LMFDB - Embedded newform 4235.2.a.bo.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-2.35862$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.35862 q^{2} +3.12567 q^{3} +3.56309 q^{4} +1.00000 q^{5} +7.37227 q^{6} -1.00000 q^{7} +3.68672 q^{8} +6.76983 q^{9} +O(q^{10})$	\(q+2.35862 q^{2} +3.12567 q^{3} +3.56309 q^{4} +1.00000 q^{5} +7.37227 q^{6} -1.00000 q^{7} +3.68672 q^{8} +6.76983 q^{9} +2.35862 q^{10} +11.1370 q^{12} +0.303615 q^{13} -2.35862 q^{14} +3.12567 q^{15} +1.56941 q^{16} -1.03365 q^{17} +15.9675 q^{18} -5.12290 q^{19} +3.56309 q^{20} -3.12567 q^{21} +8.52137 q^{23} +11.5235 q^{24} +1.00000 q^{25} +0.716112 q^{26} +11.7833 q^{27} -3.56309 q^{28} +4.31946 q^{29} +7.37227 q^{30} -2.64939 q^{31} -3.67181 q^{32} -2.43800 q^{34} -1.00000 q^{35} +24.1215 q^{36} -2.27545 q^{37} -12.0830 q^{38} +0.949001 q^{39} +3.68672 q^{40} -9.65845 q^{41} -7.37227 q^{42} +1.37993 q^{43} +6.76983 q^{45} +20.0987 q^{46} +1.07602 q^{47} +4.90546 q^{48} +1.00000 q^{49} +2.35862 q^{50} -3.23087 q^{51} +1.08181 q^{52} -9.21775 q^{53} +27.7923 q^{54} -3.68672 q^{56} -16.0125 q^{57} +10.1880 q^{58} -8.81202 q^{59} +11.1370 q^{60} -10.5463 q^{61} -6.24889 q^{62} -6.76983 q^{63} -11.7992 q^{64} +0.303615 q^{65} +13.6999 q^{67} -3.68300 q^{68} +26.6350 q^{69} -2.35862 q^{70} -7.14373 q^{71} +24.9585 q^{72} +16.1243 q^{73} -5.36691 q^{74} +3.12567 q^{75} -18.2533 q^{76} +2.23833 q^{78} -0.573402 q^{79} +1.56941 q^{80} +16.5212 q^{81} -22.7806 q^{82} +11.2134 q^{83} -11.1370 q^{84} -1.03365 q^{85} +3.25473 q^{86} +13.5012 q^{87} -14.3947 q^{89} +15.9675 q^{90} -0.303615 q^{91} +30.3624 q^{92} -8.28111 q^{93} +2.53791 q^{94} -5.12290 q^{95} -11.4769 q^{96} -3.94258 q^{97} +2.35862 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9} - 2 q^{10} + 15 q^{12} - 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} + 5 q^{17} - 2 q^{18} - 15 q^{19} + 24 q^{20} - 5 q^{21} + 4 q^{23} - 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} - 24 q^{28} + 6 q^{29} + q^{30} + 22 q^{31} + 6 q^{32} + 44 q^{34} - 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} + 38 q^{39} - 6 q^{40} - 7 q^{41} - q^{42} - 10 q^{43} + 37 q^{45} + 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} - 2 q^{50} + 11 q^{51} - 18 q^{52} + 23 q^{53} - 13 q^{54} + 6 q^{56} + 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} - 17 q^{61} - 57 q^{62} - 37 q^{63} + 64 q^{64} - 8 q^{65} + 29 q^{67} + 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} + 77 q^{72} - 3 q^{73} + 48 q^{74} + 5 q^{75} - 47 q^{76} + 10 q^{78} + 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} - 9 q^{83} - 15 q^{84} + 5 q^{85} + 25 q^{86} - 23 q^{87} + 59 q^{89} - 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} + 19 q^{94} - 15 q^{95} - 14 q^{96} + 30 q^{97} - 2 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9 - 2 * q^10 + 15 * q^12 - 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 + 5 * q^17 - 2 * q^18 - 15 * q^19 + 24 * q^20 - 5 * q^21 + 4 * q^23 - 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 - 24 * q^28 + 6 * q^29 + q^30 + 22 * q^31 + 6 * q^32 + 44 * q^34 - 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 + 38 * q^39 - 6 * q^40 - 7 * q^41 - q^42 - 10 * q^43 + 37 * q^45 + 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 - 2 * q^50 + 11 * q^51 - 18 * q^52 + 23 * q^53 - 13 * q^54 + 6 * q^56 + 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 - 17 * q^61 - 57 * q^62 - 37 * q^63 + 64 * q^64 - 8 * q^65 + 29 * q^67 + 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 + 77 * q^72 - 3 * q^73 + 48 * q^74 + 5 * q^75 - 47 * q^76 + 10 * q^78 + 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 - 9 * q^83 - 15 * q^84 + 5 * q^85 + 25 * q^86 - 23 * q^87 + 59 * q^89 - 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 + 19 * q^94 - 15 * q^95 - 14 * q^96 + 30 * q^97 - 2 * 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 $

$2$	2.35862	1.66780	0.833898	−	0.551919i	$-0.186104\pi$
$2$	2.35862	1.66780	0.833898	+	0.551919i	$0.186104\pi$
$3$	3.12567	1.80461	0.902304	−	0.431100i	$-0.141874\pi$
$3$	3.12567	1.80461	0.902304	+	0.431100i	$0.141874\pi$
$4$	3.56309	1.78154
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.37227	3.00972
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.68672	1.30345
$9$	6.76983	2.25661
$10$	2.35862	0.745861
$11$	0	0
$11$	0	0
$12$	11.1370	3.21499
$13$	0.303615	0.0842076	0.0421038	−	0.999113i	$-0.486594\pi$
$13$	0.303615	0.0842076	0.0421038	+	0.999113i	$0.486594\pi$
$14$	−2.35862	−0.630368
$15$	3.12567	0.807045
$16$	1.56941	0.392352
$17$	−1.03365	−0.250698	−0.125349	−	0.992113i	$-0.540005\pi$
$17$	−1.03365	−0.250698	−0.125349	+	0.992113i	$0.540005\pi$
$18$	15.9675	3.76357
$19$	−5.12290	−1.17527	−0.587636	−	0.809125i	$-0.699941\pi$
$19$	−5.12290	−1.17527	−0.587636	+	0.809125i	$0.699941\pi$
$20$	3.56309	0.796730
$21$	−3.12567	−0.682078
$22$	0	0
$23$	8.52137	1.77683	0.888414	−	0.459043i	$-0.151808\pi$
$23$	8.52137	1.77683	0.888414	+	0.459043i	$0.151808\pi$
$24$	11.5235	2.35222
$25$	1.00000	0.200000
$26$	0.716112	0.140441
$27$	11.7833	2.26769
$28$	−3.56309	−0.673360
$29$	4.31946	0.802103	0.401052	−	0.916055i	$-0.368645\pi$
$29$	4.31946	0.802103	0.401052	+	0.916055i	$0.368645\pi$
$30$	7.37227	1.34599
$31$	−2.64939	−0.475844	−0.237922	−	0.971284i	$-0.576466\pi$
$31$	−2.64939	−0.475844	−0.237922	+	0.971284i	$0.576466\pi$
$32$	−3.67181	−0.649091
$33$	0	0
$34$	−2.43800	−0.418113
$35$	−1.00000	−0.169031
$36$	24.1215	4.02025
$37$	−2.27545	−0.374081	−0.187041	−	0.982352i	$-0.559890\pi$
$37$	−2.27545	−0.374081	−0.187041	+	0.982352i	$0.559890\pi$
$38$	−12.0830	−1.96011
$39$	0.949001	0.151962
$40$	3.68672	0.582922
$41$	−9.65845	−1.50840	−0.754198	−	0.656647i	$-0.771974\pi$
$41$	−9.65845	−1.50840	−0.754198	+	0.656647i	$0.771974\pi$
$42$	−7.37227	−1.13757
$43$	1.37993	0.210438	0.105219	−	0.994449i	$-0.466446\pi$
$43$	1.37993	0.210438	0.105219	+	0.994449i	$0.466446\pi$
$44$	0	0
$45$	6.76983	1.00919
$46$	20.0987	2.96339
$47$	1.07602	0.156953	0.0784765	−	0.996916i	$-0.474994\pi$
$47$	1.07602	0.156953	0.0784765	+	0.996916i	$0.474994\pi$
$48$	4.90546	0.708042
$49$	1.00000	0.142857
$50$	2.35862	0.333559
$51$	−3.23087	−0.452412
$52$	1.08181	0.150019
$53$	−9.21775	−1.26616	−0.633078	−	0.774088i	$-0.718209\pi$
$53$	−9.21775	−1.26616	−0.633078	+	0.774088i	$0.718209\pi$
$54$	27.7923	3.78205
$55$	0	0
$56$	−3.68672	−0.492659
$57$	−16.0125	−2.12091
$58$	10.1880	1.33774
$59$	−8.81202	−1.14723	−0.573614	−	0.819126i	$-0.694459\pi$
$59$	−8.81202	−1.14723	−0.573614	+	0.819126i	$0.694459\pi$
$60$	11.1370	1.43779
$61$	−10.5463	−1.35031	−0.675155	−	0.737675i	$-0.735923\pi$
$61$	−10.5463	−1.35031	−0.675155	+	0.737675i	$0.735923\pi$
$62$	−6.24889	−0.793610
$63$	−6.76983	−0.852919
$64$	−11.7992	−1.47490
$65$	0.303615	0.0376588
$66$	0	0
$67$	13.6999	1.67371	0.836854	−	0.547427i	$-0.184392\pi$
$67$	13.6999	1.67371	0.836854	+	0.547427i	$0.184392\pi$
$68$	−3.68300	−0.446629
$69$	26.6350	3.20648
$70$	−2.35862	−0.281909
$71$	−7.14373	−0.847805	−0.423903	−	0.905708i	$-0.639340\pi$
$71$	−7.14373	−0.847805	−0.423903	+	0.905708i	$0.639340\pi$
$72$	24.9585	2.94139
$73$	16.1243	1.88721	0.943605	−	0.331075i	$-0.107411\pi$
$73$	16.1243	1.88721	0.943605	+	0.331075i	$0.107411\pi$
$74$	−5.36691	−0.623891
$75$	3.12567	0.360922
$76$	−18.2533	−2.09380
$77$	0	0
$78$	2.23833	0.253441
$79$	−0.573402	−0.0645127	−0.0322564	−	0.999480i	$-0.510269\pi$
$79$	−0.573402	−0.0645127	−0.0322564	+	0.999480i	$0.510269\pi$
$80$	1.56941	0.175465
$81$	16.5212	1.83568
$82$	−22.7806	−2.51570
$83$	11.2134	1.23083	0.615413	−	0.788205i	$-0.288989\pi$
$83$	11.2134	1.23083	0.615413	+	0.788205i	$0.288989\pi$
$84$	−11.1370	−1.21515
$85$	−1.03365	−0.112116
$86$	3.25473	0.350967
$87$	13.5012	1.44748
$88$	0	0
$89$	−14.3947	−1.52583	−0.762917	−	0.646496i	$-0.776234\pi$
$89$	−14.3947	−1.52583	−0.762917	+	0.646496i	$0.776234\pi$
$90$	15.9675	1.68312
$91$	−0.303615	−0.0318275
$92$	30.3624	3.16550
$93$	−8.28111	−0.858712
$94$	2.53791	0.261766
$95$	−5.12290	−0.525598
$96$	−11.4769	−1.17135
$97$	−3.94258	−0.400308	−0.200154	−	0.979764i	$-0.564144\pi$
$97$	−3.94258	−0.400308	−0.200154	+	0.979764i	$0.564144\pi$
$98$	2.35862	0.238257
$99$	0	0
$100$	3.56309	0.356309
$101$	−10.1902	−1.01397	−0.506983	−	0.861956i	$-0.669239\pi$
$101$	−10.1902	−1.01397	−0.506983	+	0.861956i	$0.669239\pi$
$102$	−7.62038	−0.754530
$103$	18.4463	1.81757	0.908783	−	0.417269i	$-0.137013\pi$
$103$	18.4463	1.81757	0.908783	+	0.417269i	$0.137013\pi$
$104$	1.11934	0.109761
$105$	−3.12567	−0.305034
$106$	−21.7412	−2.11169
$107$	17.9196	1.73235	0.866176	−	0.499738i	$-0.166570\pi$
$107$	17.9196	1.73235	0.866176	+	0.499738i	$0.166570\pi$
$108$	41.9848	4.03999
$109$	1.01822	0.0975276	0.0487638	−	0.998810i	$-0.484472\pi$
$109$	1.01822	0.0975276	0.0487638	+	0.998810i	$0.484472\pi$
$110$	0	0
$111$	−7.11230	−0.675070
$112$	−1.56941	−0.148295
$113$	−1.79756	−0.169100	−0.0845501	−	0.996419i	$-0.526945\pi$
$113$	−1.79756	−0.169100	−0.0845501	+	0.996419i	$0.526945\pi$
$114$	−37.7674	−3.53724
$115$	8.52137	0.794622
$116$	15.3906	1.42898
$117$	2.05542	0.190024
$118$	−20.7842	−1.91334
$119$	1.03365	0.0947549
$120$	11.5235	1.05195
$121$	0	0
$122$	−24.8746	−2.25204
$123$	−30.1892	−2.72206
$124$	−9.43999	−0.847736
$125$	1.00000	0.0894427
$126$	−15.9675	−1.42249
$127$	−11.2516	−0.998417	−0.499209	−	0.866482i	$-0.666376\pi$
$127$	−11.2516	−0.998417	−0.499209	+	0.866482i	$0.666376\pi$
$128$	−20.4863	−1.81075
$129$	4.31321	0.379757
$130$	0.716112	0.0628072
$131$	3.75923	0.328445	0.164223	−	0.986423i	$-0.447488\pi$
$131$	3.75923	0.328445	0.164223	+	0.986423i	$0.447488\pi$
$132$	0	0
$133$	5.12290	0.444211
$134$	32.3128	2.79140
$135$	11.7833	1.01414
$136$	−3.81080	−0.326773
$137$	15.0871	1.28898	0.644490	−	0.764613i	$-0.277070\pi$
$137$	15.0871	1.28898	0.644490	+	0.764613i	$0.277070\pi$
$138$	62.8219	5.34775
$139$	−13.3265	−1.13034	−0.565171	−	0.824974i	$-0.691190\pi$
$139$	−13.3265	−1.13034	−0.565171	+	0.824974i	$0.691190\pi$
$140$	−3.56309	−0.301136
$141$	3.36327	0.283239
$142$	−16.8493	−1.41397
$143$	0	0
$144$	10.6246	0.885386
$145$	4.31946	0.358712
$146$	38.0311	3.14748
$147$	3.12567	0.257801
$148$	−8.10761	−0.666441
$149$	2.12769	0.174307	0.0871534	−	0.996195i	$-0.472223\pi$
$149$	2.12769	0.174307	0.0871534	+	0.996195i	$0.472223\pi$
$150$	7.37227	0.601944
$151$	−15.7506	−1.28177	−0.640883	−	0.767639i	$-0.721432\pi$
$151$	−15.7506	−1.28177	−0.640883	+	0.767639i	$0.721432\pi$
$152$	−18.8867	−1.53191
$153$	−6.99767	−0.565728
$154$	0	0
$155$	−2.64939	−0.212804
$156$	3.38137	0.270726
$157$	−8.52511	−0.680378	−0.340189	−	0.940357i	$-0.610491\pi$
$157$	−8.52511	−0.680378	−0.340189	+	0.940357i	$0.610491\pi$
$158$	−1.35244	−0.107594
$159$	−28.8117	−2.28491
$160$	−3.67181	−0.290282
$161$	−8.52137	−0.671578
$162$	38.9671	3.06155
$163$	−12.1811	−0.954097	−0.477049	−	0.878877i	$-0.658293\pi$
$163$	−12.1811	−0.954097	−0.477049	+	0.878877i	$0.658293\pi$
$164$	−34.4139	−2.68727
$165$	0	0
$166$	26.4480	2.05277
$167$	8.44915	0.653815	0.326908	−	0.945056i	$-0.393993\pi$
$167$	8.44915	0.653815	0.326908	+	0.945056i	$0.393993\pi$
$168$	−11.5235	−0.889057
$169$	−12.9078	−0.992909
$170$	−2.43800	−0.186986
$171$	−34.6812	−2.65213
$172$	4.91681	0.374904
$173$	8.85874	0.673517	0.336759	−	0.941591i	$-0.390669\pi$
$173$	8.85874	0.673517	0.336759	+	0.941591i	$0.390669\pi$
$174$	31.8442	2.41411
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−27.5435	−2.07030
$178$	−33.9516	−2.54478
$179$	8.08279	0.604136	0.302068	−	0.953286i	$-0.402323\pi$
$179$	8.08279	0.604136	0.302068	+	0.953286i	$0.402323\pi$
$180$	24.1215	1.79791
$181$	−1.35065	−0.100393	−0.0501966	−	0.998739i	$-0.515985\pi$
$181$	−1.35065	−0.100393	−0.0501966	+	0.998739i	$0.515985\pi$
$182$	−0.716112	−0.0530818
$183$	−32.9642	−2.43678
$184$	31.4159	2.31601
$185$	−2.27545	−0.167294
$186$	−19.5320	−1.43216
$187$	0	0
$188$	3.83394	0.279618
$189$	−11.7833	−0.857107
$190$	−12.0830	−0.876590
$191$	12.2917	0.889396	0.444698	−	0.895680i	$-0.353311\pi$
$191$	12.2917	0.889396	0.444698	+	0.895680i	$0.353311\pi$
$192$	−36.8805	−2.66162
$193$	−18.5658	−1.33640	−0.668198	−	0.743983i	$-0.732934\pi$
$193$	−18.5658	−1.33640	−0.668198	+	0.743983i	$0.732934\pi$
$194$	−9.29904	−0.667633
$195$	0.949001	0.0679594
$196$	3.56309	0.254506
$197$	−12.8716	−0.917062	−0.458531	−	0.888678i	$-0.651624\pi$
$197$	−12.8716	−0.917062	−0.458531	+	0.888678i	$0.651624\pi$
$198$	0	0
$199$	9.93245	0.704093	0.352046	−	0.935983i	$-0.385486\pi$
$199$	9.93245	0.704093	0.352046	+	0.935983i	$0.385486\pi$
$200$	3.68672	0.260691
$201$	42.8214	3.02039
$202$	−24.0349	−1.69109
$203$	−4.31946	−0.303167
$204$	−11.5119	−0.805991
$205$	−9.65845	−0.674575
$206$	43.5078	3.03133
$207$	57.6882	4.00961
$208$	0.476496	0.0330390
$209$	0	0
$210$	−7.37227	−0.508735
$211$	−17.1478	−1.18050	−0.590252	−	0.807219i	$-0.700972\pi$
$211$	−17.1478	−1.18050	−0.590252	+	0.807219i	$0.700972\pi$
$212$	−32.8436	−2.25571
$213$	−22.3290	−1.52996
$214$	42.2655	2.88921
$215$	1.37993	0.0941105
$216$	43.4417	2.95583
$217$	2.64939	0.179852
$218$	2.40159	0.162656
$219$	50.3994	3.40567
$220$	0	0
$221$	−0.313833	−0.0211107
$222$	−16.7752	−1.12588
$223$	15.3328	1.02676	0.513380	−	0.858161i	$-0.328393\pi$
$223$	15.3328	1.02676	0.513380	+	0.858161i	$0.328393\pi$
$224$	3.67181	0.245333
$225$	6.76983	0.451322
$226$	−4.23976	−0.282025
$227$	−2.01861	−0.133980	−0.0669899	−	0.997754i	$-0.521340\pi$
$227$	−2.01861	−0.133980	−0.0669899	+	0.997754i	$0.521340\pi$
$228$	−57.0539	−3.77849
$229$	−0.312306	−0.0206377	−0.0103189	−	0.999947i	$-0.503285\pi$
$229$	−0.312306	−0.0206377	−0.0103189	+	0.999947i	$0.503285\pi$
$230$	20.0987	1.32527
$231$	0	0
$232$	15.9247	1.04550
$233$	17.3822	1.13874	0.569371	−	0.822080i	$-0.307187\pi$
$233$	17.3822	1.13874	0.569371	+	0.822080i	$0.307187\pi$
$234$	4.84796	0.316921
$235$	1.07602	0.0701915
$236$	−31.3980	−2.04383
$237$	−1.79227	−0.116420
$238$	2.43800	0.158032
$239$	22.6580	1.46562	0.732812	−	0.680431i	$-0.238207\pi$
$239$	22.6580	1.46562	0.732812	+	0.680431i	$0.238207\pi$
$240$	4.90546	0.316646
$241$	6.28549	0.404884	0.202442	−	0.979294i	$-0.435112\pi$
$241$	6.28549	0.404884	0.202442	+	0.979294i	$0.435112\pi$
$242$	0	0
$243$	16.2899	1.04500
$244$	−37.5772	−2.40564
$245$	1.00000	0.0638877
$246$	−71.2047	−4.53985
$247$	−1.55539	−0.0989669
$248$	−9.76755	−0.620240
$249$	35.0493	2.22116
$250$	2.35862	0.149172
$251$	−10.6760	−0.673861	−0.336931	−	0.941529i	$-0.609389\pi$
$251$	−10.6760	−0.673861	−0.336931	+	0.941529i	$0.609389\pi$
$252$	−24.1215	−1.51951
$253$	0	0
$254$	−26.5382	−1.66516
$255$	−3.23087	−0.202325
$256$	−24.7208	−1.54505
$257$	−17.6734	−1.10244	−0.551220	−	0.834360i	$-0.685837\pi$
$257$	−17.6734	−1.10244	−0.551220	+	0.834360i	$0.685837\pi$
$258$	10.1732	0.633358
$259$	2.27545	0.141389
$260$	1.08181	0.0670908
$261$	29.2420	1.81004
$262$	8.86659	0.547780
$263$	12.2684	0.756499	0.378250	−	0.925704i	$-0.376526\pi$
$263$	12.2684	0.756499	0.378250	+	0.925704i	$0.376526\pi$
$264$	0	0
$265$	−9.21775	−0.566242
$266$	12.0830	0.740854
$267$	−44.9931	−2.75353
$268$	48.8139	2.98178
$269$	21.5065	1.31128	0.655639	−	0.755075i	$-0.272399\pi$
$269$	21.5065	1.31128	0.655639	+	0.755075i	$0.272399\pi$
$270$	27.7923	1.69138
$271$	−4.38256	−0.266221	−0.133111	−	0.991101i	$-0.542497\pi$
$271$	−4.38256	−0.266221	−0.133111	+	0.991101i	$0.542497\pi$
$272$	−1.62223	−0.0983619
$273$	−0.949001	−0.0574362
$274$	35.5848	2.14976
$275$	0	0
$276$	94.9028	5.71248
$277$	11.4465	0.687756	0.343878	−	0.939014i	$-0.388259\pi$
$277$	11.4465	0.687756	0.343878	+	0.939014i	$0.388259\pi$
$278$	−31.4322	−1.88518
$279$	−17.9359	−1.07379
$280$	−3.68672	−0.220324
$281$	11.4639	0.683879	0.341940	−	0.939722i	$-0.388916\pi$
$281$	11.4639	0.683879	0.341940	+	0.939722i	$0.388916\pi$
$282$	7.93268	0.472384
$283$	−12.6804	−0.753772	−0.376886	−	0.926260i	$-0.623005\pi$
$283$	−12.6804	−0.753772	−0.376886	+	0.926260i	$0.623005\pi$
$284$	−25.4537	−1.51040
$285$	−16.0125	−0.948498
$286$	0	0
$287$	9.65845	0.570120
$288$	−24.8576	−1.46475
$289$	−15.9316	−0.937151
$290$	10.1880	0.598258
$291$	−12.3232	−0.722400
$292$	57.4523	3.36214
$293$	8.25289	0.482139	0.241070	−	0.970508i	$-0.422502\pi$
$293$	8.25289	0.482139	0.241070	+	0.970508i	$0.422502\pi$
$294$	7.37227	0.429960
$295$	−8.81202	−0.513056
$296$	−8.38894	−0.487597
$297$	0	0
$298$	5.01840	0.290708
$299$	2.58721	0.149622
$300$	11.1370	0.642997
$301$	−1.37993	−0.0795379
$302$	−37.1497	−2.13772
$303$	−31.8513	−1.82981
$304$	−8.03991	−0.461121
$305$	−10.5463	−0.603877
$306$	−16.5048	−0.943519
$307$	1.76640	0.100814	0.0504070	−	0.998729i	$-0.483948\pi$
$307$	1.76640	0.100814	0.0504070	+	0.998729i	$0.483948\pi$
$308$	0	0
$309$	57.6570	3.27999
$310$	−6.24889	−0.354913
$311$	−4.51683	−0.256126	−0.128063	−	0.991766i	$-0.540876\pi$
$311$	−4.51683	−0.256126	−0.128063	+	0.991766i	$0.540876\pi$
$312$	3.49871	0.198075
$313$	−6.29171	−0.355628	−0.177814	−	0.984064i	$-0.556903\pi$
$313$	−6.29171	−0.355628	−0.177814	+	0.984064i	$0.556903\pi$
$314$	−20.1075	−1.13473
$315$	−6.76983	−0.381437
$316$	−2.04308	−0.114932
$317$	3.69981	0.207802	0.103901	−	0.994588i	$-0.466867\pi$
$317$	3.69981	0.207802	0.103901	+	0.994588i	$0.466867\pi$
$318$	−67.9558	−3.81077
$319$	0	0
$320$	−11.7992	−0.659597
$321$	56.0108	3.12622
$322$	−20.0987	−1.12005
$323$	5.29530	0.294639
$324$	58.8663	3.27035
$325$	0.303615	0.0168415
$326$	−28.7306	−1.59124
$327$	3.18262	0.175999
$328$	−35.6080	−1.96612
$329$	−1.07602	−0.0593227
$330$	0	0
$331$	−20.6957	−1.13754	−0.568769	−	0.822497i	$-0.692580\pi$
$331$	−20.6957	−1.13754	−0.568769	+	0.822497i	$0.692580\pi$
$332$	39.9541	2.19277
$333$	−15.4044	−0.844156
$334$	19.9283	1.09043
$335$	13.6999	0.748505
$336$	−4.90546	−0.267615
$337$	13.8060	0.752061	0.376030	−	0.926607i	$-0.377289\pi$
$337$	13.8060	0.752061	0.376030	+	0.926607i	$0.377289\pi$
$338$	−30.4446	−1.65597
$339$	−5.61858	−0.305160
$340$	−3.68300	−0.199739
$341$	0	0
$342$	−81.7996	−4.42322
$343$	−1.00000	−0.0539949
$344$	5.08743	0.274296
$345$	26.6350	1.43398
$346$	20.8944	1.12329
$347$	2.92092	0.156803	0.0784016	−	0.996922i	$-0.475018\pi$
$347$	2.92092	0.156803	0.0784016	+	0.996922i	$0.475018\pi$
$348$	48.1060	2.57875
$349$	14.2115	0.760727	0.380363	−	0.924837i	$-0.375799\pi$
$349$	14.2115	0.760727	0.380363	+	0.924837i	$0.375799\pi$
$350$	−2.35862	−0.126074
$351$	3.57758	0.190957
$352$	0	0
$353$	−24.1977	−1.28792	−0.643958	−	0.765061i	$-0.722709\pi$
$353$	−24.1977	−1.28792	−0.643958	+	0.765061i	$0.722709\pi$
$354$	−64.9646	−3.45283
$355$	−7.14373	−0.379150
$356$	−51.2895	−2.71834
$357$	3.23087	0.170996
$358$	19.0642	1.00758
$359$	−17.3847	−0.917532	−0.458766	−	0.888557i	$-0.651708\pi$
$359$	−17.3847	−0.917532	−0.458766	+	0.888557i	$0.651708\pi$
$360$	24.9585	1.31543
$361$	7.24405	0.381266
$362$	−3.18568	−0.167435
$363$	0	0
$364$	−1.08181	−0.0567020
$365$	16.1243	0.843986
$366$	−77.7500	−4.06406
$367$	−8.65437	−0.451755	−0.225877	−	0.974156i	$-0.572525\pi$
$367$	−8.65437	−0.451755	−0.225877	+	0.974156i	$0.572525\pi$
$368$	13.3735	0.697142
$369$	−65.3861	−3.40386
$370$	−5.36691	−0.279012
$371$	9.21775	0.478562
$372$	−29.5063	−1.52983
$373$	11.7827	0.610087	0.305044	−	0.952338i	$-0.401329\pi$
$373$	11.7827	0.610087	0.305044	+	0.952338i	$0.401329\pi$
$374$	0	0
$375$	3.12567	0.161409
$376$	3.96697	0.204581
$377$	1.31145	0.0675432
$378$	−27.7923	−1.42948
$379$	3.97512	0.204188	0.102094	−	0.994775i	$-0.467446\pi$
$379$	3.97512	0.204188	0.102094	+	0.994775i	$0.467446\pi$
$380$	−18.2533	−0.936375
$381$	−35.1688	−1.80175
$382$	28.9914	1.48333
$383$	−18.7450	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$383$	−18.7450	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$384$	−64.0333	−3.26769
$385$	0	0
$386$	−43.7897	−2.22884
$387$	9.34191	0.474876
$388$	−14.0477	−0.713166
$389$	2.31336	0.117292	0.0586459	−	0.998279i	$-0.481322\pi$
$389$	2.31336	0.117292	0.0586459	+	0.998279i	$0.481322\pi$
$390$	2.23833	0.113342
$391$	−8.80815	−0.445447
$392$	3.68672	0.186208
$393$	11.7501	0.592715
$394$	−30.3592	−1.52947
$395$	−0.573402	−0.0288510
$396$	0	0
$397$	22.3968	1.12406	0.562032	−	0.827116i	$-0.310020\pi$
$397$	22.3968	1.12406	0.562032	+	0.827116i	$0.310020\pi$
$398$	23.4269	1.17428
$399$	16.0125	0.801628
$400$	1.56941	0.0784704
$401$	24.2091	1.20894	0.604472	−	0.796626i	$-0.293384\pi$
$401$	24.2091	1.20894	0.604472	+	0.796626i	$0.293384\pi$
$402$	100.999	5.03739
$403$	−0.804393	−0.0400697
$404$	−36.3086	−1.80642
$405$	16.5212	0.820943
$406$	−10.1880	−0.505620
$407$	0	0
$408$	−11.9113	−0.589698
$409$	−17.4252	−0.861622	−0.430811	−	0.902442i	$-0.641772\pi$
$409$	−17.4252	−0.861622	−0.430811	+	0.902442i	$0.641772\pi$
$410$	−22.7806	−1.12505
$411$	47.1574	2.32610
$412$	65.7257	3.23807
$413$	8.81202	0.433611
$414$	136.065	6.68721
$415$	11.2134	0.550442
$416$	−1.11482	−0.0546584
$417$	−41.6544	−2.03982
$418$	0	0
$419$	18.0980	0.884145	0.442073	−	0.896979i	$-0.354243\pi$
$419$	18.0980	0.884145	0.442073	+	0.896979i	$0.354243\pi$
$420$	−11.1370	−0.543432
$421$	19.4325	0.947082	0.473541	−	0.880772i	$-0.342976\pi$
$421$	19.4325	0.947082	0.473541	+	0.880772i	$0.342976\pi$
$422$	−40.4452	−1.96884
$423$	7.28445	0.354182
$424$	−33.9833	−1.65037
$425$	−1.03365	−0.0501396
$426$	−52.6656	−2.55165
$427$	10.5463	0.510370
$428$	63.8491	3.08626
$429$	0	0
$430$	3.25473	0.156957
$431$	7.90822	0.380926	0.190463	−	0.981694i	$-0.439001\pi$
$431$	7.90822	0.380926	0.190463	+	0.981694i	$0.439001\pi$
$432$	18.4928	0.889734
$433$	18.2620	0.877618	0.438809	−	0.898580i	$-0.355400\pi$
$433$	18.2620	0.877618	0.438809	+	0.898580i	$0.355400\pi$
$434$	6.24889	0.299956
$435$	13.5012	0.647334
$436$	3.62800	0.173750
$437$	−43.6541	−2.08826
$438$	118.873	5.67997
$439$	−24.6331	−1.17567	−0.587837	−	0.808979i	$-0.700020\pi$
$439$	−24.6331	−1.17567	−0.587837	+	0.808979i	$0.700020\pi$
$440$	0	0
$441$	6.76983	0.322373
$442$	−0.740212	−0.0352083
$443$	−16.6461	−0.790881	−0.395441	−	0.918492i	$-0.629408\pi$
$443$	−16.6461	−0.790881	−0.395441	+	0.918492i	$0.629408\pi$
$444$	−25.3417	−1.20267
$445$	−14.3947	−0.682374
$446$	36.1642	1.71243
$447$	6.65045	0.314555
$448$	11.7992	0.557461
$449$	−8.05832	−0.380296	−0.190148	−	0.981755i	$-0.560897\pi$
$449$	−8.05832	−0.380296	−0.190148	+	0.981755i	$0.560897\pi$
$450$	15.9675	0.752713
$451$	0	0
$452$	−6.40486	−0.301259
$453$	−49.2312	−2.31309
$454$	−4.76113	−0.223451
$455$	−0.303615	−0.0142337
$456$	−59.0337	−2.76450
$457$	22.9712	1.07455	0.537273	−	0.843408i	$-0.319454\pi$
$457$	22.9712	1.07455	0.537273	+	0.843408i	$0.319454\pi$
$458$	−0.736610	−0.0344195
$459$	−12.1798	−0.568506
$460$	30.3624	1.41565
$461$	−15.0286	−0.699951	−0.349975	−	0.936759i	$-0.613810\pi$
$461$	−15.0286	−0.699951	−0.349975	+	0.936759i	$0.613810\pi$
$462$	0	0
$463$	−22.9066	−1.06456	−0.532279	−	0.846569i	$-0.678664\pi$
$463$	−22.9066	−1.06456	−0.532279	+	0.846569i	$0.678664\pi$
$464$	6.77900	0.314707
$465$	−8.28111	−0.384027
$466$	40.9979	1.89919
$467$	1.64223	0.0759932	0.0379966	−	0.999278i	$-0.487902\pi$
$467$	1.64223	0.0759932	0.0379966	+	0.999278i	$0.487902\pi$
$468$	7.32365	0.338536
$469$	−13.6999	−0.632602
$470$	2.53791	0.117065
$471$	−26.6467	−1.22781
$472$	−32.4875	−1.49536
$473$	0	0
$474$	−4.22728	−0.194165
$475$	−5.12290	−0.235055
$476$	3.68300	0.168810
$477$	−62.4026	−2.85722
$478$	53.4416	2.44436
$479$	6.50665	0.297296	0.148648	−	0.988890i	$-0.452508\pi$
$479$	6.50665	0.297296	0.148648	+	0.988890i	$0.452508\pi$
$480$	−11.4769	−0.523846
$481$	−0.690859	−0.0315005
$482$	14.8251	0.675264
$483$	−26.6350	−1.21194
$484$	0	0
$485$	−3.94258	−0.179023
$486$	38.4217	1.74284
$487$	31.1060	1.40955	0.704774	−	0.709432i	$-0.251048\pi$
$487$	31.1060	1.40955	0.704774	+	0.709432i	$0.251048\pi$
$488$	−38.8812	−1.76007
$489$	−38.0741	−1.72177
$490$	2.35862	0.106552
$491$	−19.2332	−0.867984	−0.433992	−	0.900917i	$-0.642895\pi$
$491$	−19.2332	−0.867984	−0.433992	+	0.900917i	$0.642895\pi$
$492$	−107.567	−4.84947
$493$	−4.46483	−0.201086
$494$	−3.66857	−0.165057
$495$	0	0
$496$	−4.15797	−0.186698
$497$	7.14373	0.320440
$498$	82.6679	3.70444
$499$	12.4567	0.557636	0.278818	−	0.960344i	$-0.410057\pi$
$499$	12.4567	0.557636	0.278818	+	0.960344i	$0.410057\pi$
$500$	3.56309	0.159346
$501$	26.4093	1.17988
$502$	−25.1806	−1.12386
$503$	0.952980	0.0424913	0.0212456	−	0.999774i	$-0.493237\pi$
$503$	0.952980	0.0424913	0.0212456	+	0.999774i	$0.493237\pi$
$504$	−24.9585	−1.11174
$505$	−10.1902	−0.453459
$506$	0	0
$507$	−40.3456	−1.79181
$508$	−40.0904	−1.77872
$509$	30.0463	1.33178	0.665890	−	0.746050i	$-0.268052\pi$
$509$	30.0463	1.33178	0.665890	+	0.746050i	$0.268052\pi$
$510$	−7.62038	−0.337436
$511$	−16.1243	−0.713298
$512$	−17.3345	−0.766085
$513$	−60.3645	−2.66516
$514$	−41.6849	−1.83864
$515$	18.4463	0.812840
$516$	15.3684	0.676554
$517$	0	0
$518$	5.36691	0.235809
$519$	27.6895	1.21544
$520$	1.11934	0.0490865
$521$	35.3266	1.54769	0.773844	−	0.633376i	$-0.218331\pi$
$521$	35.3266	1.54769	0.773844	+	0.633376i	$0.218331\pi$
$522$	68.9708	3.01877
$523$	−3.82511	−0.167261	−0.0836303	−	0.996497i	$-0.526651\pi$
$523$	−3.82511	−0.167261	−0.0836303	+	0.996497i	$0.526651\pi$
$524$	13.3945	0.585140
$525$	−3.12567	−0.136416
$526$	28.9364	1.26169
$527$	2.73855	0.119293
$528$	0	0
$529$	49.6137	2.15712
$530$	−21.7412	−0.944376
$531$	−59.6559	−2.58885
$532$	18.2533	0.791382
$533$	−2.93245	−0.127018
$534$	−106.122	−4.59233
$535$	17.9196	0.774732
$536$	50.5077	2.18160
$537$	25.2642	1.09023
$538$	50.7258	2.18694
$539$	0	0
$540$	41.9848	1.80674
$541$	1.78673	0.0768175	0.0384087	−	0.999262i	$-0.487771\pi$
$541$	1.78673	0.0768175	0.0384087	+	0.999262i	$0.487771\pi$
$542$	−10.3368	−0.444003
$543$	−4.22170	−0.181170
$544$	3.79538	0.162726
$545$	1.01822	0.0436157
$546$	−2.23833	−0.0957918
$547$	33.1680	1.41816	0.709081	−	0.705127i	$-0.249110\pi$
$547$	33.1680	1.41816	0.709081	+	0.705127i	$0.249110\pi$
$548$	53.7567	2.29637
$549$	−71.3965	−3.04713
$550$	0	0
$551$	−22.1281	−0.942690
$552$	98.1960	4.17950
$553$	0.573402	0.0243835
$554$	26.9980	1.14704
$555$	−7.11230	−0.301900
$556$	−47.4836	−2.01375
$557$	−2.03928	−0.0864070	−0.0432035	−	0.999066i	$-0.513756\pi$
$557$	−2.03928	−0.0864070	−0.0432035	+	0.999066i	$0.513756\pi$
$558$	−42.3040	−1.79087
$559$	0.418968	0.0177204
$560$	−1.56941	−0.0663196
$561$	0	0
$562$	27.0390	1.14057
$563$	−18.5776	−0.782953	−0.391476	−	0.920188i	$-0.628036\pi$
$563$	−18.5776	−0.782953	−0.391476	+	0.920188i	$0.628036\pi$
$564$	11.9836	0.504602
$565$	−1.79756	−0.0756239
$566$	−29.9083	−1.25714
$567$	−16.5212	−0.693823
$568$	−26.3370	−1.10507
$569$	16.4095	0.687920	0.343960	−	0.938984i	$-0.388232\pi$
$569$	16.4095	0.687920	0.343960	+	0.938984i	$0.388232\pi$
$570$	−37.7674	−1.58190
$571$	18.5329	0.775578	0.387789	−	0.921748i	$-0.373239\pi$
$571$	18.5329	0.775578	0.387789	+	0.921748i	$0.373239\pi$
$572$	0	0
$573$	38.4198	1.60501
$574$	22.7806	0.950844
$575$	8.52137	0.355366
$576$	−79.8788	−3.32828
$577$	−23.7459	−0.988554	−0.494277	−	0.869304i	$-0.664567\pi$
$577$	−23.7459	−0.988554	−0.494277	+	0.869304i	$0.664567\pi$
$578$	−37.5765	−1.56298
$579$	−58.0307	−2.41167
$580$	15.3906	0.639060
$581$	−11.2134	−0.465208
$582$	−29.0658	−1.20482
$583$	0	0
$584$	59.4459	2.45989
$585$	2.05542	0.0849813
$586$	19.4654	0.804110
$587$	21.0434	0.868554	0.434277	−	0.900779i	$-0.357004\pi$
$587$	21.0434	0.868554	0.434277	+	0.900779i	$0.357004\pi$
$588$	11.1370	0.459284
$589$	13.5725	0.559246
$590$	−20.7842	−0.855672
$591$	−40.2324	−1.65494
$592$	−3.57110	−0.146771
$593$	46.2299	1.89843	0.949217	−	0.314621i	$-0.101878\pi$
$593$	46.2299	1.89843	0.949217	+	0.314621i	$0.101878\pi$
$594$	0	0
$595$	1.03365	0.0423757
$596$	7.58112	0.310535
$597$	31.0456	1.27061
$598$	6.10225	0.249540
$599$	16.7230	0.683282	0.341641	−	0.939831i	$-0.389017\pi$
$599$	16.7230	0.683282	0.341641	+	0.939831i	$0.389017\pi$
$600$	11.5235	0.470445
$601$	−10.4475	−0.426161	−0.213080	−	0.977035i	$-0.568350\pi$
$601$	−10.4475	−0.426161	−0.213080	+	0.977035i	$0.568350\pi$
$602$	−3.25473	−0.132653
$603$	92.7460	3.77691
$604$	−56.1207	−2.28352
$605$	0	0
$606$	−75.1251	−3.05175
$607$	−19.9139	−0.808279	−0.404139	−	0.914697i	$-0.632429\pi$
$607$	−19.9139	−0.808279	−0.404139	+	0.914697i	$0.632429\pi$
$608$	18.8103	0.762859
$609$	−13.5012	−0.547097
$610$	−24.8746	−1.00714
$611$	0.326694	0.0132166
$612$	−24.9333	−1.00787
$613$	17.4111	0.703229	0.351615	−	0.936145i	$-0.385633\pi$
$613$	17.4111	0.703229	0.351615	+	0.936145i	$0.385633\pi$
$614$	4.16627	0.168137
$615$	−30.1892	−1.21734
$616$	0	0
$617$	−13.6972	−0.551427	−0.275713	−	0.961240i	$-0.588914\pi$
$617$	−13.6972	−0.551427	−0.275713	+	0.961240i	$0.588914\pi$
$618$	135.991	5.47036
$619$	−31.9100	−1.28257	−0.641286	−	0.767302i	$-0.721599\pi$
$619$	−31.9100	−1.28257	−0.641286	+	0.767302i	$0.721599\pi$
$620$	−9.43999	−0.379119
$621$	100.410	4.02930
$622$	−10.6535	−0.427165
$623$	14.3947	0.576711
$624$	1.48937	0.0596225
$625$	1.00000	0.0400000
$626$	−14.8397	−0.593115
$627$	0	0
$628$	−30.3757	−1.21212
$629$	2.35203	0.0937814
$630$	−15.9675	−0.636159
$631$	22.1491	0.881742	0.440871	−	0.897570i	$-0.354670\pi$
$631$	22.1491	0.881742	0.440871	+	0.897570i	$0.354670\pi$
$632$	−2.11397	−0.0840894
$633$	−53.5985	−2.13035
$634$	8.72644	0.346571
$635$	−11.2516	−0.446506
$636$	−102.658	−4.07067
$637$	0.303615	0.0120297
$638$	0	0
$639$	−48.3619	−1.91317
$640$	−20.4863	−0.809790
$641$	47.0120	1.85686	0.928431	−	0.371506i	$-0.121158\pi$
$641$	47.0120	1.85686	0.928431	+	0.371506i	$0.121158\pi$
$642$	132.108	5.21389
$643$	−16.2825	−0.642117	−0.321059	−	0.947059i	$-0.604039\pi$
$643$	−16.2825	−0.642117	−0.321059	+	0.947059i	$0.604039\pi$
$644$	−30.3624	−1.19644
$645$	4.31321	0.169833
$646$	12.4896	0.491397
$647$	−40.8269	−1.60507	−0.802536	−	0.596604i	$-0.796516\pi$
$647$	−40.8269	−1.60507	−0.802536	+	0.596604i	$0.796516\pi$
$648$	60.9089	2.39273
$649$	0	0
$650$	0.716112	0.0280882
$651$	8.28111	0.324562
$652$	−43.4023	−1.69976
$653$	23.2768	0.910893	0.455447	−	0.890263i	$-0.349480\pi$
$653$	23.2768	0.910893	0.455447	+	0.890263i	$0.349480\pi$
$654$	7.50658	0.293531
$655$	3.75923	0.146885
$656$	−15.1580	−0.591822
$657$	109.159	4.25870
$658$	−2.53791	−0.0989381
$659$	8.17158	0.318320	0.159160	−	0.987253i	$-0.449121\pi$
$659$	8.17158	0.318320	0.159160	+	0.987253i	$0.449121\pi$
$660$	0	0
$661$	7.64860	0.297496	0.148748	−	0.988875i	$-0.452476\pi$
$661$	7.64860	0.297496	0.148748	+	0.988875i	$0.452476\pi$
$662$	−48.8133	−1.89718
$663$	−0.980939	−0.0380965
$664$	41.3405	1.60432
$665$	5.12290	0.198657
$666$	−36.3331	−1.40788
$667$	36.8077	1.42520
$668$	30.1051	1.16480
$669$	47.9253	1.85290
$670$	32.3128	1.24835
$671$	0	0
$672$	11.4769	0.442730
$673$	−14.2835	−0.550590	−0.275295	−	0.961360i	$-0.588776\pi$
$673$	−14.2835	−0.550590	−0.275295	+	0.961360i	$0.588776\pi$
$674$	32.5631	1.25428
$675$	11.7833	0.453538
$676$	−45.9917	−1.76891
$677$	28.7655	1.10555	0.552774	−	0.833331i	$-0.313569\pi$
$677$	28.7655	1.10555	0.552774	+	0.833331i	$0.313569\pi$
$678$	−13.2521	−0.508944
$679$	3.94258	0.151302
$680$	−3.81080	−0.146137
$681$	−6.30952	−0.241781
$682$	0	0
$683$	−22.0519	−0.843794	−0.421897	−	0.906644i	$-0.638636\pi$
$683$	−22.0519	−0.843794	−0.421897	+	0.906644i	$0.638636\pi$
$684$	−123.572	−4.72489
$685$	15.0871	0.576449
$686$	−2.35862	−0.0900525
$687$	−0.976166	−0.0372430
$688$	2.16568	0.0825656
$689$	−2.79865	−0.106620
$690$	62.8219	2.39159
$691$	8.92737	0.339613	0.169807	−	0.985477i	$-0.445686\pi$
$691$	8.92737	0.339613	0.169807	+	0.985477i	$0.445686\pi$
$692$	31.5644	1.19990
$693$	0	0
$694$	6.88934	0.261516
$695$	−13.3265	−0.505504
$696$	49.7753	1.88673
$697$	9.98350	0.378152
$698$	33.5196	1.26874
$699$	54.3309	2.05499
$700$	−3.56309	−0.134672
$701$	0.0337866	0.00127610	0.000638050	−	1.00000i	$-0.499797\pi$
$701$	0.0337866	0.00127610	0.000638050		1.00000i	$0.499797\pi$
$702$	8.43814	0.318477
$703$	11.6569	0.439647
$704$	0	0
$705$	3.36327	0.126668
$706$	−57.0733	−2.14798
$707$	10.1902	0.383243
$708$	−98.1398	−3.68832
$709$	−2.86944	−0.107764	−0.0538821	−	0.998547i	$-0.517160\pi$
$709$	−2.86944	−0.107764	−0.0538821	+	0.998547i	$0.517160\pi$
$710$	−16.8493	−0.632345
$711$	−3.88184	−0.145580
$712$	−53.0693	−1.98886
$713$	−22.5764	−0.845492
$714$	7.62038	0.285186
$715$	0	0
$716$	28.7997	1.07629
$717$	70.8215	2.64488
$718$	−41.0040	−1.53026
$719$	1.67521	0.0624749	0.0312375	−	0.999512i	$-0.490055\pi$
$719$	1.67521	0.0624749	0.0312375	+	0.999512i	$0.490055\pi$
$720$	10.6246	0.395957
$721$	−18.4463	−0.686975
$722$	17.0860	0.635874
$723$	19.6464	0.730657
$724$	−4.81249	−0.178855
$725$	4.31946	0.160421
$726$	0	0
$727$	0.612732	0.0227250	0.0113625	−	0.999935i	$-0.496383\pi$
$727$	0.612732	0.0227250	0.0113625	+	0.999935i	$0.496383\pi$
$728$	−1.11934	−0.0414857
$729$	1.35351	0.0501298
$730$	38.0311	1.40760
$731$	−1.42637	−0.0527563
$732$	−117.454	−4.34123
$733$	36.4732	1.34717	0.673584	−	0.739111i	$-0.264754\pi$
$733$	36.4732	1.34717	0.673584	+	0.739111i	$0.264754\pi$
$734$	−20.4124	−0.753434
$735$	3.12567	0.115292
$736$	−31.2889	−1.15332
$737$	0	0
$738$	−154.221	−5.67695
$739$	−44.7363	−1.64565	−0.822826	−	0.568293i	$-0.807604\pi$
$739$	−44.7363	−1.64565	−0.822826	+	0.568293i	$0.807604\pi$
$740$	−8.10761	−0.298042
$741$	−4.86163	−0.178597
$742$	21.7412	0.798143
$743$	−13.6791	−0.501838	−0.250919	−	0.968008i	$-0.580733\pi$
$743$	−13.6791	−0.501838	−0.250919	+	0.968008i	$0.580733\pi$
$744$	−30.5302	−1.11929
$745$	2.12769	0.0779523
$746$	27.7910	1.01750
$747$	75.9125	2.77749
$748$	0	0
$749$	−17.9196	−0.654768
$750$	7.37227	0.269197
$751$	−46.1908	−1.68553	−0.842764	−	0.538284i	$-0.819073\pi$
$751$	−46.1908	−1.68553	−0.842764	+	0.538284i	$0.819073\pi$
$752$	1.68871	0.0615808
$753$	−33.3696	−1.21606
$754$	3.09322	0.112648
$755$	−15.7506	−0.573223
$756$	−41.9848	−1.52697
$757$	51.4344	1.86942	0.934708	−	0.355417i	$-0.115661\pi$
$757$	51.4344	1.86942	0.934708	+	0.355417i	$0.115661\pi$
$758$	9.37579	0.340544
$759$	0	0
$760$	−18.8867	−0.685093
$761$	32.2686	1.16974	0.584869	−	0.811128i	$-0.301146\pi$
$761$	32.2686	1.16974	0.584869	+	0.811128i	$0.301146\pi$
$762$	−82.9498	−3.00495
$763$	−1.01822	−0.0368620
$764$	43.7964	1.58450
$765$	−6.99767	−0.253001
$766$	−44.2124	−1.59746
$767$	−2.67546	−0.0966053
$768$	−77.2692	−2.78821
$769$	20.8369	0.751399	0.375699	−	0.926742i	$-0.377403\pi$
$769$	20.8369	0.751399	0.375699	+	0.926742i	$0.377403\pi$
$770$	0	0
$771$	−55.2414	−1.98947
$772$	−66.1516	−2.38085
$773$	−39.5002	−1.42072	−0.710361	−	0.703838i	$-0.751468\pi$
$773$	−39.5002	−1.42072	−0.710361	+	0.703838i	$0.751468\pi$
$774$	22.0340	0.791996
$775$	−2.64939	−0.0951687
$776$	−14.5352	−0.521783
$777$	7.11230	0.255152
$778$	5.45633	0.195619
$779$	49.4792	1.77278
$780$	3.38137	0.121073
$781$	0	0
$782$	−20.7751	−0.742915
$783$	50.8974	1.81892
$784$	1.56941	0.0560503
$785$	−8.52511	−0.304274
$786$	27.7141	0.988528
$787$	−23.4515	−0.835954	−0.417977	−	0.908458i	$-0.637261\pi$
$787$	−23.4515	−0.835954	−0.417977	+	0.908458i	$0.637261\pi$
$788$	−45.8626	−1.63379
$789$	38.3469	1.36519
$790$	−1.35244	−0.0481175
$791$	1.79756	0.0639139
$792$	0	0
$793$	−3.20200	−0.113706
$794$	52.8255	1.87471
$795$	−28.8117	−1.02184
$796$	35.3902	1.25437
$797$	19.6169	0.694868	0.347434	−	0.937705i	$-0.387053\pi$
$797$	19.6169	0.694868	0.347434	+	0.937705i	$0.387053\pi$
$798$	37.7674	1.33695
$799$	−1.11223	−0.0393478
$800$	−3.67181	−0.129818
$801$	−97.4497	−3.44322
$802$	57.1001	2.01627
$803$	0	0
$804$	152.576	5.38095
$805$	−8.52137	−0.300339
$806$	−1.89726	−0.0668280
$807$	67.2224	2.36634
$808$	−37.5686	−1.32166
$809$	−1.20245	−0.0422757	−0.0211379	−	0.999777i	$-0.506729\pi$
$809$	−1.20245	−0.0422757	−0.0211379	+	0.999777i	$0.506729\pi$
$810$	38.9671	1.36916
$811$	−15.3789	−0.540025	−0.270012	−	0.962857i	$-0.587028\pi$
$811$	−15.3789	−0.540025	−0.270012	+	0.962857i	$0.587028\pi$
$812$	−15.3906	−0.540104
$813$	−13.6984	−0.480425
$814$	0	0
$815$	−12.1811	−0.426685
$816$	−5.07055	−0.177505
$817$	−7.06924	−0.247322
$818$	−41.0995	−1.43701
$819$	−2.05542	−0.0718223
$820$	−34.4139	−1.20178
$821$	−36.6757	−1.27999	−0.639996	−	0.768378i	$-0.721064\pi$
$821$	−36.6757	−1.27999	−0.639996	+	0.768378i	$0.721064\pi$
$822$	111.226	3.87947
$823$	−41.8158	−1.45761	−0.728804	−	0.684722i	$-0.759924\pi$
$823$	−41.8158	−1.45761	−0.728804	+	0.684722i	$0.759924\pi$
$824$	68.0063	2.36911
$825$	0	0
$826$	20.7842	0.723175
$827$	54.0547	1.87966	0.939832	−	0.341636i	$-0.110981\pi$
$827$	54.0547	1.87966	0.939832	+	0.341636i	$0.110981\pi$
$828$	205.548	7.14329
$829$	26.8067	0.931034	0.465517	−	0.885039i	$-0.345868\pi$
$829$	26.8067	0.931034	0.465517	+	0.885039i	$0.345868\pi$
$830$	26.4480	0.918025
$831$	35.7782	1.24113
$832$	−3.58242	−0.124198
$833$	−1.03365	−0.0358140
$834$	−98.2469	−3.40201
$835$	8.44915	0.292395
$836$	0	0
$837$	−31.2184	−1.07907
$838$	42.6863	1.47457
$839$	16.2884	0.562338	0.281169	−	0.959658i	$-0.409278\pi$
$839$	16.2884	0.562338	0.281169	+	0.959658i	$0.409278\pi$
$840$	−11.5235	−0.397598
$841$	−10.3423	−0.356630
$842$	45.8339	1.57954
$843$	35.8324	1.23413
$844$	−61.0991	−2.10312
$845$	−12.9078	−0.444042
$846$	17.1812	0.590703
$847$	0	0
$848$	−14.4664	−0.496779
$849$	−39.6348	−1.36026
$850$	−2.43800	−0.0836226
$851$	−19.3899	−0.664678
$852$	−79.5601	−2.72568
$853$	−30.6496	−1.04942	−0.524710	−	0.851281i	$-0.675826\pi$
$853$	−30.6496	−1.04942	−0.524710	+	0.851281i	$0.675826\pi$
$854$	24.8746	0.851192
$855$	−34.6812	−1.18607
$856$	66.0646	2.25804
$857$	42.2735	1.44404	0.722018	−	0.691875i	$-0.243215\pi$
$857$	42.2735	1.44404	0.722018	+	0.691875i	$0.243215\pi$
$858$	0	0
$859$	−13.3365	−0.455036	−0.227518	−	0.973774i	$-0.573061\pi$
$859$	−13.3365	−0.455036	−0.227518	+	0.973774i	$0.573061\pi$
$860$	4.91681	0.167662
$861$	30.1892	1.02884
$862$	18.6525	0.635306
$863$	−37.7743	−1.28585	−0.642926	−	0.765929i	$-0.722280\pi$
$863$	−37.7743	−1.28585	−0.642926	+	0.765929i	$0.722280\pi$
$864$	−43.2660	−1.47194
$865$	8.85874	0.301206
$866$	43.0732	1.46369
$867$	−49.7968	−1.69119
$868$	9.43999	0.320414
$869$	0	0
$870$	31.8442	1.07962
$871$	4.15949	0.140939
$872$	3.75389	0.127123
$873$	−26.6906	−0.903340
$874$	−102.963	−3.48279
$875$	−1.00000	−0.0338062
$876$	179.577	6.06735
$877$	8.69917	0.293750	0.146875	−	0.989155i	$-0.453078\pi$
$877$	8.69917	0.293750	0.146875	+	0.989155i	$0.453078\pi$
$878$	−58.1001	−1.96078
$879$	25.7958	0.870072
$880$	0	0
$881$	−3.89312	−0.131163	−0.0655814	−	0.997847i	$-0.520890\pi$
$881$	−3.89312	−0.131163	−0.0655814	+	0.997847i	$0.520890\pi$
$882$	15.9675	0.537652
$883$	45.1520	1.51948	0.759742	−	0.650225i	$-0.225325\pi$
$883$	45.1520	1.51948	0.759742	+	0.650225i	$0.225325\pi$
$884$	−1.11821	−0.0376096
$885$	−27.5435	−0.925864
$886$	−39.2619	−1.31903
$887$	15.6274	0.524718	0.262359	−	0.964970i	$-0.415500\pi$
$887$	15.6274	0.524718	0.262359	+	0.964970i	$0.415500\pi$
$888$	−26.2211	−0.879922
$889$	11.2516	0.377366
$890$	−33.9516	−1.13806
$891$	0	0
$892$	54.6321	1.82922
$893$	−5.51231	−0.184463
$894$	15.6859	0.524614
$895$	8.08279	0.270178
$896$	20.4863	0.684398
$897$	8.08679	0.270010
$898$	−19.0065	−0.634256
$899$	−11.4439	−0.381676
$900$	24.1215	0.804050
$901$	9.52797	0.317423
$902$	0	0
$903$	−4.31321	−0.143535
$904$	−6.62711	−0.220414
$905$	−1.35065	−0.0448972
$906$	−116.118	−3.85775
$907$	22.9194	0.761027	0.380513	−	0.924775i	$-0.375747\pi$
$907$	22.9194	0.761027	0.380513	+	0.924775i	$0.375747\pi$
$908$	−7.19248	−0.238691
$909$	−68.9861	−2.28813
$910$	−0.716112	−0.0237389
$911$	39.8282	1.31957	0.659784	−	0.751455i	$-0.270648\pi$
$911$	39.8282	1.31957	0.659784	+	0.751455i	$0.270648\pi$
$912$	−25.1301	−0.832142
$913$	0	0
$914$	54.1803	1.79212
$915$	−32.9642	−1.08976
$916$	−1.11277	−0.0367670
$917$	−3.75923	−0.124141
$918$	−28.7276	−0.948152
$919$	9.94569	0.328078	0.164039	−	0.986454i	$-0.447548\pi$
$919$	9.94569	0.328078	0.164039	+	0.986454i	$0.447548\pi$
$920$	31.4159	1.03575
$921$	5.52120	0.181930
$922$	−35.4467	−1.16737
$923$	−2.16894	−0.0713917
$924$	0	0
$925$	−2.27545	−0.0748162
$926$	−54.0278	−1.77547
$927$	124.878	4.10154
$928$	−15.8602	−0.520638
$929$	−52.2385	−1.71389	−0.856944	−	0.515409i	$-0.827640\pi$
$929$	−52.2385	−1.71389	−0.856944	+	0.515409i	$0.827640\pi$
$930$	−19.5320	−0.640479
$931$	−5.12290	−0.167896
$932$	61.9341	2.02872
$933$	−14.1181	−0.462207
$934$	3.87339	0.126741
$935$	0	0
$936$	7.57778	0.247687
$937$	−5.94143	−0.194098	−0.0970490	−	0.995280i	$-0.530940\pi$
$937$	−5.94143	−0.194098	−0.0970490	+	0.995280i	$0.530940\pi$
$938$	−32.3128	−1.05505
$939$	−19.6658	−0.641770
$940$	3.83394	0.125049
$941$	−15.7759	−0.514281	−0.257140	−	0.966374i	$-0.582780\pi$
$941$	−15.7759	−0.514281	−0.257140	+	0.966374i	$0.582780\pi$
$942$	−62.8494	−2.04774
$943$	−82.3032	−2.68016
$944$	−13.8297	−0.450117
$945$	−11.7833	−0.383310
$946$	0	0
$947$	45.1583	1.46745	0.733723	−	0.679448i	$-0.237781\pi$
$947$	45.1583	1.46745	0.733723	+	0.679448i	$0.237781\pi$
$948$	−6.38600	−0.207408
$949$	4.89558	0.158917
$950$	−12.0830	−0.392023
$951$	11.5644	0.375001
$952$	3.81080	0.123509
$953$	−38.0837	−1.23365	−0.616825	−	0.787100i	$-0.711582\pi$
$953$	−38.0837	−1.23365	−0.616825	+	0.787100i	$0.711582\pi$
$954$	−147.184	−4.76526
$955$	12.2917	0.397750
$956$	80.7324	2.61107
$957$	0	0
$958$	15.3467	0.495830
$959$	−15.0871	−0.487189
$960$	−36.8805	−1.19031
$961$	−23.9808	−0.773573
$962$	−1.62947	−0.0525364
$963$	121.313	3.90925
$964$	22.3957	0.721318
$965$	−18.5658	−0.597655
$966$	−62.8219	−2.02126
$967$	15.4735	0.497593	0.248796	−	0.968556i	$-0.419965\pi$
$967$	15.4735	0.497593	0.248796	+	0.968556i	$0.419965\pi$
$968$	0	0
$969$	16.5514	0.531707
$970$	−9.29904	−0.298574
$971$	0.473814	0.0152054	0.00760270	−	0.999971i	$-0.497580\pi$
$971$	0.473814	0.0152054	0.00760270	+	0.999971i	$0.497580\pi$
$972$	58.0424	1.86171
$973$	13.3265	0.427229
$974$	73.3673	2.35084
$975$	0.949001	0.0303924
$976$	−16.5514	−0.529797
$977$	−46.1591	−1.47676	−0.738380	−	0.674384i	$-0.764409\pi$
$977$	−46.1591	−1.47676	−0.738380	+	0.674384i	$0.764409\pi$
$978$	−89.8024	−2.87156
$979$	0	0
$980$	3.56309	0.113819
$981$	6.89317	0.220082
$982$	−45.3639	−1.44762
$983$	−51.4375	−1.64060	−0.820300	−	0.571934i	$-0.806194\pi$
$983$	−51.4375	−1.64060	−0.820300	+	0.571934i	$0.806194\pi$
$984$	−111.299	−3.54809
$985$	−12.8716	−0.410123
$986$	−10.5308	−0.335370
$987$	−3.36327	−0.107054
$988$	−5.54198	−0.176314
$989$	11.7589	0.373911
$990$	0	0
$991$	28.7757	0.914091	0.457046	−	0.889443i	$-0.348908\pi$
$991$	28.7757	0.914091	0.457046	+	0.889443i	$0.348908\pi$
$992$	9.72805	0.308866
$993$	−64.6880	−2.05281
$994$	16.8493	0.534429
$995$	9.93245	0.314880
$996$	124.884	3.95709
$997$	45.9499	1.45525	0.727625	−	0.685975i	$-0.240624\pi$
$997$	45.9499	1.45525	0.727625	+	0.685975i	$0.240624\pi$
$998$	29.3805	0.930024
$999$	−26.8122	−0.848300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bo.1.16		18
11.3	even	5		385.2.n.f.141.8	yes	36
11.4	even	5		385.2.n.f.71.8	✓	36
11.10	odd	2		4235.2.a.bp.1.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.71.8	✓	36	11.4	even	5
385.2.n.f.141.8	yes	36	11.3	even	5
4235.2.a.bo.1.16		18	1.1	even	1	trivial
4235.2.a.bp.1.3		18	11.10	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+2.35862 q^{2} +3.12567 q^{3} +3.56309 q^{4} +1.00000 q^{5} +7.37227 q^{6} -1.00000 q^{7} +3.68672 q^{8} +6.76983 q^{9} +O(q^{10})\)	\(q+2.35862 q^{2} +3.12567 q^{3} +3.56309 q^{4} +1.00000 q^{5} +7.37227 q^{6} -1.00000 q^{7} +3.68672 q^{8} +6.76983 q^{9} +2.35862 q^{10} +11.1370 q^{12} +0.303615 q^{13} -2.35862 q^{14} +3.12567 q^{15} +1.56941 q^{16} -1.03365 q^{17} +15.9675 q^{18} -5.12290 q^{19} +3.56309 q^{20} -3.12567 q^{21} +8.52137 q^{23} +11.5235 q^{24} +1.00000 q^{25} +0.716112 q^{26} +11.7833 q^{27} -3.56309 q^{28} +4.31946 q^{29} +7.37227 q^{30} -2.64939 q^{31} -3.67181 q^{32} -2.43800 q^{34} -1.00000 q^{35} +24.1215 q^{36} -2.27545 q^{37} -12.0830 q^{38} +0.949001 q^{39} +3.68672 q^{40} -9.65845 q^{41} -7.37227 q^{42} +1.37993 q^{43} +6.76983 q^{45} +20.0987 q^{46} +1.07602 q^{47} +4.90546 q^{48} +1.00000 q^{49} +2.35862 q^{50} -3.23087 q^{51} +1.08181 q^{52} -9.21775 q^{53} +27.7923 q^{54} -3.68672 q^{56} -16.0125 q^{57} +10.1880 q^{58} -8.81202 q^{59} +11.1370 q^{60} -10.5463 q^{61} -6.24889 q^{62} -6.76983 q^{63} -11.7992 q^{64} +0.303615 q^{65} +13.6999 q^{67} -3.68300 q^{68} +26.6350 q^{69} -2.35862 q^{70} -7.14373 q^{71} +24.9585 q^{72} +16.1243 q^{73} -5.36691 q^{74} +3.12567 q^{75} -18.2533 q^{76} +2.23833 q^{78} -0.573402 q^{79} +1.56941 q^{80} +16.5212 q^{81} -22.7806 q^{82} +11.2134 q^{83} -11.1370 q^{84} -1.03365 q^{85} +3.25473 q^{86} +13.5012 q^{87} -14.3947 q^{89} +15.9675 q^{90} -0.303615 q^{91} +30.3624 q^{92} -8.28111 q^{93} +2.53791 q^{94} -5.12290 q^{95} -11.4769 q^{96} -3.94258 q^{97} +2.35862 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9} - 2 q^{10} + 15 q^{12} - 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} + 5 q^{17} - 2 q^{18} - 15 q^{19} + 24 q^{20} - 5 q^{21} + 4 q^{23} - 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} - 24 q^{28} + 6 q^{29} + q^{30} + 22 q^{31} + 6 q^{32} + 44 q^{34} - 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} + 38 q^{39} - 6 q^{40} - 7 q^{41} - q^{42} - 10 q^{43} + 37 q^{45} + 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} - 2 q^{50} + 11 q^{51} - 18 q^{52} + 23 q^{53} - 13 q^{54} + 6 q^{56} + 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} - 17 q^{61} - 57 q^{62} - 37 q^{63} + 64 q^{64} - 8 q^{65} + 29 q^{67} + 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} + 77 q^{72} - 3 q^{73} + 48 q^{74} + 5 q^{75} - 47 q^{76} + 10 q^{78} + 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} - 9 q^{83} - 15 q^{84} + 5 q^{85} + 25 q^{86} - 23 q^{87} + 59 q^{89} - 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} + 19 q^{94} - 15 q^{95} - 14 q^{96} + 30 q^{97} - 2 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9 - 2 * q^10 + 15 * q^12 - 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 + 5 * q^17 - 2 * q^18 - 15 * q^19 + 24 * q^20 - 5 * q^21 + 4 * q^23 - 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 - 24 * q^28 + 6 * q^29 + q^30 + 22 * q^31 + 6 * q^32 + 44 * q^34 - 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 + 38 * q^39 - 6 * q^40 - 7 * q^41 - q^42 - 10 * q^43 + 37 * q^45 + 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 - 2 * q^50 + 11 * q^51 - 18 * q^52 + 23 * q^53 - 13 * q^54 + 6 * q^56 + 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 - 17 * q^61 - 57 * q^62 - 37 * q^63 + 64 * q^64 - 8 * q^65 + 29 * q^67 + 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 + 77 * q^72 - 3 * q^73 + 48 * q^74 + 5 * q^75 - 47 * q^76 + 10 * q^78 + 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 - 9 * q^83 - 15 * q^84 + 5 * q^85 + 25 * q^86 - 23 * q^87 + 59 * q^89 - 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 + 19 * q^94 - 15 * q^95 - 14 * q^96 + 30 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more