LMFDB - Embedded newform 15.10.b.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,10,Mod(4,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("15.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	15.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:	$7.72553754246$
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} + 939x^{6} + 217699x^{4} + 14559561x^{2} + 31136400 $ x^8 + 939x^6 + 217699x^4 + 14559561*x^2 + 31136400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{12}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.1
Root			$25.1000i$ of defining polynomial
Character	$\chi$	$=$	15.4
Dual form			15.10.b.a.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-33.3847i q^{2} -81.0000i q^{3} -602.537 q^{4} +(-1324.50 + 445.892i) q^{5} -2704.16 q^{6} +176.118i q^{7} +3022.54i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q-33.3847i q^{2} -81.0000i q^{3} -602.537 q^{4} +(-1324.50 + 445.892i) q^{5} -2704.16 q^{6} +176.118i q^{7} +3022.54i q^{8} -6561.00 q^{9} +(14886.0 + 44218.1i) q^{10} +7384.01 q^{11} +48805.5i q^{12} +104513. i q^{13} +5879.66 q^{14} +(36117.3 + 107285. i) q^{15} -207592. q^{16} -511883. i q^{17} +219037. i q^{18} -833220. q^{19} +(798061. - 268666. i) q^{20} +14265.6 q^{21} -246513. i q^{22} -868467. i q^{23} +244826. q^{24} +(1.55549e6 - 1.18117e6i) q^{25} +3.48914e6 q^{26} +531441. i q^{27} -106118. i q^{28} -5.35363e6 q^{29} +(3.58166e6 - 1.20576e6i) q^{30} -4.02269e6 q^{31} +8.47794e6i q^{32} -598105. i q^{33} -1.70891e7 q^{34} +(-78529.8 - 233269. i) q^{35} +3.95324e6 q^{36} -1.22004e7i q^{37} +2.78168e7i q^{38} +8.46556e6 q^{39} +(-1.34773e6 - 4.00337e6i) q^{40} +3.24801e7 q^{41} -476252. i q^{42} +1.40745e7i q^{43} -4.44914e6 q^{44} +(8.69006e6 - 2.92550e6i) q^{45} -2.89935e7 q^{46} -4.74310e7i q^{47} +1.68150e7i q^{48} +4.03226e7 q^{49} +(-3.94330e7 - 5.19294e7i) q^{50} -4.14625e7 q^{51} -6.29730e7i q^{52} -4.00971e7i q^{53} +1.77420e7 q^{54} +(-9.78013e6 + 3.29247e6i) q^{55} -532326. q^{56} +6.74908e7i q^{57} +1.78729e8i q^{58} +1.14018e8 q^{59} +(-2.17620e7 - 6.46430e7i) q^{60} -4.22275e7 q^{61} +1.34296e8i q^{62} -1.15551e6i q^{63} +1.76746e8 q^{64} +(-4.66016e7 - 1.38428e8i) q^{65} -1.99675e7 q^{66} -1.12743e8i q^{67} +3.08428e8i q^{68} -7.03458e7 q^{69} +(-7.78762e6 + 2.62169e6i) q^{70} -2.94605e8 q^{71} -1.98309e7i q^{72} +2.45468e8i q^{73} -4.07307e8 q^{74} +(-9.56748e7 - 1.25994e8i) q^{75} +5.02046e8 q^{76} +1.30046e6i q^{77} -2.82620e8i q^{78} +4.95230e7 q^{79} +(2.74956e8 - 9.25637e7i) q^{80} +4.30467e7 q^{81} -1.08434e9i q^{82} -1.96219e8i q^{83} -8.59554e6 q^{84} +(2.28245e8 + 6.77990e8i) q^{85} +4.69872e8 q^{86} +4.33644e8i q^{87} +2.23185e7i q^{88} -1.02076e8 q^{89} +(-9.76668e7 - 2.90115e8i) q^{90} -1.84067e7 q^{91} +5.23284e8i q^{92} +3.25838e8i q^{93} -1.58347e9 q^{94} +(1.10360e9 - 3.71526e8i) q^{95} +6.86713e8 q^{96} -1.08777e8i q^{97} -1.34616e9i q^{98} -4.84465e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9}+O(q^{10}) $ 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9	\( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9} + 67090 q^{10} - 71988 q^{11} + 416364 q^{14} + 80190 q^{15} - 1505630 q^{16} + 851584 q^{19} + 2078100 q^{20} - 1593108 q^{21} + 1242702 q^{24} + 1695500 q^{25} - 877524 q^{26} - 73572 q^{29} + 3086100 q^{30} + 474088 q^{31} - 8124388 q^{34} - 36357180 q^{35} + 7833834 q^{36} + 12959676 q^{39} - 15313390 q^{40} + 93320088 q^{41} - 74555892 q^{44} + 4527090 q^{45} - 9664072 q^{46} + 51329600 q^{49} + 67798200 q^{50} - 108196236 q^{51} - 3188646 q^{54} + 64428480 q^{55} - 67781220 q^{56} + 236526036 q^{59} + 63172710 q^{60} - 357427760 q^{61} - 12137026 q^{64} + 19848300 q^{65} + 23317308 q^{66} + 167059584 q^{69} + 200900520 q^{70} - 156890664 q^{71} - 1523381796 q^{74} - 528573600 q^{75} + 1098697344 q^{76} + 863922280 q^{79} + 630213180 q^{80} + 344373768 q^{81} + 529023636 q^{84} - 2223350420 q^{85} + 997642392 q^{86} + 357382224 q^{89} - 440177490 q^{90} + 214754328 q^{91} - 721679824 q^{94} + 1698584640 q^{95} - 475022718 q^{96} + 472313268 q^{99}+O(q^{100}) \) 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9 + 67090 * q^10 - 71988 * q^11 + 416364 * q^14 + 80190 * q^15 - 1505630 * q^16 + 851584 * q^19 + 2078100 * q^20 - 1593108 * q^21 + 1242702 * q^24 + 1695500 * q^25 - 877524 * q^26 - 73572 * q^29 + 3086100 * q^30 + 474088 * q^31 - 8124388 * q^34 - 36357180 * q^35 + 7833834 * q^36 + 12959676 * q^39 - 15313390 * q^40 + 93320088 * q^41 - 74555892 * q^44 + 4527090 * q^45 - 9664072 * q^46 + 51329600 * q^49 + 67798200 * q^50 - 108196236 * q^51 - 3188646 * q^54 + 64428480 * q^55 - 67781220 * q^56 + 236526036 * q^59 + 63172710 * q^60 - 357427760 * q^61 - 12137026 * q^64 + 19848300 * q^65 + 23317308 * q^66 + 167059584 * q^69 + 200900520 * q^70 - 156890664 * q^71 - 1523381796 * q^74 - 528573600 * q^75 + 1098697344 * q^76 + 863922280 * q^79 + 630213180 * q^80 + 344373768 * q^81 + 529023636 * q^84 - 2223350420 * q^85 + 997642392 * q^86 + 357382224 * q^89 - 440177490 * q^90 + 214754328 * q^91 - 721679824 * q^94 + 1698584640 * q^95 - 475022718 * q^96 + 472313268 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	33.3847i		−	1.47541i	−0.675124	−	0.737704i	$-0.735910\pi$
$2$		−	33.3847i		−	1.47541i	0.675124	−	0.737704i	$-0.264090\pi$
$3$		−	81.0000i		−	0.577350i
$3$		−	81.0000i		−	0.577350i
$4$	−602.537			−1.17683
$5$	−1324.50	+	445.892i	−0.947736	+	0.319054i
$5$	−1324.50	+	445.892i	−0.947736	+	0.319054i
$6$	−2704.16			−0.851827
$7$			176.118i			0.0277245i	0.999904	+	0.0138622i	$0.00441263\pi$
$7$			176.118i			0.0277245i	−0.999904	+	0.0138622i	$0.995587\pi$
$8$			3022.54i			0.260896i
$9$	−6561.00			−0.333333
$10$	14886.0	+	44218.1i	0.470736	+	1.39830i
$11$	7384.01			0.152064			0.0760318	−	0.997105i	$-0.475775\pi$
$11$	7384.01			0.152064			0.0760318	+	0.997105i	$0.475775\pi$
$12$			48805.5i			0.679443i
$13$			104513.i			1.01491i	0.861679	+	0.507453i	$0.169413\pi$
$13$			104513.i			1.01491i	−0.861679	+	0.507453i	$0.830587\pi$
$14$	5879.66			0.0409049
$15$	36117.3	+	107285.i	0.184206	+	0.547176i
$16$	−207592.			−0.791901
$17$		−	511883.i		−	1.48645i	−0.669041	−	0.743226i	$-0.733295\pi$
$17$		−	511883.i		−	1.48645i	0.669041	−	0.743226i	$-0.266705\pi$
$18$			219037.i			0.491803i
$19$	−833220.			−1.46679			−0.733396	−	0.679802i	$-0.762066\pi$
$19$	−833220.			−1.46679			−0.733396	+	0.679802i	$0.762066\pi$
$20$	798061.	−	268666.i	1.11532	−	0.375473i
$21$	14265.6			0.0160067
$22$		−	246513.i		−	0.224356i
$23$		−	868467.i		−	0.647110i	−0.946209	−	0.323555i	$-0.895122\pi$
$23$		−	868467.i		−	0.647110i	0.946209	−	0.323555i	$-0.104878\pi$
$24$	244826.			0.150628
$25$	1.55549e6	−	1.18117e6i	0.796409	−	0.604759i
$26$	3.48914e6			1.49740
$27$			531441.i			0.192450i
$28$		−	106118.i		−	0.0326270i
$29$	−5.35363e6			−1.40559			−0.702793	−	0.711395i	$-0.748064\pi$
$29$	−5.35363e6			−1.40559			−0.702793	+	0.711395i	$0.748064\pi$
$30$	3.58166e6	−	1.20576e6i	0.807308	−	0.271779i
$31$	−4.02269e6			−0.782328			−0.391164	−	0.920321i	$-0.627927\pi$
$31$	−4.02269e6			−0.782328			−0.391164	+	0.920321i	$0.627927\pi$
$32$			8.47794e6i			1.42927i
$33$		−	598105.i		−	0.0877939i
$34$	−1.70891e7			−2.19312
$35$	−78529.8	−	233269.i	−0.00884562	−	0.0262755i
$36$	3.95324e6			0.392277
$37$		−	1.22004e7i		−	1.07020i	−0.844787	−	0.535102i	$-0.820273\pi$
$37$		−	1.22004e7i		−	1.07020i	0.844787	−	0.535102i	$-0.179727\pi$
$38$			2.78168e7i			2.16412i
$39$	8.46556e6			0.585956
$40$	−1.34773e6	−	4.00337e6i	−0.0832401	−	0.247261i
$41$	3.24801e7			1.79511			0.897554	−	0.440905i	$-0.145342\pi$
$41$	3.24801e7			1.79511			0.897554	+	0.440905i	$0.145342\pi$
$42$		−	476252.i		−	0.0236165i
$43$			1.40745e7i			0.627804i	0.949455	+	0.313902i	$0.101636\pi$
$43$			1.40745e7i			0.627804i	−0.949455	+	0.313902i	$0.898364\pi$
$44$	−4.44914e6			−0.178953
$45$	8.69006e6	−	2.92550e6i	0.315912	−	0.106351i
$46$	−2.89935e7			−0.954752
$47$		−	4.74310e7i		−	1.41782i	−0.705298	−	0.708911i	$-0.749187\pi$
$47$		−	4.74310e7i		−	1.41782i	0.705298	−	0.708911i	$-0.250813\pi$
$48$			1.68150e7i			0.457204i
$49$	4.03226e7			0.999231
$50$	−3.94330e7	−	5.19294e7i	−0.892266	−	1.17503i
$51$	−4.14625e7			−0.858203
$52$		−	6.29730e7i		−	1.19437i
$53$		−	4.00971e7i		−	0.698026i	−0.937118	−	0.349013i	$-0.886517\pi$
$53$		−	4.00971e7i		−	0.698026i	0.937118	−	0.349013i	$-0.113483\pi$
$54$	1.77420e7			0.283942
$55$	−9.78013e6	+	3.29247e6i	−0.144116	+	0.0485166i
$56$	−532326.			−0.00723321
$57$			6.74908e7i			0.846853i
$58$			1.78729e8i			2.07381i
$59$	1.14018e8			1.22501			0.612503	−	0.790468i	$-0.290163\pi$
$59$	1.14018e8			1.22501			0.612503	+	0.790468i	$0.290163\pi$
$60$	−2.17620e7	−	6.46430e7i	−0.216779	−	0.643933i
$61$	−4.22275e7			−0.390491			−0.195245	−	0.980754i	$-0.562550\pi$
$61$	−4.22275e7			−0.390491			−0.195245	+	0.980754i	$0.562550\pi$
$62$			1.34296e8i			1.15425i
$63$		−	1.15551e6i		−	0.00924150i
$64$	1.76746e8			1.31686
$65$	−4.66016e7	−	1.38428e8i	−0.323810	−	0.961863i
$66$	−1.99675e7			−0.129532
$67$		−	1.12743e8i		−	0.683521i	−0.939787	−	0.341760i	$-0.888977\pi$
$67$		−	1.12743e8i		−	0.683521i	0.939787	−	0.341760i	$-0.111023\pi$
$68$			3.08428e8i			1.74930i
$69$	−7.03458e7			−0.373609
$70$	−7.78762e6	+	2.62169e6i	−0.0387671	+	0.0130509i
$71$	−2.94605e8			−1.37587			−0.687936	−	0.725771i	$-0.741483\pi$
$71$	−2.94605e8			−1.37587			−0.687936	+	0.725771i	$0.741483\pi$
$72$		−	1.98309e7i		−	0.0869654i
$73$			2.45468e8i			1.01168i	0.862629	+	0.505838i	$0.168817\pi$
$73$			2.45468e8i			1.01168i	−0.862629	+	0.505838i	$0.831183\pi$
$74$	−4.07307e8			−1.57899
$75$	−9.56748e7	−	1.25994e8i	−0.349158	−	0.459807i
$76$	5.02046e8			1.72616
$77$			1.30046e6i			0.00421589i
$78$		−	2.82620e8i		−	0.864525i
$79$	4.95230e7			0.143049			0.0715245	−	0.997439i	$-0.477214\pi$
$79$	4.95230e7			0.143049			0.0715245	+	0.997439i	$0.477214\pi$
$80$	2.74956e8	−	9.25637e7i	0.750514	−	0.252660i
$81$	4.30467e7			0.111111
$82$		−	1.08434e9i		−	2.64852i
$83$		−	1.96219e8i		−	0.453826i	−0.973915	−	0.226913i	$-0.927137\pi$
$83$		−	1.96219e8i		−	0.453826i	0.973915	−	0.226913i	$-0.0728633\pi$
$84$	−8.59554e6			−0.0188372
$85$	2.28245e8	+	6.77990e8i	0.474259	+	1.40876i
$86$	4.69872e8			0.926267
$87$			4.33644e8i			0.811515i
$88$			2.23185e7i			0.0396728i
$89$	−1.02076e8			−0.172452			−0.0862259	−	0.996276i	$-0.527481\pi$
$89$	−1.02076e8			−0.172452			−0.0862259	+	0.996276i	$0.527481\pi$
$90$	−9.76668e7	−	2.90115e8i	−0.156912	−	0.466099i
$91$	−1.84067e7			−0.0281377
$92$			5.23284e8i			0.761538i
$93$			3.25838e8i			0.451677i
$94$	−1.58347e9			−2.09187
$95$	1.10360e9	−	3.71526e8i	1.39013	−	0.467986i
$96$	6.86713e8			0.825192
$97$		−	1.08777e8i		−	0.124757i	−0.998053	−	0.0623783i	$-0.980131\pi$
$97$		−	1.08777e8i		−	0.124757i	0.998053	−	0.0623783i	$-0.0198685\pi$
$98$		−	1.34616e9i		−	1.47427i
$99$	−4.84465e7			−0.0506879
$100$	−9.37237e8	+	7.11698e8i	−0.937237	+	0.711698i
$101$	−9.90739e8			−0.947356			−0.473678	−	0.880698i	$-0.657074\pi$
$101$	−9.90739e8			−0.947356			−0.473678	+	0.880698i	$0.657074\pi$
$102$			1.38421e9i			1.26620i
$103$			4.84152e8i			0.423852i	0.977286	+	0.211926i	$0.0679736\pi$
$103$			4.84152e8i			0.423852i	−0.977286	+	0.211926i	$0.932026\pi$
$104$	−3.15896e8			−0.264785
$105$	−1.88948e7	+	6.36092e6i	−0.0151702	+	0.00510702i
$106$	−1.33863e9			−1.02987
$107$			1.22163e9i			0.900972i	0.892783	+	0.450486i	$0.148749\pi$
$107$			1.22163e9i			0.900972i	−0.892783	+	0.450486i	$0.851251\pi$
$108$		−	3.20213e8i		−	0.226481i
$109$	1.73035e9			1.17413			0.587064	−	0.809541i	$-0.300284\pi$
$109$	1.73035e9			1.17413			0.587064	+	0.809541i	$0.300284\pi$
$110$	1.09918e8	+	3.26507e8i	0.0715817	+	0.212630i
$111$	−9.88234e8			−0.617883
$112$		−	3.65608e7i		−	0.0219551i
$113$		−	1.22947e8i		−	0.0709356i	−0.999371	−	0.0354678i	$-0.988708\pi$
$113$		−	1.22947e8i		−	0.0709356i	0.999371	−	0.0354678i	$-0.0112921\pi$
$114$	2.25316e9			1.24945
$115$	3.87243e8	+	1.15029e9i	0.206463	+	0.613290i
$116$	3.22576e9			1.65414
$117$		−	6.85711e8i		−	0.338302i
$118$		−	3.80645e9i		−	1.80738i
$119$	9.01521e7			0.0412111
$120$	−3.24273e8	+	1.09166e8i	−0.142756	+	0.0480587i
$121$	−2.30342e9			−0.976877
$122$			1.40975e9i			0.576133i
$123$		−	2.63089e9i		−	1.03641i
$124$	2.42382e9			0.920667
$125$	−1.53357e9	+	2.25804e9i	−0.561834	+	0.827250i
$126$	−3.85764e7			−0.0136350
$127$		−	5.25492e9i		−	1.79246i	−0.443589	−	0.896230i	$-0.646295\pi$
$127$		−	5.25492e9i		−	1.79246i	0.443589	−	0.896230i	$-0.353705\pi$
$128$		−	1.55991e9i		−	0.513634i
$129$	1.14003e9			0.362463
$130$	−4.62137e9	+	1.55578e9i	−1.41914	+	0.477752i
$131$	−1.55082e9			−0.460088			−0.230044	−	0.973180i	$-0.573887\pi$
$131$	−1.55082e9			−0.460088			−0.230044	+	0.973180i	$0.573887\pi$
$132$			3.60380e8i			0.103319i
$133$		−	1.46745e8i		−	0.0406661i
$134$	−3.76388e9			−1.00847
$135$	−2.36965e8	−	7.03895e8i	−0.0614021	−	0.182392i
$136$	1.54719e9			0.387809
$137$		−	1.68367e9i		−	0.408332i	−0.978936	−	0.204166i	$-0.934552\pi$
$137$		−	1.68367e9i		−	0.408332i	0.978936	−	0.204166i	$-0.0654482\pi$
$138$			2.34847e9i			0.551226i
$139$	5.27031e9			1.19748			0.598742	−	0.800942i	$-0.295667\pi$
$139$	5.27031e9			1.19748			0.598742	+	0.800942i	$0.295667\pi$
$140$	4.73171e7	+	1.40553e8i	0.0104098	+	0.0309218i
$141$	−3.84191e9			−0.818580
$142$			9.83531e9i			2.02997i
$143$			7.71726e8i			0.154330i
$144$	1.36201e9			0.263967
$145$	7.09089e9	−	2.38714e9i	1.33212	−	0.448458i
$146$	8.19486e9			1.49264
$147$		−	3.26613e9i		−	0.576906i
$148$			7.35120e9i			1.25945i
$149$	−9.44826e9			−1.57041			−0.785206	−	0.619234i	$-0.787443\pi$
$149$	−9.44826e9			−1.57041			−0.785206	+	0.619234i	$0.787443\pi$
$150$	−4.20628e9	+	3.19407e9i	−0.678403	+	0.515150i
$151$	4.21457e9			0.659717			0.329858	−	0.944030i	$-0.392999\pi$
$151$	4.21457e9			0.659717			0.329858	+	0.944030i	$0.392999\pi$
$152$		−	2.51844e9i		−	0.382680i
$153$			3.35847e9i			0.495484i
$154$	4.34154e7			0.00622015
$155$	5.32806e9	−	1.79368e9i	0.741440	−	0.249605i
$156$	−5.10081e9			−0.689571
$157$			1.50022e10i			1.97064i	0.170730	+	0.985318i	$0.445387\pi$
$157$			1.50022e10i			1.97064i	−0.170730	+	0.985318i	$0.554613\pi$
$158$		−	1.65331e9i		−	0.211056i
$159$	−3.24786e9			−0.403005
$160$	−3.78025e9	−	1.12290e10i	−0.456016	−	1.35458i
$161$	1.52953e8			0.0179408
$162$		−	1.43710e9i		−	0.163934i
$163$		−	9.23375e9i		−	1.02455i	−0.858821	−	0.512276i	$-0.828803\pi$
$163$		−	9.23375e9i		−	1.02455i	0.858821	−	0.512276i	$-0.171197\pi$
$164$	−1.95705e10			−2.11254
$165$	2.66690e8	+	7.92191e8i	0.0280110	+	0.0832055i
$166$	−6.55071e9			−0.669579
$167$		−	1.54069e10i		−	1.53282i	−0.642353	−	0.766409i	$-0.722042\pi$
$167$		−	1.54069e10i		−	1.53282i	0.642353	−	0.766409i	$-0.277958\pi$
$168$			4.31184e7i			0.00417610i
$169$	−3.18495e8			−0.0300339
$170$	2.26345e10	−	7.61988e9i	2.07850	−	0.699726i
$171$	5.46676e9			0.488931
$172$		−	8.48039e9i		−	0.738818i
$173$			1.49852e10i			1.27190i	0.771729	+	0.635951i	$0.219392\pi$
$173$			1.49852e10i			1.27190i	−0.771729	+	0.635951i	$0.780608\pi$
$174$	1.44771e10			1.19732
$175$	2.08026e8	+	2.73950e8i	0.0167666	+	0.0220800i
$176$	−1.53286e9			−0.120419
$177$		−	9.23544e9i		−	0.707258i
$178$			3.40777e9i			0.254437i
$179$	1.38653e9			0.100946			0.0504732	−	0.998725i	$-0.483927\pi$
$179$	1.38653e9			0.100946			0.0504732	+	0.998725i	$0.483927\pi$
$180$	−5.23608e9	+	1.76272e9i	−0.371775	+	0.125158i
$181$	1.03199e10			0.714696			0.357348	−	0.933971i	$-0.383681\pi$
$181$	1.03199e10			0.714696			0.357348	+	0.933971i	$0.383681\pi$
$182$			6.14501e8i			0.0415147i
$183$			3.42043e9i			0.225450i
$184$	2.62498e9			0.168829
$185$	5.44007e9	+	1.61595e10i	0.341454	+	1.01427i
$186$	1.08780e10			0.666408
$187$		−	3.77975e9i		−	0.226035i
$188$			2.85789e10i			1.66854i
$189$	−9.35965e7			−0.00533558
$190$	−1.24033e10	−	3.68434e10i	−0.690471	−	2.05101i
$191$	−1.25552e10			−0.682612			−0.341306	−	0.939952i	$-0.610869\pi$
$191$	−1.25552e10			−0.682612			−0.341306	+	0.939952i	$0.610869\pi$
$192$		−	1.43164e10i		−	0.760290i
$193$			1.70439e10i			0.884220i	0.896961	+	0.442110i	$0.145770\pi$
$193$			1.70439e10i			0.884220i	−0.896961	+	0.442110i	$0.854230\pi$
$194$	−3.63148e9			−0.184067
$195$	−1.12127e10	+	3.77473e9i	−0.555332	+	0.186952i
$196$	−2.42958e10			−1.17593
$197$		−	4.93879e9i		−	0.233627i	−0.993154	−	0.116813i	$-0.962732\pi$
$197$		−	4.93879e9i		−	0.233627i	0.993154	−	0.116813i	$-0.0372680\pi$
$198$			1.61737e9i			0.0747853i
$199$	1.98630e8			0.00897855			0.00448927	−	0.999990i	$-0.498571\pi$
$199$	1.98630e8			0.00897855			0.00448927	+	0.999990i	$0.498571\pi$
$200$	3.57014e9	+	4.70152e9i	0.157779	+	0.207780i
$201$	−9.13216e9			−0.394631
$202$			3.30755e10i			1.39774i
$203$		−	9.42873e8i		−	0.0389691i
$204$	2.49827e10			1.00996
$205$	−4.30200e10	+	1.44826e10i	−1.70129	+	0.572737i
$206$	1.61633e10			0.625355
$207$			5.69801e9i			0.215703i
$208$		−	2.16961e10i		−	0.803705i
$209$	−6.15250e9			−0.223046
$210$	2.12357e8	+	6.30797e8i	0.00753494	+	0.0223822i
$211$	−1.18996e10			−0.413295			−0.206647	−	0.978415i	$-0.566255\pi$
$211$	−1.18996e10			−0.413295			−0.206647	+	0.978415i	$0.566255\pi$
$212$			2.41600e10i			0.821457i
$213$			2.38630e10i			0.794360i
$214$	4.07836e10			1.32930
$215$	−6.27570e9	−	1.86417e10i	−0.200304	−	0.594993i
$216$	−1.60630e9			−0.0502095
$217$		−	7.08469e8i		−	0.0216896i
$218$		−	5.77673e10i		−	1.73232i
$219$	1.98829e10			0.584091
$220$	5.89289e9	−	1.98384e9i	0.169600	−	0.0570957i
$221$	5.34985e10			1.50861
$222$			3.29919e10i			0.911630i
$223$		−	1.26162e10i		−	0.341630i	−0.985303	−	0.170815i	$-0.945360\pi$
$223$		−	1.26162e10i		−	0.341630i	0.985303	−	0.170815i	$-0.0546401\pi$
$224$	−1.49312e9			−0.0396259
$225$	−1.02055e10	+	7.74966e9i	−0.265470	+	0.201586i
$226$	−4.10454e9			−0.104659
$227$		−	5.89551e10i		−	1.47369i	−0.676064	−	0.736843i	$-0.736316\pi$
$227$		−	5.89551e10i		−	1.47369i	0.676064	−	0.736843i	$-0.263684\pi$
$228$		−	4.06657e10i		−	0.996601i
$229$	−2.13417e9			−0.0512826			−0.0256413	−	0.999671i	$-0.508163\pi$
$229$	−2.13417e9			−0.0512826			−0.0256413	+	0.999671i	$0.508163\pi$
$230$	3.84019e10	−	1.29280e10i	0.904853	−	0.304618i
$231$	1.05337e8			0.00243404
$232$		−	1.61816e10i		−	0.366712i
$233$		−	1.39898e10i		−	0.310964i	−0.987839	−	0.155482i	$-0.950307\pi$
$233$		−	1.39898e10i		−	0.310964i	0.987839	−	0.155482i	$-0.0496930\pi$
$234$	−2.28922e10			−0.499134
$235$	2.11491e10	+	6.28225e10i	0.452363	+	1.34372i
$236$	−6.86999e10			−1.44162
$237$		−	4.01136e9i		−	0.0825894i
$238$		−	3.00970e9i		−	0.0608032i
$239$	−2.40573e10			−0.476932			−0.238466	−	0.971151i	$-0.576645\pi$
$239$	−2.40573e10			−0.476932			−0.238466	+	0.971151i	$0.576645\pi$
$240$	−7.49766e9	−	2.22715e10i	−0.145873	−	0.433309i
$241$	1.74563e10			0.333330			0.166665	−	0.986014i	$-0.446700\pi$
$241$	1.74563e10			0.333330			0.166665	+	0.986014i	$0.446700\pi$
$242$			7.68991e10i			1.44129i
$243$		−	3.48678e9i		−	0.0641500i
$244$	2.54436e10			0.459541
$245$	−5.34073e10	+	1.79795e10i	−0.947008	+	0.318809i
$246$	−8.78314e10			−1.52912
$247$		−	8.70824e10i		−	1.48866i
$248$		−	1.21588e10i		−	0.204106i
$249$	−1.58937e10			−0.262017
$250$	7.53840e10	+	5.11977e10i	1.22053	+	0.828935i
$251$	9.83723e10			1.56438			0.782188	−	0.623042i	$-0.214104\pi$
$251$	9.83723e10			1.56438			0.782188	+	0.623042i	$0.214104\pi$
$252$			6.96239e8i			0.0108757i
$253$		−	6.41277e9i		−	0.0984019i
$254$	−1.75434e11			−2.64461
$255$	5.49172e10	−	1.84878e10i	0.813350	−	0.273814i
$256$	3.84170e10			0.559041
$257$			4.23962e10i			0.606217i	0.952956	+	0.303108i	$0.0980244\pi$
$257$			4.23962e10i			0.606217i	−0.952956	+	0.303108i	$0.901976\pi$
$258$		−	3.80596e10i		−	0.534781i
$259$	2.14872e9			0.0296709
$260$	2.80792e10	+	8.34079e10i	0.381070	+	1.13195i
$261$	3.51252e10			0.468529
$262$			5.17737e10i			0.678818i
$263$			3.13748e10i			0.404371i	0.979347	+	0.202185i	$0.0648044\pi$
$263$			3.13748e10i			0.404371i	−0.979347	+	0.202185i	$0.935196\pi$
$264$	1.80780e9			0.0229051
$265$	1.78790e10	+	5.31087e10i	0.222708	+	0.661544i
$266$	−4.89905e9			−0.0599990
$267$			8.26814e9i			0.0995651i
$268$			6.79316e10i			0.804388i
$269$	2.63108e10			0.306372			0.153186	−	0.988197i	$-0.451047\pi$
$269$	2.63108e10			0.306372			0.153186	+	0.988197i	$0.451047\pi$
$270$	−2.34993e10	+	7.91101e9i	−0.269103	+	0.0905931i
$271$	−1.78573e10			−0.201119			−0.100560	−	0.994931i	$-0.532063\pi$
$271$	−1.78573e10			−0.201119			−0.100560	+	0.994931i	$0.532063\pi$
$272$			1.06263e11i			1.17712i
$273$			1.49094e9i			0.0162453i
$274$	−5.62086e10			−0.602456
$275$	1.14857e10	−	8.72177e9i	0.121105	−	0.0919618i
$276$	4.23860e10			0.439674
$277$		−	1.22017e11i		−	1.24527i	−0.782514	−	0.622633i	$-0.786063\pi$
$277$		−	1.22017e11i		−	1.24527i	0.782514	−	0.622633i	$-0.213937\pi$
$278$		−	1.75948e11i		−	1.76678i
$279$	2.63929e10			0.260776
$280$	7.05066e8	−	2.37360e8i	0.00685518	−	0.00230779i
$281$	−7.63919e10			−0.730919			−0.365459	−	0.930827i	$-0.619088\pi$
$281$	−7.63919e10			−0.730919			−0.365459	+	0.930827i	$0.619088\pi$
$282$			1.28261e11i			1.20774i
$283$		−	1.69528e11i		−	1.57110i	−0.618801	−	0.785548i	$-0.712381\pi$
$283$		−	1.69528e11i		−	1.57110i	0.618801	−	0.785548i	$-0.287619\pi$
$284$	1.77511e11			1.61917
$285$	−3.00936e10	−	8.93917e10i	−0.270192	−	0.802593i
$286$	2.57638e10			0.227700
$287$			5.72035e9i			0.0497684i
$288$		−	5.56238e10i		−	0.476425i
$289$	−1.43437e11			−1.20954
$290$	−7.96940e10	−	2.36727e11i	−0.661659	−	1.96543i
$291$	−8.81092e9			−0.0720282
$292$		−	1.47903e11i		−	1.19057i
$293$			6.79489e10i			0.538614i	0.963054	+	0.269307i	$0.0867947\pi$
$293$			6.79489e10i			0.538614i	−0.963054	+	0.269307i	$0.913205\pi$
$294$	−1.09039e11			−0.851173
$295$	−1.51017e11	+	5.08396e10i	−1.16098	+	0.390844i
$296$	3.68763e10			0.279212
$297$			3.92417e9i			0.0292646i
$298$			3.15427e11i			2.31700i
$299$	9.07662e10			0.656756
$300$	5.76476e10	+	7.59162e10i	0.410899	+	0.541114i
$301$	−2.47877e9			−0.0174055
$302$		−	1.40702e11i		−	0.973351i
$303$			8.02499e10i			0.546956i
$304$	1.72970e11			1.16155
$305$	5.59304e10	−	1.88289e10i	0.370082	−	0.124588i
$306$	1.12121e11			0.731041
$307$			1.09788e11i			0.705397i	0.935737	+	0.352698i	$0.114736\pi$
$307$			1.09788e11i			0.705397i	−0.935737	+	0.352698i	$0.885264\pi$
$308$		−	7.83575e8i		−	0.00496138i
$309$	3.92163e10			0.244711
$310$	−5.98816e10	−	1.77875e11i	−0.368269	−	1.09393i
$311$	−1.17419e11			−0.711731			−0.355865	−	0.934537i	$-0.615814\pi$
$311$	−1.17419e11			−0.711731			−0.355865	+	0.934537i	$0.615814\pi$
$312$			2.55875e10i			0.152874i
$313$		−	8.81118e10i		−	0.518901i	−0.965756	−	0.259450i	$-0.916459\pi$
$313$		−	8.81118e10i		−	0.518901i	0.965756	−	0.259450i	$-0.0835414\pi$
$314$	5.00843e11			2.90749
$315$	5.15234e8	+	1.53048e9i	0.00294854	+	0.00875850i
$316$	−2.98394e10			−0.168344
$317$		−	1.46950e11i		−	0.817341i	−0.912682	−	0.408671i	$-0.865992\pi$
$317$		−	1.46950e11i		−	0.817341i	0.912682	−	0.408671i	$-0.134008\pi$
$318$			1.08429e11i			0.594597i
$319$	−3.95313e10			−0.213738
$320$	−2.34101e11	+	7.88097e10i	−1.24804	+	0.420151i
$321$	9.89517e10			0.520177
$322$		−	5.10629e9i		−	0.0264700i
$323$			4.26511e11i			2.18031i
$324$	−2.59372e10			−0.130759
$325$	1.23448e11	+	1.62569e11i	0.613773	+	0.808280i
$326$	−3.08266e11			−1.51163
$327$		−	1.40159e11i		−	0.677883i
$328$			9.81726e10i			0.468337i
$329$	8.35347e9			0.0393084
$330$	2.64470e10	−	8.90337e9i	0.122762	−	0.0413277i
$331$	−3.64768e11			−1.67029			−0.835144	−	0.550032i	$-0.814616\pi$
$331$	−3.64768e11			−1.67029			−0.835144	+	0.550032i	$0.814616\pi$
$332$			1.18229e11i			0.534076i
$333$			8.00469e10i			0.356735i
$334$	−5.14353e11			−2.26153
$335$	5.02711e10	+	1.49328e11i	0.218080	+	0.647797i
$336$	−2.96143e9			−0.0126758
$337$		−	5.86492e10i		−	0.247701i	−0.992301	−	0.123851i	$-0.960476\pi$
$337$		−	5.86492e10i		−	0.247701i	0.992301	−	0.123851i	$-0.0395243\pi$
$338$			1.06328e10i			0.0443123i
$339$	−9.95869e9			−0.0409547
$340$	−1.37526e11	−	4.08514e11i	−0.558122	−	1.65788i
$341$	−2.97036e10			−0.118964
$342$		−	1.82506e11i		−	0.721372i
$343$			1.42086e10i			0.0554277i
$344$	−4.25407e10			−0.163792
$345$	9.31732e10	−	3.13667e10i	0.354083	−	0.119202i
$346$	5.00275e11			1.87658
$347$			1.80488e11i			0.668292i	0.942521	+	0.334146i	$0.108448\pi$
$347$			1.80488e11i			0.668292i	−0.942521	+	0.334146i	$0.891552\pi$
$348$		−	2.61287e11i		−	0.955015i
$349$	3.68672e11			1.33023			0.665113	−	0.746743i	$-0.268383\pi$
$349$	3.68672e11			1.33023			0.665113	+	0.746743i	$0.268383\pi$
$350$	9.14572e9	−	6.94487e9i	0.0325770	−	0.0247376i
$351$	−5.55426e10			−0.195319
$352$			6.26012e10i			0.217341i
$353$			4.25422e9i			0.0145826i	0.999973	+	0.00729128i	$0.00232091\pi$
$353$			4.25422e9i			0.0145826i	−0.999973	+	0.00729128i	$0.997679\pi$
$354$	−3.08322e11			−1.04349
$355$	3.90206e11	−	1.31362e11i	1.30396	−	0.438978i
$356$	6.15045e10			0.202946
$357$		−	7.30232e9i		−	0.0237932i
$358$		−	4.62889e10i		−	0.148937i
$359$	4.35614e10			0.138413			0.0692065	−	0.997602i	$-0.477953\pi$
$359$	4.35614e10			0.138413			0.0692065	+	0.997602i	$0.477953\pi$
$360$	8.84245e9	+	2.62661e10i	0.0277467	+	0.0824203i
$361$	3.71568e11			1.15148
$362$		−	3.44526e11i		−	1.05447i
$363$			1.86577e11i			0.564000i
$364$	1.10907e10			0.0331133
$365$	−1.09452e11	−	3.25122e11i	−0.322780	−	0.958802i
$366$	1.14190e11			0.332631
$367$			6.60321e11i			1.90002i	0.312220	+	0.950010i	$0.398927\pi$
$367$			6.60321e11i			1.90002i	−0.312220	+	0.950010i	$0.601073\pi$
$368$			1.80287e11i			0.512447i
$369$	−2.13102e11			−0.598369
$370$	5.39479e11	−	1.81615e11i	1.49647	−	0.503784i
$371$	7.06184e9			0.0193524
$372$		−	1.96329e11i		−	0.531547i
$373$		−	2.84896e11i		−	0.762072i	−0.924560	−	0.381036i	$-0.875567\pi$
$373$		−	2.84896e11i		−	0.762072i	0.924560	−	0.381036i	$-0.124433\pi$
$374$	−1.26186e11			−0.333494
$375$	1.82901e11	+	1.24219e11i	0.477613	+	0.324375i
$376$	1.43362e11			0.369905
$377$		−	5.59525e11i		−	1.42654i
$378$			3.12469e9i			0.00787216i
$379$	−5.73151e11			−1.42690			−0.713448	−	0.700708i	$-0.752868\pi$
$379$	−5.73151e11			−1.42690			−0.713448	+	0.700708i	$0.752868\pi$
$380$	−6.64960e11	+	2.23858e11i	−1.63595	+	0.550740i
$381$	−4.25649e11			−1.03488
$382$			4.19152e11i			1.00713i
$383$		−	6.41450e11i		−	1.52324i	−0.648025	−	0.761619i	$-0.724405\pi$
$383$		−	6.41450e11i		−	1.52324i	0.648025	−	0.761619i	$-0.275595\pi$
$384$	−1.26353e11			−0.296547
$385$	−5.79865e8	−	1.72246e9i	−0.00134510	−	0.00399555i
$386$	5.69004e11			1.30459
$387$		−	9.23426e10i		−	0.209268i
$388$			6.55420e10i			0.146817i
$389$	−2.64193e11			−0.584989			−0.292494	−	0.956267i	$-0.594485\pi$
$389$	−2.64193e11			−0.584989			−0.292494	+	0.956267i	$0.594485\pi$
$390$	1.26018e11	+	3.74331e11i	0.275830	+	0.819341i
$391$	−4.44554e11			−0.961898
$392$			1.21877e11i			0.260696i
$393$			1.25617e11i			0.265632i
$394$	−1.64880e11			−0.344695
$395$	−6.55933e10	+	2.20819e10i	−0.135573	+	0.0456404i
$396$	2.91908e10			0.0596510
$397$			5.69726e11i			1.15109i	0.817770	+	0.575545i	$0.195210\pi$
$397$			5.69726e11i			1.15109i	−0.817770	+	0.575545i	$0.804790\pi$
$398$		−	6.63120e9i		−	0.0132470i
$399$	−1.18864e10			−0.0234786
$400$	−3.22907e11	+	2.45202e11i	−0.630677	+	0.478910i
$401$	2.22076e11			0.428896			0.214448	−	0.976735i	$-0.431205\pi$
$401$	2.22076e11			0.428896			0.214448	+	0.976735i	$0.431205\pi$
$402$			3.04874e11i			0.582242i
$403$		−	4.20424e11i		−	0.793989i
$404$	5.96957e11			1.11488
$405$	−5.70155e10	+	1.91942e10i	−0.105304	+	0.0354505i
$406$	−3.14775e10			−0.0574954
$407$		−	9.00880e10i		−	0.162739i
$408$		−	1.25322e11i		−	0.223902i
$409$	5.50237e11			0.972288			0.486144	−	0.873879i	$-0.338403\pi$
$409$	5.50237e11			0.972288			0.486144	+	0.873879i	$0.338403\pi$
$410$	4.83498e11	+	1.43621e12i	0.845021	+	2.51010i
$411$	−1.36377e11			−0.235751
$412$		−	2.91720e11i		−	0.498802i
$413$			2.00806e10i			0.0339627i
$414$	1.90226e11			0.318251
$415$	8.74925e10	+	2.59892e11i	0.144795	+	0.430108i
$416$	−8.86056e11			−1.45058
$417$		−	4.26895e11i		−	0.691368i
$418$			2.05399e11i			0.329083i
$419$	6.71669e11			1.06461			0.532307	−	0.846551i	$-0.321325\pi$
$419$	6.71669e11			1.06461			0.532307	+	0.846551i	$0.321325\pi$
$420$	1.13848e10	−	3.83269e9i	0.0178527	−	0.00601010i
$421$	1.21865e11			0.189064			0.0945319	−	0.995522i	$-0.469865\pi$
$421$	1.21865e11			0.189064			0.0945319	+	0.995522i	$0.469865\pi$
$422$			3.97263e11i			0.609779i
$423$			3.11195e11i			0.472608i
$424$	1.21195e11			0.182112
$425$	−6.04621e11	−	7.96227e11i	−0.898945	−	1.18382i
$426$	7.96660e11			1.17201
$427$		−	7.43704e9i		−	0.0108262i
$428$		−	7.36075e11i		−	1.06029i
$429$	6.25098e10			0.0891026
$430$	−6.22346e11	+	2.09512e11i	−0.877857	+	0.295530i
$431$	−1.01277e11			−0.141372			−0.0706861	−	0.997499i	$-0.522519\pi$
$431$	−1.01277e11			−0.141372			−0.0706861	+	0.997499i	$0.522519\pi$
$432$		−	1.10323e11i		−	0.152401i
$433$		−	1.29530e12i		−	1.77082i	−0.464810	−	0.885410i	$-0.653878\pi$
$433$		−	1.29530e12i		−	1.77082i	0.464810	−	0.885410i	$-0.346122\pi$
$434$	−2.36520e10			−0.0320011
$435$	−1.93358e11	−	5.74362e11i	−0.258918	−	0.769103i
$436$	−1.04260e12			−1.38175
$437$			7.23624e11i			0.949176i
$438$		−	6.63784e11i		−	0.861773i
$439$	1.02933e12			1.32271			0.661353	−	0.750075i	$-0.269983\pi$
$439$	1.02933e12			1.32271			0.661353	+	0.750075i	$0.269983\pi$
$440$	−9.95164e9	−	2.95609e10i	−0.0126578	−	0.0375994i
$441$	−2.64557e11			−0.333077
$442$		−	1.78603e12i		−	2.22581i
$443$			5.44414e11i			0.671603i	0.941933	+	0.335802i	$0.109007\pi$
$443$			5.44414e11i			0.671603i	−0.941933	+	0.335802i	$0.890993\pi$
$444$	5.95447e11			0.727143
$445$	1.35200e11	−	4.55148e10i	0.163439	−	0.0550215i
$446$	−4.21188e11			−0.504044
$447$			7.65309e11i			0.906678i
$448$			3.11283e10i			0.0365093i
$449$	9.40286e10			0.109182			0.0545911	−	0.998509i	$-0.482614\pi$
$449$	9.40286e10			0.109182			0.0545911	+	0.998509i	$0.482614\pi$
$450$	2.58720e11	+	3.40709e11i	0.297422	+	0.391676i
$451$	2.39834e11			0.272970
$452$			7.40800e10i			0.0834791i
$453$		−	3.41380e11i		−	0.380888i
$454$	−1.96820e12			−2.17429
$455$	2.43797e10	−	8.20740e9i	0.0266672	−	0.00897747i
$456$	−2.03994e11			−0.220941
$457$			7.54861e11i			0.809551i	0.914416	+	0.404775i	$0.132650\pi$
$457$			7.54861e11i			0.809551i	−0.914416	+	0.404775i	$0.867350\pi$
$458$			7.12487e10i			0.0756628i
$459$	2.72036e11			0.286068
$460$	−2.33328e11	−	6.93090e11i	−0.242972	−	0.721738i
$461$	4.43398e11			0.457235			0.228618	−	0.973516i	$-0.426579\pi$
$461$	4.43398e11			0.457235			0.228618	+	0.973516i	$0.426579\pi$
$462$		−	3.51665e9i		−	0.00359121i
$463$			1.74896e10i			0.0176875i	0.999961	+	0.00884374i	$0.00281509\pi$
$463$			1.74896e10i			0.0176875i	−0.999961	+	0.00884374i	$0.997185\pi$
$464$	1.11137e12			1.11309
$465$	−1.45288e11	−	4.31573e11i	−0.144110	−	0.428071i
$466$	−4.67045e11			−0.458798
$467$			7.94191e11i			0.772679i	0.922357	+	0.386339i	$0.126261\pi$
$467$			7.94191e11i			0.772679i	−0.922357	+	0.386339i	$0.873739\pi$
$468$			4.13166e11i			0.398124i
$469$	1.98561e10			0.0189503
$470$	2.09731e12	−	7.06056e11i	1.98254	−	0.667420i
$471$	1.21518e12			1.13775
$472$			3.44624e11i			0.319599i
$473$			1.03926e11i			0.0954661i
$474$	−1.33918e11			−0.121853
$475$	−1.29606e12	+	9.84174e11i	−1.16817	+	0.887055i
$476$	−5.43199e10			−0.0484985
$477$			2.63077e11i			0.232675i
$478$			8.03146e11i			0.703670i
$479$	−1.59322e12			−1.38282			−0.691412	−	0.722460i	$-0.743011\pi$
$479$	−1.59322e12			−1.38282			−0.691412	+	0.722460i	$0.743011\pi$
$480$	−9.09553e11	+	3.06200e11i	−0.782064	+	0.263281i
$481$	1.27510e12			1.08616
$482$		−	5.82772e11i		−	0.491798i
$483$		−	1.23892e10i		−	0.0103581i
$484$	1.38790e12			1.14962
$485$	4.85027e10	+	1.44075e11i	0.0398041	+	0.118236i
$486$	−1.16405e11			−0.0946475
$487$		−	1.15091e12i		−	0.927175i	−0.886051	−	0.463587i	$-0.846562\pi$
$487$		−	1.15091e12i		−	0.927175i	0.886051	−	0.463587i	$-0.153438\pi$
$488$		−	1.27634e11i		−	0.101878i
$489$	−7.47933e11			−0.591525
$490$	6.00241e11	+	1.78299e12i	0.470374	+	1.39722i
$491$	5.97320e11			0.463810			0.231905	−	0.972738i	$-0.425504\pi$
$491$	5.97320e11			0.463810			0.231905	+	0.972738i	$0.425504\pi$
$492$			1.58521e12i			1.21967i
$493$			2.74043e12i			2.08933i
$494$	−2.90722e12			−2.19637
$495$	6.41675e10	−	2.16019e10i	0.0480387	−	0.0161722i
$496$	8.35079e11			0.619526
$497$		−	5.18855e10i		−	0.0381454i
$498$			5.30607e11i			0.386582i
$499$	−1.65447e12			−1.19455			−0.597277	−	0.802035i	$-0.703751\pi$
$499$	−1.65447e12			−1.19455			−0.597277	+	0.802035i	$0.703751\pi$
$500$	9.24032e11	−	1.36055e12i	0.661183	−	0.973532i
$501$	−1.24796e12			−0.884972
$502$		−	3.28413e12i		−	2.30809i
$503$		−	6.44906e11i		−	0.449201i	−0.974451	−	0.224600i	$-0.927892\pi$
$503$		−	6.44906e11i		−	0.449201i	0.974451	−	0.224600i	$-0.0721076\pi$
$504$	3.49259e9			0.00241107
$505$	1.31224e12	−	4.41763e11i	0.897843	−	0.302258i
$506$	−2.14088e11			−0.145183
$507$			2.57981e10i			0.0173401i
$508$			3.16628e12i			2.10942i
$509$	−2.79055e12			−1.84272			−0.921362	−	0.388706i	$-0.872922\pi$
$509$	−2.79055e12			−1.84272			−0.921362	+	0.388706i	$0.872922\pi$
$510$	−6.17210e11	−	1.83339e12i	−0.403987	−	1.20002i
$511$	−4.32314e10			−0.0280482
$512$		−	2.08121e12i		−	1.33845i
$513$		−	4.42807e11i		−	0.282284i
$514$	1.41538e12			0.894417
$515$	−2.15880e11	−	6.41261e11i	−0.135232	−	0.401700i
$516$	−6.86911e11			−0.426557
$517$		−	3.50231e11i		−	0.215599i
$518$		−	7.17343e10i		−	0.0437767i
$519$	1.21380e12			0.734333
$520$	4.18404e11	−	1.40855e11i	0.250946	−	0.0844808i
$521$	8.87238e11			0.527558			0.263779	−	0.964583i	$-0.415031\pi$
$521$	8.87238e11			0.527558			0.263779	+	0.964583i	$0.415031\pi$
$522$		−	1.17264e12i		−	0.691271i
$523$		−	2.05833e12i		−	1.20298i	−0.798882	−	0.601488i	$-0.794575\pi$
$523$		−	2.05833e12i		−	1.20298i	0.798882	−	0.601488i	$-0.205425\pi$
$524$	9.34428e11			0.541446
$525$	2.21899e10	−	1.68501e10i	0.0127479	−	0.00968022i
$526$	1.04744e12			0.596612
$527$			2.05915e12i			1.16289i
$528$			1.24162e11i			0.0695241i
$529$	1.04692e12			0.581249
$530$	1.77302e12	−	5.96884e11i	0.976048	−	0.328586i
$531$	−7.48070e11			−0.408335
$532$			8.84195e10i			0.0478570i
$533$			3.39460e12i			1.82187i
$534$	2.76029e11			0.146899
$535$	−5.44714e11	−	1.61805e12i	−0.287459	−	0.853884i
$536$	3.40770e11			0.178328
$537$		−	1.12309e11i		−	0.0582815i
$538$		−	8.78379e11i		−	0.452024i
$539$	2.97742e11			0.151947
$540$	1.42780e11	+	4.24122e11i	0.0722598	+	0.214644i
$541$	−1.48238e12			−0.743996			−0.371998	−	0.928233i	$-0.621327\pi$
$541$	−1.48238e12			−0.743996			−0.371998	+	0.928233i	$0.621327\pi$
$542$			5.96160e11i			0.296733i
$543$		−	8.35910e11i		−	0.412630i
$544$	4.33972e12			2.12455
$545$	−2.29185e12	+	7.71550e11i	−1.11276	+	0.374611i
$546$	4.97746e10			0.0239685
$547$		−	8.85606e10i		−	0.0422958i	−0.999776	−	0.0211479i	$-0.993268\pi$
$547$		−	8.85606e10i		−	0.0422958i	0.999776	−	0.0211479i	$-0.00673209\pi$
$548$			1.01447e12i			0.480537i
$549$	2.77054e11			0.130164
$550$	−2.91174e11	−	3.83447e11i	−0.135681	−	0.178679i
$551$	4.46075e12			2.06170
$552$		−	2.12623e11i		−	0.0974732i
$553$			8.72191e9i			0.00396596i
$554$	−4.07351e12			−1.83728
$555$	1.30892e12	−	4.40646e11i	0.585590	−	0.197138i
$556$	−3.17556e12			−1.40924
$557$			1.60802e12i			0.707852i	0.935273	+	0.353926i	$0.115154\pi$
$557$			1.60802e12i			0.707852i	−0.935273	+	0.353926i	$0.884846\pi$
$558$		−	8.81117e11i		−	0.384751i
$559$	−1.47097e12			−0.637162
$560$	1.63022e10	+	4.84249e10i	0.00700486	+	0.0208076i
$561$	−3.06160e11			−0.130501
$562$			2.55032e12i			1.07840i
$563$		−	3.70689e12i		−	1.55497i	−0.628902	−	0.777485i	$-0.716495\pi$
$563$		−	3.70689e12i		−	1.55497i	0.628902	−	0.777485i	$-0.283505\pi$
$564$	2.31489e12			0.963330
$565$	5.48210e10	+	1.62843e11i	0.0226323	+	0.0672282i
$566$	−5.65964e12			−2.31801
$567$			7.58132e9i			0.00308050i
$568$		−	8.90458e11i		−	0.358960i
$569$	2.37868e12			0.951330			0.475665	−	0.879626i	$-0.342207\pi$
$569$	2.37868e12			0.951330			0.475665	+	0.879626i	$0.342207\pi$
$570$	−2.98431e12	+	1.00467e12i	−1.18415	+	0.398644i
$571$	−1.63334e12			−0.643006			−0.321503	−	0.946909i	$-0.604188\pi$
$571$	−1.63334e12			−0.643006			−0.321503	+	0.946909i	$0.604188\pi$
$572$		−	4.64993e11i		−	0.181620i
$573$			1.01697e12i			0.394106i
$574$	1.90972e11			0.0734288
$575$	−1.02581e12	−	1.35089e12i	−0.391346	−	0.515364i
$576$	−1.15963e12			−0.438954
$577$			1.63450e12i			0.613894i	0.951727	+	0.306947i	$0.0993074\pi$
$577$			1.63450e12i			0.613894i	−0.951727	+	0.306947i	$0.900693\pi$
$578$			4.78858e12i			1.78456i
$579$	1.38055e12			0.510505
$580$	−4.27252e12	+	1.43834e12i	−1.56768	+	0.527759i
$581$	3.45578e10			0.0125821
$582$			2.94150e11i			0.106271i
$583$		−	2.96077e11i		−	0.106144i
$584$	−7.41937e11			−0.263942
$585$	3.05753e11	+	9.08225e11i	0.107937	+	0.320621i
$586$	2.26845e12			0.794676
$587$		−	2.94392e12i		−	1.02342i	−0.859157	−	0.511711i	$-0.829012\pi$
$587$		−	2.94392e12i		−	1.02342i	0.859157	−	0.511711i	$-0.170988\pi$
$588$			1.96796e12i			0.678921i
$589$	3.35178e12			1.14751
$590$	1.69726e12	+	5.04164e12i	0.576654	+	1.71292i
$591$	−4.00042e11			−0.134885
$592$			2.53271e12i			0.847497i
$593$		−	2.74147e12i		−	0.910410i	−0.890387	−	0.455205i	$-0.849566\pi$
$593$		−	2.74147e12i		−	0.910410i	0.890387	−	0.455205i	$-0.150434\pi$
$594$	1.31007e11			0.0431773
$595$	−1.19407e11	+	4.01981e10i	−0.0390573	+	0.0131486i
$596$	5.69293e12			1.84811
$597$		−	1.60890e10i		−	0.00518377i
$598$		−	3.03020e12i		−	0.968983i
$599$	1.46926e12			0.466314			0.233157	−	0.972439i	$-0.425094\pi$
$599$	1.46926e12			0.466314			0.233157	+	0.972439i	$0.425094\pi$
$600$	3.80823e11	−	2.89181e11i	0.119962	−	0.0910939i
$601$	−2.17277e12			−0.679327			−0.339664	−	0.940547i	$-0.610313\pi$
$601$	−2.17277e12			−0.679327			−0.339664	+	0.940547i	$0.610313\pi$
$602$			8.27531e10i			0.0256803i
$603$			7.39705e11i			0.227840i
$604$	−2.53944e12			−0.776374
$605$	3.05089e12	−	1.02708e12i	0.925822	−	0.311677i
$606$	2.67912e12			0.806984
$607$		−	3.29269e12i		−	0.984467i	−0.870463	−	0.492234i	$-0.836181\pi$
$607$		−	3.29269e12i		−	0.984467i	0.870463	−	0.492234i	$-0.163819\pi$
$608$		−	7.06399e12i		−	2.09645i
$609$	−7.63727e10			−0.0224988
$610$	−6.28597e11	−	1.86722e12i	−0.183818	−	0.546023i
$611$	4.95716e12			1.43896
$612$		−	2.02360e12i		−	0.583100i
$613$			4.60372e12i			1.31685i	0.752646	+	0.658425i	$0.228777\pi$
$613$			4.60372e12i			1.31685i	−0.752646	+	0.658425i	$0.771223\pi$
$614$	3.66525e12			1.04075
$615$	1.17309e12	+	3.48462e12i	0.330670	+	0.982239i
$616$	−3.93070e9			−0.00109991
$617$		−	4.75429e12i		−	1.32069i	−0.750961	−	0.660347i	$-0.770409\pi$
$617$		−	4.75429e12i		−	1.32069i	0.750961	−	0.660347i	$-0.229591\pi$
$618$		−	1.30923e12i		−	0.361049i
$619$	−3.87250e12			−1.06019			−0.530095	−	0.847938i	$-0.677844\pi$
$619$	−3.87250e12			−1.06019			−0.530095	+	0.847938i	$0.677844\pi$
$620$	−3.21035e12	+	1.08076e12i	−0.872549	+	0.293743i
$621$	4.61539e11			0.124536
$622$			3.91999e12i			1.05009i
$623$		−	1.79774e10i		−	0.00478114i
$624$	−1.75738e12			−0.464020
$625$	1.02437e12	−	3.67459e12i	0.268533	−	0.963270i
$626$	−2.94158e12			−0.765591
$627$			4.98353e11i			0.128775i
$628$		−	9.03938e12i		−	2.31910i
$629$	−6.24519e12			−1.59081
$630$	5.10946e10	−	1.72009e10i	0.0129224	−	0.00435030i
$631$	−6.47451e12			−1.62583			−0.812914	−	0.582384i	$-0.802120\pi$
$631$	−6.47451e12			−1.62583			−0.812914	+	0.582384i	$0.802120\pi$
$632$			1.49685e11i			0.0373209i
$633$			9.63865e11i			0.238616i
$634$	−4.90588e12			−1.20591
$635$	2.34313e12	+	6.96016e12i	0.571892	+	1.69878i
$636$	1.95696e12			0.474269
$637$			4.21424e12i			1.01413i
$638$			1.31974e12i			0.315351i
$639$	1.93291e12			0.458624
$640$	6.95551e11	+	2.06610e12i	0.163877	+	0.486790i
$641$	−6.76006e12			−1.58157			−0.790786	−	0.612092i	$-0.790328\pi$
$641$	−6.76006e12			−1.58157			−0.790786	+	0.612092i	$0.790328\pi$
$642$		−	3.30347e12i		−	0.767473i
$643$		−	7.56832e12i		−	1.74602i	−0.487699	−	0.873012i	$-0.662164\pi$
$643$		−	7.56832e12i		−	1.74602i	0.487699	−	0.873012i	$-0.337836\pi$
$644$	−9.21599e10			−0.0211133
$645$	−1.50997e12	+	5.08331e11i	−0.343519	+	0.115645i
$646$	1.42389e13			3.21685
$647$		−	1.53691e12i		−	0.344810i	−0.985026	−	0.172405i	$-0.944846\pi$
$647$		−	1.53691e12i		−	0.344810i	0.985026	−	0.172405i	$-0.0551537\pi$
$648$			1.30111e11i			0.0289885i
$649$	8.41908e11			0.186279
$650$	5.42730e12	−	4.12126e12i	1.19254	−	0.905566i
$651$	−5.73860e10			−0.0125225
$652$			5.56367e12i			1.20572i
$653$		−	2.27119e12i		−	0.488815i	−0.969673	−	0.244408i	$-0.921406\pi$
$653$		−	2.27119e12i		−	0.488815i	0.969673	−	0.244408i	$-0.0785935\pi$
$654$	−4.67915e12			−1.00015
$655$	2.05407e12	−	6.91500e11i	0.436043	−	0.146793i
$656$	−6.74262e12			−1.42155
$657$		−	1.61051e12i		−	0.337225i
$658$		−	2.78878e11i		−	0.0579960i
$659$	1.55488e12			0.321154			0.160577	−	0.987023i	$-0.448665\pi$
$659$	1.55488e12			0.321154			0.160577	+	0.987023i	$0.448665\pi$
$660$	−1.60691e11	−	4.77324e11i	−0.0329642	−	0.0979187i
$661$	4.30537e12			0.877210			0.438605	−	0.898680i	$-0.355473\pi$
$661$	4.30537e12			0.877210			0.438605	+	0.898680i	$0.355473\pi$
$662$			1.21777e13i			2.46436i
$663$		−	4.33338e12i		−	0.870995i
$664$	5.93081e11			0.118402
$665$	6.54326e10	+	1.94365e11i	0.0129747	+	0.0385407i
$666$	2.67234e12			0.526330
$667$			4.64945e12i			0.909569i
$668$			9.28321e12i			1.80386i
$669$	−1.02191e12			−0.197240
$670$	4.98526e12	−	1.67828e12i	0.955766	−	0.321758i
$671$	−3.11808e11			−0.0593794
$672$			1.20943e11i			0.0228780i
$673$			9.14536e12i			1.71843i	0.511611	+	0.859217i	$0.329049\pi$
$673$			9.14536e12i			1.71843i	−0.511611	+	0.859217i	$0.670951\pi$
$674$	−1.95799e12			−0.365460
$675$	6.27722e11	+	8.26649e11i	0.116386	+	0.153269i
$676$	1.91905e11			0.0353448
$677$			1.06240e12i			0.194375i	0.995266	+	0.0971873i	$0.0309846\pi$
$677$			1.06240e12i			0.194375i	−0.995266	+	0.0971873i	$0.969015\pi$
$678$			3.32468e11i			0.0604249i
$679$	1.91576e10			0.00345881
$680$	−2.04926e12	+	6.89880e11i	−0.367541	+	0.123732i
$681$	−4.77536e12			−0.850833
$682$			9.91644e11i			0.175520i
$683$			6.51237e12i			1.14511i	0.819867	+	0.572554i	$0.194047\pi$
$683$			6.51237e12i			1.14511i	−0.819867	+	0.572554i	$0.805953\pi$
$684$	−3.29392e12			−0.575388
$685$	7.50733e11	+	2.23002e12i	0.130280	+	0.386991i
$686$	4.74348e11			0.0817785
$687$			1.72868e11i			0.0296080i
$688$		−	2.92175e12i		−	0.497159i
$689$	4.19067e12			0.708430
$690$	−1.04717e12	−	3.11056e12i	−0.175871	−	0.522417i
$691$	−6.24770e12			−1.04248			−0.521241	−	0.853409i	$-0.674531\pi$
$691$	−6.24770e12			−1.04248			−0.521241	+	0.853409i	$0.674531\pi$
$692$		−	9.02911e12i		−	1.49681i
$693$		−	8.53232e9i		−	0.00140530i
$694$	6.02554e12			0.986003
$695$	−6.98054e12	+	2.34999e12i	−1.13490	+	0.382063i
$696$	−1.31071e12			−0.211721
$697$		−	1.66260e13i		−	2.66834i
$698$		−	1.23080e13i		−	1.96263i
$699$	−1.13317e12			−0.179535
$700$	−1.25343e11	−	1.65065e11i	−0.0197315	−	0.0259844i
$701$	−1.14292e11			−0.0178766			−0.00893829	−	0.999960i	$-0.502845\pi$
$701$	−1.14292e11			−0.0178766			−0.00893829	+	0.999960i	$0.502845\pi$
$702$			1.85427e12i			0.288175i
$703$			1.01656e13i			1.56977i
$704$	1.30510e12			0.200247
$705$	5.08862e12	−	1.71308e12i	0.775798	−	0.261172i
$706$	1.42026e11			0.0215152
$707$		−	1.74487e11i		−	0.0262650i
$708$			5.56469e12i			0.832322i
$709$	−5.05871e11			−0.0751851			−0.0375926	−	0.999293i	$-0.511969\pi$
$709$	−5.05871e11			−0.0751851			−0.0375926	+	0.999293i	$0.511969\pi$
$710$	−4.38549e12	−	1.30269e13i	−0.647672	−	1.92388i
$711$	−3.24920e11			−0.0476830
$712$		−	3.08529e11i		−	0.0449920i
$713$			3.49357e12i			0.506252i
$714$	−2.43785e11			−0.0351048
$715$	−3.44107e11	−	1.02215e12i	−0.0492397	−	0.146264i
$716$	−8.35436e11			−0.118797
$717$			1.94864e12i			0.275357i
$718$		−	1.45428e12i		−	0.204216i
$719$	6.71434e12			0.936965			0.468483	−	0.883473i	$-0.344801\pi$
$719$	6.71434e12			0.936965			0.468483	+	0.883473i	$0.344801\pi$
$720$	−1.80399e12	+	6.07311e11i	−0.250171	+	0.0842199i
$721$	−8.52682e10			−0.0117511
$722$		−	1.24047e13i		−	1.69890i
$723$		−	1.41396e12i		−	0.192448i
$724$	−6.21811e12			−0.841075
$725$	−8.32749e12	+	6.32355e12i	−1.11942	+	0.850041i
$726$	6.22883e12			0.832130
$727$		−	1.59888e12i		−	0.212280i	−0.994351	−	0.106140i	$-0.966151\pi$
$727$		−	1.59888e12i		−	0.212280i	0.994351	−	0.106140i	$-0.0338492\pi$
$728$		−	5.56350e10i		−	0.00734103i
$729$	−2.82430e11			−0.0370370
$730$	−1.08541e13	+	3.65402e12i	−1.41462	+	0.476232i
$731$	7.20448e12			0.933200
$732$		−	2.06093e12i		−	0.265316i
$733$			9.29212e12i			1.18890i	0.804131	+	0.594452i	$0.202631\pi$
$733$			9.29212e12i			1.18890i	−0.804131	+	0.594452i	$0.797369\pi$
$734$	2.20446e13			2.80330
$735$	1.45634e12	+	4.32599e12i	0.184065	+	0.546755i
$736$	7.36281e12			0.924898
$737$		−	8.32493e11i		−	0.103939i
$738$			7.11435e12i			0.882839i
$739$	1.41486e13			1.74508			0.872538	−	0.488546i	$-0.162473\pi$
$739$	1.41486e13			1.74508			0.872538	+	0.488546i	$0.162473\pi$
$740$	−3.27784e12	−	9.73668e12i	−0.401833	−	1.19363i
$741$	−7.05368e12			−0.859476
$742$		−	2.35757e11i		−	0.0285527i
$743$		−	1.32505e13i		−	1.59508i	−0.603269	−	0.797538i	$-0.706135\pi$
$743$		−	1.32505e13i		−	1.59508i	0.603269	−	0.797538i	$-0.293865\pi$
$744$	−9.84859e11			−0.117841
$745$	1.25142e13	−	4.21291e12i	1.48834	−	0.501047i
$746$	−9.51115e12			−1.12437
$747$			1.28739e12i			0.151275i
$748$			2.27744e12i			0.266005i
$749$	−2.15151e11			−0.0249790
$750$	4.14701e12	−	6.10610e12i	0.478586	−	0.704674i
$751$	4.20152e11			0.0481978			0.0240989	−	0.999710i	$-0.492328\pi$
$751$	4.20152e11			0.0481978			0.0240989	+	0.999710i	$0.492328\pi$
$752$			9.84631e12i			1.12278i
$753$		−	7.96816e12i		−	0.903193i
$754$	−1.86795e13			−2.10472
$755$	−5.58221e12	+	1.87925e12i	−0.625237	+	0.210486i
$756$	5.63954e10			0.00627907
$757$		−	9.67841e12i		−	1.07121i	−0.844470	−	0.535603i	$-0.820085\pi$
$757$		−	9.67841e12i		−	1.07121i	0.844470	−	0.535603i	$-0.179915\pi$
$758$			1.91345e13i			2.10525i
$759$	−5.19434e11			−0.0568123
$760$	1.12295e12	+	3.33568e12i	0.122096	+	0.362680i
$761$	1.23747e13			1.33753			0.668765	−	0.743474i	$-0.266823\pi$
$761$	1.23747e13			1.33753			0.668765	+	0.743474i	$0.266823\pi$
$762$			1.42101e13i			1.52687i
$763$			3.04747e11i			0.0325521i
$764$	7.56498e12			0.803318
$765$	−1.49751e12	−	4.44829e12i	−0.158086	−	0.469588i
$766$	−2.14146e13			−2.24740
$767$			1.19164e13i			1.24327i
$768$		−	3.11178e12i		−	0.322762i
$769$	7.80487e12			0.804817			0.402408	−	0.915460i	$-0.368173\pi$
$769$	7.80487e12			0.804817			0.402408	+	0.915460i	$0.368173\pi$
$770$	−5.75038e10	+	1.93586e10i	−0.00589506	+	0.00198457i
$771$	3.43409e12			0.349999
$772$		−	1.02696e13i		−	1.04058i
$773$			1.04365e13i			1.05135i	0.850685	+	0.525676i	$0.176188\pi$
$773$			1.04365e13i			1.05135i	−0.850685	+	0.525676i	$0.823812\pi$
$774$	−3.08283e12			−0.308756
$775$	−6.25723e12	+	4.75148e12i	−0.623052	+	0.473120i
$776$	3.28783e11			0.0325485
$777$		−	1.74046e11i		−	0.0171305i
$778$			8.81999e12i			0.863097i
$779$	−2.70631e13			−2.63305
$780$	6.75604e12	−	2.27441e12i	0.653531	−	0.220011i
$781$	−2.17537e12			−0.209220
$782$			1.48413e13i			1.41919i
$783$		−	2.84514e12i		−	0.270505i
$784$	−8.37066e12			−0.791293
$785$	−6.68936e12	−	1.98704e13i	−0.628740	−	1.86764i
$786$	4.19367e12			0.391916
$787$		−	3.71509e12i		−	0.345210i	−0.984991	−	0.172605i	$-0.944782\pi$
$787$		−	3.71509e12i		−	0.345210i	0.984991	−	0.172605i	$-0.0552183\pi$
$788$			2.97580e12i			0.274939i
$789$	2.54136e12			0.233464
$790$	7.37197e11	+	2.18981e12i	0.0673382	+	0.200025i
$791$	2.16532e10			0.00196665
$792$		−	1.46432e11i		−	0.0132243i
$793$		−	4.41333e12i		−	0.396311i
$794$	1.90201e13			1.69833
$795$	4.30180e12	−	1.44820e12i	0.381943	−	0.128581i
$796$	−1.19682e11			−0.0105662
$797$			1.44080e11i			0.0126486i	0.999980	+	0.00632430i	$0.00201310\pi$
$797$			1.44080e11i			0.0126486i	−0.999980	+	0.00632430i	$0.997987\pi$
$798$			3.96823e11i			0.0346405i
$799$	−2.42791e13			−2.10752
$800$	1.00139e13	+	1.31873e13i	0.864366	+	1.13829i
$801$	6.69720e11			0.0574840
$802$		−	7.41394e12i		−	0.632797i
$803$			1.81254e12i			0.153839i
$804$	5.50246e12			0.464413
$805$	−2.02587e11	+	6.82006e10i	−0.0170031	+	0.00572409i
$806$	−1.40357e13			−1.17146
$807$		−	2.13118e12i		−	0.176884i
$808$		−	2.99455e12i		−	0.247161i
$809$	−1.71789e11			−0.0141003			−0.00705014	−	0.999975i	$-0.502244\pi$
$809$	−1.71789e11			−0.0141003			−0.00705014	+	0.999975i	$0.502244\pi$
$810$	6.40792e11	+	1.90344e12i	0.0523040	+	0.155366i
$811$	1.37282e13			1.11435			0.557174	−	0.830396i	$-0.311886\pi$
$811$	1.37282e13			1.11435			0.557174	+	0.830396i	$0.311886\pi$
$812$			5.68116e11i			0.0458601i
$813$			1.44644e12i			0.116116i
$814$	−3.00756e12			−0.240107
$815$	4.11725e12	+	1.22301e13i	0.326888	+	0.971005i
$816$	8.60730e12			0.679612
$817$		−	1.17271e13i		−	0.920857i
$818$		−	1.83695e13i		−	1.43452i
$819$	1.20766e11			0.00937925
$820$	2.59211e13	−	8.72632e12i	2.00213	−	0.674014i
$821$	7.69158e12			0.590842			0.295421	−	0.955367i	$-0.404540\pi$
$821$	7.69158e12			0.590842			0.295421	+	0.955367i	$0.404540\pi$
$822$			4.55290e12i			0.347828i
$823$		−	5.92005e12i		−	0.449807i	−0.974381	−	0.224904i	$-0.927793\pi$
$823$		−	5.92005e12i		−	0.449807i	0.974381	−	0.224904i	$-0.0722067\pi$
$824$	−1.46337e12			−0.110581
$825$	−7.06463e11	−	9.30343e11i	−0.0530942	−	0.0699198i
$826$	6.70385e11			0.0501088
$827$		−	6.24992e12i		−	0.464622i	−0.972642	−	0.232311i	$-0.925371\pi$
$827$		−	6.24992e12i		−	0.464622i	0.972642	−	0.232311i	$-0.0746287\pi$
$828$		−	3.43326e12i		−	0.253846i
$829$	1.49297e12			0.109788			0.0548939	−	0.998492i	$-0.482518\pi$
$829$	1.49297e12			0.109788			0.0548939	+	0.998492i	$0.482518\pi$
$830$	8.67642e12	−	2.92091e12i	0.634584	−	0.213632i
$831$	−9.88339e12			−0.718955
$832$			1.84723e13i			1.33649i
$833$		−	2.06405e13i		−	1.48531i
$834$	−1.42518e13			−1.02005
$835$	6.86980e12	+	2.04064e13i	0.489052	+	1.45271i
$836$	3.70711e12			0.262487
$837$		−	2.13782e12i		−	0.150559i
$838$		−	2.24235e13i		−	1.57074i
$839$	2.30128e12			0.160339			0.0801697	−	0.996781i	$-0.474454\pi$
$839$	2.30128e12			0.160339			0.0801697	+	0.996781i	$0.474454\pi$
$840$	−1.92261e10	−	5.71104e10i	−0.00133240	−	0.00395784i
$841$	1.41542e13			0.975671
$842$		−	4.06841e12i		−	0.278946i
$843$			6.18775e12i			0.421996i
$844$	7.16993e12			0.486378
$845$	4.21847e11	−	1.42014e11i	0.0284642	−	0.00958245i
$846$	1.03891e13			0.697289
$847$		−	4.05675e11i		−	0.0270834i
$848$			8.32384e12i			0.552768i
$849$	−1.37318e13			−0.907072
$850$	−2.65818e13	+	2.01851e13i	−1.74662	+	1.32631i
$851$	−1.05957e13			−0.692540
$852$		−	1.43784e13i		−	0.934827i
$853$			1.28737e13i			0.832591i	0.909229	+	0.416296i	$0.136672\pi$
$853$			1.28737e13i			0.832591i	−0.909229	+	0.416296i	$0.863328\pi$
$854$	−2.48283e11			−0.0159730
$855$	−7.24073e12	+	2.43758e12i	−0.463377	+	0.155995i
$856$	−3.69242e12			−0.235060
$857$		−	2.72042e13i		−	1.72275i	−0.507969	−	0.861375i	$-0.669604\pi$
$857$		−	2.72042e13i		−	1.72275i	0.507969	−	0.861375i	$-0.330396\pi$
$858$		−	2.08687e12i		−	0.131463i
$859$	8.43005e11			0.0528276			0.0264138	−	0.999651i	$-0.491591\pi$
$859$	8.43005e11			0.0528276			0.0264138	+	0.999651i	$0.491591\pi$
$860$	3.78134e12	+	1.12323e13i	0.235723	+	0.700205i
$861$	4.63348e11			0.0287338
$862$			3.38111e12i			0.208582i
$863$		−	1.71350e13i		−	1.05156i	−0.850620	−	0.525781i	$-0.823773\pi$
$863$		−	1.71350e13i		−	1.05156i	0.850620	−	0.525781i	$-0.176227\pi$
$864$	−4.50553e12			−0.275064
$865$	−6.68176e12	−	1.98479e13i	−0.405806	−	1.20543i
$866$	−4.32431e13			−2.61268
$867$			1.16184e13i			0.698327i
$868$			4.26879e11i			0.0255250i
$869$	3.65678e11			0.0217525
$870$	−1.91749e13	+	6.45521e12i	−1.13474	+	0.382009i
$871$	1.17831e13			0.693709
$872$			5.23007e12i			0.306325i
$873$			7.13684e11i			0.0415855i
$874$	2.41580e13			1.40042
$875$	−3.97683e11	−	2.70090e11i	−0.0229351	−	0.0155766i
$876$	−1.19802e13			−0.687376
$877$			3.31137e13i			1.89021i	0.326767	+	0.945105i	$0.394041\pi$
$877$			3.31137e13i			1.89021i	−0.326767	+	0.945105i	$0.605959\pi$
$878$		−	3.43638e13i		−	1.95153i
$879$	5.50386e12			0.310969
$880$	2.03028e12	−	6.83491e11i	0.114126	−	0.0384203i
$881$	3.55184e13			1.98638			0.993190	−	0.116508i	$-0.0371702\pi$
$881$	3.55184e13			1.98638			0.993190	+	0.116508i	$0.0371702\pi$
$882$			8.83213e12i			0.491425i
$883$			4.77239e11i			0.0264188i	0.999913	+	0.0132094i	$0.00420480\pi$
$883$			4.77239e11i			0.0264188i	−0.999913	+	0.0132094i	$0.995795\pi$
$884$	−3.22348e13			−1.77538
$885$	4.11801e12	+	1.22324e13i	0.225654	+	0.670294i
$886$	1.81751e13			0.990889
$887$			2.72348e13i			1.47730i	0.674092	+	0.738648i	$0.264535\pi$
$887$			2.72348e13i			1.47730i	−0.674092	+	0.738648i	$0.735465\pi$
$888$		−	2.98698e12i		−	0.161203i
$889$	9.25489e11			0.0496951
$890$	−1.51950e12	−	4.51360e12i	−0.0811792	−	0.241139i
$891$	3.17857e11			0.0168960
$892$			7.60172e12i			0.402041i
$893$			3.95205e13i			2.07965i
$894$	2.55496e13			1.33772
$895$	−1.83646e12	+	6.18243e11i	−0.0956706	+	0.0322074i
$896$	2.74729e11			0.0142403
$897$		−	7.35206e12i		−	0.379178i
$898$		−	3.13911e12i		−	0.161088i
$899$	2.15360e13			1.09963
$900$	6.14921e12	−	4.66945e12i	0.312412	−	0.237233i
$901$	−2.05250e13			−1.03758
$902$		−	8.00677e12i		−	0.402743i
$903$			2.00781e11i			0.0100491i
$904$	3.71612e11			0.0185068
$905$	−1.36687e13	+	4.60155e12i	−0.677343	+	0.228027i
$906$	−1.13969e13			−0.561965
$907$			3.42622e13i			1.68106i	0.541766	+	0.840529i	$0.317756\pi$
$907$			3.42622e13i			1.68106i	−0.541766	+	0.840529i	$0.682244\pi$
$908$			3.55226e13i			1.73428i
$909$	6.50024e12			0.315785
$910$	−2.74001e11	−	8.13908e11i	−0.0132454	−	0.0393450i
$911$	2.19508e12			0.105589			0.0527944	−	0.998605i	$-0.483187\pi$
$911$	2.19508e12			0.105589			0.0527944	+	0.998605i	$0.483187\pi$
$912$		−	1.40106e13i		−	0.670624i
$913$		−	1.44888e12i		−	0.0690104i
$914$	2.52008e13			1.19442
$915$	−1.52514e12	−	4.53036e12i	−0.0719308	−	0.213667i
$916$	1.28592e12			0.0603509
$917$		−	2.73128e11i		−	0.0127557i
$918$		−	9.08182e12i		−	0.422067i
$919$	3.37738e13			1.56193			0.780963	−	0.624577i	$-0.214729\pi$
$919$	3.37738e13			1.56193			0.780963	+	0.624577i	$0.214729\pi$
$920$	−3.47679e12	+	1.17046e12i	−0.160005	+	0.0538655i
$921$	8.89285e12			0.407261
$922$		−	1.48027e13i		−	0.674609i
$923$		−	3.07901e13i		−	1.39638i
$924$	−6.34696e10			−0.00286445
$925$	−1.44108e13	−	1.89776e13i	−0.647216	−	0.852320i
$926$	5.83885e11			0.0260963
$927$		−	3.17652e12i		−	0.141284i
$928$		−	4.53878e13i		−	2.00897i
$929$	−2.93838e13			−1.29431			−0.647153	−	0.762360i	$-0.724041\pi$
$929$	−2.93838e13			−1.29431			−0.647153	+	0.762360i	$0.724041\pi$
$930$	−1.44079e13	+	4.85041e12i	−0.631579	+	0.212620i
$931$	−3.35976e13			−1.46566
$932$			8.42936e12i			0.365951i
$933$			9.51092e12i			0.410918i
$934$	2.65138e13			1.14002
$935$	1.68536e12	+	5.00629e12i	0.0721175	+	0.214222i
$936$	2.07259e12			0.0882617
$937$			2.74410e12i			0.116298i	0.998308	+	0.0581490i	$0.0185198\pi$
$937$			2.74410e12i			0.116298i	−0.998308	+	0.0581490i	$0.981480\pi$
$938$		−	6.62888e11i		−	0.0279594i
$939$	−7.13705e12			−0.299588
$940$	−1.27431e13	−	3.78528e13i	−0.532354	−	1.58133i
$941$	−1.56000e13			−0.648593			−0.324297	−	0.945955i	$-0.605128\pi$
$941$	−1.56000e13			−0.648593			−0.324297	+	0.945955i	$0.605128\pi$
$942$		−	4.05683e13i		−	1.67864i
$943$		−	2.82079e13i		−	1.16163i
$944$	−2.36692e13			−0.970084
$945$	1.23969e11	−	4.17340e10i	0.00505672	−	0.00170234i
$946$	3.46954e12			0.140851
$947$		−	1.77307e13i		−	0.716393i	−0.933646	−	0.358196i	$-0.883392\pi$
$947$		−	1.77307e13i		−	0.716393i	0.933646	−	0.358196i	$-0.116608\pi$
$948$			2.41699e12i			0.0971936i
$949$	−2.56546e13			−1.02676
$950$	3.28563e13	+	4.32686e13i	1.30877	+	1.72352i
$951$	−1.19030e13			−0.471892
$952$			2.72489e11i			0.0107518i
$953$			3.08282e13i			1.21068i	0.795966	+	0.605342i	$0.206964\pi$
$953$			3.08282e13i			1.21068i	−0.795966	+	0.605342i	$0.793036\pi$
$954$	8.78274e12			0.343291
$955$	1.66294e13	−	5.59827e12i	0.646936	−	0.217790i
$956$	1.44954e13			0.561268
$957$			3.20203e12i			0.123402i
$958$			5.31893e13i			2.04023i
$959$	2.96525e11			0.0113208
$960$	6.38359e12	+	1.89622e13i	0.242574	+	0.720555i
$961$	−1.02576e13			−0.387963
$962$		−	4.25689e13i		−	1.60253i
$963$		−	8.01509e12i		−	0.300324i
$964$	−1.05180e13			−0.392273
$965$	−7.59973e12	−	2.25746e13i	−0.282114	−	0.838007i
$966$	−4.13609e11			−0.0152825
$967$			7.03976e12i			0.258904i	0.991586	+	0.129452i	$0.0413218\pi$
$967$			7.03976e12i			0.258904i	−0.991586	+	0.129452i	$0.958678\pi$
$968$		−	6.96220e12i		−	0.254863i
$969$	3.45474e13			1.25881
$970$	4.80990e12	−	1.61925e12i	0.174447	−	0.0587273i
$971$	1.42748e13			0.515326			0.257663	−	0.966235i	$-0.417048\pi$
$971$	1.42748e13			0.515326			0.257663	+	0.966235i	$0.417048\pi$
$972$			2.10092e12i			0.0754937i
$973$			9.28199e11i			0.0331996i
$974$	−3.84228e13			−1.36796
$975$	1.31681e13	−	9.99927e12i	0.466660	−	0.354362i
$976$	8.76609e12			0.309230
$977$			5.05743e12i			0.177584i	0.996050	+	0.0887921i	$0.0283007\pi$
$977$			5.05743e12i			0.177584i	−0.996050	+	0.0887921i	$0.971699\pi$
$978$			2.49695e13i			0.872741i
$979$	−7.53729e11			−0.0262236
$980$	3.21799e13	−	1.08333e13i	1.11447	−	0.375184i
$981$	−1.13528e13			−0.391376
$982$		−	1.99413e13i		−	0.684309i
$983$		−	1.51603e12i		−	0.0517865i	−0.999665	−	0.0258932i	$-0.991757\pi$
$983$		−	1.51603e12i		−	0.0517865i	0.999665	−	0.0258932i	$-0.00824300\pi$
$984$	7.95198e12			0.270394
$985$	2.20217e12	+	6.54144e12i	0.0745397	+	0.221417i
$986$	9.14885e13			3.08262
$987$		−	6.76631e11i		−	0.0226947i
$988$			5.24704e13i			1.75189i
$989$	1.22232e13			0.406258
$990$	−7.21173e11	−	2.14221e12i	−0.0238606	−	0.0708767i
$991$	−3.83328e13			−1.26252			−0.631261	−	0.775571i	$-0.717462\pi$
$991$	−3.83328e13			−1.26252			−0.631261	+	0.775571i	$0.717462\pi$
$992$		−	3.41041e13i		−	1.11816i
$993$			2.95462e13i			0.964341i
$994$	−1.73218e12			−0.0562800
$995$	−2.63086e11	+	8.85676e10i	−0.00850929	+	0.00286464i
$996$	9.57656e12			0.308349
$997$			7.71976e12i			0.247443i	0.992317	+	0.123722i	$0.0394830\pi$
$997$			7.71976e12i			0.247443i	−0.992317	+	0.123722i	$0.960517\pi$
$998$			5.52339e13i			1.76246i
$999$	6.48380e12			0.205961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.10.b.a.4.1	✓	8
3.2	odd	2		45.10.b.c.19.8		8
4.3	odd	2		240.10.f.c.49.5		8
5.2	odd	4		75.10.a.i.1.4		4
5.3	odd	4		75.10.a.l.1.1		4
5.4	even	2	inner	15.10.b.a.4.8	yes	8
15.2	even	4		225.10.a.u.1.1		4
15.8	even	4		225.10.a.q.1.4		4
15.14	odd	2		45.10.b.c.19.1		8
20.19	odd	2		240.10.f.c.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.b.a.4.1	✓	8	1.1	even	1	trivial
15.10.b.a.4.8	yes	8	5.4	even	2	inner
45.10.b.c.19.1		8	15.14	odd	2
45.10.b.c.19.8		8	3.2	odd	2
75.10.a.i.1.4		4	5.2	odd	4
75.10.a.l.1.1		4	5.3	odd	4
225.10.a.q.1.4		4	15.8	even	4
225.10.a.u.1.1		4	15.2	even	4
240.10.f.c.49.1		8	20.19	odd	2
240.10.f.c.49.5		8	4.3	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	15.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-33.3847i q^{2} -81.0000i q^{3} -602.537 q^{4} +(-1324.50 + 445.892i) q^{5} -2704.16 q^{6} +176.118i q^{7} +3022.54i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q-33.3847i q^{2} -81.0000i q^{3} -602.537 q^{4} +(-1324.50 + 445.892i) q^{5} -2704.16 q^{6} +176.118i q^{7} +3022.54i q^{8} -6561.00 q^{9} +(14886.0 + 44218.1i) q^{10} +7384.01 q^{11} +48805.5i q^{12} +104513. i q^{13} +5879.66 q^{14} +(36117.3 + 107285. i) q^{15} -207592. q^{16} -511883. i q^{17} +219037. i q^{18} -833220. q^{19} +(798061. - 268666. i) q^{20} +14265.6 q^{21} -246513. i q^{22} -868467. i q^{23} +244826. q^{24} +(1.55549e6 - 1.18117e6i) q^{25} +3.48914e6 q^{26} +531441. i q^{27} -106118. i q^{28} -5.35363e6 q^{29} +(3.58166e6 - 1.20576e6i) q^{30} -4.02269e6 q^{31} +8.47794e6i q^{32} -598105. i q^{33} -1.70891e7 q^{34} +(-78529.8 - 233269. i) q^{35} +3.95324e6 q^{36} -1.22004e7i q^{37} +2.78168e7i q^{38} +8.46556e6 q^{39} +(-1.34773e6 - 4.00337e6i) q^{40} +3.24801e7 q^{41} -476252. i q^{42} +1.40745e7i q^{43} -4.44914e6 q^{44} +(8.69006e6 - 2.92550e6i) q^{45} -2.89935e7 q^{46} -4.74310e7i q^{47} +1.68150e7i q^{48} +4.03226e7 q^{49} +(-3.94330e7 - 5.19294e7i) q^{50} -4.14625e7 q^{51} -6.29730e7i q^{52} -4.00971e7i q^{53} +1.77420e7 q^{54} +(-9.78013e6 + 3.29247e6i) q^{55} -532326. q^{56} +6.74908e7i q^{57} +1.78729e8i q^{58} +1.14018e8 q^{59} +(-2.17620e7 - 6.46430e7i) q^{60} -4.22275e7 q^{61} +1.34296e8i q^{62} -1.15551e6i q^{63} +1.76746e8 q^{64} +(-4.66016e7 - 1.38428e8i) q^{65} -1.99675e7 q^{66} -1.12743e8i q^{67} +3.08428e8i q^{68} -7.03458e7 q^{69} +(-7.78762e6 + 2.62169e6i) q^{70} -2.94605e8 q^{71} -1.98309e7i q^{72} +2.45468e8i q^{73} -4.07307e8 q^{74} +(-9.56748e7 - 1.25994e8i) q^{75} +5.02046e8 q^{76} +1.30046e6i q^{77} -2.82620e8i q^{78} +4.95230e7 q^{79} +(2.74956e8 - 9.25637e7i) q^{80} +4.30467e7 q^{81} -1.08434e9i q^{82} -1.96219e8i q^{83} -8.59554e6 q^{84} +(2.28245e8 + 6.77990e8i) q^{85} +4.69872e8 q^{86} +4.33644e8i q^{87} +2.23185e7i q^{88} -1.02076e8 q^{89} +(-9.76668e7 - 2.90115e8i) q^{90} -1.84067e7 q^{91} +5.23284e8i q^{92} +3.25838e8i q^{93} -1.58347e9 q^{94} +(1.10360e9 - 3.71526e8i) q^{95} +6.86713e8 q^{96} -1.08777e8i q^{97} -1.34616e9i q^{98} -4.84465e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9}+O(q^{10}) \) 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9	\( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9} + 67090 q^{10} - 71988 q^{11} + 416364 q^{14} + 80190 q^{15} - 1505630 q^{16} + 851584 q^{19} + 2078100 q^{20} - 1593108 q^{21} + 1242702 q^{24} + 1695500 q^{25} - 877524 q^{26} - 73572 q^{29} + 3086100 q^{30} + 474088 q^{31} - 8124388 q^{34} - 36357180 q^{35} + 7833834 q^{36} + 12959676 q^{39} - 15313390 q^{40} + 93320088 q^{41} - 74555892 q^{44} + 4527090 q^{45} - 9664072 q^{46} + 51329600 q^{49} + 67798200 q^{50} - 108196236 q^{51} - 3188646 q^{54} + 64428480 q^{55} - 67781220 q^{56} + 236526036 q^{59} + 63172710 q^{60} - 357427760 q^{61} - 12137026 q^{64} + 19848300 q^{65} + 23317308 q^{66} + 167059584 q^{69} + 200900520 q^{70} - 156890664 q^{71} - 1523381796 q^{74} - 528573600 q^{75} + 1098697344 q^{76} + 863922280 q^{79} + 630213180 q^{80} + 344373768 q^{81} + 529023636 q^{84} - 2223350420 q^{85} + 997642392 q^{86} + 357382224 q^{89} - 440177490 q^{90} + 214754328 q^{91} - 721679824 q^{94} + 1698584640 q^{95} - 475022718 q^{96} + 472313268 q^{99}+O(q^{100}) \) 8 * q - 1194 * q^4 - 690 * q^5 + 486 * q^6 - 52488 * q^9 + 67090 * q^10 - 71988 * q^11 + 416364 * q^14 + 80190 * q^15 - 1505630 * q^16 + 851584 * q^19 + 2078100 * q^20 - 1593108 * q^21 + 1242702 * q^24 + 1695500 * q^25 - 877524 * q^26 - 73572 * q^29 + 3086100 * q^30 + 474088 * q^31 - 8124388 * q^34 - 36357180 * q^35 + 7833834 * q^36 + 12959676 * q^39 - 15313390 * q^40 + 93320088 * q^41 - 74555892 * q^44 + 4527090 * q^45 - 9664072 * q^46 + 51329600 * q^49 + 67798200 * q^50 - 108196236 * q^51 - 3188646 * q^54 + 64428480 * q^55 - 67781220 * q^56 + 236526036 * q^59 + 63172710 * q^60 - 357427760 * q^61 - 12137026 * q^64 + 19848300 * q^65 + 23317308 * q^66 + 167059584 * q^69 + 200900520 * q^70 - 156890664 * q^71 - 1523381796 * q^74 - 528573600 * q^75 + 1098697344 * q^76 + 863922280 * q^79 + 630213180 * q^80 + 344373768 * q^81 + 529023636 * q^84 - 2223350420 * q^85 + 997642392 * q^86 + 357382224 * q^89 - 440177490 * q^90 + 214754328 * q^91 - 721679824 * q^94 + 1698584640 * q^95 - 475022718 * q^96 + 472313268 * q^99

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