LMFDB - Embedded newform 62.7.f.a.23.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	62.23
Dual form			62.7.f.a.27.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.74806 + 5.37999i) q^{2} +(-5.83008 + 1.89431i) q^{3} +(-25.8885 - 18.8091i) q^{4} +226.620 q^{5} -34.6772i q^{6} +(-495.718 - 360.160i) q^{7} +(146.448 - 106.400i) q^{8} +(-559.372 + 406.407i) q^{9} +(-396.147 + 1219.21i) q^{10} +(-299.900 + 412.777i) q^{11} +(186.563 + 60.6179i) q^{12} +(-412.581 + 134.056i) q^{13} +(2804.20 - 2037.37i) q^{14} +(-1321.21 + 429.289i) q^{15} +(316.433 + 973.882i) q^{16} +(-4855.40 - 6682.89i) q^{17} +(-1208.65 - 3719.84i) q^{18} +(1178.56 - 3627.24i) q^{19} +(-5866.87 - 4262.53i) q^{20} +(3572.33 + 1160.72i) q^{21} +(-1696.49 - 2335.02i) q^{22} +(-12236.5 - 16842.1i) q^{23} +(-652.247 + 897.741i) q^{24} +35731.7 q^{25} -2454.02i q^{26} +(5118.05 - 7044.39i) q^{27} +(6059.11 + 18648.0i) q^{28} +(14805.4 + 4810.56i) q^{29} -7858.54i q^{30} +(-25330.1 + 15680.8i) q^{31} -5792.62 q^{32} +(966.516 - 2974.63i) q^{33} +(44441.4 - 14439.9i) q^{34} +(-112340. - 81619.5i) q^{35} +22125.5 q^{36} -42131.6i q^{37} +(17454.3 + 12681.3i) q^{38} +(2151.44 - 1563.11i) q^{39} +(33188.0 - 24112.5i) q^{40} +(-4274.72 + 13156.2i) q^{41} +(-12489.3 + 17190.1i) q^{42} +(-27659.5 - 8987.12i) q^{43} +(15528.0 - 5045.34i) q^{44} +(-126765. + 92100.1i) q^{45} +(112000. - 36391.1i) q^{46} +(-4422.82 - 13612.0i) q^{47} +(-3689.67 - 5078.39i) q^{48} +(79665.2 + 245184. i) q^{49} +(-62461.3 + 192236. i) q^{50} +(40966.8 + 29764.2i) q^{51} +(13202.6 + 4289.78i) q^{52} +(-6002.64 - 8261.92i) q^{53} +(28952.1 + 39849.1i) q^{54} +(-67963.5 + 93543.7i) q^{55} -110918. q^{56} +23379.7i q^{57} +(-51761.5 + 71243.6i) q^{58} +(-54316.6 - 167169. i) q^{59} +(42278.9 + 13737.2i) q^{60} -81902.1i q^{61} +(-40083.8 - 163687. i) q^{62} +423662. q^{63} +(10125.9 - 31164.2i) q^{64} +(-93499.2 + 30379.7i) q^{65} +(14313.9 + 10399.7i) q^{66} -300763. q^{67} +264336. i q^{68} +(103244. + 75011.0i) q^{69} +(635489. - 461710. i) q^{70} +(-151597. + 110141. i) q^{71} +(-38676.8 + 119035. i) q^{72} +(-253935. + 349511. i) q^{73} +(226668. + 73648.8i) q^{74} +(-208319. + 67686.8i) q^{75} +(-98736.4 + 71736.2i) q^{76} +(297332. - 96608.9i) q^{77} +(4648.67 + 14307.1i) q^{78} +(58558.0 + 80598.2i) q^{79} +(71710.2 + 220701. i) q^{80} +(139265. - 428612. i) q^{81} +(-63307.9 - 45995.9i) q^{82} +(883483. + 287061. i) q^{83} +(-70650.3 - 97241.7i) q^{84} +(-1.10033e6 - 1.51448e6i) q^{85} +(96701.2 - 133098. i) q^{86} -95429.3 q^{87} +92359.9i q^{88} +(-569843. + 784322. i) q^{89} +(-273904. - 842991. i) q^{90} +(252805. + 82141.4i) q^{91} +666175. i q^{92} +(117973. - 139403. i) q^{93} +80963.9 q^{94} +(267086. - 822005. i) q^{95} +(33771.4 - 10973.0i) q^{96} +(-200620. - 145759. i) q^{97} -1.45835e6 q^{98} -352778. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) $ 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.74806	+	5.37999i	−0.218508	+	0.672499i
$2$	−1.74806	+	5.37999i	−0.218508	+	0.672499i
$3$	−5.83008	+	1.89431i	−0.215929	+	0.0701596i	−0.414984	−	0.909829i	$-0.636213\pi$
$3$	−5.83008	+	1.89431i	−0.215929	+	0.0701596i	0.199055	+	0.979988i	$0.436213\pi$
$4$	−25.8885	−	18.8091i	−0.404508	−	0.293893i
$5$	226.620			1.81296			0.906481	−	0.422248i	$-0.138759\pi$
$5$	226.620			1.81296			0.906481	+	0.422248i	$0.138759\pi$
$6$		−	34.6772i		−	0.160542i
$7$	−495.718	−	360.160i	−1.44524	−	1.05003i	−0.986914	−	0.161245i	$-0.948449\pi$
$7$	−495.718	−	360.160i	−1.44524	−	1.05003i	−0.458326	−	0.888784i	$-0.651551\pi$
$8$	146.448	−	106.400i	0.286031	−	0.207813i
$9$	−559.372	+	406.407i	−0.767314	+	0.557486i
$10$	−396.147	+	1219.21i	−0.396147	+	1.21921i
$11$	−299.900	+	412.777i	−0.225320	+	0.310126i	−0.906677	−	0.421825i	$-0.861390\pi$
$11$	−299.900	+	412.777i	−0.225320	+	0.310126i	0.681358	+	0.731950i	$0.261390\pi$
$12$	186.563	+	60.6179i	0.107964	+	0.0350798i
$13$	−412.581	+	134.056i	−0.187793	+	0.0610176i	−0.401404	−	0.915901i	$-0.631478\pi$
$13$	−412.581	+	134.056i	−0.187793	+	0.0610176i	0.213611	+	0.976919i	$0.431478\pi$
$14$	2804.20	−	2037.37i	1.02194	−	0.742483i
$15$	−1321.21	+	429.289i	−0.391471	+	0.127197i
$16$	316.433	+	973.882i	0.0772542	+	0.237764i
$17$	−4855.40	−	6682.89i	−0.988276	−	1.36025i	−0.932249	−	0.361816i	$-0.882157\pi$
$17$	−4855.40	−	6682.89i	−0.988276	−	1.36025i	−0.0560268	−	0.998429i	$-0.517843\pi$
$18$	−1208.65	−	3719.84i	−0.207244	−	0.637833i
$19$	1178.56	−	3627.24i	0.171827	−	0.528829i	−0.827647	−	0.561248i	$-0.810321\pi$
$19$	1178.56	−	3627.24i	0.171827	−	0.528829i	0.999474	+	0.0324195i	$0.0103213\pi$
$20$	−5866.87	−	4262.53i	−0.733358	−	0.532816i
$21$	3572.33	+	1160.72i	0.385739	+	0.125334i
$22$	−1696.49	−	2335.02i	−0.159325	−	0.219292i
$23$	−12236.5	−	16842.1i	−1.00571	−	1.38424i	−0.921755	−	0.387773i	$-0.873244\pi$
$23$	−12236.5	−	16842.1i	−1.00571	−	1.38424i	−0.0839563	−	0.996469i	$-0.526756\pi$
$24$	−652.247	+	897.741i	−0.0471822	+	0.0649407i
$25$	35731.7			2.28683
$26$		−	2454.02i		−	0.139623i
$27$	5118.05	−	7044.39i	0.260024	−	0.357892i
$28$	6059.11	+	18648.0i	0.276016	+	0.849491i
$29$	14805.4	+	4810.56i	0.607052	+	0.197243i	0.596383	−	0.802700i	$-0.296604\pi$
$29$	14805.4	+	4810.56i	0.607052	+	0.197243i	0.0106688	+	0.999943i	$0.496604\pi$
$30$		−	7858.54i		−	0.291057i
$31$	−25330.1	+	15680.8i	−0.850262	+	0.526360i
$31$	−25330.1	+	15680.8i	−0.850262	+	0.526360i
$32$	−5792.62			−0.176777
$33$	966.516	−	2974.63i	0.0268947	−	0.0827735i
$34$	44441.4	−	14439.9i	1.13071	−	0.367390i
$35$	−112340.	−	81619.5i	−2.62017	−	1.90366i
$36$	22125.5			0.474226
$37$		−	42131.6i		−	0.831770i	−0.909417	−	0.415885i	$-0.863472\pi$
$37$		−	42131.6i		−	0.831770i	0.909417	−	0.415885i	$-0.136528\pi$
$38$	17454.3	+	12681.3i	0.318091	+	0.231107i
$39$	2151.44	−	1563.11i	0.0362690	−	0.0263509i
$40$	33188.0	−	24112.5i	0.518563	−	0.376758i
$41$	−4274.72	+	13156.2i	−0.0620235	+	0.190889i	−0.977267	−	0.212013i	$-0.931998\pi$
$41$	−4274.72	+	13156.2i	−0.0620235	+	0.190889i	0.915243	+	0.402901i	$0.131998\pi$
$42$	−12489.3	+	17190.1i	−0.168574	+	0.232022i
$43$	−27659.5	−	8987.12i	−0.347888	−	0.113036i	0.129861	−	0.991532i	$-0.458547\pi$
$43$	−27659.5	−	8987.12i	−0.347888	−	0.113036i	−0.477749	+	0.878497i	$0.658547\pi$
$44$	15528.0	−	5045.34i	0.182287	−	0.0592288i
$45$	−126765.	+	92100.1i	−1.39111	+	1.01070i
$46$	112000.	−	36391.1i	1.15066	−	0.373871i
$47$	−4422.82	−	13612.0i	−0.0425996	−	0.131108i	0.927495	−	0.373836i	$-0.121958\pi$
$47$	−4422.82	−	13612.0i	−0.0425996	−	0.131108i	−0.970094	+	0.242728i	$0.921958\pi$
$48$	−3689.67	−	5078.39i	−0.0333629	−	0.0459200i
$49$	79665.2	+	245184.i	0.677143	+	2.08403i
$50$	−62461.3	+	192236.i	−0.499690	+	1.53789i
$51$	40966.8	+	29764.2i	0.308832	+	0.224379i
$52$	13202.6	+	4289.78i	0.0938964	+	0.0305088i
$53$	−6002.64	−	8261.92i	−0.0403194	−	0.0554949i	0.788381	−	0.615187i	$-0.210919\pi$
$53$	−6002.64	−	8261.92i	−0.0403194	−	0.0554949i	−0.828701	+	0.559692i	$0.810919\pi$
$54$	28952.1	+	39849.1i	0.183865	+	0.253068i
$55$	−67963.5	+	93543.7i	−0.408496	+	0.562246i
$56$	−110918.			−0.631593
$57$			23379.7i			0.126245i
$58$	−51761.5	+	71243.6i	−0.265291	+	0.365142i
$59$	−54316.6	−	167169.i	−0.264470	−	0.813955i	−0.991815	−	0.127683i	$-0.959246\pi$
$59$	−54316.6	−	167169.i	−0.264470	−	0.813955i	0.727345	−	0.686272i	$-0.240754\pi$
$60$	42278.9	+	13737.2i	0.195735	+	0.0635983i
$61$		−	81902.1i		−	0.360833i	−0.983590	−	0.180416i	$-0.942256\pi$
$61$		−	81902.1i		−	0.360833i	0.983590	−	0.180416i	$-0.0577445\pi$
$62$	−40083.8	−	163687.i	−0.168188	−	0.686814i
$63$	423662.			1.69433
$64$	10125.9	−	31164.2i	0.0386271	−	0.118882i
$65$	−93499.2	+	30379.7i	−0.340461	+	0.110623i
$66$	14313.9	+	10399.7i	0.0497883	+	0.0361733i
$67$	−300763.			−0.999999			−0.499999	−	0.866026i	$-0.666666\pi$
$67$	−300763.			−0.999999			−0.499999	+	0.866026i	$0.666666\pi$
$68$			264336.i			0.840678i
$69$	103244.	+	75011.0i	0.314280	+	0.228338i
$70$	635489.	−	461710.i	1.85274	−	1.34609i
$71$	−151597.	+	110141.i	−0.423560	+	0.307734i	−0.779068	−	0.626939i	$-0.784308\pi$
$71$	−151597.	+	110141.i	−0.423560	+	0.307734i	0.355509	+	0.934673i	$0.384308\pi$
$72$	−38676.8	+	119035.i	−0.103622	+	0.318916i
$73$	−253935.	+	349511.i	−0.652760	+	0.898447i	−0.999215	−	0.0396196i	$-0.987385\pi$
$73$	−253935.	+	349511.i	−0.652760	+	0.898447i	0.346455	+	0.938067i	$0.387385\pi$
$74$	226668.	+	73648.8i	0.559364	+	0.181748i
$75$	−208319.	+	67686.8i	−0.493792	+	0.160443i
$76$	−98736.4	+	71736.2i	−0.224924	+	0.163417i
$77$	297332.	−	96608.9i	0.651282	−	0.211614i
$78$	4648.67	+	14307.1i	0.00979591	+	0.0301487i
$79$	58558.0	+	80598.2i	0.118770	+	0.163472i	0.864262	−	0.503042i	$-0.167786\pi$
$79$	58558.0	+	80598.2i	0.118770	+	0.163472i	−0.745493	+	0.666514i	$0.767786\pi$
$80$	71710.2	+	220701.i	0.140059	+	0.431057i
$81$	139265.	−	428612.i	0.262051	−	0.806509i
$82$	−63307.9	−	45995.9i	−0.114820	−	0.0834214i
$83$	883483.	+	287061.i	1.54513	+	0.502042i	0.952785	−	0.303645i	$-0.0982038\pi$
$83$	883483.	+	287061.i	1.54513	+	0.502042i	0.592341	+	0.805687i	$0.298204\pi$
$84$	−70650.3	−	97241.7i	−0.119200	−	0.164065i
$85$	−1.10033e6	−	1.51448e6i	−1.79171	−	2.46607i
$86$	96701.2	−	133098.i	0.152033	−	0.209255i
$87$	−95429.3			−0.144919
$88$			92359.9i			0.135530i
$89$	−569843.	+	784322.i	−0.808324	+	1.11256i	0.183256	+	0.983065i	$0.441336\pi$
$89$	−569843.	+	784322.i	−0.808324	+	1.11256i	−0.991580	+	0.129497i	$0.958664\pi$
$90$	−273904.	−	842991.i	−0.375726	−	1.15637i
$91$	252805.	+	82141.4i	0.335476	+	0.109003i
$92$			666175.i			0.855509i
$93$	117973.	−	139403.i	0.146667	−	0.173310i
$94$	80963.9			0.0974783
$95$	267086.	−	822005.i	0.311516	−	0.958746i
$96$	33771.4	−	10973.0i	0.0381712	−	0.0124026i
$97$	−200620.	−	145759.i	−0.219815	−	0.159705i	0.472428	−	0.881369i	$-0.343378\pi$
$97$	−200620.	−	145759.i	−0.219815	−	0.159705i	−0.692244	+	0.721664i	$0.743378\pi$
$98$	−1.45835e6			−1.54947
$99$		−	352778.i		−	0.363576i
$100$	−925041.	−	672082.i	−0.925041	−	0.672082i
$101$	1.54585e6	−	1.12313e6i	1.50039	−	1.09010i	0.530165	−	0.847895i	$-0.322130\pi$
$101$	1.54585e6	−	1.12313e6i	1.50039	−	1.09010i	0.970226	−	0.242203i	$-0.0778699\pi$
$102$	−231743.	+	168371.i	−0.218377	+	0.158660i
$103$	154812.	−	476463.i	0.141675	−	0.436031i	−0.854893	−	0.518804i	$-0.826378\pi$
$103$	154812.	−	476463.i	0.141675	−	0.436031i	0.996568	+	0.0827726i	$0.0263775\pi$
$104$	−46158.0	+	63531.0i	−0.0410342	+	0.0564788i
$105$	809562.	+	263043.i	0.699330	+	0.227226i
$106$	54942.0	−	17851.7i	0.0461304	−	0.0149887i
$107$	−1.06237e6	+	771860.i	−0.867214	+	0.630068i	−0.929838	−	0.367969i	$-0.880053\pi$
$107$	−1.06237e6	+	771860.i	−0.867214	+	0.630068i	0.0626238	+	0.998037i	$0.480053\pi$
$108$	−264998.	+	86103.0i	−0.210364	+	0.0683513i
$109$	493843.	+	1.51989e6i	0.381337	+	1.17364i	0.939103	+	0.343637i	$0.111659\pi$
$109$	493843.	+	1.51989e6i	0.381337	+	1.17364i	−0.557765	+	0.829999i	$0.688341\pi$
$110$	−384459.	−	529163.i	−0.288850	−	0.397568i
$111$	79810.3	+	245631.i	0.0583566	+	0.179603i
$112$	193892.	−	596737.i	0.138008	−	0.424746i
$113$	575027.	+	417782.i	0.398523	+	0.289544i	0.768939	−	0.639322i	$-0.220785\pi$
$113$	575027.	+	417782.i	0.398523	+	0.289544i	−0.370416	+	0.928866i	$0.620785\pi$
$114$	−125782.	−	40869.1i	−0.0848994	−	0.0275855i
$115$	−2.77303e6	−	3.81675e6i	−1.82332	−	2.50958i
$116$	−292807.	−	403015.i	−0.187589	−	0.258195i
$117$	176305.	−	242663.i	0.110080	−	0.151512i
$118$	994318.			0.605173
$119$			5.06155e6i			3.00360i
$120$	−147812.	+	203446.i	−0.0855395	+	0.117735i
$121$	466997.	+	1.43727e6i	0.263608	+	0.811302i
$122$	440632.	+	143170.i	0.242659	+	0.0788448i
$123$		−	84799.6i		−	0.0455700i
$124$	950703.	+	70484.8i	0.498631	+	0.0369684i
$125$	4.55658e6			2.33297
$126$	−740589.	+	2.27930e6i	−0.370225	+	1.13943i
$127$	2.63548e6	−	856318.i	1.28661	−	0.418046i	0.415708	−	0.909498i	$-0.363534\pi$
$127$	2.63548e6	−	856318.i	1.28661	−	0.418046i	0.870905	+	0.491452i	$0.163534\pi$
$128$	149962.	+	108954.i	0.0715077	+	0.0519534i
$129$	178282.			0.0830496
$130$		−	556130.i		−	0.253132i
$131$	−2.20982e6	−	1.60553e6i	−0.982975	−	0.714173i	−0.0246035	−	0.999697i	$-0.507832\pi$
$131$	−2.20982e6	−	1.60553e6i	−0.982975	−	0.714173i	−0.958372	+	0.285524i	$0.907832\pi$
$132$	−80971.9	+	58829.5i	−0.0352057	+	0.0255784i
$133$	−1.89062e6	+	1.37362e6i	−0.803617	+	0.583862i
$134$	525752.	−	1.61810e6i	0.218508	−	0.672498i
$135$	1.15985e6	−	1.59640e6i	0.471413	−	0.648844i
$136$	−1.42212e6	−	462076.i	−0.565355	−	0.183695i
$137$	−2.79517e6	+	908205.i	−1.08704	+	0.353201i	−0.797103	−	0.603844i	$-0.793635\pi$
$137$	−2.79517e6	+	908205.i	−1.08704	+	0.353201i	−0.289939	+	0.957045i	$0.593635\pi$
$138$	−584035.	+	424327.i	−0.222230	+	0.161459i
$139$	2.37930e6	−	773082.i	0.885942	−	0.287860i	0.169520	−	0.985527i	$-0.445778\pi$
$139$	2.37930e6	−	773082.i	0.885942	−	0.287860i	0.716422	+	0.697667i	$0.245778\pi$
$140$	1.37312e6	+	4.22602e6i	0.500407	+	1.54009i
$141$	51570.8	+	70981.1i	0.0183970	+	0.0253213i
$142$	−327559.	−	1.00812e6i	−0.114400	−	0.352085i
$143$	68398.0	−	210507.i	0.0233903	−	0.0719879i
$144$	−572797.	−	416161.i	−0.191829	−	0.139372i
$145$	3.35520e6	+	1.09017e6i	1.10056	+	0.357594i
$146$	−1.43647e6	−	1.97713e6i	−0.461571	−	0.635298i
$147$	−928910.	−	1.27853e6i	−0.292430	−	0.402495i
$148$	−792459.	+	1.09073e6i	−0.244451	+	0.336458i
$149$	−2.96769e6			−0.897138			−0.448569	−	0.893748i	$-0.648066\pi$
$149$	−2.96769e6			−0.897138			−0.448569	+	0.893748i	$0.648066\pi$
$150$		−	1.23907e6i		−	0.367133i
$151$	−338692.	+	466170.i	−0.0983726	+	0.135398i	−0.855366	−	0.518025i	$-0.826668\pi$
$151$	−338692.	+	466170.i	−0.0983726	+	0.135398i	0.756993	+	0.653423i	$0.226668\pi$
$152$	−213342.	−	656600.i	−0.0607500	−	0.186969i
$153$	5.43195e6	+	1.76495e6i	1.51664	+	0.492785i
$154$			1.76852e6i			0.484226i
$155$	−5.74032e6	+	3.55359e6i	−1.54149	+	0.954271i
$156$	−85098.4			−0.0224154
$157$	15978.5	−	49176.6i	0.00412892	−	0.0127075i	−0.948971	−	0.315364i	$-0.897873\pi$
$157$	15978.5	−	49176.6i	0.00412892	−	0.0127075i	0.953100	+	0.302656i	$0.0978734\pi$
$158$	−535980.	+	174151.i	−0.135887	+	0.0441523i
$159$	50646.5	+	36796.8i	0.0125996	+	0.00915417i
$160$	−1.31272e6			−0.320489
$161$			1.27560e7i			3.05659i
$162$	2.06248e6	+	1.49848e6i	0.485116	+	0.352457i
$163$	441921.	−	321074.i	0.102043	−	0.0741383i	−0.535594	−	0.844476i	$-0.679912\pi$
$163$	441921.	−	321074.i	0.102043	−	0.0741383i	0.637637	+	0.770337i	$0.279912\pi$
$164$	358124.	−	260192.i	0.0811898	−	0.0589879i
$165$	219032.	−	674111.i	0.0487591	−	0.150065i
$166$	−3.08877e6	+	4.25133e6i	−0.675245	+	0.929395i
$167$	5.57070e6	+	1.81003e6i	1.19608	+	0.388630i	0.838318	−	0.545182i	$-0.183539\pi$
$167$	5.57070e6	+	1.81003e6i	1.19608	+	0.388630i	0.357763	+	0.933812i	$0.383539\pi$
$168$	646661.	−	210113.i	0.136379	−	0.0443123i
$169$	−3.75272e6	+	2.72651e6i	−0.777474	+	0.564868i
$170$	1.00713e7	−	3.27237e6i	2.04993	−	0.666063i
$171$	814883.	+	2.50795e6i	0.162970	+	0.501569i
$172$	547025.	+	752915.i	0.107503	+	0.147966i
$173$	−1.62362e6	−	4.99698e6i	−0.313578	−	0.965094i	−0.976336	−	0.216260i	$-0.930614\pi$
$173$	−1.62362e6	−	4.99698e6i	−0.313578	−	0.965094i	0.662758	−	0.748834i	$-0.269386\pi$
$174$	166817.	−	513409.i	0.0316659	−	0.0974575i
$175$	−1.77128e7	−	1.28691e7i	−3.30502	−	2.40124i
$176$	−496895.	−	161451.i	−0.0911437	−	0.0296144i
$177$	633341.	+	871719.i	0.114214	+	0.157201i
$178$	−3.22352e6	−	4.43680e6i	−0.571571	−	0.786701i
$179$	4.53875e6	−	6.24706e6i	0.791366	−	1.08922i	−0.202570	−	0.979268i	$-0.564930\pi$
$179$	4.53875e6	−	6.24706e6i	0.791366	−	1.08922i	0.993937	−	0.109954i	$-0.0350705\pi$
$180$	5.01408e6			0.859754
$181$		−	1.02535e7i		−	1.72917i	−0.502490	−	0.864583i	$-0.667583\pi$
$181$		−	1.02535e7i		−	1.72917i	0.502490	−	0.864583i	$-0.332417\pi$
$182$	−883839.	+	1.21650e6i	−0.146608	+	0.201789i
$183$	155148.	+	477496.i	0.0253159	+	0.0779142i
$184$	−3.58401e6	−	1.16452e6i	−0.575329	−	0.186936i
$185$		−	9.54788e6i		−	1.50797i
$186$	543765.	+	878377.i	0.0845031	+	0.136503i
$187$	4.21468e6			0.644525
$188$	−141530.	+	435585.i	−0.0212998	+	0.0655540i
$189$	−5.07421e6	+	1.64871e6i	−0.751594	+	0.244208i
$190$	3.95549e6	+	2.87383e6i	0.576687	+	0.418987i
$191$	−8.39042e6			−1.20416			−0.602079	−	0.798436i	$-0.705661\pi$
$191$	−8.39042e6			−1.20416			−0.602079	+	0.798436i	$0.705661\pi$
$192$			200872.i			0.0283801i
$193$	5.57713e6	+	4.05202e6i	0.775781	+	0.563638i	0.903710	−	0.428146i	$-0.140833\pi$
$193$	5.57713e6	+	4.05202e6i	0.775781	+	0.563638i	−0.127929	+	0.991783i	$0.540833\pi$
$194$	1.13488e6	−	824536.i	0.155433	−	0.112929i
$195$	487559.	−	354233.i	0.0657542	−	0.0477732i
$196$	2.54929e6	−	7.84590e6i	0.338572	−	1.04202i
$197$	2.79805e6	−	3.85119e6i	0.365980	−	0.503728i	−0.585823	−	0.810439i	$-0.699229\pi$
$197$	2.79805e6	−	3.85119e6i	0.365980	−	0.503728i	0.951803	+	0.306711i	$0.0992286\pi$
$198$	1.89794e6	+	616678.i	0.244505	+	0.0794444i
$199$	−6.73683e6	+	2.18893e6i	−0.854863	+	0.277762i	−0.703481	−	0.710714i	$-0.748372\pi$
$199$	−6.73683e6	+	2.18893e6i	−0.854863	+	0.277762i	−0.151382	+	0.988475i	$0.548372\pi$
$200$	5.23282e6	−	3.80187e6i	0.654103	−	0.475234i
$201$	1.75347e6	−	569737.i	0.215929	−	0.0701595i
$202$	3.34017e6	+	1.02800e7i	0.405242	+	1.24721i
$203$	−5.60672e6	−	7.71699e6i	−0.670225	−	0.922486i
$204$	−500734.	−	1.54110e6i	−0.0589816	−	0.181527i
$205$	−968738.	+	2.98147e6i	−0.112446	+	0.346074i
$206$	2.29274e6	+	1.66578e6i	0.262273	+	0.190553i
$207$	1.36895e7	+	4.44799e6i	1.54339	+	0.501479i
$208$	−261109.	−	359385.i	−0.0290156	−	0.0399365i
$209$	1.14379e6	+	1.57429e6i	0.125287	+	0.172443i
$210$	−2.83033e6	+	3.89562e6i	−0.305618	+	0.420648i
$211$	−6.01128e6			−0.639911			−0.319955	−	0.947433i	$-0.603668\pi$
$211$	−6.01128e6			−0.639911			−0.319955	+	0.947433i	$0.603668\pi$
$212$			326793.i			0.0342978i
$213$	675179.	−	929304.i	0.0698683	−	0.0961655i
$214$	−2.29550e6	−	7.06482e6i	−0.234227	−	0.720875i
$215$	−6.26820e6	−	2.03666e6i	−0.630707	−	0.204929i
$216$		−	1.57620e6i		−	0.156405i
$217$	1.82042e7	+	1.34965e6i	1.78153	+	0.132082i
$218$	−9.04027e6			−0.872593
$219$	818378.	−	2.51871e6i	0.0779151	−	0.239798i
$220$	3.51895e6	−	1.14338e6i	0.330480	−	0.107379i
$221$	2.89912e6	+	2.10634e6i	0.268590	+	0.195142i
$222$	−1.46101e6			−0.133534
$223$		−	1.74632e7i		−	1.57474i	−0.616478	−	0.787372i	$-0.711441\pi$
$223$		−	1.74632e7i		−	1.57474i	0.616478	−	0.787372i	$-0.288559\pi$
$224$	2.87150e6	+	2.08627e6i	0.255485	+	0.185621i
$225$	−1.99873e7	+	1.45216e7i	−1.75472	+	1.27488i
$226$	−3.25285e6	+	2.36333e6i	−0.281798	+	0.204738i
$227$	−3.43145e6	+	1.05609e7i	−0.293359	+	0.902867i	0.690408	+	0.723420i	$0.257431\pi$
$227$	−3.43145e6	+	1.05609e7i	−0.293359	+	0.902867i	−0.983768	+	0.179447i	$0.942569\pi$
$228$	439751.	−	605265.i	0.0371024	−	0.0510671i
$229$	−8.96490e6	−	2.91287e6i	−0.746516	−	0.242558i	−0.0890343	−	0.996029i	$-0.528378\pi$
$229$	−8.96490e6	−	2.91287e6i	−0.746516	−	0.242558i	−0.657481	+	0.753471i	$0.728378\pi$
$230$	2.53815e7	−	8.24696e6i	2.08610	−	0.677814i
$231$	−1.55046e6	+	1.12648e6i	−0.125784	+	0.0913874i
$232$	2.68006e6	−	870805.i	0.214625	−	0.0697360i
$233$	−1.39792e6	−	4.30234e6i	−0.110513	−	0.340124i	0.880472	−	0.474099i	$-0.157226\pi$
$233$	−1.39792e6	−	4.30234e6i	−0.110513	−	0.340124i	−0.990985	+	0.133975i	$0.957226\pi$
$234$	997332.	+	1.37271e6i	0.0778381	+	0.107135i
$235$	−1.00230e6	−	3.08476e6i	−0.0772314	−	0.237694i
$236$	−1.73813e6	+	5.34942e6i	−0.132235	+	0.406978i
$237$	−494076.	−	358967.i	−0.0371149	−	0.0269656i
$238$	−2.72311e7	−	8.84791e6i	−2.01992	−	0.656311i
$239$	−3.96762e6	−	5.46096e6i	−0.290627	−	0.400014i	0.638591	−	0.769547i	$-0.279518\pi$
$239$	−3.96762e6	−	5.46096e6i	−0.290627	−	0.400014i	−0.929218	+	0.369533i	$0.879518\pi$
$240$	−836153.	−	1.15087e6i	−0.0604856	−	0.0832513i
$241$	1.33724e7	−	1.84056e7i	0.955344	−	1.31492i	0.00623145	−	0.999981i	$-0.498016\pi$
$241$	1.33724e7	−	1.84056e7i	0.955344	−	1.31492i	0.949112	−	0.314937i	$-0.101984\pi$
$242$	−8.54884e6			−0.603200
$243$			9.11031e6i			0.634913i
$244$	−1.54051e6	+	2.12033e6i	−0.106046	+	0.145960i
$245$	1.80537e7	+	5.55637e7i	1.22763	+	3.77827i
$246$	456221.	+	148235.i	0.0306457	+	0.00995740i
$247$			1.65452e6i			0.109795i
$248$	−2.04110e6	+	4.99156e6i	−0.133816	+	0.327251i
$249$	−5.69456e6			−0.368861
$250$	−7.96519e6	+	2.45143e7i	−0.509772	+	1.56892i
$251$	1.67769e7	−	5.45113e6i	1.06094	−	0.344719i	0.273985	−	0.961734i	$-0.411658\pi$
$251$	1.67769e7	−	5.45113e6i	1.06094	−	0.344719i	0.786952	+	0.617015i	$0.211658\pi$
$252$	−1.09680e7	−	7.96872e6i	−0.685371	−	0.497951i
$253$	1.06218e7			0.655896
$254$			1.56757e7i			0.956592i
$255$	9.28391e6	+	6.74516e6i	0.559900	+	0.406791i
$256$	−848316.	+	616338.i	−0.0505636	+	0.0367366i
$257$	101601.	−	73817.1i	0.00598545	−	0.00434868i	−0.584789	−	0.811186i	$-0.698823\pi$
$257$	101601.	−	73817.1i	0.00598545	−	0.00434868i	0.590774	+	0.806837i	$0.298823\pi$
$258$	−311648.	+	959153.i	−0.0181470	+	0.0558507i
$259$	−1.51741e7	+	2.08854e7i	−0.873383	+	1.20211i
$260$	2.99197e6	+	972151.i	0.170231	+	0.0553113i
$261$	−1.02368e7	+	3.32613e6i	−0.575760	+	0.187076i
$262$	1.25006e7	−	9.08223e6i	0.695068	−	0.504997i
$263$	−5.88197e6	+	1.91117e6i	−0.323337	+	0.105059i	−0.466188	−	0.884686i	$-0.654373\pi$
$263$	−5.88197e6	+	1.91117e6i	−0.323337	+	0.105059i	0.142851	+	0.989744i	$0.454373\pi$
$264$	−174958.	−	538466.i	−0.00950872	−	0.0292648i
$265$	−1.36032e6	−	1.87232e6i	−0.0730976	−	0.100610i
$266$	−4.08511e6	−	1.25727e7i	−0.217050	−	0.668010i
$267$	1.83649e6	−	5.65212e6i	0.0964837	−	0.296946i
$268$	7.78631e6	+	5.65708e6i	0.404508	+	0.293892i
$269$	1.98328e7	+	6.44406e6i	1.01889	+	0.331057i	0.770389	−	0.637575i	$-0.220062\pi$
$269$	1.98328e7	+	6.44406e6i	1.01889	+	0.331057i	0.248500	+	0.968632i	$0.420062\pi$
$270$	6.56112e6	+	9.03061e6i	0.333339	+	0.458802i
$271$	−5.72883e6	−	7.88506e6i	−0.287845	−	0.396184i	0.640468	−	0.767985i	$-0.278740\pi$
$271$	−5.72883e6	−	7.88506e6i	−0.287845	−	0.396184i	−0.928313	+	0.371801i	$0.878740\pi$
$272$	4.97193e6	−	6.84328e6i	0.247069	−	0.340061i
$273$	−1.62948e6			−0.0800866
$274$		−	1.66256e7i		−	0.808211i
$275$	−1.07159e7	+	1.47492e7i	−0.515267	+	0.709204i
$276$	−1.26194e6	−	3.88385e6i	−0.0600222	−	0.184729i
$277$	−1.49283e7	−	4.85049e6i	−0.702377	−	0.228216i	−0.0640111	−	0.997949i	$-0.520389\pi$
$277$	−1.49283e7	−	4.85049e6i	−0.702377	−	0.228216i	−0.638366	+	0.769733i	$0.720389\pi$
$278$			1.41520e7i			0.658695i
$279$	7.79618e6	−	1.90658e7i	0.358979	−	0.877893i
$280$	−2.51362e7			−1.14505
$281$	9.48286e6	−	2.91852e7i	0.427386	−	1.31536i	−0.473305	−	0.880899i	$-0.656939\pi$
$281$	9.48286e6	−	2.91852e7i	0.427386	−	1.31536i	0.900691	−	0.434460i	$-0.143061\pi$
$282$	−472026.	+	153371.i	−0.0210484	+	0.00683904i
$283$	9.53214e6	+	6.92550e6i	0.420563	+	0.305557i	0.777864	−	0.628432i	$-0.216303\pi$
$283$	9.53214e6	+	6.92550e6i	0.420563	+	0.305557i	−0.357301	+	0.933989i	$0.616303\pi$
$284$	5.99628e6			0.261774
$285$			5.29830e6i			0.228877i
$286$	1.01296e6	+	735961.i	0.0433008	+	0.0314599i
$287$	6.85741e6	−	4.98220e6i	0.290078	−	0.210754i
$288$	3.24023e6	−	2.35416e6i	0.135643	−	0.0985506i
$289$	−1.36271e7	+	4.19400e7i	−0.564561	+	1.73754i
$290$	−1.17302e7	+	1.61452e7i	−0.480963	+	0.661989i
$291$	1.44574e6	+	469750.i	0.0586694	+	0.0190628i
$292$	1.31480e7	−	4.27204e6i	0.528094	−	0.171588i
$293$	3.92206e7	−	2.84955e7i	1.55924	−	1.13285i	0.622602	−	0.782539i	$-0.286076\pi$
$293$	3.92206e7	−	2.84955e7i	1.55924	−	1.13285i	0.936633	−	0.350312i	$-0.113924\pi$
$294$	8.50230e6	−	2.76256e6i	0.334576	−	0.108710i
$295$	−1.23092e7	−	3.78839e7i	−0.479474	−	1.47567i
$296$	−4.48283e6	−	6.17008e6i	−0.172853	−	0.237912i
$297$	1.37286e6	+	4.22523e6i	0.0524031	+	0.161280i
$298$	5.18771e6	−	1.59661e7i	0.196032	−	0.603324i
$299$	7.30632e6	+	5.30835e6i	0.273329	+	0.198585i
$300$	6.66620e6	+	2.16598e6i	0.246896	+	0.0802214i
$301$	1.04745e7	+	1.44169e7i	0.384091	+	0.528656i
$302$	−1.91593e6	−	2.63705e6i	−0.0695599	−	0.0957410i
$303$	−6.88490e6	+	9.47626e6i	−0.247497	+	0.340650i
$304$	3.90544e6			0.139011
$305$		−	1.85607e7i		−	0.654175i
$306$	−1.89908e7	+	2.61386e7i	−0.662794	+	0.912258i
$307$	−701612.	−	2.15934e6i	−0.0242483	−	0.0746287i	0.938200	−	0.346093i	$-0.112492\pi$
$307$	−701612.	−	2.15934e6i	−0.0242483	−	0.0746287i	−0.962448	+	0.271465i	$0.912492\pi$
$308$	−9.51462e6	−	3.09149e6i	−0.325641	−	0.105807i
$309$			3.07108e6i			0.104092i
$310$	−9.08380e6	−	3.70948e7i	−0.304918	−	1.24517i
$311$	2.20388e7			0.732667			0.366334	−	0.930484i	$-0.380613\pi$
$311$	2.20388e7			0.732667			0.366334	+	0.930484i	$0.380613\pi$
$312$	148757.	−	457828.i	0.00489796	−	0.0150744i
$313$	−2.28470e7	+	7.42345e6i	−0.745069	+	0.242088i	−0.656858	−	0.754014i	$-0.728115\pi$
$313$	−2.28470e7	+	7.42345e6i	−0.745069	+	0.242088i	−0.0882111	+	0.996102i	$0.528115\pi$
$314$	236638.	+	171928.i	0.00764357	+	0.00555338i
$315$	9.60104e7			3.07176
$316$		−	3.18799e6i		−	0.101031i
$317$	−4.51381e6	−	3.27947e6i	−0.141699	−	0.102950i	0.514678	−	0.857384i	$-0.327912\pi$
$317$	−4.51381e6	−	3.27947e6i	−0.141699	−	0.102950i	−0.656376	+	0.754434i	$0.727912\pi$
$318$	−286500.	+	208154.i	−0.00890929	+	0.00647298i
$319$	−6.42583e6	+	4.66864e6i	−0.197951	+	0.143820i
$320$	2.29473e6	−	7.06244e6i	0.0700295	−	0.215529i
$321$	4.73159e6	−	6.51248e6i	0.143051	−	0.196893i
$322$	−6.86272e7	−	2.22983e7i	−2.05555	−	0.667889i
$323$	−2.99628e7	+	9.73550e6i	−0.889150	+	0.288902i
$324$	−1.16672e7	+	8.47670e6i	−0.343029	+	0.249225i
$325$	−1.47422e7	+	4.79004e6i	−0.429450	+	0.139537i
$326$	954870.	+	2.93879e6i	0.0275608	+	0.0848233i
$327$	−5.75829e6	−	7.92560e6i	−0.164684	−	0.226667i
$328$	773807.	+	2.38153e6i	0.0219286	+	0.0674894i
$329$	−2.71004e6	+	8.34064e6i	−0.0761006	+	0.234213i
$330$	3.24383e6	+	2.35678e6i	0.0902643	+	0.0655808i
$331$	−4.25760e7	−	1.38338e7i	−1.17404	−	0.381467i	−0.343888	−	0.939011i	$-0.611744\pi$
$331$	−4.25760e7	−	1.38338e7i	−1.17404	−	0.381467i	−0.830148	+	0.557543i	$0.811744\pi$
$332$	−1.74727e7	−	2.40491e7i	−0.477470	−	0.657181i
$333$	1.71226e7	+	2.35673e7i	0.463700	+	0.638229i
$334$	−1.94759e7	+	2.68063e7i	−0.522707	+	0.719444i
$335$	−6.81589e7			−1.81296
$336$			3.84632e6i			0.101398i
$337$	4.19739e7	−	5.77722e7i	1.09671	−	1.50949i	0.257026	−	0.966405i	$-0.417257\pi$
$337$	4.19739e7	−	5.77722e7i	1.09671	−	1.50949i	0.839680	−	0.543081i	$-0.182743\pi$
$338$	−8.10860e6	−	2.49557e7i	−0.209989	−	0.646278i
$339$	−4.14386e6	−	1.34642e6i	−0.106367	−	0.0345607i
$340$			5.99039e7i			1.52412i
$341$	1.12384e6	−	1.51584e7i	0.0283427	−	0.382287i
$342$	−1.49172e7			−0.372915
$343$	2.65376e7	−	8.16744e7i	0.657627	−	2.02397i
$344$	−5.00691e6	+	1.62684e6i	−0.122997	+	0.0399641i
$345$	2.33971e7	+	1.69990e7i	0.569778	+	0.413968i
$346$	2.97219e7			0.717544
$347$		−	5.17698e7i		−	1.23905i	−0.784978	−	0.619524i	$-0.787326\pi$
$347$		−	5.17698e7i		−	1.23905i	0.784978	−	0.619524i	$-0.212674\pi$
$348$	2.47053e6	+	1.79494e6i	0.0586208	+	0.0425905i
$349$	−2.62828e6	+	1.90956e6i	−0.0618294	+	0.0449217i	−0.618271	−	0.785965i	$-0.712166\pi$
$349$	−2.62828e6	+	1.90956e6i	−0.0618294	+	0.0449217i	0.556441	+	0.830887i	$0.312166\pi$
$350$	1.00199e8	−	7.27987e7i	2.33700	−	1.69793i
$351$	−1.16727e6	+	3.59248e6i	−0.0269929	+	0.0830756i
$352$	1.73721e6	−	2.39106e6i	0.0398312	−	0.0548230i
$353$	−6.94737e7	−	2.25734e7i	−1.57942	−	0.513183i	−0.617510	−	0.786563i	$-0.711858\pi$
$353$	−6.94737e7	−	2.25734e7i	−1.57942	−	0.513183i	−0.961906	+	0.273380i	$0.911858\pi$
$354$	−5.79696e6	+	1.88355e6i	−0.130674	+	0.0424587i
$355$	−3.43548e7	+	2.49603e7i	−0.767897	+	0.557910i
$356$	2.95048e7	−	9.58670e6i	0.653948	−	0.212481i
$357$	−9.58813e6	−	2.95092e7i	−0.210731	−	0.648565i
$358$	2.56751e7	+	3.53387e7i	0.559580	+	0.770196i
$359$	2.07301e7	+	6.38006e7i	0.448040	+	1.37893i	0.879115	+	0.476610i	$0.158135\pi$
$359$	2.07301e7	+	6.38006e7i	0.448040	+	1.37893i	−0.431074	+	0.902316i	$0.641865\pi$
$360$	−8.76494e6	+	2.69757e7i	−0.187863	+	0.578183i
$361$	2.62931e7	+	1.91030e7i	0.558881	+	0.406051i
$362$	5.51637e7	+	1.79238e7i	1.16286	+	0.377837i
$363$	−5.44527e6	−	7.49477e6i	−0.113841	−	0.156689i
$364$	−4.99975e6	−	6.88156e6i	−0.103668	−	0.142687i
$365$	−5.75467e7	+	7.92063e7i	−1.18343	+	1.62885i
$366$	−2.84013e6			−0.0579289
$367$		−	2.12977e6i		−	0.0430859i	−0.999768	−	0.0215430i	$-0.993142\pi$
$367$		−	2.12977e6i		−	0.0430859i	0.999768	−	0.0215430i	$-0.00685787\pi$
$368$	1.25302e7	−	1.72463e7i	0.251428	−	0.346061i
$369$	−2.95564e6	−	9.09651e6i	−0.0588263	−	0.181049i
$370$	5.13675e7	+	1.66903e7i	1.01411	+	0.329503i
$371$			6.25749e6i			0.122540i
$372$	−5.67620e6	+	1.38999e6i	−0.110263	+	0.0270012i
$373$	−5.26257e7			−1.01408			−0.507039	−	0.861923i	$-0.669260\pi$
$373$	−5.26257e7			−1.01408			−0.507039	+	0.861923i	$0.669260\pi$
$374$	−7.36753e6	+	2.26749e7i	−0.140834	+	0.433442i
$375$	−2.65652e7	+	8.63157e6i	−0.503756	+	0.163680i
$376$	−2.09604e6	−	1.52286e6i	−0.0394308	−	0.0286482i
$377$	−6.75330e6			−0.126035
$378$		−	3.01813e7i		−	0.558807i
$379$	−2.58645e7	−	1.87917e7i	−0.475102	−	0.345182i	0.324324	−	0.945946i	$-0.394863\pi$
$379$	−2.58645e7	−	1.87917e7i	−0.475102	−	0.345182i	−0.799426	+	0.600764i	$0.794863\pi$
$380$	−2.23757e7	+	1.62569e7i	−0.407779	+	0.296269i
$381$	−1.37429e7	+	9.98481e6i	−0.248487	+	0.180536i
$382$	1.46670e7	−	4.51404e7i	0.263118	−	0.809795i
$383$	−6.02881e6	+	8.29794e6i	−0.107309	+	0.147698i	−0.859294	−	0.511482i	$-0.829097\pi$
$383$	−6.02881e6	+	8.29794e6i	−0.107309	+	0.147698i	0.751985	+	0.659180i	$0.229097\pi$
$384$	−1.08069e6	−	351136.i	−0.0190856	−	0.00620129i
$385$	6.73814e7	−	2.18935e7i	1.18075	−	0.383649i
$386$	−3.15490e7	+	2.29217e7i	−0.548560	+	0.398552i
$387$	1.91244e7	−	6.21389e6i	0.329955	−	0.107209i
$388$	2.45216e6	+	7.54696e6i	0.0419810	+	0.129204i
$389$	2.19709e7	+	3.02403e7i	0.373249	+	0.513733i	0.953780	−	0.300505i	$-0.0971552\pi$
$389$	2.19709e7	+	3.02403e7i	0.373249	+	0.513733i	−0.580531	+	0.814238i	$0.697155\pi$
$390$	1.05348e6	+	3.24228e6i	0.0177596	+	0.0546584i
$391$	−5.31407e7	+	1.63550e8i	−0.888989	+	2.73603i
$392$	3.77545e7	+	2.74303e7i	0.626774	+	0.455378i
$393$	1.59248e7	+	5.17427e6i	0.262359	+	0.0852456i
$394$	1.58282e7	+	2.17856e7i	0.258787	+	0.356189i
$395$	1.32704e7	+	1.82652e7i	0.215325	+	0.296369i
$396$	−6.63544e6	+	9.13290e6i	−0.106852	+	0.147070i
$397$	8.15149e7			1.30276			0.651382	−	0.758750i	$-0.274190\pi$
$397$	8.15149e7			1.30276			0.651382	+	0.758750i	$0.274190\pi$
$398$		−	4.00705e7i		−	0.635587i
$399$	8.42041e6	−	1.15897e7i	0.132561	−	0.182454i
$400$	1.13067e7	+	3.47984e7i	0.176667	+	0.543726i
$401$	−6.64216e7	−	2.15817e7i	−1.03009	−	0.334697i	−0.255265	−	0.966871i	$-0.582163\pi$
$401$	−6.64216e7	−	2.15817e7i	−1.03009	−	0.334697i	−0.774827	+	0.632174i	$0.782163\pi$
$402$			1.04296e7i			0.160542i
$403$	8.34863e6	−	9.86525e6i	0.127556	−	0.150728i
$404$	−6.11450e7			−0.927292
$405$	3.15601e7	−	9.71321e7i	0.475088	−	1.46217i
$406$	5.13182e7	−	1.66743e7i	0.766820	−	0.249155i
$407$	1.73910e7	+	1.26353e7i	0.257953	+	0.187414i
$408$	9.16642e6			0.134964
$409$		−	1.07480e8i		−	1.57094i	−0.618900	−	0.785470i	$-0.712421\pi$
$409$		−	1.07480e8i		−	1.57094i	0.618900	−	0.785470i	$-0.287579\pi$
$410$	−1.43469e7	−	1.04236e7i	−0.208164	−	0.151240i
$411$	1.45756e7	−	1.05898e7i	0.209943	−	0.152533i
$412$	−1.29697e7	+	9.42305e6i	−0.185455	+	0.134741i
$413$	−3.32820e7	+	1.02431e8i	−0.472454	+	1.45406i
$414$	−4.78602e7	+	6.58740e7i	−0.674487	+	0.928352i
$415$	2.00215e8	+	6.50538e7i	2.80125	+	0.910182i
$416$	2.38992e6	−	776533.i	0.0331974	−	0.0107865i
$417$	−1.24071e7	+	9.01427e6i	−0.171104	+	0.124315i
$418$	−1.04691e7	+	3.40162e6i	−0.143344	+	0.0465754i
$419$	3.88012e7	+	1.19418e8i	0.527476	+	1.62340i	0.759367	+	0.650663i	$0.225509\pi$
$419$	3.88012e7	+	1.19418e8i	0.527476	+	1.62340i	−0.231891	+	0.972742i	$0.574491\pi$
$420$	−1.60108e7	−	2.20369e7i	−0.216105	−	0.297443i
$421$	−8.39979e6	−	2.58519e7i	−0.112570	−	0.346454i	0.878863	−	0.477075i	$-0.158303\pi$
$421$	−8.39979e6	−	2.58519e7i	−0.112570	−	0.346454i	−0.991432	+	0.130621i	$0.958303\pi$
$422$	1.05081e7	−	3.23406e7i	0.139826	−	0.430339i
$423$	8.00603e6	+	5.81672e6i	0.105778	+	0.0768523i
$424$	−1.75814e6	−	571256.i	−0.0230652	−	0.00749434i
$425$	−1.73492e8	−	2.38791e8i	−2.26002	−	3.11065i
$426$	3.81939e6	+	5.25694e6i	0.0494043	+	0.0679992i
$427$	−2.94979e7	+	4.06003e7i	−0.378885	+	0.521490i
$428$	4.20214e7			0.535968
$429$			1.35684e6i			0.0171853i
$430$	2.19144e7	−	3.01626e7i	0.275629	−	0.379371i
$431$	1.49331e7	+	4.59592e7i	0.186516	+	0.574038i	0.999971	−	0.00758978i	$-0.00241592\pi$
$431$	1.49331e7	+	4.59592e7i	0.186516	+	0.574038i	−0.813455	+	0.581628i	$0.802416\pi$
$432$	8.47992e6	+	2.75529e6i	0.105182	+	0.0341757i
$433$			1.83239e7i			0.225711i	0.993611	+	0.112856i	$0.0359998\pi$
$433$			1.83239e7i			0.225711i	−0.993611	+	0.112856i	$0.964000\pi$
$434$	−3.90832e7	+	9.55791e7i	−0.478103	+	1.16921i
$435$	−2.16262e7			−0.262732
$436$	1.58030e7	−	4.86365e7i	0.190669	−	0.586818i
$437$	−7.55117e7	+	2.45352e7i	−0.904836	+	0.293999i
$438$	1.21201e7	+	8.80573e6i	0.144239	+	0.104796i
$439$	1.14523e8			1.35363			0.676814	−	0.736154i	$-0.263360\pi$
$439$	1.14523e8			1.35363			0.676814	+	0.736154i	$0.263360\pi$
$440$			2.09306e7i			0.245710i
$441$	−1.44207e8	−	1.04773e8i	−1.68140	−	1.22161i
$442$	−1.63999e7	+	1.19152e7i	−0.189922	+	0.137986i
$443$	5.35857e7	−	3.89323e7i	0.616365	−	0.447815i	−0.235285	−	0.971926i	$-0.575602\pi$
$443$	5.35857e7	−	3.89323e7i	0.616365	−	0.447815i	0.851650	+	0.524111i	$0.175602\pi$
$444$	2.55393e6	−	7.86019e6i	0.0291783	−	0.0898016i
$445$	−1.29138e8	+	1.77743e8i	−1.46546	+	2.01703i
$446$	9.39519e7	+	3.05268e7i	1.05901	+	0.344094i
$447$	1.73019e7	−	5.62171e6i	0.193718	−	0.0629428i
$448$	−1.62437e7	+	1.18017e7i	−0.180655	+	0.131254i
$449$	−2.47999e7	+	8.05797e6i	−0.273975	+	0.0890198i	−0.442782	−	0.896629i	$-0.646008\pi$
$449$	−2.47999e7	+	8.05797e6i	−0.273975	+	0.0890198i	0.168807	+	0.985649i	$0.446008\pi$
$450$	−4.31871e7	−	1.32916e8i	−0.473932	−	1.45861i
$451$	−4.14861e6	−	5.71007e6i	−0.0452244	−	0.0622461i
$452$	−7.02851e6	−	2.16315e7i	−0.0761111	−	0.234246i
$453$	1.09153e6	−	3.35939e6i	0.0117420	−	0.0361382i
$454$	−5.08192e7	−	3.69223e7i	−0.543075	−	0.394567i
$455$	5.72907e7	+	1.86149e7i	0.608205	+	0.197618i
$456$	2.48761e6	+	3.42390e6i	0.0262354	+	0.0361099i
$457$	−1.90515e7	−	2.62222e7i	−0.199610	−	0.274739i	0.697464	−	0.716619i	$-0.254312\pi$
$457$	−1.90515e7	−	2.62222e7i	−0.199610	−	0.274739i	−0.897074	+	0.441880i	$0.854312\pi$
$458$	3.13424e7	−	4.31392e7i	0.326239	−	0.449030i
$459$	−7.19270e7			−0.743796
$460$			1.50969e8i			1.55100i
$461$	3.00135e7	−	4.13100e7i	0.306347	−	0.421651i	−0.627891	−	0.778302i	$-0.716081\pi$
$461$	3.00135e7	−	4.13100e7i	0.306347	−	0.421651i	0.934238	+	0.356651i	$0.116081\pi$
$462$	−3.35012e6	−	1.03106e7i	−0.0339731	−	0.104558i
$463$	−3.80608e7	−	1.23667e7i	−0.383474	−	0.124598i	0.110935	−	0.993828i	$-0.464615\pi$
$463$	−3.80608e7	−	1.23667e7i	−0.383474	−	0.124598i	−0.494409	+	0.869230i	$0.664615\pi$
$464$			1.59409e7i			0.159573i
$465$	2.67350e7	−	3.15916e7i	0.265901	−	0.314205i
$466$	2.55902e7			0.252881
$467$	−3.50143e7	+	1.07763e8i	−0.343791	+	1.05808i	0.618437	+	0.785835i	$0.287766\pi$
$467$	−3.50143e7	+	1.07763e8i	−0.343791	+	1.05808i	−0.962228	+	0.272246i	$0.912234\pi$
$468$	−9.12856e6	+	2.96605e6i	−0.0890563	+	0.0289361i
$469$	1.49093e8	+	1.08323e8i	1.44524	+	1.05003i
$470$	1.83481e7			0.176724
$471$			316972.i			0.00303360i
$472$	−2.57414e7	−	1.87023e7i	−0.244797	−	0.177856i
$473$	1.20048e7	−	8.72198e6i	0.113441	−	0.0824199i
$474$	2.79492e6	−	2.03062e6i	0.0262442	−	0.0190675i
$475$	4.21120e7	−	1.29607e8i	0.392939	−	1.20934i
$476$	9.52033e7	−	1.31036e8i	0.882736	−	1.21498i
$477$	6.71541e6	+	2.18197e6i	0.0618753	+	0.0201045i
$478$	3.63155e7	−	1.17996e7i	0.332513	−	0.108040i
$479$	−1.08579e8	+	7.88875e7i	−0.987963	+	0.717797i	−0.959474	−	0.281797i	$-0.909070\pi$
$479$	−1.08579e8	+	7.88875e7i	−0.987963	+	0.717797i	−0.0284890	+	0.999594i	$0.509070\pi$
$480$	7.65329e6	−	2.48670e6i	0.0692029	−	0.0224854i
$481$	5.64799e6	+	1.73827e7i	0.0507526	+	0.156200i
$482$	7.56460e7	+	1.04118e8i	0.675530	+	0.929787i
$483$	−2.41638e7	−	7.43686e7i	−0.214449	−	0.660006i
$484$	1.49439e7	−	4.59927e7i	0.131804	−	0.405651i
$485$	−4.54645e7	−	3.30319e7i	−0.398517	−	0.289539i
$486$	−4.90133e7	−	1.59254e7i	−0.426978	−	0.138734i
$487$	−3.22577e7	−	4.43989e7i	−0.279284	−	0.384402i	0.646213	−	0.763158i	$-0.276352\pi$
$487$	−3.22577e7	−	4.43989e7i	−0.279284	−	0.384402i	−0.925497	+	0.378756i	$0.876352\pi$
$488$	−8.71443e6	−	1.19944e7i	−0.0749859	−	0.103209i
$489$	−1.96822e6	+	2.70902e6i	−0.0168325	+	0.0231679i
$490$	−3.30491e8			−2.80913
$491$		−	8.17403e7i		−	0.690545i	−0.938503	−	0.345272i	$-0.887787\pi$
$491$		−	8.17403e7i		−	0.690545i	0.938503	−	0.345272i	$-0.112213\pi$
$492$	−1.59501e6	+	2.19534e6i	−0.0133927	+	0.0184334i
$493$	−3.97377e7	−	1.22300e8i	−0.331636	−	1.02067i
$494$	−8.90131e6	−	2.89221e6i	−0.0738368	−	0.0239910i
$495$		−	7.99466e7i		−	0.659150i
$496$	−2.32866e7	−	1.97066e7i	−0.190836	−	0.161498i
$497$	1.14818e8			0.935275
$498$	9.95446e6	−	3.06367e7i	0.0805990	−	0.248058i
$499$	4.70973e7	−	1.53028e7i	0.379048	−	0.123160i	−0.113295	−	0.993561i	$-0.536141\pi$
$499$	4.70973e7	−	1.53028e7i	0.379048	−	0.123160i	0.492343	+	0.870401i	$0.336141\pi$
$500$	−1.17963e8	−	8.57053e7i	−0.943706	−	0.685642i
$501$	−3.59064e7			−0.285535
$502$			9.97882e7i			0.788802i
$503$	−1.50881e7	−	1.09621e7i	−0.118558	−	0.0861373i	0.526926	−	0.849911i	$-0.323344\pi$
$503$	−1.50881e7	−	1.09621e7i	−0.118558	−	0.0861373i	−0.645484	+	0.763774i	$0.723344\pi$
$504$	6.20444e7	−	4.50779e7i	0.484630	−	0.352105i
$505$	3.50322e8	−	2.54524e8i	2.72015	−	1.97630i
$506$	−1.85675e7	+	5.71449e7i	−0.143318	+	0.441089i
$507$	1.67138e7	−	2.30046e7i	0.128248	−	0.176519i
$508$	−8.43352e7	−	2.74022e7i	−0.643306	−	0.209023i
$509$	−491517.	+	159703.i	−0.00372722	+	0.00121105i	−0.310880	−	0.950449i	$-0.600624\pi$
$509$	−491517.	+	159703.i	−0.00372722	+	0.00121105i	0.307153	+	0.951660i	$0.400624\pi$
$510$	−5.25177e7	+	3.81564e7i	−0.395909	+	0.287645i
$511$	2.51760e8	−	8.18017e7i	1.88679	−	0.613055i
$512$	−1.83298e6	−	5.64133e6i	−0.0136568	−	0.0420312i
$513$	−1.95197e7	−	2.68666e7i	−0.144585	−	0.199004i
$514$	219531.	+	675647.i	0.00161661	+	0.00497543i
$515$	3.50836e7	−	1.07976e8i	0.256852	−	0.790508i
$516$	−4.61545e6	−	3.35332e6i	−0.0335943	−	0.0244077i
$517$	6.94514e6	+	2.25661e6i	0.0502585	+	0.0163300i
$518$	−8.58378e7	−	1.18146e8i	−0.617575	−	0.850019i
$519$	1.89317e7	+	2.60572e7i	0.135421	+	0.186391i
$520$	−1.04603e7	+	1.43974e7i	−0.0743935	+	0.102394i
$521$	−1.39711e8			−0.987911			−0.493955	−	0.869487i	$-0.664449\pi$
$521$	−1.39711e8			−0.987911			−0.493955	+	0.869487i	$0.664449\pi$
$522$		−	6.08880e7i		−	0.428075i
$523$	541764.	−	745674.i	0.00378708	−	0.00521247i	−0.807119	−	0.590388i	$-0.798975\pi$
$523$	541764.	−	745674.i	0.00378708	−	0.00521247i	0.810906	+	0.585176i	$0.198975\pi$
$524$	2.70104e7	+	8.31295e7i	0.187732	+	0.577778i
$525$	1.27645e8	+	4.14745e7i	0.882119	+	0.286618i
$526$		−	3.49858e7i		−	0.240400i
$527$	2.27781e8	+	9.31419e7i	1.55627	+	0.636375i
$528$	3.20278e6			0.0217583
$529$	−8.81784e7	+	2.71385e8i	−0.595656	+	1.83324i
$530$	1.24510e7	−	4.04557e6i	0.0836326	−	0.0271739i
$531$	9.83221e7	+	7.14352e7i	0.656701	+	0.477121i
$532$	7.47819e7			0.496663
$533$		−	6.00107e6i		−	0.0396321i
$534$	2.71981e7	+	1.97605e7i	0.178613	+	0.129770i
$535$	−2.40755e8	+	1.74919e8i	−1.57223	+	1.14229i
$536$	−4.40460e7	+	3.20013e7i	−0.286030	+	0.207813i
$537$	−1.46275e7	+	4.50187e7i	−0.0944595	+	0.290717i
$538$	−6.93380e7	+	9.54355e7i	−0.445271	+	0.612863i
$539$	−1.25098e8	−	4.06469e7i	−0.798886	−	0.259574i
$540$	−6.00538e7	+	1.95127e7i	−0.381381	+	0.123918i
$541$	−1.54268e6	+	1.12083e6i	−0.00974283	+	0.00707858i	−0.592646	−	0.805463i	$-0.701917\pi$
$541$	−1.54268e6	+	1.12083e6i	−0.00974283	+	0.00707858i	0.582903	+	0.812542i	$0.301917\pi$
$542$	5.24359e7	−	1.70375e7i	0.329330	−	0.107006i
$543$	1.94233e7	+	5.97788e7i	0.121318	+	0.373377i
$544$	2.81255e7	+	3.87114e7i	0.174704	+	0.240460i
$545$	1.11915e8	+	3.44438e8i	0.691350	+	2.12776i
$546$	2.84843e6	−	8.76656e6i	0.0174996	−	0.0538581i
$547$	−7.17098e7	−	5.21002e7i	−0.438144	−	0.318330i	0.346753	−	0.937956i	$-0.387284\pi$
$547$	−7.17098e7	−	5.21002e7i	−0.438144	−	0.318330i	−0.784897	+	0.619626i	$0.787284\pi$
$548$	8.94454e7	+	2.90626e7i	0.543521	+	0.176601i
$549$	3.32856e7	+	4.58137e7i	0.201159	+	0.276872i
$550$	−6.06185e7	−	8.34343e7i	−0.364349	−	0.501483i
$551$	3.48981e7	−	4.80331e7i	0.208616	−	0.287135i
$552$	2.31010e7			0.137345
$553$		−	6.10442e7i		−	0.360968i
$554$	5.21912e7	−	7.18350e7i	0.306950	−	0.422480i
$555$	1.80866e7	+	5.56649e7i	0.105798	+	0.325614i
$556$	−7.61377e7	−	2.47386e7i	−0.442971	−	0.143930i
$557$			1.72765e8i			0.999749i	0.866098	+	0.499874i	$0.166620\pi$
$557$			1.72765e8i			0.999749i	−0.866098	+	0.499874i	$0.833380\pi$
$558$	8.89453e7	+	7.52715e7i	0.511942	+	0.433239i
$559$	1.26166e7			0.0722280
$560$	4.39397e7	−	1.35233e8i	0.250204	−	0.770047i
$561$	−2.45719e7	+	7.98391e6i	−0.139172	+	0.0452196i
$562$	1.40440e8	+	1.02035e8i	0.791190	+	0.574833i
$563$	−1.37074e8			−0.768123			−0.384061	−	0.923308i	$-0.625475\pi$
$563$	−1.37074e8			−0.768123			−0.384061	+	0.923308i	$0.625475\pi$
$564$		−	2.80760e6i		−	0.0156494i
$565$	1.30313e8	+	9.46778e7i	0.722506	+	0.524931i
$566$	−5.39219e7	+	3.91766e7i	−0.297383	+	0.216061i
$567$	−2.23405e8	+	1.62313e8i	−1.22558	+	0.890439i
$568$	−1.04819e7	+	3.22599e7i	−0.0571998	+	0.176043i
$569$	7.08782e7	−	9.75555e7i	0.384747	−	0.529559i	−0.572087	−	0.820193i	$-0.693866\pi$
$569$	7.08782e7	−	9.75555e7i	0.384747	−	0.529559i	0.956834	+	0.290633i	$0.0938660\pi$
$570$	−2.85048e7	−	9.26177e6i	−0.153919	−	0.0500114i
$571$	2.85993e8	−	9.29246e7i	1.53620	−	0.499140i	0.585872	−	0.810404i	$-0.300752\pi$
$571$	2.85993e8	−	9.29246e7i	1.53620	−	0.499140i	0.950324	+	0.311264i	$0.100752\pi$
$572$	−5.73019e6	+	4.16322e6i	−0.0306183	+	0.0222455i
$573$	4.89168e7	−	1.58940e7i	0.260013	−	0.0844833i
$574$	1.48170e7	+	4.56020e7i	0.0783473	+	0.241128i
$575$	−4.37230e8	−	6.01796e8i	−2.29989	−	3.16552i
$576$	7.00125e6	+	2.15476e7i	0.0366360	+	0.112754i
$577$	−1.10785e7	+	3.40963e7i	−0.0576707	+	0.177492i	−0.975742	−	0.218923i	$-0.929746\pi$
$577$	−1.10785e7	+	3.40963e7i	−0.0576707	+	0.177492i	0.918072	+	0.396415i	$0.129746\pi$
$578$	−2.01816e8	−	1.46628e8i	−1.04513	−	0.759333i
$579$	−4.01909e7	−	1.30588e7i	−0.207058	−	0.0672773i
$580$	−6.63561e7	−	9.13313e7i	−0.340092	−	0.468097i
$581$	−3.34570e8	−	4.60496e8i	−1.70592	−	2.34800i
$582$	−5.05450e6	+	6.95692e6i	−0.0256395	+	0.0352897i
$583$	5.21053e6			0.0262952
$584$			7.82039e7i			0.392636i
$585$	3.99543e7	−	5.49923e7i	0.199570	−	0.274685i
$586$	8.47450e7	+	2.60818e8i	0.421135	+	1.29612i
$587$	−8.43953e7	−	2.74217e7i	−0.417257	−	0.135575i	0.0928615	−	0.995679i	$-0.470399\pi$
$587$	−8.43953e7	−	2.74217e7i	−0.417257	−	0.135575i	−0.510119	+	0.860104i	$0.670399\pi$
$588$			5.05714e7i			0.248756i
$589$	2.70249e7	+	1.10359e8i	0.132257	+	0.540086i
$590$	2.25332e8			1.09715
$591$	−9.01753e6	+	2.77531e7i	−0.0436843	+	0.134446i
$592$	4.10312e7	−	1.33319e7i	0.197765	−	0.0642578i
$593$	−9.53902e7	−	6.93051e7i	−0.457446	−	0.332354i	0.335083	−	0.942189i	$-0.391236\pi$
$593$	−9.53902e7	−	6.93051e7i	−0.457446	−	0.332354i	−0.792529	+	0.609835i	$0.791236\pi$
$594$	−2.51315e7			−0.119911
$595$			1.14705e9i			5.44541i
$596$	7.68291e7	+	5.58196e7i	0.362900	+	0.263662i
$597$	3.51298e7	−	2.55233e7i	0.165102	−	0.119954i
$598$	−4.13308e7	+	3.00286e7i	−0.193272	+	0.140421i
$599$	−9.19336e7	+	2.82943e8i	−0.427754	+	1.31649i	0.472579	+	0.881289i	$0.343323\pi$
$599$	−9.19336e7	+	2.82943e8i	−0.427754	+	1.31649i	−0.900332	+	0.435203i	$0.856677\pi$
$600$	−2.33059e7	+	3.20778e7i	−0.107898	+	0.148508i
$601$	−1.89689e8	−	6.16338e7i	−0.873815	−	0.283920i	−0.162428	−	0.986720i	$-0.551933\pi$
$601$	−1.89689e8	−	6.16338e7i	−0.873815	−	0.283920i	−0.711387	+	0.702801i	$0.751933\pi$
$602$	−9.58730e7	+	3.11510e7i	−0.439447	+	0.142785i
$603$	1.68238e8	−	1.22232e8i	0.767313	−	0.557485i
$604$	1.75365e7	−	5.69795e6i	0.0795851	−	0.0258588i
$605$	1.05831e8	+	3.25714e8i	0.477911	+	1.47086i
$606$	−3.89469e7	−	5.36058e7i	−0.175007	−	0.240876i
$607$	−1.23297e7	−	3.79469e7i	−0.0551298	−	0.169672i	0.919700	−	0.392621i	$-0.128432\pi$
$607$	−1.23297e7	−	3.79469e7i	−0.0551298	−	0.169672i	−0.974830	+	0.222949i	$0.928432\pi$
$608$	−6.82695e6	+	2.10112e7i	−0.0303750	+	0.0934846i
$609$	4.73060e7	+	3.43698e7i	0.209442	+	0.152169i
$610$	9.98562e7	+	3.24452e7i	0.439932	+	0.142943i
$611$	3.64954e6	+	5.02316e6i	0.0159998	+	0.0220218i
$612$	−1.07428e8	−	1.47862e8i	−0.468666	−	0.645064i
$613$	1.62543e8	−	2.23721e8i	0.705644	−	0.971236i	−0.294236	−	0.955733i	$-0.595065\pi$
$613$	1.62543e8	−	2.23721e8i	0.705644	−	0.971236i	0.999880	−	0.0155029i	$-0.00493491\pi$
$614$	1.28437e7			0.0554861
$615$		−	1.92173e7i		−	0.0826166i
$616$	3.32643e7	−	4.57844e7i	0.142310	−	0.195873i
$617$	−4.70990e7	−	1.44956e8i	−0.200519	−	0.617135i	−0.999868	−	0.0162669i	$-0.994822\pi$
$617$	−4.70990e7	−	1.44956e8i	−0.200519	−	0.617135i	0.799348	−	0.600868i	$-0.205178\pi$
$618$	−1.65224e7	−	5.36845e6i	−0.0700015	−	0.0227449i
$619$			2.77275e8i			1.16907i	0.811370	+	0.584533i	$0.198722\pi$
$619$			2.77275e8i			1.16907i	−0.811370	+	0.584533i	$0.801278\pi$
$620$	2.15448e8	+	1.59733e7i	0.903999	+	0.0670223i
$621$	−1.81269e8			−0.756918
$622$	−3.85252e7	+	1.18568e8i	−0.160094	+	0.492717i
$623$	5.64963e8	−	1.83568e8i	2.33645	−	0.759157i
$624$	2.20307e6	+	1.60063e6i	0.00906724	+	0.00658774i
$625$	4.74305e8			1.94275
$626$		−	1.35893e8i		−	0.553956i
$627$	−9.65059e6	−	7.01157e6i	−0.0391518	−	0.0284454i
$628$	−1.33863e6	+	972571.i	−0.00540482	+	0.00392683i
$629$	−2.81561e8	+	2.04566e8i	−1.13141	+	0.822018i
$630$	−1.67832e8	+	5.16535e8i	−0.671203	+	2.06575i
$631$	−3.26720e7	+	4.49691e7i	−0.130043	+	0.178989i	−0.869073	−	0.494683i	$-0.835284\pi$
$631$	−3.26720e7	+	4.49691e7i	−0.130043	+	0.178989i	0.739030	+	0.673672i	$0.235284\pi$
$632$	1.71514e7	+	5.57282e6i	0.0679435	+	0.0220762i
$633$	3.50463e7	−	1.13872e7i	0.138175	−	0.0448959i
$634$	2.55340e7	−	1.85515e7i	0.100196	−	0.0727967i
$635$	5.97252e8	−	1.94059e8i	2.33258	−	0.757901i
$636$	−619048.	−	1.90523e6i	−0.00240632	−	0.00740588i
$637$	−6.57367e7	−	9.04788e7i	−0.254325	−	0.350049i
$638$	−1.38845e7	−	4.27320e7i	−0.0534647	−	0.164547i
$639$	4.00366e7	−	1.23220e8i	0.153446	−	0.472257i
$640$	3.39845e7	+	2.46912e7i	0.129641	+	0.0941894i
$641$	−4.48889e8	−	1.45853e8i	−1.70437	−	0.553784i	−0.714992	−	0.699133i	$-0.753570\pi$
$641$	−4.48889e8	−	1.45853e8i	−1.70437	−	0.553784i	−0.989380	+	0.145349i	$0.953570\pi$
$642$	2.67659e7	+	3.68401e7i	0.101153	+	0.139225i
$643$	−1.36725e8	−	1.88185e8i	−0.514297	−	0.707869i	0.470339	−	0.882486i	$-0.344132\pi$
$643$	−1.36725e8	−	1.88185e8i	−0.514297	−	0.707869i	−0.984637	+	0.174616i	$0.944132\pi$
$644$	2.39929e8	−	3.30234e8i	0.898309	−	1.23642i
$645$	4.04022e7			0.150566
$646$		−	1.78218e8i		−	0.661079i
$647$	−1.29395e8	+	1.78097e8i	−0.477753	+	0.657571i	−0.978071	−	0.208271i	$-0.933216\pi$
$647$	−1.29395e8	+	1.78097e8i	−0.477753	+	0.657571i	0.500318	+	0.865842i	$0.333216\pi$
$648$	−2.52096e7	−	7.75871e7i	−0.0926489	−	0.285144i
$649$	8.52933e7	+	2.77135e7i	0.312019	+	0.101381i
$650$		−	8.76862e7i		−	0.319294i
$651$	−1.08689e8	+	2.66158e7i	−0.393950	+	0.0964709i
$652$	−1.74798e7			−0.0630658
$653$	1.48755e7	−	4.57821e7i	0.0534234	−	0.164420i	−0.920785	−	0.390071i	$-0.872451\pi$
$653$	1.48755e7	−	4.57821e7i	0.0534234	−	0.164420i	0.974208	+	0.225650i	$0.0724506\pi$
$654$	5.27055e7	−	1.71251e7i	0.188418	−	0.0612208i
$655$	−5.00789e8	−	3.63845e8i	−1.78210	−	1.29477i
$656$	−1.41653e7			−0.0501781
$657$		−	2.98708e8i		−	1.05330i
$658$	−4.01352e7	−	2.91600e7i	−0.140880	−	0.102355i
$659$	8.27089e6	−	6.00915e6i	0.0288999	−	0.0209970i	−0.573242	−	0.819386i	$-0.694314\pi$
$659$	8.27089e6	−	6.00915e6i	0.0288999	−	0.0209970i	0.602141	+	0.798389i	$0.294314\pi$
$660$	−1.83499e7	+	1.33320e7i	−0.0638265	+	0.0463727i
$661$	4.65731e7	−	1.43337e8i	0.161262	−	0.496312i	−0.837480	−	0.546468i	$-0.815972\pi$
$661$	4.65731e7	−	1.43337e8i	0.161262	−	0.496312i	0.998741	+	0.0501561i	$0.0159719\pi$
$662$	1.48851e8	−	2.04876e8i	0.513072	−	0.706183i
$663$	−2.08922e7	−	6.78828e6i	−0.0716875	−	0.0232927i
$664$	1.59928e8	−	5.19636e7i	0.546285	−	0.177499i
$665$	−4.28452e8	+	3.11289e8i	−1.45693	+	1.05852i
$666$	−1.56723e8	+	5.09224e7i	−0.530530	+	0.172380i
$667$	−1.00146e8	−	3.08218e8i	−0.337486	−	1.03868i
$668$	−1.10172e8	−	1.51639e8i	−0.369609	−	0.508724i
$669$	3.30807e7	+	1.01812e8i	0.110483	+	0.340033i
$670$	1.19146e8	−	3.66694e8i	0.396146	−	1.21921i
$671$	3.38073e7	+	2.45625e7i	0.111903	+	0.0813026i
$672$	−2.06931e7	−	6.72361e6i	−0.0681897	−	0.0221562i
$673$	−1.56535e8	−	2.15451e8i	−0.513529	−	0.706812i	0.470980	−	0.882144i	$-0.343900\pi$
$673$	−1.56535e8	−	2.15451e8i	−0.513529	−	0.706812i	−0.984509	+	0.175332i	$0.943900\pi$
$674$	2.37441e8	+	3.26809e8i	0.775488	+	1.06737i
$675$	1.82877e8	−	2.51708e8i	0.594630	−	0.818438i
$676$	1.48436e8			0.480505
$677$		−	4.37165e8i		−	1.40890i	−0.709754	−	0.704449i	$-0.751194\pi$
$677$		−	4.37165e8i		−	1.40890i	0.709754	−	0.704449i	$-0.248806\pi$
$678$	1.44875e7	−	1.99403e7i	0.0464840	−	0.0639798i
$679$	4.69543e7	+	1.44510e8i	0.149991	+	0.461625i
$680$	−3.22282e8	−	1.04716e8i	−1.02497	−	0.333032i
$681$		−	6.80712e7i		−	0.215537i
$682$	7.95874e7	+	3.25441e7i	0.250895	+	0.102593i
$683$	−5.31397e7			−0.166785			−0.0833924	−	0.996517i	$-0.526575\pi$
$683$	−5.31397e7			−0.166785			−0.0833924	+	0.996517i	$0.526575\pi$
$684$	2.60762e7	−	8.02544e7i	0.0814848	−	0.250784i
$685$	−6.33441e8	+	2.05818e8i	−1.97076	+	0.640340i
$686$	3.93018e8	+	2.85544e8i	1.21742	+	0.884506i
$687$	5.77840e7			0.178212
$688$		−	2.97809e7i		−	0.0914477i
$689$	3.58413e6	+	2.60402e6i	0.0109579	+	0.00796136i
$690$	−1.32354e8	+	9.61609e7i	−0.402894	+	0.292719i
$691$	4.54440e8	−	3.30170e8i	1.37735	−	1.00070i	0.380223	−	0.924895i	$-0.375847\pi$
$691$	4.54440e8	−	3.30170e8i	1.37735	−	1.00070i	0.997123	−	0.0758048i	$-0.0241526\pi$
$692$	−5.19558e7	+	1.59904e8i	−0.156789	+	0.482547i
$693$	−1.27056e8	+	1.74878e8i	−0.381766	+	0.525456i
$694$	2.78521e8	+	9.04969e7i	0.833257	+	0.270742i
$695$	5.39198e8	−	1.75196e8i	1.60618	−	0.521879i
$696$	−1.39754e7	+	1.01537e7i	−0.0414512	+	0.0301160i
$697$	1.08677e8	−	3.53114e7i	0.320952	−	0.104284i
$698$	−5.67899e6	−	1.74781e7i	−0.0166996	−	0.0513960i
$699$	1.62999e7	+	2.24349e7i	0.0477259	+	0.0656891i
$700$	2.16502e8	+	6.66326e8i	0.631202	+	1.94264i
$701$	−2.95136e7	+	9.08336e7i	−0.0856778	+	0.263689i	−0.984712	−	0.174189i	$-0.944270\pi$
$701$	−2.95136e7	+	9.08336e7i	−0.0856778	+	0.263689i	0.899034	+	0.437878i	$0.144270\pi$
$702$	−1.72871e7	−	1.25598e7i	−0.0499701	−	0.0363054i
$703$	−1.52821e8	−	4.96547e7i	−0.439864	−	0.142920i
$704$	9.82713e6	+	1.35259e7i	0.0281649	+	0.0387657i
$705$	1.16870e7	+	1.60857e7i	0.0333530	+	0.0459065i
$706$	2.42889e8	−	3.34308e8i	0.690230	−	0.950020i
$707$	−1.17081e9			−3.31306
$708$		−	3.44801e7i		−	0.0971558i
$709$	5.67783e7	−	7.81487e7i	0.159310	−	0.219272i	−0.721899	−	0.691999i	$-0.756730\pi$
$709$	5.67783e7	−	7.81487e7i	0.159310	−	0.219272i	0.881209	+	0.472727i	$0.156730\pi$
$710$	−7.42314e7	−	2.28461e8i	−0.207402	−	0.638317i
$711$	−6.55114e7	−	2.12859e7i	−0.182267	−	0.0592222i
$712$			1.75494e8i			0.486208i
$713$	5.74049e8	+	2.34734e8i	1.58373	+	0.647602i
$714$	1.75520e8			0.482205
$715$	1.55004e7	−	4.77052e7i	0.0424057	−	0.130511i
$716$	−2.35003e8	+	7.63572e7i	−0.640229	+	0.208023i
$717$	3.34763e7	+	2.43219e7i	0.0908196	+	0.0659843i
$718$	−3.79484e8			−1.02523
$719$			3.80081e8i			1.02256i	0.859413	+	0.511281i	$0.170829\pi$
$719$			3.80081e8i			1.02256i	−0.859413	+	0.511281i	$0.829171\pi$
$720$	−1.29807e8	−	9.43105e7i	−0.347778	−	0.252675i
$721$	−2.48346e8	+	1.80434e8i	−0.662600	+	0.481407i
$722$	−1.48736e8	+	1.08063e8i	−0.395189	+	0.287122i
$723$	−4.30966e7	+	1.32638e8i	−0.114032	+	0.350955i
$724$	−1.92860e8	+	2.65448e8i	−0.508189	+	0.699462i
$725$	5.29021e8	+	1.71889e8i	1.38822	+	0.451061i
$726$	4.98404e7	−	1.61941e7i	0.130248	−	0.0423202i
$727$	−9.27027e7	+	6.73525e7i	−0.241262	+	0.175287i	−0.701845	−	0.712329i	$-0.747640\pi$
$727$	−9.27027e7	+	6.73525e7i	−0.241262	+	0.175287i	0.460583	+	0.887617i	$0.347640\pi$
$728$	4.57626e7	−	1.48692e7i	0.118609	−	0.0385383i
$729$	8.42661e7	+	2.59344e8i	0.217506	+	0.669413i
$730$	−3.25533e8	−	4.48058e8i	−0.836810	−	1.15177i
$731$	7.42381e7	+	2.28482e8i	0.190053	+	0.584923i
$732$	4.96473e6	−	1.52799e7i	0.0126579	−	0.0389571i
$733$	−2.08471e8	−	1.51463e8i	−0.529340	−	0.384588i	0.290771	−	0.956793i	$-0.406088\pi$
$733$	−2.08471e8	−	1.51463e8i	−0.529340	−	0.384588i	−0.820111	+	0.572205i	$0.806088\pi$
$734$	1.14582e7	+	3.72298e6i	0.0289752	+	0.00941462i
$735$	−2.10510e8	−	2.89742e8i	−0.530164	−	0.729708i
$736$	7.08813e7	+	9.75597e7i	0.177786	+	0.244702i
$737$	9.01988e7	−	1.24148e8i	0.225319	−	0.310125i
$738$	5.41058e7			0.134609
$739$		−	1.06176e8i		−	0.263083i	−0.991311	−	0.131542i	$-0.958007\pi$
$739$		−	1.06176e8i		−	0.263083i	0.991311	−	0.131542i	$-0.0419927\pi$
$740$	−1.79587e8	+	2.47181e8i	−0.443180	+	0.609985i
$741$	−3.13418e6	−	9.64600e6i	−0.00770316	−	0.0237079i
$742$	−3.36652e7	−	1.09385e7i	−0.0824081	−	0.0267760i
$743$		−	1.77400e8i		−	0.432502i	−0.976338	−	0.216251i	$-0.930617\pi$
$743$		−	1.77400e8i		−	0.432502i	0.976338	−	0.216251i	$-0.0693829\pi$
$744$	2.44421e6	−	3.29677e7i	0.00593499	−	0.0800515i
$745$	−6.72538e8			−1.62648
$746$	9.19931e7	−	2.83126e8i	0.221584	−	0.681966i
$747$	−6.10859e8	+	1.98480e8i	−1.46548	+	0.476163i
$748$	−1.09112e8	−	7.92745e7i	−0.260716	−	0.189421i
$749$	8.04631e8			1.91492
$750$		−	1.58009e8i		−	0.374540i
$751$	−1.82841e8	−	1.32842e8i	−0.431673	−	0.313629i	0.350645	−	0.936509i	$-0.385963\pi$
$751$	−1.82841e8	−	1.32842e8i	−0.431673	−	0.313629i	−0.782317	+	0.622880i	$0.785963\pi$
$752$	1.18570e7	−	8.61460e6i	0.0278818	−	0.0202573i
$753$	−8.74844e7	+	6.35611e7i	−0.204902	+	0.148870i
$754$	1.18052e7	−	3.63327e7i	0.0275397	−	0.0847586i
$755$	−7.67544e7	+	1.05643e8i	−0.178346	+	0.245472i
$756$	1.62375e8	+	5.27588e7i	0.375797	+	0.122104i
$757$	2.33399e8	−	7.58358e7i	0.538035	−	0.174818i	−0.0273793	−	0.999625i	$-0.508716\pi$
$757$	2.33399e8	−	7.58358e7i	0.538035	−	0.174818i	0.565415	+	0.824807i	$0.308716\pi$
$758$	1.46312e8	−	1.06302e8i	0.335948	−	0.244081i
$759$	−6.19257e7	+	2.01209e7i	−0.141627	+	0.0460174i
$760$	−4.83477e7	−	1.48799e8i	−0.110137	−	0.338968i
$761$	3.99082e8	+	5.49290e8i	0.905542	+	1.24637i	0.968666	+	0.248366i	$0.0798936\pi$
$761$	3.99082e8	+	5.49290e8i	0.905542	+	1.24637i	−0.0631241	+	0.998006i	$0.520106\pi$
$762$	−2.96947e7	−	9.13908e7i	−0.0671141	−	0.206556i
$763$	3.02598e8	−	9.31300e8i	0.681227	−	2.09660i
$764$	2.17216e8	+	1.57816e8i	0.487092	+	0.353893i
$765$	1.23099e9	+	3.99973e8i	2.74960	+	0.893400i
$766$	−3.41041e7	−	4.69402e7i	−0.0758787	−	0.104438i
$767$	4.48200e7	+	6.16894e7i	0.0993312	+	0.136718i
$768$	3.77822e6	−	5.20027e6i	0.00834072	−	0.0114800i
$769$	3.82028e8			0.840070			0.420035	−	0.907508i	$-0.362018\pi$
$769$	3.82028e8			0.840070			0.420035	+	0.907508i	$0.362018\pi$
$770$			4.00782e8i			0.877882i
$771$	−452507.	+	622823.i	−0.000987330	+	0.00135894i
$772$	−6.81688e7	−	2.09802e8i	−0.148161	−	0.455992i
$773$	6.82287e8	+	2.21689e8i	1.47716	+	0.479960i	0.933264	−	0.359191i	$-0.116947\pi$
$773$	6.82287e8	+	2.21689e8i	1.47716	+	0.479960i	0.543900	+	0.839150i	$0.316947\pi$
$774$			1.13751e8i			0.245320i
$775$	−9.05089e8	+	5.60301e8i	−1.94440	+	1.20370i
$776$	−4.48891e7			−0.0960629
$777$	4.89030e7	−	1.50508e8i	0.104249	−	0.320846i
$778$	−2.01099e8	+	6.53410e7i	−0.427043	+	0.138755i
$779$	4.26828e7	+	3.10109e7i	0.0902902	+	0.0655997i
$780$	−1.92850e7			−0.0406383
$781$		−	9.56071e7i		−	0.200695i
$782$	−7.87004e8	−	5.71792e8i	−1.64572	−	1.19569i
$783$	1.09662e8	−	7.96742e7i	0.228440	−	0.165971i
$784$	−2.13572e8	+	1.55169e8i	−0.443196	+	0.322001i
$785$	3.62104e6	−	1.11444e7i	0.00748556	−	0.0230382i
$786$	−5.56751e7	+	7.66302e7i	−0.114655	+	0.157809i
$787$	2.84477e7	+	9.24321e6i	0.0583610	+	0.0189626i	0.338052	−	0.941127i	$-0.390232\pi$
$787$	2.84477e7	+	9.24321e6i	0.0583610	+	0.0189626i	−0.279691	+	0.960090i	$0.590232\pi$
$788$	−1.44875e8	+	4.70727e7i	−0.296084	+	0.0962035i
$789$	3.06720e7	−	2.22845e7i	0.0624470	−	0.0453704i
$790$	−1.21464e8	+	3.94660e7i	−0.246358	+	0.0800465i
$791$	−1.34583e8	−	4.14204e8i	−0.271932	−	0.836921i
$792$	−3.75357e7	−	5.16635e7i	−0.0755561	−	0.103994i
$793$	1.09794e7	+	3.37913e7i	0.0220171	+	0.0677618i
$794$	−1.42493e8	+	4.38549e8i	−0.284664	+	0.876107i
$795$	1.14775e7	+	8.33890e6i	0.0228427	+	0.0165962i
$796$	2.15579e8	+	7.00457e7i	0.427431	+	0.138881i
$797$	4.99771e8	+	6.87876e8i	0.987180	+	1.35874i	0.932870	+	0.360213i	$0.117296\pi$
$797$	4.99771e8	+	6.87876e8i	0.987180	+	1.35874i	0.0543103	+	0.998524i	$0.482704\pi$
$798$	4.76331e7	+	6.55613e7i	0.0937346	+	0.129015i
$799$	−6.94931e7	+	9.56490e7i	−0.136239	+	0.187517i
$800$	−2.06980e8			−0.404258
$801$		−	6.70316e8i		−	1.30431i
$802$	2.32218e8	−	3.19621e8i	0.450167	−	0.619601i
$803$	−6.81152e7	−	2.09637e8i	−0.131552	−	0.404875i
$804$	−5.61111e7	−	1.82316e7i	−0.107964	−	0.0350797i
$805$			2.89077e9i			5.54148i
$806$	3.84810e7	+	6.21606e7i	0.0734922	+	0.118716i
$807$	−1.27834e8			−0.243235
$808$	1.06885e8	−	3.28959e8i	0.202621	−	0.623603i
$809$	1.42255e8	−	4.62214e7i	0.268671	−	0.0872966i	−0.171583	−	0.985170i	$-0.554888\pi$
$809$	1.42255e8	−	4.62214e7i	0.268671	−	0.0872966i	0.440254	+	0.897873i	$0.354888\pi$
$810$	4.67401e8	+	3.39586e8i	0.879497	+	0.638992i
$811$	7.34051e8			1.37614			0.688072	−	0.725643i	$-0.258458\pi$
$811$	7.34051e8			1.37614			0.688072	+	0.725643i	$0.258458\pi$
$812$			3.05239e8i			0.570128i
$813$	4.83363e7	+	3.51184e7i	0.0899501	+	0.0653526i
$814$	−9.83783e7	+	7.14760e7i	−0.182401	+	0.132522i
$815$	1.00148e8	−	7.27619e7i	0.184999	−	0.134410i
$816$	−1.60235e7	+	4.93152e7i	−0.0294908	+	0.0907634i
$817$	−6.51969e7	+	8.97358e7i	−0.119553	+	0.164551i
$818$	5.78244e8	+	1.87883e8i	1.05646	+	0.343263i
$819$	−1.74795e8	+	5.67943e7i	−0.318183	+	0.103384i
$820$	8.11581e7	−	5.89648e7i	0.147194	−	0.106943i
$821$	−8.14216e8	+	2.64555e8i	−1.47133	+	0.478064i	−0.931510	−	0.363717i	$-0.881508\pi$
$821$	−8.14216e8	+	2.64555e8i	−1.47133	+	0.478064i	−0.539820	+	0.841781i	$0.681508\pi$
$822$	3.14940e7	+	9.69284e7i	0.0567038	+	0.174516i
$823$	−2.08013e8	−	2.86305e8i	−0.373157	−	0.513606i	0.580599	−	0.814190i	$-0.302819\pi$
$823$	−2.08013e8	−	2.86305e8i	−0.373157	−	0.513606i	−0.953755	+	0.300584i	$0.902819\pi$
$824$	−2.80240e7	−	8.62490e7i	−0.0500897	−	0.154160i
$825$	3.45352e7	−	1.06289e8i	0.0615036	−	0.189289i
$826$	−4.92901e8	−	3.58114e8i	−0.874620	−	0.635449i
$827$	−1.54972e7	−	5.03536e6i	−0.0273992	−	0.00890253i	0.295285	−	0.955409i	$-0.404585\pi$
$827$	−1.54972e7	−	5.03536e6i	−0.0273992	−	0.00890253i	−0.322685	+	0.946507i	$0.604585\pi$
$828$	−2.70738e8	−	3.72639e8i	−0.476935	−	0.656444i
$829$	−4.00053e8	−	5.50626e8i	−0.702189	−	0.966481i	−0.999930	−	0.0118340i	$-0.996233\pi$
$829$	−4.00053e8	−	5.50626e8i	−0.702189	−	0.966481i	0.297741	−	0.954647i	$-0.403767\pi$
$830$	−6.99977e8	+	9.63436e8i	−1.22419	+	1.68496i
$831$	9.62214e7			0.167675
$832$			1.42152e7i			0.0246821i
$833$	1.25173e9	−	1.72286e9i	2.16559	−	2.98068i
$834$	−2.68083e7	−	8.25075e7i	−0.0462137	−	0.142231i
$835$	1.26243e9	+	4.10190e8i	2.16845	+	0.704572i
$836$		−	6.22699e7i		−	0.106576i
$837$	−1.91792e7	+	2.58690e8i	−0.0327081	+	0.441168i
$838$	−7.10293e8			−1.20699
$839$	1.66189e8	−	5.11476e8i	0.281395	−	0.866043i	−0.706062	−	0.708150i	$-0.749530\pi$
$839$	1.66189e8	−	5.11476e8i	0.281395	−	0.866043i	0.987456	−	0.157893i	$-0.0504701\pi$
$840$	1.46546e8	−	4.76158e7i	0.247250	−	0.0803365i
$841$	−2.85164e8	−	2.07184e8i	−0.479410	−	0.348312i
$842$	1.53766e8			0.257587
$843$			1.88116e8i			0.314009i
$844$	1.55623e8	+	1.13067e8i	0.258849	+	0.188065i
$845$	−8.50442e8	+	6.17882e8i	−1.40953	+	1.02408i
$846$	−4.52889e7	+	3.29043e7i	−0.0747965	+	0.0543428i
$847$	2.86148e8	−	8.80674e8i	0.470913	−	1.44932i
$848$	6.14670e6	−	8.46021e6i	0.0100799	−	0.0138737i
$849$	−6.86922e7	−	2.23194e7i	−0.112249	−	0.0364721i
$850$	1.58797e9	−	5.15961e8i	2.58574	−	0.840157i
$851$	−7.09584e8	+	5.15543e8i	−1.15137	+	0.836520i
$852$	−3.49588e7	+	1.13588e7i	−0.0565246	+	0.0183660i
$853$	2.84222e7	+	8.74746e7i	0.0457943	+	0.140940i	0.971339	−	0.237697i	$-0.0763927\pi$
$853$	2.84222e7	+	8.74746e7i	0.0457943	+	0.140940i	−0.925545	+	0.378638i	$0.876393\pi$
$854$	−1.66865e8	−	2.29670e8i	−0.267912	−	0.368749i
$855$	1.84669e8	+	5.68352e8i	0.295458	+	0.909325i
$856$	−7.34560e7	+	2.26074e8i	−0.117113	+	0.360438i
$857$	4.29456e8	+	3.12018e8i	0.682301	+	0.495720i	0.874120	−	0.485710i	$-0.161439\pi$
$857$	4.29456e8	+	3.12018e8i	0.682301	+	0.495720i	−0.191820	+	0.981430i	$0.561439\pi$
$858$	−7.29980e6	−	2.37185e6i	−0.0115571	−	0.00375513i
$859$	1.77308e8	+	2.44043e8i	0.279736	+	0.385023i	0.925646	−	0.378390i	$-0.123522\pi$
$859$	1.77308e8	+	2.44043e8i	0.279736	+	0.385023i	−0.645910	+	0.763413i	$0.723522\pi$
$860$	1.23967e8	+	1.70626e8i	0.194899	+	0.268256i
$861$	−3.05414e7	+	4.20367e7i	−0.0478498	+	0.0658596i
$862$	−2.73364e8			−0.426795
$863$			5.25325e8i			0.817327i	0.912685	+	0.408664i	$0.134005\pi$
$863$			5.25325e8i			0.817327i	−0.912685	+	0.408664i	$0.865995\pi$
$864$	−2.96469e7	+	4.08055e7i	−0.0459661	+	0.0632670i
$865$	−3.67945e8	−	1.13242e9i	−0.568505	−	1.74968i
$866$	−9.85822e7	−	3.20313e7i	−0.151791	−	0.0493197i
$867$		−	2.70328e8i		−	0.414795i
$868$	−4.45894e8	−	3.77346e8i	−0.681825	−	0.577006i
$869$	−5.08307e7			−0.0774580
$870$	3.78040e7	−	1.16349e8i	0.0574090	−	0.176687i
$871$	1.24089e8	−	4.03189e7i	0.187793	−	0.0610175i
$872$	2.34039e8	+	1.70040e8i	0.352971	+	0.256449i
$873$	1.71458e8			0.257701
$874$		−	4.49141e8i		−	0.672742i
$875$	−2.25878e9	−	1.64110e9i	−3.37170	−	2.44969i
$876$	−6.85614e7	+	4.98127e7i	−0.101992	+	0.0741017i
$877$	−7.28354e7	+	5.29180e7i	−0.107980	+	0.0784521i	−0.640465	−	0.767987i	$-0.721258\pi$
$877$	−7.28354e7	+	5.29180e7i	−0.107980	+	0.0784521i	0.532485	+	0.846440i	$0.321258\pi$
$878$	−2.00194e8	+	6.16133e8i	−0.295779	+	0.910313i
$879$	−1.74680e8	+	2.40427e8i	−0.257204	+	0.354011i
$880$	−1.12606e8	−	3.65880e7i	−0.165240	−	0.0536897i
$881$	5.13426e8	−	1.66822e8i	0.750845	−	0.243964i	0.0915004	−	0.995805i	$-0.470834\pi$
$881$	5.13426e8	−	1.66822e8i	0.750845	−	0.243964i	0.659345	+	0.751841i	$0.270834\pi$
$882$	8.15760e8	−	5.92684e8i	1.18893	−	0.863808i
$883$	−2.76648e8	+	8.98884e7i	−0.401833	+	0.130563i	−0.502959	−	0.864310i	$-0.667755\pi$
$883$	−2.76648e8	+	8.98884e7i	−0.401833	+	0.130563i	0.101126	+	0.994874i	$0.467755\pi$
$884$	−3.54357e7	−	1.09060e8i	−0.0512962	−	0.157873i
$885$	1.43528e8	+	1.97549e8i	0.207065	+	0.285000i
$886$	1.15784e8	+	3.56347e8i	0.166474	+	0.512356i
$887$	−4.05485e8	+	1.24795e9i	−0.581037	+	1.78825i	0.0335963	+	0.999435i	$0.489304\pi$
$887$	−4.05485e8	+	1.24795e9i	−0.581037	+	1.78825i	−0.614633	+	0.788813i	$0.710696\pi$
$888$	3.78233e7	+	2.74802e7i	0.0540158	+	0.0392447i
$889$	−1.61486e9	−	5.24701e8i	−2.29843	−	0.746804i
$890$	−7.30515e8	−	1.00547e9i	−1.03624	−	1.42626i
$891$	1.35156e8	+	1.86026e8i	0.191074	+	0.262991i
$892$	−3.28468e8	+	4.52097e8i	−0.462806	+	0.636997i
$893$	−5.45866e7			−0.0766535
$894$			1.02911e8i			0.144029i
$895$	1.02857e9	−	1.41571e9i	1.43472	−	1.97472i
$896$	−3.50981e7	−	1.08021e8i	−0.0487933	−	0.150170i
$897$	−5.26521e7	−	1.71077e7i	−0.0729522	−	0.0237036i
$898$		−	1.47509e8i		−	0.203699i
$899$	−4.50456e8	+	1.10308e8i	−0.619974	+	0.151820i
$900$	7.90581e8			1.08447
$901$	−2.60683e7	+	8.02299e7i	−0.0356400	+	0.109689i
$902$	3.79721e7	−	1.23379e7i	0.0517423	−	0.0168121i
$903$	−8.83774e7	−	6.42099e7i	−0.120027	−	0.0872045i
$904$	1.28664e8			0.174161
$905$		−	2.32365e9i		−	3.13491i
$906$	1.61654e7	+	1.17449e7i	0.0217372	+	0.0157930i
$907$	8.00996e8	−	5.81957e8i	1.07352	−	0.779955i	0.0969745	−	0.995287i	$-0.469083\pi$
$907$	8.00996e8	−	5.81957e8i	1.07352	−	0.779955i	0.976541	+	0.215332i	$0.0690835\pi$
$908$	2.87477e8	−	2.08864e8i	0.384012	−	0.279001i
$909$	−4.08259e8	+	1.25649e9i	−0.543556	+	1.67289i
$910$	−2.00296e8	+	2.75683e8i	−0.265795	+	0.365836i
$911$	3.24083e8	+	1.05301e8i	0.428648	+	0.139276i	0.515392	−	0.856954i	$-0.327646\pi$
$911$	3.24083e8	+	1.05301e8i	0.428648	+	0.139276i	−0.0867443	+	0.996231i	$0.527646\pi$
$912$	−2.27690e7	+	7.39810e6i	−0.0300165	+	0.00975295i
$913$	−3.83449e8	+	2.78592e8i	−0.503843	+	0.366064i
$914$	1.74378e8	−	5.66590e7i	0.228378	−	0.0742045i
$915$	3.51596e7	+	1.08210e8i	0.0458967	+	0.141255i
$916$	1.77300e8	+	2.44032e8i	0.230686	+	0.317512i
$917$	5.17199e8	+	1.59178e9i	0.670733	+	2.06430i
$918$	1.25733e8	−	3.86967e8i	0.162525	−	0.500202i
$919$	3.31107e8	+	2.40564e8i	0.426601	+	0.309944i	0.780289	−	0.625420i	$-0.215072\pi$
$919$	3.31107e8	+	2.40564e8i	0.426601	+	0.309944i	−0.353687	+	0.935364i	$0.615072\pi$
$920$	−8.12209e8	−	2.63903e8i	−1.04305	−	0.338907i
$921$	8.18091e6	+	1.12601e7i	0.0104718	+	0.0144132i
$922$	1.69782e8	+	2.33685e8i	0.216620	+	0.298152i
$923$	4.77808e7	−	6.57646e7i	0.0607643	−	0.0836348i
$924$	6.13272e7			0.0777387
$925$		−	1.50543e9i		−	1.90211i
$926$	1.33066e8	−	1.83149e8i	0.167584	−	0.230660i
$927$	1.07041e8	+	3.29437e8i	0.134372	+	0.413555i
$928$	−8.57620e7	−	2.78658e7i	−0.107313	−	0.0348680i
$929$		−	3.51023e8i		−	0.437813i	−0.975746	−	0.218907i	$-0.929751\pi$
$929$		−	3.51023e8i		−	0.437813i	0.975746	−	0.218907i	$-0.0702490\pi$
$930$	1.23228e8	+	1.99058e8i	0.153201	+	0.247475i
$931$	9.83232e8			1.21845
$932$	−4.47333e7	+	1.37675e8i	−0.0552565	+	0.170062i
$933$	−1.28488e8	+	4.17483e7i	−0.158204	+	0.0514036i
$934$	−5.18556e8	−	3.76753e8i	−0.636436	−	0.462398i
$935$	9.55132e8			1.16850
$936$		−	5.42964e7i		−	0.0662130i
$937$	−4.13133e8	−	3.00159e8i	−0.502194	−	0.364865i	0.307660	−	0.951496i	$-0.400454\pi$
$937$	−4.13133e8	−	3.00159e8i	−0.502194	−	0.364865i	−0.809854	+	0.586631i	$0.800454\pi$
$938$	−8.43399e8	+	6.12765e8i	−1.02194	+	0.742482i
$939$	1.19138e8	−	8.65587e7i	0.143897	−	0.104548i
$940$	−3.20736e7	+	9.87123e7i	−0.0386157	+	0.118847i
$941$	−1.71864e8	+	2.36551e8i	−0.206261	+	0.283894i	−0.899597	−	0.436720i	$-0.856140\pi$
$941$	−1.71864e8	+	2.36551e8i	−0.206261	+	0.283894i	0.693336	+	0.720614i	$0.256140\pi$
$942$	−1.70531e6	−	554087.i	−0.00204009	−	0.000662866i
$943$	2.73886e8	−	8.89910e7i	0.326614	−	0.106123i
$944$	1.45616e8	−	1.05796e8i	0.173098	−	0.125763i
$945$	−1.14992e9	+	3.73631e8i	−1.36261	+	0.442739i
$946$	2.59390e7	+	7.98322e7i	0.0306394	+	0.0942984i
$947$	−3.74201e8	−	5.15043e8i	−0.440610	−	0.606448i	0.529737	−	0.848162i	$-0.322290\pi$
$947$	−3.74201e8	−	5.15043e8i	−0.440610	−	0.606448i	−0.970348	+	0.241714i	$0.922290\pi$
$948$	6.03905e6	+	1.85863e7i	0.00708832	+	0.0218156i
$949$	5.79147e7	−	1.78243e8i	0.0677626	−	0.208552i
$950$	6.23671e8	+	4.53124e8i	0.727420	+	0.528501i
$951$	3.25282e7	+	1.05691e7i	0.0378198	+	0.0122884i
$952$	5.38551e8	+	7.41252e8i	0.624189	+	0.859122i
$953$	6.71734e8	+	9.24563e8i	0.776102	+	1.06821i	0.995701	+	0.0926227i	$0.0295251\pi$
$953$	6.71734e8	+	9.24563e8i	0.776102	+	1.06821i	−0.219599	+	0.975590i	$0.570475\pi$
$954$	−2.34779e7	+	3.23146e7i	−0.0270405	+	0.0372181i
$955$	−1.90144e9			−2.18309
$956$			2.16004e8i			0.247222i
$957$	2.86193e7	−	3.93911e7i	0.0326530	−	0.0449430i
$958$	−2.34610e8	−	7.22056e8i	−0.266840	−	0.821248i
$959$	1.71271e9	+	5.56494e8i	1.94191	+	0.630964i
$960$			4.55215e7i			0.0514521i
$961$	3.95729e8	−	7.94394e8i	0.445890	−	0.895088i
$962$	−1.03392e8			−0.116134
$963$	2.80573e8	−	8.63514e8i	0.314171	−	0.966920i
$964$	−6.92386e8	+	2.24970e8i	−0.772889	+	0.251127i
$965$	1.26389e9	+	9.18270e8i	1.40646	+	1.02185i
$966$	4.42342e8			0.490712
$967$			1.58006e9i			1.74741i	0.486460	+	0.873703i	$0.338288\pi$
$967$			1.58006e9i			1.74741i	−0.486460	+	0.873703i	$0.661712\pi$
$968$	2.21317e8	+	1.60796e8i	0.243999	+	0.177276i
$969$	1.56244e8	−	1.13518e8i	0.171724	−	0.124765i
$970$	2.57186e8	−	1.86856e8i	0.281794	−	0.204735i
$971$	1.10488e8	−	3.40048e8i	0.120686	−	0.371435i	−0.872404	−	0.488785i	$-0.837440\pi$
$971$	1.10488e8	−	3.40048e8i	0.120686	−	0.371435i	0.993091	+	0.117351i	$0.0374401\pi$
$972$	1.71357e8	−	2.35853e8i	0.186596	−	0.256828i
$973$	−1.45790e9	−	4.73699e8i	−1.58266	−	0.514238i
$974$	2.95254e8	−	9.59338e7i	0.319535	−	0.103823i
$975$	7.68745e7	−	5.58526e7i	0.0829409	−	0.0602601i
$976$	7.97630e7	−	2.59166e7i	0.0857930	−	0.0278758i
$977$	−4.49571e8	−	1.38364e9i	−0.482075	−	1.48368i	−0.836172	−	0.548467i	$-0.815212\pi$
$977$	−4.49571e8	−	1.38364e9i	−0.482075	−	1.48368i	0.354097	−	0.935209i	$-0.384788\pi$
$978$	−1.11339e7	−	1.53246e7i	−0.0119023	−	0.0163822i
$979$	−1.52854e8	−	4.70437e8i	−0.162903	−	0.501364i
$980$	5.77720e8	−	1.77804e9i	0.613817	−	1.88914i
$981$	−8.93937e8	−	6.49483e8i	−0.946891	−	0.687957i
$982$	4.39762e8	+	1.42887e8i	0.464390	+	0.150890i
$983$	−8.31752e7	−	1.14481e8i	−0.0875655	−	0.120524i	0.762987	−	0.646414i	$-0.223732\pi$
$983$	−8.31752e7	−	1.14481e8i	−0.0875655	−	0.120524i	−0.850552	+	0.525891i	$0.823732\pi$
$984$	−9.02272e6	−	1.24187e7i	−0.00947005	−	0.0130344i
$985$	6.34095e8	−	8.72757e8i	0.663507	−	0.913239i
$986$	7.27436e8			0.758864
$987$		−	5.37603e7i		−	0.0559127i
$988$	3.11201e7	−	4.28332e7i	0.0322679	−	0.0444129i
$989$	1.87094e8	+	5.75815e8i	0.193406	+	0.595242i
$990$	4.30112e8	+	1.39752e8i	0.443277	+	0.144030i
$991$			1.24100e9i			1.27512i	0.770401	+	0.637559i	$0.220056\pi$
$991$			1.24100e9i			1.27512i	−0.770401	+	0.637559i	$0.779944\pi$
$992$	1.46728e8	−	9.08329e7i	0.150306	−	0.0930482i
$993$	2.74427e8			0.280272
$994$	−2.00709e8	+	6.17717e8i	−0.204365	+	0.628971i
$995$	−1.52670e9	+	4.96056e8i	−1.54983	+	0.503571i
$996$	1.47424e8	+	1.07110e8i	0.149207	+	0.108405i
$997$	−9.06098e8			−0.914302			−0.457151	−	0.889389i	$-0.651130\pi$
$997$	−9.06098e8			−0.914302			−0.457151	+	0.889389i	$0.651130\pi$
$998$			2.80133e8i			0.281821i
$999$	−2.96792e8	−	2.15632e8i	−0.297684	−	0.216280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.23.4	✓	64
31.27	odd	10	inner	62.7.f.a.27.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.23.4	✓	64	1.1	even	1	trivial
62.7.f.a.27.4	yes	64	31.27	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+(-1.74806 + 5.37999i) q^{2} +(-5.83008 + 1.89431i) q^{3} +(-25.8885 - 18.8091i) q^{4} +226.620 q^{5} -34.6772i q^{6} +(-495.718 - 360.160i) q^{7} +(146.448 - 106.400i) q^{8} +(-559.372 + 406.407i) q^{9} +(-396.147 + 1219.21i) q^{10} +(-299.900 + 412.777i) q^{11} +(186.563 + 60.6179i) q^{12} +(-412.581 + 134.056i) q^{13} +(2804.20 - 2037.37i) q^{14} +(-1321.21 + 429.289i) q^{15} +(316.433 + 973.882i) q^{16} +(-4855.40 - 6682.89i) q^{17} +(-1208.65 - 3719.84i) q^{18} +(1178.56 - 3627.24i) q^{19} +(-5866.87 - 4262.53i) q^{20} +(3572.33 + 1160.72i) q^{21} +(-1696.49 - 2335.02i) q^{22} +(-12236.5 - 16842.1i) q^{23} +(-652.247 + 897.741i) q^{24} +35731.7 q^{25} -2454.02i q^{26} +(5118.05 - 7044.39i) q^{27} +(6059.11 + 18648.0i) q^{28} +(14805.4 + 4810.56i) q^{29} -7858.54i q^{30} +(-25330.1 + 15680.8i) q^{31} -5792.62 q^{32} +(966.516 - 2974.63i) q^{33} +(44441.4 - 14439.9i) q^{34} +(-112340. - 81619.5i) q^{35} +22125.5 q^{36} -42131.6i q^{37} +(17454.3 + 12681.3i) q^{38} +(2151.44 - 1563.11i) q^{39} +(33188.0 - 24112.5i) q^{40} +(-4274.72 + 13156.2i) q^{41} +(-12489.3 + 17190.1i) q^{42} +(-27659.5 - 8987.12i) q^{43} +(15528.0 - 5045.34i) q^{44} +(-126765. + 92100.1i) q^{45} +(112000. - 36391.1i) q^{46} +(-4422.82 - 13612.0i) q^{47} +(-3689.67 - 5078.39i) q^{48} +(79665.2 + 245184. i) q^{49} +(-62461.3 + 192236. i) q^{50} +(40966.8 + 29764.2i) q^{51} +(13202.6 + 4289.78i) q^{52} +(-6002.64 - 8261.92i) q^{53} +(28952.1 + 39849.1i) q^{54} +(-67963.5 + 93543.7i) q^{55} -110918. q^{56} +23379.7i q^{57} +(-51761.5 + 71243.6i) q^{58} +(-54316.6 - 167169. i) q^{59} +(42278.9 + 13737.2i) q^{60} -81902.1i q^{61} +(-40083.8 - 163687. i) q^{62} +423662. q^{63} +(10125.9 - 31164.2i) q^{64} +(-93499.2 + 30379.7i) q^{65} +(14313.9 + 10399.7i) q^{66} -300763. q^{67} +264336. i q^{68} +(103244. + 75011.0i) q^{69} +(635489. - 461710. i) q^{70} +(-151597. + 110141. i) q^{71} +(-38676.8 + 119035. i) q^{72} +(-253935. + 349511. i) q^{73} +(226668. + 73648.8i) q^{74} +(-208319. + 67686.8i) q^{75} +(-98736.4 + 71736.2i) q^{76} +(297332. - 96608.9i) q^{77} +(4648.67 + 14307.1i) q^{78} +(58558.0 + 80598.2i) q^{79} +(71710.2 + 220701. i) q^{80} +(139265. - 428612. i) q^{81} +(-63307.9 - 45995.9i) q^{82} +(883483. + 287061. i) q^{83} +(-70650.3 - 97241.7i) q^{84} +(-1.10033e6 - 1.51448e6i) q^{85} +(96701.2 - 133098. i) q^{86} -95429.3 q^{87} +92359.9i q^{88} +(-569843. + 784322. i) q^{89} +(-273904. - 842991. i) q^{90} +(252805. + 82141.4i) q^{91} +666175. i q^{92} +(117973. - 139403. i) q^{93} +80963.9 q^{94} +(267086. - 822005. i) q^{95} +(33771.4 - 10973.0i) q^{96} +(-200620. - 145759. i) q^{97} -1.45835e6 q^{98} -352778. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) \) 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more