LMFDB - Embedded newform 483.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 37x^{5} + 71x^{4} + 312x^{3} - 629x^{2} + 112x + 180 $ x^7 - 2x^6 - 37x^5 + 71x^4 + 312x^3 - 629x^2 + 112x + 180
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.03765$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.03765 q^{2} -3.00000 q^{3} +17.3779 q^{4} +6.20452 q^{5} +15.1129 q^{6} -7.00000 q^{7} -47.2425 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.03765 q^{2} -3.00000 q^{3} +17.3779 q^{4} +6.20452 q^{5} +15.1129 q^{6} -7.00000 q^{7} -47.2425 q^{8} +9.00000 q^{9} -31.2562 q^{10} +40.7402 q^{11} -52.1337 q^{12} +3.45169 q^{13} +35.2635 q^{14} -18.6136 q^{15} +98.9680 q^{16} -73.4576 q^{17} -45.3388 q^{18} -86.1205 q^{19} +107.822 q^{20} +21.0000 q^{21} -205.235 q^{22} +23.0000 q^{23} +141.728 q^{24} -86.5039 q^{25} -17.3884 q^{26} -27.0000 q^{27} -121.645 q^{28} +58.5361 q^{29} +93.7686 q^{30} -15.3924 q^{31} -120.626 q^{32} -122.221 q^{33} +370.054 q^{34} -43.4317 q^{35} +156.401 q^{36} +73.6831 q^{37} +433.844 q^{38} -10.3551 q^{39} -293.117 q^{40} +455.360 q^{41} -105.791 q^{42} -95.5428 q^{43} +707.980 q^{44} +55.8407 q^{45} -115.866 q^{46} +357.626 q^{47} -296.904 q^{48} +49.0000 q^{49} +435.776 q^{50} +220.373 q^{51} +59.9831 q^{52} -570.113 q^{53} +136.016 q^{54} +252.774 q^{55} +330.698 q^{56} +258.361 q^{57} -294.884 q^{58} +420.781 q^{59} -323.465 q^{60} -17.6207 q^{61} +77.5413 q^{62} -63.0000 q^{63} -184.074 q^{64} +21.4161 q^{65} +615.705 q^{66} -364.098 q^{67} -1276.54 q^{68} -69.0000 q^{69} +218.793 q^{70} -484.955 q^{71} -425.183 q^{72} -527.508 q^{73} -371.189 q^{74} +259.512 q^{75} -1496.59 q^{76} -285.182 q^{77} +52.1652 q^{78} -492.947 q^{79} +614.049 q^{80} +81.0000 q^{81} -2293.94 q^{82} +353.361 q^{83} +364.936 q^{84} -455.770 q^{85} +481.311 q^{86} -175.608 q^{87} -1924.67 q^{88} -849.256 q^{89} -281.306 q^{90} -24.1618 q^{91} +399.692 q^{92} +46.1771 q^{93} -1801.59 q^{94} -534.336 q^{95} +361.877 q^{96} -183.115 q^{97} -246.845 q^{98} +366.662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9} + 11 q^{10} - 6 q^{11} - 66 q^{12} + 17 q^{13} + 14 q^{14} + 33 q^{15} + 106 q^{16} - 78 q^{17} - 18 q^{18} + 44 q^{19} + 44 q^{20} + 147 q^{21} - 477 q^{22} + 161 q^{23} - 45 q^{24} - 80 q^{25} + 288 q^{26} - 189 q^{27} - 154 q^{28} - 185 q^{29} - 33 q^{30} + 238 q^{31} - 512 q^{32} + 18 q^{33} - 27 q^{34} + 77 q^{35} + 198 q^{36} - 511 q^{37} - 413 q^{38} - 51 q^{39} - 686 q^{40} + 867 q^{41} - 42 q^{42} - 1003 q^{43} - 629 q^{44} - 99 q^{45} - 46 q^{46} + 149 q^{47} - 318 q^{48} + 343 q^{49} - 986 q^{50} + 234 q^{51} - 439 q^{52} - 1244 q^{53} + 54 q^{54} - 270 q^{55} - 105 q^{56} - 132 q^{57} - 2376 q^{58} + 1048 q^{59} - 132 q^{60} - 1380 q^{61} - 809 q^{62} - 441 q^{63} - 1835 q^{64} - 223 q^{65} + 1431 q^{66} - 500 q^{67} - 1387 q^{68} - 483 q^{69} - 77 q^{70} - 14 q^{71} + 135 q^{72} - 530 q^{73} - 738 q^{74} + 240 q^{75} - 1785 q^{76} + 42 q^{77} - 864 q^{78} - 2978 q^{79} + 1043 q^{80} + 567 q^{81} - 1986 q^{82} - 524 q^{83} + 462 q^{84} - 2674 q^{85} + 194 q^{86} + 555 q^{87} - 4504 q^{88} - 648 q^{89} + 99 q^{90} - 119 q^{91} + 506 q^{92} - 714 q^{93} - 801 q^{94} + 154 q^{95} + 1536 q^{96} - 1999 q^{97} - 98 q^{98} - 54 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9 + 11 * q^10 - 6 * q^11 - 66 * q^12 + 17 * q^13 + 14 * q^14 + 33 * q^15 + 106 * q^16 - 78 * q^17 - 18 * q^18 + 44 * q^19 + 44 * q^20 + 147 * q^21 - 477 * q^22 + 161 * q^23 - 45 * q^24 - 80 * q^25 + 288 * q^26 - 189 * q^27 - 154 * q^28 - 185 * q^29 - 33 * q^30 + 238 * q^31 - 512 * q^32 + 18 * q^33 - 27 * q^34 + 77 * q^35 + 198 * q^36 - 511 * q^37 - 413 * q^38 - 51 * q^39 - 686 * q^40 + 867 * q^41 - 42 * q^42 - 1003 * q^43 - 629 * q^44 - 99 * q^45 - 46 * q^46 + 149 * q^47 - 318 * q^48 + 343 * q^49 - 986 * q^50 + 234 * q^51 - 439 * q^52 - 1244 * q^53 + 54 * q^54 - 270 * q^55 - 105 * q^56 - 132 * q^57 - 2376 * q^58 + 1048 * q^59 - 132 * q^60 - 1380 * q^61 - 809 * q^62 - 441 * q^63 - 1835 * q^64 - 223 * q^65 + 1431 * q^66 - 500 * q^67 - 1387 * q^68 - 483 * q^69 - 77 * q^70 - 14 * q^71 + 135 * q^72 - 530 * q^73 - 738 * q^74 + 240 * q^75 - 1785 * q^76 + 42 * q^77 - 864 * q^78 - 2978 * q^79 + 1043 * q^80 + 567 * q^81 - 1986 * q^82 - 524 * q^83 + 462 * q^84 - 2674 * q^85 + 194 * q^86 + 555 * q^87 - 4504 * q^88 - 648 * q^89 + 99 * q^90 - 119 * q^91 + 506 * q^92 - 714 * q^93 - 801 * q^94 + 154 * q^95 + 1536 * q^96 - 1999 * q^97 - 98 * q^98 - 54 * 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 $

$2$	−5.03765	−1.78108	−0.890539	−	0.454908i	$-0.849672\pi$
$2$	−5.03765	−1.78108	−0.890539	+	0.454908i	$0.849672\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	17.3779	2.17224
$5$	6.20452	0.554949	0.277475	−	0.960733i	$-0.410503\pi$
$5$	6.20452	0.554949	0.277475	+	0.960733i	$0.410503\pi$
$6$	15.1129	1.02831
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−47.2425	−2.08784
$9$	9.00000	0.333333
$10$	−31.2562	−0.988408
$11$	40.7402	1.11669	0.558347	−	0.829607i	$-0.311436\pi$
$11$	40.7402	1.11669	0.558347	+	0.829607i	$0.311436\pi$
$12$	−52.1337	−1.25414
$13$	3.45169	0.0736405	0.0368202	−	0.999322i	$-0.488277\pi$
$13$	3.45169	0.0736405	0.0368202	+	0.999322i	$0.488277\pi$
$14$	35.2635	0.673184
$15$	−18.6136	−0.320400
$16$	98.9680	1.54637
$17$	−73.4576	−1.04801	−0.524003	−	0.851717i	$-0.675562\pi$
$17$	−73.4576	−1.04801	−0.524003	+	0.851717i	$0.675562\pi$
$18$	−45.3388	−0.593692
$19$	−86.1205	−1.03986	−0.519931	−	0.854208i	$-0.674042\pi$
$19$	−86.1205	−1.03986	−0.519931	+	0.854208i	$0.674042\pi$
$20$	107.822	1.20548
$21$	21.0000	0.218218
$22$	−205.235	−1.98892
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	141.728	1.20542
$25$	−86.5039	−0.692031
$26$	−17.3884	−0.131159
$27$	−27.0000	−0.192450
$28$	−121.645	−0.821028
$29$	58.5361	0.374823	0.187412	−	0.982281i	$-0.439990\pi$
$29$	58.5361	0.374823	0.187412	+	0.982281i	$0.439990\pi$
$30$	93.7686	0.570658
$31$	−15.3924	−0.0891790	−0.0445895	−	0.999005i	$-0.514198\pi$
$31$	−15.3924	−0.0891790	−0.0445895	+	0.999005i	$0.514198\pi$
$32$	−120.626	−0.666369
$33$	−122.221	−0.644724
$34$	370.054	1.86658
$35$	−43.4317	−0.209751
$36$	156.401	0.724079
$37$	73.6831	0.327390	0.163695	−	0.986511i	$-0.447659\pi$
$37$	73.6831	0.327390	0.163695	+	0.986511i	$0.447659\pi$
$38$	433.844	1.85208
$39$	−10.3551	−0.0425164
$40$	−293.117	−1.15865
$41$	455.360	1.73452	0.867260	−	0.497856i	$-0.165879\pi$
$41$	455.360	1.73452	0.867260	+	0.497856i	$0.165879\pi$
$42$	−105.791	−0.388663
$43$	−95.5428	−0.338841	−0.169420	−	0.985544i	$-0.554190\pi$
$43$	−95.5428	−0.338841	−0.169420	+	0.985544i	$0.554190\pi$
$44$	707.980	2.42573
$45$	55.8407	0.184983
$46$	−115.866	−0.371380
$47$	357.626	1.10990	0.554948	−	0.831885i	$-0.312738\pi$
$47$	357.626	1.10990	0.554948	+	0.831885i	$0.312738\pi$
$48$	−296.904	−0.892800
$49$	49.0000	0.142857
$50$	435.776	1.23256
$51$	220.373	0.605066
$52$	59.9831	0.159965
$53$	−570.113	−1.47757	−0.738783	−	0.673943i	$-0.764599\pi$
$53$	−570.113	−1.47757	−0.738783	+	0.673943i	$0.764599\pi$
$54$	136.016	0.342768
$55$	252.774	0.619709
$56$	330.698	0.789131
$57$	258.361	0.600365
$58$	−294.884	−0.667589
$59$	420.781	0.928493	0.464246	−	0.885706i	$-0.346325\pi$
$59$	420.781	0.928493	0.464246	+	0.885706i	$0.346325\pi$
$60$	−323.465	−0.695985
$61$	−17.6207	−0.0369852	−0.0184926	−	0.999829i	$-0.505887\pi$
$61$	−17.6207	−0.0369852	−0.0184926	+	0.999829i	$0.505887\pi$
$62$	77.5413	0.158835
$63$	−63.0000	−0.125988
$64$	−184.074	−0.359519
$65$	21.4161	0.0408667
$66$	615.705	1.14830
$67$	−364.098	−0.663904	−0.331952	−	0.943296i	$-0.607707\pi$
$67$	−364.098	−0.663904	−0.331952	+	0.943296i	$0.607707\pi$
$68$	−1276.54	−2.27652
$69$	−69.0000	−0.120386
$70$	218.793	0.373583
$71$	−484.955	−0.810614	−0.405307	−	0.914181i	$-0.632835\pi$
$71$	−484.955	−0.810614	−0.405307	+	0.914181i	$0.632835\pi$
$72$	−425.183	−0.695948
$73$	−527.508	−0.845756	−0.422878	−	0.906187i	$-0.638980\pi$
$73$	−527.508	−0.845756	−0.422878	+	0.906187i	$0.638980\pi$
$74$	−371.189	−0.583107
$75$	259.512	0.399544
$76$	−1496.59	−2.25883
$77$	−285.182	−0.422071
$78$	52.1652	0.0757249
$79$	−492.947	−0.702036	−0.351018	−	0.936369i	$-0.614164\pi$
$79$	−492.947	−0.702036	−0.351018	+	0.936369i	$0.614164\pi$
$80$	614.049	0.858160
$81$	81.0000	0.111111
$82$	−2293.94	−3.08931
$83$	353.361	0.467306	0.233653	−	0.972320i	$-0.424932\pi$
$83$	353.361	0.467306	0.233653	+	0.972320i	$0.424932\pi$
$84$	364.936	0.474021
$85$	−455.770	−0.581590
$86$	481.311	0.603501
$87$	−175.608	−0.216404
$88$	−1924.67	−2.33148
$89$	−849.256	−1.01147	−0.505736	−	0.862688i	$-0.668779\pi$
$89$	−849.256	−1.01147	−0.505736	+	0.862688i	$0.668779\pi$
$90$	−281.306	−0.329469
$91$	−24.1618	−0.0278335
$92$	399.692	0.452943
$93$	46.1771	0.0514875
$94$	−1801.59	−1.97681
$95$	−534.336	−0.577071
$96$	361.877	0.384729
$97$	−183.115	−0.191675	−0.0958376	−	0.995397i	$-0.530553\pi$
$97$	−183.115	−0.191675	−0.0958376	+	0.995397i	$0.530553\pi$
$98$	−246.845	−0.254440
$99$	366.662	0.372232
$100$	−1503.26	−1.50326
$101$	1598.56	1.57488	0.787439	−	0.616392i	$-0.211406\pi$
$101$	1598.56	1.57488	0.787439	+	0.616392i	$0.211406\pi$
$102$	−1110.16	−1.07767
$103$	−1549.47	−1.48227	−0.741135	−	0.671356i	$-0.765712\pi$
$103$	−1549.47	−1.48227	−0.741135	+	0.671356i	$0.765712\pi$
$104$	−163.066	−0.153750
$105$	130.295	0.121100
$106$	2872.03	2.63166
$107$	−1011.43	−0.913815	−0.456908	−	0.889514i	$-0.651043\pi$
$107$	−1011.43	−0.913815	−0.456908	+	0.889514i	$0.651043\pi$
$108$	−469.203	−0.418047
$109$	797.544	0.700833	0.350417	−	0.936594i	$-0.386040\pi$
$109$	797.544	0.700833	0.350417	+	0.936594i	$0.386040\pi$
$110$	−1273.39	−1.10375
$111$	−221.049	−0.189019
$112$	−692.776	−0.584475
$113$	−823.623	−0.685663	−0.342831	−	0.939397i	$-0.611386\pi$
$113$	−823.623	−0.685663	−0.342831	+	0.939397i	$0.611386\pi$
$114$	−1301.53	−1.06930
$115$	142.704	0.115715
$116$	1017.23	0.814205
$117$	31.0652	0.0245468
$118$	−2119.75	−1.65372
$119$	514.203	0.396109
$120$	879.352	0.668946
$121$	328.767	0.247008
$122$	88.7668	0.0658735
$123$	−1366.08	−1.00143
$124$	−267.487	−0.193718
$125$	−1312.28	−0.938992
$126$	317.372	0.224395
$127$	1594.80	1.11430	0.557148	−	0.830413i	$-0.311896\pi$
$127$	1594.80	1.11430	0.557148	+	0.830413i	$0.311896\pi$
$128$	1892.31	1.30670
$129$	286.628	0.195630
$130$	−107.887	−0.0727868
$131$	−1005.31	−0.670488	−0.335244	−	0.942131i	$-0.608819\pi$
$131$	−1005.31	−0.670488	−0.335244	+	0.942131i	$0.608819\pi$
$132$	−2123.94	−1.40049
$133$	602.843	0.393031
$134$	1834.20	1.18247
$135$	−167.522	−0.106800
$136$	3470.32	2.18807
$137$	−1533.39	−0.956252	−0.478126	−	0.878291i	$-0.658684\pi$
$137$	−1533.39	−0.956252	−0.478126	+	0.878291i	$0.658684\pi$
$138$	347.598	0.214417
$139$	−74.1641	−0.0452555	−0.0226278	−	0.999744i	$-0.507203\pi$
$139$	−74.1641	−0.0452555	−0.0226278	+	0.999744i	$0.507203\pi$
$140$	−754.751	−0.455629
$141$	−1072.88	−0.640798
$142$	2443.03	1.44377
$143$	140.623	0.0822340
$144$	890.712	0.515458
$145$	363.188	0.208008
$146$	2657.40	1.50636
$147$	−147.000	−0.0824786
$148$	1280.46	0.711168
$149$	−2423.98	−1.33275	−0.666376	−	0.745616i	$-0.732155\pi$
$149$	−2423.98	−1.33275	−0.666376	+	0.745616i	$0.732155\pi$
$150$	−1307.33	−0.711619
$151$	508.644	0.274125	0.137063	−	0.990562i	$-0.456234\pi$
$151$	508.644	0.274125	0.137063	+	0.990562i	$0.456234\pi$
$152$	4068.55	2.17107
$153$	−661.119	−0.349335
$154$	1436.64	0.751741
$155$	−95.5023	−0.0494898
$156$	−179.949	−0.0923556
$157$	−2423.79	−1.23210	−0.616050	−	0.787707i	$-0.711268\pi$
$157$	−2423.79	−1.23210	−0.616050	+	0.787707i	$0.711268\pi$
$158$	2483.29	1.25038
$159$	1710.34	0.853074
$160$	−748.425	−0.369801
$161$	−161.000	−0.0788110
$162$	−408.049	−0.197897
$163$	−2001.71	−0.961876	−0.480938	−	0.876755i	$-0.659704\pi$
$163$	−2001.71	−0.961876	−0.480938	+	0.876755i	$0.659704\pi$
$164$	7913.20	3.76779
$165$	−758.321	−0.357789
$166$	−1780.11	−0.832308
$167$	1870.98	0.866950	0.433475	−	0.901166i	$-0.357287\pi$
$167$	1870.98	0.866950	0.433475	+	0.901166i	$0.357287\pi$
$168$	−992.093	−0.455605
$169$	−2185.09	−0.994577
$170$	2296.01	1.03586
$171$	−775.084	−0.346621
$172$	−1660.33	−0.736042
$173$	−2843.28	−1.24954	−0.624771	−	0.780808i	$-0.714808\pi$
$173$	−2843.28	−1.24954	−0.624771	+	0.780808i	$0.714808\pi$
$174$	884.652	0.385433
$175$	605.527	0.261563
$176$	4031.98	1.72683
$177$	−1262.34	−0.536065
$178$	4278.25	1.80151
$179$	−142.271	−0.0594068	−0.0297034	−	0.999559i	$-0.509456\pi$
$179$	−142.271	−0.0594068	−0.0297034	+	0.999559i	$0.509456\pi$
$180$	970.394	0.401827
$181$	−492.682	−0.202325	−0.101162	−	0.994870i	$-0.532256\pi$
$181$	−492.682	−0.202325	−0.101162	+	0.994870i	$0.532256\pi$
$182$	121.719	0.0495736
$183$	52.8620	0.0213534
$184$	−1086.58	−0.435346
$185$	457.168	0.181685
$186$	−232.624	−0.0917033
$187$	−2992.68	−1.17030
$188$	6214.78	2.41096
$189$	189.000	0.0727393
$190$	2691.80	1.02781
$191$	−5200.75	−1.97023	−0.985113	−	0.171907i	$-0.945007\pi$
$191$	−5200.75	−1.97023	−0.985113	+	0.171907i	$0.945007\pi$
$192$	552.222	0.207569
$193$	−473.465	−0.176584	−0.0882922	−	0.996095i	$-0.528141\pi$
$193$	−473.465	−0.176584	−0.0882922	+	0.996095i	$0.528141\pi$
$194$	922.468	0.341388
$195$	−64.2483	−0.0235944
$196$	851.517	0.310320
$197$	223.413	0.0807995	0.0403997	−	0.999184i	$-0.487137\pi$
$197$	223.413	0.0807995	0.0403997	+	0.999184i	$0.487137\pi$
$198$	−1847.11	−0.662973
$199$	2490.67	0.887231	0.443616	−	0.896217i	$-0.353696\pi$
$199$	2490.67	0.887231	0.443616	+	0.896217i	$0.353696\pi$
$200$	4086.66	1.44485
$201$	1092.29	0.383305
$202$	−8052.99	−2.80498
$203$	−409.752	−0.141670
$204$	3829.62	1.31435
$205$	2825.29	0.962571
$206$	7805.69	2.64004
$207$	207.000	0.0695048
$208$	341.607	0.113876
$209$	−3508.57	−1.16121
$210$	−656.380	−0.215688
$211$	1109.22	0.361903	0.180951	−	0.983492i	$-0.442082\pi$
$211$	1109.22	0.361903	0.180951	+	0.983492i	$0.442082\pi$
$212$	−9907.36	−3.20962
$213$	1454.87	0.468008
$214$	5095.21	1.62758
$215$	−592.798	−0.188039
$216$	1275.55	0.401806
$217$	107.747	0.0337065
$218$	−4017.74	−1.24824
$219$	1582.53	0.488298
$220$	4392.68	1.34615
$221$	−253.553	−0.0771756
$222$	1113.57	0.336657
$223$	986.824	0.296335	0.148167	−	0.988962i	$-0.452663\pi$
$223$	986.824	0.296335	0.148167	+	0.988962i	$0.452663\pi$
$224$	844.380	0.251864
$225$	−778.535	−0.230677
$226$	4149.12	1.22122
$227$	4283.68	1.25250	0.626251	−	0.779622i	$-0.284589\pi$
$227$	4283.68	1.25250	0.626251	+	0.779622i	$0.284589\pi$
$228$	4489.78	1.30413
$229$	2858.60	0.824898	0.412449	−	0.910981i	$-0.364674\pi$
$229$	2858.60	0.824898	0.412449	+	0.910981i	$0.364674\pi$
$230$	−718.893	−0.206097
$231$	855.545	0.243683
$232$	−2765.39	−0.782572
$233$	−5015.20	−1.41012	−0.705058	−	0.709150i	$-0.749079\pi$
$233$	−5015.20	−1.41012	−0.705058	+	0.709150i	$0.749079\pi$
$234$	−156.496	−0.0437198
$235$	2218.90	0.615936
$236$	7312.29	2.01691
$237$	1478.84	0.405321
$238$	−2590.38	−0.705500
$239$	6846.17	1.85290	0.926448	−	0.376423i	$-0.122846\pi$
$239$	6846.17	1.85290	0.926448	+	0.376423i	$0.122846\pi$
$240$	−1842.15	−0.495459
$241$	−3061.00	−0.818158	−0.409079	−	0.912499i	$-0.634150\pi$
$241$	−3061.00	−0.818158	−0.409079	+	0.912499i	$0.634150\pi$
$242$	−1656.21	−0.439940
$243$	−243.000	−0.0641500
$244$	−306.210	−0.0803406
$245$	304.022	0.0792785
$246$	6881.83	1.78362
$247$	−297.261	−0.0765760
$248$	727.174	0.186192
$249$	−1060.08	−0.269799
$250$	6610.81	1.67242
$251$	1790.75	0.450322	0.225161	−	0.974322i	$-0.427709\pi$
$251$	1790.75	0.450322	0.225161	+	0.974322i	$0.427709\pi$
$252$	−1094.81	−0.273676
$253$	937.026	0.232847
$254$	−8034.04	−1.98465
$255$	1367.31	0.335781
$256$	−8060.18	−1.96782
$257$	−2983.86	−0.724233	−0.362116	−	0.932133i	$-0.617946\pi$
$257$	−2983.86	−0.724233	−0.362116	+	0.932133i	$0.617946\pi$
$258$	−1443.93	−0.348432
$259$	−515.782	−0.123742
$260$	372.166	0.0887722
$261$	526.825	0.124941
$262$	5064.38	1.19419
$263$	−2006.51	−0.470443	−0.235221	−	0.971942i	$-0.575581\pi$
$263$	−2006.51	−0.470443	−0.235221	+	0.971942i	$0.575581\pi$
$264$	5774.01	1.34608
$265$	−3537.28	−0.819975
$266$	−3036.91	−0.700019
$267$	2547.77	0.583973
$268$	−6327.25	−1.44216
$269$	3276.81	0.742716	0.371358	−	0.928490i	$-0.378892\pi$
$269$	3276.81	0.742716	0.371358	+	0.928490i	$0.378892\pi$
$270$	843.917	0.190219
$271$	−7418.04	−1.66278	−0.831391	−	0.555688i	$-0.812455\pi$
$271$	−7418.04	−1.66278	−0.831391	+	0.555688i	$0.812455\pi$
$272$	−7269.95	−1.62061
$273$	72.4855	0.0160697
$274$	7724.69	1.70316
$275$	−3524.19	−0.772788
$276$	−1199.07	−0.261507
$277$	293.350	0.0636306	0.0318153	−	0.999494i	$-0.489871\pi$
$277$	293.350	0.0636306	0.0318153	+	0.999494i	$0.489871\pi$
$278$	373.613	0.0806036
$279$	−138.531	−0.0297263
$280$	2051.82	0.437928
$281$	−5163.32	−1.09615	−0.548074	−	0.836430i	$-0.684639\pi$
$281$	−5163.32	−1.09615	−0.548074	+	0.836430i	$0.684639\pi$
$282$	5404.78	1.14131
$283$	508.700	0.106852	0.0534259	−	0.998572i	$-0.482986\pi$
$283$	508.700	0.106852	0.0534259	+	0.998572i	$0.482986\pi$
$284$	−8427.50	−1.76085
$285$	1603.01	0.333172
$286$	−708.407	−0.146465
$287$	−3187.52	−0.655587
$288$	−1085.63	−0.222123
$289$	483.023	0.0983153
$290$	−1829.61	−0.370478
$291$	549.345	0.110664
$292$	−9166.99	−1.83718
$293$	−5244.32	−1.04565	−0.522826	−	0.852439i	$-0.675122\pi$
$293$	−5244.32	−1.04565	−0.522826	+	0.852439i	$0.675122\pi$
$294$	740.534	0.146901
$295$	2610.75	0.515266
$296$	−3480.97	−0.683539
$297$	−1099.99	−0.214908
$298$	12211.1	2.37373
$299$	79.3889	0.0153551
$300$	4509.77	0.867905
$301$	668.800	0.128070
$302$	−2562.37	−0.488238
$303$	−4795.68	−0.909257
$304$	−8523.17	−1.60802
$305$	−109.328	−0.0205249
$306$	3330.48	0.622193
$307$	2368.27	0.440275	0.220138	−	0.975469i	$-0.429349\pi$
$307$	2368.27	0.440275	0.220138	+	0.975469i	$0.429349\pi$
$308$	−4955.86	−0.916838
$309$	4648.41	0.855789
$310$	481.107	0.0881452
$311$	−6137.17	−1.11899	−0.559497	−	0.828833i	$-0.689005\pi$
$311$	−6137.17	−1.11899	−0.559497	+	0.828833i	$0.689005\pi$
$312$	489.199	0.0887675
$313$	−3668.66	−0.662509	−0.331254	−	0.943542i	$-0.607472\pi$
$313$	−3668.66	−0.662509	−0.331254	+	0.943542i	$0.607472\pi$
$314$	12210.2	2.19446
$315$	−390.885	−0.0699171
$316$	−8566.38	−1.52499
$317$	−1283.25	−0.227364	−0.113682	−	0.993517i	$-0.536265\pi$
$317$	−1283.25	−0.227364	−0.113682	+	0.993517i	$0.536265\pi$
$318$	−8616.08	−1.51939
$319$	2384.77	0.418563
$320$	−1142.09	−0.199515
$321$	3034.28	0.527591
$322$	811.061	0.140369
$323$	6326.20	1.08978
$324$	1407.61	0.241360
$325$	−298.585	−0.0509615
$326$	10083.9	1.71317
$327$	−2392.63	−0.404626
$328$	−21512.4	−3.62141
$329$	−2503.38	−0.419501
$330$	3820.16	0.637250
$331$	2049.94	0.340408	0.170204	−	0.985409i	$-0.445557\pi$
$331$	2049.94	0.340408	0.170204	+	0.985409i	$0.445557\pi$
$332$	6140.66	1.01510
$333$	663.148	0.109130
$334$	−9425.33	−1.54411
$335$	−2259.05	−0.368433
$336$	2078.33	0.337447
$337$	−3061.79	−0.494915	−0.247457	−	0.968899i	$-0.579595\pi$
$337$	−3061.79	−0.494915	−0.247457	+	0.968899i	$0.579595\pi$
$338$	11007.7	1.77142
$339$	2470.87	0.395868
$340$	−7920.31	−1.26335
$341$	−627.088	−0.0995858
$342$	3904.60	0.617358
$343$	−343.000	−0.0539949
$344$	4513.68	0.707446
$345$	−428.112	−0.0668081
$346$	14323.5	2.22553
$347$	12379.1	1.91512	0.957559	−	0.288238i	$-0.0930696\pi$
$347$	12379.1	1.91512	0.957559	+	0.288238i	$0.0930696\pi$
$348$	−3051.70	−0.470081
$349$	9403.76	1.44233	0.721163	−	0.692765i	$-0.243608\pi$
$349$	9403.76	1.44233	0.721163	+	0.692765i	$0.243608\pi$
$350$	−3050.43	−0.465864
$351$	−93.1956	−0.0141721
$352$	−4914.32	−0.744131
$353$	−6288.71	−0.948199	−0.474099	−	0.880471i	$-0.657226\pi$
$353$	−6288.71	−0.948199	−0.474099	+	0.880471i	$0.657226\pi$
$354$	6359.24	0.954774
$355$	−3008.92	−0.449850
$356$	−14758.3	−2.19716
$357$	−1542.61	−0.228694
$358$	716.710	0.105808
$359$	7503.70	1.10315	0.551574	−	0.834126i	$-0.314028\pi$
$359$	7503.70	1.10315	0.551574	+	0.834126i	$0.314028\pi$
$360$	−2638.06	−0.386216
$361$	557.732	0.0813140
$362$	2481.96	0.360356
$363$	−986.302	−0.142610
$364$	−419.882	−0.0604609
$365$	−3272.94	−0.469352
$366$	−266.300	−0.0380321
$367$	−6427.51	−0.914205	−0.457102	−	0.889414i	$-0.651113\pi$
$367$	−6427.51	−0.914205	−0.457102	+	0.889414i	$0.651113\pi$
$368$	2276.26	0.322441
$369$	4098.24	0.578173
$370$	−2303.05	−0.323595
$371$	3990.79	0.558468
$372$	802.460	0.111843
$373$	−794.772	−0.110326	−0.0551632	−	0.998477i	$-0.517568\pi$
$373$	−794.772	−0.110326	−0.0551632	+	0.998477i	$0.517568\pi$
$374$	15076.1	2.08440
$375$	3936.84	0.542127
$376$	−16895.1	−2.31729
$377$	202.048	0.0276022
$378$	−952.115	−0.129554
$379$	−9097.01	−1.23293	−0.616467	−	0.787381i	$-0.711437\pi$
$379$	−9097.01	−1.23293	−0.616467	+	0.787381i	$0.711437\pi$
$380$	−9285.64	−1.25353
$381$	−4784.40	−0.643339
$382$	26199.6	3.50913
$383$	−1594.38	−0.212713	−0.106357	−	0.994328i	$-0.533919\pi$
$383$	−1594.38	−0.212713	−0.106357	+	0.994328i	$0.533919\pi$
$384$	−5676.92	−0.754424
$385$	−1769.42	−0.234228
$386$	2385.15	0.314510
$387$	−859.885	−0.112947
$388$	−3182.15	−0.416364
$389$	−13239.1	−1.72558	−0.862791	−	0.505561i	$-0.831286\pi$
$389$	−13239.1	−1.72558	−0.862791	+	0.505561i	$0.831286\pi$
$390$	323.660	0.0420235
$391$	−1689.53	−0.218524
$392$	−2314.88	−0.298263
$393$	3015.92	0.387107
$394$	−1125.47	−0.143910
$395$	−3058.50	−0.389595
$396$	6371.82	0.808575
$397$	−6335.00	−0.800868	−0.400434	−	0.916326i	$-0.631141\pi$
$397$	−6335.00	−0.800868	−0.400434	+	0.916326i	$0.631141\pi$
$398$	−12547.1	−1.58023
$399$	−1808.53	−0.226917
$400$	−8561.12	−1.07014
$401$	385.930	0.0480608	0.0240304	−	0.999711i	$-0.492350\pi$
$401$	385.930	0.0480608	0.0240304	+	0.999711i	$0.492350\pi$
$402$	−5502.59	−0.682697
$403$	−53.1296	−0.00656719
$404$	27779.6	3.42101
$405$	502.566	0.0616610
$406$	2064.19	0.252325
$407$	3001.87	0.365595
$408$	−10411.0	−1.26328
$409$	−7100.62	−0.858443	−0.429221	−	0.903199i	$-0.641212\pi$
$409$	−7100.62	−0.858443	−0.429221	+	0.903199i	$0.641212\pi$
$410$	−14232.8	−1.71441
$411$	4600.18	0.552092
$412$	−26926.5	−3.21984
$413$	−2945.47	−0.350937
$414$	−1042.79	−0.123793
$415$	2192.43	0.259331
$416$	−416.363	−0.0490718
$417$	222.492	0.0261283
$418$	17674.9	2.06820
$419$	1129.11	0.131649	0.0658243	−	0.997831i	$-0.479032\pi$
$419$	1129.11	0.131649	0.0658243	+	0.997831i	$0.479032\pi$
$420$	2264.25	0.263058
$421$	−5787.17	−0.669951	−0.334975	−	0.942227i	$-0.608728\pi$
$421$	−5787.17	−0.669951	−0.334975	+	0.942227i	$0.608728\pi$
$422$	−5587.83	−0.644577
$423$	3218.63	0.369965
$424$	26933.6	3.08493
$425$	6354.37	0.725252
$426$	−7329.10	−0.833559
$427$	123.345	0.0139791
$428$	−17576.4	−1.98502
$429$	−421.868	−0.0474778
$430$	2986.31	0.334913
$431$	−9443.51	−1.05540	−0.527700	−	0.849431i	$-0.676946\pi$
$431$	−9443.51	−1.05540	−0.527700	+	0.849431i	$0.676946\pi$
$432$	−2672.14	−0.297600
$433$	15267.8	1.69452	0.847258	−	0.531182i	$-0.178252\pi$
$433$	15267.8	1.69452	0.847258	+	0.531182i	$0.178252\pi$
$434$	−542.789	−0.0600339
$435$	−1089.56	−0.120093
$436$	13859.6	1.52238
$437$	−1980.77	−0.216826
$438$	−7972.21	−0.869696
$439$	9875.58	1.07366	0.536829	−	0.843691i	$-0.319622\pi$
$439$	9875.58	1.07366	0.536829	+	0.843691i	$0.319622\pi$
$440$	−11941.7	−1.29386
$441$	441.000	0.0476190
$442$	1277.31	0.137456
$443$	17411.9	1.86741	0.933707	−	0.358039i	$-0.116555\pi$
$443$	17411.9	1.86741	0.933707	+	0.358039i	$0.116555\pi$
$444$	−3841.37	−0.410593
$445$	−5269.23	−0.561316
$446$	−4971.27	−0.527795
$447$	7271.93	0.769465
$448$	1288.52	0.135886
$449$	3738.31	0.392922	0.196461	−	0.980512i	$-0.437055\pi$
$449$	3738.31	0.392922	0.196461	+	0.980512i	$0.437055\pi$
$450$	3921.99	0.410854
$451$	18551.5	1.93693
$452$	−14312.8	−1.48942
$453$	−1525.93	−0.158266
$454$	−21579.7	−2.23080
$455$	−149.913	−0.0154462
$456$	−12205.6	−1.25347
$457$	−12270.7	−1.25601	−0.628006	−	0.778208i	$-0.716129\pi$
$457$	−12270.7	−1.25601	−0.628006	+	0.778208i	$0.716129\pi$
$458$	−14400.6	−1.46921
$459$	1983.36	0.201689
$460$	2479.90	0.251360
$461$	−12582.6	−1.27121	−0.635606	−	0.772013i	$-0.719250\pi$
$461$	−12582.6	−1.27121	−0.635606	+	0.772013i	$0.719250\pi$
$462$	−4309.93	−0.434018
$463$	−5278.64	−0.529847	−0.264924	−	0.964269i	$-0.585347\pi$
$463$	−5278.64	−0.529847	−0.264924	+	0.964269i	$0.585347\pi$
$464$	5793.20	0.579617
$465$	286.507	0.0285730
$466$	25264.8	2.51152
$467$	−6507.19	−0.644790	−0.322395	−	0.946605i	$-0.604488\pi$
$467$	−6507.19	−0.644790	−0.322395	+	0.946605i	$0.604488\pi$
$468$	539.848	0.0533215
$469$	2548.68	0.250932
$470$	−11178.0	−1.09703
$471$	7271.38	0.711353
$472$	−19878.8	−1.93855
$473$	−3892.44	−0.378382
$474$	−7449.88	−0.721908
$475$	7449.75	0.719617
$476$	8935.77	0.860442
$477$	−5131.02	−0.492522
$478$	−34488.6	−3.30015
$479$	−14692.4	−1.40149	−0.700746	−	0.713411i	$-0.747150\pi$
$479$	−14692.4	−1.40149	−0.700746	+	0.713411i	$0.747150\pi$
$480$	2245.28	0.213505
$481$	254.331	0.0241092
$482$	15420.2	1.45720
$483$	483.000	0.0455016
$484$	5713.28	0.536559
$485$	−1136.14	−0.106370
$486$	1224.15	0.114256
$487$	15287.1	1.42243	0.711214	−	0.702975i	$-0.248146\pi$
$487$	15287.1	1.42243	0.711214	+	0.702975i	$0.248146\pi$
$488$	832.445	0.0772193
$489$	6005.12	0.555339
$490$	−1531.55	−0.141201
$491$	−20236.3	−1.85998	−0.929992	−	0.367579i	$-0.880187\pi$
$491$	−20236.3	−1.85998	−0.929992	+	0.367579i	$0.880187\pi$
$492$	−23739.6	−2.17533
$493$	−4299.92	−0.392817
$494$	1497.50	0.136388
$495$	2274.96	0.206570
$496$	−1523.35	−0.137904
$497$	3394.69	0.306383
$498$	5340.32	0.480533
$499$	−6772.29	−0.607554	−0.303777	−	0.952743i	$-0.598248\pi$
$499$	−6772.29	−0.607554	−0.303777	+	0.952743i	$0.598248\pi$
$500$	−22804.7	−2.03971
$501$	−5612.94	−0.500534
$502$	−9021.14	−0.802058
$503$	7697.81	0.682363	0.341181	−	0.939998i	$-0.389173\pi$
$503$	7697.81	0.682363	0.341181	+	0.939998i	$0.389173\pi$
$504$	2976.28	0.263044
$505$	9918.31	0.873978
$506$	−4720.40	−0.414719
$507$	6555.26	0.574219
$508$	27714.3	2.42051
$509$	17205.0	1.49823	0.749116	−	0.662439i	$-0.230479\pi$
$509$	17205.0	1.49823	0.749116	+	0.662439i	$0.230479\pi$
$510$	−6888.02	−0.598052
$511$	3692.56	0.319666
$512$	25465.9	2.19813
$513$	2325.25	0.200122
$514$	15031.6	1.28991
$515$	−9613.72	−0.822585
$516$	4981.00	0.424954
$517$	14569.8	1.23941
$518$	2598.33	0.220394
$519$	8529.85	0.721424
$520$	−1011.75	−0.0853234
$521$	8275.57	0.695891	0.347946	−	0.937515i	$-0.386879\pi$
$521$	8275.57	0.695891	0.347946	+	0.937515i	$0.386879\pi$
$522$	−2653.96	−0.222530
$523$	−16864.9	−1.41004	−0.705022	−	0.709186i	$-0.749063\pi$
$523$	−16864.9	−1.41004	−0.705022	+	0.709186i	$0.749063\pi$
$524$	−17470.1	−1.45646
$525$	−1816.58	−0.151014
$526$	10108.1	0.837895
$527$	1130.69	0.0934601
$528$	−12095.9	−0.996985
$529$	529.000	0.0434783
$530$	17819.6	1.46044
$531$	3787.03	0.309498
$532$	10476.1	0.853756
$533$	1571.76	0.127731
$534$	−12834.8	−1.04010
$535$	−6275.41	−0.507121
$536$	17200.9	1.38613
$537$	426.812	0.0342985
$538$	−16507.4	−1.32283
$539$	1996.27	0.159528
$540$	−2911.18	−0.231995
$541$	22305.5	1.77263	0.886313	−	0.463088i	$-0.153258\pi$
$541$	22305.5	1.77263	0.886313	+	0.463088i	$0.153258\pi$
$542$	37369.5	2.96154
$543$	1478.05	0.116812
$544$	8860.88	0.698359
$545$	4948.38	0.388927
$546$	−365.156	−0.0286213
$547$	7827.60	0.611854	0.305927	−	0.952055i	$-0.401034\pi$
$547$	7827.60	0.611854	0.305927	+	0.952055i	$0.401034\pi$
$548$	−26647.1	−2.07721
$549$	−158.586	−0.0123284
$550$	17753.6	1.37639
$551$	−5041.15	−0.389765
$552$	3259.73	0.251347
$553$	3450.63	0.265345
$554$	−1477.79	−0.113331
$555$	−1371.51	−0.104896
$556$	−1288.82	−0.0983057
$557$	12170.8	0.925840	0.462920	−	0.886400i	$-0.346802\pi$
$557$	12170.8	0.925840	0.462920	+	0.886400i	$0.346802\pi$
$558$	697.872	0.0529449
$559$	−329.784	−0.0249524
$560$	−4298.34	−0.324354
$561$	8978.04	0.675674
$562$	26011.0	1.95232
$563$	20529.7	1.53681	0.768406	−	0.639962i	$-0.221050\pi$
$563$	20529.7	1.53681	0.768406	+	0.639962i	$0.221050\pi$
$564$	−18644.3	−1.39197
$565$	−5110.19	−0.380508
$566$	−2562.65	−0.190311
$567$	−567.000	−0.0419961
$568$	22910.5	1.69244
$569$	13492.2	0.994064	0.497032	−	0.867732i	$-0.334423\pi$
$569$	13492.2	0.994064	0.497032	+	0.867732i	$0.334423\pi$
$570$	−8075.39	−0.593405
$571$	2603.41	0.190805	0.0954024	−	0.995439i	$-0.469586\pi$
$571$	2603.41	0.190805	0.0954024	+	0.995439i	$0.469586\pi$
$572$	2443.73	0.178632
$573$	15602.3	1.13751
$574$	16057.6	1.16765
$575$	−1989.59	−0.144298
$576$	−1656.67	−0.119840
$577$	−5511.73	−0.397671	−0.198836	−	0.980033i	$-0.563716\pi$
$577$	−5511.73	−0.397671	−0.198836	+	0.980033i	$0.563716\pi$
$578$	−2433.30	−0.175107
$579$	1420.40	0.101951
$580$	6311.45	0.451842
$581$	−2473.52	−0.176625
$582$	−2767.40	−0.197101
$583$	−23226.5	−1.64999
$584$	24920.8	1.76581
$585$	192.745	0.0136222
$586$	26419.0	1.86239
$587$	−6489.96	−0.456336	−0.228168	−	0.973622i	$-0.573274\pi$
$587$	−6489.96	−0.456336	−0.228168	+	0.973622i	$0.573274\pi$
$588$	−2554.55	−0.179163
$589$	1325.60	0.0927339
$590$	−13152.0	−0.917729
$591$	−670.238	−0.0466496
$592$	7292.27	0.506268
$593$	6744.15	0.467030	0.233515	−	0.972353i	$-0.424977\pi$
$593$	6744.15	0.467030	0.233515	+	0.972353i	$0.424977\pi$
$594$	5541.34	0.382768
$595$	3190.39	0.219820
$596$	−42123.6	−2.89505
$597$	−7472.01	−0.512243
$598$	−399.933	−0.0273486
$599$	−17075.1	−1.16472	−0.582360	−	0.812931i	$-0.697871\pi$
$599$	−17075.1	−1.16472	−0.582360	+	0.812931i	$0.697871\pi$
$600$	−12260.0	−0.834186
$601$	870.735	0.0590982	0.0295491	−	0.999563i	$-0.490593\pi$
$601$	870.735	0.0590982	0.0295491	+	0.999563i	$0.490593\pi$
$602$	−3369.18	−0.228102
$603$	−3276.88	−0.221301
$604$	8839.17	0.595464
$605$	2039.84	0.137077
$606$	24159.0	1.61946
$607$	7469.27	0.499454	0.249727	−	0.968316i	$-0.419659\pi$
$607$	7469.27	0.499454	0.249727	+	0.968316i	$0.419659\pi$
$608$	10388.3	0.692933
$609$	1229.26	0.0817931
$610$	550.756	0.0365565
$611$	1234.41	0.0817333
$612$	−11488.8	−0.758839
$613$	−22214.8	−1.46370	−0.731849	−	0.681466i	$-0.761343\pi$
$613$	−22214.8	−1.46370	−0.731849	+	0.681466i	$0.761343\pi$
$614$	−11930.5	−0.784164
$615$	−8475.88	−0.555740
$616$	13472.7	0.881218
$617$	3243.65	0.211644	0.105822	−	0.994385i	$-0.466253\pi$
$617$	3243.65	0.211644	0.105822	+	0.994385i	$0.466253\pi$
$618$	−23417.1	−1.52423
$619$	4783.29	0.310592	0.155296	−	0.987868i	$-0.450367\pi$
$619$	4783.29	0.310592	0.155296	+	0.987868i	$0.450367\pi$
$620$	−1659.63	−0.107504
$621$	−621.000	−0.0401286
$622$	30916.9	1.99301
$623$	5944.79	0.382300
$624$	−1024.82	−0.0657462
$625$	2670.91	0.170938
$626$	18481.4	1.17998
$627$	10525.7	0.670424
$628$	−42120.4	−2.67641
$629$	−5412.59	−0.343106
$630$	1969.14	0.124528
$631$	16546.9	1.04393	0.521966	−	0.852966i	$-0.325199\pi$
$631$	16546.9	1.04393	0.521966	+	0.852966i	$0.325199\pi$
$632$	23288.1	1.46574
$633$	−3327.65	−0.208945
$634$	6464.56	0.404953
$635$	9894.97	0.618378
$636$	29722.1	1.85308
$637$	169.133	0.0105201
$638$	−12013.6	−0.745493
$639$	−4364.60	−0.270205
$640$	11740.9	0.725153
$641$	3152.15	0.194232	0.0971158	−	0.995273i	$-0.469038\pi$
$641$	3152.15	0.194232	0.0971158	+	0.995273i	$0.469038\pi$
$642$	−15285.6	−0.939681
$643$	22750.6	1.39533	0.697664	−	0.716425i	$-0.254223\pi$
$643$	22750.6	1.39533	0.697664	+	0.716425i	$0.254223\pi$
$644$	−2797.84	−0.171196
$645$	1778.39	0.108565
$646$	−31869.2	−1.94099
$647$	26757.9	1.62590	0.812952	−	0.582330i	$-0.197859\pi$
$647$	26757.9	1.62590	0.812952	+	0.582330i	$0.197859\pi$
$648$	−3826.64	−0.231983
$649$	17142.7	1.03684
$650$	1504.16	0.0907664
$651$	−323.240	−0.0194605
$652$	−34785.4	−2.08942
$653$	−4418.57	−0.264796	−0.132398	−	0.991197i	$-0.542268\pi$
$653$	−4418.57	−0.264796	−0.132398	+	0.991197i	$0.542268\pi$
$654$	12053.2	0.720671
$655$	−6237.44	−0.372087
$656$	45066.1	2.68222
$657$	−4747.58	−0.281919
$658$	12611.1	0.747164
$659$	4921.87	0.290939	0.145469	−	0.989363i	$-0.453531\pi$
$659$	4921.87	0.290939	0.145469	+	0.989363i	$0.453531\pi$
$660$	−13178.0	−0.777203
$661$	−17466.0	−1.02776	−0.513880	−	0.857862i	$-0.671792\pi$
$661$	−17466.0	−1.02776	−0.513880	+	0.857862i	$0.671792\pi$
$662$	−10326.9	−0.606292
$663$	760.659	0.0445574
$664$	−16693.6	−0.975661
$665$	3740.35	0.218112
$666$	−3340.71	−0.194369
$667$	1346.33	0.0781560
$668$	32513.7	1.88322
$669$	−2960.47	−0.171089
$670$	11380.3	0.656208
$671$	−717.871	−0.0413012
$672$	−2533.14	−0.145414
$673$	−13646.9	−0.781646	−0.390823	−	0.920466i	$-0.627810\pi$
$673$	−13646.9	−0.781646	−0.390823	+	0.920466i	$0.627810\pi$
$674$	15424.2	0.881481
$675$	2335.61	0.133181
$676$	−37972.2	−2.16046
$677$	23178.2	1.31582	0.657910	−	0.753097i	$-0.271441\pi$
$677$	23178.2	1.31582	0.657910	+	0.753097i	$0.271441\pi$
$678$	−12447.4	−0.705071
$679$	1281.80	0.0724464
$680$	21531.7	1.21427
$681$	−12851.0	−0.723132
$682$	3159.05	0.177370
$683$	−32131.3	−1.80010	−0.900050	−	0.435786i	$-0.856471\pi$
$683$	−32131.3	−1.80010	−0.900050	+	0.435786i	$0.856471\pi$
$684$	−13469.3	−0.752942
$685$	−9513.97	−0.530672
$686$	1727.91	0.0961691
$687$	−8575.80	−0.476255
$688$	−9455.68	−0.523975
$689$	−1967.85	−0.108809
$690$	2156.68	0.118990
$691$	167.722	0.00923362	0.00461681	−	0.999989i	$-0.498530\pi$
$691$	167.722	0.00923362	0.00461681	+	0.999989i	$0.498530\pi$
$692$	−49410.3	−2.71430
$693$	−2566.64	−0.140690
$694$	−62361.6	−3.41097
$695$	−460.153	−0.0251145
$696$	8296.17	0.451818
$697$	−33449.7	−1.81779
$698$	−47372.8	−2.56889
$699$	15045.6	0.814131
$700$	10522.8	0.568177
$701$	8181.92	0.440837	0.220418	−	0.975405i	$-0.429258\pi$
$701$	8181.92	0.440837	0.220418	+	0.975405i	$0.429258\pi$
$702$	469.487	0.0252416
$703$	−6345.62	−0.340440
$704$	−7499.22	−0.401473
$705$	−6656.69	−0.355611
$706$	31680.3	1.68882
$707$	−11189.9	−0.595248
$708$	−21936.9	−1.16446
$709$	−20612.2	−1.09183	−0.545914	−	0.837841i	$-0.683817\pi$
$709$	−20612.2	−1.09183	−0.545914	+	0.837841i	$0.683817\pi$
$710$	15157.9	0.801217
$711$	−4436.52	−0.234012
$712$	40121.0	2.11179
$713$	−354.024	−0.0185951
$714$	7771.13	0.407321
$715$	872.497	0.0456357
$716$	−2472.37	−0.129046
$717$	−20538.5	−1.06977
$718$	−37801.0	−1.96479
$719$	17464.0	0.905836	0.452918	−	0.891552i	$-0.350383\pi$
$719$	17464.0	0.905836	0.452918	+	0.891552i	$0.350383\pi$
$720$	5526.44	0.286053
$721$	10846.3	0.560246
$722$	−2809.66	−0.144826
$723$	9182.99	0.472364
$724$	−8561.78	−0.439497
$725$	−5063.60	−0.259389
$726$	4968.64	0.253999
$727$	−775.478	−0.0395610	−0.0197805	−	0.999804i	$-0.506297\pi$
$727$	−775.478	−0.0395610	−0.0197805	+	0.999804i	$0.506297\pi$
$728$	1141.47	0.0581120
$729$	729.000	0.0370370
$730$	16487.9	0.835952
$731$	7018.35	0.355107
$732$	918.631	0.0463847
$733$	−12461.3	−0.627923	−0.313962	−	0.949436i	$-0.601656\pi$
$733$	−12461.3	−0.627923	−0.313962	+	0.949436i	$0.601656\pi$
$734$	32379.5	1.62827
$735$	−912.065	−0.0457715
$736$	−2774.39	−0.138948
$737$	−14833.4	−0.741379
$738$	−20645.5	−1.02977
$739$	−32879.2	−1.63665	−0.818324	−	0.574758i	$-0.805096\pi$
$739$	−32879.2	−1.63665	−0.818324	+	0.574758i	$0.805096\pi$
$740$	7944.62	0.394662
$741$	891.783	0.0442112
$742$	−20104.2	−0.994674
$743$	19733.3	0.974351	0.487176	−	0.873304i	$-0.338027\pi$
$743$	19733.3	0.974351	0.487176	+	0.873304i	$0.338027\pi$
$744$	−2181.52	−0.107498
$745$	−15039.6	−0.739610
$746$	4003.78	0.196500
$747$	3180.25	0.155769
$748$	−52006.5	−2.54217
$749$	7079.98	0.345390
$750$	−19832.4	−0.965570
$751$	−2741.37	−0.133201	−0.0666006	−	0.997780i	$-0.521215\pi$
$751$	−2741.37	−0.133201	−0.0666006	+	0.997780i	$0.521215\pi$
$752$	35393.5	1.71631
$753$	−5372.24	−0.259994
$754$	−1017.85	−0.0491616
$755$	3155.90	0.152126
$756$	3284.42	0.158007
$757$	−7417.14	−0.356117	−0.178059	−	0.984020i	$-0.556982\pi$
$757$	−7417.14	−0.356117	−0.178059	+	0.984020i	$0.556982\pi$
$758$	45827.5	2.19595
$759$	−2811.08	−0.134434
$760$	25243.4	1.20483
$761$	11276.5	0.537150	0.268575	−	0.963259i	$-0.413447\pi$
$761$	11276.5	0.537150	0.268575	+	0.963259i	$0.413447\pi$
$762$	24102.1	1.14584
$763$	−5582.81	−0.264890
$764$	−90378.1	−4.27980
$765$	−4101.93	−0.193863
$766$	8031.94	0.378859
$767$	1452.41	0.0683747
$768$	24180.5	1.13612
$769$	18702.2	0.877006	0.438503	−	0.898730i	$-0.355509\pi$
$769$	18702.2	0.877006	0.438503	+	0.898730i	$0.355509\pi$
$770$	8913.70	0.417178
$771$	8951.57	0.418136
$772$	−8227.83	−0.383583
$773$	18295.1	0.851264	0.425632	−	0.904896i	$-0.360052\pi$
$773$	18295.1	0.851264	0.425632	+	0.904896i	$0.360052\pi$
$774$	4331.80	0.201167
$775$	1331.50	0.0617147
$776$	8650.81	0.400188
$777$	1547.35	0.0714423
$778$	66694.2	3.07340
$779$	−39215.8	−1.80366
$780$	−1116.50	−0.0512527
$781$	−19757.2	−0.905209
$782$	8511.23	0.389209
$783$	−1580.47	−0.0721348
$784$	4849.43	0.220911
$785$	−15038.5	−0.683753
$786$	−15193.1	−0.689467
$787$	31074.0	1.40746	0.703728	−	0.710470i	$-0.251518\pi$
$787$	31074.0	1.40746	0.703728	+	0.710470i	$0.251518\pi$
$788$	3882.44	0.175516
$789$	6019.52	0.271610
$790$	15407.7	0.693898
$791$	5765.36	0.259156
$792$	−17322.0	−0.777162
$793$	−60.8211	−0.00272361
$794$	31913.5	1.42641
$795$	10611.8	0.473413
$796$	43282.6	1.92728
$797$	−19333.9	−0.859273	−0.429637	−	0.903002i	$-0.641358\pi$
$797$	−19333.9	−0.859273	−0.429637	+	0.903002i	$0.641358\pi$
$798$	9110.73	0.404156
$799$	−26270.3	−1.16318
$800$	10434.6	0.461148
$801$	−7643.30	−0.337157
$802$	−1944.18	−0.0856001
$803$	−21490.8	−0.944452
$804$	18981.7	0.832630
$805$	−998.928	−0.0437361
$806$	267.648	0.0116967
$807$	−9830.43	−0.428807
$808$	−75520.0	−3.28810
$809$	−29043.7	−1.26220	−0.631101	−	0.775701i	$-0.717397\pi$
$809$	−29043.7	−1.26220	−0.631101	+	0.775701i	$0.717397\pi$
$810$	−2531.75	−0.109823
$811$	18023.9	0.780399	0.390199	−	0.920730i	$-0.372406\pi$
$811$	18023.9	0.780399	0.390199	+	0.920730i	$0.372406\pi$
$812$	−7120.63	−0.307740
$813$	22254.1	0.960007
$814$	−15122.3	−0.651152
$815$	−12419.6	−0.533792
$816$	21809.9	0.935659
$817$	8228.19	0.352348
$818$	35770.4	1.52895
$819$	−217.456	−0.00927783
$820$	49097.6	2.09093
$821$	8904.24	0.378514	0.189257	−	0.981928i	$-0.439392\pi$
$821$	8904.24	0.378514	0.189257	+	0.981928i	$0.439392\pi$
$822$	−23174.1	−0.983319
$823$	−42723.1	−1.80952	−0.904759	−	0.425923i	$-0.859949\pi$
$823$	−42723.1	−1.80952	−0.904759	+	0.425923i	$0.859949\pi$
$824$	73200.9	3.09475
$825$	10572.6	0.446169
$826$	14838.2	0.625046
$827$	2551.42	0.107281	0.0536407	−	0.998560i	$-0.482917\pi$
$827$	2551.42	0.107281	0.0536407	+	0.998560i	$0.482917\pi$
$828$	3597.22	0.150981
$829$	6976.51	0.292285	0.146142	−	0.989264i	$-0.453314\pi$
$829$	6976.51	0.292285	0.146142	+	0.989264i	$0.453314\pi$
$830$	−11044.7	−0.461889
$831$	−880.050	−0.0367372
$832$	−635.366	−0.0264752
$833$	−3599.42	−0.149715
$834$	−1120.84	−0.0465365
$835$	11608.5	0.481114
$836$	−60971.5	−2.52242
$837$	415.594	0.0171625
$838$	−5688.07	−0.234476
$839$	32543.8	1.33914	0.669569	−	0.742750i	$-0.266479\pi$
$839$	32543.8	1.33914	0.669569	+	0.742750i	$0.266479\pi$
$840$	−6155.46	−0.252838
$841$	−20962.5	−0.859508
$842$	29153.7	1.19323
$843$	15489.9	0.632861
$844$	19275.8	0.786139
$845$	−13557.4	−0.551940
$846$	−16214.3	−0.658937
$847$	−2301.37	−0.0933601
$848$	−56422.9	−2.28487
$849$	−1526.10	−0.0616909
$850$	−32011.1	−1.29173
$851$	1694.71	0.0682655
$852$	25282.5	1.01662
$853$	−29709.2	−1.19252	−0.596262	−	0.802790i	$-0.703348\pi$
$853$	−29709.2	−1.19252	−0.596262	+	0.802790i	$0.703348\pi$
$854$	−621.367	−0.0248978
$855$	−4809.03	−0.192357
$856$	47782.3	1.90790
$857$	6312.05	0.251593	0.125797	−	0.992056i	$-0.459851\pi$
$857$	6312.05	0.251593	0.125797	+	0.992056i	$0.459851\pi$
$858$	2125.22	0.0845616
$859$	−1901.41	−0.0755241	−0.0377620	−	0.999287i	$-0.512023\pi$
$859$	−1901.41	−0.0755241	−0.0377620	+	0.999287i	$0.512023\pi$
$860$	−10301.6	−0.408466
$861$	9562.56	0.378503
$862$	47573.1	1.87975
$863$	24074.2	0.949589	0.474794	−	0.880097i	$-0.342522\pi$
$863$	24074.2	0.949589	0.474794	+	0.880097i	$0.342522\pi$
$864$	3256.90	0.128243
$865$	−17641.2	−0.693433
$866$	−76914.0	−3.01806
$867$	−1449.07	−0.0567623
$868$	1872.41	0.0732185
$869$	−20082.8	−0.783960
$870$	5488.84	0.213896
$871$	−1256.75	−0.0488903
$872$	−37678.0	−1.46323
$873$	−1648.03	−0.0638917
$874$	9978.42	0.386184
$875$	9185.97	0.354905
$876$	27501.0	1.06070
$877$	35040.8	1.34919	0.674597	−	0.738186i	$-0.264317\pi$
$877$	35040.8	1.34919	0.674597	+	0.738186i	$0.264317\pi$
$878$	−49749.7	−1.91227
$879$	15732.9	0.603708
$880$	25016.5	0.958303
$881$	39924.3	1.52677	0.763386	−	0.645943i	$-0.223536\pi$
$881$	39924.3	1.52677	0.763386	+	0.645943i	$0.223536\pi$
$882$	−2221.60	−0.0848132
$883$	6116.36	0.233105	0.116553	−	0.993185i	$-0.462816\pi$
$883$	6116.36	0.233105	0.116553	+	0.993185i	$0.462816\pi$
$884$	−4406.22	−0.167644
$885$	−7832.24	−0.297489
$886$	−87715.0	−3.32601
$887$	−18088.9	−0.684741	−0.342371	−	0.939565i	$-0.611230\pi$
$887$	−18088.9	−0.684741	−0.342371	+	0.939565i	$0.611230\pi$
$888$	10442.9	0.394641
$889$	−11163.6	−0.421164
$890$	26544.5	0.999746
$891$	3299.96	0.124077
$892$	17148.9	0.643709
$893$	−30798.9	−1.15414
$894$	−36633.4	−1.37048
$895$	−882.722	−0.0329678
$896$	−13246.1	−0.493887
$897$	−238.167	−0.00886527
$898$	−18832.3	−0.699824
$899$	−901.008	−0.0334264
$900$	−13529.3	−0.501085
$901$	41879.1	1.54850
$902$	−93455.8	−3.44982
$903$	−2006.40	−0.0739411
$904$	38910.0	1.43156
$905$	−3056.86	−0.112280
$906$	7687.11	0.281884
$907$	24484.9	0.896371	0.448185	−	0.893941i	$-0.352070\pi$
$907$	24484.9	0.896371	0.448185	+	0.893941i	$0.352070\pi$
$908$	74441.3	2.72073
$909$	14387.0	0.524960
$910$	755.207	0.0275108
$911$	26792.0	0.974377	0.487188	−	0.873297i	$-0.338023\pi$
$911$	26792.0	0.974377	0.487188	+	0.873297i	$0.338023\pi$
$912$	25569.5	0.928389
$913$	14396.0	0.521838
$914$	61815.3	2.23706
$915$	327.984	0.0118501
$916$	49676.4	1.79187
$917$	7037.14	0.253421
$918$	−9991.45	−0.359223
$919$	51216.3	1.83838	0.919189	−	0.393817i	$-0.128846\pi$
$919$	51216.3	1.83838	0.919189	+	0.393817i	$0.128846\pi$
$920$	−6741.70	−0.241595
$921$	−7104.82	−0.254193
$922$	63386.6	2.26413
$923$	−1673.91	−0.0596940
$924$	14867.6	0.529337
$925$	−6373.87	−0.226564
$926$	26591.9	0.943699
$927$	−13945.2	−0.494090
$928$	−7060.96	−0.249771
$929$	5793.17	0.204594	0.102297	−	0.994754i	$-0.467381\pi$
$929$	5793.17	0.204594	0.102297	+	0.994754i	$0.467381\pi$
$930$	−1443.32	−0.0508907
$931$	−4219.90	−0.148552
$932$	−87153.7	−3.06310
$933$	18411.5	0.646051
$934$	32780.9	1.14842
$935$	−18568.2	−0.649459
$936$	−1467.60	−0.0512500
$937$	20183.5	0.703700	0.351850	−	0.936056i	$-0.385553\pi$
$937$	20183.5	0.703700	0.351850	+	0.936056i	$0.385553\pi$
$938$	−12839.4	−0.446930
$939$	11006.0	0.382499
$940$	38559.8	1.33796
$941$	1992.80	0.0690366	0.0345183	−	0.999404i	$-0.489010\pi$
$941$	1992.80	0.0690366	0.0345183	+	0.999404i	$0.489010\pi$
$942$	−36630.6	−1.26697
$943$	10473.3	0.361672
$944$	41643.9	1.43580
$945$	1172.65	0.0403666
$946$	19608.7	0.673927
$947$	35770.7	1.22745	0.613723	−	0.789521i	$-0.289671\pi$
$947$	35770.7	1.22745	0.613723	+	0.789521i	$0.289671\pi$
$948$	25699.1	0.880453
$949$	−1820.80	−0.0622819
$950$	−37529.2	−1.28169
$951$	3849.75	0.131269
$952$	−24292.3	−0.827013
$953$	−22813.3	−0.775442	−0.387721	−	0.921777i	$-0.626738\pi$
$953$	−22813.3	−0.775442	−0.387721	+	0.921777i	$0.626738\pi$
$954$	25848.3	0.877220
$955$	−32268.2	−1.09338
$956$	118972.	4.02493
$957$	−7154.32	−0.241658
$958$	74015.4	2.49617
$959$	10733.7	0.361429
$960$	3426.27	0.115190
$961$	−29554.1	−0.992047
$962$	−1281.23	−0.0429403
$963$	−9102.83	−0.304605
$964$	−53193.6	−1.77723
$965$	−2937.63	−0.0979954
$966$	−2433.18	−0.0810418
$967$	−8348.65	−0.277637	−0.138818	−	0.990318i	$-0.544330\pi$
$967$	−8348.65	−0.277637	−0.138818	+	0.990318i	$0.544330\pi$
$968$	−15531.8	−0.515713
$969$	−18978.6	−0.629186
$970$	5723.47	0.189453
$971$	−55136.1	−1.82225	−0.911123	−	0.412134i	$-0.864784\pi$
$971$	−55136.1	−1.82225	−0.911123	+	0.412134i	$0.864784\pi$
$972$	−4222.83	−0.139349
$973$	519.149	0.0171050
$974$	−77010.8	−2.53346
$975$	895.754	0.0294226
$976$	−1743.88	−0.0571930
$977$	49923.6	1.63480	0.817400	−	0.576071i	$-0.195415\pi$
$977$	49923.6	1.63480	0.817400	+	0.576071i	$0.195415\pi$
$978$	−30251.7	−0.989102
$979$	−34598.9	−1.12951
$980$	5283.26	0.172212
$981$	7177.89	0.233611
$982$	101943.	3.31278
$983$	40795.0	1.32366	0.661831	−	0.749653i	$-0.269780\pi$
$983$	40795.0	1.32366	0.661831	+	0.749653i	$0.269780\pi$
$984$	64537.1	2.09082
$985$	1386.17	0.0448396
$986$	21661.5	0.699637
$987$	7510.14	0.242199
$988$	−5165.77	−0.166341
$989$	−2197.49	−0.0706531
$990$	−11460.5	−0.367917
$991$	35682.8	1.14379	0.571897	−	0.820325i	$-0.306208\pi$
$991$	35682.8	1.14379	0.571897	+	0.820325i	$0.306208\pi$
$992$	1856.72	0.0594262
$993$	−6149.82	−0.196534
$994$	−17101.2	−0.545692
$995$	15453.4	0.492368
$996$	−18422.0	−0.586067
$997$	−8748.48	−0.277901	−0.138950	−	0.990299i	$-0.544373\pi$
$997$	−8748.48	−0.277901	−0.138950	+	0.990299i	$0.544373\pi$
$998$	34116.4	1.08210
$999$	−1989.44	−0.0630062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.d.1.1	✓	7
3.2	odd	2		1449.4.a.g.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.d.1.1	✓	7	1.1	even	1	trivial
1449.4.a.g.1.7		7	3.2	odd	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q-5.03765 q^{2} -3.00000 q^{3} +17.3779 q^{4} +6.20452 q^{5} +15.1129 q^{6} -7.00000 q^{7} -47.2425 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.03765 q^{2} -3.00000 q^{3} +17.3779 q^{4} +6.20452 q^{5} +15.1129 q^{6} -7.00000 q^{7} -47.2425 q^{8} +9.00000 q^{9} -31.2562 q^{10} +40.7402 q^{11} -52.1337 q^{12} +3.45169 q^{13} +35.2635 q^{14} -18.6136 q^{15} +98.9680 q^{16} -73.4576 q^{17} -45.3388 q^{18} -86.1205 q^{19} +107.822 q^{20} +21.0000 q^{21} -205.235 q^{22} +23.0000 q^{23} +141.728 q^{24} -86.5039 q^{25} -17.3884 q^{26} -27.0000 q^{27} -121.645 q^{28} +58.5361 q^{29} +93.7686 q^{30} -15.3924 q^{31} -120.626 q^{32} -122.221 q^{33} +370.054 q^{34} -43.4317 q^{35} +156.401 q^{36} +73.6831 q^{37} +433.844 q^{38} -10.3551 q^{39} -293.117 q^{40} +455.360 q^{41} -105.791 q^{42} -95.5428 q^{43} +707.980 q^{44} +55.8407 q^{45} -115.866 q^{46} +357.626 q^{47} -296.904 q^{48} +49.0000 q^{49} +435.776 q^{50} +220.373 q^{51} +59.9831 q^{52} -570.113 q^{53} +136.016 q^{54} +252.774 q^{55} +330.698 q^{56} +258.361 q^{57} -294.884 q^{58} +420.781 q^{59} -323.465 q^{60} -17.6207 q^{61} +77.5413 q^{62} -63.0000 q^{63} -184.074 q^{64} +21.4161 q^{65} +615.705 q^{66} -364.098 q^{67} -1276.54 q^{68} -69.0000 q^{69} +218.793 q^{70} -484.955 q^{71} -425.183 q^{72} -527.508 q^{73} -371.189 q^{74} +259.512 q^{75} -1496.59 q^{76} -285.182 q^{77} +52.1652 q^{78} -492.947 q^{79} +614.049 q^{80} +81.0000 q^{81} -2293.94 q^{82} +353.361 q^{83} +364.936 q^{84} -455.770 q^{85} +481.311 q^{86} -175.608 q^{87} -1924.67 q^{88} -849.256 q^{89} -281.306 q^{90} -24.1618 q^{91} +399.692 q^{92} +46.1771 q^{93} -1801.59 q^{94} -534.336 q^{95} +361.877 q^{96} -183.115 q^{97} -246.845 q^{98} +366.662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9} + 11 q^{10} - 6 q^{11} - 66 q^{12} + 17 q^{13} + 14 q^{14} + 33 q^{15} + 106 q^{16} - 78 q^{17} - 18 q^{18} + 44 q^{19} + 44 q^{20} + 147 q^{21} - 477 q^{22} + 161 q^{23} - 45 q^{24} - 80 q^{25} + 288 q^{26} - 189 q^{27} - 154 q^{28} - 185 q^{29} - 33 q^{30} + 238 q^{31} - 512 q^{32} + 18 q^{33} - 27 q^{34} + 77 q^{35} + 198 q^{36} - 511 q^{37} - 413 q^{38} - 51 q^{39} - 686 q^{40} + 867 q^{41} - 42 q^{42} - 1003 q^{43} - 629 q^{44} - 99 q^{45} - 46 q^{46} + 149 q^{47} - 318 q^{48} + 343 q^{49} - 986 q^{50} + 234 q^{51} - 439 q^{52} - 1244 q^{53} + 54 q^{54} - 270 q^{55} - 105 q^{56} - 132 q^{57} - 2376 q^{58} + 1048 q^{59} - 132 q^{60} - 1380 q^{61} - 809 q^{62} - 441 q^{63} - 1835 q^{64} - 223 q^{65} + 1431 q^{66} - 500 q^{67} - 1387 q^{68} - 483 q^{69} - 77 q^{70} - 14 q^{71} + 135 q^{72} - 530 q^{73} - 738 q^{74} + 240 q^{75} - 1785 q^{76} + 42 q^{77} - 864 q^{78} - 2978 q^{79} + 1043 q^{80} + 567 q^{81} - 1986 q^{82} - 524 q^{83} + 462 q^{84} - 2674 q^{85} + 194 q^{86} + 555 q^{87} - 4504 q^{88} - 648 q^{89} + 99 q^{90} - 119 q^{91} + 506 q^{92} - 714 q^{93} - 801 q^{94} + 154 q^{95} + 1536 q^{96} - 1999 q^{97} - 98 q^{98} - 54 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9 + 11 * q^10 - 6 * q^11 - 66 * q^12 + 17 * q^13 + 14 * q^14 + 33 * q^15 + 106 * q^16 - 78 * q^17 - 18 * q^18 + 44 * q^19 + 44 * q^20 + 147 * q^21 - 477 * q^22 + 161 * q^23 - 45 * q^24 - 80 * q^25 + 288 * q^26 - 189 * q^27 - 154 * q^28 - 185 * q^29 - 33 * q^30 + 238 * q^31 - 512 * q^32 + 18 * q^33 - 27 * q^34 + 77 * q^35 + 198 * q^36 - 511 * q^37 - 413 * q^38 - 51 * q^39 - 686 * q^40 + 867 * q^41 - 42 * q^42 - 1003 * q^43 - 629 * q^44 - 99 * q^45 - 46 * q^46 + 149 * q^47 - 318 * q^48 + 343 * q^49 - 986 * q^50 + 234 * q^51 - 439 * q^52 - 1244 * q^53 + 54 * q^54 - 270 * q^55 - 105 * q^56 - 132 * q^57 - 2376 * q^58 + 1048 * q^59 - 132 * q^60 - 1380 * q^61 - 809 * q^62 - 441 * q^63 - 1835 * q^64 - 223 * q^65 + 1431 * q^66 - 500 * q^67 - 1387 * q^68 - 483 * q^69 - 77 * q^70 - 14 * q^71 + 135 * q^72 - 530 * q^73 - 738 * q^74 + 240 * q^75 - 1785 * q^76 + 42 * q^77 - 864 * q^78 - 2978 * q^79 + 1043 * q^80 + 567 * q^81 - 1986 * q^82 - 524 * q^83 + 462 * q^84 - 2674 * q^85 + 194 * q^86 + 555 * q^87 - 4504 * q^88 - 648 * q^89 + 99 * q^90 - 119 * q^91 + 506 * q^92 - 714 * q^93 - 801 * q^94 + 154 * q^95 + 1536 * q^96 - 1999 * q^97 - 98 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more