LMFDB - Embedded newform 9.9.d.a.5.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,9,Mod(2,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.2"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.66640749055$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 $ x^14 - x^13 + 427x^12 - 1362x^11 + 135762x^10 - 371244x^9 + 18261508x^8 - 29352736x^7 + 1757083840x^6 - 1434930432x^5 + 61638378240x^4 + 183604924416x^3 + 1254910111744x^2 + 1078377512960x + 872385888256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.4
Root			$-0.447645 + 0.775344i$ of defining polynomial
Character	$\chi$	$=$	9.5
Dual form			9.9.d.a.2.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34294 - 0.775344i) q^{2} +(-44.1317 - 67.9220i) q^{3} +(-126.798 + 219.620i) q^{4} +(-604.549 - 349.037i) q^{5} +(-111.929 - 56.9976i) q^{6} +(-1124.45 - 1947.61i) q^{7} +790.223i q^{8} +(-2665.79 + 5995.02i) q^{9} -1082.49 q^{10} +(18817.0 - 10864.0i) q^{11} +(20512.8 - 1079.84i) q^{12} +(-9209.84 + 15951.9i) q^{13} +(-3020.14 - 1743.68i) q^{14} +(2972.49 + 56465.7i) q^{15} +(-31847.5 - 55161.5i) q^{16} -56538.1i q^{17} +(1068.21 + 10117.8i) q^{18} -212375. q^{19} +(153311. - 88514.1i) q^{20} +(-82661.6 + 162326. i) q^{21} +(16846.7 - 29179.3i) q^{22} +(14399.3 + 8313.41i) q^{23} +(53673.5 - 34873.9i) q^{24} +(48340.5 + 83728.3i) q^{25} +28563.2i q^{26} +(524840. - 83504.2i) q^{27} +570313. q^{28} +(-294955. + 170292. i) q^{29} +(47772.2 + 73525.1i) q^{30} +(-82902.7 + 143592. i) q^{31} +(-260733. - 150534. i) q^{32} +(-1.56833e6 - 798642. i) q^{33} +(-43836.4 - 75926.9i) q^{34} +1.56990e6i q^{35} +(-978610. - 1.34562e6i) q^{36} +1.11833e6 q^{37} +(-285206. + 164664. i) q^{38} +(1.48993e6 - 78433.6i) q^{39} +(275817. - 477729. i) q^{40} +(-3.60414e6 - 2.08085e6i) q^{41} +(14849.6 + 282085. i) q^{42} +(1.28793e6 + 2.23075e6i) q^{43} +5.51012e6i q^{44} +(3.70408e6 - 2.69382e6i) q^{45} +25783.0 q^{46} +(8.10049e6 - 4.67682e6i) q^{47} +(-2.34120e6 + 4.59752e6i) q^{48} +(353608. - 612466. i) q^{49} +(129836. + 74961.1i) q^{50} +(-3.84018e6 + 2.49512e6i) q^{51} +(-2.33557e6 - 4.04533e6i) q^{52} -4.75879e6i q^{53} +(640081. - 519072. i) q^{54} -1.51677e7 q^{55} +(1.53905e6 - 888570. i) q^{56} +(9.37246e6 + 1.44249e7i) q^{57} +(-264070. + 457383. i) q^{58} +(-8.39702e6 - 4.84802e6i) q^{59} +(-1.27779e7 - 6.50691e6i) q^{60} +(-3.04570e6 - 5.27531e6i) q^{61} +257113. i q^{62} +(1.46735e7 - 1.54919e6i) q^{63} +1.58391e7 q^{64} +(1.11356e7 - 6.42914e6i) q^{65} +(-2.72539e6 + 143471. i) q^{66} +(-1.02601e7 + 1.77710e7i) q^{67} +(1.24169e7 + 7.16890e6i) q^{68} +(-70799.4 - 1.34491e6i) q^{69} +(1.21721e6 + 2.10828e6i) q^{70} +2.08627e7i q^{71} +(-4.73740e6 - 2.10657e6i) q^{72} +9.02632e6 q^{73} +(1.50184e6 - 867089. i) q^{74} +(3.55364e6 - 6.97845e6i) q^{75} +(2.69287e7 - 4.66418e7i) q^{76} +(-4.23177e7 - 2.44321e7i) q^{77} +(1.94007e6 - 1.26054e6i) q^{78} +(1.67238e7 + 2.89665e7i) q^{79} +4.44638e7i q^{80} +(-2.88338e7 - 3.19630e7i) q^{81} -6.45351e6 q^{82} +(-5.09741e7 + 2.94299e7i) q^{83} +(-2.51688e7 - 3.87368e7i) q^{84} +(-1.97339e7 + 3.41800e7i) q^{85} +(3.45920e6 + 1.99717e6i) q^{86} +(2.45835e7 + 1.25187e7i) q^{87} +(8.58499e6 + 1.48696e7i) q^{88} -8.65172e7i q^{89} +(2.88570e6 - 6.48957e6i) q^{90} +4.14242e7 q^{91} +(-3.65158e6 + 2.10824e6i) q^{92} +(1.34117e7 - 706023. i) q^{93} +(7.25229e6 - 1.25613e7i) q^{94} +(1.28391e8 + 7.41267e7i) q^{95} +(1.28199e6 + 2.43528e7i) q^{96} +(-4.68859e7 - 8.12087e7i) q^{97} -1.09667e6i q^{98} +(1.49677e7 + 1.41770e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18}+ \cdots - 511060752 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.34294	−	0.775344i	0.0839334	−	0.0484590i	−0.457446	−	0.889237i	$-0.651236\pi$
$2$	1.34294	−	0.775344i	0.0839334	−	0.0484590i	0.541379	+	0.840778i	$0.317902\pi$
$3$	−44.1317	−	67.9220i	−0.544835	−	0.838543i
$3$	−44.1317	−	67.9220i	−0.544835	−	0.838543i
$4$	−126.798	+	219.620i	−0.495303	+	0.857891i
$5$	−604.549	−	349.037i	−0.967279	−	0.558459i	−0.0688730	−	0.997625i	$-0.521940\pi$
$5$	−604.549	−	349.037i	−0.967279	−	0.558459i	−0.898405	+	0.439167i	$0.855274\pi$
$6$	−111.929	−	56.9976i	−0.0863649	−	0.0439796i
$7$	−1124.45	−	1947.61i	−0.468327	−	0.811167i	0.531017	−	0.847361i	$-0.321810\pi$
$7$	−1124.45	−	1947.61i	−0.468327	−	0.811167i	−0.999345	+	0.0361942i	$0.988477\pi$
$8$			790.223i			0.192926i
$9$	−2665.79	+	5995.02i	−0.406309	+	0.913736i
$10$	−1082.49			−0.108249
$11$	18817.0	−	10864.0i	1.28523	−	0.742026i	0.307428	−	0.951571i	$-0.400532\pi$
$11$	18817.0	−	10864.0i	1.28523	−	0.742026i	0.977799	+	0.209545i	$0.0671983\pi$
$12$	20512.8	−	1079.84i	0.989237	−	0.0520758i
$13$	−9209.84	+	15951.9i	−0.322462	+	0.558521i	−0.980995	−	0.194031i	$-0.937844\pi$
$13$	−9209.84	+	15951.9i	−0.322462	+	0.558521i	0.658533	+	0.752552i	$0.271177\pi$
$14$	−3020.14	−	1743.68i	−0.0786166	−	0.0453893i
$15$	2972.49	+	56465.7i	0.0587159	+	1.11537i
$16$	−31847.5	−	55161.5i	−0.485954	−	0.841698i
$17$		−	56538.1i		−	0.676932i	−0.940979	−	0.338466i	$-0.890092\pi$
$17$		−	56538.1i		−	0.676932i	0.940979	−	0.338466i	$-0.109908\pi$
$18$	1068.21	+	10117.8i	0.0101758	+	0.0963823i
$19$	−212375.			−1.62963			−0.814815	−	0.579721i	$-0.803162\pi$
$19$	−212375.			−1.62963			−0.814815	+	0.579721i	$0.803162\pi$
$20$	153311.	−	88514.1i	0.958193	−	0.553213i
$21$	−82661.6	+	162326.i	−0.425037	+	0.834665i
$22$	16846.7	−	29179.3i	0.0719157	−	0.124562i
$23$	14399.3	+	8313.41i	0.0514551	+	0.0297076i	0.525507	−	0.850789i	$-0.323876\pi$
$23$	14399.3	+	8313.41i	0.0514551	+	0.0297076i	−0.474052	+	0.880497i	$0.657209\pi$
$24$	53673.5	−	34873.9i	0.161776	−	0.105113i
$25$	48340.5	+	83728.3i	0.123752	+	0.214344i
$26$			28563.2i			0.0625048i
$27$	524840.	−	83504.2i	0.987578	−	0.157128i
$28$	570313.			0.927857
$29$	−294955.	+	170292.i	−0.417027	+	0.240771i	−0.693804	−	0.720163i	$-0.744067\pi$
$29$	−294955.	+	170292.i	−0.417027	+	0.240771i	0.276778	+	0.960934i	$0.410733\pi$
$30$	47772.2	+	73525.1i	0.0589781	+	0.0907717i
$31$	−82902.7	+	143592.i	−0.0897681	+	0.155483i	−0.907413	−	0.420240i	$-0.861946\pi$
$31$	−82902.7	+	143592.i	−0.0897681	+	0.155483i	0.817645	+	0.575723i	$0.195279\pi$
$32$	−260733.	−	150534.i	−0.248654	−	0.143561i
$33$	−1.56833e6	−	798642.i	−1.32246	−	0.673436i
$34$	−43836.4	−	75926.9i	−0.0328035	−	0.0568173i
$35$			1.56990e6i			1.04617i
$36$	−978610.	−	1.34562e6i	−0.582639	−	0.801145i
$37$	1.11833e6			0.596709			0.298355	−	0.954455i	$-0.403562\pi$
$37$	1.11833e6			0.596709			0.298355	+	0.954455i	$0.403562\pi$
$38$	−285206.	+	164664.i	−0.136780	+	0.0789702i
$39$	1.48993e6	−	78433.6i	0.644033	−	0.0339034i
$40$	275817.	−	477729.i	0.107741	−	0.186613i
$41$	−3.60414e6	−	2.08085e6i	−1.27546	−	0.736387i	−0.299449	−	0.954112i	$-0.596803\pi$
$41$	−3.60414e6	−	2.08085e6i	−1.27546	−	0.736387i	−0.976010	+	0.217725i	$0.930136\pi$
$42$	14849.6	+	282085.i	0.00477220	+	0.0906532i
$43$	1.28793e6	+	2.23075e6i	0.376719	+	0.652496i	0.990583	−	0.136916i	$-0.0437190\pi$
$43$	1.28793e6	+	2.23075e6i	0.376719	+	0.652496i	−0.613864	+	0.789412i	$0.710386\pi$
$44$			5.51012e6i			1.47011i
$45$	3.70408e6	−	2.69382e6i	0.903297	−	0.656930i
$46$	25783.0			0.00575841
$47$	8.10049e6	−	4.67682e6i	1.66005	−	0.958428i	0.687356	−	0.726321i	$-0.258771\pi$
$47$	8.10049e6	−	4.67682e6i	1.66005	−	0.958428i	0.972690	−	0.232107i	$-0.0745619\pi$
$48$	−2.34120e6	+	4.59752e6i	−0.441035	+	0.866080i
$49$	353608.	−	612466.i	0.0613391	−	0.106242i
$50$	129836.	+	74961.1i	0.0207738	+	0.0119938i
$51$	−3.84018e6	+	2.49512e6i	−0.567637	+	0.368817i
$52$	−2.33557e6	−	4.04533e6i	−0.319433	−	0.553275i
$53$		−	4.75879e6i		−	0.603106i	−0.953449	−	0.301553i	$-0.902495\pi$
$53$		−	4.75879e6i		−	0.603106i	0.953449	−	0.301553i	$-0.0975050\pi$
$54$	640081.	−	519072.i	0.0752766	−	0.0610453i
$55$	−1.51677e7			−1.65756
$56$	1.53905e6	−	888570.i	0.156495	−	0.0903523i
$57$	9.37246e6	+	1.44249e7i	0.887880	+	1.36652i
$58$	−264070.	+	457383.i	−0.0233350	+	0.0404174i
$59$	−8.39702e6	−	4.84802e6i	−0.692974	−	0.400089i	0.111751	−	0.993736i	$-0.464354\pi$
$59$	−8.39702e6	−	4.84802e6i	−0.692974	−	0.400089i	−0.804725	+	0.593647i	$0.797687\pi$
$60$	−1.27779e7	−	6.50691e6i	−0.985950	−	0.502076i
$61$	−3.04570e6	−	5.27531e6i	−0.219972	−	0.381003i	0.734827	−	0.678255i	$-0.237263\pi$
$61$	−3.04570e6	−	5.27531e6i	−0.219972	−	0.381003i	−0.954799	+	0.297252i	$0.903930\pi$
$62$			257113.i			0.0174003i
$63$	1.46735e7	−	1.54919e6i	0.931478	−	0.0983430i
$64$	1.58391e7			0.944082
$65$	1.11356e7	−	6.42914e6i	0.623821	−	0.360164i
$66$	−2.72539e6	+	143471.i	−0.143632	+	0.00756116i
$67$	−1.02601e7	+	1.77710e7i	−0.509158	+	0.881888i	0.490786	+	0.871280i	$0.336710\pi$
$67$	−1.02601e7	+	1.77710e7i	−0.509158	+	0.881888i	−0.999944	+	0.0106075i	$0.996623\pi$
$68$	1.24169e7	+	7.16890e6i	0.580734	+	0.335287i
$69$	−70799.4	−	1.34491e6i	−0.00312344	−	0.0593331i
$70$	1.21721e6	+	2.10828e6i	0.0506961	+	0.0878083i
$71$			2.08627e7i			0.820987i	0.911863	+	0.410494i	$0.134644\pi$
$71$			2.08627e7i			0.820987i	−0.911863	+	0.410494i	$0.865356\pi$
$72$	−4.73740e6	−	2.10657e6i	−0.176283	−	0.0783874i
$73$	9.02632e6			0.317848			0.158924	−	0.987291i	$-0.449198\pi$
$73$	9.02632e6			0.317848			0.158924	+	0.987291i	$0.449198\pi$
$74$	1.50184e6	−	867089.i	0.0500838	−	0.0289159i
$75$	3.55364e6	−	6.97845e6i	0.112313	−	0.220554i
$76$	2.69287e7	−	4.66418e7i	0.807161	−	1.39804i
$77$	−4.23177e7	−	2.44321e7i	−1.20381	−	0.695022i
$78$	1.94007e6	−	1.26054e6i	0.0524129	−	0.0340548i
$79$	1.67238e7	+	2.89665e7i	0.429366	+	0.743683i	0.996817	−	0.0797237i	$-0.0254038\pi$
$79$	1.67238e7	+	2.89665e7i	0.429366	+	0.743683i	−0.567451	+	0.823407i	$0.692070\pi$
$80$			4.44638e7i			1.08554i
$81$	−2.88338e7	−	3.19630e7i	−0.669826	−	0.742518i
$82$	−6.45351e6			−0.142738
$83$	−5.09741e7	+	2.94299e7i	−1.07408	+	0.620121i	−0.929294	−	0.369342i	$-0.879583\pi$
$83$	−5.09741e7	+	2.94299e7i	−1.07408	+	0.620121i	−0.144788	+	0.989463i	$0.546250\pi$
$84$	−2.51688e7	−	3.87368e7i	−0.505529	−	0.778048i
$85$	−1.97339e7	+	3.41800e7i	−0.378039	+	0.654782i
$86$	3.45920e6	+	1.99717e6i	0.0632386	+	0.0365108i
$87$	2.45835e7	+	1.25187e7i	0.429107	+	0.218515i
$88$	8.58499e6	+	1.48696e7i	0.143156	+	0.247953i
$89$		−	8.65172e7i		−	1.37893i	−0.724319	−	0.689465i	$-0.757846\pi$
$89$		−	8.65172e7i		−	1.37893i	0.724319	−	0.689465i	$-0.242154\pi$
$90$	2.88570e6	−	6.48957e6i	0.0439827	−	0.0989113i
$91$	4.14242e7			0.604071
$92$	−3.65158e6	+	2.10824e6i	−0.0509718	+	0.0294286i
$93$	1.34117e7	−	706023.i	0.179288	−	0.00943815i
$94$	7.25229e6	−	1.25613e7i	0.0928889	−	0.160888i
$95$	1.28391e8	+	7.41267e7i	1.57631	+	0.910081i
$96$	1.28199e6	+	2.43528e7i	0.0150939	+	0.286724i
$97$	−4.68859e7	−	8.12087e7i	−0.529609	−	0.917309i	−0.999404	−	0.0345336i	$-0.989005\pi$
$97$	−4.68859e7	−	8.12087e7i	−0.529609	−	0.917309i	0.469795	−	0.882776i	$-0.344328\pi$
$98$		−	1.09667e6i		−	0.0118897i
$99$	1.49677e7	+	1.41770e8i	0.155816	+	1.47585i
$100$	−2.45179e7			−0.245179
$101$	8.70183e6	−	5.02401e6i	0.0836229	−	0.0482797i	−0.457605	−	0.889155i	$-0.651293\pi$
$101$	8.70183e6	−	5.02401e6i	0.0836229	−	0.0482797i	0.541228	+	0.840876i	$0.317959\pi$
$102$	−3.22253e6	+	6.32824e6i	−0.0297712	+	0.0584632i
$103$	−8.92310e6	+	1.54553e7i	−0.0792806	+	0.137318i	−0.902940	−	0.429767i	$-0.858596\pi$
$103$	−8.92310e6	+	1.54553e7i	−0.0792806	+	0.137318i	0.823659	+	0.567085i	$0.191929\pi$
$104$	−1.26056e7	−	7.27783e6i	−0.107753	−	0.0622112i
$105$	1.06631e8	−	6.92824e7i	0.877255	−	0.569988i
$106$	−3.68970e6	−	6.39075e6i	−0.0292259	−	0.0506207i
$107$		−	2.12170e8i		−	1.61864i	−0.587370	−	0.809319i	$-0.699837\pi$
$107$		−	2.12170e8i		−	1.61864i	0.587370	−	0.809319i	$-0.300163\pi$
$108$	−4.82093e7	+	1.25853e8i	−0.354352	+	0.925060i
$109$	−1.64501e8			−1.16537			−0.582683	−	0.812699i	$-0.697997\pi$
$109$	−1.64501e8			−1.16537			−0.582683	+	0.812699i	$0.697997\pi$
$110$	−2.03693e7	+	1.17602e7i	−0.139125	+	0.0803239i
$111$	−4.93537e7	−	7.59591e7i	−0.325108	−	0.500366i
$112$	−7.16221e7	+	1.24053e8i	−0.455171	+	0.788380i
$113$	8.35524e7	+	4.82390e7i	0.512442	+	0.295859i	0.733837	−	0.679326i	$-0.237728\pi$
$113$	8.35524e7	+	4.82390e7i	0.512442	+	0.295859i	−0.221395	+	0.975184i	$0.571061\pi$
$114$	2.37709e7	+	1.21049e7i	0.140743	+	0.0716705i
$115$	−5.80337e6	−	1.00517e7i	−0.0331810	−	0.0574711i
$116$		−	8.63708e7i		−	0.477018i
$117$	−7.10805e7	−	9.77377e7i	−0.379321	−	0.521577i
$118$	−1.50355e7			−0.0775516
$119$	−1.10114e8	+	6.35744e7i	−0.549105	+	0.317026i
$120$	−4.46205e7	+	2.34893e6i	−0.215184	+	0.0113278i
$121$	1.28874e8	−	2.23216e8i	0.601206	−	1.04132i
$122$	−8.18035e6	−	4.72293e6i	−0.0369260	−	0.0213193i
$123$	1.77211e7	+	3.36632e8i	0.0774232	+	1.47074i
$124$	−2.10238e7	−	3.64142e7i	−0.0889249	−	0.154022i
$125$			2.05194e8i			0.840476i
$126$	1.85044e7	−	1.34575e7i	0.0734165	−	0.0533927i
$127$	2.30345e8			0.885448			0.442724	−	0.896658i	$-0.354012\pi$
$127$	2.30345e8			0.885448			0.442724	+	0.896658i	$0.354012\pi$
$128$	8.80184e7	−	5.08175e7i	0.327894	−	0.189310i
$129$	9.46789e7	−	1.85925e8i	0.341896	−	0.671398i
$130$	9.96960e6	−	1.72678e7i	0.0349063	−	0.0604595i
$131$	9.84848e7	+	5.68602e7i	0.334414	+	0.193074i	0.657799	−	0.753194i	$-0.271488\pi$
$131$	9.84848e7	+	5.68602e7i	0.334414	+	0.193074i	−0.323385	+	0.946267i	$0.604821\pi$
$132$	3.74259e8	−	2.43171e8i	1.23275	−	0.800969i
$133$	2.38806e8	+	4.13624e8i	0.763200	+	1.32190i
$134$			3.18205e7i			0.0986932i
$135$	−3.46437e8	−	1.32706e8i	−1.04301	−	0.399535i
$136$	4.46777e7			0.130598
$137$	−2.61214e8	+	1.50812e8i	−0.741505	+	0.428108i	−0.822616	−	0.568597i	$-0.807486\pi$
$137$	−2.61214e8	+	1.50812e8i	−0.741505	+	0.428108i	0.0811112	+	0.996705i	$0.474153\pi$
$138$	−1.13785e6	−	1.75123e6i	−0.00313738	−	0.00482867i
$139$	−2.17400e6	+	3.76548e6i	−0.00582372	+	0.0100870i	−0.868923	−	0.494948i	$-0.835187\pi$
$139$	−2.17400e6	+	3.76548e6i	−0.00582372	+	0.0100870i	0.863099	+	0.505035i	$0.168520\pi$
$140$	−3.44782e8	−	1.99060e8i	−0.897496	−	0.518169i
$141$	−6.75147e8	−	3.43806e8i	−1.70813	−	0.869835i
$142$	1.61757e7	+	2.80172e7i	0.0397842	+	0.0689083i
$143$			4.00223e8i			0.957102i
$144$	4.15593e8	−	4.38773e7i	0.966537	−	0.102045i
$145$	2.37753e8			0.537841
$146$	1.21218e7	−	6.99850e6i	0.0266781	−	0.0154026i
$147$	−5.72052e7	+	3.01142e6i	−0.122509	+	0.00644915i
$148$	−1.41802e8	+	2.45607e8i	−0.295552	+	0.511911i
$149$	−1.07668e8	−	6.21619e7i	−0.218444	−	0.126119i	0.386786	−	0.922170i	$-0.373585\pi$
$149$	−1.07668e8	−	6.21619e7i	−0.218444	−	0.126119i	−0.605230	+	0.796051i	$0.706919\pi$
$150$	−638390.	−	1.21269e7i	−0.00126102	−	0.0239544i
$151$	−4.29306e8	−	7.43579e8i	−0.825769	−	1.43027i	−0.901330	−	0.433133i	$-0.857408\pi$
$151$	−4.29306e8	−	7.43579e8i	−0.825769	−	1.43027i	0.0755603	−	0.997141i	$-0.475925\pi$
$152$		−	1.67824e8i		−	0.314397i
$153$	3.38947e8	+	1.50719e8i	0.618537	+	0.275044i
$154$	−7.57733e7			−0.134720
$155$	1.00238e8	−	5.78722e7i	0.173662	−	0.100264i
$156$	−1.71694e8	+	3.37164e8i	−0.289906	+	0.569302i
$157$	5.15099e7	−	8.92177e7i	0.0847797	−	0.146843i	−0.820518	−	0.571621i	$-0.806315\pi$
$157$	5.15099e7	−	8.92177e7i	0.0847797	−	0.146843i	0.905297	+	0.424779i	$0.139648\pi$
$158$	4.49180e7	+	2.59334e7i	0.0720763	+	0.0416133i
$159$	−3.23227e8	+	2.10013e8i	−0.505730	+	0.328593i
$160$	1.05084e8	+	1.82011e8i	0.160345	+	0.277726i
$161$		−	3.73922e7i		−	0.0556516i
$162$	−6.35042e7	−	2.05681e7i	−0.0922025	−	0.0298630i
$163$	−2.40441e8			−0.340610			−0.170305	−	0.985391i	$-0.554475\pi$
$163$	−2.40441e8			−0.340610			−0.170305	+	0.985391i	$0.554475\pi$
$164$	9.13994e8	−	5.27695e8i	1.26348	−	0.729470i
$165$	6.69378e8	+	1.03022e9i	0.903099	+	1.38994i
$166$	−4.56366e7	+	7.90449e7i	−0.0601009	+	0.104098i
$167$	5.13723e8	+	2.96598e8i	0.660485	+	0.381331i	0.792462	−	0.609921i	$-0.208799\pi$
$167$	5.13723e8	+	2.96598e8i	0.660485	+	0.381331i	−0.131977	+	0.991253i	$0.542132\pi$
$168$	−1.28274e8	−	6.53211e7i	−0.161028	−	0.0820005i
$169$	2.38223e8	+	4.12614e8i	0.292036	+	0.505822i
$170$			6.12021e7i			0.0732775i
$171$	5.66148e8	−	1.27319e9i	0.662134	−	1.48905i
$172$	−6.53224e8			−0.746360
$173$	4.78569e8	−	2.76302e8i	0.534269	−	0.308460i	−0.208484	−	0.978026i	$-0.566853\pi$
$173$	4.78569e8	−	2.76302e8i	0.534269	−	0.308460i	0.742753	+	0.669565i	$0.233520\pi$
$174$	4.27203e7	−	2.24890e6i	0.0466055	−	0.00245343i
$175$	1.08713e8	−	1.88297e8i	0.115913	−	0.200767i
$176$	−1.19855e9	−	6.91983e8i	−1.24912	−	0.721182i
$177$	4.12871e7	+	7.84293e8i	0.0420651	+	0.799071i
$178$	−6.70806e7	−	1.16187e8i	−0.0668216	−	0.115738i
$179$		−	4.28843e8i		−	0.417721i	−0.977945	−	0.208860i	$-0.933025\pi$
$179$		−	4.28843e8i		−	0.417721i	0.977945	−	0.208860i	$-0.0669754\pi$
$180$	1.21948e8	+	1.15506e9i	0.116168	+	1.10031i
$181$	−5.89026e8			−0.548808			−0.274404	−	0.961615i	$-0.588481\pi$
$181$	−5.89026e8			−0.548808			−0.274404	+	0.961615i	$0.588481\pi$
$182$	5.56300e7	−	3.21180e7i	0.0507018	−	0.0292727i
$183$	−2.23897e8	+	4.39678e8i	−0.199639	+	0.392040i
$184$	−6.56945e6	+	1.13786e7i	−0.00573136	+	0.00992701i
$185$	−6.76085e8	−	3.90338e8i	−0.577184	−	0.333237i
$186$	1.74636e7	−	1.13468e7i	0.0145909	−	0.00948029i
$187$	−6.14230e8	−	1.06388e9i	−0.502302	−	0.870012i
$188$			2.37204e9i			1.89885i
$189$	−7.52792e8	−	9.28287e8i	−0.589967	−	0.727503i
$190$	2.29895e8			0.176406
$191$	8.27443e8	−	4.77725e8i	0.621734	−	0.358958i	−0.155810	−	0.987787i	$-0.549799\pi$
$191$	8.27443e8	−	4.77725e8i	0.621734	−	0.358958i	0.777544	+	0.628829i	$0.216465\pi$
$192$	−6.99004e8	−	1.07582e9i	−0.514369	−	0.791653i
$193$	−9.75155e7	+	1.68902e8i	−0.0702820	+	0.121732i	−0.899025	−	0.437898i	$-0.855723\pi$
$193$	−9.75155e7	+	1.68902e8i	−0.0702820	+	0.121732i	0.828743	+	0.559630i	$0.189057\pi$
$194$	−1.25929e8	−	7.27054e7i	−0.0889038	−	0.0513286i
$195$	−9.28113e8	−	4.72624e8i	−0.641893	−	0.326871i
$196$	8.96732e7	+	1.55319e8i	0.0607629	+	0.105244i
$197$		−	3.42083e8i		−	0.227126i	−0.993531	−	0.113563i	$-0.963774\pi$
$197$		−	3.42083e8i		−	0.227126i	0.993531	−	0.113563i	$-0.0362264\pi$
$198$	1.30021e8	+	1.78782e8i	0.0845964	+	0.116322i
$199$	1.74610e9			1.11341			0.556707	−	0.830709i	$-0.312064\pi$
$199$	1.74610e9			1.11341			0.556707	+	0.830709i	$0.312064\pi$
$200$	−6.61640e7	+	3.81998e7i	−0.0413525	+	0.0238749i
$201$	1.65984e9	−	8.73780e7i	1.01691	−	0.0535325i
$202$	7.79067e6	−	1.34938e7i	0.00467917	−	0.00810456i
$203$	6.63327e8	+	3.82972e8i	0.390610	+	0.225519i
$204$	−6.10523e7	−	1.15976e9i	−0.0352518	−	0.669647i
$205$	1.45259e9	+	2.51596e9i	0.822483	+	1.42458i
$206$			2.76739e7i			0.0153674i
$207$	−8.82245e7	+	6.41620e7i	−0.0480516	+	0.0349459i
$208$	1.17324e9			0.626808
$209$	−3.99626e9	+	2.30724e9i	−2.09444	+	1.20923i
$210$	8.94807e7	−	1.75717e8i	0.0460100	−	0.0903519i
$211$	−3.91226e8	+	6.77624e8i	−0.197378	+	0.341868i	−0.947677	−	0.319230i	$-0.896576\pi$
$211$	−3.91226e8	+	6.77624e8i	−0.197378	+	0.341868i	0.750300	+	0.661098i	$0.229909\pi$
$212$	1.04513e9	+	6.03404e8i	0.517399	+	0.298720i
$213$	1.41703e9	−	9.20704e8i	0.688433	−	0.447303i
$214$	−1.64505e8	−	2.84931e8i	−0.0784375	−	0.135858i
$215$		−	1.79813e9i		−	0.841527i
$216$	6.59869e7	+	4.14740e8i	0.0303140	+	0.190529i
$217$	3.72881e8			0.168163
$218$	−2.20914e8	+	1.27545e8i	−0.0978133	+	0.0564725i
$219$	−3.98346e8	−	6.13085e8i	−0.173175	−	0.266529i
$220$	1.92323e9	−	3.33114e9i	0.820997	−	1.42201i
$221$	9.01890e8	+	5.20707e8i	0.378081	+	0.218285i
$222$	−1.25173e8	−	6.37421e7i	−0.0515347	−	0.0262430i
$223$	−7.87235e8	−	1.36353e9i	−0.318335	−	0.551373i	0.661806	−	0.749675i	$-0.269790\pi$
$223$	−7.87235e8	−	1.36353e9i	−0.318335	−	0.551373i	−0.980141	+	0.198303i	$0.936457\pi$
$224$			6.77075e8i			0.268933i
$225$	−6.30819e8	+	6.66002e7i	−0.246136	+	0.0259864i
$226$	1.49607e8			0.0573481
$227$	−7.54169e8	+	4.35419e8i	−0.284031	+	0.163985i	−0.635247	−	0.772309i	$-0.719102\pi$
$227$	−7.54169e8	+	4.35419e8i	−0.284031	+	0.163985i	0.351216	+	0.936294i	$0.385768\pi$
$228$	−4.35641e9	+	2.29332e8i	−1.61209	+	0.0848644i
$229$	−1.86296e9	+	3.22674e9i	−0.677425	+	1.17334i	0.298328	+	0.954463i	$0.403571\pi$
$229$	−1.86296e9	+	3.22674e9i	−0.677425	+	1.17334i	−0.975754	+	0.218872i	$0.929762\pi$
$230$	−1.55871e7	−	8.99921e6i	−0.00556998	−	0.00321583i
$231$	2.08071e8	+	3.95253e9i	0.0730741	+	1.38812i
$232$	−1.34569e8	−	2.33080e8i	−0.0464508	−	0.0804552i
$233$		−	3.81360e9i		−	1.29393i	−0.762519	−	0.646966i	$-0.776037\pi$
$233$		−	3.81360e9i		−	1.29393i	0.762519	−	0.646966i	$-0.223963\pi$
$234$	−1.71237e8	−	7.61436e7i	−0.0571128	−	0.0253963i
$235$	−6.52953e9			−2.14097
$236$	2.12944e9	−	1.22944e9i	0.686465	−	0.396331i
$237$	1.22941e9	−	2.41426e9i	0.389677	−	0.765227i
$238$	−9.85841e7	+	1.70753e8i	−0.0307255	+	0.0532181i
$239$	1.45580e9	+	8.40504e8i	0.446179	+	0.257601i	0.706215	−	0.707997i	$-0.250401\pi$
$239$	1.45580e9	+	8.40504e8i	0.446179	+	0.257601i	−0.260036	+	0.965599i	$0.583735\pi$
$240$	3.02007e9	−	1.96226e9i	0.910273	−	0.591441i
$241$	2.41777e8	+	4.18769e8i	0.0716714	+	0.124139i	0.899634	−	0.436645i	$-0.143833\pi$
$241$	2.41777e8	+	4.18769e8i	0.0716714	+	0.124139i	−0.827963	+	0.560783i	$0.810500\pi$
$242$		−	3.99686e8i		−	0.116535i
$243$	−8.98505e8	+	3.36903e9i	−0.257689	+	0.966228i
$244$	1.54475e9			0.435812
$245$	−4.27546e8	+	2.46844e8i	−0.118664	+	0.0685107i
$246$	2.84804e8	+	4.38335e8i	0.0777688	+	0.119692i
$247$	1.95594e9	−	3.38779e9i	0.525494	−	0.910183i
$248$	−1.13470e8	−	6.55117e7i	−0.0299966	−	0.0173186i
$249$	4.24851e9	+	2.16347e9i	1.10520	+	0.562800i
$250$	1.59096e8	+	2.75563e8i	0.0407286	+	0.0705440i
$251$		−	2.22445e9i		−	0.560438i	−0.959936	−	0.280219i	$-0.909593\pi$
$251$		−	2.22445e9i		−	0.560438i	0.959936	−	0.280219i	$-0.0904070\pi$
$252$	−1.52034e9	+	3.41904e9i	−0.376996	+	0.847816i
$253$	3.61268e8			0.0881753
$254$	3.09338e8	−	1.78596e8i	0.0743187	−	0.0429079i
$255$	3.19246e9	−	1.68059e8i	0.755032	−	0.0397467i
$256$	−1.94860e9	+	3.37507e9i	−0.453693	+	0.785820i
$257$	1.51490e9	+	8.74631e8i	0.347258	+	0.200490i	0.663477	−	0.748197i	$-0.269080\pi$
$257$	1.51490e9	+	8.74631e8i	0.347258	+	0.200490i	−0.316219	+	0.948686i	$0.602413\pi$
$258$	−1.70085e7	−	3.23095e8i	−0.00383872	−	0.0729207i
$259$	−1.25751e9	−	2.17807e9i	−0.279455	−	0.484031i
$260$			3.26080e9i			0.713561i
$261$	−2.34617e8	−	2.22223e9i	−0.0505589	−	0.478880i
$262$	1.76345e8			0.0374246
$263$	3.84885e9	−	2.22214e9i	0.804467	−	0.464459i	−0.0405638	−	0.999177i	$-0.512915\pi$
$263$	3.84885e9	−	2.22214e9i	0.804467	−	0.464459i	0.845031	+	0.534718i	$0.179582\pi$
$264$	6.31106e8	−	1.23933e9i	0.129923	−	0.255136i
$265$	−1.66099e9	+	2.87692e9i	−0.336810	+	0.583371i
$266$	6.41402e8	+	3.70313e8i	0.128116	+	0.0739678i
$267$	−5.87642e9	+	3.81815e9i	−1.15629	+	0.751290i
$268$	−2.60192e9	−	4.50665e9i	−0.504376	−	0.873604i
$269$		−	5.21729e9i		−	0.996405i	−0.867061	−	0.498203i	$-0.833994\pi$
$269$		−	5.21729e9i		−	0.996405i	0.867061	−	0.498203i	$-0.166006\pi$
$270$	−5.68135e8	+	9.03927e7i	−0.106905	+	0.0170090i
$271$	3.10877e9			0.576383			0.288191	−	0.957573i	$-0.406946\pi$
$271$	3.10877e9			0.576383			0.288191	+	0.957573i	$0.406946\pi$
$272$	−3.11872e9	+	1.80060e9i	−0.569772	+	0.328958i
$273$	−1.82812e9	−	2.81361e9i	−0.329119	−	0.506540i
$274$	−2.33862e8	+	4.05061e8i	−0.0414914	+	0.0718652i
$275$	1.81925e9	+	1.05034e9i	0.318098	+	0.183654i
$276$	3.04346e8	+	1.54983e8i	0.0524484	+	0.0267083i
$277$	2.64734e9	+	4.58533e9i	0.449667	+	0.778846i	0.998364	−	0.0571750i	$-0.0182093\pi$
$277$	2.64734e9	+	4.58533e9i	0.449667	+	0.778846i	−0.548697	+	0.836021i	$0.684876\pi$
$278$			6.74240e6i			0.00112885i
$279$	−6.39834e8	−	8.79790e8i	−0.105597	−	0.145198i
$280$	−1.24057e9			−0.201832
$281$	−8.33058e9	+	4.80966e9i	−1.33613	+	0.771417i	−0.986232	−	0.165369i	$-0.947118\pi$
$281$	−8.33058e9	+	4.80966e9i	−1.33613	+	0.771417i	−0.349902	+	0.936786i	$0.613785\pi$
$282$	−1.17325e9	+	6.17626e7i	−0.185521	+	0.00976627i
$283$	3.79931e9	−	6.58060e9i	0.592323	−	1.02593i	−0.401595	−	0.915817i	$-0.631544\pi$
$283$	3.79931e9	−	6.58060e9i	0.592323	−	1.02593i	0.993919	−	0.110117i	$-0.0351225\pi$
$284$	−4.58186e9	−	2.64534e9i	−0.704317	−	0.406638i
$285$	−6.31283e8	−	1.19919e10i	−0.0956852	−	1.81764i
$286$	3.10311e8	+	5.37474e8i	0.0463802	+	0.0803328i
$287$			9.35929e9i			1.37948i
$288$	1.59751e9	−	1.16181e9i	0.232207	−	0.168874i
$289$	3.77920e9			0.541763
$290$	3.19287e8	−	1.84340e8i	0.0451429	−	0.0260633i
$291$	−3.44671e9	+	6.76846e9i	−0.480654	+	0.943882i
$292$	−1.14452e9	+	1.98236e9i	−0.157431	+	0.272679i
$293$	−5.56560e9	−	3.21330e9i	−0.755164	−	0.435994i	0.0723925	−	0.997376i	$-0.476937\pi$
$293$	−5.56560e9	−	3.21330e9i	−0.755164	−	0.435994i	−0.827557	+	0.561382i	$0.810270\pi$
$294$	−7.44880e7	+	4.83979e7i	−0.00997004	+	0.00647794i
$295$	3.38427e9	+	5.86173e9i	0.446866	+	0.773995i
$296$			8.83730e8i			0.115120i
$297$	8.96872e9	−	7.27316e9i	1.15267	−	0.934754i
$298$	−1.92787e8			−0.0244463
$299$	−2.65230e8	+	1.53130e8i	−0.0331847	+	0.0191592i
$300$	1.08201e9	+	1.66530e9i	0.133582	+	0.205593i
$301$	2.89643e9	−	5.01676e9i	0.352855	−	0.611163i
$302$	−1.15306e9	−	6.65719e8i	−0.138619	−	0.0800319i
$303$	−7.25267e8	−	3.69328e8i	−0.0860453	−	0.0438169i
$304$	6.76362e9	+	1.17149e10i	0.791926	+	1.37166i
$305$			4.25224e9i			0.491381i
$306$	5.72043e8	−	6.03948e7i	0.0652443	−	0.00688833i
$307$	5.43787e9			0.612174			0.306087	−	0.952003i	$-0.400980\pi$
$307$	5.43787e9			0.612174			0.306087	+	0.952003i	$0.400980\pi$
$308$	1.07316e10	−	6.19588e9i	1.19251	−	0.688494i
$309$	1.44354e9	−	7.59917e7i	0.158342	−	0.00833551i
$310$	8.97417e7	−	1.55437e8i	0.00971734	−	0.0168309i
$311$	1.27840e10	+	7.38087e9i	1.36655	+	0.788980i	0.990486	−	0.137613i	$-0.0439430\pi$
$311$	1.27840e10	+	7.38087e9i	1.36655	+	0.788980i	0.376067	+	0.926593i	$0.377276\pi$
$312$	6.19801e7	+	1.17738e9i	0.00654084	+	0.124250i
$313$	−8.94368e9	−	1.54909e10i	−0.931834	−	1.61398i	−0.780184	−	0.625550i	$-0.784874\pi$
$313$	−8.94368e9	−	1.54909e10i	−0.931834	−	1.61398i	−0.151651	−	0.988434i	$-0.548459\pi$
$314$		−	1.59751e8i		−	0.0164333i
$315$	−9.41159e9	−	4.18503e9i	−0.955919	−	0.425066i
$316$	−8.48217e9			−0.850665
$317$	3.92566e9	−	2.26648e9i	0.388754	−	0.224447i	−0.292866	−	0.956154i	$-0.594609\pi$
$317$	3.92566e9	−	2.26648e9i	0.388754	−	0.224447i	0.681620	+	0.731706i	$0.261276\pi$
$318$	−2.71240e8	+	5.32646e8i	−0.0265244	+	0.0520871i
$319$	−3.70012e9	+	6.40879e9i	−0.357316	+	0.618890i
$320$	−9.57549e9	−	5.52841e9i	−0.913190	−	0.527230i
$321$	−1.44110e10	+	9.36343e9i	−1.35730	+	0.881891i
$322$	−2.89918e7	−	5.02153e7i	−0.00269682	−	0.00467103i
$323$			1.20073e10i			1.10315i
$324$	1.06758e10	−	2.27965e9i	0.968767	−	0.206866i
$325$	−1.78084e9			−0.159621
$326$	−3.22896e8	+	1.86424e8i	−0.0285886	+	0.0165056i
$327$	7.25970e9	+	1.11732e10i	0.634933	+	0.977210i
$328$	1.64434e9	−	2.84808e9i	0.142068	−	0.246069i
$329$	−1.82173e10	−	1.05177e10i	−1.55489	−	0.897716i
$330$	1.69771e9	+	8.64525e8i	0.143155	+	0.0728990i
$331$	−4.98842e9	−	8.64019e9i	−0.415576	−	0.719800i	0.579912	−	0.814679i	$-0.303087\pi$
$331$	−4.98842e9	−	8.64019e9i	−0.415576	−	0.719800i	−0.995489	+	0.0948794i	$0.969753\pi$
$332$		−	1.49266e10i		−	1.22859i
$333$	−2.98123e9	+	6.70440e9i	−0.242448	+	0.545234i
$334$	9.19862e8			0.0739157
$335$	1.24055e10	−	7.16231e9i	0.984996	−	0.568687i
$336$	1.15867e10	−	6.09954e8i	0.909084	−	0.0478564i
$337$	−6.66219e9	+	1.15392e10i	−0.516532	+	0.894660i	0.483284	+	0.875464i	$0.339444\pi$
$337$	−6.66219e9	+	1.15392e10i	−0.516532	+	0.894660i	−0.999816	+	0.0191959i	$0.993889\pi$
$338$	6.39836e8	+	3.69409e8i	0.0490232	+	0.0283036i
$339$	−4.10817e8	−	7.80391e9i	−0.0311064	−	0.590899i
$340$	−5.00441e9	−	8.66790e9i	−0.374488	−	0.648632i
$341$			3.60262e9i			0.266441i
$342$	−2.26862e8	−	2.14877e9i	−0.0165828	−	0.157068i
$343$	−1.45550e10			−1.05156
$344$	−1.76279e9	+	1.01775e9i	−0.125883	+	0.0726787i
$345$	−4.26621e8	+	8.37776e8i	−0.0301138	+	0.0591359i
$346$	4.28458e8	−	7.42111e8i	0.0298954	−	0.0517803i
$347$	7.37200e8	+	4.25623e8i	0.0508473	+	0.0293567i	0.525208	−	0.850974i	$-0.323987\pi$
$347$	7.37200e8	+	4.25623e8i	0.0508473	+	0.0293567i	−0.474361	+	0.880330i	$0.657321\pi$
$348$	−5.86647e9	+	3.81168e9i	−0.400000	+	0.259896i
$349$	1.04327e10	+	1.80700e10i	0.703228	+	1.21803i	0.967327	+	0.253531i	$0.0815919\pi$
$349$	1.04327e10	+	1.80700e10i	0.703228	+	1.21803i	−0.264099	+	0.964495i	$0.585075\pi$
$350$		−	3.37161e8i		−	0.0224681i
$351$	−3.50164e9	+	9.14126e9i	−0.230697	+	0.602251i
$352$	−6.54161e9			−0.426103
$353$	1.54516e10	−	8.92099e9i	0.995119	−	0.574532i	0.0883185	−	0.996092i	$-0.471851\pi$
$353$	1.54516e10	−	8.92099e9i	0.995119	−	0.574532i	0.906800	+	0.421560i	$0.138517\pi$
$354$	6.63543e8	+	1.02124e9i	0.0422529	+	0.0650304i
$355$	7.28183e9	−	1.26125e10i	0.458487	−	0.794123i
$356$	1.90009e10	+	1.09702e10i	1.18297	+	0.682989i
$357$	9.17762e9	+	4.67353e9i	0.565012	+	0.287721i
$358$	−3.32501e8	−	5.75908e8i	−0.0202423	−	0.0350607i
$359$			5.27791e9i			0.317749i	0.987299	+	0.158875i	$0.0507865\pi$
$359$			5.27791e9i			0.317749i	−0.987299	+	0.158875i	$0.949213\pi$
$360$	2.12872e9	+	2.92705e9i	0.126739	+	0.174269i
$361$	2.81196e10			1.65569
$362$	−7.91024e8	+	4.56698e8i	−0.0460633	+	0.0265947i
$363$	−2.08487e10	+	1.09753e9i	−1.20075	+	0.0632103i
$364$	−5.25249e9	+	9.09758e9i	−0.299199	+	0.518227i
$365$	−5.45685e9	−	3.15051e9i	−0.307447	−	0.177505i
$366$	4.02218e7	+	7.64056e8i	0.00224149	+	0.0425796i
$367$	−9.26843e9	−	1.60534e10i	−0.510907	−	0.884917i	−0.999920	−	0.0126403i	$-0.995976\pi$
$367$	−9.26843e9	−	1.60534e10i	−0.510907	−	0.884917i	0.489013	−	0.872276i	$-0.337357\pi$
$368$		−	1.05905e9i		−	0.0577462i
$369$	2.20827e10	−	1.60598e10i	1.19109	−	0.866232i
$370$	−1.21058e9			−0.0645934
$371$	−9.26828e9	+	5.35104e9i	−0.489219	+	0.282451i
$372$	−1.54551e9	+	3.03499e9i	−0.0807050	+	0.158484i
$373$	4.63639e9	−	8.03046e9i	0.239522	−	0.414864i	−0.721056	−	0.692877i	$-0.756343\pi$
$373$	4.63639e9	−	8.03046e9i	0.239522	−	0.414864i	0.960577	+	0.278014i	$0.0896761\pi$
$374$	−1.64974e9	−	9.52479e8i	−0.0843198	−	0.0486821i
$375$	1.39372e10	−	9.05557e9i	0.704775	−	0.457921i
$376$	3.69573e9	+	6.40120e9i	0.184905	+	0.320265i
$377$		−	6.27347e9i		−	0.310558i
$378$	−1.73069e9	−	6.62957e8i	−0.0847720	−	0.0324727i
$379$	−1.41434e10			−0.685485			−0.342743	−	0.939429i	$-0.611356\pi$
$379$	−1.41434e10			−0.685485			−0.342743	+	0.939429i	$0.611356\pi$
$380$	−3.25594e10	+	1.87982e10i	−1.56150	+	0.901532i
$381$	−1.01655e10	−	1.56455e10i	−0.482423	−	0.742486i
$382$	7.40802e8	−	1.28311e9i	0.0347895	−	0.0602572i
$383$	4.91342e9	+	2.83677e9i	0.228344	+	0.131834i	0.609808	−	0.792549i	$-0.291247\pi$
$383$	4.91342e9	+	2.83677e9i	0.228344	+	0.131834i	−0.381464	+	0.924384i	$0.624580\pi$
$384$	−7.33602e9	−	3.73573e9i	−0.337393	−	0.171811i
$385$	1.70554e10	+	2.95409e10i	0.776282	+	1.34456i
$386$			3.02432e8i			0.0136232i
$387$	−1.68068e10	+	1.77442e9i	−0.749273	+	0.0791064i
$388$	2.37801e10			1.04927
$389$	−3.71981e10	+	2.14764e10i	−1.62451	+	0.937912i	−0.638819	+	0.769357i	$0.720577\pi$
$389$	−3.71981e10	+	2.14764e10i	−1.62451	+	0.937912i	−0.985692	+	0.168555i	$0.946090\pi$
$390$	−1.61284e9	+	8.49039e7i	−0.0697161	+	0.00367003i
$391$	4.70024e8	−	8.14106e8i	0.0201101	−	0.0348316i
$392$	4.83985e8	+	2.79429e8i	0.0204969	+	0.0118339i
$393$	−4.84238e8	−	9.19862e9i	−0.0202996	−	0.385614i
$394$	−2.65232e8	−	4.59395e8i	−0.0110063	−	0.0190635i
$395$		−	2.33489e10i		−	0.959132i
$396$	−3.30333e10	−	1.46889e10i	−1.34329	−	0.597320i
$397$	−1.29576e10			−0.521629			−0.260815	−	0.965389i	$-0.583991\pi$
$397$	−1.29576e10			−0.521629			−0.260815	+	0.965389i	$0.583991\pi$
$398$	2.34490e9	−	1.35383e9i	0.0934527	−	0.0539550i
$399$	1.75553e10	−	3.44741e10i	0.692653	−	1.36020i
$400$	3.07905e9	−	5.33308e9i	0.120275	−	0.208323i
$401$	2.41518e10	+	1.39441e10i	0.934055	+	0.539277i	0.888092	−	0.459666i	$-0.152031\pi$
$401$	2.41518e10	+	1.39441e10i	0.934055	+	0.539277i	0.0459636	+	0.998943i	$0.485364\pi$
$402$	2.16131e9	−	1.40429e9i	0.0827585	−	0.0537715i
$403$	−1.52704e9	−	2.64491e9i	−0.0578936	−	0.100275i
$404$			2.54813e9i			0.0956524i
$405$	6.27521e9	+	2.93872e10i	0.233243	+	1.09229i
$406$	1.18774e9			0.0437137
$407$	2.10436e10	−	1.21495e10i	0.766907	−	0.442774i
$408$	−1.97170e9	−	3.03460e9i	−0.0711542	−	0.109512i
$409$	−4.27541e9	+	7.40523e9i	−0.152786	+	0.264634i	−0.932251	−	0.361813i	$-0.882158\pi$
$409$	−4.27541e9	+	7.40523e9i	−0.152786	+	0.264634i	0.779464	+	0.626446i	$0.215491\pi$
$410$	3.90146e9	+	2.25251e9i	0.138068	+	0.0797134i
$411$	2.17713e10	+	1.10866e10i	0.762985	+	0.388536i
$412$	−2.26286e9	−	3.91939e9i	−0.0785359	−	0.136028i
$413$			2.18055e10i			0.749490i
$414$	−6.87322e7	+	1.54570e8i	−0.00233969	+	0.00526166i
$415$	4.10885e10			1.38525
$416$	4.80262e9	−	2.77279e9i	0.160363	−	0.0925857i
$417$	3.51701e8	−	1.85144e7i	0.0116313	−	0.000612302i
$418$	−3.57781e9	+	6.19696e9i	−0.117196	+	0.202989i
$419$	−3.62561e10	−	2.09324e10i	−1.17632	−	0.679147i	−0.221157	−	0.975238i	$-0.570983\pi$
$419$	−3.62561e10	−	2.09324e10i	−1.17632	−	0.679147i	−0.955160	+	0.296091i	$0.904317\pi$
$420$	1.69525e9	+	3.22031e10i	0.0544800	+	1.03491i
$421$	−2.25988e10	−	3.91422e10i	−0.719377	−	1.24600i	−0.961247	−	0.275689i	$-0.911094\pi$
$421$	−2.25988e10	−	3.91422e10i	−0.719377	−	1.24600i	0.241870	−	0.970309i	$-0.422239\pi$
$422$			1.21334e9i			0.0382589i
$423$	6.44340e9	+	6.10301e10i	0.201258	+	1.90626i
$424$	3.76051e9			0.116355
$425$	4.73384e9	−	2.73308e9i	0.145097	−	0.0837716i
$426$	1.18912e9	−	2.33513e9i	0.0361067	−	0.0709044i
$427$	−6.84950e9	+	1.18637e10i	−0.206038	+	0.356868i
$428$	4.65969e10	+	2.69027e10i	1.38861	+	0.801717i
$429$	2.71840e10	−	1.76625e10i	0.802571	−	0.521463i
$430$	−1.39417e9	−	2.41478e9i	−0.0407796	−	0.0706323i
$431$		−	3.78891e10i		−	1.09801i	−0.835820	−	0.549003i	$-0.815007\pi$
$431$		−	3.78891e10i		−	1.09801i	0.835820	−	0.549003i	$-0.184993\pi$
$432$	−2.13211e10	−	2.62915e10i	−0.612172	−	0.754886i
$433$	−5.16116e10			−1.46824			−0.734118	−	0.679022i	$-0.762404\pi$
$433$	−5.16116e10			−1.46824			−0.734118	+	0.679022i	$0.762404\pi$
$434$	5.00755e8	−	2.89111e8i	0.0141145	−	0.00814903i
$435$	−1.04924e10	−	1.61487e10i	−0.293035	−	0.451003i
$436$	2.08584e10	−	3.61277e10i	0.577210	−	0.999758i
$437$	−3.05804e9	−	1.76556e9i	−0.0838528	−	0.0484124i
$438$	−1.01031e9	−	5.14478e8i	−0.0274509	−	0.0139788i
$439$	2.71931e10	+	4.70998e10i	0.732151	+	1.26812i	0.955962	+	0.293490i	$0.0948167\pi$
$439$	2.71931e10	+	4.70998e10i	0.732151	+	1.26812i	−0.223811	+	0.974633i	$0.571850\pi$
$440$		−	1.19859e10i		−	0.319786i
$441$	2.72910e9	+	3.75259e9i	0.0721549	+	0.0992150i
$442$	1.61491e9			0.0423115
$443$	1.66107e10	−	9.59019e9i	0.431293	−	0.249007i	−0.268604	−	0.963251i	$-0.586562\pi$
$443$	1.66107e10	−	9.59019e9i	0.431293	−	0.249007i	0.699897	+	0.714243i	$0.253229\pi$
$444$	2.29401e10	−	1.20762e9i	0.590287	−	0.0310741i
$445$	−3.01977e10	+	5.23039e10i	−0.770075	+	1.33381i
$446$	−2.11441e9	−	1.22075e9i	−0.0534379	−	0.0308524i
$447$	5.29388e8	+	1.00563e10i	0.0132600	+	0.251889i
$448$	−1.78103e10	−	3.08483e10i	−0.442139	−	0.765808i
$449$		−	4.22624e10i		−	1.03984i	−0.854213	−	0.519922i	$-0.825961\pi$
$449$		−	4.22624e10i		−	1.03984i	0.854213	−	0.519922i	$-0.174039\pi$
$450$	−7.95510e8	+	5.78541e8i	−0.0193997	+	0.0141086i
$451$	−9.04256e10			−2.18567
$452$	−2.11885e10	+	1.22332e10i	−0.507629	+	0.293080i
$453$	−3.15594e10	+	6.19747e10i	−0.749439	+	1.47171i
$454$	−6.75200e8	+	1.16948e9i	−0.0158931	+	0.0275277i
$455$	−2.50429e10	−	1.44586e10i	−0.584305	−	0.337349i
$456$	−1.13989e10	+	7.40634e9i	−0.263636	+	0.171295i
$457$	−1.00776e9	−	1.74548e9i	−0.0231042	−	0.0400176i	0.854242	−	0.519875i	$-0.174022\pi$
$457$	−1.00776e9	−	1.74548e9i	−0.0231042	−	0.0400176i	−0.877346	+	0.479858i	$0.840688\pi$
$458$			5.77774e9i			0.131309i
$459$	−4.72116e9	−	2.96734e10i	−0.106365	−	0.668524i
$460$	2.94342e9			0.0657386
$461$	2.17450e10	−	1.25545e10i	0.481454	−	0.277968i	−0.239568	−	0.970880i	$-0.577006\pi$
$461$	2.17450e10	−	1.25545e10i	0.481454	−	0.277968i	0.721022	+	0.692912i	$0.243673\pi$
$462$	3.34400e9	+	5.14667e9i	0.0734004	+	0.112969i
$463$	3.43212e10	−	5.94461e10i	0.746859	−	1.29360i	−0.202462	−	0.979290i	$-0.564894\pi$
$463$	3.43212e10	−	5.94461e10i	0.746859	−	1.29360i	0.949321	−	0.314308i	$-0.101772\pi$
$464$	1.87872e10	+	1.08468e10i	0.405312	+	0.234007i
$465$	−8.35444e9	−	4.25434e9i	−0.178692	−	0.0909956i
$466$	−2.95685e9	−	5.12142e9i	−0.0627027	−	0.108604i
$467$			3.96558e10i			0.833757i	0.908962	+	0.416878i	$0.136876\pi$
$467$			3.96558e10i			0.833757i	−0.908962	+	0.416878i	$0.863124\pi$
$468$	3.04780e10	−	3.21779e9i	0.635335	−	0.0670771i
$469$	4.61481e10			0.953811
$470$	−8.76873e9	+	5.06263e9i	−0.179699	+	0.103749i
$471$	−8.33306e9	+	4.38672e8i	−0.169325	+	0.00891367i
$472$	3.83102e9	−	6.63552e9i	0.0771874	−	0.133692i
$473$	4.84699e10	+	2.79841e10i	0.968338	+	0.559070i
$474$	−2.20857e8	−	4.19541e9i	−0.00437519	−	0.0831115i
$475$	−1.02663e10	−	1.77818e10i	−0.201670	−	0.349302i
$476$		−	3.22444e10i		−	0.628096i
$477$	2.85291e10	+	1.26860e10i	0.551079	+	0.245047i
$478$	2.60672e9			0.0499324
$479$	−2.67898e10	+	1.54671e10i	−0.508894	+	0.293810i	−0.732379	−	0.680897i	$-0.761590\pi$
$479$	−2.67898e10	+	1.54671e10i	−0.508894	+	0.293810i	0.223485	+	0.974707i	$0.428257\pi$
$480$	7.72499e9	−	1.51699e10i	0.145524	−	0.285771i
$481$	−1.02996e10	+	1.78395e10i	−0.192416	+	0.333274i
$482$	6.49380e8	+	3.74920e8i	0.0120313	+	0.00694625i
$483$	−2.53975e9	+	1.65018e9i	−0.0466662	+	0.0303209i
$484$	3.26818e10	+	5.66065e10i	0.595559	+	1.03154i
$485$			6.54595e10i			1.18306i
$486$	1.40552e9	+	5.22104e9i	0.0251937	+	0.0935862i
$487$	1.04034e11			1.84952			0.924761	−	0.380549i	$-0.124265\pi$
$487$	1.04034e11			1.84952			0.924761	+	0.380549i	$0.124265\pi$
$488$	4.16867e9	−	2.40678e9i	0.0735052	−	0.0424383i
$489$	1.06110e10	+	1.63312e10i	0.185576	+	0.285616i
$490$	−3.82778e8	+	6.62991e8i	−0.00663992	+	0.0115007i
$491$	−7.15518e10	−	4.13104e10i	−1.23110	−	0.710778i	−0.263843	−	0.964566i	$-0.584990\pi$
$491$	−7.15518e10	−	4.13104e10i	−1.23110	−	0.710778i	−0.967260	+	0.253788i	$0.918324\pi$
$492$	−7.61781e10	−	3.87923e10i	−1.30008	−	0.662041i
$493$	9.62801e9	+	1.66762e10i	0.162985	+	0.282299i
$494$		−	6.06611e9i		−	0.101860i
$495$	4.04341e10	−	9.09309e10i	0.673483	−	1.51457i
$496$	1.05610e10			0.174493
$497$	4.06324e10	−	2.34591e10i	0.665957	−	0.384491i
$498$	7.38291e9	−	3.88654e8i	0.120036	−	0.00631896i
$499$	−3.38096e10	+	5.85599e10i	−0.545303	+	0.944492i	0.453285	+	0.891366i	$0.350252\pi$
$499$	−3.38096e10	+	5.85599e10i	−0.545303	+	0.944492i	−0.998588	+	0.0531262i	$0.983081\pi$
$500$	−4.50648e10	−	2.60182e10i	−0.721037	−	0.416291i
$501$	−2.52591e9	−	4.79825e10i	−0.0400929	−	0.761608i
$502$	−1.72471e9	−	2.98729e9i	−0.0271582	−	0.0470395i
$503$			1.23313e11i			1.92635i	0.268867	+	0.963177i	$0.413351\pi$
$503$			1.23313e11i			1.92635i	−0.268867	+	0.963177i	$0.586649\pi$
$504$	1.22421e9	+	1.15954e10i	0.0189729	+	0.179706i
$505$	−7.01425e9			−0.107849
$506$	4.85159e8	−	2.80107e8i	0.00740086	−	0.00427289i
$507$	1.75124e10	−	3.43899e10i	0.265042	−	0.520474i
$508$	−2.92072e10	+	5.05883e10i	−0.438566	+	0.759618i
$509$	−7.57066e10	−	4.37092e10i	−1.12788	−	0.651181i	−0.184479	−	0.982837i	$-0.559060\pi$
$509$	−7.57066e10	−	4.37092e10i	−1.12788	−	0.651181i	−0.943401	+	0.331655i	$0.892393\pi$
$510$	4.15697e9	−	2.70095e9i	0.0614463	−	0.0399242i
$511$	−1.01497e10	−	1.75798e10i	−0.148857	−	0.257827i
$512$			3.20619e10i			0.466562i
$513$	−1.11463e11	+	1.77342e10i	−1.60939	+	0.256060i
$514$	2.71256e9			0.0388621
$515$	1.07889e10	−	6.22898e9i	0.153373	−	0.0885499i
$516$	2.88279e10	+	4.43683e10i	0.406644	+	0.625855i
$517$	1.01618e11	−	1.76008e11i	1.42236	−	2.46359i
$518$	−3.37751e9	−	1.95000e9i	−0.0469113	−	0.0270842i
$519$	−3.98870e10	−	2.03117e10i	−0.549746	−	0.279948i
$520$	5.08046e9	+	8.79961e9i	0.0694848	+	0.120351i
$521$			4.04435e9i			0.0548906i	0.999623	+	0.0274453i	$0.00873721\pi$
$521$			4.04435e9i			0.0548906i	−0.999623	+	0.0274453i	$0.991263\pi$
$522$	−2.03807e9	−	2.80240e9i	−0.0274496	−	0.0377440i
$523$	2.72416e10			0.364105			0.182052	−	0.983289i	$-0.441726\pi$
$523$	2.72416e10			0.364105			0.182052	+	0.983289i	$0.441726\pi$
$524$	−2.49753e10	+	1.44195e10i	−0.331272	+	0.191260i
$525$	−1.75872e10	+	9.25834e8i	−0.231505	+	0.0121870i
$526$	3.44584e9	−	5.96837e9i	0.0450145	−	0.0779673i
$527$	8.11840e9	+	4.68716e9i	0.105251	+	0.0607669i
$528$	5.89312e9	+	1.11946e11i	0.0758245	+	1.44037i
$529$	−3.90173e10	−	6.75799e10i	−0.498235	−	0.862968i
$530$			5.15136e9i			0.0652858i
$531$	5.14487e10	−	3.74165e10i	0.647137	−	0.470636i
$532$	−1.21120e11			−1.51206
$533$	6.63872e10	−	3.83287e10i	0.822575	−	0.474914i
$534$	−4.93127e9	+	9.68377e9i	−0.0606449	+	0.119091i
$535$	−7.40552e10	+	1.28267e11i	−0.903942	+	1.56567i
$536$	−1.40431e10	−	8.10778e9i	−0.170139	−	0.0982297i
$537$	−2.91279e10	+	1.89255e10i	−0.350277	+	0.227589i
$538$	−4.04520e9	−	7.00648e9i	−0.0482848	−	0.0836317i
$539$		−	1.53664e10i		−	0.182061i
$540$	7.30723e10	−	5.92578e10i	0.859365	−	0.696900i
$541$	2.24803e10			0.262429			0.131215	−	0.991354i	$-0.458112\pi$
$541$	2.24803e10			0.262429			0.131215	+	0.991354i	$0.458112\pi$
$542$	4.17487e9	−	2.41036e9i	0.0483778	−	0.0279309i
$543$	2.59947e10	+	4.00078e10i	0.299010	+	0.460199i
$544$	−8.51091e9	+	1.47413e10i	−0.0971808	+	0.168322i
$545$	9.94490e10	+	5.74169e10i	1.12723	+	0.650809i
$546$	−4.63656e9	−	2.36108e9i	−0.0521705	−	0.0265668i
$547$	5.95117e10	+	1.03077e11i	0.664742	+	1.15137i	0.979355	+	0.202147i	$0.0647917\pi$
$547$	5.95117e10	+	1.03077e11i	0.664742	+	1.15137i	−0.314614	+	0.949220i	$0.601875\pi$
$548$		−	7.64904e10i		−	0.848174i
$549$	3.97448e10	−	4.19615e9i	0.437513	−	0.0461915i
$550$	3.25751e9			0.0355988
$551$	6.26411e10	−	3.61659e10i	0.679600	−	0.392367i
$552$	1.06278e9	−	5.59473e7i	0.0114469	−	0.000602591i
$553$	3.76104e10	−	6.51430e10i	0.402167	−	0.696574i
$554$	7.11042e9	+	4.10520e9i	0.0754842	+	0.0435808i
$555$	3.32423e9	+	6.31473e10i	0.0350363	+	0.665553i
$556$	−5.51317e8	−	9.54909e8i	−0.00576902	−	0.00999224i
$557$		−	4.55371e10i		−	0.473091i	−0.971620	−	0.236545i	$-0.923985\pi$
$557$		−	4.55371e10i		−	0.473091i	0.971620	−	0.236545i	$-0.0760152\pi$
$558$	−1.54139e9	−	6.85409e8i	−0.0158993	−	0.00706990i
$559$	−4.74464e10			−0.485910
$560$	8.65982e10	−	4.99975e10i	0.880555	−	0.508389i
$561$	−4.51537e10	+	8.86704e10i	−0.455871	+	0.895215i
$562$	−7.45829e9	+	1.29181e10i	−0.0747642	+	0.129495i
$563$	4.23095e9	+	2.44274e9i	0.0421119	+	0.0243133i	0.520908	−	0.853613i	$-0.325593\pi$
$563$	4.23095e9	+	2.44274e9i	0.0421119	+	0.0243133i	−0.478796	+	0.877926i	$0.658927\pi$
$564$	1.61114e11	−	1.04682e11i	1.59227	−	1.03456i
$565$	−3.36743e10	−	5.83257e10i	−0.330450	−	0.572356i
$566$		−	1.17831e10i		−	0.114814i
$567$	−2.98292e10	+	9.20979e10i	−0.288608	+	0.891082i
$568$	−1.64862e10			−0.158389
$569$	−1.35833e11	+	7.84230e10i	−1.29585	+	0.748160i	−0.979685	−	0.200544i	$-0.935729\pi$
$569$	−1.35833e11	+	7.84230e10i	−1.29585	+	0.748160i	−0.316167	+	0.948704i	$0.602396\pi$
$570$	−1.01456e10	−	1.56149e10i	−0.0961124	−	0.147924i
$571$	2.43502e10	−	4.21758e10i	0.229065	−	0.396751i	−0.728467	−	0.685081i	$-0.759767\pi$
$571$	2.43502e10	−	4.21758e10i	0.229065	−	0.396751i	0.957531	+	0.288330i	$0.0931000\pi$
$572$	−8.78970e10	−	5.07474e10i	−0.821089	−	0.474056i
$573$	−6.89644e10	−	3.51188e10i	−0.639745	−	0.325778i
$574$	7.25667e9	+	1.25689e10i	0.0668482	+	0.115785i
$575$			1.60750e9i			0.0147055i
$576$	−4.22237e10	+	9.49555e10i	−0.383589	+	0.862641i
$577$	−1.24459e11			−1.12285			−0.561427	−	0.827526i	$-0.689747\pi$
$577$	−1.24459e11			−1.12285			−0.561427	+	0.827526i	$0.689747\pi$
$578$	5.07523e9	−	2.93018e9i	0.0454720	−	0.0262533i
$579$	1.57757e10	−	8.30469e8i	0.140370	−	0.00738940i
$580$	−3.01466e10	+	5.22154e10i	−0.266395	+	0.461409i
$581$	1.14636e11	+	6.61851e10i	1.00604	+	0.580839i
$582$	6.19179e8	+	1.17620e10i	0.00539665	+	0.102515i
$583$	−5.16996e10	−	8.95463e10i	−0.447520	−	0.775128i
$584$			7.13281e9i			0.0613210i
$585$	8.85762e9	+	8.38969e10i	0.0756299	+	0.716346i
$586$	−9.96565e9			−0.0845114
$587$	−3.54754e10	+	2.04817e10i	−0.298796	+	0.172510i	−0.641902	−	0.766787i	$-0.721854\pi$
$587$	−3.54754e10	+	2.04817e10i	−0.298796	+	0.172510i	0.343106	+	0.939297i	$0.388521\pi$
$588$	6.59212e9	−	1.29453e10i	0.0551462	−	0.108293i
$589$	1.76065e10	−	3.04953e10i	0.146289	−	0.253380i
$590$	9.08972e9	+	5.24795e9i	0.0750140	+	0.0433094i
$591$	−2.32350e10	+	1.50967e10i	−0.190455	+	0.123746i
$592$	−3.56160e10	−	6.16887e10i	−0.289973	−	0.502249i
$593$		−	1.81583e11i		−	1.46844i	−0.678909	−	0.734222i	$-0.737547\pi$
$593$		−	1.81583e11i		−	1.46844i	0.678909	−	0.734222i	$-0.262453\pi$
$594$	6.40521e9	−	1.67212e10i	0.0514503	−	0.134314i
$595$	8.87592e10			0.708183
$596$	2.73040e10	−	1.57640e10i	0.216392	−	0.124934i
$597$	−7.70583e10	−	1.18599e11i	−0.606628	−	0.933646i
$598$	−2.37457e8	+	4.11288e8i	−0.00185687	+	0.00321619i
$599$	−3.59585e10	−	2.07606e10i	−0.279315	−	0.161262i	0.353798	−	0.935322i	$-0.384890\pi$
$599$	−3.59585e10	−	2.07606e10i	−0.279315	−	0.161262i	−0.633113	+	0.774059i	$0.718223\pi$
$600$	5.51454e9	+	2.80817e9i	0.0425504	+	0.0216680i
$601$	2.34314e10	+	4.05843e10i	0.179597	+	0.311072i	0.941743	−	0.336334i	$-0.109187\pi$
$601$	2.34314e10	+	4.05843e10i	0.179597	+	0.311072i	−0.762145	+	0.647406i	$0.775854\pi$
$602$		−	8.98291e9i		−	0.0683961i
$603$	−7.91863e10	−	1.08883e11i	−0.598937	−	0.823555i
$604$	2.17740e11			1.63603
$605$	−1.55821e11	+	8.99633e10i	−1.16307	+	0.671497i
$606$	−1.26034e9	+	6.63475e7i	−0.00934540	+	0.000491965i
$607$	−9.46390e10	+	1.63920e11i	−0.697133	+	1.20747i	0.272324	+	0.962206i	$0.412208\pi$
$607$	−9.46390e10	+	1.63920e11i	−0.697133	+	1.20747i	−0.969456	+	0.245264i	$0.921125\pi$
$608$	5.53731e10	+	3.19697e10i	0.405214	+	0.233951i
$609$	−3.26150e9	−	6.19557e10i	−0.0237109	−	0.450414i
$610$	3.29695e9	+	5.71048e9i	0.0238118	+	0.0412433i
$611$			1.72291e11i			1.23623i
$612$	−7.60785e10	+	5.53287e10i	−0.542321	+	0.394407i
$613$	−2.04650e10			−0.144934			−0.0724668	−	0.997371i	$-0.523087\pi$
$613$	−2.04650e10			−0.144934			−0.0724668	+	0.997371i	$0.523087\pi$
$614$	7.30270e9	−	4.21622e9i	0.0513819	−	0.0296654i
$615$	1.06784e11	−	2.09696e11i	0.746456	−	1.46585i
$616$	1.93069e10	−	3.34404e10i	0.134088	−	0.232247i
$617$	1.33253e11	+	7.69336e10i	0.919467	+	0.530855i	0.883465	−	0.468497i	$-0.155204\pi$
$617$	1.33253e11	+	7.69336e10i	0.919467	+	0.530855i	0.0360022	+	0.999352i	$0.488538\pi$
$618$	1.87967e9	−	1.22130e9i	0.0128863	−	0.00837272i
$619$	1.26212e11	+	2.18605e11i	0.859681	+	1.48901i	0.872233	+	0.489090i	$0.162671\pi$
$619$	1.26212e11	+	2.18605e11i	0.859681	+	1.48901i	−0.0125525	+	0.999921i	$0.503996\pi$
$620$			2.93522e10i			0.198643i
$621$	8.25150e9	+	3.16081e9i	0.0554838	+	0.0212536i
$622$	2.28908e10			0.152933
$623$	−1.68502e11	+	9.72846e10i	−1.11854	+	0.645791i
$624$	−5.17771e10	−	7.96890e10i	−0.341507	−	0.525605i
$625$	9.05034e10	−	1.56756e11i	0.593123	−	1.02732i
$626$	−2.40216e10	−	1.38689e10i	−0.156424	−	0.0903115i
$627$	3.33074e11	+	1.69612e11i	2.15512	+	1.09745i
$628$	1.30627e10	+	2.26252e10i	0.0839833	+	0.145463i
$629$		−	6.32281e10i		−	0.403932i
$630$	−1.58840e10	+	1.67699e9i	−0.100832	+	0.0106456i
$631$	1.64752e11			1.03924			0.519618	−	0.854399i	$-0.326074\pi$
$631$	1.64752e11			1.03924			0.519618	+	0.854399i	$0.326074\pi$
$632$	−2.28900e10	+	1.32156e10i	−0.143476	+	0.0828357i
$633$	6.32910e10	−	3.33179e9i	0.394210	−	0.0207522i
$634$	3.51460e9	−	6.08747e9i	0.0217530	−	0.0376773i
$635$	−1.39255e11	−	8.03987e10i	−0.856475	−	0.494486i
$636$	−5.13876e9	−	9.76163e10i	−0.0314072	−	0.596615i
$637$	6.51334e9	+	1.12814e10i	0.0395591	+	0.0685183i
$638$			1.14755e10i			0.0692607i
$639$	−1.25072e11	−	5.56156e10i	−0.750165	−	0.333575i
$640$	−7.09486e10			−0.422887
$641$	2.07985e10	−	1.20080e10i	0.123197	−	0.0711276i	−0.437135	−	0.899396i	$-0.644007\pi$
$641$	2.07985e10	−	1.20080e10i	0.123197	−	0.0711276i	0.560332	+	0.828268i	$0.310674\pi$
$642$	−1.20932e10	+	2.37480e10i	−0.0711871	+	0.139793i
$643$	6.48791e10	−	1.12374e11i	0.379543	−	0.657388i	−0.611453	−	0.791281i	$-0.709415\pi$
$643$	6.48791e10	−	1.12374e11i	0.379543	−	0.657388i	0.990996	+	0.133893i	$0.0427478\pi$
$644$	8.21207e9	+	4.74124e9i	0.0477430	+	0.0275644i
$645$	−1.22133e11	+	7.93546e10i	−0.705657	+	0.458494i
$646$	9.30977e9	+	1.61250e10i	0.0534575	+	0.0925911i
$647$		−	8.11281e10i		−	0.462971i	−0.972838	−	0.231486i	$-0.925641\pi$
$647$		−	8.11281e10i		−	0.462971i	0.972838	−	0.231486i	$-0.0743587\pi$
$648$	2.52579e10	−	2.27851e10i	0.143251	−	0.129227i
$649$	−2.10676e11			−1.18751
$650$	−2.39155e9	+	1.38076e9i	−0.0133975	+	0.00773508i
$651$	−1.64559e10	−	2.53268e10i	−0.0916214	−	0.141012i
$652$	3.04873e10	−	5.28056e10i	0.168705	−	0.292206i
$653$	2.09473e11	+	1.20939e11i	1.15206	+	0.665142i	0.949388	−	0.314105i	$-0.101704\pi$
$653$	2.09473e11	+	1.20939e11i	1.15206	+	0.665142i	0.202672	+	0.979247i	$0.435038\pi$
$654$	1.84124e10	+	9.37617e9i	0.100647	+	0.0512524i
$655$	−3.96926e10	−	6.87496e10i	−0.215647	−	0.373512i
$656$			2.65080e11i			1.43140i
$657$	−2.40623e10	+	5.41129e10i	−0.129144	+	0.290429i
$658$	−3.26195e10			−0.174010
$659$	8.16111e10	−	4.71182e10i	0.432721	−	0.249831i	−0.267784	−	0.963479i	$-0.586291\pi$
$659$	8.16111e10	−	4.71182e10i	0.432721	−	0.249831i	0.700505	+	0.713647i	$0.252958\pi$
$660$	−3.11133e11	+	1.63788e10i	−1.63972	+	0.0863190i
$661$	−1.16496e11	+	2.01777e11i	−0.610245	+	1.05698i	0.380954	+	0.924594i	$0.375596\pi$
$661$	−1.16496e11	+	2.01777e11i	−0.610245	+	1.05698i	−0.991199	+	0.132381i	$0.957738\pi$
$662$	−1.33982e10	−	7.73548e9i	−0.0697615	−	0.0402768i
$663$	−4.43448e9	−	8.42378e10i	−0.0229503	−	0.435967i
$664$	−2.32562e10	−	4.02809e10i	−0.119637	−	0.207218i
$665$		−	3.33408e11i		−	1.70486i
$666$	1.19462e9	+	1.13151e10i	0.00607199	+	0.0575122i
$667$	−5.66284e9			−0.0286109
$668$	−1.30278e11	+	7.52159e10i	−0.654281	+	0.377749i
$669$	−5.78717e10	+	1.13645e11i	−0.288910	+	0.567345i
$670$	1.11065e10	−	1.92370e10i	0.0551160	−	0.0954638i
$671$	−1.14622e11	−	6.61770e10i	−0.565428	−	0.326450i
$672$	4.59883e10	−	2.98804e10i	0.225512	−	0.146524i
$673$	−8.39841e10	−	1.45465e11i	−0.409390	−	0.709084i	0.585432	−	0.810722i	$-0.300925\pi$
$673$	−8.39841e10	−	1.45465e11i	−0.409390	−	0.709084i	−0.994821	+	0.101638i	$0.967592\pi$
$674$			2.06619e10i			0.100122i
$675$	3.23627e10	+	3.99073e10i	0.155894	+	0.192237i
$676$	−1.20824e11			−0.578586
$677$	1.68287e11	−	9.71606e10i	0.801118	−	0.462526i	−0.0427441	−	0.999086i	$-0.513610\pi$
$677$	1.68287e11	−	9.71606e10i	0.801118	−	0.462526i	0.843862	+	0.536560i	$0.180277\pi$
$678$	−6.60242e9	−	1.01616e10i	−0.0312453	−	0.0480888i
$679$	−1.05442e11	+	1.82631e11i	−0.496060	+	0.859202i
$680$	−2.70099e10	−	1.55942e10i	−0.126324	−	0.0729333i
$681$	6.28573e10	+	3.20089e10i	0.292258	+	0.148827i
$682$	2.79327e9	+	4.83809e9i	0.0129115	+	0.0223633i
$683$		−	3.79500e11i		−	1.74393i	−0.489570	−	0.871964i	$-0.662846\pi$
$683$		−	3.79500e11i		−	1.74393i	0.489570	−	0.871964i	$-0.337154\pi$
$684$	2.07832e11	+	2.85775e11i	0.949486	+	1.30557i
$685$	2.10556e11			0.956323
$686$	−1.95464e10	+	1.12851e10i	−0.0882612	+	0.0509576i
$687$	3.01382e11	−	1.58655e10i	1.35298	−	0.0712240i
$688$	8.20345e10	−	1.42088e11i	0.366136	−	0.634167i
$689$	7.59119e10	+	4.38277e10i	0.336847	+	0.194479i
$690$	7.66398e7	+	1.45586e9i	0.000338110	+	0.00642277i
$691$	−3.67841e10	−	6.37120e10i	−0.161342	−	0.279453i	0.774008	−	0.633176i	$-0.218249\pi$
$691$	−3.67841e10	−	6.37120e10i	−0.161342	−	0.279453i	−0.935350	+	0.353723i	$0.884916\pi$
$692$			1.40138e11i			0.611126i
$693$	2.59282e11	−	1.88565e11i	1.12419	−	0.817574i
$694$	1.32002e9			0.00569038
$695$	2.62858e9	−	1.51761e9i	0.0112663	−	0.00650461i
$696$	−9.89253e9	+	1.94264e10i	−0.0421571	+	0.0827858i
$697$	−1.17647e11	+	2.03771e11i	−0.498484	+	0.863400i
$698$	2.80209e10	+	1.61779e10i	0.118049	+	0.0681554i
$699$	−2.59027e11	+	1.68301e11i	−1.08502	+	0.704980i
$700$	2.75692e10	+	4.77513e10i	0.114824	+	0.198881i
$701$			2.33479e11i			0.966885i	0.875376	+	0.483443i	$0.160614\pi$
$701$			2.33479e11i			0.966885i	−0.875376	+	0.483443i	$0.839386\pi$
$702$	2.38514e9	+	1.49911e10i	0.00982124	+	0.0617284i
$703$	−2.37505e11			−0.972415
$704$	2.98044e11	−	1.72076e11i	1.21336	−	0.700533i
$705$	2.88159e11	+	4.43499e11i	1.16648	+	1.79529i
$706$	1.38337e10	−	2.39606e10i	0.0556825	−	0.0964449i
$707$	−1.95696e10	−	1.12985e10i	−0.0783258	−	0.0452214i
$708$	−1.77482e11	−	9.03791e10i	−0.706351	−	0.359696i
$709$	−5.62900e10	−	9.74972e10i	−0.222765	−	0.385840i	0.732882	−	0.680356i	$-0.238175\pi$
$709$	−5.62900e10	−	9.74972e10i	−0.222765	−	0.385840i	−0.955646	+	0.294516i	$0.904842\pi$
$710$		−	2.25837e10i		−	0.0888713i
$711$	−2.18237e11	+	2.30409e10i	−0.853985	+	0.0901616i
$712$	6.83679e10			0.266031
$713$	−2.38747e9	+	1.37841e9i	−0.00923806	+	0.00533360i
$714$	1.59485e10	−	8.39570e8i	0.0613661	−	0.00323046i
$715$	1.39693e11	−	2.41955e11i	0.534502	−	0.925784i
$716$	9.41825e10	+	5.43763e10i	0.358359	+	0.206899i
$717$	−7.15797e9	−	1.35973e11i	−0.0270840	−	0.514490i
$718$	4.09220e9	+	7.08789e9i	0.0153978	+	0.0266698i
$719$		−	8.88990e10i		−	0.332645i	−0.986071	−	0.166323i	$-0.946811\pi$
$719$		−	8.88990e10i		−	0.332645i	0.986071	−	0.166323i	$-0.0531893\pi$
$720$	−2.66561e11	−	1.18531e11i	−0.991898	−	0.441065i
$721$	4.01345e10			0.148517
$722$	3.77628e10	−	2.18024e10i	0.138968	−	0.0802333i
$723$	1.77736e10	−	3.49029e10i	0.0650464	−	0.127735i
$724$	7.46872e10	−	1.29362e11i	0.271826	−	0.470817i
$725$	−2.85166e10	−	1.64641e10i	−0.103216	−	0.0595916i
$726$	−2.71475e10	+	1.76388e10i	−0.0977199	+	0.0634925i
$727$	4.33960e10	+	7.51640e10i	0.155350	+	0.269074i	0.933186	−	0.359393i	$-0.117016\pi$
$727$	4.33960e10	+	7.51640e10i	0.155350	+	0.269074i	−0.777836	+	0.628467i	$0.783683\pi$
$728$			3.27343e10i			0.116541i
$729$	2.68484e11	−	8.76526e10i	0.950622	−	0.310352i
$730$	−9.77093e9			−0.0344068
$731$	1.26123e11	−	7.28169e10i	0.441696	−	0.255013i
$732$	−6.81724e10	−	1.04923e11i	−0.237446	−	0.365447i
$733$	−2.34369e11	+	4.05939e11i	−0.811866	+	1.40619i	0.0996907	+	0.995018i	$0.468215\pi$
$733$	−2.34369e11	+	4.05939e11i	−0.811866	+	1.40619i	−0.911557	+	0.411175i	$0.865119\pi$
$734$	−2.48938e10	−	1.43724e10i	−0.0857643	−	0.0495161i
$735$	3.56345e10	+	1.81462e10i	0.122101	+	0.0621778i
$736$	−2.50290e9	−	4.33516e9i	−0.00852969	−	0.0147738i
$737$			4.45864e11i			1.51123i
$738$	1.72037e10	−	3.86889e10i	0.0579958	−	0.130425i
$739$	−3.42168e11			−1.14726			−0.573630	−	0.819114i	$-0.694465\pi$
$739$	−3.42168e11			−1.14726			−0.573630	+	0.819114i	$0.694465\pi$
$740$	1.71452e11	−	9.89878e10i	0.571762	−	0.330107i
$741$	−3.16424e11	+	1.66573e10i	−1.04954	+	0.0552501i
$742$	−8.29780e9	+	1.43722e10i	−0.0273746	+	0.0474141i
$743$	−4.81576e11	−	2.78038e11i	−1.58019	−	0.912323i	−0.994831	−	0.101549i	$-0.967620\pi$
$743$	−4.81576e11	−	2.78038e11i	−1.58019	−	0.912323i	−0.585359	−	0.810774i	$-0.699047\pi$
$744$	5.57916e8	+	1.05982e10i	0.00182086	+	0.0345892i
$745$	4.33936e10	+	7.51599e10i	0.140864	+	0.243984i
$746$		−	1.43792e10i		−	0.0464279i
$747$	−4.05465e10	−	3.84045e11i	−0.130218	−	1.23339i
$748$	3.11532e11			0.995167
$749$	−4.13225e11	+	2.38576e11i	−1.31298	+	0.758052i
$750$	1.16956e10	−	2.29672e10i	0.0369638	−	0.0725876i
$751$	1.78639e11	−	3.09411e11i	0.561585	−	0.972695i	−0.435773	−	0.900057i	$-0.643525\pi$
$751$	1.78639e11	−	3.09411e11i	0.561585	−	0.972695i	0.997358	−	0.0726379i	$-0.0231418\pi$
$752$	−5.15961e11	−	2.97890e11i	−1.61341	−	0.931505i
$753$	−1.51089e11	+	9.81685e10i	−0.469951	+	0.305346i
$754$	−4.86409e9	−	8.42486e9i	−0.0150493	−	0.0260662i
$755$			5.99373e11i			1.84463i
$756$	2.99323e11	−	4.76235e10i	0.916331	−	0.145792i
$757$	3.78993e11			1.15411			0.577056	−	0.816704i	$-0.304201\pi$
$757$	3.78993e11			1.15411			0.577056	+	0.816704i	$0.304201\pi$
$758$	−1.89937e10	+	1.09660e10i	−0.0575351	+	0.0332179i
$759$	−1.59433e10	−	2.45380e10i	−0.0480410	−	0.0739388i
$760$	−5.85766e10	+	1.01458e11i	−0.175578	+	0.304110i
$761$	−2.04721e11	−	1.18196e11i	−0.610413	−	0.352422i	0.162714	−	0.986673i	$-0.447975\pi$
$761$	−2.04721e11	−	1.18196e11i	−0.610413	−	0.352422i	−0.773127	+	0.634251i	$0.781308\pi$
$762$	−2.57822e10	−	1.31291e10i	−0.0764716	−	0.0389417i
$763$	1.84974e11	+	3.20384e11i	0.545773	+	0.945307i
$764$			2.42297e11i			0.711173i
$765$	−1.52304e11	−	2.09422e11i	−0.444697	−	0.611471i
$766$	8.79788e9			0.0255542
$767$	1.54670e11	−	8.92990e10i	0.446916	−	0.258027i
$768$	3.15236e11	−	1.65948e10i	0.906132	−	0.0477010i
$769$	2.41662e11	−	4.18571e11i	0.691040	−	1.19692i	−0.280458	−	0.959866i	$-0.590486\pi$
$769$	2.41662e11	−	4.18571e11i	0.691040	−	1.19692i	0.971498	−	0.237049i	$-0.0761803\pi$
$770$	4.58087e10	+	2.64476e10i	0.130312	+	0.0752357i
$771$	−7.44860e9	−	1.41494e11i	−0.0210793	−	0.400425i
$772$	−2.47295e10	−	4.28327e10i	−0.0696218	−	0.120589i
$773$		−	1.76968e11i		−	0.495651i	−0.968805	−	0.247825i	$-0.920284\pi$
$773$		−	1.76968e11i		−	0.495651i	0.968805	−	0.247825i	$-0.0797159\pi$
$774$	−2.11946e10	+	1.54139e10i	−0.0590557	+	0.0429487i
$775$	−1.60303e10			−0.0444359
$776$	6.41730e10	−	3.70503e10i	0.176972	−	0.102175i
$777$	−9.24429e10	+	1.81534e11i	−0.253623	+	0.498052i
$778$	−3.33031e10	+	5.76827e10i	−0.0909005	+	0.157444i
$779$	7.65430e11	+	4.41921e11i	2.07853	+	1.20004i
$780$	2.21480e11	−	1.43905e11i	0.598352	−	0.388773i
$781$	2.26652e11	+	3.92573e11i	0.609194	+	1.05515i
$782$		−	1.45772e9i		−	0.00389805i
$783$	−1.40584e11	+	1.14006e11i	−0.374015	+	0.303306i
$784$	−4.50461e10			−0.119232
$785$	−6.22805e10	+	3.59576e10i	−0.164011	+	0.0946918i
$786$	−7.78239e9	−	1.19777e10i	−0.0203903	−	0.0313822i
$787$	2.06125e10	−	3.57019e10i	0.0537318	−	0.0930662i	−0.837908	−	0.545811i	$-0.816222\pi$
$787$	2.06125e10	−	3.57019e10i	0.0537318	−	0.0930662i	0.891640	+	0.452745i	$0.149555\pi$
$788$	7.51283e10	+	4.33754e10i	0.194849	+	0.112496i
$789$	−3.20788e11	−	1.63355e11i	−0.827771	−	0.421526i
$790$	−1.81034e10	−	3.13561e10i	−0.0464786	−	0.0805032i
$791$		−	2.16970e11i		−	0.554235i
$792$	−1.12030e11	+	1.18278e10i	−0.284729	+	0.0300610i
$793$	1.12202e11			0.283731
$794$	−1.74012e10	+	1.00466e10i	−0.0437821	+	0.0252776i
$795$	2.68709e11	−	1.41455e10i	0.672688	−	0.0354119i
$796$	−2.21402e11	+	3.83479e11i	−0.551478	+	0.955188i
$797$	−5.95648e10	−	3.43897e10i	−0.147624	−	0.0852306i	0.424369	−	0.905489i	$-0.360496\pi$
$797$	−5.95648e10	−	3.43897e10i	−0.147624	−	0.0852306i	−0.571993	+	0.820259i	$0.693829\pi$
$798$	−3.15369e9	−	5.99078e10i	−0.00777693	−	0.147731i
$799$	−2.64418e11	−	4.57986e11i	−0.648791	−	1.12374i
$800$		−	2.91076e10i		−	0.0710635i
$801$	5.18672e11	+	2.30637e11i	1.25998	+	0.560272i
$802$	4.32458e10			0.104531
$803$	1.69848e11	−	9.80619e10i	0.408506	−	0.235851i
$804$	−1.91274e11	+	3.75613e11i	−0.457753	+	0.898911i
$805$	−1.30512e10	+	2.26054e10i	−0.0310791	+	0.0538306i
$806$	−4.10144e9	−	2.36797e9i	−0.00971843	−	0.00561094i
$807$	−3.54369e11	+	2.30248e11i	−0.835529	+	0.542877i
$808$	3.97009e9	+	6.87639e9i	0.00931439	+	0.0161330i
$809$		−	6.08714e11i		−	1.42108i	−0.703656	−	0.710541i	$-0.748450\pi$
$809$		−	6.08714e11i		−	1.42108i	0.703656	−	0.710541i	$-0.251550\pi$
$810$	3.12124e10	+	3.45997e10i	0.0725082	+	0.0803771i
$811$	1.12522e11			0.260109			0.130055	−	0.991507i	$-0.458485\pi$
$811$	1.12522e11			0.260109			0.130055	+	0.991507i	$0.458485\pi$
$812$	−1.68217e11	+	9.71199e10i	−0.386941	+	0.223401i
$813$	−1.37195e11	−	2.11154e11i	−0.314034	−	0.483322i
$814$	1.88401e10	−	3.26321e10i	0.0429127	−	0.0743270i
$815$	1.45358e11	+	8.39226e10i	0.329465	+	0.190217i
$816$	2.59935e11	+	1.32367e11i	0.586278	+	0.298551i
$817$	−2.73523e11	−	4.73757e11i	−0.613912	−	1.06333i
$818$			1.32596e10i			0.0296155i
$819$	−1.10428e11	+	2.48339e11i	−0.245440	+	0.551962i
$820$	−7.36739e11			−1.62951
$821$	−4.99965e11	+	2.88655e11i	−1.10044	+	0.635341i	−0.936337	−	0.351102i	$-0.885807\pi$
$821$	−4.99965e11	+	2.88655e11i	−1.10044	+	0.635341i	−0.164105	+	0.986443i	$0.552474\pi$
$822$	3.78333e10	−	1.99164e9i	0.0828680	−	0.00436237i
$823$	1.35295e9	−	2.34337e9i	0.00294905	−	0.00510790i	−0.864547	−	0.502552i	$-0.832395\pi$
$823$	1.35295e9	−	2.34337e9i	0.00294905	−	0.00510790i	0.867496	+	0.497444i	$0.165728\pi$
$824$	−1.22131e10	−	7.05125e9i	−0.0264922	−	0.0152953i
$825$	−8.94503e9	−	1.69920e11i	−0.0193093	−	0.366800i
$826$	1.69068e10	+	2.92834e10i	0.0363195	+	0.0629073i
$827$			5.07821e11i			1.08565i	0.839847	+	0.542824i	$0.182645\pi$
$827$			5.07821e11i			1.08565i	−0.839847	+	0.542824i	$0.817355\pi$
$828$	−2.90459e9	−	2.75115e10i	−0.00617964	−	0.0585318i
$829$	2.66902e11			0.565112			0.282556	−	0.959251i	$-0.408818\pi$
$829$	2.66902e11			0.565112			0.282556	+	0.959251i	$0.408818\pi$
$830$	5.51791e10	−	3.18577e10i	0.116269	−	0.0671277i
$831$	1.94613e11	−	3.82171e11i	0.408102	−	0.801408i
$832$	−1.45875e11	+	2.52663e11i	−0.304431	+	0.527289i
$833$	−3.46277e10	−	1.99923e10i	−0.0719189	−	0.0415224i
$834$	4.57957e8	−	2.97553e8i	0.000946587	−	0.000615036i
$835$	−2.07047e11	−	3.58616e11i	−0.425915	−	0.737707i
$836$		−	1.17021e12i		−	2.39574i
$837$	−3.15201e10	+	8.22854e10i	−0.0642223	+	0.167657i
$838$	−6.49194e10			−0.131643
$839$	4.56007e11	−	2.63276e11i	0.920287	−	0.531328i	0.0365604	−	0.999331i	$-0.488360\pi$
$839$	4.56007e11	−	2.63276e11i	0.920287	−	0.531328i	0.883727	+	0.468003i	$0.155027\pi$
$840$	5.47486e10	+	8.42622e10i	0.109965	+	0.169245i
$841$	−1.92124e11	+	3.32769e11i	−0.384059	+	0.665210i
$842$	−6.06974e10	−	3.50436e10i	−0.120760	−	0.0697206i
$843$	6.94324e11	+	3.53571e11i	1.37484	+	0.700111i
$844$	−9.92132e10	−	1.71842e11i	−0.195524	−	0.338657i
$845$		−	3.32594e11i		−	0.652361i
$846$	5.59724e10	+	7.69636e10i	0.109268	+	0.150246i
$847$	−5.79651e11			−1.12624
$848$	−2.62502e11	+	1.51556e11i	−0.507633	+	0.293082i
$849$	−6.14637e11	+	3.23560e10i	−1.18301	+	0.0622765i
$850$	4.23816e9	−	7.34070e9i	0.00811897	−	0.0140625i
$851$	1.61031e10	+	9.29713e9i	0.0307037	+	0.0177268i
$852$	2.25284e10	+	4.27952e11i	0.0427536	+	0.812151i
$853$	4.85818e11	+	8.41461e11i	0.917651	+	1.58942i	0.802973	+	0.596015i	$0.203250\pi$
$853$	4.85818e11	+	8.41461e11i	0.917651	+	1.58942i	0.114678	+	0.993403i	$0.463416\pi$
$854$			2.12429e10i			0.0399376i
$855$	−7.86655e11	+	5.72101e11i	−1.47204	+	1.07055i
$856$	1.67662e11			0.312277
$857$	6.11574e11	−	3.53093e11i	1.13377	−	0.654584i	0.188892	−	0.981998i	$-0.439510\pi$
$857$	6.11574e11	−	3.53093e11i	1.13377	−	0.654584i	0.944881	+	0.327414i	$0.106177\pi$
$858$	2.28118e10	−	4.47965e10i	0.0420930	−	0.0826599i
$859$	2.25749e11	−	3.91008e11i	0.414622	−	0.718147i	−0.580767	−	0.814070i	$-0.697247\pi$
$859$	2.25749e11	−	3.91008e11i	0.414622	−	0.718147i	0.995389	+	0.0959236i	$0.0305804\pi$
$860$	3.94906e11	+	2.27999e11i	0.721938	+	0.416811i
$861$	6.35702e11	−	4.13041e11i	1.15675	−	0.751589i
$862$	−2.93771e10	−	5.08826e10i	−0.0532083	−	0.0921595i
$863$			9.00374e11i			1.62323i	0.584193	+	0.811615i	$0.301411\pi$
$863$			9.00374e11i			1.62323i	−0.584193	+	0.811615i	$0.698589\pi$
$864$	−1.49413e11	−	5.72340e10i	−0.268123	−	0.102707i
$865$	−3.85758e11			−0.689049
$866$	−6.93111e10	+	4.00168e10i	−0.123234	+	0.0711493i
$867$	−1.66783e11	−	2.56691e11i	−0.295171	−	0.454291i
$868$	−4.72805e10	+	8.18922e10i	−0.0832919	+	0.144266i
$869$	6.29385e11	+	3.63376e11i	1.10367	+	0.637201i
$870$	−2.66114e10	−	1.35514e10i	−0.0464506	−	0.0236541i
$871$	−1.88988e11	−	3.27337e11i	−0.328369	−	0.568751i
$872$		−	1.29993e11i		−	0.224829i
$873$	6.11836e11	−	6.45961e10i	1.05336	−	0.111211i
$874$	−5.47567e9			−0.00938407
$875$	3.99639e11	−	2.30732e11i	0.681766	−	0.393618i
$876$	1.85155e11	−	9.74702e9i	0.314427	−	0.0165522i
$877$	5.67437e11	−	9.82830e11i	0.959222	−	1.66142i	0.234827	−	0.972037i	$-0.424548\pi$
$877$	5.67437e11	−	9.82830e11i	0.959222	−	1.66142i	0.724395	−	0.689385i	$-0.242119\pi$
$878$	7.30371e10	+	4.21680e10i	0.122904	+	0.0709586i
$879$	2.73654e10	+	5.19835e11i	0.0458401	+	0.870783i
$880$	4.83055e11	+	8.36675e11i	0.805500	+	1.39517i
$881$		−	3.16640e11i		−	0.525609i	−0.964849	−	0.262804i	$-0.915353\pi$
$881$		−	3.16640e11i		−	0.525609i	0.964849	−	0.262804i	$-0.0846474\pi$
$882$	6.57456e9	+	2.92350e9i	0.0108641	+	0.00483090i
$883$	7.48388e11			1.23107			0.615537	−	0.788108i	$-0.288939\pi$
$883$	7.48388e11			1.23107			0.615537	+	0.788108i	$0.288939\pi$
$884$	−2.28715e11	+	1.32049e11i	−0.374530	+	0.216235i
$885$	2.48787e11	−	4.88555e11i	0.405559	−	0.796416i
$886$	1.48714e10	−	2.57580e10i	0.0241333	−	0.0418001i
$887$	−6.38831e11	−	3.68829e11i	−1.03203	−	0.595841i	−0.114463	−	0.993428i	$-0.536515\pi$
$887$	−6.38831e11	−	3.68829e11i	−1.03203	−	0.595841i	−0.917565	+	0.397586i	$0.869848\pi$
$888$	6.00247e10	−	3.90005e10i	0.0965335	−	0.0627217i
$889$	−2.59012e11	−	4.48622e11i	−0.414680	−	0.718246i
$890$			9.36543e10i			0.149268i
$891$	−8.89812e11	−	2.88197e11i	−1.41185	−	0.457276i
$892$	3.99278e11			0.630690
$893$	−1.72034e12	+	9.93240e11i	−2.70526	+	1.56188i
$894$	8.50803e9	+	1.30945e10i	0.0133192	+	0.0204993i
$895$	−1.49682e11	+	2.59257e11i	−0.233280	+	0.404052i
$896$	−1.97945e11	−	1.14284e11i	−0.307124	−	0.177318i
$897$	2.21059e10	+	1.12570e10i	0.0341460	+	0.0173882i
$898$	−3.27679e10	−	5.67556e10i	−0.0503898	−	0.0872778i
$899$		−	5.64708e10i		−	0.0864541i
$900$	6.53596e10	−	1.46985e11i	0.0996184	−	0.224029i
$901$	−2.69053e11			−0.408262
$902$	−1.21436e11	+	7.01109e10i	−0.183451	+	0.105916i
$903$	−4.68573e11	+	2.46668e10i	−0.704735	+	0.0370990i
$904$	−3.81196e10	+	6.60250e10i	−0.0570787	+	0.0988633i
$905$	3.56095e11	+	2.05592e11i	0.530850	+	0.306486i
$906$	5.66945e9	+	1.07697e11i	0.00841450	+	0.159843i
$907$	4.89448e11	+	8.47748e11i	0.723231	+	1.25267i	0.959698	+	0.281034i	$0.0906773\pi$
$907$	4.89448e11	+	8.47748e11i	0.723231	+	1.25267i	−0.236467	+	0.971640i	$0.575989\pi$
$908$		−	2.20841e11i		−	0.324890i
$909$	6.92172e9	+	6.55606e10i	0.0101382	+	0.0960257i
$910$	−4.48414e10			−0.0653903
$911$	−4.63087e11	+	2.67363e11i	−0.672340	+	0.388175i	−0.796963	−	0.604029i	$-0.793561\pi$
$911$	−4.63087e11	+	2.67363e11i	−0.672340	+	0.388175i	0.124623	+	0.992204i	$0.460228\pi$
$912$	4.97212e11	−	9.76397e11i	0.718724	−	1.41139i
$913$	−6.39453e11	+	1.10757e12i	−0.920292	+	1.59399i
$914$	−2.70670e9	−	1.56271e9i	−0.00387843	−	0.00223921i
$915$	2.88821e11	−	1.87658e11i	0.412044	−	0.267722i
$916$	−4.72438e11	−	8.18286e11i	−0.671062	−	1.16231i
$917$		−	2.55747e11i		−	0.361687i
$918$	−2.93473e10	−	3.61889e10i	−0.0413236	−	0.0509572i
$919$	9.48007e11			1.32908			0.664538	−	0.747255i	$-0.268629\pi$
$919$	9.48007e11			1.32908			0.664538	+	0.747255i	$0.268629\pi$
$920$	7.94311e9	−	4.58596e9i	0.0110876	−	0.00640146i
$921$	−2.39982e11	−	3.69351e11i	−0.333534	−	0.513335i
$922$	1.94680e10	−	3.37196e10i	0.0269401	−	0.0466616i
$923$	−3.32799e11	−	1.92142e11i	−0.458539	−	0.264737i
$924$	−8.94439e11	−	4.55476e11i	−1.22705	−	0.624852i
$925$	5.40606e10	+	9.36358e10i	0.0738438	+	0.127901i
$926$		−	1.06443e11i		−	0.144768i
$927$	−6.88675e10	−	9.46948e10i	−0.0932600	−	0.128235i
$928$	1.02539e11			0.138261
$929$	7.42540e10	−	4.28705e10i	0.0996912	−	0.0575567i	−0.449326	−	0.893368i	$-0.648336\pi$
$929$	7.42540e10	−	4.28705e10i	0.0996912	−	0.0575567i	0.549017	+	0.835811i	$0.315002\pi$
$930$	−1.45180e10	+	7.64265e8i	−0.0194078	+	0.00102167i
$931$	−7.50974e10	+	1.30073e11i	−0.0999600	+	0.173136i
$932$	8.37543e11	+	4.83556e11i	1.11005	+	0.640889i
$933$	−6.28575e10	−	1.19405e12i	−0.0829528	−	1.57578i
$934$	3.07469e10	+	5.32552e10i	0.0404030	+	0.0699801i
$935$			8.57555e11i			1.12206i
$936$	7.72346e10	−	5.61695e10i	0.100626	−	0.0731808i
$937$	−1.19514e11			−0.155046			−0.0775232	−	0.996991i	$-0.524701\pi$
$937$	−1.19514e11			−0.155046			−0.0775232	+	0.996991i	$0.524701\pi$
$938$	6.19739e10	−	3.57806e10i	0.0800566	−	0.0462207i
$939$	−6.57474e11	+	1.29111e12i	−0.845699	+	1.66074i
$940$	8.27929e11	−	1.43402e12i	1.06043	−	1.83672i
$941$	−4.72022e11	−	2.72522e11i	−0.602010	−	0.347571i	0.167822	−	0.985817i	$-0.446327\pi$
$941$	−4.72022e11	−	2.72522e11i	−0.602010	−	0.347571i	−0.769832	+	0.638247i	$0.779660\pi$
$942$	−1.08506e10	+	7.05009e9i	−0.0137801	+	0.00895347i
$943$	−3.45980e10	−	5.99255e10i	−0.0437526	−	0.0757817i
$944$			6.17590e11i			0.777700i
$945$	1.31093e11	+	8.23947e11i	0.164382	+	1.03317i
$946$	8.67892e10			0.108368
$947$	8.11905e11	−	4.68754e11i	1.00950	−	0.582834i	0.0984531	−	0.995142i	$-0.468611\pi$
$947$	8.11905e11	−	4.68754e11i	1.00950	−	0.582834i	0.911045	+	0.412308i	$0.135277\pi$
$948$	3.74332e11	+	5.76126e11i	0.463473	+	0.713320i
$949$	−8.31310e10	+	1.43987e11i	−0.102494	+	0.177525i
$950$	−2.75740e10	−	1.59199e10i	−0.0338537	−	0.0195454i
$951$	−3.27190e11	−	1.66615e11i	−0.400016	−	0.203700i
$952$	−5.02380e10	−	8.70148e10i	−0.0611624	−	0.105936i
$953$		−	6.35142e11i		−	0.770015i	−0.922913	−	0.385008i	$-0.874199\pi$
$953$		−	6.35142e11i		−	0.770015i	0.922913	−	0.385008i	$-0.125801\pi$
$954$	4.81487e10	−	5.08341e9i	0.0581287	−	0.00613708i
$955$	−6.66973e11			−0.801853
$956$	−3.69183e11	+	2.13148e11i	−0.441988	+	0.255182i
$957$	5.98590e11	−	3.15112e10i	0.713644	−	0.0375680i
$958$	−2.39846e10	+	4.15426e10i	−0.0284755	+	0.0493210i
$959$	5.87446e11	+	3.39162e11i	0.694534	+	0.400989i
$960$	4.70815e10	+	8.94364e11i	0.0554326	+	1.05300i
$961$	4.12700e11	+	7.14817e11i	0.483883	+	0.838111i
$962$			3.19430e10i			0.0372972i
$963$	1.27197e12	+	5.65602e11i	1.47901	+	0.657667i
$964$	−1.22627e11			−0.141996
$965$	1.17906e11	−	6.80729e10i	0.135965	−	0.0784992i
$966$	−2.13127e9	+	4.18527e9i	−0.00244754	+	0.00480634i
$967$	−4.94231e10	+	8.56034e10i	−0.0565229	+	0.0979005i	−0.892902	−	0.450250i	$-0.851335\pi$
$967$	−4.94231e10	+	8.56034e10i	−0.0565229	+	0.0979005i	0.836379	+	0.548151i	$0.184668\pi$
$968$	1.76390e11	+	1.01839e11i	0.200897	+	0.115988i
$969$	8.15558e11	−	5.29901e11i	0.925038	−	0.601035i
$970$	5.07537e10	+	8.79079e10i	0.0573298	+	0.0992981i
$971$		−	2.77838e11i		−	0.312546i	−0.987714	−	0.156273i	$-0.950052\pi$
$971$		−	2.77838e11i		−	0.312546i	0.987714	−	0.156273i	$-0.0499480\pi$
$972$	−6.25978e11	−	6.24515e11i	−0.701284	−	0.699645i
$973$	9.77826e9			0.0109096
$974$	1.39711e11	−	8.06621e10i	0.155237	−	0.0896259i
$975$	7.85912e10	+	1.20958e11i	0.0869672	+	0.133849i
$976$	−1.93996e11	+	3.36011e11i	−0.213793	+	0.370300i
$977$	−1.06001e12	−	6.11996e11i	−1.16341	−	0.671693i	−0.211288	−	0.977424i	$-0.567766\pi$
$977$	−1.06001e12	−	6.11996e11i	−1.16341	−	0.671693i	−0.952118	+	0.305731i	$0.901099\pi$
$978$	2.69122e10	+	1.37045e10i	0.0294167	+	0.0149799i
$979$	−9.39923e11	−	1.62799e12i	−1.02320	−	1.77224i
$980$		−	1.25197e11i		−	0.135734i
$981$	4.38526e11	−	9.86187e11i	0.473499	−	1.06484i
$982$	−1.28119e11			−0.137774
$983$	1.46935e12	−	8.48329e11i	1.57366	−	0.908553i	0.577946	−	0.816075i	$-0.303854\pi$
$983$	1.46935e12	−	8.48329e11i	1.57366	−	0.908553i	0.995715	−	0.0924783i	$-0.0294789\pi$
$984$	−2.66015e11	+	1.40037e10i	−0.283743	+	0.0149369i
$985$	−1.19400e11	+	2.06806e11i	−0.126840	+	0.219694i
$986$	2.58596e10	+	1.49300e10i	0.0273598	+	0.0157962i
$987$	8.95721e10	+	1.70152e12i	0.0943852	+	1.79295i
$988$	4.96018e11	+	8.59128e11i	0.520558	+	0.901633i
$989$			4.28283e10i			0.0447657i
$990$	−1.62024e10	−	1.53465e11i	−0.0168670	−	0.159760i
$991$	−1.54307e11			−0.159990			−0.0799949	−	0.996795i	$-0.525490\pi$
$991$	−1.54307e11			−0.159990			−0.0799949	+	0.996795i	$0.525490\pi$
$992$	4.32309e10	−	2.49594e10i	0.0446424	−	0.0257743i
$993$	−3.66712e11	+	7.20129e11i	−0.377162	+	0.740651i
$994$	3.63777e10	−	6.30081e10i	0.0372641	−	0.0645433i
$995$	−1.05560e12	−	6.09453e11i	−1.07698	−	0.621796i
$996$	−1.01384e12	+	6.58734e11i	−1.03023	+	0.669380i
$997$	−8.00414e9	−	1.38636e10i	−0.00810091	−	0.0140312i	0.861947	−	0.506999i	$-0.169245\pi$
$997$	−8.00414e9	−	1.38636e10i	−0.00810091	−	0.0140312i	−0.870047	+	0.492968i	$0.835912\pi$
$998$			1.04856e11i			0.105699i
$999$	5.86943e11	−	9.33851e10i	0.589297	−	0.0937596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.9.d.a.5.4	yes	14
3.2	odd	2		27.9.d.a.17.4		14
4.3	odd	2		144.9.q.a.113.5		14
9.2	odd	6	inner	9.9.d.a.2.4	✓	14
9.4	even	3		81.9.b.a.80.8		14
9.5	odd	6		81.9.b.a.80.7		14
9.7	even	3		27.9.d.a.8.4		14
12.11	even	2		432.9.q.a.17.6		14
36.7	odd	6		432.9.q.a.305.6		14
36.11	even	6		144.9.q.a.65.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.4	✓	14	9.2	odd	6	inner
9.9.d.a.5.4	yes	14	1.1	even	1	trivial
27.9.d.a.8.4		14	9.7	even	3
27.9.d.a.17.4		14	3.2	odd	2
81.9.b.a.80.7		14	9.5	odd	6
81.9.b.a.80.8		14	9.4	even	3
144.9.q.a.65.5		14	36.11	even	6
144.9.q.a.113.5		14	4.3	odd	2
432.9.q.a.17.6		14	12.11	even	2
432.9.q.a.305.6		14	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34294 - 0.775344i) q^{2} +(-44.1317 - 67.9220i) q^{3} +(-126.798 + 219.620i) q^{4} +(-604.549 - 349.037i) q^{5} +(-111.929 - 56.9976i) q^{6} +(-1124.45 - 1947.61i) q^{7} +790.223i q^{8} +(-2665.79 + 5995.02i) q^{9} -1082.49 q^{10} +(18817.0 - 10864.0i) q^{11} +(20512.8 - 1079.84i) q^{12} +(-9209.84 + 15951.9i) q^{13} +(-3020.14 - 1743.68i) q^{14} +(2972.49 + 56465.7i) q^{15} +(-31847.5 - 55161.5i) q^{16} -56538.1i q^{17} +(1068.21 + 10117.8i) q^{18} -212375. q^{19} +(153311. - 88514.1i) q^{20} +(-82661.6 + 162326. i) q^{21} +(16846.7 - 29179.3i) q^{22} +(14399.3 + 8313.41i) q^{23} +(53673.5 - 34873.9i) q^{24} +(48340.5 + 83728.3i) q^{25} +28563.2i q^{26} +(524840. - 83504.2i) q^{27} +570313. q^{28} +(-294955. + 170292. i) q^{29} +(47772.2 + 73525.1i) q^{30} +(-82902.7 + 143592. i) q^{31} +(-260733. - 150534. i) q^{32} +(-1.56833e6 - 798642. i) q^{33} +(-43836.4 - 75926.9i) q^{34} +1.56990e6i q^{35} +(-978610. - 1.34562e6i) q^{36} +1.11833e6 q^{37} +(-285206. + 164664. i) q^{38} +(1.48993e6 - 78433.6i) q^{39} +(275817. - 477729. i) q^{40} +(-3.60414e6 - 2.08085e6i) q^{41} +(14849.6 + 282085. i) q^{42} +(1.28793e6 + 2.23075e6i) q^{43} +5.51012e6i q^{44} +(3.70408e6 - 2.69382e6i) q^{45} +25783.0 q^{46} +(8.10049e6 - 4.67682e6i) q^{47} +(-2.34120e6 + 4.59752e6i) q^{48} +(353608. - 612466. i) q^{49} +(129836. + 74961.1i) q^{50} +(-3.84018e6 + 2.49512e6i) q^{51} +(-2.33557e6 - 4.04533e6i) q^{52} -4.75879e6i q^{53} +(640081. - 519072. i) q^{54} -1.51677e7 q^{55} +(1.53905e6 - 888570. i) q^{56} +(9.37246e6 + 1.44249e7i) q^{57} +(-264070. + 457383. i) q^{58} +(-8.39702e6 - 4.84802e6i) q^{59} +(-1.27779e7 - 6.50691e6i) q^{60} +(-3.04570e6 - 5.27531e6i) q^{61} +257113. i q^{62} +(1.46735e7 - 1.54919e6i) q^{63} +1.58391e7 q^{64} +(1.11356e7 - 6.42914e6i) q^{65} +(-2.72539e6 + 143471. i) q^{66} +(-1.02601e7 + 1.77710e7i) q^{67} +(1.24169e7 + 7.16890e6i) q^{68} +(-70799.4 - 1.34491e6i) q^{69} +(1.21721e6 + 2.10828e6i) q^{70} +2.08627e7i q^{71} +(-4.73740e6 - 2.10657e6i) q^{72} +9.02632e6 q^{73} +(1.50184e6 - 867089. i) q^{74} +(3.55364e6 - 6.97845e6i) q^{75} +(2.69287e7 - 4.66418e7i) q^{76} +(-4.23177e7 - 2.44321e7i) q^{77} +(1.94007e6 - 1.26054e6i) q^{78} +(1.67238e7 + 2.89665e7i) q^{79} +4.44638e7i q^{80} +(-2.88338e7 - 3.19630e7i) q^{81} -6.45351e6 q^{82} +(-5.09741e7 + 2.94299e7i) q^{83} +(-2.51688e7 - 3.87368e7i) q^{84} +(-1.97339e7 + 3.41800e7i) q^{85} +(3.45920e6 + 1.99717e6i) q^{86} +(2.45835e7 + 1.25187e7i) q^{87} +(8.58499e6 + 1.48696e7i) q^{88} -8.65172e7i q^{89} +(2.88570e6 - 6.48957e6i) q^{90} +4.14242e7 q^{91} +(-3.65158e6 + 2.10824e6i) q^{92} +(1.34117e7 - 706023. i) q^{93} +(7.25229e6 - 1.25613e7i) q^{94} +(1.28391e8 + 7.41267e7i) q^{95} +(1.28199e6 + 2.43528e7i) q^{96} +(-4.68859e7 - 8.12087e7i) q^{97} -1.09667e6i q^{98} +(1.49677e7 + 1.41770e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18}+ \cdots - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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