LMFDB - Embedded newform 1815.4.a.bo.1.8

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} - 3 x^{11} - 69 x^{10} + 157 x^{9} + 1812 x^{8} - 2703 x^{7} - 22379 x^{6} + 16453 x^{5} + \cdots + 196416 $ x^12 - 3x^11 - 69x^10 + 157x^9 + 1812x^8 - 2703x^7 - 22379x^6 + 16453x^5 + 129167x^4 - 22672x^3 - 298084x^2 - 19392*x + 196416
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			1.8
Root			$-1.96095$ 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)

$f(q)$	$=$	$q+2.96095 q^{2} +3.00000 q^{3} +0.767233 q^{4} -5.00000 q^{5} +8.88285 q^{6} +25.4365 q^{7} -21.4159 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.96095 q^{2} +3.00000 q^{3} +0.767233 q^{4} -5.00000 q^{5} +8.88285 q^{6} +25.4365 q^{7} -21.4159 q^{8} +9.00000 q^{9} -14.8048 q^{10} +2.30170 q^{12} +53.7812 q^{13} +75.3163 q^{14} -15.0000 q^{15} -69.5492 q^{16} +109.542 q^{17} +26.6486 q^{18} -96.4672 q^{19} -3.83616 q^{20} +76.3095 q^{21} +167.125 q^{23} -64.2476 q^{24} +25.0000 q^{25} +159.243 q^{26} +27.0000 q^{27} +19.5157 q^{28} -237.044 q^{29} -44.4143 q^{30} -4.59471 q^{31} -34.6049 q^{32} +324.349 q^{34} -127.183 q^{35} +6.90510 q^{36} -36.3041 q^{37} -285.635 q^{38} +161.344 q^{39} +107.079 q^{40} -204.882 q^{41} +225.949 q^{42} +143.175 q^{43} -45.0000 q^{45} +494.849 q^{46} +169.869 q^{47} -208.648 q^{48} +304.016 q^{49} +74.0238 q^{50} +328.627 q^{51} +41.2627 q^{52} -328.491 q^{53} +79.9457 q^{54} -544.745 q^{56} -289.402 q^{57} -701.875 q^{58} +160.992 q^{59} -11.5085 q^{60} -93.1403 q^{61} -13.6047 q^{62} +228.929 q^{63} +453.930 q^{64} -268.906 q^{65} +228.879 q^{67} +84.0444 q^{68} +501.376 q^{69} -376.581 q^{70} +1038.89 q^{71} -192.743 q^{72} +832.258 q^{73} -107.495 q^{74} +75.0000 q^{75} -74.0128 q^{76} +477.730 q^{78} +695.039 q^{79} +347.746 q^{80} +81.0000 q^{81} -606.644 q^{82} -252.758 q^{83} +58.5472 q^{84} -547.711 q^{85} +423.935 q^{86} -711.132 q^{87} +931.487 q^{89} -133.243 q^{90} +1368.01 q^{91} +128.224 q^{92} -13.7841 q^{93} +502.973 q^{94} +482.336 q^{95} -103.815 q^{96} +1372.99 q^{97} +900.176 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9	\( 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9} - 45 q^{10} + 171 q^{12} + 78 q^{13} + 262 q^{14} - 180 q^{15} + 225 q^{16} + 313 q^{17} + 81 q^{18} + 51 q^{19} - 285 q^{20} + 63 q^{21} - 34 q^{23} + 369 q^{24} + 300 q^{25} + 28 q^{26} + 324 q^{27} + 376 q^{28} + 31 q^{29} - 135 q^{30} + 655 q^{31} + 1578 q^{32} - 10 q^{34} - 105 q^{35} + 513 q^{36} + 84 q^{37} - 1076 q^{38} + 234 q^{39} - 615 q^{40} + 1463 q^{41} + 786 q^{42} - 111 q^{43} - 540 q^{45} - q^{46} + 278 q^{47} + 675 q^{48} - 325 q^{49} + 225 q^{50} + 939 q^{51} + 1957 q^{52} + 517 q^{53} + 243 q^{54} + 1543 q^{56} + 153 q^{57} + 442 q^{58} - 308 q^{59} - 855 q^{60} + 604 q^{61} + 1773 q^{62} + 189 q^{63} + 4323 q^{64} - 390 q^{65} - 357 q^{67} + 2192 q^{68} - 102 q^{69} - 1310 q^{70} - 620 q^{71} + 1107 q^{72} + 1892 q^{73} + 581 q^{74} + 900 q^{75} + 378 q^{76} + 84 q^{78} + 415 q^{79} - 1125 q^{80} + 972 q^{81} - 2802 q^{82} + 3158 q^{83} + 1128 q^{84} - 1565 q^{85} + 747 q^{86} + 93 q^{87} + 1563 q^{89} - 405 q^{90} + 1434 q^{91} - 3466 q^{92} + 1965 q^{93} - 3 q^{94} - 255 q^{95} + 4734 q^{96} + 714 q^{97} + 6586 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9 - 45 * q^10 + 171 * q^12 + 78 * q^13 + 262 * q^14 - 180 * q^15 + 225 * q^16 + 313 * q^17 + 81 * q^18 + 51 * q^19 - 285 * q^20 + 63 * q^21 - 34 * q^23 + 369 * q^24 + 300 * q^25 + 28 * q^26 + 324 * q^27 + 376 * q^28 + 31 * q^29 - 135 * q^30 + 655 * q^31 + 1578 * q^32 - 10 * q^34 - 105 * q^35 + 513 * q^36 + 84 * q^37 - 1076 * q^38 + 234 * q^39 - 615 * q^40 + 1463 * q^41 + 786 * q^42 - 111 * q^43 - 540 * q^45 - q^46 + 278 * q^47 + 675 * q^48 - 325 * q^49 + 225 * q^50 + 939 * q^51 + 1957 * q^52 + 517 * q^53 + 243 * q^54 + 1543 * q^56 + 153 * q^57 + 442 * q^58 - 308 * q^59 - 855 * q^60 + 604 * q^61 + 1773 * q^62 + 189 * q^63 + 4323 * q^64 - 390 * q^65 - 357 * q^67 + 2192 * q^68 - 102 * q^69 - 1310 * q^70 - 620 * q^71 + 1107 * q^72 + 1892 * q^73 + 581 * q^74 + 900 * q^75 + 378 * q^76 + 84 * q^78 + 415 * q^79 - 1125 * q^80 + 972 * q^81 - 2802 * q^82 + 3158 * q^83 + 1128 * q^84 - 1565 * q^85 + 747 * q^86 + 93 * q^87 + 1563 * q^89 - 405 * q^90 + 1434 * q^91 - 3466 * q^92 + 1965 * q^93 - 3 * q^94 - 255 * q^95 + 4734 * q^96 + 714 * q^97 + 6586 * 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 $

$2$	2.96095	1.04685	0.523427	−	0.852070i	$-0.324653\pi$
$2$	2.96095	1.04685	0.523427	+	0.852070i	$0.324653\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	0.767233	0.0959041
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	8.88285	0.604402
$7$	25.4365	1.37344	0.686721	−	0.726921i	$-0.259049\pi$
$7$	25.4365	1.37344	0.686721	+	0.726921i	$0.259049\pi$
$8$	−21.4159	−0.946457
$9$	9.00000	0.333333
$10$	−14.8048	−0.468168
$11$	0	0
$11$	0	0
$12$	2.30170	0.0553703
$13$	53.7812	1.14740	0.573701	−	0.819065i	$-0.305507\pi$
$13$	53.7812	1.14740	0.573701	+	0.819065i	$0.305507\pi$
$14$	75.3163	1.43779
$15$	−15.0000	−0.258199
$16$	−69.5492	−1.08671
$17$	109.542	1.56282	0.781409	−	0.624019i	$-0.214501\pi$
$17$	109.542	1.56282	0.781409	+	0.624019i	$0.214501\pi$
$18$	26.6486	0.348951
$19$	−96.4672	−1.16479	−0.582397	−	0.812904i	$-0.697885\pi$
$19$	−96.4672	−1.16479	−0.582397	+	0.812904i	$0.697885\pi$
$20$	−3.83616	−0.0428896
$21$	76.3095	0.792957
$22$	0	0
$23$	167.125	1.51513	0.757565	−	0.652759i	$-0.226389\pi$
$23$	167.125	1.51513	0.757565	+	0.652759i	$0.226389\pi$
$24$	−64.2476	−0.546437
$25$	25.0000	0.200000
$26$	159.243	1.20116
$27$	27.0000	0.192450
$28$	19.5157	0.131719
$29$	−237.044	−1.51786	−0.758930	−	0.651172i	$-0.774278\pi$
$29$	−237.044	−1.51786	−0.758930	+	0.651172i	$0.774278\pi$
$30$	−44.4143	−0.270297
$31$	−4.59471	−0.0266204	−0.0133102	−	0.999911i	$-0.504237\pi$
$31$	−4.59471	−0.0266204	−0.0133102	+	0.999911i	$0.504237\pi$
$32$	−34.6049	−0.191167
$33$	0	0
$34$	324.349	1.63604
$35$	−127.183	−0.614222
$36$	6.90510	0.0319680
$37$	−36.3041	−0.161307	−0.0806535	−	0.996742i	$-0.525701\pi$
$37$	−36.3041	−0.161307	−0.0806535	+	0.996742i	$0.525701\pi$
$38$	−285.635	−1.21937
$39$	161.344	0.662452
$40$	107.079	0.423268
$41$	−204.882	−0.780418	−0.390209	−	0.920726i	$-0.627597\pi$
$41$	−204.882	−0.780418	−0.390209	+	0.920726i	$0.627597\pi$
$42$	225.949	0.830111
$43$	143.175	0.507768	0.253884	−	0.967235i	$-0.418292\pi$
$43$	143.175	0.507768	0.253884	+	0.967235i	$0.418292\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	494.849	1.58612
$47$	169.869	0.527189	0.263594	−	0.964634i	$-0.415092\pi$
$47$	169.869	0.527189	0.263594	+	0.964634i	$0.415092\pi$
$48$	−208.648	−0.627410
$49$	304.016	0.886343
$50$	74.0238	0.209371
$51$	328.627	0.902293
$52$	41.2627	0.110040
$53$	−328.491	−0.851354	−0.425677	−	0.904875i	$-0.639964\pi$
$53$	−328.491	−0.851354	−0.425677	+	0.904875i	$0.639964\pi$
$54$	79.9457	0.201467
$55$	0	0
$56$	−544.745	−1.29990
$57$	−289.402	−0.672494
$58$	−701.875	−1.58898
$59$	160.992	0.355243	0.177621	−	0.984099i	$-0.443160\pi$
$59$	160.992	0.355243	0.177621	+	0.984099i	$0.443160\pi$
$60$	−11.5085	−0.0247623
$61$	−93.1403	−0.195498	−0.0977491	−	0.995211i	$-0.531164\pi$
$61$	−93.1403	−0.195498	−0.0977491	+	0.995211i	$0.531164\pi$
$62$	−13.6047	−0.0278677
$63$	228.929	0.457814
$64$	453.930	0.886583
$65$	−268.906	−0.513133
$66$	0	0
$67$	228.879	0.417344	0.208672	−	0.977986i	$-0.433086\pi$
$67$	228.879	0.417344	0.208672	+	0.977986i	$0.433086\pi$
$68$	84.0444	0.149881
$69$	501.376	0.874761
$70$	−376.581	−0.643001
$71$	1038.89	1.73654	0.868268	−	0.496096i	$-0.165233\pi$
$71$	1038.89	1.73654	0.868268	+	0.496096i	$0.165233\pi$
$72$	−192.743	−0.315486
$73$	832.258	1.33436	0.667181	−	0.744895i	$-0.267501\pi$
$73$	832.258	1.33436	0.667181	+	0.744895i	$0.267501\pi$
$74$	−107.495	−0.168865
$75$	75.0000	0.115470
$76$	−74.0128	−0.111709
$77$	0	0
$78$	477.730	0.693491
$79$	695.039	0.989848	0.494924	−	0.868936i	$-0.335196\pi$
$79$	695.039	0.989848	0.494924	+	0.868936i	$0.335196\pi$
$80$	347.746	0.485990
$81$	81.0000	0.111111
$82$	−606.644	−0.816984
$83$	−252.758	−0.334262	−0.167131	−	0.985935i	$-0.553450\pi$
$83$	−252.758	−0.334262	−0.167131	+	0.985935i	$0.553450\pi$
$84$	58.5472	0.0760479
$85$	−547.711	−0.698913
$86$	423.935	0.531559
$87$	−711.132	−0.876337
$88$	0	0
$89$	931.487	1.10941	0.554705	−	0.832047i	$-0.312831\pi$
$89$	931.487	1.10941	0.554705	+	0.832047i	$0.312831\pi$
$90$	−133.243	−0.156056
$91$	1368.01	1.57589
$92$	128.224	0.145307
$93$	−13.7841	−0.0153693
$94$	502.973	0.551890
$95$	482.336	0.520912
$96$	−103.815	−0.110370
$97$	1372.99	1.43718	0.718589	−	0.695435i	$-0.244788\pi$
$97$	1372.99	1.43718	0.718589	+	0.695435i	$0.244788\pi$
$98$	900.176	0.927872
$99$	0	0
$100$	19.1808	0.0191808
$101$	1218.80	1.20074	0.600372	−	0.799721i	$-0.295019\pi$
$101$	1218.80	1.20074	0.600372	+	0.799721i	$0.295019\pi$
$102$	973.048	0.944570
$103$	−1556.35	−1.48885	−0.744427	−	0.667704i	$-0.767277\pi$
$103$	−1556.35	−1.48885	−0.744427	+	0.667704i	$0.767277\pi$
$104$	−1151.77	−1.08597
$105$	−381.548	−0.354621
$106$	−972.647	−0.891244
$107$	1601.34	1.44680	0.723399	−	0.690430i	$-0.242579\pi$
$107$	1601.34	1.44680	0.723399	+	0.690430i	$0.242579\pi$
$108$	20.7153	0.0184568
$109$	−421.812	−0.370663	−0.185331	−	0.982676i	$-0.559336\pi$
$109$	−421.812	−0.370663	−0.185331	+	0.982676i	$0.559336\pi$
$110$	0	0
$111$	−108.912	−0.0931306
$112$	−1769.09	−1.49253
$113$	709.977	0.591053	0.295527	−	0.955335i	$-0.404505\pi$
$113$	709.977	0.591053	0.295527	+	0.955335i	$0.404505\pi$
$114$	−856.904	−0.704004
$115$	−835.626	−0.677587
$116$	−181.868	−0.145569
$117$	484.031	0.382467
$118$	476.688	0.371887
$119$	2786.37	2.14644
$120$	321.238	0.244374
$121$	0	0
$122$	−275.784	−0.204658
$123$	−614.645	−0.450574
$124$	−3.52521	−0.00255301
$125$	−125.000	−0.0894427
$126$	677.846	0.479265
$127$	−1381.97	−0.965593	−0.482796	−	0.875733i	$-0.660379\pi$
$127$	−1381.97	−0.965593	−0.482796	+	0.875733i	$0.660379\pi$
$128$	1620.90	1.11929
$129$	429.525	0.293160
$130$	−796.217	−0.537176
$131$	2655.13	1.77084	0.885419	−	0.464793i	$-0.153871\pi$
$131$	2655.13	1.77084	0.885419	+	0.464793i	$0.153871\pi$
$132$	0	0
$133$	−2453.79	−1.59978
$134$	677.700	0.436898
$135$	−135.000	−0.0860663
$136$	−2345.94	−1.47914
$137$	−596.040	−0.371701	−0.185851	−	0.982578i	$-0.559504\pi$
$137$	−596.040	−0.371701	−0.185851	+	0.982578i	$0.559504\pi$
$138$	1484.55	0.915748
$139$	−1688.56	−1.03037	−0.515186	−	0.857078i	$-0.672277\pi$
$139$	−1688.56	−1.03037	−0.515186	+	0.857078i	$0.672277\pi$
$140$	−97.5786	−0.0589064
$141$	509.606	0.304373
$142$	3076.11	1.81790
$143$	0	0
$144$	−625.943	−0.362236
$145$	1185.22	0.678808
$146$	2464.28	1.39688
$147$	912.047	0.511731
$148$	−27.8537	−0.0154700
$149$	−1825.35	−1.00361	−0.501806	−	0.864980i	$-0.667331\pi$
$149$	−1825.35	−1.00361	−0.501806	+	0.864980i	$0.667331\pi$
$150$	222.071	0.120880
$151$	2328.78	1.25506	0.627528	−	0.778594i	$-0.284067\pi$
$151$	2328.78	1.25506	0.627528	+	0.778594i	$0.284067\pi$
$152$	2065.93	1.10243
$153$	985.880	0.520939
$154$	0	0
$155$	22.9735	0.0119050
$156$	123.788	0.0635319
$157$	310.138	0.157654	0.0788270	−	0.996888i	$-0.474883\pi$
$157$	310.138	0.157654	0.0788270	+	0.996888i	$0.474883\pi$
$158$	2057.98	1.03623
$159$	−985.474	−0.491529
$160$	173.024	0.0854924
$161$	4251.08	2.08094
$162$	239.837	0.116317
$163$	1606.22	0.771832	0.385916	−	0.922534i	$-0.373885\pi$
$163$	1606.22	0.771832	0.385916	+	0.922534i	$0.373885\pi$
$164$	−157.192	−0.0748453
$165$	0	0
$166$	−748.403	−0.349924
$167$	2900.43	1.34396	0.671981	−	0.740568i	$-0.265444\pi$
$167$	2900.43	1.34396	0.671981	+	0.740568i	$0.265444\pi$
$168$	−1634.23	−0.750500
$169$	695.415	0.316529
$170$	−1621.75	−0.731660
$171$	−868.205	−0.388265
$172$	109.849	0.0486970
$173$	−3576.53	−1.57178	−0.785891	−	0.618365i	$-0.787795\pi$
$173$	−3576.53	−1.57178	−0.785891	+	0.618365i	$0.787795\pi$
$174$	−2105.63	−0.917397
$175$	635.913	0.274688
$176$	0	0
$177$	482.975	0.205100
$178$	2758.09	1.16139
$179$	−3961.68	−1.65424	−0.827122	−	0.562023i	$-0.810023\pi$
$179$	−3961.68	−1.65424	−0.827122	+	0.562023i	$0.810023\pi$
$180$	−34.5255	−0.0142965
$181$	2122.00	0.871421	0.435710	−	0.900087i	$-0.356497\pi$
$181$	2122.00	0.871421	0.435710	+	0.900087i	$0.356497\pi$
$182$	4050.60	1.64973
$183$	−279.421	−0.112871
$184$	−3579.13	−1.43401
$185$	181.520	0.0721386
$186$	−40.8141	−0.0160894
$187$	0	0
$188$	130.329	0.0505596
$189$	686.786	0.264319
$190$	1428.17	0.545319
$191$	−892.617	−0.338154	−0.169077	−	0.985603i	$-0.554079\pi$
$191$	−892.617	−0.338154	−0.169077	+	0.985603i	$0.554079\pi$
$192$	1361.79	0.511869
$193$	−2459.03	−0.917125	−0.458563	−	0.888662i	$-0.651635\pi$
$193$	−2459.03	−0.917125	−0.458563	+	0.888662i	$0.651635\pi$
$194$	4065.36	1.50452
$195$	−806.718	−0.296258
$196$	233.251	0.0850040
$197$	−4376.73	−1.58289	−0.791445	−	0.611241i	$-0.790671\pi$
$197$	−4376.73	−1.58289	−0.791445	+	0.611241i	$0.790671\pi$
$198$	0	0
$199$	−3139.70	−1.11843	−0.559215	−	0.829023i	$-0.688897\pi$
$199$	−3139.70	−1.11843	−0.559215	+	0.829023i	$0.688897\pi$
$200$	−535.397	−0.189291
$201$	686.637	0.240954
$202$	3608.81	1.25700
$203$	−6029.57	−2.08469
$204$	252.133	0.0865336
$205$	1024.41	0.349013
$206$	−4608.28	−1.55861
$207$	1504.13	0.505044
$208$	−3740.44	−1.24689
$209$	0	0
$210$	−1129.74	−0.371237
$211$	−1963.04	−0.640478	−0.320239	−	0.947337i	$-0.603763\pi$
$211$	−1963.04	−0.640478	−0.320239	+	0.947337i	$0.603763\pi$
$212$	−252.029	−0.0816484
$213$	3116.68	1.00259
$214$	4741.49	1.51459
$215$	−715.876	−0.227081
$216$	−578.229	−0.182146
$217$	−116.873	−0.0365616
$218$	−1248.96	−0.388030
$219$	2496.77	0.770395
$220$	0	0
$221$	5891.31	1.79318
$222$	−322.484	−0.0974942
$223$	2241.05	0.672968	0.336484	−	0.941689i	$-0.390762\pi$
$223$	2241.05	0.672968	0.336484	+	0.941689i	$0.390762\pi$
$224$	−880.227	−0.262556
$225$	225.000	0.0666667
$226$	2102.21	0.618746
$227$	2762.55	0.807740	0.403870	−	0.914816i	$-0.367665\pi$
$227$	2762.55	0.807740	0.403870	+	0.914816i	$0.367665\pi$
$228$	−222.038	−0.0644950
$229$	1180.85	0.340754	0.170377	−	0.985379i	$-0.445501\pi$
$229$	1180.85	0.340754	0.170377	+	0.985379i	$0.445501\pi$
$230$	−2474.25	−0.709335
$231$	0	0
$232$	5076.50	1.43659
$233$	4539.01	1.27623	0.638113	−	0.769943i	$-0.279715\pi$
$233$	4539.01	1.27623	0.638113	+	0.769943i	$0.279715\pi$
$234$	1433.19	0.400387
$235$	−849.343	−0.235766
$236$	123.518	0.0340692
$237$	2085.12	0.571489
$238$	8250.31	2.24701
$239$	6506.14	1.76087	0.880434	−	0.474169i	$-0.157252\pi$
$239$	6506.14	1.76087	0.880434	+	0.474169i	$0.157252\pi$
$240$	1043.24	0.280586
$241$	660.229	0.176469	0.0882346	−	0.996100i	$-0.471877\pi$
$241$	660.229	0.176469	0.0882346	+	0.996100i	$0.471877\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−71.4603	−0.0187491
$245$	−1520.08	−0.396385
$246$	−1819.93	−0.471686
$247$	−5188.12	−1.33649
$248$	98.3996	0.0251951
$249$	−758.273	−0.192986
$250$	−370.119	−0.0936335
$251$	−894.294	−0.224890	−0.112445	−	0.993658i	$-0.535868\pi$
$251$	−894.294	−0.224890	−0.112445	+	0.993658i	$0.535868\pi$
$252$	175.642	0.0439063
$253$	0	0
$254$	−4091.96	−1.01084
$255$	−1643.13	−0.403518
$256$	1167.98	0.285151
$257$	−2418.92	−0.587114	−0.293557	−	0.955942i	$-0.594839\pi$
$257$	−2418.92	−0.587114	−0.293557	+	0.955942i	$0.594839\pi$
$258$	1271.80	0.306896
$259$	−923.449	−0.221546
$260$	−206.313	−0.0492116
$261$	−2133.39	−0.505953
$262$	7861.71	1.85381
$263$	−187.242	−0.0439005	−0.0219503	−	0.999759i	$-0.506988\pi$
$263$	−187.242	−0.0439005	−0.0219503	+	0.999759i	$0.506988\pi$
$264$	0	0
$265$	1642.46	0.380737
$266$	−7265.55	−1.67473
$267$	2794.46	0.640518
$268$	175.604	0.0400250
$269$	−501.808	−0.113739	−0.0568694	−	0.998382i	$-0.518112\pi$
$269$	−501.808	−0.113739	−0.0568694	+	0.998382i	$0.518112\pi$
$270$	−399.728	−0.0900989
$271$	−8044.84	−1.80328	−0.901640	−	0.432487i	$-0.857636\pi$
$271$	−8044.84	−1.80328	−0.901640	+	0.432487i	$0.857636\pi$
$272$	−7618.58	−1.69832
$273$	4104.02	0.909840
$274$	−1764.84	−0.389117
$275$	0	0
$276$	384.672	0.0838932
$277$	7553.18	1.63836	0.819182	−	0.573534i	$-0.194428\pi$
$277$	7553.18	1.63836	0.819182	+	0.573534i	$0.194428\pi$
$278$	−4999.74	−1.07865
$279$	−41.3524	−0.00887348
$280$	2723.72	0.581335
$281$	6173.47	1.31060	0.655300	−	0.755369i	$-0.272542\pi$
$281$	6173.47	1.31060	0.655300	+	0.755369i	$0.272542\pi$
$282$	1508.92	0.318634
$283$	1717.86	0.360834	0.180417	−	0.983590i	$-0.442255\pi$
$283$	1717.86	0.360834	0.180417	+	0.983590i	$0.442255\pi$
$284$	797.074	0.166541
$285$	1447.01	0.300749
$286$	0	0
$287$	−5211.47	−1.07186
$288$	−311.444	−0.0637222
$289$	7086.51	1.44240
$290$	3509.38	0.710613
$291$	4118.98	0.829755
$292$	638.536	0.127971
$293$	655.320	0.130663	0.0653314	−	0.997864i	$-0.479190\pi$
$293$	655.320	0.130663	0.0653314	+	0.997864i	$0.479190\pi$
$294$	2700.53	0.535707
$295$	−804.958	−0.158869
$296$	777.484	0.152670
$297$	0	0
$298$	−5404.76	−1.05064
$299$	8988.19	1.73846
$300$	57.5425	0.0110741
$301$	3641.88	0.697389
$302$	6895.40	1.31386
$303$	3656.40	0.693250
$304$	6709.22	1.26579
$305$	465.702	0.0874295
$306$	2919.14	0.545348
$307$	−3918.92	−0.728550	−0.364275	−	0.931292i	$-0.618683\pi$
$307$	−3918.92	−0.728550	−0.364275	+	0.931292i	$0.618683\pi$
$308$	0	0
$309$	−4669.06	−0.859590
$310$	68.0235	0.0124628
$311$	−2471.45	−0.450620	−0.225310	−	0.974287i	$-0.572340\pi$
$311$	−2471.45	−0.450620	−0.225310	+	0.974287i	$0.572340\pi$
$312$	−3455.31	−0.626983
$313$	−5346.99	−0.965591	−0.482795	−	0.875733i	$-0.660379\pi$
$313$	−5346.99	−0.965591	−0.482795	+	0.875733i	$0.660379\pi$
$314$	918.303	0.165041
$315$	−1144.64	−0.204741
$316$	533.257	0.0949305
$317$	−6432.52	−1.13970	−0.569852	−	0.821747i	$-0.693000\pi$
$317$	−6432.52	−1.13970	−0.569852	+	0.821747i	$0.693000\pi$
$318$	−2917.94	−0.514560
$319$	0	0
$320$	−2269.65	−0.396492
$321$	4804.02	0.835310
$322$	12587.2	2.17845
$323$	−10567.2	−1.82036
$324$	62.1459	0.0106560
$325$	1344.53	0.229480
$326$	4755.93	0.807996
$327$	−1265.44	−0.214002
$328$	4387.72	0.738632
$329$	4320.86	0.724063
$330$	0	0
$331$	−11559.1	−1.91947	−0.959734	−	0.280911i	$-0.909363\pi$
$331$	−11559.1	−1.91947	−0.959734	+	0.280911i	$0.909363\pi$
$332$	−193.924	−0.0320571
$333$	−326.737	−0.0537690
$334$	8588.02	1.40693
$335$	−1144.40	−0.186642
$336$	−5307.27	−0.861712
$337$	−4371.69	−0.706650	−0.353325	−	0.935501i	$-0.614949\pi$
$337$	−4371.69	−0.706650	−0.353325	+	0.935501i	$0.614949\pi$
$338$	2059.09	0.331360
$339$	2129.93	0.341245
$340$	−420.222	−0.0670287
$341$	0	0
$342$	−2570.71	−0.406457
$343$	−991.623	−0.156101
$344$	−3066.22	−0.480580
$345$	−2506.88	−0.391205
$346$	−10589.9	−1.64543
$347$	2301.28	0.356020	0.178010	−	0.984029i	$-0.443034\pi$
$347$	2301.28	0.356020	0.178010	+	0.984029i	$0.443034\pi$
$348$	−545.604	−0.0840443
$349$	4064.49	0.623401	0.311700	−	0.950180i	$-0.399101\pi$
$349$	4064.49	0.623401	0.311700	+	0.950180i	$0.399101\pi$
$350$	1882.91	0.287559
$351$	1452.09	0.220817
$352$	0	0
$353$	−8489.82	−1.28008	−0.640039	−	0.768342i	$-0.721082\pi$
$353$	−8489.82	−1.28008	−0.640039	+	0.768342i	$0.721082\pi$
$354$	1430.07	0.214709
$355$	−5194.47	−0.776602
$356$	714.668	0.106397
$357$	8359.12	1.23925
$358$	−11730.3	−1.73175
$359$	3121.60	0.458919	0.229459	−	0.973318i	$-0.426304\pi$
$359$	3121.60	0.458919	0.229459	+	0.973318i	$0.426304\pi$
$360$	963.714	0.141089
$361$	2446.92	0.356746
$362$	6283.15	0.912251
$363$	0	0
$364$	1049.58	0.151134
$365$	−4161.29	−0.596745
$366$	−827.352	−0.118159
$367$	5371.81	0.764050	0.382025	−	0.924152i	$-0.375227\pi$
$367$	5371.81	0.764050	0.382025	+	0.924152i	$0.375227\pi$
$368$	−11623.4	−1.64650
$369$	−1843.93	−0.260139
$370$	537.473	0.0755187
$371$	−8355.67	−1.16929
$372$	−10.5756	−0.00147398
$373$	−2748.02	−0.381467	−0.190733	−	0.981642i	$-0.561087\pi$
$373$	−2748.02	−0.381467	−0.190733	+	0.981642i	$0.561087\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	−3637.88	−0.498961
$377$	−12748.5	−1.74159
$378$	2033.54	0.276704
$379$	−6460.91	−0.875659	−0.437829	−	0.899058i	$-0.644253\pi$
$379$	−6460.91	−0.875659	−0.437829	+	0.899058i	$0.644253\pi$
$380$	370.064	0.0499576
$381$	−4145.92	−0.557485
$382$	−2643.00	−0.353999
$383$	−4980.09	−0.664414	−0.332207	−	0.943207i	$-0.607793\pi$
$383$	−4980.09	−0.664414	−0.332207	+	0.943207i	$0.607793\pi$
$384$	4862.71	0.646222
$385$	0	0
$386$	−7281.08	−0.960096
$387$	1288.58	0.169256
$388$	1053.41	0.137831
$389$	8892.75	1.15908	0.579538	−	0.814945i	$-0.303233\pi$
$389$	8892.75	1.15908	0.579538	+	0.814945i	$0.303233\pi$
$390$	−2388.65	−0.310139
$391$	18307.3	2.36787
$392$	−6510.76	−0.838886
$393$	7965.39	1.02239
$394$	−12959.3	−1.65705
$395$	−3475.20	−0.442674
$396$	0	0
$397$	3118.81	0.394278	0.197139	−	0.980376i	$-0.436835\pi$
$397$	3118.81	0.394278	0.197139	+	0.980376i	$0.436835\pi$
$398$	−9296.50	−1.17083
$399$	−7361.37	−0.923632
$400$	−1738.73	−0.217341
$401$	3090.84	0.384911	0.192455	−	0.981306i	$-0.438355\pi$
$401$	3090.84	0.384911	0.192455	+	0.981306i	$0.438355\pi$
$402$	2033.10	0.252243
$403$	−247.109	−0.0305443
$404$	935.103	0.115156
$405$	−405.000	−0.0496904
$406$	−17853.3	−2.18237
$407$	0	0
$408$	−7037.83	−0.853982
$409$	−11605.8	−1.40311	−0.701553	−	0.712617i	$-0.747510\pi$
$409$	−11605.8	−1.40311	−0.701553	+	0.712617i	$0.747510\pi$
$410$	3033.22	0.365366
$411$	−1788.12	−0.214602
$412$	−1194.08	−0.142787
$413$	4095.06	0.487905
$414$	4453.65	0.528707
$415$	1263.79	0.149487
$416$	−1861.09	−0.219345
$417$	−5065.68	−0.594886
$418$	0	0
$419$	1960.62	0.228598	0.114299	−	0.993446i	$-0.463538\pi$
$419$	1960.62	0.228598	0.114299	+	0.993446i	$0.463538\pi$
$420$	−292.736	−0.0340096
$421$	−6944.99	−0.803986	−0.401993	−	0.915643i	$-0.631682\pi$
$421$	−6944.99	−0.803986	−0.401993	+	0.915643i	$0.631682\pi$
$422$	−5812.45	−0.670488
$423$	1528.82	0.175730
$424$	7034.93	0.805770
$425$	2738.56	0.312564
$426$	9228.34	1.04957
$427$	−2369.16	−0.268506
$428$	1228.60	0.138754
$429$	0	0
$430$	−2119.67	−0.237720
$431$	2951.46	0.329853	0.164926	−	0.986306i	$-0.447261\pi$
$431$	2951.46	0.329853	0.164926	+	0.986306i	$0.447261\pi$
$432$	−1877.83	−0.209137
$433$	−17546.1	−1.94737	−0.973687	−	0.227888i	$-0.926818\pi$
$433$	−17546.1	−1.94737	−0.973687	+	0.227888i	$0.926818\pi$
$434$	−346.056	−0.0382747
$435$	3555.66	0.391910
$436$	−323.628	−0.0355481
$437$	−16122.1	−1.76482
$438$	7392.83	0.806491
$439$	3755.80	0.408325	0.204162	−	0.978937i	$-0.434553\pi$
$439$	3755.80	0.408325	0.204162	+	0.978937i	$0.434553\pi$
$440$	0	0
$441$	2736.14	0.295448
$442$	17443.9	1.87720
$443$	8599.54	0.922294	0.461147	−	0.887324i	$-0.347438\pi$
$443$	8599.54	0.922294	0.461147	+	0.887324i	$0.347438\pi$
$444$	−83.5611	−0.00893161
$445$	−4657.44	−0.496143
$446$	6635.64	0.704499
$447$	−5476.04	−0.579436
$448$	11546.4	1.21767
$449$	−2052.80	−0.215763	−0.107881	−	0.994164i	$-0.534407\pi$
$449$	−2052.80	−0.215763	−0.107881	+	0.994164i	$0.534407\pi$
$450$	666.214	0.0697903
$451$	0	0
$452$	544.718	0.0566844
$453$	6986.34	0.724607
$454$	8179.78	0.845586
$455$	−6840.03	−0.704759
$456$	6197.79	0.636487
$457$	1025.27	0.104946	0.0524728	−	0.998622i	$-0.483290\pi$
$457$	1025.27	0.104946	0.0524728	+	0.998622i	$0.483290\pi$
$458$	3496.43	0.356720
$459$	2957.64	0.300764
$460$	−641.120	−0.0649834
$461$	−7699.40	−0.777867	−0.388933	−	0.921266i	$-0.627156\pi$
$461$	−7699.40	−0.777867	−0.388933	+	0.921266i	$0.627156\pi$
$462$	0	0
$463$	−4962.96	−0.498161	−0.249080	−	0.968483i	$-0.580128\pi$
$463$	−4962.96	−0.498161	−0.249080	+	0.968483i	$0.580128\pi$
$464$	16486.2	1.64947
$465$	68.9206	0.00687337
$466$	13439.8	1.33602
$467$	−9989.66	−0.989864	−0.494932	−	0.868932i	$-0.664807\pi$
$467$	−9989.66	−0.989864	−0.494932	+	0.868932i	$0.664807\pi$
$468$	371.364	0.0366802
$469$	5821.88	0.573198
$470$	−2514.86	−0.246813
$471$	930.413	0.0910216
$472$	−3447.78	−0.336222
$473$	0	0
$474$	6173.93	0.598266
$475$	−2411.68	−0.232959
$476$	2137.80	0.205852
$477$	−2956.42	−0.283785
$478$	19264.4	1.84337
$479$	1419.23	0.135378	0.0676891	−	0.997706i	$-0.478437\pi$
$479$	1419.23	0.135378	0.0676891	+	0.997706i	$0.478437\pi$
$480$	519.073	0.0493590
$481$	−1952.48	−0.185084
$482$	1954.91	0.184738
$483$	12753.2	1.20143
$484$	0	0
$485$	−6864.96	−0.642726
$486$	719.511	0.0671557
$487$	−5719.23	−0.532162	−0.266081	−	0.963951i	$-0.585729\pi$
$487$	−5719.23	−0.532162	−0.266081	+	0.963951i	$0.585729\pi$
$488$	1994.68	0.185031
$489$	4818.65	0.445618
$490$	−4500.88	−0.414957
$491$	8766.84	0.805788	0.402894	−	0.915247i	$-0.368004\pi$
$491$	8766.84	0.805788	0.402894	+	0.915247i	$0.368004\pi$
$492$	−471.576	−0.0432119
$493$	−25966.3	−2.37214
$494$	−15361.8	−1.39911
$495$	0	0
$496$	319.558	0.0289286
$497$	26425.8	2.38503
$498$	−2245.21	−0.202029
$499$	−13305.8	−1.19368	−0.596842	−	0.802359i	$-0.703578\pi$
$499$	−13305.8	−1.19368	−0.596842	+	0.802359i	$0.703578\pi$
$500$	−95.9041	−0.00857793
$501$	8701.28	0.775937
$502$	−2647.96	−0.235427
$503$	18339.7	1.62570	0.812851	−	0.582471i	$-0.197914\pi$
$503$	18339.7	1.62570	0.812851	+	0.582471i	$0.197914\pi$
$504$	−4902.70	−0.433301
$505$	−6094.00	−0.536989
$506$	0	0
$507$	2086.25	0.182748
$508$	−1060.30	−0.0926043
$509$	−5835.34	−0.508147	−0.254073	−	0.967185i	$-0.581770\pi$
$509$	−5835.34	−0.508147	−0.254073	+	0.967185i	$0.581770\pi$
$510$	−4865.24	−0.422424
$511$	21169.7	1.83267
$512$	−9508.91	−0.820779
$513$	−2604.61	−0.224165
$514$	−7162.32	−0.614623
$515$	7781.76	0.665836
$516$	329.546	0.0281152
$517$	0	0
$518$	−2734.29	−0.231926
$519$	−10729.6	−0.907469
$520$	5758.85	0.485659
$521$	−1111.09	−0.0934311	−0.0467155	−	0.998908i	$-0.514875\pi$
$521$	−1111.09	−0.0934311	−0.0467155	+	0.998908i	$0.514875\pi$
$522$	−6316.88	−0.529659
$523$	−19404.1	−1.62233	−0.811167	−	0.584814i	$-0.801167\pi$
$523$	−19404.1	−1.62233	−0.811167	+	0.584814i	$0.801167\pi$
$524$	2037.10	0.169831
$525$	1907.74	0.158591
$526$	−554.415	−0.0459575
$527$	−503.315	−0.0416029
$528$	0	0
$529$	15763.8	1.29562
$530$	4863.24	0.398576
$531$	1448.92	0.118414
$532$	−1882.63	−0.153425
$533$	−11018.8	−0.895452
$534$	8274.27	0.670529
$535$	−8006.70	−0.647028
$536$	−4901.65	−0.394998
$537$	−11885.0	−0.955078
$538$	−1485.83	−0.119068
$539$	0	0
$540$	−103.576	−0.00825411
$541$	19362.6	1.53875	0.769376	−	0.638796i	$-0.220567\pi$
$541$	19362.6	1.53875	0.769376	+	0.638796i	$0.220567\pi$
$542$	−23820.4	−1.88777
$543$	6366.01	0.503115
$544$	−3790.70	−0.298759
$545$	2109.06	0.165765
$546$	12151.8	0.952470
$547$	18673.2	1.45962	0.729808	−	0.683652i	$-0.239610\pi$
$547$	18673.2	1.45962	0.729808	+	0.683652i	$0.239610\pi$
$548$	−457.301	−0.0356477
$549$	−838.263	−0.0651661
$550$	0	0
$551$	22867.0	1.76800
$552$	−10737.4	−0.827924
$553$	17679.4	1.35950
$554$	22364.6	1.71513
$555$	544.561	0.0416493
$556$	−1295.52	−0.0988170
$557$	3653.15	0.277898	0.138949	−	0.990300i	$-0.455628\pi$
$557$	3653.15	0.277898	0.138949	+	0.990300i	$0.455628\pi$
$558$	−122.442	−0.00928924
$559$	7700.13	0.582613
$560$	8845.44	0.667479
$561$	0	0
$562$	18279.4	1.37201
$563$	−20128.2	−1.50676	−0.753378	−	0.657588i	$-0.771577\pi$
$563$	−20128.2	−1.50676	−0.753378	+	0.657588i	$0.771577\pi$
$564$	390.986	0.0291906
$565$	−3549.88	−0.264327
$566$	5086.49	0.377741
$567$	2060.36	0.152605
$568$	−22248.8	−1.64356
$569$	−20107.3	−1.48145	−0.740724	−	0.671810i	$-0.765517\pi$
$569$	−20107.3	−1.48145	−0.740724	+	0.671810i	$0.765517\pi$
$570$	4284.52	0.314840
$571$	−14510.3	−1.06346	−0.531730	−	0.846914i	$-0.678458\pi$
$571$	−14510.3	−1.06346	−0.531730	+	0.846914i	$0.678458\pi$
$572$	0	0
$573$	−2677.85	−0.195234
$574$	−15430.9	−1.12208
$575$	4178.13	0.303026
$576$	4085.37	0.295528
$577$	−10060.9	−0.725893	−0.362946	−	0.931810i	$-0.618229\pi$
$577$	−10060.9	−0.725893	−0.362946	+	0.931810i	$0.618229\pi$
$578$	20982.8	1.50998
$579$	−7377.10	−0.529502
$580$	909.339	0.0651004
$581$	−6429.27	−0.459090
$582$	12196.1	0.868633
$583$	0	0
$584$	−17823.5	−1.26292
$585$	−2420.15	−0.171044
$586$	1940.37	0.136785
$587$	1968.17	0.138390	0.0691951	−	0.997603i	$-0.477957\pi$
$587$	1968.17	0.138390	0.0691951	+	0.997603i	$0.477957\pi$
$588$	699.753	0.0490771
$589$	443.239	0.0310073
$590$	−2383.44	−0.166313
$591$	−13130.2	−0.913882
$592$	2524.92	0.175293
$593$	27277.2	1.88894	0.944468	−	0.328603i	$-0.106578\pi$
$593$	27277.2	1.88894	0.944468	+	0.328603i	$0.106578\pi$
$594$	0	0
$595$	−13931.9	−0.959917
$596$	−1400.47	−0.0962505
$597$	−9419.10	−0.645726
$598$	26613.6	1.81992
$599$	28717.7	1.95889	0.979443	−	0.201720i	$-0.0646530\pi$
$599$	28717.7	1.95889	0.979443	+	0.201720i	$0.0646530\pi$
$600$	−1606.19	−0.109287
$601$	−7056.49	−0.478935	−0.239468	−	0.970904i	$-0.576973\pi$
$601$	−7056.49	−0.478935	−0.239468	+	0.970904i	$0.576973\pi$
$602$	10783.4	0.730065
$603$	2059.91	0.139115
$604$	1786.72	0.120365
$605$	0	0
$606$	10826.4	0.725732
$607$	−7595.36	−0.507885	−0.253943	−	0.967219i	$-0.581727\pi$
$607$	−7595.36	−0.507885	−0.253943	+	0.967219i	$0.581727\pi$
$608$	3338.24	0.222670
$609$	−18088.7	−1.20360
$610$	1378.92	0.0915259
$611$	9135.73	0.604897
$612$	756.400	0.0499602
$613$	11763.5	0.775076	0.387538	−	0.921854i	$-0.373326\pi$
$613$	11763.5	0.775076	0.387538	+	0.921854i	$0.373326\pi$
$614$	−11603.7	−0.762685
$615$	3073.22	0.201503
$616$	0	0
$617$	14687.0	0.958307	0.479153	−	0.877731i	$-0.340944\pi$
$617$	14687.0	0.958307	0.479153	+	0.877731i	$0.340944\pi$
$618$	−13824.8	−0.899866
$619$	18661.1	1.21172	0.605858	−	0.795573i	$-0.292830\pi$
$619$	18661.1	1.21172	0.605858	+	0.795573i	$0.292830\pi$
$620$	17.6261	0.00114174
$621$	4512.38	0.291587
$622$	−7317.83	−0.471734
$623$	23693.8	1.52371
$624$	−11221.3	−0.719891
$625$	625.000	0.0400000
$626$	−15832.2	−1.01083
$627$	0	0
$628$	237.948	0.0151197
$629$	−3976.83	−0.252093
$630$	−3389.23	−0.214334
$631$	12675.5	0.799689	0.399844	−	0.916583i	$-0.369064\pi$
$631$	12675.5	0.799689	0.399844	+	0.916583i	$0.369064\pi$
$632$	−14884.9	−0.936849
$633$	−5889.11	−0.369780
$634$	−19046.4	−1.19310
$635$	6909.87	0.431826
$636$	−756.088	−0.0471397
$637$	16350.3	1.01699
$638$	0	0
$639$	9350.05	0.578845
$640$	−8104.52	−0.500562
$641$	−13737.6	−0.846495	−0.423248	−	0.906014i	$-0.639110\pi$
$641$	−13737.6	−0.846495	−0.423248	+	0.906014i	$0.639110\pi$
$642$	14224.5	0.874447
$643$	−9820.62	−0.602313	−0.301157	−	0.953575i	$-0.597373\pi$
$643$	−9820.62	−0.602313	−0.301157	+	0.953575i	$0.597373\pi$
$644$	3261.57	0.199571
$645$	−2147.63	−0.131105
$646$	−31289.1	−1.90565
$647$	1271.24	0.0772451	0.0386226	−	0.999254i	$-0.487703\pi$
$647$	1271.24	0.0772451	0.0386226	+	0.999254i	$0.487703\pi$
$648$	−1734.69	−0.105162
$649$	0	0
$650$	3981.09	0.240232
$651$	−350.620	−0.0211089
$652$	1232.34	0.0740219
$653$	−9595.92	−0.575065	−0.287532	−	0.957771i	$-0.592835\pi$
$653$	−9595.92	−0.575065	−0.287532	+	0.957771i	$0.592835\pi$
$654$	−3746.89	−0.224029
$655$	−13275.7	−0.791943
$656$	14249.4	0.848085
$657$	7490.32	0.444788
$658$	12793.9	0.757989
$659$	−11012.3	−0.650954	−0.325477	−	0.945550i	$-0.605525\pi$
$659$	−11012.3	−0.650954	−0.325477	+	0.945550i	$0.605525\pi$
$660$	0	0
$661$	596.766	0.0351158	0.0175579	−	0.999846i	$-0.494411\pi$
$661$	596.766	0.0351158	0.0175579	+	0.999846i	$0.494411\pi$
$662$	−34225.8	−2.00940
$663$	17673.9	1.03529
$664$	5413.02	0.316365
$665$	12268.9	0.715442
$666$	−967.452	−0.0562883
$667$	−39616.0	−2.29976
$668$	2225.30	0.128891
$669$	6723.15	0.388538
$670$	−3388.50	−0.195387
$671$	0	0
$672$	−2640.68	−0.151587
$673$	19312.1	1.10613	0.553065	−	0.833138i	$-0.313458\pi$
$673$	19312.1	1.10613	0.553065	+	0.833138i	$0.313458\pi$
$674$	−12944.4	−0.739760
$675$	675.000	0.0384900
$676$	533.545	0.0303565
$677$	24749.5	1.40502	0.702512	−	0.711672i	$-0.252062\pi$
$677$	24749.5	1.40502	0.702512	+	0.711672i	$0.252062\pi$
$678$	6306.62	0.357233
$679$	34924.1	1.97388
$680$	11729.7	0.661491
$681$	8287.65	0.466349
$682$	0	0
$683$	−11001.0	−0.616314	−0.308157	−	0.951336i	$-0.599712\pi$
$683$	−11001.0	−0.616314	−0.308157	+	0.951336i	$0.599712\pi$
$684$	−666.115	−0.0372362
$685$	2980.20	0.166230
$686$	−2936.15	−0.163415
$687$	3542.54	0.196734
$688$	−9957.72	−0.551794
$689$	−17666.7	−0.976845
$690$	−7422.74	−0.409535
$691$	−21806.5	−1.20052	−0.600260	−	0.799805i	$-0.704936\pi$
$691$	−21806.5	−1.20052	−0.600260	+	0.799805i	$0.704936\pi$
$692$	−2744.03	−0.150740
$693$	0	0
$694$	6813.97	0.372701
$695$	8442.80	0.460797
$696$	15229.5	0.829415
$697$	−22443.2	−1.21965
$698$	12034.7	0.652610
$699$	13617.0	0.736829
$700$	487.893	0.0263438
$701$	−18909.5	−1.01884	−0.509418	−	0.860519i	$-0.670139\pi$
$701$	−18909.5	−1.01884	−0.509418	+	0.860519i	$0.670139\pi$
$702$	4299.57	0.231164
$703$	3502.15	0.187889
$704$	0	0
$705$	−2548.03	−0.136120
$706$	−25138.0	−1.34006
$707$	31002.0	1.64915
$708$	370.554	0.0196699
$709$	−33785.8	−1.78964	−0.894819	−	0.446429i	$-0.852695\pi$
$709$	−33785.8	−1.78964	−0.894819	+	0.446429i	$0.852695\pi$
$710$	−15380.6	−0.812990
$711$	6255.35	0.329949
$712$	−19948.6	−1.05001
$713$	−767.891	−0.0403334
$714$	24750.9	1.29731
$715$	0	0
$716$	−3039.53	−0.158649
$717$	19518.4	1.01664
$718$	9242.91	0.480421
$719$	7372.88	0.382423	0.191211	−	0.981549i	$-0.438758\pi$
$719$	7372.88	0.382423	0.191211	+	0.981549i	$0.438758\pi$
$720$	3129.71	0.161997
$721$	−39588.2	−2.04485
$722$	7245.22	0.373461
$723$	1980.69	0.101885
$724$	1628.07	0.0835729
$725$	−5926.10	−0.303572
$726$	0	0
$727$	2386.69	0.121757	0.0608785	−	0.998145i	$-0.480610\pi$
$727$	2386.69	0.121757	0.0608785	+	0.998145i	$0.480610\pi$
$728$	−29297.0	−1.49151
$729$	729.000	0.0370370
$730$	−12321.4	−0.624705
$731$	15683.7	0.793548
$732$	−214.381	−0.0108248
$733$	−17351.8	−0.874358	−0.437179	−	0.899374i	$-0.644022\pi$
$733$	−17351.8	−0.874358	−0.437179	+	0.899374i	$0.644022\pi$
$734$	15905.7	0.799849
$735$	−4560.24	−0.228853
$736$	−5783.35	−0.289643
$737$	0	0
$738$	−5459.80	−0.272328
$739$	32872.0	1.63629	0.818143	−	0.575015i	$-0.195004\pi$
$739$	32872.0	1.63629	0.818143	+	0.575015i	$0.195004\pi$
$740$	139.268	0.00691839
$741$	−15564.4	−0.771621
$742$	−24740.7	−1.22407
$743$	−37301.4	−1.84180	−0.920898	−	0.389802i	$-0.872543\pi$
$743$	−37301.4	−1.84180	−0.920898	+	0.389802i	$0.872543\pi$
$744$	295.199	0.0145464
$745$	9126.73	0.448829
$746$	−8136.75	−0.399340
$747$	−2274.82	−0.111421
$748$	0	0
$749$	40732.5	1.98709
$750$	−1110.36	−0.0540593
$751$	7293.91	0.354406	0.177203	−	0.984174i	$-0.443295\pi$
$751$	7293.91	0.354406	0.177203	+	0.984174i	$0.443295\pi$
$752$	−11814.2	−0.572900
$753$	−2682.88	−0.129840
$754$	−37747.7	−1.82320
$755$	−11643.9	−0.561278
$756$	526.925	0.0253493
$757$	−2946.61	−0.141475	−0.0707374	−	0.997495i	$-0.522535\pi$
$757$	−2946.61	−0.141475	−0.0707374	+	0.997495i	$0.522535\pi$
$758$	−19130.4	−0.916687
$759$	0	0
$760$	−10329.6	−0.493021
$761$	−26685.9	−1.27118	−0.635588	−	0.772029i	$-0.719242\pi$
$761$	−26685.9	−1.27118	−0.635588	+	0.772029i	$0.719242\pi$
$762$	−12275.9	−0.583606
$763$	−10729.4	−0.509084
$764$	−684.845	−0.0324304
$765$	−4929.40	−0.232971
$766$	−14745.8	−0.695545
$767$	8658.32	0.407606
$768$	3503.93	0.164632
$769$	22847.7	1.07140	0.535702	−	0.844407i	$-0.320047\pi$
$769$	22847.7	1.07140	0.535702	+	0.844407i	$0.320047\pi$
$770$	0	0
$771$	−7256.77	−0.338971
$772$	−1886.65	−0.0879561
$773$	−34681.6	−1.61372	−0.806862	−	0.590740i	$-0.798836\pi$
$773$	−34681.6	−1.61372	−0.806862	+	0.590740i	$0.798836\pi$
$774$	3815.41	0.177186
$775$	−114.868	−0.00532409
$776$	−29403.8	−1.36023
$777$	−2770.35	−0.127909
$778$	26331.0	1.21338
$779$	19764.4	0.909026
$780$	−618.940	−0.0284123
$781$	0	0
$782$	54206.9	2.47882
$783$	−6400.18	−0.292112
$784$	−21144.1	−0.963195
$785$	−1550.69	−0.0705050
$786$	23585.1	1.07030
$787$	4756.33	0.215432	0.107716	−	0.994182i	$-0.465646\pi$
$787$	4756.33	0.215432	0.107716	+	0.994182i	$0.465646\pi$
$788$	−3357.97	−0.151806
$789$	−561.726	−0.0253460
$790$	−10289.9	−0.463415
$791$	18059.3	0.811777
$792$	0	0
$793$	−5009.20	−0.224315
$794$	9234.63	0.412752
$795$	4927.37	0.219819
$796$	−2408.88	−0.107262
$797$	−12709.8	−0.564872	−0.282436	−	0.959286i	$-0.591143\pi$
$797$	−12709.8	−0.564872	−0.282436	+	0.959286i	$0.591143\pi$
$798$	−21796.6	−0.966908
$799$	18607.8	0.823900
$800$	−865.122	−0.0382333
$801$	8383.39	0.369803
$802$	9151.83	0.402946
$803$	0	0
$804$	526.811	0.0231084
$805$	−21255.4	−0.930627
$806$	−731.677	−0.0319755
$807$	−1505.42	−0.0656672
$808$	−26101.7	−1.13645
$809$	−3093.23	−0.134428	−0.0672139	−	0.997739i	$-0.521411\pi$
$809$	−3093.23	−0.134428	−0.0672139	+	0.997739i	$0.521411\pi$
$810$	−1199.19	−0.0520186
$811$	−10943.5	−0.473833	−0.236917	−	0.971530i	$-0.576137\pi$
$811$	−10943.5	−0.473833	−0.236917	+	0.971530i	$0.576137\pi$
$812$	−4626.08	−0.199931
$813$	−24134.5	−1.04112
$814$	0	0
$815$	−8031.09	−0.345174
$816$	−22855.7	−0.980528
$817$	−13811.7	−0.591445
$818$	−34364.2	−1.46885
$819$	12312.0	0.525296
$820$	785.959	0.0334718
$821$	−17400.8	−0.739699	−0.369850	−	0.929092i	$-0.620591\pi$
$821$	−17400.8	−0.739699	−0.369850	+	0.929092i	$0.620591\pi$
$822$	−5294.53	−0.224657
$823$	43181.6	1.82894	0.914468	−	0.404658i	$-0.132609\pi$
$823$	43181.6	1.82894	0.914468	+	0.404658i	$0.132609\pi$
$824$	33330.6	1.40914
$825$	0	0
$826$	12125.3	0.510766
$827$	21664.7	0.910951	0.455475	−	0.890248i	$-0.349469\pi$
$827$	21664.7	0.910951	0.455475	+	0.890248i	$0.349469\pi$
$828$	1154.02	0.0484358
$829$	−5507.33	−0.230733	−0.115366	−	0.993323i	$-0.536804\pi$
$829$	−5507.33	−0.230733	−0.115366	+	0.993323i	$0.536804\pi$
$830$	3742.01	0.156491
$831$	22659.5	0.945909
$832$	24412.9	1.01727
$833$	33302.6	1.38519
$834$	−14999.2	−0.622759
$835$	−14502.1	−0.601038
$836$	0	0
$837$	−124.057	−0.00512311
$838$	5805.30	0.239309
$839$	−28171.5	−1.15922	−0.579612	−	0.814892i	$-0.696796\pi$
$839$	−28171.5	−1.15922	−0.579612	+	0.814892i	$0.696796\pi$
$840$	8171.17	0.335634
$841$	31800.8	1.30390
$842$	−20563.8	−0.841657
$843$	18520.4	0.756675
$844$	−1506.11	−0.0614245
$845$	−3477.08	−0.141556
$846$	4526.75	0.183963
$847$	0	0
$848$	22846.3	0.925172
$849$	5153.57	0.208328
$850$	8108.73	0.327209
$851$	−6067.33	−0.244401
$852$	2391.22	0.0961525
$853$	−33474.8	−1.34368	−0.671838	−	0.740698i	$-0.734495\pi$
$853$	−33474.8	−1.34368	−0.671838	+	0.740698i	$0.734495\pi$
$854$	−7014.98	−0.281086
$855$	4341.02	0.173637
$856$	−34294.1	−1.36933
$857$	40467.3	1.61300	0.806498	−	0.591237i	$-0.201360\pi$
$857$	40467.3	1.61300	0.806498	+	0.591237i	$0.201360\pi$
$858$	0	0
$859$	38266.3	1.51994	0.759970	−	0.649958i	$-0.225214\pi$
$859$	38266.3	1.51994	0.759970	+	0.649958i	$0.225214\pi$
$860$	−549.243	−0.0217780
$861$	−15634.4	−0.618838
$862$	8739.12	0.345308
$863$	−2208.90	−0.0871284	−0.0435642	−	0.999051i	$-0.513871\pi$
$863$	−2208.90	−0.0871284	−0.0435642	+	0.999051i	$0.513871\pi$
$864$	−934.332	−0.0367901
$865$	17882.6	0.702922
$866$	−51953.2	−2.03862
$867$	21259.5	0.832770
$868$	−89.6690	−0.00350641
$869$	0	0
$870$	10528.1	0.410272
$871$	12309.4	0.478861
$872$	9033.47	0.350816
$873$	12356.9	0.479059
$874$	−47736.7	−1.84751
$875$	−3179.56	−0.122844
$876$	1915.61	0.0738840
$877$	−31363.6	−1.20761	−0.603804	−	0.797133i	$-0.706349\pi$
$877$	−31363.6	−1.20761	−0.603804	+	0.797133i	$0.706349\pi$
$878$	11120.7	0.427457
$879$	1965.96	0.0754382
$880$	0	0
$881$	6473.73	0.247566	0.123783	−	0.992309i	$-0.460497\pi$
$881$	6473.73	0.247566	0.123783	+	0.992309i	$0.460497\pi$
$882$	8101.58	0.309291
$883$	−36701.8	−1.39877	−0.699384	−	0.714746i	$-0.746542\pi$
$883$	−36701.8	−1.39877	−0.699384	+	0.714746i	$0.746542\pi$
$884$	4520.01	0.171973
$885$	−2414.87	−0.0917233
$886$	25462.8	0.965508
$887$	−12835.1	−0.485862	−0.242931	−	0.970044i	$-0.578109\pi$
$887$	−12835.1	−0.485862	−0.242931	+	0.970044i	$0.578109\pi$
$888$	2332.45	0.0881441
$889$	−35152.6	−1.32619
$890$	−13790.4	−0.519390
$891$	0	0
$892$	1719.41	0.0645404
$893$	−16386.7	−0.614067
$894$	−16214.3	−0.606585
$895$	19808.4	0.739800
$896$	41230.2	1.53728
$897$	26964.6	1.00370
$898$	−6078.24	−0.225872
$899$	1089.15	0.0404061
$900$	172.627	0.00639361
$901$	−35983.7	−1.33051
$902$	0	0
$903$	10925.6	0.402638
$904$	−15204.8	−0.559406
$905$	−10610.0	−0.389711
$906$	20686.2	0.758558
$907$	35611.9	1.30372	0.651859	−	0.758340i	$-0.273989\pi$
$907$	35611.9	1.30372	0.651859	+	0.758340i	$0.273989\pi$
$908$	2119.52	0.0774656
$909$	10969.2	0.400248
$910$	−20253.0	−0.737780
$911$	16321.6	0.593588	0.296794	−	0.954942i	$-0.404083\pi$
$911$	16321.6	0.593588	0.296794	+	0.954942i	$0.404083\pi$
$912$	20127.7	0.730804
$913$	0	0
$914$	3035.78	0.109863
$915$	1397.10	0.0504774
$916$	905.985	0.0326797
$917$	67537.2	2.43214
$918$	8757.43	0.314857
$919$	−24281.7	−0.871576	−0.435788	−	0.900049i	$-0.643530\pi$
$919$	−24281.7	−0.871576	−0.435788	+	0.900049i	$0.643530\pi$
$920$	17895.7	0.641307
$921$	−11756.8	−0.420628
$922$	−22797.5	−0.814313
$923$	55872.9	1.99250
$924$	0	0
$925$	−907.602	−0.0322614
$926$	−14695.1	−0.521502
$927$	−14007.2	−0.496284
$928$	8202.87	0.290164
$929$	−17907.3	−0.632420	−0.316210	−	0.948689i	$-0.602410\pi$
$929$	−17907.3	−0.632420	−0.316210	+	0.948689i	$0.602410\pi$
$930$	204.071	0.00719542
$931$	−29327.6	−1.03241
$932$	3482.48	0.122395
$933$	−7414.34	−0.260166
$934$	−29578.9	−1.03624
$935$	0	0
$936$	−10365.9	−0.361989
$937$	−37241.5	−1.29843	−0.649214	−	0.760606i	$-0.724902\pi$
$937$	−37241.5	−1.29843	−0.649214	+	0.760606i	$0.724902\pi$
$938$	17238.3	0.600054
$939$	−16041.0	−0.557484
$940$	−651.644	−0.0226109
$941$	−10912.1	−0.378029	−0.189015	−	0.981974i	$-0.560529\pi$
$941$	−10912.1	−0.378029	−0.189015	+	0.981974i	$0.560529\pi$
$942$	2754.91	0.0952864
$943$	−34240.9	−1.18243
$944$	−11196.8	−0.386045
$945$	−3433.93	−0.118207
$946$	0	0
$947$	5221.21	0.179162	0.0895811	−	0.995980i	$-0.471447\pi$
$947$	5221.21	0.179162	0.0895811	+	0.995980i	$0.471447\pi$
$948$	1599.77	0.0548082
$949$	44759.8	1.53105
$950$	−7140.87	−0.243874
$951$	−19297.6	−0.658009
$952$	−59672.6	−2.03151
$953$	−28646.7	−0.973723	−0.486861	−	0.873479i	$-0.661858\pi$
$953$	−28646.7	−0.973723	−0.486861	+	0.873479i	$0.661858\pi$
$954$	−8753.82	−0.297081
$955$	4463.09	0.151227
$956$	4991.73	0.168874
$957$	0	0
$958$	4202.26	0.141721
$959$	−15161.2	−0.510510
$960$	−6808.96	−0.228915
$961$	−29769.9	−0.999291
$962$	−5781.19	−0.193756
$963$	14412.1	0.482266
$964$	506.549	0.0169241
$965$	12295.2	0.410151
$966$	37761.7	1.25773
$967$	−47857.8	−1.59152	−0.795762	−	0.605610i	$-0.792929\pi$
$967$	−47857.8	−1.59152	−0.795762	+	0.605610i	$0.792929\pi$
$968$	0	0
$969$	−31701.7	−1.05099
$970$	−20326.8	−0.672840
$971$	38062.7	1.25797	0.628985	−	0.777417i	$-0.283471\pi$
$971$	38062.7	1.25797	0.628985	+	0.777417i	$0.283471\pi$
$972$	186.438	0.00615225
$973$	−42951.1	−1.41516
$974$	−16934.4	−0.557096
$975$	4033.59	0.132490
$976$	6477.84	0.212449
$977$	32007.7	1.04813	0.524063	−	0.851680i	$-0.324416\pi$
$977$	32007.7	1.04813	0.524063	+	0.851680i	$0.324416\pi$
$978$	14267.8	0.466497
$979$	0	0
$980$	−1166.25	−0.0380149
$981$	−3796.31	−0.123554
$982$	25958.2	0.843543
$983$	−41454.3	−1.34505	−0.672526	−	0.740073i	$-0.734791\pi$
$983$	−41454.3	−1.34505	−0.672526	+	0.740073i	$0.734791\pi$
$984$	13163.2	0.426449
$985$	21883.7	0.707890
$986$	−76885.0	−2.48328
$987$	12962.6	0.418038
$988$	−3980.50	−0.128175
$989$	23928.2	0.769334
$990$	0	0
$991$	22836.0	0.731998	0.365999	−	0.930615i	$-0.380727\pi$
$991$	22836.0	0.731998	0.365999	+	0.930615i	$0.380727\pi$
$992$	158.999	0.00508894
$993$	−34677.2	−1.10821
$994$	78245.6	2.49678
$995$	15698.5	0.500177
$996$	−581.772	−0.0185082
$997$	−10140.2	−0.322111	−0.161055	−	0.986945i	$-0.551490\pi$
$997$	−10140.2	−0.322111	−0.161055	+	0.986945i	$0.551490\pi$
$998$	−39397.8	−1.24961
$999$	−980.210	−0.0310435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bo.1.8		12
11.7	odd	10		165.4.m.d.16.3	✓	24
11.8	odd	10		165.4.m.d.31.3	yes	24
11.10	odd	2		1815.4.a.bg.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.d.16.3	✓	24	11.7	odd	10
165.4.m.d.31.3	yes	24	11.8	odd	10
1815.4.a.bg.1.5		12	11.10	odd	2
1815.4.a.bo.1.8		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)

\(f(q)\)	\(=\)	\(q+2.96095 q^{2} +3.00000 q^{3} +0.767233 q^{4} -5.00000 q^{5} +8.88285 q^{6} +25.4365 q^{7} -21.4159 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.96095 q^{2} +3.00000 q^{3} +0.767233 q^{4} -5.00000 q^{5} +8.88285 q^{6} +25.4365 q^{7} -21.4159 q^{8} +9.00000 q^{9} -14.8048 q^{10} +2.30170 q^{12} +53.7812 q^{13} +75.3163 q^{14} -15.0000 q^{15} -69.5492 q^{16} +109.542 q^{17} +26.6486 q^{18} -96.4672 q^{19} -3.83616 q^{20} +76.3095 q^{21} +167.125 q^{23} -64.2476 q^{24} +25.0000 q^{25} +159.243 q^{26} +27.0000 q^{27} +19.5157 q^{28} -237.044 q^{29} -44.4143 q^{30} -4.59471 q^{31} -34.6049 q^{32} +324.349 q^{34} -127.183 q^{35} +6.90510 q^{36} -36.3041 q^{37} -285.635 q^{38} +161.344 q^{39} +107.079 q^{40} -204.882 q^{41} +225.949 q^{42} +143.175 q^{43} -45.0000 q^{45} +494.849 q^{46} +169.869 q^{47} -208.648 q^{48} +304.016 q^{49} +74.0238 q^{50} +328.627 q^{51} +41.2627 q^{52} -328.491 q^{53} +79.9457 q^{54} -544.745 q^{56} -289.402 q^{57} -701.875 q^{58} +160.992 q^{59} -11.5085 q^{60} -93.1403 q^{61} -13.6047 q^{62} +228.929 q^{63} +453.930 q^{64} -268.906 q^{65} +228.879 q^{67} +84.0444 q^{68} +501.376 q^{69} -376.581 q^{70} +1038.89 q^{71} -192.743 q^{72} +832.258 q^{73} -107.495 q^{74} +75.0000 q^{75} -74.0128 q^{76} +477.730 q^{78} +695.039 q^{79} +347.746 q^{80} +81.0000 q^{81} -606.644 q^{82} -252.758 q^{83} +58.5472 q^{84} -547.711 q^{85} +423.935 q^{86} -711.132 q^{87} +931.487 q^{89} -133.243 q^{90} +1368.01 q^{91} +128.224 q^{92} -13.7841 q^{93} +502.973 q^{94} +482.336 q^{95} -103.815 q^{96} +1372.99 q^{97} +900.176 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9	\( 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9} - 45 q^{10} + 171 q^{12} + 78 q^{13} + 262 q^{14} - 180 q^{15} + 225 q^{16} + 313 q^{17} + 81 q^{18} + 51 q^{19} - 285 q^{20} + 63 q^{21} - 34 q^{23} + 369 q^{24} + 300 q^{25} + 28 q^{26} + 324 q^{27} + 376 q^{28} + 31 q^{29} - 135 q^{30} + 655 q^{31} + 1578 q^{32} - 10 q^{34} - 105 q^{35} + 513 q^{36} + 84 q^{37} - 1076 q^{38} + 234 q^{39} - 615 q^{40} + 1463 q^{41} + 786 q^{42} - 111 q^{43} - 540 q^{45} - q^{46} + 278 q^{47} + 675 q^{48} - 325 q^{49} + 225 q^{50} + 939 q^{51} + 1957 q^{52} + 517 q^{53} + 243 q^{54} + 1543 q^{56} + 153 q^{57} + 442 q^{58} - 308 q^{59} - 855 q^{60} + 604 q^{61} + 1773 q^{62} + 189 q^{63} + 4323 q^{64} - 390 q^{65} - 357 q^{67} + 2192 q^{68} - 102 q^{69} - 1310 q^{70} - 620 q^{71} + 1107 q^{72} + 1892 q^{73} + 581 q^{74} + 900 q^{75} + 378 q^{76} + 84 q^{78} + 415 q^{79} - 1125 q^{80} + 972 q^{81} - 2802 q^{82} + 3158 q^{83} + 1128 q^{84} - 1565 q^{85} + 747 q^{86} + 93 q^{87} + 1563 q^{89} - 405 q^{90} + 1434 q^{91} - 3466 q^{92} + 1965 q^{93} - 3 q^{94} - 255 q^{95} + 4734 q^{96} + 714 q^{97} + 6586 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9 - 45 * q^10 + 171 * q^12 + 78 * q^13 + 262 * q^14 - 180 * q^15 + 225 * q^16 + 313 * q^17 + 81 * q^18 + 51 * q^19 - 285 * q^20 + 63 * q^21 - 34 * q^23 + 369 * q^24 + 300 * q^25 + 28 * q^26 + 324 * q^27 + 376 * q^28 + 31 * q^29 - 135 * q^30 + 655 * q^31 + 1578 * q^32 - 10 * q^34 - 105 * q^35 + 513 * q^36 + 84 * q^37 - 1076 * q^38 + 234 * q^39 - 615 * q^40 + 1463 * q^41 + 786 * q^42 - 111 * q^43 - 540 * q^45 - q^46 + 278 * q^47 + 675 * q^48 - 325 * q^49 + 225 * q^50 + 939 * q^51 + 1957 * q^52 + 517 * q^53 + 243 * q^54 + 1543 * q^56 + 153 * q^57 + 442 * q^58 - 308 * q^59 - 855 * q^60 + 604 * q^61 + 1773 * q^62 + 189 * q^63 + 4323 * q^64 - 390 * q^65 - 357 * q^67 + 2192 * q^68 - 102 * q^69 - 1310 * q^70 - 620 * q^71 + 1107 * q^72 + 1892 * q^73 + 581 * q^74 + 900 * q^75 + 378 * q^76 + 84 * q^78 + 415 * q^79 - 1125 * q^80 + 972 * q^81 - 2802 * q^82 + 3158 * q^83 + 1128 * q^84 - 1565 * q^85 + 747 * q^86 + 93 * q^87 + 1563 * q^89 - 405 * q^90 + 1434 * q^91 - 3466 * q^92 + 1965 * q^93 - 3 * q^94 - 255 * q^95 + 4734 * q^96 + 714 * q^97 + 6586 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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