LMFDB - Embedded newform 1850.2.b.o.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(149,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, 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("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3182656.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{3} + 25x^{2} - 10x + 2 $ x^6 - 2x^3 + 25x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.2
Root			$0.203364 - 0.203364i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.o.149.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} -2.91729i q^{7} +1.00000i q^{8} +2.83457 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} -2.91729i q^{7} +1.00000i q^{8} +2.83457 q^{9} +6.51056 q^{11} -0.406728i q^{12} -0.813457i q^{13} -2.91729 q^{14} +1.00000 q^{16} +2.51056i q^{17} -2.83457i q^{18} -0.406728 q^{19} +1.18654 q^{21} -6.51056i q^{22} +5.02112i q^{23} -0.406728 q^{24} -0.813457 q^{26} +2.37309i q^{27} +2.91729i q^{28} +5.32401 q^{29} -8.75186 q^{31} -1.00000i q^{32} +2.64803i q^{33} +2.51056 q^{34} -2.83457 q^{36} +1.00000i q^{37} +0.406728i q^{38} +0.330856 q^{39} +6.34513 q^{41} -1.18654i q^{42} -7.32401i q^{43} -6.51056 q^{44} +5.02112 q^{46} +5.42784i q^{47} +0.406728i q^{48} -1.51056 q^{49} -1.02112 q^{51} +0.813457i q^{52} -2.34513i q^{53} +2.37309 q^{54} +2.91729 q^{56} -0.165428i q^{57} -5.32401i q^{58} +1.42784 q^{59} -1.32401 q^{61} +8.75186i q^{62} -8.26926i q^{63} -1.00000 q^{64} +2.64803 q^{66} +5.42784i q^{67} -2.51056i q^{68} -2.04223 q^{69} +14.6480 q^{71} +2.83457i q^{72} -11.0211i q^{73} +1.00000 q^{74} +0.406728 q^{76} -18.9932i q^{77} -0.330856i q^{78} +1.75870 q^{79} +7.53851 q^{81} -6.34513i q^{82} -7.05476i q^{83} -1.18654 q^{84} -7.32401 q^{86} +2.16543i q^{87} +6.51056i q^{88} -6.00000 q^{89} -2.37309 q^{91} -5.02112i q^{92} -3.55963i q^{93} +5.42784 q^{94} +0.406728 q^{96} -2.34513i q^{97} +1.51056i q^{98} +18.4546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 22 * q^9	$ 6 q - 6 q^{4} - 22 q^{9} + 22 q^{11} + 2 q^{14} + 6 q^{16} + 12 q^{21} + 10 q^{29} + 6 q^{31} - 2 q^{34} + 22 q^{36} + 80 q^{39} - 18 q^{41} - 22 q^{44} - 4 q^{46} + 8 q^{49} + 28 q^{51} + 24 q^{54} - 2 q^{56} - 28 q^{59} + 14 q^{61} - 6 q^{64} - 28 q^{66} + 56 q^{69} + 44 q^{71} + 6 q^{74} + 52 q^{79} + 94 q^{81} - 12 q^{84} - 22 q^{86} - 36 q^{89} - 24 q^{91} - 4 q^{94} - 38 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 22 * q^9 + 22 * q^11 + 2 * q^14 + 6 * q^16 + 12 * q^21 + 10 * q^29 + 6 * q^31 - 2 * q^34 + 22 * q^36 + 80 * q^39 - 18 * q^41 - 22 * q^44 - 4 * q^46 + 8 * q^49 + 28 * q^51 + 24 * q^54 - 2 * q^56 - 28 * q^59 + 14 * q^61 - 6 * q^64 - 28 * q^66 + 56 * q^69 + 44 * q^71 + 6 * q^74 + 52 * q^79 + 94 * q^81 - 12 * q^84 - 22 * q^86 - 36 * q^89 - 24 * q^91 - 4 * q^94 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$1$	$-1$

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
$3$	0.406728i	0.234825i	0.993083	+	0.117412i	$0.0374599\pi$
$3$	0.406728i	0.234825i	−0.993083	+	0.117412i	$0.962540\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.406728	0.166046
$7$	− 2.91729i	− 1.10263i	−0.834297	−	0.551315i	$-0.814126\pi$
$7$	− 2.91729i	− 1.10263i	0.834297	−	0.551315i	$-0.185874\pi$
$8$	1.00000i	0.353553i
$9$	2.83457	0.944857
$10$	0	0
$11$	6.51056	1.96301	0.981503	−	0.191444i	$-0.0613171\pi$
$11$	6.51056	1.96301	0.981503	+	0.191444i	$0.0613171\pi$
$12$	− 0.406728i	− 0.117412i
$13$	− 0.813457i	− 0.225612i	−0.993617	−	0.112806i	$-0.964016\pi$
$13$	− 0.813457i	− 0.225612i	0.993617	−	0.112806i	$-0.0359839\pi$
$14$	−2.91729	−0.779677
$15$	0	0
$16$	1.00000	0.250000
$17$	2.51056i	0.608900i	0.952528	+	0.304450i	$0.0984726\pi$
$17$	2.51056i	0.608900i	−0.952528	+	0.304450i	$0.901527\pi$
$18$	− 2.83457i	− 0.668115i
$19$	−0.406728	−0.0933099	−0.0466550	−	0.998911i	$-0.514856\pi$
$19$	−0.406728	−0.0933099	−0.0466550	+	0.998911i	$0.514856\pi$
$20$	0	0
$21$	1.18654	0.258925
$22$	− 6.51056i	− 1.38806i
$23$	5.02112i	1.04697i	0.852033	+	0.523487i	$0.175369\pi$
$23$	5.02112i	1.04697i	−0.852033	+	0.523487i	$0.824631\pi$
$24$	−0.406728	−0.0830231
$25$	0	0
$26$	−0.813457	−0.159532
$27$	2.37309i	0.456701i
$28$	2.91729i	0.551315i
$29$	5.32401	0.988645	0.494322	−	0.869279i	$-0.335416\pi$
$29$	5.32401	0.988645	0.494322	+	0.869279i	$0.335416\pi$
$30$	0	0
$31$	−8.75186	−1.57188	−0.785940	−	0.618303i	$-0.787821\pi$
$31$	−8.75186	−1.57188	−0.785940	+	0.618303i	$0.787821\pi$
$32$	− 1.00000i	− 0.176777i
$33$	2.64803i	0.460963i
$34$	2.51056	0.430557
$35$	0	0
$36$	−2.83457	−0.472429
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	0.406728i	0.0659801i
$39$	0.330856	0.0529794
$40$	0	0
$41$	6.34513	0.990943	0.495471	−	0.868624i	$-0.334995\pi$
$41$	6.34513	0.990943	0.495471	+	0.868624i	$0.334995\pi$
$42$	− 1.18654i	− 0.183088i
$43$	− 7.32401i	− 1.11690i	−0.829538	−	0.558451i	$-0.811396\pi$
$43$	− 7.32401i	− 1.11690i	0.829538	−	0.558451i	$-0.188604\pi$
$44$	−6.51056	−0.981503
$45$	0	0
$46$	5.02112	0.740323
$47$	5.42784i	0.791732i	0.918308	+	0.395866i	$0.129556\pi$
$47$	5.42784i	0.791732i	−0.918308	+	0.395866i	$0.870444\pi$
$48$	0.406728i	0.0587062i
$49$	−1.51056	−0.215794
$50$	0	0
$51$	−1.02112	−0.142985
$52$	0.813457i	0.112806i
$53$	− 2.34513i	− 0.322128i	−0.986944	−	0.161064i	$-0.948507\pi$
$53$	− 2.34513i	− 0.322128i	0.986944	−	0.161064i	$-0.0514926\pi$
$54$	2.37309	0.322936
$55$	0	0
$56$	2.91729	0.389839
$57$	− 0.165428i	− 0.0219115i
$58$	− 5.32401i	− 0.699077i
$59$	1.42784	0.185889	0.0929447	−	0.995671i	$-0.470372\pi$
$59$	1.42784	0.185889	0.0929447	+	0.995671i	$0.470372\pi$
$60$	0	0
$61$	−1.32401	−0.169523	−0.0847613	−	0.996401i	$-0.527013\pi$
$61$	−1.32401	−0.169523	−0.0847613	+	0.996401i	$0.527013\pi$
$62$	8.75186i	1.11149i
$63$	− 8.26926i	− 1.04183i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.64803	0.325950
$67$	5.42784i	0.663117i	0.943435	+	0.331558i	$0.107574\pi$
$67$	5.42784i	0.663117i	−0.943435	+	0.331558i	$0.892426\pi$
$68$	− 2.51056i	− 0.304450i
$69$	−2.04223	−0.245856
$70$	0	0
$71$	14.6480	1.73840	0.869201	−	0.494460i	$-0.164634\pi$
$71$	14.6480	1.73840	0.869201	+	0.494460i	$0.164634\pi$
$72$	2.83457i	0.334058i
$73$	− 11.0211i	− 1.28992i	−0.764215	−	0.644962i	$-0.776873\pi$
$73$	− 11.0211i	− 1.28992i	0.764215	−	0.644962i	$-0.223127\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	0.406728	0.0466550
$77$	− 18.9932i	− 2.16447i
$78$	− 0.330856i	− 0.0374621i
$79$	1.75870	0.197869	0.0989346	−	0.995094i	$-0.468457\pi$
$79$	1.75870	0.197869	0.0989346	+	0.995094i	$0.468457\pi$
$80$	0	0
$81$	7.53851	0.837613
$82$	− 6.34513i	− 0.700702i
$83$	− 7.05476i	− 0.774360i	−0.922004	−	0.387180i	$-0.873449\pi$
$83$	− 7.05476i	− 0.774360i	0.922004	−	0.387180i	$-0.126551\pi$
$84$	−1.18654	−0.129462
$85$	0	0
$86$	−7.32401	−0.789769
$87$	2.16543i	0.232158i
$88$	6.51056i	0.694028i
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−2.37309	−0.248767
$92$	− 5.02112i	− 0.523487i
$93$	− 3.55963i	− 0.369116i
$94$	5.42784	0.559839
$95$	0	0
$96$	0.406728	0.0415115
$97$	− 2.34513i	− 0.238112i	−0.992888	−	0.119056i	$-0.962013\pi$
$97$	− 2.34513i	− 0.238112i	0.992888	−	0.119056i	$-0.0379868\pi$
$98$	1.51056i	0.152589i
$99$	18.4546	1.85476
$100$	0	0
$101$	−8.20766	−0.816693	−0.408346	−	0.912827i	$-0.633894\pi$
$101$	−8.20766	−0.816693	−0.408346	+	0.912827i	$0.633894\pi$
$102$	1.02112i	0.101105i
$103$	− 8.81346i	− 0.868416i	−0.900813	−	0.434208i	$-0.857028\pi$
$103$	− 8.81346i	− 0.868416i	0.900813	−	0.434208i	$-0.142972\pi$
$104$	0.813457	0.0797660
$105$	0	0
$106$	−2.34513	−0.227779
$107$	− 15.2624i	− 1.47547i	−0.675089	−	0.737737i	$-0.735895\pi$
$107$	− 15.2624i	− 1.47547i	0.675089	−	0.737737i	$-0.264105\pi$
$108$	− 2.37309i	− 0.228350i
$109$	−4.30290	−0.412143	−0.206072	−	0.978537i	$-0.566068\pi$
$109$	−4.30290	−0.412143	−0.206072	+	0.978537i	$0.566068\pi$
$110$	0	0
$111$	−0.406728	−0.0386050
$112$	− 2.91729i	− 0.275658i
$113$	− 9.15859i	− 0.861567i	−0.902455	−	0.430784i	$-0.858237\pi$
$113$	− 9.15859i	− 0.861567i	0.902455	−	0.430784i	$-0.141763\pi$
$114$	−0.165428	−0.0154938
$115$	0	0
$116$	−5.32401	−0.494322
$117$	− 2.30580i	− 0.213171i
$118$	− 1.42784i	− 0.131444i
$119$	7.32401	0.671391
$120$	0	0
$121$	31.3874	2.85340
$122$	1.32401i	0.119871i
$123$	2.58074i	0.232698i
$124$	8.75186	0.785940
$125$	0	0
$126$	−8.26926	−0.736684
$127$	8.61439i	0.764403i	0.924079	+	0.382202i	$0.124834\pi$
$127$	8.61439i	0.764403i	−0.924079	+	0.382202i	$0.875166\pi$
$128$	1.00000i	0.0883883i
$129$	2.97888	0.262276
$130$	0	0
$131$	13.4278	1.17320	0.586598	−	0.809878i	$-0.300467\pi$
$131$	13.4278	1.17320	0.586598	+	0.809878i	$0.300467\pi$
$132$	− 2.64803i	− 0.230481i
$133$	1.18654i	0.102886i
$134$	5.42784	0.468894
$135$	0	0
$136$	−2.51056	−0.215279
$137$	14.6903i	1.25507i	0.778587	+	0.627537i	$0.215937\pi$
$137$	14.6903i	1.25507i	−0.778587	+	0.627537i	$0.784063\pi$
$138$	2.04223i	0.173846i
$139$	−17.3662	−1.47299	−0.736493	−	0.676445i	$-0.763519\pi$
$139$	−17.3662	−1.47299	−0.736493	+	0.676445i	$0.763519\pi$
$140$	0	0
$141$	−2.20766	−0.185918
$142$	− 14.6480i	− 1.22924i
$143$	− 5.29606i	− 0.442879i
$144$	2.83457	0.236214
$145$	0	0
$146$	−11.0211	−0.912114
$147$	− 0.614387i	− 0.0506738i
$148$	− 1.00000i	− 0.0821995i
$149$	0.207658	0.0170120	0.00850601	−	0.999964i	$-0.497292\pi$
$149$	0.207658	0.0170120	0.00850601	+	0.999964i	$0.497292\pi$
$150$	0	0
$151$	0.813457	0.0661982	0.0330991	−	0.999452i	$-0.489462\pi$
$151$	0.813457	0.0661982	0.0330991	+	0.999452i	$0.489462\pi$
$152$	− 0.406728i	− 0.0329900i
$153$	7.11636i	0.575323i
$154$	−18.9932	−1.53051
$155$	0	0
$156$	−0.330856	−0.0264897
$157$	− 5.32401i	− 0.424903i	−0.977172	−	0.212451i	$-0.931855\pi$
$157$	− 5.32401i	− 0.424903i	0.977172	−	0.212451i	$-0.0681447\pi$
$158$	− 1.75870i	− 0.139915i
$159$	0.953831	0.0756437
$160$	0	0
$161$	14.6480	1.15443
$162$	− 7.53851i	− 0.592282i
$163$	15.2008i	1.19062i	0.803496	+	0.595310i	$0.202971\pi$
$163$	15.2008i	1.19062i	−0.803496	+	0.595310i	$0.797029\pi$
$164$	−6.34513	−0.495471
$165$	0	0
$166$	−7.05476	−0.547555
$167$	12.4826i	0.965933i	0.875639	+	0.482966i	$0.160441\pi$
$167$	12.4826i	0.965933i	−0.875639	+	0.482966i	$0.839559\pi$
$168$	1.18654i	0.0915438i
$169$	12.3383	0.949099
$170$	0	0
$171$	−1.15290	−0.0881645
$172$	7.32401i	0.558451i
$173$	23.0354i	1.75135i	0.482903	+	0.875674i	$0.339583\pi$
$173$	23.0354i	1.75135i	−0.482903	+	0.875674i	$0.660417\pi$
$174$	2.16543	0.164161
$175$	0	0
$176$	6.51056	0.490752
$177$	0.580745i	0.0436514i
$178$	6.00000i	0.449719i
$179$	−24.2835	−1.81504	−0.907518	−	0.420013i	$-0.862026\pi$
$179$	−24.2835	−1.81504	−0.907518	+	0.420013i	$0.862026\pi$
$180$	0	0
$181$	2.16543	0.160955	0.0804775	−	0.996756i	$-0.474355\pi$
$181$	2.16543	0.160955	0.0804775	+	0.996756i	$0.474355\pi$
$182$	2.37309i	0.175905i
$183$	− 0.538514i	− 0.0398081i
$184$	−5.02112	−0.370162
$185$	0	0
$186$	−3.55963	−0.261005
$187$	16.3451i	1.19527i
$188$	− 5.42784i	− 0.395866i
$189$	6.92297	0.503572
$190$	0	0
$191$	−19.3326	−1.39886	−0.699429	−	0.714702i	$-0.746562\pi$
$191$	−19.3326	−1.39886	−0.699429	+	0.714702i	$0.746562\pi$
$192$	− 0.406728i	− 0.0293531i
$193$	− 20.0422i	− 1.44267i	−0.692586	−	0.721336i	$-0.743529\pi$
$193$	− 20.0422i	− 1.44267i	0.692586	−	0.721336i	$-0.256471\pi$
$194$	−2.34513	−0.168370
$195$	0	0
$196$	1.51056	0.107897
$197$	− 15.6269i	− 1.11337i	−0.830723	−	0.556686i	$-0.812073\pi$
$197$	− 15.6269i	− 1.11337i	0.830723	−	0.556686i	$-0.187927\pi$
$198$	− 18.4546i	− 1.31151i
$199$	−20.2835	−1.43786	−0.718931	−	0.695082i	$-0.755368\pi$
$199$	−20.2835	−1.43786	−0.718931	+	0.695082i	$0.755368\pi$
$200$	0	0
$201$	−2.20766	−0.155716
$202$	8.20766i	0.577489i
$203$	− 15.5317i	− 1.09011i
$204$	1.02112	0.0714924
$205$	0	0
$206$	−8.81346	−0.614063
$207$	14.2327i	0.989242i
$208$	− 0.813457i	− 0.0564031i
$209$	−2.64803	−0.183168
$210$	0	0
$211$	18.7182	1.28862	0.644308	−	0.764766i	$-0.277146\pi$
$211$	18.7182	1.28862	0.644308	+	0.764766i	$0.277146\pi$
$212$	2.34513i	0.161064i
$213$	5.95777i	0.408220i
$214$	−15.2624	−1.04332
$215$	0	0
$216$	−2.37309	−0.161468
$217$	25.5317i	1.73320i
$218$	4.30290i	0.291429i
$219$	4.48260	0.302906
$220$	0	0
$221$	2.04223	0.137375
$222$	0.406728i	0.0272978i
$223$	− 15.7307i	− 1.05341i	−0.850049	−	0.526704i	$-0.823428\pi$
$223$	− 15.7307i	− 1.05341i	0.850049	−	0.526704i	$-0.176572\pi$
$224$	−2.91729	−0.194919
$225$	0	0
$226$	−9.15859	−0.609220
$227$	− 12.8836i	− 0.855117i	−0.903988	−	0.427559i	$-0.859374\pi$
$227$	− 12.8836i	− 0.855117i	0.903988	−	0.427559i	$-0.140626\pi$
$228$	0.165428i	0.0109557i
$229$	−5.25383	−0.347183	−0.173591	−	0.984818i	$-0.555537\pi$
$229$	−5.25383	−0.347183	−0.173591	+	0.984818i	$0.555537\pi$
$230$	0	0
$231$	7.72506	0.508271
$232$	5.32401i	0.349539i
$233$	28.3172i	1.85512i	0.373675	+	0.927560i	$0.378098\pi$
$233$	28.3172i	1.85512i	−0.373675	+	0.927560i	$0.621902\pi$
$234$	−2.30580	−0.150735
$235$	0	0
$236$	−1.42784	−0.0929447
$237$	0.715313i	0.0464646i
$238$	− 7.32401i	− 0.474745i
$239$	−14.3788	−0.930085	−0.465043	−	0.885288i	$-0.653961\pi$
$239$	−14.3788	−0.930085	−0.465043	+	0.885288i	$0.653961\pi$
$240$	0	0
$241$	18.2749	1.17719	0.588596	−	0.808427i	$-0.299681\pi$
$241$	18.2749	1.17719	0.588596	+	0.808427i	$0.299681\pi$
$242$	− 31.3874i	− 2.01766i
$243$	10.1854i	0.653393i
$244$	1.32401	0.0847613
$245$	0	0
$246$	2.58074	0.164542
$247$	0.330856i	0.0210519i
$248$	− 8.75186i	− 0.555744i
$249$	2.86937	0.181839
$250$	0	0
$251$	−1.22019	−0.0770174	−0.0385087	−	0.999258i	$-0.512261\pi$
$251$	−1.22019	−0.0770174	−0.0385087	+	0.999258i	$0.512261\pi$
$252$	8.26926i	0.520914i
$253$	32.6903i	2.05522i
$254$	8.61439	0.540515
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 27.1306i	− 1.69236i	−0.532895	−	0.846181i	$-0.678896\pi$
$257$	− 27.1306i	− 1.69236i	0.532895	−	0.846181i	$-0.321104\pi$
$258$	− 2.97888i	− 0.185457i
$259$	2.91729	0.181271
$260$	0	0
$261$	15.0913	0.934128
$262$	− 13.4278i	− 0.829575i
$263$	− 20.2133i	− 1.24641i	−0.782059	−	0.623204i	$-0.785831\pi$
$263$	− 20.2133i	− 1.24641i	0.782059	−	0.623204i	$-0.214169\pi$
$264$	−2.64803	−0.162975
$265$	0	0
$266$	1.18654	0.0727516
$267$	− 2.44037i	− 0.149348i
$268$	− 5.42784i	− 0.331558i
$269$	0.207658	0.0126611	0.00633057	−	0.999980i	$-0.497985\pi$
$269$	0.207658	0.0126611	0.00633057	+	0.999980i	$0.497985\pi$
$270$	0	0
$271$	−30.6480	−1.86174	−0.930868	−	0.365357i	$-0.880947\pi$
$271$	−30.6480	−1.86174	−0.930868	+	0.365357i	$0.880947\pi$
$272$	2.51056i	0.152225i
$273$	− 0.965202i	− 0.0584167i
$274$	14.6903	0.887471
$275$	0	0
$276$	2.04223	0.122928
$277$	16.8135i	1.01022i	0.863054	+	0.505111i	$0.168549\pi$
$277$	16.8135i	1.01022i	−0.863054	+	0.505111i	$0.831451\pi$
$278$	17.3662i	1.04156i
$279$	−24.8078	−1.48520
$280$	0	0
$281$	−14.2749	−0.851572	−0.425786	−	0.904824i	$-0.640002\pi$
$281$	−14.2749	−0.851572	−0.425786	+	0.904824i	$0.640002\pi$
$282$	2.20766i	0.131464i
$283$	− 13.2288i	− 0.786369i	−0.919460	−	0.393184i	$-0.871373\pi$
$283$	− 13.2288i	− 0.786369i	0.919460	−	0.393184i	$-0.128627\pi$
$284$	−14.6480	−0.869201
$285$	0	0
$286$	−5.29606	−0.313162
$287$	− 18.5106i	− 1.09264i
$288$	− 2.83457i	− 0.167029i
$289$	10.6971	0.629241
$290$	0	0
$291$	0.953831	0.0559146
$292$	11.0211i	0.644962i
$293$	2.34513i	0.137004i	0.997651	+	0.0685020i	$0.0218219\pi$
$293$	2.34513i	0.137004i	−0.997651	+	0.0685020i	$0.978178\pi$
$294$	−0.614387	−0.0358318
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	15.4501i	0.896507i
$298$	− 0.207658i	− 0.0120293i
$299$	4.08446	0.236210
$300$	0	0
$301$	−21.3662	−1.23153
$302$	− 0.813457i	− 0.0468092i
$303$	− 3.33829i	− 0.191780i
$304$	−0.406728	−0.0233275
$305$	0	0
$306$	7.11636	0.406815
$307$	23.2624i	1.32766i	0.747885	+	0.663828i	$0.231069\pi$
$307$	23.2624i	1.32766i	−0.747885	+	0.663828i	$0.768931\pi$
$308$	18.9932i	1.08224i
$309$	3.58468	0.203926
$310$	0	0
$311$	−31.3999	−1.78052	−0.890262	−	0.455449i	$-0.849479\pi$
$311$	−31.3999	−1.78052	−0.890262	+	0.455449i	$0.849479\pi$
$312$	0.330856i	0.0187310i
$313$	− 8.04223i	− 0.454574i	−0.973828	−	0.227287i	$-0.927014\pi$
$313$	− 8.04223i	− 0.454574i	0.973828	−	0.227287i	$-0.0729855\pi$
$314$	−5.32401	−0.300452
$315$	0	0
$316$	−1.75870	−0.0989346
$317$	12.3029i	0.691000i	0.938419	+	0.345500i	$0.112291\pi$
$317$	12.3029i	0.691000i	−0.938419	+	0.345500i	$0.887709\pi$
$318$	− 0.953831i	− 0.0534882i
$319$	34.6623	1.94072
$320$	0	0
$321$	6.20766	0.346478
$322$	− 14.6480i	− 0.816303i
$323$	− 1.02112i	− 0.0568164i
$324$	−7.53851	−0.418806
$325$	0	0
$326$	15.2008	0.841895
$327$	− 1.75011i	− 0.0967814i
$328$	6.34513i	0.350351i
$329$	15.8346	0.872988
$330$	0	0
$331$	−6.77981	−0.372652	−0.186326	−	0.982488i	$-0.559658\pi$
$331$	−6.77981	−0.372652	−0.186326	+	0.982488i	$0.559658\pi$
$332$	7.05476i	0.387180i
$333$	2.83457i	0.155334i
$334$	12.4826	0.683018
$335$	0	0
$336$	1.18654	0.0647312
$337$	− 10.6903i	− 0.582336i	−0.956672	−	0.291168i	$-0.905956\pi$
$337$	− 10.6903i	− 0.582336i	0.956672	−	0.291168i	$-0.0940438\pi$
$338$	− 12.3383i	− 0.671114i
$339$	3.72506	0.202317
$340$	0	0
$341$	−56.9795	−3.08561
$342$	1.15290i	0.0623417i
$343$	− 16.0143i	− 0.864689i
$344$	7.32401	0.394884
$345$	0	0
$346$	23.0354	1.23839
$347$	− 5.62691i	− 0.302069i	−0.988529	−	0.151034i	$-0.951740\pi$
$347$	− 5.62691i	− 0.302069i	0.988529	−	0.151034i	$-0.0482604\pi$
$348$	− 2.16543i	− 0.116079i
$349$	−15.1306	−0.809924	−0.404962	−	0.914334i	$-0.632715\pi$
$349$	−15.1306	−0.809924	−0.404962	+	0.914334i	$0.632715\pi$
$350$	0	0
$351$	1.93040	0.103037
$352$	− 6.51056i	− 0.347014i
$353$	35.7816i	1.90446i	0.305381	+	0.952230i	$0.401216\pi$
$353$	35.7816i	1.90446i	−0.305381	+	0.952230i	$0.598784\pi$
$354$	0.580745	0.0308662
$355$	0	0
$356$	6.00000	0.317999
$357$	2.97888i	0.157659i
$358$	24.2835i	1.28342i
$359$	−4.48260	−0.236583	−0.118291	−	0.992979i	$-0.537742\pi$
$359$	−4.48260	−0.236583	−0.118291	+	0.992979i	$0.537742\pi$
$360$	0	0
$361$	−18.8346	−0.991293
$362$	− 2.16543i	− 0.113812i
$363$	12.7661i	0.670048i
$364$	2.37309	0.124384
$365$	0	0
$366$	−0.538514	−0.0281486
$367$	21.5653i	1.12570i	0.826559	+	0.562850i	$0.190295\pi$
$367$	21.5653i	1.12570i	−0.826559	+	0.562850i	$0.809705\pi$
$368$	5.02112i	0.261744i
$369$	17.9857	0.936300
$370$	0	0
$371$	−6.84141	−0.355188
$372$	3.55963i	0.184558i
$373$	16.9230i	0.876238i	0.898917	+	0.438119i	$0.144355\pi$
$373$	16.9230i	0.876238i	−0.898917	+	0.438119i	$0.855645\pi$
$374$	16.3451	0.845187
$375$	0	0
$376$	−5.42784	−0.279920
$377$	− 4.33086i	− 0.223050i
$378$	− 6.92297i	− 0.356079i
$379$	−31.2710	−1.60628	−0.803142	−	0.595788i	$-0.796840\pi$
$379$	−31.2710	−1.60628	−0.803142	+	0.595788i	$0.796840\pi$
$380$	0	0
$381$	−3.50372	−0.179501
$382$	19.3326i	0.989142i
$383$	1.62691i	0.0831314i	0.999136	+	0.0415657i	$0.0132346\pi$
$383$	1.62691i	0.0831314i	−0.999136	+	0.0415657i	$0.986765\pi$
$384$	−0.406728	−0.0207558
$385$	0	0
$386$	−20.0422	−1.02012
$387$	− 20.7604i	− 1.05531i
$388$	2.34513i	0.119056i
$389$	31.6412	1.60427	0.802136	−	0.597141i	$-0.203697\pi$
$389$	31.6412	1.60427	0.802136	+	0.597141i	$0.203697\pi$
$390$	0	0
$391$	−12.6058	−0.637503
$392$	− 1.51056i	− 0.0762947i
$393$	5.46149i	0.275496i
$394$	−15.6269	−0.787273
$395$	0	0
$396$	−18.4546	−0.927381
$397$	39.2961i	1.97221i	0.166116	+	0.986106i	$0.446878\pi$
$397$	39.2961i	1.97221i	−0.166116	+	0.986106i	$0.553122\pi$
$398$	20.2835i	1.01672i
$399$	−0.482601	−0.0241603
$400$	0	0
$401$	−9.66914	−0.482854	−0.241427	−	0.970419i	$-0.577615\pi$
$401$	−9.66914	−0.482854	−0.241427	+	0.970419i	$0.577615\pi$
$402$	2.20766i	0.110108i
$403$	7.11926i	0.354636i
$404$	8.20766	0.408346
$405$	0	0
$406$	−15.5317	−0.770824
$407$	6.51056i	0.322716i
$408$	− 1.02112i	− 0.0505527i
$409$	26.2749	1.29921	0.649606	−	0.760271i	$-0.274934\pi$
$409$	26.2749	1.29921	0.649606	+	0.760271i	$0.274934\pi$
$410$	0	0
$411$	−5.97495	−0.294722
$412$	8.81346i	0.434208i
$413$	− 4.16543i	− 0.204967i
$414$	14.2327	0.699500
$415$	0	0
$416$	−0.813457	−0.0398830
$417$	− 7.06335i	− 0.345894i
$418$	2.64803i	0.129519i
$419$	30.1940	1.47507	0.737536	−	0.675308i	$-0.235989\pi$
$419$	30.1940	1.47507	0.737536	+	0.675308i	$0.235989\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	− 18.7182i	− 0.911188i
$423$	15.3856i	0.748074i
$424$	2.34513	0.113890
$425$	0	0
$426$	5.95777	0.288655
$427$	3.86253i	0.186921i
$428$	15.2624i	0.737737i
$429$	2.15406	0.103999
$430$	0	0
$431$	25.5653	1.23144	0.615719	−	0.787966i	$-0.288866\pi$
$431$	25.5653	1.23144	0.615719	+	0.787966i	$0.288866\pi$
$432$	2.37309i	0.114175i
$433$	32.0422i	1.53985i	0.638134	+	0.769926i	$0.279707\pi$
$433$	32.0422i	1.53985i	−0.638134	+	0.769926i	$0.720293\pi$
$434$	25.5317	1.22556
$435$	0	0
$436$	4.30290	0.206072
$437$	− 2.04223i	− 0.0976931i
$438$	− 4.48260i	− 0.214187i
$439$	−3.93840	−0.187970	−0.0939848	−	0.995574i	$-0.529961\pi$
$439$	−3.93840	−0.187970	−0.0939848	+	0.995574i	$0.529961\pi$
$440$	0	0
$441$	−4.28178	−0.203894
$442$	− 2.04223i	− 0.0971390i
$443$	− 0.0758724i	− 0.00360481i	−0.999998	−	0.00180240i	$-0.999426\pi$
$443$	− 0.0758724i	− 0.00360481i	0.999998	−	0.00180240i	$-0.000573723\pi$
$444$	0.406728	0.0193025
$445$	0	0
$446$	−15.7307	−0.744872
$447$	0.0844605i	0.00399485i
$448$	2.91729i	0.137829i
$449$	−19.2961	−0.910637	−0.455319	−	0.890329i	$-0.650475\pi$
$449$	−19.2961	−0.910637	−0.455319	+	0.890329i	$0.650475\pi$
$450$	0	0
$451$	41.3103	1.94523
$452$	9.15859i	0.430784i
$453$	0.330856i	0.0155450i
$454$	−12.8836	−0.604659
$455$	0	0
$456$	0.165428	0.00774688
$457$	− 3.00684i	− 0.140654i	−0.997524	−	0.0703271i	$-0.977596\pi$
$457$	− 3.00684i	− 0.140654i	0.997524	−	0.0703271i	$-0.0224043\pi$
$458$	5.25383i	0.245495i
$459$	−5.95777	−0.278085
$460$	0	0
$461$	−0.633755	−0.0295169	−0.0147585	−	0.999891i	$-0.504698\pi$
$461$	−0.633755	−0.0295169	−0.0147585	+	0.999891i	$0.504698\pi$
$462$	− 7.72506i	− 0.359402i
$463$	18.0422i	0.838494i	0.907872	+	0.419247i	$0.137706\pi$
$463$	18.0422i	0.838494i	−0.907872	+	0.419247i	$0.862294\pi$
$464$	5.32401	0.247161
$465$	0	0
$466$	28.3172	1.31177
$467$	23.4758i	1.08633i	0.839626	+	0.543164i	$0.182774\pi$
$467$	23.4758i	1.08633i	−0.839626	+	0.543164i	$0.817226\pi$
$468$	2.30580i	0.106586i
$469$	15.8346	0.731173
$470$	0	0
$471$	2.16543	0.0997777
$472$	1.42784i	0.0657218i
$473$	− 47.6834i	− 2.19249i
$474$	0.715313	0.0328554
$475$	0	0
$476$	−7.32401	−0.335696
$477$	− 6.64744i	− 0.304365i
$478$	14.3788i	0.657670i
$479$	8.19907	0.374625	0.187313	−	0.982300i	$-0.440022\pi$
$479$	8.19907	0.374625	0.187313	+	0.982300i	$0.440022\pi$
$480$	0	0
$481$	0.813457	0.0370904
$482$	− 18.2749i	− 0.832401i
$483$	5.95777i	0.271088i
$484$	−31.3874	−1.42670
$485$	0	0
$486$	10.1854	0.462019
$487$	− 0.953831i	− 0.0432222i	−0.999766	−	0.0216111i	$-0.993120\pi$
$487$	− 0.953831i	− 0.0432222i	0.999766	−	0.0216111i	$-0.00687956\pi$
$488$	− 1.32401i	− 0.0599353i
$489$	−6.18260	−0.279587
$490$	0	0
$491$	19.3383	0.872725	0.436362	−	0.899771i	$-0.356267\pi$
$491$	19.3383	0.872725	0.436362	+	0.899771i	$0.356267\pi$
$492$	− 2.58074i	− 0.116349i
$493$	13.3662i	0.601985i
$494$	0.330856	0.0148859
$495$	0	0
$496$	−8.75186	−0.392970
$497$	− 42.7325i	− 1.91681i
$498$	− 2.86937i	− 0.128580i
$499$	5.63550	0.252280	0.126140	−	0.992012i	$-0.459741\pi$
$499$	5.63550	0.252280	0.126140	+	0.992012i	$0.459741\pi$
$500$	0	0
$501$	−5.07703	−0.226825
$502$	1.22019i	0.0544595i
$503$	− 33.6269i	− 1.49935i	−0.661806	−	0.749675i	$-0.730210\pi$
$503$	− 33.6269i	− 1.49935i	0.661806	−	0.749675i	$-0.269790\pi$
$504$	8.26926	0.368342
$505$	0	0
$506$	32.6903	1.45326
$507$	5.01833i	0.222872i
$508$	− 8.61439i	− 0.382202i
$509$	18.6903	0.828431	0.414216	−	0.910179i	$-0.364056\pi$
$509$	18.6903	0.828431	0.414216	+	0.910179i	$0.364056\pi$
$510$	0	0
$511$	−32.1517	−1.42231
$512$	− 1.00000i	− 0.0441942i
$513$	− 0.965202i	− 0.0426147i
$514$	−27.1306	−1.19668
$515$	0	0
$516$	−2.97888	−0.131138
$517$	35.3383i	1.55418i
$518$	− 2.91729i	− 0.128178i
$519$	−9.36915	−0.411260
$520$	0	0
$521$	25.1586	1.10222	0.551109	−	0.834433i	$-0.314205\pi$
$521$	25.1586	1.10222	0.551109	+	0.834433i	$0.314205\pi$
$522$	− 15.0913i	− 0.660528i
$523$	− 7.25383i	− 0.317188i	−0.987344	−	0.158594i	$-0.949304\pi$
$523$	− 7.25383i	− 0.317188i	0.987344	−	0.158594i	$-0.0506960\pi$
$524$	−13.4278	−0.586598
$525$	0	0
$526$	−20.2133	−0.881344
$527$	− 21.9720i	− 0.957117i
$528$	2.64803i	0.115241i
$529$	−2.21160	−0.0961564
$530$	0	0
$531$	4.04733	0.175639
$532$	− 1.18654i	− 0.0514432i
$533$	− 5.16149i	− 0.223569i
$534$	−2.44037	−0.105605
$535$	0	0
$536$	−5.42784	−0.234447
$537$	− 9.87680i	− 0.426215i
$538$	− 0.207658i	− 0.00895278i
$539$	−9.83457	−0.423605
$540$	0	0
$541$	16.0422	0.689709	0.344855	−	0.938656i	$-0.387928\pi$
$541$	16.0422	0.689709	0.344855	+	0.938656i	$0.387928\pi$
$542$	30.6480i	1.31645i
$543$	0.880741i	0.0377962i
$544$	2.51056	0.107639
$545$	0	0
$546$	−0.965202	−0.0413068
$547$	− 16.0143i	− 0.684721i	−0.939569	−	0.342360i	$-0.888774\pi$
$547$	− 16.0143i	− 0.684721i	0.939569	−	0.342360i	$-0.111226\pi$
$548$	− 14.6903i	− 0.627537i
$549$	−3.75301	−0.160175
$550$	0	0
$551$	−2.16543	−0.0922503
$552$	− 2.04223i	− 0.0869231i
$553$	− 5.13063i	− 0.218177i
$554$	16.8135	0.714335
$555$	0	0
$556$	17.3662	0.736493
$557$	10.8557i	0.459970i	0.973194	+	0.229985i	$0.0738678\pi$
$557$	10.8557i	0.459970i	−0.973194	+	0.229985i	$0.926132\pi$
$558$	24.8078i	1.05020i
$559$	−5.95777	−0.251987
$560$	0	0
$561$	−6.64803	−0.280680
$562$	14.2749i	0.602152i
$563$	31.0776i	1.30977i	0.755731	+	0.654883i	$0.227282\pi$
$563$	31.0776i	1.30977i	−0.755731	+	0.654883i	$0.772718\pi$
$564$	2.20766	0.0929592
$565$	0	0
$566$	−13.2288	−0.556047
$567$	− 21.9920i	− 0.923577i
$568$	14.6480i	0.614618i
$569$	−30.0845	−1.26121	−0.630603	−	0.776105i	$-0.717192\pi$
$569$	−30.0845	−1.26121	−0.630603	+	0.776105i	$0.717192\pi$
$570$	0	0
$571$	5.55673	0.232542	0.116271	−	0.993218i	$-0.462906\pi$
$571$	5.55673	0.232542	0.116271	+	0.993218i	$0.462906\pi$
$572$	5.29606i	0.221439i
$573$	− 7.86312i	− 0.328487i
$574$	−18.5106	−0.772616
$575$	0	0
$576$	−2.83457	−0.118107
$577$	22.2499i	0.926275i	0.886286	+	0.463137i	$0.153276\pi$
$577$	22.2499i	0.926275i	−0.886286	+	0.463137i	$0.846724\pi$
$578$	− 10.6971i	− 0.444941i
$579$	8.15174	0.338775
$580$	0	0
$581$	−20.5807	−0.853833
$582$	− 0.953831i	− 0.0395376i
$583$	− 15.2681i	− 0.632340i
$584$	11.0211	0.456057
$585$	0	0
$586$	2.34513	0.0968764
$587$	− 45.3103i	− 1.87016i	−0.354440	−	0.935079i	$-0.615328\pi$
$587$	− 45.3103i	− 1.87016i	0.354440	−	0.935079i	$-0.384672\pi$
$588$	0.614387i	0.0253369i
$589$	3.55963	0.146672
$590$	0	0
$591$	6.35591	0.261447
$592$	1.00000i	0.0410997i
$593$	− 0.232712i	− 0.00955635i	−0.999989	−	0.00477817i	$-0.998479\pi$
$593$	− 0.232712i	− 0.00955635i	0.999989	−	0.00477817i	$-0.00152095\pi$
$594$	15.4501	0.633926
$595$	0	0
$596$	−0.207658	−0.00850601
$597$	− 8.24989i	− 0.337645i
$598$	− 4.08446i	− 0.167026i
$599$	−43.4056	−1.77350	−0.886752	−	0.462246i	$-0.847044\pi$
$599$	−43.4056	−1.77350	−0.886752	+	0.462246i	$0.847044\pi$
$600$	0	0
$601$	35.5317	1.44937	0.724684	−	0.689082i	$-0.241986\pi$
$601$	35.5317	1.44937	0.724684	+	0.689082i	$0.241986\pi$
$602$	21.3662i	0.870823i
$603$	15.3856i	0.626551i
$604$	−0.813457	−0.0330991
$605$	0	0
$606$	−3.33829	−0.135609
$607$	− 26.7325i	− 1.08504i	−0.840043	−	0.542519i	$-0.817471\pi$
$607$	− 26.7325i	− 1.08504i	0.840043	−	0.542519i	$-0.182529\pi$
$608$	0.406728i	0.0164950i
$609$	6.31717	0.255985
$610$	0	0
$611$	4.41532	0.178625
$612$	− 7.11636i	− 0.287662i
$613$	48.0565i	1.94098i	0.241134	+	0.970492i	$0.422481\pi$
$613$	48.0565i	1.94098i	−0.241134	+	0.970492i	$0.577519\pi$
$614$	23.2624	0.938795
$615$	0	0
$616$	18.9932	0.765256
$617$	− 12.9789i	− 0.522510i	−0.965270	−	0.261255i	$-0.915864\pi$
$617$	− 12.9789i	− 0.522510i	0.965270	−	0.261255i	$-0.0841364\pi$
$618$	− 3.58468i	− 0.144197i
$619$	−25.3662	−1.01956	−0.509778	−	0.860306i	$-0.670272\pi$
$619$	−25.3662	−1.01956	−0.509778	+	0.860306i	$0.670272\pi$
$620$	0	0
$621$	−11.9155	−0.478154
$622$	31.3999i	1.25902i
$623$	17.5037i	0.701272i
$624$	0.330856	0.0132448
$625$	0	0
$626$	−8.04223	−0.321432
$627$	− 1.07703i	− 0.0430124i
$628$	5.32401i	0.212451i
$629$	−2.51056	−0.100102
$630$	0	0
$631$	−31.6075	−1.25828	−0.629138	−	0.777293i	$-0.716592\pi$
$631$	−31.6075	−1.25828	−0.629138	+	0.777293i	$0.716592\pi$
$632$	1.75870i	0.0699573i
$633$	7.61323i	0.302599i
$634$	12.3029	0.488611
$635$	0	0
$636$	−0.953831	−0.0378219
$637$	1.22877i	0.0486858i
$638$	− 34.6623i	− 1.37229i
$639$	41.5209	1.64254
$640$	0	0
$641$	−23.8625	−0.942513	−0.471257	−	0.881996i	$-0.656199\pi$
$641$	−23.8625	−0.942513	−0.471257	+	0.881996i	$0.656199\pi$
$642$	− 6.20766i	− 0.244997i
$643$	32.8277i	1.29460i	0.762236	+	0.647300i	$0.224102\pi$
$643$	32.8277i	1.29460i	−0.762236	+	0.647300i	$0.775898\pi$
$644$	−14.6480	−0.577213
$645$	0	0
$646$	−1.02112	−0.0401752
$647$	13.9578i	0.548737i	0.961625	+	0.274368i	$0.0884687\pi$
$647$	13.9578i	0.548737i	−0.961625	+	0.274368i	$0.911531\pi$
$648$	7.53851i	0.296141i
$649$	9.29606	0.364902
$650$	0	0
$651$	−10.3845	−0.406999
$652$	− 15.2008i	− 0.595310i
$653$	28.5921i	1.11890i	0.828865	+	0.559448i	$0.188987\pi$
$653$	28.5921i	1.11890i	−0.828865	+	0.559448i	$0.811013\pi$
$654$	−1.75011	−0.0684348
$655$	0	0
$656$	6.34513	0.247736
$657$	− 31.2401i	− 1.21879i
$658$	− 15.8346i	− 0.617296i
$659$	5.62691	0.219193	0.109597	−	0.993976i	$-0.465044\pi$
$659$	5.62691	0.219193	0.109597	+	0.993976i	$0.465044\pi$
$660$	0	0
$661$	13.3240	0.518244	0.259122	−	0.965845i	$-0.416567\pi$
$661$	13.3240	0.518244	0.259122	+	0.965845i	$0.416567\pi$
$662$	6.77981i	0.263505i
$663$	0.830633i	0.0322591i
$664$	7.05476	0.273778
$665$	0	0
$666$	2.83457	0.109837
$667$	26.7325i	1.03509i
$668$	− 12.4826i	− 0.482966i
$669$	6.39814	0.247366
$670$	0	0
$671$	−8.62007	−0.332774
$672$	− 1.18654i	− 0.0457719i
$673$	29.6691i	1.14366i	0.820372	+	0.571831i	$0.193767\pi$
$673$	29.6691i	1.14366i	−0.820372	+	0.571831i	$0.806233\pi$
$674$	−10.6903	−0.411773
$675$	0	0
$676$	−12.3383	−0.474550
$677$	1.25383i	0.0481885i	0.999710	+	0.0240943i	$0.00767018\pi$
$677$	1.25383i	0.0481885i	−0.999710	+	0.0240943i	$0.992330\pi$
$678$	− 3.72506i	− 0.143060i
$679$	−6.84141	−0.262549
$680$	0	0
$681$	5.24014	0.200803
$682$	56.9795i	2.18186i
$683$	− 4.76045i	− 0.182153i	−0.995844	−	0.0910767i	$-0.970969\pi$
$683$	− 4.76045i	− 0.182153i	0.995844	−	0.0910767i	$-0.0290308\pi$
$684$	1.15290	0.0440823
$685$	0	0
$686$	−16.0143	−0.611428
$687$	− 2.13688i	− 0.0815271i
$688$	− 7.32401i	− 0.279225i
$689$	−1.90766	−0.0726761
$690$	0	0
$691$	−20.2219	−0.769279	−0.384639	−	0.923067i	$-0.625674\pi$
$691$	−20.2219	−0.769279	−0.384639	+	0.923067i	$0.625674\pi$
$692$	− 23.0354i	− 0.875674i
$693$	− 53.8375i	− 2.04512i
$694$	−5.62691	−0.213595
$695$	0	0
$696$	−2.16543	−0.0820803
$697$	15.9298i	0.603385i
$698$	15.1306i	0.572703i
$699$	−11.5174	−0.435628
$700$	0	0
$701$	−22.0845	−0.834119	−0.417059	−	0.908879i	$-0.636939\pi$
$701$	−22.0845	−0.834119	−0.417059	+	0.908879i	$0.636939\pi$
$702$	− 1.93040i	− 0.0728584i
$703$	− 0.406728i	− 0.0153401i
$704$	−6.51056	−0.245376
$705$	0	0
$706$	35.7816	1.34666
$707$	23.9441i	0.900510i
$708$	− 0.580745i	− 0.0218257i
$709$	−5.59896	−0.210273	−0.105137	−	0.994458i	$-0.533528\pi$
$709$	−5.59896	−0.210273	−0.105137	+	0.994458i	$0.533528\pi$
$710$	0	0
$711$	4.98516	0.186958
$712$	− 6.00000i	− 0.224860i
$713$	− 43.9441i	− 1.64572i
$714$	2.97888	0.111482
$715$	0	0
$716$	24.2835	0.907518
$717$	− 5.84826i	− 0.218407i
$718$	4.48260i	0.167289i
$719$	−40.2921	−1.50264	−0.751321	−	0.659937i	$-0.770583\pi$
$719$	−40.2921	−1.50264	−0.751321	+	0.659937i	$0.770583\pi$
$720$	0	0
$721$	−25.7114	−0.957542
$722$	18.8346i	0.700950i
$723$	7.43294i	0.276434i
$724$	−2.16543	−0.0804775
$725$	0	0
$726$	12.7661	0.473796
$727$	− 11.2538i	− 0.417381i	−0.977982	−	0.208691i	$-0.933080\pi$
$727$	− 11.2538i	− 0.417381i	0.977982	−	0.208691i	$-0.0669202\pi$
$728$	− 2.37309i	− 0.0879524i
$729$	18.4729	0.684180
$730$	0	0
$731$	18.3874	0.680081
$732$	0.538514i	0.0199041i
$733$	− 42.2892i	− 1.56199i	−0.624539	−	0.780994i	$-0.714713\pi$
$733$	− 42.2892i	− 1.56199i	0.624539	−	0.780994i	$-0.285287\pi$
$734$	21.5653	0.795990
$735$	0	0
$736$	5.02112	0.185081
$737$	35.3383i	1.30170i
$738$	− 17.9857i	− 0.662064i
$739$	29.3103	1.07820	0.539099	−	0.842242i	$-0.318765\pi$
$739$	29.3103	1.07820	0.539099	+	0.842242i	$0.318765\pi$
$740$	0	0
$741$	−0.134569	−0.00494350
$742$	6.84141i	0.251156i
$743$	− 4.39245i	− 0.161144i	−0.996749	−	0.0805718i	$-0.974325\pi$
$743$	− 4.39245i	− 0.161144i	0.996749	−	0.0805718i	$-0.0256746\pi$
$744$	3.55963	0.130502
$745$	0	0
$746$	16.9230	0.619594
$747$	− 19.9972i	− 0.731660i
$748$	− 16.3451i	− 0.597637i
$749$	−44.5248	−1.62690
$750$	0	0
$751$	2.58074	0.0941727	0.0470864	−	0.998891i	$-0.485006\pi$
$751$	2.58074	0.0941727	0.0470864	+	0.998891i	$0.485006\pi$
$752$	5.42784i	0.197933i
$753$	− 0.496284i	− 0.0180856i
$754$	−4.33086	−0.157720
$755$	0	0
$756$	−6.92297	−0.251786
$757$	− 27.3805i	− 0.995162i	−0.867418	−	0.497581i	$-0.834222\pi$
$757$	− 27.3805i	− 0.995162i	0.867418	−	0.497581i	$-0.165778\pi$
$758$	31.2710i	1.13581i
$759$	−13.2961	−0.482616
$760$	0	0
$761$	−42.9509	−1.55697	−0.778485	−	0.627663i	$-0.784011\pi$
$761$	−42.9509	−1.55697	−0.778485	+	0.627663i	$0.784011\pi$
$762$	3.50372i	0.126926i
$763$	12.5528i	0.454441i
$764$	19.3326	0.699429
$765$	0	0
$766$	1.62691	0.0587828
$767$	− 1.16149i	− 0.0419389i
$768$	0.406728i	0.0146765i
$769$	13.0633	0.471076	0.235538	−	0.971865i	$-0.424315\pi$
$769$	13.0633	0.471076	0.235538	+	0.971865i	$0.424315\pi$
$770$	0	0
$771$	11.0348	0.397409
$772$	20.0422i	0.721336i
$773$	− 15.3662i	− 0.552685i	−0.961059	−	0.276343i	$-0.910878\pi$
$773$	− 15.3662i	− 0.552685i	0.961059	−	0.276343i	$-0.0891225\pi$
$774$	−20.7604	−0.746219
$775$	0	0
$776$	2.34513	0.0841852
$777$	1.18654i	0.0425670i
$778$	− 31.6412i	− 1.13439i
$779$	−2.58074	−0.0924648
$780$	0	0
$781$	95.3668	3.41249
$782$	12.6058i	0.450782i
$783$	12.6343i	0.451515i
$784$	−1.51056	−0.0539485
$785$	0	0
$786$	5.46149	0.194805
$787$	− 10.9316i	− 0.389668i	−0.980836	−	0.194834i	$-0.937583\pi$
$787$	− 10.9316i	− 0.389668i	0.980836	−	0.194834i	$-0.0624168\pi$
$788$	15.6269i	0.556686i
$789$	8.22134	0.292688
$790$	0	0
$791$	−26.7182	−0.949990
$792$	18.4546i	0.655757i
$793$	1.07703i	0.0382464i
$794$	39.2961	1.39456
$795$	0	0
$796$	20.2835	0.718931
$797$	24.2921i	0.860471i	0.902717	+	0.430235i	$0.141569\pi$
$797$	24.2921i	0.860471i	−0.902717	+	0.430235i	$0.858431\pi$
$798$	0.482601i	0.0170839i
$799$	−13.6269	−0.482086
$800$	0	0
$801$	−17.0074	−0.600928
$802$	9.66914i	0.341429i
$803$	− 71.7536i	− 2.53213i
$804$	2.20766	0.0778581
$805$	0	0
$806$	7.11926	0.250765
$807$	0.0844605i	0.00297315i
$808$	− 8.20766i	− 0.288744i
$809$	40.0422	1.40781	0.703905	−	0.710294i	$-0.251438\pi$
$809$	40.0422	1.40781	0.703905	+	0.710294i	$0.251438\pi$
$810$	0	0
$811$	−40.6343	−1.42686	−0.713432	−	0.700724i	$-0.752860\pi$
$811$	−40.6343	−1.42686	−0.713432	+	0.700724i	$0.752860\pi$
$812$	15.5317i	0.545055i
$813$	− 12.4654i	− 0.437182i
$814$	6.51056	0.228195
$815$	0	0
$816$	−1.02112	−0.0357462
$817$	2.97888i	0.104218i
$818$	− 26.2749i	− 0.918682i
$819$	−6.72668	−0.235049
$820$	0	0
$821$	−41.4787	−1.44762	−0.723808	−	0.690002i	$-0.757610\pi$
$821$	−41.4787	−1.44762	−0.723808	+	0.690002i	$0.757610\pi$
$822$	5.97495i	0.208400i
$823$	− 5.27610i	− 0.183913i	−0.995763	−	0.0919566i	$-0.970688\pi$
$823$	− 5.27610i	− 0.183913i	0.995763	−	0.0919566i	$-0.0293121\pi$
$824$	8.81346	0.307031
$825$	0	0
$826$	−4.16543	−0.144934
$827$	− 1.76438i	− 0.0613537i	−0.999529	−	0.0306768i	$-0.990234\pi$
$827$	− 1.76438i	− 0.0613537i	0.999529	−	0.0306768i	$-0.00976627\pi$
$828$	− 14.2327i	− 0.494621i
$829$	−16.3029	−0.566223	−0.283112	−	0.959087i	$-0.591367\pi$
$829$	−16.3029	−0.566223	−0.283112	+	0.959087i	$0.591367\pi$
$830$	0	0
$831$	−6.83851	−0.237225
$832$	0.813457i	0.0282015i
$833$	− 3.79234i	− 0.131397i
$834$	−7.06335	−0.244584
$835$	0	0
$836$	2.64803	0.0915840
$837$	− 20.7689i	− 0.717879i
$838$	− 30.1940i	− 1.04303i
$839$	−14.3731	−0.496214	−0.248107	−	0.968733i	$-0.579808\pi$
$839$	−14.3731	−0.496214	−0.248107	+	0.968733i	$0.579808\pi$
$840$	0	0
$841$	−0.654870	−0.0225817
$842$	− 22.0000i	− 0.758170i
$843$	− 5.80602i	− 0.199970i
$844$	−18.7182	−0.644308
$845$	0	0
$846$	15.3856	0.528968
$847$	− 91.5659i	− 3.14624i
$848$	− 2.34513i	− 0.0805321i
$849$	5.38052	0.184659
$850$	0	0
$851$	−5.02112	−0.172122
$852$	− 5.95777i	− 0.204110i
$853$	43.2961i	1.48243i	0.671268	+	0.741214i	$0.265750\pi$
$853$	43.2961i	1.48243i	−0.671268	+	0.741214i	$0.734250\pi$
$854$	3.86253	0.132173
$855$	0	0
$856$	15.2624	0.521659
$857$	49.0776i	1.67646i	0.545317	+	0.838230i	$0.316409\pi$
$857$	49.0776i	1.67646i	−0.545317	+	0.838230i	$0.683591\pi$
$858$	− 2.15406i	− 0.0735383i
$859$	−15.5374	−0.530128	−0.265064	−	0.964231i	$-0.585393\pi$
$859$	−15.5374	−0.530128	−0.265064	+	0.964231i	$0.585393\pi$
$860$	0	0
$861$	7.52877	0.256580
$862$	− 25.5653i	− 0.870758i
$863$	− 36.0901i	− 1.22852i	−0.789103	−	0.614261i	$-0.789454\pi$
$863$	− 36.0901i	− 1.22852i	0.789103	−	0.614261i	$-0.210546\pi$
$864$	2.37309	0.0807340
$865$	0	0
$866$	32.0422	1.08884
$867$	4.35081i	0.147761i
$868$	− 25.5317i	− 0.866601i
$869$	11.4501	0.388419
$870$	0	0
$871$	4.41532	0.149607
$872$	− 4.30290i	− 0.145715i
$873$	− 6.64744i	− 0.224982i
$874$	−2.04223	−0.0690795
$875$	0	0
$876$	−4.48260	−0.151453
$877$	− 29.3240i	− 0.990202i	−0.868836	−	0.495101i	$-0.835131\pi$
$877$	− 29.3240i	− 0.990202i	0.868836	−	0.495101i	$-0.164869\pi$
$878$	3.93840i	0.132915i
$879$	−0.953831	−0.0321719
$880$	0	0
$881$	23.8066	0.802065	0.401033	−	0.916064i	$-0.368651\pi$
$881$	23.8066	0.802065	0.401033	+	0.916064i	$0.368651\pi$
$882$	4.28178i	0.144175i
$883$	− 3.94699i	− 0.132827i	−0.997792	−	0.0664134i	$-0.978844\pi$
$883$	− 3.94699i	− 0.132827i	0.997792	−	0.0664134i	$-0.0211556\pi$
$884$	−2.04223	−0.0686876
$885$	0	0
$886$	−0.0758724	−0.00254898
$887$	− 1.96346i	− 0.0659264i	−0.999457	−	0.0329632i	$-0.989506\pi$
$887$	− 1.96346i	− 0.0659264i	0.999457	−	0.0329632i	$-0.0104944\pi$
$888$	− 0.406728i	− 0.0136489i
$889$	25.1306	0.842854
$890$	0	0
$891$	49.0799	1.64424
$892$	15.7307i	0.526704i
$893$	− 2.20766i	− 0.0738765i
$894$	0.0844605	0.00282478
$895$	0	0
$896$	2.91729	0.0974597
$897$	1.66127i	0.0554681i
$898$	19.2961i	0.643918i
$899$	−46.5950	−1.55403
$900$	0	0
$901$	5.88758	0.196144
$902$	− 41.3103i	− 1.37548i
$903$	− 8.69026i	− 0.289194i
$904$	9.15859	0.304610
$905$	0	0
$906$	0.330856	0.0109920
$907$	− 5.89049i	− 0.195590i	−0.995207	−	0.0977952i	$-0.968821\pi$
$907$	− 5.89049i	− 0.195590i	0.995207	−	0.0977952i	$-0.0311790\pi$
$908$	12.8836i	0.427559i
$909$	−23.2652	−0.771658
$910$	0	0
$911$	−27.9527	−0.926113	−0.463057	−	0.886329i	$-0.653247\pi$
$911$	−27.9527	−0.926113	−0.463057	+	0.886329i	$0.653247\pi$
$912$	− 0.165428i	− 0.00547787i
$913$	− 45.9304i	− 1.52007i
$914$	−3.00684	−0.0994575
$915$	0	0
$916$	5.25383	0.173591
$917$	− 39.1729i	− 1.29360i
$918$	5.95777i	0.196636i
$919$	−17.7587	−0.585805	−0.292903	−	0.956142i	$-0.594621\pi$
$919$	−17.7587	−0.585805	−0.292903	+	0.956142i	$0.594621\pi$
$920$	0	0
$921$	−9.46149	−0.311767
$922$	0.633755i	0.0208716i
$923$	− 11.9155i	− 0.392205i
$924$	−7.72506	−0.254136
$925$	0	0
$926$	18.0422	0.592904
$927$	− 24.9824i	− 0.820529i
$928$	− 5.32401i	− 0.174769i
$929$	−34.2892	−1.12499	−0.562496	−	0.826800i	$-0.690159\pi$
$929$	−34.2892	−1.12499	−0.562496	+	0.826800i	$0.690159\pi$
$930$	0	0
$931$	0.614387	0.0201357
$932$	− 28.3172i	− 0.927560i
$933$	− 12.7712i	− 0.418111i
$934$	23.4758	0.768150
$935$	0	0
$936$	2.30580	0.0753675
$937$	14.0845i	0.460119i	0.973177	+	0.230060i	$0.0738921\pi$
$937$	14.0845i	0.460119i	−0.973177	+	0.230060i	$0.926108\pi$
$938$	− 15.8346i	− 0.517017i
$939$	3.27100	0.106745
$940$	0	0
$941$	14.2499	0.464533	0.232267	−	0.972652i	$-0.425386\pi$
$941$	14.2499	0.464533	0.232267	+	0.972652i	$0.425386\pi$
$942$	− 2.16543i	− 0.0705535i
$943$	31.8596i	1.03749i
$944$	1.42784	0.0464723
$945$	0	0
$946$	−47.6834	−1.55032
$947$	29.8203i	0.969029i	0.874783	+	0.484515i	$0.161004\pi$
$947$	29.8203i	0.969029i	−0.874783	+	0.484515i	$0.838996\pi$
$948$	− 0.715313i	− 0.0232323i
$949$	−8.96520	−0.291023
$950$	0	0
$951$	−5.00394	−0.162264
$952$	7.32401i	0.237373i
$953$	8.64803i	0.280137i	0.990142	+	0.140069i	$0.0447323\pi$
$953$	8.64803i	0.280137i	−0.990142	+	0.140069i	$0.955268\pi$
$954$	−6.64744	−0.215219
$955$	0	0
$956$	14.3788	0.465043
$957$	14.0981i	0.455728i
$958$	− 8.19907i	− 0.264900i
$959$	42.8557	1.38388
$960$	0	0
$961$	45.5950	1.47081
$962$	− 0.813457i	− 0.0262269i
$963$	− 43.2624i	− 1.39411i
$964$	−18.2749	−0.588596
$965$	0	0
$966$	5.95777	0.191688
$967$	45.0325i	1.44815i	0.689723	+	0.724074i	$0.257732\pi$
$967$	45.0325i	1.44815i	−0.689723	+	0.724074i	$0.742268\pi$
$968$	31.3874i	1.00883i
$969$	0.415317	0.0133419
$970$	0	0
$971$	26.3029	0.844100	0.422050	−	0.906573i	$-0.361311\pi$
$971$	26.3029	0.844100	0.422050	+	0.906573i	$0.361311\pi$
$972$	− 10.1854i	− 0.326696i
$973$	50.6623i	1.62416i
$974$	−0.953831	−0.0305627
$975$	0	0
$976$	−1.32401	−0.0423807
$977$	− 25.6549i	− 0.820772i	−0.911912	−	0.410386i	$-0.865394\pi$
$977$	− 25.6549i	− 0.820772i	0.911912	−	0.410386i	$-0.134606\pi$
$978$	6.18260i	0.197698i
$979$	−39.0633	−1.24847
$980$	0	0
$981$	−12.1969	−0.389416
$982$	− 19.3383i	− 0.617110i
$983$	− 55.3611i	− 1.76575i	−0.469611	−	0.882873i	$-0.655606\pi$
$983$	− 55.3611i	− 1.76575i	0.469611	−	0.882873i	$-0.344394\pi$
$984$	−2.58074	−0.0822711
$985$	0	0
$986$	13.3662	0.425668
$987$	6.44037i	0.204999i
$988$	− 0.330856i	− 0.0105259i
$989$	36.7747	1.16937
$990$	0	0
$991$	−3.24814	−0.103181	−0.0515903	−	0.998668i	$-0.516429\pi$
$991$	−3.24814	−0.103181	−0.0515903	+	0.998668i	$0.516429\pi$
$992$	8.75186i	0.277872i
$993$	− 2.75754i	− 0.0875080i
$994$	−42.7325	−1.35539
$995$	0	0
$996$	−2.86937	−0.0909195
$997$	12.6480i	0.400567i	0.979738	+	0.200284i	$0.0641863\pi$
$997$	12.6480i	0.400567i	−0.979738	+	0.200284i	$0.935814\pi$
$998$	− 5.63550i	− 0.178389i
$999$	−2.37309	−0.0750811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.o.149.2		6
5.2	odd	4		370.2.a.g.1.2	✓	3
5.3	odd	4		1850.2.a.z.1.2		3
5.4	even	2	inner	1850.2.b.o.149.5		6
15.2	even	4		3330.2.a.bg.1.3		3
20.7	even	4		2960.2.a.u.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.a.g.1.2	✓	3	5.2	odd	4
1850.2.a.z.1.2		3	5.3	odd	4
1850.2.b.o.149.2		6	1.1	even	1	trivial
1850.2.b.o.149.5		6	5.4	even	2	inner
2960.2.a.u.1.2		3	20.7	even	4
3330.2.a.bg.1.3		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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} -2.91729i q^{7} +1.00000i q^{8} +2.83457 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} -2.91729i q^{7} +1.00000i q^{8} +2.83457 q^{9} +6.51056 q^{11} -0.406728i q^{12} -0.813457i q^{13} -2.91729 q^{14} +1.00000 q^{16} +2.51056i q^{17} -2.83457i q^{18} -0.406728 q^{19} +1.18654 q^{21} -6.51056i q^{22} +5.02112i q^{23} -0.406728 q^{24} -0.813457 q^{26} +2.37309i q^{27} +2.91729i q^{28} +5.32401 q^{29} -8.75186 q^{31} -1.00000i q^{32} +2.64803i q^{33} +2.51056 q^{34} -2.83457 q^{36} +1.00000i q^{37} +0.406728i q^{38} +0.330856 q^{39} +6.34513 q^{41} -1.18654i q^{42} -7.32401i q^{43} -6.51056 q^{44} +5.02112 q^{46} +5.42784i q^{47} +0.406728i q^{48} -1.51056 q^{49} -1.02112 q^{51} +0.813457i q^{52} -2.34513i q^{53} +2.37309 q^{54} +2.91729 q^{56} -0.165428i q^{57} -5.32401i q^{58} +1.42784 q^{59} -1.32401 q^{61} +8.75186i q^{62} -8.26926i q^{63} -1.00000 q^{64} +2.64803 q^{66} +5.42784i q^{67} -2.51056i q^{68} -2.04223 q^{69} +14.6480 q^{71} +2.83457i q^{72} -11.0211i q^{73} +1.00000 q^{74} +0.406728 q^{76} -18.9932i q^{77} -0.330856i q^{78} +1.75870 q^{79} +7.53851 q^{81} -6.34513i q^{82} -7.05476i q^{83} -1.18654 q^{84} -7.32401 q^{86} +2.16543i q^{87} +6.51056i q^{88} -6.00000 q^{89} -2.37309 q^{91} -5.02112i q^{92} -3.55963i q^{93} +5.42784 q^{94} +0.406728 q^{96} -2.34513i q^{97} +1.51056i q^{98} +18.4546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 22 * q^9	\( 6 q - 6 q^{4} - 22 q^{9} + 22 q^{11} + 2 q^{14} + 6 q^{16} + 12 q^{21} + 10 q^{29} + 6 q^{31} - 2 q^{34} + 22 q^{36} + 80 q^{39} - 18 q^{41} - 22 q^{44} - 4 q^{46} + 8 q^{49} + 28 q^{51} + 24 q^{54} - 2 q^{56} - 28 q^{59} + 14 q^{61} - 6 q^{64} - 28 q^{66} + 56 q^{69} + 44 q^{71} + 6 q^{74} + 52 q^{79} + 94 q^{81} - 12 q^{84} - 22 q^{86} - 36 q^{89} - 24 q^{91} - 4 q^{94} - 38 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 22 * q^9 + 22 * q^11 + 2 * q^14 + 6 * q^16 + 12 * q^21 + 10 * q^29 + 6 * q^31 - 2 * q^34 + 22 * q^36 + 80 * q^39 - 18 * q^41 - 22 * q^44 - 4 * q^46 + 8 * q^49 + 28 * q^51 + 24 * q^54 - 2 * q^56 - 28 * q^59 + 14 * q^61 - 6 * q^64 - 28 * q^66 + 56 * q^69 + 44 * q^71 + 6 * q^74 + 52 * q^79 + 94 * q^81 - 12 * q^84 - 22 * q^86 - 36 * q^89 - 24 * q^91 - 4 * q^94 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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