LMFDB - Embedded newform 3525.2.a.be.1.6

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 $ x^8 - 3x^7 - 7x^6 + 24x^5 + 8x^4 - 47x^3 + 8x^2 + 13*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.60965$ 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)

$f(q)$	$=$	$q+1.60965 q^{2} -1.00000 q^{3} +0.590961 q^{4} -1.60965 q^{6} +2.89141 q^{7} -2.26805 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.60965 q^{2} -1.00000 q^{3} +0.590961 q^{4} -1.60965 q^{6} +2.89141 q^{7} -2.26805 q^{8} +1.00000 q^{9} -2.05110 q^{11} -0.590961 q^{12} +4.52660 q^{13} +4.65415 q^{14} -4.83269 q^{16} -4.14437 q^{17} +1.60965 q^{18} +3.21947 q^{19} -2.89141 q^{21} -3.30155 q^{22} +2.15638 q^{23} +2.26805 q^{24} +7.28623 q^{26} -1.00000 q^{27} +1.70871 q^{28} +9.10114 q^{29} +0.697696 q^{31} -3.24281 q^{32} +2.05110 q^{33} -6.67097 q^{34} +0.590961 q^{36} -8.61642 q^{37} +5.18220 q^{38} -4.52660 q^{39} +3.28361 q^{41} -4.65415 q^{42} +4.46014 q^{43} -1.21212 q^{44} +3.47101 q^{46} +1.00000 q^{47} +4.83269 q^{48} +1.36026 q^{49} +4.14437 q^{51} +2.67505 q^{52} +2.71638 q^{53} -1.60965 q^{54} -6.55788 q^{56} -3.21947 q^{57} +14.6496 q^{58} -8.56992 q^{59} +8.48391 q^{61} +1.12304 q^{62} +2.89141 q^{63} +4.44560 q^{64} +3.30155 q^{66} +13.9564 q^{67} -2.44916 q^{68} -2.15638 q^{69} -15.7695 q^{71} -2.26805 q^{72} +8.88127 q^{73} -13.8694 q^{74} +1.90258 q^{76} -5.93059 q^{77} -7.28623 q^{78} +15.6685 q^{79} +1.00000 q^{81} +5.28545 q^{82} +5.17115 q^{83} -1.70871 q^{84} +7.17925 q^{86} -9.10114 q^{87} +4.65202 q^{88} +14.5447 q^{89} +13.0883 q^{91} +1.27434 q^{92} -0.697696 q^{93} +1.60965 q^{94} +3.24281 q^{96} -0.136874 q^{97} +2.18954 q^{98} -2.05110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * 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 $

$2$	1.60965	1.13819	0.569096	−	0.822271i	$-0.307293\pi$
$2$	1.60965	1.13819	0.569096	+	0.822271i	$0.307293\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.590961	0.295481
$5$	0	0
$5$	0	0
$6$	−1.60965	−0.657135
$7$	2.89141	1.09285	0.546425	−	0.837508i	$-0.315988\pi$
$7$	2.89141	1.09285	0.546425	+	0.837508i	$0.315988\pi$
$8$	−2.26805	−0.801878
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.05110	−0.618431	−0.309216	−	0.950992i	$-0.600066\pi$
$11$	−2.05110	−0.618431	−0.309216	+	0.950992i	$0.600066\pi$
$12$	−0.590961	−0.170596
$13$	4.52660	1.25545	0.627727	−	0.778434i	$-0.283985\pi$
$13$	4.52660	1.25545	0.627727	+	0.778434i	$0.283985\pi$
$14$	4.65415	1.24387
$15$	0	0
$16$	−4.83269	−1.20817
$17$	−4.14437	−1.00516	−0.502579	−	0.864532i	$-0.667615\pi$
$17$	−4.14437	−1.00516	−0.502579	+	0.864532i	$0.667615\pi$
$18$	1.60965	0.379397
$19$	3.21947	0.738597	0.369298	−	0.929311i	$-0.379598\pi$
$19$	3.21947	0.738597	0.369298	+	0.929311i	$0.379598\pi$
$20$	0	0
$21$	−2.89141	−0.630958
$22$	−3.30155	−0.703893
$23$	2.15638	0.449637	0.224818	−	0.974401i	$-0.427821\pi$
$23$	2.15638	0.449637	0.224818	+	0.974401i	$0.427821\pi$
$24$	2.26805	0.462965
$25$	0	0
$26$	7.28623	1.42895
$27$	−1.00000	−0.192450
$28$	1.70871	0.322916
$29$	9.10114	1.69004	0.845020	−	0.534735i	$-0.179589\pi$
$29$	9.10114	1.69004	0.845020	+	0.534735i	$0.179589\pi$
$30$	0	0
$31$	0.697696	0.125310	0.0626550	−	0.998035i	$-0.480043\pi$
$31$	0.697696	0.125310	0.0626550	+	0.998035i	$0.480043\pi$
$32$	−3.24281	−0.573253
$33$	2.05110	0.357052
$34$	−6.67097	−1.14406
$35$	0	0
$36$	0.590961	0.0984935
$37$	−8.61642	−1.41653	−0.708265	−	0.705946i	$-0.750522\pi$
$37$	−8.61642	−1.41653	−0.708265	+	0.705946i	$0.750522\pi$
$38$	5.18220	0.840665
$39$	−4.52660	−0.724837
$40$	0	0
$41$	3.28361	0.512813	0.256407	−	0.966569i	$-0.417461\pi$
$41$	3.28361	0.512813	0.256407	+	0.966569i	$0.417461\pi$
$42$	−4.65415	−0.718151
$43$	4.46014	0.680166	0.340083	−	0.940396i	$-0.389545\pi$
$43$	4.46014	0.680166	0.340083	+	0.940396i	$0.389545\pi$
$44$	−1.21212	−0.182734
$45$	0	0
$46$	3.47101	0.511773
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	4.83269	0.697538
$49$	1.36026	0.194323
$50$	0	0
$51$	4.14437	0.580328
$52$	2.67505	0.370962
$53$	2.71638	0.373124	0.186562	−	0.982443i	$-0.440266\pi$
$53$	2.71638	0.373124	0.186562	+	0.982443i	$0.440266\pi$
$54$	−1.60965	−0.219045
$55$	0	0
$56$	−6.55788	−0.876333
$57$	−3.21947	−0.426429
$58$	14.6496	1.92359
$59$	−8.56992	−1.11571	−0.557854	−	0.829939i	$-0.688375\pi$
$59$	−8.56992	−1.11571	−0.557854	+	0.829939i	$0.688375\pi$
$60$	0	0
$61$	8.48391	1.08625	0.543127	−	0.839651i	$-0.317240\pi$
$61$	8.48391	1.08625	0.543127	+	0.839651i	$0.317240\pi$
$62$	1.12304	0.142627
$63$	2.89141	0.364284
$64$	4.44560	0.555700
$65$	0	0
$66$	3.30155	0.406393
$67$	13.9564	1.70505	0.852524	−	0.522687i	$-0.175071\pi$
$67$	13.9564	1.70505	0.852524	+	0.522687i	$0.175071\pi$
$68$	−2.44916	−0.297004
$69$	−2.15638	−0.259598
$70$	0	0
$71$	−15.7695	−1.87149	−0.935746	−	0.352674i	$-0.885273\pi$
$71$	−15.7695	−1.87149	−0.935746	+	0.352674i	$0.885273\pi$
$72$	−2.26805	−0.267293
$73$	8.88127	1.03947	0.519737	−	0.854326i	$-0.326030\pi$
$73$	8.88127	1.03947	0.519737	+	0.854326i	$0.326030\pi$
$74$	−13.8694	−1.61228
$75$	0	0
$76$	1.90258	0.218241
$77$	−5.93059	−0.675853
$78$	−7.28623	−0.825003
$79$	15.6685	1.76284	0.881421	−	0.472332i	$-0.156588\pi$
$79$	15.6685	1.76284	0.881421	+	0.472332i	$0.156588\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.28545	0.583680
$83$	5.17115	0.567607	0.283804	−	0.958882i	$-0.408404\pi$
$83$	5.17115	0.567607	0.283804	+	0.958882i	$0.408404\pi$
$84$	−1.70871	−0.186436
$85$	0	0
$86$	7.17925	0.774159
$87$	−9.10114	−0.975745
$88$	4.65202	0.495907
$89$	14.5447	1.54174	0.770868	−	0.636994i	$-0.219823\pi$
$89$	14.5447	1.54174	0.770868	+	0.636994i	$0.219823\pi$
$90$	0	0
$91$	13.0883	1.37202
$92$	1.27434	0.132859
$93$	−0.697696	−0.0723477
$94$	1.60965	0.166022
$95$	0	0
$96$	3.24281	0.330968
$97$	−0.136874	−0.0138975	−0.00694874	−	0.999976i	$-0.502212\pi$
$97$	−0.136874	−0.0138975	−0.00694874	+	0.999976i	$0.502212\pi$
$98$	2.18954	0.221177
$99$	−2.05110	−0.206144
$100$	0	0
$101$	−7.06652	−0.703145	−0.351572	−	0.936161i	$-0.614353\pi$
$101$	−7.06652	−0.703145	−0.351572	+	0.936161i	$0.614353\pi$
$102$	6.67097	0.660524
$103$	8.01574	0.789814	0.394907	−	0.918721i	$-0.370777\pi$
$103$	8.01574	0.789814	0.394907	+	0.918721i	$0.370777\pi$
$104$	−10.2666	−1.00672
$105$	0	0
$106$	4.37241	0.424686
$107$	19.7935	1.91351	0.956753	−	0.290900i	$-0.0939547\pi$
$107$	19.7935	1.91351	0.956753	+	0.290900i	$0.0939547\pi$
$108$	−0.590961	−0.0568653
$109$	−1.61314	−0.154511	−0.0772554	−	0.997011i	$-0.524616\pi$
$109$	−1.61314	−0.154511	−0.0772554	+	0.997011i	$0.524616\pi$
$110$	0	0
$111$	8.61642	0.817835
$112$	−13.9733	−1.32035
$113$	−6.17689	−0.581073	−0.290536	−	0.956864i	$-0.593834\pi$
$113$	−6.17689	−0.581073	−0.290536	+	0.956864i	$0.593834\pi$
$114$	−5.18220	−0.485358
$115$	0	0
$116$	5.37842	0.499374
$117$	4.52660	0.418485
$118$	−13.7945	−1.26989
$119$	−11.9831	−1.09849
$120$	0	0
$121$	−6.79297	−0.617543
$122$	13.6561	1.23636
$123$	−3.28361	−0.296073
$124$	0.412311	0.0370266
$125$	0	0
$126$	4.65415	0.414625
$127$	7.60694	0.675006	0.337503	−	0.941324i	$-0.390418\pi$
$127$	7.60694	0.675006	0.337503	+	0.941324i	$0.390418\pi$
$128$	13.6415	1.20575
$129$	−4.46014	−0.392694
$130$	0	0
$131$	−16.1974	−1.41517	−0.707585	−	0.706628i	$-0.750215\pi$
$131$	−16.1974	−1.41517	−0.707585	+	0.706628i	$0.750215\pi$
$132$	1.21212	0.105502
$133$	9.30881	0.807176
$134$	22.4649	1.94067
$135$	0	0
$136$	9.39965	0.806014
$137$	13.7313	1.17315	0.586573	−	0.809896i	$-0.300477\pi$
$137$	13.7313	1.17315	0.586573	+	0.809896i	$0.300477\pi$
$138$	−3.47101	−0.295472
$139$	0.415128	0.0352107	0.0176053	−	0.999845i	$-0.494396\pi$
$139$	0.415128	0.0352107	0.0176053	+	0.999845i	$0.494396\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−25.3833	−2.13012
$143$	−9.28454	−0.776412
$144$	−4.83269	−0.402724
$145$	0	0
$146$	14.2957	1.18312
$147$	−1.36026	−0.112192
$148$	−5.09197	−0.418557
$149$	−7.34727	−0.601911	−0.300956	−	0.953638i	$-0.597306\pi$
$149$	−7.34727	−0.601911	−0.300956	+	0.953638i	$0.597306\pi$
$150$	0	0
$151$	5.58738	0.454695	0.227347	−	0.973814i	$-0.426995\pi$
$151$	5.58738	0.454695	0.227347	+	0.973814i	$0.426995\pi$
$152$	−7.30193	−0.592265
$153$	−4.14437	−0.335052
$154$	−9.54615	−0.769251
$155$	0	0
$156$	−2.67505	−0.214175
$157$	−13.6795	−1.09175	−0.545873	−	0.837868i	$-0.683802\pi$
$157$	−13.6795	−1.09175	−0.545873	+	0.837868i	$0.683802\pi$
$158$	25.2207	2.00645
$159$	−2.71638	−0.215423
$160$	0	0
$161$	6.23499	0.491386
$162$	1.60965	0.126466
$163$	−17.5811	−1.37706	−0.688530	−	0.725208i	$-0.741744\pi$
$163$	−17.5811	−1.37706	−0.688530	+	0.725208i	$0.741744\pi$
$164$	1.94048	0.151526
$165$	0	0
$166$	8.32372	0.646046
$167$	1.61778	0.125188	0.0625938	−	0.998039i	$-0.480063\pi$
$167$	1.61778	0.125188	0.0625938	+	0.998039i	$0.480063\pi$
$168$	6.55788	0.505951
$169$	7.49013	0.576164
$170$	0	0
$171$	3.21947	0.246199
$172$	2.63577	0.200976
$173$	11.9840	0.911129	0.455565	−	0.890203i	$-0.349437\pi$
$173$	11.9840	0.911129	0.455565	+	0.890203i	$0.349437\pi$
$174$	−14.6496	−1.11058
$175$	0	0
$176$	9.91235	0.747171
$177$	8.56992	0.644154
$178$	23.4118	1.75479
$179$	13.5550	1.01315	0.506574	−	0.862197i	$-0.330912\pi$
$179$	13.5550	1.01315	0.506574	+	0.862197i	$0.330912\pi$
$180$	0	0
$181$	−5.72613	−0.425620	−0.212810	−	0.977094i	$-0.568262\pi$
$181$	−5.72613	−0.425620	−0.212810	+	0.977094i	$0.568262\pi$
$182$	21.0675	1.56163
$183$	−8.48391	−0.627149
$184$	−4.89079	−0.360554
$185$	0	0
$186$	−1.12304	−0.0823456
$187$	8.50054	0.621621
$188$	0.590961	0.0431003
$189$	−2.89141	−0.210319
$190$	0	0
$191$	8.20512	0.593701	0.296851	−	0.954924i	$-0.404064\pi$
$191$	8.20512	0.593701	0.296851	+	0.954924i	$0.404064\pi$
$192$	−4.44560	−0.320834
$193$	21.2576	1.53016	0.765079	−	0.643936i	$-0.222700\pi$
$193$	21.2576	1.53016	0.765079	+	0.643936i	$0.222700\pi$
$194$	−0.220319	−0.0158180
$195$	0	0
$196$	0.803861	0.0574186
$197$	3.62958	0.258597	0.129298	−	0.991606i	$-0.458727\pi$
$197$	3.62958	0.258597	0.129298	+	0.991606i	$0.458727\pi$
$198$	−3.30155	−0.234631
$199$	3.79766	0.269209	0.134605	−	0.990899i	$-0.457024\pi$
$199$	3.79766	0.269209	0.134605	+	0.990899i	$0.457024\pi$
$200$	0	0
$201$	−13.9564	−0.984410
$202$	−11.3746	−0.800314
$203$	26.3151	1.84696
$204$	2.44916	0.171476
$205$	0	0
$206$	12.9025	0.898960
$207$	2.15638	0.149879
$208$	−21.8757	−1.51680
$209$	−6.60347	−0.456771
$210$	0	0
$211$	14.6034	1.00534	0.502669	−	0.864479i	$-0.332352\pi$
$211$	14.6034	1.00534	0.502669	+	0.864479i	$0.332352\pi$
$212$	1.60528	0.110251
$213$	15.7695	1.08051
$214$	31.8605	2.17794
$215$	0	0
$216$	2.26805	0.154322
$217$	2.01733	0.136945
$218$	−2.59658	−0.175863
$219$	−8.88127	−0.600140
$220$	0	0
$221$	−18.7599	−1.26193
$222$	13.8694	0.930853
$223$	23.7647	1.59140	0.795701	−	0.605689i	$-0.207102\pi$
$223$	23.7647	1.59140	0.795701	+	0.605689i	$0.207102\pi$
$224$	−9.37629	−0.626480
$225$	0	0
$226$	−9.94261	−0.661372
$227$	−6.10001	−0.404872	−0.202436	−	0.979295i	$-0.564886\pi$
$227$	−6.10001	−0.404872	−0.202436	+	0.979295i	$0.564886\pi$
$228$	−1.90258	−0.126001
$229$	−22.3505	−1.47696	−0.738482	−	0.674274i	$-0.764457\pi$
$229$	−22.3505	−1.47696	−0.738482	+	0.674274i	$0.764457\pi$
$230$	0	0
$231$	5.93059	0.390204
$232$	−20.6419	−1.35521
$233$	6.55140	0.429197	0.214598	−	0.976702i	$-0.431156\pi$
$233$	6.55140	0.429197	0.214598	+	0.976702i	$0.431156\pi$
$234$	7.28623	0.476316
$235$	0	0
$236$	−5.06449	−0.329670
$237$	−15.6685	−1.01778
$238$	−19.2885	−1.25029
$239$	−26.9521	−1.74339	−0.871693	−	0.490053i	$-0.836978\pi$
$239$	−26.9521	−1.74339	−0.871693	+	0.490053i	$0.836978\pi$
$240$	0	0
$241$	16.0041	1.03091	0.515457	−	0.856915i	$-0.327622\pi$
$241$	16.0041	1.03091	0.515457	+	0.856915i	$0.327622\pi$
$242$	−10.9343	−0.702882
$243$	−1.00000	−0.0641500
$244$	5.01366	0.320967
$245$	0	0
$246$	−5.28545	−0.336988
$247$	14.5733	0.927274
$248$	−1.58241	−0.100483
$249$	−5.17115	−0.327708
$250$	0	0
$251$	−26.5909	−1.67840	−0.839201	−	0.543821i	$-0.816977\pi$
$251$	−26.5909	−1.67840	−0.839201	+	0.543821i	$0.816977\pi$
$252$	1.70871	0.107639
$253$	−4.42297	−0.278070
$254$	12.2445	0.768287
$255$	0	0
$256$	13.0667	0.816670
$257$	−2.59505	−0.161875	−0.0809373	−	0.996719i	$-0.525791\pi$
$257$	−2.59505	−0.161875	−0.0809373	+	0.996719i	$0.525791\pi$
$258$	−7.17925	−0.446961
$259$	−24.9136	−1.54806
$260$	0	0
$261$	9.10114	0.563346
$262$	−26.0720	−1.61074
$263$	−2.09258	−0.129034	−0.0645170	−	0.997917i	$-0.520551\pi$
$263$	−2.09258	−0.129034	−0.0645170	+	0.997917i	$0.520551\pi$
$264$	−4.65202	−0.286312
$265$	0	0
$266$	14.9839	0.918721
$267$	−14.5447	−0.890122
$268$	8.24771	0.503809
$269$	11.9754	0.730153	0.365077	−	0.930977i	$-0.381043\pi$
$269$	11.9754	0.730153	0.365077	+	0.930977i	$0.381043\pi$
$270$	0	0
$271$	13.4698	0.818230	0.409115	−	0.912483i	$-0.365837\pi$
$271$	13.4698	0.818230	0.409115	+	0.912483i	$0.365837\pi$
$272$	20.0284	1.21440
$273$	−13.0883	−0.792138
$274$	22.1026	1.33527
$275$	0	0
$276$	−1.27434	−0.0767062
$277$	11.6830	0.701965	0.350982	−	0.936382i	$-0.385848\pi$
$277$	11.6830	0.701965	0.350982	+	0.936382i	$0.385848\pi$
$278$	0.668209	0.0400765
$279$	0.697696	0.0417700
$280$	0	0
$281$	−26.0065	−1.55142	−0.775710	−	0.631090i	$-0.782608\pi$
$281$	−26.0065	−1.55142	−0.775710	+	0.631090i	$0.782608\pi$
$282$	−1.60965	−0.0958530
$283$	−14.4211	−0.857246	−0.428623	−	0.903484i	$-0.641001\pi$
$283$	−14.4211	−0.857246	−0.428623	+	0.903484i	$0.641001\pi$
$284$	−9.31915	−0.552990
$285$	0	0
$286$	−14.9448	−0.883706
$287$	9.49426	0.560428
$288$	−3.24281	−0.191084
$289$	0.175799	0.0103411
$290$	0	0
$291$	0.136874	0.00802372
$292$	5.24848	0.307144
$293$	−5.61335	−0.327936	−0.163968	−	0.986466i	$-0.552429\pi$
$293$	−5.61335	−0.327936	−0.163968	+	0.986466i	$0.552429\pi$
$294$	−2.18954	−0.127696
$295$	0	0
$296$	19.5425	1.13589
$297$	2.05110	0.119017
$298$	−11.8265	−0.685091
$299$	9.76109	0.564498
$300$	0	0
$301$	12.8961	0.743319
$302$	8.99371	0.517530
$303$	7.06652	0.405961
$304$	−15.5587	−0.892352
$305$	0	0
$306$	−6.67097	−0.381354
$307$	−13.5331	−0.772375	−0.386187	−	0.922420i	$-0.626208\pi$
$307$	−13.5331	−0.772375	−0.386187	+	0.922420i	$0.626208\pi$
$308$	−3.50475	−0.199701
$309$	−8.01574	−0.455999
$310$	0	0
$311$	−0.849986	−0.0481983	−0.0240991	−	0.999710i	$-0.507672\pi$
$311$	−0.849986	−0.0481983	−0.0240991	+	0.999710i	$0.507672\pi$
$312$	10.2666	0.581231
$313$	2.68904	0.151993	0.0759966	−	0.997108i	$-0.475786\pi$
$313$	2.68904	0.151993	0.0759966	+	0.997108i	$0.475786\pi$
$314$	−22.0192	−1.24262
$315$	0	0
$316$	9.25946	0.520885
$317$	4.65829	0.261635	0.130818	−	0.991406i	$-0.458240\pi$
$317$	4.65829	0.261635	0.130818	+	0.991406i	$0.458240\pi$
$318$	−4.37241	−0.245193
$319$	−18.6674	−1.04517
$320$	0	0
$321$	−19.7935	−1.10476
$322$	10.0361	0.559292
$323$	−13.3427	−0.742406
$324$	0.590961	0.0328312
$325$	0	0
$326$	−28.2994	−1.56736
$327$	1.61314	0.0892068
$328$	−7.44740	−0.411214
$329$	2.89141	0.159409
$330$	0	0
$331$	−17.7902	−0.977837	−0.488918	−	0.872330i	$-0.662608\pi$
$331$	−17.7902	−0.977837	−0.488918	+	0.872330i	$0.662608\pi$
$332$	3.05595	0.167717
$333$	−8.61642	−0.472177
$334$	2.60405	0.142487
$335$	0	0
$336$	13.9733	0.762305
$337$	−34.0593	−1.85533	−0.927663	−	0.373419i	$-0.878185\pi$
$337$	−34.0593	−1.85533	−0.927663	+	0.373419i	$0.878185\pi$
$338$	12.0565	0.655785
$339$	6.17689	0.335483
$340$	0	0
$341$	−1.43105	−0.0774956
$342$	5.18220	0.280222
$343$	−16.3068	−0.880485
$344$	−10.1158	−0.545410
$345$	0	0
$346$	19.2901	1.03704
$347$	22.5182	1.20884	0.604419	−	0.796667i	$-0.293405\pi$
$347$	22.5182	1.20884	0.604419	+	0.796667i	$0.293405\pi$
$348$	−5.37842	−0.288314
$349$	26.7475	1.43176	0.715879	−	0.698224i	$-0.246026\pi$
$349$	26.7475	1.43176	0.715879	+	0.698224i	$0.246026\pi$
$350$	0	0
$351$	−4.52660	−0.241612
$352$	6.65134	0.354518
$353$	−13.9790	−0.744025	−0.372013	−	0.928228i	$-0.621332\pi$
$353$	−13.9790	−0.744025	−0.372013	+	0.928228i	$0.621332\pi$
$354$	13.7945	0.733171
$355$	0	0
$356$	8.59536	0.455553
$357$	11.9831	0.634212
$358$	21.8187	1.15316
$359$	8.06400	0.425602	0.212801	−	0.977096i	$-0.431741\pi$
$359$	8.06400	0.425602	0.212801	+	0.977096i	$0.431741\pi$
$360$	0	0
$361$	−8.63503	−0.454475
$362$	−9.21705	−0.484437
$363$	6.79297	0.356538
$364$	7.73466	0.405406
$365$	0	0
$366$	−13.6561	−0.713816
$367$	4.15872	0.217083	0.108542	−	0.994092i	$-0.465382\pi$
$367$	4.15872	0.217083	0.108542	+	0.994092i	$0.465382\pi$
$368$	−10.4211	−0.543239
$369$	3.28361	0.170938
$370$	0	0
$371$	7.85418	0.407768
$372$	−0.412311	−0.0213773
$373$	−3.98023	−0.206089	−0.103044	−	0.994677i	$-0.532858\pi$
$373$	−3.98023	−0.206089	−0.103044	+	0.994677i	$0.532858\pi$
$374$	13.6829	0.707524
$375$	0	0
$376$	−2.26805	−0.116966
$377$	41.1972	2.12177
$378$	−4.65415	−0.239384
$379$	4.75448	0.244221	0.122111	−	0.992516i	$-0.461034\pi$
$379$	4.75448	0.244221	0.122111	+	0.992516i	$0.461034\pi$
$380$	0	0
$381$	−7.60694	−0.389715
$382$	13.2073	0.675746
$383$	7.55458	0.386021	0.193010	−	0.981197i	$-0.438175\pi$
$383$	7.55458	0.386021	0.193010	+	0.981197i	$0.438175\pi$
$384$	−13.6415	−0.696138
$385$	0	0
$386$	34.2173	1.74161
$387$	4.46014	0.226722
$388$	−0.0808874	−0.00410644
$389$	12.0545	0.611189	0.305594	−	0.952162i	$-0.401145\pi$
$389$	12.0545	0.611189	0.305594	+	0.952162i	$0.401145\pi$
$390$	0	0
$391$	−8.93685	−0.451956
$392$	−3.08514	−0.155823
$393$	16.1974	0.817049
$394$	5.84234	0.294333
$395$	0	0
$396$	−1.21212	−0.0609115
$397$	5.70537	0.286344	0.143172	−	0.989698i	$-0.454270\pi$
$397$	5.70537	0.286344	0.143172	+	0.989698i	$0.454270\pi$
$398$	6.11289	0.306412
$399$	−9.30881	−0.466023
$400$	0	0
$401$	−25.6860	−1.28270	−0.641349	−	0.767249i	$-0.721625\pi$
$401$	−25.6860	−1.28270	−0.641349	+	0.767249i	$0.721625\pi$
$402$	−22.4649	−1.12045
$403$	3.15819	0.157321
$404$	−4.17604	−0.207766
$405$	0	0
$406$	42.3581	2.10220
$407$	17.6732	0.876027
$408$	−9.39965	−0.465352
$409$	−37.8814	−1.87311	−0.936557	−	0.350515i	$-0.886006\pi$
$409$	−37.8814	−1.87311	−0.936557	+	0.350515i	$0.886006\pi$
$410$	0	0
$411$	−13.7313	−0.677316
$412$	4.73699	0.233375
$413$	−24.7792	−1.21930
$414$	3.47101	0.170591
$415$	0	0
$416$	−14.6789	−0.719693
$417$	−0.415128	−0.0203289
$418$	−10.6292	−0.519893
$419$	−39.3561	−1.92267	−0.961336	−	0.275377i	$-0.911197\pi$
$419$	−39.3561	−1.92267	−0.961336	+	0.275377i	$0.911197\pi$
$420$	0	0
$421$	−12.9116	−0.629273	−0.314636	−	0.949212i	$-0.601883\pi$
$421$	−12.9116	−0.629273	−0.314636	+	0.949212i	$0.601883\pi$
$422$	23.5063	1.14427
$423$	1.00000	0.0486217
$424$	−6.16090	−0.299200
$425$	0	0
$426$	25.3833	1.22982
$427$	24.5305	1.18711
$428$	11.6972	0.565404
$429$	9.28454	0.448262
$430$	0	0
$431$	−3.38916	−0.163250	−0.0816250	−	0.996663i	$-0.526011\pi$
$431$	−3.38916	−0.163250	−0.0816250	+	0.996663i	$0.526011\pi$
$432$	4.83269	0.232513
$433$	34.1171	1.63956	0.819782	−	0.572676i	$-0.194095\pi$
$433$	34.1171	1.63956	0.819782	+	0.572676i	$0.194095\pi$
$434$	3.24718	0.155870
$435$	0	0
$436$	−0.953303	−0.0456549
$437$	6.94241	0.332100
$438$	−14.2957	−0.683075
$439$	−13.2170	−0.630811	−0.315406	−	0.948957i	$-0.602141\pi$
$439$	−13.2170	−0.630811	−0.315406	+	0.948957i	$0.602141\pi$
$440$	0	0
$441$	1.36026	0.0647743
$442$	−30.1968	−1.43632
$443$	−28.3665	−1.34773	−0.673867	−	0.738853i	$-0.735368\pi$
$443$	−28.3665	−1.34773	−0.673867	+	0.738853i	$0.735368\pi$
$444$	5.09197	0.241654
$445$	0	0
$446$	38.2528	1.81132
$447$	7.34727	0.347514
$448$	12.8541	0.607297
$449$	−5.94981	−0.280789	−0.140394	−	0.990096i	$-0.544837\pi$
$449$	−5.94981	−0.280789	−0.140394	+	0.990096i	$0.544837\pi$
$450$	0	0
$451$	−6.73502	−0.317140
$452$	−3.65030	−0.171696
$453$	−5.58738	−0.262518
$454$	−9.81886	−0.460822
$455$	0	0
$456$	7.30193	0.341944
$457$	−6.58351	−0.307963	−0.153982	−	0.988074i	$-0.549210\pi$
$457$	−6.58351	−0.307963	−0.153982	+	0.988074i	$0.549210\pi$
$458$	−35.9764	−1.68107
$459$	4.14437	0.193443
$460$	0	0
$461$	−35.2196	−1.64034	−0.820171	−	0.572118i	$-0.806122\pi$
$461$	−35.2196	−1.64034	−0.820171	+	0.572118i	$0.806122\pi$
$462$	9.54615	0.444127
$463$	13.7978	0.641239	0.320619	−	0.947208i	$-0.396109\pi$
$463$	13.7978	0.641239	0.320619	+	0.947208i	$0.396109\pi$
$464$	−43.9830	−2.04186
$465$	0	0
$466$	10.5454	0.488508
$467$	8.02180	0.371205	0.185602	−	0.982625i	$-0.440576\pi$
$467$	8.02180	0.371205	0.185602	+	0.982625i	$0.440576\pi$
$468$	2.67505	0.123654
$469$	40.3538	1.86336
$470$	0	0
$471$	13.6795	0.630320
$472$	19.4370	0.894662
$473$	−9.14822	−0.420636
$474$	−25.2207	−1.15843
$475$	0	0
$476$	−7.08153	−0.324582
$477$	2.71638	0.124375
$478$	−43.3833	−1.98431
$479$	−0.339149	−0.0154961	−0.00774806	−	0.999970i	$-0.502466\pi$
$479$	−0.339149	−0.0154961	−0.00774806	+	0.999970i	$0.502466\pi$
$480$	0	0
$481$	−39.0031	−1.77839
$482$	25.7609	1.17338
$483$	−6.23499	−0.283702
$484$	−4.01438	−0.182472
$485$	0	0
$486$	−1.60965	−0.0730150
$487$	−32.9320	−1.49229	−0.746146	−	0.665782i	$-0.768098\pi$
$487$	−32.9320	−1.49229	−0.746146	+	0.665782i	$0.768098\pi$
$488$	−19.2420	−0.871043
$489$	17.5811	0.795046
$490$	0	0
$491$	2.35165	0.106129	0.0530643	−	0.998591i	$-0.483101\pi$
$491$	2.35165	0.106129	0.0530643	+	0.998591i	$0.483101\pi$
$492$	−1.94048	−0.0874838
$493$	−37.7185	−1.69876
$494$	23.4578	1.05542
$495$	0	0
$496$	−3.37175	−0.151396
$497$	−45.5960	−2.04526
$498$	−8.32372	−0.372995
$499$	−3.77188	−0.168853	−0.0844263	−	0.996430i	$-0.526906\pi$
$499$	−3.77188	−0.168853	−0.0844263	+	0.996430i	$0.526906\pi$
$500$	0	0
$501$	−1.61778	−0.0722771
$502$	−42.8019	−1.91034
$503$	−0.270322	−0.0120530	−0.00602652	−	0.999982i	$-0.501918\pi$
$503$	−0.270322	−0.0120530	−0.00602652	+	0.999982i	$0.501918\pi$
$504$	−6.55788	−0.292111
$505$	0	0
$506$	−7.11941	−0.316497
$507$	−7.49013	−0.332648
$508$	4.49540	0.199451
$509$	−0.465277	−0.0206230	−0.0103115	−	0.999947i	$-0.503282\pi$
$509$	−0.465277	−0.0206230	−0.0103115	+	0.999947i	$0.503282\pi$
$510$	0	0
$511$	25.6794	1.13599
$512$	−6.25011	−0.276219
$513$	−3.21947	−0.142143
$514$	−4.17711	−0.184244
$515$	0	0
$516$	−2.63577	−0.116033
$517$	−2.05110	−0.0902075
$518$	−40.1021	−1.76199
$519$	−11.9840	−0.526041
$520$	0	0
$521$	−20.3235	−0.890387	−0.445193	−	0.895434i	$-0.646865\pi$
$521$	−20.3235	−0.890387	−0.445193	+	0.895434i	$0.646865\pi$
$522$	14.6496	0.641196
$523$	43.0920	1.88428	0.942140	−	0.335219i	$-0.108810\pi$
$523$	43.0920	1.88428	0.942140	+	0.335219i	$0.108810\pi$
$524$	−9.57201	−0.418155
$525$	0	0
$526$	−3.36831	−0.146865
$527$	−2.89151	−0.125956
$528$	−9.91235	−0.431380
$529$	−18.3500	−0.797827
$530$	0	0
$531$	−8.56992	−0.371903
$532$	5.50114	0.238505
$533$	14.8636	0.643813
$534$	−23.4118	−1.01313
$535$	0	0
$536$	−31.6539	−1.36724
$537$	−13.5550	−0.584941
$538$	19.2762	0.831054
$539$	−2.79003	−0.120175
$540$	0	0
$541$	−27.1465	−1.16712	−0.583560	−	0.812070i	$-0.698341\pi$
$541$	−27.1465	−1.16712	−0.583560	+	0.812070i	$0.698341\pi$
$542$	21.6816	0.931303
$543$	5.72613	0.245732
$544$	13.4394	0.576209
$545$	0	0
$546$	−21.0675	−0.901605
$547$	6.65030	0.284346	0.142173	−	0.989842i	$-0.454591\pi$
$547$	6.65030	0.284346	0.142173	+	0.989842i	$0.454591\pi$
$548$	8.11468	0.346642
$549$	8.48391	0.362085
$550$	0	0
$551$	29.3008	1.24826
$552$	4.89079	0.208166
$553$	45.3040	1.92652
$554$	18.8055	0.798970
$555$	0	0
$556$	0.245324	0.0104041
$557$	7.78871	0.330018	0.165009	−	0.986292i	$-0.447235\pi$
$557$	7.78871	0.330018	0.165009	+	0.986292i	$0.447235\pi$
$558$	1.12304	0.0475422
$559$	20.1893	0.853916
$560$	0	0
$561$	−8.50054	−0.358893
$562$	−41.8613	−1.76581
$563$	−17.8053	−0.750405	−0.375203	−	0.926943i	$-0.622427\pi$
$563$	−17.8053	−0.750405	−0.375203	+	0.926943i	$0.622427\pi$
$564$	−0.590961	−0.0248840
$565$	0	0
$566$	−23.2129	−0.975710
$567$	2.89141	0.121428
$568$	35.7660	1.50071
$569$	−1.15450	−0.0483993	−0.0241996	−	0.999707i	$-0.507704\pi$
$569$	−1.15450	−0.0483993	−0.0241996	+	0.999707i	$0.507704\pi$
$570$	0	0
$571$	−45.8755	−1.91983	−0.959914	−	0.280293i	$-0.909568\pi$
$571$	−45.8755	−1.91983	−0.959914	+	0.280293i	$0.909568\pi$
$572$	−5.48680	−0.229415
$573$	−8.20512	−0.342774
$574$	15.2824	0.637875
$575$	0	0
$576$	4.44560	0.185233
$577$	−17.1596	−0.714362	−0.357181	−	0.934035i	$-0.616262\pi$
$577$	−17.1596	−0.714362	−0.357181	+	0.934035i	$0.616262\pi$
$578$	0.282975	0.0117702
$579$	−21.2576	−0.883437
$580$	0	0
$581$	14.9519	0.620310
$582$	0.220319	0.00913253
$583$	−5.57158	−0.230751
$584$	−20.1432	−0.833531
$585$	0	0
$586$	−9.03551	−0.373254
$587$	36.9440	1.52484	0.762422	−	0.647080i	$-0.224010\pi$
$587$	36.9440	1.52484	0.762422	+	0.647080i	$0.224010\pi$
$588$	−0.803861	−0.0331507
$589$	2.24621	0.0925535
$590$	0	0
$591$	−3.62958	−0.149301
$592$	41.6405	1.71141
$593$	−13.9078	−0.571127	−0.285563	−	0.958360i	$-0.592181\pi$
$593$	−13.9078	−0.571127	−0.285563	+	0.958360i	$0.592181\pi$
$594$	3.30155	0.135464
$595$	0	0
$596$	−4.34195	−0.177853
$597$	−3.79766	−0.155428
$598$	15.7119	0.642507
$599$	39.5466	1.61583	0.807916	−	0.589298i	$-0.200596\pi$
$599$	39.5466	1.61583	0.807916	+	0.589298i	$0.200596\pi$
$600$	0	0
$601$	8.97526	0.366109	0.183054	−	0.983103i	$-0.441402\pi$
$601$	8.97526	0.366109	0.183054	+	0.983103i	$0.441402\pi$
$602$	20.7582	0.846040
$603$	13.9564	0.568350
$604$	3.30192	0.134353
$605$	0	0
$606$	11.3746	0.462061
$607$	−0.157215	−0.00638115	−0.00319058	−	0.999995i	$-0.501016\pi$
$607$	−0.157215	−0.00638115	−0.00319058	+	0.999995i	$0.501016\pi$
$608$	−10.4401	−0.423403
$609$	−26.3151	−1.06634
$610$	0	0
$611$	4.52660	0.183127
$612$	−2.44916	−0.0990015
$613$	−9.37271	−0.378560	−0.189280	−	0.981923i	$-0.560615\pi$
$613$	−9.37271	−0.378560	−0.189280	+	0.981923i	$0.560615\pi$
$614$	−21.7835	−0.879111
$615$	0	0
$616$	13.4509	0.541952
$617$	−46.0532	−1.85403	−0.927017	−	0.375020i	$-0.877636\pi$
$617$	−46.0532	−1.85403	−0.927017	+	0.375020i	$0.877636\pi$
$618$	−12.9025	−0.519015
$619$	32.5780	1.30942	0.654710	−	0.755880i	$-0.272791\pi$
$619$	32.5780	1.30942	0.654710	+	0.755880i	$0.272791\pi$
$620$	0	0
$621$	−2.15638	−0.0865327
$622$	−1.36818	−0.0548589
$623$	42.0548	1.68489
$624$	21.8757	0.875727
$625$	0	0
$626$	4.32840	0.172997
$627$	6.60347	0.263717
$628$	−8.08407	−0.322590
$629$	35.7096	1.42384
$630$	0	0
$631$	−31.6591	−1.26033	−0.630163	−	0.776462i	$-0.717012\pi$
$631$	−31.6591	−1.26033	−0.630163	+	0.776462i	$0.717012\pi$
$632$	−35.5370	−1.41358
$633$	−14.6034	−0.580432
$634$	7.49819	0.297791
$635$	0	0
$636$	−1.60528	−0.0636533
$637$	6.15736	0.243963
$638$	−30.0479	−1.18961
$639$	−15.7695	−0.623831
$640$	0	0
$641$	−13.6035	−0.537306	−0.268653	−	0.963237i	$-0.586579\pi$
$641$	−13.6035	−0.537306	−0.268653	+	0.963237i	$0.586579\pi$
$642$	−31.8605	−1.25743
$643$	−4.19435	−0.165409	−0.0827045	−	0.996574i	$-0.526356\pi$
$643$	−4.19435	−0.165409	−0.0827045	+	0.996574i	$0.526356\pi$
$644$	3.68464	0.145195
$645$	0	0
$646$	−21.4770	−0.845000
$647$	−21.9387	−0.862499	−0.431249	−	0.902233i	$-0.641927\pi$
$647$	−21.9387	−0.862499	−0.431249	+	0.902233i	$0.641927\pi$
$648$	−2.26805	−0.0890976
$649$	17.5778	0.689989
$650$	0	0
$651$	−2.01733	−0.0790652
$652$	−10.3898	−0.406895
$653$	3.23345	0.126534	0.0632672	−	0.997997i	$-0.479848\pi$
$653$	3.23345	0.126534	0.0632672	+	0.997997i	$0.479848\pi$
$654$	2.59658	0.101534
$655$	0	0
$656$	−15.8686	−0.619567
$657$	8.88127	0.346491
$658$	4.65415	0.181438
$659$	−15.4658	−0.602461	−0.301230	−	0.953551i	$-0.597397\pi$
$659$	−15.4658	−0.602461	−0.301230	+	0.953551i	$0.597397\pi$
$660$	0	0
$661$	23.2375	0.903835	0.451917	−	0.892060i	$-0.350740\pi$
$661$	23.2375	0.903835	0.451917	+	0.892060i	$0.350740\pi$
$662$	−28.6359	−1.11297
$663$	18.7599	0.728575
$664$	−11.7284	−0.455152
$665$	0	0
$666$	−13.8694	−0.537428
$667$	19.6255	0.759904
$668$	0.956045	0.0369905
$669$	−23.7647	−0.918797
$670$	0	0
$671$	−17.4014	−0.671773
$672$	9.37629	0.361698
$673$	−44.2939	−1.70741	−0.853703	−	0.520760i	$-0.825649\pi$
$673$	−44.2939	−1.70741	−0.853703	+	0.520760i	$0.825649\pi$
$674$	−54.8233	−2.11172
$675$	0	0
$676$	4.42638	0.170245
$677$	−3.26240	−0.125384	−0.0626921	−	0.998033i	$-0.519969\pi$
$677$	−3.26240	−0.125384	−0.0626921	+	0.998033i	$0.519969\pi$
$678$	9.94261	0.381844
$679$	−0.395760	−0.0151879
$680$	0	0
$681$	6.10001	0.233753
$682$	−2.30348	−0.0882048
$683$	46.2534	1.76984	0.884918	−	0.465747i	$-0.154214\pi$
$683$	46.2534	1.76984	0.884918	+	0.465747i	$0.154214\pi$
$684$	1.90258	0.0727470
$685$	0	0
$686$	−26.2482	−1.00216
$687$	22.3505	0.852725
$688$	−21.5545	−0.821757
$689$	12.2960	0.468439
$690$	0	0
$691$	18.4048	0.700153	0.350077	−	0.936721i	$-0.386156\pi$
$691$	18.4048	0.700153	0.350077	+	0.936721i	$0.386156\pi$
$692$	7.08210	0.269221
$693$	−5.93059	−0.225284
$694$	36.2463	1.37589
$695$	0	0
$696$	20.6419	0.782428
$697$	−13.6085	−0.515458
$698$	43.0540	1.62962
$699$	−6.55140	−0.247797
$700$	0	0
$701$	−18.0583	−0.682051	−0.341026	−	0.940054i	$-0.610774\pi$
$701$	−18.0583	−0.682051	−0.341026	+	0.940054i	$0.610774\pi$
$702$	−7.28623	−0.275001
$703$	−27.7403	−1.04624
$704$	−9.11839	−0.343662
$705$	0	0
$706$	−22.5012	−0.846844
$707$	−20.4322	−0.768432
$708$	5.06449	0.190335
$709$	40.7703	1.53116	0.765580	−	0.643340i	$-0.222452\pi$
$709$	40.7703	1.53116	0.765580	+	0.643340i	$0.222452\pi$
$710$	0	0
$711$	15.6685	0.587614
$712$	−32.9882	−1.23629
$713$	1.50450	0.0563440
$714$	19.2885	0.721855
$715$	0	0
$716$	8.01047	0.299365
$717$	26.9521	1.00654
$718$	12.9802	0.484416
$719$	7.63475	0.284728	0.142364	−	0.989814i	$-0.454530\pi$
$719$	7.63475	0.284728	0.142364	+	0.989814i	$0.454530\pi$
$720$	0	0
$721$	23.1768	0.863149
$722$	−13.8993	−0.517280
$723$	−16.0041	−0.595199
$724$	−3.38392	−0.125762
$725$	0	0
$726$	10.9343	0.405809
$727$	−9.38310	−0.348000	−0.174000	−	0.984746i	$-0.555669\pi$
$727$	−9.38310	−0.348000	−0.174000	+	0.984746i	$0.555669\pi$
$728$	−29.6849	−1.10020
$729$	1.00000	0.0370370
$730$	0	0
$731$	−18.4845	−0.683673
$732$	−5.01366	−0.185310
$733$	8.20997	0.303242	0.151621	−	0.988439i	$-0.451551\pi$
$733$	8.20997	0.303242	0.151621	+	0.988439i	$0.451551\pi$
$734$	6.69407	0.247083
$735$	0	0
$736$	−6.99274	−0.257756
$737$	−28.6261	−1.05446
$738$	5.28545	0.194560
$739$	53.7810	1.97837	0.989184	−	0.146683i	$-0.0468596\pi$
$739$	53.7810	1.97837	0.989184	+	0.146683i	$0.0468596\pi$
$740$	0	0
$741$	−14.5733	−0.535362
$742$	12.6424	0.464119
$743$	6.71423	0.246321	0.123161	−	0.992387i	$-0.460697\pi$
$743$	6.71423	0.246321	0.123161	+	0.992387i	$0.460697\pi$
$744$	1.58241	0.0580141
$745$	0	0
$746$	−6.40676	−0.234568
$747$	5.17115	0.189202
$748$	5.02349	0.183677
$749$	57.2311	2.09118
$750$	0	0
$751$	15.4143	0.562476	0.281238	−	0.959638i	$-0.409255\pi$
$751$	15.4143	0.562476	0.281238	+	0.959638i	$0.409255\pi$
$752$	−4.83269	−0.176230
$753$	26.5909	0.969026
$754$	66.3130	2.41498
$755$	0	0
$756$	−1.70871	−0.0621452
$757$	−21.9633	−0.798269	−0.399135	−	0.916892i	$-0.630689\pi$
$757$	−21.9633	−0.798269	−0.399135	+	0.916892i	$0.630689\pi$
$758$	7.65303	0.277971
$759$	4.42297	0.160544
$760$	0	0
$761$	23.5171	0.852494	0.426247	−	0.904607i	$-0.359835\pi$
$761$	23.5171	0.852494	0.426247	+	0.904607i	$0.359835\pi$
$762$	−12.2445	−0.443571
$763$	−4.66425	−0.168857
$764$	4.84890	0.175427
$765$	0	0
$766$	12.1602	0.439366
$767$	−38.7926	−1.40072
$768$	−13.0667	−0.471505
$769$	−49.0593	−1.76912	−0.884562	−	0.466422i	$-0.845543\pi$
$769$	−49.0593	−1.76912	−0.884562	+	0.466422i	$0.845543\pi$
$770$	0	0
$771$	2.59505	0.0934584
$772$	12.5624	0.452132
$773$	−15.5967	−0.560973	−0.280487	−	0.959858i	$-0.590496\pi$
$773$	−15.5967	−0.560973	−0.280487	+	0.959858i	$0.590496\pi$
$774$	7.17925	0.258053
$775$	0	0
$776$	0.310439	0.0111441
$777$	24.9136	0.893771
$778$	19.4035	0.695650
$779$	10.5715	0.378762
$780$	0	0
$781$	32.3448	1.15739
$782$	−14.3852	−0.514412
$783$	−9.10114	−0.325248
$784$	−6.57371	−0.234775
$785$	0	0
$786$	26.0720	0.929958
$787$	7.26119	0.258833	0.129417	−	0.991590i	$-0.458690\pi$
$787$	7.26119	0.258833	0.129417	+	0.991590i	$0.458690\pi$
$788$	2.14494	0.0764104
$789$	2.09258	0.0744978
$790$	0	0
$791$	−17.8599	−0.635026
$792$	4.65202	0.165302
$793$	38.4033	1.36374
$794$	9.18362	0.325914
$795$	0	0
$796$	2.24427	0.0795461
$797$	−15.4601	−0.547624	−0.273812	−	0.961783i	$-0.588285\pi$
$797$	−15.4601	−0.547624	−0.273812	+	0.961783i	$0.588285\pi$
$798$	−14.9839	−0.530424
$799$	−4.14437	−0.146617
$800$	0	0
$801$	14.5447	0.513912
$802$	−41.3454	−1.45996
$803$	−18.2164	−0.642843
$804$	−8.24771	−0.290874
$805$	0	0
$806$	5.08357	0.179061
$807$	−11.9754	−0.421554
$808$	16.0272	0.563837
$809$	−50.3702	−1.77092	−0.885461	−	0.464713i	$-0.846158\pi$
$809$	−50.3702	−1.77092	−0.885461	+	0.464713i	$0.846158\pi$
$810$	0	0
$811$	−39.0167	−1.37006	−0.685032	−	0.728513i	$-0.740212\pi$
$811$	−39.0167	−1.37006	−0.685032	+	0.728513i	$0.740212\pi$
$812$	15.5512	0.545741
$813$	−13.4698	−0.472405
$814$	28.4476	0.997087
$815$	0	0
$816$	−20.0284	−0.701136
$817$	14.3593	0.502368
$818$	−60.9756	−2.13196
$819$	13.0883	0.457341
$820$	0	0
$821$	17.5530	0.612604	0.306302	−	0.951934i	$-0.400908\pi$
$821$	17.5530	0.612604	0.306302	+	0.951934i	$0.400908\pi$
$822$	−22.1026	−0.770916
$823$	−11.6225	−0.405134	−0.202567	−	0.979268i	$-0.564928\pi$
$823$	−11.6225	−0.405134	−0.202567	+	0.979268i	$0.564928\pi$
$824$	−18.1801	−0.633335
$825$	0	0
$826$	−39.8857	−1.38780
$827$	4.12817	0.143550	0.0717752	−	0.997421i	$-0.477134\pi$
$827$	4.12817	0.143550	0.0717752	+	0.997421i	$0.477134\pi$
$828$	1.27434	0.0442863
$829$	35.8722	1.24589	0.622946	−	0.782265i	$-0.285936\pi$
$829$	35.8722	1.24589	0.622946	+	0.782265i	$0.285936\pi$
$830$	0	0
$831$	−11.6830	−0.405279
$832$	20.1235	0.697656
$833$	−5.63742	−0.195325
$834$	−0.668209	−0.0231382
$835$	0	0
$836$	−3.90239	−0.134967
$837$	−0.697696	−0.0241159
$838$	−63.3494	−2.18837
$839$	36.0129	1.24330	0.621652	−	0.783294i	$-0.286462\pi$
$839$	36.0129	1.24330	0.621652	+	0.783294i	$0.286462\pi$
$840$	0	0
$841$	53.8307	1.85623
$842$	−20.7831	−0.716233
$843$	26.0065	0.895713
$844$	8.63002	0.297058
$845$	0	0
$846$	1.60965	0.0553408
$847$	−19.6413	−0.674882
$848$	−13.1274	−0.450797
$849$	14.4211	0.494931
$850$	0	0
$851$	−18.5803	−0.636925
$852$	9.31915	0.319269
$853$	−12.6467	−0.433014	−0.216507	−	0.976281i	$-0.569466\pi$
$853$	−12.6467	−0.433014	−0.216507	+	0.976281i	$0.569466\pi$
$854$	39.4854	1.35116
$855$	0	0
$856$	−44.8927	−1.53440
$857$	−7.19169	−0.245664	−0.122832	−	0.992428i	$-0.539198\pi$
$857$	−7.19169	−0.245664	−0.122832	+	0.992428i	$0.539198\pi$
$858$	14.9448	0.510208
$859$	35.7583	1.22006	0.610028	−	0.792379i	$-0.291158\pi$
$859$	35.7583	1.22006	0.610028	+	0.792379i	$0.291158\pi$
$860$	0	0
$861$	−9.49426	−0.323564
$862$	−5.45535	−0.185810
$863$	26.9381	0.916984	0.458492	−	0.888699i	$-0.348390\pi$
$863$	26.9381	0.916984	0.458492	+	0.888699i	$0.348390\pi$
$864$	3.24281	0.110323
$865$	0	0
$866$	54.9165	1.86614
$867$	−0.175799	−0.00597046
$868$	1.19216	0.0404646
$869$	−32.1377	−1.09020
$870$	0	0
$871$	63.1752	2.14061
$872$	3.65869	0.123899
$873$	−0.136874	−0.00463250
$874$	11.1748	0.377994
$875$	0	0
$876$	−5.24848	−0.177330
$877$	45.4016	1.53310	0.766552	−	0.642182i	$-0.221971\pi$
$877$	45.4016	1.53310	0.766552	+	0.642182i	$0.221971\pi$
$878$	−21.2746	−0.717984
$879$	5.61335	0.189334
$880$	0	0
$881$	13.6687	0.460511	0.230255	−	0.973130i	$-0.426044\pi$
$881$	13.6687	0.460511	0.230255	+	0.973130i	$0.426044\pi$
$882$	2.18954	0.0737255
$883$	−7.44286	−0.250472	−0.125236	−	0.992127i	$-0.539969\pi$
$883$	−7.44286	−0.250472	−0.125236	+	0.992127i	$0.539969\pi$
$884$	−11.0864	−0.372875
$885$	0	0
$886$	−45.6601	−1.53398
$887$	10.6253	0.356762	0.178381	−	0.983962i	$-0.442914\pi$
$887$	10.6253	0.356762	0.178381	+	0.983962i	$0.442914\pi$
$888$	−19.5425	−0.655804
$889$	21.9948	0.737681
$890$	0	0
$891$	−2.05110	−0.0687146
$892$	14.0440	0.470229
$893$	3.21947	0.107735
$894$	11.8265	0.395537
$895$	0	0
$896$	39.4431	1.31770
$897$	−9.76109	−0.325913
$898$	−9.57709	−0.319592
$899$	6.34983	0.211779
$900$	0	0
$901$	−11.2577	−0.375048
$902$	−10.8410	−0.360966
$903$	−12.8961	−0.429156
$904$	14.0095	0.465950
$905$	0	0
$906$	−8.99371	−0.298796
$907$	2.96687	0.0985133	0.0492566	−	0.998786i	$-0.484315\pi$
$907$	2.96687	0.0985133	0.0492566	+	0.998786i	$0.484315\pi$
$908$	−3.60487	−0.119632
$909$	−7.06652	−0.234382
$910$	0	0
$911$	−2.44851	−0.0811227	−0.0405614	−	0.999177i	$-0.512915\pi$
$911$	−2.44851	−0.0811227	−0.0405614	+	0.999177i	$0.512915\pi$
$912$	15.5587	0.515199
$913$	−10.6066	−0.351026
$914$	−10.5971	−0.350521
$915$	0	0
$916$	−13.2083	−0.436414
$917$	−46.8332	−1.54657
$918$	6.67097	0.220175
$919$	−2.21230	−0.0729769	−0.0364885	−	0.999334i	$-0.511617\pi$
$919$	−2.21230	−0.0729769	−0.0364885	+	0.999334i	$0.511617\pi$
$920$	0	0
$921$	13.5331	0.445931
$922$	−56.6912	−1.86702
$923$	−71.3822	−2.34957
$924$	3.50475	0.115298
$925$	0	0
$926$	22.2096	0.729853
$927$	8.01574	0.263271
$928$	−29.5133	−0.968820
$929$	14.9520	0.490558	0.245279	−	0.969453i	$-0.421120\pi$
$929$	14.9520	0.490558	0.245279	+	0.969453i	$0.421120\pi$
$930$	0	0
$931$	4.37931	0.143526
$932$	3.87162	0.126819
$933$	0.849986	0.0278273
$934$	12.9123	0.422502
$935$	0	0
$936$	−10.2666	−0.335574
$937$	0.266191	0.00869607	0.00434804	−	0.999991i	$-0.498616\pi$
$937$	0.266191	0.00869607	0.00434804	+	0.999991i	$0.498616\pi$
$938$	64.9553	2.12087
$939$	−2.68904	−0.0877533
$940$	0	0
$941$	51.4216	1.67630	0.838149	−	0.545442i	$-0.183638\pi$
$941$	51.4216	1.67630	0.838149	+	0.545442i	$0.183638\pi$
$942$	22.0192	0.717424
$943$	7.08072	0.230580
$944$	41.4157	1.34797
$945$	0	0
$946$	−14.7254	−0.478764
$947$	−27.9541	−0.908385	−0.454192	−	0.890904i	$-0.650072\pi$
$947$	−27.9541	−0.908385	−0.454192	+	0.890904i	$0.650072\pi$
$948$	−9.25946	−0.300733
$949$	40.2020	1.30501
$950$	0	0
$951$	−4.65829	−0.151055
$952$	27.1783	0.880853
$953$	3.48949	0.113036	0.0565178	−	0.998402i	$-0.482000\pi$
$953$	3.48949	0.113036	0.0565178	+	0.998402i	$0.482000\pi$
$954$	4.37241	0.141562
$955$	0	0
$956$	−15.9276	−0.515137
$957$	18.6674	0.603431
$958$	−0.545910	−0.0176376
$959$	39.7029	1.28207
$960$	0	0
$961$	−30.5132	−0.984297
$962$	−62.7812	−2.02415
$963$	19.7935	0.637836
$964$	9.45780	0.304615
$965$	0	0
$966$	−10.0361	−0.322907
$967$	−15.8726	−0.510430	−0.255215	−	0.966884i	$-0.582146\pi$
$967$	−15.8726	−0.510430	−0.255215	+	0.966884i	$0.582146\pi$
$968$	15.4068	0.495194
$969$	13.3427	0.428628
$970$	0	0
$971$	44.2670	1.42060	0.710298	−	0.703901i	$-0.248560\pi$
$971$	44.2670	1.42060	0.710298	+	0.703901i	$0.248560\pi$
$972$	−0.590961	−0.0189551
$973$	1.20031	0.0384800
$974$	−53.0089	−1.69851
$975$	0	0
$976$	−41.0001	−1.31238
$977$	−0.648897	−0.0207601	−0.0103800	−	0.999946i	$-0.503304\pi$
$977$	−0.648897	−0.0207601	−0.0103800	+	0.999946i	$0.503304\pi$
$978$	28.2994	0.904915
$979$	−29.8327	−0.953458
$980$	0	0
$981$	−1.61314	−0.0515036
$982$	3.78533	0.120795
$983$	28.4868	0.908586	0.454293	−	0.890852i	$-0.349892\pi$
$983$	28.4868	0.908586	0.454293	+	0.890852i	$0.349892\pi$
$984$	7.44740	0.237414
$985$	0	0
$986$	−60.7134	−1.93351
$987$	−2.89141	−0.0920346
$988$	8.61223	0.273991
$989$	9.61778	0.305828
$990$	0	0
$991$	45.7840	1.45438	0.727189	−	0.686437i	$-0.240826\pi$
$991$	45.7840	1.45438	0.727189	+	0.686437i	$0.240826\pi$
$992$	−2.26249	−0.0718343
$993$	17.7902	0.564554
$994$	−73.3935	−2.32790
$995$	0	0
$996$	−3.05595	−0.0968314
$997$	44.8082	1.41909	0.709546	−	0.704659i	$-0.248900\pi$
$997$	44.8082	1.41909	0.709546	+	0.704659i	$0.248900\pi$
$998$	−6.07140	−0.192187
$999$	8.61642	0.272612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.be.1.6	yes	8
5.4	even	2		3525.2.a.bd.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.bd.1.3	✓	8	5.4	even	2
3525.2.a.be.1.6	yes	8	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.60965 q^{2} -1.00000 q^{3} +0.590961 q^{4} -1.60965 q^{6} +2.89141 q^{7} -2.26805 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.60965 q^{2} -1.00000 q^{3} +0.590961 q^{4} -1.60965 q^{6} +2.89141 q^{7} -2.26805 q^{8} +1.00000 q^{9} -2.05110 q^{11} -0.590961 q^{12} +4.52660 q^{13} +4.65415 q^{14} -4.83269 q^{16} -4.14437 q^{17} +1.60965 q^{18} +3.21947 q^{19} -2.89141 q^{21} -3.30155 q^{22} +2.15638 q^{23} +2.26805 q^{24} +7.28623 q^{26} -1.00000 q^{27} +1.70871 q^{28} +9.10114 q^{29} +0.697696 q^{31} -3.24281 q^{32} +2.05110 q^{33} -6.67097 q^{34} +0.590961 q^{36} -8.61642 q^{37} +5.18220 q^{38} -4.52660 q^{39} +3.28361 q^{41} -4.65415 q^{42} +4.46014 q^{43} -1.21212 q^{44} +3.47101 q^{46} +1.00000 q^{47} +4.83269 q^{48} +1.36026 q^{49} +4.14437 q^{51} +2.67505 q^{52} +2.71638 q^{53} -1.60965 q^{54} -6.55788 q^{56} -3.21947 q^{57} +14.6496 q^{58} -8.56992 q^{59} +8.48391 q^{61} +1.12304 q^{62} +2.89141 q^{63} +4.44560 q^{64} +3.30155 q^{66} +13.9564 q^{67} -2.44916 q^{68} -2.15638 q^{69} -15.7695 q^{71} -2.26805 q^{72} +8.88127 q^{73} -13.8694 q^{74} +1.90258 q^{76} -5.93059 q^{77} -7.28623 q^{78} +15.6685 q^{79} +1.00000 q^{81} +5.28545 q^{82} +5.17115 q^{83} -1.70871 q^{84} +7.17925 q^{86} -9.10114 q^{87} +4.65202 q^{88} +14.5447 q^{89} +13.0883 q^{91} +1.27434 q^{92} -0.697696 q^{93} +1.60965 q^{94} +3.24281 q^{96} -0.136874 q^{97} +2.18954 q^{98} -2.05110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * q^99

Introduction

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