LMFDB - Embedded newform 9.8.c.a.4.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,8,Mod(4,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.4"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	9.c (of order $3$, degree $2$, 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:	$2.81146522936$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 $ x^12 - 6x^11 + 375x^10 - 1820x^9 + 50808x^8 - 192378x^7 + 3002887x^6 - 8342916x^5 + 72369348x^4 - 131054670x^3 + 513267363x^2 - 449098992*x + 754412211
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.5
Root			$0.500000 + 9.08282i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.8.c.a.7.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.11595 + 12.3252i) q^{2} +(45.7172 - 9.84574i) q^{3} +(-37.2735 + 64.5595i) q^{4} +(-145.304 + 251.673i) q^{5} +(446.672 + 493.411i) q^{6} +(-555.940 - 962.916i) q^{7} +760.739 q^{8} +(1993.12 - 900.239i) q^{9} -4135.89 q^{10} +(-2245.36 - 3889.07i) q^{11} +(-1068.40 + 3318.46i) q^{12} +(-1218.29 + 2110.14i) q^{13} +(7912.08 - 13704.1i) q^{14} +(-4164.96 + 12936.4i) q^{15} +(10184.4 + 17639.9i) q^{16} +15905.4 q^{17} +(25278.6 + 18159.5i) q^{18} -49949.6 q^{19} +(-10831.9 - 18761.5i) q^{20} +(-34896.6 - 38548.2i) q^{21} +(31955.7 - 55348.9i) q^{22} +(-34692.5 + 60089.2i) q^{23} +(34778.8 - 7490.04i) q^{24} +(-3163.73 - 5479.74i) q^{25} -34677.2 q^{26} +(82256.4 - 60780.2i) q^{27} +82887.2 q^{28} +(47035.8 + 81468.4i) q^{29} +(-189081. + 40720.9i) q^{30} +(9963.58 - 17257.4i) q^{31} +(-96255.8 + 166720. i) q^{32} +(-140942. - 155690. i) q^{33} +(113182. + 196037. i) q^{34} +323120. q^{35} +(-16171.5 + 162230. i) q^{36} +331750. q^{37} +(-355439. - 615638. i) q^{38} +(-34920.9 + 108465. i) q^{39} +(-110538. + 191457. i) q^{40} +(-121133. + 209809. i) q^{41} +(226791. - 704414. i) q^{42} +(-415713. - 720036. i) q^{43} +334769. q^{44} +(-63041.7 + 632423. i) q^{45} -987481. q^{46} +(80005.3 + 138573. i) q^{47} +(639279. + 706172. i) q^{48} +(-206366. + 357437. i) q^{49} +(45025.8 - 77987.1i) q^{50} +(727150. - 156600. i) q^{51} +(-90819.7 - 157304. i) q^{52} +311589. q^{53} +(1.33446e6 + 581317. i) q^{54} +1.30503e6 q^{55} +(-422925. - 732527. i) q^{56} +(-2.28356e6 + 491791. i) q^{57} +(-669408. + 1.15945e6i) q^{58} +(156177. - 270506. i) q^{59} +(-679926. - 751072. i) q^{60} +(28723.9 + 49751.3i) q^{61} +283601. q^{62} +(-1.97491e6 - 1.41873e6i) q^{63} -132603. q^{64} +(-354044. - 613221. i) q^{65} +(915973. - 2.84502e6i) q^{66} +(2.05100e6 - 3.55243e6i) q^{67} +(-592849. + 1.02684e6i) q^{68} +(-994422. + 3.08869e6i) q^{69} +(2.29930e6 + 3.98251e6i) q^{70} -403110. q^{71} +(1.51625e6 - 684847. i) q^{72} -823496. q^{73} +(2.36072e6 + 4.08889e6i) q^{74} +(-198589. - 219369. i) q^{75} +(1.86180e6 - 3.22472e6i) q^{76} +(-2.49656e6 + 4.32418e6i) q^{77} +(-1.58534e6 + 341422. i) q^{78} +(-489414. - 847689. i) q^{79} -5.91931e6 q^{80} +(3.16211e6 - 3.58858e6i) q^{81} -3.44791e6 q^{82} +(1.85204e6 + 3.20782e6i) q^{83} +(3.78937e6 - 816086. i) q^{84} +(-2.31111e6 + 4.00296e6i) q^{85} +(5.91638e6 - 1.02475e7i) q^{86} +(2.95246e6 + 3.26140e6i) q^{87} +(-1.70813e6 - 2.95857e6i) q^{88} +2.09023e6 q^{89} +(-8.24334e6 + 3.72329e6i) q^{90} +2.70918e6 q^{91} +(-2.58622e6 - 4.47947e6i) q^{92} +(285595. - 887060. i) q^{93} +(-1.13863e6 + 1.97216e6i) q^{94} +(7.25786e6 - 1.25710e7i) q^{95} +(-2.75906e6 + 8.56968e6i) q^{96} +(-1.75125e6 - 3.03325e6i) q^{97} -5.87396e6 q^{98} +(-7.97637e6 - 5.73004e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{2} + 24 q^{3} - 321 q^{4} - 180 q^{5} - 1233 q^{6} - 84 q^{7} + 5922 q^{8} + 990 q^{9} + 252 q^{10} - 8460 q^{11} + 8052 q^{12} - 1848 q^{13} - 16272 q^{14} - 1188 q^{15} - 12417 q^{16} + 30564 q^{17}+ \cdots - 49382676 q^{99}+O(q^{100}) $ 12 * q - 9 * q^2 + 24 * q^3 - 321 * q^4 - 180 * q^5 - 1233 * q^6 - 84 * q^7 + 5922 * q^8 + 990 * q^9 + 252 * q^10 - 8460 * q^11 + 8052 * q^12 - 1848 * q^13 - 16272 * q^14 - 1188 * q^15 - 12417 * q^16 + 30564 * q^17 + 42876 * q^18 + 24432 * q^19 - 40788 * q^20 - 187224 * q^21 - 35001 * q^22 - 51588 * q^23 + 215469 * q^24 + 4746 * q^25 + 536472 * q^26 + 322272 * q^27 + 75516 * q^28 - 414648 * q^29 - 1112112 * q^30 + 8196 * q^31 - 1048977 * q^32 - 148518 * q^33 - 106623 * q^34 + 2210616 * q^35 + 2501811 * q^36 + 139344 * q^37 - 1952685 * q^38 - 2057316 * q^39 + 305496 * q^40 - 1731582 * q^41 + 538866 * q^42 + 408372 * q^43 + 5169114 * q^44 + 2687580 * q^45 - 1684008 * q^46 - 1631484 * q^47 - 7434525 * q^48 - 179010 * q^49 - 1654461 * q^50 + 2525688 * q^51 + 681594 * q^52 + 2835648 * q^53 + 5816529 * q^54 - 16056 * q^55 - 1784466 * q^56 - 3071850 * q^57 - 948384 * q^58 - 2055636 * q^59 + 371484 * q^60 - 2723196 * q^61 - 1026828 * q^62 - 2238804 * q^63 + 7178178 * q^64 - 1387620 * q^65 + 5754762 * q^66 + 3806556 * q^67 + 2142639 * q^68 - 3002292 * q^69 + 953442 * q^70 + 2408400 * q^71 - 9638325 * q^72 - 10670052 * q^73 + 9846504 * q^74 + 19174632 * q^75 - 6727827 * q^76 + 3478824 * q^77 - 13339962 * q^78 + 6020916 * q^79 - 38072448 * q^80 - 28538730 * q^81 + 9403002 * q^82 + 9605052 * q^83 + 30090090 * q^84 - 1698624 * q^85 + 34278561 * q^86 + 10290708 * q^87 - 16459029 * q^88 - 24630264 * q^89 - 13660596 * q^90 + 13570104 * q^91 + 39143394 * q^92 + 27331212 * q^93 + 12602808 * q^94 + 10422072 * q^95 - 3404376 * q^96 + 9977226 * q^97 - 95833314 * q^98 - 49382676 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	7.11595	+	12.3252i	0.628967	+	1.08940i	0.987759	+	0.155985i	$0.0498553\pi$
$2$	7.11595	+	12.3252i	0.628967	+	1.08940i	−0.358792	+	0.933417i	$0.616811\pi$
$3$	45.7172	−	9.84574i	0.977586	−	0.210535i
$3$	45.7172	−	9.84574i	0.977586	−	0.210535i
$4$	−37.2735	+	64.5595i	−0.291199	+	0.504371i
$5$	−145.304	+	251.673i	−0.519854	+	0.900413i	0.479880	+	0.877334i	$0.340680\pi$
$5$	−145.304	+	251.673i	−0.519854	+	0.900413i	−0.999734	+	0.0230788i	$0.992653\pi$
$6$	446.672	+	493.411i	0.844227	+	0.932566i
$7$	−555.940	−	962.916i	−0.612611	−	1.06107i	−0.990799	−	0.135344i	$-0.956786\pi$
$7$	−555.940	−	962.916i	−0.612611	−	1.06107i	0.378188	−	0.925729i	$-0.376547\pi$
$8$	760.739			0.525316
$9$	1993.12	−	900.239i	0.911350	−	0.411632i
$10$	−4135.89			−1.30788
$11$	−2245.36	−	3889.07i	−0.508640	−	0.880991i	−0.999950	−	0.0100060i	$-0.996815\pi$
$11$	−2245.36	−	3889.07i	−0.508640	−	0.880991i	0.491310	−	0.870985i	$-0.336518\pi$
$12$	−1068.40	+	3318.46i	−0.178484	+	0.554374i
$13$	−1218.29	+	2110.14i	−0.153797	+	0.266385i	−0.932620	−	0.360859i	$-0.882484\pi$
$13$	−1218.29	+	2110.14i	−0.153797	+	0.266385i	0.778823	+	0.627244i	$0.215817\pi$
$14$	7912.08	−	13704.1i	0.770624	−	1.33476i
$15$	−4164.96	+	12936.4i	−0.318633	+	0.989679i
$16$	10184.4	+	17639.9i	0.621605	+	1.07665i
$17$	15905.4			0.785187			0.392593	−	0.919712i	$-0.371578\pi$
$17$	15905.4			0.785187			0.392593	+	0.919712i	$0.371578\pi$
$18$	25278.6	+	18159.5i	1.02164	+	0.733924i
$19$	−49949.6			−1.67069			−0.835343	−	0.549730i	$-0.814731\pi$
$19$	−49949.6			−1.67069			−0.835343	+	0.549730i	$0.814731\pi$
$20$	−10831.9	−	18761.5i	−0.302762	−	0.524399i
$21$	−34896.6	−	38548.2i	−0.822273	−	0.908314i
$22$	31955.7	−	55348.9i	0.639836	−	1.10823i
$23$	−34692.5	+	60089.2i	−0.594550	+	1.02979i	0.399060	+	0.916925i	$0.369337\pi$
$23$	−34692.5	+	60089.2i	−0.594550	+	1.02979i	−0.993610	+	0.112867i	$0.963997\pi$
$24$	34778.8	−	7490.04i	0.513542	−	0.110597i
$25$	−3163.73	−	5479.74i	−0.0404957	−	0.0701406i
$26$	−34677.2			−0.386934
$27$	82256.4	−	60780.2i	0.804260	−	0.594277i
$28$	82887.2			0.713566
$29$	47035.8	+	81468.4i	0.358126	+	0.620292i	0.987648	−	0.156691i	$-0.0500826\pi$
$29$	47035.8	+	81468.4i	0.358126	+	0.620292i	−0.629522	+	0.776983i	$0.716749\pi$
$30$	−189081.	+	40720.9i	−1.27857	+	0.275355i
$31$	9963.58	−	17257.4i	0.0600689	−	0.104042i	−0.834427	−	0.551118i	$-0.814201\pi$
$31$	9963.58	−	17257.4i	0.0600689	−	0.104042i	0.894496	+	0.447076i	$0.147535\pi$
$32$	−96255.8	+	166720.i	−0.519280	+	0.899420i
$33$	−140942.	−	155690.i	−0.682719	−	0.754158i
$34$	113182.	+	196037.i	0.493857	+	0.855385i
$35$	323120.			1.27387
$36$	−16171.5	+	162230.i	−0.0577687	+	0.579526i
$37$	331750.			1.07673			0.538363	−	0.842713i	$-0.319043\pi$
$37$	331750.			1.07673			0.538363	+	0.842713i	$0.319043\pi$
$38$	−355439.	−	615638.i	−1.05081	−	1.82005i
$39$	−34920.9	+	108465.i	−0.0942669	+	0.292794i
$40$	−110538.	+	191457.i	−0.273087	+	0.473001i
$41$	−121133.	+	209809.i	−0.274486	+	0.475423i	−0.970005	−	0.243084i	$-0.921841\pi$
$41$	−121133.	+	209809.i	−0.274486	+	0.475423i	0.695520	+	0.718507i	$0.255174\pi$
$42$	226791.	−	704414.i	0.472338	−	1.46709i
$43$	−415713.	−	720036.i	−0.797359	−	1.38107i	−0.921330	−	0.388781i	$-0.872896\pi$
$43$	−415713.	−	720036.i	−0.797359	−	1.38107i	0.123971	−	0.992286i	$-0.460437\pi$
$44$	334769.			0.592462
$45$	−63041.7	+	632423.i	−0.103130	+	1.03458i
$46$	−987481.			−1.49581
$47$	80005.3	+	138573.i	0.112403	+	0.194687i	0.916738	−	0.399488i	$-0.130812\pi$
$47$	80005.3	+	138573.i	0.112403	+	0.194687i	−0.804336	+	0.594175i	$0.797479\pi$
$48$	639279.	+	706172.i	0.834346	+	0.921651i
$49$	−206366.	+	357437.i	−0.250583	+	0.434023i
$50$	45025.8	−	77987.1i	0.0509409	−	0.0882323i
$51$	727150.	−	156600.i	0.767588	−	0.165309i
$52$	−90819.7	−	157304.i	−0.0895712	−	0.155142i
$53$	311589.			0.287486			0.143743	−	0.989615i	$-0.454086\pi$
$53$	311589.			0.287486			0.143743	+	0.989615i	$0.454086\pi$
$54$	1.33446e6	+	581317.i	1.15326	+	0.502383i
$55$	1.30503e6			1.05767
$56$	−422925.	−	732527.i	−0.321814	−	0.557398i
$57$	−2.28356e6	+	491791.i	−1.63324	+	0.351738i
$58$	−669408.	+	1.15945e6i	−0.450498	+	0.780286i
$59$	156177.	−	270506.i	0.0989997	−	0.171473i	−0.812271	−	0.583280i	$-0.801769\pi$
$59$	156177.	−	270506.i	0.0989997	−	0.171473i	0.911271	+	0.411807i	$0.135102\pi$
$60$	−679926.	−	751072.i	−0.406380	−	0.448903i
$61$	28723.9	+	49751.3i	0.0162028	+	0.0280640i	0.874013	−	0.485902i	$-0.161509\pi$
$61$	28723.9	+	49751.3i	0.0162028	+	0.0280640i	−0.857810	+	0.513966i	$0.828176\pi$
$62$	283601.			0.151125
$63$	−1.97491e6	−	1.41873e6i	−0.995074	−	0.714838i
$64$	−132603.			−0.0632302
$65$	−354044.	−	613221.i	−0.159904	−	0.276962i
$66$	915973.	−	2.84502e6i	0.392174	−	1.21810i
$67$	2.05100e6	−	3.55243e6i	0.833111	−	1.44299i	−0.0624478	−	0.998048i	$-0.519891\pi$
$67$	2.05100e6	−	3.55243e6i	0.833111	−	1.44299i	0.895559	−	0.444943i	$-0.146776\pi$
$68$	−592849.	+	1.02684e6i	−0.228646	+	0.396026i
$69$	−994422.	+	3.08869e6i	−0.364417	+	1.13188i
$70$	2.29930e6	+	3.98251e6i	0.801223	+	1.38776i
$71$	−403110.			−0.133666			−0.0668328	−	0.997764i	$-0.521289\pi$
$71$	−403110.			−0.133666			−0.0668328	+	0.997764i	$0.521289\pi$
$72$	1.51625e6	−	684847.i	0.478747	−	0.216237i
$73$	−823496.			−0.247760			−0.123880	−	0.992297i	$-0.539534\pi$
$73$	−823496.			−0.247760			−0.123880	+	0.992297i	$0.539534\pi$
$74$	2.36072e6	+	4.08889e6i	0.677226	+	1.17299i
$75$	−198589.	−	219369.i	−0.0543551	−	0.0600428i
$76$	1.86180e6	−	3.22472e6i	0.486502	−	0.842646i
$77$	−2.49656e6	+	4.32418e6i	−0.623197	+	1.07941i
$78$	−1.58534e6	+	341422.i	−0.378261	+	0.0814631i
$79$	−489414.	−	847689.i	−0.111682	−	0.193438i	0.804767	−	0.593591i	$-0.202290\pi$
$79$	−489414.	−	847689.i	−0.111682	−	0.193438i	−0.916448	+	0.400153i	$0.868957\pi$
$80$	−5.91931e6			−1.29258
$81$	3.16211e6	−	3.58858e6i	0.661118	−	0.750282i
$82$	−3.44791e6			−0.690569
$83$	1.85204e6	+	3.20782e6i	0.355530	+	0.615796i	0.987209	−	0.159434i	$-0.0509670\pi$
$83$	1.85204e6	+	3.20782e6i	0.355530	+	0.615796i	−0.631678	+	0.775231i	$0.717634\pi$
$84$	3.78937e6	−	816086.i	0.697572	−	0.150231i
$85$	−2.31111e6	+	4.00296e6i	−0.408182	+	0.706993i
$86$	5.91638e6	−	1.02475e7i	1.00303	−	1.73729i
$87$	2.95246e6	+	3.26140e6i	0.480692	+	0.530991i
$88$	−1.70813e6	−	2.95857e6i	−0.267197	−	0.462799i
$89$	2.09023e6			0.314289			0.157145	−	0.987576i	$-0.449771\pi$
$89$	2.09023e6			0.314289			0.157145	+	0.987576i	$0.449771\pi$
$90$	−8.24334e6	+	3.72329e6i	−1.19194	+	0.538367i
$91$	2.70918e6			0.376872
$92$	−2.58622e6	−	4.47947e6i	−0.346265	−	0.599748i
$93$	285595.	−	887060.i	0.0368180	−	0.114357i
$94$	−1.13863e6	+	1.97216e6i	−0.141395	+	0.244903i
$95$	7.25786e6	−	1.25710e7i	0.868512	−	1.50431i
$96$	−2.75906e6	+	8.56968e6i	−0.318282	+	0.988587i
$97$	−1.75125e6	−	3.03325e6i	−0.194826	−	0.337448i	0.752018	−	0.659143i	$-0.229081\pi$
$97$	−1.75125e6	−	3.03325e6i	−0.194826	−	0.337448i	−0.946843	+	0.321695i	$0.895747\pi$
$98$	−5.87396e6			−0.630435
$99$	−7.97637e6	−	5.73004e6i	−0.826194	−	0.593519i
$100$	471692.			0.0471692
$101$	−277361.	−	480403.i	−0.0267868	−	0.0463960i	0.852321	−	0.523019i	$-0.175194\pi$
$101$	−277361.	−	480403.i	−0.0267868	−	0.0463960i	−0.879108	+	0.476623i	$0.841861\pi$
$102$	7.10449e6	+	7.84789e6i	0.662876	+	0.732238i
$103$	−1.01746e7	+	1.76229e7i	−0.917459	+	1.58909i	−0.114199	+	0.993458i	$0.536430\pi$
$103$	−1.01746e7	+	1.76229e7i	−0.917459	+	1.58909i	−0.803260	+	0.595628i	$0.796903\pi$
$104$	−926800.	+	1.60527e6i	−0.0807922	+	0.139936i
$105$	1.47721e7	−	3.18136e6i	1.24532	−	0.268194i
$106$	2.21725e6	+	3.84039e6i	0.180819	+	0.313188i
$107$	6.49941e6			0.512897			0.256449	−	0.966558i	$-0.417448\pi$
$107$	6.49941e6			0.512897			0.256449	+	0.966558i	$0.417448\pi$
$108$	857958.	+	7.57592e6i	0.0655365	+	0.578699i
$109$	2.79312e6			0.206584			0.103292	−	0.994651i	$-0.467062\pi$
$109$	2.79312e6			0.206584			0.103292	+	0.994651i	$0.467062\pi$
$110$	9.28655e6	+	1.60848e7i	0.665242	+	1.15223i
$111$	1.51667e7	−	3.26633e6i	1.05259	−	0.226689i
$112$	1.13238e7	−	1.96134e7i	0.761604	−	1.31914i
$113$	−1.04172e7	+	1.80431e7i	−0.679167	+	1.17635i	0.296065	+	0.955168i	$0.404326\pi$
$113$	−1.04172e7	+	1.80431e7i	−0.679167	+	1.17635i	−0.975232	+	0.221184i	$0.929008\pi$
$114$	−2.23111e7	−	2.46457e7i	−1.41044	−	1.55802i
$115$	−1.00819e7	−	1.74624e7i	−0.618158	−	1.07068i
$116$	−7.01274e6			−0.417143
$117$	−528570.	+	5.30252e6i	−0.0305107	+	0.306078i
$118$	4.44538e6			0.249070
$119$	−8.84244e6	−	1.53155e7i	−0.481014	−	0.833140i
$120$	−3.16845e6	+	9.84123e6i	−0.167383	+	0.519894i
$121$	−339665.	+	588316.i	−0.0174302	+	0.0301899i
$122$	−408796.	+	708055.i	−0.0203820	+	0.0353027i
$123$	−3.47214e6	+	1.07845e7i	−0.168240	+	0.522556i
$124$	742754.	+	1.28649e6i	0.0349840	+	0.0605940i
$125$	−2.08649e7			−0.955500
$126$	3.43275e6	−	3.44367e7i	0.152878	−	1.53365i
$127$	8.89911e6			0.385508			0.192754	−	0.981247i	$-0.438258\pi$
$127$	8.89911e6			0.385508			0.192754	+	0.981247i	$0.438258\pi$
$128$	1.13771e7	+	1.97058e7i	0.479511	+	0.830537i
$129$	−2.60945e7	−	2.88250e7i	−1.07025	−	1.18224i
$130$	5.03871e6	−	8.72731e6i	0.201149	−	0.348400i
$131$	−6.35869e6	+	1.10136e7i	−0.247126	+	0.428034i	−0.962727	−	0.270475i	$-0.912819\pi$
$131$	−6.35869e6	+	1.10136e7i	−0.247126	+	0.428034i	0.715601	+	0.698509i	$0.246153\pi$
$132$	1.53047e7	−	3.29605e6i	0.579183	−	0.124734i
$133$	2.77690e7	+	4.80973e7i	1.02348	+	1.77272i
$134$	5.83791e7			2.09600
$135$	3.34459e6	+	2.95333e7i	0.116997	+	1.03310i
$136$	1.20998e7			0.412471
$137$	−2.45052e7	−	4.24442e7i	−0.814209	−	1.41025i	−0.909895	−	0.414840i	$-0.863838\pi$
$137$	−2.45052e7	−	4.24442e7i	−0.814209	−	1.41025i	0.0956855	−	0.995412i	$-0.469496\pi$
$138$	−4.51449e7	+	9.72249e6i	−1.46228	+	0.314920i
$139$	789537.	−	1.36752e6i	0.0249357	−	0.0431898i	−0.853288	−	0.521439i	$-0.825395\pi$
$139$	789537.	−	1.36752e6i	0.0249357	−	0.0431898i	0.878224	+	0.478250i	$0.158729\pi$
$140$	−1.20438e7	+	2.08605e7i	−0.370950	+	0.642504i
$141$	5.02198e6	+	5.54747e6i	0.150872	+	0.166659i
$142$	−2.86851e6	−	4.96841e6i	−0.0840713	−	0.145616i
$143$	1.09420e7			0.312910
$144$	3.61788e7	+	2.59900e7i	1.00968	+	0.725334i
$145$	−2.73379e7			−0.744692
$146$	−5.85996e6	−	1.01497e7i	−0.155833	−	0.269911i
$147$	−5.91525e6	+	1.83728e7i	−0.153590	+	0.477052i
$148$	−1.23655e7	+	2.14177e7i	−0.313542	+	0.543070i
$149$	1.95734e7	−	3.39021e7i	0.484746	−	0.839605i	−0.515100	−	0.857130i	$-0.672245\pi$
$149$	1.95734e7	−	3.39021e7i	0.484746	−	0.839605i	0.999846	+	0.0175249i	$0.00557863\pi$
$150$	1.29061e6	−	4.00866e6i	0.0312232	−	0.0969795i
$151$	−9.19094e6	−	1.59192e7i	−0.217240	−	0.376271i	0.736723	−	0.676195i	$-0.236372\pi$
$151$	−9.19094e6	−	1.59192e7i	−0.217240	−	0.376271i	−0.953963	+	0.299923i	$0.903039\pi$
$152$	−3.79986e7			−0.877638
$153$	3.17014e7	−	1.43187e7i	0.715580	−	0.323208i
$154$	−7.10617e7			−1.56788
$155$	2.89549e6	+	5.01513e6i	0.0624540	+	0.108174i
$156$	−5.70080e6	−	6.29733e6i	−0.120226	−	0.132807i
$157$	3.32168e7	−	5.75332e7i	0.685029	−	1.18650i	−0.288399	−	0.957510i	$-0.593123\pi$
$157$	3.32168e7	−	5.75332e7i	0.685029	−	1.18650i	0.973428	−	0.228994i	$-0.0735437\pi$
$158$	6.96529e6	−	1.20642e7i	0.140488	−	0.243332i
$159$	1.42450e7	−	3.06783e6i	0.281042	−	0.0605258i
$160$	−2.79726e7	−	4.84500e7i	−0.539900	−	0.935134i
$161$	7.71478e7			1.45691
$162$	6.67312e7	+	1.34374e7i	1.23318	+	0.248321i
$163$	−3.94682e7			−0.713823			−0.356912	−	0.934138i	$-0.616170\pi$
$163$	−3.94682e7			−0.713823			−0.356912	+	0.934138i	$0.616170\pi$
$164$	−9.03010e6	−	1.56406e7i	−0.159860	−	0.276885i
$165$	5.96624e7	−	1.28490e7i	1.03397	−	0.222677i
$166$	−2.63580e7	+	4.56534e7i	−0.447234	+	0.774631i
$167$	−4.86177e7	+	8.42084e7i	−0.807769	+	1.39910i	0.106637	+	0.994298i	$0.465992\pi$
$167$	−4.86177e7	+	8.42084e7i	−0.807769	+	1.39910i	−0.914406	+	0.404799i	$0.867342\pi$
$168$	−2.65472e7	−	2.93251e7i	−0.431953	−	0.477152i
$169$	2.84058e7	+	4.92003e7i	0.452693	+	0.784087i
$170$	−6.57829e7			−1.02693
$171$	−9.95557e7	+	4.49666e7i	−1.52258	+	0.687708i
$172$	6.19802e7			0.928760
$173$	−2.77015e7	−	4.79804e7i	−0.406763	−	0.704534i	0.587762	−	0.809034i	$-0.300009\pi$
$173$	−2.77015e7	−	4.79804e7i	−0.406763	−	0.704534i	−0.994525	+	0.104500i	$0.966676\pi$
$174$	−1.91878e7	+	5.95976e7i	−0.276124	+	0.857643i
$175$	−3.51768e6	+	6.09281e6i	−0.0496162	+	0.0859378i
$176$	4.57351e7	−	7.92156e7i	0.632347	−	1.09526i
$177$	4.47662e6	−	1.39044e7i	0.0606798	−	0.188472i
$178$	1.48740e7	+	2.57625e7i	0.197678	+	0.342388i
$179$	9.87173e7			1.28649			0.643247	−	0.765659i	$-0.277587\pi$
$179$	9.87173e7			1.28649			0.643247	+	0.765659i	$0.277587\pi$
$180$	−3.84792e7	−	2.76425e7i	−0.491781	−	0.353284i
$181$	9.03305e7			1.13230			0.566148	−	0.824304i	$-0.308433\pi$
$181$	9.03305e7			1.13230			0.566148	+	0.824304i	$0.308433\pi$
$182$	1.92784e7	+	3.33912e7i	0.237040	+	0.410565i
$183$	1.80301e6	+	1.99168e6i	0.0217481	+	0.0240237i
$184$	−2.63920e7	+	4.57122e7i	−0.312327	+	0.540966i
$185$	−4.82045e7	+	8.34927e7i	−0.559740	+	0.969499i
$186$	1.29655e7	−	2.79226e6i	0.147738	−	0.0318172i
$187$	−3.57133e7	−	6.18572e7i	−0.399378	−	0.691743i
$188$	−1.19283e7			−0.130926
$189$	−1.04256e8	−	4.54159e7i	−1.12327	−	0.489318i
$190$	2.06586e8			2.18506
$191$	5.20912e7	+	9.02247e7i	0.540938	+	0.936933i	0.998850	+	0.0479353i	$0.0152641\pi$
$191$	5.20912e7	+	9.02247e7i	0.540938	+	0.936933i	−0.457912	+	0.888998i	$0.651403\pi$
$192$	−6.06225e6	+	1.30558e6i	−0.0618130	+	0.0133122i
$193$	−6.65147e6	+	1.15207e7i	−0.0665989	+	0.115353i	−0.897402	−	0.441214i	$-0.854548\pi$
$193$	−6.65147e6	+	1.15207e7i	−0.0665989	+	0.115353i	0.830803	+	0.556566i	$0.187881\pi$
$194$	2.49236e7	−	4.31689e7i	0.245078	−	0.424487i
$195$	−2.22235e7	−	2.45489e7i	−0.214630	−	0.237089i
$196$	−1.53840e7	−	2.66458e7i	−0.145939	−	0.252774i
$197$	−1.71308e8			−1.59641			−0.798206	−	0.602384i	$-0.794217\pi$
$197$	−1.71308e8			−1.59641			−0.798206	+	0.602384i	$0.794217\pi$
$198$	1.38644e7	−	1.39085e8i	0.126932	−	1.27336i
$199$	−1.24021e8			−1.11561			−0.557803	−	0.829974i	$-0.688355\pi$
$199$	−1.24021e8			−1.11561			−0.557803	+	0.829974i	$0.688355\pi$
$200$	−2.40677e6	−	4.16865e6i	−0.0212730	−	0.0368460i
$201$	5.87895e7	−	1.82601e8i	0.510638	−	1.58605i
$202$	3.94737e6	−	6.83704e6i	0.0336960	−	0.0583631i
$203$	5.22981e7	−	9.05830e7i	0.438783	−	0.759994i
$204$	−1.69933e7	+	5.27815e7i	−0.140144	+	0.435287i
$205$	−3.52021e7	−	6.09719e7i	−0.285385	−	0.494301i
$206$	−2.89608e8			−2.30821
$207$	−1.50518e7	+	1.50997e8i	−0.117948	+	1.18324i
$208$	−4.96301e7			−0.382405
$209$	1.12155e8	+	1.94258e8i	0.849778	+	1.47186i
$210$	1.44329e8	+	1.59431e8i	1.07544	+	1.18797i
$211$	9.32487e7	−	1.61511e8i	0.683367	−	1.18363i	−0.290580	−	0.956851i	$-0.593848\pi$
$211$	9.32487e7	−	1.61511e8i	0.683367	−	1.18363i	0.973947	−	0.226776i	$-0.0728185\pi$
$212$	−1.16140e7	+	2.01160e7i	−0.0837156	+	0.145000i
$213$	−1.84291e7	+	3.96892e6i	−0.130670	+	0.0281413i
$214$	4.62495e7	+	8.01064e7i	0.322596	+	0.558752i
$215$	2.41618e8			1.65804
$216$	6.25757e7	−	4.62379e7i	0.422491	−	0.312183i
$217$	−2.21566e7			−0.147195
$218$	1.98757e7	+	3.44257e7i	0.129935	+	0.225053i
$219$	−3.76479e7	+	8.10793e6i	−0.242207	+	0.0521622i
$220$	−4.86431e7	+	8.42523e7i	−0.307994	+	0.533461i
$221$	−1.93774e7	+	3.35626e7i	−0.120760	+	0.209162i
$222$	1.48184e8	+	1.63689e8i	0.909002	+	1.00412i
$223$	2.10250e7	+	3.64164e7i	0.126961	+	0.219902i	0.922498	−	0.386003i	$-0.126144\pi$
$223$	2.10250e7	+	3.64164e7i	0.126961	+	0.219902i	−0.795537	+	0.605905i	$0.792811\pi$
$224$	2.14050e8			1.27247
$225$	−1.12388e7	−	8.07368e6i	−0.0657779	−	0.0472533i
$226$	−2.96513e8			−1.70869
$227$	−1.56517e8	−	2.71095e8i	−0.888117	−	1.53826i	−0.842098	−	0.539324i	$-0.818680\pi$
$227$	−1.56517e8	−	2.71095e8i	−0.888117	−	1.53826i	−0.0460190	−	0.998941i	$-0.514653\pi$
$228$	5.33662e7	−	1.65756e8i	0.298191	−	0.926184i
$229$	−8.35576e7	+	1.44726e8i	−0.459792	+	0.796384i	−0.998950	−	0.0458213i	$-0.985410\pi$
$229$	−8.35576e7	+	1.44726e8i	−0.459792	+	0.796384i	0.539157	+	0.842205i	$0.318743\pi$
$230$	1.43485e8	−	2.48522e8i	0.777602	−	1.34685i
$231$	−7.15612e7	+	2.22270e8i	−0.381976	+	1.18642i
$232$	3.57819e7	+	6.19761e7i	0.188129	+	0.325849i
$233$	−2.55430e8			−1.32290			−0.661449	−	0.749990i	$-0.730058\pi$
$233$	−2.55430e8			−1.32290			−0.661449	+	0.749990i	$0.730058\pi$
$234$	−6.91158e7	+	3.12177e7i	−0.352632	+	0.159274i
$235$	−4.65002e7			−0.233732
$236$	1.16425e7	+	2.01654e7i	0.0576572	+	0.0998652i
$237$	−3.07207e7	−	3.39353e7i	−0.149904	−	0.165590i
$238$	1.25845e8	−	2.17969e8i	0.605084	−	1.04804i
$239$	8.84471e7	−	1.53195e8i	0.419074	−	0.725858i	−0.576772	−	0.816905i	$-0.695688\pi$
$239$	8.84471e7	−	1.53195e8i	0.419074	−	0.725858i	0.995847	+	0.0910472i	$0.0290214\pi$
$240$	−2.70614e8	+	5.82800e7i	−1.26360	+	0.272132i
$241$	1.56994e8	+	2.71922e8i	0.722478	+	1.25137i	0.960004	+	0.279987i	$0.0903303\pi$
$241$	1.56994e8	+	2.71922e8i	0.722478	+	1.25137i	−0.237526	+	0.971381i	$0.576336\pi$
$242$	−9.66814e6			−0.0438520
$243$	1.09230e8	−	1.95193e8i	0.488339	−	0.872654i
$244$	−4.28256e6			−0.0188729
$245$	−5.99715e7	−	1.03874e8i	−0.260533	−	0.451257i
$246$	−1.57629e8	+	3.39472e7i	−0.675091	+	0.145389i
$247$	6.08531e7	−	1.05401e8i	0.256947	−	0.445045i
$248$	7.57968e6	−	1.31284e7i	0.0315551	−	0.0546551i
$249$	1.16253e8	+	1.28418e8i	0.477208	+	0.527143i
$250$	−1.48473e8	−	2.57163e8i	−0.600978	−	1.04092i
$251$	1.34891e8			0.538425			0.269212	−	0.963081i	$-0.413237\pi$
$251$	1.34891e8			0.538425			0.269212	+	0.963081i	$0.413237\pi$
$252$	1.65204e8	−	7.46183e7i	0.650308	−	0.293727i
$253$	3.11588e8			1.20965
$254$	6.33256e7	+	1.09683e8i	0.242472	+	0.419974i
$255$	−6.62453e7	+	2.05759e8i	−0.250187	+	0.777083i
$256$	−1.70405e8	+	2.95150e8i	−0.634808	+	1.09952i
$257$	−1.17761e8	+	2.03969e8i	−0.432750	+	0.749545i	−0.997109	−	0.0759845i	$-0.975790\pi$
$257$	−1.17761e8	+	2.03969e8i	−0.432750	+	0.749545i	0.564359	+	0.825529i	$0.309123\pi$
$258$	1.69586e8	−	5.26737e8i	0.614783	−	1.90952i
$259$	−1.84433e8	−	3.19448e8i	−0.659614	−	1.14249i
$260$	5.27857e7			0.186256
$261$	1.67089e8	+	1.20033e8i	0.581710	+	0.417887i
$262$	−1.80992e8			−0.621736
$263$	8.33326e7	+	1.44336e8i	0.282468	+	0.489249i	0.971992	−	0.235014i	$-0.0755135\pi$
$263$	8.33326e7	+	1.44336e8i	0.282468	+	0.489249i	−0.689524	+	0.724263i	$0.742180\pi$
$264$	−1.07220e8	−	1.18440e8i	−0.358643	−	0.396171i
$265$	−4.52750e7	+	7.84186e7i	−0.149451	+	0.258856i
$266$	−3.95205e8	+	6.84515e8i	−1.28747	+	2.22996i
$267$	9.55596e7	−	2.05799e7i	0.307245	−	0.0661689i
$268$	1.52895e8	+	2.64823e8i	0.485202	+	0.840395i
$269$	−1.49508e8			−0.468308			−0.234154	−	0.972200i	$-0.575232\pi$
$269$	−1.49508e8			−0.468308			−0.234154	+	0.972200i	$0.575232\pi$
$270$	−3.40204e8	+	2.51380e8i	−1.05188	+	0.777245i
$271$	3.02665e8			0.923783			0.461892	−	0.886936i	$-0.347171\pi$
$271$	3.02665e8			0.923783			0.461892	+	0.886936i	$0.347171\pi$
$272$	1.61987e8	+	2.80569e8i	0.488076	+	0.845373i
$273$	1.23856e8	−	2.66739e7i	0.368424	−	0.0793446i
$274$	3.48755e8	−	6.04062e8i	1.02422	−	1.77400i
$275$	−1.42074e7	+	2.46079e7i	−0.0411955	+	0.0713527i
$276$	−1.62338e8	−	1.79325e8i	−0.464772	−	0.513405i
$277$	−1.63479e7	−	2.83153e7i	−0.0462148	−	0.0800465i	0.841993	−	0.539489i	$-0.181383\pi$
$277$	−1.63479e7	−	2.83153e7i	−0.0462148	−	0.0800465i	−0.888207	+	0.459443i	$0.848049\pi$
$278$	2.24732e7			0.0627348
$279$	4.32282e6	−	4.33658e7i	0.0119166	−	0.119545i
$280$	2.45810e8			0.669185
$281$	−2.50968e8	−	4.34689e8i	−0.674755	−	1.16871i	−0.976540	−	0.215334i	$-0.930916\pi$
$281$	−2.50968e8	−	4.34689e8i	−0.674755	−	1.16871i	0.301786	−	0.953376i	$-0.402417\pi$
$282$	−3.26375e7	+	1.01372e8i	−0.0866652	+	0.269183i
$283$	−1.62635e8	+	2.81691e8i	−0.426541	+	0.738790i	−0.996563	−	0.0828391i	$-0.973601\pi$
$283$	−1.62635e8	+	2.81691e8i	−0.426541	+	0.738790i	0.570022	+	0.821629i	$0.306935\pi$
$284$	1.50253e7	−	2.60246e7i	0.0389233	−	0.0674171i
$285$	2.08038e8	−	6.46169e8i	0.532336	−	1.65344i
$286$	7.78626e7	+	1.34862e8i	0.196810	+	0.340885i
$287$	2.69371e8			0.672611
$288$	−4.17617e7	+	4.18946e8i	−0.103016	+	1.03344i
$289$	−1.57357e8			−0.383481
$290$	−1.94535e8	−	3.36944e8i	−0.468386	−	0.811269i
$291$	−1.09927e8	−	1.21429e8i	−0.261504	−	0.288867i
$292$	3.06945e7	−	5.31645e7i	0.0721475	−	0.124963i
$293$	7.17572e7	−	1.24287e8i	0.166659	−	0.288662i	−0.770584	−	0.637338i	$-0.780035\pi$
$293$	7.17572e7	−	1.24287e8i	0.166659	−	0.288662i	0.937243	+	0.348676i	$0.113369\pi$
$294$	−2.68541e8	+	5.78335e7i	−0.616304	+	0.132728i
$295$	4.53860e7	+	7.86109e7i	0.102931	+	0.178281i
$296$	2.52375e8			0.565622
$297$	−4.21074e8	−	1.83428e8i	−0.932632	−	0.406273i
$298$	5.57133e8			1.21956
$299$	−8.45311e7	−	1.46412e8i	−0.182881	−	0.316758i
$300$	2.15644e7	−	4.64416e6i	0.0461120	−	0.00993077i
$301$	−4.62223e8	+	8.00593e8i	−0.976941	+	1.69211i
$302$	1.30805e8	−	2.26560e8i	0.273274	−	0.473325i
$303$	−1.74101e7	−	1.92318e7i	−0.0359543	−	0.0397166i
$304$	−5.08706e8	−	8.81105e8i	−1.03851	−	1.79875i
$305$	−1.66947e7			−0.0336923
$306$	4.02066e8	+	2.88835e8i	0.802180	+	0.576268i
$307$	−6.60558e8			−1.30295			−0.651474	−	0.758671i	$-0.725849\pi$
$307$	−6.60558e8			−1.30295			−0.651474	+	0.758671i	$0.725849\pi$
$308$	−1.86111e8	−	3.22354e8i	−0.362949	−	0.628645i
$309$	−2.91643e8	+	9.05847e8i	−0.562338	+	1.74663i
$310$	−4.12083e7	+	7.13748e7i	−0.0785630	+	0.136075i
$311$	−5.28703e7	+	9.15740e7i	−0.0996667	+	0.172628i	−0.911547	−	0.411197i	$-0.865111\pi$
$311$	−5.28703e7	+	9.15740e7i	−0.0996667	+	0.172628i	0.811880	+	0.583824i	$0.198444\pi$
$312$	−2.65657e7	+	8.25133e7i	−0.0495199	+	0.153809i
$313$	5.93605e7	+	1.02815e8i	0.109419	+	0.189519i	0.915535	−	0.402238i	$-0.131768\pi$
$313$	5.93605e7	+	1.02815e8i	0.109419	+	0.189519i	−0.806116	+	0.591757i	$0.798434\pi$
$314$	9.45476e8			1.72344
$315$	6.44018e8	−	2.90885e8i	1.16094	−	0.524366i
$316$	7.29686e7			0.130086
$317$	2.17334e8	+	3.76434e8i	0.383196	+	0.663715i	0.991517	−	0.129976i	$-0.0414901\pi$
$317$	2.17334e8	+	3.76434e8i	0.383196	+	0.663715i	−0.608321	+	0.793691i	$0.708157\pi$
$318$	1.39178e8	+	1.53741e8i	0.242703	+	0.268100i
$319$	2.11224e8	−	3.65851e8i	0.364314	−	0.631011i
$320$	1.92677e7	−	3.33727e7i	0.0328705	−	0.0569333i
$321$	2.97135e8	−	6.39915e7i	0.501402	−	0.107983i
$322$	5.48980e8	+	9.50861e8i	0.916349	+	1.58716i
$323$	−7.94468e8			−1.31180
$324$	1.13814e8	+	3.37903e8i	0.185904	+	0.551930i
$325$	1.54173e7			0.0249125
$326$	−2.80854e8	−	4.86453e8i	−0.448971	−	0.777641i
$327$	1.27694e8	−	2.75004e7i	0.201954	−	0.0434932i
$328$	−9.21507e7	+	1.59610e8i	−0.144192	+	0.249747i
$329$	8.89563e7	−	1.54077e8i	0.137718	−	0.238535i
$330$	5.82921e8	+	6.43918e8i	0.892917	+	0.986351i
$331$	−3.67129e8	−	6.35887e8i	−0.556444	−	0.963789i	−0.997790	−	0.0664518i	$-0.978832\pi$
$331$	−3.67129e8	−	6.35887e8i	−0.556444	−	0.963789i	0.441346	−	0.897337i	$-0.354501\pi$
$332$	−2.76127e8			−0.414120
$333$	6.61219e8	−	2.98655e8i	0.981275	−	0.443215i
$334$	−1.38385e9			−2.03224
$335$	5.96034e8	+	1.03236e9i	0.866192	+	1.50029i
$336$	3.24584e8	−	1.00816e9i	0.466809	−	1.44991i
$337$	2.35772e8	−	4.08370e8i	0.335574	−	0.581231i	−0.648021	−	0.761622i	$-0.724403\pi$
$337$	2.35772e8	−	4.08370e8i	0.335574	−	0.581231i	0.983595	+	0.180391i	$0.0577364\pi$
$338$	−4.04268e8	+	7.00213e8i	−0.569458	+	0.986329i
$339$	−2.98597e8	+	9.27446e8i	−0.416281	+	1.29297i
$340$	−1.72286e8	−	2.98408e8i	−0.237724	−	0.411751i
$341$	−8.94871e7			−0.122214
$342$	−1.26266e9	−	9.07063e8i	−1.70684	−	1.22616i
$343$	−4.56772e8			−0.611181
$344$	−3.16249e8	−	5.47759e8i	−0.418866	−	0.725496i
$345$	−6.32846e8	−	6.99066e8i	−0.829719	−	0.916540i
$346$	3.94244e8	−	6.82851e8i	0.511681	−	0.886257i
$347$	5.53356e8	−	9.58441e8i	0.710970	−	1.23144i	−0.253523	−	0.967329i	$-0.581589\pi$
$347$	5.53356e8	−	9.58441e8i	0.710970	−	1.23144i	0.964493	−	0.264107i	$-0.0850773\pi$
$348$	−3.20603e8	+	6.90457e7i	−0.407793	+	0.0878232i
$349$	3.98088e7	+	6.89509e7i	0.0501291	+	0.0868262i	0.890001	−	0.455958i	$-0.150703\pi$
$349$	3.98088e7	+	6.89509e7i	0.0501291	+	0.0868262i	−0.839872	+	0.542784i	$0.817370\pi$
$350$	−1.00127e8			−0.124828
$351$	2.80425e7	+	2.47620e8i	0.0346132	+	0.305641i
$352$	8.64514e8			1.05651
$353$	5.09107e7	+	8.81799e7i	0.0616024	+	0.106698i	0.895182	−	0.445701i	$-0.147046\pi$
$353$	5.09107e7	+	8.81799e7i	0.0616024	+	0.106698i	−0.833579	+	0.552400i	$0.813712\pi$
$354$	2.03230e8	−	4.37681e7i	0.243488	−	0.0524380i
$355$	5.85734e7	−	1.01452e8i	0.0694866	−	0.120354i
$356$	−7.79102e7	+	1.34944e8i	−0.0915207	+	0.158518i
$357$	−5.55044e8	−	6.13123e8i	−0.645638	−	0.713196i
$358$	7.02468e8	+	1.21671e9i	0.809162	+	1.40151i
$359$	9.69307e7			0.110568			0.0552842	−	0.998471i	$-0.482394\pi$
$359$	9.69307e7			0.110568			0.0552842	+	0.998471i	$0.482394\pi$
$360$	−4.79583e7	+	4.81109e8i	−0.0541757	+	0.543481i
$361$	1.60109e9			1.79119
$362$	6.42788e8	+	1.11334e9i	0.712176	+	1.23353i
$363$	−9.73610e6	+	3.02404e7i	−0.0106835	+	0.0331829i
$364$	−1.00981e8	+	1.74903e8i	−0.109745	+	0.190083i
$365$	1.19657e8	−	2.07252e8i	0.128799	−	0.223086i
$366$	−1.17177e7	+	3.63952e7i	−0.0124927	+	0.0388025i
$367$	7.72007e8	+	1.33716e9i	0.815249	+	1.41205i	0.909149	+	0.416471i	$0.136733\pi$
$367$	7.72007e8	+	1.33716e9i	0.815249	+	1.41205i	−0.0939003	+	0.995582i	$0.529933\pi$
$368$	−1.41329e9			−1.47830
$369$	−5.25551e7	+	5.27223e8i	−0.0544531	+	0.546264i
$370$	−1.37208e9			−1.40823
$371$	−1.73225e8	−	3.00034e8i	−0.176117	−	0.305043i
$372$	4.66230e7	+	5.15016e7i	0.0469570	+	0.0518705i
$373$	6.74772e8	−	1.16874e9i	0.673250	−	1.16610i	−0.303727	−	0.952759i	$-0.598231\pi$
$373$	6.74772e8	−	1.16874e9i	0.673250	−	1.16610i	0.976977	−	0.213344i	$-0.0684355\pi$
$374$	5.08268e8	−	8.80345e8i	0.502391	−	0.870167i
$375$	−9.53883e8	+	2.05430e8i	−0.934084	+	0.201166i
$376$	6.08632e7	+	1.05418e8i	0.0590469	+	0.102272i
$377$	−2.29213e8			−0.220315
$378$	−1.82120e8	−	1.60815e9i	−0.173435	−	1.53146i
$379$	1.61145e9			1.52048			0.760238	−	0.649645i	$-0.225082\pi$
$379$	1.61145e9			1.52048			0.760238	+	0.649645i	$0.225082\pi$
$380$	5.41051e8	+	9.37127e8i	0.505819	+	0.876105i
$381$	4.06842e8	−	8.76183e7i	0.376867	−	0.0811629i
$382$	−7.41357e8	+	1.28407e9i	−0.680465	+	1.17860i
$383$	−6.32119e8	+	1.09486e9i	−0.574915	+	0.995781i	0.421136	+	0.906997i	$0.361631\pi$
$383$	−6.32119e8	+	1.09486e9i	−0.574915	+	0.995781i	−0.996051	+	0.0887840i	$0.971702\pi$
$384$	7.14149e8	+	7.88877e8i	0.643620	+	0.710968i
$385$	−7.25519e8	−	1.25664e9i	−0.647942	−	1.12227i
$386$	−1.89326e8			−0.167554
$387$	−1.47677e9	−	1.06088e9i	−1.29516	−	0.930417i
$388$	2.61100e8			0.226932
$389$	9.18665e8	+	1.59117e9i	0.791286	+	1.37055i	0.925171	+	0.379551i	$0.123921\pi$
$389$	9.18665e8	+	1.59117e9i	0.791286	+	1.37055i	−0.133885	+	0.990997i	$0.542745\pi$
$390$	1.44429e8	−	4.48598e8i	0.123290	−	0.382940i
$391$	−5.51798e8	+	9.55743e8i	−0.466833	+	0.808579i
$392$	−1.56991e8	+	2.71916e8i	−0.131635	+	0.227999i
$393$	−1.82265e8	+	5.66115e8i	−0.151471	+	0.470469i
$394$	−1.21902e9	−	2.11140e9i	−1.00409	−	1.73914i
$395$	2.84454e8			0.232232
$396$	6.67235e8	−	3.01372e8i	0.539940	−	0.243876i
$397$	−1.85478e9			−1.48773			−0.743867	−	0.668327i	$-0.767011\pi$
$397$	−1.85478e9			−1.48773			−0.743867	+	0.668327i	$0.767011\pi$
$398$	−8.82529e8	−	1.52859e9i	−0.701679	−	1.21534i
$399$	1.74307e9	+	1.92547e9i	1.37376	+	1.51751i
$400$	6.44412e7	−	1.11615e8i	0.0503447	−	0.0871996i
$401$	6.04284e8	−	1.04665e9i	0.467989	−	0.810580i	−0.531342	−	0.847157i	$-0.678312\pi$
$401$	6.04284e8	−	1.04665e9i	0.467989	−	0.810580i	0.999331	+	0.0365770i	$0.0116454\pi$
$402$	2.66893e9	−	5.74786e8i	2.04902	−	0.441281i
$403$	2.42770e7	+	4.20491e7i	0.0184769	+	0.0320029i
$404$	4.13528e7			0.0312011
$405$	4.43683e8	+	1.31725e9i	0.331879	+	0.985316i
$406$	1.48860e9			1.10392
$407$	−7.44898e8	−	1.29020e9i	−0.547667	−	0.948587i
$408$	5.53171e8	−	1.19132e8i	0.403226	−	0.0868396i
$409$	6.10716e8	−	1.05779e9i	0.441375	−	0.764484i	−0.556417	−	0.830903i	$-0.687824\pi$
$409$	6.10716e8	−	1.05779e9i	0.441375	−	0.764484i	0.997792	+	0.0664194i	$0.0211575\pi$
$410$	5.00993e8	−	8.67746e8i	0.358995	−	0.621798i
$411$	−1.53820e9	−	1.69916e9i	−1.09287	−	1.20722i
$412$	−7.58485e8	−	1.31373e9i	−0.534326	−	0.925480i
$413$	−3.47299e8			−0.242593
$414$	−1.96817e9	+	8.88970e8i	−1.36321	+	0.615724i
$415$	−1.07643e9			−0.739295
$416$	−2.34535e8	−	4.06226e8i	−0.159728	−	0.276657i
$417$	2.26312e7	−	7.02927e7i	0.0152838	−	0.0474716i
$418$	−1.59617e9	+	2.76466e9i	−1.06896	+	1.85150i
$419$	−7.60350e8	+	1.31697e9i	−0.504969	+	0.874632i	0.495014	+	0.868885i	$0.335163\pi$
$419$	−7.60350e8	+	1.31697e9i	−0.504969	+	0.874632i	−0.999983	+	0.00574729i	$0.998171\pi$
$420$	−3.45222e8	+	1.07226e9i	−0.227366	+	0.706201i
$421$	−5.43681e8	−	9.41684e8i	−0.355105	−	0.615060i	0.632031	−	0.774943i	$-0.282222\pi$
$421$	−5.43681e8	−	9.41684e8i	−0.355105	−	0.615060i	−0.987136	+	0.159883i	$0.948888\pi$
$422$	2.65421e9			1.71926
$423$	2.84210e8	+	2.04170e8i	0.182578	+	0.131160i
$424$	2.37038e8			0.151021
$425$	−5.03203e7	−	8.71573e7i	−0.0317967	−	0.0550735i
$426$	−1.80058e8	−	1.98899e8i	−0.112844	−	0.124652i
$427$	3.19375e7	−	5.53174e7i	0.0198520	−	0.0343846i
$428$	−2.42255e8	+	4.19599e8i	−0.149355	+	0.258691i
$429$	5.00236e8	−	1.07732e8i	0.305897	−	0.0658785i
$430$	1.71934e9	+	2.97799e9i	1.04285	+	1.80627i
$431$	−1.33391e9			−0.802521			−0.401261	−	0.915964i	$-0.631428\pi$
$431$	−1.33391e9			−0.802521			−0.401261	+	0.915964i	$0.631428\pi$
$432$	1.90989e9	+	8.31984e8i	1.13976	+	0.496503i
$433$	−3.41286e8			−0.202027			−0.101014	−	0.994885i	$-0.532209\pi$
$433$	−3.41286e8			−0.202027			−0.101014	+	0.994885i	$0.532209\pi$
$434$	−1.57665e8	−	2.73084e8i	−0.0925810	−	0.160355i
$435$	−1.24981e9	+	2.69162e8i	−0.728000	+	0.156784i
$436$	−1.04109e8	+	1.80323e8i	−0.0601571	+	0.104195i
$437$	1.73288e9	−	3.00144e9i	0.993307	−	1.72046i
$438$	−3.67832e8	−	4.06322e8i	−0.209166	−	0.231053i
$439$	6.78117e8	+	1.17453e9i	0.382541	+	0.662581i	0.991425	−	0.130679i	$-0.0417156\pi$
$439$	6.78117e8	+	1.17453e9i	0.382541	+	0.662581i	−0.608883	+	0.793260i	$0.708382\pi$
$440$	9.92789e8			0.555613
$441$	−8.95345e7	+	8.98194e8i	−0.0497113	+	0.498695i
$442$	−5.51554e8			−0.303815
$443$	5.79697e8	+	1.00407e9i	0.316802	+	0.548717i	0.979819	−	0.199887i	$-0.0640575\pi$
$443$	5.79697e8	+	1.00407e9i	0.316802	+	0.548717i	−0.663017	+	0.748605i	$0.730724\pi$
$444$	−3.54443e8	+	1.10090e9i	−0.192179	+	0.596909i
$445$	−3.03718e8	+	5.26055e8i	−0.163384	+	0.282990i
$446$	−2.99226e8	+	5.18274e8i	−0.159708	+	0.276622i
$447$	5.61049e8	−	1.74262e9i	0.297115	−	0.922842i
$448$	7.37195e7	+	1.27686e8i	0.0387355	+	0.0670918i
$449$	9.76057e8			0.508877			0.254439	−	0.967089i	$-0.418109\pi$
$449$	9.76057e8			0.508877			0.254439	+	0.967089i	$0.418109\pi$
$450$	1.95350e7	−	1.95972e8i	0.0101058	−	0.101379i
$451$	1.08795e9			0.558458
$452$	−7.76570e8	−	1.34506e9i	−0.395545	−	0.685105i
$453$	−5.76920e8	−	6.37288e8i	−0.291590	−	0.322101i
$454$	2.22753e9	−	3.85820e9i	1.11719	−	1.93504i
$455$	−3.93654e8	+	6.81828e8i	−0.195918	+	0.339340i
$456$	−1.73719e9	+	3.74125e8i	−0.857967	+	0.184773i
$457$	9.44190e8	+	1.63539e9i	0.462757	+	0.801518i	0.999097	−	0.0424836i	$-0.0135270\pi$
$457$	9.44190e8	+	1.63539e9i	0.462757	+	0.801518i	−0.536340	+	0.844002i	$0.680194\pi$
$458$	−2.37837e9			−1.15678
$459$	1.30832e9	−	9.66733e8i	0.631495	−	0.466619i
$460$	1.50315e9			0.720028
$461$	7.07086e8	+	1.22471e9i	0.336139	+	0.582210i	0.983703	−	0.179801i	$-0.0575454\pi$
$461$	7.07086e8	+	1.22471e9i	0.336139	+	0.582210i	−0.647564	+	0.762011i	$0.724212\pi$
$462$	−3.24874e9	+	6.99655e8i	−1.53274	+	0.330094i
$463$	5.13035e8	−	8.88602e8i	0.240222	−	0.416077i	−0.720555	−	0.693398i	$-0.756113\pi$
$463$	5.13035e8	−	8.88602e8i	0.240222	−	0.416077i	0.960778	+	0.277320i	$0.0894463\pi$
$464$	−9.58061e8	+	1.65941e9i	−0.445226	+	0.771153i
$465$	1.81751e8	+	2.00769e8i	0.0838285	+	0.0926002i
$466$	−1.81763e9	−	3.14822e9i	−0.832059	−	1.44117i
$467$	4.39875e8			0.199858			0.0999288	−	0.994995i	$-0.468139\pi$
$467$	4.39875e8			0.199858			0.0999288	+	0.994995i	$0.468139\pi$
$468$	−3.22627e8	−	2.31767e8i	−0.145492	−	0.104518i
$469$	−4.56092e9			−2.04149
$470$	−3.30893e8	−	5.73124e8i	−0.147009	−	0.254628i
$471$	9.52121e8	−	2.95730e9i	0.419874	−	1.30413i
$472$	1.18810e8	−	2.05784e8i	0.0520061	−	0.0900773i
$473$	−1.86685e9	+	3.23347e9i	−0.811138	+	1.40493i
$474$	1.99652e8	−	6.20121e8i	0.0861092	−	0.267456i
$475$	1.58027e8	+	2.73711e8i	0.0676556	+	0.117183i
$476$	1.31835e9			0.560283
$477$	6.21035e8	−	2.80505e8i	0.262000	−	0.118338i
$478$	2.51754e9			1.05434
$479$	−1.23369e9	−	2.13681e9i	−0.512899	−	0.888367i	−0.999888	−	0.0149590i	$-0.995238\pi$
$479$	−1.23369e9	−	2.13681e9i	−0.512899	−	0.888367i	0.486989	−	0.873408i	$-0.338095\pi$
$480$	−1.75586e9	−	1.93959e9i	−0.724677	−	0.800506i
$481$	−4.04168e8	+	7.00040e8i	−0.165598	+	0.286824i
$482$	−2.23433e9	+	3.86997e9i	−0.908830	+	1.57414i
$483$	3.52698e9	−	7.59578e8i	1.42426	−	0.306731i
$484$	−2.53209e7	−	4.38572e7i	−0.0101513	−	0.0175825i
$485$	1.01785e9			0.405123
$486$	3.18307e9	−	4.26970e7i	1.25782	−	0.0168721i
$487$	9.54719e8			0.374563			0.187281	−	0.982306i	$-0.440032\pi$
$487$	9.54719e8			0.374563			0.187281	+	0.982306i	$0.440032\pi$
$488$	2.18514e7	+	3.78477e7i	0.00851157	+	0.0147425i
$489$	−1.80438e9	+	3.88594e8i	−0.697824	+	0.150285i
$490$	8.53508e8	−	1.47832e9i	0.327734	−	0.567652i
$491$	−9.83801e8	+	1.70399e9i	−0.375079	+	0.649655i	−0.990339	−	0.138669i	$-0.955718\pi$
$491$	−9.83801e8	+	1.70399e9i	−0.375079	+	0.649655i	0.615260	+	0.788324i	$0.289051\pi$
$492$	−5.66824e8	−	6.26136e8i	−0.214571	−	0.237023i
$493$	7.48122e8	+	1.29579e9i	0.281196	+	0.487045i
$494$	1.73211e9			0.646445
$495$	2.60109e9	−	1.17484e9i	0.963912	−	0.435373i
$496$	4.05891e8			0.149356
$497$	2.24105e8	+	3.88161e8i	0.0818850	+	0.141829i
$498$	−7.55522e8	+	2.34666e9i	−0.274122	+	0.851427i
$499$	−5.22725e8	+	9.05387e8i	−0.188331	+	0.326199i	−0.944694	−	0.327953i	$-0.893641\pi$
$499$	−5.22725e8	+	9.05387e8i	−0.188331	+	0.326199i	0.756363	+	0.654152i	$0.226974\pi$
$500$	7.77706e8	−	1.34703e9i	0.278241	−	0.481927i
$501$	−1.39357e9	+	4.32845e9i	−0.495105	+	1.53780i
$502$	9.59877e8	+	1.66256e9i	0.338651	+	0.586561i
$503$	1.15052e9			0.403093			0.201546	−	0.979479i	$-0.435403\pi$
$503$	1.15052e9			0.403093			0.201546	+	0.979479i	$0.435403\pi$
$504$	−1.50239e9	−	1.07928e9i	−0.522728	−	0.375516i
$505$	1.61206e8			0.0557008
$506$	2.21725e9	+	3.84039e9i	0.760830	+	1.31780i
$507$	1.78305e9	+	1.96962e9i	0.607624	+	0.671205i
$508$	−3.31701e8	+	5.74522e8i	−0.112260	+	0.194439i
$509$	2.50094e9	−	4.33176e9i	0.840603	−	1.45597i	−0.0487822	−	0.998809i	$-0.515534\pi$
$509$	2.50094e9	−	4.33176e9i	0.840603	−	1.45597i	0.889385	−	0.457158i	$-0.151133\pi$
$510$	−3.00741e9	+	6.47682e8i	−1.00392	+	0.216205i
$511$	4.57814e8	+	7.92957e8i	0.151781	+	0.262892i
$512$	−1.93782e9			−0.638071
$513$	−4.10868e9	+	3.03595e9i	−1.34367	+	0.992850i
$514$	−3.35194e9			−1.08874
$515$	−2.95681e9	−	5.12134e9i	−0.953889	−	1.65218i
$516$	2.83356e9	−	6.10242e8i	0.907944	−	0.195536i
$517$	3.59281e8	−	6.22293e8i	0.114345	−	0.198051i
$518$	2.62483e9	−	4.54635e9i	0.829751	−	1.43717i
$519$	−1.73884e9	−	1.92079e9i	−0.545975	−	0.603105i
$520$	−2.69335e8	−	4.66501e8i	−0.0840003	−	0.145493i
$521$	−1.31851e9			−0.408460			−0.204230	−	0.978923i	$-0.565469\pi$
$521$	−1.31851e9			−0.408460			−0.204230	+	0.978923i	$0.565469\pi$
$522$	−2.90431e8	+	2.91355e9i	−0.0893709	+	0.896553i
$523$	1.46804e9			0.448727			0.224363	−	0.974506i	$-0.427970\pi$
$523$	1.46804e9			0.448727			0.224363	+	0.974506i	$0.427970\pi$
$524$	−4.74020e8	−	8.21028e8i	−0.143925	−	0.249286i
$525$	−1.00830e8	+	3.13180e8i	−0.0304112	+	0.0944575i
$526$	−1.18598e9	+	2.05418e9i	−0.355326	+	0.615443i
$527$	1.58475e8	−	2.74486e8i	0.0471653	−	0.0816927i
$528$	1.31095e9	−	4.07181e9i	0.387584	−	1.20384i
$529$	−7.04732e8	−	1.22063e9i	−0.206980	−	0.358501i
$530$	−1.28870e9			−0.375998
$531$	6.77591e7	−	6.79748e8i	0.0196398	−	0.197023i
$532$	−4.14018e9			−1.19214
$533$	−2.95151e8	−	5.11216e8i	−0.0844303	−	0.146238i
$534$	9.33648e8	+	1.03134e9i	0.265331	+	0.293095i
$535$	−9.44387e8	+	1.63573e9i	−0.266632	+	0.461820i
$536$	1.56027e9	−	2.70247e9i	0.437647	−	0.758026i
$537$	4.51308e9	−	9.71946e8i	1.25766	−	0.270852i
$538$	−1.06389e9	−	1.84271e9i	−0.294550	−	0.510176i
$539$	1.85346e9			0.509827
$540$	−2.03132e9	−	8.84883e8i	−0.555137	−	0.241829i
$541$	3.28515e9			0.892000			0.446000	−	0.895033i	$-0.352848\pi$
$541$	3.28515e9			0.892000			0.446000	+	0.895033i	$0.352848\pi$
$542$	2.15375e9	+	3.73040e9i	0.581029	+	1.00637i
$543$	4.12966e9	−	8.89371e8i	1.10692	−	0.238388i
$544$	−1.53099e9	+	2.65175e9i	−0.407732	+	0.706213i
$545$	−4.05850e8	+	7.02954e8i	−0.107394	+	0.186011i
$546$	1.21012e9	+	1.33674e9i	0.318165	+	0.351457i
$547$	−1.71890e9	−	2.97722e9i	−0.449050	−	0.777778i	0.549274	−	0.835642i	$-0.314904\pi$
$547$	−1.71890e9	−	2.97722e9i	−0.449050	−	0.777778i	−0.998324	+	0.0578644i	$0.981571\pi$
$548$	3.65357e9			0.948387
$549$	1.02038e8	+	7.33020e7i	0.0263184	+	0.0189066i
$550$	−4.04396e8			−0.103642
$551$	−2.34942e9	−	4.06931e9i	−0.598315	−	1.03631i
$552$	−7.56496e8	+	2.34968e9i	−0.191434	+	0.594597i
$553$	−5.44169e8	+	9.42528e8i	−0.136835	+	0.237004i
$554$	2.32661e8	−	4.02981e8i	0.0581352	−	0.100693i
$555$	−1.38173e9	+	4.29166e9i	−0.343081	+	1.06561i
$556$	5.88576e7	+	1.01944e8i	0.0145225	+	0.0251537i
$557$	−7.14256e9			−1.75130			−0.875651	−	0.482945i	$-0.839567\pi$
$557$	−7.14256e9			−1.75130			−0.875651	+	0.482945i	$0.839567\pi$
$558$	5.65252e8	−	2.55309e8i	0.137728	−	0.0622080i
$559$	2.02584e9			0.490527
$560$	3.29078e9	+	5.69979e9i	0.791845	+	1.37152i
$561$	−2.24174e9	−	2.47631e9i	−0.536062	−	0.592155i
$562$	3.57175e9	−	6.18645e9i	0.848797	−	1.47016i
$563$	−2.31348e9	+	4.00706e9i	−0.546369	+	0.946338i	0.452151	+	0.891941i	$0.350657\pi$
$563$	−2.31348e9	+	4.00706e9i	−0.546369	+	0.946338i	−0.998519	+	0.0543966i	$0.982676\pi$
$564$	−5.45328e8	+	1.17443e8i	−0.127992	+	0.0275645i
$565$	−3.02731e9	−	5.24346e9i	−0.706135	−	1.22306i
$566$	−4.62920e9			−1.07312
$567$	−5.21344e9	−	1.04981e9i	−1.20111	−	0.241864i
$568$	−3.06662e8			−0.0702167
$569$	2.82742e9	+	4.89724e9i	0.643425	+	1.11444i	0.984663	+	0.174468i	$0.0558204\pi$
$569$	2.82742e9	+	4.89724e9i	0.643425	+	1.11444i	−0.341238	+	0.939977i	$0.610846\pi$
$570$	9.44454e9	−	2.03399e9i	2.13609	−	0.460032i
$571$	−3.84013e9	+	6.65130e9i	−0.863216	+	1.49513i	0.00559216	+	0.999984i	$0.498220\pi$
$571$	−3.84013e9	+	6.65130e9i	−0.863216	+	1.49513i	−0.868808	+	0.495149i	$0.835113\pi$
$572$	−4.07845e8	+	7.06409e8i	−0.0911191	+	0.157823i
$573$	3.26979e9	+	3.61194e9i	0.726071	+	0.802046i
$574$	1.91683e9	+	3.32005e9i	0.423050	+	0.732744i
$575$	4.39031e8			0.0963070
$576$	−2.64295e8	+	1.19375e8i	−0.0576249	+	0.0260276i
$577$	2.51579e9			0.545204			0.272602	−	0.962127i	$-0.412116\pi$
$577$	2.51579e9			0.545204			0.272602	+	0.962127i	$0.412116\pi$
$578$	−1.11975e9	−	1.93946e9i	−0.241197	−	0.417766i
$579$	−1.90657e8	+	5.92182e8i	−0.0408204	+	0.126789i
$580$	1.01898e9	−	1.76492e9i	0.216853	−	0.375601i
$581$	2.05924e9	−	3.56671e9i	0.435603	−	0.754487i
$582$	7.14406e8	−	2.21895e9i	0.150215	−	0.466570i
$583$	−6.99628e8	−	1.21179e9i	−0.146227	−	0.253273i
$584$	−6.26465e8			−0.130152
$585$	−1.25770e9	−	9.03502e8i	−0.259735	−	0.186588i
$586$	2.04248e9			0.419292
$587$	2.25025e9	+	3.89755e9i	0.459196	+	0.795351i	0.998919	−	0.0464920i	$-0.0148042\pi$
$587$	2.25025e9	+	3.89755e9i	0.459196	+	0.795351i	−0.539723	+	0.841843i	$0.681471\pi$
$588$	−9.65659e8	−	1.06670e9i	−0.195886	−	0.216383i
$589$	−4.97677e8	+	8.62002e8i	−0.100356	+	0.173822i
$590$	−6.45929e8	+	1.11878e9i	−0.129480	+	0.224266i
$591$	−7.83171e9	+	1.68665e9i	−1.56063	+	0.336101i
$592$	3.37867e9	+	5.85203e9i	0.669299	+	1.15926i
$593$	8.41758e9			1.65766			0.828831	−	0.559499i	$-0.189007\pi$
$593$	8.41758e9			1.65766			0.828831	+	0.559499i	$0.189007\pi$
$594$	−7.35554e8	−	6.49507e9i	−0.144000	−	1.27154i
$595$	5.13935e9			1.00023
$596$	1.45914e9	+	2.52730e9i	0.282315	+	0.488984i
$597$	−5.66990e9	+	1.22108e9i	−1.09060	+	0.234874i
$598$	1.20304e9	−	2.08372e9i	0.230052	−	0.398461i
$599$	−1.91250e9	+	3.31254e9i	−0.363586	+	0.629749i	−0.988548	−	0.150906i	$-0.951781\pi$
$599$	−1.91250e9	+	3.31254e9i	−0.363586	+	0.629749i	0.624963	+	0.780655i	$0.285114\pi$
$600$	−1.51074e8	−	1.66882e8i	−0.0285536	−	0.0315414i
$601$	3.62512e8	+	6.27889e8i	0.0681179	+	0.117984i	0.898073	−	0.439847i	$-0.144967\pi$
$601$	3.62512e8	+	6.27889e8i	0.0681179	+	0.117984i	−0.829955	+	0.557830i	$0.811634\pi$
$602$	−1.31566e10			−2.45786
$603$	8.89850e8	−	8.92681e9i	0.165275	−	1.65801i
$604$	1.37031e9			0.253041
$605$	−9.87089e7	−	1.70969e8i	−0.0181223	−	0.0313887i
$606$	1.13147e8	−	3.51435e8i	0.0206532	−	0.0641492i
$607$	5.42460e9	−	9.39569e9i	0.984481	−	1.70517i	0.340263	−	0.940330i	$-0.389484\pi$
$607$	5.42460e9	−	9.39569e9i	0.984481	−	1.70517i	0.644218	−	0.764842i	$-0.277183\pi$
$608$	4.80794e9	−	8.32760e9i	0.867554	−	1.50265i
$609$	1.49907e9	−	4.65611e9i	0.268943	−	0.835339i
$610$	−1.18799e8	−	2.05766e8i	−0.0211913	−	0.0367044i
$611$	−3.89879e8			−0.0691489
$612$	−2.57215e8	+	2.58033e9i	−0.0453592	+	0.455036i
$613$	−7.59484e9			−1.33170			−0.665851	−	0.746085i	$-0.731931\pi$
$613$	−7.59484e9			−1.33170			−0.665851	+	0.746085i	$0.731931\pi$
$614$	−4.70050e9	−	8.14150e9i	−0.819511	−	1.41943i
$615$	−2.20966e9	−	2.44087e9i	−0.383056	−	0.423138i
$616$	−1.89923e9	+	3.28957e9i	−0.327375	+	0.567031i
$617$	−5.91168e8	+	1.02393e9i	−0.101324	+	0.175498i	−0.912230	−	0.409678i	$-0.865641\pi$
$617$	−5.91168e8	+	1.02393e9i	−0.101324	+	0.175498i	0.810906	+	0.585176i	$0.198975\pi$
$618$	−1.32400e10	+	2.85140e9i	−2.25647	+	0.485958i
$619$	4.81004e9	+	8.33123e9i	0.815138	+	1.41186i	0.909229	+	0.416297i	$0.136672\pi$
$619$	4.81004e9	+	8.33123e9i	0.815138	+	1.41186i	−0.0940908	+	0.995564i	$0.529994\pi$
$620$	−4.31699e8			−0.0727462
$621$	7.98551e8	+	7.05135e9i	0.133808	+	1.18155i
$622$	−1.50489e9			−0.250748
$623$	−1.16204e9	−	2.01272e9i	−0.192537	−	0.333484i
$624$	−2.26895e9	+	4.88645e8i	−0.373834	+	0.0805096i
$625$	3.27891e9	−	5.67923e9i	0.537216	−	0.930485i
$626$	−8.44813e8	+	1.46326e9i	−0.137642	+	0.238403i
$627$	7.04001e9	+	7.77667e9i	1.14061	+	1.25996i
$628$	2.47621e9	+	4.28892e9i	0.398959	+	0.691018i
$629$	5.27662e9			0.845432
$630$	8.16801e9	+	5.86771e9i	1.30144	+	0.934925i
$631$	−4.21153e9			−0.667325			−0.333662	−	0.942693i	$-0.608285\pi$
$631$	−4.21153e9			−0.667325			−0.333662	+	0.942693i	$0.608285\pi$
$632$	−3.72316e8	−	6.44870e8i	−0.0586681	−	0.101616i
$633$	2.67287e9	−	8.30195e9i	0.418856	−	1.30097i
$634$	−3.09308e9	+	5.35737e9i	−0.482035	+	0.834909i
$635$	−1.29307e9	+	2.23967e9i	−0.200408	+	0.347116i
$636$	−3.32902e8	+	1.03400e9i	−0.0513117	+	0.159375i
$637$	−5.02828e8	−	8.70923e8i	−0.0770781	−	0.133503i
$638$	6.01224e9			0.916567
$639$	−8.03449e8	+	3.62896e8i	−0.121816	+	0.0550211i
$640$	−6.61256e9			−0.997102
$641$	3.96142e9	+	6.86139e9i	0.594084	+	1.02898i	0.993675	+	0.112291i	$0.0358188\pi$
$641$	3.96142e9	+	6.86139e9i	0.594084	+	1.02898i	−0.399591	+	0.916694i	$0.630848\pi$
$642$	2.90310e9	+	3.20688e9i	0.433002	+	0.478311i
$643$	1.46169e9	−	2.53172e9i	0.216829	−	0.375558i	−0.737008	−	0.675884i	$-0.763762\pi$
$643$	1.46169e9	−	2.53172e9i	0.216829	−	0.375558i	0.953837	+	0.300326i	$0.0970953\pi$
$644$	−2.87557e9	+	4.98063e9i	−0.424251	+	0.734824i
$645$	1.10461e10	−	2.37891e9i	1.62088	−	0.349075i
$646$	−5.65340e9	−	9.79197e9i	−0.825079	−	1.42908i
$647$	1.00413e10			1.45755			0.728774	−	0.684754i	$-0.240090\pi$
$647$	1.00413e10			1.45755			0.728774	+	0.684754i	$0.240090\pi$
$648$	2.40554e9	−	2.72997e9i	0.347296	−	0.394135i
$649$	−1.40269e9			−0.201421
$650$	1.09709e8	+	1.90022e8i	0.0156692	+	0.0271398i
$651$	−1.01294e9	+	2.18148e8i	−0.143896	+	0.0309897i
$652$	1.47112e9	−	2.54805e9i	0.207865	−	0.360032i
$653$	−7.41652e8	+	1.28458e9i	−0.104233	+	0.180536i	−0.913424	−	0.407008i	$-0.866572\pi$
$653$	−7.41652e8	+	1.28458e9i	−0.104233	+	0.180536i	0.809192	+	0.587545i	$0.199905\pi$
$654$	1.24761e9	+	1.37816e9i	0.174404	+	0.192653i
$655$	−1.84788e9	−	3.20062e9i	−0.256938	−	0.445030i
$656$	−4.93466e9			−0.682487
$657$	−1.64133e9	+	7.41344e8i	−0.225796	+	0.101986i
$658$	2.53203e9			0.346480
$659$	1.67543e9	+	2.90193e9i	0.228048	+	0.394991i	0.957230	−	0.289329i	$-0.0934323\pi$
$659$	1.67543e9	+	2.90193e9i	0.228048	+	0.394991i	−0.729181	+	0.684320i	$0.760099\pi$
$660$	−1.39430e9	+	4.33071e9i	−0.188778	+	0.586347i
$661$	−1.70018e9	+	2.94480e9i	−0.228976	+	0.396598i	−0.957505	−	0.288417i	$-0.906871\pi$
$661$	−1.70018e9	+	2.94480e9i	−0.228976	+	0.396598i	0.728529	+	0.685015i	$0.240204\pi$
$662$	5.22495e9	−	9.04988e9i	0.699969	−	1.21238i
$663$	−5.55430e8	+	1.72517e9i	−0.0740171	+	0.229898i
$664$	1.40892e9	+	2.44032e9i	0.186766	+	0.323488i
$665$	−1.61397e10			−2.12824
$666$	8.38618e9	+	6.02444e9i	1.10003	+	0.790236i
$667$	−6.52716e9			−0.851695
$668$	−3.62430e9	−	6.27748e9i	−0.470443	−	0.814831i
$669$	1.31975e9	+	1.45785e9i	0.170412	+	0.188244i
$670$	−8.48269e9	+	1.46925e10i	−1.08961	+	1.88726i
$671$	1.28991e8	−	2.23419e8i	0.0164828	−	0.0285490i
$672$	9.78575e9	−	2.10748e9i	1.24395	−	0.267899i
$673$	−4.48300e9	−	7.76478e9i	−0.566912	−	0.981921i	−0.996869	−	0.0790714i	$-0.974804\pi$
$673$	−4.48300e9	−	7.76478e9i	−0.566912	−	0.981921i	0.429957	−	0.902850i	$-0.358529\pi$
$674$	6.71098e9			0.844260
$675$	−5.93296e8	−	2.58452e8i	−0.0742521	−	0.0323457i
$676$	−4.23513e9			−0.527294
$677$	−7.44416e9	−	1.28937e10i	−0.922052	−	1.59704i	−0.796235	−	0.604987i	$-0.793178\pi$
$677$	−7.44416e9	−	1.28937e10i	−0.922052	−	1.59704i	−0.125816	−	0.992054i	$-0.540155\pi$
$678$	−1.35557e10	+	2.91939e9i	−1.67040	+	0.359740i
$679$	−1.94717e9	+	3.37261e9i	−0.238705	+	0.413448i
$680$	−1.75815e9	+	3.04521e9i	−0.214425	+	0.371395i
$681$	−9.82464e9	−	1.08527e10i	−1.19207	−	1.31681i
$682$	−6.36786e8	−	1.10295e9i	−0.0768684	−	0.133140i
$683$	7.71503e9			0.926542			0.463271	−	0.886217i	$-0.346676\pi$
$683$	7.71503e9			0.926542			0.463271	+	0.886217i	$0.346676\pi$
$684$	8.07763e8	−	8.10333e9i	0.0965133	−	0.968205i
$685$	1.42428e10			1.69308
$686$	−3.25037e9	−	5.62980e9i	−0.384413	−	0.665822i
$687$	−2.39508e9	+	7.43915e9i	−0.281820	+	0.875336i
$688$	8.46756e9	−	1.46662e10i	0.991285	−	1.71696i
$689$	−3.79606e8	+	6.57496e8i	−0.0442146	+	0.0765819i
$690$	4.11282e9	−	1.27745e10i	0.476615	−	1.48037i
$691$	1.26498e9	+	2.19101e9i	0.145851	+	0.252622i	0.929690	−	0.368342i	$-0.120075\pi$
$691$	1.26498e9	+	2.19101e9i	0.145851	+	0.252622i	−0.783839	+	0.620964i	$0.786741\pi$
$692$	4.13012e9			0.473796
$693$	−1.08317e9	+	1.08661e10i	−0.123631	+	1.24025i
$694$	1.57506e10			1.78871
$695$	2.29445e8	+	3.97411e8i	0.0259258	+	0.0449048i
$696$	2.24605e9	+	2.48108e9i	0.252515	+	0.278938i
$697$	−1.92667e9	+	3.33709e9i	−0.215522	+	0.373296i
$698$	−5.66555e8	+	9.81302e8i	−0.0630591	+	0.109222i
$699$	−1.16775e10	+	2.51490e9i	−1.29325	+	0.278516i
$700$	−2.62232e8	−	4.54200e8i	−0.0288964	−	0.0500500i
$701$	1.41167e10			1.54782			0.773908	−	0.633298i	$-0.218299\pi$
$701$	1.41167e10			1.54782			0.773908	+	0.633298i	$0.218299\pi$
$702$	−2.85242e9	+	2.10768e9i	−0.311196	+	0.229946i
$703$	−1.65708e10			−1.79887
$704$	2.97742e8	+	5.15704e8i	0.0321614	+	0.0557053i
$705$	−2.12586e9	+	4.57829e8i	−0.228493	+	0.0492087i
$706$	−7.24555e8	+	1.25497e9i	−0.0774917	+	0.134220i
$707$	−3.08392e8	+	5.34150e8i	−0.0328197	+	0.0568454i
$708$	7.30805e8	+	8.07275e8i	0.0773900	+	0.0854880i
$709$	6.46733e9	+	1.12017e10i	0.681496	+	1.18039i	0.974524	+	0.224282i	$0.0720037\pi$
$709$	6.46733e9	+	1.12017e10i	0.681496	+	1.18039i	−0.293028	+	0.956104i	$0.594663\pi$
$710$	1.66722e9			0.174819
$711$	−1.73858e9	−	1.24896e9i	−0.181406	−	0.130318i
$712$	1.59012e9			0.165101
$713$	6.91324e8	+	1.19741e9i	0.0714279	+	0.123717i
$714$	3.60719e9	−	1.12040e10i	0.370873	−	1.15194i
$715$	−1.58991e9	+	2.75380e9i	−0.162668	+	0.281748i
$716$	−3.67954e9	+	6.37314e9i	−0.374626	+	0.648871i
$717$	2.53523e9	−	7.87446e9i	0.256863	−	0.797818i
$718$	6.89754e8	+	1.19469e9i	0.0695438	+	0.120453i
$719$	−1.22962e10			−1.23373			−0.616864	−	0.787070i	$-0.711597\pi$
$719$	−1.22962e10			−1.23373			−0.616864	+	0.787070i	$0.711597\pi$
$720$	−1.17979e10	+	5.32879e9i	−1.17799	+	0.532065i
$721$	2.26258e10			2.24818
$722$	1.13933e10	+	1.97338e10i	1.12660	+	1.95133i
$723$	9.85462e9	+	1.08858e10i	0.969741	+	1.07121i
$724$	−3.36693e9	+	5.83170e9i	−0.329723	+	0.571097i
$725$	2.97617e8	−	5.15487e8i	0.0290051	−	0.0502383i
$726$	−4.42000e8	+	9.51901e7i	−0.0428691	+	0.00923238i
$727$	−3.37402e9	−	5.84398e9i	−0.325670	−	0.564077i	0.655978	−	0.754780i	$-0.272256\pi$
$727$	−3.37402e9	−	5.84398e9i	−0.325670	−	0.564077i	−0.981648	+	0.190704i	$0.938923\pi$
$728$	2.06098e9			0.197977
$729$	3.07189e9	−	9.99912e9i	0.293670	−	0.955907i
$730$	3.40589e9			0.324041
$731$	−6.61208e9	−	1.14525e10i	−0.626076	−	1.08440i
$732$	−1.95786e8	+	4.21650e7i	−0.0184499	+	0.00397341i
$733$	−1.87123e9	+	3.24106e9i	−0.175494	+	0.303965i	−0.940332	−	0.340258i	$-0.889486\pi$
$733$	−1.87123e9	+	3.24106e9i	−0.175494	+	0.303965i	0.764838	+	0.644223i	$0.222819\pi$
$734$	−1.09871e10	+	1.90303e10i	−1.02553	+	1.77627i
$735$	−3.76444e9	−	4.15835e9i	−0.349699	−	0.386291i
$736$	−6.67872e9	−	1.15679e10i	−0.617477	−	1.06950i
$737$	−1.84209e10			−1.69502
$738$	−6.87211e9	+	3.10394e9i	−0.629350	+	0.284261i
$739$	1.27399e9			0.116121			0.0580606	−	0.998313i	$-0.481508\pi$
$739$	1.27399e9			0.116121			0.0580606	+	0.998313i	$0.481508\pi$
$740$	−3.59350e9	−	6.22412e9i	−0.325992	−	0.564634i
$741$	1.74429e9	−	5.41777e9i	0.157490	−	0.489166i
$742$	2.46532e9	−	4.27005e9i	0.221543	−	0.383724i
$743$	−3.62517e9	+	6.27897e9i	−0.324240	+	0.561601i	−0.981358	−	0.192187i	$-0.938442\pi$
$743$	−3.62517e9	+	6.27897e9i	−0.324240	+	0.561601i	0.657118	+	0.753788i	$0.271775\pi$
$744$	2.17263e8	−	6.74821e8i	0.0193411	−	0.0600735i
$745$	5.68817e9	+	9.85220e9i	0.503994	+	0.872944i
$746$	1.92066e10			1.69381
$747$	6.57915e9	+	4.72631e9i	0.577494	+	0.414858i
$748$	5.32463e9			0.465194
$749$	−3.61328e9	−	6.25838e9i	−0.314206	−	0.544221i
$750$	−9.31975e9	−	1.02950e10i	−0.806659	−	0.891067i
$751$	9.82411e9	−	1.70159e10i	0.846357	−	1.46593i	−0.0380804	−	0.999275i	$-0.512124\pi$
$751$	9.82411e9	−	1.70159e10i	0.846357	−	1.46593i	0.884437	−	0.466659i	$-0.154542\pi$
$752$	−1.62961e9	+	2.82257e9i	−0.139740	+	0.242037i
$753$	6.16684e9	−	1.32810e9i	0.526357	−	0.113357i
$754$	−1.63107e9	−	2.82509e9i	−0.138571	−	0.240012i
$755$	5.34190e9			0.451733
$756$	6.81800e9	−	5.03790e9i	0.573893	−	0.424056i
$757$	−1.81025e10			−1.51671			−0.758356	−	0.651841i	$-0.773997\pi$
$757$	−1.81025e10			−1.51671			−0.758356	+	0.651841i	$0.773997\pi$
$758$	1.14670e10	+	1.98614e10i	0.956329	+	1.65641i
$759$	1.42449e10	−	3.06782e9i	1.18254	−	0.254673i
$760$	5.52133e9	−	9.56323e9i	0.456243	−	0.790236i
$761$	2.43280e9	−	4.21373e9i	0.200106	−	0.346593i	−0.748457	−	0.663184i	$-0.769205\pi$
$761$	2.43280e9	−	4.21373e9i	0.200106	−	0.346593i	0.948562	+	0.316590i	$0.102538\pi$
$762$	3.97498e9	+	4.39092e9i	0.325456	+	0.359512i
$763$	−1.55281e9	−	2.68954e9i	−0.126556	−	0.219201i
$764$	−7.76648e9			−0.630083
$765$	−1.00270e9	+	1.00589e10i	−0.0809762	+	0.812339i
$766$	−1.79925e10			−1.44641
$767$	3.80537e8	+	6.59109e8i	0.0304518	+	0.0527440i
$768$	−4.88446e9	+	1.51712e10i	−0.389092	+	1.20852i
$769$	3.32352e9	−	5.75651e9i	0.263546	−	0.456475i	−0.703636	−	0.710561i	$-0.748441\pi$
$769$	3.32352e9	−	5.75651e9i	0.263546	−	0.456475i	0.967182	+	0.254086i	$0.0817746\pi$
$770$	1.03255e10	−	1.78843e10i	0.815069	−	1.41174i
$771$	−3.37550e9	+	1.04843e10i	−0.265245	+	0.823854i
$772$	−4.95846e8	−	8.58831e8i	−0.0387870	−	0.0671811i
$773$	−1.79263e10			−1.39593			−0.697963	−	0.716134i	$-0.745910\pi$
$773$	−1.79263e10			−1.39593			−0.697963	+	0.716134i	$0.745910\pi$
$774$	2.56690e9	−	2.57506e10i	0.198983	−	1.99616i
$775$	−1.26088e8			−0.00973012
$776$	−1.33224e9	−	2.30751e9i	−0.102345	−	0.177267i
$777$	−1.15770e10	−	1.27884e10i	−0.885363	−	0.978006i
$778$	−1.30743e10	+	2.26454e10i	−0.995385	+	1.72406i
$779$	6.05056e9	−	1.04799e10i	0.458579	−	0.794282i
$780$	2.41321e9	−	5.19715e8i	0.182081	−	0.0392133i
$781$	9.05127e8	+	1.56773e9i	0.0679878	+	0.117758i
$782$	−1.57063e10			−1.17449
$783$	8.82066e9	+	3.84245e9i	0.656651	+	0.286050i
$784$	−8.40685e9			−0.623056
$785$	9.65303e9	+	1.67195e10i	0.712229	+	1.23362i
$786$	−8.27446e9	+	1.78200e9i	−0.607800	+	0.130897i
$787$	−4.95269e9	+	8.57831e9i	−0.362184	+	0.627321i	−0.988320	−	0.152393i	$-0.951302\pi$
$787$	−4.95269e9	+	8.57831e9i	−0.362184	+	0.627321i	0.626136	+	0.779714i	$0.284635\pi$
$788$	6.38523e9	−	1.10595e10i	0.464873	−	0.805185i
$789$	5.23083e9	+	5.77818e9i	0.379141	+	0.418814i
$790$	2.02416e9	+	3.50595e9i	0.146066	+	0.252994i
$791$	2.31653e10			1.66426
$792$	−6.06793e9	−	4.35906e9i	−0.434013	−	0.311785i
$793$	−1.39976e8			−0.00996777
$794$	−1.31985e10	−	2.28605e10i	−0.935736	−	1.62074i
$795$	−1.29776e9	+	4.03084e9i	−0.0916026	+	0.284519i
$796$	4.62270e9	−	8.00676e9i	0.324863	−	0.562679i
$797$	1.18602e10	−	2.05424e10i	0.829824	−	1.43730i	−0.0683515	−	0.997661i	$-0.521774\pi$
$797$	1.18602e10	−	2.05424e10i	0.829824	−	1.43730i	0.898176	−	0.439637i	$-0.144893\pi$
$798$	−1.13281e10	+	3.51852e10i	−0.789128	+	2.45104i
$799$	1.27252e9	+	2.20406e9i	0.0882571	+	0.152866i
$800$	1.21811e9			0.0841145
$801$	4.16609e9	−	1.88171e9i	0.286428	−	0.129372i
$802$	1.72002e10			1.17740
$803$	1.84904e9	+	3.20263e9i	0.126021	+	0.218275i
$804$	9.59732e9	+	1.06016e10i	0.651259	+	0.719406i
$805$	−1.12099e10	+	1.94160e10i	−0.757381	+	1.31182i
$806$	−3.45508e8	+	5.98438e8i	−0.0232427	+	0.0402575i
$807$	−6.83509e9	+	1.47202e9i	−0.457811	+	0.0985952i
$808$	−2.10999e8	−	3.65461e8i	−0.0140715	−	0.0243726i
$809$	−2.49700e10			−1.65805			−0.829027	−	0.559208i	$-0.811105\pi$
$809$	−2.49700e10			−1.65805			−0.829027	+	0.559208i	$0.811105\pi$
$810$	−1.30781e10	+	1.48420e10i	−0.864665	+	0.981281i
$811$	−1.12321e9			−0.0739412			−0.0369706	−	0.999316i	$-0.511771\pi$
$811$	−1.12321e9			−0.0739412			−0.0369706	+	0.999316i	$0.511771\pi$
$812$	3.89866e9	+	6.75268e9i	0.255546	+	0.442619i
$813$	1.38370e10	−	2.97996e9i	0.903078	−	0.194489i
$814$	1.06013e10	−	1.83620e10i	0.688929	−	1.19326i
$815$	5.73487e9	−	9.93308e9i	0.371084	−	0.642736i
$816$	1.01680e10	+	1.12319e10i	0.655117	+	0.723668i
$817$	2.07647e10	+	3.59655e10i	1.33214	+	2.30733i
$818$	1.73833e10			1.11044
$819$	5.39973e9	−	2.43891e9i	0.343462	−	0.155132i
$820$	5.24842e9			0.332415
$821$	7.45639e9	+	1.29148e10i	0.470249	+	0.814494i	0.999421	−	0.0340198i	$-0.0108309\pi$
$821$	7.45639e9	+	1.29148e10i	0.470249	+	0.814494i	−0.529173	+	0.848514i	$0.677498\pi$
$822$	9.99667e9	−	3.10498e10i	0.627775	−	1.94988i
$823$	1.40501e9	−	2.43356e9i	0.0878580	−	0.152175i	−0.818747	−	0.574154i	$-0.805331\pi$
$823$	1.40501e9	−	2.43356e9i	0.0878580	−	0.152175i	0.906605	+	0.421979i	$0.138664\pi$
$824$	−7.74021e9	+	1.34064e10i	−0.481956	+	0.834772i
$825$	−4.07239e8	+	1.26489e9i	−0.0252499	+	0.0784265i
$826$	−2.47136e9	−	4.28053e9i	−0.152583	−	0.264282i
$827$	1.92634e10			1.18430			0.592151	−	0.805827i	$-0.298279\pi$
$827$	1.92634e10			1.18430			0.592151	+	0.805827i	$0.298279\pi$
$828$	−9.18725e9	−	6.59991e9i	−0.562444	−	0.404047i
$829$	−3.12798e10			−1.90688			−0.953440	−	0.301582i	$-0.902485\pi$
$829$	−3.12798e10			−1.90688			−0.953440	+	0.301582i	$0.902485\pi$
$830$	−7.65982e9	−	1.32672e10i	−0.464992	−	0.805390i
$831$	−1.02616e9	−	1.13354e9i	−0.0620316	−	0.0685225i
$832$	1.61549e8	−	2.79812e8i	0.00972464	−	0.0168436i
$833$	−3.28233e9	+	5.68517e9i	−0.196755	+	0.340789i
$834$	1.02741e9	−	2.21266e8i	0.0613287	−	0.0132079i
$835$	−1.41287e10	−	2.44716e10i	−0.839843	−	1.45465i
$836$	−1.67216e10			−0.989818
$837$	−2.29341e8	−	2.02512e9i	−0.0135189	−	0.119375i
$838$	−2.16425e10			−1.27044
$839$	−7.65355e9	−	1.32563e10i	−0.447400	−	0.774920i	0.550816	−	0.834627i	$-0.314317\pi$
$839$	−7.65355e9	−	1.32563e10i	−0.447400	−	0.774920i	−0.998216	+	0.0597070i	$0.980983\pi$
$840$	1.12377e10	−	2.42018e9i	0.654186	−	0.140887i
$841$	4.20021e9	−	7.27498e9i	0.243492	−	0.421741i
$842$	7.73762e9	−	1.34019e10i	0.446699	−	0.773705i
$843$	−1.57534e10	−	1.74018e10i	−0.905685	−	1.00046i
$844$	6.95140e9	+	1.20402e10i	0.397992	+	0.689342i
$845$	−1.65099e10			−0.941336
$846$	−4.94008e8	+	4.95580e9i	−0.0280503	+	0.281396i
$847$	7.55332e8			0.0427116
$848$	3.17334e9	+	5.49639e9i	0.178703	+	0.309522i
$849$	−4.66174e9	+	1.44794e10i	−0.261439	+	0.812033i
$850$	7.16154e8	−	1.24041e9i	0.0399982	−	0.0692788i
$851$	−1.15093e10	+	1.99346e10i	−0.640168	+	1.10880i
$852$	4.30684e8	−	1.33771e9i	0.0238572	−	0.0741008i
$853$	−1.59603e10	−	2.76441e10i	−0.880480	−	1.52504i	−0.850808	−	0.525477i	$-0.823887\pi$
$853$	−1.59603e10	−	2.76441e10i	−0.880480	−	1.52504i	−0.0296720	−	0.999560i	$-0.509446\pi$
$854$	9.09063e8			0.0499449
$855$	3.14891e9	−	3.15893e10i	0.172297	−	1.72846i
$856$	4.94435e9			0.269433
$857$	1.48319e10	+	2.56895e10i	0.804938	+	1.39419i	0.916333	+	0.400417i	$0.131135\pi$
$857$	1.48319e10	+	2.56895e10i	0.804938	+	1.39419i	−0.111395	+	0.993776i	$0.535532\pi$
$858$	4.88747e9	+	5.39889e9i	0.264167	+	0.291809i
$859$	8.51597e9	−	1.47501e10i	0.458414	−	0.793997i	−0.540463	−	0.841368i	$-0.681751\pi$
$859$	8.51597e9	−	1.47501e10i	0.458414	−	0.793997i	0.998877	+	0.0473709i	$0.0150843\pi$
$860$	−9.00595e9	+	1.55988e10i	−0.482820	+	0.836268i
$861$	1.23149e10	−	2.65216e9i	0.657535	−	0.141608i
$862$	−9.49204e9	−	1.64407e10i	−0.504759	−	0.874269i
$863$	−3.16249e9			−0.167491			−0.0837454	−	0.996487i	$-0.526688\pi$
$863$	−3.16249e9			−0.167491			−0.0837454	+	0.996487i	$0.526688\pi$
$864$	2.21561e9	+	1.95642e10i	0.116868	+	1.03196i
$865$	1.61005e10			0.845829
$866$	−2.42857e9	−	4.20641e9i	−0.127069	−	0.220089i
$867$	−7.19393e9	+	1.54930e9i	−0.374886	+	0.0807362i
$868$	8.25853e8	−	1.43042e9i	0.0428631	−	0.0742411i
$869$	−2.19782e9	+	3.80673e9i	−0.113611	+	0.196781i
$870$	−1.22110e10	−	1.34888e10i	−0.628689	−	0.694474i
$871$	4.99741e9	+	8.65578e9i	0.256261	+	0.443856i
$872$	2.12484e9			0.108522
$873$	−6.22110e9	−	4.46909e9i	−0.316459	−	0.227337i
$874$	4.93243e10			2.49903
$875$	1.15996e10	+	2.00911e10i	0.585349	+	1.01385i
$876$	8.79824e8	−	2.73274e9i	0.0442213	−	0.137352i
$877$	−3.19898e9	+	5.54079e9i	−0.160145	+	0.277379i	−0.934920	−	0.354857i	$-0.884529\pi$
$877$	−3.19898e9	+	5.54079e9i	−0.160145	+	0.277379i	0.774776	+	0.632236i	$0.217863\pi$
$878$	−9.65089e9	+	1.67158e10i	−0.481212	+	0.833484i
$879$	2.05684e9	−	6.38856e9i	0.102150	−	0.317280i
$880$	1.32910e10	+	2.30206e10i	0.657456	+	1.13875i
$881$	−1.45065e10			−0.714739			−0.357369	−	0.933963i	$-0.616326\pi$
$881$	−1.45065e10			−0.714739			−0.357369	+	0.933963i	$0.616326\pi$
$882$	−1.17075e10	+	5.28797e9i	−0.574547	+	0.259507i
$883$	2.39105e10			1.16876			0.584382	−	0.811479i	$-0.301337\pi$
$883$	2.39105e10			1.16876			0.584382	+	0.811479i	$0.301337\pi$
$884$	−1.44452e9	−	2.50199e9i	−0.0703302	−	0.121815i
$885$	2.84890e9	+	3.14701e9i	0.138158	+	0.152615i
$886$	−8.25019e9	+	1.42898e10i	−0.398516	+	0.690250i
$887$	1.54012e10	−	2.66757e10i	0.741007	−	1.28346i	−0.211030	−	0.977480i	$-0.567682\pi$
$887$	1.54012e10	−	2.66757e10i	0.741007	−	1.28346i	0.952037	−	0.305982i	$-0.0989849\pi$
$888$	1.15379e10	−	2.48482e9i	0.552944	−	0.119083i
$889$	−4.94737e9	−	8.56909e9i	−0.236166	−	0.409052i
$890$	−8.64497e9			−0.411054
$891$	−2.10563e10	−	4.24003e9i	−0.997263	−	0.200815i
$892$	−3.13470e9			−0.147883
$893$	−3.99624e9	−	6.92168e9i	−0.187789	−	0.325261i
$894$	2.54706e10	−	5.48539e9i	1.19222	−	0.256759i
$895$	−1.43440e10	+	2.48445e10i	−0.668789	+	1.15838i
$896$	1.26500e10	−	2.19105e10i	0.587507	−	1.01759i
$897$	−5.30606e9	−	5.86128e9i	−0.245470	−	0.271156i
$898$	6.94557e9	+	1.20301e10i	0.320067	+	0.554372i
$899$	1.87458e9			0.0860488
$900$	9.40140e8	−	4.24636e8i	0.0429877	−	0.0194164i
$901$	4.95594e9			0.225730
$902$	7.74178e9	+	1.34092e10i	0.351252	+	0.608385i
$903$	−1.32491e10	+	4.11518e10i	−0.598796	+	1.85987i
$904$	−7.92477e9	+	1.37261e10i	−0.356777	+	0.617957i
$905$	−1.31253e10	+	2.27338e10i	−0.588628	+	1.01953i
$906$	3.74936e9	−	1.16456e10i	0.167498	−	0.520249i
$907$	−6.06562e9	−	1.05060e10i	−0.269929	−	0.467531i	0.698914	−	0.715206i	$-0.253667\pi$
$907$	−6.06562e9	−	1.05060e10i	−0.269929	−	0.467531i	−0.968843	+	0.247675i	$0.920334\pi$
$908$	2.33357e10			1.03448
$909$	−9.85291e8	−	7.07811e8i	−0.0435102	−	0.0312567i
$910$	−1.12049e10			−0.492904
$911$	−9.73568e9	−	1.68627e10i	−0.426630	−	0.738945i	0.569941	−	0.821686i	$-0.306966\pi$
$911$	−9.73568e9	−	1.68627e10i	−0.426630	−	0.738945i	−0.996571	+	0.0827403i	$0.973633\pi$
$912$	−3.19317e10	−	3.52730e10i	−1.39393	−	1.53979i
$913$	8.31697e9	−	1.44054e10i	0.361674	−	0.626438i
$914$	−1.34376e10	+	2.32746e10i	−0.582117	+	1.00826i
$915$	−7.63237e8	+	1.64372e8i	−0.0329371	+	0.00709340i
$916$	−6.22896e9	−	1.07889e10i	−0.267782	−	0.463812i
$917$	1.41402e10			0.605567
$918$	2.12251e10	+	9.24607e9i	0.905525	+	0.394465i
$919$	2.10755e10			0.895721			0.447861	−	0.894103i	$-0.352186\pi$
$919$	2.10755e10			0.895721			0.447861	+	0.894103i	$0.352186\pi$
$920$	−7.66969e9	−	1.32843e10i	−0.324729	−	0.562446i
$921$	−3.01989e10	+	6.50369e9i	−1.27374	+	0.274316i
$922$	−1.00632e10	+	1.74299e10i	−0.422841	+	0.732382i
$923$	4.91105e8	−	8.50619e8i	0.0205574	−	0.0356065i
$924$	−1.16823e10	−	1.29047e10i	−0.487165	−	0.538142i
$925$	−1.04957e9	−	1.81791e9i	−0.0436028	−	0.0755223i
$926$	1.46029e10			0.604368
$927$	−4.41437e9	+	4.42842e10i	−0.182008	+	1.82587i
$928$	−1.81099e10			−0.743870
$929$	−3.48141e9	−	6.02997e9i	−0.142462	−	0.246752i	0.785961	−	0.618276i	$-0.212169\pi$
$929$	−3.48141e9	−	6.02997e9i	−0.142462	−	0.246752i	−0.928423	+	0.371524i	$0.878835\pi$
$930$	−1.18119e9	+	3.66878e9i	−0.0481536	+	0.149566i
$931$	1.03079e10	−	1.78538e10i	0.418646	−	0.725116i
$932$	9.52076e9	−	1.64904e10i	0.385226	−	0.667232i
$933$	−1.51547e9	+	4.70705e9i	−0.0610886	+	0.189742i
$934$	3.13013e9	+	5.42155e9i	0.125704	+	0.217725i
$935$	2.07571e10			0.830472
$936$	−4.02104e8	+	4.03383e9i	−0.0160278	+	0.160788i
$937$	1.58623e10			0.629908			0.314954	−	0.949107i	$-0.398011\pi$
$937$	1.58623e10			0.629908			0.314954	+	0.949107i	$0.398011\pi$
$938$	−3.24553e10	−	5.62142e10i	−1.28403	−	2.22401i
$939$	3.72609e9	+	4.11599e9i	0.146867	+	0.162235i
$940$	1.73322e9	−	3.00203e9i	0.0680624	−	0.117888i
$941$	1.62492e10	−	2.81444e10i	0.635722	−	1.10110i	−0.350640	−	0.936510i	$-0.614036\pi$
$941$	1.62492e10	−	2.81444e10i	0.635722	−	1.10110i	0.986362	−	0.164592i	$-0.0526308\pi$
$942$	4.32245e10	−	9.30891e9i	1.68481	−	0.362845i
$943$	−8.40483e9	−	1.45576e10i	−0.326391	−	0.565326i
$944$	6.36225e9			0.246155
$945$	2.65787e10	−	1.96393e10i	1.02452	−	0.757032i
$946$	−5.31376e10			−2.04072
$947$	−2.70871e9	−	4.69162e9i	−0.103642	−	0.179514i	0.809540	−	0.587064i	$-0.199716\pi$
$947$	−2.70871e9	−	4.69162e9i	−0.103642	−	0.179514i	−0.913183	+	0.407550i	$0.866383\pi$
$948$	3.33592e9	−	7.18430e8i	0.127170	−	0.0273877i
$949$	1.00326e9	−	1.73769e9i	0.0381049	−	0.0659996i
$950$	−2.24902e9	+	3.89542e9i	−0.0851063	+	0.147408i
$951$	1.36422e10	+	1.50697e10i	0.514342	+	0.568162i
$952$	−6.72678e9	−	1.16511e10i	−0.252684	−	0.437662i
$953$	2.62658e9			0.0983028			0.0491514	−	0.998791i	$-0.484348\pi$
$953$	2.62658e9			0.0983028			0.0491514	+	0.998791i	$0.484348\pi$
$954$	7.87653e9	+	5.65832e9i	0.293708	+	0.210993i
$955$	−3.02762e10			−1.12484
$956$	6.59346e9	+	1.14202e10i	0.244068	+	0.422738i
$957$	6.05450e9	−	1.88053e10i	0.223299	−	0.693568i
$958$	1.75578e10	−	3.04109e10i	0.645193	−	1.11751i
$959$	−2.72468e10	+	4.71928e10i	−0.997586	+	1.72787i
$960$	5.52288e8	−	1.71541e9i	0.0201473	−	0.0625776i
$961$	1.35578e10	+	2.34827e10i	0.492783	+	0.853526i
$962$	−1.15042e10			−0.416622
$963$	1.29541e10	−	5.85102e9i	0.467429	−	0.211125i
$964$	−2.34069e10			−0.841539
$965$	−1.93296e9	−	3.34799e9i	−0.0692433	−	0.119933i
$966$	3.44598e10	+	3.80656e10i	1.22996	+	1.35867i
$967$	−1.95753e10	+	3.39054e10i	−0.696171	+	1.20580i	0.273614	+	0.961840i	$0.411781\pi$
$967$	−1.95753e10	+	3.39054e10i	−0.696171	+	1.20580i	−0.969784	+	0.243963i	$0.921552\pi$
$968$	−2.58396e8	+	4.47555e8i	−0.00915635	+	0.0158593i
$969$	−3.63209e10	+	7.82213e9i	−1.28240	+	0.276180i
$970$	7.24296e9	+	1.25452e10i	0.254809	+	0.441343i
$971$	−2.49003e10			−0.872846			−0.436423	−	0.899742i	$-0.643755\pi$
$971$	−2.49003e10			−0.872846			−0.436423	+	0.899742i	$0.643755\pi$
$972$	8.53016e9	+	1.43274e10i	0.297938	+	0.500420i
$973$	−1.75574e9			−0.0611034
$974$	6.79373e9	+	1.17671e10i	0.235587	+	0.408050i
$975$	7.04838e8	−	1.51795e8i	0.0243542	−	0.00524496i
$976$	−5.85070e8	+	1.01337e9i	−0.0201434	+	0.0348895i
$977$	−2.22902e9	+	3.86078e9i	−0.0764686	+	0.132448i	−0.901724	−	0.432312i	$-0.857698\pi$
$977$	−2.22902e9	+	3.86078e9i	−0.0764686	+	0.132448i	0.825255	+	0.564760i	$0.191031\pi$
$978$	−1.76293e10	−	1.94740e10i	−0.602629	−	0.665687i
$979$	−4.69332e9	−	8.12906e9i	−0.159860	−	0.276886i
$980$	8.94137e9			0.303468
$981$	5.56703e9	−	2.51448e9i	0.188271	−	0.0850367i
$982$	−2.80027e10			−0.943648
$983$	1.32778e10	+	2.29979e10i	0.445851	+	0.772237i	0.998111	−	0.0614353i	$-0.0195678\pi$
$983$	1.32778e10	+	2.29979e10i	0.445851	+	0.772237i	−0.552260	+	0.833672i	$0.686234\pi$
$984$	−2.64139e9	+	8.20420e9i	−0.0883793	+	0.274507i
$985$	2.48916e10	−	4.31135e10i	0.829901	−	1.43743i
$986$	−1.06472e10	+	1.84415e10i	−0.353725	+	0.612670i
$987$	2.54983e9	−	7.91980e9i	0.0844114	−	0.262183i
$988$	4.53641e9	+	7.85730e9i	0.149645	+	0.259193i
$989$	5.76886e10			1.89628
$990$	3.29894e10	+	2.36988e10i	1.08056	+	0.776253i
$991$	6.89473e9			0.225040			0.112520	−	0.993649i	$-0.464108\pi$
$991$	6.89473e9			0.225040			0.112520	+	0.993649i	$0.464108\pi$
$992$	1.91810e9	+	3.32225e9i	0.0623852	+	0.108054i
$993$	−2.30449e10	−	2.54563e10i	−0.746883	−	0.825036i
$994$	−3.18944e9	+	5.52427e9i	−0.103006	+	0.178411i
$995$	1.80207e10	−	3.12128e10i	0.579951	−	1.00451i
$996$	−1.26238e10	+	2.71868e9i	−0.404838	+	0.0871867i
$997$	2.56614e8	+	4.44468e8i	0.00820062	+	0.0142039i	0.870097	−	0.492881i	$-0.164056\pi$
$997$	2.56614e8	+	4.44468e8i	0.00820062	+	0.0142039i	−0.861896	+	0.507085i	$0.830723\pi$
$998$	−1.48787e10			−0.473816
$999$	2.72886e10	−	2.01639e10i	0.865969	−	0.639874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.8.c.a.4.5	✓	12
3.2	odd	2		27.8.c.a.10.2		12
4.3	odd	2		144.8.i.c.49.1		12
9.2	odd	6		27.8.c.a.19.2		12
9.4	even	3		81.8.a.e.1.2		6
9.5	odd	6		81.8.a.c.1.5		6
9.7	even	3	inner	9.8.c.a.7.5	yes	12
12.11	even	2		432.8.i.c.145.5		12
36.7	odd	6		144.8.i.c.97.1		12
36.11	even	6		432.8.i.c.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.8.c.a.4.5	✓	12	1.1	even	1	trivial
9.8.c.a.7.5	yes	12	9.7	even	3	inner
27.8.c.a.10.2		12	3.2	odd	2
27.8.c.a.19.2		12	9.2	odd	6
81.8.a.c.1.5		6	9.5	odd	6
81.8.a.e.1.2		6	9.4	even	3
144.8.i.c.49.1		12	4.3	odd	2
144.8.i.c.97.1		12	36.7	odd	6
432.8.i.c.145.5		12	12.11	even	2
432.8.i.c.289.5		12	36.11	even	6

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.11595 + 12.3252i) q^{2} +(45.7172 - 9.84574i) q^{3} +(-37.2735 + 64.5595i) q^{4} +(-145.304 + 251.673i) q^{5} +(446.672 + 493.411i) q^{6} +(-555.940 - 962.916i) q^{7} +760.739 q^{8} +(1993.12 - 900.239i) q^{9} -4135.89 q^{10} +(-2245.36 - 3889.07i) q^{11} +(-1068.40 + 3318.46i) q^{12} +(-1218.29 + 2110.14i) q^{13} +(7912.08 - 13704.1i) q^{14} +(-4164.96 + 12936.4i) q^{15} +(10184.4 + 17639.9i) q^{16} +15905.4 q^{17} +(25278.6 + 18159.5i) q^{18} -49949.6 q^{19} +(-10831.9 - 18761.5i) q^{20} +(-34896.6 - 38548.2i) q^{21} +(31955.7 - 55348.9i) q^{22} +(-34692.5 + 60089.2i) q^{23} +(34778.8 - 7490.04i) q^{24} +(-3163.73 - 5479.74i) q^{25} -34677.2 q^{26} +(82256.4 - 60780.2i) q^{27} +82887.2 q^{28} +(47035.8 + 81468.4i) q^{29} +(-189081. + 40720.9i) q^{30} +(9963.58 - 17257.4i) q^{31} +(-96255.8 + 166720. i) q^{32} +(-140942. - 155690. i) q^{33} +(113182. + 196037. i) q^{34} +323120. q^{35} +(-16171.5 + 162230. i) q^{36} +331750. q^{37} +(-355439. - 615638. i) q^{38} +(-34920.9 + 108465. i) q^{39} +(-110538. + 191457. i) q^{40} +(-121133. + 209809. i) q^{41} +(226791. - 704414. i) q^{42} +(-415713. - 720036. i) q^{43} +334769. q^{44} +(-63041.7 + 632423. i) q^{45} -987481. q^{46} +(80005.3 + 138573. i) q^{47} +(639279. + 706172. i) q^{48} +(-206366. + 357437. i) q^{49} +(45025.8 - 77987.1i) q^{50} +(727150. - 156600. i) q^{51} +(-90819.7 - 157304. i) q^{52} +311589. q^{53} +(1.33446e6 + 581317. i) q^{54} +1.30503e6 q^{55} +(-422925. - 732527. i) q^{56} +(-2.28356e6 + 491791. i) q^{57} +(-669408. + 1.15945e6i) q^{58} +(156177. - 270506. i) q^{59} +(-679926. - 751072. i) q^{60} +(28723.9 + 49751.3i) q^{61} +283601. q^{62} +(-1.97491e6 - 1.41873e6i) q^{63} -132603. q^{64} +(-354044. - 613221. i) q^{65} +(915973. - 2.84502e6i) q^{66} +(2.05100e6 - 3.55243e6i) q^{67} +(-592849. + 1.02684e6i) q^{68} +(-994422. + 3.08869e6i) q^{69} +(2.29930e6 + 3.98251e6i) q^{70} -403110. q^{71} +(1.51625e6 - 684847. i) q^{72} -823496. q^{73} +(2.36072e6 + 4.08889e6i) q^{74} +(-198589. - 219369. i) q^{75} +(1.86180e6 - 3.22472e6i) q^{76} +(-2.49656e6 + 4.32418e6i) q^{77} +(-1.58534e6 + 341422. i) q^{78} +(-489414. - 847689. i) q^{79} -5.91931e6 q^{80} +(3.16211e6 - 3.58858e6i) q^{81} -3.44791e6 q^{82} +(1.85204e6 + 3.20782e6i) q^{83} +(3.78937e6 - 816086. i) q^{84} +(-2.31111e6 + 4.00296e6i) q^{85} +(5.91638e6 - 1.02475e7i) q^{86} +(2.95246e6 + 3.26140e6i) q^{87} +(-1.70813e6 - 2.95857e6i) q^{88} +2.09023e6 q^{89} +(-8.24334e6 + 3.72329e6i) q^{90} +2.70918e6 q^{91} +(-2.58622e6 - 4.47947e6i) q^{92} +(285595. - 887060. i) q^{93} +(-1.13863e6 + 1.97216e6i) q^{94} +(7.25786e6 - 1.25710e7i) q^{95} +(-2.75906e6 + 8.56968e6i) q^{96} +(-1.75125e6 - 3.03325e6i) q^{97} -5.87396e6 q^{98} +(-7.97637e6 - 5.73004e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{2} + 24 q^{3} - 321 q^{4} - 180 q^{5} - 1233 q^{6} - 84 q^{7} + 5922 q^{8} + 990 q^{9} + 252 q^{10} - 8460 q^{11} + 8052 q^{12} - 1848 q^{13} - 16272 q^{14} - 1188 q^{15} - 12417 q^{16} + 30564 q^{17}+ \cdots - 49382676 q^{99}+O(q^{100}) \) 12 * q - 9 * q^2 + 24 * q^3 - 321 * q^4 - 180 * q^5 - 1233 * q^6 - 84 * q^7 + 5922 * q^8 + 990 * q^9 + 252 * q^10 - 8460 * q^11 + 8052 * q^12 - 1848 * q^13 - 16272 * q^14 - 1188 * q^15 - 12417 * q^16 + 30564 * q^17 + 42876 * q^18 + 24432 * q^19 - 40788 * q^20 - 187224 * q^21 - 35001 * q^22 - 51588 * q^23 + 215469 * q^24 + 4746 * q^25 + 536472 * q^26 + 322272 * q^27 + 75516 * q^28 - 414648 * q^29 - 1112112 * q^30 + 8196 * q^31 - 1048977 * q^32 - 148518 * q^33 - 106623 * q^34 + 2210616 * q^35 + 2501811 * q^36 + 139344 * q^37 - 1952685 * q^38 - 2057316 * q^39 + 305496 * q^40 - 1731582 * q^41 + 538866 * q^42 + 408372 * q^43 + 5169114 * q^44 + 2687580 * q^45 - 1684008 * q^46 - 1631484 * q^47 - 7434525 * q^48 - 179010 * q^49 - 1654461 * q^50 + 2525688 * q^51 + 681594 * q^52 + 2835648 * q^53 + 5816529 * q^54 - 16056 * q^55 - 1784466 * q^56 - 3071850 * q^57 - 948384 * q^58 - 2055636 * q^59 + 371484 * q^60 - 2723196 * q^61 - 1026828 * q^62 - 2238804 * q^63 + 7178178 * q^64 - 1387620 * q^65 + 5754762 * q^66 + 3806556 * q^67 + 2142639 * q^68 - 3002292 * q^69 + 953442 * q^70 + 2408400 * q^71 - 9638325 * q^72 - 10670052 * q^73 + 9846504 * q^74 + 19174632 * q^75 - 6727827 * q^76 + 3478824 * q^77 - 13339962 * q^78 + 6020916 * q^79 - 38072448 * q^80 - 28538730 * q^81 + 9403002 * q^82 + 9605052 * q^83 + 30090090 * q^84 - 1698624 * q^85 + 34278561 * q^86 + 10290708 * q^87 - 16459029 * q^88 - 24630264 * q^89 - 13660596 * q^90 + 13570104 * q^91 + 39143394 * q^92 + 27331212 * q^93 + 12602808 * q^94 + 10422072 * q^95 - 3404376 * q^96 + 9977226 * q^97 - 95833314 * q^98 - 49382676 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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