405506	+	0.0702357i	−0.885588	−	0.464471i	$-0.846245\pi$
$823$	−6.48480e8	+	1.12320e9i	−0.0405506	+	0.0702357i	0.845038	+	0.534707i	$0.179578\pi$
$824$	−1.02110e9	−	1.76859e9i	−0.0635803	−	0.110124i
$825$	1.05360e9			0.0653259
$826$	−1.16785e10	−	6.09721e9i	−0.721037	−	0.376445i
$827$	−2.74361e9			−0.168676			−0.0843380	−	0.996437i	$-0.526878\pi$
$827$	−2.74361e9			−0.168676			−0.0843380	+	0.996437i	$0.526878\pi$
$828$	8.26054e8	+	1.43077e9i	0.0505711	+	0.0875917i
$829$	5.28560e9	−	9.15492e9i	0.322221	−	0.558102i	−0.658725	−	0.752383i	$-0.728904\pi$
$829$	5.28560e9	−	9.15492e9i	0.322221	−	0.558102i	0.980946	+	0.194281i	$0.0622374\pi$
$830$	4.23748e9	−	7.33953e9i	0.257238	−	0.445548i
$831$	1.72738e9	+	2.99191e9i	0.104420	+	0.180861i
$832$	1.80613e9			0.108722
$833$	3.21150e9	−	2.73232e8i	0.192509	−	0.0163785i
$834$	9.88829e9			0.590256
$835$	−5.12715e9	−	8.88048e9i	−0.304771	−	0.527878i
$836$	−3.47115e9	+	6.01221e9i	−0.205472	+	0.355887i
$837$	1.89670e9	−	3.28518e9i	0.111805	−	0.193651i
$838$	−1.22916e9	−	2.12896e9i	−0.0721527	−	0.124972i
$839$	1.32550e10			0.774842			0.387421	−	0.921903i	$-0.373366\pi$
$839$	1.32550e10			0.774842			0.387421	+	0.921903i	$0.373366\pi$
$840$	1.39010e9	+	7.25753e8i	0.0809222	+	0.0422485i
$841$	1.01882e10			0.590626
$842$	−1.08157e10	−	1.87333e10i	−0.624397	−	1.08149i
$843$	1.49264e9	−	2.58533e9i	0.0858140	−	0.148634i
$844$	4.02414e9	−	6.97002e9i	0.230396	−	0.399058i
$845$	−9.54926e8	−	1.65398e9i	−0.0544467	−	0.0943044i
$846$	5.79983e9			0.329321
$847$	−5.10129e8	−	1.20135e10i	−0.0288462	−	0.679327i
$848$	5.63046e9			0.317072
$849$	−1.06665e9	−	1.84749e9i	−0.0598199	−	0.103611i
$850$	2.44607e8	−	4.23671e8i	0.0136616	−	0.0236626i
$851$	1.64808e9	−	2.85455e9i	0.0916693	−	0.158776i
$852$	1.07616e9	+	1.86396e9i	0.0596125	+	0.103252i
$853$	−2.62779e10			−1.44967			−0.724834	−	0.688923i	$-0.758084\pi$
$853$	−2.62779e10			−1.44967			−0.724834	+	0.688923i	$0.758084\pi$
$854$	−1.41591e10	+	8.99659e9i	−0.777919	+	0.494282i
$855$	−3.95795e9			−0.216566
$856$	2.82233e9	+	4.88841e9i	0.153797	+	0.266385i
$857$	1.56837e9	−	2.71649e9i	0.0851167	−	0.147426i	−0.820324	−	0.571899i	$-0.806207\pi$
$857$	1.56837e9	−	2.71649e9i	0.0851167	−	0.147426i	0.905441	+	0.424472i	$0.139540\pi$
$858$	−1.85833e9	+	3.21872e9i	−0.100442	+	0.173971i
$859$	6.12799e9	+	1.06140e10i	0.329870	+	0.571351i	0.982486	−	0.186338i	$-0.0596619\pi$
$859$	6.12799e9	+	1.06140e10i	0.329870	+	0.571351i	−0.652616	+	0.757689i	$0.726329\pi$
$860$	1.72950e9			0.0927207
$861$	−6.58069e9	+	4.18131e9i	−0.351366	+	0.223255i
$862$	−1.42309e10			−0.756758
$863$	−1.02377e10	−	1.77322e10i	−0.542205	−	0.939126i	−0.998777	−	0.0494398i	$-0.984256\pi$
$863$	−1.02377e10	−	1.77322e10i	−0.542205	−	0.939126i	0.456572	−	0.889686i	$-0.349077\pi$
$864$	−3.22486e8	+	5.58563e8i	−0.0170103	+	0.0294628i
$865$	−4.56199e9	+	7.90159e9i	−0.239661	+	0.415105i
$866$	−3.48776e9	−	6.04098e9i	−0.182488	−	0.316079i
$867$	−1.06656e10			−0.555799
$868$	−4.74874e8	−	1.11833e10i	−0.0246467	−	0.580431i
$869$	−1.15172e10			−0.595359
$870$	2.23620e9	+	3.87321e9i	0.115131	+	0.199413i
$871$	5.88820e9	−	1.01987e10i	0.301939	−	0.522974i
$872$	−3.26947e9	+	5.66289e9i	−0.166982	+	0.289221i
$873$	−3.22277e8	−	5.58200e8i	−0.0163938	−	0.0283949i
$874$	−1.23042e10			−0.623396
$875$	1.57120e9	+	8.20304e8i	0.0792872	+	0.0413949i
$876$	7.10605e9			0.357161
$877$	1.12179e10	+	1.94300e10i	0.561583	+	0.972690i	0.997359	+	0.0726348i	$0.0231408\pi$
$877$	1.12179e10	+	1.94300e10i	0.561583	+	0.972690i	−0.435776	+	0.900055i	$0.643526\pi$
$878$	−1.56340e9	+	2.70790e9i	−0.0779544	+	0.135021i
$879$	−8.71930e9	+	1.51023e10i	−0.433032	+	0.750034i
$880$	6.39338e8	+	1.10737e9i	0.0316258	+	0.0547774i
$881$	−1.20844e10			−0.595400			−0.297700	−	0.954659i	$-0.596220\pi$
$881$	−1.20844e10			−0.595400			−0.297700	+	0.954659i	$0.596220\pi$
$882$	−4.78561e9	+	4.07155e8i	−0.234854	+	0.0199811i
$883$	−3.39014e10			−1.65713			−0.828563	−	0.559896i	$-0.810841\pi$
$883$	−3.39014e10			−1.65713			−0.828563	+	0.559896i	$0.810841\pi$
$884$	8.62872e8	+	1.49454e9i	0.0420111	+	0.0727653i
$885$	3.06225e9	−	5.30397e9i	0.148504	−	0.257217i
$886$	−6.59011e9	+	1.14144e10i	−0.318328	+	0.551360i
$887$	−1.74091e10	−	3.01535e10i	−0.837614	−	1.45079i	−0.891884	−	0.452264i	$-0.850617\pi$
$887$	−1.74091e10	−	3.01535e10i	−0.837614	−	1.45079i	0.0542703	−	0.998526i	$-0.482717\pi$
$888$	1.28680e9			0.0616687
$889$	1.51206e10	+	7.89427e9i	0.721792	+	0.376839i
$890$	5.53781e9			0.263314
$891$	−6.63614e8	−	1.14941e9i	−0.0314299	−	0.0544382i
$892$	−6.92843e9	+	1.20004e10i	−0.326857	+	0.566133i
$893$	−2.15974e10	+	3.74078e10i	−1.01490	+	1.75785i
$894$	1.86437e9	+	3.22918e9i	0.0872669	+	0.151151i
$895$	−7.23010e9			−0.337104
$896$	8.07404e7	+	1.90144e9i	0.00374984	+	0.0883088i
$897$	−6.58723e9			−0.304740
$898$	−1.40088e9	−	2.42640e9i	−0.0645556	−	0.111814i
$899$	1.59619e10	−	2.76468e10i	0.732699	−	1.26907i
$900$	−3.64500e8	+	6.31333e8i	−0.0166667	+	0.0288675i
$901$	2.68994e9	+	4.65911e9i	0.122520	+	0.212210i
$902$	−6.35748e9			−0.288444
$903$	−4.47093e9	+	2.84079e9i	−0.202065	+	0.128390i
$904$	8.97280e9			0.403960
$905$	−7.14118e9	−	1.23689e10i	−0.320258	−	0.554703i
$906$	−4.78426e9	+	8.28659e9i	−0.213730	+	0.370192i
$907$	9.41917e9	−	1.63145e10i	0.419167	−	0.726018i	−0.576689	−	0.816964i	$-0.695656\pi$
$907$	9.41917e9	−	1.63145e10i	0.419167	−	0.726018i	0.995856	+	0.0909453i	$0.0289889\pi$
$908$	5.99425e9	+	1.03823e10i	0.265726	+	0.460251i
$909$	−3.23724e9			−0.142956
$910$	−5.27729e9	+	3.35314e9i	−0.232149	+	0.147505i
$911$	3.81103e9			0.167004			0.0835021	−	0.996508i	$-0.473389\pi$
$911$	3.81103e9			0.167004			0.0835021	+	0.996508i	$0.473389\pi$
$912$	−2.40175e9	−	4.15994e9i	−0.104844	−	0.181596i
$913$	−1.05827e10	+	1.83298e10i	−0.460204	+	0.797096i
$914$	7.86527e9	−	1.36231e10i	0.340724	−	0.590150i
$915$	−3.89931e9	−	6.75381e9i	−0.168273	−	0.291457i
$916$	7.37262e9			0.316948
$917$	−1.61545e9	−	3.80438e10i	−0.0691831	−	1.62926i
$918$	−6.16268e8			−0.0262918
$919$	−1.49597e10	−	2.59110e10i	−0.635798	−	1.10123i	−0.986346	−	0.164689i	$-0.947338\pi$
$919$	−1.49597e10	−	2.59110e10i	−0.635798	−	1.10123i	0.350548	−	0.936545i	$-0.385995\pi$
$920$	−1.13313e9	+	1.96264e9i	−0.0479760	+	0.0830968i
$921$	−1.32829e10	+	2.30067e10i	−0.560255	+	0.970389i
$922$	−1.39161e10	−	2.41034e10i	−0.584735	−	1.01279i
$923$	−8.58164e9			−0.359223
$924$	−3.47165e9	−	1.81250e9i	−0.144772	−	0.0755835i
$925$	1.45444e9			0.0604227
$926$	−1.81991e9	−	3.15217e9i	−0.0753200	−	0.130458i
$927$	−1.45387e9	+	2.51817e9i	−0.0599441	+	0.103826i
$928$	−2.71392e9	+	4.70065e9i	−0.111475	+	0.193081i
$929$	5.41279e9	+	9.37522e9i	0.221496	+	0.383642i	0.955262	−	0.295760i	$-0.0955727\pi$
$929$	5.41279e9	+	9.37522e9i	0.221496	+	0.383642i	−0.733766	+	0.679402i	$0.762239\pi$
$930$	5.20357e9			0.212134
$931$	1.51946e10	−	3.23824e10i	0.617113	−	1.31518i
$932$	−3.93583e9			−0.159250
$933$	−1.20737e8	−	2.09122e8i	−0.00486692	−	0.00842975i
$934$	−3.52733e9	+	6.10951e9i	−0.141655	+	0.245354i
$935$	−6.10884e8	+	1.05808e9i	−0.0244409	+	0.0423330i
$936$	−1.28581e9	−	2.22708e9i	−0.0512519	−	0.0887710i
$937$	1.31959e9			0.0524023			0.0262011	−	0.999657i	$-0.491659\pi$
$937$	1.31959e9			0.0524023			0.0262011	+	0.999657i	$0.491659\pi$
$938$	1.10001e10	+	5.74301e9i	0.435197	+	0.227211i
$939$	−1.01341e9			−0.0399445
$940$	3.97794e9	+	6.88999e9i	0.156211	+	0.270565i
$941$	1.09052e10	−	1.88884e10i	0.426649	−	0.738977i	−0.569924	−	0.821697i	$-0.693027\pi$
$941$	1.09052e10	−	1.88884e10i	0.426649	−	0.738977i	0.996573	+	0.0827200i	$0.0263607\pi$
$942$	−7.52282e9	+	1.30299e10i	−0.293226	+	0.507882i
$943$	−5.63386e9	−	9.75813e9i	−0.218784	−	0.378944i
$944$	7.43286e9			0.287577
$945$	−9.47244e7	−	2.23076e9i	−0.00365133	−	0.0859888i
$946$	−4.31928e9			−0.165879
$947$	1.24162e9	+	2.15055e9i	0.0475078	+	0.0822859i	0.888801	−	0.458292i	$-0.151539\pi$
$947$	1.24162e9	+	2.15055e9i	0.0475078	+	0.0822859i	−0.841294	+	0.540578i	$0.818205\pi$
$948$	3.98448e9	−	6.90131e9i	0.151894	−	0.263089i
$949$	−1.41665e10	+	2.45371e10i	−0.538061	+	0.931948i
$950$	−2.71465e9	−	4.70191e9i	−0.102726	−	0.177927i
$951$	1.31750e10			0.496726
$952$	−1.53483e9	+	9.75218e8i	−0.0576543	+	0.0366330i
$953$	1.52662e10			0.571354			0.285677	−	0.958326i	$-0.407782\pi$
$953$	1.52662e10			0.571354			0.285677	+	0.958326i	$0.407782\pi$
$954$	−4.00840e9	−	6.94276e9i	−0.149469	−	0.258889i
$955$	3.87835e9	−	6.71749e9i	0.144090	−	0.249572i
$956$	−6.61248e9	+	1.14532e10i	−0.244772	+	0.423958i
$957$	−5.58472e9	−	9.67301e9i	−0.205973	−	0.356755i
$958$	−2.68338e9			−0.0986059
$959$	−1.20202e10	+	7.63749e9i	−0.440094	+	0.279631i
$960$	−8.84736e8			−0.0322749
$961$	−4.81513e9	−	8.34005e9i	−0.175015	−	0.303136i
$962$	−2.56534e9	+	4.44329e9i	−0.0929034	+	0.160913i
$963$	4.01851e9	−	6.96026e9i	0.145002	−	0.251150i
$964$	−3.20052e9	−	5.54347e9i	−0.115067	−	0.199302i
$965$	−5.38723e8			−0.0192983
$966$	−2.94473e8	−	6.93485e9i	−0.0105106	−	0.247524i
$967$	−2.94595e10			−1.04769			−0.523844	−	0.851814i	$-0.675503\pi$
$967$	−2.94595e10			−1.04769			−0.523844	+	0.851814i	$0.675503\pi$
$968$	3.39203e9	+	5.87516e9i	0.120197	+	0.208188i
$969$	2.29486e9	−	3.97481e9i	0.0810256	−	0.140340i
$970$	4.42081e8	−	7.65706e8i	0.0155525	−	0.0269377i
$971$	1.05953e10	+	1.83516e10i	0.371403	+	0.643289i	0.989782	−	0.142591i	$-0.0455434\pi$
$971$	1.05953e10	+	1.83516e10i	0.371403	+	0.643289i	−0.618378	+	0.785880i	$0.712210\pi$
$972$	9.18330e8			0.0320750
$973$	−3.68272e10	−	1.92270e10i	−1.28166	−	0.669141i
$974$	−3.30829e9			−0.114722
$975$	−1.45332e9	−	2.51723e9i	−0.0502164	−	0.0869774i
$976$	4.73232e9	−	8.19662e9i	0.162930	−	0.282202i
$977$	1.37105e9	−	2.37473e9i	0.0470351	−	0.0814672i	−0.841549	−	0.540180i	$-0.818356\pi$
$977$	1.37105e9	−	2.37473e9i	0.0470351	−	0.0814672i	0.888584	+	0.458713i	$0.151689\pi$
$978$	−3.71945e9	−	6.44227e9i	−0.127143	−	0.220218i
$979$	−1.38302e10			−0.471074
$980$	−3.76600e9	−	5.40588e9i	−0.127817	−	0.183474i
$981$	9.31033e9			0.314864
$982$	1.25830e10	+	2.17944e10i	0.424028	+	0.734438i
$983$	−8.54131e9	+	1.47940e10i	−0.286805	+	0.496761i	−0.973045	−	0.230614i	$-0.925927\pi$
$983$	−8.54131e9	+	1.47940e10i	−0.286805	+	0.496761i	0.686240	+	0.727375i	$0.259260\pi$
$984$	2.19942e9	−	3.80951e9i	0.0735912	−	0.127464i
$985$	3.76912e9	+	6.52831e9i	0.125665	+	0.217658i
$986$	−5.18627e9			−0.172300
$987$	−2.16005e10	−	1.12773e10i	−0.715077	−	0.373333i
$988$	1.91523e10			0.631789
$989$	−3.82765e9	−	6.62969e9i	−0.125819	−	0.217924i
$990$	9.10307e8	−	1.57670e9i	0.0298171	−	0.0516447i
$991$	−7.44419e9	+	1.28937e10i	−0.242974	+	0.420843i	−0.961560	−	0.274595i	$-0.911456\pi$
$991$	−7.44419e9	+	1.28937e10i	−0.242974	+	0.420843i	0.718586	+	0.695438i	$0.244790\pi$
$992$	3.15760e9	+	5.46913e9i	0.102699	+	0.177880i
$993$	7.19088e9			0.233056
$994$	−3.83630e8	−	9.03450e9i	−0.0123897	−	0.291778i
$995$	−1.99501e10			−0.642042
$996$	−7.32236e9	−	1.26827e10i	−0.234825	−	0.406728i
$997$	−7.71555e9	+	1.33637e10i	−0.246566	+	0.427065i	−0.962571	−	0.271030i	$-0.912636\pi$
$997$	−7.71555e9	+	1.33637e10i	−0.246566	+	0.427065i	0.716005	+	0.698096i	$0.245969\pi$
$998$	6.96712e9	−	1.20674e10i	0.221869	−	0.384288i
$999$	−9.16089e8	−	1.58671e9i	−0.0290709	−	0.0503523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.8.i.b.151.1	yes	4
7.2	even	3	inner	210.8.i.b.121.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.8.i.b.121.1	✓	4	7.2	even	3	inner
210.8.i.b.151.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	210.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(62.5000 + 108.253i) q^{5} +216.000 q^{6} +(-804.454 - 419.996i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(62.5000 + 108.253i) q^{5} +216.000 q^{6} +(-804.454 - 419.996i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(500.000 - 866.025i) q^{10} +(-1248.71 + 2162.82i) q^{11} +(-864.000 - 1496.49i) q^{12} +6889.83 q^{13} +(308.000 + 7253.41i) q^{14} -3375.00 q^{15} +(-2048.00 - 3547.24i) q^{16} +(1956.85 - 3389.37i) q^{17} +(-2916.00 + 5050.66i) q^{18} +(-21717.2 - 37615.2i) q^{19} -8000.00 q^{20} +(20680.8 - 13140.4i) q^{21} +19979.3 q^{22} +(17705.2 + 30666.3i) q^{23} +(-6912.00 + 11971.9i) q^{24} +(-7812.50 + 13531.6i) q^{25} +(-27559.3 - 47734.1i) q^{26} +19683.0 q^{27} +(49021.1 - 31147.5i) q^{28} +165644. q^{29} +(13500.0 + 23382.7i) q^{30} +(96362.4 - 166905. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-33715.1 - 58396.2i) q^{33} -31309.7 q^{34} +(-4812.50 - 113334. i) q^{35} +46656.0 q^{36} +(-46542.1 - 80613.3i) q^{37} +(-173737. + 300922. i) q^{38} +(-93012.7 + 161103. i) q^{39} +(32000.0 + 55425.6i) q^{40} -318203. q^{41} +(-173762. - 90719.1i) q^{42} -216188. q^{43} +(-79917.2 - 138421. i) q^{44} +(45562.5 - 78916.6i) q^{45} +(141642. - 245331. i) q^{46} +(-497242. - 861249. i) q^{47} +110592. q^{48} +(470750. + 675735. i) q^{49} +125000. q^{50} +(52835.0 + 91513.0i) q^{51} +(-220474. + 381873. i) q^{52} +(-687312. + 1.19046e6i) q^{53} +(-78732.0 - 136368. i) q^{54} -312177. q^{55} +(-411881. - 215038. i) q^{56} +1.17273e6 q^{57} +(-662578. - 1.14762e6i) q^{58} +(-907332. + 1.57155e6i) q^{59} +(108000. - 187061. i) q^{60} +(1.15535e6 + 2.00113e6i) q^{61} -1.54180e6 q^{62} +(28066.5 + 660967. i) q^{63} +262144. q^{64} +(430614. + 745846. i) q^{65} +(-269721. + 467170. i) q^{66} +(854623. - 1.48025e6i) q^{67} +(125239. + 216920. i) q^{68} -956081. q^{69} +(-765954. + 486680. i) q^{70} -1.24555e6 q^{71} +(-186624. - 323242. i) q^{72} +(-2.05615e6 + 3.56136e6i) q^{73} +(-372337. + 644907. i) q^{74} +(-210938. - 365354. i) q^{75} +2.77980e6 q^{76} +(1.91290e6 - 1.21544e6i) q^{77} +1.48820e6 q^{78} +(2.30583e6 + 3.99382e6i) q^{79} +(256000. - 443405. i) q^{80} +(-265720. + 460241. i) q^{81} +(1.27281e6 + 2.20458e6i) q^{82} +8.47496e6 q^{83} +(66528.0 + 1.56674e6i) q^{84} +489213. q^{85} +(864751. + 1.49779e6i) q^{86} +(-2.23620e6 + 3.87321e6i) q^{87} +(-639338. + 1.10737e6i) q^{88} +(2.76891e6 + 4.79589e6i) q^{89} -729000. q^{90} +(-5.54255e6 - 2.89370e6i) q^{91} -2.26627e6 q^{92} +(2.60179e6 + 4.50643e6i) q^{93} +(-3.97794e6 + 6.88999e6i) q^{94} +(2.71465e6 - 4.70191e6i) q^{95} +(-442368. - 766204. i) q^{96} +884161. q^{97} +(2.79863e6 - 5.96439e6i) q^{98} +1.82061e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 250 q^{5} + 864 q^{6} - 77 q^{7} + 2048 q^{8} - 1458 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 54 * q^3 - 128 * q^4 + 250 * q^5 + 864 * q^6 - 77 * q^7 + 2048 * q^8 - 1458 * q^9	\( 4 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 250 q^{5} + 864 q^{6} - 77 q^{7} + 2048 q^{8} - 1458 q^{9} + 2000 q^{10} + 5325 q^{11} - 3456 q^{12} - 13720 q^{13} + 1232 q^{14} - 13500 q^{15} - 8192 q^{16} - 21786 q^{17} - 11664 q^{18} - 44692 q^{19} - 32000 q^{20} - 2079 q^{21} - 85200 q^{22} + 46143 q^{23} - 27648 q^{24} - 31250 q^{25} + 54880 q^{26} + 78732 q^{27} - 4928 q^{28} + 481308 q^{29} + 54000 q^{30} + 341927 q^{31} - 65536 q^{32} + 143775 q^{33} + 348576 q^{34} - 19250 q^{35} + 186624 q^{36} - 258856 q^{37} - 357536 q^{38} + 185220 q^{39} + 128000 q^{40} - 641958 q^{41} - 16632 q^{42} - 1980190 q^{43} + 340800 q^{44} + 182250 q^{45} + 369144 q^{46} - 1722897 q^{47} + 442368 q^{48} + 1641157 q^{49} + 500000 q^{50} - 588222 q^{51} + 439040 q^{52} - 2994681 q^{53} - 314928 q^{54} + 1331250 q^{55} - 39424 q^{56} + 2413368 q^{57} - 1925232 q^{58} + 858450 q^{59} + 432000 q^{60} + 3920558 q^{61} - 5470832 q^{62} + 112266 q^{63} + 1048576 q^{64} - 857500 q^{65} + 1150200 q^{66} + 4109921 q^{67} - 1394304 q^{68} - 2491722 q^{69} + 77000 q^{70} - 12572220 q^{71} - 746496 q^{72} - 4115065 q^{73} - 2070848 q^{74} - 843750 q^{75} + 5720576 q^{76} + 16411353 q^{77} - 2963520 q^{78} + 1753115 q^{79} + 1024000 q^{80} - 1062882 q^{81} + 2567832 q^{82} + 31085664 q^{83} + 266112 q^{84} - 5446500 q^{85} + 7920760 q^{86} - 6497658 q^{87} + 2726400 q^{88} + 5883408 q^{89} - 2916000 q^{90} - 32148571 q^{91} - 5906304 q^{92} + 9232029 q^{93} - 13783176 q^{94} + 5586500 q^{95} - 1769472 q^{96} - 21519892 q^{97} + 13129256 q^{98} - 7763850 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 54 * q^3 - 128 * q^4 + 250 * q^5 + 864 * q^6 - 77 * q^7 + 2048 * q^8 - 1458 * q^9 + 2000 * q^10 + 5325 * q^11 - 3456 * q^12 - 13720 * q^13 + 1232 * q^14 - 13500 * q^15 - 8192 * q^16 - 21786 * q^17 - 11664 * q^18 - 44692 * q^19 - 32000 * q^20 - 2079 * q^21 - 85200 * q^22 + 46143 * q^23 - 27648 * q^24 - 31250 * q^25 + 54880 * q^26 + 78732 * q^27 - 4928 * q^28 + 481308 * q^29 + 54000 * q^30 + 341927 * q^31 - 65536 * q^32 + 143775 * q^33 + 348576 * q^34 - 19250 * q^35 + 186624 * q^36 - 258856 * q^37 - 357536 * q^38 + 185220 * q^39 + 128000 * q^40 - 641958 * q^41 - 16632 * q^42 - 1980190 * q^43 + 340800 * q^44 + 182250 * q^45 + 369144 * q^46 - 1722897 * q^47 + 442368 * q^48 + 1641157 * q^49 + 500000 * q^50 - 588222 * q^51 + 439040 * q^52 - 2994681 * q^53 - 314928 * q^54 + 1331250 * q^55 - 39424 * q^56 + 2413368 * q^57 - 1925232 * q^58 + 858450 * q^59 + 432000 * q^60 + 3920558 * q^61 - 5470832 * q^62 + 112266 * q^63 + 1048576 * q^64 - 857500 * q^65 + 1150200 * q^66 + 4109921 * q^67 - 1394304 * q^68 - 2491722 * q^69 + 77000 * q^70 - 12572220 * q^71 - 746496 * q^72 - 4115065 * q^73 - 2070848 * q^74 - 843750 * q^75 + 5720576 * q^76 + 16411353 * q^77 - 2963520 * q^78 + 1753115 * q^79 + 1024000 * q^80 - 1062882 * q^81 + 2567832 * q^82 + 31085664 * q^83 + 266112 * q^84 - 5446500 * q^85 + 7920760 * q^86 - 6497658 * q^87 + 2726400 * q^88 + 5883408 * q^89 - 2916000 * q^90 - 32148571 * q^91 - 5906304 * q^92 + 9232029 * q^93 - 13783176 * q^94 + 5586500 * q^95 - 1769472 * q^96 - 21519892 * q^97 + 13129256 * q^98 - 7763850 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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