LMFDB - Embedded newform 1815.4.a.bn.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 59 x^{10} + 269 x^{9} + 1318 x^{8} - 5253 x^{7} - 13369 x^{6} + 44853 x^{5} + \cdots + 17600 $ x^12 - 5x^11 - 59x^10 + 269x^9 + 1318x^8 - 5253x^7 - 13369x^6 + 44853x^5 + 57849x^4 - 151000x^3 - 76540x^2 + 100800*x + 17600
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-2.69379$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.69379 q^{2} +3.00000 q^{3} +5.64411 q^{4} +5.00000 q^{5} +11.0814 q^{6} +0.0404379 q^{7} -8.70216 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.69379 q^{2} +3.00000 q^{3} +5.64411 q^{4} +5.00000 q^{5} +11.0814 q^{6} +0.0404379 q^{7} -8.70216 q^{8} +9.00000 q^{9} +18.4690 q^{10} +16.9323 q^{12} +63.3853 q^{13} +0.149369 q^{14} +15.0000 q^{15} -77.2969 q^{16} -2.67629 q^{17} +33.2441 q^{18} +0.783900 q^{19} +28.2206 q^{20} +0.121314 q^{21} +69.9301 q^{23} -26.1065 q^{24} +25.0000 q^{25} +234.132 q^{26} +27.0000 q^{27} +0.228236 q^{28} -46.1166 q^{29} +55.4069 q^{30} +198.879 q^{31} -215.902 q^{32} -9.88568 q^{34} +0.202190 q^{35} +50.7970 q^{36} -27.1655 q^{37} +2.89556 q^{38} +190.156 q^{39} -43.5108 q^{40} +221.307 q^{41} +0.448108 q^{42} +367.226 q^{43} +45.0000 q^{45} +258.307 q^{46} +419.488 q^{47} -231.891 q^{48} -342.998 q^{49} +92.3449 q^{50} -8.02888 q^{51} +357.754 q^{52} -122.921 q^{53} +99.7324 q^{54} -0.351897 q^{56} +2.35170 q^{57} -170.345 q^{58} +41.5124 q^{59} +84.6617 q^{60} +446.643 q^{61} +734.617 q^{62} +0.363941 q^{63} -179.121 q^{64} +316.927 q^{65} +438.401 q^{67} -15.1053 q^{68} +209.790 q^{69} +0.746847 q^{70} -631.494 q^{71} -78.3194 q^{72} -749.387 q^{73} -100.344 q^{74} +75.0000 q^{75} +4.42442 q^{76} +702.397 q^{78} +508.299 q^{79} -386.484 q^{80} +81.0000 q^{81} +817.463 q^{82} +1098.09 q^{83} +0.684709 q^{84} -13.3815 q^{85} +1356.46 q^{86} -138.350 q^{87} +587.440 q^{89} +166.221 q^{90} +2.56317 q^{91} +394.693 q^{92} +596.636 q^{93} +1549.50 q^{94} +3.91950 q^{95} -647.705 q^{96} -983.797 q^{97} -1266.97 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9	\( 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9} + 35 q^{10} + 147 q^{12} + 172 q^{13} - 30 q^{14} + 180 q^{15} + 161 q^{16} + 317 q^{17} + 63 q^{18} + 237 q^{19} + 245 q^{20} + 231 q^{21} + 210 q^{23} + 333 q^{24} + 300 q^{25} + 8 q^{26} + 324 q^{27} + 542 q^{28} + 759 q^{29} + 105 q^{30} - 193 q^{31} + 410 q^{32} - 78 q^{34} + 385 q^{35} + 441 q^{36} + 286 q^{37} - 168 q^{38} + 516 q^{39} + 555 q^{40} + 1189 q^{41} - 90 q^{42} + 775 q^{43} + 540 q^{45} + 529 q^{46} + 382 q^{47} + 483 q^{48} + 1195 q^{49} + 175 q^{50} + 951 q^{51} + 1741 q^{52} + 275 q^{53} + 189 q^{54} - 419 q^{56} + 711 q^{57} - 418 q^{58} + 646 q^{59} + 735 q^{60} + 1340 q^{61} + 983 q^{62} + 693 q^{63} - 1489 q^{64} + 860 q^{65} - 185 q^{67} + 3322 q^{68} + 630 q^{69} - 150 q^{70} - 932 q^{71} + 999 q^{72} + 2860 q^{73} + 4187 q^{74} + 900 q^{75} + 1594 q^{76} + 24 q^{78} + 1429 q^{79} + 805 q^{80} + 972 q^{81} - 30 q^{82} + 2590 q^{83} + 1626 q^{84} + 1585 q^{85} - 3195 q^{86} + 2277 q^{87} - 473 q^{89} + 315 q^{90} - 4302 q^{91} + 5462 q^{92} - 579 q^{93} + 2875 q^{94} + 1185 q^{95} + 1230 q^{96} + 318 q^{97} - 194 q^{98}+O(q^{100}) \) 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9 + 35 * q^10 + 147 * q^12 + 172 * q^13 - 30 * q^14 + 180 * q^15 + 161 * q^16 + 317 * q^17 + 63 * q^18 + 237 * q^19 + 245 * q^20 + 231 * q^21 + 210 * q^23 + 333 * q^24 + 300 * q^25 + 8 * q^26 + 324 * q^27 + 542 * q^28 + 759 * q^29 + 105 * q^30 - 193 * q^31 + 410 * q^32 - 78 * q^34 + 385 * q^35 + 441 * q^36 + 286 * q^37 - 168 * q^38 + 516 * q^39 + 555 * q^40 + 1189 * q^41 - 90 * q^42 + 775 * q^43 + 540 * q^45 + 529 * q^46 + 382 * q^47 + 483 * q^48 + 1195 * q^49 + 175 * q^50 + 951 * q^51 + 1741 * q^52 + 275 * q^53 + 189 * q^54 - 419 * q^56 + 711 * q^57 - 418 * q^58 + 646 * q^59 + 735 * q^60 + 1340 * q^61 + 983 * q^62 + 693 * q^63 - 1489 * q^64 + 860 * q^65 - 185 * q^67 + 3322 * q^68 + 630 * q^69 - 150 * q^70 - 932 * q^71 + 999 * q^72 + 2860 * q^73 + 4187 * q^74 + 900 * q^75 + 1594 * q^76 + 24 * q^78 + 1429 * q^79 + 805 * q^80 + 972 * q^81 - 30 * q^82 + 2590 * q^83 + 1626 * q^84 + 1585 * q^85 - 3195 * q^86 + 2277 * q^87 - 473 * q^89 + 315 * q^90 - 4302 * q^91 + 5462 * q^92 - 579 * q^93 + 2875 * q^94 + 1185 * q^95 + 1230 * q^96 + 318 * q^97 - 194 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.69379	1.30595	0.652977	−	0.757378i	$-0.273520\pi$
$2$	3.69379	1.30595	0.652977	+	0.757378i	$0.273520\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.64411	0.705514
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	11.0814	0.753993
$7$	0.0404379	0.00218344	0.00109172	−	0.999999i	$-0.499652\pi$
$7$	0.0404379	0.00218344	0.00109172	+	0.999999i	$0.499652\pi$
$8$	−8.70216	−0.384585
$9$	9.00000	0.333333
$10$	18.4690	0.584040
$11$	0	0
$11$	0	0
$12$	16.9323	0.407329
$13$	63.3853	1.35230	0.676151	−	0.736763i	$-0.263647\pi$
$13$	63.3853	1.35230	0.676151	+	0.736763i	$0.263647\pi$
$14$	0.149369	0.00285147
$15$	15.0000	0.258199
$16$	−77.2969	−1.20776
$17$	−2.67629	−0.0381822	−0.0190911	−	0.999818i	$-0.506077\pi$
$17$	−2.67629	−0.0381822	−0.0190911	+	0.999818i	$0.506077\pi$
$18$	33.2441	0.435318
$19$	0.783900	0.00946521	0.00473260	−	0.999989i	$-0.498494\pi$
$19$	0.783900	0.00946521	0.00473260	+	0.999989i	$0.498494\pi$
$20$	28.2206	0.315516
$21$	0.121314	0.00126061
$22$	0	0
$23$	69.9301	0.633975	0.316988	−	0.948430i	$-0.397329\pi$
$23$	69.9301	0.633975	0.316988	+	0.948430i	$0.397329\pi$
$24$	−26.1065	−0.222040
$25$	25.0000	0.200000
$26$	234.132	1.76604
$27$	27.0000	0.192450
$28$	0.228236	0.00154045
$29$	−46.1166	−0.295298	−0.147649	−	0.989040i	$-0.547171\pi$
$29$	−46.1166	−0.295298	−0.147649	+	0.989040i	$0.547171\pi$
$30$	55.4069	0.337196
$31$	198.879	1.15225	0.576124	−	0.817363i	$-0.304565\pi$
$31$	198.879	1.15225	0.576124	+	0.817363i	$0.304565\pi$
$32$	−215.902	−1.19270
$33$	0	0
$34$	−9.88568	−0.0498641
$35$	0.202190	0.000976465 0
$36$	50.7970	0.235171
$37$	−27.1655	−0.120702	−0.0603511	−	0.998177i	$-0.519222\pi$
$37$	−27.1655	−0.120702	−0.0603511	+	0.998177i	$0.519222\pi$
$38$	2.89556	0.0123611
$39$	190.156	0.780752
$40$	−43.5108	−0.171991
$41$	221.307	0.842984	0.421492	−	0.906832i	$-0.361507\pi$
$41$	221.307	0.842984	0.421492	+	0.906832i	$0.361507\pi$
$42$	0.448108	0.00164630
$43$	367.226	1.30236	0.651180	−	0.758923i	$-0.274274\pi$
$43$	367.226	1.30236	0.651180	+	0.758923i	$0.274274\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	258.307	0.827942
$47$	419.488	1.30188	0.650942	−	0.759127i	$-0.274374\pi$
$47$	419.488	1.30188	0.650942	+	0.759127i	$0.274374\pi$
$48$	−231.891	−0.697303
$49$	−342.998	−0.999995
$50$	92.3449	0.261191
$51$	−8.02888	−0.0220445
$52$	357.754	0.954069
$53$	−122.921	−0.318575	−0.159287	−	0.987232i	$-0.550920\pi$
$53$	−122.921	−0.318575	−0.159287	+	0.987232i	$0.550920\pi$
$54$	99.7324	0.251331
$55$	0	0
$56$	−0.351897	−0.000839718 0
$57$	2.35170	0.00546474
$58$	−170.345	−0.385645
$59$	41.5124	0.0916010	0.0458005	−	0.998951i	$-0.485416\pi$
$59$	41.5124	0.0916010	0.0458005	+	0.998951i	$0.485416\pi$
$60$	84.6617	0.182163
$61$	446.643	0.937488	0.468744	−	0.883334i	$-0.344707\pi$
$61$	446.643	0.937488	0.468744	+	0.883334i	$0.344707\pi$
$62$	734.617	1.50478
$63$	0.363941	0.000727814 0
$64$	−179.121	−0.349845
$65$	316.927	0.604768
$66$	0	0
$67$	438.401	0.799391	0.399695	−	0.916648i	$-0.369116\pi$
$67$	438.401	0.799391	0.399695	+	0.916648i	$0.369116\pi$
$68$	−15.1053	−0.0269381
$69$	209.790	0.366026
$70$	0.746847	0.00127522
$71$	−631.494	−1.05556	−0.527778	−	0.849382i	$-0.676975\pi$
$71$	−631.494	−1.05556	−0.527778	+	0.849382i	$0.676975\pi$
$72$	−78.3194	−0.128195
$73$	−749.387	−1.20150	−0.600748	−	0.799439i	$-0.705130\pi$
$73$	−749.387	−1.20150	−0.600748	+	0.799439i	$0.705130\pi$
$74$	−100.344	−0.157631
$75$	75.0000	0.115470
$76$	4.42442	0.00667784
$77$	0	0
$78$	702.397	1.01963
$79$	508.299	0.723900	0.361950	−	0.932198i	$-0.382111\pi$
$79$	508.299	0.723900	0.361950	+	0.932198i	$0.382111\pi$
$80$	−386.484	−0.540128
$81$	81.0000	0.111111
$82$	817.463	1.10090
$83$	1098.09	1.45218	0.726089	−	0.687600i	$-0.241336\pi$
$83$	1098.09	1.45218	0.726089	+	0.687600i	$0.241336\pi$
$84$	0.684709	0.000889379 0
$85$	−13.3815	−0.0170756
$86$	1356.46	1.70082
$87$	−138.350	−0.170490
$88$	0	0
$89$	587.440	0.699646	0.349823	−	0.936816i	$-0.386242\pi$
$89$	587.440	0.699646	0.349823	+	0.936816i	$0.386242\pi$
$90$	166.221	0.194680
$91$	2.56317	0.00295267
$92$	394.693	0.447279
$93$	596.636	0.665250
$94$	1549.50	1.70020
$95$	3.91950	0.00423297
$96$	−647.705	−0.688605
$97$	−983.797	−1.02979	−0.514894	−	0.857254i	$-0.672169\pi$
$97$	−983.797	−1.02979	−0.514894	+	0.857254i	$0.672169\pi$
$98$	−1266.97	−1.30595
$99$	0	0
$100$	141.103	0.141103
$101$	−422.751	−0.416488	−0.208244	−	0.978077i	$-0.566775\pi$
$101$	−422.751	−0.416488	−0.208244	+	0.978077i	$0.566775\pi$
$102$	−29.6570	−0.0287891
$103$	−361.646	−0.345962	−0.172981	−	0.984925i	$-0.555340\pi$
$103$	−361.646	−0.345962	−0.172981	+	0.984925i	$0.555340\pi$
$104$	−551.589	−0.520075
$105$	0.606569	0.000563762 0
$106$	−454.044	−0.416044
$107$	1480.67	1.33778	0.668888	−	0.743363i	$-0.266771\pi$
$107$	1480.67	1.33778	0.668888	+	0.743363i	$0.266771\pi$
$108$	152.391	0.135776
$109$	−2088.79	−1.83550	−0.917750	−	0.397159i	$-0.869996\pi$
$109$	−2088.79	−1.83550	−0.917750	+	0.397159i	$0.869996\pi$
$110$	0	0
$111$	−81.4965	−0.0696874
$112$	−3.12573	−0.00263708
$113$	1132.06	0.942434	0.471217	−	0.882017i	$-0.343815\pi$
$113$	1132.06	0.942434	0.471217	+	0.882017i	$0.343815\pi$
$114$	8.68669	0.00713670
$115$	349.650	0.283522
$116$	−260.287	−0.208337
$117$	570.468	0.450767
$118$	153.338	0.119627
$119$	−0.108224	−8.33686e−5 0
$120$	−130.532	−0.0992993
$121$	0	0
$122$	1649.81	1.22432
$123$	663.921	0.486697
$124$	1122.49	0.812927
$125$	125.000	0.0894427
$126$	1.34432	0.000950491 0
$127$	2640.74	1.84510	0.922549	−	0.385879i	$-0.126102\pi$
$127$	2640.74	1.84510	0.922549	+	0.385879i	$0.126102\pi$
$128$	1065.58	0.735817
$129$	1101.68	0.751918
$130$	1170.66	0.789799
$131$	−278.290	−0.185605	−0.0928027	−	0.995685i	$-0.529583\pi$
$131$	−278.290	−0.185605	−0.0928027	+	0.995685i	$0.529583\pi$
$132$	0	0
$133$	0.0316993	2.06667e−5 0
$134$	1619.36	1.04397
$135$	135.000	0.0860663
$136$	23.2895	0.0146843
$137$	−546.287	−0.340675	−0.170338	−	0.985386i	$-0.554486\pi$
$137$	−546.287	−0.340675	−0.170338	+	0.985386i	$0.554486\pi$
$138$	774.922	0.478013
$139$	1117.61	0.681976	0.340988	−	0.940068i	$-0.389239\pi$
$139$	1117.61	0.681976	0.340988	+	0.940068i	$0.389239\pi$
$140$	1.14118	0.000688910 0
$141$	1258.46	0.751643
$142$	−2332.61	−1.37851
$143$	0	0
$144$	−695.672	−0.402588
$145$	−230.583	−0.132061
$146$	−2768.08	−1.56910
$147$	−1029.00	−0.577348
$148$	−153.325	−0.0851571
$149$	2895.17	1.59182	0.795911	−	0.605414i	$-0.206992\pi$
$149$	2895.17	1.59182	0.795911	+	0.605414i	$0.206992\pi$
$150$	277.035	0.150799
$151$	−3342.60	−1.80144	−0.900719	−	0.434402i	$-0.856960\pi$
$151$	−3342.60	−1.80144	−0.900719	+	0.434402i	$0.856960\pi$
$152$	−6.82162	−0.00364017
$153$	−24.0867	−0.0127274
$154$	0	0
$155$	994.393	0.515301
$156$	1073.26	0.550832
$157$	−848.828	−0.431490	−0.215745	−	0.976450i	$-0.569218\pi$
$157$	−848.828	−0.431490	−0.215745	+	0.976450i	$0.569218\pi$
$158$	1877.55	0.945379
$159$	−368.762	−0.183929
$160$	−1079.51	−0.533391
$161$	2.82783	0.00138425
$162$	299.197	0.145106
$163$	2584.81	1.24207	0.621036	−	0.783782i	$-0.286712\pi$
$163$	2584.81	1.24207	0.621036	+	0.783782i	$0.286712\pi$
$164$	1249.08	0.594737
$165$	0	0
$166$	4056.11	1.89648
$167$	−101.377	−0.0469746	−0.0234873	−	0.999724i	$-0.507477\pi$
$167$	−101.377	−0.0469746	−0.0234873	+	0.999724i	$0.507477\pi$
$168$	−1.05569	−0.000484812 0
$169$	1820.70	0.828721
$170$	−49.4284	−0.0222999
$171$	7.05510	0.00315507
$172$	2072.67	0.918834
$173$	1546.93	0.679833	0.339916	−	0.940456i	$-0.389601\pi$
$173$	1546.93	0.679833	0.339916	+	0.940456i	$0.389601\pi$
$174$	−511.036	−0.222652
$175$	1.01095	0.000436689 0
$176$	0	0
$177$	124.537	0.0528858
$178$	2169.88	0.913705
$179$	−2394.73	−0.999947	−0.499974	−	0.866041i	$-0.666657\pi$
$179$	−2394.73	−0.999947	−0.499974	+	0.866041i	$0.666657\pi$
$180$	253.985	0.105172
$181$	2773.71	1.13905	0.569526	−	0.821973i	$-0.307127\pi$
$181$	2773.71	1.13905	0.569526	+	0.821973i	$0.307127\pi$
$182$	9.46783	0.00385606
$183$	1339.93	0.541259
$184$	−608.543	−0.243817
$185$	−135.827	−0.0539796
$186$	2203.85	0.868786
$187$	0	0
$188$	2367.64	0.918498
$189$	1.09182	0.000420204 0
$190$	14.4778	0.00552806
$191$	−3142.52	−1.19050	−0.595248	−	0.803542i	$-0.702946\pi$
$191$	−3142.52	−1.19050	−0.595248	+	0.803542i	$0.702946\pi$
$192$	−537.362	−0.201983
$193$	−4922.60	−1.83594	−0.917970	−	0.396650i	$-0.870173\pi$
$193$	−4922.60	−1.83594	−0.917970	+	0.396650i	$0.870173\pi$
$194$	−3633.94	−1.34486
$195$	950.780	0.349163
$196$	−1935.92	−0.705511
$197$	−2010.24	−0.727025	−0.363512	−	0.931589i	$-0.618423\pi$
$197$	−2010.24	−0.727025	−0.363512	+	0.931589i	$0.618423\pi$
$198$	0	0
$199$	−1814.84	−0.646485	−0.323243	−	0.946316i	$-0.604773\pi$
$199$	−1814.84	−0.646485	−0.323243	+	0.946316i	$0.604773\pi$
$200$	−217.554	−0.0769169
$201$	1315.20	0.461528
$202$	−1561.56	−0.543914
$203$	−1.86486	−0.000644766 0
$204$	−45.3159	−0.0155527
$205$	1106.54	0.376994
$206$	−1335.85	−0.451810
$207$	629.371	0.211325
$208$	−4899.49	−1.63326
$209$	0	0
$210$	2.24054	0.000736247 0
$211$	2961.91	0.966380	0.483190	−	0.875515i	$-0.339478\pi$
$211$	2961.91	0.966380	0.483190	+	0.875515i	$0.339478\pi$
$212$	−693.778	−0.224759
$213$	−1894.48	−0.609426
$214$	5469.30	1.74707
$215$	1836.13	0.582433
$216$	−234.958	−0.0740133
$217$	8.04224	0.00251587
$218$	−7715.55	−2.39708
$219$	−2248.16	−0.693684
$220$	0	0
$221$	−169.638	−0.0516338
$222$	−301.031	−0.0910085
$223$	−1756.72	−0.527527	−0.263764	−	0.964587i	$-0.584964\pi$
$223$	−1756.72	−0.527527	−0.263764	+	0.964587i	$0.584964\pi$
$224$	−8.73061	−0.00260419
$225$	225.000	0.0666667
$226$	4181.59	1.23078
$227$	−5127.19	−1.49914	−0.749568	−	0.661928i	$-0.769739\pi$
$227$	−5127.19	−1.49914	−0.749568	+	0.661928i	$0.769739\pi$
$228$	13.2733	0.00385545
$229$	−1514.30	−0.436978	−0.218489	−	0.975839i	$-0.570113\pi$
$229$	−1514.30	−0.436978	−0.218489	+	0.975839i	$0.570113\pi$
$230$	1291.54	0.370267
$231$	0	0
$232$	401.314	0.113567
$233$	−2581.48	−0.725830	−0.362915	−	0.931822i	$-0.618218\pi$
$233$	−2581.48	−0.725830	−0.362915	+	0.931822i	$0.618218\pi$
$234$	2107.19	0.588681
$235$	2097.44	0.582220
$236$	234.301	0.0646258
$237$	1524.90	0.417944
$238$	−0.399756	−0.000108875 0
$239$	895.538	0.242375	0.121187	−	0.992630i	$-0.461330\pi$
$239$	895.538	0.242375	0.121187	+	0.992630i	$0.461330\pi$
$240$	−1159.45	−0.311843
$241$	358.286	0.0957644	0.0478822	−	0.998853i	$-0.484753\pi$
$241$	358.286	0.0957644	0.0478822	+	0.998853i	$0.484753\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	2520.90	0.661411
$245$	−1714.99	−0.447211
$246$	2452.39	0.635604
$247$	49.6878	0.0127998
$248$	−1730.67	−0.443137
$249$	3294.27	0.838416
$250$	461.724	0.116808
$251$	−133.878	−0.0336666	−0.0168333	−	0.999858i	$-0.505358\pi$
$251$	−133.878	−0.0336666	−0.0168333	+	0.999858i	$0.505358\pi$
$252$	2.05413	0.000513483 0
$253$	0	0
$254$	9754.34	2.40961
$255$	−40.1444	−0.00985859
$256$	5368.99	1.31079
$257$	−5877.64	−1.42660	−0.713302	−	0.700856i	$-0.752801\pi$
$257$	−5877.64	−1.42660	−0.713302	+	0.700856i	$0.752801\pi$
$258$	4069.38	0.981970
$259$	−1.09852	−0.000263546 0
$260$	1788.77	0.426672
$261$	−415.050	−0.0984327
$262$	−1027.95	−0.242392
$263$	5487.60	1.28662	0.643308	−	0.765607i	$-0.277561\pi$
$263$	5487.60	1.28662	0.643308	+	0.765607i	$0.277561\pi$
$264$	0	0
$265$	−614.603	−0.142471
$266$	0.117091	2.69898e−5 0
$267$	1762.32	0.403941
$268$	2474.38	0.563982
$269$	−4002.94	−0.907300	−0.453650	−	0.891180i	$-0.649878\pi$
$269$	−4002.94	−0.907300	−0.453650	+	0.891180i	$0.649878\pi$
$270$	498.662	0.112399
$271$	1333.17	0.298835	0.149418	−	0.988774i	$-0.452260\pi$
$271$	1333.17	0.298835	0.149418	+	0.988774i	$0.452260\pi$
$272$	206.869	0.0461150
$273$	7.68951	0.00170473
$274$	−2017.87	−0.444906
$275$	0	0
$276$	1184.08	0.258236
$277$	2278.90	0.494317	0.247159	−	0.968975i	$-0.420503\pi$
$277$	2278.90	0.494317	0.247159	+	0.968975i	$0.420503\pi$
$278$	4128.23	0.890628
$279$	1789.91	0.384082
$280$	−1.75949	−0.000375534 0
$281$	5084.11	1.07933	0.539666	−	0.841879i	$-0.318550\pi$
$281$	5084.11	1.07933	0.539666	+	0.841879i	$0.318550\pi$
$282$	4648.50	0.981611
$283$	−7423.54	−1.55931	−0.779653	−	0.626212i	$-0.784605\pi$
$283$	−7423.54	−1.55931	−0.779653	+	0.626212i	$0.784605\pi$
$284$	−3564.22	−0.744710
$285$	11.7585	0.00244391
$286$	0	0
$287$	8.94920	0.00184061
$288$	−1943.11	−0.397566
$289$	−4905.84	−0.998542
$290$	−851.726	−0.172466
$291$	−2951.39	−0.594549
$292$	−4229.63	−0.847672
$293$	4228.69	0.843149	0.421574	−	0.906794i	$-0.361478\pi$
$293$	4228.69	0.843149	0.421574	+	0.906794i	$0.361478\pi$
$294$	−3800.90	−0.753989
$295$	207.562	0.0409652
$296$	236.398	0.0464202
$297$	0	0
$298$	10694.2	2.07884
$299$	4432.54	0.857326
$300$	423.309	0.0814658
$301$	14.8499	0.00284363
$302$	−12346.9	−2.35259
$303$	−1268.25	−0.240460
$304$	−60.5930	−0.0114317
$305$	2233.22	0.419258
$306$	−88.9711	−0.0166214
$307$	458.603	0.0852568	0.0426284	−	0.999091i	$-0.486427\pi$
$307$	458.603	0.0852568	0.0426284	+	0.999091i	$0.486427\pi$
$308$	0	0
$309$	−1084.94	−0.199741
$310$	3673.08	0.672959
$311$	−7400.53	−1.34934	−0.674672	−	0.738118i	$-0.735715\pi$
$311$	−7400.53	−1.34934	−0.674672	+	0.738118i	$0.735715\pi$
$312$	−1654.77	−0.300265
$313$	9039.59	1.63242	0.816211	−	0.577755i	$-0.196071\pi$
$313$	9039.59	1.63242	0.816211	+	0.577755i	$0.196071\pi$
$314$	−3135.40	−0.563505
$315$	1.81971	0.000325488 0
$316$	2868.90	0.510722
$317$	−1920.73	−0.340313	−0.170156	−	0.985417i	$-0.554427\pi$
$317$	−1920.73	−0.340313	−0.170156	+	0.985417i	$0.554427\pi$
$318$	−1362.13	−0.240203
$319$	0	0
$320$	−895.603	−0.156455
$321$	4442.02	0.772365
$322$	10.4454	0.00180776
$323$	−2.09795	−0.000361402 0
$324$	457.173	0.0783905
$325$	1584.63	0.270460
$326$	9547.74	1.62209
$327$	−6266.36	−1.05973
$328$	−1925.85	−0.324199
$329$	16.9632	0.00284259
$330$	0	0
$331$	−9831.40	−1.63258	−0.816288	−	0.577645i	$-0.803972\pi$
$331$	−9831.40	−1.63258	−0.816288	+	0.577645i	$0.803972\pi$
$332$	6197.74	1.02453
$333$	−244.489	−0.0402340
$334$	−374.465	−0.0613467
$335$	2192.00	0.357498
$336$	−9.37718	−0.00152252
$337$	6487.18	1.04860	0.524301	−	0.851533i	$-0.324326\pi$
$337$	6487.18	1.04860	0.524301	+	0.851533i	$0.324326\pi$
$338$	6725.29	1.08227
$339$	3396.17	0.544115
$340$	−75.5266	−0.0120471
$341$	0	0
$342$	26.0601	0.00412037
$343$	−27.7403	−0.00436687
$344$	−3195.66	−0.500868
$345$	1048.95	0.163692
$346$	5714.05	0.887830
$347$	−4861.11	−0.752041	−0.376021	−	0.926611i	$-0.622708\pi$
$347$	−4861.11	−0.752041	−0.376021	+	0.926611i	$0.622708\pi$
$348$	−780.862	−0.120283
$349$	3215.74	0.493223	0.246612	−	0.969114i	$-0.420683\pi$
$349$	3215.74	0.493223	0.246612	+	0.969114i	$0.420683\pi$
$350$	3.73423	0.000570295 0
$351$	1711.40	0.260251
$352$	0	0
$353$	11549.1	1.74134	0.870672	−	0.491864i	$-0.163684\pi$
$353$	11549.1	1.74134	0.870672	+	0.491864i	$0.163684\pi$
$354$	460.015	0.0690664
$355$	−3157.47	−0.472059
$356$	3315.58	0.493610
$357$	−0.324671	−4.81329e−5 0
$358$	−8845.64	−1.30588
$359$	3496.98	0.514105	0.257053	−	0.966397i	$-0.417249\pi$
$359$	3496.98	0.514105	0.257053	+	0.966397i	$0.417249\pi$
$360$	−391.597	−0.0573305
$361$	−6858.39	−0.999910
$362$	10245.5	1.48755
$363$	0	0
$364$	14.4668	0.00208315
$365$	−3746.94	−0.537325
$366$	4949.42	0.706859
$367$	−9254.06	−1.31623	−0.658117	−	0.752915i	$-0.728647\pi$
$367$	−9254.06	−1.31623	−0.658117	+	0.752915i	$0.728647\pi$
$368$	−5405.38	−0.765692
$369$	1991.76	0.280995
$370$	−501.719	−0.0704949
$371$	−4.97066	−0.000695589 0
$372$	3367.48	0.469344
$373$	5894.65	0.818267	0.409133	−	0.912475i	$-0.365831\pi$
$373$	5894.65	0.818267	0.409133	+	0.912475i	$0.365831\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	−3650.45	−0.500685
$377$	−2923.12	−0.399332
$378$	4.03297	0.000548766 0
$379$	−632.403	−0.0857108	−0.0428554	−	0.999081i	$-0.513645\pi$
$379$	−632.403	−0.0857108	−0.0428554	+	0.999081i	$0.513645\pi$
$380$	22.1221	0.00298642
$381$	7922.21	1.06527
$382$	−11607.8	−1.55473
$383$	−8223.12	−1.09708	−0.548541	−	0.836124i	$-0.684816\pi$
$383$	−8223.12	−1.09708	−0.548541	+	0.836124i	$0.684816\pi$
$384$	3196.73	0.424824
$385$	0	0
$386$	−18183.1	−2.39765
$387$	3305.04	0.434120
$388$	−5552.66	−0.726530
$389$	13565.2	1.76808	0.884039	−	0.467413i	$-0.154814\pi$
$389$	13565.2	1.76808	0.884039	+	0.467413i	$0.154814\pi$
$390$	3511.99	0.455991
$391$	−187.154	−0.0242065
$392$	2984.83	0.384583
$393$	−834.870	−0.107159
$394$	−7425.42	−0.949460
$395$	2541.49	0.323738
$396$	0	0
$397$	−8160.73	−1.03168	−0.515838	−	0.856686i	$-0.672519\pi$
$397$	−8160.73	−1.03168	−0.515838	+	0.856686i	$0.672519\pi$
$398$	−6703.64	−0.844279
$399$	0.0950978	1.19319e−5 0
$400$	−1932.42	−0.241553
$401$	−1647.42	−0.205158	−0.102579	−	0.994725i	$-0.532709\pi$
$401$	−1647.42	−0.205158	−0.102579	+	0.994725i	$0.532709\pi$
$402$	4858.09	0.602735
$403$	12606.0	1.55819
$404$	−2386.06	−0.293838
$405$	405.000	0.0496904
$406$	−6.88841	−0.000842035 0
$407$	0	0
$408$	69.8686	0.00847797
$409$	−5981.37	−0.723129	−0.361565	−	0.932347i	$-0.617757\pi$
$409$	−5981.37	−0.723129	−0.361565	+	0.932347i	$0.617757\pi$
$410$	4087.31	0.492337
$411$	−1638.86	−0.196689
$412$	−2041.17	−0.244081
$413$	1.67868	0.000200005 0
$414$	2324.77	0.275981
$415$	5490.44	0.649434
$416$	−13685.0	−1.61289
$417$	3352.84	0.393739
$418$	0	0
$419$	−16036.5	−1.86977	−0.934885	−	0.354950i	$-0.884498\pi$
$419$	−16036.5	−1.86977	−0.934885	+	0.354950i	$0.884498\pi$
$420$	3.42354	0.000397742 0
$421$	7718.11	0.893486	0.446743	−	0.894662i	$-0.352584\pi$
$421$	7718.11	0.893486	0.446743	+	0.894662i	$0.352584\pi$
$422$	10940.7	1.26205
$423$	3775.39	0.433961
$424$	1069.68	0.122519
$425$	−66.9074	−0.00763643
$426$	−6997.82	−0.795882
$427$	18.0613	0.00204695
$428$	8357.08	0.943820
$429$	0	0
$430$	6782.29	0.760631
$431$	3906.55	0.436593	0.218297	−	0.975882i	$-0.429950\pi$
$431$	3906.55	0.436593	0.218297	+	0.975882i	$0.429950\pi$
$432$	−2087.02	−0.232434
$433$	8120.16	0.901224	0.450612	−	0.892720i	$-0.351206\pi$
$433$	8120.16	0.901224	0.450612	+	0.892720i	$0.351206\pi$
$434$	29.7064	0.00328560
$435$	−691.749	−0.0762456
$436$	−11789.4	−1.29497
$437$	54.8182	0.00600071
$438$	−8304.25	−0.905919
$439$	−2899.99	−0.315282	−0.157641	−	0.987496i	$-0.550389\pi$
$439$	−2899.99	−0.315282	−0.157641	+	0.987496i	$0.550389\pi$
$440$	0	0
$441$	−3086.99	−0.333332
$442$	−626.607	−0.0674314
$443$	−12000.9	−1.28709	−0.643543	−	0.765410i	$-0.722536\pi$
$443$	−12000.9	−1.28709	−0.643543	+	0.765410i	$0.722536\pi$
$444$	−459.975	−0.0491655
$445$	2937.20	0.312891
$446$	−6488.95	−0.688926
$447$	8685.51	0.919039
$448$	−7.24327	−0.000763867 0
$449$	−15852.1	−1.66616	−0.833080	−	0.553152i	$-0.813425\pi$
$449$	−15852.1	−1.66616	−0.833080	+	0.553152i	$0.813425\pi$
$450$	831.104	0.0870636
$451$	0	0
$452$	6389.47	0.664901
$453$	−10027.8	−1.04006
$454$	−18938.8	−1.95780
$455$	12.8159	0.00132048
$456$	−20.4649	−0.00210166
$457$	9910.64	1.01444	0.507221	−	0.861816i	$-0.330673\pi$
$457$	9910.64	1.01444	0.507221	+	0.861816i	$0.330673\pi$
$458$	−5593.52	−0.570673
$459$	−72.2600	−0.00734816
$460$	1973.47	0.200029
$461$	5102.66	0.515519	0.257760	−	0.966209i	$-0.417016\pi$
$461$	5102.66	0.515519	0.257760	+	0.966209i	$0.417016\pi$
$462$	0	0
$463$	5889.70	0.591182	0.295591	−	0.955315i	$-0.404483\pi$
$463$	5889.70	0.591182	0.295591	+	0.955315i	$0.404483\pi$
$464$	3564.67	0.356650
$465$	2983.18	0.297509
$466$	−9535.46	−0.947900
$467$	−8958.05	−0.887643	−0.443822	−	0.896115i	$-0.646378\pi$
$467$	−8958.05	−0.887643	−0.443822	+	0.896115i	$0.646378\pi$
$468$	3219.79	0.318023
$469$	17.7280	0.00174542
$470$	7747.50	0.760353
$471$	−2546.48	−0.249121
$472$	−361.248	−0.0352283
$473$	0	0
$474$	5632.65	0.545815
$475$	19.5975	0.00189304
$476$	−0.610828	−5.88177e−5 0
$477$	−1106.29	−0.106192
$478$	3307.93	0.316530
$479$	11844.6	1.12984	0.564920	−	0.825146i	$-0.308907\pi$
$479$	11844.6	1.12984	0.564920	+	0.825146i	$0.308907\pi$
$480$	−3238.52	−0.307953
$481$	−1721.89	−0.163226
$482$	1323.43	0.125064
$483$	8.48348	0.000799196 0
$484$	0	0
$485$	−4918.99	−0.460535
$486$	897.592	0.0837769
$487$	−12539.3	−1.16675	−0.583376	−	0.812202i	$-0.698269\pi$
$487$	−12539.3	−1.16675	−0.583376	+	0.812202i	$0.698269\pi$
$488$	−3886.76	−0.360544
$489$	7754.42	0.717110
$490$	−6334.83	−0.584037
$491$	−15705.5	−1.44355	−0.721773	−	0.692130i	$-0.756673\pi$
$491$	−15705.5	−1.44355	−0.721773	+	0.692130i	$0.756673\pi$
$492$	3747.25	0.343372
$493$	123.422	0.0112751
$494$	183.536	0.0167160
$495$	0	0
$496$	−15372.7	−1.39164
$497$	−25.5363	−0.00230475
$498$	12168.3	1.09493
$499$	−3043.63	−0.273049	−0.136525	−	0.990637i	$-0.543593\pi$
$499$	−3043.63	−0.273049	−0.136525	+	0.990637i	$0.543593\pi$
$500$	705.514	0.0631031
$501$	−304.130	−0.0271208
$502$	−494.518	−0.0439670
$503$	5107.89	0.452782	0.226391	−	0.974036i	$-0.427307\pi$
$503$	5107.89	0.452782	0.226391	+	0.974036i	$0.427307\pi$
$504$	−3.16707	−0.000279906 0
$505$	−2113.76	−0.186259
$506$	0	0
$507$	5462.10	0.478463
$508$	14904.6	1.30174
$509$	−8161.42	−0.710704	−0.355352	−	0.934733i	$-0.615639\pi$
$509$	−8161.42	−0.710704	−0.355352	+	0.934733i	$0.615639\pi$
$510$	−148.285	−0.0128749
$511$	−30.3037	−0.00262340
$512$	11307.3	0.976011
$513$	21.1653	0.00182158
$514$	−21710.8	−1.86308
$515$	−1808.23	−0.154719
$516$	6218.00	0.530489
$517$	0	0
$518$	−4.05769	−0.000344179 0
$519$	4640.80	0.392502
$520$	−2757.95	−0.232584
$521$	−20203.2	−1.69889	−0.849444	−	0.527680i	$-0.823062\pi$
$521$	−20203.2	−1.69889	−0.849444	+	0.527680i	$0.823062\pi$
$522$	−1533.11	−0.128548
$523$	−16730.5	−1.39880	−0.699400	−	0.714730i	$-0.746549\pi$
$523$	−16730.5	−1.39880	−0.699400	+	0.714730i	$0.746549\pi$
$524$	−1570.70	−0.130947
$525$	3.03284	0.000252122 0
$526$	20270.1	1.68026
$527$	−532.258	−0.0439953
$528$	0	0
$529$	−7276.78	−0.598075
$530$	−2270.22	−0.186060
$531$	373.612	0.0305337
$532$	0.178914	1.45807e−5 0
$533$	14027.6	1.13997
$534$	6509.64	0.527528
$535$	7403.36	0.598271
$536$	−3815.03	−0.307433
$537$	−7184.19	−0.577320
$538$	−14786.0	−1.18489
$539$	0	0
$540$	761.955	0.0607210
$541$	6564.44	0.521677	0.260838	−	0.965382i	$-0.416001\pi$
$541$	6564.44	0.521677	0.260838	+	0.965382i	$0.416001\pi$
$542$	4924.46	0.390265
$543$	8321.14	0.657632
$544$	577.816	0.0455398
$545$	−10443.9	−0.820860
$546$	28.4035	0.00222629
$547$	12075.1	0.943867	0.471933	−	0.881634i	$-0.343556\pi$
$547$	12075.1	0.943867	0.471933	+	0.881634i	$0.343556\pi$
$548$	−3083.31	−0.240351
$549$	4019.79	0.312496
$550$	0	0
$551$	−36.1508	−0.00279506
$552$	−1825.63	−0.140768
$553$	20.5545	0.00158059
$554$	8417.79	0.645556
$555$	−407.482	−0.0311652
$556$	6307.93	0.481144
$557$	−2970.66	−0.225980	−0.112990	−	0.993596i	$-0.536043\pi$
$557$	−2970.66	−0.225980	−0.112990	+	0.993596i	$0.536043\pi$
$558$	6611.55	0.501594
$559$	23276.8	1.76118
$560$	−15.6286	−0.00117934
$561$	0	0
$562$	18779.6	1.40956
$563$	−15522.2	−1.16196	−0.580979	−	0.813919i	$-0.697330\pi$
$563$	−15522.2	−1.16196	−0.580979	+	0.813919i	$0.697330\pi$
$564$	7102.91	0.530295
$565$	5660.29	0.421469
$566$	−27421.0	−2.03638
$567$	3.27547	0.000242605 0
$568$	5495.36	0.405951
$569$	20414.4	1.50407	0.752034	−	0.659124i	$-0.229073\pi$
$569$	20414.4	1.50407	0.752034	+	0.659124i	$0.229073\pi$
$570$	43.4335	0.00319163
$571$	−10858.2	−0.795796	−0.397898	−	0.917430i	$-0.630260\pi$
$571$	−10858.2	−0.795796	−0.397898	+	0.917430i	$0.630260\pi$
$572$	0	0
$573$	−9427.56	−0.687333
$574$	33.0565	0.00240375
$575$	1748.25	0.126795
$576$	−1612.09	−0.116615
$577$	7855.17	0.566750	0.283375	−	0.959009i	$-0.408546\pi$
$577$	7855.17	0.566750	0.283375	+	0.959009i	$0.408546\pi$
$578$	−18121.2	−1.30405
$579$	−14767.8	−1.05998
$580$	−1301.44	−0.0931711
$581$	44.4044	0.00317075
$582$	−10901.8	−0.776453
$583$	0	0
$584$	6521.29	0.462077
$585$	2852.34	0.201589
$586$	15619.9	1.10111
$587$	12563.4	0.883384	0.441692	−	0.897167i	$-0.354378\pi$
$587$	12563.4	0.883384	0.441692	+	0.897167i	$0.354378\pi$
$588$	−5807.77	−0.407327
$589$	155.901	0.0109063
$590$	766.692	0.0534986
$591$	−6030.73	−0.419748
$592$	2099.81	0.145780
$593$	103.440	0.00716321	0.00358160	−	0.999994i	$-0.498860\pi$
$593$	103.440	0.00716321	0.00358160	+	0.999994i	$0.498860\pi$
$594$	0	0
$595$	−0.541119	−3.72836e−5 0
$596$	16340.7	1.12305
$597$	−5444.52	−0.373248
$598$	16372.9	1.11963
$599$	−6530.65	−0.445468	−0.222734	−	0.974879i	$-0.571498\pi$
$599$	−6530.65	−0.445468	−0.222734	+	0.974879i	$0.571498\pi$
$600$	−652.662	−0.0444080
$601$	−9148.12	−0.620898	−0.310449	−	0.950590i	$-0.600479\pi$
$601$	−9148.12	−0.620898	−0.310449	+	0.950590i	$0.600479\pi$
$602$	54.8524	0.00371365
$603$	3945.61	0.266464
$604$	−18866.0	−1.27094
$605$	0	0
$606$	−4684.67	−0.314029
$607$	−13120.8	−0.877357	−0.438679	−	0.898644i	$-0.644553\pi$
$607$	−13120.8	−0.877357	−0.438679	+	0.898644i	$0.644553\pi$
$608$	−169.245	−0.0112891
$609$	−5.59458	−0.000372256 0
$610$	8249.04	0.547531
$611$	26589.4	1.76054
$612$	−135.948	−0.00897935
$613$	14125.9	0.930734	0.465367	−	0.885118i	$-0.345922\pi$
$613$	14125.9	0.930734	0.465367	+	0.885118i	$0.345922\pi$
$614$	1693.98	0.111341
$615$	3319.61	0.217658
$616$	0	0
$617$	−11220.7	−0.732135	−0.366067	−	0.930588i	$-0.619296\pi$
$617$	−11220.7	−0.732135	−0.366067	+	0.930588i	$0.619296\pi$
$618$	−4007.54	−0.260852
$619$	−6634.84	−0.430818	−0.215409	−	0.976524i	$-0.569109\pi$
$619$	−6634.84	−0.430818	−0.215409	+	0.976524i	$0.569109\pi$
$620$	5612.47	0.363552
$621$	1888.11	0.122009
$622$	−27336.0	−1.76218
$623$	23.7548	0.00152764
$624$	−14698.5	−0.942964
$625$	625.000	0.0400000
$626$	33390.4	2.13187
$627$	0	0
$628$	−4790.88	−0.304422
$629$	72.7028	0.00460867
$630$	6.72162	0.000425073 0
$631$	−25589.1	−1.61440	−0.807200	−	0.590278i	$-0.799018\pi$
$631$	−25589.1	−1.61440	−0.807200	+	0.590278i	$0.799018\pi$
$632$	−4423.30	−0.278401
$633$	8885.73	0.557940
$634$	−7094.80	−0.444433
$635$	13203.7	0.825153
$636$	−2081.34	−0.129765
$637$	−21741.1	−1.35230
$638$	0	0
$639$	−5683.44	−0.351852
$640$	5327.89	0.329068
$641$	−12096.9	−0.745393	−0.372697	−	0.927953i	$-0.621567\pi$
$641$	−12096.9	−0.745393	−0.372697	+	0.927953i	$0.621567\pi$
$642$	16407.9	1.00867
$643$	14512.2	0.890053	0.445027	−	0.895517i	$-0.353194\pi$
$643$	14512.2	0.890053	0.445027	+	0.895517i	$0.353194\pi$
$644$	15.9606	0.000976607 0
$645$	5508.40	0.336268
$646$	−7.74938	−0.000471974 0
$647$	20351.3	1.23662	0.618308	−	0.785936i	$-0.287818\pi$
$647$	20351.3	1.23662	0.618308	+	0.785936i	$0.287818\pi$
$648$	−704.875	−0.0427316
$649$	0	0
$650$	5853.31	0.353209
$651$	24.1267	0.00145254
$652$	14588.9	0.876299
$653$	18697.4	1.12050	0.560249	−	0.828324i	$-0.310706\pi$
$653$	18697.4	1.12050	0.560249	+	0.828324i	$0.310706\pi$
$654$	−23146.6	−1.38395
$655$	−1391.45	−0.0830053
$656$	−17106.3	−1.01813
$657$	−6744.49	−0.400498
$658$	62.6586	0.00371229
$659$	−12558.6	−0.742356	−0.371178	−	0.928562i	$-0.621046\pi$
$659$	−12558.6	−0.742356	−0.371178	+	0.928562i	$0.621046\pi$
$660$	0	0
$661$	−13572.8	−0.798667	−0.399333	−	0.916806i	$-0.630758\pi$
$661$	−13572.8	−0.798667	−0.399333	+	0.916806i	$0.630758\pi$
$662$	−36315.2	−2.13207
$663$	−508.914	−0.0298108
$664$	−9555.74	−0.558486
$665$	0.158496	9.24245e−6 0
$666$	−903.093	−0.0525438
$667$	−3224.94	−0.187212
$668$	−572.182	−0.0331413
$669$	−5270.15	−0.304568
$670$	8096.81	0.466876
$671$	0	0
$672$	−26.1918	−0.00150353
$673$	−1488.16	−0.0852367	−0.0426183	−	0.999091i	$-0.513570\pi$
$673$	−1488.16	−0.0852367	−0.0426183	+	0.999091i	$0.513570\pi$
$674$	23962.3	1.36943
$675$	675.000	0.0384900
$676$	10276.2	0.584675
$677$	−1106.70	−0.0628274	−0.0314137	−	0.999506i	$-0.510001\pi$
$677$	−1106.70	−0.0628274	−0.0314137	+	0.999506i	$0.510001\pi$
$678$	12544.8	0.710588
$679$	−39.7827	−0.00224848
$680$	116.448	0.00656701
$681$	−15381.6	−0.865526
$682$	0	0
$683$	26534.9	1.48657	0.743287	−	0.668973i	$-0.233266\pi$
$683$	26534.9	1.48657	0.743287	+	0.668973i	$0.233266\pi$
$684$	39.8198	0.00222595
$685$	−2731.44	−0.152354
$686$	−102.467	−0.00570293
$687$	−4542.91	−0.252289
$688$	−28385.5	−1.57294
$689$	−7791.37	−0.430809
$690$	3874.61	0.213774
$691$	20848.2	1.14776	0.573881	−	0.818939i	$-0.305437\pi$
$691$	20848.2	1.14776	0.573881	+	0.818939i	$0.305437\pi$
$692$	8731.06	0.479632
$693$	0	0
$694$	−17956.0	−0.982131
$695$	5588.06	0.304989
$696$	1203.94	0.0655680
$697$	−592.283	−0.0321870
$698$	11878.3	0.644126
$699$	−7744.44	−0.419058
$700$	5.70591	0.000308090 0
$701$	−16348.4	−0.880844	−0.440422	−	0.897791i	$-0.645171\pi$
$701$	−16348.4	−0.880844	−0.440422	+	0.897791i	$0.645171\pi$
$702$	6321.57	0.339875
$703$	−21.2950	−0.00114247
$704$	0	0
$705$	6292.31	0.336145
$706$	42659.9	2.27411
$707$	−17.0952	−0.000909378 0
$708$	702.902	0.0373117
$709$	17235.6	0.912973	0.456486	−	0.889730i	$-0.349108\pi$
$709$	17235.6	0.912973	0.456486	+	0.889730i	$0.349108\pi$
$710$	−11663.0	−0.616487
$711$	4574.69	0.241300
$712$	−5111.99	−0.269073
$713$	13907.6	0.730496
$714$	−1.19927	−6.28593e−5 0
$715$	0	0
$716$	−13516.1	−0.705477
$717$	2686.61	0.139935
$718$	12917.1	0.671397
$719$	−1353.29	−0.0701937	−0.0350968	−	0.999384i	$-0.511174\pi$
$719$	−1353.29	−0.0701937	−0.0350968	+	0.999384i	$0.511174\pi$
$720$	−3478.36	−0.180043
$721$	−14.6242	−0.000755387 0
$722$	−25333.5	−1.30584
$723$	1074.86	0.0552896
$724$	15655.1	0.803617
$725$	−1152.92	−0.0590596
$726$	0	0
$727$	−2052.50	−0.104708	−0.0523542	−	0.998629i	$-0.516672\pi$
$727$	−2052.50	−0.104708	−0.0523542	+	0.998629i	$0.516672\pi$
$728$	−22.3051	−0.00113555
$729$	729.000	0.0370370
$730$	−13840.4	−0.701721
$731$	−982.806	−0.0497269
$732$	7562.71	0.381866
$733$	−25717.9	−1.29593	−0.647963	−	0.761672i	$-0.724379\pi$
$733$	−25717.9	−1.29593	−0.647963	+	0.761672i	$0.724379\pi$
$734$	−34182.6	−1.71894
$735$	−5144.98	−0.258198
$736$	−15098.0	−0.756141
$737$	0	0
$738$	7357.16	0.366966
$739$	−35541.3	−1.76916	−0.884578	−	0.466392i	$-0.845554\pi$
$739$	−35541.3	−1.76916	−0.884578	+	0.466392i	$0.845554\pi$
$740$	−766.626	−0.0380834
$741$	149.063	0.00738998
$742$	−18.3606	−0.000908407 0
$743$	8009.99	0.395502	0.197751	−	0.980252i	$-0.436636\pi$
$743$	8009.99	0.395502	0.197751	+	0.980252i	$0.436636\pi$
$744$	−5192.02	−0.255845
$745$	14475.8	0.711884
$746$	21773.6	1.06862
$747$	9882.80	0.484060
$748$	0	0
$749$	59.8753	0.00292096
$750$	1385.17	0.0674391
$751$	−37661.3	−1.82993	−0.914966	−	0.403530i	$-0.867783\pi$
$751$	−37661.3	−1.82993	−0.914966	+	0.403530i	$0.867783\pi$
$752$	−32425.1	−1.57237
$753$	−401.634	−0.0194374
$754$	−10797.4	−0.521509
$755$	−16713.0	−0.805628
$756$	6.16238	0.000296460 0
$757$	23072.3	1.10776	0.553881	−	0.832596i	$-0.313146\pi$
$757$	23072.3	1.10776	0.553881	+	0.832596i	$0.313146\pi$
$758$	−2335.97	−0.111934
$759$	0	0
$760$	−34.1081	−0.00162794
$761$	26599.7	1.26707	0.633534	−	0.773715i	$-0.281604\pi$
$761$	26599.7	1.26707	0.633534	+	0.773715i	$0.281604\pi$
$762$	29263.0	1.39119
$763$	−84.4662	−0.00400771
$764$	−17736.7	−0.839912
$765$	−120.433	−0.00569186
$766$	−30374.5	−1.43274
$767$	2631.28	0.123872
$768$	16107.0	0.756784
$769$	−3516.05	−0.164879	−0.0824396	−	0.996596i	$-0.526271\pi$
$769$	−3516.05	−0.164879	−0.0824396	+	0.996596i	$0.526271\pi$
$770$	0	0
$771$	−17632.9	−0.823651
$772$	−27783.7	−1.29528
$773$	−8190.87	−0.381119	−0.190559	−	0.981676i	$-0.561030\pi$
$773$	−8190.87	−0.381119	−0.190559	+	0.981676i	$0.561030\pi$
$774$	12208.1	0.566941
$775$	4971.97	0.230449
$776$	8561.16	0.396041
$777$	−3.29555	−0.000152158 0
$778$	50107.0	2.30903
$779$	173.483	0.00797902
$780$	5366.31	0.246339
$781$	0	0
$782$	−691.307	−0.0316126
$783$	−1245.15	−0.0568301
$784$	26512.7	1.20776
$785$	−4244.14	−0.192968
$786$	−3083.84	−0.139945
$787$	9699.98	0.439348	0.219674	−	0.975573i	$-0.429501\pi$
$787$	9699.98	0.439348	0.219674	+	0.975573i	$0.429501\pi$
$788$	−11346.0	−0.512926
$789$	16462.8	0.742828
$790$	9387.75	0.422786
$791$	45.7781	0.00205775
$792$	0	0
$793$	28310.6	1.26777
$794$	−30144.0	−1.34732
$795$	−1843.81	−0.0822556
$796$	−10243.2	−0.456105
$797$	−38694.4	−1.71973	−0.859866	−	0.510519i	$-0.829453\pi$
$797$	−38694.4	−1.71973	−0.859866	+	0.510519i	$0.829453\pi$
$798$	0.351272	1.55826e−5 0
$799$	−1122.67	−0.0497088
$800$	−5397.54	−0.238540
$801$	5286.96	0.233215
$802$	−6085.24	−0.267927
$803$	0	0
$804$	7423.15	0.325615
$805$	14.1391	0.000619055 0
$806$	46563.9	2.03492
$807$	−12008.8	−0.523830
$808$	3678.85	0.160175
$809$	35467.5	1.54137	0.770687	−	0.637214i	$-0.219913\pi$
$809$	35467.5	1.54137	0.770687	+	0.637214i	$0.219913\pi$
$810$	1495.99	0.0648933
$811$	12823.6	0.555235	0.277618	−	0.960692i	$-0.410455\pi$
$811$	12823.6	0.555235	0.277618	+	0.960692i	$0.410455\pi$
$812$	−10.5255	−0.000454892 0
$813$	3999.52	0.172533
$814$	0	0
$815$	12924.0	0.555471
$816$	620.608	0.0266245
$817$	287.869	0.0123271
$818$	−22094.0	−0.944373
$819$	23.0685	0.000984225 0
$820$	6245.41	0.265975
$821$	19914.6	0.846557	0.423279	−	0.906000i	$-0.360879\pi$
$821$	19914.6	0.846557	0.423279	+	0.906000i	$0.360879\pi$
$822$	−6053.62	−0.256866
$823$	35553.4	1.50585	0.752924	−	0.658107i	$-0.228643\pi$
$823$	35553.4	1.50585	0.752924	+	0.658107i	$0.228643\pi$
$824$	3147.10	0.133051
$825$	0	0
$826$	6.20068	0.000261198 0
$827$	−44031.1	−1.85140	−0.925702	−	0.378254i	$-0.876525\pi$
$827$	−44031.1	−1.85140	−0.925702	+	0.378254i	$0.876525\pi$
$828$	3552.24	0.149093
$829$	−33136.0	−1.38825	−0.694126	−	0.719853i	$-0.744209\pi$
$829$	−33136.0	−1.38825	−0.694126	+	0.719853i	$0.744209\pi$
$830$	20280.6	0.848131
$831$	6836.71	0.285394
$832$	−11353.6	−0.473096
$833$	917.965	0.0381820
$834$	12384.7	0.514205
$835$	−506.883	−0.0210077
$836$	0	0
$837$	5369.72	0.221750
$838$	−59235.5	−2.44183
$839$	22537.4	0.927388	0.463694	−	0.885995i	$-0.346524\pi$
$839$	22537.4	0.927388	0.463694	+	0.885995i	$0.346524\pi$
$840$	−5.27846	−0.000216814 0
$841$	−22262.3	−0.912799
$842$	28509.1	1.16685
$843$	15252.3	0.623153
$844$	16717.4	0.681795
$845$	9103.51	0.370615
$846$	13945.5	0.566733
$847$	0	0
$848$	9501.39	0.384763
$849$	−22270.6	−0.900266
$850$	−247.142	−0.00997283
$851$	−1899.68	−0.0765221
$852$	−10692.7	−0.429959
$853$	19111.1	0.767119	0.383560	−	0.923516i	$-0.374698\pi$
$853$	19111.1	0.767119	0.383560	+	0.923516i	$0.374698\pi$
$854$	66.7148	0.00267322
$855$	35.2755	0.00141099
$856$	−12885.0	−0.514488
$857$	−39383.9	−1.56981	−0.784906	−	0.619615i	$-0.787289\pi$
$857$	−39383.9	−1.56981	−0.784906	+	0.619615i	$0.787289\pi$
$858$	0	0
$859$	2996.24	0.119011	0.0595056	−	0.998228i	$-0.481048\pi$
$859$	2996.24	0.119011	0.0595056	+	0.998228i	$0.481048\pi$
$860$	10363.3	0.410915
$861$	26.8476	0.00106268
$862$	14430.0	0.570171
$863$	35553.7	1.40239	0.701194	−	0.712970i	$-0.252650\pi$
$863$	35553.7	1.40239	0.701194	+	0.712970i	$0.252650\pi$
$864$	−5829.34	−0.229535
$865$	7734.66	0.304030
$866$	29994.2	1.17696
$867$	−14717.5	−0.576509
$868$	45.3913	0.00177498
$869$	0	0
$870$	−2555.18	−0.0995732
$871$	27788.2	1.08102
$872$	18176.9	0.705905
$873$	−8854.18	−0.343263
$874$	202.487	0.00783664
$875$	5.05474	0.000195293 0
$876$	−12688.9	−0.489404
$877$	−4648.55	−0.178986	−0.0894929	−	0.995987i	$-0.528525\pi$
$877$	−4648.55	−0.178986	−0.0894929	+	0.995987i	$0.528525\pi$
$878$	−10712.0	−0.411744
$879$	12686.1	0.486792
$880$	0	0
$881$	−28852.3	−1.10336	−0.551680	−	0.834056i	$-0.686013\pi$
$881$	−28852.3	−1.10336	−0.551680	+	0.834056i	$0.686013\pi$
$882$	−11402.7	−0.435316
$883$	3627.05	0.138233	0.0691166	−	0.997609i	$-0.477982\pi$
$883$	3627.05	0.138233	0.0691166	+	0.997609i	$0.477982\pi$
$884$	−957.455	−0.0364284
$885$	622.686	0.0236513
$886$	−44328.8	−1.68087
$887$	9742.54	0.368796	0.184398	−	0.982852i	$-0.440966\pi$
$887$	9742.54	0.368796	0.184398	+	0.982852i	$0.440966\pi$
$888$	709.195	0.0268007
$889$	106.786	0.00402867
$890$	10849.4	0.408621
$891$	0	0
$892$	−9915.12	−0.372178
$893$	328.836	0.0123226
$894$	32082.5	1.20022
$895$	−11973.6	−0.447190
$896$	43.0897	0.00160661
$897$	13297.6	0.494977
$898$	−58554.3	−2.17593
$899$	−9171.61	−0.340256
$900$	1269.93	0.0470343
$901$	328.972	0.0121639
$902$	0	0
$903$	44.5496	0.00164177
$904$	−9851.35	−0.362446
$905$	13868.6	0.509400
$906$	−37040.7	−1.35827
$907$	−37939.9	−1.38895	−0.694473	−	0.719519i	$-0.744362\pi$
$907$	−37939.9	−1.38895	−0.694473	+	0.719519i	$0.744362\pi$
$908$	−28938.5	−1.05766
$909$	−3804.76	−0.138829
$910$	47.3391	0.00172448
$911$	16855.0	0.612988	0.306494	−	0.951873i	$-0.400844\pi$
$911$	16855.0	0.612988	0.306494	+	0.951873i	$0.400844\pi$
$912$	−181.779	−0.00660012
$913$	0	0
$914$	36607.8	1.32481
$915$	6699.65	0.242058
$916$	−8546.89	−0.308294
$917$	−11.2535	−0.000405259 0
$918$	−266.913	−0.00959636
$919$	−25498.3	−0.915247	−0.457623	−	0.889146i	$-0.651299\pi$
$919$	−25498.3	−0.915247	−0.457623	+	0.889146i	$0.651299\pi$
$920$	−3042.71	−0.109038
$921$	1375.81	0.0492231
$922$	18848.2	0.673244
$923$	−40027.4	−1.42743
$924$	0	0
$925$	−679.137	−0.0241404
$926$	21755.3	0.772057
$927$	−3254.81	−0.115321
$928$	9956.65	0.352201
$929$	−31622.1	−1.11678	−0.558390	−	0.829579i	$-0.688581\pi$
$929$	−31622.1	−1.11678	−0.558390	+	0.829579i	$0.688581\pi$
$930$	11019.3	0.388533
$931$	−268.876	−0.00946516
$932$	−14570.2	−0.512083
$933$	−22201.6	−0.779044
$934$	−33089.2	−1.15922
$935$	0	0
$936$	−4964.30	−0.173358
$937$	45760.9	1.59546	0.797728	−	0.603018i	$-0.206035\pi$
$937$	45760.9	1.59546	0.797728	+	0.603018i	$0.206035\pi$
$938$	65.4836	0.00227944
$939$	27118.8	0.942479
$940$	11838.2	0.410765
$941$	24472.1	0.847786	0.423893	−	0.905712i	$-0.360663\pi$
$941$	24472.1	0.847786	0.423893	+	0.905712i	$0.360663\pi$
$942$	−9406.19	−0.325340
$943$	15476.0	0.534431
$944$	−3208.78	−0.110632
$945$	5.45912	0.000187921 0
$946$	0	0
$947$	−46500.5	−1.59563	−0.797816	−	0.602901i	$-0.794011\pi$
$947$	−46500.5	−1.59563	−0.797816	+	0.602901i	$0.794011\pi$
$948$	8606.69	0.294865
$949$	−47500.2	−1.62478
$950$	72.3891	0.00247222
$951$	−5762.20	−0.196480
$952$	0.941780	3.20623e−5 0
$953$	35809.6	1.21719	0.608597	−	0.793480i	$-0.291733\pi$
$953$	35809.6	1.21719	0.608597	+	0.793480i	$0.291733\pi$
$954$	−4086.39	−0.138681
$955$	−15712.6	−0.532406
$956$	5054.52	0.170999
$957$	0	0
$958$	43751.5	1.47552
$959$	−22.0907	−0.000743844 0
$960$	−2686.81	−0.0903296
$961$	9761.72	0.327673
$962$	−6360.32	−0.213165
$963$	13326.1	0.445925
$964$	2022.21	0.0675632
$965$	−24613.0	−0.821057
$966$	31.3362	0.00104371
$967$	−28182.3	−0.937210	−0.468605	−	0.883408i	$-0.655243\pi$
$967$	−28182.3	−0.937210	−0.468605	+	0.883408i	$0.655243\pi$
$968$	0	0
$969$	−6.29384	−0.000208656 0
$970$	−18169.7	−0.601438
$971$	45727.2	1.51128	0.755641	−	0.654985i	$-0.227325\pi$
$971$	45727.2	1.51128	0.755641	+	0.654985i	$0.227325\pi$
$972$	1371.52	0.0452588
$973$	45.1939	0.00148905
$974$	−46317.5	−1.52372
$975$	4753.90	0.156150
$976$	−34524.1	−1.13226
$977$	52027.3	1.70369	0.851843	−	0.523797i	$-0.175485\pi$
$977$	52027.3	1.70369	0.851843	+	0.523797i	$0.175485\pi$
$978$	28643.2	0.936513
$979$	0	0
$980$	−9679.61	−0.315514
$981$	−18799.1	−0.611833
$982$	−58013.0	−1.88520
$983$	36479.0	1.18362	0.591811	−	0.806077i	$-0.298413\pi$
$983$	36479.0	1.18362	0.591811	+	0.806077i	$0.298413\pi$
$984$	−5777.55	−0.187176
$985$	−10051.2	−0.325135
$986$	455.894	0.0147248
$987$	50.8896	0.00164117
$988$	280.443	0.00903046
$989$	25680.2	0.825664
$990$	0	0
$991$	−28559.8	−0.915472	−0.457736	−	0.889088i	$-0.651340\pi$
$991$	−28559.8	−0.915472	−0.457736	+	0.889088i	$0.651340\pi$
$992$	−42938.2	−1.37428
$993$	−29494.2	−0.942568
$994$	−94.3258	−0.00300989
$995$	−9074.20	−0.289117
$996$	18593.2	0.591514
$997$	−20820.1	−0.661362	−0.330681	−	0.943743i	$-0.607278\pi$
$997$	−20820.1	−0.661362	−0.330681	+	0.943743i	$0.607278\pi$
$998$	−11242.5	−0.356589
$999$	−733.468	−0.0232291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bn.1.9		12
11.3	even	5		165.4.m.a.31.5	yes	24
11.4	even	5		165.4.m.a.16.5	✓	24
11.10	odd	2		1815.4.a.bh.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.a.16.5	✓	24	11.4	even	5
165.4.m.a.31.5	yes	24	11.3	even	5
1815.4.a.bh.1.4		12	11.10	odd	2
1815.4.a.bn.1.9		12	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+3.69379 q^{2} +3.00000 q^{3} +5.64411 q^{4} +5.00000 q^{5} +11.0814 q^{6} +0.0404379 q^{7} -8.70216 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.69379 q^{2} +3.00000 q^{3} +5.64411 q^{4} +5.00000 q^{5} +11.0814 q^{6} +0.0404379 q^{7} -8.70216 q^{8} +9.00000 q^{9} +18.4690 q^{10} +16.9323 q^{12} +63.3853 q^{13} +0.149369 q^{14} +15.0000 q^{15} -77.2969 q^{16} -2.67629 q^{17} +33.2441 q^{18} +0.783900 q^{19} +28.2206 q^{20} +0.121314 q^{21} +69.9301 q^{23} -26.1065 q^{24} +25.0000 q^{25} +234.132 q^{26} +27.0000 q^{27} +0.228236 q^{28} -46.1166 q^{29} +55.4069 q^{30} +198.879 q^{31} -215.902 q^{32} -9.88568 q^{34} +0.202190 q^{35} +50.7970 q^{36} -27.1655 q^{37} +2.89556 q^{38} +190.156 q^{39} -43.5108 q^{40} +221.307 q^{41} +0.448108 q^{42} +367.226 q^{43} +45.0000 q^{45} +258.307 q^{46} +419.488 q^{47} -231.891 q^{48} -342.998 q^{49} +92.3449 q^{50} -8.02888 q^{51} +357.754 q^{52} -122.921 q^{53} +99.7324 q^{54} -0.351897 q^{56} +2.35170 q^{57} -170.345 q^{58} +41.5124 q^{59} +84.6617 q^{60} +446.643 q^{61} +734.617 q^{62} +0.363941 q^{63} -179.121 q^{64} +316.927 q^{65} +438.401 q^{67} -15.1053 q^{68} +209.790 q^{69} +0.746847 q^{70} -631.494 q^{71} -78.3194 q^{72} -749.387 q^{73} -100.344 q^{74} +75.0000 q^{75} +4.42442 q^{76} +702.397 q^{78} +508.299 q^{79} -386.484 q^{80} +81.0000 q^{81} +817.463 q^{82} +1098.09 q^{83} +0.684709 q^{84} -13.3815 q^{85} +1356.46 q^{86} -138.350 q^{87} +587.440 q^{89} +166.221 q^{90} +2.56317 q^{91} +394.693 q^{92} +596.636 q^{93} +1549.50 q^{94} +3.91950 q^{95} -647.705 q^{96} -983.797 q^{97} -1266.97 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9	\( 12 q + 7 q^{2} + 36 q^{3} + 49 q^{4} + 60 q^{5} + 21 q^{6} + 77 q^{7} + 111 q^{8} + 108 q^{9} + 35 q^{10} + 147 q^{12} + 172 q^{13} - 30 q^{14} + 180 q^{15} + 161 q^{16} + 317 q^{17} + 63 q^{18} + 237 q^{19} + 245 q^{20} + 231 q^{21} + 210 q^{23} + 333 q^{24} + 300 q^{25} + 8 q^{26} + 324 q^{27} + 542 q^{28} + 759 q^{29} + 105 q^{30} - 193 q^{31} + 410 q^{32} - 78 q^{34} + 385 q^{35} + 441 q^{36} + 286 q^{37} - 168 q^{38} + 516 q^{39} + 555 q^{40} + 1189 q^{41} - 90 q^{42} + 775 q^{43} + 540 q^{45} + 529 q^{46} + 382 q^{47} + 483 q^{48} + 1195 q^{49} + 175 q^{50} + 951 q^{51} + 1741 q^{52} + 275 q^{53} + 189 q^{54} - 419 q^{56} + 711 q^{57} - 418 q^{58} + 646 q^{59} + 735 q^{60} + 1340 q^{61} + 983 q^{62} + 693 q^{63} - 1489 q^{64} + 860 q^{65} - 185 q^{67} + 3322 q^{68} + 630 q^{69} - 150 q^{70} - 932 q^{71} + 999 q^{72} + 2860 q^{73} + 4187 q^{74} + 900 q^{75} + 1594 q^{76} + 24 q^{78} + 1429 q^{79} + 805 q^{80} + 972 q^{81} - 30 q^{82} + 2590 q^{83} + 1626 q^{84} + 1585 q^{85} - 3195 q^{86} + 2277 q^{87} - 473 q^{89} + 315 q^{90} - 4302 q^{91} + 5462 q^{92} - 579 q^{93} + 2875 q^{94} + 1185 q^{95} + 1230 q^{96} + 318 q^{97} - 194 q^{98}+O(q^{100}) \) 12 * q + 7 * q^2 + 36 * q^3 + 49 * q^4 + 60 * q^5 + 21 * q^6 + 77 * q^7 + 111 * q^8 + 108 * q^9 + 35 * q^10 + 147 * q^12 + 172 * q^13 - 30 * q^14 + 180 * q^15 + 161 * q^16 + 317 * q^17 + 63 * q^18 + 237 * q^19 + 245 * q^20 + 231 * q^21 + 210 * q^23 + 333 * q^24 + 300 * q^25 + 8 * q^26 + 324 * q^27 + 542 * q^28 + 759 * q^29 + 105 * q^30 - 193 * q^31 + 410 * q^32 - 78 * q^34 + 385 * q^35 + 441 * q^36 + 286 * q^37 - 168 * q^38 + 516 * q^39 + 555 * q^40 + 1189 * q^41 - 90 * q^42 + 775 * q^43 + 540 * q^45 + 529 * q^46 + 382 * q^47 + 483 * q^48 + 1195 * q^49 + 175 * q^50 + 951 * q^51 + 1741 * q^52 + 275 * q^53 + 189 * q^54 - 419 * q^56 + 711 * q^57 - 418 * q^58 + 646 * q^59 + 735 * q^60 + 1340 * q^61 + 983 * q^62 + 693 * q^63 - 1489 * q^64 + 860 * q^65 - 185 * q^67 + 3322 * q^68 + 630 * q^69 - 150 * q^70 - 932 * q^71 + 999 * q^72 + 2860 * q^73 + 4187 * q^74 + 900 * q^75 + 1594 * q^76 + 24 * q^78 + 1429 * q^79 + 805 * q^80 + 972 * q^81 - 30 * q^82 + 2590 * q^83 + 1626 * q^84 + 1585 * q^85 - 3195 * q^86 + 2277 * q^87 - 473 * q^89 + 315 * q^90 - 4302 * q^91 + 5462 * q^92 - 579 * q^93 + 2875 * q^94 + 1185 * q^95 + 1230 * q^96 + 318 * q^97 - 194 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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