LMFDB - Embedded newform 15.11.c.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(11,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("15.11");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.c (of order $2$, degree $1$, 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:	$9.53035879011$
Analytic rank:	$0$
Dimension:	$14$
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} + 11554 x^{12} + 52224391 x^{10} + 115670558124 x^{8} + 127683454012911 x^{6} + \cdots + 62\!\cdots\!00 $ x^14 + 11554x^12 + 52224391x^10 + 115670558124x^8 + 127683454012911x^6 + 62207430110604450x^4 + 9049402196955729225x^2 + 62911149236536050000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{20}\cdot 5^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.13
Root			$54.9539i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.11.c.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+52.7178i q^{2} +(-210.660 + 121.125i) q^{3} -1755.17 q^{4} +1397.54i q^{5} +(-6385.47 - 11105.5i) q^{6} -8585.72 q^{7} -38545.6i q^{8} +(29706.2 - 51032.6i) q^{9} +O(q^{10})$	\(q+52.7178i q^{2} +(-210.660 + 121.125i) q^{3} -1755.17 q^{4} +1397.54i q^{5} +(-6385.47 - 11105.5i) q^{6} -8585.72 q^{7} -38545.6i q^{8} +(29706.2 - 51032.6i) q^{9} -73675.4 q^{10} +184175. i q^{11} +(369744. - 212595. i) q^{12} +490018. q^{13} -452620. i q^{14} +(-169278. - 294406. i) q^{15} +234746. q^{16} -1.29033e6i q^{17} +(2.69033e6 + 1.56605e6i) q^{18} -4.09260e6 q^{19} -2.45292e6i q^{20} +(1.80867e6 - 1.03995e6i) q^{21} -9.70928e6 q^{22} -7.15208e6i q^{23} +(4.66885e6 + 8.12001e6i) q^{24} -1.95312e6 q^{25} +2.58327e7i q^{26} +(-76572.7 + 1.43487e7i) q^{27} +1.50694e7 q^{28} +1.25838e7i q^{29} +(1.55205e7 - 8.92396e6i) q^{30} -3.43282e7 q^{31} -2.70954e7i q^{32} +(-2.23082e7 - 3.87982e7i) q^{33} +6.80234e7 q^{34} -1.19989e7i q^{35} +(-5.21394e7 + 8.95707e7i) q^{36} -5.32490e7 q^{37} -2.15753e8i q^{38} +(-1.03227e8 + 5.93536e7i) q^{39} +5.38690e7 q^{40} +4.13097e6i q^{41} +(5.48238e7 + 9.53490e7i) q^{42} +2.40945e8 q^{43} -3.23257e8i q^{44} +(7.13202e7 + 4.15157e7i) q^{45} +3.77042e8 q^{46} +2.08997e8i q^{47} +(-4.94515e7 + 2.84337e7i) q^{48} -2.08761e8 q^{49} -1.02964e8i q^{50} +(1.56292e8 + 2.71821e8i) q^{51} -8.60063e8 q^{52} +3.98526e8i q^{53} +(-7.56432e8 - 4.03675e6i) q^{54} -2.57392e8 q^{55} +3.30941e8i q^{56} +(8.62146e8 - 4.95718e8i) q^{57} -6.63392e8 q^{58} +1.05848e8i q^{59} +(2.97111e8 + 5.16732e8i) q^{60} +1.44239e8 q^{61} -1.80971e9i q^{62} +(-2.55049e8 + 4.38151e8i) q^{63} +1.66879e9 q^{64} +6.84821e8i q^{65} +(2.04536e9 - 1.17604e9i) q^{66} -2.05801e9 q^{67} +2.26474e9i q^{68} +(8.66299e8 + 1.50666e9i) q^{69} +6.32556e8 q^{70} -5.86016e8i q^{71} +(-1.96708e9 - 1.14504e9i) q^{72} -1.45815e9 q^{73} -2.80717e9i q^{74} +(4.11445e8 - 2.36573e8i) q^{75} +7.18319e9 q^{76} -1.58127e9i q^{77} +(-3.12899e9 - 5.44191e9i) q^{78} -3.28039e9 q^{79} +3.28067e8i q^{80} +(-1.72186e9 - 3.03197e9i) q^{81} -2.17776e8 q^{82} +6.81301e9i q^{83} +(-3.17451e9 + 1.82529e9i) q^{84} +1.80329e9 q^{85} +1.27021e10i q^{86} +(-1.52422e9 - 2.65091e9i) q^{87} +7.09911e9 q^{88} -5.70384e9i q^{89} +(-2.18862e9 + 3.75984e9i) q^{90} -4.20715e9 q^{91} +1.25531e10i q^{92} +(7.23157e9 - 4.15802e9i) q^{93} -1.10179e10 q^{94} -5.71958e9i q^{95} +(3.28194e9 + 5.70791e9i) q^{96} +8.16165e9 q^{97} -1.10054e10i q^{98} +(9.39890e9 + 5.47113e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) $ 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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 $

$2$			52.7178i			1.64743i	0.567003	+	0.823716i	$0.308103\pi$
$2$			52.7178i			1.64743i	−0.567003	+	0.823716i	$0.691897\pi$
$3$	−210.660	+	121.125i	−0.866913	+	0.498459i
$3$	−210.660	+	121.125i	−0.866913	+	0.498459i
$4$	−1755.17			−1.71403
$5$			1397.54i			0.447214i
$5$			1397.54i			0.447214i
$6$	−6385.47	−	11105.5i	−0.821177	−	1.42818i
$7$	−8585.72			−0.510842			−0.255421	−	0.966830i	$-0.582214\pi$
$7$	−8585.72			−0.510842			−0.255421	+	0.966830i	$0.582214\pi$
$8$		−	38545.6i		−	1.17632i
$9$	29706.2	−	51032.6i	0.503078	−	0.864241i
$10$	−73675.4			−0.736754
$11$			184175.i			1.14358i	0.820400	+	0.571790i	$0.193751\pi$
$11$			184175.i			1.14358i	−0.820400	+	0.571790i	$0.806249\pi$
$12$	369744.	−	212595.i	1.48592	−	0.854374i
$13$	490018.			1.31976			0.659880	−	0.751371i	$-0.270607\pi$
$13$	490018.			1.31976			0.659880	+	0.751371i	$0.270607\pi$
$14$		−	452620.i		−	0.841577i
$15$	−169278.	−	294406.i	−0.222918	−	0.387695i
$16$	234746.			0.223871
$17$		−	1.29033e6i		−	0.908774i	−0.890804	−	0.454387i	$-0.849858\pi$
$17$		−	1.29033e6i		−	0.908774i	0.890804	−	0.454387i	$-0.150142\pi$
$18$	2.69033e6	+	1.56605e6i	1.42378	+	0.828786i
$19$	−4.09260e6			−1.65284			−0.826420	−	0.563054i	$-0.809626\pi$
$19$	−4.09260e6			−1.65284			−0.826420	+	0.563054i	$0.809626\pi$
$20$		−	2.45292e6i		−	0.766538i
$21$	1.80867e6	−	1.03995e6i	0.442856	−	0.254634i
$22$	−9.70928e6			−1.88397
$23$		−	7.15208e6i		−	1.11120i	−0.831449	−	0.555601i	$-0.812488\pi$
$23$		−	7.15208e6i		−	1.11120i	0.831449	−	0.555601i	$-0.187512\pi$
$24$	4.66885e6	+	8.12001e6i	0.586345	+	1.01977i
$25$	−1.95312e6			−0.200000
$26$			2.58327e7i			2.17421i
$27$	−76572.7	+	1.43487e7i	−0.00533649	+	0.999986i
$28$	1.50694e7			0.875599
$29$			1.25838e7i			0.613512i	0.951788	+	0.306756i	$0.0992435\pi$
$29$			1.25838e7i			0.613512i	−0.951788	+	0.306756i	$0.900756\pi$
$30$	1.55205e7	−	8.92396e6i	0.638702	−	0.367241i
$31$	−3.43282e7			−1.19906			−0.599532	−	0.800351i	$-0.704647\pi$
$31$	−3.43282e7			−1.19906			−0.599532	+	0.800351i	$0.704647\pi$
$32$		−	2.70954e7i		−	0.807505i
$33$	−2.23082e7	−	3.87982e7i	−0.570027	−	0.991384i
$34$	6.80234e7			1.49714
$35$		−	1.19989e7i		−	0.228455i
$36$	−5.21394e7	+	8.95707e7i	−0.862291	+	1.48134i
$37$	−5.32490e7			−0.767897			−0.383949	−	0.923354i	$-0.625436\pi$
$37$	−5.32490e7			−0.767897			−0.383949	+	0.923354i	$0.625436\pi$
$38$		−	2.15753e8i		−	2.72294i
$39$	−1.03227e8	+	5.93536e7i	−1.14412	+	0.657846i
$40$	5.38690e7			0.526065
$41$			4.13097e6i			0.0356560i	0.999841	+	0.0178280i	$0.00567514\pi$
$41$			4.13097e6i			0.0356560i	−0.999841	+	0.0178280i	$0.994325\pi$
$42$	5.48238e7	+	9.53490e7i	0.419491	+	0.729574i
$43$	2.40945e8			1.63899			0.819495	−	0.573086i	$-0.194254\pi$
$43$	2.40945e8			1.63899			0.819495	+	0.573086i	$0.194254\pi$
$44$		−	3.23257e8i		−	1.96013i
$45$	7.13202e7	+	4.15157e7i	0.386500	+	0.224983i
$46$	3.77042e8			1.83063
$47$			2.08997e8i			0.911277i	0.890165	+	0.455639i	$0.150589\pi$
$47$			2.08997e8i			0.911277i	−0.890165	+	0.455639i	$0.849411\pi$
$48$	−4.94515e7	+	2.84337e7i	−0.194077	+	0.111590i
$49$	−2.08761e8			−0.739041
$50$		−	1.02964e8i		−	0.329486i
$51$	1.56292e8	+	2.71821e8i	0.452986	+	0.787829i
$52$	−8.60063e8			−2.26211
$53$			3.98526e8i			0.952967i	0.879183	+	0.476483i	$0.158089\pi$
$53$			3.98526e8i			0.952967i	−0.879183	+	0.476483i	$0.841911\pi$
$54$	−7.56432e8	−	4.03675e6i	−1.64741	−	0.00879149i
$55$	−2.57392e8			−0.511424
$56$			3.30941e8i			0.600912i
$57$	8.62146e8	−	4.95718e8i	1.43287	−	0.823873i
$58$	−6.63392e8			−1.01072
$59$			1.05848e8i			0.148055i	0.997256	+	0.0740273i	$0.0235852\pi$
$59$			1.05848e8i			0.148055i	−0.997256	+	0.0740273i	$0.976415\pi$
$60$	2.97111e8	+	5.16732e8i	0.382087	+	0.664522i
$61$	1.44239e8			0.170779			0.0853895	−	0.996348i	$-0.472787\pi$
$61$	1.44239e8			0.170779			0.0853895	+	0.996348i	$0.472787\pi$
$62$		−	1.80971e9i		−	1.97538i
$63$	−2.55049e8	+	4.38151e8i	−0.256993	+	0.441491i
$64$	1.66879e9			1.55418
$65$			6.84821e8i			0.590215i
$66$	2.04536e9	−	1.17604e9i	1.63324	−	0.939080i
$67$	−2.05801e9			−1.52431			−0.762157	−	0.647393i	$-0.775859\pi$
$67$	−2.05801e9			−1.52431			−0.762157	+	0.647393i	$0.775859\pi$
$68$			2.26474e9i			1.55767i
$69$	8.66299e8	+	1.50666e9i	0.553888	+	0.963316i
$70$	6.32556e8			0.376365
$71$		−	5.86016e8i		−	0.324802i	−0.986725	−	0.162401i	$-0.948076\pi$
$71$		−	5.86016e8i		−	0.324802i	0.986725	−	0.162401i	$-0.0519237\pi$
$72$	−1.96708e9	−	1.14504e9i	−1.01662	−	0.591779i
$73$	−1.45815e9			−0.703378			−0.351689	−	0.936117i	$-0.614392\pi$
$73$	−1.45815e9			−0.703378			−0.351689	+	0.936117i	$0.614392\pi$
$74$		−	2.80717e9i		−	1.26506i
$75$	4.11445e8	−	2.36573e8i	0.173383	−	0.0996917i
$76$	7.18319e9			2.83302
$77$		−	1.58127e9i		−	0.584188i
$78$	−3.12899e9	−	5.44191e9i	−1.08376	−	1.88486i
$79$	−3.28039e9			−1.06608			−0.533040	−	0.846090i	$-0.678951\pi$
$79$	−3.28039e9			−1.06608			−0.533040	+	0.846090i	$0.678951\pi$
$80$			3.28067e8i			0.100118i
$81$	−1.72186e9	−	3.03197e9i	−0.493825	−	0.869561i
$82$	−2.17776e8			−0.0587409
$83$			6.81301e9i			1.72961i	0.502107	+	0.864805i	$0.332558\pi$
$83$			6.81301e9i			1.72961i	−0.502107	+	0.864805i	$0.667442\pi$
$84$	−3.17451e9	+	1.82529e9i	−0.759068	+	0.436450i
$85$	1.80329e9			0.406416
$86$			1.27021e10i			2.70012i
$87$	−1.52422e9	−	2.65091e9i	−0.305810	−	0.531862i
$88$	7.09911e9			1.34521
$89$		−	5.70384e9i		−	1.02145i	−0.859744	−	0.510725i	$-0.829377\pi$
$89$		−	5.70384e9i		−	1.02145i	0.859744	−	0.510725i	$-0.170623\pi$
$90$	−2.18862e9	+	3.75984e9i	−0.370645	+	0.636733i
$91$	−4.20715e9			−0.674189
$92$			1.25531e10i			1.90463i
$93$	7.23157e9	−	4.15802e9i	1.03948	−	0.597684i
$94$	−1.10179e10			−1.50127
$95$		−	5.71958e9i		−	0.739173i
$96$	3.28194e9	+	5.70791e9i	0.402508	+	0.700037i
$97$	8.16165e9			0.950429			0.475214	−	0.879870i	$-0.342371\pi$
$97$	8.16165e9			0.950429			0.475214	+	0.879870i	$0.342371\pi$
$98$		−	1.10054e10i		−	1.21752i
$99$	9.39890e9	+	5.47113e9i	0.988328	+	0.575309i
$100$	3.42806e9			0.342806
$101$			5.61592e9i			0.534335i	0.963650	+	0.267168i	$0.0860878\pi$
$101$			5.61592e9i			0.534335i	−0.963650	+	0.267168i	$0.913912\pi$
$102$	−1.43298e10	+	8.23936e9i	−1.29789	+	0.746264i
$103$	−3.90259e9			−0.336641			−0.168321	−	0.985732i	$-0.553834\pi$
$103$	−3.90259e9			−0.336641			−0.168321	+	0.985732i	$0.553834\pi$
$104$		−	1.88880e10i		−	1.55246i
$105$	1.45337e9	+	2.52769e9i	0.113876	+	0.198051i
$106$	−2.10094e10			−1.56995
$107$		−	7.09114e9i		−	0.505588i	−0.967520	−	0.252794i	$-0.918650\pi$
$107$		−	7.09114e9i		−	0.505588i	0.967520	−	0.252794i	$-0.0813495\pi$
$108$	1.34398e8	−	2.51844e10i	0.00914690	−	1.71401i
$109$	−4.10379e9			−0.266718			−0.133359	−	0.991068i	$-0.542576\pi$
$109$	−4.10379e9			−0.266718			−0.133359	+	0.991068i	$0.542576\pi$
$110$		−	1.35691e10i		−	0.842536i
$111$	1.12174e10	−	6.44981e9i	0.665700	−	0.382765i
$112$	−2.01546e9			−0.114363
$113$			9.51044e9i			0.516189i	0.966120	+	0.258094i	$0.0830945\pi$
$113$			9.51044e9i			0.516189i	−0.966120	+	0.258094i	$0.916905\pi$
$114$	2.61332e10	+	4.54505e10i	1.35727	+	2.36056i
$115$	9.99533e9			0.496945
$116$		−	2.20867e10i		−	1.05158i
$117$	1.45566e10	−	2.50069e10i	0.663942	−	1.14059i
$118$	−5.58007e9			−0.243910
$119$			1.10784e10i			0.464240i
$120$	−1.13481e10	+	6.52491e9i	−0.456053	+	0.262222i
$121$	−7.98284e9			−0.307773
$122$			7.60398e9i			0.281347i
$123$	−5.00366e8	−	8.70231e8i	−0.0177731	−	0.0309107i
$124$	6.02517e10			2.05523
$125$		−	2.72958e9i		−	0.0894427i
$126$	−2.30984e10	−	1.34456e10i	−0.727325	−	0.423379i
$127$	1.44905e10			0.438597			0.219299	−	0.975658i	$-0.429623\pi$
$127$	1.44905e10			0.438597			0.219299	+	0.975658i	$0.429623\pi$
$128$			6.02292e10i			1.75290i
$129$	−5.07576e10	+	2.91846e10i	−1.42086	+	0.816969i
$130$	−3.61022e10			−0.972338
$131$		−	9.50064e8i		−	0.0246261i	−0.999924	−	0.0123131i	$-0.996081\pi$
$131$		−	9.50064e8i		−	0.0246261i	0.999924	−	0.0123131i	$-0.00391947\pi$
$132$	3.91547e10	+	6.80974e10i	0.977044	+	1.69926i
$133$	3.51379e10			0.844340
$134$		−	1.08494e11i		−	2.51120i
$135$	−2.00529e10	−	1.07014e8i	−0.447207	−	0.00238655i
$136$	−4.97365e10			−1.06901
$137$		−	6.05991e10i		−	1.25563i	−0.778361	−	0.627817i	$-0.783949\pi$
$137$		−	6.05991e10i		−	1.25563i	0.778361	−	0.627817i	$-0.216051\pi$
$138$	−7.94276e10	+	4.56694e10i	−1.58700	+	0.912493i
$139$	−5.59447e10			−1.07817			−0.539083	−	0.842253i	$-0.681229\pi$
$139$	−5.59447e10			−1.07817			−0.539083	+	0.842253i	$0.681229\pi$
$140$			2.10601e10i			0.391580i
$141$	−2.53148e10	−	4.40273e10i	−0.454234	−	0.789998i
$142$	3.08935e10			0.535088
$143$			9.02488e10i			1.50925i
$144$	6.97341e9	−	1.19797e10i	0.112624	−	0.193478i
$145$	−1.75864e10			−0.274371
$146$		−	7.68706e10i		−	1.15877i
$147$	4.39775e10	−	2.52862e10i	0.640684	−	0.368381i
$148$	9.34610e10			1.31620
$149$			1.02629e11i			1.39746i	0.715387	+	0.698729i	$0.246251\pi$
$149$			1.02629e11i			1.39746i	−0.715387	+	0.698729i	$0.753749\pi$
$150$	1.24716e10	+	2.16905e10i	0.164235	+	0.285636i
$151$	6.86648e10			0.874681			0.437340	−	0.899296i	$-0.355920\pi$
$151$	6.86648e10			0.874681			0.437340	+	0.899296i	$0.355920\pi$
$152$			1.57751e11i			1.94426i
$153$	−6.58488e10	−	3.83308e10i	−0.785400	−	0.457184i
$154$	8.33611e10			0.962410
$155$		−	4.79751e10i		−	0.536238i
$156$	1.81181e11	−	1.04176e11i	1.96105	−	1.12757i
$157$	−1.69286e10			−0.177469			−0.0887344	−	0.996055i	$-0.528282\pi$
$157$	−1.69286e10			−0.177469			−0.0887344	+	0.996055i	$0.528282\pi$
$158$		−	1.72935e11i		−	1.75629i
$159$	−4.82717e10	−	8.39536e10i	−0.475015	−	0.826140i
$160$	3.78669e10			0.361127
$161$			6.14057e10i			0.567648i
$162$	1.59839e11	−	9.07728e10i	1.43254	−	0.813543i
$163$	−6.79037e10			−0.590140			−0.295070	−	0.955476i	$-0.595343\pi$
$163$	−6.79037e10			−0.590140			−0.295070	+	0.955476i	$0.595343\pi$
$164$		−	7.25055e9i		−	0.0611156i
$165$	5.42221e10	−	3.11767e10i	0.443360	−	0.254924i
$166$	−3.59167e11			−2.84942
$167$			5.79714e10i			0.446305i	0.974784	+	0.223152i	$0.0716348\pi$
$167$			5.79714e10i			0.446305i	−0.974784	+	0.223152i	$0.928365\pi$
$168$	−4.00854e10	−	6.97161e10i	−0.299530	−	0.520939i
$169$	1.02259e11			0.741767
$170$			9.50655e10i			0.669543i
$171$	−1.21576e11	+	2.08856e11i	−0.831508	+	1.42845i
$172$	−4.22900e11			−2.80928
$173$		−	6.15009e9i		−	0.0396872i	−0.999803	−	0.0198436i	$-0.993683\pi$
$173$		−	6.15009e9i		−	0.0396872i	0.999803	−	0.0198436i	$-0.00631684\pi$
$174$	1.39750e11	−	8.03537e10i	0.876206	−	0.503802i
$175$	1.67690e10			0.102168
$176$			4.32342e10i			0.256014i
$177$	−1.28209e10	−	2.22979e10i	−0.0737991	−	0.128351i
$178$	3.00694e11			1.68277
$179$			2.98317e11i			1.62335i	0.584109	+	0.811675i	$0.301444\pi$
$179$			2.98317e11i			1.62335i	−0.584109	+	0.811675i	$0.698556\pi$
$180$	−1.25179e11	−	7.28671e10i	−0.662474	−	0.385628i
$181$	4.64324e10			0.239017			0.119508	−	0.992833i	$-0.461868\pi$
$181$	4.64324e10			0.239017			0.119508	+	0.992833i	$0.461868\pi$
$182$		−	2.21792e11i		−	1.11068i
$183$	−3.03854e10	+	1.74711e10i	−0.148051	+	0.0851263i
$184$	−2.75681e11			−1.30713
$185$		−	7.44178e10i		−	0.343414i
$186$	2.19201e11	+	3.81233e11i	0.984643	+	1.71248i
$187$	2.37646e11			1.03926
$188$		−	3.66825e11i		−	1.56196i
$189$	6.57432e8	−	1.23194e11i	0.00272610	−	0.510835i
$190$	3.01524e11			1.21774
$191$			3.22608e11i			1.26914i	0.772867	+	0.634568i	$0.218822\pi$
$191$			3.22608e11i			1.26914i	−0.772867	+	0.634568i	$0.781178\pi$
$192$	−3.51547e11	+	2.02133e11i	−1.34734	+	0.774695i
$193$	2.83812e11			1.05985			0.529925	−	0.848045i	$-0.322220\pi$
$193$	2.83812e11			1.05985			0.529925	+	0.848045i	$0.322220\pi$
$194$			4.30265e11i			1.56577i
$195$	−8.29492e10	−	1.44264e11i	−0.294198	−	0.511665i
$196$	3.66410e11			1.26674
$197$			1.62705e10i			0.0548365i	0.999624	+	0.0274183i	$0.00872860\pi$
$197$			1.62705e10i			0.0548365i	−0.999624	+	0.0274183i	$0.991271\pi$
$198$	−2.88426e11	+	4.95490e11i	−0.947783	+	1.62820i
$199$	−4.49674e11			−1.44089			−0.720447	−	0.693510i	$-0.756063\pi$
$199$	−4.49674e11			−1.44089			−0.720447	+	0.693510i	$0.756063\pi$
$200$			7.52843e10i			0.235263i
$201$	4.33541e11	−	2.49278e11i	1.32145	−	0.759807i
$202$	−2.96059e11			−0.880281
$203$		−	1.08041e11i		−	0.313408i
$204$	−2.74318e11	−	4.77091e11i	−0.776433	−	1.35036i
$205$	−5.77321e9			−0.0159459
$206$		−	2.05736e11i		−	0.554593i
$207$	−3.64989e11	−	2.12461e11i	−0.960346	−	0.559021i
$208$	1.15030e11			0.295456
$209$		−	7.53752e11i		−	1.89015i
$210$	−1.33254e11	+	7.66187e10i	−0.326276	+	0.187602i
$211$	−1.19879e11			−0.286636			−0.143318	−	0.989677i	$-0.545777\pi$
$211$	−1.19879e11			−0.286636			−0.143318	+	0.989677i	$0.545777\pi$
$212$		−	6.99481e11i		−	1.63341i
$213$	7.09815e10	+	1.23450e11i	0.161900	+	0.281575i
$214$	3.73829e11			0.832922
$215$			3.36731e11i			0.732979i
$216$	5.53079e11	+	2.95154e9i	1.17630	+	0.00627740i
$217$	2.94732e11			0.612532
$218$		−	2.16343e11i		−	0.439400i
$219$	3.07174e11	−	1.76619e11i	0.609768	−	0.350605i
$220$	4.51766e11			0.876597
$221$		−	6.32284e11i		−	1.19936i
$222$	3.40020e11	+	5.91359e11i	0.630579	+	1.09670i
$223$	−1.73350e11			−0.314341			−0.157170	−	0.987572i	$-0.550237\pi$
$223$	−1.73350e11			−0.314341			−0.157170	+	0.987572i	$0.550237\pi$
$224$			2.32633e11i			0.412507i
$225$	−5.80200e10	+	9.96730e10i	−0.100616	+	0.172848i
$226$	−5.01370e11			−0.850385
$227$			2.67143e11i			0.443216i	0.975136	+	0.221608i	$0.0711305\pi$
$227$			2.67143e11i			0.443216i	−0.975136	+	0.221608i	$0.928870\pi$
$228$	−1.51321e12	+	8.70068e11i	−2.45598	+	1.41214i
$229$	−5.44556e11			−0.864699			−0.432350	−	0.901706i	$-0.642315\pi$
$229$	−5.44556e11			−0.864699			−0.432350	+	0.901706i	$0.642315\pi$
$230$			5.26932e11i			0.818682i
$231$	1.91532e11	+	3.33111e11i	0.291194	+	0.506440i
$232$	4.85051e11			0.721685
$233$		−	3.68173e11i		−	0.536132i	−0.963401	−	0.268066i	$-0.913615\pi$
$233$		−	3.68173e11i		−	0.536132i	0.963401	−	0.268066i	$-0.0863846\pi$
$234$	1.31831e12	+	7.67391e11i	1.87905	+	1.09380i
$235$	−2.92082e11			−0.407536
$236$		−	1.85781e11i		−	0.253770i
$237$	6.91047e11	−	3.97339e11i	0.924200	−	0.531397i
$238$	−5.84029e11			−0.764804
$239$			7.10968e11i			0.911719i	0.890052	+	0.455859i	$0.150668\pi$
$239$			7.10968e11i			0.911719i	−0.890052	+	0.455859i	$0.849332\pi$
$240$	−3.97373e10	−	6.91106e10i	−0.0499047	−	0.0867937i
$241$	−6.84147e10			−0.0841519			−0.0420760	−	0.999114i	$-0.513397\pi$
$241$	−6.84147e10			−0.0841519			−0.0420760	+	0.999114i	$0.513397\pi$
$242$		−	4.20838e11i		−	0.507035i
$243$	7.29977e11	+	4.30154e11i	0.861544	+	0.507683i
$244$	−2.53164e11			−0.292720
$245$		−	2.91752e11i		−	0.330509i
$246$	4.58767e10	−	2.63782e10i	0.0509233	−	0.0292799i
$247$	−2.00545e12			−2.18135
$248$			1.32320e12i			1.41048i
$249$	−8.25229e11	−	1.43523e12i	−0.862139	−	1.49942i
$250$	1.43897e11			0.147351
$251$		−	1.09154e12i		−	1.09564i	−0.836595	−	0.547822i	$-0.815457\pi$
$251$		−	1.09154e12i		−	1.09564i	0.836595	−	0.547822i	$-0.184543\pi$
$252$	4.47655e11	−	7.69029e11i	0.440494	−	0.756728i
$253$	1.31723e12			1.27075
$254$			7.63910e11i			0.722559i
$255$	−3.79881e11	+	2.18424e11i	−0.352328	+	0.202582i
$256$	−1.46631e12			−1.33360
$257$			1.91831e12i			1.71101i	0.517791	+	0.855507i	$0.326755\pi$
$257$			1.91831e12i			1.71101i	−0.517791	+	0.855507i	$0.673245\pi$
$258$	−1.53855e12	−	2.67583e12i	−1.34590	−	2.34077i
$259$	4.57181e11			0.392274
$260$		−	1.20197e12i		−	1.01165i
$261$	6.42185e11	+	3.73818e11i	0.530222	+	0.308644i
$262$	5.00853e10			0.0405699
$263$			1.68131e12i			1.33619i	0.744075	+	0.668097i	$0.232891\pi$
$263$			1.68131e12i			1.33619i	−0.744075	+	0.668097i	$0.767109\pi$
$264$	−1.49550e12	+	8.59883e11i	−1.16618	+	0.670532i
$265$	−5.56958e11			−0.426180
$266$			1.85239e12i			1.39099i
$267$	6.90880e11	+	1.20157e12i	0.509151	+	0.885509i
$268$	3.61216e12			2.61272
$269$		−	2.03485e12i		−	1.44468i	−0.691538	−	0.722340i	$-0.743067\pi$
$269$		−	2.03485e12i		−	1.44468i	0.691538	−	0.722340i	$-0.256933\pi$
$270$	5.64152e9	−	1.05715e12i	0.00393168	−	0.736743i
$271$	5.92309e11			0.405230			0.202615	−	0.979258i	$-0.435056\pi$
$271$	5.92309e11			0.405230			0.202615	+	0.979258i	$0.435056\pi$
$272$		−	3.02899e11i		−	0.203448i
$273$	8.86279e11	−	5.09593e11i	0.584463	−	0.336055i
$274$	3.19465e12			2.06857
$275$		−	3.59716e11i		−	0.228716i
$276$	−1.52050e12	−	2.64443e12i	−0.949381	−	1.65115i
$277$	5.00326e11			0.306799			0.153400	−	0.988164i	$-0.450978\pi$
$277$	5.00326e11			0.306799			0.153400	+	0.988164i	$0.450978\pi$
$278$		−	2.94928e12i		−	1.77620i
$279$	−1.01976e12	+	1.75185e12i	−0.603222	+	1.03628i
$280$	−4.62505e11			−0.268736
$281$			1.48516e12i			0.847701i	0.905732	+	0.423850i	$0.139322\pi$
$281$			1.48516e12i			0.847701i	−0.905732	+	0.423850i	$0.860678\pi$
$282$	2.32102e12	−	1.33454e12i	1.30147	−	0.748320i
$283$	2.64964e12			1.45967			0.729835	−	0.683623i	$-0.239597\pi$
$283$	2.64964e12			1.45967			0.729835	+	0.683623i	$0.239597\pi$
$284$			1.02856e12i			0.556720i
$285$	6.92787e11	+	1.20489e12i	0.368447	+	0.640799i
$286$	−4.75772e12			−2.48639
$287$		−	3.54674e10i		−	0.0182146i
$288$	−1.38275e12	−	8.04902e11i	−0.697879	−	0.406238i
$289$	3.51043e11			0.174129
$290$		−	9.27119e11i		−	0.452007i
$291$	−1.71933e12	+	9.88584e11i	−0.823939	+	0.473749i
$292$	2.55930e12			1.20561
$293$		−	2.14889e11i		−	0.0995121i	−0.998761	−	0.0497560i	$-0.984156\pi$
$293$		−	2.14889e11i		−	0.0995121i	0.998761	−	0.0497560i	$-0.0158444\pi$
$294$	1.33303e12	+	2.31840e12i	0.606883	+	1.05548i
$295$	−1.47927e11			−0.0662120
$296$			2.05251e12i			0.903290i
$297$	−2.64267e12	−	1.41027e10i	−1.14356	−	0.00610269i
$298$	−5.41037e12			−2.30222
$299$		−	3.50464e12i		−	1.46652i
$300$	−7.22155e11	+	4.15226e11i	−0.297183	+	0.170875i
$301$	−2.06869e12			−0.837265
$302$			3.61986e12i			1.44098i
$303$	−6.80231e11	−	1.18305e12i	−0.266344	−	0.463223i
$304$	−9.60719e11			−0.370023
$305$			2.01581e11i			0.0763747i
$306$	2.02072e12	−	3.47141e12i	0.753180	−	1.29389i
$307$	−1.78342e12			−0.653976			−0.326988	−	0.945028i	$-0.606034\pi$
$307$	−1.78342e12			−0.653976			−0.326988	+	0.945028i	$0.606034\pi$
$308$			2.77540e12i			1.00132i
$309$	8.22120e11	−	4.72703e11i	0.291839	−	0.167802i
$310$	2.52914e12			0.883415
$311$		−	1.62831e12i		−	0.559675i	−0.960047	−	0.279837i	$-0.909719\pi$
$311$		−	1.62831e12i		−	0.559675i	0.960047	−	0.279837i	$-0.0902805\pi$
$312$	2.28782e12	+	3.97895e12i	0.773835	+	1.34585i
$313$	−3.65821e12			−1.21772			−0.608859	−	0.793278i	$-0.708373\pi$
$313$	−3.65821e12			−1.21772			−0.608859	+	0.793278i	$0.708373\pi$
$314$		−	8.92437e11i		−	0.292368i
$315$	−6.12335e11	−	3.56442e11i	−0.197441	−	0.114931i
$316$	5.75763e12			1.82729
$317$			2.41571e12i			0.754656i	0.926080	+	0.377328i	$0.123157\pi$
$317$			2.41571e12i			0.754656i	−0.926080	+	0.377328i	$0.876843\pi$
$318$	4.42585e12	−	2.54478e12i	1.36101	−	0.782554i
$319$	−2.31762e12			−0.701599
$320$			2.33220e12i			0.695050i
$321$	8.58917e11	+	1.49382e12i	0.252015	+	0.438301i
$322$	−3.23717e12			−0.935162
$323$			5.28080e12i			1.50206i
$324$	3.02216e12	+	5.32162e12i	0.846432	+	1.49045i
$325$	−9.57066e11			−0.263952
$326$		−	3.57973e12i		−	0.972216i
$327$	8.64505e11	−	4.97074e11i	0.231222	−	0.132948i
$328$	1.59231e11			0.0419428
$329$		−	1.79439e12i		−	0.465519i
$330$	1.64357e12	+	2.85847e12i	0.419970	+	0.730406i
$331$	4.62559e12			1.16420			0.582100	−	0.813117i	$-0.302231\pi$
$331$	4.62559e12			1.16420			0.582100	+	0.813117i	$0.302231\pi$
$332$		−	1.19580e13i		−	2.96461i
$333$	−1.58183e12	+	2.71743e12i	−0.386312	+	0.663648i
$334$	−3.05613e12			−0.735257
$335$		−	2.87616e12i		−	0.681694i
$336$	4.24577e11	−	2.44124e11i	0.0991425	−	0.0570050i
$337$	7.31346e12			1.68257			0.841285	−	0.540591i	$-0.181799\pi$
$337$	7.31346e12			1.68257			0.841285	+	0.540591i	$0.181799\pi$
$338$			5.39086e12i			1.22201i
$339$	−1.15196e12	−	2.00347e12i	−0.257299	−	0.447491i
$340$	−3.16508e12			−0.696610
$341$		−	6.32238e12i		−	1.37122i
$342$	−1.10104e13	−	6.40921e12i	−2.35328	−	1.36985i
$343$	4.21761e12			0.888375
$344$		−	9.28737e12i		−	1.92797i
$345$	−2.10562e12	+	1.21069e12i	−0.430808	+	0.247706i
$346$	3.24219e11			0.0653820
$347$		−	3.89811e12i		−	0.774831i	−0.921905	−	0.387415i	$-0.873368\pi$
$347$		−	3.89811e12i		−	0.774831i	0.921905	−	0.387415i	$-0.126632\pi$
$348$	2.67527e12	+	4.65279e12i	0.524168	+	0.911627i
$349$	−7.78009e12			−1.50265			−0.751325	−	0.659933i	$-0.770585\pi$
$349$	−7.78009e12			−1.50265			−0.751325	+	0.659933i	$0.770585\pi$
$350$			8.84024e11i			0.168315i
$351$	−3.75220e10	+	7.03112e12i	−0.00704288	+	1.31974i
$352$	4.99028e12			0.923446
$353$		−	6.00660e12i		−	1.09586i	−0.836524	−	0.547930i	$-0.815416\pi$
$353$		−	6.00660e12i		−	1.09586i	0.836524	−	0.547930i	$-0.184584\pi$
$354$	1.17550e12	−	6.75888e11i	0.211449	−	0.121579i
$355$	8.18983e11			0.145256
$356$			1.00112e13i			1.75080i
$357$	−1.34188e12	−	2.33378e12i	−0.231404	−	0.402456i
$358$	−1.57266e13			−2.67436
$359$			4.95033e12i			0.830159i	0.909785	+	0.415080i	$0.136246\pi$
$359$			4.95033e12i			0.830159i	−0.909785	+	0.415080i	$0.863754\pi$
$360$	1.60025e12	−	2.74908e12i	0.264652	−	0.454647i
$361$	1.06183e13			1.73188
$362$			2.44781e12i			0.393764i
$363$	1.68167e12	−	9.66926e11i	0.266813	−	0.153412i
$364$	7.38426e12			1.15558
$365$		−	2.03783e12i		−	0.314560i
$366$	−9.21036e11	−	1.60185e12i	−0.140240	−	0.243903i
$367$	−9.92742e11			−0.149110			−0.0745548	−	0.997217i	$-0.523754\pi$
$367$	−9.92742e11			−0.149110			−0.0745548	+	0.997217i	$0.523754\pi$
$368$		−	1.67892e12i		−	0.248766i
$369$	2.10814e11	+	1.22716e11i	0.0308154	+	0.0179378i
$370$	3.92314e12			0.565751
$371$		−	3.42164e12i		−	0.486815i
$372$	−1.26926e13	+	7.29801e12i	−1.78171	+	1.02445i
$373$	1.18539e13			1.64178			0.820891	−	0.571085i	$-0.193477\pi$
$373$	1.18539e13			1.64178			0.820891	+	0.571085i	$0.193477\pi$
$374$			1.25282e13i			1.71210i
$375$	3.30621e11	+	5.75012e11i	0.0445835	+	0.0775391i
$376$	8.05590e12			1.07195
$377$			6.16630e12i			0.809689i
$378$	6.49451e12	+	3.46584e10i	0.841565	+	0.00449106i
$379$	7.82563e12			1.00075			0.500373	−	0.865810i	$-0.333196\pi$
$379$	7.82563e12			1.00075			0.500373	+	0.865810i	$0.333196\pi$
$380$			1.00388e13i			1.26697i
$381$	−3.05258e12	+	1.75517e12i	−0.380226	+	0.218623i
$382$	−1.70072e13			−2.09082
$383$		−	6.65124e12i		−	0.807065i	−0.914965	−	0.403533i	$-0.867782\pi$
$383$		−	6.65124e12i		−	0.807065i	0.914965	−	0.403533i	$-0.132218\pi$
$384$	−7.29529e12	−	1.26879e13i	−0.873748	−	1.51961i
$385$	2.20989e12			0.261257
$386$			1.49620e13i			1.74603i
$387$	7.15758e12	−	1.22961e13i	0.824540	−	1.41648i
$388$	−1.43251e13			−1.62906
$389$			1.29264e13i			1.45121i	0.688112	+	0.725604i	$0.258440\pi$
$389$			1.29264e13i			1.45121i	−0.688112	+	0.725604i	$0.741560\pi$
$390$	7.60530e12	−	4.37290e12i	0.842933	−	0.484670i
$391$	−9.22854e12			−1.00983
$392$			8.04680e12i			0.869346i
$393$	1.15077e11	+	2.00140e11i	0.0122751	+	0.0213487i
$394$	−8.57746e11			−0.0903395
$395$		−	4.58448e12i		−	0.476766i
$396$	−1.64966e13	−	9.60276e12i	−1.69402	−	0.986098i
$397$	−3.10825e12			−0.315183			−0.157592	−	0.987504i	$-0.550373\pi$
$397$	−3.10825e12			−0.315183			−0.157592	+	0.987504i	$0.550373\pi$
$398$		−	2.37058e13i		−	2.37377i
$399$	−7.40215e12	+	4.25609e12i	−0.731970	+	0.420869i
$400$	−4.58488e11			−0.0447742
$401$			1.06402e13i			1.02619i	0.858331	+	0.513097i	$0.171502\pi$
$401$			1.06402e13i			1.02619i	−0.858331	+	0.513097i	$0.828498\pi$
$402$	1.31414e13	+	2.28553e13i	1.25173	+	2.17699i
$403$	−1.68214e13			−1.58248
$404$		−	9.85688e12i		−	0.915867i
$405$	4.23731e12	−	2.40638e12i	0.388880	−	0.220845i
$406$	5.69570e12			0.516318
$407$		−	9.80712e12i		−	0.878151i
$408$	1.04775e13	−	6.02435e12i	0.926736	−	0.532856i
$409$	−1.29027e13			−1.12736			−0.563681	−	0.825993i	$-0.690615\pi$
$409$	−1.29027e13			−1.12736			−0.563681	+	0.825993i	$0.690615\pi$
$410$		−	3.04351e11i		−	0.0262697i
$411$	7.34009e12	+	1.27658e13i	0.625882	+	1.08853i
$412$	6.84970e12			0.577013
$413$		−	9.08780e11i		−	0.0756325i
$414$	1.12005e13	−	1.92414e13i	0.920949	−	1.58210i
$415$	−9.52147e12			−0.773505
$416$		−	1.32772e13i		−	1.06571i
$417$	1.17853e13	−	6.77633e12i	0.934676	−	0.537421i
$418$	3.97362e13			3.11390
$419$			2.28141e12i			0.176658i	0.996091	+	0.0883291i	$0.0281527\pi$
$419$			2.28141e12i			0.176658i	−0.996091	+	0.0883291i	$0.971847\pi$
$420$	−2.55091e12	−	4.43652e12i	−0.195186	−	0.339466i
$421$	−8.12936e12			−0.614676			−0.307338	−	0.951600i	$-0.599438\pi$
$421$	−8.12936e12			−0.614676			−0.307338	+	0.951600i	$0.599438\pi$
$422$		−	6.31976e12i		−	0.472214i
$423$	1.06656e13	+	6.20851e12i	0.787563	+	0.458443i
$424$	1.53614e13			1.12099
$425$			2.52018e12i			0.181755i
$426$	−6.50803e12	+	3.74199e12i	−0.463875	+	0.266719i
$427$	−1.23840e12			−0.0872411
$428$			1.24461e13i			0.866594i
$429$	−1.09314e13	−	1.90118e13i	−0.752299	−	1.30839i
$430$	−1.77517e13			−1.20753
$431$		−	2.21129e13i		−	1.48682i	−0.668835	−	0.743411i	$-0.733207\pi$
$431$		−	2.21129e13i		−	1.48682i	0.668835	−	0.743411i	$-0.266793\pi$
$432$	−1.79751e10	+	3.36830e12i	−0.00119468	+	0.223868i
$433$	−2.74404e13			−1.80281			−0.901407	−	0.432973i	$-0.857464\pi$
$433$	−2.74404e13			−1.80281			−0.901407	+	0.432973i	$0.857464\pi$
$434$			1.55376e13i			1.00910i
$435$	3.70476e12	−	2.13017e12i	0.237856	−	0.136763i
$436$	7.20285e12			0.457164
$437$			2.92706e13i			1.83664i
$438$	9.31099e12	+	1.61936e13i	0.577597	+	1.00455i
$439$	1.88919e13			1.15865			0.579325	−	0.815097i	$-0.303316\pi$
$439$	1.88919e13			1.15865			0.579325	+	0.815097i	$0.303316\pi$
$440$			9.92131e12i			0.601597i
$441$	−6.20150e12	+	1.06536e13i	−0.371795	+	0.638709i
$442$	3.33326e13			1.97587
$443$			1.49540e13i			0.876472i	0.898860	+	0.438236i	$0.144397\pi$
$443$			1.49540e13i			0.876472i	−0.898860	+	0.438236i	$0.855603\pi$
$444$	−1.96885e13	+	1.13205e13i	−1.14103	+	0.656071i
$445$	7.97135e12			0.456806
$446$		−	9.13866e12i		−	0.517855i
$447$	−1.24310e13	−	2.16198e13i	−0.696575	−	1.21147i
$448$	−1.43277e13			−0.793940
$449$			1.55241e13i			0.850697i	0.905030	+	0.425349i	$0.139849\pi$
$449$			1.55241e13i			0.850697i	−0.905030	+	0.425349i	$0.860151\pi$
$450$	−5.25454e12	−	3.05869e12i	−0.284756	−	0.165757i
$451$	−7.60820e11			−0.0407755
$452$		−	1.66924e13i		−	0.884763i
$453$	−1.44649e13	+	8.31706e12i	−0.758273	+	0.435992i
$454$	−1.40832e13			−0.730167
$455$		−	5.87968e12i		−	0.301506i
$456$	−1.91077e13	−	3.32319e13i	−0.969136	−	1.68551i
$457$	−1.29107e13			−0.647694			−0.323847	−	0.946110i	$-0.604976\pi$
$457$	−1.29107e13			−0.647694			−0.323847	+	0.946110i	$0.604976\pi$
$458$		−	2.87078e13i		−	1.42453i
$459$	1.85146e13	+	9.88041e10i	0.908761	+	0.00484966i
$460$	−1.75435e13			−0.851778
$461$		−	2.31686e13i		−	1.11274i	−0.830934	−	0.556371i	$-0.812193\pi$
$461$		−	2.31686e13i		−	1.11274i	0.830934	−	0.556371i	$-0.187807\pi$
$462$	−1.75609e13	+	1.00972e13i	−0.834326	+	0.479722i
$463$	1.37624e13			0.646829			0.323415	−	0.946257i	$-0.395169\pi$
$463$	1.37624e13			0.646829			0.323415	+	0.946257i	$0.395169\pi$
$464$			2.95400e12i			0.137347i
$465$	5.81100e12	+	1.01064e13i	0.267292	+	0.464872i
$466$	1.94093e13			0.883241
$467$		−	1.15233e13i		−	0.518793i	−0.965771	−	0.259397i	$-0.916476\pi$
$467$		−	1.15233e13i		−	0.518793i	0.965771	−	0.259397i	$-0.0835237\pi$
$468$	−2.55492e13	+	4.38912e13i	−1.13802	+	1.95501i
$469$	1.76695e13			0.778683
$470$		−	1.53979e13i		−	0.671387i
$471$	3.56617e12	−	2.05048e12i	0.153850	−	0.0884609i
$472$	4.07996e12			0.174159
$473$			4.43760e13i			1.87432i
$474$	2.09468e13	+	3.64305e13i	0.875440	+	1.52256i
$475$	7.99335e12			0.330568
$476$		−	1.94445e13i		−	0.795722i
$477$	2.03378e13	+	1.18387e13i	0.823593	+	0.479417i
$478$	−3.74807e13			−1.50199
$479$			3.33568e13i			1.32284i	0.750016	+	0.661419i	$0.230046\pi$
$479$			3.33568e13i			1.32284i	−0.750016	+	0.661419i	$0.769954\pi$
$480$	−7.97705e12	+	4.58665e12i	−0.313066	+	0.180007i
$481$	−2.60930e13			−1.01344
$482$		−	3.60667e12i		−	0.138635i
$483$	−7.43780e12	−	1.29357e13i	−0.282949	−	0.492102i
$484$	1.40112e13			0.527533
$485$			1.14063e13i			0.425045i
$486$	−2.26768e13	+	3.84828e13i	−0.836373	+	1.41933i
$487$	2.91600e13			1.06449			0.532247	−	0.846589i	$-0.321348\pi$
$487$	2.91600e13			1.06449			0.532247	+	0.846589i	$0.321348\pi$
$488$		−	5.55978e12i		−	0.200890i
$489$	1.43046e13	−	8.22487e12i	0.511601	−	0.294161i
$490$	1.53805e13			0.544491
$491$		−	1.80549e13i		−	0.632685i	−0.948645	−	0.316343i	$-0.897545\pi$
$491$		−	1.80549e13i		−	0.632685i	0.948645	−	0.316343i	$-0.102455\pi$
$492$	8.78226e11	+	1.52740e12i	0.0304636	+	0.0529819i
$493$	1.62373e13			0.557544
$494$		−	1.05723e14i		−	3.59363i
$495$	−7.64614e12	+	1.31354e13i	−0.257286	+	0.441994i
$496$	−8.05839e12			−0.268435
$497$			5.03137e12i			0.165922i
$498$	7.56621e13	−	4.35042e13i	2.47020	−	1.42032i
$499$	−6.75804e12			−0.218433			−0.109217	−	0.994018i	$-0.534834\pi$
$499$	−6.75804e12			−0.218433			−0.109217	+	0.994018i	$0.534834\pi$
$500$			4.79086e12i			0.153308i
$501$	−7.02181e12	−	1.22123e13i	−0.222464	−	0.386908i
$502$	5.75434e13			1.80500
$503$		−	4.57456e13i		−	1.42072i	−0.703837	−	0.710362i	$-0.748531\pi$
$503$		−	4.57456e13i		−	1.42072i	0.703837	−	0.710362i	$-0.251469\pi$
$504$	1.68888e13	+	9.83102e12i	0.519333	+	0.302305i
$505$	−7.84848e12			−0.238962
$506$			6.94415e13i			2.09347i
$507$	−2.15418e13	+	1.23861e13i	−0.643048	+	0.369740i
$508$	−2.54333e13			−0.751769
$509$		−	1.40193e13i		−	0.410334i	−0.978727	−	0.205167i	$-0.934226\pi$
$509$		−	1.40193e13i		−	0.410334i	0.978727	−	0.205167i	$-0.0657738\pi$
$510$	−1.15149e13	−	2.00265e13i	−0.333740	−	0.580436i
$511$	1.25193e13			0.359315
$512$		−	1.56261e13i		−	0.444120i
$513$	3.13381e11	−	5.87235e13i	0.00882036	−	1.65282i
$514$	−1.01129e14			−2.81878
$515$		−	5.45404e12i		−	0.150550i
$516$	8.90880e13	−	5.12239e13i	2.43540	−	1.40031i
$517$	−3.84919e13			−1.04212
$518$			2.41016e13i			0.646245i
$519$	7.44932e11	+	1.29558e12i	0.0197825	+	0.0344054i
$520$	2.63968e13			0.694280
$521$			4.32955e13i			1.12786i	0.825823	+	0.563929i	$0.190711\pi$
$521$			4.32955e13i			1.12786i	−0.825823	+	0.563929i	$0.809289\pi$
$522$	−1.97069e13	+	3.38546e13i	−0.508470	+	0.873505i
$523$	9.10128e12			0.232592			0.116296	−	0.993215i	$-0.462898\pi$
$523$	9.10128e12			0.232592			0.116296	+	0.993215i	$0.462898\pi$
$524$			1.66752e12i			0.0422099i
$525$	−3.53255e12	+	2.03115e12i	−0.0885711	+	0.0509267i
$526$	−8.86350e13			−2.20129
$527$			4.42947e13i			1.08968i
$528$	−5.23676e12	−	9.10771e12i	−0.127612	−	0.221942i
$529$	−9.72568e12			−0.234769
$530$		−	2.93616e13i		−	0.702102i
$531$	5.40169e12	+	3.14434e12i	0.127955	+	0.0744830i
$532$	−6.16729e13			−1.44723
$533$			2.02425e12i			0.0470574i
$534$	−6.33441e13	+	3.64217e13i	−1.45882	+	0.838791i
$535$	9.91016e12			0.226106
$536$			7.93273e13i			1.79308i
$537$	−3.61337e13	−	6.28434e13i	−0.809173	−	1.40730i
$538$	1.07273e14			2.38001
$539$		−	3.84484e13i		−	0.845151i
$540$	3.51962e13	+	1.87827e11i	0.766527	+	0.00409062i
$541$	6.44217e13			1.39010			0.695050	−	0.718961i	$-0.255382\pi$
$541$	6.44217e13			1.39010			0.695050	+	0.718961i	$0.255382\pi$
$542$			3.12252e13i			0.667589i
$543$	−9.78145e12	+	5.62415e12i	−0.207207	+	0.119140i
$544$	−3.49620e13			−0.733840
$545$		−	5.73523e12i		−	0.119280i
$546$	2.68647e13	+	4.67227e13i	0.553628	+	0.962863i
$547$	−1.96392e13			−0.401040			−0.200520	−	0.979690i	$-0.564263\pi$
$547$	−1.96392e13			−0.401040			−0.200520	+	0.979690i	$0.564263\pi$
$548$			1.06361e14i			2.15219i
$549$	4.28481e12	−	7.36090e12i	0.0859151	−	0.147594i
$550$	1.89634e13			0.376794
$551$		−	5.15006e13i		−	1.01404i
$552$	5.80749e13	−	3.33920e13i	1.13316	−	0.651548i
$553$	2.81645e13			0.544599
$554$			2.63761e13i			0.505430i
$555$	9.01389e12	+	1.56768e13i	0.171178	+	0.297710i
$556$	9.81924e13			1.84801
$557$			3.47665e13i			0.648462i	0.945978	+	0.324231i	$0.105105\pi$
$557$			3.47665e13i			0.648462i	−0.945978	+	0.324231i	$0.894895\pi$
$558$	−9.23540e13	−	5.37596e13i	−1.70720	−	0.993768i
$559$	1.18068e14			2.16307
$560$		−	2.81669e12i		−	0.0511445i
$561$	−5.00625e13	+	2.87850e13i	−0.900944	+	0.518026i
$562$	−7.82945e13			−1.39653
$563$		−	7.28553e13i		−	1.28801i	−0.765022	−	0.644005i	$-0.777272\pi$
$563$		−	7.28553e13i		−	1.28801i	0.765022	−	0.644005i	$-0.222728\pi$
$564$	4.44318e13	+	7.72752e13i	0.778571	+	1.35408i
$565$	−1.32912e13			−0.230847
$566$			1.39683e14i			2.40471i
$567$	1.47834e13	+	2.60317e13i	0.252267	+	0.444208i
$568$	−2.25883e13			−0.382070
$569$		−	3.56988e13i		−	0.598539i	−0.954169	−	0.299270i	$-0.903257\pi$
$569$		−	3.56988e13i		−	0.598539i	0.954169	−	0.299270i	$-0.0967430\pi$
$570$	−6.35190e13	+	3.65222e13i	−1.05567	+	0.606991i
$571$	−1.01836e14			−1.67773			−0.838864	−	0.544342i	$-0.816780\pi$
$571$	−1.01836e14			−1.67773			−0.838864	+	0.544342i	$0.816780\pi$
$572$		−	1.58402e14i		−	2.58690i
$573$	−3.90761e13	−	6.79606e13i	−0.632612	−	1.10023i
$574$	1.86976e12			0.0300073
$575$			1.39689e13i			0.222240i
$576$	4.95734e13	−	8.51626e13i	0.781874	−	1.34319i
$577$	−2.01671e13			−0.315329			−0.157665	−	0.987493i	$-0.550396\pi$
$577$	−2.01671e13			−0.315329			−0.157665	+	0.987493i	$0.550396\pi$
$578$			1.85062e13i			0.286866i
$579$	−5.97878e13	+	3.43769e13i	−0.918798	+	0.528291i
$580$	3.08672e13			0.470280
$581$		−	5.84946e13i		−	0.883557i
$582$	−5.21160e13	−	9.06395e13i	−0.780470	−	1.35738i
$583$	−7.33984e13			−1.08979
$584$			5.62053e13i			0.827395i
$585$	3.49482e13	+	2.03434e13i	0.510088	+	0.296924i
$586$	1.13285e13			0.163939
$587$			7.52727e13i			1.08006i	0.841647	+	0.540029i	$0.181587\pi$
$587$			7.52727e13i			1.08006i	−0.841647	+	0.540029i	$0.818413\pi$
$588$	−7.71879e13	+	4.43816e13i	−1.09815	+	0.631417i
$589$	1.40491e14			1.98186
$590$		−	7.79838e12i		−	0.109080i
$591$	−1.97077e12	−	3.42755e12i	−0.0273338	−	0.0475385i
$592$	−1.25000e13			−0.171910
$593$			3.90993e13i			0.533207i	0.963806	+	0.266603i	$0.0859014\pi$
$593$			3.90993e13i			0.533207i	−0.963806	+	0.266603i	$0.914099\pi$
$594$	7.43466e11	−	1.39316e14i	0.0100538	−	1.88394i
$595$	−1.54825e13			−0.207614
$596$		−	1.80131e14i		−	2.39529i
$597$	9.47282e13	−	5.44669e13i	1.24913	−	0.718226i
$598$	1.84757e14			2.41599
$599$		−	1.39062e13i		−	0.180333i	−0.995927	−	0.0901663i	$-0.971260\pi$
$599$		−	1.39062e13i		−	0.180333i	0.995927	−	0.0901663i	$-0.0287399\pi$
$600$	−9.11884e12	−	1.58594e13i	−0.117269	−	0.203953i
$601$	1.04746e14			1.33588			0.667939	−	0.744216i	$-0.267177\pi$
$601$	1.04746e14			1.33588			0.667939	+	0.744216i	$0.267177\pi$
$602$		−	1.09057e14i		−	1.37934i
$603$	−6.11358e13	+	1.05026e14i	−0.766848	+	1.31737i
$604$	−1.20518e14			−1.49923
$605$		−	1.11564e13i		−	0.137640i
$606$	6.23678e13	−	3.58603e13i	0.763127	−	0.438784i
$607$	−7.58314e13			−0.920249			−0.460125	−	0.887854i	$-0.652195\pi$
$607$	−7.58314e13			−0.920249			−0.460125	+	0.887854i	$0.652195\pi$
$608$			1.10890e14i			1.33468i
$609$	1.30865e13	+	2.27600e13i	0.156221	+	0.271697i
$610$	−1.06269e13			−0.125822
$611$			1.02412e14i			1.20267i
$612$	1.15576e14	+	6.72771e13i	1.34620	+	0.783628i
$613$	−2.78096e13			−0.321286			−0.160643	−	0.987013i	$-0.551357\pi$
$613$	−2.78096e13			−0.321286			−0.160643	+	0.987013i	$0.551357\pi$
$614$		−	9.40180e13i		−	1.07738i
$615$	1.21618e12	−	6.99283e11i	0.0138237	−	0.00794836i
$616$	−6.09510e13			−0.687190
$617$			8.07234e12i			0.0902763i	0.998981	+	0.0451382i	$0.0143728\pi$
$617$			8.07234e12i			0.0902763i	−0.998981	+	0.0451382i	$0.985627\pi$
$618$	2.49199e13	+	4.33404e13i	0.276442	+	0.480784i
$619$	−3.68186e13			−0.405149			−0.202574	−	0.979267i	$-0.564931\pi$
$619$	−3.68186e13			−0.405149			−0.202574	+	0.979267i	$0.564931\pi$
$620$			8.42043e13i			0.919128i
$621$	1.02623e14	+	5.47654e11i	1.11119	+	0.00592991i
$622$	8.58410e13			0.922026
$623$			4.89715e13i			0.521799i
$624$	−2.42321e13	+	1.39330e13i	−0.256135	+	0.147273i
$625$	3.81470e12			0.0400000
$626$		−	1.92853e14i		−	2.00611i
$627$	9.12986e13	+	1.58785e14i	0.942164	+	1.63860i
$628$	2.97125e13			0.304187
$629$			6.87088e13i			0.697845i
$630$	1.87909e13	−	3.22810e13i	0.189341	−	0.325270i
$631$	−3.53798e13			−0.353678			−0.176839	−	0.984240i	$-0.556587\pi$
$631$	−3.53798e13			−0.353678			−0.176839	+	0.984240i	$0.556587\pi$
$632$			1.26444e14i			1.25405i
$633$	2.52537e13	−	1.45204e13i	0.248489	−	0.142876i
$634$	−1.27351e14			−1.24324
$635$			2.02511e13i			0.196147i
$636$	8.47249e13	+	1.47353e14i	0.814190	+	1.41603i
$637$	−1.02296e14			−0.975356
$638$		−	1.22180e14i		−	1.15584i
$639$	−2.99059e13	−	1.74083e13i	−0.280707	−	0.163400i
$640$	−8.41729e13			−0.783921
$641$		−	9.06348e12i		−	0.0837539i	−0.999123	−	0.0418769i	$-0.986666\pi$
$641$		−	9.06348e12i		−	0.0837539i	0.999123	−	0.0418769i	$-0.0133337\pi$
$642$	−7.87508e13	+	4.52802e13i	−0.722071	+	0.415177i
$643$	−2.89867e13			−0.263720			−0.131860	−	0.991268i	$-0.542095\pi$
$643$	−2.89867e13			−0.263720			−0.131860	+	0.991268i	$0.542095\pi$
$644$		−	1.07777e14i		−	0.972967i
$645$	−4.07868e13	−	7.09358e13i	−0.365360	−	0.635429i
$646$	−2.78392e14			−2.47454
$647$		−	1.05647e14i		−	0.931824i	−0.884831	−	0.465912i	$-0.845726\pi$
$647$		−	1.05647e14i		−	0.931824i	0.884831	−	0.465912i	$-0.154274\pi$
$648$	−1.16869e14	+	6.63701e13i	−1.02288	+	0.580895i
$649$	−1.94945e13			−0.169312
$650$		−	5.04544e13i		−	0.434843i
$651$	−6.20882e13	+	3.56996e13i	−0.531012	+	0.305322i
$652$	1.19182e14			1.01152
$653$		−	2.10855e14i		−	1.77590i	−0.459940	−	0.887950i	$-0.652129\pi$
$653$		−	2.10855e14i		−	1.77590i	0.459940	−	0.887950i	$-0.347871\pi$
$654$	2.62046e13	+	4.55748e13i	0.219023	+	0.380922i
$655$	1.32775e12			0.0110131
$656$			9.69728e11i			0.00798235i
$657$	−4.33162e13	+	7.44133e13i	−0.353854	+	0.607888i
$658$	9.45962e13			0.766910
$659$		−	4.35263e12i		−	0.0350207i	−0.999847	−	0.0175103i	$-0.994426\pi$
$659$		−	4.35263e12i		−	0.0350207i	0.999847	−	0.0175103i	$-0.00557400\pi$
$660$	−9.51689e13	+	5.47203e13i	−0.759933	+	0.436947i
$661$	−8.82844e13			−0.699643			−0.349822	−	0.936816i	$-0.613758\pi$
$661$	−8.82844e13			−0.699643			−0.349822	+	0.936816i	$0.613758\pi$
$662$			2.43851e14i			1.91794i
$663$	7.65857e13	+	1.33197e14i	0.597833	+	1.03974i
$664$	2.62611e14			2.03457
$665$			4.91067e13i			0.377600i
$666$	−1.43257e14	−	8.33905e13i	−1.09332	−	0.636423i
$667$	9.00005e13			0.681736
$668$		−	1.01750e14i		−	0.764980i
$669$	3.65180e13	−	2.09972e13i	0.272506	−	0.156686i
$670$	1.51625e14			1.12304
$671$			2.65652e13i			0.195299i
$672$	−2.81778e13	−	4.90065e13i	−0.205618	−	0.357608i
$673$	−4.17130e13			−0.302131			−0.151066	−	0.988524i	$-0.548271\pi$
$673$	−4.17130e13			−0.302131			−0.151066	+	0.988524i	$0.548271\pi$
$674$			3.85550e14i			2.77192i
$675$	1.49556e11	−	2.80248e13i	0.00106730	−	0.199997i
$676$	−1.79481e14			−1.27141
$677$		−	2.14210e14i		−	1.50625i	−0.657878	−	0.753124i	$-0.728546\pi$
$677$		−	2.14210e14i		−	1.50625i	0.657878	−	0.753124i	$-0.271454\pi$
$678$	1.05619e14	−	6.07286e13i	0.737211	−	0.423882i
$679$	−7.00737e13			−0.485519
$680$		−	6.95088e13i		−	0.478074i
$681$	−3.23579e13	−	5.62764e13i	−0.220925	−	0.384230i
$682$	3.33302e14			2.25900
$683$		−	7.65144e13i		−	0.514801i	−0.966305	−	0.257401i	$-0.917134\pi$
$683$		−	7.65144e13i		−	0.514801i	0.966305	−	0.257401i	$-0.0828660\pi$
$684$	2.13386e14	−	3.66577e14i	1.42523	−	2.44841i
$685$	8.46897e13			0.561536
$686$			2.22343e14i			1.46354i
$687$	1.14716e14	−	6.59596e13i	0.749619	−	0.431017i
$688$	5.65609e13			0.366922
$689$			1.95285e14i			1.25769i
$690$	−6.38249e13	−	1.11003e14i	−0.408079	−	0.709727i
$691$	−3.58651e13			−0.227657			−0.113829	−	0.993500i	$-0.536311\pi$
$691$	−3.58651e13			−0.227657			−0.113829	+	0.993500i	$0.536311\pi$
$692$			1.07944e13i			0.0680252i
$693$	−8.06963e13	−	4.69736e13i	−0.504879	−	0.293892i
$694$	2.05500e14			1.27648
$695$		−	7.81852e13i		−	0.482170i
$696$	−1.02181e14	+	5.87520e13i	−0.625638	+	0.359730i
$697$	5.33032e12			0.0324033
$698$		−	4.10149e14i		−	2.47551i
$699$	4.45951e13	+	7.75593e13i	0.267240	+	0.464780i
$700$	−2.94324e13			−0.175120
$701$			4.69125e13i			0.277140i	0.990353	+	0.138570i	$0.0442505\pi$
$701$			4.69125e13i			0.277140i	−0.990353	+	0.138570i	$0.955749\pi$
$702$	−3.70665e14	−	1.97808e12i	−2.17418	−	0.0116027i
$703$	2.17927e14			1.26921
$704$			3.07348e14i			1.77733i
$705$	6.15300e13	−	3.53786e13i	0.353298	−	0.203140i
$706$	3.16655e14			1.80535
$707$		−	4.82167e13i		−	0.272961i
$708$	2.25028e13	+	3.91366e13i	0.126494	+	0.219997i
$709$	−2.65121e14			−1.47983			−0.739917	−	0.672698i	$-0.765135\pi$
$709$	−2.65121e14			−1.47983			−0.739917	+	0.672698i	$0.765135\pi$
$710$			4.31750e13i			0.239299i
$711$	−9.74481e13	+	1.67407e14i	−0.536322	+	0.921351i
$712$	−2.19858e14			−1.20155
$713$			2.45518e14i			1.33240i
$714$	1.23032e14	−	7.07408e13i	0.663019	−	0.381223i
$715$	−1.26127e14			−0.674957
$716$		−	5.23596e14i		−	2.78247i
$717$	−8.61164e13	−	1.49773e14i	−0.454454	−	0.790381i
$718$	−2.60970e14			−1.36763
$719$		−	1.91958e14i		−	0.998994i	−0.866316	−	0.499497i	$-0.833518\pi$
$719$		−	1.91958e14i		−	0.998994i	0.866316	−	0.499497i	$-0.166482\pi$
$720$	1.67421e13	+	9.74564e12i	0.0865262	+	0.0503672i
$721$	3.35066e13			0.171970
$722$			5.59773e14i			2.85316i
$723$	1.44122e13	−	8.28676e12i	0.0729525	−	0.0419463i
$724$	−8.14967e13			−0.409682
$725$		−	2.45778e13i		−	0.122702i
$726$	5.09742e13	+	8.86537e13i	0.252736	+	0.439556i
$727$	−1.76621e14			−0.869701			−0.434850	−	0.900503i	$-0.643199\pi$
$727$	−1.76621e14			−0.869701			−0.434850	+	0.900503i	$0.643199\pi$
$728$			1.62167e14i			0.793060i
$729$	−2.05879e14	−	2.19744e12i	−0.999943	−	0.0106728i
$730$	1.07430e14			0.518216
$731$		−	3.10899e14i		−	1.48947i
$732$	5.33316e13	−	3.06646e13i	0.253763	−	0.145909i
$733$	2.26158e14			1.06879			0.534394	−	0.845236i	$-0.320540\pi$
$733$	2.26158e14			1.06879			0.534394	+	0.845236i	$0.320540\pi$
$734$		−	5.23352e13i		−	0.245648i
$735$	3.53386e13	+	6.14604e13i	0.164745	+	0.286523i
$736$	−1.93788e14			−0.897301
$737$		−	3.79034e14i		−	1.74317i
$738$	−6.46930e12	+	1.11137e13i	−0.0295512	+	0.0507663i
$739$	−7.57588e12			−0.0343725			−0.0171862	−	0.999852i	$-0.505471\pi$
$739$	−7.57588e12			−0.0343725			−0.0171862	+	0.999852i	$0.505471\pi$
$740$			1.30616e14i			0.588622i
$741$	4.22467e14	−	2.42910e14i	1.89104	−	1.08731i
$742$	1.80381e14			0.801995
$743$			3.48216e13i			0.153782i	0.997040	+	0.0768908i	$0.0244993\pi$
$743$			3.48216e13i			0.153782i	−0.997040	+	0.0768908i	$0.975501\pi$
$744$	−1.60273e14	−	2.78745e14i	−0.703065	−	1.22276i
$745$	−1.43428e14			−0.624962
$746$			6.24909e14i			2.70472i
$747$	3.47685e14	+	2.02389e14i	1.49480	+	0.870129i
$748$	−4.17108e14			−1.78132
$749$			6.08825e13i			0.258276i
$750$	−3.03134e13	+	1.74296e13i	−0.127740	+	0.0734483i
$751$	1.35563e14			0.567467			0.283733	−	0.958903i	$-0.408427\pi$
$751$	1.35563e14			0.567467			0.283733	+	0.958903i	$0.408427\pi$
$752$			4.90611e13i			0.204008i
$753$	1.32213e14	+	2.29943e14i	0.546134	+	0.949829i
$754$	−3.25074e14			−1.33391
$755$			9.59620e13i			0.391169i
$756$	−1.15390e12	+	2.16226e14i	−0.00467262	+	0.875586i
$757$	3.08860e14			1.24246			0.621231	−	0.783628i	$-0.286633\pi$
$757$	3.08860e14			1.24246			0.621231	+	0.783628i	$0.286633\pi$
$758$			4.12550e14i			1.64866i
$759$	−2.77488e14	+	1.59550e14i	−1.10163	+	0.633415i
$760$	−2.20464e14			−0.869502
$761$			4.75721e14i			1.86393i	0.362552	+	0.931964i	$0.381906\pi$
$761$			4.75721e14i			1.86393i	−0.362552	+	0.931964i	$0.618094\pi$
$762$	−9.25289e13	−	1.60925e14i	−0.360166	−	0.626396i
$763$	3.52340e13			0.136251
$764$		−	5.66231e14i		−	2.17534i
$765$	5.35690e13	−	9.20266e13i	0.204459	−	0.351242i
$766$	3.50639e14			1.32958
$767$			5.18673e13i			0.195397i
$768$	3.08893e14	−	1.77608e14i	1.15612	−	0.664746i
$769$	2.11554e14			0.786663			0.393332	−	0.919397i	$-0.371322\pi$
$769$	2.11554e14			0.786663			0.393332	+	0.919397i	$0.371322\pi$
$770$			1.16501e14i			0.430403i
$771$	−2.32356e14	−	4.04112e14i	−0.852870	−	1.48330i
$772$	−4.98138e14			−1.81662
$773$			3.66903e14i			1.32939i	0.747113	+	0.664697i	$0.231440\pi$
$773$			3.66903e14i			1.32939i	−0.747113	+	0.664697i	$0.768560\pi$
$774$	6.48222e14	+	3.77332e14i	2.33356	+	1.35837i
$775$	6.70472e13			0.239813
$776$		−	3.14595e14i		−	1.11801i
$777$	−9.63098e13	+	5.53763e13i	−0.340068	+	0.195532i
$778$	−6.81452e14			−2.39077
$779$		−	1.69064e13i		−	0.0589338i
$780$	1.45590e14	+	2.53208e14i	0.504264	+	0.877010i
$781$	1.07929e14			0.371436
$782$		−	4.86508e14i		−	1.66363i
$783$	−1.80562e14	−	9.63579e11i	−0.613503	−	0.00327400i
$784$	−4.90057e13			−0.165450
$785$		−	2.36584e13i		−	0.0793665i
$786$	−1.05510e13	+	6.06660e12i	−0.0351706	+	0.0202224i
$787$	1.97912e14			0.655539			0.327770	−	0.944758i	$-0.393703\pi$
$787$	1.97912e14			0.655539			0.327770	+	0.944758i	$0.393703\pi$
$788$		−	2.85575e13i		−	0.0939915i
$789$	−2.03650e14	−	3.54185e14i	−0.666037	−	1.15836i
$790$	2.41684e14			0.785439
$791$		−	8.16540e13i		−	0.263691i
$792$	2.10888e14	−	3.62286e14i	0.676746	−	1.16259i
$793$	7.06798e13			0.225387
$794$		−	1.63860e14i		−	0.519242i
$795$	1.17329e14	−	6.74618e13i	0.369461	−	0.212433i
$796$	7.89253e14			2.46974
$797$		−	2.31079e14i		−	0.718569i	−0.933228	−	0.359285i	$-0.883021\pi$
$797$		−	2.31079e14i		−	0.718569i	0.933228	−	0.359285i	$-0.116979\pi$
$798$	−2.24372e14	−	3.90225e14i	−0.693352	−	1.20587i
$799$	2.69675e14			0.828145
$800$			5.29206e13i			0.161501i
$801$	−2.91081e14	−	1.69440e14i	−0.882779	−	0.513869i
$802$	−5.60930e14			−1.69058
$803$		−	2.68555e14i		−	0.804368i
$804$	−7.60937e14	+	4.37524e14i	−2.26500	+	1.30233i
$805$	−8.58171e13			−0.253860
$806$		−	8.86788e14i		−	2.60702i
$807$	2.46473e14	+	4.28662e14i	0.720113	+	1.25241i
$808$	2.16469e14			0.628548
$809$		−	1.78183e14i		−	0.514189i	−0.966386	−	0.257095i	$-0.917235\pi$
$809$		−	1.78183e14i		−	0.514189i	0.966386	−	0.257095i	$-0.0827652\pi$
$810$	1.26859e14	+	2.23382e14i	0.363828	+	0.640652i
$811$	2.15462e14			0.614138			0.307069	−	0.951687i	$-0.400652\pi$
$811$	2.15462e14			0.614138			0.307069	+	0.951687i	$0.400652\pi$
$812$			1.89631e14i			0.537190i
$813$	−1.24776e14	+	7.17437e13i	−0.351300	+	0.201991i
$814$	5.17010e14			1.44669
$815$		−	9.48983e13i		−	0.263919i
$816$	3.66888e13	+	6.38087e13i	0.101410	+	0.176372i
$817$	−9.86093e14			−2.70899
$818$		−	6.80201e14i		−	1.85725i
$819$	−1.24979e14	+	2.14702e14i	−0.339169	+	0.582662i
$820$	1.01330e13			0.0273317
$821$			6.62457e14i			1.77600i	0.459847	+	0.887998i	$0.347904\pi$
$821$			6.62457e14i			1.77600i	−0.459847	+	0.887998i	$0.652096\pi$
$822$	−6.72985e14	+	3.86953e14i	−1.79327	+	1.03110i
$823$	−2.57560e14			−0.682149			−0.341074	−	0.940036i	$-0.610791\pi$
$823$	−2.57560e14			−0.682149			−0.341074	+	0.940036i	$0.610791\pi$
$824$			1.50428e14i			0.395997i
$825$	4.35708e13	+	7.57777e13i	0.114005	+	0.198277i
$826$	4.79089e13			0.124599
$827$		−	9.26700e13i		−	0.239559i	−0.992801	−	0.119779i	$-0.961781\pi$
$827$		−	9.26700e13i		−	0.239559i	0.992801	−	0.119779i	$-0.0382187\pi$
$828$	6.40617e14	+	3.72905e14i	1.64606	+	0.958179i
$829$	4.06274e14			1.03764			0.518820	−	0.854884i	$-0.326372\pi$
$829$	4.06274e14			1.03764			0.518820	+	0.854884i	$0.326372\pi$
$830$		−	5.01951e14i		−	1.27430i
$831$	−1.05399e14	+	6.06022e13i	−0.265968	+	0.152927i
$832$	8.17736e14			2.05114
$833$			2.69370e14i			0.671621i
$834$	3.57233e14	+	6.21296e14i	0.885364	+	1.53981i
$835$	−8.10175e13			−0.199594
$836$			1.32296e15i			3.23978i
$837$	2.62860e12	−	4.92565e14i	0.00639878	−	1.19905i
$838$	−1.20271e14			−0.291032
$839$		−	5.41664e14i		−	1.30293i	−0.758680	−	0.651463i	$-0.774156\pi$
$839$		−	5.41664e14i		−	1.30293i	0.758680	−	0.651463i	$-0.225844\pi$
$840$	9.74312e13	−	5.60211e13i	0.232971	−	0.133954i
$841$	2.62354e14			0.623603
$842$		−	4.28562e14i		−	1.01264i
$843$	−1.79891e14	−	3.12864e14i	−0.422544	−	0.734883i
$844$	2.10408e14			0.491304
$845$			1.42911e14i			0.331728i
$846$	−3.27299e14	+	5.62270e14i	−0.755254	+	1.29746i
$847$	6.85385e13			0.157223
$848$			9.35524e13i			0.213342i
$849$	−5.58173e14	+	3.20939e14i	−1.26541	+	0.727585i
$850$	−1.32858e14			−0.299429
$851$			3.80841e14i			0.853289i
$852$	−1.24584e14	−	2.16676e14i	−0.277502	−	0.482628i
$853$	4.75923e14			1.05388			0.526941	−	0.849902i	$-0.323339\pi$
$853$	4.75923e14			1.05388			0.526941	+	0.849902i	$0.323339\pi$
$854$		−	6.52856e13i		−	0.143724i
$855$	−2.91885e14	−	1.69907e14i	−0.638824	−	0.371862i
$856$	−2.73332e14			−0.594732
$857$			8.19167e14i			1.77202i	0.463667	+	0.886009i	$0.346533\pi$
$857$			8.19167e14i			1.77202i	−0.463667	+	0.886009i	$0.653467\pi$
$858$	1.00226e15	−	5.76281e14i	2.15548	−	1.23936i
$859$	−6.18721e14			−1.32291			−0.661453	−	0.749986i	$-0.730060\pi$
$859$	−6.18721e14			−1.32291			−0.661453	+	0.749986i	$0.730060\pi$
$860$		−	5.91020e14i		−	1.25635i
$861$	4.29600e12	+	7.47156e12i	0.00907922	+	0.0157905i
$862$	1.16574e15			2.44944
$863$			4.64074e14i			0.969468i	0.874662	+	0.484734i	$0.161083\pi$
$863$			4.64074e14i			0.969468i	−0.874662	+	0.484734i	$0.838917\pi$
$864$	3.88783e14	+	2.07477e12i	0.807493	+	0.00430924i
$865$	8.59501e12			0.0177487
$866$		−	1.44660e15i		−	2.97001i
$867$	−7.39508e13	+	4.25203e13i	−0.150955	+	0.0867962i
$868$	−5.17304e14			−1.04990
$869$		−	6.04164e14i		−	1.21915i
$870$	1.12298e14	+	1.95307e14i	0.225307	+	0.391851i
$871$	−1.00846e15			−2.01173
$872$			1.58183e14i			0.313745i
$873$	2.42452e14	−	4.16510e14i	0.478140	−	0.821399i
$874$	−1.54308e15			−3.02574
$875$			2.34354e13i			0.0456911i
$876$	−5.39142e14	+	3.09997e14i	−1.04516	+	0.600947i
$877$	−7.21752e14			−1.39120			−0.695600	−	0.718429i	$-0.744862\pi$
$877$	−7.21752e14			−1.39120			−0.695600	+	0.718429i	$0.744862\pi$
$878$			9.95938e14i			1.90880i
$879$	2.60285e13	+	4.52685e13i	0.0496027	+	0.0862684i
$880$	−6.04216e13			−0.114493
$881$			1.04627e15i			1.97136i	0.168633	+	0.985679i	$0.446065\pi$
$881$			1.04627e15i			1.97136i	−0.168633	+	0.985679i	$0.553935\pi$
$882$	−5.61634e14	−	3.26929e14i	−1.05223	−	0.612507i
$883$	9.92061e14			1.84814			0.924070	−	0.382223i	$-0.124841\pi$
$883$	9.92061e14			1.84814			0.924070	+	0.382223i	$0.124841\pi$
$884$			1.10976e15i			2.05575i
$885$	3.11623e13	−	1.79177e13i	0.0574001	−	0.0330040i
$886$	−7.88341e14			−1.44393
$887$			6.08007e14i			1.10736i	0.832728	+	0.553682i	$0.186778\pi$
$887$			6.08007e14i			1.10736i	−0.832728	+	0.553682i	$0.813222\pi$
$888$	−2.48612e14	−	4.32382e14i	−0.450253	−	0.783075i
$889$	−1.24412e14			−0.224054
$890$			4.20232e14i			0.752557i
$891$	5.58412e14	−	3.17123e14i	0.994412	−	0.564728i
$892$	3.04259e14			0.538790
$893$		−	8.55340e14i		−	1.50620i
$894$	1.13975e15	−	6.55334e14i	1.99582	−	1.14756i
$895$	−4.16910e14			−0.725984
$896$		−	5.17111e14i		−	0.895455i
$897$	4.24502e14	+	7.38288e14i	0.731000	+	1.27135i
$898$	−8.18397e14			−1.40147
$899$		−	4.31980e14i		−	0.735640i
$900$	1.01835e14	−	1.74943e14i	0.172458	−	0.296267i
$901$	5.14231e14			0.866032
$902$		−	4.01088e13i		−	0.0671749i
$903$	4.35790e14	−	2.50571e14i	0.725836	−	0.417342i
$904$	3.66585e14			0.607201
$905$			6.48913e13i			0.106892i
$906$	−4.38457e14	−	7.62560e14i	−0.718268	−	1.24920i
$907$	7.23803e14			1.17919			0.589595	−	0.807699i	$-0.299287\pi$
$907$	7.23803e14			1.17919			0.589595	+	0.807699i	$0.299287\pi$
$908$		−	4.68881e14i		−	0.759685i
$909$	2.86595e14	+	1.66828e14i	0.461795	+	0.268812i
$910$	3.09964e14			0.496711
$911$		−	1.03516e15i		−	1.64975i	−0.565317	−	0.824873i	$-0.691246\pi$
$911$		−	1.03516e15i		−	1.64975i	0.565317	−	0.824873i	$-0.308754\pi$
$912$	2.02385e14	−	1.16368e14i	0.320778	−	0.184441i
$913$	−1.25478e15			−1.97795
$914$		−	6.80625e14i		−	1.06703i
$915$	−2.44165e13	−	4.24650e13i	−0.0380696	−	0.0662102i
$916$	9.55787e14			1.48212
$917$			8.15698e12i			0.0125801i
$918$	−5.20873e12	+	9.76047e14i	−0.00798948	+	1.49712i
$919$	8.05335e14			1.22857			0.614284	−	0.789085i	$-0.289445\pi$
$919$	8.05335e14			1.22857			0.614284	+	0.789085i	$0.289445\pi$
$920$		−	3.85276e14i		−	0.584564i
$921$	3.75695e14	−	2.16018e14i	0.566941	−	0.325980i
$922$	1.22140e15			1.83317
$923$		−	2.87158e14i		−	0.428660i
$924$	−3.36171e14	−	5.84665e14i	−0.499115	−	0.868055i
$925$	1.04002e14			0.153579
$926$			7.25524e14i			1.06561i
$927$	−1.15931e14	+	1.99159e14i	−0.169357	+	0.290939i
$928$	3.40964e14			0.495414
$929$			1.30557e15i			1.88678i	0.331686	+	0.943390i	$0.392382\pi$
$929$			1.30557e15i			1.88678i	−0.331686	+	0.943390i	$0.607618\pi$
$930$	−5.32789e14	+	3.06343e14i	−0.765844	+	0.440346i
$931$	8.54373e14			1.22152
$932$			6.46205e14i			0.918947i
$933$	1.97230e14	+	3.43020e14i	0.278975	+	0.485189i
$934$	6.07486e14			0.854676
$935$			3.32120e14i			0.464769i
$936$	−9.63903e14	−	5.61092e14i	−1.34170	−	0.781006i
$937$	−5.31650e14			−0.736085			−0.368043	−	0.929809i	$-0.619972\pi$
$937$	−5.31650e14			−0.736085			−0.368043	+	0.929809i	$0.619972\pi$
$938$			9.31499e14i			1.28283i
$939$	7.70639e14	−	4.43102e14i	1.05566	−	0.606983i
$940$	5.12653e14			0.698528
$941$		−	6.64570e14i		−	0.900726i	−0.892846	−	0.450363i	$-0.851295\pi$
$941$		−	6.64570e14i		−	0.900726i	0.892846	−	0.450363i	$-0.148705\pi$
$942$	1.08097e14	+	1.88001e14i	0.145733	+	0.253458i
$943$	2.95450e13			0.0396211
$944$			2.48473e13i			0.0331451i
$945$	1.72169e14	+	9.18789e11i	0.228452	+	0.00121915i
$946$	−2.33941e15			−3.08781
$947$		−	7.04459e14i		−	0.924923i	−0.886639	−	0.462462i	$-0.846966\pi$
$947$		−	7.04459e14i		−	0.924923i	0.886639	−	0.462462i	$-0.153034\pi$
$948$	−1.21290e15	+	6.97396e14i	−1.58411	+	0.910831i
$949$	−7.14520e14			−0.928290
$950$			4.21392e14i			0.544588i
$951$	−2.92604e14	−	5.08894e14i	−0.376165	−	0.654221i
$952$	4.27023e14			0.546093
$953$			1.81791e14i			0.231264i	0.993292	+	0.115632i	$0.0368893\pi$
$953$			1.81791e14i			0.231264i	−0.993292	+	0.115632i	$0.963111\pi$
$954$	−6.24112e14	+	1.07217e15i	−0.789806	+	1.35681i
$955$	−4.50859e14			−0.567575
$956$		−	1.24787e15i		−	1.56271i
$957$	4.88230e14	−	2.80723e14i	0.608226	−	0.349718i
$958$	−1.75850e15			−2.17929
$959$			5.20286e14i			0.641430i
$960$	−2.82489e14	−	4.91302e14i	−0.346454	−	0.602549i
$961$	3.58795e14			0.437753
$962$		−	1.37556e15i		−	1.66957i
$963$	−3.61879e14	−	2.10651e14i	−0.436950	−	0.254350i
$964$	1.20079e14			0.144239
$965$			3.96639e14i			0.473979i
$966$	6.81943e14	−	3.92104e14i	0.810704	−	0.466140i
$967$	1.16026e14			0.137221			0.0686107	−	0.997644i	$-0.478143\pi$
$967$	1.16026e14			0.137221			0.0686107	+	0.997644i	$0.478143\pi$
$968$			3.07703e14i			0.362039i
$969$	−6.39639e14	−	1.11245e15i	−0.748715	−	1.30216i
$970$	−6.01313e14			−0.700232
$971$			9.14338e14i			1.05928i	0.848223	+	0.529640i	$0.177673\pi$
$971$			9.14338e14i			1.05928i	−0.848223	+	0.529640i	$0.822327\pi$
$972$	−1.28123e15	−	7.54992e14i	−1.47671	−	0.870184i
$973$	4.80326e14			0.550772
$974$			1.53725e15i			1.75368i
$975$	2.01615e14	−	1.15925e14i	0.228824	−	0.131569i
$976$	3.38595e13			0.0382324
$977$			6.57398e14i			0.738509i	0.929328	+	0.369254i	$0.120387\pi$
$977$			6.57398e14i			0.738509i	−0.929328	+	0.369254i	$0.879613\pi$
$978$	4.33597e14	+	7.54107e14i	0.484610	+	0.842827i
$979$	1.05050e15			1.16811
$980$			5.12074e14i			0.566503i
$981$	−1.21908e14	+	2.09427e14i	−0.134180	+	0.230509i
$982$	9.51815e14			1.04231
$983$			7.31629e13i			0.0797120i	0.999205	+	0.0398560i	$0.0126899\pi$
$983$			7.31629e13i			0.0797120i	−0.999205	+	0.0398560i	$0.987310\pi$
$984$	−3.35435e13	+	1.92869e13i	−0.0363608	+	0.0209068i
$985$	−2.27387e13			−0.0245236
$986$			8.55995e14i			0.918515i
$987$	2.17346e14	+	3.78006e14i	0.232042	+	0.403564i
$988$	3.51989e15			3.73891
$989$		−	1.72326e15i		−	1.82125i
$990$	−6.92468e14	−	4.03088e14i	−0.728154	−	0.423861i
$991$	−1.59368e15			−1.66737			−0.833687	−	0.552237i	$-0.813774\pi$
$991$	−1.59368e15			−1.66737			−0.833687	+	0.552237i	$0.813774\pi$
$992$			9.30135e14i			0.968250i
$993$	−9.74427e14	+	5.60277e14i	−1.00926	+	0.580305i
$994$	−2.65243e14			−0.273346
$995$		−	6.28438e14i		−	0.644387i
$996$	1.44841e15	+	2.51907e15i	1.47773	+	2.57006i
$997$	−1.04837e15			−1.06423			−0.532117	−	0.846671i	$-0.678603\pi$
$997$	−1.04837e15			−1.06423			−0.532117	+	0.846671i	$0.678603\pi$
$998$		−	3.56269e14i		−	0.359853i
$999$	4.07742e12	−	7.64054e14i	0.00409787	−	0.767886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.c.a.11.13	yes	14
3.2	odd	2	inner	15.11.c.a.11.2	✓	14
4.3	odd	2		240.11.l.b.161.11		14
5.2	odd	4		75.11.d.d.74.4		28
5.3	odd	4		75.11.d.d.74.25		28
5.4	even	2		75.11.c.g.26.2		14
12.11	even	2		240.11.l.b.161.12		14
15.2	even	4		75.11.d.d.74.26		28
15.8	even	4		75.11.d.d.74.3		28
15.14	odd	2		75.11.c.g.26.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.c.a.11.2	✓	14	3.2	odd	2	inner
15.11.c.a.11.13	yes	14	1.1	even	1	trivial
75.11.c.g.26.2		14	5.4	even	2
75.11.c.g.26.13		14	15.14	odd	2
75.11.d.d.74.3		28	15.8	even	4
75.11.d.d.74.4		28	5.2	odd	4
75.11.d.d.74.25		28	5.3	odd	4
75.11.d.d.74.26		28	15.2	even	4
240.11.l.b.161.11		14	4.3	odd	2
240.11.l.b.161.12		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+52.7178i q^{2} +(-210.660 + 121.125i) q^{3} -1755.17 q^{4} +1397.54i q^{5} +(-6385.47 - 11105.5i) q^{6} -8585.72 q^{7} -38545.6i q^{8} +(29706.2 - 51032.6i) q^{9} +O(q^{10})\)	\(q+52.7178i q^{2} +(-210.660 + 121.125i) q^{3} -1755.17 q^{4} +1397.54i q^{5} +(-6385.47 - 11105.5i) q^{6} -8585.72 q^{7} -38545.6i q^{8} +(29706.2 - 51032.6i) q^{9} -73675.4 q^{10} +184175. i q^{11} +(369744. - 212595. i) q^{12} +490018. q^{13} -452620. i q^{14} +(-169278. - 294406. i) q^{15} +234746. q^{16} -1.29033e6i q^{17} +(2.69033e6 + 1.56605e6i) q^{18} -4.09260e6 q^{19} -2.45292e6i q^{20} +(1.80867e6 - 1.03995e6i) q^{21} -9.70928e6 q^{22} -7.15208e6i q^{23} +(4.66885e6 + 8.12001e6i) q^{24} -1.95312e6 q^{25} +2.58327e7i q^{26} +(-76572.7 + 1.43487e7i) q^{27} +1.50694e7 q^{28} +1.25838e7i q^{29} +(1.55205e7 - 8.92396e6i) q^{30} -3.43282e7 q^{31} -2.70954e7i q^{32} +(-2.23082e7 - 3.87982e7i) q^{33} +6.80234e7 q^{34} -1.19989e7i q^{35} +(-5.21394e7 + 8.95707e7i) q^{36} -5.32490e7 q^{37} -2.15753e8i q^{38} +(-1.03227e8 + 5.93536e7i) q^{39} +5.38690e7 q^{40} +4.13097e6i q^{41} +(5.48238e7 + 9.53490e7i) q^{42} +2.40945e8 q^{43} -3.23257e8i q^{44} +(7.13202e7 + 4.15157e7i) q^{45} +3.77042e8 q^{46} +2.08997e8i q^{47} +(-4.94515e7 + 2.84337e7i) q^{48} -2.08761e8 q^{49} -1.02964e8i q^{50} +(1.56292e8 + 2.71821e8i) q^{51} -8.60063e8 q^{52} +3.98526e8i q^{53} +(-7.56432e8 - 4.03675e6i) q^{54} -2.57392e8 q^{55} +3.30941e8i q^{56} +(8.62146e8 - 4.95718e8i) q^{57} -6.63392e8 q^{58} +1.05848e8i q^{59} +(2.97111e8 + 5.16732e8i) q^{60} +1.44239e8 q^{61} -1.80971e9i q^{62} +(-2.55049e8 + 4.38151e8i) q^{63} +1.66879e9 q^{64} +6.84821e8i q^{65} +(2.04536e9 - 1.17604e9i) q^{66} -2.05801e9 q^{67} +2.26474e9i q^{68} +(8.66299e8 + 1.50666e9i) q^{69} +6.32556e8 q^{70} -5.86016e8i q^{71} +(-1.96708e9 - 1.14504e9i) q^{72} -1.45815e9 q^{73} -2.80717e9i q^{74} +(4.11445e8 - 2.36573e8i) q^{75} +7.18319e9 q^{76} -1.58127e9i q^{77} +(-3.12899e9 - 5.44191e9i) q^{78} -3.28039e9 q^{79} +3.28067e8i q^{80} +(-1.72186e9 - 3.03197e9i) q^{81} -2.17776e8 q^{82} +6.81301e9i q^{83} +(-3.17451e9 + 1.82529e9i) q^{84} +1.80329e9 q^{85} +1.27021e10i q^{86} +(-1.52422e9 - 2.65091e9i) q^{87} +7.09911e9 q^{88} -5.70384e9i q^{89} +(-2.18862e9 + 3.75984e9i) q^{90} -4.20715e9 q^{91} +1.25531e10i q^{92} +(7.23157e9 - 4.15802e9i) q^{93} -1.10179e10 q^{94} -5.71958e9i q^{95} +(3.28194e9 + 5.70791e9i) q^{96} +8.16165e9 q^{97} -1.10054e10i q^{98} +(9.39890e9 + 5.47113e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more