LMFDB - Embedded newform 2550.2.a.bo.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(1,2550)]

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, 0, 0]))

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

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

chi := DirichletCharacter("2550.1");

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.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$20.3618525154$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 510)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.12489$ of defining polynomial
Character	$\chi$	$=$	2550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.64002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.64002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +6.24977 q^{11} +1.00000 q^{12} +2.00000 q^{13} +4.64002 q^{14} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -4.24977 q^{19} +4.64002 q^{21} +6.24977 q^{22} -3.67030 q^{23} +1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} +4.64002 q^{28} -9.85952 q^{29} +2.39025 q^{31} +1.00000 q^{32} +6.24977 q^{33} -1.00000 q^{34} +1.00000 q^{36} -4.88979 q^{37} -4.24977 q^{38} +2.00000 q^{39} +5.21949 q^{41} +4.64002 q^{42} -8.24977 q^{43} +6.24977 q^{44} -3.67030 q^{46} -3.21949 q^{47} +1.00000 q^{48} +14.5298 q^{49} -1.00000 q^{51} +2.00000 q^{52} -3.28005 q^{53} +1.00000 q^{54} +4.64002 q^{56} -4.24977 q^{57} -9.85952 q^{58} -7.03028 q^{59} -14.1698 q^{61} +2.39025 q^{62} +4.64002 q^{63} +1.00000 q^{64} +6.24977 q^{66} -2.06055 q^{67} -1.00000 q^{68} -3.67030 q^{69} -12.8292 q^{71} +1.00000 q^{72} +2.31032 q^{73} -4.88979 q^{74} -4.24977 q^{76} +28.9991 q^{77} +2.00000 q^{78} +5.60975 q^{79} +1.00000 q^{81} +5.21949 q^{82} +8.24977 q^{83} +4.64002 q^{84} -8.24977 q^{86} -9.85952 q^{87} +6.24977 q^{88} -3.03028 q^{89} +9.28005 q^{91} -3.67030 q^{92} +2.39025 q^{93} -3.21949 q^{94} +1.00000 q^{96} +6.96972 q^{97} +14.5298 q^{98} +6.24977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 4 q^{19} + 6 q^{21} + 2 q^{22} - 4 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} + 6 q^{28} - 4 q^{29} + 16 q^{31} + 3 q^{32} + 2 q^{33} - 3 q^{34} + 3 q^{36} + 10 q^{37} + 4 q^{38} + 6 q^{39} - 2 q^{41} + 6 q^{42} - 8 q^{43} + 2 q^{44} - 4 q^{46} + 8 q^{47} + 3 q^{48} + 11 q^{49} - 3 q^{51} + 6 q^{52} + 6 q^{53} + 3 q^{54} + 6 q^{56} + 4 q^{57} - 4 q^{58} - 22 q^{59} - 2 q^{61} + 16 q^{62} + 6 q^{63} + 3 q^{64} + 2 q^{66} - 8 q^{67} - 3 q^{68} - 4 q^{69} - 12 q^{71} + 3 q^{72} - 8 q^{73} + 10 q^{74} + 4 q^{76} + 20 q^{77} + 6 q^{78} + 8 q^{79} + 3 q^{81} - 2 q^{82} + 8 q^{83} + 6 q^{84} - 8 q^{86} - 4 q^{87} + 2 q^{88} - 10 q^{89} + 12 q^{91} - 4 q^{92} + 16 q^{93} + 8 q^{94} + 3 q^{96} + 20 q^{97} + 11 q^{98} + 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 4 * q^19 + 6 * q^21 + 2 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 + 6 * q^28 - 4 * q^29 + 16 * q^31 + 3 * q^32 + 2 * q^33 - 3 * q^34 + 3 * q^36 + 10 * q^37 + 4 * q^38 + 6 * q^39 - 2 * q^41 + 6 * q^42 - 8 * q^43 + 2 * q^44 - 4 * q^46 + 8 * q^47 + 3 * q^48 + 11 * q^49 - 3 * q^51 + 6 * q^52 + 6 * q^53 + 3 * q^54 + 6 * q^56 + 4 * q^57 - 4 * q^58 - 22 * q^59 - 2 * q^61 + 16 * q^62 + 6 * q^63 + 3 * q^64 + 2 * q^66 - 8 * q^67 - 3 * q^68 - 4 * q^69 - 12 * q^71 + 3 * q^72 - 8 * q^73 + 10 * q^74 + 4 * q^76 + 20 * q^77 + 6 * q^78 + 8 * q^79 + 3 * q^81 - 2 * q^82 + 8 * q^83 + 6 * q^84 - 8 * q^86 - 4 * q^87 + 2 * q^88 - 10 * q^89 + 12 * q^91 - 4 * q^92 + 16 * q^93 + 8 * q^94 + 3 * q^96 + 20 * q^97 + 11 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	4.64002	1.75376	0.876882	−	0.480706i	$-0.159619\pi$
$7$	4.64002	1.75376	0.876882	+	0.480706i	$0.159619\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	6.24977	1.88438	0.942188	−	0.335084i	$-0.108765\pi$
$11$	6.24977	1.88438	0.942188	+	0.335084i	$0.108765\pi$
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	4.64002	1.24010
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−4.24977	−0.974964	−0.487482	−	0.873133i	$-0.662085\pi$
$19$	−4.24977	−0.974964	−0.487482	+	0.873133i	$0.662085\pi$
$20$	0	0
$21$	4.64002	1.01254
$22$	6.24977	1.33246
$23$	−3.67030	−0.765310	−0.382655	−	0.923891i	$-0.624990\pi$
$23$	−3.67030	−0.765310	−0.382655	+	0.923891i	$0.624990\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	4.64002	0.876882
$29$	−9.85952	−1.83087	−0.915433	−	0.402470i	$-0.868152\pi$
$29$	−9.85952	−1.83087	−0.915433	+	0.402470i	$0.868152\pi$
$30$	0	0
$31$	2.39025	0.429302	0.214651	−	0.976691i	$-0.431139\pi$
$31$	2.39025	0.429302	0.214651	+	0.976691i	$0.431139\pi$
$32$	1.00000	0.176777
$33$	6.24977	1.08795
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.88979	−0.803877	−0.401939	−	0.915667i	$-0.631663\pi$
$37$	−4.88979	−0.803877	−0.401939	+	0.915667i	$0.631663\pi$
$38$	−4.24977	−0.689404
$39$	2.00000	0.320256
$40$	0	0
$41$	5.21949	0.815148	0.407574	−	0.913172i	$-0.366375\pi$
$41$	5.21949	0.815148	0.407574	+	0.913172i	$0.366375\pi$
$42$	4.64002	0.715971
$43$	−8.24977	−1.25808	−0.629039	−	0.777374i	$-0.716551\pi$
$43$	−8.24977	−1.25808	−0.629039	+	0.777374i	$0.716551\pi$
$44$	6.24977	0.942188
$45$	0	0
$46$	−3.67030	−0.541156
$47$	−3.21949	−0.469612	−0.234806	−	0.972042i	$-0.575445\pi$
$47$	−3.21949	−0.469612	−0.234806	+	0.972042i	$0.575445\pi$
$48$	1.00000	0.144338
$49$	14.5298	2.07569
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000	0.277350
$53$	−3.28005	−0.450549	−0.225275	−	0.974295i	$-0.572328\pi$
$53$	−3.28005	−0.450549	−0.225275	+	0.974295i	$0.572328\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.64002	0.620049
$57$	−4.24977	−0.562896
$58$	−9.85952	−1.29462
$59$	−7.03028	−0.915264	−0.457632	−	0.889142i	$-0.651302\pi$
$59$	−7.03028	−0.915264	−0.457632	+	0.889142i	$0.651302\pi$
$60$	0	0
$61$	−14.1698	−1.81426	−0.907131	−	0.420848i	$-0.861733\pi$
$61$	−14.1698	−1.81426	−0.907131	+	0.420848i	$0.861733\pi$
$62$	2.39025	0.303562
$63$	4.64002	0.584588
$64$	1.00000	0.125000
$65$	0	0
$66$	6.24977	0.769294
$67$	−2.06055	−0.251737	−0.125868	−	0.992047i	$-0.540172\pi$
$67$	−2.06055	−0.251737	−0.125868	+	0.992047i	$0.540172\pi$
$68$	−1.00000	−0.121268
$69$	−3.67030	−0.441852
$70$	0	0
$71$	−12.8292	−1.52255	−0.761275	−	0.648429i	$-0.775426\pi$
$71$	−12.8292	−1.52255	−0.761275	+	0.648429i	$0.775426\pi$
$72$	1.00000	0.117851
$73$	2.31032	0.270403	0.135201	−	0.990818i	$-0.456832\pi$
$73$	2.31032	0.270403	0.135201	+	0.990818i	$0.456832\pi$
$74$	−4.88979	−0.568427
$75$	0	0
$76$	−4.24977	−0.487482
$77$	28.9991	3.30475
$78$	2.00000	0.226455
$79$	5.60975	0.631146	0.315573	−	0.948901i	$-0.397803\pi$
$79$	5.60975	0.631146	0.315573	+	0.948901i	$0.397803\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.21949	0.576397
$83$	8.24977	0.905530	0.452765	−	0.891630i	$-0.350438\pi$
$83$	8.24977	0.905530	0.452765	+	0.891630i	$0.350438\pi$
$84$	4.64002	0.506268
$85$	0	0
$86$	−8.24977	−0.889596
$87$	−9.85952	−1.05705
$88$	6.24977	0.666228
$89$	−3.03028	−0.321209	−0.160604	−	0.987019i	$-0.551344\pi$
$89$	−3.03028	−0.321209	−0.160604	+	0.987019i	$0.551344\pi$
$90$	0	0
$91$	9.28005	0.972813
$92$	−3.67030	−0.382655
$93$	2.39025	0.247858
$94$	−3.21949	−0.332066
$95$	0	0
$96$	1.00000	0.102062
$97$	6.96972	0.707668	0.353834	−	0.935308i	$-0.384878\pi$
$97$	6.96972	0.707668	0.353834	+	0.935308i	$0.384878\pi$
$98$	14.5298	1.46773
$99$	6.24977	0.628126
$100$	0	0
$101$	−9.03028	−0.898546	−0.449273	−	0.893395i	$-0.648317\pi$
$101$	−9.03028	−0.898546	−0.449273	+	0.893395i	$0.648317\pi$
$102$	−1.00000	−0.0990148
$103$	2.24977	0.221677	0.110838	−	0.993838i	$-0.464646\pi$
$103$	2.24977	0.221677	0.110838	+	0.993838i	$0.464646\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−3.28005	−0.318586
$107$	−15.7190	−1.51962	−0.759808	−	0.650147i	$-0.774707\pi$
$107$	−15.7190	−1.51962	−0.759808	+	0.650147i	$0.774707\pi$
$108$	1.00000	0.0962250
$109$	10.1698	0.974094	0.487047	−	0.873376i	$-0.338074\pi$
$109$	10.1698	0.974094	0.487047	+	0.873376i	$0.338074\pi$
$110$	0	0
$111$	−4.88979	−0.464119
$112$	4.64002	0.438441
$113$	7.28005	0.684849	0.342425	−	0.939545i	$-0.388752\pi$
$113$	7.28005	0.684849	0.342425	+	0.939545i	$0.388752\pi$
$114$	−4.24977	−0.398028
$115$	0	0
$116$	−9.85952	−0.915433
$117$	2.00000	0.184900
$118$	−7.03028	−0.647189
$119$	−4.64002	−0.425350
$120$	0	0
$121$	28.0596	2.55088
$122$	−14.1698	−1.28288
$123$	5.21949	0.470626
$124$	2.39025	0.214651
$125$	0	0
$126$	4.64002	0.413366
$127$	15.5298	1.37805	0.689024	−	0.724738i	$-0.258039\pi$
$127$	15.5298	1.37805	0.689024	+	0.724738i	$0.258039\pi$
$128$	1.00000	0.0883883
$129$	−8.24977	−0.726352
$130$	0	0
$131$	−6.24977	−0.546045	−0.273023	−	0.962008i	$-0.588023\pi$
$131$	−6.24977	−0.546045	−0.273023	+	0.962008i	$0.588023\pi$
$132$	6.24977	0.543973
$133$	−19.7190	−1.70986
$134$	−2.06055	−0.178005
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	19.5298	1.66854	0.834272	−	0.551352i	$-0.185888\pi$
$137$	19.5298	1.66854	0.834272	+	0.551352i	$0.185888\pi$
$138$	−3.67030	−0.312437
$139$	−3.34060	−0.283346	−0.141673	−	0.989914i	$-0.545248\pi$
$139$	−3.34060	−0.283346	−0.141673	+	0.989914i	$0.545248\pi$
$140$	0	0
$141$	−3.21949	−0.271130
$142$	−12.8292	−1.07661
$143$	12.4995	1.04526
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.31032	0.191204
$147$	14.5298	1.19840
$148$	−4.88979	−0.401939
$149$	−5.68968	−0.466116	−0.233058	−	0.972463i	$-0.574873\pi$
$149$	−5.68968	−0.466116	−0.233058	+	0.972463i	$0.574873\pi$
$150$	0	0
$151$	16.4995	1.34271	0.671357	−	0.741134i	$-0.265712\pi$
$151$	16.4995	1.34271	0.671357	+	0.741134i	$0.265712\pi$
$152$	−4.24977	−0.344702
$153$	−1.00000	−0.0808452
$154$	28.9991	2.33681
$155$	0	0
$156$	2.00000	0.160128
$157$	15.2800	1.21948	0.609740	−	0.792601i	$-0.291274\pi$
$157$	15.2800	1.21948	0.609740	+	0.792601i	$0.291274\pi$
$158$	5.60975	0.446288
$159$	−3.28005	−0.260125
$160$	0	0
$161$	−17.0303	−1.34217
$162$	1.00000	0.0785674
$163$	8.49954	0.665735	0.332868	−	0.942974i	$-0.391984\pi$
$163$	8.49954	0.665735	0.332868	+	0.942974i	$0.391984\pi$
$164$	5.21949	0.407574
$165$	0	0
$166$	8.24977	0.640306
$167$	−14.2304	−1.10118	−0.550590	−	0.834776i	$-0.685597\pi$
$167$	−14.2304	−1.10118	−0.550590	+	0.834776i	$0.685597\pi$
$168$	4.64002	0.357986
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−4.24977	−0.324988
$172$	−8.24977	−0.629039
$173$	16.8898	1.28411	0.642054	−	0.766660i	$-0.278083\pi$
$173$	16.8898	1.28411	0.642054	+	0.766660i	$0.278083\pi$
$174$	−9.85952	−0.747448
$175$	0	0
$176$	6.24977	0.471094
$177$	−7.03028	−0.528428
$178$	−3.03028	−0.227129
$179$	1.34060	0.100201	0.0501005	−	0.998744i	$-0.484046\pi$
$179$	1.34060	0.100201	0.0501005	+	0.998744i	$0.484046\pi$
$180$	0	0
$181$	−6.32970	−0.470483	−0.235241	−	0.971937i	$-0.575588\pi$
$181$	−6.32970	−0.470483	−0.235241	+	0.971937i	$0.575588\pi$
$182$	9.28005	0.687883
$183$	−14.1698	−1.04746
$184$	−3.67030	−0.270578
$185$	0	0
$186$	2.39025	0.175262
$187$	−6.24977	−0.457029
$188$	−3.21949	−0.234806
$189$	4.64002	0.337512
$190$	0	0
$191$	−15.2195	−1.10124	−0.550622	−	0.834755i	$-0.685609\pi$
$191$	−15.2195	−1.10124	−0.550622	+	0.834755i	$0.685609\pi$
$192$	1.00000	0.0721688
$193$	11.4693	0.825576	0.412788	−	0.910827i	$-0.364555\pi$
$193$	11.4693	0.825576	0.412788	+	0.910827i	$0.364555\pi$
$194$	6.96972	0.500397
$195$	0	0
$196$	14.5298	1.03784
$197$	15.6097	1.11215	0.556074	−	0.831133i	$-0.312307\pi$
$197$	15.6097	1.11215	0.556074	+	0.831133i	$0.312307\pi$
$198$	6.24977	0.444152
$199$	−5.60975	−0.397664	−0.198832	−	0.980034i	$-0.563715\pi$
$199$	−5.60975	−0.397664	−0.198832	+	0.980034i	$0.563715\pi$
$200$	0	0
$201$	−2.06055	−0.145340
$202$	−9.03028	−0.635368
$203$	−45.7484	−3.21091
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	2.24977	0.156749
$207$	−3.67030	−0.255103
$208$	2.00000	0.138675
$209$	−26.5601	−1.83720
$210$	0	0
$211$	−11.8401	−0.815109	−0.407554	−	0.913181i	$-0.633618\pi$
$211$	−11.8401	−0.815109	−0.407554	+	0.913181i	$0.633618\pi$
$212$	−3.28005	−0.225275
$213$	−12.8292	−0.879045
$214$	−15.7190	−1.07453
$215$	0	0
$216$	1.00000	0.0680414
$217$	11.0908	0.752894
$218$	10.1698	0.688789
$219$	2.31032	0.156117
$220$	0	0
$221$	−2.00000	−0.134535
$222$	−4.88979	−0.328182
$223$	8.18922	0.548391	0.274195	−	0.961674i	$-0.411589\pi$
$223$	8.18922	0.548391	0.274195	+	0.961674i	$0.411589\pi$
$224$	4.64002	0.310025
$225$	0	0
$226$	7.28005	0.484262
$227$	−1.93945	−0.128726	−0.0643628	−	0.997927i	$-0.520501\pi$
$227$	−1.93945	−0.128726	−0.0643628	+	0.997927i	$0.520501\pi$
$228$	−4.24977	−0.281448
$229$	−7.93945	−0.524653	−0.262327	−	0.964979i	$-0.584490\pi$
$229$	−7.93945	−0.524653	−0.262327	+	0.964979i	$0.584490\pi$
$230$	0	0
$231$	28.9991	1.90800
$232$	−9.85952	−0.647309
$233$	2.78051	0.182157	0.0910785	−	0.995844i	$-0.470969\pi$
$233$	2.78051	0.182157	0.0910785	+	0.995844i	$0.470969\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−7.03028	−0.457632
$237$	5.60975	0.364392
$238$	−4.64002	−0.300768
$239$	3.34060	0.216085	0.108043	−	0.994146i	$-0.465542\pi$
$239$	3.34060	0.216085	0.108043	+	0.994146i	$0.465542\pi$
$240$	0	0
$241$	−5.21949	−0.336217	−0.168109	−	0.985768i	$-0.553766\pi$
$241$	−5.21949	−0.336217	−0.168109	+	0.985768i	$0.553766\pi$
$242$	28.0596	1.80374
$243$	1.00000	0.0641500
$244$	−14.1698	−0.907131
$245$	0	0
$246$	5.21949	0.332783
$247$	−8.49954	−0.540813
$248$	2.39025	0.151781
$249$	8.24977	0.522808
$250$	0	0
$251$	20.2791	1.28001	0.640004	−	0.768372i	$-0.278933\pi$
$251$	20.2791	1.28001	0.640004	+	0.768372i	$0.278933\pi$
$252$	4.64002	0.292294
$253$	−22.9385	−1.44213
$254$	15.5298	0.974427
$255$	0	0
$256$	1.00000	0.0625000
$257$	3.52982	0.220184	0.110092	−	0.993921i	$-0.464885\pi$
$257$	3.52982	0.220184	0.110092	+	0.993921i	$0.464885\pi$
$258$	−8.24977	−0.513608
$259$	−22.6888	−1.40981
$260$	0	0
$261$	−9.85952	−0.610289
$262$	−6.24977	−0.386112
$263$	−7.21949	−0.445173	−0.222587	−	0.974913i	$-0.571450\pi$
$263$	−7.21949	−0.445173	−0.222587	+	0.974913i	$0.571450\pi$
$264$	6.24977	0.384647
$265$	0	0
$266$	−19.7190	−1.20905
$267$	−3.03028	−0.185450
$268$	−2.06055	−0.125868
$269$	4.41961	0.269469	0.134734	−	0.990882i	$-0.456982\pi$
$269$	4.41961	0.269469	0.134734	+	0.990882i	$0.456982\pi$
$270$	0	0
$271$	−10.0606	−0.611135	−0.305568	−	0.952170i	$-0.598846\pi$
$271$	−10.0606	−0.611135	−0.305568	+	0.952170i	$0.598846\pi$
$272$	−1.00000	−0.0606339
$273$	9.28005	0.561654
$274$	19.5298	1.17984
$275$	0	0
$276$	−3.67030	−0.220926
$277$	10.0487	0.603770	0.301885	−	0.953344i	$-0.402384\pi$
$277$	10.0487	0.603770	0.301885	+	0.953344i	$0.402384\pi$
$278$	−3.34060	−0.200356
$279$	2.39025	0.143101
$280$	0	0
$281$	−32.1505	−1.91794	−0.958968	−	0.283515i	$-0.908500\pi$
$281$	−32.1505	−1.91794	−0.958968	+	0.283515i	$0.908500\pi$
$282$	−3.21949	−0.191718
$283$	0.659401	0.0391973	0.0195987	−	0.999808i	$-0.493761\pi$
$283$	0.659401	0.0391973	0.0195987	+	0.999808i	$0.493761\pi$
$284$	−12.8292	−0.761275
$285$	0	0
$286$	12.4995	0.739113
$287$	24.2186	1.42958
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	6.96972	0.408572
$292$	2.31032	0.135201
$293$	31.1202	1.81806	0.909030	−	0.416730i	$-0.136824\pi$
$293$	31.1202	1.81806	0.909030	+	0.416730i	$0.136824\pi$
$294$	14.5298	0.847396
$295$	0	0
$296$	−4.88979	−0.284214
$297$	6.24977	0.362648
$298$	−5.68968	−0.329594
$299$	−7.34060	−0.424518
$300$	0	0
$301$	−38.2791	−2.20637
$302$	16.4995	0.949442
$303$	−9.03028	−0.518776
$304$	−4.24977	−0.243741
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	16.2498	0.927423	0.463712	−	0.885986i	$-0.346517\pi$
$307$	16.2498	0.927423	0.463712	+	0.885986i	$0.346517\pi$
$308$	28.9991	1.65238
$309$	2.24977	0.127985
$310$	0	0
$311$	−6.39025	−0.362358	−0.181179	−	0.983450i	$-0.557991\pi$
$311$	−6.39025	−0.362358	−0.181179	+	0.983450i	$0.557991\pi$
$312$	2.00000	0.113228
$313$	−23.5904	−1.33341	−0.666703	−	0.745323i	$-0.732295\pi$
$313$	−23.5904	−1.33341	−0.666703	+	0.745323i	$0.732295\pi$
$314$	15.2800	0.862303
$315$	0	0
$316$	5.60975	0.315573
$317$	−27.3288	−1.53494	−0.767469	−	0.641086i	$-0.778484\pi$
$317$	−27.3288	−1.53494	−0.767469	+	0.641086i	$0.778484\pi$
$318$	−3.28005	−0.183936
$319$	−61.6197	−3.45004
$320$	0	0
$321$	−15.7190	−0.877351
$322$	−17.0303	−0.949060
$323$	4.24977	0.236464
$324$	1.00000	0.0555556
$325$	0	0
$326$	8.49954	0.470746
$327$	10.1698	0.562394
$328$	5.21949	0.288198
$329$	−14.9385	−0.823588
$330$	0	0
$331$	16.4995	0.906897	0.453448	−	0.891283i	$-0.350194\pi$
$331$	16.4995	0.906897	0.453448	+	0.891283i	$0.350194\pi$
$332$	8.24977	0.452765
$333$	−4.88979	−0.267959
$334$	−14.2304	−0.778652
$335$	0	0
$336$	4.64002	0.253134
$337$	−12.8704	−0.701096	−0.350548	−	0.936545i	$-0.614005\pi$
$337$	−12.8704	−0.701096	−0.350548	+	0.936545i	$0.614005\pi$
$338$	−9.00000	−0.489535
$339$	7.28005	0.395398
$340$	0	0
$341$	14.9385	0.808967
$342$	−4.24977	−0.229801
$343$	34.9385	1.88650
$344$	−8.24977	−0.444798
$345$	0	0
$346$	16.8898	0.908001
$347$	−1.43991	−0.0772982	−0.0386491	−	0.999253i	$-0.512305\pi$
$347$	−1.43991	−0.0772982	−0.0386491	+	0.999253i	$0.512305\pi$
$348$	−9.85952	−0.528526
$349$	19.1589	1.02555	0.512777	−	0.858522i	$-0.328617\pi$
$349$	19.1589	1.02555	0.512777	+	0.858522i	$0.328617\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	6.24977	0.333114
$353$	9.87890	0.525801	0.262900	−	0.964823i	$-0.415321\pi$
$353$	9.87890	0.525801	0.262900	+	0.964823i	$0.415321\pi$
$354$	−7.03028	−0.373655
$355$	0	0
$356$	−3.03028	−0.160604
$357$	−4.64002	−0.245576
$358$	1.34060	0.0708529
$359$	−14.6812	−0.774844	−0.387422	−	0.921902i	$-0.626634\pi$
$359$	−14.6812	−0.774844	−0.387422	+	0.921902i	$0.626634\pi$
$360$	0	0
$361$	−0.939448	−0.0494446
$362$	−6.32970	−0.332682
$363$	28.0596	1.47275
$364$	9.28005	0.486407
$365$	0	0
$366$	−14.1698	−0.740669
$367$	−7.23887	−0.377866	−0.188933	−	0.981990i	$-0.560503\pi$
$367$	−7.23887	−0.377866	−0.188933	+	0.981990i	$0.560503\pi$
$368$	−3.67030	−0.191328
$369$	5.21949	0.271716
$370$	0	0
$371$	−15.2195	−0.790157
$372$	2.39025	0.123929
$373$	12.5601	0.650337	0.325169	−	0.945656i	$-0.394579\pi$
$373$	12.5601	0.650337	0.325169	+	0.945656i	$0.394579\pi$
$374$	−6.24977	−0.323168
$375$	0	0
$376$	−3.21949	−0.166033
$377$	−19.7190	−1.01558
$378$	4.64002	0.238657
$379$	10.4390	0.536215	0.268107	−	0.963389i	$-0.413602\pi$
$379$	10.4390	0.536215	0.268107	+	0.963389i	$0.413602\pi$
$380$	0	0
$381$	15.5298	0.795617
$382$	−15.2195	−0.778697
$383$	−9.15894	−0.468000	−0.234000	−	0.972237i	$-0.575182\pi$
$383$	−9.15894	−0.468000	−0.234000	+	0.972237i	$0.575182\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	11.4693	0.583770
$387$	−8.24977	−0.419359
$388$	6.96972	0.353834
$389$	10.8099	0.548082	0.274041	−	0.961718i	$-0.411640\pi$
$389$	10.8099	0.548082	0.274041	+	0.961718i	$0.411640\pi$
$390$	0	0
$391$	3.67030	0.185615
$392$	14.5298	0.733867
$393$	−6.24977	−0.315259
$394$	15.6097	0.786408
$395$	0	0
$396$	6.24977	0.314063
$397$	−4.88979	−0.245412	−0.122706	−	0.992443i	$-0.539157\pi$
$397$	−4.88979	−0.245412	−0.122706	+	0.992443i	$0.539157\pi$
$398$	−5.60975	−0.281191
$399$	−19.7190	−0.987187
$400$	0	0
$401$	−35.6585	−1.78070	−0.890350	−	0.455277i	$-0.849540\pi$
$401$	−35.6585	−1.78070	−0.890350	+	0.455277i	$0.849540\pi$
$402$	−2.06055	−0.102771
$403$	4.78051	0.238134
$404$	−9.03028	−0.449273
$405$	0	0
$406$	−45.7484	−2.27045
$407$	−30.5601	−1.51481
$408$	−1.00000	−0.0495074
$409$	21.4693	1.06159	0.530793	−	0.847501i	$-0.321894\pi$
$409$	21.4693	1.06159	0.530793	+	0.847501i	$0.321894\pi$
$410$	0	0
$411$	19.5298	0.963335
$412$	2.24977	0.110838
$413$	−32.6206	−1.60516
$414$	−3.67030	−0.180385
$415$	0	0
$416$	2.00000	0.0980581
$417$	−3.34060	−0.163590
$418$	−26.5601	−1.29910
$419$	25.5904	1.25017	0.625086	−	0.780556i	$-0.285064\pi$
$419$	25.5904	1.25017	0.625086	+	0.780556i	$0.285064\pi$
$420$	0	0
$421$	−14.7805	−0.720358	−0.360179	−	0.932883i	$-0.617284\pi$
$421$	−14.7805	−0.720358	−0.360179	+	0.932883i	$0.617284\pi$
$422$	−11.8401	−0.576369
$423$	−3.21949	−0.156537
$424$	−3.28005	−0.159293
$425$	0	0
$426$	−12.8292	−0.621579
$427$	−65.7484	−3.18179
$428$	−15.7190	−0.759808
$429$	12.4995	0.603484
$430$	0	0
$431$	10.8898	0.524543	0.262271	−	0.964994i	$-0.415528\pi$
$431$	10.8898	0.524543	0.262271	+	0.964994i	$0.415528\pi$
$432$	1.00000	0.0481125
$433$	36.4683	1.75256	0.876279	−	0.481805i	$-0.160019\pi$
$433$	36.4683	1.75256	0.876279	+	0.481805i	$0.160019\pi$
$434$	11.0908	0.532377
$435$	0	0
$436$	10.1698	0.487047
$437$	15.5979	0.746150
$438$	2.31032	0.110392
$439$	20.2909	0.968434	0.484217	−	0.874948i	$-0.339105\pi$
$439$	20.2909	0.968434	0.484217	+	0.874948i	$0.339105\pi$
$440$	0	0
$441$	14.5298	0.691896
$442$	−2.00000	−0.0951303
$443$	1.43991	0.0684120	0.0342060	−	0.999415i	$-0.489110\pi$
$443$	1.43991	0.0684120	0.0342060	+	0.999415i	$0.489110\pi$
$444$	−4.88979	−0.232059
$445$	0	0
$446$	8.18922	0.387771
$447$	−5.68968	−0.269112
$448$	4.64002	0.219221
$449$	0.220411	0.0104019	0.00520093	−	0.999986i	$-0.498344\pi$
$449$	0.220411	0.0104019	0.00520093	+	0.999986i	$0.498344\pi$
$450$	0	0
$451$	32.6206	1.53605
$452$	7.28005	0.342425
$453$	16.4995	0.775216
$454$	−1.93945	−0.0910228
$455$	0	0
$456$	−4.24977	−0.199014
$457$	−15.4693	−0.723622	−0.361811	−	0.932252i	$-0.617841\pi$
$457$	−15.4693	−0.723622	−0.361811	+	0.932252i	$0.617841\pi$
$458$	−7.93945	−0.370986
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−27.4693	−1.27937	−0.639686	−	0.768637i	$-0.720935\pi$
$461$	−27.4693	−1.27937	−0.639686	+	0.768637i	$0.720935\pi$
$462$	28.9991	1.34916
$463$	−39.1277	−1.81842	−0.909210	−	0.416337i	$-0.863314\pi$
$463$	−39.1277	−1.81842	−0.909210	+	0.416337i	$0.863314\pi$
$464$	−9.85952	−0.457717
$465$	0	0
$466$	2.78051	0.128804
$467$	−33.1202	−1.53262	−0.766310	−	0.642471i	$-0.777909\pi$
$467$	−33.1202	−1.53262	−0.766310	+	0.642471i	$0.777909\pi$
$468$	2.00000	0.0924500
$469$	−9.56101	−0.441486
$470$	0	0
$471$	15.2800	0.704067
$472$	−7.03028	−0.323595
$473$	−51.5592	−2.37069
$474$	5.60975	0.257664
$475$	0	0
$476$	−4.64002	−0.212675
$477$	−3.28005	−0.150183
$478$	3.34060	0.152795
$479$	2.26915	0.103680	0.0518400	−	0.998655i	$-0.483491\pi$
$479$	2.26915	0.103680	0.0518400	+	0.998655i	$0.483491\pi$
$480$	0	0
$481$	−9.77959	−0.445911
$482$	−5.21949	−0.237741
$483$	−17.0303	−0.774904
$484$	28.0596	1.27544
$485$	0	0
$486$	1.00000	0.0453609
$487$	43.0403	1.95034	0.975170	−	0.221457i	$-0.0710813\pi$
$487$	43.0403	1.95034	0.975170	+	0.221457i	$0.0710813\pi$
$488$	−14.1698	−0.641439
$489$	8.49954	0.384363
$490$	0	0
$491$	−10.3397	−0.466623	−0.233312	−	0.972402i	$-0.574956\pi$
$491$	−10.3397	−0.466623	−0.233312	+	0.972402i	$0.574956\pi$
$492$	5.21949	0.235313
$493$	9.85952	0.444050
$494$	−8.49954	−0.382412
$495$	0	0
$496$	2.39025	0.107326
$497$	−59.5280	−2.67020
$498$	8.24977	0.369681
$499$	42.1580	1.88725	0.943626	−	0.331013i	$-0.107390\pi$
$499$	42.1580	1.88725	0.943626	+	0.331013i	$0.107390\pi$
$500$	0	0
$501$	−14.2304	−0.635767
$502$	20.2791	0.905102
$503$	35.7290	1.59308	0.796539	−	0.604587i	$-0.206662\pi$
$503$	35.7290	1.59308	0.796539	+	0.604587i	$0.206662\pi$
$504$	4.64002	0.206683
$505$	0	0
$506$	−22.9385	−1.01974
$507$	−9.00000	−0.399704
$508$	15.5298	0.689024
$509$	−34.6888	−1.53755	−0.768776	−	0.639518i	$-0.779134\pi$
$509$	−34.6888	−1.53755	−0.768776	+	0.639518i	$0.779134\pi$
$510$	0	0
$511$	10.7200	0.474223
$512$	1.00000	0.0441942
$513$	−4.24977	−0.187632
$514$	3.52982	0.155694
$515$	0	0
$516$	−8.24977	−0.363176
$517$	−20.1211	−0.884925
$518$	−22.6888	−0.996887
$519$	16.8898	0.741380
$520$	0	0
$521$	30.3397	1.32921	0.664603	−	0.747197i	$-0.268601\pi$
$521$	30.3397	1.32921	0.664603	+	0.747197i	$0.268601\pi$
$522$	−9.85952	−0.431539
$523$	21.9394	0.959345	0.479673	−	0.877448i	$-0.340755\pi$
$523$	21.9394	0.959345	0.479673	+	0.877448i	$0.340755\pi$
$524$	−6.24977	−0.273023
$525$	0	0
$526$	−7.21949	−0.314785
$527$	−2.39025	−0.104121
$528$	6.24977	0.271986
$529$	−9.52890	−0.414300
$530$	0	0
$531$	−7.03028	−0.305088
$532$	−19.7190	−0.854929
$533$	10.4390	0.452163
$534$	−3.03028	−0.131133
$535$	0	0
$536$	−2.06055	−0.0890023
$537$	1.34060	0.0578511
$538$	4.41961	0.190543
$539$	90.8080	3.91138
$540$	0	0
$541$	0.269148	0.0115716	0.00578579	−	0.999983i	$-0.498158\pi$
$541$	0.269148	0.0115716	0.00578579	+	0.999983i	$0.498158\pi$
$542$	−10.0606	−0.432138
$543$	−6.32970	−0.271633
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	9.28005	0.397149
$547$	7.21949	0.308683	0.154342	−	0.988018i	$-0.450674\pi$
$547$	7.21949	0.308683	0.154342	+	0.988018i	$0.450674\pi$
$548$	19.5298	0.834272
$549$	−14.1698	−0.604754
$550$	0	0
$551$	41.9007	1.78503
$552$	−3.67030	−0.156218
$553$	26.0294	1.10688
$554$	10.0487	0.426930
$555$	0	0
$556$	−3.34060	−0.141673
$557$	32.2791	1.36771	0.683855	−	0.729618i	$-0.260302\pi$
$557$	32.2791	1.36771	0.683855	+	0.729618i	$0.260302\pi$
$558$	2.39025	0.101187
$559$	−16.4995	−0.697856
$560$	0	0
$561$	−6.24977	−0.263866
$562$	−32.1505	−1.35619
$563$	3.30941	0.139475	0.0697374	−	0.997565i	$-0.477784\pi$
$563$	3.30941	0.139475	0.0697374	+	0.997565i	$0.477784\pi$
$564$	−3.21949	−0.135565
$565$	0	0
$566$	0.659401	0.0277167
$567$	4.64002	0.194863
$568$	−12.8292	−0.538303
$569$	−14.1211	−0.591987	−0.295994	−	0.955190i	$-0.595651\pi$
$569$	−14.1211	−0.591987	−0.295994	+	0.955190i	$0.595651\pi$
$570$	0	0
$571$	18.5601	0.776716	0.388358	−	0.921509i	$-0.373042\pi$
$571$	18.5601	0.776716	0.388358	+	0.921509i	$0.373042\pi$
$572$	12.4995	0.522632
$573$	−15.2195	−0.635804
$574$	24.2186	1.01086
$575$	0	0
$576$	1.00000	0.0416667
$577$	−3.37935	−0.140684	−0.0703422	−	0.997523i	$-0.522409\pi$
$577$	−3.37935	−0.140684	−0.0703422	+	0.997523i	$0.522409\pi$
$578$	1.00000	0.0415945
$579$	11.4693	0.476646
$580$	0	0
$581$	38.2791	1.58809
$582$	6.96972	0.288904
$583$	−20.4995	−0.849004
$584$	2.31032	0.0956018
$585$	0	0
$586$	31.1202	1.28556
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	14.5298	0.599200
$589$	−10.1580	−0.418554
$590$	0	0
$591$	15.6097	0.642099
$592$	−4.88979	−0.200969
$593$	−13.9688	−0.573630	−0.286815	−	0.957986i	$-0.592597\pi$
$593$	−13.9688	−0.573630	−0.286815	+	0.957986i	$0.592597\pi$
$594$	6.24977	0.256431
$595$	0	0
$596$	−5.68968	−0.233058
$597$	−5.60975	−0.229592
$598$	−7.34060	−0.300179
$599$	41.4986	1.69559	0.847794	−	0.530326i	$-0.177930\pi$
$599$	41.4986	1.69559	0.847794	+	0.530326i	$0.177930\pi$
$600$	0	0
$601$	33.6803	1.37385	0.686924	−	0.726730i	$-0.258961\pi$
$601$	33.6803	1.37385	0.686924	+	0.726730i	$0.258961\pi$
$602$	−38.2791	−1.56014
$603$	−2.06055	−0.0839122
$604$	16.4995	0.671357
$605$	0	0
$606$	−9.03028	−0.366830
$607$	13.5804	0.551211	0.275605	−	0.961271i	$-0.411122\pi$
$607$	13.5804	0.551211	0.275605	+	0.961271i	$0.411122\pi$
$608$	−4.24977	−0.172351
$609$	−45.7484	−1.85382
$610$	0	0
$611$	−6.43899	−0.260494
$612$	−1.00000	−0.0404226
$613$	−13.2195	−0.533930	−0.266965	−	0.963706i	$-0.586021\pi$
$613$	−13.2195	−0.533930	−0.266965	+	0.963706i	$0.586021\pi$
$614$	16.2498	0.655787
$615$	0	0
$616$	28.9991	1.16841
$617$	−36.7200	−1.47829	−0.739145	−	0.673547i	$-0.764770\pi$
$617$	−36.7200	−1.47829	−0.739145	+	0.673547i	$0.764770\pi$
$618$	2.24977	0.0904991
$619$	−10.9385	−0.439657	−0.219828	−	0.975539i	$-0.570550\pi$
$619$	−10.9385	−0.439657	−0.219828	+	0.975539i	$0.570550\pi$
$620$	0	0
$621$	−3.67030	−0.147284
$622$	−6.39025	−0.256226
$623$	−14.0606	−0.563324
$624$	2.00000	0.0800641
$625$	0	0
$626$	−23.5904	−0.942861
$627$	−26.5601	−1.06071
$628$	15.2800	0.609740
$629$	4.88979	0.194969
$630$	0	0
$631$	−5.77959	−0.230082	−0.115041	−	0.993361i	$-0.536700\pi$
$631$	−5.77959	−0.230082	−0.115041	+	0.993361i	$0.536700\pi$
$632$	5.60975	0.223144
$633$	−11.8401	−0.470603
$634$	−27.3288	−1.08536
$635$	0	0
$636$	−3.28005	−0.130062
$637$	29.0596	1.15138
$638$	−61.6197	−2.43955
$639$	−12.8292	−0.507517
$640$	0	0
$641$	19.9007	0.786030	0.393015	−	0.919532i	$-0.371432\pi$
$641$	19.9007	0.786030	0.393015	+	0.919532i	$0.371432\pi$
$642$	−15.7190	−0.620381
$643$	12.1211	0.478010	0.239005	−	0.971018i	$-0.423179\pi$
$643$	12.1211	0.478010	0.239005	+	0.971018i	$0.423179\pi$
$644$	−17.0303	−0.671087
$645$	0	0
$646$	4.24977	0.167205
$647$	34.4002	1.35241	0.676206	−	0.736712i	$-0.263623\pi$
$647$	34.4002	1.35241	0.676206	+	0.736712i	$0.263623\pi$
$648$	1.00000	0.0392837
$649$	−43.9376	−1.72470
$650$	0	0
$651$	11.0908	0.434684
$652$	8.49954	0.332868
$653$	−13.5492	−0.530221	−0.265110	−	0.964218i	$-0.585408\pi$
$653$	−13.5492	−0.530221	−0.265110	+	0.964218i	$0.585408\pi$
$654$	10.1698	0.397672
$655$	0	0
$656$	5.21949	0.203787
$657$	2.31032	0.0901343
$658$	−14.9385	−0.582365
$659$	−27.5298	−1.07241	−0.536205	−	0.844088i	$-0.680142\pi$
$659$	−27.5298	−1.07241	−0.536205	+	0.844088i	$0.680142\pi$
$660$	0	0
$661$	19.6585	0.764626	0.382313	−	0.924033i	$-0.375128\pi$
$661$	19.6585	0.764626	0.382313	+	0.924033i	$0.375128\pi$
$662$	16.4995	0.641273
$663$	−2.00000	−0.0776736
$664$	8.24977	0.320153
$665$	0	0
$666$	−4.88979	−0.189476
$667$	36.1874	1.40118
$668$	−14.2304	−0.550590
$669$	8.18922	0.316613
$670$	0	0
$671$	−88.5583	−3.41875
$672$	4.64002	0.178993
$673$	−27.4693	−1.05886	−0.529431	−	0.848353i	$-0.677595\pi$
$673$	−27.4693	−1.05886	−0.529431	+	0.848353i	$0.677595\pi$
$674$	−12.8704	−0.495750
$675$	0	0
$676$	−9.00000	−0.346154
$677$	13.5104	0.519248	0.259624	−	0.965710i	$-0.416401\pi$
$677$	13.5104	0.519248	0.259624	+	0.965710i	$0.416401\pi$
$678$	7.28005	0.279589
$679$	32.3397	1.24108
$680$	0	0
$681$	−1.93945	−0.0743198
$682$	14.9385	0.572026
$683$	−4.49954	−0.172170	−0.0860851	−	0.996288i	$-0.527436\pi$
$683$	−4.49954	−0.172170	−0.0860851	+	0.996288i	$0.527436\pi$
$684$	−4.24977	−0.162494
$685$	0	0
$686$	34.9385	1.33396
$687$	−7.93945	−0.302909
$688$	−8.24977	−0.314520
$689$	−6.56009	−0.249920
$690$	0	0
$691$	31.0984	1.18304	0.591519	−	0.806291i	$-0.298528\pi$
$691$	31.0984	1.18304	0.591519	+	0.806291i	$0.298528\pi$
$692$	16.8898	0.642054
$693$	28.9991	1.10158
$694$	−1.43991	−0.0546581
$695$	0	0
$696$	−9.85952	−0.373724
$697$	−5.21949	−0.197702
$698$	19.1589	0.725177
$699$	2.78051	0.105168
$700$	0	0
$701$	−42.5289	−1.60629	−0.803147	−	0.595781i	$-0.796843\pi$
$701$	−42.5289	−1.60629	−0.803147	+	0.595781i	$0.796843\pi$
$702$	2.00000	0.0754851
$703$	20.7805	0.783752
$704$	6.24977	0.235547
$705$	0	0
$706$	9.87890	0.371797
$707$	−41.9007	−1.57584
$708$	−7.03028	−0.264214
$709$	21.2682	0.798745	0.399373	−	0.916789i	$-0.369228\pi$
$709$	21.2682	0.798745	0.399373	+	0.916789i	$0.369228\pi$
$710$	0	0
$711$	5.60975	0.210382
$712$	−3.03028	−0.113564
$713$	−8.77294	−0.328549
$714$	−4.64002	−0.173649
$715$	0	0
$716$	1.34060	0.0501005
$717$	3.34060	0.124757
$718$	−14.6812	−0.547897
$719$	−9.32878	−0.347905	−0.173952	−	0.984754i	$-0.555654\pi$
$719$	−9.32878	−0.347905	−0.173952	+	0.984754i	$0.555654\pi$
$720$	0	0
$721$	10.4390	0.388768
$722$	−0.939448	−0.0349626
$723$	−5.21949	−0.194115
$724$	−6.32970	−0.235241
$725$	0	0
$726$	28.0596	1.04139
$727$	−16.5289	−0.613023	−0.306512	−	0.951867i	$-0.599162\pi$
$727$	−16.5289	−0.613023	−0.306512	+	0.951867i	$0.599162\pi$
$728$	9.28005	0.343941
$729$	1.00000	0.0370370
$730$	0	0
$731$	8.24977	0.305129
$732$	−14.1698	−0.523732
$733$	−41.6803	−1.53950	−0.769748	−	0.638348i	$-0.779618\pi$
$733$	−41.6803	−1.53950	−0.769748	+	0.638348i	$0.779618\pi$
$734$	−7.23887	−0.267192
$735$	0	0
$736$	−3.67030	−0.135289
$737$	−12.8780	−0.474366
$738$	5.21949	0.192132
$739$	−28.2498	−1.03918	−0.519592	−	0.854414i	$-0.673916\pi$
$739$	−28.2498	−1.03918	−0.519592	+	0.854414i	$0.673916\pi$
$740$	0	0
$741$	−8.49954	−0.312238
$742$	−15.2195	−0.558725
$743$	24.5095	0.899167	0.449584	−	0.893238i	$-0.351572\pi$
$743$	24.5095	0.899167	0.449584	+	0.893238i	$0.351572\pi$
$744$	2.39025	0.0876309
$745$	0	0
$746$	12.5601	0.459858
$747$	8.24977	0.301843
$748$	−6.24977	−0.228514
$749$	−72.9367	−2.66505
$750$	0	0
$751$	6.92855	0.252826	0.126413	−	0.991978i	$-0.459653\pi$
$751$	6.92855	0.252826	0.126413	+	0.991978i	$0.459653\pi$
$752$	−3.21949	−0.117403
$753$	20.2791	0.739013
$754$	−19.7190	−0.718125
$755$	0	0
$756$	4.64002	0.168756
$757$	−17.8401	−0.648411	−0.324205	−	0.945987i	$-0.605097\pi$
$757$	−17.8401	−0.648411	−0.324205	+	0.945987i	$0.605097\pi$
$758$	10.4390	0.379161
$759$	−22.9385	−0.832616
$760$	0	0
$761$	−34.9991	−1.26872	−0.634358	−	0.773039i	$-0.718735\pi$
$761$	−34.9991	−1.26872	−0.634358	+	0.773039i	$0.718735\pi$
$762$	15.5298	0.562586
$763$	47.1883	1.70833
$764$	−15.2195	−0.550622
$765$	0	0
$766$	−9.15894	−0.330926
$767$	−14.0606	−0.507697
$768$	1.00000	0.0360844
$769$	44.4977	1.60463	0.802314	−	0.596902i	$-0.203602\pi$
$769$	44.4977	1.60463	0.802314	+	0.596902i	$0.203602\pi$
$770$	0	0
$771$	3.52982	0.127123
$772$	11.4693	0.412788
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	−8.24977	−0.296532
$775$	0	0
$776$	6.96972	0.250199
$777$	−22.6888	−0.813955
$778$	10.8099	0.387552
$779$	−22.1817	−0.794740
$780$	0	0
$781$	−80.1798	−2.86906
$782$	3.67030	0.131250
$783$	−9.85952	−0.352350
$784$	14.5298	0.518922
$785$	0	0
$786$	−6.24977	−0.222922
$787$	27.2195	0.970270	0.485135	−	0.874439i	$-0.338770\pi$
$787$	27.2195	0.970270	0.485135	+	0.874439i	$0.338770\pi$
$788$	15.6097	0.556074
$789$	−7.21949	−0.257021
$790$	0	0
$791$	33.7796	1.20106
$792$	6.24977	0.222076
$793$	−28.3397	−1.00637
$794$	−4.88979	−0.173532
$795$	0	0
$796$	−5.60975	−0.198832
$797$	−4.71995	−0.167189	−0.0835947	−	0.996500i	$-0.526640\pi$
$797$	−4.71995	−0.167189	−0.0835947	+	0.996500i	$0.526640\pi$
$798$	−19.7190	−0.698046
$799$	3.21949	0.113898
$800$	0	0
$801$	−3.03028	−0.107070
$802$	−35.6585	−1.25914
$803$	14.4390	0.509541
$804$	−2.06055	−0.0726701
$805$	0	0
$806$	4.78051	0.168386
$807$	4.41961	0.155578
$808$	−9.03028	−0.317684
$809$	8.27913	0.291079	0.145539	−	0.989352i	$-0.453508\pi$
$809$	8.27913	0.291079	0.145539	+	0.989352i	$0.453508\pi$
$810$	0	0
$811$	−24.6206	−0.864548	−0.432274	−	0.901742i	$-0.642289\pi$
$811$	−24.6206	−0.864548	−0.432274	+	0.901742i	$0.642289\pi$
$812$	−45.7484	−1.60545
$813$	−10.0606	−0.352839
$814$	−30.5601	−1.07113
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	35.0596	1.22658
$818$	21.4693	0.750655
$819$	9.28005	0.324271
$820$	0	0
$821$	−8.36089	−0.291797	−0.145899	−	0.989300i	$-0.546607\pi$
$821$	−8.36089	−0.291797	−0.145899	+	0.989300i	$0.546607\pi$
$822$	19.5298	0.681181
$823$	2.70058	0.0941361	0.0470681	−	0.998892i	$-0.485012\pi$
$823$	2.70058	0.0941361	0.0470681	+	0.998892i	$0.485012\pi$
$824$	2.24977	0.0783745
$825$	0	0
$826$	−32.6206	−1.13502
$827$	−5.40115	−0.187816	−0.0939082	−	0.995581i	$-0.529936\pi$
$827$	−5.40115	−0.187816	−0.0939082	+	0.995581i	$0.529936\pi$
$828$	−3.67030	−0.127552
$829$	−52.4390	−1.82128	−0.910641	−	0.413199i	$-0.864411\pi$
$829$	−52.4390	−1.82128	−0.910641	+	0.413199i	$0.864411\pi$
$830$	0	0
$831$	10.0487	0.348587
$832$	2.00000	0.0693375
$833$	−14.5298	−0.503428
$834$	−3.34060	−0.115675
$835$	0	0
$836$	−26.5601	−0.918600
$837$	2.39025	0.0826192
$838$	25.5904	0.884005
$839$	−17.5710	−0.606618	−0.303309	−	0.952892i	$-0.598091\pi$
$839$	−17.5710	−0.606618	−0.303309	+	0.952892i	$0.598091\pi$
$840$	0	0
$841$	68.2101	2.35207
$842$	−14.7805	−0.509370
$843$	−32.1505	−1.10732
$844$	−11.8401	−0.407554
$845$	0	0
$846$	−3.21949	−0.110689
$847$	130.197	4.47363
$848$	−3.28005	−0.112637
$849$	0.659401	0.0226306
$850$	0	0
$851$	17.9470	0.615216
$852$	−12.8292	−0.439523
$853$	−10.6694	−0.365313	−0.182656	−	0.983177i	$-0.558470\pi$
$853$	−10.6694	−0.365313	−0.182656	+	0.983177i	$0.558470\pi$
$854$	−65.7484	−2.24986
$855$	0	0
$856$	−15.7190	−0.537266
$857$	25.0596	0.856021	0.428010	−	0.903774i	$-0.359215\pi$
$857$	25.0596	0.856021	0.428010	+	0.903774i	$0.359215\pi$
$858$	12.4995	0.426727
$859$	46.5601	1.58861	0.794305	−	0.607519i	$-0.207835\pi$
$859$	46.5601	1.58861	0.794305	+	0.607519i	$0.207835\pi$
$860$	0	0
$861$	24.2186	0.825367
$862$	10.8898	0.370908
$863$	4.24221	0.144406	0.0722032	−	0.997390i	$-0.476997\pi$
$863$	4.24221	0.144406	0.0722032	+	0.997390i	$0.476997\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	36.4683	1.23924
$867$	1.00000	0.0339618
$868$	11.0908	0.376447
$869$	35.0596	1.18932
$870$	0	0
$871$	−4.12110	−0.139638
$872$	10.1698	0.344394
$873$	6.96972	0.235889
$874$	15.5979	0.527608
$875$	0	0
$876$	2.31032	0.0780586
$877$	−15.7309	−0.531193	−0.265597	−	0.964084i	$-0.585569\pi$
$877$	−15.7309	−0.531193	−0.265597	+	0.964084i	$0.585569\pi$
$878$	20.2909	0.684786
$879$	31.1202	1.04966
$880$	0	0
$881$	3.93945	0.132723	0.0663617	−	0.997796i	$-0.478861\pi$
$881$	3.93945	0.132723	0.0663617	+	0.997796i	$0.478861\pi$
$882$	14.5298	0.489244
$883$	−20.3784	−0.685789	−0.342895	−	0.939374i	$-0.611407\pi$
$883$	−20.3784	−0.685789	−0.342895	+	0.939374i	$0.611407\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	1.43991	0.0483746
$887$	−27.1084	−0.910210	−0.455105	−	0.890438i	$-0.650398\pi$
$887$	−27.1084	−0.910210	−0.455105	+	0.890438i	$0.650398\pi$
$888$	−4.88979	−0.164091
$889$	72.0587	2.41677
$890$	0	0
$891$	6.24977	0.209375
$892$	8.18922	0.274195
$893$	13.6821	0.457855
$894$	−5.68968	−0.190291
$895$	0	0
$896$	4.64002	0.155012
$897$	−7.34060	−0.245095
$898$	0.220411	0.00735522
$899$	−23.5667	−0.785995
$900$	0	0
$901$	3.28005	0.109274
$902$	32.6206	1.08615
$903$	−38.2791	−1.27385
$904$	7.28005	0.242131
$905$	0	0
$906$	16.4995	0.548161
$907$	−22.8998	−0.760375	−0.380187	−	0.924910i	$-0.624140\pi$
$907$	−22.8998	−0.760375	−0.380187	+	0.924910i	$0.624140\pi$
$908$	−1.93945	−0.0643628
$909$	−9.03028	−0.299515
$910$	0	0
$911$	41.5710	1.37731	0.688654	−	0.725090i	$-0.258202\pi$
$911$	41.5710	1.37731	0.688654	+	0.725090i	$0.258202\pi$
$912$	−4.24977	−0.140724
$913$	51.5592	1.70636
$914$	−15.4693	−0.511678
$915$	0	0
$916$	−7.93945	−0.262327
$917$	−28.9991	−0.957634
$918$	−1.00000	−0.0330049
$919$	−45.8771	−1.51334	−0.756672	−	0.653794i	$-0.773176\pi$
$919$	−45.8771	−1.51334	−0.756672	+	0.653794i	$0.773176\pi$
$920$	0	0
$921$	16.2498	0.535448
$922$	−27.4693	−0.904652
$923$	−25.6585	−0.844559
$924$	28.9991	0.954000
$925$	0	0
$926$	−39.1277	−1.28582
$927$	2.24977	0.0738922
$928$	−9.85952	−0.323655
$929$	47.1589	1.54723	0.773617	−	0.633653i	$-0.218445\pi$
$929$	47.1589	1.54723	0.773617	+	0.633653i	$0.218445\pi$
$930$	0	0
$931$	−61.7484	−2.02372
$932$	2.78051	0.0910785
$933$	−6.39025	−0.209207
$934$	−33.1202	−1.08373
$935$	0	0
$936$	2.00000	0.0653720
$937$	13.6509	0.445956	0.222978	−	0.974823i	$-0.428422\pi$
$937$	13.6509	0.445956	0.222978	+	0.974823i	$0.428422\pi$
$938$	−9.56101	−0.312178
$939$	−23.5904	−0.769843
$940$	0	0
$941$	29.8595	0.973392	0.486696	−	0.873571i	$-0.338202\pi$
$941$	29.8595	0.973392	0.486696	+	0.873571i	$0.338202\pi$
$942$	15.2800	0.497851
$943$	−19.1571	−0.623841
$944$	−7.03028	−0.228816
$945$	0	0
$946$	−51.5592	−1.67633
$947$	11.0984	0.360649	0.180325	−	0.983607i	$-0.442285\pi$
$947$	11.0984	0.360649	0.180325	+	0.983607i	$0.442285\pi$
$948$	5.60975	0.182196
$949$	4.62065	0.149993
$950$	0	0
$951$	−27.3288	−0.886197
$952$	−4.64002	−0.150384
$953$	11.8183	0.382834	0.191417	−	0.981509i	$-0.438692\pi$
$953$	11.8183	0.382834	0.191417	+	0.981509i	$0.438692\pi$
$954$	−3.28005	−0.106195
$955$	0	0
$956$	3.34060	0.108043
$957$	−61.6197	−1.99188
$958$	2.26915	0.0733129
$959$	90.6188	2.92623
$960$	0	0
$961$	−25.2867	−0.815700
$962$	−9.77959	−0.315307
$963$	−15.7190	−0.506539
$964$	−5.21949	−0.168109
$965$	0	0
$966$	−17.0303	−0.547940
$967$	−21.7502	−0.699440	−0.349720	−	0.936854i	$-0.613723\pi$
$967$	−21.7502	−0.699440	−0.349720	+	0.936854i	$0.613723\pi$
$968$	28.0596	0.901871
$969$	4.24977	0.136522
$970$	0	0
$971$	−40.4078	−1.29675	−0.648374	−	0.761322i	$-0.724551\pi$
$971$	−40.4078	−1.29675	−0.648374	+	0.761322i	$0.724551\pi$
$972$	1.00000	0.0320750
$973$	−15.5005	−0.496922
$974$	43.0403	1.37910
$975$	0	0
$976$	−14.1698	−0.453566
$977$	−10.5307	−0.336908	−0.168454	−	0.985710i	$-0.553877\pi$
$977$	−10.5307	−0.336908	−0.168454	+	0.985710i	$0.553877\pi$
$978$	8.49954	0.271785
$979$	−18.9385	−0.605278
$980$	0	0
$981$	10.1698	0.324698
$982$	−10.3397	−0.329953
$983$	48.5095	1.54721	0.773607	−	0.633666i	$-0.218451\pi$
$983$	48.5095	1.54721	0.773607	+	0.633666i	$0.218451\pi$
$984$	5.21949	0.166391
$985$	0	0
$986$	9.85952	0.313991
$987$	−14.9385	−0.475499
$988$	−8.49954	−0.270406
$989$	30.2791	0.962820
$990$	0	0
$991$	−13.9494	−0.443118	−0.221559	−	0.975147i	$-0.571115\pi$
$991$	−13.9494	−0.443118	−0.221559	+	0.975147i	$0.571115\pi$
$992$	2.39025	0.0758906
$993$	16.4995	0.523597
$994$	−59.5280	−1.88811
$995$	0	0
$996$	8.24977	0.261404
$997$	−36.9485	−1.17017	−0.585086	−	0.810972i	$-0.698939\pi$
$997$	−36.9485	−1.17017	−0.585086	+	0.810972i	$0.698939\pi$
$998$	42.1580	1.33449
$999$	−4.88979	−0.154706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.a.bo.1.3		3
3.2	odd	2		7650.2.a.dl.1.3		3
5.2	odd	4		510.2.d.d.409.4	yes	6
5.3	odd	4		510.2.d.d.409.1	✓	6
5.4	even	2		2550.2.a.bn.1.1		3
15.2	even	4		1530.2.d.i.919.3		6
15.8	even	4		1530.2.d.i.919.6		6
15.14	odd	2		7650.2.a.dm.1.1		3
20.3	even	4		4080.2.m.p.2449.1		6
20.7	even	4		4080.2.m.p.2449.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.d.d.409.1	✓	6	5.3	odd	4
510.2.d.d.409.4	yes	6	5.2	odd	4
1530.2.d.i.919.3		6	15.2	even	4
1530.2.d.i.919.6		6	15.8	even	4
2550.2.a.bn.1.1		3	5.4	even	2
2550.2.a.bo.1.3		3	1.1	even	1	trivial
4080.2.m.p.2449.1		6	20.3	even	4
4080.2.m.p.2449.4		6	20.7	even	4
7650.2.a.dl.1.3		3	3.2	odd	2
7650.2.a.dm.1.1		3	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.64002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.64002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +6.24977 q^{11} +1.00000 q^{12} +2.00000 q^{13} +4.64002 q^{14} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -4.24977 q^{19} +4.64002 q^{21} +6.24977 q^{22} -3.67030 q^{23} +1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} +4.64002 q^{28} -9.85952 q^{29} +2.39025 q^{31} +1.00000 q^{32} +6.24977 q^{33} -1.00000 q^{34} +1.00000 q^{36} -4.88979 q^{37} -4.24977 q^{38} +2.00000 q^{39} +5.21949 q^{41} +4.64002 q^{42} -8.24977 q^{43} +6.24977 q^{44} -3.67030 q^{46} -3.21949 q^{47} +1.00000 q^{48} +14.5298 q^{49} -1.00000 q^{51} +2.00000 q^{52} -3.28005 q^{53} +1.00000 q^{54} +4.64002 q^{56} -4.24977 q^{57} -9.85952 q^{58} -7.03028 q^{59} -14.1698 q^{61} +2.39025 q^{62} +4.64002 q^{63} +1.00000 q^{64} +6.24977 q^{66} -2.06055 q^{67} -1.00000 q^{68} -3.67030 q^{69} -12.8292 q^{71} +1.00000 q^{72} +2.31032 q^{73} -4.88979 q^{74} -4.24977 q^{76} +28.9991 q^{77} +2.00000 q^{78} +5.60975 q^{79} +1.00000 q^{81} +5.21949 q^{82} +8.24977 q^{83} +4.64002 q^{84} -8.24977 q^{86} -9.85952 q^{87} +6.24977 q^{88} -3.03028 q^{89} +9.28005 q^{91} -3.67030 q^{92} +2.39025 q^{93} -3.21949 q^{94} +1.00000 q^{96} +6.96972 q^{97} +14.5298 q^{98} +6.24977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 4 q^{19} + 6 q^{21} + 2 q^{22} - 4 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} + 6 q^{28} - 4 q^{29} + 16 q^{31} + 3 q^{32} + 2 q^{33} - 3 q^{34} + 3 q^{36} + 10 q^{37} + 4 q^{38} + 6 q^{39} - 2 q^{41} + 6 q^{42} - 8 q^{43} + 2 q^{44} - 4 q^{46} + 8 q^{47} + 3 q^{48} + 11 q^{49} - 3 q^{51} + 6 q^{52} + 6 q^{53} + 3 q^{54} + 6 q^{56} + 4 q^{57} - 4 q^{58} - 22 q^{59} - 2 q^{61} + 16 q^{62} + 6 q^{63} + 3 q^{64} + 2 q^{66} - 8 q^{67} - 3 q^{68} - 4 q^{69} - 12 q^{71} + 3 q^{72} - 8 q^{73} + 10 q^{74} + 4 q^{76} + 20 q^{77} + 6 q^{78} + 8 q^{79} + 3 q^{81} - 2 q^{82} + 8 q^{83} + 6 q^{84} - 8 q^{86} - 4 q^{87} + 2 q^{88} - 10 q^{89} + 12 q^{91} - 4 q^{92} + 16 q^{93} + 8 q^{94} + 3 q^{96} + 20 q^{97} + 11 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 4 * q^19 + 6 * q^21 + 2 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 + 6 * q^28 - 4 * q^29 + 16 * q^31 + 3 * q^32 + 2 * q^33 - 3 * q^34 + 3 * q^36 + 10 * q^37 + 4 * q^38 + 6 * q^39 - 2 * q^41 + 6 * q^42 - 8 * q^43 + 2 * q^44 - 4 * q^46 + 8 * q^47 + 3 * q^48 + 11 * q^49 - 3 * q^51 + 6 * q^52 + 6 * q^53 + 3 * q^54 + 6 * q^56 + 4 * q^57 - 4 * q^58 - 22 * q^59 - 2 * q^61 + 16 * q^62 + 6 * q^63 + 3 * q^64 + 2 * q^66 - 8 * q^67 - 3 * q^68 - 4 * q^69 - 12 * q^71 + 3 * q^72 - 8 * q^73 + 10 * q^74 + 4 * q^76 + 20 * q^77 + 6 * q^78 + 8 * q^79 + 3 * q^81 - 2 * q^82 + 8 * q^83 + 6 * q^84 - 8 * q^86 - 4 * q^87 + 2 * q^88 - 10 * q^89 + 12 * q^91 - 4 * q^92 + 16 * q^93 + 8 * q^94 + 3 * q^96 + 20 * q^97 + 11 * q^98 + 2 * q^99

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