LMFDB - Embedded newform 25.8.d.a.11.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,8,Mod(6,25)] 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("25.6"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, 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:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	25.11
Dual form			25.8.d.a.16.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.59067 + 5.51494i) q^{2} +(19.6452 - 60.4618i) q^{3} +(-12.3506 + 38.0111i) q^{4} +(279.098 - 15.1508i) q^{5} +(184.323 + 567.288i) q^{6} -1041.08 q^{7} +(-487.000 - 1498.83i) q^{8} +(-1500.38 - 1090.09i) q^{9} +(-2034.98 + 1654.21i) q^{10} +(6018.53 - 4372.72i) q^{11} +(2055.59 + 1493.47i) q^{12} +(-10155.7 - 7378.57i) q^{13} +(7902.50 - 5741.50i) q^{14} +(4566.89 - 17172.4i) q^{15} +(7823.85 + 5684.36i) q^{16} +(-4604.79 - 14172.1i) q^{17} +17400.6 q^{18} +(-10295.5 - 31686.3i) q^{19} +(-2871.11 + 10795.9i) q^{20} +(-20452.3 + 62945.7i) q^{21} +(-21569.4 + 66383.7i) q^{22} +(-54287.3 + 39442.0i) q^{23} -100189. q^{24} +(77665.9 - 8457.12i) q^{25} +117781. q^{26} +(17097.7 - 12422.2i) q^{27} +(12857.9 - 39572.6i) q^{28} +(12141.8 - 37368.6i) q^{29} +(60039.0 + 155536. i) q^{30} +(75355.5 + 231920. i) q^{31} +110986. q^{32} +(-146147. - 449794. i) q^{33} +(113112. + 82180.5i) q^{34} +(-290563. + 15773.2i) q^{35} +(59965.9 - 43567.7i) q^{36} +(-41143.9 - 29892.8i) q^{37} +(252898. + 183741. i) q^{38} +(-645634. + 469080. i) q^{39} +(-158629. - 410942. i) q^{40} +(79881.6 + 58037.4i) q^{41} +(-191895. - 590593. i) q^{42} +759929. q^{43} +(91879.6 + 282776. i) q^{44} +(-435267. - 281509. i) q^{45} +(194556. - 598782. i) q^{46} +(-15281.1 + 47030.3i) q^{47} +(497388. - 361374. i) q^{48} +260308. q^{49} +(-542895. + 492518. i) q^{50} -947333. q^{51} +(405897. - 294901. i) q^{52} +(83795.2 - 257895. i) q^{53} +(-61275.1 + 188585. i) q^{54} +(1.61351e6 - 1.31160e6i) q^{55} +(507007. + 1.56041e6i) q^{56} -2.11807e6 q^{57} +(113921. + 350614. i) q^{58} +(61011.7 + 44327.6i) q^{59} +(596338. + 385681. i) q^{60} +(329818. - 239627. i) q^{61} +(-1.85102e6 - 1.34485e6i) q^{62} +(1.56201e6 + 1.13487e6i) q^{63} +(-1.84391e6 + 1.33968e6i) q^{64} +(-2.94623e6 - 1.90547e6i) q^{65} +(3.58994e6 + 2.60825e6i) q^{66} +(396700. + 1.22092e6i) q^{67} +595568. q^{68} +(1.31825e6 + 4.05715e6i) q^{69} +(2.11858e6 - 1.72217e6i) q^{70} +(-171818. + 528802. i) q^{71} +(-903174. + 2.77968e6i) q^{72} +(-2.14937e6 + 1.56161e6i) q^{73} +477167. q^{74} +(1.01443e6 - 4.86196e6i) q^{75} +1.33159e6 q^{76} +(-6.26578e6 + 4.55236e6i) q^{77} +(2.31384e6 - 7.12126e6i) q^{78} +(763891. - 2.35102e6i) q^{79} +(2.26974e6 + 1.46795e6i) q^{80} +(-1.66853e6 - 5.13522e6i) q^{81} -926427. q^{82} +(1.90359e6 + 5.85863e6i) q^{83} +(-2.14004e6 - 1.55483e6i) q^{84} +(-1.49991e6 - 3.88563e6i) q^{85} +(-5.76837e6 + 4.19097e6i) q^{86} +(-2.02084e6 - 1.46823e6i) q^{87} +(-9.48500e6 - 6.89125e6i) q^{88} +(4.48162e6 - 3.25609e6i) q^{89} +(4.85647e6 - 263634. i) q^{90} +(1.05729e7 + 7.68170e6i) q^{91} +(-828756. - 2.55065e6i) q^{92} +1.55027e7 q^{93} +(-143376. - 441265. i) q^{94} +(-3.35353e6 - 8.68760e6i) q^{95} +(2.18035e6 - 6.71044e6i) q^{96} +(3.82641e6 - 1.17765e7i) q^{97} +(-1.97591e6 + 1.43558e6i) q^{98} -1.37967e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) $ 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−7.59067	+	5.51494i	−0.670926	+	0.487457i	−0.870335	−	0.492460i	$-0.836098\pi$
$2$	−7.59067	+	5.51494i	−0.670926	+	0.487457i	0.199409	+	0.979916i	$0.436098\pi$
$3$	19.6452	−	60.4618i	0.420081	−	1.29288i	−0.487546	−	0.873097i	$-0.662108\pi$
$3$	19.6452	−	60.4618i	0.420081	−	1.29288i	0.907627	−	0.419778i	$-0.137892\pi$
$4$	−12.3506	+	38.0111i	−0.0964887	+	0.296962i
$5$	279.098	−	15.1508i	0.998530	−	0.0542053i
$5$	279.098	−	15.1508i	0.998530	−	0.0542053i
$6$	184.323	+	567.288i	0.348377	+	1.07220i
$7$	−1041.08			−1.14721			−0.573603	−	0.819133i	$-0.694455\pi$
$7$	−1041.08			−1.14721			−0.573603	+	0.819133i	$0.694455\pi$
$8$	−487.000	−	1498.83i	−0.336290	−	1.03499i
$9$	−1500.38	−	1090.09i	−0.686043	−	0.498439i
$10$	−2034.98	+	1654.21i	−0.643517	+	0.523108i
$11$	6018.53	−	4372.72i	1.36338	−	0.990551i	0.365155	−	0.930947i	$-0.381016\pi$
$11$	6018.53	−	4372.72i	1.36338	−	0.990551i	0.998222	−	0.0596047i	$-0.0189840\pi$
$12$	2055.59	+	1493.47i	0.343401	+	0.249496i
$13$	−10155.7	−	7378.57i	−1.28206	−	0.931474i	−0.282450	−	0.959282i	$-0.591147\pi$
$13$	−10155.7	−	7378.57i	−1.28206	−	0.931474i	−0.999613	+	0.0278081i	$0.991147\pi$
$14$	7902.50	−	5741.50i	0.769691	−	0.559213i
$15$	4566.89	−	17172.4i	0.349383	−	1.31375i
$16$	7823.85	+	5684.36i	0.477530	+	0.346946i
$17$	−4604.79	−	14172.1i	−0.227321	−	0.699621i	−0.998048	−	0.0624555i	$-0.980107\pi$
$17$	−4604.79	−	14172.1i	−0.227321	−	0.699621i	0.770727	−	0.637165i	$-0.219893\pi$
$18$	17400.6			0.703252
$19$	−10295.5	−	31686.3i	−0.344358	−	1.05983i	−0.961926	−	0.273309i	$-0.911882\pi$
$19$	−10295.5	−	31686.3i	−0.344358	−	1.05983i	0.617568	−	0.786517i	$-0.288118\pi$
$20$	−2871.11	+	10795.9i	−0.0802499	+	0.301755i
$21$	−20452.3	+	62945.7i	−0.481919	+	1.48320i
$22$	−21569.4	+	66383.7i	−0.431875	+	1.32917i
$23$	−54287.3	+	39442.0i	−0.930359	+	0.675945i	−0.946081	−	0.323931i	$-0.894995\pi$
$23$	−54287.3	+	39442.0i	−0.930359	+	0.675945i	0.0157216	+	0.999876i	$0.494995\pi$
$24$	−100189.			−1.47939
$25$	77665.9	−	8457.12i	0.994124	−	0.108251i
$26$	117781.			1.31422
$27$	17097.7	−	12422.2i	0.167172	−	0.121458i
$28$	12857.9	−	39572.6i	0.110692	−	0.340676i
$29$	12141.8	−	37368.6i	0.0924463	−	0.284521i	−0.894133	−	0.447801i	$-0.852207\pi$
$29$	12141.8	−	37368.6i	0.0924463	−	0.284521i	0.986580	+	0.163280i	$0.0522074\pi$
$30$	60039.0	+	155536.i	0.405984	+	1.05174i
$31$	75355.5	+	231920.i	0.454306	+	1.39821i	0.871948	+	0.489599i	$0.162857\pi$
$31$	75355.5	+	231920.i	0.454306	+	1.39821i	−0.417641	+	0.908612i	$0.637143\pi$
$32$	110986.			0.598749
$33$	−146147.	−	449794.i	−0.707931	−	2.17879i
$34$	113112.	+	82180.5i	0.493550	+	0.358585i
$35$	−290563.	+	15773.2i	−1.14552	+	0.0621846i
$36$	59965.9	−	43567.7i	0.214213	−	0.155635i
$37$	−41143.9	−	29892.8i	−0.133536	−	0.0970198i	0.519012	−	0.854767i	$-0.326300\pi$
$37$	−41143.9	−	29892.8i	−0.133536	−	0.0970198i	−0.652548	+	0.757747i	$0.726300\pi$
$38$	252898.	+	183741.i	0.747658	+	0.543205i
$39$	−645634.	+	469080.i	−1.74285	+	1.26625i
$40$	−158629.	−	410942.i	−0.391898	−	1.01524i
$41$	79881.6	+	58037.4i	0.181010	+	0.131512i	0.674601	−	0.738183i	$-0.264316\pi$
$41$	79881.6	+	58037.4i	0.181010	+	0.131512i	−0.493590	+	0.869694i	$0.664316\pi$
$42$	−191895.	−	590593.i	−0.399661	−	1.23003i
$43$	759929.			1.45758			0.728792	−	0.684735i	$-0.240082\pi$
$43$	759929.			1.45758			0.728792	+	0.684735i	$0.240082\pi$
$44$	91879.6	+	282776.i	0.162605	+	0.500448i
$45$	−435267.	−	281509.i	−0.712052	−	0.460519i
$46$	194556.	−	598782.i	0.294708	−	0.907019i
$47$	−15281.1	+	47030.3i	−0.0214690	+	0.0660747i	−0.961217	−	0.275793i	$-0.911060\pi$
$47$	−15281.1	+	47030.3i	−0.0214690	+	0.0660747i	0.939748	+	0.341868i	$0.111060\pi$
$48$	497388.	−	361374.i	0.649159	−	0.471642i
$49$	260308.			0.316083
$50$	−542895.	+	492518.i	−0.614216	+	0.557221i
$51$	−947333.			−1.00002
$52$	405897.	−	294901.i	0.400317	−	0.290847i
$53$	83795.2	−	257895.i	0.0773132	−	0.237946i	−0.904929	−	0.425562i	$-0.860076\pi$
$53$	83795.2	−	257895.i	0.0773132	−	0.237946i	0.982242	+	0.187617i	$0.0600763\pi$
$54$	−61275.1	+	188585.i	−0.0529549	+	0.162978i
$55$	1.61351e6	−	1.31160e6i	1.30768	−	1.06300i
$56$	507007.	+	1.56041e6i	0.385794	+	1.18735i
$57$	−2.11807e6			−1.51488
$58$	113921.	+	350614.i	0.0766667	+	0.235956i
$59$	61011.7	+	44327.6i	0.0386751	+	0.0280991i	0.606955	−	0.794736i	$-0.292391\pi$
$59$	61011.7	+	44327.6i	0.0386751	+	0.0280991i	−0.568280	+	0.822835i	$0.692391\pi$
$60$	596338.	+	385681.i	0.356421	+	0.230515i
$61$	329818.	−	239627.i	0.186046	−	0.135170i	−0.490864	−	0.871236i	$-0.663319\pi$
$61$	329818.	−	239627.i	0.186046	−	0.135170i	0.676910	+	0.736066i	$0.263319\pi$
$62$	−1.85102e6	−	1.34485e6i	−0.986373	−	0.716642i
$63$	1.56201e6	+	1.13487e6i	0.787033	+	0.571813i
$64$	−1.84391e6	+	1.33968e6i	−0.879247	+	0.638810i
$65$	−2.94623e6	−	1.90547e6i	−1.33067	−	0.860610i
$66$	3.58994e6	+	2.60825e6i	1.53703	+	1.11672i
$67$	396700.	+	1.22092e6i	0.161139	+	0.495934i	0.998731	−	0.0503618i	$-0.0160375\pi$
$67$	396700.	+	1.22092e6i	0.161139	+	0.495934i	−0.837592	+	0.546296i	$0.816037\pi$
$68$	595568.			0.229694
$69$	1.31825e6	+	4.05715e6i	0.483088	+	1.48679i
$70$	2.11858e6	−	1.72217e6i	0.738247	−	0.600112i
$71$	−171818.	+	528802.i	−0.0569724	+	0.175343i	−0.975493	−	0.220030i	$-0.929385\pi$
$71$	−171818.	+	528802.i	−0.0569724	+	0.175343i	0.918521	+	0.395373i	$0.129385\pi$
$72$	−903174.	+	2.77968e6i	−0.285173	+	0.877671i
$73$	−2.14937e6	+	1.56161e6i	−0.646666	+	0.469831i	−0.862134	−	0.506680i	$-0.830872\pi$
$73$	−2.14937e6	+	1.56161e6i	−0.646666	+	0.469831i	0.215468	+	0.976511i	$0.430872\pi$
$74$	477167.			0.136886
$75$	1.01443e6	−	4.86196e6i	0.277657	−	1.33075i
$76$	1.33159e6			0.347954
$77$	−6.26578e6	+	4.55236e6i	−1.56407	+	1.13637i
$78$	2.31384e6	−	7.12126e6i	0.552080	−	1.69913i
$79$	763891.	−	2.35102e6i	0.174316	−	0.536489i	−0.825286	−	0.564715i	$-0.808986\pi$
$79$	763891.	−	2.35102e6i	0.174316	−	0.536489i	0.999602	+	0.0282265i	$0.00898597\pi$
$80$	2.26974e6	+	1.46795e6i	0.495634	+	0.320551i
$81$	−1.66853e6	−	5.13522e6i	−0.348849	−	1.07365i
$82$	−926427.			−0.185551
$83$	1.90359e6	+	5.85863e6i	0.365426	+	1.12466i	0.949714	+	0.313119i	$0.101374\pi$
$83$	1.90359e6	+	5.85863e6i	0.365426	+	1.12466i	−0.584288	+	0.811546i	$0.698626\pi$
$84$	−2.14004e6	−	1.55483e6i	−0.393952	−	0.286223i
$85$	−1.49991e6	−	3.88563e6i	−0.264910	−	0.686270i
$86$	−5.76837e6	+	4.19097e6i	−0.977932	+	0.710509i
$87$	−2.02084e6	−	1.46823e6i	−0.329015	−	0.239043i
$88$	−9.48500e6	−	6.89125e6i	−1.48371	−	1.07798i
$89$	4.48162e6	−	3.25609e6i	0.673860	−	0.489588i	−0.197455	−	0.980312i	$-0.563268\pi$
$89$	4.48162e6	−	3.25609e6i	0.673860	−	0.489588i	0.871315	+	0.490724i	$0.163268\pi$
$90$	4.85647e6	−	263634.i	0.702218	−	0.0381199i
$91$	1.05729e7	+	7.68170e6i	1.47079	+	1.06859i
$92$	−828756.	−	2.55065e6i	−0.110961	−	0.341502i
$93$	1.55027e7			1.99856
$94$	−143376.	−	441265.i	−0.0178044	−	0.0547964i
$95$	−3.35353e6	−	8.68760e6i	−0.401300	−	1.03960i
$96$	2.18035e6	−	6.71044e6i	0.251523	−	0.774108i
$97$	3.82641e6	−	1.17765e7i	0.425687	−	1.31013i	−0.476648	−	0.879094i	$-0.658148\pi$
$97$	3.82641e6	−	1.17765e7i	0.425687	−	1.31013i	0.902335	−	0.431036i	$-0.141852\pi$
$98$	−1.97591e6	+	1.43558e6i	−0.212068	+	0.154077i
$99$	−1.37967e7			−1.42906
$100$	−637752.	+	3.05662e6i	−0.0637752	+	0.305662i
$101$	−9.56648e6			−0.923905			−0.461953	−	0.886905i	$-0.652851\pi$
$101$	−9.56648e6			−0.923905			−0.461953	+	0.886905i	$0.652851\pi$
$102$	7.19088e6	−	5.22448e6i	0.670937	−	0.487464i
$103$	−1.44152e6	+	4.43653e6i	−0.129984	+	0.400049i	−0.994776	−	0.102081i	$-0.967450\pi$
$103$	−1.44152e6	+	4.43653e6i	−0.129984	+	0.400049i	0.864792	+	0.502130i	$0.167450\pi$
$104$	−6.11340e6	+	1.88151e7i	−0.532925	+	1.64017i
$105$	−4.75451e6	+	1.78779e7i	−0.400814	+	1.50714i
$106$	786215.	+	2.41972e6i	0.0641167	+	0.197331i
$107$	1.83851e7			1.45085			0.725427	−	0.688299i	$-0.241642\pi$
$107$	1.83851e7			1.45085			0.725427	+	0.688299i	$0.241642\pi$
$108$	261015.	+	803323.i	0.0199381	+	0.0613630i
$109$	1.69110e6	+	1.22866e6i	0.125077	+	0.0908738i	0.648565	−	0.761159i	$-0.275369\pi$
$109$	1.69110e6	+	1.22866e6i	0.125077	+	0.0908738i	−0.523488	+	0.852033i	$0.675369\pi$
$110$	−5.01419e6	+	1.88543e7i	−0.359192	+	1.35063i
$111$	−2.61565e6	+	1.90038e6i	−0.181531	+	0.131890i
$112$	−8.14527e6	−	5.91788e6i	−0.547826	−	0.398019i
$113$	−5.50739e6	−	4.00135e6i	−0.359063	−	0.260875i	0.393598	−	0.919283i	$-0.371230\pi$
$113$	−5.50739e6	−	4.00135e6i	−0.359063	−	0.260875i	−0.752661	+	0.658408i	$0.771230\pi$
$114$	1.60776e7	−	1.16810e7i	1.01637	−	0.738439i
$115$	−1.45539e7	+	1.18307e7i	−0.892352	+	0.725382i
$116$	1.27046e6	+	923045.i	0.0755717	+	0.0549060i
$117$	7.19413e6	+	2.21413e7i	0.415267	+	1.27806i
$118$	−707583.			−0.0396452
$119$	4.79396e6	+	1.47543e7i	0.260784	+	0.802610i
$120$	−2.79626e7	+	1.51795e6i	−1.47721	+	0.0801906i
$121$	1.10802e7	−	3.41013e7i	0.568588	−	1.74993i
$122$	−1.18201e6	+	3.63786e6i	−0.0589335	+	0.181379i
$123$	5.07834e6	−	3.68963e6i	0.246067	−	0.178778i
$124$	−9.74622e6			−0.459050
$125$	2.15482e7	−	3.53706e6i	0.986794	−	0.161979i
$126$	−1.81155e7			−0.806775
$127$	5.27105e6	−	3.82964e6i	0.228341	−	0.165900i	−0.467732	−	0.883870i	$-0.654929\pi$
$127$	5.27105e6	−	3.82964e6i	0.228341	−	0.165900i	0.696073	+	0.717971i	$0.254929\pi$
$128$	2.21829e6	−	6.82720e6i	0.0934940	−	0.287745i
$129$	1.49290e7	−	4.59467e7i	0.612303	−	1.88448i
$130$	3.28724e7	−	1.78448e6i	1.31229	−	0.0712378i
$131$	5.70396e6	+	1.75550e7i	0.221680	+	0.682262i	0.998612	+	0.0526764i	$0.0167752\pi$
$131$	5.70396e6	+	1.75550e7i	0.221680	+	0.682262i	−0.776931	+	0.629585i	$0.783225\pi$
$132$	1.89022e7			0.715324
$133$	1.07185e7	+	3.29881e7i	0.395050	+	1.21584i
$134$	−9.74449e6	−	7.07979e6i	−0.349858	−	0.254187i
$135$	4.58372e6	−	3.72605e6i	0.160343	−	0.130341i
$136$	−1.89991e7	+	1.38036e7i	−0.647658	+	0.470551i
$137$	8.83261e6	+	6.41726e6i	0.293472	+	0.213220i	0.724772	−	0.688989i	$-0.241945\pi$
$137$	8.83261e6	+	6.41726e6i	0.293472	+	0.213220i	−0.431300	+	0.902209i	$0.641945\pi$
$138$	−3.23814e7	−	2.35264e7i	−1.04886	−	0.762043i
$139$	7.48205e6	−	5.43603e6i	0.236303	−	0.171684i	−0.463332	−	0.886185i	$-0.653346\pi$
$139$	7.48205e6	−	5.43603e6i	0.236303	−	0.171684i	0.699635	+	0.714501i	$0.253346\pi$
$140$	2.98906e6	−	1.12394e7i	0.0920633	−	0.346176i
$141$	2.54334e6	+	1.84784e6i	0.0764076	+	0.0555134i
$142$	−1.61210e6	−	4.96152e6i	−0.0472478	−	0.145414i
$143$	−9.33870e7			−2.67061
$144$	−5.54227e6	−	1.70574e7i	−0.154675	−	0.476040i
$145$	2.82258e6	−	1.06134e7i	0.0768879	−	0.289113i
$146$	7.70295e6	−	2.37073e7i	0.204844	−	0.630444i
$147$	5.11380e6	−	1.57387e7i	0.132780	−	0.408655i
$148$	1.64441e6	−	1.19473e6i	0.0416959	−	0.0302939i
$149$	1.01288e7			0.250845			0.125423	−	0.992103i	$-0.459971\pi$
$149$	1.01288e7			0.250845			0.125423	+	0.992103i	$0.459971\pi$
$150$	1.91132e7	+	4.25001e7i	0.462397	+	1.02818i
$151$	−4.85342e7			−1.14717			−0.573587	−	0.819145i	$-0.694448\pi$
$151$	−4.85342e7			−1.14717			−0.573587	+	0.819145i	$0.694448\pi$
$152$	−4.24786e7	+	3.08625e7i	−0.981110	+	0.712818i
$153$	−8.53989e6	+	2.62831e7i	−0.192767	+	0.593275i
$154$	2.24555e7	−	6.91108e7i	0.495450	−	1.52484i
$155$	2.45453e7	+	6.35867e7i	0.529429	+	1.37153i
$156$	−9.85632e6	−	3.03346e7i	−0.207864	−	0.639739i
$157$	3.12764e7			0.645013			0.322507	−	0.946567i	$-0.395475\pi$
$157$	3.12764e7			0.645013			0.322507	+	0.946567i	$0.395475\pi$
$158$	7.16727e6	+	2.20586e7i	0.144562	+	0.444916i
$159$	−1.39466e7	−	1.01328e7i	−0.275156	−	0.199913i
$160$	3.09760e7	−	1.68154e6i	0.597869	−	0.0324554i
$161$	5.65175e7	−	4.10623e7i	1.06731	−	0.775449i
$162$	4.09857e7	+	2.97779e7i	0.757408	+	0.550289i
$163$	−874084.	−	635059.i	−0.0158087	−	0.0114857i	0.579853	−	0.814721i	$-0.303110\pi$
$163$	−874084.	−	635059.i	−0.0158087	−	0.0114857i	−0.595662	+	0.803236i	$0.703110\pi$
$164$	−3.19265e6	+	2.31959e6i	−0.0565194	+	0.0410637i
$165$	−4.76040e7	−	1.23322e8i	−0.824992	−	2.13721i
$166$	−4.67595e7	−	3.39728e7i	−0.793399	−	0.576438i
$167$	216303.	+	665713.i	0.00359381	+	0.0110606i	0.952837	−	0.303481i	$-0.0981490\pi$
$167$	216303.	+	665713.i	0.00359381	+	0.0110606i	−0.949244	+	0.314542i	$0.898149\pi$
$168$	1.04305e8			1.69716
$169$	2.93052e7	+	9.01923e7i	0.467027	+	1.43736i
$170$	3.28143e7	+	2.12226e7i	0.512262	+	0.331305i
$171$	−1.90937e7	+	5.87644e7i	−0.292014	+	0.898728i
$172$	−9.38555e6	+	2.88857e7i	−0.140640	+	0.432847i
$173$	−4.91386e7	+	3.57013e7i	−0.721542	+	0.524231i	−0.886876	−	0.462007i	$-0.847130\pi$
$173$	−4.91386e7	+	3.57013e7i	−0.721542	+	0.524231i	0.165335	+	0.986238i	$0.447130\pi$
$174$	2.34367e7			0.337268
$175$	−8.08565e7	+	8.80455e6i	−1.14046	+	0.124186i
$176$	7.19442e7			0.994722
$177$	3.87872e6	−	2.81805e6i	0.0525753	−	0.0381982i
$178$	−1.60613e7	+	4.94317e7i	−0.213458	+	0.656955i
$179$	8.32025e6	−	2.56071e7i	0.108430	−	0.333714i	−0.882090	−	0.471081i	$-0.843864\pi$
$179$	8.32025e6	−	2.56071e7i	0.108430	−	0.333714i	0.990520	+	0.137367i	$0.0438639\pi$
$180$	1.60762e7	−	1.30682e7i	0.205462	−	0.167017i
$181$	−1.46827e7	−	4.51886e7i	−0.184047	−	0.566440i	0.815883	−	0.578217i	$-0.196251\pi$
$181$	−1.46827e7	−	4.51886e7i	−0.184047	−	0.566440i	−0.999931	+	0.0117771i	$0.996251\pi$
$182$	−1.22620e8			−1.50769
$183$	−8.00893e6	−	2.46489e7i	−0.0966041	−	0.297317i
$184$	8.55549e7	+	6.21593e7i	1.01247	+	0.735603i
$185$	−1.19361e7	−	7.71964e6i	−0.138599	−	0.0896388i
$186$	−1.17676e8	+	8.54964e7i	−1.34089	+	0.974210i
$187$	−8.96846e7	−	6.51597e7i	−1.00293	−	0.728674i
$188$	−1.59894e6	−	1.16170e6i	−0.0175501	−	0.0127509i
$189$	−1.78001e7	+	1.29325e7i	−0.191781	+	0.139337i
$190$	7.33671e7	+	4.74501e7i	0.776004	+	0.501880i
$191$	1.19406e7	+	8.67535e6i	0.123996	+	0.0900887i	0.648055	−	0.761594i	$-0.275583\pi$
$191$	1.19406e7	+	8.67535e6i	0.123996	+	0.0900887i	−0.524058	+	0.851682i	$0.675583\pi$
$192$	4.47755e7	+	1.37805e8i	0.456547	+	1.40511i
$193$	1.00874e8			1.01002			0.505008	−	0.863115i	$-0.331490\pi$
$193$	1.00874e8			1.01002			0.505008	+	0.863115i	$0.331490\pi$
$194$	3.59016e7	+	1.10494e8i	0.353027	+	1.08650i
$195$	−1.73088e8	+	1.40701e8i	−1.67165	+	1.35886i
$196$	−3.21494e6	+	9.89457e6i	−0.0304984	+	0.0938644i
$197$	6.30862e7	−	1.94159e8i	0.587899	−	1.80937i	0.000595128	−	1.00000i	$-0.499811\pi$
$197$	6.30862e7	−	1.94159e8i	0.587899	−	1.80937i	0.587304	−	0.809367i	$-0.300189\pi$
$198$	1.04726e8	−	7.60880e7i	0.958797	−	0.696607i
$199$	−1.03143e8			−0.927795			−0.463898	−	0.885889i	$-0.653549\pi$
$199$	−1.03143e8			−0.927795			−0.463898	+	0.885889i	$0.653549\pi$
$200$	−5.04991e7	−	1.12290e8i	−0.446353	−	0.992509i
$201$	8.16120e7			0.708872
$202$	7.26160e7	−	5.27586e7i	0.619873	−	0.450364i
$203$	−1.26406e7	+	3.89037e7i	−0.106055	+	0.326404i
$204$	1.17001e7	−	3.60091e7i	0.0964902	−	0.296966i
$205$	2.31741e7	+	1.49878e7i	0.187873	+	0.121507i
$206$	−1.35251e7	−	4.16261e7i	−0.107797	−	0.331765i
$207$	1.24447e8			0.975184
$208$	−3.75145e7	−	1.15458e8i	−0.289053	−	0.889614i
$209$	−2.00519e8	−	1.45686e8i	−1.51930	−	1.10384i
$210$	−6.25055e7	−	1.61926e8i	−0.465747	−	1.20656i
$211$	1.66007e8	−	1.20611e8i	1.21657	−	0.883891i	0.220761	−	0.975328i	$-0.429146\pi$
$211$	1.66007e8	−	1.20611e8i	1.21657	−	0.883891i	0.995811	+	0.0914365i	$0.0291459\pi$
$212$	8.76796e6	+	6.37030e6i	0.0632009	+	0.0459181i
$213$	2.85969e7	+	2.07769e7i	0.202764	+	0.147316i
$214$	−1.39555e8	+	1.01393e8i	−0.973416	+	0.707228i
$215$	2.12094e8	−	1.15136e7i	1.45544	−	0.0790087i
$216$	−2.69454e7	−	1.95770e7i	−0.181926	−	0.132177i
$217$	−7.84512e7	−	2.41448e8i	−0.521183	−	1.60404i
$218$	−1.96126e7			−0.128215
$219$	5.21927e7	+	1.60633e8i	0.335781	+	1.03343i
$220$	2.99277e7	+	7.75301e7i	0.189493	+	0.490898i
$221$	−5.78048e7	+	1.77905e8i	−0.360239	+	1.10870i
$222$	9.37405e6	−	2.88504e7i	0.0575032	−	0.176977i
$223$	1.95399e8	−	1.41965e8i	1.17993	−	0.857266i	0.187762	−	0.982215i	$-0.439877\pi$
$223$	1.95399e8	−	1.41965e8i	1.17993	−	0.857266i	0.992163	+	0.124949i	$0.0398767\pi$
$224$	−1.15546e8			−0.686889
$225$	−1.25747e8	−	7.19737e7i	−0.735968	−	0.421245i
$226$	6.38720e7			0.368070
$227$	−2.78564e8	+	2.02389e8i	−1.58065	+	1.14841i	−0.664696	+	0.747114i	$0.731439\pi$
$227$	−2.78564e8	+	2.02389e8i	−1.58065	+	1.14841i	−0.915950	+	0.401293i	$0.868561\pi$
$228$	2.61594e7	−	8.05102e7i	0.146169	−	0.449862i
$229$	−4.04051e7	+	1.24354e8i	−0.222337	+	0.684284i	0.776214	+	0.630470i	$0.217138\pi$
$229$	−4.04051e7	+	1.24354e8i	−0.222337	+	0.684284i	−0.998551	+	0.0538139i	$0.982862\pi$
$230$	4.52281e7	−	1.70066e8i	0.245110	−	0.921661i
$231$	1.52151e8	+	4.68272e8i	0.812143	+	2.49952i
$232$	−6.19223e7			−0.325566
$233$	−3.40101e7	−	1.04672e8i	−0.176142	−	0.542108i	0.823542	−	0.567255i	$-0.191995\pi$
$233$	−3.40101e7	−	1.04672e8i	−0.176142	−	0.542108i	−0.999684	+	0.0251471i	$0.991995\pi$
$234$	−1.76716e8	−	1.28392e8i	−0.901614	−	0.655061i
$235$	−3.55236e6	+	1.33576e7i	−0.0178558	+	0.0671413i
$236$	−2.43847e6	+	1.77165e6i	−0.0120761	+	0.00877377i
$237$	−1.27140e8	−	9.23725e7i	−0.620387	−	0.450737i
$238$	−1.17758e8	−	8.55565e7i	−0.566204	−	0.411371i
$239$	2.92132e8	−	2.12247e8i	1.38416	−	1.00565i	0.387685	−	0.921792i	$-0.373275\pi$
$239$	2.92132e8	−	2.12247e8i	1.38416	−	1.00565i	0.996477	−	0.0838612i	$-0.0267252\pi$
$240$	1.33345e8	−	1.08394e8i	0.622639	−	0.506136i
$241$	1.28643e8	+	9.34645e7i	0.592006	+	0.430118i	0.843032	−	0.537863i	$-0.180768\pi$
$241$	1.28643e8	+	9.34645e7i	0.592006	+	0.430118i	−0.251026	+	0.967980i	$0.580768\pi$
$242$	1.03961e8	+	3.19958e8i	0.471536	+	1.45124i
$243$	−2.97044e8			−1.32800
$244$	5.03505e6	+	1.54963e7i	0.0221891	+	0.0682909i
$245$	7.26512e7	−	3.94388e6i	0.315618	−	0.0171333i
$246$	−1.81999e7	+	5.60135e7i	−0.0779463	+	0.239894i
$247$	−1.29241e8	+	3.97764e8i	−0.545711	+	1.67953i
$248$	3.10911e8	−	2.25890e8i	1.29436	−	0.940409i
$249$	3.91620e8			1.60756
$250$	−1.44059e8	+	1.45686e8i	−0.583109	+	0.589695i
$251$	4.06328e8			1.62188			0.810941	−	0.585128i	$-0.198956\pi$
$251$	4.06328e8			1.62188			0.810941	+	0.585128i	$0.198956\pi$
$252$	−6.24293e7	+	4.53576e7i	−0.245746	+	0.178545i
$253$	−1.54261e8	+	4.74766e8i	−0.598872	+	1.84314i
$254$	−1.88905e7	+	5.81391e7i	−0.0723313	+	0.222613i
$255$	−2.64398e8	+	1.43529e7i	−0.998546	+	0.0542061i
$256$	−6.93387e7	−	2.13403e8i	−0.258307	−	0.794987i
$257$	1.72438e8			0.633675			0.316837	−	0.948480i	$-0.397379\pi$
$257$	1.72438e8			0.633675			0.316837	+	0.948480i	$0.397379\pi$
$258$	1.40072e8	+	4.31099e8i	0.507789	+	1.56282i
$259$	4.28342e7	+	3.11208e7i	0.153194	+	0.111302i
$260$	1.08817e8	−	8.84558e7i	0.383963	−	0.312119i
$261$	−5.89522e7	+	4.28313e7i	−0.205238	+	0.149114i
$262$	−1.40112e8	−	1.01797e8i	−0.481304	−	0.349688i
$263$	−2.69124e8	−	1.95530e8i	−0.912236	−	0.662778i	0.0293431	−	0.999569i	$-0.490658\pi$
$263$	−2.69124e8	−	1.95530e8i	−0.912236	−	0.662778i	−0.941579	+	0.336791i	$0.890658\pi$
$264$	−6.02993e8	+	4.38100e8i	−2.01696	+	1.46541i
$265$	1.94797e7	−	7.32475e7i	0.0643016	−	0.241787i
$266$	−2.63288e8	−	1.91290e8i	−0.857718	−	0.623169i
$267$	−1.08826e8	−	3.34933e8i	−0.349901	−	1.07688i
$268$	−5.13078e7			−0.162821
$269$	1.73409e7	+	5.33697e7i	0.0543173	+	0.167171i	0.974535	−	0.224236i	$-0.0719885\pi$
$269$	1.73409e7	+	5.33697e7i	0.0543173	+	0.167171i	−0.920218	+	0.391407i	$0.871988\pi$
$270$	−1.42445e7	+	5.35621e7i	−0.0440428	+	0.165609i
$271$	−1.26011e8	+	3.87821e8i	−0.384605	+	1.18369i	0.552161	+	0.833737i	$0.313803\pi$
$271$	−1.26011e8	+	3.87821e8i	−0.384605	+	1.18369i	−0.936766	+	0.349956i	$0.886197\pi$
$272$	4.45321e7	−	1.37056e8i	0.134178	−	0.412958i
$273$	6.72157e8	−	4.88351e8i	1.99941	−	1.45266i
$274$	−1.02436e8			−0.300834
$275$	4.30454e8	−	3.90510e8i	1.24814	−	1.13232i
$276$	−1.70498e8			−0.488132
$277$	2.67855e8	−	1.94608e8i	0.757218	−	0.550151i	−0.140838	−	0.990033i	$-0.544980\pi$
$277$	2.67855e8	−	1.94608e8i	0.757218	−	0.550151i	0.898056	+	0.439882i	$0.144980\pi$
$278$	−2.68144e7	+	8.25261e7i	−0.0748533	+	0.230375i
$279$	1.39752e8	−	4.30111e8i	0.385250	−	1.18568i
$280$	1.65146e8	+	4.27824e8i	0.449588	+	1.16469i
$281$	−9.87347e7	−	3.03874e8i	−0.265459	−	0.816999i	−0.991587	−	0.129440i	$-0.958682\pi$
$281$	−9.87347e7	−	3.03874e8i	−0.265459	−	0.816999i	0.726128	−	0.687559i	$-0.241318\pi$
$282$	−2.94963e7			−0.0783243
$283$	2.11379e8	+	6.50557e8i	0.554381	+	1.70621i	0.697572	+	0.716515i	$0.254264\pi$
$283$	2.11379e8	+	6.50557e8i	0.554381	+	1.70621i	−0.143190	+	0.989695i	$0.545736\pi$
$284$	−1.79783e7	−	1.30620e7i	−0.0465730	−	0.0338372i
$285$	−5.91149e8	+	3.20905e7i	−1.51265	+	0.0821146i
$286$	7.08869e8	−	5.15024e8i	1.79178	−	1.30181i
$287$	−8.31632e7	−	6.04216e7i	−0.207656	−	0.150871i
$288$	−1.66521e8	−	1.20985e8i	−0.410768	−	0.298440i
$289$	1.52327e8	−	1.10672e8i	0.371222	−	0.269709i
$290$	3.71072e7	+	9.61294e7i	0.0893441	+	0.231453i
$291$	−6.36857e8	−	4.62703e8i	−1.51501	−	1.10072i
$292$	−3.28125e7	−	1.00986e8i	−0.0771257	−	0.237368i
$293$	−8.22935e7			−0.191130			−0.0955650	−	0.995423i	$-0.530466\pi$
$293$	−8.22935e7			−0.191130			−0.0955650	+	0.995423i	$0.530466\pi$
$294$	4.79807e7	+	1.47669e8i	0.110116	+	0.338902i
$295$	1.76998e7	+	1.14473e7i	0.0401413	+	0.0259614i
$296$	−2.47672e7	+	7.62256e7i	−0.0555081	+	0.170836i
$297$	4.85842e7	−	1.49527e8i	0.107609	−	0.331185i
$298$	−7.68843e7	+	5.58597e7i	−0.168299	+	0.122276i
$299$	8.42353e8			1.82241
$300$	1.72280e8	+	9.86076e7i	0.368392	+	0.210856i
$301$	−7.91148e8			−1.67215
$302$	3.68407e8	−	2.67664e8i	0.769669	−	0.559197i
$303$	−1.87936e8	+	5.78407e8i	−0.388115	+	1.19450i
$304$	9.95661e7	−	3.06433e8i	0.203261	−	0.625573i
$305$	8.84209e7	−	7.18763e7i	0.178445	−	0.145056i
$306$	−8.01262e7	−	2.46603e8i	−0.159864	−	0.492010i
$307$	−5.18731e8			−1.02319			−0.511597	−	0.859225i	$-0.670946\pi$
$307$	−5.18731e8			−1.02319			−0.511597	+	0.859225i	$0.670946\pi$
$308$	−9.56541e7	−	2.94393e8i	−0.186542	−	0.574117i
$309$	2.39922e8	+	1.74313e8i	0.462610	+	0.336106i
$310$	−5.36992e8	−	3.47299e8i	−1.02377	−	0.662122i
$311$	−5.34468e8	+	3.88314e8i	−1.00754	+	0.732017i	−0.963691	−	0.267021i	$-0.913961\pi$
$311$	−5.34468e8	+	3.88314e8i	−1.00754	+	0.732017i	−0.0438445	+	0.999038i	$0.513961\pi$
$312$	1.01750e9	+	7.39254e8i	1.89667	+	1.37801i
$313$	−2.70917e8	−	1.96833e8i	−0.499381	−	0.362821i	0.309400	−	0.950932i	$-0.399872\pi$
$313$	−2.70917e8	−	1.96833e8i	−0.499381	−	0.362821i	−0.808780	+	0.588111i	$0.799872\pi$
$314$	−2.37409e8	+	1.72488e8i	−0.432756	+	0.314416i
$315$	4.53148e8	+	2.93073e8i	0.816871	+	0.528311i
$316$	7.99302e7	+	5.80727e7i	0.142497	+	0.103530i
$317$	1.11320e8	+	3.42608e8i	0.196275	+	0.604074i	0.999959	+	0.00901730i	$0.00287034\pi$
$317$	1.11320e8	+	3.42608e8i	0.196275	+	0.604074i	−0.803684	+	0.595057i	$0.797130\pi$
$318$	1.61746e8			0.282058
$319$	−9.03265e7	−	2.77997e8i	−0.155793	−	0.479482i
$320$	−4.94335e8	+	4.01839e8i	−0.843327	+	0.685531i
$321$	3.61180e8	−	1.11160e9i	0.609476	−	1.87577i
$322$	−2.02549e8	+	6.23381e8i	−0.338091	+	1.04054i
$323$	−4.01653e8	+	2.91818e8i	−0.663197	+	0.481841i
$324$	2.15803e8			0.352492
$325$	−8.51156e8	−	4.87175e8i	−1.37536	−	0.787215i
$326$	1.01372e7			0.0162053
$327$	1.07509e8	−	7.81100e7i	0.170031	−	0.123535i
$328$	4.80859e7	−	1.47993e8i	0.0752419	−	0.231571i
$329$	1.59088e7	−	4.89623e7i	0.0246293	−	0.0758013i
$330$	1.04146e9	+	6.73564e8i	1.59531	+	1.03176i
$331$	4.78511e7	+	1.47271e8i	0.0725260	+	0.223212i	0.980748	−	0.195276i	$-0.0625602\pi$
$331$	4.78511e7	+	1.47271e8i	0.0725260	+	0.223212i	−0.908222	+	0.418488i	$0.862560\pi$
$332$	−2.46203e8			−0.369242
$333$	2.91456e7	+	8.97009e7i	0.0432532	+	0.133120i
$334$	−5.31326e6	−	3.86031e6i	−0.00780276	−	0.00566904i
$335$	1.29216e8	+	3.34744e8i	0.187784	+	0.486470i
$336$	−5.17822e8	+	3.76220e8i	−0.744720	+	0.541071i
$337$	2.30050e8	+	1.67141e8i	0.327430	+	0.237892i	0.739339	−	0.673333i	$-0.235138\pi$
$337$	2.30050e8	+	1.67141e8i	0.327430	+	0.237892i	−0.411909	+	0.911225i	$0.635138\pi$
$338$	−7.19851e8	−	5.23003e8i	−1.01399	−	0.736708i
$339$	−3.50123e8	+	2.54379e8i	−0.488114	+	0.354636i
$340$	1.66222e8	−	9.02336e6i	0.229357	−	0.0124506i
$341$	1.46765e9	+	1.06631e9i	2.00439	+	1.45628i
$342$	−1.79148e8	−	5.51362e8i	−0.242171	−	0.745325i
$343$	5.86374e8			0.784594
$344$	−3.70086e8	−	1.13901e9i	−0.490171	−	1.50859i
$345$	4.29389e8	+	1.11237e9i	0.562969	+	1.45842i
$346$	1.76104e8	−	5.41993e8i	0.228562	−	0.703441i
$347$	4.75006e7	−	1.46192e8i	0.0610303	−	0.187832i	−0.915893	−	0.401423i	$-0.868516\pi$
$347$	4.75006e7	−	1.46192e8i	0.0610303	−	0.187832i	0.976923	+	0.213591i	$0.0685159\pi$
$348$	8.07675e7	−	5.86810e7i	0.102733	−	0.0746398i
$349$	4.65176e8			0.585771			0.292886	−	0.956147i	$-0.405384\pi$
$349$	4.65176e8			0.585771			0.292886	+	0.956147i	$0.405384\pi$
$350$	5.65198e8	−	5.12751e8i	0.704633	−	0.639247i
$351$	−2.65298e8			−0.327460
$352$	6.67975e8	−	4.85312e8i	0.816321	−	0.593092i
$353$	−3.60241e8	+	1.10871e9i	−0.435895	+	1.34155i	0.456272	+	0.889840i	$0.349184\pi$
$353$	−3.60241e8	+	1.10871e9i	−0.435895	+	1.34155i	−0.892167	+	0.451706i	$0.850816\pi$
$354$	−1.39006e7	+	4.27818e7i	−0.0166542	+	0.0512563i
$355$	−3.99422e7	+	1.50190e8i	−0.0473841	+	0.178173i
$356$	6.84170e7	+	2.10566e8i	0.0803690	+	0.247350i
$357$	9.86250e8			1.14722
$358$	7.80654e7	+	2.40261e8i	0.0899224	+	0.276753i
$359$	−1.33623e9	−	9.70831e8i	−1.52423	−	1.10742i	−0.959338	−	0.282260i	$-0.908916\pi$
$359$	−1.33623e9	−	9.70831e8i	−1.52423	−	1.10742i	−0.564897	−	0.825161i	$-0.691084\pi$
$360$	−2.09959e8	+	7.89487e8i	−0.237179	+	0.891838i
$361$	−1.74870e8	+	1.27050e8i	−0.195632	+	0.142135i
$362$	3.60663e8	+	2.62037e8i	0.399597	+	0.290324i
$363$	−1.84415e9	−	1.33985e9i	−2.02359	−	1.47023i
$364$	−4.22571e8	+	3.07016e8i	−0.459246	+	0.333662i
$365$	−5.76223e8	+	4.68405e8i	−0.620248	+	0.504193i
$366$	1.96731e8	+	1.42933e8i	0.209743	+	0.152387i
$367$	1.26939e8	+	3.90677e8i	0.134049	+	0.412560i	0.995441	−	0.0953810i	$-0.0304069\pi$
$367$	1.26939e8	+	3.90677e8i	0.134049	+	0.412560i	−0.861392	+	0.507941i	$0.830407\pi$
$368$	−6.48938e8			−0.678791
$369$	−5.65866e7	−	1.74156e8i	−0.0586302	−	0.180445i
$370$	1.33176e8	−	7.22947e6i	0.136685	−	0.00741994i
$371$	−8.72376e7	+	2.68490e8i	−0.0886942	+	0.272973i
$372$	−1.91467e8	+	5.89274e8i	−0.192838	+	0.593495i
$373$	−9.71975e7	+	7.06181e7i	−0.0969782	+	0.0704588i	−0.635218	−	0.772333i	$-0.719090\pi$
$373$	−9.71975e7	+	7.06181e7i	−0.0969782	+	0.0704588i	0.538239	+	0.842792i	$0.319090\pi$
$374$	1.04012e9			1.02809
$375$	2.09463e8	−	1.37233e9i	0.205115	−	1.34385i
$376$	7.79324e7			0.0756067
$377$	−3.99036e8	+	2.89916e8i	−0.383545	+	0.278662i
$378$	6.37924e7	−	1.96333e8i	0.0607502	−	0.186970i
$379$	5.65605e8	−	1.74075e9i	0.533674	−	1.64248i	−0.212824	−	0.977090i	$-0.568266\pi$
$379$	5.65605e8	−	1.74075e9i	0.533674	−	1.64248i	0.746498	−	0.665388i	$-0.231734\pi$
$380$	3.71643e8	−	2.01747e7i	0.347443	−	0.0188610i
$381$	−1.27996e8	−	3.93931e8i	−0.118566	−	0.364908i
$382$	−1.38481e8			−0.127107
$383$	1.31569e8	+	4.04928e8i	0.119663	+	0.368283i	0.992891	−	0.119028i	$-0.0379777\pi$
$383$	1.31569e8	+	4.04928e8i	0.119663	+	0.368283i	−0.873228	+	0.487311i	$0.837978\pi$
$384$	−3.69206e8	−	2.68244e8i	−0.332743	−	0.241752i
$385$	−1.67979e9	+	1.36548e9i	−1.50018	+	1.21948i
$386$	−7.65700e8	+	5.56313e8i	−0.677646	+	0.492339i
$387$	−1.14018e9	−	8.28389e8i	−0.999965	−	0.726517i
$388$	4.00379e8	+	2.90892e8i	0.347984	+	0.252825i
$389$	−1.25658e9	+	9.12959e8i	−1.08235	+	0.786371i	−0.978091	−	0.208179i	$-0.933246\pi$
$389$	−1.25658e9	+	9.12959e8i	−1.08235	+	0.786371i	−0.104256	+	0.994550i	$0.533246\pi$
$390$	5.37894e8	−	2.02258e9i	0.459167	−	1.72656i
$391$	8.08957e8	+	5.87742e8i	0.684395	+	0.497242i
$392$	−1.26770e8	−	3.90157e8i	−0.106295	−	0.327144i
$393$	1.17346e9			0.975203
$394$	5.91911e8	+	1.82172e9i	0.487551	+	1.50053i
$395$	1.77580e8	−	6.67736e8i	0.144979	−	0.545149i
$396$	1.70397e8	−	5.24428e8i	0.137889	−	0.424377i
$397$	5.51106e8	−	1.69613e9i	0.442047	−	1.36048i	−0.443643	−	0.896203i	$-0.646314\pi$
$397$	5.51106e8	−	1.69613e9i	0.442047	−	1.36048i	0.885690	−	0.464277i	$-0.153686\pi$
$398$	7.82921e8	−	5.68825e8i	0.622482	−	0.452260i
$399$	2.20509e9			1.73788
$400$	6.55720e8	+	3.75314e8i	0.512281	+	0.293214i
$401$	1.19159e8			0.0922828			0.0461414	−	0.998935i	$-0.485308\pi$
$401$	1.19159e8			0.0922828			0.0461414	+	0.998935i	$0.485308\pi$
$402$	−6.19490e8	+	4.50086e8i	−0.475601	+	0.345544i
$403$	9.45950e8	−	2.91134e9i	0.719947	−	2.21577i
$404$	1.18151e8	−	3.63632e8i	0.0891464	−	0.274364i
$405$	−5.43487e8	−	1.40795e9i	−0.406533	−	1.05316i
$406$	−1.18601e8	−	3.65017e8i	−0.0879525	−	0.270690i
$407$	−3.78339e8			−0.278164
$408$	4.61351e8	+	1.41989e9i	0.336295	+	1.03501i
$409$	−1.59063e9	−	1.15566e9i	−1.14957	−	0.835215i	−0.161151	−	0.986930i	$-0.551520\pi$
$409$	−1.59063e9	−	1.15566e9i	−1.14957	−	0.835215i	−0.988424	+	0.151715i	$0.951520\pi$
$410$	−2.58564e8	+	1.40361e7i	−0.185278	+	0.0100578i
$411$	5.61518e8	−	4.07967e8i	0.398949	−	0.289853i
$412$	−1.50834e8	−	1.09587e8i	−0.106257	−	0.0772004i
$413$	−6.35181e7	−	4.61486e7i	−0.0443683	−	0.0322354i
$414$	−9.44632e8	+	6.86315e8i	−0.654277	+	0.475360i
$415$	6.20049e8	+	1.60629e9i	0.425851	+	1.10320i
$416$	−1.12715e9	−	8.18921e8i	−0.767634	−	0.557719i
$417$	−1.81685e8	−	5.59170e8i	−0.122700	−	0.377631i
$418$	2.32552e9			1.55741
$419$	8.03243e8	+	2.47213e9i	0.533455	+	1.64181i	0.746964	+	0.664864i	$0.231511\pi$
$419$	8.03243e8	+	2.47213e9i	0.533455	+	1.64181i	−0.213510	+	0.976941i	$0.568489\pi$
$420$	−6.20836e8	−	4.01525e8i	−0.408888	−	0.264448i
$421$	4.99337e8	−	1.53680e9i	0.326142	−	1.00376i	−0.644781	−	0.764367i	$-0.723051\pi$
$421$	4.99337e8	−	1.53680e9i	0.326142	−	1.00376i	0.970923	−	0.239393i	$-0.0769485\pi$
$422$	−5.94940e8	+	1.83104e9i	−0.385372	+	1.18605i
$423$	7.41944e7	−	5.39054e7i	0.0476628	−	0.0346291i
$424$	−4.27350e8			−0.272272
$425$	−4.77490e8	−	1.06175e9i	−0.301720	−	0.670902i
$426$	−3.31653e8			−0.207850
$427$	−3.43368e8	+	2.49471e8i	−0.213433	+	0.155068i
$428$	−2.27067e8	+	6.98839e8i	−0.139991	+	0.430848i
$429$	−1.83461e9	+	5.64635e9i	−1.12187	+	3.45277i
$430$	−1.54644e9	+	1.25708e9i	−0.937981	+	0.762473i
$431$	3.13074e8	+	9.63541e8i	0.188354	+	0.579695i	0.999990	−	0.00446866i	$-0.00142242\pi$
$431$	3.13074e8	+	9.63541e8i	0.188354	+	0.579695i	−0.811636	+	0.584164i	$0.801422\pi$
$432$	2.04382e8			0.121969
$433$	8.77716e8	+	2.70133e9i	0.519573	+	1.59908i	0.774804	+	0.632201i	$0.217848\pi$
$433$	8.77716e8	+	2.70133e9i	0.519573	+	1.59908i	−0.255231	+	0.966880i	$0.582152\pi$
$434$	1.92707e9	+	1.40010e9i	1.13157	+	0.822136i
$435$	−5.86258e8	−	3.79162e8i	−0.341488	−	0.220857i
$436$	−6.75888e7	+	4.91061e7i	−0.0390546	+	0.0283748i
$437$	1.80869e9	+	1.31409e9i	1.03676	+	0.753251i
$438$	−1.28206e9	−	9.31469e8i	−0.729034	−	0.529675i
$439$	1.59576e9	−	1.15939e9i	0.900206	−	0.654038i	−0.0383132	−	0.999266i	$-0.512198\pi$
$439$	1.59576e9	−	1.15939e9i	0.900206	−	0.654038i	0.938519	+	0.345228i	$0.112198\pi$
$440$	−2.75165e9	−	1.77963e9i	−1.53996	−	0.995966i
$441$	−3.90559e8	−	2.83758e8i	−0.216846	−	0.157548i
$442$	−5.42358e8	−	1.66921e9i	−0.298750	−	0.919458i
$443$	−1.53821e9			−0.840625			−0.420313	−	0.907379i	$-0.638080\pi$
$443$	−1.53821e9			−0.840625			−0.420313	+	0.907379i	$0.638080\pi$
$444$	−3.99309e7	−	1.22895e8i	−0.0216505	−	0.0666335i
$445$	1.20148e9	−	9.76666e8i	0.646332	−	0.525395i
$446$	−7.00275e8	+	2.15522e9i	−0.373763	+	1.15032i
$447$	1.98983e8	−	6.12405e8i	0.105375	−	0.324312i
$448$	1.91966e9	−	1.39472e9i	1.00868	−	0.732847i
$449$	−2.62754e9			−1.36990			−0.684948	−	0.728592i	$-0.740175\pi$
$449$	−2.62754e9			−1.36990			−0.684948	+	0.728592i	$0.740175\pi$
$450$	1.35143e9	−	1.47159e8i	0.699119	−	0.0761278i
$451$	7.34551e8			0.377054
$452$	2.20115e8	−	1.59923e8i	0.112115	−	0.0814566i
$453$	−9.53467e8	+	2.93447e9i	−0.481905	+	1.48315i
$454$	9.98325e8	−	3.07253e9i	0.500699	−	1.54099i
$455$	3.06727e9	+	1.98375e9i	1.52655	+	0.987297i
$456$	1.03150e9	+	3.17463e9i	0.509440	+	1.56789i
$457$	−3.96919e9			−1.94534			−0.972670	−	0.232192i	$-0.925410\pi$
$457$	−3.96919e9			−1.94534			−0.972670	+	0.232192i	$0.925410\pi$
$458$	−3.79104e8	−	1.16676e9i	−0.184387	−	0.567484i
$459$	−2.54780e8	−	1.85108e8i	−0.122976	−	0.0893473i
$460$	−2.69948e8	−	6.99324e8i	−0.129309	−	0.334985i
$461$	−8.15675e8	+	5.92623e8i	−0.387761	+	0.281725i	−0.764537	−	0.644579i	$-0.777032\pi$
$461$	−8.15675e8	+	5.92623e8i	−0.387761	+	0.281725i	0.376776	+	0.926304i	$0.377032\pi$
$462$	−3.73742e9	−	2.71540e9i	−1.76330	−	1.28111i
$463$	1.82525e9	+	1.32612e9i	0.854651	+	0.620940i	0.926425	−	0.376481i	$-0.122866\pi$
$463$	1.82525e9	+	1.32612e9i	0.854651	+	0.620940i	−0.0717734	+	0.997421i	$0.522866\pi$
$464$	3.07412e8	−	2.23348e8i	0.142859	−	0.103793i
$465$	4.32676e9	−	2.34879e8i	1.99562	−	0.108332i
$466$	8.35420e8	+	6.06968e8i	0.382432	+	0.277853i
$467$	1.02231e9	+	3.14634e9i	0.464485	+	1.42954i	0.859629	+	0.510920i	$0.170695\pi$
$467$	1.02231e9	+	3.14634e9i	0.464485	+	1.42954i	−0.395143	+	0.918620i	$0.629305\pi$
$468$	−9.30465e8			−0.419604
$469$	−4.12997e8	−	1.27107e9i	−0.184859	−	0.568939i
$470$	−4.67014e7	−	1.20984e8i	−0.0207485	−	0.0537508i
$471$	6.14433e8	−	1.89103e9i	0.270958	−	0.833922i
$472$	3.67269e7	−	1.13034e8i	0.0160764	−	0.0494779i
$473$	4.57366e9	−	3.32296e9i	1.98724	−	1.44381i
$474$	1.47450e9			0.635949
$475$	−1.06759e9	−	2.37388e9i	−0.457062	−	1.01632i
$476$	−6.20035e8			−0.263507
$477$	−4.06852e8	+	2.95596e8i	−0.171642	+	0.124705i
$478$	−1.04695e9	+	3.22219e9i	−0.438459	+	1.34944i
$479$	−2.34040e8	+	7.20302e8i	−0.0973008	+	0.299461i	−0.987846	−	0.155433i	$-0.950323\pi$
$479$	−2.34040e8	+	7.20302e8i	−0.0973008	+	0.299461i	0.890546	+	0.454894i	$0.150323\pi$
$480$	5.06863e8	−	1.90590e9i	0.209192	−	0.786604i
$481$	1.97280e8	+	6.07167e8i	0.0808307	+	0.248771i
$482$	−1.49194e9			−0.606856
$483$	−1.37241e9	−	4.22383e9i	−0.554201	−	1.70566i
$484$	1.15938e9	+	8.42339e8i	0.464801	+	0.337698i
$485$	8.89518e8	−	3.34476e9i	0.354045	−	1.33128i
$486$	2.25476e9	−	1.63818e9i	0.890990	−	0.647342i
$487$	5.27257e8	+	3.83075e8i	0.206858	+	0.150291i	0.686391	−	0.727233i	$-0.259194\pi$
$487$	5.27257e8	+	3.83075e8i	0.206858	+	0.150291i	−0.479533	+	0.877524i	$0.659194\pi$
$488$	−5.19782e8	−	3.77644e8i	−0.202466	−	0.147100i
$489$	−5.55684e7	+	4.03728e7i	−0.0214905	+	0.0156138i
$490$	−5.29721e8	+	4.30604e8i	−0.203405	+	0.165345i
$491$	5.07673e8	+	3.68846e8i	0.193552	+	0.140624i	0.680341	−	0.732896i	$-0.261832\pi$
$491$	5.07673e8	+	3.68846e8i	0.193552	+	0.140624i	−0.486788	+	0.873520i	$0.661832\pi$
$492$	7.75265e7	+	2.38602e8i	0.0293476	+	0.0903226i
$493$	−5.85501e8			−0.220071
$494$	−1.21262e9	−	3.73206e9i	−0.452564	−	1.39285i
$495$	−3.85062e9	+	2.09031e8i	−1.42696	+	0.0774628i
$496$	−7.28749e8	+	2.24286e9i	−0.268159	+	0.825308i
$497$	1.78877e8	−	5.50525e8i	0.0653591	−	0.201155i
$498$	−2.97266e9	+	2.15976e9i	−1.07855	+	0.783616i
$499$	−4.24539e9			−1.52956			−0.764779	−	0.644293i	$-0.777152\pi$
$499$	−4.24539e9			−1.52956			−0.764779	+	0.644293i	$0.777152\pi$
$500$	−1.31685e8	+	8.62757e8i	−0.0471130	+	0.308669i
$501$	4.44996e7			0.0158097
$502$	−3.08430e9	+	2.24088e9i	−1.08816	+	0.790597i
$503$	6.24861e8	−	1.92312e9i	0.218925	−	0.673782i	−0.779927	−	0.625871i	$-0.784744\pi$
$503$	6.24861e8	−	1.92312e9i	0.218925	−	0.673782i	0.998852	−	0.0479109i	$-0.0152564\pi$
$504$	9.40278e8	−	2.89388e9i	0.327152	−	1.00687i
$505$	−2.66998e9	+	1.44940e8i	−0.922547	+	0.0500805i
$506$	−1.44736e9	−	4.45453e9i	−0.496651	−	1.52853i
$507$	6.02890e9			2.05452
$508$	8.04685e7	+	2.47657e8i	0.0272335	+	0.0838160i
$509$	7.75412e8	+	5.63370e8i	0.260628	+	0.189357i	0.710424	−	0.703774i	$-0.248503\pi$
$509$	7.75412e8	+	5.63370e8i	0.260628	+	0.189357i	−0.449796	+	0.893131i	$0.648503\pi$
$510$	1.92780e9	−	1.56709e9i	0.643527	−	0.523116i
$511$	2.23766e9	−	1.62576e9i	0.741860	−	0.538993i
$512$	2.44660e9	+	1.77756e9i	0.805597	+	0.585300i
$513$	−5.69644e8	−	4.13870e8i	−0.186291	−	0.135349i
$514$	−1.30892e9	+	9.50984e8i	−0.425149	+	0.308889i
$515$	−3.35106e8	+	1.26006e9i	−0.108108	+	0.406507i
$516$	1.56210e9	+	1.13493e9i	0.500537	+	0.363661i
$517$	1.13681e8	+	3.49873e8i	0.0361801	+	0.111351i
$518$	−4.96769e8			−0.157037
$519$	1.19323e9	+	3.67237e9i	0.374660	+	1.15308i
$520$	−1.42117e9	+	5.34387e9i	−0.443235	+	1.66665i
$521$	−1.05172e9	+	3.23686e9i	−0.325813	+	1.00275i	0.645259	+	0.763964i	$0.276749\pi$
$521$	−1.05172e9	+	3.23686e9i	−0.325813	+	1.00275i	−0.971072	+	0.238786i	$0.923251\pi$
$522$	2.11275e8	−	6.50236e8i	0.0650130	−	0.200090i
$523$	−1.73260e9	+	1.25881e9i	−0.529594	+	0.384772i	−0.820206	−	0.572069i	$-0.806141\pi$
$523$	−1.73260e9	+	1.25881e9i	−0.529594	+	0.384772i	0.290612	+	0.956841i	$0.406141\pi$
$524$	−7.37731e8			−0.223995
$525$	−1.05611e9	+	5.06170e9i	−0.318530	+	1.52665i
$526$	3.12117e9			0.935119
$527$	2.93980e9	−	2.13589e9i	0.874944	−	0.635684i
$528$	1.41336e9	−	4.34988e9i	0.417863	−	1.28605i
$529$	3.39287e8	−	1.04422e9i	0.0996488	−	0.306688i
$530$	2.56092e8	+	6.63427e8i	0.0747188	+	0.193565i
$531$	−4.32195e7	−	1.33016e8i	−0.0125271	−	0.0385543i
$532$	−1.38629e9			−0.399175
$533$	−3.83023e8	−	1.17882e9i	−0.109567	−	0.337213i
$534$	2.67320e9	+	1.94220e9i	0.759692	+	0.551949i
$535$	5.13125e9	−	2.78550e8i	1.44872	−	0.0786439i
$536$	1.63676e9	−	1.18917e9i	0.459100	−	0.333555i
$537$	−1.38480e9	−	1.00611e9i	−0.385902	−	0.280374i
$538$	−4.25960e8	−	3.09478e8i	−0.117932	−	0.0856824i
$539$	1.56667e9	−	1.13825e9i	0.430940	−	0.313096i
$540$	8.50198e7	+	2.20251e8i	0.0232349	+	0.0601921i
$541$	−3.71234e9	−	2.69718e9i	−1.00799	−	0.732350i	−0.0442063	−	0.999022i	$-0.514076\pi$
$541$	−3.71234e9	−	2.69718e9i	−1.00799	−	0.732350i	−0.963787	+	0.266672i	$0.914076\pi$
$542$	−1.18231e9	−	3.63876e9i	−0.318957	−	0.981649i
$543$	−3.02063e9			−0.809651
$544$	−5.11069e8	−	1.57291e9i	−0.136108	−	0.418897i
$545$	4.90598e8	+	3.17294e8i	0.129819	+	0.0839604i
$546$	−2.40889e9	+	7.41382e9i	−0.633350	+	1.94925i
$547$	−2.32355e8	+	7.15116e8i	−0.0607011	+	0.186819i	−0.976809	−	0.214113i	$-0.931314\pi$
$547$	−2.32355e8	+	7.15116e8i	−0.0607011	+	0.186819i	0.916108	+	0.400932i	$0.131314\pi$
$548$	−3.53015e8	+	2.56480e8i	−0.0916349	+	0.0665766i
$549$	−7.56065e8			−0.195010
$550$	−1.11379e9	+	5.33816e9i	−0.285452	+	1.36811i
$551$	−1.30908e9			−0.333377
$552$	5.43901e9	−	3.95167e9i	1.37636	−	0.999986i
$553$	−7.95273e8	+	2.44760e9i	−0.199976	+	0.615463i
$554$	−9.59946e8	+	2.95441e9i	−0.239863	+	0.738222i
$555$	−7.01230e8	+	5.70022e8i	−0.174115	+	0.141536i
$556$	1.14222e8	+	3.51539e8i	0.0281830	+	0.0867384i
$557$	4.45745e9			1.09293			0.546466	−	0.837481i	$-0.315973\pi$
$557$	4.45745e9			1.09293			0.546466	+	0.837481i	$0.315973\pi$
$558$	1.31123e9	+	4.03555e9i	0.319492	+	0.983294i
$559$	−7.71764e9	−	5.60719e9i	−1.86872	−	1.35770i
$560$	−2.36299e9	−	1.52826e9i	−0.568595	−	0.367738i
$561$	−5.70155e9	+	4.14242e9i	−1.36340	+	0.990567i
$562$	2.42531e9	+	1.76209e9i	0.576355	+	0.418747i
$563$	4.64199e9	+	3.37260e9i	1.09629	+	0.796501i	0.980450	−	0.196767i	$-0.0630444\pi$
$563$	4.64199e9	+	3.37260e9i	1.09629	+	0.796501i	0.115839	+	0.993268i	$0.463044\pi$
$564$	−1.01650e8	+	7.38531e7i	−0.0238578	+	0.0173337i
$565$	−1.59772e9	−	1.03333e9i	−0.372676	−	0.241028i
$566$	−5.19229e9	−	3.77242e9i	−1.20365	−	0.874505i
$567$	1.73708e9	+	5.34618e9i	0.400202	+	1.23169i
$568$	8.76260e8			0.200638
$569$	1.74276e9	+	5.36367e9i	0.396593	+	1.22059i	0.927714	+	0.373292i	$0.121771\pi$
$569$	1.74276e9	+	5.36367e9i	0.396593	+	1.22059i	−0.531120	+	0.847296i	$0.678229\pi$
$570$	4.31023e9	−	3.50374e9i	0.974853	−	0.792446i
$571$	2.27532e9	−	7.00272e9i	0.511466	−	1.57413i	−0.278156	−	0.960536i	$-0.589723\pi$
$571$	2.27532e9	−	7.00272e9i	0.511466	−	1.57413i	0.789622	−	0.613594i	$-0.210277\pi$
$572$	1.15338e9	−	3.54974e9i	0.257684	−	0.793068i
$573$	7.59104e8	−	5.51521e8i	0.168562	−	0.122468i
$574$	9.64486e8			0.212865
$575$	−3.88270e9	+	3.52241e9i	−0.851720	+	0.772686i
$576$	4.22693e9			0.921609
$577$	−5.20942e9	+	3.78487e9i	−1.12895	+	0.820229i	−0.985541	−	0.169435i	$-0.945806\pi$
$577$	−5.20942e9	+	3.78487e9i	−1.12895	+	0.820229i	−0.143407	+	0.989664i	$0.545806\pi$
$578$	−5.45913e8	+	1.68015e9i	−0.117592	+	0.361909i
$579$	1.98169e9	−	6.09902e9i	0.424288	−	1.30582i
$580$	3.68568e8	+	2.38371e8i	0.0784368	+	0.0507289i
$581$	−1.98179e9	−	6.09932e9i	−0.419219	−	1.29022i
$582$	7.38595e9			1.55302
$583$	−6.23379e8	−	1.91856e9i	−0.130290	−	0.400992i
$584$	3.38733e9	+	2.46104e9i	0.703740	+	0.511297i
$585$	2.34332e9	+	6.07058e9i	0.483935	+	1.25367i
$586$	6.24662e8	−	4.53844e8i	0.128234	−	0.0931676i
$587$	−3.73612e9	−	2.71445e9i	−0.762408	−	0.553922i	0.137240	−	0.990538i	$-0.456177\pi$
$587$	−3.73612e9	−	2.71445e9i	−0.762408	−	0.553922i	−0.899648	+	0.436616i	$0.856177\pi$
$588$	5.35086e8	+	3.88762e8i	0.108543	+	0.0788613i
$589$	6.57288e9	−	4.77548e9i	1.32542	−	0.962971i
$590$	−1.97485e8	+	1.07205e7i	−0.0395869	+	0.00214898i
$591$	−1.04999e10	−	7.62861e9i	−2.09232	−	1.52016i
$592$	−1.51982e8	−	4.67754e8i	−0.0301070	−	0.0926598i
$593$	−1.45846e9			−0.287212			−0.143606	−	0.989635i	$-0.545870\pi$
$593$	−1.45846e9			−0.287212			−0.143606	+	0.989635i	$0.545870\pi$
$594$	4.55845e8	+	1.40295e9i	0.0892410	+	0.274656i
$595$	1.56152e9	+	4.04526e9i	0.303906	+	0.787294i
$596$	−1.25096e8	+	3.85007e8i	−0.0242037	+	0.0744914i
$597$	−2.02626e9	+	6.23619e9i	−0.389749	+	1.19952i
$598$	−6.39402e9	+	4.64553e9i	−1.22270	+	0.888343i
$599$	6.81103e8			0.129485			0.0647424	−	0.997902i	$-0.479377\pi$
$599$	6.81103e8			0.129485			0.0647424	+	0.997902i	$0.479377\pi$
$600$	−7.78130e9	+	8.47313e8i	−1.47070	+	0.160145i
$601$	6.48635e8			0.121882			0.0609410	−	0.998141i	$-0.480590\pi$
$601$	6.48635e8			0.121882			0.0609410	+	0.998141i	$0.480590\pi$
$602$	6.00534e9	−	4.36314e9i	1.12189	−	0.815100i
$603$	7.35706e8	−	2.26427e9i	0.136645	−	0.420550i
$604$	5.99425e8	−	1.84484e9i	0.110689	−	0.340666i
$605$	2.57579e9	−	9.68545e9i	0.472896	−	1.77818i
$606$	−1.76332e9	−	5.42695e9i	−0.321868	−	0.990607i
$607$	−1.69210e9			−0.307089			−0.153545	−	0.988142i	$-0.549069\pi$
$607$	−1.69210e9			−0.307089			−0.153545	+	0.988142i	$0.549069\pi$
$608$	−1.14266e9	−	3.51675e9i	−0.206184	−	0.634570i
$609$	2.10386e9	+	1.52855e9i	0.377448	+	0.274232i
$610$	−2.74780e8	+	1.03323e9i	−0.0490152	+	0.184306i
$611$	5.02207e8	−	3.64874e8i	0.0890714	−	0.0647142i
$612$	−8.93576e8	−	6.49221e8i	−0.157580	−	0.114489i
$613$	5.21050e9	+	3.78565e9i	0.913624	+	0.663787i	0.941929	−	0.335812i	$-0.109011\pi$
$613$	5.21050e9	+	3.78565e9i	0.913624	+	0.663787i	−0.0283045	+	0.999599i	$0.509011\pi$
$614$	3.93752e9	−	2.86077e9i	0.686488	−	0.498763i
$615$	1.36145e9	−	1.10671e9i	0.236015	−	0.191854i
$616$	9.87465e9	+	7.17436e9i	1.70212	+	1.23666i
$617$	−5.39663e8	−	1.66091e9i	−0.0924963	−	0.284674i	0.894097	−	0.447874i	$-0.147819\pi$
$617$	−5.39663e8	−	1.66091e9i	−0.0924963	−	0.284674i	−0.986593	+	0.163199i	$0.947819\pi$
$618$	−2.78249e9			−0.474214
$619$	−6.66451e8	−	2.05113e9i	−0.112941	−	0.347596i	0.878571	−	0.477612i	$-0.158497\pi$
$619$	−6.66451e8	−	2.05113e9i	−0.112941	−	0.347596i	−0.991512	+	0.130015i	$0.958497\pi$
$620$	−2.72015e9	+	1.47663e8i	−0.458376	+	0.0248829i
$621$	−4.38230e8	+	1.34873e9i	−0.0734314	+	0.225999i
$622$	1.91544e9	−	5.89512e9i	0.319155	−	0.982259i
$623$	−4.66573e9	+	3.38985e9i	−0.773057	+	0.561659i
$624$	−7.71777e9			−1.27159
$625$	5.96047e9	−	1.31366e9i	0.976563	−	0.215230i
$626$	3.14196e9			0.511907
$627$	−1.27477e10	+	9.26173e9i	−2.06536	+	1.50057i
$628$	−3.86281e8	+	1.18885e9i	−0.0622365	+	0.191544i
$629$	−2.34184e8	+	7.20745e8i	−0.0375215	+	0.115479i
$630$	−5.05598e9	+	2.74464e8i	−0.805589	+	0.0437314i
$631$	2.87307e9	+	8.84239e9i	0.455243	+	1.40109i	0.870850	+	0.491549i	$0.163569\pi$
$631$	2.87307e9	+	8.84239e9i	0.455243	+	1.40109i	−0.415607	+	0.909544i	$0.636431\pi$
$632$	−3.89579e9			−0.613884
$633$	−4.03112e9	−	1.24065e10i	−0.631703	−	1.94418i
$634$	−2.73446e9	−	1.98670e9i	−0.426146	−	0.309613i
$635$	1.41311e9	−	1.14870e9i	0.219013	−	0.178033i
$636$	5.57408e8	−	4.04981e8i	0.0859159	−	0.0624215i
$637$	−2.64361e9	−	1.92070e9i	−0.405238	−	0.294423i
$638$	2.21877e9	+	1.61203e9i	0.338252	+	0.245755i
$639$	8.34231e8	−	6.06104e8i	0.126483	−	0.0918956i
$640$	5.15682e8	−	1.93906e9i	0.0777592	−	0.292390i
$641$	3.57516e9	+	2.59751e9i	0.536158	+	0.389542i	0.822656	−	0.568539i	$-0.192491\pi$
$641$	3.57516e9	+	2.59751e9i	0.536158	+	0.389542i	−0.286498	+	0.958081i	$0.592491\pi$
$642$	3.38880e9	+	1.04297e10i	0.505445	+	1.55560i
$643$	−2.54722e9			−0.377857			−0.188928	−	0.981991i	$-0.560501\pi$
$643$	−2.54722e9			−0.377857			−0.188928	+	0.981991i	$0.560501\pi$
$644$	8.62803e8	+	2.65543e9i	0.127295	+	0.391773i
$645$	3.47051e9	−	1.30498e10i	0.509254	−	1.91489i
$646$	1.43945e9	−	4.43019e9i	0.210080	−	0.646559i
$647$	1.29370e9	−	3.98159e9i	0.187788	−	0.577952i	−0.812197	−	0.583383i	$-0.801729\pi$
$647$	1.29370e9	−	3.98159e9i	0.187788	−	0.577952i	0.999985	+	0.00543079i	$0.00172868\pi$
$648$	−6.88426e9	+	5.00171e9i	−0.993904	+	0.722114i
$649$	5.61033e8			0.0805623
$650$	9.14758e9	−	9.96089e8i	1.30650	−	0.142266i
$651$	−1.61396e10			−2.29276
$652$	3.49347e7	−	2.53815e7i	0.00493617	−	0.00358634i
$653$	8.78458e8	−	2.70361e9i	0.123460	−	0.379969i	−0.870158	−	0.492773i	$-0.835983\pi$
$653$	8.78458e8	−	2.70361e9i	0.123460	−	0.379969i	0.993617	+	0.112804i	$0.0359832\pi$
$654$	−3.85294e8	+	1.18581e9i	−0.0538605	+	0.165765i
$655$	1.85793e9	+	4.81313e9i	0.258337	+	0.669242i
$656$	2.95076e8	+	9.08152e8i	0.0408104	+	0.125602i
$657$	4.92714e9			0.677823
$658$	1.49266e8	+	4.59393e8i	0.0204254	+	0.0628628i
$659$	6.11790e9	+	4.44491e9i	0.832729	+	0.605013i	0.920330	−	0.391143i	$-0.127920\pi$
$659$	6.11790e9	+	4.44491e9i	0.832729	+	0.605013i	−0.0876014	+	0.996156i	$0.527920\pi$
$660$	5.27555e9	−	2.86384e8i	0.714272	−	0.0387743i
$661$	8.90945e9	−	6.47309e9i	1.19990	−	0.871780i	0.205627	−	0.978631i	$-0.434077\pi$
$661$	8.90945e9	−	6.47309e9i	1.19990	−	0.871780i	0.994275	+	0.106851i	$0.0340767\pi$
$662$	−1.17541e9	−	8.53985e8i	−0.157466	−	0.114406i
$663$	9.62086e9	+	6.98996e9i	1.28208	+	0.931489i
$664$	7.85406e9	−	5.70631e9i	1.04113	−	0.756427i
$665$	3.49130e9	+	9.04450e9i	0.460374	+	1.19264i
$666$	−7.15929e8	−	5.20153e8i	−0.0939097	−	0.0682294i
$667$	8.14748e8	+	2.50754e9i	0.106312	+	0.327195i
$668$	−2.79760e7			−0.00363134
$669$	−4.74483e9	−	1.46031e10i	−0.612674	−	1.88562i
$670$	−2.82693e9	−	1.82831e9i	−0.363122	−	0.234849i
$671$	9.37200e8	−	2.88440e9i	0.119758	−	0.368576i
$672$	−2.26993e9	+	6.98611e9i	−0.288549	+	0.888062i
$673$	−1.05430e9	+	7.65991e8i	−0.133324	+	0.0968659i	−0.652449	−	0.757833i	$-0.726258\pi$
$673$	−1.05430e9	+	7.65991e8i	−0.133324	+	0.0968659i	0.519124	+	0.854699i	$0.326258\pi$
$674$	−2.66801e9			−0.335643
$675$	1.22285e9	−	1.10938e9i	0.153042	−	0.138841i
$676$	−3.79024e9			−0.471904
$677$	−8.10815e8	+	5.89091e8i	−0.100429	+	0.0729663i	−0.636867	−	0.770974i	$-0.719770\pi$
$677$	−8.10815e8	+	5.89091e8i	−0.100429	+	0.0729663i	0.536437	+	0.843940i	$0.319770\pi$
$678$	1.25478e9	−	3.86182e9i	0.154619	−	0.475869i
$679$	−3.98360e9	+	1.22603e10i	−0.488351	+	1.50299i
$680$	−5.09345e9	+	4.14041e9i	−0.621200	+	0.504966i
$681$	6.76433e9	+	2.08185e10i	0.820748	+	2.52600i
$682$	−1.70211e10			−2.05467
$683$	−1.81829e8	−	5.59612e8i	−0.0218369	−	0.0672070i	0.939544	−	0.342428i	$-0.111249\pi$
$683$	−1.81829e8	−	5.59612e8i	−0.0218369	−	0.0672070i	−0.961381	+	0.275221i	$0.911249\pi$
$684$	−1.99788e9	−	1.45155e9i	−0.238712	−	0.173434i
$685$	2.56239e9	+	1.65722e9i	0.304598	+	0.196999i
$686$	−4.45097e9	+	3.23382e9i	−0.526405	+	0.382456i
$687$	6.72491e9	+	4.88594e9i	0.791294	+	0.574909i
$688$	5.94558e9	+	4.31971e9i	0.696040	+	0.505703i
$689$	−2.75390e9	+	2.00083e9i	−0.320761	+	0.233046i
$690$	−9.39400e9	−	6.07557e9i	−1.08863	−	0.704069i
$691$	3.63023e9	+	2.63752e9i	0.418564	+	0.304104i	0.777060	−	0.629427i	$-0.216710\pi$
$691$	3.63023e9	+	2.63752e9i	0.418564	+	0.304104i	−0.358496	+	0.933531i	$0.616710\pi$
$692$	−7.50156e8	−	2.30874e9i	−0.0860558	−	0.264853i
$693$	1.43635e10			1.63943
$694$	4.45678e8	+	1.37165e9i	0.0506131	+	0.155771i
$695$	2.00586e9	−	1.63054e9i	0.226649	−	0.184240i
$696$	−1.21648e9	+	3.74393e9i	−0.136764	+	0.420916i
$697$	4.54673e8	−	1.39934e9i	0.0508609	−	0.156534i
$698$	−3.53099e9	+	2.56542e9i	−0.393009	+	0.285538i
$699$	−6.99681e9			−0.774872
$700$	6.63952e8	−	3.18219e9i	0.0731634	−	0.350657i
$701$	−5.20045e9			−0.570201			−0.285100	−	0.958498i	$-0.592027\pi$
$701$	−5.20045e9			−0.570201			−0.285100	+	0.958498i	$0.592027\pi$
$702$	2.01379e9	−	1.46310e9i	0.219702	−	0.159623i
$703$	−5.23596e8	+	1.61146e9i	−0.0568398	+	0.174935i
$704$	−5.23960e9	+	1.61258e10i	−0.565971	+	1.74188i
$705$	7.37835e8	+	4.77194e8i	0.0793044	+	0.0512901i
$706$	−3.37999e9	−	1.04025e10i	−0.361492	−	1.11256i
$707$	9.95949e9			1.05991
$708$	5.92129e7	+	1.82239e8i	0.00627047	+	0.0192985i
$709$	5.97005e9	+	4.33750e9i	0.629095	+	0.457064i	0.856087	−	0.516832i	$-0.172889\pi$
$709$	5.97005e9	+	4.33750e9i	0.629095	+	0.457064i	−0.226992	+	0.973897i	$0.572889\pi$
$710$	−5.25103e8	−	1.36032e9i	−0.0550605	−	0.142639i
$711$	−3.70893e9	+	2.69470e9i	−0.386995	+	0.281168i
$712$	−7.06288e9	−	5.13148e9i	−0.733334	−	0.532798i
$713$	−1.32382e10	−	9.61815e9i	−1.36778	−	0.993752i
$714$	−7.48630e9	+	5.43911e9i	−0.769703	+	0.559222i
$715$	−2.60641e10	+	1.41489e9i	−2.66668	+	0.144761i
$716$	8.70594e8	+	6.32523e8i	0.0886380	+	0.0643993i
$717$	−7.09381e9	−	2.18325e10i	−0.718724	−	2.21201i
$718$	1.54970e10			1.56247
$719$	4.96640e9	+	1.52850e10i	0.498300	+	1.53361i	0.811751	+	0.584004i	$0.198515\pi$
$719$	4.96640e9	+	1.52850e10i	0.498300	+	1.53361i	−0.313451	+	0.949604i	$0.601485\pi$
$720$	−1.80527e9	−	4.67670e9i	−0.180251	−	0.466956i
$721$	1.50074e9	−	4.61879e9i	0.149118	−	0.458939i
$722$	6.26702e8	−	1.92879e9i	0.0619699	−	0.190724i
$723$	8.17825e9	−	5.94185e9i	0.804779	−	0.584706i
$724$	1.89901e9			0.185969
$725$	6.26972e8	−	3.00495e9i	0.0611034	−	0.292856i
$726$	2.13876e10			2.07435
$727$	6.18596e9	−	4.49436e9i	0.597086	−	0.433808i	−0.247758	−	0.968822i	$-0.579694\pi$
$727$	6.18596e9	−	4.49436e9i	0.597086	−	0.433808i	0.844843	+	0.535014i	$0.179694\pi$
$728$	6.36455e9	−	1.95881e10i	0.611375	−	1.88162i
$729$	−2.18641e9	+	6.72907e9i	−0.209018	+	0.643293i
$730$	1.79069e9	−	6.73334e9i	0.170369	−	0.640620i
$731$	−3.49932e9	−	1.07698e10i	−0.331339	−	1.01976i
$732$	1.03585e9			0.0976129
$733$	7.95241e8	+	2.44750e9i	0.0745821	+	0.229540i	0.981397	−	0.191989i	$-0.0614936\pi$
$733$	7.95241e8	+	2.44750e9i	0.0745821	+	0.229540i	−0.906815	+	0.421529i	$0.861494\pi$
$734$	−3.11811e9	−	2.26544e9i	−0.291042	−	0.211454i
$735$	1.18880e9	−	4.47010e9i	0.110434	−	0.415252i
$736$	−6.02515e9	+	4.37753e9i	−0.557052	+	0.404722i
$737$	7.72627e9	+	5.61346e9i	0.710941	+	0.516529i
$738$	1.38999e9	+	1.00989e9i	0.127296	+	0.0924858i
$739$	−1.04489e9	+	7.59157e8i	−0.0952390	+	0.0691952i	−0.634386	−	0.773017i	$-0.718747\pi$
$739$	−1.04489e9	+	7.59157e8i	−0.0952390	+	0.0691952i	0.539147	+	0.842212i	$0.318747\pi$
$740$	4.40849e8	−	3.58361e8i	0.0399925	−	0.0325095i
$741$	2.15106e10	+	1.56283e10i	1.94217	+	1.41107i
$742$	−8.18514e8	−	2.51913e9i	−0.0735550	−	0.226379i
$743$	−5.30477e9			−0.474467			−0.237233	−	0.971453i	$-0.576241\pi$
$743$	−5.30477e9			−0.474467			−0.237233	+	0.971453i	$0.576241\pi$
$744$	−7.54981e9	−	2.32359e10i	−0.672096	−	2.06850i
$745$	2.82692e9	−	1.53460e8i	0.250476	−	0.0135971i
$746$	3.48339e8	−	1.07208e9i	0.0307196	−	0.0945453i
$747$	3.53033e9	−	1.08652e10i	0.309879	−	0.953711i
$748$	3.58445e9	−	2.60425e9i	0.313160	−	0.227524i
$749$	−1.91404e10			−1.66443
$750$	5.97837e9	+	1.15721e10i	0.517450	+	1.00161i
$751$	1.38844e10			1.19615			0.598075	−	0.801440i	$-0.295932\pi$
$751$	1.38844e10			1.19615			0.598075	+	0.801440i	$0.295932\pi$
$752$	−3.86894e8	+	2.81095e8i	−0.0331764	+	0.0241041i
$753$	7.98242e9	−	2.45674e10i	0.681321	−	2.09689i
$754$	1.43007e9	−	4.40132e9i	0.121495	−	0.373924i
$755$	−1.35458e10	+	7.35334e8i	−1.14549	+	0.0621828i
$756$	−2.71738e8	−	8.36324e8i	−0.0228731	−	0.0703961i
$757$	−2.21325e10			−1.85437			−0.927183	−	0.374609i	$-0.877777\pi$
$757$	−2.21325e10			−1.85437			−0.927183	+	0.374609i	$0.877777\pi$
$758$	5.30683e9	+	1.63327e10i	0.442581	+	1.36212i
$759$	2.56747e10	+	1.86538e10i	2.13137	+	1.54853i
$760$	−1.13881e10	+	9.25724e9i	−0.941029	+	0.764951i
$761$	−3.16257e9	+	2.29775e9i	−0.260132	+	0.188997i	−0.710205	−	0.703994i	$-0.751398\pi$
$761$	−3.16257e9	+	2.29775e9i	−0.260132	+	0.188997i	0.450073	+	0.892992i	$0.351398\pi$
$762$	3.14408e9	+	2.28431e9i	0.257426	+	0.187031i
$763$	−1.76058e9	−	1.27913e9i	−0.143489	−	0.104251i
$764$	−4.77233e8	+	3.46730e8i	−0.0387172	+	0.0281297i
$765$	−1.98525e9	+	7.46493e9i	−0.160325	+	0.602852i
$766$	−3.23185e9	−	2.34808e9i	−0.259807	−	0.188761i
$767$	−2.92544e8	−	9.00358e8i	−0.0234103	−	0.0720496i
$768$	−1.42649e10			−1.13633
$769$	−7.15536e9	−	2.20219e10i	−0.567400	−	1.74628i	−0.660712	−	0.750640i	$-0.729745\pi$
$769$	−7.15536e9	−	2.20219e10i	−0.567400	−	1.74628i	0.0933123	−	0.995637i	$-0.470255\pi$
$770$	5.22018e9	−	1.96289e10i	0.412067	−	1.54945i
$771$	3.38758e9	−	1.04259e10i	0.266195	−	0.819263i
$772$	−1.24585e9	+	3.83433e9i	−0.0974551	+	0.299936i
$773$	−5.39569e9	+	3.92020e9i	−0.420164	+	0.305267i	−0.777704	−	0.628631i	$-0.783616\pi$
$773$	−5.39569e9	+	3.92020e9i	−0.420164	+	0.305267i	0.357540	+	0.933898i	$0.383616\pi$
$774$	1.32232e10			1.02505
$775$	7.81393e9	+	1.73750e10i	0.602995	+	1.34082i
$776$	−1.95144e10			−1.49913
$777$	2.72311e9	−	1.97845e9i	0.208253	−	0.151305i
$778$	4.50336e9	−	1.38599e10i	0.342853	−	1.05519i
$779$	1.01657e9	−	3.12868e9i	0.0770471	−	0.237126i
$780$	−3.21047e9	−	8.31699e9i	−0.242235	−	0.627531i
$781$	1.27821e9	+	3.93392e9i	0.0960114	+	0.295493i
$782$	−9.38189e9			−0.701563
$783$	−2.56603e8	−	7.89744e8i	−0.0191028	−	0.0587923i
$784$	2.03661e9	+	1.47968e9i	0.150939	+	0.109664i
$785$	8.72918e9	−	4.73864e8i	0.644065	−	0.0349631i
$786$	−8.90736e9	+	6.47157e9i	−0.654290	+	0.475369i
$787$	3.40979e8	+	2.47736e8i	0.0249354	+	0.0181166i	0.600183	−	0.799863i	$-0.295094\pi$
$787$	3.40979e8	+	2.47736e8i	0.0249354	+	0.0181166i	−0.575248	+	0.817979i	$0.695094\pi$
$788$	6.60106e9	+	4.79595e9i	0.480587	+	0.349167i
$789$	−1.71091e10	+	1.24305e10i	−1.24010	+	0.900988i
$790$	2.33457e9	+	6.04791e9i	0.168466	+	0.436426i
$791$	5.73364e9	+	4.16573e9i	0.411920	+	0.299277i
$792$	6.71899e9	+	2.06789e10i	0.480580	+	1.47907i
$793$	−5.11765e9			−0.364430
$794$	5.17079e9	+	1.59141e10i	0.366594	+	1.12826i
$795$	−4.04599e9	−	2.61674e9i	−0.285588	−	0.184704i
$796$	1.27387e9	−	3.92056e9i	0.0895217	−	0.275520i
$797$	−5.56488e9	+	1.71269e10i	−0.389360	+	1.19833i	0.543908	+	0.839145i	$0.316944\pi$
$797$	−5.56488e9	+	1.71269e10i	−0.389360	+	1.19833i	−0.933268	+	0.359182i	$0.883056\pi$
$798$	−1.67381e10	+	1.21609e10i	−1.16599	+	0.847142i
$799$	7.36883e8			0.0511075
$800$	8.61986e9	−	9.38625e8i	0.595231	−	0.0648153i
$801$	−1.02735e10			−0.706327
$802$	−9.04494e8	+	6.57154e8i	−0.0619149	+	0.0449838i
$803$	−6.10756e9	+	1.87971e10i	−0.416259	+	1.28111i
$804$	−1.00795e9	+	3.10216e9i	−0.0683982	+	0.210508i
$805$	1.51518e10	−	1.23167e10i	1.02371	−	0.832163i
$806$	8.87545e9	+	2.73158e10i	0.597060	+	1.83756i
$807$	3.56750e9			0.238950
$808$	4.65888e9	+	1.43386e10i	0.310700	+	0.956237i
$809$	−1.67606e10	−	1.21773e10i	−1.11294	−	0.808595i	−0.129813	−	0.991539i	$-0.541438\pi$
$809$	−1.67606e10	−	1.21773e10i	−1.11294	−	0.808595i	−0.983124	+	0.182943i	$0.941438\pi$
$810$	1.18902e10	+	7.68996e9i	0.786123	+	0.508425i
$811$	−3.17177e9	+	2.30443e9i	−0.208799	+	0.151701i	−0.687270	−	0.726402i	$-0.741191\pi$
$811$	−3.17177e9	+	2.30443e9i	−0.208799	+	0.151701i	0.478471	+	0.878103i	$0.341191\pi$
$812$	−1.32266e9	−	9.60965e8i	−0.0866963	−	0.0629885i
$813$	2.09729e10	+	1.52377e10i	1.36880	+	0.994493i
$814$	2.87184e9	−	2.08651e9i	0.186627	−	0.135593i
$815$	−2.53576e8	−	1.64000e8i	−0.0164081	−	0.0106119i
$816$	−7.41179e9	−	5.38498e9i	−0.477538	−	0.346951i
$817$	−7.82387e9	−	2.40794e10i	−0.501931	−	1.54479i
$818$	1.84473e10			1.17841
$819$	−7.48968e9	−	2.30509e10i	−0.476398	−	1.46620i
$820$	−8.55916e8	+	6.95764e8i	−0.0542104	+	0.0440670i
$821$	1.76046e8	−	5.41815e8i	0.0111026	−	0.0341704i	−0.945352	−	0.326052i	$-0.894281\pi$
$821$	1.76046e8	−	5.41815e8i	0.0111026	−	0.0341704i	0.956454	+	0.291882i	$0.0942814\pi$
$822$	−2.01238e9	+	6.19348e9i	−0.126374	+	0.388941i
$823$	−1.86363e10	+	1.35401e10i	−1.16536	+	0.846684i	−0.990446	−	0.137899i	$-0.955965\pi$
$823$	−1.86363e10	+	1.35401e10i	−1.16536	+	0.846684i	−0.174915	+	0.984584i	$0.555965\pi$
$824$	7.35163e9			0.457761
$825$	−1.51546e10	−	3.36977e10i	−0.939628	−	2.08935i
$826$	7.36652e8			0.0454812
$827$	7.72596e9	−	5.61324e9i	0.474989	−	0.345100i	−0.324394	−	0.945922i	$-0.605160\pi$
$827$	7.72596e9	−	5.61324e9i	0.474989	−	0.345100i	0.799382	+	0.600823i	$0.205160\pi$
$828$	−1.53698e9	+	4.73035e9i	−0.0940942	+	0.289592i
$829$	2.75976e8	−	8.49367e8i	0.0168240	−	0.0517791i	−0.942292	−	0.334792i	$-0.891334\pi$
$829$	2.75976e8	−	8.49367e8i	0.0168240	−	0.0517791i	0.959116	+	0.283013i	$0.0913339\pi$
$830$	−1.35652e10	−	8.77327e9i	−0.823478	−	0.532584i
$831$	−6.50429e9	−	2.00181e10i	−0.393184	−	1.21010i
$832$	2.86112e10			1.72229
$833$	−1.19866e9	−	3.68910e9i	−0.0718521	−	0.221138i
$834$	4.46290e9	+	3.24249e9i	0.266401	+	0.193552i
$835$	7.04559e7	+	1.82522e8i	0.00418808	+	0.0108496i
$836$	8.01420e9	−	5.82266e9i	0.474393	−	0.344667i
$837$	4.16936e9	+	3.02922e9i	0.245771	+	0.178563i
$838$	−1.97308e10	−	1.43352e10i	−1.15822	−	0.841494i
$839$	2.30903e10	−	1.67761e10i	1.34978	−	0.980671i	0.350755	−	0.936467i	$-0.385925\pi$
$839$	2.30903e10	−	1.67761e10i	1.34978	−	0.980671i	0.999023	−	0.0442037i	$-0.0140750\pi$
$840$	2.91114e10	−	1.58031e9i	1.69467	−	0.0919952i
$841$	1.27065e10	+	9.23178e9i	0.736611	+	0.535179i
$842$	4.68507e9	+	1.44191e10i	0.270473	+	0.832429i
$843$	−2.03125e10			−1.16779
$844$	2.53428e9	+	7.79972e9i	0.145096	+	0.446561i
$845$	9.54551e9	+	2.47284e10i	0.544253	+	1.40993i
$846$	−2.65900e8	+	8.18356e8i	−0.0150981	+	0.0464671i
$847$	−1.15354e10	+	3.55022e10i	−0.652288	+	2.00754i
$848$	2.12157e9	−	1.54141e9i	0.119474	−	0.0868027i
$849$	4.34864e10			2.43880
$850$	9.47993e9	+	5.42602e9i	0.529467	+	0.303051i
$851$	3.41262e9			0.189817
$852$	−1.14294e9	+	8.30394e8i	−0.0633118	+	0.0459987i
$853$	−5.25111e8	+	1.61612e9i	−0.0289687	+	0.0891565i	−0.964496	−	0.264099i	$-0.914925\pi$
$853$	−5.25111e8	+	1.61612e9i	−0.0289687	+	0.0891565i	0.935527	+	0.353256i	$0.114925\pi$
$854$	1.23057e9	−	3.78730e9i	0.0676089	−	0.208079i
$855$	−4.43868e9	+	1.66903e10i	−0.242869	+	0.913235i
$856$	−8.95356e9	−	2.75562e10i	−0.487908	−	1.50163i
$857$	−2.42132e10			−1.31407			−0.657037	−	0.753858i	$-0.728190\pi$
$857$	−2.42132e10			−1.31407			−0.657037	+	0.753858i	$0.728190\pi$
$858$	−1.72134e10	−	5.29773e10i	−0.930380	−	2.86341i
$859$	−4.01641e9	−	2.91809e9i	−0.216203	−	0.157081i	0.474413	−	0.880303i	$-0.342660\pi$
$859$	−4.01641e9	−	2.91809e9i	−0.216203	−	0.157081i	−0.690616	+	0.723222i	$0.742660\pi$
$860$	−2.18184e9	+	8.20414e9i	−0.116971	+	0.439834i
$861$	−5.28696e9	+	3.84120e9i	−0.282290	+	0.205096i
$862$	−7.69031e9	−	5.58734e9i	−0.408948	−	0.297118i
$863$	−1.89978e9	−	1.38027e9i	−0.100616	−	0.0731016i	0.536340	−	0.844002i	$-0.319807\pi$
$863$	−1.89978e9	−	1.38027e9i	−0.100616	−	0.0731016i	−0.636956	+	0.770901i	$0.719807\pi$
$864$	1.89761e9	−	1.37870e9i	0.100094	−	0.0727227i
$865$	−1.31736e10	+	1.07086e10i	−0.692065	+	0.562572i
$866$	−2.15601e10	−	1.56644e10i	−1.12808	−	0.819597i
$867$	−3.69893e9	−	1.13841e10i	−0.192757	−	0.593244i
$868$	1.01466e10			0.526626
$869$	−5.68282e9	−	1.74899e10i	−0.293762	−	0.904105i
$870$	6.54114e9	−	3.55086e8i	0.336772	−	0.0182817i
$871$	4.97984e9	−	1.53264e10i	0.255359	−	0.785915i
$872$	1.01799e9	−	3.13304e9i	0.0519917	−	0.160014i
$873$	−1.85784e10	+	1.34980e10i	−0.945060	+	0.686626i
$874$	−2.09763e10			−1.06277
$875$	−2.24335e10	+	3.68237e9i	−1.13206	+	0.185823i
$876$	−6.75043e9			−0.339287
$877$	9.33730e6	−	6.78395e6i	0.000467437	−	0.000339613i	−0.587552	−	0.809187i	$-0.699908\pi$
$877$	9.33730e6	−	6.78395e6i	0.000467437	−	0.000339613i	0.588019	+	0.808847i	$0.299908\pi$
$878$	−5.71893e9	+	1.76010e10i	−0.285157	+	0.877622i
$879$	−1.61667e9	+	4.97561e9i	−0.0802900	+	0.247107i
$880$	2.00795e10	−	1.09001e9i	0.993259	−	0.0539191i
$881$	7.88282e9	+	2.42608e10i	0.388388	+	1.19534i	0.933993	+	0.357292i	$0.116300\pi$
$881$	7.88282e9	+	2.42608e10i	0.388388	+	1.19534i	−0.545605	+	0.838043i	$0.683700\pi$
$882$	4.52951e9			0.222286
$883$	−3.83729e9	−	1.18100e10i	−0.187569	−	0.577279i	0.812414	−	0.583081i	$-0.198153\pi$
$883$	−3.83729e9	−	1.18100e10i	−0.187569	−	0.577279i	−0.999983	+	0.00580219i	$0.998153\pi$
$884$	−6.04843e9	−	4.39444e9i	−0.294483	−	0.213954i
$885$	1.03984e9	−	8.45277e8i	0.0504274	−	0.0409919i
$886$	1.16760e10	−	8.48313e9i	0.563998	−	0.409768i
$887$	2.52073e10	+	1.83142e10i	1.21281	+	0.881159i	0.995483	−	0.0949391i	$-0.0302657\pi$
$887$	2.52073e10	+	1.83142e10i	1.21281	+	0.881159i	0.217329	+	0.976098i	$0.430266\pi$
$888$	4.12218e9	+	2.99494e9i	0.197552	+	0.143530i
$889$	−5.48759e9	+	3.98697e9i	−0.261954	+	0.190321i
$890$	−3.73375e9	+	1.40396e10i	−0.177533	+	0.667560i
$891$	−3.24970e10	−	2.36104e10i	−1.53912	−	1.11823i
$892$	2.98298e9	+	9.18066e9i	0.140726	+	0.433109i
$893$	1.64754e9			0.0774207
$894$	1.86697e9	+	5.74594e9i	0.0873888	+	0.268955i
$895$	1.93419e9	−	7.27294e9i	0.0901818	−	0.339101i
$896$	−2.30942e9	+	7.10767e9i	−0.107257	+	0.330103i
$897$	1.65482e10	−	5.09302e10i	0.765557	−	2.35614i
$898$	1.99448e10	−	1.44907e10i	0.919099	−	0.667765i
$899$	9.58148e9			0.439819
$900$	4.28884e9	−	3.89087e9i	0.196106	−	0.177909i
$901$	−4.04077e9			−0.184047
$902$	−5.57573e9	+	4.05100e9i	−0.252976	+	0.183798i
$903$	−1.55423e10	+	4.78343e10i	−0.702438	+	2.16188i
$904$	−3.31526e9	+	1.02033e10i	−0.149255	+	0.459358i
$905$	−4.78254e9	−	1.23896e10i	−0.214481	−	0.555630i
$906$	−8.94598e9	−	2.75329e10i	−0.399649	−	1.22999i
$907$	4.41064e10			1.96280			0.981401	−	0.191970i	$-0.0614878\pi$
$907$	4.41064e10			1.96280			0.981401	+	0.191970i	$0.0614878\pi$
$908$	−4.25259e9	−	1.30881e10i	−0.188518	−	0.580199i
$909$	1.43533e10	+	1.04283e10i	0.633839	+	0.460511i
$910$	−3.42229e10	+	1.85779e9i	−1.50547	+	0.0817245i
$911$	1.84279e10	−	1.33887e10i	0.807536	−	0.586710i	−0.105579	−	0.994411i	$-0.533670\pi$
$911$	1.84279e10	−	1.33887e10i	0.807536	−	0.586710i	0.913115	+	0.407701i	$0.133670\pi$
$912$	−1.65715e10	−	1.20399e10i	−0.723402	−	0.525582i
$913$	3.70749e10	+	2.69365e10i	1.61225	+	1.17137i
$914$	3.01288e10	−	2.18899e10i	1.30518	−	0.948269i
$915$	−2.60872e9	−	6.75812e9i	−0.112578	−	0.291643i
$916$	−4.22781e9	−	3.07169e9i	−0.181753	−	0.132051i
$917$	−5.93829e9	−	1.82762e10i	−0.254313	−	0.782695i
$918$	2.95481e9			0.126061
$919$	1.42046e9	+	4.37174e9i	0.0603706	+	0.185802i	0.976694	−	0.214638i	$-0.0688573\pi$
$919$	1.42046e9	+	4.37174e9i	0.0603706	+	0.185802i	−0.916323	+	0.400440i	$0.868857\pi$
$920$	2.48199e10	+	1.60523e10i	1.05086	+	0.679640i
$921$	−1.01906e10	+	3.13634e10i	−0.429824	+	1.32286i
$922$	2.92324e9	−	8.99680e9i	0.122830	−	0.378033i
$923$	5.64674e9	−	4.10260e9i	0.236370	−	0.171733i
$924$	−1.96787e10			−0.820624
$925$	−3.44829e9	−	1.97369e9i	−0.143254	−	0.0819942i
$926$	−2.11683e10			−0.876089
$927$	6.99902e9	−	5.08508e9i	0.288575	−	0.209662i
$928$	1.34757e9	−	4.14740e9i	0.0553522	−	0.170356i
$929$	9.30291e8	−	2.86314e9i	0.0380683	−	0.117162i	−0.930216	−	0.367011i	$-0.880381\pi$
$929$	9.30291e8	−	2.86314e9i	0.0380683	−	0.117162i	0.968285	+	0.249849i	$0.0803810\pi$
$930$	−3.15477e10	+	2.56447e10i	−1.28611	+	1.04546i
$931$	−2.68000e9	−	8.24820e9i	−0.108846	−	0.334993i
$932$	4.39875e9			0.177981
$933$	1.29784e10	+	3.99434e10i	0.523161	+	1.61012i
$934$	−2.51118e10	−	1.82448e10i	−1.00847	−	0.732699i
$935$	−2.60180e10	−	1.68271e10i	−1.04096	−	0.673239i
$936$	2.96825e10	−	2.15656e10i	1.18314	−	0.859599i
$937$	1.21531e10	+	8.82977e9i	0.482614	+	0.350639i	0.802337	−	0.596872i	$-0.203590\pi$
$937$	1.21531e10	+	8.82977e9i	0.482614	+	0.350639i	−0.319723	+	0.947511i	$0.603590\pi$
$938$	1.01448e10	+	7.37063e9i	0.401360	+	0.291605i
$939$	−1.72231e10	+	1.25133e10i	−0.678863	+	0.493223i
$940$	−4.63862e8	−	3.00002e8i	−0.0182155	−	0.0117809i
$941$	−3.12623e10	−	2.27134e10i	−1.22309	−	0.888624i	−0.226734	−	0.973957i	$-0.572805\pi$
$941$	−3.12623e10	−	2.27134e10i	−1.22309	−	0.888624i	−0.996353	+	0.0853323i	$0.972805\pi$
$942$	5.76497e9	+	1.77427e10i	0.224708	+	0.691580i
$943$	−6.62566e9			−0.257299
$944$	2.25372e8	+	6.93625e8i	0.00871965	+	0.0268363i
$945$	−4.77202e9	+	3.87912e9i	−0.183946	+	0.149528i
$946$	−1.63912e10	+	5.04469e10i	−0.629494	+	1.93738i
$947$	−1.81369e9	+	5.58197e9i	−0.0693966	+	0.213581i	−0.979740	−	0.200272i	$-0.935817\pi$
$947$	−1.81369e9	+	5.58197e9i	−0.0693966	+	0.213581i	0.910344	+	0.413853i	$0.135817\pi$
$948$	5.08143e9	−	3.69187e9i	0.193712	−	0.140740i
$949$	3.33508e10			1.26670
$950$	2.11955e10	+	1.21316e10i	0.802067	+	0.459079i
$951$	2.29016e10			0.863444
$952$	1.97796e10	−	1.43707e10i	0.742998	−	0.539819i
$953$	1.18546e10	−	3.64847e10i	0.443671	−	1.36548i	−0.440264	−	0.897869i	$-0.645115\pi$
$953$	1.18546e10	−	3.64847e10i	0.443671	−	1.36548i	0.883935	−	0.467611i	$-0.154885\pi$
$954$	1.45809e9	−	4.48753e9i	0.0543706	−	0.167336i
$955$	3.46403e9	+	2.24036e9i	0.128697	+	0.0832350i
$956$	4.45973e9	+	1.37256e10i	0.165084	+	0.508077i
$957$	−1.85827e10			−0.685356
$958$	−2.19590e9	−	6.75829e9i	−0.0806926	−	0.248346i
$959$	−9.19546e9	−	6.68089e9i	−0.336673	−	0.244607i
$960$	1.45846e10	+	3.77826e10i	0.532041	+	1.37830i
$961$	−2.58504e10	+	1.87814e10i	−0.939583	+	0.682647i
$962$	−4.84598e9	−	3.52081e9i	−0.175497	−	0.127506i
$963$	−2.75846e10	−	2.00414e10i	−0.995348	−	0.723163i
$964$	−5.14150e9	+	3.73552e9i	−0.184850	+	0.134302i
$965$	2.81537e10	−	1.52832e9i	1.00853	−	0.0547482i
$966$	3.37116e10	+	2.44929e10i	1.20326	+	0.874220i
$967$	4.09875e9	+	1.26147e10i	0.145767	+	0.448624i	0.997109	−	0.0759870i	$-0.0242108\pi$
$967$	4.09875e9	+	1.26147e10i	0.145767	+	0.448624i	−0.851342	+	0.524611i	$0.824211\pi$
$968$	−5.65081e10			−2.00238
$969$	9.75328e9	+	3.00175e10i	0.344364	+	1.05984i
$970$	1.16941e10	+	3.02946e10i	0.411402	+	1.06577i
$971$	3.76501e9	−	1.15875e10i	0.131977	−	0.406184i	−0.863130	−	0.504981i	$-0.831499\pi$
$971$	3.76501e9	−	1.15875e10i	0.131977	−	0.406184i	0.995108	+	0.0987971i	$0.0314995\pi$
$972$	3.66865e9	−	1.12910e10i	0.128137	−	0.394365i
$973$	−7.78942e9	+	5.65935e9i	−0.271088	+	0.196957i
$974$	−6.11487e9			−0.212046
$975$	−4.61767e10	+	4.18917e10i	−1.59553	+	1.44748i
$976$	3.94258e9			0.135739
$977$	3.21447e9	−	2.33545e9i	0.110275	−	0.0801198i	−0.531281	−	0.847196i	$-0.678289\pi$
$977$	3.21447e9	−	2.33545e9i	0.110275	−	0.0801198i	0.641556	+	0.767076i	$0.278289\pi$
$978$	1.99147e8	−	6.12913e8i	0.00680752	−	0.0209514i
$979$	1.27348e10	−	3.91937e10i	0.433764	−	1.33499i
$980$	−7.47372e8	+	2.81026e9i	−0.0253656	+	0.0953796i
$981$	−1.19795e9	−	3.68690e9i	−0.0405132	−	0.124687i
$982$	−5.88774e9			−0.198408
$983$	−2.78475e9	−	8.57057e9i	−0.0935079	−	0.287788i	0.893354	−	0.449353i	$-0.148346\pi$
$983$	−2.78475e9	−	8.57057e9i	−0.0935079	−	0.287788i	−0.986862	+	0.161566i	$0.948346\pi$
$984$	−8.00328e9	−	5.81473e9i	−0.267784	−	0.194557i
$985$	1.46655e10	−	5.51452e10i	0.488957	−	1.83857i
$986$	4.44435e9	−	3.22901e9i	0.147652	−	0.107275i
$987$	−2.64782e9	−	1.92375e9i	−0.0876553	−	0.0636853i
$988$	−1.35233e10	−	9.82522e9i	−0.446100	−	0.324110i
$989$	−4.12545e10	+	2.99731e10i	−1.35608	+	0.985247i
$990$	2.80760e10	−	2.28227e10i	0.919628	−	0.747555i
$991$	7.22420e9	+	5.24869e9i	0.235794	+	0.171314i	0.699407	−	0.714723i	$-0.253447\pi$
$991$	7.22420e9	+	5.24869e9i	0.235794	+	0.171314i	−0.463614	+	0.886037i	$0.653447\pi$
$992$	8.36343e9	+	2.57400e10i	0.272015	+	0.837178i
$993$	9.84429e9			0.319052
$994$	1.67832e9	+	5.16535e9i	0.0542030	+	0.166820i
$995$	−2.87868e10	+	1.56270e9i	−0.926431	+	0.0502914i
$996$	−4.83672e9	+	1.48859e10i	−0.155111	+	0.477384i
$997$	−8.68073e9	+	2.67165e10i	−0.277411	+	0.853782i	0.711161	+	0.703029i	$0.248170\pi$
$997$	−8.68073e9	+	2.67165e10i	−0.277411	+	0.853782i	−0.988571	+	0.150753i	$0.951830\pi$
$998$	3.22253e10	−	2.34131e10i	1.02622	−	0.745593i
$999$	−1.07480e9			−0.0341074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.11.6	✓	68
25.4	even	10		625.8.a.c.1.12		34
25.16	even	5	inner	25.8.d.a.16.6	yes	68
25.21	even	5		625.8.a.d.1.23		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.11.6	✓	68	1.1	even	1	trivial
25.8.d.a.16.6	yes	68	25.16	even	5	inner
625.8.a.c.1.12		34	25.4	even	10
625.8.a.d.1.23		34	25.21	even	5

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.59067 + 5.51494i) q^{2} +(19.6452 - 60.4618i) q^{3} +(-12.3506 + 38.0111i) q^{4} +(279.098 - 15.1508i) q^{5} +(184.323 + 567.288i) q^{6} -1041.08 q^{7} +(-487.000 - 1498.83i) q^{8} +(-1500.38 - 1090.09i) q^{9} +(-2034.98 + 1654.21i) q^{10} +(6018.53 - 4372.72i) q^{11} +(2055.59 + 1493.47i) q^{12} +(-10155.7 - 7378.57i) q^{13} +(7902.50 - 5741.50i) q^{14} +(4566.89 - 17172.4i) q^{15} +(7823.85 + 5684.36i) q^{16} +(-4604.79 - 14172.1i) q^{17} +17400.6 q^{18} +(-10295.5 - 31686.3i) q^{19} +(-2871.11 + 10795.9i) q^{20} +(-20452.3 + 62945.7i) q^{21} +(-21569.4 + 66383.7i) q^{22} +(-54287.3 + 39442.0i) q^{23} -100189. q^{24} +(77665.9 - 8457.12i) q^{25} +117781. q^{26} +(17097.7 - 12422.2i) q^{27} +(12857.9 - 39572.6i) q^{28} +(12141.8 - 37368.6i) q^{29} +(60039.0 + 155536. i) q^{30} +(75355.5 + 231920. i) q^{31} +110986. q^{32} +(-146147. - 449794. i) q^{33} +(113112. + 82180.5i) q^{34} +(-290563. + 15773.2i) q^{35} +(59965.9 - 43567.7i) q^{36} +(-41143.9 - 29892.8i) q^{37} +(252898. + 183741. i) q^{38} +(-645634. + 469080. i) q^{39} +(-158629. - 410942. i) q^{40} +(79881.6 + 58037.4i) q^{41} +(-191895. - 590593. i) q^{42} +759929. q^{43} +(91879.6 + 282776. i) q^{44} +(-435267. - 281509. i) q^{45} +(194556. - 598782. i) q^{46} +(-15281.1 + 47030.3i) q^{47} +(497388. - 361374. i) q^{48} +260308. q^{49} +(-542895. + 492518. i) q^{50} -947333. q^{51} +(405897. - 294901. i) q^{52} +(83795.2 - 257895. i) q^{53} +(-61275.1 + 188585. i) q^{54} +(1.61351e6 - 1.31160e6i) q^{55} +(507007. + 1.56041e6i) q^{56} -2.11807e6 q^{57} +(113921. + 350614. i) q^{58} +(61011.7 + 44327.6i) q^{59} +(596338. + 385681. i) q^{60} +(329818. - 239627. i) q^{61} +(-1.85102e6 - 1.34485e6i) q^{62} +(1.56201e6 + 1.13487e6i) q^{63} +(-1.84391e6 + 1.33968e6i) q^{64} +(-2.94623e6 - 1.90547e6i) q^{65} +(3.58994e6 + 2.60825e6i) q^{66} +(396700. + 1.22092e6i) q^{67} +595568. q^{68} +(1.31825e6 + 4.05715e6i) q^{69} +(2.11858e6 - 1.72217e6i) q^{70} +(-171818. + 528802. i) q^{71} +(-903174. + 2.77968e6i) q^{72} +(-2.14937e6 + 1.56161e6i) q^{73} +477167. q^{74} +(1.01443e6 - 4.86196e6i) q^{75} +1.33159e6 q^{76} +(-6.26578e6 + 4.55236e6i) q^{77} +(2.31384e6 - 7.12126e6i) q^{78} +(763891. - 2.35102e6i) q^{79} +(2.26974e6 + 1.46795e6i) q^{80} +(-1.66853e6 - 5.13522e6i) q^{81} -926427. q^{82} +(1.90359e6 + 5.85863e6i) q^{83} +(-2.14004e6 - 1.55483e6i) q^{84} +(-1.49991e6 - 3.88563e6i) q^{85} +(-5.76837e6 + 4.19097e6i) q^{86} +(-2.02084e6 - 1.46823e6i) q^{87} +(-9.48500e6 - 6.89125e6i) q^{88} +(4.48162e6 - 3.25609e6i) q^{89} +(4.85647e6 - 263634. i) q^{90} +(1.05729e7 + 7.68170e6i) q^{91} +(-828756. - 2.55065e6i) q^{92} +1.55027e7 q^{93} +(-143376. - 441265. i) q^{94} +(-3.35353e6 - 8.68760e6i) q^{95} +(2.18035e6 - 6.71044e6i) q^{96} +(3.82641e6 - 1.17765e7i) q^{97} +(-1.97591e6 + 1.43558e6i) q^{98} -1.37967e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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