LMFDB - Embedded newform 8450.2.a.bt.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8450,2,Mod(1,8450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8450, 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("8450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8450 = 2 \cdot 5^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8450.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:	$67.4735897080$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	8450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.67513 q^{3} +1.00000 q^{4} +1.67513 q^{6} +1.80606 q^{7} -1.00000 q^{8} -0.193937 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.67513 q^{3} +1.00000 q^{4} +1.67513 q^{6} +1.80606 q^{7} -1.00000 q^{8} -0.193937 q^{9} -6.44358 q^{11} -1.67513 q^{12} -1.80606 q^{14} +1.00000 q^{16} -0.481194 q^{17} +0.193937 q^{18} +6.28726 q^{19} -3.02539 q^{21} +6.44358 q^{22} -7.11871 q^{23} +1.67513 q^{24} +5.35026 q^{27} +1.80606 q^{28} +2.31265 q^{29} -3.25694 q^{31} -1.00000 q^{32} +10.7938 q^{33} +0.481194 q^{34} -0.193937 q^{36} +3.06300 q^{37} -6.28726 q^{38} -7.50659 q^{41} +3.02539 q^{42} +2.00000 q^{43} -6.44358 q^{44} +7.11871 q^{46} +2.19394 q^{47} -1.67513 q^{48} -3.73813 q^{49} +0.806063 q^{51} +0.906679 q^{53} -5.35026 q^{54} -1.80606 q^{56} -10.5320 q^{57} -2.31265 q^{58} -6.57452 q^{59} -10.9502 q^{61} +3.25694 q^{62} -0.350262 q^{63} +1.00000 q^{64} -10.7938 q^{66} +0.649738 q^{67} -0.481194 q^{68} +11.9248 q^{69} -3.66291 q^{71} +0.193937 q^{72} -2.60720 q^{73} -3.06300 q^{74} +6.28726 q^{76} -11.6375 q^{77} -2.29455 q^{79} -8.38058 q^{81} +7.50659 q^{82} +13.3380 q^{83} -3.02539 q^{84} -2.00000 q^{86} -3.87399 q^{87} +6.44358 q^{88} +1.15633 q^{89} -7.11871 q^{92} +5.45580 q^{93} -2.19394 q^{94} +1.67513 q^{96} +13.8315 q^{97} +3.73813 q^{98} +1.24965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9} - 3 q^{11} - 5 q^{14} + 3 q^{16} + 4 q^{17} + q^{18} + 13 q^{19} + 6 q^{21} + 3 q^{22} + 6 q^{27} + 5 q^{28} - 14 q^{29} - 6 q^{31} - 3 q^{32} + 6 q^{33} - 4 q^{34} - q^{36} + 5 q^{37} - 13 q^{38} - 2 q^{41} - 6 q^{42} + 6 q^{43} - 3 q^{44} + 7 q^{47} - 2 q^{49} + 2 q^{51} + 9 q^{53} - 6 q^{54} - 5 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 4 q^{61} + 6 q^{62} + 9 q^{63} + 3 q^{64} - 6 q^{66} + 12 q^{67} + 4 q^{68} + 14 q^{69} + 20 q^{71} + q^{72} + 6 q^{73} - 5 q^{74} + 13 q^{76} - 19 q^{77} - 14 q^{79} - 13 q^{81} + 2 q^{82} + 4 q^{83} + 6 q^{84} - 6 q^{86} - 20 q^{87} + 3 q^{88} - 7 q^{89} + 26 q^{93} - 7 q^{94} + 26 q^{97} + 2 q^{98} - 13 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9 - 3 * q^11 - 5 * q^14 + 3 * q^16 + 4 * q^17 + q^18 + 13 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^27 + 5 * q^28 - 14 * q^29 - 6 * q^31 - 3 * q^32 + 6 * q^33 - 4 * q^34 - q^36 + 5 * q^37 - 13 * q^38 - 2 * q^41 - 6 * q^42 + 6 * q^43 - 3 * q^44 + 7 * q^47 - 2 * q^49 + 2 * q^51 + 9 * q^53 - 6 * q^54 - 5 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 4 * q^61 + 6 * q^62 + 9 * q^63 + 3 * q^64 - 6 * q^66 + 12 * q^67 + 4 * q^68 + 14 * q^69 + 20 * q^71 + q^72 + 6 * q^73 - 5 * q^74 + 13 * q^76 - 19 * q^77 - 14 * q^79 - 13 * q^81 + 2 * q^82 + 4 * q^83 + 6 * q^84 - 6 * q^86 - 20 * q^87 + 3 * q^88 - 7 * q^89 + 26 * q^93 - 7 * q^94 + 26 * q^97 + 2 * q^98 - 13 * q^99

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
$3$	−1.67513	−0.967137	−0.483569	−	0.875306i	$-0.660660\pi$
$3$	−1.67513	−0.967137	−0.483569	+	0.875306i	$0.660660\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.67513	0.683869
$7$	1.80606	0.682628	0.341314	−	0.939949i	$-0.389128\pi$
$7$	1.80606	0.682628	0.341314	+	0.939949i	$0.389128\pi$
$8$	−1.00000	−0.353553
$9$	−0.193937	−0.0646455
$10$	0	0
$11$	−6.44358	−1.94281	−0.971407	−	0.237422i	$-0.923698\pi$
$11$	−6.44358	−1.94281	−0.971407	+	0.237422i	$0.923698\pi$
$12$	−1.67513	−0.483569
$13$	0	0
$13$	0	0
$14$	−1.80606	−0.482691
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.481194	−0.116707	−0.0583534	−	0.998296i	$-0.518585\pi$
$17$	−0.481194	−0.116707	−0.0583534	+	0.998296i	$0.518585\pi$
$18$	0.193937	0.0457113
$19$	6.28726	1.44240	0.721198	−	0.692729i	$-0.243592\pi$
$19$	6.28726	1.44240	0.721198	+	0.692729i	$0.243592\pi$
$20$	0	0
$21$	−3.02539	−0.660195
$22$	6.44358	1.37378
$23$	−7.11871	−1.48435	−0.742177	−	0.670204i	$-0.766207\pi$
$23$	−7.11871	−1.48435	−0.742177	+	0.670204i	$0.766207\pi$
$24$	1.67513	0.341935
$25$	0	0
$26$	0	0
$27$	5.35026	1.02966
$28$	1.80606	0.341314
$29$	2.31265	0.429448	0.214724	−	0.976675i	$-0.431115\pi$
$29$	2.31265	0.429448	0.214724	+	0.976675i	$0.431115\pi$
$30$	0	0
$31$	−3.25694	−0.584964	−0.292482	−	0.956271i	$-0.594481\pi$
$31$	−3.25694	−0.584964	−0.292482	+	0.956271i	$0.594481\pi$
$32$	−1.00000	−0.176777
$33$	10.7938	1.87897
$34$	0.481194	0.0825241
$35$	0	0
$36$	−0.193937	−0.0323228
$37$	3.06300	0.503555	0.251777	−	0.967785i	$-0.418985\pi$
$37$	3.06300	0.503555	0.251777	+	0.967785i	$0.418985\pi$
$38$	−6.28726	−1.01993
$39$	0	0
$40$	0	0
$41$	−7.50659	−1.17233	−0.586166	−	0.810191i	$-0.699363\pi$
$41$	−7.50659	−1.17233	−0.586166	+	0.810191i	$0.699363\pi$
$42$	3.02539	0.466828
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	−6.44358	−0.971407
$45$	0	0
$46$	7.11871	1.04960
$47$	2.19394	0.320019	0.160009	−	0.987116i	$-0.448848\pi$
$47$	2.19394	0.320019	0.160009	+	0.987116i	$0.448848\pi$
$48$	−1.67513	−0.241784
$49$	−3.73813	−0.534019
$50$	0	0
$51$	0.806063	0.112871
$52$	0	0
$53$	0.906679	0.124542	0.0622710	−	0.998059i	$-0.480166\pi$
$53$	0.906679	0.124542	0.0622710	+	0.998059i	$0.480166\pi$
$54$	−5.35026	−0.728078
$55$	0	0
$56$	−1.80606	−0.241345
$57$	−10.5320	−1.39499
$58$	−2.31265	−0.303666
$59$	−6.57452	−0.855929	−0.427965	−	0.903796i	$-0.640769\pi$
$59$	−6.57452	−0.855929	−0.427965	+	0.903796i	$0.640769\pi$
$60$	0	0
$61$	−10.9502	−1.40203	−0.701013	−	0.713149i	$-0.747268\pi$
$61$	−10.9502	−1.40203	−0.701013	+	0.713149i	$0.747268\pi$
$62$	3.25694	0.413632
$63$	−0.350262	−0.0441288
$64$	1.00000	0.125000
$65$	0	0
$66$	−10.7938	−1.32863
$67$	0.649738	0.0793782	0.0396891	−	0.999212i	$-0.487363\pi$
$67$	0.649738	0.0793782	0.0396891	+	0.999212i	$0.487363\pi$
$68$	−0.481194	−0.0583534
$69$	11.9248	1.43557
$70$	0	0
$71$	−3.66291	−0.434708	−0.217354	−	0.976093i	$-0.569743\pi$
$71$	−3.66291	−0.434708	−0.217354	+	0.976093i	$0.569743\pi$
$72$	0.193937	0.0228556
$73$	−2.60720	−0.305150	−0.152575	−	0.988292i	$-0.548757\pi$
$73$	−2.60720	−0.305150	−0.152575	+	0.988292i	$0.548757\pi$
$74$	−3.06300	−0.356067
$75$	0	0
$76$	6.28726	0.721198
$77$	−11.6375	−1.32622
$78$	0	0
$79$	−2.29455	−0.258157	−0.129079	−	0.991634i	$-0.541202\pi$
$79$	−2.29455	−0.258157	−0.129079	+	0.991634i	$0.541202\pi$
$80$	0	0
$81$	−8.38058	−0.931175
$82$	7.50659	0.828964
$83$	13.3380	1.46404	0.732020	−	0.681283i	$-0.238578\pi$
$83$	13.3380	1.46404	0.732020	+	0.681283i	$0.238578\pi$
$84$	−3.02539	−0.330097
$85$	0	0
$86$	−2.00000	−0.215666
$87$	−3.87399	−0.415336
$88$	6.44358	0.686888
$89$	1.15633	0.122570	0.0612851	−	0.998120i	$-0.480480\pi$
$89$	1.15633	0.122570	0.0612851	+	0.998120i	$0.480480\pi$
$90$	0	0
$91$	0	0
$92$	−7.11871	−0.742177
$93$	5.45580	0.565740
$94$	−2.19394	−0.226287
$95$	0	0
$96$	1.67513	0.170967
$97$	13.8315	1.40437	0.702186	−	0.711994i	$-0.252208\pi$
$97$	13.8315	1.40437	0.702186	+	0.711994i	$0.252208\pi$
$98$	3.73813	0.377609
$99$	1.24965	0.125594
$100$	0	0
$101$	−9.59991	−0.955227	−0.477613	−	0.878570i	$-0.658498\pi$
$101$	−9.59991	−0.955227	−0.477613	+	0.878570i	$0.658498\pi$
$102$	−0.806063	−0.0798122
$103$	−3.07522	−0.303011	−0.151505	−	0.988456i	$-0.548412\pi$
$103$	−3.07522	−0.303011	−0.151505	+	0.988456i	$0.548412\pi$
$104$	0	0
$105$	0	0
$106$	−0.906679	−0.0880644
$107$	1.67513	0.161941	0.0809705	−	0.996716i	$-0.474198\pi$
$107$	1.67513	0.161941	0.0809705	+	0.996716i	$0.474198\pi$
$108$	5.35026	0.514829
$109$	−10.8872	−1.04280	−0.521401	−	0.853312i	$-0.674590\pi$
$109$	−10.8872	−1.04280	−0.521401	+	0.853312i	$0.674590\pi$
$110$	0	0
$111$	−5.13093	−0.487007
$112$	1.80606	0.170657
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	10.5320	0.986410
$115$	0	0
$116$	2.31265	0.214724
$117$	0	0
$118$	6.57452	0.605233
$119$	−0.869067	−0.0796673
$120$	0	0
$121$	30.5198	2.77452
$122$	10.9502	0.991382
$123$	12.5745	1.13381
$124$	−3.25694	−0.292482
$125$	0	0
$126$	0.350262	0.0312038
$127$	5.18664	0.460240	0.230120	−	0.973162i	$-0.426088\pi$
$127$	5.18664	0.460240	0.230120	+	0.973162i	$0.426088\pi$
$128$	−1.00000	−0.0883883
$129$	−3.35026	−0.294974
$130$	0	0
$131$	−10.8011	−0.943700	−0.471850	−	0.881679i	$-0.656414\pi$
$131$	−10.8011	−0.943700	−0.471850	+	0.881679i	$0.656414\pi$
$132$	10.7938	0.939484
$133$	11.3552	0.984620
$134$	−0.649738	−0.0561288
$135$	0	0
$136$	0.481194	0.0412621
$137$	−6.14411	−0.524926	−0.262463	−	0.964942i	$-0.584535\pi$
$137$	−6.14411	−0.524926	−0.262463	+	0.964942i	$0.584535\pi$
$138$	−11.9248	−1.01510
$139$	10.3380	0.876861	0.438431	−	0.898765i	$-0.355534\pi$
$139$	10.3380	0.876861	0.438431	+	0.898765i	$0.355534\pi$
$140$	0	0
$141$	−3.67513	−0.309502
$142$	3.66291	0.307385
$143$	0	0
$144$	−0.193937	−0.0161614
$145$	0	0
$146$	2.60720	0.215774
$147$	6.26187	0.516470
$148$	3.06300	0.251777
$149$	16.0508	1.31493	0.657466	−	0.753484i	$-0.271628\pi$
$149$	16.0508	1.31493	0.657466	+	0.753484i	$0.271628\pi$
$150$	0	0
$151$	−9.31757	−0.758253	−0.379127	−	0.925345i	$-0.623776\pi$
$151$	−9.31757	−0.758253	−0.379127	+	0.925345i	$0.623776\pi$
$152$	−6.28726	−0.509964
$153$	0.0933212	0.00754457
$154$	11.6375	0.937778
$155$	0	0
$156$	0	0
$157$	14.7562	1.17768	0.588838	−	0.808251i	$-0.299586\pi$
$157$	14.7562	1.17768	0.588838	+	0.808251i	$0.299586\pi$
$158$	2.29455	0.182545
$159$	−1.51881	−0.120449
$160$	0	0
$161$	−12.8568	−1.01326
$162$	8.38058	0.658440
$163$	−13.5247	−1.05934	−0.529668	−	0.848205i	$-0.677683\pi$
$163$	−13.5247	−1.05934	−0.529668	+	0.848205i	$0.677683\pi$
$164$	−7.50659	−0.586166
$165$	0	0
$166$	−13.3380	−1.03523
$167$	23.4241	1.81261	0.906304	−	0.422625i	$-0.138891\pi$
$167$	23.4241	1.81261	0.906304	+	0.422625i	$0.138891\pi$
$168$	3.02539	0.233414
$169$	0	0
$170$	0	0
$171$	−1.21933	−0.0932444
$172$	2.00000	0.152499
$173$	4.62435	0.351582	0.175791	−	0.984427i	$-0.443752\pi$
$173$	4.62435	0.351582	0.175791	+	0.984427i	$0.443752\pi$
$174$	3.87399	0.293687
$175$	0	0
$176$	−6.44358	−0.485703
$177$	11.0132	0.827801
$178$	−1.15633	−0.0866702
$179$	−8.31265	−0.621317	−0.310658	−	0.950522i	$-0.600549\pi$
$179$	−8.31265	−0.621317	−0.310658	+	0.950522i	$0.600549\pi$
$180$	0	0
$181$	−1.02539	−0.0762168	−0.0381084	−	0.999274i	$-0.512133\pi$
$181$	−1.02539	−0.0762168	−0.0381084	+	0.999274i	$0.512133\pi$
$182$	0	0
$183$	18.3430	1.35595
$184$	7.11871	0.524799
$185$	0	0
$186$	−5.45580	−0.400039
$187$	3.10062	0.226739
$188$	2.19394	0.160009
$189$	9.66291	0.702873
$190$	0	0
$191$	0.355186	0.0257004	0.0128502	−	0.999917i	$-0.495910\pi$
$191$	0.355186	0.0257004	0.0128502	+	0.999917i	$0.495910\pi$
$192$	−1.67513	−0.120892
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−13.8315	−0.993041
$195$	0	0
$196$	−3.73813	−0.267010
$197$	−14.1065	−1.00505	−0.502523	−	0.864564i	$-0.667595\pi$
$197$	−14.1065	−1.00505	−0.502523	+	0.864564i	$0.667595\pi$
$198$	−1.24965	−0.0888085
$199$	−3.14903	−0.223229	−0.111614	−	0.993752i	$-0.535602\pi$
$199$	−3.14903	−0.223229	−0.111614	+	0.993752i	$0.535602\pi$
$200$	0	0
$201$	−1.08840	−0.0767696
$202$	9.59991	0.675447
$203$	4.17679	0.293153
$204$	0.806063	0.0564357
$205$	0	0
$206$	3.07522	0.214261
$207$	1.38058	0.0959569
$208$	0	0
$209$	−40.5125	−2.80231
$210$	0	0
$211$	3.09332	0.212953	0.106477	−	0.994315i	$-0.466043\pi$
$211$	3.09332	0.212953	0.106477	+	0.994315i	$0.466043\pi$
$212$	0.906679	0.0622710
$213$	6.13586	0.420422
$214$	−1.67513	−0.114510
$215$	0	0
$216$	−5.35026	−0.364039
$217$	−5.88224	−0.399313
$218$	10.8872	0.737372
$219$	4.36741	0.295122
$220$	0	0
$221$	0	0
$222$	5.13093	0.344366
$223$	22.1939	1.48622	0.743108	−	0.669172i	$-0.233351\pi$
$223$	22.1939	1.48622	0.743108	+	0.669172i	$0.233351\pi$
$224$	−1.80606	−0.120673
$225$	0	0
$226$	14.0000	0.931266
$227$	−13.3357	−0.885120	−0.442560	−	0.896739i	$-0.645930\pi$
$227$	−13.3357	−0.885120	−0.442560	+	0.896739i	$0.645930\pi$
$228$	−10.5320	−0.697497
$229$	−26.1744	−1.72965	−0.864827	−	0.502069i	$-0.832572\pi$
$229$	−26.1744	−1.72965	−0.864827	+	0.502069i	$0.832572\pi$
$230$	0	0
$231$	19.4944	1.28264
$232$	−2.31265	−0.151833
$233$	−20.8691	−1.36718	−0.683589	−	0.729867i	$-0.739582\pi$
$233$	−20.8691	−1.36718	−0.683589	+	0.729867i	$0.739582\pi$
$234$	0	0
$235$	0	0
$236$	−6.57452	−0.427965
$237$	3.84367	0.249674
$238$	0.869067	0.0563333
$239$	15.2931	0.989231	0.494615	−	0.869112i	$-0.335309\pi$
$239$	15.2931	0.989231	0.494615	+	0.869112i	$0.335309\pi$
$240$	0	0
$241$	12.7685	0.822488	0.411244	−	0.911525i	$-0.365094\pi$
$241$	12.7685	0.822488	0.411244	+	0.911525i	$0.365094\pi$
$242$	−30.5198	−1.96188
$243$	−2.01222	−0.129084
$244$	−10.9502	−0.701013
$245$	0	0
$246$	−12.5745	−0.801722
$247$	0	0
$248$	3.25694	0.206816
$249$	−22.3430	−1.41593
$250$	0	0
$251$	−4.21203	−0.265861	−0.132931	−	0.991125i	$-0.542439\pi$
$251$	−4.21203	−0.265861	−0.132931	+	0.991125i	$0.542439\pi$
$252$	−0.350262	−0.0220644
$253$	45.8700	2.88382
$254$	−5.18664	−0.325439
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.6253	−1.16181	−0.580907	−	0.813970i	$-0.697302\pi$
$257$	−18.6253	−1.16181	−0.580907	+	0.813970i	$0.697302\pi$
$258$	3.35026	0.208578
$259$	5.53198	0.343740
$260$	0	0
$261$	−0.448507	−0.0277619
$262$	10.8011	0.667297
$263$	23.0205	1.41950	0.709751	−	0.704452i	$-0.248807\pi$
$263$	23.0205	1.41950	0.709751	+	0.704452i	$0.248807\pi$
$264$	−10.7938	−0.664315
$265$	0	0
$266$	−11.3552	−0.696231
$267$	−1.93700	−0.118542
$268$	0.649738	0.0396891
$269$	−13.4739	−0.821518	−0.410759	−	0.911744i	$-0.634736\pi$
$269$	−13.4739	−0.821518	−0.410759	+	0.911744i	$0.634736\pi$
$270$	0	0
$271$	17.9003	1.08737	0.543684	−	0.839290i	$-0.317029\pi$
$271$	17.9003	1.08737	0.543684	+	0.839290i	$0.317029\pi$
$272$	−0.481194	−0.0291767
$273$	0	0
$274$	6.14411	0.371179
$275$	0	0
$276$	11.9248	0.717787
$277$	−8.48849	−0.510024	−0.255012	−	0.966938i	$-0.582079\pi$
$277$	−8.48849	−0.510024	−0.255012	+	0.966938i	$0.582079\pi$
$278$	−10.3380	−0.620035
$279$	0.631640	0.0378153
$280$	0	0
$281$	16.5296	0.986074	0.493037	−	0.870008i	$-0.335887\pi$
$281$	16.5296	0.986074	0.493037	+	0.870008i	$0.335887\pi$
$282$	3.67513	0.218851
$283$	−1.53690	−0.0913595	−0.0456797	−	0.998956i	$-0.514545\pi$
$283$	−1.53690	−0.0913595	−0.0456797	+	0.998956i	$0.514545\pi$
$284$	−3.66291	−0.217354
$285$	0	0
$286$	0	0
$287$	−13.5574	−0.800266
$288$	0.193937	0.0114278
$289$	−16.7685	−0.986380
$290$	0	0
$291$	−23.1695	−1.35822
$292$	−2.60720	−0.152575
$293$	5.92970	0.346417	0.173208	−	0.984885i	$-0.444587\pi$
$293$	5.92970	0.346417	0.173208	+	0.984885i	$0.444587\pi$
$294$	−6.26187	−0.365199
$295$	0	0
$296$	−3.06300	−0.178033
$297$	−34.4749	−2.00043
$298$	−16.0508	−0.929797
$299$	0	0
$300$	0	0
$301$	3.61213	0.208200
$302$	9.31757	0.536166
$303$	16.0811	0.923835
$304$	6.28726	0.360599
$305$	0	0
$306$	−0.0933212	−0.00533482
$307$	17.9756	1.02592	0.512960	−	0.858413i	$-0.328549\pi$
$307$	17.9756	1.02592	0.512960	+	0.858413i	$0.328549\pi$
$308$	−11.6375	−0.663109
$309$	5.15140	0.293053
$310$	0	0
$311$	15.9575	0.904865	0.452432	−	0.891799i	$-0.350556\pi$
$311$	15.9575	0.904865	0.452432	+	0.891799i	$0.350556\pi$
$312$	0	0
$313$	−23.4372	−1.32475	−0.662376	−	0.749172i	$-0.730452\pi$
$313$	−23.4372	−1.32475	−0.662376	+	0.749172i	$0.730452\pi$
$314$	−14.7562	−0.832742
$315$	0	0
$316$	−2.29455	−0.129079
$317$	20.6507	1.15986	0.579929	−	0.814667i	$-0.303080\pi$
$317$	20.6507	1.15986	0.579929	+	0.814667i	$0.303080\pi$
$318$	1.51881	0.0851704
$319$	−14.9018	−0.834338
$320$	0	0
$321$	−2.80606	−0.156619
$322$	12.8568	0.716484
$323$	−3.02539	−0.168337
$324$	−8.38058	−0.465588
$325$	0	0
$326$	13.5247	0.749063
$327$	18.2374	1.00853
$328$	7.50659	0.414482
$329$	3.96239	0.218454
$330$	0	0
$331$	26.6761	1.46625	0.733125	−	0.680094i	$-0.238061\pi$
$331$	26.6761	1.46625	0.733125	+	0.680094i	$0.238061\pi$
$332$	13.3380	0.732020
$333$	−0.594028	−0.0325526
$334$	−23.4241	−1.28171
$335$	0	0
$336$	−3.02539	−0.165049
$337$	−8.40597	−0.457902	−0.228951	−	0.973438i	$-0.573530\pi$
$337$	−8.40597	−0.457902	−0.228951	+	0.973438i	$0.573530\pi$
$338$	0	0
$339$	23.4518	1.27373
$340$	0	0
$341$	20.9864	1.13648
$342$	1.21933	0.0659338
$343$	−19.3938	−1.04716
$344$	−2.00000	−0.107833
$345$	0	0
$346$	−4.62435	−0.248606
$347$	−21.1514	−1.13547	−0.567733	−	0.823213i	$-0.692180\pi$
$347$	−21.1514	−1.13547	−0.567733	+	0.823213i	$0.692180\pi$
$348$	−3.87399	−0.207668
$349$	−5.47390	−0.293011	−0.146506	−	0.989210i	$-0.546803\pi$
$349$	−5.47390	−0.293011	−0.146506	+	0.989210i	$0.546803\pi$
$350$	0	0
$351$	0	0
$352$	6.44358	0.343444
$353$	30.1441	1.60441	0.802204	−	0.597049i	$-0.203660\pi$
$353$	30.1441	1.60441	0.802204	+	0.597049i	$0.203660\pi$
$354$	−11.0132	−0.585344
$355$	0	0
$356$	1.15633	0.0612851
$357$	1.45580	0.0770492
$358$	8.31265	0.439337
$359$	8.38787	0.442695	0.221348	−	0.975195i	$-0.428954\pi$
$359$	8.38787	0.442695	0.221348	+	0.975195i	$0.428954\pi$
$360$	0	0
$361$	20.5296	1.08051
$362$	1.02539	0.0538934
$363$	−51.1246	−2.68335
$364$	0	0
$365$	0	0
$366$	−18.3430	−0.958802
$367$	−19.5125	−1.01854	−0.509271	−	0.860606i	$-0.670085\pi$
$367$	−19.5125	−1.01854	−0.509271	+	0.860606i	$0.670085\pi$
$368$	−7.11871	−0.371089
$369$	1.45580	0.0757860
$370$	0	0
$371$	1.63752	0.0850158
$372$	5.45580	0.282870
$373$	−8.51388	−0.440832	−0.220416	−	0.975406i	$-0.570741\pi$
$373$	−8.51388	−0.440832	−0.220416	+	0.975406i	$0.570741\pi$
$374$	−3.10062	−0.160329
$375$	0	0
$376$	−2.19394	−0.113144
$377$	0	0
$378$	−9.66291	−0.497007
$379$	19.7186	1.01288	0.506439	−	0.862276i	$-0.330962\pi$
$379$	19.7186	1.01288	0.506439	+	0.862276i	$0.330962\pi$
$380$	0	0
$381$	−8.68830	−0.445115
$382$	−0.355186	−0.0181729
$383$	−27.7196	−1.41640	−0.708202	−	0.706010i	$-0.750493\pi$
$383$	−27.7196	−1.41640	−0.708202	+	0.706010i	$0.750493\pi$
$384$	1.67513	0.0854837
$385$	0	0
$386$	−14.0000	−0.712581
$387$	−0.387873	−0.0197167
$388$	13.8315	0.702186
$389$	9.15140	0.463994	0.231997	−	0.972716i	$-0.425474\pi$
$389$	9.15140	0.463994	0.231997	+	0.972716i	$0.425474\pi$
$390$	0	0
$391$	3.42548	0.173234
$392$	3.73813	0.188804
$393$	18.0933	0.912687
$394$	14.1065	0.710675
$395$	0	0
$396$	1.24965	0.0627971
$397$	−1.43041	−0.0717902	−0.0358951	−	0.999356i	$-0.511428\pi$
$397$	−1.43041	−0.0717902	−0.0358951	+	0.999356i	$0.511428\pi$
$398$	3.14903	0.157847
$399$	−19.0214	−0.952262
$400$	0	0
$401$	−21.6702	−1.08216	−0.541079	−	0.840972i	$-0.681984\pi$
$401$	−21.6702	−1.08216	−0.541079	+	0.840972i	$0.681984\pi$
$402$	1.08840	0.0542843
$403$	0	0
$404$	−9.59991	−0.477613
$405$	0	0
$406$	−4.17679	−0.207291
$407$	−19.7367	−0.978313
$408$	−0.806063	−0.0399061
$409$	−9.08110	−0.449032	−0.224516	−	0.974470i	$-0.572080\pi$
$409$	−9.08110	−0.449032	−0.224516	+	0.974470i	$0.572080\pi$
$410$	0	0
$411$	10.2922	0.507676
$412$	−3.07522	−0.151505
$413$	−11.8740	−0.584281
$414$	−1.38058	−0.0678518
$415$	0	0
$416$	0	0
$417$	−17.3176	−0.848045
$418$	40.5125	1.98153
$419$	−15.5428	−0.759315	−0.379657	−	0.925127i	$-0.623958\pi$
$419$	−15.5428	−0.759315	−0.379657	+	0.925127i	$0.623958\pi$
$420$	0	0
$421$	4.96476	0.241968	0.120984	−	0.992654i	$-0.461395\pi$
$421$	4.96476	0.241968	0.120984	+	0.992654i	$0.461395\pi$
$422$	−3.09332	−0.150581
$423$	−0.425485	−0.0206878
$424$	−0.906679	−0.0440322
$425$	0	0
$426$	−6.13586	−0.297283
$427$	−19.7767	−0.957062
$428$	1.67513	0.0809705
$429$	0	0
$430$	0	0
$431$	32.9706	1.58814	0.794070	−	0.607826i	$-0.207958\pi$
$431$	32.9706	1.58814	0.794070	+	0.607826i	$0.207958\pi$
$432$	5.35026	0.257415
$433$	−16.1114	−0.774265	−0.387133	−	0.922024i	$-0.626534\pi$
$433$	−16.1114	−0.774265	−0.387133	+	0.922024i	$0.626534\pi$
$434$	5.88224	0.282357
$435$	0	0
$436$	−10.8872	−0.521401
$437$	−44.7572	−2.14103
$438$	−4.36741	−0.208683
$439$	−0.0834721	−0.00398390	−0.00199195	−	0.999998i	$-0.500634\pi$
$439$	−0.0834721	−0.00398390	−0.00199195	+	0.999998i	$0.500634\pi$
$440$	0	0
$441$	0.724961	0.0345220
$442$	0	0
$443$	40.9135	1.94386	0.971930	−	0.235271i	$-0.0755977\pi$
$443$	40.9135	1.94386	0.971930	+	0.235271i	$0.0755977\pi$
$444$	−5.13093	−0.243503
$445$	0	0
$446$	−22.1939	−1.05091
$447$	−26.8872	−1.27172
$448$	1.80606	0.0853285
$449$	29.1319	1.37482	0.687409	−	0.726270i	$-0.258748\pi$
$449$	29.1319	1.37482	0.687409	+	0.726270i	$0.258748\pi$
$450$	0	0
$451$	48.3693	2.27762
$452$	−14.0000	−0.658505
$453$	15.6082	0.733335
$454$	13.3357	0.625874
$455$	0	0
$456$	10.5320	0.493205
$457$	32.6678	1.52814	0.764068	−	0.645135i	$-0.223199\pi$
$457$	32.6678	1.52814	0.764068	+	0.645135i	$0.223199\pi$
$458$	26.1744	1.22305
$459$	−2.57452	−0.120168
$460$	0	0
$461$	19.1006	0.889604	0.444802	−	0.895629i	$-0.353274\pi$
$461$	19.1006	0.889604	0.444802	+	0.895629i	$0.353274\pi$
$462$	−19.4944	−0.906960
$463$	−8.29218	−0.385370	−0.192685	−	0.981261i	$-0.561720\pi$
$463$	−8.29218	−0.385370	−0.192685	+	0.981261i	$0.561720\pi$
$464$	2.31265	0.107362
$465$	0	0
$466$	20.8691	0.966741
$467$	−23.5369	−1.08916	−0.544579	−	0.838710i	$-0.683311\pi$
$467$	−23.5369	−1.08916	−0.544579	+	0.838710i	$0.683311\pi$
$468$	0	0
$469$	1.17347	0.0541857
$470$	0	0
$471$	−24.7186	−1.13897
$472$	6.57452	0.302617
$473$	−12.8872	−0.592553
$474$	−3.84367	−0.176546
$475$	0	0
$476$	−0.869067	−0.0398336
$477$	−0.175838	−0.00805108
$478$	−15.2931	−0.699492
$479$	−6.55642	−0.299570	−0.149785	−	0.988719i	$-0.547858\pi$
$479$	−6.55642	−0.299570	−0.149785	+	0.988719i	$0.547858\pi$
$480$	0	0
$481$	0	0
$482$	−12.7685	−0.581587
$483$	21.5369	0.979963
$484$	30.5198	1.38726
$485$	0	0
$486$	2.01222	0.0912761
$487$	13.5599	0.614459	0.307229	−	0.951635i	$-0.400598\pi$
$487$	13.5599	0.614459	0.307229	+	0.951635i	$0.400598\pi$
$488$	10.9502	0.495691
$489$	22.6556	1.02452
$490$	0	0
$491$	4.95746	0.223727	0.111864	−	0.993724i	$-0.464318\pi$
$491$	4.95746	0.223727	0.111864	+	0.993724i	$0.464318\pi$
$492$	12.5745	0.566903
$493$	−1.11283	−0.0501195
$494$	0	0
$495$	0	0
$496$	−3.25694	−0.146241
$497$	−6.61545	−0.296744
$498$	22.3430	1.00121
$499$	13.8700	0.620907	0.310454	−	0.950588i	$-0.399519\pi$
$499$	13.8700	0.620907	0.310454	+	0.950588i	$0.399519\pi$
$500$	0	0
$501$	−39.2384	−1.75304
$502$	4.21203	0.187992
$503$	−3.44851	−0.153761	−0.0768807	−	0.997040i	$-0.524496\pi$
$503$	−3.44851	−0.153761	−0.0768807	+	0.997040i	$0.524496\pi$
$504$	0.350262	0.0156019
$505$	0	0
$506$	−45.8700	−2.03917
$507$	0	0
$508$	5.18664	0.230120
$509$	30.9624	1.37238	0.686192	−	0.727421i	$-0.259281\pi$
$509$	30.9624	1.37238	0.686192	+	0.727421i	$0.259281\pi$
$510$	0	0
$511$	−4.70877	−0.208304
$512$	−1.00000	−0.0441942
$513$	33.6385	1.48517
$514$	18.6253	0.821527
$515$	0	0
$516$	−3.35026	−0.147487
$517$	−14.1368	−0.621736
$518$	−5.53198	−0.243061
$519$	−7.74638	−0.340029
$520$	0	0
$521$	14.2506	0.624330	0.312165	−	0.950028i	$-0.398946\pi$
$521$	14.2506	0.624330	0.312165	+	0.950028i	$0.398946\pi$
$522$	0.448507	0.0196306
$523$	10.5139	0.459740	0.229870	−	0.973221i	$-0.426170\pi$
$523$	10.5139	0.459740	0.229870	+	0.973221i	$0.426170\pi$
$524$	−10.8011	−0.471850
$525$	0	0
$526$	−23.0205	−1.00374
$527$	1.56722	0.0682692
$528$	10.7938	0.469742
$529$	27.6761	1.20331
$530$	0	0
$531$	1.27504	0.0553320
$532$	11.3552	0.492310
$533$	0	0
$534$	1.93700	0.0838220
$535$	0	0
$536$	−0.649738	−0.0280644
$537$	13.9248	0.600898
$538$	13.4739	0.580901
$539$	24.0870	1.03750
$540$	0	0
$541$	−15.5345	−0.667882	−0.333941	−	0.942594i	$-0.608379\pi$
$541$	−15.5345	−0.667882	−0.333941	+	0.942594i	$0.608379\pi$
$542$	−17.9003	−0.768885
$543$	1.71767	0.0737121
$544$	0.481194	0.0206310
$545$	0	0
$546$	0	0
$547$	23.5515	1.00699	0.503495	−	0.863998i	$-0.332047\pi$
$547$	23.5515	1.00699	0.503495	+	0.863998i	$0.332047\pi$
$548$	−6.14411	−0.262463
$549$	2.12364	0.0906347
$550$	0	0
$551$	14.5402	0.619435
$552$	−11.9248	−0.507552
$553$	−4.14411	−0.176225
$554$	8.48849	0.360641
$555$	0	0
$556$	10.3380	0.438431
$557$	20.0459	0.849370	0.424685	−	0.905341i	$-0.360385\pi$
$557$	20.0459	0.849370	0.424685	+	0.905341i	$0.360385\pi$
$558$	−0.631640	−0.0267394
$559$	0	0
$560$	0	0
$561$	−5.19394	−0.219288
$562$	−16.5296	−0.697260
$563$	12.5745	0.529953	0.264976	−	0.964255i	$-0.414636\pi$
$563$	12.5745	0.529953	0.264976	+	0.964255i	$0.414636\pi$
$564$	−3.67513	−0.154751
$565$	0	0
$566$	1.53690	0.0646009
$567$	−15.1359	−0.635646
$568$	3.66291	0.153692
$569$	4.28963	0.179831	0.0899153	−	0.995949i	$-0.471340\pi$
$569$	4.28963	0.179831	0.0899153	+	0.995949i	$0.471340\pi$
$570$	0	0
$571$	6.39280	0.267530	0.133765	−	0.991013i	$-0.457293\pi$
$571$	6.39280	0.267530	0.133765	+	0.991013i	$0.457293\pi$
$572$	0	0
$573$	−0.594984	−0.0248558
$574$	13.5574	0.565874
$575$	0	0
$576$	−0.193937	−0.00808069
$577$	37.8169	1.57434	0.787168	−	0.616738i	$-0.211546\pi$
$577$	37.8169	1.57434	0.787168	+	0.616738i	$0.211546\pi$
$578$	16.7685	0.697476
$579$	−23.4518	−0.974625
$580$	0	0
$581$	24.0894	0.999395
$582$	23.1695	0.960407
$583$	−5.84226	−0.241962
$584$	2.60720	0.107887
$585$	0	0
$586$	−5.92970	−0.244954
$587$	−22.5501	−0.930741	−0.465371	−	0.885116i	$-0.654079\pi$
$587$	−22.5501	−0.930741	−0.465371	+	0.885116i	$0.654079\pi$
$588$	6.26187	0.258235
$589$	−20.4772	−0.843749
$590$	0	0
$591$	23.6302	0.972018
$592$	3.06300	0.125889
$593$	−8.38787	−0.344449	−0.172224	−	0.985058i	$-0.555095\pi$
$593$	−8.38787	−0.344449	−0.172224	+	0.985058i	$0.555095\pi$
$594$	34.4749	1.41452
$595$	0	0
$596$	16.0508	0.657466
$597$	5.27504	0.215893
$598$	0	0
$599$	29.0884	1.18852	0.594260	−	0.804273i	$-0.297445\pi$
$599$	29.0884	1.18852	0.594260	+	0.804273i	$0.297445\pi$
$600$	0	0
$601$	−43.0118	−1.75449	−0.877243	−	0.480046i	$-0.840620\pi$
$601$	−43.0118	−1.75449	−0.877243	+	0.480046i	$0.840620\pi$
$602$	−3.61213	−0.147219
$603$	−0.126008	−0.00513144
$604$	−9.31757	−0.379127
$605$	0	0
$606$	−16.0811	−0.653250
$607$	21.7513	0.882858	0.441429	−	0.897296i	$-0.354472\pi$
$607$	21.7513	0.882858	0.441429	+	0.897296i	$0.354472\pi$
$608$	−6.28726	−0.254982
$609$	−6.99668	−0.283520
$610$	0	0
$611$	0	0
$612$	0.0933212	0.00377228
$613$	−30.8129	−1.24452	−0.622261	−	0.782810i	$-0.713786\pi$
$613$	−30.8129	−1.24452	−0.622261	+	0.782810i	$0.713786\pi$
$614$	−17.9756	−0.725435
$615$	0	0
$616$	11.6375	0.468889
$617$	46.0870	1.85539	0.927696	−	0.373336i	$-0.121786\pi$
$617$	46.0870	1.85539	0.927696	+	0.373336i	$0.121786\pi$
$618$	−5.15140	−0.207220
$619$	13.5564	0.544878	0.272439	−	0.962173i	$-0.412170\pi$
$619$	13.5564	0.544878	0.272439	+	0.962173i	$0.412170\pi$
$620$	0	0
$621$	−38.0870	−1.52838
$622$	−15.9575	−0.639836
$623$	2.08840	0.0836698
$624$	0	0
$625$	0	0
$626$	23.4372	0.936741
$627$	67.8637	2.71021
$628$	14.7562	0.588838
$629$	−1.47390	−0.0587682
$630$	0	0
$631$	5.35026	0.212991	0.106495	−	0.994313i	$-0.466037\pi$
$631$	5.35026	0.212991	0.106495	+	0.994313i	$0.466037\pi$
$632$	2.29455	0.0912724
$633$	−5.18172	−0.205955
$634$	−20.6507	−0.820144
$635$	0	0
$636$	−1.51881	−0.0602246
$637$	0	0
$638$	14.9018	0.589966
$639$	0.710373	0.0281019
$640$	0	0
$641$	12.3806	0.489003	0.244502	−	0.969649i	$-0.421376\pi$
$641$	12.3806	0.489003	0.244502	+	0.969649i	$0.421376\pi$
$642$	2.80606	0.110746
$643$	−11.5247	−0.454489	−0.227245	−	0.973838i	$-0.572972\pi$
$643$	−11.5247	−0.454489	−0.227245	+	0.973838i	$0.572972\pi$
$644$	−12.8568	−0.506631
$645$	0	0
$646$	3.02539	0.119032
$647$	−3.67021	−0.144291	−0.0721453	−	0.997394i	$-0.522985\pi$
$647$	−3.67021	−0.144291	−0.0721453	+	0.997394i	$0.522985\pi$
$648$	8.38058	0.329220
$649$	42.3634	1.66291
$650$	0	0
$651$	9.85352	0.386190
$652$	−13.5247	−0.529668
$653$	−8.10650	−0.317232	−0.158616	−	0.987340i	$-0.550703\pi$
$653$	−8.10650	−0.317232	−0.158616	+	0.987340i	$0.550703\pi$
$654$	−18.2374	−0.713140
$655$	0	0
$656$	−7.50659	−0.293083
$657$	0.505632	0.0197266
$658$	−3.96239	−0.154470
$659$	18.5442	0.722379	0.361190	−	0.932492i	$-0.382371\pi$
$659$	18.5442	0.722379	0.361190	+	0.932492i	$0.382371\pi$
$660$	0	0
$661$	−46.4119	−1.80521	−0.902606	−	0.430468i	$-0.858349\pi$
$661$	−46.4119	−1.80521	−0.902606	+	0.430468i	$0.858349\pi$
$662$	−26.6761	−1.03680
$663$	0	0
$664$	−13.3380	−0.517616
$665$	0	0
$666$	0.594028	0.0230181
$667$	−16.4631	−0.637454
$668$	23.4241	0.906304
$669$	−37.1777	−1.43737
$670$	0	0
$671$	70.5583	2.72387
$672$	3.02539	0.116707
$673$	40.4095	1.55767	0.778836	−	0.627228i	$-0.215811\pi$
$673$	40.4095	1.55767	0.778836	+	0.627228i	$0.215811\pi$
$674$	8.40597	0.323786
$675$	0	0
$676$	0	0
$677$	14.2473	0.547567	0.273784	−	0.961791i	$-0.411725\pi$
$677$	14.2473	0.547567	0.273784	+	0.961791i	$0.411725\pi$
$678$	−23.4518	−0.900662
$679$	24.9805	0.958663
$680$	0	0
$681$	22.3390	0.856032
$682$	−20.9864	−0.803610
$683$	5.80351	0.222065	0.111033	−	0.993817i	$-0.464584\pi$
$683$	5.80351	0.222065	0.111033	+	0.993817i	$0.464584\pi$
$684$	−1.21933	−0.0466222
$685$	0	0
$686$	19.3938	0.740457
$687$	43.8456	1.67281
$688$	2.00000	0.0762493
$689$	0	0
$690$	0	0
$691$	19.2398	0.731916	0.365958	−	0.930631i	$-0.380741\pi$
$691$	19.2398	0.731916	0.365958	+	0.930631i	$0.380741\pi$
$692$	4.62435	0.175791
$693$	2.25694	0.0857341
$694$	21.1514	0.802896
$695$	0	0
$696$	3.87399	0.146843
$697$	3.61213	0.136819
$698$	5.47390	0.207190
$699$	34.9584	1.32225
$700$	0	0
$701$	45.3742	1.71376	0.856881	−	0.515515i	$-0.172399\pi$
$701$	45.3742	1.71376	0.856881	+	0.515515i	$0.172399\pi$
$702$	0	0
$703$	19.2579	0.726325
$704$	−6.44358	−0.242852
$705$	0	0
$706$	−30.1441	−1.13449
$707$	−17.3380	−0.652064
$708$	11.0132	0.413900
$709$	−3.97319	−0.149216	−0.0746082	−	0.997213i	$-0.523771\pi$
$709$	−3.97319	−0.149216	−0.0746082	+	0.997213i	$0.523771\pi$
$710$	0	0
$711$	0.444998	0.0166887
$712$	−1.15633	−0.0433351
$713$	23.1852	0.868294
$714$	−1.45580	−0.0544820
$715$	0	0
$716$	−8.31265	−0.310658
$717$	−25.6180	−0.956722
$718$	−8.38787	−0.313033
$719$	45.6991	1.70429	0.852145	−	0.523306i	$-0.175302\pi$
$719$	45.6991	1.70429	0.852145	+	0.523306i	$0.175302\pi$
$720$	0	0
$721$	−5.55405	−0.206844
$722$	−20.5296	−0.764033
$723$	−21.3888	−0.795459
$724$	−1.02539	−0.0381084
$725$	0	0
$726$	51.1246	1.89741
$727$	24.7948	0.919588	0.459794	−	0.888026i	$-0.347923\pi$
$727$	24.7948	0.919588	0.459794	+	0.888026i	$0.347923\pi$
$728$	0	0
$729$	28.5125	1.05602
$730$	0	0
$731$	−0.962389	−0.0355952
$732$	18.3430	0.677976
$733$	45.8651	1.69407	0.847033	−	0.531540i	$-0.178387\pi$
$733$	45.8651	1.69407	0.847033	+	0.531540i	$0.178387\pi$
$734$	19.5125	0.720218
$735$	0	0
$736$	7.11871	0.262399
$737$	−4.18664	−0.154217
$738$	−1.45580	−0.0535888
$739$	−34.9633	−1.28615	−0.643074	−	0.765804i	$-0.722341\pi$
$739$	−34.9633	−1.28615	−0.643074	+	0.765804i	$0.722341\pi$
$740$	0	0
$741$	0	0
$742$	−1.63752	−0.0601152
$743$	−6.86670	−0.251915	−0.125957	−	0.992036i	$-0.540200\pi$
$743$	−6.86670	−0.251915	−0.125957	+	0.992036i	$0.540200\pi$
$744$	−5.45580	−0.200019
$745$	0	0
$746$	8.51388	0.311715
$747$	−2.58673	−0.0946437
$748$	3.10062	0.113370
$749$	3.02539	0.110545
$750$	0	0
$751$	4.80018	0.175161	0.0875806	−	0.996157i	$-0.472086\pi$
$751$	4.80018	0.175161	0.0875806	+	0.996157i	$0.472086\pi$
$752$	2.19394	0.0800046
$753$	7.05571	0.257124
$754$	0	0
$755$	0	0
$756$	9.66291	0.351437
$757$	27.7753	1.00951	0.504755	−	0.863263i	$-0.331583\pi$
$757$	27.7753	1.00951	0.504755	+	0.863263i	$0.331583\pi$
$758$	−19.7186	−0.716213
$759$	−76.8383	−2.78905
$760$	0	0
$761$	3.16220	0.114630	0.0573149	−	0.998356i	$-0.481746\pi$
$761$	3.16220	0.114630	0.0573149	+	0.998356i	$0.481746\pi$
$762$	8.68830	0.314744
$763$	−19.6629	−0.711845
$764$	0.355186	0.0128502
$765$	0	0
$766$	27.7196	1.00155
$767$	0	0
$768$	−1.67513	−0.0604461
$769$	−8.15633	−0.294125	−0.147062	−	0.989127i	$-0.546982\pi$
$769$	−8.15633	−0.294125	−0.147062	+	0.989127i	$0.546982\pi$
$770$	0	0
$771$	31.1998	1.12363
$772$	14.0000	0.503871
$773$	5.87892	0.211450	0.105725	−	0.994395i	$-0.466284\pi$
$773$	5.87892	0.211450	0.105725	+	0.994395i	$0.466284\pi$
$774$	0.387873	0.0139418
$775$	0	0
$776$	−13.8315	−0.496520
$777$	−9.26679	−0.332444
$778$	−9.15140	−0.328094
$779$	−47.1958	−1.69097
$780$	0	0
$781$	23.6023	0.844556
$782$	−3.42548	−0.122495
$783$	12.3733	0.442185
$784$	−3.73813	−0.133505
$785$	0	0
$786$	−18.0933	−0.645367
$787$	23.7015	0.844866	0.422433	−	0.906394i	$-0.361176\pi$
$787$	23.7015	0.844866	0.422433	+	0.906394i	$0.361176\pi$
$788$	−14.1065	−0.502523
$789$	−38.5623	−1.37285
$790$	0	0
$791$	−25.2849	−0.899027
$792$	−1.24965	−0.0444042
$793$	0	0
$794$	1.43041	0.0507633
$795$	0	0
$796$	−3.14903	−0.111614
$797$	48.5198	1.71866	0.859329	−	0.511423i	$-0.170881\pi$
$797$	48.5198	1.71866	0.859329	+	0.511423i	$0.170881\pi$
$798$	19.0214	0.673351
$799$	−1.05571	−0.0373483
$800$	0	0
$801$	−0.224254	−0.00792362
$802$	21.6702	0.765202
$803$	16.7997	0.592849
$804$	−1.08840	−0.0383848
$805$	0	0
$806$	0	0
$807$	22.5705	0.794521
$808$	9.59991	0.337724
$809$	−17.1187	−0.601862	−0.300931	−	0.953646i	$-0.597297\pi$
$809$	−17.1187	−0.601862	−0.300931	+	0.953646i	$0.597297\pi$
$810$	0	0
$811$	7.67372	0.269461	0.134730	−	0.990882i	$-0.456983\pi$
$811$	7.67372	0.269461	0.134730	+	0.990882i	$0.456983\pi$
$812$	4.17679	0.146577
$813$	−29.9854	−1.05163
$814$	19.7367	0.691772
$815$	0	0
$816$	0.806063	0.0282179
$817$	12.5745	0.439927
$818$	9.08110	0.317513
$819$	0	0
$820$	0	0
$821$	53.7866	1.87716	0.938582	−	0.345057i	$-0.112140\pi$
$821$	53.7866	1.87716	0.938582	+	0.345057i	$0.112140\pi$
$822$	−10.2922	−0.358981
$823$	−9.77575	−0.340761	−0.170381	−	0.985378i	$-0.554500\pi$
$823$	−9.77575	−0.340761	−0.170381	+	0.985378i	$0.554500\pi$
$824$	3.07522	0.107130
$825$	0	0
$826$	11.8740	0.413149
$827$	28.1598	0.979213	0.489607	−	0.871943i	$-0.337140\pi$
$827$	28.1598	0.979213	0.489607	+	0.871943i	$0.337140\pi$
$828$	1.38058	0.0479784
$829$	20.2130	0.702026	0.351013	−	0.936371i	$-0.385837\pi$
$829$	20.2130	0.702026	0.351013	+	0.936371i	$0.385837\pi$
$830$	0	0
$831$	14.2193	0.493263
$832$	0	0
$833$	1.79877	0.0623237
$834$	17.3176	0.599659
$835$	0	0
$836$	−40.5125	−1.40115
$837$	−17.4255	−0.602313
$838$	15.5428	0.536917
$839$	−12.5926	−0.434745	−0.217373	−	0.976089i	$-0.569749\pi$
$839$	−12.5926	−0.434745	−0.217373	+	0.976089i	$0.569749\pi$
$840$	0	0
$841$	−23.6516	−0.815574
$842$	−4.96476	−0.171097
$843$	−27.6893	−0.953669
$844$	3.09332	0.106477
$845$	0	0
$846$	0.425485	0.0146285
$847$	55.1206	1.89397
$848$	0.906679	0.0311355
$849$	2.57452	0.0883571
$850$	0	0
$851$	−21.8046	−0.747454
$852$	6.13586	0.210211
$853$	−45.7704	−1.56715	−0.783574	−	0.621299i	$-0.786605\pi$
$853$	−45.7704	−1.56715	−0.783574	+	0.621299i	$0.786605\pi$
$854$	19.7767	0.676745
$855$	0	0
$856$	−1.67513	−0.0572548
$857$	27.8169	0.950206	0.475103	−	0.879930i	$-0.342411\pi$
$857$	27.8169	0.950206	0.475103	+	0.879930i	$0.342411\pi$
$858$	0	0
$859$	25.9706	0.886107	0.443053	−	0.896495i	$-0.353895\pi$
$859$	25.9706	0.886107	0.443053	+	0.896495i	$0.353895\pi$
$860$	0	0
$861$	22.7104	0.773967
$862$	−32.9706	−1.12298
$863$	18.7210	0.637270	0.318635	−	0.947877i	$-0.396776\pi$
$863$	18.7210	0.637270	0.318635	+	0.947877i	$0.396776\pi$
$864$	−5.35026	−0.182020
$865$	0	0
$866$	16.1114	0.547488
$867$	28.0894	0.953964
$868$	−5.88224	−0.199656
$869$	14.7851	0.501551
$870$	0	0
$871$	0	0
$872$	10.8872	0.368686
$873$	−2.68243	−0.0907863
$874$	44.7572	1.51393
$875$	0	0
$876$	4.36741	0.147561
$877$	−22.6859	−0.766050	−0.383025	−	0.923738i	$-0.625118\pi$
$877$	−22.6859	−0.766050	−0.383025	+	0.923738i	$0.625118\pi$
$878$	0.0834721	0.00281705
$879$	−9.93303	−0.335033
$880$	0	0
$881$	−2.47627	−0.0834276	−0.0417138	−	0.999130i	$-0.513282\pi$
$881$	−2.47627	−0.0834276	−0.0417138	+	0.999130i	$0.513282\pi$
$882$	−0.724961	−0.0244107
$883$	31.4641	1.05885	0.529425	−	0.848357i	$-0.322408\pi$
$883$	31.4641	1.05885	0.529425	+	0.848357i	$0.322408\pi$
$884$	0	0
$885$	0	0
$886$	−40.9135	−1.37452
$887$	−39.7163	−1.33354	−0.666771	−	0.745263i	$-0.732324\pi$
$887$	−39.7163	−1.33354	−0.666771	+	0.745263i	$0.732324\pi$
$888$	5.13093	0.172183
$889$	9.36741	0.314173
$890$	0	0
$891$	54.0010	1.80910
$892$	22.1939	0.743108
$893$	13.7938	0.461593
$894$	26.8872	0.899241
$895$	0	0
$896$	−1.80606	−0.0603363
$897$	0	0
$898$	−29.1319	−0.972144
$899$	−7.53216	−0.251212
$900$	0	0
$901$	−0.436289	−0.0145349
$902$	−48.3693	−1.61052
$903$	−6.05079	−0.201358
$904$	14.0000	0.465633
$905$	0	0
$906$	−15.6082	−0.518546
$907$	53.5755	1.77894	0.889472	−	0.456989i	$-0.151072\pi$
$907$	53.5755	1.77894	0.889472	+	0.456989i	$0.151072\pi$
$908$	−13.3357	−0.442560
$909$	1.86177	0.0617511
$910$	0	0
$911$	14.6253	0.484558	0.242279	−	0.970207i	$-0.422105\pi$
$911$	14.6253	0.484558	0.242279	+	0.970207i	$0.422105\pi$
$912$	−10.5320	−0.348749
$913$	−85.9448	−2.84436
$914$	−32.6678	−1.08056
$915$	0	0
$916$	−26.1744	−0.864827
$917$	−19.5075	−0.644196
$918$	2.57452	0.0849717
$919$	53.0494	1.74994	0.874969	−	0.484180i	$-0.160882\pi$
$919$	53.0494	1.74994	0.874969	+	0.484180i	$0.160882\pi$
$920$	0	0
$921$	−30.1114	−0.992205
$922$	−19.1006	−0.629045
$923$	0	0
$924$	19.4944	0.641318
$925$	0	0
$926$	8.29218	0.272498
$927$	0.596398	0.0195883
$928$	−2.31265	−0.0759165
$929$	10.4504	0.342867	0.171434	−	0.985196i	$-0.445160\pi$
$929$	10.4504	0.342867	0.171434	+	0.985196i	$0.445160\pi$
$930$	0	0
$931$	−23.5026	−0.770267
$932$	−20.8691	−0.683589
$933$	−26.7308	−0.875128
$934$	23.5369	0.770151
$935$	0	0
$936$	0	0
$937$	−10.5745	−0.345454	−0.172727	−	0.984970i	$-0.555258\pi$
$937$	−10.5745	−0.345454	−0.172727	+	0.984970i	$0.555258\pi$
$938$	−1.17347	−0.0383151
$939$	39.2605	1.28122
$940$	0	0
$941$	16.6107	0.541494	0.270747	−	0.962651i	$-0.412729\pi$
$941$	16.6107	0.541494	0.270747	+	0.962651i	$0.412729\pi$
$942$	24.7186	0.805376
$943$	53.4372	1.74016
$944$	−6.57452	−0.213982
$945$	0	0
$946$	12.8872	0.418998
$947$	−42.4871	−1.38064	−0.690322	−	0.723502i	$-0.742531\pi$
$947$	−42.4871	−1.38064	−0.690322	+	0.723502i	$0.742531\pi$
$948$	3.84367	0.124837
$949$	0	0
$950$	0	0
$951$	−34.5926	−1.12174
$952$	0.869067	0.0281666
$953$	45.0214	1.45839	0.729193	−	0.684308i	$-0.239895\pi$
$953$	45.0214	1.45839	0.729193	+	0.684308i	$0.239895\pi$
$954$	0.175838	0.00569297
$955$	0	0
$956$	15.2931	0.494615
$957$	24.9624	0.806919
$958$	6.55642	0.211828
$959$	−11.0966	−0.358329
$960$	0	0
$961$	−20.3923	−0.657817
$962$	0	0
$963$	−0.324869	−0.0104688
$964$	12.7685	0.411244
$965$	0	0
$966$	−21.5369	−0.692939
$967$	24.4763	0.787104	0.393552	−	0.919302i	$-0.371246\pi$
$967$	24.4763	0.787104	0.393552	+	0.919302i	$0.371246\pi$
$968$	−30.5198	−0.980942
$969$	5.06793	0.162805
$970$	0	0
$971$	−56.4046	−1.81011	−0.905054	−	0.425296i	$-0.860170\pi$
$971$	−56.4046	−1.81011	−0.905054	+	0.425296i	$0.860170\pi$
$972$	−2.01222	−0.0645419
$973$	18.6712	0.598570
$974$	−13.5599	−0.434488
$975$	0	0
$976$	−10.9502	−0.350506
$977$	13.5125	0.432302	0.216151	−	0.976360i	$-0.430650\pi$
$977$	13.5125	0.432302	0.216151	+	0.976360i	$0.430650\pi$
$978$	−22.6556	−0.724447
$979$	−7.45088	−0.238131
$980$	0	0
$981$	2.11142	0.0674124
$982$	−4.95746	−0.158199
$983$	30.1187	0.960638	0.480319	−	0.877094i	$-0.340521\pi$
$983$	30.1187	0.960638	0.480319	+	0.877094i	$0.340521\pi$
$984$	−12.5745	−0.400861
$985$	0	0
$986$	1.11283	0.0354399
$987$	−6.63752	−0.211275
$988$	0	0
$989$	−14.2374	−0.452724
$990$	0	0
$991$	35.3258	1.12216	0.561081	−	0.827761i	$-0.310386\pi$
$991$	35.3258	1.12216	0.561081	+	0.827761i	$0.310386\pi$
$992$	3.25694	0.103408
$993$	−44.6859	−1.41807
$994$	6.61545	0.209829
$995$	0	0
$996$	−22.3430	−0.707964
$997$	−16.8169	−0.532596	−0.266298	−	0.963891i	$-0.585800\pi$
$997$	−16.8169	−0.532596	−0.266298	+	0.963891i	$0.585800\pi$
$998$	−13.8700	−0.439048
$999$	16.3879	0.518489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8450.2.a.bt.1.1		3
5.2	odd	4		1690.2.b.b.339.3		6
5.3	odd	4		1690.2.b.b.339.4		6
5.4	even	2		8450.2.a.ca.1.3		3
13.4	even	6		650.2.e.j.601.3		6
13.10	even	6		650.2.e.j.451.3		6
13.12	even	2		8450.2.a.cb.1.1		3
65.4	even	6		650.2.e.k.601.1		6
65.8	even	4		1690.2.c.b.1689.2		6
65.12	odd	4		1690.2.b.c.339.6		6
65.17	odd	12		130.2.n.a.29.6	yes	12
65.18	even	4		1690.2.c.c.1689.2		6
65.23	odd	12		130.2.n.a.9.6	yes	12
65.38	odd	4		1690.2.b.c.339.1		6
65.43	odd	12		130.2.n.a.29.1	yes	12
65.47	even	4		1690.2.c.c.1689.5		6
65.49	even	6		650.2.e.k.451.1		6
65.57	even	4		1690.2.c.b.1689.5		6
65.62	odd	12		130.2.n.a.9.1	✓	12
65.64	even	2		8450.2.a.bu.1.3		3
195.17	even	12		1170.2.bp.h.289.3		12
195.23	even	12		1170.2.bp.h.919.3		12
195.62	even	12		1170.2.bp.h.919.6		12
195.173	even	12		1170.2.bp.h.289.6		12
260.23	even	12		1040.2.dh.b.529.2		12
260.43	even	12		1040.2.dh.b.289.5		12
260.127	even	12		1040.2.dh.b.529.5		12
260.147	even	12		1040.2.dh.b.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.1	✓	12	65.62	odd	12
130.2.n.a.9.6	yes	12	65.23	odd	12
130.2.n.a.29.1	yes	12	65.43	odd	12
130.2.n.a.29.6	yes	12	65.17	odd	12
650.2.e.j.451.3		6	13.10	even	6
650.2.e.j.601.3		6	13.4	even	6
650.2.e.k.451.1		6	65.49	even	6
650.2.e.k.601.1		6	65.4	even	6
1040.2.dh.b.289.2		12	260.147	even	12
1040.2.dh.b.289.5		12	260.43	even	12
1040.2.dh.b.529.2		12	260.23	even	12
1040.2.dh.b.529.5		12	260.127	even	12
1170.2.bp.h.289.3		12	195.17	even	12
1170.2.bp.h.289.6		12	195.173	even	12
1170.2.bp.h.919.3		12	195.23	even	12
1170.2.bp.h.919.6		12	195.62	even	12
1690.2.b.b.339.3		6	5.2	odd	4
1690.2.b.b.339.4		6	5.3	odd	4
1690.2.b.c.339.1		6	65.38	odd	4
1690.2.b.c.339.6		6	65.12	odd	4
1690.2.c.b.1689.2		6	65.8	even	4
1690.2.c.b.1689.5		6	65.57	even	4
1690.2.c.c.1689.2		6	65.18	even	4
1690.2.c.c.1689.5		6	65.47	even	4
8450.2.a.bt.1.1		3	1.1	even	1	trivial
8450.2.a.bu.1.3		3	65.64	even	2
8450.2.a.ca.1.3		3	5.4	even	2
8450.2.a.cb.1.1		3	13.12	even	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:	\( N \)	\(=\)	\( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.67513 q^{3} +1.00000 q^{4} +1.67513 q^{6} +1.80606 q^{7} -1.00000 q^{8} -0.193937 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.67513 q^{3} +1.00000 q^{4} +1.67513 q^{6} +1.80606 q^{7} -1.00000 q^{8} -0.193937 q^{9} -6.44358 q^{11} -1.67513 q^{12} -1.80606 q^{14} +1.00000 q^{16} -0.481194 q^{17} +0.193937 q^{18} +6.28726 q^{19} -3.02539 q^{21} +6.44358 q^{22} -7.11871 q^{23} +1.67513 q^{24} +5.35026 q^{27} +1.80606 q^{28} +2.31265 q^{29} -3.25694 q^{31} -1.00000 q^{32} +10.7938 q^{33} +0.481194 q^{34} -0.193937 q^{36} +3.06300 q^{37} -6.28726 q^{38} -7.50659 q^{41} +3.02539 q^{42} +2.00000 q^{43} -6.44358 q^{44} +7.11871 q^{46} +2.19394 q^{47} -1.67513 q^{48} -3.73813 q^{49} +0.806063 q^{51} +0.906679 q^{53} -5.35026 q^{54} -1.80606 q^{56} -10.5320 q^{57} -2.31265 q^{58} -6.57452 q^{59} -10.9502 q^{61} +3.25694 q^{62} -0.350262 q^{63} +1.00000 q^{64} -10.7938 q^{66} +0.649738 q^{67} -0.481194 q^{68} +11.9248 q^{69} -3.66291 q^{71} +0.193937 q^{72} -2.60720 q^{73} -3.06300 q^{74} +6.28726 q^{76} -11.6375 q^{77} -2.29455 q^{79} -8.38058 q^{81} +7.50659 q^{82} +13.3380 q^{83} -3.02539 q^{84} -2.00000 q^{86} -3.87399 q^{87} +6.44358 q^{88} +1.15633 q^{89} -7.11871 q^{92} +5.45580 q^{93} -2.19394 q^{94} +1.67513 q^{96} +13.8315 q^{97} +3.73813 q^{98} +1.24965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9} - 3 q^{11} - 5 q^{14} + 3 q^{16} + 4 q^{17} + q^{18} + 13 q^{19} + 6 q^{21} + 3 q^{22} + 6 q^{27} + 5 q^{28} - 14 q^{29} - 6 q^{31} - 3 q^{32} + 6 q^{33} - 4 q^{34} - q^{36} + 5 q^{37} - 13 q^{38} - 2 q^{41} - 6 q^{42} + 6 q^{43} - 3 q^{44} + 7 q^{47} - 2 q^{49} + 2 q^{51} + 9 q^{53} - 6 q^{54} - 5 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 4 q^{61} + 6 q^{62} + 9 q^{63} + 3 q^{64} - 6 q^{66} + 12 q^{67} + 4 q^{68} + 14 q^{69} + 20 q^{71} + q^{72} + 6 q^{73} - 5 q^{74} + 13 q^{76} - 19 q^{77} - 14 q^{79} - 13 q^{81} + 2 q^{82} + 4 q^{83} + 6 q^{84} - 6 q^{86} - 20 q^{87} + 3 q^{88} - 7 q^{89} + 26 q^{93} - 7 q^{94} + 26 q^{97} + 2 q^{98} - 13 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9 - 3 * q^11 - 5 * q^14 + 3 * q^16 + 4 * q^17 + q^18 + 13 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^27 + 5 * q^28 - 14 * q^29 - 6 * q^31 - 3 * q^32 + 6 * q^33 - 4 * q^34 - q^36 + 5 * q^37 - 13 * q^38 - 2 * q^41 - 6 * q^42 + 6 * q^43 - 3 * q^44 + 7 * q^47 - 2 * q^49 + 2 * q^51 + 9 * q^53 - 6 * q^54 - 5 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 4 * q^61 + 6 * q^62 + 9 * q^63 + 3 * q^64 - 6 * q^66 + 12 * q^67 + 4 * q^68 + 14 * q^69 + 20 * q^71 + q^72 + 6 * q^73 - 5 * q^74 + 13 * q^76 - 19 * q^77 - 14 * q^79 - 13 * q^81 + 2 * q^82 + 4 * q^83 + 6 * q^84 - 6 * q^86 - 20 * q^87 + 3 * q^88 - 7 * q^89 + 26 * q^93 - 7 * q^94 + 26 * q^97 + 2 * q^98 - 13 * q^99

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