LMFDB - Embedded newform 1573.4.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 69 x^{13} + 418 x^{12} + 1806 x^{11} - 10742 x^{10} - 24098 x^{9} + 129758 x^{8} + \cdots + 47232 $ x^15 - 6x^14 - 69x^13 + 418x^12 + 1806x^11 - 10742x^10 - 24098x^9 + 129758x^8 + 183825x^7 - 750764x^6 - 813769x^5 + 1744424x^4 + 1731312x^3 - 516000x^2 - 352704x + 47232
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.13862$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.13862 q^{2} +4.96398 q^{3} +1.85094 q^{4} -20.3862 q^{5} -15.5801 q^{6} -8.13132 q^{7} +19.2996 q^{8} -2.35886 q^{9} +O(q^{10})$	\(q-3.13862 q^{2} +4.96398 q^{3} +1.85094 q^{4} -20.3862 q^{5} -15.5801 q^{6} -8.13132 q^{7} +19.2996 q^{8} -2.35886 q^{9} +63.9846 q^{10} +9.18804 q^{12} -13.0000 q^{13} +25.5211 q^{14} -101.197 q^{15} -75.3815 q^{16} +20.7657 q^{17} +7.40358 q^{18} +33.3930 q^{19} -37.7337 q^{20} -40.3637 q^{21} +44.7246 q^{23} +95.8027 q^{24} +290.597 q^{25} +40.8021 q^{26} -145.737 q^{27} -15.0506 q^{28} -97.3868 q^{29} +317.618 q^{30} +68.0003 q^{31} +82.1976 q^{32} -65.1756 q^{34} +165.767 q^{35} -4.36612 q^{36} +343.891 q^{37} -104.808 q^{38} -64.5318 q^{39} -393.445 q^{40} -334.660 q^{41} +126.686 q^{42} +92.5971 q^{43} +48.0883 q^{45} -140.373 q^{46} +89.1504 q^{47} -374.193 q^{48} -276.882 q^{49} -912.075 q^{50} +103.081 q^{51} -24.0622 q^{52} +541.370 q^{53} +457.413 q^{54} -156.931 q^{56} +165.762 q^{57} +305.660 q^{58} +305.622 q^{59} -187.309 q^{60} -69.4004 q^{61} -213.427 q^{62} +19.1807 q^{63} +345.065 q^{64} +265.021 q^{65} +881.590 q^{67} +38.4361 q^{68} +222.012 q^{69} -520.279 q^{70} +427.313 q^{71} -45.5251 q^{72} +1092.99 q^{73} -1079.34 q^{74} +1442.52 q^{75} +61.8085 q^{76} +202.541 q^{78} -453.847 q^{79} +1536.74 q^{80} -659.746 q^{81} +1050.37 q^{82} +720.357 q^{83} -74.7109 q^{84} -423.334 q^{85} -290.627 q^{86} -483.427 q^{87} -1436.03 q^{89} -150.931 q^{90} +105.707 q^{91} +82.7826 q^{92} +337.552 q^{93} -279.809 q^{94} -680.756 q^{95} +408.028 q^{96} -578.549 q^{97} +869.027 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) $ 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9} + 16 q^{10} - 3 q^{12} - 195 q^{13} + 60 q^{14} + 202 q^{15} + 282 q^{16} - 136 q^{17} - 351 q^{18} - 136 q^{19} - 62 q^{20} - 625 q^{21} - 176 q^{23} + 227 q^{24} + 479 q^{25} + 78 q^{26} - 13 q^{27} + 86 q^{28} - 344 q^{29} - 542 q^{30} + 275 q^{31} + 170 q^{32} - 1505 q^{34} - 655 q^{35} + 623 q^{36} + 346 q^{37} - 848 q^{38} - 26 q^{39} - 256 q^{40} - 38 q^{41} + 575 q^{42} - 534 q^{43} - 633 q^{45} + 375 q^{46} + 276 q^{47} - 723 q^{48} + 773 q^{49} - 1684 q^{50} - 1111 q^{51} - 702 q^{52} + 706 q^{53} + 178 q^{54} - 2056 q^{56} - 1320 q^{57} - 983 q^{58} - 174 q^{59} + 2004 q^{60} - 1078 q^{61} - 1365 q^{62} + 2055 q^{63} + 1338 q^{64} + 26 q^{65} - 260 q^{67} - 559 q^{68} + 154 q^{69} - 1161 q^{70} + 2910 q^{71} - 6171 q^{72} - 1000 q^{73} - 688 q^{74} - 553 q^{75} - 178 q^{76} - 325 q^{78} + 386 q^{79} + 1702 q^{80} - 2805 q^{81} + 3380 q^{82} - 4318 q^{83} - 6681 q^{84} + 1391 q^{85} + 4139 q^{86} - 3144 q^{87} - 810 q^{89} + 3789 q^{90} + 364 q^{91} - 4857 q^{92} + 394 q^{93} + 116 q^{94} - 5204 q^{95} + 893 q^{96} - 1860 q^{97} - 8 q^{98}+O(q^{100}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9 + 16 * q^10 - 3 * q^12 - 195 * q^13 + 60 * q^14 + 202 * q^15 + 282 * q^16 - 136 * q^17 - 351 * q^18 - 136 * q^19 - 62 * q^20 - 625 * q^21 - 176 * q^23 + 227 * q^24 + 479 * q^25 + 78 * q^26 - 13 * q^27 + 86 * q^28 - 344 * q^29 - 542 * q^30 + 275 * q^31 + 170 * q^32 - 1505 * q^34 - 655 * q^35 + 623 * q^36 + 346 * q^37 - 848 * q^38 - 26 * q^39 - 256 * q^40 - 38 * q^41 + 575 * q^42 - 534 * q^43 - 633 * q^45 + 375 * q^46 + 276 * q^47 - 723 * q^48 + 773 * q^49 - 1684 * q^50 - 1111 * q^51 - 702 * q^52 + 706 * q^53 + 178 * q^54 - 2056 * q^56 - 1320 * q^57 - 983 * q^58 - 174 * q^59 + 2004 * q^60 - 1078 * q^61 - 1365 * q^62 + 2055 * q^63 + 1338 * q^64 + 26 * q^65 - 260 * q^67 - 559 * q^68 + 154 * q^69 - 1161 * q^70 + 2910 * q^71 - 6171 * q^72 - 1000 * q^73 - 688 * q^74 - 553 * q^75 - 178 * q^76 - 325 * q^78 + 386 * q^79 + 1702 * q^80 - 2805 * q^81 + 3380 * q^82 - 4318 * q^83 - 6681 * q^84 + 1391 * q^85 + 4139 * q^86 - 3144 * q^87 - 810 * q^89 + 3789 * q^90 + 364 * q^91 - 4857 * q^92 + 394 * q^93 + 116 * q^94 - 5204 * q^95 + 893 * q^96 - 1860 * q^97 - 8 * q^98

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 $

$2$	−3.13862	−1.10967	−0.554835	−	0.831960i	$-0.687219\pi$
$2$	−3.13862	−1.10967	−0.554835	+	0.831960i	$0.687219\pi$
$3$	4.96398	0.955319	0.477660	−	0.878545i	$-0.341485\pi$
$3$	4.96398	0.955319	0.477660	+	0.878545i	$0.341485\pi$
$4$	1.85094	0.231368
$5$	−20.3862	−1.82340	−0.911699	−	0.410859i	$-0.865229\pi$
$5$	−20.3862	−1.82340	−0.911699	+	0.410859i	$0.865229\pi$
$6$	−15.5801	−1.06009
$7$	−8.13132	−0.439050	−0.219525	−	0.975607i	$-0.570451\pi$
$7$	−8.13132	−0.439050	−0.219525	+	0.975607i	$0.570451\pi$
$8$	19.2996	0.852928
$9$	−2.35886	−0.0873654
$10$	63.9846	2.02337
$11$	0	0
$11$	0	0
$12$	9.18804	0.221030
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	25.5211	0.487201
$15$	−101.197	−1.74193
$16$	−75.3815	−1.17784
$17$	20.7657	0.296260	0.148130	−	0.988968i	$-0.452675\pi$
$17$	20.7657	0.296260	0.148130	+	0.988968i	$0.452675\pi$
$18$	7.40358	0.0969467
$19$	33.3930	0.403204	0.201602	−	0.979468i	$-0.435385\pi$
$19$	33.3930	0.403204	0.201602	+	0.979468i	$0.435385\pi$
$20$	−37.7337	−0.421875
$21$	−40.3637	−0.419433
$22$	0	0
$23$	44.7246	0.405466	0.202733	−	0.979234i	$-0.435018\pi$
$23$	44.7246	0.405466	0.202733	+	0.979234i	$0.435018\pi$
$24$	95.8027	0.814819
$25$	290.597	2.32478
$26$	40.8021	0.307767
$27$	−145.737	−1.03878
$28$	−15.0506	−0.101582
$29$	−97.3868	−0.623596	−0.311798	−	0.950148i	$-0.600931\pi$
$29$	−97.3868	−0.623596	−0.311798	+	0.950148i	$0.600931\pi$
$30$	317.618	1.93296
$31$	68.0003	0.393975	0.196987	−	0.980406i	$-0.436884\pi$
$31$	68.0003	0.393975	0.196987	+	0.980406i	$0.436884\pi$
$32$	82.1976	0.454082
$33$	0	0
$34$	−65.1756	−0.328751
$35$	165.767	0.800563
$36$	−4.36612	−0.0202135
$37$	343.891	1.52798	0.763990	−	0.645228i	$-0.223238\pi$
$37$	343.891	1.52798	0.763990	+	0.645228i	$0.223238\pi$
$38$	−104.808	−0.447424
$39$	−64.5318	−0.264958
$40$	−393.445	−1.55523
$41$	−334.660	−1.27476	−0.637380	−	0.770550i	$-0.719982\pi$
$41$	−334.660	−1.27476	−0.637380	+	0.770550i	$0.719982\pi$
$42$	126.686	0.465432
$43$	92.5971	0.328394	0.164197	−	0.986428i	$-0.447497\pi$
$43$	92.5971	0.328394	0.164197	+	0.986428i	$0.447497\pi$
$44$	0	0
$45$	48.0883	0.159302
$46$	−140.373	−0.449934
$47$	89.1504	0.276679	0.138340	−	0.990385i	$-0.455823\pi$
$47$	89.1504	0.276679	0.138340	+	0.990385i	$0.455823\pi$
$48$	−374.193	−1.12521
$49$	−276.882	−0.807235
$50$	−912.075	−2.57974
$51$	103.081	0.283023
$52$	−24.0622	−0.0641699
$53$	541.370	1.40307	0.701537	−	0.712633i	$-0.252497\pi$
$53$	541.370	1.40307	0.701537	+	0.712633i	$0.252497\pi$
$54$	457.413	1.15270
$55$	0	0
$56$	−156.931	−0.374478
$57$	165.762	0.385189
$58$	305.660	0.691986
$59$	305.622	0.674382	0.337191	−	0.941436i	$-0.390523\pi$
$59$	305.622	0.674382	0.337191	+	0.941436i	$0.390523\pi$
$60$	−187.309	−0.403026
$61$	−69.4004	−0.145669	−0.0728345	−	0.997344i	$-0.523204\pi$
$61$	−69.4004	−0.145669	−0.0728345	+	0.997344i	$0.523204\pi$
$62$	−213.427	−0.437182
$63$	19.1807	0.0383578
$64$	345.065	0.673956
$65$	265.021	0.505719
$66$	0	0
$67$	881.590	1.60751	0.803757	−	0.594958i	$-0.202831\pi$
$67$	881.590	1.60751	0.803757	+	0.594958i	$0.202831\pi$
$68$	38.4361	0.0685450
$69$	222.012	0.387349
$70$	−520.279	−0.888360
$71$	427.313	0.714264	0.357132	−	0.934054i	$-0.383755\pi$
$71$	427.313	0.714264	0.357132	+	0.934054i	$0.383755\pi$
$72$	−45.5251	−0.0745164
$73$	1092.99	1.75239	0.876197	−	0.481953i	$-0.160073\pi$
$73$	1092.99	1.75239	0.876197	+	0.481953i	$0.160073\pi$
$74$	−1079.34	−1.69555
$75$	1442.52	2.22090
$76$	61.8085	0.0932884
$77$	0	0
$78$	202.541	0.294016
$79$	−453.847	−0.646352	−0.323176	−	0.946339i	$-0.604751\pi$
$79$	−453.847	−0.646352	−0.323176	+	0.946339i	$0.604751\pi$
$80$	1536.74	2.14766
$81$	−659.746	−0.905002
$82$	1050.37	1.41456
$83$	720.357	0.952645	0.476322	−	0.879271i	$-0.341970\pi$
$83$	720.357	0.952645	0.476322	+	0.879271i	$0.341970\pi$
$84$	−74.7109	−0.0970432
$85$	−423.334	−0.540200
$86$	−290.627	−0.364409
$87$	−483.427	−0.595733
$88$	0	0
$89$	−1436.03	−1.71033	−0.855165	−	0.518356i	$-0.826544\pi$
$89$	−1436.03	−1.71033	−0.855165	+	0.518356i	$0.826544\pi$
$90$	−150.931	−0.176772
$91$	105.707	0.121771
$92$	82.7826	0.0938117
$93$	337.552	0.376371
$94$	−279.809	−0.307023
$95$	−680.756	−0.735201
$96$	408.028	0.433793
$97$	−578.549	−0.605595	−0.302798	−	0.953055i	$-0.597921\pi$
$97$	−578.549	−0.605595	−0.302798	+	0.953055i	$0.597921\pi$
$98$	869.027	0.895765
$99$	0	0
$100$	537.879	0.537879
$101$	215.654	0.212459	0.106230	−	0.994342i	$-0.466122\pi$
$101$	215.654	0.212459	0.106230	+	0.994342i	$0.466122\pi$
$102$	−323.531	−0.314062
$103$	−1357.05	−1.29820	−0.649098	−	0.760705i	$-0.724854\pi$
$103$	−1357.05	−1.29820	−0.649098	+	0.760705i	$0.724854\pi$
$104$	−250.894	−0.236560
$105$	822.863	0.764793
$106$	−1699.16	−1.55695
$107$	−1557.63	−1.40731	−0.703655	−	0.710542i	$-0.748450\pi$
$107$	−1557.63	−1.40731	−0.703655	+	0.710542i	$0.748450\pi$
$108$	−269.751	−0.240340
$109$	−87.2243	−0.0766474	−0.0383237	−	0.999265i	$-0.512202\pi$
$109$	−87.2243	−0.0766474	−0.0383237	+	0.999265i	$0.512202\pi$
$110$	0	0
$111$	1707.07	1.45971
$112$	612.951	0.517129
$113$	1191.81	0.992180	0.496090	−	0.868271i	$-0.334769\pi$
$113$	1191.81	0.992180	0.496090	+	0.868271i	$0.334769\pi$
$114$	−520.265	−0.427432
$115$	−911.764	−0.739326
$116$	−180.257	−0.144280
$117$	30.6652	0.0242308
$118$	−959.230	−0.748342
$119$	−168.852	−0.130073
$120$	−1953.05	−1.48574
$121$	0	0
$122$	217.821	0.161644
$123$	−1661.25	−1.21780
$124$	125.865	0.0911530
$125$	−3375.90	−2.41560
$126$	−60.2009	−0.0425645
$127$	345.185	0.241183	0.120591	−	0.992702i	$-0.461521\pi$
$127$	345.185	0.241183	0.120591	+	0.992702i	$0.461521\pi$
$128$	−1740.61	−1.20195
$129$	459.651	0.313721
$130$	−831.799	−0.561182
$131$	−1665.47	−1.11078	−0.555391	−	0.831589i	$-0.687431\pi$
$131$	−1665.47	−1.11078	−0.555391	+	0.831589i	$0.687431\pi$
$132$	0	0
$133$	−271.529	−0.177027
$134$	−2766.98	−1.78381
$135$	2971.02	1.89411
$136$	400.769	0.252689
$137$	2920.05	1.82100	0.910498	−	0.413514i	$-0.135699\pi$
$137$	2920.05	1.82100	0.910498	+	0.413514i	$0.135699\pi$
$138$	−696.812	−0.429830
$139$	−1741.75	−1.06283	−0.531416	−	0.847111i	$-0.678340\pi$
$139$	−1741.75	−1.06283	−0.531416	+	0.847111i	$0.678340\pi$
$140$	306.825	0.185224
$141$	442.541	0.264317
$142$	−1341.17	−0.792597
$143$	0	0
$144$	177.815	0.102902
$145$	1985.35	1.13706
$146$	−3430.48	−1.94458
$147$	−1374.44	−0.771167
$148$	636.522	0.353525
$149$	1908.42	1.04929	0.524645	−	0.851321i	$-0.324198\pi$
$149$	1908.42	1.04929	0.524645	+	0.851321i	$0.324198\pi$
$150$	−4527.52	−2.46447
$151$	−1441.95	−0.777117	−0.388558	−	0.921424i	$-0.627027\pi$
$151$	−1441.95	−0.777117	−0.388558	+	0.921424i	$0.627027\pi$
$152$	644.470	0.343904
$153$	−48.9835	−0.0258829
$154$	0	0
$155$	−1386.27	−0.718372
$156$	−119.445	−0.0613027
$157$	−457.888	−0.232761	−0.116380	−	0.993205i	$-0.537129\pi$
$157$	−457.888	−0.232761	−0.116380	+	0.993205i	$0.537129\pi$
$158$	1424.46	0.717238
$159$	2687.35	1.34038
$160$	−1675.70	−0.827972
$161$	−363.670	−0.178020
$162$	2070.69	1.00425
$163$	−2411.48	−1.15878	−0.579392	−	0.815049i	$-0.696710\pi$
$163$	−2411.48	−1.15878	−0.579392	+	0.815049i	$0.696710\pi$
$164$	−619.437	−0.294938
$165$	0	0
$166$	−2260.93	−1.05712
$167$	−2073.87	−0.960964	−0.480482	−	0.877005i	$-0.659538\pi$
$167$	−2073.87	−0.960964	−0.480482	+	0.877005i	$0.659538\pi$
$168$	−779.003	−0.357746
$169$	169.000	0.0769231
$170$	1328.68	0.599443
$171$	−78.7696	−0.0352261
$172$	171.392	0.0759797
$173$	−1201.75	−0.528134	−0.264067	−	0.964504i	$-0.585064\pi$
$173$	−1201.75	−0.528134	−0.264067	+	0.964504i	$0.585064\pi$
$174$	1517.29	0.661067
$175$	−2362.94	−1.02069
$176$	0	0
$177$	1517.10	0.644250
$178$	4507.17	1.89790
$179$	1082.87	0.452167	0.226083	−	0.974108i	$-0.427408\pi$
$179$	1082.87	0.452167	0.226083	+	0.974108i	$0.427408\pi$
$180$	89.0086	0.0368573
$181$	−63.9439	−0.0262592	−0.0131296	−	0.999914i	$-0.504179\pi$
$181$	−63.9439	−0.0262592	−0.0131296	+	0.999914i	$0.504179\pi$
$182$	−331.775	−0.135125
$183$	−344.502	−0.139160
$184$	863.165	0.345833
$185$	−7010.62	−2.78612
$186$	−1059.45	−0.417648
$187$	0	0
$188$	165.012	0.0640147
$189$	1185.03	0.456077
$190$	2136.64	0.815831
$191$	−4240.14	−1.60631	−0.803156	−	0.595768i	$-0.796848\pi$
$191$	−4240.14	−1.60631	−0.803156	+	0.595768i	$0.796848\pi$
$192$	1712.90	0.643843
$193$	−4980.43	−1.85751	−0.928754	−	0.370698i	$-0.879119\pi$
$193$	−4980.43	−1.85751	−0.928754	+	0.370698i	$0.879119\pi$
$194$	1815.85	0.672011
$195$	1315.56	0.483123
$196$	−512.492	−0.186768
$197$	2778.85	1.00500	0.502500	−	0.864577i	$-0.332414\pi$
$197$	2778.85	1.00500	0.502500	+	0.864577i	$0.332414\pi$
$198$	0	0
$199$	4684.26	1.66864	0.834318	−	0.551284i	$-0.185862\pi$
$199$	4684.26	1.66864	0.834318	+	0.551284i	$0.185862\pi$
$200$	5608.40	1.98287
$201$	4376.20	1.53569
$202$	−676.856	−0.235759
$203$	791.883	0.273790
$204$	190.796	0.0654823
$205$	6822.45	2.32439
$206$	4259.27	1.44057
$207$	−105.499	−0.0354237
$208$	979.960	0.326673
$209$	0	0
$210$	−2582.66	−0.848668
$211$	−898.317	−0.293093	−0.146547	−	0.989204i	$-0.546816\pi$
$211$	−898.317	−0.293093	−0.146547	+	0.989204i	$0.546816\pi$
$212$	1002.04	0.324626
$213$	2121.17	0.682350
$214$	4888.82	1.56165
$215$	−1887.70	−0.598792
$216$	−2812.66	−0.886006
$217$	−552.932	−0.172975
$218$	273.764	0.0850534
$219$	5425.58	1.67410
$220$	0	0
$221$	−269.954	−0.0821677
$222$	−5357.84	−1.61980
$223$	3475.18	1.04357	0.521784	−	0.853078i	$-0.325267\pi$
$223$	3475.18	1.04357	0.521784	+	0.853078i	$0.325267\pi$
$224$	−668.375	−0.199365
$225$	−685.480	−0.203105
$226$	−3740.65	−1.10099
$227$	2007.70	0.587030	0.293515	−	0.955954i	$-0.405175\pi$
$227$	2007.70	0.587030	0.293515	+	0.955954i	$0.405175\pi$
$228$	306.816	0.0891202
$229$	3293.75	0.950468	0.475234	−	0.879859i	$-0.342363\pi$
$229$	3293.75	0.950468	0.475234	+	0.879859i	$0.342363\pi$
$230$	2861.68	0.820408
$231$	0	0
$232$	−1879.52	−0.531883
$233$	−4113.47	−1.15658	−0.578289	−	0.815832i	$-0.696279\pi$
$233$	−4113.47	−1.15658	−0.578289	+	0.815832i	$0.696279\pi$
$234$	−96.2466	−0.0268882
$235$	−1817.44	−0.504496
$236$	565.688	0.156030
$237$	−2252.89	−0.617473
$238$	529.964	0.144338
$239$	−5695.20	−1.54139	−0.770694	−	0.637206i	$-0.780090\pi$
$239$	−5695.20	−1.54139	−0.770694	+	0.637206i	$0.780090\pi$
$240$	7628.37	2.05170
$241$	−5633.34	−1.50571	−0.752854	−	0.658188i	$-0.771323\pi$
$241$	−5633.34	−1.50571	−0.752854	+	0.658188i	$0.771323\pi$
$242$	0	0
$243$	659.927	0.174215
$244$	−128.456	−0.0337031
$245$	5644.57	1.47191
$246$	5214.03	1.35136
$247$	−434.109	−0.111829
$248$	1312.38	0.336032
$249$	3575.84	0.910080
$250$	10595.7	2.68052
$251$	−4304.56	−1.08248	−0.541238	−	0.840869i	$-0.682044\pi$
$251$	−4304.56	−1.08248	−0.541238	+	0.840869i	$0.682044\pi$
$252$	35.5023	0.00887475
$253$	0	0
$254$	−1083.41	−0.267633
$255$	−2101.42	−0.516063
$256$	2702.59	0.659813
$257$	−1125.41	−0.273157	−0.136578	−	0.990629i	$-0.543611\pi$
$257$	−1125.41	−0.273157	−0.136578	+	0.990629i	$0.543611\pi$
$258$	−1442.67	−0.348127
$259$	−2796.28	−0.670860
$260$	490.538	0.117007
$261$	229.722	0.0544807
$262$	5227.27	1.23260
$263$	−1481.44	−0.347336	−0.173668	−	0.984804i	$-0.555562\pi$
$263$	−1481.44	−0.347336	−0.173668	+	0.984804i	$0.555562\pi$
$264$	0	0
$265$	−11036.5	−2.55836
$266$	852.227	0.196441
$267$	−7128.45	−1.63391
$268$	1631.77	0.371927
$269$	544.761	0.123475	0.0617373	−	0.998092i	$-0.480336\pi$
$269$	544.761	0.123475	0.0617373	+	0.998092i	$0.480336\pi$
$270$	−9324.91	−2.10184
$271$	8432.45	1.89017	0.945083	−	0.326830i	$-0.105980\pi$
$271$	8432.45	1.89017	0.945083	+	0.326830i	$0.105980\pi$
$272$	−1565.35	−0.348946
$273$	524.729	0.116330
$274$	−9164.92	−2.02070
$275$	0	0
$276$	410.931	0.0896202
$277$	4518.99	0.980217	0.490108	−	0.871661i	$-0.336957\pi$
$277$	4518.99	0.980217	0.490108	+	0.871661i	$0.336957\pi$
$278$	5466.70	1.17939
$279$	−160.403	−0.0344197
$280$	3199.23	0.682822
$281$	−1521.25	−0.322954	−0.161477	−	0.986876i	$-0.551626\pi$
$281$	−1521.25	−0.322954	−0.161477	+	0.986876i	$0.551626\pi$
$282$	−1388.97	−0.293305
$283$	7123.35	1.49625	0.748126	−	0.663557i	$-0.230954\pi$
$283$	7123.35	1.49625	0.748126	+	0.663557i	$0.230954\pi$
$284$	790.931	0.165258
$285$	−3379.26	−0.702352
$286$	0	0
$287$	2721.23	0.559683
$288$	−193.893	−0.0396710
$289$	−4481.79	−0.912230
$290$	−6231.25	−1.26176
$291$	−2871.91	−0.578537
$292$	2023.06	0.405447
$293$	−6722.30	−1.34034	−0.670172	−	0.742205i	$-0.733780\pi$
$293$	−6722.30	−1.34034	−0.670172	+	0.742205i	$0.733780\pi$
$294$	4313.83	0.855741
$295$	−6230.46	−1.22967
$296$	6636.94	1.30326
$297$	0	0
$298$	−5989.82	−1.16437
$299$	−581.419	−0.112456
$300$	2670.02	0.513846
$301$	−752.937	−0.144181
$302$	4525.75	0.862343
$303$	1070.50	0.202966
$304$	−2517.22	−0.474909
$305$	1414.81	0.265612
$306$	153.741	0.0287214
$307$	7735.10	1.43800	0.718999	−	0.695011i	$-0.244601\pi$
$307$	7735.10	1.43800	0.718999	+	0.695011i	$0.244601\pi$
$308$	0	0
$309$	−6736.38	−1.24019
$310$	4350.97	0.797156
$311$	−1013.68	−0.184824	−0.0924121	−	0.995721i	$-0.529458\pi$
$311$	−1013.68	−0.184824	−0.0924121	+	0.995721i	$0.529458\pi$
$312$	−1245.44	−0.225990
$313$	2201.95	0.397640	0.198820	−	0.980036i	$-0.436289\pi$
$313$	2201.95	0.397640	0.198820	+	0.980036i	$0.436289\pi$
$314$	1437.14	0.258288
$315$	−391.021	−0.0699414
$316$	−840.045	−0.149545
$317$	−6439.10	−1.14087	−0.570435	−	0.821343i	$-0.693225\pi$
$317$	−6439.10	−1.14087	−0.570435	+	0.821343i	$0.693225\pi$
$318$	−8434.58	−1.48738
$319$	0	0
$320$	−7034.57	−1.22889
$321$	−7732.07	−1.34443
$322$	1141.42	0.197543
$323$	693.429	0.119453
$324$	−1221.15	−0.209388
$325$	−3777.76	−0.644777
$326$	7568.73	1.28587
$327$	−432.980	−0.0732228
$328$	−6458.80	−1.08728
$329$	−724.911	−0.121476
$330$	0	0
$331$	−11033.2	−1.83215	−0.916073	−	0.401011i	$-0.868659\pi$
$331$	−11033.2	−1.83215	−0.916073	+	0.401011i	$0.868659\pi$
$332$	1333.34	0.220411
$333$	−811.192	−0.133493
$334$	6509.10	1.06635
$335$	−17972.3	−2.93114
$336$	3042.68	0.494023
$337$	−10411.5	−1.68294	−0.841470	−	0.540304i	$-0.818309\pi$
$337$	−10411.5	−1.68294	−0.841470	+	0.540304i	$0.818309\pi$
$338$	−530.427	−0.0853592
$339$	5916.14	0.947848
$340$	−783.566	−0.124985
$341$	0	0
$342$	247.228	0.0390893
$343$	5040.46	0.793467
$344$	1787.08	0.280096
$345$	−4525.98	−0.706292
$346$	3771.83	0.586054
$347$	−412.136	−0.0637597	−0.0318799	−	0.999492i	$-0.510149\pi$
$347$	−412.136	−0.0637597	−0.0318799	+	0.999492i	$0.510149\pi$
$348$	−894.795	−0.137833
$349$	5470.88	0.839111	0.419555	−	0.907730i	$-0.362186\pi$
$349$	5470.88	0.839111	0.419555	+	0.907730i	$0.362186\pi$
$350$	7416.37	1.13263
$351$	1894.58	0.288106
$352$	0	0
$353$	722.493	0.108936	0.0544681	−	0.998516i	$-0.482654\pi$
$353$	722.493	0.108936	0.0544681	+	0.998516i	$0.482654\pi$
$354$	−4761.60	−0.714905
$355$	−8711.29	−1.30239
$356$	−2658.02	−0.395715
$357$	−838.181	−0.124261
$358$	−3398.73	−0.501756
$359$	−9499.35	−1.39654	−0.698268	−	0.715837i	$-0.746046\pi$
$359$	−9499.35	−1.39654	−0.698268	+	0.715837i	$0.746046\pi$
$360$	928.083	0.135873
$361$	−5743.91	−0.837426
$362$	200.696	0.0291391
$363$	0	0
$364$	195.658	0.0281738
$365$	−22281.9	−3.19531
$366$	1081.26	0.154422
$367$	3676.54	0.522926	0.261463	−	0.965214i	$-0.415795\pi$
$367$	3676.54	0.522926	0.261463	+	0.965214i	$0.415795\pi$
$368$	−3371.41	−0.477573
$369$	789.419	0.111370
$370$	22003.7	3.09167
$371$	−4402.05	−0.616020
$372$	624.790	0.0870802
$373$	9665.29	1.34169	0.670844	−	0.741598i	$-0.265932\pi$
$373$	9665.29	1.34169	0.670844	+	0.741598i	$0.265932\pi$
$374$	0	0
$375$	−16757.9	−2.30767
$376$	1720.56	0.235988
$377$	1266.03	0.172954
$378$	−3719.37	−0.506095
$379$	−1824.13	−0.247228	−0.123614	−	0.992330i	$-0.539448\pi$
$379$	−1824.13	−0.247228	−0.123614	+	0.992330i	$0.539448\pi$
$380$	−1260.04	−0.170102
$381$	1713.49	0.230407
$382$	13308.2	1.78248
$383$	−1368.77	−0.182613	−0.0913063	−	0.995823i	$-0.529104\pi$
$383$	−1368.77	−0.182613	−0.0913063	+	0.995823i	$0.529104\pi$
$384$	−8640.36	−1.14825
$385$	0	0
$386$	15631.7	2.06122
$387$	−218.424	−0.0286902
$388$	−1070.86	−0.140115
$389$	−5956.27	−0.776336	−0.388168	−	0.921589i	$-0.626892\pi$
$389$	−5956.27	−0.776336	−0.388168	+	0.921589i	$0.626892\pi$
$390$	−4129.04	−0.536108
$391$	928.737	0.120123
$392$	−5343.69	−0.688514
$393$	−8267.35	−1.06115
$394$	−8721.76	−1.11522
$395$	9252.23	1.17856
$396$	0	0
$397$	10388.6	1.31332	0.656660	−	0.754187i	$-0.271969\pi$
$397$	10388.6	1.31332	0.656660	+	0.754187i	$0.271969\pi$
$398$	−14702.1	−1.85163
$399$	−1347.87	−0.169117
$400$	−21905.7	−2.73821
$401$	2936.05	0.365634	0.182817	−	0.983147i	$-0.441478\pi$
$401$	2936.05	0.365634	0.182817	+	0.983147i	$0.441478\pi$
$402$	−13735.2	−1.70411
$403$	−884.004	−0.109269
$404$	399.163	0.0491562
$405$	13449.7	1.65018
$406$	−2485.42	−0.303816
$407$	0	0
$408$	1989.41	0.241398
$409$	−749.773	−0.0906452	−0.0453226	−	0.998972i	$-0.514432\pi$
$409$	−749.773	−0.0906452	−0.0453226	+	0.998972i	$0.514432\pi$
$410$	−21413.1	−2.57931
$411$	14495.1	1.73963
$412$	−2511.82	−0.300361
$413$	−2485.11	−0.296087
$414$	331.122	0.0393086
$415$	−14685.4	−1.73705
$416$	−1068.57	−0.125940
$417$	−8646.03	−1.01534
$418$	0	0
$419$	1926.64	0.224636	0.112318	−	0.993672i	$-0.464172\pi$
$419$	1926.64	0.224636	0.112318	+	0.993672i	$0.464172\pi$
$420$	1523.07	0.176948
$421$	−12115.3	−1.40253	−0.701264	−	0.712902i	$-0.747380\pi$
$421$	−12115.3	−1.40253	−0.701264	+	0.712902i	$0.747380\pi$
$422$	2819.48	0.325237
$423$	−210.294	−0.0241722
$424$	10448.2	1.19672
$425$	6034.45	0.688739
$426$	−6657.56	−0.757183
$427$	564.316	0.0639559
$428$	−2883.09	−0.325606
$429$	0	0
$430$	5924.79	0.664462
$431$	−12936.6	−1.44579	−0.722893	−	0.690960i	$-0.757188\pi$
$431$	−12936.6	−1.44579	−0.722893	+	0.690960i	$0.757188\pi$
$432$	10985.9	1.22351
$433$	−7228.01	−0.802207	−0.401104	−	0.916033i	$-0.631373\pi$
$433$	−7228.01	−0.802207	−0.401104	+	0.916033i	$0.631373\pi$
$434$	1735.44	0.191945
$435$	9855.23	1.08626
$436$	−161.447	−0.0177337
$437$	1493.49	0.163486
$438$	−17028.8	−1.85769
$439$	9024.65	0.981145	0.490573	−	0.871400i	$-0.336788\pi$
$439$	9024.65	0.981145	0.490573	+	0.871400i	$0.336788\pi$
$440$	0	0
$441$	653.126	0.0705244
$442$	847.283	0.0911791
$443$	−8462.02	−0.907545	−0.453773	−	0.891117i	$-0.649922\pi$
$443$	−8462.02	−0.907545	−0.453773	+	0.891117i	$0.649922\pi$
$444$	3159.68	0.337730
$445$	29275.3	3.11861
$446$	−10907.3	−1.15802
$447$	9473.38	1.00241
$448$	−2805.84	−0.295900
$449$	−10534.2	−1.10722	−0.553609	−	0.832776i	$-0.686750\pi$
$449$	−10534.2	−1.10722	−0.553609	+	0.832776i	$0.686750\pi$
$450$	2151.46	0.225380
$451$	0	0
$452$	2205.98	0.229558
$453$	−7157.84	−0.742394
$454$	−6301.41	−0.651409
$455$	−2154.97	−0.222036
$456$	3199.14	0.328538
$457$	8487.53	0.868774	0.434387	−	0.900726i	$-0.356965\pi$
$457$	8487.53	0.868774	0.434387	+	0.900726i	$0.356965\pi$
$458$	−10337.8	−1.05471
$459$	−3026.33	−0.307749
$460$	−1687.62	−0.171056
$461$	−15303.9	−1.54614	−0.773072	−	0.634318i	$-0.781281\pi$
$461$	−15303.9	−1.54614	−0.773072	+	0.634318i	$0.781281\pi$
$462$	0	0
$463$	18990.8	1.90622	0.953108	−	0.302630i	$-0.0978646\pi$
$463$	18990.8	1.90622	0.953108	+	0.302630i	$0.0978646\pi$
$464$	7341.17	0.734494
$465$	−6881.41	−0.686275
$466$	12910.6	1.28342
$467$	−1311.88	−0.129992	−0.0649962	−	0.997886i	$-0.520704\pi$
$467$	−1311.88	−0.129992	−0.0649962	+	0.997886i	$0.520704\pi$
$468$	56.7596	0.00560622
$469$	−7168.49	−0.705779
$470$	5704.25	0.559824
$471$	−2272.95	−0.222361
$472$	5898.36	0.575200
$473$	0	0
$474$	7070.97	0.685191
$475$	9703.91	0.937360
$476$	−312.536	−0.0300947
$477$	−1277.02	−0.122580
$478$	17875.1	1.71043
$479$	−9416.47	−0.898224	−0.449112	−	0.893475i	$-0.648260\pi$
$479$	−9416.47	−0.898224	−0.449112	+	0.893475i	$0.648260\pi$
$480$	−8318.13	−0.790977
$481$	−4470.58	−0.423785
$482$	17680.9	1.67084
$483$	−1805.25	−0.170066
$484$	0	0
$485$	11794.4	1.10424
$486$	−2071.26	−0.193321
$487$	6507.42	0.605502	0.302751	−	0.953070i	$-0.402095\pi$
$487$	6507.42	0.605502	0.302751	+	0.953070i	$0.402095\pi$
$488$	−1339.40	−0.124245
$489$	−11970.6	−1.10701
$490$	−17716.2	−1.63333
$491$	−21515.6	−1.97757	−0.988784	−	0.149356i	$-0.952280\pi$
$491$	−21515.6	−1.97757	−0.988784	+	0.149356i	$0.952280\pi$
$492$	−3074.87	−0.281760
$493$	−2022.30	−0.184747
$494$	1362.50	0.124093
$495$	0	0
$496$	−5125.97	−0.464038
$497$	−3474.62	−0.313597
$498$	−11223.2	−1.00989
$499$	14766.7	1.32474	0.662372	−	0.749175i	$-0.269550\pi$
$499$	14766.7	1.32474	0.662372	+	0.749175i	$0.269550\pi$
$500$	−6248.59	−0.558891
$501$	−10294.7	−0.918027
$502$	13510.4	1.20119
$503$	−1432.44	−0.126977	−0.0634884	−	0.997983i	$-0.520223\pi$
$503$	−1432.44	−0.126977	−0.0634884	+	0.997983i	$0.520223\pi$
$504$	370.179	0.0327164
$505$	−4396.36	−0.387397
$506$	0	0
$507$	838.913	0.0734861
$508$	638.917	0.0558019
$509$	8760.75	0.762895	0.381447	−	0.924391i	$-0.375426\pi$
$509$	8760.75	0.762895	0.381447	+	0.924391i	$0.375426\pi$
$510$	6595.56	0.572660
$511$	−8887.45	−0.769388
$512$	5442.46	0.469776
$513$	−4866.59	−0.418841
$514$	3532.24	0.303114
$515$	27665.1	2.36713
$516$	850.787	0.0725849
$517$	0	0
$518$	8776.48	0.744433
$519$	−5965.45	−0.504536
$520$	5114.78	0.431342
$521$	13713.0	1.15312	0.576562	−	0.817053i	$-0.304394\pi$
$521$	13713.0	1.15312	0.576562	+	0.817053i	$0.304394\pi$
$522$	−721.012	−0.0604556
$523$	13938.3	1.16535	0.582675	−	0.812706i	$-0.302006\pi$
$523$	13938.3	1.16535	0.582675	+	0.812706i	$0.302006\pi$
$524$	−3082.68	−0.256999
$525$	−11729.6	−0.975088
$526$	4649.67	0.385428
$527$	1412.07	0.116719
$528$	0	0
$529$	−10166.7	−0.835597
$530$	34639.3	2.83894
$531$	−720.920	−0.0589176
$532$	−502.585	−0.0409583
$533$	4350.58	0.353555
$534$	22373.5	1.81310
$535$	31754.3	2.56609
$536$	17014.3	1.37109
$537$	5375.37	0.431963
$538$	−1709.80	−0.137016
$539$	0	0
$540$	5499.19	0.438236
$541$	−14671.6	−1.16595	−0.582976	−	0.812489i	$-0.698112\pi$
$541$	−14671.6	−1.16595	−0.582976	+	0.812489i	$0.698112\pi$
$542$	−26466.3	−2.09746
$543$	−317.417	−0.0250859
$544$	1706.89	0.134526
$545$	1778.17	0.139759
$546$	−1646.92	−0.129088
$547$	−18586.1	−1.45281	−0.726404	−	0.687268i	$-0.758810\pi$
$547$	−18586.1	−1.45281	−0.726404	+	0.687268i	$0.758810\pi$
$548$	5404.84	0.421320
$549$	163.706	0.0127264
$550$	0	0
$551$	−3252.04	−0.251436
$552$	4284.74	0.330381
$553$	3690.38	0.283781
$554$	−14183.4	−1.08772
$555$	−34800.6	−2.66163
$556$	−3223.88	−0.245905
$557$	−22681.2	−1.72538	−0.862688	−	0.505736i	$-0.831221\pi$
$557$	−22681.2	−1.72538	−0.862688	+	0.505736i	$0.831221\pi$
$558$	503.446	0.0381945
$559$	−1203.76	−0.0910800
$560$	−12495.8	−0.942932
$561$	0	0
$562$	4774.62	0.358372
$563$	−21431.5	−1.60432	−0.802158	−	0.597112i	$-0.796315\pi$
$563$	−21431.5	−1.60432	−0.802158	+	0.597112i	$0.796315\pi$
$564$	819.118	0.0611544
$565$	−24296.5	−1.80914
$566$	−22357.5	−1.66035
$567$	5364.61	0.397341
$568$	8246.95	0.609216
$569$	3490.95	0.257203	0.128601	−	0.991696i	$-0.458951\pi$
$569$	3490.95	0.257203	0.128601	+	0.991696i	$0.458951\pi$
$570$	10606.2	0.779379
$571$	−3814.58	−0.279571	−0.139786	−	0.990182i	$-0.544641\pi$
$571$	−3814.58	−0.279571	−0.139786	+	0.990182i	$0.544641\pi$
$572$	0	0
$573$	−21048.0	−1.53454
$574$	−8540.91	−0.621064
$575$	12996.8	0.942619
$576$	−813.962	−0.0588804
$577$	7703.54	0.555810	0.277905	−	0.960609i	$-0.410360\pi$
$577$	7703.54	0.555810	0.277905	+	0.960609i	$0.410360\pi$
$578$	14066.6	1.01227
$579$	−24722.8	−1.77451
$580$	3674.76	0.263080
$581$	−5857.46	−0.418259
$582$	9013.83	0.641985
$583$	0	0
$584$	21094.2	1.49467
$585$	−625.148	−0.0441824
$586$	21098.8	1.48734
$587$	27215.9	1.91366	0.956832	−	0.290641i	$-0.0938684\pi$
$587$	27215.9	1.91366	0.956832	+	0.290641i	$0.0938684\pi$
$588$	−2544.00	−0.178423
$589$	2270.73	0.158852
$590$	19555.1	1.36452
$591$	13794.2	0.960095
$592$	−25923.0	−1.79971
$593$	−6898.68	−0.477732	−0.238866	−	0.971053i	$-0.576776\pi$
$593$	−6898.68	−0.477732	−0.238866	+	0.971053i	$0.576776\pi$
$594$	0	0
$595$	3442.26	0.237175
$596$	3532.38	0.242772
$597$	23252.6	1.59408
$598$	1824.86	0.124789
$599$	−14777.5	−1.00800	−0.503999	−	0.863704i	$-0.668138\pi$
$599$	−14777.5	−1.00800	−0.503999	+	0.863704i	$0.668138\pi$
$600$	27840.0	1.89427
$601$	4980.78	0.338053	0.169027	−	0.985611i	$-0.445938\pi$
$601$	4980.78	0.338053	0.169027	+	0.985611i	$0.445938\pi$
$602$	2363.18	0.159994
$603$	−2079.55	−0.140441
$604$	−2668.97	−0.179800
$605$	0	0
$606$	−3359.90	−0.225226
$607$	22716.4	1.51899	0.759496	−	0.650512i	$-0.225446\pi$
$607$	22716.4	1.51899	0.759496	+	0.650512i	$0.225446\pi$
$608$	2744.82	0.183088
$609$	3930.90	0.261557
$610$	−4440.55	−0.294742
$611$	−1158.96	−0.0767370
$612$	−90.6655	−0.00598846
$613$	11773.3	0.775726	0.387863	−	0.921717i	$-0.373213\pi$
$613$	11773.3	0.775726	0.387863	+	0.921717i	$0.373213\pi$
$614$	−24277.5	−1.59570
$615$	33866.5	2.22054
$616$	0	0
$617$	6297.68	0.410916	0.205458	−	0.978666i	$-0.434132\pi$
$617$	6297.68	0.410916	0.205458	+	0.978666i	$0.434132\pi$
$618$	21142.9	1.37620
$619$	19127.8	1.24202	0.621012	−	0.783801i	$-0.286722\pi$
$619$	19127.8	1.24202	0.621012	+	0.783801i	$0.286722\pi$
$620$	−2565.90	−0.166208
$621$	−6518.02	−0.421190
$622$	3181.55	0.205094
$623$	11676.9	0.750920
$624$	4864.51	0.312077
$625$	32497.1	2.07982
$626$	−6911.08	−0.441249
$627$	0	0
$628$	−847.524	−0.0538533
$629$	7141.13	0.452679
$630$	1227.27	0.0776119
$631$	15626.8	0.985884	0.492942	−	0.870062i	$-0.335921\pi$
$631$	15626.8	0.985884	0.492942	+	0.870062i	$0.335921\pi$
$632$	−8759.06	−0.551292
$633$	−4459.23	−0.279998
$634$	20209.9	1.26599
$635$	−7037.01	−0.439772
$636$	4974.13	0.310121
$637$	3599.46	0.223887
$638$	0	0
$639$	−1007.97	−0.0624019
$640$	35484.4	2.19163
$641$	13942.8	0.859139	0.429570	−	0.903034i	$-0.358665\pi$
$641$	13942.8	0.859139	0.429570	+	0.903034i	$0.358665\pi$
$642$	24268.0	1.49187
$643$	4409.96	0.270469	0.135235	−	0.990814i	$-0.456821\pi$
$643$	4409.96	0.270469	0.135235	+	0.990814i	$0.456821\pi$
$644$	−673.132	−0.0411880
$645$	−9370.53	−0.572038
$646$	−2176.41	−0.132554
$647$	−7323.38	−0.444995	−0.222497	−	0.974933i	$-0.571421\pi$
$647$	−7323.38	−0.444995	−0.222497	+	0.974933i	$0.571421\pi$
$648$	−12732.8	−0.771902
$649$	0	0
$650$	11857.0	0.715490
$651$	−2744.75	−0.165246
$652$	−4463.51	−0.268105
$653$	−9502.50	−0.569466	−0.284733	−	0.958607i	$-0.591905\pi$
$653$	−9502.50	−0.569466	−0.284733	+	0.958607i	$0.591905\pi$
$654$	1358.96	0.0812531
$655$	33952.5	2.02540
$656$	25227.2	1.50146
$657$	−2578.21	−0.153099
$658$	2275.22	0.134798
$659$	13116.3	0.775327	0.387663	−	0.921801i	$-0.373282\pi$
$659$	13116.3	0.775327	0.387663	+	0.921801i	$0.373282\pi$
$660$	0	0
$661$	−2810.22	−0.165363	−0.0826813	−	0.996576i	$-0.526348\pi$
$661$	−2810.22	−0.165363	−0.0826813	+	0.996576i	$0.526348\pi$
$662$	34629.1	2.03308
$663$	−1340.05	−0.0784964
$664$	13902.6	0.812537
$665$	5535.45	0.322790
$666$	2546.02	0.148133
$667$	−4355.58	−0.252847
$668$	−3838.61	−0.222336
$669$	17250.8	0.996940
$670$	56408.2	3.25259
$671$	0	0
$672$	−3317.80	−0.190457
$673$	6579.13	0.376830	0.188415	−	0.982089i	$-0.439665\pi$
$673$	6579.13	0.376830	0.188415	+	0.982089i	$0.439665\pi$
$674$	32677.8	1.86751
$675$	−42350.8	−2.41494
$676$	312.809	0.0177975
$677$	11954.7	0.678667	0.339334	−	0.940666i	$-0.389798\pi$
$677$	11954.7	0.678667	0.339334	+	0.940666i	$0.389798\pi$
$678$	−18568.5	−1.05180
$679$	4704.37	0.265887
$680$	−8170.15	−0.460752
$681$	9966.19	0.560801
$682$	0	0
$683$	−10200.3	−0.571455	−0.285727	−	0.958311i	$-0.592235\pi$
$683$	−10200.3	−0.571455	−0.285727	+	0.958311i	$0.592235\pi$
$684$	−145.798	−0.00815018
$685$	−59528.7	−3.32040
$686$	−15820.1	−0.880486
$687$	16350.1	0.908000
$688$	−6980.11	−0.386794
$689$	−7037.81	−0.389143
$690$	14205.3	0.783751
$691$	913.344	0.0502825	0.0251413	−	0.999684i	$-0.491996\pi$
$691$	913.344	0.0502825	0.0251413	+	0.999684i	$0.491996\pi$
$692$	−2224.36	−0.122193
$693$	0	0
$694$	1293.54	0.0707523
$695$	35507.7	1.93796
$696$	−9329.92	−0.508118
$697$	−6949.45	−0.377660
$698$	−17171.0	−0.931136
$699$	−20419.2	−1.10490
$700$	−4373.66	−0.236156
$701$	−17623.2	−0.949530	−0.474765	−	0.880112i	$-0.657467\pi$
$701$	−17623.2	−0.949530	−0.474765	+	0.880112i	$0.657467\pi$
$702$	−5946.37	−0.319703
$703$	11483.5	0.616088
$704$	0	0
$705$	−9021.74	−0.481955
$706$	−2267.63	−0.120883
$707$	−1753.55	−0.0932802
$708$	2808.07	0.149059
$709$	5018.18	0.265813	0.132907	−	0.991129i	$-0.457569\pi$
$709$	5018.18	0.265813	0.132907	+	0.991129i	$0.457569\pi$
$710$	27341.4	1.44522
$711$	1070.56	0.0564688
$712$	−27714.8	−1.45879
$713$	3041.28	0.159743
$714$	2630.73	0.137889
$715$	0	0
$716$	2004.34	0.104617
$717$	−28270.9	−1.47252
$718$	29814.9	1.54969
$719$	8260.90	0.428483	0.214242	−	0.976781i	$-0.431272\pi$
$719$	8260.90	0.428483	0.214242	+	0.976781i	$0.431272\pi$
$720$	−3624.97	−0.187631
$721$	11034.6	0.569973
$722$	18027.9	0.929267
$723$	−27963.8	−1.43843
$724$	−118.357	−0.00607553
$725$	−28300.3	−1.44972
$726$	0	0
$727$	−294.181	−0.0150077	−0.00750384	−	0.999972i	$-0.502389\pi$
$727$	−294.181	−0.0150077	−0.00750384	+	0.999972i	$0.502389\pi$
$728$	2040.10	0.103862
$729$	21089.0	1.07143
$730$	69934.4	3.54574
$731$	1922.84	0.0972899
$732$	−637.654	−0.0321972
$733$	−32021.1	−1.61354	−0.806772	−	0.590863i	$-0.798788\pi$
$733$	−32021.1	−1.61354	−0.806772	+	0.590863i	$0.798788\pi$
$734$	−11539.3	−0.580275
$735$	28019.5	1.40614
$736$	3676.25	0.184115
$737$	0	0
$738$	−2477.69	−0.123584
$739$	9709.27	0.483303	0.241652	−	0.970363i	$-0.422311\pi$
$739$	9709.27	0.483303	0.241652	+	0.970363i	$0.422311\pi$
$740$	−12976.3	−0.644617
$741$	−2154.91	−0.106832
$742$	13816.4	0.683579
$743$	31181.4	1.53962	0.769808	−	0.638275i	$-0.220352\pi$
$743$	31181.4	1.53962	0.769808	+	0.638275i	$0.220352\pi$
$744$	6514.61	0.321018
$745$	−38905.5	−1.91327
$746$	−30335.7	−1.48883
$747$	−1699.23	−0.0832281
$748$	0	0
$749$	12665.6	0.617880
$750$	52596.7	2.56075
$751$	−30323.4	−1.47339	−0.736696	−	0.676225i	$-0.763615\pi$
$751$	−30323.4	−1.47339	−0.736696	+	0.676225i	$0.763615\pi$
$752$	−6720.30	−0.325883
$753$	−21367.8	−1.03411
$754$	−3973.58	−0.191922
$755$	29396.0	1.41699
$756$	2193.43	0.105521
$757$	30895.4	1.48337	0.741685	−	0.670749i	$-0.234027\pi$
$757$	30895.4	1.48337	0.741685	+	0.670749i	$0.234027\pi$
$758$	5725.26	0.274341
$759$	0	0
$760$	−13138.3	−0.627074
$761$	2946.49	0.140355	0.0701774	−	0.997535i	$-0.477643\pi$
$761$	2946.49	0.140355	0.0701774	+	0.997535i	$0.477643\pi$
$762$	−5378.01	−0.255675
$763$	709.248	0.0336521
$764$	−7848.25	−0.371649
$765$	998.587	0.0471947
$766$	4296.04	0.202640
$767$	−3973.08	−0.187040
$768$	13415.6	0.630332
$769$	17519.6	0.821550	0.410775	−	0.911737i	$-0.365258\pi$
$769$	17519.6	0.821550	0.410775	+	0.911737i	$0.365258\pi$
$770$	0	0
$771$	−5586.53	−0.260952
$772$	−9218.48	−0.429767
$773$	−1563.04	−0.0727279	−0.0363640	−	0.999339i	$-0.511578\pi$
$773$	−1563.04	−0.0727279	−0.0363640	+	0.999339i	$0.511578\pi$
$774$	685.551	0.0318367
$775$	19760.7	0.915903
$776$	−11165.7	−0.516529
$777$	−13880.7	−0.640885
$778$	18694.5	0.861477
$779$	−11175.3	−0.513989
$780$	2435.02	0.111779
$781$	0	0
$782$	−2914.95	−0.133297
$783$	14192.9	0.647780
$784$	20871.8	0.950791
$785$	9334.59	0.424415
$786$	25948.1	1.17753
$787$	−15895.8	−0.719979	−0.359989	−	0.932956i	$-0.617220\pi$
$787$	−15895.8	−0.719979	−0.359989	+	0.932956i	$0.617220\pi$
$788$	5143.49	0.232524
$789$	−7353.83	−0.331817
$790$	−29039.2	−1.30781
$791$	−9691.01	−0.435616
$792$	0	0
$793$	902.205	0.0404013
$794$	−32605.8	−1.45735
$795$	−54784.9	−2.44405
$796$	8670.29	0.386068
$797$	13724.8	0.609985	0.304992	−	0.952355i	$-0.401346\pi$
$797$	13724.8	0.609985	0.304992	+	0.952355i	$0.401346\pi$
$798$	4230.44	0.187664
$799$	1851.27	0.0819690
$800$	23886.4	1.05564
$801$	3387.41	0.149424
$802$	−9215.15	−0.405734
$803$	0	0
$804$	8100.09	0.355309
$805$	7413.85	0.324601
$806$	2774.55	0.121252
$807$	2704.18	0.117958
$808$	4162.03	0.181212
$809$	−25269.3	−1.09817	−0.549087	−	0.835765i	$-0.685024\pi$
$809$	−25269.3	−1.09817	−0.549087	+	0.835765i	$0.685024\pi$
$810$	−42213.6	−1.83115
$811$	−7632.86	−0.330488	−0.165244	−	0.986253i	$-0.552841\pi$
$811$	−7632.86	−0.330488	−0.165244	+	0.986253i	$0.552841\pi$
$812$	1465.73	0.0633461
$813$	41858.6	1.80571
$814$	0	0
$815$	49161.0	2.11292
$816$	−7770.37	−0.333355
$817$	3092.10	0.132410
$818$	2353.25	0.100586
$819$	−249.349	−0.0106385
$820$	12628.0	0.537790
$821$	−10912.9	−0.463900	−0.231950	−	0.972728i	$-0.574511\pi$
$821$	−10912.9	−0.463900	−0.231950	+	0.972728i	$0.574511\pi$
$822$	−45494.5	−1.93042
$823$	−31419.2	−1.33075	−0.665374	−	0.746510i	$-0.731728\pi$
$823$	−31419.2	−1.33075	−0.665374	+	0.746510i	$0.731728\pi$
$824$	−26190.5	−1.10727
$825$	0	0
$826$	7799.81	0.328559
$827$	34824.5	1.46429	0.732144	−	0.681150i	$-0.238520\pi$
$827$	34824.5	1.46429	0.732144	+	0.681150i	$0.238520\pi$
$828$	−195.273	−0.00819590
$829$	−32263.1	−1.35168	−0.675841	−	0.737047i	$-0.736220\pi$
$829$	−32263.1	−1.35168	−0.675841	+	0.737047i	$0.736220\pi$
$830$	46091.8	1.92755
$831$	22432.2	0.936420
$832$	−4485.85	−0.186922
$833$	−5749.64	−0.239151
$834$	27136.6	1.12670
$835$	42278.4	1.75222
$836$	0	0
$837$	−9910.15	−0.409253
$838$	−6046.99	−0.249272
$839$	−6547.32	−0.269414	−0.134707	−	0.990885i	$-0.543009\pi$
$839$	−6547.32	−0.269414	−0.134707	+	0.990885i	$0.543009\pi$
$840$	15880.9	0.652313
$841$	−14904.8	−0.611128
$842$	38025.4	1.55634
$843$	−7551.45	−0.308524
$844$	−1662.73	−0.0678123
$845$	−3445.27	−0.140261
$846$	660.033	0.0268232
$847$	0	0
$848$	−40809.3	−1.65259
$849$	35360.2	1.42940
$850$	−18939.9	−0.764273
$851$	15380.4	0.619544
$852$	3926.17	0.157874
$853$	−28258.5	−1.13429	−0.567147	−	0.823616i	$-0.691953\pi$
$853$	−28258.5	−1.13429	−0.567147	+	0.823616i	$0.691953\pi$
$854$	−1771.18	−0.0709700
$855$	1605.81	0.0642311
$856$	−30061.7	−1.20033
$857$	6893.03	0.274751	0.137375	−	0.990519i	$-0.456133\pi$
$857$	6893.03	0.274751	0.137375	+	0.990519i	$0.456133\pi$
$858$	0	0
$859$	−31941.4	−1.26871	−0.634357	−	0.773040i	$-0.718735\pi$
$859$	−31941.4	−1.26871	−0.634357	+	0.773040i	$0.718735\pi$
$860$	−3494.03	−0.138541
$861$	13508.1	0.534676
$862$	40603.0	1.60434
$863$	5366.78	0.211689	0.105844	−	0.994383i	$-0.466245\pi$
$863$	5366.78	0.211689	0.105844	+	0.994383i	$0.466245\pi$
$864$	−11979.2	−0.471692
$865$	24499.1	0.962998
$866$	22686.0	0.890186
$867$	−22247.5	−0.871471
$868$	−1023.44	−0.0400207
$869$	0	0
$870$	−30931.8	−1.20539
$871$	−11460.7	−0.445844
$872$	−1683.39	−0.0653748
$873$	1364.72	0.0529080
$874$	−4687.49	−0.181415
$875$	27450.5	1.06057
$876$	10042.4	0.387332
$877$	−11774.6	−0.453365	−0.226683	−	0.973969i	$-0.572788\pi$
$877$	−11774.6	−0.453365	−0.226683	+	0.973969i	$0.572788\pi$
$878$	−28324.9	−1.08875
$879$	−33369.4	−1.28046
$880$	0	0
$881$	30439.0	1.16404	0.582018	−	0.813176i	$-0.302263\pi$
$881$	30439.0	1.16404	0.582018	+	0.813176i	$0.302263\pi$
$882$	−2049.92	−0.0782588
$883$	13638.5	0.519786	0.259893	−	0.965637i	$-0.416313\pi$
$883$	13638.5	0.519786	0.259893	+	0.965637i	$0.416313\pi$
$884$	−499.669	−0.0190110
$885$	−30927.9	−1.17472
$886$	26559.1	1.00708
$887$	2685.50	0.101657	0.0508287	−	0.998707i	$-0.483814\pi$
$887$	2685.50	0.101657	0.0508287	+	0.998707i	$0.483814\pi$
$888$	32945.7	1.24503
$889$	−2806.81	−0.105891
$890$	−91884.0	−3.46063
$891$	0	0
$892$	6432.36	0.241448
$893$	2977.00	0.111558
$894$	−29733.4	−1.11234
$895$	−22075.7	−0.824480
$896$	14153.5	0.527716
$897$	−2886.16	−0.107431
$898$	33063.0	1.22865
$899$	−6622.33	−0.245681
$900$	−1268.78	−0.0469920
$901$	11241.9	0.415675
$902$	0	0
$903$	−3737.57	−0.137739
$904$	23001.5	0.846258
$905$	1303.57	0.0478810
$906$	22465.7	0.823813
$907$	244.207	0.00894021	0.00447011	−	0.999990i	$-0.498577\pi$
$907$	244.207	0.00894021	0.00447011	+	0.999990i	$0.498577\pi$
$908$	3716.14	0.135820
$909$	−508.698	−0.0185616
$910$	6763.63	0.246387
$911$	4588.20	0.166865	0.0834325	−	0.996513i	$-0.473412\pi$
$911$	4588.20	0.166865	0.0834325	+	0.996513i	$0.473412\pi$
$912$	−12495.4	−0.453689
$913$	0	0
$914$	−26639.1	−0.964053
$915$	7023.09	0.253745
$916$	6096.54	0.219908
$917$	13542.4	0.487689
$918$	9498.50	0.341500
$919$	36500.5	1.31016	0.655082	−	0.755557i	$-0.272634\pi$
$919$	36500.5	1.31016	0.655082	+	0.755557i	$0.272634\pi$
$920$	−17596.7	−0.630592
$921$	38396.9	1.37375
$922$	48033.0	1.71571
$923$	−5555.07	−0.198101
$924$	0	0
$925$	99933.7	3.55222
$926$	−59605.0	−2.11527
$927$	3201.10	0.113417
$928$	−8004.96	−0.283164
$929$	−15075.2	−0.532403	−0.266201	−	0.963917i	$-0.585769\pi$
$929$	−15075.2	−0.532403	−0.266201	+	0.963917i	$0.585769\pi$
$930$	21598.1	0.761538
$931$	−9245.91	−0.325481
$932$	−7613.80	−0.267595
$933$	−5031.88	−0.176566
$934$	4117.49	0.144249
$935$	0	0
$936$	591.826	0.0206671
$937$	−49203.8	−1.71550	−0.857748	−	0.514071i	$-0.828137\pi$
$937$	−49203.8	−1.71550	−0.857748	+	0.514071i	$0.828137\pi$
$938$	22499.2	0.783182
$939$	10930.4	0.379873
$940$	−3363.97	−0.116724
$941$	33599.2	1.16398	0.581988	−	0.813197i	$-0.302275\pi$
$941$	33599.2	1.16398	0.581988	+	0.813197i	$0.302275\pi$
$942$	7133.92	0.246747
$943$	−14967.5	−0.516872
$944$	−23038.2	−0.794312
$945$	−24158.3	−0.831609
$946$	0	0
$947$	49814.0	1.70933	0.854666	−	0.519178i	$-0.173762\pi$
$947$	49814.0	1.70933	0.854666	+	0.519178i	$0.173762\pi$
$948$	−4169.97	−0.142863
$949$	−14208.9	−0.486027
$950$	−30456.9	−1.04016
$951$	−31963.6	−1.08990
$952$	−3258.78	−0.110943
$953$	1334.93	0.0453752	0.0226876	−	0.999743i	$-0.492778\pi$
$953$	1334.93	0.0453752	0.0226876	+	0.999743i	$0.492778\pi$
$954$	4008.08	0.136023
$955$	86440.3	2.92895
$956$	−10541.5	−0.356627
$957$	0	0
$958$	29554.7	0.996733
$959$	−23743.8	−0.799508
$960$	−34919.5	−1.17398
$961$	−25167.0	−0.844784
$962$	14031.5	0.470262
$963$	3674.25	0.122950
$964$	−10427.0	−0.348372
$965$	101532.	3.38697
$966$	5666.00	0.188717
$967$	6948.63	0.231079	0.115539	−	0.993303i	$-0.463140\pi$
$967$	6948.63	0.231079	0.115539	+	0.993303i	$0.463140\pi$
$968$	0	0
$969$	3442.17	0.114116
$970$	−37018.2	−1.22534
$971$	−29864.0	−0.987005	−0.493503	−	0.869744i	$-0.664284\pi$
$971$	−29864.0	−0.987005	−0.493503	+	0.869744i	$0.664284\pi$
$972$	1221.49	0.0403078
$973$	14162.8	0.466636
$974$	−20424.3	−0.671907
$975$	−18752.8	−0.615968
$976$	5231.51	0.171574
$977$	−39658.8	−1.29867	−0.649333	−	0.760504i	$-0.724952\pi$
$977$	−39658.8	−1.29867	−0.649333	+	0.760504i	$0.724952\pi$
$978$	37571.0	1.22841
$979$	0	0
$980$	10447.8	0.340553
$981$	205.750	0.00669633
$982$	67529.3	2.19445
$983$	38885.2	1.26169	0.630846	−	0.775908i	$-0.282708\pi$
$983$	38885.2	1.26169	0.630846	+	0.775908i	$0.282708\pi$
$984$	−32061.4	−1.03870
$985$	−56650.2	−1.83251
$986$	6347.25	0.205008
$987$	−3598.44	−0.116048
$988$	−803.510	−0.0258736
$989$	4141.37	0.133152
$990$	0	0
$991$	−10413.2	−0.333790	−0.166895	−	0.985975i	$-0.553374\pi$
$991$	−10413.2	−0.333790	−0.166895	+	0.985975i	$0.553374\pi$
$992$	5589.46	0.178897
$993$	−54768.7	−1.75028
$994$	10905.5	0.347990
$995$	−95494.3	−3.04259
$996$	6618.68	0.210563
$997$	28072.1	0.891726	0.445863	−	0.895101i	$-0.352897\pi$
$997$	28072.1	0.891726	0.445863	+	0.895101i	$0.352897\pi$
$998$	−46347.0	−1.47003
$999$	−50117.6	−1.58724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.h.1.5	✓	15
11.10	odd	2		1573.4.a.k.1.11	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1573.4.a.h.1.5	✓	15	1.1	even	1	trivial
1573.4.a.k.1.11	yes	15	11.10	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-3.13862 q^{2} +4.96398 q^{3} +1.85094 q^{4} -20.3862 q^{5} -15.5801 q^{6} -8.13132 q^{7} +19.2996 q^{8} -2.35886 q^{9} +O(q^{10})\)	\(q-3.13862 q^{2} +4.96398 q^{3} +1.85094 q^{4} -20.3862 q^{5} -15.5801 q^{6} -8.13132 q^{7} +19.2996 q^{8} -2.35886 q^{9} +63.9846 q^{10} +9.18804 q^{12} -13.0000 q^{13} +25.5211 q^{14} -101.197 q^{15} -75.3815 q^{16} +20.7657 q^{17} +7.40358 q^{18} +33.3930 q^{19} -37.7337 q^{20} -40.3637 q^{21} +44.7246 q^{23} +95.8027 q^{24} +290.597 q^{25} +40.8021 q^{26} -145.737 q^{27} -15.0506 q^{28} -97.3868 q^{29} +317.618 q^{30} +68.0003 q^{31} +82.1976 q^{32} -65.1756 q^{34} +165.767 q^{35} -4.36612 q^{36} +343.891 q^{37} -104.808 q^{38} -64.5318 q^{39} -393.445 q^{40} -334.660 q^{41} +126.686 q^{42} +92.5971 q^{43} +48.0883 q^{45} -140.373 q^{46} +89.1504 q^{47} -374.193 q^{48} -276.882 q^{49} -912.075 q^{50} +103.081 q^{51} -24.0622 q^{52} +541.370 q^{53} +457.413 q^{54} -156.931 q^{56} +165.762 q^{57} +305.660 q^{58} +305.622 q^{59} -187.309 q^{60} -69.4004 q^{61} -213.427 q^{62} +19.1807 q^{63} +345.065 q^{64} +265.021 q^{65} +881.590 q^{67} +38.4361 q^{68} +222.012 q^{69} -520.279 q^{70} +427.313 q^{71} -45.5251 q^{72} +1092.99 q^{73} -1079.34 q^{74} +1442.52 q^{75} +61.8085 q^{76} +202.541 q^{78} -453.847 q^{79} +1536.74 q^{80} -659.746 q^{81} +1050.37 q^{82} +720.357 q^{83} -74.7109 q^{84} -423.334 q^{85} -290.627 q^{86} -483.427 q^{87} -1436.03 q^{89} -150.931 q^{90} +105.707 q^{91} +82.7826 q^{92} +337.552 q^{93} -279.809 q^{94} -680.756 q^{95} +408.028 q^{96} -578.549 q^{97} +869.027 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9} + 16 q^{10} - 3 q^{12} - 195 q^{13} + 60 q^{14} + 202 q^{15} + 282 q^{16} - 136 q^{17} - 351 q^{18} - 136 q^{19} - 62 q^{20} - 625 q^{21} - 176 q^{23} + 227 q^{24} + 479 q^{25} + 78 q^{26} - 13 q^{27} + 86 q^{28} - 344 q^{29} - 542 q^{30} + 275 q^{31} + 170 q^{32} - 1505 q^{34} - 655 q^{35} + 623 q^{36} + 346 q^{37} - 848 q^{38} - 26 q^{39} - 256 q^{40} - 38 q^{41} + 575 q^{42} - 534 q^{43} - 633 q^{45} + 375 q^{46} + 276 q^{47} - 723 q^{48} + 773 q^{49} - 1684 q^{50} - 1111 q^{51} - 702 q^{52} + 706 q^{53} + 178 q^{54} - 2056 q^{56} - 1320 q^{57} - 983 q^{58} - 174 q^{59} + 2004 q^{60} - 1078 q^{61} - 1365 q^{62} + 2055 q^{63} + 1338 q^{64} + 26 q^{65} - 260 q^{67} - 559 q^{68} + 154 q^{69} - 1161 q^{70} + 2910 q^{71} - 6171 q^{72} - 1000 q^{73} - 688 q^{74} - 553 q^{75} - 178 q^{76} - 325 q^{78} + 386 q^{79} + 1702 q^{80} - 2805 q^{81} + 3380 q^{82} - 4318 q^{83} - 6681 q^{84} + 1391 q^{85} + 4139 q^{86} - 3144 q^{87} - 810 q^{89} + 3789 q^{90} + 364 q^{91} - 4857 q^{92} + 394 q^{93} + 116 q^{94} - 5204 q^{95} + 893 q^{96} - 1860 q^{97} - 8 q^{98}+O(q^{100}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9 + 16 * q^10 - 3 * q^12 - 195 * q^13 + 60 * q^14 + 202 * q^15 + 282 * q^16 - 136 * q^17 - 351 * q^18 - 136 * q^19 - 62 * q^20 - 625 * q^21 - 176 * q^23 + 227 * q^24 + 479 * q^25 + 78 * q^26 - 13 * q^27 + 86 * q^28 - 344 * q^29 - 542 * q^30 + 275 * q^31 + 170 * q^32 - 1505 * q^34 - 655 * q^35 + 623 * q^36 + 346 * q^37 - 848 * q^38 - 26 * q^39 - 256 * q^40 - 38 * q^41 + 575 * q^42 - 534 * q^43 - 633 * q^45 + 375 * q^46 + 276 * q^47 - 723 * q^48 + 773 * q^49 - 1684 * q^50 - 1111 * q^51 - 702 * q^52 + 706 * q^53 + 178 * q^54 - 2056 * q^56 - 1320 * q^57 - 983 * q^58 - 174 * q^59 + 2004 * q^60 - 1078 * q^61 - 1365 * q^62 + 2055 * q^63 + 1338 * q^64 + 26 * q^65 - 260 * q^67 - 559 * q^68 + 154 * q^69 - 1161 * q^70 + 2910 * q^71 - 6171 * q^72 - 1000 * q^73 - 688 * q^74 - 553 * q^75 - 178 * q^76 - 325 * q^78 + 386 * q^79 + 1702 * q^80 - 2805 * q^81 + 3380 * q^82 - 4318 * q^83 - 6681 * q^84 + 1391 * q^85 + 4139 * q^86 - 3144 * q^87 - 810 * q^89 + 3789 * q^90 + 364 * q^91 - 4857 * q^92 + 394 * q^93 + 116 * q^94 - 5204 * q^95 + 893 * q^96 - 1860 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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