LMFDB - Embedded newform 15.9.c.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,9,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, 9, names="a")

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

chi := DirichletCharacter("15.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
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:	$6.11067915092$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 433 x^{8} - 2220 x^{7} + 49747 x^{6} + 744964 x^{5} + 4580249 x^{4} + 16418988 x^{3} + \cdots + 53656344 $ x^10 - 4x^9 - 433x^8 - 2220x^7 + 49747x^6 + 744964x^5 + 4580249x^4 + 16418988x^3 + 38943804x^2 + 57910464*x + 53656344
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{10}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.3
Root			$-7.95862 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.9.c.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.2357i q^{2} +(-57.8099 + 56.7364i) q^{3} +151.230 q^{4} -279.508i q^{5} +(580.739 + 591.726i) q^{6} +3448.05 q^{7} -4168.30i q^{8} +(122.959 - 6559.85i) q^{9} +O(q^{10})$	\(q-10.2357i q^{2} +(-57.8099 + 56.7364i) q^{3} +151.230 q^{4} -279.508i q^{5} +(580.739 + 591.726i) q^{6} +3448.05 q^{7} -4168.30i q^{8} +(122.959 - 6559.85i) q^{9} -2860.98 q^{10} -7123.65i q^{11} +(-8742.57 + 8580.23i) q^{12} +41361.3 q^{13} -35293.4i q^{14} +(15858.3 + 16158.3i) q^{15} -3950.77 q^{16} +119540. i q^{17} +(-67144.9 - 1258.58i) q^{18} -86288.8 q^{19} -42270.0i q^{20} +(-199331. + 195630. i) q^{21} -72915.8 q^{22} -317353. i q^{23} +(236494. + 240969. i) q^{24} -78125.0 q^{25} -423364. i q^{26} +(365074. + 386200. i) q^{27} +521448. q^{28} +59853.0i q^{29} +(165393. - 162321. i) q^{30} -1.02106e6 q^{31} -1.02664e6i q^{32} +(404170. + 411817. i) q^{33} +1.22358e6 q^{34} -963760. i q^{35} +(18595.0 - 992044. i) q^{36} +877366. q^{37} +883230. i q^{38} +(-2.39109e6 + 2.34669e6i) q^{39} -1.16507e6 q^{40} -1.55753e6i q^{41} +(2.00242e6 + 2.04030e6i) q^{42} -2.56966e6 q^{43} -1.07731e6i q^{44} +(-1.83353e6 - 34368.1i) q^{45} -3.24834e6 q^{46} +8.98739e6i q^{47} +(228394. - 224153. i) q^{48} +6.12427e6 q^{49} +799667. i q^{50} +(-6.78229e6 - 6.91061e6i) q^{51} +6.25506e6 q^{52} +6.22182e6i q^{53} +(3.95304e6 - 3.73680e6i) q^{54} -1.99112e6 q^{55} -1.43725e7i q^{56} +(4.98835e6 - 4.89572e6i) q^{57} +612639. q^{58} +3.96940e6i q^{59} +(2.39825e6 + 2.44362e6i) q^{60} -563629. q^{61} +1.04513e7i q^{62} +(423969. - 2.26187e7i) q^{63} -1.15199e7 q^{64} -1.15608e7i q^{65} +(4.21525e6 - 4.13698e6i) q^{66} +1.34009e7 q^{67} +1.80781e7i q^{68} +(1.80055e7 + 1.83461e7i) q^{69} -9.86480e6 q^{70} +3.56270e7i q^{71} +(-2.73434e7 - 512529. i) q^{72} +970897. q^{73} -8.98049e6i q^{74} +(4.51640e6 - 4.43253e6i) q^{75} -1.30494e7 q^{76} -2.45627e7i q^{77} +(2.40201e7 + 2.44746e7i) q^{78} -2.78755e7 q^{79} +1.10427e6i q^{80} +(-4.30165e7 - 1.61318e6i) q^{81} -1.59425e7 q^{82} -2.25794e7i q^{83} +(-3.01448e7 + 2.95851e7i) q^{84} +3.34126e7 q^{85} +2.63024e7i q^{86} +(-3.39584e6 - 3.46009e6i) q^{87} -2.96935e7 q^{88} -5.73209e7i q^{89} +(-351783. + 1.87676e7i) q^{90} +1.42616e8 q^{91} -4.79932e7i q^{92} +(5.90274e7 - 5.79313e7i) q^{93} +9.19926e7 q^{94} +2.41185e7i q^{95} +(5.82481e7 + 5.93502e7i) q^{96} -3.31851e7 q^{97} -6.26864e7i q^{98} +(-4.67301e7 - 875917. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9}+O(q^{10}) $ 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} - 8750 q^{10} - 3812 q^{12} - 55464 q^{13} - 21250 q^{15} + 280386 q^{16} - 419800 q^{18} - 231516 q^{19} + 289572 q^{21} + 1129940 q^{22} + 1136334 q^{24} - 781250 q^{25} - 335512 q^{27} - 3340724 q^{28} - 965000 q^{30} + 881620 q^{31} + 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} + 4672616 q^{37} + 1826792 q^{39} + 2913750 q^{40} - 5392860 q^{42} + 7731336 q^{43} - 2142500 q^{45} - 25424604 q^{46} + 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} + 21064016 q^{52} - 7979798 q^{54} - 4377500 q^{55} - 2856304 q^{57} - 4351100 q^{58} + 23016250 q^{60} + 22417020 q^{61} + 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} - 46646024 q^{67} + 33562632 q^{69} - 62992500 q^{70} + 54175560 q^{72} - 129964884 q^{73} + 8750000 q^{75} + 198922436 q^{76} + 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} + 202877560 q^{82} - 197346768 q^{84} - 110682500 q^{85} - 168322540 q^{87} - 484775700 q^{88} + 171878750 q^{90} + 444288464 q^{91} + 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} - 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9 - 8750 * q^10 - 3812 * q^12 - 55464 * q^13 - 21250 * q^15 + 280386 * q^16 - 419800 * q^18 - 231516 * q^19 + 289572 * q^21 + 1129940 * q^22 + 1136334 * q^24 - 781250 * q^25 - 335512 * q^27 - 3340724 * q^28 - 965000 * q^30 + 881620 * q^31 + 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 + 4672616 * q^37 + 1826792 * q^39 + 2913750 * q^40 - 5392860 * q^42 + 7731336 * q^43 - 2142500 * q^45 - 25424604 * q^46 + 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 + 21064016 * q^52 - 7979798 * q^54 - 4377500 * q^55 - 2856304 * q^57 - 4351100 * q^58 + 23016250 * q^60 + 22417020 * q^61 + 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 - 46646024 * q^67 + 33562632 * q^69 - 62992500 * q^70 + 54175560 * q^72 - 129964884 * q^73 + 8750000 * q^75 + 198922436 * q^76 + 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 + 202877560 * q^82 - 197346768 * q^84 - 110682500 * q^85 - 168322540 * q^87 - 484775700 * q^88 + 171878750 * q^90 + 444288464 * q^91 + 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 - 258825724 * q^97 - 33965200 * 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 $

$2$		−	10.2357i		−	0.639734i	−0.947463	−	0.319867i	$-0.896362\pi$
$2$		−	10.2357i		−	0.639734i	0.947463	−	0.319867i	$-0.103638\pi$
$3$	−57.8099	+	56.7364i	−0.713702	+	0.700450i
$3$	−57.8099	+	56.7364i	−0.713702	+	0.700450i
$4$	151.230			0.590741
$5$		−	279.508i		−	0.447214i
$5$		−	279.508i		−	0.447214i
$6$	580.739	+	591.726i	0.448101	+	0.456579i
$7$	3448.05			1.43609			0.718045	−	0.695996i	$-0.245037\pi$
$7$	3448.05			1.43609			0.718045	+	0.695996i	$0.245037\pi$
$8$		−	4168.30i		−	1.01765i
$9$	122.959	−	6559.85i	0.0187409	−	0.999824i
$10$	−2860.98			−0.286098
$11$		−	7123.65i		−	0.486555i	−0.969957	−	0.243277i	$-0.921777\pi$
$11$		−	7123.65i		−	0.486555i	0.969957	−	0.243277i	$-0.0782225\pi$
$12$	−8742.57	+	8580.23i	−0.421613	+	0.413784i
$13$	41361.3			1.44818			0.724088	−	0.689708i	$-0.242261\pi$
$13$	41361.3			1.44818			0.724088	+	0.689708i	$0.242261\pi$
$14$		−	35293.4i		−	0.918715i
$15$	15858.3	+	16158.3i	0.313251	+	0.319177i
$16$	−3950.77			−0.0602840
$17$			119540.i			1.43126i	0.698479	+	0.715631i	$0.253861\pi$
$17$			119540.i			1.43126i	−0.698479	+	0.715631i	$0.746139\pi$
$18$	−67144.9	−	1258.58i	−0.639621	−	0.0119892i
$19$	−86288.8			−0.662125			−0.331063	−	0.943609i	$-0.607407\pi$
$19$	−86288.8			−0.662125			−0.331063	+	0.943609i	$0.607407\pi$
$20$		−	42270.0i		−	0.264187i
$21$	−199331.	+	195630.i	−1.02494	+	1.00591i
$22$	−72915.8			−0.311265
$23$		−	317353.i		−	1.13405i	−0.823701	−	0.567024i	$-0.808095\pi$
$23$		−	317353.i		−	1.13405i	0.823701	−	0.567024i	$-0.191905\pi$
$24$	236494.	+	240969.i	0.712813	+	0.726299i
$25$	−78125.0			−0.200000
$26$		−	423364.i		−	0.926447i
$27$	365074.	+	386200.i	0.686951	+	0.726704i
$28$	521448.			0.848358
$29$			59853.0i			0.0846240i	0.999104	+	0.0423120i	$0.0134724\pi$
$29$			59853.0i			0.0846240i	−0.999104	+	0.0423120i	$0.986528\pi$
$30$	165393.	−	162321.i	0.204188	−	0.200397i
$31$	−1.02106e6			−1.10562			−0.552809	−	0.833308i	$-0.686444\pi$
$31$	−1.02106e6			−1.10562			−0.552809	+	0.833308i	$0.686444\pi$
$32$		−	1.02664e6i		−	0.979085i
$33$	404170.	+	411817.i	0.340807	+	0.347255i
$34$	1.22358e6			0.915626
$35$		−	963760.i		−	0.642239i
$36$	18595.0	−	992044.i	0.0110710	−	0.590637i
$37$	877366.			0.468138			0.234069	−	0.972220i	$-0.424796\pi$
$37$	877366.			0.468138			0.234069	+	0.972220i	$0.424796\pi$
$38$			883230.i			0.423584i
$39$	−2.39109e6	+	2.34669e6i	−1.03357	+	1.01437i
$40$	−1.16507e6			−0.455107
$41$		−	1.55753e6i		−	0.551189i	−0.961274	−	0.275595i	$-0.911125\pi$
$41$		−	1.55753e6i		−	0.551189i	0.961274	−	0.275595i	$-0.0888747\pi$
$42$	2.00242e6	+	2.04030e6i	0.643514	+	0.655689i
$43$	−2.56966e6			−0.751626			−0.375813	−	0.926696i	$-0.622636\pi$
$43$	−2.56966e6			−0.751626			−0.375813	+	0.926696i	$0.622636\pi$
$44$		−	1.07731e6i		−	0.287428i
$45$	−1.83353e6	−	34368.1i	−0.447135	−	0.00838118i
$46$	−3.24834e6			−0.725489
$47$			8.98739e6i			1.84180i	0.389800	+	0.920899i	$0.372544\pi$
$47$			8.98739e6i			1.84180i	−0.389800	+	0.920899i	$0.627456\pi$
$48$	228394.	−	224153.i	0.0430248	−	0.0422259i
$49$	6.12427e6			1.06236
$50$			799667.i			0.127947i
$51$	−6.78229e6	−	6.91061e6i	−1.00253	−	1.02149i
$52$	6.25506e6			0.855497
$53$			6.22182e6i			0.788522i	0.918999	+	0.394261i	$0.128999\pi$
$53$			6.22182e6i			0.788522i	−0.918999	+	0.394261i	$0.871001\pi$
$54$	3.95304e6	−	3.73680e6i	0.464897	−	0.439466i
$55$	−1.99112e6			−0.217594
$56$		−	1.43725e7i		−	1.46144i
$57$	4.98835e6	−	4.89572e6i	0.472560	−	0.463785i
$58$	612639.			0.0541368
$59$			3.96940e6i			0.327580i	0.986495	+	0.163790i	$0.0523719\pi$
$59$			3.96940e6i			0.327580i	−0.986495	+	0.163790i	$0.947628\pi$
$60$	2.39825e6	+	2.44362e6i	0.185050	+	0.188551i
$61$	−563629.			−0.0407074			−0.0203537	−	0.999793i	$-0.506479\pi$
$61$	−563629.			−0.0407074			−0.0203537	+	0.999793i	$0.506479\pi$
$62$			1.04513e7i			0.707300i
$63$	423969.	−	2.26187e7i	0.0269136	−	1.43584i
$64$	−1.15199e7			−0.686637
$65$		−	1.15608e7i		−	0.647644i
$66$	4.21525e6	−	4.13698e6i	0.222151	−	0.218026i
$67$	1.34009e7			0.665021			0.332510	−	0.943100i	$-0.392104\pi$
$67$	1.34009e7			0.665021			0.332510	+	0.943100i	$0.392104\pi$
$68$			1.80781e7i			0.845505i
$69$	1.80055e7	+	1.83461e7i	0.794343	+	0.809372i
$70$	−9.86480e6			−0.410862
$71$			3.56270e7i			1.40199i	0.713165	+	0.700997i	$0.247261\pi$
$71$			3.56270e7i			1.40199i	−0.713165	+	0.700997i	$0.752739\pi$
$72$	−2.73434e7	−	512529.i	−1.01747	−	0.0190717i
$73$	970897.			0.0341886			0.0170943	−	0.999854i	$-0.494558\pi$
$73$	970897.			0.0341886			0.0170943	+	0.999854i	$0.494558\pi$
$74$		−	8.98049e6i		−	0.299484i
$75$	4.51640e6	−	4.43253e6i	0.142740	−	0.140090i
$76$	−1.30494e7			−0.391145
$77$		−	2.45627e7i		−	0.698737i
$78$	2.40201e7	+	2.44746e7i	0.648929	+	0.661207i
$79$	−2.78755e7			−0.715672			−0.357836	−	0.933784i	$-0.616485\pi$
$79$	−2.78755e7			−0.715672			−0.357836	+	0.933784i	$0.616485\pi$
$80$			1.10427e6i			0.0269598i
$81$	−4.30165e7	−	1.61318e6i	−0.999298	−	0.0374752i
$82$	−1.59425e7			−0.352614
$83$		−	2.25794e7i		−	0.475773i	−0.971293	−	0.237886i	$-0.923545\pi$
$83$		−	2.25794e7i		−	0.475773i	0.971293	−	0.237886i	$-0.0764546\pi$
$84$	−3.01448e7	+	2.95851e7i	−0.605474	+	0.594232i
$85$	3.34126e7			0.640080
$86$			2.63024e7i			0.480840i
$87$	−3.39584e6	−	3.46009e6i	−0.0592749	−	0.0603963i
$88$	−2.96935e7			−0.495143
$89$		−	5.73209e7i		−	0.913593i	−0.889571	−	0.456796i	$-0.848997\pi$
$89$		−	5.73209e7i		−	0.913593i	0.889571	−	0.456796i	$-0.151003\pi$
$90$	−351783.	+	1.87676e7i	−0.00536172	+	0.286047i
$91$	1.42616e8			2.07971
$92$		−	4.79932e7i		−	0.669929i
$93$	5.90274e7	−	5.79313e7i	0.789081	−	0.774429i
$94$	9.19926e7			1.17826
$95$			2.41185e7i			0.296111i
$96$	5.82481e7	+	5.93502e7i	0.685799	+	0.698775i
$97$	−3.31851e7			−0.374848			−0.187424	−	0.982279i	$-0.560014\pi$
$97$	−3.31851e7			−0.374848			−0.187424	+	0.982279i	$0.560014\pi$
$98$		−	6.26864e7i		−	0.679625i
$99$	−4.67301e7	−	875917.i	−0.486469	−	0.00911847i
$100$	−1.18148e7			−0.118148
$101$			65955.2i			0.000633816i	1.00000		0.000316908i	$0.000100875\pi$
$101$			65955.2i			0.000633816i	−1.00000		0.000316908i	$0.999899\pi$
$102$	−7.07352e7	+	6.94218e7i	−0.653484	+	0.641350i
$103$	−2.03592e8			−1.80889			−0.904444	−	0.426593i	$-0.859714\pi$
$103$	−2.03592e8			−1.80889			−0.904444	+	0.426593i	$0.859714\pi$
$104$		−	1.72406e8i		−	1.47374i
$105$	5.46803e7	+	5.57148e7i	0.449856	+	0.458367i
$106$	6.36849e7			0.504444
$107$		−	3.26956e7i		−	0.249433i	−0.992192	−	0.124716i	$-0.960198\pi$
$107$		−	3.26956e7i		−	0.249433i	0.992192	−	0.124716i	$-0.0398021\pi$
$108$	5.52100e7	+	5.84049e7i	0.405810	+	0.429294i
$109$	−6.88723e7			−0.487909			−0.243954	−	0.969787i	$-0.578445\pi$
$109$	−6.88723e7			−0.487909			−0.243954	+	0.969787i	$0.578445\pi$
$110$			2.03806e7i			0.139202i
$111$	−5.07204e7	+	4.97786e7i	−0.334111	+	0.327907i
$112$	−1.36225e7			−0.0865733
$113$			2.24841e8i			1.37899i	0.724289	+	0.689497i	$0.242168\pi$
$113$			2.24841e8i			1.37899i	−0.724289	+	0.689497i	$0.757832\pi$
$114$	−5.01113e7	−	5.10594e7i	−0.296699	−	0.302313i
$115$	−8.87029e7			−0.507162
$116$			9.05155e6i			0.0499909i
$117$	5.08575e6	−	2.71324e8i	0.0271401	−	1.44792i
$118$	4.06297e7			0.209564
$119$			4.12182e8i			2.05542i
$120$	6.73528e7	−	6.61021e7i	0.324811	−	0.318780i
$121$	1.63612e8			0.763264
$122$			5.76915e6i			0.0260419i
$123$	8.83686e7	+	9.00405e7i	0.386080	+	0.393385i
$124$	−1.54415e8			−0.653133
$125$			2.18366e7i			0.0894427i
$126$	−2.31519e8	−	4.33964e6i	−0.918554	−	0.0172175i
$127$	−1.02495e7			−0.0393993			−0.0196996	−	0.999806i	$-0.506271\pi$
$127$	−1.02495e7			−0.0393993			−0.0196996	+	0.999806i	$0.506271\pi$
$128$		−	1.44907e8i		−	0.539820i
$129$	1.48552e8	−	1.45793e8i	0.536437	−	0.526476i
$130$	−1.18334e8			−0.414320
$131$			8.55607e7i			0.290529i	0.989393	+	0.145264i	$0.0464033\pi$
$131$			8.55607e7i			0.290529i	−0.989393	+	0.145264i	$0.953597\pi$
$132$	6.11226e7	+	6.22790e7i	0.201329	+	0.205138i
$133$	−2.97529e8			−0.950872
$134$		−	1.37168e8i		−	0.425436i
$135$	1.07946e8	−	1.02041e8i	0.324992	−	0.307214i
$136$	4.98280e8			1.45652
$137$			2.41199e7i			0.0684688i	0.999414	+	0.0342344i	$0.0108993\pi$
$137$			2.41199e7i			0.0684688i	−0.999414	+	0.0342344i	$0.989101\pi$
$138$	1.87786e8	−	1.84299e8i	0.517783	−	0.508168i
$139$	4.84604e8			1.29816			0.649079	−	0.760721i	$-0.275154\pi$
$139$	4.84604e8			1.29816			0.649079	+	0.760721i	$0.275154\pi$
$140$		−	1.45749e8i		−	0.379397i
$141$	−5.09912e8	−	5.19560e8i	−1.29009	−	1.31450i
$142$	3.64669e8			0.896902
$143$		−	2.94644e8i		−	0.704617i
$144$	−485783.	+	2.59165e7i	−0.00112978	+	0.0602734i
$145$	1.67294e7			0.0378450
$146$		−	9.93784e6i		−	0.0218716i
$147$	−3.54043e8	+	3.47469e8i	−0.758206	+	0.744127i
$148$	1.32684e8			0.276548
$149$			6.26323e8i			1.27073i	0.772212	+	0.635365i	$0.219150\pi$
$149$			6.26323e8i			1.27073i	−0.772212	+	0.635365i	$0.780850\pi$
$150$	−4.53702e7	−	4.62286e7i	−0.0896202	−	0.0913158i
$151$	−9.61203e8			−1.84887			−0.924437	−	0.381334i	$-0.875465\pi$
$151$	−9.61203e8			−1.84887			−0.924437	+	0.381334i	$0.875465\pi$
$152$			3.59677e8i			0.673812i
$153$	7.84167e8	+	1.46986e7i	1.43101	+	0.0268231i
$154$	−2.51418e8			−0.447005
$155$			2.85395e8i			0.494447i
$156$	−3.61604e8	+	3.54890e8i	−0.610570	+	0.599232i
$157$	9.24294e8			1.52129			0.760644	−	0.649169i	$-0.224883\pi$
$157$	9.24294e8			1.52129			0.760644	+	0.649169i	$0.224883\pi$
$158$			2.85326e8i			0.457839i
$159$	−3.53004e8	−	3.59682e8i	−0.552320	−	0.562770i
$160$	−2.86956e8			−0.437860
$161$		−	1.09425e9i		−	1.62860i
$162$	−1.65121e7	+	4.40305e8i	−0.0239741	+	0.639284i
$163$	−1.30110e9			−1.84315			−0.921575	−	0.388200i	$-0.873097\pi$
$163$	−1.30110e9			−1.84315			−0.921575	+	0.388200i	$0.873097\pi$
$164$		−	2.35545e8i		−	0.325610i
$165$	1.15106e8	−	1.12969e8i	0.155297	−	0.152414i
$166$	−2.31117e8			−0.304368
$167$			1.12208e9i			1.44263i	0.692605	+	0.721317i	$0.256463\pi$
$167$			1.12208e9i			1.44263i	−0.692605	+	0.721317i	$0.743537\pi$
$168$	8.15444e8	+	8.30873e8i	1.02366	+	1.04303i
$169$	8.95030e8			1.09721
$170$		−	3.42002e8i		−	0.409480i
$171$	−1.06100e7	+	5.66042e8i	−0.0124088	+	0.662009i
$172$	−3.88609e8			−0.444016
$173$		−	1.21708e9i		−	1.35874i	−0.733797	−	0.679369i	$-0.762254\pi$
$173$		−	1.21708e9i		−	1.35874i	0.733797	−	0.679369i	$-0.237746\pi$
$174$	−3.54166e7	+	3.47590e7i	−0.0386376	+	0.0379201i
$175$	−2.69379e8			−0.287218
$176$			2.81439e7i			0.0293315i
$177$	−2.25210e8	−	2.29471e8i	−0.229453	−	0.233794i
$178$	−5.86721e8			−0.584456
$179$		−	3.40141e8i		−	0.331320i	−0.986183	−	0.165660i	$-0.947025\pi$
$179$		−	3.40141e8i		−	0.331320i	0.986183	−	0.165660i	$-0.0529754\pi$
$180$	−2.77285e8	−	5.19747e6i	−0.264141	−	0.00495111i
$181$	1.89427e9			1.76493			0.882466	−	0.470377i	$-0.155882\pi$
$181$	1.89427e9			1.76493			0.882466	+	0.470377i	$0.155882\pi$
$182$		−	1.45978e9i		−	1.33046i
$183$	3.25833e7	−	3.19783e7i	0.0290530	−	0.0285135i
$184$	−1.32282e9			−1.15406
$185$		−	2.45231e8i		−	0.209358i
$186$	−5.92970e8	−	6.04189e8i	−0.495428	−	0.504802i
$187$	8.51564e8			0.696387
$188$			1.35916e9i			1.08803i
$189$	1.25879e9	+	1.33164e9i	0.986524	+	1.04361i
$190$	2.46870e8			0.189432
$191$		−	1.22208e9i		−	0.918262i	−0.888369	−	0.459131i	$-0.848161\pi$
$191$		−	1.22208e9i		−	0.918262i	0.888369	−	0.459131i	$-0.151839\pi$
$192$	6.65962e8	−	6.53596e8i	0.490054	−	0.480955i
$193$	3.63918e8			0.262286			0.131143	−	0.991363i	$-0.458135\pi$
$193$	3.63918e8			0.262286			0.131143	+	0.991363i	$0.458135\pi$
$194$			3.39674e8i			0.239803i
$195$	6.55921e8	+	6.68331e8i	0.453642	+	0.462225i
$196$	9.26172e8			0.627577
$197$		−	1.98338e9i		−	1.31687i	−0.752639	−	0.658434i	$-0.771219\pi$
$197$		−	1.98338e9i		−	1.31687i	0.752639	−	0.658434i	$-0.228781\pi$
$198$	−8.96565e6	+	4.78317e8i	−0.00583339	+	0.311211i
$199$	6.06495e8			0.386736			0.193368	−	0.981126i	$-0.438059\pi$
$199$	6.06495e8			0.386736			0.193368	+	0.981126i	$0.438059\pi$
$200$			3.25648e8i			0.203530i
$201$	−7.74705e8	+	7.60320e8i	−0.474627	+	0.465814i
$202$	675100.			0.000405474
$203$			2.06376e8i			0.121528i
$204$	−1.02568e9	−	1.04509e9i	−0.592233	−	0.603438i
$205$	−4.35343e8			−0.246499
$206$			2.08391e9i			1.15721i
$207$	−2.08179e9	−	3.90214e7i	−1.13385	−	0.0212531i
$208$	−1.63409e8			−0.0873019
$209$			6.14691e8i			0.322160i
$210$	5.70282e8	−	5.59693e8i	0.293233	−	0.287788i
$211$	−4.10164e8			−0.206932			−0.103466	−	0.994633i	$-0.532993\pi$
$211$	−4.10164e8			−0.206932			−0.103466	+	0.994633i	$0.532993\pi$
$212$			9.40924e8i			0.465812i
$213$	−2.02135e9	−	2.05959e9i	−0.982026	−	1.00061i
$214$	−3.34663e8			−0.159571
$215$			7.18242e8i			0.336137i
$216$	1.60980e9	−	1.52174e9i	0.739530	−	0.699076i
$217$	−3.52067e9			−1.58777
$218$			7.04958e8i			0.312131i
$219$	−5.61274e7	+	5.50852e7i	−0.0244005	+	0.0239474i
$220$	−3.01117e8			−0.128542
$221$			4.94435e9i			2.07272i
$222$	5.09521e8	+	5.19161e8i	0.209773	+	0.213742i
$223$	−4.68112e8			−0.189291			−0.0946455	−	0.995511i	$-0.530172\pi$
$223$	−4.68112e8			−0.189291			−0.0946455	+	0.995511i	$0.530172\pi$
$224$		−	3.53993e9i		−	1.40605i
$225$	−9.60617e6	+	5.12488e8i	−0.00374818	+	0.199965i
$226$	2.30142e9			0.882188
$227$			2.13615e9i			0.804503i	0.915529	+	0.402251i	$0.131772\pi$
$227$			2.13615e9i			0.804503i	−0.915529	+	0.402251i	$0.868228\pi$
$228$	7.54386e8	−	7.40378e8i	0.279161	−	0.273977i
$229$	−7.50976e8			−0.273076			−0.136538	−	0.990635i	$-0.543598\pi$
$229$	−7.50976e8			−0.273076			−0.136538	+	0.990635i	$0.543598\pi$
$230$			9.07939e8i			0.324448i
$231$	1.39360e9	+	1.41997e9i	0.489430	+	0.498690i
$232$	2.49485e8			0.0861177
$233$		−	2.03107e9i		−	0.689129i	−0.938763	−	0.344565i	$-0.888027\pi$
$233$		−	2.03107e9i		−	0.689129i	0.938763	−	0.344565i	$-0.111973\pi$
$234$	−2.77720e9	−	5.20564e7i	−0.926284	−	0.0173624i
$235$	2.51205e9			0.823677
$236$			6.00291e8i			0.193515i
$237$	1.61148e9	−	1.58156e9i	0.510777	−	0.501292i
$238$	4.21898e9			1.31492
$239$		−	1.54091e9i		−	0.472265i	−0.971721	−	0.236133i	$-0.924120\pi$
$239$		−	1.54091e9i		−	0.472265i	0.971721	−	0.236133i	$-0.0758800\pi$
$240$	−6.26526e7	−	6.38380e7i	−0.0188840	−	0.0192413i
$241$	−9.80028e8			−0.290516			−0.145258	−	0.989394i	$-0.546401\pi$
$241$	−9.80028e8			−0.290516			−0.145258	+	0.989394i	$0.546401\pi$
$242$		−	1.67469e9i		−	0.488286i
$243$	2.57830e9	−	2.34734e9i	0.739450	−	0.673211i
$244$	−8.52374e7			−0.0240475
$245$		−	1.71179e9i		−	0.475100i
$246$	9.21631e8	−	9.04518e8i	0.251661	−	0.246988i
$247$	−3.56902e9			−0.958874
$248$			4.25608e9i			1.12513i
$249$	1.28107e9	+	1.30531e9i	0.333255	+	0.339560i
$250$	2.23514e8			0.0572195
$251$		−	3.36978e9i		−	0.848997i	−0.905429	−	0.424499i	$-0.860450\pi$
$251$		−	3.36978e9i		−	0.848997i	0.905429	−	0.424499i	$-0.139550\pi$
$252$	6.41167e7	−	3.42062e9i	0.0158990	−	0.848209i
$253$	−2.26071e9			−0.551777
$254$			1.04911e8i			0.0252050i
$255$	−1.93157e9	+	1.89571e9i	−0.456826	+	0.448343i
$256$	−4.43231e9			−1.03198
$257$			6.58864e8i			0.151030i	0.997145	+	0.0755150i	$0.0240601\pi$
$257$			6.58864e8i			0.151030i	−0.997145	+	0.0755150i	$0.975940\pi$
$258$	−1.49230e9	−	1.52054e9i	−0.336804	−	0.343177i
$259$	3.02521e9			0.672289
$260$		−	1.74834e9i		−	0.382590i
$261$	3.92626e8	+	7.35946e6i	0.0846092	+	0.00158593i
$262$	8.75777e8			0.185861
$263$		−	1.12759e9i		−	0.235682i	−0.993032	−	0.117841i	$-0.962403\pi$
$263$		−	1.12759e9i		−	0.235682i	0.993032	−	0.117841i	$-0.0375973\pi$
$264$	1.71658e9	−	1.68470e9i	0.353384	−	0.346822i
$265$	1.73905e9			0.352638
$266$			3.04542e9i			0.608305i
$267$	3.25218e9	+	3.31371e9i	0.639926	+	0.652033i
$268$	2.02662e9			0.392855
$269$			5.06830e9i			0.967950i	0.875082	+	0.483975i	$0.160807\pi$
$269$			5.06830e9i			0.967950i	−0.875082	+	0.483975i	$0.839193\pi$
$270$	−1.04447e9	−	1.10491e9i	−0.196535	−	0.207908i
$271$	−2.89969e9			−0.537618			−0.268809	−	0.963194i	$-0.586630\pi$
$271$	−2.89969e9			−0.537618			−0.268809	+	0.963194i	$0.586630\pi$
$272$		−	4.72277e8i		−	0.0862822i
$273$	−8.24462e9	+	8.09153e9i	−1.48429	+	1.45673i
$274$	2.46885e8			0.0438018
$275$			5.56535e8i			0.0973110i
$276$	2.72296e9	+	2.77448e9i	0.469251	+	0.478129i
$277$	6.70508e9			1.13890			0.569449	−	0.822027i	$-0.307157\pi$
$277$	6.70508e9			1.13890			0.569449	+	0.822027i	$0.307157\pi$
$278$		−	4.96028e9i		−	0.830476i
$279$	−1.25549e8	+	6.69800e9i	−0.0207202	+	1.10542i
$280$	−4.01724e9			−0.653575
$281$		−	1.08727e10i		−	1.74387i	−0.489625	−	0.871933i	$-0.662866\pi$
$281$		−	1.08727e10i		−	1.74387i	0.489625	−	0.871933i	$-0.337134\pi$
$282$	−5.31808e9	+	5.21933e9i	−0.840927	+	0.825312i
$283$	3.48119e9			0.542728			0.271364	−	0.962477i	$-0.412525\pi$
$283$	3.48119e9			0.542728			0.271364	+	0.962477i	$0.412525\pi$
$284$			5.38786e9i			0.828215i
$285$	−1.36840e9	−	1.39428e9i	−0.207411	−	0.211335i
$286$	−3.01590e9			−0.450767
$287$		−	5.37044e9i		−	0.791558i
$288$	−6.73463e9	−	1.26235e8i	−0.978913	−	0.0183489i
$289$	−7.31415e9			−1.04851
$290$		−	1.71238e8i		−	0.0242107i
$291$	1.91842e9	−	1.88280e9i	0.267530	−	0.262562i
$292$	1.46828e8			0.0201966
$293$			9.46915e9i			1.28481i	0.766364	+	0.642407i	$0.222064\pi$
$293$			9.46915e9i			1.28481i	−0.766364	+	0.642407i	$0.777936\pi$
$294$	3.55660e9	+	3.62389e9i	0.476043	+	0.485050i
$295$	1.10948e9			0.146498
$296$		−	3.65712e9i		−	0.476401i
$297$	2.75115e9	−	2.60066e9i	0.353581	−	0.334239i
$298$	6.41088e9			0.812929
$299$		−	1.31262e10i		−	1.64230i
$300$	6.83013e8	−	6.70331e8i	0.0843226	−	0.0827569i
$301$	−8.86032e9			−1.07940
$302$			9.83862e9i			1.18279i
$303$	−3.74206e6	−	3.81286e6i	−0.000443956	−	0.000452356i
$304$	3.40908e8			0.0399156
$305$			1.57539e8i			0.0182049i
$306$	1.50451e8	−	8.02652e9i	0.0171596	−	0.915465i
$307$	8.28984e9			0.933239			0.466619	−	0.884458i	$-0.345472\pi$
$307$	8.28984e9			0.933239			0.466619	+	0.884458i	$0.345472\pi$
$308$		−	3.71461e9i		−	0.412773i
$309$	1.17696e10	−	1.15511e10i	1.29101	−	1.26703i
$310$	2.92123e9			0.316314
$311$		−	8.23247e9i		−	0.880012i	−0.897995	−	0.440006i	$-0.854976\pi$
$311$		−	8.23247e9i		−	0.880012i	0.897995	−	0.440006i	$-0.145024\pi$
$312$	9.78172e9	+	9.96679e9i	1.03228	+	1.05181i
$313$	1.27222e10			1.32551			0.662757	−	0.748835i	$-0.269386\pi$
$313$	1.27222e10			1.32551			0.662757	+	0.748835i	$0.269386\pi$
$314$		−	9.46083e9i		−	0.973219i
$315$	−6.32212e9	−	1.18503e8i	−0.642126	−	0.0120361i
$316$	−4.21560e9			−0.422777
$317$			6.36014e9i			0.629839i	0.949118	+	0.314920i	$0.101978\pi$
$317$			6.36014e9i			0.629839i	−0.949118	+	0.314920i	$0.898022\pi$
$318$	−3.68161e9	+	3.61325e9i	−0.360023	+	0.353338i
$319$	4.26372e8			0.0411742
$320$			3.21990e9i			0.307074i
$321$	1.85503e9	+	1.89013e9i	0.174715	+	0.178021i
$322$	−1.12005e10			−1.04187
$323$		−	1.03150e10i		−	0.947674i
$324$	−6.50537e9	−	2.43961e8i	−0.590326	−	0.0221381i
$325$	−3.23136e9			−0.289635
$326$			1.33177e10i			1.17913i
$327$	3.98150e9	−	3.90757e9i	0.348221	−	0.341755i
$328$	−6.49224e9			−0.560918
$329$			3.09890e10i			2.64499i
$330$	−1.15632e9	−	1.17820e9i	−0.0975041	−	0.0993488i
$331$	1.25518e9			0.104567			0.0522836	−	0.998632i	$-0.483350\pi$
$331$	1.25518e9			0.104567			0.0522836	+	0.998632i	$0.483350\pi$
$332$		−	3.41467e9i		−	0.281059i
$333$	1.07880e8	−	5.75539e9i	0.00877332	−	0.468056i
$334$	1.14853e10			0.922902
$335$		−	3.74567e9i		−	0.297406i
$336$	7.87514e8	−	7.72891e8i	0.0617875	−	0.0606402i
$337$	−8.02773e9			−0.622405			−0.311203	−	0.950344i	$-0.600732\pi$
$337$	−8.02773e9			−0.622405			−0.311203	+	0.950344i	$0.600732\pi$
$338$		−	9.16129e9i		−	0.701924i
$339$	−1.27567e10	−	1.29980e10i	−0.965915	−	0.984190i
$340$	5.05297e9			0.378121
$341$			7.27368e9i			0.537943i
$342$	5.79385e9	+	1.08601e8i	0.423509	+	0.00793834i
$343$	1.23948e9			0.0895491
$344$			1.07111e10i			0.764892i
$345$	5.12790e9	−	5.03268e9i	0.361962	−	0.355241i
$346$	−1.24577e10			−0.869230
$347$			6.89272e9i			0.475415i	0.971337	+	0.237707i	$0.0763960\pi$
$347$			6.89272e9i			0.475415i	−0.971337	+	0.237707i	$0.923604\pi$
$348$	−5.13552e8	−	5.23269e8i	−0.0350161	−	0.0356786i
$349$	−1.26058e10			−0.849703			−0.424852	−	0.905263i	$-0.639674\pi$
$349$	−1.26058e10			−0.849703			−0.424852	+	0.905263i	$0.639674\pi$
$350$			2.75729e9i			0.183743i
$351$	1.51000e10	+	1.59738e10i	0.994826	+	1.05239i
$352$	−7.31346e9			−0.476378
$353$			1.83440e10i			1.18139i	0.806894	+	0.590697i	$0.201147\pi$
$353$			1.83440e10i			1.18139i	−0.806894	+	0.590697i	$0.798853\pi$
$354$	−2.34880e9	+	2.30519e9i	−0.149566	+	0.146789i
$355$	9.95805e9			0.626990
$356$		−	8.66862e9i		−	0.539697i
$357$	−2.33857e10	−	2.38282e10i	−1.43972	−	1.46696i
$358$	−3.48160e9			−0.211956
$359$		−	1.55471e7i		−	0.000935992i	−1.00000		0.000467996i	$-0.999851\pi$
$359$		−	1.55471e7i		−	0.000935992i	1.00000		0.000467996i	$-0.000148968\pi$
$360$	−1.43256e8	+	7.64271e9i	−0.00852911	+	0.455027i
$361$	−9.53780e9			−0.561590
$362$		−	1.93893e10i		−	1.12909i
$363$	−9.45842e9	+	9.28279e9i	−0.544743	+	0.534628i
$364$	2.15678e10			1.22857
$365$		−	2.71374e8i		−	0.0152896i
$366$	−3.27321e8	−	3.33514e8i	−0.0182410	−	0.0185862i
$367$	−4.76932e9			−0.262901			−0.131450	−	0.991323i	$-0.541963\pi$
$367$	−4.76932e9			−0.262901			−0.131450	+	0.991323i	$0.541963\pi$
$368$			1.25379e9i			0.0683650i
$369$	−1.02172e10	−	1.91512e8i	−0.551092	−	0.0103298i
$370$	−2.51012e9			−0.133933
$371$			2.14532e10i			1.13239i
$372$	8.92669e9	−	8.76094e9i	0.466143	−	0.457487i
$373$	2.29205e10			1.18410			0.592051	−	0.805901i	$-0.298319\pi$
$373$	2.29205e10			1.18410			0.592051	+	0.805901i	$0.298319\pi$
$374$		−	8.71638e9i		−	0.445502i
$375$	−1.23893e9	−	1.26237e9i	−0.0626501	−	0.0638354i
$376$	3.74621e10			1.87431
$377$			2.47560e9i			0.122550i
$378$	1.36303e10	−	1.28847e10i	0.667634	−	0.631112i
$379$	−6.81528e9			−0.330314			−0.165157	−	0.986267i	$-0.552813\pi$
$379$	−6.81528e9			−0.330314			−0.165157	+	0.986267i	$0.552813\pi$
$380$			3.64743e9i			0.174925i
$381$	5.92522e8	−	5.81520e8i	0.0281193	−	0.0275972i
$382$	−1.25089e10			−0.587443
$383$		−	1.07682e10i		−	0.500437i	−0.968189	−	0.250219i	$-0.919497\pi$
$383$		−	1.07682e10i		−	0.500437i	0.968189	−	0.250219i	$-0.0805025\pi$
$384$	8.22149e9	+	8.37704e9i	0.378116	+	0.385270i
$385$	−6.86549e9			−0.312485
$386$		−	3.72497e9i		−	0.167793i
$387$	−3.15963e8	+	1.68566e10i	−0.0140861	+	0.751494i
$388$	−5.01857e9			−0.221438
$389$		−	3.21668e10i		−	1.40479i	−0.711790	−	0.702393i	$-0.752115\pi$
$389$		−	3.21668e10i		−	1.40479i	0.711790	−	0.702393i	$-0.247885\pi$
$390$	6.84086e9	−	6.71383e9i	0.295701	−	0.290210i
$391$	3.79365e10			1.62312
$392$		−	2.55278e10i		−	1.08111i
$393$	−4.85441e9	−	4.94625e9i	−0.203501	−	0.207351i
$394$	−2.03014e10			−0.842444
$395$			7.79144e9i			0.320058i
$396$	−7.06697e9	−	1.32465e8i	−0.287377	−	0.00538665i
$397$	3.26005e10			1.31239			0.656194	−	0.754592i	$-0.272165\pi$
$397$	3.26005e10			1.31239			0.656194	+	0.754592i	$0.272165\pi$
$398$		−	6.20792e9i		−	0.247408i
$399$	1.72001e10	−	1.68807e10i	0.678639	−	0.666038i
$400$	3.08654e8			0.0120568
$401$			2.38085e10i			0.920778i	0.887717	+	0.460389i	$0.152290\pi$
$401$			2.38085e10i			0.920778i	−0.887717	+	0.460389i	$0.847710\pi$
$402$	7.78244e9	+	7.92968e9i	0.297997	+	0.303635i
$403$	−4.22324e10			−1.60113
$404$			9.97438e6i			0.000374421i
$405$	−4.50899e8	+	1.20235e10i	−0.0167594	+	0.446899i
$406$	2.11241e9			0.0777454
$407$		−	6.25005e9i		−	0.227775i
$408$	−2.88055e10	+	2.82706e10i	−1.03952	+	1.02022i
$409$	−3.89304e10			−1.39122			−0.695609	−	0.718420i	$-0.744866\pi$
$409$	−3.89304e10			−1.39122			−0.695609	+	0.718420i	$0.744866\pi$
$410$			4.45605e9i			0.157694i
$411$	−1.36847e9	−	1.39437e9i	−0.0479589	−	0.0488663i
$412$	−3.07891e10			−1.06858
$413$			1.36867e10i			0.470434i
$414$	−3.99413e8	+	2.13086e10i	−0.0135963	+	0.725361i
$415$	−6.31113e9			−0.212772
$416$		−	4.24634e10i		−	1.41789i
$417$	−2.80149e10	+	2.74947e10i	−0.926498	+	0.909295i
$418$	6.29182e9			0.206097
$419$		−	3.25983e10i		−	1.05764i	−0.848733	−	0.528821i	$-0.822634\pi$
$419$		−	3.25983e10i		−	1.05764i	0.848733	−	0.528821i	$-0.177366\pi$
$420$	8.26929e9	+	8.42574e9i	0.265748	+	0.270776i
$421$	−4.59023e9			−0.146119			−0.0730594	−	0.997328i	$-0.523276\pi$
$421$	−4.59023e9			−0.146119			−0.0730594	+	0.997328i	$0.523276\pi$
$422$			4.19833e9i			0.132381i
$423$	5.89559e10	+	1.10508e9i	1.84148	+	0.0345169i
$424$	2.59344e10			0.802440
$425$		−	9.33909e9i		−	0.286252i
$426$	−2.10814e10	+	2.06900e10i	−0.640121	+	0.628235i
$427$	−1.94342e9			−0.0584596
$428$		−	4.94454e9i		−	0.147350i
$429$	1.67170e10	+	1.70333e10i	0.493549	+	0.502886i
$430$	7.35173e9			0.215038
$431$			1.76624e10i			0.511848i	0.966697	+	0.255924i	$0.0823797\pi$
$431$			1.76624e10i			0.511848i	−0.966697	+	0.255924i	$0.917620\pi$
$432$	−1.44232e9	−	1.52579e9i	−0.0414122	−	0.0438086i
$433$	−2.38480e10			−0.678424			−0.339212	−	0.940710i	$-0.610160\pi$
$433$	−2.38480e10			−0.678424			−0.339212	+	0.940710i	$0.610160\pi$
$434$			3.60367e10i			1.01575i
$435$	−9.67125e8	+	9.49167e8i	−0.0270101	+	0.0265085i
$436$	−1.04155e10			−0.288228
$437$			2.73840e10i			0.750882i
$438$	5.63838e8	+	5.74505e8i	0.0153200	+	0.0156098i
$439$	1.28782e10			0.346734			0.173367	−	0.984857i	$-0.444535\pi$
$439$	1.28782e10			0.346734			0.173367	+	0.984857i	$0.444535\pi$
$440$			8.29958e9i			0.221435i
$441$	7.53034e8	−	4.01743e10i	0.0199095	−	1.06217i
$442$	5.06091e10			1.32599
$443$			1.07169e10i			0.278261i	0.990274	+	0.139131i	$0.0444308\pi$
$443$			1.07169e10i			0.278261i	−0.990274	+	0.139131i	$0.955569\pi$
$444$	−7.67043e9	+	7.52800e9i	−0.197373	+	0.193708i
$445$	−1.60217e10			−0.408571
$446$			4.79147e9i			0.121096i
$447$	−3.55353e10	−	3.62076e10i	−0.890082	−	0.906923i
$448$	−3.97211e10			−0.986073
$449$		−	1.78639e10i		−	0.439532i	−0.975553	−	0.219766i	$-0.929471\pi$
$449$		−	1.78639e10i		−	0.439532i	0.975553	−	0.219766i	$-0.0705294\pi$
$450$	5.24569e9	+	9.83262e7i	0.127924	+	0.00239783i
$451$	−1.10953e10			−0.268184
$452$			3.40027e10i			0.814628i
$453$	5.55670e10	−	5.45352e10i	1.31955	−	1.29504i
$454$	2.18650e10			0.514667
$455$		−	3.98624e10i		−	0.930075i
$456$	−2.04068e10	−	2.07929e10i	−0.471971	−	0.480901i
$457$	6.60639e10			1.51460			0.757302	−	0.653064i	$-0.226517\pi$
$457$	6.60639e10			1.51460			0.757302	+	0.653064i	$0.226517\pi$
$458$			7.68679e9i			0.174696i
$459$	−4.61665e10	+	4.36411e10i	−1.04010	+	0.983207i
$460$	−1.34145e10			−0.299601
$461$		−	6.51600e10i		−	1.44270i	−0.692569	−	0.721352i	$-0.743521\pi$
$461$		−	6.51600e10i		−	1.44270i	0.692569	−	0.721352i	$-0.256479\pi$
$462$	1.45344e10	−	1.42645e10i	0.319029	−	0.313105i
$463$	1.65087e10			0.359244			0.179622	−	0.983736i	$-0.442513\pi$
$463$	1.65087e10			0.359244			0.179622	+	0.983736i	$0.442513\pi$
$464$		−	2.36466e8i		−	0.00510148i
$465$	−1.61923e10	−	1.64987e10i	−0.346335	−	0.352888i
$466$	−2.07895e10			−0.440859
$467$		−	3.64524e10i		−	0.766404i	−0.923664	−	0.383202i	$-0.874821\pi$
$467$		−	3.64524e10i		−	0.766404i	0.923664	−	0.383202i	$-0.125179\pi$
$468$	7.69116e8	−	4.10323e10i	0.0160328	−	0.855347i
$469$	4.62071e10			0.955030
$470$		−	2.57127e10i		−	0.526934i
$471$	−5.34333e10	+	5.24411e10i	−1.08575	+	1.06559i
$472$	1.65456e10			0.333362
$473$			1.83054e10i			0.365707i
$474$	−1.61884e10	−	1.64947e10i	−0.320693	−	0.326761i
$475$	6.74132e9			0.132425
$476$			6.23341e10i			1.21422i
$477$	4.08142e10	+	7.65028e8i	0.788384	+	0.0147776i
$478$	−1.57724e10			−0.302124
$479$			5.54555e10i			1.05342i	0.850044	+	0.526711i	$0.176575\pi$
$479$			5.54555e10i			1.05342i	−0.850044	+	0.526711i	$0.823425\pi$
$480$	1.65889e10	−	1.62808e10i	0.312502	−	0.306699i
$481$	3.62890e10			0.677946
$482$			1.00313e10i			0.185853i
$483$	6.20839e10	+	6.32585e10i	1.14075	+	1.16233i
$484$	2.47431e10			0.450892
$485$			9.27551e9i			0.167637i
$486$	−2.40268e10	−	2.63908e10i	−0.430676	−	0.473051i
$487$	−4.92651e10			−0.875837			−0.437919	−	0.899015i	$-0.644284\pi$
$487$	−4.92651e10			−0.875837			−0.437919	+	0.899015i	$0.644284\pi$
$488$			2.34937e9i			0.0414259i
$489$	7.52165e10	−	7.38198e10i	1.31546	−	1.29103i
$490$	−1.75214e10			−0.303937
$491$		−	6.73149e10i		−	1.15820i	−0.815255	−	0.579102i	$-0.803403\pi$
$491$		−	6.73149e10i		−	1.15820i	0.815255	−	0.579102i	$-0.196597\pi$
$492$	1.33640e10	+	1.36168e10i	0.228073	+	0.232389i
$493$	−7.15485e9			−0.121119
$494$			3.65316e10i			0.613424i
$495$	−2.44826e8	+	1.30614e10i	−0.00407790	+	0.217556i
$496$	4.03398e9			0.0666511
$497$			1.22844e11i			2.01339i
$498$	1.33608e10	−	1.31127e10i	0.217228	−	0.213194i
$499$	−8.14015e10			−1.31290			−0.656448	−	0.754371i	$-0.727942\pi$
$499$	−8.14015e10			−1.31290			−0.656448	+	0.754371i	$0.727942\pi$
$500$			3.30234e9i			0.0528375i
$501$	−6.36626e10	−	6.48670e10i	−1.01049	−	1.02961i
$502$	−3.44922e10			−0.543132
$503$			4.27491e10i			0.667814i	0.942606	+	0.333907i	$0.108367\pi$
$503$			4.27491e10i			0.667814i	−0.942606	+	0.333907i	$0.891633\pi$
$504$	−9.42815e10	−	1.76723e9i	−1.46118	−	0.0273886i
$505$	1.84350e7			0.000283451
$506$			2.31401e10i			0.352990i
$507$	−5.17416e10	+	5.07808e10i	−0.783083	+	0.768542i
$508$	−1.55003e9			−0.0232748
$509$		−	6.30456e10i		−	0.939255i	−0.882865	−	0.469628i	$-0.844388\pi$
$509$		−	6.30456e10i		−	0.939255i	0.882865	−	0.469628i	$-0.155612\pi$
$510$	1.94040e10	+	1.97711e10i	0.286820	+	0.292247i
$511$	3.34770e9			0.0490980
$512$			8.27185e9i			0.120371i
$513$	−3.15018e10	−	3.33248e10i	−0.454848	−	0.481169i
$514$	6.74396e9			0.0966189
$515$			5.69057e10i			0.808959i
$516$	2.24654e10	−	2.20483e10i	0.316895	−	0.311011i
$517$	6.40230e10			0.896136
$518$		−	3.09652e10i		−	0.430086i
$519$	6.90529e10	+	7.03594e10i	0.951727	+	0.969734i
$520$	−4.81890e10			−0.659075
$521$			7.92618e10i			1.07575i	0.843023	+	0.537877i	$0.180774\pi$
$521$			7.92618e10i			1.07575i	−0.843023	+	0.537877i	$0.819226\pi$
$522$	7.53295e7	−	4.01882e9i	0.00101457	−	0.0541273i
$523$	−8.10207e10			−1.08290			−0.541451	−	0.840732i	$-0.682125\pi$
$523$	−8.10207e10			−1.08290			−0.541451	+	0.840732i	$0.682125\pi$
$524$			1.29393e10i			0.171627i
$525$	1.55728e10	−	1.52836e10i	0.204988	−	0.201182i
$526$	−1.15417e10			−0.150774
$527$		−	1.22058e11i		−	1.58243i
$528$	−1.59679e9	−	1.62700e9i	−0.0205452	−	0.0209339i
$529$	−2.24020e10			−0.286065
$530$		−	1.78005e10i		−	0.225594i
$531$	2.60387e10	+	4.88073e8i	0.327522	+	0.00613913i
$532$	−4.49951e10			−0.561719
$533$		−	6.44215e10i		−	0.798219i
$534$	3.39183e10	−	3.32885e10i	0.417127	−	0.409382i
$535$	−9.13869e9			−0.111550
$536$		−	5.58590e10i		−	0.676759i
$537$	1.92984e10	+	1.96635e10i	0.232073	+	0.236463i
$538$	5.18778e10			0.619230
$539$		−	4.36272e10i		−	0.516895i
$540$	1.63247e10	−	1.54317e10i	0.191986	−	0.181484i
$541$	7.57616e10			0.884423			0.442212	−	0.896911i	$-0.354194\pi$
$541$	7.57616e10			0.884423			0.442212	+	0.896911i	$0.354194\pi$
$542$			2.96804e10i			0.343932i
$543$	−1.09508e11	+	1.07474e11i	−1.25963	+	1.23625i
$544$	1.22726e11			1.40133
$545$			1.92504e10i			0.218199i
$546$	8.28227e10	+	8.43897e10i	0.931921	+	0.949553i
$547$	1.08131e11			1.20782			0.603909	−	0.797053i	$-0.293609\pi$
$547$	1.08131e11			1.20782			0.603909	+	0.797053i	$0.293609\pi$
$548$			3.64764e9i			0.0404473i
$549$	−6.93032e7	+	3.69732e9i	−0.000762893	+	0.0407003i
$550$	5.69655e9			0.0622531
$551$		−	5.16464e9i		−	0.0560317i
$552$	7.64721e10	−	7.50522e10i	0.823658	−	0.808364i
$553$	−9.61162e10			−1.02777
$554$		−	6.86314e10i		−	0.728591i
$555$	1.39135e10	+	1.41768e10i	0.146644	+	0.149419i
$556$	7.32865e10			0.766876
$557$		−	1.02611e11i		−	1.06604i	−0.846103	−	0.533019i	$-0.821057\pi$
$557$		−	1.02611e11i		−	1.06604i	0.846103	−	0.533019i	$-0.178943\pi$
$558$	6.85590e10	+	1.28508e9i	0.707176	+	0.0132554i
$559$	−1.06285e11			−1.08849
$560$			3.80760e9i			0.0387168i
$561$	−4.92288e10	+	4.83147e10i	−0.497013	+	0.487784i
$562$	−1.11290e11			−1.11561
$563$		−	8.67308e10i		−	0.863256i	−0.902052	−	0.431628i	$-0.857939\pi$
$563$		−	8.67308e10i		−	0.863256i	0.902052	−	0.431628i	$-0.142061\pi$
$564$	−7.71139e10	−	7.85729e10i	−0.762107	−	0.776526i
$565$	6.28450e10			0.616705
$566$		−	3.56326e10i		−	0.347201i
$567$	−1.48323e11	−	5.56235e9i	−1.43508	−	0.0538178i
$568$	1.48504e11			1.42674
$569$			1.42835e11i			1.36265i	0.731981	+	0.681325i	$0.238596\pi$
$569$			1.42835e11i			1.36265i	−0.731981	+	0.681325i	$0.761404\pi$
$570$	−1.42715e10	+	1.40065e10i	−0.135198	+	0.132688i
$571$	4.15522e10			0.390886			0.195443	−	0.980715i	$-0.437386\pi$
$571$	4.15522e10			0.390886			0.195443	+	0.980715i	$0.437386\pi$
$572$		−	4.45589e10i		−	0.416246i
$573$	6.93365e10	+	7.06483e10i	0.643196	+	0.655365i
$574$	−5.49704e10			−0.506386
$575$			2.47932e10i			0.226810i
$576$	−1.41647e9	+	7.55685e10i	−0.0128682	+	0.686517i
$577$	−1.37843e11			−1.24360			−0.621800	−	0.783176i	$-0.713598\pi$
$577$	−1.37843e11			−1.24360			−0.621800	+	0.783176i	$0.713598\pi$
$578$			7.48657e10i			0.670767i
$579$	−2.10381e10	+	2.06474e10i	−0.187194	+	0.183718i
$580$	2.52998e9			0.0223566
$581$		−	7.78549e10i		−	0.683253i
$582$	−1.92719e10	−	1.96365e10i	−0.167970	−	0.171148i
$583$	4.43221e10			0.383659
$584$		−	4.04699e9i		−	0.0347921i
$585$	−7.58374e10	−	1.42151e9i	−0.647530	−	0.0121374i
$586$	9.69237e10			0.821939
$587$		−	2.08977e11i		−	1.76014i	−0.474848	−	0.880068i	$-0.657497\pi$
$587$		−	2.08977e11i		−	1.76014i	0.474848	−	0.880068i	$-0.342503\pi$
$588$	−5.35419e10	+	5.25477e10i	−0.447903	+	0.439586i
$589$	8.81061e10			0.732057
$590$		−	1.13564e10i		−	0.0937197i
$591$	1.12530e11	+	1.14659e11i	0.922399	+	0.939851i
$592$	−3.46627e9			−0.0282212
$593$		−	4.25547e10i		−	0.344135i	−0.985085	−	0.172067i	$-0.944955\pi$
$593$		−	4.25547e10i		−	0.344135i	0.985085	−	0.172067i	$-0.0550447\pi$
$594$	−2.66197e10	−	2.81601e10i	−0.213824	−	0.226198i
$595$	1.15208e11			0.919212
$596$			9.47187e10i			0.750672i
$597$	−3.50614e10	+	3.44104e10i	−0.276014	+	0.270889i
$598$	−1.34356e11			−1.05063
$599$			6.86408e10i			0.533182i	0.963810	+	0.266591i	$0.0858972\pi$
$599$			6.86408e10i			0.533182i	−0.963810	+	0.266591i	$0.914103\pi$
$600$	−1.84761e10	−	1.88257e10i	−0.142563	−	0.145260i
$601$	−2.16080e11			−1.65622			−0.828109	−	0.560567i	$-0.810583\pi$
$601$	−2.16080e11			−1.65622			−0.828109	+	0.560567i	$0.810583\pi$
$602$			9.06919e10i			0.690530i
$603$	1.64776e9	−	8.79080e10i	0.0124631	−	0.664904i
$604$	−1.45363e11			−1.09221
$605$		−	4.57311e10i		−	0.341342i
$606$	−3.90274e7	+	3.83027e7i	−0.000289387	+	0.000284014i
$607$	2.36866e10			0.174481			0.0872405	−	0.996187i	$-0.472195\pi$
$607$	2.36866e10			0.174481			0.0872405	+	0.996187i	$0.472195\pi$
$608$			8.85880e10i			0.648277i
$609$	−1.17090e10	−	1.19306e10i	−0.0851241	−	0.0867346i
$610$	1.61253e9			0.0116463
$611$			3.71731e11i			2.66725i
$612$	1.18589e11	+	2.22286e9i	0.845356	+	0.0158455i
$613$	1.04944e9			0.00743219			0.00371609	−	0.999993i	$-0.498817\pi$
$613$	1.04944e9			0.00743219			0.00371609	+	0.999993i	$0.498817\pi$
$614$		−	8.48526e10i		−	0.597024i
$615$	2.51671e10	−	2.46998e10i	0.175927	−	0.172660i
$616$	−1.02385e11			−0.711070
$617$			1.92658e11i			1.32937i	0.747124	+	0.664684i	$0.231434\pi$
$617$			1.92658e11i			1.32937i	−0.747124	+	0.664684i	$0.768566\pi$
$618$	−1.18234e11	−	1.20471e11i	−0.810565	−	0.825900i
$619$	3.90898e10			0.266257			0.133129	−	0.991099i	$-0.457498\pi$
$619$	3.90898e10			0.266257			0.133129	+	0.991099i	$0.457498\pi$
$620$			4.31602e10i			0.292090i
$621$	1.22562e11	−	1.15857e11i	0.824117	−	0.779036i
$622$	−8.42654e10			−0.562973
$623$		−	1.97645e11i		−	1.31200i
$624$	9.44667e9	−	9.27126e9i	0.0623075	−	0.0611506i
$625$	6.10352e9			0.0400000
$626$		−	1.30221e11i		−	0.847976i
$627$	−3.48754e10	−	3.55352e10i	−0.225657	−	0.229926i
$628$	1.39781e11			0.898687
$629$			1.04881e11i			0.670028i
$630$	−1.21297e9	+	6.47116e10i	−0.00769992	+	0.410790i
$631$	−1.46902e10			−0.0926636			−0.0463318	−	0.998926i	$-0.514753\pi$
$631$	−1.46902e10			−0.0926636			−0.0463318	+	0.998926i	$0.514753\pi$
$632$			1.16193e11i			0.728304i
$633$	2.37115e10	−	2.32712e10i	0.147688	−	0.144945i
$634$	6.51007e10			0.402929
$635$			2.86482e9i			0.0176199i
$636$	−5.33846e10	−	5.43947e10i	−0.326278	−	0.332451i
$637$	2.53308e11			1.53848
$638$		−	4.36423e9i		−	0.0263405i
$639$	2.33708e11	+	4.38066e9i	1.40175	+	0.0262746i
$640$	−4.05027e10			−0.241415
$641$		−	1.98992e11i		−	1.17870i	−0.807879	−	0.589349i	$-0.799384\pi$
$641$		−	1.98992e11i		−	1.17870i	0.807879	−	0.589349i	$-0.200616\pi$
$642$	1.93468e10	−	1.89876e10i	0.113886	−	0.111771i
$643$	1.32563e11			0.775495			0.387748	−	0.921766i	$-0.373253\pi$
$643$	1.32563e11			0.775495			0.387748	+	0.921766i	$0.373253\pi$
$644$		−	1.65483e11i		−	0.962078i
$645$	−4.07505e10	−	4.15214e10i	−0.235447	−	0.239902i
$646$	−1.05582e11			−0.606259
$647$		−	1.66551e10i		−	0.0950453i	−0.998870	−	0.0475227i	$-0.984867\pi$
$647$		−	1.66551e10i		−	0.0950453i	0.998870	−	0.0475227i	$-0.0151326\pi$
$648$	−6.72423e9	+	1.79305e11i	−0.0381366	+	1.01694i
$649$	2.82766e10			0.159385
$650$			3.30753e10i			0.185289i
$651$	2.03530e11	−	1.99750e11i	1.13319	−	1.11215i
$652$	−1.96765e11			−1.08882
$653$		−	6.15244e10i		−	0.338372i	−0.985584	−	0.169186i	$-0.945886\pi$
$653$		−	6.15244e10i		−	0.338372i	0.985584	−	0.169186i	$-0.0541139\pi$
$654$	−3.99968e10	−	4.07535e10i	−0.218632	−	0.222769i
$655$	2.39150e10			0.129928
$656$			6.15344e9i			0.0332279i
$657$	1.19380e8	−	6.36894e9i	0.000640725	−	0.0341826i
$658$	3.17195e11			1.69209
$659$		−	6.62231e10i		−	0.351130i	−0.984468	−	0.175565i	$-0.943825\pi$
$659$		−	6.62231e10i		−	0.351130i	0.984468	−	0.175565i	$-0.0561752\pi$
$660$	1.74075e10	−	1.70843e10i	0.0917404	−	0.0900370i
$661$	−3.16830e11			−1.65966			−0.829832	−	0.558014i	$-0.811564\pi$
$661$	−3.16830e11			−1.65966			−0.829832	+	0.558014i	$0.811564\pi$
$662$		−	1.28477e10i		−	0.0668951i
$663$	−2.80525e11	−	2.85832e11i	−1.45183	−	1.47930i
$664$	−9.41176e10			−0.484171
$665$			8.31617e10i			0.425243i
$666$	−5.89106e10	−	1.10423e9i	−0.299431	−	0.00561259i
$667$	1.89945e10			0.0959677
$668$			1.69691e11i			0.852223i
$669$	2.70615e10	−	2.65590e10i	0.135097	−	0.132589i
$670$	−3.83397e10			−0.190261
$671$			4.01509e9i			0.0198064i
$672$	2.00843e11	+	2.04643e11i	0.984870	+	1.00350i
$673$	−2.15656e10			−0.105124			−0.0525618	−	0.998618i	$-0.516739\pi$
$673$	−2.15656e10			−0.105124			−0.0525618	+	0.998618i	$0.516739\pi$
$674$			8.21697e10i			0.398173i
$675$	−2.85214e10	−	3.01719e10i	−0.137390	−	0.145341i
$676$	1.35355e11			0.648169
$677$			2.05571e11i			0.978605i	0.872114	+	0.489303i	$0.162749\pi$
$677$			2.05571e11i			0.978605i	−0.872114	+	0.489303i	$0.837251\pi$
$678$	−1.33045e11	+	1.30574e11i	−0.629620	+	0.617928i
$679$	−1.14424e11			−0.538316
$680$		−	1.39273e11i		−	0.651377i
$681$	−1.21197e11	−	1.23490e11i	−0.563514	−	0.574175i
$682$	7.44515e10			0.344140
$683$			3.27181e11i			1.50351i	0.659445	+	0.751753i	$0.270791\pi$
$683$			3.27181e11i			1.50351i	−0.659445	+	0.751753i	$0.729209\pi$
$684$	−1.60455e9	+	8.56023e10i	−0.00733040	+	0.391076i
$685$	6.74171e9			0.0306202
$686$		−	1.26869e10i		−	0.0572876i
$687$	4.34138e10	−	4.26077e10i	0.194895	−	0.191276i
$688$	1.01521e10			0.0453110
$689$			2.57343e11i			1.14192i
$690$	−5.15132e10	−	5.24879e10i	−0.227260	−	0.231559i
$691$	5.11252e10			0.224245			0.112122	−	0.993694i	$-0.464235\pi$
$691$	5.11252e10			0.224245			0.112122	+	0.993694i	$0.464235\pi$
$692$		−	1.84059e11i		−	0.802662i
$693$	−1.61128e11	−	3.02021e9i	−0.698614	−	0.0130949i
$694$	7.05521e10			0.304139
$695$		−	1.35451e11i		−	0.580554i
$696$	−1.44227e10	+	1.41549e10i	−0.0614624	+	0.0603211i
$697$	1.86188e11			0.788896
$698$			1.29029e11i			0.543584i
$699$	1.15235e11	+	1.17416e11i	0.482700	+	0.491833i
$700$	−4.07381e10			−0.169672
$701$		−	1.49396e11i		−	0.618681i	−0.950951	−	0.309341i	$-0.899892\pi$
$701$		−	1.49396e11i		−	0.618681i	0.950951	−	0.309341i	$-0.100108\pi$
$702$	1.63503e11	−	1.54559e11i	0.673252	−	0.636424i
$703$	−7.57069e10			−0.309966
$704$			8.20635e10i			0.334087i
$705$	−1.45221e11	+	1.42525e11i	−0.587860	+	0.576944i
$706$	1.87764e11			0.755777
$707$			2.27417e8i			0.000910218i
$708$	−3.40584e10	−	3.47028e10i	−0.135547	−	0.138112i
$709$	1.80177e10			0.0713041			0.0356520	−	0.999364i	$-0.488649\pi$
$709$	1.80177e10			0.0713041			0.0356520	+	0.999364i	$0.488649\pi$
$710$		−	1.01928e11i		−	0.401107i
$711$	−3.42754e9	+	1.82859e11i	−0.0134123	+	0.715546i
$712$	−2.38930e11			−0.929718
$713$			3.24037e11i			1.25382i
$714$	−2.43899e11	+	2.39370e11i	−0.938462	+	0.921036i
$715$	−8.23554e10			−0.315114
$716$		−	5.14395e10i		−	0.195724i
$717$	8.74258e10	+	8.90799e10i	0.330798	+	0.337057i
$718$	−1.59136e8			−0.000598785
$719$		−	4.58130e11i		−	1.71425i	−0.515112	−	0.857123i	$-0.672250\pi$
$719$		−	4.58130e11i		−	1.71425i	0.515112	−	0.857123i	$-0.327750\pi$
$720$	7.24388e9	+	1.35781e8i	0.0269551	+	0.000505251i
$721$	−7.01996e11			−2.59773
$722$			9.76264e10i			0.359268i
$723$	5.66552e10	−	5.56032e10i	0.207342	−	0.203492i
$724$	2.86470e11			1.04262
$725$		−	4.67601e9i		−	0.0169248i
$726$	9.50162e10	+	9.68138e10i	0.342020	+	0.348491i
$727$	−1.27196e11			−0.455342			−0.227671	−	0.973738i	$-0.573111\pi$
$727$	−1.27196e11			−0.455342			−0.227671	+	0.973738i	$0.573111\pi$
$728$		−	5.94466e11i		−	2.11642i
$729$	−1.58715e10	+	2.81983e11i	−0.0561963	+	0.998420i
$730$	−2.77771e9			−0.00978128
$731$		−	3.07178e11i		−	1.07577i
$732$	4.92756e9	−	4.83606e9i	0.0171628	−	0.0168441i
$733$	2.10630e11			0.729631			0.364816	−	0.931080i	$-0.381132\pi$
$733$	2.10630e11			0.729631			0.364816	+	0.931080i	$0.381132\pi$
$734$			4.88175e10i			0.168186i
$735$	9.71206e10	+	9.89581e10i	0.332784	+	0.339080i
$736$	−3.25809e11			−1.11033
$737$		−	9.54634e10i		−	0.323569i
$738$	−1.96027e9	+	1.04580e11i	−0.00660830	+	0.352552i
$739$	2.18560e11			0.732811			0.366405	−	0.930455i	$-0.380588\pi$
$739$	2.18560e11			0.732811			0.366405	+	0.930455i	$0.380588\pi$
$740$		−	3.70863e10i		−	0.123676i
$741$	2.06325e11	−	2.02494e11i	0.684350	−	0.671643i
$742$	2.19589e11			0.724427
$743$		−	1.82763e11i		−	0.599700i	−0.953986	−	0.299850i	$-0.903063\pi$
$743$		−	1.82763e11i		−	0.599700i	0.953986	−	0.299850i	$-0.0969366\pi$
$744$	−2.41475e11	−	2.46044e11i	−0.788098	−	0.803009i
$745$	1.75063e11			0.568288
$746$		−	2.34608e11i		−	0.757509i
$747$	−1.48117e11	−	2.77634e9i	−0.475689	−	0.00891641i
$748$	1.28782e11			0.411384
$749$		−	1.12736e11i		−	0.358208i
$750$	−1.29213e10	+	1.26814e10i	−0.0408377	+	0.0400794i
$751$	5.51243e11			1.73294			0.866469	−	0.499230i	$-0.166384\pi$
$751$	5.51243e11			1.73294			0.866469	+	0.499230i	$0.166384\pi$
$752$		−	3.55071e10i		−	0.111031i
$753$	1.91189e11	+	1.94806e11i	0.594680	+	0.605931i
$754$	2.53396e10			0.0783996
$755$			2.68665e11i			0.826842i
$756$	1.90367e11	+	2.01383e11i	0.582780	+	0.616505i
$757$	−4.36075e10			−0.132794			−0.0663969	−	0.997793i	$-0.521150\pi$
$757$	−4.36075e10			−0.132794			−0.0663969	+	0.997793i	$0.521150\pi$
$758$			6.97594e10i			0.211313i
$759$	1.30691e11	−	1.28265e11i	0.393804	−	0.386492i
$760$	1.00533e11			0.301338
$761$			4.60493e11i			1.37304i	0.727110	+	0.686521i	$0.240863\pi$
$761$			4.60493e11i			1.37304i	−0.727110	+	0.686521i	$0.759137\pi$
$762$	−5.95229e9	−	6.06490e9i	−0.0176548	−	0.0179889i
$763$	−2.37475e11			−0.700681
$764$		−	1.84815e11i		−	0.542455i
$765$	4.10837e9	−	2.19181e11i	0.0119957	−	0.639967i
$766$	−1.10221e11			−0.320147
$767$			1.64180e11i			0.474393i
$768$	2.56231e11	−	2.51473e11i	0.736525	−	0.722849i
$769$	−1.46976e11			−0.420281			−0.210140	−	0.977671i	$-0.567392\pi$
$769$	−1.46976e11			−0.420281			−0.210140	+	0.977671i	$0.567392\pi$
$770$			7.02733e10i			0.199907i
$771$	−3.73816e10	−	3.80888e10i	−0.105789	−	0.107790i
$772$	5.50352e10			0.154943
$773$		−	1.06663e11i		−	0.298741i	−0.988781	−	0.149371i	$-0.952275\pi$
$773$		−	1.06663e11i		−	0.298741i	0.988781	−	0.149371i	$-0.0477247\pi$
$774$	1.72539e11	+	3.23411e9i	0.480756	+	0.00901137i
$775$	7.97704e10			0.221123
$776$			1.38325e11i			0.381465i
$777$	−1.74887e11	+	1.71639e11i	−0.479814	+	0.470904i
$778$	−3.29251e11			−0.898688
$779$			1.34397e11i			0.364956i
$780$	9.91947e10	+	1.01071e11i	0.267985	+	0.273055i
$781$	2.53794e11			0.682147
$782$		−	3.88308e11i		−	1.03836i
$783$	−2.31152e10	+	2.18508e10i	−0.0614966	+	0.0581326i
$784$	−2.41956e10			−0.0640431
$785$		−	2.58348e11i		−	0.680341i
$786$	−5.06285e10	+	4.96885e10i	−0.132649	+	0.130186i
$787$	−6.64587e11			−1.73242			−0.866209	−	0.499682i	$-0.833450\pi$
$787$	−6.64587e11			−1.73242			−0.866209	+	0.499682i	$0.833450\pi$
$788$		−	2.99947e11i		−	0.777928i
$789$	6.39752e10	+	6.51856e10i	0.165083	+	0.168207i
$790$	7.97511e10			0.204752
$791$			7.75265e11i			1.98036i
$792$	−3.65108e9	+	1.94785e11i	−0.00927941	+	0.495056i
$793$	−2.33124e10			−0.0589515
$794$		−	3.33690e11i		−	0.839578i
$795$	−1.00534e11	+	9.86675e10i	−0.251678	+	0.247005i
$796$	9.17201e10			0.228461
$797$			2.85566e11i			0.707738i	0.935295	+	0.353869i	$0.115134\pi$
$797$			2.85566e11i			0.707738i	−0.935295	+	0.353869i	$0.884866\pi$
$798$	−1.72786e11	−	1.76055e11i	−0.426087	−	0.434148i
$799$	−1.07436e12			−2.63610
$800$			8.02066e10i			0.195817i
$801$	−3.76016e11	−	7.04811e9i	−0.913432	−	0.0171215i
$802$	2.43698e11			0.589052
$803$		−	6.91633e9i		−	0.0166346i
$804$	−1.17158e11	+	1.14983e11i	−0.280381	+	0.275175i
$805$	−3.05852e11			−0.728330
$806$			4.32280e11i			1.02430i
$807$	−2.87557e11	−	2.92998e11i	−0.678000	−	0.690828i
$808$	2.74921e8			0.000645003
$809$		−	6.31328e10i		−	0.147388i	−0.997281	−	0.0736938i	$-0.976521\pi$
$809$		−	6.31328e10i		−	0.147388i	0.997281	−	0.0736938i	$-0.0234788\pi$
$810$	1.23069e11	+	4.61528e9i	0.285897	+	0.0107216i
$811$	6.09177e11			1.40819			0.704093	−	0.710107i	$-0.251354\pi$
$811$	6.09177e11			1.40819			0.704093	+	0.710107i	$0.251354\pi$
$812$			3.12102e10i			0.0717914i
$813$	1.67630e11	−	1.64518e11i	0.383699	−	0.376574i
$814$	−6.39738e10			−0.145715
$815$			3.63669e11i			0.824282i
$816$	2.67953e10	+	2.73023e10i	0.0604363	+	0.0615798i
$817$	2.21733e11			0.497671
$818$			3.98481e11i			0.890009i
$819$	1.75359e10	−	9.35540e11i	0.0389756	−	2.07935i
$820$	−6.58367e10			−0.145617
$821$		−	4.63422e11i		−	1.02001i	−0.860172	−	0.510004i	$-0.829644\pi$
$821$		−	4.63422e11i		−	1.02001i	0.860172	−	0.510004i	$-0.170356\pi$
$822$	−1.42724e10	+	1.40073e10i	−0.0312614	+	0.0306809i
$823$	6.84569e11			1.49217			0.746085	−	0.665851i	$-0.231931\pi$
$823$	6.84569e11			1.49217			0.746085	+	0.665851i	$0.231931\pi$
$824$			8.48631e11i			1.84082i
$825$	−3.15758e10	−	3.21732e10i	−0.0681614	−	0.0694510i
$826$	1.40094e11			0.300952
$827$		−	5.73805e11i		−	1.22671i	−0.789807	−	0.613355i	$-0.789819\pi$
$827$		−	5.73805e11i		−	1.22671i	0.789807	−	0.613355i	$-0.210181\pi$
$828$	−3.14828e11	−	5.90120e9i	−0.669811	−	0.0125551i
$829$	5.68680e11			1.20407			0.602033	−	0.798471i	$-0.294358\pi$
$829$	5.68680e11			1.20407			0.602033	+	0.798471i	$0.294358\pi$
$830$			6.45991e10i			0.136117i
$831$	−3.87620e11	+	3.80422e11i	−0.812834	+	0.797741i
$832$	−4.76477e11			−0.994371
$833$			7.32098e11i			1.52051i
$834$	2.81428e11	+	2.86753e11i	0.581706	+	0.592712i
$835$	3.13630e11			0.645166
$836$			9.29596e10i			0.190313i
$837$	−3.72763e11	−	3.94334e11i	−0.759505	−	0.803456i
$838$	−3.33668e11			−0.676609
$839$		−	2.49035e10i		−	0.0502588i	−0.999684	−	0.0251294i	$-0.992000\pi$
$839$		−	2.49035e10i		−	0.0502588i	0.999684	−	0.0251294i	$-0.00799977\pi$
$840$	2.32236e11	−	2.27924e11i	0.466458	−	0.457796i
$841$	4.96664e11			0.992839
$842$			4.69844e10i			0.0934772i
$843$	6.16880e11	+	6.28551e11i	1.22149	+	1.24460i
$844$	−6.20289e10			−0.122243
$845$		−	2.50169e11i		−	0.490689i
$846$	1.13113e10	−	6.03457e11i	0.0220816	−	1.17805i
$847$	5.64145e11			1.09612
$848$		−	2.45810e10i		−	0.0475353i
$849$	−2.01247e11	+	1.97510e11i	−0.387346	+	0.380154i
$850$	−9.55925e10			−0.183125
$851$		−	2.78435e11i		−	0.530891i
$852$	−3.05688e11	−	3.11471e11i	−0.580123	−	0.591099i
$853$	−7.97637e11			−1.50664			−0.753319	−	0.657655i	$-0.771549\pi$
$853$	−7.97637e11			−1.50664			−0.753319	+	0.657655i	$0.771549\pi$
$854$			1.98924e10i			0.0373985i
$855$	1.58213e11	+	2.96558e9i	0.296059	+	0.00554939i
$856$	−1.36285e11			−0.253836
$857$		−	7.68355e11i		−	1.42442i	−0.701965	−	0.712211i	$-0.747694\pi$
$857$		−	7.68355e11i		−	1.42442i	0.701965	−	0.712211i	$-0.252306\pi$
$858$	1.74348e11	−	1.71111e11i	0.321713	−	0.315740i
$859$	−5.30152e10			−0.0973706			−0.0486853	−	0.998814i	$-0.515503\pi$
$859$	−5.30152e10			−0.0973706			−0.0486853	+	0.998814i	$0.515503\pi$
$860$			1.08619e11i			0.198570i
$861$	3.04700e11	+	3.10465e11i	0.554446	+	0.564936i
$862$	1.80788e11			0.327447
$863$		−	8.01812e11i		−	1.44554i	−0.691090	−	0.722769i	$-0.742869\pi$
$863$		−	8.01812e11i		−	1.44554i	0.691090	−	0.722769i	$-0.257131\pi$
$864$	3.96490e11	−	3.74801e11i	0.711504	−	0.672583i
$865$	−3.40185e11			−0.607646
$866$			2.44102e11i			0.434010i
$867$	4.22830e11	−	4.14978e11i	0.748323	−	0.734428i
$868$	−5.32430e11			−0.937959
$869$			1.98575e11i			0.348214i
$870$	9.71542e9	+	9.89924e9i	0.0169584	+	0.0172792i
$871$	5.54280e11			0.963067
$872$			2.87080e11i			0.496520i
$873$	−4.08040e9	+	2.17689e11i	−0.00702499	+	0.374783i
$874$	2.80296e11			0.480364
$875$			7.52938e10i			0.128448i
$876$	−8.48813e9	+	8.33052e9i	−0.0144144	+	0.0141467i
$877$	5.88957e11			0.995601			0.497800	−	0.867292i	$-0.334141\pi$
$877$	5.88957e11			0.995601			0.497800	+	0.867292i	$0.334141\pi$
$878$		−	1.31818e11i		−	0.221817i
$879$	−5.37245e11	−	5.47410e11i	−0.899948	−	0.916974i
$880$	7.86647e9			0.0131174
$881$		−	7.89776e11i		−	1.31099i	−0.755198	−	0.655497i	$-0.772459\pi$
$881$		−	7.89776e11i		−	1.31099i	0.755198	−	0.655497i	$-0.227541\pi$
$882$	−4.11213e11	−	7.70786e9i	−0.679506	−	0.0127368i
$883$	−4.30157e11			−0.707594			−0.353797	−	0.935322i	$-0.615110\pi$
$883$	−4.30157e11			−0.707594			−0.353797	+	0.935322i	$0.615110\pi$
$884$			7.47733e11i			1.22444i
$885$	−6.41390e10	+	6.29480e10i	−0.104556	+	0.102615i
$886$	1.09695e11			0.178013
$887$			1.14158e12i			1.84421i	0.386934	+	0.922107i	$0.373534\pi$
$887$			1.14158e12i			1.84421i	−0.386934	+	0.922107i	$0.626466\pi$
$888$	2.07492e11	+	2.11418e11i	0.333695	+	0.340008i
$889$	−3.53408e10			−0.0565809
$890$			1.63994e11i			0.261377i
$891$	−1.14918e10	+	3.06434e11i	−0.0182337	+	0.486213i
$892$	−7.07924e10			−0.111822
$893$		−	7.75511e11i		−	1.21950i
$894$	−3.70612e11	+	3.63730e11i	−0.580189	+	0.569416i
$895$	−9.50724e10			−0.148171
$896$		−	4.99646e11i		−	0.775230i
$897$	7.44731e11	+	7.58821e11i	1.15035	+	1.17211i
$898$	−1.82850e11			−0.281183
$899$		−	6.11135e10i		−	0.0935618i
$900$	−1.45274e9	+	7.75034e10i	−0.00221420	+	0.118127i
$901$	−7.43759e11			−1.12858
$902$			1.13568e11i			0.171566i
$903$	5.12214e11	−	5.02703e11i	0.770372	−	0.756067i
$904$	9.37205e11			1.40333
$905$		−	5.29465e11i		−	0.789301i
$906$	−5.58208e11	−	5.68769e11i	−0.828483	−	0.844158i
$907$	−3.91779e11			−0.578911			−0.289455	−	0.957191i	$-0.593474\pi$
$907$	−3.91779e11			−0.578911			−0.289455	+	0.957191i	$0.593474\pi$
$908$			3.23049e11i			0.475253i
$909$	4.32656e8	+	8.10978e6i	0.000633705	+	1.18783e-5i
$910$	−4.08021e11			−0.595000
$911$			2.39414e11i			0.347597i	0.984781	+	0.173799i	$0.0556042\pi$
$911$			2.39414e11i			0.347597i	−0.984781	+	0.173799i	$0.944396\pi$
$912$	−1.97078e10	+	1.93419e10i	−0.0284878	+	0.0279588i
$913$	−1.60848e11			−0.231490
$914$		−	6.76212e11i		−	0.968943i
$915$	−8.93820e9	−	9.10731e9i	−0.0127516	−	0.0129929i
$916$	−1.13570e11			−0.161317
$917$			2.95018e11i			0.417226i
$918$	4.46699e11	+	4.72548e11i	0.628990	+	0.665389i
$919$	2.64317e11			0.370563			0.185282	−	0.982685i	$-0.440680\pi$
$919$	2.64317e11			0.370563			0.185282	+	0.982685i	$0.440680\pi$
$920$			3.69740e11i			0.516113i
$921$	−4.79235e11	+	4.70336e11i	−0.666054	+	0.653687i
$922$	−6.66960e11			−0.922946
$923$			1.47358e12i			2.03033i
$924$	2.10754e11	+	2.14741e11i	0.289126	+	0.294597i
$925$	−6.85442e10			−0.0936276
$926$		−	1.68979e11i		−	0.229820i
$927$	−2.50335e10	+	1.33553e12i	−0.0339002	+	1.80857i
$928$	6.14477e10			0.0828541
$929$		−	8.24093e11i		−	1.10640i	−0.833047	−	0.553202i	$-0.813406\pi$
$929$		−	8.24093e11i		−	1.10640i	0.833047	−	0.553202i	$-0.186594\pi$
$930$	−1.68876e11	+	1.65740e11i	−0.225754	+	0.221562i
$931$	−5.28456e11			−0.703413
$932$		−	3.07158e11i		−	0.407097i
$933$	4.67081e11	+	4.75918e11i	0.616404	+	0.628066i
$934$	−3.73117e11			−0.490295
$935$		−	2.38019e11i		−	0.311434i
$936$	−1.13096e12	−	2.11989e10i	−1.47348	−	0.0276191i
$937$	3.88885e11			0.504502			0.252251	−	0.967662i	$-0.418829\pi$
$937$	3.88885e11			0.504502			0.252251	+	0.967662i	$0.418829\pi$
$938$		−	4.72964e11i		−	0.610965i
$939$	−7.35467e11	+	7.21811e11i	−0.946022	+	0.928455i
$940$	3.79897e11			0.486580
$941$		−	5.71451e11i		−	0.728821i	−0.931239	−	0.364410i	$-0.881271\pi$
$941$		−	5.71451e11i		−	0.728821i	0.931239	−	0.364410i	$-0.118729\pi$
$942$	5.36774e11	+	5.46929e11i	0.681691	+	0.694588i
$943$	−4.94287e11			−0.625075
$944$		−	1.56822e10i		−	0.0197478i
$945$	3.72204e11	−	3.51844e11i	0.466718	−	0.441187i
$946$	1.87369e11			0.233955
$947$			7.99848e10i			0.0994507i	0.998763	+	0.0497253i	$0.0158346\pi$
$947$			7.99848e10i			0.0994507i	−0.998763	+	0.0497253i	$0.984165\pi$
$948$	2.43703e11	−	2.39178e11i	0.301737	−	0.296134i
$949$	4.01576e10			0.0495111
$950$		−	6.90023e10i		−	0.0847168i
$951$	−3.60852e11	−	3.67679e11i	−0.441171	−	0.449517i
$952$	1.71810e12			2.09170
$953$		−	1.05398e12i		−	1.27779i	−0.769294	−	0.638894i	$-0.779392\pi$
$953$		−	1.05398e12i		−	1.27779i	0.769294	−	0.638894i	$-0.220608\pi$
$954$	7.83063e9	−	4.17763e11i	0.00945373	−	0.504355i
$955$	−3.41582e11			−0.410659
$956$		−	2.33032e11i		−	0.278987i
$957$	−2.46485e10	+	2.41908e10i	−0.0293861	+	0.0288405i
$958$	5.67628e11			0.673910
$959$			8.31666e10i			0.0983274i
$960$	−1.82686e11	−	1.86142e11i	−0.215090	−	0.219159i
$961$	1.89674e11			0.222389
$962$		−	3.71445e11i		−	0.433705i
$963$	−2.14478e11	−	4.02021e9i	−0.249389	−	0.00467459i
$964$	−1.48209e11			−0.171620
$965$		−	1.01718e11i		−	0.117298i
$966$	6.47497e11	−	6.35474e11i	0.743583	−	0.729775i
$967$	−4.82707e11			−0.552049			−0.276025	−	0.961151i	$-0.589017\pi$
$967$	−4.82707e11			−0.552049			−0.276025	+	0.961151i	$0.589017\pi$
$968$		−	6.81985e11i		−	0.776736i
$969$	5.85236e11	+	5.96309e11i	0.663798	+	0.676357i
$970$	9.49417e10			0.107243
$971$			9.01068e11i			1.01363i	0.862054	+	0.506817i	$0.169178\pi$
$971$			9.01068e11i			1.01363i	−0.862054	+	0.506817i	$0.830822\pi$
$972$	3.89916e11	−	3.54988e11i	0.436823	−	0.397694i
$973$	1.67094e12			1.86427
$974$			5.04264e11i			0.560302i
$975$	1.86804e11	−	1.83336e11i	0.206713	−	0.202875i
$976$	2.22677e9			0.00245401
$977$		−	2.30964e11i		−	0.253493i	−0.991935	−	0.126747i	$-0.959546\pi$
$977$		−	2.30964e11i		−	0.253493i	0.991935	−	0.126747i	$-0.0404535\pi$
$978$	−7.55600e11	−	7.69896e11i	−0.825918	−	0.841544i
$979$	−4.08334e11			−0.444513
$980$		−	2.58873e11i		−	0.280661i
$981$	−8.46846e9	+	4.51792e11i	−0.00914384	+	0.487823i
$982$	−6.89017e11			−0.740942
$983$			1.09320e10i			0.0117080i	0.999983	+	0.00585402i	$0.00186340\pi$
$983$			1.09320e10i			0.0117080i	−0.999983	+	0.00585402i	$0.998137\pi$
$984$	3.75316e11	−	3.68346e11i	0.400328	−	0.392895i
$985$	−5.54373e11			−0.588921
$986$			7.32351e10i			0.0774840i
$987$	−1.75820e12	−	1.79147e12i	−1.85268	−	1.88773i
$988$	−5.39742e11			−0.566446
$989$			8.15489e11i			0.852380i
$990$	1.33694e11	+	2.50598e9i	0.139178	+	0.00260877i
$991$	5.43139e10			0.0563140			0.0281570	−	0.999604i	$-0.491036\pi$
$991$	5.43139e10			0.0563140			0.0281570	+	0.999604i	$0.491036\pi$
$992$			1.04827e12i			1.08249i
$993$	−7.25620e10	+	7.12146e10i	−0.0746298	+	0.0732440i
$994$	1.25740e12			1.28803
$995$		−	1.69521e11i		−	0.172954i
$996$	1.93736e11	+	1.97402e11i	0.196867	+	0.200592i
$997$	1.85628e12			1.87872			0.939361	−	0.342929i	$-0.111419\pi$
$997$	1.85628e12			1.87872			0.939361	+	0.342929i	$0.111419\pi$
$998$			8.33205e11i			0.839904i
$999$	3.20304e11	+	3.38839e11i	0.321588	+	0.340198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.9.c.a.11.3	✓	10
3.2	odd	2	inner	15.9.c.a.11.8	yes	10
4.3	odd	2		240.9.l.b.161.7		10
5.2	odd	4		75.9.d.c.74.16		20
5.3	odd	4		75.9.d.c.74.5		20
5.4	even	2		75.9.c.g.26.8		10
12.11	even	2		240.9.l.b.161.8		10
15.2	even	4		75.9.d.c.74.6		20
15.8	even	4		75.9.d.c.74.15		20
15.14	odd	2		75.9.c.g.26.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.3	✓	10	1.1	even	1	trivial
15.9.c.a.11.8	yes	10	3.2	odd	2	inner
75.9.c.g.26.3		10	15.14	odd	2
75.9.c.g.26.8		10	5.4	even	2
75.9.d.c.74.5		20	5.3	odd	4
75.9.d.c.74.6		20	15.2	even	4
75.9.d.c.74.15		20	15.8	even	4
75.9.d.c.74.16		20	5.2	odd	4
240.9.l.b.161.7		10	4.3	odd	2
240.9.l.b.161.8		10	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.2357i q^{2} +(-57.8099 + 56.7364i) q^{3} +151.230 q^{4} -279.508i q^{5} +(580.739 + 591.726i) q^{6} +3448.05 q^{7} -4168.30i q^{8} +(122.959 - 6559.85i) q^{9} +O(q^{10})\)	\(q-10.2357i q^{2} +(-57.8099 + 56.7364i) q^{3} +151.230 q^{4} -279.508i q^{5} +(580.739 + 591.726i) q^{6} +3448.05 q^{7} -4168.30i q^{8} +(122.959 - 6559.85i) q^{9} -2860.98 q^{10} -7123.65i q^{11} +(-8742.57 + 8580.23i) q^{12} +41361.3 q^{13} -35293.4i q^{14} +(15858.3 + 16158.3i) q^{15} -3950.77 q^{16} +119540. i q^{17} +(-67144.9 - 1258.58i) q^{18} -86288.8 q^{19} -42270.0i q^{20} +(-199331. + 195630. i) q^{21} -72915.8 q^{22} -317353. i q^{23} +(236494. + 240969. i) q^{24} -78125.0 q^{25} -423364. i q^{26} +(365074. + 386200. i) q^{27} +521448. q^{28} +59853.0i q^{29} +(165393. - 162321. i) q^{30} -1.02106e6 q^{31} -1.02664e6i q^{32} +(404170. + 411817. i) q^{33} +1.22358e6 q^{34} -963760. i q^{35} +(18595.0 - 992044. i) q^{36} +877366. q^{37} +883230. i q^{38} +(-2.39109e6 + 2.34669e6i) q^{39} -1.16507e6 q^{40} -1.55753e6i q^{41} +(2.00242e6 + 2.04030e6i) q^{42} -2.56966e6 q^{43} -1.07731e6i q^{44} +(-1.83353e6 - 34368.1i) q^{45} -3.24834e6 q^{46} +8.98739e6i q^{47} +(228394. - 224153. i) q^{48} +6.12427e6 q^{49} +799667. i q^{50} +(-6.78229e6 - 6.91061e6i) q^{51} +6.25506e6 q^{52} +6.22182e6i q^{53} +(3.95304e6 - 3.73680e6i) q^{54} -1.99112e6 q^{55} -1.43725e7i q^{56} +(4.98835e6 - 4.89572e6i) q^{57} +612639. q^{58} +3.96940e6i q^{59} +(2.39825e6 + 2.44362e6i) q^{60} -563629. q^{61} +1.04513e7i q^{62} +(423969. - 2.26187e7i) q^{63} -1.15199e7 q^{64} -1.15608e7i q^{65} +(4.21525e6 - 4.13698e6i) q^{66} +1.34009e7 q^{67} +1.80781e7i q^{68} +(1.80055e7 + 1.83461e7i) q^{69} -9.86480e6 q^{70} +3.56270e7i q^{71} +(-2.73434e7 - 512529. i) q^{72} +970897. q^{73} -8.98049e6i q^{74} +(4.51640e6 - 4.43253e6i) q^{75} -1.30494e7 q^{76} -2.45627e7i q^{77} +(2.40201e7 + 2.44746e7i) q^{78} -2.78755e7 q^{79} +1.10427e6i q^{80} +(-4.30165e7 - 1.61318e6i) q^{81} -1.59425e7 q^{82} -2.25794e7i q^{83} +(-3.01448e7 + 2.95851e7i) q^{84} +3.34126e7 q^{85} +2.63024e7i q^{86} +(-3.39584e6 - 3.46009e6i) q^{87} -2.96935e7 q^{88} -5.73209e7i q^{89} +(-351783. + 1.87676e7i) q^{90} +1.42616e8 q^{91} -4.79932e7i q^{92} +(5.90274e7 - 5.79313e7i) q^{93} +9.19926e7 q^{94} +2.41185e7i q^{95} +(5.82481e7 + 5.93502e7i) q^{96} -3.31851e7 q^{97} -6.26864e7i q^{98} +(-4.67301e7 - 875917. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9}+O(q^{10}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} - 8750 q^{10} - 3812 q^{12} - 55464 q^{13} - 21250 q^{15} + 280386 q^{16} - 419800 q^{18} - 231516 q^{19} + 289572 q^{21} + 1129940 q^{22} + 1136334 q^{24} - 781250 q^{25} - 335512 q^{27} - 3340724 q^{28} - 965000 q^{30} + 881620 q^{31} + 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} + 4672616 q^{37} + 1826792 q^{39} + 2913750 q^{40} - 5392860 q^{42} + 7731336 q^{43} - 2142500 q^{45} - 25424604 q^{46} + 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} + 21064016 q^{52} - 7979798 q^{54} - 4377500 q^{55} - 2856304 q^{57} - 4351100 q^{58} + 23016250 q^{60} + 22417020 q^{61} + 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} - 46646024 q^{67} + 33562632 q^{69} - 62992500 q^{70} + 54175560 q^{72} - 129964884 q^{73} + 8750000 q^{75} + 198922436 q^{76} + 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} + 202877560 q^{82} - 197346768 q^{84} - 110682500 q^{85} - 168322540 q^{87} - 484775700 q^{88} + 171878750 q^{90} + 444288464 q^{91} + 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} - 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9 - 8750 * q^10 - 3812 * q^12 - 55464 * q^13 - 21250 * q^15 + 280386 * q^16 - 419800 * q^18 - 231516 * q^19 + 289572 * q^21 + 1129940 * q^22 + 1136334 * q^24 - 781250 * q^25 - 335512 * q^27 - 3340724 * q^28 - 965000 * q^30 + 881620 * q^31 + 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 + 4672616 * q^37 + 1826792 * q^39 + 2913750 * q^40 - 5392860 * q^42 + 7731336 * q^43 - 2142500 * q^45 - 25424604 * q^46 + 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 + 21064016 * q^52 - 7979798 * q^54 - 4377500 * q^55 - 2856304 * q^57 - 4351100 * q^58 + 23016250 * q^60 + 22417020 * q^61 + 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 - 46646024 * q^67 + 33562632 * q^69 - 62992500 * q^70 + 54175560 * q^72 - 129964884 * q^73 + 8750000 * q^75 + 198922436 * q^76 + 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 + 202877560 * q^82 - 197346768 * q^84 - 110682500 * q^85 - 168322540 * q^87 - 484775700 * q^88 + 171878750 * q^90 + 444288464 * q^91 + 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 - 258825724 * q^97 - 33965200 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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