LMFDB - Embedded newform 1421.4.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1421,4,Mod(1,1421)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1421, 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("1421.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1421 = 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1421.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:	$83.8417141182$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.13458092.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 $ x^5 - x^4 - 14x^3 + 18x^2 + 20*x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.27399$ of defining polynomial
Character	$\chi$	$=$	1421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.63099 q^{2} -9.87991 q^{3} -5.33986 q^{4} +16.8209 q^{5} -16.1141 q^{6} -21.7572 q^{8} +70.6126 q^{9} +O(q^{10})$	\(q+1.63099 q^{2} -9.87991 q^{3} -5.33986 q^{4} +16.8209 q^{5} -16.1141 q^{6} -21.7572 q^{8} +70.6126 q^{9} +27.4348 q^{10} -8.55158 q^{11} +52.7573 q^{12} +11.3429 q^{13} -166.189 q^{15} +7.23299 q^{16} -68.4740 q^{17} +115.169 q^{18} -6.93014 q^{19} -89.8214 q^{20} -13.9476 q^{22} -132.042 q^{23} +214.959 q^{24} +157.944 q^{25} +18.5001 q^{26} -430.889 q^{27} -29.0000 q^{29} -271.054 q^{30} +0.419319 q^{31} +185.855 q^{32} +84.4888 q^{33} -111.681 q^{34} -377.061 q^{36} +395.483 q^{37} -11.3030 q^{38} -112.067 q^{39} -365.977 q^{40} +447.209 q^{41} +184.132 q^{43} +45.6642 q^{44} +1187.77 q^{45} -215.360 q^{46} +97.2612 q^{47} -71.4613 q^{48} +257.605 q^{50} +676.516 q^{51} -60.5693 q^{52} -209.547 q^{53} -702.776 q^{54} -143.845 q^{55} +68.4691 q^{57} -47.2988 q^{58} -45.9651 q^{59} +887.427 q^{60} -427.655 q^{61} +0.683906 q^{62} +245.264 q^{64} +190.798 q^{65} +137.801 q^{66} -405.055 q^{67} +365.641 q^{68} +1304.57 q^{69} -557.971 q^{71} -1536.33 q^{72} +381.988 q^{73} +645.031 q^{74} -1560.47 q^{75} +37.0060 q^{76} -182.780 q^{78} +577.208 q^{79} +121.666 q^{80} +2350.60 q^{81} +729.396 q^{82} +353.745 q^{83} -1151.80 q^{85} +300.318 q^{86} +286.517 q^{87} +186.059 q^{88} +277.871 q^{89} +1937.24 q^{90} +705.088 q^{92} -4.14283 q^{93} +158.632 q^{94} -116.571 q^{95} -1836.23 q^{96} -677.917 q^{97} -603.849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9}+O(q^{10}) $ 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9} + 64 q^{10} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 74 q^{15} + 146 q^{16} - 66 q^{17} - 108 q^{18} - 214 q^{19} - 6 q^{20} - 98 q^{22} + 164 q^{23} - 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} - 145 q^{29} - 234 q^{30} - 420 q^{31} - 652 q^{32} + 576 q^{33} - 204 q^{34} - 260 q^{36} + 378 q^{37} + 496 q^{38} - 374 q^{39} + 80 q^{40} + 1158 q^{41} - 204 q^{43} + 784 q^{44} + 1506 q^{45} + 580 q^{46} - 248 q^{47} + 1880 q^{48} + 908 q^{50} + 228 q^{51} - 1482 q^{52} - 554 q^{53} - 918 q^{54} - 546 q^{55} + 44 q^{57} - 440 q^{59} + 636 q^{60} - 618 q^{61} - 1250 q^{62} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} - 692 q^{71} - 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} - 1302 q^{78} + 272 q^{79} + 890 q^{80} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 1628 q^{85} + 2446 q^{86} + 232 q^{87} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 3468 q^{92} - 40 q^{93} + 5942 q^{94} + 2244 q^{95} - 7386 q^{96} - 1562 q^{97} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9 + 64 * q^10 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 74 * q^15 + 146 * q^16 - 66 * q^17 - 108 * q^18 - 214 * q^19 - 6 * q^20 - 98 * q^22 + 164 * q^23 - 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 - 145 * q^29 - 234 * q^30 - 420 * q^31 - 652 * q^32 + 576 * q^33 - 204 * q^34 - 260 * q^36 + 378 * q^37 + 496 * q^38 - 374 * q^39 + 80 * q^40 + 1158 * q^41 - 204 * q^43 + 784 * q^44 + 1506 * q^45 + 580 * q^46 - 248 * q^47 + 1880 * q^48 + 908 * q^50 + 228 * q^51 - 1482 * q^52 - 554 * q^53 - 918 * q^54 - 546 * q^55 + 44 * q^57 - 440 * q^59 + 636 * q^60 - 618 * q^61 - 1250 * q^62 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 - 692 * q^71 - 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 - 1302 * q^78 + 272 * q^79 + 890 * q^80 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 1628 * q^85 + 2446 * q^86 + 232 * q^87 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 3468 * q^92 - 40 * q^93 + 5942 * q^94 + 2244 * q^95 - 7386 * q^96 - 1562 * q^97 - 238 * 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 $

$2$	1.63099	0.576643	0.288322	−	0.957534i	$-0.406903\pi$
$2$	1.63099	0.576643	0.288322	+	0.957534i	$0.406903\pi$
$3$	−9.87991	−1.90139	−0.950695	−	0.310128i	$-0.899628\pi$
$3$	−9.87991	−1.90139	−0.950695	+	0.310128i	$0.899628\pi$
$4$	−5.33986	−0.667483
$5$	16.8209	1.50451	0.752255	−	0.658872i	$-0.228966\pi$
$5$	16.8209	1.50451	0.752255	+	0.658872i	$0.228966\pi$
$6$	−16.1141	−1.09642
$7$	0	0
$7$	0	0
$8$	−21.7572	−0.961543
$9$	70.6126	2.61528
$10$	27.4348	0.867565
$11$	−8.55158	−0.234400	−0.117200	−	0.993108i	$-0.537392\pi$
$11$	−8.55158	−0.234400	−0.117200	+	0.993108i	$0.537392\pi$
$12$	52.7573	1.26914
$13$	11.3429	0.241996	0.120998	−	0.992653i	$-0.461391\pi$
$13$	11.3429	0.241996	0.120998	+	0.992653i	$0.461391\pi$
$14$	0	0
$15$	−166.189	−2.86066
$16$	7.23299	0.113016
$17$	−68.4740	−0.976904	−0.488452	−	0.872591i	$-0.662438\pi$
$17$	−68.4740	−0.976904	−0.488452	+	0.872591i	$0.662438\pi$
$18$	115.169	1.50808
$19$	−6.93014	−0.0836780	−0.0418390	−	0.999124i	$-0.513322\pi$
$19$	−6.93014	−0.0836780	−0.0418390	+	0.999124i	$0.513322\pi$
$20$	−89.8214	−1.00423
$21$	0	0
$22$	−13.9476	−0.135165
$23$	−132.042	−1.19708	−0.598538	−	0.801095i	$-0.704251\pi$
$23$	−132.042	−1.19708	−0.598538	+	0.801095i	$0.704251\pi$
$24$	214.959	1.82827
$25$	157.944	1.26355
$26$	18.5001	0.139545
$27$	−430.889	−3.07128
$28$	0	0
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−271.054	−1.64958
$31$	0.419319	0.00242941	0.00121471	−	0.999999i	$-0.499613\pi$
$31$	0.419319	0.00242941	0.00121471	+	0.999999i	$0.499613\pi$
$32$	185.855	1.02671
$33$	84.4888	0.445685
$34$	−111.681	−0.563325
$35$	0	0
$36$	−377.061	−1.74565
$37$	395.483	1.75722	0.878609	−	0.477542i	$-0.158472\pi$
$37$	395.483	1.75722	0.878609	+	0.477542i	$0.158472\pi$
$38$	−11.3030	−0.0482524
$39$	−112.067	−0.460128
$40$	−365.977	−1.44665
$41$	447.209	1.70347	0.851736	−	0.523971i	$-0.175550\pi$
$41$	447.209	1.70347	0.851736	+	0.523971i	$0.175550\pi$
$42$	0	0
$43$	184.132	0.653020	0.326510	−	0.945194i	$-0.394127\pi$
$43$	184.132	0.653020	0.326510	+	0.945194i	$0.394127\pi$
$44$	45.6642	0.156458
$45$	1187.77	3.93472
$46$	−215.360	−0.690285
$47$	97.2612	0.301851	0.150926	−	0.988545i	$-0.451775\pi$
$47$	97.2612	0.301851	0.150926	+	0.988545i	$0.451775\pi$
$48$	−71.4613	−0.214886
$49$	0	0
$50$	257.605	0.728617
$51$	676.516	1.85748
$52$	−60.5693	−0.161528
$53$	−209.547	−0.543086	−0.271543	−	0.962426i	$-0.587534\pi$
$53$	−209.547	−0.543086	−0.271543	+	0.962426i	$0.587534\pi$
$54$	−702.776	−1.77103
$55$	−143.845	−0.352657
$56$	0	0
$57$	68.4691	0.159105
$58$	−47.2988	−0.107080
$59$	−45.9651	−0.101426	−0.0507131	−	0.998713i	$-0.516149\pi$
$59$	−45.9651	−0.101426	−0.0507131	+	0.998713i	$0.516149\pi$
$60$	887.427	1.90944
$61$	−427.655	−0.897634	−0.448817	−	0.893624i	$-0.648154\pi$
$61$	−427.655	−0.897634	−0.448817	+	0.893624i	$0.648154\pi$
$62$	0.683906	0.00140091
$63$	0	0
$64$	245.264	0.479031
$65$	190.798	0.364085
$66$	137.801	0.257001
$67$	−405.055	−0.738588	−0.369294	−	0.929313i	$-0.620400\pi$
$67$	−405.055	−0.738588	−0.369294	+	0.929313i	$0.620400\pi$
$68$	365.641	0.652067
$69$	1304.57	2.27611
$70$	0	0
$71$	−557.971	−0.932662	−0.466331	−	0.884610i	$-0.654424\pi$
$71$	−557.971	−0.932662	−0.466331	+	0.884610i	$0.654424\pi$
$72$	−1536.33	−2.51470
$73$	381.988	0.612443	0.306222	−	0.951960i	$-0.400935\pi$
$73$	381.988	0.612443	0.306222	+	0.951960i	$0.400935\pi$
$74$	645.031	1.01329
$75$	−1560.47	−2.40250
$76$	37.0060	0.0558536
$77$	0	0
$78$	−182.780	−0.265330
$79$	577.208	0.822038	0.411019	−	0.911627i	$-0.365173\pi$
$79$	577.208	0.822038	0.411019	+	0.911627i	$0.365173\pi$
$80$	121.666	0.170033
$81$	2350.60	3.22442
$82$	729.396	0.982296
$83$	353.745	0.467813	0.233907	−	0.972259i	$-0.424849\pi$
$83$	353.745	0.467813	0.233907	+	0.972259i	$0.424849\pi$
$84$	0	0
$85$	−1151.80	−1.46976
$86$	300.318	0.376560
$87$	286.517	0.353079
$88$	186.059	0.225385
$89$	277.871	0.330947	0.165473	−	0.986214i	$-0.447085\pi$
$89$	277.871	0.330947	0.165473	+	0.986214i	$0.447085\pi$
$90$	1937.24	2.26893
$91$	0	0
$92$	705.088	0.799027
$93$	−4.14283	−0.00461926
$94$	158.632	0.174060
$95$	−116.571	−0.125894
$96$	−1836.23	−1.95218
$97$	−677.917	−0.709609	−0.354804	−	0.934941i	$-0.615453\pi$
$97$	−677.917	−0.709609	−0.354804	+	0.934941i	$0.615453\pi$
$98$	0	0
$99$	−603.849	−0.613022
$100$	−843.397	−0.843397
$101$	−567.816	−0.559404	−0.279702	−	0.960087i	$-0.590236\pi$
$101$	−567.816	−0.559404	−0.279702	+	0.960087i	$0.590236\pi$
$102$	1103.39	1.07110
$103$	−319.205	−0.305362	−0.152681	−	0.988276i	$-0.548791\pi$
$103$	−319.205	−0.305362	−0.152681	+	0.988276i	$0.548791\pi$
$104$	−246.789	−0.232689
$105$	0	0
$106$	−341.771	−0.313167
$107$	−79.6547	−0.0719674	−0.0359837	−	0.999352i	$-0.511456\pi$
$107$	−79.6547	−0.0719674	−0.0359837	+	0.999352i	$0.511456\pi$
$108$	2300.88	2.05003
$109$	−1708.43	−1.50126	−0.750632	−	0.660721i	$-0.770251\pi$
$109$	−1708.43	−1.50126	−0.750632	+	0.660721i	$0.770251\pi$
$110$	−234.611	−0.203357
$111$	−3907.34	−3.34116
$112$	0	0
$113$	1050.31	0.874383	0.437191	−	0.899369i	$-0.355973\pi$
$113$	1050.31	0.874383	0.437191	+	0.899369i	$0.355973\pi$
$114$	111.673	0.0917465
$115$	−2221.08	−1.80101
$116$	154.856	0.123948
$117$	800.950	0.632887
$118$	−74.9687	−0.0584867
$119$	0	0
$120$	3615.82	2.75065
$121$	−1257.87	−0.945057
$122$	−697.503	−0.517615
$123$	−4418.39	−3.23896
$124$	−2.23910	−0.00162159
$125$	554.143	0.396513
$126$	0	0
$127$	366.926	0.256373	0.128187	−	0.991750i	$-0.459084\pi$
$127$	366.926	0.256373	0.128187	+	0.991750i	$0.459084\pi$
$128$	−1086.81	−0.750482
$129$	−1819.21	−1.24165
$130$	311.190	0.209947
$131$	−2310.86	−1.54123	−0.770614	−	0.637302i	$-0.780050\pi$
$131$	−2310.86	−1.54123	−0.770614	+	0.637302i	$0.780050\pi$
$132$	−451.158	−0.297487
$133$	0	0
$134$	−660.643	−0.425902
$135$	−7247.95	−4.62077
$136$	1489.80	0.939335
$137$	1899.65	1.18466	0.592329	−	0.805696i	$-0.298209\pi$
$137$	1899.65	1.18466	0.592329	+	0.805696i	$0.298209\pi$
$138$	2127.74	1.31250
$139$	−1309.49	−0.799061	−0.399531	−	0.916720i	$-0.630827\pi$
$139$	−1309.49	−0.799061	−0.399531	+	0.916720i	$0.630827\pi$
$140$	0	0
$141$	−960.932	−0.573937
$142$	−910.047	−0.537813
$143$	−96.9994	−0.0567238
$144$	510.740	0.295567
$145$	−487.807	−0.279380
$146$	623.020	0.353161
$147$	0	0
$148$	−2111.83	−1.17291
$149$	1782.98	0.980320	0.490160	−	0.871632i	$-0.336938\pi$
$149$	1782.98	0.980320	0.490160	+	0.871632i	$0.336938\pi$
$150$	−2545.12	−1.38539
$151$	−1631.96	−0.879515	−0.439758	−	0.898116i	$-0.644936\pi$
$151$	−1631.96	−0.879515	−0.439758	+	0.898116i	$0.644936\pi$
$152$	150.781	0.0804600
$153$	−4835.12	−2.55488
$154$	0	0
$155$	7.05333	0.00365508
$156$	598.420	0.307128
$157$	−852.817	−0.433517	−0.216759	−	0.976225i	$-0.569548\pi$
$157$	−852.817	−0.433517	−0.216759	+	0.976225i	$0.569548\pi$
$158$	941.422	0.474022
$159$	2070.31	1.03262
$160$	3126.25	1.54470
$161$	0	0
$162$	3833.81	1.85934
$163$	3280.24	1.57625	0.788123	−	0.615518i	$-0.211053\pi$
$163$	3280.24	1.57625	0.788123	+	0.615518i	$0.211053\pi$
$164$	−2388.04	−1.13704
$165$	1421.18	0.670538
$166$	576.955	0.269761
$167$	1682.26	0.779504	0.389752	−	0.920920i	$-0.372561\pi$
$167$	1682.26	0.779504	0.389752	+	0.920920i	$0.372561\pi$
$168$	0	0
$169$	−2068.34	−0.941438
$170$	−1878.57	−0.847528
$171$	−489.355	−0.218842
$172$	−983.239	−0.435879
$173$	1590.22	0.698854	0.349427	−	0.936964i	$-0.386376\pi$
$173$	1590.22	0.698854	0.349427	+	0.936964i	$0.386376\pi$
$174$	467.308	0.203601
$175$	0	0
$176$	−61.8535	−0.0264908
$177$	454.131	0.192851
$178$	453.206	0.190838
$179$	−1794.60	−0.749356	−0.374678	−	0.927155i	$-0.622247\pi$
$179$	−1794.60	−0.749356	−0.374678	+	0.927155i	$0.622247\pi$
$180$	−6342.52	−2.62635
$181$	−2353.41	−0.966450	−0.483225	−	0.875496i	$-0.660535\pi$
$181$	−2353.41	−0.966450	−0.483225	+	0.875496i	$0.660535\pi$
$182$	0	0
$183$	4225.20	1.70675
$184$	2872.88	1.15104
$185$	6652.40	2.64375
$186$	−6.75693	−0.00266367
$187$	585.560	0.228986
$188$	−519.361	−0.201480
$189$	0	0
$190$	−190.127	−0.0725962
$191$	−2184.35	−0.827508	−0.413754	−	0.910389i	$-0.635783\pi$
$191$	−2184.35	−0.827508	−0.413754	+	0.910389i	$0.635783\pi$
$192$	−2423.19	−0.910825
$193$	−3109.71	−1.15980	−0.579901	−	0.814687i	$-0.696909\pi$
$193$	−3109.71	−1.15980	−0.579901	+	0.814687i	$0.696909\pi$
$194$	−1105.68	−0.409191
$195$	−1885.06	−0.692267
$196$	0	0
$197$	923.756	0.334086	0.167043	−	0.985950i	$-0.446578\pi$
$197$	923.756	0.334086	0.167043	+	0.985950i	$0.446578\pi$
$198$	−984.874	−0.353495
$199$	−4548.71	−1.62035	−0.810174	−	0.586189i	$-0.800628\pi$
$199$	−4548.71	−1.62035	−0.810174	+	0.586189i	$0.800628\pi$
$200$	−3436.42	−1.21496
$201$	4001.91	1.40434
$202$	−926.103	−0.322576
$203$	0	0
$204$	−3612.50	−1.23983
$205$	7522.48	2.56289
$206$	−520.622	−0.176085
$207$	−9323.85	−3.13069
$208$	82.0429	0.0273493
$209$	59.2636	0.0196141
$210$	0	0
$211$	−318.664	−0.103970	−0.0519851	−	0.998648i	$-0.516555\pi$
$211$	−318.664	−0.103970	−0.0519851	+	0.998648i	$0.516555\pi$
$212$	1118.95	0.362500
$213$	5512.70	1.77335
$214$	−129.916	−0.0414995
$215$	3097.27	0.982475
$216$	9374.94	2.95317
$217$	0	0
$218$	−2786.44	−0.865694
$219$	−3774.01	−1.16449
$220$	768.115	0.235392
$221$	−776.691	−0.236407
$222$	−6372.85	−1.92666
$223$	−1706.70	−0.512509	−0.256254	−	0.966609i	$-0.582488\pi$
$223$	−1706.70	−0.512509	−0.256254	+	0.966609i	$0.582488\pi$
$224$	0	0
$225$	11152.8	3.30454
$226$	1713.06	0.504207
$227$	−3043.63	−0.889925	−0.444962	−	0.895549i	$-0.646783\pi$
$227$	−3043.63	−0.889925	−0.444962	+	0.895549i	$0.646783\pi$
$228$	−365.616	−0.106199
$229$	2621.57	0.756500	0.378250	−	0.925704i	$-0.376526\pi$
$229$	2621.57	0.756500	0.378250	+	0.925704i	$0.376526\pi$
$230$	−3622.56	−1.03854
$231$	0	0
$232$	630.960	0.178554
$233$	−2778.73	−0.781291	−0.390646	−	0.920541i	$-0.627748\pi$
$233$	−2778.73	−0.781291	−0.390646	+	0.920541i	$0.627748\pi$
$234$	1306.34	0.364950
$235$	1636.02	0.454138
$236$	245.447	0.0677002
$237$	−5702.76	−1.56301
$238$	0	0
$239$	4722.67	1.27818	0.639088	−	0.769133i	$-0.279312\pi$
$239$	4722.67	1.27818	0.639088	+	0.769133i	$0.279312\pi$
$240$	−1202.05	−0.323299
$241$	4704.13	1.25734	0.628672	−	0.777671i	$-0.283599\pi$
$241$	4704.13	1.25734	0.628672	+	0.777671i	$0.283599\pi$
$242$	−2051.58	−0.544961
$243$	−11589.7	−3.05959
$244$	2283.62	0.599155
$245$	0	0
$246$	−7206.36	−1.86773
$247$	−78.6076	−0.0202497
$248$	−9.12321	−0.00233599
$249$	−3494.96	−0.889496
$250$	903.804	0.228646
$251$	−4449.07	−1.11882	−0.559408	−	0.828893i	$-0.688971\pi$
$251$	−4449.07	−1.11882	−0.559408	+	0.828893i	$0.688971\pi$
$252$	0	0
$253$	1129.17	0.280594
$254$	598.454	0.147836
$255$	11379.6	2.79459
$256$	−3734.70	−0.911792
$257$	−7226.68	−1.75404	−0.877019	−	0.480456i	$-0.840471\pi$
$257$	−7226.68	−1.75404	−0.877019	+	0.480456i	$0.840471\pi$
$258$	−2967.11	−0.715986
$259$	0	0
$260$	−1018.83	−0.243020
$261$	−2047.77	−0.485646
$262$	−3769.00	−0.888739
$263$	−4789.59	−1.12296	−0.561481	−	0.827490i	$-0.689768\pi$
$263$	−4789.59	−1.12296	−0.561481	+	0.827490i	$0.689768\pi$
$264$	−1838.24	−0.428545
$265$	−3524.78	−0.817078
$266$	0	0
$267$	−2745.34	−0.629259
$268$	2162.94	0.492995
$269$	47.0448	0.0106631	0.00533154	−	0.999986i	$-0.498303\pi$
$269$	47.0448	0.0106631	0.00533154	+	0.999986i	$0.498303\pi$
$270$	−11821.4	−2.66454
$271$	−7721.78	−1.73087	−0.865433	−	0.501025i	$-0.832956\pi$
$271$	−7721.78	−1.73087	−0.865433	+	0.501025i	$0.832956\pi$
$272$	−495.272	−0.110405
$273$	0	0
$274$	3098.32	0.683125
$275$	−1350.67	−0.296176
$276$	−6966.20	−1.51926
$277$	−7554.66	−1.63868	−0.819342	−	0.573305i	$-0.805661\pi$
$277$	−7554.66	−1.63868	−0.819342	+	0.573305i	$0.805661\pi$
$278$	−2135.77	−0.460773
$279$	29.6092	0.00635360
$280$	0	0
$281$	−2094.83	−0.444723	−0.222361	−	0.974964i	$-0.571377\pi$
$281$	−2094.83	−0.444723	−0.222361	+	0.974964i	$0.571377\pi$
$282$	−1567.27	−0.330957
$283$	8200.83	1.72257	0.861287	−	0.508119i	$-0.169659\pi$
$283$	8200.83	1.72257	0.861287	+	0.508119i	$0.169659\pi$
$284$	2979.49	0.622536
$285$	1151.71	0.239374
$286$	−158.205	−0.0327094
$287$	0	0
$288$	13123.7	2.68514
$289$	−224.318	−0.0456580
$290$	−795.610	−0.161103
$291$	6697.76	1.34924
$292$	−2039.76	−0.408795
$293$	−3518.87	−0.701620	−0.350810	−	0.936447i	$-0.614094\pi$
$293$	−3518.87	−0.701620	−0.350810	+	0.936447i	$0.614094\pi$
$294$	0	0
$295$	−773.175	−0.152597
$296$	−8604.62	−1.68964
$297$	3684.78	0.719907
$298$	2908.03	0.565295
$299$	−1497.74	−0.289687
$300$	8332.69	1.60363
$301$	0	0
$302$	−2661.71	−0.507167
$303$	5609.97	1.06364
$304$	−50.1256	−0.00945691
$305$	−7193.56	−1.35050
$306$	−7886.06	−1.47325
$307$	8725.36	1.62209	0.811046	−	0.584982i	$-0.198898\pi$
$307$	8725.36	1.62209	0.811046	+	0.584982i	$0.198898\pi$
$308$	0	0
$309$	3153.72	0.580611
$310$	11.5039	0.00210768
$311$	−2640.09	−0.481370	−0.240685	−	0.970603i	$-0.577372\pi$
$311$	−2640.09	−0.481370	−0.240685	+	0.970603i	$0.577372\pi$
$312$	2438.26	0.442433
$313$	1938.00	0.349976	0.174988	−	0.984571i	$-0.444011\pi$
$313$	1938.00	0.349976	0.174988	+	0.984571i	$0.444011\pi$
$314$	−1390.94	−0.249985
$315$	0	0
$316$	−3082.21	−0.548696
$317$	−5546.11	−0.982651	−0.491326	−	0.870976i	$-0.663488\pi$
$317$	−5546.11	−0.982651	−0.491326	+	0.870976i	$0.663488\pi$
$318$	3376.66	0.595452
$319$	247.996	0.0435270
$320$	4125.57	0.720707
$321$	786.981	0.136838
$322$	0	0
$323$	474.534	0.0817454
$324$	−12551.9	−2.15224
$325$	1791.53	0.305774
$326$	5350.04	0.908931
$327$	16879.1	2.85449
$328$	−9730.04	−1.63796
$329$	0	0
$330$	2317.94	0.386661
$331$	185.492	0.0308023	0.0154012	−	0.999881i	$-0.495097\pi$
$331$	185.492	0.0308023	0.0154012	+	0.999881i	$0.495097\pi$
$332$	−1888.95	−0.312257
$333$	27926.1	4.59562
$334$	2743.76	0.449496
$335$	−6813.41	−1.11121
$336$	0	0
$337$	−8508.32	−1.37530	−0.687652	−	0.726040i	$-0.741359\pi$
$337$	−8508.32	−1.37530	−0.687652	+	0.726040i	$0.741359\pi$
$338$	−3373.45	−0.542874
$339$	−10377.0	−1.66254
$340$	6150.43	0.981041
$341$	−3.58584	−0.000569454 0
$342$	−798.135	−0.126194
$343$	0	0
$344$	−4006.20	−0.627906
$345$	21944.0	3.42442
$346$	2593.63	0.402990
$347$	7853.53	1.21498	0.607492	−	0.794326i	$-0.292176\pi$
$347$	7853.53	1.21498	0.607492	+	0.794326i	$0.292176\pi$
$348$	−1529.96	−0.235674
$349$	−6328.33	−0.970624	−0.485312	−	0.874341i	$-0.661294\pi$
$349$	−6328.33	−0.970624	−0.485312	+	0.874341i	$0.661294\pi$
$350$	0	0
$351$	−4887.51	−0.743237
$352$	−1589.35	−0.240661
$353$	7973.45	1.20222	0.601111	−	0.799166i	$-0.294725\pi$
$353$	7973.45	1.20222	0.601111	+	0.799166i	$0.294725\pi$
$354$	740.684	0.111206
$355$	−9385.59	−1.40320
$356$	−1483.79	−0.220901
$357$	0	0
$358$	−2926.98	−0.432111
$359$	−10059.4	−1.47887	−0.739435	−	0.673228i	$-0.764907\pi$
$359$	−10059.4	−1.47887	−0.739435	+	0.673228i	$0.764907\pi$
$360$	−25842.6	−3.78340
$361$	−6810.97	−0.992998
$362$	−3838.39	−0.557297
$363$	12427.6	1.79692
$364$	0	0
$365$	6425.40	0.921426
$366$	6891.27	0.984187
$367$	3032.67	0.431346	0.215673	−	0.976466i	$-0.430805\pi$
$367$	3032.67	0.431346	0.215673	+	0.976466i	$0.430805\pi$
$368$	−955.061	−0.135288
$369$	31578.6	4.45506
$370$	10850.0	1.52450
$371$	0	0
$372$	22.1221	0.00308328
$373$	−11109.4	−1.54215	−0.771077	−	0.636742i	$-0.780282\pi$
$373$	−11109.4	−1.54215	−0.771077	+	0.636742i	$0.780282\pi$
$374$	955.045	0.132043
$375$	−5474.89	−0.753925
$376$	−2116.13	−0.290243
$377$	−328.943	−0.0449375
$378$	0	0
$379$	4510.20	0.611275	0.305638	−	0.952148i	$-0.401130\pi$
$379$	4510.20	0.611275	0.305638	+	0.952148i	$0.401130\pi$
$380$	622.475	0.0840323
$381$	−3625.20	−0.487466
$382$	−3562.66	−0.477177
$383$	−7810.96	−1.04209	−0.521047	−	0.853528i	$-0.674458\pi$
$383$	−7810.96	−1.04209	−0.521047	+	0.853528i	$0.674458\pi$
$384$	10737.6	1.42696
$385$	0	0
$386$	−5071.92	−0.668792
$387$	13002.0	1.70783
$388$	3619.98	0.473652
$389$	9221.90	1.20198	0.600989	−	0.799258i	$-0.294774\pi$
$389$	9221.90	1.20198	0.600989	+	0.799258i	$0.294774\pi$
$390$	−3074.53	−0.399191
$391$	9041.46	1.16943
$392$	0	0
$393$	22831.1	2.93047
$394$	1506.64	0.192648
$395$	9709.17	1.23676
$396$	3224.47	0.409181
$397$	10034.3	1.26854	0.634268	−	0.773113i	$-0.281301\pi$
$397$	10034.3	1.26854	0.634268	+	0.773113i	$0.281301\pi$
$398$	−7418.91	−0.934363
$399$	0	0
$400$	1142.41	0.142801
$401$	−8193.64	−1.02038	−0.510188	−	0.860063i	$-0.670424\pi$
$401$	−8193.64	−1.02038	−0.510188	+	0.860063i	$0.670424\pi$
$402$	6527.09	0.809805
$403$	4.75628	0.000587908 0
$404$	3032.06	0.373392
$405$	39539.3	4.85117
$406$	0	0
$407$	−3382.01	−0.411892
$408$	−14719.1	−1.78604
$409$	−3921.69	−0.474120	−0.237060	−	0.971495i	$-0.576184\pi$
$409$	−3921.69	−0.474120	−0.237060	+	0.971495i	$0.576184\pi$
$410$	12269.1	1.47787
$411$	−18768.4	−2.25250
$412$	1704.51	0.203824
$413$	0	0
$414$	−15207.1	−1.80529
$415$	5950.31	0.703830
$416$	2108.13	0.248460
$417$	12937.6	1.51933
$418$	96.6586	0.0113103
$419$	−3026.66	−0.352892	−0.176446	−	0.984310i	$-0.556460\pi$
$419$	−3026.66	−0.352892	−0.176446	+	0.984310i	$0.556460\pi$
$420$	0	0
$421$	4823.43	0.558384	0.279192	−	0.960235i	$-0.409933\pi$
$421$	4823.43	0.558384	0.279192	+	0.960235i	$0.409933\pi$
$422$	−519.739	−0.0599538
$423$	6867.87	0.789426
$424$	4559.17	0.522200
$425$	−10815.0	−1.23437
$426$	8991.19	1.02259
$427$	0	0
$428$	425.345	0.0480370
$429$	958.346	0.107854
$430$	5051.63	0.566537
$431$	−2029.51	−0.226816	−0.113408	−	0.993548i	$-0.536177\pi$
$431$	−2029.51	−0.226816	−0.113408	+	0.993548i	$0.536177\pi$
$432$	−3116.61	−0.347102
$433$	535.808	0.0594672	0.0297336	−	0.999558i	$-0.490534\pi$
$433$	535.808	0.0594672	0.0297336	+	0.999558i	$0.490534\pi$
$434$	0	0
$435$	4819.49	0.531211
$436$	9122.77	1.00207
$437$	915.072	0.100169
$438$	−6155.38	−0.671497
$439$	−8791.74	−0.955824	−0.477912	−	0.878408i	$-0.658606\pi$
$439$	−8791.74	−0.955824	−0.477912	+	0.878408i	$0.658606\pi$
$440$	3129.68	0.339095
$441$	0	0
$442$	−1266.78	−0.136322
$443$	13916.9	1.49258	0.746291	−	0.665619i	$-0.231833\pi$
$443$	13916.9	1.49258	0.746291	+	0.665619i	$0.231833\pi$
$444$	20864.7	2.23016
$445$	4674.05	0.497912
$446$	−2783.62	−0.295535
$447$	−17615.7	−1.86397
$448$	0	0
$449$	2129.54	0.223829	0.111915	−	0.993718i	$-0.464302\pi$
$449$	2129.54	0.223829	0.111915	+	0.993718i	$0.464302\pi$
$450$	18190.2	1.90554
$451$	−3824.35	−0.399294
$452$	−5608.53	−0.583635
$453$	16123.6	1.67230
$454$	−4964.14	−0.513169
$455$	0	0
$456$	−1489.70	−0.152986
$457$	1932.25	0.197783	0.0988915	−	0.995098i	$-0.468470\pi$
$457$	1932.25	0.197783	0.0988915	+	0.995098i	$0.468470\pi$
$458$	4275.77	0.436231
$459$	29504.6	3.00035
$460$	11860.2	1.20214
$461$	16518.3	1.66884	0.834418	−	0.551132i	$-0.185804\pi$
$461$	16518.3	1.66884	0.834418	+	0.551132i	$0.185804\pi$
$462$	0	0
$463$	11535.2	1.15785	0.578926	−	0.815380i	$-0.303472\pi$
$463$	11535.2	1.15785	0.578926	+	0.815380i	$0.303472\pi$
$464$	−209.757	−0.0209865
$465$	−69.6863	−0.00694973
$466$	−4532.10	−0.450526
$467$	−15667.8	−1.55250	−0.776250	−	0.630425i	$-0.782880\pi$
$467$	−15667.8	−1.55250	−0.776250	+	0.630425i	$0.782880\pi$
$468$	−4276.96	−0.422441
$469$	0	0
$470$	2668.34	0.261876
$471$	8425.75	0.824285
$472$	1000.07	0.0975255
$473$	−1574.62	−0.153068
$474$	−9301.17	−0.901301
$475$	−1094.57	−0.105731
$476$	0	0
$477$	−14796.7	−1.42032
$478$	7702.65	0.737052
$479$	−4672.28	−0.445682	−0.222841	−	0.974855i	$-0.571533\pi$
$479$	−4672.28	−0.445682	−0.222841	+	0.974855i	$0.571533\pi$
$480$	−30887.1	−2.93707
$481$	4485.92	0.425239
$482$	7672.41	0.725038
$483$	0	0
$484$	6716.85	0.630809
$485$	−11403.2	−1.06761
$486$	−18902.8	−1.76429
$487$	−8465.76	−0.787722	−0.393861	−	0.919170i	$-0.628861\pi$
$487$	−8465.76	−0.787722	−0.393861	+	0.919170i	$0.628861\pi$
$488$	9304.60	0.863113
$489$	−32408.4	−2.99706
$490$	0	0
$491$	−12302.6	−1.13077	−0.565385	−	0.824827i	$-0.691272\pi$
$491$	−12302.6	−1.13077	−0.565385	+	0.824827i	$0.691272\pi$
$492$	23593.6	2.16195
$493$	1985.74	0.181407
$494$	−128.209	−0.0116769
$495$	−10157.3	−0.922297
$496$	3.03293	0.000274562 0
$497$	0	0
$498$	−5700.26	−0.512922
$499$	−2781.31	−0.249516	−0.124758	−	0.992187i	$-0.539815\pi$
$499$	−2781.31	−0.249516	−0.124758	+	0.992187i	$0.539815\pi$
$500$	−2959.05	−0.264665
$501$	−16620.6	−1.48214
$502$	−7256.40	−0.645158
$503$	13673.9	1.21211	0.606054	−	0.795424i	$-0.292752\pi$
$503$	13673.9	1.21211	0.606054	+	0.795424i	$0.292752\pi$
$504$	0	0
$505$	−9551.18	−0.841628
$506$	1841.67	0.161803
$507$	20435.0	1.79004
$508$	−1959.33	−0.171125
$509$	−7431.68	−0.647158	−0.323579	−	0.946201i	$-0.604886\pi$
$509$	−7431.68	−0.647158	−0.323579	+	0.946201i	$0.604886\pi$
$510$	18560.1	1.61148
$511$	0	0
$512$	2603.24	0.224704
$513$	2986.12	0.256999
$514$	−11786.7	−1.01145
$515$	−5369.33	−0.459419
$516$	9714.31	0.828776
$517$	−831.737	−0.0707538
$518$	0	0
$519$	−15711.2	−1.32879
$520$	−4151.23	−0.350083
$521$	−7797.86	−0.655721	−0.327860	−	0.944726i	$-0.606328\pi$
$521$	−7797.86	−0.655721	−0.327860	+	0.944726i	$0.606328\pi$
$522$	−3339.89	−0.280044
$523$	16670.9	1.39382	0.696908	−	0.717160i	$-0.254558\pi$
$523$	16670.9	1.39382	0.696908	+	0.717160i	$0.254558\pi$
$524$	12339.7	1.02874
$525$	0	0
$526$	−7811.79	−0.647548
$527$	−28.7124	−0.00237331
$528$	611.107	0.0503693
$529$	5268.18	0.432990
$530$	−5748.90	−0.471163
$531$	−3245.71	−0.265258
$532$	0	0
$533$	5072.64	0.412233
$534$	−4477.63	−0.362858
$535$	−1339.87	−0.108276
$536$	8812.88	0.710184
$537$	17730.5	1.42482
$538$	76.7297	0.00614880
$539$	0	0
$540$	38703.0	3.08428
$541$	13400.1	1.06491	0.532455	−	0.846458i	$-0.321270\pi$
$541$	13400.1	1.06491	0.532455	+	0.846458i	$0.321270\pi$
$542$	−12594.2	−0.998092
$543$	23251.5	1.83760
$544$	−12726.2	−1.00300
$545$	−28737.4	−2.25867
$546$	0	0
$547$	−17339.4	−1.35535	−0.677677	−	0.735360i	$-0.737013\pi$
$547$	−17339.4	−1.35535	−0.677677	+	0.735360i	$0.737013\pi$
$548$	−10143.9	−0.790739
$549$	−30197.9	−2.34757
$550$	−2202.93	−0.170788
$551$	200.974	0.0155386
$552$	−28383.7	−2.18857
$553$	0	0
$554$	−12321.6	−0.944936
$555$	−65725.1	−5.02680
$556$	6992.50	0.533360
$557$	−7790.90	−0.592659	−0.296330	−	0.955086i	$-0.595763\pi$
$557$	−7790.90	−0.592659	−0.296330	+	0.955086i	$0.595763\pi$
$558$	48.2924	0.00366376
$559$	2088.58	0.158028
$560$	0	0
$561$	−5785.28	−0.435392
$562$	−3416.66	−0.256447
$563$	21514.2	1.61051	0.805253	−	0.592932i	$-0.202030\pi$
$563$	21514.2	1.61051	0.805253	+	0.592932i	$0.202030\pi$
$564$	5131.24	0.383093
$565$	17667.3	1.31552
$566$	13375.5	0.993311
$567$	0	0
$568$	12139.9	0.896794
$569$	16993.5	1.25203	0.626015	−	0.779811i	$-0.284685\pi$
$569$	16993.5	1.25203	0.626015	+	0.779811i	$0.284685\pi$
$570$	1878.44	0.138034
$571$	16791.4	1.23064	0.615321	−	0.788277i	$-0.289027\pi$
$571$	16791.4	1.23064	0.615321	+	0.788277i	$0.289027\pi$
$572$	517.963	0.0378621
$573$	21581.2	1.57342
$574$	0	0
$575$	−20855.3	−1.51256
$576$	17318.7	1.25280
$577$	−8108.87	−0.585055	−0.292527	−	0.956257i	$-0.594496\pi$
$577$	−8108.87	−0.585055	−0.292527	+	0.956257i	$0.594496\pi$
$578$	−365.860	−0.0263284
$579$	30723.7	2.20524
$580$	2604.82	0.186482
$581$	0	0
$582$	10924.0	0.778032
$583$	1791.96	0.127299
$584$	−8311.00	−0.588890
$585$	13472.7	0.952185
$586$	−5739.25	−0.404584
$587$	−16076.3	−1.13039	−0.565197	−	0.824956i	$-0.691200\pi$
$587$	−16076.3	−1.13039	−0.565197	+	0.824956i	$0.691200\pi$
$588$	0	0
$589$	−2.90594	−0.000203289 0
$590$	−1261.04	−0.0879938
$591$	−9126.63	−0.635227
$592$	2860.53	0.198593
$593$	4341.83	0.300671	0.150335	−	0.988635i	$-0.451965\pi$
$593$	4341.83	0.300671	0.150335	+	0.988635i	$0.451965\pi$
$594$	6009.85	0.415130
$595$	0	0
$596$	−9520.88	−0.654346
$597$	44940.8	3.08091
$598$	−2442.80	−0.167046
$599$	−10540.1	−0.718960	−0.359480	−	0.933153i	$-0.617046\pi$
$599$	−10540.1	−0.718960	−0.359480	+	0.933153i	$0.617046\pi$
$600$	33951.5	2.31011
$601$	−16485.6	−1.11890	−0.559451	−	0.828863i	$-0.688988\pi$
$601$	−16485.6	−1.11890	−0.559451	+	0.828863i	$0.688988\pi$
$602$	0	0
$603$	−28602.0	−1.93162
$604$	8714.43	0.587061
$605$	−21158.6	−1.42185
$606$	9149.82	0.613343
$607$	−13326.5	−0.891112	−0.445556	−	0.895254i	$-0.646994\pi$
$607$	−13326.5	−0.891112	−0.445556	+	0.895254i	$0.646994\pi$
$608$	−1288.00	−0.0859132
$609$	0	0
$610$	−11732.7	−0.778756
$611$	1103.22	0.0730467
$612$	25818.9	1.70534
$613$	20459.4	1.34804	0.674019	−	0.738714i	$-0.264567\pi$
$613$	20459.4	1.34804	0.674019	+	0.738714i	$0.264567\pi$
$614$	14231.0	0.935369
$615$	−74321.4	−4.87305
$616$	0	0
$617$	−3108.50	−0.202826	−0.101413	−	0.994844i	$-0.532336\pi$
$617$	−3108.50	−0.202826	−0.101413	+	0.994844i	$0.532336\pi$
$618$	5143.70	0.334806
$619$	−10426.3	−0.677012	−0.338506	−	0.940964i	$-0.609922\pi$
$619$	−10426.3	−0.677012	−0.338506	+	0.940964i	$0.609922\pi$
$620$	−37.6638	−0.00243970
$621$	56895.5	3.67655
$622$	−4305.97	−0.277579
$623$	0	0
$624$	−810.576	−0.0520016
$625$	−10421.8	−0.666992
$626$	3160.87	0.201811
$627$	−585.519	−0.0372941
$628$	4553.92	0.289365
$629$	−27080.3	−1.71663
$630$	0	0
$631$	18018.2	1.13675	0.568377	−	0.822768i	$-0.307572\pi$
$631$	18018.2	1.13675	0.568377	+	0.822768i	$0.307572\pi$
$632$	−12558.4	−0.790424
$633$	3148.37	0.197688
$634$	−9045.67	−0.566639
$635$	6172.04	0.385716
$636$	−11055.2	−0.689255
$637$	0	0
$638$	404.479	0.0250995
$639$	−39399.8	−2.43917
$640$	−18281.2	−1.12911
$641$	15178.7	0.935295	0.467648	−	0.883915i	$-0.345102\pi$
$641$	15178.7	0.935295	0.467648	+	0.883915i	$0.345102\pi$
$642$	1283.56	0.0789067
$643$	−23957.1	−1.46932	−0.734662	−	0.678433i	$-0.762659\pi$
$643$	−23957.1	−1.46932	−0.734662	+	0.678433i	$0.762659\pi$
$644$	0	0
$645$	−30600.7	−1.86807
$646$	773.962	0.0471379
$647$	12835.2	0.779915	0.389958	−	0.920833i	$-0.372490\pi$
$647$	12835.2	0.779915	0.389958	+	0.920833i	$0.372490\pi$
$648$	−51142.5	−3.10041
$649$	393.074	0.0237743
$650$	2921.98	0.176322
$651$	0	0
$652$	−17516.0	−1.05212
$653$	−4355.97	−0.261045	−0.130523	−	0.991445i	$-0.541665\pi$
$653$	−4355.97	−0.261045	−0.130523	+	0.991445i	$0.541665\pi$
$654$	27529.7	1.64602
$655$	−38870.8	−2.31879
$656$	3234.66	0.192519
$657$	26973.2	1.60171
$658$	0	0
$659$	−32704.1	−1.93319	−0.966594	−	0.256313i	$-0.917492\pi$
$659$	−32704.1	−1.93319	−0.966594	+	0.256313i	$0.917492\pi$
$660$	−7588.91	−0.447572
$661$	2839.66	0.167095	0.0835475	−	0.996504i	$-0.473375\pi$
$661$	2839.66	0.167095	0.0835475	+	0.996504i	$0.473375\pi$
$662$	302.536	0.0177620
$663$	7673.64	0.449501
$664$	−7696.50	−0.449823
$665$	0	0
$666$	45547.3	2.65003
$667$	3829.23	0.222291
$668$	−8983.04	−0.520306
$669$	16862.1	0.974478
$670$	−11112.6	−0.640773
$671$	3657.13	0.210405
$672$	0	0
$673$	−18569.9	−1.06362	−0.531810	−	0.846864i	$-0.678488\pi$
$673$	−18569.9	−1.06362	−0.531810	+	0.846864i	$0.678488\pi$
$674$	−13877.0	−0.793060
$675$	−68056.1	−3.88071
$676$	11044.6	0.628393
$677$	−18106.5	−1.02790	−0.513952	−	0.857819i	$-0.671819\pi$
$677$	−18106.5	−1.02790	−0.513952	+	0.857819i	$0.671819\pi$
$678$	−16924.8	−0.958693
$679$	0	0
$680$	25059.9	1.41324
$681$	30070.8	1.69209
$682$	−5.84848	−0.000328372 0
$683$	−5510.97	−0.308743	−0.154371	−	0.988013i	$-0.549335\pi$
$683$	−5510.97	−0.308743	−0.154371	+	0.988013i	$0.549335\pi$
$684$	2613.09	0.146073
$685$	31953.9	1.78233
$686$	0	0
$687$	−25900.9	−1.43840
$688$	1331.82	0.0738014
$689$	−2376.87	−0.131425
$690$	35790.6	1.97467
$691$	−24652.0	−1.35717	−0.678587	−	0.734520i	$-0.737408\pi$
$691$	−24652.0	−1.35717	−0.678587	+	0.734520i	$0.737408\pi$
$692$	−8491.53	−0.466473
$693$	0	0
$694$	12809.1	0.700613
$695$	−22026.9	−1.20220
$696$	−6233.82	−0.339501
$697$	−30622.2	−1.66413
$698$	−10321.5	−0.559704
$699$	27453.6	1.48554
$700$	0	0
$701$	−3399.10	−0.183142	−0.0915708	−	0.995799i	$-0.529189\pi$
$701$	−3399.10	−0.183142	−0.0915708	+	0.995799i	$0.529189\pi$
$702$	−7971.50	−0.428582
$703$	−2740.75	−0.147041
$704$	−2097.39	−0.112285
$705$	−16163.8	−0.863493
$706$	13004.7	0.693253
$707$	0	0
$708$	−2424.99	−0.128724
$709$	26329.1	1.39465	0.697327	−	0.716753i	$-0.254373\pi$
$709$	26329.1	1.39465	0.697327	+	0.716753i	$0.254373\pi$
$710$	−15307.8	−0.809145
$711$	40758.2	2.14986
$712$	−6045.70	−0.318219
$713$	−55.3678	−0.00290819
$714$	0	0
$715$	−1631.62	−0.0853415
$716$	9582.91	0.500182
$717$	−46659.6	−2.43031
$718$	−16406.8	−0.852781
$719$	−22345.6	−1.15904	−0.579521	−	0.814957i	$-0.696760\pi$
$719$	−22345.6	−1.15904	−0.579521	+	0.814957i	$0.696760\pi$
$720$	8591.13	0.444684
$721$	0	0
$722$	−11108.7	−0.572606
$723$	−46476.4	−2.39070
$724$	12566.9	0.645089
$725$	−4580.37	−0.234635
$726$	20269.4	1.03618
$727$	29862.8	1.52345	0.761727	−	0.647898i	$-0.224352\pi$
$727$	29862.8	1.52345	0.761727	+	0.647898i	$0.224352\pi$
$728$	0	0
$729$	51039.2	2.59306
$730$	10479.8	0.531334
$731$	−12608.2	−0.637938
$732$	−22562.0	−1.13923
$733$	987.919	0.0497812	0.0248906	−	0.999690i	$-0.492076\pi$
$733$	987.919	0.0497812	0.0248906	+	0.999690i	$0.492076\pi$
$734$	4946.27	0.248733
$735$	0	0
$736$	−24540.7	−1.22905
$737$	3463.86	0.173125
$738$	51504.5	2.56898
$739$	−35870.9	−1.78556	−0.892782	−	0.450489i	$-0.851250\pi$
$739$	−35870.9	−1.78556	−0.892782	+	0.450489i	$0.851250\pi$
$740$	−35522.9	−1.76466
$741$	776.636	0.0385026
$742$	0	0
$743$	8322.20	0.410918	0.205459	−	0.978666i	$-0.434131\pi$
$743$	8322.20	0.410918	0.205459	+	0.978666i	$0.434131\pi$
$744$	90.1365	0.00444162
$745$	29991.4	1.47490
$746$	−18119.4	−0.889273
$747$	24978.8	1.22346
$748$	−3126.81	−0.152844
$749$	0	0
$750$	−8929.50	−0.434746
$751$	20781.2	1.00974	0.504872	−	0.863194i	$-0.331540\pi$
$751$	20781.2	1.00974	0.504872	+	0.863194i	$0.331540\pi$
$752$	703.489	0.0341139
$753$	43956.4	2.12730
$754$	−536.504	−0.0259129
$755$	−27451.0	−1.32324
$756$	0	0
$757$	−16424.7	−0.788596	−0.394298	−	0.918983i	$-0.629012\pi$
$757$	−16424.7	−0.788596	−0.394298	+	0.918983i	$0.629012\pi$
$758$	7356.10	0.352488
$759$	−11156.1	−0.533519
$760$	2536.27	0.121053
$761$	−416.312	−0.0198309	−0.00991543	−	0.999951i	$-0.503156\pi$
$761$	−416.312	−0.0198309	−0.00991543	+	0.999951i	$0.503156\pi$
$762$	−5912.67	−0.281094
$763$	0	0
$764$	11664.1	0.552347
$765$	−81331.3	−3.84384
$766$	−12739.6	−0.600916
$767$	−521.376	−0.0245447
$768$	36898.5	1.73367
$769$	37129.2	1.74111	0.870554	−	0.492073i	$-0.163761\pi$
$769$	37129.2	1.74111	0.870554	+	0.492073i	$0.163761\pi$
$770$	0	0
$771$	71398.9	3.33511
$772$	16605.4	0.774148
$773$	2182.83	0.101567	0.0507833	−	0.998710i	$-0.483828\pi$
$773$	2182.83	0.101567	0.0507833	+	0.998710i	$0.483828\pi$
$774$	21206.2	0.984809
$775$	66.2287	0.00306969
$776$	14749.6	0.682319
$777$	0	0
$778$	15040.9	0.693112
$779$	−3099.22	−0.142543
$780$	10066.0	0.462076
$781$	4771.53	0.218616
$782$	14746.6	0.674343
$783$	12495.8	0.570322
$784$	0	0
$785$	−14345.2	−0.652231
$786$	37237.4	1.68984
$787$	−7068.15	−0.320143	−0.160071	−	0.987105i	$-0.551172\pi$
$787$	−7068.15	−0.320143	−0.160071	+	0.987105i	$0.551172\pi$
$788$	−4932.73	−0.222996
$789$	47320.7	2.13519
$790$	15835.6	0.713171
$791$	0	0
$792$	13138.1	0.589446
$793$	−4850.84	−0.217224
$794$	16365.9	0.731493
$795$	34824.5	1.55358
$796$	24289.5	1.08155
$797$	−15086.0	−0.670482	−0.335241	−	0.942132i	$-0.608818\pi$
$797$	−15086.0	−0.670482	−0.335241	+	0.942132i	$0.608818\pi$
$798$	0	0
$799$	−6659.86	−0.294880
$800$	29354.6	1.29730
$801$	19621.2	0.865519
$802$	−13363.8	−0.588393
$803$	−3266.60	−0.143557
$804$	−21369.6	−0.937375
$805$	0	0
$806$	7.75746	0.000339013 0
$807$	−464.798	−0.0202747
$808$	12354.1	0.537890
$809$	−21798.3	−0.947326	−0.473663	−	0.880706i	$-0.657069\pi$
$809$	−21798.3	−0.947326	−0.473663	+	0.880706i	$0.657069\pi$
$810$	64488.3	2.79739
$811$	−5569.61	−0.241153	−0.120577	−	0.992704i	$-0.538474\pi$
$811$	−5569.61	−0.241153	−0.120577	+	0.992704i	$0.538474\pi$
$812$	0	0
$813$	76290.4	3.29105
$814$	−5516.03	−0.237515
$815$	55176.6	2.37148
$816$	4893.24	0.209924
$817$	−1276.06	−0.0546434
$818$	−6396.25	−0.273398
$819$	0	0
$820$	−40169.0	−1.71069
$821$	21281.8	0.904676	0.452338	−	0.891847i	$-0.350590\pi$
$821$	21281.8	0.904676	0.452338	+	0.891847i	$0.350590\pi$
$822$	−30611.1	−1.29889
$823$	16799.0	0.711514	0.355757	−	0.934578i	$-0.384223\pi$
$823$	16799.0	0.711514	0.355757	+	0.934578i	$0.384223\pi$
$824$	6945.02	0.293618
$825$	13344.5	0.563145
$826$	0	0
$827$	7360.62	0.309497	0.154748	−	0.987954i	$-0.450543\pi$
$827$	7360.62	0.309497	0.154748	+	0.987954i	$0.450543\pi$
$828$	49788.1	2.08968
$829$	11634.6	0.487438	0.243719	−	0.969846i	$-0.421633\pi$
$829$	11634.6	0.487438	0.243719	+	0.969846i	$0.421633\pi$
$830$	9704.92	0.405859
$831$	74639.4	3.11578
$832$	2782.00	0.115924
$833$	0	0
$834$	21101.2	0.876110
$835$	28297.2	1.17277
$836$	−316.459	−0.0130921
$837$	−180.680	−0.00746141
$838$	−4936.46	−0.203493
$839$	32151.0	1.32297	0.661486	−	0.749957i	$-0.269926\pi$
$839$	32151.0	1.32297	0.661486	+	0.749957i	$0.269926\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	7866.99	0.321988
$843$	20696.7	0.845592
$844$	1701.62	0.0693984
$845$	−34791.4	−1.41640
$846$	11201.4	0.455217
$847$	0	0
$848$	−1515.66	−0.0613771
$849$	−81023.4	−3.27528
$850$	−17639.2	−0.711789
$851$	−52220.6	−2.10352
$852$	−29437.1	−1.18368
$853$	−35044.9	−1.40670	−0.703349	−	0.710844i	$-0.748313\pi$
$853$	−35044.9	−1.40670	−0.703349	+	0.710844i	$0.748313\pi$
$854$	0	0
$855$	−8231.41	−0.329249
$856$	1733.07	0.0691997
$857$	−7143.05	−0.284716	−0.142358	−	0.989815i	$-0.545468\pi$
$857$	−7143.05	−0.284716	−0.142358	+	0.989815i	$0.545468\pi$
$858$	1563.06	0.0621933
$859$	−33960.3	−1.34891	−0.674454	−	0.738317i	$-0.735621\pi$
$859$	−33960.3	−1.34891	−0.674454	+	0.738317i	$0.735621\pi$
$860$	−16539.0	−0.655785
$861$	0	0
$862$	−3310.11	−0.130792
$863$	45823.4	1.80747	0.903736	−	0.428090i	$-0.140814\pi$
$863$	45823.4	1.80747	0.903736	+	0.428090i	$0.140814\pi$
$864$	−80082.7	−3.15332
$865$	26748.9	1.05143
$866$	873.900	0.0342914
$867$	2216.24	0.0868136
$868$	0	0
$869$	−4936.04	−0.192685
$870$	7860.55	0.306319
$871$	−4594.49	−0.178735
$872$	37170.7	1.44353
$873$	−47869.5	−1.85583
$874$	1492.48	0.0577617
$875$	0	0
$876$	20152.7	0.777279
$877$	−21281.3	−0.819406	−0.409703	−	0.912219i	$-0.634368\pi$
$877$	−21281.3	−0.819406	−0.409703	+	0.912219i	$0.634368\pi$
$878$	−14339.3	−0.551169
$879$	34766.1	1.33405
$880$	−1040.43	−0.0398557
$881$	−1359.32	−0.0519826	−0.0259913	−	0.999662i	$-0.508274\pi$
$881$	−1359.32	−0.0519826	−0.0259913	+	0.999662i	$0.508274\pi$
$882$	0	0
$883$	−47928.2	−1.82663	−0.913313	−	0.407257i	$-0.866485\pi$
$883$	−47928.2	−1.82663	−0.913313	+	0.407257i	$0.866485\pi$
$884$	4147.42	0.157797
$885$	7638.90	0.290146
$886$	22698.5	0.860688
$887$	−3100.58	−0.117370	−0.0586851	−	0.998277i	$-0.518691\pi$
$887$	−3100.58	−0.117370	−0.0586851	+	0.998277i	$0.518691\pi$
$888$	85012.9	3.21266
$889$	0	0
$890$	7623.34	0.287118
$891$	−20101.3	−0.755803
$892$	9113.56	0.342090
$893$	−674.033	−0.0252583
$894$	−28731.1	−1.07485
$895$	−30186.8	−1.12741
$896$	0	0
$897$	14797.5	0.550808
$898$	3473.27	0.129070
$899$	−12.1602	−0.000451131 0
$900$	−59554.5	−2.20572
$901$	14348.5	0.530543
$902$	−6237.48	−0.230250
$903$	0	0
$904$	−22851.9	−0.840756
$905$	−39586.5	−1.45403
$906$	26297.5	0.964321
$907$	23428.1	0.857680	0.428840	−	0.903380i	$-0.358922\pi$
$907$	23428.1	0.857680	0.428840	+	0.903380i	$0.358922\pi$
$908$	16252.6	0.594009
$909$	−40094.9	−1.46300
$910$	0	0
$911$	−12868.3	−0.467999	−0.234000	−	0.972237i	$-0.575181\pi$
$911$	−12868.3	−0.467999	−0.234000	+	0.972237i	$0.575181\pi$
$912$	495.237	0.0179813
$913$	−3025.07	−0.109655
$914$	3151.49	0.114050
$915$	71071.7	2.56782
$916$	−13998.8	−0.504950
$917$	0	0
$918$	48121.9	1.73013
$919$	3938.41	0.141367	0.0706834	−	0.997499i	$-0.477482\pi$
$919$	3938.41	0.141367	0.0706834	+	0.997499i	$0.477482\pi$
$920$	48324.4	1.73175
$921$	−86205.7	−3.08423
$922$	26941.2	0.962323
$923$	−6328.99	−0.225700
$924$	0	0
$925$	62464.1	2.22033
$926$	18813.8	0.667667
$927$	−22539.9	−0.798607
$928$	−5389.79	−0.190656
$929$	15856.7	0.560001	0.280001	−	0.960000i	$-0.409665\pi$
$929$	15856.7	0.560001	0.280001	+	0.960000i	$0.409665\pi$
$930$	−113.658	−0.00400751
$931$	0	0
$932$	14838.0	0.521498
$933$	26083.9	0.915271
$934$	−25554.0	−0.895238
$935$	9849.67	0.344512
$936$	−17426.4	−0.608548
$937$	18559.7	0.647085	0.323542	−	0.946214i	$-0.395126\pi$
$937$	18559.7	0.647085	0.323542	+	0.946214i	$0.395126\pi$
$938$	0	0
$939$	−19147.3	−0.665441
$940$	−8736.14	−0.303129
$941$	−24125.6	−0.835785	−0.417892	−	0.908497i	$-0.637231\pi$
$941$	−24125.6	−0.835785	−0.417892	+	0.908497i	$0.637231\pi$
$942$	13742.4	0.475318
$943$	−59050.6	−2.03919
$944$	−332.465	−0.0114627
$945$	0	0
$946$	−2568.19	−0.0882655
$947$	−6883.31	−0.236196	−0.118098	−	0.993002i	$-0.537680\pi$
$947$	−6883.31	−0.236196	−0.118098	+	0.993002i	$0.537680\pi$
$948$	30452.0	1.04328
$949$	4332.84	0.148209
$950$	−1785.24	−0.0609693
$951$	54795.0	1.86840
$952$	0	0
$953$	37573.8	1.27716	0.638580	−	0.769555i	$-0.279522\pi$
$953$	37573.8	1.27716	0.638580	+	0.769555i	$0.279522\pi$
$954$	−24133.3	−0.819020
$955$	−36742.8	−1.24499
$956$	−25218.4	−0.853161
$957$	−2450.18	−0.0827617
$958$	−7620.45	−0.257000
$959$	0	0
$960$	−40760.2	−1.37034
$961$	−29790.8	−0.999994
$962$	7316.50	0.245211
$963$	−5624.63	−0.188215
$964$	−25119.4	−0.839255
$965$	−52308.2	−1.74493
$966$	0	0
$967$	−1584.28	−0.0526856	−0.0263428	−	0.999653i	$-0.508386\pi$
$967$	−1584.28	−0.0526856	−0.0263428	+	0.999653i	$0.508386\pi$
$968$	27367.8	0.908712
$969$	−4688.35	−0.155430
$970$	−18598.5	−0.615632
$971$	−36569.1	−1.20861	−0.604304	−	0.796754i	$-0.706549\pi$
$971$	−36569.1	−1.20861	−0.604304	+	0.796754i	$0.706549\pi$
$972$	61887.5	2.04222
$973$	0	0
$974$	−13807.6	−0.454234
$975$	−17700.2	−0.581395
$976$	−3093.23	−0.101447
$977$	−33583.0	−1.09971	−0.549854	−	0.835261i	$-0.685317\pi$
$977$	−33583.0	−1.09971	−0.549854	+	0.835261i	$0.685317\pi$
$978$	−52858.0	−1.72823
$979$	−2376.23	−0.0775738
$980$	0	0
$981$	−120637.	−3.92623
$982$	−20065.4	−0.652051
$983$	25900.6	0.840387	0.420193	−	0.907435i	$-0.361962\pi$
$983$	25900.6	0.840387	0.420193	+	0.907435i	$0.361962\pi$
$984$	96131.9	3.11440
$985$	15538.4	0.502635
$986$	3238.74	0.104607
$987$	0	0
$988$	419.754	0.0135163
$989$	−24313.2	−0.781714
$990$	−16566.5	−0.531836
$991$	29604.3	0.948951	0.474475	−	0.880269i	$-0.342638\pi$
$991$	29604.3	0.948951	0.474475	+	0.880269i	$0.342638\pi$
$992$	77.9324	0.00249431
$993$	−1832.65	−0.0585672
$994$	0	0
$995$	−76513.5	−2.43783
$996$	18662.6	0.593723
$997$	−39267.2	−1.24735	−0.623673	−	0.781685i	$-0.714360\pi$
$997$	−39267.2	−1.24735	−0.623673	+	0.781685i	$0.714360\pi$
$998$	−4536.30	−0.143882
$999$	−170409.	−5.39691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1421.4.a.e.1.3		5
7.6	odd	2		29.4.a.b.1.3	✓	5
21.20	even	2		261.4.a.f.1.3		5
28.27	even	2		464.4.a.l.1.1		5
35.34	odd	2		725.4.a.c.1.3		5
56.13	odd	2		1856.4.a.y.1.1		5
56.27	even	2		1856.4.a.bb.1.5		5
203.202	odd	2		841.4.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.b.1.3	✓	5	7.6	odd	2
261.4.a.f.1.3		5	21.20	even	2
464.4.a.l.1.1		5	28.27	even	2
725.4.a.c.1.3		5	35.34	odd	2
841.4.a.b.1.3		5	203.202	odd	2
1421.4.a.e.1.3		5	1.1	even	1	trivial
1856.4.a.y.1.1		5	56.13	odd	2
1856.4.a.bb.1.5		5	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1421 = 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1421.a (trivial)

\(f(q)\)	\(=\)	\(q+1.63099 q^{2} -9.87991 q^{3} -5.33986 q^{4} +16.8209 q^{5} -16.1141 q^{6} -21.7572 q^{8} +70.6126 q^{9} +O(q^{10})\)	\(q+1.63099 q^{2} -9.87991 q^{3} -5.33986 q^{4} +16.8209 q^{5} -16.1141 q^{6} -21.7572 q^{8} +70.6126 q^{9} +27.4348 q^{10} -8.55158 q^{11} +52.7573 q^{12} +11.3429 q^{13} -166.189 q^{15} +7.23299 q^{16} -68.4740 q^{17} +115.169 q^{18} -6.93014 q^{19} -89.8214 q^{20} -13.9476 q^{22} -132.042 q^{23} +214.959 q^{24} +157.944 q^{25} +18.5001 q^{26} -430.889 q^{27} -29.0000 q^{29} -271.054 q^{30} +0.419319 q^{31} +185.855 q^{32} +84.4888 q^{33} -111.681 q^{34} -377.061 q^{36} +395.483 q^{37} -11.3030 q^{38} -112.067 q^{39} -365.977 q^{40} +447.209 q^{41} +184.132 q^{43} +45.6642 q^{44} +1187.77 q^{45} -215.360 q^{46} +97.2612 q^{47} -71.4613 q^{48} +257.605 q^{50} +676.516 q^{51} -60.5693 q^{52} -209.547 q^{53} -702.776 q^{54} -143.845 q^{55} +68.4691 q^{57} -47.2988 q^{58} -45.9651 q^{59} +887.427 q^{60} -427.655 q^{61} +0.683906 q^{62} +245.264 q^{64} +190.798 q^{65} +137.801 q^{66} -405.055 q^{67} +365.641 q^{68} +1304.57 q^{69} -557.971 q^{71} -1536.33 q^{72} +381.988 q^{73} +645.031 q^{74} -1560.47 q^{75} +37.0060 q^{76} -182.780 q^{78} +577.208 q^{79} +121.666 q^{80} +2350.60 q^{81} +729.396 q^{82} +353.745 q^{83} -1151.80 q^{85} +300.318 q^{86} +286.517 q^{87} +186.059 q^{88} +277.871 q^{89} +1937.24 q^{90} +705.088 q^{92} -4.14283 q^{93} +158.632 q^{94} -116.571 q^{95} -1836.23 q^{96} -677.917 q^{97} -603.849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9} + 64 q^{10} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 74 q^{15} + 146 q^{16} - 66 q^{17} - 108 q^{18} - 214 q^{19} - 6 q^{20} - 98 q^{22} + 164 q^{23} - 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} - 145 q^{29} - 234 q^{30} - 420 q^{31} - 652 q^{32} + 576 q^{33} - 204 q^{34} - 260 q^{36} + 378 q^{37} + 496 q^{38} - 374 q^{39} + 80 q^{40} + 1158 q^{41} - 204 q^{43} + 784 q^{44} + 1506 q^{45} + 580 q^{46} - 248 q^{47} + 1880 q^{48} + 908 q^{50} + 228 q^{51} - 1482 q^{52} - 554 q^{53} - 918 q^{54} - 546 q^{55} + 44 q^{57} - 440 q^{59} + 636 q^{60} - 618 q^{61} - 1250 q^{62} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} - 692 q^{71} - 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} - 1302 q^{78} + 272 q^{79} + 890 q^{80} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 1628 q^{85} + 2446 q^{86} + 232 q^{87} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 3468 q^{92} - 40 q^{93} + 5942 q^{94} + 2244 q^{95} - 7386 q^{96} - 1562 q^{97} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9 + 64 * q^10 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 74 * q^15 + 146 * q^16 - 66 * q^17 - 108 * q^18 - 214 * q^19 - 6 * q^20 - 98 * q^22 + 164 * q^23 - 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 - 145 * q^29 - 234 * q^30 - 420 * q^31 - 652 * q^32 + 576 * q^33 - 204 * q^34 - 260 * q^36 + 378 * q^37 + 496 * q^38 - 374 * q^39 + 80 * q^40 + 1158 * q^41 - 204 * q^43 + 784 * q^44 + 1506 * q^45 + 580 * q^46 - 248 * q^47 + 1880 * q^48 + 908 * q^50 + 228 * q^51 - 1482 * q^52 - 554 * q^53 - 918 * q^54 - 546 * q^55 + 44 * q^57 - 440 * q^59 + 636 * q^60 - 618 * q^61 - 1250 * q^62 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 - 692 * q^71 - 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 - 1302 * q^78 + 272 * q^79 + 890 * q^80 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 1628 * q^85 + 2446 * q^86 + 232 * q^87 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 3468 * q^92 - 40 * q^93 + 5942 * q^94 + 2244 * q^95 - 7386 * q^96 - 1562 * q^97 - 238 * q^99

Introduction

L-functions

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