LMFDB - Embedded newform 1775.4.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1775,4,Mod(1,1775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1775, 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("1775.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1775 = 5^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1775.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:	$104.728390260$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} - 89 x^{18} + 952 x^{17} + 2911 x^{16} - 41549 x^{15} - 37799 x^{14} + \cdots - 106929408 $ x^20 - 9x^19 - 89x^18 + 952x^17 + 2911x^16 - 41549x^15 - 37799x^14 + 974485x^13 - 43478x^12 - 13402754x^11 + 6726996x^10 + 110353987x^9 - 76601582x^8 - 528296868x^7 + 380540584x^6 + 1335398700x^5 - 833784408x^4 - 1402468992x^3 + 573826752x^2 + 308840768*x - 106929408
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 355)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-2.71848$ of defining polynomial
Character	$\chi$	$=$	1775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.71848 q^{2} -8.68292 q^{3} -0.609867 q^{4} -23.6043 q^{6} -33.0011 q^{7} -23.4058 q^{8} +48.3931 q^{9} +O(q^{10})$	\(q+2.71848 q^{2} -8.68292 q^{3} -0.609867 q^{4} -23.6043 q^{6} -33.0011 q^{7} -23.4058 q^{8} +48.3931 q^{9} +37.5555 q^{11} +5.29543 q^{12} -35.5285 q^{13} -89.7127 q^{14} -58.7491 q^{16} +45.5250 q^{17} +131.556 q^{18} -84.7351 q^{19} +286.546 q^{21} +102.094 q^{22} +137.202 q^{23} +203.230 q^{24} -96.5835 q^{26} -185.755 q^{27} +20.1263 q^{28} +269.622 q^{29} -171.082 q^{31} +27.5377 q^{32} -326.092 q^{33} +123.759 q^{34} -29.5134 q^{36} -110.527 q^{37} -230.351 q^{38} +308.491 q^{39} -231.349 q^{41} +778.968 q^{42} +291.806 q^{43} -22.9039 q^{44} +372.980 q^{46} +620.295 q^{47} +510.114 q^{48} +746.070 q^{49} -395.290 q^{51} +21.6676 q^{52} -208.870 q^{53} -504.971 q^{54} +772.414 q^{56} +735.748 q^{57} +732.962 q^{58} +711.267 q^{59} -612.219 q^{61} -465.084 q^{62} -1597.02 q^{63} +544.854 q^{64} -886.473 q^{66} -9.03382 q^{67} -27.7642 q^{68} -1191.31 q^{69} +71.0000 q^{71} -1132.68 q^{72} +125.186 q^{73} -300.464 q^{74} +51.6771 q^{76} -1239.37 q^{77} +838.627 q^{78} -195.974 q^{79} +306.281 q^{81} -628.917 q^{82} -385.077 q^{83} -174.755 q^{84} +793.269 q^{86} -2341.11 q^{87} -879.015 q^{88} +865.972 q^{89} +1172.48 q^{91} -83.6748 q^{92} +1485.50 q^{93} +1686.26 q^{94} -239.108 q^{96} -1454.32 q^{97} +2028.18 q^{98} +1817.43 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9}+O(q^{10}) $ 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9	\( 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9} + 62 q^{11} - 160 q^{12} - 232 q^{13} + 56 q^{14} + 387 q^{16} - 314 q^{17} - 224 q^{18} + 54 q^{19} + 58 q^{21} + 123 q^{22} - 344 q^{23} + 419 q^{24} - 387 q^{26} - 326 q^{27} - 786 q^{28} + 748 q^{29} - 18 q^{31} - 345 q^{32} - 746 q^{33} - 142 q^{34} + 90 q^{36} - 858 q^{37} - 723 q^{38} + 210 q^{39} + 386 q^{41} + 237 q^{42} - 1210 q^{43} + 1105 q^{44} - 57 q^{46} - 320 q^{47} - 2280 q^{48} + 1576 q^{49} - 350 q^{51} - 780 q^{52} - 2066 q^{53} - 536 q^{54} + 938 q^{56} - 710 q^{57} - 1852 q^{58} + 1198 q^{59} + 284 q^{61} - 2444 q^{62} - 732 q^{63} + 1118 q^{64} - 219 q^{66} - 976 q^{67} - 2904 q^{68} + 1026 q^{69} + 1420 q^{71} - 3374 q^{72} - 4310 q^{73} + 955 q^{74} + 740 q^{76} - 5196 q^{77} - 61 q^{78} - 340 q^{79} + 2556 q^{81} - 1191 q^{82} + 354 q^{83} - 1955 q^{84} + 1248 q^{86} - 3392 q^{87} - 135 q^{88} - 1446 q^{89} - 240 q^{91} - 4114 q^{92} + 1066 q^{93} - 3985 q^{94} - 2145 q^{96} - 3282 q^{97} + 4708 q^{98} - 6506 q^{99}+O(q^{100}) \) 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9 + 62 * q^11 - 160 * q^12 - 232 * q^13 + 56 * q^14 + 387 * q^16 - 314 * q^17 - 224 * q^18 + 54 * q^19 + 58 * q^21 + 123 * q^22 - 344 * q^23 + 419 * q^24 - 387 * q^26 - 326 * q^27 - 786 * q^28 + 748 * q^29 - 18 * q^31 - 345 * q^32 - 746 * q^33 - 142 * q^34 + 90 * q^36 - 858 * q^37 - 723 * q^38 + 210 * q^39 + 386 * q^41 + 237 * q^42 - 1210 * q^43 + 1105 * q^44 - 57 * q^46 - 320 * q^47 - 2280 * q^48 + 1576 * q^49 - 350 * q^51 - 780 * q^52 - 2066 * q^53 - 536 * q^54 + 938 * q^56 - 710 * q^57 - 1852 * q^58 + 1198 * q^59 + 284 * q^61 - 2444 * q^62 - 732 * q^63 + 1118 * q^64 - 219 * q^66 - 976 * q^67 - 2904 * q^68 + 1026 * q^69 + 1420 * q^71 - 3374 * q^72 - 4310 * q^73 + 955 * q^74 + 740 * q^76 - 5196 * q^77 - 61 * q^78 - 340 * q^79 + 2556 * q^81 - 1191 * q^82 + 354 * q^83 - 1955 * q^84 + 1248 * q^86 - 3392 * q^87 - 135 * q^88 - 1446 * q^89 - 240 * q^91 - 4114 * q^92 + 1066 * q^93 - 3985 * q^94 - 2145 * q^96 - 3282 * q^97 + 4708 * q^98 - 6506 * 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 $

$2$	2.71848	0.961128	0.480564	−	0.876960i	$-0.340432\pi$
$2$	2.71848	0.961128	0.480564	+	0.876960i	$0.340432\pi$
$3$	−8.68292	−1.67103	−0.835515	−	0.549468i	$-0.814830\pi$
$3$	−8.68292	−1.67103	−0.835515	+	0.549468i	$0.814830\pi$
$4$	−0.609867	−0.0762334
$5$	0	0
$5$	0	0
$6$	−23.6043	−1.60607
$7$	−33.0011	−1.78189	−0.890945	−	0.454112i	$-0.849957\pi$
$7$	−33.0011	−1.78189	−0.890945	+	0.454112i	$0.849957\pi$
$8$	−23.4058	−1.03440
$9$	48.3931	1.79234
$10$	0	0
$11$	37.5555	1.02940	0.514700	−	0.857370i	$-0.327903\pi$
$11$	37.5555	1.02940	0.514700	+	0.857370i	$0.327903\pi$
$12$	5.29543	0.127388
$13$	−35.5285	−0.757987	−0.378993	−	0.925399i	$-0.623730\pi$
$13$	−35.5285	−0.757987	−0.378993	+	0.925399i	$0.623730\pi$
$14$	−89.7127	−1.71262
$15$	0	0
$16$	−58.7491	−0.917955
$17$	45.5250	0.649496	0.324748	−	0.945801i	$-0.394721\pi$
$17$	45.5250	0.649496	0.324748	+	0.945801i	$0.394721\pi$
$18$	131.556	1.72267
$19$	−84.7351	−1.02314	−0.511568	−	0.859243i	$-0.670935\pi$
$19$	−84.7351	−1.02314	−0.511568	+	0.859243i	$0.670935\pi$
$20$	0	0
$21$	286.546	2.97759
$22$	102.094	0.989386
$23$	137.202	1.24385	0.621924	−	0.783077i	$-0.286351\pi$
$23$	137.202	1.24385	0.621924	+	0.783077i	$0.286351\pi$
$24$	203.230	1.72851
$25$	0	0
$26$	−96.5835	−0.728522
$27$	−185.755	−1.32402
$28$	20.1263	0.135839
$29$	269.622	1.72647	0.863234	−	0.504804i	$-0.168435\pi$
$29$	269.622	1.72647	0.863234	+	0.504804i	$0.168435\pi$
$30$	0	0
$31$	−171.082	−0.991204	−0.495602	−	0.868550i	$-0.665052\pi$
$31$	−171.082	−0.991204	−0.495602	+	0.868550i	$0.665052\pi$
$32$	27.5377	0.152126
$33$	−326.092	−1.72016
$34$	123.759	0.624248
$35$	0	0
$36$	−29.5134	−0.136636
$37$	−110.527	−0.491093	−0.245547	−	0.969385i	$-0.578967\pi$
$37$	−110.527	−0.491093	−0.245547	+	0.969385i	$0.578967\pi$
$38$	−230.351	−0.983364
$39$	308.491	1.26662
$40$	0	0
$41$	−231.349	−0.881235	−0.440617	−	0.897695i	$-0.645240\pi$
$41$	−231.349	−0.881235	−0.440617	+	0.897695i	$0.645240\pi$
$42$	778.968	2.86184
$43$	291.806	1.03488	0.517442	−	0.855718i	$-0.326884\pi$
$43$	291.806	1.03488	0.517442	+	0.855718i	$0.326884\pi$
$44$	−22.9039	−0.0784747
$45$	0	0
$46$	372.980	1.19550
$47$	620.295	1.92509	0.962547	−	0.271116i	$-0.0873927\pi$
$47$	620.295	1.92509	0.962547	+	0.271116i	$0.0873927\pi$
$48$	510.114	1.53393
$49$	746.070	2.17513
$50$	0	0
$51$	−395.290	−1.08533
$52$	21.6676	0.0577839
$53$	−208.870	−0.541331	−0.270666	−	0.962673i	$-0.587244\pi$
$53$	−208.870	−0.541331	−0.270666	+	0.962673i	$0.587244\pi$
$54$	−504.971	−1.27255
$55$	0	0
$56$	772.414	1.84318
$57$	735.748	1.70969
$58$	732.962	1.65936
$59$	711.267	1.56948	0.784738	−	0.619828i	$-0.212798\pi$
$59$	711.267	1.56948	0.784738	+	0.619828i	$0.212798\pi$
$60$	0	0
$61$	−612.219	−1.28503	−0.642513	−	0.766274i	$-0.722108\pi$
$61$	−612.219	−1.28503	−0.642513	+	0.766274i	$0.722108\pi$
$62$	−465.084	−0.952673
$63$	−1597.02	−3.19375
$64$	544.854	1.06417
$65$	0	0
$66$	−886.473	−1.65329
$67$	−9.03382	−0.0164725	−0.00823625	−	0.999966i	$-0.502622\pi$
$67$	−9.03382	−0.0164725	−0.00823625	+	0.999966i	$0.502622\pi$
$68$	−27.7642	−0.0495133
$69$	−1191.31	−2.07851
$70$	0	0
$71$	71.0000	0.118678
$71$	71.0000	0.118678
$72$	−1132.68	−1.85399
$73$	125.186	0.200711	0.100356	−	0.994952i	$-0.468002\pi$
$73$	125.186	0.200711	0.100356	+	0.994952i	$0.468002\pi$
$74$	−300.464	−0.472003
$75$	0	0
$76$	51.6771	0.0779970
$77$	−1239.37	−1.83428
$78$	838.627	1.21738
$79$	−195.974	−0.279098	−0.139549	−	0.990215i	$-0.544565\pi$
$79$	−195.974	−0.279098	−0.139549	+	0.990215i	$0.544565\pi$
$80$	0	0
$81$	306.281	0.420139
$82$	−628.917	−0.846979
$83$	−385.077	−0.509249	−0.254625	−	0.967040i	$-0.581952\pi$
$83$	−385.077	−0.509249	−0.254625	+	0.967040i	$0.581952\pi$
$84$	−174.755	−0.226992
$85$	0	0
$86$	793.269	0.994656
$87$	−2341.11	−2.88498
$88$	−879.015	−1.06481
$89$	865.972	1.03138	0.515690	−	0.856775i	$-0.327536\pi$
$89$	865.972	1.03138	0.515690	+	0.856775i	$0.327536\pi$
$90$	0	0
$91$	1172.48	1.35065
$92$	−83.6748	−0.0948228
$93$	1485.50	1.65633
$94$	1686.26	1.85026
$95$	0	0
$96$	−239.108	−0.254206
$97$	−1454.32	−1.52231	−0.761153	−	0.648573i	$-0.775366\pi$
$97$	−1454.32	−1.52231	−0.761153	+	0.648573i	$0.775366\pi$
$98$	2028.18	2.09058
$99$	1817.43	1.84503
$100$	0	0
$101$	−1862.53	−1.83494	−0.917470	−	0.397806i	$-0.869772\pi$
$101$	−1862.53	−1.83494	−0.917470	+	0.397806i	$0.869772\pi$
$102$	−1074.59	−1.04314
$103$	76.5244	0.0732056	0.0366028	−	0.999330i	$-0.488346\pi$
$103$	76.5244	0.0732056	0.0366028	+	0.999330i	$0.488346\pi$
$104$	831.571	0.784060
$105$	0	0
$106$	−567.810	−0.520289
$107$	981.030	0.886353	0.443176	−	0.896434i	$-0.353852\pi$
$107$	981.030	0.886353	0.443176	+	0.896434i	$0.353852\pi$
$108$	113.286	0.100935
$109$	334.488	0.293928	0.146964	−	0.989142i	$-0.453050\pi$
$109$	334.488	0.293928	0.146964	+	0.989142i	$0.453050\pi$
$110$	0	0
$111$	959.693	0.820631
$112$	1938.78	1.63569
$113$	−1202.63	−1.00119	−0.500593	−	0.865683i	$-0.666885\pi$
$113$	−1202.63	−1.00119	−0.500593	+	0.865683i	$0.666885\pi$
$114$	2000.12	1.64323
$115$	0	0
$116$	−164.434	−0.131614
$117$	−1719.33	−1.35857
$118$	1933.56	1.50847
$119$	−1502.37	−1.15733
$120$	0	0
$121$	79.4157	0.0596662
$122$	−1664.31	−1.23507
$123$	2008.78	1.47257
$124$	104.338	0.0755628
$125$	0	0
$126$	−4341.48	−3.06960
$127$	1858.67	1.29866	0.649331	−	0.760506i	$-0.275049\pi$
$127$	1858.67	1.29866	0.649331	+	0.760506i	$0.275049\pi$
$128$	1260.87	0.870675
$129$	−2533.73	−1.72932
$130$	0	0
$131$	545.635	0.363911	0.181956	−	0.983307i	$-0.441757\pi$
$131$	545.635	0.363911	0.181956	+	0.983307i	$0.441757\pi$
$132$	198.872	0.131134
$133$	2796.35	1.82311
$134$	−24.5583	−0.0158322
$135$	0	0
$136$	−1065.55	−0.671837
$137$	−1328.72	−0.828615	−0.414307	−	0.910137i	$-0.635976\pi$
$137$	−1328.72	−0.828615	−0.414307	+	0.910137i	$0.635976\pi$
$138$	−3238.56	−1.99771
$139$	−2211.55	−1.34951	−0.674753	−	0.738044i	$-0.735750\pi$
$139$	−2211.55	−1.34951	−0.674753	+	0.738044i	$0.735750\pi$
$140$	0	0
$141$	−5385.98	−3.21689
$142$	193.012	0.114065
$143$	−1334.29	−0.780272
$144$	−2843.05	−1.64529
$145$	0	0
$146$	340.316	0.192909
$147$	−6478.06	−3.63471
$148$	67.4065	0.0374377
$149$	1392.62	0.765690	0.382845	−	0.923813i	$-0.374944\pi$
$149$	1392.62	0.765690	0.382845	+	0.923813i	$0.374944\pi$
$150$	0	0
$151$	1975.67	1.06475	0.532377	−	0.846508i	$-0.321299\pi$
$151$	1975.67	1.06475	0.532377	+	0.846508i	$0.321299\pi$
$152$	1983.29	1.05833
$153$	2203.10	1.16412
$154$	−3369.21	−1.76298
$155$	0	0
$156$	−188.139	−0.0965586
$157$	1952.14	0.992342	0.496171	−	0.868225i	$-0.334739\pi$
$157$	1952.14	0.992342	0.496171	+	0.868225i	$0.334739\pi$
$158$	−532.750	−0.268249
$159$	1813.61	0.904580
$160$	0	0
$161$	−4527.80	−2.21640
$162$	832.619	0.403807
$163$	1828.13	0.878466	0.439233	−	0.898373i	$-0.355250\pi$
$163$	1828.13	0.878466	0.439233	+	0.898373i	$0.355250\pi$
$164$	141.092	0.0671795
$165$	0	0
$166$	−1046.82	−0.489453
$167$	−2721.96	−1.26127	−0.630634	−	0.776081i	$-0.717205\pi$
$167$	−2721.96	−1.26127	−0.630634	+	0.776081i	$0.717205\pi$
$168$	−6706.81	−3.08001
$169$	−934.727	−0.425456
$170$	0	0
$171$	−4100.60	−1.83380
$172$	−177.963	−0.0788927
$173$	−95.2802	−0.0418729	−0.0209365	−	0.999781i	$-0.506665\pi$
$173$	−95.2802	−0.0418729	−0.0209365	+	0.999781i	$0.506665\pi$
$174$	−6364.26	−2.77283
$175$	0	0
$176$	−2206.35	−0.944944
$177$	−6175.88	−2.62264
$178$	2354.13	0.991288
$179$	−2469.60	−1.03121	−0.515604	−	0.856827i	$-0.672433\pi$
$179$	−2469.60	−1.03121	−0.515604	+	0.856827i	$0.672433\pi$
$180$	0	0
$181$	−3009.42	−1.23585	−0.617924	−	0.786238i	$-0.712026\pi$
$181$	−3009.42	−1.23585	−0.617924	+	0.786238i	$0.712026\pi$
$182$	3187.36	1.29815
$183$	5315.85	2.14732
$184$	−3211.31	−1.28663
$185$	0	0
$186$	4038.29	1.59194
$187$	1709.71	0.668592
$188$	−378.298	−0.146756
$189$	6130.11	2.35926
$190$	0	0
$191$	2523.33	0.955926	0.477963	−	0.878380i	$-0.341375\pi$
$191$	2523.33	0.955926	0.477963	+	0.878380i	$0.341375\pi$
$192$	−4730.92	−1.77825
$193$	−989.128	−0.368907	−0.184453	−	0.982841i	$-0.559051\pi$
$193$	−989.128	−0.368907	−0.184453	+	0.982841i	$0.559051\pi$
$194$	−3953.53	−1.46313
$195$	0	0
$196$	−455.003	−0.165817
$197$	485.236	0.175491	0.0877453	−	0.996143i	$-0.472034\pi$
$197$	485.236	0.175491	0.0877453	+	0.996143i	$0.472034\pi$
$198$	4940.64	1.77331
$199$	543.990	0.193781	0.0968905	−	0.995295i	$-0.469110\pi$
$199$	543.990	0.193781	0.0968905	+	0.995295i	$0.469110\pi$
$200$	0	0
$201$	78.4400	0.0275260
$202$	−5063.26	−1.76361
$203$	−8897.81	−3.07638
$204$	241.074	0.0827381
$205$	0	0
$206$	208.030	0.0703599
$207$	6639.62	2.22940
$208$	2087.27	0.695798
$209$	−3182.27	−1.05322
$210$	0	0
$211$	3806.59	1.24197	0.620986	−	0.783821i	$-0.286732\pi$
$211$	3806.59	1.24197	0.620986	+	0.783821i	$0.286732\pi$
$212$	127.383	0.0412675
$213$	−616.487	−0.198315
$214$	2666.91	0.851898
$215$	0	0
$216$	4347.73	1.36956
$217$	5645.90	1.76622
$218$	909.298	0.282502
$219$	−1086.98	−0.335395
$220$	0	0
$221$	−1617.43	−0.492309
$222$	2608.91	0.788731
$223$	−841.626	−0.252733	−0.126366	−	0.991984i	$-0.540332\pi$
$223$	−841.626	−0.252733	−0.126366	+	0.991984i	$0.540332\pi$
$224$	−908.773	−0.271071
$225$	0	0
$226$	−3269.33	−0.962268
$227$	4852.17	1.41872	0.709360	−	0.704846i	$-0.248984\pi$
$227$	4852.17	1.41872	0.709360	+	0.704846i	$0.248984\pi$
$228$	−448.709	−0.130335
$229$	−1202.01	−0.346860	−0.173430	−	0.984846i	$-0.555485\pi$
$229$	−1202.01	−0.346860	−0.173430	+	0.984846i	$0.555485\pi$
$230$	0	0
$231$	10761.4	3.06513
$232$	−6310.71	−1.78585
$233$	−5732.51	−1.61180	−0.805899	−	0.592052i	$-0.798318\pi$
$233$	−5732.51	−1.61180	−0.805899	+	0.592052i	$0.798318\pi$
$234$	−4673.98	−1.30576
$235$	0	0
$236$	−433.778	−0.119646
$237$	1701.62	0.466381
$238$	−4084.17	−1.11234
$239$	2962.09	0.801680	0.400840	−	0.916148i	$-0.368718\pi$
$239$	2962.09	0.801680	0.400840	+	0.916148i	$0.368718\pi$
$240$	0	0
$241$	−4305.40	−1.15077	−0.575384	−	0.817883i	$-0.695148\pi$
$241$	−4305.40	−1.15077	−0.575384	+	0.817883i	$0.695148\pi$
$242$	215.890	0.0573469
$243$	2355.97	0.621957
$244$	373.372	0.0979619
$245$	0	0
$246$	5460.84	1.41533
$247$	3010.51	0.775523
$248$	4004.31	1.02530
$249$	3343.59	0.850970
$250$	0	0
$251$	−3528.88	−0.887413	−0.443706	−	0.896172i	$-0.646337\pi$
$251$	−3528.88	−0.887413	−0.443706	+	0.896172i	$0.646337\pi$
$252$	973.973	0.243470
$253$	5152.68	1.28042
$254$	5052.75	1.24818
$255$	0	0
$256$	−931.173	−0.227337
$257$	703.796	0.170823	0.0854116	−	0.996346i	$-0.472779\pi$
$257$	703.796	0.170823	0.0854116	+	0.996346i	$0.472779\pi$
$258$	−6887.89	−1.66210
$259$	3647.49	0.875074
$260$	0	0
$261$	13047.9	3.09442
$262$	1483.30	0.349765
$263$	−4170.20	−0.977740	−0.488870	−	0.872357i	$-0.662591\pi$
$263$	−4170.20	−0.977740	−0.488870	+	0.872357i	$0.662591\pi$
$264$	7632.42	1.77933
$265$	0	0
$266$	7601.82	1.75225
$267$	−7519.17	−1.72347
$268$	5.50943	0.00125575
$269$	3278.14	0.743017	0.371509	−	0.928430i	$-0.378841\pi$
$269$	3278.14	0.743017	0.371509	+	0.928430i	$0.378841\pi$
$270$	0	0
$271$	−1821.29	−0.408248	−0.204124	−	0.978945i	$-0.565435\pi$
$271$	−1821.29	−0.408248	−0.204124	+	0.978945i	$0.565435\pi$
$272$	−2674.55	−0.596208
$273$	−10180.5	−2.25697
$274$	−3612.10	−0.796405
$275$	0	0
$276$	726.541	0.158452
$277$	−1851.18	−0.401541	−0.200771	−	0.979638i	$-0.564345\pi$
$277$	−1851.18	−0.401541	−0.200771	+	0.979638i	$0.564345\pi$
$278$	−6012.05	−1.29705
$279$	−8279.22	−1.77657
$280$	0	0
$281$	8053.71	1.70977	0.854883	−	0.518821i	$-0.173629\pi$
$281$	8053.71	1.70977	0.854883	+	0.518821i	$0.173629\pi$
$282$	−14641.7	−3.09184
$283$	4228.20	0.888128	0.444064	−	0.895995i	$-0.353536\pi$
$283$	4228.20	0.888128	0.444064	+	0.895995i	$0.353536\pi$
$284$	−43.3006	−0.00904724
$285$	0	0
$286$	−3627.24	−0.749941
$287$	7634.76	1.57026
$288$	1332.63	0.272661
$289$	−2840.48	−0.578155
$290$	0	0
$291$	12627.7	2.54382
$292$	−76.3469	−0.0153009
$293$	−8021.65	−1.59942	−0.799709	−	0.600387i	$-0.795013\pi$
$293$	−8021.65	−1.59942	−0.799709	+	0.600387i	$0.795013\pi$
$294$	−17610.5	−3.49342
$295$	0	0
$296$	2586.96	0.507986
$297$	−6976.12	−1.36295
$298$	3785.81	0.735926
$299$	−4874.57	−0.942821
$300$	0	0
$301$	−9629.91	−1.84405
$302$	5370.82	1.02336
$303$	16172.2	3.06624
$304$	4978.11	0.939192
$305$	0	0
$306$	5989.07	1.11886
$307$	−2731.63	−0.507826	−0.253913	−	0.967227i	$-0.581718\pi$
$307$	−2731.63	−0.507826	−0.253913	+	0.967227i	$0.581718\pi$
$308$	755.852	0.139833
$309$	−664.455	−0.122329
$310$	0	0
$311$	1144.13	0.208609	0.104305	−	0.994545i	$-0.466738\pi$
$311$	1144.13	0.208609	0.104305	+	0.994545i	$0.466738\pi$
$312$	−7220.47	−1.31019
$313$	8366.24	1.51082	0.755412	−	0.655250i	$-0.227437\pi$
$313$	8366.24	1.51082	0.755412	+	0.655250i	$0.227437\pi$
$314$	5306.85	0.953768
$315$	0	0
$316$	119.518	0.0212766
$317$	6420.00	1.13749	0.568743	−	0.822515i	$-0.307430\pi$
$317$	6420.00	1.13749	0.568743	+	0.822515i	$0.307430\pi$
$318$	4930.25	0.869417
$319$	10125.8	1.77723
$320$	0	0
$321$	−8518.21	−1.48112
$322$	−12308.7	−2.13024
$323$	−3857.56	−0.664522
$324$	−186.791	−0.0320286
$325$	0	0
$326$	4969.73	0.844318
$327$	−2904.33	−0.491161
$328$	5414.89	0.911547
$329$	−20470.4	−3.43030
$330$	0	0
$331$	−7528.70	−1.25020	−0.625098	−	0.780547i	$-0.714941\pi$
$331$	−7528.70	−1.25020	−0.625098	+	0.780547i	$0.714941\pi$
$332$	234.846	0.0388218
$333$	−5348.73	−0.880205
$334$	−7399.60	−1.21224
$335$	0	0
$336$	−16834.3	−2.73329
$337$	−4338.18	−0.701233	−0.350617	−	0.936519i	$-0.614028\pi$
$337$	−4338.18	−0.701233	−0.350617	+	0.936519i	$0.614028\pi$
$338$	−2541.04	−0.408918
$339$	10442.4	1.67301
$340$	0	0
$341$	−6425.09	−1.02035
$342$	−11147.4	−1.76252
$343$	−13301.7	−2.09395
$344$	−6829.94	−1.07048
$345$	0	0
$346$	−259.017	−0.0402452
$347$	−6731.46	−1.04139	−0.520697	−	0.853742i	$-0.674328\pi$
$347$	−6731.46	−1.04139	−0.520697	+	0.853742i	$0.674328\pi$
$348$	1427.76	0.219932
$349$	−1848.21	−0.283475	−0.141737	−	0.989904i	$-0.545269\pi$
$349$	−1848.21	−0.283475	−0.141737	+	0.989904i	$0.545269\pi$
$350$	0	0
$351$	6599.59	1.00359
$352$	1034.19	0.156598
$353$	12585.1	1.89755	0.948775	−	0.315953i	$-0.102324\pi$
$353$	12585.1	1.89755	0.948775	+	0.315953i	$0.102324\pi$
$354$	−16789.0	−2.52069
$355$	0	0
$356$	−528.128	−0.0786256
$357$	13045.0	1.93393
$358$	−6713.55	−0.991123
$359$	−11256.9	−1.65492	−0.827461	−	0.561523i	$-0.810216\pi$
$359$	−11256.9	−1.65492	−0.827461	+	0.561523i	$0.810216\pi$
$360$	0	0
$361$	321.040	0.0468057
$362$	−8181.04	−1.18781
$363$	−689.561	−0.0997040
$364$	−715.055	−0.102965
$365$	0	0
$366$	14451.0	2.06385
$367$	11103.1	1.57923	0.789617	−	0.613600i	$-0.210279\pi$
$367$	11103.1	1.57923	0.789617	+	0.613600i	$0.210279\pi$
$368$	−8060.48	−1.14180
$369$	−11195.7	−1.57947
$370$	0	0
$371$	6892.94	0.964592
$372$	−905.955	−0.126268
$373$	−4003.92	−0.555805	−0.277902	−	0.960609i	$-0.589639\pi$
$373$	−4003.92	−0.555805	−0.277902	+	0.960609i	$0.589639\pi$
$374$	4647.82	0.642602
$375$	0	0
$376$	−14518.5	−1.99131
$377$	−9579.27	−1.30864
$378$	16664.6	2.26755
$379$	7262.31	0.984274	0.492137	−	0.870518i	$-0.336216\pi$
$379$	7262.31	0.984274	0.492137	+	0.870518i	$0.336216\pi$
$380$	0	0
$381$	−16138.7	−2.17010
$382$	6859.63	0.918767
$383$	−4740.30	−0.632423	−0.316211	−	0.948689i	$-0.602411\pi$
$383$	−4740.30	−0.632423	−0.316211	+	0.948689i	$0.602411\pi$
$384$	−10948.1	−1.45492
$385$	0	0
$386$	−2688.92	−0.354566
$387$	14121.4	1.85486
$388$	886.941	0.116050
$389$	9395.93	1.22466	0.612330	−	0.790603i	$-0.290233\pi$
$389$	9395.93	1.22466	0.612330	+	0.790603i	$0.290233\pi$
$390$	0	0
$391$	6246.10	0.807875
$392$	−17462.3	−2.24995
$393$	−4737.71	−0.608106
$394$	1319.10	0.168669
$395$	0	0
$396$	−1108.39	−0.140653
$397$	1484.03	0.187611	0.0938054	−	0.995591i	$-0.470097\pi$
$397$	1484.03	0.187611	0.0938054	+	0.995591i	$0.470097\pi$
$398$	1478.83	0.186248
$399$	−24280.5	−3.04648
$400$	0	0
$401$	3705.09	0.461405	0.230703	−	0.973024i	$-0.425898\pi$
$401$	3705.09	0.461405	0.230703	+	0.973024i	$0.425898\pi$
$402$	213.238	0.0264560
$403$	6078.30	0.751319
$404$	1135.90	0.139884
$405$	0	0
$406$	−24188.5	−2.95679
$407$	−4150.88	−0.505532
$408$	9252.05	1.12266
$409$	−2007.14	−0.242657	−0.121329	−	0.992612i	$-0.538715\pi$
$409$	−2007.14	−0.242657	−0.121329	+	0.992612i	$0.538715\pi$
$410$	0	0
$411$	11537.2	1.38464
$412$	−46.6697	−0.00558071
$413$	−23472.6	−2.79663
$414$	18049.7	2.14274
$415$	0	0
$416$	−978.372	−0.115309
$417$	19202.7	2.25506
$418$	−8650.94	−1.01228
$419$	7168.99	0.835867	0.417933	−	0.908478i	$-0.362755\pi$
$419$	7168.99	0.835867	0.417933	+	0.908478i	$0.362755\pi$
$420$	0	0
$421$	7936.42	0.918759	0.459379	−	0.888240i	$-0.348072\pi$
$421$	7936.42	0.918759	0.459379	+	0.888240i	$0.348072\pi$
$422$	10348.1	1.19369
$423$	30018.0	3.45042
$424$	4888.77	0.559952
$425$	0	0
$426$	−1675.91	−0.190606
$427$	20203.9	2.28978
$428$	−598.298	−0.0675697
$429$	11585.5	1.30386
$430$	0	0
$431$	16678.4	1.86396	0.931982	−	0.362504i	$-0.118078\pi$
$431$	16678.4	1.86396	0.931982	+	0.362504i	$0.118078\pi$
$432$	10912.9	1.21539
$433$	−3118.80	−0.346143	−0.173071	−	0.984909i	$-0.555369\pi$
$433$	−3118.80	−0.346143	−0.173071	+	0.984909i	$0.555369\pi$
$434$	15348.3	1.69756
$435$	0	0
$436$	−203.993	−0.0224071
$437$	−11625.8	−1.27263
$438$	−2954.94	−0.322357
$439$	11383.4	1.23759	0.618793	−	0.785554i	$-0.287622\pi$
$439$	11383.4	1.23759	0.618793	+	0.785554i	$0.287622\pi$
$440$	0	0
$441$	36104.6	3.89857
$442$	−4396.96	−0.473172
$443$	−10169.9	−1.09071	−0.545357	−	0.838204i	$-0.683606\pi$
$443$	−10169.9	−1.09071	−0.545357	+	0.838204i	$0.683606\pi$
$444$	−585.285	−0.0625595
$445$	0	0
$446$	−2287.94	−0.242909
$447$	−12092.0	−1.27949
$448$	−17980.7	−1.89623
$449$	5673.06	0.596276	0.298138	−	0.954523i	$-0.403634\pi$
$449$	5673.06	0.596276	0.298138	+	0.954523i	$0.403634\pi$
$450$	0	0
$451$	−8688.42	−0.907144
$452$	733.445	0.0763238
$453$	−17154.6	−1.77923
$454$	13190.5	1.36357
$455$	0	0
$456$	−17220.7	−1.76850
$457$	−6104.30	−0.624830	−0.312415	−	0.949946i	$-0.601138\pi$
$457$	−6104.30	−0.624830	−0.312415	+	0.949946i	$0.601138\pi$
$458$	−3267.64	−0.333377
$459$	−8456.49	−0.859946
$460$	0	0
$461$	−4956.09	−0.500712	−0.250356	−	0.968154i	$-0.580548\pi$
$461$	−4956.09	−0.500712	−0.250356	+	0.968154i	$0.580548\pi$
$462$	29254.5	2.94598
$463$	8257.18	0.828820	0.414410	−	0.910090i	$-0.363988\pi$
$463$	8257.18	0.828820	0.414410	+	0.910090i	$0.363988\pi$
$464$	−15840.1	−1.58482
$465$	0	0
$466$	−15583.7	−1.54914
$467$	−4037.55	−0.400076	−0.200038	−	0.979788i	$-0.564107\pi$
$467$	−4037.55	−0.400076	−0.200038	+	0.979788i	$0.564107\pi$
$468$	1048.57	0.103568
$469$	298.126	0.0293522
$470$	0	0
$471$	−16950.3	−1.65823
$472$	−16647.7	−1.62346
$473$	10958.9	1.06531
$474$	4625.83	0.448252
$475$	0	0
$476$	916.247	0.0882271
$477$	−10107.9	−0.970249
$478$	8052.38	0.770517
$479$	−12833.4	−1.22416	−0.612081	−	0.790795i	$-0.709667\pi$
$479$	−12833.4	−1.22416	−0.612081	+	0.790795i	$0.709667\pi$
$480$	0	0
$481$	3926.84	0.372242
$482$	−11704.1	−1.10604
$483$	39314.5	3.70367
$484$	−48.4330	−0.00454856
$485$	0	0
$486$	6404.65	0.597780
$487$	−18965.6	−1.76471	−0.882354	−	0.470586i	$-0.844043\pi$
$487$	−18965.6	−1.76471	−0.882354	+	0.470586i	$0.844043\pi$
$488$	14329.4	1.32923
$489$	−15873.5	−1.46794
$490$	0	0
$491$	−14125.6	−1.29833	−0.649163	−	0.760649i	$-0.724881\pi$
$491$	−14125.6	−1.29833	−0.649163	+	0.760649i	$0.724881\pi$
$492$	−1225.09	−0.112259
$493$	12274.5	1.12133
$494$	8184.01	0.745377
$495$	0	0
$496$	10050.9	0.909880
$497$	−2343.07	−0.211471
$498$	9089.49	0.817891
$499$	−14352.5	−1.28758	−0.643792	−	0.765200i	$-0.722640\pi$
$499$	−14352.5	−1.28758	−0.643792	+	0.765200i	$0.722640\pi$
$500$	0	0
$501$	23634.6	2.10761
$502$	−9593.18	−0.852917
$503$	−13872.5	−1.22971	−0.614855	−	0.788640i	$-0.710786\pi$
$503$	−13872.5	−1.22971	−0.614855	+	0.788640i	$0.710786\pi$
$504$	37379.6	3.30361
$505$	0	0
$506$	14007.4	1.23065
$507$	8116.16	0.710949
$508$	−1133.54	−0.0990014
$509$	20524.6	1.78730	0.893650	−	0.448764i	$-0.148136\pi$
$509$	20524.6	1.78730	0.893650	+	0.448764i	$0.148136\pi$
$510$	0	0
$511$	−4131.28	−0.357646
$512$	−12618.4	−1.08918
$513$	15740.0	1.35465
$514$	1913.26	0.164183
$515$	0	0
$516$	1545.24	0.131832
$517$	23295.5	1.98169
$518$	9915.63	0.841058
$519$	827.310	0.0699709
$520$	0	0
$521$	239.408	0.0201318	0.0100659	−	0.999949i	$-0.496796\pi$
$521$	239.408	0.0201318	0.0100659	+	0.999949i	$0.496796\pi$
$522$	35470.3	2.97413
$523$	4173.77	0.348960	0.174480	−	0.984661i	$-0.444176\pi$
$523$	4173.77	0.348960	0.174480	+	0.984661i	$0.444176\pi$
$524$	−332.765	−0.0277422
$525$	0	0
$526$	−11336.6	−0.939733
$527$	−7788.52	−0.643782
$528$	19157.6	1.57903
$529$	6657.29	0.547160
$530$	0	0
$531$	34420.4	2.81303
$532$	−1705.40	−0.138982
$533$	8219.48	0.667964
$534$	−20440.7	−1.65647
$535$	0	0
$536$	211.443	0.0170391
$537$	21443.3	1.72318
$538$	8911.55	0.714134
$539$	28019.0	2.23908
$540$	0	0
$541$	672.250	0.0534238	0.0267119	−	0.999643i	$-0.491496\pi$
$541$	672.250	0.0534238	0.0267119	+	0.999643i	$0.491496\pi$
$542$	−4951.13	−0.392379
$543$	26130.5	2.06514
$544$	1253.65	0.0988050
$545$	0	0
$546$	−27675.6	−2.16924
$547$	6679.64	0.522122	0.261061	−	0.965322i	$-0.415928\pi$
$547$	6679.64	0.522122	0.261061	+	0.965322i	$0.415928\pi$
$548$	810.342	0.0631681
$549$	−29627.2	−2.30320
$550$	0	0
$551$	−22846.5	−1.76641
$552$	27883.5	2.15000
$553$	6467.34	0.497322
$554$	−5032.41	−0.385932
$555$	0	0
$556$	1348.75	0.102877
$557$	4904.37	0.373079	0.186539	−	0.982447i	$-0.440273\pi$
$557$	4904.37	0.373079	0.186539	+	0.982447i	$0.440273\pi$
$558$	−22506.9	−1.70751
$559$	−10367.4	−0.784429
$560$	0	0
$561$	−14845.3	−1.11724
$562$	21893.9	1.64330
$563$	11827.8	0.885403	0.442702	−	0.896669i	$-0.354020\pi$
$563$	11827.8	0.885403	0.442702	+	0.896669i	$0.354020\pi$
$564$	3284.73	0.245234
$565$	0	0
$566$	11494.3	0.853605
$567$	−10107.6	−0.748641
$568$	−1661.81	−0.122760
$569$	−8561.24	−0.630766	−0.315383	−	0.948964i	$-0.602133\pi$
$569$	−8561.24	−0.630766	−0.315383	+	0.948964i	$0.602133\pi$
$570$	0	0
$571$	24468.3	1.79329	0.896643	−	0.442755i	$-0.145999\pi$
$571$	24468.3	1.79329	0.896643	+	0.442755i	$0.145999\pi$
$572$	813.739	0.0594828
$573$	−21909.9	−1.59738
$574$	20754.9	1.50922
$575$	0	0
$576$	26367.2	1.90735
$577$	8195.48	0.591304	0.295652	−	0.955296i	$-0.404463\pi$
$577$	8195.48	0.591304	0.295652	+	0.955296i	$0.404463\pi$
$578$	−7721.78	−0.555681
$579$	8588.52	0.616454
$580$	0	0
$581$	12707.9	0.907426
$582$	34328.2	2.44493
$583$	−7844.23	−0.557247
$584$	−2930.08	−0.207615
$585$	0	0
$586$	−21806.7	−1.53725
$587$	−12575.1	−0.884211	−0.442106	−	0.896963i	$-0.645768\pi$
$587$	−12575.1	−0.884211	−0.442106	+	0.896963i	$0.645768\pi$
$588$	3950.76	0.277086
$589$	14496.7	1.01414
$590$	0	0
$591$	−4213.27	−0.293250
$592$	6493.34	0.450802
$593$	15089.8	1.04497	0.522483	−	0.852650i	$-0.325006\pi$
$593$	15089.8	1.04497	0.522483	+	0.852650i	$0.325006\pi$
$594$	−18964.4	−1.30997
$595$	0	0
$596$	−849.313	−0.0583711
$597$	−4723.42	−0.323814
$598$	−13251.4	−0.906171
$599$	−27594.7	−1.88228	−0.941142	−	0.338013i	$-0.890245\pi$
$599$	−27594.7	−1.88228	−0.941142	+	0.338013i	$0.890245\pi$
$600$	0	0
$601$	−12582.7	−0.854005	−0.427003	−	0.904250i	$-0.640430\pi$
$601$	−12582.7	−0.854005	−0.427003	+	0.904250i	$0.640430\pi$
$602$	−26178.7	−1.77237
$603$	−437.175	−0.0295243
$604$	−1204.90	−0.0811697
$605$	0	0
$606$	43963.9	2.94705
$607$	−11156.7	−0.746025	−0.373013	−	0.927826i	$-0.621675\pi$
$607$	−11156.7	−0.746025	−0.373013	+	0.927826i	$0.621675\pi$
$608$	−2333.41	−0.155645
$609$	77259.0	5.14071
$610$	0	0
$611$	−22038.2	−1.45920
$612$	−1343.60	−0.0887445
$613$	−11974.3	−0.788968	−0.394484	−	0.918903i	$-0.629077\pi$
$613$	−11974.3	−0.788968	−0.394484	+	0.918903i	$0.629077\pi$
$614$	−7425.89	−0.488086
$615$	0	0
$616$	29008.4	1.89737
$617$	18947.9	1.23632	0.618162	−	0.786050i	$-0.287877\pi$
$617$	18947.9	1.23632	0.618162	+	0.786050i	$0.287877\pi$
$618$	−1806.31	−0.117573
$619$	−7936.17	−0.515317	−0.257659	−	0.966236i	$-0.582951\pi$
$619$	−7936.17	−0.515317	−0.257659	+	0.966236i	$0.582951\pi$
$620$	0	0
$621$	−25485.9	−1.64688
$622$	3110.29	0.200500
$623$	−28578.0	−1.83781
$624$	−18123.6	−1.16270
$625$	0	0
$626$	22743.5	1.45209
$627$	27631.4	1.75996
$628$	−1190.55	−0.0756496
$629$	−5031.72	−0.318963
$630$	0	0
$631$	18436.0	1.16311	0.581556	−	0.813506i	$-0.302444\pi$
$631$	18436.0	1.16311	0.581556	+	0.813506i	$0.302444\pi$
$632$	4586.91	0.288699
$633$	−33052.3	−2.07537
$634$	17452.6	1.09327
$635$	0	0
$636$	−1106.06	−0.0689592
$637$	−26506.7	−1.64872
$638$	27526.8	1.70814
$639$	3435.91	0.212711
$640$	0	0
$641$	5266.34	0.324505	0.162253	−	0.986749i	$-0.448124\pi$
$641$	5266.34	0.324505	0.162253	+	0.986749i	$0.448124\pi$
$642$	−23156.6	−1.42355
$643$	16593.8	1.01772	0.508862	−	0.860848i	$-0.330066\pi$
$643$	16593.8	1.01772	0.508862	+	0.860848i	$0.330066\pi$
$644$	2761.36	0.168964
$645$	0	0
$646$	−10486.7	−0.638691
$647$	−7826.41	−0.475561	−0.237781	−	0.971319i	$-0.576420\pi$
$647$	−7826.41	−0.475561	−0.237781	+	0.971319i	$0.576420\pi$
$648$	−7168.74	−0.434590
$649$	26712.0	1.61562
$650$	0	0
$651$	−49022.9	−2.95140
$652$	−1114.91	−0.0669684
$653$	7106.17	0.425859	0.212929	−	0.977068i	$-0.431700\pi$
$653$	7106.17	0.425859	0.212929	+	0.977068i	$0.431700\pi$
$654$	−7895.36	−0.472069
$655$	0	0
$656$	13591.5	0.808934
$657$	6058.15	0.359743
$658$	−55648.4	−3.29696
$659$	−21812.0	−1.28934	−0.644671	−	0.764460i	$-0.723005\pi$
$659$	−21812.0	−1.28934	−0.644671	+	0.764460i	$0.723005\pi$
$660$	0	0
$661$	−8297.96	−0.488280	−0.244140	−	0.969740i	$-0.578506\pi$
$661$	−8297.96	−0.488280	−0.244140	+	0.969740i	$0.578506\pi$
$662$	−20466.6	−1.20160
$663$	14044.0	0.822663
$664$	9013.01	0.526766
$665$	0	0
$666$	−14540.4	−0.845990
$667$	36992.6	2.14747
$668$	1660.03	0.0961507
$669$	7307.77	0.422324
$670$	0	0
$671$	−22992.2	−1.32281
$672$	7890.80	0.452968
$673$	−15526.1	−0.889284	−0.444642	−	0.895708i	$-0.646669\pi$
$673$	−15526.1	−0.889284	−0.444642	+	0.895708i	$0.646669\pi$
$674$	−11793.3	−0.673975
$675$	0	0
$676$	570.059	0.0324339
$677$	9210.09	0.522855	0.261427	−	0.965223i	$-0.415807\pi$
$677$	9210.09	0.522855	0.261427	+	0.965223i	$0.415807\pi$
$678$	28387.3	1.60798
$679$	47994.0	2.71258
$680$	0	0
$681$	−42131.0	−2.37072
$682$	−17466.5	−0.980683
$683$	−7620.76	−0.426940	−0.213470	−	0.976950i	$-0.568477\pi$
$683$	−7620.76	−0.426940	−0.213470	+	0.976950i	$0.568477\pi$
$684$	2500.82	0.139797
$685$	0	0
$686$	−36160.5	−2.01255
$687$	10437.0	0.579614
$688$	−17143.4	−0.949977
$689$	7420.85	0.410322
$690$	0	0
$691$	−33408.0	−1.83922	−0.919610	−	0.392833i	$-0.871495\pi$
$691$	−33408.0	−1.83922	−0.919610	+	0.392833i	$0.871495\pi$
$692$	58.1082	0.00319211
$693$	−59977.1	−3.28765
$694$	−18299.3	−1.00091
$695$	0	0
$696$	54795.4	2.98422
$697$	−10532.2	−0.572358
$698$	−5024.33	−0.272455
$699$	49774.9	2.69336
$700$	0	0
$701$	−26746.0	−1.44106	−0.720528	−	0.693426i	$-0.756101\pi$
$701$	−26746.0	−1.44106	−0.720528	+	0.693426i	$0.756101\pi$
$702$	17940.9	0.964578
$703$	9365.48	0.502455
$704$	20462.3	1.09545
$705$	0	0
$706$	34212.2	1.82379
$707$	61465.5	3.26966
$708$	3766.46	0.199933
$709$	−17877.9	−0.946993	−0.473496	−	0.880796i	$-0.657008\pi$
$709$	−17877.9	−0.946993	−0.473496	+	0.880796i	$0.657008\pi$
$710$	0	0
$711$	−9483.78	−0.500238
$712$	−20268.7	−1.06686
$713$	−23472.8	−1.23291
$714$	35462.5	1.85876
$715$	0	0
$716$	1506.13	0.0786125
$717$	−25719.6	−1.33963
$718$	−30601.7	−1.59059
$719$	−17648.6	−0.915414	−0.457707	−	0.889103i	$-0.651329\pi$
$719$	−17648.6	−0.915414	−0.457707	+	0.889103i	$0.651329\pi$
$720$	0	0
$721$	−2525.39	−0.130444
$722$	872.741	0.0449862
$723$	37383.5	1.92297
$724$	1835.35	0.0942128
$725$	0	0
$726$	−1874.56	−0.0958283
$727$	7103.37	0.362379	0.181189	−	0.983448i	$-0.442005\pi$
$727$	7103.37	0.362379	0.181189	+	0.983448i	$0.442005\pi$
$728$	−27442.7	−1.39711
$729$	−28726.3	−1.45945
$730$	0	0
$731$	13284.5	0.672153
$732$	−3241.96	−0.163697
$733$	−5682.65	−0.286348	−0.143174	−	0.989697i	$-0.545731\pi$
$733$	−5682.65	−0.286348	−0.143174	+	0.989697i	$0.545731\pi$
$734$	30183.6	1.51785
$735$	0	0
$736$	3778.22	0.189221
$737$	−339.270	−0.0169568
$738$	−30435.3	−1.51807
$739$	−28152.2	−1.40135	−0.700675	−	0.713481i	$-0.747118\pi$
$739$	−28152.2	−1.40135	−0.700675	+	0.713481i	$0.747118\pi$
$740$	0	0
$741$	−26140.0	−1.29592
$742$	18738.3	0.927097
$743$	23595.6	1.16506	0.582530	−	0.812809i	$-0.302063\pi$
$743$	23595.6	1.16506	0.582530	+	0.812809i	$0.302063\pi$
$744$	−34769.1	−1.71330
$745$	0	0
$746$	−10884.6	−0.534199
$747$	−18635.1	−0.912747
$748$	−1042.70	−0.0509690
$749$	−32375.0	−1.57938
$750$	0	0
$751$	−11215.4	−0.544948	−0.272474	−	0.962163i	$-0.587842\pi$
$751$	−11215.4	−0.544948	−0.272474	+	0.962163i	$0.587842\pi$
$752$	−36441.8	−1.76715
$753$	30641.0	1.48289
$754$	−26041.0	−1.25777
$755$	0	0
$756$	−3738.55	−0.179854
$757$	10851.6	0.521015	0.260507	−	0.965472i	$-0.416110\pi$
$757$	10851.6	0.521015	0.260507	+	0.965472i	$0.416110\pi$
$758$	19742.4	0.946013
$759$	−44740.3	−2.13962
$760$	0	0
$761$	1795.40	0.0855232	0.0427616	−	0.999085i	$-0.486384\pi$
$761$	1795.40	0.0855232	0.0427616	+	0.999085i	$0.486384\pi$
$762$	−43872.7	−2.08575
$763$	−11038.4	−0.523746
$764$	−1538.90	−0.0728735
$765$	0	0
$766$	−12886.4	−0.607839
$767$	−25270.2	−1.18964
$768$	8085.31	0.379887
$769$	36190.2	1.69707	0.848537	−	0.529135i	$-0.177484\pi$
$769$	36190.2	1.69707	0.848537	+	0.529135i	$0.177484\pi$
$770$	0	0
$771$	−6111.01	−0.285451
$772$	603.236	0.0281230
$773$	−13205.3	−0.614438	−0.307219	−	0.951639i	$-0.599398\pi$
$773$	−13205.3	−0.614438	−0.307219	+	0.951639i	$0.599398\pi$
$774$	38388.8	1.78276
$775$	0	0
$776$	34039.4	1.57467
$777$	−31670.9	−1.46227
$778$	25542.6	1.17705
$779$	19603.4	0.901622
$780$	0	0
$781$	2666.44	0.122167
$782$	16979.9	0.776471
$783$	−50083.6	−2.28588
$784$	−43830.9	−1.99667
$785$	0	0
$786$	−12879.4	−0.584468
$787$	−13164.5	−0.596270	−0.298135	−	0.954524i	$-0.596365\pi$
$787$	−13164.5	−0.596270	−0.298135	+	0.954524i	$0.596365\pi$
$788$	−295.929	−0.0133782
$789$	36209.5	1.63383
$790$	0	0
$791$	39688.1	1.78400
$792$	−42538.3	−1.90850
$793$	21751.2	0.974033
$794$	4034.31	0.180318
$795$	0	0
$796$	−331.761	−0.0147726
$797$	−13434.3	−0.597075	−0.298537	−	0.954398i	$-0.596499\pi$
$797$	−13434.3	−0.597075	−0.298537	+	0.954398i	$0.596499\pi$
$798$	−66006.0	−2.92805
$799$	28238.9	1.25034
$800$	0	0
$801$	41907.1	1.84858
$802$	10072.2	0.443470
$803$	4701.43	0.206613
$804$	−47.8380	−0.00209840
$805$	0	0
$806$	16523.7	0.722114
$807$	−28463.8	−1.24160
$808$	43594.0	1.89806
$809$	30140.3	1.30986	0.654929	−	0.755690i	$-0.272698\pi$
$809$	30140.3	1.30986	0.654929	+	0.755690i	$0.272698\pi$
$810$	0	0
$811$	1939.83	0.0839911	0.0419956	−	0.999118i	$-0.486628\pi$
$811$	1939.83	0.0839911	0.0419956	+	0.999118i	$0.486628\pi$
$812$	5426.48	0.234522
$813$	15814.1	0.682195
$814$	−11284.1	−0.485881
$815$	0	0
$816$	23222.9	0.996281
$817$	−24726.2	−1.05883
$818$	−5456.38	−0.233225
$819$	56739.9	2.42082
$820$	0	0
$821$	9709.77	0.412757	0.206378	−	0.978472i	$-0.433832\pi$
$821$	9709.77	0.412757	0.206378	+	0.978472i	$0.433832\pi$
$822$	31363.6	1.33082
$823$	2355.96	0.0997855	0.0498927	−	0.998755i	$-0.484112\pi$
$823$	2355.96	0.0997855	0.0498927	+	0.998755i	$0.484112\pi$
$824$	−1791.11	−0.0757237
$825$	0	0
$826$	−63809.7	−2.68792
$827$	−11326.6	−0.476255	−0.238128	−	0.971234i	$-0.576534\pi$
$827$	−11326.6	−0.476255	−0.238128	+	0.971234i	$0.576534\pi$
$828$	−4049.28	−0.169955
$829$	−11034.9	−0.462314	−0.231157	−	0.972916i	$-0.574251\pi$
$829$	−11034.9	−0.462314	−0.231157	+	0.972916i	$0.574251\pi$
$830$	0	0
$831$	16073.7	0.670987
$832$	−19357.8	−0.806625
$833$	33964.8	1.41274
$834$	52202.2	2.16740
$835$	0	0
$836$	1940.76	0.0802902
$837$	31779.4	1.31237
$838$	19488.8	0.803375
$839$	−17501.5	−0.720166	−0.360083	−	0.932920i	$-0.617252\pi$
$839$	−17501.5	−0.720166	−0.360083	+	0.932920i	$0.617252\pi$
$840$	0	0
$841$	48307.1	1.98069
$842$	21575.0	0.883045
$843$	−69929.8	−2.85707
$844$	−2321.51	−0.0946798
$845$	0	0
$846$	81603.4	3.31629
$847$	−2620.80	−0.106319
$848$	12271.0	0.496918
$849$	−36713.1	−1.48409
$850$	0	0
$851$	−15164.4	−0.610846
$852$	375.975	0.0151182
$853$	−29749.0	−1.19412	−0.597061	−	0.802196i	$-0.703665\pi$
$853$	−29749.0	−1.19412	−0.597061	+	0.802196i	$0.703665\pi$
$854$	54923.8	2.20077
$855$	0	0
$856$	−22961.7	−0.916841
$857$	27262.2	1.08665	0.543324	−	0.839523i	$-0.317165\pi$
$857$	27262.2	1.08665	0.543324	+	0.839523i	$0.317165\pi$
$858$	31495.1	1.25317
$859$	−884.768	−0.0351431	−0.0175715	−	0.999846i	$-0.505593\pi$
$859$	−884.768	−0.0351431	−0.0175715	+	0.999846i	$0.505593\pi$
$860$	0	0
$861$	−66292.0	−2.62396
$862$	45339.8	1.79151
$863$	16476.8	0.649914	0.324957	−	0.945729i	$-0.394650\pi$
$863$	16476.8	0.649914	0.324957	+	0.945729i	$0.394650\pi$
$864$	−5115.26	−0.201417
$865$	0	0
$866$	−8478.39	−0.332688
$867$	24663.6	0.966114
$868$	−3443.25	−0.134645
$869$	−7359.89	−0.287304
$870$	0	0
$871$	320.958	0.0124859
$872$	−7828.93	−0.304038
$873$	−70379.0	−2.72849
$874$	−31604.5	−1.22316
$875$	0	0
$876$	662.914	0.0255683
$877$	−23402.0	−0.901059	−0.450530	−	0.892761i	$-0.648765\pi$
$877$	−23402.0	−0.901059	−0.450530	+	0.892761i	$0.648765\pi$
$878$	30945.6	1.18948
$879$	69651.3	2.67268
$880$	0	0
$881$	−45316.7	−1.73298	−0.866492	−	0.499191i	$-0.833631\pi$
$881$	−45316.7	−1.73298	−0.866492	+	0.499191i	$0.833631\pi$
$882$	98149.8	3.74702
$883$	−38988.0	−1.48590	−0.742950	−	0.669347i	$-0.766574\pi$
$883$	−38988.0	−1.48590	−0.742950	+	0.669347i	$0.766574\pi$
$884$	986.419	0.0375304
$885$	0	0
$886$	−27646.7	−1.04832
$887$	16291.8	0.616712	0.308356	−	0.951271i	$-0.400221\pi$
$887$	16291.8	0.616712	0.308356	+	0.951271i	$0.400221\pi$
$888$	−22462.3	−0.848859
$889$	−61338.0	−2.31407
$890$	0	0
$891$	11502.5	0.432491
$892$	513.280	0.0192667
$893$	−52560.8	−1.96963
$894$	−32871.9	−1.22975
$895$	0	0
$896$	−41610.1	−1.55145
$897$	42325.5	1.57548
$898$	15422.1	0.573098
$899$	−46127.6	−1.71128
$900$	0	0
$901$	−9508.82	−0.351592
$902$	−23619.3	−0.871881
$903$	83615.8	3.08146
$904$	28148.5	1.03562
$905$	0	0
$906$	−46634.4	−1.71007
$907$	40519.0	1.48337	0.741683	−	0.670751i	$-0.234028\pi$
$907$	40519.0	1.48337	0.741683	+	0.670751i	$0.234028\pi$
$908$	−2959.18	−0.108154
$909$	−90133.8	−3.28883
$910$	0	0
$911$	7629.82	0.277483	0.138742	−	0.990329i	$-0.455694\pi$
$911$	7629.82	0.277483	0.138742	+	0.990329i	$0.455694\pi$
$912$	−43224.6	−1.56942
$913$	−14461.8	−0.524221
$914$	−16594.4	−0.600541
$915$	0	0
$916$	733.066	0.0264423
$917$	−18006.5	−0.648449
$918$	−22988.8	−0.826518
$919$	35596.5	1.27772	0.638858	−	0.769324i	$-0.279407\pi$
$919$	35596.5	1.27772	0.638858	+	0.769324i	$0.279407\pi$
$920$	0	0
$921$	23718.6	0.848592
$922$	−13473.0	−0.481248
$923$	−2522.52	−0.0899565
$924$	−6563.00	−0.233665
$925$	0	0
$926$	22447.0	0.796602
$927$	3703.26	0.131209
$928$	7424.77	0.262640
$929$	13538.2	0.478120	0.239060	−	0.971005i	$-0.423161\pi$
$929$	13538.2	0.478120	0.239060	+	0.971005i	$0.423161\pi$
$930$	0	0
$931$	−63218.3	−2.22545
$932$	3496.07	0.122873
$933$	−9934.37	−0.348592
$934$	−10976.0	−0.384525
$935$	0	0
$936$	40242.3	1.40530
$937$	−37269.4	−1.29940	−0.649701	−	0.760190i	$-0.725106\pi$
$937$	−37269.4	−1.29940	−0.649701	+	0.760190i	$0.725106\pi$
$938$	810.449	0.0282112
$939$	−72643.4	−2.52463
$940$	0	0
$941$	3061.81	0.106070	0.0530352	−	0.998593i	$-0.483110\pi$
$941$	3061.81	0.106070	0.0530352	+	0.998593i	$0.483110\pi$
$942$	−46079.0	−1.59377
$943$	−31741.5	−1.09612
$944$	−41786.3	−1.44071
$945$	0	0
$946$	29791.6	1.02390
$947$	−12279.4	−0.421361	−0.210680	−	0.977555i	$-0.567568\pi$
$947$	−12279.4	−0.421361	−0.210680	+	0.977555i	$0.567568\pi$
$948$	−1037.76	−0.0355538
$949$	−4447.68	−0.152137
$950$	0	0
$951$	−55744.4	−1.90077
$952$	35164.1	1.19714
$953$	−30851.1	−1.04865	−0.524326	−	0.851518i	$-0.675683\pi$
$953$	−30851.1	−1.04865	−0.524326	+	0.851518i	$0.675683\pi$
$954$	−27478.1	−0.932533
$955$	0	0
$956$	−1806.48	−0.0611148
$957$	−87921.5	−2.96980
$958$	−34887.3	−1.17658
$959$	43849.2	1.47650
$960$	0	0
$961$	−521.806	−0.0175156
$962$	10675.0	0.357772
$963$	47475.1	1.58864
$964$	2625.72	0.0877270
$965$	0	0
$966$	106876.	3.55970
$967$	−6257.68	−0.208101	−0.104050	−	0.994572i	$-0.533180\pi$
$967$	−6257.68	−0.208101	−0.104050	+	0.994572i	$0.533180\pi$
$968$	−1858.79	−0.0617186
$969$	33494.9	1.11044
$970$	0	0
$971$	−25874.0	−0.855135	−0.427568	−	0.903983i	$-0.640629\pi$
$971$	−25874.0	−0.855135	−0.427568	+	0.903983i	$0.640629\pi$
$972$	−1436.83	−0.0474139
$973$	72983.5	2.40467
$974$	−51557.6	−1.69611
$975$	0	0
$976$	35967.3	1.17960
$977$	−41040.7	−1.34392	−0.671959	−	0.740588i	$-0.734547\pi$
$977$	−41040.7	−1.34392	−0.671959	+	0.740588i	$0.734547\pi$
$978$	−43151.7	−1.41088
$979$	32522.0	1.06170
$980$	0	0
$981$	16186.9	0.526818
$982$	−38400.1	−1.24786
$983$	−30927.7	−1.00350	−0.501749	−	0.865013i	$-0.667310\pi$
$983$	−30927.7	−1.00350	−0.501749	+	0.865013i	$0.667310\pi$
$984$	−47017.1	−1.52322
$985$	0	0
$986$	33368.1	1.07774
$987$	177743.	5.73214
$988$	−1836.01	−0.0591207
$989$	40036.3	1.28724
$990$	0	0
$991$	33782.1	1.08287	0.541435	−	0.840743i	$-0.317881\pi$
$991$	33782.1	1.08287	0.541435	+	0.840743i	$0.317881\pi$
$992$	−4711.21	−0.150787
$993$	65371.1	2.08911
$994$	−6369.60	−0.203251
$995$	0	0
$996$	−2039.15	−0.0648723
$997$	−11831.4	−0.375832	−0.187916	−	0.982185i	$-0.560173\pi$
$997$	−11831.4	−0.375832	−0.187916	+	0.982185i	$0.560173\pi$
$998$	−39016.9	−1.23753
$999$	20530.8	0.650218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.4.a.g.1.15		20
5.4	even	2		355.4.a.d.1.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
355.4.a.d.1.6	✓	20	5.4	even	2
1775.4.a.g.1.15		20	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:	\( N \)	\(=\)	\( 1775 = 5^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1775.a (trivial)

\(f(q)\)	\(=\)	\(q+2.71848 q^{2} -8.68292 q^{3} -0.609867 q^{4} -23.6043 q^{6} -33.0011 q^{7} -23.4058 q^{8} +48.3931 q^{9} +O(q^{10})\)	\(q+2.71848 q^{2} -8.68292 q^{3} -0.609867 q^{4} -23.6043 q^{6} -33.0011 q^{7} -23.4058 q^{8} +48.3931 q^{9} +37.5555 q^{11} +5.29543 q^{12} -35.5285 q^{13} -89.7127 q^{14} -58.7491 q^{16} +45.5250 q^{17} +131.556 q^{18} -84.7351 q^{19} +286.546 q^{21} +102.094 q^{22} +137.202 q^{23} +203.230 q^{24} -96.5835 q^{26} -185.755 q^{27} +20.1263 q^{28} +269.622 q^{29} -171.082 q^{31} +27.5377 q^{32} -326.092 q^{33} +123.759 q^{34} -29.5134 q^{36} -110.527 q^{37} -230.351 q^{38} +308.491 q^{39} -231.349 q^{41} +778.968 q^{42} +291.806 q^{43} -22.9039 q^{44} +372.980 q^{46} +620.295 q^{47} +510.114 q^{48} +746.070 q^{49} -395.290 q^{51} +21.6676 q^{52} -208.870 q^{53} -504.971 q^{54} +772.414 q^{56} +735.748 q^{57} +732.962 q^{58} +711.267 q^{59} -612.219 q^{61} -465.084 q^{62} -1597.02 q^{63} +544.854 q^{64} -886.473 q^{66} -9.03382 q^{67} -27.7642 q^{68} -1191.31 q^{69} +71.0000 q^{71} -1132.68 q^{72} +125.186 q^{73} -300.464 q^{74} +51.6771 q^{76} -1239.37 q^{77} +838.627 q^{78} -195.974 q^{79} +306.281 q^{81} -628.917 q^{82} -385.077 q^{83} -174.755 q^{84} +793.269 q^{86} -2341.11 q^{87} -879.015 q^{88} +865.972 q^{89} +1172.48 q^{91} -83.6748 q^{92} +1485.50 q^{93} +1686.26 q^{94} -239.108 q^{96} -1454.32 q^{97} +2028.18 q^{98} +1817.43 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9}+O(q^{10}) \) 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9	\( 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9} + 62 q^{11} - 160 q^{12} - 232 q^{13} + 56 q^{14} + 387 q^{16} - 314 q^{17} - 224 q^{18} + 54 q^{19} + 58 q^{21} + 123 q^{22} - 344 q^{23} + 419 q^{24} - 387 q^{26} - 326 q^{27} - 786 q^{28} + 748 q^{29} - 18 q^{31} - 345 q^{32} - 746 q^{33} - 142 q^{34} + 90 q^{36} - 858 q^{37} - 723 q^{38} + 210 q^{39} + 386 q^{41} + 237 q^{42} - 1210 q^{43} + 1105 q^{44} - 57 q^{46} - 320 q^{47} - 2280 q^{48} + 1576 q^{49} - 350 q^{51} - 780 q^{52} - 2066 q^{53} - 536 q^{54} + 938 q^{56} - 710 q^{57} - 1852 q^{58} + 1198 q^{59} + 284 q^{61} - 2444 q^{62} - 732 q^{63} + 1118 q^{64} - 219 q^{66} - 976 q^{67} - 2904 q^{68} + 1026 q^{69} + 1420 q^{71} - 3374 q^{72} - 4310 q^{73} + 955 q^{74} + 740 q^{76} - 5196 q^{77} - 61 q^{78} - 340 q^{79} + 2556 q^{81} - 1191 q^{82} + 354 q^{83} - 1955 q^{84} + 1248 q^{86} - 3392 q^{87} - 135 q^{88} - 1446 q^{89} - 240 q^{91} - 4114 q^{92} + 1066 q^{93} - 3985 q^{94} - 2145 q^{96} - 3282 q^{97} + 4708 q^{98} - 6506 q^{99}+O(q^{100}) \) 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9 + 62 * q^11 - 160 * q^12 - 232 * q^13 + 56 * q^14 + 387 * q^16 - 314 * q^17 - 224 * q^18 + 54 * q^19 + 58 * q^21 + 123 * q^22 - 344 * q^23 + 419 * q^24 - 387 * q^26 - 326 * q^27 - 786 * q^28 + 748 * q^29 - 18 * q^31 - 345 * q^32 - 746 * q^33 - 142 * q^34 + 90 * q^36 - 858 * q^37 - 723 * q^38 + 210 * q^39 + 386 * q^41 + 237 * q^42 - 1210 * q^43 + 1105 * q^44 - 57 * q^46 - 320 * q^47 - 2280 * q^48 + 1576 * q^49 - 350 * q^51 - 780 * q^52 - 2066 * q^53 - 536 * q^54 + 938 * q^56 - 710 * q^57 - 1852 * q^58 + 1198 * q^59 + 284 * q^61 - 2444 * q^62 - 732 * q^63 + 1118 * q^64 - 219 * q^66 - 976 * q^67 - 2904 * q^68 + 1026 * q^69 + 1420 * q^71 - 3374 * q^72 - 4310 * q^73 + 955 * q^74 + 740 * q^76 - 5196 * q^77 - 61 * q^78 - 340 * q^79 + 2556 * q^81 - 1191 * q^82 + 354 * q^83 - 1955 * q^84 + 1248 * q^86 - 3392 * q^87 - 135 * q^88 - 1446 * q^89 - 240 * q^91 - 4114 * q^92 + 1066 * q^93 - 3985 * q^94 - 2145 * q^96 - 3282 * q^97 + 4708 * q^98 - 6506 * q^99

Introduction

L-functions

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