LMFDB - Embedded newform 575.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} - 2x + 1 $ x^4 - 5x^2 - 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.751024$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.751024 q^{2} -0.580491 q^{3} -1.43596 q^{4} +0.435963 q^{6} +0.315061 q^{7} +2.58049 q^{8} -2.66303 q^{9} +O(q^{10})$	\(q-0.751024 q^{2} -0.580491 q^{3} -1.43596 q^{4} +0.435963 q^{6} +0.315061 q^{7} +2.58049 q^{8} -2.66303 q^{9} -4.34797 q^{11} +0.833563 q^{12} +4.58049 q^{13} -0.236619 q^{14} +0.933914 q^{16} +0.917461 q^{17} +2.00000 q^{18} +2.76748 q^{19} -0.182890 q^{21} +3.26543 q^{22} -1.00000 q^{23} -1.49795 q^{24} -3.44006 q^{26} +3.28734 q^{27} -0.452416 q^{28} +7.03291 q^{29} -0.867829 q^{31} -5.86237 q^{32} +2.52396 q^{33} -0.689035 q^{34} +3.82401 q^{36} +4.68904 q^{37} -2.07844 q^{38} -2.65893 q^{39} +4.69184 q^{41} +0.137355 q^{42} +9.08944 q^{43} +6.24352 q^{44} +0.751024 q^{46} +8.24762 q^{47} -0.542129 q^{48} -6.90074 q^{49} -0.532578 q^{51} -6.57741 q^{52} +10.9048 q^{53} -2.46887 q^{54} +0.813013 q^{56} -1.60650 q^{57} -5.28188 q^{58} +1.50205 q^{59} +11.4634 q^{61} +0.651760 q^{62} -0.839018 q^{63} +2.53496 q^{64} -1.89555 q^{66} -1.68494 q^{67} -1.31744 q^{68} +0.580491 q^{69} -5.36578 q^{71} -6.87193 q^{72} -10.1484 q^{73} -3.52158 q^{74} -3.97400 q^{76} -1.36988 q^{77} +1.99692 q^{78} +7.39760 q^{79} +6.08082 q^{81} -3.52369 q^{82} -15.3052 q^{83} +0.262624 q^{84} -6.82639 q^{86} -4.08254 q^{87} -11.2199 q^{88} -10.9326 q^{89} +1.44314 q^{91} +1.43596 q^{92} +0.503767 q^{93} -6.19416 q^{94} +3.40306 q^{96} +14.2158 q^{97} +5.18262 q^{98} +11.5788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9} + 2 q^{11} - 10 q^{12} + 14 q^{13} - 4 q^{14} + 2 q^{16} + 14 q^{17} + 8 q^{18} - 4 q^{19} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 12 q^{24} + 6 q^{26} + 14 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{32} + 14 q^{33} + 14 q^{34} - 8 q^{36} + 2 q^{37} - 10 q^{38} - 8 q^{39} - 8 q^{41} - 24 q^{42} + 4 q^{43} + 6 q^{44} + 2 q^{47} + 10 q^{51} + 18 q^{52} + 4 q^{53} + 22 q^{54} + 14 q^{56} - 8 q^{61} - 28 q^{62} - 12 q^{63} - 20 q^{64} - 8 q^{66} - 2 q^{67} + 8 q^{68} - 2 q^{69} - 24 q^{71} - 12 q^{72} + 18 q^{73} - 36 q^{74} - 18 q^{76} + 4 q^{77} - 32 q^{78} + 24 q^{79} + 8 q^{81} + 32 q^{82} - 6 q^{83} + 2 q^{84} + 14 q^{86} - 6 q^{87} - 10 q^{88} - 8 q^{89} + 26 q^{91} - 2 q^{92} + 2 q^{93} - 42 q^{94} + 30 q^{96} + 34 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9 + 2 * q^11 - 10 * q^12 + 14 * q^13 - 4 * q^14 + 2 * q^16 + 14 * q^17 + 8 * q^18 - 4 * q^19 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 12 * q^24 + 6 * q^26 + 14 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^32 + 14 * q^33 + 14 * q^34 - 8 * q^36 + 2 * q^37 - 10 * q^38 - 8 * q^39 - 8 * q^41 - 24 * q^42 + 4 * q^43 + 6 * q^44 + 2 * q^47 + 10 * q^51 + 18 * q^52 + 4 * q^53 + 22 * q^54 + 14 * q^56 - 8 * q^61 - 28 * q^62 - 12 * q^63 - 20 * q^64 - 8 * q^66 - 2 * q^67 + 8 * q^68 - 2 * q^69 - 24 * q^71 - 12 * q^72 + 18 * q^73 - 36 * q^74 - 18 * q^76 + 4 * q^77 - 32 * q^78 + 24 * q^79 + 8 * q^81 + 32 * q^82 - 6 * q^83 + 2 * q^84 + 14 * q^86 - 6 * q^87 - 10 * q^88 - 8 * q^89 + 26 * q^91 - 2 * q^92 + 2 * q^93 - 42 * q^94 + 30 * q^96 + 34 * q^97 - 28 * q^98 + 36 * 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 $

$2$	−0.751024	−0.531054	−0.265527	−	0.964103i	$-0.585546\pi$
$2$	−0.751024	−0.531054	−0.265527	+	0.964103i	$0.585546\pi$
$3$	−0.580491	−0.335147	−0.167573	−	0.985860i	$-0.553593\pi$
$3$	−0.580491	−0.335147	−0.167573	+	0.985860i	$0.553593\pi$
$4$	−1.43596	−0.717981
$5$	0	0
$5$	0	0
$6$	0.435963	0.177981
$7$	0.315061	0.119082	0.0595410	−	0.998226i	$-0.481036\pi$
$7$	0.315061	0.119082	0.0595410	+	0.998226i	$0.481036\pi$
$8$	2.58049	0.912341
$9$	−2.66303	−0.887677
$10$	0	0
$11$	−4.34797	−1.31096	−0.655481	−	0.755212i	$-0.727534\pi$
$11$	−4.34797	−1.31096	−0.655481	+	0.755212i	$0.727534\pi$
$12$	0.833563	0.240629
$13$	4.58049	1.27040	0.635200	−	0.772348i	$-0.280918\pi$
$13$	4.58049	1.27040	0.635200	+	0.772348i	$0.280918\pi$
$14$	−0.236619	−0.0632390
$15$	0	0
$16$	0.933914	0.233479
$17$	0.917461	0.222517	0.111258	−	0.993792i	$-0.464512\pi$
$17$	0.917461	0.222517	0.111258	+	0.993792i	$0.464512\pi$
$18$	2.00000	0.471405
$19$	2.76748	0.634903	0.317451	−	0.948275i	$-0.397173\pi$
$19$	2.76748	0.634903	0.317451	+	0.948275i	$0.397173\pi$
$20$	0	0
$21$	−0.182890	−0.0399099
$22$	3.26543	0.696192
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.49795	−0.305768
$25$	0	0
$26$	−3.44006	−0.674651
$27$	3.28734	0.632648
$28$	−0.452416	−0.0854987
$29$	7.03291	1.30598	0.652989	−	0.757367i	$-0.273515\pi$
$29$	7.03291	1.30598	0.652989	+	0.757367i	$0.273515\pi$
$30$	0	0
$31$	−0.867829	−0.155867	−0.0779333	−	0.996959i	$-0.524832\pi$
$31$	−0.867829	−0.155867	−0.0779333	+	0.996959i	$0.524832\pi$
$32$	−5.86237	−1.03633
$33$	2.52396	0.439364
$34$	−0.689035	−0.118169
$35$	0	0
$36$	3.82401	0.637335
$37$	4.68904	0.770873	0.385436	−	0.922734i	$-0.374051\pi$
$37$	4.68904	0.770873	0.385436	+	0.922734i	$0.374051\pi$
$38$	−2.07844	−0.337168
$39$	−2.65893	−0.425770
$40$	0	0
$41$	4.69184	0.732742	0.366371	−	0.930469i	$-0.380600\pi$
$41$	4.69184	0.732742	0.366371	+	0.930469i	$0.380600\pi$
$42$	0.137355	0.0211943
$43$	9.08944	1.38613	0.693063	−	0.720877i	$-0.256261\pi$
$43$	9.08944	1.38613	0.693063	+	0.720877i	$0.256261\pi$
$44$	6.24352	0.941246
$45$	0	0
$46$	0.751024	0.110732
$47$	8.24762	1.20304	0.601519	−	0.798858i	$-0.294562\pi$
$47$	8.24762	1.20304	0.601519	+	0.798858i	$0.294562\pi$
$48$	−0.542129	−0.0782496
$49$	−6.90074	−0.985819
$50$	0	0
$51$	−0.532578	−0.0745758
$52$	−6.57741	−0.912123
$53$	10.9048	1.49789	0.748947	−	0.662630i	$-0.230560\pi$
$53$	10.9048	1.49789	0.748947	+	0.662630i	$0.230560\pi$
$54$	−2.46887	−0.335971
$55$	0	0
$56$	0.813013	0.108643
$57$	−1.60650	−0.212786
$58$	−5.28188	−0.693545
$59$	1.50205	0.195550	0.0977750	−	0.995209i	$-0.468827\pi$
$59$	1.50205	0.195550	0.0977750	+	0.995209i	$0.468827\pi$
$60$	0	0
$61$	11.4634	1.46774	0.733870	−	0.679290i	$-0.237712\pi$
$61$	11.4634	1.46774	0.733870	+	0.679290i	$0.237712\pi$
$62$	0.651760	0.0827737
$63$	−0.839018	−0.105706
$64$	2.53496	0.316869
$65$	0	0
$66$	−1.89555	−0.233326
$67$	−1.68494	−0.205848	−0.102924	−	0.994689i	$-0.532820\pi$
$67$	−1.68494	−0.205848	−0.102924	+	0.994689i	$0.532820\pi$
$68$	−1.31744	−0.159763
$69$	0.580491	0.0698829
$70$	0	0
$71$	−5.36578	−0.636801	−0.318401	−	0.947956i	$-0.603146\pi$
$71$	−5.36578	−0.636801	−0.318401	+	0.947956i	$0.603146\pi$
$72$	−6.87193	−0.809864
$73$	−10.1484	−1.18778	−0.593888	−	0.804548i	$-0.702408\pi$
$73$	−10.1484	−1.18778	−0.593888	+	0.804548i	$0.702408\pi$
$74$	−3.52158	−0.409375
$75$	0	0
$76$	−3.97400	−0.455848
$77$	−1.36988	−0.156112
$78$	1.99692	0.226107
$79$	7.39760	0.832295	0.416148	−	0.909297i	$-0.363380\pi$
$79$	7.39760	0.832295	0.416148	+	0.909297i	$0.363380\pi$
$80$	0	0
$81$	6.08082	0.675647
$82$	−3.52369	−0.389126
$83$	−15.3052	−1.67997	−0.839984	−	0.542611i	$-0.817436\pi$
$83$	−15.3052	−1.67997	−0.839984	+	0.542611i	$0.817436\pi$
$84$	0.262624	0.0286546
$85$	0	0
$86$	−6.82639	−0.736109
$87$	−4.08254	−0.437694
$88$	−11.2199	−1.19604
$89$	−10.9326	−1.15885	−0.579424	−	0.815026i	$-0.696723\pi$
$89$	−10.9326	−1.15885	−0.579424	+	0.815026i	$0.696723\pi$
$90$	0	0
$91$	1.44314	0.151282
$92$	1.43596	0.149709
$93$	0.503767	0.0522382
$94$	−6.19416	−0.638879
$95$	0	0
$96$	3.40306	0.347323
$97$	14.2158	1.44340	0.721698	−	0.692208i	$-0.243362\pi$
$97$	14.2158	1.44340	0.721698	+	0.692208i	$0.243362\pi$
$98$	5.18262	0.523524
$99$	11.5788	1.16371
$100$	0	0
$101$	−8.16508	−0.812456	−0.406228	−	0.913772i	$-0.633156\pi$
$101$	−8.16508	−0.812456	−0.406228	+	0.913772i	$0.633156\pi$
$102$	0.399979	0.0396038
$103$	0.287338	0.0283122	0.0141561	−	0.999900i	$-0.495494\pi$
$103$	0.287338	0.0283122	0.0141561	+	0.999900i	$0.495494\pi$
$104$	11.8199	1.15904
$105$	0	0
$106$	−8.18979	−0.795463
$107$	−14.0935	−1.36247	−0.681237	−	0.732063i	$-0.738558\pi$
$107$	−14.0935	−1.36247	−0.681237	+	0.732063i	$0.738558\pi$
$108$	−4.72049	−0.454230
$109$	1.76338	0.168901	0.0844506	−	0.996428i	$-0.473086\pi$
$109$	1.76338	0.168901	0.0844506	+	0.996428i	$0.473086\pi$
$110$	0	0
$111$	−2.72194	−0.258355
$112$	0.294240	0.0278031
$113$	−0.315061	−0.0296385	−0.0148192	−	0.999890i	$-0.504717\pi$
$113$	−0.315061	−0.0296385	−0.0148192	+	0.999890i	$0.504717\pi$
$114$	1.20652	0.113001
$115$	0	0
$116$	−10.0990	−0.937668
$117$	−12.1980	−1.12770
$118$	−1.12807	−0.103848
$119$	0.289056	0.0264978
$120$	0	0
$121$	7.90483	0.718621
$122$	−8.60930	−0.779450
$123$	−2.72357	−0.245576
$124$	1.24617	0.111909
$125$	0	0
$126$	0.630123	0.0561358
$127$	21.3284	1.89259	0.946296	−	0.323300i	$-0.104792\pi$
$127$	21.3284	1.89259	0.946296	+	0.323300i	$0.104792\pi$
$128$	9.82094	0.868056
$129$	−5.27634	−0.464556
$130$	0	0
$131$	8.11373	0.708900	0.354450	−	0.935075i	$-0.384668\pi$
$131$	8.11373	0.708900	0.354450	+	0.935075i	$0.384668\pi$
$132$	−3.62431	−0.315455
$133$	0.871925	0.0756055
$134$	1.26543	0.109316
$135$	0	0
$136$	2.36750	0.203011
$137$	7.22680	0.617427	0.308713	−	0.951155i	$-0.400102\pi$
$137$	7.22680	0.617427	0.308713	+	0.951155i	$0.400102\pi$
$138$	−0.435963	−0.0371116
$139$	−10.8431	−0.919701	−0.459850	−	0.887996i	$-0.652097\pi$
$139$	−10.8431	−0.919701	−0.459850	+	0.887996i	$0.652097\pi$
$140$	0	0
$141$	−4.78767	−0.403194
$142$	4.02983	0.338176
$143$	−19.9158	−1.66545
$144$	−2.48704	−0.207254
$145$	0	0
$146$	7.62166	0.630773
$147$	4.00582	0.330394
$148$	−6.73328	−0.553472
$149$	−7.90074	−0.647254	−0.323627	−	0.946185i	$-0.604902\pi$
$149$	−7.90074	−0.647254	−0.323627	+	0.946185i	$0.604902\pi$
$150$	0	0
$151$	−8.03700	−0.654042	−0.327021	−	0.945017i	$-0.606045\pi$
$151$	−8.03700	−0.654042	−0.327021	+	0.945017i	$0.606045\pi$
$152$	7.14145	0.579248
$153$	−2.44323	−0.197523
$154$	1.02881	0.0829039
$155$	0	0
$156$	3.81813	0.305695
$157$	4.75928	0.379832	0.189916	−	0.981800i	$-0.439178\pi$
$157$	4.75928	0.379832	0.189916	+	0.981800i	$0.439178\pi$
$158$	−5.55578	−0.441994
$159$	−6.33016	−0.502014
$160$	0	0
$161$	−0.315061	−0.0248303
$162$	−4.56684	−0.358805
$163$	2.11545	0.165695	0.0828473	−	0.996562i	$-0.473599\pi$
$163$	2.11545	0.165695	0.0828473	+	0.996562i	$0.473599\pi$
$164$	−6.73731	−0.526095
$165$	0	0
$166$	11.4946	0.892154
$167$	−15.8760	−1.22852	−0.614262	−	0.789102i	$-0.710546\pi$
$167$	−15.8760	−1.22852	−0.614262	+	0.789102i	$0.710546\pi$
$168$	−0.471947	−0.0364115
$169$	7.98090	0.613915
$170$	0	0
$171$	−7.36988	−0.563589
$172$	−13.0521	−0.995213
$173$	−0.0767241	−0.00583323	−0.00291661	−	0.999996i	$-0.500928\pi$
$173$	−0.0767241	−0.00583323	−0.00291661	+	0.999996i	$0.500928\pi$
$174$	3.06609	0.232439
$175$	0	0
$176$	−4.06063	−0.306082
$177$	−0.871925	−0.0655379
$178$	8.21061	0.615412
$179$	−20.7247	−1.54904	−0.774520	−	0.632549i	$-0.782009\pi$
$179$	−20.7247	−1.54904	−0.774520	+	0.632549i	$0.782009\pi$
$180$	0	0
$181$	−11.5610	−0.859319	−0.429660	−	0.902991i	$-0.641366\pi$
$181$	−11.5610	−0.859319	−0.429660	+	0.902991i	$0.641366\pi$
$182$	−1.08383	−0.0803388
$183$	−6.65441	−0.491908
$184$	−2.58049	−0.190236
$185$	0	0
$186$	−0.378341	−0.0277413
$187$	−3.98909	−0.291711
$188$	−11.8433	−0.863759
$189$	1.03571	0.0753371
$190$	0	0
$191$	21.9683	1.58957	0.794784	−	0.606892i	$-0.207584\pi$
$191$	21.9683	1.58957	0.794784	+	0.606892i	$0.207584\pi$
$192$	−1.47152	−0.106198
$193$	20.2914	1.46061	0.730305	−	0.683122i	$-0.239378\pi$
$193$	20.2914	1.46061	0.730305	+	0.683122i	$0.239378\pi$
$194$	−10.6764	−0.766521
$195$	0	0
$196$	9.90920	0.707800
$197$	8.62159	0.614263	0.307131	−	0.951667i	$-0.400631\pi$
$197$	8.62159	0.614263	0.307131	+	0.951667i	$0.400631\pi$
$198$	−8.69594	−0.617993
$199$	20.7796	1.47302	0.736512	−	0.676424i	$-0.236471\pi$
$199$	20.7796	1.47302	0.736512	+	0.676424i	$0.236471\pi$
$200$	0	0
$201$	0.978092	0.0689893
$202$	6.13217	0.431458
$203$	2.21580	0.155519
$204$	0.764762	0.0535440
$205$	0	0
$206$	−0.215798	−0.0150353
$207$	2.66303	0.185093
$208$	4.27779	0.296611
$209$	−12.0329	−0.832334
$210$	0	0
$211$	−4.16508	−0.286736	−0.143368	−	0.989669i	$-0.545793\pi$
$211$	−4.16508	−0.286736	−0.143368	+	0.989669i	$0.545793\pi$
$212$	−15.6589	−1.07546
$213$	3.11479	0.213422
$214$	10.5846	0.723548
$215$	0	0
$216$	8.48295	0.577191
$217$	−0.273419	−0.0185609
$218$	−1.32434	−0.0896958
$219$	5.89103	0.398079
$220$	0	0
$221$	4.20242	0.282685
$222$	2.04424	0.137201
$223$	18.7618	1.25638	0.628190	−	0.778060i	$-0.283796\pi$
$223$	18.7618	1.25638	0.628190	+	0.778060i	$0.283796\pi$
$224$	−1.84701	−0.123408
$225$	0	0
$226$	0.236619	0.0157396
$227$	−10.9637	−0.727689	−0.363845	−	0.931460i	$-0.618536\pi$
$227$	−10.9637	−0.727689	−0.363845	+	0.931460i	$0.618536\pi$
$228$	2.30687	0.152776
$229$	25.9367	1.71394	0.856971	−	0.515364i	$-0.172343\pi$
$229$	25.9367	1.71394	0.856971	+	0.515364i	$0.172343\pi$
$230$	0	0
$231$	0.795201	0.0523204
$232$	18.1484	1.19150
$233$	8.23942	0.539783	0.269891	−	0.962891i	$-0.413012\pi$
$233$	8.23942	0.539783	0.269891	+	0.962891i	$0.413012\pi$
$234$	9.16098	0.598872
$235$	0	0
$236$	−2.15689	−0.140401
$237$	−4.29424	−0.278941
$238$	−0.217088	−0.0140718
$239$	16.0508	1.03824	0.519120	−	0.854701i	$-0.326260\pi$
$239$	16.0508	1.03824	0.519120	+	0.854701i	$0.326260\pi$
$240$	0	0
$241$	−2.09755	−0.135115	−0.0675574	−	0.997715i	$-0.521521\pi$
$241$	−2.09755	−0.135115	−0.0675574	+	0.997715i	$0.521521\pi$
$242$	−5.93672	−0.381627
$243$	−13.3919	−0.859089
$244$	−16.4610	−1.05381
$245$	0	0
$246$	2.04547	0.130414
$247$	12.6764	0.806580
$248$	−2.23942	−0.142204
$249$	8.88455	0.563036
$250$	0	0
$251$	−13.7018	−0.864847	−0.432423	−	0.901671i	$-0.642341\pi$
$251$	−13.7018	−0.864847	−0.432423	+	0.901671i	$0.642341\pi$
$252$	1.20480	0.0758952
$253$	4.34797	0.273354
$254$	−16.0182	−1.00507
$255$	0	0
$256$	−12.4457	−0.777854
$257$	−0.998281	−0.0622711	−0.0311355	−	0.999515i	$-0.509912\pi$
$257$	−0.998281	−0.0622711	−0.0311355	+	0.999515i	$0.509912\pi$
$258$	3.96266	0.246704
$259$	1.47733	0.0917971
$260$	0	0
$261$	−18.7288	−1.15929
$262$	−6.09361	−0.376464
$263$	9.18527	0.566388	0.283194	−	0.959063i	$-0.408606\pi$
$263$	9.18527	0.566388	0.283194	+	0.959063i	$0.408606\pi$
$264$	6.51305	0.400850
$265$	0	0
$266$	−0.654837	−0.0401506
$267$	6.34625	0.388384
$268$	2.41951	0.147795
$269$	21.4398	1.30721	0.653603	−	0.756837i	$-0.273256\pi$
$269$	21.4398	1.30721	0.653603	+	0.756837i	$0.273256\pi$
$270$	0	0
$271$	−25.2488	−1.53376	−0.766878	−	0.641793i	$-0.778191\pi$
$271$	−25.2488	−1.53376	−0.766878	+	0.641793i	$0.778191\pi$
$272$	0.856830	0.0519529
$273$	−0.837727	−0.0507016
$274$	−5.42750	−0.327887
$275$	0	0
$276$	−0.833563	−0.0501746
$277$	30.8114	1.85128	0.925638	−	0.378409i	$-0.123529\pi$
$277$	30.8114	1.85128	0.925638	+	0.378409i	$0.123529\pi$
$278$	8.14344	0.488411
$279$	2.31105	0.138359
$280$	0	0
$281$	3.60821	0.215248	0.107624	−	0.994192i	$-0.465676\pi$
$281$	3.60821	0.215248	0.107624	+	0.994192i	$0.465676\pi$
$282$	3.59565	0.214118
$283$	−5.23942	−0.311451	−0.155726	−	0.987800i	$-0.549772\pi$
$283$	−5.23942	−0.311451	−0.155726	+	0.987800i	$0.549772\pi$
$284$	7.70506	0.457211
$285$	0	0
$286$	14.9573	0.884442
$287$	1.47822	0.0872565
$288$	15.6117	0.919927
$289$	−16.1583	−0.950486
$290$	0	0
$291$	−8.25214	−0.483749
$292$	14.5727	0.852800
$293$	1.90074	0.111042	0.0555211	−	0.998458i	$-0.482318\pi$
$293$	1.90074	0.111042	0.0555211	+	0.998458i	$0.482318\pi$
$294$	−3.00846	−0.175457
$295$	0	0
$296$	12.1000	0.703299
$297$	−14.2932	−0.829378
$298$	5.93364	0.343727
$299$	−4.58049	−0.264897
$300$	0	0
$301$	2.86373	0.165063
$302$	6.03598	0.347332
$303$	4.73975	0.272292
$304$	2.58459	0.148236
$305$	0	0
$306$	1.83492	0.104895
$307$	2.82467	0.161213	0.0806063	−	0.996746i	$-0.474314\pi$
$307$	2.82467	0.161213	0.0806063	+	0.996746i	$0.474314\pi$
$308$	1.96709	0.112086
$309$	−0.166797	−0.00948875
$310$	0	0
$311$	16.1028	0.913107	0.456554	−	0.889696i	$-0.349084\pi$
$311$	16.1028	0.913107	0.456554	+	0.889696i	$0.349084\pi$
$312$	−6.86135	−0.388448
$313$	26.3740	1.49075	0.745373	−	0.666648i	$-0.232272\pi$
$313$	26.3740	1.49075	0.745373	+	0.666648i	$0.232272\pi$
$314$	−3.57434	−0.201712
$315$	0	0
$316$	−10.6227	−0.597572
$317$	−15.5020	−0.870682	−0.435341	−	0.900266i	$-0.643372\pi$
$317$	−15.5020	−0.870682	−0.435341	+	0.900266i	$0.643372\pi$
$318$	4.75410	0.266597
$319$	−30.5789	−1.71209
$320$	0	0
$321$	8.18117	0.456628
$322$	0.236619	0.0131862
$323$	2.53905	0.141277
$324$	−8.73183	−0.485102
$325$	0	0
$326$	−1.58875	−0.0879928
$327$	−1.02363	−0.0566067
$328$	12.1073	0.668511
$329$	2.59851	0.143260
$330$	0	0
$331$	19.0302	1.04599	0.522997	−	0.852335i	$-0.324814\pi$
$331$	19.0302	1.04599	0.522997	+	0.852335i	$0.324814\pi$
$332$	21.9778	1.20619
$333$	−12.4870	−0.684286
$334$	11.9233	0.652413
$335$	0	0
$336$	−0.170804	−0.00931812
$337$	−4.09354	−0.222989	−0.111495	−	0.993765i	$-0.535564\pi$
$337$	−4.09354	−0.222989	−0.111495	+	0.993765i	$0.535564\pi$
$338$	−5.99385	−0.326022
$339$	0.182890	0.00993324
$340$	0	0
$341$	3.77329	0.204335
$342$	5.53496	0.299296
$343$	−4.37959	−0.236475
$344$	23.4552	1.26462
$345$	0	0
$346$	0.0576217	0.00309776
$347$	−17.4357	−0.935997	−0.467998	−	0.883729i	$-0.655025\pi$
$347$	−17.4357	−0.935997	−0.467998	+	0.883729i	$0.655025\pi$
$348$	5.86237	0.314256
$349$	8.48770	0.454336	0.227168	−	0.973856i	$-0.427053\pi$
$349$	8.48770	0.454336	0.227168	+	0.973856i	$0.427053\pi$
$350$	0	0
$351$	15.0576	0.803716
$352$	25.4894	1.35859
$353$	20.5696	1.09481	0.547404	−	0.836868i	$-0.315616\pi$
$353$	20.5696	1.09481	0.547404	+	0.836868i	$0.315616\pi$
$354$	0.654837	0.0348042
$355$	0	0
$356$	15.6987	0.832032
$357$	−0.167795	−0.00888064
$358$	15.5648	0.822625
$359$	−22.4121	−1.18286	−0.591432	−	0.806355i	$-0.701437\pi$
$359$	−22.4121	−1.18286	−0.591432	+	0.806355i	$0.701437\pi$
$360$	0	0
$361$	−11.3411	−0.596898
$362$	8.68256	0.456345
$363$	−4.58868	−0.240843
$364$	−2.07229	−0.108617
$365$	0	0
$366$	4.99762	0.261230
$367$	−21.9401	−1.14526	−0.572632	−	0.819812i	$-0.694078\pi$
$367$	−21.9401	−1.14526	−0.572632	+	0.819812i	$0.694078\pi$
$368$	−0.933914	−0.0486837
$369$	−12.4945	−0.650438
$370$	0	0
$371$	3.43569	0.178372
$372$	−0.723390	−0.0375060
$373$	0.853821	0.0442092	0.0221046	−	0.999756i	$-0.492963\pi$
$373$	0.853821	0.0442092	0.0221046	+	0.999756i	$0.492963\pi$
$374$	2.99590	0.154914
$375$	0	0
$376$	21.2829	1.09758
$377$	32.2142	1.65911
$378$	−0.777846	−0.0400081
$379$	−2.52049	−0.129469	−0.0647345	−	0.997903i	$-0.520620\pi$
$379$	−2.52049	−0.129469	−0.0647345	+	0.997903i	$0.520620\pi$
$380$	0	0
$381$	−12.3810	−0.634296
$382$	−16.4987	−0.844147
$383$	−13.5983	−0.694841	−0.347420	−	0.937709i	$-0.612942\pi$
$383$	−13.5983	−0.694841	−0.347420	+	0.937709i	$0.612942\pi$
$384$	−5.70096	−0.290926
$385$	0	0
$386$	−15.2394	−0.775663
$387$	−24.2055	−1.23043
$388$	−20.4134	−1.03633
$389$	10.7398	0.544527	0.272264	−	0.962223i	$-0.412228\pi$
$389$	10.7398	0.544527	0.272264	+	0.962223i	$0.412228\pi$
$390$	0	0
$391$	−0.917461	−0.0463980
$392$	−17.8073	−0.899404
$393$	−4.70995	−0.237585
$394$	−6.47502	−0.326207
$395$	0	0
$396$	−16.6267	−0.835522
$397$	19.5868	0.983031	0.491516	−	0.870869i	$-0.336443\pi$
$397$	19.5868	0.983031	0.491516	+	0.870869i	$0.336443\pi$
$398$	−15.6060	−0.782256
$399$	−0.506145	−0.0253389
$400$	0	0
$401$	−8.01209	−0.400105	−0.200052	−	0.979785i	$-0.564111\pi$
$401$	−8.01209	−0.400105	−0.200052	+	0.979785i	$0.564111\pi$
$402$	−0.734570	−0.0366370
$403$	−3.97508	−0.198013
$404$	11.7247	0.583328
$405$	0	0
$406$	−1.66412	−0.0825888
$407$	−20.3878	−1.01058
$408$	−1.37431	−0.0680386
$409$	−28.2350	−1.39613	−0.698065	−	0.716034i	$-0.745955\pi$
$409$	−28.2350	−1.39613	−0.698065	+	0.716034i	$0.745955\pi$
$410$	0	0
$411$	−4.19509	−0.206929
$412$	−0.412607	−0.0203277
$413$	0.473237	0.0232865
$414$	−2.00000	−0.0982946
$415$	0	0
$416$	−26.8526	−1.31655
$417$	6.29433	0.308235
$418$	9.03700	0.442014
$419$	−21.9470	−1.07218	−0.536091	−	0.844160i	$-0.680100\pi$
$419$	−21.9470	−1.07218	−0.536091	+	0.844160i	$0.680100\pi$
$420$	0	0
$421$	0.747198	0.0364162	0.0182081	−	0.999834i	$-0.494204\pi$
$421$	0.747198	0.0364162	0.0182081	+	0.999834i	$0.494204\pi$
$422$	3.12807	0.152272
$423$	−21.9637	−1.06791
$424$	28.1398	1.36659
$425$	0	0
$426$	−2.33928	−0.113339
$427$	3.61168	0.174781
$428$	20.2378	0.978231
$429$	11.5610	0.558168
$430$	0	0
$431$	27.3642	1.31808	0.659042	−	0.752106i	$-0.270962\pi$
$431$	27.3642	1.31808	0.659042	+	0.752106i	$0.270962\pi$
$432$	3.07009	0.147710
$433$	25.4265	1.22192	0.610960	−	0.791662i	$-0.290784\pi$
$433$	25.4265	1.22192	0.610960	+	0.791662i	$0.290784\pi$
$434$	0.205345	0.00985685
$435$	0	0
$436$	−2.53215	−0.121268
$437$	−2.76748	−0.132386
$438$	−4.42430	−0.211401
$439$	−30.8097	−1.47047	−0.735233	−	0.677815i	$-0.762927\pi$
$439$	−30.8097	−1.47047	−0.735233	+	0.677815i	$0.762927\pi$
$440$	0	0
$441$	18.3769	0.875089
$442$	−3.15612	−0.150121
$443$	−24.5778	−1.16773	−0.583863	−	0.811852i	$-0.698459\pi$
$443$	−24.5778	−1.16773	−0.583863	+	0.811852i	$0.698459\pi$
$444$	3.90861	0.185494
$445$	0	0
$446$	−14.0905	−0.667206
$447$	4.58631	0.216925
$448$	0.798667	0.0377335
$449$	38.6816	1.82550	0.912749	−	0.408522i	$-0.133956\pi$
$449$	38.6816	1.82550	0.912749	+	0.408522i	$0.133956\pi$
$450$	0	0
$451$	−20.4000	−0.960597
$452$	0.452416	0.0212799
$453$	4.66541	0.219200
$454$	8.23404	0.386443
$455$	0	0
$456$	−4.14555	−0.194133
$457$	−6.40041	−0.299398	−0.149699	−	0.988732i	$-0.547831\pi$
$457$	−6.40041	−0.299398	−0.149699	+	0.988732i	$0.547831\pi$
$458$	−19.4791	−0.910196
$459$	3.01600	0.140775
$460$	0	0
$461$	−23.8337	−1.11005	−0.555024	−	0.831835i	$-0.687291\pi$
$461$	−23.8337	−1.11005	−0.555024	+	0.831835i	$0.687291\pi$
$462$	−0.597215	−0.0277850
$463$	−26.5529	−1.23402	−0.617008	−	0.786957i	$-0.711655\pi$
$463$	−26.5529	−1.23402	−0.617008	+	0.786957i	$0.711655\pi$
$464$	6.56813	0.304918
$465$	0	0
$466$	−6.18801	−0.286654
$467$	18.6049	0.860931	0.430465	−	0.902607i	$-0.358349\pi$
$467$	18.6049	0.860931	0.430465	+	0.902607i	$0.358349\pi$
$468$	17.5159	0.809671
$469$	−0.530859	−0.0245128
$470$	0	0
$471$	−2.76272	−0.127300
$472$	3.87602	0.178408
$473$	−39.5206	−1.81716
$474$	3.22508	0.148133
$475$	0	0
$476$	−0.415074	−0.0190249
$477$	−29.0399	−1.32965
$478$	−12.0545	−0.551362
$479$	29.9627	1.36903	0.684514	−	0.728999i	$-0.260014\pi$
$479$	29.9627	1.36903	0.684514	+	0.728999i	$0.260014\pi$
$480$	0	0
$481$	21.4781	0.979316
$482$	1.57531	0.0717533
$483$	0.182890	0.00832180
$484$	−11.3510	−0.515957
$485$	0	0
$486$	10.0576	0.456223
$487$	−37.2265	−1.68689	−0.843446	−	0.537214i	$-0.819477\pi$
$487$	−37.2265	−1.68689	−0.843446	+	0.537214i	$0.819477\pi$
$488$	29.5812	1.33908
$489$	−1.22800	−0.0555320
$490$	0	0
$491$	−0.691841	−0.0312224	−0.0156112	−	0.999878i	$-0.504969\pi$
$491$	−0.691841	−0.0312224	−0.0156112	+	0.999878i	$0.504969\pi$
$492$	3.91095	0.176319
$493$	6.45242	0.290602
$494$	−9.52029	−0.428338
$495$	0	0
$496$	−0.810478	−0.0363915
$497$	−1.69055	−0.0758315
$498$	−6.67251	−0.299003
$499$	−24.7988	−1.11014	−0.555072	−	0.831802i	$-0.687309\pi$
$499$	−24.7988	−1.11014	−0.555072	+	0.831802i	$0.687309\pi$
$500$	0	0
$501$	9.21589	0.411735
$502$	10.2903	0.459281
$503$	22.6049	1.00790	0.503951	−	0.863732i	$-0.331879\pi$
$503$	22.6049	1.00790	0.503951	+	0.863732i	$0.331879\pi$
$504$	−2.16508	−0.0964403
$505$	0	0
$506$	−3.26543	−0.145166
$507$	−4.63284	−0.205752
$508$	−30.6268	−1.35885
$509$	−19.1240	−0.847655	−0.423828	−	0.905743i	$-0.639314\pi$
$509$	−19.1240	−0.847655	−0.423828	+	0.905743i	$0.639314\pi$
$510$	0	0
$511$	−3.19735	−0.141443
$512$	−10.2949	−0.454973
$513$	9.09763	0.401670
$514$	0.749733	0.0330693
$515$	0	0
$516$	7.57663	0.333542
$517$	−35.8604	−1.57714
$518$	−1.10951	−0.0487492
$519$	0.0445377	0.00195499
$520$	0	0
$521$	12.8425	0.562638	0.281319	−	0.959614i	$-0.409228\pi$
$521$	12.8425	0.562638	0.281319	+	0.959614i	$0.409228\pi$
$522$	14.0658	0.615644
$523$	−32.8289	−1.43551	−0.717753	−	0.696298i	$-0.754829\pi$
$523$	−32.8289	−1.43551	−0.717753	+	0.696298i	$0.754829\pi$
$524$	−11.6510	−0.508977
$525$	0	0
$526$	−6.89836	−0.300783
$527$	−0.796199	−0.0346830
$528$	2.35716	0.102582
$529$	1.00000	0.0434783
$530$	0	0
$531$	−4.00000	−0.173585
$532$	−1.25205	−0.0542834
$533$	21.4909	0.930876
$534$	−4.76619	−0.206253
$535$	0	0
$536$	−4.34797	−0.187804
$537$	12.0305	0.519156
$538$	−16.1018	−0.694198
$539$	30.0042	1.29237
$540$	0	0
$541$	−25.7261	−1.10605	−0.553026	−	0.833164i	$-0.686527\pi$
$541$	−25.7261	−1.10605	−0.553026	+	0.833164i	$0.686527\pi$
$542$	18.9625	0.814507
$543$	6.71103	0.287998
$544$	−5.37850	−0.230601
$545$	0	0
$546$	0.629153	0.0269253
$547$	36.0191	1.54006	0.770032	−	0.638005i	$-0.220240\pi$
$547$	36.0191	1.54006	0.770032	+	0.638005i	$0.220240\pi$
$548$	−10.3774	−0.443301
$549$	−30.5274	−1.30288
$550$	0	0
$551$	19.4634	0.829169
$552$	1.49795	0.0637571
$553$	2.33070	0.0991114
$554$	−23.1401	−0.983128
$555$	0	0
$556$	15.5703	0.660328
$557$	−36.2148	−1.53447	−0.767235	−	0.641366i	$-0.778368\pi$
$557$	−36.2148	−1.53447	−0.767235	+	0.641366i	$0.778368\pi$
$558$	−1.73566	−0.0734763
$559$	41.6341	1.76094
$560$	0	0
$561$	2.31563	0.0977660
$562$	−2.70986	−0.114308
$563$	−23.3308	−0.983277	−0.491638	−	0.870799i	$-0.663602\pi$
$563$	−23.3308	−0.983277	−0.491638	+	0.870799i	$0.663602\pi$
$564$	6.87491	0.289486
$565$	0	0
$566$	3.93493	0.165398
$567$	1.91583	0.0804574
$568$	−13.8463	−0.580980
$569$	15.6845	0.657529	0.328764	−	0.944412i	$-0.393368\pi$
$569$	15.6845	0.657529	0.328764	+	0.944412i	$0.393368\pi$
$570$	0	0
$571$	38.7600	1.62206	0.811028	−	0.585007i	$-0.198908\pi$
$571$	38.7600	1.62206	0.811028	+	0.585007i	$0.198908\pi$
$572$	28.5984	1.19576
$573$	−12.7524	−0.532738
$574$	−1.11018	−0.0463379
$575$	0	0
$576$	−6.75066	−0.281278
$577$	21.5902	0.898812	0.449406	−	0.893328i	$-0.351636\pi$
$577$	21.5902	0.898812	0.449406	+	0.893328i	$0.351636\pi$
$578$	12.1352	0.504760
$579$	−11.7790	−0.489518
$580$	0	0
$581$	−4.82209	−0.200054
$582$	6.19756	0.256897
$583$	−47.4139	−1.96368
$584$	−26.1877	−1.08366
$585$	0	0
$586$	−1.42750	−0.0589694
$587$	−24.3902	−1.00669	−0.503345	−	0.864086i	$-0.667897\pi$
$587$	−24.3902	−1.00669	−0.503345	+	0.864086i	$0.667897\pi$
$588$	−5.75220	−0.237217
$589$	−2.40170	−0.0989602
$590$	0	0
$591$	−5.00476	−0.205868
$592$	4.37916	0.179982
$593$	13.9747	0.573874	0.286937	−	0.957949i	$-0.407363\pi$
$593$	13.9747	0.573874	0.286937	+	0.957949i	$0.407363\pi$
$594$	10.7346	0.440445
$595$	0	0
$596$	11.3452	0.464716
$597$	−12.0623	−0.493679
$598$	3.44006	0.140674
$599$	−20.9932	−0.857758	−0.428879	−	0.903362i	$-0.641091\pi$
$599$	−20.9932	−0.857758	−0.428879	+	0.903362i	$0.641091\pi$
$600$	0	0
$601$	−13.3007	−0.542546	−0.271273	−	0.962502i	$-0.587445\pi$
$601$	−13.3007	−0.542546	−0.271273	+	0.962502i	$0.587445\pi$
$602$	−2.15073	−0.0876573
$603$	4.48704	0.182726
$604$	11.5408	0.469590
$605$	0	0
$606$	−3.55967	−0.144602
$607$	12.3549	0.501469	0.250734	−	0.968056i	$-0.419328\pi$
$607$	12.3549	0.501469	0.250734	+	0.968056i	$0.419328\pi$
$608$	−16.2240	−0.657970
$609$	−1.28625	−0.0521215
$610$	0	0
$611$	37.7781	1.52834
$612$	3.50838	0.141818
$613$	14.6291	0.590865	0.295432	−	0.955364i	$-0.404536\pi$
$613$	14.6291	0.590865	0.295432	+	0.955364i	$0.404536\pi$
$614$	−2.12140	−0.0856126
$615$	0	0
$616$	−3.53496	−0.142427
$617$	−17.3723	−0.699384	−0.349692	−	0.936865i	$-0.613714\pi$
$617$	−17.3723	−0.699384	−0.349692	+	0.936865i	$0.613714\pi$
$618$	0.125269	0.00503904
$619$	40.0049	1.60793	0.803967	−	0.594674i	$-0.202719\pi$
$619$	40.0049	1.60793	0.803967	+	0.594674i	$0.202719\pi$
$620$	0	0
$621$	−3.28734	−0.131916
$622$	−12.0936	−0.484909
$623$	−3.44443	−0.137998
$624$	−2.48322	−0.0994082
$625$	0	0
$626$	−19.8075	−0.791667
$627$	6.98499	0.278954
$628$	−6.83416	−0.272712
$629$	4.30201	0.171532
$630$	0	0
$631$	15.7992	0.628956	0.314478	−	0.949265i	$-0.398171\pi$
$631$	15.7992	0.628956	0.314478	+	0.949265i	$0.398171\pi$
$632$	19.0894	0.759337
$633$	2.41779	0.0960985
$634$	11.6424	0.462379
$635$	0	0
$636$	9.08987	0.360437
$637$	−31.6088	−1.25238
$638$	22.9655	0.909211
$639$	14.2892	0.565273
$640$	0	0
$641$	−37.3861	−1.47666	−0.738332	−	0.674437i	$-0.764386\pi$
$641$	−37.3861	−1.47666	−0.738332	+	0.674437i	$0.764386\pi$
$642$	−6.14426	−0.242495
$643$	44.1766	1.74216	0.871078	−	0.491145i	$-0.163421\pi$
$643$	44.1766	1.74216	0.871078	+	0.491145i	$0.163421\pi$
$644$	0.452416	0.0178277
$645$	0	0
$646$	−1.90689	−0.0750256
$647$	4.88521	0.192058	0.0960288	−	0.995379i	$-0.469386\pi$
$647$	4.88521	0.192058	0.0960288	+	0.995379i	$0.469386\pi$
$648$	15.6915	0.616420
$649$	−6.53086	−0.256359
$650$	0	0
$651$	0.158717	0.00622063
$652$	−3.03770	−0.118966
$653$	−36.6211	−1.43309	−0.716546	−	0.697540i	$-0.754278\pi$
$653$	−36.6211	−1.43309	−0.716546	+	0.697540i	$0.754278\pi$
$654$	0.768769	0.0300612
$655$	0	0
$656$	4.38178	0.171080
$657$	27.0254	1.05436
$658$	−1.95154	−0.0760790
$659$	−10.3388	−0.402743	−0.201371	−	0.979515i	$-0.564540\pi$
$659$	−10.3388	−0.402743	−0.201371	+	0.979515i	$0.564540\pi$
$660$	0	0
$661$	6.46980	0.251646	0.125823	−	0.992053i	$-0.459843\pi$
$661$	6.46980	0.251646	0.125823	+	0.992053i	$0.459843\pi$
$662$	−14.2921	−0.555480
$663$	−2.43947	−0.0947411
$664$	−39.4950	−1.53270
$665$	0	0
$666$	9.37807	0.363393
$667$	−7.03291	−0.272315
$668$	22.7974	0.882057
$669$	−10.8910	−0.421071
$670$	0	0
$671$	−49.8426	−1.92415
$672$	1.07217	0.0413599
$673$	−30.1889	−1.16370	−0.581849	−	0.813297i	$-0.697670\pi$
$673$	−30.1889	−1.16370	−0.581849	+	0.813297i	$0.697670\pi$
$674$	3.07435	0.118419
$675$	0	0
$676$	−11.4603	−0.440780
$677$	−0.443226	−0.0170345	−0.00851727	−	0.999964i	$-0.502711\pi$
$677$	−0.443226	−0.0170345	−0.00851727	+	0.999964i	$0.502711\pi$
$678$	−0.137355	−0.00527509
$679$	4.47885	0.171882
$680$	0	0
$681$	6.36436	0.243883
$682$	−2.83383	−0.108513
$683$	−25.7553	−0.985498	−0.492749	−	0.870171i	$-0.664008\pi$
$683$	−25.7553	−0.985498	−0.492749	+	0.870171i	$0.664008\pi$
$684$	10.5829	0.404646
$685$	0	0
$686$	3.28917	0.125581
$687$	−15.0560	−0.574422
$688$	8.48876	0.323631
$689$	49.9495	1.90292
$690$	0	0
$691$	16.1707	0.615162	0.307581	−	0.951522i	$-0.400480\pi$
$691$	16.1707	0.615162	0.307581	+	0.951522i	$0.400480\pi$
$692$	0.110173	0.00418815
$693$	3.64802	0.138577
$694$	13.0946	0.497065
$695$	0	0
$696$	−10.5350	−0.399326
$697$	4.30458	0.163048
$698$	−6.37447	−0.241277
$699$	−4.78291	−0.180906
$700$	0	0
$701$	−26.5049	−1.00107	−0.500537	−	0.865715i	$-0.666864\pi$
$701$	−26.5049	−1.00107	−0.500537	+	0.865715i	$0.666864\pi$
$702$	−11.3086	−0.426817
$703$	12.9768	0.489429
$704$	−11.0219	−0.415404
$705$	0	0
$706$	−15.4483	−0.581403
$707$	−2.57250	−0.0967489
$708$	1.25205	0.0470550
$709$	38.6885	1.45298	0.726488	−	0.687179i	$-0.241151\pi$
$709$	38.6885	1.45298	0.726488	+	0.687179i	$0.241151\pi$
$710$	0	0
$711$	−19.7000	−0.738809
$712$	−28.2114	−1.05727
$713$	0.867829	0.0325004
$714$	0.126018	0.00471610
$715$	0	0
$716$	29.7600	1.11218
$717$	−9.31735	−0.347963
$718$	16.8320	0.628165
$719$	43.7242	1.63064	0.815319	−	0.579012i	$-0.196562\pi$
$719$	43.7242	1.63064	0.815319	+	0.579012i	$0.196562\pi$
$720$	0	0
$721$	0.0905291	0.00337148
$722$	8.51741	0.316985
$723$	1.21761	0.0452833
$724$	16.6011	0.616975
$725$	0	0
$726$	3.44621	0.127901
$727$	−37.2280	−1.38071	−0.690355	−	0.723471i	$-0.742545\pi$
$727$	−37.2280	−1.38071	−0.690355	+	0.723471i	$0.742545\pi$
$728$	3.72400	0.138021
$729$	−10.4686	−0.387726
$730$	0	0
$731$	8.33921	0.308437
$732$	9.55548	0.353181
$733$	−27.9656	−1.03293	−0.516466	−	0.856308i	$-0.672753\pi$
$733$	−27.9656	−1.03293	−0.516466	+	0.856308i	$0.672753\pi$
$734$	16.4776	0.608198
$735$	0	0
$736$	5.86237	0.216090
$737$	7.32606	0.269859
$738$	9.38368	0.345418
$739$	−30.4555	−1.12032	−0.560162	−	0.828383i	$-0.689261\pi$
$739$	−30.4555	−1.12032	−0.560162	+	0.828383i	$0.689261\pi$
$740$	0	0
$741$	−7.35854	−0.270323
$742$	−2.58029	−0.0947253
$743$	−1.97918	−0.0726090	−0.0363045	−	0.999341i	$-0.511559\pi$
$743$	−1.97918	−0.0726090	−0.0363045	+	0.999341i	$0.511559\pi$
$744$	1.29997	0.0476591
$745$	0	0
$746$	−0.641240	−0.0234775
$747$	40.7583	1.49127
$748$	5.72819	0.209443
$749$	−4.44033	−0.162246
$750$	0	0
$751$	5.77719	0.210813	0.105406	−	0.994429i	$-0.466386\pi$
$751$	5.77719	0.210813	0.105406	+	0.994429i	$0.466386\pi$
$752$	7.70257	0.280884
$753$	7.95374	0.289851
$754$	−24.1936	−0.881080
$755$	0	0
$756$	−1.48725	−0.0540906
$757$	26.9857	0.980814	0.490407	−	0.871494i	$-0.336848\pi$
$757$	26.9857	0.980814	0.490407	+	0.871494i	$0.336848\pi$
$758$	1.89295	0.0687550
$759$	−2.52396	−0.0916138
$760$	0	0
$761$	5.95209	0.215763	0.107881	−	0.994164i	$-0.465593\pi$
$761$	5.95209	0.215763	0.107881	+	0.994164i	$0.465593\pi$
$762$	9.29840	0.336846
$763$	0.555573	0.0201131
$764$	−31.5456	−1.14128
$765$	0	0
$766$	10.2127	0.368998
$767$	6.88012	0.248427
$768$	7.22460	0.260695
$769$	−29.5669	−1.06621	−0.533104	−	0.846050i	$-0.678975\pi$
$769$	−29.5669	−1.06621	−0.533104	+	0.846050i	$0.678975\pi$
$770$	0	0
$771$	0.579493	0.0208699
$772$	−29.1377	−1.04869
$773$	−2.24223	−0.0806474	−0.0403237	−	0.999187i	$-0.512839\pi$
$773$	−2.24223	−0.0806474	−0.0403237	+	0.999187i	$0.512839\pi$
$774$	18.1789	0.653426
$775$	0	0
$776$	36.6837	1.31687
$777$	−0.857579	−0.0307655
$778$	−8.06581	−0.289173
$779$	12.9846	0.465220
$780$	0	0
$781$	23.3302	0.834822
$782$	0.689035	0.0246398
$783$	23.1195	0.826225
$784$	−6.44470	−0.230168
$785$	0	0
$786$	3.53728	0.126171
$787$	6.28634	0.224084	0.112042	−	0.993703i	$-0.464261\pi$
$787$	6.28634	0.224084	0.112042	+	0.993703i	$0.464261\pi$
$788$	−12.3803	−0.441029
$789$	−5.33197	−0.189823
$790$	0	0
$791$	−0.0992637	−0.00352941
$792$	29.8789	1.06170
$793$	52.5081	1.86462
$794$	−14.7101	−0.522043
$795$	0	0
$796$	−29.8387	−1.05760
$797$	15.5627	0.551258	0.275629	−	0.961264i	$-0.411114\pi$
$797$	15.5627	0.551258	0.275629	+	0.961264i	$0.411114\pi$
$798$	0.380127	0.0134564
$799$	7.56687	0.267696
$800$	0	0
$801$	29.1137	1.02868
$802$	6.01727	0.212477
$803$	44.1247	1.55713
$804$	−1.40450	−0.0495330
$805$	0	0
$806$	2.98538	0.105156
$807$	−12.4456	−0.438106
$808$	−21.0699	−0.741237
$809$	7.48638	0.263207	0.131604	−	0.991302i	$-0.457987\pi$
$809$	7.48638	0.263207	0.131604	+	0.991302i	$0.457987\pi$
$810$	0	0
$811$	−39.7694	−1.39649	−0.698246	−	0.715858i	$-0.746036\pi$
$811$	−39.7694	−1.39649	−0.698246	+	0.715858i	$0.746036\pi$
$812$	−3.18180	−0.111659
$813$	14.6567	0.514033
$814$	15.3117	0.536675
$815$	0	0
$816$	−0.497382	−0.0174119
$817$	25.1548	0.880056
$818$	21.2052	0.741421
$819$	−3.84311	−0.134289
$820$	0	0
$821$	30.2829	1.05688	0.528440	−	0.848970i	$-0.322777\pi$
$821$	30.2829	1.05688	0.528440	+	0.848970i	$0.322777\pi$
$822$	3.15061	0.109890
$823$	−7.15992	−0.249579	−0.124790	−	0.992183i	$-0.539826\pi$
$823$	−7.15992	−0.249579	−0.124790	+	0.992183i	$0.539826\pi$
$824$	0.741473	0.0258304
$825$	0	0
$826$	−0.355413	−0.0123664
$827$	29.1034	1.01202	0.506011	−	0.862527i	$-0.331119\pi$
$827$	29.1034	1.01202	0.506011	+	0.862527i	$0.331119\pi$
$828$	−3.82401	−0.132894
$829$	−42.4480	−1.47428	−0.737140	−	0.675740i	$-0.763824\pi$
$829$	−42.4480	−1.47428	−0.737140	+	0.675740i	$0.763824\pi$
$830$	0	0
$831$	−17.8857	−0.620449
$832$	11.6113	0.402551
$833$	−6.33115	−0.219362
$834$	−4.72719	−0.163689
$835$	0	0
$836$	17.2788	0.597600
$837$	−2.85285	−0.0986088
$838$	16.4827	0.569387
$839$	−32.2617	−1.11380	−0.556898	−	0.830581i	$-0.688009\pi$
$839$	−32.2617	−1.11380	−0.556898	+	0.830581i	$0.688009\pi$
$840$	0	0
$841$	20.4618	0.705579
$842$	−0.561164	−0.0193390
$843$	−2.09454	−0.0721396
$844$	5.98090	0.205871
$845$	0	0
$846$	16.4952	0.567118
$847$	2.49051	0.0855749
$848$	10.1842	0.349726
$849$	3.04144	0.104382
$850$	0	0
$851$	−4.68904	−0.160738
$852$	−4.47272	−0.153233
$853$	12.3883	0.424168	0.212084	−	0.977251i	$-0.431975\pi$
$853$	12.3883	0.424168	0.212084	+	0.977251i	$0.431975\pi$
$854$	−2.71246	−0.0928184
$855$	0	0
$856$	−36.3682	−1.24304
$857$	11.8646	0.405287	0.202643	−	0.979253i	$-0.435047\pi$
$857$	11.8646	0.405287	0.202643	+	0.979253i	$0.435047\pi$
$858$	−8.68256	−0.296418
$859$	6.57949	0.224489	0.112245	−	0.993681i	$-0.464196\pi$
$859$	6.57949	0.224489	0.112245	+	0.993681i	$0.464196\pi$
$860$	0	0
$861$	−0.858092	−0.0292437
$862$	−20.5511	−0.699975
$863$	41.6998	1.41948	0.709739	−	0.704464i	$-0.248813\pi$
$863$	41.6998	1.41948	0.709739	+	0.704464i	$0.248813\pi$
$864$	−19.2716	−0.655633
$865$	0	0
$866$	−19.0959	−0.648906
$867$	9.37973	0.318552
$868$	0.392620	0.0133264
$869$	−32.1645	−1.09111
$870$	0	0
$871$	−7.71785	−0.261509
$872$	4.55039	0.154096
$873$	−37.8571	−1.28127
$874$	2.07844	0.0703044
$875$	0	0
$876$	−8.45930	−0.285813
$877$	−20.9988	−0.709079	−0.354540	−	0.935041i	$-0.615362\pi$
$877$	−20.9988	−0.709079	−0.354540	+	0.935041i	$0.615362\pi$
$878$	23.1388	0.780897
$879$	−1.10336	−0.0372154
$880$	0	0
$881$	−12.3401	−0.415747	−0.207874	−	0.978156i	$-0.566654\pi$
$881$	−12.3401	−0.415747	−0.207874	+	0.978156i	$0.566654\pi$
$882$	−13.8015	−0.464720
$883$	35.5426	1.19610	0.598052	−	0.801457i	$-0.295942\pi$
$883$	35.5426	1.19610	0.598052	+	0.801457i	$0.295942\pi$
$884$	−6.03452	−0.202963
$885$	0	0
$886$	18.4585	0.620126
$887$	19.1997	0.644663	0.322331	−	0.946627i	$-0.395533\pi$
$887$	19.1997	0.644663	0.322331	+	0.946627i	$0.395533\pi$
$888$	−7.02395	−0.235708
$889$	6.71977	0.225374
$890$	0	0
$891$	−26.4392	−0.885747
$892$	−26.9412	−0.902057
$893$	22.8251	0.763813
$894$	−3.44443	−0.115199
$895$	0	0
$896$	3.09420	0.103370
$897$	2.65893	0.0887792
$898$	−29.0508	−0.969438
$899$	−6.10336	−0.203558
$900$	0	0
$901$	10.0048	0.333307
$902$	15.3209	0.510129
$903$	−1.66237	−0.0553202
$904$	−0.813013	−0.0270404
$905$	0	0
$906$	−3.50383	−0.116407
$907$	−54.5806	−1.81232	−0.906159	−	0.422937i	$-0.860999\pi$
$907$	−54.5806	−1.81232	−0.906159	+	0.422937i	$0.860999\pi$
$908$	15.7435	0.522467
$909$	21.7439	0.721198
$910$	0	0
$911$	24.7619	0.820397	0.410199	−	0.911996i	$-0.365459\pi$
$911$	24.7619	0.820397	0.410199	+	0.911996i	$0.365459\pi$
$912$	−1.50033	−0.0496809
$913$	66.5467	2.20237
$914$	4.80686	0.158997
$915$	0	0
$916$	−37.2441	−1.23058
$917$	2.55632	0.0844172
$918$	−2.26509	−0.0747592
$919$	9.32187	0.307500	0.153750	−	0.988110i	$-0.450865\pi$
$919$	9.32187	0.307500	0.153750	+	0.988110i	$0.450865\pi$
$920$	0	0
$921$	−1.63970	−0.0540298
$922$	17.8997	0.589495
$923$	−24.5779	−0.808992
$924$	−1.14188	−0.0375651
$925$	0	0
$926$	19.9418	0.655329
$927$	−0.765190	−0.0251321
$928$	−41.2295	−1.35343
$929$	−16.9227	−0.555217	−0.277608	−	0.960694i	$-0.589542\pi$
$929$	−16.9227	−0.555217	−0.277608	+	0.960694i	$0.589542\pi$
$930$	0	0
$931$	−19.0976	−0.625900
$932$	−11.8315	−0.387554
$933$	−9.34754	−0.306025
$934$	−13.9727	−0.457201
$935$	0	0
$936$	−31.4768	−1.02885
$937$	32.3925	1.05822	0.529109	−	0.848554i	$-0.322526\pi$
$937$	32.3925	1.05822	0.529109	+	0.848554i	$0.322526\pi$
$938$	0.398688	0.0130176
$939$	−15.3099	−0.499618
$940$	0	0
$941$	39.8390	1.29871	0.649357	−	0.760484i	$-0.275038\pi$
$941$	39.8390	1.29871	0.649357	+	0.760484i	$0.275038\pi$
$942$	2.07487	0.0676029
$943$	−4.69184	−0.152787
$944$	1.40278	0.0456567
$945$	0	0
$946$	29.6809	0.965010
$947$	12.7594	0.414624	0.207312	−	0.978275i	$-0.433528\pi$
$947$	12.7594	0.414624	0.207312	+	0.978275i	$0.433528\pi$
$948$	6.16637	0.200274
$949$	−46.4844	−1.50895
$950$	0	0
$951$	8.99880	0.291806
$952$	0.745908	0.0241750
$953$	−7.04791	−0.228304	−0.114152	−	0.993463i	$-0.536415\pi$
$953$	−7.04791	−0.228304	−0.114152	+	0.993463i	$0.536415\pi$
$954$	21.8097	0.706114
$955$	0	0
$956$	−23.0484	−0.745437
$957$	17.7508	0.573800
$958$	−22.5027	−0.727029
$959$	2.27688	0.0735244
$960$	0	0
$961$	−30.2469	−0.975706
$962$	−16.1306	−0.520070
$963$	37.5315	1.20944
$964$	3.01200	0.0970099
$965$	0	0
$966$	−0.137355	−0.00441933
$967$	−9.27901	−0.298393	−0.149196	−	0.988808i	$-0.547669\pi$
$967$	−9.27901	−0.298393	−0.149196	+	0.988808i	$0.547669\pi$
$968$	20.3983	0.655628
$969$	−1.47390	−0.0473484
$970$	0	0
$971$	0.0274304	0.000880284 0	0.000440142	−	1.00000i	$-0.499860\pi$
$971$	0.0274304	0.000880284 0	0.000440142		1.00000i	$0.499860\pi$
$972$	19.2302	0.616810
$973$	−3.41625	−0.109520
$974$	27.9580	0.895831
$975$	0	0
$976$	10.7058	0.342686
$977$	29.9665	0.958714	0.479357	−	0.877620i	$-0.340870\pi$
$977$	29.9665	0.958714	0.479357	+	0.877620i	$0.340870\pi$
$978$	0.922256	0.0294905
$979$	47.5344	1.51921
$980$	0	0
$981$	−4.69594	−0.149930
$982$	0.519589	0.0165808
$983$	−5.80749	−0.185230	−0.0926151	−	0.995702i	$-0.529523\pi$
$983$	−5.80749	−0.185230	−0.0926151	+	0.995702i	$0.529523\pi$
$984$	−7.02815	−0.224049
$985$	0	0
$986$	−4.84592	−0.154326
$987$	−1.50841	−0.0480132
$988$	−18.2028	−0.579110
$989$	−9.08944	−0.289027
$990$	0	0
$991$	17.5926	0.558847	0.279423	−	0.960168i	$-0.409857\pi$
$991$	17.5926	0.558847	0.279423	+	0.960168i	$0.409857\pi$
$992$	5.08754	0.161529
$993$	−11.0469	−0.350561
$994$	1.26964	0.0402707
$995$	0	0
$996$	−12.7579	−0.404249
$997$	−24.2200	−0.767055	−0.383527	−	0.923530i	$-0.625291\pi$
$997$	−24.2200	−0.767055	−0.383527	+	0.923530i	$0.625291\pi$
$998$	18.6245	0.589547
$999$	15.4144	0.487691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.j.1.2		4
3.2	odd	2		5175.2.a.bw.1.3		4
4.3	odd	2		9200.2.a.ck.1.3		4
5.2	odd	4		115.2.b.b.24.3	✓	8
5.3	odd	4		115.2.b.b.24.6	yes	8
5.4	even	2		575.2.a.i.1.3		4
15.2	even	4		1035.2.b.e.829.6		8
15.8	even	4		1035.2.b.e.829.3		8
15.14	odd	2		5175.2.a.bv.1.2		4
20.3	even	4		1840.2.e.d.369.5		8
20.7	even	4		1840.2.e.d.369.4		8
20.19	odd	2		9200.2.a.cq.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.b.b.24.3	✓	8	5.2	odd	4
115.2.b.b.24.6	yes	8	5.3	odd	4
575.2.a.i.1.3		4	5.4	even	2
575.2.a.j.1.2		4	1.1	even	1	trivial
1035.2.b.e.829.3		8	15.8	even	4
1035.2.b.e.829.6		8	15.2	even	4
1840.2.e.d.369.4		8	20.7	even	4
1840.2.e.d.369.5		8	20.3	even	4
5175.2.a.bv.1.2		4	15.14	odd	2
5175.2.a.bw.1.3		4	3.2	odd	2
9200.2.a.ck.1.3		4	4.3	odd	2
9200.2.a.cq.1.2		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q-0.751024 q^{2} -0.580491 q^{3} -1.43596 q^{4} +0.435963 q^{6} +0.315061 q^{7} +2.58049 q^{8} -2.66303 q^{9} +O(q^{10})\)	\(q-0.751024 q^{2} -0.580491 q^{3} -1.43596 q^{4} +0.435963 q^{6} +0.315061 q^{7} +2.58049 q^{8} -2.66303 q^{9} -4.34797 q^{11} +0.833563 q^{12} +4.58049 q^{13} -0.236619 q^{14} +0.933914 q^{16} +0.917461 q^{17} +2.00000 q^{18} +2.76748 q^{19} -0.182890 q^{21} +3.26543 q^{22} -1.00000 q^{23} -1.49795 q^{24} -3.44006 q^{26} +3.28734 q^{27} -0.452416 q^{28} +7.03291 q^{29} -0.867829 q^{31} -5.86237 q^{32} +2.52396 q^{33} -0.689035 q^{34} +3.82401 q^{36} +4.68904 q^{37} -2.07844 q^{38} -2.65893 q^{39} +4.69184 q^{41} +0.137355 q^{42} +9.08944 q^{43} +6.24352 q^{44} +0.751024 q^{46} +8.24762 q^{47} -0.542129 q^{48} -6.90074 q^{49} -0.532578 q^{51} -6.57741 q^{52} +10.9048 q^{53} -2.46887 q^{54} +0.813013 q^{56} -1.60650 q^{57} -5.28188 q^{58} +1.50205 q^{59} +11.4634 q^{61} +0.651760 q^{62} -0.839018 q^{63} +2.53496 q^{64} -1.89555 q^{66} -1.68494 q^{67} -1.31744 q^{68} +0.580491 q^{69} -5.36578 q^{71} -6.87193 q^{72} -10.1484 q^{73} -3.52158 q^{74} -3.97400 q^{76} -1.36988 q^{77} +1.99692 q^{78} +7.39760 q^{79} +6.08082 q^{81} -3.52369 q^{82} -15.3052 q^{83} +0.262624 q^{84} -6.82639 q^{86} -4.08254 q^{87} -11.2199 q^{88} -10.9326 q^{89} +1.44314 q^{91} +1.43596 q^{92} +0.503767 q^{93} -6.19416 q^{94} +3.40306 q^{96} +14.2158 q^{97} +5.18262 q^{98} +11.5788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9} + 2 q^{11} - 10 q^{12} + 14 q^{13} - 4 q^{14} + 2 q^{16} + 14 q^{17} + 8 q^{18} - 4 q^{19} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 12 q^{24} + 6 q^{26} + 14 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{32} + 14 q^{33} + 14 q^{34} - 8 q^{36} + 2 q^{37} - 10 q^{38} - 8 q^{39} - 8 q^{41} - 24 q^{42} + 4 q^{43} + 6 q^{44} + 2 q^{47} + 10 q^{51} + 18 q^{52} + 4 q^{53} + 22 q^{54} + 14 q^{56} - 8 q^{61} - 28 q^{62} - 12 q^{63} - 20 q^{64} - 8 q^{66} - 2 q^{67} + 8 q^{68} - 2 q^{69} - 24 q^{71} - 12 q^{72} + 18 q^{73} - 36 q^{74} - 18 q^{76} + 4 q^{77} - 32 q^{78} + 24 q^{79} + 8 q^{81} + 32 q^{82} - 6 q^{83} + 2 q^{84} + 14 q^{86} - 6 q^{87} - 10 q^{88} - 8 q^{89} + 26 q^{91} - 2 q^{92} + 2 q^{93} - 42 q^{94} + 30 q^{96} + 34 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9 + 2 * q^11 - 10 * q^12 + 14 * q^13 - 4 * q^14 + 2 * q^16 + 14 * q^17 + 8 * q^18 - 4 * q^19 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 12 * q^24 + 6 * q^26 + 14 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^32 + 14 * q^33 + 14 * q^34 - 8 * q^36 + 2 * q^37 - 10 * q^38 - 8 * q^39 - 8 * q^41 - 24 * q^42 + 4 * q^43 + 6 * q^44 + 2 * q^47 + 10 * q^51 + 18 * q^52 + 4 * q^53 + 22 * q^54 + 14 * q^56 - 8 * q^61 - 28 * q^62 - 12 * q^63 - 20 * q^64 - 8 * q^66 - 2 * q^67 + 8 * q^68 - 2 * q^69 - 24 * q^71 - 12 * q^72 + 18 * q^73 - 36 * q^74 - 18 * q^76 + 4 * q^77 - 32 * q^78 + 24 * q^79 + 8 * q^81 + 32 * q^82 - 6 * q^83 + 2 * q^84 + 14 * q^86 - 6 * q^87 - 10 * q^88 - 8 * q^89 + 26 * q^91 - 2 * q^92 + 2 * q^93 - 42 * q^94 + 30 * q^96 + 34 * q^97 - 28 * q^98 + 36 * q^99

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