LMFDB - Embedded newform 9.9.d.a.2.7

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			2.7
Root			$-8.68602 - 15.0446i$ of defining polynomial
Character	$\chi$	$=$	9.2
Dual form			9.9.d.a.5.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(26.0581 + 15.0446i) q^{2} +(-77.6435 + 23.0757i) q^{3} +(324.682 + 562.365i) q^{4} +(189.131 - 109.195i) q^{5} +(-2370.40 - 566.810i) q^{6} +(1404.67 - 2432.96i) q^{7} +11836.0i q^{8} +(5496.03 - 3583.35i) q^{9} +6571.17 q^{10} +(-4502.73 - 2599.65i) q^{11} +(-38186.4 - 36171.7i) q^{12} +(-5261.39 - 9112.99i) q^{13} +(73205.9 - 42265.5i) q^{14} +(-12165.0 + 12842.6i) q^{15} +(-94949.8 + 164458. i) q^{16} -15221.5i q^{17} +(197126. - 10689.5i) q^{18} -92696.3 q^{19} +(122815. + 70907.0i) q^{20} +(-52921.3 + 221317. i) q^{21} +(-78221.6 - 135484. i) q^{22} +(-53108.9 + 30662.4i) q^{23} +(-273124. - 918989. i) q^{24} +(-171466. + 296987. i) q^{25} -316622. i q^{26} +(-344043. + 405048. i) q^{27} +1.82428e6 q^{28} +(759877. + 438715. i) q^{29} +(-510209. + 151634. i) q^{30} +(-814808. - 1.41129e6i) q^{31} +(-2.32434e6 + 1.34196e6i) q^{32} +(409597. + 97942.6i) q^{33} +(229001. - 396642. i) q^{34} -613530. i q^{35} +(3.79961e6 + 1.92732e6i) q^{36} -1.66998e6 q^{37} +(-2.41549e6 - 1.39458e6i) q^{38} +(618801. + 586154. i) q^{39} +(1.29243e6 + 2.23855e6i) q^{40} +(4.15258e6 - 2.39749e6i) q^{41} +(-4.70866e6 + 4.97091e6i) q^{42} +(256358. - 444024. i) q^{43} -3.37624e6i q^{44} +(648185. - 1.27786e6i) q^{45} -1.84522e6 q^{46} +(1.08416e6 + 625937. i) q^{47} +(3.57726e6 - 1.49601e7i) q^{48} +(-1.06379e6 - 1.84254e6i) q^{49} +(-8.93612e6 + 5.15927e6i) q^{50} +(351246. + 1.18185e6i) q^{51} +(3.41655e6 - 5.91764e6i) q^{52} +8.87435e6i q^{53} +(-1.50589e7 + 5.37879e6i) q^{54} -1.13547e6 q^{55} +(2.87965e7 + 1.66257e7i) q^{56} +(7.19727e6 - 2.13903e6i) q^{57} +(1.32006e7 + 2.28641e7i) q^{58} +(-8.34796e6 + 4.81970e6i) q^{59} +(-1.11720e7 - 2.67144e6i) q^{60} +(-4.51315e6 + 7.81701e6i) q^{61} -4.90339e7i q^{62} +(-998047. - 1.84050e7i) q^{63} -3.21428e7 q^{64} +(-1.99018e6 - 1.14903e6i) q^{65} +(9.19978e6 + 8.71442e6i) q^{66} +(-5.32613e6 - 9.22513e6i) q^{67} +(8.56002e6 - 4.94213e6i) q^{68} +(3.41600e6 - 3.60626e6i) q^{69} +(9.23033e6 - 1.59874e7i) q^{70} +2.16518e7i q^{71} +(4.24126e7 + 6.50510e7i) q^{72} +2.00444e7 q^{73} +(-4.35165e7 - 2.51242e7i) q^{74} +(6.46001e6 - 2.70158e7i) q^{75} +(-3.00968e7 - 5.21292e7i) q^{76} +(-1.26497e7 + 7.30331e6i) q^{77} +(7.30628e6 + 2.45837e7i) q^{78} +(-2.83077e7 + 4.90305e7i) q^{79} +4.14720e7i q^{80} +(1.73659e7 - 3.93884e7i) q^{81} +1.44278e8 q^{82} +(-1.29077e6 - 745226. i) q^{83} +(-1.41644e8 + 4.20965e7i) q^{84} +(-1.66210e6 - 2.87885e6i) q^{85} +(1.33604e7 - 7.71361e6i) q^{86} +(-6.91232e7 - 1.65287e7i) q^{87} +(3.07695e7 - 5.32944e7i) q^{88} +5.42495e7i q^{89} +(3.61153e7 - 2.35468e7i) q^{90} -2.95620e7 q^{91} +(-3.44870e7 - 1.99111e7i) q^{92} +(9.58309e7 + 9.07751e7i) q^{93} +(1.88340e7 + 3.26214e7i) q^{94} +(-1.75317e7 + 1.01219e7i) q^{95} +(1.49503e8 - 1.57830e8i) q^{96} +(-3.06695e6 + 5.31212e6i) q^{97} -6.40174e7i q^{98} +(-3.40626e7 + 1.84711e6i) 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 $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	26.0581	+	15.0446i	1.62863	+	0.940289i	0.984503	+	0.175370i	$0.0561121\pi$
$2$	26.0581	+	15.0446i	1.62863	+	0.940289i	0.644126	+	0.764919i	$0.277221\pi$
$3$	−77.6435	+	23.0757i	−0.958562	+	0.284885i
$3$	−77.6435	+	23.0757i	−0.958562	+	0.284885i
$4$	324.682	+	562.365i	1.26829	+	2.19674i
$5$	189.131	−	109.195i	0.302609	−	0.174711i	−0.341005	−	0.940061i	$-0.610767\pi$
$5$	189.131	−	109.195i	0.302609	−	0.174711i	0.643614	+	0.765350i	$0.277434\pi$
$6$	−2370.40	−	566.810i	−1.82902	−	0.437354i
$7$	1404.67	−	2432.96i	0.585035	−	1.01331i	−0.409836	−	0.912159i	$-0.634414\pi$
$7$	1404.67	−	2432.96i	0.585035	−	1.01331i	0.994871	−	0.101151i	$-0.0322527\pi$
$8$			11836.0i			2.88965i
$9$	5496.03	−	3583.35i	0.837681	−	0.546159i
$10$	6571.17			0.657117
$11$	−4502.73	−	2599.65i	−0.307543	−	0.177560i	0.338284	−	0.941044i	$-0.390154\pi$
$11$	−4502.73	−	2599.65i	−0.307543	−	0.177560i	−0.645826	+	0.763484i	$0.723487\pi$
$12$	−38186.4	−	36171.7i	−1.84155	−	1.74439i
$13$	−5261.39	−	9112.99i	−0.184216	−	0.319071i	0.759096	−	0.650978i	$-0.225641\pi$
$13$	−5261.39	−	9112.99i	−0.184216	−	0.319071i	−0.943312	+	0.331907i	$0.892308\pi$
$14$	73205.9	−	42265.5i	1.90561	−	1.10020i
$15$	−12165.0	+	12842.6i	−0.240297	+	0.253680i
$16$	−94949.8	+	164458.i	−1.44882	+	2.50943i
$17$		−	15221.5i		−	0.182247i	−0.995840	−	0.0911236i	$-0.970954\pi$
$17$		−	15221.5i		−	0.182247i	0.995840	−	0.0911236i	$-0.0290458\pi$
$18$	197126.	−	10689.5i	1.87782	−	0.101828i
$19$	−92696.3			−0.711292			−0.355646	−	0.934621i	$-0.615739\pi$
$19$	−92696.3			−0.711292			−0.355646	+	0.934621i	$0.615739\pi$
$20$	122815.	+	70907.0i	0.767591	+	0.443169i
$21$	−52921.3	+	221317.i	−0.272116	+	1.13799i
$22$	−78221.6	−	135484.i	−0.333915	−	0.578358i
$23$	−53108.9	+	30662.4i	−0.189782	+	0.109571i	−0.591881	−	0.806026i	$-0.701614\pi$
$23$	−53108.9	+	30662.4i	−0.189782	+	0.109571i	0.402098	+	0.915597i	$0.368281\pi$
$24$	−273124.	−	918989.i	−0.823217	−	2.76991i
$25$	−171466.	+	296987.i	−0.438952	+	0.760287i
$26$		−	316622.i		−	0.692865i
$27$	−344043.	+	405048.i	−0.647377	+	0.762170i
$28$	1.82428e6			2.96797
$29$	759877.	+	438715.i	1.07436	+	0.620284i	0.929370	−	0.369149i	$-0.120351\pi$
$29$	759877.	+	438715.i	1.07436	+	0.620284i	0.144993	+	0.989433i	$0.453684\pi$
$30$	−510209.	+	151634.i	−0.629887	+	0.187203i
$31$	−814808.	−	1.41129e6i	−0.882284	−	1.52816i	−0.848796	−	0.528721i	$-0.822672\pi$
$31$	−814808.	−	1.41129e6i	−0.882284	−	1.52816i	−0.0334881	−	0.999439i	$-0.510662\pi$
$32$	−2.32434e6	+	1.34196e6i	−2.21667	+	1.27979i
$33$	409597.	+	97942.6i	0.345383	+	0.0825878i
$34$	229001.	−	396642.i	0.171365	−	0.296813i
$35$		−	613530.i		−	0.408849i
$36$	3.79961e6	+	1.92732e6i	2.26219	+	1.14748i
$37$	−1.66998e6			−0.891055			−0.445528	−	0.895268i	$-0.646984\pi$
$37$	−1.66998e6			−0.891055			−0.445528	+	0.895268i	$0.646984\pi$
$38$	−2.41549e6	−	1.39458e6i	−1.15843	−	0.668820i
$39$	618801.	+	586154.i	0.267481	+	0.253369i
$40$	1.29243e6	+	2.23855e6i	0.504855	+	0.874434i
$41$	4.15258e6	−	2.39749e6i	1.46954	−	0.848442i	0.470128	−	0.882598i	$-0.344208\pi$
$41$	4.15258e6	−	2.39749e6i	1.46954	−	0.848442i	0.999417	+	0.0341559i	$0.0108743\pi$
$42$	−4.70866e6	+	4.97091e6i	−1.51321	+	1.59749i
$43$	256358.	−	444024.i	0.0749846	−	0.129877i	−0.826095	−	0.563531i	$-0.809443\pi$
$43$	256358.	−	444024.i	0.0749846	−	0.129877i	0.901080	+	0.433654i	$0.142776\pi$
$44$		−	3.37624e6i		−	0.900788i
$45$	648185.	−	1.27786e6i	0.158070	−	0.311625i
$46$	−1.84522e6			−0.412113
$47$	1.08416e6	+	625937.i	0.222177	+	0.128274i	0.606958	−	0.794734i	$-0.292390\pi$
$47$	1.08416e6	+	625937.i	0.222177	+	0.128274i	−0.384781	+	0.923008i	$0.625723\pi$
$48$	3.57726e6	−	1.49601e7i	0.673884	−	2.81819i
$49$	−1.06379e6	−	1.84254e6i	−0.184532	−	0.319619i
$50$	−8.93612e6	+	5.15927e6i	−1.42978	+	0.825483i
$51$	351246.	+	1.18185e6i	0.0519195	+	0.174695i
$52$	3.41655e6	−	5.91764e6i	0.467277	−	0.809348i
$53$			8.87435e6i			1.12469i	0.826903	+	0.562345i	$0.190101\pi$
$53$			8.87435e6i			1.12469i	−0.826903	+	0.562345i	$0.809899\pi$
$54$	−1.50589e7	+	5.37879e6i	−1.77100	+	0.632571i
$55$	−1.13547e6			−0.124087
$56$	2.87965e7	+	1.66257e7i	2.92811	+	1.69055i
$57$	7.19727e6	−	2.13903e6i	0.681818	−	0.202636i
$58$	1.32006e7	+	2.28641e7i	1.16649	+	2.02043i
$59$	−8.34796e6	+	4.81970e6i	−0.688926	+	0.397752i	−0.803210	−	0.595697i	$-0.796876\pi$
$59$	−8.34796e6	+	4.81970e6i	−0.688926	+	0.397752i	0.114284	+	0.993448i	$0.463543\pi$
$60$	−1.11720e7	−	2.67144e6i	−0.862035	−	0.206130i
$61$	−4.51315e6	+	7.81701e6i	−0.325957	+	0.564574i	−0.981706	−	0.190405i	$-0.939020\pi$
$61$	−4.51315e6	+	7.81701e6i	−0.325957	+	0.564574i	0.655748	+	0.754979i	$0.272353\pi$
$62$		−	4.90339e7i		−	3.31841i
$63$	−998047.	−	1.84050e7i	−0.0633561	−	1.16835i
$64$	−3.21428e7			−1.91586
$65$	−1.99018e6	−	1.14903e6i	−0.111491	−	0.0643692i
$66$	9.19978e6	+	8.71442e6i	0.484844	+	0.459265i
$67$	−5.32613e6	−	9.22513e6i	−0.264309	−	0.457797i	0.703073	−	0.711118i	$-0.251811\pi$
$67$	−5.32613e6	−	9.22513e6i	−0.264309	−	0.457797i	−0.967382	+	0.253320i	$0.918477\pi$
$68$	8.56002e6	−	4.94213e6i	0.400350	−	0.231142i
$69$	3.41600e6	−	3.60626e6i	0.150703	−	0.159097i
$70$	9.23033e6	−	1.59874e7i	0.384437	−	0.665864i
$71$			2.16518e7i			0.852042i	0.904713	+	0.426021i	$0.140085\pi$
$71$			2.16518e7i			0.852042i	−0.904713	+	0.426021i	$0.859915\pi$
$72$	4.24126e7	+	6.50510e7i	1.57821	+	2.42061i
$73$	2.00444e7			0.705833			0.352917	−	0.935655i	$-0.385190\pi$
$73$	2.00444e7			0.705833			0.352917	+	0.935655i	$0.385190\pi$
$74$	−4.35165e7	−	2.51242e7i	−1.45120	−	0.837850i
$75$	6.46001e6	−	2.70158e7i	0.204168	−	0.853833i
$76$	−3.00968e7	−	5.21292e7i	−0.902123	−	1.56252i
$77$	−1.26497e7	+	7.30331e6i	−0.359847	+	0.207758i
$78$	7.30628e6	+	2.45837e7i	0.197387	+	0.664153i
$79$	−2.83077e7	+	4.90305e7i	−0.726770	+	1.25880i	0.231471	+	0.972842i	$0.425646\pi$
$79$	−2.83077e7	+	4.90305e7i	−0.726770	+	1.25880i	−0.958241	+	0.285961i	$0.907687\pi$
$80$			4.14720e7i			1.01250i
$81$	1.73659e7	−	3.93884e7i	0.403420	−	0.915015i
$82$	1.44278e8			3.19112
$83$	−1.29077e6	−	745226.i	−0.0271980	−	0.0157028i	0.486339	−	0.873770i	$-0.338332\pi$
$83$	−1.29077e6	−	745226.i	−0.0271980	−	0.0157028i	−0.513537	+	0.858067i	$0.671665\pi$
$84$	−1.41644e8	+	4.20965e7i	−2.84498	+	0.845530i
$85$	−1.66210e6	−	2.87885e6i	−0.0318407	−	0.0551497i
$86$	1.33604e7	−	7.71361e6i	0.244244	−	0.141014i
$87$	−6.91232e7	−	1.65287e7i	−1.20655	−	0.288511i
$88$	3.07695e7	−	5.32944e7i	0.513086	−	0.888691i
$89$			5.42495e7i			0.864641i	0.901720	+	0.432321i	$0.142305\pi$
$89$			5.42495e7i			0.864641i	−0.901720	+	0.432321i	$0.857695\pi$
$90$	3.61153e7	−	2.35468e7i	0.550455	−	0.358891i
$91$	−2.95620e7			−0.431091
$92$	−3.44870e7	−	1.99111e7i	−0.481397	−	0.277935i
$93$	9.58309e7	+	9.07751e7i	1.28107	+	1.21349i
$94$	1.88340e7	+	3.26214e7i	0.241230	+	0.417822i
$95$	−1.75317e7	+	1.01219e7i	−0.215244	+	0.124271i
$96$	1.49503e8	−	1.57830e8i	1.76022	−	1.85825i
$97$	−3.06695e6	+	5.31212e6i	−0.0346434	+	0.0600041i	−0.882827	−	0.469698i	$-0.844363\pi$
$97$	−3.06695e6	+	5.31212e6i	−0.0346434	+	0.0600041i	0.848184	+	0.529702i	$0.177696\pi$
$98$		−	6.40174e7i		−	0.694055i
$99$	−3.40626e7	+	1.84711e6i	−0.354599	+	0.0192288i
$100$	−2.22687e8			−2.22687
$101$	8.02563e7	+	4.63360e7i	0.771247	+	0.445280i	0.833319	−	0.552792i	$-0.186438\pi$
$101$	8.02563e7	+	4.63360e7i	0.771247	+	0.445280i	−0.0620722	+	0.998072i	$0.519771\pi$
$102$	−8.62769e6	+	3.60810e7i	−0.0797065	+	0.333333i
$103$	−9.31684e7	−	1.61372e8i	−0.827789	−	1.43377i	−0.899769	−	0.436367i	$-0.856265\pi$
$103$	−9.31684e7	−	1.61372e8i	−0.827789	−	1.43377i	0.0719798	−	0.997406i	$-0.477068\pi$
$104$	1.07861e8	−	6.22738e7i	0.922004	−	0.532319i
$105$	1.41576e7	+	4.76366e7i	0.116475	+	0.391907i
$106$	−1.33511e8	+	2.31248e8i	−1.05753	+	1.83170i
$107$		−	2.13043e8i		−	1.62530i	−0.582754	−	0.812648i	$-0.698025\pi$
$107$		−	2.13043e8i		−	1.62530i	0.582754	−	0.812648i	$-0.301975\pi$
$108$	−3.39489e8	−	6.19657e7i	−2.49535	−	0.455466i
$109$	1.52786e8			1.08238			0.541188	−	0.840901i	$-0.317975\pi$
$109$	1.52786e8			1.08238			0.541188	+	0.840901i	$0.317975\pi$
$110$	−2.95882e7	−	1.70828e7i	−0.202092	−	0.116678i
$111$	1.29663e8	−	3.85359e7i	0.854132	−	0.253848i
$112$	2.66746e8	+	4.62018e8i	1.69522	+	2.93621i
$113$	2.32734e8	−	1.34369e8i	1.42740	−	0.824109i	0.430484	−	0.902598i	$-0.358343\pi$
$113$	2.32734e8	−	1.34369e8i	1.42740	−	0.824109i	0.996915	+	0.0784888i	$0.0250095\pi$
$114$	2.19728e8	+	5.25412e7i	1.30096	+	0.311086i
$115$	−6.69635e6	+	1.15984e7i	−0.0382866	+	0.0663143i
$116$			5.69771e8i			3.14679i
$117$	−6.15718e7	−	3.12318e7i	−0.328578	−	0.166669i
$118$	−2.90042e8			−1.49601
$119$	−3.70332e7	−	2.13811e7i	−0.184673	−	0.106621i
$120$	−1.52005e8	−	1.43985e8i	−0.733048	−	0.694374i
$121$	−9.36630e7	−	1.62229e8i	−0.436945	−	0.756811i
$122$	−2.35208e8	+	1.35797e8i	−1.06173	+	0.612988i
$123$	−2.67097e8	+	2.81974e8i	−1.16694	+	1.23194i
$124$	5.29106e8	−	9.16439e8i	2.23798	−	3.87629i
$125$			1.60201e8i			0.656183i
$126$	2.50890e8	−	4.94615e8i	0.995407	−	1.96239i
$127$	6.54444e7			0.251569			0.125785	−	0.992058i	$-0.459855\pi$
$127$	6.54444e7			0.251569			0.125785	+	0.992058i	$0.459855\pi$
$128$	−2.42548e8	−	1.40035e8i	−0.903563	−	0.521672i
$129$	−9.65834e6	+	4.03912e7i	−0.0348774	+	0.145857i
$130$	−3.45735e7	−	5.98830e7i	−0.121051	−	0.209667i
$131$	−2.29305e7	+	1.32389e7i	−0.0778624	+	0.0449539i	−0.538426	−	0.842673i	$-0.680981\pi$
$131$	−2.29305e7	+	1.32389e7i	−0.0778624	+	0.0449539i	0.460563	+	0.887627i	$0.347647\pi$
$132$	7.79090e7	+	2.62143e8i	0.256621	+	0.863461i
$133$	−1.30208e8	+	2.25526e8i	−0.416131	+	0.720760i
$134$		−	3.20518e8i		−	0.994109i
$135$	−2.08399e7	+	1.14175e8i	−0.0627422	+	0.343744i
$136$	1.80161e8			0.526631
$137$	−3.91502e8	−	2.26034e8i	−1.11135	−	0.641640i	−0.172174	−	0.985067i	$-0.555079\pi$
$137$	−3.91502e8	−	2.26034e8i	−1.11135	−	0.641640i	−0.939180	+	0.343426i	$0.888412\pi$
$138$	1.43269e8	−	4.25797e7i	0.395036	−	0.117405i
$139$	2.17967e8	+	3.77529e8i	0.583890	+	1.01133i	0.995013	+	0.0997472i	$0.0318034\pi$
$139$	2.17967e8	+	3.77529e8i	0.583890	+	1.01133i	−0.411123	+	0.911580i	$0.634863\pi$
$140$	3.45028e8	−	1.99202e8i	0.898135	−	0.518539i
$141$	−9.86215e7	−	2.35824e7i	−0.249514	−	0.0596638i
$142$	−3.25744e8	+	5.64205e8i	−0.801166	+	1.38766i
$143$			5.47111e7i			0.130837i
$144$	6.74638e7	+	1.24410e9i	0.156899	+	2.89339i
$145$	1.91621e8			0.433483
$146$	5.22319e8	+	3.01561e8i	1.14954	+	0.663687i
$147$	1.25114e8	+	1.18514e8i	0.267940	+	0.253805i
$148$	−5.42212e8	−	9.39139e8i	−1.13011	−	1.95742i
$149$	−2.83553e8	+	1.63710e8i	−0.575294	+	0.332146i	−0.759261	−	0.650786i	$-0.774439\pi$
$149$	−2.83553e8	+	1.63710e8i	−0.575294	+	0.332146i	0.183967	+	0.982932i	$0.441106\pi$
$150$	5.74778e8	−	6.06791e8i	1.13536	−	1.19860i
$151$	−7.34134e6	+	1.27156e7i	−0.0141211	+	0.0244584i	−0.873000	−	0.487721i	$-0.837828\pi$
$151$	−7.34134e6	+	1.27156e7i	−0.0141211	+	0.0244584i	0.858879	+	0.512179i	$0.171162\pi$
$152$		−	1.09715e9i		−	2.05539i
$153$	−5.45439e7	−	8.36576e7i	−0.0995361	−	0.152665i
$154$	−4.39502e8			−0.781409
$155$	−3.08210e8	−	1.77945e8i	−0.533974	−	0.308290i
$156$	−1.28719e8	+	5.38306e8i	−0.217343	+	0.908930i
$157$	−7.90150e6	−	1.36858e7i	−0.0130050	−	0.0225253i	0.859450	−	0.511220i	$-0.170806\pi$
$157$	−7.90150e6	−	1.36858e7i	−0.0130050	−	0.0225253i	−0.872455	+	0.488695i	$0.837473\pi$
$158$	−1.47529e9	+	8.51759e8i	−2.36728	+	1.36675i
$159$	−2.04782e8	−	6.89035e8i	−0.320407	−	1.07809i
$160$	−2.93070e8	+	5.07612e8i	−0.447189	+	0.774554i
$161$			1.72282e8i			0.256411i
$162$	1.04511e9	−	7.65122e8i	1.51740	−	1.11089i
$163$	1.05884e9			1.49996			0.749979	−	0.661462i	$-0.230064\pi$
$163$	1.05884e9			1.49996			0.749979	+	0.661462i	$0.230064\pi$
$164$	2.69653e9	+	1.55684e9i	3.72761	+	2.15214i
$165$	8.81621e7	−	2.62018e7i	0.118945	−	0.0353505i
$166$	−2.24233e7	−	3.88383e7i	−0.0295303	−	0.0511479i
$167$	6.11861e8	−	3.53258e8i	0.786659	−	0.454178i	−0.0521260	−	0.998641i	$-0.516600\pi$
$167$	6.11861e8	−	3.53258e8i	0.786659	−	0.454178i	0.838785	+	0.544463i	$0.183266\pi$
$168$	−2.61951e9	−	6.26377e8i	−3.28839	−	0.786319i
$169$	3.52501e8	−	6.10550e8i	0.432129	−	0.748470i
$170$		−	1.00023e8i		−	0.119758i
$171$	−5.09461e8	+	3.32164e8i	−0.595836	+	0.388479i
$172$	3.32938e8			0.380408
$173$	−9.42825e8	−	5.44340e8i	−1.05256	−	0.607695i	−0.129195	−	0.991619i	$-0.541239\pi$
$173$	−9.42825e8	−	5.44340e8i	−1.05256	−	0.607695i	−0.923365	+	0.383924i	$0.874573\pi$
$174$	−1.55255e9	−	1.47064e9i	−1.69374	−	1.60439i
$175$	4.81705e8	+	8.34337e8i	0.513605	+	0.889589i
$176$	8.55067e8	−	4.93673e8i	0.891147	−	0.514504i
$177$	5.36947e8	−	5.66853e8i	0.547065	−	0.577534i
$178$	−8.16164e8	+	1.41364e9i	−0.813013	+	1.40818i
$179$			1.28580e8i			0.125245i	0.998037	+	0.0626225i	$0.0199464\pi$
$179$			1.28580e8i			0.125245i	−0.998037	+	0.0626225i	$0.980054\pi$
$180$	9.29077e8	−	5.03809e7i	0.885037	−	0.0479928i
$181$	−5.51510e8			−0.513853			−0.256927	−	0.966431i	$-0.582710\pi$
$181$	−5.51510e8			−0.513853			−0.256927	+	0.966431i	$0.582710\pi$
$182$	−7.70329e8	−	4.44750e8i	−0.702087	−	0.405350i
$183$	1.70034e8	−	7.11084e8i	0.151611	−	0.634040i
$184$	−3.62921e8	−	6.28597e8i	−0.316622	−	0.548405i
$185$	−3.15845e8	+	1.82353e8i	−0.269641	+	0.155678i
$186$	1.13149e9	+	3.80716e9i	0.945364	+	3.18090i
$187$	−3.95706e7	+	6.85382e7i	−0.0323598	+	0.0560488i
$188$			8.12921e8i			0.650754i
$189$	5.02200e8	+	1.40600e9i	0.393577	+	1.10189i
$190$	−6.09123e8			−0.467402
$191$	1.01356e9	+	5.85182e8i	0.761584	+	0.439701i	0.829864	−	0.557965i	$-0.188418\pi$
$191$	1.01356e9	+	5.85182e8i	0.761584	+	0.439701i	−0.0682799	+	0.997666i	$0.521751\pi$
$192$	2.49568e9	−	7.41718e8i	1.83647	−	0.545800i
$193$	−6.08669e8	−	1.05425e9i	−0.438684	−	0.759823i	0.558904	−	0.829232i	$-0.311222\pi$
$193$	−6.08669e8	−	1.05425e9i	−0.438684	−	0.759823i	−0.997588	+	0.0694089i	$0.977889\pi$
$194$	−1.59838e8	+	9.22824e7i	−0.112842	+	0.0651496i
$195$	1.81039e8	+	4.32900e7i	0.125209	+	0.0299398i
$196$	6.90788e8	−	1.19648e9i	0.468080	−	0.810739i
$197$			1.16248e9i			0.771826i	0.922535	+	0.385913i	$0.126114\pi$
$197$			1.16248e9i			0.771826i	−0.922535	+	0.385913i	$0.873886\pi$
$198$	−9.15395e8	−	4.64327e8i	−0.595590	−	0.302109i
$199$	−2.31429e9			−1.47572			−0.737861	−	0.674952i	$-0.764164\pi$
$199$	−2.31429e9			−1.47572			−0.737861	+	0.674952i	$0.764164\pi$
$200$	−3.51514e9	−	2.02947e9i	−2.19696	−	1.26842i
$201$	6.26415e8	+	5.93367e8i	0.383776	+	0.363529i
$202$	1.39422e9	+	2.41485e9i	0.837383	+	1.45039i
$203$	2.13475e9	−	1.23250e9i	1.25708	−	0.725776i
$204$	−5.50587e8	+	5.81253e8i	−0.317911	+	0.335617i
$205$	5.23587e8	−	9.06880e8i	0.296465	−	0.513493i
$206$		−	5.60673e9i		−	3.11344i
$207$	−1.82014e8	+	3.58829e8i	−0.0991340	+	0.195437i
$208$	1.99827e9			1.06758
$209$	4.17387e8	+	2.40978e8i	0.218753	+	0.126297i
$210$	−3.47755e8	+	1.45431e9i	−0.178812	+	0.747792i
$211$	1.17351e9	+	2.03258e9i	0.592048	+	1.02546i	0.993956	+	0.109777i	$0.0350136\pi$
$211$	1.17351e9	+	2.03258e9i	0.592048	+	1.02546i	−0.401909	+	0.915680i	$0.631653\pi$
$212$	−4.99062e9	+	2.88134e9i	−2.47065	+	1.42643i
$213$	−4.99630e8	−	1.68112e9i	−0.242734	−	0.816735i
$214$	3.20516e9	−	5.55149e9i	1.52825	−	2.64700i
$215$		−	1.11972e8i		−	0.0524027i
$216$	−4.79416e9	−	4.07209e9i	−2.20240	−	1.87069i
$217$	−4.57814e9			−2.06467
$218$	3.98131e9	+	2.29861e9i	1.76279	+	1.01775i
$219$	−1.55632e9	+	4.62539e8i	−0.676585	+	0.201081i
$220$	−3.68667e8	−	6.38550e8i	−0.157378	−	0.272587i
$221$	−1.38713e8	+	8.00861e7i	−0.0581498	+	0.0335728i
$222$	3.95853e9	+	9.46563e8i	1.62975	+	0.389706i
$223$	5.96084e8	−	1.03245e9i	0.241039	−	0.417492i	−0.719971	−	0.694004i	$-0.755845\pi$
$223$	5.96084e8	−	1.03245e9i	0.241039	−	0.417492i	0.961011	+	0.276511i	$0.0891784\pi$
$224$			7.54004e9i			2.99489i
$225$	1.21830e8	+	2.24667e9i	0.0475361	+	0.876616i
$226$	8.08612e9			3.09960
$227$	−3.54419e7	−	2.04624e7i	−0.0133479	−	0.00770643i	0.493311	−	0.869853i	$-0.335786\pi$
$227$	−3.54419e7	−	2.04624e7i	−0.0133479	−	0.00770643i	−0.506659	+	0.862146i	$0.669120\pi$
$228$	3.53974e9	+	3.35299e9i	1.30988	+	1.24077i
$229$	−1.51873e9	−	2.63052e9i	−0.552255	−	0.956534i	−0.998111	−	0.0614295i	$-0.980434\pi$
$229$	−1.51873e9	−	2.63052e9i	−0.552255	−	0.956534i	0.445856	−	0.895105i	$-0.352899\pi$
$230$	−3.48988e8	+	2.01488e8i	−0.124709	+	0.0720009i
$231$	8.13638e8	−	8.58955e8i	0.285748	−	0.301663i
$232$	−5.19264e9	+	8.99391e9i	−1.79240	+	3.10453i
$233$			2.47142e9i			0.838537i	0.907862	+	0.419269i	$0.137713\pi$
$233$			2.47142e9i			0.838537i	−0.907862	+	0.419269i	$0.862287\pi$
$234$	−1.13457e9	−	1.74017e9i	−0.378414	−	0.580400i
$235$	2.73396e8			0.0896439
$236$	−5.42086e9	−	3.12974e9i	−1.74751	−	1.00893i
$237$	1.06650e9	−	4.46012e9i	0.338040	−	1.41369i
$238$	−6.43343e8	−	1.11430e9i	−0.200509	−	0.347292i
$239$	2.68255e9	−	1.54877e9i	0.822159	−	0.474674i	−0.0290013	−	0.999579i	$-0.509233\pi$
$239$	2.68255e9	−	1.54877e9i	0.822159	−	0.474674i	0.851160	+	0.524906i	$0.175899\pi$
$240$	−9.56995e8	−	3.22003e9i	−0.288446	−	0.970545i
$241$	−2.94024e7	+	5.09264e7i	−0.00871594	+	0.0150965i	−0.870350	−	0.492433i	$-0.836108\pi$
$241$	−2.94024e7	+	5.09264e7i	−0.00871594	+	0.0150965i	0.861635	+	0.507529i	$0.169441\pi$
$242$		−	5.63650e9i		−	1.64342i
$243$	−4.39436e8	+	3.45898e9i	−0.126029	+	0.992027i
$244$	−5.86135e9			−1.65363
$245$	−4.02392e8	−	2.32321e8i	−0.111682	−	0.0644799i
$246$	−1.12022e10	+	3.32930e9i	−3.05889	+	0.909103i
$247$	4.87711e8	+	8.44741e8i	0.131031	+	0.226953i
$248$	1.67040e10	−	9.64407e9i	4.41585	−	2.54949i
$249$	1.17416e8	+	2.80766e7i	0.0305444	+	0.00730377i
$250$	−2.41016e9	+	4.17452e9i	−0.617001	+	1.06868i
$251$			3.40153e9i			0.856997i	0.903542	+	0.428499i	$0.140957\pi$
$251$			3.40153e9i			0.856997i	−0.903542	+	0.428499i	$0.859043\pi$
$252$	1.00263e10	−	6.53704e9i	2.48621	−	1.62099i
$253$	3.18847e8			0.0778216
$254$	1.70535e9	+	9.84587e8i	0.409713	+	0.236548i
$255$	1.95483e8	+	1.85170e8i	0.0462326	+	0.0437935i
$256$	−9.92756e7	−	1.71950e8i	−0.0231144	−	0.0400353i
$257$	−4.27262e9	+	2.46680e9i	−0.979405	+	0.565459i	−0.902090	−	0.431547i	$-0.857968\pi$
$257$	−4.27262e9	+	2.46680e9i	−0.979405	+	0.565459i	−0.0773142	+	0.997007i	$0.524634\pi$
$258$	−8.59348e8	+	9.07211e8i	−0.193950	+	0.204753i
$259$	−2.34577e9	+	4.06300e9i	−0.521299	+	0.902916i
$260$		−	1.49228e9i		−	0.326555i
$261$	5.74838e9	−	3.11716e8i	1.23875	−	0.0671734i
$262$	−7.96698e8			−0.169079
$263$	−5.66211e9	−	3.26902e9i	−1.18347	−	0.683274i	−0.226652	−	0.973976i	$-0.572778\pi$
$263$	−5.66211e9	−	3.26902e9i	−1.18347	−	0.683274i	−0.956814	+	0.290702i	$0.906111\pi$
$264$	−1.15925e9	+	4.84799e9i	−0.238650	+	0.998035i
$265$	9.69031e8	+	1.67841e9i	0.196496	+	0.340342i
$266$	−6.78592e9	+	3.91785e9i	−1.35545	+	0.782567i
$267$	−1.25184e9	−	4.21212e9i	−0.246323	−	0.828812i
$268$	3.45859e9	−	5.99046e9i	0.670440	−	1.16124i
$269$			3.91317e9i			0.747343i	0.927561	+	0.373672i	$0.121901\pi$
$269$			3.91317e9i			0.747343i	−0.927561	+	0.373672i	$0.878099\pi$
$270$	−2.26076e9	+	2.66164e9i	−0.425402	+	0.500835i
$271$	5.50493e9			1.02064			0.510322	−	0.859983i	$-0.329526\pi$
$271$	5.50493e9			1.02064			0.510322	+	0.859983i	$0.329526\pi$
$272$	2.50329e9	+	1.44528e9i	0.457336	+	0.264043i
$273$	2.29530e9	−	6.82164e8i	0.413227	−	0.122811i
$274$	−6.80119e9	−	1.17800e10i	−1.20665	−	2.08999i
$275$	1.54413e9	−	8.91502e8i	0.269993	−	0.155880i
$276$	3.13715e9	+	7.50155e8i	0.540629	+	0.129275i
$277$	2.81367e9	−	4.87342e9i	0.477919	−	0.827780i	−0.521760	−	0.853092i	$-0.674724\pi$
$277$	2.81367e9	−	4.87342e9i	0.477919	−	0.827780i	0.999680	+	0.0253117i	$0.00805783\pi$
$278$			1.31169e10i			2.19610i
$279$	−9.53535e9	−	4.83673e9i	−1.57369	−	0.798244i
$280$	7.26174e9			1.18143
$281$	3.55445e9	+	2.05216e9i	0.570095	+	0.329145i	0.757187	−	0.653198i	$-0.226573\pi$
$281$	3.55445e9	+	2.05216e9i	0.570095	+	0.329145i	−0.187092	+	0.982342i	$0.559906\pi$
$282$	−2.21510e9	−	2.09823e9i	−0.350265	−	0.331786i
$283$	2.48538e9	+	4.30480e9i	0.387477	+	0.671130i	0.992109	−	0.125374i	$-0.0400132\pi$
$283$	2.48538e9	+	4.30480e9i	0.387477	+	0.671130i	−0.604632	+	0.796505i	$0.706680\pi$
$284$	−1.21762e10	+	7.02995e9i	−1.87171	+	1.08063i
$285$	1.12765e9	−	1.19046e9i	0.170921	−	0.180441i
$286$	−8.23109e8	+	1.42567e9i	−0.123025	+	0.213085i
$287$		−	1.34708e10i		−	1.98547i
$288$	−7.96593e9	+	1.57044e10i	−1.15789	+	2.28271i
$289$	6.74406e9			0.966786
$290$	4.99328e9	+	2.88287e9i	0.705983	+	0.407599i
$291$	1.15548e8	−	4.83224e8i	0.0161136	−	0.0673870i
$292$	6.50806e9	+	1.12723e10i	0.895200	+	1.55053i
$293$	−2.65351e9	+	1.53201e9i	−0.360040	+	0.207869i	−0.669098	−	0.743174i	$-0.733320\pi$
$293$	−2.65351e9	+	1.53201e9i	−0.360040	+	0.207869i	0.309058	+	0.951043i	$0.399986\pi$
$294$	1.47725e9	+	4.97054e9i	0.197726	+	0.665295i
$295$	−1.05257e9	+	1.82311e9i	−0.138984	+	0.240726i
$296$		−	1.97659e10i		−	2.57484i
$297$	2.60212e9	−	9.29434e8i	0.334427	−	0.119452i
$298$	−9.85180e9			−1.24925
$299$	5.58853e8	+	3.22654e8i	0.0699218	+	0.0403694i
$300$	1.72902e10	−	5.13865e9i	2.13459	−	0.634401i
$301$	−7.20195e8	−	1.24741e9i	−0.0877373	−	0.151965i
$302$	−3.82602e8	+	2.20895e8i	−0.0459959	+	0.0265558i
$303$	−7.30061e9	−	1.74572e9i	−0.866141	−	0.207112i
$304$	8.80150e9	−	1.52446e10i	1.03053	−	1.78494i
$305$			1.97125e9i			0.227794i
$306$	−1.62710e8	−	3.00055e9i	−0.0185579	−	0.342227i
$307$	−3.87276e9			−0.435980			−0.217990	−	0.975951i	$-0.569950\pi$
$307$	−3.87276e9			−0.435980			−0.217990	+	0.975951i	$0.569950\pi$
$308$	−8.21425e9	−	4.74250e9i	−0.912778	−	0.526993i
$309$	1.09577e10	+	1.03796e10i	1.20195	+	1.13854i
$310$	−5.35424e9	−	9.27382e9i	−0.579764	−	1.00418i
$311$	3.98486e9	−	2.30066e9i	0.425962	−	0.245930i	−0.271663	−	0.962393i	$-0.587573\pi$
$311$	3.98486e9	−	2.30066e9i	0.425962	−	0.245930i	0.697625	+	0.716463i	$0.254240\pi$
$312$	−6.93773e9	+	7.32413e9i	−0.732148	+	0.772926i
$313$	2.25805e9	−	3.91106e9i	0.235264	−	0.407490i	−0.724085	−	0.689711i	$-0.757738\pi$
$313$	2.25805e9	−	3.91106e9i	0.235264	−	0.407490i	0.959349	+	0.282221i	$0.0910711\pi$
$314$		−	4.75500e8i		−	0.0489139i
$315$	−2.19849e9	−	3.37198e9i	−0.223297	−	0.342486i
$316$	−3.67640e10			−3.68701
$317$	−7.55534e9	−	4.36208e9i	−0.748199	−	0.431973i	0.0768439	−	0.997043i	$-0.475516\pi$
$317$	−7.55534e9	−	4.36208e9i	−0.748199	−	0.431973i	−0.825043	+	0.565070i	$0.808849\pi$
$318$	5.03007e9	−	2.10358e10i	0.491887	−	2.05708i
$319$	−2.28102e9	−	3.95083e9i	−0.220275	−	0.381528i
$320$	−6.07920e9	+	3.50983e9i	−0.579758	+	0.334723i
$321$	4.91612e9	+	1.65414e10i	0.463022	+	1.55795i
$322$	−2.59192e9	+	4.48934e9i	−0.241101	+	0.417599i
$323$			1.41097e9i			0.129631i
$324$	2.77890e10	−	3.02271e9i	2.52170	−	0.274294i
$325$	3.60859e9			0.323447
$326$	2.75913e10	+	1.59298e10i	2.44287	+	1.41039i
$327$	−1.18629e10	+	3.52565e9i	−1.03752	+	0.308353i
$328$	2.83768e10	+	4.91500e10i	2.45170	+	4.24647i
$329$	3.04576e9	−	1.75847e9i	0.259963	−	0.150090i
$330$	2.69153e9	+	6.43598e8i	0.226957	+	0.0542699i
$331$	−8.13688e9	+	1.40935e10i	−0.677869	+	1.17410i	0.297753	+	0.954643i	$0.403763\pi$
$331$	−8.13688e9	+	1.40935e10i	−0.677869	+	1.17410i	−0.975621	+	0.219460i	$0.929570\pi$
$332$		−	9.67845e8i		−	0.0796624i
$333$	−9.17826e9	+	5.98413e9i	−0.746420	+	0.486658i
$334$	2.12585e10			1.70823
$335$	−2.01467e9	−	1.16317e9i	−0.159965	−	0.0923557i
$336$	−3.13725e10	−	2.97173e10i	−2.46145	−	2.33159i
$337$	−8.51751e9	−	1.47528e10i	−0.660378	−	1.14381i	−0.980516	−	0.196438i	$-0.937063\pi$
$337$	−8.51751e9	−	1.47528e10i	−0.660378	−	1.14381i	0.320138	−	0.947371i	$-0.396271\pi$
$338$	1.83710e10	−	1.06065e10i	1.40756	−	0.812653i
$339$	−1.49696e10	+	1.58034e10i	−1.13347	+	1.19660i
$340$	1.07931e9	−	1.86942e9i	0.0807663	−	0.139891i
$341$			8.47287e9i			0.626633i
$342$	−1.82729e10	+	9.90879e8i	−1.33568	+	0.0724296i
$343$	1.02182e10			0.738239
$344$	5.25547e9	+	3.03425e9i	0.375300	+	0.216679i
$345$	2.52287e8	−	1.05506e9i	0.0178081	−	0.0744737i
$346$	−1.63788e10	−	2.83689e10i	−1.14282	−	1.97942i
$347$	2.89724e9	−	1.67272e9i	0.199833	−	0.115374i	−0.396745	−	0.917929i	$-0.629860\pi$
$347$	2.89724e9	−	1.67272e9i	0.199833	−	0.115374i	0.596577	+	0.802555i	$0.296527\pi$
$348$	−1.31478e10	−	4.42390e10i	−0.896474	−	3.01640i
$349$	−4.03503e9	+	6.98888e9i	−0.271985	+	0.471092i	−0.969370	−	0.245605i	$-0.921013\pi$
$349$	−4.03503e9	+	6.98888e9i	−0.271985	+	0.471092i	0.697385	+	0.716697i	$0.254347\pi$
$350$			2.89883e10i			1.93175i
$351$	5.50134e9	+	1.00414e9i	0.362444	+	0.0661554i
$352$	1.39545e10			0.908959
$353$	−1.32067e9	−	7.62489e8i	−0.0850541	−	0.0491060i	0.456870	−	0.889534i	$-0.348971\pi$
$353$	−1.32067e9	−	7.62489e8i	−0.0850541	−	0.0491060i	−0.541924	+	0.840428i	$0.682304\pi$
$354$	2.25199e10	−	6.69292e9i	1.43401	−	0.426189i
$355$	2.36426e9	+	4.09503e9i	0.148862	+	0.257836i
$356$	−3.05080e10	+	1.76138e10i	−1.89939	+	1.09661i
$357$	3.36877e9	+	8.05540e8i	0.207395	+	0.0495923i
$358$	−1.93443e9	+	3.35054e9i	−0.117766	+	0.203977i
$359$		−	2.58143e10i		−	1.55411i	−0.629430	−	0.777057i	$-0.716712\pi$
$359$		−	2.58143e10i		−	1.55411i	0.629430	−	0.777057i	$-0.283288\pi$
$360$	1.51247e10	+	7.67192e9i	0.900488	+	0.456766i
$361$	−8.39096e9			−0.494063
$362$	−1.43713e10	−	8.29726e9i	−0.836876	−	0.483170i
$363$	1.10159e10	+	1.04347e10i	0.634443	+	0.600971i
$364$	−9.59825e9	−	1.66247e10i	−0.546747	−	0.946994i
$365$	3.79102e9	−	2.18874e9i	0.213592	−	0.123317i
$366$	1.51288e10	−	1.59714e10i	0.843099	−	0.890057i
$367$	7.78832e9	−	1.34898e10i	0.429318	−	0.743601i	−0.567494	−	0.823377i	$-0.692087\pi$
$367$	7.78832e9	−	1.34898e10i	0.429318	−	0.743601i	0.996813	+	0.0797760i	$0.0254205\pi$
$368$		−	1.16456e10i		−	0.634994i
$369$	1.42316e10	−	2.80569e10i	0.767626	−	1.51333i
$370$	−1.09737e10			−0.585528
$371$	2.15909e10	+	1.24655e10i	1.13966	+	0.657983i
$372$	−1.99342e10	+	8.33650e10i	−1.04094	+	4.35323i
$373$	−6.74347e9	−	1.16800e10i	−0.348376	−	0.603405i	0.637585	−	0.770380i	$-0.279933\pi$
$373$	−6.74347e9	−	1.16800e10i	−0.348376	−	0.603405i	−0.985961	+	0.166975i	$0.946600\pi$
$374$	−2.06226e9	+	1.19065e9i	−0.105404	+	0.0608551i
$375$	−3.69674e9	−	1.24386e10i	−0.186936	−	0.628992i
$376$	−7.40860e9	+	1.28321e10i	−0.370668	+	0.642015i
$377$		−	9.23300e9i		−	0.457065i
$378$	−8.06639e9	+	4.41931e10i	−0.395104	+	2.16465i
$379$	1.75878e10			0.852422			0.426211	−	0.904624i	$-0.359848\pi$
$379$	1.75878e10			0.852422			0.426211	+	0.904624i	$0.359848\pi$
$380$	−1.13845e10	−	6.57282e9i	−0.545981	−	0.315222i
$381$	−5.08133e9	+	1.51017e9i	−0.241145	+	0.0716683i
$382$	1.76077e10	+	3.04974e10i	0.826892	+	1.43222i
$383$	−8.70594e8	+	5.02638e8i	−0.0404595	+	0.0233593i	−0.520093	−	0.854109i	$-0.674103\pi$
$383$	−8.70594e8	+	5.02638e8i	−0.0404595	+	0.0233593i	0.479634	+	0.877469i	$0.340770\pi$
$384$	2.20637e10	+	5.27587e9i	1.01474	+	0.242644i
$385$	−1.59496e9	+	2.76256e9i	−0.0725952	+	0.125739i
$386$		−	3.66288e10i		−	1.64996i
$387$	−1.82147e8	−	3.35899e9i	−0.00812043	−	0.149749i
$388$	−3.98314e9			−0.175751
$389$	2.58931e8	+	1.49494e8i	0.0113080	+	0.00652866i	0.505643	−	0.862743i	$-0.331255\pi$
$389$	2.58931e8	+	1.49494e8i	0.0113080	+	0.00652866i	−0.494335	+	0.869271i	$0.664589\pi$
$390$	4.06625e9	+	3.85172e9i	0.175766	+	0.166493i
$391$	4.66728e8	+	8.08396e8i	0.0199690	+	0.0345873i
$392$	2.18083e10	−	1.25911e10i	0.923588	−	0.533234i
$393$	1.47491e9	−	1.55705e9i	0.0618292	−	0.0652729i
$394$	−1.74890e10	+	3.02919e10i	−0.725740	+	1.25702i
$395$			1.23642e10i			0.507900i
$396$	−1.20983e10	−	1.85559e10i	−0.491974	−	0.754573i
$397$	−4.25871e9			−0.171442			−0.0857208	−	0.996319i	$-0.527319\pi$
$397$	−4.25871e9			−0.171442			−0.0857208	+	0.996319i	$0.527319\pi$
$398$	−6.03058e10	−	3.48176e10i	−2.40340	−	1.38761i
$399$	4.90561e9	−	2.05153e10i	0.193554	−	0.809442i
$400$	−3.25612e10	−	5.63977e10i	−1.27192	−	2.20304i
$401$	−2.35315e10	+	1.35859e10i	−0.910064	+	0.525426i	−0.880452	−	0.474136i	$-0.842761\pi$
$401$	−2.35315e10	+	1.35859e10i	−0.910064	+	0.525426i	−0.0296123	+	0.999561i	$0.509427\pi$
$402$	7.39618e9	+	2.48862e10i	0.283207	+	0.952915i
$403$	−8.57404e9	+	1.48507e10i	−0.325061	+	0.563023i
$404$			6.01778e10i			2.25897i
$405$	−1.01658e9	−	9.34582e9i	−0.0377851	−	0.347374i
$406$	7.41700e10			2.72976
$407$	7.51948e9	+	4.34137e9i	0.274038	+	0.158216i
$408$	−1.39884e10	+	4.15735e9i	−0.504808	+	0.150029i
$409$	6.53265e9	+	1.13149e10i	0.233451	+	0.404349i	0.958821	−	0.284010i	$-0.0916647\pi$
$409$	6.53265e9	+	1.13149e10i	0.233451	+	0.404349i	−0.725370	+	0.688359i	$0.758331\pi$
$410$	2.72873e10	−	1.57543e10i	0.965663	−	0.557526i
$411$	3.56135e10	+	8.51589e9i	1.24809	+	0.298444i
$412$	6.05001e10	−	1.04789e11i	2.09975	−	3.63687i
$413$			2.70803e10i			0.930795i
$414$	−1.01414e10	+	6.61207e9i	−0.345220	+	0.225080i
$415$	−3.25499e8			−0.0109738
$416$	2.44585e10	+	1.41211e10i	0.816690	+	0.471516i
$417$	−2.56354e10	−	2.42830e10i	−0.847806	−	0.803078i
$418$	7.25086e9	+	1.25589e10i	0.237511	+	0.411382i
$419$	−4.96679e10	+	2.86758e10i	−1.61146	+	0.930377i	−0.622429	+	0.782677i	$0.713854\pi$
$419$	−4.96679e10	+	2.86758e10i	−1.61146	+	0.930377i	−0.989032	+	0.147701i	$0.952813\pi$
$420$	−2.21924e10	+	2.34285e10i	−0.713194	+	0.752916i
$421$	9.15566e8	−	1.58581e9i	0.0291448	−	0.0504803i	−0.851085	−	0.525028i	$-0.824055\pi$
$421$	9.15566e8	−	1.58581e9i	0.0291448	−	0.0504803i	0.880230	+	0.474547i	$0.157388\pi$
$422$			7.06200e10i			2.22678i
$423$	8.20150e9	−	4.44741e8i	0.256172	−	0.0138914i
$424$	−1.05037e11			−3.24996
$425$	4.52058e9	+	2.60996e9i	0.138560	+	0.0799978i
$426$	1.22725e10	−	5.13236e10i	0.372644	−	1.55840i
$427$	1.26790e10	+	2.19606e10i	0.381393	+	0.660592i
$428$	1.19808e11	−	6.91712e10i	3.57035	−	2.06134i
$429$	−1.26250e9	−	4.24796e9i	−0.0372736	−	0.125416i
$430$	1.68457e9	−	2.91776e9i	0.0492737	−	0.0853445i
$431$		−	2.14254e10i		−	0.620896i	−0.950590	−	0.310448i	$-0.899521\pi$
$431$		−	2.14254e10i		−	0.620896i	0.950590	−	0.310448i	$-0.100479\pi$
$432$	−3.39466e10	−	9.50398e10i	−0.974680	−	2.72879i
$433$	−2.13129e10			−0.606306			−0.303153	−	0.952942i	$-0.598039\pi$
$433$	−2.13129e10			−0.606306			−0.303153	+	0.952942i	$0.598039\pi$
$434$	−1.19297e11	−	6.88764e10i	−3.36258	−	1.94139i
$435$	−1.48782e10	+	4.42179e9i	−0.415520	+	0.123493i
$436$	4.96069e10	+	8.59217e10i	1.37276	+	2.37770i
$437$	4.92300e9	−	2.84230e9i	0.134991	−	0.0779370i
$438$	−4.75134e10	−	1.13614e10i	−1.29098	−	0.308699i
$439$	−7.43152e6	+	1.28718e7i	−0.000200087	+	0.000346561i	−0.866125	−	0.499827i	$-0.833397\pi$
$439$	−7.43152e6	+	1.28718e7i	−0.000200087	+	0.000346561i	0.865925	+	0.500173i	$0.166730\pi$
$440$		−	1.34395e10i		−	0.358568i
$441$	−1.24491e10	−	6.31472e9i	−0.329143	−	0.166955i
$442$	−4.81946e9			−0.126273
$443$	4.49699e10	+	2.59634e10i	1.16764	+	0.674135i	0.953122	−	0.302586i	$-0.0978501\pi$
$443$	4.49699e10	+	2.59634e10i	1.16764	+	0.674135i	0.214513	+	0.976721i	$0.431183\pi$
$444$	6.37705e10	+	6.04061e10i	1.64092	+	1.55435i
$445$	5.92376e9	+	1.02602e10i	0.151063	+	0.261648i
$446$	3.10656e10	−	1.79357e10i	0.785127	−	0.453293i
$447$	1.82384e10	−	1.92542e10i	0.456831	−	0.482275i
$448$	−4.51501e10	+	7.82022e10i	−1.12085	+	1.94136i
$449$		−	6.25399e9i		−	0.153876i	−0.997036	−	0.0769382i	$-0.975486\pi$
$449$		−	6.25399e9i		−	0.153876i	0.997036	−	0.0769382i	$-0.0245144\pi$
$450$	−3.06257e10	+	6.03767e10i	−0.746854	+	1.47238i
$451$	−2.49306e10			−0.602597
$452$	1.51129e11	+	8.72542e10i	3.62071	+	2.09042i
$453$	2.76587e8	−	1.15669e9i	0.00656808	−	0.0274678i
$454$	−6.15699e8	−	1.06642e9i	−0.0144925	−	0.0251018i
$455$	−5.59109e9	+	3.22802e9i	−0.130452	+	0.0753165i
$456$	2.53176e10	+	8.51869e10i	0.585548	+	1.97021i
$457$	1.20762e10	−	2.09166e10i	0.276864	−	0.479542i	−0.693740	−	0.720226i	$-0.744038\pi$
$457$	1.20762e10	−	2.09166e10i	0.276864	−	0.479542i	0.970604	+	0.240684i	$0.0773716\pi$
$458$		−	9.13952e10i		−	2.07712i
$459$	6.16543e9	+	5.23683e9i	0.138903	+	0.117983i
$460$	−8.69673e9			−0.194234
$461$	−3.92832e10	−	2.26802e10i	−0.869768	−	0.502161i	−0.00249716	−	0.999997i	$-0.500795\pi$
$461$	−3.92832e10	−	2.26802e10i	−0.869768	−	0.502161i	−0.867271	+	0.497836i	$0.834128\pi$
$462$	3.41245e10	−	1.01418e10i	0.749028	−	0.222611i
$463$	−1.79234e10	−	3.10442e10i	−0.390029	−	0.675549i	0.602424	−	0.798176i	$-0.294202\pi$
$463$	−1.79234e10	−	3.10442e10i	−0.390029	−	0.675549i	−0.992453	+	0.122627i	$0.960868\pi$
$464$	−1.44300e11	+	8.33118e10i	−3.11312	+	1.79736i
$465$	2.80367e10	+	6.70414e9i	0.599674	+	0.143394i
$466$	−3.71815e10	+	6.44003e10i	−0.788467	+	1.36567i
$467$		−	2.44598e10i		−	0.514262i	−0.966376	−	0.257131i	$-0.917223\pi$
$467$		−	2.44598e10i		−	0.514262i	0.966376	−	0.257131i	$-0.0827773\pi$
$468$	−2.42753e9	−	4.47662e10i	−0.0506036	−	0.933183i
$469$	−2.99258e10			−0.618521
$470$	7.12417e9	+	4.11314e9i	0.145997	+	0.0842912i
$471$	9.29309e8	+	8.80281e8i	0.0188832	+	0.0178870i
$472$	−5.70460e10	−	9.88065e10i	−1.14936	−	1.99075i
$473$	−2.30862e9	+	1.33288e9i	−0.0461220	+	0.0266285i
$474$	9.48918e10	−	1.00177e11i	1.87982	−	1.98451i
$475$	1.58942e10	−	2.75296e10i	0.312223	−	0.540786i
$476$		−	2.77683e10i		−	0.540905i
$477$	3.17999e10	+	4.87736e10i	0.614260	+	0.942132i
$478$	9.32027e10			1.78532
$479$	2.25111e10	+	1.29968e10i	0.427617	+	0.246885i	0.698331	−	0.715775i	$-0.253926\pi$
$479$	2.25111e10	+	1.29968e10i	0.427617	+	0.246885i	−0.270714	+	0.962660i	$0.587260\pi$
$480$	1.10415e10	−	4.61755e10i	0.207999	−	0.869855i
$481$	8.78642e9	+	1.52185e10i	0.164146	+	0.284310i
$482$	−1.53234e9	+	8.84696e8i	−0.0283901	+	0.0163910i
$483$	−3.97553e9	−	1.33766e10i	−0.0730477	−	0.245786i
$484$	6.08213e10	−	1.05346e11i	1.10834	−	1.91971i
$485$			1.33958e9i			0.0242104i
$486$	−6.34899e10	+	8.35232e10i	−1.13805	+	1.49714i
$487$	−8.78432e10			−1.56168			−0.780840	−	0.624731i	$-0.785209\pi$
$487$	−8.78432e10			−1.56168			−0.780840	+	0.624731i	$0.785209\pi$
$488$	−9.25221e10	−	5.34177e10i	−1.63142	−	0.941902i
$489$	−8.22119e10	+	2.44334e10i	−1.43780	+	0.427315i
$490$	−6.99036e9	−	1.21077e10i	−0.121259	−	0.210027i
$491$	3.74608e10	−	2.16280e10i	0.644541	−	0.372126i	−0.141820	−	0.989892i	$-0.545296\pi$
$491$	3.74608e10	−	2.16280e10i	0.644541	−	0.372126i	0.786362	+	0.617766i	$0.211962\pi$
$492$	−2.45294e11	−	5.86545e10i	−4.18626	−	1.00102i
$493$	6.67789e9	−	1.15664e10i	0.113045	−	0.195800i
$494$			2.93497e10i			0.492829i
$495$	−6.24059e9	+	4.06880e9i	−0.103945	+	0.0677713i
$496$	3.09463e11			5.11308
$497$	5.26780e10	+	3.04137e10i	0.863384	+	0.498475i
$498$	2.63724e9	+	2.49811e9i	0.0428778	+	0.0406157i
$499$	1.60632e10	+	2.78224e10i	0.259078	+	0.448737i	0.965995	−	0.258560i	$-0.0832479\pi$
$499$	1.60632e10	+	2.78224e10i	0.259078	+	0.448737i	−0.706917	+	0.707297i	$0.749915\pi$
$500$	−9.00913e10	+	5.20143e10i	−1.44146	+	0.832228i
$501$	−3.93553e10	+	4.15473e10i	−0.624673	+	0.659465i
$502$	−5.11748e10	+	8.86373e10i	−0.805825	+	1.39573i
$503$			6.78797e10i			1.06040i	0.847874	+	0.530198i	$0.177882\pi$
$503$			6.78797e10i			1.06040i	−0.847874	+	0.530198i	$0.822118\pi$
$504$	2.17842e11	−	1.18129e10i	3.37613	−	0.183077i
$505$	2.02386e10			0.311182
$506$	8.30853e9	+	4.79693e9i	0.126742	+	0.0731748i
$507$	−1.32806e10	+	5.55394e10i	−0.200995	+	0.840561i
$508$	2.12486e10	+	3.68037e10i	0.319062	+	0.552632i
$509$	8.45265e10	−	4.88014e10i	1.25928	−	0.727045i	0.286344	−	0.958127i	$-0.407560\pi$
$509$	8.45265e10	−	4.88014e10i	1.25928	−	0.727045i	0.972934	+	0.231082i	$0.0742265\pi$
$510$	2.30810e9	+	7.76613e9i	0.0341172	+	0.114795i
$511$	2.81558e10	−	4.87673e10i	0.412937	−	0.715228i
$512$			6.57238e10i			0.956408i
$513$	3.18915e10	−	3.75465e10i	0.460474	−	0.542126i
$514$	−1.48448e11			−2.12678
$515$	−3.52420e10	−	2.03470e10i	−0.500993	−	0.289248i
$516$	−2.58505e10	+	7.68277e9i	−0.364645	+	0.108373i
$517$	−3.25444e9	−	5.63686e9i	−0.0455527	−	0.0788996i
$518$	−1.22253e11	+	7.05825e10i	−1.69800	+	0.980343i
$519$	8.57652e10	+	2.05082e10i	1.18207	+	0.282655i
$520$	1.35999e10	−	2.35558e10i	0.186005	−	0.322169i
$521$		−	1.29018e11i		−	1.75106i	−0.483166	−	0.875529i	$-0.660513\pi$
$521$		−	1.29018e11i		−	1.75106i	0.483166	−	0.875529i	$-0.339487\pi$
$522$	1.54481e11	+	7.83594e10i	2.08062	+	1.05538i
$523$	6.06027e10			0.810000			0.405000	−	0.914317i	$-0.367272\pi$
$523$	6.06027e10			0.810000			0.405000	+	0.914317i	$0.367272\pi$
$524$	−1.48902e10	−	8.59686e9i	−0.197504	−	0.114029i
$525$	−5.66541e10	−	5.36652e10i	−0.745752	−	0.706408i
$526$	−9.83624e10	−	1.70369e11i	−1.28495	−	2.22560i
$527$	−2.14819e10	+	1.24026e10i	−0.278503	+	0.160794i
$528$	−5.49986e10	+	5.80618e10i	−0.707645	+	0.747058i
$529$	−3.72751e10	+	6.45624e10i	−0.475988	+	0.824436i
$530$			5.83149e10i			0.739053i
$531$	−2.86100e10	+	5.64029e10i	−0.359865	+	0.709452i
$532$	−1.69104e11			−2.11110
$533$	−4.36967e10	−	2.52283e10i	−0.541427	−	0.312593i
$534$	3.07492e10	−	1.28593e11i	0.378154	−	1.58144i
$535$	−2.32632e10	−	4.02930e10i	−0.283958	−	0.491830i
$536$	1.09189e11	−	6.30401e10i	1.32287	−	0.763761i
$537$	−2.96706e9	−	9.98337e9i	−0.0356804	−	0.120055i
$538$	−5.88723e10	+	1.01970e11i	−0.702719	+	1.21714i
$539$			1.10620e10i			0.131062i
$540$	−7.09742e10	+	2.53508e10i	−0.834690	+	0.298138i
$541$	7.82943e10			0.913990			0.456995	−	0.889469i	$-0.348926\pi$
$541$	7.82943e10			0.913990			0.456995	+	0.889469i	$0.348926\pi$
$542$	1.43448e11	+	8.28196e10i	1.66225	+	0.959701i
$543$	4.28212e10	−	1.27265e10i	0.492560	−	0.146389i
$544$	2.04266e10	+	3.53799e10i	0.233239	+	0.403981i
$545$	2.88966e10	−	1.66834e10i	0.327537	−	0.189104i
$546$	7.00740e10	+	1.67561e10i	0.788472	+	0.188539i
$547$	2.08950e10	−	3.61912e10i	0.233396	−	0.404253i	−0.725410	−	0.688317i	$-0.758350\pi$
$547$	2.08950e10	−	3.61912e10i	0.233396	−	0.404253i	0.958805	+	0.284064i	$0.0916830\pi$
$548$		−	2.93556e11i		−	3.25514i
$549$	3.20669e9	+	5.91347e10i	0.0352994	+	0.650958i
$550$	5.36493e10			0.586291
$551$	−7.04378e10	−	4.06673e10i	−0.764187	−	0.441203i
$552$	4.26837e10	+	4.04319e10i	0.459734	+	0.435479i
$553$	7.95261e10	+	1.37743e11i	0.850372	+	1.47289i
$554$	1.46638e11	−	8.46613e10i	1.55671	−	0.898765i
$555$	2.03154e10	−	2.14469e10i	0.214118	−	0.226043i
$556$	−1.41540e11	+	2.45154e11i	−1.48108	+	2.56531i
$557$		−	5.58671e10i		−	0.580410i	−0.956964	−	0.290205i	$-0.906276\pi$
$557$		−	5.58671e10i		−	0.580410i	0.956964	−	0.290205i	$-0.0937235\pi$
$558$	−1.75706e11	−	2.69492e11i	−1.81238	−	2.77977i
$559$	−5.39519e9			−0.0552534
$560$	1.00900e11	+	5.82545e10i	1.02598	+	0.592349i
$561$	1.49083e9	−	6.23466e9i	0.0150514	−	0.0629451i
$562$	6.17481e10	+	1.06951e11i	0.618982	+	1.07211i
$563$	−1.64465e11	+	9.49538e10i	−1.63697	+	0.945103i	−0.655096	+	0.755546i	$0.727372\pi$
$563$	−1.64465e11	+	9.49538e10i	−1.63697	+	0.945103i	−0.981870	+	0.189557i	$0.939295\pi$
$564$	−1.87587e10	−	6.31181e10i	−0.185390	−	0.623788i
$565$	2.93447e10	−	5.08266e10i	0.287963	−	0.498766i
$566$			1.49566e11i			1.45736i
$567$	−7.14370e10	−	9.75782e10i	−0.691180	−	0.944106i
$568$	−2.56271e11			−2.46210
$569$	7.94261e10	+	4.58567e10i	0.757729	+	0.437475i	0.828480	−	0.560019i	$-0.189206\pi$
$569$	7.94261e10	+	4.58567e10i	0.757729	+	0.437475i	−0.0707506	+	0.997494i	$0.522539\pi$
$570$	4.72945e10	−	1.40559e10i	0.448034	−	0.133156i
$571$	−5.88051e10	−	1.01853e11i	−0.553185	−	0.958145i	−0.998042	−	0.0625430i	$-0.980079\pi$
$571$	−5.88051e10	−	1.01853e11i	−0.553185	−	0.958145i	0.444857	−	0.895601i	$-0.353254\pi$
$572$	−3.07676e10	+	1.77637e10i	−0.287415	+	0.165939i
$573$	−9.22002e10	−	2.20469e10i	−0.855290	−	0.204517i
$574$	2.02662e11	−	3.51022e11i	1.86692	−	3.23360i
$575$		−	2.10302e10i		−	0.192385i
$576$	−1.76658e11	+	1.15179e11i	−1.60488	+	1.04637i
$577$	7.31119e10			0.659606			0.329803	−	0.944050i	$-0.393018\pi$
$577$	7.31119e10			0.659606			0.329803	+	0.944050i	$0.393018\pi$
$578$	1.75737e11	+	1.01462e11i	1.57454	+	0.909058i
$579$	7.15866e10	+	6.78099e10i	0.636968	+	0.603363i
$580$	6.22160e10	+	1.07761e11i	0.549781	+	0.952249i
$581$	−3.62621e9	+	2.09359e9i	−0.0318235	+	0.0183733i
$582$	1.02809e10	−	1.08535e10i	0.0896063	−	0.0945970i
$583$	2.30702e10	−	3.99588e10i	0.199700	−	0.345890i
$584$			2.37246e11i			2.03961i
$585$	−1.50555e10	+	8.16410e8i	−0.128550	+	0.00697084i
$586$	−9.21939e10			−0.781829
$587$	−1.35807e11	−	7.84084e10i	−1.14385	−	0.660404i	−0.196472	−	0.980509i	$-0.562948\pi$
$587$	−1.35807e11	−	7.84084e10i	−1.14385	−	0.660404i	−0.947382	+	0.320105i	$0.896282\pi$
$588$	−2.60256e10	+	1.08839e11i	−0.217717	+	0.910492i
$589$	7.55297e10	+	1.30821e11i	0.627562	+	1.08697i
$590$	−5.48559e10	+	3.16711e10i	−0.452705	+	0.261369i
$591$	−2.68249e10	−	9.02588e10i	−0.219882	−	0.739843i
$592$	1.58564e11	−	2.74642e11i	1.29098	−	2.23604i
$593$			1.86748e11i			1.51021i	0.655603	+	0.755106i	$0.272415\pi$
$593$			1.86748e11i			1.51021i	−0.655603	+	0.755106i	$0.727585\pi$
$594$	8.17891e10	+	1.49286e10i	0.656976	+	0.119915i
$595$	−9.33883e9			−0.0745117
$596$	−1.84129e11	−	1.06307e11i	−1.45928	−	0.842514i
$597$	1.79689e11	−	5.34037e10i	1.41457	−	0.420411i
$598$	9.70842e9	+	1.68155e10i	0.0759178	+	0.131494i
$599$	−1.30393e11	+	7.52824e10i	−1.01285	+	0.584771i	−0.912026	−	0.410133i	$-0.865482\pi$
$599$	−1.30393e11	+	7.52824e10i	−1.01285	+	0.584771i	−0.100828	+	0.994904i	$0.532149\pi$
$600$	3.19759e11	+	7.64607e10i	2.46728	+	0.589975i
$601$	−1.24614e11	+	2.15838e11i	−0.955145	+	1.65436i	−0.221109	+	0.975249i	$0.570968\pi$
$601$	−1.24614e11	+	2.15838e11i	−0.955145	+	1.65436i	−0.734036	+	0.679110i	$0.762366\pi$
$602$		−	4.33403e10i		−	0.329994i
$603$	−6.23294e10	−	3.16161e10i	−0.471437	−	0.239133i
$604$	−9.53439e9			−0.0716383
$605$	−3.54291e10	−	2.04550e10i	−0.264447	−	0.152679i
$606$	−1.63976e11	−	1.55325e11i	−1.21588	−	1.15173i
$607$	1.80399e10	+	3.12461e10i	0.132886	+	0.230166i	0.924788	−	0.380483i	$-0.124242\pi$
$607$	1.80399e10	+	3.12461e10i	0.132886	+	0.230166i	−0.791902	+	0.610649i	$0.790909\pi$
$608$	2.15458e11	−	1.24395e11i	1.57670	−	0.910306i
$609$	−1.37309e11	+	1.44956e11i	−0.998227	+	1.05382i
$610$	−2.96567e10	+	5.13669e10i	−0.214192	+	0.370992i
$611$		−	1.31732e10i		−	0.0945206i
$612$	2.93367e10	−	5.78357e10i	0.209125	−	0.412278i
$613$	1.35788e11			0.961658			0.480829	−	0.876814i	$-0.340336\pi$
$613$	1.35788e11			0.961658			0.480829	+	0.876814i	$0.340336\pi$
$614$	−1.00916e11	−	5.82642e10i	−0.710050	−	0.409947i
$615$	−1.97263e10	+	8.24954e10i	−0.137894	+	0.576673i
$616$	−8.64420e10	−	1.49722e11i	−0.600346	−	1.03983i
$617$	1.99576e11	−	1.15225e11i	1.37711	−	0.795072i	0.385295	−	0.922793i	$-0.374100\pi$
$617$	1.99576e11	−	1.15225e11i	1.37711	−	0.795072i	0.991810	+	0.127721i	$0.0407662\pi$
$618$	1.29379e11	+	4.35327e11i	0.886973	+	2.98443i
$619$	−4.64661e10	+	8.04816e10i	−0.316500	+	0.548194i	−0.979755	−	0.200199i	$-0.935841\pi$
$619$	−4.64661e10	+	8.04816e10i	−0.316500	+	0.548194i	0.663255	+	0.748393i	$0.269174\pi$
$620$		−	2.31102e11i		−	1.56400i
$621$	5.85195e9	−	3.20609e10i	0.0393490	−	0.215580i
$622$	1.38450e11			0.924980
$623$	1.31987e11	+	7.62026e10i	0.876150	+	0.505845i
$624$	−1.55153e11	+	4.61114e10i	−1.02334	+	0.304138i
$625$	−4.94857e10	−	8.57117e10i	−0.324309	−	0.561720i
$626$	1.17681e11	−	6.79430e10i	0.766316	−	0.442433i
$627$	−3.79681e10	−	9.07892e9i	−0.245668	−	0.0587441i
$628$	5.13094e9	−	8.88705e9i	0.0329882	−	0.0571372i
$629$			2.54196e10i			0.162392i
$630$	−6.55834e9	−	1.20943e11i	−0.0416324	−	0.767745i
$631$	−8.34022e10			−0.526090			−0.263045	−	0.964784i	$-0.584727\pi$
$631$	−8.34022e10			−0.526090			−0.263045	+	0.964784i	$0.584727\pi$
$632$	−5.80325e11	−	3.35051e11i	−3.63750	−	2.10011i
$633$	−1.38018e11	−	1.30737e11i	−0.859651	−	0.814298i
$634$	−1.31252e11	−	2.27335e11i	−0.812359	−	1.40705i
$635$	1.23775e10	−	7.14618e9i	0.0761272	−	0.0439520i
$636$	3.21001e11	−	3.38879e11i	1.96190	−	2.07117i
$637$	−1.11940e10	+	1.93887e10i	−0.0679876	+	0.117758i
$638$		−	1.37268e11i		−	0.828489i
$639$	7.75861e10	+	1.18999e11i	0.465351	+	0.713740i
$640$	−6.11645e10			−0.364569
$641$	−1.75293e11	−	1.01205e11i	−1.03832	−	0.599476i	−0.118965	−	0.992898i	$-0.537958\pi$
$641$	−1.75293e11	−	1.01205e11i	−1.03832	−	0.599476i	−0.919358	+	0.393423i	$0.871291\pi$
$642$	−1.20755e11	+	5.04999e11i	−0.710829	+	2.97269i
$643$	−1.46356e11	−	2.53496e11i	−0.856184	−	1.48295i	−0.875543	−	0.483141i	$-0.839496\pi$
$643$	−1.46356e11	−	2.53496e11i	−0.856184	−	1.48295i	0.0193590	−	0.999813i	$-0.493837\pi$
$644$	−9.68856e10	+	5.59369e10i	−0.563269	+	0.325203i
$645$	2.58382e9	+	8.69386e9i	0.0149287	+	0.0502312i
$646$	−2.12276e10	+	3.67673e10i	−0.121891	+	0.211121i
$647$			5.77437e10i			0.329524i	0.986333	+	0.164762i	$0.0526856\pi$
$647$			5.77437e10i			0.329524i	−0.986333	+	0.164762i	$0.947314\pi$
$648$	4.66201e11	+	2.05543e11i	2.64407	+	1.16574i
$649$	5.01182e10			0.282499
$650$	9.40328e10	+	5.42898e10i	0.526776	+	0.304134i
$651$	3.55463e11	−	1.05644e11i	1.97911	−	0.588193i
$652$	3.43785e11	+	5.95453e11i	1.90238	+	3.29502i
$653$	1.97662e11	−	1.14120e11i	1.08710	−	0.627639i	0.154299	−	0.988024i	$-0.450688\pi$
$653$	1.97662e11	−	1.14120e11i	1.08710	−	0.627639i	0.932804	+	0.360385i	$0.117355\pi$
$654$	−3.62165e11	−	8.66009e10i	−1.97968	−	0.473381i
$655$	−2.89124e9	+	5.00777e9i	−0.0157079	+	0.0272069i
$656$			9.10566e11i			4.91696i
$657$	1.10165e11	−	7.18262e10i	0.591263	−	0.385498i
$658$	1.05822e11			0.564512
$659$	2.84269e11	+	1.64123e11i	1.50726	+	0.870217i	0.999964	+	0.00844460i	$0.00268803\pi$
$659$	2.84269e11	+	1.64123e11i	1.50726	+	0.870217i	0.507295	+	0.861772i	$0.330645\pi$
$660$	4.33596e10	+	4.10720e10i	0.228512	+	0.216456i
$661$	−1.43424e11	−	2.48417e11i	−0.751304	−	1.30130i	−0.947191	−	0.320670i	$-0.896092\pi$
$661$	−1.43424e11	−	2.48417e11i	−0.751304	−	1.30130i	0.195888	−	0.980626i	$-0.437241\pi$
$662$	−4.24062e11	+	2.44833e11i	−2.20799	+	1.27479i
$663$	8.92213e9	−	9.41906e9i	0.0461758	−	0.0487476i
$664$	8.82050e9	−	1.52776e10i	0.0453755	−	0.0785926i
$665$			5.68719e10i			0.290811i
$666$	−3.29197e11	+	1.78513e10i	−1.67324	+	0.0907346i
$667$	−5.38083e10			−0.271860
$668$	3.97320e11	+	2.29393e11i	1.99542	+	1.15206i
$669$	−2.24576e10	+	9.39179e10i	−0.112114	+	0.468861i
$670$	−3.49989e10	−	6.06199e10i	−0.173682	−	0.300826i
$671$	4.06430e10	−	2.34653e10i	0.200491	−	0.115754i
$672$	−1.73991e11	−	5.85435e11i	−0.853200	−	2.87079i
$673$	2.95892e10	−	5.12500e10i	0.144236	−	0.249824i	−0.784852	−	0.619684i	$-0.787261\pi$
$673$	2.95892e10	−	5.12500e10i	0.144236	−	0.249824i	0.929088	+	0.369860i	$0.120594\pi$
$674$		−	5.12571e11i		−	2.48379i
$675$	−6.13027e10	−	1.71628e11i	−0.295301	−	0.826748i
$676$	4.57802e11			2.19226
$677$	−1.63457e11	−	9.43721e10i	−0.778126	−	0.449251i	0.0576400	−	0.998337i	$-0.481642\pi$
$677$	−1.63457e11	−	9.43721e10i	−0.778126	−	0.449251i	−0.835766	+	0.549086i	$0.814976\pi$
$678$	−6.27834e11	+	1.86593e11i	−2.97116	+	0.883030i
$679$	8.61612e9	+	1.49236e10i	0.0405352	+	0.0702090i
$680$	3.40741e10	−	1.96727e10i	0.159363	−	0.0920084i
$681$	3.22402e9	+	7.70927e8i	0.0149903	+	0.00358447i
$682$	−1.27471e11	+	2.20787e11i	−0.589216	+	1.02055i
$683$		−	8.88600e10i		−	0.408342i	−0.978935	−	0.204171i	$-0.934550\pi$
$683$		−	8.88600e10i		−	0.408342i	0.978935	−	0.204171i	$-0.0654498\pi$
$684$	−3.52210e11	−	1.78656e11i	−1.60908	−	0.816193i
$685$	−9.87268e10			−0.448408
$686$	2.66266e11	+	1.53729e11i	1.20232	+	0.694158i
$687$	1.78621e11	+	1.69197e11i	0.801873	+	0.759568i
$688$	4.86822e10	+	8.43200e10i	0.217278	+	0.376337i
$689$	8.08718e10	−	4.66914e10i	0.358856	−	0.207186i
$690$	2.24472e10	−	2.36974e10i	0.0990296	−	0.104545i
$691$	−2.25765e10	+	3.91037e10i	−0.0990251	+	0.171516i	−0.911281	−	0.411784i	$-0.864906\pi$
$691$	−2.25765e10	+	3.91037e10i	−0.0990251	+	0.171516i	0.812256	+	0.583301i	$0.198239\pi$
$692$		−	7.06949e11i		−	3.08293i
$693$	−4.33528e10	+	8.54675e10i	−0.187968	+	0.370568i
$694$	1.00662e11			0.433938
$695$	8.24484e10	+	4.76016e10i	0.353381	+	0.204025i
$696$	1.95634e11	−	8.18142e11i	0.833695	−	3.48652i
$697$	−3.64934e10	−	6.32084e10i	−0.154626	−	0.267821i
$698$	−2.10290e11	+	1.21411e11i	−0.885926	+	0.511489i
$699$	−5.70296e10	−	1.91889e11i	−0.238887	−	0.803790i
$700$	−3.12801e11	+	5.41788e11i	−1.30280	+	2.25651i
$701$			1.98855e11i			0.823500i	0.911297	+	0.411750i	$0.135082\pi$
$701$			1.98855e11i			0.823500i	−0.911297	+	0.411750i	$0.864918\pi$
$702$	1.28247e11	+	1.08932e11i	0.528081	+	0.448544i
$703$	1.54801e11			0.633801
$704$	1.44731e11	+	8.35603e10i	0.589210	+	0.340180i
$705$	−2.12274e10	+	6.30880e9i	−0.0859292	+	0.0255382i
$706$	−2.29427e10	−	3.97380e10i	−0.0923477	−	0.159951i
$707$	2.25467e11	−	1.30173e11i	0.902413	−	0.521009i
$708$	4.93115e11	+	1.17914e11i	1.96253	+	0.469279i
$709$	4.68743e10	−	8.11887e10i	0.185503	−	0.321300i	−0.758243	−	0.651972i	$-0.773942\pi$
$709$	4.68743e10	−	8.11887e10i	0.185503	−	0.321300i	0.943746	+	0.330672i	$0.107275\pi$
$710$			1.42278e11i			0.559892i
$711$	2.01132e10	+	3.70909e11i	0.0787052	+	1.45141i
$712$	−6.42098e11			−2.49851
$713$	8.65471e10	+	4.99680e10i	0.334884	+	0.193345i
$714$	7.56646e10	+	7.16727e10i	0.291139	+	0.275779i
$715$	5.97417e9	+	1.03476e10i	0.0228588	+	0.0395926i
$716$	−7.23087e10	+	4.17474e10i	−0.275130	+	0.158847i
$717$	−1.72544e11	+	1.82154e11i	−0.652863	+	0.689225i
$718$	3.88367e11	−	6.72671e11i	1.46132	−	2.53108i
$719$			1.69858e11i			0.635582i	0.948161	+	0.317791i	$0.102941\pi$
$719$			1.69858e11i			0.635582i	−0.948161	+	0.317791i	$0.897059\pi$
$720$	1.48609e11	+	2.27931e11i	0.552987	+	0.848153i
$721$	−5.23483e11			−1.93714
$722$	−2.18652e11	−	1.26239e11i	−0.804646	−	0.464562i
$723$	1.10774e9	−	4.63258e9i	0.00405402	−	0.0169539i
$724$	−1.79065e11	−	3.10150e11i	−0.651713	−	1.12880i
$725$	−2.60585e11	+	1.50449e11i	−0.943188	+	0.544550i
$726$	1.30066e11	+	4.37638e11i	0.468185	+	1.57532i
$727$	−1.36204e11	+	2.35912e11i	−0.487587	+	0.844526i	−0.999898	−	0.0142744i	$-0.995456\pi$
$727$	−1.36204e11	+	2.35912e11i	−0.487587	+	0.844526i	0.512311	+	0.858800i	$0.328789\pi$
$728$		−	3.49897e11i		−	1.24570i
$729$	−4.56990e10	−	2.78708e11i	−0.161807	−	0.986822i
$730$	1.31715e11			0.463815
$731$	−6.75870e9	−	3.90214e9i	−0.0236698	−	0.0136657i
$732$	4.55096e11	−	1.35255e11i	1.58511	−	0.471094i
$733$	1.52152e11	+	2.63536e11i	0.527064	+	0.912901i	0.999503	+	0.0315378i	$0.0100404\pi$
$733$	1.52152e11	+	2.63536e11i	0.527064	+	0.912901i	−0.472439	+	0.881363i	$0.656626\pi$
$734$	4.05897e11	−	2.34345e11i	1.39840	−	0.807367i
$735$	3.66041e10	+	8.75275e9i	0.125424	+	0.0299913i
$736$	8.22955e10	−	1.42540e11i	0.280456	−	0.485764i
$737$			5.53844e10i			0.187723i
$738$	7.92954e11	−	5.16998e11i	2.67314	−	1.74286i
$739$	−7.86648e10			−0.263756			−0.131878	−	0.991266i	$-0.542101\pi$
$739$	−7.86648e10			−0.263756			−0.131878	+	0.991266i	$0.542101\pi$
$740$	−2.05098e11	−	1.18413e11i	−0.683966	−	0.394888i
$741$	−5.73606e10	−	5.43344e10i	−0.190257	−	0.180219i
$742$	3.75078e11	+	6.49655e11i	1.23739	+	2.14322i
$743$	−3.53569e11	+	2.04133e11i	−1.16016	+	0.669821i	−0.951343	−	0.308133i	$-0.900296\pi$
$743$	−3.53569e11	+	2.04133e11i	−1.16016	+	0.669821i	−0.208820	+	0.977954i	$0.566962\pi$
$744$	−1.07441e12	+	1.13426e12i	−3.50655	+	3.70185i
$745$	−3.57524e10	+	6.19251e10i	−0.116059	+	0.201021i
$746$		−	4.05812e11i		−	1.31030i
$747$	−9.76451e9	+	5.29499e8i	−0.0313594	+	0.00170052i
$748$	−5.13913e10			−0.164166
$749$	−5.18325e11	−	2.99255e11i	−1.64693	−	0.950856i
$750$	9.08035e10	−	3.79741e11i	0.286984	−	1.20017i
$751$	1.30881e11	+	2.26693e11i	0.411450	+	0.712652i	0.995049	−	0.0993900i	$-0.0316891\pi$
$751$	1.30881e11	+	2.26693e11i	0.411450	+	0.712652i	−0.583599	+	0.812042i	$0.698356\pi$
$752$	−2.05881e11	+	1.18865e11i	−0.643790	+	0.371692i
$753$	−7.84926e10	−	2.64107e11i	−0.244146	−	0.821485i
$754$	1.38907e11	−	2.40594e11i	0.429773	−	0.744388i
$755$			3.20654e9i			0.00986844i
$756$	−6.27630e11	+	7.38922e11i	−1.92140	+	2.26210i
$757$	8.69747e10			0.264856			0.132428	−	0.991193i	$-0.457723\pi$
$757$	8.69747e10			0.264856			0.132428	+	0.991193i	$0.457723\pi$
$758$	4.58304e11	+	2.64602e11i	1.38828	+	0.801523i
$759$	−2.47564e10	+	7.35761e9i	−0.0745968	+	0.0221702i
$760$	−1.19803e11	−	2.07506e11i	−0.359099	−	0.621978i
$761$	5.62723e11	−	3.24888e11i	1.67786	−	0.968713i	0.714839	−	0.699289i	$-0.246500\pi$
$761$	5.62723e11	−	3.24888e11i	1.67786	−	0.968713i	0.963022	−	0.269424i	$-0.0868334\pi$
$762$	−1.55130e11	−	3.70946e10i	−0.460124	−	0.110025i
$763$	2.14614e11	−	3.71723e11i	0.633228	−	1.09678i
$764$			7.59991e11i			2.23067i
$765$	−1.94509e10	−	9.86632e9i	−0.0567929	−	0.0288078i
$766$	−3.02480e10			−0.0878580
$767$	8.78437e10	+	5.07166e10i	0.253822	+	0.146544i
$768$	1.16760e10	+	1.10600e10i	0.0335620	+	0.0317914i
$769$	9.15317e8	+	1.58538e9i	0.00261738	+	0.00453343i	0.867331	−	0.497732i	$-0.165834\pi$
$769$	9.15317e8	+	1.58538e9i	0.00261738	+	0.00453343i	−0.864714	+	0.502265i	$0.832500\pi$
$770$	−8.31234e10	+	4.79913e10i	−0.236461	+	0.136521i
$771$	2.74818e11	−	2.90125e11i	0.777729	−	0.821045i
$772$	3.95247e11	−	6.84588e11i	1.11276	−	1.92735i
$773$			4.83772e11i			1.35495i	0.735547	+	0.677474i	$0.236925\pi$
$773$			4.83772e11i			1.35495i	−0.735547	+	0.677474i	$0.763075\pi$
$774$	4.57883e10	−	9.02691e10i	0.127582	−	0.251521i
$775$	5.58846e11			1.54912
$776$	−6.28743e10	−	3.63005e10i	−0.173391	−	0.100107i
$777$	8.83776e10	−	3.69595e11i	0.242470	−	1.01401i
$778$	4.49815e9	+	7.79103e9i	0.0122777	+	0.0212655i
$779$	−3.84929e11	+	2.22239e11i	−1.04528	+	0.603490i
$780$	3.44353e10	+	1.15866e11i	0.0930305	+	0.313023i
$781$	5.62873e10	−	9.74924e10i	0.151289	−	0.262039i
$782$			2.80870e10i			0.0751065i
$783$	−4.39131e11	+	1.56850e11i	−1.16828	+	0.417290i
$784$	4.04028e11			1.06942
$785$	−2.98883e9	−	1.72560e9i	−0.00787087	−	0.00454425i
$786$	6.18584e10	−	1.83843e10i	0.162072	−	0.0481679i
$787$	5.63882e10	+	9.76673e10i	0.146991	+	0.254595i	0.930114	−	0.367271i	$-0.119708\pi$
$787$	5.63882e10	+	9.76673e10i	0.146991	+	0.254595i	−0.783123	+	0.621867i	$0.786375\pi$
$788$	−6.53736e11	+	3.77435e11i	−1.69550	+	0.978897i
$789$	5.15061e11	+	1.23161e11i	1.32908	+	0.317809i
$790$	−1.86015e11	+	3.22188e11i	−0.477573	+	0.827181i
$791$		−	7.54975e11i		−	1.92853i
$792$	−2.18624e10	−	4.03165e11i	−0.0555644	−	1.02467i
$793$	9.49818e10			0.240186
$794$	−1.10974e11	−	6.40708e10i	−0.279215	−	0.161205i
$795$	−1.13969e11	−	1.07957e11i	−0.285312	−	0.270260i
$796$	−7.51406e11	−	1.30147e12i	−1.87164	−	3.24178i
$797$	−2.85447e11	+	1.64803e11i	−0.707443	+	0.408443i	−0.810114	−	0.586273i	$-0.800595\pi$
$797$	−2.85447e11	+	1.64803e11i	−0.707443	+	0.408443i	0.102670	+	0.994715i	$0.467261\pi$
$798$	4.36475e11	−	4.60785e11i	1.07634	−	1.13628i
$799$	9.52769e9	−	1.65024e10i	0.0233776	−	0.0404912i
$800$		−	9.20399e11i		−	2.24707i
$801$	1.94395e11	+	2.98157e11i	0.472232	+	0.724294i
$802$	−8.17580e11			−1.97621
$803$	−9.02547e10	−	5.21086e10i	−0.217074	−	0.125328i
$804$	−1.30303e11	+	5.44929e11i	−0.311840	+	1.30412i
$805$	1.88123e10	+	3.25839e10i	0.0447980	+	0.0775924i
$806$	−4.46845e11	+	2.57986e11i	−1.05881	+	0.611303i
$807$	−9.02991e10	−	3.03833e11i	−0.212907	−	0.716375i
$808$	−5.48433e11	+	9.49914e11i	−1.28670	+	2.22863i
$809$			7.47472e10i			0.174502i	0.996186	+	0.0872511i	$0.0278082\pi$
$809$			7.47472e10i			0.174502i	−0.996186	+	0.0872511i	$0.972192\pi$
$810$	1.14114e11	−	2.58828e11i	0.265094	−	0.601272i
$811$	−3.26425e10			−0.0754570			−0.0377285	−	0.999288i	$-0.512012\pi$
$811$	−3.26425e10			−0.0754570			−0.0377285	+	0.999288i	$0.512012\pi$
$812$	1.38623e12	+	8.00340e11i	3.18868	+	1.84099i
$813$	−4.27422e11	+	1.27030e11i	−0.978351	+	0.290766i
$814$	1.30629e11	+	2.26256e11i	0.297537	+	0.515349i
$815$	2.00259e11	−	1.15619e11i	0.453901	−	0.262060i
$816$	−2.27715e11	−	5.44511e10i	−0.513607	−	0.122814i
$817$	−2.37634e10	+	4.11594e10i	−0.0533360	+	0.0923806i
$818$			3.93125e11i			0.878047i
$819$	−1.62474e11	+	1.05931e11i	−0.361117	+	0.235444i
$820$	6.79997e11			1.50401
$821$	−2.33044e11	−	1.34548e11i	−0.512939	−	0.296145i	0.221102	−	0.975251i	$-0.429035\pi$
$821$	−2.33044e11	−	1.34548e11i	−0.512939	−	0.296145i	−0.734041	+	0.679105i	$0.762368\pi$
$822$	7.99900e11	+	7.57699e11i	1.75206	+	1.65962i
$823$	3.47774e11	+	6.02362e11i	0.758049	+	1.31298i	0.943844	+	0.330391i	$0.107181\pi$
$823$	3.47774e11	+	6.02362e11i	0.758049	+	1.31298i	−0.185795	+	0.982589i	$0.559486\pi$
$824$	1.91000e12	−	1.10274e12i	4.14310	−	2.39202i
$825$	−9.93194e10	+	1.04851e11i	−0.214397	+	0.226338i
$826$	−4.07414e11	+	7.05661e11i	−0.875216	+	1.51592i
$827$		−	5.94239e11i		−	1.27040i	−0.772349	−	0.635198i	$-0.780918\pi$
$827$		−	5.94239e11i		−	1.27040i	0.772349	−	0.635198i	$-0.219082\pi$
$828$	−2.60890e11	+	1.41472e10i	−0.555054	+	0.0300988i
$829$	4.75360e10			0.100648			0.0503239	−	0.998733i	$-0.483975\pi$
$829$	4.75360e10			0.100648			0.0503239	+	0.998733i	$0.483975\pi$
$830$	−8.48187e9	−	4.89701e9i	−0.0178723	−	0.0103186i
$831$	−1.06006e11	+	4.43317e11i	−0.222293	+	0.929631i
$832$	1.69116e11	+	2.92917e11i	0.352932	+	0.611296i
$833$	−2.80462e10	+	1.61925e10i	−0.0582498	+	0.0336305i
$834$	−3.02682e11	−	1.01844e12i	−0.625636	−	2.10510i
$835$	7.71477e10	−	1.33624e11i	0.158700	−	0.274877i
$836$			3.12965e11i			0.640723i
$837$	8.51969e11	+	1.55507e11i	1.73589	+	0.316845i
$838$	−1.72567e12			−3.49929
$839$	3.49558e11	+	2.01818e11i	0.705459	+	0.407297i	0.809377	−	0.587289i	$-0.199805\pi$
$839$	3.49558e11	+	2.01818e11i	0.705459	+	0.407297i	−0.103919	+	0.994586i	$0.533138\pi$
$840$	−5.63827e11	+	1.67570e11i	−1.13248	+	0.336572i
$841$	1.34819e11	+	2.33513e11i	0.269505	+	0.466796i
$842$	4.77157e10	−	2.75487e10i	0.0949321	−	0.0548091i
$843$	−3.23335e11	−	7.73158e10i	−0.640240	−	0.153094i
$844$	−7.62034e11	+	1.31988e12i	−1.50177	+	2.60115i
$845$		−	1.53965e11i		−	0.301992i
$846$	2.20406e11	+	1.11799e11i	0.430271	+	0.218252i
$847$	−5.26262e11			−1.02251
$848$	−1.45946e12	−	8.42617e11i	−2.82233	−	1.62947i
$849$	−2.92309e11	−	2.76888e11i	−0.562616	−	0.532933i
$850$	7.85317e10	+	1.36021e11i	0.150442	+	0.260573i
$851$	8.86909e10	−	5.12057e10i	0.169107	−	0.0976338i
$852$	7.83184e11	−	8.26805e11i	1.48630	−	1.56908i
$853$	4.49610e11	−	7.78748e11i	0.849259	−	1.47096i	−0.0326111	−	0.999468i	$-0.510382\pi$
$853$	4.49610e11	−	7.78748e11i	0.849259	−	1.47096i	0.881870	−	0.471492i	$-0.156284\pi$
$854$			7.63002e11i			1.43448i
$855$	−6.00843e10	+	1.18453e11i	−0.112434	+	0.221657i
$856$	2.52158e12			4.69654
$857$	−1.05952e11	−	6.11716e10i	−0.196421	−	0.113404i	0.398564	−	0.917140i	$-0.369509\pi$
$857$	−1.05952e11	−	6.11716e10i	−0.196421	−	0.113404i	−0.594985	+	0.803737i	$0.702842\pi$
$858$	3.10108e10	−	1.29688e11i	0.0572222	−	0.239303i
$859$	−6.24886e10	−	1.08233e11i	−0.114770	−	0.198787i	0.802918	−	0.596090i	$-0.203280\pi$
$859$	−6.24886e10	−	1.08233e11i	−0.114770	−	0.198787i	−0.917688	+	0.397302i	$0.869946\pi$
$860$	6.29689e10	−	3.63551e10i	0.115115	−	0.0664617i
$861$	3.10847e11	+	1.04592e12i	0.565631	+	1.90320i
$862$	3.22337e11	−	5.58303e11i	0.583822	−	1.01121i
$863$			2.94209e11i			0.530411i	0.964192	+	0.265205i	$0.0854397\pi$
$863$			2.94209e11i			0.530411i	−0.964192	+	0.265205i	$0.914560\pi$
$864$	2.56114e11	−	1.40316e12i	0.459598	−	2.51798i
$865$	−2.37756e11			−0.424685
$866$	−5.55374e11	−	3.20645e11i	−0.987447	−	0.570103i
$867$	−5.23633e11	+	1.55624e11i	−0.926724	+	0.275423i
$868$	−1.48644e12	−	2.57459e12i	−2.61859	−	4.53554i
$869$	2.54924e11	−	1.47181e11i	0.447026	−	0.258090i
$870$	−4.54220e11	−	1.08613e11i	−0.792847	−	0.189585i
$871$	−5.60457e10	+	9.70739e10i	−0.0973799	+	0.168667i
$872$			1.80838e12i			3.12769i
$873$	2.17913e9	+	4.01855e10i	0.00375169	+	0.0691851i
$874$	1.71045e11			0.293133
$875$	3.89762e11	+	2.25029e11i	0.664917	+	0.383890i
$876$	−7.65424e11	−	7.25042e11i	−1.29983	−	1.23125i
$877$	−5.03683e11	−	8.72404e11i	−0.851449	−	1.47475i	−0.879900	−	0.475158i	$-0.842391\pi$
$877$	−5.03683e11	−	8.72404e11i	−0.851449	−	1.47475i	0.0284512	−	0.999595i	$-0.490942\pi$
$878$	−3.87302e8	+	2.23609e8i	−0.000651736	+	0.000376280i
$879$	1.70676e11	−	1.80182e11i	0.285902	−	0.301825i
$880$	1.07813e11	−	1.86738e11i	0.179780	−	0.311387i
$881$			4.62844e11i			0.768300i	0.923271	+	0.384150i	$0.125505\pi$
$881$			4.62844e11i			0.768300i	−0.923271	+	0.384150i	$0.874495\pi$
$882$	−2.29397e11	−	3.51842e11i	−0.379065	−	0.581397i
$883$	3.39859e11			0.559057			0.279528	−	0.960137i	$-0.409822\pi$
$883$	3.39859e11			0.559057			0.279528	+	0.960137i	$0.409822\pi$
$884$	−9.00752e10	−	5.20049e10i	−0.147501	−	0.0851600i
$885$	3.96559e10	−	1.65841e11i	0.0646449	−	0.270346i
$886$	7.81219e11	+	1.35311e12i	1.26776	+	2.19583i
$887$	3.07275e11	−	1.77405e11i	0.496401	−	0.286598i	−0.230825	−	0.972995i	$-0.574142\pi$
$887$	3.07275e11	−	1.77405e11i	0.496401	−	0.286598i	0.727226	+	0.686398i	$0.240809\pi$
$888$	4.56112e11	+	1.53469e12i	0.733532	+	2.46814i
$889$	9.19278e10	−	1.59224e11i	0.147177	−	0.254918i
$890$			3.56483e11i			0.568170i
$891$	−1.80590e11	+	1.32210e11i	−0.286539	+	0.209775i
$892$	7.74150e11			1.22283
$893$	−1.00497e11	−	5.80221e10i	−0.158033	−	0.0912405i
$894$	7.64929e11	−	2.27337e11i	1.19749	−	0.355893i
$895$	1.40402e10	+	2.43184e10i	0.0218817	+	0.0379003i
$896$	−6.81401e11	+	3.93407e11i	−1.05723	+	0.610393i
$897$	−5.08368e10	−	1.21561e10i	−0.0785250	−	0.0187769i
$898$	9.40890e10	−	1.62967e11i	0.144688	−	0.250608i
$899$		−	1.42987e12i		−	2.18907i
$900$	−1.22389e12	+	7.97965e11i	−1.86541	+	1.21623i
$901$	1.35081e11			0.204972
$902$	−6.49644e11	−	3.75072e11i	−0.981407	−	0.566615i
$903$	8.47034e10	+	8.02347e10i	0.127394	+	0.120673i
$904$	1.59039e12	+	2.75464e12i	2.38139	+	4.12468i
$905$	−1.04307e11	+	6.02219e10i	−0.155497	+	0.0897760i
$906$	2.46092e10	−	2.59799e10i	0.0365246	−	0.0385589i
$907$	−4.71072e11	+	8.15921e11i	−0.696079	+	1.20564i	0.273737	+	0.961805i	$0.411740\pi$
$907$	−4.71072e11	+	8.15921e11i	−0.696079	+	1.20564i	−0.969816	+	0.243839i	$0.921593\pi$
$908$		−	2.65751e10i		−	0.0390959i
$909$	6.07129e11	−	3.29227e10i	0.889253	−	0.0482214i
$910$	−1.94257e11			−0.283277
$911$	−9.27030e10	−	5.35221e10i	−0.134592	−	0.0777069i	0.431192	−	0.902260i	$-0.358093\pi$
$911$	−9.27030e10	−	5.35221e10i	−0.134592	−	0.0777069i	−0.565784	+	0.824553i	$0.691427\pi$
$912$	−3.31599e11	+	1.38675e12i	−0.479329	+	2.00456i
$913$	3.87466e9	+	6.71111e9i	0.00557636	+	0.00965853i
$914$	6.29365e11	−	3.63364e11i	0.901816	−	0.520664i
$915$	−4.54879e10	−	1.53055e11i	−0.0648950	−	0.218354i
$916$	9.86210e11	−	1.70817e12i	1.40084	−	2.42632i
$917$			7.43852e10i			0.105198i
$918$	8.18730e10	+	2.29218e11i	0.115284	+	0.322759i
$919$	−9.49552e11			−1.33124			−0.665621	−	0.746290i	$-0.731833\pi$
$919$	−9.49552e11			−1.33124			−0.665621	+	0.746290i	$0.731833\pi$
$920$	−1.37279e11	−	7.92580e10i	−0.191625	−	0.110635i
$921$	3.00694e11	−	8.93664e10i	0.417914	−	0.124204i
$922$	−6.82430e11	−	1.18200e12i	−0.944353	−	1.63567i
$923$	1.97313e11	−	1.13919e11i	0.271862	−	0.156960i
$924$	7.47220e11	+	1.78675e11i	1.02509	+	0.245118i
$925$	2.86344e11	−	4.95963e11i	0.391130	−	0.677458i
$926$		−	1.07860e12i		−	1.46696i
$927$	−1.09031e12	−	5.53052e11i	−1.47649	−	0.748940i
$928$	−2.35495e12			−3.17534
$929$	9.88848e11	+	5.70912e11i	1.32760	+	0.766489i	0.984928	−	0.172966i	$-0.0553351\pi$
$929$	9.88848e11	+	5.70912e11i	1.32760	+	0.766489i	0.342671	+	0.939456i	$0.388668\pi$
$930$	6.29722e11	+	5.96499e11i	0.841815	+	0.797403i
$931$	9.86097e10	+	1.70797e11i	0.131256	+	0.227343i
$932$	−1.38984e12	+	8.02424e11i	−1.84205	+	1.06351i
$933$	−2.56309e11	+	2.70584e11i	−0.338250	+	0.357089i
$934$	3.67988e11	−	6.37374e11i	0.483555	−	0.837543i
$935$			1.72836e10i			0.0226145i
$936$	3.69660e11	−	7.28764e11i	0.481614	−	0.949475i
$937$	−6.05876e11			−0.786005			−0.393002	−	0.919537i	$-0.628564\pi$
$937$	−6.05876e11			−0.786005			−0.393002	+	0.919537i	$0.628564\pi$
$938$	−7.79808e11	−	4.50223e11i	−1.00734	−	0.581589i
$939$	−8.50726e10	+	3.55774e11i	−0.109428	+	0.457627i
$940$	8.87667e10	+	1.53748e11i	0.113694	+	0.196924i
$941$	−1.05979e12	+	6.11870e11i	−1.35164	+	0.780370i	−0.988479	−	0.151356i	$-0.951636\pi$
$941$	−1.05979e12	+	6.11870e11i	−1.35164	+	0.780370i	−0.363161	+	0.931726i	$0.618303\pi$
$942$	1.09725e10	+	3.69195e10i	0.0139348	+	0.0468870i
$943$	−1.47026e11	+	2.54657e11i	−0.185929	+	0.322039i
$944$		−	1.83052e12i		−	2.30508i
$945$	2.48509e11	+	2.11080e11i	0.311613	+	0.264680i
$946$	−8.02108e10			−0.100154
$947$	1.15908e10	+	6.69195e9i	0.0144116	+	0.00832057i	0.507189	−	0.861835i	$-0.330685\pi$
$947$	1.15908e10	+	6.69195e9i	0.0144116	+	0.00832057i	−0.492777	+	0.870156i	$0.664018\pi$
$948$	2.85449e12	−	8.48354e11i	3.53423	−	1.05037i
$949$	−1.05461e11	−	1.82665e11i	−0.130026	−	0.225211i
$950$	8.28345e11	−	4.78245e11i	1.01699	−	0.587160i
$951$	6.87281e11	+	1.64342e11i	0.840257	+	0.200922i
$952$	2.53067e11	−	4.38325e11i	0.308098	−	0.533641i
$953$			8.41398e11i			1.02007i	0.860154	+	0.510035i	$0.170367\pi$
$953$			8.41398e11i			1.02007i	−0.860154	+	0.510035i	$0.829633\pi$
$954$	9.48625e10	+	1.74936e12i	0.114525	+	2.11197i
$955$	2.55595e11			0.307283
$956$	1.74195e12	+	1.00571e12i	2.08547	+	1.20405i
$957$	2.68274e11	+	2.54121e11i	0.319839	+	0.302965i
$958$	3.91064e11	+	6.77343e11i	0.464286	+	0.804167i
$959$	−1.09986e12	+	6.35006e11i	−1.30036	+	0.750764i
$960$	3.91019e11	−	4.12797e11i	0.460376	−	0.486017i
$961$	−9.01377e11	+	1.56123e12i	−1.05685	+	1.83052i
$962$			5.28754e11i			0.617381i
$963$	−7.63409e11	−	1.17089e12i	−0.887671	−	1.36148i
$964$	−3.81856e10			−0.0442173
$965$	−2.30236e11	−	1.32927e11i	−0.265500	−	0.153286i
$966$	9.76514e10	−	4.08379e11i	0.112142	−	0.468980i
$967$	1.04286e10	+	1.80629e10i	0.0119267	+	0.0206577i	0.871927	−	0.489636i	$-0.162870\pi$
$967$	1.04286e10	+	1.80629e10i	0.0119267	+	0.0206577i	−0.860000	+	0.510293i	$0.829537\pi$
$968$	1.92014e12	−	1.10860e12i	2.18692	−	1.26262i
$969$	−3.25592e10	−	1.09553e11i	−0.0369299	−	0.124259i
$970$	−2.01535e10	+	3.49069e10i	−0.0227648	+	0.0394297i
$971$		−	1.21234e11i		−	0.136379i	−0.997672	−	0.0681894i	$-0.978278\pi$
$971$		−	1.21234e11i		−	0.136379i	0.997672	−	0.0681894i	$-0.0217222\pi$
$972$	−2.08789e12	+	8.75945e11i	−2.33906	+	0.981322i
$973$	1.22469e12			1.36638
$974$	−2.28902e12	−	1.32157e12i	−2.54340	−	1.46843i
$975$	−2.80183e11	+	8.32706e10i	−0.310044	+	0.0921453i
$976$	−8.57046e11	−	1.48445e12i	−0.944506	−	1.63593i
$977$	4.44845e11	−	2.56831e11i	0.488236	−	0.281883i	−0.235606	−	0.971849i	$-0.575708\pi$
$977$	4.44845e11	−	2.56831e11i	0.488236	−	0.281883i	0.723842	+	0.689965i	$0.242374\pi$
$978$	−2.50987e12	−	6.00160e11i	−2.74345	−	0.656012i
$979$	1.41030e11	−	2.44271e11i	0.153526	−	0.265914i
$980$		−	3.01721e11i		−	0.327116i
$981$	8.39718e11	−	5.47487e11i	0.906687	−	0.591150i
$982$	1.30154e12			1.39962
$983$	8.13405e11	+	4.69620e11i	0.871150	+	0.502959i	0.867730	−	0.497035i	$-0.165578\pi$
$983$	8.13405e11	+	4.69620e11i	0.871150	+	0.502959i	0.00341979	+	0.999994i	$0.498911\pi$
$984$	−3.33744e12	−	3.16136e12i	−3.55986	−	3.37205i
$985$	1.26936e11	+	2.19860e11i	0.134847	+	0.233562i
$986$	3.48026e11	−	2.00933e11i	0.368217	−	0.212590i
$987$	−1.95906e11	+	2.06817e11i	−0.206433	+	0.217930i
$988$	−3.16702e11	+	5.48544e11i	−0.332371	+	0.575683i
$989$			3.14422e10i			0.0328645i
$990$	−2.23831e11	+	1.21377e10i	−0.233013	+	0.0126356i
$991$	5.00750e11			0.519190			0.259595	−	0.965718i	$-0.416411\pi$
$991$	5.00750e11			0.519190			0.259595	+	0.965718i	$0.416411\pi$
$992$	3.78778e12	+	2.18688e12i	3.91146	+	2.25828i
$993$	3.06559e11	−	1.28203e12i	0.315295	−	1.31857i
$994$	9.15124e11	+	1.58504e12i	0.937421	+	1.62366i
$995$	−4.37703e11	+	2.52708e11i	−0.446567	+	0.257826i
$996$	2.23337e10	+	7.51469e10i	0.0226946	+	0.0763614i
$997$	4.68011e11	−	8.10618e11i	0.473669	−	0.820419i	−0.525876	−	0.850561i	$-0.676263\pi$
$997$	4.68011e11	−	8.10618e11i	0.473669	−	0.820419i	0.999546	+	0.0301419i	$0.00959593\pi$
$998$			9.66662e11i			0.974434i
$999$	5.74545e11	−	6.76423e11i	0.576848	−	0.679136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.9.d.a.2.7	✓	14
3.2	odd	2		27.9.d.a.8.1		14
4.3	odd	2		144.9.q.a.65.6		14
9.2	odd	6		81.9.b.a.80.14		14
9.4	even	3		27.9.d.a.17.1		14
9.5	odd	6	inner	9.9.d.a.5.7	yes	14
9.7	even	3		81.9.b.a.80.1		14
12.11	even	2		432.9.q.a.305.4		14
36.23	even	6		144.9.q.a.113.6		14
36.31	odd	6		432.9.q.a.17.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.7	✓	14	1.1	even	1	trivial
9.9.d.a.5.7	yes	14	9.5	odd	6	inner
27.9.d.a.8.1		14	3.2	odd	2
27.9.d.a.17.1		14	9.4	even	3
81.9.b.a.80.1		14	9.7	even	3
81.9.b.a.80.14		14	9.2	odd	6
144.9.q.a.65.6		14	4.3	odd	2
144.9.q.a.113.6		14	36.23	even	6
432.9.q.a.17.4		14	36.31	odd	6
432.9.q.a.305.4		14	12.11	even	2

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+(26.0581 + 15.0446i) q^{2} +(-77.6435 + 23.0757i) q^{3} +(324.682 + 562.365i) q^{4} +(189.131 - 109.195i) q^{5} +(-2370.40 - 566.810i) q^{6} +(1404.67 - 2432.96i) q^{7} +11836.0i q^{8} +(5496.03 - 3583.35i) q^{9} +6571.17 q^{10} +(-4502.73 - 2599.65i) q^{11} +(-38186.4 - 36171.7i) q^{12} +(-5261.39 - 9112.99i) q^{13} +(73205.9 - 42265.5i) q^{14} +(-12165.0 + 12842.6i) q^{15} +(-94949.8 + 164458. i) q^{16} -15221.5i q^{17} +(197126. - 10689.5i) q^{18} -92696.3 q^{19} +(122815. + 70907.0i) q^{20} +(-52921.3 + 221317. i) q^{21} +(-78221.6 - 135484. i) q^{22} +(-53108.9 + 30662.4i) q^{23} +(-273124. - 918989. i) q^{24} +(-171466. + 296987. i) q^{25} -316622. i q^{26} +(-344043. + 405048. i) q^{27} +1.82428e6 q^{28} +(759877. + 438715. i) q^{29} +(-510209. + 151634. i) q^{30} +(-814808. - 1.41129e6i) q^{31} +(-2.32434e6 + 1.34196e6i) q^{32} +(409597. + 97942.6i) q^{33} +(229001. - 396642. i) q^{34} -613530. i q^{35} +(3.79961e6 + 1.92732e6i) q^{36} -1.66998e6 q^{37} +(-2.41549e6 - 1.39458e6i) q^{38} +(618801. + 586154. i) q^{39} +(1.29243e6 + 2.23855e6i) q^{40} +(4.15258e6 - 2.39749e6i) q^{41} +(-4.70866e6 + 4.97091e6i) q^{42} +(256358. - 444024. i) q^{43} -3.37624e6i q^{44} +(648185. - 1.27786e6i) q^{45} -1.84522e6 q^{46} +(1.08416e6 + 625937. i) q^{47} +(3.57726e6 - 1.49601e7i) q^{48} +(-1.06379e6 - 1.84254e6i) q^{49} +(-8.93612e6 + 5.15927e6i) q^{50} +(351246. + 1.18185e6i) q^{51} +(3.41655e6 - 5.91764e6i) q^{52} +8.87435e6i q^{53} +(-1.50589e7 + 5.37879e6i) q^{54} -1.13547e6 q^{55} +(2.87965e7 + 1.66257e7i) q^{56} +(7.19727e6 - 2.13903e6i) q^{57} +(1.32006e7 + 2.28641e7i) q^{58} +(-8.34796e6 + 4.81970e6i) q^{59} +(-1.11720e7 - 2.67144e6i) q^{60} +(-4.51315e6 + 7.81701e6i) q^{61} -4.90339e7i q^{62} +(-998047. - 1.84050e7i) q^{63} -3.21428e7 q^{64} +(-1.99018e6 - 1.14903e6i) q^{65} +(9.19978e6 + 8.71442e6i) q^{66} +(-5.32613e6 - 9.22513e6i) q^{67} +(8.56002e6 - 4.94213e6i) q^{68} +(3.41600e6 - 3.60626e6i) q^{69} +(9.23033e6 - 1.59874e7i) q^{70} +2.16518e7i q^{71} +(4.24126e7 + 6.50510e7i) q^{72} +2.00444e7 q^{73} +(-4.35165e7 - 2.51242e7i) q^{74} +(6.46001e6 - 2.70158e7i) q^{75} +(-3.00968e7 - 5.21292e7i) q^{76} +(-1.26497e7 + 7.30331e6i) q^{77} +(7.30628e6 + 2.45837e7i) q^{78} +(-2.83077e7 + 4.90305e7i) q^{79} +4.14720e7i q^{80} +(1.73659e7 - 3.93884e7i) q^{81} +1.44278e8 q^{82} +(-1.29077e6 - 745226. i) q^{83} +(-1.41644e8 + 4.20965e7i) q^{84} +(-1.66210e6 - 2.87885e6i) q^{85} +(1.33604e7 - 7.71361e6i) q^{86} +(-6.91232e7 - 1.65287e7i) q^{87} +(3.07695e7 - 5.32944e7i) q^{88} +5.42495e7i q^{89} +(3.61153e7 - 2.35468e7i) q^{90} -2.95620e7 q^{91} +(-3.44870e7 - 1.99111e7i) q^{92} +(9.58309e7 + 9.07751e7i) q^{93} +(1.88340e7 + 3.26214e7i) q^{94} +(-1.75317e7 + 1.01219e7i) q^{95} +(1.49503e8 - 1.57830e8i) q^{96} +(-3.06695e6 + 5.31212e6i) q^{97} -6.40174e7i q^{98} +(-3.40626e7 + 1.84711e6i) 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

Representations

Groups

Database

Properties

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