LMFDB - Embedded newform 850.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(1,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.a (trivial)

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:	yes
Analytic conductor:	$6.78728417181$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} -0.414214 q^{6} +0.414214 q^{7} -1.00000 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} -0.414214 q^{6} +0.414214 q^{7} -1.00000 q^{8} -2.82843 q^{9} +2.00000 q^{11} +0.414214 q^{12} -6.65685 q^{13} -0.414214 q^{14} +1.00000 q^{16} -1.00000 q^{17} +2.82843 q^{18} +0.828427 q^{19} +0.171573 q^{21} -2.00000 q^{22} -7.65685 q^{23} -0.414214 q^{24} +6.65685 q^{26} -2.41421 q^{27} +0.414214 q^{28} -4.00000 q^{29} +1.58579 q^{31} -1.00000 q^{32} +0.828427 q^{33} +1.00000 q^{34} -2.82843 q^{36} -5.65685 q^{37} -0.828427 q^{38} -2.75736 q^{39} +7.65685 q^{41} -0.171573 q^{42} +11.3137 q^{43} +2.00000 q^{44} +7.65685 q^{46} -3.17157 q^{47} +0.414214 q^{48} -6.82843 q^{49} -0.414214 q^{51} -6.65685 q^{52} -5.82843 q^{53} +2.41421 q^{54} -0.414214 q^{56} +0.343146 q^{57} +4.00000 q^{58} -8.00000 q^{59} -3.65685 q^{61} -1.58579 q^{62} -1.17157 q^{63} +1.00000 q^{64} -0.828427 q^{66} +7.31371 q^{67} -1.00000 q^{68} -3.17157 q^{69} -13.2426 q^{71} +2.82843 q^{72} -1.65685 q^{73} +5.65685 q^{74} +0.828427 q^{76} +0.828427 q^{77} +2.75736 q^{78} +1.24264 q^{79} +7.48528 q^{81} -7.65685 q^{82} -2.34315 q^{83} +0.171573 q^{84} -11.3137 q^{86} -1.65685 q^{87} -2.00000 q^{88} -2.00000 q^{89} -2.75736 q^{91} -7.65685 q^{92} +0.656854 q^{93} +3.17157 q^{94} -0.414214 q^{96} +6.82843 q^{98} -5.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 4 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{17} - 4 q^{19} + 6 q^{21} - 4 q^{22} - 4 q^{23} + 2 q^{24} + 2 q^{26} - 2 q^{27} - 2 q^{28} - 8 q^{29} + 6 q^{31} - 2 q^{32} - 4 q^{33} + 2 q^{34} + 4 q^{38} - 14 q^{39} + 4 q^{41} - 6 q^{42} + 4 q^{44} + 4 q^{46} - 12 q^{47} - 2 q^{48} - 8 q^{49} + 2 q^{51} - 2 q^{52} - 6 q^{53} + 2 q^{54} + 2 q^{56} + 12 q^{57} + 8 q^{58} - 16 q^{59} + 4 q^{61} - 6 q^{62} - 8 q^{63} + 2 q^{64} + 4 q^{66} - 8 q^{67} - 2 q^{68} - 12 q^{69} - 18 q^{71} + 8 q^{73} - 4 q^{76} - 4 q^{77} + 14 q^{78} - 6 q^{79} - 2 q^{81} - 4 q^{82} - 16 q^{83} + 6 q^{84} + 8 q^{87} - 4 q^{88} - 4 q^{89} - 14 q^{91} - 4 q^{92} - 10 q^{93} + 12 q^{94} + 2 q^{96} + 8 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 4 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^17 - 4 * q^19 + 6 * q^21 - 4 * q^22 - 4 * q^23 + 2 * q^24 + 2 * q^26 - 2 * q^27 - 2 * q^28 - 8 * q^29 + 6 * q^31 - 2 * q^32 - 4 * q^33 + 2 * q^34 + 4 * q^38 - 14 * q^39 + 4 * q^41 - 6 * q^42 + 4 * q^44 + 4 * q^46 - 12 * q^47 - 2 * q^48 - 8 * q^49 + 2 * q^51 - 2 * q^52 - 6 * q^53 + 2 * q^54 + 2 * q^56 + 12 * q^57 + 8 * q^58 - 16 * q^59 + 4 * q^61 - 6 * q^62 - 8 * q^63 + 2 * q^64 + 4 * q^66 - 8 * q^67 - 2 * q^68 - 12 * q^69 - 18 * q^71 + 8 * q^73 - 4 * q^76 - 4 * q^77 + 14 * q^78 - 6 * q^79 - 2 * q^81 - 4 * q^82 - 16 * q^83 + 6 * q^84 + 8 * q^87 - 4 * q^88 - 4 * q^89 - 14 * q^91 - 4 * q^92 - 10 * q^93 + 12 * q^94 + 2 * q^96 + 8 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.414214	0.239146	0.119573	−	0.992825i	$-0.461847\pi$
$3$	0.414214	0.239146	0.119573	+	0.992825i	$0.461847\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−0.414214	−0.169102
$7$	0.414214	0.156558	0.0782790	−	0.996931i	$-0.475058\pi$
$7$	0.414214	0.156558	0.0782790	+	0.996931i	$0.475058\pi$
$8$	−1.00000	−0.353553
$9$	−2.82843	−0.942809
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0.414214	0.119573
$13$	−6.65685	−1.84628	−0.923140	−	0.384465i	$-0.874386\pi$
$13$	−6.65685	−1.84628	−0.923140	+	0.384465i	$0.874386\pi$
$14$	−0.414214	−0.110703
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.82843	0.666667
$19$	0.828427	0.190054	0.0950271	−	0.995475i	$-0.469706\pi$
$19$	0.828427	0.190054	0.0950271	+	0.995475i	$0.469706\pi$
$20$	0	0
$21$	0.171573	0.0374403
$22$	−2.00000	−0.426401
$23$	−7.65685	−1.59656	−0.798282	−	0.602284i	$-0.794258\pi$
$23$	−7.65685	−1.59656	−0.798282	+	0.602284i	$0.794258\pi$
$24$	−0.414214	−0.0845510
$25$	0	0
$26$	6.65685	1.30552
$27$	−2.41421	−0.464616
$28$	0.414214	0.0782790
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	0	0
$31$	1.58579	0.284816	0.142408	−	0.989808i	$-0.454516\pi$
$31$	1.58579	0.284816	0.142408	+	0.989808i	$0.454516\pi$
$32$	−1.00000	−0.176777
$33$	0.828427	0.144211
$34$	1.00000	0.171499
$35$	0	0
$36$	−2.82843	−0.471405
$37$	−5.65685	−0.929981	−0.464991	−	0.885316i	$-0.653942\pi$
$37$	−5.65685	−0.929981	−0.464991	+	0.885316i	$0.653942\pi$
$38$	−0.828427	−0.134389
$39$	−2.75736	−0.441531
$40$	0	0
$41$	7.65685	1.19580	0.597900	−	0.801571i	$-0.296002\pi$
$41$	7.65685	1.19580	0.597900	+	0.801571i	$0.296002\pi$
$42$	−0.171573	−0.0264743
$43$	11.3137	1.72532	0.862662	−	0.505781i	$-0.168795\pi$
$43$	11.3137	1.72532	0.862662	+	0.505781i	$0.168795\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	7.65685	1.12894
$47$	−3.17157	−0.462621	−0.231311	−	0.972880i	$-0.574301\pi$
$47$	−3.17157	−0.462621	−0.231311	+	0.972880i	$0.574301\pi$
$48$	0.414214	0.0597866
$49$	−6.82843	−0.975490
$50$	0	0
$51$	−0.414214	−0.0580015
$52$	−6.65685	−0.923140
$53$	−5.82843	−0.800596	−0.400298	−	0.916385i	$-0.631093\pi$
$53$	−5.82843	−0.800596	−0.400298	+	0.916385i	$0.631093\pi$
$54$	2.41421	0.328533
$55$	0	0
$56$	−0.414214	−0.0553516
$57$	0.343146	0.0454508
$58$	4.00000	0.525226
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	−3.65685	−0.468212	−0.234106	−	0.972211i	$-0.575216\pi$
$61$	−3.65685	−0.468212	−0.234106	+	0.972211i	$0.575216\pi$
$62$	−1.58579	−0.201395
$63$	−1.17157	−0.147604
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.828427	−0.101972
$67$	7.31371	0.893512	0.446756	−	0.894656i	$-0.352579\pi$
$67$	7.31371	0.893512	0.446756	+	0.894656i	$0.352579\pi$
$68$	−1.00000	−0.121268
$69$	−3.17157	−0.381813
$70$	0	0
$71$	−13.2426	−1.57161	−0.785806	−	0.618473i	$-0.787752\pi$
$71$	−13.2426	−1.57161	−0.785806	+	0.618473i	$0.787752\pi$
$72$	2.82843	0.333333
$73$	−1.65685	−0.193920	−0.0969601	−	0.995288i	$-0.530912\pi$
$73$	−1.65685	−0.193920	−0.0969601	+	0.995288i	$0.530912\pi$
$74$	5.65685	0.657596
$75$	0	0
$76$	0.828427	0.0950271
$77$	0.828427	0.0944080
$78$	2.75736	0.312209
$79$	1.24264	0.139808	0.0699040	−	0.997554i	$-0.477731\pi$
$79$	1.24264	0.139808	0.0699040	+	0.997554i	$0.477731\pi$
$80$	0	0
$81$	7.48528	0.831698
$82$	−7.65685	−0.845558
$83$	−2.34315	−0.257194	−0.128597	−	0.991697i	$-0.541047\pi$
$83$	−2.34315	−0.257194	−0.128597	+	0.991697i	$0.541047\pi$
$84$	0.171573	0.0187201
$85$	0	0
$86$	−11.3137	−1.21999
$87$	−1.65685	−0.177633
$88$	−2.00000	−0.213201
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	−2.75736	−0.289050
$92$	−7.65685	−0.798282
$93$	0.656854	0.0681126
$94$	3.17157	0.327123
$95$	0	0
$96$	−0.414214	−0.0422755
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	6.82843	0.689775
$99$	−5.65685	−0.568535
$100$	0	0
$101$	−1.34315	−0.133648	−0.0668240	−	0.997765i	$-0.521287\pi$
$101$	−1.34315	−0.133648	−0.0668240	+	0.997765i	$0.521287\pi$
$102$	0.414214	0.0410133
$103$	1.51472	0.149250	0.0746248	−	0.997212i	$-0.476224\pi$
$103$	1.51472	0.149250	0.0746248	+	0.997212i	$0.476224\pi$
$104$	6.65685	0.652758
$105$	0	0
$106$	5.82843	0.566107
$107$	−16.0711	−1.55365	−0.776824	−	0.629717i	$-0.783171\pi$
$107$	−16.0711	−1.55365	−0.776824	+	0.629717i	$0.783171\pi$
$108$	−2.41421	−0.232308
$109$	15.3137	1.46679	0.733394	−	0.679804i	$-0.237935\pi$
$109$	15.3137	1.46679	0.733394	+	0.679804i	$0.237935\pi$
$110$	0	0
$111$	−2.34315	−0.222402
$112$	0.414214	0.0391395
$113$	−6.34315	−0.596713	−0.298356	−	0.954455i	$-0.596438\pi$
$113$	−6.34315	−0.596713	−0.298356	+	0.954455i	$0.596438\pi$
$114$	−0.343146	−0.0321385
$115$	0	0
$116$	−4.00000	−0.371391
$117$	18.8284	1.74069
$118$	8.00000	0.736460
$119$	−0.414214	−0.0379709
$120$	0	0
$121$	−7.00000	−0.636364
$122$	3.65685	0.331076
$123$	3.17157	0.285971
$124$	1.58579	0.142408
$125$	0	0
$126$	1.17157	0.104372
$127$	1.65685	0.147022	0.0735110	−	0.997294i	$-0.476580\pi$
$127$	1.65685	0.147022	0.0735110	+	0.997294i	$0.476580\pi$
$128$	−1.00000	−0.0883883
$129$	4.68629	0.412605
$130$	0	0
$131$	−12.8995	−1.12703	−0.563517	−	0.826104i	$-0.690552\pi$
$131$	−12.8995	−1.12703	−0.563517	+	0.826104i	$0.690552\pi$
$132$	0.828427	0.0721053
$133$	0.343146	0.0297545
$134$	−7.31371	−0.631808
$135$	0	0
$136$	1.00000	0.0857493
$137$	13.4853	1.15213	0.576063	−	0.817406i	$-0.304588\pi$
$137$	13.4853	1.15213	0.576063	+	0.817406i	$0.304588\pi$
$138$	3.17157	0.269982
$139$	−21.3848	−1.81383	−0.906917	−	0.421310i	$-0.861570\pi$
$139$	−21.3848	−1.81383	−0.906917	+	0.421310i	$0.861570\pi$
$140$	0	0
$141$	−1.31371	−0.110634
$142$	13.2426	1.11130
$143$	−13.3137	−1.11335
$144$	−2.82843	−0.235702
$145$	0	0
$146$	1.65685	0.137122
$147$	−2.82843	−0.233285
$148$	−5.65685	−0.464991
$149$	−9.14214	−0.748953	−0.374476	−	0.927236i	$-0.622178\pi$
$149$	−9.14214	−0.748953	−0.374476	+	0.927236i	$0.622178\pi$
$150$	0	0
$151$	2.48528	0.202249	0.101125	−	0.994874i	$-0.467756\pi$
$151$	2.48528	0.202249	0.101125	+	0.994874i	$0.467756\pi$
$152$	−0.828427	−0.0671943
$153$	2.82843	0.228665
$154$	−0.828427	−0.0667566
$155$	0	0
$156$	−2.75736	−0.220765
$157$	16.1716	1.29063	0.645316	−	0.763916i	$-0.276726\pi$
$157$	16.1716	1.29063	0.645316	+	0.763916i	$0.276726\pi$
$158$	−1.24264	−0.0988592
$159$	−2.41421	−0.191460
$160$	0	0
$161$	−3.17157	−0.249955
$162$	−7.48528	−0.588099
$163$	19.5858	1.53408	0.767039	−	0.641601i	$-0.221729\pi$
$163$	19.5858	1.53408	0.767039	+	0.641601i	$0.221729\pi$
$164$	7.65685	0.597900
$165$	0	0
$166$	2.34315	0.181863
$167$	7.65685	0.592505	0.296253	−	0.955110i	$-0.404263\pi$
$167$	7.65685	0.592505	0.296253	+	0.955110i	$0.404263\pi$
$168$	−0.171573	−0.0132371
$169$	31.3137	2.40875
$170$	0	0
$171$	−2.34315	−0.179185
$172$	11.3137	0.862662
$173$	10.9706	0.834076	0.417038	−	0.908889i	$-0.363068\pi$
$173$	10.9706	0.834076	0.417038	+	0.908889i	$0.363068\pi$
$174$	1.65685	0.125606
$175$	0	0
$176$	2.00000	0.150756
$177$	−3.31371	−0.249074
$178$	2.00000	0.149906
$179$	24.8284	1.85576	0.927882	−	0.372874i	$-0.121628\pi$
$179$	24.8284	1.85576	0.927882	+	0.372874i	$0.121628\pi$
$180$	0	0
$181$	19.6569	1.46108	0.730541	−	0.682869i	$-0.239268\pi$
$181$	19.6569	1.46108	0.730541	+	0.682869i	$0.239268\pi$
$182$	2.75736	0.204389
$183$	−1.51472	−0.111971
$184$	7.65685	0.564471
$185$	0	0
$186$	−0.656854	−0.0481629
$187$	−2.00000	−0.146254
$188$	−3.17157	−0.231311
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−14.4853	−1.04812	−0.524059	−	0.851682i	$-0.675583\pi$
$191$	−14.4853	−1.04812	−0.524059	+	0.851682i	$0.675583\pi$
$192$	0.414214	0.0298933
$193$	9.65685	0.695116	0.347558	−	0.937659i	$-0.387011\pi$
$193$	9.65685	0.695116	0.347558	+	0.937659i	$0.387011\pi$
$194$	0	0
$195$	0	0
$196$	−6.82843	−0.487745
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	5.65685	0.402015
$199$	−4.34315	−0.307877	−0.153939	−	0.988080i	$-0.549196\pi$
$199$	−4.34315	−0.307877	−0.153939	+	0.988080i	$0.549196\pi$
$200$	0	0
$201$	3.02944	0.213680
$202$	1.34315	0.0945034
$203$	−1.65685	−0.116288
$204$	−0.414214	−0.0290008
$205$	0	0
$206$	−1.51472	−0.105535
$207$	21.6569	1.50526
$208$	−6.65685	−0.461570
$209$	1.65685	0.114607
$210$	0	0
$211$	−9.72792	−0.669698	−0.334849	−	0.942272i	$-0.608685\pi$
$211$	−9.72792	−0.669698	−0.334849	+	0.942272i	$0.608685\pi$
$212$	−5.82843	−0.400298
$213$	−5.48528	−0.375845
$214$	16.0711	1.09860
$215$	0	0
$216$	2.41421	0.164266
$217$	0.656854	0.0445902
$218$	−15.3137	−1.03718
$219$	−0.686292	−0.0463753
$220$	0	0
$221$	6.65685	0.447788
$222$	2.34315	0.157262
$223$	18.4853	1.23787	0.618933	−	0.785444i	$-0.287565\pi$
$223$	18.4853	1.23787	0.618933	+	0.785444i	$0.287565\pi$
$224$	−0.414214	−0.0276758
$225$	0	0
$226$	6.34315	0.421940
$227$	13.2426	0.878945	0.439472	−	0.898256i	$-0.355165\pi$
$227$	13.2426	0.878945	0.439472	+	0.898256i	$0.355165\pi$
$228$	0.343146	0.0227254
$229$	−12.3137	−0.813713	−0.406856	−	0.913492i	$-0.633375\pi$
$229$	−12.3137	−0.813713	−0.406856	+	0.913492i	$0.633375\pi$
$230$	0	0
$231$	0.343146	0.0225773
$232$	4.00000	0.262613
$233$	−20.0000	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$234$	−18.8284	−1.23085
$235$	0	0
$236$	−8.00000	−0.520756
$237$	0.514719	0.0334346
$238$	0.414214	0.0268495
$239$	8.97056	0.580257	0.290129	−	0.956988i	$-0.406302\pi$
$239$	8.97056	0.580257	0.290129	+	0.956988i	$0.406302\pi$
$240$	0	0
$241$	20.6274	1.32873	0.664364	−	0.747409i	$-0.268702\pi$
$241$	20.6274	1.32873	0.664364	+	0.747409i	$0.268702\pi$
$242$	7.00000	0.449977
$243$	10.3431	0.663513
$244$	−3.65685	−0.234106
$245$	0	0
$246$	−3.17157	−0.202212
$247$	−5.51472	−0.350893
$248$	−1.58579	−0.100698
$249$	−0.970563	−0.0615069
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	−1.17157	−0.0738022
$253$	−15.3137	−0.962765
$254$	−1.65685	−0.103960
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.5147	0.655890	0.327945	−	0.944697i	$-0.393644\pi$
$257$	10.5147	0.655890	0.327945	+	0.944697i	$0.393644\pi$
$258$	−4.68629	−0.291756
$259$	−2.34315	−0.145596
$260$	0	0
$261$	11.3137	0.700301
$262$	12.8995	0.796933
$263$	−10.3431	−0.637786	−0.318893	−	0.947791i	$-0.603311\pi$
$263$	−10.3431	−0.637786	−0.318893	+	0.947791i	$0.603311\pi$
$264$	−0.828427	−0.0509862
$265$	0	0
$266$	−0.343146	−0.0210396
$267$	−0.828427	−0.0506989
$268$	7.31371	0.446756
$269$	28.6274	1.74544	0.872722	−	0.488217i	$-0.162353\pi$
$269$	28.6274	1.74544	0.872722	+	0.488217i	$0.162353\pi$
$270$	0	0
$271$	−22.4853	−1.36588	−0.682942	−	0.730473i	$-0.739300\pi$
$271$	−22.4853	−1.36588	−0.682942	+	0.730473i	$0.739300\pi$
$272$	−1.00000	−0.0606339
$273$	−1.14214	−0.0691252
$274$	−13.4853	−0.814676
$275$	0	0
$276$	−3.17157	−0.190906
$277$	−23.6569	−1.42140	−0.710701	−	0.703494i	$-0.751622\pi$
$277$	−23.6569	−1.42140	−0.710701	+	0.703494i	$0.751622\pi$
$278$	21.3848	1.28257
$279$	−4.48528	−0.268527
$280$	0	0
$281$	6.65685	0.397115	0.198557	−	0.980089i	$-0.436374\pi$
$281$	6.65685	0.397115	0.198557	+	0.980089i	$0.436374\pi$
$282$	1.31371	0.0782302
$283$	18.9706	1.12768	0.563841	−	0.825883i	$-0.309323\pi$
$283$	18.9706	1.12768	0.563841	+	0.825883i	$0.309323\pi$
$284$	−13.2426	−0.785806
$285$	0	0
$286$	13.3137	0.787256
$287$	3.17157	0.187212
$288$	2.82843	0.166667
$289$	1.00000	0.0588235
$290$	0	0
$291$	0	0
$292$	−1.65685	−0.0969601
$293$	−25.3137	−1.47884	−0.739421	−	0.673243i	$-0.764901\pi$
$293$	−25.3137	−1.47884	−0.739421	+	0.673243i	$0.764901\pi$
$294$	2.82843	0.164957
$295$	0	0
$296$	5.65685	0.328798
$297$	−4.82843	−0.280174
$298$	9.14214	0.529590
$299$	50.9706	2.94770
$300$	0	0
$301$	4.68629	0.270113
$302$	−2.48528	−0.143012
$303$	−0.556349	−0.0319614
$304$	0.828427	0.0475136
$305$	0	0
$306$	−2.82843	−0.161690
$307$	−9.65685	−0.551146	−0.275573	−	0.961280i	$-0.588868\pi$
$307$	−9.65685	−0.551146	−0.275573	+	0.961280i	$0.588868\pi$
$308$	0.828427	0.0472040
$309$	0.627417	0.0356925
$310$	0	0
$311$	20.2132	1.14619	0.573093	−	0.819490i	$-0.305743\pi$
$311$	20.2132	1.14619	0.573093	+	0.819490i	$0.305743\pi$
$312$	2.75736	0.156105
$313$	22.9706	1.29837	0.649186	−	0.760629i	$-0.275109\pi$
$313$	22.9706	1.29837	0.649186	+	0.760629i	$0.275109\pi$
$314$	−16.1716	−0.912615
$315$	0	0
$316$	1.24264	0.0699040
$317$	−2.68629	−0.150877	−0.0754386	−	0.997150i	$-0.524036\pi$
$317$	−2.68629	−0.150877	−0.0754386	+	0.997150i	$0.524036\pi$
$318$	2.41421	0.135382
$319$	−8.00000	−0.447914
$320$	0	0
$321$	−6.65685	−0.371549
$322$	3.17157	0.176745
$323$	−0.828427	−0.0460949
$324$	7.48528	0.415849
$325$	0	0
$326$	−19.5858	−1.08476
$327$	6.34315	0.350777
$328$	−7.65685	−0.422779
$329$	−1.31371	−0.0724271
$330$	0	0
$331$	−14.4853	−0.796183	−0.398092	−	0.917346i	$-0.630327\pi$
$331$	−14.4853	−0.796183	−0.398092	+	0.917346i	$0.630327\pi$
$332$	−2.34315	−0.128597
$333$	16.0000	0.876795
$334$	−7.65685	−0.418964
$335$	0	0
$336$	0.171573	0.00936007
$337$	−28.9706	−1.57813	−0.789064	−	0.614312i	$-0.789434\pi$
$337$	−28.9706	−1.57813	−0.789064	+	0.614312i	$0.789434\pi$
$338$	−31.3137	−1.70324
$339$	−2.62742	−0.142702
$340$	0	0
$341$	3.17157	0.171750
$342$	2.34315	0.126703
$343$	−5.72792	−0.309279
$344$	−11.3137	−0.609994
$345$	0	0
$346$	−10.9706	−0.589781
$347$	−33.5858	−1.80298	−0.901490	−	0.432800i	$-0.857525\pi$
$347$	−33.5858	−1.80298	−0.901490	+	0.432800i	$0.857525\pi$
$348$	−1.65685	−0.0888167
$349$	16.1716	0.865644	0.432822	−	0.901479i	$-0.357518\pi$
$349$	16.1716	0.865644	0.432822	+	0.901479i	$0.357518\pi$
$350$	0	0
$351$	16.0711	0.857810
$352$	−2.00000	−0.106600
$353$	−21.3431	−1.13598	−0.567991	−	0.823035i	$-0.692279\pi$
$353$	−21.3431	−1.13598	−0.567991	+	0.823035i	$0.692279\pi$
$354$	3.31371	0.176122
$355$	0	0
$356$	−2.00000	−0.106000
$357$	−0.171573	−0.00908060
$358$	−24.8284	−1.31222
$359$	−20.1421	−1.06306	−0.531531	−	0.847039i	$-0.678383\pi$
$359$	−20.1421	−1.06306	−0.531531	+	0.847039i	$0.678383\pi$
$360$	0	0
$361$	−18.3137	−0.963879
$362$	−19.6569	−1.03314
$363$	−2.89949	−0.152184
$364$	−2.75736	−0.144525
$365$	0	0
$366$	1.51472	0.0791756
$367$	−29.0416	−1.51596	−0.757980	−	0.652277i	$-0.773814\pi$
$367$	−29.0416	−1.51596	−0.757980	+	0.652277i	$0.773814\pi$
$368$	−7.65685	−0.399141
$369$	−21.6569	−1.12741
$370$	0	0
$371$	−2.41421	−0.125340
$372$	0.656854	0.0340563
$373$	27.0000	1.39801	0.699004	−	0.715118i	$-0.253627\pi$
$373$	27.0000	1.39801	0.699004	+	0.715118i	$0.253627\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	3.17157	0.163561
$377$	26.6274	1.37138
$378$	1.00000	0.0514344
$379$	4.07107	0.209117	0.104558	−	0.994519i	$-0.466657\pi$
$379$	4.07107	0.209117	0.104558	+	0.994519i	$0.466657\pi$
$380$	0	0
$381$	0.686292	0.0351598
$382$	14.4853	0.741131
$383$	21.7990	1.11388	0.556938	−	0.830554i	$-0.311976\pi$
$383$	21.7990	1.11388	0.556938	+	0.830554i	$0.311976\pi$
$384$	−0.414214	−0.0211377
$385$	0	0
$386$	−9.65685	−0.491521
$387$	−32.0000	−1.62665
$388$	0	0
$389$	−14.0000	−0.709828	−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000	−0.709828	−0.354914	+	0.934899i	$0.615490\pi$
$390$	0	0
$391$	7.65685	0.387224
$392$	6.82843	0.344888
$393$	−5.34315	−0.269526
$394$	−2.00000	−0.100759
$395$	0	0
$396$	−5.65685	−0.284268
$397$	4.97056	0.249465	0.124733	−	0.992190i	$-0.460193\pi$
$397$	4.97056	0.249465	0.124733	+	0.992190i	$0.460193\pi$
$398$	4.34315	0.217702
$399$	0.142136	0.00711568
$400$	0	0
$401$	26.0000	1.29838	0.649189	−	0.760627i	$-0.275108\pi$
$401$	26.0000	1.29838	0.649189	+	0.760627i	$0.275108\pi$
$402$	−3.02944	−0.151095
$403$	−10.5563	−0.525849
$404$	−1.34315	−0.0668240
$405$	0	0
$406$	1.65685	0.0822283
$407$	−11.3137	−0.560800
$408$	0.414214	0.0205066
$409$	−29.9706	−1.48195	−0.740974	−	0.671533i	$-0.765636\pi$
$409$	−29.9706	−1.48195	−0.740974	+	0.671533i	$0.765636\pi$
$410$	0	0
$411$	5.58579	0.275527
$412$	1.51472	0.0746248
$413$	−3.31371	−0.163057
$414$	−21.6569	−1.06438
$415$	0	0
$416$	6.65685	0.326379
$417$	−8.85786	−0.433771
$418$	−1.65685	−0.0810394
$419$	6.68629	0.326647	0.163323	−	0.986573i	$-0.447779\pi$
$419$	6.68629	0.326647	0.163323	+	0.986573i	$0.447779\pi$
$420$	0	0
$421$	−18.3137	−0.892556	−0.446278	−	0.894894i	$-0.647251\pi$
$421$	−18.3137	−0.892556	−0.446278	+	0.894894i	$0.647251\pi$
$422$	9.72792	0.473548
$423$	8.97056	0.436164
$424$	5.82843	0.283053
$425$	0	0
$426$	5.48528	0.265763
$427$	−1.51472	−0.0733024
$428$	−16.0711	−0.776824
$429$	−5.51472	−0.266253
$430$	0	0
$431$	−34.5563	−1.66452	−0.832260	−	0.554385i	$-0.812954\pi$
$431$	−34.5563	−1.66452	−0.832260	+	0.554385i	$0.812954\pi$
$432$	−2.41421	−0.116154
$433$	−14.6863	−0.705778	−0.352889	−	0.935665i	$-0.614801\pi$
$433$	−14.6863	−0.705778	−0.352889	+	0.935665i	$0.614801\pi$
$434$	−0.656854	−0.0315300
$435$	0	0
$436$	15.3137	0.733394
$437$	−6.34315	−0.303434
$438$	0.686292	0.0327923
$439$	−35.8701	−1.71198	−0.855992	−	0.516989i	$-0.827053\pi$
$439$	−35.8701	−1.71198	−0.855992	+	0.516989i	$0.827053\pi$
$440$	0	0
$441$	19.3137	0.919700
$442$	−6.65685	−0.316634
$443$	5.51472	0.262012	0.131006	−	0.991382i	$-0.458179\pi$
$443$	5.51472	0.262012	0.131006	+	0.991382i	$0.458179\pi$
$444$	−2.34315	−0.111201
$445$	0	0
$446$	−18.4853	−0.875303
$447$	−3.78680	−0.179109
$448$	0.414214	0.0195698
$449$	18.3431	0.865667	0.432833	−	0.901474i	$-0.357514\pi$
$449$	18.3431	0.865667	0.432833	+	0.901474i	$0.357514\pi$
$450$	0	0
$451$	15.3137	0.721094
$452$	−6.34315	−0.298356
$453$	1.02944	0.0483672
$454$	−13.2426	−0.621508
$455$	0	0
$456$	−0.343146	−0.0160693
$457$	25.1421	1.17610	0.588050	−	0.808825i	$-0.299896\pi$
$457$	25.1421	1.17610	0.588050	+	0.808825i	$0.299896\pi$
$458$	12.3137	0.575382
$459$	2.41421	0.112686
$460$	0	0
$461$	−12.6274	−0.588117	−0.294059	−	0.955787i	$-0.595006\pi$
$461$	−12.6274	−0.588117	−0.294059	+	0.955787i	$0.595006\pi$
$462$	−0.343146	−0.0159646
$463$	−2.34315	−0.108895	−0.0544476	−	0.998517i	$-0.517340\pi$
$463$	−2.34315	−0.108895	−0.0544476	+	0.998517i	$0.517340\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	20.0000	0.926482
$467$	−33.1127	−1.53227	−0.766136	−	0.642678i	$-0.777823\pi$
$467$	−33.1127	−1.53227	−0.766136	+	0.642678i	$0.777823\pi$
$468$	18.8284	0.870344
$469$	3.02944	0.139886
$470$	0	0
$471$	6.69848	0.308650
$472$	8.00000	0.368230
$473$	22.6274	1.04041
$474$	−0.514719	−0.0236418
$475$	0	0
$476$	−0.414214	−0.0189854
$477$	16.4853	0.754809
$478$	−8.97056	−0.410304
$479$	−33.3137	−1.52214	−0.761071	−	0.648668i	$-0.775326\pi$
$479$	−33.3137	−1.52214	−0.761071	+	0.648668i	$0.775326\pi$
$480$	0	0
$481$	37.6569	1.71700
$482$	−20.6274	−0.939553
$483$	−1.31371	−0.0597758
$484$	−7.00000	−0.318182
$485$	0	0
$486$	−10.3431	−0.469175
$487$	−36.6274	−1.65975	−0.829873	−	0.557952i	$-0.811587\pi$
$487$	−36.6274	−1.65975	−0.829873	+	0.557952i	$0.811587\pi$
$488$	3.65685	0.165538
$489$	8.11270	0.366869
$490$	0	0
$491$	1.65685	0.0747728	0.0373864	−	0.999301i	$-0.488097\pi$
$491$	1.65685	0.0747728	0.0373864	+	0.999301i	$0.488097\pi$
$492$	3.17157	0.142986
$493$	4.00000	0.180151
$494$	5.51472	0.248119
$495$	0	0
$496$	1.58579	0.0712039
$497$	−5.48528	−0.246048
$498$	0.970563	0.0434920
$499$	30.3553	1.35889	0.679446	−	0.733726i	$-0.262220\pi$
$499$	30.3553	1.35889	0.679446	+	0.733726i	$0.262220\pi$
$500$	0	0
$501$	3.17157	0.141695
$502$	4.00000	0.178529
$503$	30.9706	1.38091	0.690455	−	0.723376i	$-0.257411\pi$
$503$	30.9706	1.38091	0.690455	+	0.723376i	$0.257411\pi$
$504$	1.17157	0.0521860
$505$	0	0
$506$	15.3137	0.680777
$507$	12.9706	0.576043
$508$	1.65685	0.0735110
$509$	35.1421	1.55765	0.778824	−	0.627243i	$-0.215817\pi$
$509$	35.1421	1.55765	0.778824	+	0.627243i	$0.215817\pi$
$510$	0	0
$511$	−0.686292	−0.0303597
$512$	−1.00000	−0.0441942
$513$	−2.00000	−0.0883022
$514$	−10.5147	−0.463784
$515$	0	0
$516$	4.68629	0.206302
$517$	−6.34315	−0.278971
$518$	2.34315	0.102952
$519$	4.54416	0.199466
$520$	0	0
$521$	−38.2843	−1.67726	−0.838632	−	0.544698i	$-0.816644\pi$
$521$	−38.2843	−1.67726	−0.838632	+	0.544698i	$0.816644\pi$
$522$	−11.3137	−0.495188
$523$	−2.34315	−0.102459	−0.0512293	−	0.998687i	$-0.516314\pi$
$523$	−2.34315	−0.102459	−0.0512293	+	0.998687i	$0.516314\pi$
$524$	−12.8995	−0.563517
$525$	0	0
$526$	10.3431	0.450983
$527$	−1.58579	−0.0690779
$528$	0.828427	0.0360527
$529$	35.6274	1.54902
$530$	0	0
$531$	22.6274	0.981946
$532$	0.343146	0.0148773
$533$	−50.9706	−2.20778
$534$	0.828427	0.0358495
$535$	0	0
$536$	−7.31371	−0.315904
$537$	10.2843	0.443799
$538$	−28.6274	−1.23422
$539$	−13.6569	−0.588242
$540$	0	0
$541$	40.9706	1.76146	0.880731	−	0.473617i	$-0.157052\pi$
$541$	40.9706	1.76146	0.880731	+	0.473617i	$0.157052\pi$
$542$	22.4853	0.965826
$543$	8.14214	0.349412
$544$	1.00000	0.0428746
$545$	0	0
$546$	1.14214	0.0488789
$547$	7.92893	0.339017	0.169508	−	0.985529i	$-0.445782\pi$
$547$	7.92893	0.339017	0.169508	+	0.985529i	$0.445782\pi$
$548$	13.4853	0.576063
$549$	10.3431	0.441435
$550$	0	0
$551$	−3.31371	−0.141169
$552$	3.17157	0.134991
$553$	0.514719	0.0218881
$554$	23.6569	1.00508
$555$	0	0
$556$	−21.3848	−0.906917
$557$	−19.6274	−0.831640	−0.415820	−	0.909447i	$-0.636505\pi$
$557$	−19.6274	−0.831640	−0.415820	+	0.909447i	$0.636505\pi$
$558$	4.48528	0.189877
$559$	−75.3137	−3.18543
$560$	0	0
$561$	−0.828427	−0.0349762
$562$	−6.65685	−0.280802
$563$	−35.4558	−1.49429	−0.747143	−	0.664664i	$-0.768575\pi$
$563$	−35.4558	−1.49429	−0.747143	+	0.664664i	$0.768575\pi$
$564$	−1.31371	−0.0553171
$565$	0	0
$566$	−18.9706	−0.797392
$567$	3.10051	0.130209
$568$	13.2426	0.555649
$569$	−28.6274	−1.20012	−0.600062	−	0.799954i	$-0.704857\pi$
$569$	−28.6274	−1.20012	−0.600062	+	0.799954i	$0.704857\pi$
$570$	0	0
$571$	10.0711	0.421461	0.210731	−	0.977544i	$-0.432416\pi$
$571$	10.0711	0.421461	0.210731	+	0.977544i	$0.432416\pi$
$572$	−13.3137	−0.556674
$573$	−6.00000	−0.250654
$574$	−3.17157	−0.132379
$575$	0	0
$576$	−2.82843	−0.117851
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	−1.00000	−0.0415945
$579$	4.00000	0.166234
$580$	0	0
$581$	−0.970563	−0.0402657
$582$	0	0
$583$	−11.6569	−0.482778
$584$	1.65685	0.0685611
$585$	0	0
$586$	25.3137	1.04570
$587$	−15.3137	−0.632064	−0.316032	−	0.948748i	$-0.602351\pi$
$587$	−15.3137	−0.632064	−0.316032	+	0.948748i	$0.602351\pi$
$588$	−2.82843	−0.116642
$589$	1.31371	0.0541304
$590$	0	0
$591$	0.828427	0.0340769
$592$	−5.65685	−0.232495
$593$	−3.34315	−0.137287	−0.0686433	−	0.997641i	$-0.521867\pi$
$593$	−3.34315	−0.137287	−0.0686433	+	0.997641i	$0.521867\pi$
$594$	4.82843	0.198113
$595$	0	0
$596$	−9.14214	−0.374476
$597$	−1.79899	−0.0736278
$598$	−50.9706	−2.08434
$599$	14.3431	0.586045	0.293023	−	0.956106i	$-0.405339\pi$
$599$	14.3431	0.586045	0.293023	+	0.956106i	$0.405339\pi$
$600$	0	0
$601$	−25.6569	−1.04656	−0.523282	−	0.852159i	$-0.675293\pi$
$601$	−25.6569	−1.04656	−0.523282	+	0.852159i	$0.675293\pi$
$602$	−4.68629	−0.190999
$603$	−20.6863	−0.842411
$604$	2.48528	0.101125
$605$	0	0
$606$	0.556349	0.0226001
$607$	40.0711	1.62643	0.813217	−	0.581960i	$-0.197714\pi$
$607$	40.0711	1.62643	0.813217	+	0.581960i	$0.197714\pi$
$608$	−0.828427	−0.0335972
$609$	−0.686292	−0.0278099
$610$	0	0
$611$	21.1127	0.854128
$612$	2.82843	0.114332
$613$	13.1421	0.530806	0.265403	−	0.964138i	$-0.414495\pi$
$613$	13.1421	0.530806	0.265403	+	0.964138i	$0.414495\pi$
$614$	9.65685	0.389719
$615$	0	0
$616$	−0.828427	−0.0333783
$617$	8.97056	0.361141	0.180571	−	0.983562i	$-0.442206\pi$
$617$	8.97056	0.361141	0.180571	+	0.983562i	$0.442206\pi$
$618$	−0.627417	−0.0252384
$619$	37.3137	1.49976	0.749882	−	0.661571i	$-0.230110\pi$
$619$	37.3137	1.49976	0.749882	+	0.661571i	$0.230110\pi$
$620$	0	0
$621$	18.4853	0.741789
$622$	−20.2132	−0.810476
$623$	−0.828427	−0.0331902
$624$	−2.75736	−0.110383
$625$	0	0
$626$	−22.9706	−0.918088
$627$	0.686292	0.0274078
$628$	16.1716	0.645316
$629$	5.65685	0.225554
$630$	0	0
$631$	−32.9706	−1.31254	−0.656269	−	0.754527i	$-0.727866\pi$
$631$	−32.9706	−1.31254	−0.656269	+	0.754527i	$0.727866\pi$
$632$	−1.24264	−0.0494296
$633$	−4.02944	−0.160156
$634$	2.68629	0.106686
$635$	0	0
$636$	−2.41421	−0.0957298
$637$	45.4558	1.80103
$638$	8.00000	0.316723
$639$	37.4558	1.48173
$640$	0	0
$641$	36.2843	1.43314	0.716571	−	0.697514i	$-0.245710\pi$
$641$	36.2843	1.43314	0.716571	+	0.697514i	$0.245710\pi$
$642$	6.65685	0.262725
$643$	29.8701	1.17796	0.588980	−	0.808148i	$-0.299530\pi$
$643$	29.8701	1.17796	0.588980	+	0.808148i	$0.299530\pi$
$644$	−3.17157	−0.124977
$645$	0	0
$646$	0.828427	0.0325940
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	−7.48528	−0.294050
$649$	−16.0000	−0.628055
$650$	0	0
$651$	0.272078	0.0106636
$652$	19.5858	0.767039
$653$	8.28427	0.324189	0.162094	−	0.986775i	$-0.448175\pi$
$653$	8.28427	0.324189	0.162094	+	0.986775i	$0.448175\pi$
$654$	−6.34315	−0.248037
$655$	0	0
$656$	7.65685	0.298950
$657$	4.68629	0.182830
$658$	1.31371	0.0512137
$659$	−4.14214	−0.161355	−0.0806773	−	0.996740i	$-0.525708\pi$
$659$	−4.14214	−0.161355	−0.0806773	+	0.996740i	$0.525708\pi$
$660$	0	0
$661$	−26.1716	−1.01796	−0.508978	−	0.860779i	$-0.669977\pi$
$661$	−26.1716	−1.01796	−0.508978	+	0.860779i	$0.669977\pi$
$662$	14.4853	0.562986
$663$	2.75736	0.107087
$664$	2.34315	0.0909317
$665$	0	0
$666$	−16.0000	−0.619987
$667$	30.6274	1.18590
$668$	7.65685	0.296253
$669$	7.65685	0.296031
$670$	0	0
$671$	−7.31371	−0.282343
$672$	−0.171573	−0.00661857
$673$	18.0000	0.693849	0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000	0.693849	0.346925	+	0.937893i	$0.387226\pi$
$674$	28.9706	1.11590
$675$	0	0
$676$	31.3137	1.20437
$677$	−17.9411	−0.689533	−0.344767	−	0.938688i	$-0.612042\pi$
$677$	−17.9411	−0.689533	−0.344767	+	0.938688i	$0.612042\pi$
$678$	2.62742	0.100905
$679$	0	0
$680$	0	0
$681$	5.48528	0.210196
$682$	−3.17157	−0.121446
$683$	11.9289	0.456448	0.228224	−	0.973609i	$-0.426708\pi$
$683$	11.9289	0.456448	0.228224	+	0.973609i	$0.426708\pi$
$684$	−2.34315	−0.0895924
$685$	0	0
$686$	5.72792	0.218693
$687$	−5.10051	−0.194596
$688$	11.3137	0.431331
$689$	38.7990	1.47812
$690$	0	0
$691$	−20.3553	−0.774354	−0.387177	−	0.922005i	$-0.626550\pi$
$691$	−20.3553	−0.774354	−0.387177	+	0.922005i	$0.626550\pi$
$692$	10.9706	0.417038
$693$	−2.34315	−0.0890087
$694$	33.5858	1.27490
$695$	0	0
$696$	1.65685	0.0628029
$697$	−7.65685	−0.290024
$698$	−16.1716	−0.612103
$699$	−8.28427	−0.313340
$700$	0	0
$701$	8.62742	0.325853	0.162927	−	0.986638i	$-0.447907\pi$
$701$	8.62742	0.325853	0.162927	+	0.986638i	$0.447907\pi$
$702$	−16.0711	−0.606563
$703$	−4.68629	−0.176747
$704$	2.00000	0.0753778
$705$	0	0
$706$	21.3431	0.803260
$707$	−0.556349	−0.0209237
$708$	−3.31371	−0.124537
$709$	−31.6569	−1.18890	−0.594449	−	0.804133i	$-0.702630\pi$
$709$	−31.6569	−1.18890	−0.594449	+	0.804133i	$0.702630\pi$
$710$	0	0
$711$	−3.51472	−0.131812
$712$	2.00000	0.0749532
$713$	−12.1421	−0.454727
$714$	0.171573	0.00642095
$715$	0	0
$716$	24.8284	0.927882
$717$	3.71573	0.138766
$718$	20.1421	0.751698
$719$	12.8995	0.481070	0.240535	−	0.970640i	$-0.422677\pi$
$719$	12.8995	0.481070	0.240535	+	0.970640i	$0.422677\pi$
$720$	0	0
$721$	0.627417	0.0233662
$722$	18.3137	0.681566
$723$	8.54416	0.317761
$724$	19.6569	0.730541
$725$	0	0
$726$	2.89949	0.107610
$727$	40.8284	1.51424	0.757121	−	0.653274i	$-0.226605\pi$
$727$	40.8284	1.51424	0.757121	+	0.653274i	$0.226605\pi$
$728$	2.75736	0.102195
$729$	−18.1716	−0.673021
$730$	0	0
$731$	−11.3137	−0.418453
$732$	−1.51472	−0.0559856
$733$	−0.171573	−0.00633719	−0.00316859	−	0.999995i	$-0.501009\pi$
$733$	−0.171573	−0.00633719	−0.00316859	+	0.999995i	$0.501009\pi$
$734$	29.0416	1.07195
$735$	0	0
$736$	7.65685	0.282235
$737$	14.6274	0.538808
$738$	21.6569	0.797200
$739$	−4.82843	−0.177617	−0.0888083	−	0.996049i	$-0.528306\pi$
$739$	−4.82843	−0.177617	−0.0888083	+	0.996049i	$0.528306\pi$
$740$	0	0
$741$	−2.28427	−0.0839148
$742$	2.41421	0.0886286
$743$	−23.9289	−0.877867	−0.438934	−	0.898519i	$-0.644644\pi$
$743$	−23.9289	−0.877867	−0.438934	+	0.898519i	$0.644644\pi$
$744$	−0.656854	−0.0240814
$745$	0	0
$746$	−27.0000	−0.988540
$747$	6.62742	0.242485
$748$	−2.00000	−0.0731272
$749$	−6.65685	−0.243236
$750$	0	0
$751$	−22.2843	−0.813165	−0.406582	−	0.913614i	$-0.633280\pi$
$751$	−22.2843	−0.813165	−0.406582	+	0.913614i	$0.633280\pi$
$752$	−3.17157	−0.115655
$753$	−1.65685	−0.0603791
$754$	−26.6274	−0.969713
$755$	0	0
$756$	−1.00000	−0.0363696
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	−4.07107	−0.147868
$759$	−6.34315	−0.230242
$760$	0	0
$761$	−8.51472	−0.308658	−0.154329	−	0.988019i	$-0.549322\pi$
$761$	−8.51472	−0.308658	−0.154329	+	0.988019i	$0.549322\pi$
$762$	−0.686292	−0.0248617
$763$	6.34315	0.229637
$764$	−14.4853	−0.524059
$765$	0	0
$766$	−21.7990	−0.787630
$767$	53.2548	1.92292
$768$	0.414214	0.0149466
$769$	−47.1421	−1.69999	−0.849994	−	0.526792i	$-0.823395\pi$
$769$	−47.1421	−1.69999	−0.849994	+	0.526792i	$0.823395\pi$
$770$	0	0
$771$	4.35534	0.156854
$772$	9.65685	0.347558
$773$	−20.9411	−0.753200	−0.376600	−	0.926376i	$-0.622907\pi$
$773$	−20.9411	−0.753200	−0.376600	+	0.926376i	$0.622907\pi$
$774$	32.0000	1.15022
$775$	0	0
$776$	0	0
$777$	−0.970563	−0.0348187
$778$	14.0000	0.501924
$779$	6.34315	0.227267
$780$	0	0
$781$	−26.4853	−0.947718
$782$	−7.65685	−0.273809
$783$	9.65685	0.345108
$784$	−6.82843	−0.243872
$785$	0	0
$786$	5.34315	0.190584
$787$	5.10051	0.181813	0.0909067	−	0.995859i	$-0.471023\pi$
$787$	5.10051	0.181813	0.0909067	+	0.995859i	$0.471023\pi$
$788$	2.00000	0.0712470
$789$	−4.28427	−0.152524
$790$	0	0
$791$	−2.62742	−0.0934202
$792$	5.65685	0.201008
$793$	24.3431	0.864450
$794$	−4.97056	−0.176399
$795$	0	0
$796$	−4.34315	−0.153939
$797$	22.1716	0.785357	0.392679	−	0.919676i	$-0.371548\pi$
$797$	22.1716	0.785357	0.392679	+	0.919676i	$0.371548\pi$
$798$	−0.142136	−0.00503155
$799$	3.17157	0.112202
$800$	0	0
$801$	5.65685	0.199875
$802$	−26.0000	−0.918092
$803$	−3.31371	−0.116938
$804$	3.02944	0.106840
$805$	0	0
$806$	10.5563	0.371832
$807$	11.8579	0.417417
$808$	1.34315	0.0472517
$809$	10.6863	0.375710	0.187855	−	0.982197i	$-0.439846\pi$
$809$	10.6863	0.375710	0.187855	+	0.982197i	$0.439846\pi$
$810$	0	0
$811$	−44.6985	−1.56958	−0.784788	−	0.619764i	$-0.787228\pi$
$811$	−44.6985	−1.56958	−0.784788	+	0.619764i	$0.787228\pi$
$812$	−1.65685	−0.0581442
$813$	−9.31371	−0.326646
$814$	11.3137	0.396545
$815$	0	0
$816$	−0.414214	−0.0145004
$817$	9.37258	0.327905
$818$	29.9706	1.04790
$819$	7.79899	0.272519
$820$	0	0
$821$	−19.6569	−0.686029	−0.343014	−	0.939330i	$-0.611448\pi$
$821$	−19.6569	−0.686029	−0.343014	+	0.939330i	$0.611448\pi$
$822$	−5.58579	−0.194827
$823$	−27.1838	−0.947567	−0.473783	−	0.880641i	$-0.657112\pi$
$823$	−27.1838	−0.947567	−0.473783	+	0.880641i	$0.657112\pi$
$824$	−1.51472	−0.0527677
$825$	0	0
$826$	3.31371	0.115299
$827$	−3.37258	−0.117276	−0.0586381	−	0.998279i	$-0.518676\pi$
$827$	−3.37258	−0.117276	−0.0586381	+	0.998279i	$0.518676\pi$
$828$	21.6569	0.752628
$829$	34.4558	1.19670	0.598350	−	0.801234i	$-0.295823\pi$
$829$	34.4558	1.19670	0.598350	+	0.801234i	$0.295823\pi$
$830$	0	0
$831$	−9.79899	−0.339923
$832$	−6.65685	−0.230785
$833$	6.82843	0.236591
$834$	8.85786	0.306723
$835$	0	0
$836$	1.65685	0.0573035
$837$	−3.82843	−0.132330
$838$	−6.68629	−0.230974
$839$	−31.2426	−1.07862	−0.539308	−	0.842109i	$-0.681314\pi$
$839$	−31.2426	−1.07862	−0.539308	+	0.842109i	$0.681314\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	18.3137	0.631132
$843$	2.75736	0.0949685
$844$	−9.72792	−0.334849
$845$	0	0
$846$	−8.97056	−0.308414
$847$	−2.89949	−0.0996278
$848$	−5.82843	−0.200149
$849$	7.85786	0.269681
$850$	0	0
$851$	43.3137	1.48477
$852$	−5.48528	−0.187923
$853$	37.3137	1.27760	0.638799	−	0.769374i	$-0.279432\pi$
$853$	37.3137	1.27760	0.638799	+	0.769374i	$0.279432\pi$
$854$	1.51472	0.0518326
$855$	0	0
$856$	16.0711	0.549298
$857$	−1.65685	−0.0565971	−0.0282985	−	0.999600i	$-0.509009\pi$
$857$	−1.65685	−0.0565971	−0.0282985	+	0.999600i	$0.509009\pi$
$858$	5.51472	0.188269
$859$	12.1421	0.414284	0.207142	−	0.978311i	$-0.433584\pi$
$859$	12.1421	0.414284	0.207142	+	0.978311i	$0.433584\pi$
$860$	0	0
$861$	1.31371	0.0447711
$862$	34.5563	1.17699
$863$	−43.5980	−1.48409	−0.742046	−	0.670349i	$-0.766145\pi$
$863$	−43.5980	−1.48409	−0.742046	+	0.670349i	$0.766145\pi$
$864$	2.41421	0.0821332
$865$	0	0
$866$	14.6863	0.499061
$867$	0.414214	0.0140674
$868$	0.656854	0.0222951
$869$	2.48528	0.0843074
$870$	0	0
$871$	−48.6863	−1.64967
$872$	−15.3137	−0.518588
$873$	0	0
$874$	6.34315	0.214560
$875$	0	0
$876$	−0.686292	−0.0231876
$877$	−31.3137	−1.05739	−0.528694	−	0.848812i	$-0.677318\pi$
$877$	−31.3137	−1.05739	−0.528694	+	0.848812i	$0.677318\pi$
$878$	35.8701	1.21056
$879$	−10.4853	−0.353660
$880$	0	0
$881$	−38.9706	−1.31295	−0.656476	−	0.754347i	$-0.727954\pi$
$881$	−38.9706	−1.31295	−0.656476	+	0.754347i	$0.727954\pi$
$882$	−19.3137	−0.650326
$883$	−31.4558	−1.05857	−0.529287	−	0.848443i	$-0.677540\pi$
$883$	−31.4558	−1.05857	−0.529287	+	0.848443i	$0.677540\pi$
$884$	6.65685	0.223894
$885$	0	0
$886$	−5.51472	−0.185271
$887$	34.4142	1.15552	0.577758	−	0.816208i	$-0.303928\pi$
$887$	34.4142	1.15552	0.577758	+	0.816208i	$0.303928\pi$
$888$	2.34315	0.0786308
$889$	0.686292	0.0230175
$890$	0	0
$891$	14.9706	0.501533
$892$	18.4853	0.618933
$893$	−2.62742	−0.0879232
$894$	3.78680	0.126649
$895$	0	0
$896$	−0.414214	−0.0138379
$897$	21.1127	0.704932
$898$	−18.3431	−0.612119
$899$	−6.34315	−0.211556
$900$	0	0
$901$	5.82843	0.194173
$902$	−15.3137	−0.509891
$903$	1.94113	0.0645966
$904$	6.34315	0.210970
$905$	0	0
$906$	−1.02944	−0.0342008
$907$	17.3137	0.574892	0.287446	−	0.957797i	$-0.407194\pi$
$907$	17.3137	0.574892	0.287446	+	0.957797i	$0.407194\pi$
$908$	13.2426	0.439472
$909$	3.79899	0.126005
$910$	0	0
$911$	−3.72792	−0.123512	−0.0617558	−	0.998091i	$-0.519670\pi$
$911$	−3.72792	−0.123512	−0.0617558	+	0.998091i	$0.519670\pi$
$912$	0.343146	0.0113627
$913$	−4.68629	−0.155094
$914$	−25.1421	−0.831628
$915$	0	0
$916$	−12.3137	−0.406856
$917$	−5.34315	−0.176446
$918$	−2.41421	−0.0796809
$919$	−38.3431	−1.26482	−0.632412	−	0.774632i	$-0.717935\pi$
$919$	−38.3431	−1.26482	−0.632412	+	0.774632i	$0.717935\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	12.6274	0.415862
$923$	88.1543	2.90164
$924$	0.343146	0.0112887
$925$	0	0
$926$	2.34315	0.0770005
$927$	−4.28427	−0.140714
$928$	4.00000	0.131306
$929$	8.00000	0.262471	0.131236	−	0.991351i	$-0.458106\pi$
$929$	8.00000	0.262471	0.131236	+	0.991351i	$0.458106\pi$
$930$	0	0
$931$	−5.65685	−0.185396
$932$	−20.0000	−0.655122
$933$	8.37258	0.274106
$934$	33.1127	1.08348
$935$	0	0
$936$	−18.8284	−0.615426
$937$	−17.0000	−0.555366	−0.277683	−	0.960673i	$-0.589566\pi$
$937$	−17.0000	−0.555366	−0.277683	+	0.960673i	$0.589566\pi$
$938$	−3.02944	−0.0989146
$939$	9.51472	0.310501
$940$	0	0
$941$	7.65685	0.249606	0.124803	−	0.992182i	$-0.460170\pi$
$941$	7.65685	0.249606	0.124803	+	0.992182i	$0.460170\pi$
$942$	−6.69848	−0.218248
$943$	−58.6274	−1.90917
$944$	−8.00000	−0.260378
$945$	0	0
$946$	−22.6274	−0.735681
$947$	−1.31371	−0.0426898	−0.0213449	−	0.999772i	$-0.506795\pi$
$947$	−1.31371	−0.0426898	−0.0213449	+	0.999772i	$0.506795\pi$
$948$	0.514719	0.0167173
$949$	11.0294	0.358031
$950$	0	0
$951$	−1.11270	−0.0360817
$952$	0.414214	0.0134247
$953$	32.1127	1.04023	0.520116	−	0.854096i	$-0.325889\pi$
$953$	32.1127	1.04023	0.520116	+	0.854096i	$0.325889\pi$
$954$	−16.4853	−0.533731
$955$	0	0
$956$	8.97056	0.290129
$957$	−3.31371	−0.107117
$958$	33.3137	1.07632
$959$	5.58579	0.180374
$960$	0	0
$961$	−28.4853	−0.918880
$962$	−37.6569	−1.21411
$963$	45.4558	1.46479
$964$	20.6274	0.664364
$965$	0	0
$966$	1.31371	0.0422679
$967$	−10.6274	−0.341755	−0.170877	−	0.985292i	$-0.554660\pi$
$967$	−10.6274	−0.341755	−0.170877	+	0.985292i	$0.554660\pi$
$968$	7.00000	0.224989
$969$	−0.343146	−0.0110234
$970$	0	0
$971$	53.9411	1.73105	0.865527	−	0.500863i	$-0.166984\pi$
$971$	53.9411	1.73105	0.865527	+	0.500863i	$0.166984\pi$
$972$	10.3431	0.331757
$973$	−8.85786	−0.283970
$974$	36.6274	1.17362
$975$	0	0
$976$	−3.65685	−0.117053
$977$	22.3137	0.713879	0.356939	−	0.934128i	$-0.383820\pi$
$977$	22.3137	0.713879	0.356939	+	0.934128i	$0.383820\pi$
$978$	−8.11270	−0.259415
$979$	−4.00000	−0.127841
$980$	0	0
$981$	−43.3137	−1.38290
$982$	−1.65685	−0.0528723
$983$	−4.41421	−0.140792	−0.0703958	−	0.997519i	$-0.522426\pi$
$983$	−4.41421	−0.140792	−0.0703958	+	0.997519i	$0.522426\pi$
$984$	−3.17157	−0.101106
$985$	0	0
$986$	−4.00000	−0.127386
$987$	−0.544156	−0.0173207
$988$	−5.51472	−0.175447
$989$	−86.6274	−2.75459
$990$	0	0
$991$	37.1838	1.18118	0.590591	−	0.806971i	$-0.298895\pi$
$991$	37.1838	1.18118	0.590591	+	0.806971i	$0.298895\pi$
$992$	−1.58579	−0.0503488
$993$	−6.00000	−0.190404
$994$	5.48528	0.173983
$995$	0	0
$996$	−0.970563	−0.0307535
$997$	38.6274	1.22334	0.611671	−	0.791112i	$-0.290498\pi$
$997$	38.6274	1.22334	0.611671	+	0.791112i	$0.290498\pi$
$998$	−30.3553	−0.960881
$999$	13.6569	0.432084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.a.m.1.2	✓	2
3.2	odd	2		7650.2.a.dc.1.2		2
4.3	odd	2		6800.2.a.bi.1.1		2
5.2	odd	4		850.2.c.j.749.1		4
5.3	odd	4		850.2.c.j.749.4		4
5.4	even	2		850.2.a.o.1.1	yes	2
15.14	odd	2		7650.2.a.cw.1.1		2
20.19	odd	2		6800.2.a.bc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.a.m.1.2	✓	2	1.1	even	1	trivial
850.2.a.o.1.1	yes	2	5.4	even	2
850.2.c.j.749.1		4	5.2	odd	4
850.2.c.j.749.4		4	5.3	odd	4
6800.2.a.bc.1.2		2	20.19	odd	2
6800.2.a.bi.1.1		2	4.3	odd	2
7650.2.a.cw.1.1		2	15.14	odd	2
7650.2.a.dc.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} -0.414214 q^{6} +0.414214 q^{7} -1.00000 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} -0.414214 q^{6} +0.414214 q^{7} -1.00000 q^{8} -2.82843 q^{9} +2.00000 q^{11} +0.414214 q^{12} -6.65685 q^{13} -0.414214 q^{14} +1.00000 q^{16} -1.00000 q^{17} +2.82843 q^{18} +0.828427 q^{19} +0.171573 q^{21} -2.00000 q^{22} -7.65685 q^{23} -0.414214 q^{24} +6.65685 q^{26} -2.41421 q^{27} +0.414214 q^{28} -4.00000 q^{29} +1.58579 q^{31} -1.00000 q^{32} +0.828427 q^{33} +1.00000 q^{34} -2.82843 q^{36} -5.65685 q^{37} -0.828427 q^{38} -2.75736 q^{39} +7.65685 q^{41} -0.171573 q^{42} +11.3137 q^{43} +2.00000 q^{44} +7.65685 q^{46} -3.17157 q^{47} +0.414214 q^{48} -6.82843 q^{49} -0.414214 q^{51} -6.65685 q^{52} -5.82843 q^{53} +2.41421 q^{54} -0.414214 q^{56} +0.343146 q^{57} +4.00000 q^{58} -8.00000 q^{59} -3.65685 q^{61} -1.58579 q^{62} -1.17157 q^{63} +1.00000 q^{64} -0.828427 q^{66} +7.31371 q^{67} -1.00000 q^{68} -3.17157 q^{69} -13.2426 q^{71} +2.82843 q^{72} -1.65685 q^{73} +5.65685 q^{74} +0.828427 q^{76} +0.828427 q^{77} +2.75736 q^{78} +1.24264 q^{79} +7.48528 q^{81} -7.65685 q^{82} -2.34315 q^{83} +0.171573 q^{84} -11.3137 q^{86} -1.65685 q^{87} -2.00000 q^{88} -2.00000 q^{89} -2.75736 q^{91} -7.65685 q^{92} +0.656854 q^{93} +3.17157 q^{94} -0.414214 q^{96} +6.82843 q^{98} -5.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 4 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{17} - 4 q^{19} + 6 q^{21} - 4 q^{22} - 4 q^{23} + 2 q^{24} + 2 q^{26} - 2 q^{27} - 2 q^{28} - 8 q^{29} + 6 q^{31} - 2 q^{32} - 4 q^{33} + 2 q^{34} + 4 q^{38} - 14 q^{39} + 4 q^{41} - 6 q^{42} + 4 q^{44} + 4 q^{46} - 12 q^{47} - 2 q^{48} - 8 q^{49} + 2 q^{51} - 2 q^{52} - 6 q^{53} + 2 q^{54} + 2 q^{56} + 12 q^{57} + 8 q^{58} - 16 q^{59} + 4 q^{61} - 6 q^{62} - 8 q^{63} + 2 q^{64} + 4 q^{66} - 8 q^{67} - 2 q^{68} - 12 q^{69} - 18 q^{71} + 8 q^{73} - 4 q^{76} - 4 q^{77} + 14 q^{78} - 6 q^{79} - 2 q^{81} - 4 q^{82} - 16 q^{83} + 6 q^{84} + 8 q^{87} - 4 q^{88} - 4 q^{89} - 14 q^{91} - 4 q^{92} - 10 q^{93} + 12 q^{94} + 2 q^{96} + 8 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 4 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^17 - 4 * q^19 + 6 * q^21 - 4 * q^22 - 4 * q^23 + 2 * q^24 + 2 * q^26 - 2 * q^27 - 2 * q^28 - 8 * q^29 + 6 * q^31 - 2 * q^32 - 4 * q^33 + 2 * q^34 + 4 * q^38 - 14 * q^39 + 4 * q^41 - 6 * q^42 + 4 * q^44 + 4 * q^46 - 12 * q^47 - 2 * q^48 - 8 * q^49 + 2 * q^51 - 2 * q^52 - 6 * q^53 + 2 * q^54 + 2 * q^56 + 12 * q^57 + 8 * q^58 - 16 * q^59 + 4 * q^61 - 6 * q^62 - 8 * q^63 + 2 * q^64 + 4 * q^66 - 8 * q^67 - 2 * q^68 - 12 * q^69 - 18 * q^71 + 8 * q^73 - 4 * q^76 - 4 * q^77 + 14 * q^78 - 6 * q^79 - 2 * q^81 - 4 * q^82 - 16 * q^83 + 6 * q^84 + 8 * q^87 - 4 * q^88 - 4 * q^89 - 14 * q^91 - 4 * q^92 - 10 * q^93 + 12 * q^94 + 2 * q^96 + 8 * q^98

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