LMFDB - Embedded newform 6.25.b.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,25,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 25, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 25);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	6.b (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:	$21.8980291355$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9921984x^{6} + 31297402621425x^{4} + 35629505313218665424x^{2} + 11190322069687119538557504 $ x^8 + 9921984x^6 + 31297402621425x^4 + 35629505313218665424*x^2 + 11190322069687119538557504
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{53}\cdot 3^{32}\cdot 17^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.8
Root			$-1246.64i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.25.b.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2896.31i q^{2} +(473275. - 241744. i) q^{3} -8.38861e6 q^{4} -7.85820e7i q^{5} +(7.00165e8 + 1.37075e9i) q^{6} +2.19870e9 q^{7} -2.42960e10i q^{8} +(1.65549e11 - 2.28823e11i) q^{9} +O(q^{10})$	\(q+2896.31i q^{2} +(473275. - 241744. i) q^{3} -8.38861e6 q^{4} -7.85820e7i q^{5} +(7.00165e8 + 1.37075e9i) q^{6} +2.19870e9 q^{7} -2.42960e10i q^{8} +(1.65549e11 - 2.28823e11i) q^{9} +2.27598e11 q^{10} -1.55920e12i q^{11} +(-3.97012e12 + 2.02789e12i) q^{12} -3.72207e13 q^{13} +6.36811e12i q^{14} +(-1.89967e13 - 3.71909e13i) q^{15} +7.03687e13 q^{16} -6.73556e14i q^{17} +(6.62742e14 + 4.79482e14i) q^{18} +9.37274e14 q^{19} +6.59193e14i q^{20} +(1.04059e15 - 5.31522e14i) q^{21} +4.51594e15 q^{22} -3.13424e16i q^{23} +(-5.87341e15 - 1.14987e16i) q^{24} +5.34295e16 q^{25} -1.07803e17i q^{26} +(2.30339e16 - 1.48317e17i) q^{27} -1.84440e16 q^{28} -2.21159e17i q^{29} +(1.07716e17 - 5.50203e16i) q^{30} +6.76426e17 q^{31} +2.03810e17i q^{32} +(-3.76928e17 - 7.37933e17i) q^{33} +1.95083e18 q^{34} -1.72778e17i q^{35} +(-1.38873e18 + 1.91950e18i) q^{36} -4.23578e18 q^{37} +2.71464e18i q^{38} +(-1.76157e19 + 8.99789e18i) q^{39} -1.90923e18 q^{40} +2.43094e19i q^{41} +(1.53945e18 + 3.01387e18i) q^{42} +2.27505e19 q^{43} +1.30796e19i q^{44} +(-1.79813e19 - 1.30092e19i) q^{45} +9.07774e19 q^{46} -6.93806e19i q^{47} +(3.33038e19 - 1.70112e19i) q^{48} -1.86747e20 q^{49} +1.54748e20i q^{50} +(-1.62828e20 - 3.18777e20i) q^{51} +3.12230e20 q^{52} -8.43863e20i q^{53} +(4.29571e20 + 6.67133e19i) q^{54} -1.22525e20 q^{55} -5.34196e19i q^{56} +(4.43589e20 - 2.26580e20i) q^{57} +6.40546e20 q^{58} +2.79071e21i q^{59} +(1.59356e20 + 3.11980e20i) q^{60} -4.56793e21 q^{61} +1.95914e21i q^{62} +(3.63993e20 - 5.03112e20i) q^{63} -5.90296e20 q^{64} +2.92488e21i q^{65} +(2.13728e21 - 1.09170e21i) q^{66} -1.20142e21 q^{67} +5.65019e21i q^{68} +(-7.57684e21 - 1.48336e22i) q^{69} +5.00419e20 q^{70} +1.60117e22i q^{71} +(-5.55948e21 - 4.02219e21i) q^{72} +2.60444e22 q^{73} -1.22681e22i q^{74} +(2.52869e22 - 1.29163e22i) q^{75} -7.86242e21 q^{76} -3.42822e21i q^{77} +(-2.60607e22 - 5.10204e22i) q^{78} +8.00431e22 q^{79} -5.52971e21i q^{80} +(-2.49533e22 - 7.57629e22i) q^{81} -7.04077e22 q^{82} +1.65147e23i q^{83} +(-8.72910e21 + 4.45873e21i) q^{84} -5.29293e22 q^{85} +6.58923e22i q^{86} +(-5.34639e22 - 1.04669e23i) q^{87} -3.78824e22 q^{88} +4.33073e23i q^{89} +(3.76786e22 - 5.20795e22i) q^{90} -8.18372e22 q^{91} +2.62919e23i q^{92} +(3.20136e23 - 1.63522e23i) q^{93} +2.00948e23 q^{94} -7.36528e22i q^{95} +(4.92697e22 + 9.64581e22i) q^{96} -4.08706e23 q^{97} -5.40877e23i q^{98} +(-3.56782e23 - 2.58125e23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9}+O(q^{10}) $ 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9	$ 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 36\!\cdots\!36 q^{21}+ \cdots + 69\!\cdots\!44 q^{99}+O(q^{100}) $ 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9 - 1863369424896 * q^10 + 1106289623040 * q^12 + 50568363679120 * q^13 - 348034956760512 * q^15 + 562949953421312 * q^16 - 514738292981760 * q^18 - 978083631341264 * q^19 + 3640012304241936 * q^21 - 336450979430400 * q^22 - 282849366245376 * q^24 + 7630618767014024 * q^25 - 86594528606057640 * q^27 + 85234923203461120 * q^28 - 725410188900237312 * q^30 + 3092119786822709104 * q^31 - 8158685952668529600 * q^33 + 3821138032531341312 * q^34 - 2476057486864416768 * q^36 + 22590293223992782480 * q^37 - 40190176581881465040 * q^39 + 15631075664637984768 * q^40 - 79119883835565342720 * q^42 + 226487466371803896880 * q^43 - 347709996757177504128 * q^45 + 139842130561120468992 * q^46 - 9280229982150328320 * q^48 + 104686700473616731800 * q^49 + 558091874936566543104 * q^51 - 424198180105575464960 * q^52 + 334066775626796728320 * q^54 - 2212687664250467338368 * q^55 + 3588879995640760725840 * q^57 - 1867706355469718323200 * q^58 + 2919528822560885047296 * q^60 - 6507010783838092385648 * q^61 + 10112982777612899380080 * q^63 - 4722366482869645213696 * q^64 - 1924112442339530440704 * q^66 - 7042120118150060144720 * q^67 - 4323335967368731345536 * q^69 + 16481910236435553583104 * q^70 + 4317937762413135790080 * q^72 + 36259820324758576687120 * q^73 - 108081978448612908655272 * q^75 + 8204760174538377920512 * q^76 - 74188898027329578270720 * q^78 + 316807052777330015315824 * q^79 - 268518660504396776813304 * q^81 + 83114941529654645882880 * q^82 - 30534636335462338265088 * q^84 - 222512862545524200678912 * q^85 + 449461577201807342128320 * q^87 + 2822355377657688883200 * q^88 + 612683975543382025371648 * q^90 - 1196839602335690774367520 * q^91 + 873237537450828783745680 * q^93 - 1298887117621773403422720 * q^94 + 2372712456480891076608 * q^96 + 816517576248201265716880 * q^97 + 695858883367208922313344 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$			2896.31i			0.707107i
$2$			2896.31i			0.707107i
$3$	473275.	−	241744.i	0.890551	−	0.454884i
$3$	473275.	−	241744.i	0.890551	−	0.454884i
$4$	−8.38861e6			−0.500000
$5$		−	7.85820e7i		−	0.321872i	−0.986965	−	0.160936i	$-0.948549\pi$
$5$		−	7.85820e7i		−	0.321872i	0.986965	−	0.160936i	$-0.0514512\pi$
$6$	7.00165e8	+	1.37075e9i	0.321651	+	0.629715i
$7$	2.19870e9			0.158851			0.0794254	−	0.996841i	$-0.474691\pi$
$7$	2.19870e9			0.158851			0.0794254	+	0.996841i	$0.474691\pi$
$8$		−	2.42960e10i		−	0.353553i
$9$	1.65549e11	−	2.28823e11i	0.586162	−	0.810194i
$10$	2.27598e11			0.227598
$11$		−	1.55920e12i		−	0.496811i	−0.968656	−	0.248405i	$-0.920094\pi$
$11$		−	1.55920e12i		−	0.496811i	0.968656	−	0.248405i	$-0.0799065\pi$
$12$	−3.97012e12	+	2.02789e12i	−0.445275	+	0.227442i
$13$	−3.72207e13			−1.59759			−0.798794	−	0.601605i	$-0.794528\pi$
$13$	−3.72207e13			−1.59759			−0.798794	+	0.601605i	$0.794528\pi$
$14$			6.36811e12i			0.112324i
$15$	−1.89967e13	−	3.71909e13i	−0.146414	−	0.286643i
$16$	7.03687e13			0.250000
$17$		−	6.73556e14i		−	1.15608i	−0.816010	−	0.578038i	$-0.803819\pi$
$17$		−	6.73556e14i		−	1.15608i	0.816010	−	0.578038i	$-0.196181\pi$
$18$	6.62742e14	+	4.79482e14i	0.572894	+	0.414479i
$19$	9.37274e14			0.423471			0.211735	−	0.977327i	$-0.432089\pi$
$19$	9.37274e14			0.423471			0.211735	+	0.977327i	$0.432089\pi$
$20$			6.59193e14i			0.160936i
$21$	1.04059e15	−	5.31522e14i	0.141465	−	0.0722586i
$22$	4.51594e15			0.351298
$23$		−	3.13424e16i		−	1.43021i	−0.699019	−	0.715103i	$-0.746380\pi$
$23$		−	3.13424e16i		−	1.43021i	0.699019	−	0.715103i	$-0.253620\pi$
$24$	−5.87341e15	−	1.14987e16i	−0.160826	−	0.314857i
$25$	5.34295e16			0.896399
$26$		−	1.07803e17i		−	1.12967i
$27$	2.30339e16	−	1.48317e17i	0.153462	−	0.988154i
$28$	−1.84440e16			−0.0794254
$29$		−	2.21159e17i		−	0.625071i	−0.949906	−	0.312535i	$-0.898822\pi$
$29$		−	2.21159e17i		−	0.625071i	0.949906	−	0.312535i	$-0.101178\pi$
$30$	1.07716e17	−	5.50203e16i	0.202687	−	0.103530i
$31$	6.76426e17			0.858776			0.429388	−	0.903120i	$-0.358729\pi$
$31$	6.76426e17			0.858776			0.429388	+	0.903120i	$0.358729\pi$
$32$			2.03810e17i			0.176777i
$33$	−3.76928e17	−	7.37933e17i	−0.225991	−	0.442435i
$34$	1.95083e18			0.817469
$35$		−	1.72778e17i		−	0.0511296i
$36$	−1.38873e18	+	1.91950e18i	−0.293081	+	0.405097i
$37$	−4.23578e18			−0.643448			−0.321724	−	0.946834i	$-0.604262\pi$
$37$	−4.23578e18			−0.643448			−0.321724	+	0.946834i	$0.604262\pi$
$38$			2.71464e18i			0.299439i
$39$	−1.76157e19	+	8.99789e18i	−1.42273	+	0.726717i
$40$	−1.90923e18			−0.113799
$41$			2.43094e19i			1.07738i	0.842504	+	0.538690i	$0.181081\pi$
$41$			2.43094e19i			1.07738i	−0.842504	+	0.538690i	$0.818919\pi$
$42$	1.53945e18	+	3.01387e18i	0.0510946	+	0.100031i
$43$	2.27505e19			0.569336			0.284668	−	0.958626i	$-0.408117\pi$
$43$	2.27505e19			0.569336			0.284668	+	0.958626i	$0.408117\pi$
$44$			1.30796e19i			0.248405i
$45$	−1.79813e19	−	1.30092e19i	−0.260779	−	0.188669i
$46$	9.07774e19			1.01131
$47$		−	6.93806e19i		−	0.597123i	−0.954390	−	0.298561i	$-0.903493\pi$
$47$		−	6.93806e19i		−	0.597123i	0.954390	−	0.298561i	$-0.0965068\pi$
$48$	3.33038e19	−	1.70112e19i	0.222638	−	0.113721i
$49$	−1.86747e20			−0.974766
$50$			1.54748e20i			0.633850i
$51$	−1.62828e20	−	3.18777e20i	−0.525880	−	1.02954i
$52$	3.12230e20			0.798794
$53$		−	8.43863e20i		−	1.71776i	−0.512180	−	0.858878i	$-0.671162\pi$
$53$		−	8.43863e20i		−	1.71776i	0.512180	−	0.858878i	$-0.328838\pi$
$54$	4.29571e20	+	6.67133e19i	0.698731	+	0.108514i
$55$	−1.22525e20			−0.159909
$56$		−	5.34196e19i		−	0.0561622i
$57$	4.43589e20	−	2.26580e20i	0.377122	−	0.192630i
$58$	6.40546e20			0.441992
$59$			2.79071e21i			1.56852i	0.620432	+	0.784260i	$0.286957\pi$
$59$			2.79071e21i			1.56852i	−0.620432	+	0.784260i	$0.713043\pi$
$60$	1.59356e20	+	3.11980e20i	0.0732071	+	0.143322i
$61$	−4.56793e21			−1.72092			−0.860461	−	0.509517i	$-0.829824\pi$
$61$	−4.56793e21			−1.72092			−0.860461	+	0.509517i	$0.829824\pi$
$62$			1.95914e21i			0.607246i
$63$	3.63993e20	−	5.03112e20i	0.0931122	−	0.128700i
$64$	−5.90296e20			−0.125000
$65$			2.92488e21i			0.514218i
$66$	2.13728e21	−	1.09170e21i	0.312849	−	0.159800i
$67$	−1.20142e21			−0.146824			−0.0734118	−	0.997302i	$-0.523389\pi$
$67$	−1.20142e21			−0.146824			−0.0734118	+	0.997302i	$0.523389\pi$
$68$			5.65019e21i			0.578038i
$69$	−7.57684e21	−	1.48336e22i	−0.650577	−	1.27367i
$70$	5.00419e20			0.0361541
$71$			1.60117e22i			0.975748i	0.872914	+	0.487874i	$0.162227\pi$
$71$			1.60117e22i			0.975748i	−0.872914	+	0.487874i	$0.837773\pi$
$72$	−5.55948e21	−	4.02219e21i	−0.286447	−	0.207239i
$73$	2.60444e22			1.13721			0.568605	−	0.822611i	$-0.307483\pi$
$73$	2.60444e22			1.13721			0.568605	+	0.822611i	$0.307483\pi$
$74$		−	1.22681e22i		−	0.454986i
$75$	2.52869e22	−	1.29163e22i	0.798289	−	0.407757i
$76$	−7.86242e21			−0.211735
$77$		−	3.42822e21i		−	0.0789187i
$78$	−2.60607e22	−	5.10204e22i	−0.513866	−	1.00602i
$79$	8.00431e22			1.35456			0.677281	−	0.735725i	$-0.263158\pi$
$79$	8.00431e22			1.35456			0.677281	+	0.735725i	$0.263158\pi$
$80$		−	5.52971e21i		−	0.0804679i
$81$	−2.49533e22	−	7.57629e22i	−0.312829	−	0.949809i
$82$	−7.04077e22			−0.761823
$83$			1.65147e23i			1.54502i	0.635002	+	0.772511i	$0.280999\pi$
$83$			1.65147e23i			1.54502i	−0.635002	+	0.772511i	$0.719001\pi$
$84$	−8.72910e21	+	4.45873e21i	−0.0707323	+	0.0361293i
$85$	−5.29293e22			−0.372108
$86$			6.58923e22i			0.402581i
$87$	−5.34639e22	−	1.04669e23i	−0.284335	−	0.556657i
$88$	−3.78824e22			−0.175649
$89$			4.33073e23i			1.75340i	0.481038	+	0.876700i	$0.340260\pi$
$89$			4.33073e23i			1.75340i	−0.481038	+	0.876700i	$0.659740\pi$
$90$	3.76786e22	−	5.20795e22i	0.133409	−	0.184398i
$91$	−8.18372e22			−0.253778
$92$			2.62919e23i			0.715103i
$93$	3.20136e23	−	1.63522e23i	0.764784	−	0.390643i
$94$	2.00948e23			0.422230
$95$		−	7.36528e22i		−	0.136303i
$96$	4.92697e22	+	9.64581e22i	0.0804128	+	0.157429i
$97$	−4.08706e23			−0.589048			−0.294524	−	0.955644i	$-0.595161\pi$
$97$	−4.08706e23			−0.589048			−0.294524	+	0.955644i	$0.595161\pi$
$98$		−	5.40877e23i		−	0.689264i
$99$	−3.56782e23	−	2.58125e23i	−0.402513	−	0.291211i
$100$	−4.48199e23			−0.448199
$101$		−	8.79558e23i		−	0.780563i	−0.920696	−	0.390281i	$-0.872378\pi$
$101$		−	8.79558e23i		−	0.780563i	0.920696	−	0.390281i	$-0.127622\pi$
$102$	9.23277e23	−	4.71600e23i	0.727998	−	0.371853i
$103$	−4.26954e23			−0.299457			−0.149728	−	0.988727i	$-0.547840\pi$
$103$	−4.26954e23			−0.299457			−0.149728	+	0.988727i	$0.547840\pi$
$104$			9.04315e23i			0.564833i
$105$	−4.17680e22	−	8.17716e22i	−0.0232580	−	0.0455335i
$106$	2.44409e24			1.21464
$107$		−	3.07226e24i		−	1.36412i	−0.731297	−	0.682059i	$-0.761085\pi$
$107$		−	3.07226e24i		−	1.36412i	0.731297	−	0.682059i	$-0.238915\pi$
$108$	−1.93222e23	+	1.24417e24i	−0.0767312	+	0.494077i
$109$	2.05754e24			0.731527			0.365763	−	0.930708i	$-0.380808\pi$
$109$	2.05754e24			0.731527			0.365763	+	0.930708i	$0.380808\pi$
$110$		−	3.54871e23i		−	0.113073i
$111$	−2.00469e24	+	1.02397e24i	−0.573023	+	0.292694i
$112$	1.54720e23			0.0397127
$113$			2.56925e24i			0.592742i	0.955073	+	0.296371i	$0.0957764\pi$
$113$			2.56925e24i			0.592742i	−0.955073	+	0.296371i	$0.904224\pi$
$114$	6.56247e23	+	1.28477e24i	0.136210	+	0.266666i
$115$	−2.46295e24			−0.460343
$116$			1.85522e24i			0.312535i
$117$	−6.16187e24	+	8.51695e24i	−0.936445	+	1.29436i
$118$	−8.08275e24			−1.10911
$119$		−	1.48095e24i		−	0.183644i
$120$	−9.03590e23	+	4.61544e23i	−0.101344	+	0.0517652i
$121$	7.41861e24			0.753179
$122$		−	1.32301e25i		−	1.21688i
$123$	5.87666e24	+	1.15051e25i	0.490083	+	0.959461i
$124$	−5.67427e24			−0.429388
$125$		−	8.88245e24i		−	0.610397i
$126$	1.45717e24	+	1.05424e24i	0.0910046	+	0.0658403i
$127$	1.69658e25			0.963673			0.481836	−	0.876261i	$-0.339970\pi$
$127$	1.69658e25			0.963673			0.481836	+	0.876261i	$0.339970\pi$
$128$		−	1.70968e24i		−	0.0883883i
$129$	1.07672e25	−	5.49978e24i	0.507023	−	0.258982i
$130$	−8.47135e24			−0.363607
$131$		−	1.19460e25i		−	0.467701i	−0.972273	−	0.233851i	$-0.924867\pi$
$131$		−	1.19460e25i		−	0.467701i	0.972273	−	0.233851i	$-0.0751326\pi$
$132$	3.16190e24	+	6.19023e24i	0.112996	+	0.221218i
$133$	2.06078e24			0.0672686
$134$		−	3.47967e24i		−	0.103820i
$135$	−1.16550e25	−	1.81005e24i	−0.318059	−	0.0493952i
$136$	−1.63647e25			−0.408735
$137$		−	2.33983e25i		−	0.535226i	−0.963527	−	0.267613i	$-0.913765\pi$
$137$		−	2.33983e25i		−	0.535226i	0.963527	−	0.267613i	$-0.0862348\pi$
$138$	4.29627e25	−	2.19449e25i	0.900622	−	0.460028i
$139$	1.59193e25			0.306018			0.153009	−	0.988225i	$-0.451104\pi$
$139$	1.59193e25			0.306018			0.153009	+	0.988225i	$0.451104\pi$
$140$			1.44937e24i			0.0255648i
$141$	−1.67723e25	−	3.28361e25i	−0.271621	−	0.531768i
$142$	−4.63749e25			−0.689958
$143$			5.80348e25i			0.793699i
$144$	1.16495e25	−	1.61020e25i	0.146540	−	0.202549i
$145$	−1.73791e25			−0.201193
$146$			7.54328e25i			0.804129i
$147$	−8.83827e25	+	4.51449e25i	−0.868079	+	0.443405i
$148$	3.55323e25			0.321724
$149$			1.86675e26i			1.55901i	0.626393	+	0.779507i	$0.284531\pi$
$149$			1.86675e26i			1.55901i	−0.626393	+	0.779507i	$0.715469\pi$
$150$	3.74095e25	+	7.32386e25i	0.288328	+	0.564475i
$151$	1.57212e24			0.0111883			0.00559414	−	0.999984i	$-0.498219\pi$
$151$	1.57212e24			0.0111883			0.00559414	+	0.999984i	$0.498219\pi$
$152$		−	2.27720e25i		−	0.149720i
$153$	−1.54125e26	−	1.11507e26i	−0.936646	−	0.677647i
$154$	9.92919e24			0.0558040
$155$		−	5.31549e25i		−	0.276416i
$156$	1.47771e26	−	7.54797e25i	0.711367	−	0.363358i
$157$	2.61155e26			1.16440			0.582199	−	0.813046i	$-0.302192\pi$
$157$	2.61155e26			1.16440			0.582199	+	0.813046i	$0.302192\pi$
$158$			2.31830e26i			0.957820i
$159$	−2.03999e26	−	3.99379e26i	−0.781379	−	1.52975i
$160$	1.60158e25			0.0568994
$161$		−	6.89125e25i		−	0.227189i
$162$	2.19433e26	−	7.22724e25i	0.671617	−	0.221204i
$163$	−1.85589e26			−0.527596			−0.263798	−	0.964578i	$-0.584975\pi$
$163$	−1.85589e26			−0.527596			−0.263798	+	0.964578i	$0.584975\pi$
$164$		−	2.03922e26i		−	0.538690i
$165$	−5.79882e25	+	2.96198e25i	−0.142407	+	0.0727401i
$166$	−4.78318e26			−1.09250
$167$		−	4.33404e25i		−	0.0921076i	−0.998939	−	0.0460538i	$-0.985335\pi$
$167$		−	4.33404e25i		−	0.0921076i	0.998939	−	0.0460538i	$-0.0146646\pi$
$168$	−1.29139e25	−	2.52822e25i	−0.0255473	−	0.0500153i
$169$	8.42583e26			1.55229
$170$		−	1.53300e26i		−	0.263120i
$171$	1.55165e26	−	2.14470e26i	0.248222	−	0.343094i
$172$	−1.90845e26			−0.284668
$173$			5.82910e26i			0.811051i	0.914084	+	0.405525i	$0.132911\pi$
$173$			5.82910e26i			0.811051i	−0.914084	+	0.405525i	$0.867089\pi$
$174$	3.03154e26	−	1.54848e26i	0.393616	−	0.201055i
$175$	1.17475e26			0.142394
$176$		−	1.09719e26i		−	0.124203i
$177$	6.74636e26	+	1.32077e27i	0.713494	+	1.39685i
$178$	−1.25431e27			−1.23984
$179$		−	4.62261e26i		−	0.427219i	−0.976919	−	0.213610i	$-0.931478\pi$
$179$		−	4.62261e26i		−	0.427219i	0.976919	−	0.213610i	$-0.0685221\pi$
$180$	1.50838e26	+	1.09129e26i	0.130389	+	0.0943344i
$181$	4.20265e26			0.339923			0.169961	−	0.985451i	$-0.445636\pi$
$181$	4.20265e26			0.339923			0.169961	+	0.985451i	$0.445636\pi$
$182$		−	2.37026e26i		−	0.179448i
$183$	−2.16189e27	+	1.10427e27i	−1.53257	+	0.782819i
$184$	−7.61496e26			−0.505654
$185$			3.32856e26i			0.207108i
$186$	4.73610e26	+	9.27212e26i	0.276226	+	0.540784i
$187$	−1.05021e27			−0.574351
$188$			5.82006e26i			0.298561i
$189$	5.06446e25	−	3.26104e26i	0.0243776	−	0.156969i
$190$	2.13321e26			0.0963809
$191$		−	2.10635e27i		−	0.893571i	−0.894641	−	0.446786i	$-0.852569\pi$
$191$		−	2.10635e27i		−	0.893571i	0.894641	−	0.446786i	$-0.147431\pi$
$192$	−2.79372e26	+	1.42700e26i	−0.111319	+	0.0568605i
$193$	2.28503e27			0.855467			0.427734	−	0.903905i	$-0.359312\pi$
$193$	2.28503e27			0.855467			0.427734	+	0.903905i	$0.359312\pi$
$194$		−	1.18374e27i		−	0.416520i
$195$	7.07071e26	+	1.38427e27i	0.233910	+	0.457938i
$196$	1.56655e27			0.487383
$197$		−	3.36890e27i		−	0.986037i	−0.870019	−	0.493019i	$-0.835893\pi$
$197$		−	3.36890e27i		−	0.986037i	0.870019	−	0.493019i	$-0.164107\pi$
$198$	7.47611e26	−	1.03335e27i	0.205917	−	0.284620i
$199$	1.75228e27			0.454324			0.227162	−	0.973857i	$-0.427055\pi$
$199$	1.75228e27			0.454324			0.227162	+	0.973857i	$0.427055\pi$
$200$		−	1.29812e27i		−	0.316925i
$201$	−5.68600e26	+	2.90435e26i	−0.130754	+	0.0667876i
$202$	2.54747e27			0.551941
$203$		−	4.86263e26i		−	0.0992929i
$204$	1.36590e27	+	2.67410e27i	0.262940	+	0.514772i
$205$	1.91028e27			0.346778
$206$		−	1.23659e27i		−	0.211748i
$207$	−7.17186e27	−	5.18872e27i	−1.15874	−	0.838332i
$208$	−2.61918e27			−0.399397
$209$		−	1.46140e27i		−	0.210385i
$210$	2.36836e26	−	1.20973e26i	0.0321970	−	0.0164459i
$211$	−1.49978e28			−1.92592			−0.962962	−	0.269638i	$-0.913096\pi$
$211$	−1.49978e28			−1.92592			−0.962962	+	0.269638i	$0.913096\pi$
$212$			7.07884e27i			0.858878i
$213$	3.87073e27	+	7.57795e27i	0.443852	+	0.868953i
$214$	8.89821e27			0.964578
$215$		−	1.78778e27i		−	0.183253i
$216$	−3.60350e27	−	5.59632e26i	−0.349365	−	0.0542572i
$217$	1.48726e27			0.136417
$218$			5.95927e27i			0.517268i
$219$	1.23262e28	−	6.29609e27i	1.01274	−	0.517299i
$220$	1.02782e27			0.0799547
$221$			2.50702e28i			1.84693i
$222$	−2.96575e27	−	5.80621e27i	−0.206966	−	0.405188i
$223$	−2.04706e28			−1.35354			−0.676771	−	0.736194i	$-0.736621\pi$
$223$	−2.04706e28			−1.35354			−0.676771	+	0.736194i	$0.736621\pi$
$224$			4.48116e26i			0.0280811i
$225$	8.84522e27	−	1.22259e28i	0.525434	−	0.726257i
$226$	−7.44135e27			−0.419132
$227$			1.50976e28i			0.806485i	0.915093	+	0.403243i	$0.132117\pi$
$227$			1.50976e28i			0.806485i	−0.915093	+	0.403243i	$0.867883\pi$
$228$	−3.72109e27	+	1.90069e27i	−0.188561	+	0.0963150i
$229$	2.46646e28			1.18590			0.592950	−	0.805239i	$-0.297963\pi$
$229$	2.46646e28			1.18590			0.592950	+	0.805239i	$0.297963\pi$
$230$		−	7.13346e27i		−	0.325512i
$231$	−8.28751e26	−	1.62249e27i	−0.0358988	−	0.0702811i
$232$	−5.37329e27			−0.220996
$233$			1.81404e28i			0.708559i	0.935140	+	0.354279i	$0.115274\pi$
$233$			1.81404e28i			0.708559i	−0.935140	+	0.354279i	$0.884726\pi$
$234$	−2.46677e28	−	1.78467e28i	−0.915248	−	0.662166i
$235$	−5.45206e27			−0.192197
$236$		−	2.34101e28i		−	0.784260i
$237$	3.78824e28	−	1.93499e28i	1.20631	−	0.616168i
$238$	4.28928e27			0.129856
$239$		−	6.04731e28i		−	1.74096i	−0.492208	−	0.870478i	$-0.663810\pi$
$239$		−	6.04731e28i		−	1.74096i	0.492208	−	0.870478i	$-0.336190\pi$
$240$	−1.33677e27	−	2.61708e27i	−0.0366036	−	0.0716608i
$241$	3.08193e28			0.802820			0.401410	−	0.915899i	$-0.368520\pi$
$241$	3.08193e28			0.802820			0.401410	+	0.915899i	$0.368520\pi$
$242$			2.14866e28i			0.532578i
$243$	−3.01250e28	−	2.98244e28i	−0.710643	−	0.703553i
$244$	3.83185e28			0.860461
$245$			1.46749e28i			0.313750i
$246$	−3.33222e28	+	1.70206e28i	−0.678442	+	0.346541i
$247$	−3.48860e28			−0.676532
$248$		−	1.64344e28i		−	0.303623i
$249$	3.99234e28	+	7.81601e28i	0.702805	+	1.37592i
$250$	2.57263e28			0.431616
$251$			2.37397e28i			0.379656i	0.981817	+	0.189828i	$0.0607931\pi$
$251$			2.37397e28i			0.379656i	−0.981817	+	0.189828i	$0.939207\pi$
$252$	−3.05339e27	+	4.22041e27i	−0.0465561	+	0.0643500i
$253$	−4.88693e28			−0.710542
$254$			4.91382e28i			0.681419i
$255$	−2.50501e28	+	1.27953e28i	−0.331381	+	0.169266i
$256$	4.95176e27			0.0625000
$257$			1.17021e28i			0.140951i	0.997514	+	0.0704754i	$0.0224516\pi$
$257$			1.17021e28i			0.140951i	−0.997514	+	0.0704754i	$0.977548\pi$
$258$	1.59291e28	+	3.11852e28i	0.183128	+	0.358519i
$259$	−9.31321e27			−0.102212
$260$		−	2.45357e28i		−	0.257109i
$261$	−5.06063e28	−	3.66128e28i	−0.506429	−	0.366392i
$262$	3.45994e28			0.330715
$263$		−	5.43156e28i		−	0.495971i	−0.968764	−	0.247985i	$-0.920232\pi$
$263$		−	5.43156e28i		−	0.495971i	0.968764	−	0.247985i	$-0.0797685\pi$
$264$	−1.79288e28	+	9.15785e27i	−0.156424	+	0.0798999i
$265$	−6.63124e28			−0.552897
$266$			5.96866e27i			0.0475661i
$267$	1.04693e29	+	2.04963e29i	0.797593	+	1.56149i
$268$	1.00782e28			0.0734118
$269$		−	1.47463e29i		−	1.02720i	−0.858028	−	0.513602i	$-0.828311\pi$
$269$		−	1.47463e29i		−	1.02720i	0.858028	−	0.513602i	$-0.171689\pi$
$270$	5.24246e27	−	3.37565e28i	0.0349277	−	0.224902i
$271$	−2.09550e29			−1.33554			−0.667770	−	0.744368i	$-0.732751\pi$
$271$	−2.09550e29			−1.33554			−0.667770	+	0.744368i	$0.732751\pi$
$272$		−	4.73973e28i		−	0.289019i
$273$	−3.87315e28	+	1.97836e28i	−0.226002	+	0.115439i
$274$	6.77686e28			0.378462
$275$		−	8.33076e28i		−	0.445340i
$276$	6.35591e28	+	1.24433e29i	0.325289	+	0.636836i
$277$	8.59896e28			0.421394			0.210697	−	0.977551i	$-0.432427\pi$
$277$	8.59896e28			0.421394			0.210697	+	0.977551i	$0.432427\pi$
$278$			4.61073e28i			0.216388i
$279$	1.11982e29	−	1.54782e29i	0.503381	−	0.695775i
$280$	−4.19782e27			−0.0180770
$281$		−	2.34014e29i		−	0.965530i	−0.875750	−	0.482765i	$-0.839633\pi$
$281$		−	2.34014e29i		−	0.965530i	0.875750	−	0.482765i	$-0.160367\pi$
$282$	9.51035e28	−	4.85779e28i	0.376017	−	0.192065i
$283$	4.67446e29			1.77131			0.885654	−	0.464346i	$-0.153711\pi$
$283$	4.67446e29			1.77131			0.885654	+	0.464346i	$0.153711\pi$
$284$		−	1.34316e29i		−	0.487874i
$285$	−1.78051e28	−	3.48581e28i	−0.0620021	−	0.121385i
$286$	−1.68087e29			−0.561230
$287$			5.34491e28i			0.171143i
$288$	4.66363e28	+	3.37406e28i	0.143223	+	0.103620i
$289$	−1.14229e29			−0.336512
$290$		−	5.03353e28i		−	0.142265i
$291$	−1.93431e29	+	9.88022e28i	−0.524577	+	0.267948i
$292$	−2.18477e29			−0.568605
$293$			3.03480e29i			0.758085i	0.925379	+	0.379043i	$0.123747\pi$
$293$			3.03480e29i			0.758085i	−0.925379	+	0.379043i	$0.876253\pi$
$294$	−1.30754e29	−	2.55984e29i	−0.313535	−	0.613825i
$295$	2.19299e29			0.504862
$296$			1.02913e29i			0.227493i
$297$	−2.31256e29	−	3.59146e28i	−0.490926	−	0.0762418i
$298$	−5.40668e29			−1.10239
$299$			1.16659e30i			2.28488i
$300$	−2.12122e29	+	1.08349e29i	−0.399144	+	0.203879i
$301$	5.00214e28			0.0904394
$302$			4.55336e27i			0.00791131i
$303$	−2.12628e29	−	4.16273e29i	−0.355065	−	0.695131i
$304$	6.59548e28			0.105868
$305$			3.58957e29i			0.553916i
$306$	3.22958e29	−	4.46393e29i	0.479169	−	0.662309i
$307$	9.11333e29			1.30022			0.650110	−	0.759840i	$-0.274723\pi$
$307$	9.11333e29			1.30022			0.650110	+	0.759840i	$0.274723\pi$
$308$			2.87580e28i			0.0394594i
$309$	−2.02067e29	+	1.03213e29i	−0.266681	+	0.136218i
$310$	1.53953e29			0.195455
$311$		−	4.35089e29i		−	0.531439i	−0.964050	−	0.265719i	$-0.914391\pi$
$311$		−	4.35089e29i		−	0.531439i	0.964050	−	0.265719i	$-0.0856095\pi$
$312$	2.18613e29	+	4.27990e29i	0.256933	+	0.503012i
$313$	2.73884e29			0.309767			0.154883	−	0.987933i	$-0.450500\pi$
$313$	2.73884e29			0.309767			0.154883	+	0.987933i	$0.450500\pi$
$314$			7.56384e29i			0.823354i
$315$	−3.95355e28	−	2.86033e28i	−0.0414249	−	0.0299702i
$316$	−6.71450e29			−0.677281
$317$		−	5.05172e29i		−	0.490600i	−0.969447	−	0.245300i	$-0.921113\pi$
$317$		−	5.05172e29i		−	0.490600i	0.969447	−	0.245300i	$-0.0788865\pi$
$318$	1.15673e30	−	5.90843e29i	1.08170	−	0.552519i
$319$	−3.44833e29			−0.310542
$320$			4.63866e28i			0.0402340i
$321$	−7.42699e29	−	1.45402e30i	−0.620515	−	1.21482i
$322$	1.99592e29			0.160647
$323$		−	6.31306e29i		−	0.489564i
$324$	2.09323e29	+	6.35545e29i	0.156415	+	0.474905i
$325$	−1.98869e30			−1.43208
$326$		−	5.37524e29i		−	0.373067i
$327$	9.73783e29	−	4.97398e29i	0.651462	−	0.332760i
$328$	5.90622e29			0.380911
$329$		−	1.52547e29i		−	0.0948534i
$330$	−8.57880e28	−	1.67952e29i	−0.0514350	−	0.100697i
$331$	1.25611e30			0.726260			0.363130	−	0.931738i	$-0.381708\pi$
$331$	1.25611e30			0.726260			0.363130	+	0.931738i	$0.381708\pi$
$332$		−	1.38536e30i		−	0.772511i
$333$	−7.01231e29	+	9.69244e29i	−0.377164	+	0.521317i
$334$	1.25527e29			0.0651299
$335$			9.44096e28i			0.0472583i
$336$	7.32250e28	−	3.74025e28i	0.0353662	−	0.0180647i
$337$	2.14072e29			0.0997704			0.0498852	−	0.998755i	$-0.484114\pi$
$337$	2.14072e29			0.0997704			0.0498852	+	0.998755i	$0.484114\pi$
$338$			2.44038e30i			1.09763i
$339$	6.21101e29	+	1.21596e30i	0.269629	+	0.527867i
$340$	4.44003e29			0.186054
$341$		−	1.05469e30i		−	0.426649i
$342$	6.21170e29	+	4.49406e29i	0.242604	+	0.175520i
$343$	−8.31830e29			−0.313693
$344$		−	5.52745e29i		−	0.201291i
$345$	−1.16565e30	+	5.95403e29i	−0.409959	+	0.209402i
$346$	−1.68829e30			−0.573499
$347$			3.33922e30i			1.09570i	0.836577	+	0.547849i	$0.184553\pi$
$347$			3.33922e30i			1.09570i	−0.836577	+	0.547849i	$0.815447\pi$
$348$	4.48488e29	+	8.78029e29i	0.142167	+	0.278329i
$349$	−4.90589e29			−0.150249			−0.0751247	−	0.997174i	$-0.523935\pi$
$349$	−4.90589e29			−0.150249			−0.0751247	+	0.997174i	$0.523935\pi$
$350$			3.40245e29i			0.100687i
$351$	−8.57339e29	+	5.52046e30i	−0.245170	+	1.57866i
$352$	3.17781e29			0.0878246
$353$		−	3.94390e30i		−	1.05349i	−0.850024	−	0.526744i	$-0.823413\pi$
$353$		−	3.94390e30i		−	1.05349i	0.850024	−	0.526744i	$-0.176587\pi$
$354$	−3.82537e30	+	1.95396e30i	−0.987720	+	0.504517i
$355$	1.25823e30			0.314066
$356$		−	3.63288e30i		−	0.876700i
$357$	−3.58010e29	−	7.00895e29i	−0.0835364	−	0.163544i
$358$	1.33885e30			0.302090
$359$		−	2.87184e30i		−	0.626653i	−0.949646	−	0.313326i	$-0.898557\pi$
$359$		−	2.87184e30i		−	0.626653i	0.949646	−	0.313326i	$-0.101443\pi$
$360$	−3.16071e29	+	4.36875e29i	−0.0667045	+	0.0921992i
$361$	−4.02028e30			−0.820673
$362$			1.21722e30i			0.240362i
$363$	3.51105e30	−	1.79340e30i	0.670744	−	0.342609i
$364$	6.86500e29			0.126889
$365$		−	2.04662e30i		−	0.366036i
$366$	−3.19830e30	−	6.26149e30i	−0.553537	−	1.08369i
$367$	1.02914e31			1.72378			0.861889	−	0.507097i	$-0.169281\pi$
$367$	1.02914e31			1.72378			0.861889	+	0.507097i	$0.169281\pi$
$368$		−	2.20553e30i		−	0.357552i
$369$	5.56256e30	+	4.02441e30i	0.872887	+	0.631519i
$370$	−9.64055e29			−0.146447
$371$		−	1.85540e30i		−	0.272867i
$372$	−2.68549e30	+	1.37172e30i	−0.382392	+	0.195322i
$373$	6.01783e30			0.829724			0.414862	−	0.909884i	$-0.363830\pi$
$373$	6.01783e30			0.829724			0.414862	+	0.909884i	$0.363830\pi$
$374$		−	3.04174e30i		−	0.406127i
$375$	−2.14728e30	−	4.20384e30i	−0.277660	−	0.543590i
$376$	−1.68567e30			−0.211115
$377$			8.23171e30i			0.998605i
$378$	9.44497e29	+	1.46682e29i	0.110994	+	0.0172376i
$379$	−1.59790e31			−1.81920			−0.909598	−	0.415489i	$-0.863610\pi$
$379$	−1.59790e31			−1.81920			−0.909598	+	0.415489i	$0.863610\pi$
$380$			6.17845e29i			0.0681516i
$381$	8.02949e30	−	4.10138e30i	0.858199	−	0.438359i
$382$	6.10063e30			0.631850
$383$			9.46058e29i			0.0949582i	0.998872	+	0.0474791i	$0.0151188\pi$
$383$			9.46058e29i			0.0949582i	−0.998872	+	0.0474791i	$0.984881\pi$
$384$	−4.13304e29	−	8.09149e29i	−0.0402064	−	0.0787143i
$385$	−2.69396e29			−0.0254017
$386$			6.61814e30i			0.604907i
$387$	3.76632e30	−	5.20582e30i	0.333723	−	0.461273i
$388$	3.42848e30			0.294524
$389$			1.00139e31i			0.834084i	0.908887	+	0.417042i	$0.136933\pi$
$389$			1.00139e31i			0.834084i	−0.908887	+	0.417042i	$0.863067\pi$
$390$	−4.00928e30	+	2.04790e30i	−0.323811	+	0.165399i
$391$	−2.11109e31			−1.65343
$392$			4.53720e30i			0.344632i
$393$	−2.88788e30	−	5.65376e30i	−0.212750	−	0.416512i
$394$	9.75738e30			0.697234
$395$		−	6.28994e30i		−	0.435995i
$396$	2.99290e30	+	2.16531e30i	0.201257	+	0.145606i
$397$	−9.09072e30			−0.593079			−0.296539	−	0.955021i	$-0.595833\pi$
$397$	−9.09072e30			−0.593079			−0.296539	+	0.955021i	$0.595833\pi$
$398$			5.07513e30i			0.321255i
$399$	9.75317e29	−	4.98182e29i	0.0599061	−	0.0305994i
$400$	3.75977e30			0.224100
$401$			1.62871e31i			0.942129i	0.882099	+	0.471064i	$0.156130\pi$
$401$			1.62871e31i			0.942129i	−0.882099	+	0.471064i	$0.843870\pi$
$402$	−8.41189e29	−	1.64684e30i	−0.0472260	−	0.0924569i
$403$	−2.51771e31			−1.37197
$404$			7.37827e30i			0.390281i
$405$	−5.95360e30	+	1.96088e30i	−0.305717	+	0.100691i
$406$	1.40837e30			0.0702107
$407$			6.60445e30i			0.319672i
$408$	−7.74501e30	+	3.95607e30i	−0.363999	+	0.185927i
$409$	4.21235e31			1.92240			0.961202	−	0.275844i	$-0.0889574\pi$
$409$	4.21235e31			1.92240			0.961202	+	0.275844i	$0.0889574\pi$
$410$			5.53277e30i			0.245209i
$411$	−5.65639e30	−	1.10738e31i	−0.243465	−	0.476646i
$412$	3.58155e30			0.149728
$413$			6.13592e30i			0.249161i
$414$	1.50281e31	−	2.07719e31i	0.592790	−	0.819356i
$415$	1.29776e31			0.497299
$416$		−	7.58595e30i		−	0.282416i
$417$	7.53423e30	−	3.84840e30i	0.272525	−	0.139203i
$418$	4.23267e30			0.148764
$419$		−	3.32650e31i		−	1.13611i	−0.822992	−	0.568054i	$-0.807697\pi$
$419$		−	3.32650e31i		−	1.13611i	0.822992	−	0.568054i	$-0.192303\pi$
$420$	3.50376e29	+	6.85950e29i	0.0116290	+	0.0227667i
$421$	2.84585e31			0.917966			0.458983	−	0.888445i	$-0.348214\pi$
$421$	2.84585e31			0.917966			0.458983	+	0.888445i	$0.348214\pi$
$422$		−	4.34384e31i		−	1.36183i
$423$	−1.58759e31	−	1.14859e31i	−0.483785	−	0.350010i
$424$	−2.05025e31			−0.607319
$425$		−	3.59878e31i		−	1.03630i
$426$	−2.19481e31	+	1.12108e31i	−0.614443	+	0.313851i
$427$	−1.00435e31			−0.273370
$428$			2.57720e31i			0.682059i
$429$	1.40295e31	+	2.74664e31i	0.361041	+	0.706829i
$430$	5.17795e30			0.129580
$431$			3.37981e31i			0.822554i	0.911510	+	0.411277i	$0.134917\pi$
$431$			3.37981e31i			0.822554i	−0.911510	+	0.411277i	$0.865083\pi$
$432$	1.62087e30	−	1.04369e31i	0.0383656	−	0.247039i
$433$	−2.18119e31			−0.502155			−0.251077	−	0.967967i	$-0.580785\pi$
$433$	−2.18119e31			−0.502155			−0.251077	+	0.967967i	$0.580785\pi$
$434$			4.30755e30i			0.0964615i
$435$	−8.22511e30	+	4.20130e30i	−0.179172	+	0.0915192i
$436$	−1.72599e31			−0.365763
$437$		−	2.93764e31i		−	0.605650i
$438$	1.82354e31	+	3.57005e31i	0.365785	+	0.716118i
$439$	2.90476e31			0.566938			0.283469	−	0.958981i	$-0.408515\pi$
$439$	2.90476e31			0.566938			0.283469	+	0.958981i	$0.408515\pi$
$440$			2.97688e30i			0.0565365i
$441$	−3.09158e31	+	4.27320e31i	−0.571371	+	0.789750i
$442$	−7.26112e31			−1.30598
$443$			2.02953e30i			0.0355263i	0.999842	+	0.0177632i	$0.00565449\pi$
$443$			2.02953e30i			0.0355263i	−0.999842	+	0.0177632i	$0.994346\pi$
$444$	1.68166e31	−	8.58972e30i	0.286511	−	0.146347i
$445$	3.40317e31			0.564370
$446$		−	5.92891e31i		−	0.957098i
$447$	4.51275e31	+	8.83485e31i	0.709171	+	1.38838i
$448$	−1.29788e30			−0.0198563
$449$			2.79159e31i			0.415810i	0.978149	+	0.207905i	$0.0666645\pi$
$449$			2.79159e31i			0.415810i	−0.978149	+	0.207905i	$0.933335\pi$
$450$	3.54100e31	+	2.56185e31i	0.513541	+	0.371538i
$451$	3.79034e31			0.535254
$452$		−	2.15525e31i		−	0.296371i
$453$	7.44048e29	−	3.80051e29i	0.00996374	−	0.00508937i
$454$	−4.37272e31			−0.570271
$455$			6.43093e30i			0.0816840i
$456$	−5.50499e30	−	1.07774e31i	−0.0681050	−	0.133333i
$457$	7.70981e30			0.0929072			0.0464536	−	0.998920i	$-0.485208\pi$
$457$	7.70981e30			0.0929072			0.0464536	+	0.998920i	$0.485208\pi$
$458$			7.14363e31i			0.838558i
$459$	−9.98995e31	−	1.55146e31i	−1.14238	−	0.177414i
$460$	2.06607e31			0.230171
$461$			1.16682e31i			0.126646i	0.997993	+	0.0633230i	$0.0201698\pi$
$461$			1.16682e31i			0.126646i	−0.997993	+	0.0633230i	$0.979830\pi$
$462$	4.69924e30	−	2.40032e30i	0.0496963	−	0.0253843i
$463$	−1.20430e32			−1.24098			−0.620488	−	0.784216i	$-0.713066\pi$
$463$	−1.20430e32			−1.24098			−0.620488	+	0.784216i	$0.713066\pi$
$464$		−	1.55627e31i		−	0.156268i
$465$	−1.28499e31	−	2.51569e31i	−0.125737	−	0.246162i
$466$	−5.25402e31			−0.501027
$467$		−	1.03648e32i		−	0.963297i	−0.876365	−	0.481648i	$-0.840038\pi$
$467$		−	1.03648e32i		−	0.963297i	0.876365	−	0.481648i	$-0.159962\pi$
$468$	5.16895e31	−	7.14454e31i	0.468222	−	0.647178i
$469$	−2.64155e30			−0.0233230
$470$		−	1.57909e31i		−	0.135904i
$471$	1.23598e32	−	6.31325e31i	1.03696	−	0.529666i
$472$	6.78030e31			0.554556
$473$		−	3.54726e31i		−	0.282852i
$474$	5.60434e31	+	1.09719e32i	0.435697	+	0.852987i
$475$	5.00781e31			0.379599
$476$			1.24231e31i			0.0918218i
$477$	−1.93095e32	−	1.39701e32i	−1.39172	−	1.00688i
$478$	1.75149e32			1.23104
$479$		−	1.27488e32i		−	0.873863i	−0.899495	−	0.436931i	$-0.856065\pi$
$479$		−	1.27488e32i		−	0.873863i	0.899495	−	0.436931i	$-0.143935\pi$
$480$	7.57986e30	−	3.87171e30i	0.0506718	−	0.0258826i
$481$	1.57659e32			1.02796
$482$			8.92622e31i			0.567679i
$483$	−1.66592e31	−	3.26146e31i	−0.103345	−	0.202324i
$484$	−6.22318e31			−0.376590
$485$			3.21169e31i			0.189598i
$486$	8.63807e31	−	8.72513e31i	0.497487	−	0.502501i
$487$	7.43336e31			0.417674			0.208837	−	0.977950i	$-0.433032\pi$
$487$	7.43336e31			0.417674			0.208837	+	0.977950i	$0.433032\pi$
$488$			1.10982e32i			0.608438i
$489$	−8.78348e31	+	4.48651e31i	−0.469851	+	0.239995i
$490$	−4.25032e31			−0.221855
$491$			3.80259e32i			1.93687i	0.249258	+	0.968437i	$0.419813\pi$
$491$			3.80259e32i			1.93687i	−0.249258	+	0.968437i	$0.580187\pi$
$492$	−4.92970e31	−	9.65114e31i	−0.245041	−	0.479731i
$493$	−1.48963e32			−0.722629
$494$		−	1.01041e32i		−	0.478380i
$495$	−2.02840e31	+	2.80366e31i	−0.0937327	+	0.129558i
$496$	4.75992e31			0.214694
$497$			3.52049e31i			0.154998i
$498$	−2.26376e32	+	1.15630e32i	−0.972922	+	0.496958i
$499$	−1.36860e32			−0.574207			−0.287104	−	0.957900i	$-0.592692\pi$
$499$	−1.36860e32			−0.574207			−0.287104	+	0.957900i	$0.592692\pi$
$500$			7.45114e31i			0.305199i
$501$	−1.04773e31	−	2.05119e31i	−0.0418982	−	0.0820265i
$502$	−6.87576e31			−0.268458
$503$			2.04771e32i			0.780645i	0.920678	+	0.390323i	$0.127636\pi$
$503$			2.04771e32i			0.780645i	−0.920678	+	0.390323i	$0.872364\pi$
$504$	−1.22236e31	−	8.84358e30i	−0.0455023	−	0.0329201i
$505$	−6.91174e31			−0.251241
$506$		−	1.41541e32i		−	0.502429i
$507$	3.98773e32	−	2.03689e32i	1.38239	−	0.706110i
$508$	−1.42319e32			−0.481836
$509$			2.83630e32i			0.937861i	0.883235	+	0.468931i	$0.155361\pi$
$509$			2.83630e32i			0.937861i	−0.883235	+	0.468931i	$0.844639\pi$
$510$	−3.70593e31	−	7.25529e31i	−0.119689	−	0.234322i
$511$	5.72639e31			0.180647
$512$			1.43418e31i			0.0441942i
$513$	2.15891e31	−	1.39013e32i	0.0649869	−	0.418454i
$514$	−3.38930e31			−0.0996673
$515$			3.35508e31i			0.0963866i
$516$	−9.03220e31	+	4.61355e31i	−0.253511	+	0.129491i
$517$	−1.08179e32			−0.296657
$518$		−	2.69739e31i		−	0.0722749i
$519$	1.40915e32	+	2.75877e32i	0.368934	+	0.722282i
$520$	7.10629e31			0.181804
$521$		−	2.17793e32i		−	0.544493i	−0.962228	−	0.272246i	$-0.912233\pi$
$521$		−	2.17793e32i		−	0.544493i	0.962228	−	0.272246i	$-0.0877666\pi$
$522$	1.06042e32	−	1.46571e32i	0.259079	−	0.358099i
$523$	4.75878e32			1.13625			0.568127	−	0.822941i	$-0.307668\pi$
$523$	4.75878e32			1.13625			0.568127	+	0.822941i	$0.307668\pi$
$524$			1.00211e32i			0.233851i
$525$	5.55982e31	−	2.83990e31i	0.126809	−	0.0647725i
$526$	1.57315e32			0.350704
$527$		−	4.55610e32i		−	0.992810i
$528$	−2.65240e31	−	5.19274e31i	−0.0564978	−	0.110609i
$529$	−5.02097e32			−1.04549
$530$		−	1.92061e32i		−	0.390957i
$531$	6.38577e32	+	4.62000e32i	1.27081	+	0.919406i
$532$	−1.72871e31			−0.0336343
$533$		−	9.04816e32i		−	1.72121i
$534$	−5.93635e32	+	3.03223e32i	−1.10414	+	0.563984i
$535$	−2.41424e32			−0.439071
$536$			2.91896e31i			0.0519100i
$537$	−1.11749e32	−	2.18777e32i	−0.194335	−	0.380460i
$538$	4.27100e32			0.726343
$539$			2.91177e32i			0.484274i
$540$	9.77694e31	+	1.51838e31i	0.159029	+	0.0246976i
$541$	3.58979e32			0.571086			0.285543	−	0.958366i	$-0.407826\pi$
$541$	3.58979e32			0.571086			0.285543	+	0.958366i	$0.407826\pi$
$542$		−	6.06923e32i		−	0.944370i
$543$	1.98901e32	−	1.01597e32i	0.302719	−	0.154625i
$544$	1.37277e32			0.204367
$545$		−	1.61686e32i		−	0.235458i
$546$	−5.72995e31	−	1.12178e32i	−0.0816280	−	0.159808i
$547$	−6.21413e32			−0.866028			−0.433014	−	0.901387i	$-0.642550\pi$
$547$	−6.21413e32			−0.866028			−0.433014	+	0.901387i	$0.642550\pi$
$548$			1.96279e32i			0.267613i
$549$	−7.56217e32	+	1.04525e33i	−1.00874	+	1.39428i
$550$	2.41284e32			0.314903
$551$		−	2.07287e32i		−	0.264699i
$552$	−3.60397e32	+	1.84087e32i	−0.450311	+	0.230014i
$553$	1.75991e32			0.215173
$554$			2.49053e32i			0.297971i
$555$	8.04660e31	+	1.57533e32i	0.0942099	+	0.184440i
$556$	−1.33541e32			−0.153009
$557$		−	2.54222e32i		−	0.285070i	−0.989790	−	0.142535i	$-0.954475\pi$
$557$		−	2.54222e32i		−	0.285070i	0.989790	−	0.142535i	$-0.0455254\pi$
$558$	4.48296e32	+	3.24334e32i	0.491987	+	0.355944i
$559$	−8.46789e32			−0.909564
$560$		−	1.21582e31i		−	0.0127824i
$561$	−4.97039e32	+	2.53882e32i	−0.511489	+	0.261263i
$562$	6.77776e32			0.682733
$563$			1.20736e33i			1.19052i	0.803533	+	0.595261i	$0.202951\pi$
$563$			1.20736e33i			1.19052i	−0.803533	+	0.595261i	$0.797049\pi$
$564$	1.40696e32	+	2.75449e32i	0.135811	+	0.265884i
$565$	2.01897e32			0.190787
$566$			1.35387e33i			1.25250i
$567$	−5.48647e31	−	1.66580e32i	−0.0496932	−	0.150878i
$568$	3.89021e32			0.344979
$569$			6.61064e32i			0.573980i	0.957934	+	0.286990i	$0.0926546\pi$
$569$			6.61064e32i			0.573980i	−0.957934	+	0.286990i	$0.907345\pi$
$570$	1.00960e32	−	5.15691e31i	0.0858321	−	0.0438421i
$571$	−1.14492e33			−0.953105			−0.476553	−	0.879146i	$-0.658114\pi$
$571$	−1.14492e33			−0.953105			−0.476553	+	0.879146i	$0.658114\pi$
$572$		−	4.86831e32i		−	0.396849i
$573$	−5.09196e32	−	9.96881e32i	−0.406471	−	0.795771i
$574$	−1.54805e32			−0.121016
$575$		−	1.67461e33i		−	1.28203i
$576$	−9.77231e31	+	1.35073e32i	−0.0732702	+	0.101274i
$577$	2.27547e33			1.67094			0.835470	−	0.549537i	$-0.185196\pi$
$577$	2.27547e33			1.67094			0.835470	+	0.549537i	$0.185196\pi$
$578$		−	3.30841e32i		−	0.237950i
$579$	1.08145e33	−	5.52391e32i	0.761837	−	0.389138i
$580$	1.45787e32			0.100596
$581$			3.63109e32i			0.245428i
$582$	−2.86162e32	−	5.60235e32i	−0.189468	−	0.370932i
$583$	−1.31576e33			−0.853400
$584$		−	6.32776e32i		−	0.402065i
$585$	6.69279e32	+	4.84212e32i	0.416617	+	0.301415i
$586$	−8.78971e32			−0.536047
$587$		−	2.64271e33i		−	1.57904i	−0.613725	−	0.789520i	$-0.710330\pi$
$587$		−	2.64271e33i		−	1.57904i	0.613725	−	0.789520i	$-0.289670\pi$
$588$	7.41408e32	−	3.78703e32i	0.434040	−	0.221703i
$589$	6.33996e32			0.363666
$590$			6.35158e32i			0.356992i
$591$	−8.14411e32	−	1.59442e33i	−0.448532	−	0.878116i
$592$	−2.98067e32			−0.160862
$593$			3.60659e33i			1.90739i	0.300772	+	0.953696i	$0.402756\pi$
$593$			3.60659e33i			1.90739i	−0.300772	+	0.953696i	$0.597244\pi$
$594$	1.04020e32	−	6.69789e32i	0.0539111	−	0.347137i
$595$	−1.16376e32			−0.0591097
$596$		−	1.56594e33i		−	0.779507i
$597$	8.29309e32	−	4.23602e32i	0.404598	−	0.206665i
$598$	−3.37880e33			−1.61565
$599$			2.13018e33i			0.998379i	0.866493	+	0.499189i	$0.166369\pi$
$599$			2.13018e33i			0.998379i	−0.866493	+	0.499189i	$0.833631\pi$
$600$	−3.13813e32	−	6.14370e32i	−0.144164	−	0.282238i
$601$	3.19212e33			1.43743			0.718713	−	0.695306i	$-0.244731\pi$
$601$	3.19212e33			1.43743			0.718713	+	0.695306i	$0.244731\pi$
$602$			1.44877e32i			0.0639503i
$603$	−1.98894e32	+	2.74911e32i	−0.0860623	+	0.118956i
$604$	−1.31879e31			−0.00559414
$605$		−	5.82969e32i		−	0.242427i
$606$	1.20566e33	−	6.15836e32i	0.491532	−	0.251069i
$607$	1.31960e33			0.527446			0.263723	−	0.964598i	$-0.415049\pi$
$607$	1.31960e33			0.527446			0.263723	+	0.964598i	$0.415049\pi$
$608$			1.91025e32i			0.0748598i
$609$	−1.17551e32	−	2.30136e32i	−0.0451667	−	0.0884254i
$610$	−1.03965e33			−0.391678
$611$			2.58240e33i			0.953956i
$612$	1.29289e33	+	9.35386e32i	0.468323	+	0.338824i
$613$	1.42736e33			0.506999			0.253499	−	0.967336i	$-0.418418\pi$
$613$	1.42736e33			0.506999			0.253499	+	0.967336i	$0.418418\pi$
$614$			2.63950e33i			0.919394i
$615$	9.04090e32	−	4.61799e32i	0.308824	−	0.157744i
$616$	−8.32921e31			−0.0279020
$617$		−	5.36476e32i		−	0.176250i	−0.996109	−	0.0881248i	$-0.971913\pi$
$617$		−	5.36476e32i		−	0.176250i	0.996109	−	0.0881248i	$-0.0280874\pi$
$618$	−2.98938e32	−	5.85247e32i	−0.0963206	−	0.188572i
$619$	−3.63419e33			−1.14847			−0.574235	−	0.818691i	$-0.694700\pi$
$619$	−3.63419e33			−1.14847			−0.574235	+	0.818691i	$0.694700\pi$
$620$			4.45895e32i			0.138208i
$621$	−4.64861e33	−	7.21938e32i	−1.41326	−	0.219483i
$622$	1.26015e33			0.375784
$623$			9.52197e32i			0.278529i
$624$	−1.23959e33	+	6.33170e32i	−0.355683	+	0.181679i
$625$	2.48665e33			0.699929
$626$			7.93253e32i			0.219038i
$627$	−3.53285e32	−	6.91645e32i	−0.0957006	−	0.187358i
$628$	−2.19072e33			−0.582199
$629$			2.85304e33i			0.743874i
$630$	8.28440e31	−	1.14507e32i	0.0211921	−	0.0292918i
$631$	−6.10564e33			−1.53242			−0.766212	−	0.642588i	$-0.777861\pi$
$631$	−6.10564e33			−1.53242			−0.766212	+	0.642588i	$0.777861\pi$
$632$		−	1.94473e33i		−	0.478910i
$633$	−7.09810e33	+	3.62563e33i	−1.71513	+	0.876071i
$634$	1.46313e33			0.346907
$635$		−	1.33321e33i		−	0.310179i
$636$	1.71127e33	+	3.35024e33i	0.390690	+	0.764875i
$637$	6.95086e33			1.55728
$638$		−	9.98742e32i		−	0.219586i
$639$	3.66385e33	+	2.65073e33i	0.790545	+	0.571946i
$640$	−1.34350e32			−0.0284497
$641$		−	9.25569e33i		−	1.92359i	−0.273771	−	0.961795i	$-0.588271\pi$
$641$		−	9.25569e33i		−	1.92359i	0.273771	−	0.961795i	$-0.411729\pi$
$642$	4.21130e33	−	2.15109e33i	0.859005	−	0.438771i
$643$	9.93440e32			0.198889			0.0994443	−	0.995043i	$-0.468293\pi$
$643$	9.93440e32			0.198889			0.0994443	+	0.995043i	$0.468293\pi$
$644$			5.78080e32i			0.113595i
$645$	−4.32184e32	−	8.46110e32i	−0.0833589	−	0.163196i
$646$	1.82846e33			0.346174
$647$		−	6.13374e33i		−	1.13992i	−0.821673	−	0.569960i	$-0.806959\pi$
$647$		−	6.13374e33i		−	1.13992i	0.821673	−	0.569960i	$-0.193041\pi$
$648$	−1.84074e33	+	6.06265e32i	−0.335808	+	0.110602i
$649$	4.35128e33			0.779258
$650$		−	5.75985e33i		−	1.01263i
$651$	7.03882e32	−	3.59535e32i	0.121486	−	0.0620540i
$652$	1.55684e33			0.263798
$653$			4.06146e33i			0.675653i	0.941208	+	0.337826i	$0.109692\pi$
$653$			4.06146e33i			0.675653i	−0.941208	+	0.337826i	$0.890308\pi$
$654$	1.44062e33	+	2.82038e33i	0.235297	+	0.460653i
$655$	−9.38743e32			−0.150540
$656$			1.71063e33i			0.269345i
$657$	4.31164e33	−	5.95956e33i	0.666589	−	0.921361i
$658$	4.41823e32			0.0670715
$659$		−	9.06217e33i		−	1.35085i	−0.737428	−	0.675425i	$-0.763960\pi$
$659$		−	9.06217e33i		−	1.35085i	0.737428	−	0.675425i	$-0.236040\pi$
$660$	4.86440e32	−	2.48469e32i	0.0712037	−	0.0363701i
$661$	−1.08028e34			−1.55281			−0.776403	−	0.630236i	$-0.782958\pi$
$661$	−1.08028e34			−1.55281			−0.776403	+	0.630236i	$0.782958\pi$
$662$			3.63809e33i			0.513544i
$663$	6.06058e33	+	1.18651e34i	0.840140	+	1.64479i
$664$	4.01242e33			0.546248
$665$		−	1.61940e32i		−	0.0216519i
$666$	−2.80723e33	−	2.03098e33i	−0.368627	−	0.266695i
$667$	−6.93167e33			−0.893980
$668$			3.63566e32i			0.0460538i
$669$	−9.68821e33	+	4.94863e33i	−1.20540	+	0.615704i
$670$	−2.73439e32			−0.0334167
$671$			7.12233e33i			0.854972i
$672$	1.08329e32	+	2.12082e32i	0.0127736	+	0.0250077i
$673$	1.84641e33			0.213869			0.106934	−	0.994266i	$-0.465897\pi$
$673$	1.84641e33			0.213869			0.106934	+	0.994266i	$0.465897\pi$
$674$			6.20019e32i			0.0705483i
$675$	1.23069e33	−	7.92449e33i	0.137564	−	0.885780i
$676$	−7.06810e33			−0.776144
$677$		−	1.58418e34i		−	1.70899i	−0.519458	−	0.854496i	$-0.673866\pi$
$677$		−	1.58418e34i		−	1.70899i	0.519458	−	0.854496i	$-0.326134\pi$
$678$	−3.52181e33	+	1.79890e33i	−0.373258	+	0.190656i
$679$	−8.98622e32			−0.0935706
$680$			1.28597e33i			0.131560i
$681$	3.64974e33	+	7.14530e33i	0.366857	+	0.718216i
$682$	3.05470e33			0.301686
$683$			1.01164e34i			0.981699i	0.871244	+	0.490849i	$0.163313\pi$
$683$			1.01164e34i			0.981699i	−0.871244	+	0.490849i	$0.836687\pi$
$684$	−1.30162e33	+	1.79910e33i	−0.124111	+	0.171547i
$685$	−1.83868e33			−0.172274
$686$		−	2.40924e33i		−	0.221814i
$687$	1.16731e34	−	5.96251e33i	1.05610	−	0.539447i
$688$	1.60092e33			0.142334
$689$			3.14092e34i			2.74427i
$690$	−1.72447e33	−	3.37609e33i	−0.148070	−	0.289885i
$691$	1.09063e33			0.0920320			0.0460160	−	0.998941i	$-0.485347\pi$
$691$	1.09063e33			0.0920320			0.0460160	+	0.998941i	$0.485347\pi$
$692$		−	4.88980e33i		−	0.405525i
$693$	−7.84455e32	−	5.67540e32i	−0.0639395	−	0.0462591i
$694$	−9.67141e33			−0.774776
$695$		−	1.25097e33i		−	0.0984987i
$696$	−2.54304e33	+	1.29896e33i	−0.196808	+	0.100527i
$697$	1.63738e34			1.24553
$698$		−	1.42090e33i		−	0.106242i
$699$	4.38533e33	+	8.58540e33i	0.322312	+	0.631008i
$700$	−9.85455e32			−0.0711968
$701$		−	1.22710e33i		−	0.0871493i	−0.999050	−	0.0435746i	$-0.986125\pi$
$701$		−	1.22710e33i		−	0.0871493i	0.999050	−	0.0435746i	$-0.0138746\pi$
$702$	−1.59890e34	−	2.48312e33i	−1.11628	−	0.173361i
$703$	−3.97009e33			−0.272481
$704$			9.20392e32i			0.0621013i
$705$	−2.58033e33	+	1.31800e33i	−0.171161	+	0.0874272i
$706$	1.14228e34			0.744928
$707$		−	1.93388e33i		−	0.123993i
$708$	−5.65926e33	−	1.10794e34i	−0.356747	−	0.698423i
$709$	−1.02023e34			−0.632327			−0.316163	−	0.948705i	$-0.602395\pi$
$709$	−1.02023e34			−0.632327			−0.316163	+	0.948705i	$0.602395\pi$
$710$			3.64423e33i			0.222078i
$711$	1.32511e34	−	1.83157e34i	0.793992	−	1.09746i
$712$	1.05219e34			0.619921
$713$		−	2.12008e34i		−	1.22823i
$714$	2.03001e33	−	1.03691e33i	0.115643	−	0.0590692i
$715$	4.56048e33			0.255469
$716$			3.87773e33i			0.213610i
$717$	−1.46190e34	−	2.86204e34i	−0.791932	−	1.55041i
$718$	8.31774e33			0.443110
$719$			3.09786e34i			1.62299i	0.584362	+	0.811493i	$0.301345\pi$
$719$			3.09786e34i			1.62299i	−0.584362	+	0.811493i	$0.698655\pi$
$720$	−1.26532e33	−	9.15440e32i	−0.0651946	−	0.0471672i
$721$	−9.38742e32			−0.0475689
$722$		−	1.16440e34i		−	0.580303i
$723$	1.45860e34	−	7.45037e33i	0.714952	−	0.365190i
$724$	−3.52544e33			−0.169961
$725$		−	1.18164e34i		−	0.560313i
$726$	5.19425e33	+	1.01691e34i	0.242261	+	0.474288i
$727$	1.06499e34			0.488578			0.244289	−	0.969702i	$-0.421445\pi$
$727$	1.06499e34			0.488578			0.244289	+	0.969702i	$0.421445\pi$
$728$			1.98832e33i			0.0897241i
$729$	−2.14673e34	−	6.83262e33i	−0.952899	−	0.303289i
$730$	5.92766e33			0.258826
$731$		−	1.53237e34i		−	0.658196i
$732$	1.81352e34	−	9.26327e33i	0.766284	−	0.391410i
$733$	−1.29281e34			−0.537389			−0.268694	−	0.963226i	$-0.586592\pi$
$733$	−1.29281e34			−0.537389			−0.268694	+	0.963226i	$0.586592\pi$
$734$			2.98071e34i			1.21890i
$735$	3.54758e33	+	6.94529e33i	0.142720	+	0.279410i
$736$	6.38789e33			0.252827
$737$			1.87325e33i			0.0729435i
$738$	−1.16559e34	+	1.61109e34i	−0.446551	+	0.617224i
$739$	−4.14836e34			−1.56366			−0.781832	−	0.623489i	$-0.785715\pi$
$739$	−4.14836e34			−1.56366			−0.781832	+	0.623489i	$0.785715\pi$
$740$		−	2.79220e33i		−	0.103554i
$741$	−1.65107e34	+	8.43348e33i	−0.602486	+	0.307743i
$742$	5.37381e33			0.192946
$743$			3.70596e34i			1.30929i	0.755938	+	0.654643i	$0.227181\pi$
$743$			3.70596e34i			1.30929i	−0.755938	+	0.654643i	$0.772819\pi$
$744$	−3.97293e33	−	7.77802e33i	−0.138113	−	0.270392i
$745$	1.46693e34			0.501803
$746$			1.74295e34i			0.586704i
$747$	3.77895e34	+	2.73400e34i	1.25177	+	0.905632i
$748$	8.80981e33			0.287175
$749$		−	6.75497e33i		−	0.216691i
$750$	1.21756e34	−	6.21918e33i	0.384376	−	0.196335i
$751$	−4.89324e33			−0.152026			−0.0760129	−	0.997107i	$-0.524219\pi$
$751$	−4.89324e33			−0.152026			−0.0760129	+	0.997107i	$0.524219\pi$
$752$		−	4.88222e33i		−	0.149281i
$753$	5.73893e33	+	1.12354e34i	0.172700	+	0.338103i
$754$	−2.38416e34			−0.706121
$755$		−	1.23541e32i		−	0.00360119i
$756$	−4.24838e32	+	2.73556e33i	−0.0121888	+	0.0784845i
$757$	−4.02832e34			−1.13756			−0.568779	−	0.822490i	$-0.692584\pi$
$757$	−4.02832e34			−1.13756			−0.568779	+	0.822490i	$0.692584\pi$
$758$		−	4.62802e34i		−	1.28637i
$759$	−2.31286e34	+	1.18138e34i	−0.632773	+	0.323214i
$760$	−1.78947e33			−0.0481905
$761$			2.31833e34i			0.614554i	0.951620	+	0.307277i	$0.0994177\pi$
$761$			2.31833e34i			0.614554i	−0.951620	+	0.307277i	$0.900582\pi$
$762$	1.18789e34	+	2.32559e34i	0.309967	+	0.606839i
$763$	4.52391e33			0.116204
$764$			1.76693e34i			0.446786i
$765$	−8.76241e33	+	1.21114e34i	−0.218116	+	0.301480i
$766$	−2.74008e33			−0.0671456
$767$		−	1.03872e35i		−	2.50585i
$768$	2.34355e33	−	1.19706e33i	0.0556594	−	0.0284302i
$769$	2.72124e34			0.636283			0.318141	−	0.948043i	$-0.396941\pi$
$769$	2.72124e34			0.636283			0.318141	+	0.948043i	$0.396941\pi$
$770$		−	7.80255e32i		−	0.0179617i
$771$	2.82892e33	+	5.53833e33i	0.0641162	+	0.125524i
$772$	−1.91682e34			−0.427734
$773$		−	2.28163e34i		−	0.501292i	−0.968079	−	0.250646i	$-0.919357\pi$
$773$		−	2.28163e34i		−	0.501292i	0.968079	−	0.250646i	$-0.0806429\pi$
$774$	1.50777e34	+	1.09084e34i	0.326169	+	0.235978i
$775$	3.61411e34			0.769806
$776$			9.92993e33i			0.208260i
$777$	−4.40771e33	+	2.25141e33i	−0.0910251	+	0.0464946i
$778$	−2.90035e34			−0.589787
$779$			2.27846e34i			0.456239i
$780$	−5.93135e33	−	1.16121e34i	−0.116955	−	0.228969i
$781$	2.49655e34			0.484762
$782$		−	6.11436e34i		−	1.16915i
$783$	−3.28016e34	−	5.09416e33i	−0.617666	−	0.0959249i
$784$	−1.31411e34			−0.243692
$785$		−	2.05220e34i		−	0.374787i
$786$	1.63750e34	−	8.36420e33i	0.294518	−	0.150437i
$787$	2.07484e34			0.367525			0.183763	−	0.982971i	$-0.441172\pi$
$787$	2.07484e34			0.367525			0.183763	+	0.982971i	$0.441172\pi$
$788$			2.82604e34i			0.493019i
$789$	−1.31305e34	−	2.57062e34i	−0.225609	−	0.441687i
$790$	1.82176e34			0.308295
$791$			5.64901e33i			0.0941575i
$792$	−6.27141e33	+	8.66837e33i	−0.102959	+	0.142310i
$793$	1.70022e35			2.74932
$794$		−	2.63295e34i		−	0.419370i
$795$	−3.13840e34	+	1.60306e34i	−0.492383	+	0.251504i
$796$	−1.46992e34			−0.227162
$797$		−	1.12075e34i		−	0.170611i	−0.996355	−	0.0853056i	$-0.972813\pi$
$797$		−	1.12075e34i		−	0.170611i	0.996355	−	0.0853056i	$-0.0271867\pi$
$798$	1.44289e33	+	2.82482e33i	0.0216370	+	0.0423600i
$799$	−4.67317e34			−0.690319
$800$			1.08895e34i			0.158462i
$801$	9.90970e34	+	7.16949e34i	1.42059	+	1.02778i
$802$	−4.71724e34			−0.666186
$803$		−	4.06086e34i		−	0.564978i
$804$	4.76976e33	−	2.43634e33i	0.0653769	−	0.0333938i
$805$	−5.41528e33			−0.0731258
$806$		−	7.29206e34i		−	0.970129i
$807$	−3.56484e34	−	6.97908e34i	−0.467259	−	0.914778i
$808$	−2.13697e34			−0.275971
$809$			1.26096e35i			1.60443i	0.597038	+	0.802213i	$0.296344\pi$
$809$			1.26096e35i			1.60443i	−0.597038	+	0.802213i	$0.703656\pi$
$810$	−5.67931e33	−	1.72435e34i	−0.0711992	−	0.216174i
$811$	1.69590e33			0.0209483			0.0104742	−	0.999945i	$-0.496666\pi$
$811$	1.69590e33			0.0209483			0.0104742	+	0.999945i	$0.496666\pi$
$812$			4.07907e33i			0.0496465i
$813$	−9.91750e34	+	5.06575e34i	−1.18937	+	0.607516i
$814$	−1.91285e34			−0.226042
$815$			1.45840e34i			0.169818i
$816$	−1.14580e34	−	2.24320e34i	−0.131470	−	0.257386i
$817$	2.13234e34			0.241097
$818$			1.22003e35i			1.35935i
$819$	−1.35481e34	+	1.87262e34i	−0.148755	+	0.205609i
$820$	−1.60246e34			−0.173389
$821$			9.56150e33i			0.101955i	0.998700	+	0.0509775i	$0.0162337\pi$
$821$			9.56150e33i			0.101955i	−0.998700	+	0.0509775i	$0.983766\pi$
$822$	3.20732e34	−	1.63826e34i	0.337039	−	0.172156i
$823$	−1.72348e35			−1.78488			−0.892438	−	0.451170i	$-0.851007\pi$
$823$	−1.72348e35			−1.78488			−0.892438	+	0.451170i	$0.851007\pi$
$824$			1.03733e34i			0.105874i
$825$	−2.01391e34	−	3.94274e34i	−0.202578	−	0.396598i
$826$	−1.77715e34			−0.176183
$827$			5.71639e34i			0.558541i	0.960212	+	0.279271i	$0.0900927\pi$
$827$			5.71639e34i			0.558541i	−0.960212	+	0.279271i	$0.909907\pi$
$828$	6.01619e34	+	4.35261e34i	0.579372	+	0.419166i
$829$	−3.17589e34			−0.301447			−0.150724	−	0.988576i	$-0.548160\pi$
$829$	−3.17589e34			−0.301447			−0.150724	+	0.988576i	$0.548160\pi$
$830$			3.75871e34i			0.351643i
$831$	4.06968e34	−	2.07875e34i	0.375273	−	0.191685i
$832$	2.19712e34			0.199698
$833$			1.25784e35i			1.12690i
$834$	1.11462e34	+	2.18215e34i	0.0984313	+	0.192704i
$835$	−3.40577e33			−0.0296468
$836$			1.22591e34i			0.105192i
$837$	1.55807e34	−	1.00325e35i	0.131790	−	0.848603i
$838$	9.63458e34			0.803349
$839$		−	1.39267e35i		−	1.14474i	−0.819996	−	0.572369i	$-0.806025\pi$
$839$		−	1.39267e35i		−	1.14474i	0.819996	−	0.572369i	$-0.193975\pi$
$840$	−1.98672e33	+	1.01480e33i	−0.0160985	+	0.00822295i
$841$	7.62735e34			0.609287
$842$			8.24246e34i			0.649100i
$843$	−5.65714e34	−	1.10753e35i	−0.439204	−	0.859853i
$844$	1.25811e35			0.962962
$845$		−	6.62118e34i		−	0.499637i
$846$	3.32667e34	−	4.59814e34i	0.247495	−	0.342088i
$847$	1.63113e34			0.119643
$848$		−	5.93816e34i		−	0.429439i
$849$	2.21230e35	−	1.13002e35i	1.57744	−	0.805739i
$850$	1.04232e35			0.732778
$851$			1.32760e35i			0.920263i
$852$	−3.24701e34	−	6.35684e34i	−0.221926	−	0.434477i
$853$	−2.47404e35			−1.66732			−0.833659	−	0.552279i	$-0.813758\pi$
$853$	−2.47404e35			−1.66732			−0.833659	+	0.552279i	$0.813758\pi$
$854$		−	2.90891e34i		−	0.193302i
$855$	−1.68534e34	−	1.21932e34i	−0.110432	−	0.0798957i
$856$	−7.46436e34			−0.482289
$857$		−	4.02332e34i		−	0.256339i	−0.991752	−	0.128169i	$-0.959090\pi$
$857$		−	4.02332e34i		−	0.256339i	0.991752	−	0.128169i	$-0.0409101\pi$
$858$	−7.95512e34	+	4.06339e34i	−0.499804	+	0.255294i
$859$	6.66573e33			0.0412981			0.0206490	−	0.999787i	$-0.493427\pi$
$859$	6.66573e33			0.0412981			0.0206490	+	0.999787i	$0.493427\pi$
$860$			1.49969e34i			0.0916266i
$861$	1.29210e34	+	2.52962e34i	0.0778500	+	0.152411i
$862$	−9.78896e34			−0.581634
$863$		−	3.97364e34i		−	0.232841i	−0.993200	−	0.116421i	$-0.962858\pi$
$863$		−	3.97364e34i		−	0.232841i	0.993200	−	0.116421i	$-0.0371420\pi$
$864$	3.02284e34	+	4.69453e33i	0.174683	+	0.0271286i
$865$	4.58062e34			0.261054
$866$		−	6.31739e34i		−	0.355077i
$867$	−5.40615e34	+	2.76140e34i	−0.299681	+	0.153074i
$868$	−1.24760e34			−0.0682086
$869$		−	1.24804e35i		−	0.672961i
$870$	−1.21683e34	−	2.38225e34i	−0.0647139	−	0.126694i
$871$	4.47176e34			0.234563
$872$		−	4.99900e34i		−	0.258634i
$873$	−6.76610e34	+	9.35213e34i	−0.345277	+	0.477243i
$874$	8.50833e34			0.428259
$875$		−	1.95298e34i		−	0.0969620i
$876$	−1.03400e35	+	5.28154e34i	−0.506372	+	0.258649i
$877$	−1.05268e35			−0.508513			−0.254257	−	0.967137i	$-0.581831\pi$
$877$	−1.05268e35			−0.508513			−0.254257	+	0.967137i	$0.581831\pi$
$878$			8.41307e34i			0.400885i
$879$	7.33643e34	+	1.43629e35i	0.344841	+	0.675113i
$880$	−8.62196e33			−0.0399773
$881$			1.06383e34i			0.0486587i	0.999704	+	0.0243293i	$0.00774503\pi$
$881$			1.06383e34i			0.0486587i	−0.999704	+	0.0243293i	$0.992255\pi$
$882$	−1.23765e35	−	8.95418e34i	−0.558438	−	0.404020i
$883$	3.78664e35			1.68549			0.842743	−	0.538316i	$-0.180939\pi$
$883$	3.78664e35			1.68549			0.842743	+	0.538316i	$0.180939\pi$
$884$		−	2.10304e35i		−	0.923467i
$885$	1.03789e35	−	5.30142e34i	0.449606	−	0.229654i
$886$	−5.87814e33			−0.0251209
$887$			3.25185e35i			1.37103i	0.728058	+	0.685516i	$0.240423\pi$
$887$			3.25185e35i			1.37103i	−0.728058	+	0.685516i	$0.759577\pi$
$888$	2.48785e34	+	4.87060e34i	0.103483	+	0.202594i
$889$	3.73027e34			0.153080
$890$			9.85664e34i			0.399070i
$891$	−1.18130e35	+	3.89073e34i	−0.471875	+	0.155417i
$892$	1.71720e35			0.676771
$893$		−	6.50286e34i		−	0.252864i
$894$	−2.55885e35	+	1.30703e35i	−0.981734	+	0.501459i
$895$	−3.63254e34			−0.137510
$896$		−	3.75907e33i		−	0.0140406i
$897$	2.82016e35	+	5.52117e35i	1.03935	+	2.03480i
$898$	−8.08530e34			−0.294022
$899$		−	1.49598e35i		−	0.536796i
$900$	−7.41991e34	+	1.02558e35i	−0.262717	+	0.363128i
$901$	−5.68389e35			−1.98586
$902$			1.09780e35i			0.378482i
$903$	2.36739e34	−	1.20924e34i	0.0805409	−	0.0411394i
$904$	6.24226e34			0.209566
$905$		−	3.30253e34i		−	0.109412i
$906$	1.10075e33	+	2.15499e33i	0.00359873	+	0.00704543i
$907$	−1.19080e35			−0.384195			−0.192098	−	0.981376i	$-0.561529\pi$
$907$	−1.19080e35			−0.384195			−0.192098	+	0.981376i	$0.561529\pi$
$908$		−	1.26647e35i		−	0.403243i
$909$	−2.01263e35	−	1.45610e35i	−0.632408	−	0.457536i
$910$	−1.86260e34			−0.0577593
$911$		−	2.21662e34i		−	0.0678377i	−0.999425	−	0.0339189i	$-0.989201\pi$
$911$		−	2.21662e34i		−	0.0678377i	0.999425	−	0.0339189i	$-0.0107988\pi$
$912$	3.12148e34	−	1.59442e34i	0.0942805	−	0.0481575i
$913$	2.57499e35			0.767583
$914$			2.23300e34i			0.0656953i
$915$	8.67756e34	+	1.69885e35i	0.251967	+	0.493290i
$916$	−2.06902e35			−0.592950
$917$		−	2.62657e34i		−	0.0742946i
$918$	4.49351e34	−	2.89340e35i	0.125451	−	0.807786i
$919$	3.46304e35			0.954269			0.477135	−	0.878830i	$-0.341675\pi$
$919$	3.46304e35			0.954269			0.477135	+	0.878830i	$0.341675\pi$
$920$			5.98398e34i			0.162756i
$921$	4.31311e35	−	2.20309e35i	1.15791	−	0.591449i
$922$	−3.37946e34			−0.0895522
$923$		−	5.95968e35i		−	1.55884i
$924$	6.95207e33	+	1.36104e34i	0.0179494	+	0.0351406i
$925$	−2.26316e35			−0.576785
$926$		−	3.48803e35i		−	0.877503i
$927$	−7.06819e34	+	9.76967e34i	−0.175530	+	0.242618i
$928$	4.50744e34			0.110498
$929$		−	1.56816e35i		−	0.379492i	−0.981833	−	0.189746i	$-0.939234\pi$
$929$		−	1.56816e35i		−	0.379492i	0.981833	−	0.189746i	$-0.0607664\pi$
$930$	7.28621e34	−	3.72172e34i	0.174063	−	0.0889095i
$931$	−1.75033e35			−0.412785
$932$		−	1.52173e35i		−	0.354279i
$933$	−1.05180e35	−	2.05917e35i	−0.241743	−	0.473273i
$934$	3.00198e35			0.681154
$935$			8.25277e34i			0.184867i
$936$	2.06928e35	+	1.49709e35i	0.457624	+	0.331083i
$937$	−1.98499e35			−0.433395			−0.216697	−	0.976239i	$-0.569528\pi$
$937$	−1.98499e35			−0.433395			−0.216697	+	0.976239i	$0.569528\pi$
$938$		−	7.65075e33i		−	0.0164919i
$939$	1.29623e35	−	6.62098e34i	0.275863	−	0.140908i
$940$	4.57352e34			0.0960985
$941$		−	8.42043e34i		−	0.174686i	−0.996178	−	0.0873431i	$-0.972162\pi$
$941$		−	8.42043e34i		−	0.174686i	0.996178	−	0.0873431i	$-0.0278376\pi$
$942$	1.82851e35	+	3.57978e35i	0.374530	+	0.733239i
$943$	7.61917e35			1.54088
$944$			1.96379e35i			0.392130i
$945$	−2.56259e34	−	3.97975e33i	−0.0505239	−	0.00784647i
$946$	1.02740e35			0.200007
$947$			5.46530e35i			1.05054i	0.850934	+	0.525272i	$0.176036\pi$
$947$			5.46530e35i			1.05054i	−0.850934	+	0.525272i	$0.823964\pi$
$948$	−3.17781e35	+	1.62319e35i	−0.603153	+	0.308084i
$949$	−9.69394e35			−1.81679
$950$			1.45042e35i			0.268417i
$951$	−1.22122e35	−	2.39085e35i	−0.223166	−	0.436905i
$952$	−3.59811e34			−0.0649278
$953$			2.79844e35i			0.498657i	0.968419	+	0.249328i	$0.0802098\pi$
$953$			2.79844e35i			0.498657i	−0.968419	+	0.249328i	$0.919790\pi$
$954$	4.04617e35	−	5.59263e35i	0.711974	−	0.984092i
$955$	−1.65521e35			−0.287615
$956$			5.07285e35i			0.870478i
$957$	−1.63201e35	+	8.33612e34i	−0.276553	+	0.141260i
$958$	3.69245e35			0.617914
$959$		−	5.14457e34i		−	0.0850210i
$960$	1.12137e34	+	2.19536e34i	0.0183018	+	0.0358304i
$961$	−1.62861e35			−0.262504
$962$			4.56629e35i			0.726880i
$963$	−7.03002e35	−	5.08610e35i	−1.10520	−	0.799594i
$964$	−2.58531e35			−0.401410
$965$		−	1.79562e35i		−	0.275351i
$966$	9.44620e34	−	4.82502e34i	0.143064	−	0.0730757i
$967$	7.32290e35			1.09538			0.547691	−	0.836681i	$-0.315507\pi$
$967$	7.32290e35			1.09538			0.547691	+	0.836681i	$0.315507\pi$
$968$		−	1.80243e35i		−	0.266289i
$969$	−1.52614e35	−	2.98782e35i	−0.222695	−	0.435982i
$970$	−9.30206e34			−0.134066
$971$			2.41941e35i			0.344412i	0.985061	+	0.172206i	$0.0550895\pi$
$971$			2.41941e35i			0.344412i	−0.985061	+	0.172206i	$0.944911\pi$
$972$	2.52707e35	+	2.50185e35i	0.355322	+	0.351776i
$973$	3.50018e34			0.0486112
$974$			2.15293e35i			0.295340i
$975$	−9.41196e35	+	4.80753e35i	−1.27534	+	0.651428i
$976$	−3.21439e35			−0.430230
$977$			9.95253e35i			1.31583i	0.753094	+	0.657913i	$0.228561\pi$
$977$			9.95253e35i			1.31583i	−0.753094	+	0.657913i	$0.771439\pi$
$978$	−1.29943e35	−	2.54397e35i	−0.169702	−	0.332235i
$979$	6.75249e35			0.871108
$980$		−	1.23102e35i		−	0.156875i
$981$	3.40624e35	−	4.70812e35i	0.428793	−	0.592679i
$982$	−1.10135e36			−1.36958
$983$			1.39864e36i			1.71816i	0.511839	+	0.859081i	$0.328964\pi$
$983$			1.39864e36i			1.71816i	−0.511839	+	0.859081i	$0.671036\pi$
$984$	2.79527e35	−	1.42779e35i	0.339221	−	0.173270i
$985$	−2.64735e35			−0.317378
$986$		−	4.31443e35i		−	0.510976i
$987$	−3.68773e34	−	7.21967e34i	−0.0431473	−	0.0844717i
$988$	2.92645e35			0.338266
$989$		−	7.13054e35i		−	0.814268i
$990$	−8.12026e34	−	5.87487e34i	−0.0916111	−	0.0662790i
$991$	6.96850e35			0.776703			0.388352	−	0.921511i	$-0.373045\pi$
$991$	6.96850e35			0.776703			0.388352	+	0.921511i	$0.373045\pi$
$992$			1.37862e35i			0.151812i
$993$	5.94487e35	−	3.03657e35i	0.646772	−	0.330364i
$994$	−1.01964e35			−0.109600
$995$		−	1.37697e35i		−	0.146234i
$996$	−3.34901e35	−	6.55655e35i	−0.351403	−	0.687960i
$997$	−4.39776e35			−0.455921			−0.227961	−	0.973670i	$-0.573206\pi$
$997$	−4.39776e35			−0.455921			−0.227961	+	0.973670i	$0.573206\pi$
$998$		−	3.96388e35i		−	0.406026i
$999$	−9.75666e34	+	6.28237e35i	−0.0987451	+	0.635826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.25.b.a.5.8	yes	8
3.2	odd	2	inner	6.25.b.a.5.4	✓	8
4.3	odd	2		48.25.e.d.17.2		8
12.11	even	2		48.25.e.d.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.25.b.a.5.4	✓	8	3.2	odd	2	inner
6.25.b.a.5.8	yes	8	1.1	even	1	trivial
48.25.e.d.17.1		8	12.11	even	2
48.25.e.d.17.2		8	4.3	odd	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2896.31i q^{2} +(473275. - 241744. i) q^{3} -8.38861e6 q^{4} -7.85820e7i q^{5} +(7.00165e8 + 1.37075e9i) q^{6} +2.19870e9 q^{7} -2.42960e10i q^{8} +(1.65549e11 - 2.28823e11i) q^{9} +O(q^{10})\)	\(q+2896.31i q^{2} +(473275. - 241744. i) q^{3} -8.38861e6 q^{4} -7.85820e7i q^{5} +(7.00165e8 + 1.37075e9i) q^{6} +2.19870e9 q^{7} -2.42960e10i q^{8} +(1.65549e11 - 2.28823e11i) q^{9} +2.27598e11 q^{10} -1.55920e12i q^{11} +(-3.97012e12 + 2.02789e12i) q^{12} -3.72207e13 q^{13} +6.36811e12i q^{14} +(-1.89967e13 - 3.71909e13i) q^{15} +7.03687e13 q^{16} -6.73556e14i q^{17} +(6.62742e14 + 4.79482e14i) q^{18} +9.37274e14 q^{19} +6.59193e14i q^{20} +(1.04059e15 - 5.31522e14i) q^{21} +4.51594e15 q^{22} -3.13424e16i q^{23} +(-5.87341e15 - 1.14987e16i) q^{24} +5.34295e16 q^{25} -1.07803e17i q^{26} +(2.30339e16 - 1.48317e17i) q^{27} -1.84440e16 q^{28} -2.21159e17i q^{29} +(1.07716e17 - 5.50203e16i) q^{30} +6.76426e17 q^{31} +2.03810e17i q^{32} +(-3.76928e17 - 7.37933e17i) q^{33} +1.95083e18 q^{34} -1.72778e17i q^{35} +(-1.38873e18 + 1.91950e18i) q^{36} -4.23578e18 q^{37} +2.71464e18i q^{38} +(-1.76157e19 + 8.99789e18i) q^{39} -1.90923e18 q^{40} +2.43094e19i q^{41} +(1.53945e18 + 3.01387e18i) q^{42} +2.27505e19 q^{43} +1.30796e19i q^{44} +(-1.79813e19 - 1.30092e19i) q^{45} +9.07774e19 q^{46} -6.93806e19i q^{47} +(3.33038e19 - 1.70112e19i) q^{48} -1.86747e20 q^{49} +1.54748e20i q^{50} +(-1.62828e20 - 3.18777e20i) q^{51} +3.12230e20 q^{52} -8.43863e20i q^{53} +(4.29571e20 + 6.67133e19i) q^{54} -1.22525e20 q^{55} -5.34196e19i q^{56} +(4.43589e20 - 2.26580e20i) q^{57} +6.40546e20 q^{58} +2.79071e21i q^{59} +(1.59356e20 + 3.11980e20i) q^{60} -4.56793e21 q^{61} +1.95914e21i q^{62} +(3.63993e20 - 5.03112e20i) q^{63} -5.90296e20 q^{64} +2.92488e21i q^{65} +(2.13728e21 - 1.09170e21i) q^{66} -1.20142e21 q^{67} +5.65019e21i q^{68} +(-7.57684e21 - 1.48336e22i) q^{69} +5.00419e20 q^{70} +1.60117e22i q^{71} +(-5.55948e21 - 4.02219e21i) q^{72} +2.60444e22 q^{73} -1.22681e22i q^{74} +(2.52869e22 - 1.29163e22i) q^{75} -7.86242e21 q^{76} -3.42822e21i q^{77} +(-2.60607e22 - 5.10204e22i) q^{78} +8.00431e22 q^{79} -5.52971e21i q^{80} +(-2.49533e22 - 7.57629e22i) q^{81} -7.04077e22 q^{82} +1.65147e23i q^{83} +(-8.72910e21 + 4.45873e21i) q^{84} -5.29293e22 q^{85} +6.58923e22i q^{86} +(-5.34639e22 - 1.04669e23i) q^{87} -3.78824e22 q^{88} +4.33073e23i q^{89} +(3.76786e22 - 5.20795e22i) q^{90} -8.18372e22 q^{91} +2.62919e23i q^{92} +(3.20136e23 - 1.63522e23i) q^{93} +2.00948e23 q^{94} -7.36528e22i q^{95} +(4.92697e22 + 9.64581e22i) q^{96} -4.08706e23 q^{97} -5.40877e23i q^{98} +(-3.56782e23 - 2.58125e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9}+O(q^{10}) \) 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9	\( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 36\!\cdots\!36 q^{21}+ \cdots + 69\!\cdots\!44 q^{99}+O(q^{100}) \) 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9 - 1863369424896 * q^10 + 1106289623040 * q^12 + 50568363679120 * q^13 - 348034956760512 * q^15 + 562949953421312 * q^16 - 514738292981760 * q^18 - 978083631341264 * q^19 + 3640012304241936 * q^21 - 336450979430400 * q^22 - 282849366245376 * q^24 + 7630618767014024 * q^25 - 86594528606057640 * q^27 + 85234923203461120 * q^28 - 725410188900237312 * q^30 + 3092119786822709104 * q^31 - 8158685952668529600 * q^33 + 3821138032531341312 * q^34 - 2476057486864416768 * q^36 + 22590293223992782480 * q^37 - 40190176581881465040 * q^39 + 15631075664637984768 * q^40 - 79119883835565342720 * q^42 + 226487466371803896880 * q^43 - 347709996757177504128 * q^45 + 139842130561120468992 * q^46 - 9280229982150328320 * q^48 + 104686700473616731800 * q^49 + 558091874936566543104 * q^51 - 424198180105575464960 * q^52 + 334066775626796728320 * q^54 - 2212687664250467338368 * q^55 + 3588879995640760725840 * q^57 - 1867706355469718323200 * q^58 + 2919528822560885047296 * q^60 - 6507010783838092385648 * q^61 + 10112982777612899380080 * q^63 - 4722366482869645213696 * q^64 - 1924112442339530440704 * q^66 - 7042120118150060144720 * q^67 - 4323335967368731345536 * q^69 + 16481910236435553583104 * q^70 + 4317937762413135790080 * q^72 + 36259820324758576687120 * q^73 - 108081978448612908655272 * q^75 + 8204760174538377920512 * q^76 - 74188898027329578270720 * q^78 + 316807052777330015315824 * q^79 - 268518660504396776813304 * q^81 + 83114941529654645882880 * q^82 - 30534636335462338265088 * q^84 - 222512862545524200678912 * q^85 + 449461577201807342128320 * q^87 + 2822355377657688883200 * q^88 + 612683975543382025371648 * q^90 - 1196839602335690774367520 * q^91 + 873237537450828783745680 * q^93 - 1298887117621773403422720 * q^94 + 2372712456480891076608 * q^96 + 816517576248201265716880 * q^97 + 695858883367208922313344 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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