LMFDB - Embedded newform 950.2.b.g.799.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.4227136.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 22x^{2} + 9 $ x^6 + 9x^4 + 22x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.5
Root			$-1.91223i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.g.799.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.25561i q^{3} -1.00000 q^{4} +2.25561 q^{6} +4.22547i q^{7} -1.00000i q^{8} -2.08777 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.25561i q^{3} -1.00000 q^{4} +2.25561 q^{6} +4.22547i q^{7} -1.00000i q^{8} -2.08777 q^{9} -5.13770 q^{11} +2.25561i q^{12} -3.16784i q^{13} -4.22547 q^{14} +1.00000 q^{16} -6.48108i q^{17} -2.08777i q^{18} +1.00000 q^{19} +9.53101 q^{21} -5.13770i q^{22} -7.56885i q^{23} -2.25561 q^{24} +3.16784 q^{26} -2.05763i q^{27} -4.22547i q^{28} -0.832162 q^{29} -4.51122 q^{31} +1.00000i q^{32} +11.5886i q^{33} +6.48108 q^{34} +2.08777 q^{36} +0.137699i q^{37} +1.00000i q^{38} -7.14540 q^{39} -11.6489 q^{41} +9.53101i q^{42} +2.51122i q^{43} +5.13770 q^{44} +7.56885 q^{46} -5.96216i q^{47} -2.25561i q^{48} -10.8546 q^{49} -14.6188 q^{51} +3.16784i q^{52} -0.225470i q^{53} +2.05763 q^{54} +4.22547 q^{56} -2.25561i q^{57} -0.832162i q^{58} -5.39331 q^{59} +14.4509 q^{61} -4.51122i q^{62} -8.82181i q^{63} -1.00000 q^{64} -11.5886 q^{66} -4.11021i q^{67} +6.48108i q^{68} -17.0724 q^{69} +3.82446 q^{71} +2.08777i q^{72} -4.70655i q^{73} -0.137699 q^{74} -1.00000 q^{76} -21.7092i q^{77} -7.14540i q^{78} -10.6265 q^{79} -10.9045 q^{81} -11.6489i q^{82} +12.0999i q^{83} -9.53101 q^{84} -2.51122 q^{86} +1.87703i q^{87} +5.13770i q^{88} +10.0000 q^{89} +13.3856 q^{91} +7.56885i q^{92} +10.1755i q^{93} +5.96216 q^{94} +2.25561 q^{96} +3.93972i q^{97} -10.8546i q^{98} +10.7263 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9	$ 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} + 6 q^{19} - 22 q^{21} - 4 q^{24} - 4 q^{26} - 28 q^{29} - 8 q^{31} + 8 q^{34} + 26 q^{36} - 58 q^{39} - 16 q^{41} - 4 q^{44} + 28 q^{46} - 50 q^{49} - 22 q^{51} + 14 q^{54} + 4 q^{56} + 12 q^{59} + 44 q^{61} - 6 q^{64} + 8 q^{66} - 16 q^{69} - 4 q^{71} + 34 q^{74} - 6 q^{76} - 48 q^{79} - 2 q^{81} + 22 q^{84} + 4 q^{86} + 60 q^{89} - 14 q^{91} - 26 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 + 6 * q^19 - 22 * q^21 - 4 * q^24 - 4 * q^26 - 28 * q^29 - 8 * q^31 + 8 * q^34 + 26 * q^36 - 58 * q^39 - 16 * q^41 - 4 * q^44 + 28 * q^46 - 50 * q^49 - 22 * q^51 + 14 * q^54 + 4 * q^56 + 12 * q^59 + 44 * q^61 - 6 * q^64 + 8 * q^66 - 16 * q^69 - 4 * q^71 + 34 * q^74 - 6 * q^76 - 48 * q^79 - 2 * q^81 + 22 * q^84 + 4 * q^86 + 60 * q^89 - 14 * q^91 - 26 * q^94 + 4 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 2.25561i	− 1.30228i	−0.758959	−	0.651138i	$-0.774292\pi$
$3$	− 2.25561i	− 1.30228i	0.758959	−	0.651138i	$-0.225708\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.25561	0.920848
$7$	4.22547i	1.59708i	0.601943	+	0.798539i	$0.294393\pi$
$7$	4.22547i	1.59708i	−0.601943	+	0.798539i	$0.705607\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−2.08777	−0.695924
$10$	0	0
$11$	−5.13770	−1.54907	−0.774537	−	0.632528i	$-0.782017\pi$
$11$	−5.13770	−1.54907	−0.774537	+	0.632528i	$0.782017\pi$
$12$	2.25561i	0.651138i
$13$	− 3.16784i	− 0.878600i	−0.898340	−	0.439300i	$-0.855226\pi$
$13$	− 3.16784i	− 0.878600i	0.898340	−	0.439300i	$-0.144774\pi$
$14$	−4.22547	−1.12930
$15$	0	0
$16$	1.00000	0.250000
$17$	− 6.48108i	− 1.57189i	−0.618295	−	0.785946i	$-0.712176\pi$
$17$	− 6.48108i	− 1.57189i	0.618295	−	0.785946i	$-0.287824\pi$
$18$	− 2.08777i	− 0.492092i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	9.53101	2.07984
$22$	− 5.13770i	− 1.09536i
$23$	− 7.56885i	− 1.57821i	−0.614256	−	0.789107i	$-0.710544\pi$
$23$	− 7.56885i	− 1.57821i	0.614256	−	0.789107i	$-0.289456\pi$
$24$	−2.25561	−0.460424
$25$	0	0
$26$	3.16784	0.621264
$27$	− 2.05763i	− 0.395991i
$28$	− 4.22547i	− 0.798539i
$29$	−0.832162	−0.154529	−0.0772643	−	0.997011i	$-0.524619\pi$
$29$	−0.832162	−0.154529	−0.0772643	+	0.997011i	$0.524619\pi$
$30$	0	0
$31$	−4.51122	−0.810239	−0.405119	−	0.914264i	$-0.632770\pi$
$31$	−4.51122	−0.810239	−0.405119	+	0.914264i	$0.632770\pi$
$32$	1.00000i	0.176777i
$33$	11.5886i	2.01732i
$34$	6.48108	1.11150
$35$	0	0
$36$	2.08777	0.347962
$37$	0.137699i	0.0226376i	0.999936	+	0.0113188i	$0.00360296\pi$
$37$	0.137699i	0.0226376i	−0.999936	+	0.0113188i	$0.996397\pi$
$38$	1.00000i	0.162221i
$39$	−7.14540	−1.14418
$40$	0	0
$41$	−11.6489	−1.81926	−0.909628	−	0.415425i	$-0.863633\pi$
$41$	−11.6489	−1.81926	−0.909628	+	0.415425i	$0.863633\pi$
$42$	9.53101i	1.47067i
$43$	2.51122i	0.382957i	0.981497	+	0.191479i	$0.0613282\pi$
$43$	2.51122i	0.382957i	−0.981497	+	0.191479i	$0.938672\pi$
$44$	5.13770	0.774537
$45$	0	0
$46$	7.56885	1.11597
$47$	− 5.96216i	− 0.869670i	−0.900510	−	0.434835i	$-0.856807\pi$
$47$	− 5.96216i	− 0.869670i	0.900510	−	0.434835i	$-0.143193\pi$
$48$	− 2.25561i	− 0.325569i
$49$	−10.8546	−1.55066
$50$	0	0
$51$	−14.6188	−2.04704
$52$	3.16784i	0.439300i
$53$	− 0.225470i	− 0.0309707i	−0.999880	−	0.0154853i	$-0.995071\pi$
$53$	− 0.225470i	− 0.0309707i	0.999880	−	0.0154853i	$-0.00492934\pi$
$54$	2.05763	0.280008
$55$	0	0
$56$	4.22547	0.564652
$57$	− 2.25561i	− 0.298763i
$58$	− 0.832162i	− 0.109268i
$59$	−5.39331	−0.702149	−0.351074	−	0.936348i	$-0.614184\pi$
$59$	−5.39331	−0.702149	−0.351074	+	0.936348i	$0.614184\pi$
$60$	0	0
$61$	14.4509	1.85025	0.925127	−	0.379659i	$-0.123959\pi$
$61$	14.4509	1.85025	0.925127	+	0.379659i	$0.123959\pi$
$62$	− 4.51122i	− 0.572925i
$63$	− 8.82181i	− 1.11144i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−11.5886	−1.42646
$67$	− 4.11021i	− 0.502142i	−0.967969	−	0.251071i	$-0.919217\pi$
$67$	− 4.11021i	− 0.502142i	0.967969	−	0.251071i	$-0.0807827\pi$
$68$	6.48108i	0.785946i
$69$	−17.0724	−2.05527
$70$	0	0
$71$	3.82446	0.453880	0.226940	−	0.973909i	$-0.427128\pi$
$71$	3.82446	0.453880	0.226940	+	0.973909i	$0.427128\pi$
$72$	2.08777i	0.246046i
$73$	− 4.70655i	− 0.550860i	−0.961321	−	0.275430i	$-0.911180\pi$
$73$	− 4.70655i	− 0.550860i	0.961321	−	0.275430i	$-0.0888202\pi$
$74$	−0.137699	−0.0160072
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 21.7092i	− 2.47399i
$78$	− 7.14540i	− 0.809058i
$79$	−10.6265	−1.19557	−0.597786	−	0.801655i	$-0.703953\pi$
$79$	−10.6265	−1.19557	−0.597786	+	0.801655i	$0.703953\pi$
$80$	0	0
$81$	−10.9045	−1.21161
$82$	− 11.6489i	− 1.28641i
$83$	12.0999i	1.32813i	0.747674	+	0.664066i	$0.231171\pi$
$83$	12.0999i	1.32813i	−0.747674	+	0.664066i	$0.768829\pi$
$84$	−9.53101	−1.03992
$85$	0	0
$86$	−2.51122	−0.270792
$87$	1.87703i	0.201239i
$88$	5.13770i	0.547681i
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	13.3856	1.40319
$92$	7.56885i	0.789107i
$93$	10.1755i	1.05515i
$94$	5.96216	0.614950
$95$	0	0
$96$	2.25561	0.230212
$97$	3.93972i	0.400018i	0.979794	+	0.200009i	$0.0640972\pi$
$97$	3.93972i	0.400018i	−0.979794	+	0.200009i	$0.935903\pi$
$98$	− 10.8546i	− 1.09648i
$99$	10.7263	1.07804
$100$	0	0
$101$	3.19798	0.318211	0.159105	−	0.987262i	$-0.449139\pi$
$101$	3.19798	0.318211	0.159105	+	0.987262i	$0.449139\pi$
$102$	− 14.6188i	− 1.44747i
$103$	10.6868i	1.05300i	0.850176	+	0.526499i	$0.176496\pi$
$103$	10.6868i	1.05300i	−0.850176	+	0.526499i	$0.823504\pi$
$104$	−3.16784	−0.310632
$105$	0	0
$106$	0.225470	0.0218996
$107$	10.8168i	1.04570i	0.852426	+	0.522848i	$0.175130\pi$
$107$	10.8168i	1.04570i	−0.852426	+	0.522848i	$0.824870\pi$
$108$	2.05763i	0.197996i
$109$	−9.24791	−0.885789	−0.442894	−	0.896574i	$-0.646048\pi$
$109$	−9.24791	−0.885789	−0.442894	+	0.896574i	$0.646048\pi$
$110$	0	0
$111$	0.310596	0.0294804
$112$	4.22547i	0.399269i
$113$	− 17.6489i	− 1.66027i	−0.557562	−	0.830135i	$-0.688263\pi$
$113$	− 17.6489i	− 1.66027i	0.557562	−	0.830135i	$-0.311737\pi$
$114$	2.25561	0.211257
$115$	0	0
$116$	0.832162	0.0772643
$117$	6.61372i	0.611439i
$118$	− 5.39331i	− 0.496494i
$119$	27.3856	2.51043
$120$	0	0
$121$	15.3960	1.39963
$122$	14.4509i	1.30833i
$123$	26.2754i	2.36917i
$124$	4.51122	0.405119
$125$	0	0
$126$	8.82181	0.785910
$127$	− 12.7866i	− 1.13463i	−0.823501	−	0.567314i	$-0.807982\pi$
$127$	− 12.7866i	− 1.13463i	0.823501	−	0.567314i	$-0.192018\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	5.66432	0.498716
$130$	0	0
$131$	−2.11526	−0.184811	−0.0924057	−	0.995721i	$-0.529456\pi$
$131$	−2.11526	−0.184811	−0.0924057	+	0.995721i	$0.529456\pi$
$132$	− 11.5886i	− 1.00866i
$133$	4.22547i	0.366395i
$134$	4.11021	0.355068
$135$	0	0
$136$	−6.48108	−0.555748
$137$	− 5.36317i	− 0.458206i	−0.973402	−	0.229103i	$-0.926421\pi$
$137$	− 5.36317i	− 0.458206i	0.973402	−	0.229103i	$-0.0735793\pi$
$138$	− 17.0724i	− 1.45330i
$139$	10.1601	0.861771	0.430886	−	0.902407i	$-0.358201\pi$
$139$	10.1601	0.861771	0.430886	+	0.902407i	$0.358201\pi$
$140$	0	0
$141$	−13.4483	−1.13255
$142$	3.82446i	0.320941i
$143$	16.2754i	1.36102i
$144$	−2.08777	−0.173981
$145$	0	0
$146$	4.70655	0.389517
$147$	24.4837i	2.01938i
$148$	− 0.137699i	− 0.0113188i
$149$	5.93972	0.486601	0.243301	−	0.969951i	$-0.421770\pi$
$149$	5.93972	0.486601	0.243301	+	0.969951i	$0.421770\pi$
$150$	0	0
$151$	−15.2978	−1.24492	−0.622460	−	0.782652i	$-0.713867\pi$
$151$	−15.2978	−1.24492	−0.622460	+	0.782652i	$0.713867\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	13.5310i	1.09392i
$154$	21.7092	1.74938
$155$	0	0
$156$	7.14540	0.572090
$157$	− 12.7866i	− 1.02048i	−0.860031	−	0.510242i	$-0.829556\pi$
$157$	− 12.7866i	− 1.02048i	0.860031	−	0.510242i	$-0.170444\pi$
$158$	− 10.6265i	− 0.845397i
$159$	−0.508572	−0.0403324
$160$	0	0
$161$	31.9819	2.52053
$162$	− 10.9045i	− 0.856740i
$163$	11.4734i	0.898664i	0.893365	+	0.449332i	$0.148338\pi$
$163$	11.4734i	0.898664i	−0.893365	+	0.449332i	$0.851662\pi$
$164$	11.6489	0.909628
$165$	0	0
$166$	−12.0999	−0.939131
$167$	19.4131i	1.50223i	0.660171	+	0.751115i	$0.270484\pi$
$167$	19.4131i	1.50223i	−0.660171	+	0.751115i	$0.729516\pi$
$168$	− 9.53101i	− 0.735333i
$169$	2.96480	0.228062
$170$	0	0
$171$	−2.08777	−0.159656
$172$	− 2.51122i	− 0.191479i
$173$	− 9.78662i	− 0.744063i	−0.928220	−	0.372031i	$-0.878661\pi$
$173$	− 9.78662i	− 0.744063i	0.928220	−	0.372031i	$-0.121339\pi$
$174$	−1.87703	−0.142297
$175$	0	0
$176$	−5.13770	−0.387269
$177$	12.1652i	0.914392i
$178$	10.0000i	0.749532i
$179$	6.82446	0.510084	0.255042	−	0.966930i	$-0.417911\pi$
$179$	6.82446	0.510084	0.255042	+	0.966930i	$0.417911\pi$
$180$	0	0
$181$	−0.137699	−0.0102351	−0.00511755	−	0.999987i	$-0.501629\pi$
$181$	−0.137699	−0.0102351	−0.00511755	+	0.999987i	$0.501629\pi$
$182$	13.3856i	0.992207i
$183$	− 32.5957i	− 2.40954i
$184$	−7.56885	−0.557983
$185$	0	0
$186$	−10.1755	−0.746107
$187$	33.2978i	2.43498i
$188$	5.96216i	0.434835i
$189$	8.69446	0.632429
$190$	0	0
$191$	19.3779	1.40214	0.701068	−	0.713095i	$-0.252707\pi$
$191$	19.3779	1.40214	0.701068	+	0.713095i	$0.252707\pi$
$192$	2.25561i	0.162785i
$193$	5.42851i	0.390752i	0.980728	+	0.195376i	$0.0625928\pi$
$193$	5.42851i	0.390752i	−0.980728	+	0.195376i	$0.937407\pi$
$194$	−3.93972	−0.282856
$195$	0	0
$196$	10.8546	0.775328
$197$	− 15.6489i	− 1.11494i	−0.830197	−	0.557470i	$-0.811772\pi$
$197$	− 15.6489i	− 1.11494i	0.830197	−	0.557470i	$-0.188228\pi$
$198$	10.7263i	0.762288i
$199$	−18.0499	−1.27953	−0.639763	−	0.768572i	$-0.720967\pi$
$199$	−18.0499	−1.27953	−0.639763	+	0.768572i	$0.720967\pi$
$200$	0	0
$201$	−9.27102	−0.653927
$202$	3.19798i	0.225009i
$203$	− 3.51628i	− 0.246794i
$204$	14.6188	1.02352
$205$	0	0
$206$	−10.6868	−0.744582
$207$	15.8020i	1.09832i
$208$	− 3.16784i	− 0.219650i
$209$	−5.13770	−0.355382
$210$	0	0
$211$	−7.50857	−0.516911	−0.258456	−	0.966023i	$-0.583214\pi$
$211$	−7.50857	−0.516911	−0.258456	+	0.966023i	$0.583214\pi$
$212$	0.225470i	0.0154853i
$213$	− 8.62648i	− 0.591077i
$214$	−10.8168	−0.739418
$215$	0	0
$216$	−2.05763	−0.140004
$217$	− 19.0620i	− 1.29401i
$218$	− 9.24791i	− 0.626347i
$219$	−10.6161	−0.717372
$220$	0	0
$221$	−20.5310	−1.38106
$222$	0.310596i	0.0208458i
$223$	− 27.8091i	− 1.86223i	−0.364723	−	0.931116i	$-0.618836\pi$
$223$	− 27.8091i	− 1.86223i	0.364723	−	0.931116i	$-0.381164\pi$
$224$	−4.22547	−0.282326
$225$	0	0
$226$	17.6489	1.17399
$227$	8.91223i	0.591525i	0.955261	+	0.295763i	$0.0955738\pi$
$227$	8.91223i	0.591525i	−0.955261	+	0.295763i	$0.904426\pi$
$228$	2.25561i	0.149381i
$229$	13.6489	0.901946	0.450973	−	0.892538i	$-0.351077\pi$
$229$	13.6489	0.901946	0.450973	+	0.892538i	$0.351077\pi$
$230$	0	0
$231$	−48.9674	−3.22182
$232$	0.832162i	0.0546341i
$233$	− 23.2754i	− 1.52482i	−0.647093	−	0.762411i	$-0.724015\pi$
$233$	− 23.2754i	− 1.52482i	0.647093	−	0.762411i	$-0.275985\pi$
$234$	−6.61372	−0.432352
$235$	0	0
$236$	5.39331	0.351074
$237$	23.9692i	1.55697i
$238$	27.3856i	1.77515i
$239$	−3.72898	−0.241208	−0.120604	−	0.992701i	$-0.538483\pi$
$239$	−3.72898	−0.241208	−0.120604	+	0.992701i	$0.538483\pi$
$240$	0	0
$241$	−1.48878	−0.0959009	−0.0479505	−	0.998850i	$-0.515269\pi$
$241$	−1.48878	−0.0959009	−0.0479505	+	0.998850i	$0.515269\pi$
$242$	15.3960i	0.989689i
$243$	18.4234i	1.18186i
$244$	−14.4509	−0.925127
$245$	0	0
$246$	−26.2754	−1.67526
$247$	− 3.16784i	− 0.201565i
$248$	4.51122i	0.286463i
$249$	27.2925	1.72959
$250$	0	0
$251$	−8.78662	−0.554606	−0.277303	−	0.960782i	$-0.589441\pi$
$251$	−8.78662	−0.554606	−0.277303	+	0.960782i	$0.589441\pi$
$252$	8.82181i	0.555722i
$253$	38.8865i	2.44477i
$254$	12.7866	0.802304
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.74175i	0.171025i	0.996337	+	0.0855127i	$0.0272528\pi$
$257$	2.74175i	0.171025i	−0.996337	+	0.0855127i	$0.972747\pi$
$258$	5.66432i	0.352645i
$259$	−0.581844	−0.0361540
$260$	0	0
$261$	1.73736	0.107540
$262$	− 2.11526i	− 0.130681i
$263$	− 2.74704i	− 0.169390i	−0.996407	−	0.0846948i	$-0.973008\pi$
$263$	− 2.74704i	− 0.169390i	0.996407	−	0.0846948i	$-0.0269915\pi$
$264$	11.5886	0.713231
$265$	0	0
$266$	−4.22547	−0.259080
$267$	− 22.5561i	− 1.38041i
$268$	4.11021i	0.251071i
$269$	9.74175	0.593965	0.296982	−	0.954883i	$-0.404020\pi$
$269$	9.74175	0.593965	0.296982	+	0.954883i	$0.404020\pi$
$270$	0	0
$271$	26.3555	1.60098	0.800490	−	0.599346i	$-0.204573\pi$
$271$	26.3555	1.60098	0.800490	+	0.599346i	$0.204573\pi$
$272$	− 6.48108i	− 0.392973i
$273$	− 30.1927i	− 1.82734i
$274$	5.36317	0.324001
$275$	0	0
$276$	17.0724	1.02764
$277$	− 0.962158i	− 0.0578104i	−0.999582	−	0.0289052i	$-0.990798\pi$
$277$	− 0.962158i	− 0.0578104i	0.999582	−	0.0289052i	$-0.00920210\pi$
$278$	10.1601i	0.609364i
$279$	9.41839	0.563864
$280$	0	0
$281$	−14.6714	−0.875219	−0.437610	−	0.899165i	$-0.644175\pi$
$281$	−14.6714	−0.875219	−0.437610	+	0.899165i	$0.644175\pi$
$282$	− 13.4483i	− 0.800834i
$283$	26.1601i	1.55506i	0.628847	+	0.777529i	$0.283527\pi$
$283$	26.1601i	1.55506i	−0.628847	+	0.777529i	$0.716473\pi$
$284$	−3.82446	−0.226940
$285$	0	0
$286$	−16.2754	−0.962384
$287$	− 49.2221i	− 2.90549i
$288$	− 2.08777i	− 0.123023i
$289$	−25.0044	−1.47085
$290$	0	0
$291$	8.88647	0.520934
$292$	4.70655i	0.275430i
$293$	22.4657i	1.31246i	0.754562	+	0.656229i	$0.227850\pi$
$293$	22.4657i	1.31246i	−0.754562	+	0.656229i	$0.772150\pi$
$294$	−24.4837	−1.42792
$295$	0	0
$296$	0.137699	0.00800360
$297$	10.5715i	0.613420i
$298$	5.93972i	0.344079i
$299$	−23.9769	−1.38662
$300$	0	0
$301$	−10.6111	−0.611612
$302$	− 15.2978i	− 0.880291i
$303$	− 7.21338i	− 0.414398i
$304$	1.00000	0.0573539
$305$	0	0
$306$	−13.5310	−0.773516
$307$	17.2204i	0.982821i	0.870928	+	0.491410i	$0.163518\pi$
$307$	17.2204i	0.982821i	−0.870928	+	0.491410i	$0.836482\pi$
$308$	21.7092i	1.23700i
$309$	24.1051	1.37129
$310$	0	0
$311$	−7.87439	−0.446516	−0.223258	−	0.974759i	$-0.571669\pi$
$311$	−7.87439	−0.446516	−0.223258	+	0.974759i	$0.571669\pi$
$312$	7.14540i	0.404529i
$313$	25.1678i	1.42257i	0.702904	+	0.711285i	$0.251887\pi$
$313$	25.1678i	1.42257i	−0.702904	+	0.711285i	$0.748113\pi$
$314$	12.7866	0.721590
$315$	0	0
$316$	10.6265	0.597786
$317$	− 23.9045i	− 1.34261i	−0.741180	−	0.671306i	$-0.765734\pi$
$317$	− 23.9045i	− 1.34261i	0.741180	−	0.671306i	$-0.234266\pi$
$318$	− 0.508572i	− 0.0285193i
$319$	4.27540	0.239376
$320$	0	0
$321$	24.3984	1.36178
$322$	31.9819i	1.78228i
$323$	− 6.48108i	− 0.360617i
$324$	10.9045	0.605807
$325$	0	0
$326$	−11.4734	−0.635451
$327$	20.8597i	1.15354i
$328$	11.6489i	0.643204i
$329$	25.1929	1.38893
$330$	0	0
$331$	30.7565	1.69053	0.845264	−	0.534348i	$-0.179443\pi$
$331$	30.7565	1.69053	0.845264	+	0.534348i	$0.179443\pi$
$332$	− 12.0999i	− 0.664066i
$333$	− 0.287484i	− 0.0157540i
$334$	−19.4131	−1.06224
$335$	0	0
$336$	9.53101	0.519959
$337$	13.4734i	0.733942i	0.930232	+	0.366971i	$0.119605\pi$
$337$	13.4734i	0.733942i	−0.930232	+	0.366971i	$0.880395\pi$
$338$	2.96480i	0.161264i
$339$	−39.8091	−2.16213
$340$	0	0
$341$	23.1773	1.25512
$342$	− 2.08777i	− 0.112894i
$343$	− 16.2875i	− 0.879441i
$344$	2.51122	0.135396
$345$	0	0
$346$	9.78662	0.526132
$347$	28.9468i	1.55394i	0.629536	+	0.776971i	$0.283245\pi$
$347$	28.9468i	1.55394i	−0.629536	+	0.776971i	$0.716755\pi$
$348$	− 1.87703i	− 0.100619i
$349$	−27.9243	−1.49475	−0.747377	−	0.664400i	$-0.768687\pi$
$349$	−27.9243	−1.49475	−0.747377	+	0.664400i	$0.768687\pi$
$350$	0	0
$351$	−6.51825	−0.347918
$352$	− 5.13770i	− 0.273840i
$353$	− 28.3099i	− 1.50678i	−0.657571	−	0.753392i	$-0.728416\pi$
$353$	− 28.3099i	− 1.50678i	0.657571	−	0.753392i	$-0.271584\pi$
$354$	−12.1652	−0.646573
$355$	0	0
$356$	−10.0000	−0.529999
$357$	− 61.7712i	− 3.26928i
$358$	6.82446i	0.360684i
$359$	−2.60163	−0.137309	−0.0686545	−	0.997640i	$-0.521871\pi$
$359$	−2.60163	−0.137309	−0.0686545	+	0.997640i	$0.521871\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 0.137699i	− 0.00723731i
$363$	− 34.7272i	− 1.82271i
$364$	−13.3856	−0.701596
$365$	0	0
$366$	32.5957	1.70380
$367$	11.6489i	0.608069i	0.952661	+	0.304034i	$0.0983337\pi$
$367$	11.6489i	0.608069i	−0.952661	+	0.304034i	$0.901666\pi$
$368$	− 7.56885i	− 0.394554i
$369$	24.3203	1.26606
$370$	0	0
$371$	0.952717	0.0494626
$372$	− 10.1755i	− 0.527577i
$373$	12.8064i	0.663091i	0.943439	+	0.331545i	$0.107570\pi$
$373$	12.8064i	0.663091i	−0.943439	+	0.331545i	$0.892430\pi$
$374$	−33.2978	−1.72179
$375$	0	0
$376$	−5.96216	−0.307475
$377$	2.63615i	0.135769i
$378$	8.69446i	0.447195i
$379$	20.9122	1.07419	0.537095	−	0.843522i	$-0.319522\pi$
$379$	20.9122	1.07419	0.537095	+	0.843522i	$0.319522\pi$
$380$	0	0
$381$	−28.8416	−1.47760
$382$	19.3779i	0.991460i
$383$	− 10.3511i	− 0.528916i	−0.964397	−	0.264458i	$-0.914807\pi$
$383$	− 10.3511i	− 0.528916i	0.964397	−	0.264458i	$-0.0851930\pi$
$384$	−2.25561	−0.115106
$385$	0	0
$386$	−5.42851	−0.276304
$387$	− 5.24285i	− 0.266509i
$388$	− 3.93972i	− 0.200009i
$389$	−6.56620	−0.332920	−0.166460	−	0.986048i	$-0.553234\pi$
$389$	−6.56620	−0.332920	−0.166460	+	0.986048i	$0.553234\pi$
$390$	0	0
$391$	−49.0543	−2.48078
$392$	10.8546i	0.548240i
$393$	4.77121i	0.240676i
$394$	15.6489	0.788381
$395$	0	0
$396$	−10.7263	−0.539019
$397$	23.5284i	1.18085i	0.807091	+	0.590427i	$0.201041\pi$
$397$	23.5284i	1.18085i	−0.807091	+	0.590427i	$0.798959\pi$
$398$	− 18.0499i	− 0.904761i
$399$	9.53101	0.477147
$400$	0	0
$401$	6.22041	0.310633	0.155316	−	0.987865i	$-0.450360\pi$
$401$	6.22041	0.310633	0.155316	+	0.987865i	$0.450360\pi$
$402$	− 9.27102i	− 0.462396i
$403$	14.2908i	0.711876i
$404$	−3.19798	−0.159105
$405$	0	0
$406$	3.51628	0.174510
$407$	− 0.707457i	− 0.0350674i
$408$	14.6188i	0.723737i
$409$	34.4905	1.70545	0.852723	−	0.522363i	$-0.174949\pi$
$409$	34.4905	1.70545	0.852723	+	0.522363i	$0.174949\pi$
$410$	0	0
$411$	−12.0972	−0.596711
$412$	− 10.6868i	− 0.526499i
$413$	− 22.7893i	− 1.12139i
$414$	−15.8020	−0.776627
$415$	0	0
$416$	3.16784	0.155316
$417$	− 22.9173i	− 1.12226i
$418$	− 5.13770i	− 0.251293i
$419$	10.6265	0.519138	0.259569	−	0.965725i	$-0.416420\pi$
$419$	10.6265	0.519138	0.259569	+	0.965725i	$0.416420\pi$
$420$	0	0
$421$	−1.98021	−0.0965095	−0.0482548	−	0.998835i	$-0.515366\pi$
$421$	−1.98021	−0.0965095	−0.0482548	+	0.998835i	$0.515366\pi$
$422$	− 7.50857i	− 0.365512i
$423$	12.4476i	0.605224i
$424$	−0.225470	−0.0109498
$425$	0	0
$426$	8.62648	0.417954
$427$	61.0620i	2.95500i
$428$	− 10.8168i	− 0.522848i
$429$	36.7109	1.77242
$430$	0	0
$431$	15.0774	0.726254	0.363127	−	0.931740i	$-0.381709\pi$
$431$	15.0774	0.726254	0.363127	+	0.931740i	$0.381709\pi$
$432$	− 2.05763i	− 0.0989979i
$433$	− 13.5337i	− 0.650386i	−0.945648	−	0.325193i	$-0.894571\pi$
$433$	− 13.5337i	− 0.650386i	0.945648	−	0.325193i	$-0.105429\pi$
$434$	19.0620	0.915006
$435$	0	0
$436$	9.24791	0.442894
$437$	− 7.56885i	− 0.362067i
$438$	− 10.6161i	− 0.507258i
$439$	−39.1773	−1.86983	−0.934915	−	0.354872i	$-0.884524\pi$
$439$	−39.1773	−1.86983	−0.934915	+	0.354872i	$0.884524\pi$
$440$	0	0
$441$	22.6619	1.07914
$442$	− 20.5310i	− 0.976560i
$443$	− 19.3132i	− 0.917600i	−0.888540	−	0.458800i	$-0.848279\pi$
$443$	− 19.3132i	− 0.917600i	0.888540	−	0.458800i	$-0.151721\pi$
$444$	−0.310596	−0.0147402
$445$	0	0
$446$	27.8091	1.31680
$447$	− 13.3977i	− 0.633689i
$448$	− 4.22547i	− 0.199635i
$449$	−41.4131	−1.95440	−0.977202	−	0.212310i	$-0.931901\pi$
$449$	−41.4131	−1.95440	−0.977202	+	0.212310i	$0.931901\pi$
$450$	0	0
$451$	59.8486	2.81816
$452$	17.6489i	0.830135i
$453$	34.5059i	1.62123i
$454$	−8.91223	−0.418272
$455$	0	0
$456$	−2.25561	−0.105629
$457$	− 37.8392i	− 1.77004i	−0.465551	−	0.885021i	$-0.654144\pi$
$457$	− 37.8392i	− 1.77004i	0.465551	−	0.885021i	$-0.345856\pi$
$458$	13.6489i	0.637772i
$459$	−13.3357	−0.622456
$460$	0	0
$461$	1.58864	0.0739903	0.0369952	−	0.999315i	$-0.488221\pi$
$461$	1.58864	0.0739903	0.0369952	+	0.999315i	$0.488221\pi$
$462$	− 48.9674i	− 2.27817i
$463$	− 40.3581i	− 1.87560i	−0.347175	−	0.937800i	$-0.612859\pi$
$463$	− 40.3581i	− 1.87560i	0.347175	−	0.937800i	$-0.387141\pi$
$464$	−0.832162	−0.0386322
$465$	0	0
$466$	23.2754	1.07821
$467$	− 39.5130i	− 1.82844i	−0.405217	−	0.914221i	$-0.632804\pi$
$467$	− 39.5130i	− 1.82844i	0.405217	−	0.914221i	$-0.367196\pi$
$468$	− 6.61372i	− 0.305719i
$469$	17.3676	0.801959
$470$	0	0
$471$	−28.8416	−1.32895
$472$	5.39331i	0.248247i
$473$	− 12.9019i	− 0.593229i
$474$	−23.9692	−1.10094
$475$	0	0
$476$	−27.3856	−1.25522
$477$	0.470730i	0.0215532i
$478$	− 3.72898i	− 0.170560i
$479$	−7.61107	−0.347759	−0.173879	−	0.984767i	$-0.555630\pi$
$479$	−7.61107	−0.347759	−0.173879	+	0.984767i	$0.555630\pi$
$480$	0	0
$481$	0.436209	0.0198894
$482$	− 1.48878i	− 0.0678122i
$483$	− 72.1388i	− 3.28243i
$484$	−15.3960	−0.699816
$485$	0	0
$486$	−18.4234	−0.835705
$487$	− 20.3907i	− 0.923989i	−0.886883	−	0.461995i	$-0.847134\pi$
$487$	− 20.3907i	− 0.923989i	0.886883	−	0.461995i	$-0.152866\pi$
$488$	− 14.4509i	− 0.654163i
$489$	25.8794	1.17031
$490$	0	0
$491$	25.0224	1.12925	0.564623	−	0.825349i	$-0.309021\pi$
$491$	25.0224	1.12925	0.564623	+	0.825349i	$0.309021\pi$
$492$	− 26.2754i	− 1.18459i
$493$	5.39331i	0.242902i
$494$	3.16784	0.142528
$495$	0	0
$496$	−4.51122	−0.202560
$497$	16.1601i	0.724881i
$498$	27.2925i	1.22301i
$499$	−22.6111	−1.01221	−0.506105	−	0.862472i	$-0.668915\pi$
$499$	−22.6111	−1.01221	−0.506105	+	0.862472i	$0.668915\pi$
$500$	0	0
$501$	43.7884	1.95632
$502$	− 8.78662i	− 0.392166i
$503$	− 11.5035i	− 0.512916i	−0.966555	−	0.256458i	$-0.917444\pi$
$503$	− 11.5035i	− 0.512916i	0.966555	−	0.256458i	$-0.0825556\pi$
$504$	−8.82181	−0.392955
$505$	0	0
$506$	−38.8865	−1.72871
$507$	− 6.68744i	− 0.296999i
$508$	12.7866i	0.567314i
$509$	−9.11526	−0.404027	−0.202013	−	0.979383i	$-0.564748\pi$
$509$	−9.11526	−0.404027	−0.202013	+	0.979383i	$0.564748\pi$
$510$	0	0
$511$	19.8874	0.879766
$512$	1.00000i	0.0441942i
$513$	− 2.05763i	− 0.0908467i
$514$	−2.74175	−0.120933
$515$	0	0
$516$	−5.66432	−0.249358
$517$	30.6318i	1.34718i
$518$	− 0.581844i	− 0.0255648i
$519$	−22.0748	−0.968975
$520$	0	0
$521$	15.4888	0.678576	0.339288	−	0.940683i	$-0.389814\pi$
$521$	15.4888	0.678576	0.339288	+	0.940683i	$0.389814\pi$
$522$	1.73736i	0.0760423i
$523$	− 4.34073i	− 0.189807i	−0.995486	−	0.0949035i	$-0.969746\pi$
$523$	− 4.34073i	− 0.189807i	0.995486	−	0.0949035i	$-0.0302543\pi$
$524$	2.11526	0.0924057
$525$	0	0
$526$	2.74704	0.119776
$527$	29.2376i	1.27361i
$528$	11.5886i	0.504331i
$529$	−34.2875	−1.49076
$530$	0	0
$531$	11.2600	0.488642
$532$	− 4.22547i	− 0.183197i
$533$	36.9019i	1.59840i
$534$	22.5561	0.976097
$535$	0	0
$536$	−4.11021	−0.177534
$537$	− 15.3933i	− 0.664270i
$538$	9.74175i	0.419996i
$539$	55.7677	2.40208
$540$	0	0
$541$	19.5491	0.840480	0.420240	−	0.907413i	$-0.361946\pi$
$541$	19.5491	0.840480	0.420240	+	0.907413i	$0.361946\pi$
$542$	26.3555i	1.13206i
$543$	0.310596i	0.0133289i
$544$	6.48108	0.277874
$545$	0	0
$546$	30.1927	1.29213
$547$	− 41.8038i	− 1.78740i	−0.448665	−	0.893700i	$-0.648100\pi$
$547$	− 41.8038i	− 1.78740i	0.448665	−	0.893700i	$-0.351900\pi$
$548$	5.36317i	0.229103i
$549$	−30.1703	−1.28763
$550$	0	0
$551$	−0.832162	−0.0354513
$552$	17.0724i	0.726648i
$553$	− 44.9019i	− 1.90942i
$554$	0.962158	0.0408782
$555$	0	0
$556$	−10.1601	−0.430886
$557$	− 9.76418i	− 0.413722i	−0.978370	−	0.206861i	$-0.933675\pi$
$557$	− 9.76418i	− 0.413722i	0.978370	−	0.206861i	$-0.0663247\pi$
$558$	9.41839i	0.398712i
$559$	7.95513	0.336466
$560$	0	0
$561$	75.1069	3.17102
$562$	− 14.6714i	− 0.618874i
$563$	− 11.4509i	− 0.482600i	−0.970451	−	0.241300i	$-0.922426\pi$
$563$	− 11.4509i	− 0.482600i	0.970451	−	0.241300i	$-0.0775737\pi$
$564$	13.4483	0.566275
$565$	0	0
$566$	−26.1601	−1.09959
$567$	− 46.0767i	− 1.93504i
$568$	− 3.82446i	− 0.160471i
$569$	13.4338	0.563174	0.281587	−	0.959536i	$-0.409139\pi$
$569$	13.4338	0.563174	0.281587	+	0.959536i	$0.409139\pi$
$570$	0	0
$571$	37.6335	1.57491	0.787457	−	0.616370i	$-0.211397\pi$
$571$	37.6335	1.57491	0.787457	+	0.616370i	$0.211397\pi$
$572$	− 16.2754i	− 0.680509i
$573$	− 43.7090i	− 1.82597i
$574$	49.2221	2.05449
$575$	0	0
$576$	2.08777	0.0869905
$577$	1.56885i	0.0653121i	0.999467	+	0.0326560i	$0.0103966\pi$
$577$	1.56885i	0.0653121i	−0.999467	+	0.0326560i	$0.989603\pi$
$578$	− 25.0044i	− 1.04005i
$579$	12.2446	0.508868
$580$	0	0
$581$	−51.1276	−2.12113
$582$	8.88647i	0.368356i
$583$	1.15840i	0.0479759i
$584$	−4.70655	−0.194758
$585$	0	0
$586$	−22.4657	−0.928048
$587$	25.8693i	1.06774i	0.845566	+	0.533871i	$0.179263\pi$
$587$	25.8693i	1.06774i	−0.845566	+	0.533871i	$0.820737\pi$
$588$	− 24.4837i	− 1.00969i
$589$	−4.51122	−0.185881
$590$	0	0
$591$	−35.2978	−1.45196
$592$	0.137699i	0.00565940i
$593$	28.9243i	1.18778i	0.804547	+	0.593890i	$0.202408\pi$
$593$	28.9243i	1.18778i	−0.804547	+	0.593890i	$0.797592\pi$
$594$	−10.5715	−0.433754
$595$	0	0
$596$	−5.93972	−0.243301
$597$	40.7136i	1.66630i
$598$	− 23.9769i	− 0.980488i
$599$	−41.3581	−1.68985	−0.844923	−	0.534887i	$-0.820354\pi$
$599$	−41.3581	−1.68985	−0.844923	+	0.534887i	$0.820354\pi$
$600$	0	0
$601$	2.68147	0.109379	0.0546897	−	0.998503i	$-0.482583\pi$
$601$	2.68147	0.109379	0.0546897	+	0.998503i	$0.482583\pi$
$602$	− 10.6111i	− 0.432475i
$603$	8.58117i	0.349452i
$604$	15.2978	0.622460
$605$	0	0
$606$	7.21338	0.293024
$607$	3.31324i	0.134480i	0.997737	+	0.0672401i	$0.0214194\pi$
$607$	3.31324i	0.134480i	−0.997737	+	0.0672401i	$0.978581\pi$
$608$	1.00000i	0.0405554i
$609$	−7.93134	−0.321394
$610$	0	0
$611$	−18.8871	−0.764092
$612$	− 13.5310i	− 0.546959i
$613$	10.0603i	0.406331i	0.979144	+	0.203165i	$0.0651229\pi$
$613$	10.0603i	0.406331i	−0.979144	+	0.203165i	$0.934877\pi$
$614$	−17.2204	−0.694959
$615$	0	0
$616$	−21.7092	−0.874688
$617$	− 27.6265i	− 1.11220i	−0.831115	−	0.556100i	$-0.812297\pi$
$617$	− 27.6265i	− 1.11220i	0.831115	−	0.556100i	$-0.187703\pi$
$618$	24.1051i	0.969651i
$619$	−16.6714	−0.670078	−0.335039	−	0.942204i	$-0.608750\pi$
$619$	−16.6714	−0.670078	−0.335039	+	0.942204i	$0.608750\pi$
$620$	0	0
$621$	−15.5739	−0.624959
$622$	− 7.87439i	− 0.315734i
$623$	42.2547i	1.69290i
$624$	−7.14540	−0.286045
$625$	0	0
$626$	−25.1678	−1.00591
$627$	11.5886i	0.462806i
$628$	12.7866i	0.510242i
$629$	0.892439	0.0355839
$630$	0	0
$631$	−0.709194	−0.0282326	−0.0141163	−	0.999900i	$-0.504494\pi$
$631$	−0.709194	−0.0282326	−0.0141163	+	0.999900i	$0.504494\pi$
$632$	10.6265i	0.422699i
$633$	16.9364i	0.673162i
$634$	23.9045	0.949370
$635$	0	0
$636$	0.508572	0.0201662
$637$	34.3856i	1.36241i
$638$	4.27540i	0.169265i
$639$	−7.98459	−0.315866
$640$	0	0
$641$	−2.43553	−0.0961978	−0.0480989	−	0.998843i	$-0.515316\pi$
$641$	−2.43553	−0.0961978	−0.0480989	+	0.998843i	$0.515316\pi$
$642$	24.3984i	0.962927i
$643$	− 7.70390i	− 0.303812i	−0.988395	−	0.151906i	$-0.951459\pi$
$643$	− 7.70390i	− 0.303812i	0.988395	−	0.151906i	$-0.0485411\pi$
$644$	−31.9819	−1.26027
$645$	0	0
$646$	6.48108	0.254995
$647$	− 10.0499i	− 0.395103i	−0.980292	−	0.197552i	$-0.936701\pi$
$647$	− 10.0499i	− 0.395103i	0.980292	−	0.197552i	$-0.0632990\pi$
$648$	10.9045i	0.428370i
$649$	27.7092	1.08768
$650$	0	0
$651$	−42.9964	−1.68516
$652$	− 11.4734i	− 0.449332i
$653$	7.09283i	0.277564i	0.990323	+	0.138782i	$0.0443187\pi$
$653$	7.09283i	0.277564i	−0.990323	+	0.138782i	$0.955681\pi$
$654$	−20.8597	−0.815677
$655$	0	0
$656$	−11.6489	−0.454814
$657$	9.82620i	0.383356i
$658$	25.1929i	0.982122i
$659$	1.16346	0.0453218	0.0226609	−	0.999743i	$-0.492786\pi$
$659$	1.16346	0.0453218	0.0226609	+	0.999743i	$0.492786\pi$
$660$	0	0
$661$	1.79432	0.0697909	0.0348955	−	0.999391i	$-0.488890\pi$
$661$	1.79432	0.0697909	0.0348955	+	0.999391i	$0.488890\pi$
$662$	30.7565i	1.19538i
$663$	46.3099i	1.79853i
$664$	12.0999	0.469566
$665$	0	0
$666$	0.287484	0.0111398
$667$	6.29851i	0.243879i
$668$	− 19.4131i	− 0.751115i
$669$	−62.7263	−2.42514
$670$	0	0
$671$	−74.2446	−2.86618
$672$	9.53101i	0.367667i
$673$	25.2824i	0.974566i	0.873244	+	0.487283i	$0.162012\pi$
$673$	25.2824i	0.974566i	−0.873244	+	0.487283i	$0.837988\pi$
$674$	−13.4734	−0.518975
$675$	0	0
$676$	−2.96480	−0.114031
$677$	− 4.89682i	− 0.188200i	−0.995563	−	0.0941001i	$-0.970003\pi$
$677$	− 4.89682i	− 0.188200i	0.995563	−	0.0941001i	$-0.0299974\pi$
$678$	− 39.8091i	− 1.52886i
$679$	−16.6472	−0.638860
$680$	0	0
$681$	20.1025	0.770330
$682$	23.1773i	0.887504i
$683$	− 10.1980i	− 0.390215i	−0.980782	−	0.195107i	$-0.937494\pi$
$683$	− 10.1980i	− 0.390215i	0.980782	−	0.195107i	$-0.0625055\pi$
$684$	2.08777	0.0798279
$685$	0	0
$686$	16.2875	0.621859
$687$	− 30.7866i	− 1.17458i
$688$	2.51122i	0.0957393i
$689$	−0.714253	−0.0272109
$690$	0	0
$691$	−39.9846	−1.52109	−0.760543	−	0.649288i	$-0.775067\pi$
$691$	−39.9846	−1.52109	−0.760543	+	0.649288i	$0.775067\pi$
$692$	9.78662i	0.372031i
$693$	45.3238i	1.72171i
$694$	−28.9468	−1.09880
$695$	0	0
$696$	1.87703	0.0711487
$697$	75.4975i	2.85967i
$698$	− 27.9243i	− 1.05695i
$699$	−52.5002	−1.98574
$700$	0	0
$701$	4.91729	0.185723	0.0928617	−	0.995679i	$-0.470399\pi$
$701$	4.91729	0.185723	0.0928617	+	0.995679i	$0.470399\pi$
$702$	− 6.51825i	− 0.246015i
$703$	0.137699i	0.00519342i
$704$	5.13770	0.193634
$705$	0	0
$706$	28.3099	1.06546
$707$	13.5130i	0.508207i
$708$	− 12.1652i	− 0.457196i
$709$	36.8865	1.38530	0.692650	−	0.721274i	$-0.256443\pi$
$709$	36.8865	1.38530	0.692650	+	0.721274i	$0.256443\pi$
$710$	0	0
$711$	22.1857	0.832027
$712$	− 10.0000i	− 0.374766i
$713$	34.1447i	1.27873i
$714$	61.7712	2.31173
$715$	0	0
$716$	−6.82446	−0.255042
$717$	8.41113i	0.314119i
$718$	− 2.60163i	− 0.0970921i
$719$	23.8891	0.890914	0.445457	−	0.895303i	$-0.353041\pi$
$719$	23.8891	0.890914	0.445457	+	0.895303i	$0.353041\pi$
$720$	0	0
$721$	−45.1566	−1.68172
$722$	1.00000i	0.0372161i
$723$	3.35811i	0.124889i
$724$	0.137699	0.00511755
$725$	0	0
$726$	34.7272	1.28885
$727$	19.6894i	0.730240i	0.930961	+	0.365120i	$0.118972\pi$
$727$	19.6894i	0.730240i	−0.930961	+	0.365120i	$0.881028\pi$
$728$	− 13.3856i	− 0.496104i
$729$	8.84251	0.327500
$730$	0	0
$731$	16.2754	0.601967
$732$	32.5957i	1.20477i
$733$	− 1.76418i	− 0.0651615i	−0.999469	−	0.0325808i	$-0.989627\pi$
$733$	− 1.76418i	− 0.0651615i	0.999469	−	0.0325808i	$-0.0103726\pi$
$734$	−11.6489	−0.429969
$735$	0	0
$736$	7.56885	0.278991
$737$	21.1170i	0.777855i
$738$	24.3203i	0.895241i
$739$	−28.1755	−1.03645	−0.518227	−	0.855243i	$-0.673408\pi$
$739$	−28.1755	−1.03645	−0.518227	+	0.855243i	$0.673408\pi$
$740$	0	0
$741$	−7.14540	−0.262493
$742$	0.952717i	0.0349753i
$743$	5.42851i	0.199153i	0.995030	+	0.0995763i	$0.0317487\pi$
$743$	5.42851i	0.199153i	−0.995030	+	0.0995763i	$0.968251\pi$
$744$	10.1755	0.373053
$745$	0	0
$746$	−12.8064	−0.468876
$747$	− 25.2617i	− 0.924278i
$748$	− 33.2978i	− 1.21749i
$749$	−45.7059	−1.67006
$750$	0	0
$751$	25.8640	0.943792	0.471896	−	0.881654i	$-0.343570\pi$
$751$	25.8640	0.943792	0.471896	+	0.881654i	$0.343570\pi$
$752$	− 5.96216i	− 0.217418i
$753$	19.8192i	0.722251i
$754$	−2.63615	−0.0960031
$755$	0	0
$756$	−8.69446	−0.316215
$757$	− 3.76947i	− 0.137004i	−0.997651	−	0.0685019i	$-0.978178\pi$
$757$	− 3.76947i	− 0.137004i	0.997651	−	0.0685019i	$-0.0218219\pi$
$758$	20.9122i	0.759566i
$759$	87.7127	3.18377
$760$	0	0
$761$	18.3605	0.665568	0.332784	−	0.943003i	$-0.392012\pi$
$761$	18.3605	0.665568	0.332784	+	0.943003i	$0.392012\pi$
$762$	− 28.8416i	− 1.04482i
$763$	− 39.0767i	− 1.41467i
$764$	−19.3779	−0.701068
$765$	0	0
$766$	10.3511	0.374000
$767$	17.0851i	0.616908i
$768$	− 2.25561i	− 0.0813923i
$769$	38.1300	1.37500	0.687501	−	0.726183i	$-0.258708\pi$
$769$	38.1300	1.37500	0.687501	+	0.726183i	$0.258708\pi$
$770$	0	0
$771$	6.18431	0.222722
$772$	− 5.42851i	− 0.195376i
$773$	29.1575i	1.04872i	0.851496	+	0.524361i	$0.175696\pi$
$773$	29.1575i	1.04872i	−0.851496	+	0.524361i	$0.824304\pi$
$774$	5.24285	0.188450
$775$	0	0
$776$	3.93972	0.141428
$777$	1.31241i	0.0470825i
$778$	− 6.56620i	− 0.235410i
$779$	−11.6489	−0.417366
$780$	0	0
$781$	−19.6489	−0.703094
$782$	− 49.0543i	− 1.75418i
$783$	1.71228i	0.0611920i
$784$	−10.8546	−0.387664
$785$	0	0
$786$	−4.77121	−0.170183
$787$	− 47.0165i	− 1.67596i	−0.545704	−	0.837978i	$-0.683738\pi$
$787$	− 47.0165i	− 1.67596i	0.545704	−	0.837978i	$-0.316262\pi$
$788$	15.6489i	0.557470i
$789$	−6.19624	−0.220592
$790$	0	0
$791$	74.5750	2.65158
$792$	− 10.7263i	− 0.381144i
$793$	− 45.7782i	− 1.62563i
$794$	−23.5284	−0.834990
$795$	0	0
$796$	18.0499	0.639763
$797$	− 42.6359i	− 1.51024i	−0.655586	−	0.755121i	$-0.727578\pi$
$797$	− 42.6359i	− 1.51024i	0.655586	−	0.755121i	$-0.272422\pi$
$798$	9.53101i	0.337394i
$799$	−38.6412	−1.36703
$800$	0	0
$801$	−20.8777	−0.737678
$802$	6.22041i	0.219650i
$803$	24.1808i	0.853323i
$804$	9.27102	0.326964
$805$	0	0
$806$	−14.2908	−0.503372
$807$	− 21.9736i	− 0.773506i
$808$	− 3.19798i	− 0.112504i
$809$	−49.4630	−1.73903	−0.869514	−	0.493909i	$-0.835568\pi$
$809$	−49.4630	−1.73903	−0.869514	+	0.493909i	$0.835568\pi$
$810$	0	0
$811$	−16.7816	−0.589280	−0.294640	−	0.955608i	$-0.595200\pi$
$811$	−16.7816	−0.589280	−0.294640	+	0.955608i	$0.595200\pi$
$812$	3.51628i	0.123397i
$813$	− 59.4476i	− 2.08492i
$814$	0.707457	0.0247964
$815$	0	0
$816$	−14.6188	−0.511760
$817$	2.51122i	0.0878564i
$818$	34.4905i	1.20593i
$819$	−27.9461	−0.976515
$820$	0	0
$821$	11.5337	0.402527	0.201264	−	0.979537i	$-0.435495\pi$
$821$	11.5337	0.402527	0.201264	+	0.979537i	$0.435495\pi$
$822$	− 12.0972i	− 0.421939i
$823$	− 32.6309i	− 1.13744i	−0.822531	−	0.568720i	$-0.807439\pi$
$823$	− 32.6309i	− 1.13744i	0.822531	−	0.568720i	$-0.192561\pi$
$824$	10.6868	0.372291
$825$	0	0
$826$	22.7893	0.792940
$827$	6.64650i	0.231122i	0.993300	+	0.115561i	$0.0368665\pi$
$827$	6.64650i	0.231122i	−0.993300	+	0.115561i	$0.963133\pi$
$828$	− 15.8020i	− 0.549158i
$829$	30.9217	1.07395	0.536977	−	0.843597i	$-0.319566\pi$
$829$	30.9217	1.07395	0.536977	+	0.843597i	$0.319566\pi$
$830$	0	0
$831$	−2.17025	−0.0752852
$832$	3.16784i	0.109825i
$833$	70.3495i	2.43747i
$834$	22.9173	0.793561
$835$	0	0
$836$	5.13770	0.177691
$837$	9.28243i	0.320848i
$838$	10.6265i	0.367086i
$839$	48.7109	1.68169	0.840844	−	0.541277i	$-0.182059\pi$
$839$	48.7109	1.68169	0.840844	+	0.541277i	$0.182059\pi$
$840$	0	0
$841$	−28.3075	−0.976121
$842$	− 1.98021i	− 0.0682426i
$843$	33.0928i	1.13978i
$844$	7.50857	0.258456
$845$	0	0
$846$	−12.4476	−0.427958
$847$	65.0551i	2.23532i
$848$	− 0.225470i	− 0.00774267i
$849$	59.0070	2.02512
$850$	0	0
$851$	1.04222	0.0357270
$852$	8.62648i	0.295538i
$853$	− 46.1447i	− 1.57997i	−0.613129	−	0.789983i	$-0.710089\pi$
$853$	− 46.1447i	− 1.57997i	0.613129	−	0.789983i	$-0.289911\pi$
$854$	−61.0620	−2.08950
$855$	0	0
$856$	10.8168	0.369709
$857$	− 8.40607i	− 0.287146i	−0.989640	−	0.143573i	$-0.954141\pi$
$857$	− 8.40607i	− 0.287146i	0.989640	−	0.143573i	$-0.0458592\pi$
$858$	36.7109i	1.25329i
$859$	8.49581	0.289873	0.144937	−	0.989441i	$-0.453702\pi$
$859$	8.49581	0.289873	0.144937	+	0.989441i	$0.453702\pi$
$860$	0	0
$861$	−111.026	−3.78375
$862$	15.0774i	0.513539i
$863$	− 3.37352i	− 0.114836i	−0.998350	−	0.0574179i	$-0.981713\pi$
$863$	− 3.37352i	− 0.114836i	0.998350	−	0.0574179i	$-0.0182868\pi$
$864$	2.05763	0.0700021
$865$	0	0
$866$	13.5337	0.459892
$867$	56.4001i	1.91545i
$868$	19.0620i	0.647007i
$869$	54.5957	1.85203
$870$	0	0
$871$	−13.0205	−0.441182
$872$	9.24791i	0.313174i
$873$	− 8.22524i	− 0.278382i
$874$	7.56885	0.256020
$875$	0	0
$876$	10.6161	0.358686
$877$	− 13.2780i	− 0.448368i	−0.974547	−	0.224184i	$-0.928028\pi$
$877$	− 13.2780i	− 0.448368i	0.974547	−	0.224184i	$-0.0719716\pi$
$878$	− 39.1773i	− 1.32217i
$879$	50.6738	1.70918
$880$	0	0
$881$	−26.6489	−0.897825	−0.448912	−	0.893576i	$-0.648188\pi$
$881$	−26.6489	−0.897825	−0.448912	+	0.893576i	$0.648188\pi$
$882$	22.6619i	0.763066i
$883$	47.7884i	1.60821i	0.594490	+	0.804103i	$0.297354\pi$
$883$	47.7884i	1.60821i	−0.594490	+	0.804103i	$0.702646\pi$
$884$	20.5310	0.690532
$885$	0	0
$886$	19.3132	0.648841
$887$	− 36.3304i	− 1.21985i	−0.792457	−	0.609927i	$-0.791199\pi$
$887$	− 36.3304i	− 1.21985i	0.792457	−	0.609927i	$-0.208801\pi$
$888$	− 0.310596i	− 0.0104229i
$889$	54.0295	1.81209
$890$	0	0
$891$	56.0242	1.87688
$892$	27.8091i	0.931116i
$893$	− 5.96216i	− 0.199516i
$894$	13.3977	0.448086
$895$	0	0
$896$	4.22547	0.141163
$897$	54.0825i	1.80576i
$898$	− 41.4131i	− 1.38197i
$899$	3.75406	0.125205
$900$	0	0
$901$	−1.46129	−0.0486826
$902$	59.8486i	1.99274i
$903$	23.9344i	0.796488i
$904$	−17.6489	−0.586994
$905$	0	0
$906$	−34.5059	−1.14638
$907$	− 39.3873i	− 1.30784i	−0.756566	−	0.653918i	$-0.773124\pi$
$907$	− 39.3873i	− 1.30784i	0.756566	−	0.653918i	$-0.226876\pi$
$908$	− 8.91223i	− 0.295763i
$909$	−6.67664	−0.221450
$910$	0	0
$911$	−20.5561	−0.681054	−0.340527	−	0.940235i	$-0.610605\pi$
$911$	−20.5561	−0.681054	−0.340527	+	0.940235i	$0.610605\pi$
$912$	− 2.25561i	− 0.0746907i
$913$	− 62.1654i	− 2.05738i
$914$	37.8392	1.25161
$915$	0	0
$916$	−13.6489	−0.450973
$917$	− 8.93799i	− 0.295158i
$918$	− 13.3357i	− 0.440143i
$919$	−12.4054	−0.409216	−0.204608	−	0.978844i	$-0.565592\pi$
$919$	−12.4054	−0.409216	−0.204608	+	0.978844i	$0.565592\pi$
$920$	0	0
$921$	38.8425	1.27990
$922$	1.58864i	0.0523190i
$923$	− 12.1153i	− 0.398779i
$924$	48.9674	1.61091
$925$	0	0
$926$	40.3581	1.32625
$927$	− 22.3115i	− 0.732806i
$928$	− 0.832162i	− 0.0273171i
$929$	31.3330	1.02800	0.514002	−	0.857789i	$-0.328162\pi$
$929$	31.3330	1.02800	0.514002	+	0.857789i	$0.328162\pi$
$930$	0	0
$931$	−10.8546	−0.355745
$932$	23.2754i	0.762411i
$933$	17.7615i	0.581487i
$934$	39.5130	1.29290
$935$	0	0
$936$	6.61372	0.216176
$937$	7.27299i	0.237598i	0.992918	+	0.118799i	$0.0379044\pi$
$937$	7.27299i	0.237598i	−0.992918	+	0.118799i	$0.962096\pi$
$938$	17.3676i	0.567071i
$939$	56.7688	1.85258
$940$	0	0
$941$	6.72128	0.219107	0.109554	−	0.993981i	$-0.465058\pi$
$941$	6.72128	0.219107	0.109554	+	0.993981i	$0.465058\pi$
$942$	− 28.8416i	− 0.939710i
$943$	88.1689i	2.87117i
$944$	−5.39331	−0.175537
$945$	0	0
$946$	12.9019	0.419476
$947$	10.0757i	0.327416i	0.986509	+	0.163708i	$0.0523454\pi$
$947$	10.0757i	0.327416i	−0.986509	+	0.163708i	$0.947655\pi$
$948$	− 23.9692i	− 0.778483i
$949$	−14.9096	−0.483986
$950$	0	0
$951$	−53.9193	−1.74845
$952$	− 27.3856i	− 0.887573i
$953$	8.14473i	0.263834i	0.991261	+	0.131917i	$0.0421132\pi$
$953$	8.14473i	0.263834i	−0.991261	+	0.131917i	$0.957887\pi$
$954$	−0.470730	−0.0152404
$955$	0	0
$956$	3.72898	0.120604
$957$	− 9.64363i	− 0.311734i
$958$	− 7.61107i	− 0.245903i
$959$	22.6619	0.731791
$960$	0	0
$961$	−10.6489	−0.343513
$962$	0.436209i	0.0140639i
$963$	− 22.5829i	− 0.727724i
$964$	1.48878	0.0479505
$965$	0	0
$966$	72.1388	2.32103
$967$	47.1773i	1.51712i	0.651604	+	0.758560i	$0.274097\pi$
$967$	47.1773i	1.51712i	−0.651604	+	0.758560i	$0.725903\pi$
$968$	− 15.3960i	− 0.494845i
$969$	−14.6188	−0.469623
$970$	0	0
$971$	0.230528	0.00739801	0.00369901	−	0.999993i	$-0.498823\pi$
$971$	0.230528	0.00739801	0.00369901	+	0.999993i	$0.498823\pi$
$972$	− 18.4234i	− 0.590932i
$973$	42.9313i	1.37632i
$974$	20.3907	0.653359
$975$	0	0
$976$	14.4509	0.462563
$977$	− 5.80905i	− 0.185848i	−0.995673	−	0.0929240i	$-0.970379\pi$
$977$	− 5.80905i	− 0.185848i	0.995673	−	0.0929240i	$-0.0296214\pi$
$978$	25.8794i	0.827533i
$979$	−51.3770	−1.64202
$980$	0	0
$981$	19.3075	0.616441
$982$	25.0224i	0.798498i
$983$	22.3511i	0.712889i	0.934317	+	0.356444i	$0.116011\pi$
$983$	22.3511i	0.712889i	−0.934317	+	0.356444i	$0.883989\pi$
$984$	26.2754	0.837629
$985$	0	0
$986$	−5.39331	−0.171758
$987$	− 56.8254i	− 1.80877i
$988$	3.16784i	0.100782i
$989$	19.0070	0.604388
$990$	0	0
$991$	−34.9415	−1.10995	−0.554976	−	0.831866i	$-0.687273\pi$
$991$	−34.9415	−1.10995	−0.554976	+	0.831866i	$0.687273\pi$
$992$	− 4.51122i	− 0.143231i
$993$	− 69.3746i	− 2.20154i
$994$	−16.1601	−0.512568
$995$	0	0
$996$	−27.2925	−0.864797
$997$	− 9.35282i	− 0.296207i	−0.988972	−	0.148103i	$-0.952683\pi$
$997$	− 9.35282i	− 0.296207i	0.988972	−	0.148103i	$-0.0473168\pi$
$998$	− 22.6111i	− 0.715741i
$999$	0.283334	0.00896430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.b.g.799.5		6
5.2	odd	4		950.2.a.k.1.2	✓	3
5.3	odd	4		950.2.a.m.1.2	yes	3
5.4	even	2	inner	950.2.b.g.799.2		6
15.2	even	4		8550.2.a.co.1.1		3
15.8	even	4		8550.2.a.cj.1.3		3
20.3	even	4		7600.2.a.bm.1.2		3
20.7	even	4		7600.2.a.cb.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.k.1.2	✓	3	5.2	odd	4
950.2.a.m.1.2	yes	3	5.3	odd	4
950.2.b.g.799.2		6	5.4	even	2	inner
950.2.b.g.799.5		6	1.1	even	1	trivial
7600.2.a.bm.1.2		3	20.3	even	4
7600.2.a.cb.1.2		3	20.7	even	4
8550.2.a.cj.1.3		3	15.8	even	4
8550.2.a.co.1.1		3	15.2	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.25561i q^{3} -1.00000 q^{4} +2.25561 q^{6} +4.22547i q^{7} -1.00000i q^{8} -2.08777 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -2.25561i q^{3} -1.00000 q^{4} +2.25561 q^{6} +4.22547i q^{7} -1.00000i q^{8} -2.08777 q^{9} -5.13770 q^{11} +2.25561i q^{12} -3.16784i q^{13} -4.22547 q^{14} +1.00000 q^{16} -6.48108i q^{17} -2.08777i q^{18} +1.00000 q^{19} +9.53101 q^{21} -5.13770i q^{22} -7.56885i q^{23} -2.25561 q^{24} +3.16784 q^{26} -2.05763i q^{27} -4.22547i q^{28} -0.832162 q^{29} -4.51122 q^{31} +1.00000i q^{32} +11.5886i q^{33} +6.48108 q^{34} +2.08777 q^{36} +0.137699i q^{37} +1.00000i q^{38} -7.14540 q^{39} -11.6489 q^{41} +9.53101i q^{42} +2.51122i q^{43} +5.13770 q^{44} +7.56885 q^{46} -5.96216i q^{47} -2.25561i q^{48} -10.8546 q^{49} -14.6188 q^{51} +3.16784i q^{52} -0.225470i q^{53} +2.05763 q^{54} +4.22547 q^{56} -2.25561i q^{57} -0.832162i q^{58} -5.39331 q^{59} +14.4509 q^{61} -4.51122i q^{62} -8.82181i q^{63} -1.00000 q^{64} -11.5886 q^{66} -4.11021i q^{67} +6.48108i q^{68} -17.0724 q^{69} +3.82446 q^{71} +2.08777i q^{72} -4.70655i q^{73} -0.137699 q^{74} -1.00000 q^{76} -21.7092i q^{77} -7.14540i q^{78} -10.6265 q^{79} -10.9045 q^{81} -11.6489i q^{82} +12.0999i q^{83} -9.53101 q^{84} -2.51122 q^{86} +1.87703i q^{87} +5.13770i q^{88} +10.0000 q^{89} +13.3856 q^{91} +7.56885i q^{92} +10.1755i q^{93} +5.96216 q^{94} +2.25561 q^{96} +3.93972i q^{97} -10.8546i q^{98} +10.7263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9	\( 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} + 6 q^{19} - 22 q^{21} - 4 q^{24} - 4 q^{26} - 28 q^{29} - 8 q^{31} + 8 q^{34} + 26 q^{36} - 58 q^{39} - 16 q^{41} - 4 q^{44} + 28 q^{46} - 50 q^{49} - 22 q^{51} + 14 q^{54} + 4 q^{56} + 12 q^{59} + 44 q^{61} - 6 q^{64} + 8 q^{66} - 16 q^{69} - 4 q^{71} + 34 q^{74} - 6 q^{76} - 48 q^{79} - 2 q^{81} + 22 q^{84} + 4 q^{86} + 60 q^{89} - 14 q^{91} - 26 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 + 6 * q^19 - 22 * q^21 - 4 * q^24 - 4 * q^26 - 28 * q^29 - 8 * q^31 + 8 * q^34 + 26 * q^36 - 58 * q^39 - 16 * q^41 - 4 * q^44 + 28 * q^46 - 50 * q^49 - 22 * q^51 + 14 * q^54 + 4 * q^56 + 12 * q^59 + 44 * q^61 - 6 * q^64 + 8 * q^66 - 16 * q^69 - 4 * q^71 + 34 * q^74 - 6 * q^76 - 48 * q^79 - 2 * q^81 + 22 * q^84 + 4 * q^86 + 60 * q^89 - 14 * q^91 - 26 * q^94 + 4 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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