LMFDB - Embedded newform 27.10.c.a.10.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not 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:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 $ x^16 - 8x^15 + 1984x^14 - 13748x^13 + 1552498x^12 - 9136628x^11 + 609566956x^10 - 2964409064x^9 + 126210674407x^8 - 487156186164x^7 + 13162328064828x^6 - 37794288146040x^5 + 578928267028062x^4 - 1095428523832956x^3 + 5807598664427172x^2 - 5266103139591300*x + 1336504689748125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{40}\cdot 17^{2} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.8
Root			$0.500000 + 23.8209i$ of defining polynomial
Character	$\chi$	$=$	27.10
Dual form			27.10.c.a.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.8795 + 34.4322i) q^{2} +(-534.387 + 925.585i) q^{4} +(-423.223 + 733.045i) q^{5} +(3521.99 + 6100.27i) q^{7} -22136.7 q^{8} +O(q^{10})$	\(q+(19.8795 + 34.4322i) q^{2} +(-534.387 + 925.585i) q^{4} +(-423.223 + 733.045i) q^{5} +(3521.99 + 6100.27i) q^{7} -22136.7 q^{8} -33653.8 q^{10} +(-45051.5 - 78031.5i) q^{11} +(-34294.5 + 59399.8i) q^{13} +(-140031. + 242540. i) q^{14} +(-166460. - 288317. i) q^{16} +235749. q^{17} -232999. q^{19} +(-452330. - 783458. i) q^{20} +(1.79120e6 - 3.10245e6i) q^{22} +(-133126. + 230581. i) q^{23} +(618326. + 1.07097e6i) q^{25} -2.72703e6 q^{26} -7.52842e6 q^{28} +(1.53091e6 + 2.65162e6i) q^{29} +(-1.79575e6 + 3.11033e6i) q^{31} +(951277. - 1.64766e6i) q^{32} +(4.68656e6 + 8.11736e6i) q^{34} -5.96236e6 q^{35} +5.13436e6 q^{37} +(-4.63189e6 - 8.02267e6i) q^{38} +(9.36877e6 - 1.62272e7i) q^{40} +(-2.25103e6 + 3.89890e6i) q^{41} +(1.64956e7 + 2.85712e7i) q^{43} +9.62997e7 q^{44} -1.05859e7 q^{46} +(6.21541e6 + 1.07654e7i) q^{47} +(-4.63206e6 + 8.02297e6i) q^{49} +(-2.45840e7 + 4.25807e7i) q^{50} +(-3.66530e7 - 6.34849e7i) q^{52} -3.42506e7 q^{53} +7.62674e7 q^{55} +(-7.79653e7 - 1.35040e8i) q^{56} +(-6.08675e7 + 1.05426e8i) q^{58} +(-2.27808e7 + 3.94575e7i) q^{59} +(-3.08230e7 - 5.33870e7i) q^{61} -1.42794e8 q^{62} -9.48116e7 q^{64} +(-2.90285e7 - 5.02788e7i) q^{65} +(-2.92242e6 + 5.06178e6i) q^{67} +(-1.25981e8 + 2.18205e8i) q^{68} +(-1.18529e8 - 2.05297e8i) q^{70} +2.53018e8 q^{71} +3.59593e8 q^{73} +(1.02068e8 + 1.76788e8i) q^{74} +(1.24511e8 - 2.15660e8i) q^{76} +(3.17342e8 - 5.49653e8i) q^{77} +(-1.44462e8 - 2.50215e8i) q^{79} +2.81799e8 q^{80} -1.78997e8 q^{82} +(-2.26650e8 - 3.92569e8i) q^{83} +(-9.97744e7 + 1.72814e8i) q^{85} +(-6.55848e8 + 1.13596e9i) q^{86} +(9.97292e8 + 1.72736e9i) q^{88} +5.93996e8 q^{89} -4.83140e8 q^{91} +(-1.42281e8 - 2.46438e8i) q^{92} +(-2.47118e8 + 4.28021e8i) q^{94} +(9.86105e7 - 1.70798e8i) q^{95} +(1.49505e8 + 2.58951e8i) q^{97} -3.68332e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) $ 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22} - 1064559 q^{23} - 2293229 q^{25} - 2436312 q^{26} + 1225724 q^{28} + 1309053 q^{29} - 2359819 q^{31} - 5760063 q^{32} + 981801 q^{34} + 31066554 q^{35} + 16391516 q^{37} - 39490203 q^{38} - 16760496 q^{40} - 54747318 q^{41} + 15249608 q^{43} + 332509926 q^{44} + 2390520 q^{46} - 156295545 q^{47} + 15239583 q^{49} - 315590163 q^{50} - 19773358 q^{52} + 525516228 q^{53} - 7579770 q^{55} - 470339790 q^{56} + 55408560 q^{58} - 307774074 q^{59} + 69192125 q^{61} + 914436924 q^{62} - 403588478 q^{64} - 482470359 q^{65} + 14328044 q^{67} - 915409575 q^{68} - 229271934 q^{70} + 1239601392 q^{71} + 598613198 q^{73} - 1022736000 q^{74} + 119954093 q^{76} - 717995541 q^{77} + 30257531 q^{79} + 2927826528 q^{80} - 202376022 q^{82} - 1176168291 q^{83} + 4818366 q^{85} - 1426944009 q^{86} + 911312427 q^{88} + 3317041296 q^{89} - 739230122 q^{91} + 76813998 q^{92} - 1954316784 q^{94} + 391400652 q^{95} - 267311278 q^{97} - 4827300318 q^{98}+O(q^{100}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	19.8795	+	34.4322i	0.878557	+	1.52170i	0.852925	+	0.522033i	$0.174826\pi$
$2$	19.8795	+	34.4322i	0.878557	+	1.52170i	0.0256316	+	0.999671i	$0.491840\pi$
$3$		0			0
$3$		0			0
$4$	−534.387	+	925.585i	−1.04372	+	1.80778i
$5$	−423.223	+	733.045i	−0.302834	+	0.524524i	−0.976777	−	0.214260i	$-0.931266\pi$
$5$	−423.223	+	733.045i	−0.302834	+	0.524524i	0.673943	+	0.738784i	$0.264599\pi$
$6$		0			0
$7$	3521.99	+	6100.27i	0.554431	+	0.960302i	0.997948	+	0.0640361i	$0.0203973\pi$
$7$	3521.99	+	6100.27i	0.554431	+	0.960302i	−0.443517	+	0.896266i	$0.646269\pi$
$8$	−22136.7			−1.91077
$9$		0			0
$10$	−33653.8			−1.06423
$11$	−45051.5	−	78031.5i	−0.927774	−	1.60695i	−0.787037	−	0.616905i	$-0.788386\pi$
$11$	−45051.5	−	78031.5i	−0.927774	−	1.60695i	−0.140737	−	0.990047i	$-0.544947\pi$
$12$		0			0
$13$	−34294.5	+	59399.8i	−0.333027	+	0.576820i	−0.983104	−	0.183049i	$-0.941403\pi$
$13$	−34294.5	+	59399.8i	−0.333027	+	0.576820i	0.650077	+	0.759869i	$0.274737\pi$
$14$	−140031.	+	242540.i	−0.974198	+	1.68736i
$15$		0			0
$16$	−166460.	−	288317.i	−0.634995	−	1.09984i
$17$	235749.			0.684588			0.342294	−	0.939593i	$-0.388796\pi$
$17$	235749.			0.684588			0.342294	+	0.939593i	$0.388796\pi$
$18$		0			0
$19$	−232999.			−0.410168			−0.205084	−	0.978744i	$-0.565747\pi$
$19$	−232999.			−0.410168			−0.205084	+	0.978744i	$0.565747\pi$
$20$	−452330.	−	783458.i	−0.632150	−	1.09492i
$21$		0			0
$22$	1.79120e6	−	3.10245e6i	1.63020	−	2.82360i
$23$	−133126.	+	230581.i	−0.0991944	+	0.171810i	−0.911351	−	0.411629i	$-0.864960\pi$
$23$	−133126.	+	230581.i	−0.0991944	+	0.171810i	0.812157	+	0.583439i	$0.198293\pi$
$24$		0			0
$25$	618326.	+	1.07097e6i	0.316583	+	0.548338i
$26$	−2.72703e6			−1.17033
$27$		0			0
$28$	−7.52842e6			−2.31469
$29$	1.53091e6	+	2.65162e6i	0.401938	+	0.696178i	0.993960	−	0.109744i	$-0.0350032\pi$
$29$	1.53091e6	+	2.65162e6i	0.401938	+	0.696178i	−0.592021	+	0.805922i	$0.701670\pi$
$30$		0			0
$31$	−1.79575e6	+	3.11033e6i	−0.349235	+	0.604893i	−0.986114	−	0.166071i	$-0.946892\pi$
$31$	−1.79575e6	+	3.11033e6i	−0.349235	+	0.604893i	0.636879	+	0.770964i	$0.280225\pi$
$32$	951277.	−	1.64766e6i	0.160373	−	0.277775i
$33$		0			0
$34$	4.68656e6	+	8.11736e6i	0.601449	+	1.04174i
$35$	−5.96236e6			−0.671602
$36$		0			0
$37$	5.13436e6			0.450380			0.225190	−	0.974315i	$-0.427700\pi$
$37$	5.13436e6			0.450380			0.225190	+	0.974315i	$0.427700\pi$
$38$	−4.63189e6	−	8.02267e6i	−0.360356	−	0.624155i
$39$		0			0
$40$	9.36877e6	−	1.62272e7i	0.578646	−	1.00224i
$41$	−2.25103e6	+	3.89890e6i	−0.124410	+	0.215484i	−0.921502	−	0.388374i	$-0.873037\pi$
$41$	−2.25103e6	+	3.89890e6i	−0.124410	+	0.215484i	0.797092	+	0.603857i	$0.206370\pi$
$42$		0			0
$43$	1.64956e7	+	2.85712e7i	0.735801	+	1.27444i	0.954371	+	0.298623i	$0.0965273\pi$
$43$	1.64956e7	+	2.85712e7i	0.735801	+	1.27444i	−0.218571	+	0.975821i	$0.570139\pi$
$44$	9.62997e7			3.87336
$45$		0			0
$46$	−1.05859e7			−0.348592
$47$	6.21541e6	+	1.07654e7i	0.185793	+	0.321803i	0.943843	−	0.330393i	$-0.107181\pi$
$47$	6.21541e6	+	1.07654e7i	0.185793	+	0.321803i	−0.758050	+	0.652196i	$0.773848\pi$
$48$		0			0
$49$	−4.63206e6	+	8.02297e6i	−0.114787	+	0.198817i
$50$	−2.45840e7	+	4.25807e7i	−0.556272	+	0.963492i
$51$		0			0
$52$	−3.66530e7	−	6.34849e7i	−0.695176	−	1.20408i
$53$	−3.42506e7			−0.596248			−0.298124	−	0.954527i	$-0.596361\pi$
$53$	−3.42506e7			−0.596248			−0.298124	+	0.954527i	$0.596361\pi$
$54$		0			0
$55$	7.62674e7			1.12385
$56$	−7.79653e7	−	1.35040e8i	−1.05939	−	1.83491i
$57$		0			0
$58$	−6.08675e7	+	1.05426e8i	−0.706251	+	1.22326i
$59$	−2.27808e7	+	3.94575e7i	−0.244757	+	0.423932i	−0.962063	−	0.272826i	$-0.912042\pi$
$59$	−2.27808e7	+	3.94575e7i	−0.244757	+	0.423932i	0.717306	+	0.696758i	$0.245375\pi$
$60$		0			0
$61$	−3.08230e7	−	5.33870e7i	−0.285030	−	0.493686i	0.687587	−	0.726102i	$-0.258670\pi$
$61$	−3.08230e7	−	5.33870e7i	−0.285030	−	0.493686i	−0.972616	+	0.232416i	$0.925337\pi$
$62$	−1.42794e8			−1.22729
$63$		0			0
$64$	−9.48116e7			−0.706401
$65$	−2.90285e7	−	5.02788e7i	−0.201704	−	0.349361i
$66$		0			0
$67$	−2.92242e6	+	5.06178e6i	−0.0177176	+	0.0306879i	−0.874748	−	0.484578i	$-0.838973\pi$
$67$	−2.92242e6	+	5.06178e6i	−0.0177176	+	0.0306879i	0.857031	+	0.515265i	$0.172307\pi$
$68$	−1.25981e8	+	2.18205e8i	−0.714520	+	1.23759i
$69$		0			0
$70$	−1.18529e8	−	2.05297e8i	−0.590040	−	1.02198i
$71$	2.53018e8			1.18165			0.590825	−	0.806800i	$-0.298802\pi$
$71$	2.53018e8			1.18165			0.590825	+	0.806800i	$0.298802\pi$
$72$		0			0
$73$	3.59593e8			1.48203			0.741017	−	0.671486i	$-0.234344\pi$
$73$	3.59593e8			1.48203			0.741017	+	0.671486i	$0.234344\pi$
$74$	1.02068e8	+	1.76788e8i	0.395684	+	0.685345i
$75$		0			0
$76$	1.24511e8	−	2.15660e8i	0.428102	−	0.741495i
$77$	3.17342e8	−	5.49653e8i	1.02877	−	1.78189i
$78$		0			0
$79$	−1.44462e8	−	2.50215e8i	−0.417283	−	0.722755i	0.578382	−	0.815766i	$-0.303684\pi$
$79$	−1.44462e8	−	2.50215e8i	−0.417283	−	0.722755i	−0.995665	+	0.0930107i	$0.970351\pi$
$80$	2.81799e8			0.769192
$81$		0			0
$82$	−1.78997e8			−0.437204
$83$	−2.26650e8	−	3.92569e8i	−0.524208	−	0.907956i	−0.999603	−	0.0281829i	$-0.991028\pi$
$83$	−2.26650e8	−	3.92569e8i	−0.524208	−	0.907956i	0.475394	−	0.879773i	$-0.342305\pi$
$84$		0			0
$85$	−9.97744e7	+	1.72814e8i	−0.207316	+	0.359083i
$86$	−6.55848e8	+	1.13596e9i	−1.29289	+	2.23934i
$87$		0			0
$88$	9.97292e8	+	1.72736e9i	1.77276	+	3.07051i
$89$	5.93996e8			1.00353			0.501763	−	0.865005i	$-0.332685\pi$
$89$	5.93996e8			1.00353			0.501763	+	0.865005i	$0.332685\pi$
$90$		0			0
$91$	−4.83140e8			−0.738562
$92$	−1.42281e8	−	2.46438e8i	−0.207063	−	0.358644i
$93$		0			0
$94$	−2.47118e8	+	4.28021e8i	−0.326460	+	0.565445i
$95$	9.86105e7	−	1.70798e8i	0.124213	−	0.215143i
$96$		0			0
$97$	1.49505e8	+	2.58951e8i	0.171468	+	0.296992i	0.938933	−	0.344099i	$-0.111816\pi$
$97$	1.49505e8	+	2.58951e8i	0.171468	+	0.296992i	−0.767465	+	0.641091i	$0.778482\pi$
$98$	−3.68332e8			−0.403387
$99$		0			0
$100$	−1.32170e9			−1.32170
$101$	−3.93716e6	−	6.81936e6i	−0.00376476	−	0.00652075i	0.864137	−	0.503257i	$-0.167865\pi$
$101$	−3.93716e6	−	6.81936e6i	−0.00376476	−	0.00652075i	−0.867902	+	0.496736i	$0.834532\pi$
$102$		0			0
$103$	9.12453e8	−	1.58041e9i	0.798809	−	1.38358i	−0.121583	−	0.992581i	$-0.538797\pi$
$103$	9.12453e8	−	1.58041e9i	0.798809	−	1.38358i	0.920392	−	0.390996i	$-0.127869\pi$
$104$	7.59167e8	−	1.31492e9i	0.636338	−	1.10217i
$105$		0			0
$106$	−6.80884e8	−	1.17933e9i	−0.523838	−	0.907313i
$107$	−4.67288e8			−0.344634			−0.172317	−	0.985042i	$-0.555125\pi$
$107$	−4.67288e8			−0.344634			−0.172317	+	0.985042i	$0.555125\pi$
$108$		0			0
$109$	1.80762e9			1.22656			0.613279	−	0.789866i	$-0.289850\pi$
$109$	1.80762e9			1.22656			0.613279	+	0.789866i	$0.289850\pi$
$110$	1.51616e9	+	2.62606e9i	0.987363	+	1.71016i
$111$		0			0
$112$	1.17254e9	−	2.03090e9i	0.704121	−	1.21957i
$113$	5.18834e8	−	8.98647e8i	0.299347	−	0.518485i	−0.676639	−	0.736315i	$-0.736564\pi$
$113$	5.18834e8	−	8.98647e8i	0.299347	−	0.518485i	0.975987	+	0.217830i	$0.0698977\pi$
$114$		0			0
$115$	−1.12684e8	−	1.95174e8i	−0.0600789	−	0.104060i
$116$	−3.27240e9			−1.67805
$117$		0			0
$118$	−1.81148e9			−0.860132
$119$	8.30305e8	+	1.43813e9i	0.379556	+	0.657411i
$120$		0			0
$121$	−2.88030e9	+	4.98883e9i	−1.22153	+	2.11575i
$122$	1.22549e9	−	2.12261e9i	0.500830	−	0.867463i
$123$		0			0
$124$	−1.91925e9	−	3.32423e9i	−0.729010	−	1.26268i
$125$	−2.69998e9			−0.989157
$126$		0			0
$127$	5.65026e9			1.92731			0.963655	−	0.267150i	$-0.0860818\pi$
$127$	5.65026e9			1.92731			0.963655	+	0.267150i	$0.0860818\pi$
$128$	−2.37186e9	−	4.10818e9i	−0.780987	−	1.35271i
$129$		0			0
$130$	1.15414e9	−	1.99903e9i	0.354417	−	0.613867i
$131$	−3.24241e9	+	5.61602e9i	−0.961939	+	1.66613i	−0.244314	+	0.969696i	$0.578563\pi$
$131$	−3.24241e9	+	5.61602e9i	−0.961939	+	1.66613i	−0.717625	+	0.696430i	$0.754771\pi$
$132$		0			0
$133$	−8.20619e8	−	1.42135e9i	−0.227410	−	0.393886i
$134$	−2.32385e8			−0.0622638
$135$		0			0
$136$	−5.21870e9			−1.30809
$137$	−1.29715e9	−	2.24673e9i	−0.314592	−	0.544889i	0.664759	−	0.747058i	$-0.268534\pi$
$137$	−1.29715e9	−	2.24673e9i	−0.314592	−	0.544889i	−0.979351	+	0.202169i	$0.935201\pi$
$138$		0			0
$139$	−2.19078e9	+	3.79454e9i	−0.497773	+	0.862169i	−0.999997	−	0.00256931i	$-0.999182\pi$
$139$	−2.19078e9	+	3.79454e9i	−0.497773	+	0.862169i	0.502223	+	0.864738i	$0.332515\pi$
$140$	3.18620e9	−	5.51867e9i	0.700967	−	1.21411i
$141$		0			0
$142$	5.02986e9	+	8.71198e9i	1.03815	+	1.79812i
$143$	6.18008e9			1.23590
$144$		0			0
$145$	−2.59167e9			−0.486883
$146$	7.14852e9	+	1.23816e10i	1.30205	+	2.25522i
$147$		0			0
$148$	−2.74373e9	+	4.75229e9i	−0.470072	+	0.814189i
$149$	−1.88301e9	+	3.26147e9i	−0.312978	+	0.542094i	−0.979006	−	0.203833i	$-0.934660\pi$
$149$	−1.88301e9	+	3.26147e9i	−0.312978	+	0.542094i	0.666028	+	0.745927i	$0.267993\pi$
$150$		0			0
$151$	−4.60600e9	−	7.97783e9i	−0.720988	−	1.24879i	−0.960604	−	0.277920i	$-0.910355\pi$
$151$	−4.60600e9	−	7.97783e9i	−0.720988	−	1.24879i	0.239616	−	0.970868i	$-0.422978\pi$
$152$	5.15782e9			0.783737
$153$		0			0
$154$	2.52344e10			3.61534
$155$	−1.52001e9	−	2.63273e9i	−0.211521	−	0.366364i
$156$		0			0
$157$	1.74126e9	−	3.01595e9i	0.228726	−	0.396165i	−0.728705	−	0.684828i	$-0.759877\pi$
$157$	1.74126e9	−	3.01595e9i	0.228726	−	0.396165i	0.957431	+	0.288663i	$0.0932107\pi$
$158$	5.74364e9	−	9.94828e9i	0.733213	−	1.26996i
$159$		0			0
$160$	8.05205e8	+	1.39466e9i	0.0971330	+	0.168239i
$161$	−1.87547e9			−0.219986
$162$		0			0
$163$	−6.34728e9			−0.704277			−0.352139	−	0.935948i	$-0.614545\pi$
$163$	−6.34728e9			−0.704277			−0.352139	+	0.935948i	$0.614545\pi$
$164$	−2.40584e9	−	4.16704e9i	−0.259699	−	0.449811i
$165$		0			0
$166$	9.01136e9	−	1.56081e10i	0.921094	−	1.59538i
$167$	3.40727e9	−	5.90156e9i	0.338986	−	0.587142i	−0.645256	−	0.763966i	$-0.723249\pi$
$167$	3.40727e9	−	5.90156e9i	0.338986	−	0.587142i	0.984242	+	0.176825i	$0.0565826\pi$
$168$		0			0
$169$	2.95002e9	+	5.10959e9i	0.278186	+	0.481832i
$170$	−7.93385e9			−0.728557
$171$		0			0
$172$	−3.52601e10			−3.07189
$173$	4.95185e9	+	8.57685e9i	0.420300	+	0.727982i	0.995969	−	0.0897016i	$-0.0285913\pi$
$173$	4.95185e9	+	8.57685e9i	0.420300	+	0.727982i	−0.575668	+	0.817683i	$0.695258\pi$
$174$		0			0
$175$	−4.35548e9	+	7.54392e9i	−0.351047	+	0.608031i
$176$	−1.49986e10	+	2.59783e10i	−1.17826	+	2.04081i
$177$		0			0
$178$	1.18083e10	+	2.04526e10i	0.881654	+	1.52707i
$179$	−1.34679e9			−0.0980532			−0.0490266	−	0.998797i	$-0.515612\pi$
$179$	−1.34679e9			−0.0980532			−0.0490266	+	0.998797i	$0.515612\pi$
$180$		0			0
$181$	−1.53579e10			−1.06360			−0.531800	−	0.846870i	$-0.678484\pi$
$181$	−1.53579e10			−1.06360			−0.531800	+	0.846870i	$0.678484\pi$
$182$	−9.60457e9	−	1.66356e10i	−0.648868	−	1.12387i
$183$		0			0
$184$	2.94697e9	−	5.10430e9i	0.189538	−	0.328289i
$185$	−2.17298e9	+	3.76372e9i	−0.136390	+	0.236235i
$186$		0			0
$187$	−1.06208e10	−	1.83958e10i	−0.635143	−	1.10010i
$188$	−1.32857e10			−0.775667
$189$		0			0
$190$	7.84130e9			0.436512
$191$	−1.39313e10	−	2.41297e10i	−0.757429	−	1.31191i	−0.944158	−	0.329494i	$-0.893122\pi$
$191$	−1.39313e10	−	2.41297e10i	−0.757429	−	1.31191i	0.186729	−	0.982412i	$-0.440211\pi$
$192$		0			0
$193$	7.38764e9	−	1.27958e10i	0.383264	−	0.663832i	−0.608263	−	0.793736i	$-0.708133\pi$
$193$	7.38764e9	−	1.27958e10i	0.383264	−	0.663832i	0.991527	+	0.129903i	$0.0414667\pi$
$194$	−5.94417e9	+	1.02956e10i	−0.301289	+	0.521848i
$195$		0			0
$196$	−4.95062e9	−	8.57473e9i	−0.239611	−	0.415019i
$197$	2.08977e10			0.988554			0.494277	−	0.869304i	$-0.335433\pi$
$197$	2.08977e10			0.988554			0.494277	+	0.869304i	$0.335433\pi$
$198$		0			0
$199$	2.77242e10			1.25320			0.626600	−	0.779341i	$-0.284446\pi$
$199$	2.77242e10			1.25320			0.626600	+	0.779341i	$0.284446\pi$
$200$	−1.36877e10	−	2.37078e10i	−0.604917	−	1.04775i
$201$		0			0
$202$	1.56537e8	−	2.71131e8i	0.00661510	−	0.0114577i
$203$	−1.07837e10	+	1.86780e10i	−0.445694	+	0.771965i
$204$		0			0
$205$	−1.90538e9	−	3.30021e9i	−0.0753509	−	0.130512i
$206$	7.25563e10			2.80720
$207$		0			0
$208$	2.28347e10			0.845881
$209$	1.04969e10	+	1.81812e10i	0.380544	+	0.659121i
$210$		0			0
$211$	5.45826e9	−	9.45399e9i	0.189576	−	0.328355i	−0.755533	−	0.655111i	$-0.772622\pi$
$211$	5.45826e9	−	9.45399e9i	0.189576	−	0.328355i	0.945109	+	0.326755i	$0.105955\pi$
$212$	1.83031e10	−	3.17018e10i	0.622318	−	1.07789i
$213$		0			0
$214$	−9.28944e9	−	1.60898e10i	−0.302780	−	0.524431i
$215$	−2.79253e10			−0.891302
$216$		0			0
$217$	−2.52985e10			−0.774507
$218$	3.59346e10	+	6.22405e10i	1.07760	+	1.86646i
$219$		0			0
$220$	−4.07563e10	+	7.05920e10i	−1.17299	+	2.03167i
$221$	−8.08489e9	+	1.40034e10i	−0.227986	+	0.394884i
$222$		0			0
$223$	2.80127e10	+	4.85194e10i	0.758547	+	1.31384i	0.943591	+	0.331113i	$0.107424\pi$
$223$	2.80127e10	+	4.85194e10i	0.758547	+	1.31384i	−0.185044	+	0.982730i	$0.559243\pi$
$224$	1.34016e10			0.355663
$225$		0			0
$226$	4.12566e10			1.05197
$227$	−1.28104e10	−	2.21883e10i	−0.320219	−	0.554636i	0.660314	−	0.750990i	$-0.270423\pi$
$227$	−1.28104e10	−	2.21883e10i	−0.320219	−	0.554636i	−0.980533	+	0.196354i	$0.937090\pi$
$228$		0			0
$229$	−4.04705e9	+	7.00970e9i	−0.0972477	+	0.168438i	−0.910544	−	0.413411i	$-0.864337\pi$
$229$	−4.04705e9	+	7.00970e9i	−0.0972477	+	0.168438i	0.813297	+	0.581849i	$0.197671\pi$
$230$	4.48019e9	−	7.75992e9i	0.105565	−	0.182845i
$231$		0			0
$232$	−3.38894e10	−	5.86981e10i	−0.768011	−	1.33023i
$233$	2.40857e10			0.535374			0.267687	−	0.963506i	$-0.413741\pi$
$233$	2.40857e10			0.535374			0.267687	+	0.963506i	$0.413741\pi$
$234$		0			0
$235$	−1.05220e10			−0.225058
$236$	−2.43475e10	−	4.21711e10i	−0.510917	−	0.884935i
$237$		0			0
$238$	−3.30121e10	+	5.71785e10i	−0.666924	+	1.15515i
$239$	1.83170e10	−	3.17260e10i	0.363132	−	0.628963i	−0.625342	−	0.780350i	$-0.715041\pi$
$239$	1.83170e10	−	3.17260e10i	0.363132	−	0.628963i	0.988475	+	0.151387i	$0.0483740\pi$
$240$		0			0
$241$	4.13227e10	+	7.15730e10i	0.789063	+	1.36670i	0.926542	+	0.376193i	$0.122767\pi$
$241$	4.13227e10	+	7.15730e10i	0.789063	+	1.36670i	−0.137478	+	0.990505i	$0.543900\pi$
$242$	−2.29036e11			−4.29273
$243$		0			0
$244$	6.58855e10			1.18997
$245$	−3.92079e9	−	6.79102e9i	−0.0695227	−	0.120417i
$246$		0			0
$247$	7.99057e9	−	1.38401e10i	0.136597	−	0.236593i
$248$	3.97520e10	−	6.88524e10i	0.667307	−	1.15581i
$249$		0			0
$250$	−5.36741e10	−	9.29663e10i	−0.869030	−	1.50520i
$251$	8.40180e10			1.33611			0.668053	−	0.744114i	$-0.267128\pi$
$251$	8.40180e10			1.33611			0.668053	+	0.744114i	$0.267128\pi$
$252$		0			0
$253$	2.39901e10			0.368120
$254$	1.12324e11	+	1.94551e11i	1.69325	+	2.93280i
$255$		0			0
$256$	7.00307e10	−	1.21297e11i	1.01908	−	1.76510i
$257$	−6.19866e10	+	1.07364e11i	−0.886337	+	1.53518i	−0.0421632	+	0.999111i	$0.513425\pi$
$257$	−6.19866e10	+	1.07364e11i	−0.886337	+	1.53518i	−0.844174	+	0.536070i	$0.819908\pi$
$258$		0			0
$259$	1.80832e10	+	3.13210e10i	0.249704	+	0.432501i
$260$	6.20497e10			0.842092
$261$		0			0
$262$	−2.57830e11			−3.38047
$263$	−5.38774e10	−	9.33183e10i	−0.694393	−	1.20272i	−0.970385	−	0.241564i	$-0.922340\pi$
$263$	−5.38774e10	−	9.33183e10i	−0.694393	−	1.20272i	0.275992	−	0.961160i	$-0.410994\pi$
$264$		0			0
$265$	1.44957e10	−	2.51072e10i	0.180564	−	0.312746i
$266$	3.26270e10	−	5.65115e10i	0.399585	−	0.692101i
$267$		0			0
$268$	−3.12340e9	−	5.40989e9i	−0.0369846	−	0.0640593i
$269$	5.47369e10			0.637375			0.318688	−	0.947860i	$-0.396758\pi$
$269$	5.47369e10			0.637375			0.318688	+	0.947860i	$0.396758\pi$
$270$		0			0
$271$	7.34345e9			0.0827063			0.0413531	−	0.999145i	$-0.486833\pi$
$271$	7.34345e9			0.0827063			0.0413531	+	0.999145i	$0.486833\pi$
$272$	−3.92427e10	−	6.79704e10i	−0.434709	−	0.752939i
$273$		0			0
$274$	5.15733e10	−	8.93276e10i	0.552774	−	0.957432i
$275$	5.57131e10	−	9.64979e10i	0.587435	−	1.01747i
$276$		0			0
$277$	−3.80128e10	−	6.58400e10i	−0.387945	−	0.671941i	0.604228	−	0.796812i	$-0.293482\pi$
$277$	−3.80128e10	−	6.58400e10i	−0.387945	−	0.671941i	−0.992173	+	0.124871i	$0.960148\pi$
$278$	−1.74206e11			−1.74929
$279$		0			0
$280$	1.31987e11			1.28328
$281$	1.14192e10	+	1.97787e10i	0.109259	+	0.189243i	0.915470	−	0.402385i	$-0.131819\pi$
$281$	1.14192e10	+	1.97787e10i	0.109259	+	0.189243i	−0.806211	+	0.591628i	$0.798485\pi$
$282$		0			0
$283$	9.92192e10	−	1.71853e11i	0.919511	−	1.59264i	0.119352	−	0.992852i	$-0.461918\pi$
$283$	9.92192e10	−	1.71853e11i	0.919511	−	1.59264i	0.800159	−	0.599788i	$-0.204748\pi$
$284$	−1.35209e11	+	2.34190e11i	−1.23332	+	2.13617i
$285$		0			0
$286$	1.22857e11	+	2.12794e11i	1.08580	+	1.88067i
$287$	−3.17124e10			−0.275906
$288$		0			0
$289$	−6.30104e10			−0.531340
$290$	−5.15211e10	−	8.92371e10i	−0.427754	−	0.740892i
$291$		0			0
$292$	−1.92162e11	+	3.32834e11i	−1.54683	+	2.67920i
$293$	2.07685e10	−	3.59722e10i	0.164627	−	0.285143i	−0.771896	−	0.635749i	$-0.780691\pi$
$293$	2.07685e10	−	3.59722e10i	0.164627	−	0.285143i	0.936523	+	0.350607i	$0.114025\pi$
$294$		0			0
$295$	−1.92828e10	−	3.33987e10i	−0.148242	−	0.256762i
$296$	−1.13658e11			−0.860571
$297$		0			0
$298$	−1.49733e11			−1.09988
$299$	−9.13097e9	−	1.58153e10i	−0.0660688	−	0.114435i
$300$		0			0
$301$	−1.16195e11	+	2.01255e11i	−0.815901	+	1.41318i
$302$	1.83130e11	−	3.17190e11i	1.26686	−	2.19426i
$303$		0			0
$304$	3.87849e10	+	6.71775e10i	0.260455	+	0.451121i
$305$	5.21800e10			0.345267
$306$		0			0
$307$	1.45036e10			0.0931864			0.0465932	−	0.998914i	$-0.485164\pi$
$307$	1.45036e10			0.0931864			0.0465932	+	0.998914i	$0.485164\pi$
$308$	3.39167e11	+	5.87454e11i	2.14751	+	3.71960i
$309$		0			0
$310$	6.04338e10	−	1.04674e11i	0.371666	−	0.643744i
$311$	−1.48065e10	+	2.56457e10i	−0.0897494	+	0.155450i	−0.907405	−	0.420257i	$-0.861940\pi$
$311$	−1.48065e10	+	2.56457e10i	−0.0897494	+	0.155450i	0.817656	+	0.575707i	$0.195273\pi$
$312$		0			0
$313$	4.63427e10	+	8.02679e10i	0.272918	+	0.472707i	0.969608	−	0.244665i	$-0.0786780\pi$
$313$	4.63427e10	+	8.02679e10i	0.272918	+	0.472707i	−0.696690	+	0.717372i	$0.745345\pi$
$314$	1.38461e11			0.803795
$315$		0			0
$316$	3.08793e11			1.74211
$317$	−6.83738e10	−	1.18427e11i	−0.380297	−	0.658694i	0.610807	−	0.791779i	$-0.290845\pi$
$317$	−6.83738e10	−	1.18427e11i	−0.380297	−	0.658694i	−0.991105	+	0.133085i	$0.957512\pi$
$318$		0			0
$319$	1.37940e11	−	2.38919e11i	0.745816	−	1.29179i
$320$	4.01265e10	−	6.95011e10i	0.213922	−	0.370524i
$321$		0			0
$322$	−3.72834e10	−	6.45768e10i	−0.193270	−	0.334753i
$323$	−5.49291e10			−0.280796
$324$		0			0
$325$	−8.48208e10			−0.421723
$326$	−1.26181e11	−	2.18551e11i	−0.618747	−	1.07170i
$327$		0			0
$328$	4.98304e10	−	8.63088e10i	0.237718	−	0.411740i
$329$	−4.37813e10	+	7.58314e10i	−0.206019	+	0.356835i
$330$		0			0
$331$	−1.56804e11	−	2.71592e11i	−0.718009	−	1.24363i	−0.961787	−	0.273797i	$-0.911720\pi$
$331$	−1.56804e11	−	2.71592e11i	−0.718009	−	1.24363i	0.243778	−	0.969831i	$-0.421613\pi$
$332$	4.84475e11			2.18852
$333$		0			0
$334$	2.70939e11			1.19128
$335$	−2.47367e9	−	4.28453e9i	−0.0107310	−	0.0185867i
$336$		0			0
$337$	−1.44549e11	+	2.50366e11i	−0.610493	+	1.05740i	0.380664	+	0.924713i	$0.375695\pi$
$337$	−1.44549e11	+	2.50366e11i	−0.610493	+	1.05740i	−0.991157	+	0.132692i	$0.957638\pi$
$338$	−1.17290e11	+	2.03152e11i	−0.488804	+	0.846634i
$339$		0			0
$340$	−1.06636e11	−	1.84699e11i	−0.432762	−	0.749566i
$341$	3.23605e11			1.29605
$342$		0			0
$343$	2.18994e11			0.854296
$344$	−3.65158e11	−	6.32473e11i	−1.40594	−	2.43517i
$345$		0			0
$346$	−1.96880e11	+	3.41007e11i	−0.738516	+	1.27915i
$347$	−1.12430e11	+	1.94734e11i	−0.416293	+	0.721040i	−0.995563	−	0.0940954i	$-0.970004\pi$
$347$	−1.12430e11	+	1.94734e11i	−0.416293	+	0.721040i	0.579271	+	0.815135i	$0.303337\pi$
$348$		0			0
$349$	4.39959e10	+	7.62031e10i	0.158744	+	0.274953i	0.934416	−	0.356183i	$-0.115922\pi$
$349$	4.39959e10	+	7.62031e10i	0.158744	+	0.274953i	−0.775672	+	0.631136i	$0.782589\pi$
$350$	−3.46339e11			−1.23366
$351$		0			0
$352$	−1.71426e11			−0.595161
$353$	1.91051e11	+	3.30911e11i	0.654884	+	1.13429i	0.981923	+	0.189281i	$0.0606157\pi$
$353$	1.91051e11	+	3.30911e11i	0.654884	+	1.13429i	−0.327039	+	0.945011i	$0.606051\pi$
$354$		0			0
$355$	−1.07083e11	+	1.85473e11i	−0.357844	+	0.619804i
$356$	−3.17424e11	+	5.49794e11i	−1.04740	+	1.81416i
$357$		0			0
$358$	−2.67735e10	−	4.63731e10i	−0.0861453	−	0.149208i
$359$	−4.78348e11			−1.51991			−0.759957	−	0.649973i	$-0.774780\pi$
$359$	−4.78348e11			−1.51991			−0.759957	+	0.649973i	$0.774780\pi$
$360$		0			0
$361$	−2.68399e11			−0.831762
$362$	−3.05307e11	−	5.28807e11i	−0.934433	−	1.61849i
$363$		0			0
$364$	2.58184e11	−	4.47187e11i	0.770854	−	1.33516i
$365$	−1.52188e11	+	2.63598e11i	−0.448811	+	0.777363i
$366$		0			0
$367$	−1.13258e11	−	1.96169e11i	−0.325892	−	0.564461i	0.655801	−	0.754934i	$-0.272331\pi$
$367$	−1.13258e11	−	1.96169e11i	−0.325892	−	0.564461i	−0.981692	+	0.190473i	$0.938998\pi$
$368$	8.86405e10			0.251952
$369$		0			0
$370$	−1.72791e11			−0.479307
$371$	−1.20630e11	−	2.08938e11i	−0.330578	−	0.572578i
$372$		0			0
$373$	−2.38579e11	+	4.13231e11i	−0.638180	+	1.10536i	0.347652	+	0.937624i	$0.386979\pi$
$373$	−2.38579e11	+	4.13231e11i	−0.638180	+	1.10536i	−0.985832	+	0.167736i	$0.946354\pi$
$374$	4.22273e11	−	7.31399e11i	1.11602	−	1.93300i
$375$		0			0
$376$	−1.37589e11	−	2.38311e11i	−0.355008	−	0.614891i
$377$	−2.10008e11			−0.535426
$378$		0			0
$379$	−5.69565e10			−0.141797			−0.0708985	−	0.997484i	$-0.522587\pi$
$379$	−5.69565e10			−0.141797			−0.0708985	+	0.997484i	$0.522587\pi$
$380$	1.05392e11	+	1.82545e11i	0.259288	+	0.449100i
$381$		0			0
$382$	5.53894e11	−	9.59373e11i	1.33089	−	2.30517i
$383$	−1.11903e10	+	1.93822e10i	−0.0265734	+	0.0460265i	−0.879006	−	0.476810i	$-0.841793\pi$
$383$	−1.11903e10	+	1.93822e10i	−0.0265734	+	0.0460265i	0.852433	+	0.522837i	$0.175126\pi$
$384$		0			0
$385$	2.68613e11	+	4.65252e11i	0.623095	+	1.07923i
$386$	5.87449e11			1.34688
$387$		0			0
$388$	−3.19575e11			−0.715862
$389$	2.11354e11	+	3.66075e11i	0.467990	+	0.810583i	0.999331	−	0.0365755i	$-0.0116449\pi$
$389$	2.11354e11	+	3.66075e11i	0.467990	+	0.810583i	−0.531341	+	0.847158i	$0.678312\pi$
$390$		0			0
$391$	−3.13842e10	+	5.43591e10i	−0.0679073	+	0.117619i
$392$	1.02539e11	−	1.77602e11i	0.219331	−	0.379892i
$393$		0			0
$394$	4.15435e11	+	7.19555e11i	0.868501	+	1.50429i
$395$	2.44558e11			0.505470
$396$		0			0
$397$	5.15461e11			1.04145			0.520725	−	0.853724i	$-0.325662\pi$
$397$	5.15461e11			1.04145			0.520725	+	0.853724i	$0.325662\pi$
$398$	5.51143e11	+	9.54608e11i	1.10101	+	1.90700i
$399$		0			0
$400$	2.05853e11	−	3.56548e11i	0.402057	−	0.696383i
$401$	3.20829e9	−	5.55693e9i	0.00619619	−	0.0107321i	−0.862911	−	0.505356i	$-0.831361\pi$
$401$	3.20829e9	−	5.55693e9i	0.00619619	−	0.0107321i	0.869107	+	0.494624i	$0.164694\pi$
$402$		0			0
$403$	−1.23169e11	−	2.13334e11i	−0.232610	−	0.402891i
$404$	8.41586e9			0.0157175
$405$		0			0
$406$	−8.57499e11			−1.56627
$407$	−2.31311e11	−	4.00642e11i	−0.417851	−	0.723739i
$408$		0			0
$409$	1.74242e11	−	3.01796e11i	0.307891	−	0.533284i	−0.670009	−	0.742353i	$-0.733710\pi$
$409$	1.74242e11	−	3.01796e11i	0.307891	−	0.533284i	0.977901	+	0.209069i	$0.0670433\pi$
$410$	7.57558e10	−	1.31213e11i	0.132400	−	0.229324i
$411$		0			0
$412$	9.75205e11	+	1.68910e12i	1.66747	+	2.88815i
$413$	−3.20935e11			−0.542803
$414$		0			0
$415$	3.83694e11			0.634993
$416$	6.52471e10	+	1.13011e11i	0.106817	+	0.185013i
$417$		0			0
$418$	−4.17347e11	+	7.22867e11i	−0.668658	+	1.15815i
$419$	1.89634e11	−	3.28456e11i	0.300575	−	0.520611i	−0.675691	−	0.737185i	$-0.736155\pi$
$419$	1.89634e11	−	3.28456e11i	0.300575	−	0.520611i	0.976266	+	0.216573i	$0.0694881\pi$
$420$		0			0
$421$	−5.72178e11	−	9.91041e11i	−0.887690	−	1.53752i	−0.842599	−	0.538542i	$-0.818975\pi$
$421$	−5.72178e11	−	9.91041e11i	−0.887690	−	1.53752i	−0.0450917	−	0.998983i	$-0.514358\pi$
$422$	4.34030e11			0.666213
$423$		0			0
$424$	7.58196e11			1.13929
$425$	1.45770e11	+	2.52480e11i	0.216729	+	0.375385i
$426$		0			0
$427$	2.17117e11	−	3.76057e11i	0.316059	−	0.547430i
$428$	2.49713e11	−	4.32515e11i	0.359703	−	0.623023i
$429$		0			0
$430$	−5.55140e11	−	9.61531e11i	−0.783059	−	1.35630i
$431$	3.08594e11			0.430764			0.215382	−	0.976530i	$-0.430900\pi$
$431$	3.08594e11			0.430764			0.215382	+	0.976530i	$0.430900\pi$
$432$		0			0
$433$	−3.53112e11			−0.482744			−0.241372	−	0.970433i	$-0.577597\pi$
$433$	−3.53112e11			−0.482744			−0.241372	+	0.970433i	$0.577597\pi$
$434$	−5.02920e11	−	8.71083e11i	−0.680448	−	1.17857i
$435$		0			0
$436$	−9.65969e11	+	1.67311e12i	−1.28019	+	2.21735i
$437$	3.10181e10	−	5.37250e10i	0.0406864	−	0.0704709i
$438$		0			0
$439$	2.97352e11	+	5.15030e11i	0.382104	+	0.661823i	0.991363	−	0.131148i	$-0.0418664\pi$
$439$	2.97352e11	+	5.15030e11i	0.382104	+	0.661823i	−0.609259	+	0.792971i	$0.708533\pi$
$440$	−1.68831e12			−2.14741
$441$		0			0
$442$	−6.42893e11			−0.801195
$443$	−9.53500e10	−	1.65151e11i	−0.117626	−	0.203735i	0.801200	−	0.598396i	$-0.204195\pi$
$443$	−9.53500e10	−	1.65151e11i	−0.117626	−	0.203735i	−0.918827	+	0.394662i	$0.870862\pi$
$444$		0			0
$445$	−2.51393e11	+	4.35426e11i	−0.303902	+	0.526373i
$446$	−1.11375e12	+	1.92908e12i	−1.33285	+	2.30857i
$447$		0			0
$448$	−3.33926e11	−	5.78376e11i	−0.391650	−	0.678358i
$449$	−2.55836e11			−0.297066			−0.148533	−	0.988907i	$-0.547455\pi$
$449$	−2.55836e11			−0.297066			−0.148533	+	0.988907i	$0.547455\pi$
$450$		0			0
$451$	4.05649e11			0.461696
$452$	5.54516e11	+	9.60450e11i	0.624872	+	1.08231i
$453$		0			0
$454$	5.09329e11	−	8.82184e11i	0.562662	−	0.974559i
$455$	2.04476e11	−	3.54163e11i	0.223662	−	0.387393i
$456$		0			0
$457$	−2.02347e11	−	3.50475e11i	−0.217007	−	0.375867i	0.736885	−	0.676019i	$-0.236296\pi$
$457$	−2.02347e11	−	3.50475e11i	−0.217007	−	0.375867i	−0.953892	+	0.300152i	$0.902963\pi$
$458$	−3.21813e11			−0.341750
$459$		0			0
$460$	2.40867e11			0.250823
$461$	2.83018e11	+	4.90201e11i	0.291850	+	0.505499i	0.974247	−	0.225483i	$-0.0723959\pi$
$461$	2.83018e11	+	4.90201e11i	0.291850	+	0.505499i	−0.682397	+	0.730982i	$0.739063\pi$
$462$		0			0
$463$	2.30932e11	−	3.99986e11i	0.233544	−	0.404511i	−0.725304	−	0.688428i	$-0.758301\pi$
$463$	2.30932e11	−	3.99986e11i	0.233544	−	0.404511i	0.958849	+	0.283918i	$0.0916343\pi$
$464$	5.09672e11	−	8.82777e11i	0.510457	−	0.884138i
$465$		0			0
$466$	4.78811e11	+	8.29324e11i	0.470357	+	0.814682i
$467$	1.14378e12			1.11280			0.556398	−	0.830916i	$-0.312183\pi$
$467$	1.14378e12			1.11280			0.556398	+	0.830916i	$0.312183\pi$
$468$		0			0
$469$	−4.11710e10			−0.0392928
$470$	−2.09172e11	−	3.62297e11i	−0.197726	−	0.342472i
$471$		0			0
$472$	5.04292e11	−	8.73460e11i	0.467674	−	0.810035i
$473$	1.48630e12	−	2.57435e12i	1.36531	−	2.36479i
$474$		0			0
$475$	−1.44069e11	−	2.49535e11i	−0.129852	−	0.224911i
$476$	−1.77482e12			−1.58461
$477$		0			0
$478$	1.45653e12			1.27613
$479$	−7.19646e11	−	1.24646e12i	−0.624610	−	1.08186i	−0.988616	−	0.150460i	$-0.951924\pi$
$479$	−7.19646e11	−	1.24646e12i	−0.624610	−	1.08186i	0.364006	−	0.931397i	$-0.381409\pi$
$480$		0			0
$481$	−1.76080e11	+	3.04980e11i	−0.149989	+	0.259788i
$482$	−1.64295e12	+	2.84567e12i	−1.38647	+	2.40144i
$483$		0			0
$484$	−3.07839e12	−	5.33193e12i	−2.54988	−	4.41652i
$485$	−2.53097e11			−0.207706
$486$		0			0
$487$	3.07201e11			0.247481			0.123740	−	0.992315i	$-0.460511\pi$
$487$	3.07201e11			0.247481			0.123740	+	0.992315i	$0.460511\pi$
$488$	6.82319e11	+	1.18181e12i	0.544626	+	0.943320i
$489$		0			0
$490$	1.55887e11	−	2.70004e11i	0.122159	−	0.211586i
$491$	6.64994e11	−	1.15180e12i	0.516358	−	0.894358i	−0.483462	−	0.875365i	$-0.660621\pi$
$491$	6.64994e11	−	1.15180e12i	0.516358	−	0.894358i	0.999820	−	0.0189926i	$-0.00604588\pi$
$492$		0			0
$493$	3.60911e11	+	6.25116e11i	0.275162	+	0.476595i
$494$	6.35393e11			0.480033
$495$		0			0
$496$	1.19568e12			0.887050
$497$	8.91128e11	+	1.54348e12i	0.655143	+	1.13474i
$498$		0			0
$499$	1.35791e11	−	2.35197e11i	0.0980433	−	0.169816i	−0.812831	−	0.582499i	$-0.802075\pi$
$499$	1.35791e11	−	2.35197e11i	0.0980433	−	0.169816i	0.910875	+	0.412683i	$0.135408\pi$
$500$	1.44283e12	−	2.49906e12i	1.03241	−	1.78818i
$501$		0			0
$502$	1.67023e12	+	2.89293e12i	1.17384	+	2.03316i
$503$	−2.43504e12			−1.69610			−0.848049	−	0.529917i	$-0.822223\pi$
$503$	−2.43504e12			−1.69610			−0.848049	+	0.529917i	$0.822223\pi$
$504$		0			0
$505$	6.66519e9			0.00456039
$506$	4.76910e11	+	8.26033e11i	0.323414	+	0.560170i
$507$		0			0
$508$	−3.01942e12	+	5.22979e12i	−2.01158	+	3.48416i
$509$	−1.24976e12	+	2.16465e12i	−0.825272	+	1.42941i	0.0764398	+	0.997074i	$0.475645\pi$
$509$	−1.24976e12	+	2.16465e12i	−0.825272	+	1.42941i	−0.901711	+	0.432338i	$0.857689\pi$
$510$		0			0
$511$	1.26648e12	+	2.19361e12i	0.821686	+	1.42320i
$512$	3.13991e12			2.01931
$513$		0			0
$514$	−4.92904e12			−3.11479
$515$	7.72343e11	+	1.33774e12i	0.483813	+	0.837989i
$516$		0			0
$517$	5.60028e11	−	9.69996e11i	0.344748	−	0.597121i
$518$	−7.18968e11	+	1.24529e12i	−0.438759	+	0.759953i
$519$		0			0
$520$	6.42595e11	+	1.11301e12i	0.385409	+	0.667549i
$521$	−1.97181e11			−0.117245			−0.0586225	−	0.998280i	$-0.518671\pi$
$521$	−1.97181e11			−0.117245			−0.0586225	+	0.998280i	$0.518671\pi$
$522$		0			0
$523$	−1.84314e12			−1.07721			−0.538606	−	0.842558i	$-0.681049\pi$
$523$	−1.84314e12			−1.07721			−0.538606	+	0.842558i	$0.681049\pi$
$524$	−3.46540e12	−	6.00225e12i	−2.00800	−	3.47795i
$525$		0			0
$526$	2.14211e12	−	3.71024e12i	1.22013	−	2.11332i
$527$	−4.23345e11	+	7.33256e11i	−0.239082	+	0.414102i
$528$		0			0
$529$	8.65131e11	+	1.49845e12i	0.480321	+	0.831940i
$530$	1.15266e12			0.634543
$531$		0			0
$532$	1.75411e12			0.949412
$533$	−1.54396e11	−	2.67422e11i	−0.0828635	−	0.143524i
$534$		0			0
$535$	1.97767e11	−	3.42543e11i	0.104367	−	0.180769i
$536$	6.46927e10	−	1.12051e11i	0.0338543	−	0.0586374i
$537$		0			0
$538$	1.08814e12	+	1.88472e12i	0.559970	+	0.969897i
$539$	8.34726e11			0.425985
$540$		0			0
$541$	1.54291e12			0.774378			0.387189	−	0.922000i	$-0.373446\pi$
$541$	1.54291e12			0.774378			0.387189	+	0.922000i	$0.373446\pi$
$542$	1.45984e11	+	2.52852e11i	0.0726621	+	0.125855i
$543$		0			0
$544$	2.24262e11	−	3.88434e11i	0.109790	−	0.190161i
$545$	−7.65028e11	+	1.32507e12i	−0.371444	+	0.643359i
$546$		0			0
$547$	−5.29052e11	−	9.16345e11i	−0.252671	−	0.437639i	0.711589	−	0.702596i	$-0.247976\pi$
$547$	−5.29052e11	−	9.16345e11i	−0.252671	−	0.437639i	−0.964260	+	0.264957i	$0.914642\pi$
$548$	2.77272e12			1.31339
$549$		0			0
$550$	4.43019e12			2.06438
$551$	−3.56701e11	−	6.17824e11i	−0.164862	−	0.285550i
$552$		0			0
$553$	1.01759e12	−	1.76251e12i	0.462709	−	0.801435i
$554$	1.51135e12	−	2.61773e12i	0.681664	−	1.18068i
$555$		0			0
$556$	−2.34144e12	−	4.05550e12i	−1.03908	−	1.79973i
$557$	−3.41690e11			−0.150413			−0.0752063	−	0.997168i	$-0.523962\pi$
$557$	−3.41690e11			−0.150413			−0.0752063	+	0.997168i	$0.523962\pi$
$558$		0			0
$559$	−2.26283e12			−0.980166
$560$	9.92494e11	+	1.71905e12i	0.426464	+	0.738657i
$561$		0			0
$562$	−4.54017e11	+	7.86380e11i	−0.191981	+	0.332521i
$563$	−1.19658e12	+	2.07253e12i	−0.501941	+	0.869387i	0.498056	+	0.867145i	$0.334047\pi$
$563$	−1.19658e12	+	2.07253e12i	−0.501941	+	0.869387i	−0.999997	+	0.00224278i	$0.999286\pi$
$564$		0			0
$565$	4.39166e11	+	7.60657e11i	0.181305	+	0.314030i
$566$	7.88970e12			3.23137
$567$		0			0
$568$	−5.60099e12			−2.25786
$569$	−6.66747e11	−	1.15484e12i	−0.266659	−	0.461866i	0.701338	−	0.712829i	$-0.252586\pi$
$569$	−6.66747e11	−	1.15484e12i	−0.266659	−	0.461866i	−0.967997	+	0.250962i	$0.919253\pi$
$570$		0			0
$571$	−7.84355e11	+	1.35854e12i	−0.308781	+	0.534824i	−0.978096	−	0.208155i	$-0.933254\pi$
$571$	−7.84355e11	+	1.35854e12i	−0.308781	+	0.534824i	0.669315	+	0.742979i	$0.266588\pi$
$572$	−3.30255e12	+	5.72019e12i	−1.28993	+	2.23423i
$573$		0			0
$574$	−6.30427e11	−	1.09193e12i	−0.242399	−	0.419848i
$575$	−3.29261e11			−0.125613
$576$		0			0
$577$	−1.18747e12			−0.445996			−0.222998	−	0.974819i	$-0.571584\pi$
$577$	−1.18747e12			−0.445996			−0.222998	+	0.974819i	$0.571584\pi$
$578$	−1.25261e12	−	2.16959e12i	−0.466812	−	0.808542i
$579$		0			0
$580$	1.38496e12	−	2.39881e12i	0.508171	−	0.880178i
$581$	1.59652e12	−	2.76525e12i	0.581275	−	1.00680i
$582$		0			0
$583$	1.54304e12	+	2.67263e12i	0.553184	+	0.958142i
$584$	−7.96020e12			−2.83182
$585$		0			0
$586$	1.65147e12			0.578537
$587$	2.78979e12	+	4.83205e12i	0.969839	+	1.67981i	0.696010	+	0.718032i	$0.254957\pi$
$587$	2.78979e12	+	4.83205e12i	0.969839	+	1.67981i	0.273829	+	0.961778i	$0.411710\pi$
$588$		0			0
$589$	4.18407e11	−	7.24702e11i	0.143245	−	0.248108i
$590$	7.66662e11	−	1.32790e12i	0.260477	−	0.451160i
$591$		0			0
$592$	−8.54666e11	−	1.48033e12i	−0.285989	−	0.495347i
$593$	−3.44549e12			−1.14421			−0.572105	−	0.820181i	$-0.693873\pi$
$593$	−3.44549e12			−1.14421			−0.572105	+	0.820181i	$0.693873\pi$
$594$		0			0
$595$	−1.40562e12			−0.459771
$596$	−2.01251e12	−	3.48577e12i	−0.653325	−	1.13159i
$597$		0			0
$598$	3.63038e11	−	6.28800e11i	0.116090	−	0.201075i
$599$	9.21832e11	−	1.59666e12i	0.292571	−	0.506748i	−0.681846	−	0.731496i	$-0.738823\pi$
$599$	9.21832e11	−	1.59666e12i	0.292571	−	0.506748i	0.974417	+	0.224748i	$0.0721559\pi$
$600$		0			0
$601$	−2.52084e12	−	4.36622e12i	−0.788152	−	1.36512i	−0.927098	−	0.374819i	$-0.877705\pi$
$601$	−2.52084e12	−	4.36622e12i	−0.788152	−	1.36512i	0.138946	−	0.990300i	$-0.455628\pi$
$602$	−9.23956e12			−2.86726
$603$		0			0
$604$	9.84554e12			3.01005
$605$	−2.43802e12	−	4.22278e12i	−0.739842	−	1.28144i
$606$		0			0
$607$	−4.91499e11	+	8.51302e11i	−0.146951	+	0.254527i	−0.930099	−	0.367308i	$-0.880279\pi$
$607$	−4.91499e11	+	8.51302e11i	−0.146951	+	0.254527i	0.783148	+	0.621836i	$0.213613\pi$
$608$	−2.21646e11	+	3.83902e11i	−0.0657800	+	0.113934i
$609$		0			0
$610$	1.03731e12	+	1.79668e12i	0.303337	+	0.525394i
$611$	−8.52618e11			−0.247497
$612$		0			0
$613$	−5.27728e12			−1.50952			−0.754758	−	0.656003i	$-0.772246\pi$
$613$	−5.27728e12			−1.50952			−0.754758	+	0.656003i	$0.772246\pi$
$614$	2.88324e11	+	4.99391e11i	0.0818696	+	0.141802i
$615$		0			0
$616$	−7.02491e12	+	1.21675e13i	−1.96575	+	3.40477i
$617$	2.50229e12	−	4.33409e12i	0.695111	−	1.20397i	−0.275032	−	0.961435i	$-0.588688\pi$
$617$	2.50229e12	−	4.33409e12i	0.695111	−	1.20397i	0.970143	−	0.242533i	$-0.0779783\pi$
$618$		0			0
$619$	−2.62154e12	−	4.54063e12i	−0.717708	−	1.24311i	−0.961906	−	0.273382i	$-0.911858\pi$
$619$	−2.62154e12	−	4.54063e12i	−0.717708	−	1.24311i	0.244197	−	0.969726i	$-0.421476\pi$
$620$	3.24908e12			0.883076
$621$		0			0
$622$	−1.17738e12			−0.315400
$623$	2.09205e12	+	3.62354e12i	0.556386	+	0.963688i
$624$		0			0
$625$	−6.49748e10	+	1.12540e11i	−0.0170328	+	0.0295016i
$626$	−1.84254e12	+	3.19137e12i	−0.479548	+	0.830601i
$627$		0			0
$628$	1.86101e12	+	3.22337e12i	0.477453	+	0.826974i
$629$	1.21042e12			0.308324
$630$		0			0
$631$	4.84088e12			1.21560			0.607802	−	0.794089i	$-0.292052\pi$
$631$	4.84088e12			1.21560			0.607802	+	0.794089i	$0.292052\pi$
$632$	3.19790e12	+	5.53893e12i	0.797331	+	1.38102i
$633$		0			0
$634$	2.71847e12	−	4.70853e12i	0.668225	−	1.15740i
$635$	−2.39132e12	+	4.14189e12i	−0.583655	+	1.01092i
$636$		0			0
$637$	−3.17709e11	−	5.50287e11i	−0.0764542	−	0.132423i
$638$	1.09687e13			2.62097
$639$		0			0
$640$	4.01530e12			0.946037
$641$	1.22108e12	+	2.11497e12i	0.285682	+	0.494816i	0.972774	−	0.231754i	$-0.0744466\pi$
$641$	1.22108e12	+	2.11497e12i	0.285682	+	0.494816i	−0.687092	+	0.726570i	$0.741113\pi$
$642$		0			0
$643$	−2.79975e12	+	4.84930e12i	−0.645906	+	1.11874i	0.338185	+	0.941080i	$0.390187\pi$
$643$	−2.79975e12	+	4.84930e12i	−0.645906	+	1.11874i	−0.984091	+	0.177663i	$0.943146\pi$
$644$	1.00223e12	−	1.73591e12i	0.229604	−	0.397686i
$645$		0			0
$646$	−1.09196e12	−	1.89133e12i	−0.246695	−	0.427289i
$647$	7.09599e12			1.59200			0.796002	−	0.605295i	$-0.206945\pi$
$647$	7.09599e12			1.59200			0.796002	+	0.605295i	$0.206945\pi$
$648$		0			0
$649$	4.10524e12			0.908317
$650$	−1.68619e12	−	2.92057e12i	−0.370507	−	0.641738i
$651$		0			0
$652$	3.39190e12	−	5.87495e12i	0.735071	−	1.27318i
$653$	−9.88559e10	+	1.71223e11i	−0.0212762	+	0.0368514i	−0.876467	−	0.481461i	$-0.840106\pi$
$653$	−9.88559e10	+	1.71223e11i	−0.0212762	+	0.0368514i	0.855191	+	0.518313i	$0.173440\pi$
$654$		0			0
$655$	−2.74453e12	−	4.75366e12i	−0.582615	−	1.00912i
$656$	1.49883e12			0.315998
$657$		0			0
$658$	−3.48139e12			−0.723997
$659$	−2.47784e12	−	4.29174e12i	−0.511786	−	0.886440i	−0.999907	−	0.0136635i	$-0.995651\pi$
$659$	−2.47784e12	−	4.29174e12i	−0.511786	−	0.886440i	0.488120	−	0.872776i	$-0.337683\pi$
$660$		0			0
$661$	1.81202e12	−	3.13852e12i	0.369196	−	0.639467i	−0.620244	−	0.784409i	$-0.712966\pi$
$661$	1.81202e12	−	3.13852e12i	0.369196	−	0.639467i	0.989440	+	0.144942i	$0.0462997\pi$
$662$	6.23434e12	−	1.07982e13i	1.26162	−	2.18520i
$663$		0			0
$664$	5.01728e12	+	8.69019e12i	1.00164	+	1.73489i
$665$	1.38922e12			0.275470
$666$		0			0
$667$	−8.15216e11			−0.159480
$668$	3.64160e12	+	6.30743e12i	0.707616	+	1.22563i
$669$		0			0
$670$	9.83506e10	−	1.70348e11i	0.0188556	−	0.0326589i
$671$	−2.77724e12	+	4.81033e12i	−0.528887	+	0.916059i
$672$		0			0
$673$	1.66766e12	+	2.88846e12i	0.313356	+	0.542749i	0.979087	−	0.203443i	$-0.0652132\pi$
$673$	1.66766e12	+	2.88846e12i	0.313356	+	0.542749i	−0.665730	+	0.746192i	$0.731880\pi$
$674$	−1.14942e13			−2.14541
$675$		0			0
$676$	−6.30581e12			−1.16140
$677$	−2.09334e12	−	3.62577e12i	−0.382993	−	0.663363i	0.608496	−	0.793557i	$-0.291773\pi$
$677$	−2.09334e12	−	3.62577e12i	−0.382993	−	0.663363i	−0.991489	+	0.130194i	$0.958440\pi$
$678$		0			0
$679$	−1.05311e12	+	1.82405e12i	−0.190135	+	0.329323i
$680$	2.20868e12	−	3.82554e12i	0.396134	−	0.686124i
$681$		0			0
$682$	6.43309e12	+	1.11424e13i	1.13865	+	1.97220i
$683$	−3.28484e12			−0.577591			−0.288796	−	0.957391i	$-0.593255\pi$
$683$	−3.28484e12			−0.577591			−0.288796	+	0.957391i	$0.593255\pi$
$684$		0			0
$685$	2.19594e12			0.381077
$686$	4.35348e12	+	7.54045e12i	0.750548	+	1.29999i
$687$		0			0
$688$	5.49172e12	−	9.51193e12i	0.934459	−	1.61853i
$689$	1.17461e12	−	2.03448e12i	0.198567	−	0.343928i
$690$		0			0
$691$	1.34766e12	+	2.33422e12i	0.224869	+	0.389485i	0.956280	−	0.292452i	$-0.0944712\pi$
$691$	1.34766e12	+	2.33422e12i	0.224869	+	0.389485i	−0.731411	+	0.681937i	$0.761138\pi$
$692$	−1.05848e13			−1.75471
$693$		0			0
$694$	−8.94018e12			−1.46295
$695$	−1.85438e12	−	3.21187e12i	−0.301485	−	0.522188i
$696$		0			0
$697$	−5.30677e11	+	9.19160e11i	−0.0851693	+	0.147518i
$698$	−1.74923e12	+	3.02975e12i	−0.278931	+	0.483123i
$699$		0			0
$700$	−4.65502e12	−	8.06273e12i	−0.732792	−	1.26923i
$701$	−8.26238e12			−1.29233			−0.646166	−	0.763197i	$-0.723628\pi$
$701$	−8.26238e12			−1.29233			−0.646166	+	0.763197i	$0.723628\pi$
$702$		0			0
$703$	−1.19630e12			−0.184732
$704$	4.27140e12	+	7.39829e12i	0.655381	+	1.13515i
$705$		0			0
$706$	−7.59600e12	+	1.31567e13i	−1.15070	+	1.99308i
$707$	2.77333e10	−	4.80355e10i	0.00417459	−	0.00723061i
$708$		0			0
$709$	3.94697e12	+	6.83635e12i	0.586619	+	1.01605i	0.994672	+	0.103095i	$0.0328745\pi$
$709$	3.94697e12	+	6.83635e12i	0.586619	+	1.01605i	−0.408053	+	0.912958i	$0.633792\pi$
$710$	−8.51503e12			−1.25754
$711$		0			0
$712$	−1.31491e13			−1.91751
$713$	−4.78121e11	−	8.28130e11i	−0.0692843	−	0.120004i
$714$		0			0
$715$	−2.61555e12	+	4.53027e12i	−0.374271	+	0.648257i
$716$	7.19708e11	−	1.24657e12i	0.102340	−	0.177259i
$717$		0			0
$718$	−9.50931e12	−	1.64706e13i	−1.33533	−	2.31286i
$719$	9.37950e12			1.30888			0.654440	−	0.756114i	$-0.272904\pi$
$719$	9.37950e12			1.30888			0.654440	+	0.756114i	$0.272904\pi$
$720$		0			0
$721$	1.28546e13			1.77154
$722$	−5.33564e12	−	9.24159e12i	−0.730750	−	1.26570i
$723$		0			0
$724$	8.20706e12	−	1.42150e13i	1.11010	−	1.92276i
$725$	−1.89321e12	+	3.27913e12i	−0.254494	+	0.440796i
$726$		0			0
$727$	−1.89555e11	−	3.28319e11i	−0.0251670	−	0.0435905i	0.853168	−	0.521637i	$-0.174678\pi$
$727$	−1.89555e11	−	3.28319e11i	−0.0251670	−	0.0435905i	−0.878335	+	0.478046i	$0.841345\pi$
$728$	1.06951e13			1.41122
$729$		0			0
$730$	−1.21017e13			−1.57722
$731$	3.88882e12	+	6.73563e12i	0.503720	+	0.872469i
$732$		0			0
$733$	4.04935e12	−	7.01368e12i	0.518104	−	0.897383i	−0.481674	−	0.876350i	$-0.659971\pi$
$733$	4.04935e12	−	7.01368e12i	0.518104	−	0.897383i	0.999779	−	0.0210328i	$-0.00669544\pi$
$734$	4.50304e12	−	7.79949e12i	0.572629	−	0.991822i
$735$		0			0
$736$	2.53279e11	+	4.38692e11i	0.0318163	+	0.0551074i
$737$	5.26638e11			0.0657519
$738$		0			0
$739$	5.44252e12			0.671274			0.335637	−	0.941991i	$-0.391048\pi$
$739$	5.44252e12			0.671274			0.335637	+	0.941991i	$0.391048\pi$
$740$	−2.32243e12	−	4.02256e12i	−0.284708	−	0.493128i
$741$		0			0
$742$	4.79614e12	−	8.30715e12i	0.580863	−	1.00608i
$743$	−5.15614e12	+	8.93070e12i	−0.620691	+	1.07507i	0.368667	+	0.929562i	$0.379814\pi$
$743$	−5.15614e12	+	8.93070e12i	−0.620691	+	1.07507i	−0.989357	+	0.145506i	$0.953519\pi$
$744$		0			0
$745$	−1.59387e12	−	2.76066e12i	−0.189561	−	0.328329i
$746$	−1.89713e13			−2.24271
$747$		0			0
$748$	2.27025e13			2.65165
$749$	−1.64579e12	−	2.85059e12i	−0.191076	−	0.330953i
$750$		0			0
$751$	1.31578e12	−	2.27900e12i	0.150940	−	0.261435i	−0.780633	−	0.624989i	$-0.785103\pi$
$751$	1.31578e12	−	2.27900e12i	0.150940	−	0.261435i	0.931573	+	0.363554i	$0.118437\pi$
$752$	2.06924e12	−	3.58402e12i	0.235955	−	0.408686i
$753$		0			0
$754$	−4.17484e12	−	7.23104e12i	−0.470402	−	0.814760i
$755$	7.79747e12			0.873359
$756$		0			0
$757$	−4.56786e12			−0.505570			−0.252785	−	0.967523i	$-0.581346\pi$
$757$	−4.56786e12			−0.505570			−0.252785	+	0.967523i	$0.581346\pi$
$758$	−1.13226e12	−	1.96114e12i	−0.124577	−	0.215773i
$759$		0			0
$760$	−2.18291e12	+	3.78091e12i	−0.237342	+	0.411089i
$761$	2.74282e12	−	4.75071e12i	0.296461	−	0.513485i	−0.678863	−	0.734265i	$-0.737527\pi$
$761$	2.74282e12	−	4.75071e12i	0.296461	−	0.513485i	0.975324	+	0.220780i	$0.0708604\pi$
$762$		0			0
$763$	6.36643e12	+	1.10270e13i	0.680042	+	1.17787i
$764$	2.97788e13			3.16219
$765$		0			0
$766$	−8.89830e11			−0.0933851
$767$	−1.56251e12	−	2.70635e12i	−0.163021	−	0.282361i
$768$		0			0
$769$	−4.54800e12	+	7.87737e12i	−0.468977	+	0.812293i	−0.999371	−	0.0354588i	$-0.988711\pi$
$769$	−4.54800e12	+	7.87737e12i	−0.468977	+	0.812293i	0.530394	+	0.847751i	$0.322044\pi$
$770$	−1.06798e13	+	1.84979e13i	−1.09485	+	1.89633i
$771$		0			0
$772$	7.89571e12	+	1.36758e13i	0.800043	+	1.38572i
$773$	4.56540e12			0.459908			0.229954	−	0.973202i	$-0.426142\pi$
$773$	4.56540e12			0.459908			0.229954	+	0.973202i	$0.426142\pi$
$774$		0			0
$775$	−4.44143e12			−0.442248
$776$	−3.30955e12	−	5.73232e12i	−0.327636	−	0.567483i
$777$		0			0
$778$	−8.40320e12	+	1.45548e13i	−0.822312	+	1.42429i
$779$	5.24487e11	−	9.08438e11i	0.0510289	−	0.0883846i
$780$		0			0
$781$	−1.13988e13	−	1.97434e13i	−1.09630	−	1.89886i
$782$	−2.49561e12			−0.238642
$783$		0			0
$784$	3.08421e12			0.291556
$785$	1.47389e12	+	2.55284e12i	0.138532	+	0.239944i
$786$		0			0
$787$	−1.46658e12	+	2.54020e12i	−0.136276	+	0.236037i	−0.926084	−	0.377317i	$-0.876847\pi$
$787$	−1.46658e12	+	2.54020e12i	−0.136276	+	0.236037i	0.789808	+	0.613354i	$0.210180\pi$
$788$	−1.11675e13	+	1.93426e13i	−1.03178	+	1.78709i
$789$		0			0
$790$	4.86169e12	+	8.42069e12i	0.444084	+	0.769176i
$791$	7.30932e12			0.663870
$792$		0			0
$793$	4.22824e12			0.379691
$794$	1.02471e13	+	1.77485e13i	0.914973	+	1.58478i
$795$		0			0
$796$	−1.48155e13	+	2.56611e13i	−1.30800	+	2.26551i
$797$	8.53371e12	−	1.47808e13i	0.749162	−	1.29759i	−0.199063	−	0.979987i	$-0.563790\pi$
$797$	8.53371e12	−	1.47808e13i	0.749162	−	1.29759i	0.948225	−	0.317600i	$-0.102877\pi$
$798$		0			0
$799$	1.46528e12	+	2.53793e12i	0.127192	+	0.220302i
$800$	2.35280e12			0.203086
$801$		0			0
$802$	2.55117e11			0.0217748
$803$	−1.62002e13	−	2.80596e13i	−1.37499	−	2.38156i
$804$		0			0
$805$	7.93744e11	−	1.37481e12i	0.0666192	−	0.115388i
$806$	4.89705e12	−	8.48195e12i	0.408721	−	0.707926i
$807$		0			0
$808$	8.71557e10	+	1.50958e11i	0.00719358	+	0.0124596i
$809$	−1.70485e13			−1.39932			−0.699662	−	0.714474i	$-0.746666\pi$
$809$	−1.70485e13			−1.39932			−0.699662	+	0.714474i	$0.746666\pi$
$810$		0			0
$811$	1.00699e13			0.817390			0.408695	−	0.912671i	$-0.365984\pi$
$811$	1.00699e13			0.817390			0.408695	+	0.912671i	$0.365984\pi$
$812$	−1.15254e13	−	1.99625e13i	−0.930363	−	1.61144i
$813$		0			0
$814$	9.19667e12	−	1.59291e13i	0.734211	−	1.27169i
$815$	2.68632e12	−	4.65284e12i	0.213279	−	0.369410i
$816$		0			0
$817$	−3.84345e12	−	6.65706e12i	−0.301802	−	0.522737i
$818$	1.38553e13			1.08200
$819$		0			0
$820$	4.07283e12			0.314582
$821$	6.38604e12	+	1.10610e13i	0.490555	+	0.849666i	0.999941	−	0.0108721i	$-0.00346076\pi$
$821$	6.38604e12	+	1.10610e13i	0.490555	+	0.849666i	−0.509386	+	0.860538i	$0.670127\pi$
$822$		0			0
$823$	−4.34146e12	+	7.51964e12i	−0.329865	+	0.571344i	−0.982485	−	0.186342i	$-0.940337\pi$
$823$	−4.34146e12	+	7.51964e12i	−0.329865	+	0.571344i	0.652619	+	0.757686i	$0.273670\pi$
$824$	−2.01987e13	+	3.49852e13i	−1.52634	+	2.64370i
$825$		0			0
$826$	−6.38003e12	−	1.10505e13i	−0.476883	−	0.825986i
$827$	1.72868e13			1.28511			0.642554	−	0.766240i	$-0.277875\pi$
$827$	1.72868e13			1.28511			0.642554	+	0.766240i	$0.277875\pi$
$828$		0			0
$829$	1.88685e12			0.138753			0.0693763	−	0.997591i	$-0.477899\pi$
$829$	1.88685e12			0.138753			0.0693763	+	0.997591i	$0.477899\pi$
$830$	7.62764e12	+	1.32115e13i	0.557877	+	0.966271i
$831$		0			0
$832$	3.25152e12	−	5.63179e12i	0.235251	−	0.407466i
$833$	−1.09200e12	+	1.89140e12i	−0.0785817	+	0.136107i
$834$		0			0
$835$	2.88407e12	+	4.99536e12i	0.205313	+	0.355613i
$836$	−2.24377e13			−1.58873
$837$		0			0
$838$	1.50793e13			1.05629
$839$	4.82969e12	+	8.36527e12i	0.336504	+	0.582843i	0.983773	−	0.179420i	$-0.0574220\pi$
$839$	4.82969e12	+	8.36527e12i	0.336504	+	0.582843i	−0.647268	+	0.762262i	$0.724089\pi$
$840$		0			0
$841$	2.56618e12	−	4.44476e12i	0.176891	−	0.306384i
$842$	2.27492e13	−	3.94027e13i	1.55977	−	2.70161i
$843$		0			0
$844$	5.83364e12	+	1.01042e13i	0.395730	+	0.685424i
$845$	−4.99408e12			−0.336977
$846$		0			0
$847$	−4.05776e13			−2.70902
$848$	5.70136e12	+	9.87504e12i	0.378614	+	0.655779i
$849$		0			0
$850$	−5.79564e12	+	1.00384e13i	−0.380817	+	0.659595i
$851$	−6.83517e11	+	1.18389e12i	−0.0446751	+	0.0773796i
$852$		0			0
$853$	−6.32883e12	−	1.09619e13i	−0.409311	−	0.708947i	0.585502	−	0.810671i	$-0.300897\pi$
$853$	−6.32883e12	−	1.09619e13i	−0.409311	−	0.708947i	−0.994813	+	0.101724i	$0.967564\pi$
$854$	1.72647e13			1.11070
$855$		0			0
$856$	1.03442e13			0.658515
$857$	8.15121e12	+	1.41183e13i	0.516189	+	0.894065i	0.999823	+	0.0187949i	$0.00598294\pi$
$857$	8.15121e12	+	1.41183e13i	0.516189	+	0.894065i	−0.483635	+	0.875270i	$0.660684\pi$
$858$		0			0
$859$	1.32805e13	−	2.30024e13i	0.832231	−	1.44147i	−0.0640344	−	0.997948i	$-0.520397\pi$
$859$	1.32805e13	−	2.30024e13i	0.832231	−	1.44147i	0.896265	−	0.443518i	$-0.146270\pi$
$860$	1.49229e13	−	2.58472e13i	0.930273	−	1.61128i
$861$		0			0
$862$	6.13468e12	+	1.06256e13i	0.378450	+	0.655495i
$863$	−1.50602e13			−0.924234			−0.462117	−	0.886819i	$-0.652910\pi$
$863$	−1.50602e13			−0.924234			−0.462117	+	0.886819i	$0.652910\pi$
$864$		0			0
$865$	−8.38295e12			−0.509125
$866$	−7.01968e12	−	1.21584e13i	−0.424118	−	0.734594i
$867$		0			0
$868$	1.35192e13	−	2.34159e13i	0.808371	−	1.40014i
$869$	−1.30164e13	+	2.25451e13i	−0.774289	+	1.34111i
$870$		0			0
$871$	−2.00446e11	−	3.47182e11i	−0.0118009	−	0.0204398i
$872$	−4.00148e13			−2.34367
$873$		0			0
$874$	2.46650e12			0.142981
$875$	−9.50930e12	−	1.64706e13i	−0.548419	−	0.949889i
$876$		0			0
$877$	1.33232e13	−	2.30765e13i	0.760520	−	1.31726i	−0.182064	−	0.983287i	$-0.558278\pi$
$877$	1.33232e13	−	2.30765e13i	0.760520	−	1.31726i	0.942583	−	0.333972i	$-0.108389\pi$
$878$	−1.18224e13	+	2.04770e13i	−0.671399	+	1.16290i
$879$		0			0
$880$	−1.26955e13	−	2.19892e13i	−0.713636	−	1.23605i
$881$	3.46233e13			1.93632			0.968159	−	0.250336i	$-0.0805412\pi$
$881$	3.46233e13			1.93632			0.968159	+	0.250336i	$0.0805412\pi$
$882$		0			0
$883$	5.22763e12			0.289389			0.144694	−	0.989476i	$-0.453780\pi$
$883$	5.22763e12			0.289389			0.144694	+	0.989476i	$0.453780\pi$
$884$	−8.64091e12	−	1.49665e13i	−0.475909	−	0.824299i
$885$		0			0
$886$	3.79102e12	−	6.56623e12i	0.206683	−	0.357985i
$887$	−1.70993e13	+	2.96169e13i	−0.927518	+	1.60651i	−0.140057	+	0.990143i	$0.544729\pi$
$887$	−1.70993e13	+	2.96169e13i	−0.927518	+	1.60651i	−0.787461	+	0.616365i	$0.788605\pi$
$888$		0			0
$889$	1.99002e13	+	3.44681e13i	1.06856	+	1.85080i
$890$	−1.99902e13			−1.06798
$891$		0			0
$892$	−5.98784e13			−3.16686
$893$	−1.44818e12	−	2.50833e12i	−0.0762064	−	0.131993i
$894$		0			0
$895$	5.69994e11	−	9.87259e11i	0.0296939	−	0.0514313i
$896$	1.67073e13	−	2.89379e13i	0.866006	−	1.49997i
$897$		0			0
$898$	−5.08589e12	−	8.80901e12i	−0.260990	−	0.452047i
$899$	−1.09965e13			−0.561484
$900$		0			0
$901$	−8.07454e12			−0.408184
$902$	8.06409e12	+	1.39674e13i	0.405626	+	0.702565i
$903$		0			0
$904$	−1.14853e13	+	1.98931e13i	−0.571984	+	0.990705i
$905$	6.49982e12	−	1.12580e13i	0.322094	−	0.557884i
$906$		0			0
$907$	3.67941e12	+	6.37292e12i	0.180528	+	0.312684i	0.942061	−	0.335443i	$-0.108886\pi$
$907$	3.67941e12	+	6.37292e12i	0.180528	+	0.312684i	−0.761532	+	0.648127i	$0.775553\pi$
$908$	2.73829e13			1.33688
$909$		0			0
$910$	1.62595e13			0.785998
$911$	−6.52165e12	−	1.12958e13i	−0.313708	−	0.543358i	0.665454	−	0.746439i	$-0.268238\pi$
$911$	−6.52165e12	−	1.12958e13i	−0.313708	−	0.543358i	−0.979162	+	0.203081i	$0.934905\pi$
$912$		0			0
$913$	−2.04218e13	+	3.53717e13i	−0.972694	+	1.68476i
$914$	8.04509e12	−	1.39345e13i	0.381306	−	0.660441i
$915$		0			0
$916$	−4.32538e12	−	7.49178e12i	−0.202999	−	0.351605i
$917$	−4.56790e13			−2.13331
$918$		0			0
$919$	−6.75575e12			−0.312431			−0.156215	−	0.987723i	$-0.549929\pi$
$919$	−6.75575e12			−0.312431			−0.156215	+	0.987723i	$0.549929\pi$
$920$	2.49445e12	+	4.32052e12i	0.114797	+	0.198834i
$921$		0			0
$922$	−1.12525e13	+	1.94899e13i	−0.512813	+	0.888219i
$923$	−8.67713e12	+	1.50292e13i	−0.393521	+	0.681599i
$924$		0			0
$925$	3.17471e12	+	5.49876e12i	0.142583	+	0.246960i
$926$	1.83632e13			0.820727
$927$		0			0
$928$	5.82529e12			0.257841
$929$	8.69637e12	+	1.50625e13i	0.383060	+	0.663480i	0.991498	−	0.130122i	$-0.0415368\pi$
$929$	8.69637e12	+	1.50625e13i	0.383060	+	0.663480i	−0.608438	+	0.793602i	$0.708204\pi$
$930$		0			0
$931$	1.07926e12	−	1.86934e12i	0.0470819	−	0.0815483i
$932$	−1.28711e13	+	2.22933e13i	−0.558783	+	0.967840i
$933$		0			0
$934$	2.27377e13	+	3.93828e13i	0.977654	+	1.69335i
$935$	1.79799e13			0.769372
$936$		0			0
$937$	−6.24202e12			−0.264544			−0.132272	−	0.991213i	$-0.542227\pi$
$937$	−6.24202e12			−0.264544			−0.132272	+	0.991213i	$0.542227\pi$
$938$	−8.18457e11	−	1.41761e12i	−0.0345210	−	0.0597921i
$939$		0			0
$940$	5.62283e12	−	9.73903e12i	0.234898	−	0.406856i
$941$	3.56277e12	−	6.17090e12i	0.148127	−	0.256564i	−0.782408	−	0.622766i	$-0.786009\pi$
$941$	3.56277e12	−	6.17090e12i	0.148127	−	0.256564i	0.930535	+	0.366202i	$0.119342\pi$
$942$		0			0
$943$	−5.99341e11	−	1.03809e12i	−0.0246815	−	0.0427496i
$944$	1.51684e13			0.621678
$945$		0			0
$946$	1.18188e14			4.79802
$947$	9.20632e12	+	1.59458e13i	0.371973	+	0.644276i	0.989869	−	0.141984i	$-0.0453481\pi$
$947$	9.20632e12	+	1.59458e13i	0.371973	+	0.644276i	−0.617896	+	0.786260i	$0.712015\pi$
$948$		0			0
$949$	−1.23321e13	+	2.13598e13i	−0.493558	+	0.854867i
$950$	5.72804e12	−	9.92125e12i	0.228165	−	0.395194i
$951$		0			0
$952$	−1.83802e13	−	3.18355e13i	−0.725244	−	1.25616i
$953$	−8.34892e12			−0.327878			−0.163939	−	0.986470i	$-0.552420\pi$
$953$	−8.34892e12			−0.327878			−0.163939	+	0.986470i	$0.552420\pi$
$954$		0			0
$955$	2.35842e13			0.917501
$956$	1.95768e13	+	3.39079e13i	0.758019	+	1.31293i
$957$		0			0
$958$	2.86124e13	−	4.95581e13i	1.09751	−	1.90095i
$959$	9.13711e12	−	1.58259e13i	0.348839	−	0.604207i
$960$		0			0
$961$	6.77038e12	+	1.17266e13i	0.256070	+	0.443526i
$962$	−1.40015e13			−0.527094
$963$		0			0
$964$	−8.83291e13			−3.29426
$965$	6.25325e12	+	1.08309e13i	0.232131	+	0.402062i
$966$		0			0
$967$	1.50380e13	−	2.60466e13i	0.553059	−	0.957927i	−0.444992	−	0.895534i	$-0.646794\pi$
$967$	1.50380e13	−	2.60466e13i	0.553059	−	0.957927i	0.998052	−	0.0623927i	$-0.0198731\pi$
$968$	6.37605e13	−	1.10436e14i	2.33406	−	4.04271i
$969$		0			0
$970$	−5.03143e12	−	8.71469e12i	−0.182481	−	0.316067i
$971$	4.68313e12			0.169064			0.0845318	−	0.996421i	$-0.473061\pi$
$971$	4.68313e12			0.169064			0.0845318	+	0.996421i	$0.473061\pi$
$972$		0			0
$973$	−3.08636e13			−1.10392
$974$	6.10699e12	+	1.05776e13i	0.217426	+	0.376593i
$975$		0			0
$976$	−1.02616e13	+	1.77736e13i	−0.361985	+	0.626976i
$977$	7.81803e12	−	1.35412e13i	0.274519	−	0.475480i	−0.695495	−	0.718531i	$-0.744815\pi$
$977$	7.81803e12	−	1.35412e13i	0.274519	−	0.475480i	0.970014	+	0.243051i	$0.0781482\pi$
$978$		0			0
$979$	−2.67604e13	−	4.63504e13i	−0.931045	−	1.61262i
$980$	8.38088e12			0.290250
$981$		0			0
$982$	5.28789e13			1.81460
$983$	−2.31834e12	−	4.01548e12i	−0.0791929	−	0.137166i	0.823709	−	0.567013i	$-0.191901\pi$
$983$	−2.31834e12	−	4.01548e12i	−0.0791929	−	0.137166i	−0.902902	+	0.429847i	$0.858568\pi$
$984$		0			0
$985$	−8.84440e12	+	1.53189e13i	−0.299368	+	0.518520i
$986$	−1.43494e13	+	2.48539e13i	−0.483491	+	0.837431i
$987$		0			0
$988$	8.54011e12	+	1.47919e13i	0.285139	+	0.493876i
$989$	−8.78397e12			−0.291949
$990$		0			0
$991$	2.04024e13			0.671970			0.335985	−	0.941867i	$-0.390931\pi$
$991$	2.04024e13			0.671970			0.335985	+	0.941867i	$0.390931\pi$
$992$	3.41651e12	+	5.91756e12i	0.112016	+	0.194017i
$993$		0			0
$994$	−3.54303e13	+	6.13671e13i	−1.15116	+	1.99387i
$995$	−1.17335e13	+	2.03231e13i	−0.379512	+	0.657334i
$996$		0			0
$997$	1.05858e13	+	1.83351e13i	0.339308	+	0.587699i	0.984303	−	0.176488i	$-0.0564738\pi$
$997$	1.05858e13	+	1.83351e13i	0.339308	+	0.587699i	−0.644995	+	0.764187i	$0.723140\pi$
$998$	1.07978e13			0.344547
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.c.a.10.8		16
3.2	odd	2		9.10.c.a.4.1	✓	16
9.2	odd	6		9.10.c.a.7.1	yes	16
9.4	even	3		81.10.a.d.1.1		8
9.5	odd	6		81.10.a.c.1.8		8
9.7	even	3	inner	27.10.c.a.19.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.1	✓	16	3.2	odd	2
9.10.c.a.7.1	yes	16	9.2	odd	6
27.10.c.a.10.8		16	1.1	even	1	trivial
27.10.c.a.19.8		16	9.7	even	3	inner
81.10.a.c.1.8		8	9.5	odd	6
81.10.a.d.1.1		8	9.4	even	3

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(19.8795 + 34.4322i) q^{2} +(-534.387 + 925.585i) q^{4} +(-423.223 + 733.045i) q^{5} +(3521.99 + 6100.27i) q^{7} -22136.7 q^{8} +O(q^{10})\)	\(q+(19.8795 + 34.4322i) q^{2} +(-534.387 + 925.585i) q^{4} +(-423.223 + 733.045i) q^{5} +(3521.99 + 6100.27i) q^{7} -22136.7 q^{8} -33653.8 q^{10} +(-45051.5 - 78031.5i) q^{11} +(-34294.5 + 59399.8i) q^{13} +(-140031. + 242540. i) q^{14} +(-166460. - 288317. i) q^{16} +235749. q^{17} -232999. q^{19} +(-452330. - 783458. i) q^{20} +(1.79120e6 - 3.10245e6i) q^{22} +(-133126. + 230581. i) q^{23} +(618326. + 1.07097e6i) q^{25} -2.72703e6 q^{26} -7.52842e6 q^{28} +(1.53091e6 + 2.65162e6i) q^{29} +(-1.79575e6 + 3.11033e6i) q^{31} +(951277. - 1.64766e6i) q^{32} +(4.68656e6 + 8.11736e6i) q^{34} -5.96236e6 q^{35} +5.13436e6 q^{37} +(-4.63189e6 - 8.02267e6i) q^{38} +(9.36877e6 - 1.62272e7i) q^{40} +(-2.25103e6 + 3.89890e6i) q^{41} +(1.64956e7 + 2.85712e7i) q^{43} +9.62997e7 q^{44} -1.05859e7 q^{46} +(6.21541e6 + 1.07654e7i) q^{47} +(-4.63206e6 + 8.02297e6i) q^{49} +(-2.45840e7 + 4.25807e7i) q^{50} +(-3.66530e7 - 6.34849e7i) q^{52} -3.42506e7 q^{53} +7.62674e7 q^{55} +(-7.79653e7 - 1.35040e8i) q^{56} +(-6.08675e7 + 1.05426e8i) q^{58} +(-2.27808e7 + 3.94575e7i) q^{59} +(-3.08230e7 - 5.33870e7i) q^{61} -1.42794e8 q^{62} -9.48116e7 q^{64} +(-2.90285e7 - 5.02788e7i) q^{65} +(-2.92242e6 + 5.06178e6i) q^{67} +(-1.25981e8 + 2.18205e8i) q^{68} +(-1.18529e8 - 2.05297e8i) q^{70} +2.53018e8 q^{71} +3.59593e8 q^{73} +(1.02068e8 + 1.76788e8i) q^{74} +(1.24511e8 - 2.15660e8i) q^{76} +(3.17342e8 - 5.49653e8i) q^{77} +(-1.44462e8 - 2.50215e8i) q^{79} +2.81799e8 q^{80} -1.78997e8 q^{82} +(-2.26650e8 - 3.92569e8i) q^{83} +(-9.97744e7 + 1.72814e8i) q^{85} +(-6.55848e8 + 1.13596e9i) q^{86} +(9.97292e8 + 1.72736e9i) q^{88} +5.93996e8 q^{89} -4.83140e8 q^{91} +(-1.42281e8 - 2.46438e8i) q^{92} +(-2.47118e8 + 4.28021e8i) q^{94} +(9.86105e7 - 1.70798e8i) q^{95} +(1.49505e8 + 2.58951e8i) q^{97} -3.68332e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22} - 1064559 q^{23} - 2293229 q^{25} - 2436312 q^{26} + 1225724 q^{28} + 1309053 q^{29} - 2359819 q^{31} - 5760063 q^{32} + 981801 q^{34} + 31066554 q^{35} + 16391516 q^{37} - 39490203 q^{38} - 16760496 q^{40} - 54747318 q^{41} + 15249608 q^{43} + 332509926 q^{44} + 2390520 q^{46} - 156295545 q^{47} + 15239583 q^{49} - 315590163 q^{50} - 19773358 q^{52} + 525516228 q^{53} - 7579770 q^{55} - 470339790 q^{56} + 55408560 q^{58} - 307774074 q^{59} + 69192125 q^{61} + 914436924 q^{62} - 403588478 q^{64} - 482470359 q^{65} + 14328044 q^{67} - 915409575 q^{68} - 229271934 q^{70} + 1239601392 q^{71} + 598613198 q^{73} - 1022736000 q^{74} + 119954093 q^{76} - 717995541 q^{77} + 30257531 q^{79} + 2927826528 q^{80} - 202376022 q^{82} - 1176168291 q^{83} + 4818366 q^{85} - 1426944009 q^{86} + 911312427 q^{88} + 3317041296 q^{89} - 739230122 q^{91} + 76813998 q^{92} - 1954316784 q^{94} + 391400652 q^{95} - 267311278 q^{97} - 4827300318 q^{98}+O(q^{100}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

Introduction

L-functions

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