LMFDB - Embedded newform 2550.2.d.l.2449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(2449,2550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2550, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2550.2449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.d (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:	$20.3618525154$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2449.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	2550.2449
Dual form			2550.2.d.l.2449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -5.00000 q^{11} -1.00000i q^{12} -4.00000i q^{13} +3.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} -3.00000 q^{21} +5.00000i q^{22} +4.00000i q^{23} -1.00000 q^{24} -4.00000 q^{26} -1.00000i q^{27} -3.00000i q^{28} +4.00000 q^{29} -1.00000 q^{31} -1.00000i q^{32} -5.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} -9.00000i q^{37} -1.00000i q^{38} +4.00000 q^{39} -10.0000 q^{41} +3.00000i q^{42} -11.0000i q^{43} +5.00000 q^{44} +4.00000 q^{46} +9.00000i q^{47} +1.00000i q^{48} -2.00000 q^{49} +1.00000 q^{51} +4.00000i q^{52} -3.00000i q^{53} -1.00000 q^{54} -3.00000 q^{56} +1.00000i q^{57} -4.00000i q^{58} +8.00000 q^{59} -14.0000 q^{61} +1.00000i q^{62} -3.00000i q^{63} -1.00000 q^{64} -5.00000 q^{66} -7.00000i q^{67} +1.00000i q^{68} -4.00000 q^{69} +14.0000 q^{71} -1.00000i q^{72} -2.00000i q^{73} -9.00000 q^{74} -1.00000 q^{76} -15.0000i q^{77} -4.00000i q^{78} +5.00000 q^{79} +1.00000 q^{81} +10.0000i q^{82} -8.00000i q^{83} +3.00000 q^{84} -11.0000 q^{86} +4.00000i q^{87} -5.00000i q^{88} +2.00000 q^{89} +12.0000 q^{91} -4.00000i q^{92} -1.00000i q^{93} +9.00000 q^{94} +1.00000 q^{96} -14.0000i q^{97} +2.00000i q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} - 10 q^{11} + 6 q^{14} + 2 q^{16} + 2 q^{19} - 6 q^{21} - 2 q^{24} - 8 q^{26} + 8 q^{29} - 2 q^{31} - 2 q^{34} + 2 q^{36} + 8 q^{39} - 20 q^{41} + 10 q^{44} + 8 q^{46} - 4 q^{49} + 2 q^{51} - 2 q^{54} - 6 q^{56} + 16 q^{59} - 28 q^{61} - 2 q^{64} - 10 q^{66} - 8 q^{69} + 28 q^{71} - 18 q^{74} - 2 q^{76} + 10 q^{79} + 2 q^{81} + 6 q^{84} - 22 q^{86} + 4 q^{89} + 24 q^{91} + 18 q^{94} + 2 q^{96} + 10 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 - 10 * q^11 + 6 * q^14 + 2 * q^16 + 2 * q^19 - 6 * q^21 - 2 * q^24 - 8 * q^26 + 8 * q^29 - 2 * q^31 - 2 * q^34 + 2 * q^36 + 8 * q^39 - 20 * q^41 + 10 * q^44 + 8 * q^46 - 4 * q^49 + 2 * q^51 - 2 * q^54 - 6 * q^56 + 16 * q^59 - 28 * q^61 - 2 * q^64 - 10 * q^66 - 8 * q^69 + 28 * q^71 - 18 * q^74 - 2 * q^76 + 10 * q^79 + 2 * q^81 + 6 * q^84 - 22 * q^86 + 4 * q^89 + 24 * q^91 + 18 * q^94 + 2 * q^96 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2550\mathbb{Z}\right)^\times$.

$n$	$751$	$851$	$1327$
$\chi(n)$	$1$	$1$	$-1$

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
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	3.00000i	1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$	3.00000i	1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 4.00000i	− 1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	− 4.00000i	− 1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$	3.00000	0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	− 1.00000i	− 0.242536i
$17$	− 1.00000i	− 0.242536i
$18$	1.00000i	0.235702i
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	5.00000i	1.06600i
$23$	4.00000i	0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$	4.00000i	0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−4.00000	−0.784465
$27$	− 1.00000i	− 0.192450i
$28$	− 3.00000i	− 0.566947i
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 5.00000i	− 0.870388i
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	− 9.00000i	− 1.47959i	−0.672832	−	0.739795i	$-0.734922\pi$
$37$	− 9.00000i	− 1.47959i	0.672832	−	0.739795i	$-0.265078\pi$
$38$	− 1.00000i	− 0.162221i
$39$	4.00000	0.640513
$40$	0	0
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	3.00000i	0.462910i
$43$	− 11.0000i	− 1.67748i	−0.544529	−	0.838742i	$-0.683292\pi$
$43$	− 11.0000i	− 1.67748i	0.544529	−	0.838742i	$-0.316708\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	4.00000	0.589768
$47$	9.00000i	1.31278i	0.754420	+	0.656392i	$0.227918\pi$
$47$	9.00000i	1.31278i	−0.754420	+	0.656392i	$0.772082\pi$
$48$	1.00000i	0.144338i
$49$	−2.00000	−0.285714
$50$	0	0
$51$	1.00000	0.140028
$52$	4.00000i	0.554700i
$53$	− 3.00000i	− 0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$	− 3.00000i	− 0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.00000	−0.400892
$57$	1.00000i	0.132453i
$58$	− 4.00000i	− 0.525226i
$59$	8.00000	1.04151	0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000	1.04151	0.520756	+	0.853706i	$0.325650\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	1.00000i	0.127000i
$63$	− 3.00000i	− 0.377964i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−5.00000	−0.615457
$67$	− 7.00000i	− 0.855186i	−0.903971	−	0.427593i	$-0.859362\pi$
$67$	− 7.00000i	− 0.855186i	0.903971	−	0.427593i	$-0.140638\pi$
$68$	1.00000i	0.121268i
$69$	−4.00000	−0.481543
$70$	0	0
$71$	14.0000	1.66149	0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000	1.66149	0.830747	+	0.556650i	$0.187914\pi$
$72$	− 1.00000i	− 0.117851i
$73$	− 2.00000i	− 0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$	− 2.00000i	− 0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$	−9.00000	−1.04623
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 15.0000i	− 1.70941i
$78$	− 4.00000i	− 0.452911i
$79$	5.00000	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.0000i	1.10432i
$83$	− 8.00000i	− 0.878114i	−0.898459	−	0.439057i	$-0.855313\pi$
$83$	− 8.00000i	− 0.878114i	0.898459	−	0.439057i	$-0.144687\pi$
$84$	3.00000	0.327327
$85$	0	0
$86$	−11.0000	−1.18616
$87$	4.00000i	0.428845i
$88$	− 5.00000i	− 0.533002i
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	12.0000	1.25794
$92$	− 4.00000i	− 0.417029i
$93$	− 1.00000i	− 0.103695i
$94$	9.00000	0.928279
$95$	0	0
$96$	1.00000	0.102062
$97$	− 14.0000i	− 1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$	− 14.0000i	− 1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	2.00000i	0.202031i
$99$	5.00000	0.502519
$100$	0	0
$101$	9.00000	0.895533	0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000	0.895533	0.447767	+	0.894150i	$0.352219\pi$
$102$	− 1.00000i	− 0.0990148i
$103$	− 14.0000i	− 1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$	− 14.0000i	− 1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	−3.00000	−0.291386
$107$	− 15.0000i	− 1.45010i	−0.688694	−	0.725052i	$-0.741816\pi$
$107$	− 15.0000i	− 1.45010i	0.688694	−	0.725052i	$-0.258184\pi$
$108$	1.00000i	0.0962250i
$109$	−1.00000	−0.0957826	−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000	−0.0957826	−0.0478913	+	0.998853i	$0.515250\pi$
$110$	0	0
$111$	9.00000	0.854242
$112$	3.00000i	0.283473i
$113$	3.00000i	0.282216i	0.989994	+	0.141108i	$0.0450665\pi$
$113$	3.00000i	0.282216i	−0.989994	+	0.141108i	$0.954933\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	−4.00000	−0.371391
$117$	4.00000i	0.369800i
$118$	− 8.00000i	− 0.736460i
$119$	3.00000	0.275010
$120$	0	0
$121$	14.0000	1.27273
$122$	14.0000i	1.26750i
$123$	− 10.0000i	− 0.901670i
$124$	1.00000	0.0898027
$125$	0	0
$126$	−3.00000	−0.267261
$127$	− 2.00000i	− 0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$	− 2.00000i	− 0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	1.00000i	0.0883883i
$129$	11.0000	0.968496
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	5.00000i	0.435194i
$133$	3.00000i	0.260133i
$134$	−7.00000	−0.604708
$135$	0	0
$136$	1.00000	0.0857493
$137$	− 6.00000i	− 0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$	− 6.00000i	− 0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$	4.00000i	0.340503i
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	−9.00000	−0.757937
$142$	− 14.0000i	− 1.17485i
$143$	20.0000i	1.67248i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−2.00000	−0.165521
$147$	− 2.00000i	− 0.164957i
$148$	9.00000i	0.739795i
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	−24.0000	−1.95309	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000	−1.95309	−0.976546	+	0.215308i	$0.930924\pi$
$152$	1.00000i	0.0811107i
$153$	1.00000i	0.0808452i
$154$	−15.0000	−1.20873
$155$	0	0
$156$	−4.00000	−0.320256
$157$	− 24.0000i	− 1.91541i	−0.287754	−	0.957704i	$-0.592909\pi$
$157$	− 24.0000i	− 1.91541i	0.287754	−	0.957704i	$-0.407091\pi$
$158$	− 5.00000i	− 0.397779i
$159$	3.00000	0.237915
$160$	0	0
$161$	−12.0000	−0.945732
$162$	− 1.00000i	− 0.0785674i
$163$	18.0000i	1.40987i	0.709273	+	0.704934i	$0.249024\pi$
$163$	18.0000i	1.40987i	−0.709273	+	0.704934i	$0.750976\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	−8.00000	−0.620920
$167$	18.0000i	1.39288i	0.717614	+	0.696441i	$0.245234\pi$
$167$	18.0000i	1.39288i	−0.717614	+	0.696441i	$0.754766\pi$
$168$	− 3.00000i	− 0.231455i
$169$	−3.00000	−0.230769
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	11.0000i	0.838742i
$173$	14.0000i	1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$	14.0000i	1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$	4.00000	0.303239
$175$	0	0
$176$	−5.00000	−0.376889
$177$	8.00000i	0.601317i
$178$	− 2.00000i	− 0.149906i
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−5.00000	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$182$	− 12.0000i	− 0.889499i
$183$	− 14.0000i	− 1.03491i
$184$	−4.00000	−0.294884
$185$	0	0
$186$	−1.00000	−0.0733236
$187$	5.00000i	0.365636i
$188$	− 9.00000i	− 0.656392i
$189$	3.00000	0.218218
$190$	0	0
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 6.00000i	− 0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$	− 6.00000i	− 0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	− 12.0000i	− 0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$	− 12.0000i	− 0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	− 5.00000i	− 0.355335i
$199$	1.00000	0.0708881	0.0354441	−	0.999372i	$-0.488715\pi$
$199$	1.00000	0.0708881	0.0354441	+	0.999372i	$0.488715\pi$
$200$	0	0
$201$	7.00000	0.493742
$202$	− 9.00000i	− 0.633238i
$203$	12.0000i	0.842235i
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	−14.0000	−0.975426
$207$	− 4.00000i	− 0.278019i
$208$	− 4.00000i	− 0.277350i
$209$	−5.00000	−0.345857
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	3.00000i	0.206041i
$213$	14.0000i	0.959264i
$214$	−15.0000	−1.02538
$215$	0	0
$216$	1.00000	0.0680414
$217$	− 3.00000i	− 0.203653i
$218$	1.00000i	0.0677285i
$219$	2.00000	0.135147
$220$	0	0
$221$	−4.00000	−0.269069
$222$	− 9.00000i	− 0.604040i
$223$	− 6.00000i	− 0.401790i	−0.979613	−	0.200895i	$-0.935615\pi$
$223$	− 6.00000i	− 0.401790i	0.979613	−	0.200895i	$-0.0643850\pi$
$224$	3.00000	0.200446
$225$	0	0
$226$	3.00000	0.199557
$227$	− 21.0000i	− 1.39382i	−0.717159	−	0.696909i	$-0.754558\pi$
$227$	− 21.0000i	− 1.39382i	0.717159	−	0.696909i	$-0.245442\pi$
$228$	− 1.00000i	− 0.0662266i
$229$	12.0000	0.792982	0.396491	−	0.918039i	$-0.370228\pi$
$229$	12.0000	0.792982	0.396491	+	0.918039i	$0.370228\pi$
$230$	0	0
$231$	15.0000	0.986928
$232$	4.00000i	0.262613i
$233$	6.00000i	0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$	6.00000i	0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	−8.00000	−0.520756
$237$	5.00000i	0.324785i
$238$	− 3.00000i	− 0.194461i
$239$	−5.00000	−0.323423	−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000	−0.323423	−0.161712	+	0.986838i	$0.551701\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	− 14.0000i	− 0.899954i
$243$	1.00000i	0.0641500i
$244$	14.0000	0.896258
$245$	0	0
$246$	−10.0000	−0.637577
$247$	− 4.00000i	− 0.254514i
$248$	− 1.00000i	− 0.0635001i
$249$	8.00000	0.506979
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	3.00000i	0.188982i
$253$	− 20.0000i	− 1.25739i
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 12.0000i	− 0.748539i	−0.927320	−	0.374270i	$-0.877893\pi$
$257$	− 12.0000i	− 0.748539i	0.927320	−	0.374270i	$-0.122107\pi$
$258$	− 11.0000i	− 0.684830i
$259$	27.0000	1.67770
$260$	0	0
$261$	−4.00000	−0.247594
$262$	− 4.00000i	− 0.247121i
$263$	7.00000i	0.431638i	0.976433	+	0.215819i	$0.0692422\pi$
$263$	7.00000i	0.431638i	−0.976433	+	0.215819i	$0.930758\pi$
$264$	5.00000	0.307729
$265$	0	0
$266$	3.00000	0.183942
$267$	2.00000i	0.122398i
$268$	7.00000i	0.427593i
$269$	−28.0000	−1.70719	−0.853595	−	0.520937i	$-0.825583\pi$
$269$	−28.0000	−1.70719	−0.853595	+	0.520937i	$0.825583\pi$
$270$	0	0
$271$	4.00000	0.242983	0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000	0.242983	0.121491	+	0.992592i	$0.461232\pi$
$272$	− 1.00000i	− 0.0606339i
$273$	12.0000i	0.726273i
$274$	−6.00000	−0.362473
$275$	0	0
$276$	4.00000	0.240772
$277$	− 13.0000i	− 0.781094i	−0.920583	−	0.390547i	$-0.872286\pi$
$277$	− 13.0000i	− 0.781094i	0.920583	−	0.390547i	$-0.127714\pi$
$278$	8.00000i	0.479808i
$279$	1.00000	0.0598684
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	9.00000i	0.535942i
$283$	− 22.0000i	− 1.30776i	−0.756596	−	0.653882i	$-0.773139\pi$
$283$	− 22.0000i	− 1.30776i	0.756596	−	0.653882i	$-0.226861\pi$
$284$	−14.0000	−0.830747
$285$	0	0
$286$	20.0000	1.18262
$287$	− 30.0000i	− 1.77084i
$288$	1.00000i	0.0589256i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	14.0000	0.820695
$292$	2.00000i	0.117041i
$293$	18.0000i	1.05157i	0.850617	+	0.525786i	$0.176229\pi$
$293$	18.0000i	1.05157i	−0.850617	+	0.525786i	$0.823771\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	9.00000	0.523114
$297$	5.00000i	0.290129i
$298$	14.0000i	0.810998i
$299$	16.0000	0.925304
$300$	0	0
$301$	33.0000	1.90209
$302$	24.0000i	1.38104i
$303$	9.00000i	0.517036i
$304$	1.00000	0.0573539
$305$	0	0
$306$	1.00000	0.0571662
$307$	8.00000i	0.456584i	0.973593	+	0.228292i	$0.0733141\pi$
$307$	8.00000i	0.456584i	−0.973593	+	0.228292i	$0.926686\pi$
$308$	15.0000i	0.854704i
$309$	14.0000	0.796432
$310$	0	0
$311$	10.0000	0.567048	0.283524	−	0.958965i	$-0.408496\pi$
$311$	10.0000	0.567048	0.283524	+	0.958965i	$0.408496\pi$
$312$	4.00000i	0.226455i
$313$	16.0000i	0.904373i	0.891923	+	0.452187i	$0.149356\pi$
$313$	16.0000i	0.904373i	−0.891923	+	0.452187i	$0.850644\pi$
$314$	−24.0000	−1.35440
$315$	0	0
$316$	−5.00000	−0.281272
$317$	4.00000i	0.224662i	0.993671	+	0.112331i	$0.0358318\pi$
$317$	4.00000i	0.224662i	−0.993671	+	0.112331i	$0.964168\pi$
$318$	− 3.00000i	− 0.168232i
$319$	−20.0000	−1.11979
$320$	0	0
$321$	15.0000	0.837218
$322$	12.0000i	0.668734i
$323$	− 1.00000i	− 0.0556415i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	18.0000	0.996928
$327$	− 1.00000i	− 0.0553001i
$328$	− 10.0000i	− 0.552158i
$329$	−27.0000	−1.48856
$330$	0	0
$331$	5.00000	0.274825	0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000	0.274825	0.137412	+	0.990514i	$0.456121\pi$
$332$	8.00000i	0.439057i
$333$	9.00000i	0.493197i
$334$	18.0000	0.984916
$335$	0	0
$336$	−3.00000	−0.163663
$337$	24.0000i	1.30736i	0.756770	+	0.653682i	$0.226776\pi$
$337$	24.0000i	1.30736i	−0.756770	+	0.653682i	$0.773224\pi$
$338$	3.00000i	0.163178i
$339$	−3.00000	−0.162938
$340$	0	0
$341$	5.00000	0.270765
$342$	1.00000i	0.0540738i
$343$	15.0000i	0.809924i
$344$	11.0000	0.593080
$345$	0	0
$346$	14.0000	0.752645
$347$	11.0000i	0.590511i	0.955418	+	0.295255i	$0.0954048\pi$
$347$	11.0000i	0.590511i	−0.955418	+	0.295255i	$0.904595\pi$
$348$	− 4.00000i	− 0.214423i
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	5.00000i	0.266501i
$353$	− 24.0000i	− 1.27739i	−0.769460	−	0.638696i	$-0.779474\pi$
$353$	− 24.0000i	− 1.27739i	0.769460	−	0.638696i	$-0.220526\pi$
$354$	8.00000	0.425195
$355$	0	0
$356$	−2.00000	−0.106000
$357$	3.00000i	0.158777i
$358$	− 12.0000i	− 0.634220i
$359$	25.0000	1.31945	0.659725	−	0.751507i	$-0.270673\pi$
$359$	25.0000	1.31945	0.659725	+	0.751507i	$0.270673\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	5.00000i	0.262794i
$363$	14.0000i	0.734809i
$364$	−12.0000	−0.628971
$365$	0	0
$366$	−14.0000	−0.731792
$367$	25.0000i	1.30499i	0.757793	+	0.652495i	$0.226278\pi$
$367$	25.0000i	1.30499i	−0.757793	+	0.652495i	$0.773722\pi$
$368$	4.00000i	0.208514i
$369$	10.0000	0.520579
$370$	0	0
$371$	9.00000	0.467257
$372$	1.00000i	0.0518476i
$373$	− 6.00000i	− 0.310668i	−0.987862	−	0.155334i	$-0.950355\pi$
$373$	− 6.00000i	− 0.310668i	0.987862	−	0.155334i	$-0.0496454\pi$
$374$	5.00000	0.258544
$375$	0	0
$376$	−9.00000	−0.464140
$377$	− 16.0000i	− 0.824042i
$378$	− 3.00000i	− 0.154303i
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	0	0
$381$	2.00000	0.102463
$382$	9.00000i	0.460480i
$383$	12.0000i	0.613171i	0.951843	+	0.306586i	$0.0991866\pi$
$383$	12.0000i	0.613171i	−0.951843	+	0.306586i	$0.900813\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−6.00000	−0.305392
$387$	11.0000i	0.559161i
$388$	14.0000i	0.710742i
$389$	−21.0000	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$390$	0	0
$391$	4.00000	0.202289
$392$	− 2.00000i	− 0.101015i
$393$	4.00000i	0.201773i
$394$	−12.0000	−0.604551
$395$	0	0
$396$	−5.00000	−0.251259
$397$	15.0000i	0.752828i	0.926451	+	0.376414i	$0.122843\pi$
$397$	15.0000i	0.752828i	−0.926451	+	0.376414i	$0.877157\pi$
$398$	− 1.00000i	− 0.0501255i
$399$	−3.00000	−0.150188
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	− 7.00000i	− 0.349128i
$403$	4.00000i	0.199254i
$404$	−9.00000	−0.447767
$405$	0	0
$406$	12.0000	0.595550
$407$	45.0000i	2.23057i
$408$	1.00000i	0.0495074i
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	14.0000i	0.689730i
$413$	24.0000i	1.18096i
$414$	−4.00000	−0.196589
$415$	0	0
$416$	−4.00000	−0.196116
$417$	− 8.00000i	− 0.391762i
$418$	5.00000i	0.244558i
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	24.0000	1.16969	0.584844	−	0.811146i	$-0.301156\pi$
$421$	24.0000	1.16969	0.584844	+	0.811146i	$0.301156\pi$
$422$	12.0000i	0.584151i
$423$	− 9.00000i	− 0.437595i
$424$	3.00000	0.145693
$425$	0	0
$426$	14.0000	0.678302
$427$	− 42.0000i	− 2.03252i
$428$	15.0000i	0.725052i
$429$	−20.0000	−0.965609
$430$	0	0
$431$	14.0000	0.674356	0.337178	−	0.941441i	$-0.390528\pi$
$431$	14.0000	0.674356	0.337178	+	0.941441i	$0.390528\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 27.0000i	− 1.29754i	−0.760986	−	0.648769i	$-0.775284\pi$
$433$	− 27.0000i	− 1.29754i	0.760986	−	0.648769i	$-0.224716\pi$
$434$	−3.00000	−0.144005
$435$	0	0
$436$	1.00000	0.0478913
$437$	4.00000i	0.191346i
$438$	− 2.00000i	− 0.0955637i
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	4.00000i	0.190261i
$443$	38.0000i	1.80543i	0.430234	+	0.902717i	$0.358431\pi$
$443$	38.0000i	1.80543i	−0.430234	+	0.902717i	$0.641569\pi$
$444$	−9.00000	−0.427121
$445$	0	0
$446$	−6.00000	−0.284108
$447$	− 14.0000i	− 0.662177i
$448$	− 3.00000i	− 0.141737i
$449$	41.0000	1.93491	0.967455	−	0.253044i	$-0.0814317\pi$
$449$	41.0000	1.93491	0.967455	+	0.253044i	$0.0814317\pi$
$450$	0	0
$451$	50.0000	2.35441
$452$	− 3.00000i	− 0.141108i
$453$	− 24.0000i	− 1.12762i
$454$	−21.0000	−0.985579
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	37.0000i	1.73079i	0.501093	+	0.865393i	$0.332931\pi$
$457$	37.0000i	1.73079i	−0.501093	+	0.865393i	$0.667069\pi$
$458$	− 12.0000i	− 0.560723i
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−5.00000	−0.232873	−0.116437	−	0.993198i	$-0.537147\pi$
$461$	−5.00000	−0.232873	−0.116437	+	0.993198i	$0.537147\pi$
$462$	− 15.0000i	− 0.697863i
$463$	− 36.0000i	− 1.67306i	−0.547920	−	0.836531i	$-0.684580\pi$
$463$	− 36.0000i	− 1.67306i	0.547920	−	0.836531i	$-0.315420\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	6.00000	0.277945
$467$	− 6.00000i	− 0.277647i	−0.990317	−	0.138823i	$-0.955668\pi$
$467$	− 6.00000i	− 0.277647i	0.990317	−	0.138823i	$-0.0443321\pi$
$468$	− 4.00000i	− 0.184900i
$469$	21.0000	0.969690
$470$	0	0
$471$	24.0000	1.10586
$472$	8.00000i	0.368230i
$473$	55.0000i	2.52890i
$474$	5.00000	0.229658
$475$	0	0
$476$	−3.00000	−0.137505
$477$	3.00000i	0.137361i
$478$	5.00000i	0.228695i
$479$	−30.0000	−1.37073	−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000	−1.37073	−0.685367	+	0.728197i	$0.740358\pi$
$480$	0	0
$481$	−36.0000	−1.64146
$482$	8.00000i	0.364390i
$483$	− 12.0000i	− 0.546019i
$484$	−14.0000	−0.636364
$485$	0	0
$486$	1.00000	0.0453609
$487$	− 8.00000i	− 0.362515i	−0.983436	−	0.181257i	$-0.941983\pi$
$487$	− 8.00000i	− 0.362515i	0.983436	−	0.181257i	$-0.0580167\pi$
$488$	− 14.0000i	− 0.633750i
$489$	−18.0000	−0.813988
$490$	0	0
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	10.0000i	0.450835i
$493$	− 4.00000i	− 0.180151i
$494$	−4.00000	−0.179969
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	42.0000i	1.88396i
$498$	− 8.00000i	− 0.358489i
$499$	38.0000	1.70111	0.850557	−	0.525883i	$-0.176265\pi$
$499$	38.0000	1.70111	0.850557	+	0.525883i	$0.176265\pi$
$500$	0	0
$501$	−18.0000	−0.804181
$502$	18.0000i	0.803379i
$503$	− 34.0000i	− 1.51599i	−0.652263	−	0.757993i	$-0.726180\pi$
$503$	− 34.0000i	− 1.51599i	0.652263	−	0.757993i	$-0.273820\pi$
$504$	3.00000	0.133631
$505$	0	0
$506$	−20.0000	−0.889108
$507$	− 3.00000i	− 0.133235i
$508$	2.00000i	0.0887357i
$509$	9.00000	0.398918	0.199459	−	0.979906i	$-0.436082\pi$
$509$	9.00000	0.398918	0.199459	+	0.979906i	$0.436082\pi$
$510$	0	0
$511$	6.00000	0.265424
$512$	− 1.00000i	− 0.0441942i
$513$	− 1.00000i	− 0.0441511i
$514$	−12.0000	−0.529297
$515$	0	0
$516$	−11.0000	−0.484248
$517$	− 45.0000i	− 1.97910i
$518$	− 27.0000i	− 1.18631i
$519$	−14.0000	−0.614532
$520$	0	0
$521$	15.0000	0.657162	0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000	0.657162	0.328581	+	0.944476i	$0.393430\pi$
$522$	4.00000i	0.175075i
$523$	20.0000i	0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$	20.0000i	0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	7.00000	0.305215
$527$	1.00000i	0.0435607i
$528$	− 5.00000i	− 0.217597i
$529$	7.00000	0.304348
$530$	0	0
$531$	−8.00000	−0.347170
$532$	− 3.00000i	− 0.130066i
$533$	40.0000i	1.73259i
$534$	2.00000	0.0865485
$535$	0	0
$536$	7.00000	0.302354
$537$	12.0000i	0.517838i
$538$	28.0000i	1.20717i
$539$	10.0000	0.430730
$540$	0	0
$541$	23.0000	0.988847	0.494424	−	0.869221i	$-0.335379\pi$
$541$	23.0000	0.988847	0.494424	+	0.869221i	$0.335379\pi$
$542$	− 4.00000i	− 0.171815i
$543$	− 5.00000i	− 0.214571i
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	12.0000	0.513553
$547$	2.00000i	0.0855138i	0.999086	+	0.0427569i	$0.0136141\pi$
$547$	2.00000i	0.0855138i	−0.999086	+	0.0427569i	$0.986386\pi$
$548$	6.00000i	0.256307i
$549$	14.0000	0.597505
$550$	0	0
$551$	4.00000	0.170406
$552$	− 4.00000i	− 0.170251i
$553$	15.0000i	0.637865i
$554$	−13.0000	−0.552317
$555$	0	0
$556$	8.00000	0.339276
$557$	9.00000i	0.381342i	0.981654	+	0.190671i	$0.0610664\pi$
$557$	9.00000i	0.381342i	−0.981654	+	0.190671i	$0.938934\pi$
$558$	− 1.00000i	− 0.0423334i
$559$	−44.0000	−1.86100
$560$	0	0
$561$	−5.00000	−0.211100
$562$	18.0000i	0.759284i
$563$	− 16.0000i	− 0.674320i	−0.941447	−	0.337160i	$-0.890534\pi$
$563$	− 16.0000i	− 0.674320i	0.941447	−	0.337160i	$-0.109466\pi$
$564$	9.00000	0.378968
$565$	0	0
$566$	−22.0000	−0.924729
$567$	3.00000i	0.125988i
$568$	14.0000i	0.587427i
$569$	−14.0000	−0.586911	−0.293455	−	0.955973i	$-0.594805\pi$
$569$	−14.0000	−0.586911	−0.293455	+	0.955973i	$0.594805\pi$
$570$	0	0
$571$	−26.0000	−1.08807	−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000	−1.08807	−0.544033	+	0.839064i	$0.683103\pi$
$572$	− 20.0000i	− 0.836242i
$573$	− 9.00000i	− 0.375980i
$574$	−30.0000	−1.25218
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 45.0000i	− 1.87337i	−0.350167	−	0.936687i	$-0.613875\pi$
$577$	− 45.0000i	− 1.87337i	0.350167	−	0.936687i	$-0.386125\pi$
$578$	1.00000i	0.0415945i
$579$	6.00000	0.249351
$580$	0	0
$581$	24.0000	0.995688
$582$	− 14.0000i	− 0.580319i
$583$	15.0000i	0.621237i
$584$	2.00000	0.0827606
$585$	0	0
$586$	18.0000	0.743573
$587$	6.00000i	0.247647i	0.992304	+	0.123823i	$0.0395156\pi$
$587$	6.00000i	0.247647i	−0.992304	+	0.123823i	$0.960484\pi$
$588$	2.00000i	0.0824786i
$589$	−1.00000	−0.0412043
$590$	0	0
$591$	12.0000	0.493614
$592$	− 9.00000i	− 0.369898i
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	5.00000	0.205152
$595$	0	0
$596$	14.0000	0.573462
$597$	1.00000i	0.0409273i
$598$	− 16.0000i	− 0.654289i
$599$	−39.0000	−1.59350	−0.796748	−	0.604311i	$-0.793448\pi$
$599$	−39.0000	−1.59350	−0.796748	+	0.604311i	$0.793448\pi$
$600$	0	0
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	− 33.0000i	− 1.34498i
$603$	7.00000i	0.285062i
$604$	24.0000	0.976546
$605$	0	0
$606$	9.00000	0.365600
$607$	32.0000i	1.29884i	0.760430	+	0.649420i	$0.224988\pi$
$607$	32.0000i	1.29884i	−0.760430	+	0.649420i	$0.775012\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	−12.0000	−0.486265
$610$	0	0
$611$	36.0000	1.45640
$612$	− 1.00000i	− 0.0404226i
$613$	10.0000i	0.403896i	0.979396	+	0.201948i	$0.0647272\pi$
$613$	10.0000i	0.403896i	−0.979396	+	0.201948i	$0.935273\pi$
$614$	8.00000	0.322854
$615$	0	0
$616$	15.0000	0.604367
$617$	19.0000i	0.764911i	0.923974	+	0.382456i	$0.124922\pi$
$617$	19.0000i	0.764911i	−0.923974	+	0.382456i	$0.875078\pi$
$618$	− 14.0000i	− 0.563163i
$619$	40.0000	1.60774	0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000	1.60774	0.803868	+	0.594808i	$0.202772\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	− 10.0000i	− 0.400963i
$623$	6.00000i	0.240385i
$624$	4.00000	0.160128
$625$	0	0
$626$	16.0000	0.639489
$627$	− 5.00000i	− 0.199681i
$628$	24.0000i	0.957704i
$629$	−9.00000	−0.358854
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	5.00000i	0.198889i
$633$	− 12.0000i	− 0.476957i
$634$	4.00000	0.158860
$635$	0	0
$636$	−3.00000	−0.118958
$637$	8.00000i	0.316972i
$638$	20.0000i	0.791808i
$639$	−14.0000	−0.553831
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	− 15.0000i	− 0.592003i
$643$	− 44.0000i	− 1.73519i	−0.497271	−	0.867595i	$-0.665665\pi$
$643$	− 44.0000i	− 1.73519i	0.497271	−	0.867595i	$-0.334335\pi$
$644$	12.0000	0.472866
$645$	0	0
$646$	−1.00000	−0.0393445
$647$	8.00000i	0.314512i	0.987558	+	0.157256i	$0.0502649\pi$
$647$	8.00000i	0.314512i	−0.987558	+	0.157256i	$0.949735\pi$
$648$	1.00000i	0.0392837i
$649$	−40.0000	−1.57014
$650$	0	0
$651$	3.00000	0.117579
$652$	− 18.0000i	− 0.704934i
$653$	10.0000i	0.391330i	0.980671	+	0.195665i	$0.0626866\pi$
$653$	10.0000i	0.391330i	−0.980671	+	0.195665i	$0.937313\pi$
$654$	−1.00000	−0.0391031
$655$	0	0
$656$	−10.0000	−0.390434
$657$	2.00000i	0.0780274i
$658$	27.0000i	1.05257i
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	− 5.00000i	− 0.194331i
$663$	− 4.00000i	− 0.155347i
$664$	8.00000	0.310460
$665$	0	0
$666$	9.00000	0.348743
$667$	16.0000i	0.619522i
$668$	− 18.0000i	− 0.696441i
$669$	6.00000	0.231973
$670$	0	0
$671$	70.0000	2.70232
$672$	3.00000i	0.115728i
$673$	− 4.00000i	− 0.154189i	−0.997024	−	0.0770943i	$-0.975436\pi$
$673$	− 4.00000i	− 0.154189i	0.997024	−	0.0770943i	$-0.0245643\pi$
$674$	24.0000	0.924445
$675$	0	0
$676$	3.00000	0.115385
$677$	18.0000i	0.691796i	0.938272	+	0.345898i	$0.112426\pi$
$677$	18.0000i	0.691796i	−0.938272	+	0.345898i	$0.887574\pi$
$678$	3.00000i	0.115214i
$679$	42.0000	1.61181
$680$	0	0
$681$	21.0000	0.804722
$682$	− 5.00000i	− 0.191460i
$683$	8.00000i	0.306111i	0.988218	+	0.153056i	$0.0489114\pi$
$683$	8.00000i	0.306111i	−0.988218	+	0.153056i	$0.951089\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	15.0000	0.572703
$687$	12.0000i	0.457829i
$688$	− 11.0000i	− 0.419371i
$689$	−12.0000	−0.457164
$690$	0	0
$691$	6.00000	0.228251	0.114125	−	0.993466i	$-0.463593\pi$
$691$	6.00000	0.228251	0.114125	+	0.993466i	$0.463593\pi$
$692$	− 14.0000i	− 0.532200i
$693$	15.0000i	0.569803i
$694$	11.0000	0.417554
$695$	0	0
$696$	−4.00000	−0.151620
$697$	10.0000i	0.378777i
$698$	− 10.0000i	− 0.378506i
$699$	−6.00000	−0.226941
$700$	0	0
$701$	22.0000	0.830929	0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000	0.830929	0.415464	+	0.909610i	$0.363619\pi$
$702$	4.00000i	0.150970i
$703$	− 9.00000i	− 0.339441i
$704$	5.00000	0.188445
$705$	0	0
$706$	−24.0000	−0.903252
$707$	27.0000i	1.01544i
$708$	− 8.00000i	− 0.300658i
$709$	−49.0000	−1.84023	−0.920117	−	0.391644i	$-0.871906\pi$
$709$	−49.0000	−1.84023	−0.920117	+	0.391644i	$0.871906\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	2.00000i	0.0749532i
$713$	− 4.00000i	− 0.149801i
$714$	3.00000	0.112272
$715$	0	0
$716$	−12.0000	−0.448461
$717$	− 5.00000i	− 0.186728i
$718$	− 25.0000i	− 0.932992i
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	0	0
$721$	42.0000	1.56416
$722$	18.0000i	0.669891i
$723$	− 8.00000i	− 0.297523i
$724$	5.00000	0.185824
$725$	0	0
$726$	14.0000	0.519589
$727$	32.0000i	1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$	32.0000i	1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$	12.0000i	0.444750i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−11.0000	−0.406850
$732$	14.0000i	0.517455i
$733$	2.00000i	0.0738717i	0.999318	+	0.0369358i	$0.0117597\pi$
$733$	2.00000i	0.0738717i	−0.999318	+	0.0369358i	$0.988240\pi$
$734$	25.0000	0.922767
$735$	0	0
$736$	4.00000	0.147442
$737$	35.0000i	1.28924i
$738$	− 10.0000i	− 0.368105i
$739$	17.0000	0.625355	0.312678	−	0.949859i	$-0.398774\pi$
$739$	17.0000	0.625355	0.312678	+	0.949859i	$0.398774\pi$
$740$	0	0
$741$	4.00000	0.146944
$742$	− 9.00000i	− 0.330400i
$743$	− 38.0000i	− 1.39408i	−0.717030	−	0.697042i	$-0.754499\pi$
$743$	− 38.0000i	− 1.39408i	0.717030	−	0.697042i	$-0.245501\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	−6.00000	−0.219676
$747$	8.00000i	0.292705i
$748$	− 5.00000i	− 0.182818i
$749$	45.0000	1.64426
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	9.00000i	0.328196i
$753$	− 18.0000i	− 0.655956i
$754$	−16.0000	−0.582686
$755$	0	0
$756$	−3.00000	−0.109109
$757$	− 46.0000i	− 1.67190i	−0.548807	−	0.835949i	$-0.684918\pi$
$757$	− 46.0000i	− 1.67190i	0.548807	−	0.835949i	$-0.315082\pi$
$758$	− 4.00000i	− 0.145287i
$759$	20.0000	0.725954
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	− 2.00000i	− 0.0724524i
$763$	− 3.00000i	− 0.108607i
$764$	9.00000	0.325609
$765$	0	0
$766$	12.0000	0.433578
$767$	− 32.0000i	− 1.15545i
$768$	1.00000i	0.0360844i
$769$	−11.0000	−0.396670	−0.198335	−	0.980134i	$-0.563553\pi$
$769$	−11.0000	−0.396670	−0.198335	+	0.980134i	$0.563553\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	6.00000i	0.215945i
$773$	− 22.0000i	− 0.791285i	−0.918405	−	0.395643i	$-0.870522\pi$
$773$	− 22.0000i	− 0.791285i	0.918405	−	0.395643i	$-0.129478\pi$
$774$	11.0000	0.395387
$775$	0	0
$776$	14.0000	0.502571
$777$	27.0000i	0.968620i
$778$	21.0000i	0.752886i
$779$	−10.0000	−0.358287
$780$	0	0
$781$	−70.0000	−2.50480
$782$	− 4.00000i	− 0.143040i
$783$	− 4.00000i	− 0.142948i
$784$	−2.00000	−0.0714286
$785$	0	0
$786$	4.00000	0.142675
$787$	50.0000i	1.78231i	0.453701	+	0.891154i	$0.350103\pi$
$787$	50.0000i	1.78231i	−0.453701	+	0.891154i	$0.649897\pi$
$788$	12.0000i	0.427482i
$789$	−7.00000	−0.249207
$790$	0	0
$791$	−9.00000	−0.320003
$792$	5.00000i	0.177667i
$793$	56.0000i	1.98862i
$794$	15.0000	0.532330
$795$	0	0
$796$	−1.00000	−0.0354441
$797$	− 39.0000i	− 1.38145i	−0.723117	−	0.690725i	$-0.757291\pi$
$797$	− 39.0000i	− 1.38145i	0.723117	−	0.690725i	$-0.242709\pi$
$798$	3.00000i	0.106199i
$799$	9.00000	0.318397
$800$	0	0
$801$	−2.00000	−0.0706665
$802$	30.0000i	1.05934i
$803$	10.0000i	0.352892i
$804$	−7.00000	−0.246871
$805$	0	0
$806$	4.00000	0.140894
$807$	− 28.0000i	− 0.985647i
$808$	9.00000i	0.316619i
$809$	−39.0000	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$810$	0	0
$811$	−22.0000	−0.772524	−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000	−0.772524	−0.386262	+	0.922389i	$0.626234\pi$
$812$	− 12.0000i	− 0.421117i
$813$	4.00000i	0.140286i
$814$	45.0000	1.57725
$815$	0	0
$816$	1.00000	0.0350070
$817$	− 11.0000i	− 0.384841i
$818$	− 26.0000i	− 0.909069i
$819$	−12.0000	−0.419314
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	− 6.00000i	− 0.209274i
$823$	− 8.00000i	− 0.278862i	−0.990232	−	0.139431i	$-0.955473\pi$
$823$	− 8.00000i	− 0.278862i	0.990232	−	0.139431i	$-0.0445274\pi$
$824$	14.0000	0.487713
$825$	0	0
$826$	24.0000	0.835067
$827$	− 39.0000i	− 1.35616i	−0.734987	−	0.678081i	$-0.762812\pi$
$827$	− 39.0000i	− 1.35616i	0.734987	−	0.678081i	$-0.237188\pi$
$828$	4.00000i	0.139010i
$829$	24.0000	0.833554	0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000	0.833554	0.416777	+	0.909009i	$0.363160\pi$
$830$	0	0
$831$	13.0000	0.450965
$832$	4.00000i	0.138675i
$833$	2.00000i	0.0692959i
$834$	−8.00000	−0.277017
$835$	0	0
$836$	5.00000	0.172929
$837$	1.00000i	0.0345651i
$838$	28.0000i	0.967244i
$839$	−10.0000	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	− 24.0000i	− 0.827095i
$843$	− 18.0000i	− 0.619953i
$844$	12.0000	0.413057
$845$	0	0
$846$	−9.00000	−0.309426
$847$	42.0000i	1.44314i
$848$	− 3.00000i	− 0.103020i
$849$	22.0000	0.755038
$850$	0	0
$851$	36.0000	1.23406
$852$	− 14.0000i	− 0.479632i
$853$	− 9.00000i	− 0.308154i	−0.988059	−	0.154077i	$-0.950760\pi$
$853$	− 9.00000i	− 0.308154i	0.988059	−	0.154077i	$-0.0492404\pi$
$854$	−42.0000	−1.43721
$855$	0	0
$856$	15.0000	0.512689
$857$	− 5.00000i	− 0.170797i	−0.996347	−	0.0853984i	$-0.972784\pi$
$857$	− 5.00000i	− 0.170797i	0.996347	−	0.0853984i	$-0.0272163\pi$
$858$	20.0000i	0.682789i
$859$	25.0000	0.852989	0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000	0.852989	0.426494	+	0.904490i	$0.359748\pi$
$860$	0	0
$861$	30.0000	1.02240
$862$	− 14.0000i	− 0.476842i
$863$	− 17.0000i	− 0.578687i	−0.957225	−	0.289343i	$-0.906563\pi$
$863$	− 17.0000i	− 0.578687i	0.957225	−	0.289343i	$-0.0934369\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−27.0000	−0.917497
$867$	− 1.00000i	− 0.0339618i
$868$	3.00000i	0.101827i
$869$	−25.0000	−0.848067
$870$	0	0
$871$	−28.0000	−0.948744
$872$	− 1.00000i	− 0.0338643i
$873$	14.0000i	0.473828i
$874$	4.00000	0.135302
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	46.0000i	1.55331i	0.629926	+	0.776655i	$0.283085\pi$
$877$	46.0000i	1.55331i	−0.629926	+	0.776655i	$0.716915\pi$
$878$	20.0000i	0.674967i
$879$	−18.0000	−0.607125
$880$	0	0
$881$	−35.0000	−1.17918	−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000	−1.17918	−0.589590	+	0.807703i	$0.700711\pi$
$882$	− 2.00000i	− 0.0673435i
$883$	− 48.0000i	− 1.61533i	−0.589643	−	0.807664i	$-0.700731\pi$
$883$	− 48.0000i	− 1.61533i	0.589643	−	0.807664i	$-0.299269\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	38.0000	1.27663
$887$	− 12.0000i	− 0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$	− 12.0000i	− 0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$	9.00000i	0.302020i
$889$	6.00000	0.201234
$890$	0	0
$891$	−5.00000	−0.167506
$892$	6.00000i	0.200895i
$893$	9.00000i	0.301174i
$894$	−14.0000	−0.468230
$895$	0	0
$896$	−3.00000	−0.100223
$897$	16.0000i	0.534224i
$898$	− 41.0000i	− 1.36819i
$899$	−4.00000	−0.133407
$900$	0	0
$901$	−3.00000	−0.0999445
$902$	− 50.0000i	− 1.66482i
$903$	33.0000i	1.09817i
$904$	−3.00000	−0.0997785
$905$	0	0
$906$	−24.0000	−0.797347
$907$	24.0000i	0.796907i	0.917189	+	0.398453i	$0.130453\pi$
$907$	24.0000i	0.796907i	−0.917189	+	0.398453i	$0.869547\pi$
$908$	21.0000i	0.696909i
$909$	−9.00000	−0.298511
$910$	0	0
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	1.00000i	0.0331133i
$913$	40.0000i	1.32381i
$914$	37.0000	1.22385
$915$	0	0
$916$	−12.0000	−0.396491
$917$	12.0000i	0.396275i
$918$	1.00000i	0.0330049i
$919$	14.0000	0.461817	0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000	0.461817	0.230909	+	0.972975i	$0.425830\pi$
$920$	0	0
$921$	−8.00000	−0.263609
$922$	5.00000i	0.164666i
$923$	− 56.0000i	− 1.84326i
$924$	−15.0000	−0.493464
$925$	0	0
$926$	−36.0000	−1.18303
$927$	14.0000i	0.459820i
$928$	− 4.00000i	− 0.131306i
$929$	−1.00000	−0.0328089	−0.0164045	−	0.999865i	$-0.505222\pi$
$929$	−1.00000	−0.0328089	−0.0164045	+	0.999865i	$0.505222\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	− 6.00000i	− 0.196537i
$933$	10.0000i	0.327385i
$934$	−6.00000	−0.196326
$935$	0	0
$936$	−4.00000	−0.130744
$937$	− 38.0000i	− 1.24141i	−0.784046	−	0.620703i	$-0.786847\pi$
$937$	− 38.0000i	− 1.24141i	0.784046	−	0.620703i	$-0.213153\pi$
$938$	− 21.0000i	− 0.685674i
$939$	−16.0000	−0.522140
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	− 24.0000i	− 0.781962i
$943$	− 40.0000i	− 1.30258i
$944$	8.00000	0.260378
$945$	0	0
$946$	55.0000	1.78820
$947$	− 29.0000i	− 0.942373i	−0.882034	−	0.471187i	$-0.843826\pi$
$947$	− 29.0000i	− 0.942373i	0.882034	−	0.471187i	$-0.156174\pi$
$948$	− 5.00000i	− 0.162392i
$949$	−8.00000	−0.259691
$950$	0	0
$951$	−4.00000	−0.129709
$952$	3.00000i	0.0972306i
$953$	− 12.0000i	− 0.388718i	−0.980930	−	0.194359i	$-0.937737\pi$
$953$	− 12.0000i	− 0.388718i	0.980930	−	0.194359i	$-0.0622627\pi$
$954$	3.00000	0.0971286
$955$	0	0
$956$	5.00000	0.161712
$957$	− 20.0000i	− 0.646508i
$958$	30.0000i	0.969256i
$959$	18.0000	0.581250
$960$	0	0
$961$	−30.0000	−0.967742
$962$	36.0000i	1.16069i
$963$	15.0000i	0.483368i
$964$	8.00000	0.257663
$965$	0	0
$966$	−12.0000	−0.386094
$967$	− 24.0000i	− 0.771788i	−0.922543	−	0.385894i	$-0.873893\pi$
$967$	− 24.0000i	− 0.771788i	0.922543	−	0.385894i	$-0.126107\pi$
$968$	14.0000i	0.449977i
$969$	1.00000	0.0321246
$970$	0	0
$971$	−10.0000	−0.320915	−0.160458	−	0.987043i	$-0.551297\pi$
$971$	−10.0000	−0.320915	−0.160458	+	0.987043i	$0.551297\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 24.0000i	− 0.769405i
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−14.0000	−0.448129
$977$	− 48.0000i	− 1.53566i	−0.640656	−	0.767828i	$-0.721338\pi$
$977$	− 48.0000i	− 1.53566i	0.640656	−	0.767828i	$-0.278662\pi$
$978$	18.0000i	0.575577i
$979$	−10.0000	−0.319601
$980$	0	0
$981$	1.00000	0.0319275
$982$	30.0000i	0.957338i
$983$	28.0000i	0.893061i	0.894768	+	0.446531i	$0.147341\pi$
$983$	28.0000i	0.893061i	−0.894768	+	0.446531i	$0.852659\pi$
$984$	10.0000	0.318788
$985$	0	0
$986$	−4.00000	−0.127386
$987$	− 27.0000i	− 0.859419i
$988$	4.00000i	0.127257i
$989$	44.0000	1.39912
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	1.00000i	0.0317500i
$993$	5.00000i	0.158670i
$994$	42.0000	1.33216
$995$	0	0
$996$	−8.00000	−0.253490
$997$	− 25.0000i	− 0.791758i	−0.918303	−	0.395879i	$-0.870440\pi$
$997$	− 25.0000i	− 0.791758i	0.918303	−	0.395879i	$-0.129560\pi$
$998$	− 38.0000i	− 1.20287i
$999$	−9.00000	−0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.d.l.2449.1		2
5.2	odd	4		2550.2.a.bb.1.1	yes	1
5.3	odd	4		2550.2.a.f.1.1	✓	1
5.4	even	2	inner	2550.2.d.l.2449.2		2
15.2	even	4		7650.2.a.f.1.1		1
15.8	even	4		7650.2.a.ch.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.f.1.1	✓	1	5.3	odd	4
2550.2.a.bb.1.1	yes	1	5.2	odd	4
2550.2.d.l.2449.1		2	1.1	even	1	trivial
2550.2.d.l.2449.2		2	5.4	even	2	inner
7650.2.a.f.1.1		1	15.2	even	4
7650.2.a.ch.1.1		1	15.8	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:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -5.00000 q^{11} -1.00000i q^{12} -4.00000i q^{13} +3.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} -3.00000 q^{21} +5.00000i q^{22} +4.00000i q^{23} -1.00000 q^{24} -4.00000 q^{26} -1.00000i q^{27} -3.00000i q^{28} +4.00000 q^{29} -1.00000 q^{31} -1.00000i q^{32} -5.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} -9.00000i q^{37} -1.00000i q^{38} +4.00000 q^{39} -10.0000 q^{41} +3.00000i q^{42} -11.0000i q^{43} +5.00000 q^{44} +4.00000 q^{46} +9.00000i q^{47} +1.00000i q^{48} -2.00000 q^{49} +1.00000 q^{51} +4.00000i q^{52} -3.00000i q^{53} -1.00000 q^{54} -3.00000 q^{56} +1.00000i q^{57} -4.00000i q^{58} +8.00000 q^{59} -14.0000 q^{61} +1.00000i q^{62} -3.00000i q^{63} -1.00000 q^{64} -5.00000 q^{66} -7.00000i q^{67} +1.00000i q^{68} -4.00000 q^{69} +14.0000 q^{71} -1.00000i q^{72} -2.00000i q^{73} -9.00000 q^{74} -1.00000 q^{76} -15.0000i q^{77} -4.00000i q^{78} +5.00000 q^{79} +1.00000 q^{81} +10.0000i q^{82} -8.00000i q^{83} +3.00000 q^{84} -11.0000 q^{86} +4.00000i q^{87} -5.00000i q^{88} +2.00000 q^{89} +12.0000 q^{91} -4.00000i q^{92} -1.00000i q^{93} +9.00000 q^{94} +1.00000 q^{96} -14.0000i q^{97} +2.00000i q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} - 10 q^{11} + 6 q^{14} + 2 q^{16} + 2 q^{19} - 6 q^{21} - 2 q^{24} - 8 q^{26} + 8 q^{29} - 2 q^{31} - 2 q^{34} + 2 q^{36} + 8 q^{39} - 20 q^{41} + 10 q^{44} + 8 q^{46} - 4 q^{49} + 2 q^{51} - 2 q^{54} - 6 q^{56} + 16 q^{59} - 28 q^{61} - 2 q^{64} - 10 q^{66} - 8 q^{69} + 28 q^{71} - 18 q^{74} - 2 q^{76} + 10 q^{79} + 2 q^{81} + 6 q^{84} - 22 q^{86} + 4 q^{89} + 24 q^{91} + 18 q^{94} + 2 q^{96} + 10 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 - 10 * q^11 + 6 * q^14 + 2 * q^16 + 2 * q^19 - 6 * q^21 - 2 * q^24 - 8 * q^26 + 8 * q^29 - 2 * q^31 - 2 * q^34 + 2 * q^36 + 8 * q^39 - 20 * q^41 + 10 * q^44 + 8 * q^46 - 4 * q^49 + 2 * q^51 - 2 * q^54 - 6 * q^56 + 16 * q^59 - 28 * q^61 - 2 * q^64 - 10 * q^66 - 8 * q^69 + 28 * q^71 - 18 * q^74 - 2 * q^76 + 10 * q^79 + 2 * q^81 + 6 * q^84 - 22 * q^86 + 4 * q^89 + 24 * q^91 + 18 * q^94 + 2 * q^96 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more