LMFDB - Embedded newform 3525.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 141)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} +2.56155 q^{6} +1.56155 q^{7} +6.56155 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} +2.56155 q^{6} +1.56155 q^{7} +6.56155 q^{8} +1.00000 q^{9} +5.56155 q^{11} +4.56155 q^{12} -1.12311 q^{13} +4.00000 q^{14} +7.68466 q^{16} -5.12311 q^{17} +2.56155 q^{18} +6.00000 q^{19} +1.56155 q^{21} +14.2462 q^{22} -4.68466 q^{23} +6.56155 q^{24} -2.87689 q^{26} +1.00000 q^{27} +7.12311 q^{28} -9.56155 q^{29} -1.12311 q^{31} +6.56155 q^{32} +5.56155 q^{33} -13.1231 q^{34} +4.56155 q^{36} -7.56155 q^{37} +15.3693 q^{38} -1.12311 q^{39} +7.12311 q^{41} +4.00000 q^{42} -2.87689 q^{43} +25.3693 q^{44} -12.0000 q^{46} -1.00000 q^{47} +7.68466 q^{48} -4.56155 q^{49} -5.12311 q^{51} -5.12311 q^{52} +12.2462 q^{53} +2.56155 q^{54} +10.2462 q^{56} +6.00000 q^{57} -24.4924 q^{58} +7.12311 q^{59} +2.00000 q^{61} -2.87689 q^{62} +1.56155 q^{63} +1.43845 q^{64} +14.2462 q^{66} -5.12311 q^{67} -23.3693 q^{68} -4.68466 q^{69} +3.12311 q^{71} +6.56155 q^{72} -9.12311 q^{73} -19.3693 q^{74} +27.3693 q^{76} +8.68466 q^{77} -2.87689 q^{78} -9.56155 q^{79} +1.00000 q^{81} +18.2462 q^{82} -7.12311 q^{83} +7.12311 q^{84} -7.36932 q^{86} -9.56155 q^{87} +36.4924 q^{88} -8.24621 q^{89} -1.75379 q^{91} -21.3693 q^{92} -1.12311 q^{93} -2.56155 q^{94} +6.56155 q^{96} +16.9309 q^{97} -11.6847 q^{98} +5.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} + 5 q^{4} + q^{6} - q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 + 5 * q^4 + q^6 - q^7 + 9 * q^8 + 2 * q^9	$ 2 q + q^{2} + 2 q^{3} + 5 q^{4} + q^{6} - q^{7} + 9 q^{8} + 2 q^{9} + 7 q^{11} + 5 q^{12} + 6 q^{13} + 8 q^{14} + 3 q^{16} - 2 q^{17} + q^{18} + 12 q^{19} - q^{21} + 12 q^{22} + 3 q^{23} + 9 q^{24} - 14 q^{26} + 2 q^{27} + 6 q^{28} - 15 q^{29} + 6 q^{31} + 9 q^{32} + 7 q^{33} - 18 q^{34} + 5 q^{36} - 11 q^{37} + 6 q^{38} + 6 q^{39} + 6 q^{41} + 8 q^{42} - 14 q^{43} + 26 q^{44} - 24 q^{46} - 2 q^{47} + 3 q^{48} - 5 q^{49} - 2 q^{51} - 2 q^{52} + 8 q^{53} + q^{54} + 4 q^{56} + 12 q^{57} - 16 q^{58} + 6 q^{59} + 4 q^{61} - 14 q^{62} - q^{63} + 7 q^{64} + 12 q^{66} - 2 q^{67} - 22 q^{68} + 3 q^{69} - 2 q^{71} + 9 q^{72} - 10 q^{73} - 14 q^{74} + 30 q^{76} + 5 q^{77} - 14 q^{78} - 15 q^{79} + 2 q^{81} + 20 q^{82} - 6 q^{83} + 6 q^{84} + 10 q^{86} - 15 q^{87} + 40 q^{88} - 20 q^{91} - 18 q^{92} + 6 q^{93} - q^{94} + 9 q^{96} + 5 q^{97} - 11 q^{98} + 7 q^{99}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 + 5 * q^4 + q^6 - q^7 + 9 * q^8 + 2 * q^9 + 7 * q^11 + 5 * q^12 + 6 * q^13 + 8 * q^14 + 3 * q^16 - 2 * q^17 + q^18 + 12 * q^19 - q^21 + 12 * q^22 + 3 * q^23 + 9 * q^24 - 14 * q^26 + 2 * q^27 + 6 * q^28 - 15 * q^29 + 6 * q^31 + 9 * q^32 + 7 * q^33 - 18 * q^34 + 5 * q^36 - 11 * q^37 + 6 * q^38 + 6 * q^39 + 6 * q^41 + 8 * q^42 - 14 * q^43 + 26 * q^44 - 24 * q^46 - 2 * q^47 + 3 * q^48 - 5 * q^49 - 2 * q^51 - 2 * q^52 + 8 * q^53 + q^54 + 4 * q^56 + 12 * q^57 - 16 * q^58 + 6 * q^59 + 4 * q^61 - 14 * q^62 - q^63 + 7 * q^64 + 12 * q^66 - 2 * q^67 - 22 * q^68 + 3 * q^69 - 2 * q^71 + 9 * q^72 - 10 * q^73 - 14 * q^74 + 30 * q^76 + 5 * q^77 - 14 * q^78 - 15 * q^79 + 2 * q^81 + 20 * q^82 - 6 * q^83 + 6 * q^84 + 10 * q^86 - 15 * q^87 + 40 * q^88 - 20 * q^91 - 18 * q^92 + 6 * q^93 - q^94 + 9 * q^96 + 5 * q^97 - 11 * q^98 + 7 * 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 $

$2$	2.56155	1.81129	0.905646	−	0.424035i	$-0.139387\pi$
$2$	2.56155	1.81129	0.905646	+	0.424035i	$0.139387\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.56155	2.28078
$5$	0	0
$5$	0	0
$6$	2.56155	1.04575
$7$	1.56155	0.590211	0.295106	−	0.955465i	$-0.404645\pi$
$7$	1.56155	0.590211	0.295106	+	0.955465i	$0.404645\pi$
$8$	6.56155	2.31986
$9$	1.00000	0.333333
$10$	0	0
$11$	5.56155	1.67687	0.838436	−	0.545001i	$-0.183471\pi$
$11$	5.56155	1.67687	0.838436	+	0.545001i	$0.183471\pi$
$12$	4.56155	1.31681
$13$	−1.12311	−0.311493	−0.155747	−	0.987797i	$-0.549778\pi$
$13$	−1.12311	−0.311493	−0.155747	+	0.987797i	$0.549778\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	7.68466	1.92116
$17$	−5.12311	−1.24254	−0.621268	−	0.783598i	$-0.713382\pi$
$17$	−5.12311	−1.24254	−0.621268	+	0.783598i	$0.713382\pi$
$18$	2.56155	0.603764
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	0	0
$21$	1.56155	0.340759
$22$	14.2462	3.03730
$23$	−4.68466	−0.976819	−0.488409	−	0.872615i	$-0.662423\pi$
$23$	−4.68466	−0.976819	−0.488409	+	0.872615i	$0.662423\pi$
$24$	6.56155	1.33937
$25$	0	0
$26$	−2.87689	−0.564205
$27$	1.00000	0.192450
$28$	7.12311	1.34614
$29$	−9.56155	−1.77554	−0.887768	−	0.460291i	$-0.847745\pi$
$29$	−9.56155	−1.77554	−0.887768	+	0.460291i	$0.847745\pi$
$30$	0	0
$31$	−1.12311	−0.201716	−0.100858	−	0.994901i	$-0.532159\pi$
$31$	−1.12311	−0.201716	−0.100858	+	0.994901i	$0.532159\pi$
$32$	6.56155	1.15993
$33$	5.56155	0.968142
$34$	−13.1231	−2.25059
$35$	0	0
$36$	4.56155	0.760259
$37$	−7.56155	−1.24311	−0.621556	−	0.783370i	$-0.713499\pi$
$37$	−7.56155	−1.24311	−0.621556	+	0.783370i	$0.713499\pi$
$38$	15.3693	2.49323
$39$	−1.12311	−0.179841
$40$	0	0
$41$	7.12311	1.11244	0.556221	−	0.831034i	$-0.312251\pi$
$41$	7.12311	1.11244	0.556221	+	0.831034i	$0.312251\pi$
$42$	4.00000	0.617213
$43$	−2.87689	−0.438722	−0.219361	−	0.975644i	$-0.570397\pi$
$43$	−2.87689	−0.438722	−0.219361	+	0.975644i	$0.570397\pi$
$44$	25.3693	3.82457
$45$	0	0
$46$	−12.0000	−1.76930
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	7.68466	1.10918
$49$	−4.56155	−0.651650
$50$	0	0
$51$	−5.12311	−0.717378
$52$	−5.12311	−0.710447
$53$	12.2462	1.68215	0.841073	−	0.540921i	$-0.181924\pi$
$53$	12.2462	1.68215	0.841073	+	0.540921i	$0.181924\pi$
$54$	2.56155	0.348583
$55$	0	0
$56$	10.2462	1.36921
$57$	6.00000	0.794719
$58$	−24.4924	−3.21601
$59$	7.12311	0.927349	0.463675	−	0.886006i	$-0.346531\pi$
$59$	7.12311	0.927349	0.463675	+	0.886006i	$0.346531\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−2.87689	−0.365366
$63$	1.56155	0.196737
$64$	1.43845	0.179806
$65$	0	0
$66$	14.2462	1.75359
$67$	−5.12311	−0.625887	−0.312943	−	0.949772i	$-0.601315\pi$
$67$	−5.12311	−0.625887	−0.312943	+	0.949772i	$0.601315\pi$
$68$	−23.3693	−2.83395
$69$	−4.68466	−0.563967
$70$	0	0
$71$	3.12311	0.370644	0.185322	−	0.982678i	$-0.440667\pi$
$71$	3.12311	0.370644	0.185322	+	0.982678i	$0.440667\pi$
$72$	6.56155	0.773286
$73$	−9.12311	−1.06778	−0.533889	−	0.845554i	$-0.679270\pi$
$73$	−9.12311	−1.06778	−0.533889	+	0.845554i	$0.679270\pi$
$74$	−19.3693	−2.25164
$75$	0	0
$76$	27.3693	3.13948
$77$	8.68466	0.989709
$78$	−2.87689	−0.325744
$79$	−9.56155	−1.07576	−0.537879	−	0.843022i	$-0.680774\pi$
$79$	−9.56155	−1.07576	−0.537879	+	0.843022i	$0.680774\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	18.2462	2.01496
$83$	−7.12311	−0.781862	−0.390931	−	0.920420i	$-0.627847\pi$
$83$	−7.12311	−0.781862	−0.390931	+	0.920420i	$0.627847\pi$
$84$	7.12311	0.777195
$85$	0	0
$86$	−7.36932	−0.794654
$87$	−9.56155	−1.02511
$88$	36.4924	3.89011
$89$	−8.24621	−0.874097	−0.437048	−	0.899438i	$-0.643976\pi$
$89$	−8.24621	−0.874097	−0.437048	+	0.899438i	$0.643976\pi$
$90$	0	0
$91$	−1.75379	−0.183847
$92$	−21.3693	−2.22791
$93$	−1.12311	−0.116461
$94$	−2.56155	−0.264204
$95$	0	0
$96$	6.56155	0.669686
$97$	16.9309	1.71907	0.859535	−	0.511077i	$-0.170753\pi$
$97$	16.9309	1.71907	0.859535	+	0.511077i	$0.170753\pi$
$98$	−11.6847	−1.18033
$99$	5.56155	0.558957
$100$	0	0
$101$	10.8769	1.08229	0.541146	−	0.840929i	$-0.317991\pi$
$101$	10.8769	1.08229	0.541146	+	0.840929i	$0.317991\pi$
$102$	−13.1231	−1.29938
$103$	−9.56155	−0.942128	−0.471064	−	0.882099i	$-0.656130\pi$
$103$	−9.56155	−0.942128	−0.471064	+	0.882099i	$0.656130\pi$
$104$	−7.36932	−0.722621
$105$	0	0
$106$	31.3693	3.04686
$107$	−1.56155	−0.150961	−0.0754805	−	0.997147i	$-0.524049\pi$
$107$	−1.56155	−0.150961	−0.0754805	+	0.997147i	$0.524049\pi$
$108$	4.56155	0.438936
$109$	9.12311	0.873835	0.436918	−	0.899502i	$-0.356070\pi$
$109$	9.12311	0.873835	0.436918	+	0.899502i	$0.356070\pi$
$110$	0	0
$111$	−7.56155	−0.717711
$112$	12.0000	1.13389
$113$	8.87689	0.835068	0.417534	−	0.908661i	$-0.362894\pi$
$113$	8.87689	0.835068	0.417534	+	0.908661i	$0.362894\pi$
$114$	15.3693	1.43947
$115$	0	0
$116$	−43.6155	−4.04960
$117$	−1.12311	−0.103831
$118$	18.2462	1.67970
$119$	−8.00000	−0.733359
$120$	0	0
$121$	19.9309	1.81190
$122$	5.12311	0.463824
$123$	7.12311	0.642269
$124$	−5.12311	−0.460068
$125$	0	0
$126$	4.00000	0.356348
$127$	−1.12311	−0.0996595	−0.0498298	−	0.998758i	$-0.515868\pi$
$127$	−1.12311	−0.0996595	−0.0498298	+	0.998758i	$0.515868\pi$
$128$	−9.43845	−0.834249
$129$	−2.87689	−0.253296
$130$	0	0
$131$	0.876894	0.0766146	0.0383073	−	0.999266i	$-0.487803\pi$
$131$	0.876894	0.0766146	0.0383073	+	0.999266i	$0.487803\pi$
$132$	25.3693	2.20812
$133$	9.36932	0.812423
$134$	−13.1231	−1.13366
$135$	0	0
$136$	−33.6155	−2.88251
$137$	23.1231	1.97554	0.987770	−	0.155917i	$-0.0498333\pi$
$137$	23.1231	1.97554	0.987770	+	0.155917i	$0.0498333\pi$
$138$	−12.0000	−1.02151
$139$	3.75379	0.318392	0.159196	−	0.987247i	$-0.449110\pi$
$139$	3.75379	0.318392	0.159196	+	0.987247i	$0.449110\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	8.00000	0.671345
$143$	−6.24621	−0.522334
$144$	7.68466	0.640388
$145$	0	0
$146$	−23.3693	−1.93406
$147$	−4.56155	−0.376231
$148$	−34.4924	−2.83526
$149$	−11.3693	−0.931411	−0.465705	−	0.884940i	$-0.654199\pi$
$149$	−11.3693	−0.931411	−0.465705	+	0.884940i	$0.654199\pi$
$150$	0	0
$151$	8.24621	0.671067	0.335534	−	0.942028i	$-0.391083\pi$
$151$	8.24621	0.671067	0.335534	+	0.942028i	$0.391083\pi$
$152$	39.3693	3.19327
$153$	−5.12311	−0.414179
$154$	22.2462	1.79265
$155$	0	0
$156$	−5.12311	−0.410177
$157$	−9.80776	−0.782745	−0.391372	−	0.920232i	$-0.628000\pi$
$157$	−9.80776	−0.782745	−0.391372	+	0.920232i	$0.628000\pi$
$158$	−24.4924	−1.94851
$159$	12.2462	0.971188
$160$	0	0
$161$	−7.31534	−0.576530
$162$	2.56155	0.201255
$163$	−8.24621	−0.645893	−0.322947	−	0.946417i	$-0.604673\pi$
$163$	−8.24621	−0.645893	−0.322947	+	0.946417i	$0.604673\pi$
$164$	32.4924	2.53723
$165$	0	0
$166$	−18.2462	−1.41618
$167$	12.6847	0.981568	0.490784	−	0.871281i	$-0.336710\pi$
$167$	12.6847	0.981568	0.490784	+	0.871281i	$0.336710\pi$
$168$	10.2462	0.790512
$169$	−11.7386	−0.902972
$170$	0	0
$171$	6.00000	0.458831
$172$	−13.1231	−1.00063
$173$	−16.2462	−1.23518	−0.617588	−	0.786502i	$-0.711890\pi$
$173$	−16.2462	−1.23518	−0.617588	+	0.786502i	$0.711890\pi$
$174$	−24.4924	−1.85677
$175$	0	0
$176$	42.7386	3.22155
$177$	7.12311	0.535405
$178$	−21.1231	−1.58324
$179$	−0.192236	−0.0143684	−0.00718419	−	0.999974i	$-0.502287\pi$
$179$	−0.192236	−0.0143684	−0.00718419	+	0.999974i	$0.502287\pi$
$180$	0	0
$181$	4.24621	0.315618	0.157809	−	0.987470i	$-0.449557\pi$
$181$	4.24621	0.315618	0.157809	+	0.987470i	$0.449557\pi$
$182$	−4.49242	−0.333001
$183$	2.00000	0.147844
$184$	−30.7386	−2.26608
$185$	0	0
$186$	−2.87689	−0.210944
$187$	−28.4924	−2.08357
$188$	−4.56155	−0.332685
$189$	1.56155	0.113586
$190$	0	0
$191$	−20.4924	−1.48278	−0.741390	−	0.671075i	$-0.765833\pi$
$191$	−20.4924	−1.48278	−0.741390	+	0.671075i	$0.765833\pi$
$192$	1.43845	0.103811
$193$	18.4924	1.33111	0.665557	−	0.746347i	$-0.268194\pi$
$193$	18.4924	1.33111	0.665557	+	0.746347i	$0.268194\pi$
$194$	43.3693	3.11374
$195$	0	0
$196$	−20.8078	−1.48627
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	14.2462	1.01243
$199$	−13.1231	−0.930272	−0.465136	−	0.885239i	$-0.653995\pi$
$199$	−13.1231	−0.930272	−0.465136	+	0.885239i	$0.653995\pi$
$200$	0	0
$201$	−5.12311	−0.361356
$202$	27.8617	1.96035
$203$	−14.9309	−1.04794
$204$	−23.3693	−1.63618
$205$	0	0
$206$	−24.4924	−1.70647
$207$	−4.68466	−0.325606
$208$	−8.63068	−0.598430
$209$	33.3693	2.30820
$210$	0	0
$211$	−9.12311	−0.628060	−0.314030	−	0.949413i	$-0.601679\pi$
$211$	−9.12311	−0.628060	−0.314030	+	0.949413i	$0.601679\pi$
$212$	55.8617	3.83660
$213$	3.12311	0.213992
$214$	−4.00000	−0.273434
$215$	0	0
$216$	6.56155	0.446457
$217$	−1.75379	−0.119055
$218$	23.3693	1.58277
$219$	−9.12311	−0.616482
$220$	0	0
$221$	5.75379	0.387042
$222$	−19.3693	−1.29998
$223$	17.6155	1.17962	0.589812	−	0.807541i	$-0.299202\pi$
$223$	17.6155	1.17962	0.589812	+	0.807541i	$0.299202\pi$
$224$	10.2462	0.684604
$225$	0	0
$226$	22.7386	1.51255
$227$	−0.192236	−0.0127591	−0.00637957	−	0.999980i	$-0.502031\pi$
$227$	−0.192236	−0.0127591	−0.00637957	+	0.999980i	$0.502031\pi$
$228$	27.3693	1.81258
$229$	−6.87689	−0.454438	−0.227219	−	0.973844i	$-0.572963\pi$
$229$	−6.87689	−0.454438	−0.227219	+	0.973844i	$0.572963\pi$
$230$	0	0
$231$	8.68466	0.571409
$232$	−62.7386	−4.11899
$233$	3.31534	0.217195	0.108598	−	0.994086i	$-0.465364\pi$
$233$	3.31534	0.217195	0.108598	+	0.994086i	$0.465364\pi$
$234$	−2.87689	−0.188068
$235$	0	0
$236$	32.4924	2.11508
$237$	−9.56155	−0.621090
$238$	−20.4924	−1.32833
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	2.68466	0.172934	0.0864670	−	0.996255i	$-0.472442\pi$
$241$	2.68466	0.172934	0.0864670	+	0.996255i	$0.472442\pi$
$242$	51.0540	3.28187
$243$	1.00000	0.0641500
$244$	9.12311	0.584047
$245$	0	0
$246$	18.2462	1.16334
$247$	−6.73863	−0.428769
$248$	−7.36932	−0.467952
$249$	−7.12311	−0.451408
$250$	0	0
$251$	−8.49242	−0.536037	−0.268018	−	0.963414i	$-0.586369\pi$
$251$	−8.49242	−0.536037	−0.268018	+	0.963414i	$0.586369\pi$
$252$	7.12311	0.448713
$253$	−26.0540	−1.63800
$254$	−2.87689	−0.180512
$255$	0	0
$256$	−27.0540	−1.69087
$257$	8.68466	0.541734	0.270867	−	0.962617i	$-0.412690\pi$
$257$	8.68466	0.541734	0.270867	+	0.962617i	$0.412690\pi$
$258$	−7.36932	−0.458794
$259$	−11.8078	−0.733699
$260$	0	0
$261$	−9.56155	−0.591845
$262$	2.24621	0.138771
$263$	−17.3693	−1.07104	−0.535519	−	0.844523i	$-0.679884\pi$
$263$	−17.3693	−1.07104	−0.535519	+	0.844523i	$0.679884\pi$
$264$	36.4924	2.24595
$265$	0	0
$266$	24.0000	1.47153
$267$	−8.24621	−0.504660
$268$	−23.3693	−1.42751
$269$	3.36932	0.205431	0.102715	−	0.994711i	$-0.467247\pi$
$269$	3.36932	0.205431	0.102715	+	0.994711i	$0.467247\pi$
$270$	0	0
$271$	−9.56155	−0.580823	−0.290411	−	0.956902i	$-0.593792\pi$
$271$	−9.56155	−0.580823	−0.290411	+	0.956902i	$0.593792\pi$
$272$	−39.3693	−2.38712
$273$	−1.75379	−0.106144
$274$	59.2311	3.57828
$275$	0	0
$276$	−21.3693	−1.28628
$277$	10.4924	0.630429	0.315214	−	0.949021i	$-0.397924\pi$
$277$	10.4924	0.630429	0.315214	+	0.949021i	$0.397924\pi$
$278$	9.61553	0.576701
$279$	−1.12311	−0.0672386
$280$	0	0
$281$	−9.56155	−0.570394	−0.285197	−	0.958469i	$-0.592059\pi$
$281$	−9.56155	−0.570394	−0.285197	+	0.958469i	$0.592059\pi$
$282$	−2.56155	−0.152538
$283$	10.9309	0.649773	0.324886	−	0.945753i	$-0.394674\pi$
$283$	10.9309	0.649773	0.324886	+	0.945753i	$0.394674\pi$
$284$	14.2462	0.845357
$285$	0	0
$286$	−16.0000	−0.946100
$287$	11.1231	0.656576
$288$	6.56155	0.386643
$289$	9.24621	0.543895
$290$	0	0
$291$	16.9309	0.992505
$292$	−41.6155	−2.43536
$293$	−2.93087	−0.171223	−0.0856116	−	0.996329i	$-0.527284\pi$
$293$	−2.93087	−0.171223	−0.0856116	+	0.996329i	$0.527284\pi$
$294$	−11.6847	−0.681463
$295$	0	0
$296$	−49.6155	−2.88384
$297$	5.56155	0.322714
$298$	−29.1231	−1.68706
$299$	5.26137	0.304273
$300$	0	0
$301$	−4.49242	−0.258939
$302$	21.1231	1.21550
$303$	10.8769	0.624861
$304$	46.1080	2.64447
$305$	0	0
$306$	−13.1231	−0.750198
$307$	28.6847	1.63712	0.818560	−	0.574421i	$-0.194773\pi$
$307$	28.6847	1.63712	0.818560	+	0.574421i	$0.194773\pi$
$308$	39.6155	2.25730
$309$	−9.56155	−0.543938
$310$	0	0
$311$	9.56155	0.542186	0.271093	−	0.962553i	$-0.412615\pi$
$311$	9.56155	0.542186	0.271093	+	0.962553i	$0.412615\pi$
$312$	−7.36932	−0.417205
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	−25.1231	−1.41778
$315$	0	0
$316$	−43.6155	−2.45357
$317$	−3.80776	−0.213865	−0.106933	−	0.994266i	$-0.534103\pi$
$317$	−3.80776	−0.213865	−0.106933	+	0.994266i	$0.534103\pi$
$318$	31.3693	1.75910
$319$	−53.1771	−2.97734
$320$	0	0
$321$	−1.56155	−0.0871574
$322$	−18.7386	−1.04426
$323$	−30.7386	−1.71034
$324$	4.56155	0.253420
$325$	0	0
$326$	−21.1231	−1.16990
$327$	9.12311	0.504509
$328$	46.7386	2.58071
$329$	−1.56155	−0.0860912
$330$	0	0
$331$	22.2462	1.22276	0.611381	−	0.791336i	$-0.290614\pi$
$331$	22.2462	1.22276	0.611381	+	0.791336i	$0.290614\pi$
$332$	−32.4924	−1.78325
$333$	−7.56155	−0.414371
$334$	32.4924	1.77791
$335$	0	0
$336$	12.0000	0.654654
$337$	−18.6847	−1.01782	−0.508909	−	0.860820i	$-0.669951\pi$
$337$	−18.6847	−1.01782	−0.508909	+	0.860820i	$0.669951\pi$
$338$	−30.0691	−1.63555
$339$	8.87689	0.482127
$340$	0	0
$341$	−6.24621	−0.338251
$342$	15.3693	0.831077
$343$	−18.0540	−0.974823
$344$	−18.8769	−1.01777
$345$	0	0
$346$	−41.6155	−2.23726
$347$	−8.87689	−0.476537	−0.238268	−	0.971199i	$-0.576580\pi$
$347$	−8.87689	−0.476537	−0.238268	+	0.971199i	$0.576580\pi$
$348$	−43.6155	−2.33804
$349$	25.6155	1.37117	0.685584	−	0.727994i	$-0.259547\pi$
$349$	25.6155	1.37117	0.685584	+	0.727994i	$0.259547\pi$
$350$	0	0
$351$	−1.12311	−0.0599469
$352$	36.4924	1.94505
$353$	−23.3693	−1.24382	−0.621912	−	0.783087i	$-0.713644\pi$
$353$	−23.3693	−1.24382	−0.621912	+	0.783087i	$0.713644\pi$
$354$	18.2462	0.969775
$355$	0	0
$356$	−37.6155	−1.99362
$357$	−8.00000	−0.423405
$358$	−0.492423	−0.0260253
$359$	22.0540	1.16396	0.581982	−	0.813202i	$-0.302277\pi$
$359$	22.0540	1.16396	0.581982	+	0.813202i	$0.302277\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	10.8769	0.571677
$363$	19.9309	1.04610
$364$	−8.00000	−0.419314
$365$	0	0
$366$	5.12311	0.267789
$367$	−12.7386	−0.664951	−0.332476	−	0.943112i	$-0.607884\pi$
$367$	−12.7386	−0.664951	−0.332476	+	0.943112i	$0.607884\pi$
$368$	−36.0000	−1.87663
$369$	7.12311	0.370814
$370$	0	0
$371$	19.1231	0.992822
$372$	−5.12311	−0.265621
$373$	−6.87689	−0.356072	−0.178036	−	0.984024i	$-0.556974\pi$
$373$	−6.87689	−0.356072	−0.178036	+	0.984024i	$0.556974\pi$
$374$	−72.9848	−3.77396
$375$	0	0
$376$	−6.56155	−0.338386
$377$	10.7386	0.553068
$378$	4.00000	0.205738
$379$	−31.4233	−1.61411	−0.807053	−	0.590479i	$-0.798939\pi$
$379$	−31.4233	−1.61411	−0.807053	+	0.590479i	$0.798939\pi$
$380$	0	0
$381$	−1.12311	−0.0575384
$382$	−52.4924	−2.68575
$383$	27.1231	1.38593	0.692963	−	0.720973i	$-0.256305\pi$
$383$	27.1231	1.38593	0.692963	+	0.720973i	$0.256305\pi$
$384$	−9.43845	−0.481654
$385$	0	0
$386$	47.3693	2.41103
$387$	−2.87689	−0.146241
$388$	77.2311	3.92081
$389$	−21.8617	−1.10843	−0.554217	−	0.832372i	$-0.686982\pi$
$389$	−21.8617	−1.10843	−0.554217	+	0.832372i	$0.686982\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	−29.9309	−1.51174
$393$	0.876894	0.0442335
$394$	5.12311	0.258098
$395$	0	0
$396$	25.3693	1.27486
$397$	6.49242	0.325845	0.162923	−	0.986639i	$-0.447908\pi$
$397$	6.49242	0.325845	0.162923	+	0.986639i	$0.447908\pi$
$398$	−33.6155	−1.68499
$399$	9.36932	0.469053
$400$	0	0
$401$	16.7386	0.835887	0.417944	−	0.908473i	$-0.362751\pi$
$401$	16.7386	0.835887	0.417944	+	0.908473i	$0.362751\pi$
$402$	−13.1231	−0.654521
$403$	1.26137	0.0628331
$404$	49.6155	2.46846
$405$	0	0
$406$	−38.2462	−1.89813
$407$	−42.0540	−2.08454
$408$	−33.6155	−1.66422
$409$	−18.0000	−0.890043	−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000	−0.890043	−0.445021	+	0.895520i	$0.646804\pi$
$410$	0	0
$411$	23.1231	1.14058
$412$	−43.6155	−2.14878
$413$	11.1231	0.547332
$414$	−12.0000	−0.589768
$415$	0	0
$416$	−7.36932	−0.361310
$417$	3.75379	0.183824
$418$	85.4773	4.18083
$419$	−6.43845	−0.314539	−0.157269	−	0.987556i	$-0.550269\pi$
$419$	−6.43845	−0.314539	−0.157269	+	0.987556i	$0.550269\pi$
$420$	0	0
$421$	−30.8769	−1.50485	−0.752424	−	0.658679i	$-0.771115\pi$
$421$	−30.8769	−1.50485	−0.752424	+	0.658679i	$0.771115\pi$
$422$	−23.3693	−1.13760
$423$	−1.00000	−0.0486217
$424$	80.3542	3.90234
$425$	0	0
$426$	8.00000	0.387601
$427$	3.12311	0.151138
$428$	−7.12311	−0.344308
$429$	−6.24621	−0.301570
$430$	0	0
$431$	22.2462	1.07156	0.535781	−	0.844357i	$-0.320017\pi$
$431$	22.2462	1.07156	0.535781	+	0.844357i	$0.320017\pi$
$432$	7.68466	0.369728
$433$	28.2462	1.35743	0.678713	−	0.734403i	$-0.262538\pi$
$433$	28.2462	1.35743	0.678713	+	0.734403i	$0.262538\pi$
$434$	−4.49242	−0.215643
$435$	0	0
$436$	41.6155	1.99302
$437$	−28.1080	−1.34459
$438$	−23.3693	−1.11663
$439$	−35.8078	−1.70901	−0.854506	−	0.519442i	$-0.826140\pi$
$439$	−35.8078	−1.70901	−0.854506	+	0.519442i	$0.826140\pi$
$440$	0	0
$441$	−4.56155	−0.217217
$442$	14.7386	0.701045
$443$	−24.4924	−1.16367	−0.581835	−	0.813307i	$-0.697665\pi$
$443$	−24.4924	−1.16367	−0.581835	+	0.813307i	$0.697665\pi$
$444$	−34.4924	−1.63694
$445$	0	0
$446$	45.1231	2.13664
$447$	−11.3693	−0.537750
$448$	2.24621	0.106124
$449$	20.6847	0.976169	0.488085	−	0.872796i	$-0.337696\pi$
$449$	20.6847	0.976169	0.488085	+	0.872796i	$0.337696\pi$
$450$	0	0
$451$	39.6155	1.86542
$452$	40.4924	1.90460
$453$	8.24621	0.387441
$454$	−0.492423	−0.0231105
$455$	0	0
$456$	39.3693	1.84364
$457$	−27.1771	−1.27129	−0.635645	−	0.771981i	$-0.719266\pi$
$457$	−27.1771	−1.27129	−0.635645	+	0.771981i	$0.719266\pi$
$458$	−17.6155	−0.823120
$459$	−5.12311	−0.239126
$460$	0	0
$461$	0.192236	0.00895332	0.00447666	−	0.999990i	$-0.498575\pi$
$461$	0.192236	0.00895332	0.00447666	+	0.999990i	$0.498575\pi$
$462$	22.2462	1.03499
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	−73.4773	−3.41110
$465$	0	0
$466$	8.49242	0.393404
$467$	19.8078	0.916594	0.458297	−	0.888799i	$-0.348460\pi$
$467$	19.8078	0.916594	0.458297	+	0.888799i	$0.348460\pi$
$468$	−5.12311	−0.236816
$469$	−8.00000	−0.369406
$470$	0	0
$471$	−9.80776	−0.451918
$472$	46.7386	2.15132
$473$	−16.0000	−0.735681
$474$	−24.4924	−1.12497
$475$	0	0
$476$	−36.4924	−1.67263
$477$	12.2462	0.560715
$478$	−20.4924	−0.937302
$479$	17.3693	0.793624	0.396812	−	0.917900i	$-0.370116\pi$
$479$	17.3693	0.793624	0.396812	+	0.917900i	$0.370116\pi$
$480$	0	0
$481$	8.49242	0.387221
$482$	6.87689	0.313234
$483$	−7.31534	−0.332860
$484$	90.9157	4.13253
$485$	0	0
$486$	2.56155	0.116194
$487$	−22.7386	−1.03039	−0.515193	−	0.857074i	$-0.672280\pi$
$487$	−22.7386	−1.03039	−0.515193	+	0.857074i	$0.672280\pi$
$488$	13.1231	0.594055
$489$	−8.24621	−0.372907
$490$	0	0
$491$	−11.6155	−0.524201	−0.262101	−	0.965041i	$-0.584415\pi$
$491$	−11.6155	−0.524201	−0.262101	+	0.965041i	$0.584415\pi$
$492$	32.4924	1.46487
$493$	48.9848	2.20617
$494$	−17.2614	−0.776626
$495$	0	0
$496$	−8.63068	−0.387529
$497$	4.87689	0.218759
$498$	−18.2462	−0.817632
$499$	−17.6155	−0.788579	−0.394290	−	0.918986i	$-0.629009\pi$
$499$	−17.6155	−0.788579	−0.394290	+	0.918986i	$0.629009\pi$
$500$	0	0
$501$	12.6847	0.566709
$502$	−21.7538	−0.970919
$503$	15.3153	0.682877	0.341439	−	0.939904i	$-0.389086\pi$
$503$	15.3153	0.682877	0.341439	+	0.939904i	$0.389086\pi$
$504$	10.2462	0.456403
$505$	0	0
$506$	−66.7386	−2.96689
$507$	−11.7386	−0.521331
$508$	−5.12311	−0.227301
$509$	9.36932	0.415288	0.207644	−	0.978204i	$-0.433420\pi$
$509$	9.36932	0.415288	0.207644	+	0.978204i	$0.433420\pi$
$510$	0	0
$511$	−14.2462	−0.630215
$512$	−50.4233	−2.22842
$513$	6.00000	0.264906
$514$	22.2462	0.981238
$515$	0	0
$516$	−13.1231	−0.577713
$517$	−5.56155	−0.244597
$518$	−30.2462	−1.32894
$519$	−16.2462	−0.713130
$520$	0	0
$521$	42.4924	1.86163	0.930813	−	0.365495i	$-0.119100\pi$
$521$	42.4924	1.86163	0.930813	+	0.365495i	$0.119100\pi$
$522$	−24.4924	−1.07200
$523$	−18.0540	−0.789445	−0.394723	−	0.918800i	$-0.629159\pi$
$523$	−18.0540	−0.789445	−0.394723	+	0.918800i	$0.629159\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	−44.4924	−1.93996
$527$	5.75379	0.250639
$528$	42.7386	1.85996
$529$	−1.05398	−0.0458250
$530$	0	0
$531$	7.12311	0.309116
$532$	42.7386	1.85295
$533$	−8.00000	−0.346518
$534$	−21.1231	−0.914086
$535$	0	0
$536$	−33.6155	−1.45197
$537$	−0.192236	−0.00829559
$538$	8.63068	0.372095
$539$	−25.3693	−1.09273
$540$	0	0
$541$	−14.4924	−0.623078	−0.311539	−	0.950233i	$-0.600844\pi$
$541$	−14.4924	−0.623078	−0.311539	+	0.950233i	$0.600844\pi$
$542$	−24.4924	−1.05204
$543$	4.24621	0.182222
$544$	−33.6155	−1.44125
$545$	0	0
$546$	−4.49242	−0.192258
$547$	4.24621	0.181555	0.0907774	−	0.995871i	$-0.471065\pi$
$547$	4.24621	0.181555	0.0907774	+	0.995871i	$0.471065\pi$
$548$	105.477	4.50577
$549$	2.00000	0.0853579
$550$	0	0
$551$	−57.3693	−2.44402
$552$	−30.7386	−1.30832
$553$	−14.9309	−0.634925
$554$	26.8769	1.14189
$555$	0	0
$556$	17.1231	0.726181
$557$	−0.192236	−0.00814530	−0.00407265	−	0.999992i	$-0.501296\pi$
$557$	−0.192236	−0.00814530	−0.00407265	+	0.999992i	$0.501296\pi$
$558$	−2.87689	−0.121789
$559$	3.23106	0.136659
$560$	0	0
$561$	−28.4924	−1.20295
$562$	−24.4924	−1.03315
$563$	38.7386	1.63264	0.816319	−	0.577601i	$-0.196011\pi$
$563$	38.7386	1.63264	0.816319	+	0.577601i	$0.196011\pi$
$564$	−4.56155	−0.192076
$565$	0	0
$566$	28.0000	1.17693
$567$	1.56155	0.0655791
$568$	20.4924	0.859843
$569$	−11.3153	−0.474364	−0.237182	−	0.971465i	$-0.576224\pi$
$569$	−11.3153	−0.474364	−0.237182	+	0.971465i	$0.576224\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−28.4924	−1.19133
$573$	−20.4924	−0.856083
$574$	28.4924	1.18925
$575$	0	0
$576$	1.43845	0.0599353
$577$	−43.3693	−1.80549	−0.902744	−	0.430178i	$-0.858451\pi$
$577$	−43.3693	−1.80549	−0.902744	+	0.430178i	$0.858451\pi$
$578$	23.6847	0.985152
$579$	18.4924	0.768519
$580$	0	0
$581$	−11.1231	−0.461464
$582$	43.3693	1.79772
$583$	68.1080	2.82074
$584$	−59.8617	−2.47710
$585$	0	0
$586$	−7.50758	−0.310135
$587$	1.75379	0.0723866	0.0361933	−	0.999345i	$-0.488477\pi$
$587$	1.75379	0.0723866	0.0361933	+	0.999345i	$0.488477\pi$
$588$	−20.8078	−0.858098
$589$	−6.73863	−0.277661
$590$	0	0
$591$	2.00000	0.0822690
$592$	−58.1080	−2.38822
$593$	41.8617	1.71906	0.859528	−	0.511089i	$-0.170758\pi$
$593$	41.8617	1.71906	0.859528	+	0.511089i	$0.170758\pi$
$594$	14.2462	0.584529
$595$	0	0
$596$	−51.8617	−2.12434
$597$	−13.1231	−0.537093
$598$	13.4773	0.551126
$599$	−8.68466	−0.354846	−0.177423	−	0.984135i	$-0.556776\pi$
$599$	−8.68466	−0.354846	−0.177423	+	0.984135i	$0.556776\pi$
$600$	0	0
$601$	38.6847	1.57798	0.788990	−	0.614406i	$-0.210604\pi$
$601$	38.6847	1.57798	0.788990	+	0.614406i	$0.210604\pi$
$602$	−11.5076	−0.469014
$603$	−5.12311	−0.208629
$604$	37.6155	1.53055
$605$	0	0
$606$	27.8617	1.13181
$607$	29.6155	1.20206	0.601029	−	0.799228i	$-0.294758\pi$
$607$	29.6155	1.20206	0.601029	+	0.799228i	$0.294758\pi$
$608$	39.3693	1.59664
$609$	−14.9309	−0.605029
$610$	0	0
$611$	1.12311	0.0454360
$612$	−23.3693	−0.944649
$613$	−4.93087	−0.199156	−0.0995780	−	0.995030i	$-0.531749\pi$
$613$	−4.93087	−0.199156	−0.0995780	+	0.995030i	$0.531749\pi$
$614$	73.4773	2.96530
$615$	0	0
$616$	56.9848	2.29598
$617$	18.4924	0.744477	0.372238	−	0.928137i	$-0.378590\pi$
$617$	18.4924	0.744477	0.372238	+	0.928137i	$0.378590\pi$
$618$	−24.4924	−0.985230
$619$	30.9309	1.24322	0.621608	−	0.783328i	$-0.286480\pi$
$619$	30.9309	1.24322	0.621608	+	0.783328i	$0.286480\pi$
$620$	0	0
$621$	−4.68466	−0.187989
$622$	24.4924	0.982057
$623$	−12.8769	−0.515902
$624$	−8.63068	−0.345504
$625$	0	0
$626$	−5.12311	−0.204760
$627$	33.3693	1.33264
$628$	−44.7386	−1.78527
$629$	38.7386	1.54461
$630$	0	0
$631$	−33.2311	−1.32291	−0.661454	−	0.749986i	$-0.730060\pi$
$631$	−33.2311	−1.32291	−0.661454	+	0.749986i	$0.730060\pi$
$632$	−62.7386	−2.49561
$633$	−9.12311	−0.362611
$634$	−9.75379	−0.387372
$635$	0	0
$636$	55.8617	2.21506
$637$	5.12311	0.202985
$638$	−136.216	−5.39284
$639$	3.12311	0.123548
$640$	0	0
$641$	23.3153	0.920901	0.460450	−	0.887685i	$-0.347688\pi$
$641$	23.3153	0.920901	0.460450	+	0.887685i	$0.347688\pi$
$642$	−4.00000	−0.157867
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−33.3693	−1.31494
$645$	0	0
$646$	−78.7386	−3.09793
$647$	−14.6307	−0.575192	−0.287596	−	0.957752i	$-0.592856\pi$
$647$	−14.6307	−0.575192	−0.287596	+	0.957752i	$0.592856\pi$
$648$	6.56155	0.257762
$649$	39.6155	1.55505
$650$	0	0
$651$	−1.75379	−0.0687364
$652$	−37.6155	−1.47314
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	23.3693	0.913813
$655$	0	0
$656$	54.7386	2.13718
$657$	−9.12311	−0.355926
$658$	−4.00000	−0.155936
$659$	7.12311	0.277477	0.138738	−	0.990329i	$-0.455695\pi$
$659$	7.12311	0.277477	0.138738	+	0.990329i	$0.455695\pi$
$660$	0	0
$661$	−38.0000	−1.47803	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000	−1.47803	−0.739014	+	0.673690i	$0.764708\pi$
$662$	56.9848	2.21478
$663$	5.75379	0.223459
$664$	−46.7386	−1.81381
$665$	0	0
$666$	−19.3693	−0.750546
$667$	44.7926	1.73438
$668$	57.8617	2.23874
$669$	17.6155	0.681056
$670$	0	0
$671$	11.1231	0.429403
$672$	10.2462	0.395256
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	−47.8617	−1.84357
$675$	0	0
$676$	−53.5464	−2.05948
$677$	32.1080	1.23401	0.617004	−	0.786960i	$-0.288346\pi$
$677$	32.1080	1.23401	0.617004	+	0.786960i	$0.288346\pi$
$678$	22.7386	0.873272
$679$	26.4384	1.01461
$680$	0	0
$681$	−0.192236	−0.00736650
$682$	−16.0000	−0.612672
$683$	42.2462	1.61651	0.808253	−	0.588835i	$-0.200413\pi$
$683$	42.2462	1.61651	0.808253	+	0.588835i	$0.200413\pi$
$684$	27.3693	1.04649
$685$	0	0
$686$	−46.2462	−1.76569
$687$	−6.87689	−0.262370
$688$	−22.1080	−0.842858
$689$	−13.7538	−0.523978
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	−74.1080	−2.81716
$693$	8.68466	0.329903
$694$	−22.7386	−0.863147
$695$	0	0
$696$	−62.7386	−2.37810
$697$	−36.4924	−1.38225
$698$	65.6155	2.48358
$699$	3.31534	0.125398
$700$	0	0
$701$	20.6847	0.781249	0.390624	−	0.920550i	$-0.372259\pi$
$701$	20.6847	0.781249	0.390624	+	0.920550i	$0.372259\pi$
$702$	−2.87689	−0.108581
$703$	−45.3693	−1.71114
$704$	8.00000	0.301511
$705$	0	0
$706$	−59.8617	−2.25293
$707$	16.9848	0.638781
$708$	32.4924	1.22114
$709$	−12.9309	−0.485629	−0.242815	−	0.970073i	$-0.578071\pi$
$709$	−12.9309	−0.485629	−0.242815	+	0.970073i	$0.578071\pi$
$710$	0	0
$711$	−9.56155	−0.358586
$712$	−54.1080	−2.02778
$713$	5.26137	0.197040
$714$	−20.4924	−0.766910
$715$	0	0
$716$	−0.876894	−0.0327711
$717$	−8.00000	−0.298765
$718$	56.4924	2.10828
$719$	12.8769	0.480227	0.240114	−	0.970745i	$-0.422815\pi$
$719$	12.8769	0.480227	0.240114	+	0.970745i	$0.422815\pi$
$720$	0	0
$721$	−14.9309	−0.556055
$722$	43.5464	1.62063
$723$	2.68466	0.0998435
$724$	19.3693	0.719855
$725$	0	0
$726$	51.0540	1.89479
$727$	36.7386	1.36256	0.681280	−	0.732023i	$-0.261424\pi$
$727$	36.7386	1.36256	0.681280	+	0.732023i	$0.261424\pi$
$728$	−11.5076	−0.426499
$729$	1.00000	0.0370370
$730$	0	0
$731$	14.7386	0.545128
$732$	9.12311	0.337200
$733$	0.930870	0.0343825	0.0171912	−	0.999852i	$-0.494528\pi$
$733$	0.930870	0.0343825	0.0171912	+	0.999852i	$0.494528\pi$
$734$	−32.6307	−1.20442
$735$	0	0
$736$	−30.7386	−1.13304
$737$	−28.4924	−1.04953
$738$	18.2462	0.671652
$739$	32.1922	1.18421	0.592105	−	0.805861i	$-0.298297\pi$
$739$	32.1922	1.18421	0.592105	+	0.805861i	$0.298297\pi$
$740$	0	0
$741$	−6.73863	−0.247550
$742$	48.9848	1.79829
$743$	40.4924	1.48552	0.742761	−	0.669556i	$-0.233516\pi$
$743$	40.4924	1.48552	0.742761	+	0.669556i	$0.233516\pi$
$744$	−7.36932	−0.270172
$745$	0	0
$746$	−17.6155	−0.644950
$747$	−7.12311	−0.260621
$748$	−129.970	−4.75216
$749$	−2.43845	−0.0890989
$750$	0	0
$751$	42.1080	1.53654	0.768270	−	0.640125i	$-0.221118\pi$
$751$	42.1080	1.53654	0.768270	+	0.640125i	$0.221118\pi$
$752$	−7.68466	−0.280231
$753$	−8.49242	−0.309481
$754$	27.5076	1.00177
$755$	0	0
$756$	7.12311	0.259065
$757$	17.6155	0.640247	0.320124	−	0.947376i	$-0.396276\pi$
$757$	17.6155	0.640247	0.320124	+	0.947376i	$0.396276\pi$
$758$	−80.4924	−2.92362
$759$	−26.0540	−0.945699
$760$	0	0
$761$	34.1080	1.23641	0.618206	−	0.786016i	$-0.287860\pi$
$761$	34.1080	1.23641	0.618206	+	0.786016i	$0.287860\pi$
$762$	−2.87689	−0.104219
$763$	14.2462	0.515747
$764$	−93.4773	−3.38189
$765$	0	0
$766$	69.4773	2.51032
$767$	−8.00000	−0.288863
$768$	−27.0540	−0.976226
$769$	−36.7386	−1.32483	−0.662415	−	0.749138i	$-0.730468\pi$
$769$	−36.7386	−1.32483	−0.662415	+	0.749138i	$0.730468\pi$
$770$	0	0
$771$	8.68466	0.312770
$772$	84.3542	3.03597
$773$	20.2462	0.728206	0.364103	−	0.931359i	$-0.381376\pi$
$773$	20.2462	0.728206	0.364103	+	0.931359i	$0.381376\pi$
$774$	−7.36932	−0.264885
$775$	0	0
$776$	111.093	3.98800
$777$	−11.8078	−0.423601
$778$	−56.0000	−2.00770
$779$	42.7386	1.53127
$780$	0	0
$781$	17.3693	0.621523
$782$	61.4773	2.19842
$783$	−9.56155	−0.341702
$784$	−35.0540	−1.25193
$785$	0	0
$786$	2.24621	0.0801197
$787$	−3.75379	−0.133808	−0.0669041	−	0.997759i	$-0.521312\pi$
$787$	−3.75379	−0.133808	−0.0669041	+	0.997759i	$0.521312\pi$
$788$	9.12311	0.324997
$789$	−17.3693	−0.618364
$790$	0	0
$791$	13.8617	0.492867
$792$	36.4924	1.29670
$793$	−2.24621	−0.0797653
$794$	16.6307	0.590201
$795$	0	0
$796$	−59.8617	−2.12174
$797$	−23.3153	−0.825872	−0.412936	−	0.910760i	$-0.635497\pi$
$797$	−23.3153	−0.825872	−0.412936	+	0.910760i	$0.635497\pi$
$798$	24.0000	0.849591
$799$	5.12311	0.181242
$800$	0	0
$801$	−8.24621	−0.291366
$802$	42.8769	1.51404
$803$	−50.7386	−1.79053
$804$	−23.3693	−0.824172
$805$	0	0
$806$	3.23106	0.113809
$807$	3.36932	0.118606
$808$	71.3693	2.51076
$809$	−35.4233	−1.24542	−0.622708	−	0.782454i	$-0.713968\pi$
$809$	−35.4233	−1.24542	−0.622708	+	0.782454i	$0.713968\pi$
$810$	0	0
$811$	51.8078	1.81922	0.909608	−	0.415467i	$-0.136382\pi$
$811$	51.8078	1.81922	0.909608	+	0.415467i	$0.136382\pi$
$812$	−68.1080	−2.39012
$813$	−9.56155	−0.335338
$814$	−107.723	−3.77571
$815$	0	0
$816$	−39.3693	−1.37820
$817$	−17.2614	−0.603899
$818$	−46.1080	−1.61213
$819$	−1.75379	−0.0612823
$820$	0	0
$821$	−35.1231	−1.22580	−0.612902	−	0.790159i	$-0.709998\pi$
$821$	−35.1231	−1.22580	−0.612902	+	0.790159i	$0.709998\pi$
$822$	59.2311	2.06592
$823$	−0.684658	−0.0238657	−0.0119328	−	0.999929i	$-0.503798\pi$
$823$	−0.684658	−0.0238657	−0.0119328	+	0.999929i	$0.503798\pi$
$824$	−62.7386	−2.18560
$825$	0	0
$826$	28.4924	0.991378
$827$	1.26137	0.0438620	0.0219310	−	0.999759i	$-0.493019\pi$
$827$	1.26137	0.0438620	0.0219310	+	0.999759i	$0.493019\pi$
$828$	−21.3693	−0.742635
$829$	−5.50758	−0.191286	−0.0956430	−	0.995416i	$-0.530491\pi$
$829$	−5.50758	−0.191286	−0.0956430	+	0.995416i	$0.530491\pi$
$830$	0	0
$831$	10.4924	0.363978
$832$	−1.61553	−0.0560084
$833$	23.3693	0.809699
$834$	9.61553	0.332959
$835$	0	0
$836$	152.216	5.26450
$837$	−1.12311	−0.0388202
$838$	−16.4924	−0.569721
$839$	51.8078	1.78860	0.894301	−	0.447465i	$-0.147673\pi$
$839$	51.8078	1.78860	0.894301	+	0.447465i	$0.147673\pi$
$840$	0	0
$841$	62.4233	2.15253
$842$	−79.0928	−2.72572
$843$	−9.56155	−0.329317
$844$	−41.6155	−1.43247
$845$	0	0
$846$	−2.56155	−0.0880680
$847$	31.1231	1.06940
$848$	94.1080	3.23168
$849$	10.9309	0.375146
$850$	0	0
$851$	35.4233	1.21429
$852$	14.2462	0.488067
$853$	−51.4773	−1.76255	−0.881274	−	0.472606i	$-0.843314\pi$
$853$	−51.4773	−1.76255	−0.881274	+	0.472606i	$0.843314\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	−10.2462	−0.350208
$857$	−6.43845	−0.219933	−0.109967	−	0.993935i	$-0.535074\pi$
$857$	−6.43845	−0.219933	−0.109967	+	0.993935i	$0.535074\pi$
$858$	−16.0000	−0.546231
$859$	18.9848	0.647755	0.323877	−	0.946099i	$-0.395014\pi$
$859$	18.9848	0.647755	0.323877	+	0.946099i	$0.395014\pi$
$860$	0	0
$861$	11.1231	0.379074
$862$	56.9848	1.94091
$863$	20.1080	0.684483	0.342241	−	0.939612i	$-0.388814\pi$
$863$	20.1080	0.684483	0.342241	+	0.939612i	$0.388814\pi$
$864$	6.56155	0.223229
$865$	0	0
$866$	72.3542	2.45869
$867$	9.24621	0.314018
$868$	−8.00000	−0.271538
$869$	−53.1771	−1.80391
$870$	0	0
$871$	5.75379	0.194960
$872$	59.8617	2.02717
$873$	16.9309	0.573023
$874$	−72.0000	−2.43544
$875$	0	0
$876$	−41.6155	−1.40606
$877$	−40.2462	−1.35902	−0.679509	−	0.733667i	$-0.737807\pi$
$877$	−40.2462	−1.35902	−0.679509	+	0.733667i	$0.737807\pi$
$878$	−91.7235	−3.09552
$879$	−2.93087	−0.0988558
$880$	0	0
$881$	−15.8078	−0.532577	−0.266289	−	0.963893i	$-0.585797\pi$
$881$	−15.8078	−0.532577	−0.266289	+	0.963893i	$0.585797\pi$
$882$	−11.6847	−0.393443
$883$	4.00000	0.134611	0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000	0.134611	0.0673054	+	0.997732i	$0.478560\pi$
$884$	26.2462	0.882756
$885$	0	0
$886$	−62.7386	−2.10775
$887$	−4.49242	−0.150841	−0.0754204	−	0.997152i	$-0.524030\pi$
$887$	−4.49242	−0.150841	−0.0754204	+	0.997152i	$0.524030\pi$
$888$	−49.6155	−1.66499
$889$	−1.75379	−0.0588202
$890$	0	0
$891$	5.56155	0.186319
$892$	80.3542	2.69046
$893$	−6.00000	−0.200782
$894$	−29.1231	−0.974022
$895$	0	0
$896$	−14.7386	−0.492383
$897$	5.26137	0.175672
$898$	52.9848	1.76813
$899$	10.7386	0.358153
$900$	0	0
$901$	−62.7386	−2.09013
$902$	101.477	3.37882
$903$	−4.49242	−0.149498
$904$	58.2462	1.93724
$905$	0	0
$906$	21.1231	0.701768
$907$	−37.1771	−1.23444	−0.617222	−	0.786789i	$-0.711742\pi$
$907$	−37.1771	−1.23444	−0.617222	+	0.786789i	$0.711742\pi$
$908$	−0.876894	−0.0291008
$909$	10.8769	0.360764
$910$	0	0
$911$	−34.7386	−1.15094	−0.575471	−	0.817822i	$-0.695181\pi$
$911$	−34.7386	−1.15094	−0.575471	+	0.817822i	$0.695181\pi$
$912$	46.1080	1.52679
$913$	−39.6155	−1.31108
$914$	−69.6155	−2.30268
$915$	0	0
$916$	−31.3693	−1.03647
$917$	1.36932	0.0452188
$918$	−13.1231	−0.433127
$919$	13.6155	0.449135	0.224567	−	0.974459i	$-0.427903\pi$
$919$	13.6155	0.449135	0.224567	+	0.974459i	$0.427903\pi$
$920$	0	0
$921$	28.6847	0.945192
$922$	0.492423	0.0162171
$923$	−3.50758	−0.115453
$924$	39.6155	1.30326
$925$	0	0
$926$	35.8617	1.17849
$927$	−9.56155	−0.314043
$928$	−62.7386	−2.05950
$929$	−15.8617	−0.520407	−0.260203	−	0.965554i	$-0.583790\pi$
$929$	−15.8617	−0.520407	−0.260203	+	0.965554i	$0.583790\pi$
$930$	0	0
$931$	−27.3693	−0.896993
$932$	15.1231	0.495374
$933$	9.56155	0.313031
$934$	50.7386	1.66022
$935$	0	0
$936$	−7.36932	−0.240874
$937$	40.7386	1.33087	0.665437	−	0.746454i	$-0.268245\pi$
$937$	40.7386	1.33087	0.665437	+	0.746454i	$0.268245\pi$
$938$	−20.4924	−0.669101
$939$	−2.00000	−0.0652675
$940$	0	0
$941$	2.00000	0.0651981	0.0325991	−	0.999469i	$-0.489622\pi$
$941$	2.00000	0.0651981	0.0325991	+	0.999469i	$0.489622\pi$
$942$	−25.1231	−0.818555
$943$	−33.3693	−1.08665
$944$	54.7386	1.78159
$945$	0	0
$946$	−40.9848	−1.33253
$947$	−58.2462	−1.89275	−0.946374	−	0.323074i	$-0.895284\pi$
$947$	−58.2462	−1.89275	−0.946374	+	0.323074i	$0.895284\pi$
$948$	−43.6155	−1.41657
$949$	10.2462	0.332606
$950$	0	0
$951$	−3.80776	−0.123475
$952$	−52.4924	−1.70129
$953$	32.7926	1.06226	0.531128	−	0.847291i	$-0.321768\pi$
$953$	32.7926	1.06226	0.531128	+	0.847291i	$0.321768\pi$
$954$	31.3693	1.01562
$955$	0	0
$956$	−36.4924	−1.18025
$957$	−53.1771	−1.71897
$958$	44.4924	1.43748
$959$	36.1080	1.16599
$960$	0	0
$961$	−29.7386	−0.959311
$962$	21.7538	0.701370
$963$	−1.56155	−0.0503203
$964$	12.2462	0.394424
$965$	0	0
$966$	−18.7386	−0.602906
$967$	−38.0540	−1.22373	−0.611867	−	0.790961i	$-0.709581\pi$
$967$	−38.0540	−1.22373	−0.611867	+	0.790961i	$0.709581\pi$
$968$	130.777	4.20335
$969$	−30.7386	−0.987467
$970$	0	0
$971$	−42.9309	−1.37772	−0.688859	−	0.724896i	$-0.741888\pi$
$971$	−42.9309	−1.37772	−0.688859	+	0.724896i	$0.741888\pi$
$972$	4.56155	0.146312
$973$	5.86174	0.187919
$974$	−58.2462	−1.86633
$975$	0	0
$976$	15.3693	0.491960
$977$	48.7386	1.55929	0.779644	−	0.626224i	$-0.215400\pi$
$977$	48.7386	1.55929	0.779644	+	0.626224i	$0.215400\pi$
$978$	−21.1231	−0.675442
$979$	−45.8617	−1.46575
$980$	0	0
$981$	9.12311	0.291278
$982$	−29.7538	−0.949482
$983$	−52.0000	−1.65854	−0.829271	−	0.558846i	$-0.811244\pi$
$983$	−52.0000	−1.65854	−0.829271	+	0.558846i	$0.811244\pi$
$984$	46.7386	1.48997
$985$	0	0
$986$	125.477	3.99601
$987$	−1.56155	−0.0497048
$988$	−30.7386	−0.977926
$989$	13.4773	0.428552
$990$	0	0
$991$	−2.43845	−0.0774598	−0.0387299	−	0.999250i	$-0.512331\pi$
$991$	−2.43845	−0.0774598	−0.0387299	+	0.999250i	$0.512331\pi$
$992$	−7.36932	−0.233976
$993$	22.2462	0.705962
$994$	12.4924	0.396236
$995$	0	0
$996$	−32.4924	−1.02956
$997$	1.12311	0.0355691	0.0177846	−	0.999842i	$-0.494339\pi$
$997$	1.12311	0.0355691	0.0177846	+	0.999842i	$0.494339\pi$
$998$	−45.1231	−1.42835
$999$	−7.56155	−0.239237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.q.1.2		2
5.4	even	2		141.2.a.f.1.1	✓	2
15.14	odd	2		423.2.a.h.1.2		2
20.19	odd	2		2256.2.a.s.1.1		2
35.34	odd	2		6909.2.a.m.1.1		2
40.19	odd	2		9024.2.a.ca.1.2		2
40.29	even	2		9024.2.a.cf.1.2		2
60.59	even	2		6768.2.a.y.1.2		2
235.234	odd	2		6627.2.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
141.2.a.f.1.1	✓	2	5.4	even	2
423.2.a.h.1.2		2	15.14	odd	2
2256.2.a.s.1.1		2	20.19	odd	2
3525.2.a.q.1.2		2	1.1	even	1	trivial
6627.2.a.k.1.1		2	235.234	odd	2
6768.2.a.y.1.2		2	60.59	even	2
6909.2.a.m.1.1		2	35.34	odd	2
9024.2.a.ca.1.2		2	40.19	odd	2
9024.2.a.cf.1.2		2	40.29	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} +2.56155 q^{6} +1.56155 q^{7} +6.56155 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} +2.56155 q^{6} +1.56155 q^{7} +6.56155 q^{8} +1.00000 q^{9} +5.56155 q^{11} +4.56155 q^{12} -1.12311 q^{13} +4.00000 q^{14} +7.68466 q^{16} -5.12311 q^{17} +2.56155 q^{18} +6.00000 q^{19} +1.56155 q^{21} +14.2462 q^{22} -4.68466 q^{23} +6.56155 q^{24} -2.87689 q^{26} +1.00000 q^{27} +7.12311 q^{28} -9.56155 q^{29} -1.12311 q^{31} +6.56155 q^{32} +5.56155 q^{33} -13.1231 q^{34} +4.56155 q^{36} -7.56155 q^{37} +15.3693 q^{38} -1.12311 q^{39} +7.12311 q^{41} +4.00000 q^{42} -2.87689 q^{43} +25.3693 q^{44} -12.0000 q^{46} -1.00000 q^{47} +7.68466 q^{48} -4.56155 q^{49} -5.12311 q^{51} -5.12311 q^{52} +12.2462 q^{53} +2.56155 q^{54} +10.2462 q^{56} +6.00000 q^{57} -24.4924 q^{58} +7.12311 q^{59} +2.00000 q^{61} -2.87689 q^{62} +1.56155 q^{63} +1.43845 q^{64} +14.2462 q^{66} -5.12311 q^{67} -23.3693 q^{68} -4.68466 q^{69} +3.12311 q^{71} +6.56155 q^{72} -9.12311 q^{73} -19.3693 q^{74} +27.3693 q^{76} +8.68466 q^{77} -2.87689 q^{78} -9.56155 q^{79} +1.00000 q^{81} +18.2462 q^{82} -7.12311 q^{83} +7.12311 q^{84} -7.36932 q^{86} -9.56155 q^{87} +36.4924 q^{88} -8.24621 q^{89} -1.75379 q^{91} -21.3693 q^{92} -1.12311 q^{93} -2.56155 q^{94} +6.56155 q^{96} +16.9309 q^{97} -11.6847 q^{98} +5.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} + 5 q^{4} + q^{6} - q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 + 5 * q^4 + q^6 - q^7 + 9 * q^8 + 2 * q^9	\( 2 q + q^{2} + 2 q^{3} + 5 q^{4} + q^{6} - q^{7} + 9 q^{8} + 2 q^{9} + 7 q^{11} + 5 q^{12} + 6 q^{13} + 8 q^{14} + 3 q^{16} - 2 q^{17} + q^{18} + 12 q^{19} - q^{21} + 12 q^{22} + 3 q^{23} + 9 q^{24} - 14 q^{26} + 2 q^{27} + 6 q^{28} - 15 q^{29} + 6 q^{31} + 9 q^{32} + 7 q^{33} - 18 q^{34} + 5 q^{36} - 11 q^{37} + 6 q^{38} + 6 q^{39} + 6 q^{41} + 8 q^{42} - 14 q^{43} + 26 q^{44} - 24 q^{46} - 2 q^{47} + 3 q^{48} - 5 q^{49} - 2 q^{51} - 2 q^{52} + 8 q^{53} + q^{54} + 4 q^{56} + 12 q^{57} - 16 q^{58} + 6 q^{59} + 4 q^{61} - 14 q^{62} - q^{63} + 7 q^{64} + 12 q^{66} - 2 q^{67} - 22 q^{68} + 3 q^{69} - 2 q^{71} + 9 q^{72} - 10 q^{73} - 14 q^{74} + 30 q^{76} + 5 q^{77} - 14 q^{78} - 15 q^{79} + 2 q^{81} + 20 q^{82} - 6 q^{83} + 6 q^{84} + 10 q^{86} - 15 q^{87} + 40 q^{88} - 20 q^{91} - 18 q^{92} + 6 q^{93} - q^{94} + 9 q^{96} + 5 q^{97} - 11 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 + 5 * q^4 + q^6 - q^7 + 9 * q^8 + 2 * q^9 + 7 * q^11 + 5 * q^12 + 6 * q^13 + 8 * q^14 + 3 * q^16 - 2 * q^17 + q^18 + 12 * q^19 - q^21 + 12 * q^22 + 3 * q^23 + 9 * q^24 - 14 * q^26 + 2 * q^27 + 6 * q^28 - 15 * q^29 + 6 * q^31 + 9 * q^32 + 7 * q^33 - 18 * q^34 + 5 * q^36 - 11 * q^37 + 6 * q^38 + 6 * q^39 + 6 * q^41 + 8 * q^42 - 14 * q^43 + 26 * q^44 - 24 * q^46 - 2 * q^47 + 3 * q^48 - 5 * q^49 - 2 * q^51 - 2 * q^52 + 8 * q^53 + q^54 + 4 * q^56 + 12 * q^57 - 16 * q^58 + 6 * q^59 + 4 * q^61 - 14 * q^62 - q^63 + 7 * q^64 + 12 * q^66 - 2 * q^67 - 22 * q^68 + 3 * q^69 - 2 * q^71 + 9 * q^72 - 10 * q^73 - 14 * q^74 + 30 * q^76 + 5 * q^77 - 14 * q^78 - 15 * q^79 + 2 * q^81 + 20 * q^82 - 6 * q^83 + 6 * q^84 + 10 * q^86 - 15 * q^87 + 40 * q^88 - 20 * q^91 - 18 * q^92 + 6 * q^93 - q^94 + 9 * q^96 + 5 * q^97 - 11 * q^98 + 7 * q^99

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