LMFDB - Embedded newform 1250.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1250,2,Mod(1,1250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1250, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1250.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1250 = 2 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1250.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:	$9.98130025266$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.85410 q^{9} +4.23607 q^{11} +0.381966 q^{12} -1.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} -1.14590 q^{17} -2.85410 q^{18} +5.85410 q^{19} +1.14590 q^{21} +4.23607 q^{22} +1.76393 q^{23} +0.381966 q^{24} -1.00000 q^{26} -2.23607 q^{27} +3.00000 q^{28} -9.47214 q^{29} -0.236068 q^{31} +1.00000 q^{32} +1.61803 q^{33} -1.14590 q^{34} -2.85410 q^{36} +8.32624 q^{37} +5.85410 q^{38} -0.381966 q^{39} +1.47214 q^{41} +1.14590 q^{42} +6.23607 q^{43} +4.23607 q^{44} +1.76393 q^{46} +11.9443 q^{47} +0.381966 q^{48} +2.00000 q^{49} -0.437694 q^{51} -1.00000 q^{52} -10.4721 q^{53} -2.23607 q^{54} +3.00000 q^{56} +2.23607 q^{57} -9.47214 q^{58} -4.47214 q^{59} -8.85410 q^{61} -0.236068 q^{62} -8.56231 q^{63} +1.00000 q^{64} +1.61803 q^{66} +10.2361 q^{67} -1.14590 q^{68} +0.673762 q^{69} -3.00000 q^{71} -2.85410 q^{72} -7.70820 q^{73} +8.32624 q^{74} +5.85410 q^{76} +12.7082 q^{77} -0.381966 q^{78} -7.23607 q^{79} +7.70820 q^{81} +1.47214 q^{82} +4.52786 q^{83} +1.14590 q^{84} +6.23607 q^{86} -3.61803 q^{87} +4.23607 q^{88} +4.47214 q^{89} -3.00000 q^{91} +1.76393 q^{92} -0.0901699 q^{93} +11.9443 q^{94} +0.381966 q^{96} -9.56231 q^{97} +2.00000 q^{98} -12.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 6 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 6 * q^7 + 2 * q^8 + q^9	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 6 q^{7} + 2 q^{8} + q^{9} + 4 q^{11} + 3 q^{12} - 2 q^{13} + 6 q^{14} + 2 q^{16} - 9 q^{17} + q^{18} + 5 q^{19} + 9 q^{21} + 4 q^{22} + 8 q^{23} + 3 q^{24} - 2 q^{26} + 6 q^{28} - 10 q^{29} + 4 q^{31} + 2 q^{32} + q^{33} - 9 q^{34} + q^{36} + q^{37} + 5 q^{38} - 3 q^{39} - 6 q^{41} + 9 q^{42} + 8 q^{43} + 4 q^{44} + 8 q^{46} + 6 q^{47} + 3 q^{48} + 4 q^{49} - 21 q^{51} - 2 q^{52} - 12 q^{53} + 6 q^{56} - 10 q^{58} - 11 q^{61} + 4 q^{62} + 3 q^{63} + 2 q^{64} + q^{66} + 16 q^{67} - 9 q^{68} + 17 q^{69} - 6 q^{71} + q^{72} - 2 q^{73} + q^{74} + 5 q^{76} + 12 q^{77} - 3 q^{78} - 10 q^{79} + 2 q^{81} - 6 q^{82} + 18 q^{83} + 9 q^{84} + 8 q^{86} - 5 q^{87} + 4 q^{88} - 6 q^{91} + 8 q^{92} + 11 q^{93} + 6 q^{94} + 3 q^{96} + q^{97} + 4 q^{98} - 13 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 6 * q^7 + 2 * q^8 + q^9 + 4 * q^11 + 3 * q^12 - 2 * q^13 + 6 * q^14 + 2 * q^16 - 9 * q^17 + q^18 + 5 * q^19 + 9 * q^21 + 4 * q^22 + 8 * q^23 + 3 * q^24 - 2 * q^26 + 6 * q^28 - 10 * q^29 + 4 * q^31 + 2 * q^32 + q^33 - 9 * q^34 + q^36 + q^37 + 5 * q^38 - 3 * q^39 - 6 * q^41 + 9 * q^42 + 8 * q^43 + 4 * q^44 + 8 * q^46 + 6 * q^47 + 3 * q^48 + 4 * q^49 - 21 * q^51 - 2 * q^52 - 12 * q^53 + 6 * q^56 - 10 * q^58 - 11 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 + q^66 + 16 * q^67 - 9 * q^68 + 17 * q^69 - 6 * q^71 + q^72 - 2 * q^73 + q^74 + 5 * q^76 + 12 * q^77 - 3 * q^78 - 10 * q^79 + 2 * q^81 - 6 * q^82 + 18 * q^83 + 9 * q^84 + 8 * q^86 - 5 * q^87 + 4 * q^88 - 6 * q^91 + 8 * q^92 + 11 * q^93 + 6 * q^94 + 3 * q^96 + q^97 + 4 * q^98 - 13 * 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
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.381966	0.155937
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	1.00000	0.353553
$9$	−2.85410	−0.951367
$10$	0	0
$11$	4.23607	1.27722	0.638611	−	0.769529i	$-0.279509\pi$
$11$	4.23607	1.27722	0.638611	+	0.769529i	$0.279509\pi$
$12$	0.381966	0.110264
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	3.00000	0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.14590	−0.277921	−0.138961	−	0.990298i	$-0.544376\pi$
$17$	−1.14590	−0.277921	−0.138961	+	0.990298i	$0.544376\pi$
$18$	−2.85410	−0.672718
$19$	5.85410	1.34302	0.671512	−	0.740994i	$-0.265645\pi$
$19$	5.85410	1.34302	0.671512	+	0.740994i	$0.265645\pi$
$20$	0	0
$21$	1.14590	0.250055
$22$	4.23607	0.903133
$23$	1.76393	0.367805	0.183903	−	0.982944i	$-0.441127\pi$
$23$	1.76393	0.367805	0.183903	+	0.982944i	$0.441127\pi$
$24$	0.381966	0.0779685
$25$	0	0
$26$	−1.00000	−0.196116
$27$	−2.23607	−0.430331
$28$	3.00000	0.566947
$29$	−9.47214	−1.75893	−0.879466	−	0.475962i	$-0.842100\pi$
$29$	−9.47214	−1.75893	−0.879466	+	0.475962i	$0.842100\pi$
$30$	0	0
$31$	−0.236068	−0.0423991	−0.0211995	−	0.999775i	$-0.506749\pi$
$31$	−0.236068	−0.0423991	−0.0211995	+	0.999775i	$0.506749\pi$
$32$	1.00000	0.176777
$33$	1.61803	0.281664
$34$	−1.14590	−0.196520
$35$	0	0
$36$	−2.85410	−0.475684
$37$	8.32624	1.36883	0.684413	−	0.729095i	$-0.260059\pi$
$37$	8.32624	1.36883	0.684413	+	0.729095i	$0.260059\pi$
$38$	5.85410	0.949661
$39$	−0.381966	−0.0611635
$40$	0	0
$41$	1.47214	0.229909	0.114955	−	0.993371i	$-0.463328\pi$
$41$	1.47214	0.229909	0.114955	+	0.993371i	$0.463328\pi$
$42$	1.14590	0.176816
$43$	6.23607	0.950991	0.475496	−	0.879718i	$-0.342269\pi$
$43$	6.23607	0.950991	0.475496	+	0.879718i	$0.342269\pi$
$44$	4.23607	0.638611
$45$	0	0
$46$	1.76393	0.260078
$47$	11.9443	1.74225	0.871126	−	0.491060i	$-0.163391\pi$
$47$	11.9443	1.74225	0.871126	+	0.491060i	$0.163391\pi$
$48$	0.381966	0.0551320
$49$	2.00000	0.285714
$50$	0	0
$51$	−0.437694	−0.0612894
$52$	−1.00000	−0.138675
$53$	−10.4721	−1.43846	−0.719229	−	0.694773i	$-0.755505\pi$
$53$	−10.4721	−1.43846	−0.719229	+	0.694773i	$0.755505\pi$
$54$	−2.23607	−0.304290
$55$	0	0
$56$	3.00000	0.400892
$57$	2.23607	0.296174
$58$	−9.47214	−1.24375
$59$	−4.47214	−0.582223	−0.291111	−	0.956689i	$-0.594025\pi$
$59$	−4.47214	−0.582223	−0.291111	+	0.956689i	$0.594025\pi$
$60$	0	0
$61$	−8.85410	−1.13365	−0.566826	−	0.823838i	$-0.691829\pi$
$61$	−8.85410	−1.13365	−0.566826	+	0.823838i	$0.691829\pi$
$62$	−0.236068	−0.0299807
$63$	−8.56231	−1.07875
$64$	1.00000	0.125000
$65$	0	0
$66$	1.61803	0.199166
$67$	10.2361	1.25053	0.625267	−	0.780411i	$-0.284990\pi$
$67$	10.2361	1.25053	0.625267	+	0.780411i	$0.284990\pi$
$68$	−1.14590	−0.138961
$69$	0.673762	0.0811114
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	−2.85410	−0.336359
$73$	−7.70820	−0.902177	−0.451089	−	0.892479i	$-0.648964\pi$
$73$	−7.70820	−0.902177	−0.451089	+	0.892479i	$0.648964\pi$
$74$	8.32624	0.967905
$75$	0	0
$76$	5.85410	0.671512
$77$	12.7082	1.44823
$78$	−0.381966	−0.0432491
$79$	−7.23607	−0.814121	−0.407061	−	0.913401i	$-0.633446\pi$
$79$	−7.23607	−0.814121	−0.407061	+	0.913401i	$0.633446\pi$
$80$	0	0
$81$	7.70820	0.856467
$82$	1.47214	0.162570
$83$	4.52786	0.496998	0.248499	−	0.968632i	$-0.420063\pi$
$83$	4.52786	0.496998	0.248499	+	0.968632i	$0.420063\pi$
$84$	1.14590	0.125028
$85$	0	0
$86$	6.23607	0.672453
$87$	−3.61803	−0.387894
$88$	4.23607	0.451566
$89$	4.47214	0.474045	0.237023	−	0.971504i	$-0.423828\pi$
$89$	4.47214	0.474045	0.237023	+	0.971504i	$0.423828\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	1.76393	0.183903
$93$	−0.0901699	−0.00935019
$94$	11.9443	1.23196
$95$	0	0
$96$	0.381966	0.0389842
$97$	−9.56231	−0.970905	−0.485453	−	0.874263i	$-0.661345\pi$
$97$	−9.56231	−0.970905	−0.485453	+	0.874263i	$0.661345\pi$
$98$	2.00000	0.202031
$99$	−12.0902	−1.21511
$100$	0	0
$101$	0.618034	0.0614967	0.0307483	−	0.999527i	$-0.490211\pi$
$101$	0.618034	0.0614967	0.0307483	+	0.999527i	$0.490211\pi$
$102$	−0.437694	−0.0433382
$103$	13.1459	1.29530	0.647652	−	0.761936i	$-0.275751\pi$
$103$	13.1459	1.29530	0.647652	+	0.761936i	$0.275751\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−10.4721	−1.01714
$107$	1.09017	0.105391	0.0526954	−	0.998611i	$-0.483219\pi$
$107$	1.09017	0.105391	0.0526954	+	0.998611i	$0.483219\pi$
$108$	−2.23607	−0.215166
$109$	−15.0000	−1.43674	−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000	−1.43674	−0.718370	+	0.695662i	$0.755111\pi$
$110$	0	0
$111$	3.18034	0.301865
$112$	3.00000	0.283473
$113$	−3.76393	−0.354081	−0.177040	−	0.984204i	$-0.556652\pi$
$113$	−3.76393	−0.354081	−0.177040	+	0.984204i	$0.556652\pi$
$114$	2.23607	0.209427
$115$	0	0
$116$	−9.47214	−0.879466
$117$	2.85410	0.263862
$118$	−4.47214	−0.411693
$119$	−3.43769	−0.315133
$120$	0	0
$121$	6.94427	0.631297
$122$	−8.85410	−0.801613
$123$	0.562306	0.0507014
$124$	−0.236068	−0.0211995
$125$	0	0
$126$	−8.56231	−0.762791
$127$	3.52786	0.313047	0.156524	−	0.987674i	$-0.449971\pi$
$127$	3.52786	0.313047	0.156524	+	0.987674i	$0.449971\pi$
$128$	1.00000	0.0883883
$129$	2.38197	0.209720
$130$	0	0
$131$	−16.4164	−1.43431	−0.717154	−	0.696915i	$-0.754556\pi$
$131$	−16.4164	−1.43431	−0.717154	+	0.696915i	$0.754556\pi$
$132$	1.61803	0.140832
$133$	17.5623	1.52285
$134$	10.2361	0.884262
$135$	0	0
$136$	−1.14590	−0.0982599
$137$	−5.09017	−0.434883	−0.217441	−	0.976073i	$-0.569771\pi$
$137$	−5.09017	−0.434883	−0.217441	+	0.976073i	$0.569771\pi$
$138$	0.673762	0.0573544
$139$	−5.32624	−0.451766	−0.225883	−	0.974154i	$-0.572527\pi$
$139$	−5.32624	−0.451766	−0.225883	+	0.974154i	$0.572527\pi$
$140$	0	0
$141$	4.56231	0.384215
$142$	−3.00000	−0.251754
$143$	−4.23607	−0.354238
$144$	−2.85410	−0.237842
$145$	0	0
$146$	−7.70820	−0.637935
$147$	0.763932	0.0630081
$148$	8.32624	0.684413
$149$	2.23607	0.183186	0.0915929	−	0.995797i	$-0.470804\pi$
$149$	2.23607	0.183186	0.0915929	+	0.995797i	$0.470804\pi$
$150$	0	0
$151$	−9.70820	−0.790042	−0.395021	−	0.918672i	$-0.629263\pi$
$151$	−9.70820	−0.790042	−0.395021	+	0.918672i	$0.629263\pi$
$152$	5.85410	0.474830
$153$	3.27051	0.264405
$154$	12.7082	1.02406
$155$	0	0
$156$	−0.381966	−0.0305818
$157$	−4.56231	−0.364112	−0.182056	−	0.983288i	$-0.558275\pi$
$157$	−4.56231	−0.364112	−0.182056	+	0.983288i	$0.558275\pi$
$158$	−7.23607	−0.575671
$159$	−4.00000	−0.317221
$160$	0	0
$161$	5.29180	0.417052
$162$	7.70820	0.605614
$163$	−1.85410	−0.145224	−0.0726122	−	0.997360i	$-0.523134\pi$
$163$	−1.85410	−0.145224	−0.0726122	+	0.997360i	$0.523134\pi$
$164$	1.47214	0.114955
$165$	0	0
$166$	4.52786	0.351430
$167$	−13.3820	−1.03553	−0.517764	−	0.855524i	$-0.673235\pi$
$167$	−13.3820	−1.03553	−0.517764	+	0.855524i	$0.673235\pi$
$168$	1.14590	0.0884080
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−16.7082	−1.27771
$172$	6.23607	0.475496
$173$	1.23607	0.0939765	0.0469883	−	0.998895i	$-0.485038\pi$
$173$	1.23607	0.0939765	0.0469883	+	0.998895i	$0.485038\pi$
$174$	−3.61803	−0.274282
$175$	0	0
$176$	4.23607	0.319306
$177$	−1.70820	−0.128396
$178$	4.47214	0.335201
$179$	11.1803	0.835658	0.417829	−	0.908526i	$-0.362791\pi$
$179$	11.1803	0.835658	0.417829	+	0.908526i	$0.362791\pi$
$180$	0	0
$181$	5.41641	0.402598	0.201299	−	0.979530i	$-0.435484\pi$
$181$	5.41641	0.402598	0.201299	+	0.979530i	$0.435484\pi$
$182$	−3.00000	−0.222375
$183$	−3.38197	−0.250002
$184$	1.76393	0.130039
$185$	0	0
$186$	−0.0901699	−0.00661158
$187$	−4.85410	−0.354967
$188$	11.9443	0.871126
$189$	−6.70820	−0.487950
$190$	0	0
$191$	−13.6525	−0.987858	−0.493929	−	0.869502i	$-0.664440\pi$
$191$	−13.6525	−0.987858	−0.493929	+	0.869502i	$0.664440\pi$
$192$	0.381966	0.0275660
$193$	14.6525	1.05471	0.527354	−	0.849646i	$-0.323184\pi$
$193$	14.6525	1.05471	0.527354	+	0.849646i	$0.323184\pi$
$194$	−9.56231	−0.686534
$195$	0	0
$196$	2.00000	0.142857
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	−12.0902	−0.859211
$199$	2.56231	0.181637	0.0908185	−	0.995867i	$-0.471052\pi$
$199$	2.56231	0.181637	0.0908185	+	0.995867i	$0.471052\pi$
$200$	0	0
$201$	3.90983	0.275778
$202$	0.618034	0.0434847
$203$	−28.4164	−1.99444
$204$	−0.437694	−0.0306447
$205$	0	0
$206$	13.1459	0.915918
$207$	−5.03444	−0.349918
$208$	−1.00000	−0.0693375
$209$	24.7984	1.71534
$210$	0	0
$211$	−22.2705	−1.53317	−0.766583	−	0.642146i	$-0.778044\pi$
$211$	−22.2705	−1.53317	−0.766583	+	0.642146i	$0.778044\pi$
$212$	−10.4721	−0.719229
$213$	−1.14590	−0.0785156
$214$	1.09017	0.0745225
$215$	0	0
$216$	−2.23607	−0.152145
$217$	−0.708204	−0.0480760
$218$	−15.0000	−1.01593
$219$	−2.94427	−0.198955
$220$	0	0
$221$	1.14590	0.0770814
$222$	3.18034	0.213450
$223$	9.00000	0.602685	0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000	0.602685	0.301342	+	0.953516i	$0.402565\pi$
$224$	3.00000	0.200446
$225$	0	0
$226$	−3.76393	−0.250373
$227$	−29.3607	−1.94874	−0.974368	−	0.224958i	$-0.927775\pi$
$227$	−29.3607	−1.94874	−0.974368	+	0.224958i	$0.927775\pi$
$228$	2.23607	0.148087
$229$	−2.56231	−0.169322	−0.0846610	−	0.996410i	$-0.526981\pi$
$229$	−2.56231	−0.169322	−0.0846610	+	0.996410i	$0.526981\pi$
$230$	0	0
$231$	4.85410	0.319376
$232$	−9.47214	−0.621876
$233$	−14.2918	−0.936287	−0.468143	−	0.883653i	$-0.655077\pi$
$233$	−14.2918	−0.936287	−0.468143	+	0.883653i	$0.655077\pi$
$234$	2.85410	0.186578
$235$	0	0
$236$	−4.47214	−0.291111
$237$	−2.76393	−0.179537
$238$	−3.43769	−0.222833
$239$	−6.90983	−0.446960	−0.223480	−	0.974709i	$-0.571742\pi$
$239$	−6.90983	−0.446960	−0.223480	+	0.974709i	$0.571742\pi$
$240$	0	0
$241$	15.6180	1.00605	0.503023	−	0.864273i	$-0.332221\pi$
$241$	15.6180	1.00605	0.503023	+	0.864273i	$0.332221\pi$
$242$	6.94427	0.446395
$243$	9.65248	0.619207
$244$	−8.85410	−0.566826
$245$	0	0
$246$	0.562306	0.0358513
$247$	−5.85410	−0.372488
$248$	−0.236068	−0.0149903
$249$	1.72949	0.109602
$250$	0	0
$251$	0.819660	0.0517365	0.0258682	−	0.999665i	$-0.491765\pi$
$251$	0.819660	0.0517365	0.0258682	+	0.999665i	$0.491765\pi$
$252$	−8.56231	−0.539375
$253$	7.47214	0.469769
$254$	3.52786	0.221358
$255$	0	0
$256$	1.00000	0.0625000
$257$	−25.7426	−1.60578	−0.802891	−	0.596126i	$-0.796706\pi$
$257$	−25.7426	−1.60578	−0.802891	+	0.596126i	$0.796706\pi$
$258$	2.38197	0.148295
$259$	24.9787	1.55210
$260$	0	0
$261$	27.0344	1.67339
$262$	−16.4164	−1.01421
$263$	−4.61803	−0.284760	−0.142380	−	0.989812i	$-0.545476\pi$
$263$	−4.61803	−0.284760	−0.142380	+	0.989812i	$0.545476\pi$
$264$	1.61803	0.0995831
$265$	0	0
$266$	17.5623	1.07681
$267$	1.70820	0.104540
$268$	10.2361	0.625267
$269$	1.90983	0.116444	0.0582222	−	0.998304i	$-0.481457\pi$
$269$	1.90983	0.116444	0.0582222	+	0.998304i	$0.481457\pi$
$270$	0	0
$271$	28.5066	1.73165	0.865826	−	0.500346i	$-0.166794\pi$
$271$	28.5066	1.73165	0.865826	+	0.500346i	$0.166794\pi$
$272$	−1.14590	−0.0694803
$273$	−1.14590	−0.0693529
$274$	−5.09017	−0.307508
$275$	0	0
$276$	0.673762	0.0405557
$277$	−0.291796	−0.0175323	−0.00876616	−	0.999962i	$-0.502790\pi$
$277$	−0.291796	−0.0175323	−0.00876616	+	0.999962i	$0.502790\pi$
$278$	−5.32624	−0.319447
$279$	0.673762	0.0403371
$280$	0	0
$281$	3.18034	0.189723	0.0948616	−	0.995490i	$-0.469759\pi$
$281$	3.18034	0.189723	0.0948616	+	0.995490i	$0.469759\pi$
$282$	4.56231	0.271681
$283$	12.2918	0.730671	0.365336	−	0.930876i	$-0.380954\pi$
$283$	12.2918	0.730671	0.365336	+	0.930876i	$0.380954\pi$
$284$	−3.00000	−0.178017
$285$	0	0
$286$	−4.23607	−0.250484
$287$	4.41641	0.260692
$288$	−2.85410	−0.168180
$289$	−15.6869	−0.922760
$290$	0	0
$291$	−3.65248	−0.214112
$292$	−7.70820	−0.451089
$293$	−8.56231	−0.500215	−0.250108	−	0.968218i	$-0.580466\pi$
$293$	−8.56231	−0.500215	−0.250108	+	0.968218i	$0.580466\pi$
$294$	0.763932	0.0445534
$295$	0	0
$296$	8.32624	0.483953
$297$	−9.47214	−0.549629
$298$	2.23607	0.129532
$299$	−1.76393	−0.102011
$300$	0	0
$301$	18.7082	1.07832
$302$	−9.70820	−0.558644
$303$	0.236068	0.0135618
$304$	5.85410	0.335756
$305$	0	0
$306$	3.27051	0.186963
$307$	23.1246	1.31979	0.659896	−	0.751357i	$-0.270600\pi$
$307$	23.1246	1.31979	0.659896	+	0.751357i	$0.270600\pi$
$308$	12.7082	0.724117
$309$	5.02129	0.285651
$310$	0	0
$311$	−9.90983	−0.561935	−0.280967	−	0.959717i	$-0.590655\pi$
$311$	−9.90983	−0.561935	−0.280967	+	0.959717i	$0.590655\pi$
$312$	−0.381966	−0.0216246
$313$	16.5623	0.936157	0.468078	−	0.883687i	$-0.344946\pi$
$313$	16.5623	0.936157	0.468078	+	0.883687i	$0.344946\pi$
$314$	−4.56231	−0.257466
$315$	0	0
$316$	−7.23607	−0.407061
$317$	−8.38197	−0.470778	−0.235389	−	0.971901i	$-0.575636\pi$
$317$	−8.38197	−0.470778	−0.235389	+	0.971901i	$0.575636\pi$
$318$	−4.00000	−0.224309
$319$	−40.1246	−2.24655
$320$	0	0
$321$	0.416408	0.0232416
$322$	5.29180	0.294900
$323$	−6.70820	−0.373254
$324$	7.70820	0.428234
$325$	0	0
$326$	−1.85410	−0.102689
$327$	−5.72949	−0.316842
$328$	1.47214	0.0812851
$329$	35.8328	1.97553
$330$	0	0
$331$	−15.5623	−0.855382	−0.427691	−	0.903925i	$-0.640673\pi$
$331$	−15.5623	−0.855382	−0.427691	+	0.903925i	$0.640673\pi$
$332$	4.52786	0.248499
$333$	−23.7639	−1.30226
$334$	−13.3820	−0.732229
$335$	0	0
$336$	1.14590	0.0625139
$337$	4.58359	0.249684	0.124842	−	0.992177i	$-0.460158\pi$
$337$	4.58359	0.249684	0.124842	+	0.992177i	$0.460158\pi$
$338$	−12.0000	−0.652714
$339$	−1.43769	−0.0780848
$340$	0	0
$341$	−1.00000	−0.0541530
$342$	−16.7082	−0.903476
$343$	−15.0000	−0.809924
$344$	6.23607	0.336226
$345$	0	0
$346$	1.23607	0.0664514
$347$	21.0902	1.13218	0.566090	−	0.824344i	$-0.308456\pi$
$347$	21.0902	1.13218	0.566090	+	0.824344i	$0.308456\pi$
$348$	−3.61803	−0.193947
$349$	−17.7639	−0.950881	−0.475441	−	0.879748i	$-0.657711\pi$
$349$	−17.7639	−0.950881	−0.475441	+	0.879748i	$0.657711\pi$
$350$	0	0
$351$	2.23607	0.119352
$352$	4.23607	0.225783
$353$	21.2361	1.13028	0.565141	−	0.824994i	$-0.308822\pi$
$353$	21.2361	1.13028	0.565141	+	0.824994i	$0.308822\pi$
$354$	−1.70820	−0.0907900
$355$	0	0
$356$	4.47214	0.237023
$357$	−1.31308	−0.0694957
$358$	11.1803	0.590899
$359$	−8.09017	−0.426983	−0.213491	−	0.976945i	$-0.568484\pi$
$359$	−8.09017	−0.426983	−0.213491	+	0.976945i	$0.568484\pi$
$360$	0	0
$361$	15.2705	0.803711
$362$	5.41641	0.284680
$363$	2.65248	0.139219
$364$	−3.00000	−0.157243
$365$	0	0
$366$	−3.38197	−0.176778
$367$	−35.5410	−1.85523	−0.927613	−	0.373543i	$-0.878143\pi$
$367$	−35.5410	−1.85523	−0.927613	+	0.373543i	$0.878143\pi$
$368$	1.76393	0.0919513
$369$	−4.20163	−0.218728
$370$	0	0
$371$	−31.4164	−1.63106
$372$	−0.0901699	−0.00467509
$373$	11.7639	0.609113	0.304557	−	0.952494i	$-0.401492\pi$
$373$	11.7639	0.609113	0.304557	+	0.952494i	$0.401492\pi$
$374$	−4.85410	−0.251000
$375$	0	0
$376$	11.9443	0.615979
$377$	9.47214	0.487840
$378$	−6.70820	−0.345033
$379$	9.47214	0.486551	0.243275	−	0.969957i	$-0.421778\pi$
$379$	9.47214	0.486551	0.243275	+	0.969957i	$0.421778\pi$
$380$	0	0
$381$	1.34752	0.0690358
$382$	−13.6525	−0.698521
$383$	−11.3262	−0.578744	−0.289372	−	0.957217i	$-0.593446\pi$
$383$	−11.3262	−0.578744	−0.289372	+	0.957217i	$0.593446\pi$
$384$	0.381966	0.0194921
$385$	0	0
$386$	14.6525	0.745791
$387$	−17.7984	−0.904742
$388$	−9.56231	−0.485453
$389$	18.2148	0.923526	0.461763	−	0.887003i	$-0.347217\pi$
$389$	18.2148	0.923526	0.461763	+	0.887003i	$0.347217\pi$
$390$	0	0
$391$	−2.02129	−0.102221
$392$	2.00000	0.101015
$393$	−6.27051	−0.316305
$394$	−12.0000	−0.604551
$395$	0	0
$396$	−12.0902	−0.607554
$397$	10.2361	0.513734	0.256867	−	0.966447i	$-0.417310\pi$
$397$	10.2361	0.513734	0.256867	+	0.966447i	$0.417310\pi$
$398$	2.56231	0.128437
$399$	6.70820	0.335830
$400$	0	0
$401$	−14.1803	−0.708132	−0.354066	−	0.935220i	$-0.615201\pi$
$401$	−14.1803	−0.708132	−0.354066	+	0.935220i	$0.615201\pi$
$402$	3.90983	0.195005
$403$	0.236068	0.0117594
$404$	0.618034	0.0307483
$405$	0	0
$406$	−28.4164	−1.41028
$407$	35.2705	1.74829
$408$	−0.437694	−0.0216691
$409$	−6.70820	−0.331699	−0.165850	−	0.986151i	$-0.553037\pi$
$409$	−6.70820	−0.331699	−0.165850	+	0.986151i	$0.553037\pi$
$410$	0	0
$411$	−1.94427	−0.0959039
$412$	13.1459	0.647652
$413$	−13.4164	−0.660178
$414$	−5.03444	−0.247429
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	−2.03444	−0.0996270
$418$	24.7984	1.21293
$419$	22.7639	1.11209	0.556045	−	0.831152i	$-0.312318\pi$
$419$	22.7639	1.11209	0.556045	+	0.831152i	$0.312318\pi$
$420$	0	0
$421$	21.2705	1.03666	0.518331	−	0.855180i	$-0.326554\pi$
$421$	21.2705	1.03666	0.518331	+	0.855180i	$0.326554\pi$
$422$	−22.2705	−1.08411
$423$	−34.0902	−1.65752
$424$	−10.4721	−0.508572
$425$	0	0
$426$	−1.14590	−0.0555189
$427$	−26.5623	−1.28544
$428$	1.09017	0.0526954
$429$	−1.61803	−0.0781194
$430$	0	0
$431$	26.0689	1.25569	0.627847	−	0.778337i	$-0.283936\pi$
$431$	26.0689	1.25569	0.627847	+	0.778337i	$0.283936\pi$
$432$	−2.23607	−0.107583
$433$	21.3607	1.02653	0.513264	−	0.858231i	$-0.328436\pi$
$433$	21.3607	1.02653	0.513264	+	0.858231i	$0.328436\pi$
$434$	−0.708204	−0.0339949
$435$	0	0
$436$	−15.0000	−0.718370
$437$	10.3262	0.493971
$438$	−2.94427	−0.140683
$439$	25.6525	1.22433	0.612163	−	0.790732i	$-0.290300\pi$
$439$	25.6525	1.22433	0.612163	+	0.790732i	$0.290300\pi$
$440$	0	0
$441$	−5.70820	−0.271819
$442$	1.14590	0.0545048
$443$	−19.4164	−0.922501	−0.461251	−	0.887270i	$-0.652599\pi$
$443$	−19.4164	−0.922501	−0.461251	+	0.887270i	$0.652599\pi$
$444$	3.18034	0.150932
$445$	0	0
$446$	9.00000	0.426162
$447$	0.854102	0.0403976
$448$	3.00000	0.141737
$449$	−3.94427	−0.186142	−0.0930709	−	0.995659i	$-0.529668\pi$
$449$	−3.94427	−0.186142	−0.0930709	+	0.995659i	$0.529668\pi$
$450$	0	0
$451$	6.23607	0.293645
$452$	−3.76393	−0.177040
$453$	−3.70820	−0.174227
$454$	−29.3607	−1.37796
$455$	0	0
$456$	2.23607	0.104713
$457$	−40.2148	−1.88117	−0.940584	−	0.339561i	$-0.889722\pi$
$457$	−40.2148	−1.88117	−0.940584	+	0.339561i	$0.889722\pi$
$458$	−2.56231	−0.119729
$459$	2.56231	0.119598
$460$	0	0
$461$	5.81966	0.271049	0.135524	−	0.990774i	$-0.456728\pi$
$461$	5.81966	0.271049	0.135524	+	0.990774i	$0.456728\pi$
$462$	4.85410	0.225833
$463$	34.9787	1.62560	0.812799	−	0.582544i	$-0.197943\pi$
$463$	34.9787	1.62560	0.812799	+	0.582544i	$0.197943\pi$
$464$	−9.47214	−0.439733
$465$	0	0
$466$	−14.2918	−0.662055
$467$	19.1803	0.887560	0.443780	−	0.896136i	$-0.353637\pi$
$467$	19.1803	0.887560	0.443780	+	0.896136i	$0.353637\pi$
$468$	2.85410	0.131931
$469$	30.7082	1.41797
$470$	0	0
$471$	−1.74265	−0.0802969
$472$	−4.47214	−0.205847
$473$	26.4164	1.21463
$474$	−2.76393	−0.126952
$475$	0	0
$476$	−3.43769	−0.157566
$477$	29.8885	1.36850
$478$	−6.90983	−0.316048
$479$	−15.2016	−0.694580	−0.347290	−	0.937758i	$-0.612898\pi$
$479$	−15.2016	−0.694580	−0.347290	+	0.937758i	$0.612898\pi$
$480$	0	0
$481$	−8.32624	−0.379644
$482$	15.6180	0.711382
$483$	2.02129	0.0919717
$484$	6.94427	0.315649
$485$	0	0
$486$	9.65248	0.437845
$487$	−22.1246	−1.00256	−0.501281	−	0.865285i	$-0.667138\pi$
$487$	−22.1246	−1.00256	−0.501281	+	0.865285i	$0.667138\pi$
$488$	−8.85410	−0.400806
$489$	−0.708204	−0.0320261
$490$	0	0
$491$	19.2361	0.868112	0.434056	−	0.900886i	$-0.357082\pi$
$491$	19.2361	0.868112	0.434056	+	0.900886i	$0.357082\pi$
$492$	0.562306	0.0253507
$493$	10.8541	0.488844
$494$	−5.85410	−0.263388
$495$	0	0
$496$	−0.236068	−0.0105998
$497$	−9.00000	−0.403705
$498$	1.72949	0.0775003
$499$	34.1459	1.52858	0.764290	−	0.644873i	$-0.223090\pi$
$499$	34.1459	1.52858	0.764290	+	0.644873i	$0.223090\pi$
$500$	0	0
$501$	−5.11146	−0.228363
$502$	0.819660	0.0365832
$503$	30.5066	1.36022	0.680111	−	0.733110i	$-0.261932\pi$
$503$	30.5066	1.36022	0.680111	+	0.733110i	$0.261932\pi$
$504$	−8.56231	−0.381395
$505$	0	0
$506$	7.47214	0.332177
$507$	−4.58359	−0.203564
$508$	3.52786	0.156524
$509$	−1.90983	−0.0846517	−0.0423259	−	0.999104i	$-0.513477\pi$
$509$	−1.90983	−0.0846517	−0.0423259	+	0.999104i	$0.513477\pi$
$510$	0	0
$511$	−23.1246	−1.02297
$512$	1.00000	0.0441942
$513$	−13.0902	−0.577945
$514$	−25.7426	−1.13546
$515$	0	0
$516$	2.38197	0.104860
$517$	50.5967	2.22524
$518$	24.9787	1.09750
$519$	0.472136	0.0207245
$520$	0	0
$521$	−23.4508	−1.02740	−0.513700	−	0.857970i	$-0.671726\pi$
$521$	−23.4508	−1.02740	−0.513700	+	0.857970i	$0.671726\pi$
$522$	27.0344	1.18327
$523$	4.65248	0.203439	0.101719	−	0.994813i	$-0.467566\pi$
$523$	4.65248	0.203439	0.101719	+	0.994813i	$0.467566\pi$
$524$	−16.4164	−0.717154
$525$	0	0
$526$	−4.61803	−0.201356
$527$	0.270510	0.0117836
$528$	1.61803	0.0704159
$529$	−19.8885	−0.864719
$530$	0	0
$531$	12.7639	0.553907
$532$	17.5623	0.761423
$533$	−1.47214	−0.0637653
$534$	1.70820	0.0739212
$535$	0	0
$536$	10.2361	0.442131
$537$	4.27051	0.184286
$538$	1.90983	0.0823386
$539$	8.47214	0.364921
$540$	0	0
$541$	15.2918	0.657446	0.328723	−	0.944426i	$-0.393382\pi$
$541$	15.2918	0.657446	0.328723	+	0.944426i	$0.393382\pi$
$542$	28.5066	1.22446
$543$	2.06888	0.0887843
$544$	−1.14590	−0.0491300
$545$	0	0
$546$	−1.14590	−0.0490399
$547$	−8.38197	−0.358387	−0.179193	−	0.983814i	$-0.557349\pi$
$547$	−8.38197	−0.358387	−0.179193	+	0.983814i	$0.557349\pi$
$548$	−5.09017	−0.217441
$549$	25.2705	1.07852
$550$	0	0
$551$	−55.4508	−2.36229
$552$	0.673762	0.0286772
$553$	−21.7082	−0.923127
$554$	−0.291796	−0.0123972
$555$	0	0
$556$	−5.32624	−0.225883
$557$	−24.8885	−1.05456	−0.527281	−	0.849691i	$-0.676788\pi$
$557$	−24.8885	−1.05456	−0.527281	+	0.849691i	$0.676788\pi$
$558$	0.673762	0.0285226
$559$	−6.23607	−0.263758
$560$	0	0
$561$	−1.85410	−0.0782802
$562$	3.18034	0.134155
$563$	28.1459	1.18621	0.593104	−	0.805126i	$-0.297902\pi$
$563$	28.1459	1.18621	0.593104	+	0.805126i	$0.297902\pi$
$564$	4.56231	0.192108
$565$	0	0
$566$	12.2918	0.516663
$567$	23.1246	0.971142
$568$	−3.00000	−0.125877
$569$	17.7639	0.744703	0.372351	−	0.928092i	$-0.378552\pi$
$569$	17.7639	0.744703	0.372351	+	0.928092i	$0.378552\pi$
$570$	0	0
$571$	17.3262	0.725080	0.362540	−	0.931968i	$-0.381910\pi$
$571$	17.3262	0.725080	0.362540	+	0.931968i	$0.381910\pi$
$572$	−4.23607	−0.177119
$573$	−5.21478	−0.217851
$574$	4.41641	0.184337
$575$	0	0
$576$	−2.85410	−0.118921
$577$	43.0000	1.79011	0.895057	−	0.445952i	$-0.147135\pi$
$577$	43.0000	1.79011	0.895057	+	0.445952i	$0.147135\pi$
$578$	−15.6869	−0.652490
$579$	5.59675	0.232593
$580$	0	0
$581$	13.5836	0.563542
$582$	−3.65248	−0.151400
$583$	−44.3607	−1.83723
$584$	−7.70820	−0.318968
$585$	0	0
$586$	−8.56231	−0.353706
$587$	34.1803	1.41077	0.705387	−	0.708823i	$-0.250773\pi$
$587$	34.1803	1.41077	0.705387	+	0.708823i	$0.250773\pi$
$588$	0.763932	0.0315040
$589$	−1.38197	−0.0569429
$590$	0	0
$591$	−4.58359	−0.188544
$592$	8.32624	0.342206
$593$	−29.0132	−1.19143	−0.595714	−	0.803197i	$-0.703131\pi$
$593$	−29.0132	−1.19143	−0.595714	+	0.803197i	$0.703131\pi$
$594$	−9.47214	−0.388646
$595$	0	0
$596$	2.23607	0.0915929
$597$	0.978714	0.0400561
$598$	−1.76393	−0.0721325
$599$	8.94427	0.365453	0.182727	−	0.983164i	$-0.441508\pi$
$599$	8.94427	0.365453	0.182727	+	0.983164i	$0.441508\pi$
$600$	0	0
$601$	38.8328	1.58402	0.792012	−	0.610506i	$-0.209034\pi$
$601$	38.8328	1.58402	0.792012	+	0.610506i	$0.209034\pi$
$602$	18.7082	0.762489
$603$	−29.2148	−1.18972
$604$	−9.70820	−0.395021
$605$	0	0
$606$	0.236068	0.00958961
$607$	33.8541	1.37410	0.687048	−	0.726612i	$-0.258906\pi$
$607$	33.8541	1.37410	0.687048	+	0.726612i	$0.258906\pi$
$608$	5.85410	0.237415
$609$	−10.8541	−0.439830
$610$	0	0
$611$	−11.9443	−0.483214
$612$	3.27051	0.132203
$613$	21.4377	0.865860	0.432930	−	0.901427i	$-0.357480\pi$
$613$	21.4377	0.865860	0.432930	+	0.901427i	$0.357480\pi$
$614$	23.1246	0.933233
$615$	0	0
$616$	12.7082	0.512028
$617$	−14.3607	−0.578139	−0.289070	−	0.957308i	$-0.593346\pi$
$617$	−14.3607	−0.578139	−0.289070	+	0.957308i	$0.593346\pi$
$618$	5.02129	0.201986
$619$	46.9574	1.88738	0.943689	−	0.330833i	$-0.107330\pi$
$619$	46.9574	1.88738	0.943689	+	0.330833i	$0.107330\pi$
$620$	0	0
$621$	−3.94427	−0.158278
$622$	−9.90983	−0.397348
$623$	13.4164	0.537517
$624$	−0.381966	−0.0152909
$625$	0	0
$626$	16.5623	0.661963
$627$	9.47214	0.378281
$628$	−4.56231	−0.182056
$629$	−9.54102	−0.380425
$630$	0	0
$631$	−44.8328	−1.78477	−0.892383	−	0.451279i	$-0.850968\pi$
$631$	−44.8328	−1.78477	−0.892383	+	0.451279i	$0.850968\pi$
$632$	−7.23607	−0.287835
$633$	−8.50658	−0.338106
$634$	−8.38197	−0.332890
$635$	0	0
$636$	−4.00000	−0.158610
$637$	−2.00000	−0.0792429
$638$	−40.1246	−1.58855
$639$	8.56231	0.338720
$640$	0	0
$641$	−30.3607	−1.19917	−0.599587	−	0.800309i	$-0.704669\pi$
$641$	−30.3607	−1.19917	−0.599587	+	0.800309i	$0.704669\pi$
$642$	0.416408	0.0164343
$643$	31.7639	1.25265	0.626324	−	0.779563i	$-0.284559\pi$
$643$	31.7639	1.25265	0.626324	+	0.779563i	$0.284559\pi$
$644$	5.29180	0.208526
$645$	0	0
$646$	−6.70820	−0.263931
$647$	23.6525	0.929875	0.464937	−	0.885344i	$-0.346077\pi$
$647$	23.6525	0.929875	0.464937	+	0.885344i	$0.346077\pi$
$648$	7.70820	0.302807
$649$	−18.9443	−0.743628
$650$	0	0
$651$	−0.270510	−0.0106021
$652$	−1.85410	−0.0726122
$653$	8.59675	0.336417	0.168208	−	0.985751i	$-0.446202\pi$
$653$	8.59675	0.336417	0.168208	+	0.985751i	$0.446202\pi$
$654$	−5.72949	−0.224041
$655$	0	0
$656$	1.47214	0.0574773
$657$	22.0000	0.858302
$658$	35.8328	1.39691
$659$	−25.6525	−0.999279	−0.499639	−	0.866234i	$-0.666534\pi$
$659$	−25.6525	−0.999279	−0.499639	+	0.866234i	$0.666534\pi$
$660$	0	0
$661$	−27.2705	−1.06070	−0.530350	−	0.847779i	$-0.677939\pi$
$661$	−27.2705	−1.06070	−0.530350	+	0.847779i	$0.677939\pi$
$662$	−15.5623	−0.604846
$663$	0.437694	0.0169986
$664$	4.52786	0.175715
$665$	0	0
$666$	−23.7639	−0.920834
$667$	−16.7082	−0.646944
$668$	−13.3820	−0.517764
$669$	3.43769	0.132909
$670$	0	0
$671$	−37.5066	−1.44793
$672$	1.14590	0.0442040
$673$	−3.23607	−0.124741	−0.0623706	−	0.998053i	$-0.519866\pi$
$673$	−3.23607	−0.124741	−0.0623706	+	0.998053i	$0.519866\pi$
$674$	4.58359	0.176553
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−8.38197	−0.322145	−0.161073	−	0.986943i	$-0.551495\pi$
$677$	−8.38197	−0.322145	−0.161073	+	0.986943i	$0.551495\pi$
$678$	−1.43769	−0.0552143
$679$	−28.6869	−1.10090
$680$	0	0
$681$	−11.2148	−0.429751
$682$	−1.00000	−0.0382920
$683$	11.3607	0.434704	0.217352	−	0.976093i	$-0.430258\pi$
$683$	11.3607	0.434704	0.217352	+	0.976093i	$0.430258\pi$
$684$	−16.7082	−0.638854
$685$	0	0
$686$	−15.0000	−0.572703
$687$	−0.978714	−0.0373403
$688$	6.23607	0.237748
$689$	10.4721	0.398957
$690$	0	0
$691$	−32.2705	−1.22763	−0.613814	−	0.789451i	$-0.710366\pi$
$691$	−32.2705	−1.22763	−0.613814	+	0.789451i	$0.710366\pi$
$692$	1.23607	0.0469883
$693$	−36.2705	−1.37780
$694$	21.0902	0.800572
$695$	0	0
$696$	−3.61803	−0.137141
$697$	−1.68692	−0.0638966
$698$	−17.7639	−0.672375
$699$	−5.45898	−0.206478
$700$	0	0
$701$	18.1803	0.686662	0.343331	−	0.939214i	$-0.388445\pi$
$701$	18.1803	0.686662	0.343331	+	0.939214i	$0.388445\pi$
$702$	2.23607	0.0843949
$703$	48.7426	1.83836
$704$	4.23607	0.159653
$705$	0	0
$706$	21.2361	0.799230
$707$	1.85410	0.0697307
$708$	−1.70820	−0.0641982
$709$	12.2361	0.459535	0.229768	−	0.973246i	$-0.426203\pi$
$709$	12.2361	0.459535	0.229768	+	0.973246i	$0.426203\pi$
$710$	0	0
$711$	20.6525	0.774528
$712$	4.47214	0.167600
$713$	−0.416408	−0.0155946
$714$	−1.31308	−0.0491409
$715$	0	0
$716$	11.1803	0.417829
$717$	−2.63932	−0.0985672
$718$	−8.09017	−0.301922
$719$	11.5066	0.429123	0.214561	−	0.976710i	$-0.431168\pi$
$719$	11.5066	0.429123	0.214561	+	0.976710i	$0.431168\pi$
$720$	0	0
$721$	39.4377	1.46874
$722$	15.2705	0.568310
$723$	5.96556	0.221861
$724$	5.41641	0.201299
$725$	0	0
$726$	2.65248	0.0984426
$727$	−2.65248	−0.0983749	−0.0491874	−	0.998790i	$-0.515663\pi$
$727$	−2.65248	−0.0983749	−0.0491874	+	0.998790i	$0.515663\pi$
$728$	−3.00000	−0.111187
$729$	−19.4377	−0.719915
$730$	0	0
$731$	−7.14590	−0.264301
$732$	−3.38197	−0.125001
$733$	−31.7771	−1.17371	−0.586857	−	0.809691i	$-0.699635\pi$
$733$	−31.7771	−1.17371	−0.586857	+	0.809691i	$0.699635\pi$
$734$	−35.5410	−1.31184
$735$	0	0
$736$	1.76393	0.0650194
$737$	43.3607	1.59721
$738$	−4.20163	−0.154664
$739$	30.0000	1.10357	0.551784	−	0.833987i	$-0.313947\pi$
$739$	30.0000	1.10357	0.551784	+	0.833987i	$0.313947\pi$
$740$	0	0
$741$	−2.23607	−0.0821440
$742$	−31.4164	−1.15333
$743$	−15.2705	−0.560221	−0.280110	−	0.959968i	$-0.590371\pi$
$743$	−15.2705	−0.560221	−0.280110	+	0.959968i	$0.590371\pi$
$744$	−0.0901699	−0.00330579
$745$	0	0
$746$	11.7639	0.430708
$747$	−12.9230	−0.472827
$748$	−4.85410	−0.177484
$749$	3.27051	0.119502
$750$	0	0
$751$	7.85410	0.286600	0.143300	−	0.989679i	$-0.454229\pi$
$751$	7.85410	0.286600	0.143300	+	0.989679i	$0.454229\pi$
$752$	11.9443	0.435563
$753$	0.313082	0.0114094
$754$	9.47214	0.344955
$755$	0	0
$756$	−6.70820	−0.243975
$757$	16.4164	0.596664	0.298332	−	0.954462i	$-0.403570\pi$
$757$	16.4164	0.596664	0.298332	+	0.954462i	$0.403570\pi$
$758$	9.47214	0.344043
$759$	2.85410	0.103597
$760$	0	0
$761$	26.9230	0.975957	0.487979	−	0.872856i	$-0.337734\pi$
$761$	26.9230	0.975957	0.487979	+	0.872856i	$0.337734\pi$
$762$	1.34752	0.0488156
$763$	−45.0000	−1.62911
$764$	−13.6525	−0.493929
$765$	0	0
$766$	−11.3262	−0.409234
$767$	4.47214	0.161479
$768$	0.381966	0.0137830
$769$	3.41641	0.123199	0.0615994	−	0.998101i	$-0.480380\pi$
$769$	3.41641	0.123199	0.0615994	+	0.998101i	$0.480380\pi$
$770$	0	0
$771$	−9.83282	−0.354120
$772$	14.6525	0.527354
$773$	−30.7984	−1.10774	−0.553870	−	0.832603i	$-0.686850\pi$
$773$	−30.7984	−1.10774	−0.553870	+	0.832603i	$0.686850\pi$
$774$	−17.7984	−0.639749
$775$	0	0
$776$	−9.56231	−0.343267
$777$	9.54102	0.342282
$778$	18.2148	0.653032
$779$	8.61803	0.308773
$780$	0	0
$781$	−12.7082	−0.454735
$782$	−2.02129	−0.0722810
$783$	21.1803	0.756924
$784$	2.00000	0.0714286
$785$	0	0
$786$	−6.27051	−0.223662
$787$	11.4164	0.406951	0.203475	−	0.979080i	$-0.434776\pi$
$787$	11.4164	0.406951	0.203475	+	0.979080i	$0.434776\pi$
$788$	−12.0000	−0.427482
$789$	−1.76393	−0.0627976
$790$	0	0
$791$	−11.2918	−0.401490
$792$	−12.0902	−0.429605
$793$	8.85410	0.314418
$794$	10.2361	0.363264
$795$	0	0
$796$	2.56231	0.0908185
$797$	−5.61803	−0.199001	−0.0995005	−	0.995038i	$-0.531724\pi$
$797$	−5.61803	−0.199001	−0.0995005	+	0.995038i	$0.531724\pi$
$798$	6.70820	0.237468
$799$	−13.6869	−0.484208
$800$	0	0
$801$	−12.7639	−0.450991
$802$	−14.1803	−0.500725
$803$	−32.6525	−1.15228
$804$	3.90983	0.137889
$805$	0	0
$806$	0.236068	0.00831514
$807$	0.729490	0.0256793
$808$	0.618034	0.0217424
$809$	−2.23607	−0.0786160	−0.0393080	−	0.999227i	$-0.512515\pi$
$809$	−2.23607	−0.0786160	−0.0393080	+	0.999227i	$0.512515\pi$
$810$	0	0
$811$	40.9443	1.43775	0.718874	−	0.695140i	$-0.244658\pi$
$811$	40.9443	1.43775	0.718874	+	0.695140i	$0.244658\pi$
$812$	−28.4164	−0.997220
$813$	10.8885	0.381878
$814$	35.2705	1.23623
$815$	0	0
$816$	−0.437694	−0.0153224
$817$	36.5066	1.27720
$818$	−6.70820	−0.234547
$819$	8.56231	0.299191
$820$	0	0
$821$	39.1591	1.36666	0.683330	−	0.730109i	$-0.260531\pi$
$821$	39.1591	1.36666	0.683330	+	0.730109i	$0.260531\pi$
$822$	−1.94427	−0.0678143
$823$	20.8328	0.726186	0.363093	−	0.931753i	$-0.381721\pi$
$823$	20.8328	0.726186	0.363093	+	0.931753i	$0.381721\pi$
$824$	13.1459	0.457959
$825$	0	0
$826$	−13.4164	−0.466817
$827$	5.03444	0.175065	0.0875323	−	0.996162i	$-0.472102\pi$
$827$	5.03444	0.175065	0.0875323	+	0.996162i	$0.472102\pi$
$828$	−5.03444	−0.174959
$829$	53.4164	1.85523	0.927614	−	0.373540i	$-0.121856\pi$
$829$	53.4164	1.85523	0.927614	+	0.373540i	$0.121856\pi$
$830$	0	0
$831$	−0.111456	−0.00386637
$832$	−1.00000	−0.0346688
$833$	−2.29180	−0.0794060
$834$	−2.03444	−0.0704470
$835$	0	0
$836$	24.7984	0.857670
$837$	0.527864	0.0182457
$838$	22.7639	0.786367
$839$	−55.2492	−1.90742	−0.953708	−	0.300736i	$-0.902768\pi$
$839$	−55.2492	−1.90742	−0.953708	+	0.300736i	$0.902768\pi$
$840$	0	0
$841$	60.7214	2.09384
$842$	21.2705	0.733030
$843$	1.21478	0.0418393
$844$	−22.2705	−0.766583
$845$	0	0
$846$	−34.0902	−1.17204
$847$	20.8328	0.715824
$848$	−10.4721	−0.359615
$849$	4.69505	0.161134
$850$	0	0
$851$	14.6869	0.503461
$852$	−1.14590	−0.0392578
$853$	18.1459	0.621304	0.310652	−	0.950524i	$-0.399453\pi$
$853$	18.1459	0.621304	0.310652	+	0.950524i	$0.399453\pi$
$854$	−26.5623	−0.908943
$855$	0	0
$856$	1.09017	0.0372612
$857$	56.3394	1.92452	0.962259	−	0.272137i	$-0.0877304\pi$
$857$	56.3394	1.92452	0.962259	+	0.272137i	$0.0877304\pi$
$858$	−1.61803	−0.0552388
$859$	34.3951	1.17355	0.586773	−	0.809751i	$-0.300398\pi$
$859$	34.3951	1.17355	0.586773	+	0.809751i	$0.300398\pi$
$860$	0	0
$861$	1.68692	0.0574900
$862$	26.0689	0.887910
$863$	11.2361	0.382480	0.191240	−	0.981543i	$-0.438749\pi$
$863$	11.2361	0.382480	0.191240	+	0.981543i	$0.438749\pi$
$864$	−2.23607	−0.0760726
$865$	0	0
$866$	21.3607	0.725865
$867$	−5.99187	−0.203495
$868$	−0.708204	−0.0240380
$869$	−30.6525	−1.03981
$870$	0	0
$871$	−10.2361	−0.346836
$872$	−15.0000	−0.507964
$873$	27.2918	0.923687
$874$	10.3262	0.349290
$875$	0	0
$876$	−2.94427	−0.0994777
$877$	−4.43769	−0.149850	−0.0749251	−	0.997189i	$-0.523872\pi$
$877$	−4.43769	−0.149850	−0.0749251	+	0.997189i	$0.523872\pi$
$878$	25.6525	0.865729
$879$	−3.27051	−0.110312
$880$	0	0
$881$	38.1803	1.28633	0.643164	−	0.765728i	$-0.277621\pi$
$881$	38.1803	1.28633	0.643164	+	0.765728i	$0.277621\pi$
$882$	−5.70820	−0.192205
$883$	41.6869	1.40288	0.701438	−	0.712730i	$-0.252542\pi$
$883$	41.6869	1.40288	0.701438	+	0.712730i	$0.252542\pi$
$884$	1.14590	0.0385407
$885$	0	0
$886$	−19.4164	−0.652307
$887$	−33.1803	−1.11409	−0.557043	−	0.830483i	$-0.688064\pi$
$887$	−33.1803	−1.11409	−0.557043	+	0.830483i	$0.688064\pi$
$888$	3.18034	0.106725
$889$	10.5836	0.354962
$890$	0	0
$891$	32.6525	1.09390
$892$	9.00000	0.301342
$893$	69.9230	2.33988
$894$	0.854102	0.0285654
$895$	0	0
$896$	3.00000	0.100223
$897$	−0.673762	−0.0224963
$898$	−3.94427	−0.131622
$899$	2.23607	0.0745770
$900$	0	0
$901$	12.0000	0.399778
$902$	6.23607	0.207638
$903$	7.14590	0.237801
$904$	−3.76393	−0.125187
$905$	0	0
$906$	−3.70820	−0.123197
$907$	−25.6180	−0.850633	−0.425316	−	0.905045i	$-0.639837\pi$
$907$	−25.6180	−0.850633	−0.425316	+	0.905045i	$0.639837\pi$
$908$	−29.3607	−0.974368
$909$	−1.76393	−0.0585059
$910$	0	0
$911$	−16.4164	−0.543900	−0.271950	−	0.962311i	$-0.587669\pi$
$911$	−16.4164	−0.543900	−0.271950	+	0.962311i	$0.587669\pi$
$912$	2.23607	0.0740436
$913$	19.1803	0.634777
$914$	−40.2148	−1.33019
$915$	0	0
$916$	−2.56231	−0.0846610
$917$	−49.2492	−1.62635
$918$	2.56231	0.0845687
$919$	−5.65248	−0.186458	−0.0932290	−	0.995645i	$-0.529719\pi$
$919$	−5.65248	−0.186458	−0.0932290	+	0.995645i	$0.529719\pi$
$920$	0	0
$921$	8.83282	0.291051
$922$	5.81966	0.191660
$923$	3.00000	0.0987462
$924$	4.85410	0.159688
$925$	0	0
$926$	34.9787	1.14947
$927$	−37.5197	−1.23231
$928$	−9.47214	−0.310938
$929$	−52.8885	−1.73522	−0.867608	−	0.497248i	$-0.834344\pi$
$929$	−52.8885	−1.73522	−0.867608	+	0.497248i	$0.834344\pi$
$930$	0	0
$931$	11.7082	0.383721
$932$	−14.2918	−0.468143
$933$	−3.78522	−0.123922
$934$	19.1803	0.627600
$935$	0	0
$936$	2.85410	0.0932892
$937$	−41.9230	−1.36956	−0.684782	−	0.728748i	$-0.740103\pi$
$937$	−41.9230	−1.36956	−0.684782	+	0.728748i	$0.740103\pi$
$938$	30.7082	1.00266
$939$	6.32624	0.206449
$940$	0	0
$941$	−9.38197	−0.305843	−0.152922	−	0.988238i	$-0.548868\pi$
$941$	−9.38197	−0.305843	−0.152922	+	0.988238i	$0.548868\pi$
$942$	−1.74265	−0.0567785
$943$	2.59675	0.0845617
$944$	−4.47214	−0.145556
$945$	0	0
$946$	26.4164	0.858872
$947$	39.3820	1.27974	0.639871	−	0.768482i	$-0.278988\pi$
$947$	39.3820	1.27974	0.639871	+	0.768482i	$0.278988\pi$
$948$	−2.76393	−0.0897683
$949$	7.70820	0.250219
$950$	0	0
$951$	−3.20163	−0.103820
$952$	−3.43769	−0.111416
$953$	−44.6180	−1.44532	−0.722660	−	0.691204i	$-0.757081\pi$
$953$	−44.6180	−1.44532	−0.722660	+	0.691204i	$0.757081\pi$
$954$	29.8885	0.967677
$955$	0	0
$956$	−6.90983	−0.223480
$957$	−15.3262	−0.495427
$958$	−15.2016	−0.491142
$959$	−15.2705	−0.493110
$960$	0	0
$961$	−30.9443	−0.998202
$962$	−8.32624	−0.268449
$963$	−3.11146	−0.100265
$964$	15.6180	0.503023
$965$	0	0
$966$	2.02129	0.0650338
$967$	13.1246	0.422059	0.211030	−	0.977480i	$-0.432318\pi$
$967$	13.1246	0.422059	0.211030	+	0.977480i	$0.432318\pi$
$968$	6.94427	0.223197
$969$	−2.56231	−0.0823131
$970$	0	0
$971$	6.06888	0.194760	0.0973799	−	0.995247i	$-0.468954\pi$
$971$	6.06888	0.194760	0.0973799	+	0.995247i	$0.468954\pi$
$972$	9.65248	0.309603
$973$	−15.9787	−0.512254
$974$	−22.1246	−0.708918
$975$	0	0
$976$	−8.85410	−0.283413
$977$	−50.0132	−1.60006	−0.800031	−	0.599958i	$-0.795184\pi$
$977$	−50.0132	−1.60006	−0.800031	+	0.599958i	$0.795184\pi$
$978$	−0.708204	−0.0226459
$979$	18.9443	0.605462
$980$	0	0
$981$	42.8115	1.36687
$982$	19.2361	0.613848
$983$	−38.4853	−1.22749	−0.613745	−	0.789504i	$-0.710338\pi$
$983$	−38.4853	−1.22749	−0.613745	+	0.789504i	$0.710338\pi$
$984$	0.562306	0.0179257
$985$	0	0
$986$	10.8541	0.345665
$987$	13.6869	0.435659
$988$	−5.85410	−0.186244
$989$	11.0000	0.349780
$990$	0	0
$991$	−3.45085	−0.109620	−0.0548099	−	0.998497i	$-0.517455\pi$
$991$	−3.45085	−0.109620	−0.0548099	+	0.998497i	$0.517455\pi$
$992$	−0.236068	−0.00749517
$993$	−5.94427	−0.188636
$994$	−9.00000	−0.285463
$995$	0	0
$996$	1.72949	0.0548010
$997$	−27.2492	−0.862992	−0.431496	−	0.902115i	$-0.642014\pi$
$997$	−27.2492	−0.862992	−0.431496	+	0.902115i	$0.642014\pi$
$998$	34.1459	1.08087
$999$	−18.6180	−0.589049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.2.a.d.1.1		2
4.3	odd	2		10000.2.a.a.1.2		2
5.2	odd	4		1250.2.b.b.1249.4		4
5.3	odd	4		1250.2.b.b.1249.1		4
5.4	even	2		1250.2.a.a.1.2		2
20.19	odd	2		10000.2.a.n.1.1		2
25.2	odd	20		250.2.e.b.149.2		8
25.9	even	10		50.2.d.a.31.1	yes	4
25.11	even	5		250.2.d.a.101.1		4
25.12	odd	20		250.2.e.b.99.1		8
25.13	odd	20		250.2.e.b.99.2		8
25.14	even	10		50.2.d.a.21.1	✓	4
25.16	even	5		250.2.d.a.151.1		4
25.23	odd	20		250.2.e.b.149.1		8
75.14	odd	10		450.2.h.a.271.1		4
75.59	odd	10		450.2.h.a.181.1		4
100.39	odd	10		400.2.u.c.321.1		4
100.59	odd	10		400.2.u.c.81.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.21.1	✓	4	25.14	even	10
50.2.d.a.31.1	yes	4	25.9	even	10
250.2.d.a.101.1		4	25.11	even	5
250.2.d.a.151.1		4	25.16	even	5
250.2.e.b.99.1		8	25.12	odd	20
250.2.e.b.99.2		8	25.13	odd	20
250.2.e.b.149.1		8	25.23	odd	20
250.2.e.b.149.2		8	25.2	odd	20
400.2.u.c.81.1		4	100.59	odd	10
400.2.u.c.321.1		4	100.39	odd	10
450.2.h.a.181.1		4	75.59	odd	10
450.2.h.a.271.1		4	75.14	odd	10
1250.2.a.a.1.2		2	5.4	even	2
1250.2.a.d.1.1		2	1.1	even	1	trivial
1250.2.b.b.1249.1		4	5.3	odd	4
1250.2.b.b.1249.4		4	5.2	odd	4
10000.2.a.a.1.2		2	4.3	odd	2
10000.2.a.n.1.1		2	20.19	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:	\( N \)	\(=\)	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1250.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.85410 q^{9} +4.23607 q^{11} +0.381966 q^{12} -1.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} -1.14590 q^{17} -2.85410 q^{18} +5.85410 q^{19} +1.14590 q^{21} +4.23607 q^{22} +1.76393 q^{23} +0.381966 q^{24} -1.00000 q^{26} -2.23607 q^{27} +3.00000 q^{28} -9.47214 q^{29} -0.236068 q^{31} +1.00000 q^{32} +1.61803 q^{33} -1.14590 q^{34} -2.85410 q^{36} +8.32624 q^{37} +5.85410 q^{38} -0.381966 q^{39} +1.47214 q^{41} +1.14590 q^{42} +6.23607 q^{43} +4.23607 q^{44} +1.76393 q^{46} +11.9443 q^{47} +0.381966 q^{48} +2.00000 q^{49} -0.437694 q^{51} -1.00000 q^{52} -10.4721 q^{53} -2.23607 q^{54} +3.00000 q^{56} +2.23607 q^{57} -9.47214 q^{58} -4.47214 q^{59} -8.85410 q^{61} -0.236068 q^{62} -8.56231 q^{63} +1.00000 q^{64} +1.61803 q^{66} +10.2361 q^{67} -1.14590 q^{68} +0.673762 q^{69} -3.00000 q^{71} -2.85410 q^{72} -7.70820 q^{73} +8.32624 q^{74} +5.85410 q^{76} +12.7082 q^{77} -0.381966 q^{78} -7.23607 q^{79} +7.70820 q^{81} +1.47214 q^{82} +4.52786 q^{83} +1.14590 q^{84} +6.23607 q^{86} -3.61803 q^{87} +4.23607 q^{88} +4.47214 q^{89} -3.00000 q^{91} +1.76393 q^{92} -0.0901699 q^{93} +11.9443 q^{94} +0.381966 q^{96} -9.56231 q^{97} +2.00000 q^{98} -12.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 6 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 6 * q^7 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 6 q^{7} + 2 q^{8} + q^{9} + 4 q^{11} + 3 q^{12} - 2 q^{13} + 6 q^{14} + 2 q^{16} - 9 q^{17} + q^{18} + 5 q^{19} + 9 q^{21} + 4 q^{22} + 8 q^{23} + 3 q^{24} - 2 q^{26} + 6 q^{28} - 10 q^{29} + 4 q^{31} + 2 q^{32} + q^{33} - 9 q^{34} + q^{36} + q^{37} + 5 q^{38} - 3 q^{39} - 6 q^{41} + 9 q^{42} + 8 q^{43} + 4 q^{44} + 8 q^{46} + 6 q^{47} + 3 q^{48} + 4 q^{49} - 21 q^{51} - 2 q^{52} - 12 q^{53} + 6 q^{56} - 10 q^{58} - 11 q^{61} + 4 q^{62} + 3 q^{63} + 2 q^{64} + q^{66} + 16 q^{67} - 9 q^{68} + 17 q^{69} - 6 q^{71} + q^{72} - 2 q^{73} + q^{74} + 5 q^{76} + 12 q^{77} - 3 q^{78} - 10 q^{79} + 2 q^{81} - 6 q^{82} + 18 q^{83} + 9 q^{84} + 8 q^{86} - 5 q^{87} + 4 q^{88} - 6 q^{91} + 8 q^{92} + 11 q^{93} + 6 q^{94} + 3 q^{96} + q^{97} + 4 q^{98} - 13 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 6 * q^7 + 2 * q^8 + q^9 + 4 * q^11 + 3 * q^12 - 2 * q^13 + 6 * q^14 + 2 * q^16 - 9 * q^17 + q^18 + 5 * q^19 + 9 * q^21 + 4 * q^22 + 8 * q^23 + 3 * q^24 - 2 * q^26 + 6 * q^28 - 10 * q^29 + 4 * q^31 + 2 * q^32 + q^33 - 9 * q^34 + q^36 + q^37 + 5 * q^38 - 3 * q^39 - 6 * q^41 + 9 * q^42 + 8 * q^43 + 4 * q^44 + 8 * q^46 + 6 * q^47 + 3 * q^48 + 4 * q^49 - 21 * q^51 - 2 * q^52 - 12 * q^53 + 6 * q^56 - 10 * q^58 - 11 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 + q^66 + 16 * q^67 - 9 * q^68 + 17 * q^69 - 6 * q^71 + q^72 - 2 * q^73 + q^74 + 5 * q^76 + 12 * q^77 - 3 * q^78 - 10 * q^79 + 2 * q^81 - 6 * q^82 + 18 * q^83 + 9 * q^84 + 8 * q^86 - 5 * q^87 + 4 * q^88 - 6 * q^91 + 8 * q^92 + 11 * q^93 + 6 * q^94 + 3 * q^96 + q^97 + 4 * q^98 - 13 * q^99

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