LMFDB - Embedded newform 38.10.c.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
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} - 3 x^{13} + 93094 x^{12} + 3763497 x^{11} + 6525212431 x^{10} + 244392759522 x^{9} + \cdots + 37\!\cdots\!25 $ x^14 - 3x^13 + 93094x^12 + 3763497x^11 + 6525212431x^10 + 244392759522x^9 + 198778066371639x^8 + 9216645483921129x^7 + 4530154246073222607x^6 + 142122715974381300066x^5 + 8185019559882294055671x^4 - 135327799885026117969495x^3 + 2044710563339570147369550x^2 - 9649457865335314261798875*x + 37683939484136051622500625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.5
Root			$-25.7605 - 44.6185i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(37.7605 + 65.4031i) q^{3} +(-128.000 + 221.703i) q^{4} +(-802.961 - 1390.77i) q^{5} +(-604.168 + 1046.45i) q^{6} +1586.11 q^{7} -4096.00 q^{8} +(6989.79 - 12106.7i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(37.7605 + 65.4031i) q^{3} +(-128.000 + 221.703i) q^{4} +(-802.961 - 1390.77i) q^{5} +(-604.168 + 1046.45i) q^{6} +1586.11 q^{7} -4096.00 q^{8} +(6989.79 - 12106.7i) q^{9} +(12847.4 - 22252.3i) q^{10} +22906.4 q^{11} -19333.4 q^{12} +(74050.5 - 128259. i) q^{13} +(12688.9 + 21977.8i) q^{14} +(60640.4 - 105032. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(227226. + 393567. i) q^{17} +223673. q^{18} +(-562019. + 82596.3i) q^{19} +411116. q^{20} +(59892.4 + 103737. i) q^{21} +(183251. + 317401. i) q^{22} +(1.04035e6 - 1.80194e6i) q^{23} +(-154667. - 267891. i) q^{24} +(-312929. + 542010. i) q^{25} +2.36962e6 q^{26} +2.54223e6 q^{27} +(-203022. + 351645. i) q^{28} +(-1.07872e6 + 1.86840e6i) q^{29} +1.94049e6 q^{30} +3.63339e6 q^{31} +(524288. - 908093. i) q^{32} +(864959. + 1.49815e6i) q^{33} +(-3.63561e6 + 6.29706e6i) q^{34} +(-1.27359e6 - 2.20592e6i) q^{35} +(1.78939e6 + 3.09931e6i) q^{36} +2.01484e7 q^{37} +(-5.64064e6 - 7.12680e6i) q^{38} +1.11847e7 q^{39} +(3.28893e6 + 5.69659e6i) q^{40} +(-7.28282e6 - 1.26142e7i) q^{41} +(-958278. + 1.65979e6i) q^{42} +(-1.16317e7 - 2.01467e7i) q^{43} +(-2.93202e6 + 5.07841e6i) q^{44} -2.24501e7 q^{45} +3.32913e7 q^{46} +(1.58577e7 - 2.74664e7i) q^{47} +(2.47467e6 - 4.28626e6i) q^{48} -3.78379e7 q^{49} -1.00137e7 q^{50} +(-1.71603e7 + 2.97225e7i) q^{51} +(1.89569e7 + 3.28344e7i) q^{52} +(-2.60871e7 + 4.51842e7i) q^{53} +(2.03379e7 + 3.52262e7i) q^{54} +(-1.83930e7 - 3.18576e7i) q^{55} -6.49672e6 q^{56} +(-2.66242e7 - 3.36389e7i) q^{57} -3.45191e7 q^{58} +(-8.43766e7 - 1.46145e8i) q^{59} +(1.55239e7 + 2.68883e7i) q^{60} +(-3.37688e7 + 5.84893e7i) q^{61} +(2.90672e7 + 5.03458e7i) q^{62} +(1.10866e7 - 1.92025e7i) q^{63} +1.67772e7 q^{64} -2.37839e8 q^{65} +(-1.38393e7 + 2.39704e7i) q^{66} +(-5.27851e7 + 9.14264e7i) q^{67} -1.16340e8 q^{68} +1.57137e8 q^{69} +(2.03774e7 - 3.52946e7i) q^{70} +(-5.27425e7 - 9.13527e7i) q^{71} +(-2.86302e7 + 4.95889e7i) q^{72} +(4.53734e7 + 7.85890e7i) q^{73} +(1.61187e8 + 2.79185e8i) q^{74} -4.72655e7 q^{75} +(5.36266e7 - 1.35173e8i) q^{76} +3.63322e7 q^{77} +(8.94779e7 + 1.54980e8i) q^{78} +(-5.02318e7 - 8.70039e7i) q^{79} +(-5.26228e7 + 9.11454e7i) q^{80} +(-4.15840e7 - 7.20257e7i) q^{81} +(1.16525e8 - 2.01827e8i) q^{82} +5.84251e8 q^{83} -3.06649e7 q^{84} +(3.64907e8 - 6.32037e8i) q^{85} +(1.86107e8 - 3.22348e8i) q^{86} -1.62932e8 q^{87} -9.38248e7 q^{88} +(2.88444e8 - 4.99600e8i) q^{89} +(-1.79601e8 - 3.11078e8i) q^{90} +(1.17452e8 - 2.03434e8i) q^{91} +(2.66330e8 + 4.61297e8i) q^{92} +(1.37199e8 + 2.37635e8i) q^{93} +5.07448e8 q^{94} +(5.66152e8 + 7.15317e8i) q^{95} +7.91895e7 q^{96} +(4.47210e8 + 7.74591e8i) q^{97} +(-3.02703e8 - 5.24297e8i) q^{98} +(1.60111e8 - 2.77321e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) $ 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$3$	37.7605	+	65.4031i	0.269149	+	0.466179i	0.968642	−	0.248460i	$-0.0799244\pi$
$3$	37.7605	+	65.4031i	0.269149	+	0.466179i	−0.699494	+	0.714639i	$0.746591\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−802.961	−	1390.77i	−0.574552	−	0.995153i	−0.996090	−	0.0883425i	$-0.971843\pi$
$5$	−802.961	−	1390.77i	−0.574552	−	0.995153i	0.421538	−	0.906811i	$-0.361490\pi$
$6$	−604.168	+	1046.45i	−0.190317	+	0.329638i
$7$	1586.11			0.249685			0.124843	−	0.992177i	$-0.460157\pi$
$7$	1586.11			0.249685			0.124843	+	0.992177i	$0.460157\pi$
$8$	−4096.00			−0.353553
$9$	6989.79	−	12106.7i	0.355118	−	0.615082i
$10$	12847.4	−	22252.3i	0.406270	−	0.703680i
$11$	22906.4			0.471727			0.235863	−	0.971786i	$-0.424208\pi$
$11$	22906.4			0.471727			0.235863	+	0.971786i	$0.424208\pi$
$12$	−19333.4			−0.269149
$13$	74050.5	−	128259.i	0.719090	−	1.24550i	−0.242271	−	0.970209i	$-0.577892\pi$
$13$	74050.5	−	128259.i	0.719090	−	1.24550i	0.961361	−	0.275291i	$-0.0887744\pi$
$14$	12688.9	+	21977.8i	0.0882770	+	0.152900i
$15$	60640.4	−	105032.i	0.309280	−	0.535688i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	227226.	+	393567.i	0.659838	+	1.14287i	0.980657	+	0.195733i	$0.0627085\pi$
$17$	227226.	+	393567.i	0.659838	+	1.14287i	−0.320819	+	0.947140i	$0.603958\pi$
$18$	223673.			0.502213
$19$	−562019.	+	82596.3i	−0.989373	+	0.145402i
$19$	−562019.	+	82596.3i	−0.989373	+	0.145402i
$20$	411116.			0.574552
$21$	59892.4	+	103737.i	0.0672024	+	0.116398i
$22$	183251.	+	317401.i	0.166781	+	0.288872i
$23$	1.04035e6	−	1.80194e6i	0.775184	−	1.34266i	−0.159507	−	0.987197i	$-0.550990\pi$
$23$	1.04035e6	−	1.80194e6i	0.775184	−	1.34266i	0.934691	−	0.355462i	$-0.115676\pi$
$24$	−154667.	−	267891.i	−0.0951584	−	0.164819i
$25$	−312929.	+	542010.i	−0.160220	+	0.277509i
$26$	2.36962e6			1.01695
$27$	2.54223e6			0.920615
$28$	−203022.	+	351645.i	−0.0624213	+	0.108117i
$29$	−1.07872e6	+	1.86840e6i	−0.283216	+	0.490545i	−0.972175	−	0.234256i	$-0.924735\pi$
$29$	−1.07872e6	+	1.86840e6i	−0.283216	+	0.490545i	0.688959	+	0.724801i	$0.258068\pi$
$30$	1.94049e6			0.437388
$31$	3.63339e6			0.706618			0.353309	−	0.935507i	$-0.385056\pi$
$31$	3.63339e6			0.706618			0.353309	+	0.935507i	$0.385056\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	864959.	+	1.49815e6i	0.126965	+	0.219909i
$34$	−3.63561e6	+	6.29706e6i	−0.466576	+	0.808133i
$35$	−1.27359e6	−	2.20592e6i	−0.143457	−	0.248475i
$36$	1.78939e6	+	3.09931e6i	0.177559	+	0.307541i
$37$	2.01484e7			1.76739			0.883696	−	0.468060i	$-0.155047\pi$
$37$	2.01484e7			1.76739			0.883696	+	0.468060i	$0.155047\pi$
$38$	−5.64064e6	−	7.12680e6i	−0.438836	−	0.554457i
$39$	1.11847e7			0.774168
$40$	3.28893e6	+	5.69659e6i	0.203135	+	0.351840i
$41$	−7.28282e6	−	1.26142e7i	−0.402506	−	0.697160i	0.591522	−	0.806289i	$-0.298527\pi$
$41$	−7.28282e6	−	1.26142e7i	−0.402506	−	0.697160i	−0.994028	+	0.109129i	$0.965194\pi$
$42$	−958278.	+	1.65979e6i	−0.0475193	+	0.0823058i
$43$	−1.16317e7	−	2.01467e7i	−0.518843	−	0.898662i	−0.999760	−	0.0218961i	$-0.993030\pi$
$43$	−1.16317e7	−	2.01467e7i	−0.518843	−	0.898662i	0.480918	−	0.876766i	$-0.340304\pi$
$44$	−2.93202e6	+	5.07841e6i	−0.117932	+	0.204264i
$45$	−2.24501e7			−0.816135
$46$	3.32913e7			1.09628
$47$	1.58577e7	−	2.74664e7i	0.474025	−	0.821035i	−0.525533	−	0.850773i	$-0.676134\pi$
$47$	1.58577e7	−	2.74664e7i	0.474025	−	0.821035i	0.999558	+	0.0297381i	$0.00946733\pi$
$48$	2.47467e6	−	4.28626e6i	0.0672872	−	0.116545i
$49$	−3.78379e7			−0.937657
$50$	−1.00137e7			−0.226585
$51$	−1.71603e7	+	2.97225e7i	−0.355189	+	0.615205i
$52$	1.89569e7	+	3.28344e7i	0.359545	+	0.622750i
$53$	−2.60871e7	+	4.51842e7i	−0.454135	+	0.786585i	−0.998638	−	0.0521742i	$-0.983385\pi$
$53$	−2.60871e7	+	4.51842e7i	−0.454135	+	0.786585i	0.544503	+	0.838759i	$0.316718\pi$
$54$	2.03379e7	+	3.52262e7i	0.325487	+	0.563759i
$55$	−1.83930e7	−	3.18576e7i	−0.271031	−	0.469440i
$56$	−6.49672e6			−0.0882770
$57$	−2.66242e7	−	3.36389e7i	−0.334072	−	0.422090i
$58$	−3.45191e7			−0.400528
$59$	−8.43766e7	−	1.46145e8i	−0.906542	−	1.57018i	−0.818834	−	0.574031i	$-0.805379\pi$
$59$	−8.43766e7	−	1.46145e8i	−0.906542	−	1.57018i	−0.0877081	−	0.996146i	$-0.527954\pi$
$60$	1.55239e7	+	2.68883e7i	0.154640	+	0.267844i
$61$	−3.37688e7	+	5.84893e7i	−0.312271	+	0.540869i	−0.978854	−	0.204562i	$-0.934423\pi$
$61$	−3.37688e7	+	5.84893e7i	−0.312271	+	0.540869i	0.666583	+	0.745431i	$0.267756\pi$
$62$	2.90672e7	+	5.03458e7i	0.249827	+	0.432714i
$63$	1.10866e7	−	1.92025e7i	0.0886677	−	0.153577i
$64$	1.67772e7			0.125000
$65$	−2.37839e8			−1.65262
$66$	−1.38393e7	+	2.39704e7i	−0.0897775	+	0.155499i
$67$	−5.27851e7	+	9.14264e7i	−0.320018	+	0.554287i	−0.980491	−	0.196562i	$-0.937022\pi$
$67$	−5.27851e7	+	9.14264e7i	−0.320018	+	0.554287i	0.660473	+	0.750849i	$0.270356\pi$
$68$	−1.16340e8			−0.659838
$69$	1.57137e8			0.834559
$70$	2.03774e7	−	3.52946e7i	0.101439	−	0.175698i
$71$	−5.27425e7	−	9.13527e7i	−0.246319	−	0.426637i	0.716183	−	0.697913i	$-0.245888\pi$
$71$	−5.27425e7	−	9.13527e7i	−0.246319	−	0.426637i	−0.962502	+	0.271276i	$0.912554\pi$
$72$	−2.86302e7	+	4.95889e7i	−0.125553	+	0.217464i
$73$	4.53734e7	+	7.85890e7i	0.187003	+	0.323898i	0.944250	−	0.329231i	$-0.106789\pi$
$73$	4.53734e7	+	7.85890e7i	0.187003	+	0.323898i	−0.757247	+	0.653129i	$0.773456\pi$
$74$	1.61187e8	+	2.79185e8i	0.624868	+	1.08230i
$75$	−4.72655e7			−0.172492
$76$	5.36266e7	−	1.35173e8i	0.184382	−	0.464761i
$77$	3.63322e7			0.117783
$78$	8.94779e7	+	1.54980e8i	0.273710	+	0.474079i
$79$	−5.02318e7	−	8.70039e7i	−0.145096	−	0.251314i	0.784313	−	0.620366i	$-0.213016\pi$
$79$	−5.02318e7	−	8.70039e7i	−0.145096	−	0.251314i	−0.929409	+	0.369052i	$0.879683\pi$
$80$	−5.26228e7	+	9.11454e7i	−0.143638	+	0.248788i
$81$	−4.15840e7	−	7.20257e7i	−0.107336	−	0.185911i
$82$	1.16525e8	−	2.01827e8i	0.284614	−	0.492967i
$83$	5.84251e8			1.35129			0.675644	−	0.737228i	$-0.263866\pi$
$83$	5.84251e8			1.35129			0.675644	+	0.737228i	$0.263866\pi$
$84$	−3.06649e7			−0.0672024
$85$	3.64907e8	−	6.32037e8i	0.758223	−	1.31328i
$86$	1.86107e8	−	3.22348e8i	0.366877	−	0.635450i
$87$	−1.62932e8			−0.304909
$88$	−9.38248e7			−0.166781
$89$	2.88444e8	−	4.99600e8i	0.487312	−	0.844049i	−0.512582	−	0.858638i	$-0.671311\pi$
$89$	2.88444e8	−	4.99600e8i	0.487312	−	0.844049i	0.999894	+	0.0145897i	$0.00464422\pi$
$90$	−1.79601e8	−	3.11078e8i	−0.288547	−	0.499779i
$91$	1.17452e8	−	2.03434e8i	0.179546	−	0.310983i
$92$	2.66330e8	+	4.61297e8i	0.387592	+	0.671329i
$93$	1.37199e8	+	2.37635e8i	0.190185	+	0.329411i
$94$	5.07448e8			0.670372
$95$	5.66152e8	+	7.15317e8i	0.713143	+	0.901037i
$96$	7.91895e7			0.0951584
$97$	4.47210e8	+	7.74591e8i	0.512907	+	0.888382i	0.999888	+	0.0149689i	$0.00476493\pi$
$97$	4.47210e8	+	7.74591e8i	0.512907	+	0.888382i	−0.486981	+	0.873413i	$0.661902\pi$
$98$	−3.02703e8	−	5.24297e8i	−0.331512	−	0.574196i
$99$	1.60111e8	−	2.77321e8i	0.167519	−	0.290151i
$100$	−8.01099e7	−	1.38754e8i	−0.0801099	−	0.138754i
$101$	−6.05327e8	+	1.04846e9i	−0.578820	+	1.00255i	0.416795	+	0.909001i	$0.363153\pi$
$101$	−6.05327e8	+	1.04846e9i	−0.578820	+	1.00255i	−0.995615	+	0.0935453i	$0.970180\pi$
$102$	−5.49130e8			−0.502313
$103$	−1.29218e9			−1.13124			−0.565622	−	0.824665i	$-0.691364\pi$
$103$	−1.29218e9			−1.13124			−0.565622	+	0.824665i	$0.691364\pi$
$104$	−3.03311e8	+	5.25350e8i	−0.254237	+	0.440351i
$105$	9.61825e7	−	1.66593e8i	0.0772226	−	0.133753i
$106$	−8.34788e8			−0.642244
$107$	6.81399e8			0.502544			0.251272	−	0.967916i	$-0.419151\pi$
$107$	6.81399e8			0.502544			0.251272	+	0.967916i	$0.419151\pi$
$108$	−3.25406e8	+	5.63619e8i	−0.230154	+	0.398638i
$109$	6.69834e8	+	1.16019e9i	0.454514	+	0.787242i	0.998660	−	0.0517487i	$-0.0164795\pi$
$109$	6.69834e8	+	1.16019e9i	0.454514	+	0.787242i	−0.544146	+	0.838991i	$0.683146\pi$
$110$	2.94287e8	−	5.09721e8i	0.191648	−	0.331944i
$111$	7.60814e8	+	1.31777e9i	0.475691	+	0.823922i
$112$	−5.19737e7	−	9.00211e7i	−0.0312106	−	0.0540584i
$113$	1.83847e9			1.06073			0.530364	−	0.847770i	$-0.322055\pi$
$113$	1.83847e9			1.06073			0.530364	+	0.847770i	$0.322055\pi$
$114$	2.53121e8	−	6.38027e8i	0.140364	−	0.353808i
$115$	−3.34145e9			−1.78153
$116$	−2.76153e8	−	4.78310e8i	−0.141608	−	0.245272i
$117$	−1.03520e9	−	1.79301e9i	−0.510724	−	0.884599i
$118$	1.35003e9	−	2.33831e9i	0.641022	−	1.11028i
$119$	3.60406e8	+	6.24241e8i	0.164752	+	0.285358i
$120$	−2.48383e8	+	4.30212e8i	−0.109347	+	0.189394i
$121$	−1.83324e9			−0.777474
$122$	−1.08060e9			−0.441618
$123$	5.50006e8	−	9.52638e8i	0.216668	−	0.375279i
$124$	−4.65075e8	+	8.05533e8i	−0.176655	+	0.305975i
$125$	−2.13149e9			−0.780885
$126$	3.54771e8			0.125395
$127$	−2.84390e8	+	4.92579e8i	−0.0970059	+	0.168019i	−0.910444	−	0.413632i	$-0.864260\pi$
$127$	−2.84390e8	+	4.92579e8i	−0.0970059	+	0.168019i	0.813438	+	0.581651i	$0.197593\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	8.78439e8	−	1.52150e9i	0.279292	−	0.483747i
$130$	−1.90271e9	−	3.29559e9i	−0.584289	−	1.01202i
$131$	2.26690e9	+	3.92639e9i	0.672531	+	1.16486i	0.977184	+	0.212394i	$0.0681262\pi$
$131$	2.26690e9	+	3.92639e9i	0.672531	+	1.16486i	−0.304653	+	0.952463i	$0.598540\pi$
$132$	−4.42859e8			−0.126965
$133$	−8.91425e8	+	1.31007e8i	−0.247032	+	0.0363046i
$134$	−1.68912e9			−0.452574
$135$	−2.04131e9	−	3.53566e9i	−0.528941	−	0.916153i
$136$	−9.30717e8	−	1.61205e9i	−0.233288	−	0.404067i
$137$	−1.22064e9	+	2.11421e9i	−0.296037	+	0.512750i	−0.975225	−	0.221213i	$-0.928998\pi$
$137$	−1.22064e9	+	2.11421e9i	−0.296037	+	0.512750i	0.679189	+	0.733963i	$0.262332\pi$
$138$	1.25709e9	+	2.17735e9i	0.295061	+	0.511061i
$139$	−1.93022e9	+	3.34324e9i	−0.438571	+	0.759628i	−0.997580	−	0.0695343i	$-0.977849\pi$
$139$	−1.93022e9	+	3.34324e9i	−0.438571	+	0.759628i	0.559008	+	0.829162i	$0.311182\pi$
$140$	6.52076e8			0.143457
$141$	2.39519e9			0.510333
$142$	8.43880e8	−	1.46164e9i	0.174174	−	0.301678i
$143$	1.69623e9	−	2.93796e9i	0.339214	−	0.587536i
$144$	−9.16166e8			−0.177559
$145$	3.46468e9			0.650890
$146$	−7.25974e8	+	1.25742e9i	−0.132231	+	0.229031i
$147$	−1.42878e9	−	2.47471e9i	−0.252369	−	0.437116i
$148$	−2.57900e9	+	4.46695e9i	−0.441848	+	0.765304i
$149$	1.92493e9	+	3.33408e9i	0.319946	+	0.554163i	0.980477	−	0.196636i	$-0.0630018\pi$
$149$	1.92493e9	+	3.33408e9i	0.319946	+	0.554163i	−0.660530	+	0.750800i	$0.729668\pi$
$150$	−3.78124e8	−	6.54930e8i	−0.0609851	−	0.105629i
$151$	9.40087e8			0.147154			0.0735770	−	0.997290i	$-0.476559\pi$
$151$	9.40087e8			0.147154			0.0735770	+	0.997290i	$0.476559\pi$
$152$	2.30203e9	−	3.38314e8i	0.349796	−	0.0514072i
$153$	6.35304e9			0.937282
$154$	2.90657e8	+	5.03433e8i	0.0416426	+	0.0721271i
$155$	−2.91747e9	−	5.05321e9i	−0.405989	−	0.703194i
$156$	−1.43165e9	+	2.47969e9i	−0.193542	+	0.335225i
$157$	5.53767e9	+	9.59152e9i	0.727409	+	1.25991i	0.957975	+	0.286852i	$0.0926088\pi$
$157$	5.53767e9	+	9.59152e9i	0.727409	+	1.25991i	−0.230566	+	0.973057i	$0.574058\pi$
$158$	8.03708e8	−	1.39206e9i	0.102599	−	0.177706i
$159$	−3.94025e9			−0.488919
$160$	−1.68393e9			−0.203135
$161$	1.65011e9	−	2.85808e9i	0.193552	−	0.335242i
$162$	6.65345e8	−	1.15241e9i	0.0758978	−	0.131459i
$163$	−5.19038e9			−0.575911			−0.287955	−	0.957644i	$-0.592975\pi$
$163$	−5.19038e9			−0.575911			−0.287955	+	0.957644i	$0.592975\pi$
$164$	3.72880e9			0.402506
$165$	1.38906e9	−	2.40591e9i	0.145895	−	0.252698i
$166$	4.67401e9	+	8.09562e9i	0.477753	+	0.827492i
$167$	2.26060e9	−	3.91547e9i	0.224905	−	0.389547i	−0.731386	−	0.681964i	$-0.761126\pi$
$167$	2.26060e9	−	3.91547e9i	0.224905	−	0.389547i	0.956291	+	0.292417i	$0.0944595\pi$
$168$	−2.45319e8	−	4.24905e8i	−0.0237596	−	0.0411529i
$169$	−5.66471e9	−	9.81157e9i	−0.534180	−	0.925227i
$170$	1.16770e10			1.07229
$171$	−2.92843e9	+	7.38151e9i	−0.261910	+	0.660181i
$172$	5.95544e9			0.518843
$173$	5.52904e9	+	9.57659e9i	0.469291	+	0.812837i	0.999384	−	0.0351033i	$-0.0111760\pi$
$173$	5.52904e9	+	9.57659e9i	0.469291	+	0.812837i	−0.530092	+	0.847940i	$0.677843\pi$
$174$	−1.30346e9	−	2.25766e9i	−0.107802	−	0.186718i
$175$	−4.96341e8	+	8.59688e8i	−0.0400045	+	0.0692898i
$176$	−7.50598e8	−	1.30007e9i	−0.0589658	−	0.102132i
$177$	6.37221e9	−	1.10370e10i	0.487989	−	0.845222i
$178$	9.23022e9			0.689163
$179$	−2.94330e9			−0.214287			−0.107144	−	0.994244i	$-0.534170\pi$
$179$	−2.94330e9			−0.214287			−0.107144	+	0.994244i	$0.534170\pi$
$180$	2.87361e9	−	4.97724e9i	0.204034	−	0.353397i
$181$	8.44821e9	−	1.46327e10i	0.585074	−	1.01338i	−0.409792	−	0.912179i	$-0.634399\pi$
$181$	8.44821e9	−	1.46327e10i	0.585074	−	1.01338i	0.994866	−	0.101199i	$-0.0322679\pi$
$182$	3.75848e9			0.253916
$183$	−5.10051e9			−0.336189
$184$	−4.26128e9	+	7.38075e9i	−0.274069	+	0.474701i
$185$	−1.61784e10	−	2.80218e10i	−1.01546	−	1.75883i
$186$	−2.19518e9	+	3.80217e9i	−0.134481	+	0.232929i
$187$	5.20493e9	+	9.01521e9i	0.311263	+	0.539124i
$188$	4.05958e9	+	7.03141e9i	0.237012	+	0.410518i
$189$	4.03226e9			0.229864
$190$	−5.38251e9	+	1.35674e10i	−0.299636	+	0.755274i
$191$	4.35774e9			0.236925			0.118463	−	0.992959i	$-0.462203\pi$
$191$	4.35774e9			0.236925			0.118463	+	0.992959i	$0.462203\pi$
$192$	6.33516e8	+	1.09728e9i	0.0336436	+	0.0582724i
$193$	1.79393e9	+	3.10718e9i	0.0930673	+	0.161197i	0.908800	−	0.417231i	$-0.136999\pi$
$193$	1.79393e9	+	3.10718e9i	0.0930673	+	0.161197i	−0.815733	+	0.578429i	$0.803666\pi$
$194$	−7.15536e9	+	1.23935e10i	−0.362680	+	0.628181i
$195$	−8.98091e9	−	1.55554e10i	−0.444800	−	0.770416i
$196$	4.84325e9	−	8.38875e9i	0.234414	−	0.406018i
$197$	1.39268e10			0.658799			0.329399	−	0.944191i	$-0.393154\pi$
$197$	1.39268e10			0.658799			0.329399	+	0.944191i	$0.393154\pi$
$198$	5.12356e9			0.236907
$199$	−1.97683e10	+	3.42397e10i	−0.893573	+	1.54771i	−0.0580118	+	0.998316i	$0.518476\pi$
$199$	−1.97683e10	+	3.42397e10i	−0.893573	+	1.54771i	−0.835561	+	0.549398i	$0.814857\pi$
$200$	1.28176e9	−	2.22007e9i	0.0566463	−	0.0981142i
$201$	−7.97276e9			−0.344530
$202$	−1.93705e10			−0.818575
$203$	−1.71097e9	+	2.96349e9i	−0.0707149	+	0.122482i
$204$	−4.39304e9	−	7.60897e9i	−0.177595	−	0.307603i
$205$	−1.16956e10	+	2.02574e10i	−0.462521	+	0.801109i
$206$	−1.03375e10	−	1.79050e10i	−0.399955	−	0.692743i
$207$	−1.45437e10	−	2.51904e10i	−0.550564	−	0.953604i
$208$	−9.70595e9			−0.359545
$209$	−1.28739e10	+	1.89199e9i	−0.466713	+	0.0685898i
$210$	3.07784e9			0.109209
$211$	−8.90289e9	−	1.54203e10i	−0.309215	−	0.535576i	0.668976	−	0.743284i	$-0.266733\pi$
$211$	−8.90289e9	−	1.54203e10i	−0.309215	−	0.535576i	−0.978191	+	0.207708i	$0.933400\pi$
$212$	−6.67830e9	−	1.15672e10i	−0.227067	−	0.393292i
$213$	3.98317e9	−	6.89905e9i	0.132593	−	0.229658i
$214$	5.45119e9	+	9.44174e9i	0.177676	+	0.307744i
$215$	−1.86796e10	+	3.23541e10i	−0.596204	+	1.03266i
$216$	−1.04130e10			−0.325487
$217$	5.76297e9			0.176432
$218$	−1.07173e10	+	1.85630e10i	−0.321390	+	0.556664i
$219$	−3.42664e9	+	5.93512e9i	−0.100663	+	0.174354i
$220$	9.41720e9			0.271031
$221$	6.73048e10			1.89793
$222$	−1.21730e10	+	2.10843e10i	−0.336365	+	0.582601i
$223$	−1.09478e10	−	1.89622e10i	−0.296453	−	0.513471i	0.678869	−	0.734259i	$-0.262470\pi$
$223$	−1.09478e10	−	1.89622e10i	−0.296453	−	0.513471i	−0.975322	+	0.220788i	$0.929137\pi$
$224$	8.31580e8	−	1.44034e9i	0.0220693	−	0.0382251i
$225$	4.37462e9	+	7.57706e9i	0.113794	+	0.197097i
$226$	1.47078e10	+	2.54746e10i	0.375024	+	0.649560i
$227$	−7.28196e10			−1.82025			−0.910127	−	0.414330i	$-0.864016\pi$
$227$	−7.28196e10			−1.82025			−0.910127	+	0.414330i	$0.864016\pi$
$228$	1.08657e10	−	1.59687e9i	0.266288	−	0.0391347i
$229$	4.06447e10			0.976661			0.488331	−	0.872659i	$-0.337606\pi$
$229$	4.06447e10			0.976661			0.488331	+	0.872659i	$0.337606\pi$
$230$	−2.67316e10	−	4.63004e10i	−0.629867	−	1.09096i
$231$	1.37192e9	+	2.37624e9i	0.0317012	+	0.0549080i
$232$	4.41844e9	−	7.65297e9i	0.100132	−	0.173434i
$233$	−2.05691e9	−	3.56267e9i	−0.0457208	−	0.0791908i	0.842259	−	0.539073i	$-0.181225\pi$
$233$	−2.05691e9	−	3.56267e9i	−0.0457208	−	0.0791908i	−0.887980	+	0.459882i	$0.847892\pi$
$234$	1.65631e10	−	2.86882e10i	0.361136	−	0.625506i
$235$	−5.09326e10			−1.08941
$236$	4.32008e10			0.906542
$237$	3.79355e9	−	6.57063e9i	0.0781050	−	0.135282i
$238$	−5.76649e9	+	9.98785e9i	−0.116497	+	0.201779i
$239$	5.68395e10			1.12683			0.563417	−	0.826173i	$-0.309486\pi$
$239$	5.68395e10			1.12683			0.563417	+	0.826173i	$0.309486\pi$
$240$	−7.94826e9			−0.154640
$241$	−4.92295e10	+	8.52679e10i	−0.940044	+	1.62820i	−0.174663	+	0.984628i	$0.555883\pi$
$241$	−4.92295e10	+	8.52679e10i	−0.940044	+	1.62820i	−0.765382	+	0.643576i	$0.777450\pi$
$242$	−1.46659e10	−	2.54022e10i	−0.274879	−	0.476104i
$243$	2.81598e10	−	4.87743e10i	0.518086	−	0.897352i
$244$	−8.64482e9	−	1.49733e10i	−0.156136	−	0.270435i
$245$	3.03823e10	+	5.26237e10i	0.538733	+	0.933113i
$246$	1.76002e10			0.306414
$247$	−3.10241e10	+	7.82005e10i	−0.530350	+	1.33682i
$248$	−1.48824e10			−0.249827
$249$	2.20616e10	+	3.82118e10i	0.363697	+	0.629943i
$250$	−1.70519e10	−	2.95347e10i	−0.276085	−	0.478193i
$251$	1.80223e10	−	3.12156e10i	0.286602	−	0.496410i	−0.686394	−	0.727230i	$-0.740808\pi$
$251$	1.80223e10	−	3.12156e10i	0.286602	−	0.496410i	0.972996	+	0.230820i	$0.0741409\pi$
$252$	2.83817e9	+	4.91585e9i	0.0443338	+	0.0767885i
$253$	2.38307e10	−	4.12761e10i	0.365675	−	0.633368i
$254$	−9.10049e9			−0.137187
$255$	5.51162e10			0.816298
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	6.04590e10	−	1.04718e11i	0.864493	−	1.49735i	−0.00305587	−	0.999995i	$-0.500973\pi$
$257$	6.04590e10	−	1.04718e11i	0.864493	−	1.49735i	0.867549	−	0.497351i	$-0.165694\pi$
$258$	2.81100e10			0.394978
$259$	3.19576e10			0.441292
$260$	3.04434e10	−	5.27294e10i	0.413154	−	0.715604i
$261$	1.50801e10	+	2.61194e10i	0.201150	+	0.348403i
$262$	−3.62705e10	+	6.28223e10i	−0.475551	+	0.823679i
$263$	−5.13870e10	−	8.90049e10i	−0.662296	−	1.14713i	−0.980011	−	0.198944i	$-0.936249\pi$
$263$	−5.13870e10	−	8.90049e10i	−0.662296	−	1.14713i	0.317714	−	0.948186i	$-0.397085\pi$
$264$	−3.54287e9	−	6.13643e9i	−0.0448888	−	0.0777496i
$265$	8.37878e10			1.04370
$266$	−8.94669e9	−	1.13039e10i	−0.109571	−	0.138440i
$267$	4.35672e10			0.524637
$268$	−1.35130e10	−	2.34052e10i	−0.160009	−	0.277144i
$269$	4.59020e10	+	7.95046e10i	0.534499	+	0.925779i	0.999187	+	0.0403048i	$0.0128329\pi$
$269$	4.59020e10	+	7.95046e10i	0.534499	+	0.925779i	−0.464689	+	0.885474i	$0.653834\pi$
$270$	3.26610e10	−	5.65705e10i	0.374018	−	0.647818i
$271$	6.32678e9	+	1.09583e10i	0.0712559	+	0.123419i	0.899452	−	0.437020i	$-0.143966\pi$
$271$	6.32678e9	+	1.09583e10i	0.0712559	+	0.123419i	−0.828196	+	0.560438i	$0.810633\pi$
$272$	1.48915e10	−	2.57928e10i	0.164960	−	0.285718i
$273$	1.77403e10			0.193298
$274$	−3.90605e10			−0.418659
$275$	−7.16810e9	+	1.24155e10i	−0.0755800	+	0.130908i
$276$	−2.01135e10	+	3.48376e10i	−0.208640	+	0.361375i
$277$	−7.98480e10			−0.814901			−0.407451	−	0.913227i	$-0.633582\pi$
$277$	−7.98480e10			−0.814901			−0.407451	+	0.913227i	$0.633582\pi$
$278$	−6.17670e10			−0.620233
$279$	2.53967e10	−	4.39883e10i	0.250933	−	0.434629i
$280$	5.21661e9	+	9.03543e9i	0.0507197	+	0.0878492i
$281$	5.99385e10	−	1.03817e11i	0.573492	−	0.993318i	−0.422711	−	0.906264i	$-0.638922\pi$
$281$	5.99385e10	−	1.03817e11i	0.573492	−	0.993318i	0.996204	−	0.0870534i	$-0.0277451\pi$
$282$	1.91615e10	+	3.31887e10i	0.180430	+	0.312514i
$283$	8.47968e10	+	1.46872e11i	0.785851	+	1.36113i	0.928489	+	0.371360i	$0.121108\pi$
$283$	8.47968e10	+	1.46872e11i	0.785851	+	1.36113i	−0.142638	+	0.989775i	$0.545558\pi$
$284$	2.70042e10			0.246319
$285$	−2.54058e10	+	6.40388e10i	−0.228103	+	0.574965i
$286$	5.42795e10			0.479721
$287$	−1.15514e10	−	2.00075e10i	−0.100500	−	0.174071i
$288$	−7.32932e9	−	1.26948e10i	−0.0627766	−	0.108732i
$289$	−4.39691e10	+	7.61568e10i	−0.370773	+	0.642197i
$290$	2.77175e10	+	4.80081e10i	0.230124	+	0.398587i
$291$	−3.37738e10	+	5.84979e10i	−0.276097	+	0.478213i
$292$	−2.32312e10			−0.187003
$293$	−1.45449e11			−1.15294			−0.576469	−	0.817119i	$-0.695570\pi$
$293$	−1.45449e11			−1.15294			−0.576469	+	0.817119i	$0.695570\pi$
$294$	2.28604e10	−	3.95954e10i	0.178452	−	0.309088i
$295$	−1.35502e11	+	2.34697e11i	−1.04171	+	1.80430i
$296$	−8.25279e10			−0.624868
$297$	5.82335e10			0.434279
$298$	−3.07989e10	+	5.33453e10i	−0.226236	+	0.391853i
$299$	−1.54077e11	−	2.66870e11i	−1.11485	−	1.93098i
$300$	6.04998e9	−	1.04789e10i	0.0431229	−	0.0746911i
$301$	−1.84492e10	−	3.19550e10i	−0.129547	−	0.224383i
$302$	7.52070e9	+	1.30262e10i	0.0520268	+	0.0901130i
$303$	−9.14298e10			−0.623155
$304$	2.31041e10	+	2.91914e10i	0.155152	+	0.196030i
$305$	1.08460e11			0.717664
$306$	5.08243e10	+	8.80303e10i	0.331379	+	0.573965i
$307$	−4.19179e10	−	7.26039e10i	−0.269325	−	0.466485i	0.699363	−	0.714767i	$-0.253467\pi$
$307$	−4.19179e10	−	7.26039e10i	−0.269325	−	0.466485i	−0.968688	+	0.248282i	$0.920134\pi$
$308$	−4.65052e9	+	8.05493e9i	−0.0294458	+	0.0510016i
$309$	−4.87935e10	−	8.45128e10i	−0.304473	−	0.527362i
$310$	4.66796e10	−	8.08514e10i	0.287078	−	0.497233i
$311$	−7.24440e10			−0.439117			−0.219559	−	0.975599i	$-0.570462\pi$
$311$	−7.24440e10			−0.439117			−0.219559	+	0.975599i	$0.570462\pi$
$312$	−4.58127e10			−0.273710
$313$	−1.36607e10	+	2.36610e10i	−0.0804493	+	0.139342i	−0.903443	−	0.428708i	$-0.858969\pi$
$313$	−1.36607e10	+	2.36610e10i	−0.0804493	+	0.139342i	0.822994	+	0.568050i	$0.192302\pi$
$314$	−8.86027e10	+	1.53464e11i	−0.514356	+	0.890890i
$315$	−3.56084e10			−0.203777
$316$	2.57187e10			0.145096
$317$	9.05785e10	−	1.56887e11i	0.503800	−	0.872607i	−0.496190	−	0.868214i	$-0.665268\pi$
$317$	9.05785e10	−	1.56887e11i	0.503800	−	0.872607i	0.999990	−	0.00439358i	$-0.00139853\pi$
$318$	−3.15220e10	−	5.45977e10i	−0.172859	−	0.299401i
$319$	−2.47097e10	+	4.27984e10i	−0.133601	+	0.231403i
$320$	−1.34714e10	−	2.33332e10i	−0.0718190	−	0.124394i
$321$	2.57300e10	+	4.45656e10i	0.135259	+	0.234276i
$322$	5.28037e10			0.273724
$323$	−1.60212e11	−	2.02424e11i	−0.819001	−	1.03479i
$324$	2.12910e10			0.107336
$325$	4.63452e10	+	8.02722e10i	0.230425	+	0.399108i
$326$	−4.15231e10	−	7.19200e10i	−0.203615	−	0.352672i
$327$	−5.05865e10	+	8.76184e10i	−0.244664	+	0.423770i
$328$	2.98304e10	+	5.16678e10i	0.142307	+	0.246483i
$329$	2.51522e10	−	4.35648e10i	0.118357	−	0.205000i
$330$	4.44498e10			0.206327
$331$	−2.65282e11			−1.21474			−0.607369	−	0.794420i	$-0.707775\pi$
$331$	−2.65282e11			−1.21474			−0.607369	+	0.794420i	$0.707775\pi$
$332$	−7.47841e10	+	1.29530e11i	−0.337822	+	0.585125i
$333$	1.40833e11	−	2.43930e11i	0.627633	−	1.08709i
$334$	7.23391e10			0.318064
$335$	1.69537e11			0.735468
$336$	3.92511e9	−	6.79849e9i	0.0168006	−	0.0290995i
$337$	−3.59987e10	−	6.23516e10i	−0.152038	−	0.263338i	0.779939	−	0.625856i	$-0.215250\pi$
$337$	−3.59987e10	−	6.23516e10i	−0.152038	−	0.263338i	−0.931977	+	0.362518i	$0.881917\pi$
$338$	9.06354e10	−	1.56985e11i	0.377723	−	0.654235i
$339$	6.94216e10	+	1.20242e11i	0.285493	+	0.494489i
$340$	9.34161e10	+	1.61801e11i	0.379111	+	0.656640i
$341$	8.32281e10			0.333331
$342$	−1.25709e11	+	1.84746e10i	−0.496876	+	0.0730226i
$343$	−1.24020e11			−0.483804
$344$	4.76435e10	+	8.25210e10i	0.183439	+	0.317725i
$345$	−1.26175e11	−	2.18541e11i	−0.479497	−	0.830514i
$346$	−8.84647e10	+	1.53225e11i	−0.331839	+	0.574762i
$347$	8.45543e10	+	1.46452e11i	0.313078	+	0.542268i	0.979027	−	0.203730i	$-0.0653064\pi$
$347$	8.45543e10	+	1.46452e11i	0.313078	+	0.542268i	−0.665949	+	0.745997i	$0.731973\pi$
$348$	2.08553e10	−	3.61225e10i	0.0762273	−	0.132029i
$349$	−5.10748e11			−1.84286			−0.921431	−	0.388543i	$-0.872979\pi$
$349$	−5.10748e11			−1.84286			−0.921431	+	0.388543i	$0.872979\pi$
$350$	−1.58829e10			−0.0565749
$351$	1.88254e11	−	3.26065e11i	0.662005	−	1.14663i
$352$	1.20096e10	−	2.08012e10i	0.0416951	−	0.0722181i
$353$	2.76119e11			0.946476			0.473238	−	0.880935i	$-0.343085\pi$
$353$	2.76119e11			0.946476			0.473238	+	0.880935i	$0.343085\pi$
$354$	2.03911e11			0.690121
$355$	−8.47003e10	+	1.46705e11i	−0.283046	+	0.490250i
$356$	7.38417e10	+	1.27898e11i	0.243656	+	0.422024i
$357$	−2.72182e10	+	4.71433e10i	−0.0886854	+	0.153608i
$358$	−2.35464e10	−	4.07836e10i	−0.0757620	−	0.131224i
$359$	2.14740e11	+	3.71941e11i	0.682320	+	1.18181i	0.974271	+	0.225379i	$0.0723621\pi$
$359$	2.14740e11	+	3.71941e11i	0.682320	+	1.18181i	−0.291952	+	0.956433i	$0.594305\pi$
$360$	9.19556e10			0.288547
$361$	3.09043e11	−	9.28414e10i	0.957717	−	0.287713i
$362$	2.70343e11			0.827420
$363$	−6.92242e10	−	1.19900e11i	−0.209256	−	0.362442i
$364$	3.00678e10	+	5.20790e10i	0.0897730	+	0.155491i
$365$	7.28661e10	−	1.26208e11i	0.214886	−	0.372193i
$366$	−4.08041e10	−	7.06748e10i	−0.118861	−	0.205873i
$367$	−5.11098e10	+	8.85248e10i	−0.147064	+	0.254723i	−0.930141	−	0.367202i	$-0.880316\pi$
$367$	−5.11098e10	+	8.85248e10i	−0.147064	+	0.254723i	0.783077	+	0.621925i	$0.213649\pi$
$368$	−1.36361e11			−0.387592
$369$	−2.03621e11			−0.571748
$370$	2.58854e11	−	4.48349e11i	0.718038	−	1.24368i
$371$	−4.13771e10	+	7.16672e10i	−0.113391	+	0.196398i
$372$	−7.02458e10			−0.190185
$373$	−1.38332e11			−0.370026			−0.185013	−	0.982736i	$-0.559233\pi$
$373$	−1.38332e11			−0.370026			−0.185013	+	0.982736i	$0.559233\pi$
$374$	−8.32789e10	+	1.44243e11i	−0.220096	+	0.381218i
$375$	−8.04860e10	−	1.39406e11i	−0.210174	−	0.364032i
$376$	−6.49533e10	+	1.12502e11i	−0.167593	+	0.290280i
$377$	1.59760e11	+	2.76712e11i	0.407316	+	0.705492i
$378$	3.22581e10	+	5.58727e10i	0.0812692	+	0.140762i
$379$	5.54133e11			1.37955			0.689776	−	0.724023i	$-0.257709\pi$
$379$	5.54133e11			1.37955			0.689776	+	0.724023i	$0.257709\pi$
$380$	−2.31055e11	+	3.39566e10i	−0.568446	+	0.0835408i
$381$	−4.29549e10			−0.104436
$382$	3.48619e10	+	6.03827e10i	0.0837657	+	0.145087i
$383$	1.12421e11	+	1.94718e11i	0.266963	+	0.462394i	0.968076	−	0.250657i	$-0.0806465\pi$
$383$	1.12421e11	+	1.94718e11i	0.266963	+	0.462394i	−0.701113	+	0.713050i	$0.747313\pi$
$384$	−1.01363e10	+	1.75565e10i	−0.0237896	+	0.0412048i
$385$	−2.91733e10	−	5.05296e10i	−0.0676725	−	0.117212i
$386$	−2.87029e10	+	4.97148e10i	−0.0658085	+	0.113984i
$387$	−3.25213e11			−0.737002
$388$	−2.28972e11			−0.512907
$389$	1.35134e11	−	2.34060e11i	0.299221	−	0.518267i	−0.676737	−	0.736225i	$-0.736606\pi$
$389$	1.35134e11	−	2.34060e11i	0.299221	−	0.518267i	0.975958	+	0.217959i	$0.0699398\pi$
$390$	1.43695e11	−	2.48886e11i	0.314521	−	0.544766i
$391$	9.45579e11			2.04598
$392$	1.54984e11			0.331512
$393$	−1.71199e11	+	2.96525e11i	−0.362022	+	0.627040i
$394$	1.11414e11	+	1.92975e11i	0.232920	+	0.403430i
$395$	−8.06682e10	+	1.39722e11i	−0.166731	+	0.288786i
$396$	4.09884e10	+	7.09941e10i	0.0837593	+	0.145075i
$397$	1.54384e11	+	2.67402e11i	0.311922	+	0.540265i	0.978778	−	0.204921i	$-0.0656938\pi$
$397$	1.54384e11	+	2.67402e11i	0.311922	+	0.540265i	−0.666856	+	0.745186i	$0.732360\pi$
$398$	−6.32585e11			−1.26370
$399$	−4.22289e10	−	5.33551e10i	−0.0834127	−	0.105390i
$400$	4.10163e10			0.0801099
$401$	3.92208e11	+	6.79324e11i	0.757472	+	1.31198i	0.944136	+	0.329557i	$0.106899\pi$
$401$	3.92208e11	+	6.79324e11i	0.757472	+	1.31198i	−0.186663	+	0.982424i	$0.559767\pi$
$402$	−6.37821e10	−	1.10474e11i	−0.121810	−	0.210980i
$403$	2.69055e11	−	4.66017e11i	0.508122	−	0.880093i
$404$	−1.54964e11	−	2.68405e11i	−0.289410	−	0.501273i
$405$	−6.67807e10	+	1.15668e11i	−0.123340	+	0.213631i
$406$	−5.47511e10			−0.100006
$407$	4.61528e11			0.833726
$408$	7.02887e10	−	1.21744e11i	0.125578	−	0.217508i
$409$	−4.88322e10	+	8.45799e10i	−0.0862883	+	0.149456i	−0.905939	−	0.423407i	$-0.860834\pi$
$409$	−4.88322e10	+	8.45799e10i	−0.0862883	+	0.149456i	0.819651	+	0.572863i	$0.194167\pi$
$410$	−3.74260e11			−0.654103
$411$	−1.84368e11			−0.318711
$412$	1.65399e11	−	2.86480e11i	0.282811	−	0.489843i
$413$	−1.33831e11	−	2.31802e11i	−0.226350	−	0.392050i
$414$	2.32699e11	−	4.03046e11i	0.389307	−	0.674300i
$415$	−4.69131e11	−	8.12558e11i	−0.776385	−	1.34474i
$416$	−7.76476e10	−	1.34490e11i	−0.127118	−	0.220175i
$417$	−2.91544e11			−0.472163
$418$	−1.29207e11	−	1.63249e11i	−0.207011	−	0.261552i
$419$	4.86127e11			0.770524			0.385262	−	0.922807i	$-0.374111\pi$
$419$	4.86127e11			0.770524			0.385262	+	0.922807i	$0.374111\pi$
$420$	2.46227e10	+	4.26478e10i	0.0386113	+	0.0668767i
$421$	−4.34077e11	−	7.51843e11i	−0.673437	−	1.16643i	−0.976923	−	0.213591i	$-0.931484\pi$
$421$	−4.34077e11	−	7.51843e11i	−0.673437	−	1.16643i	0.303486	−	0.952836i	$-0.401849\pi$
$422$	1.42446e11	−	2.46724e11i	0.218648	−	0.378709i
$423$	−2.21685e11	−	3.83969e11i	−0.336670	−	0.583129i
$424$	1.06853e11	−	1.85075e11i	0.160561	−	0.278100i
$425$	−2.84422e11			−0.422877
$426$	1.27461e11			0.187515
$427$	−5.35612e10	+	9.27706e10i	−0.0779695	+	0.135047i
$428$	−8.72191e10	+	1.51068e11i	−0.125636	+	0.217608i
$429$	2.56203e11			0.365196
$430$	−5.97748e11			−0.843160
$431$	−6.84879e10	+	1.18624e11i	−0.0956018	+	0.165587i	−0.909860	−	0.414916i	$-0.863811\pi$
$431$	−6.84879e10	+	1.18624e11i	−0.0956018	+	0.165587i	0.814258	+	0.580503i	$0.197144\pi$
$432$	−8.33039e10	−	1.44287e11i	−0.115077	−	0.199319i
$433$	−4.15303e11	+	7.19326e11i	−0.567766	+	0.983400i	0.429020	+	0.903295i	$0.358859\pi$
$433$	−4.15303e11	+	7.19326e11i	−0.567766	+	0.983400i	−0.996786	+	0.0801052i	$0.974474\pi$
$434$	4.61038e10	+	7.98541e10i	0.0623782	+	0.108042i
$435$	1.30828e11	+	2.26601e11i	0.175186	+	0.303431i
$436$	−3.42955e11			−0.454514
$437$	−4.35864e11	+	1.09866e12i	−0.571721	+	1.44110i
$438$	−1.09653e11			−0.142359
$439$	4.48148e11	+	7.76215e11i	0.575878	+	0.997451i	0.995946	+	0.0899576i	$0.0286732\pi$
$439$	4.48148e11	+	7.76215e11i	0.575878	+	0.997451i	−0.420067	+	0.907493i	$0.637993\pi$
$440$	7.53376e10	+	1.30489e11i	0.0958241	+	0.165972i
$441$	−2.64479e11	+	4.58090e11i	−0.332979	+	0.576737i
$442$	5.38438e11	+	9.32602e11i	0.671020	+	1.16224i
$443$	4.39046e11	−	7.60450e11i	0.541618	−	0.938110i	−0.457193	−	0.889367i	$-0.651145\pi$
$443$	4.39046e11	−	7.60450e11i	0.541618	−	0.938110i	0.998811	−	0.0487425i	$-0.0155214\pi$
$444$	−3.89537e11			−0.475691
$445$	−9.26438e11			−1.11994
$446$	1.75165e11	−	3.03395e11i	0.209624	−	0.363079i
$447$	−1.45373e11	+	2.51793e11i	−0.172226	+	0.298305i
$448$	2.66105e10			0.0312106
$449$	−8.80958e11			−1.02293			−0.511466	−	0.859304i	$-0.670897\pi$
$449$	−8.80958e11			−1.02293			−0.511466	+	0.859304i	$0.670897\pi$
$450$	−6.99939e10	+	1.21233e11i	−0.0804644	+	0.139368i
$451$	−1.66823e11	−	2.88946e11i	−0.189873	−	0.328869i
$452$	−2.35324e11	+	4.07594e11i	−0.265182	+	0.459309i
$453$	3.54982e10	+	6.14846e10i	0.0396063	+	0.0686001i
$454$	−5.82557e11	−	1.00902e12i	−0.643557	−	1.11467i
$455$	−3.77239e11			−0.412634
$456$	1.09053e11	+	1.37785e11i	0.118112	+	0.149231i
$457$	−1.50869e12			−1.61800			−0.808998	−	0.587812i	$-0.799990\pi$
$457$	−1.50869e12			−1.61800			−0.808998	+	0.587812i	$0.799990\pi$
$458$	3.25157e11	+	5.63189e11i	0.345302	+	0.598080i
$459$	5.77661e11	+	1.00054e12i	0.607457	+	1.05215i
$460$	4.27705e11	−	7.40807e11i	0.445384	−	0.771427i
$461$	5.56595e11	+	9.64051e11i	0.573965	+	0.994136i	0.996153	+	0.0876279i	$0.0279286\pi$
$461$	5.56595e11	+	9.64051e11i	0.573965	+	0.994136i	−0.422189	+	0.906508i	$0.638738\pi$
$462$	−2.19507e10	+	3.80198e10i	−0.0224161	+	0.0388258i
$463$	−3.12075e11			−0.315605			−0.157803	−	0.987471i	$-0.550441\pi$
$463$	−3.12075e11			−0.315605			−0.157803	+	0.987471i	$0.550441\pi$
$464$	1.41390e11			0.141608
$465$	2.20331e11	−	3.81624e11i	0.218543	−	0.378527i
$466$	3.29106e10	−	5.70028e10i	0.0323295	−	0.0559963i
$467$	7.91645e11			0.770202			0.385101	−	0.922874i	$-0.374167\pi$
$467$	7.91645e11			0.770202			0.385101	+	0.922874i	$0.374167\pi$
$468$	5.30020e11			0.510724
$469$	−8.37230e10	+	1.45013e11i	−0.0799037	+	0.138397i
$470$	−4.07461e11	−	7.05743e11i	−0.385164	−	0.667123i
$471$	−4.18210e11	+	7.24361e11i	−0.391562	+	0.678205i
$472$	3.45607e11	+	5.98608e11i	0.320511	+	0.555141i
$473$	−2.66441e11	−	4.61490e11i	−0.244752	−	0.423923i
$474$	1.21394e11			0.110457
$475$	1.31104e11	−	3.30467e11i	0.118167	−	0.297856i
$476$	−1.84528e11			−0.164752
$477$	3.64687e11	+	6.31656e11i	0.322543	+	0.558661i
$478$	4.54716e11	+	7.87592e11i	0.398396	+	0.690042i
$479$	2.42303e11	−	4.19680e11i	0.210304	−	0.364258i	−0.741505	−	0.670947i	$-0.765888\pi$
$479$	2.42303e11	−	4.19680e11i	0.210304	−	0.364258i	0.951810	+	0.306689i	$0.0992212\pi$
$480$	−6.35861e10	−	1.10134e11i	−0.0546734	−	0.0946972i
$481$	1.49200e12	−	2.58422e12i	1.27091	−	2.20129i
$482$	−1.57534e12			−1.32942
$483$	2.49237e11			0.208377
$484$	2.34655e11	−	4.06435e11i	0.194368	−	0.336656i
$485$	7.18185e11	−	1.24393e12i	0.589384	−	1.02084i
$486$	9.01115e11			0.732685
$487$	2.13820e12			1.72253			0.861266	−	0.508155i	$-0.169672\pi$
$487$	2.13820e12			1.72253			0.861266	+	0.508155i	$0.169672\pi$
$488$	1.38317e11	−	2.39572e11i	0.110405	−	0.191226i
$489$	−1.95991e11	−	3.39467e11i	−0.155006	−	0.268478i
$490$	−4.86117e11	+	8.41979e11i	−0.380942	+	0.659810i
$491$	−3.66997e11	−	6.35658e11i	−0.284968	−	0.493579i	0.687633	−	0.726058i	$-0.258650\pi$
$491$	−3.66997e11	−	6.35658e11i	−0.284968	−	0.493579i	−0.972601	+	0.232479i	$0.925316\pi$
$492$	1.40801e11	+	2.43875e11i	0.108334	+	0.187640i
$493$	−9.80453e11			−0.747508
$494$	−1.33177e12	+	1.95722e11i	−1.00614	+	0.147866i
$495$	−5.14252e11			−0.384993
$496$	−1.19059e11	−	2.06216e11i	−0.0883273	−	0.152987i
$497$	−8.36555e10	−	1.44896e11i	−0.0615022	−	0.106525i
$498$	−3.52986e11	+	6.11389e11i	−0.257173	+	0.445437i
$499$	5.67108e10	+	9.82260e10i	0.0409462	+	0.0709208i	0.885772	−	0.464120i	$-0.153629\pi$
$499$	5.67108e10	+	9.82260e10i	0.0409462	+	0.0709208i	−0.844826	+	0.535041i	$0.820296\pi$
$500$	2.72830e11	−	4.72556e11i	0.195221	−	0.338133i
$501$	3.41445e11			0.242131
$502$	5.76715e11			0.405317
$503$	1.01627e12	−	1.76024e12i	0.707872	−	1.22607i	−0.257774	−	0.966205i	$-0.582989\pi$
$503$	1.01627e12	−	1.76024e12i	0.707872	−	1.22607i	0.965645	−	0.259864i	$-0.0836778\pi$
$504$	−4.54107e10	+	7.86536e10i	−0.0313488	+	0.0542977i
$505$	1.94421e12			1.33025
$506$	7.62584e11			0.517143
$507$	4.27805e11	−	7.40980e11i	0.287548	−	0.498047i
$508$	−7.28040e10	−	1.26100e11i	−0.0485030	−	0.0840096i
$509$	−1.10287e12	+	1.91022e12i	−0.728270	+	1.26140i	0.229344	+	0.973345i	$0.426342\pi$
$509$	−1.10287e12	+	1.91022e12i	−0.728270	+	1.26140i	−0.957614	+	0.288055i	$0.906991\pi$
$510$	4.40930e11	+	7.63713e11i	0.288605	+	0.499879i
$511$	7.19672e10	+	1.24651e11i	0.0466918	+	0.0808726i
$512$	−6.87195e10			−0.0441942
$513$	−1.42878e12	+	2.09979e11i	−0.910832	+	0.133859i
$514$	1.93469e12			1.22258
$515$	1.03757e12	+	1.79713e12i	0.649959	+	1.12576i
$516$	2.24880e11	+	3.89504e11i	0.139646	+	0.241874i
$517$	3.63244e11	−	6.29158e11i	0.223610	−	0.387304i
$518$	2.55661e11	+	4.42818e11i	0.156020	+	0.270235i
$519$	−4.17559e11	+	7.23234e11i	−0.252618	+	0.437548i
$520$	9.74187e11			0.584289
$521$	1.44731e12			0.860582			0.430291	−	0.902690i	$-0.358411\pi$
$521$	1.44731e12			0.860582			0.430291	+	0.902690i	$0.358411\pi$
$522$	−2.41281e11	+	4.17911e11i	−0.142235	+	0.246358i
$523$	6.31388e11	−	1.09360e12i	0.369010	−	0.639145i	−0.620401	−	0.784285i	$-0.713030\pi$
$523$	6.31388e11	−	1.09360e12i	0.369010	−	0.639145i	0.989411	+	0.145140i	$0.0463633\pi$
$524$	−1.16065e12			−0.672531
$525$	−7.49684e10			−0.0430686
$526$	8.22192e11	−	1.42408e12i	0.468314	−	0.811144i
$527$	8.25601e11	+	1.42998e12i	0.466254	+	0.807575i
$528$	5.66859e10	−	9.81829e10i	0.0317411	−	0.0549773i
$529$	−1.26409e12	−	2.18946e12i	−0.701821	−	1.21559i
$530$	6.70302e11	+	1.16100e12i	0.369002	+	0.639131i
$531$	−2.35910e12			−1.28772
$532$	8.50579e10	−	2.14400e11i	0.0460375	−	0.116044i
$533$	−2.15719e12			−1.15775
$534$	3.48538e11	+	6.03685e11i	0.185487	+	0.321273i
$535$	−5.47137e11	−	9.47668e11i	−0.288738	−	0.500109i
$536$	2.16208e11	−	3.74483e11i	0.113143	−	0.195970i
$537$	−1.11141e11	−	1.92501e11i	−0.0576751	−	0.0998963i
$538$	−7.34432e11	+	1.27207e12i	−0.377948	+	0.654625i
$539$	−8.66730e11			−0.442318
$540$	1.04515e12			0.528941
$541$	6.06857e11	−	1.05111e12i	0.304578	−	0.527545i	−0.672589	−	0.740016i	$-0.734818\pi$
$541$	6.06857e11	−	1.05111e12i	0.304578	−	0.527545i	0.977167	+	0.212471i	$0.0681511\pi$
$542$	−1.01229e11	+	1.75333e11i	−0.0503856	+	0.0872703i
$543$	1.27603e12			0.629888
$544$	4.76527e11			0.233288
$545$	1.07570e12	−	1.86317e12i	0.522284	−	0.904623i
$546$	1.41922e11	+	2.45816e11i	0.0683413	+	0.118371i
$547$	−1.86550e12	+	3.23114e12i	−0.890948	+	1.54317i	−0.0522080	+	0.998636i	$0.516626\pi$
$547$	−1.86550e12	+	3.23114e12i	−0.890948	+	1.54317i	−0.838740	+	0.544532i	$0.816707\pi$
$548$	−3.12484e11	−	5.41238e11i	−0.148018	−	0.256375i
$549$	4.72074e11	+	8.17656e11i	0.221786	+	0.384145i
$550$	−2.29379e11			−0.106886
$551$	4.51939e11	−	1.13917e12i	0.208880	−	0.526512i
$552$	−6.43632e11			−0.295061
$553$	−7.96732e10	−	1.37998e11i	−0.0362284	−	0.0627494i
$554$	−6.38784e11	−	1.10641e12i	−0.288111	−	0.499023i
$555$	1.22181e12	−	2.11623e12i	0.546619	−	0.946772i
$556$	−4.94136e11	−	8.55869e11i	−0.219286	−	0.379814i
$557$	−1.95823e12	+	3.39176e12i	−0.862017	+	1.49306i	0.00796276	+	0.999968i	$0.497465\pi$
$557$	−1.95823e12	+	3.39176e12i	−0.862017	+	1.49306i	−0.869979	+	0.493088i	$0.835868\pi$
$558$	8.12693e11			0.354873
$559$	−3.44534e12			−1.49238
$560$	−8.34657e10	+	1.44567e11i	−0.0358643	+	0.0621187i
$561$	−3.93082e11	+	6.80837e11i	−0.167552	+	0.290209i
$562$	1.91803e12			0.811041
$563$	−1.15076e12			−0.482722			−0.241361	−	0.970435i	$-0.577594\pi$
$563$	−1.15076e12			−0.482722			−0.241361	+	0.970435i	$0.577594\pi$
$564$	−3.06584e11	+	5.31019e11i	−0.127583	+	0.220981i
$565$	−1.47622e12	−	2.55689e12i	−0.609443	−	1.05559i
$566$	−1.35675e12	+	2.34996e12i	−0.555681	+	0.962468i
$567$	−6.59569e10	−	1.14241e11i	−0.0268001	−	0.0464192i
$568$	2.16033e11	+	3.74181e11i	0.0870869	+	0.150839i
$569$	−1.84423e12			−0.737582			−0.368791	−	0.929512i	$-0.620228\pi$
$569$	−1.84423e12			−0.737582			−0.368791	+	0.929512i	$0.620228\pi$
$570$	−1.09059e12	+	1.60278e11i	−0.432739	+	0.0635969i
$571$	3.23916e12			1.27518			0.637588	−	0.770377i	$-0.279932\pi$
$571$	3.23916e12			1.27518			0.637588	+	0.770377i	$0.279932\pi$
$572$	4.34236e11	+	7.52119e11i	0.169607	+	0.293768i
$573$	1.64551e11	+	2.85010e11i	0.0637681	+	0.110450i
$574$	1.84822e11	−	3.20121e11i	0.0710640	−	0.123086i
$575$	6.51113e11	+	1.12776e12i	0.248400	+	0.430241i
$576$	1.17269e11	−	2.03116e11i	0.0443898	−	0.0768853i
$577$	−7.96551e11			−0.299173			−0.149587	−	0.988749i	$-0.547794\pi$
$577$	−7.96551e11			−0.299173			−0.149587	+	0.988749i	$0.547794\pi$
$578$	−1.40701e12			−0.524352
$579$	−1.35479e11	+	2.34657e11i	−0.0500979	+	0.0867721i
$580$	−4.43479e11	+	7.68129e11i	−0.162722	+	0.281844i
$581$	9.26688e11			0.337397
$582$	−1.08076e12			−0.390460
$583$	−5.97563e11	+	1.03501e12i	−0.214227	+	0.371053i
$584$	−1.85849e11	−	3.21900e11i	−0.0661155	−	0.114515i
$585$	−1.66244e12	+	2.87943e12i	−0.586874	+	1.01650i
$586$	−1.16359e12	−	2.01540e12i	−0.407625	−	0.706028i
$587$	8.11180e11	+	1.40501e12i	0.281998	+	0.488435i	0.971877	−	0.235490i	$-0.0756695\pi$
$587$	8.11180e11	+	1.40501e12i	0.281998	+	0.488435i	−0.689879	+	0.723925i	$0.742336\pi$
$588$	7.31534e11			0.252369
$589$	−2.04204e12	+	3.00105e11i	−0.699109	+	0.102743i
$590$	−4.33607e12			−1.47320
$591$	5.25882e11	+	9.10855e11i	0.177315	+	0.307118i
$592$	−6.60223e11	−	1.14354e12i	−0.220924	−	0.382652i
$593$	1.80752e12	−	3.13072e12i	0.600257	−	1.03968i	−0.392524	−	0.919742i	$-0.628398\pi$
$593$	1.80752e12	−	3.13072e12i	0.600257	−	1.03968i	0.992782	−	0.119935i	$-0.0382685\pi$
$594$	4.65868e11	+	8.06907e11i	0.153541	+	0.265940i
$595$	5.78783e11	−	1.00248e12i	0.189317	−	0.327906i
$596$	−9.85565e11			−0.319946
$597$	−2.98584e12			−0.962016
$598$	2.46524e12	−	4.26991e12i	0.788321	−	1.36541i
$599$	1.28900e12	−	2.23261e12i	0.409102	−	0.708585i	−0.585688	−	0.810537i	$-0.699175\pi$
$599$	1.28900e12	−	2.23261e12i	0.409102	−	0.708585i	0.994789	+	0.101952i	$0.0325088\pi$
$600$	1.93599e11			0.0609851
$601$	3.40980e12			1.06609			0.533044	−	0.846087i	$-0.321048\pi$
$601$	3.40980e12			1.06609			0.533044	+	0.846087i	$0.321048\pi$
$602$	2.95187e11	−	5.11279e11i	0.0916038	−	0.158662i
$603$	7.37913e11	+	1.27810e12i	0.227288	+	0.393675i
$604$	−1.20331e11	+	2.08420e11i	−0.0367885	+	0.0637195i
$605$	1.47202e12	+	2.54962e12i	0.446699	+	0.773706i
$606$	−7.31438e11	−	1.26689e12i	−0.220318	−	0.381603i
$607$	−3.99979e12			−1.19588			−0.597941	−	0.801540i	$-0.704014\pi$
$607$	−3.99979e12			−1.19588			−0.597941	+	0.801540i	$0.704014\pi$
$608$	−2.19655e11	+	5.53670e11i	−0.0651890	+	0.164318i
$609$	−2.58429e11			−0.0761313
$610$	8.67682e11	+	1.50287e12i	0.253733	+	0.439478i
$611$	−2.34855e12	−	4.06781e12i	−0.681733	−	1.18080i
$612$	−8.13189e11	+	1.40848e12i	−0.234320	+	0.405855i
$613$	2.69935e12	+	4.67540e12i	0.772123	+	1.33736i	0.936397	+	0.350941i	$0.114138\pi$
$613$	2.69935e12	+	4.67540e12i	0.772123	+	1.33736i	−0.164275	+	0.986415i	$0.552528\pi$
$614$	6.70686e11	−	1.16166e12i	0.190442	−	0.329854i
$615$	−1.76653e12			−0.497947
$616$	−1.48817e11			−0.0416426
$617$	1.26035e12	−	2.18299e12i	0.350113	−	0.606414i	−0.636156	−	0.771561i	$-0.719476\pi$
$617$	1.26035e12	−	2.18299e12i	0.350113	−	0.606414i	0.986269	+	0.165147i	$0.0528097\pi$
$618$	7.80696e11	−	1.35220e12i	0.215295	−	0.372902i
$619$	1.53209e12			0.419447			0.209723	−	0.977761i	$-0.432744\pi$
$619$	1.53209e12			0.419447			0.209723	+	0.977761i	$0.432744\pi$
$620$	1.49375e12			0.405989
$621$	2.64482e12	−	4.58095e12i	0.713646	−	1.23607i
$622$	−5.79552e11	−	1.00381e12i	−0.155251	−	0.268903i
$623$	4.57505e11	−	7.92422e11i	0.121674	−	0.210746i
$624$	−3.66502e11	−	6.34800e11i	−0.0967710	−	0.167612i
$625$	2.32269e12	+	4.02302e12i	0.608879	+	1.05461i
$626$	−4.37141e11			−0.113772
$627$	−6.09865e11	−	7.70548e11i	−0.157590	−	0.199111i
$628$	−2.83529e12			−0.727409
$629$	4.57824e12	+	7.92974e12i	1.16619	+	2.01991i
$630$	−2.84867e11	−	4.93404e11i	−0.0720460	−	0.124787i
$631$	2.01758e12	−	3.49454e12i	0.506638	−	0.877522i	−0.493333	−	0.869841i	$-0.664221\pi$
$631$	2.01758e12	−	3.49454e12i	0.506638	−	0.877522i	0.999970	−	0.00768172i	$-0.00244519\pi$
$632$	2.05749e11	+	3.56368e11i	0.0512993	+	0.0888530i
$633$	6.72356e11	−	1.16455e12i	0.166449	−	0.288299i
$634$	2.89851e12			0.712481
$635$	9.13417e11			0.222940
$636$	5.04352e11	−	8.73564e11i	0.122230	−	0.211708i
$637$	−2.80191e12	+	4.85306e12i	−0.674260	+	1.16785i
$638$	−7.90709e11			−0.188940
$639$	−1.47464e12			−0.349889
$640$	2.15543e11	−	3.73332e11i	0.0507837	−	0.0879599i
$641$	−2.55035e12	−	4.41734e12i	−0.596677	−	1.03347i	−0.993308	−	0.115497i	$-0.963154\pi$
$641$	−2.55035e12	−	4.41734e12i	−0.596677	−	1.03347i	0.396631	−	0.917978i	$-0.370179\pi$
$642$	−4.11680e11	+	7.13050e11i	−0.0956427	+	0.165658i
$643$	4.20771e12	+	7.28797e12i	0.970726	+	1.68135i	0.693373	+	0.720578i	$0.256124\pi$
$643$	4.20771e12	+	7.28797e12i	0.970726	+	1.68135i	0.277353	+	0.960768i	$0.410543\pi$
$644$	4.22429e11	+	7.31669e11i	0.0967760	+	0.167621i
$645$	−2.82141e12			−0.641870
$646$	1.52317e12	−	3.83936e12i	0.344114	−	0.867386i
$647$	−4.62557e12			−1.03776			−0.518879	−	0.854847i	$-0.673651\pi$
$647$	−4.62557e12			−1.03776			−0.518879	+	0.854847i	$0.673651\pi$
$648$	1.70328e11	+	2.95017e11i	0.0379489	+	0.0657294i
$649$	−1.93277e12	−	3.34765e12i	−0.427640	−	0.740694i
$650$	−7.41523e11	+	1.28436e12i	−0.162935	+	0.282212i
$651$	2.17613e11	+	3.76916e11i	0.0474865	+	0.0822490i
$652$	6.64369e11	−	1.15072e12i	0.143978	−	0.249377i
$653$	5.43811e12			1.17041			0.585206	−	0.810884i	$-0.301014\pi$
$653$	5.43811e12			1.17041			0.585206	+	0.810884i	$0.301014\pi$
$654$	−1.61877e12			−0.346007
$655$	3.64047e12	−	6.30548e12i	0.772808	−	1.33854i
$656$	−4.77287e11	+	8.26685e11i	−0.100626	+	0.174290i
$657$	1.26860e12			0.265632
$658$	8.04869e11			0.167382
$659$	−1.23441e12	+	2.13806e12i	−0.254961	+	0.441606i	−0.964885	−	0.262673i	$-0.915396\pi$
$659$	−1.23441e12	+	2.13806e12i	−0.254961	+	0.441606i	0.709924	+	0.704279i	$0.248729\pi$
$660$	3.55598e11	+	6.15914e11i	0.0729477	+	0.126349i
$661$	2.02507e12	−	3.50753e12i	0.412605	−	0.714653i	−0.582569	−	0.812781i	$-0.697952\pi$
$661$	2.02507e12	−	3.50753e12i	0.412605	−	0.714653i	0.995174	+	0.0981287i	$0.0312857\pi$
$662$	−2.12226e12	−	3.67586e12i	−0.429474	−	0.743872i
$663$	2.54146e12	+	4.40194e12i	0.510826	+	0.884776i
$664$	−2.39309e12			−0.477753
$665$	8.97980e11	+	1.13457e12i	0.178061	+	0.224975i
$666$	4.50666e12			0.887607
$667$	2.24450e12	+	3.88759e12i	0.439090	+	0.760525i
$668$	5.78713e11	+	1.00236e12i	0.112452	+	0.194773i
$669$	8.26790e11	−	1.43204e12i	0.159580	−	0.276400i
$670$	1.35630e12	+	2.34918e12i	0.260027	+	0.450380i
$671$	−7.73524e11	+	1.33978e12i	−0.147307	+	0.255143i
$672$	1.25603e11			0.0237596
$673$	1.40960e12			0.264867			0.132434	−	0.991192i	$-0.457721\pi$
$673$	1.40960e12			0.264867			0.132434	+	0.991192i	$0.457721\pi$
$674$	5.75979e11	−	9.97626e11i	0.107507	−	0.186208i
$675$	−7.95539e11	+	1.37791e12i	−0.147501	+	0.255479i
$676$	2.90033e12			0.534180
$677$	3.98192e12			0.728524			0.364262	−	0.931296i	$-0.381321\pi$
$677$	3.98192e12			0.728524			0.364262	+	0.931296i	$0.381321\pi$
$678$	−1.11075e12	+	1.92387e12i	−0.201874	+	0.349657i
$679$	7.09326e11	+	1.22859e12i	0.128065	+	0.221816i
$680$	−1.49466e12	+	2.58882e12i	−0.268072	+	0.464315i
$681$	−2.74970e12	−	4.76263e12i	−0.489919	−	0.848564i
$682$	6.65825e11	+	1.15324e12i	0.117850	+	0.204123i
$683$	−3.21673e11			−0.0565615			−0.0282808	−	0.999600i	$-0.509003\pi$
$683$	−3.21673e11			−0.0565615			−0.0282808	+	0.999600i	$0.509003\pi$
$684$	−1.26166e12	−	1.59407e12i	−0.220389	−	0.278456i
$685$	3.92051e12			0.680353
$686$	−9.92163e11	−	1.71848e12i	−0.171051	−	0.296268i
$687$	1.53476e12	+	2.65829e12i	0.262867	+	0.455299i
$688$	−7.62296e11	+	1.32034e12i	−0.129711	+	0.224665i
$689$	3.86353e12	+	6.69183e12i	0.653127	+	1.13125i
$690$	2.01880e12	−	3.49666e12i	0.339056	−	0.587262i
$691$	−1.14733e13			−1.91442			−0.957211	−	0.289392i	$-0.906547\pi$
$691$	−1.14733e13			−1.91442			−0.957211	+	0.289392i	$0.906547\pi$
$692$	−2.83087e12			−0.469291
$693$	2.53954e11	−	4.39862e11i	0.0418269	−	0.0724463i
$694$	−1.35287e12	+	2.34324e12i	−0.221380	+	0.383441i
$695$	6.19956e12			1.00793
$696$	6.67370e11			0.107802
$697$	3.30969e12	−	5.73255e12i	0.531177	−	0.920026i
$698$	−4.08599e12	−	7.07714e12i	−0.651550	−	1.12852i
$699$	1.55340e11	−	2.69057e11i	0.0246114	−	0.0426282i
$700$	−1.27063e11	−	2.20080e11i	−0.0200023	−	0.0346449i
$701$	−1.61926e12	−	2.80464e12i	−0.253271	−	0.438678i	0.711154	−	0.703037i	$-0.248173\pi$
$701$	−1.61926e12	−	2.80464e12i	−0.253271	−	0.438678i	−0.964424	+	0.264359i	$0.914840\pi$
$702$	6.02412e12			0.936217
$703$	−1.13238e13	+	1.66418e12i	−1.74861	+	0.256982i
$704$	3.84306e11			0.0589658
$705$	−1.92324e12	−	3.33115e12i	−0.293213	−	0.507859i
$706$	2.20895e12	+	3.82601e12i	0.334630	+	0.579596i
$707$	−9.60116e11	+	1.66297e12i	−0.144523	+	0.250321i
$708$	1.63128e12	+	2.82547e12i	0.243995	+	0.422611i
$709$	−4.62052e12	+	8.00298e12i	−0.686725	+	1.18944i	0.286166	+	0.958180i	$0.407619\pi$
$709$	−4.62052e12	+	8.00298e12i	−0.686725	+	1.18944i	−0.972891	+	0.231263i	$0.925714\pi$
$710$	−2.71041e12			−0.400288
$711$	−1.40444e12			−0.206105
$712$	−1.18147e12	+	2.04636e12i	−0.172291	+	0.298416i
$713$	3.78001e12	−	6.54717e12i	0.547759	−	0.948747i
$714$	−8.70982e11			−0.125420
$715$	−5.44804e12			−0.779584
$716$	3.76743e11	−	6.52538e11i	0.0535718	−	0.0927891i
$717$	2.14629e12	+	3.71748e12i	0.303286	+	0.525306i
$718$	−3.43584e12	+	5.95105e12i	−0.482473	+	0.835667i
$719$	−2.35892e12	−	4.08576e12i	−0.329179	−	0.570155i	0.653170	−	0.757211i	$-0.273439\pi$
$719$	−2.35892e12	−	4.08576e12i	−0.329179	−	0.570155i	−0.982349	+	0.187056i	$0.940105\pi$
$720$	7.35645e11	+	1.27417e12i	0.102017	+	0.176698i
$721$	−2.04955e12			−0.282455
$722$	3.75880e12	+	3.53950e12i	0.514791	+	0.484757i
$723$	−7.43572e12			−1.01205
$724$	2.16274e12	+	3.74598e12i	0.292537	+	0.506689i
$725$	−6.75127e11	−	1.16935e12i	−0.0907537	−	0.157190i
$726$	1.10759e12	−	1.91840e12i	0.147966	−	0.256285i
$727$	−6.92532e12	−	1.19950e13i	−0.919465	−	1.59256i	−0.800230	−	0.599693i	$-0.795289\pi$
$727$	−6.92532e12	−	1.19950e13i	−0.919465	−	1.59256i	−0.119235	−	0.992866i	$-0.538044\pi$
$728$	−4.81085e11	+	8.33264e11i	−0.0634791	+	0.109949i
$729$	2.61632e12			0.343097
$730$	2.33171e12			0.303894
$731$	5.28605e12	−	9.15571e12i	0.684704	−	1.18594i
$732$	6.52866e11	−	1.13080e12i	0.0840473	−	0.145574i
$733$	−5.05292e12			−0.646509			−0.323255	−	0.946312i	$-0.604777\pi$
$733$	−5.05292e12			−0.646509			−0.323255	+	0.946312i	$0.604777\pi$
$734$	−1.63551e12			−0.207980
$735$	−2.29450e12	+	3.97420e12i	−0.289998	+	0.502292i
$736$	−1.09089e12	−	1.88947e12i	−0.137034	−	0.237351i
$737$	−1.20912e12	+	2.09425e12i	−0.150961	+	0.261472i
$738$	−1.62897e12	−	2.82146e12i	−0.202143	−	0.350123i
$739$	−4.00121e12	−	6.93031e12i	−0.493505	−	0.854776i	0.506467	−	0.862260i	$-0.330951\pi$
$739$	−4.00121e12	−	6.93031e12i	−0.493505	−	0.854776i	−0.999972	+	0.00748316i	$0.997618\pi$
$740$	8.28333e12			1.01546
$741$	−6.28604e12	+	9.23818e11i	−0.765941	+	0.112565i
$742$	−1.32407e12			−0.160359
$743$	2.59945e12	+	4.50237e12i	0.312918	+	0.541990i	0.978993	−	0.203895i	$-0.0653600\pi$
$743$	2.59945e12	+	4.50237e12i	0.312918	+	0.541990i	−0.666074	+	0.745885i	$0.732027\pi$
$744$	−5.61966e11	−	9.73354e11i	−0.0672407	−	0.116464i
$745$	3.09129e12	−	5.35427e12i	0.367652	−	0.636791i
$746$	−1.10665e12	−	1.91678e12i	−0.130824	−	0.226594i
$747$	4.08379e12	−	7.07333e12i	0.479867	−	0.831154i
$748$	−2.66492e12			−0.311263
$749$	1.08078e12			0.125478
$750$	1.28778e12	−	2.23049e12i	0.148616	−	0.257410i
$751$	8.15931e11	−	1.41323e12i	0.0935996	−	0.162119i	−0.815424	−	0.578865i	$-0.803496\pi$
$751$	8.15931e11	−	1.41323e12i	0.0935996	−	0.162119i	0.909023	+	0.416745i	$0.136829\pi$
$752$	−2.07851e12			−0.237012
$753$	2.72213e12			0.308554
$754$	−2.55616e12	+	4.42739e12i	−0.288016	+	0.498858i
$755$	−7.54853e11	−	1.30744e12i	−0.0845476	−	0.146441i
$756$	−5.16130e11	+	8.93963e11i	−0.0574660	+	0.0995340i
$757$	4.10515e12	+	7.11033e12i	0.454357	+	0.786970i	0.998651	−	0.0519247i	$-0.0165356\pi$
$757$	4.10515e12	+	7.11033e12i	0.454357	+	0.786970i	−0.544294	+	0.838895i	$0.683202\pi$
$758$	4.43307e12	+	7.67830e12i	0.487745	+	0.844799i
$759$	3.59944e12			0.393684
$760$	−2.31896e12	−	2.92994e12i	−0.252134	−	0.318565i
$761$	7.46928e12			0.807324			0.403662	−	0.914908i	$-0.367737\pi$
$761$	7.46928e12			0.807324			0.403662	+	0.914908i	$0.367737\pi$
$762$	−3.43639e11	−	5.95201e11i	−0.0369237	−	0.0639538i
$763$	1.06243e12	+	1.84018e12i	0.113485	+	0.196563i
$764$	−5.57791e11	+	9.66122e11i	−0.0592313	+	0.102592i
$765$	−5.10124e12	−	8.83561e12i	−0.538517	−	0.932739i
$766$	−1.79873e12	+	3.11549e12i	−0.188771	+	0.326962i
$767$	−2.49925e13			−2.60754
$768$	−3.24360e11			−0.0336436
$769$	−4.05438e12	+	7.02239e12i	−0.418076	+	0.724129i	−0.995746	−	0.0921413i	$-0.970629\pi$
$769$	−4.05438e12	+	7.02239e12i	−0.418076	+	0.724129i	0.577670	+	0.816271i	$0.303962\pi$
$770$	4.66773e11	−	8.08474e11i	0.0478517	−	0.0828816i
$771$	9.13185e12			0.930709
$772$	−9.18491e11			−0.0930673
$773$	−7.42005e12	+	1.28519e13i	−0.747480	+	1.29467i	0.201548	+	0.979479i	$0.435403\pi$
$773$	−7.42005e12	+	1.28519e13i	−0.747480	+	1.29467i	−0.949027	+	0.315194i	$0.897930\pi$
$774$	−2.60170e12	−	4.50628e12i	−0.260569	−	0.451319i
$775$	−1.13700e12	+	1.96933e12i	−0.113214	+	0.196093i
$776$	−1.83177e12	−	3.17272e12i	−0.181340	−	0.314090i
$777$	1.20674e12	+	2.09013e12i	0.118773	+	0.205721i
$778$	4.32430e12			0.423163
$779$	5.13497e12	+	6.48789e12i	0.499596	+	0.631226i
$780$	4.59823e12			0.444800
$781$	−1.20814e12	−	2.09256e12i	−0.116195	−	0.201256i
$782$	7.56463e12	+	1.31023e13i	0.723365	+	1.25290i
$783$	−2.74236e12	+	4.74991e12i	−0.260733	+	0.451603i
$784$	1.23987e12	+	2.14752e12i	0.117207	+	0.203009i
$785$	8.89306e12	−	1.54032e13i	0.835868	−	1.44777i
$786$	−5.47836e12			−0.511976
$787$	−1.44374e13			−1.34154			−0.670770	−	0.741666i	$-0.734036\pi$
$787$	−1.44374e13			−1.34154			−0.670770	+	0.741666i	$0.734036\pi$
$788$	−1.78263e12	+	3.08760e12i	−0.164700	+	0.285268i
$789$	3.88080e12	−	6.72174e12i	0.356512	−	0.617497i
$790$	−2.58138e12			−0.235793
$791$	2.91602e12			0.264848
$792$	−6.55815e11	+	1.13591e12i	−0.0592268	+	0.102584i
$793$	5.00120e12	+	8.66233e12i	0.449102	+	0.777867i
$794$	−2.47015e12	+	4.27843e12i	−0.220562	+	0.382025i
$795$	3.16387e12	+	5.47998e12i	0.280909	+	0.486549i
$796$	−5.06068e12	−	8.76535e12i	−0.446786	−	0.773857i
$797$	−1.68486e13			−1.47911			−0.739557	−	0.673094i	$-0.764965\pi$
$797$	−1.68486e13			−1.47911			−0.739557	+	0.673094i	$0.764965\pi$
$798$	4.01479e11	−	1.01198e12i	0.0350469	−	0.0883405i
$799$	1.44132e13			1.25112
$800$	3.28130e11	+	5.68338e11i	0.0283231	+	0.0490571i
$801$	−4.03233e12	−	6.98420e12i	−0.346106	−	0.599474i
$802$	−6.27533e12	+	1.08692e13i	−0.535614	+	0.927710i
$803$	1.03934e12	+	1.80019e12i	0.0882142	+	0.152791i
$804$	1.02051e12	−	1.76758e12i	0.0861324	−	0.149186i
$805$	−5.29991e12			−0.444823
$806$	8.60976e12			0.718593
$807$	−3.46657e12	+	6.00427e12i	−0.287719	+	0.498344i
$808$	2.47942e12	−	4.29448e12i	0.204644	−	0.354454i
$809$	2.38409e13			1.95684			0.978419	−	0.206633i	$-0.0662505\pi$
$809$	2.38409e13			1.95684			0.978419	+	0.206633i	$0.0662505\pi$
$810$	−2.13698e12			−0.174429
$811$	4.31468e12	−	7.47325e12i	0.350231	−	0.606619i	−0.636058	−	0.771641i	$-0.719436\pi$
$811$	4.31468e12	−	7.47325e12i	0.350231	−	0.606619i	0.986290	+	0.165022i	$0.0527696\pi$
$812$	−4.38009e11	−	7.58654e11i	−0.0353574	−	0.0612409i
$813$	−4.77805e11	+	8.27583e11i	−0.0383569	+	0.0664361i
$814$	3.69223e12	+	6.39512e12i	0.294767	+	0.510551i
$815$	4.16767e12	+	7.21862e12i	0.330891	+	0.573119i
$816$	2.24924e12			0.177595
$817$	8.20129e12	+	1.03621e13i	0.643996	+	0.813671i
$818$	−1.56263e12			−0.122030
$819$	−1.64194e12	−	2.84392e12i	−0.127520	−	0.220871i
$820$	−2.99408e12	−	5.18590e12i	−0.231260	−	0.400555i
$821$	9.07982e12	−	1.57267e13i	0.697482	−	1.20807i	−0.271855	−	0.962338i	$-0.587637\pi$
$821$	9.07982e12	−	1.57267e13i	0.697482	−	1.20807i	0.969337	−	0.245736i	$-0.0790297\pi$
$822$	−1.47494e12	−	2.55468e12i	−0.112681	−	0.195170i
$823$	7.84478e12	−	1.35876e13i	0.596048	−	1.03239i	−0.397350	−	0.917667i	$-0.630070\pi$
$823$	7.84478e12	−	1.35876e13i	0.596048	−	1.03239i	0.993398	−	0.114719i	$-0.0365966\pi$
$824$	5.29278e12			0.399955
$825$	−1.08268e12			−0.0813690
$826$	2.14129e12	−	3.70883e12i	0.160054	−	0.277221i
$827$	−1.20367e13	+	2.08482e13i	−0.894816	+	1.54987i	−0.0607833	+	0.998151i	$0.519360\pi$
$827$	−1.20367e13	+	2.08482e13i	−0.894816	+	1.54987i	−0.834032	+	0.551715i	$0.813973\pi$
$828$	7.44636e12			0.550564
$829$	5.84860e12			0.430087			0.215044	−	0.976604i	$-0.431011\pi$
$829$	5.84860e12			0.430087			0.215044	+	0.976604i	$0.431011\pi$
$830$	7.50609e12	−	1.30009e13i	0.548987	−	0.950874i
$831$	−3.01510e12	−	5.22231e12i	−0.219330	−	0.379890i
$832$	1.24236e12	−	2.15183e12i	0.0898862	−	0.155688i
$833$	−8.59774e12	−	1.48917e13i	−0.618702	−	1.07162i
$834$	−2.33235e12	−	4.03976e12i	−0.166935	−	0.289140i
$835$	−7.26068e12			−0.516878
$836$	1.22840e12	−	3.09634e12i	0.0869781	−	0.219240i
$837$	9.23693e12			0.650524
$838$	3.88901e12	+	6.73597e12i	0.272422	+	0.471848i
$839$	−1.08529e12	−	1.87978e12i	−0.0756167	−	0.130972i	0.825738	−	0.564054i	$-0.190759\pi$
$839$	−1.08529e12	−	1.87978e12i	−0.0756167	−	0.130972i	−0.901354	+	0.433082i	$0.857426\pi$
$840$	−3.93963e11	+	6.82365e11i	−0.0273023	+	0.0472890i
$841$	4.92629e12	+	8.53259e12i	0.339577	+	0.588165i
$842$	6.94523e12	−	1.20295e13i	0.476192	−	0.824788i
$843$	9.05324e12			0.617419
$844$	4.55828e12			0.309215
$845$	−9.09709e12	+	1.57566e13i	−0.613829	+	1.06318i
$846$	3.54695e12	−	6.14350e12i	0.238061	−	0.412334i
$847$	−2.90773e12			−0.194124
$848$	3.41929e12			0.227067
$849$	−6.40394e12	+	1.10919e13i	−0.423022	+	0.732695i
$850$	−2.27538e12	−	3.94107e12i	−0.149509	−	0.258958i
$851$	2.09614e13	−	3.63063e13i	1.37005	−	2.37300i
$852$	1.01969e12	+	1.76616e12i	0.0662964	+	0.114829i
$853$	9.43272e12	+	1.63380e13i	0.610052	+	1.05664i	0.991231	+	0.132139i	$0.0421846\pi$
$853$	9.43272e12	+	1.63380e13i	0.610052	+	1.05664i	−0.381180	+	0.924501i	$0.624482\pi$
$854$	−1.71396e12			−0.110265
$855$	1.26174e13	−	1.85430e12i	0.807462	−	0.118667i
$856$	−2.79101e12			−0.177676
$857$	−2.05944e12	−	3.56706e12i	−0.130418	−	0.225890i	0.793420	−	0.608675i	$-0.208298\pi$
$857$	−2.05944e12	−	3.56706e12i	−0.130418	−	0.225890i	−0.923838	+	0.382785i	$0.874965\pi$
$858$	2.04962e12	+	3.55005e12i	0.129116	+	0.223636i
$859$	−1.19630e13	+	2.07205e13i	−0.749670	+	1.29847i	0.198312	+	0.980139i	$0.436454\pi$
$859$	−1.19630e13	+	2.07205e13i	−0.749670	+	1.29847i	−0.947981	+	0.318327i	$0.896879\pi$
$860$	−4.78198e12	−	8.28264e12i	−0.298102	−	0.516328i
$861$	8.72371e11	−	1.51099e12i	0.0540987	−	0.0937017i
$862$	−2.19161e12			−0.135201
$863$	1.91137e13			1.17300			0.586498	−	0.809951i	$-0.300506\pi$
$863$	1.91137e13			1.17300			0.586498	+	0.809951i	$0.300506\pi$
$864$	1.33286e12	−	2.30858e12i	0.0813717	−	0.140940i
$865$	8.87921e12	−	1.53792e13i	0.539265	−	0.934034i
$866$	−1.32897e13			−0.802943
$867$	−6.64119e12			−0.399172
$868$	−7.37660e11	+	1.27767e12i	−0.0441080	+	0.0763974i
$869$	−1.15063e12	−	1.99295e12i	−0.0684458	−	0.118552i
$870$	−2.09325e12	+	3.62562e12i	−0.123875	+	0.214558i
$871$	7.81752e12	+	1.35403e13i	0.460243	+	0.797165i
$872$	−2.74364e12	−	4.75212e12i	−0.160695	−	0.278332i
$873$	1.25036e13			0.728571
$874$	−1.87103e13	+	2.74973e12i	−1.08463	+	0.159400i
$875$	−3.38077e12			−0.194975
$876$	−8.77220e11	−	1.51939e12i	−0.0503315	−	0.0871768i
$877$	−1.82098e12	−	3.15402e12i	−0.103946	−	0.180039i	0.809361	−	0.587311i	$-0.199813\pi$
$877$	−1.82098e12	−	3.15402e12i	−0.103946	−	0.180039i	−0.913307	+	0.407272i	$0.866480\pi$
$878$	−7.17036e12	+	1.24194e13i	−0.407208	+	0.705304i
$879$	−5.49222e12	−	9.51281e12i	−0.310312	−	0.537476i
$880$	−1.20540e12	+	2.08782e12i	−0.0677579	+	0.117360i
$881$	5.33441e12			0.298329			0.149164	−	0.988812i	$-0.452342\pi$
$881$	5.33441e12			0.298329			0.149164	+	0.988812i	$0.452342\pi$
$882$	−8.46332e12			−0.470903
$883$	−6.05613e12	+	1.04895e13i	−0.335252	+	0.580674i	−0.983533	−	0.180727i	$-0.942155\pi$
$883$	−6.05613e12	+	1.04895e13i	−0.335252	+	0.580674i	0.648281	+	0.761401i	$0.275488\pi$
$884$	−8.61501e12	+	1.49216e13i	−0.474483	+	0.821828i
$885$	−2.04665e13			−1.12150
$886$	1.40495e13			0.765963
$887$	−5.24847e12	+	9.09062e12i	−0.284693	+	0.493102i	−0.972535	−	0.232758i	$-0.925225\pi$
$887$	−5.24847e12	+	9.09062e12i	−0.284693	+	0.493102i	0.687842	+	0.725861i	$0.258558\pi$
$888$	−3.11630e12	−	5.39758e12i	−0.168182	−	0.291300i
$889$	−4.51075e11	+	7.81285e11i	−0.0242209	+	0.0419519i
$890$	−7.41150e12	−	1.28371e13i	−0.395960	−	0.685823i
$891$	−9.52542e11	−	1.64985e12i	−0.0506331	−	0.0876991i
$892$	5.60528e12			0.296453
$893$	−6.64373e12	+	1.67464e13i	−0.349607	+	0.881234i
$894$	−4.65193e12			−0.243565
$895$	2.36336e12	+	4.09346e12i	0.123119	+	0.213249i
$896$	2.12884e11	+	3.68727e11i	0.0110346	+	0.0191125i
$897$	1.16361e13	−	2.01543e13i	0.600123	−	1.03944i
$898$	−7.04766e12	−	1.22069e13i	−0.361661	−	0.626415i
$899$	−3.91942e12	+	6.78863e12i	−0.200126	+	0.346628i
$900$	−2.23981e12			−0.113794
$901$	−2.37107e13			−1.19862
$902$	2.66917e12	−	4.62314e12i	0.134260	−	0.232546i
$903$	1.39330e12	−	2.41327e12i	0.0697350	−	0.120784i
$904$	−7.53038e12			−0.375024
$905$	−2.71343e13			−1.34462
$906$	−5.67971e11	+	9.83754e11i	−0.0280059	+	0.0485076i
$907$	9.59377e12	+	1.66169e13i	0.470713	+	0.815299i	0.999439	−	0.0334933i	$-0.0106633\pi$
$907$	9.59377e12	+	1.66169e13i	0.470713	+	0.815299i	−0.528726	+	0.848793i	$0.677330\pi$
$908$	9.32091e12	−	1.61443e13i	0.455063	−	0.788193i
$909$	8.46221e12	+	1.46570e13i	0.411099	+	0.712044i
$910$	−3.01791e12	−	5.22717e12i	−0.145888	−	0.252686i
$911$	4.33392e12			0.208472			0.104236	−	0.994553i	$-0.466760\pi$
$911$	4.33392e12			0.208472			0.104236	+	0.994553i	$0.466760\pi$
$912$	−1.03678e12	+	2.61336e12i	−0.0496263	+	0.125090i
$913$	1.33831e13			0.637439
$914$	−1.20695e13	−	2.09050e13i	−0.572048	−	0.990816i
$915$	4.09551e12	+	7.09363e12i	0.193158	+	0.334560i
$916$	−5.20252e12	+	9.01102e12i	−0.244165	+	0.422907i
$917$	3.59556e12	+	6.22770e12i	0.167921	+	0.290848i
$918$	−9.24257e12	+	1.60086e13i	−0.429537	+	0.743980i
$919$	−1.25217e13			−0.579087			−0.289543	−	0.957165i	$-0.593503\pi$
$919$	−1.25217e13			−0.579087			−0.289543	+	0.957165i	$0.593503\pi$
$920$	1.36866e13			0.629867
$921$	3.16568e12	−	5.48312e12i	0.144977	−	0.251107i
$922$	−8.90552e12	+	1.54248e13i	−0.405854	+	0.702960i
$923$	−1.56224e13			−0.708502
$924$	−7.02424e11			−0.0317012
$925$	−6.30503e12	+	1.09206e13i	−0.283171	+	0.490467i
$926$	−2.49660e12	−	4.32423e12i	−0.111583	−	0.193268i
$927$	−9.03208e12	+	1.56440e13i	−0.401725	+	0.695809i
$928$	1.13112e12	+	1.95916e12i	0.0500660	+	0.0867169i
$929$	−8.00409e12	−	1.38635e13i	−0.352567	−	0.610663i	0.634132	−	0.773225i	$-0.281358\pi$
$929$	−8.00409e12	−	1.38635e13i	−0.352567	−	0.610663i	−0.986698	+	0.162562i	$0.948024\pi$
$930$	7.05058e12			0.309066
$931$	2.12656e13	−	3.12527e12i	0.927693	−	0.136337i
$932$	1.05314e12			0.0457208
$933$	−2.73552e12	−	4.73806e12i	−0.118188	−	0.204707i
$934$	6.33316e12	+	1.09694e13i	0.272308	+	0.471651i
$935$	8.35871e12	−	1.44777e13i	0.357674	−	0.619509i
$936$	4.24016e12	+	7.34417e12i	0.180568	+	0.312753i
$937$	−1.35178e13	+	2.34136e13i	−0.572900	+	0.992291i	0.423367	+	0.905958i	$0.360848\pi$
$937$	−1.35178e13	+	2.34136e13i	−0.572900	+	0.992291i	−0.996266	+	0.0863330i	$0.972485\pi$
$938$	−2.67914e12			−0.113001
$939$	−2.06333e12			−0.0866113
$940$	6.51937e12	−	1.12919e13i	0.272352	−	0.471727i
$941$	−9.16436e12	+	1.58731e13i	−0.381021	+	0.659948i	−0.991208	−	0.132309i	$-0.957761\pi$
$941$	−9.16436e12	+	1.58731e13i	−0.381021	+	0.659948i	0.610187	+	0.792257i	$0.291094\pi$
$942$	−1.33827e13			−0.553752
$943$	−3.03068e13			−1.24806
$944$	−5.52970e12	+	9.57773e12i	−0.226635	+	0.392544i
$945$	−3.23775e12	−	5.60795e12i	−0.132069	−	0.228750i
$946$	4.26306e12	−	7.38383e12i	0.173066	−	0.299759i
$947$	−1.26380e13	−	2.18897e13i	−0.510628	−	0.884434i	−0.999924	−	0.0123165i	$-0.996079\pi$
$947$	−1.26380e13	−	2.18897e13i	−0.510628	−	0.884434i	0.489296	−	0.872118i	$-0.337254\pi$
$948$	9.71150e11	+	1.68208e12i	0.0390525	+	0.0676409i
$949$	1.34397e13			0.537887
$950$	5.62791e12	−	8.27098e11i	0.224177	−	0.0329458i
$951$	1.36812e13			0.542388
$952$	−1.47622e12	−	2.55689e12i	−0.0582485	−	0.100889i
$953$	−2.47415e13	−	4.28535e13i	−0.971646	−	1.68294i	−0.690587	−	0.723249i	$-0.742648\pi$
$953$	−2.47415e13	−	4.28535e13i	−0.971646	−	1.68294i	−0.281059	−	0.959691i	$-0.590686\pi$
$954$	−5.83499e12	+	1.01065e13i	−0.228072	+	0.395033i
$955$	−3.49910e12	−	6.06061e12i	−0.136126	−	0.235777i
$956$	−7.27546e12	+	1.26015e13i	−0.281708	+	0.487933i
$957$	−3.73220e12			−0.143834
$958$	7.75368e12			0.297415
$959$	−1.93607e12	+	3.35338e12i	−0.0739159	+	0.128026i
$960$	1.01738e12	−	1.76215e12i	0.0386600	−	0.0669610i
$961$	−1.32381e13			−0.500690
$962$	4.77440e13			1.79734
$963$	4.76283e12	−	8.24947e12i	0.178463	−	0.309106i
$964$	−1.26027e13	−	2.18286e13i	−0.470022	−	0.814102i
$965$	2.88091e12	−	4.98988e12i	0.106944	−	0.185232i
$966$	1.99389e12	+	3.45352e12i	0.0736724	+	0.127604i
$967$	2.44131e13	+	4.22847e13i	0.897850	+	1.55512i	0.830237	+	0.557410i	$0.188205\pi$
$967$	2.44131e13	+	4.22847e13i	0.897850	+	1.55512i	0.0676130	+	0.997712i	$0.478462\pi$
$968$	7.50896e12			0.274879
$969$	7.18946e12	−	1.81220e13i	0.261962	−	0.660313i
$970$	2.29819e13			0.833515
$971$	−1.06745e13	−	1.84887e13i	−0.385354	−	0.667452i	0.606464	−	0.795111i	$-0.292587\pi$
$971$	−1.06745e13	−	1.84887e13i	−0.385354	−	0.667452i	−0.991818	+	0.127658i	$0.959254\pi$
$972$	7.20892e12	+	1.24862e13i	0.259043	+	0.448676i
$973$	−3.06155e12	+	5.30275e12i	−0.109505	+	0.189668i
$974$	1.71056e13	+	2.96277e13i	0.609007	+	1.05483i
$975$	−3.50003e12	+	6.06224e12i	−0.124037	+	0.214839i
$976$	4.42615e12			0.156136
$977$	1.11835e13			0.392693			0.196346	−	0.980535i	$-0.437092\pi$
$977$	1.11835e13			0.392693			0.196346	+	0.980535i	$0.437092\pi$
$978$	3.13586e12	−	5.43147e12i	0.109605	−	0.189842i
$979$	6.60723e12	−	1.14441e13i	0.229878	−	0.398160i
$980$	−1.55557e13			−0.538733
$981$	1.87280e13			0.645625
$982$	5.87196e12	−	1.01705e13i	0.201503	−	0.349013i
$983$	3.24220e12	+	5.61565e12i	0.110751	+	0.191827i	0.916073	−	0.401011i	$-0.131341\pi$
$983$	3.24220e12	+	5.61565e12i	0.110751	+	0.191827i	−0.805322	+	0.592837i	$0.798008\pi$
$984$	−2.25282e12	+	3.90200e12i	−0.0766036	+	0.132681i
$985$	−1.11827e13	−	1.93689e13i	−0.378514	−	0.655605i
$986$	−7.84362e12	−	1.35856e13i	−0.264284	−	0.457753i
$987$	3.79903e12			0.127422
$988$	−1.33662e13	−	1.68878e13i	−0.446273	−	0.563853i
$989$	−4.84043e13			−1.60879
$990$	−4.11401e12	−	7.12568e12i	−0.136115	−	0.235759i
$991$	−4.71682e12	−	8.16977e12i	−0.155352	−	0.269078i	0.777835	−	0.628469i	$-0.216318\pi$
$991$	−4.71682e12	−	8.16977e12i	−0.155352	−	0.269078i	−0.933187	+	0.359390i	$0.882985\pi$
$992$	1.90495e12	−	3.29946e12i	0.0624568	−	0.108178i
$993$	−1.00172e13	−	1.73503e13i	−0.326945	−	0.566285i
$994$	1.33849e12	−	2.31833e12i	0.0434886	−	0.0753245i
$995$	6.34926e13			2.05362
$996$	−1.12955e13			−0.363697
$997$	−1.76174e13	+	3.05143e13i	−0.564696	+	0.978082i	0.432382	+	0.901691i	$0.357673\pi$
$997$	−1.76174e13	+	3.05143e13i	−0.564696	+	0.978082i	−0.997078	+	0.0763914i	$0.975660\pi$
$998$	−9.07373e11	+	1.57162e12i	−0.0289533	+	0.0501486i
$999$	5.12219e13			1.62709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.a.7.5	✓	14
19.11	even	3	inner	38.10.c.a.11.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.a.7.5	✓	14	1.1	even	1	trivial
38.10.c.a.11.5	yes	14	19.11	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(37.7605 + 65.4031i) q^{3} +(-128.000 + 221.703i) q^{4} +(-802.961 - 1390.77i) q^{5} +(-604.168 + 1046.45i) q^{6} +1586.11 q^{7} -4096.00 q^{8} +(6989.79 - 12106.7i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(37.7605 + 65.4031i) q^{3} +(-128.000 + 221.703i) q^{4} +(-802.961 - 1390.77i) q^{5} +(-604.168 + 1046.45i) q^{6} +1586.11 q^{7} -4096.00 q^{8} +(6989.79 - 12106.7i) q^{9} +(12847.4 - 22252.3i) q^{10} +22906.4 q^{11} -19333.4 q^{12} +(74050.5 - 128259. i) q^{13} +(12688.9 + 21977.8i) q^{14} +(60640.4 - 105032. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(227226. + 393567. i) q^{17} +223673. q^{18} +(-562019. + 82596.3i) q^{19} +411116. q^{20} +(59892.4 + 103737. i) q^{21} +(183251. + 317401. i) q^{22} +(1.04035e6 - 1.80194e6i) q^{23} +(-154667. - 267891. i) q^{24} +(-312929. + 542010. i) q^{25} +2.36962e6 q^{26} +2.54223e6 q^{27} +(-203022. + 351645. i) q^{28} +(-1.07872e6 + 1.86840e6i) q^{29} +1.94049e6 q^{30} +3.63339e6 q^{31} +(524288. - 908093. i) q^{32} +(864959. + 1.49815e6i) q^{33} +(-3.63561e6 + 6.29706e6i) q^{34} +(-1.27359e6 - 2.20592e6i) q^{35} +(1.78939e6 + 3.09931e6i) q^{36} +2.01484e7 q^{37} +(-5.64064e6 - 7.12680e6i) q^{38} +1.11847e7 q^{39} +(3.28893e6 + 5.69659e6i) q^{40} +(-7.28282e6 - 1.26142e7i) q^{41} +(-958278. + 1.65979e6i) q^{42} +(-1.16317e7 - 2.01467e7i) q^{43} +(-2.93202e6 + 5.07841e6i) q^{44} -2.24501e7 q^{45} +3.32913e7 q^{46} +(1.58577e7 - 2.74664e7i) q^{47} +(2.47467e6 - 4.28626e6i) q^{48} -3.78379e7 q^{49} -1.00137e7 q^{50} +(-1.71603e7 + 2.97225e7i) q^{51} +(1.89569e7 + 3.28344e7i) q^{52} +(-2.60871e7 + 4.51842e7i) q^{53} +(2.03379e7 + 3.52262e7i) q^{54} +(-1.83930e7 - 3.18576e7i) q^{55} -6.49672e6 q^{56} +(-2.66242e7 - 3.36389e7i) q^{57} -3.45191e7 q^{58} +(-8.43766e7 - 1.46145e8i) q^{59} +(1.55239e7 + 2.68883e7i) q^{60} +(-3.37688e7 + 5.84893e7i) q^{61} +(2.90672e7 + 5.03458e7i) q^{62} +(1.10866e7 - 1.92025e7i) q^{63} +1.67772e7 q^{64} -2.37839e8 q^{65} +(-1.38393e7 + 2.39704e7i) q^{66} +(-5.27851e7 + 9.14264e7i) q^{67} -1.16340e8 q^{68} +1.57137e8 q^{69} +(2.03774e7 - 3.52946e7i) q^{70} +(-5.27425e7 - 9.13527e7i) q^{71} +(-2.86302e7 + 4.95889e7i) q^{72} +(4.53734e7 + 7.85890e7i) q^{73} +(1.61187e8 + 2.79185e8i) q^{74} -4.72655e7 q^{75} +(5.36266e7 - 1.35173e8i) q^{76} +3.63322e7 q^{77} +(8.94779e7 + 1.54980e8i) q^{78} +(-5.02318e7 - 8.70039e7i) q^{79} +(-5.26228e7 + 9.11454e7i) q^{80} +(-4.15840e7 - 7.20257e7i) q^{81} +(1.16525e8 - 2.01827e8i) q^{82} +5.84251e8 q^{83} -3.06649e7 q^{84} +(3.64907e8 - 6.32037e8i) q^{85} +(1.86107e8 - 3.22348e8i) q^{86} -1.62932e8 q^{87} -9.38248e7 q^{88} +(2.88444e8 - 4.99600e8i) q^{89} +(-1.79601e8 - 3.11078e8i) q^{90} +(1.17452e8 - 2.03434e8i) q^{91} +(2.66330e8 + 4.61297e8i) q^{92} +(1.37199e8 + 2.37635e8i) q^{93} +5.07448e8 q^{94} +(5.66152e8 + 7.15317e8i) q^{95} +7.91895e7 q^{96} +(4.47210e8 + 7.74591e8i) q^{97} +(-3.02703e8 - 5.24297e8i) q^{98} +(1.60111e8 - 2.77321e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more