LMFDB - Embedded newform 8450.2.a.ca.1.2

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:	$1$
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			1.2
Root			$2.17009$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.539189 q^{3} +1.00000 q^{4} +0.539189 q^{6} +0.709275 q^{7} +1.00000 q^{8} -2.70928 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.539189 q^{3} +1.00000 q^{4} +0.539189 q^{6} +0.709275 q^{7} +1.00000 q^{8} -2.70928 q^{9} +4.51026 q^{11} +0.539189 q^{12} +0.709275 q^{14} +1.00000 q^{16} -3.17009 q^{17} -2.70928 q^{18} +0.120638 q^{19} +0.382433 q^{21} +4.51026 q^{22} -4.97107 q^{23} +0.539189 q^{24} -3.07838 q^{27} +0.709275 q^{28} -7.26180 q^{29} -9.66701 q^{31} +1.00000 q^{32} +2.43188 q^{33} -3.17009 q^{34} -2.70928 q^{36} -6.95774 q^{37} +0.120638 q^{38} -0.447480 q^{41} +0.382433 q^{42} -2.00000 q^{43} +4.51026 q^{44} -4.97107 q^{46} -4.70928 q^{47} +0.539189 q^{48} -6.49693 q^{49} -1.70928 q^{51} -9.58864 q^{53} -3.07838 q^{54} +0.709275 q^{56} +0.0650468 q^{57} -7.26180 q^{58} +5.75872 q^{59} +7.06278 q^{61} -9.66701 q^{62} -1.92162 q^{63} +1.00000 q^{64} +2.43188 q^{66} -2.92162 q^{67} -3.17009 q^{68} -2.68035 q^{69} +8.18342 q^{71} -2.70928 q^{72} +6.74539 q^{73} -6.95774 q^{74} +0.120638 q^{76} +3.19902 q^{77} -16.0072 q^{79} +6.46800 q^{81} -0.447480 q^{82} -0.355771 q^{83} +0.382433 q^{84} -2.00000 q^{86} -3.91548 q^{87} +4.51026 q^{88} -3.63090 q^{89} -4.97107 q^{92} -5.21235 q^{93} -4.70928 q^{94} +0.539189 q^{96} -7.90829 q^{97} -6.49693 q^{98} -12.2195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.539189	0.311301	0.155650	−	0.987812i	$-0.450253\pi$
$3$	0.539189	0.311301	0.155650	+	0.987812i	$0.450253\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.539189	0.220123
$7$	0.709275	0.268081	0.134040	−	0.990976i	$-0.457205\pi$
$7$	0.709275	0.268081	0.134040	+	0.990976i	$0.457205\pi$
$8$	1.00000	0.353553
$9$	−2.70928	−0.903092
$10$	0	0
$11$	4.51026	1.35989	0.679947	−	0.733261i	$-0.262003\pi$
$11$	4.51026	1.35989	0.679947	+	0.733261i	$0.262003\pi$
$12$	0.539189	0.155650
$13$	0	0
$13$	0	0
$14$	0.709275	0.189562
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.17009	−0.768859	−0.384429	−	0.923154i	$-0.625602\pi$
$17$	−3.17009	−0.768859	−0.384429	+	0.923154i	$0.625602\pi$
$18$	−2.70928	−0.638582
$19$	0.120638	0.0276763	0.0138381	−	0.999904i	$-0.495595\pi$
$19$	0.120638	0.0276763	0.0138381	+	0.999904i	$0.495595\pi$
$20$	0	0
$21$	0.382433	0.0834538
$22$	4.51026	0.961591
$23$	−4.97107	−1.03654	−0.518270	−	0.855217i	$-0.673424\pi$
$23$	−4.97107	−1.03654	−0.518270	+	0.855217i	$0.673424\pi$
$24$	0.539189	0.110061
$25$	0	0
$26$	0	0
$27$	−3.07838	−0.592434
$28$	0.709275	0.134040
$29$	−7.26180	−1.34848	−0.674241	−	0.738512i	$-0.735529\pi$
$29$	−7.26180	−1.34848	−0.674241	+	0.738512i	$0.735529\pi$
$30$	0	0
$31$	−9.66701	−1.73625	−0.868124	−	0.496348i	$-0.834674\pi$
$31$	−9.66701	−1.73625	−0.868124	+	0.496348i	$0.834674\pi$
$32$	1.00000	0.176777
$33$	2.43188	0.423336
$34$	−3.17009	−0.543665
$35$	0	0
$36$	−2.70928	−0.451546
$37$	−6.95774	−1.14385	−0.571923	−	0.820308i	$-0.693802\pi$
$37$	−6.95774	−1.14385	−0.571923	+	0.820308i	$0.693802\pi$
$38$	0.120638	0.0195701
$39$	0	0
$40$	0	0
$41$	−0.447480	−0.0698847	−0.0349423	−	0.999389i	$-0.511125\pi$
$41$	−0.447480	−0.0698847	−0.0349423	+	0.999389i	$0.511125\pi$
$42$	0.382433	0.0590108
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	4.51026	0.679947
$45$	0	0
$46$	−4.97107	−0.732944
$47$	−4.70928	−0.686918	−0.343459	−	0.939168i	$-0.611599\pi$
$47$	−4.70928	−0.686918	−0.343459	+	0.939168i	$0.611599\pi$
$48$	0.539189	0.0778252
$49$	−6.49693	−0.928133
$50$	0	0
$51$	−1.70928	−0.239346
$52$	0	0
$53$	−9.58864	−1.31710	−0.658550	−	0.752537i	$-0.728830\pi$
$53$	−9.58864	−1.31710	−0.658550	+	0.752537i	$0.728830\pi$
$54$	−3.07838	−0.418914
$55$	0	0
$56$	0.709275	0.0947809
$57$	0.0650468	0.00861565
$58$	−7.26180	−0.953520
$59$	5.75872	0.749722	0.374861	−	0.927081i	$-0.377690\pi$
$59$	5.75872	0.749722	0.374861	+	0.927081i	$0.377690\pi$
$60$	0	0
$61$	7.06278	0.904296	0.452148	−	0.891943i	$-0.350658\pi$
$61$	7.06278	0.904296	0.452148	+	0.891943i	$0.350658\pi$
$62$	−9.66701	−1.22771
$63$	−1.92162	−0.242102
$64$	1.00000	0.125000
$65$	0	0
$66$	2.43188	0.299344
$67$	−2.92162	−0.356933	−0.178466	−	0.983946i	$-0.557114\pi$
$67$	−2.92162	−0.356933	−0.178466	+	0.983946i	$0.557114\pi$
$68$	−3.17009	−0.384429
$69$	−2.68035	−0.322676
$70$	0	0
$71$	8.18342	0.971193	0.485596	−	0.874183i	$-0.338602\pi$
$71$	8.18342	0.971193	0.485596	+	0.874183i	$0.338602\pi$
$72$	−2.70928	−0.319291
$73$	6.74539	0.789488	0.394744	−	0.918791i	$-0.370833\pi$
$73$	6.74539	0.789488	0.394744	+	0.918791i	$0.370833\pi$
$74$	−6.95774	−0.808821
$75$	0	0
$76$	0.120638	0.0138381
$77$	3.19902	0.364562
$78$	0	0
$79$	−16.0072	−1.80095	−0.900475	−	0.434908i	$-0.856781\pi$
$79$	−16.0072	−1.80095	−0.900475	+	0.434908i	$0.856781\pi$
$80$	0	0
$81$	6.46800	0.718667
$82$	−0.447480	−0.0494159
$83$	−0.355771	−0.0390510	−0.0195255	−	0.999809i	$-0.506216\pi$
$83$	−0.355771	−0.0390510	−0.0195255	+	0.999809i	$0.506216\pi$
$84$	0.382433	0.0417269
$85$	0	0
$86$	−2.00000	−0.215666
$87$	−3.91548	−0.419783
$88$	4.51026	0.480795
$89$	−3.63090	−0.384874	−0.192437	−	0.981309i	$-0.561639\pi$
$89$	−3.63090	−0.384874	−0.192437	+	0.981309i	$0.561639\pi$
$90$	0	0
$91$	0	0
$92$	−4.97107	−0.518270
$93$	−5.21235	−0.540495
$94$	−4.70928	−0.485725
$95$	0	0
$96$	0.539189	0.0550307
$97$	−7.90829	−0.802965	−0.401483	−	0.915867i	$-0.631505\pi$
$97$	−7.90829	−0.802965	−0.401483	+	0.915867i	$0.631505\pi$
$98$	−6.49693	−0.656289
$99$	−12.2195	−1.22811
$100$	0	0
$101$	6.14116	0.611068	0.305534	−	0.952181i	$-0.401165\pi$
$101$	6.14116	0.611068	0.305534	+	0.952181i	$0.401165\pi$
$102$	−1.70928	−0.169243
$103$	17.6803	1.74210	0.871048	−	0.491198i	$-0.163441\pi$
$103$	17.6803	1.74210	0.871048	+	0.491198i	$0.163441\pi$
$104$	0	0
$105$	0	0
$106$	−9.58864	−0.931331
$107$	−0.539189	−0.0521254	−0.0260627	−	0.999660i	$-0.508297\pi$
$107$	−0.539189	−0.0521254	−0.0260627	+	0.999660i	$0.508297\pi$
$108$	−3.07838	−0.296217
$109$	11.0205	1.05557	0.527787	−	0.849377i	$-0.323022\pi$
$109$	11.0205	1.05557	0.527787	+	0.849377i	$0.323022\pi$
$110$	0	0
$111$	−3.75154	−0.356080
$112$	0.709275	0.0670202
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	0.0650468	0.00609219
$115$	0	0
$116$	−7.26180	−0.674241
$117$	0	0
$118$	5.75872	0.530133
$119$	−2.24846	−0.206116
$120$	0	0
$121$	9.34244	0.849313
$122$	7.06278	0.639434
$123$	−0.241276	−0.0217552
$124$	−9.66701	−0.868124
$125$	0	0
$126$	−1.92162	−0.171192
$127$	12.1773	1.08056	0.540279	−	0.841486i	$-0.318319\pi$
$127$	12.1773	1.08056	0.540279	+	0.841486i	$0.318319\pi$
$128$	1.00000	0.0883883
$129$	−1.07838	−0.0949459
$130$	0	0
$131$	−17.4547	−1.52502	−0.762511	−	0.646976i	$-0.776034\pi$
$131$	−17.4547	−1.52502	−0.762511	+	0.646976i	$0.776034\pi$
$132$	2.43188	0.211668
$133$	0.0855657	0.00741948
$134$	−2.92162	−0.252390
$135$	0	0
$136$	−3.17009	−0.271833
$137$	−9.35350	−0.799124	−0.399562	−	0.916706i	$-0.630838\pi$
$137$	−9.35350	−0.799124	−0.399562	+	0.916706i	$0.630838\pi$
$138$	−2.68035	−0.228166
$139$	−2.64423	−0.224281	−0.112140	−	0.993692i	$-0.535771\pi$
$139$	−2.64423	−0.224281	−0.112140	+	0.993692i	$0.535771\pi$
$140$	0	0
$141$	−2.53919	−0.213838
$142$	8.18342	0.686737
$143$	0	0
$144$	−2.70928	−0.225773
$145$	0	0
$146$	6.74539	0.558253
$147$	−3.50307	−0.288928
$148$	−6.95774	−0.571923
$149$	9.23513	0.756572	0.378286	−	0.925689i	$-0.376514\pi$
$149$	9.23513	0.756572	0.378286	+	0.925689i	$0.376514\pi$
$150$	0	0
$151$	9.42574	0.767056	0.383528	−	0.923529i	$-0.374709\pi$
$151$	9.42574	0.767056	0.383528	+	0.923529i	$0.374709\pi$
$152$	0.120638	0.00978505
$153$	8.58864	0.694350
$154$	3.19902	0.257784
$155$	0	0
$156$	0	0
$157$	5.77205	0.460660	0.230330	−	0.973113i	$-0.426019\pi$
$157$	5.77205	0.460660	0.230330	+	0.973113i	$0.426019\pi$
$158$	−16.0072	−1.27346
$159$	−5.17009	−0.410015
$160$	0	0
$161$	−3.52586	−0.277877
$162$	6.46800	0.508174
$163$	−16.8215	−1.31756	−0.658781	−	0.752335i	$-0.728928\pi$
$163$	−16.8215	−1.31756	−0.658781	+	0.752335i	$0.728928\pi$
$164$	−0.447480	−0.0349423
$165$	0	0
$166$	−0.355771	−0.0276132
$167$	18.1194	1.40212	0.701061	−	0.713101i	$-0.252710\pi$
$167$	18.1194	1.40212	0.701061	+	0.713101i	$0.252710\pi$
$168$	0.382433	0.0295054
$169$	0	0
$170$	0	0
$171$	−0.326842	−0.0249942
$172$	−2.00000	−0.152499
$173$	−10.3041	−0.783403	−0.391701	−	0.920092i	$-0.628113\pi$
$173$	−10.3041	−0.783403	−0.391701	+	0.920092i	$0.628113\pi$
$174$	−3.91548	−0.296832
$175$	0	0
$176$	4.51026	0.339974
$177$	3.10504	0.233389
$178$	−3.63090	−0.272147
$179$	1.26180	0.0943110	0.0471555	−	0.998888i	$-0.484984\pi$
$179$	1.26180	0.0943110	0.0471555	+	0.998888i	$0.484984\pi$
$180$	0	0
$181$	2.38243	0.177085	0.0885424	−	0.996072i	$-0.471779\pi$
$181$	2.38243	0.177085	0.0885424	+	0.996072i	$0.471779\pi$
$182$	0	0
$183$	3.80817	0.281508
$184$	−4.97107	−0.366472
$185$	0	0
$186$	−5.21235	−0.382188
$187$	−14.2979	−1.04557
$188$	−4.70928	−0.343459
$189$	−2.18342	−0.158820
$190$	0	0
$191$	−11.0856	−0.802123	−0.401062	−	0.916051i	$-0.631359\pi$
$191$	−11.0856	−0.802123	−0.401062	+	0.916051i	$0.631359\pi$
$192$	0.539189	0.0389126
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−7.90829	−0.567782
$195$	0	0
$196$	−6.49693	−0.464066
$197$	−8.69368	−0.619399	−0.309699	−	0.950835i	$-0.600228\pi$
$197$	−8.69368	−0.619399	−0.309699	+	0.950835i	$0.600228\pi$
$198$	−12.2195	−0.868405
$199$	21.5174	1.52533	0.762666	−	0.646793i	$-0.223890\pi$
$199$	21.5174	1.52533	0.762666	+	0.646793i	$0.223890\pi$
$200$	0	0
$201$	−1.57531	−0.111114
$202$	6.14116	0.432090
$203$	−5.15061	−0.361502
$204$	−1.70928	−0.119673
$205$	0	0
$206$	17.6803	1.23185
$207$	13.4680	0.936091
$208$	0	0
$209$	0.544109	0.0376368
$210$	0	0
$211$	−5.58864	−0.384738	−0.192369	−	0.981323i	$-0.561617\pi$
$211$	−5.58864	−0.384738	−0.192369	+	0.981323i	$0.561617\pi$
$212$	−9.58864	−0.658550
$213$	4.41241	0.302333
$214$	−0.539189	−0.0368582
$215$	0	0
$216$	−3.07838	−0.209457
$217$	−6.85658	−0.465455
$218$	11.0205	0.746404
$219$	3.63704	0.245768
$220$	0	0
$221$	0	0
$222$	−3.75154	−0.251787
$223$	−24.7093	−1.65466	−0.827328	−	0.561720i	$-0.810140\pi$
$223$	−24.7093	−1.65466	−0.827328	+	0.561720i	$0.810140\pi$
$224$	0.709275	0.0473905
$225$	0	0
$226$	14.0000	0.931266
$227$	−28.6947	−1.90454	−0.952268	−	0.305264i	$-0.901255\pi$
$227$	−28.6947	−1.90454	−0.952268	+	0.305264i	$0.901255\pi$
$228$	0.0650468	0.00430783
$229$	1.89988	0.125548	0.0627738	−	0.998028i	$-0.480005\pi$
$229$	1.89988	0.125548	0.0627738	+	0.998028i	$0.480005\pi$
$230$	0	0
$231$	1.72487	0.113488
$232$	−7.26180	−0.476760
$233$	22.2485	1.45755	0.728773	−	0.684756i	$-0.240091\pi$
$233$	22.2485	1.45755	0.728773	+	0.684756i	$0.240091\pi$
$234$	0	0
$235$	0	0
$236$	5.75872	0.374861
$237$	−8.63090	−0.560637
$238$	−2.24846	−0.145746
$239$	−24.8710	−1.60877	−0.804384	−	0.594110i	$-0.797505\pi$
$239$	−24.8710	−1.60877	−0.804384	+	0.594110i	$0.797505\pi$
$240$	0	0
$241$	2.95055	0.190062	0.0950309	−	0.995474i	$-0.469705\pi$
$241$	2.95055	0.190062	0.0950309	+	0.995474i	$0.469705\pi$
$242$	9.34244	0.600555
$243$	12.7226	0.816156
$244$	7.06278	0.452148
$245$	0	0
$246$	−0.241276	−0.0153832
$247$	0	0
$248$	−9.66701	−0.613856
$249$	−0.191828	−0.0121566
$250$	0	0
$251$	16.5597	1.04524	0.522620	−	0.852566i	$-0.324955\pi$
$251$	16.5597	1.04524	0.522620	+	0.852566i	$0.324955\pi$
$252$	−1.92162	−0.121051
$253$	−22.4208	−1.40958
$254$	12.1773	0.764070
$255$	0	0
$256$	1.00000	0.0625000
$257$	−0.523590	−0.0326607	−0.0163303	−	0.999867i	$-0.505198\pi$
$257$	−0.523590	−0.0326607	−0.0163303	+	0.999867i	$0.505198\pi$
$258$	−1.07838	−0.0671369
$259$	−4.93495	−0.306643
$260$	0	0
$261$	19.6742	1.21780
$262$	−17.4547	−1.07835
$263$	−28.7815	−1.77474	−0.887372	−	0.461054i	$-0.847471\pi$
$263$	−28.7815	−1.77474	−0.887372	+	0.461054i	$0.847471\pi$
$264$	2.43188	0.149672
$265$	0	0
$266$	0.0855657	0.00524637
$267$	−1.95774	−0.119812
$268$	−2.92162	−0.178466
$269$	10.0566	0.613164	0.306582	−	0.951844i	$-0.400815\pi$
$269$	10.0566	0.613164	0.306582	+	0.951844i	$0.400815\pi$
$270$	0	0
$271$	−18.1256	−1.10105	−0.550525	−	0.834819i	$-0.685572\pi$
$271$	−18.1256	−1.10105	−0.550525	+	0.834819i	$0.685572\pi$
$272$	−3.17009	−0.192215
$273$	0	0
$274$	−9.35350	−0.565066
$275$	0	0
$276$	−2.68035	−0.161338
$277$	24.7165	1.48507	0.742534	−	0.669808i	$-0.233624\pi$
$277$	24.7165	1.48507	0.742534	+	0.669808i	$0.233624\pi$
$278$	−2.64423	−0.158590
$279$	26.1906	1.56799
$280$	0	0
$281$	−22.9854	−1.37120	−0.685598	−	0.727980i	$-0.740459\pi$
$281$	−22.9854	−1.37120	−0.685598	+	0.727980i	$0.740459\pi$
$282$	−2.53919	−0.151206
$283$	−18.0989	−1.07587	−0.537934	−	0.842987i	$-0.680795\pi$
$283$	−18.0989	−1.07587	−0.537934	+	0.842987i	$0.680795\pi$
$284$	8.18342	0.485596
$285$	0	0
$286$	0	0
$287$	−0.317387	−0.0187347
$288$	−2.70928	−0.159646
$289$	−6.95055	−0.408856
$290$	0	0
$291$	−4.26406	−0.249964
$292$	6.74539	0.394744
$293$	17.8443	1.04247	0.521237	−	0.853412i	$-0.325471\pi$
$293$	17.8443	1.04247	0.521237	+	0.853412i	$0.325471\pi$
$294$	−3.50307	−0.204303
$295$	0	0
$296$	−6.95774	−0.404410
$297$	−13.8843	−0.805648
$298$	9.23513	0.534977
$299$	0	0
$300$	0	0
$301$	−1.41855	−0.0817639
$302$	9.42574	0.542390
$303$	3.31124	0.190226
$304$	0.120638	0.00691907
$305$	0	0
$306$	8.58864	0.490980
$307$	3.44521	0.196629	0.0983143	−	0.995155i	$-0.468655\pi$
$307$	3.44521	0.196629	0.0983143	+	0.995155i	$0.468655\pi$
$308$	3.19902	0.182281
$309$	9.53305	0.542316
$310$	0	0
$311$	17.8238	1.01069	0.505347	−	0.862916i	$-0.331365\pi$
$311$	17.8238	1.01069	0.505347	+	0.862916i	$0.331365\pi$
$312$	0	0
$313$	−32.2245	−1.82143	−0.910717	−	0.413031i	$-0.864470\pi$
$313$	−32.2245	−1.82143	−0.910717	+	0.413031i	$0.864470\pi$
$314$	5.77205	0.325736
$315$	0	0
$316$	−16.0072	−0.900475
$317$	1.90602	0.107053	0.0535265	−	0.998566i	$-0.482954\pi$
$317$	1.90602	0.107053	0.0535265	+	0.998566i	$0.482954\pi$
$318$	−5.17009	−0.289924
$319$	−32.7526	−1.83379
$320$	0	0
$321$	−0.290725	−0.0162267
$322$	−3.52586	−0.196488
$323$	−0.382433	−0.0212792
$324$	6.46800	0.359333
$325$	0	0
$326$	−16.8215	−0.931657
$327$	5.94214	0.328601
$328$	−0.447480	−0.0247080
$329$	−3.34017	−0.184150
$330$	0	0
$331$	0.711543	0.0391099	0.0195550	−	0.999809i	$-0.493775\pi$
$331$	0.711543	0.0391099	0.0195550	+	0.999809i	$0.493775\pi$
$332$	−0.355771	−0.0195255
$333$	18.8504	1.03300
$334$	18.1194	0.991450
$335$	0	0
$336$	0.382433	0.0208635
$337$	−9.85043	−0.536587	−0.268294	−	0.963337i	$-0.586460\pi$
$337$	−9.85043	−0.536587	−0.268294	+	0.963337i	$0.586460\pi$
$338$	0	0
$339$	7.54864	0.409986
$340$	0	0
$341$	−43.6007	−2.36111
$342$	−0.326842	−0.0176736
$343$	−9.57304	−0.516896
$344$	−2.00000	−0.107833
$345$	0	0
$346$	−10.3041	−0.553949
$347$	25.5330	1.37069	0.685343	−	0.728221i	$-0.259652\pi$
$347$	25.5330	1.37069	0.685343	+	0.728221i	$0.259652\pi$
$348$	−3.91548	−0.209892
$349$	18.0566	0.966550	0.483275	−	0.875469i	$-0.339447\pi$
$349$	18.0566	0.966550	0.483275	+	0.875469i	$0.339447\pi$
$350$	0	0
$351$	0	0
$352$	4.51026	0.240398
$353$	−14.6465	−0.779554	−0.389777	−	0.920909i	$-0.627448\pi$
$353$	−14.6465	−0.779554	−0.389777	+	0.920909i	$0.627448\pi$
$354$	3.10504	0.165031
$355$	0	0
$356$	−3.63090	−0.192437
$357$	−1.21235	−0.0641642
$358$	1.26180	0.0666879
$359$	13.4186	0.708204	0.354102	−	0.935207i	$-0.384787\pi$
$359$	13.4186	0.708204	0.354102	+	0.935207i	$0.384787\pi$
$360$	0	0
$361$	−18.9854	−0.999234
$362$	2.38243	0.125218
$363$	5.03734	0.264392
$364$	0	0
$365$	0	0
$366$	3.80817	0.199056
$367$	−21.5441	−1.12459	−0.562297	−	0.826936i	$-0.690082\pi$
$367$	−21.5441	−1.12459	−0.562297	+	0.826936i	$0.690082\pi$
$368$	−4.97107	−0.259135
$369$	1.21235	0.0631123
$370$	0	0
$371$	−6.80098	−0.353090
$372$	−5.21235	−0.270248
$373$	21.3340	1.10463	0.552317	−	0.833634i	$-0.313744\pi$
$373$	21.3340	1.10463	0.552317	+	0.833634i	$0.313744\pi$
$374$	−14.2979	−0.739327
$375$	0	0
$376$	−4.70928	−0.242862
$377$	0	0
$378$	−2.18342	−0.112303
$379$	−8.11223	−0.416697	−0.208349	−	0.978055i	$-0.566809\pi$
$379$	−8.11223	−0.416697	−0.208349	+	0.978055i	$0.566809\pi$
$380$	0	0
$381$	6.56585	0.336379
$382$	−11.0856	−0.567187
$383$	−24.9399	−1.27437	−0.637184	−	0.770712i	$-0.719901\pi$
$383$	−24.9399	−1.27437	−0.637184	+	0.770712i	$0.719901\pi$
$384$	0.539189	0.0275154
$385$	0	0
$386$	−14.0000	−0.712581
$387$	5.41855	0.275440
$388$	−7.90829	−0.401483
$389$	13.5330	0.686153	0.343076	−	0.939308i	$-0.388531\pi$
$389$	13.5330	0.686153	0.343076	+	0.939308i	$0.388531\pi$
$390$	0	0
$391$	15.7587	0.796953
$392$	−6.49693	−0.328144
$393$	−9.41136	−0.474740
$394$	−8.69368	−0.437981
$395$	0	0
$396$	−12.2195	−0.614055
$397$	4.59478	0.230605	0.115303	−	0.993330i	$-0.463216\pi$
$397$	4.59478	0.230605	0.115303	+	0.993330i	$0.463216\pi$
$398$	21.5174	1.07857
$399$	0.0461361	0.00230969
$400$	0	0
$401$	−29.7031	−1.48330	−0.741652	−	0.670785i	$-0.765957\pi$
$401$	−29.7031	−1.48330	−0.741652	+	0.670785i	$0.765957\pi$
$402$	−1.57531	−0.0785691
$403$	0	0
$404$	6.14116	0.305534
$405$	0	0
$406$	−5.15061	−0.255621
$407$	−31.3812	−1.55551
$408$	−1.70928	−0.0846217
$409$	10.3112	0.509858	0.254929	−	0.966960i	$-0.417948\pi$
$409$	10.3112	0.509858	0.254929	+	0.966960i	$0.417948\pi$
$410$	0	0
$411$	−5.04331	−0.248768
$412$	17.6803	0.871048
$413$	4.08452	0.200986
$414$	13.4680	0.661916
$415$	0	0
$416$	0	0
$417$	−1.42574	−0.0698187
$418$	0.544109	0.0266133
$419$	38.0905	1.86084	0.930421	−	0.366492i	$-0.119441\pi$
$419$	38.0905	1.86084	0.930421	+	0.366492i	$0.119441\pi$
$420$	0	0
$421$	26.7103	1.30178	0.650891	−	0.759171i	$-0.274396\pi$
$421$	26.7103	1.30178	0.650891	+	0.759171i	$0.274396\pi$
$422$	−5.58864	−0.272051
$423$	12.7587	0.620350
$424$	−9.58864	−0.465665
$425$	0	0
$426$	4.41241	0.213782
$427$	5.00946	0.242425
$428$	−0.539189	−0.0260627
$429$	0	0
$430$	0	0
$431$	20.7187	0.997986	0.498993	−	0.866606i	$-0.333703\pi$
$431$	20.7187	0.997986	0.498993	+	0.866606i	$0.333703\pi$
$432$	−3.07838	−0.148109
$433$	−15.8576	−0.762069	−0.381034	−	0.924561i	$-0.624432\pi$
$433$	−15.8576	−0.762069	−0.381034	+	0.924561i	$0.624432\pi$
$434$	−6.85658	−0.329126
$435$	0	0
$436$	11.0205	0.527787
$437$	−0.599701	−0.0286876
$438$	3.63704	0.173785
$439$	−9.73925	−0.464829	−0.232415	−	0.972617i	$-0.574663\pi$
$439$	−9.73925	−0.464829	−0.232415	+	0.972617i	$0.574663\pi$
$440$	0	0
$441$	17.6020	0.838189
$442$	0	0
$443$	9.23060	0.438559	0.219279	−	0.975662i	$-0.429629\pi$
$443$	9.23060	0.438559	0.219279	+	0.975662i	$0.429629\pi$
$444$	−3.75154	−0.178040
$445$	0	0
$446$	−24.7093	−1.17002
$447$	4.97948	0.235521
$448$	0.709275	0.0335101
$449$	2.92389	0.137987	0.0689934	−	0.997617i	$-0.478021\pi$
$449$	2.92389	0.137987	0.0689934	+	0.997617i	$0.478021\pi$
$450$	0	0
$451$	−2.01825	−0.0950358
$452$	14.0000	0.658505
$453$	5.08225	0.238785
$454$	−28.6947	−1.34671
$455$	0	0
$456$	0.0650468	0.00304609
$457$	−11.6526	−0.545087	−0.272544	−	0.962143i	$-0.587865\pi$
$457$	−11.6526	−0.545087	−0.272544	+	0.962143i	$0.587865\pi$
$458$	1.89988	0.0887756
$459$	9.75872	0.455498
$460$	0	0
$461$	30.2979	1.41111	0.705557	−	0.708653i	$-0.250697\pi$
$461$	30.2979	1.41111	0.705557	+	0.708653i	$0.250697\pi$
$462$	1.72487	0.0802484
$463$	−7.04331	−0.327330	−0.163665	−	0.986516i	$-0.552332\pi$
$463$	−7.04331	−0.327330	−0.163665	+	0.986516i	$0.552332\pi$
$464$	−7.26180	−0.337120
$465$	0	0
$466$	22.2485	1.03064
$467$	3.90110	0.180522	0.0902608	−	0.995918i	$-0.471230\pi$
$467$	3.90110	0.180522	0.0902608	+	0.995918i	$0.471230\pi$
$468$	0	0
$469$	−2.07223	−0.0956869
$470$	0	0
$471$	3.11223	0.143404
$472$	5.75872	0.265067
$473$	−9.02052	−0.414764
$474$	−8.63090	−0.396430
$475$	0	0
$476$	−2.24846	−0.103058
$477$	25.9783	1.18946
$478$	−24.8710	−1.13757
$479$	−17.5103	−0.800064	−0.400032	−	0.916501i	$-0.631001\pi$
$479$	−17.5103	−0.800064	−0.400032	+	0.916501i	$0.631001\pi$
$480$	0	0
$481$	0	0
$482$	2.95055	0.134394
$483$	−1.90110	−0.0865032
$484$	9.34244	0.424656
$485$	0	0
$486$	12.7226	0.577109
$487$	38.5318	1.74604	0.873022	−	0.487681i	$-0.162157\pi$
$487$	38.5318	1.74604	0.873022	+	0.487681i	$0.162157\pi$
$488$	7.06278	0.319717
$489$	−9.06997	−0.410158
$490$	0	0
$491$	6.82377	0.307952	0.153976	−	0.988075i	$-0.450792\pi$
$491$	6.82377	0.307952	0.153976	+	0.988075i	$0.450792\pi$
$492$	−0.241276	−0.0108776
$493$	23.0205	1.03679
$494$	0	0
$495$	0	0
$496$	−9.66701	−0.434062
$497$	5.80430	0.260358
$498$	−0.191828	−0.00859602
$499$	−9.57918	−0.428823	−0.214412	−	0.976743i	$-0.568783\pi$
$499$	−9.57918	−0.428823	−0.214412	+	0.976743i	$0.568783\pi$
$500$	0	0
$501$	9.76979	0.436482
$502$	16.5597	0.739096
$503$	−16.6742	−0.743466	−0.371733	−	0.928340i	$-0.621236\pi$
$503$	−16.6742	−0.743466	−0.371733	+	0.928340i	$0.621236\pi$
$504$	−1.92162	−0.0855959
$505$	0	0
$506$	−22.4208	−0.996727
$507$	0	0
$508$	12.1773	0.540279
$509$	23.6598	1.04870	0.524352	−	0.851502i	$-0.324308\pi$
$509$	23.6598	1.04870	0.524352	+	0.851502i	$0.324308\pi$
$510$	0	0
$511$	4.78434	0.211647
$512$	1.00000	0.0441942
$513$	−0.371370	−0.0163964
$514$	−0.523590	−0.0230946
$515$	0	0
$516$	−1.07838	−0.0474729
$517$	−21.2401	−0.934136
$518$	−4.93495	−0.216829
$519$	−5.55583	−0.243874
$520$	0	0
$521$	−24.0472	−1.05353	−0.526763	−	0.850012i	$-0.676594\pi$
$521$	−24.0472	−1.05353	−0.526763	+	0.850012i	$0.676594\pi$
$522$	19.6742	0.861116
$523$	−23.3340	−1.02033	−0.510163	−	0.860078i	$-0.670415\pi$
$523$	−23.3340	−1.02033	−0.510163	+	0.860078i	$0.670415\pi$
$524$	−17.4547	−0.762511
$525$	0	0
$526$	−28.7815	−1.25493
$527$	30.6453	1.33493
$528$	2.43188	0.105834
$529$	1.71154	0.0744149
$530$	0	0
$531$	−15.6020	−0.677068
$532$	0.0855657	0.00370974
$533$	0	0
$534$	−1.95774	−0.0847197
$535$	0	0
$536$	−2.92162	−0.126195
$537$	0.680346	0.0293591
$538$	10.0566	0.433572
$539$	−29.3028	−1.26216
$540$	0	0
$541$	33.1494	1.42520	0.712602	−	0.701569i	$-0.247517\pi$
$541$	33.1494	1.42520	0.712602	+	0.701569i	$0.247517\pi$
$542$	−18.1256	−0.778559
$543$	1.28458	0.0551267
$544$	−3.17009	−0.135916
$545$	0	0
$546$	0	0
$547$	−43.6742	−1.86737	−0.933687	−	0.358090i	$-0.883428\pi$
$547$	−43.6742	−1.86737	−0.933687	+	0.358090i	$0.883428\pi$
$548$	−9.35350	−0.399562
$549$	−19.1350	−0.816662
$550$	0	0
$551$	−0.876050	−0.0373210
$552$	−2.68035	−0.114083
$553$	−11.3535	−0.482800
$554$	24.7165	1.05010
$555$	0	0
$556$	−2.64423	−0.112140
$557$	−22.3991	−0.949079	−0.474540	−	0.880234i	$-0.657385\pi$
$557$	−22.3991	−0.949079	−0.474540	+	0.880234i	$0.657385\pi$
$558$	26.1906	1.10874
$559$	0	0
$560$	0	0
$561$	−7.70928	−0.325486
$562$	−22.9854	−0.969583
$563$	−0.241276	−0.0101686	−0.00508429	−	0.999987i	$-0.501618\pi$
$563$	−0.241276	−0.0101686	−0.00508429	+	0.999987i	$0.501618\pi$
$564$	−2.53919	−0.106919
$565$	0	0
$566$	−18.0989	−0.760753
$567$	4.58759	0.192661
$568$	8.18342	0.343369
$569$	27.1711	1.13907	0.569537	−	0.821966i	$-0.307123\pi$
$569$	27.1711	1.13907	0.569537	+	0.821966i	$0.307123\pi$
$570$	0	0
$571$	2.25461	0.0943524	0.0471762	−	0.998887i	$-0.484978\pi$
$571$	2.25461	0.0943524	0.0471762	+	0.998887i	$0.484978\pi$
$572$	0	0
$573$	−5.97721	−0.249702
$574$	−0.317387	−0.0132475
$575$	0	0
$576$	−2.70928	−0.112886
$577$	7.86481	0.327416	0.163708	−	0.986509i	$-0.447654\pi$
$577$	7.86481	0.327416	0.163708	+	0.986509i	$0.447654\pi$
$578$	−6.95055	−0.289105
$579$	−7.54864	−0.313711
$580$	0	0
$581$	−0.252340	−0.0104688
$582$	−4.26406	−0.176751
$583$	−43.2472	−1.79112
$584$	6.74539	0.279126
$585$	0	0
$586$	17.8443	0.737141
$587$	−11.2039	−0.462436	−0.231218	−	0.972902i	$-0.574271\pi$
$587$	−11.2039	−0.462436	−0.231218	+	0.972902i	$0.574271\pi$
$588$	−3.50307	−0.144464
$589$	−1.16621	−0.0480529
$590$	0	0
$591$	−4.68753	−0.192819
$592$	−6.95774	−0.285961
$593$	13.4186	0.551034	0.275517	−	0.961296i	$-0.411151\pi$
$593$	13.4186	0.551034	0.275517	+	0.961296i	$0.411151\pi$
$594$	−13.8843	−0.569679
$595$	0	0
$596$	9.23513	0.378286
$597$	11.6020	0.474837
$598$	0	0
$599$	29.5753	1.20841	0.604207	−	0.796827i	$-0.293490\pi$
$599$	29.5753	1.20841	0.604207	+	0.796827i	$0.293490\pi$
$600$	0	0
$601$	24.9832	1.01909	0.509543	−	0.860445i	$-0.329815\pi$
$601$	24.9832	1.01909	0.509543	+	0.860445i	$0.329815\pi$
$602$	−1.41855	−0.0578158
$603$	7.91548	0.322343
$604$	9.42574	0.383528
$605$	0	0
$606$	3.31124	0.134510
$607$	−10.3919	−0.421794	−0.210897	−	0.977508i	$-0.567638\pi$
$607$	−10.3919	−0.421794	−0.210897	+	0.977508i	$0.567638\pi$
$608$	0.120638	0.00489252
$609$	−2.77715	−0.112536
$610$	0	0
$611$	0	0
$612$	8.58864	0.347175
$613$	−30.5285	−1.23303	−0.616517	−	0.787341i	$-0.711457\pi$
$613$	−30.5285	−1.23303	−0.616517	+	0.787341i	$0.711457\pi$
$614$	3.44521	0.139037
$615$	0	0
$616$	3.19902	0.128892
$617$	7.30283	0.294001	0.147000	−	0.989136i	$-0.453038\pi$
$617$	7.30283	0.294001	0.147000	+	0.989136i	$0.453038\pi$
$618$	9.53305	0.383475
$619$	24.5103	0.985151	0.492575	−	0.870270i	$-0.336056\pi$
$619$	24.5103	0.985151	0.492575	+	0.870270i	$0.336056\pi$
$620$	0	0
$621$	15.3028	0.614082
$622$	17.8238	0.714668
$623$	−2.57531	−0.103177
$624$	0	0
$625$	0	0
$626$	−32.2245	−1.28795
$627$	0.293378	0.0117164
$628$	5.77205	0.230330
$629$	22.0566	0.879456
$630$	0	0
$631$	3.07838	0.122548	0.0612741	−	0.998121i	$-0.480484\pi$
$631$	3.07838	0.122548	0.0612741	+	0.998121i	$0.480484\pi$
$632$	−16.0072	−0.636732
$633$	−3.01333	−0.119769
$634$	1.90602	0.0756979
$635$	0	0
$636$	−5.17009	−0.205007
$637$	0	0
$638$	−32.7526	−1.29669
$639$	−22.1711	−0.877076
$640$	0	0
$641$	−2.46800	−0.0974801	−0.0487401	−	0.998811i	$-0.515521\pi$
$641$	−2.46800	−0.0974801	−0.0487401	+	0.998811i	$0.515521\pi$
$642$	−0.290725	−0.0114740
$643$	−18.8215	−0.742248	−0.371124	−	0.928583i	$-0.621027\pi$
$643$	−18.8215	−0.742248	−0.371124	+	0.928583i	$0.621027\pi$
$644$	−3.52586	−0.138938
$645$	0	0
$646$	−0.382433	−0.0150466
$647$	11.7031	0.460098	0.230049	−	0.973179i	$-0.426111\pi$
$647$	11.7031	0.460098	0.230049	+	0.973179i	$0.426111\pi$
$648$	6.46800	0.254087
$649$	25.9733	1.01954
$650$	0	0
$651$	−3.69699	−0.144896
$652$	−16.8215	−0.658781
$653$	−14.6937	−0.575008	−0.287504	−	0.957779i	$-0.592825\pi$
$653$	−14.6937	−0.575008	−0.287504	+	0.957779i	$0.592825\pi$
$654$	5.94214	0.232356
$655$	0	0
$656$	−0.447480	−0.0174712
$657$	−18.2751	−0.712981
$658$	−3.34017	−0.130213
$659$	18.7877	0.731863	0.365932	−	0.930642i	$-0.380750\pi$
$659$	18.7877	0.731863	0.365932	+	0.930642i	$0.380750\pi$
$660$	0	0
$661$	5.84202	0.227228	0.113614	−	0.993525i	$-0.463757\pi$
$661$	5.84202	0.227228	0.113614	+	0.993525i	$0.463757\pi$
$662$	0.711543	0.0276549
$663$	0	0
$664$	−0.355771	−0.0138066
$665$	0	0
$666$	18.8504	0.730439
$667$	36.0989	1.39775
$668$	18.1194	0.701061
$669$	−13.3230	−0.515096
$670$	0	0
$671$	31.8550	1.22975
$672$	0.382433	0.0147527
$673$	40.8925	1.57629	0.788145	−	0.615489i	$-0.211042\pi$
$673$	40.8925	1.57629	0.788145	+	0.615489i	$0.211042\pi$
$674$	−9.85043	−0.379424
$675$	0	0
$676$	0	0
$677$	28.2700	1.08651	0.543253	−	0.839569i	$-0.317193\pi$
$677$	28.2700	1.08651	0.543253	+	0.839569i	$0.317193\pi$
$678$	7.54864	0.289904
$679$	−5.60916	−0.215260
$680$	0	0
$681$	−15.4719	−0.592884
$682$	−43.6007	−1.66956
$683$	−41.5052	−1.58815	−0.794075	−	0.607819i	$-0.792045\pi$
$683$	−41.5052	−1.58815	−0.794075	+	0.607819i	$0.792045\pi$
$684$	−0.326842	−0.0124971
$685$	0	0
$686$	−9.57304	−0.365500
$687$	1.02439	0.0390831
$688$	−2.00000	−0.0762493
$689$	0	0
$690$	0	0
$691$	24.1084	0.917125	0.458562	−	0.888662i	$-0.348365\pi$
$691$	24.1084	0.917125	0.458562	+	0.888662i	$0.348365\pi$
$692$	−10.3041	−0.391701
$693$	−8.66701	−0.329233
$694$	25.5330	0.969221
$695$	0	0
$696$	−3.91548	−0.148416
$697$	1.41855	0.0537314
$698$	18.0566	0.683454
$699$	11.9961	0.453735
$700$	0	0
$701$	−14.1822	−0.535654	−0.267827	−	0.963467i	$-0.586306\pi$
$701$	−14.1822	−0.535654	−0.267827	+	0.963467i	$0.586306\pi$
$702$	0	0
$703$	−0.839369	−0.0316574
$704$	4.51026	0.169987
$705$	0	0
$706$	−14.6465	−0.551228
$707$	4.35577	0.163816
$708$	3.10504	0.116695
$709$	46.4957	1.74618	0.873091	−	0.487556i	$-0.162112\pi$
$709$	46.4957	1.74618	0.873091	+	0.487556i	$0.162112\pi$
$710$	0	0
$711$	43.3679	1.62642
$712$	−3.63090	−0.136074
$713$	48.0554	1.79969
$714$	−1.21235	−0.0453709
$715$	0	0
$716$	1.26180	0.0471555
$717$	−13.4101	−0.500811
$718$	13.4186	0.500776
$719$	−12.7214	−0.474428	−0.237214	−	0.971457i	$-0.576234\pi$
$719$	−12.7214	−0.474428	−0.237214	+	0.971457i	$0.576234\pi$
$720$	0	0
$721$	12.5402	0.467023
$722$	−18.9854	−0.706565
$723$	1.59090	0.0591664
$724$	2.38243	0.0885424
$725$	0	0
$726$	5.03734	0.186953
$727$	13.2595	0.491769	0.245884	−	0.969299i	$-0.420922\pi$
$727$	13.2595	0.491769	0.245884	+	0.969299i	$0.420922\pi$
$728$	0	0
$729$	−12.5441	−0.464597
$730$	0	0
$731$	6.34017	0.234500
$732$	3.80817	0.140754
$733$	−31.5848	−1.16661	−0.583305	−	0.812253i	$-0.698241\pi$
$733$	−31.5848	−1.16661	−0.583305	+	0.812253i	$0.698241\pi$
$734$	−21.5441	−0.795208
$735$	0	0
$736$	−4.97107	−0.183236
$737$	−13.1773	−0.485391
$738$	1.21235	0.0446271
$739$	−2.83218	−0.104183	−0.0520917	−	0.998642i	$-0.516589\pi$
$739$	−2.83218	−0.104183	−0.0520917	+	0.998642i	$0.516589\pi$
$740$	0	0
$741$	0	0
$742$	−6.80098	−0.249672
$743$	−20.8020	−0.763152	−0.381576	−	0.924337i	$-0.624619\pi$
$743$	−20.8020	−0.763152	−0.381576	+	0.924337i	$0.624619\pi$
$744$	−5.21235	−0.191094
$745$	0	0
$746$	21.3340	0.781094
$747$	0.963883	0.0352666
$748$	−14.2979	−0.522783
$749$	−0.382433	−0.0139738
$750$	0	0
$751$	36.2823	1.32396	0.661980	−	0.749521i	$-0.269716\pi$
$751$	36.2823	1.32396	0.661980	+	0.749521i	$0.269716\pi$
$752$	−4.70928	−0.171730
$753$	8.92881	0.325384
$754$	0	0
$755$	0	0
$756$	−2.18342	−0.0794101
$757$	40.8687	1.48540	0.742699	−	0.669626i	$-0.233545\pi$
$757$	40.8687	1.48540	0.742699	+	0.669626i	$0.233545\pi$
$758$	−8.11223	−0.294649
$759$	−12.0891	−0.438805
$760$	0	0
$761$	−35.6225	−1.29131	−0.645657	−	0.763627i	$-0.723416\pi$
$761$	−35.6225	−1.29131	−0.645657	+	0.763627i	$0.723416\pi$
$762$	6.56585	0.237856
$763$	7.81658	0.282979
$764$	−11.0856	−0.401062
$765$	0	0
$766$	−24.9399	−0.901114
$767$	0	0
$768$	0.539189	0.0194563
$769$	−3.36910	−0.121493	−0.0607465	−	0.998153i	$-0.519348\pi$
$769$	−3.36910	−0.121493	−0.0607465	+	0.998153i	$0.519348\pi$
$770$	0	0
$771$	−0.282314	−0.0101673
$772$	−14.0000	−0.503871
$773$	11.0794	0.398499	0.199250	−	0.979949i	$-0.436150\pi$
$773$	11.0794	0.398499	0.199250	+	0.979949i	$0.436150\pi$
$774$	5.41855	0.194766
$775$	0	0
$776$	−7.90829	−0.283891
$777$	−2.66087	−0.0954582
$778$	13.5330	0.485183
$779$	−0.0539832	−0.00193415
$780$	0	0
$781$	36.9093	1.32072
$782$	15.7587	0.563531
$783$	22.3545	0.798886
$784$	−6.49693	−0.232033
$785$	0	0
$786$	−9.41136	−0.335692
$787$	5.67089	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$787$	5.67089	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$788$	−8.69368	−0.309699
$789$	−15.5187	−0.552479
$790$	0	0
$791$	9.92986	0.353065
$792$	−12.2195	−0.434202
$793$	0	0
$794$	4.59478	0.163063
$795$	0	0
$796$	21.5174	0.762666
$797$	−27.3424	−0.968519	−0.484259	−	0.874924i	$-0.660911\pi$
$797$	−27.3424	−0.968519	−0.484259	+	0.874924i	$0.660911\pi$
$798$	0.0461361	0.00163320
$799$	14.9288	0.528143
$800$	0	0
$801$	9.83710	0.347577
$802$	−29.7031	−1.04885
$803$	30.4235	1.07362
$804$	−1.57531	−0.0555568
$805$	0	0
$806$	0	0
$807$	5.42243	0.190878
$808$	6.14116	0.216045
$809$	−5.02893	−0.176808	−0.0884039	−	0.996085i	$-0.528177\pi$
$809$	−5.02893	−0.176808	−0.0884039	+	0.996085i	$0.528177\pi$
$810$	0	0
$811$	−47.3390	−1.66230	−0.831148	−	0.556052i	$-0.812316\pi$
$811$	−47.3390	−1.66230	−0.831148	+	0.556052i	$0.812316\pi$
$812$	−5.15061	−0.180751
$813$	−9.77310	−0.342758
$814$	−31.3812	−1.09991
$815$	0	0
$816$	−1.70928	−0.0598366
$817$	−0.241276	−0.00844119
$818$	10.3112	0.360524
$819$	0	0
$820$	0	0
$821$	20.6816	0.721792	0.360896	−	0.932606i	$-0.382471\pi$
$821$	20.6816	0.721792	0.360896	+	0.932606i	$0.382471\pi$
$822$	−5.04331	−0.175905
$823$	19.8371	0.691478	0.345739	−	0.938331i	$-0.387628\pi$
$823$	19.8371	0.691478	0.345739	+	0.938331i	$0.387628\pi$
$824$	17.6803	0.615924
$825$	0	0
$826$	4.08452	0.142119
$827$	39.6730	1.37956	0.689782	−	0.724017i	$-0.257706\pi$
$827$	39.6730	1.37956	0.689782	+	0.724017i	$0.257706\pi$
$828$	13.4680	0.468045
$829$	−25.3874	−0.881739	−0.440870	−	0.897571i	$-0.645330\pi$
$829$	−25.3874	−0.881739	−0.440870	+	0.897571i	$0.645330\pi$
$830$	0	0
$831$	13.3268	0.462303
$832$	0	0
$833$	20.5958	0.713603
$834$	−1.42574	−0.0493693
$835$	0	0
$836$	0.544109	0.0188184
$837$	29.7587	1.02861
$838$	38.0905	1.31581
$839$	23.0277	0.795005	0.397502	−	0.917601i	$-0.369877\pi$
$839$	23.0277	0.795005	0.397502	+	0.917601i	$0.369877\pi$
$840$	0	0
$841$	23.7337	0.818402
$842$	26.7103	0.920498
$843$	−12.3935	−0.426855
$844$	−5.58864	−0.192369
$845$	0	0
$846$	12.7587	0.438654
$847$	6.62636	0.227685
$848$	−9.58864	−0.329275
$849$	−9.75872	−0.334919
$850$	0	0
$851$	34.5874	1.18564
$852$	4.41241	0.151167
$853$	−13.7047	−0.469241	−0.234621	−	0.972087i	$-0.575385\pi$
$853$	−13.7047	−0.469241	−0.234621	+	0.972087i	$0.575385\pi$
$854$	5.00946	0.171420
$855$	0	0
$856$	−0.539189	−0.0184291
$857$	17.8648	0.610250	0.305125	−	0.952312i	$-0.401302\pi$
$857$	17.8648	0.610250	0.305125	+	0.952312i	$0.401302\pi$
$858$	0	0
$859$	13.7187	0.468077	0.234039	−	0.972227i	$-0.424806\pi$
$859$	13.7187	0.468077	0.234039	+	0.972227i	$0.424806\pi$
$860$	0	0
$861$	−0.171131	−0.00583214
$862$	20.7187	0.705683
$863$	−19.9383	−0.678706	−0.339353	−	0.940659i	$-0.610208\pi$
$863$	−19.9383	−0.678706	−0.339353	+	0.940659i	$0.610208\pi$
$864$	−3.07838	−0.104729
$865$	0	0
$866$	−15.8576	−0.538864
$867$	−3.74766	−0.127277
$868$	−6.85658	−0.232727
$869$	−72.1966	−2.44910
$870$	0	0
$871$	0	0
$872$	11.0205	0.373202
$873$	21.4257	0.725151
$874$	−0.599701	−0.0202852
$875$	0	0
$876$	3.63704	0.122884
$877$	−21.6163	−0.729932	−0.364966	−	0.931021i	$-0.618919\pi$
$877$	−21.6163	−0.729932	−0.364966	+	0.931021i	$0.618919\pi$
$878$	−9.73925	−0.328684
$879$	9.62144	0.324523
$880$	0	0
$881$	−7.99386	−0.269320	−0.134660	−	0.990892i	$-0.542994\pi$
$881$	−7.99386	−0.269320	−0.134660	+	0.990892i	$0.542994\pi$
$882$	17.6020	0.592689
$883$	−26.2713	−0.884098	−0.442049	−	0.896991i	$-0.645748\pi$
$883$	−26.2713	−0.884098	−0.442049	+	0.896991i	$0.645748\pi$
$884$	0	0
$885$	0	0
$886$	9.23060	0.310108
$887$	−17.1627	−0.576268	−0.288134	−	0.957590i	$-0.593035\pi$
$887$	−17.1627	−0.576268	−0.288134	+	0.957590i	$0.593035\pi$
$888$	−3.75154	−0.125893
$889$	8.63704	0.289677
$890$	0	0
$891$	29.1724	0.977311
$892$	−24.7093	−0.827328
$893$	−0.568118	−0.0190114
$894$	4.97948	0.166539
$895$	0	0
$896$	0.709275	0.0236952
$897$	0	0
$898$	2.92389	0.0975715
$899$	70.1999	2.34130
$900$	0	0
$901$	30.3968	1.01266
$902$	−2.01825	−0.0672004
$903$	−0.764867	−0.0254532
$904$	14.0000	0.465633
$905$	0	0
$906$	5.08225	0.168847
$907$	−16.4136	−0.545006	−0.272503	−	0.962155i	$-0.587851\pi$
$907$	−16.4136	−0.545006	−0.272503	+	0.962155i	$0.587851\pi$
$908$	−28.6947	−0.952268
$909$	−16.6381	−0.551850
$910$	0	0
$911$	−4.52359	−0.149873	−0.0749366	−	0.997188i	$-0.523875\pi$
$911$	−4.52359	−0.149873	−0.0749366	+	0.997188i	$0.523875\pi$
$912$	0.0650468	0.00215391
$913$	−1.60462	−0.0531052
$914$	−11.6526	−0.385435
$915$	0	0
$916$	1.89988	0.0627738
$917$	−12.3802	−0.408829
$918$	9.75872	0.322086
$919$	−7.64301	−0.252120	−0.126060	−	0.992023i	$-0.540233\pi$
$919$	−7.64301	−0.252120	−0.126060	+	0.992023i	$0.540233\pi$
$920$	0	0
$921$	1.85762	0.0612107
$922$	30.2979	0.997809
$923$	0	0
$924$	1.72487	0.0567442
$925$	0	0
$926$	−7.04331	−0.231457
$927$	−47.9009	−1.57327
$928$	−7.26180	−0.238380
$929$	−59.3295	−1.94654	−0.973269	−	0.229669i	$-0.926236\pi$
$929$	−59.3295	−1.94654	−0.973269	+	0.229669i	$0.926236\pi$
$930$	0	0
$931$	−0.783777	−0.0256873
$932$	22.2485	0.728773
$933$	9.61038	0.314630
$934$	3.90110	0.127648
$935$	0	0
$936$	0	0
$937$	−1.75872	−0.0574550	−0.0287275	−	0.999587i	$-0.509146\pi$
$937$	−1.75872	−0.0574550	−0.0287275	+	0.999587i	$0.509146\pi$
$938$	−2.07223	−0.0676609
$939$	−17.3751	−0.567014
$940$	0	0
$941$	−42.2967	−1.37883	−0.689416	−	0.724365i	$-0.742133\pi$
$941$	−42.2967	−1.37883	−0.689416	+	0.724365i	$0.742133\pi$
$942$	3.11223	0.101402
$943$	2.22446	0.0724382
$944$	5.75872	0.187430
$945$	0	0
$946$	−9.02052	−0.293282
$947$	4.83832	0.157224	0.0786122	−	0.996905i	$-0.474951\pi$
$947$	4.83832	0.157224	0.0786122	+	0.996905i	$0.474951\pi$
$948$	−8.63090	−0.280319
$949$	0	0
$950$	0	0
$951$	1.02771	0.0333257
$952$	−2.24846	−0.0728731
$953$	−25.9539	−0.840728	−0.420364	−	0.907356i	$-0.638098\pi$
$953$	−25.9539	−0.840728	−0.420364	+	0.907356i	$0.638098\pi$
$954$	25.9783	0.841077
$955$	0	0
$956$	−24.8710	−0.804384
$957$	−17.6598	−0.570861
$958$	−17.5103	−0.565731
$959$	−6.63421	−0.214230
$960$	0	0
$961$	62.4512	2.01455
$962$	0	0
$963$	1.46081	0.0470740
$964$	2.95055	0.0950309
$965$	0	0
$966$	−1.90110	−0.0611670
$967$	−29.9939	−0.964537	−0.482269	−	0.876023i	$-0.660187\pi$
$967$	−29.9939	−0.964537	−0.482269	+	0.876023i	$0.660187\pi$
$968$	9.34244	0.300277
$969$	−0.206204	−0.00662422
$970$	0	0
$971$	15.7286	0.504754	0.252377	−	0.967629i	$-0.418788\pi$
$971$	15.7286	0.504754	0.252377	+	0.967629i	$0.418788\pi$
$972$	12.7226	0.408078
$973$	−1.87549	−0.0601253
$974$	38.5318	1.23464
$975$	0	0
$976$	7.06278	0.226074
$977$	27.5441	0.881214	0.440607	−	0.897700i	$-0.354763\pi$
$977$	27.5441	0.881214	0.440607	+	0.897700i	$0.354763\pi$
$978$	−9.06997	−0.290026
$979$	−16.3763	−0.523389
$980$	0	0
$981$	−29.8576	−0.953280
$982$	6.82377	0.217755
$983$	−18.0289	−0.575034	−0.287517	−	0.957776i	$-0.592830\pi$
$983$	−18.0289	−0.575034	−0.287517	+	0.957776i	$0.592830\pi$
$984$	−0.241276	−0.00769161
$985$	0	0
$986$	23.0205	0.733123
$987$	−1.80098	−0.0573260
$988$	0	0
$989$	9.94214	0.316142
$990$	0	0
$991$	11.6332	0.369540	0.184770	−	0.982782i	$-0.440846\pi$
$991$	11.6332	0.369540	0.184770	+	0.982782i	$0.440846\pi$
$992$	−9.66701	−0.306928
$993$	0.383656	0.0121750
$994$	5.80430	0.184101
$995$	0	0
$996$	−0.191828	−0.00607830
$997$	−28.8648	−0.914158	−0.457079	−	0.889426i	$-0.651104\pi$
$997$	−28.8648	−0.914158	−0.457079	+	0.889426i	$0.651104\pi$
$998$	−9.57918	−0.303224
$999$	21.4186	0.677653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8450.2.a.ca.1.2		3
5.2	odd	4		1690.2.b.b.339.5		6
5.3	odd	4		1690.2.b.b.339.2		6
5.4	even	2		8450.2.a.bt.1.2		3
13.4	even	6		650.2.e.k.601.2		6
13.10	even	6		650.2.e.k.451.2		6
13.12	even	2		8450.2.a.bu.1.2		3
65.4	even	6		650.2.e.j.601.2		6
65.8	even	4		1690.2.c.c.1689.4		6
65.12	odd	4		1690.2.b.c.339.2		6
65.17	odd	12		130.2.n.a.29.2	yes	12
65.18	even	4		1690.2.c.b.1689.4		6
65.23	odd	12		130.2.n.a.9.2	✓	12
65.38	odd	4		1690.2.b.c.339.5		6
65.43	odd	12		130.2.n.a.29.5	yes	12
65.47	even	4		1690.2.c.b.1689.3		6
65.49	even	6		650.2.e.j.451.2		6
65.57	even	4		1690.2.c.c.1689.3		6
65.62	odd	12		130.2.n.a.9.5	yes	12
65.64	even	2		8450.2.a.cb.1.2		3
195.17	even	12		1170.2.bp.h.289.5		12
195.23	even	12		1170.2.bp.h.919.5		12
195.62	even	12		1170.2.bp.h.919.2		12
195.173	even	12		1170.2.bp.h.289.2		12
260.23	even	12		1040.2.dh.b.529.4		12
260.43	even	12		1040.2.dh.b.289.3		12
260.127	even	12		1040.2.dh.b.529.3		12
260.147	even	12		1040.2.dh.b.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.2	✓	12	65.23	odd	12
130.2.n.a.9.5	yes	12	65.62	odd	12
130.2.n.a.29.2	yes	12	65.17	odd	12
130.2.n.a.29.5	yes	12	65.43	odd	12
650.2.e.j.451.2		6	65.49	even	6
650.2.e.j.601.2		6	65.4	even	6
650.2.e.k.451.2		6	13.10	even	6
650.2.e.k.601.2		6	13.4	even	6
1040.2.dh.b.289.3		12	260.43	even	12
1040.2.dh.b.289.4		12	260.147	even	12
1040.2.dh.b.529.3		12	260.127	even	12
1040.2.dh.b.529.4		12	260.23	even	12
1170.2.bp.h.289.2		12	195.173	even	12
1170.2.bp.h.289.5		12	195.17	even	12
1170.2.bp.h.919.2		12	195.62	even	12
1170.2.bp.h.919.5		12	195.23	even	12
1690.2.b.b.339.2		6	5.3	odd	4
1690.2.b.b.339.5		6	5.2	odd	4
1690.2.b.c.339.2		6	65.12	odd	4
1690.2.b.c.339.5		6	65.38	odd	4
1690.2.c.b.1689.3		6	65.47	even	4
1690.2.c.b.1689.4		6	65.18	even	4
1690.2.c.c.1689.3		6	65.57	even	4
1690.2.c.c.1689.4		6	65.8	even	4
8450.2.a.bt.1.2		3	5.4	even	2
8450.2.a.bu.1.2		3	13.12	even	2
8450.2.a.ca.1.2		3	1.1	even	1	trivial
8450.2.a.cb.1.2		3	65.64	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.539189 q^{3} +1.00000 q^{4} +0.539189 q^{6} +0.709275 q^{7} +1.00000 q^{8} -2.70928 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.539189 q^{3} +1.00000 q^{4} +0.539189 q^{6} +0.709275 q^{7} +1.00000 q^{8} -2.70928 q^{9} +4.51026 q^{11} +0.539189 q^{12} +0.709275 q^{14} +1.00000 q^{16} -3.17009 q^{17} -2.70928 q^{18} +0.120638 q^{19} +0.382433 q^{21} +4.51026 q^{22} -4.97107 q^{23} +0.539189 q^{24} -3.07838 q^{27} +0.709275 q^{28} -7.26180 q^{29} -9.66701 q^{31} +1.00000 q^{32} +2.43188 q^{33} -3.17009 q^{34} -2.70928 q^{36} -6.95774 q^{37} +0.120638 q^{38} -0.447480 q^{41} +0.382433 q^{42} -2.00000 q^{43} +4.51026 q^{44} -4.97107 q^{46} -4.70928 q^{47} +0.539189 q^{48} -6.49693 q^{49} -1.70928 q^{51} -9.58864 q^{53} -3.07838 q^{54} +0.709275 q^{56} +0.0650468 q^{57} -7.26180 q^{58} +5.75872 q^{59} +7.06278 q^{61} -9.66701 q^{62} -1.92162 q^{63} +1.00000 q^{64} +2.43188 q^{66} -2.92162 q^{67} -3.17009 q^{68} -2.68035 q^{69} +8.18342 q^{71} -2.70928 q^{72} +6.74539 q^{73} -6.95774 q^{74} +0.120638 q^{76} +3.19902 q^{77} -16.0072 q^{79} +6.46800 q^{81} -0.447480 q^{82} -0.355771 q^{83} +0.382433 q^{84} -2.00000 q^{86} -3.91548 q^{87} +4.51026 q^{88} -3.63090 q^{89} -4.97107 q^{92} -5.21235 q^{93} -4.70928 q^{94} +0.539189 q^{96} -7.90829 q^{97} -6.49693 q^{98} -12.2195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 5 q^{7} + 3 q^{8} - q^{9}+O(q^{10}) \) 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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