LMFDB - Embedded newform 10.26.b.a.9.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	10.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:	$39.5996779952$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 1406300109694 x^{10} + \cdots + 56\!\cdots\!01 $ x^12 + 1406300109694x^10 + 721371039010841274826815x^8 + 163583579306250445630287276512319780x^6 + 14727031184488621294308896513370084274619782815x^4 + 213559114414440049199738916498397853721503585895983619294*x^2 + 562442837480837791206109989109268286491448310078170789537309341601
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{8}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.8
Root			$-508420. i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.26.b.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00i q^{2} -1.01684e6i q^{3} -1.67772e7 q^{4} +(-2.64029e8 + 4.77820e8i) q^{5} +4.16497e9 q^{6} -1.16326e10i q^{7} -6.87195e10i q^{8} -1.86674e11 q^{9} +(-1.95715e12 - 1.08146e12i) q^{10} -5.94667e12 q^{11} +1.70597e13i q^{12} +8.19186e13i q^{13} +4.76472e13 q^{14} +(4.85866e14 + 2.68475e14i) q^{15} +2.81475e14 q^{16} +1.37679e15i q^{17} -7.64617e14i q^{18} -4.66320e15 q^{19} +(4.42968e15 - 8.01649e15i) q^{20} -1.18285e16 q^{21} -2.43576e16i q^{22} -9.70196e16i q^{23} -6.98767e16 q^{24} +(-1.58600e17 - 2.52317e17i) q^{25} -3.35539e17 q^{26} -6.71739e17i q^{27} +1.95163e17i q^{28} +1.92842e18 q^{29} +(-1.09968e18 + 1.99011e18i) q^{30} +5.14163e18 q^{31} +1.15292e18i q^{32} +6.04681e18i q^{33} -5.63933e18 q^{34} +(5.55829e18 + 3.07135e18i) q^{35} +3.13187e18 q^{36} -4.77086e19i q^{37} -1.91005e19i q^{38} +8.32981e19 q^{39} +(3.28355e19 + 1.81440e19i) q^{40} +1.13507e20 q^{41} -4.84495e19i q^{42} -9.41611e18i q^{43} +9.97685e19 q^{44} +(4.92874e19 - 8.91965e19i) q^{45} +3.97392e20 q^{46} -1.09883e21i q^{47} -2.86215e20i q^{48} +1.20575e21 q^{49} +(1.03349e21 - 6.49627e20i) q^{50} +1.39998e21 q^{51} -1.37437e21i q^{52} -6.11805e20i q^{53} +2.75144e21 q^{54} +(1.57009e21 - 2.84144e21i) q^{55} -7.99387e20 q^{56} +4.74172e21i q^{57} +7.89879e21i q^{58} +1.74642e22 q^{59} +(-8.15148e21 - 4.50427e21i) q^{60} +2.94578e21 q^{61} +2.10601e22i q^{62} +2.17151e21i q^{63} -4.72237e21 q^{64} +(-3.91423e22 - 2.16289e22i) q^{65} -2.47677e22 q^{66} -5.85392e22i q^{67} -2.30987e22i q^{68} -9.86533e22 q^{69} +(-1.25802e22 + 2.27668e22i) q^{70} -2.27224e23 q^{71} +1.28281e22i q^{72} +2.69974e23i q^{73} +1.95415e23 q^{74} +(-2.56566e23 + 1.61271e23i) q^{75} +7.82355e22 q^{76} +6.91753e22i q^{77} +3.41189e23i q^{78} +9.35155e23 q^{79} +(-7.43176e22 + 1.34494e23i) q^{80} -8.41218e23 q^{81} +4.64926e23i q^{82} -1.71255e24i q^{83} +1.98449e23 q^{84} +(-6.57858e23 - 3.63513e23i) q^{85} +3.85684e22 q^{86} -1.96089e24i q^{87} +4.08652e23i q^{88} +2.89830e24 q^{89} +(3.65349e23 + 2.01881e23i) q^{90} +9.52927e23 q^{91} +1.62772e24i q^{92} -5.22821e24i q^{93} +4.50081e24 q^{94} +(1.23122e24 - 2.22817e24i) q^{95} +1.17234e24 q^{96} +1.13099e24i q^{97} +4.93876e24i q^{98} +1.11009e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 201326592 q^{4} - 490295340 q^{5} - 6565199872 q^{6} - 1082937564236 q^{9} + 1636528619520 q^{10} + 19723089228624 q^{11} + 278591122243584 q^{14} - 449884766537680 q^{15} + 33\!\cdots\!72 q^{16}+ \cdots + 41\!\cdots\!28 q^{99}+O(q^{100}) $ 12 * q - 201326592 * q^4 - 490295340 * q^5 - 6565199872 * q^6 - 1082937564236 * q^9 + 1636528619520 * q^10 + 19723089228624 * q^11 + 278591122243584 * q^14 - 449884766537680 * q^15 + 3377699720527872 * q^16 - 4015312977833040 * q^19 + 8225790822973440 * q^20 - 56363420582029456 * q^21 + 110145776335716352 * q^24 - 1047554086248996900 * q^25 - 252210272532037632 * q^26 + 5852064063311009640 * q^29 - 3747916483574824960 * q^30 + 158585871554029824 * q^31 + 28121800210885115904 * q^34 - 42730948507221221040 * q^35 + 18168677429701246976 * q^36 - 249453273245123586912 * q^39 - 27456394139868856320 * q^40 + 206458603439752488024 * q^41 - 330898528175898230784 * q^44 + 957114913653485255020 * q^45 - 1111751773656740462592 * q^46 - 3432561496278055389084 * q^49 + 346631457781510963200 * q^50 - 3032451787323924027136 * q^51 + 6455741354411915345920 * q^54 - 7824754202169531625680 * q^55 - 4673983433563013382144 * q^56 + 24998150261761560337680 * q^59 + 7547813903312229498880 * q^60 + 7374571220622236593224 * q^61 - 56668397794435742564352 * q^64 + 20652620138653742557920 * q^65 + 56072959085731865952256 * q^66 - 370250651964757999709072 * q^69 + 157367128964587932549120 * q^70 + 149137752442507323299424 * q^71 + 27409492362780459270144 * q^74 + 1032897211530510645911200 * q^75 + 67365773136708124016640 * q^76 + 801700633747623249599040 * q^79 - 138005869407843165143040 * q^80 - 2864220237232227656687428 * q^81 + 945621281603553901674496 * q^84 + 2004099032091709203221760 * q^85 - 1363071174568488987328512 * q^86 - 5964345056120682049233480 * q^89 + 4840324611668628597309440 * q^90 - 14003423438242038482629536 * q^91 + 3325183945859356082110464 * q^94 + 18644670331946084490382800 * q^95 - 1847939481072001752236032 * q^96 + 4107440578564823447146928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

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

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 $

$2$			4096.00i			0.707107i
$2$			4096.00i			0.707107i
$3$		−	1.01684e6i		−	1.10468i	−0.833619	−	0.552340i	$-0.813735\pi$
$3$		−	1.01684e6i		−	1.10468i	0.833619	−	0.552340i	$-0.186265\pi$
$4$	−1.67772e7			−0.500000
$5$	−2.64029e8	+	4.77820e8i	−0.483645	+	0.875264i
$5$	−2.64029e8	+	4.77820e8i	−0.483645	+	0.875264i
$6$	4.16497e9			0.781127
$7$		−	1.16326e10i		−	0.317652i	−0.987307	−	0.158826i	$-0.949229\pi$
$7$		−	1.16326e10i		−	0.317652i	0.987307	−	0.158826i	$-0.0507709\pi$
$8$		−	6.87195e10i		−	0.353553i
$9$	−1.86674e11			−0.220319
$10$	−1.95715e12	−	1.08146e12i	−0.618905	−	0.341989i
$11$	−5.94667e12			−0.571301			−0.285651	−	0.958334i	$-0.592210\pi$
$11$	−5.94667e12			−0.571301			−0.285651	+	0.958334i	$0.592210\pi$
$12$			1.70597e13i			0.552340i
$13$			8.19186e13i			0.975193i	0.873069	+	0.487597i	$0.162126\pi$
$13$			8.19186e13i			0.975193i	−0.873069	+	0.487597i	$0.837874\pi$
$14$	4.76472e13			0.224614
$15$	4.85866e14	+	2.68475e14i	0.966887	+	0.534274i
$16$	2.81475e14			0.250000
$17$			1.37679e15i			0.573134i	0.958060	+	0.286567i	$0.0925141\pi$
$17$			1.37679e15i			0.573134i	−0.958060	+	0.286567i	$0.907486\pi$
$18$		−	7.64617e14i		−	0.155789i
$19$	−4.66320e15			−0.483352			−0.241676	−	0.970357i	$-0.577697\pi$
$19$	−4.66320e15			−0.483352			−0.241676	+	0.970357i	$0.577697\pi$
$20$	4.42968e15	−	8.01649e15i	0.241823	−	0.437632i
$21$	−1.18285e16			−0.350904
$22$		−	2.43576e16i		−	0.403971i
$23$		−	9.70196e16i		−	0.923127i	−0.887107	−	0.461563i	$-0.847289\pi$
$23$		−	9.70196e16i		−	0.923127i	0.887107	−	0.461563i	$-0.152711\pi$
$24$	−6.98767e16			−0.390564
$25$	−1.58600e17	−	2.52317e17i	−0.532174	−	0.846635i
$26$	−3.35539e17			−0.689566
$27$		−	6.71739e17i		−	0.861298i
$28$			1.95163e17i			0.158826i
$29$	1.92842e18			1.01211			0.506053	−	0.862503i	$-0.331104\pi$
$29$	1.92842e18			1.01211			0.506053	+	0.862503i	$0.331104\pi$
$30$	−1.09968e18	+	1.99011e18i	−0.377788	+	0.683693i
$31$	5.14163e18			1.17241			0.586205	−	0.810163i	$-0.300621\pi$
$31$	5.14163e18			1.17241			0.586205	+	0.810163i	$0.300621\pi$
$32$			1.15292e18i			0.176777i
$33$			6.04681e18i			0.631105i
$34$	−5.63933e18			−0.405267
$35$	5.55829e18	+	3.07135e18i	0.278029	+	0.153631i
$36$	3.13187e18			0.110160
$37$		−	4.77086e19i		−	1.19145i	−0.803189	−	0.595725i	$-0.796865\pi$
$37$		−	4.77086e19i		−	1.19145i	0.803189	−	0.595725i	$-0.203135\pi$
$38$		−	1.91005e19i		−	0.341782i
$39$	8.32981e19			1.07728
$40$	3.28355e19	+	1.81440e19i	0.309453	+	0.170994i
$41$	1.13507e20			0.785644			0.392822	−	0.919615i	$-0.371499\pi$
$41$	1.13507e20			0.785644			0.392822	+	0.919615i	$0.371499\pi$
$42$		−	4.84495e19i		−	0.248127i
$43$		−	9.41611e18i		−	0.0359348i	−0.999839	−	0.0179674i	$-0.994280\pi$
$43$		−	9.41611e18i		−	0.0359348i	0.999839	−	0.0179674i	$-0.00571951\pi$
$44$	9.97685e19			0.285651
$45$	4.92874e19	−	8.91965e19i	0.106556	−	0.192838i
$46$	3.97392e20			0.652749
$47$		−	1.09883e21i		−	1.37946i	−0.724069	−	0.689728i	$-0.757730\pi$
$47$		−	1.09883e21i		−	1.37946i	0.724069	−	0.689728i	$-0.242270\pi$
$48$		−	2.86215e20i		−	0.276170i
$49$	1.20575e21			0.899097
$50$	1.03349e21	−	6.49627e20i	0.598661	−	0.376304i
$51$	1.39998e21			0.633130
$52$		−	1.37437e21i		−	0.487597i
$53$		−	6.11805e20i		−	0.171066i	−0.996335	−	0.0855331i	$-0.972741\pi$
$53$		−	6.11805e20i		−	0.171066i	0.996335	−	0.0855331i	$-0.0272594\pi$
$54$	2.75144e21			0.609030
$55$	1.57009e21	−	2.84144e21i	0.276307	−	0.500039i
$56$	−7.99387e20			−0.112307
$57$			4.74172e21i			0.533950i
$58$			7.89879e21i			0.715667i
$59$	1.74642e22			1.27791			0.638954	−	0.769245i	$-0.279368\pi$
$59$	1.74642e22			1.27791			0.638954	+	0.769245i	$0.279368\pi$
$60$	−8.15148e21	−	4.50427e21i	−0.483444	−	0.267137i
$61$	2.94578e21			0.142095			0.0710473	−	0.997473i	$-0.477366\pi$
$61$	2.94578e21			0.142095			0.0710473	+	0.997473i	$0.477366\pi$
$62$			2.10601e22i			0.829019i
$63$			2.17151e21i			0.0699849i
$64$	−4.72237e21			−0.125000
$65$	−3.91423e22	−	2.16289e22i	−0.853552	−	0.471648i
$66$	−2.47677e22			−0.446259
$67$		−	5.85392e22i		−	0.874001i	−0.899461	−	0.437000i	$-0.856041\pi$
$67$		−	5.85392e22i		−	0.874001i	0.899461	−	0.437000i	$-0.143959\pi$
$68$		−	2.30987e22i		−	0.286567i
$69$	−9.86533e22			−1.01976
$70$	−1.25802e22	+	2.27668e22i	−0.108633	+	0.196597i
$71$	−2.27224e23			−1.64333			−0.821665	−	0.569970i	$-0.806955\pi$
$71$	−2.27224e23			−1.64333			−0.821665	+	0.569970i	$0.806955\pi$
$72$			1.28281e22i			0.0778946i
$73$			2.69974e23i			1.37971i	0.723949	+	0.689853i	$0.242325\pi$
$73$			2.69974e23i			1.37971i	−0.723949	+	0.689853i	$0.757675\pi$
$74$	1.95415e23			0.842482
$75$	−2.56566e23	+	1.61271e23i	−0.935261	+	0.587883i
$76$	7.82355e22			0.241676
$77$			6.91753e22i			0.181475i
$78$			3.41189e23i			0.761750i
$79$	9.35155e23			1.78051			0.890257	−	0.455459i	$-0.150525\pi$
$79$	9.35155e23			1.78051			0.890257	+	0.455459i	$0.150525\pi$
$80$	−7.43176e22	+	1.34494e23i	−0.120911	+	0.218816i
$81$	−8.41218e23			−1.17178
$82$			4.64926e23i			0.555534i
$83$		−	1.71255e24i		−	1.75860i	−0.476264	−	0.879302i	$-0.658009\pi$
$83$		−	1.71255e24i		−	1.75860i	0.476264	−	0.879302i	$-0.341991\pi$
$84$	1.98449e23			0.175452
$85$	−6.57858e23	−	3.63513e23i	−0.501644	−	0.277194i
$86$	3.85684e22			0.0254098
$87$		−	1.96089e24i		−	1.11805i
$88$			4.08652e23i			0.201985i
$89$	2.89830e24			1.24385			0.621926	−	0.783076i	$-0.286350\pi$
$89$	2.89830e24			1.24385			0.621926	+	0.783076i	$0.286350\pi$
$90$	3.65349e23	+	2.01881e23i	0.136357	+	0.0753467i
$91$	9.52927e23			0.309772
$92$			1.62772e24i			0.461563i
$93$		−	5.22821e24i		−	1.29514i
$94$	4.50081e24			0.975422
$95$	1.23122e24	−	2.22817e24i	0.233771	−	0.423061i
$96$	1.17234e24			0.195282
$97$			1.13099e24i			0.165506i	0.996570	+	0.0827529i	$0.0263712\pi$
$97$			1.13099e24i			0.165506i	−0.996570	+	0.0827529i	$0.973629\pi$
$98$			4.93876e24i			0.635758i
$99$	1.11009e24			0.125869
$100$	2.66087e24	+	4.23317e24i	0.266087	+	0.423317i
$101$	−1.20834e25			−1.06702			−0.533510	−	0.845794i	$-0.679127\pi$
$101$	−1.20834e25			−1.06702			−0.533510	+	0.845794i	$0.679127\pi$
$102$			5.73430e24i			0.447691i
$103$		−	1.70464e23i		−	0.0117806i	−0.999983	−	0.00589030i	$-0.998125\pi$
$103$		−	1.70464e23i		−	0.0117806i	0.999983	−	0.00589030i	$-0.00187495\pi$
$104$	5.62940e24			0.344783
$105$	3.12307e24	−	5.65189e24i	0.169713	−	0.307134i
$106$	2.50595e24			0.120962
$107$		−	1.25315e25i		−	0.537906i	−0.963153	−	0.268953i	$-0.913322\pi$
$107$		−	1.25315e25i		−	0.537906i	0.963153	−	0.268953i	$-0.0866776\pi$
$108$			1.12699e25i			0.430649i
$109$	−5.31922e25			−1.81141			−0.905704	−	0.423910i	$-0.860657\pi$
$109$	−5.31922e25			−1.81141			−0.905704	+	0.423910i	$0.860657\pi$
$110$	1.16385e25	+	6.43111e24i	0.353581	+	0.195379i
$111$	−4.85120e25			−1.31617
$112$		−	3.27429e24i		−	0.0794130i
$113$			1.81999e25i			0.394991i	0.980304	+	0.197496i	$0.0632808\pi$
$113$			1.81999e25i			0.394991i	−0.980304	+	0.197496i	$0.936719\pi$
$114$	−1.94221e25			−0.377560
$115$	4.63579e25	+	2.56160e25i	0.807980	+	0.446466i
$116$	−3.23535e25			−0.506053
$117$		−	1.52921e25i		−	0.214854i
$118$			7.15335e25i			0.903617i
$119$	1.60157e25			0.182057
$120$	1.84495e25	−	3.33885e25i	0.188894	−	0.341846i
$121$	−7.29842e25			−0.673615
$122$			1.20659e25i			0.100476i
$123$		−	1.15419e26i		−	0.867886i
$124$	−8.62622e25			−0.586205
$125$	1.62437e26	−	9.16337e24i	0.998413	−	0.0563223i
$126$	−8.89449e24			−0.0494868
$127$			4.54166e25i			0.228912i	0.993428	+	0.114456i	$0.0365125\pi$
$127$			4.54166e25i			0.228912i	−0.993428	+	0.114456i	$0.963488\pi$
$128$		−	1.93428e25i		−	0.0883883i
$129$	−9.57467e24			−0.0396965
$130$	8.85920e25	−	1.60327e26i	0.333505	−	0.603552i
$131$	3.22369e26			1.10271			0.551356	−	0.834270i	$-0.314110\pi$
$131$	3.22369e26			1.10271			0.551356	+	0.834270i	$0.314110\pi$
$132$		−	1.01449e26i		−	0.315553i
$133$			5.42452e25i			0.153538i
$134$	2.39777e26			0.618012
$135$	3.20970e26	+	1.77359e26i	0.753863	+	0.416563i
$136$	9.46123e25			0.202634
$137$			5.61602e26i			1.09754i	0.835973	+	0.548771i	$0.184904\pi$
$137$			5.61602e26i			1.09754i	−0.835973	+	0.548771i	$0.815096\pi$
$138$		−	4.04084e26i		−	0.721079i
$139$	7.44482e26			1.21386			0.606931	−	0.794755i	$-0.292400\pi$
$139$	7.44482e26			1.21386			0.606931	+	0.794755i	$0.292400\pi$
$140$	−9.32527e25	−	5.15287e25i	−0.139015	−	0.0768155i
$141$	−1.11733e27			−1.52386
$142$		−	9.30710e26i		−	1.16201i
$143$		−	4.87143e26i		−	0.557129i
$144$	−5.25441e25			−0.0550798
$145$	−5.09158e26	+	9.21435e26i	−0.489500	+	0.885860i
$146$	−1.10581e27			−0.975600
$147$		−	1.22606e27i		−	0.993215i
$148$			8.00418e26i			0.595725i
$149$	9.58450e26			0.655754			0.327877	−	0.944720i	$-0.393667\pi$
$149$	9.58450e26			0.655754			0.327877	+	0.944720i	$0.393667\pi$
$150$	−6.60566e26	−	1.05089e27i	−0.415696	−	0.661329i
$151$	8.90889e26			0.515955			0.257978	−	0.966151i	$-0.416944\pi$
$151$	8.90889e26			0.515955			0.257978	+	0.966151i	$0.416944\pi$
$152$			3.20452e26i			0.170891i
$153$		−	2.57011e26i		−	0.126273i
$154$	−2.83342e26			−0.128322
$155$	−1.35754e27	+	2.45677e27i	−0.567031	+	1.02617i
$156$	−1.39751e27			−0.538639
$157$			4.44904e27i			1.58314i	0.611076	+	0.791572i	$0.290737\pi$
$157$			4.44904e27i			1.58314i	−0.611076	+	0.791572i	$0.709263\pi$
$158$			3.83040e27i			1.25901i
$159$	−6.22107e26			−0.188974
$160$	−5.50889e26	−	3.04405e26i	−0.154726	−	0.0854972i
$161$	−1.12859e27			−0.293233
$162$		−	3.44563e27i		−	0.828573i
$163$			1.89357e27i			0.421634i	0.977526	+	0.210817i	$0.0676124\pi$
$163$			1.89357e27i			0.421634i	−0.977526	+	0.210817i	$0.932388\pi$
$164$	−1.90434e27			−0.392822
$165$	−2.88928e27	−	1.59653e27i	−0.552384	−	0.305231i
$166$	7.01462e27			1.24352
$167$		−	2.78772e27i		−	0.458451i	−0.973373	−	0.229226i	$-0.926381\pi$
$167$		−	2.78772e27i		−	0.458451i	0.973373	−	0.229226i	$-0.0736194\pi$
$168$			8.12848e26i			0.124063i
$169$	3.45751e26			0.0489982
$170$	1.48895e27	−	2.69459e27i	0.196006	−	0.354716i
$171$	8.70498e26			0.106492
$172$			1.57976e26i			0.0179674i
$173$		−	1.54571e28i		−	1.63513i	−0.575836	−	0.817565i	$-0.695323\pi$
$173$		−	1.54571e28i		−	1.63513i	0.575836	−	0.817565i	$-0.304677\pi$
$174$	8.03180e27			0.790583
$175$	−2.93510e27	+	1.84494e27i	−0.268935	+	0.169046i
$176$	−1.67384e27			−0.142825
$177$		−	1.77583e28i		−	1.41168i
$178$			1.18715e28i			0.879536i
$179$	−1.48885e28			−1.02846			−0.514232	−	0.857651i	$-0.671923\pi$
$179$	−1.48885e28			−1.02846			−0.514232	+	0.857651i	$0.671923\pi$
$180$	−8.26905e26	+	1.49647e27i	−0.0532782	+	0.0964188i
$181$	2.99166e28			1.79858			0.899291	−	0.437351i	$-0.144083\pi$
$181$	2.99166e28			1.79858			0.899291	+	0.437351i	$0.144083\pi$
$182$			3.90319e27i			0.219042i
$183$		−	2.99539e27i		−	0.156969i
$184$	−6.66713e27			−0.326375
$185$	2.27961e28	+	1.25965e28i	1.04283	+	0.576239i
$186$	2.14148e28			0.915802
$187$		−	8.18732e27i		−	0.327432i
$188$			1.84353e28i			0.689728i
$189$	−7.81408e27			−0.273593
$190$	9.12658e27	+	5.04308e27i	0.299149	+	0.165301i
$191$	1.13139e28			0.347292			0.173646	−	0.984808i	$-0.444445\pi$
$191$	1.13139e28			0.347292			0.173646	+	0.984808i	$0.444445\pi$
$192$			4.80189e27i			0.138085i
$193$		−	6.86928e26i		−	0.0185116i	−0.999957	−	0.00925582i	$-0.997054\pi$
$193$		−	6.86928e26i		−	0.0185116i	0.999957	−	0.00925582i	$-0.00294626\pi$
$194$	−4.63255e27			−0.117030
$195$	−2.19931e28	+	3.98015e28i	−0.521020	+	0.942902i
$196$	−2.02291e28			−0.449549
$197$		−	7.22234e28i		−	1.50609i	−0.657970	−	0.753044i	$-0.728585\pi$
$197$		−	7.22234e28i		−	1.50609i	0.657970	−	0.753044i	$-0.271415\pi$
$198$			4.54692e27i			0.0890026i
$199$	−6.41046e28			−1.17822			−0.589110	−	0.808053i	$-0.700521\pi$
$199$	−6.41046e28			−1.17822			−0.589110	+	0.808053i	$0.700521\pi$
$200$	−1.73391e28	+	1.08989e28i	−0.299331	+	0.188152i
$201$	−5.95250e28			−0.965492
$202$		−	4.94936e28i		−	0.754497i
$203$		−	2.24325e28i		−	0.321497i
$204$	−2.34877e28			−0.316565
$205$	−2.99693e28	+	5.42361e28i	−0.379973	+	0.687646i
$206$	6.98220e26			0.00833014
$207$			1.81110e28i			0.203383i
$208$			2.30580e28i			0.243798i
$209$	2.77305e28			0.276140
$210$	2.31501e28	+	1.27921e28i	0.217176	+	0.120005i
$211$	−2.74461e28			−0.242633			−0.121317	−	0.992614i	$-0.538712\pi$
$211$	−2.74461e28			−0.242633			−0.121317	+	0.992614i	$0.538712\pi$
$212$			1.02644e28i			0.0855331i
$213$			2.31050e29i			1.81536i
$214$	5.13290e28			0.380357
$215$	4.49920e27	+	2.48613e27i	0.0314525	+	0.0173797i
$216$	−4.61616e28			−0.304515
$217$		−	5.98106e28i		−	0.372419i
$218$		−	2.17875e29i		−	1.28086i
$219$	2.74521e29			1.52414
$220$	−2.63418e28	+	4.76714e28i	−0.138154	+	0.250020i
$221$	−1.12785e29			−0.558917
$222$		−	1.98705e29i		−	0.930673i
$223$			2.58596e29i			1.14502i	0.819899	+	0.572508i	$0.194029\pi$
$223$			2.58596e29i			1.14502i	−0.819899	+	0.572508i	$0.805971\pi$
$224$	1.34115e28			0.0561535
$225$	2.96066e28	+	4.71010e28i	0.117248	+	0.186530i
$226$	−7.45466e28			−0.279301
$227$		−	4.86361e29i		−	1.72439i	−0.506578	−	0.862194i	$-0.669090\pi$
$227$		−	4.86361e29i		−	1.72439i	0.506578	−	0.862194i	$-0.330910\pi$
$228$		−	7.95529e28i		−	0.266975i
$229$	4.91096e29			1.56035			0.780176	−	0.625560i	$-0.215130\pi$
$229$	4.91096e29			1.56035			0.780176	+	0.625560i	$0.215130\pi$
$230$	−1.04923e29	+	1.89882e29i	−0.315699	+	0.571328i
$231$	7.03402e28			0.200472
$232$		−	1.32520e29i		−	0.357833i
$233$			2.93368e29i			0.750696i	0.926884	+	0.375348i	$0.122477\pi$
$233$			2.93368e29i			0.750696i	−0.926884	+	0.375348i	$0.877523\pi$
$234$	6.26363e28			0.151925
$235$	5.25043e29	+	2.90124e29i	1.20739	+	0.667167i
$236$	−2.93001e29			−0.638954
$237$		−	9.50903e29i		−	1.96690i
$238$			6.56002e28i			0.128734i
$239$	2.65452e28			0.0494324			0.0247162	−	0.999695i	$-0.492132\pi$
$239$	2.65452e28			0.0494324			0.0247162	+	0.999695i	$0.492132\pi$
$240$	1.36759e29	+	7.55691e28i	0.241722	+	0.133568i
$241$	−6.46401e27			−0.0108465			−0.00542324	−	0.999985i	$-0.501726\pi$
$241$	−6.46401e27			−0.0108465			−0.00542324	+	0.999985i	$0.501726\pi$
$242$		−	2.98943e29i		−	0.476318i
$243$			2.86226e29i			0.433143i
$244$	−4.94220e28			−0.0710473
$245$	−3.18354e29	+	5.76132e29i	−0.434844	+	0.786947i
$246$	4.72755e29			0.613688
$247$		−	3.82003e29i		−	0.471362i
$248$		−	3.53330e29i		−	0.414510i
$249$	−1.74139e30			−1.94270
$250$	3.75332e28	+	6.65342e29i	0.0398259	+	0.705984i
$251$	−5.06787e29			−0.511569			−0.255785	−	0.966734i	$-0.582334\pi$
$251$	−5.06787e29			−0.511569			−0.255785	+	0.966734i	$0.582334\pi$
$252$		−	3.64318e28i		−	0.0349924i
$253$			5.76943e29i			0.527383i
$254$	−1.86026e29			−0.161865
$255$	−3.69634e29	+	6.68936e29i	−0.306210	+	0.554156i
$256$	7.92282e28			0.0625000
$257$		−	8.16135e29i		−	0.613194i	−0.951839	−	0.306597i	$-0.900810\pi$
$257$		−	8.16135e29i		−	0.613194i	0.951839	−	0.306597i	$-0.0991904\pi$
$258$		−	3.92178e28i		−	0.0280697i
$259$	−5.54976e29			−0.378466
$260$	6.56699e29	+	3.62873e29i	0.426776	+	0.235824i
$261$	−3.59985e29			−0.222986
$262$			1.32042e30i			0.779736i
$263$			1.16241e30i			0.654505i	0.944937	+	0.327253i	$0.106123\pi$
$263$			1.16241e30i			0.654505i	−0.944937	+	0.327253i	$0.893877\pi$
$264$	4.15533e29			0.223129
$265$	2.92332e29	+	1.61534e29i	0.149728	+	0.0827354i
$266$	−2.22188e29			−0.108568
$267$		−	2.94711e30i		−	1.37406i
$268$			9.82125e29i			0.437000i
$269$	−1.07881e30			−0.458184			−0.229092	−	0.973405i	$-0.573576\pi$
$269$	−1.07881e30			−0.458184			−0.229092	+	0.973405i	$0.573576\pi$
$270$	−7.26461e29	+	1.31469e30i	−0.294554	+	0.533062i
$271$	2.07856e30			0.804723			0.402362	−	0.915481i	$-0.368189\pi$
$271$	2.07856e30			0.804723			0.402362	+	0.915481i	$0.368189\pi$
$272$			3.87532e29i			0.143284i
$273$		−	9.68974e29i		−	0.342199i
$274$	−2.30032e30			−0.776080
$275$	9.43144e29	+	1.50044e30i	0.304032	+	0.483683i
$276$	1.65513e30			0.509880
$277$		−	4.81866e30i		−	1.41883i	−0.704793	−	0.709413i	$-0.748960\pi$
$277$		−	4.81866e30i		−	1.41883i	0.704793	−	0.709413i	$-0.251040\pi$
$278$			3.04940e30i			0.858330i
$279$	−9.59809e29			−0.258305
$280$	2.11062e29	−	3.81963e29i	0.0543167	−	0.0982983i
$281$	3.81522e30			0.939054			0.469527	−	0.882918i	$-0.344424\pi$
$281$	3.81522e30			0.939054			0.469527	+	0.882918i	$0.344424\pi$
$282$		−	4.57660e30i		−	1.07753i
$283$		−	3.50448e30i		−	0.789392i	−0.918812	−	0.394696i	$-0.870850\pi$
$283$		−	3.50448e30i		−	0.789392i	0.918812	−	0.394696i	$-0.129150\pi$
$284$	3.81219e30			0.821665
$285$	−2.26569e30	−	1.25195e30i	−0.467347	−	0.258242i
$286$	1.99534e30			0.393950
$287$		−	1.32039e30i		−	0.249561i
$288$		−	2.15220e29i		−	0.0389473i
$289$	3.87508e30			0.671517
$290$	−3.77420e30	−	2.08551e30i	−0.626397	−	0.346129i
$291$	1.15004e30			0.182831
$292$		−	4.52942e30i		−	0.689853i
$293$			1.01157e30i			0.147622i	0.997272	+	0.0738111i	$0.0235162\pi$
$293$			1.01157e30i			0.147622i	−0.997272	+	0.0738111i	$0.976484\pi$
$294$	5.02192e30			0.702309
$295$	−4.61107e30	+	8.34476e30i	−0.618054	+	1.11851i
$296$	−3.27851e30			−0.421241
$297$			3.99461e30i			0.492061i
$298$			3.92581e30i			0.463688i
$299$	7.94771e30			0.900227
$300$	4.30446e30	−	2.70568e30i	0.467630	−	0.293941i
$301$	−1.09534e29			−0.0114148
$302$			3.64908e30i			0.364835i
$303$			1.22869e31i			1.17872i
$304$	−1.31257e30			−0.120838
$305$	−7.77772e29	+	1.40755e30i	−0.0687234	+	0.124370i
$306$	1.05272e30			0.0892882
$307$			1.27764e31i			1.04035i	0.854060	+	0.520174i	$0.174133\pi$
$307$			1.27764e31i			1.04035i	−0.854060	+	0.520174i	$0.825867\pi$
$308$		−	1.16057e30i		−	0.0907375i
$309$	−1.73334e29			−0.0130138
$310$	−1.00629e31	−	5.56049e30i	−0.725611	−	0.400951i
$311$	−1.19771e31			−0.829556			−0.414778	−	0.909923i	$-0.636141\pi$
$311$	−1.19771e31			−0.829556			−0.414778	+	0.909923i	$0.636141\pi$
$312$		−	5.72420e30i		−	0.380875i
$313$		−	2.39996e31i		−	1.53426i	−0.641492	−	0.767130i	$-0.721684\pi$
$313$		−	2.39996e31i		−	1.53426i	0.641492	−	0.767130i	$-0.278316\pi$
$314$	−1.82233e31			−1.11945
$315$	−1.03759e30	−	5.73341e29i	−0.0612553	−	0.0338479i
$316$	−1.56893e31			−0.890257
$317$			5.21982e30i			0.284718i	0.989815	+	0.142359i	$0.0454687\pi$
$317$			5.21982e30i			0.284718i	−0.989815	+	0.142359i	$0.954531\pi$
$318$		−	2.54815e30i		−	0.133625i
$319$	−1.14677e31			−0.578217
$320$	1.24684e30	−	2.25644e30i	0.0604557	−	0.109408i
$321$	−1.27425e31			−0.594214
$322$		−	4.62271e30i		−	0.207347i
$323$		−	6.42025e30i		−	0.277026i
$324$	1.41133e31			0.585889
$325$	2.06694e31	−	1.29923e31i	0.825632	−	0.518973i
$326$	−7.75605e30			−0.298140
$327$			5.40879e31i			2.00103i
$328$		−	7.80017e30i		−	0.277767i
$329$	−1.27823e31			−0.438187
$330$	6.53940e30	−	1.18345e31i	0.215831	−	0.390594i
$331$	2.99801e31			0.952759			0.476379	−	0.879240i	$-0.341949\pi$
$331$	2.99801e31			0.952759			0.476379	+	0.879240i	$0.341949\pi$
$332$			2.87319e31i			0.879302i
$333$			8.90596e30i			0.262499i
$334$	1.14185e31			0.324174
$335$	2.79712e31	+	1.54561e31i	0.764981	+	0.422706i
$336$	−3.32943e30			−0.0877260
$337$		−	2.25223e31i		−	0.571792i	−0.958261	−	0.285896i	$-0.907709\pi$
$337$		−	2.25223e31i		−	0.571792i	0.958261	−	0.285896i	$-0.0922913\pi$
$338$			1.41620e30i			0.0346469i
$339$	1.85063e31			0.436339
$340$	1.10370e31	+	6.09874e30i	0.250822	+	0.138597i
$341$	−3.05756e31			−0.669800
$342$			3.56556e30i			0.0753011i
$343$		−	2.96262e31i		−	0.603252i
$344$	−6.47070e29			−0.0127049
$345$	2.60474e31	−	4.71385e31i	0.493202	−	0.892559i
$346$	6.33124e31			1.15621
$347$			1.77495e31i			0.312656i	0.987705	+	0.156328i	$0.0499657\pi$
$347$			1.77495e31i			0.312656i	−0.987705	+	0.156328i	$0.950034\pi$
$348$			3.28983e31i			0.559027i
$349$	−6.99151e31			−1.14618			−0.573091	−	0.819492i	$-0.694256\pi$
$349$	−6.99151e31			−1.14618			−0.573091	+	0.819492i	$0.694256\pi$
$350$	−7.55686e30	−	1.20222e31i	−0.119534	−	0.190166i
$351$	5.50279e31			0.839932
$352$		−	6.85604e30i		−	0.100993i
$353$		−	5.98918e31i		−	0.851498i	−0.904841	−	0.425749i	$-0.860011\pi$
$353$		−	5.98918e31i		−	0.851498i	0.904841	−	0.425749i	$-0.139989\pi$
$354$	7.27381e31			0.998208
$355$	5.99938e31	−	1.08572e32i	0.794789	−	1.43835i
$356$	−4.86255e31			−0.621926
$357$		−	1.62854e31i		−	0.201115i
$358$		−	6.09835e31i		−	0.727234i
$359$	−2.70071e31			−0.311027			−0.155513	−	0.987834i	$-0.549703\pi$
$359$	−2.70071e31			−0.311027			−0.155513	+	0.987834i	$0.549703\pi$
$360$	−6.12954e30	−	3.38700e30i	−0.0681784	−	0.0376734i
$361$	−7.13311e31			−0.766371
$362$			1.22538e32i			1.27179i
$363$			7.42132e31i			0.744129i
$364$	−1.59875e31			−0.154886
$365$	−1.28999e32	−	7.12811e31i	−1.20761	−	0.667289i
$366$	1.22691e31			0.110994
$367$			1.68905e32i			1.47678i	0.674372	+	0.738392i	$0.264415\pi$
$367$			1.68905e32i			1.47678i	−0.674372	+	0.738392i	$0.735585\pi$
$368$		−	2.73086e31i		−	0.230782i
$369$	−2.11889e31			−0.173093
$370$	−5.15952e31	+	9.33730e31i	−0.407462	+	0.737394i
$371$	−7.11689e30			−0.0543396
$372$			8.77149e31i			0.647570i
$373$		−	5.83575e31i		−	0.416616i	−0.978063	−	0.208308i	$-0.933204\pi$
$373$		−	5.83575e31i		−	0.416616i	0.978063	−	0.208308i	$-0.0667957\pi$
$374$	3.35352e31			0.231530
$375$	−9.31768e30	−	1.65172e32i	−0.0622181	−	1.10293i
$376$	−7.55111e31			−0.487711
$377$			1.57973e32i			0.986998i
$378$		−	3.20065e31i		−	0.193460i
$379$	1.51743e32			0.887399			0.443700	−	0.896176i	$-0.353666\pi$
$379$	1.51743e32			0.887399			0.443700	+	0.896176i	$0.353666\pi$
$380$	−2.06564e31	+	3.73825e31i	−0.116886	+	0.211530i
$381$	4.61814e31			0.252874
$382$			4.63416e31i			0.245572i
$383$			2.03117e32i			1.04174i	0.853635	+	0.520872i	$0.174393\pi$
$383$			2.03117e32i			1.04174i	−0.853635	+	0.520872i	$0.825607\pi$
$384$	−1.96685e31			−0.0976409
$385$	−3.30533e31	−	1.82643e31i	−0.158839	−	0.0877696i
$386$	2.81366e30			0.0130897
$387$			1.75774e30i			0.00791714i
$388$		−	1.89749e31i		−	0.0827529i
$389$	−4.00318e32			−1.69058			−0.845289	−	0.534310i	$-0.820572\pi$
$389$	−4.00318e32			−1.69058			−0.845289	+	0.534310i	$0.820572\pi$
$390$	−1.63027e32	−	9.00839e31i	−0.666732	−	0.368417i
$391$	1.33576e32			0.529076
$392$		−	8.28586e31i		−	0.317879i
$393$		−	3.27798e32i		−	1.21815i
$394$	2.95827e32			1.06496
$395$	−2.46908e32	+	4.46836e32i	−0.861137	+	1.55842i
$396$	−1.86242e31			−0.0629343
$397$		−	9.71109e31i		−	0.317970i	−0.987281	−	0.158985i	$-0.949178\pi$
$397$		−	9.71109e31i		−	0.317970i	0.987281	−	0.158985i	$-0.0508222\pi$
$398$		−	2.62573e32i		−	0.833127i
$399$	5.51586e31			0.169610
$400$	−4.46420e31	−	7.10209e31i	−0.133044	−	0.211659i
$401$	1.47073e32			0.424842			0.212421	−	0.977178i	$-0.431865\pi$
$401$	1.47073e32			0.424842			0.212421	+	0.977178i	$0.431865\pi$
$402$		−	2.43814e32i		−	0.682706i
$403$			4.21195e32i			1.14333i
$404$	2.02726e32			0.533510
$405$	2.22106e32	−	4.01950e32i	0.566725	−	1.02562i
$406$	9.18836e31			0.227333
$407$			2.83708e32i			0.680676i
$408$		−	9.62056e31i		−	0.223845i
$409$	4.55653e32			1.02824			0.514118	−	0.857720i	$-0.328119\pi$
$409$	4.55653e32			1.02824			0.514118	+	0.857720i	$0.328119\pi$
$410$	−2.22151e32	−	1.22754e32i	−0.486239	−	0.268681i
$411$	5.71059e32			1.21243
$412$			2.85991e30i			0.00589030i
$413$		−	2.03155e32i		−	0.405930i
$414$	−7.41828e31			−0.143813
$415$	8.18292e32	+	4.52164e32i	1.53924	+	0.850541i
$416$	−9.44457e31			−0.172391
$417$		−	7.57019e32i		−	1.34093i
$418$			1.13584e32i			0.195260i
$419$	−1.07085e33			−1.78670			−0.893350	−	0.449361i	$-0.851652\pi$
$419$	−1.07085e33			−1.78670			−0.893350	+	0.449361i	$0.851652\pi$
$420$	−5.23964e31	+	9.48230e31i	−0.0848566	+	0.153567i
$421$	4.34132e32			0.682489			0.341244	−	0.939975i	$-0.389152\pi$
$421$	4.34132e32			0.682489			0.341244	+	0.939975i	$0.389152\pi$
$422$		−	1.12419e32i		−	0.171568i
$423$			2.05123e32i			0.303921i
$424$	−4.20429e31			−0.0604811
$425$	3.47387e32	−	2.18359e32i	0.485235	−	0.305007i
$426$	−9.46382e32			−1.28365
$427$		−	3.42671e31i		−	0.0451366i
$428$			2.10244e32i			0.268953i
$429$	−4.95346e32			−0.615450
$430$	−1.01832e31	+	1.84287e31i	−0.0122893	+	0.0222403i
$431$	−7.49364e32			−0.878470			−0.439235	−	0.898372i	$-0.644750\pi$
$431$	−7.49364e32			−0.878470			−0.439235	+	0.898372i	$0.644750\pi$
$432$		−	1.89078e32i		−	0.215325i
$433$		−	3.10398e32i		−	0.343416i	−0.985148	−	0.171708i	$-0.945072\pi$
$433$		−	3.10398e32i		−	0.343416i	0.985148	−	0.171708i	$-0.0549285\pi$
$434$	2.44984e32			0.263340
$435$	9.36952e32	+	5.17732e32i	0.978592	+	0.540741i
$436$	8.92417e32			0.905704
$437$			4.52421e32i			0.446195i
$438$			1.12444e33i			1.07773i
$439$	−3.93993e32			−0.367013			−0.183507	−	0.983018i	$-0.558745\pi$
$439$	−3.93993e32			−0.367013			−0.183507	+	0.983018i	$0.558745\pi$
$440$	−1.95262e32	−	1.07896e32i	−0.176791	−	0.0976893i
$441$	−2.25082e32			−0.198088
$442$		−	4.61966e32i		−	0.395214i
$443$			1.28865e33i			1.07174i	0.844301	+	0.535869i	$0.180016\pi$
$443$			1.28865e33i			1.07174i	−0.844301	+	0.535869i	$0.819984\pi$
$444$	8.13897e32			0.658085
$445$	−7.65237e32	+	1.38487e33i	−0.601583	+	1.08870i
$446$	−1.05921e33			−0.809649
$447$		−	9.74590e32i		−	0.724399i
$448$			5.49335e31i			0.0397065i
$449$	−2.64778e33			−1.86124			−0.930619	−	0.365990i	$-0.880731\pi$
$449$	−2.64778e33			−1.86124			−0.930619	+	0.365990i	$0.880731\pi$
$450$	−1.92926e32	+	1.21268e32i	−0.131897	+	0.0829071i
$451$	−6.74991e32			−0.448839
$452$		−	3.05343e32i		−	0.197496i
$453$		−	9.05891e32i		−	0.569966i
$454$	1.99213e33			1.21933
$455$	−2.51601e32	+	4.55328e32i	−0.149820	+	0.271132i
$456$	3.25849e32			0.188780
$457$		−	3.41528e33i		−	1.92519i	−0.270947	−	0.962594i	$-0.587337\pi$
$457$		−	3.41528e33i		−	1.92519i	0.270947	−	0.962594i	$-0.412663\pi$
$458$			2.01153e33i			1.10334i
$459$	9.24844e32			0.493639
$460$	−7.77756e32	−	4.29765e32i	−0.403990	−	0.223233i
$461$	−3.55950e33			−1.79940			−0.899700	−	0.436510i	$-0.856214\pi$
$461$	−3.55950e33			−1.79940			−0.899700	+	0.436510i	$0.856214\pi$
$462$			2.88113e32i			0.141755i
$463$		−	2.37447e33i		−	1.13712i	−0.822643	−	0.568558i	$-0.807501\pi$
$463$		−	2.37447e33i		−	1.13712i	0.822643	−	0.568558i	$-0.192499\pi$
$464$	5.42801e32			0.253026
$465$	2.49814e33	+	1.38040e33i	1.13359	+	0.626388i
$466$	−1.20164e33			−0.530822
$467$		−	1.47044e33i		−	0.632392i	−0.948694	−	0.316196i	$-0.897594\pi$
$467$		−	1.47044e33i		−	0.632392i	0.948694	−	0.316196i	$-0.102406\pi$
$468$			2.56558e32i			0.107427i
$469$	−6.80964e32			−0.277628
$470$	−1.18835e33	+	2.15058e33i	−0.471758	+	0.853752i
$471$	4.52396e33			1.74887
$472$		−	1.20013e33i		−	0.451808i
$473$			5.59945e31i			0.0205296i
$474$	3.89490e33			1.39081
$475$	7.39585e32	+	1.17660e33i	0.257228	+	0.409223i
$476$	−2.68698e32			−0.0910286
$477$			1.14208e32i			0.0376892i
$478$			1.08729e32i			0.0349540i
$479$	1.56346e33			0.489657			0.244829	−	0.969566i	$-0.421268\pi$
$479$	1.56346e33			0.489657			0.244829	+	0.969566i	$0.421268\pi$
$480$	−3.09531e32	+	5.60165e32i	−0.0944471	+	0.170923i
$481$	3.90823e33			1.16189
$482$		−	2.64766e31i		−	0.00766962i
$483$			1.14760e33i			0.323929i
$484$	1.22447e33			0.336807
$485$	−5.40411e32	−	2.98615e32i	−0.144861	−	0.0800461i
$486$	−1.17238e33			−0.306278
$487$		−	4.18200e33i		−	1.06481i	−0.846490	−	0.532405i	$-0.821289\pi$
$487$		−	4.18200e33i		−	1.06481i	0.846490	−	0.532405i	$-0.178711\pi$
$488$		−	2.02432e32i		−	0.0502380i
$489$	1.92545e33			0.465771
$490$	−2.35984e33	−	1.30398e33i	−0.556456	−	0.307481i
$491$	4.13591e32			0.0950719			0.0475360	−	0.998870i	$-0.484863\pi$
$491$	4.13591e32			0.0950719			0.0475360	+	0.998870i	$0.484863\pi$
$492$			1.93641e33i			0.433943i
$493$			2.65502e33i			0.580072i
$494$	1.56468e33			0.333303
$495$	−2.93096e32	+	5.30422e32i	−0.0608758	+	0.110168i
$496$	1.44724e33			0.293103
$497$			2.64321e33i			0.522007i
$498$		−	7.13275e33i		−	1.37369i
$499$	−5.19785e33			−0.976264			−0.488132	−	0.872770i	$-0.662321\pi$
$499$	−5.19785e33			−0.976264			−0.488132	+	0.872770i	$0.662321\pi$
$500$	−2.72524e33	+	1.53736e32i	−0.499206	+	0.0281611i
$501$	−2.83466e33			−0.506442
$502$		−	2.07580e33i		−	0.361734i
$503$			3.59933e33i			0.611817i	0.952061	+	0.305909i	$0.0989602\pi$
$503$			3.59933e33i			0.611817i	−0.952061	+	0.305909i	$0.901040\pi$
$504$	1.49225e32			0.0247434
$505$	3.19037e33	−	5.77369e33i	0.516059	−	0.933924i
$506$	−2.36316e33			−0.372916
$507$		−	3.51573e32i		−	0.0541273i
$508$		−	7.61964e32i		−	0.114456i
$509$	−1.19327e34			−1.74891			−0.874453	−	0.485109i	$-0.838780\pi$
$509$	−1.19327e34			−1.74891			−0.874453	+	0.485109i	$0.838780\pi$
$510$	−2.73996e33	−	1.51402e33i	−0.391848	−	0.216524i
$511$	3.14051e33			0.438267
$512$			3.24519e32i			0.0441942i
$513$			3.13245e33i			0.416310i
$514$	3.34289e33			0.433594
$515$	8.14511e31	+	4.50075e31i	0.0103111	+	0.00569763i
$516$	1.60636e32			0.0198483
$517$			6.53438e33i			0.788085i
$518$		−	2.27318e33i		−	0.267616i
$519$	−1.57174e34			−1.80630
$520$	−1.48633e33	+	2.68984e33i	−0.166753	+	0.301776i
$521$	1.63355e34			1.78921			0.894605	−	0.446859i	$-0.147457\pi$
$521$	1.63355e34			1.78921			0.894605	+	0.446859i	$0.147457\pi$
$522$		−	1.47450e33i		−	0.157675i
$523$			9.46552e33i			0.988265i	0.869387	+	0.494133i	$0.164514\pi$
$523$			9.46552e33i			0.988265i	−0.869387	+	0.494133i	$0.835486\pi$
$524$	−5.40846e33			−0.551356
$525$	1.87600e33	+	2.98453e33i	0.186742	+	0.297088i
$526$	−4.76124e33			−0.462805
$527$			7.07895e33i			0.671949i
$528$			1.70202e33i			0.157776i
$529$	1.63297e33			0.147837
$530$	−6.61645e32	+	1.19739e33i	−0.0585028	+	0.105874i
$531$	−3.26012e33			−0.281548
$532$		−	9.10083e32i		−	0.0767689i
$533$			9.29836e33i			0.766155i
$534$	1.20714e34			0.971607
$535$	5.98780e33	+	3.30868e33i	0.470809	+	0.260156i
$536$	−4.02278e33			−0.309006
$537$			1.51393e34i			1.13612i
$538$		−	4.41879e33i		−	0.323985i
$539$	−7.17020e33			−0.513655
$540$	−5.38499e33	−	2.97559e33i	−0.376932	−	0.208281i
$541$	1.13679e34			0.777528			0.388764	−	0.921337i	$-0.372902\pi$
$541$	1.13679e34			0.777528			0.388764	+	0.921337i	$0.372902\pi$
$542$			8.51379e33i			0.569025i
$543$		−	3.04204e34i		−	1.98686i
$544$	−1.58733e33			−0.101317
$545$	1.40443e34	−	2.54163e34i	0.876079	−	1.58546i
$546$	3.96892e33			0.241971
$547$		−	2.60600e34i		−	1.55286i	−0.630204	−	0.776430i	$-0.717029\pi$
$547$		−	2.60600e34i		−	1.55286i	0.630204	−	0.776430i	$-0.282971\pi$
$548$		−	9.42211e33i		−	0.548771i
$549$	−5.49901e32			−0.0313062
$550$	−6.14582e33	+	3.86312e33i	−0.342016	+	0.214983i
$551$	−8.99258e33			−0.489203
$552$			6.77940e33i			0.360540i
$553$		−	1.08783e34i		−	0.565584i
$554$	1.97372e34			1.00326
$555$	1.28086e34	−	2.31800e34i	0.636560	−	1.15200i
$556$	−1.24903e34			−0.606931
$557$			3.30593e34i			1.57074i	0.619029	+	0.785368i	$0.287526\pi$
$557$			3.30593e34i			1.57074i	−0.619029	+	0.785368i	$0.712474\pi$
$558$		−	3.93138e33i		−	0.182649i
$559$	7.71354e32			0.0350434
$560$	1.56452e33	+	8.64508e32i	0.0695074	+	0.0384077i
$561$	−8.32519e33			−0.361708
$562$			1.56271e34i			0.664011i
$563$		−	1.77408e34i		−	0.737255i	−0.929577	−	0.368628i	$-0.879828\pi$
$563$		−	1.77408e34i		−	0.737255i	0.929577	−	0.368628i	$-0.120172\pi$
$564$	1.87458e34			0.761929
$565$	−8.69626e33	−	4.80530e33i	−0.345722	−	0.191036i
$566$	1.43543e34			0.558184
$567$			9.78556e33i			0.372218i
$568$			1.56147e34i			0.581005i
$569$	3.24647e34			1.18170			0.590851	−	0.806781i	$-0.298792\pi$
$569$	3.24647e34			1.18170			0.590851	+	0.806781i	$0.298792\pi$
$570$	5.12800e33	−	9.28026e33i	0.182605	−	0.330464i
$571$	−1.08523e34			−0.378068			−0.189034	−	0.981971i	$-0.560536\pi$
$571$	−1.08523e34			−0.378068			−0.189034	+	0.981971i	$0.560536\pi$
$572$			8.17290e33i			0.278565i
$573$		−	1.15044e34i		−	0.383646i
$574$	5.40830e33			0.176467
$575$	−2.44797e34	+	1.53873e34i	−0.781551	+	0.491264i
$576$	8.81543e32			0.0275399
$577$			5.40061e34i			1.65099i	0.564406	+	0.825497i	$0.309105\pi$
$577$			5.40061e34i			1.65099i	−0.564406	+	0.825497i	$0.690895\pi$
$578$			1.58723e34i			0.474834i
$579$	−6.98496e32			−0.0204495
$580$	8.54226e33	−	1.54591e34i	0.244750	−	0.442930i
$581$	−1.99215e34			−0.558625
$582$			4.71056e33i			0.129281i
$583$			3.63820e33i			0.0977304i
$584$	1.85525e34			0.487800
$585$	7.30686e33	+	4.03756e33i	0.188054	+	0.103913i
$586$	−4.14340e33			−0.104385
$587$		−	5.41910e34i		−	1.33644i	−0.743962	−	0.668222i	$-0.767056\pi$
$587$		−	5.41910e34i		−	1.33644i	0.743962	−	0.668222i	$-0.232944\pi$
$588$			2.05698e34i			0.496608i
$589$	−2.39764e34			−0.566687
$590$	−3.41801e34	−	1.88869e34i	−0.790903	−	0.437030i
$591$	−7.34396e34			−1.66375
$592$		−	1.34288e34i		−	0.297862i
$593$		−	3.87147e34i		−	0.840799i	−0.907339	−	0.420400i	$-0.861890\pi$
$593$		−	3.87147e34i		−	0.840799i	0.907339	−	0.420400i	$-0.138110\pi$
$594$	−1.63619e34			−0.347939
$595$	−4.22861e33	+	7.65260e33i	−0.0880512	+	0.159348i
$596$	−1.60801e34			−0.327877
$597$			6.51841e34i			1.30156i
$598$			3.25538e34i			0.636557i
$599$	−9.20898e33			−0.176350			−0.0881751	−	0.996105i	$-0.528104\pi$
$599$	−9.20898e33			−0.176350			−0.0881751	+	0.996105i	$0.528104\pi$
$600$	1.10825e34	+	1.76311e34i	0.207848	+	0.330665i
$601$	3.98144e34			0.731324			0.365662	−	0.930748i	$-0.380843\pi$
$601$	3.98144e34			0.731324			0.365662	+	0.930748i	$0.380843\pi$
$602$		−	4.48651e32i		−	0.00807147i
$603$			1.09277e34i			0.192559i
$604$	−1.49466e34			−0.257978
$605$	1.92700e34	−	3.48733e34i	0.325791	−	0.589591i
$606$	−5.03271e34			−0.833478
$607$		−	3.32966e34i		−	0.540184i	−0.962835	−	0.270092i	$-0.912946\pi$
$607$		−	3.32966e34i		−	0.540184i	0.962835	−	0.270092i	$-0.0870540\pi$
$608$		−	5.37630e33i		−	0.0854454i
$609$	−2.28103e34			−0.355152
$610$	−5.76533e33	−	3.18575e33i	−0.0879430	−	0.0485947i
$611$	9.00147e34			1.34524
$612$			4.31193e33i			0.0631363i
$613$			5.68278e34i			0.815277i	0.913143	+	0.407639i	$0.133648\pi$
$613$			5.68278e34i			0.815277i	−0.913143	+	0.407639i	$0.866352\pi$
$614$	−5.23321e34			−0.735637
$615$	5.51494e34	+	3.04739e34i	0.759629	+	0.419749i
$616$	4.75369e33			0.0641611
$617$		−	9.70987e33i		−	0.128425i	−0.997936	−	0.0642124i	$-0.979546\pi$
$617$		−	9.70987e33i		−	0.128425i	0.997936	−	0.0642124i	$-0.0204535\pi$
$618$		−	7.09978e32i		−	0.00920214i
$619$	−3.18717e34			−0.404829			−0.202415	−	0.979300i	$-0.564879\pi$
$619$	−3.18717e34			−0.404829			−0.202415	+	0.979300i	$0.564879\pi$
$620$	2.27758e34	−	4.12178e34i	0.283515	−	0.513084i
$621$	−6.51718e34			−0.795087
$622$		−	4.90581e34i		−	0.586584i
$623$		−	3.37148e34i		−	0.395112i
$624$	2.34463e34			0.269319
$625$	−3.85097e34	+	8.00351e34i	−0.433581	+	0.901115i
$626$	9.83022e34			1.08489
$627$		−	2.81975e34i		−	0.305046i
$628$		−	7.46425e34i		−	0.791572i
$629$	6.56848e34			0.682860
$630$	2.34841e33	−	4.24996e33i	0.0239341	−	0.0433140i
$631$	1.18827e35			1.18726			0.593632	−	0.804737i	$-0.297693\pi$
$631$	1.18827e35			1.18726			0.593632	+	0.804737i	$0.297693\pi$
$632$		−	6.42634e34i		−	0.629506i
$633$			2.79083e34i			0.268032i
$634$	−2.13804e34			−0.201326
$635$	−2.17010e34	−	1.19913e34i	−0.200358	−	0.110712i
$636$	1.04372e34			0.0944868
$637$			9.87734e34i			0.876793i
$638$		−	4.69715e34i		−	0.408861i
$639$	4.24168e34			0.362057
$640$	9.24238e33	+	5.10707e33i	0.0773631	+	0.0427486i
$641$	1.95210e35			1.60242			0.801212	−	0.598381i	$-0.204189\pi$
$641$	1.95210e35			1.60242			0.801212	+	0.598381i	$0.204189\pi$
$642$		−	5.21934e34i		−	0.420173i
$643$			5.50965e34i			0.434998i	0.976061	+	0.217499i	$0.0697899\pi$
$643$			5.50965e34i			0.434998i	−0.976061	+	0.217499i	$0.930210\pi$
$644$	1.89346e34			0.146617
$645$	2.52799e33	−	4.57497e33i	0.0191990	−	0.0347449i
$646$	2.62973e34			0.195887
$647$		−	1.62013e35i		−	1.18371i	−0.806045	−	0.591855i	$-0.798396\pi$
$647$		−	1.62013e35i		−	1.18371i	0.806045	−	0.591855i	$-0.201604\pi$
$648$			5.78080e34i			0.414286i
$649$	−1.03854e35			−0.730070
$650$	5.32165e34	+	8.46620e34i	0.366969	+	0.583810i
$651$	−6.08178e34			−0.411404
$652$		−	3.17688e34i		−	0.210817i
$653$		−	6.88298e34i		−	0.448086i	−0.974579	−	0.224043i	$-0.928074\pi$
$653$		−	6.88298e34i		−	0.448086i	0.974579	−	0.224043i	$-0.0719256\pi$
$654$	−2.21544e35			−1.41494
$655$	−8.51149e34	+	1.54034e35i	−0.533322	+	0.965165i
$656$	3.19495e34			0.196411
$657$		−	5.03972e34i		−	0.303976i
$658$		−	5.23562e34i		−	0.309845i
$659$	8.31458e34			0.482806			0.241403	−	0.970425i	$-0.422392\pi$
$659$	8.31458e34			0.482806			0.241403	+	0.970425i	$0.422392\pi$
$660$	4.84741e34	+	2.67854e34i	0.276192	+	0.152616i
$661$	−9.81505e34			−0.548749			−0.274375	−	0.961623i	$-0.588471\pi$
$661$	−9.81505e34			−0.548749			−0.274375	+	0.961623i	$0.588471\pi$
$662$			1.22798e35i			0.673702i
$663$			1.14684e35i			0.617424i
$664$	−1.17686e35			−0.621761
$665$	−2.59194e34	−	1.43223e34i	−0.134386	−	0.0742579i
$666$	−3.64788e34			−0.185615
$667$		−	1.87094e35i		−	0.934302i
$668$			4.67702e34i			0.229226i
$669$	2.62951e35			1.26488
$670$	−6.33080e34	+	1.14570e35i	−0.298898	+	0.540923i
$671$	−1.75176e34			−0.0811788
$672$		−	1.36373e34i		−	0.0620317i
$673$			1.38294e34i			0.0617470i	0.999523	+	0.0308735i	$0.00982891\pi$
$673$			1.38294e34i			0.0617470i	−0.999523	+	0.0308735i	$0.990171\pi$
$674$	9.22512e34			0.404318
$675$	−1.69491e35	+	1.06538e35i	−0.729205	+	0.458361i
$676$	−5.80074e33			−0.0244991
$677$		−	3.23088e35i		−	1.33956i	−0.742559	−	0.669780i	$-0.766388\pi$
$677$		−	3.23088e35i		−	1.33956i	0.742559	−	0.669780i	$-0.233612\pi$
$678$			7.58020e34i			0.308538i
$679$	1.31564e34			0.0525732
$680$	−2.49804e34	+	4.52076e34i	−0.0980028	+	0.177358i
$681$	−4.94551e35			−1.90490
$682$		−	1.25238e35i		−	0.473620i
$683$			4.94645e35i			1.83669i	0.395785	+	0.918343i	$0.370473\pi$
$683$			4.94645e35i			1.83669i	−0.395785	+	0.918343i	$0.629527\pi$
$684$	−1.46045e34			−0.0532459
$685$	−2.68344e35	−	1.48279e35i	−0.960639	−	0.530821i
$686$	1.21349e35			0.426564
$687$		−	4.99365e35i		−	1.72369i
$688$		−	2.65040e33i		−	0.00898371i
$689$	5.01182e34			0.166823
$690$	1.93079e35	+	1.06690e35i	0.631135	+	0.348747i
$691$	−3.23399e35			−1.03816			−0.519079	−	0.854726i	$-0.673725\pi$
$691$	−3.23399e35			−1.03816			−0.519079	+	0.854726i	$0.673725\pi$
$692$			2.59328e35i			0.817565i
$693$		−	1.29132e34i		−	0.0399824i
$694$	−7.27017e34			−0.221081
$695$	−1.96565e35	+	3.55728e35i	−0.587079	+	1.06245i
$696$	−1.34751e35			−0.395292
$697$			1.56276e35i			0.450279i
$698$		−	2.86372e35i		−	0.810472i
$699$	2.98308e35			0.829279
$700$	4.92429e34	−	3.09529e34i	0.134468	−	0.0845232i
$701$	3.02063e35			0.810256			0.405128	−	0.914260i	$-0.367227\pi$
$701$	3.02063e35			0.810256			0.405128	+	0.914260i	$0.367227\pi$
$702$			2.25394e35i			0.593922i
$703$			2.22475e35i			0.575890i
$704$	2.80823e34			0.0714127
$705$	2.95009e35	−	5.33885e35i	0.737007	−	1.33378i
$706$	2.45317e35			0.602100
$707$			1.40562e35i			0.338941i
$708$			2.97935e35i			0.705840i
$709$	4.34959e35			1.01244			0.506222	−	0.862403i	$-0.331042\pi$
$709$	4.34959e35			1.01244			0.506222	+	0.862403i	$0.331042\pi$
$710$	4.44712e35	+	2.45735e35i	1.01707	+	0.562001i
$711$	−1.74569e35			−0.392281
$712$		−	1.99170e35i		−	0.439768i
$713$		−	4.98839e35i		−	1.08228i
$714$	6.67049e34			0.142210
$715$	2.32766e35	+	1.28620e35i	0.487635	+	0.269453i
$716$	2.49788e35			0.514232
$717$		−	2.69922e34i		−	0.0546071i
$718$		−	1.10621e35i		−	0.219929i
$719$	2.50423e35			0.489286			0.244643	−	0.969613i	$-0.421329\pi$
$719$	2.50423e35			0.489286			0.244643	+	0.969613i	$0.421329\pi$
$720$	1.38732e34	−	2.51066e34i	0.0266391	−	0.0482094i
$721$	−1.98294e33			−0.00374213
$722$		−	2.92172e35i		−	0.541906i
$723$			6.57286e33i			0.0119819i
$724$	−5.01917e35			−0.899291
$725$	−3.05847e35	−	4.86572e35i	−0.538617	−	0.856884i
$726$	−3.03977e35			−0.526179
$727$			6.25077e34i			0.106354i	0.998585	+	0.0531770i	$0.0169347\pi$
$727$			6.25077e34i			0.106354i	−0.998585	+	0.0531770i	$0.983065\pi$
$728$		−	6.54847e34i		−	0.109521i
$729$	−4.21708e35			−0.693294
$730$	2.91967e35	−	5.28380e35i	0.471844	−	0.853908i
$731$	1.29640e34			0.0205955
$732$			5.02542e34i			0.0784845i
$733$		−	8.87732e35i		−	1.36296i	−0.731838	−	0.681479i	$-0.761337\pi$
$733$		−	8.87732e35i		−	1.36296i	0.731838	−	0.681479i	$-0.238663\pi$
$734$	−6.91835e35			−1.04424
$735$	5.85833e35	+	3.23714e35i	0.869326	+	0.480364i
$736$	1.11856e35			0.163187
$737$			3.48113e35i			0.499318i
$738$		−	8.67896e34i		−	0.122395i
$739$	6.31553e35			0.875698			0.437849	−	0.899048i	$-0.355740\pi$
$739$	6.31553e35			0.875698			0.437849	+	0.899048i	$0.355740\pi$
$740$	−3.82456e35	−	2.11334e35i	−0.521416	−	0.288119i
$741$	−3.88435e35			−0.520704
$742$		−	2.91508e34i		−	0.0384239i
$743$		−	1.51703e35i		−	0.196623i	−0.995156	−	0.0983113i	$-0.968656\pi$
$743$		−	1.51703e35i		−	0.196623i	0.995156	−	0.0983113i	$-0.0313441\pi$
$744$	−3.59280e35			−0.457901
$745$	−2.53059e35	+	4.57967e35i	−0.317153	+	0.573958i
$746$	2.39032e35			0.294592
$747$			3.19689e35i			0.387455i
$748$			1.37360e35i			0.163716i
$749$	−1.45774e35			−0.170867
$750$	6.76546e35	−	3.81652e34i	0.779887	−	0.0439948i
$751$	1.36888e36			1.55191			0.775954	−	0.630789i	$-0.217269\pi$
$751$	1.36888e36			1.55191			0.775954	+	0.630789i	$0.217269\pi$
$752$		−	3.09293e35i		−	0.344864i
$753$			5.15322e35i			0.565121i
$754$	−6.47058e35			−0.697913
$755$	−2.35221e35	+	4.25685e35i	−0.249539	+	0.451597i
$756$	1.31099e35			0.136797
$757$			1.53344e36i			1.57386i	0.617040	+	0.786931i	$0.288331\pi$
$757$			1.53344e36i			1.57386i	−0.617040	+	0.786931i	$0.711669\pi$
$758$			6.21540e35i			0.627486i
$759$	5.86659e35			0.582590
$760$	−1.53119e35	−	8.46088e34i	−0.149575	−	0.0826505i
$761$	−1.14959e36			−1.10467			−0.552337	−	0.833621i	$-0.686264\pi$
$761$	−1.14959e36			−1.10467			−0.552337	+	0.833621i	$0.686264\pi$
$762$			1.89159e35i			0.178809i
$763$			6.18764e35i			0.575398i
$764$	−1.89815e35			−0.173646
$765$	1.22805e35	+	6.78584e34i	0.110522	+	0.0610711i
$766$	−8.31967e35			−0.736625
$767$			1.43065e36i			1.24621i
$768$		−	8.05623e34i		−	0.0690425i
$769$	−1.22160e36			−1.03003			−0.515015	−	0.857181i	$-0.672214\pi$
$769$	−1.22160e36			−1.03003			−0.515015	+	0.857181i	$0.672214\pi$
$770$	7.48106e34	−	1.35386e35i	0.0620624	−	0.112316i
$771$	−8.29879e35			−0.677384
$772$			1.15247e34i			0.00925582i
$773$		−	6.78971e35i		−	0.536547i	−0.963343	−	0.268273i	$-0.913547\pi$
$773$		−	6.78971e35i		−	0.536547i	0.963343	−	0.268273i	$-0.0864530\pi$
$774$	−7.19971e33			−0.00559826
$775$	−8.15464e35	−	1.29732e36i	−0.623927	−	0.992603i
$776$	7.77212e34			0.0585151
$777$			5.64322e35i			0.418084i
$778$		−	1.63970e36i		−	1.19542i
$779$	−5.29307e35			−0.379743
$780$	3.68983e35	−	6.67758e35i	0.260510	−	0.471451i
$781$	1.35123e36			0.938837
$782$			5.47126e35i			0.374113i
$783$		−	1.29539e36i		−	0.871725i
$784$	3.39389e35			0.224774
$785$	−2.12584e36	−	1.17468e36i	−1.38567	−	0.765680i
$786$	1.34266e36			0.861359
$787$			9.85723e35i			0.622402i	0.950344	+	0.311201i	$0.100731\pi$
$787$			9.85723e35i			0.622402i	−0.950344	+	0.311201i	$0.899269\pi$
$788$			1.21171e36i			0.753044i
$789$	1.18199e36			0.723019
$790$	−1.83024e36	−	1.01134e36i	−1.10197	−	0.608916i
$791$	2.11712e35			0.125470
$792$		−	7.62847e34i		−	0.0445013i
$793$			2.41314e35i			0.138570i
$794$	3.97766e35			0.224839
$795$	1.64254e35	−	2.97255e35i	0.0913962	−	0.165402i
$796$	1.07550e36			0.589110
$797$		−	1.15299e36i		−	0.621722i	−0.950455	−	0.310861i	$-0.899383\pi$
$797$		−	1.15299e36i		−	0.621722i	0.950455	−	0.310861i	$-0.100617\pi$
$798$			2.25930e35i			0.119933i
$799$	1.51286e36			0.790613
$800$	2.90901e35	−	1.82854e35i	0.149665	−	0.0940760i
$801$	−5.41038e35			−0.274045
$802$			6.02410e35i			0.300409i
$803$		−	1.60545e36i		−	0.788228i
$804$	9.98663e35			0.482746
$805$	2.97981e35	−	5.39263e35i	0.141821	−	0.256656i
$806$	−1.72522e36			−0.808454
$807$			1.09697e36i			0.506147i
$808$			8.30366e35i			0.377248i
$809$	1.76491e36			0.789526			0.394763	−	0.918783i	$-0.370827\pi$
$809$	1.76491e36			0.789526			0.394763	+	0.918783i	$0.370827\pi$
$810$	1.64639e36	+	9.09746e35i	0.725220	+	0.400735i
$811$	3.26639e36			1.41680			0.708398	−	0.705814i	$-0.249418\pi$
$811$	3.26639e36			1.41680			0.708398	+	0.705814i	$0.249418\pi$
$812$			3.76355e35i			0.160749i
$813$		−	2.11356e36i		−	0.888962i
$814$	−1.16207e36			−0.481311
$815$	−9.04784e35	−	4.99957e35i	−0.369041	−	0.203921i
$816$	3.94058e35			0.158283
$817$			4.39092e34i			0.0173692i
$818$			1.86635e36i			0.727072i
$819$	−1.77887e35			−0.0682488
$820$	5.02801e35	−	9.09930e35i	0.189987	−	0.343823i
$821$	8.67287e35			0.322755			0.161378	−	0.986893i	$-0.448406\pi$
$821$	8.67287e35			0.322755			0.161378	+	0.986893i	$0.448406\pi$
$822$			2.33906e36i			0.857320i
$823$			1.77728e36i			0.641589i	0.947149	+	0.320794i	$0.103950\pi$
$823$			1.77728e36i			0.641589i	−0.947149	+	0.320794i	$0.896050\pi$
$824$	−1.17142e34			−0.00416507
$825$	1.52571e36	−	9.59026e35i	0.534316	−	0.335858i
$826$	8.32121e35			0.287036
$827$		−	1.78322e36i		−	0.605880i	−0.953010	−	0.302940i	$-0.902032\pi$
$827$		−	1.78322e36i		−	0.605880i	0.953010	−	0.302940i	$-0.0979682\pi$
$828$		−	3.03853e35i		−	0.101691i
$829$	2.64368e36			0.871521			0.435760	−	0.900063i	$-0.356479\pi$
$829$	2.64368e36			0.871521			0.435760	+	0.900063i	$0.356479\pi$
$830$	−1.85207e36	+	3.35173e36i	−0.601423	+	1.08841i
$831$	−4.89981e36			−1.56735
$832$		−	3.86850e35i		−	0.121899i
$833$			1.66007e36i			0.515303i
$834$	3.10075e36			0.948180
$835$	1.33203e36	+	7.36040e35i	0.401266	+	0.221728i
$836$	−4.65240e35			−0.138070
$837$		−	3.45383e36i		−	1.00980i
$838$		−	4.38619e36i		−	1.26339i
$839$	−6.66972e36			−1.89271			−0.946354	−	0.323133i	$-0.895264\pi$
$839$	−6.66972e36			−1.89271			−0.946354	+	0.323133i	$0.895264\pi$
$840$	−3.88395e35	−	2.14616e35i	−0.108588	−	0.0600027i
$841$	8.84259e34			0.0243573
$842$			1.77820e36i			0.482593i
$843$		−	3.87947e36i		−	1.03735i
$844$	4.60469e35			0.121317
$845$	−9.12884e34	+	1.65207e35i	−0.0236977	+	0.0428863i
$846$	−8.40185e35			−0.214904
$847$			8.48997e35i			0.213975i
$848$		−	1.72208e35i		−	0.0427666i
$849$	−3.56349e36			−0.872026
$850$	8.94400e35	+	1.42290e36i	0.215673	+	0.343113i
$851$	−4.62867e36			−1.09986
$852$		−	3.87638e36i		−	0.907678i
$853$			5.04065e36i			1.16312i	0.813504	+	0.581559i	$0.197557\pi$
$853$			5.04065e36i			1.16312i	−0.813504	+	0.581559i	$0.802443\pi$
$854$	1.40358e35			0.0319164
$855$	−2.29837e35	+	4.15941e35i	−0.0515043	+	0.0932085i
$856$	−8.61159e35			−0.190178
$857$			1.92537e36i			0.419038i	0.977805	+	0.209519i	$0.0671899\pi$
$857$			1.92537e36i			0.419038i	−0.977805	+	0.209519i	$0.932810\pi$
$858$		−	2.02894e36i		−	0.435189i
$859$	−4.40642e36			−0.931474			−0.465737	−	0.884923i	$-0.654211\pi$
$859$	−4.40642e36			−0.931474			−0.465737	+	0.884923i	$0.654211\pi$
$860$	−7.54841e34	−	4.17103e34i	−0.0157262	−	0.00868986i
$861$	−1.34262e36			−0.275686
$862$		−	3.06940e36i		−	0.621172i
$863$			8.01223e36i			1.59815i	0.601229	+	0.799077i	$0.294678\pi$
$863$			8.01223e36i			1.59815i	−0.601229	+	0.799077i	$0.705322\pi$
$864$	7.74462e35			0.152257
$865$	7.38572e36	+	4.08113e36i	1.43117	+	0.790823i
$866$	1.27139e36			0.242831
$867$		−	3.94033e36i		−	0.741812i
$868$			1.00346e36i			0.186209i
$869$	−5.56106e36			−1.01721
$870$	−2.12063e36	+	3.83775e36i	−0.382362	+	0.691969i
$871$	4.79545e36			0.852319
$872$			3.65534e36i			0.640430i
$873$		−	2.11127e35i		−	0.0364641i
$874$	−1.85312e36			−0.315508
$875$	−1.06594e35	−	1.88957e36i	−0.0178909	−	0.317148i
$876$	−4.60569e36			−0.762068
$877$			4.46078e36i			0.727639i	0.931469	+	0.363820i	$0.118528\pi$
$877$			4.46078e36i			0.727639i	−0.931469	+	0.363820i	$0.881472\pi$
$878$		−	1.61379e36i		−	0.259518i
$879$	1.02861e36			0.163075
$880$	4.41942e35	−	7.99793e35i	0.0690768	−	0.125010i
$881$	3.24157e36			0.499525			0.249762	−	0.968307i	$-0.419648\pi$
$881$	3.24157e36			0.499525			0.249762	+	0.968307i	$0.419648\pi$
$882$		−	9.21937e35i		−	0.140070i
$883$		−	4.92118e35i		−	0.0737157i	−0.999321	−	0.0368579i	$-0.988265\pi$
$883$		−	4.92118e35i		−	0.0737157i	0.999321	−	0.0368579i	$-0.0117349\pi$
$884$	1.89221e36			0.279458
$885$	8.48528e36	+	4.68872e36i	1.23559	+	0.682752i
$886$	−5.27831e36			−0.757833
$887$		−	1.07566e37i		−	1.52276i	−0.648306	−	0.761380i	$-0.724522\pi$
$887$		−	1.07566e37i		−	1.52276i	0.648306	−	0.761380i	$-0.275478\pi$
$888$			3.33372e36i			0.465337i
$889$	5.28314e35			0.0727143
$890$	−5.67242e36	−	3.13441e36i	−0.769827	−	0.425384i
$891$	5.00244e36			0.669439
$892$		−	4.33853e36i		−	0.572508i
$893$			5.12407e36i			0.666763i
$894$	3.99192e36			0.512228
$895$	3.93101e36	−	7.11404e36i	0.497412	−	0.900178i
$896$	−2.25007e35			−0.0280767
$897$		−	8.08154e36i		−	0.994463i
$898$		−	1.08453e37i		−	1.31609i
$899$	9.91520e36			1.18660
$900$	−4.96716e35	−	7.90223e35i	−0.0586241	−	0.0932650i
$901$	8.42327e35			0.0980439
$902$		−	2.76476e36i		−	0.317377i
$903$			1.11378e35i			0.0126097i
$904$	1.25069e36			0.139651
$905$	−7.89886e36	+	1.42947e37i	−0.869875	+	1.57423i
$906$	3.71053e36			0.403026
$907$		−	5.76079e35i		−	0.0617151i	−0.999524	−	0.0308575i	$-0.990176\pi$
$907$		−	5.76079e35i		−	0.0617151i	0.999524	−	0.0308575i	$-0.00982381\pi$
$908$			8.15978e36i			0.862194i
$909$	2.25566e36			0.235085
$910$	−1.86502e36	−	1.03056e36i	−0.191720	−	0.105939i
$911$	−2.28818e36			−0.232012			−0.116006	−	0.993249i	$-0.537009\pi$
$911$	−2.28818e36			−0.232012			−0.116006	+	0.993249i	$0.537009\pi$
$912$			1.33468e36i			0.133487i
$913$			1.01840e37i			1.00469i
$914$	1.39890e37			1.36131
$915$	1.43125e36	+	7.90869e35i	0.137389	+	0.0759174i
$916$	−8.23922e36			−0.780176
$917$		−	3.75000e36i		−	0.350279i
$918$			3.78816e36i			0.349056i
$919$	−3.48143e36			−0.316457			−0.158228	−	0.987403i	$-0.550578\pi$
$919$	−3.48143e36			−0.316457			−0.158228	+	0.987403i	$0.550578\pi$
$920$	1.76032e36	−	3.18569e36i	0.157850	−	0.285664i
$921$	1.29915e37			1.14925
$922$		−	1.45797e37i		−	1.27237i
$923$		−	1.86139e37i		−	1.60256i
$924$	−1.18011e36			−0.100236
$925$	−1.20377e37	+	7.56661e36i	−1.00872	+	0.634059i
$926$	9.72584e36			0.804063
$927$			3.18212e34i			0.00259549i
$928$			2.22331e36i			0.178917i
$929$	4.39451e36			0.348910			0.174455	−	0.984665i	$-0.444184\pi$
$929$	4.39451e36			0.348910			0.174455	+	0.984665i	$0.444184\pi$
$930$	−5.65412e36	+	1.02324e37i	−0.442923	+	0.801568i
$931$	−5.62265e36			−0.434581
$932$		−	4.92190e36i		−	0.375348i
$933$			1.21788e37i			0.916394i
$934$	6.02292e36			0.447168
$935$	3.91206e36	+	2.16169e36i	0.286590	+	0.158361i
$936$	−1.05086e36			−0.0759623
$937$		−	2.04937e37i		−	1.46176i	−0.682508	−	0.730878i	$-0.739111\pi$
$937$		−	2.04937e37i		−	1.46176i	0.682508	−	0.730878i	$-0.260889\pi$
$938$		−	2.78923e36i		−	0.196313i
$939$	−2.44037e37			−1.69487
$940$	−8.80876e36	−	4.86747e36i	−0.603694	−	0.333584i
$941$	−7.85670e36			−0.531337			−0.265668	−	0.964064i	$-0.585593\pi$
$941$	−7.85670e36			−0.531337			−0.265668	+	0.964064i	$0.585593\pi$
$942$			1.85301e37i			1.23664i
$943$		−	1.10124e37i		−	0.725249i
$944$	4.91574e36			0.319477
$945$	2.06315e36	−	3.73372e36i	0.132322	−	0.239466i
$946$	−2.29353e35			−0.0145166
$947$			7.10609e36i			0.443870i	0.975061	+	0.221935i	$0.0712373\pi$
$947$			7.10609e36i			0.443870i	−0.975061	+	0.221935i	$0.928763\pi$
$948$			1.59535e37i			0.983449i
$949$	−2.21159e37			−1.34548
$950$	−4.81937e36	+	3.02934e36i	−0.289364	+	0.181887i
$951$	5.30772e36			0.314522
$952$		−	1.10059e36i		−	0.0643670i
$953$		−	1.19839e37i		−	0.691729i	−0.938285	−	0.345864i	$-0.887586\pi$
$953$		−	1.19839e37i		−	0.691729i	0.938285	−	0.345864i	$-0.112414\pi$
$954$	−4.67796e35			−0.0266503
$955$	−2.98719e36	+	5.40599e36i	−0.167966	+	0.303972i
$956$	−4.45354e35			−0.0247162
$957$			1.16608e37i			0.638745i
$958$			6.40392e36i			0.346240i
$959$	6.53289e36			0.348637
$960$	−2.29444e36	−	1.26784e36i	−0.120861	−	0.0667842i
$961$	7.20357e36			0.374546
$962$			1.60081e37i			0.821583i
$963$			2.33931e36i			0.118511i
$964$	1.08448e35			0.00542324
$965$	3.28228e35	+	1.81369e35i	0.0162026	+	0.00895307i
$966$	−4.70055e36			−0.229052
$967$			3.63759e37i			1.74978i	0.484322	+	0.874890i	$0.339066\pi$
$967$			3.63759e37i			1.74978i	−0.484322	+	0.874890i	$0.660934\pi$
$968$			5.01544e36i			0.238159i
$969$	−6.52836e36			−0.306025
$970$	1.22313e36	−	2.21352e36i	0.0566011	−	0.102432i
$971$	−2.46036e36			−0.112398			−0.0561990	−	0.998420i	$-0.517898\pi$
$971$	−2.46036e36			−0.112398			−0.0561990	+	0.998420i	$0.517898\pi$
$972$		−	4.80208e36i		−	0.216572i
$973$		−	8.66027e36i		−	0.385586i
$974$	1.71295e37			0.752934
$975$	−1.32111e37	−	2.10175e37i	−0.573299	−	0.912060i
$976$	8.29163e35			0.0355236
$977$		−	7.12253e36i		−	0.301268i	−0.988590	−	0.150634i	$-0.951869\pi$
$977$		−	7.12253e36i		−	0.301268i	0.988590	−	0.150634i	$-0.0481314\pi$
$978$			7.88666e36i			0.329350i
$979$	−1.72353e37			−0.710614
$980$	5.34109e36	−	9.66589e36i	0.217422	−	0.393474i
$981$	9.92960e36			0.399088
$982$			1.69407e36i			0.0672260i
$983$		−	3.14802e37i		−	1.23344i	−0.787183	−	0.616720i	$-0.788461\pi$
$983$		−	3.14802e37i		−	1.23344i	0.787183	−	0.616720i	$-0.211539\pi$
$984$	−7.93152e36			−0.306844
$985$	3.45098e37	+	1.90691e37i	1.31822	+	0.728412i
$986$	−1.08750e37			−0.410173
$987$			1.29975e37i			0.484057i
$988$			6.40894e36i			0.235681i
$989$	−9.13547e35			−0.0331724
$990$	−2.17261e36	−	1.20052e36i	−0.0779008	−	0.0430457i
$991$	2.04047e37			0.722454			0.361227	−	0.932478i	$-0.382358\pi$
$991$	2.04047e37			0.722454			0.361227	+	0.932478i	$0.382358\pi$
$992$			5.92790e36i			0.207255i
$993$		−	3.04849e37i		−	1.05249i
$994$	−1.08266e37			−0.369115
$995$	1.69255e37	−	3.06305e37i	0.569840	−	1.03125i
$996$	2.92157e37			0.971348
$997$		−	1.06204e37i		−	0.348700i	−0.984684	−	0.174350i	$-0.944218\pi$
$997$		−	1.06204e37i		−	0.348700i	0.984684	−	0.174350i	$-0.0557825\pi$
$998$		−	2.12904e37i		−	0.690323i
$999$	−3.20478e37			−1.02619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.b.a.9.8	yes	12
5.2	odd	4		50.26.a.k.1.2		6
5.3	odd	4		50.26.a.l.1.5		6
5.4	even	2	inner	10.26.b.a.9.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.5	✓	12	5.4	even	2	inner
10.26.b.a.9.8	yes	12	1.1	even	1	trivial
50.26.a.k.1.2		6	5.2	odd	4
50.26.a.l.1.5		6	5.3	odd	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4096.00i q^{2} -1.01684e6i q^{3} -1.67772e7 q^{4} +(-2.64029e8 + 4.77820e8i) q^{5} +4.16497e9 q^{6} -1.16326e10i q^{7} -6.87195e10i q^{8} -1.86674e11 q^{9} +(-1.95715e12 - 1.08146e12i) q^{10} -5.94667e12 q^{11} +1.70597e13i q^{12} +8.19186e13i q^{13} +4.76472e13 q^{14} +(4.85866e14 + 2.68475e14i) q^{15} +2.81475e14 q^{16} +1.37679e15i q^{17} -7.64617e14i q^{18} -4.66320e15 q^{19} +(4.42968e15 - 8.01649e15i) q^{20} -1.18285e16 q^{21} -2.43576e16i q^{22} -9.70196e16i q^{23} -6.98767e16 q^{24} +(-1.58600e17 - 2.52317e17i) q^{25} -3.35539e17 q^{26} -6.71739e17i q^{27} +1.95163e17i q^{28} +1.92842e18 q^{29} +(-1.09968e18 + 1.99011e18i) q^{30} +5.14163e18 q^{31} +1.15292e18i q^{32} +6.04681e18i q^{33} -5.63933e18 q^{34} +(5.55829e18 + 3.07135e18i) q^{35} +3.13187e18 q^{36} -4.77086e19i q^{37} -1.91005e19i q^{38} +8.32981e19 q^{39} +(3.28355e19 + 1.81440e19i) q^{40} +1.13507e20 q^{41} -4.84495e19i q^{42} -9.41611e18i q^{43} +9.97685e19 q^{44} +(4.92874e19 - 8.91965e19i) q^{45} +3.97392e20 q^{46} -1.09883e21i q^{47} -2.86215e20i q^{48} +1.20575e21 q^{49} +(1.03349e21 - 6.49627e20i) q^{50} +1.39998e21 q^{51} -1.37437e21i q^{52} -6.11805e20i q^{53} +2.75144e21 q^{54} +(1.57009e21 - 2.84144e21i) q^{55} -7.99387e20 q^{56} +4.74172e21i q^{57} +7.89879e21i q^{58} +1.74642e22 q^{59} +(-8.15148e21 - 4.50427e21i) q^{60} +2.94578e21 q^{61} +2.10601e22i q^{62} +2.17151e21i q^{63} -4.72237e21 q^{64} +(-3.91423e22 - 2.16289e22i) q^{65} -2.47677e22 q^{66} -5.85392e22i q^{67} -2.30987e22i q^{68} -9.86533e22 q^{69} +(-1.25802e22 + 2.27668e22i) q^{70} -2.27224e23 q^{71} +1.28281e22i q^{72} +2.69974e23i q^{73} +1.95415e23 q^{74} +(-2.56566e23 + 1.61271e23i) q^{75} +7.82355e22 q^{76} +6.91753e22i q^{77} +3.41189e23i q^{78} +9.35155e23 q^{79} +(-7.43176e22 + 1.34494e23i) q^{80} -8.41218e23 q^{81} +4.64926e23i q^{82} -1.71255e24i q^{83} +1.98449e23 q^{84} +(-6.57858e23 - 3.63513e23i) q^{85} +3.85684e22 q^{86} -1.96089e24i q^{87} +4.08652e23i q^{88} +2.89830e24 q^{89} +(3.65349e23 + 2.01881e23i) q^{90} +9.52927e23 q^{91} +1.62772e24i q^{92} -5.22821e24i q^{93} +4.50081e24 q^{94} +(1.23122e24 - 2.22817e24i) q^{95} +1.17234e24 q^{96} +1.13099e24i q^{97} +4.93876e24i q^{98} +1.11009e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 201326592 q^{4} - 490295340 q^{5} - 6565199872 q^{6} - 1082937564236 q^{9} + 1636528619520 q^{10} + 19723089228624 q^{11} + 278591122243584 q^{14} - 449884766537680 q^{15} + 33\!\cdots\!72 q^{16}+ \cdots + 41\!\cdots\!28 q^{99}+O(q^{100}) \) 12 * q - 201326592 * q^4 - 490295340 * q^5 - 6565199872 * q^6 - 1082937564236 * q^9 + 1636528619520 * q^10 + 19723089228624 * q^11 + 278591122243584 * q^14 - 449884766537680 * q^15 + 3377699720527872 * q^16 - 4015312977833040 * q^19 + 8225790822973440 * q^20 - 56363420582029456 * q^21 + 110145776335716352 * q^24 - 1047554086248996900 * q^25 - 252210272532037632 * q^26 + 5852064063311009640 * q^29 - 3747916483574824960 * q^30 + 158585871554029824 * q^31 + 28121800210885115904 * q^34 - 42730948507221221040 * q^35 + 18168677429701246976 * q^36 - 249453273245123586912 * q^39 - 27456394139868856320 * q^40 + 206458603439752488024 * q^41 - 330898528175898230784 * q^44 + 957114913653485255020 * q^45 - 1111751773656740462592 * q^46 - 3432561496278055389084 * q^49 + 346631457781510963200 * q^50 - 3032451787323924027136 * q^51 + 6455741354411915345920 * q^54 - 7824754202169531625680 * q^55 - 4673983433563013382144 * q^56 + 24998150261761560337680 * q^59 + 7547813903312229498880 * q^60 + 7374571220622236593224 * q^61 - 56668397794435742564352 * q^64 + 20652620138653742557920 * q^65 + 56072959085731865952256 * q^66 - 370250651964757999709072 * q^69 + 157367128964587932549120 * q^70 + 149137752442507323299424 * q^71 + 27409492362780459270144 * q^74 + 1032897211530510645911200 * q^75 + 67365773136708124016640 * q^76 + 801700633747623249599040 * q^79 - 138005869407843165143040 * q^80 - 2864220237232227656687428 * q^81 + 945621281603553901674496 * q^84 + 2004099032091709203221760 * q^85 - 1363071174568488987328512 * q^86 - 5964345056120682049233480 * q^89 + 4840324611668628597309440 * q^90 - 14003423438242038482629536 * q^91 + 3325183945859356082110464 * q^94 + 18644670331946084490382800 * q^95 - 1847939481072001752236032 * q^96 + 4107440578564823447146928 * q^99

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