LMFDB - Embedded newform 1617.4.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 28x^{3} - 11x^{2} + 108x - 64 $ x^5 - 28x^3 - 11x^2 + 108*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.30014$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.300143 q^{2} -3.00000 q^{3} -7.90991 q^{4} +20.3930 q^{5} +0.900430 q^{6} +4.77526 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.300143 q^{2} -3.00000 q^{3} -7.90991 q^{4} +20.3930 q^{5} +0.900430 q^{6} +4.77526 q^{8} +9.00000 q^{9} -6.12084 q^{10} +11.0000 q^{11} +23.7297 q^{12} -14.2196 q^{13} -61.1791 q^{15} +61.8460 q^{16} -137.618 q^{17} -2.70129 q^{18} +44.1690 q^{19} -161.307 q^{20} -3.30158 q^{22} +71.7916 q^{23} -14.3258 q^{24} +290.876 q^{25} +4.26793 q^{26} -27.0000 q^{27} -59.5108 q^{29} +18.3625 q^{30} +207.490 q^{31} -56.7647 q^{32} -33.0000 q^{33} +41.3053 q^{34} -71.1892 q^{36} +126.287 q^{37} -13.2570 q^{38} +42.6589 q^{39} +97.3821 q^{40} +283.938 q^{41} -179.170 q^{43} -87.0091 q^{44} +183.537 q^{45} -21.5478 q^{46} -94.8748 q^{47} -185.538 q^{48} -87.3047 q^{50} +412.855 q^{51} +112.476 q^{52} +727.121 q^{53} +8.10387 q^{54} +224.324 q^{55} -132.507 q^{57} +17.8618 q^{58} -677.153 q^{59} +483.922 q^{60} -210.226 q^{61} -62.2767 q^{62} -477.731 q^{64} -289.981 q^{65} +9.90474 q^{66} -428.085 q^{67} +1088.55 q^{68} -215.375 q^{69} +419.232 q^{71} +42.9773 q^{72} -921.181 q^{73} -37.9042 q^{74} -872.629 q^{75} -349.373 q^{76} -12.8038 q^{78} +895.977 q^{79} +1261.23 q^{80} +81.0000 q^{81} -85.2222 q^{82} -1180.59 q^{83} -2806.46 q^{85} +53.7767 q^{86} +178.532 q^{87} +52.5278 q^{88} -8.28883 q^{89} -55.0876 q^{90} -567.866 q^{92} -622.469 q^{93} +28.4760 q^{94} +900.740 q^{95} +170.294 q^{96} +828.982 q^{97} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9	\( 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9} - 55 q^{10} + 55 q^{11} - 63 q^{12} - 111 q^{13} + 21 q^{15} + 201 q^{16} - 136 q^{17} + 45 q^{18} - 111 q^{19} - 219 q^{20} + 55 q^{22} - 28 q^{23} - 180 q^{24} + 190 q^{25} + q^{26} - 135 q^{27} + 61 q^{29} + 165 q^{30} + 280 q^{31} + 535 q^{32} - 165 q^{33} + 572 q^{34} + 189 q^{36} - 41 q^{37} - 267 q^{38} + 333 q^{39} + 336 q^{40} - 426 q^{41} + 424 q^{43} + 231 q^{44} - 63 q^{45} + 140 q^{46} - 75 q^{47} - 603 q^{48} + 490 q^{50} + 408 q^{51} + 269 q^{52} + 1500 q^{53} - 135 q^{54} - 77 q^{55} + 333 q^{57} - 1767 q^{58} - 757 q^{59} + 657 q^{60} - 658 q^{61} + 568 q^{62} - 748 q^{64} + 537 q^{65} - 165 q^{66} - 583 q^{67} + 1650 q^{68} + 84 q^{69} - 764 q^{71} + 540 q^{72} - 875 q^{73} - 825 q^{74} - 570 q^{75} - 213 q^{76} - 3 q^{78} - 244 q^{79} + 2577 q^{80} + 405 q^{81} + 2006 q^{82} - 924 q^{83} - 1402 q^{85} + 1272 q^{86} - 183 q^{87} + 660 q^{88} + 1110 q^{89} - 495 q^{90} - 2046 q^{92} - 840 q^{93} + 3349 q^{94} + 1923 q^{95} - 1605 q^{96} + 852 q^{97} + 495 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9 - 55 * q^10 + 55 * q^11 - 63 * q^12 - 111 * q^13 + 21 * q^15 + 201 * q^16 - 136 * q^17 + 45 * q^18 - 111 * q^19 - 219 * q^20 + 55 * q^22 - 28 * q^23 - 180 * q^24 + 190 * q^25 + q^26 - 135 * q^27 + 61 * q^29 + 165 * q^30 + 280 * q^31 + 535 * q^32 - 165 * q^33 + 572 * q^34 + 189 * q^36 - 41 * q^37 - 267 * q^38 + 333 * q^39 + 336 * q^40 - 426 * q^41 + 424 * q^43 + 231 * q^44 - 63 * q^45 + 140 * q^46 - 75 * q^47 - 603 * q^48 + 490 * q^50 + 408 * q^51 + 269 * q^52 + 1500 * q^53 - 135 * q^54 - 77 * q^55 + 333 * q^57 - 1767 * q^58 - 757 * q^59 + 657 * q^60 - 658 * q^61 + 568 * q^62 - 748 * q^64 + 537 * q^65 - 165 * q^66 - 583 * q^67 + 1650 * q^68 + 84 * q^69 - 764 * q^71 + 540 * q^72 - 875 * q^73 - 825 * q^74 - 570 * q^75 - 213 * q^76 - 3 * q^78 - 244 * q^79 + 2577 * q^80 + 405 * q^81 + 2006 * q^82 - 924 * q^83 - 1402 * q^85 + 1272 * q^86 - 183 * q^87 + 660 * q^88 + 1110 * q^89 - 495 * q^90 - 2046 * q^92 - 840 * q^93 + 3349 * q^94 + 1923 * q^95 - 1605 * q^96 + 852 * q^97 + 495 * 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 $

$2$	−0.300143	−0.106117	−0.0530584	−	0.998591i	$-0.516897\pi$
$2$	−0.300143	−0.106117	−0.0530584	+	0.998591i	$0.516897\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.90991	−0.988739
$5$	20.3930	1.82401	0.912005	−	0.410179i	$-0.134534\pi$
$5$	20.3930	1.82401	0.912005	+	0.410179i	$0.134534\pi$
$6$	0.900430	0.0612665
$7$	0	0
$7$	0	0
$8$	4.77526	0.211039
$9$	9.00000	0.333333
$10$	−6.12084	−0.193558
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	23.7297	0.570849
$13$	−14.2196	−0.303370	−0.151685	−	0.988429i	$-0.548470\pi$
$13$	−14.2196	−0.303370	−0.151685	+	0.988429i	$0.548470\pi$
$14$	0	0
$15$	−61.1791	−1.05309
$16$	61.8460	0.966345
$17$	−137.618	−1.96337	−0.981687	−	0.190500i	$-0.938989\pi$
$17$	−137.618	−1.96337	−0.981687	+	0.190500i	$0.938989\pi$
$18$	−2.70129	−0.0353723
$19$	44.1690	0.533319	0.266660	−	0.963791i	$-0.414080\pi$
$19$	44.1690	0.533319	0.266660	+	0.963791i	$0.414080\pi$
$20$	−161.307	−1.80347
$21$	0	0
$22$	−3.30158	−0.0319954
$23$	71.7916	0.650852	0.325426	−	0.945568i	$-0.394492\pi$
$23$	71.7916	0.650852	0.325426	+	0.945568i	$0.394492\pi$
$24$	−14.3258	−0.121843
$25$	290.876	2.32701
$26$	4.26793	0.0321927
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−59.5108	−0.381065	−0.190532	−	0.981681i	$-0.561021\pi$
$29$	−59.5108	−0.381065	−0.190532	+	0.981681i	$0.561021\pi$
$30$	18.3625	0.111751
$31$	207.490	1.20214	0.601068	−	0.799198i	$-0.294742\pi$
$31$	207.490	1.20214	0.601068	+	0.799198i	$0.294742\pi$
$32$	−56.7647	−0.313584
$33$	−33.0000	−0.174078
$34$	41.3053	0.208347
$35$	0	0
$36$	−71.1892	−0.329580
$37$	126.287	0.561120	0.280560	−	0.959836i	$-0.409480\pi$
$37$	126.287	0.561120	0.280560	+	0.959836i	$0.409480\pi$
$38$	−13.2570	−0.0565941
$39$	42.6589	0.175151
$40$	97.3821	0.384936
$41$	283.938	1.08155	0.540777	−	0.841166i	$-0.318130\pi$
$41$	283.938	1.08155	0.540777	+	0.841166i	$0.318130\pi$
$42$	0	0
$43$	−179.170	−0.635423	−0.317711	−	0.948188i	$-0.602914\pi$
$43$	−179.170	−0.635423	−0.317711	+	0.948188i	$0.602914\pi$
$44$	−87.0091	−0.298116
$45$	183.537	0.608003
$46$	−21.5478	−0.0690663
$47$	−94.8748	−0.294445	−0.147222	−	0.989103i	$-0.547033\pi$
$47$	−94.8748	−0.294445	−0.147222	+	0.989103i	$0.547033\pi$
$48$	−185.538	−0.557919
$49$	0	0
$50$	−87.3047	−0.246935
$51$	412.855	1.13355
$52$	112.476	0.299954
$53$	727.121	1.88449	0.942244	−	0.334929i	$-0.108712\pi$
$53$	727.121	1.88449	0.942244	+	0.334929i	$0.108712\pi$
$54$	8.10387	0.0204222
$55$	224.324	0.549960
$56$	0	0
$57$	−132.507	−0.307912
$58$	17.8618	0.0404374
$59$	−677.153	−1.49420	−0.747100	−	0.664712i	$-0.768554\pi$
$59$	−677.153	−1.49420	−0.747100	+	0.664712i	$0.768554\pi$
$60$	483.922	1.04123
$61$	−210.226	−0.441257	−0.220628	−	0.975358i	$-0.570811\pi$
$61$	−210.226	−0.441257	−0.220628	+	0.975358i	$0.570811\pi$
$62$	−62.2767	−0.127567
$63$	0	0
$64$	−477.731	−0.933068
$65$	−289.981	−0.553350
$66$	9.90474	0.0184726
$67$	−428.085	−0.780581	−0.390290	−	0.920692i	$-0.627625\pi$
$67$	−428.085	−0.780581	−0.390290	+	0.920692i	$0.627625\pi$
$68$	1088.55	1.94127
$69$	−215.375	−0.375769
$70$	0	0
$71$	419.232	0.700756	0.350378	−	0.936608i	$-0.386053\pi$
$71$	419.232	0.700756	0.350378	+	0.936608i	$0.386053\pi$
$72$	42.9773	0.0703462
$73$	−921.181	−1.47693	−0.738466	−	0.674291i	$-0.764449\pi$
$73$	−921.181	−1.47693	−0.738466	+	0.674291i	$0.764449\pi$
$74$	−37.9042	−0.0595443
$75$	−872.629	−1.34350
$76$	−349.373	−0.527313
$77$	0	0
$78$	−12.8038	−0.0185864
$79$	895.977	1.27602	0.638008	−	0.770030i	$-0.279759\pi$
$79$	895.977	1.27602	0.638008	+	0.770030i	$0.279759\pi$
$80$	1261.23	1.76262
$81$	81.0000	0.111111
$82$	−85.2222	−0.114771
$83$	−1180.59	−1.56128	−0.780639	−	0.624982i	$-0.785106\pi$
$83$	−1180.59	−1.56128	−0.780639	+	0.624982i	$0.785106\pi$
$84$	0	0
$85$	−2806.46	−3.58121
$86$	53.7767	0.0674290
$87$	178.532	0.220008
$88$	52.5278	0.0636305
$89$	−8.28883	−0.00987207	−0.00493603	−	0.999988i	$-0.501571\pi$
$89$	−8.28883	−0.00987207	−0.00493603	+	0.999988i	$0.501571\pi$
$90$	−55.0876	−0.0645193
$91$	0	0
$92$	−567.866	−0.643523
$93$	−622.469	−0.694054
$94$	28.4760	0.0312455
$95$	900.740	0.972779
$96$	170.294	0.181048
$97$	828.982	0.867735	0.433868	−	0.900977i	$-0.357149\pi$
$97$	828.982	0.867735	0.433868	+	0.900977i	$0.357149\pi$
$98$	0	0
$99$	99.0000	0.100504
$100$	−2300.81	−2.30081
$101$	483.553	0.476389	0.238194	−	0.971217i	$-0.423444\pi$
$101$	483.553	0.476389	0.238194	+	0.971217i	$0.423444\pi$
$102$	−123.916	−0.120289
$103$	775.895	0.742245	0.371122	−	0.928584i	$-0.378973\pi$
$103$	775.895	0.742245	0.371122	+	0.928584i	$0.378973\pi$
$104$	−67.9023	−0.0640228
$105$	0	0
$106$	−218.241	−0.199976
$107$	26.1791	0.0236526	0.0118263	−	0.999930i	$-0.496235\pi$
$107$	26.1791	0.0236526	0.0118263	+	0.999930i	$0.496235\pi$
$108$	213.568	0.190283
$109$	−2101.76	−1.84690	−0.923451	−	0.383716i	$-0.874644\pi$
$109$	−2101.76	−1.84690	−0.923451	+	0.383716i	$0.874644\pi$
$110$	−67.3292	−0.0583599
$111$	−378.861	−0.323963
$112$	0	0
$113$	2386.80	1.98700	0.993500	−	0.113831i	$-0.0363122\pi$
$113$	2386.80	1.98700	0.993500	+	0.113831i	$0.0363122\pi$
$114$	39.7711	0.0326746
$115$	1464.05	1.18716
$116$	470.725	0.376774
$117$	−127.977	−0.101123
$118$	203.243	0.158560
$119$	0	0
$120$	−292.146	−0.222243
$121$	121.000	0.0909091
$122$	63.0979	0.0468247
$123$	−851.815	−0.624435
$124$	−1641.23	−1.18860
$125$	3382.73	2.42048
$126$	0	0
$127$	764.562	0.534204	0.267102	−	0.963668i	$-0.413934\pi$
$127$	764.562	0.534204	0.267102	+	0.963668i	$0.413934\pi$
$128$	597.506	0.412598
$129$	537.510	0.366861
$130$	87.0360	0.0587197
$131$	−1101.78	−0.734829	−0.367414	−	0.930057i	$-0.619757\pi$
$131$	−1101.78	−0.734829	−0.367414	+	0.930057i	$0.619757\pi$
$132$	261.027	0.172117
$133$	0	0
$134$	128.487	0.0828327
$135$	−550.612	−0.351031
$136$	−657.163	−0.414348
$137$	3014.79	1.88008	0.940038	−	0.341069i	$-0.110789\pi$
$137$	3014.79	1.88008	0.940038	+	0.341069i	$0.110789\pi$
$138$	64.6434	0.0398754
$139$	1200.40	0.732496	0.366248	−	0.930517i	$-0.380642\pi$
$139$	1200.40	0.732496	0.366248	+	0.930517i	$0.380642\pi$
$140$	0	0
$141$	284.624	0.169998
$142$	−125.830	−0.0743620
$143$	−156.416	−0.0914696
$144$	556.614	0.322115
$145$	−1213.61	−0.695066
$146$	276.486	0.156727
$147$	0	0
$148$	−998.919	−0.554802
$149$	−2105.74	−1.15778	−0.578888	−	0.815407i	$-0.696513\pi$
$149$	−2105.74	−1.15778	−0.578888	+	0.815407i	$0.696513\pi$
$150$	261.914	0.142568
$151$	2283.81	1.23082	0.615410	−	0.788207i	$-0.288991\pi$
$151$	2283.81	1.23082	0.615410	+	0.788207i	$0.288991\pi$
$152$	210.918	0.112551
$153$	−1238.57	−0.654458
$154$	0	0
$155$	4231.35	2.19271
$156$	−337.428	−0.173179
$157$	1053.76	0.535663	0.267832	−	0.963466i	$-0.413693\pi$
$157$	1053.76	0.535663	0.267832	+	0.963466i	$0.413693\pi$
$158$	−268.922	−0.135407
$159$	−2181.36	−1.08801
$160$	−1157.61	−0.571980
$161$	0	0
$162$	−24.3116	−0.0117908
$163$	1613.39	0.775281	0.387640	−	0.921811i	$-0.373290\pi$
$163$	1613.39	0.775281	0.387640	+	0.921811i	$0.373290\pi$
$164$	−2245.93	−1.06937
$165$	−672.971	−0.317519
$166$	354.345	0.165678
$167$	2561.31	1.18683	0.593413	−	0.804898i	$-0.297780\pi$
$167$	2561.31	1.18683	0.593413	+	0.804898i	$0.297780\pi$
$168$	0	0
$169$	−1994.80	−0.907967
$170$	842.340	0.380027
$171$	397.521	0.177773
$172$	1417.22	0.628267
$173$	−1674.42	−0.735862	−0.367931	−	0.929853i	$-0.619934\pi$
$173$	−1674.42	−0.735862	−0.367931	+	0.929853i	$0.619934\pi$
$174$	−53.5854	−0.0233465
$175$	0	0
$176$	680.307	0.291364
$177$	2031.46	0.862676
$178$	2.48784	0.00104759
$179$	−967.196	−0.403864	−0.201932	−	0.979400i	$-0.564722\pi$
$179$	−967.196	−0.403864	−0.201932	+	0.979400i	$0.564722\pi$
$180$	−1451.77	−0.601157
$181$	−978.790	−0.401950	−0.200975	−	0.979596i	$-0.564411\pi$
$181$	−978.790	−0.401950	−0.200975	+	0.979596i	$0.564411\pi$
$182$	0	0
$183$	630.677	0.254760
$184$	342.824	0.137355
$185$	2575.38	1.02349
$186$	186.830	0.0736508
$187$	−1513.80	−0.591980
$188$	750.451	0.291129
$189$	0	0
$190$	−270.351	−0.103228
$191$	−2366.16	−0.896385	−0.448192	−	0.893937i	$-0.647932\pi$
$191$	−2366.16	−0.896385	−0.448192	+	0.893937i	$0.647932\pi$
$192$	1433.19	0.538707
$193$	2909.83	1.08525	0.542627	−	0.839974i	$-0.317430\pi$
$193$	2909.83	1.08525	0.542627	+	0.839974i	$0.317430\pi$
$194$	−248.813	−0.0920812
$195$	869.944	0.319477
$196$	0	0
$197$	−1312.10	−0.474533	−0.237267	−	0.971445i	$-0.576252\pi$
$197$	−1312.10	−0.474533	−0.237267	+	0.971445i	$0.576252\pi$
$198$	−29.7142	−0.0106651
$199$	974.539	0.347152	0.173576	−	0.984820i	$-0.444468\pi$
$199$	974.539	0.347152	0.173576	+	0.984820i	$0.444468\pi$
$200$	1389.01	0.491089
$201$	1284.26	0.450669
$202$	−145.135	−0.0505528
$203$	0	0
$204$	−3265.65	−1.12079
$205$	5790.36	1.97276
$206$	−232.880	−0.0787646
$207$	646.125	0.216951
$208$	−879.427	−0.293160
$209$	485.859	0.160802
$210$	0	0
$211$	2997.95	0.978141	0.489070	−	0.872244i	$-0.337336\pi$
$211$	2997.95	0.978141	0.489070	+	0.872244i	$0.337336\pi$
$212$	−5751.47	−1.86327
$213$	−1257.70	−0.404582
$214$	−7.85747	−0.00250993
$215$	−3653.82	−1.15902
$216$	−128.932	−0.0406144
$217$	0	0
$218$	630.830	0.195987
$219$	2763.54	0.852707
$220$	−1774.38	−0.543767
$221$	1956.88	0.595629
$222$	113.713	0.0343779
$223$	2342.96	0.703569	0.351785	−	0.936081i	$-0.385575\pi$
$223$	2342.96	0.703569	0.351785	+	0.936081i	$0.385575\pi$
$224$	0	0
$225$	2617.89	0.775670
$226$	−716.382	−0.210854
$227$	1048.67	0.306619	0.153310	−	0.988178i	$-0.451007\pi$
$227$	1048.67	0.306619	0.153310	+	0.988178i	$0.451007\pi$
$228$	1048.12	0.304445
$229$	2738.04	0.790108	0.395054	−	0.918658i	$-0.370726\pi$
$229$	2738.04	0.790108	0.395054	+	0.918658i	$0.370726\pi$
$230$	−439.425	−0.125978
$231$	0	0
$232$	−284.179	−0.0804194
$233$	5144.84	1.44657	0.723283	−	0.690552i	$-0.242632\pi$
$233$	5144.84	1.44657	0.723283	+	0.690552i	$0.242632\pi$
$234$	38.4113	0.0107309
$235$	−1934.79	−0.537070
$236$	5356.22	1.47737
$237$	−2687.93	−0.736708
$238$	0	0
$239$	1971.83	0.533670	0.266835	−	0.963742i	$-0.414022\pi$
$239$	1971.83	0.533670	0.266835	+	0.963742i	$0.414022\pi$
$240$	−3783.69	−1.01765
$241$	−2316.64	−0.619202	−0.309601	−	0.950867i	$-0.600195\pi$
$241$	−2316.64	−0.619202	−0.309601	+	0.950867i	$0.600195\pi$
$242$	−36.3174	−0.00964698
$243$	−243.000	−0.0641500
$244$	1662.87	0.436288
$245$	0	0
$246$	255.667	0.0662630
$247$	−628.066	−0.161793
$248$	990.817	0.253697
$249$	3541.76	0.901404
$250$	−1015.30	−0.256854
$251$	5215.47	1.31154	0.655772	−	0.754959i	$-0.272343\pi$
$251$	5215.47	1.31154	0.655772	+	0.754959i	$0.272343\pi$
$252$	0	0
$253$	789.708	0.196239
$254$	−229.478	−0.0566880
$255$	8419.38	2.06761
$256$	3642.51	0.889284
$257$	4071.13	0.988133	0.494067	−	0.869424i	$-0.335510\pi$
$257$	4071.13	0.988133	0.494067	+	0.869424i	$0.335510\pi$
$258$	−161.330	−0.0389301
$259$	0	0
$260$	2293.73	0.547119
$261$	−535.597	−0.127022
$262$	330.691	0.0779777
$263$	7805.80	1.83014	0.915069	−	0.403298i	$-0.132136\pi$
$263$	7805.80	1.83014	0.915069	+	0.403298i	$0.132136\pi$
$264$	−157.583	−0.0367371
$265$	14828.2	3.43732
$266$	0	0
$267$	24.8665	0.00569964
$268$	3386.12	0.771791
$269$	−3856.06	−0.874008	−0.437004	−	0.899460i	$-0.643960\pi$
$269$	−3856.06	−0.874008	−0.437004	+	0.899460i	$0.643960\pi$
$270$	165.263	0.0372503
$271$	−176.549	−0.0395742	−0.0197871	−	0.999804i	$-0.506299\pi$
$271$	−176.549	−0.0395742	−0.0197871	+	0.999804i	$0.506299\pi$
$272$	−8511.15	−1.89730
$273$	0	0
$274$	−904.868	−0.199508
$275$	3199.64	0.701620
$276$	1703.60	0.371538
$277$	4173.74	0.905327	0.452664	−	0.891681i	$-0.350474\pi$
$277$	4173.74	0.905327	0.452664	+	0.891681i	$0.350474\pi$
$278$	−360.293	−0.0777301
$279$	1867.41	0.400712
$280$	0	0
$281$	−4696.41	−0.997026	−0.498513	−	0.866882i	$-0.666120\pi$
$281$	−4696.41	−0.997026	−0.498513	+	0.866882i	$0.666120\pi$
$282$	−85.4281	−0.0180396
$283$	−5431.69	−1.14092	−0.570460	−	0.821325i	$-0.693235\pi$
$283$	−5431.69	−1.14092	−0.570460	+	0.821325i	$0.693235\pi$
$284$	−3316.09	−0.692865
$285$	−2702.22	−0.561634
$286$	46.9472	0.00970645
$287$	0	0
$288$	−510.883	−0.104528
$289$	14025.8	2.85484
$290$	364.256	0.0737581
$291$	−2486.94	−0.500987
$292$	7286.46	1.46030
$293$	6169.95	1.23021	0.615107	−	0.788444i	$-0.289113\pi$
$293$	6169.95	1.23021	0.615107	+	0.788444i	$0.289113\pi$
$294$	0	0
$295$	−13809.2	−2.72543
$296$	603.053	0.118418
$297$	−297.000	−0.0580259
$298$	632.023	0.122859
$299$	−1020.85	−0.197449
$300$	6902.42	1.32837
$301$	0	0
$302$	−685.470	−0.130611
$303$	−1450.66	−0.275043
$304$	2731.68	0.515370
$305$	−4287.14	−0.804856
$306$	371.747	0.0694490
$307$	3433.80	0.638363	0.319182	−	0.947694i	$-0.396592\pi$
$307$	3433.80	0.638363	0.319182	+	0.947694i	$0.396592\pi$
$308$	0	0
$309$	−2327.68	−0.428535
$310$	−1270.01	−0.232683
$311$	2397.11	0.437066	0.218533	−	0.975830i	$-0.429873\pi$
$311$	2397.11	0.437066	0.218533	+	0.975830i	$0.429873\pi$
$312$	203.707	0.0369636
$313$	−8508.97	−1.53660	−0.768299	−	0.640091i	$-0.778897\pi$
$313$	−8508.97	−1.53660	−0.768299	+	0.640091i	$0.778897\pi$
$314$	−316.279	−0.0568428
$315$	0	0
$316$	−7087.10	−1.26165
$317$	1000.49	0.177266	0.0886330	−	0.996064i	$-0.471750\pi$
$317$	1000.49	0.177266	0.0886330	+	0.996064i	$0.471750\pi$
$318$	654.722	0.115456
$319$	−654.619	−0.114895
$320$	−9742.39	−1.70193
$321$	−78.5372	−0.0136558
$322$	0	0
$323$	−6078.47	−1.04710
$324$	−640.703	−0.109860
$325$	−4136.15	−0.705946
$326$	−484.250	−0.0822703
$327$	6305.29	1.06631
$328$	1355.88	0.228249
$329$	0	0
$330$	201.988	0.0336941
$331$	602.659	0.100076	0.0500380	−	0.998747i	$-0.484066\pi$
$331$	602.659	0.100076	0.0500380	+	0.998747i	$0.484066\pi$
$332$	9338.33	1.54370
$333$	1136.58	0.187040
$334$	−768.759	−0.125942
$335$	−8729.96	−1.42379
$336$	0	0
$337$	7700.41	1.24471	0.622356	−	0.782734i	$-0.286175\pi$
$337$	7700.41	1.24471	0.622356	+	0.782734i	$0.286175\pi$
$338$	598.727	0.0963505
$339$	−7160.39	−1.14720
$340$	22198.8	3.54089
$341$	2282.39	0.362458
$342$	−119.313	−0.0188647
$343$	0	0
$344$	−855.583	−0.134099
$345$	−4392.15	−0.685407
$346$	502.567	0.0780872
$347$	1967.23	0.304341	0.152170	−	0.988354i	$-0.451374\pi$
$347$	1967.23	0.304341	0.152170	+	0.988354i	$0.451374\pi$
$348$	−1412.18	−0.217530
$349$	−6122.38	−0.939035	−0.469518	−	0.882923i	$-0.655572\pi$
$349$	−6122.38	−0.939035	−0.469518	+	0.882923i	$0.655572\pi$
$350$	0	0
$351$	383.930	0.0583836
$352$	−624.412	−0.0945491
$353$	7052.14	1.06331	0.531654	−	0.846962i	$-0.321571\pi$
$353$	7052.14	1.06331	0.531654	+	0.846962i	$0.321571\pi$
$354$	−609.729	−0.0915444
$355$	8549.42	1.27819
$356$	65.5639	0.00976090
$357$	0	0
$358$	290.298	0.0428567
$359$	−454.072	−0.0667549	−0.0333774	−	0.999443i	$-0.510626\pi$
$359$	−454.072	−0.0667549	−0.0333774	+	0.999443i	$0.510626\pi$
$360$	876.438	0.128312
$361$	−4908.10	−0.715571
$362$	293.777	0.0426536
$363$	−363.000	−0.0524864
$364$	0	0
$365$	−18785.7	−2.69394
$366$	−189.294	−0.0270343
$367$	9890.82	1.40680	0.703401	−	0.710793i	$-0.251664\pi$
$367$	9890.82	1.40680	0.703401	+	0.710793i	$0.251664\pi$
$368$	4440.03	0.628947
$369$	2555.44	0.360518
$370$	−772.982	−0.108609
$371$	0	0
$372$	4923.68	0.686238
$373$	383.615	0.0532515	0.0266258	−	0.999645i	$-0.491524\pi$
$373$	383.615	0.0532515	0.0266258	+	0.999645i	$0.491524\pi$
$374$	454.358	0.0628190
$375$	−10148.2	−1.39747
$376$	−453.051	−0.0621392
$377$	846.221	0.115604
$378$	0	0
$379$	−3609.50	−0.489202	−0.244601	−	0.969624i	$-0.578657\pi$
$379$	−3609.50	−0.489202	−0.244601	+	0.969624i	$0.578657\pi$
$380$	−7124.78	−0.961825
$381$	−2293.69	−0.308423
$382$	710.188	0.0951215
$383$	8251.46	1.10086	0.550431	−	0.834881i	$-0.314463\pi$
$383$	8251.46	1.10086	0.550431	+	0.834881i	$0.314463\pi$
$384$	−1792.52	−0.238214
$385$	0	0
$386$	−873.366	−0.115164
$387$	−1612.53	−0.211808
$388$	−6557.17	−0.857964
$389$	−8928.88	−1.16378	−0.581892	−	0.813266i	$-0.697687\pi$
$389$	−8928.88	−1.16378	−0.581892	+	0.813266i	$0.697687\pi$
$390$	−261.108	−0.0339019
$391$	−9879.85	−1.27787
$392$	0	0
$393$	3305.33	0.424254
$394$	393.818	0.0503559
$395$	18271.7	2.32747
$396$	−783.081	−0.0993720
$397$	6704.24	0.847547	0.423773	−	0.905768i	$-0.360705\pi$
$397$	6704.24	0.847547	0.423773	+	0.905768i	$0.360705\pi$
$398$	−292.502	−0.0368386
$399$	0	0
$400$	17989.6	2.24869
$401$	10113.8	1.25950	0.629750	−	0.776798i	$-0.283157\pi$
$401$	10113.8	1.25950	0.629750	+	0.776798i	$0.283157\pi$
$402$	−385.461	−0.0478235
$403$	−2950.42	−0.364693
$404$	−3824.86	−0.471024
$405$	1651.84	0.202668
$406$	0	0
$407$	1389.16	0.169184
$408$	1971.49	0.239224
$409$	−2855.16	−0.345179	−0.172590	−	0.984994i	$-0.555213\pi$
$409$	−2855.16	−0.345179	−0.172590	+	0.984994i	$0.555213\pi$
$410$	−1737.94	−0.209343
$411$	−9044.36	−1.08546
$412$	−6137.26	−0.733886
$413$	0	0
$414$	−193.930	−0.0230221
$415$	−24075.7	−2.84779
$416$	807.173	0.0951320
$417$	−3601.21	−0.422907
$418$	−145.827	−0.0170638
$419$	5415.96	0.631473	0.315736	−	0.948847i	$-0.397749\pi$
$419$	5415.96	0.631473	0.315736	+	0.948847i	$0.397749\pi$
$420$	0	0
$421$	−1047.16	−0.121224	−0.0606122	−	0.998161i	$-0.519305\pi$
$421$	−1047.16	−0.121224	−0.0606122	+	0.998161i	$0.519305\pi$
$422$	−899.816	−0.103797
$423$	−853.873	−0.0981483
$424$	3472.19	0.397699
$425$	−40029.9	−4.56879
$426$	377.489	0.0429329
$427$	0	0
$428$	−207.074	−0.0233862
$429$	469.247	0.0528100
$430$	1096.67	0.122991
$431$	7975.35	0.891320	0.445660	−	0.895202i	$-0.352969\pi$
$431$	7975.35	0.891320	0.445660	+	0.895202i	$0.352969\pi$
$432$	−1669.84	−0.185973
$433$	−15938.4	−1.76894	−0.884468	−	0.466600i	$-0.845479\pi$
$433$	−15938.4	−1.76894	−0.884468	+	0.466600i	$0.845479\pi$
$434$	0	0
$435$	3640.82	0.401297
$436$	16624.8	1.82610
$437$	3170.96	0.347112
$438$	−829.459	−0.0904865
$439$	13129.6	1.42743	0.713713	−	0.700439i	$-0.247012\pi$
$439$	13129.6	1.42743	0.713713	+	0.700439i	$0.247012\pi$
$440$	1071.20	0.116063
$441$	0	0
$442$	−587.345	−0.0632062
$443$	4868.10	0.522100	0.261050	−	0.965325i	$-0.415931\pi$
$443$	4868.10	0.522100	0.261050	+	0.965325i	$0.415931\pi$
$444$	2996.76	0.320315
$445$	−169.034	−0.0180067
$446$	−703.223	−0.0746605
$447$	6317.21	0.668442
$448$	0	0
$449$	−3270.54	−0.343755	−0.171878	−	0.985118i	$-0.554983\pi$
$449$	−3270.54	−0.343755	−0.171878	+	0.985118i	$0.554983\pi$
$450$	−785.742	−0.0823116
$451$	3123.32	0.326101
$452$	−18879.4	−1.96463
$453$	−6851.43	−0.710614
$454$	−314.751	−0.0325374
$455$	0	0
$456$	−632.755	−0.0649813
$457$	−8156.03	−0.834843	−0.417421	−	0.908713i	$-0.637066\pi$
$457$	−8156.03	−0.834843	−0.417421	+	0.908713i	$0.637066\pi$
$458$	−821.805	−0.0838437
$459$	3715.70	0.377852
$460$	−11580.5	−1.17379
$461$	−17797.9	−1.79812	−0.899058	−	0.437830i	$-0.855747\pi$
$461$	−17797.9	−1.79812	−0.899058	+	0.437830i	$0.855747\pi$
$462$	0	0
$463$	6141.60	0.616468	0.308234	−	0.951311i	$-0.400262\pi$
$463$	6141.60	0.616468	0.308234	+	0.951311i	$0.400262\pi$
$464$	−3680.51	−0.368240
$465$	−12694.0	−1.26596
$466$	−1544.19	−0.153505
$467$	−2423.85	−0.240177	−0.120088	−	0.992763i	$-0.538318\pi$
$467$	−2423.85	−0.240177	−0.120088	+	0.992763i	$0.538318\pi$
$468$	1012.28	0.0999847
$469$	0	0
$470$	580.713	0.0569922
$471$	−3161.28	−0.309265
$472$	−3233.58	−0.315334
$473$	−1970.87	−0.191587
$474$	806.765	0.0781771
$475$	12847.7	1.24104
$476$	0	0
$477$	6544.09	0.628162
$478$	−591.832	−0.0566313
$479$	−12080.1	−1.15231	−0.576154	−	0.817341i	$-0.695447\pi$
$479$	−12080.1	−1.15231	−0.576154	+	0.817341i	$0.695447\pi$
$480$	3472.82	0.330233
$481$	−1795.75	−0.170227
$482$	695.323	0.0657077
$483$	0	0
$484$	−957.100	−0.0898854
$485$	16905.5	1.58276
$486$	72.9349	0.00680739
$487$	6229.98	0.579686	0.289843	−	0.957074i	$-0.406397\pi$
$487$	6229.98	0.579686	0.289843	+	0.957074i	$0.406397\pi$
$488$	−1003.88	−0.0931221
$489$	−4840.18	−0.447608
$490$	0	0
$491$	−263.710	−0.0242384	−0.0121192	−	0.999927i	$-0.503858\pi$
$491$	−263.710	−0.0242384	−0.0121192	+	0.999927i	$0.503858\pi$
$492$	6737.78	0.617404
$493$	8189.78	0.748173
$494$	188.510	0.0171690
$495$	2018.91	0.183320
$496$	12832.4	1.16168
$497$	0	0
$498$	−1063.04	−0.0956541
$499$	5544.42	0.497400	0.248700	−	0.968581i	$-0.419997\pi$
$499$	5544.42	0.497400	0.248700	+	0.968581i	$0.419997\pi$
$500$	−26757.1	−2.39323
$501$	−7683.92	−0.685214
$502$	−1565.39	−0.139177
$503$	6759.56	0.599193	0.299596	−	0.954066i	$-0.403148\pi$
$503$	6759.56	0.599193	0.299596	+	0.954066i	$0.403148\pi$
$504$	0	0
$505$	9861.11	0.868938
$506$	−237.026	−0.0208243
$507$	5984.41	0.524215
$508$	−6047.62	−0.528189
$509$	−14876.4	−1.29545	−0.647726	−	0.761873i	$-0.724280\pi$
$509$	−14876.4	−1.29545	−0.647726	+	0.761873i	$0.724280\pi$
$510$	−2527.02	−0.219409
$511$	0	0
$512$	−5873.32	−0.506966
$513$	−1192.56	−0.102637
$514$	−1221.92	−0.104857
$515$	15822.9	1.35386
$516$	−4251.66	−0.362730
$517$	−1043.62	−0.0887785
$518$	0	0
$519$	5023.27	0.424850
$520$	−1384.74	−0.116778
$521$	1449.03	0.121848	0.0609241	−	0.998142i	$-0.480595\pi$
$521$	1449.03	0.121848	0.0609241	+	0.998142i	$0.480595\pi$
$522$	160.756	0.0134791
$523$	22320.4	1.86617	0.933083	−	0.359662i	$-0.117108\pi$
$523$	22320.4	1.86617	0.933083	+	0.359662i	$0.117108\pi$
$524$	8714.95	0.726554
$525$	0	0
$526$	−2342.86	−0.194208
$527$	−28554.4	−2.36024
$528$	−2040.92	−0.168219
$529$	−7012.96	−0.576392
$530$	−4450.59	−0.364758
$531$	−6094.37	−0.498066
$532$	0	0
$533$	−4037.49	−0.328111
$534$	−7.46351	−0.000604827 0
$535$	533.871	0.0431425
$536$	−2044.22	−0.164733
$537$	2901.59	0.233171
$538$	1157.37	0.0927468
$539$	0	0
$540$	4355.30	0.347078
$541$	−9285.38	−0.737910	−0.368955	−	0.929447i	$-0.620284\pi$
$541$	−9285.38	−0.737910	−0.368955	+	0.929447i	$0.620284\pi$
$542$	52.9902	0.00419949
$543$	2936.37	0.232066
$544$	7811.87	0.615683
$545$	−42861.3	−3.36877
$546$	0	0
$547$	−13289.4	−1.03878	−0.519391	−	0.854537i	$-0.673841\pi$
$547$	−13289.4	−1.03878	−0.519391	+	0.854537i	$0.673841\pi$
$548$	−23846.7	−1.85891
$549$	−1892.03	−0.147086
$550$	−960.351	−0.0744537
$551$	−2628.53	−0.203229
$552$	−1028.47	−0.0793018
$553$	0	0
$554$	−1252.72	−0.0960704
$555$	−7726.13	−0.590911
$556$	−9495.09	−0.724247
$557$	−2006.74	−0.152654	−0.0763270	−	0.997083i	$-0.524319\pi$
$557$	−2006.74	−0.152654	−0.0763270	+	0.997083i	$0.524319\pi$
$558$	−560.490	−0.0425223
$559$	2547.73	0.192768
$560$	0	0
$561$	4541.41	0.341780
$562$	1409.60	0.105801
$563$	538.433	0.0403059	0.0201530	−	0.999797i	$-0.493585\pi$
$563$	538.433	0.0403059	0.0201530	+	0.999797i	$0.493585\pi$
$564$	−2251.35	−0.168084
$565$	48674.1	3.62431
$566$	1630.29	0.121071
$567$	0	0
$568$	2001.94	0.147887
$569$	2431.81	0.179168	0.0895841	−	0.995979i	$-0.471446\pi$
$569$	2431.81	0.179168	0.0895841	+	0.995979i	$0.471446\pi$
$570$	811.054	0.0595988
$571$	20061.2	1.47029	0.735143	−	0.677912i	$-0.237115\pi$
$571$	20061.2	1.47029	0.735143	+	0.677912i	$0.237115\pi$
$572$	1237.24	0.0904395
$573$	7098.49	0.517528
$574$	0	0
$575$	20882.5	1.51454
$576$	−4299.58	−0.311023
$577$	−17450.9	−1.25908	−0.629540	−	0.776968i	$-0.716757\pi$
$577$	−17450.9	−1.25908	−0.629540	+	0.776968i	$0.716757\pi$
$578$	−4209.76	−0.302946
$579$	−8729.49	−0.626572
$580$	9599.53	0.687239
$581$	0	0
$582$	746.440	0.0531631
$583$	7998.34	0.568194
$584$	−4398.87	−0.311690
$585$	−2609.83	−0.184450
$586$	−1851.87	−0.130546
$587$	278.808	0.0196041	0.00980206	−	0.999952i	$-0.496880\pi$
$587$	278.808	0.0196041	0.00980206	+	0.999952i	$0.496880\pi$
$588$	0	0
$589$	9164.61	0.641122
$590$	4144.74	0.289214
$591$	3936.29	0.273972
$592$	7810.35	0.542235
$593$	22867.9	1.58359	0.791797	−	0.610785i	$-0.209146\pi$
$593$	22867.9	1.58359	0.791797	+	0.610785i	$0.209146\pi$
$594$	89.1426	0.00615752
$595$	0	0
$596$	16656.2	1.14474
$597$	−2923.62	−0.200428
$598$	306.401	0.0209527
$599$	212.492	0.0144945	0.00724725	−	0.999974i	$-0.497693\pi$
$599$	212.492	0.0144945	0.00724725	+	0.999974i	$0.497693\pi$
$600$	−4167.03	−0.283530
$601$	8413.31	0.571025	0.285512	−	0.958375i	$-0.407836\pi$
$601$	8413.31	0.571025	0.285512	+	0.958375i	$0.407836\pi$
$602$	0	0
$603$	−3852.77	−0.260194
$604$	−18064.7	−1.21696
$605$	2467.56	0.165819
$606$	435.405	0.0291867
$607$	26805.6	1.79243	0.896216	−	0.443618i	$-0.146305\pi$
$607$	26805.6	1.79243	0.896216	+	0.443618i	$0.146305\pi$
$608$	−2507.24	−0.167240
$609$	0	0
$610$	1286.76	0.0854087
$611$	1349.08	0.0893258
$612$	9796.95	0.647088
$613$	11415.9	0.752178	0.376089	−	0.926583i	$-0.377269\pi$
$613$	11415.9	0.752178	0.376089	+	0.926583i	$0.377269\pi$
$614$	−1030.63	−0.0677410
$615$	−17371.1	−1.13898
$616$	0	0
$617$	15755.1	1.02800	0.514000	−	0.857790i	$-0.328163\pi$
$617$	15755.1	1.02800	0.514000	+	0.857790i	$0.328163\pi$
$618$	698.640	0.0454748
$619$	23455.5	1.52303	0.761515	−	0.648147i	$-0.224456\pi$
$619$	23455.5	1.52303	0.761515	+	0.648147i	$0.224456\pi$
$620$	−33469.6	−2.16802
$621$	−1938.37	−0.125256
$622$	−719.477	−0.0463800
$623$	0	0
$624$	2638.28	0.169256
$625$	32624.5	2.08797
$626$	2553.91	0.163059
$627$	−1457.58	−0.0928389
$628$	−8335.14	−0.529631
$629$	−17379.4	−1.10169
$630$	0	0
$631$	4496.85	0.283703	0.141852	−	0.989888i	$-0.454694\pi$
$631$	4496.85	0.283703	0.141852	+	0.989888i	$0.454694\pi$
$632$	4278.52	0.269289
$633$	−8993.86	−0.564730
$634$	−300.292	−0.0188109
$635$	15591.8	0.974394
$636$	17254.4	1.07576
$637$	0	0
$638$	196.480	0.0121923
$639$	3773.09	0.233585
$640$	12185.0	0.752583
$641$	−14888.5	−0.917409	−0.458704	−	0.888589i	$-0.651686\pi$
$641$	−14888.5	−0.917409	−0.458704	+	0.888589i	$0.651686\pi$
$642$	23.5724	0.00144911
$643$	−29338.5	−1.79937	−0.899687	−	0.436535i	$-0.856206\pi$
$643$	−29338.5	−1.79937	−0.899687	+	0.436535i	$0.856206\pi$
$644$	0	0
$645$	10961.5	0.669159
$646$	1824.41	0.111115
$647$	−15639.5	−0.950312	−0.475156	−	0.879902i	$-0.657608\pi$
$647$	−15639.5	−0.950312	−0.475156	+	0.879902i	$0.657608\pi$
$648$	386.796	0.0234487
$649$	−7448.68	−0.450518
$650$	1241.44	0.0749127
$651$	0	0
$652$	−12761.8	−0.766550
$653$	−9632.69	−0.577268	−0.288634	−	0.957439i	$-0.593201\pi$
$653$	−9632.69	−0.577268	−0.288634	+	0.957439i	$0.593201\pi$
$654$	−1892.49	−0.113153
$655$	−22468.6	−1.34033
$656$	17560.5	1.04515
$657$	−8290.63	−0.492311
$658$	0	0
$659$	−5224.42	−0.308823	−0.154412	−	0.988007i	$-0.549348\pi$
$659$	−5224.42	−0.308823	−0.154412	+	0.988007i	$0.549348\pi$
$660$	5323.14	0.313944
$661$	−11467.7	−0.674799	−0.337399	−	0.941362i	$-0.609547\pi$
$661$	−11467.7	−0.674799	−0.337399	+	0.941362i	$0.609547\pi$
$662$	−180.884	−0.0106197
$663$	−5870.64	−0.343887
$664$	−5637.60	−0.329490
$665$	0	0
$666$	−341.138	−0.0198481
$667$	−4272.38	−0.248017
$668$	−20259.7	−1.17346
$669$	−7028.87	−0.406206
$670$	2620.24	0.151088
$671$	−2312.48	−0.133044
$672$	0	0
$673$	−10955.3	−0.627480	−0.313740	−	0.949509i	$-0.601582\pi$
$673$	−10955.3	−0.627480	−0.313740	+	0.949509i	$0.601582\pi$
$674$	−2311.23	−0.132085
$675$	−7853.66	−0.447834
$676$	15778.7	0.897742
$677$	19092.9	1.08390	0.541949	−	0.840411i	$-0.317687\pi$
$677$	19092.9	1.08390	0.541949	+	0.840411i	$0.317687\pi$
$678$	2149.15	0.121737
$679$	0	0
$680$	−13401.6	−0.755774
$681$	−3146.00	−0.177027
$682$	−685.043	−0.0384629
$683$	−27127.0	−1.51974	−0.759872	−	0.650072i	$-0.774739\pi$
$683$	−27127.0	−1.51974	−0.759872	+	0.650072i	$0.774739\pi$
$684$	−3144.36	−0.175771
$685$	61480.7	3.42928
$686$	0	0
$687$	−8214.12	−0.456169
$688$	−11081.0	−0.614037
$689$	−10339.4	−0.571697
$690$	1318.28	0.0727332
$691$	4331.47	0.238461	0.119231	−	0.992867i	$-0.461957\pi$
$691$	4331.47	0.238461	0.119231	+	0.992867i	$0.461957\pi$
$692$	13244.5	0.727575
$693$	0	0
$694$	−590.451	−0.0322957
$695$	24479.9	1.33608
$696$	852.538	0.0464301
$697$	−39075.1	−2.12349
$698$	1837.59	0.0996474
$699$	−15434.5	−0.835175
$700$	0	0
$701$	−26769.8	−1.44234	−0.721172	−	0.692756i	$-0.756396\pi$
$701$	−26769.8	−1.44234	−0.721172	+	0.692756i	$0.756396\pi$
$702$	−115.234	−0.00619548
$703$	5577.97	0.299256
$704$	−5255.04	−0.281331
$705$	5804.36	0.310078
$706$	−2116.65	−0.112835
$707$	0	0
$708$	−16068.7	−0.852962
$709$	8000.36	0.423780	0.211890	−	0.977294i	$-0.432038\pi$
$709$	8000.36	0.423780	0.211890	+	0.977294i	$0.432038\pi$
$710$	−2566.05	−0.135637
$711$	8063.79	0.425339
$712$	−39.5813	−0.00208339
$713$	14896.0	0.782413
$714$	0	0
$715$	−3189.80	−0.166841
$716$	7650.44	0.399316
$717$	−5915.49	−0.308114
$718$	136.287	0.00708381
$719$	6828.84	0.354204	0.177102	−	0.984193i	$-0.443328\pi$
$719$	6828.84	0.354204	0.177102	+	0.984193i	$0.443328\pi$
$720$	11351.1	0.587541
$721$	0	0
$722$	1473.13	0.0759341
$723$	6949.91	0.357496
$724$	7742.14	0.397423
$725$	−17310.3	−0.886742
$726$	108.952	0.00556968
$727$	−7640.53	−0.389782	−0.194891	−	0.980825i	$-0.562435\pi$
$727$	−7640.53	−0.389782	−0.194891	+	0.980825i	$0.562435\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	5638.40	0.285872
$731$	24657.1	1.24757
$732$	−4988.60	−0.251891
$733$	24968.8	1.25817	0.629087	−	0.777335i	$-0.283429\pi$
$733$	24968.8	1.25817	0.629087	+	0.777335i	$0.283429\pi$
$734$	−2968.66	−0.149285
$735$	0	0
$736$	−4075.23	−0.204097
$737$	−4708.94	−0.235354
$738$	−767.000	−0.0382570
$739$	24256.7	1.20744	0.603720	−	0.797196i	$-0.293684\pi$
$739$	24256.7	1.20744	0.603720	+	0.797196i	$0.293684\pi$
$740$	−20371.0	−1.01196
$741$	1884.20	0.0934113
$742$	0	0
$743$	33315.2	1.64498	0.822488	−	0.568782i	$-0.192585\pi$
$743$	33315.2	1.64498	0.822488	+	0.568782i	$0.192585\pi$
$744$	−2972.45	−0.146472
$745$	−42942.4	−2.11179
$746$	−115.140	−0.00565088
$747$	−10625.3	−0.520426
$748$	11974.0	0.585314
$749$	0	0
$750$	3045.91	0.148295
$751$	510.164	0.0247885	0.0123942	−	0.999923i	$-0.496055\pi$
$751$	510.164	0.0247885	0.0123942	+	0.999923i	$0.496055\pi$
$752$	−5867.63	−0.284535
$753$	−15646.4	−0.757220
$754$	−253.988	−0.0122675
$755$	46573.8	2.24503
$756$	0	0
$757$	−13170.8	−0.632365	−0.316183	−	0.948698i	$-0.602401\pi$
$757$	−13170.8	−0.632365	−0.316183	+	0.948698i	$0.602401\pi$
$758$	1083.37	0.0519125
$759$	−2369.12	−0.113299
$760$	4301.27	0.205294
$761$	−2098.03	−0.0999388	−0.0499694	−	0.998751i	$-0.515912\pi$
$761$	−2098.03	−0.0999388	−0.0499694	+	0.998751i	$0.515912\pi$
$762$	688.435	0.0327288
$763$	0	0
$764$	18716.1	0.886291
$765$	−25258.1	−1.19374
$766$	−2476.62	−0.116820
$767$	9628.85	0.453296
$768$	−10927.5	−0.513429
$769$	−27039.1	−1.26795	−0.633976	−	0.773353i	$-0.718578\pi$
$769$	−27039.1	−1.26795	−0.633976	+	0.773353i	$0.718578\pi$
$770$	0	0
$771$	−12213.4	−0.570499
$772$	−23016.5	−1.07303
$773$	−12497.4	−0.581501	−0.290750	−	0.956799i	$-0.593905\pi$
$773$	−12497.4	−0.581501	−0.290750	+	0.956799i	$0.593905\pi$
$774$	483.990	0.0224763
$775$	60353.9	2.79739
$776$	3958.60	0.183126
$777$	0	0
$778$	2679.94	0.123497
$779$	12541.3	0.576813
$780$	−6881.18	−0.315879
$781$	4611.55	0.211286
$782$	2965.37	0.135603
$783$	1606.79	0.0733360
$784$	0	0
$785$	21489.4	0.977055
$786$	−992.072	−0.0450204
$787$	17525.8	0.793810	0.396905	−	0.917860i	$-0.370084\pi$
$787$	17525.8	0.793810	0.396905	+	0.917860i	$0.370084\pi$
$788$	10378.6	0.469190
$789$	−23417.4	−1.05663
$790$	−5484.13	−0.246983
$791$	0	0
$792$	472.750	0.0212102
$793$	2989.33	0.133864
$794$	−2012.23	−0.0899389
$795$	−44484.7	−1.98454
$796$	−7708.52	−0.343243
$797$	−31769.5	−1.41196	−0.705981	−	0.708231i	$-0.749494\pi$
$797$	−31769.5	−1.41196	−0.705981	+	0.708231i	$0.749494\pi$
$798$	0	0
$799$	13056.5	0.578106
$800$	−16511.5	−0.729713
$801$	−74.5995	−0.00329069
$802$	−3035.59	−0.133654
$803$	−10133.0	−0.445312
$804$	−10158.4	−0.445594
$805$	0	0
$806$	885.551	0.0387000
$807$	11568.2	0.504609
$808$	2309.09	0.100536
$809$	32782.7	1.42470	0.712348	−	0.701826i	$-0.247632\pi$
$809$	32782.7	1.42470	0.712348	+	0.701826i	$0.247632\pi$
$810$	−495.788	−0.0215064
$811$	−27108.1	−1.17373	−0.586865	−	0.809685i	$-0.699638\pi$
$811$	−27108.1	−1.17373	−0.586865	+	0.809685i	$0.699638\pi$
$812$	0	0
$813$	529.648	0.0228482
$814$	−416.946	−0.0179533
$815$	32902.0	1.41412
$816$	25533.5	1.09540
$817$	−7913.76	−0.338883
$818$	856.957	0.0366293
$819$	0	0
$820$	−45801.3	−1.95055
$821$	13323.1	0.566358	0.283179	−	0.959067i	$-0.408611\pi$
$821$	13323.1	0.566358	0.283179	+	0.959067i	$0.408611\pi$
$822$	2714.60	0.115186
$823$	19594.1	0.829898	0.414949	−	0.909845i	$-0.363799\pi$
$823$	19594.1	0.829898	0.414949	+	0.909845i	$0.363799\pi$
$824$	3705.10	0.156642
$825$	−9598.92	−0.405081
$826$	0	0
$827$	11716.8	0.492662	0.246331	−	0.969186i	$-0.420775\pi$
$827$	11716.8	0.492662	0.246331	+	0.969186i	$0.420775\pi$
$828$	−5110.79	−0.214508
$829$	−27947.0	−1.17085	−0.585427	−	0.810725i	$-0.699073\pi$
$829$	−27947.0	−1.17085	−0.585427	+	0.810725i	$0.699073\pi$
$830$	7226.18	0.302198
$831$	−12521.2	−0.522691
$832$	6793.15	0.283065
$833$	0	0
$834$	1080.88	0.0448775
$835$	52232.8	2.16478
$836$	−3843.10	−0.158991
$837$	−5602.22	−0.231351
$838$	−1625.57	−0.0670098
$839$	−19042.6	−0.783581	−0.391791	−	0.920054i	$-0.628144\pi$
$839$	−19042.6	−0.783581	−0.391791	+	0.920054i	$0.628144\pi$
$840$	0	0
$841$	−20847.5	−0.854790
$842$	314.298	0.0128639
$843$	14089.2	0.575633
$844$	−23713.6	−0.967126
$845$	−40680.1	−1.65614
$846$	256.284	0.0104152
$847$	0	0
$848$	44969.6	1.82106
$849$	16295.1	0.658711
$850$	12014.7	0.484826
$851$	9066.35	0.365206
$852$	9948.27	0.400026
$853$	−28671.8	−1.15088	−0.575441	−	0.817843i	$-0.695170\pi$
$853$	−28671.8	−1.15088	−0.575441	+	0.817843i	$0.695170\pi$
$854$	0	0
$855$	8106.66	0.324260
$856$	125.012	0.00499160
$857$	−4893.18	−0.195038	−0.0975191	−	0.995234i	$-0.531091\pi$
$857$	−4893.18	−0.195038	−0.0975191	+	0.995234i	$0.531091\pi$
$858$	−140.842	−0.00560402
$859$	2934.03	0.116540	0.0582700	−	0.998301i	$-0.481442\pi$
$859$	2934.03	0.116540	0.0582700	+	0.998301i	$0.481442\pi$
$860$	28901.4	1.14597
$861$	0	0
$862$	−2393.75	−0.0945840
$863$	−33600.9	−1.32536	−0.662680	−	0.748902i	$-0.730581\pi$
$863$	−33600.9	−1.32536	−0.662680	+	0.748902i	$0.730581\pi$
$864$	1532.65	0.0603492
$865$	−34146.6	−1.34222
$866$	4783.80	0.187714
$867$	−42077.5	−1.64824
$868$	0	0
$869$	9855.74	0.384733
$870$	−1092.77	−0.0425843
$871$	6087.21	0.236805
$872$	−10036.5	−0.389768
$873$	7460.83	0.289245
$874$	−951.744	−0.0368344
$875$	0	0
$876$	−21859.4	−0.843105
$877$	21202.1	0.816357	0.408179	−	0.912902i	$-0.366164\pi$
$877$	21202.1	0.816357	0.408179	+	0.912902i	$0.366164\pi$
$878$	−3940.75	−0.151474
$879$	−18509.9	−0.710264
$880$	13873.5	0.531450
$881$	−7032.42	−0.268931	−0.134466	−	0.990918i	$-0.542932\pi$
$881$	−7032.42	−0.268931	−0.134466	+	0.990918i	$0.542932\pi$
$882$	0	0
$883$	−27321.9	−1.04129	−0.520644	−	0.853774i	$-0.674308\pi$
$883$	−27321.9	−1.04129	−0.520644	+	0.853774i	$0.674308\pi$
$884$	−15478.8	−0.588922
$885$	41427.6	1.57353
$886$	−1461.13	−0.0554036
$887$	−14447.0	−0.546879	−0.273439	−	0.961889i	$-0.588161\pi$
$887$	−14447.0	−0.546879	−0.273439	+	0.961889i	$0.588161\pi$
$888$	−1809.16	−0.0683687
$889$	0	0
$890$	50.7346	0.00191082
$891$	891.000	0.0335013
$892$	−18532.6	−0.695646
$893$	−4190.52	−0.157033
$894$	−1896.07	−0.0709329
$895$	−19724.1	−0.736652
$896$	0	0
$897$	3062.55	0.113997
$898$	981.630	0.0364782
$899$	−12347.9	−0.458092
$900$	−20707.3	−0.766936
$901$	−100065.	−3.69995
$902$	−937.444	−0.0346047
$903$	0	0
$904$	11397.6	0.419334
$905$	−19960.5	−0.733160
$906$	2056.41	0.0754080
$907$	−45955.9	−1.68241	−0.841203	−	0.540720i	$-0.818152\pi$
$907$	−45955.9	−1.68241	−0.841203	+	0.540720i	$0.818152\pi$
$908$	−8294.87	−0.303166
$909$	4351.97	0.158796
$910$	0	0
$911$	36320.1	1.32090	0.660450	−	0.750870i	$-0.270366\pi$
$911$	36320.1	1.32090	0.660450	+	0.750870i	$0.270366\pi$
$912$	−8195.03	−0.297549
$913$	−12986.4	−0.470743
$914$	2447.98	0.0885908
$915$	12861.4	0.464684
$916$	−21657.7	−0.781211
$917$	0	0
$918$	−1115.24	−0.0400964
$919$	−29575.2	−1.06158	−0.530791	−	0.847503i	$-0.678105\pi$
$919$	−29575.2	−1.06158	−0.530791	+	0.847503i	$0.678105\pi$
$920$	6991.22	0.250537
$921$	−10301.4	−0.368559
$922$	5341.93	0.190810
$923$	−5961.32	−0.212589
$924$	0	0
$925$	36733.9	1.30573
$926$	−1843.36	−0.0654175
$927$	6983.05	0.247415
$928$	3378.12	0.119496
$929$	−26451.9	−0.934188	−0.467094	−	0.884208i	$-0.654699\pi$
$929$	−26451.9	−0.934188	−0.467094	+	0.884208i	$0.654699\pi$
$930$	3810.03	0.134340
$931$	0	0
$932$	−40695.3	−1.43028
$933$	−7191.33	−0.252340
$934$	727.503	0.0254868
$935$	−30871.0	−1.07978
$936$	−611.121	−0.0213409
$937$	−10132.1	−0.353255	−0.176628	−	0.984278i	$-0.556519\pi$
$937$	−10132.1	−0.353255	−0.176628	+	0.984278i	$0.556519\pi$
$938$	0	0
$939$	25526.9	0.887156
$940$	15304.0	0.531022
$941$	−1338.60	−0.0463731	−0.0231865	−	0.999731i	$-0.507381\pi$
$941$	−1338.60	−0.0463731	−0.0231865	+	0.999731i	$0.507381\pi$
$942$	948.837	0.0328182
$943$	20384.4	0.703931
$944$	−41879.2	−1.44391
$945$	0	0
$946$	591.544	0.0203306
$947$	−38658.7	−1.32655	−0.663273	−	0.748378i	$-0.730833\pi$
$947$	−38658.7	−1.32655	−0.663273	+	0.748378i	$0.730833\pi$
$948$	21261.3	0.728412
$949$	13098.8	0.448057
$950$	−3856.16	−0.131695
$951$	−3001.48	−0.102345
$952$	0	0
$953$	9358.77	0.318111	0.159056	−	0.987270i	$-0.449155\pi$
$953$	9358.77	0.318111	0.159056	+	0.987270i	$0.449155\pi$
$954$	−1964.17	−0.0666585
$955$	−48253.3	−1.63501
$956$	−15597.0	−0.527660
$957$	1963.86	0.0663349
$958$	3625.77	0.122279
$959$	0	0
$960$	29227.2	0.982607
$961$	13261.0	0.445133
$962$	538.983	0.0180640
$963$	235.612	0.00788419
$964$	18324.4	0.612229
$965$	59340.3	1.97951
$966$	0	0
$967$	−48585.8	−1.61573	−0.807866	−	0.589366i	$-0.799378\pi$
$967$	−48585.8	−1.61573	−0.807866	+	0.589366i	$0.799378\pi$
$968$	577.806	0.0191853
$969$	18235.4	0.604546
$970$	−5074.06	−0.167957
$971$	18291.4	0.604530	0.302265	−	0.953224i	$-0.402257\pi$
$971$	18291.4	0.604530	0.302265	+	0.953224i	$0.402257\pi$
$972$	1922.11	0.0634277
$973$	0	0
$974$	−1869.89	−0.0615144
$975$	12408.5	0.407578
$976$	−13001.6	−0.426406
$977$	−54334.8	−1.77925	−0.889623	−	0.456695i	$-0.849033\pi$
$977$	−54334.8	−1.77925	−0.889623	+	0.456695i	$0.849033\pi$
$978$	1452.75	0.0474988
$979$	−91.1771	−0.00297654
$980$	0	0
$981$	−18915.9	−0.615634
$982$	79.1508	0.00257210
$983$	10277.9	0.333485	0.166742	−	0.986001i	$-0.446675\pi$
$983$	10277.9	0.333485	0.166742	+	0.986001i	$0.446675\pi$
$984$	−4067.63	−0.131780
$985$	−26757.7	−0.865554
$986$	−2458.11	−0.0793937
$987$	0	0
$988$	4967.95	0.159971
$989$	−12862.9	−0.413566
$990$	−605.963	−0.0194533
$991$	34615.9	1.10960	0.554798	−	0.831985i	$-0.312796\pi$
$991$	34615.9	1.10960	0.554798	+	0.831985i	$0.312796\pi$
$992$	−11778.1	−0.376971
$993$	−1807.98	−0.0577789
$994$	0	0
$995$	19873.8	0.633209
$996$	−28015.0	−0.891254
$997$	−31429.7	−0.998383	−0.499191	−	0.866492i	$-0.666370\pi$
$997$	−31429.7	−0.998383	−0.499191	+	0.866492i	$0.666370\pi$
$998$	−1664.12	−0.0527825
$999$	−3409.75	−0.107988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.p.1.2		5
7.6	odd	2		231.4.a.l.1.2	✓	5
21.20	even	2		693.4.a.n.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.l.1.2	✓	5	7.6	odd	2
693.4.a.n.1.4		5	21.20	even	2
1617.4.a.p.1.2		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-0.300143 q^{2} -3.00000 q^{3} -7.90991 q^{4} +20.3930 q^{5} +0.900430 q^{6} +4.77526 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.300143 q^{2} -3.00000 q^{3} -7.90991 q^{4} +20.3930 q^{5} +0.900430 q^{6} +4.77526 q^{8} +9.00000 q^{9} -6.12084 q^{10} +11.0000 q^{11} +23.7297 q^{12} -14.2196 q^{13} -61.1791 q^{15} +61.8460 q^{16} -137.618 q^{17} -2.70129 q^{18} +44.1690 q^{19} -161.307 q^{20} -3.30158 q^{22} +71.7916 q^{23} -14.3258 q^{24} +290.876 q^{25} +4.26793 q^{26} -27.0000 q^{27} -59.5108 q^{29} +18.3625 q^{30} +207.490 q^{31} -56.7647 q^{32} -33.0000 q^{33} +41.3053 q^{34} -71.1892 q^{36} +126.287 q^{37} -13.2570 q^{38} +42.6589 q^{39} +97.3821 q^{40} +283.938 q^{41} -179.170 q^{43} -87.0091 q^{44} +183.537 q^{45} -21.5478 q^{46} -94.8748 q^{47} -185.538 q^{48} -87.3047 q^{50} +412.855 q^{51} +112.476 q^{52} +727.121 q^{53} +8.10387 q^{54} +224.324 q^{55} -132.507 q^{57} +17.8618 q^{58} -677.153 q^{59} +483.922 q^{60} -210.226 q^{61} -62.2767 q^{62} -477.731 q^{64} -289.981 q^{65} +9.90474 q^{66} -428.085 q^{67} +1088.55 q^{68} -215.375 q^{69} +419.232 q^{71} +42.9773 q^{72} -921.181 q^{73} -37.9042 q^{74} -872.629 q^{75} -349.373 q^{76} -12.8038 q^{78} +895.977 q^{79} +1261.23 q^{80} +81.0000 q^{81} -85.2222 q^{82} -1180.59 q^{83} -2806.46 q^{85} +53.7767 q^{86} +178.532 q^{87} +52.5278 q^{88} -8.28883 q^{89} -55.0876 q^{90} -567.866 q^{92} -622.469 q^{93} +28.4760 q^{94} +900.740 q^{95} +170.294 q^{96} +828.982 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9	\( 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9} - 55 q^{10} + 55 q^{11} - 63 q^{12} - 111 q^{13} + 21 q^{15} + 201 q^{16} - 136 q^{17} + 45 q^{18} - 111 q^{19} - 219 q^{20} + 55 q^{22} - 28 q^{23} - 180 q^{24} + 190 q^{25} + q^{26} - 135 q^{27} + 61 q^{29} + 165 q^{30} + 280 q^{31} + 535 q^{32} - 165 q^{33} + 572 q^{34} + 189 q^{36} - 41 q^{37} - 267 q^{38} + 333 q^{39} + 336 q^{40} - 426 q^{41} + 424 q^{43} + 231 q^{44} - 63 q^{45} + 140 q^{46} - 75 q^{47} - 603 q^{48} + 490 q^{50} + 408 q^{51} + 269 q^{52} + 1500 q^{53} - 135 q^{54} - 77 q^{55} + 333 q^{57} - 1767 q^{58} - 757 q^{59} + 657 q^{60} - 658 q^{61} + 568 q^{62} - 748 q^{64} + 537 q^{65} - 165 q^{66} - 583 q^{67} + 1650 q^{68} + 84 q^{69} - 764 q^{71} + 540 q^{72} - 875 q^{73} - 825 q^{74} - 570 q^{75} - 213 q^{76} - 3 q^{78} - 244 q^{79} + 2577 q^{80} + 405 q^{81} + 2006 q^{82} - 924 q^{83} - 1402 q^{85} + 1272 q^{86} - 183 q^{87} + 660 q^{88} + 1110 q^{89} - 495 q^{90} - 2046 q^{92} - 840 q^{93} + 3349 q^{94} + 1923 q^{95} - 1605 q^{96} + 852 q^{97} + 495 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9 - 55 * q^10 + 55 * q^11 - 63 * q^12 - 111 * q^13 + 21 * q^15 + 201 * q^16 - 136 * q^17 + 45 * q^18 - 111 * q^19 - 219 * q^20 + 55 * q^22 - 28 * q^23 - 180 * q^24 + 190 * q^25 + q^26 - 135 * q^27 + 61 * q^29 + 165 * q^30 + 280 * q^31 + 535 * q^32 - 165 * q^33 + 572 * q^34 + 189 * q^36 - 41 * q^37 - 267 * q^38 + 333 * q^39 + 336 * q^40 - 426 * q^41 + 424 * q^43 + 231 * q^44 - 63 * q^45 + 140 * q^46 - 75 * q^47 - 603 * q^48 + 490 * q^50 + 408 * q^51 + 269 * q^52 + 1500 * q^53 - 135 * q^54 - 77 * q^55 + 333 * q^57 - 1767 * q^58 - 757 * q^59 + 657 * q^60 - 658 * q^61 + 568 * q^62 - 748 * q^64 + 537 * q^65 - 165 * q^66 - 583 * q^67 + 1650 * q^68 + 84 * q^69 - 764 * q^71 + 540 * q^72 - 875 * q^73 - 825 * q^74 - 570 * q^75 - 213 * q^76 - 3 * q^78 - 244 * q^79 + 2577 * q^80 + 405 * q^81 + 2006 * q^82 - 924 * q^83 - 1402 * q^85 + 1272 * q^86 - 183 * q^87 + 660 * q^88 + 1110 * q^89 - 495 * q^90 - 2046 * q^92 - 840 * q^93 + 3349 * q^94 + 1923 * q^95 - 1605 * q^96 + 852 * q^97 + 495 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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