LMFDB - Embedded newform 6.25.b.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 25);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	6.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.8980291355$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9921984x^{6} + 31297402621425x^{4} + 35629505313218665424x^{2} + 11190322069687119538557504 $ x^8 + 9921984x^6 + 31297402621425x^4 + 35629505313218665424*x^2 + 11190322069687119538557504
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{53}\cdot 3^{32}\cdot 17^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.3
Root			$-708.500i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.25.b.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2896.31i q^{2} +(269557. - 458005. i) q^{3} -8.38861e6 q^{4} -4.56581e8i q^{5} +(-1.32652e9 - 7.80721e8i) q^{6} +1.81935e9 q^{7} +2.42960e10i q^{8} +(-1.37107e11 - 2.46917e11i) q^{9} +O(q^{10})$	\(q-2896.31i q^{2} +(269557. - 458005. i) q^{3} -8.38861e6 q^{4} -4.56581e8i q^{5} +(-1.32652e9 - 7.80721e8i) q^{6} +1.81935e9 q^{7} +2.42960e10i q^{8} +(-1.37107e11 - 2.46917e11i) q^{9} -1.32240e12 q^{10} -3.36073e12i q^{11} +(-2.26121e12 + 3.84202e12i) q^{12} +3.10150e13 q^{13} -5.26941e12i q^{14} +(-2.09116e14 - 1.23075e14i) q^{15} +7.03687e13 q^{16} +1.14524e14i q^{17} +(-7.15148e14 + 3.97105e14i) q^{18} +9.25261e14 q^{19} +3.83008e15i q^{20} +(4.90420e14 - 8.33273e14i) q^{21} -9.73371e15 q^{22} +2.51730e16i q^{23} +(1.11277e16 + 6.54917e15i) q^{24} -1.48862e17 q^{25} -8.98290e16i q^{26} +(-1.50047e17 - 3.76256e15i) q^{27} -1.52619e16 q^{28} +5.38831e17i q^{29} +(-3.56463e17 + 6.05666e17i) q^{30} +4.67868e17 q^{31} -2.03810e17i q^{32} +(-1.53923e18 - 9.05909e17i) q^{33} +3.31696e17 q^{34} -8.30683e17i q^{35} +(1.15014e18 + 2.07129e18i) q^{36} +3.11155e18 q^{37} -2.67984e18i q^{38} +(8.36032e18 - 1.42050e19i) q^{39} +1.10931e19 q^{40} -1.15365e19i q^{41} +(-2.41342e18 - 1.42041e18i) q^{42} +5.41569e19 q^{43} +2.81918e19i q^{44} +(-1.12738e20 + 6.26006e19i) q^{45} +7.29088e19 q^{46} -1.41317e20i q^{47} +(1.89684e19 - 3.22292e19i) q^{48} -1.88271e20 q^{49} +4.31150e20i q^{50} +(5.24524e19 + 3.08707e19i) q^{51} -2.60173e20 q^{52} -5.85803e20i q^{53} +(-1.08975e19 + 4.34584e20i) q^{54} -1.53445e21 q^{55} +4.42030e19i q^{56} +(2.49411e20 - 4.23774e20i) q^{57} +1.56062e21 q^{58} +1.22231e21i q^{59} +(1.75420e21 + 1.03243e21i) q^{60} +3.16259e21 q^{61} -1.35509e21i q^{62} +(-2.49447e20 - 4.49230e20i) q^{63} -5.90296e20 q^{64} -1.41609e22i q^{65} +(-2.62379e21 + 4.45808e21i) q^{66} -2.88702e21 q^{67} -9.60695e20i q^{68} +(1.15294e22 + 6.78557e21i) q^{69} -2.40592e21 q^{70} +5.86562e21i q^{71} +(5.99910e21 - 3.33116e21i) q^{72} -4.89426e21 q^{73} -9.01201e21i q^{74} +(-4.01268e22 + 6.81794e22i) q^{75} -7.76165e21 q^{76} -6.11435e21i q^{77} +(-4.11421e22 - 2.42141e22i) q^{78} +4.71039e22 q^{79} -3.21290e22i q^{80} +(-4.21697e22 + 6.77082e22i) q^{81} -3.34133e22 q^{82} -1.25799e23i q^{83} +(-4.11394e21 + 6.99000e21i) q^{84} +5.22894e22 q^{85} -1.56855e23i q^{86} +(2.46787e23 + 1.45246e23i) q^{87} +8.16522e22 q^{88} -4.49583e22i q^{89} +(1.81311e23 + 3.26523e23i) q^{90} +5.64273e22 q^{91} -2.11166e23i q^{92} +(1.26117e23 - 2.14286e23i) q^{93} -4.09298e23 q^{94} -4.22457e23i q^{95} +(-9.33458e22 - 5.49384e22i) q^{96} -2.08004e23 q^{97} +5.45292e23i q^{98} +(-8.29821e23 + 4.60780e23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9}+O(q^{10}) $ 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9	$ 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 36\!\cdots\!36 q^{21}+ \cdots + 69\!\cdots\!44 q^{99}+O(q^{100}) $ 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9 - 1863369424896 * q^10 + 1106289623040 * q^12 + 50568363679120 * q^13 - 348034956760512 * q^15 + 562949953421312 * q^16 - 514738292981760 * q^18 - 978083631341264 * q^19 + 3640012304241936 * q^21 - 336450979430400 * q^22 - 282849366245376 * q^24 + 7630618767014024 * q^25 - 86594528606057640 * q^27 + 85234923203461120 * q^28 - 725410188900237312 * q^30 + 3092119786822709104 * q^31 - 8158685952668529600 * q^33 + 3821138032531341312 * q^34 - 2476057486864416768 * q^36 + 22590293223992782480 * q^37 - 40190176581881465040 * q^39 + 15631075664637984768 * q^40 - 79119883835565342720 * q^42 + 226487466371803896880 * q^43 - 347709996757177504128 * q^45 + 139842130561120468992 * q^46 - 9280229982150328320 * q^48 + 104686700473616731800 * q^49 + 558091874936566543104 * q^51 - 424198180105575464960 * q^52 + 334066775626796728320 * q^54 - 2212687664250467338368 * q^55 + 3588879995640760725840 * q^57 - 1867706355469718323200 * q^58 + 2919528822560885047296 * q^60 - 6507010783838092385648 * q^61 + 10112982777612899380080 * q^63 - 4722366482869645213696 * q^64 - 1924112442339530440704 * q^66 - 7042120118150060144720 * q^67 - 4323335967368731345536 * q^69 + 16481910236435553583104 * q^70 + 4317937762413135790080 * q^72 + 36259820324758576687120 * q^73 - 108081978448612908655272 * q^75 + 8204760174538377920512 * q^76 - 74188898027329578270720 * q^78 + 316807052777330015315824 * q^79 - 268518660504396776813304 * q^81 + 83114941529654645882880 * q^82 - 30534636335462338265088 * q^84 - 222512862545524200678912 * q^85 + 449461577201807342128320 * q^87 + 2822355377657688883200 * q^88 + 612683975543382025371648 * q^90 - 1196839602335690774367520 * q^91 + 873237537450828783745680 * q^93 - 1298887117621773403422720 * q^94 + 2372712456480891076608 * q^96 + 816517576248201265716880 * q^97 + 695858883367208922313344 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	2896.31i		−	0.707107i
$2$		−	2896.31i		−	0.707107i
$3$	269557.	−	458005.i	0.507220	−	0.861817i
$3$	269557.	−	458005.i	0.507220	−	0.861817i
$4$	−8.38861e6			−0.500000
$5$		−	4.56581e8i		−	1.87016i	−0.354441	−	0.935078i	$-0.615329\pi$
$5$		−	4.56581e8i		−	1.87016i	0.354441	−	0.935078i	$-0.384671\pi$
$6$	−1.32652e9	−	7.80721e8i	−0.609396	−	0.358658i
$7$	1.81935e9			0.131444			0.0657220	−	0.997838i	$-0.479065\pi$
$7$	1.81935e9			0.131444			0.0657220	+	0.997838i	$0.479065\pi$
$8$			2.42960e10i			0.353553i
$9$	−1.37107e11	−	2.46917e11i	−0.485456	−	0.874261i
$10$	−1.32240e12			−1.32240
$11$		−	3.36073e12i		−	1.07083i	−0.844589	−	0.535416i	$-0.820155\pi$
$11$		−	3.36073e12i		−	1.07083i	0.844589	−	0.535416i	$-0.179845\pi$
$12$	−2.26121e12	+	3.84202e12i	−0.253610	+	0.430908i
$13$	3.10150e13			1.33123			0.665613	−	0.746297i	$-0.268170\pi$
$13$	3.10150e13			1.33123			0.665613	+	0.746297i	$0.268170\pi$
$14$		−	5.26941e12i		−	0.0929450i
$15$	−2.09116e14	−	1.23075e14i	−1.61173	−	0.948580i
$16$	7.03687e13			0.250000
$17$			1.14524e14i			0.196566i	0.995159	+	0.0982830i	$0.0313350\pi$
$17$			1.14524e14i			0.196566i	−0.995159	+	0.0982830i	$0.968665\pi$
$18$	−7.15148e14	+	3.97105e14i	−0.618196	+	0.343269i
$19$	9.25261e14			0.418043			0.209022	−	0.977911i	$-0.432972\pi$
$19$	9.25261e14			0.418043			0.209022	+	0.977911i	$0.432972\pi$
$20$			3.83008e15i			0.935078i
$21$	4.90420e14	−	8.33273e14i	0.0666710	−	0.113281i
$22$	−9.73371e15			−0.757192
$23$			2.51730e16i			1.14869i	0.818615	+	0.574343i	$0.194742\pi$
$23$			2.51730e16i			1.14869i	−0.818615	+	0.574343i	$0.805258\pi$
$24$	1.11277e16	+	6.54917e15i	0.304698	+	0.179329i
$25$	−1.48862e17			−2.49749
$26$		−	8.98290e16i		−	0.941318i
$27$	−1.50047e17	−	3.76256e15i	−0.999686	−	0.0250679i
$28$	−1.52619e16			−0.0657220
$29$			5.38831e17i			1.52292i	0.648213	+	0.761459i	$0.275517\pi$
$29$			5.38831e17i			1.52292i	−0.648213	+	0.761459i	$0.724483\pi$
$30$	−3.56463e17	+	6.05666e17i	−0.670748	+	1.13967i
$31$	4.67868e17			0.593995			0.296998	−	0.954878i	$-0.404015\pi$
$31$	4.67868e17			0.593995			0.296998	+	0.954878i	$0.404015\pi$
$32$		−	2.03810e17i		−	0.176777i
$33$	−1.53923e18	−	9.05909e17i	−0.922860	−	0.543147i
$34$	3.31696e17			0.138993
$35$		−	8.30683e17i		−	0.245821i
$36$	1.15014e18	+	2.07129e18i	0.242728	+	0.437130i
$37$	3.11155e18			0.472668			0.236334	−	0.971672i	$-0.424054\pi$
$37$	3.11155e18			0.472668			0.236334	+	0.971672i	$0.424054\pi$
$38$		−	2.67984e18i		−	0.295601i
$39$	8.36032e18	−	1.42050e19i	0.675224	−	1.14727i
$40$	1.10931e19			0.661200
$41$		−	1.15365e19i		−	0.511291i	−0.966771	−	0.255646i	$-0.917712\pi$
$41$		−	1.15365e19i		−	0.511291i	0.966771	−	0.255646i	$-0.0822881\pi$
$42$	−2.41342e18	−	1.42041e18i	−0.0801015	−	0.0471435i
$43$	5.41569e19			1.35529			0.677645	−	0.735390i	$-0.263001\pi$
$43$	5.41569e19			1.35529			0.677645	+	0.735390i	$0.263001\pi$
$44$			2.81918e19i			0.535416i
$45$	−1.12738e20	+	6.26006e19i	−1.63500	+	0.907879i
$46$	7.29088e19			0.812243
$47$		−	1.41317e20i		−	1.21624i	−0.793844	−	0.608122i	$-0.791923\pi$
$47$		−	1.41317e20i		−	1.21624i	0.793844	−	0.608122i	$-0.208077\pi$
$48$	1.89684e19	−	3.22292e19i	0.126805	−	0.215454i
$49$	−1.88271e20			−0.982722
$50$			4.31150e20i			1.76599i
$51$	5.24524e19	+	3.08707e19i	0.169404	+	0.0997022i
$52$	−2.60173e20			−0.665613
$53$		−	5.85803e20i		−	1.19245i	−0.802816	−	0.596226i	$-0.796666\pi$
$53$		−	5.85803e20i		−	1.19245i	0.802816	−	0.596226i	$-0.203334\pi$
$54$	−1.08975e19	+	4.34584e20i	−0.0177257	+	0.706885i
$55$	−1.53445e21			−2.00262
$56$			4.42030e19i			0.0464725i
$57$	2.49411e20	−	4.23774e20i	0.212040	−	0.360277i
$58$	1.56062e21			1.07687
$59$			1.22231e21i			0.686998i	0.939153	+	0.343499i	$0.111612\pi$
$59$			1.22231e21i			0.686998i	−0.939153	+	0.343499i	$0.888388\pi$
$60$	1.75420e21	+	1.03243e21i	0.805866	+	0.474290i
$61$	3.16259e21			1.19148			0.595738	−	0.803179i	$-0.296860\pi$
$61$	3.16259e21			1.19148			0.595738	+	0.803179i	$0.296860\pi$
$62$		−	1.35509e21i		−	0.420018i
$63$	−2.49447e20	−	4.49230e20i	−0.0638103	−	0.114916i
$64$	−5.90296e20			−0.125000
$65$		−	1.41609e22i		−	2.48960i
$66$	−2.62379e21	+	4.45808e21i	−0.384063	+	0.652561i
$67$	−2.88702e21			−0.352820			−0.176410	−	0.984317i	$-0.556448\pi$
$67$	−2.88702e21			−0.352820			−0.176410	+	0.984317i	$0.556448\pi$
$68$		−	9.60695e20i		−	0.0982830i
$69$	1.15294e22	+	6.78557e21i	0.989956	+	0.582636i
$70$	−2.40592e21			−0.173822
$71$			5.86562e21i			0.357449i	0.983899	+	0.178724i	$0.0571970\pi$
$71$			5.86562e21i			0.357449i	−0.983899	+	0.178724i	$0.942803\pi$
$72$	5.99910e21	−	3.33116e21i	0.309098	−	0.171635i
$73$	−4.89426e21			−0.213704			−0.106852	−	0.994275i	$-0.534077\pi$
$73$	−4.89426e21			−0.213704			−0.106852	+	0.994275i	$0.534077\pi$
$74$		−	9.01201e21i		−	0.334227i
$75$	−4.01268e22	+	6.81794e22i	−1.26677	+	2.15238i
$76$	−7.76165e21			−0.209022
$77$		−	6.11435e21i		−	0.140754i
$78$	−4.11421e22	−	2.42141e22i	−0.811244	−	0.477455i
$79$	4.71039e22			0.797135			0.398567	−	0.917139i	$-0.369507\pi$
$79$	4.71039e22			0.797135			0.398567	+	0.917139i	$0.369507\pi$
$80$		−	3.21290e22i		−	0.467539i
$81$	−4.21697e22	+	6.77082e22i	−0.528664	+	0.848831i
$82$	−3.34133e22			−0.361538
$83$		−	1.25799e23i		−	1.17690i	−0.808534	−	0.588449i	$-0.799739\pi$
$83$		−	1.25799e23i		−	1.17690i	0.808534	−	0.588449i	$-0.200261\pi$
$84$	−4.11394e21	+	6.99000e21i	−0.0333355	+	0.0566403i
$85$	5.22894e22			0.367609
$86$		−	1.56855e23i		−	0.958334i
$87$	2.46787e23	+	1.45246e23i	1.31248	+	0.772454i
$88$	8.16522e22			0.378596
$89$		−	4.49583e22i		−	0.182024i	−0.995850	−	0.0910122i	$-0.970990\pi$
$89$		−	4.49583e22i		−	0.182024i	0.995850	−	0.0910122i	$-0.0290102\pi$
$90$	1.81311e23	+	3.26523e23i	0.641968	+	1.15612i
$91$	5.64273e22			0.174982
$92$		−	2.11166e23i		−	0.574343i
$93$	1.26117e23	−	2.14286e23i	0.301286	−	0.511915i
$94$	−4.09298e23			−0.860014
$95$		−	4.22457e23i		−	0.781806i
$96$	−9.33458e22	−	5.49384e22i	−0.152349	−	0.0896646i
$97$	−2.08004e23			−0.299786			−0.149893	−	0.988702i	$-0.547893\pi$
$97$	−2.08004e23			−0.299786			−0.149893	+	0.988702i	$0.547893\pi$
$98$			5.45292e23i			0.694890i
$99$	−8.29821e23	+	4.60780e23i	−0.936186	+	0.519842i
$100$	1.24874e24			1.24874
$101$			4.79708e23i			0.425717i	0.977083	+	0.212858i	$0.0682773\pi$
$101$			4.79708e23i			0.425717i	−0.977083	+	0.212858i	$0.931723\pi$
$102$	8.94112e22	−	1.51918e23i	0.0705001	−	0.119787i
$103$	−2.07015e24			−1.45196			−0.725982	−	0.687714i	$-0.758614\pi$
$103$	−2.07015e24			−1.45196			−0.725982	+	0.687714i	$0.758614\pi$
$104$			7.53541e23i			0.470659i
$105$	−3.80457e23	−	2.23917e23i	−0.211853	−	0.124685i
$106$	−1.69667e24			−0.843192
$107$		−	2.26189e24i		−	1.00430i	−0.864779	−	0.502152i	$-0.832542\pi$
$107$		−	2.26189e24i		−	1.00430i	0.864779	−	0.502152i	$-0.167458\pi$
$108$	1.25869e24	+	3.15627e22i	0.499843	+	0.0125340i
$109$	4.92671e23			0.175162			0.0875808	−	0.996157i	$-0.472086\pi$
$109$	4.92671e23			0.175162			0.0875808	+	0.996157i	$0.472086\pi$
$110$			4.44423e24i			1.41607i
$111$	8.38741e23	−	1.42511e24i	0.239747	−	0.407353i
$112$	1.28026e23			0.0328610
$113$			3.60667e24i			0.832080i	0.909346	+	0.416040i	$0.136582\pi$
$113$			3.60667e24i			0.832080i	−0.909346	+	0.416040i	$0.863418\pi$
$114$	−1.22738e24	−	7.22371e23i	−0.254754	−	0.149935i
$115$	1.14935e25			2.14822
$116$		−	4.52004e24i		−	0.761459i
$117$	−4.25238e24	−	7.65813e24i	−0.646252	−	1.16384i
$118$	3.54017e24			0.485781
$119$			2.08359e23i			0.0258374i
$120$	2.99023e24	−	5.08069e24i	0.335374	−	0.569833i
$121$	−1.44476e24			−0.146680
$122$		−	9.15984e24i		−	0.842500i
$123$	−5.28378e24	−	3.10975e24i	−0.440640	−	0.259337i
$124$	−3.92476e24			−0.296998
$125$			4.07531e25i			2.80053i
$126$	−1.30111e24	+	7.22475e23i	−0.0812581	+	0.0451207i
$127$	1.55723e24			0.0884519			0.0442259	−	0.999022i	$-0.485918\pi$
$127$	1.55723e24			0.0884519			0.0442259	+	0.999022i	$0.485918\pi$
$128$			1.70968e24i			0.0883883i
$129$	1.45984e25	−	2.48041e25i	0.687429	−	1.16801i
$130$	−4.10143e25			−1.76041
$131$			3.80638e24i			0.149024i	0.997220	+	0.0745121i	$0.0237399\pi$
$131$			3.80638e24i			0.149024i	−0.997220	+	0.0745121i	$0.976260\pi$
$132$	1.29120e25	+	7.59931e24i	0.461430	+	0.271573i
$133$	1.68338e24			0.0549493
$134$			8.36171e24i			0.249481i
$135$	−1.71792e24	+	6.85089e25i	−0.0468810	+	1.86957i
$136$	−2.78247e24			−0.0694966
$137$		−	2.25473e25i		−	0.515760i	−0.966177	−	0.257880i	$-0.916976\pi$
$137$		−	2.25473e25i		−	0.515760i	0.966177	−	0.257880i	$-0.0830239\pi$
$138$	1.96531e25	−	3.33926e25i	0.411986	−	0.700005i
$139$	−7.62088e25			−1.46497			−0.732483	−	0.680785i	$-0.761639\pi$
$139$	−7.62088e25			−1.46497			−0.732483	+	0.680785i	$0.761639\pi$
$140$			6.96828e24i			0.122910i
$141$	−6.47239e25	−	3.80931e25i	−1.04818	−	0.616903i
$142$	1.69886e25			0.252754
$143$		−	1.04233e26i		−	1.42552i
$144$	−9.64806e24	−	1.73752e25i	−0.121364	−	0.218565i
$145$	2.46020e26			2.84810
$146$			1.41753e25i			0.151112i
$147$	−5.07499e25	+	8.62291e25i	−0.498456	+	0.846927i
$148$	−2.61016e25			−0.236334
$149$		−	2.27765e25i		−	0.190218i	−0.995467	−	0.0951089i	$-0.969680\pi$
$149$		−	2.27765e25i		−	0.190218i	0.995467	−	0.0951089i	$-0.0303199\pi$
$150$	1.97469e26	+	1.16220e26i	1.52196	+	0.895745i
$151$	1.16110e26			0.826314			0.413157	−	0.910660i	$-0.364426\pi$
$151$	1.16110e26			0.826314			0.413157	+	0.910660i	$0.364426\pi$
$152$			2.24802e25i			0.147801i
$153$	2.82779e25	−	1.57020e25i	0.171850	−	0.0954242i
$154$	−1.77091e25			−0.0995284
$155$		−	2.13620e26i		−	1.11086i
$156$	−7.01315e25	+	1.19160e26i	−0.337612	+	0.573636i
$157$	−3.85801e26			−1.72015			−0.860077	−	0.510164i	$-0.829585\pi$
$157$	−3.85801e26			−1.72015			−0.860077	+	0.510164i	$0.829585\pi$
$158$		−	1.36427e26i		−	0.563660i
$159$	−2.68301e26	−	1.57908e26i	−1.02768	−	0.604836i
$160$	−9.30557e25			−0.330600
$161$			4.57986e25i			0.150988i
$162$	1.96104e26	+	1.22136e26i	0.600214	+	0.373822i
$163$	3.94400e26			1.12121			0.560604	−	0.828084i	$-0.310569\pi$
$163$	3.94400e26			1.12121			0.560604	+	0.828084i	$0.310569\pi$
$164$			9.67753e25i			0.255646i
$165$	−4.13621e26	+	7.02783e26i	−1.01577	+	1.72589i
$166$	−3.64352e26			−0.832193
$167$		−	2.99402e26i		−	0.636292i	−0.948042	−	0.318146i	$-0.896940\pi$
$167$		−	2.99402e26i		−	0.636292i	0.948042	−	0.318146i	$-0.103060\pi$
$168$	2.02452e25	+	1.19153e25i	0.0400508	+	0.0235718i
$169$	4.19130e26			0.772161
$170$		−	1.51446e26i		−	0.259939i
$171$	−1.26860e26	−	2.28463e26i	−0.202942	−	0.365479i
$172$	−4.54301e26			−0.677645
$173$			1.10874e27i			1.54268i	0.636424	+	0.771339i	$0.280413\pi$
$173$			1.10874e27i			1.54268i	−0.636424	+	0.771339i	$0.719587\pi$
$174$	4.20677e26	−	7.14772e26i	0.546208	−	0.928061i
$175$	−2.70832e26			−0.328280
$176$		−	2.36490e26i		−	0.267708i
$177$	5.59822e26	+	3.29481e26i	0.592067	+	0.348459i
$178$	−1.30213e26			−0.128711
$179$			2.47530e26i			0.228766i	0.993437	+	0.114383i	$0.0364891\pi$
$179$			2.47530e26i			0.228766i	−0.993437	+	0.114383i	$0.963511\pi$
$180$	9.45713e26	−	5.25132e26i	0.817502	−	0.453940i
$181$	9.06907e26			0.733533			0.366767	−	0.930313i	$-0.380465\pi$
$181$	9.06907e26			0.733533			0.366767	+	0.930313i	$0.380465\pi$
$182$		−	1.63431e26i		−	0.123731i
$183$	8.52500e26	−	1.44848e27i	0.604340	−	1.02683i
$184$	−6.11603e26			−0.406121
$185$		−	1.42068e27i		−	0.883963i
$186$	−6.20638e26	−	3.65275e26i	−0.361979	−	0.213041i
$187$	3.84883e26			0.210489
$188$			1.18545e27i			0.608122i
$189$	−2.72990e26	−	6.84543e24i	−0.131403	−	0.00329503i
$190$	−1.22357e27			−0.552821
$191$			2.37087e27i			1.00579i	0.864348	+	0.502895i	$0.167732\pi$
$191$			2.37087e27i			1.00579i	−0.864348	+	0.502895i	$0.832268\pi$
$192$	−1.59119e26	+	2.70358e26i	−0.0634025	+	0.107727i
$193$	5.09004e27			1.90561			0.952804	−	0.303585i	$-0.0981835\pi$
$193$	5.09004e27			1.90561			0.952804	+	0.303585i	$0.0981835\pi$
$194$			6.02444e26i			0.211980i
$195$	−6.48575e27	−	3.81717e27i	−2.14558	−	1.26277i
$196$	1.57933e27			0.491361
$197$			4.72370e27i			1.38257i	0.722582	+	0.691285i	$0.242955\pi$
$197$			4.72370e27i			1.38257i	−0.722582	+	0.691285i	$0.757045\pi$
$198$	1.33456e27	+	2.40342e27i	0.367584	+	0.661983i
$199$	−7.31715e27			−1.89716			−0.948582	−	0.316530i	$-0.897482\pi$
$199$	−7.31715e27			−1.89716			−0.948582	+	0.316530i	$0.897482\pi$
$200$		−	3.61675e27i		−	0.882995i
$201$	−7.78219e26	+	1.32227e27i	−0.178957	+	0.304066i
$202$	1.38938e27			0.301027
$203$			9.80325e26i			0.200179i
$204$	−4.40003e26	−	2.58962e26i	−0.0847020	−	0.0498511i
$205$	−5.26736e27			−0.956195
$206$			5.99580e27i			1.02669i
$207$	6.21564e27	−	3.45140e27i	1.00425	−	0.557636i
$208$	2.18249e27			0.332806
$209$		−	3.10955e27i		−	0.447654i
$210$	−6.48532e26	+	1.10192e27i	−0.0881658	+	0.149802i
$211$	5.52494e27			0.709476			0.354738	−	0.934966i	$-0.384570\pi$
$211$	5.52494e27			0.709476			0.354738	+	0.934966i	$0.384570\pi$
$212$			4.91407e27i			0.596226i
$213$	2.68648e27	+	1.58112e27i	0.308055	+	0.181305i
$214$	−6.55112e27			−0.710150
$215$		−	2.47270e28i		−	2.53460i
$216$	9.14152e25	−	3.64555e27i	0.00886285	−	0.353442i
$217$	8.51218e26			0.0780771
$218$		−	1.42693e27i		−	0.123858i
$219$	−1.31928e27	+	2.24160e27i	−0.108395	+	0.184174i
$220$	1.28719e28			1.00131
$221$			3.55195e27i			0.261674i
$222$	−4.12755e27	−	2.42925e27i	−0.288042	−	0.169526i
$223$	−2.65651e27			−0.175652			−0.0878261	−	0.996136i	$-0.527992\pi$
$223$	−2.65651e27			−0.175652			−0.0878261	+	0.996136i	$0.527992\pi$
$224$		−	3.70802e26i		−	0.0232362i
$225$	2.04100e28	+	3.67565e28i	1.21242	+	2.18345i
$226$	1.04460e28			0.588369
$227$		−	3.79716e27i		−	0.202837i	−0.994844	−	0.101419i	$-0.967662\pi$
$227$		−	3.79716e27i		−	0.202837i	0.994844	−	0.101419i	$-0.0323382\pi$
$228$	−2.09221e27	+	3.55487e27i	−0.106020	+	0.180138i
$229$	1.19916e28			0.576570			0.288285	−	0.957545i	$-0.406915\pi$
$229$	1.19916e28			0.576570			0.288285	+	0.957545i	$0.406915\pi$
$230$		−	3.32888e28i		−	1.51902i
$231$	−2.80040e27	−	1.64817e27i	−0.121304	−	0.0713934i
$232$	−1.30914e28			−0.538433
$233$			2.52886e28i			0.987766i	0.869528	+	0.493883i	$0.164423\pi$
$233$			2.52886e28i			0.987766i	−0.869528	+	0.493883i	$0.835577\pi$
$234$	−2.21803e28	+	1.23162e28i	−0.822958	+	0.456969i
$235$	−6.45227e28			−2.27457
$236$		−	1.02534e28i		−	0.343499i
$237$	1.26972e28	−	2.15738e28i	0.404323	−	0.686984i
$238$	6.03473e26			0.0182698
$239$		−	2.31937e28i		−	0.667720i	−0.942623	−	0.333860i	$-0.891649\pi$
$239$		−	2.31937e28i		−	0.667720i	0.942623	−	0.333860i	$-0.108351\pi$
$240$	−1.47153e28	−	8.66062e27i	−0.402933	−	0.237145i
$241$	−9.28349e27			−0.241828			−0.120914	−	0.992663i	$-0.538583\pi$
$241$	−9.28349e27			−0.241828			−0.120914	+	0.992663i	$0.538583\pi$
$242$			4.18446e27i			0.103718i
$243$	1.96435e28	+	3.75652e28i	0.463388	+	0.886156i
$244$	−2.65297e28			−0.595738
$245$			8.59611e28i			1.83785i
$246$	−9.00681e27	+	1.53035e28i	−0.183379	+	0.311579i
$247$	2.86970e28			0.556510
$248$			1.13673e28i			0.210009i
$249$	−5.76164e28	−	3.39100e28i	−1.01427	−	0.596946i
$250$	1.18034e29			1.98028
$251$		−	1.06381e29i		−	1.70129i	−0.525742	−	0.850644i	$-0.676212\pi$
$251$		−	1.06381e29i		−	1.70129i	0.525742	−	0.850644i	$-0.323788\pi$
$252$	2.09251e27	+	3.76841e27i	0.0319052	+	0.0574582i
$253$	8.45996e28			1.23005
$254$		−	4.51021e27i		−	0.0625449i
$255$	1.40950e28	−	2.39488e28i	0.186459	−	0.316812i
$256$	4.95176e27			0.0625000
$257$			7.43493e28i			0.895528i	0.894152	+	0.447764i	$0.147780\pi$
$257$			7.43493e28i			0.895528i	−0.894152	+	0.447764i	$0.852220\pi$
$258$	−7.18403e28	−	4.22814e28i	−0.825908	−	0.486086i
$259$	5.66101e27			0.0621294
$260$			1.18790e29i			1.24480i
$261$	1.33047e29	−	7.38776e28i	1.33143	−	0.739310i
$262$	1.10245e28			0.105376
$263$		−	1.08384e29i		−	0.989685i	−0.868983	−	0.494843i	$-0.835226\pi$
$263$		−	1.08384e29i		−	0.989685i	0.868983	−	0.494843i	$-0.164774\pi$
$264$	2.20100e28	−	3.73971e28i	0.192031	−	0.326280i
$265$	−2.67467e29			−2.23007
$266$		−	4.87558e27i		−	0.0388550i
$267$	−2.05911e28	−	1.21188e28i	−0.156872	−	0.0923264i
$268$	2.42181e28			0.176410
$269$		−	1.29861e29i		−	0.904591i	−0.891868	−	0.452296i	$-0.850605\pi$
$269$		−	1.29861e29i		−	0.904591i	0.891868	−	0.452296i	$-0.149395\pi$
$270$	1.98423e29	+	4.97561e27i	1.32198	+	0.0331498i
$271$	−4.00692e28			−0.255375			−0.127688	−	0.991814i	$-0.540756\pi$
$271$	−4.00692e28			−0.255375			−0.127688	+	0.991814i	$0.540756\pi$
$272$			8.05889e27i			0.0491415i
$273$	1.52104e28	−	2.58440e28i	0.0887541	−	0.150802i
$274$	−6.53040e28			−0.364697
$275$			5.00284e29i			2.67439i
$276$	−9.67152e28	−	5.69215e28i	−0.494978	−	0.291318i
$277$	1.01057e29			0.495232			0.247616	−	0.968858i	$-0.420353\pi$
$277$	1.01057e29			0.495232			0.247616	+	0.968858i	$0.420353\pi$
$278$			2.20724e29i			1.03589i
$279$	−6.41481e28	−	1.15525e29i	−0.288359	−	0.519307i
$280$	2.01823e28			0.0869108
$281$			5.95802e28i			0.245825i	0.992418	+	0.122912i	$0.0392234\pi$
$281$			5.95802e28i			0.245825i	−0.992418	+	0.122912i	$0.960777\pi$
$282$	−1.10329e29	+	1.87460e29i	−0.436216	+	0.741174i
$283$	−1.57986e29			−0.598663			−0.299332	−	0.954149i	$-0.596764\pi$
$283$	−1.57986e29			−0.598663			−0.299332	+	0.954149i	$0.596764\pi$
$284$		−	4.92044e28i		−	0.178724i
$285$	−1.93487e29	−	1.13876e29i	−0.673774	−	0.396548i
$286$	−3.01891e29			−1.00799
$287$		−	2.09890e28i		−	0.0672062i
$288$	−5.03241e28	+	2.79438e28i	−0.154549	+	0.0858174i
$289$	3.26333e29			0.961362
$290$		−	7.12550e29i		−	2.01391i
$291$	−5.60690e28	+	9.52668e28i	−0.152057	+	0.258360i
$292$	4.10561e28			0.106852
$293$		−	3.62941e29i		−	0.906618i	−0.891354	−	0.453309i	$-0.850244\pi$
$293$		−	3.62941e29i		−	0.906618i	0.891354	−	0.453309i	$-0.149756\pi$
$294$	2.49746e29	+	1.46987e29i	0.598868	+	0.352462i
$295$	5.58082e29			1.28479
$296$			7.55982e28i			0.167113i
$297$	−1.26449e28	+	5.04269e29i	−0.0268435	+	1.07049i
$298$	−6.59677e28			−0.134504
$299$			7.80741e29i			1.52916i
$300$	3.36608e29	−	5.71930e29i	0.633387	−	1.07619i
$301$	9.85305e28			0.178145
$302$		−	3.36290e29i		−	0.584292i
$303$	2.19709e29	+	1.29309e29i	0.366890	+	0.215932i
$304$	6.51095e28			0.104511
$305$		−	1.44398e30i		−	2.22825i
$306$	−4.54779e28	−	8.19015e28i	−0.0674751	−	0.121516i
$307$	1.61139e29			0.229901			0.114950	−	0.993371i	$-0.463329\pi$
$307$	1.61139e29			0.229901			0.114950	+	0.993371i	$0.463329\pi$
$308$			5.12909e28i			0.0703772i
$309$	−5.58025e29	+	9.48140e29i	−0.736465	+	1.25133i
$310$	−6.18709e29			−0.785500
$311$		−	7.23373e29i		−	0.883563i	−0.897123	−	0.441781i	$-0.854347\pi$
$311$		−	7.23373e29i		−	0.883563i	0.897123	−	0.441781i	$-0.145653\pi$
$312$	3.45125e29	+	2.03122e29i	0.405622	+	0.238728i
$313$	5.06999e29			0.573423			0.286711	−	0.958017i	$-0.407438\pi$
$313$	5.06999e29			0.573423			0.286711	+	0.958017i	$0.407438\pi$
$314$			1.11740e30i			1.21633i
$315$	−2.05110e29	+	1.13893e29i	−0.214912	+	0.119335i
$316$	−3.95136e29			−0.398567
$317$			3.48880e29i			0.338817i	0.985546	+	0.169409i	$0.0541857\pi$
$317$			3.48880e29i			0.338817i	−0.985546	+	0.169409i	$0.945814\pi$
$318$	−4.57349e29	+	7.77082e29i	−0.427683	+	0.726677i
$319$	1.81086e30			1.63079
$320$			2.69518e29i			0.233770i
$321$	−1.03595e30	−	6.09708e29i	−0.865526	−	0.509403i
$322$	1.32647e29			0.106764
$323$			1.05964e29i			0.0821731i
$324$	3.53745e29	−	5.67978e29i	0.264332	−	0.424416i
$325$	−4.61695e30			−3.32472
$326$		−	1.14231e30i		−	0.792813i
$327$	1.32803e29	−	2.25646e29i	0.0888454	−	0.150957i
$328$	2.80291e29			0.180769
$329$		−	2.57106e29i		−	0.159868i
$330$	2.03548e30	+	1.19797e30i	1.22039	+	0.718258i
$331$	−1.05153e30			−0.607976			−0.303988	−	0.952676i	$-0.598318\pi$
$331$	−1.05153e30			−0.607976			−0.303988	+	0.952676i	$0.598318\pi$
$332$			1.05528e30i			0.588449i
$333$	−4.26616e29	−	7.68295e29i	−0.229460	−	0.413235i
$334$	−8.67160e29			−0.449927
$335$			1.31816e30i			0.659828i
$336$	3.45103e28	−	5.86364e28i	0.0166678	−	0.0283202i
$337$	2.48164e30			1.15659			0.578295	−	0.815828i	$-0.303718\pi$
$337$	2.48164e30			1.15659			0.578295	+	0.815828i	$0.303718\pi$
$338$		−	1.21393e30i		−	0.546000i
$339$	1.65187e30	+	9.72204e29i	0.717100	+	0.422047i
$340$	−4.38635e29			−0.183805
$341$		−	1.57238e30i		−	0.636069i
$342$	−6.61699e29	+	3.67426e29i	−0.258433	+	0.143501i
$343$	−6.91086e29			−0.260617
$344$			1.31580e30i			0.479167i
$345$	3.09816e30	−	5.26409e30i	1.08962	−	1.85137i
$346$	3.21125e30			1.09084
$347$			3.73656e30i			1.22608i	0.790052	+	0.613040i	$0.210053\pi$
$347$			3.73656e30i			1.22608i	−0.790052	+	0.613040i	$0.789947\pi$
$348$	−2.07020e30	−	1.21841e30i	−0.656238	−	0.386227i
$349$	5.31023e30			1.62633			0.813164	−	0.582035i	$-0.197743\pi$
$349$	5.31023e30			1.62633			0.813164	+	0.582035i	$0.197743\pi$
$350$			7.84414e29i			0.232129i
$351$	−4.65372e30	−	1.16696e29i	−1.33081	−	0.0333711i
$352$	−6.84949e29			−0.189298
$353$		−	1.35177e28i		−	0.00361082i	−0.999998	−	0.00180541i	$-0.999425\pi$
$353$		−	1.35177e28i		−	0.00361082i	0.999998	−	0.00180541i	$-0.000574680\pi$
$354$	9.54280e29	−	1.62142e30i	0.246398	−	0.418654i
$355$	2.67813e30			0.668485
$356$			3.77137e29i			0.0910122i
$357$	9.54296e28	+	5.61648e28i	0.0222671	+	0.0131053i
$358$	7.16923e29			0.161762
$359$			1.08720e30i			0.237234i	0.992940	+	0.118617i	$0.0378460\pi$
$359$			1.08720e30i			0.237234i	−0.992940	+	0.118617i	$0.962154\pi$
$360$	−1.52094e30	−	2.73908e30i	−0.320984	−	0.578062i
$361$	−4.04265e30			−0.825240
$362$		−	2.62668e30i		−	0.518686i
$363$	−3.89444e29	+	6.61705e29i	−0.0743988	+	0.126411i
$364$	−4.73346e29			−0.0874908
$365$			2.23463e30i			0.399660i
$366$	−4.19525e30	−	2.46910e30i	−0.726081	−	0.427333i
$367$	−4.97294e30			−0.832952			−0.416476	−	0.909147i	$-0.636735\pi$
$367$	−4.97294e30			−0.832952			−0.416476	+	0.909147i	$0.636735\pi$
$368$			1.77139e30i			0.287171i
$369$	−2.84856e30	+	1.58174e30i	−0.447002	+	0.248210i
$370$	−4.11472e30			−0.625056
$371$		−	1.06578e30i		−	0.156741i
$372$	−1.05795e30	+	1.79756e30i	−0.150643	+	0.255958i
$373$	−4.16953e30			−0.574885			−0.287443	−	0.957798i	$-0.592805\pi$
$373$	−4.16953e30			−0.574885			−0.287443	+	0.957798i	$0.592805\pi$
$374$		−	1.11474e30i		−	0.148838i
$375$	1.86651e31	+	1.09853e31i	2.41355	+	1.42049i
$376$	3.43344e30			0.430007
$377$			1.67118e31i			2.02735i
$378$	−1.98265e28	+	7.90662e29i	−0.00232994	+	0.0929158i
$379$	−5.25196e30			−0.597931			−0.298966	−	0.954264i	$-0.596642\pi$
$379$	−5.25196e30			−0.597931			−0.298966	+	0.954264i	$0.596642\pi$
$380$			3.54383e30i			0.390903i
$381$	4.19762e29	−	7.13217e29i	0.0448645	−	0.0762293i
$382$	6.86677e30			0.711200
$383$		−	1.79845e31i		−	1.80515i	−0.430532	−	0.902575i	$-0.641674\pi$
$383$		−	1.79845e31i		−	1.80515i	0.430532	−	0.902575i	$-0.358326\pi$
$384$	7.83041e29	+	4.60857e29i	0.0761746	+	0.0448323i
$385$	−2.79170e30			−0.263233
$386$		−	1.47423e31i		−	1.34747i
$387$	−7.42530e30	−	1.33723e31i	−0.657934	−	1.18488i
$388$	1.74486e30			0.149893
$389$		−	5.39514e30i		−	0.449374i	−0.974431	−	0.224687i	$-0.927864\pi$
$389$		−	5.39514e30i		−	0.449374i	0.974431	−	0.224687i	$-0.0721359\pi$
$390$	−1.10557e31	+	1.87847e31i	−0.892916	+	1.51715i
$391$	−2.88291e30			−0.225793
$392$		−	4.57424e30i		−	0.347445i
$393$	1.74334e30	+	1.02604e30i	0.128432	+	0.0755880i
$394$	1.36813e31			0.977625
$395$		−	2.15068e31i		−	1.49077i
$396$	6.96104e30	−	3.86530e30i	0.468093	−	0.259921i
$397$	1.06217e31			0.692958			0.346479	−	0.938058i	$-0.387377\pi$
$397$	1.06217e31			0.692958			0.346479	+	0.938058i	$0.387377\pi$
$398$			2.11927e31i			1.34150i
$399$	4.53767e29	−	7.70995e29i	0.0278714	−	0.0473562i
$400$	−1.04752e31			−0.624372
$401$		−	3.13328e30i		−	0.181245i	−0.995885	−	0.0906226i	$-0.971114\pi$
$401$		−	3.13328e30i		−	0.181245i	0.995885	−	0.0906226i	$-0.0288857\pi$
$402$	3.82971e30	+	2.25396e30i	0.215007	+	0.126542i
$403$	1.45109e31			0.790742
$404$		−	4.02408e30i		−	0.212858i
$405$	3.09143e31	+	1.92539e31i	1.58745	+	0.988685i
$406$	2.83932e30			0.141548
$407$		−	1.04571e31i		−	0.506148i
$408$	−7.50035e29	+	1.27438e30i	−0.0352500	+	0.0598933i
$409$	−2.02665e31			−0.924909			−0.462454	−	0.886643i	$-0.653031\pi$
$409$	−2.02665e31			−0.924909			−0.462454	+	0.886643i	$0.653031\pi$
$410$			1.52559e31i			0.676132i
$411$	−1.03268e31	−	6.07779e30i	−0.444491	−	0.261604i
$412$	1.73657e31			0.725982
$413$			2.22381e30i			0.0903018i
$414$	−9.99632e30	−	1.80024e31i	−0.394309	−	0.710112i
$415$	−5.74373e31			−2.20098
$416$		−	6.32116e30i		−	0.235330i
$417$	−2.05426e31	+	3.49040e31i	−0.743060	+	1.26253i
$418$	−9.00622e30			−0.316539
$419$			1.73826e31i			0.593674i	0.954928	+	0.296837i	$0.0959317\pi$
$419$			1.73826e31i			0.593674i	−0.954928	+	0.296837i	$0.904068\pi$
$420$	3.19150e30	+	1.87835e30i	0.105926	+	0.0623426i
$421$	3.94616e31			1.27289			0.636443	−	0.771324i	$-0.280405\pi$
$421$	3.94616e31			1.27289			0.636443	+	0.771324i	$0.280405\pi$
$422$		−	1.60019e31i		−	0.501675i
$423$	−3.48936e31	+	1.93756e31i	−1.06331	+	0.590433i
$424$	1.42327e31			0.421596
$425$		−	1.70482e31i		−	0.490921i
$426$	4.57941e30	−	7.78088e30i	0.128202	−	0.217828i
$427$	5.75388e30			0.156612
$428$			1.89741e31i			0.502152i
$429$	−4.77392e31	−	2.80968e31i	−1.22854	−	0.723051i
$430$	−7.16171e31			−1.79224
$431$			5.04053e31i			1.22673i	0.789799	+	0.613365i	$0.210185\pi$
$431$			5.04053e31i			1.22673i	−0.789799	+	0.613365i	$0.789815\pi$
$432$	−1.05587e31	−	2.64767e29i	−0.249921	−	0.00626698i
$433$	7.89926e31			1.81858			0.909289	−	0.416166i	$-0.136627\pi$
$433$	7.89926e31			1.81858			0.909289	+	0.416166i	$0.136627\pi$
$434$		−	2.46539e30i		−	0.0552089i
$435$	6.63165e31	−	1.12678e32i	1.44461	−	2.45454i
$436$	−4.13282e30			−0.0875808
$437$			2.32916e31i			0.480200i
$438$	6.49236e30	+	3.82106e30i	0.130231	+	0.0766468i
$439$	2.86248e31			0.558687			0.279344	−	0.960191i	$-0.409883\pi$
$439$	2.86248e31			0.558687			0.279344	+	0.960191i	$0.409883\pi$
$440$		−	3.72809e31i		−	0.708034i
$441$	2.58133e31	+	4.64874e31i	0.477069	+	0.859156i
$442$	1.02876e31			0.185031
$443$			4.49140e31i			0.786206i	0.919494	+	0.393103i	$0.128599\pi$
$443$			4.49140e31i			0.786206i	−0.919494	+	0.393103i	$0.871401\pi$
$444$	−7.03587e30	+	1.19546e31i	−0.119873	+	0.203677i
$445$	−2.05271e31			−0.340414
$446$			7.69408e30i			0.124205i
$447$	−1.04317e31	−	6.13956e30i	−0.163933	−	0.0964822i
$448$	−1.07396e30			−0.0164305
$449$			5.39778e31i			0.804006i	0.915638	+	0.402003i	$0.131686\pi$
$449$			5.39778e31i			0.804006i	−0.915638	+	0.402003i	$0.868314\pi$
$450$	1.06458e32	−	5.91137e31i	1.54394	−	0.857311i
$451$	−3.87711e31			−0.547507
$452$		−	3.02549e31i		−	0.416040i
$453$	3.12982e31	−	5.31788e31i	0.419123	−	0.712132i
$454$	−1.09977e31			−0.143428
$455$		−	2.57636e31i		−	0.327243i
$456$	1.02960e31	+	6.05969e30i	0.127377	+	0.0749674i
$457$	−2.97204e31			−0.358146			−0.179073	−	0.983836i	$-0.557310\pi$
$457$	−2.97204e31			−0.358146			−0.179073	+	0.983836i	$0.557310\pi$
$458$		−	3.47315e31i		−	0.407697i
$459$	4.30903e29	−	1.71840e31i	0.00492750	−	0.196504i
$460$	−9.64146e31			−1.07411
$461$			2.21817e31i			0.240759i	0.992728	+	0.120380i	$0.0384112\pi$
$461$			2.21817e31i			0.240759i	−0.992728	+	0.120380i	$0.961589\pi$
$462$	−4.77361e30	+	8.11084e30i	−0.0504828	+	0.0857752i
$463$	1.34906e32			1.39014			0.695072	−	0.718940i	$-0.255372\pi$
$463$	1.34906e32			1.39014			0.695072	+	0.718940i	$0.255372\pi$
$464$			3.79169e31i			0.380730i
$465$	−9.78389e31	−	5.75828e31i	−0.957361	−	0.563452i
$466$	7.32437e31			0.698456
$467$		−	2.20131e31i		−	0.204587i	−0.994754	−	0.102294i	$-0.967382\pi$
$467$		−	2.20131e31i		−	0.204587i	0.994754	−	0.102294i	$-0.0326181\pi$
$468$	3.56716e31	+	6.42411e31i	0.323126	+	0.581919i
$469$	−5.25252e30			−0.0463760
$470$			1.86878e32i			1.60836i
$471$	−1.03995e32	+	1.76699e32i	−0.872496	+	1.48246i
$472$	−2.96971e31			−0.242891
$473$		−	1.82006e32i		−	1.45129i
$474$	−6.24844e31	−	3.67750e31i	−0.485771	−	0.285899i
$475$	−1.37736e32			−1.04406
$476$		−	1.74784e30i		−	0.0129187i
$477$	−1.44645e32	+	8.03178e31i	−1.04251	+	0.578884i
$478$	−6.71760e31			−0.472150
$479$		−	1.84865e32i		−	1.26715i	−0.773681	−	0.633575i	$-0.781587\pi$
$479$		−	1.84865e32i		−	1.26715i	0.773681	−	0.633575i	$-0.218413\pi$
$480$	−2.50838e31	+	4.26199e31i	−0.167687	+	0.284917i
$481$	9.65047e31			0.629228
$482$			2.68879e31i			0.170998i
$483$	2.09760e31	+	1.23454e31i	0.130124	+	0.0765840i
$484$	1.21195e31			0.0733398
$485$			9.49707e31i			0.560646i
$486$	1.08800e32	−	5.68938e31i	0.626607	−	0.327665i
$487$	−8.47310e31			−0.476096			−0.238048	−	0.971253i	$-0.576508\pi$
$487$	−8.47310e31			−0.476096			−0.238048	+	0.971253i	$0.576508\pi$
$488$			7.68383e31i			0.421250i
$489$	1.06314e32	−	1.80637e32i	0.568699	−	0.966275i
$490$	2.48970e32			1.29955
$491$			8.67400e31i			0.441816i	0.975295	+	0.220908i	$0.0709021\pi$
$491$			8.67400e31i			0.441816i	−0.975295	+	0.220908i	$0.929098\pi$
$492$	4.43236e31	+	2.60865e31i	0.220320	+	0.129669i
$493$	−6.17090e31			−0.299354
$494$		−	8.31153e31i		−	0.393512i
$495$	2.10383e32	+	3.78881e32i	0.972186	+	1.75081i
$496$	3.29233e31			0.148499
$497$			1.06716e31i			0.0469845i
$498$	−9.82137e31	+	1.66875e32i	−0.422105	+	0.717198i
$499$	2.49415e32			1.04645			0.523223	−	0.852196i	$-0.324730\pi$
$499$	2.49415e32			1.04645			0.523223	+	0.852196i	$0.324730\pi$
$500$		−	3.41862e32i		−	1.40027i
$501$	−1.37127e32	−	8.07059e31i	−0.548367	−	0.322740i
$502$	−3.08111e32			−1.20299
$503$		−	4.71984e32i		−	1.79933i	−0.436579	−	0.899666i	$-0.643810\pi$
$503$		−	4.71984e32i		−	1.79933i	0.436579	−	0.899666i	$-0.356190\pi$
$504$	1.09145e31	−	6.06056e30i	0.0406291	−	0.0225604i
$505$	2.19026e32			0.796157
$506$		−	2.45027e32i		−	0.869775i
$507$	1.12979e32	−	1.91963e32i	0.391655	−	0.665461i
$508$	−1.30630e31			−0.0442259
$509$		−	1.88162e32i		−	0.622183i	−0.950380	−	0.311091i	$-0.899306\pi$
$509$		−	1.88162e32i		−	0.622183i	0.950380	−	0.311091i	$-0.100694\pi$
$510$	−6.93631e31	−	4.08235e31i	−0.224020	−	0.131846i
$511$	−8.90440e30			−0.0280901
$512$		−	1.43418e31i		−	0.0441942i
$513$	−1.38833e32	−	3.48135e30i	−0.417912	−	0.0104795i
$514$	2.15338e32			0.633234
$515$			9.45193e32i			2.71540i
$516$	−1.22460e32	+	2.08072e32i	−0.343715	+	0.584005i
$517$	−4.74928e32			−1.30239
$518$		−	1.63960e31i		−	0.0439321i
$519$	5.07807e32	+	2.98868e32i	1.32951	+	0.782477i
$520$	3.44053e32			0.880207
$521$			6.65852e31i			0.166466i	0.996530	+	0.0832329i	$0.0265245\pi$
$521$			6.65852e31i			0.166466i	−0.996530	+	0.0832329i	$0.973475\pi$
$522$	−2.13972e32	−	3.85344e32i	−0.522771	−	0.941462i
$523$	−7.70218e30			−0.0183905			−0.00919525	−	0.999958i	$-0.502927\pi$
$523$	−7.70218e30			−0.0183905			−0.00919525	+	0.999958i	$0.502927\pi$
$524$		−	3.19303e31i		−	0.0745121i
$525$	−7.30049e31	+	1.24043e32i	−0.166510	+	0.282917i
$526$	−3.13914e32			−0.699813
$527$			5.35820e31i			0.116759i
$528$	−1.08314e32	−	6.37477e31i	−0.230715	−	0.135787i
$529$	−1.53429e32			−0.319477
$530$			7.74666e32i			1.57690i
$531$	3.01808e32	−	1.67587e32i	0.600616	−	0.333508i
$532$	−1.41212e31			−0.0274746
$533$		−	3.57805e32i		−	0.680644i
$534$	−3.50999e31	+	5.96382e31i	−0.0652846	+	0.110925i
$535$	−1.03273e33			−1.87821
$536$		−	7.01431e31i		−	0.124741i
$537$	1.13370e32	+	6.67235e31i	0.197154	+	0.116035i
$538$	−3.76118e32			−0.639643
$539$			6.32728e32i			1.05233i
$540$	1.44109e31	−	5.74694e32i	0.0234405	−	0.934785i
$541$	6.06284e32			0.964514			0.482257	−	0.876030i	$-0.339817\pi$
$541$	6.06284e32			0.964514			0.482257	+	0.876030i	$0.339817\pi$
$542$			1.16053e32i			0.180578i
$543$	2.44463e32	−	4.15368e32i	0.372062	−	0.632171i
$544$	2.33410e31			0.0347483
$545$		−	2.24944e32i		−	0.327580i
$546$	−7.48521e31	−	4.40540e31i	−0.106633	−	0.0627586i
$547$	−8.04943e32			−1.12180			−0.560902	−	0.827882i	$-0.689546\pi$
$547$	−8.04943e32			−1.12180			−0.560902	+	0.827882i	$0.689546\pi$
$548$			1.89140e32i			0.257880i
$549$	−4.33614e32	−	7.80898e32i	−0.578409	−	1.04166i
$550$	1.44898e33			1.89108
$551$			4.98559e32i			0.636646i
$552$	−1.64862e32	+	2.80117e32i	−0.205993	+	0.350002i
$553$	8.56987e31			0.104779
$554$		−	2.92692e32i		−	0.350182i
$555$	−6.50676e32	−	3.82954e32i	−0.761814	−	0.448364i
$556$	6.39286e32			0.732483
$557$		−	9.36098e32i		−	1.04968i	−0.851200	−	0.524842i	$-0.824124\pi$
$557$		−	9.36098e32i		−	1.04968i	0.851200	−	0.524842i	$-0.175876\pi$
$558$	−3.34595e32	+	1.85793e32i	−0.367205	+	0.203900i
$559$	1.67967e33			1.80420
$560$		−	5.84541e31i		−	0.0614552i
$561$	1.03748e32	−	1.76278e32i	0.106764	−	0.181403i
$562$	1.72563e32			0.173824
$563$			3.63395e32i			0.358326i	0.983819	+	0.179163i	$0.0573389\pi$
$563$			3.63395e32i			0.358326i	−0.983819	+	0.179163i	$0.942661\pi$
$564$	5.42943e32	+	3.19548e32i	0.524089	+	0.308451i
$565$	1.64674e33			1.55612
$566$			4.57577e32i			0.423319i
$567$	−7.67216e31	+	1.23185e32i	−0.0694898	+	0.111574i
$568$	−1.42511e32			−0.126377
$569$			1.56580e33i			1.35953i	0.733431	+	0.679764i	$0.237918\pi$
$569$			1.56580e33i			1.35953i	−0.733431	+	0.679764i	$0.762082\pi$
$570$	−3.29821e32	+	5.60399e32i	−0.280401	+	0.476430i
$571$	−1.35659e33			−1.12932			−0.564659	−	0.825324i	$-0.690992\pi$
$571$	−1.35659e33			−1.12932			−0.564659	+	0.825324i	$0.690992\pi$
$572$			8.74369e32i			0.712759i
$573$	1.08587e33	+	6.39085e32i	0.866806	+	0.510156i
$574$	−6.07907e31			−0.0475220
$575$		−	3.74730e33i		−	2.86883i
$576$	8.09338e31	+	1.45754e32i	0.0606820	+	0.109283i
$577$	−1.34896e33			−0.990578			−0.495289	−	0.868728i	$-0.664938\pi$
$577$	−1.34896e33			−0.990578			−0.495289	+	0.868728i	$0.664938\pi$
$578$		−	9.45161e32i		−	0.679785i
$579$	1.37206e33	−	2.33126e33i	0.966562	−	1.64229i
$580$	−2.06377e33			−1.42405
$581$		−	2.28872e32i		−	0.154696i
$582$	2.75922e32	+	1.62393e32i	0.182688	+	0.107521i
$583$	−1.96872e33			−1.27692
$584$		−	1.18911e32i		−	0.0755558i
$585$	−3.49656e33	+	1.94156e33i	−2.17656	+	1.20859i
$586$	−1.05119e33			−0.641075
$587$			3.28919e33i			1.96531i	0.185437	+	0.982656i	$0.440630\pi$
$587$			3.28919e33i			1.96531i	−0.185437	+	0.982656i	$0.559370\pi$
$588$	4.25721e32	−	7.23342e32i	0.249228	−	0.423463i
$589$	4.32900e32			0.248316
$590$		−	1.61638e33i		−	0.908487i
$591$	2.16348e33	+	1.27331e33i	1.19152	+	0.701267i
$592$	2.18956e32			0.118167
$593$			1.50339e33i			0.795088i	0.917583	+	0.397544i	$0.130137\pi$
$593$			1.50339e33i			0.795088i	−0.917583	+	0.397544i	$0.869863\pi$
$594$	1.46052e33	+	3.66237e31i	0.756954	+	0.0189812i
$595$	9.51330e31			0.0483201
$596$			1.91063e32i			0.0951089i
$597$	−1.97239e33	+	3.35129e33i	−0.962279	+	1.63501i
$598$	2.26127e33			1.08128
$599$		−	2.92781e33i		−	1.37221i	−0.727501	−	0.686107i	$-0.759318\pi$
$599$		−	2.92781e33i		−	1.37221i	0.727501	−	0.686107i	$-0.240682\pi$
$600$	−1.65649e33	−	9.74921e32i	−0.760980	−	0.447872i
$601$	1.78506e33			0.803821			0.401910	−	0.915679i	$-0.368346\pi$
$601$	1.78506e33			0.803821			0.401910	+	0.915679i	$0.368346\pi$
$602$		−	2.85375e32i		−	0.125967i
$603$	3.95832e32	+	7.12856e32i	0.171279	+	0.308456i
$604$	−9.73999e32			−0.413157
$605$			6.59648e32i			0.274314i
$606$	3.74518e32	−	6.36344e32i	0.152687	−	0.259430i
$607$	2.30435e32			0.0921050			0.0460525	−	0.998939i	$-0.485336\pi$
$607$	2.30435e32			0.0921050			0.0460525	+	0.998939i	$0.485336\pi$
$608$		−	1.88577e32i		−	0.0739003i
$609$	4.48993e32	+	2.64254e32i	0.172517	+	0.101534i
$610$	−4.18221e33			−1.57561
$611$		−	4.38295e33i		−	1.61909i
$612$	−2.37212e32	+	1.31718e32i	−0.0859250	+	0.0477121i
$613$	4.46344e33			1.58542			0.792710	−	0.609599i	$-0.208670\pi$
$613$	4.46344e33			1.58542			0.792710	+	0.609599i	$0.208670\pi$
$614$		−	4.66709e32i		−	0.162564i
$615$	−1.41986e33	+	2.41248e33i	−0.485001	+	0.824065i
$616$	1.48554e32			0.0497642
$617$		−	3.92178e32i		−	0.128843i	−0.997923	−	0.0644216i	$-0.979480\pi$
$617$		−	3.92178e32i		−	0.128843i	0.997923	−	0.0644216i	$-0.0205203\pi$
$618$	2.74611e33	+	1.61621e33i	0.884822	+	0.520759i
$619$	−2.74576e32			−0.0867710			−0.0433855	−	0.999058i	$-0.513814\pi$
$619$	−2.74576e32			−0.0867710			−0.0433855	+	0.999058i	$0.513814\pi$
$620$			1.79197e33i			0.555432i
$621$	9.47150e31	−	3.77715e33i	0.0287952	−	1.14832i
$622$	−2.09511e33			−0.624773
$623$		−	8.17950e31i		−	0.0239260i
$624$	5.88305e32	−	9.99589e32i	0.168806	−	0.286818i
$625$	9.73426e33			2.73995
$626$		−	1.46843e33i		−	0.405471i
$627$	−1.42419e33	−	8.38202e32i	−0.385796	−	0.227059i
$628$	3.23633e33			0.860077
$629$			3.56346e32i			0.0929105i
$630$	3.29868e32	+	5.94062e32i	0.0843828	+	0.151965i
$631$	−7.59300e33			−1.90573			−0.952864	−	0.303397i	$-0.901879\pi$
$631$	−7.59300e33			−1.90573			−0.952864	+	0.303397i	$0.901879\pi$
$632$			1.14444e33i			0.281830i
$633$	1.48929e33	−	2.53045e33i	0.359860	−	0.611439i
$634$	1.01047e33			0.239580
$635$		−	7.11000e32i		−	0.165419i
$636$	2.25067e33	+	1.32462e33i	0.513838	+	0.302418i
$637$	−5.83923e33			−1.30823
$638$		−	5.24482e33i		−	1.15314i
$639$	1.44832e33	−	8.04219e32i	0.312503	−	0.173526i
$640$	7.80607e32			0.165300
$641$			5.38294e33i			1.11872i	0.828924	+	0.559362i	$0.188954\pi$
$641$			5.38294e33i			1.11872i	−0.828924	+	0.559362i	$0.811046\pi$
$642$	−1.76590e33	+	3.00044e33i	−0.360202	+	0.612020i
$643$	−5.58872e32			−0.111887			−0.0559436	−	0.998434i	$-0.517817\pi$
$643$	−5.58872e32			−0.111887			−0.0559436	+	0.998434i	$0.517817\pi$
$644$		−	3.84187e32i		−	0.0754939i
$645$	−1.13251e34	−	6.66535e33i	−2.18436	−	1.28560i
$646$	3.06906e32			0.0581052
$647$			9.97296e33i			1.85342i	0.375783	+	0.926708i	$0.377374\pi$
$647$			9.97296e33i			1.85342i	−0.375783	+	0.926708i	$0.622626\pi$
$648$	−1.64504e33	−	1.02455e33i	−0.300107	−	0.186911i
$649$	4.10784e33			0.735659
$650$			1.33721e34i			2.35093i
$651$	2.29452e32	−	3.89862e32i	0.0396023	−	0.0672882i
$652$	−3.30847e33			−0.560604
$653$			6.38820e32i			0.106272i	0.998587	+	0.0531362i	$0.0169217\pi$
$653$			6.38820e32i			0.106272i	−0.998587	+	0.0531362i	$0.983078\pi$
$654$	−6.53539e32	−	3.84639e32i	−0.106743	−	0.0628232i
$655$	1.73792e33			0.278699
$656$		−	8.11810e32i		−	0.127823i
$657$	6.71039e32	+	1.20848e33i	0.103744	+	0.186833i
$658$	−7.44658e32			−0.113044
$659$		−	6.90599e33i		−	1.02944i	−0.857359	−	0.514720i	$-0.827896\pi$
$659$		−	6.90599e33i		−	1.02944i	0.857359	−	0.514720i	$-0.172104\pi$
$660$	3.46970e33	−	5.89537e33i	0.507885	−	0.862947i
$661$	−1.70554e33			−0.245156			−0.122578	−	0.992459i	$-0.539116\pi$
$661$	−1.70554e33			−0.245156			−0.122578	+	0.992459i	$0.539116\pi$
$662$			3.04556e33i			0.429904i
$663$	1.62681e33	+	9.57455e32i	0.225515	+	0.132726i
$664$	3.05641e33			0.416096
$665$		−	7.68599e32i		−	0.102764i
$666$	−2.22522e33	+	1.23561e33i	−0.292201	+	0.162252i
$667$	−1.35640e34			−1.74935
$668$			2.51156e33i			0.318146i
$669$	−7.16083e32	+	1.21670e33i	−0.0890943	+	0.151380i
$670$	3.81780e33			0.466569
$671$		−	1.06286e34i		−	1.27587i
$672$	−1.69829e32	−	9.99524e31i	−0.0200254	−	0.0117859i
$673$	5.28039e33			0.611625			0.305813	−	0.952092i	$-0.401072\pi$
$673$	5.28039e33			0.611625			0.305813	+	0.952092i	$0.401072\pi$
$674$		−	7.18758e33i		−	0.817832i
$675$	2.23363e34	+	5.60102e32i	2.49670	+	0.0626068i
$676$	−3.51591e33			−0.386080
$677$			1.06855e34i			1.15274i	0.817188	+	0.576371i	$0.195532\pi$
$677$			1.06855e34i			1.15274i	−0.817188	+	0.576371i	$0.804468\pi$
$678$	2.81580e33	−	4.78433e33i	0.298432	−	0.507066i
$679$	−3.78433e32			−0.0394050
$680$			1.27042e33i			0.129970i
$681$	−1.73912e33	−	1.02355e33i	−0.174809	−	0.102883i
$682$	−4.55409e33			−0.449769
$683$			6.35426e32i			0.0616618i	0.999525	+	0.0308309i	$0.00981534\pi$
$683$			6.35426e32i			0.0616618i	−0.999525	+	0.0308309i	$0.990185\pi$
$684$	1.06418e33	+	1.91649e33i	0.101471	+	0.182739i
$685$	−1.02947e34			−0.964552
$686$			2.00160e33i			0.184284i
$687$	3.23243e33	−	5.49222e33i	0.292448	−	0.496898i
$688$	3.81095e33			0.338822
$689$		−	1.81687e34i		−	1.58742i
$690$	−1.52464e34	−	8.97324e33i	−1.30912	−	0.770478i
$691$	2.02979e34			1.71283			0.856417	−	0.516284i	$-0.172685\pi$
$691$	2.02979e34			1.71283			0.856417	+	0.516284i	$0.172685\pi$
$692$		−	9.30076e33i		−	0.771339i
$693$	−1.50974e33	+	8.38322e32i	−0.123056	+	0.0683301i
$694$	1.08222e34			0.866969
$695$			3.47955e34i			2.73972i
$696$	−3.52889e33	+	5.99594e33i	−0.273104	+	0.464031i
$697$	1.32121e33			0.100503
$698$		−	1.53801e34i		−	1.14999i
$699$	1.15823e34	+	6.81673e33i	0.851274	+	0.501014i
$700$	2.27191e33			0.164140
$701$		−	1.31882e34i		−	0.936633i	−0.883561	−	0.468317i	$-0.844861\pi$
$701$		−	1.31882e34i		−	0.936633i	0.883561	−	0.468317i	$-0.155139\pi$
$702$	−3.37987e32	+	1.34786e34i	−0.0235969	+	0.941023i
$703$	2.87900e33			0.197596
$704$			1.98382e33i			0.133854i
$705$	−1.73926e34	+	2.95517e34i	−1.15370	+	1.96026i
$706$	−3.91514e31			−0.00255324
$707$			8.72759e32i			0.0559579i
$708$	−4.69613e33	−	2.76389e33i	−0.296033	−	0.174230i
$709$	1.70214e34			1.05497			0.527487	−	0.849563i	$-0.323134\pi$
$709$	1.70214e34			1.05497			0.527487	+	0.849563i	$0.323134\pi$
$710$		−	7.75670e33i		−	0.472690i
$711$	−6.45829e33	−	1.16308e34i	−0.386974	−	0.696904i
$712$	1.09231e33			0.0643553
$713$			1.17776e34i			0.682313i
$714$	1.62671e32	−	2.76394e32i	0.00926682	−	0.0157452i
$715$	−4.75908e34			−2.66594
$716$		−	2.07643e33i		−	0.114383i
$717$	−1.06228e34	−	6.25202e33i	−0.575453	−	0.338681i
$718$	3.14887e33			0.167750
$719$			9.84142e33i			0.515598i	0.966199	+	0.257799i	$0.0829972\pi$
$719$			9.84142e33i			0.515598i	−0.966199	+	0.257799i	$0.917003\pi$
$720$	−7.93321e33	+	4.40512e33i	−0.408751	+	0.226970i
$721$	−3.76634e33			−0.190852
$722$			1.17088e34i			0.583533i
$723$	−2.50243e33	+	4.25188e33i	−0.122660	+	0.208411i
$724$	−7.60768e33			−0.366767
$725$		−	8.02114e34i		−	3.80347i
$726$	1.91650e33	+	1.12795e33i	0.0893861	+	0.0526079i
$727$	−3.38827e34			−1.55441			−0.777205	−	0.629247i	$-0.783363\pi$
$727$	−3.38827e34			−1.55441			−0.777205	+	0.629247i	$0.783363\pi$
$728$			1.37096e33i			0.0618653i
$729$	2.25001e34	+	1.12913e33i	0.998743	+	0.0501201i
$730$	6.47218e33			0.282603
$731$			6.20225e33i			0.266404i
$732$	−7.15129e33	+	1.21507e34i	−0.302170	+	0.513417i
$733$	6.94273e33			0.288591			0.144295	−	0.989535i	$-0.453908\pi$
$733$	6.94273e33			0.288591			0.144295	+	0.989535i	$0.453908\pi$
$734$			1.44032e34i			0.588986i
$735$	3.93706e34	+	2.31714e34i	1.58389	+	0.932191i
$736$	5.13050e33			0.203061
$737$			9.70250e33i			0.377810i
$738$	4.58121e33	+	8.25032e33i	0.175511	+	0.316078i
$739$	4.80426e34			1.81090			0.905448	−	0.424458i	$-0.139535\pi$
$739$	4.80426e34			1.81090			0.905448	+	0.424458i	$0.139535\pi$
$740$			1.19175e34i			0.441982i
$741$	7.73548e33	−	1.31434e34i	0.282273	−	0.479609i
$742$	−3.08684e33			−0.110832
$743$			5.57616e33i			0.197001i	0.995137	+	0.0985007i	$0.0314047\pi$
$743$			5.57616e33i			0.197001i	−0.995137	+	0.0985007i	$0.968595\pi$
$744$	5.20629e33	+	3.06415e33i	0.180989	+	0.106521i
$745$	−1.03993e34			−0.355737
$746$			1.20762e34i			0.406505i
$747$	−3.10618e34	+	1.72479e34i	−1.02892	+	0.571333i
$748$	−3.22863e33			−0.105245
$749$		−	4.11517e33i		−	0.132010i
$750$	3.18168e34	−	5.40600e34i	1.00444	−	1.70664i
$751$	2.09656e34			0.651371			0.325685	−	0.945478i	$-0.394405\pi$
$751$	2.09656e34			0.651371			0.325685	+	0.945478i	$0.394405\pi$
$752$		−	9.94431e33i		−	0.304061i
$753$	−4.87228e34	−	2.86757e34i	−1.46620	−	0.862927i
$754$	4.84027e34			1.43355
$755$		−	5.30135e34i		−	1.54534i
$756$	2.29000e33	+	5.74237e31i	0.0657014	+	0.00164751i
$757$	−2.59094e34			−0.731657			−0.365829	−	0.930682i	$-0.619214\pi$
$757$	−2.59094e34			−0.731657			−0.365829	+	0.930682i	$0.619214\pi$
$758$			1.52113e34i			0.422801i
$759$	2.28044e34	−	3.87470e34i	0.623905	−	1.06008i
$760$	1.02640e34			0.276410
$761$			6.37561e34i			1.69008i	0.534707	+	0.845038i	$0.320422\pi$
$761$			6.37561e34i			1.69008i	−0.534707	+	0.845038i	$0.679578\pi$
$762$	−2.06570e33	−	1.21576e33i	−0.0539023	−	0.0317240i
$763$	8.96343e32			0.0230239
$764$		−	1.98883e34i		−	0.502895i
$765$	−7.16925e33	−	1.29111e34i	−0.178458	−	0.321387i
$766$	−5.20887e34			−1.27643
$767$			3.79098e34i			0.914549i
$768$	1.33478e33	−	2.26793e33i	0.0317012	−	0.0538635i
$769$	4.52884e34			1.05894			0.529470	−	0.848329i	$-0.322391\pi$
$769$	4.52884e34			1.05894			0.529470	+	0.848329i	$0.322391\pi$
$770$			8.08563e33i			0.186134i
$771$	3.40523e34	+	2.00414e34i	0.771781	+	0.454230i
$772$	−4.26984e34			−0.952804
$773$		−	2.41056e34i		−	0.529619i	−0.964301	−	0.264810i	$-0.914691\pi$
$773$		−	2.41056e34i		−	0.529619i	0.964301	−	0.264810i	$-0.0853091\pi$
$774$	−3.87302e34	+	2.15060e34i	−0.837834	+	0.465229i
$775$	−6.96477e34			−1.48350
$776$		−	5.05366e33i		−	0.105990i
$777$	1.52597e33	−	2.59277e33i	0.0315132	−	0.0535441i
$778$	−1.56260e34			−0.317755
$779$		−	1.06743e34i		−	0.213742i
$780$	5.44064e34	+	3.20207e34i	1.07279	+	0.631387i
$781$	1.97127e34			0.382767
$782$			8.34979e33i			0.159659i
$783$	2.02739e33	−	8.08502e34i	0.0381764	−	1.52244i
$784$	−1.32484e34			−0.245681
$785$			1.76149e35i			3.21696i
$786$	2.97173e33	−	5.04926e33i	0.0534488	−	0.0908149i
$787$	−2.11726e33			−0.0375040			−0.0187520	−	0.999824i	$-0.505969\pi$
$787$	−2.11726e33			−0.0375040			−0.0187520	+	0.999824i	$0.505969\pi$
$788$		−	3.96252e34i		−	0.691285i
$789$	−4.96405e34	−	2.92158e34i	−0.852927	−	0.501988i
$790$	−6.22902e34			−1.05413
$791$			6.56181e33i			0.109372i
$792$	−1.11951e34	−	2.01613e34i	−0.183792	−	0.330992i
$793$	9.80878e34			1.58612
$794$		−	3.07636e34i		−	0.489995i
$795$	−7.20976e34	+	1.22501e35i	−1.13114	+	1.92192i
$796$	6.13807e34			0.948582
$797$			1.31847e34i			0.200711i	0.994952	+	0.100355i	$0.0319979\pi$
$797$			1.31847e34i			0.200711i	−0.994952	+	0.100355i	$0.968002\pi$
$798$	−2.23304e33	−	1.31425e33i	−0.0334859	−	0.0197080i
$799$	1.61842e34			0.239072
$800$			3.03395e34i			0.441497i
$801$	−1.11010e34	+	6.16410e33i	−0.159137	+	0.0883649i
$802$	−9.07495e33			−0.128160
$803$			1.64483e34i			0.228841i
$804$	6.52817e33	−	1.10920e34i	0.0894785	−	0.152033i
$805$	2.09108e34			0.282371
$806$		−	4.20281e34i		−	0.559139i
$807$	−5.94771e34	−	3.50051e34i	−0.779592	−	0.458826i
$808$	−1.16550e34			−0.150514
$809$		−	5.48800e34i		−	0.698284i	−0.937070	−	0.349142i	$-0.886473\pi$
$809$		−	5.48800e34i		−	0.698284i	0.937070	−	0.349142i	$-0.113527\pi$
$810$	5.57652e34	−	8.95374e34i	0.699106	−	1.12249i
$811$	−2.02114e34			−0.249659			−0.124829	−	0.992178i	$-0.539838\pi$
$811$	−2.02114e34			−0.249659			−0.124829	+	0.992178i	$0.539838\pi$
$812$		−	8.22356e33i		−	0.100089i
$813$	−1.08009e34	+	1.83519e34i	−0.129531	+	0.220087i
$814$	−3.02869e34			−0.357900
$815$		−	1.80076e35i		−	2.09683i
$816$	3.69101e33	+	2.17233e33i	0.0423510	+	0.0249255i
$817$	5.01092e34			0.566569
$818$			5.86980e34i			0.654009i
$819$	−7.73659e33	−	1.39329e34i	−0.0849459	−	0.152980i
$820$	4.41858e34			0.478098
$821$			4.91287e34i			0.523862i	0.965087	+	0.261931i	$0.0843593\pi$
$821$			4.91287e34i			0.523862i	−0.965087	+	0.261931i	$0.915641\pi$
$822$	−1.76032e34	+	2.99095e34i	−0.184982	+	0.314302i
$823$	1.85256e35			1.91856			0.959279	−	0.282461i	$-0.0911507\pi$
$823$	1.85256e35			1.91856			0.959279	+	0.282461i	$0.0911507\pi$
$824$		−	5.02964e34i		−	0.513347i
$825$	2.29132e35	+	1.34855e35i	2.30483	+	1.35650i
$826$	6.44083e33			0.0638530
$827$		−	1.63343e35i		−	1.59600i	−0.602654	−	0.798002i	$-0.705890\pi$
$827$		−	1.63343e35i		−	1.59600i	0.602654	−	0.798002i	$-0.294110\pi$
$828$	−5.21406e34	+	2.89524e34i	−0.502125	+	0.278818i
$829$	−1.13394e35			−1.07630			−0.538152	−	0.842848i	$-0.680877\pi$
$829$	−1.13394e35			−1.07630			−0.538152	+	0.842848i	$0.680877\pi$
$830$			1.66356e35i			1.55633i
$831$	2.72406e34	−	4.62845e34i	0.251191	−	0.426799i
$832$	−1.83080e34			−0.166403
$833$		−	2.15615e34i		−	0.193170i
$834$	1.01093e35	+	5.94978e34i	0.892745	+	0.525422i
$835$	−1.36701e35			−1.18997
$836$			2.60848e34i			0.223827i
$837$	−7.02024e34	−	1.76038e33i	−0.593809	−	0.0148902i
$838$	5.03455e34			0.419791
$839$			2.05511e34i			0.168924i	0.996427	+	0.0844622i	$0.0269172\pi$
$839$			2.05511e34i			0.168924i	−0.996427	+	0.0844622i	$0.973083\pi$
$840$	5.44028e33	−	9.24358e33i	0.0440829	−	0.0749012i
$841$	−1.65154e35			−1.31928
$842$		−	1.14293e35i		−	0.900066i
$843$	2.72880e34	+	1.60603e34i	0.211856	+	0.124687i
$844$	−4.63465e34			−0.354738
$845$		−	1.91367e35i		−	1.44406i
$846$	5.61177e34	+	1.01063e35i	0.417499	+	0.751876i
$847$	−2.62852e33			−0.0192802
$848$		−	4.12222e34i		−	0.298113i
$849$	−4.25864e34	+	7.23585e34i	−0.303654	+	0.515938i
$850$	−4.93769e34			−0.347134
$851$			7.83271e34i			0.542947i
$852$	−2.25358e34	−	1.32634e34i	−0.154028	−	0.0906525i
$853$	−1.23579e35			−0.832832			−0.416416	−	0.909174i	$-0.636714\pi$
$853$	−1.23579e35			−0.832832			−0.416416	+	0.909174i	$0.636714\pi$
$854$		−	1.66650e34i		−	0.110742i
$855$	−1.04312e35	+	5.79219e34i	−0.683503	+	0.379533i
$856$	5.49548e34			0.355075
$857$			1.56805e35i			0.999055i	0.866298	+	0.499527i	$0.166493\pi$
$857$			1.56805e35i			0.999055i	−0.866298	+	0.499527i	$0.833507\pi$
$858$	−8.13769e34	+	1.38267e35i	−0.511274	+	0.868706i
$859$	−1.59845e35			−0.990330			−0.495165	−	0.868799i	$-0.664892\pi$
$859$	−1.59845e35			−0.990330			−0.495165	+	0.868799i	$0.664892\pi$
$860$			2.07425e35i			1.26730i
$861$	−9.61307e33	−	5.65774e33i	−0.0579194	−	0.0340883i
$862$	1.45989e35			0.867430
$863$			6.37895e34i			0.373783i	0.982381	+	0.186892i	$0.0598413\pi$
$863$			6.37895e34i			0.373783i	−0.982381	+	0.186892i	$0.940159\pi$
$864$	−7.66846e32	+	3.05811e34i	−0.00443143	+	0.176721i
$865$	5.06229e35			2.88505
$866$		−	2.28787e35i		−	1.28593i
$867$	8.79655e34	−	1.49462e35i	0.487622	−	0.828518i
$868$	−7.14053e33			−0.0390386
$869$		−	1.58303e35i		−	0.853597i
$870$	−3.26352e35	−	1.92073e35i	−1.73562	−	1.02149i
$871$	−8.95411e34			−0.469682
$872$			1.19699e34i			0.0619290i
$873$	2.85188e34	+	5.13597e34i	0.145533	+	0.262091i
$874$	6.74597e34			0.339553
$875$			7.41444e34i			0.368114i
$876$	1.10670e34	−	1.88039e34i	0.0541975	−	0.0920869i
$877$	−3.55972e35			−1.71957			−0.859787	−	0.510652i	$-0.829404\pi$
$877$	−3.55972e35			−1.71957			−0.859787	+	0.510652i	$0.829404\pi$
$878$		−	8.29064e34i		−	0.395051i
$879$	−1.66229e35	−	9.78333e34i	−0.781338	−	0.459854i
$880$	−1.07977e35			−0.500656
$881$			1.83672e35i			0.840101i	0.907501	+	0.420050i	$0.137988\pi$
$881$			1.83672e35i			0.840101i	−0.907501	+	0.420050i	$0.862012\pi$
$882$	1.34642e35	−	7.47634e34i	0.607515	−	0.337339i
$883$	1.85716e35			0.826647			0.413324	−	0.910584i	$-0.364368\pi$
$883$	1.85716e35			0.826647			0.413324	+	0.910584i	$0.364368\pi$
$884$		−	2.97960e34i		−	0.130837i
$885$	1.50435e35	−	2.55604e35i	0.651673	−	1.10726i
$886$	1.30085e35			0.555932
$887$			2.36928e35i			0.998926i	0.866335	+	0.499463i	$0.166469\pi$
$887$			2.36928e35i			0.998926i	−0.866335	+	0.499463i	$0.833531\pi$
$888$	3.46244e34	+	2.03781e34i	0.144021	+	0.0847632i
$889$	2.83315e33			0.0116265
$890$			5.94529e34i			0.240709i
$891$	2.27549e35	+	1.41721e35i	0.908955	+	0.566110i
$892$	2.22844e34			0.0878261
$893$		−	1.30755e35i		−	0.508442i
$894$	−1.77821e34	+	3.02135e34i	−0.0682232	+	0.115918i
$895$	1.13018e35			0.427828
$896$			3.11051e33i			0.0116181i
$897$	3.57583e35	+	2.10454e35i	1.31785	+	0.775619i
$898$	1.56337e35			0.568518
$899$			2.52102e35i			0.904606i
$900$	−1.71212e35	−	3.08336e35i	−0.606210	−	1.09173i
$901$	6.70884e34			0.234396
$902$			1.12293e35i			0.387146i
$903$	2.65596e34	−	4.51274e34i	0.0903585	−	0.153528i
$904$	−8.76276e34			−0.294185
$905$		−	4.14077e35i		−	1.37182i
$906$	−1.54022e35	−	9.06494e34i	−0.503553	−	0.296365i
$907$	5.44825e35			1.75780			0.878901	−	0.477004i	$-0.158277\pi$
$907$	5.44825e35			1.75780			0.878901	+	0.477004i	$0.158277\pi$
$908$			3.18529e34i			0.101419i
$909$	1.18448e35	−	6.57714e34i	0.372187	−	0.206667i
$910$	−7.46195e34			−0.231396
$911$			9.49061e34i			0.290452i	0.989399	+	0.145226i	$0.0463908\pi$
$911$			9.49061e34i			0.290452i	−0.989399	+	0.145226i	$0.953609\pi$
$912$	1.75507e34	−	2.98204e34i	0.0530099	−	0.0900692i
$913$	−4.22775e35			−1.26026
$914$			8.60795e34i			0.253248i
$915$	−6.61350e35	−	3.89235e35i	−1.92034	−	1.13021i
$916$	−1.00593e35			−0.288285
$917$			6.92516e33i			0.0195883i
$918$	−4.97702e34	−	1.24803e33i	−0.138950	−	0.00348427i
$919$	−2.17698e35			−0.599885			−0.299943	−	0.953957i	$-0.596968\pi$
$919$	−2.17698e35			−0.599885			−0.299943	+	0.953957i	$0.596968\pi$
$920$			2.79247e35i			0.759511i
$921$	4.34362e34	−	7.38025e34i	0.116610	−	0.198132i
$922$	6.42450e34			0.170243
$923$			1.81922e35i			0.475845i
$924$	2.34915e34	+	1.38258e34i	0.0606522	+	0.0356967i
$925$	−4.63191e35			−1.18048
$926$		−	3.90730e35i		−	0.982981i
$927$	2.83833e35	+	5.11156e35i	0.704865	+	1.26940i
$928$	1.09819e35			0.269216
$929$			7.35473e35i			1.77983i	0.456127	+	0.889915i	$0.349236\pi$
$929$			7.35473e35i			1.77983i	−0.456127	+	0.889915i	$0.650764\pi$
$930$	−1.66778e35	+	2.83372e35i	−0.398421	+	0.676957i
$931$	−1.74200e35			−0.410820
$932$		−	2.12136e35i		−	0.493883i
$933$	−3.31308e35	−	1.94990e35i	−0.761469	−	0.448160i
$934$	−6.37567e34			−0.144665
$935$		−	1.75730e35i		−	0.393648i
$936$	1.86062e35	−	1.03316e35i	0.411479	−	0.228485i
$937$	−6.48186e35			−1.41522			−0.707611	−	0.706602i	$-0.750227\pi$
$937$	−6.48186e35			−1.41522			−0.707611	+	0.706602i	$0.750227\pi$
$938$			1.52129e34i			0.0327928i
$939$	1.36665e35	−	2.32208e35i	0.290851	−	0.494185i
$940$	5.41256e35			1.13728
$941$		−	3.85253e35i		−	0.799229i	−0.916683	−	0.399614i	$-0.869144\pi$
$941$		−	3.85253e35i		−	0.799229i	0.916683	−	0.399614i	$-0.130856\pi$
$942$	5.11774e35	+	3.01203e35i	1.04826	+	0.616948i
$943$	2.90409e35			0.587313
$944$			8.60121e34i			0.171750i
$945$	−3.12550e33	+	1.24642e35i	−0.00616222	+	0.245744i
$946$	−5.27147e35			−1.02621
$947$		−	4.72280e35i		−	0.907820i	−0.891048	−	0.453910i	$-0.850029\pi$
$947$		−	4.72280e35i		−	0.907820i	0.891048	−	0.453910i	$-0.149971\pi$
$948$	−1.06512e35	+	1.80974e35i	−0.202161	+	0.343492i
$949$	−1.51796e35			−0.284488
$950$			3.98926e35i			0.738260i
$951$	1.59789e35	+	9.40432e34i	0.291998	+	0.171855i
$952$	−5.06230e33			−0.00913491
$953$			1.06604e36i			1.89959i	0.312877	+	0.949794i	$0.398707\pi$
$953$			1.06604e36i			1.89959i	−0.312877	+	0.949794i	$0.601293\pi$
$954$	2.32625e35	+	4.18936e35i	0.409333	+	0.737169i
$955$	1.08249e36			1.88098
$956$			1.94563e35i			0.333860i
$957$	4.88132e35	−	8.29384e35i	0.827168	−	1.40544i
$958$	−5.35426e35			−0.896011
$959$		−	4.10215e34i		−	0.0677936i
$960$	1.23441e35	+	7.26506e34i	0.201467	+	0.118573i
$961$	−4.01512e35			−0.647170
$962$		−	2.79508e35i		−	0.444931i
$963$	−5.58498e35	+	3.10121e35i	−0.878024	+	0.487546i
$964$	7.78755e34			0.120914
$965$		−	2.32402e36i		−	3.56379i
$966$	3.57560e34	−	6.07529e34i	0.0541531	−	0.0920114i
$967$	1.18623e36			1.77439			0.887197	−	0.461391i	$-0.152649\pi$
$967$	1.18623e36			1.77439			0.887197	+	0.461391i	$0.152649\pi$
$968$		−	3.51018e34i		−	0.0518591i
$969$	4.85322e34	+	2.85635e34i	0.0708182	+	0.0416798i
$970$	2.75064e35			0.396437
$971$		−	9.47421e35i		−	1.34869i	−0.738416	−	0.674345i	$-0.764426\pi$
$971$		−	9.47421e35i		−	1.34869i	0.738416	−	0.674345i	$-0.235574\pi$
$972$	−1.64782e35	−	3.15119e35i	−0.231694	−	0.443078i
$973$	−1.38651e35			−0.192561
$974$			2.45407e35i			0.336651i
$975$	−1.24453e36	+	2.11458e36i	−1.68636	+	2.86530i
$976$	2.22548e35			0.297869
$977$		−	3.91558e35i		−	0.517679i	−0.965920	−	0.258840i	$-0.916660\pi$
$977$		−	3.91558e35i		−	0.517679i	0.965920	−	0.258840i	$-0.0833401\pi$
$978$	−5.23181e35	−	3.07917e35i	−0.683260	−	0.402131i
$979$	−1.51093e35			−0.194917
$980$		−	7.21094e35i		−	0.918923i
$981$	−6.75487e34	−	1.21649e35i	−0.0850333	−	0.153137i
$982$	2.51226e35			0.312411
$983$		−	8.43619e35i		−	1.03634i	−0.855276	−	0.518172i	$-0.826613\pi$
$983$		−	8.43619e35i		−	1.03634i	0.855276	−	0.518172i	$-0.173387\pi$
$984$	7.55546e34	−	1.28375e35i	0.0916895	−	0.155790i
$985$	2.15675e36			2.58562
$986$			1.78728e35i			0.211675i
$987$	−1.17756e35	−	6.93048e34i	−0.137777	−	0.0810882i
$988$	−2.40728e35			−0.278255
$989$			1.36329e36i			1.55680i
$990$	1.09736e36	−	6.09336e35i	1.23801	−	0.687439i
$991$	−1.42451e36			−1.58775			−0.793876	−	0.608079i	$-0.791940\pi$
$991$	−1.42451e36			−1.58775			−0.793876	+	0.608079i	$0.791940\pi$
$992$		−	9.53560e34i		−	0.105005i
$993$	−2.83448e35	+	4.81606e35i	−0.308377	+	0.523964i
$994$	3.09084e34			0.0332230
$995$			3.34087e36i			3.54800i
$996$	4.83321e35	+	2.84457e35i	0.507135	+	0.298473i
$997$	8.85938e35			0.918463			0.459231	−	0.888317i	$-0.348125\pi$
$997$	8.85938e35			0.918463			0.459231	+	0.888317i	$0.348125\pi$
$998$		−	7.22384e35i		−	0.739949i
$999$	−4.66880e35	−	1.17074e34i	−0.472519	−	0.0118488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.25.b.a.5.3	✓	8
3.2	odd	2	inner	6.25.b.a.5.7	yes	8
4.3	odd	2		48.25.e.d.17.4		8
12.11	even	2		48.25.e.d.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.25.b.a.5.3	✓	8	1.1	even	1	trivial
6.25.b.a.5.7	yes	8	3.2	odd	2	inner
48.25.e.d.17.3		8	12.11	even	2
48.25.e.d.17.4		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2896.31i q^{2} +(269557. - 458005. i) q^{3} -8.38861e6 q^{4} -4.56581e8i q^{5} +(-1.32652e9 - 7.80721e8i) q^{6} +1.81935e9 q^{7} +2.42960e10i q^{8} +(-1.37107e11 - 2.46917e11i) q^{9} +O(q^{10})\)	\(q-2896.31i q^{2} +(269557. - 458005. i) q^{3} -8.38861e6 q^{4} -4.56581e8i q^{5} +(-1.32652e9 - 7.80721e8i) q^{6} +1.81935e9 q^{7} +2.42960e10i q^{8} +(-1.37107e11 - 2.46917e11i) q^{9} -1.32240e12 q^{10} -3.36073e12i q^{11} +(-2.26121e12 + 3.84202e12i) q^{12} +3.10150e13 q^{13} -5.26941e12i q^{14} +(-2.09116e14 - 1.23075e14i) q^{15} +7.03687e13 q^{16} +1.14524e14i q^{17} +(-7.15148e14 + 3.97105e14i) q^{18} +9.25261e14 q^{19} +3.83008e15i q^{20} +(4.90420e14 - 8.33273e14i) q^{21} -9.73371e15 q^{22} +2.51730e16i q^{23} +(1.11277e16 + 6.54917e15i) q^{24} -1.48862e17 q^{25} -8.98290e16i q^{26} +(-1.50047e17 - 3.76256e15i) q^{27} -1.52619e16 q^{28} +5.38831e17i q^{29} +(-3.56463e17 + 6.05666e17i) q^{30} +4.67868e17 q^{31} -2.03810e17i q^{32} +(-1.53923e18 - 9.05909e17i) q^{33} +3.31696e17 q^{34} -8.30683e17i q^{35} +(1.15014e18 + 2.07129e18i) q^{36} +3.11155e18 q^{37} -2.67984e18i q^{38} +(8.36032e18 - 1.42050e19i) q^{39} +1.10931e19 q^{40} -1.15365e19i q^{41} +(-2.41342e18 - 1.42041e18i) q^{42} +5.41569e19 q^{43} +2.81918e19i q^{44} +(-1.12738e20 + 6.26006e19i) q^{45} +7.29088e19 q^{46} -1.41317e20i q^{47} +(1.89684e19 - 3.22292e19i) q^{48} -1.88271e20 q^{49} +4.31150e20i q^{50} +(5.24524e19 + 3.08707e19i) q^{51} -2.60173e20 q^{52} -5.85803e20i q^{53} +(-1.08975e19 + 4.34584e20i) q^{54} -1.53445e21 q^{55} +4.42030e19i q^{56} +(2.49411e20 - 4.23774e20i) q^{57} +1.56062e21 q^{58} +1.22231e21i q^{59} +(1.75420e21 + 1.03243e21i) q^{60} +3.16259e21 q^{61} -1.35509e21i q^{62} +(-2.49447e20 - 4.49230e20i) q^{63} -5.90296e20 q^{64} -1.41609e22i q^{65} +(-2.62379e21 + 4.45808e21i) q^{66} -2.88702e21 q^{67} -9.60695e20i q^{68} +(1.15294e22 + 6.78557e21i) q^{69} -2.40592e21 q^{70} +5.86562e21i q^{71} +(5.99910e21 - 3.33116e21i) q^{72} -4.89426e21 q^{73} -9.01201e21i q^{74} +(-4.01268e22 + 6.81794e22i) q^{75} -7.76165e21 q^{76} -6.11435e21i q^{77} +(-4.11421e22 - 2.42141e22i) q^{78} +4.71039e22 q^{79} -3.21290e22i q^{80} +(-4.21697e22 + 6.77082e22i) q^{81} -3.34133e22 q^{82} -1.25799e23i q^{83} +(-4.11394e21 + 6.99000e21i) q^{84} +5.22894e22 q^{85} -1.56855e23i q^{86} +(2.46787e23 + 1.45246e23i) q^{87} +8.16522e22 q^{88} -4.49583e22i q^{89} +(1.81311e23 + 3.26523e23i) q^{90} +5.64273e22 q^{91} -2.11166e23i q^{92} +(1.26117e23 - 2.14286e23i) q^{93} -4.09298e23 q^{94} -4.22457e23i q^{95} +(-9.33458e22 - 5.49384e22i) q^{96} -2.08004e23 q^{97} +5.45292e23i q^{98} +(-8.29821e23 + 4.60780e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9}+O(q^{10}) \) 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9	\( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 36\!\cdots\!36 q^{21}+ \cdots + 69\!\cdots\!44 q^{99}+O(q^{100}) \) 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9 - 1863369424896 * q^10 + 1106289623040 * q^12 + 50568363679120 * q^13 - 348034956760512 * q^15 + 562949953421312 * q^16 - 514738292981760 * q^18 - 978083631341264 * q^19 + 3640012304241936 * q^21 - 336450979430400 * q^22 - 282849366245376 * q^24 + 7630618767014024 * q^25 - 86594528606057640 * q^27 + 85234923203461120 * q^28 - 725410188900237312 * q^30 + 3092119786822709104 * q^31 - 8158685952668529600 * q^33 + 3821138032531341312 * q^34 - 2476057486864416768 * q^36 + 22590293223992782480 * q^37 - 40190176581881465040 * q^39 + 15631075664637984768 * q^40 - 79119883835565342720 * q^42 + 226487466371803896880 * q^43 - 347709996757177504128 * q^45 + 139842130561120468992 * q^46 - 9280229982150328320 * q^48 + 104686700473616731800 * q^49 + 558091874936566543104 * q^51 - 424198180105575464960 * q^52 + 334066775626796728320 * q^54 - 2212687664250467338368 * q^55 + 3588879995640760725840 * q^57 - 1867706355469718323200 * q^58 + 2919528822560885047296 * q^60 - 6507010783838092385648 * q^61 + 10112982777612899380080 * q^63 - 4722366482869645213696 * q^64 - 1924112442339530440704 * q^66 - 7042120118150060144720 * q^67 - 4323335967368731345536 * q^69 + 16481910236435553583104 * q^70 + 4317937762413135790080 * q^72 + 36259820324758576687120 * q^73 - 108081978448612908655272 * q^75 + 8204760174538377920512 * q^76 - 74188898027329578270720 * q^78 + 316807052777330015315824 * q^79 - 268518660504396776813304 * q^81 + 83114941529654645882880 * q^82 - 30534636335462338265088 * q^84 - 222512862545524200678912 * q^85 + 449461577201807342128320 * q^87 + 2822355377657688883200 * q^88 + 612683975543382025371648 * q^90 - 1196839602335690774367520 * q^91 + 873237537450828783745680 * q^93 - 1298887117621773403422720 * q^94 + 2372712456480891076608 * q^96 + 816517576248201265716880 * q^97 + 695858883367208922313344 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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