LMFDB - Embedded newform 1475.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1475,2,Mod(1,1475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1475, 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("1475.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1475 = 5^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1475.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:	$11.7779342981$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.138136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 4x - 2 $ x^5 - x^4 - 6x^3 + 3x^2 + 4*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 59)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.05592$ of defining polynomial
Character	$\chi$	$=$	1475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.554026 q^{2} -0.0831139 q^{3} -1.69306 q^{4} +0.0460472 q^{6} +1.22679 q^{7} +2.04605 q^{8} -2.99309 q^{9} +O(q^{10})$	\(q-0.554026 q^{2} -0.0831139 q^{3} -1.69306 q^{4} +0.0460472 q^{6} +1.22679 q^{7} +2.04605 q^{8} -2.99309 q^{9} -3.51176 q^{11} +0.140716 q^{12} +1.51176 q^{13} -0.679674 q^{14} +2.25255 q^{16} -6.63866 q^{17} +1.65825 q^{18} +3.12861 q^{19} -0.101963 q^{21} +1.94560 q^{22} +6.11183 q^{23} -0.170055 q^{24} -0.837553 q^{26} +0.498109 q^{27} -2.07703 q^{28} -4.44667 q^{29} +9.83969 q^{31} -5.34006 q^{32} +0.291876 q^{33} +3.67799 q^{34} +5.06747 q^{36} -0.0543954 q^{37} -1.73333 q^{38} -0.125648 q^{39} +0.486822 q^{41} +0.0564904 q^{42} -0.600073 q^{43} +5.94560 q^{44} -3.38611 q^{46} +5.10805 q^{47} -0.187218 q^{48} -5.49498 q^{49} +0.551765 q^{51} -2.55949 q^{52} -2.70292 q^{53} -0.275965 q^{54} +2.51007 q^{56} -0.260031 q^{57} +2.46357 q^{58} +1.00000 q^{59} +9.72786 q^{61} -5.45144 q^{62} -3.67190 q^{63} -1.54657 q^{64} -0.161707 q^{66} +8.29780 q^{67} +11.2396 q^{68} -0.507978 q^{69} -3.43851 q^{71} -6.12401 q^{72} +5.36637 q^{73} +0.0301365 q^{74} -5.29691 q^{76} -4.30820 q^{77} +0.0696123 q^{78} +6.77418 q^{79} +8.93788 q^{81} -0.269712 q^{82} +5.07450 q^{83} +0.172630 q^{84} +0.332456 q^{86} +0.369581 q^{87} -7.18523 q^{88} +0.820696 q^{89} +1.85461 q^{91} -10.3477 q^{92} -0.817816 q^{93} -2.82999 q^{94} +0.443834 q^{96} +16.2434 q^{97} +3.04436 q^{98} +10.5110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9	$ 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9} - 2 q^{11} + 22 q^{12} - 8 q^{13} - 18 q^{14} + 10 q^{16} + q^{17} + 2 q^{18} + 6 q^{19} + 15 q^{21} - 8 q^{22} + 8 q^{23} + 6 q^{24} + 8 q^{26} + 11 q^{27} + 2 q^{28} + 14 q^{29} + 2 q^{32} + 14 q^{33} - 2 q^{34} + 42 q^{36} - 18 q^{37} - 18 q^{39} - 10 q^{41} - 34 q^{42} + 4 q^{43} + 12 q^{44} + 16 q^{46} + 20 q^{47} + 54 q^{48} + q^{49} - 12 q^{51} - 28 q^{52} + 10 q^{53} - 26 q^{54} - 38 q^{56} + 3 q^{57} + 38 q^{58} + 5 q^{59} + 22 q^{61} - 48 q^{62} + 12 q^{63} + 18 q^{64} + 28 q^{66} + 14 q^{68} - 4 q^{69} + 3 q^{71} - 28 q^{72} + 8 q^{73} + 8 q^{74} + 14 q^{76} - 2 q^{77} - 20 q^{78} + 10 q^{79} - 3 q^{81} + 48 q^{82} - 6 q^{83} + 28 q^{84} - 8 q^{86} - 11 q^{87} + 24 q^{88} + 10 q^{89} + 6 q^{91} - 4 q^{92} - 6 q^{93} - 36 q^{94} + 42 q^{96} + 22 q^{97} - 24 q^{98} - 4 q^{99}+O(q^{100}) $ 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9 - 2 * q^11 + 22 * q^12 - 8 * q^13 - 18 * q^14 + 10 * q^16 + q^17 + 2 * q^18 + 6 * q^19 + 15 * q^21 - 8 * q^22 + 8 * q^23 + 6 * q^24 + 8 * q^26 + 11 * q^27 + 2 * q^28 + 14 * q^29 + 2 * q^32 + 14 * q^33 - 2 * q^34 + 42 * q^36 - 18 * q^37 - 18 * q^39 - 10 * q^41 - 34 * q^42 + 4 * q^43 + 12 * q^44 + 16 * q^46 + 20 * q^47 + 54 * q^48 + q^49 - 12 * q^51 - 28 * q^52 + 10 * q^53 - 26 * q^54 - 38 * q^56 + 3 * q^57 + 38 * q^58 + 5 * q^59 + 22 * q^61 - 48 * q^62 + 12 * q^63 + 18 * q^64 + 28 * q^66 + 14 * q^68 - 4 * q^69 + 3 * q^71 - 28 * q^72 + 8 * q^73 + 8 * q^74 + 14 * q^76 - 2 * q^77 - 20 * q^78 + 10 * q^79 - 3 * q^81 + 48 * q^82 - 6 * q^83 + 28 * q^84 - 8 * q^86 - 11 * q^87 + 24 * q^88 + 10 * q^89 + 6 * q^91 - 4 * q^92 - 6 * q^93 - 36 * q^94 + 42 * q^96 + 22 * q^97 - 24 * q^98 - 4 * 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 $

$2$	−0.554026	−0.391755	−0.195878	−	0.980628i	$-0.562756\pi$
$2$	−0.554026	−0.391755	−0.195878	+	0.980628i	$0.562756\pi$
$3$	−0.0831139	−0.0479858	−0.0239929	−	0.999712i	$-0.507638\pi$
$3$	−0.0831139	−0.0479858	−0.0239929	+	0.999712i	$0.507638\pi$
$4$	−1.69306	−0.846528
$5$	0	0
$5$	0	0
$6$	0.0460472	0.0187987
$7$	1.22679	0.463684	0.231842	−	0.972754i	$-0.425525\pi$
$7$	1.22679	0.463684	0.231842	+	0.972754i	$0.425525\pi$
$8$	2.04605	0.723387
$9$	−2.99309	−0.997697
$10$	0	0
$11$	−3.51176	−1.05884	−0.529418	−	0.848361i	$-0.677590\pi$
$11$	−3.51176	−1.05884	−0.529418	+	0.848361i	$0.677590\pi$
$12$	0.140716	0.0406214
$13$	1.51176	0.419287	0.209643	−	0.977778i	$-0.432770\pi$
$13$	1.51176	0.419287	0.209643	+	0.977778i	$0.432770\pi$
$14$	−0.679674	−0.181650
$15$	0	0
$16$	2.25255	0.563137
$17$	−6.63866	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$17$	−6.63866	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$18$	1.65825	0.390853
$19$	3.12861	0.717752	0.358876	−	0.933385i	$-0.383160\pi$
$19$	3.12861	0.717752	0.358876	+	0.933385i	$0.383160\pi$
$20$	0	0
$21$	−0.101963	−0.0222502
$22$	1.94560	0.414804
$23$	6.11183	1.27441	0.637203	−	0.770696i	$-0.280091\pi$
$23$	6.11183	1.27441	0.637203	+	0.770696i	$0.280091\pi$
$24$	−0.170055	−0.0347123
$25$	0	0
$26$	−0.837553	−0.164258
$27$	0.498109	0.0958612
$28$	−2.07703	−0.392521
$29$	−4.44667	−0.825727	−0.412863	−	0.910793i	$-0.635471\pi$
$29$	−4.44667	−0.825727	−0.412863	+	0.910793i	$0.635471\pi$
$30$	0	0
$31$	9.83969	1.76726	0.883631	−	0.468185i	$-0.155092\pi$
$31$	9.83969	1.76726	0.883631	+	0.468185i	$0.155092\pi$
$32$	−5.34006	−0.943999
$33$	0.291876	0.0508091
$34$	3.67799	0.630770
$35$	0	0
$36$	5.06747	0.844579
$37$	−0.0543954	−0.00894255	−0.00447128	−	0.999990i	$-0.501423\pi$
$37$	−0.0543954	−0.00894255	−0.00447128	+	0.999990i	$0.501423\pi$
$38$	−1.73333	−0.281183
$39$	−0.125648	−0.0201198
$40$	0	0
$41$	0.486822	0.0760289	0.0380144	−	0.999277i	$-0.487897\pi$
$41$	0.486822	0.0760289	0.0380144	+	0.999277i	$0.487897\pi$
$42$	0.0564904	0.00871665
$43$	−0.600073	−0.0915102	−0.0457551	−	0.998953i	$-0.514569\pi$
$43$	−0.600073	−0.0915102	−0.0457551	+	0.998953i	$0.514569\pi$
$44$	5.94560	0.896334
$45$	0	0
$46$	−3.38611	−0.499255
$47$	5.10805	0.745086	0.372543	−	0.928015i	$-0.378486\pi$
$47$	5.10805	0.745086	0.372543	+	0.928015i	$0.378486\pi$
$48$	−0.187218	−0.0270226
$49$	−5.49498	−0.784998
$50$	0	0
$51$	0.551765	0.0772626
$52$	−2.55949	−0.354938
$53$	−2.70292	−0.371275	−0.185638	−	0.982618i	$-0.559435\pi$
$53$	−2.70292	−0.371275	−0.185638	+	0.982618i	$0.559435\pi$
$54$	−0.275965	−0.0375541
$55$	0	0
$56$	2.51007	0.335423
$57$	−0.260031	−0.0344419
$58$	2.46357	0.323483
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0	0
$61$	9.72786	1.24553	0.622763	−	0.782411i	$-0.286010\pi$
$61$	9.72786	1.24553	0.622763	+	0.782411i	$0.286010\pi$
$62$	−5.45144	−0.692334
$63$	−3.67190	−0.462616
$64$	−1.54657	−0.193321
$65$	0	0
$66$	−0.161707	−0.0199047
$67$	8.29780	1.01374	0.506869	−	0.862023i	$-0.330803\pi$
$67$	8.29780	1.01374	0.506869	+	0.862023i	$0.330803\pi$
$68$	11.2396	1.36300
$69$	−0.507978	−0.0611534
$70$	0	0
$71$	−3.43851	−0.408077	−0.204038	−	0.978963i	$-0.565407\pi$
$71$	−3.43851	−0.408077	−0.204038	+	0.978963i	$0.565407\pi$
$72$	−6.12401	−0.721721
$73$	5.36637	0.628087	0.314043	−	0.949409i	$-0.398316\pi$
$73$	5.36637	0.628087	0.314043	+	0.949409i	$0.398316\pi$
$74$	0.0301365	0.00350329
$75$	0	0
$76$	−5.29691	−0.607597
$77$	−4.30820	−0.490965
$78$	0.0696123	0.00788205
$79$	6.77418	0.762155	0.381077	−	0.924543i	$-0.375553\pi$
$79$	6.77418	0.762155	0.381077	+	0.924543i	$0.375553\pi$
$80$	0	0
$81$	8.93788	0.993097
$82$	−0.269712	−0.0297847
$83$	5.07450	0.556998	0.278499	−	0.960436i	$-0.410163\pi$
$83$	5.07450	0.556998	0.278499	+	0.960436i	$0.410163\pi$
$84$	0.172630	0.0188355
$85$	0	0
$86$	0.332456	0.0358496
$87$	0.369581	0.0396232
$88$	−7.18523	−0.765948
$89$	0.820696	0.0869936	0.0434968	−	0.999054i	$-0.486150\pi$
$89$	0.820696	0.0869936	0.0434968	+	0.999054i	$0.486150\pi$
$90$	0	0
$91$	1.85461	0.194416
$92$	−10.3477	−1.07882
$93$	−0.817816	−0.0848035
$94$	−2.82999	−0.291891
$95$	0	0
$96$	0.443834	0.0452986
$97$	16.2434	1.64927	0.824634	−	0.565667i	$-0.191381\pi$
$97$	16.2434	1.64927	0.824634	+	0.565667i	$0.191381\pi$
$98$	3.04436	0.307527
$99$	10.5110	1.05640
$100$	0	0
$101$	0.0949750	0.00945036	0.00472518	−	0.999989i	$-0.498496\pi$
$101$	0.0949750	0.00945036	0.00472518	+	0.999989i	$0.498496\pi$
$102$	−0.305692	−0.0302680
$103$	1.72950	0.170413	0.0852065	−	0.996363i	$-0.472845\pi$
$103$	1.72950	0.170413	0.0852065	+	0.996363i	$0.472845\pi$
$104$	3.09313	0.303307
$105$	0	0
$106$	1.49749	0.145449
$107$	15.7861	1.52610	0.763051	−	0.646338i	$-0.223701\pi$
$107$	15.7861	1.52610	0.763051	+	0.646338i	$0.223701\pi$
$108$	−0.843327	−0.0811492
$109$	14.4037	1.37963	0.689813	−	0.723988i	$-0.257693\pi$
$109$	14.4037	1.37963	0.689813	+	0.723988i	$0.257693\pi$
$110$	0	0
$111$	0.00452102	0.000429116 0
$112$	2.76341	0.261117
$113$	10.9900	1.03385	0.516924	−	0.856031i	$-0.327077\pi$
$113$	10.9900	1.03385	0.516924	+	0.856031i	$0.327077\pi$
$114$	0.144064	0.0134928
$115$	0	0
$116$	7.52847	0.699001
$117$	−4.52484	−0.418321
$118$	−0.554026	−0.0510022
$119$	−8.14425	−0.746582
$120$	0	0
$121$	1.33246	0.121132
$122$	−5.38948	−0.487941
$123$	−0.0404617	−0.00364831
$124$	−16.6592	−1.49604
$125$	0	0
$126$	2.03433	0.181232
$127$	−15.2435	−1.35264	−0.676320	−	0.736608i	$-0.736426\pi$
$127$	−15.2435	−1.35264	−0.676320	+	0.736608i	$0.736426\pi$
$128$	11.5370	1.01973
$129$	0.0498744	0.00439120
$130$	0	0
$131$	16.6229	1.45235	0.726173	−	0.687512i	$-0.241297\pi$
$131$	16.6229	1.45235	0.726173	+	0.687512i	$0.241297\pi$
$132$	−0.494162	−0.0430113
$133$	3.83815	0.332810
$134$	−4.59719	−0.397137
$135$	0	0
$136$	−13.5830	−1.16473
$137$	11.4840	0.981145	0.490573	−	0.871400i	$-0.336788\pi$
$137$	11.4840	0.981145	0.490573	+	0.871400i	$0.336788\pi$
$138$	0.281433	0.0239572
$139$	16.3874	1.38996	0.694979	−	0.719030i	$-0.255414\pi$
$139$	16.3874	1.38996	0.694979	+	0.719030i	$0.255414\pi$
$140$	0	0
$141$	−0.424550	−0.0357536
$142$	1.90503	0.159866
$143$	−5.30894	−0.443956
$144$	−6.74209	−0.561841
$145$	0	0
$146$	−2.97311	−0.246056
$147$	0.456710	0.0376688
$148$	0.0920945	0.00757012
$149$	−4.70151	−0.385162	−0.192581	−	0.981281i	$-0.561686\pi$
$149$	−4.70151	−0.385162	−0.192581	+	0.981281i	$0.561686\pi$
$150$	0	0
$151$	−16.6634	−1.35605	−0.678025	−	0.735038i	$-0.737164\pi$
$151$	−16.6634	−1.35605	−0.678025	+	0.735038i	$0.737164\pi$
$152$	6.40128	0.519213
$153$	19.8701	1.60640
$154$	2.38685	0.192338
$155$	0	0
$156$	0.212730	0.0170320
$157$	−11.5484	−0.921659	−0.460830	−	0.887489i	$-0.652448\pi$
$157$	−11.5484	−0.921659	−0.460830	+	0.887489i	$0.652448\pi$
$158$	−3.75307	−0.298578
$159$	0.224651	0.0178160
$160$	0	0
$161$	7.49794	0.590921
$162$	−4.95181	−0.389051
$163$	−21.6697	−1.69731	−0.848653	−	0.528951i	$-0.822586\pi$
$163$	−21.6697	−1.69731	−0.848653	+	0.528951i	$0.822586\pi$
$164$	−0.824217	−0.0643606
$165$	0	0
$166$	−2.81140	−0.218207
$167$	−8.23649	−0.637359	−0.318680	−	0.947863i	$-0.603239\pi$
$167$	−8.23649	−0.637359	−0.318680	+	0.947863i	$0.603239\pi$
$168$	−0.208622	−0.0160955
$169$	−10.7146	−0.824199
$170$	0	0
$171$	−9.36422	−0.716099
$172$	1.01596	0.0774660
$173$	13.4058	1.01923	0.509614	−	0.860403i	$-0.329788\pi$
$173$	13.4058	1.01923	0.509614	+	0.860403i	$0.329788\pi$
$174$	−0.204757	−0.0155226
$175$	0	0
$176$	−7.91041	−0.596270
$177$	−0.0831139	−0.00624722
$178$	−0.454687	−0.0340802
$179$	15.5523	1.16244	0.581218	−	0.813748i	$-0.302576\pi$
$179$	15.5523	1.16244	0.581218	+	0.813748i	$0.302576\pi$
$180$	0	0
$181$	−4.58657	−0.340917	−0.170459	−	0.985365i	$-0.554525\pi$
$181$	−4.58657	−0.340917	−0.170459	+	0.985365i	$0.554525\pi$
$182$	−1.02750	−0.0761636
$183$	−0.808521	−0.0597676
$184$	12.5051	0.921888
$185$	0	0
$186$	0.453091	0.0332222
$187$	23.3134	1.70484
$188$	−8.64821	−0.630736
$189$	0.611076	0.0444493
$190$	0	0
$191$	−16.7722	−1.21360	−0.606798	−	0.794856i	$-0.707546\pi$
$191$	−16.7722	−1.21360	−0.606798	+	0.794856i	$0.707546\pi$
$192$	0.128541	0.00927666
$193$	0.162527	0.0116990	0.00584948	−	0.999983i	$-0.498138\pi$
$193$	0.162527	0.0116990	0.00584948	+	0.999983i	$0.498138\pi$
$194$	−8.99926	−0.646109
$195$	0	0
$196$	9.30331	0.664522
$197$	−0.631098	−0.0449638	−0.0224819	−	0.999747i	$-0.507157\pi$
$197$	−0.631098	−0.0449638	−0.0224819	+	0.999747i	$0.507157\pi$
$198$	−5.82337	−0.413849
$199$	2.94041	0.208440	0.104220	−	0.994554i	$-0.466765\pi$
$199$	2.94041	0.208440	0.104220	+	0.994554i	$0.466765\pi$
$200$	0	0
$201$	−0.689662	−0.0486450
$202$	−0.0526186	−0.00370223
$203$	−5.45514	−0.382876
$204$	−0.934169	−0.0654049
$205$	0	0
$206$	−0.958189	−0.0667602
$207$	−18.2933	−1.27147
$208$	3.40531	0.236116
$209$	−10.9869	−0.759981
$210$	0	0
$211$	−0.634730	−0.0436966	−0.0218483	−	0.999761i	$-0.506955\pi$
$211$	−0.634730	−0.0436966	−0.0218483	+	0.999761i	$0.506955\pi$
$212$	4.57620	0.314295
$213$	0.285788	0.0195819
$214$	−8.74591	−0.597858
$215$	0	0
$216$	1.01916	0.0693447
$217$	12.0713	0.819450
$218$	−7.98002	−0.540475
$219$	−0.446020	−0.0301393
$220$	0	0
$221$	−10.0361	−0.675098
$222$	−0.00250476	−0.000168108 0
$223$	−17.4410	−1.16794	−0.583969	−	0.811776i	$-0.698501\pi$
$223$	−17.4410	−1.16794	−0.583969	+	0.811776i	$0.698501\pi$
$224$	−6.55115	−0.437717
$225$	0	0
$226$	−6.08872	−0.405016
$227$	−7.93179	−0.526451	−0.263226	−	0.964734i	$-0.584786\pi$
$227$	−7.93179	−0.526451	−0.263226	+	0.964734i	$0.584786\pi$
$228$	0.440247	0.0291561
$229$	7.70812	0.509367	0.254684	−	0.967024i	$-0.418029\pi$
$229$	7.70812	0.509367	0.254684	+	0.967024i	$0.418029\pi$
$230$	0	0
$231$	0.358071	0.0235593
$232$	−9.09811	−0.597320
$233$	1.63095	0.106847	0.0534235	−	0.998572i	$-0.482987\pi$
$233$	1.63095	0.106847	0.0534235	+	0.998572i	$0.482987\pi$
$234$	2.50687	0.163880
$235$	0	0
$236$	−1.69306	−0.110209
$237$	−0.563028	−0.0365726
$238$	4.51212	0.292478
$239$	−5.67412	−0.367028	−0.183514	−	0.983017i	$-0.558747\pi$
$239$	−5.67412	−0.367028	−0.183514	+	0.983017i	$0.558747\pi$
$240$	0	0
$241$	15.0844	0.971675	0.485837	−	0.874049i	$-0.338515\pi$
$241$	15.0844	0.971675	0.485837	+	0.874049i	$0.338515\pi$
$242$	−0.738214	−0.0474542
$243$	−2.23719	−0.143516
$244$	−16.4698	−1.05437
$245$	0	0
$246$	0.0224168	0.00142924
$247$	4.72971	0.300944
$248$	20.1325	1.27841
$249$	−0.421761	−0.0267280
$250$	0	0
$251$	−23.9990	−1.51480	−0.757402	−	0.652949i	$-0.773532\pi$
$251$	−23.9990	−1.51480	−0.757402	+	0.652949i	$0.773532\pi$
$252$	6.21673	0.391617
$253$	−21.4633	−1.34939
$254$	8.44528	0.529904
$255$	0	0
$256$	−3.29864	−0.206165
$257$	−3.00905	−0.187699	−0.0938497	−	0.995586i	$-0.529917\pi$
$257$	−3.00905	−0.187699	−0.0938497	+	0.995586i	$0.529917\pi$
$258$	−0.0276317	−0.00172027
$259$	−0.0667318	−0.00414651
$260$	0	0
$261$	13.3093	0.823825
$262$	−9.20949	−0.568964
$263$	−8.76260	−0.540325	−0.270163	−	0.962815i	$-0.587077\pi$
$263$	−8.76260	−0.540325	−0.270163	+	0.962815i	$0.587077\pi$
$264$	0.597192	0.0367546
$265$	0	0
$266$	−2.12643	−0.130380
$267$	−0.0682113	−0.00417446
$268$	−14.0486	−0.858157
$269$	0.677248	0.0412925	0.0206463	−	0.999787i	$-0.493428\pi$
$269$	0.677248	0.0412925	0.0206463	+	0.999787i	$0.493428\pi$
$270$	0	0
$271$	19.9270	1.21048	0.605239	−	0.796044i	$-0.293078\pi$
$271$	19.9270	1.21048	0.605239	+	0.796044i	$0.293078\pi$
$272$	−14.9539	−0.906714
$273$	−0.154144	−0.00932923
$274$	−6.36244	−0.384369
$275$	0	0
$276$	0.860036	0.0517681
$277$	10.4598	0.628468	0.314234	−	0.949346i	$-0.398252\pi$
$277$	10.4598	0.628468	0.314234	+	0.949346i	$0.398252\pi$
$278$	−9.07902	−0.544523
$279$	−29.4511	−1.76319
$280$	0	0
$281$	−13.4514	−0.802445	−0.401222	−	0.915981i	$-0.631415\pi$
$281$	−13.4514	−0.802445	−0.401222	+	0.915981i	$0.631415\pi$
$282$	0.235212	0.0140066
$283$	−7.30104	−0.434002	−0.217001	−	0.976171i	$-0.569627\pi$
$283$	−7.30104	−0.434002	−0.217001	+	0.976171i	$0.569627\pi$
$284$	5.82160	0.345448
$285$	0	0
$286$	2.94129	0.173922
$287$	0.597230	0.0352533
$288$	15.9833	0.941825
$289$	27.0718	1.59246
$290$	0	0
$291$	−1.35005	−0.0791415
$292$	−9.08557	−0.531693
$293$	−31.5375	−1.84244	−0.921221	−	0.389039i	$-0.872807\pi$
$293$	−31.5375	−1.84244	−0.921221	+	0.389039i	$0.872807\pi$
$294$	−0.253029	−0.0147569
$295$	0	0
$296$	−0.111296	−0.00646892
$297$	−1.74924	−0.101501
$298$	2.60475	0.150889
$299$	9.23962	0.534341
$300$	0	0
$301$	−0.736164	−0.0424318
$302$	9.23197	0.531240
$303$	−0.00789374	−0.000453484 0
$304$	7.04735	0.404193
$305$	0	0
$306$	−11.0086	−0.629317
$307$	14.8416	0.847056	0.423528	−	0.905883i	$-0.360791\pi$
$307$	14.8416	0.847056	0.423528	+	0.905883i	$0.360791\pi$
$308$	7.29402	0.415615
$309$	−0.143746	−0.00817741
$310$	0	0
$311$	28.1095	1.59395	0.796973	−	0.604015i	$-0.206433\pi$
$311$	28.1095	1.59395	0.796973	+	0.604015i	$0.206433\pi$
$312$	−0.257082	−0.0145544
$313$	15.9377	0.900853	0.450426	−	0.892814i	$-0.351272\pi$
$313$	15.9377	0.900853	0.450426	+	0.892814i	$0.351272\pi$
$314$	6.39808	0.361065
$315$	0	0
$316$	−11.4691	−0.645185
$317$	26.4868	1.48765	0.743824	−	0.668376i	$-0.233010\pi$
$317$	26.4868	1.48765	0.743824	+	0.668376i	$0.233010\pi$
$318$	−0.124462	−0.00697949
$319$	15.6157	0.874309
$320$	0	0
$321$	−1.31205	−0.0732313
$322$	−4.15405	−0.231496
$323$	−20.7698	−1.15566
$324$	−15.1323	−0.840685
$325$	0	0
$326$	12.0056	0.664928
$327$	−1.19715	−0.0662025
$328$	0.996062	0.0549983
$329$	6.26651	0.345484
$330$	0	0
$331$	11.8053	0.648876	0.324438	−	0.945907i	$-0.394825\pi$
$331$	11.8053	0.648876	0.324438	+	0.945907i	$0.394825\pi$
$332$	−8.59141	−0.471515
$333$	0.162810	0.00892196
$334$	4.56323	0.249689
$335$	0	0
$336$	−0.229678	−0.0125299
$337$	29.8075	1.62372	0.811860	−	0.583852i	$-0.198455\pi$
$337$	29.8075	1.62372	0.811860	+	0.583852i	$0.198455\pi$
$338$	5.93615	0.322884
$339$	−0.913419	−0.0496101
$340$	0	0
$341$	−34.5546	−1.87124
$342$	5.18801	0.280536
$343$	−15.3287	−0.827674
$344$	−1.22778	−0.0661973
$345$	0	0
$346$	−7.42718	−0.399288
$347$	−10.1332	−0.543979	−0.271990	−	0.962300i	$-0.587682\pi$
$347$	−10.1332	−0.543979	−0.271990	+	0.962300i	$0.587682\pi$
$348$	−0.625720	−0.0335421
$349$	20.8787	1.11761	0.558805	−	0.829299i	$-0.311260\pi$
$349$	20.8787	1.11761	0.558805	+	0.829299i	$0.311260\pi$
$350$	0	0
$351$	0.753022	0.0401933
$352$	18.7530	0.999539
$353$	−14.1831	−0.754889	−0.377445	−	0.926032i	$-0.623197\pi$
$353$	−14.1831	−0.754889	−0.377445	+	0.926032i	$0.623197\pi$
$354$	0.0460472	0.00244738
$355$	0	0
$356$	−1.38948	−0.0736425
$357$	0.676901	0.0358254
$358$	−8.61639	−0.455391
$359$	10.7071	0.565098	0.282549	−	0.959253i	$-0.408820\pi$
$359$	10.7071	0.565098	0.282549	+	0.959253i	$0.408820\pi$
$360$	0	0
$361$	−9.21180	−0.484832
$362$	2.54108	0.133556
$363$	−0.110746	−0.00581264
$364$	−3.13996	−0.164579
$365$	0	0
$366$	0.447941	0.0234143
$367$	19.7442	1.03064	0.515319	−	0.856998i	$-0.327673\pi$
$367$	19.7442	1.03064	0.515319	+	0.856998i	$0.327673\pi$
$368$	13.7672	0.717665
$369$	−1.45710	−0.0758538
$370$	0	0
$371$	−3.31592	−0.172154
$372$	1.38461	0.0717885
$373$	−28.1245	−1.45623	−0.728116	−	0.685454i	$-0.759604\pi$
$373$	−28.1245	−1.45623	−0.728116	+	0.685454i	$0.759604\pi$
$374$	−12.9162	−0.667881
$375$	0	0
$376$	10.4513	0.538985
$377$	−6.72230	−0.346216
$378$	−0.338552	−0.0174132
$379$	−8.35227	−0.429027	−0.214514	−	0.976721i	$-0.568817\pi$
$379$	−8.35227	−0.429027	−0.214514	+	0.976721i	$0.568817\pi$
$380$	0	0
$381$	1.26695	0.0649076
$382$	9.29224	0.475432
$383$	−6.79985	−0.347456	−0.173728	−	0.984794i	$-0.555581\pi$
$383$	−6.79985	−0.347456	−0.173728	+	0.984794i	$0.555581\pi$
$384$	−0.958882	−0.0489328
$385$	0	0
$386$	−0.0900441	−0.00458313
$387$	1.79607	0.0912995
$388$	−27.5010	−1.39615
$389$	2.45846	0.124649	0.0623243	−	0.998056i	$-0.480149\pi$
$389$	2.45846	0.124649	0.0623243	+	0.998056i	$0.480149\pi$
$390$	0	0
$391$	−40.5744	−2.05193
$392$	−11.2430	−0.567857
$393$	−1.38159	−0.0696920
$394$	0.349644	0.0176148
$395$	0	0
$396$	−17.7957	−0.894270
$397$	−13.6689	−0.686025	−0.343012	−	0.939331i	$-0.611447\pi$
$397$	−13.6689	−0.686025	−0.343012	+	0.939331i	$0.611447\pi$
$398$	−1.62906	−0.0816574
$399$	−0.319004	−0.0159702
$400$	0	0
$401$	−15.8050	−0.789266	−0.394633	−	0.918839i	$-0.629128\pi$
$401$	−15.8050	−0.789266	−0.394633	+	0.918839i	$0.629128\pi$
$402$	0.382091	0.0190569
$403$	14.8753	0.740989
$404$	−0.160798	−0.00800000
$405$	0	0
$406$	3.02229	0.149994
$407$	0.191024	0.00946869
$408$	1.12894	0.0558907
$409$	−14.2978	−0.706981	−0.353490	−	0.935438i	$-0.615005\pi$
$409$	−14.2978	−0.706981	−0.353490	+	0.935438i	$0.615005\pi$
$410$	0	0
$411$	−0.954481	−0.0470811
$412$	−2.92814	−0.144259
$413$	1.22679	0.0603665
$414$	10.1349	0.498105
$415$	0	0
$416$	−8.07289	−0.395806
$417$	−1.36202	−0.0666983
$418$	6.08704	0.297727
$419$	−13.0370	−0.636897	−0.318449	−	0.947940i	$-0.603162\pi$
$419$	−13.0370	−0.636897	−0.318449	+	0.947940i	$0.603162\pi$
$420$	0	0
$421$	2.97171	0.144832	0.0724161	−	0.997375i	$-0.476929\pi$
$421$	2.97171	0.144832	0.0724161	+	0.997375i	$0.476929\pi$
$422$	0.351657	0.0171184
$423$	−15.2889	−0.743370
$424$	−5.53031	−0.268576
$425$	0	0
$426$	−0.158334	−0.00767131
$427$	11.9341	0.577530
$428$	−26.7268	−1.29189
$429$	0.441246	0.0213036
$430$	0	0
$431$	19.3224	0.930728	0.465364	−	0.885119i	$-0.345923\pi$
$431$	19.3224	0.930728	0.465364	+	0.885119i	$0.345923\pi$
$432$	1.12202	0.0539830
$433$	7.70767	0.370407	0.185204	−	0.982700i	$-0.440706\pi$
$433$	7.70767	0.370407	0.185204	+	0.982700i	$0.440706\pi$
$434$	−6.68778	−0.321024
$435$	0	0
$436$	−24.3863	−1.16789
$437$	19.1215	0.914707
$438$	0.247107	0.0118072
$439$	−8.88996	−0.424294	−0.212147	−	0.977238i	$-0.568046\pi$
$439$	−8.88996	−0.424294	−0.212147	+	0.977238i	$0.568046\pi$
$440$	0	0
$441$	16.4470	0.783190
$442$	5.56023	0.264473
$443$	−26.5070	−1.25939	−0.629694	−	0.776844i	$-0.716820\pi$
$443$	−26.5070	−1.25939	−0.629694	+	0.776844i	$0.716820\pi$
$444$	−0.00765433	−0.000363259 0
$445$	0	0
$446$	9.66277	0.457545
$447$	0.390761	0.0184823
$448$	−1.89731	−0.0896396
$449$	−29.7086	−1.40204	−0.701018	−	0.713144i	$-0.747271\pi$
$449$	−29.7086	−1.40204	−0.701018	+	0.713144i	$0.747271\pi$
$450$	0	0
$451$	−1.70960	−0.0805021
$452$	−18.6066	−0.875182
$453$	1.38496	0.0650712
$454$	4.39441	0.206240
$455$	0	0
$456$	−0.532036	−0.0249149
$457$	−32.0351	−1.49854	−0.749270	−	0.662265i	$-0.769595\pi$
$457$	−32.0351	−1.49854	−0.749270	+	0.662265i	$0.769595\pi$
$458$	−4.27050	−0.199547
$459$	−3.30678	−0.154347
$460$	0	0
$461$	9.60727	0.447455	0.223728	−	0.974652i	$-0.428177\pi$
$461$	9.60727	0.447455	0.223728	+	0.974652i	$0.428177\pi$
$462$	−0.198381	−0.00922950
$463$	22.7451	1.05706	0.528528	−	0.848916i	$-0.322744\pi$
$463$	22.7451	1.05706	0.528528	+	0.848916i	$0.322744\pi$
$464$	−10.0164	−0.464998
$465$	0	0
$466$	−0.903587	−0.0418579
$467$	3.93858	0.182256	0.0911278	−	0.995839i	$-0.470953\pi$
$467$	3.93858	0.182256	0.0911278	+	0.995839i	$0.470953\pi$
$468$	7.66080	0.354121
$469$	10.1797	0.470053
$470$	0	0
$471$	0.959829	0.0442266
$472$	2.04605	0.0941770
$473$	2.10731	0.0968943
$474$	0.311932	0.0143275
$475$	0	0
$476$	13.7887	0.632003
$477$	8.09010	0.370420
$478$	3.14361	0.143785
$479$	−15.4762	−0.707126	−0.353563	−	0.935411i	$-0.615030\pi$
$479$	−15.4762	−0.707126	−0.353563	+	0.935411i	$0.615030\pi$
$480$	0	0
$481$	−0.0822328	−0.00374949
$482$	−8.35717	−0.380659
$483$	−0.623183	−0.0283558
$484$	−2.25592	−0.102542
$485$	0	0
$486$	1.23946	0.0562231
$487$	23.6476	1.07158	0.535788	−	0.844352i	$-0.320015\pi$
$487$	23.6476	1.07158	0.535788	+	0.844352i	$0.320015\pi$
$488$	19.9037	0.900997
$489$	1.80106	0.0814466
$490$	0	0
$491$	−23.3963	−1.05586	−0.527931	−	0.849287i	$-0.677032\pi$
$491$	−23.3963	−1.05586	−0.527931	+	0.849287i	$0.677032\pi$
$492$	0.0685039	0.00308840
$493$	29.5200	1.32951
$494$	−2.62038	−0.117896
$495$	0	0
$496$	22.1644	0.995211
$497$	−4.21834	−0.189218
$498$	0.233667	0.0104708
$499$	−25.6394	−1.14778	−0.573889	−	0.818933i	$-0.694566\pi$
$499$	−25.6394	−1.14778	−0.573889	+	0.818933i	$0.694566\pi$
$500$	0	0
$501$	0.684567	0.0305842
$502$	13.2961	0.593433
$503$	19.5345	0.871002	0.435501	−	0.900188i	$-0.356571\pi$
$503$	19.5345	0.871002	0.435501	+	0.900188i	$0.356571\pi$
$504$	−7.51288	−0.334650
$505$	0	0
$506$	11.8912	0.528629
$507$	0.890531	0.0395499
$508$	25.8081	1.14505
$509$	12.3592	0.547811	0.273905	−	0.961757i	$-0.411684\pi$
$509$	12.3592	0.547811	0.273905	+	0.961757i	$0.411684\pi$
$510$	0	0
$511$	6.58342	0.291233
$512$	−21.2464	−0.938967
$513$	1.55839	0.0688046
$514$	1.66709	0.0735322
$515$	0	0
$516$	−0.0844401	−0.00371727
$517$	−17.9382	−0.788923
$518$	0.0369711	0.00162442
$519$	−1.11421	−0.0489085
$520$	0	0
$521$	−9.47799	−0.415238	−0.207619	−	0.978210i	$-0.566571\pi$
$521$	−9.47799	−0.415238	−0.207619	+	0.978210i	$0.566571\pi$
$522$	−7.37370	−0.322738
$523$	4.16535	0.182138	0.0910689	−	0.995845i	$-0.470972\pi$
$523$	4.16535	0.182138	0.0910689	+	0.995845i	$0.470972\pi$
$524$	−28.1434	−1.22945
$525$	0	0
$526$	4.85470	0.211675
$527$	−65.3224	−2.84549
$528$	0.657465	0.0286125
$529$	14.3545	0.624108
$530$	0	0
$531$	−2.99309	−0.129889
$532$	−6.49820	−0.281733
$533$	0.735958	0.0318779
$534$	0.0377908	0.00163537
$535$	0	0
$536$	16.9777	0.733324
$537$	−1.29262	−0.0557805
$538$	−0.375213	−0.0161766
$539$	19.2971	0.831183
$540$	0	0
$541$	−6.59864	−0.283698	−0.141849	−	0.989888i	$-0.545305\pi$
$541$	−6.59864	−0.283698	−0.141849	+	0.989888i	$0.545305\pi$
$542$	−11.0401	−0.474211
$543$	0.381208	0.0163592
$544$	35.4509	1.51994
$545$	0	0
$546$	0.0853998	0.00365478
$547$	20.0812	0.858608	0.429304	−	0.903160i	$-0.358759\pi$
$547$	20.0812	0.858608	0.429304	+	0.903160i	$0.358759\pi$
$548$	−19.4431	−0.830567
$549$	−29.1164	−1.24266
$550$	0	0
$551$	−13.9119	−0.592667
$552$	−1.03935	−0.0442376
$553$	8.31050	0.353399
$554$	−5.79499	−0.246206
$555$	0	0
$556$	−27.7447	−1.17664
$557$	1.70165	0.0721011	0.0360506	−	0.999350i	$-0.488522\pi$
$557$	1.70165	0.0721011	0.0360506	+	0.999350i	$0.488522\pi$
$558$	16.3167	0.690740
$559$	−0.907166	−0.0383690
$560$	0	0
$561$	−1.93767	−0.0818083
$562$	7.45243	0.314362
$563$	27.8050	1.17184	0.585921	−	0.810368i	$-0.300733\pi$
$563$	27.8050	1.17184	0.585921	+	0.810368i	$0.300733\pi$
$564$	0.718787	0.0302664
$565$	0	0
$566$	4.04496	0.170023
$567$	10.9649	0.460483
$568$	−7.03536	−0.295197
$569$	21.0455	0.882272	0.441136	−	0.897440i	$-0.354576\pi$
$569$	21.0455	0.882272	0.441136	+	0.897440i	$0.354576\pi$
$570$	0	0
$571$	19.1805	0.802681	0.401340	−	0.915929i	$-0.368544\pi$
$571$	19.1805	0.802681	0.401340	+	0.915929i	$0.368544\pi$
$572$	8.98832	0.375821
$573$	1.39401	0.0582354
$574$	−0.330880	−0.0138107
$575$	0	0
$576$	4.62901	0.192876
$577$	21.4091	0.891273	0.445637	−	0.895214i	$-0.352977\pi$
$577$	21.4091	0.891273	0.445637	+	0.895214i	$0.352977\pi$
$578$	−14.9985	−0.623854
$579$	−0.0135083	−0.000561384 0
$580$	0	0
$581$	6.22535	0.258271
$582$	0.747964	0.0310041
$583$	9.49202	0.393119
$584$	10.9799	0.454350
$585$	0	0
$586$	17.4726	0.721787
$587$	1.12380	0.0463844	0.0231922	−	0.999731i	$-0.492617\pi$
$587$	1.12380	0.0463844	0.0231922	+	0.999731i	$0.492617\pi$
$588$	−0.773235	−0.0318877
$589$	30.7846	1.26846
$590$	0	0
$591$	0.0524530	0.00215763
$592$	−0.122528	−0.00503588
$593$	17.8023	0.731052	0.365526	−	0.930801i	$-0.380889\pi$
$593$	17.8023	0.731052	0.365526	+	0.930801i	$0.380889\pi$
$594$	0.969124	0.0397636
$595$	0	0
$596$	7.95991	0.326051
$597$	−0.244389	−0.0100022
$598$	−5.11899	−0.209331
$599$	8.68580	0.354892	0.177446	−	0.984131i	$-0.443216\pi$
$599$	8.68580	0.354892	0.177446	+	0.984131i	$0.443216\pi$
$600$	0	0
$601$	39.5416	1.61294	0.806468	−	0.591278i	$-0.201376\pi$
$601$	39.5416	1.61294	0.806468	+	0.591278i	$0.201376\pi$
$602$	0.407854	0.0166229
$603$	−24.8361	−1.01140
$604$	28.2121	1.14793
$605$	0	0
$606$	0.00437334	0.000177655 0
$607$	35.2136	1.42928	0.714639	−	0.699494i	$-0.246591\pi$
$607$	35.2136	1.42928	0.714639	+	0.699494i	$0.246591\pi$
$608$	−16.7070	−0.677557
$609$	0.453398	0.0183726
$610$	0	0
$611$	7.72215	0.312405
$612$	−33.6412	−1.35987
$613$	−41.4559	−1.67439	−0.837195	−	0.546905i	$-0.815806\pi$
$613$	−41.4559	−1.67439	−0.837195	+	0.546905i	$0.815806\pi$
$614$	−8.22264	−0.331839
$615$	0	0
$616$	−8.81477	−0.355157
$617$	−19.2672	−0.775668	−0.387834	−	0.921729i	$-0.626777\pi$
$617$	−19.2672	−0.775668	−0.387834	+	0.921729i	$0.626777\pi$
$618$	0.0796388	0.00320354
$619$	11.9040	0.478464	0.239232	−	0.970962i	$-0.423104\pi$
$619$	11.9040	0.478464	0.239232	+	0.970962i	$0.423104\pi$
$620$	0	0
$621$	3.04436	0.122166
$622$	−15.5734	−0.624436
$623$	1.00682	0.0403375
$624$	−0.283029	−0.0113302
$625$	0	0
$626$	−8.82990	−0.352914
$627$	0.913166	0.0364683
$628$	19.5520	0.780210
$629$	0.361113	0.0143985
$630$	0	0
$631$	1.56023	0.0621119	0.0310559	−	0.999518i	$-0.490113\pi$
$631$	1.56023	0.0621119	0.0310559	+	0.999518i	$0.490113\pi$
$632$	13.8603	0.551333
$633$	0.0527549	0.00209682
$634$	−14.6744	−0.582794
$635$	0	0
$636$	−0.380346	−0.0150817
$637$	−8.30709	−0.329139
$638$	−8.65147	−0.342515
$639$	10.2918	0.407137
$640$	0	0
$641$	11.9081	0.470342	0.235171	−	0.971954i	$-0.424435\pi$
$641$	11.9081	0.470342	0.235171	+	0.971954i	$0.424435\pi$
$642$	0.726907	0.0286887
$643$	8.88323	0.350321	0.175160	−	0.984540i	$-0.443956\pi$
$643$	8.88323	0.350321	0.175160	+	0.984540i	$0.443956\pi$
$644$	−12.6944	−0.500231
$645$	0	0
$646$	11.5070	0.452736
$647$	−5.67660	−0.223170	−0.111585	−	0.993755i	$-0.535593\pi$
$647$	−5.67660	−0.223170	−0.111585	+	0.993755i	$0.535593\pi$
$648$	18.2873	0.718394
$649$	−3.51176	−0.137849
$650$	0	0
$651$	−1.00329	−0.0393220
$652$	36.6881	1.43682
$653$	−19.1897	−0.750952	−0.375476	−	0.926832i	$-0.622521\pi$
$653$	−19.1897	−0.750952	−0.375476	+	0.926832i	$0.622521\pi$
$654$	0.663251	0.0259352
$655$	0	0
$656$	1.09659	0.0428147
$657$	−16.0620	−0.626640
$658$	−3.47181	−0.135345
$659$	−49.5041	−1.92840	−0.964202	−	0.265167i	$-0.914573\pi$
$659$	−49.5041	−1.92840	−0.964202	+	0.265167i	$0.914573\pi$
$660$	0	0
$661$	21.9398	0.853359	0.426680	−	0.904403i	$-0.359683\pi$
$661$	21.9398	0.853359	0.426680	+	0.904403i	$0.359683\pi$
$662$	−6.54042	−0.254200
$663$	0.834136	0.0323952
$664$	10.3827	0.402925
$665$	0	0
$666$	−0.0902012	−0.00349522
$667$	−27.1773	−1.05231
$668$	13.9448	0.539542
$669$	1.44959	0.0560444
$670$	0	0
$671$	−34.1619	−1.31881
$672$	0.544491	0.0210042
$673$	49.8824	1.92282	0.961412	−	0.275112i	$-0.0887151\pi$
$673$	49.8824	1.92282	0.961412	+	0.275112i	$0.0887151\pi$
$674$	−16.5141	−0.636101
$675$	0	0
$676$	18.1404	0.697707
$677$	0.357534	0.0137412	0.00687058	−	0.999976i	$-0.497813\pi$
$677$	0.357534	0.0137412	0.00687058	+	0.999976i	$0.497813\pi$
$678$	0.506058	0.0194350
$679$	19.9273	0.764738
$680$	0	0
$681$	0.659242	0.0252622
$682$	19.1442	0.733068
$683$	30.1267	1.15277	0.576383	−	0.817179i	$-0.304463\pi$
$683$	30.1267	1.15277	0.576383	+	0.817179i	$0.304463\pi$
$684$	15.8541	0.606198
$685$	0	0
$686$	8.49251	0.324246
$687$	−0.640652	−0.0244424
$688$	−1.35169	−0.0515328
$689$	−4.08617	−0.155671
$690$	0	0
$691$	−0.152788	−0.00581232	−0.00290616	−	0.999996i	$-0.500925\pi$
$691$	−0.152788	−0.00581232	−0.00290616	+	0.999996i	$0.500925\pi$
$692$	−22.6968	−0.862805
$693$	12.8948	0.489834
$694$	5.61406	0.213107
$695$	0	0
$696$	0.756179	0.0286629
$697$	−3.23185	−0.122415
$698$	−11.5673	−0.437829
$699$	−0.135555	−0.00512714
$700$	0	0
$701$	10.0003	0.377706	0.188853	−	0.982005i	$-0.439523\pi$
$701$	10.0003	0.377706	0.188853	+	0.982005i	$0.439523\pi$
$702$	−0.417193	−0.0157459
$703$	−0.170182	−0.00641854
$704$	5.43117	0.204695
$705$	0	0
$706$	7.85779	0.295732
$707$	0.116514	0.00438198
$708$	0.140716	0.00528845
$709$	26.7168	1.00337	0.501686	−	0.865050i	$-0.332713\pi$
$709$	26.7168	1.00337	0.501686	+	0.865050i	$0.332713\pi$
$710$	0	0
$711$	−20.2757	−0.760400
$712$	1.67918	0.0629300
$713$	60.1386	2.25221
$714$	−0.375020	−0.0140348
$715$	0	0
$716$	−26.3310	−0.984035
$717$	0.471598	0.0176122
$718$	−5.93199	−0.221380
$719$	52.4577	1.95634	0.978171	−	0.207802i	$-0.0666309\pi$
$719$	52.4577	1.95634	0.978171	+	0.207802i	$0.0666309\pi$
$720$	0	0
$721$	2.12174	0.0790177
$722$	5.10357	0.189935
$723$	−1.25373	−0.0466266
$724$	7.76532	0.288596
$725$	0	0
$726$	0.0613559	0.00227713
$727$	14.3795	0.533306	0.266653	−	0.963793i	$-0.414082\pi$
$727$	14.3795	0.533306	0.266653	+	0.963793i	$0.414082\pi$
$728$	3.79463	0.140638
$729$	−26.6277	−0.986211
$730$	0	0
$731$	3.98368	0.147342
$732$	1.36887	0.0505949
$733$	14.6110	0.539671	0.269835	−	0.962906i	$-0.413031\pi$
$733$	14.6110	0.539671	0.269835	+	0.962906i	$0.413031\pi$
$734$	−10.9388	−0.403758
$735$	0	0
$736$	−32.6376	−1.20304
$737$	−29.1399	−1.07338
$738$	0.807273	0.0297161
$739$	16.9697	0.624240	0.312120	−	0.950043i	$-0.398961\pi$
$739$	16.9697	0.624240	0.312120	+	0.950043i	$0.398961\pi$
$740$	0	0
$741$	−0.393104	−0.0144410
$742$	1.83711	0.0674423
$743$	−17.2224	−0.631829	−0.315915	−	0.948788i	$-0.602311\pi$
$743$	−17.2224	−0.631829	−0.315915	+	0.948788i	$0.602311\pi$
$744$	−1.67329	−0.0613458
$745$	0	0
$746$	15.5817	0.570487
$747$	−15.1884	−0.555716
$748$	−39.4708	−1.44320
$749$	19.3663	0.707628
$750$	0	0
$751$	−39.0434	−1.42471	−0.712357	−	0.701817i	$-0.752372\pi$
$751$	−39.0434	−1.42471	−0.712357	+	0.701817i	$0.752372\pi$
$752$	11.5061	0.419586
$753$	1.99465	0.0726892
$754$	3.72433	0.135632
$755$	0	0
$756$	−1.03459	−0.0376275
$757$	−14.3786	−0.522600	−0.261300	−	0.965258i	$-0.584151\pi$
$757$	−14.3786	−0.522600	−0.261300	+	0.965258i	$0.584151\pi$
$758$	4.62737	0.168074
$759$	1.78390	0.0647514
$760$	0	0
$761$	−3.66157	−0.132732	−0.0663660	−	0.997795i	$-0.521140\pi$
$761$	−3.66157	−0.132732	−0.0663660	+	0.997795i	$0.521140\pi$
$762$	−0.701920	−0.0254279
$763$	17.6703	0.639709
$764$	28.3963	1.02734
$765$	0	0
$766$	3.76729	0.136118
$767$	1.51176	0.0545865
$768$	0.274163	0.00989301
$769$	−3.36527	−0.121355	−0.0606774	−	0.998157i	$-0.519326\pi$
$769$	−3.36527	−0.121355	−0.0606774	+	0.998157i	$0.519326\pi$
$770$	0	0
$771$	0.250094	0.00900691
$772$	−0.275167	−0.00990349
$773$	30.0104	1.07940	0.539700	−	0.841857i	$-0.318538\pi$
$773$	30.0104	1.07940	0.539700	+	0.841857i	$0.318538\pi$
$774$	−0.995070	−0.0357671
$775$	0	0
$776$	33.2348	1.19306
$777$	0.00554634	0.000198974 0
$778$	−1.36205	−0.0488318
$779$	1.52308	0.0545699
$780$	0	0
$781$	12.0752	0.432086
$782$	22.4792	0.803856
$783$	−2.21493	−0.0791552
$784$	−12.3777	−0.442061
$785$	0	0
$786$	0.765436	0.0273022
$787$	−48.9816	−1.74600	−0.873002	−	0.487716i	$-0.837830\pi$
$787$	−48.9816	−1.74600	−0.873002	+	0.487716i	$0.837830\pi$
$788$	1.06848	0.0380631
$789$	0.728294	0.0259280
$790$	0	0
$791$	13.4824	0.479379
$792$	21.5060	0.764184
$793$	14.7062	0.522232
$794$	7.57295	0.268754
$795$	0	0
$796$	−4.97827	−0.176450
$797$	6.64859	0.235505	0.117753	−	0.993043i	$-0.462431\pi$
$797$	6.64859	0.235505	0.117753	+	0.993043i	$0.462431\pi$
$798$	0.176736	0.00625640
$799$	−33.9106	−1.19967
$800$	0	0
$801$	−2.45642	−0.0867933
$802$	8.75639	0.309199
$803$	−18.8454	−0.665040
$804$	1.16764	0.0411794
$805$	0	0
$806$	−8.24127	−0.290286
$807$	−0.0562887	−0.00198146
$808$	0.194323	0.00683627
$809$	33.7196	1.18552	0.592759	−	0.805380i	$-0.298039\pi$
$809$	33.7196	1.18552	0.592759	+	0.805380i	$0.298039\pi$
$810$	0	0
$811$	36.5045	1.28185	0.640924	−	0.767605i	$-0.278552\pi$
$811$	36.5045	1.28185	0.640924	+	0.767605i	$0.278552\pi$
$812$	9.23586	0.324115
$813$	−1.65621	−0.0580858
$814$	−0.105832	−0.00370941
$815$	0	0
$816$	1.24288	0.0435094
$817$	−1.87739	−0.0656817
$818$	7.92135	0.276963
$819$	−5.55103	−0.193969
$820$	0	0
$821$	40.0498	1.39775	0.698874	−	0.715245i	$-0.253685\pi$
$821$	40.0498	1.39775	0.698874	+	0.715245i	$0.253685\pi$
$822$	0.528807	0.0184443
$823$	−15.9713	−0.556723	−0.278362	−	0.960476i	$-0.589791\pi$
$823$	−15.9713	−0.556723	−0.278362	+	0.960476i	$0.589791\pi$
$824$	3.53864	0.123274
$825$	0	0
$826$	−0.679674	−0.0236489
$827$	12.7942	0.444898	0.222449	−	0.974944i	$-0.428595\pi$
$827$	12.7942	0.444898	0.222449	+	0.974944i	$0.428595\pi$
$828$	30.9715	1.07634
$829$	−29.8277	−1.03596	−0.517980	−	0.855393i	$-0.673316\pi$
$829$	−29.8277	−1.03596	−0.517980	+	0.855393i	$0.673316\pi$
$830$	0	0
$831$	−0.869354	−0.0301576
$832$	−2.33804	−0.0810568
$833$	36.4793	1.26393
$834$	0.754593	0.0261294
$835$	0	0
$836$	18.6015	0.643345
$837$	4.90124	0.169412
$838$	7.22281	0.249508
$839$	−18.8556	−0.650966	−0.325483	−	0.945548i	$-0.605527\pi$
$839$	−18.8556	−0.650966	−0.325483	+	0.945548i	$0.605527\pi$
$840$	0	0
$841$	−9.22708	−0.318175
$842$	−1.64640	−0.0567387
$843$	1.11800	0.0385060
$844$	1.07463	0.0369904
$845$	0	0
$846$	8.47042	0.291219
$847$	1.63465	0.0561671
$848$	−6.08847	−0.209079
$849$	0.606818	0.0208259
$850$	0	0
$851$	−0.332456	−0.0113964
$852$	−0.483856	−0.0165766
$853$	18.8027	0.643791	0.321896	−	0.946775i	$-0.395680\pi$
$853$	18.8027	0.643791	0.321896	+	0.946775i	$0.395680\pi$
$854$	−6.61177	−0.226250
$855$	0	0
$856$	32.2991	1.10396
$857$	−33.6436	−1.14924	−0.574622	−	0.818419i	$-0.694851\pi$
$857$	−33.6436	−1.14924	−0.574622	+	0.818419i	$0.694851\pi$
$858$	−0.244462	−0.00834579
$859$	6.28090	0.214301	0.107151	−	0.994243i	$-0.465827\pi$
$859$	6.28090	0.214301	0.107151	+	0.994243i	$0.465827\pi$
$860$	0	0
$861$	−0.0496381	−0.00169166
$862$	−10.7051	−0.364618
$863$	39.4634	1.34335	0.671676	−	0.740845i	$-0.265575\pi$
$863$	39.4634	1.34335	0.671676	+	0.740845i	$0.265575\pi$
$864$	−2.65994	−0.0904929
$865$	0	0
$866$	−4.27025	−0.145109
$867$	−2.25004	−0.0764155
$868$	−20.4373	−0.693687
$869$	−23.7893	−0.806996
$870$	0	0
$871$	12.5443	0.425047
$872$	29.4707	0.998003
$873$	−48.6180	−1.64547
$874$	−10.5938	−0.358341
$875$	0	0
$876$	0.755137	0.0255137
$877$	−10.5159	−0.355097	−0.177548	−	0.984112i	$-0.556817\pi$
$877$	−10.5159	−0.355097	−0.177548	+	0.984112i	$0.556817\pi$
$878$	4.92526	0.166220
$879$	2.62121	0.0884112
$880$	0	0
$881$	24.1606	0.813993	0.406996	−	0.913430i	$-0.366576\pi$
$881$	24.1606	0.813993	0.406996	+	0.913430i	$0.366576\pi$
$882$	−9.11205	−0.306819
$883$	1.52562	0.0513412	0.0256706	−	0.999670i	$-0.491828\pi$
$883$	1.52562	0.0513412	0.0256706	+	0.999670i	$0.491828\pi$
$884$	16.9916	0.571490
$885$	0	0
$886$	14.6856	0.493372
$887$	44.7628	1.50299	0.751495	−	0.659739i	$-0.229333\pi$
$887$	44.7628	1.50299	0.751495	+	0.659739i	$0.229333\pi$
$888$	0.00925021	0.000310417 0
$889$	−18.7006	−0.627197
$890$	0	0
$891$	−31.3877	−1.05153
$892$	29.5286	0.988691
$893$	15.9811	0.534787
$894$	−0.216491	−0.00724055
$895$	0	0
$896$	14.1535	0.472834
$897$	−0.767941	−0.0256408
$898$	16.4593	0.549255
$899$	−43.7539	−1.45928
$900$	0	0
$901$	17.9438	0.597795
$902$	0.947164	0.0315371
$903$	0.0611855	0.00203613
$904$	22.4860	0.747873
$905$	0	0
$906$	−0.767305	−0.0254920
$907$	−11.3166	−0.375761	−0.187881	−	0.982192i	$-0.560162\pi$
$907$	−11.3166	−0.375761	−0.187881	+	0.982192i	$0.560162\pi$
$908$	13.4290	0.445656
$909$	−0.284269	−0.00942860
$910$	0	0
$911$	−16.3511	−0.541737	−0.270869	−	0.962616i	$-0.587311\pi$
$911$	−16.3511	−0.541737	−0.270869	+	0.962616i	$0.587311\pi$
$912$	−0.585732	−0.0193955
$913$	−17.8204	−0.589770
$914$	17.7483	0.587061
$915$	0	0
$916$	−13.0503	−0.431193
$917$	20.3928	0.673429
$918$	1.83204	0.0604663
$919$	−25.6887	−0.847391	−0.423696	−	0.905805i	$-0.639267\pi$
$919$	−25.6887	−0.847391	−0.423696	+	0.905805i	$0.639267\pi$
$920$	0	0
$921$	−1.23355	−0.0406467
$922$	−5.32267	−0.175293
$923$	−5.19821	−0.171101
$924$	−0.606234	−0.0199436
$925$	0	0
$926$	−12.6014	−0.414107
$927$	−5.17656	−0.170021
$928$	23.7455	0.779485
$929$	−16.1930	−0.531275	−0.265637	−	0.964073i	$-0.585582\pi$
$929$	−16.1930	−0.531275	−0.265637	+	0.964073i	$0.585582\pi$
$930$	0	0
$931$	−17.1917	−0.563434
$932$	−2.76129	−0.0904490
$933$	−2.33629	−0.0764868
$934$	−2.18207	−0.0713996
$935$	0	0
$936$	−9.25803	−0.302608
$937$	3.46633	0.113240	0.0566200	−	0.998396i	$-0.481968\pi$
$937$	3.46633	0.113240	0.0566200	+	0.998396i	$0.481968\pi$
$938$	−5.63980	−0.184146
$939$	−1.32465	−0.0432282
$940$	0	0
$941$	−18.4147	−0.600303	−0.300151	−	0.953892i	$-0.597037\pi$
$941$	−18.4147	−0.600303	−0.300151	+	0.953892i	$0.597037\pi$
$942$	−0.531770	−0.0173260
$943$	2.97538	0.0968916
$944$	2.25255	0.0733142
$945$	0	0
$946$	−1.16750	−0.0379588
$947$	26.7851	0.870397	0.435199	−	0.900334i	$-0.356678\pi$
$947$	26.7851	0.870397	0.435199	+	0.900334i	$0.356678\pi$
$948$	0.953238	0.0309597
$949$	8.11267	0.263348
$950$	0	0
$951$	−2.20142	−0.0713860
$952$	−16.6635	−0.540068
$953$	11.1607	0.361530	0.180765	−	0.983526i	$-0.442143\pi$
$953$	11.1607	0.361530	0.180765	+	0.983526i	$0.442143\pi$
$954$	−4.48212	−0.145114
$955$	0	0
$956$	9.60660	0.310700
$957$	−1.29788	−0.0419544
$958$	8.57422	0.277020
$959$	14.0885	0.454941
$960$	0	0
$961$	65.8196	2.12321
$962$	0.0455591	0.00146888
$963$	−47.2493	−1.52259
$964$	−25.5388	−0.822550
$965$	0	0
$966$	0.345260	0.0111085
$967$	−41.1562	−1.32349	−0.661747	−	0.749727i	$-0.730185\pi$
$967$	−41.1562	−1.32349	−0.661747	+	0.749727i	$0.730185\pi$
$968$	2.72627	0.0876255
$969$	1.72626	0.0554554
$970$	0	0
$971$	18.9541	0.608267	0.304133	−	0.952629i	$-0.401633\pi$
$971$	18.9541	0.608267	0.304133	+	0.952629i	$0.401633\pi$
$972$	3.78769	0.121490
$973$	20.1039	0.644501
$974$	−13.1014	−0.419796
$975$	0	0
$976$	21.9125	0.701402
$977$	30.1231	0.963722	0.481861	−	0.876248i	$-0.339961\pi$
$977$	30.1231	0.963722	0.481861	+	0.876248i	$0.339961\pi$
$978$	−0.997832	−0.0319071
$979$	−2.88209	−0.0921119
$980$	0	0
$981$	−43.1116	−1.37645
$982$	12.9622	0.413639
$983$	−33.9131	−1.08166	−0.540830	−	0.841132i	$-0.681890\pi$
$983$	−33.9131	−1.08166	−0.540830	+	0.841132i	$0.681890\pi$
$984$	−0.0827866	−0.00263914
$985$	0	0
$986$	−16.3548	−0.520843
$987$	−0.520834	−0.0165783
$988$	−8.00765	−0.254757
$989$	−3.66754	−0.116621
$990$	0	0
$991$	−54.7652	−1.73967	−0.869837	−	0.493339i	$-0.835776\pi$
$991$	−54.7652	−1.73967	−0.869837	+	0.493339i	$0.835776\pi$
$992$	−52.5446	−1.66829
$993$	−0.981181	−0.0311368
$994$	2.33707	0.0741273
$995$	0	0
$996$	0.714065	0.0226260
$997$	59.9210	1.89772	0.948859	−	0.315702i	$-0.102240\pi$
$997$	59.9210	1.89772	0.948859	+	0.315702i	$0.102240\pi$
$998$	14.2049	0.449648
$999$	−0.0270949	−0.000857244 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1475.2.a.i.1.3		5
5.2	odd	4		1475.2.b.e.1299.5		10
5.3	odd	4		1475.2.b.e.1299.6		10
5.4	even	2		59.2.a.a.1.3	✓	5
15.14	odd	2		531.2.a.f.1.3		5
20.19	odd	2		944.2.a.n.1.3		5
35.34	odd	2		2891.2.a.f.1.3		5
40.19	odd	2		3776.2.a.bl.1.3		5
40.29	even	2		3776.2.a.bn.1.3		5
55.54	odd	2		7139.2.a.k.1.3		5
60.59	even	2		8496.2.a.bv.1.1		5
65.64	even	2		9971.2.a.d.1.3		5
295.294	odd	2		3481.2.a.d.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.a.a.1.3	✓	5	5.4	even	2
531.2.a.f.1.3		5	15.14	odd	2
944.2.a.n.1.3		5	20.19	odd	2
1475.2.a.i.1.3		5	1.1	even	1	trivial
1475.2.b.e.1299.5		10	5.2	odd	4
1475.2.b.e.1299.6		10	5.3	odd	4
2891.2.a.f.1.3		5	35.34	odd	2
3481.2.a.d.1.3		5	295.294	odd	2
3776.2.a.bl.1.3		5	40.19	odd	2
3776.2.a.bn.1.3		5	40.29	even	2
7139.2.a.k.1.3		5	55.54	odd	2
8496.2.a.bv.1.1		5	60.59	even	2
9971.2.a.d.1.3		5	65.64	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1475 = 5^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1475.a (trivial)

\(f(q)\)	\(=\)	\(q-0.554026 q^{2} -0.0831139 q^{3} -1.69306 q^{4} +0.0460472 q^{6} +1.22679 q^{7} +2.04605 q^{8} -2.99309 q^{9} +O(q^{10})\)	\(q-0.554026 q^{2} -0.0831139 q^{3} -1.69306 q^{4} +0.0460472 q^{6} +1.22679 q^{7} +2.04605 q^{8} -2.99309 q^{9} -3.51176 q^{11} +0.140716 q^{12} +1.51176 q^{13} -0.679674 q^{14} +2.25255 q^{16} -6.63866 q^{17} +1.65825 q^{18} +3.12861 q^{19} -0.101963 q^{21} +1.94560 q^{22} +6.11183 q^{23} -0.170055 q^{24} -0.837553 q^{26} +0.498109 q^{27} -2.07703 q^{28} -4.44667 q^{29} +9.83969 q^{31} -5.34006 q^{32} +0.291876 q^{33} +3.67799 q^{34} +5.06747 q^{36} -0.0543954 q^{37} -1.73333 q^{38} -0.125648 q^{39} +0.486822 q^{41} +0.0564904 q^{42} -0.600073 q^{43} +5.94560 q^{44} -3.38611 q^{46} +5.10805 q^{47} -0.187218 q^{48} -5.49498 q^{49} +0.551765 q^{51} -2.55949 q^{52} -2.70292 q^{53} -0.275965 q^{54} +2.51007 q^{56} -0.260031 q^{57} +2.46357 q^{58} +1.00000 q^{59} +9.72786 q^{61} -5.45144 q^{62} -3.67190 q^{63} -1.54657 q^{64} -0.161707 q^{66} +8.29780 q^{67} +11.2396 q^{68} -0.507978 q^{69} -3.43851 q^{71} -6.12401 q^{72} +5.36637 q^{73} +0.0301365 q^{74} -5.29691 q^{76} -4.30820 q^{77} +0.0696123 q^{78} +6.77418 q^{79} +8.93788 q^{81} -0.269712 q^{82} +5.07450 q^{83} +0.172630 q^{84} +0.332456 q^{86} +0.369581 q^{87} -7.18523 q^{88} +0.820696 q^{89} +1.85461 q^{91} -10.3477 q^{92} -0.817816 q^{93} -2.82999 q^{94} +0.443834 q^{96} +16.2434 q^{97} +3.04436 q^{98} +10.5110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9	\( 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9} - 2 q^{11} + 22 q^{12} - 8 q^{13} - 18 q^{14} + 10 q^{16} + q^{17} + 2 q^{18} + 6 q^{19} + 15 q^{21} - 8 q^{22} + 8 q^{23} + 6 q^{24} + 8 q^{26} + 11 q^{27} + 2 q^{28} + 14 q^{29} + 2 q^{32} + 14 q^{33} - 2 q^{34} + 42 q^{36} - 18 q^{37} - 18 q^{39} - 10 q^{41} - 34 q^{42} + 4 q^{43} + 12 q^{44} + 16 q^{46} + 20 q^{47} + 54 q^{48} + q^{49} - 12 q^{51} - 28 q^{52} + 10 q^{53} - 26 q^{54} - 38 q^{56} + 3 q^{57} + 38 q^{58} + 5 q^{59} + 22 q^{61} - 48 q^{62} + 12 q^{63} + 18 q^{64} + 28 q^{66} + 14 q^{68} - 4 q^{69} + 3 q^{71} - 28 q^{72} + 8 q^{73} + 8 q^{74} + 14 q^{76} - 2 q^{77} - 20 q^{78} + 10 q^{79} - 3 q^{81} + 48 q^{82} - 6 q^{83} + 28 q^{84} - 8 q^{86} - 11 q^{87} + 24 q^{88} + 10 q^{89} + 6 q^{91} - 4 q^{92} - 6 q^{93} - 36 q^{94} + 42 q^{96} + 22 q^{97} - 24 q^{98} - 4 q^{99}+O(q^{100}) \) 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9 - 2 * q^11 + 22 * q^12 - 8 * q^13 - 18 * q^14 + 10 * q^16 + q^17 + 2 * q^18 + 6 * q^19 + 15 * q^21 - 8 * q^22 + 8 * q^23 + 6 * q^24 + 8 * q^26 + 11 * q^27 + 2 * q^28 + 14 * q^29 + 2 * q^32 + 14 * q^33 - 2 * q^34 + 42 * q^36 - 18 * q^37 - 18 * q^39 - 10 * q^41 - 34 * q^42 + 4 * q^43 + 12 * q^44 + 16 * q^46 + 20 * q^47 + 54 * q^48 + q^49 - 12 * q^51 - 28 * q^52 + 10 * q^53 - 26 * q^54 - 38 * q^56 + 3 * q^57 + 38 * q^58 + 5 * q^59 + 22 * q^61 - 48 * q^62 + 12 * q^63 + 18 * q^64 + 28 * q^66 + 14 * q^68 - 4 * q^69 + 3 * q^71 - 28 * q^72 + 8 * q^73 + 8 * q^74 + 14 * q^76 - 2 * q^77 - 20 * q^78 + 10 * q^79 - 3 * q^81 + 48 * q^82 - 6 * q^83 + 28 * q^84 - 8 * q^86 - 11 * q^87 + 24 * q^88 + 10 * q^89 + 6 * q^91 - 4 * q^92 - 6 * q^93 - 36 * q^94 + 42 * q^96 + 22 * q^97 - 24 * q^98 - 4 * q^99

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