LMFDB - Embedded newform 63.8.h.a.25.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,8,Mod(25,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("63.25");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	63.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.6802566055$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.11
Character	$\chi$	$=$	63.25
Dual form			63.8.h.a.58.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-15.9040 q^{2} +(1.05606 + 46.7534i) q^{3} +124.937 q^{4} +(223.705 - 387.469i) q^{5} +(-16.7956 - 743.566i) q^{6} +(357.985 - 833.900i) q^{7} +48.7143 q^{8} +(-2184.77 + 98.7492i) q^{9} +(-3557.80 + 6162.30i) q^{10} +(4.13107 + 7.15522i) q^{11} +(131.941 + 5841.23i) q^{12} +(36.8566 + 63.8375i) q^{13} +(-5693.39 + 13262.3i) q^{14} +(18351.7 + 10049.8i) q^{15} -16766.7 q^{16} +(3590.42 - 6218.79i) q^{17} +(34746.6 - 1570.51i) q^{18} +(-4823.33 - 8354.25i) q^{19} +(27949.0 - 48409.2i) q^{20} +(39365.8 + 15856.4i) q^{21} +(-65.7005 - 113.797i) q^{22} +(-44889.6 + 77751.1i) q^{23} +(51.4454 + 2277.56i) q^{24} +(-61025.5 - 105699. i) q^{25} +(-586.167 - 1015.27i) q^{26} +(-6924.12 - 102041. i) q^{27} +(44725.5 - 104185. i) q^{28} +(35422.2 - 61353.0i) q^{29} +(-291866. - 159832. i) q^{30} -304092. q^{31} +260422. q^{32} +(-330.168 + 200.698i) q^{33} +(-57102.0 + 98903.5i) q^{34} +(-243027. - 325256. i) q^{35} +(-272958. + 12337.4i) q^{36} +(-144039. - 249482. i) q^{37} +(76710.1 + 132866. i) q^{38} +(-2945.70 + 1790.59i) q^{39} +(10897.6 - 18875.3i) q^{40} +(349003. + 604491. i) q^{41} +(-626073. - 252180. i) q^{42} +(473928. - 820867. i) q^{43} +(516.123 + 893.951i) q^{44} +(-450482. + 868620. i) q^{45} +(713925. - 1.23655e6i) q^{46} -566768. q^{47} +(-17706.7 - 783900. i) q^{48} +(-567237. - 597047. i) q^{49} +(970549. + 1.68104e6i) q^{50} +(294541. + 161297. i) q^{51} +(4604.75 + 7975.67i) q^{52} +(28361.1 - 49122.8i) q^{53} +(110121. + 1.62286e6i) q^{54} +3696.56 q^{55} +(17439.0 - 40622.9i) q^{56} +(385496. - 234330. i) q^{57} +(-563354. + 975758. i) q^{58} -183272. q^{59} +(2.29281e6 + 1.25559e6i) q^{60} +1.45871e6 q^{61} +4.83628e6 q^{62} +(-699767. + 1.85723e6i) q^{63} -1.99561e6 q^{64} +32980.1 q^{65} +(5251.00 - 3191.90i) q^{66} -3.09622e6 q^{67} +(448576. - 776956. i) q^{68} +(-3.68254e6 - 2.01664e6i) q^{69} +(3.86510e6 + 5.17286e6i) q^{70} -980257. q^{71} +(-106430. + 4810.50i) q^{72} +(-633108. + 1.09658e6i) q^{73} +(2.29079e6 + 3.96776e6i) q^{74} +(4.87736e6 - 2.96478e6i) q^{75} +(-602612. - 1.04375e6i) q^{76} +(7445.60 - 883.439i) q^{77} +(46848.4 - 28477.5i) q^{78} -7.91984e6 q^{79} +(-3.75079e6 + 6.49657e6i) q^{80} +(4.76347e6 - 431488. i) q^{81} +(-5.55054e6 - 9.61382e6i) q^{82} +(3.73104e6 - 6.46235e6i) q^{83} +(4.91824e6 + 1.98105e6i) q^{84} +(-1.60639e6 - 2.78235e6i) q^{85} +(-7.53735e6 + 1.30551e7i) q^{86} +(2.90587e6 + 1.59132e6i) q^{87} +(201.242 + 348.562i) q^{88} +(-4.11617e6 - 7.12941e6i) q^{89} +(7.16446e6 - 1.38145e7i) q^{90} +(66428.3 - 7881.88i) q^{91} +(-5.60838e6 + 9.71399e6i) q^{92} +(-321141. - 1.42174e7i) q^{93} +9.01387e6 q^{94} -4.31601e6 q^{95} +(275022. + 1.21756e7i) q^{96} +(-1.34912e6 + 2.33674e6i) q^{97} +(9.02133e6 + 9.49544e6i) q^{98} +(-9732.00 - 15224.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{2} - q^{3} + 6654 q^{4} - 499 q^{5} + 796 q^{6} - 84 q^{7} - 264 q^{8} - 2083 q^{9} - 258 q^{10} - 2953 q^{11} - 4262 q^{12} + 1845 q^{13} - 6064 q^{14} - 4756 q^{15} + 392958 q^{16} - 25695 q^{17}+ \cdots - 27043330 q^{99}+O(q^{100}) $ 108 * q - 2 * q^2 - q^3 + 6654 * q^4 - 499 * q^5 + 796 * q^6 - 84 * q^7 - 264 * q^8 - 2083 * q^9 - 258 * q^10 - 2953 * q^11 - 4262 * q^12 + 1845 * q^13 - 6064 * q^14 - 4756 * q^15 + 392958 * q^16 - 25695 * q^17 + 18628 * q^18 - 22344 * q^19 - 128642 * q^20 + 26395 * q^21 - 258 * q^22 + 24588 * q^23 + 9582 * q^24 - 718749 * q^25 - 184322 * q^26 - 108115 * q^27 - 37764 * q^28 - 46252 * q^29 - 368195 * q^30 + 215046 * q^31 - 896314 * q^32 - 508675 * q^33 + 126 * q^34 - 13856 * q^35 - 725486 * q^36 - 6219 * q^37 - 574289 * q^38 + 863855 * q^39 + 45102 * q^40 - 472490 * q^41 - 1455340 * q^42 - 48054 * q^43 - 763907 * q^44 - 1979983 * q^45 - 301266 * q^46 + 2767914 * q^47 + 3830059 * q^48 - 179010 * q^49 + 1454999 * q^50 - 1705518 * q^51 + 439809 * q^52 - 942852 * q^53 + 690229 * q^54 - 1333590 * q^55 - 960744 * q^56 - 4103881 * q^57 - 346383 * q^58 + 10263900 * q^59 + 1690429 * q^60 - 5446392 * q^61 + 17542716 * q^62 - 3666923 * q^63 + 20938488 * q^64 + 9110336 * q^65 + 8839522 * q^66 + 2503716 * q^67 - 3564510 * q^68 - 14621034 * q^69 + 5170071 * q^70 - 15030822 * q^71 + 10036926 * q^72 + 5865900 * q^73 - 10298901 * q^74 - 20070398 * q^75 - 5703426 * q^76 - 13731494 * q^77 + 18441853 * q^78 + 1098144 * q^79 - 22433777 * q^80 - 8145607 * q^81 + 126 * q^82 - 24302862 * q^83 + 10191035 * q^84 - 1239627 * q^85 - 8642455 * q^86 + 25559693 * q^87 + 2064129 * q^88 - 16002211 * q^89 + 28857805 * q^90 - 77007 * q^91 + 17446044 * q^92 - 1086678 * q^93 - 23171394 * q^94 + 8775674 * q^95 + 11149883 * q^96 - 3307419 * q^97 + 30910129 * q^98 - 27043330 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−15.9040			−1.40573			−0.702864	−	0.711324i	$-0.748096\pi$
$2$	−15.9040			−1.40573			−0.702864	+	0.711324i	$0.748096\pi$
$3$	1.05606	+	46.7534i	0.0225822	+	0.999745i
$3$	1.05606	+	46.7534i	0.0225822	+	0.999745i
$4$	124.937			0.976070
$5$	223.705	−	387.469i	0.800352	−	1.38625i	−0.119033	−	0.992890i	$-0.537979\pi$
$5$	223.705	−	387.469i	0.800352	−	1.38625i	0.919385	−	0.393360i	$-0.128687\pi$
$6$	−16.7956	−	743.566i	−0.0317444	−	1.40537i
$7$	357.985	−	833.900i	0.394477	−	0.918906i
$7$	357.985	−	833.900i	0.394477	−	0.918906i
$8$	48.7143			0.0336389
$9$	−2184.77	+	98.7492i	−0.998980	+	0.0451528i
$10$	−3557.80	+	6162.30i	−1.12508	+	1.94869i
$11$	4.13107	+	7.15522i	0.000935810	+	0.00162087i	0.866493	−	0.499189i	$-0.166369\pi$
$11$	4.13107	+	7.15522i	0.000935810	+	0.00162087i	−0.865557	+	0.500810i	$0.833035\pi$
$12$	131.941	+	5841.23i	0.0220418	+	0.975821i
$13$	36.8566	+	63.8375i	0.00465279	+	0.00805887i	0.868342	−	0.495965i	$-0.165186\pi$
$13$	36.8566	+	63.8375i	0.00465279	+	0.00805887i	−0.863690	+	0.504024i	$0.831852\pi$
$14$	−5693.39	+	13262.3i	−0.554527	+	1.29173i
$15$	18351.7	+	10049.8i	1.40397	+	0.768843i
$16$	−16766.7			−1.02336
$17$	3590.42	−	6218.79i	0.177245	−	0.306997i	−0.763691	−	0.645582i	$-0.776615\pi$
$17$	3590.42	−	6218.79i	0.177245	−	0.306997i	0.940936	+	0.338585i	$0.109948\pi$
$18$	34746.6	−	1570.51i	1.40429	−	0.0634725i
$19$	−4823.33	−	8354.25i	−0.161328	−	0.279428i	0.774017	−	0.633164i	$-0.218244\pi$
$19$	−4823.33	−	8354.25i	−0.161328	−	0.279428i	−0.935345	+	0.353737i	$0.884911\pi$
$20$	27949.0	−	48409.2i	0.781200	−	1.35308i
$21$	39365.8	+	15856.4i	0.927580	+	0.373625i
$22$	−65.7005	−	113.797i	−0.00131549	−	0.00227850i
$23$	−44889.6	+	77751.1i	−0.769305	+	1.33248i	0.168635	+	0.985679i	$0.446064\pi$
$23$	−44889.6	+	77751.1i	−0.769305	+	1.33248i	−0.937940	+	0.346797i	$0.887269\pi$
$24$	51.4454	+	2277.56i	0.000759639	+	0.0336303i
$25$	−61025.5	−	105699.i	−0.781126	−	1.35295i
$26$	−586.167	−	1015.27i	−0.00654056	−	0.0113286i
$27$	−6924.12	−	102041.i	−0.0677004	−	0.997706i
$28$	44725.5	−	104185.i	0.385037	−	0.896917i
$29$	35422.2	−	61353.0i	0.269701	−	0.467135i	−0.699084	−	0.715040i	$-0.746409\pi$
$29$	35422.2	−	61353.0i	0.269701	−	0.467135i	0.968785	+	0.247904i	$0.0797419\pi$
$30$	−291866.	−	159832.i	−1.97360	−	1.08078i
$31$	−304092.			−1.83333			−0.916663	−	0.399662i	$-0.869128\pi$
$31$	−304092.			−1.83333			−0.916663	+	0.399662i	$0.869128\pi$
$32$	260422.			1.40492
$33$	−330.168	+	200.698i	−0.00159933	+	0.000972174i
$34$	−57102.0	+	98903.5i	−0.249158	+	0.431554i
$35$	−243027.	−	325256.i	−0.958113	−	1.28229i
$36$	−272958.	+	12337.4i	−0.975075	+	0.0440723i
$37$	−144039.	−	249482.i	−0.467491	−	0.809717i	0.531820	−	0.846858i	$-0.321508\pi$
$37$	−144039.	−	249482.i	−0.467491	−	0.809717i	−0.999310	+	0.0371404i	$0.988175\pi$
$38$	76710.1	+	132866.i	0.226783	+	0.392799i
$39$	−2945.70	+	1790.59i	−0.00795175	+	0.00483359i
$40$	10897.6	−	18875.3i	0.0269230	−	0.0466319i
$41$	349003.	+	604491.i	0.790835	+	1.36977i	0.925451	+	0.378868i	$0.123687\pi$
$41$	349003.	+	604491.i	0.790835	+	1.36977i	−0.134616	+	0.990898i	$0.542980\pi$
$42$	−626073.	−	252180.i	−1.30392	−	0.525215i
$43$	473928.	−	820867.i	0.909019	−	1.57447i	0.0935884	−	0.995611i	$-0.470166\pi$
$43$	473928.	−	820867.i	0.909019	−	1.57447i	0.815430	−	0.578855i	$-0.196500\pi$
$44$	516.123	+	893.951i	0.000913417	+	0.00158208i
$45$	−450482.	+	868620.i	−0.736942	+	1.42097i
$46$	713925.	−	1.23655e6i	1.08143	−	1.87310i
$47$	−566768.			−0.796274			−0.398137	−	0.917326i	$-0.630343\pi$
$47$	−566768.			−0.796274			−0.398137	+	0.917326i	$0.630343\pi$
$48$	−17706.7	−	783900.i	−0.0231096	−	1.02310i
$49$	−567237.	−	597047.i	−0.688776	−	0.724974i
$50$	970549.	+	1.68104e6i	1.09805	+	1.90188i
$51$	294541.	+	161297.i	0.310921	+	0.170267i
$52$	4604.75	+	7975.67i	0.00454145	+	0.00786603i
$53$	28361.1	−	49122.8i	0.0261672	−	0.0453229i	−0.852645	−	0.522490i	$-0.825003\pi$
$53$	28361.1	−	49122.8i	0.0261672	−	0.0453229i	0.878812	+	0.477167i	$0.158336\pi$
$54$	110121.	+	1.62286e6i	0.0951683	+	1.40250i
$55$	3696.56			0.00299591
$56$	17439.0	−	40622.9i	0.0132698	−	0.0309110i
$57$	385496.	−	234330.i	0.275713	−	0.167597i
$58$	−563354.	+	975758.i	−0.379126	+	0.656665i
$59$	−183272.			−0.116175			−0.0580877	−	0.998311i	$-0.518500\pi$
$59$	−183272.			−0.116175			−0.0580877	+	0.998311i	$0.518500\pi$
$60$	2.29281e6	+	1.25559e6i	1.37037	+	0.750445i
$61$	1.45871e6			0.822837			0.411418	−	0.911447i	$-0.365033\pi$
$61$	1.45871e6			0.822837			0.411418	+	0.911447i	$0.365033\pi$
$62$	4.83628e6			2.57716
$63$	−699767.	+	1.85723e6i	−0.352583	+	0.935780i
$64$	−1.99561e6			−0.951581
$65$	32980.1			0.0148955
$66$	5251.00	−	3191.90i	0.00224822	−	0.00136661i
$67$	−3.09622e6			−1.25768			−0.628840	−	0.777534i	$-0.716470\pi$
$67$	−3.09622e6			−1.25768			−0.628840	+	0.777534i	$0.716470\pi$
$68$	448576.	−	776956.i	0.173003	−	0.299651i
$69$	−3.68254e6	−	2.01664e6i	−1.34951	−	0.739019i
$70$	3.86510e6	+	5.17286e6i	1.34685	+	1.80255i
$71$	−980257.			−0.325039			−0.162520	−	0.986705i	$-0.551962\pi$
$71$	−980257.			−0.325039			−0.162520	+	0.986705i	$0.551962\pi$
$72$	−106430.	+	4810.50i	−0.0336046	+	0.00151889i
$73$	−633108.	+	1.09658e6i	−0.190479	+	0.329920i	−0.945409	−	0.325886i	$-0.894338\pi$
$73$	−633108.	+	1.09658e6i	−0.190479	+	0.329920i	0.754930	+	0.655806i	$0.227671\pi$
$74$	2.29079e6	+	3.96776e6i	0.657164	+	1.13824i
$75$	4.87736e6	−	2.96478e6i	1.33497	−	0.811479i
$76$	−602612.	−	1.04375e6i	−0.157467	−	0.272741i
$77$	7445.60	−	883.439i	0.00185858	−	0.000220526i
$78$	46848.4	−	28477.5i	0.0111780	−	0.00679472i
$79$	−7.91984e6			−1.80726			−0.903632	−	0.428309i	$-0.859109\pi$
$79$	−7.91984e6			−1.80726			−0.903632	+	0.428309i	$0.859109\pi$
$80$	−3.75079e6	+	6.49657e6i	−0.819046	+	1.41863i
$81$	4.76347e6	−	431488.i	0.995922	−	0.0902135i
$82$	−5.55054e6	−	9.61382e6i	−1.11170	−	1.92552i
$83$	3.73104e6	−	6.46235e6i	0.716237	−	1.24056i	−0.246244	−	0.969208i	$-0.579196\pi$
$83$	3.73104e6	−	6.46235e6i	0.716237	−	1.24056i	0.962481	−	0.271350i	$-0.0874702\pi$
$84$	4.91824e6	+	1.98105e6i	0.905383	+	0.364685i
$85$	−1.60639e6	−	2.78235e6i	−0.283717	−	0.491411i
$86$	−7.53735e6	+	1.30551e7i	−1.27783	+	2.21327i
$87$	2.90587e6	+	1.59132e6i	0.473107	+	0.259083i
$88$	201.242	+	348.562i	3.14796e−5	+	5.45243e-5i
$89$	−4.11617e6	−	7.12941e6i	−0.618910	−	1.07198i	−0.989685	−	0.143261i	$-0.954241\pi$
$89$	−4.11617e6	−	7.12941e6i	−0.618910	−	1.07198i	0.370774	−	0.928723i	$-0.379092\pi$
$90$	7.16446e6	−	1.38145e7i	1.03594	−	1.99750i
$91$	66428.3	−	7881.88i	0.00924077	−	0.00109644i
$92$	−5.60838e6	+	9.71399e6i	−0.750896	+	1.30059i
$93$	−321141.	−	1.42174e7i	−0.0414004	−	1.83286i
$94$	9.01387e6			1.11934
$95$	−4.31601e6			−0.516476
$96$	275022.	+	1.21756e7i	0.0317262	+	1.40456i
$97$	−1.34912e6	+	2.33674e6i	−0.150089	+	0.259962i	−0.931260	−	0.364356i	$-0.881289\pi$
$97$	−1.34912e6	+	2.33674e6i	−0.150089	+	0.259962i	0.781171	+	0.624317i	$0.214623\pi$
$98$	9.02133e6	+	9.49544e6i	0.968232	+	1.01912i
$99$	−9732.00	−	15224.6i	−0.00100804	−	0.00157696i
$100$	−7.62434e6	−	1.32057e7i	−0.762434	−	1.32057i
$101$	−2.20140e6	−	3.81293e6i	−0.212605	−	0.368243i	0.739924	−	0.672690i	$-0.234861\pi$
$101$	−2.20140e6	−	3.81293e6i	−0.212605	−	0.368243i	−0.952529	+	0.304448i	$0.901528\pi$
$102$	−4.68438e6	−	2.56527e6i	−0.437071	−	0.239349i
$103$	−5.30070e6	+	9.18109e6i	−0.477973	+	0.827873i	−0.999681	−	0.0252508i	$-0.991962\pi$
$103$	−5.30070e6	+	9.18109e6i	−0.477973	+	0.827873i	0.521708	+	0.853124i	$0.325295\pi$
$104$	1795.45	+	3109.80i	0.000156515	+	0.000271092i
$105$	1.49502e7	−	1.17059e7i	1.26033	−	0.986826i
$106$	−451054.	+	781249.i	−0.0367839	+	0.0637116i
$107$	−3.12112e6	−	5.40593e6i	−0.246301	−	0.426606i	0.716195	−	0.697900i	$-0.245882\pi$
$107$	−3.12112e6	−	5.40593e6i	−0.246301	−	0.426606i	−0.962497	+	0.271293i	$0.912549\pi$
$108$	−865078.	−	1.27487e7i	−0.0660803	−	0.973831i
$109$	1.73153e6	−	2.99909e6i	0.128067	−	0.221818i	−0.794861	−	0.606792i	$-0.792456\pi$
$109$	1.73153e6	−	2.99909e6i	0.128067	−	0.221818i	0.922928	+	0.384974i	$0.125789\pi$
$110$	−58790.1			−0.00421143
$111$	1.15120e7	−	6.99777e6i	0.798954	−	0.485656i
$112$	−6.00222e6	+	1.39817e7i	−0.403691	+	0.940369i
$113$	7.16405e6	+	1.24085e7i	0.467072	+	0.808992i	0.999292	−	0.0376135i	$-0.0119756\pi$
$113$	7.16405e6	+	1.24085e7i	0.467072	+	0.808992i	−0.532220	+	0.846606i	$0.678642\pi$
$114$	−6.13093e6	+	3.72678e6i	−0.387578	+	0.235595i
$115$	2.00841e7	+	3.47867e7i	1.23143	+	2.13290i
$116$	4.42554e6	−	7.66526e6i	0.263247	−	0.455957i
$117$	−86827.1	−	135831.i	−0.00501193	−	0.00784057i
$118$	2.91476e6			0.163311
$119$	−3.90053e6	−	5.22028e6i	−0.212182	−	0.283975i
$120$	893993.	+	489569.i	0.0472280	+	0.0258630i
$121$	9.74355e6	−	1.68763e7i	0.499998	−	0.866022i
$122$	−2.31993e7			−1.15668
$123$	−2.78935e7	+	1.69555e7i	−1.35156	+	0.821566i
$124$	−3.79924e7			−1.78945
$125$	−1.96529e7			−0.899999
$126$	1.11291e7	−	2.95374e7i	0.495636	−	1.31545i
$127$	−2.94497e7			−1.27576			−0.637879	−	0.770137i	$-0.720188\pi$
$127$	−2.94497e7			−1.27576			−0.637879	+	0.770137i	$0.720188\pi$
$128$	−1.59581e6			−0.0672586
$129$	3.88789e7	+	2.12909e7i	1.59459	+	0.873232i
$130$	−524515.			−0.0209390
$131$	−7.97334e6	+	1.38102e7i	−0.309878	+	0.536725i	−0.978335	−	0.207026i	$-0.933622\pi$
$131$	−7.97334e6	+	1.38102e7i	−0.309878	+	0.536725i	0.668457	+	0.743750i	$0.266955\pi$
$132$	−41250.2	+	25074.6i	−0.00156105	+	0.000948910i
$133$	−8.69329e6	+	1.03148e6i	−0.320408	+	0.0380172i
$134$	4.92423e7			1.76796
$135$	−4.10867e7	−	2.01443e7i	−1.43725	−	0.704666i
$136$	174905.	−	302944.i	0.00596232	−	0.0103270i
$137$	−1.86210e7	−	3.22526e7i	−0.618703	−	1.07162i	−0.989723	−	0.143000i	$-0.954325\pi$
$137$	−1.86210e7	−	3.22526e7i	−0.618703	−	1.07162i	0.371020	−	0.928625i	$-0.379008\pi$
$138$	5.85671e7	+	3.20726e7i	1.89704	+	1.03886i
$139$	−8.84161e6	−	1.53141e7i	−0.279241	−	0.483660i	0.691955	−	0.721941i	$-0.256750\pi$
$139$	−8.84161e6	−	1.53141e7i	−0.279241	−	0.483660i	−0.971196	+	0.238280i	$0.923416\pi$
$140$	−3.03631e7	−	4.06365e7i	−0.935186	−	1.25161i
$141$	−598542.	−	2.64983e7i	−0.0179816	−	0.796071i
$142$	1.55900e7			0.456917
$143$	−304.514	+	527.434i	−8.70826e−6	+	1.50832e-5i
$144$	3.66313e7	−	1.65570e6i	1.02231	−	0.0462074i
$145$	−1.58482e7	−	2.74500e7i	−0.431711	−	0.747745i
$146$	1.00689e7	−	1.74399e7i	0.267762	−	0.463777i
$147$	2.73150e7	−	2.71508e7i	0.709235	−	0.704972i
$148$	−1.79957e7	−	3.11695e7i	−0.456304	−	0.790341i
$149$	1.92208e7	−	3.32914e7i	0.476013	−	0.824479i	−0.523609	−	0.851959i	$-0.675415\pi$
$149$	1.92208e7	−	3.32914e7i	0.476013	−	0.824479i	0.999622	+	0.0274797i	$0.00874816\pi$
$150$	−7.75694e7	+	4.71518e7i	−1.87660	+	1.14072i
$151$	1.30824e7	+	2.26594e7i	0.309221	+	0.535586i	0.978192	−	0.207702i	$-0.0665984\pi$
$151$	1.30824e7	+	2.26594e7i	0.309221	+	0.535586i	−0.668971	+	0.743288i	$0.733265\pi$
$152$	−234965.	−	406972.i	−0.00542689	−	0.00939965i
$153$	−7.23013e6	+	1.39412e7i	−0.163202	+	0.314687i
$154$	−118415.	+	14050.2i	−0.00261266	+	0.000309999i
$155$	−6.80270e7	+	1.17826e8i	−1.46731	+	2.54145i
$156$	−368027.	+	223711.i	−0.00776146	+	0.00471793i
$157$	2.63573e7			0.543566			0.271783	−	0.962359i	$-0.412387\pi$
$157$	2.63573e7			0.543566			0.271783	+	0.962359i	$0.412387\pi$
$158$	1.25957e8			2.54052
$159$	2.32661e6	+	1.27410e6i	0.0459022	+	0.0251370i
$160$	5.82577e7	−	1.00905e8i	1.12443	−	1.94757i
$161$	4.87669e7	+	6.52672e7i	0.920947	+	1.23255i
$162$	−7.57581e7	+	6.86239e6i	−1.40000	+	0.126816i
$163$	2.38661e7	+	4.13374e7i	0.431644	+	0.747629i	0.997015	−	0.0772074i	$-0.0246004\pi$
$163$	2.38661e7	+	4.13374e7i	0.431644	+	0.747629i	−0.565371	+	0.824837i	$0.691267\pi$
$164$	4.36034e7	+	7.55233e7i	0.771910	+	1.33699i
$165$	3903.80	+	172827.i	6.76541e−5	+	0.00299515i
$166$	−5.93384e7	+	1.02777e8i	−1.00683	+	1.74389i
$167$	8.87002e6	+	1.53633e7i	0.147373	+	0.255257i	0.930256	−	0.366912i	$-0.119585\pi$
$167$	8.87002e6	+	1.53633e7i	0.147373	+	0.255257i	−0.782883	+	0.622169i	$0.786252\pi$
$168$	1.91768e6	+	772433.i	0.0312028	+	0.0125683i
$169$	3.13715e7	−	5.43371e7i	0.499957	−	0.865950i
$170$	2.55480e7	+	4.42505e7i	0.398828	+	0.690791i
$171$	1.13628e7	+	1.77758e7i	0.173780	+	0.271858i
$172$	5.92111e7	−	1.02557e8i	0.887266	−	1.53679i
$173$	−6.47646e6			−0.0950991			−0.0475495	−	0.998869i	$-0.515141\pi$
$173$	−6.47646e6			−0.0950991			−0.0475495	+	0.998869i	$0.515141\pi$
$174$	−4.62150e7	−	2.53083e7i	−0.665059	−	0.364200i
$175$	−1.09989e8	+	1.30504e7i	−1.55137	+	0.184074i
$176$	−69264.3	−	119969.i	−0.000957668	−	0.00165873i
$177$	−193547.	−	8.56859e6i	−0.00262349	−	0.116146i
$178$	6.54635e7	+	1.13386e8i	0.870020	+	1.50692i
$179$	3.31880e7	−	5.74833e7i	0.432509	−	0.749128i	−0.564579	−	0.825379i	$-0.690962\pi$
$179$	3.31880e7	−	5.74833e7i	0.432509	−	0.749128i	0.997089	+	0.0762508i	$0.0242950\pi$
$180$	−5.62819e7	+	1.08523e8i	−0.719308	+	1.38697i
$181$	6.40444e7			0.802798			0.401399	−	0.915903i	$-0.368524\pi$
$181$	6.40444e7			0.802798			0.401399	+	0.915903i	$0.368524\pi$
$182$	−1.05647e6	+	125353.i	−0.0129900	+	0.00154130i
$183$	1.54049e6	+	6.81996e7i	0.0185814	+	0.822627i
$184$	−2.18677e6	+	3.78760e6i	−0.0258786	+	0.0448230i
$185$	−1.28889e8			−1.49663
$186$	5.10742e6	+	2.26113e8i	0.0581977	+	2.57650i
$187$	59329.0			0.000663470
$188$	−7.08102e7			−0.777219
$189$	−8.75709e7	−	3.07552e7i	−0.943504	−	0.331361i
$190$	6.86418e7			0.726024
$191$	1.62963e8			1.69227			0.846137	−	0.532965i	$-0.178922\pi$
$191$	1.62963e8			1.69227			0.846137	+	0.532965i	$0.178922\pi$
$192$	−2.10749e6	−	9.33017e7i	−0.0214888	−	0.951339i
$193$	−1.37564e8			−1.37738			−0.688691	−	0.725055i	$-0.741814\pi$
$193$	−1.37564e8			−1.37738			−0.688691	+	0.725055i	$0.741814\pi$
$194$	2.14563e7	−	3.71635e7i	0.210984	−	0.365435i
$195$	34829.0	+	1.54193e6i	0.000336372	+	0.0148917i
$196$	−7.08688e7	−	7.45933e7i	−0.672294	−	0.707626i
$197$	3.48701e7			0.324954			0.162477	−	0.986712i	$-0.448052\pi$
$197$	3.48701e7			0.324954			0.162477	+	0.986712i	$0.448052\pi$
$198$	154778.	+	242131.i	0.00141703	+	0.00221678i
$199$	9.37158e7	−	1.62321e8i	0.842999	−	1.46012i	−0.0443486	−	0.999016i	$-0.514121\pi$
$199$	9.37158e7	−	1.62321e8i	0.842999	−	1.46012i	0.887348	−	0.461101i	$-0.152545\pi$
$200$	−2.97282e6	−	5.14907e6i	−0.0262762	−	0.0455118i
$201$	−3.26981e6	−	1.44759e8i	−0.0284011	−	1.25736i
$202$	3.50110e7	+	6.06408e7i	0.298865	+	0.517649i
$203$	−3.84817e7	−	5.15020e7i	−0.322863	−	0.432104i
$204$	3.67991e7	+	2.01520e7i	0.303481	+	0.166193i
$205$	3.12295e8			2.53178
$206$	8.43023e7	−	1.46016e8i	0.671899	−	1.16376i
$207$	9.03957e7	−	1.74301e8i	0.708356	−	1.36585i
$208$	−617963.	−	1.07034e6i	−0.00476147	−	0.00824711i
$209$	39851.0	−	69023.9i	0.000301944	−	0.000522983i
$210$	−2.37767e8	+	1.86170e8i	−1.77168	+	1.38721i
$211$	2.31349e7	+	4.00709e7i	0.169543	+	0.293657i	0.938259	−	0.345933i	$-0.112438\pi$
$211$	2.31349e7	+	4.00709e7i	0.169543	+	0.293657i	−0.768716	+	0.639590i	$0.779104\pi$
$212$	3.54335e6	−	6.13725e6i	0.0255410	−	0.0442383i
$213$	−1.03521e6	−	4.58304e7i	−0.00734009	−	0.324956i
$214$	4.96382e7	+	8.59759e7i	0.346233	+	0.599692i
$215$	−2.12040e8	−	3.67264e8i	−1.45507	−	2.52025i
$216$	−337304.	−	4.97087e6i	−0.00227737	−	0.0335617i
$217$	−1.08860e8	+	2.53583e8i	−0.723204	+	1.68465i
$218$	−2.75382e7	+	4.76975e7i	−0.180027	+	0.311816i
$219$	−5.19373e7	−	2.84419e7i	−0.334137	−	0.182980i
$220$	461837.			0.00292422
$221$	529323.			0.00329874
$222$	−1.83087e8	+	1.11292e8i	−1.12311	+	0.682701i
$223$	−1.37640e8	+	2.38399e8i	−0.831146	+	1.43959i	0.0659847	+	0.997821i	$0.478981\pi$
$223$	−1.37640e8	+	2.38399e8i	−0.831146	+	1.43959i	−0.897130	+	0.441766i	$0.854352\pi$
$224$	9.32271e7	−	2.17166e8i	0.554209	−	1.29099i
$225$	1.43764e8	+	2.24902e8i	0.841419	+	1.31630i
$226$	−1.13937e8	−	1.97345e8i	−0.656576	−	1.13722i
$227$	−1.00528e8	−	1.74119e8i	−0.570422	−	0.987999i	−0.996523	−	0.0833235i	$-0.973447\pi$
$227$	−1.00528e8	−	1.74119e8i	−0.570422	−	0.987999i	0.426101	−	0.904676i	$-0.359887\pi$
$228$	4.81627e7	−	2.92765e7i	0.269116	−	0.163586i
$229$	5.29404e7	−	9.16955e7i	0.291315	−	0.504573i	−0.682806	−	0.730600i	$-0.739240\pi$
$229$	5.29404e7	−	9.16955e7i	0.291315	−	0.504573i	0.974121	+	0.226027i	$0.0725738\pi$
$230$	−3.19417e8	−	5.53247e8i	−1.73105	−	2.99827i
$231$	49166.8	+	347174.i	0.000262440	+	0.00185313i
$232$	1.72557e6	−	2.98877e6i	0.00907244	−	0.0157139i
$233$	9.62973e7	+	1.66792e8i	0.498733	+	0.863831i	0.999999	−	0.00146207i	$-0.000465391\pi$
$233$	9.62973e7	+	1.66792e8i	0.498733	+	0.863831i	−0.501266	+	0.865293i	$0.667132\pi$
$234$	1.38090e6	+	2.16025e6i	0.00704541	+	0.0110217i
$235$	−1.26789e8	+	2.19605e8i	−0.637299	+	1.10383i
$236$	−2.28974e7			−0.113395
$237$	−8.36385e6	−	3.70280e8i	−0.0408119	−	1.80680i
$238$	6.20340e7	+	8.30233e7i	0.298271	+	0.399191i
$239$	−1.20811e8	−	2.09251e8i	−0.572418	−	0.991457i	−0.996317	−	0.0857475i	$-0.972672\pi$
$239$	−1.20811e8	−	2.09251e8i	−0.572418	−	0.991457i	0.423899	−	0.905709i	$-0.360661\pi$
$240$	−3.07698e8	−	1.68502e8i	−1.43676	−	0.786801i
$241$	−1.01088e8	−	1.75089e8i	−0.465198	−	0.805747i	0.534012	−	0.845477i	$-0.320684\pi$
$241$	−1.01088e8	−	1.75089e8i	−0.465198	−	0.805747i	−0.999210	+	0.0397300i	$0.987350\pi$
$242$	−1.54961e8	+	2.68401e8i	−0.702861	+	1.21739i
$243$	2.52041e7	+	2.22253e8i	0.112681	+	0.993631i
$244$	1.82246e8			0.803147
$245$	−3.58231e8	+	8.62239e7i	−1.55626	+	0.374581i
$246$	4.43618e8	−	2.69660e8i	1.89992	−	1.15490i
$247$	355543.	−	615819.i	0.00150125	−	0.00260024i
$248$	−1.48137e7			−0.0616711
$249$	3.06077e8	+	1.67614e8i	1.25642	+	0.688039i
$250$	3.12560e8			1.26515
$251$	−4.99073e7			−0.199208			−0.0996039	−	0.995027i	$-0.531758\pi$
$251$	−4.99073e7			−0.199208			−0.0996039	+	0.995027i	$0.531758\pi$
$252$	−8.74268e7	+	2.32037e8i	−0.344146	+	0.913387i
$253$	−741768.			−0.00287970
$254$	4.68368e8			1.79337
$255$	1.28388e8	−	7.80426e7i	0.484879	−	0.294741i
$256$	2.80818e8			1.04613
$257$	−2.28137e8	+	3.95144e8i	−0.838357	+	1.45208i	0.0529107	+	0.998599i	$0.483150\pi$
$257$	−2.28137e8	+	3.95144e8i	−0.838357	+	1.45208i	−0.891268	+	0.453478i	$0.850183\pi$
$258$	−6.18329e8	−	3.38610e8i	−2.24156	−	1.22753i
$259$	−2.59607e8	+	3.08030e7i	−0.928468	+	0.110165i
$260$	4.12043e6			0.0145390
$261$	−7.13307e7	+	1.37540e8i	−0.248333	+	0.478837i
$262$	1.26808e8	−	2.19638e8i	0.435604	−	0.754489i
$263$	1.98585e8	+	3.43960e8i	0.673135	+	1.16590i	0.977010	+	0.213192i	$0.0683859\pi$
$263$	1.98585e8	+	3.43960e8i	0.673135	+	1.16590i	−0.303876	+	0.952712i	$0.598281\pi$
$264$	−16083.9	+	9776.87i	−5.37995e−5	+	3.27029e-5i
$265$	−1.26890e7	−	2.19780e7i	−0.0418859	−	0.0725485i
$266$	1.38258e8	−	1.64047e7i	0.450406	−	0.0534418i
$267$	3.28977e8	−	1.99974e8i	1.05773	−	0.642960i
$268$	−3.86833e8			−1.22758
$269$	−1.14124e8	+	1.97669e8i	−0.357474	+	0.619163i	−0.987538	−	0.157380i	$-0.949695\pi$
$269$	−1.14124e8	+	1.97669e8i	−0.357474	+	0.619163i	0.630064	+	0.776543i	$0.283029\pi$
$270$	6.53443e8	+	3.20374e8i	2.02039	+	0.990568i
$271$	3.13684e8	+	5.43316e8i	0.957413	+	1.65829i	0.728747	+	0.684783i	$0.240103\pi$
$271$	3.13684e8	+	5.43316e8i	0.957413	+	1.65829i	0.228665	+	0.973505i	$0.426564\pi$
$272$	−6.01994e7	+	1.04268e8i	−0.181385	+	0.314168i
$273$	438657.	+	3.09743e6i	0.00130484	+	0.00921365i
$274$	2.96149e8	+	5.12945e8i	0.869728	+	1.50641i
$275$	504201.	−	873301.i	0.00146197	−	0.00253221i
$276$	−4.60085e8	−	2.51952e8i	−1.31721	−	0.721334i
$277$	−1.03848e8	−	1.79869e8i	−0.293574	−	0.508484i	0.681079	−	0.732210i	$-0.261511\pi$
$277$	−1.03848e8	−	1.79869e8i	−0.293574	−	0.508484i	−0.974652	+	0.223726i	$0.928178\pi$
$278$	1.40617e8	+	2.43556e8i	0.392537	+	0.679894i
$279$	6.64372e8	−	3.00289e7i	1.83146	−	0.0827798i
$280$	−1.18389e7	−	1.58446e7i	−0.0322299	−	0.0431349i
$281$	−1.12761e6	+	1.95308e6i	−0.00303171	+	0.00525108i	−0.867537	−	0.497372i	$-0.834298\pi$
$281$	−1.12761e6	+	1.95308e6i	−0.00303171	+	0.00525108i	0.864506	+	0.502623i	$0.167632\pi$
$282$	9.51921e6	+	4.21429e8i	0.0252772	+	1.11906i
$283$	7.38298e7			0.193633			0.0968165	−	0.995302i	$-0.469134\pi$
$283$	7.38298e7			0.193633			0.0968165	+	0.995302i	$0.469134\pi$
$284$	−1.22470e8			−0.317261
$285$	−4.55798e6	−	2.01788e8i	−0.0116631	−	0.516344i
$286$	4842.99	−	8388.31i	1.22414e−5	−	2.12028e-5i
$287$	6.29023e8	−	7.46352e7i	1.57065	−	0.186362i
$288$	−5.68962e8	+	2.57164e7i	−1.40349	+	0.0634362i
$289$	1.79387e8	+	3.10708e8i	0.437168	+	0.757198i
$290$	2.52050e8	+	4.36564e8i	0.606868	+	1.05113i
$291$	−1.10675e8	−	6.06081e7i	−0.263285	−	0.144180i
$292$	−7.90986e7	+	1.37003e8i	−0.185921	+	0.322025i
$293$	4.78993e7	+	8.29641e7i	0.111248	+	0.192687i	0.916274	−	0.400553i	$-0.131182\pi$
$293$	4.78993e7	+	8.29641e7i	0.111248	+	0.192687i	−0.805026	+	0.593240i	$0.797848\pi$
$294$	−4.34417e8	+	4.31806e8i	−0.996992	+	0.990998i
$295$	−4.09989e7	+	7.10121e7i	−0.0929811	+	0.161048i
$296$	−7.01674e6	−	1.21534e7i	−0.0157259	−	0.0272380i
$297$	701523.	−	471083.i	0.00155380	−	0.00104340i
$298$	−3.05687e8	+	5.29465e8i	−0.669145	+	1.15899i
$299$	−6.61792e6			−0.0143177
$300$	6.09362e8	−	3.70410e8i	1.30302	−	0.792061i
$301$	−5.14863e8	−	6.89067e8i	−1.08820	−	1.45639i
$302$	−2.08063e8	−	3.60375e8i	−0.434681	−	0.752889i
$303$	1.75943e8	−	1.06950e8i	0.363348	−	0.220866i
$304$	8.08712e7	+	1.40073e8i	0.165096	+	0.285955i
$305$	3.26320e8	−	5.65203e8i	0.658559	−	1.14066i
$306$	1.14988e8	−	2.21720e8i	0.229418	−	0.442364i
$307$	−3.59188e8			−0.708496			−0.354248	−	0.935152i	$-0.615263\pi$
$307$	−3.59188e8			−0.708496			−0.354248	+	0.935152i	$0.615263\pi$
$308$	930231.	−	110374.i	0.00181411	−	0.000215248i
$309$	−4.34845e8	−	2.38130e8i	−0.838456	−	0.459156i
$310$	1.08190e9	−	1.87391e9i	2.06263	−	3.57258i
$311$	4.55186e8			0.858080			0.429040	−	0.903285i	$-0.358852\pi$
$311$	4.55186e8			0.858080			0.429040	+	0.903285i	$0.358852\pi$
$312$	−143498.	+	87227.4i	−0.000267488	+	0.000162597i
$313$	−2.45501e8			−0.452530			−0.226265	−	0.974066i	$-0.572652\pi$
$313$	−2.45501e8			−0.452530			−0.226265	+	0.974066i	$0.572652\pi$
$314$	−4.19187e8			−0.764106
$315$	5.63077e8	+	6.86610e8i	1.01503	+	1.23772i
$316$	−9.89481e8			−1.76402
$317$	1.31614e8			0.232056			0.116028	−	0.993246i	$-0.462984\pi$
$317$	1.31614e8			0.232056			0.116028	+	0.993246i	$0.462984\pi$
$318$	−3.70024e7	−	2.02633e7i	−0.0645260	−	0.0353358i
$319$	585325.			0.00100955
$320$	−4.46428e8	+	7.73237e8i	−0.761600	+	1.31913i
$321$	2.49450e8	−	1.51632e8i	0.420936	−	0.255872i
$322$	−7.75588e8	−	1.03801e9i	−1.29460	−	1.73263i
$323$	−6.92710e7			−0.114378
$324$	5.95133e8	−	5.39088e7i	0.972090	−	0.0880547i
$325$	4.49839e6	−	7.79143e6i	0.00726884	−	0.0125900i
$326$	−3.79567e8	−	6.57429e8i	−0.606774	−	1.05096i
$327$	1.42047e8	+	7.77876e7i	0.224654	+	0.123025i
$328$	1.70015e7	+	2.94474e7i	0.0266028	+	0.0460774i
$329$	−2.02894e8	+	4.72628e8i	−0.314112	+	0.731701i
$330$	−62086.1	−	2.74864e6i	−9.51033e−5	−	0.00421036i
$331$	−3.65162e8			−0.553461			−0.276731	−	0.960948i	$-0.589251\pi$
$331$	−3.65162e8			−0.553461			−0.276731	+	0.960948i	$0.589251\pi$
$332$	4.66145e8	−	8.07386e8i	0.699097	−	1.21087i
$333$	3.39327e8	+	5.30837e8i	0.503575	+	0.787783i
$334$	−1.41069e8	−	2.44338e8i	−0.207166	−	0.358822i
$335$	−6.92641e8	+	1.19969e9i	−1.00659	+	1.74346i
$336$	−6.60033e8	−	2.65859e8i	−0.949245	−	0.382352i
$337$	3.56787e8	+	6.17974e8i	0.507814	+	0.879560i	0.999959	+	0.00904664i	$0.00287967\pi$
$337$	3.56787e8	+	6.17974e8i	0.507814	+	0.879560i	−0.492145	+	0.870513i	$0.663787\pi$
$338$	−4.98933e8	+	8.64177e8i	−0.702803	+	1.21729i
$339$	−5.72574e8	+	3.48048e8i	−0.798239	+	0.485222i
$340$	−2.00697e8	−	3.47618e8i	−0.276927	−	0.479652i
$341$	−1.25623e6	−	2.17585e6i	−0.00171564	−	0.00297158i
$342$	−1.80714e8	−	2.82706e8i	−0.244288	−	0.382159i
$343$	−7.00940e8	+	2.59285e8i	−0.937889	+	0.346935i
$344$	2.30871e7	−	3.99880e7i	0.0305784	−	0.0529633i
$345$	−1.60519e9	+	9.75737e8i	−2.10455	+	1.27928i
$346$	1.03002e8			0.133683
$347$	1.03806e9			1.33373			0.666866	−	0.745178i	$-0.267635\pi$
$347$	1.03806e9			1.33373			0.666866	+	0.745178i	$0.267635\pi$
$348$	3.63051e8	+	1.98814e8i	0.461785	+	0.252883i
$349$	4.33005e8	−	7.49987e8i	0.545260	−	0.944419i	−0.453330	−	0.891343i	$-0.649764\pi$
$349$	4.33005e8	−	7.49987e8i	0.545260	−	0.944419i	0.998590	−	0.0530759i	$-0.0169025\pi$
$350$	1.74926e9	−	2.07554e8i	2.18080	−	0.258758i
$351$	6.25886e6	−	4.20291e6i	0.00772539	−	0.00518771i
$352$	1.07582e6	+	1.86337e6i	0.00131474	+	0.00227720i
$353$	3.65394e8	+	6.32881e8i	0.442130	+	0.765792i	0.997847	−	0.0655796i	$-0.0208896\pi$
$353$	3.65394e8	+	6.32881e8i	0.442130	+	0.765792i	−0.555717	+	0.831371i	$0.687556\pi$
$354$	3.07817e6	+	1.36275e8i	0.00368791	+	0.163269i
$355$	−2.19289e8	+	3.79819e8i	−0.260146	+	0.450586i
$356$	−5.14261e8	−	8.90727e8i	−0.604100	−	1.04633i
$357$	2.39947e8	−	1.87876e8i	0.279111	−	0.218541i
$358$	−5.27822e8	+	9.14214e8i	−0.607990	+	1.05307i
$359$	6.44597e8	+	1.11647e9i	0.735288	+	1.27356i	0.954597	+	0.297901i	$0.0962865\pi$
$359$	6.44597e8	+	1.11647e9i	0.735288	+	1.27356i	−0.219309	+	0.975655i	$0.570380\pi$
$360$	−2.19449e7	+	4.23143e7i	−0.0247899	+	0.0478000i
$361$	4.00407e8	−	6.93525e8i	0.447947	−	0.775866i
$362$	−1.01856e9			−1.12852
$363$	7.99316e8	+	4.37722e8i	0.877093	+	0.480314i
$364$	8.29935e6	−	984738.i	0.00901964	−	0.00107020i
$365$	2.83259e8	+	4.90619e8i	0.304901	+	0.528104i
$366$	−2.44999e7	−	1.08465e9i	−0.0261204	−	1.15639i
$367$	−3.34593e8	−	5.79532e8i	−0.353334	−	0.611993i	0.633497	−	0.773745i	$-0.281619\pi$
$367$	−3.34593e8	−	5.79532e8i	−0.353334	−	0.611993i	−0.986831	+	0.161752i	$0.948285\pi$
$368$	7.52650e8	−	1.30363e9i	0.787274	−	1.36360i
$369$	−8.22184e8	−	1.28621e9i	−0.851877	−	1.33266i
$370$	2.04984e9			2.10385
$371$	−3.08107e7	−	4.12355e7i	−0.0313251	−	0.0419240i
$372$	−4.01223e7	−	1.77627e9i	−0.0404097	−	1.78900i
$373$	7.65518e8	−	1.32592e9i	0.763791	−	1.32292i	−0.177093	−	0.984194i	$-0.556669\pi$
$373$	7.65518e8	−	1.32592e9i	0.763791	−	1.32292i	0.940884	−	0.338730i	$-0.109997\pi$
$374$	−943568.			−0.000932659
$375$	−2.07547e7	−	9.18842e8i	−0.0203239	−	0.899770i
$376$	−2.76097e7			−0.0267858
$377$	5.22217e6			0.00501945
$378$	1.39273e9	+	4.89130e8i	1.32631	+	0.465804i
$379$	4.22507e7			0.0398654			0.0199327	−	0.999801i	$-0.493655\pi$
$379$	4.22507e7			0.0398654			0.0199327	+	0.999801i	$0.493655\pi$
$380$	−5.39229e8			−0.504117
$381$	−3.11008e7	−	1.37688e9i	−0.0288094	−	1.27543i
$382$	−2.59175e9			−2.37888
$383$	9.33011e8	−	1.61602e9i	0.848577	−	1.46978i	−0.0339013	−	0.999425i	$-0.510793\pi$
$383$	9.33011e8	−	1.61602e9i	0.848577	−	1.46978i	0.882478	−	0.470353i	$-0.155873\pi$
$384$	−1.68528e6	−	7.46098e7i	−0.00151884	−	0.0672414i
$385$	1.32331e6	−	3.08257e6i	0.00118182	−	0.00275296i
$386$	2.18782e9			1.93622
$387$	−9.54363e8	+	1.84021e9i	−0.837000	+	1.61391i
$388$	−1.68555e8	+	2.91945e8i	−0.146497	+	0.253741i
$389$	6.05977e8	+	1.04958e9i	0.521955	+	0.904052i	0.999674	+	0.0255392i	$0.00813027\pi$
$389$	6.05977e8	+	1.04958e9i	0.521955	+	0.904052i	−0.477719	+	0.878513i	$0.658536\pi$
$390$	−553920.	−	2.45229e7i	−0.000472848	−	0.0209337i
$391$	3.22345e8	+	5.58318e8i	0.272711	+	0.472349i
$392$	−2.76326e7	−	2.90848e7i	−0.0231697	−	0.0243873i
$393$	−6.54096e8	−	3.58197e8i	−0.543585	−	0.297679i
$394$	−5.54574e8			−0.456797
$395$	−1.77171e9	+	3.06869e9i	−1.44645	+	2.50532i
$396$	−1.21589e6	−	1.90211e6i	−0.000983920	−	0.00153923i
$397$	−8.71337e8	−	1.50920e9i	−0.698907	−	1.21054i	−0.968846	−	0.247665i	$-0.920337\pi$
$397$	−8.71337e8	−	1.50920e9i	−0.698907	−	1.21054i	0.269938	−	0.962878i	$-0.412997\pi$
$398$	−1.49046e9	+	2.58154e9i	−1.18503	+	2.05253i
$399$	−5.74059e7	−	4.05352e8i	−0.0452430	−	0.319468i
$400$	1.02319e9	+	1.77223e9i	0.799371	+	1.38455i
$401$	−1.78791e8	+	3.09674e8i	−0.138465	+	0.239828i	−0.926916	−	0.375270i	$-0.877550\pi$
$401$	−1.78791e8	+	3.09674e8i	−0.138465	+	0.239828i	0.788451	+	0.615098i	$0.210883\pi$
$402$	5.20030e7	+	2.30225e9i	0.0399243	+	1.76751i
$403$	−1.12078e7	−	1.94125e7i	−0.00853008	−	0.0147745i
$404$	−2.75036e8	−	4.76376e8i	−0.207517	−	0.359431i
$405$	8.98424e8	−	1.94222e9i	0.672030	−	1.45280i
$406$	6.12012e8	+	8.19087e8i	0.453857	+	0.607420i
$407$	1.19007e6	−	2.06125e6i	0.000874965	−	0.00151548i
$408$	1.43484e7	+	7.85748e6i	0.0104591	+	0.00572760i
$409$	−6.23692e8			−0.450753			−0.225376	−	0.974272i	$-0.572361\pi$
$409$	−6.23692e8			−0.450753			−0.225376	+	0.974272i	$0.572361\pi$
$410$	−4.96674e9			−3.55900
$411$	1.48826e9	−	9.04659e8i	1.05738	−	0.642745i
$412$	−6.62254e8	+	1.14706e9i	−0.466535	+	0.808062i
$413$	−6.56086e7	+	1.52831e8i	−0.0458285	+	0.106754i
$414$	−1.43765e9	+	2.77208e9i	−0.995755	+	1.92002i
$415$	−1.66931e9	−	2.89132e9i	−1.14648	−	1.98577i
$416$	9.59827e6	+	1.66247e7i	0.00653681	+	0.0113221i
$417$	7.06651e8	−	4.29548e8i	0.477231	−	0.290092i
$418$	−633790.	+	1.09776e6i	−0.000424452	+	0.000735172i
$419$	−6.38676e8	−	1.10622e9i	−0.424162	−	0.734670i	0.572180	−	0.820128i	$-0.306098\pi$
$419$	−6.38676e8	−	1.10622e9i	−0.424162	−	0.734670i	−0.996342	+	0.0854584i	$0.972765\pi$
$420$	1.86783e9	−	1.46249e9i	1.23017	−	0.963211i
$421$	7.07030e8	−	1.22461e9i	0.461796	−	0.799854i	−0.537254	−	0.843420i	$-0.680538\pi$
$421$	7.07030e8	−	1.22461e9i	0.461796	−	0.799854i	0.999051	+	0.0435658i	$0.0138718\pi$
$422$	−3.67938e8	−	6.37287e8i	−0.238331	−	0.412802i
$423$	1.23826e9	−	5.59678e7i	0.795462	−	0.0359540i
$424$	1.38159e6	−	2.39298e6i	0.000880235	−	0.00152461i
$425$	−8.76428e8			−0.553802
$426$	1.64640e7	+	7.28887e8i	0.0103182	+	0.456800i
$427$	5.22195e8	−	1.21642e9i	0.324590	−	0.756110i
$428$	−3.89943e8	−	6.75401e8i	−0.240407	−	0.416398i
$429$	−24981.0	−	13680.1i	−1.52760e−5	−	8.36543e-6i
$430$	3.37229e9	+	5.84097e9i	2.04543	+	3.54279i
$431$	6.61159e7	−	1.14516e8i	0.0397773	−	0.0688964i	−0.845451	−	0.534052i	$-0.820668\pi$
$431$	6.61159e7	−	1.14516e8i	0.0397773	−	0.0688964i	0.885229	+	0.465156i	$0.154002\pi$
$432$	1.16095e8	+	1.71089e9i	0.0692817	+	1.02101i
$433$	−2.24495e9			−1.32892			−0.664460	−	0.747324i	$-0.731338\pi$
$433$	−2.24495e9			−1.32892			−0.664460	+	0.747324i	$0.731338\pi$
$434$	1.73132e9	−	4.03298e9i	1.01663	−	2.36816i
$435$	1.26664e9	−	7.69949e8i	0.737806	−	0.448487i
$436$	2.16332e8	−	3.74698e8i	0.125002	−	0.216510i
$437$	8.66070e8			0.496441
$438$	8.26010e8	+	4.52340e8i	0.469706	+	0.257221i
$439$	1.62092e9			0.914401			0.457201	−	0.889364i	$-0.348852\pi$
$439$	1.62092e9			0.914401			0.457201	+	0.889364i	$0.348852\pi$
$440$	180076.			0.000100779
$441$	1.29824e9	+	1.24840e9i	0.720808	+	0.693135i
$442$	−8.41834e6			−0.00463712
$443$	1.24264e9			0.679098			0.339549	−	0.940588i	$-0.389725\pi$
$443$	1.24264e9			0.679098			0.339549	+	0.940588i	$0.389725\pi$
$444$	1.43828e9	−	8.74280e8i	0.779835	−	0.474035i
$445$	−3.68323e9			−1.98138
$446$	2.18902e9	−	3.79150e9i	1.16836	−	2.02367i
$447$	1.57678e9	+	8.63480e8i	0.835018	+	0.457273i
$448$	−7.14398e8	+	1.66414e9i	−0.375377	+	0.874414i
$449$	−2.73486e9			−1.42585			−0.712923	−	0.701242i	$-0.752629\pi$
$449$	−2.73486e9			−1.42585			−0.712923	+	0.701242i	$0.752629\pi$
$450$	−2.28643e9	−	3.57684e9i	−1.18281	−	1.85036i
$451$	−2.88351e6	+	4.99439e6i	−0.00148014	+	0.00256368i
$452$	8.95054e8	+	1.55028e9i	0.455895	+	0.789633i
$453$	−1.04559e9	+	6.35578e8i	−0.528467	+	0.321237i
$454$	1.59879e9	+	2.76919e9i	0.801857	+	1.38886i
$455$	1.18064e7	−	2.75021e7i	0.00587592	−	0.0136876i
$456$	1.87792e7	−	1.14152e7i	0.00927470	−	0.00563777i
$457$	2.96663e9			1.45397			0.726986	−	0.686652i	$-0.240920\pi$
$457$	2.96663e9			1.45397			0.726986	+	0.686652i	$0.240920\pi$
$458$	−8.41964e8	+	1.45832e9i	−0.409510	+	0.709292i
$459$	−6.59433e8	−	3.23311e8i	−0.318292	−	0.156054i
$460$	2.50925e9	+	4.34614e9i	1.20196	+	2.08186i
$461$	1.24974e9	−	2.16461e9i	0.594109	−	1.02903i	−0.399563	−	0.916706i	$-0.630838\pi$
$461$	1.24974e9	−	2.16461e9i	0.594109	−	1.02903i	0.993672	−	0.112321i	$-0.0358286\pi$
$462$	−781949.	−	5.52146e6i	−0.000368919	−	0.00260500i
$463$	8.69737e8	+	1.50643e9i	0.407244	+	0.705367i	0.994580	−	0.103976i	$-0.0331565\pi$
$463$	8.69737e8	+	1.50643e9i	0.407244	+	0.705367i	−0.587336	+	0.809343i	$0.699823\pi$
$464$	−5.93912e8	+	1.02869e9i	−0.276000	+	0.478046i
$465$	−5.58062e9	−	3.05607e9i	−2.57393	−	1.40954i
$466$	−1.53151e9	−	2.65266e9i	−0.701083	−	1.21431i
$467$	−2.03516e9	−	3.52500e9i	−0.924676	−	1.60159i	−0.792082	−	0.610415i	$-0.791003\pi$
$467$	−2.03516e9	−	3.52500e9i	−0.924676	−	1.60159i	−0.132594	−	0.991170i	$-0.542331\pi$
$468$	−1.08479e7	−	1.69703e7i	−0.00489199	−	0.00765294i
$469$	−1.10840e9	+	2.58194e9i	−0.496126	+	1.15569i
$470$	2.01645e9	−	3.49259e9i	0.895869	−	1.55169i
$471$	2.78350e7	+	1.23230e9i	0.0122749	+	0.543428i
$472$	−8.92797e6			−0.00390801
$473$	7.83131e6			0.00340268
$474$	1.33019e8	+	5.88893e9i	0.0573705	+	2.53987i
$475$	−5.88692e8	+	1.01964e9i	−0.252035	+	0.436537i
$476$	−4.87321e8	−	6.52206e8i	−0.207105	−	0.277179i
$477$	−5.71115e7	+	1.10123e8i	−0.0240940	+	0.0464582i
$478$	1.92137e9	+	3.32792e9i	0.804664	+	1.39372i
$479$	−5.87978e8	−	1.01841e9i	−0.244448	−	0.423397i	0.717528	−	0.696530i	$-0.245273\pi$
$479$	−5.87978e8	−	1.01841e9i	−0.244448	−	0.423397i	−0.961976	+	0.273133i	$0.911940\pi$
$480$	4.77919e9	+	2.61719e9i	1.97247	+	1.08017i
$481$	1.06176e7	−	1.83901e7i	0.00435027	−	0.00753490i
$482$	1.60770e9	+	2.78461e9i	0.653942	+	1.13266i
$483$	−2.99997e9	+	2.34895e9i	−1.21144	+	0.948546i
$484$	1.21733e9	−	2.10848e9i	0.488033	−	0.845299i
$485$	6.03609e8	+	1.04548e9i	0.240248	+	0.416121i
$486$	−4.00846e8	−	3.53471e9i	−0.158398	−	1.39677i
$487$	1.96818e9	−	3.40900e9i	0.772173	−	1.33744i	−0.164197	−	0.986428i	$-0.552503\pi$
$487$	1.96818e9	−	3.40900e9i	0.772173	−	1.33744i	0.936370	−	0.351015i	$-0.114163\pi$
$488$	7.10600e7			0.0276793
$489$	−1.90746e9	+	1.15948e9i	−0.737691	+	0.448417i
$490$	5.69730e9	−	1.37130e9i	2.18768	−	0.526559i
$491$	1.76295e9	+	3.05351e9i	0.672131	+	1.16416i	0.977299	+	0.211866i	$0.0679541\pi$
$491$	1.76295e9	+	3.05351e9i	0.672131	+	1.16416i	−0.305168	+	0.952299i	$0.598713\pi$
$492$	−3.48493e9	+	2.11837e9i	−1.31922	+	0.801906i
$493$	−2.54361e8	−	4.40566e8i	−0.0956062	−	0.165595i
$494$	−5.65455e6	+	9.79397e6i	−0.00211035	+	0.00365523i
$495$	−8.07614e6	+	365033.i	−0.00299285	+	0.000135274i
$496$	5.09862e9			1.87615
$497$	−3.50917e8	+	8.17437e8i	−0.128220	+	0.298681i
$498$	−4.86785e9	−	2.66574e9i	−1.76618	−	0.967196i
$499$	−1.88907e9	+	3.27197e9i	−0.680608	+	1.17885i	0.294187	+	0.955748i	$0.404951\pi$
$499$	−1.88907e9	+	3.27197e9i	−0.680608	+	1.17885i	−0.974796	+	0.223100i	$0.928382\pi$
$500$	−2.45538e9			−0.878462
$501$	−7.08921e8	+	4.30929e8i	−0.251864	+	0.153099i
$502$	7.93726e8			0.280032
$503$	−1.03897e9			−0.364012			−0.182006	−	0.983297i	$-0.558259\pi$
$503$	−1.03897e9			−0.364012			−0.182006	+	0.983297i	$0.558259\pi$
$504$	−3.40887e7	+	9.04738e7i	−0.0118605	+	0.0314786i
$505$	−1.96985e9			−0.680635
$506$	1.17971e7			0.00404807
$507$	2.57358e9	+	1.40934e9i	0.877020	+	0.480274i
$508$	−3.67936e9			−1.24523
$509$	1.35294e9	−	2.34335e9i	0.454742	−	0.787636i	−0.543932	−	0.839130i	$-0.683065\pi$
$509$	1.35294e9	−	2.34335e9i	0.454742	−	0.787636i	0.998673	+	0.0514938i	$0.0163983\pi$
$510$	−2.04188e9	+	1.24119e9i	−0.681608	+	0.414326i
$511$	6.87792e8	+	9.20506e8i	0.228026	+	0.305178i
$512$	−4.26186e9			−1.40331
$513$	−8.19080e8	+	5.50024e8i	−0.267865	+	0.179875i
$514$	3.62828e9	−	6.28437e9i	1.17850	−	2.04122i
$515$	2.37159e9	+	4.10771e9i	0.765093	+	1.32518i
$516$	4.85741e9	+	2.66002e9i	1.55643	+	0.852336i
$517$	−2.34136e6	−	4.05535e6i	−0.000745161	−	0.00129066i
$518$	4.12879e9	−	4.89891e8i	1.30517	−	0.154862i
$519$	−6.83955e6	−	3.02797e8i	−0.00214754	−	0.0950748i
$520$	1.60660e6			0.000501068
$521$	1.53215e9	−	2.65376e9i	0.474645	−	0.822109i	−0.524934	−	0.851143i	$-0.675910\pi$
$521$	1.53215e9	−	2.65376e9i	0.474645	−	0.822109i	0.999578	+	0.0290343i	$0.00924322\pi$
$522$	1.13444e9	−	2.18744e9i	0.349089	−	0.673114i
$523$	−1.16267e9	−	2.01380e9i	−0.355385	−	0.615545i	0.631799	−	0.775133i	$-0.282317\pi$
$523$	−1.16267e9	−	2.01380e9i	−0.355385	−	0.615545i	−0.987184	+	0.159587i	$0.948984\pi$
$524$	−9.96165e8	+	1.72541e9i	−0.302463	+	0.523881i
$525$	−7.26308e8	−	5.12857e9i	−0.219060	−	1.54682i
$526$	−3.15830e9	−	5.47033e9i	−0.946244	−	1.63894i
$527$	−1.09182e9	+	1.89109e9i	−0.324948	+	0.562826i
$528$	5.53583e6	−	3.36504e6i	0.00163668	−	0.000994882i
$529$	−2.32775e9	−	4.03178e9i	−0.683661	−	1.18414i
$530$	2.01806e8	+	3.49539e8i	0.0588802	+	0.101983i
$531$	4.00407e8	−	1.80980e7i	0.116057	−	0.00524564i
$532$	−1.08611e9	+	1.28870e8i	−0.312741	+	0.0371075i
$533$	−2.57262e7	+	4.45590e7i	−0.00735918	+	0.0127465i
$534$	−5.23206e9	+	3.18039e9i	−1.48689	+	0.903827i
$535$	−2.79284e9			−0.788511
$536$	−1.50830e8			−0.0423070
$537$	2.72259e9	+	1.49095e9i	0.758704	+	0.415482i
$538$	1.81503e9	−	3.14372e9i	0.502511	−	0.870375i
$539$	1.92871e6	−	6.52514e6i	0.000530526	−	0.00179486i
$540$	−5.13325e9	−	2.51676e9i	−1.40286	−	0.687803i
$541$	−3.85199e8	−	6.67185e8i	−0.104591	−	0.181157i	0.808980	−	0.587836i	$-0.200020\pi$
$541$	−3.85199e8	−	6.67185e8i	−0.104591	−	0.181157i	−0.913571	+	0.406679i	$0.866687\pi$
$542$	−4.98882e9	−	8.64089e9i	−1.34586	−	2.33110i
$543$	6.76350e7	+	2.99430e9i	0.0181289	+	0.802594i
$544$	9.35023e8	−	1.61951e9i	0.249015	−	0.431307i
$545$	−7.74703e8	−	1.34182e9i	−0.204997	−	0.355065i
$546$	−6.97640e6	−	4.92614e7i	−0.00183424	−	0.0129519i
$547$	1.59560e9	−	2.76366e9i	0.416838	−	0.721985i	−0.578781	−	0.815483i	$-0.696471\pi$
$547$	1.59560e9	−	2.76366e9i	0.416838	−	0.721985i	0.995619	+	0.0934977i	$0.0298048\pi$
$548$	−2.32646e9	−	4.02954e9i	−0.603897	−	1.04598i
$549$	−3.18694e9	+	1.44046e8i	−0.821998	+	0.0371534i
$550$	−8.01880e6	+	1.38890e7i	−0.00205513	+	0.00355960i
$551$	−6.83411e8			−0.174041
$552$	−1.79393e8	−	9.82391e7i	−0.0453960	−	0.0248598i
$553$	−2.83518e9	+	6.60436e9i	−0.712924	+	1.66071i
$554$	1.65159e9	+	2.86064e9i	0.412684	+	0.714790i
$555$	−1.36115e8	−	6.02599e9i	−0.0337971	−	1.49625i
$556$	−1.10464e9	−	1.91330e9i	−0.272559	−	0.472086i
$557$	−8.58889e8	+	1.48764e9i	−0.210593	+	0.364758i	−0.951900	−	0.306408i	$-0.900873\pi$
$557$	−8.58889e8	+	1.48764e9i	−0.210593	+	0.364758i	0.741307	+	0.671166i	$0.234206\pi$
$558$	−1.05662e10	+	4.77579e8i	−2.57453	+	0.116366i
$559$	6.98695e7			0.0169179
$560$	4.07476e9	+	5.45346e9i	0.980492	+	1.31224i
$561$	62655.2	+	2.77384e6i	1.49826e−5	+	0.000663301i
$562$	1.79336e7	−	3.10618e7i	0.00426176	−	0.00738159i
$563$	7.71493e9			1.82202			0.911009	−	0.412387i	$-0.135305\pi$
$563$	7.71493e9			1.82202			0.911009	+	0.412387i	$0.135305\pi$
$564$	−7.47801e7	−	3.31062e9i	−0.0175513	−	0.777021i
$565$	6.41053e9			1.49529
$566$	−1.17419e9			−0.272195
$567$	1.34543e9	−	4.12672e9i	0.309971	−	0.950746i
$568$	−4.77526e7			−0.0109340
$569$	3.70736e9			0.843669			0.421835	−	0.906673i	$-0.361386\pi$
$569$	3.70736e9			0.843669			0.421835	+	0.906673i	$0.361386\pi$
$570$	7.24901e7	+	3.20924e9i	0.0163952	+	0.725839i
$571$	−1.65785e8			−0.0372666			−0.0186333	−	0.999826i	$-0.505932\pi$
$571$	−1.65785e8			−0.0372666			−0.0186333	+	0.999826i	$0.505932\pi$
$572$	−38045.1	+	65896.0i	−8.49988e−6	+	1.47222e-5i
$573$	1.72099e8	+	7.61906e9i	0.0382152	+	1.69184i
$574$	−1.00040e10	+	1.18700e9i	−2.20791	+	0.261974i
$575$	1.09576e10			2.40370
$576$	4.35995e9	−	1.97065e8i	0.950611	−	0.0429666i
$577$	−3.41897e8	+	5.92184e8i	−0.0740935	+	0.128334i	−0.900692	−	0.434459i	$-0.856940\pi$
$577$	−3.41897e8	+	5.92184e8i	−0.0740935	+	0.128334i	0.826598	+	0.562793i	$0.190273\pi$
$578$	−2.85297e9	−	4.94149e9i	−0.614540	−	1.06441i
$579$	−1.45276e8	−	6.43159e9i	−0.0311042	−	1.37703i
$580$	−1.98003e9	−	3.42952e9i	−0.421380	−	0.729852i
$581$	−4.05330e9	−	5.42474e9i	−0.857417	−	1.14753i
$582$	1.76018e9	+	9.63911e8i	0.370106	+	0.202678i
$583$	468646.			9.79501e−5
$584$	−3.08414e7	+	5.34189e7i	−0.00640752	+	0.0110981i
$585$	−7.20538e7	+	3.25675e6i	−0.0148803	+	0.000672573i
$586$	−7.61791e8	−	1.31946e9i	−0.156385	−	0.270866i
$587$	−4.18507e9	+	7.24875e9i	−0.854022	+	1.47921i	0.0235269	+	0.999723i	$0.492510\pi$
$587$	−4.18507e9	+	7.24875e9i	−0.854022	+	1.47921i	−0.877549	+	0.479487i	$0.840823\pi$
$588$	3.41265e9	−	3.39214e9i	0.692263	−	0.688102i
$589$	1.46674e9	+	2.54046e9i	0.295766	+	0.512282i
$590$	6.52046e8	−	1.12938e9i	0.130706	−	0.226390i
$591$	3.68251e7	+	1.63030e9i	0.00733816	+	0.324871i
$592$	2.41505e9	+	4.18299e9i	0.478410	+	0.828630i
$593$	−1.82985e9	−	3.16940e9i	−0.360350	−	0.624145i	0.627668	−	0.778481i	$-0.284009\pi$
$593$	−1.82985e9	−	3.16940e9i	−0.360350	−	0.624145i	−0.988018	+	0.154336i	$0.950676\pi$
$594$	−1.11570e7	+	7.49210e6i	−0.00218422	+	0.00146673i
$595$	−2.89526e9	+	3.43530e8i	−0.563481	+	0.0668584i
$596$	2.40139e9	−	4.15932e9i	0.464622	−	0.804749i
$597$	7.68801e9	+	4.21012e9i	1.47878	+	0.809811i
$598$	1.05251e8			0.0201267
$599$	−2.27517e9			−0.432533			−0.216267	−	0.976334i	$-0.569388\pi$
$599$	−2.27517e9			−0.432533			−0.216267	+	0.976334i	$0.569388\pi$
$600$	2.37597e8	−	1.44427e8i	0.0449068	−	0.0272973i
$601$	2.19860e9	−	3.80809e9i	0.413130	−	0.715561i	−0.582101	−	0.813117i	$-0.697769\pi$
$601$	2.19860e9	−	3.80809e9i	0.413130	−	0.715561i	0.995230	+	0.0975555i	$0.0311023\pi$
$602$	8.18837e9	+	1.09589e10i	1.52971	+	2.04729i
$603$	6.76453e9	−	3.05749e8i	1.25640	−	0.0567878i
$604$	1.63448e9	+	2.83100e9i	0.301821	+	0.522770i
$605$	−4.35937e9	−	7.55064e9i	−0.800349	−	1.38625i
$606$	−2.79819e9	+	1.70093e9i	−0.510768	+	0.310478i
$607$	9.78583e8	−	1.69496e9i	0.177598	−	0.307608i	−0.763460	−	0.645856i	$-0.776501\pi$
$607$	9.78583e8	−	1.69496e9i	0.177598	−	0.307608i	0.941057	+	0.338248i	$0.109834\pi$
$608$	−1.25610e9	−	2.17563e9i	−0.226653	−	0.392575i
$609$	2.36726e9	−	1.85354e9i	0.424703	−	0.332538i
$610$	−5.18980e9	+	8.98899e9i	−0.925755	+	1.60345i
$611$	−2.08891e7	−	3.61810e7i	−0.00370490	−	0.00641707i
$612$	−9.03311e8	+	1.74177e9i	−0.159297	+	0.307157i
$613$	2.40688e8	−	4.16884e8i	0.0422030	−	0.0730977i	−0.844152	−	0.536103i	$-0.819896\pi$
$613$	2.40688e8	−	4.16884e8i	0.0422030	−	0.0730977i	0.886355	+	0.463006i	$0.153229\pi$
$614$	5.71252e9			0.995952
$615$	3.29803e8	+	1.46009e10i	0.0571732	+	2.53114i
$616$	362707.	−	43036.1i	6.25207e−5	−	7.41824e-6i
$617$	2.23827e9	+	3.87679e9i	0.383631	+	0.664468i	0.991578	−	0.129509i	$-0.0413401\pi$
$617$	2.23827e9	+	3.87679e9i	0.383631	+	0.664468i	−0.607947	+	0.793977i	$0.708007\pi$
$618$	6.91578e9	+	3.78722e9i	1.17864	+	0.645448i
$619$	3.47973e9	+	6.02707e9i	0.589697	+	1.02138i	0.994272	+	0.106880i	$0.0340860\pi$
$619$	3.47973e9	+	6.02707e9i	0.589697	+	1.02138i	−0.404575	+	0.914505i	$0.632581\pi$
$620$	−8.49909e9	+	1.47209e10i	−1.43219	+	2.48063i
$621$	8.24464e9	+	4.04224e9i	1.38150	+	0.677331i
$622$	−7.23928e9			−1.20623
$623$	−7.41874e9	+	8.80252e8i	−1.22920	+	0.145847i
$624$	4.93897e7	−	3.00223e7i	0.00813748	−	0.00494649i
$625$	3.71155e8	−	6.42860e8i	0.0608101	−	0.105326i
$626$	3.90444e9			0.636135
$627$	3.26919e6	+	1.79028e6i	0.000529668	+	0.000290057i
$628$	3.29300e9			0.530559
$629$	−2.06863e9			−0.331441
$630$	−8.95518e9	−	1.09198e10i	−1.42686	−	1.73990i
$631$	1.51928e9			0.240732			0.120366	−	0.992730i	$-0.461593\pi$
$631$	1.51928e9			0.240732			0.120366	+	0.992730i	$0.461593\pi$
$632$	−3.85810e8			−0.0607944
$633$	−1.84902e9	+	1.12395e9i	−0.289753	+	0.176131i
$634$	−2.09318e9			−0.326208
$635$	−6.58805e9	+	1.14108e10i	−1.02105	+	1.76852i
$636$	2.90680e8	+	1.59182e8i	0.0448038	+	0.0245355i
$637$	1.72076e7	−	5.82161e7i	0.00263774	−	0.00892391i
$638$	−9.30901e6			−0.00141916
$639$	2.14164e9	−	9.67996e7i	0.324708	−	0.0146764i
$640$	−3.56992e8	+	6.18328e8i	−0.0538305	+	0.0932372i
$641$	7.10715e8	+	1.23100e9i	0.106584	+	0.184609i	0.914384	−	0.404847i	$-0.132675\pi$
$641$	7.10715e8	+	1.23100e9i	0.106584	+	0.184609i	−0.807800	+	0.589456i	$0.799342\pi$
$642$	−3.96725e9	+	2.41155e9i	−0.591721	+	0.359687i
$643$	1.47619e9	+	2.55684e9i	0.218980	+	0.379285i	0.954496	−	0.298222i	$-0.0963937\pi$
$643$	1.47619e9	+	2.55684e9i	0.218980	+	0.379285i	−0.735516	+	0.677507i	$0.763060\pi$
$644$	6.09279e9	+	8.15429e9i	0.898909	+	1.20306i
$645$	1.69470e10	−	1.03015e10i	2.48675	−	1.51161i
$646$	1.10169e9			0.160784
$647$	−1.02949e9	+	1.78314e9i	−0.149437	+	0.258833i	−0.931020	−	0.364969i	$-0.881080\pi$
$647$	−1.02949e9	+	1.78314e9i	−0.149437	+	0.258833i	0.781582	+	0.623802i	$0.214413\pi$
$648$	2.32049e8	−	2.10197e7i	0.0335017	−	0.00303468i
$649$	−757109.	−	1.31135e6i	−0.000108718	−	0.000188305i
$650$	−7.15423e7	+	1.23915e8i	−0.0102180	+	0.0176981i
$651$	−1.19708e10	−	4.82180e9i	−1.70056	−	0.684977i
$652$	2.98176e9	+	5.16457e9i	0.421315	+	0.729739i
$653$	1.21478e9	−	2.10407e9i	0.170727	−	0.295708i	−0.767947	−	0.640513i	$-0.778722\pi$
$653$	1.21478e9	−	2.10407e9i	0.170727	−	0.295708i	0.938674	+	0.344805i	$0.112055\pi$
$654$	−2.25911e9	−	1.23713e9i	−0.315802	−	0.172940i
$655$	3.56736e9	+	6.17884e9i	0.496023	+	0.859137i
$656$	−5.85163e9	−	1.01353e10i	−0.809307	−	1.40176i
$657$	1.27491e9	−	2.45828e9i	0.175388	−	0.338184i
$658$	3.22683e9	−	7.51667e9i	0.441555	−	1.02857i
$659$	2.22166e9	−	3.84802e9i	0.302397	−	0.523768i	−0.674281	−	0.738475i	$-0.735546\pi$
$659$	2.22166e9	−	3.84802e9i	0.302397	−	0.523768i	0.976678	+	0.214707i	$0.0688797\pi$
$660$	487729.	+	2.15925e7i	6.60352e−5	+	0.00292347i
$661$	2.30412e9			0.310313			0.155157	−	0.987890i	$-0.450412\pi$
$661$	2.30412e9			0.310313			0.155157	+	0.987890i	$0.450412\pi$
$662$	5.80753e9			0.778016
$663$	558998.	+	2.47477e7i	7.44926e−5	+	0.00329789i
$664$	1.81755e8	−	3.14809e8i	0.0240934	−	0.0417310i
$665$	−1.54507e9	+	3.59912e9i	−0.203738	+	0.474593i
$666$	−5.39666e9	−	8.44243e9i	−0.707889	−	1.10741i
$667$	3.18018e9	+	5.50823e9i	0.414964	+	0.718739i
$668$	1.10819e9	+	1.91945e9i	0.143846	+	0.249149i
$669$	−1.12913e10	−	6.18337e9i	−1.45799	−	0.798425i
$670$	1.10158e10	−	1.90799e10i	1.41499	−	2.45083i
$671$	6.02602e6	+	1.04374e7i	0.000770019	+	0.00133371i
$672$	1.02517e10	+	4.12935e9i	1.30318	+	0.524915i
$673$	−3.59016e9	+	6.21833e9i	−0.454005	+	0.786360i	−0.998630	−	0.0523196i	$-0.983339\pi$
$673$	−3.59016e9	+	6.21833e9i	−0.454005	+	0.786360i	0.544625	+	0.838679i	$0.316672\pi$
$674$	−5.67434e9	−	9.82825e9i	−0.713848	−	1.23642i
$675$	−1.03631e10	+	6.95899e9i	−1.29696	+	0.870929i
$676$	3.91947e9	−	6.78871e9i	0.487993	−	0.845228i
$677$	−4.92958e9			−0.610590			−0.305295	−	0.952258i	$-0.598755\pi$
$677$	−4.92958e9			−0.610590			−0.305295	+	0.952258i	$0.598755\pi$
$678$	9.10621e9	−	5.53535e9i	1.12211	−	0.682089i
$679$	1.46564e9	+	1.96155e9i	0.179674	+	0.240466i
$680$	−7.82542e7	−	1.35540e8i	−0.00954391	−	0.0165305i
$681$	8.03452e9	−	4.88390e9i	0.974866	−	0.592587i
$682$	1.99790e7	+	3.46047e7i	0.00241173	+	0.00417724i
$683$	−6.50914e9	+	1.12742e10i	−0.781719	+	1.35398i	0.149220	+	0.988804i	$0.452324\pi$
$683$	−6.50914e9	+	1.12742e10i	−0.781719	+	1.35398i	−0.930939	+	0.365174i	$0.881010\pi$
$684$	1.41964e9	+	2.22086e9i	0.169622	+	0.265353i
$685$	−1.66625e10			−1.98072
$686$	1.11477e10	−	4.12367e9i	1.31842	−	0.487696i
$687$	4.34299e9	+	2.37831e9i	0.511023	+	0.279847i
$688$	−7.94620e9	+	1.37632e10i	−0.930251	+	1.61124i
$689$	4.18117e6			0.000487002
$690$	2.55289e10	−	1.55181e10i	2.95842	−	1.79832i
$691$	1.18841e9			0.137022			0.0685112	−	0.997650i	$-0.478175\pi$
$691$	1.18841e9			0.137022			0.0685112	+	0.997650i	$0.478175\pi$
$692$	−8.09149e8			−0.0928234
$693$	−1.61797e7	+	2.66536e6i	−0.00184673	+	0.000304221i
$694$	−1.65093e10			−1.87486
$695$	−7.91166e9			−0.893965
$696$	1.41558e8	+	7.75199e7i	0.0159148	+	0.00871527i
$697$	5.01227e9			0.560686
$698$	−6.88651e9	+	1.19278e10i	−0.766487	+	1.32760i
$699$	−7.69640e9	+	4.67837e9i	−0.852349	+	0.518113i
$700$	−1.37417e10	+	1.63048e9i	−1.51425	+	0.179669i
$701$	−4.01569e9			−0.440299			−0.220149	−	0.975466i	$-0.570655\pi$
$701$	−4.01569e9			−0.440299			−0.220149	+	0.975466i	$0.570655\pi$
$702$	−9.95409e7	+	6.68431e7i	−0.0108598	+	0.00729250i
$703$	−1.38949e9	+	2.40667e9i	−0.150838	+	0.261260i
$704$	−8.24400e6	−	1.42790e7i	−0.000890500	−	0.00154239i
$705$	−1.04012e10	−	5.69590e9i	−1.11794	−	0.612210i
$706$	−5.81122e9	−	1.00653e10i	−0.621514	−	1.07649i
$707$	−3.96767e9	+	4.70774e8i	−0.422248	+	0.0501008i
$708$	−2.41811e7	−	1.07053e9i	−0.00256071	−	0.113366i
$709$	2.02799e8			0.0213699			0.0106850	−	0.999943i	$-0.496599\pi$
$709$	2.02799e8			0.0213699			0.0106850	+	0.999943i	$0.496599\pi$
$710$	3.48756e9	−	6.04064e9i	0.365694	−	0.633401i
$711$	1.73030e10	−	7.82078e8i	1.80542	−	0.0816030i
$712$	−2.00516e8	−	3.47304e8i	−0.0208195	−	0.0360604i
$713$	1.36506e10	−	2.36435e10i	1.41039	−	2.44286i
$714$	−3.81611e9	+	2.98798e9i	−0.392354	+	0.307209i
$715$	136243.	+	235980.i	1.39394e−5	+	2.41437e-5i
$716$	4.14641e9	−	7.18179e9i	0.422159	−	0.731201i
$717$	9.65560e9	−	5.86930e9i	0.978278	−	0.594661i
$718$	−1.02517e10	−	1.77564e10i	−1.03361	−	1.79027i
$719$	6.72725e9	+	1.16519e10i	0.674973	+	1.16909i	0.976477	+	0.215622i	$0.0691779\pi$
$719$	6.72725e9	+	1.16519e10i	0.674973	+	1.16909i	−0.301504	+	0.953465i	$0.597489\pi$
$720$	7.55309e9	−	1.45639e10i	0.754155	−	1.45416i
$721$	5.75854e9	+	7.70695e9i	0.572188	+	0.765789i
$722$	−6.36807e9	+	1.10298e10i	−0.629691	+	1.09066i
$723$	8.07925e9	−	4.91109e9i	0.795036	−	0.483275i
$724$	8.00152e9			0.783587
$725$	−8.64662e9			−0.842681
$726$	−1.27123e10	−	6.96153e9i	−1.23295	−	0.675191i
$727$	1.20757e9	−	2.09158e9i	0.116558	−	0.201885i	−0.801843	−	0.597534i	$-0.796147\pi$
$727$	1.20757e9	−	2.09158e9i	0.116558	−	0.201885i	0.918402	+	0.395649i	$0.129480\pi$
$728$	3.23601e6	−	383960.i	0.000310849	−	3.68830e-5i
$729$	−1.03645e10	+	1.41309e9i	−0.990833	+	0.135090i
$730$	−4.50495e9	−	7.80280e9i	−0.428608	−	0.742370i
$731$	−3.40320e9	−	5.89451e9i	−0.322238	−	0.558132i
$732$	1.92464e8	+	8.52065e9i	0.0181368	+	0.802942i
$733$	1.30163e7	−	2.25449e7i	0.00122074	−	0.00211439i	−0.865414	−	0.501057i	$-0.832945\pi$
$733$	1.30163e7	−	2.25449e7i	0.00122074	−	0.00211439i	0.866635	+	0.498942i	$0.166278\pi$
$734$	5.32137e9	+	9.21688e9i	0.496692	+	0.860295i
$735$	−4.40958e9	−	1.66575e10i	−0.409630	−	1.54740i
$736$	−1.16902e10	+	2.02481e10i	−1.08081	+	1.87203i
$737$	−1.27907e7	−	2.21541e7i	−0.00117695	−	0.00203854i
$738$	1.30760e10	+	2.04559e10i	1.19751	+	1.87336i
$739$	1.00421e10	−	1.73934e10i	0.915312	−	1.58537i	0.108867	−	0.994056i	$-0.465278\pi$
$739$	1.00421e10	−	1.73934e10i	0.915312	−	1.58537i	0.806444	−	0.591310i	$-0.201389\pi$
$740$	−1.61030e10			−1.46081
$741$	2.91671e7	+	1.59725e7i	0.00263348	+	0.00144215i
$742$	4.90013e8	+	6.55809e8i	0.0440346	+	0.0589337i
$743$	−4.25927e9	−	7.37727e9i	−0.380955	−	0.659834i	0.610244	−	0.792214i	$-0.291072\pi$
$743$	−4.25927e9	−	7.37727e9i	−0.380955	−	0.659834i	−0.991199	+	0.132380i	$0.957738\pi$
$744$	−1.56442e7	−	6.92590e8i	−0.00139267	−	0.0616553i
$745$	−8.59957e9	−	1.48949e10i	−0.761956	−	1.31975i
$746$	−1.21748e10	+	2.10873e10i	−1.07368	+	1.85967i
$747$	−7.51331e9	+	1.44872e10i	−0.659491	+	1.27163i
$748$	7.41239e6			0.000647594
$749$	−5.62532e9	+	6.67458e8i	−0.489171	+	0.0580414i
$750$	3.30083e8	+	1.46133e10i	0.0285699	+	1.26483i
$751$	−1.10056e9	+	1.90622e9i	−0.0948141	+	0.164223i	−0.909531	−	0.415636i	$-0.863559\pi$
$751$	−1.10056e9	+	1.90622e9i	−0.0948141	+	0.164223i	0.814717	+	0.579859i	$0.196892\pi$
$752$	9.50281e9			0.814873
$753$	−5.27053e7	−	2.33334e9i	−0.00449854	−	0.199157i
$754$	−8.30533e7			−0.00705598
$755$	1.17064e10			0.989942
$756$	−1.09408e10	−	3.84246e9i	−0.920926	−	0.323432i
$757$	−2.99424e9			−0.250871			−0.125436	−	0.992102i	$-0.540033\pi$
$757$	−2.99424e9			−0.250871			−0.125436	+	0.992102i	$0.540033\pi$
$758$	−6.71954e8			−0.0560399
$759$	−783354.	−	3.46802e7i	−6.50297e−5	−	0.00287896i
$760$	−2.10252e8			−0.0173737
$761$	1.71934e9	−	2.97799e9i	0.141422	−	0.244950i	−0.786610	−	0.617450i	$-0.788166\pi$
$761$	1.71934e9	−	2.97799e9i	0.141422	−	0.244950i	0.928032	+	0.372500i	$0.121499\pi$
$762$	4.94626e8	+	2.18978e10i	0.0404981	+	1.79291i
$763$	−1.88108e9	−	2.51755e9i	−0.153311	−	0.205183i
$764$	2.03600e10			1.65178
$765$	3.78435e9	+	5.92016e9i	0.305616	+	0.478100i
$766$	−1.48386e10	+	2.57012e10i	−1.19287	+	2.06611i
$767$	−6.75478e6	−	1.16996e7i	−0.000540540	−	0.000936242i
$768$	2.96561e8	+	1.31292e10i	0.0236238	+	1.04586i
$769$	4.71655e9	+	8.16930e9i	0.374009	+	0.647803i	0.990178	−	0.139811i	$-0.0446496\pi$
$769$	4.71655e9	+	8.16930e9i	0.374009	+	0.647803i	−0.616169	+	0.787614i	$0.711316\pi$
$770$	−2.10460e7	+	4.90251e7i	−0.00166131	+	0.00386991i
$771$	−1.87153e10	−	1.02489e10i	−1.47064	−	0.805352i
$772$	−1.71868e10			−1.34442
$773$	6.46521e9	−	1.11981e10i	0.503448	−	0.871997i	−0.496544	−	0.868011i	$-0.665398\pi$
$773$	6.46521e9	−	1.11981e10i	0.503448	−	0.871997i	0.999992	−	0.00398581i	$-0.00126873\pi$
$774$	1.51782e10	−	2.92666e10i	1.17659	−	2.26871i
$775$	1.85574e10	+	3.21423e10i	1.43206	+	2.48040i
$776$	−6.57213e7	+	1.13833e8i	−0.00504882	+	0.00874482i
$777$	−1.71431e9	−	1.21050e10i	−0.131104	−	0.925744i
$778$	−9.63746e9	−	1.66926e10i	−0.733726	−	1.27085i
$779$	3.36671e9	−	5.83132e9i	0.255167	−	0.441963i
$780$	4.35143e6	+	1.92644e8i	0.000328323	+	0.0145353i
$781$	−4.04951e6	−	7.01396e6i	−0.000304175	−	0.000526847i
$782$	−5.12657e9	−	8.87949e9i	−0.383357	−	0.663994i
$783$	−6.50580e9	−	3.18971e9i	−0.484322	−	0.237457i
$784$	9.51068e9	+	1.00105e10i	0.704864	+	0.741908i
$785$	5.89627e9	−	1.02126e10i	0.435044	−	0.753519i
$786$	1.04027e10	+	5.69676e9i	0.764133	+	0.418455i
$787$	−1.16844e10			−0.854466			−0.427233	−	0.904142i	$-0.640512\pi$
$787$	−1.16844e10			−0.854466			−0.427233	+	0.904142i	$0.640512\pi$
$788$	4.35657e9			0.317178
$789$	−1.58716e10	+	9.64779e9i	−1.15041	+	0.699292i
$790$	2.81773e10	−	4.88044e10i	2.03331	−	3.52180i
$791$	1.29121e10	−	1.53205e9i	0.927637	−	0.110066i
$792$	−474088.	−	741655.i	−3.39095e−5	−	5.30473e-5i
$793$	5.37630e7	+	9.31203e7i	0.00382849	+	0.00663114i
$794$	1.38577e10	+	2.40023e10i	0.982473	+	1.70169i
$795$	1.01415e9	−	6.16466e8i	0.0715841	−	0.0435135i
$796$	1.17086e10	−	2.02798e10i	0.822826	−	1.42518i
$797$	7.69557e9	+	1.33291e10i	0.538439	+	0.932604i	0.998988	+	0.0449698i	$0.0143192\pi$
$797$	7.69557e9	+	1.33291e10i	0.538439	+	0.932604i	−0.460549	+	0.887634i	$0.652348\pi$
$798$	9.12983e8	+	6.44671e9i	0.0635993	+	0.449085i
$799$	−2.03493e9	+	3.52461e9i	−0.141136	+	0.244454i
$800$	−1.58924e10	−	2.75264e10i	−1.09742	−	1.90079i
$801$	9.69690e9	+	1.51696e10i	0.666682	+	1.04295i
$802$	2.84348e9	−	4.92506e9i	0.194644	−	0.337133i
$803$	−1.04616e7			−0.000713010
$804$	−4.08520e8	−	1.80858e10i	−0.0277215	−	1.22727i
$805$	3.61984e10	−	4.29503e9i	2.44570	−	0.290189i
$806$	1.78249e8	+	3.08736e8i	0.0119910	+	0.0207690i
$807$	−9.36222e9	−	5.12695e9i	−0.627078	−	0.343401i
$808$	−1.07240e8	−	1.85744e8i	−0.00715180	−	0.0123873i
$809$	−1.86525e9	+	3.23070e9i	−0.123856	+	0.214525i	−0.921285	−	0.388888i	$-0.872859\pi$
$809$	−1.86525e9	+	3.23070e9i	−0.123856	+	0.214525i	0.797429	+	0.603412i	$0.206193\pi$
$810$	−1.42885e10	+	3.08891e10i	−0.944691	+	2.04224i
$811$	−1.47321e10			−0.969822			−0.484911	−	0.874564i	$-0.661148\pi$
$811$	−1.47321e10			−0.969822			−0.484911	+	0.874564i	$0.661148\pi$
$812$	−4.80779e9	−	6.43450e9i	−0.315137	−	0.421764i
$813$	−2.50706e10	+	1.52396e10i	−1.63624	+	0.994616i
$814$	−1.89268e7	+	3.27822e7i	−0.00122996	+	0.00213036i
$815$	2.13559e10			1.38187
$816$	−4.93848e9	−	2.70442e9i	−0.318184	−	0.174244i
$817$	−9.14364e9			−0.586600
$818$	9.91919e9			0.633636
$819$	−1.44352e8	+	2.37798e7i	−0.00918183	+	0.00151257i
$820$	3.90172e10			2.47120
$821$	−1.91170e10			−1.20564			−0.602822	−	0.797876i	$-0.705957\pi$
$821$	−1.91170e10			−1.20564			−0.602822	+	0.797876i	$0.705957\pi$
$822$	−2.36692e10	+	1.43877e10i	−1.48639	+	0.903524i
$823$	−6.71460e9			−0.419875			−0.209938	−	0.977715i	$-0.567326\pi$
$823$	−6.71460e9			−0.419875			−0.209938	+	0.977715i	$0.567326\pi$
$824$	−2.58220e8	+	4.47251e8i	−0.0160785	+	0.0278487i
$825$	4.13623e7	+	2.26509e7i	0.00256458	+	0.00140442i
$826$	1.04344e9	−	2.43062e9i	0.0644224	−	0.150067i
$827$	−1.79908e10			−1.10606			−0.553032	−	0.833160i	$-0.686529\pi$
$827$	−1.79908e10			−1.10606			−0.553032	+	0.833160i	$0.686529\pi$
$828$	1.12938e10	−	2.17767e10i	0.691405	−	1.33317i
$829$	1.17843e9	−	2.04109e9i	0.0718392	−	0.124429i	−0.827868	−	0.560923i	$-0.810446\pi$
$829$	1.17843e9	−	2.04109e9i	0.0718392	−	0.124429i	0.899707	+	0.436494i	$0.143780\pi$
$830$	2.65486e10	+	4.59836e10i	1.61164	+	2.79145i
$831$	8.29983e9	−	5.04518e9i	0.501725	−	0.304981i
$832$	−7.35515e7	−	1.27395e8i	−0.00442751	−	0.00766867i
$833$	−5.74953e9	+	1.38387e9i	−0.344647	+	0.0829543i
$834$	−1.12386e10	+	6.83154e9i	−0.670857	+	0.407791i
$835$	7.93708e9			0.471800
$836$	4.97886e6	−	8.62364e6i	0.000294719	−	0.000510468i
$837$	2.10557e9	+	3.10300e10i	0.124117	+	1.82912i
$838$	1.01575e10	+	1.75933e10i	0.596256	+	1.03275i
$839$	1.07177e10	−	1.85635e10i	0.626518	−	1.08516i	−0.361727	−	0.932284i	$-0.617813\pi$
$839$	1.07177e10	−	1.85635e10i	0.626518	−	1.08516i	0.988245	−	0.152877i	$-0.0488538\pi$
$840$	7.28288e8	−	5.70243e8i	0.0423961	−	0.0331957i
$841$	6.11548e9	+	1.05923e10i	0.354523	+	0.614052i
$842$	−1.12446e10	+	1.94762e10i	−0.649160	+	1.12438i
$843$	−9.25042e7	−	5.06572e7i	−0.00531820	−	0.00291236i
$844$	2.89041e9	+	5.00633e9i	0.165486	+	0.286630i
$845$	−1.40360e10	−	2.43110e10i	−0.800283	−	1.38613i
$846$	−1.96932e10	+	8.90112e8i	−1.11820	+	0.0505415i
$847$	−1.05851e10	−	1.41666e10i	−0.598555	−	0.801077i
$848$	−4.75521e8	+	8.23626e8i	−0.0267784	+	0.0463815i
$849$	7.79689e7	+	3.45180e9i	0.00437265	+	0.193584i
$850$	1.39387e10			0.778495
$851$	2.58634e10			1.43857
$852$	−1.29336e8	−	5.72591e9i	−0.00716444	−	0.317180i
$853$	1.43355e10	−	2.48299e10i	0.790847	−	1.36979i	−0.134596	−	0.990901i	$-0.542974\pi$
$853$	1.43355e10	−	2.48299e10i	0.790847	−	1.36979i	0.925443	−	0.378886i	$-0.123693\pi$
$854$	−8.30499e9	+	1.93459e10i	−0.456285	+	1.06288i
$855$	9.42949e9	−	4.26203e8i	0.515949	−	0.0233203i
$856$	−1.52043e8	−	2.63346e8i	−0.00828531	−	0.0143506i
$857$	−7.31312e9	−	1.26667e10i	−0.396890	−	0.687433i	0.596451	−	0.802650i	$-0.296577\pi$
$857$	−7.31312e9	−	1.26667e10i	−0.396890	−	0.687433i	−0.993340	+	0.115217i	$0.963244\pi$
$858$	397297.	+	217568.i	2.14738e−5	+	1.17595e-5i
$859$	9.27158e9	−	1.60588e10i	0.499089	−	0.864447i	−0.500911	−	0.865499i	$-0.667002\pi$
$859$	9.27158e9	−	1.60588e10i	0.499089	−	0.864447i	0.999999	+	0.00105200i	$0.000334861\pi$
$860$	−2.64917e10	−	4.58849e10i	−1.42025	−	2.45994i
$861$	4.15374e9	+	2.93302e10i	0.221783	+	1.56604i
$862$	−1.05151e9	+	1.82126e9i	−0.0559161	+	0.0968495i
$863$	−3.40006e9	−	5.88908e9i	−0.180073	−	0.311896i	0.761832	−	0.647775i	$-0.224300\pi$
$863$	−3.40006e9	−	5.88908e9i	−0.180073	−	0.311896i	−0.941905	+	0.335879i	$0.890967\pi$
$864$	−1.80319e9	−	2.65738e10i	−0.0951138	−	1.40170i
$865$	−1.44882e9	+	2.50943e9i	−0.0761127	+	0.131831i
$866$	3.57036e10			1.86810
$867$	−1.43372e10	+	8.71509e9i	−0.747133	+	0.454156i
$868$	−1.36007e10	+	3.16819e10i	−0.705898	+	1.64434i
$869$	−3.27174e7	−	5.66682e7i	−0.00169126	−	0.00292934i
$870$	−2.01447e10	+	1.22453e10i	−1.03715	+	0.630450i
$871$	−1.14116e8	−	1.97655e8i	−0.00585173	−	0.0101355i
$872$	8.43502e7	−	1.46099e8i	0.00430803	−	0.00746172i
$873$	2.71676e9	−	5.23846e9i	0.138198	−	0.266473i
$874$	−1.37740e10			−0.697861
$875$	−7.03545e9	+	1.63886e10i	−0.355029	+	0.827015i
$876$	−6.48889e9	−	3.55345e9i	−0.326141	−	0.178602i
$877$	−7.37290e9	+	1.27702e10i	−0.369097	+	0.639294i	−0.989425	−	0.145048i	$-0.953666\pi$
$877$	−7.37290e9	+	1.27702e10i	−0.369097	+	0.639294i	0.620328	+	0.784343i	$0.287000\pi$
$878$	−2.57792e10			−1.28540
$879$	−3.82827e9	+	2.32707e9i	−0.190126	+	0.115571i
$880$	−6.19791e7			−0.00306589
$881$	−3.80590e10			−1.87518			−0.937588	−	0.347748i	$-0.886946\pi$
$881$	−3.80590e10			−1.87518			−0.937588	+	0.347748i	$0.886946\pi$
$882$	−2.06472e10	−	1.98545e10i	−1.01326	−	0.974358i
$883$	3.17735e10			1.55311			0.776555	−	0.630050i	$-0.216965\pi$
$883$	3.17735e10			1.55311			0.776555	+	0.630050i	$0.216965\pi$
$884$	6.61320e7			0.00321980
$885$	−3.36336e9	−	1.84185e9i	−0.163107	−	0.0893206i
$886$	−1.97630e10			−0.954627
$887$	9.73490e9	−	1.68613e10i	0.468381	−	0.811259i	−0.530966	−	0.847393i	$-0.678171\pi$
$887$	9.73490e9	−	1.68613e10i	0.468381	−	0.811259i	0.999347	+	0.0361337i	$0.0115042\pi$
$888$	5.60801e8	−	3.40892e8i	0.0268759	−	0.0163370i
$889$	−1.05426e10	+	2.45581e10i	−0.503257	+	1.17230i
$890$	5.85781e10			2.78529
$891$	2.27656e7	+	3.23011e7i	0.00107822	+	0.00152984i
$892$	−1.71963e10	+	2.97849e10i	−0.811256	+	1.40514i
$893$	2.73371e9	+	4.73492e9i	0.128461	+	0.222501i
$894$	−2.50772e10	−	1.37328e10i	−1.17381	−	0.642802i
$895$	−1.48486e10	−	2.57186e10i	−0.692319	−	1.19913i
$896$	−5.71277e8	+	1.33075e9i	−0.0265319	+	0.0618043i
$897$	−6.98894e6	−	3.09411e8i	−0.000323324	−	0.0143140i
$898$	4.34952e10			2.00435
$899$	−1.07716e10	+	1.86570e10i	−0.494449	+	0.856411i
$900$	1.79615e10	+	2.80986e10i	0.821284	+	1.28480i
$901$	−2.03656e8	−	3.52743e8i	−0.00927600	−	0.0160665i
$902$	4.58593e7	−	7.94307e7i	0.00208068	−	0.00360384i
$903$	3.16725e10	−	2.47993e10i	1.43145	−	1.12081i
$904$	3.48992e8	+	6.04471e8i	0.0157118	+	0.0272136i
$905$	1.43271e10	−	2.48152e10i	0.642521	−	1.11288i
$906$	1.66291e10	−	1.01082e10i	0.742881	−	0.451572i
$907$	1.24214e10	+	2.15146e10i	0.552773	+	0.957431i	0.998073	+	0.0620495i	$0.0197637\pi$
$907$	1.24214e10	+	2.15146e10i	0.552773	+	0.957431i	−0.445300	+	0.895381i	$0.646903\pi$
$908$	−1.25596e10	−	2.17539e10i	−0.556771	−	0.964356i
$909$	5.18607e9	+	8.11299e9i	0.229015	+	0.358267i
$910$	−1.87768e8	+	4.37393e8i	−0.00825995	+	0.0192410i
$911$	1.83042e10	−	3.17038e10i	0.802115	−	1.38930i	−0.116107	−	0.993237i	$-0.537042\pi$
$911$	1.83042e10	−	3.17038e10i	0.802115	−	1.38930i	0.918222	−	0.396067i	$-0.129625\pi$
$912$	−6.46349e9	+	3.92893e9i	−0.282153	+	0.171511i
$913$	6.16527e7			0.00268105
$914$	−4.71812e10			−2.04389
$915$	2.67698e10	+	1.46597e10i	1.15524	+	0.632633i
$916$	6.61422e9	−	1.14562e10i	0.284344	−	0.492498i
$917$	8.66202e9	+	1.15928e10i	0.370960	+	0.496474i
$918$	1.04876e10	+	5.14194e9i	0.447432	+	0.219370i
$919$	−1.12005e9	−	1.93999e9i	−0.0476029	−	0.0824507i	0.841242	−	0.540659i	$-0.181825\pi$
$919$	−1.12005e9	−	1.93999e9i	−0.0476029	−	0.0824507i	−0.888845	+	0.458208i	$0.848492\pi$
$920$	9.78383e8	+	1.69461e9i	0.0414240	+	0.0717484i
$921$	−3.79325e8	−	1.67933e10i	−0.0159994	−	0.708315i
$922$	−1.98758e10	+	3.44260e10i	−0.835156	+	1.44653i
$923$	−3.61290e7	−	6.25772e7i	−0.00151234	−	0.00261945i
$924$	6.14275e6	+	4.33749e7i	0.000256160	+	0.00180878i
$925$	−1.75800e10	+	3.04495e10i	−0.730338	+	1.26498i
$926$	−1.38323e10	−	2.39582e10i	−0.572474	−	0.991554i
$927$	1.06742e10	−	2.05820e10i	0.440104	−	0.848610i
$928$	9.22470e9	−	1.59777e10i	0.378909	−	0.656289i
$929$	1.72230e10			0.704782			0.352391	−	0.935853i	$-0.385369\pi$
$929$	1.72230e10			0.704782			0.352391	+	0.935853i	$0.385369\pi$
$930$	8.87542e10	+	4.86036e10i	3.61825	+	1.98143i
$931$	−2.25191e9	+	7.61859e9i	−0.0914593	+	0.309422i
$932$	1.20311e10	+	2.08385e10i	0.486799	+	0.843160i
$933$	4.80705e8	+	2.12815e10i	0.0193773	+	0.857861i
$934$	3.23672e10	+	5.60616e10i	1.29984	+	2.25139i
$935$	1.32722e7	−	2.29881e7i	0.000531010	−	0.000919736i
$936$	−4.22973e6	−	6.61690e6i	−0.000168596	−	0.000263748i
$937$	−1.17791e9			−0.0467762			−0.0233881	−	0.999726i	$-0.507445\pi$
$937$	−1.17791e9			−0.0467762			−0.0233881	+	0.999726i	$0.507445\pi$
$938$	1.76280e10	−	4.10632e10i	0.697418	−	1.62459i
$939$	−2.59264e8	−	1.14780e10i	−0.0102191	−	0.452415i
$940$	−1.58406e10	+	2.74367e10i	−0.622049	+	1.07742i
$941$	−1.46697e10			−0.573928			−0.286964	−	0.957941i	$-0.592646\pi$
$941$	−1.46697e10			−0.573928			−0.286964	+	0.957941i	$0.592646\pi$
$942$	−4.42687e8	−	1.95984e10i	−0.0172552	−	0.763911i
$943$	−6.26665e10			−2.43357
$944$	3.07286e9			0.118889
$945$	−3.15067e10	+	2.70509e10i	−1.21448	+	1.04273i
$946$	−1.24549e8			−0.00478324
$947$	−2.10216e10			−0.804343			−0.402171	−	0.915564i	$-0.631744\pi$
$947$	−2.10216e10			−0.804343			−0.402171	+	0.915564i	$0.631744\pi$
$948$	−1.04495e9	−	4.62617e10i	−0.0398353	−	1.76357i
$949$	−9.33369e7			−0.00354504
$950$	9.36255e9	−	1.62164e10i	0.354292	−	0.613652i
$951$	1.38992e8	+	6.15339e9i	0.00524033	+	0.231997i
$952$	−1.90012e8	−	2.54303e8i	−0.00713759	−	0.00955260i
$953$	1.50279e10			0.562436			0.281218	−	0.959644i	$-0.409262\pi$
$953$	1.50279e10			0.562436			0.281218	+	0.959644i	$0.409262\pi$
$954$	9.08302e8	−	1.75139e9i	0.0338697	−	0.0653075i
$955$	3.64555e10	−	6.31429e10i	1.35442	−	2.34592i
$956$	−1.50937e10	−	2.61431e10i	−0.558720	−	0.967731i
$957$	618140.	+	2.73660e7i	2.27979e−5	+	0.00100930i
$958$	9.35120e9	+	1.61968e10i	0.343628	+	0.595181i
$959$	−3.35615e10	+	3.98216e9i	−1.22879	+	0.145799i
$960$	−3.66229e10	−	2.00555e10i	−1.33599	−	0.731617i
$961$	6.49595e10			2.36108
$962$	−1.68861e8	+	2.92477e8i	−0.00611530	+	0.0105920i
$963$	7.35275e9	+	1.15025e10i	0.265313	+	0.415050i
$964$	−1.26296e10	−	2.18751e10i	−0.454066	−	0.786465i
$965$	−3.07738e10	+	5.33017e10i	−1.10239	+	1.90939i
$966$	4.77114e10	−	3.73576e10i	1.70295	−	1.33340i
$967$	3.04945e9	+	5.28180e9i	0.108450	+	0.187840i	0.915142	−	0.403131i	$-0.132078\pi$
$967$	3.04945e9	+	5.28180e9i	0.108450	+	0.187840i	−0.806693	+	0.590971i	$0.798745\pi$
$968$	4.74651e8	−	8.22119e8i	0.0168194	−	0.0291320i
$969$	−7.31546e7	−	3.23866e9i	−0.00258290	−	0.114349i
$970$	−9.59979e9	−	1.66273e10i	−0.337723	−	0.584953i
$971$	1.92395e10	+	3.33239e10i	0.674415	+	1.16812i	0.976639	+	0.214884i	$0.0689375\pi$
$971$	1.92395e10	+	3.33239e10i	0.674415	+	1.16812i	−0.302224	+	0.953237i	$0.597729\pi$
$972$	3.14892e9	+	2.77676e10i	0.109984	+	0.969854i
$973$	−1.59356e10	+	1.89080e9i	−0.554592	+	0.0658037i
$974$	−3.13020e10	+	5.42166e10i	−1.08546	+	1.88008i
$975$	3.69027e8	+	2.02087e8i	0.0127509	+	0.00698267i
$976$	−2.44577e10			−0.842056
$977$	−5.13148e9			−0.176040			−0.0880201	−	0.996119i	$-0.528054\pi$
$977$	−5.13148e9			−0.176040			−0.0880201	+	0.996119i	$0.528054\pi$
$978$	3.03362e10	−	1.84404e10i	1.03699	−	0.630352i
$979$	3.40083e7	−	5.89041e7i	0.00115837	−	0.00200635i
$980$	−4.47563e10	+	1.07725e10i	−1.51902	+	0.365618i
$981$	−3.48683e9	+	6.72331e9i	−0.117920	+	0.227374i
$982$	−2.80379e10	−	4.85630e10i	−0.944833	−	1.63650i
$983$	−1.72082e10	−	2.98056e10i	−0.577829	−	1.00083i	−0.995728	−	0.0923357i	$-0.970567\pi$
$983$	−1.72082e10	−	2.98056e10i	−0.577829	−	1.00083i	0.417899	−	0.908494i	$-0.362767\pi$
$984$	−1.35881e9	+	8.25975e8i	−0.0454649	+	0.0276366i
$985$	7.80063e9	−	1.35111e10i	0.260077	−	0.450467i
$986$	4.04535e9	+	7.00675e9i	0.134396	+	0.232781i
$987$	−2.23112e10	−	8.98688e9i	−0.738608	−	0.297508i
$988$	4.44205e7	−	7.69385e7i	0.00146532	−	0.00253802i
$989$	4.25489e10	+	7.36969e10i	1.39863	+	2.42249i
$990$	1.28443e8	−	5.80548e6i	0.00420714	−	0.000190158i
$991$	7.88933e9	−	1.36647e10i	0.257503	−	0.446008i	−0.708069	−	0.706143i	$-0.750434\pi$
$991$	7.88933e9	−	1.36647e10i	0.257503	−	0.446008i	0.965572	+	0.260135i	$0.0837670\pi$
$992$	−7.91923e10			−2.57568
$993$	−3.85634e8	−	1.70726e10i	−0.0124984	−	0.553320i
$994$	5.58099e9	−	1.30005e10i	0.180243	−	0.419864i
$995$	−4.19294e10	−	7.26239e10i	−1.34939	−	2.33721i
$996$	3.82404e10	+	2.09412e10i	1.22635	+	0.671575i
$997$	−1.84473e10	−	3.19516e10i	−0.589521	−	1.02108i	−0.994295	−	0.106663i	$-0.965983\pi$
$997$	−1.84473e10	−	3.19516e10i	−0.589521	−	1.02108i	0.404774	−	0.914417i	$-0.367350\pi$
$998$	3.00438e10	−	5.20374e10i	0.956750	−	1.65714i
$999$	−2.44601e10	+	1.64253e10i	−0.776210	+	0.521236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.8.h.a.25.11	yes	108
7.2	even	3		63.8.g.a.16.44	yes	108
9.4	even	3		63.8.g.a.4.44	✓	108
63.58	even	3	inner	63.8.h.a.58.11	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.8.g.a.4.44	✓	108	9.4	even	3
63.8.g.a.16.44	yes	108	7.2	even	3
63.8.h.a.25.11	yes	108	1.1	even	1	trivial
63.8.h.a.58.11	yes	108	63.58	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	63.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-15.9040 q^{2} +(1.05606 + 46.7534i) q^{3} +124.937 q^{4} +(223.705 - 387.469i) q^{5} +(-16.7956 - 743.566i) q^{6} +(357.985 - 833.900i) q^{7} +48.7143 q^{8} +(-2184.77 + 98.7492i) q^{9} +(-3557.80 + 6162.30i) q^{10} +(4.13107 + 7.15522i) q^{11} +(131.941 + 5841.23i) q^{12} +(36.8566 + 63.8375i) q^{13} +(-5693.39 + 13262.3i) q^{14} +(18351.7 + 10049.8i) q^{15} -16766.7 q^{16} +(3590.42 - 6218.79i) q^{17} +(34746.6 - 1570.51i) q^{18} +(-4823.33 - 8354.25i) q^{19} +(27949.0 - 48409.2i) q^{20} +(39365.8 + 15856.4i) q^{21} +(-65.7005 - 113.797i) q^{22} +(-44889.6 + 77751.1i) q^{23} +(51.4454 + 2277.56i) q^{24} +(-61025.5 - 105699. i) q^{25} +(-586.167 - 1015.27i) q^{26} +(-6924.12 - 102041. i) q^{27} +(44725.5 - 104185. i) q^{28} +(35422.2 - 61353.0i) q^{29} +(-291866. - 159832. i) q^{30} -304092. q^{31} +260422. q^{32} +(-330.168 + 200.698i) q^{33} +(-57102.0 + 98903.5i) q^{34} +(-243027. - 325256. i) q^{35} +(-272958. + 12337.4i) q^{36} +(-144039. - 249482. i) q^{37} +(76710.1 + 132866. i) q^{38} +(-2945.70 + 1790.59i) q^{39} +(10897.6 - 18875.3i) q^{40} +(349003. + 604491. i) q^{41} +(-626073. - 252180. i) q^{42} +(473928. - 820867. i) q^{43} +(516.123 + 893.951i) q^{44} +(-450482. + 868620. i) q^{45} +(713925. - 1.23655e6i) q^{46} -566768. q^{47} +(-17706.7 - 783900. i) q^{48} +(-567237. - 597047. i) q^{49} +(970549. + 1.68104e6i) q^{50} +(294541. + 161297. i) q^{51} +(4604.75 + 7975.67i) q^{52} +(28361.1 - 49122.8i) q^{53} +(110121. + 1.62286e6i) q^{54} +3696.56 q^{55} +(17439.0 - 40622.9i) q^{56} +(385496. - 234330. i) q^{57} +(-563354. + 975758. i) q^{58} -183272. q^{59} +(2.29281e6 + 1.25559e6i) q^{60} +1.45871e6 q^{61} +4.83628e6 q^{62} +(-699767. + 1.85723e6i) q^{63} -1.99561e6 q^{64} +32980.1 q^{65} +(5251.00 - 3191.90i) q^{66} -3.09622e6 q^{67} +(448576. - 776956. i) q^{68} +(-3.68254e6 - 2.01664e6i) q^{69} +(3.86510e6 + 5.17286e6i) q^{70} -980257. q^{71} +(-106430. + 4810.50i) q^{72} +(-633108. + 1.09658e6i) q^{73} +(2.29079e6 + 3.96776e6i) q^{74} +(4.87736e6 - 2.96478e6i) q^{75} +(-602612. - 1.04375e6i) q^{76} +(7445.60 - 883.439i) q^{77} +(46848.4 - 28477.5i) q^{78} -7.91984e6 q^{79} +(-3.75079e6 + 6.49657e6i) q^{80} +(4.76347e6 - 431488. i) q^{81} +(-5.55054e6 - 9.61382e6i) q^{82} +(3.73104e6 - 6.46235e6i) q^{83} +(4.91824e6 + 1.98105e6i) q^{84} +(-1.60639e6 - 2.78235e6i) q^{85} +(-7.53735e6 + 1.30551e7i) q^{86} +(2.90587e6 + 1.59132e6i) q^{87} +(201.242 + 348.562i) q^{88} +(-4.11617e6 - 7.12941e6i) q^{89} +(7.16446e6 - 1.38145e7i) q^{90} +(66428.3 - 7881.88i) q^{91} +(-5.60838e6 + 9.71399e6i) q^{92} +(-321141. - 1.42174e7i) q^{93} +9.01387e6 q^{94} -4.31601e6 q^{95} +(275022. + 1.21756e7i) q^{96} +(-1.34912e6 + 2.33674e6i) q^{97} +(9.02133e6 + 9.49544e6i) q^{98} +(-9732.00 - 15224.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{2} - q^{3} + 6654 q^{4} - 499 q^{5} + 796 q^{6} - 84 q^{7} - 264 q^{8} - 2083 q^{9} - 258 q^{10} - 2953 q^{11} - 4262 q^{12} + 1845 q^{13} - 6064 q^{14} - 4756 q^{15} + 392958 q^{16} - 25695 q^{17}+ \cdots - 27043330 q^{99}+O(q^{100}) \) 108 * q - 2 * q^2 - q^3 + 6654 * q^4 - 499 * q^5 + 796 * q^6 - 84 * q^7 - 264 * q^8 - 2083 * q^9 - 258 * q^10 - 2953 * q^11 - 4262 * q^12 + 1845 * q^13 - 6064 * q^14 - 4756 * q^15 + 392958 * q^16 - 25695 * q^17 + 18628 * q^18 - 22344 * q^19 - 128642 * q^20 + 26395 * q^21 - 258 * q^22 + 24588 * q^23 + 9582 * q^24 - 718749 * q^25 - 184322 * q^26 - 108115 * q^27 - 37764 * q^28 - 46252 * q^29 - 368195 * q^30 + 215046 * q^31 - 896314 * q^32 - 508675 * q^33 + 126 * q^34 - 13856 * q^35 - 725486 * q^36 - 6219 * q^37 - 574289 * q^38 + 863855 * q^39 + 45102 * q^40 - 472490 * q^41 - 1455340 * q^42 - 48054 * q^43 - 763907 * q^44 - 1979983 * q^45 - 301266 * q^46 + 2767914 * q^47 + 3830059 * q^48 - 179010 * q^49 + 1454999 * q^50 - 1705518 * q^51 + 439809 * q^52 - 942852 * q^53 + 690229 * q^54 - 1333590 * q^55 - 960744 * q^56 - 4103881 * q^57 - 346383 * q^58 + 10263900 * q^59 + 1690429 * q^60 - 5446392 * q^61 + 17542716 * q^62 - 3666923 * q^63 + 20938488 * q^64 + 9110336 * q^65 + 8839522 * q^66 + 2503716 * q^67 - 3564510 * q^68 - 14621034 * q^69 + 5170071 * q^70 - 15030822 * q^71 + 10036926 * q^72 + 5865900 * q^73 - 10298901 * q^74 - 20070398 * q^75 - 5703426 * q^76 - 13731494 * q^77 + 18441853 * q^78 + 1098144 * q^79 - 22433777 * q^80 - 8145607 * q^81 + 126 * q^82 - 24302862 * q^83 + 10191035 * q^84 - 1239627 * q^85 - 8642455 * q^86 + 25559693 * q^87 + 2064129 * q^88 - 16002211 * q^89 + 28857805 * q^90 - 77007 * q^91 + 17446044 * q^92 - 1086678 * q^93 - 23171394 * q^94 + 8775674 * q^95 + 11149883 * q^96 - 3307419 * q^97 + 30910129 * q^98 - 27043330 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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