LMFDB - Embedded newform 1450.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
Analytic rank:	$1$
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 290)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.381966 q^{3} +1.00000 q^{4} -0.381966 q^{6} -2.61803 q^{7} +1.00000 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.381966 q^{3} +1.00000 q^{4} -0.381966 q^{6} -2.61803 q^{7} +1.00000 q^{8} -2.85410 q^{9} +2.00000 q^{11} -0.381966 q^{12} -0.381966 q^{13} -2.61803 q^{14} +1.00000 q^{16} -3.38197 q^{17} -2.85410 q^{18} -2.00000 q^{19} +1.00000 q^{21} +2.00000 q^{22} -4.85410 q^{23} -0.381966 q^{24} -0.381966 q^{26} +2.23607 q^{27} -2.61803 q^{28} -1.00000 q^{29} -3.85410 q^{31} +1.00000 q^{32} -0.763932 q^{33} -3.38197 q^{34} -2.85410 q^{36} -8.94427 q^{37} -2.00000 q^{38} +0.145898 q^{39} +7.70820 q^{41} +1.00000 q^{42} -3.38197 q^{43} +2.00000 q^{44} -4.85410 q^{46} -1.52786 q^{47} -0.381966 q^{48} -0.145898 q^{49} +1.29180 q^{51} -0.381966 q^{52} -9.38197 q^{53} +2.23607 q^{54} -2.61803 q^{56} +0.763932 q^{57} -1.00000 q^{58} +2.85410 q^{59} -10.8541 q^{61} -3.85410 q^{62} +7.47214 q^{63} +1.00000 q^{64} -0.763932 q^{66} +8.94427 q^{67} -3.38197 q^{68} +1.85410 q^{69} -5.70820 q^{71} -2.85410 q^{72} +5.56231 q^{73} -8.94427 q^{74} -2.00000 q^{76} -5.23607 q^{77} +0.145898 q^{78} +6.56231 q^{79} +7.70820 q^{81} +7.70820 q^{82} -14.9443 q^{83} +1.00000 q^{84} -3.38197 q^{86} +0.381966 q^{87} +2.00000 q^{88} +2.00000 q^{89} +1.00000 q^{91} -4.85410 q^{92} +1.47214 q^{93} -1.52786 q^{94} -0.381966 q^{96} -7.14590 q^{97} -0.145898 q^{98} -5.70820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + q^9	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + q^{9} + 4 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} + 2 q^{16} - 9 q^{17} + q^{18} - 4 q^{19} + 2 q^{21} + 4 q^{22} - 3 q^{23} - 3 q^{24} - 3 q^{26} - 3 q^{28} - 2 q^{29} - q^{31} + 2 q^{32} - 6 q^{33} - 9 q^{34} + q^{36} - 4 q^{38} + 7 q^{39} + 2 q^{41} + 2 q^{42} - 9 q^{43} + 4 q^{44} - 3 q^{46} - 12 q^{47} - 3 q^{48} - 7 q^{49} + 16 q^{51} - 3 q^{52} - 21 q^{53} - 3 q^{56} + 6 q^{57} - 2 q^{58} - q^{59} - 15 q^{61} - q^{62} + 6 q^{63} + 2 q^{64} - 6 q^{66} - 9 q^{68} - 3 q^{69} + 2 q^{71} + q^{72} - 9 q^{73} - 4 q^{76} - 6 q^{77} + 7 q^{78} - 7 q^{79} + 2 q^{81} + 2 q^{82} - 12 q^{83} + 2 q^{84} - 9 q^{86} + 3 q^{87} + 4 q^{88} + 4 q^{89} + 2 q^{91} - 3 q^{92} - 6 q^{93} - 12 q^{94} - 3 q^{96} - 21 q^{97} - 7 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + q^9 + 4 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 + 2 * q^16 - 9 * q^17 + q^18 - 4 * q^19 + 2 * q^21 + 4 * q^22 - 3 * q^23 - 3 * q^24 - 3 * q^26 - 3 * q^28 - 2 * q^29 - q^31 + 2 * q^32 - 6 * q^33 - 9 * q^34 + q^36 - 4 * q^38 + 7 * q^39 + 2 * q^41 + 2 * q^42 - 9 * q^43 + 4 * q^44 - 3 * q^46 - 12 * q^47 - 3 * q^48 - 7 * q^49 + 16 * q^51 - 3 * q^52 - 21 * q^53 - 3 * q^56 + 6 * q^57 - 2 * q^58 - q^59 - 15 * q^61 - q^62 + 6 * q^63 + 2 * q^64 - 6 * q^66 - 9 * q^68 - 3 * q^69 + 2 * q^71 + q^72 - 9 * q^73 - 4 * q^76 - 6 * q^77 + 7 * q^78 - 7 * q^79 + 2 * q^81 + 2 * q^82 - 12 * q^83 + 2 * q^84 - 9 * q^86 + 3 * q^87 + 4 * q^88 + 4 * q^89 + 2 * q^91 - 3 * q^92 - 6 * q^93 - 12 * q^94 - 3 * q^96 - 21 * q^97 - 7 * 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
$3$	−0.381966	−0.220528	−0.110264	−	0.993902i	$-0.535170\pi$
$3$	−0.381966	−0.220528	−0.110264	+	0.993902i	$0.535170\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−0.381966	−0.155937
$7$	−2.61803	−0.989524	−0.494762	−	0.869029i	$-0.664745\pi$
$7$	−2.61803	−0.989524	−0.494762	+	0.869029i	$0.664745\pi$
$8$	1.00000	0.353553
$9$	−2.85410	−0.951367
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−0.381966	−0.110264
$13$	−0.381966	−0.105938	−0.0529692	−	0.998596i	$-0.516869\pi$
$13$	−0.381966	−0.105938	−0.0529692	+	0.998596i	$0.516869\pi$
$14$	−2.61803	−0.699699
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.38197	−0.820247	−0.410124	−	0.912030i	$-0.634514\pi$
$17$	−3.38197	−0.820247	−0.410124	+	0.912030i	$0.634514\pi$
$18$	−2.85410	−0.672718
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	2.00000	0.426401
$23$	−4.85410	−1.01215	−0.506075	−	0.862489i	$-0.668904\pi$
$23$	−4.85410	−1.01215	−0.506075	+	0.862489i	$0.668904\pi$
$24$	−0.381966	−0.0779685
$25$	0	0
$26$	−0.381966	−0.0749097
$27$	2.23607	0.430331
$28$	−2.61803	−0.494762
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−3.85410	−0.692217	−0.346109	−	0.938194i	$-0.612497\pi$
$31$	−3.85410	−0.692217	−0.346109	+	0.938194i	$0.612497\pi$
$32$	1.00000	0.176777
$33$	−0.763932	−0.132983
$34$	−3.38197	−0.580002
$35$	0	0
$36$	−2.85410	−0.475684
$37$	−8.94427	−1.47043	−0.735215	−	0.677834i	$-0.762919\pi$
$37$	−8.94427	−1.47043	−0.735215	+	0.677834i	$0.762919\pi$
$38$	−2.00000	−0.324443
$39$	0.145898	0.0233624
$40$	0	0
$41$	7.70820	1.20382	0.601910	−	0.798564i	$-0.294407\pi$
$41$	7.70820	1.20382	0.601910	+	0.798564i	$0.294407\pi$
$42$	1.00000	0.154303
$43$	−3.38197	−0.515745	−0.257872	−	0.966179i	$-0.583021\pi$
$43$	−3.38197	−0.515745	−0.257872	+	0.966179i	$0.583021\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−4.85410	−0.715698
$47$	−1.52786	−0.222862	−0.111431	−	0.993772i	$-0.535543\pi$
$47$	−1.52786	−0.222862	−0.111431	+	0.993772i	$0.535543\pi$
$48$	−0.381966	−0.0551320
$49$	−0.145898	−0.0208426
$50$	0	0
$51$	1.29180	0.180888
$52$	−0.381966	−0.0529692
$53$	−9.38197	−1.28871	−0.644356	−	0.764726i	$-0.722875\pi$
$53$	−9.38197	−1.28871	−0.644356	+	0.764726i	$0.722875\pi$
$54$	2.23607	0.304290
$55$	0	0
$56$	−2.61803	−0.349850
$57$	0.763932	0.101185
$58$	−1.00000	−0.131306
$59$	2.85410	0.371572	0.185786	−	0.982590i	$-0.440517\pi$
$59$	2.85410	0.371572	0.185786	+	0.982590i	$0.440517\pi$
$60$	0	0
$61$	−10.8541	−1.38973	−0.694863	−	0.719142i	$-0.744535\pi$
$61$	−10.8541	−1.38973	−0.694863	+	0.719142i	$0.744535\pi$
$62$	−3.85410	−0.489471
$63$	7.47214	0.941401
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.763932	−0.0940335
$67$	8.94427	1.09272	0.546358	−	0.837552i	$-0.316014\pi$
$67$	8.94427	1.09272	0.546358	+	0.837552i	$0.316014\pi$
$68$	−3.38197	−0.410124
$69$	1.85410	0.223208
$70$	0	0
$71$	−5.70820	−0.677439	−0.338720	−	0.940887i	$-0.609994\pi$
$71$	−5.70820	−0.677439	−0.338720	+	0.940887i	$0.609994\pi$
$72$	−2.85410	−0.336359
$73$	5.56231	0.651019	0.325509	−	0.945539i	$-0.394464\pi$
$73$	5.56231	0.651019	0.325509	+	0.945539i	$0.394464\pi$
$74$	−8.94427	−1.03975
$75$	0	0
$76$	−2.00000	−0.229416
$77$	−5.23607	−0.596705
$78$	0.145898	0.0165197
$79$	6.56231	0.738317	0.369159	−	0.929366i	$-0.379646\pi$
$79$	6.56231	0.738317	0.369159	+	0.929366i	$0.379646\pi$
$80$	0	0
$81$	7.70820	0.856467
$82$	7.70820	0.851229
$83$	−14.9443	−1.64035	−0.820173	−	0.572115i	$-0.806123\pi$
$83$	−14.9443	−1.64035	−0.820173	+	0.572115i	$0.806123\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	−3.38197	−0.364687
$87$	0.381966	0.0409511
$88$	2.00000	0.213201
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−4.85410	−0.506075
$93$	1.47214	0.152653
$94$	−1.52786	−0.157587
$95$	0	0
$96$	−0.381966	−0.0389842
$97$	−7.14590	−0.725556	−0.362778	−	0.931876i	$-0.618172\pi$
$97$	−7.14590	−0.725556	−0.362778	+	0.931876i	$0.618172\pi$
$98$	−0.145898	−0.0147379
$99$	−5.70820	−0.573696
$100$	0	0
$101$	10.8541	1.08002	0.540012	−	0.841657i	$-0.318420\pi$
$101$	10.8541	1.08002	0.540012	+	0.841657i	$0.318420\pi$
$102$	1.29180	0.127907
$103$	−7.41641	−0.730760	−0.365380	−	0.930858i	$-0.619061\pi$
$103$	−7.41641	−0.730760	−0.365380	+	0.930858i	$0.619061\pi$
$104$	−0.381966	−0.0374548
$105$	0	0
$106$	−9.38197	−0.911257
$107$	14.1803	1.37087	0.685433	−	0.728136i	$-0.259613\pi$
$107$	14.1803	1.37087	0.685433	+	0.728136i	$0.259613\pi$
$108$	2.23607	0.215166
$109$	19.4164	1.85975	0.929877	−	0.367870i	$-0.119913\pi$
$109$	19.4164	1.85975	0.929877	+	0.367870i	$0.119913\pi$
$110$	0	0
$111$	3.41641	0.324271
$112$	−2.61803	−0.247381
$113$	−4.09017	−0.384771	−0.192385	−	0.981319i	$-0.561622\pi$
$113$	−4.09017	−0.384771	−0.192385	+	0.981319i	$0.561622\pi$
$114$	0.763932	0.0715488
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	1.09017	0.100786
$118$	2.85410	0.262741
$119$	8.85410	0.811654
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−10.8541	−0.982684
$123$	−2.94427	−0.265476
$124$	−3.85410	−0.346109
$125$	0	0
$126$	7.47214	0.665671
$127$	8.29180	0.735778	0.367889	−	0.929870i	$-0.380081\pi$
$127$	8.29180	0.735778	0.367889	+	0.929870i	$0.380081\pi$
$128$	1.00000	0.0883883
$129$	1.29180	0.113736
$130$	0	0
$131$	21.4164	1.87116	0.935580	−	0.353114i	$-0.114877\pi$
$131$	21.4164	1.87116	0.935580	+	0.353114i	$0.114877\pi$
$132$	−0.763932	−0.0664917
$133$	5.23607	0.454025
$134$	8.94427	0.772667
$135$	0	0
$136$	−3.38197	−0.290001
$137$	4.85410	0.414714	0.207357	−	0.978265i	$-0.433514\pi$
$137$	4.85410	0.414714	0.207357	+	0.978265i	$0.433514\pi$
$138$	1.85410	0.157832
$139$	−5.56231	−0.471789	−0.235894	−	0.971779i	$-0.575802\pi$
$139$	−5.56231	−0.471789	−0.235894	+	0.971779i	$0.575802\pi$
$140$	0	0
$141$	0.583592	0.0491473
$142$	−5.70820	−0.479022
$143$	−0.763932	−0.0638832
$144$	−2.85410	−0.237842
$145$	0	0
$146$	5.56231	0.460340
$147$	0.0557281	0.00459638
$148$	−8.94427	−0.735215
$149$	−21.4164	−1.75450	−0.877250	−	0.480033i	$-0.840625\pi$
$149$	−21.4164	−1.75450	−0.877250	+	0.480033i	$0.840625\pi$
$150$	0	0
$151$	4.29180	0.349261	0.174631	−	0.984634i	$-0.444127\pi$
$151$	4.29180	0.349261	0.174631	+	0.984634i	$0.444127\pi$
$152$	−2.00000	−0.162221
$153$	9.65248	0.780356
$154$	−5.23607	−0.421934
$155$	0	0
$156$	0.145898	0.0116812
$157$	−9.70820	−0.774799	−0.387400	−	0.921912i	$-0.626627\pi$
$157$	−9.70820	−0.774799	−0.387400	+	0.921912i	$0.626627\pi$
$158$	6.56231	0.522069
$159$	3.58359	0.284197
$160$	0	0
$161$	12.7082	1.00155
$162$	7.70820	0.605614
$163$	−7.41641	−0.580898	−0.290449	−	0.956890i	$-0.593805\pi$
$163$	−7.41641	−0.580898	−0.290449	+	0.956890i	$0.593805\pi$
$164$	7.70820	0.601910
$165$	0	0
$166$	−14.9443	−1.15990
$167$	−2.61803	−0.202590	−0.101295	−	0.994856i	$-0.532299\pi$
$167$	−2.61803	−0.202590	−0.101295	+	0.994856i	$0.532299\pi$
$168$	1.00000	0.0771517
$169$	−12.8541	−0.988777
$170$	0	0
$171$	5.70820	0.436517
$172$	−3.38197	−0.257872
$173$	−17.5066	−1.33100	−0.665500	−	0.746398i	$-0.731782\pi$
$173$	−17.5066	−1.33100	−0.665500	+	0.746398i	$0.731782\pi$
$174$	0.381966	0.0289568
$175$	0	0
$176$	2.00000	0.150756
$177$	−1.09017	−0.0819422
$178$	2.00000	0.149906
$179$	9.14590	0.683597	0.341798	−	0.939773i	$-0.388964\pi$
$179$	9.14590	0.683597	0.341798	+	0.939773i	$0.388964\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	1.00000	0.0741249
$183$	4.14590	0.306474
$184$	−4.85410	−0.357849
$185$	0	0
$186$	1.47214	0.107942
$187$	−6.76393	−0.494628
$188$	−1.52786	−0.111431
$189$	−5.85410	−0.425823
$190$	0	0
$191$	23.2705	1.68379	0.841897	−	0.539637i	$-0.181439\pi$
$191$	23.2705	1.68379	0.841897	+	0.539637i	$0.181439\pi$
$192$	−0.381966	−0.0275660
$193$	2.56231	0.184439	0.0922194	−	0.995739i	$-0.470604\pi$
$193$	2.56231	0.184439	0.0922194	+	0.995739i	$0.470604\pi$
$194$	−7.14590	−0.513046
$195$	0	0
$196$	−0.145898	−0.0104213
$197$	−9.38197	−0.668437	−0.334219	−	0.942496i	$-0.608472\pi$
$197$	−9.38197	−0.668437	−0.334219	+	0.942496i	$0.608472\pi$
$198$	−5.70820	−0.405664
$199$	19.1246	1.35571	0.677854	−	0.735197i	$-0.262910\pi$
$199$	19.1246	1.35571	0.677854	+	0.735197i	$0.262910\pi$
$200$	0	0
$201$	−3.41641	−0.240975
$202$	10.8541	0.763692
$203$	2.61803	0.183750
$204$	1.29180	0.0904438
$205$	0	0
$206$	−7.41641	−0.516726
$207$	13.8541	0.962927
$208$	−0.381966	−0.0264846
$209$	−4.00000	−0.276686
$210$	0	0
$211$	−11.4164	−0.785938	−0.392969	−	0.919552i	$-0.628552\pi$
$211$	−11.4164	−0.785938	−0.392969	+	0.919552i	$0.628552\pi$
$212$	−9.38197	−0.644356
$213$	2.18034	0.149394
$214$	14.1803	0.969348
$215$	0	0
$216$	2.23607	0.152145
$217$	10.0902	0.684965
$218$	19.4164	1.31505
$219$	−2.12461	−0.143568
$220$	0	0
$221$	1.29180	0.0868956
$222$	3.41641	0.229294
$223$	26.5623	1.77874	0.889372	−	0.457185i	$-0.151142\pi$
$223$	26.5623	1.77874	0.889372	+	0.457185i	$0.151142\pi$
$224$	−2.61803	−0.174925
$225$	0	0
$226$	−4.09017	−0.272074
$227$	−16.4721	−1.09329	−0.546647	−	0.837363i	$-0.684096\pi$
$227$	−16.4721	−1.09329	−0.546647	+	0.837363i	$0.684096\pi$
$228$	0.763932	0.0505926
$229$	−8.14590	−0.538296	−0.269148	−	0.963099i	$-0.586742\pi$
$229$	−8.14590	−0.538296	−0.269148	+	0.963099i	$0.586742\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	−1.00000	−0.0656532
$233$	11.2361	0.736099	0.368050	−	0.929806i	$-0.380026\pi$
$233$	11.2361	0.736099	0.368050	+	0.929806i	$0.380026\pi$
$234$	1.09017	0.0712666
$235$	0	0
$236$	2.85410	0.185786
$237$	−2.50658	−0.162820
$238$	8.85410	0.573926
$239$	5.70820	0.369233	0.184617	−	0.982811i	$-0.440896\pi$
$239$	5.70820	0.369233	0.184617	+	0.982811i	$0.440896\pi$
$240$	0	0
$241$	−8.85410	−0.570343	−0.285171	−	0.958477i	$-0.592051\pi$
$241$	−8.85410	−0.570343	−0.285171	+	0.958477i	$0.592051\pi$
$242$	−7.00000	−0.449977
$243$	−9.65248	−0.619207
$244$	−10.8541	−0.694863
$245$	0	0
$246$	−2.94427	−0.187720
$247$	0.763932	0.0486078
$248$	−3.85410	−0.244736
$249$	5.70820	0.361743
$250$	0	0
$251$	−29.1246	−1.83833	−0.919165	−	0.393874i	$-0.871135\pi$
$251$	−29.1246	−1.83833	−0.919165	+	0.393874i	$0.871135\pi$
$252$	7.47214	0.470700
$253$	−9.70820	−0.610350
$254$	8.29180	0.520274
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.29180	−0.142958	−0.0714792	−	0.997442i	$-0.522772\pi$
$257$	−2.29180	−0.142958	−0.0714792	+	0.997442i	$0.522772\pi$
$258$	1.29180	0.0804237
$259$	23.4164	1.45502
$260$	0	0
$261$	2.85410	0.176664
$262$	21.4164	1.32311
$263$	21.5967	1.33171	0.665856	−	0.746080i	$-0.268066\pi$
$263$	21.5967	1.33171	0.665856	+	0.746080i	$0.268066\pi$
$264$	−0.763932	−0.0470168
$265$	0	0
$266$	5.23607	0.321044
$267$	−0.763932	−0.0467519
$268$	8.94427	0.546358
$269$	3.27051	0.199407	0.0997033	−	0.995017i	$-0.468211\pi$
$269$	3.27051	0.199407	0.0997033	+	0.995017i	$0.468211\pi$
$270$	0	0
$271$	23.4164	1.42245	0.711223	−	0.702967i	$-0.248142\pi$
$271$	23.4164	1.42245	0.711223	+	0.702967i	$0.248142\pi$
$272$	−3.38197	−0.205062
$273$	−0.381966	−0.0231176
$274$	4.85410	0.293247
$275$	0	0
$276$	1.85410	0.111604
$277$	30.0000	1.80253	0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000	1.80253	0.901263	+	0.433273i	$0.142641\pi$
$278$	−5.56231	−0.333605
$279$	11.0000	0.658553
$280$	0	0
$281$	−17.5623	−1.04768	−0.523840	−	0.851817i	$-0.675501\pi$
$281$	−17.5623	−1.04768	−0.523840	+	0.851817i	$0.675501\pi$
$282$	0.583592	0.0347524
$283$	6.76393	0.402074	0.201037	−	0.979584i	$-0.435569\pi$
$283$	6.76393	0.402074	0.201037	+	0.979584i	$0.435569\pi$
$284$	−5.70820	−0.338720
$285$	0	0
$286$	−0.763932	−0.0451722
$287$	−20.1803	−1.19121
$288$	−2.85410	−0.168180
$289$	−5.56231	−0.327194
$290$	0	0
$291$	2.72949	0.160006
$292$	5.56231	0.325509
$293$	19.4164	1.13432	0.567159	−	0.823608i	$-0.308042\pi$
$293$	19.4164	1.13432	0.567159	+	0.823608i	$0.308042\pi$
$294$	0.0557281	0.00325013
$295$	0	0
$296$	−8.94427	−0.519875
$297$	4.47214	0.259500
$298$	−21.4164	−1.24062
$299$	1.85410	0.107225
$300$	0	0
$301$	8.85410	0.510342
$302$	4.29180	0.246965
$303$	−4.14590	−0.238176
$304$	−2.00000	−0.114708
$305$	0	0
$306$	9.65248	0.551795
$307$	24.0000	1.36975	0.684876	−	0.728659i	$-0.259856\pi$
$307$	24.0000	1.36975	0.684876	+	0.728659i	$0.259856\pi$
$308$	−5.23607	−0.298353
$309$	2.83282	0.161153
$310$	0	0
$311$	−34.5623	−1.95985	−0.979924	−	0.199370i	$-0.936110\pi$
$311$	−34.5623	−1.95985	−0.979924	+	0.199370i	$0.936110\pi$
$312$	0.145898	0.00825985
$313$	12.7639	0.721460	0.360730	−	0.932670i	$-0.382528\pi$
$313$	12.7639	0.721460	0.360730	+	0.932670i	$0.382528\pi$
$314$	−9.70820	−0.547866
$315$	0	0
$316$	6.56231	0.369159
$317$	20.1803	1.13344	0.566720	−	0.823910i	$-0.308212\pi$
$317$	20.1803	1.13344	0.566720	+	0.823910i	$0.308212\pi$
$318$	3.58359	0.200958
$319$	−2.00000	−0.111979
$320$	0	0
$321$	−5.41641	−0.302314
$322$	12.7082	0.708201
$323$	6.76393	0.376355
$324$	7.70820	0.428234
$325$	0	0
$326$	−7.41641	−0.410757
$327$	−7.41641	−0.410128
$328$	7.70820	0.425614
$329$	4.00000	0.220527
$330$	0	0
$331$	27.1246	1.49090	0.745452	−	0.666560i	$-0.232234\pi$
$331$	27.1246	1.49090	0.745452	+	0.666560i	$0.232234\pi$
$332$	−14.9443	−0.820173
$333$	25.5279	1.39892
$334$	−2.61803	−0.143252
$335$	0	0
$336$	1.00000	0.0545545
$337$	−8.61803	−0.469454	−0.234727	−	0.972061i	$-0.575420\pi$
$337$	−8.61803	−0.469454	−0.234727	+	0.972061i	$0.575420\pi$
$338$	−12.8541	−0.699171
$339$	1.56231	0.0848528
$340$	0	0
$341$	−7.70820	−0.417423
$342$	5.70820	0.308664
$343$	18.7082	1.01015
$344$	−3.38197	−0.182343
$345$	0	0
$346$	−17.5066	−0.941159
$347$	6.00000	0.322097	0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000	0.322097	0.161048	+	0.986947i	$0.448512\pi$
$348$	0.381966	0.0204755
$349$	−24.8328	−1.32927	−0.664635	−	0.747168i	$-0.731413\pi$
$349$	−24.8328	−1.32927	−0.664635	+	0.747168i	$0.731413\pi$
$350$	0	0
$351$	−0.854102	−0.0455886
$352$	2.00000	0.106600
$353$	3.05573	0.162640	0.0813200	−	0.996688i	$-0.474086\pi$
$353$	3.05573	0.162640	0.0813200	+	0.996688i	$0.474086\pi$
$354$	−1.09017	−0.0579419
$355$	0	0
$356$	2.00000	0.106000
$357$	−3.38197	−0.178993
$358$	9.14590	0.483376
$359$	0.270510	0.0142770	0.00713848	−	0.999975i	$-0.497728\pi$
$359$	0.270510	0.0142770	0.00713848	+	0.999975i	$0.497728\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−10.0000	−0.525588
$363$	2.67376	0.140336
$364$	1.00000	0.0524142
$365$	0	0
$366$	4.14590	0.216710
$367$	−35.1246	−1.83349	−0.916745	−	0.399473i	$-0.869193\pi$
$367$	−35.1246	−1.83349	−0.916745	+	0.399473i	$0.869193\pi$
$368$	−4.85410	−0.253038
$369$	−22.0000	−1.14527
$370$	0	0
$371$	24.5623	1.27521
$372$	1.47214	0.0763267
$373$	−15.2705	−0.790677	−0.395339	−	0.918535i	$-0.629373\pi$
$373$	−15.2705	−0.790677	−0.395339	+	0.918535i	$0.629373\pi$
$374$	−6.76393	−0.349755
$375$	0	0
$376$	−1.52786	−0.0787936
$377$	0.381966	0.0196723
$378$	−5.85410	−0.301103
$379$	26.0000	1.33553	0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000	1.33553	0.667765	+	0.744372i	$0.267251\pi$
$380$	0	0
$381$	−3.16718	−0.162260
$382$	23.2705	1.19062
$383$	7.85410	0.401326	0.200663	−	0.979660i	$-0.435690\pi$
$383$	7.85410	0.401326	0.200663	+	0.979660i	$0.435690\pi$
$384$	−0.381966	−0.0194921
$385$	0	0
$386$	2.56231	0.130418
$387$	9.65248	0.490663
$388$	−7.14590	−0.362778
$389$	−20.8328	−1.05627	−0.528133	−	0.849162i	$-0.677108\pi$
$389$	−20.8328	−1.05627	−0.528133	+	0.849162i	$0.677108\pi$
$390$	0	0
$391$	16.4164	0.830213
$392$	−0.145898	−0.00736896
$393$	−8.18034	−0.412644
$394$	−9.38197	−0.472657
$395$	0	0
$396$	−5.70820	−0.286848
$397$	1.96556	0.0986485	0.0493243	−	0.998783i	$-0.484293\pi$
$397$	1.96556	0.0986485	0.0493243	+	0.998783i	$0.484293\pi$
$398$	19.1246	0.958630
$399$	−2.00000	−0.100125
$400$	0	0
$401$	21.9787	1.09756	0.548782	−	0.835965i	$-0.315092\pi$
$401$	21.9787	1.09756	0.548782	+	0.835965i	$0.315092\pi$
$402$	−3.41641	−0.170395
$403$	1.47214	0.0733323
$404$	10.8541	0.540012
$405$	0	0
$406$	2.61803	0.129931
$407$	−17.8885	−0.886702
$408$	1.29180	0.0639534
$409$	−7.12461	−0.352289	−0.176145	−	0.984364i	$-0.556363\pi$
$409$	−7.12461	−0.352289	−0.176145	+	0.984364i	$0.556363\pi$
$410$	0	0
$411$	−1.85410	−0.0914561
$412$	−7.41641	−0.365380
$413$	−7.47214	−0.367680
$414$	13.8541	0.680892
$415$	0	0
$416$	−0.381966	−0.0187274
$417$	2.12461	0.104043
$418$	−4.00000	−0.195646
$419$	−21.8541	−1.06764	−0.533821	−	0.845597i	$-0.679245\pi$
$419$	−21.8541	−1.06764	−0.533821	+	0.845597i	$0.679245\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−11.4164	−0.555742
$423$	4.36068	0.212024
$424$	−9.38197	−0.455629
$425$	0	0
$426$	2.18034	0.105638
$427$	28.4164	1.37517
$428$	14.1803	0.685433
$429$	0.291796	0.0140880
$430$	0	0
$431$	−33.4164	−1.60961	−0.804806	−	0.593538i	$-0.797731\pi$
$431$	−33.4164	−1.60961	−0.804806	+	0.593538i	$0.797731\pi$
$432$	2.23607	0.107583
$433$	16.4721	0.791600	0.395800	−	0.918337i	$-0.370467\pi$
$433$	16.4721	0.791600	0.395800	+	0.918337i	$0.370467\pi$
$434$	10.0902	0.484344
$435$	0	0
$436$	19.4164	0.929877
$437$	9.70820	0.464406
$438$	−2.12461	−0.101518
$439$	−37.1246	−1.77186	−0.885931	−	0.463818i	$-0.846479\pi$
$439$	−37.1246	−1.77186	−0.885931	+	0.463818i	$0.846479\pi$
$440$	0	0
$441$	0.416408	0.0198289
$442$	1.29180	0.0614445
$443$	1.90983	0.0907388	0.0453694	−	0.998970i	$-0.485554\pi$
$443$	1.90983	0.0907388	0.0453694	+	0.998970i	$0.485554\pi$
$444$	3.41641	0.162136
$445$	0	0
$446$	26.5623	1.25776
$447$	8.18034	0.386917
$448$	−2.61803	−0.123690
$449$	−4.58359	−0.216313	−0.108157	−	0.994134i	$-0.534495\pi$
$449$	−4.58359	−0.216313	−0.108157	+	0.994134i	$0.534495\pi$
$450$	0	0
$451$	15.4164	0.725930
$452$	−4.09017	−0.192385
$453$	−1.63932	−0.0770220
$454$	−16.4721	−0.773076
$455$	0	0
$456$	0.763932	0.0357744
$457$	14.2918	0.668542	0.334271	−	0.942477i	$-0.391510\pi$
$457$	14.2918	0.668542	0.334271	+	0.942477i	$0.391510\pi$
$458$	−8.14590	−0.380633
$459$	−7.56231	−0.352978
$460$	0	0
$461$	−24.1459	−1.12459	−0.562293	−	0.826938i	$-0.690081\pi$
$461$	−24.1459	−1.12459	−0.562293	+	0.826938i	$0.690081\pi$
$462$	2.00000	0.0930484
$463$	17.8885	0.831351	0.415676	−	0.909513i	$-0.363545\pi$
$463$	17.8885	0.831351	0.415676	+	0.909513i	$0.363545\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	11.2361	0.520501
$467$	−34.7984	−1.61028	−0.805138	−	0.593087i	$-0.797909\pi$
$467$	−34.7984	−1.61028	−0.805138	+	0.593087i	$0.797909\pi$
$468$	1.09017	0.0503931
$469$	−23.4164	−1.08127
$470$	0	0
$471$	3.70820	0.170865
$472$	2.85410	0.131371
$473$	−6.76393	−0.311006
$474$	−2.50658	−0.115131
$475$	0	0
$476$	8.85410	0.405827
$477$	26.7771	1.22604
$478$	5.70820	0.261087
$479$	−18.9787	−0.867160	−0.433580	−	0.901115i	$-0.642750\pi$
$479$	−18.9787	−0.867160	−0.433580	+	0.901115i	$0.642750\pi$
$480$	0	0
$481$	3.41641	0.155775
$482$	−8.85410	−0.403293
$483$	−4.85410	−0.220869
$484$	−7.00000	−0.318182
$485$	0	0
$486$	−9.65248	−0.437845
$487$	−38.5623	−1.74742	−0.873712	−	0.486443i	$-0.838294\pi$
$487$	−38.5623	−1.74742	−0.873712	+	0.486443i	$0.838294\pi$
$488$	−10.8541	−0.491342
$489$	2.83282	0.128104
$490$	0	0
$491$	−6.29180	−0.283945	−0.141972	−	0.989871i	$-0.545344\pi$
$491$	−6.29180	−0.283945	−0.141972	+	0.989871i	$0.545344\pi$
$492$	−2.94427	−0.132738
$493$	3.38197	0.152316
$494$	0.763932	0.0343709
$495$	0	0
$496$	−3.85410	−0.173054
$497$	14.9443	0.670342
$498$	5.70820	0.255791
$499$	28.5623	1.27862	0.639312	−	0.768947i	$-0.279219\pi$
$499$	28.5623	1.27862	0.639312	+	0.768947i	$0.279219\pi$
$500$	0	0
$501$	1.00000	0.0446767
$502$	−29.1246	−1.29990
$503$	−32.9443	−1.46891	−0.734456	−	0.678656i	$-0.762563\pi$
$503$	−32.9443	−1.46891	−0.734456	+	0.678656i	$0.762563\pi$
$504$	7.47214	0.332835
$505$	0	0
$506$	−9.70820	−0.431582
$507$	4.90983	0.218053
$508$	8.29180	0.367889
$509$	−21.1246	−0.936332	−0.468166	−	0.883641i	$-0.655085\pi$
$509$	−21.1246	−0.936332	−0.468166	+	0.883641i	$0.655085\pi$
$510$	0	0
$511$	−14.5623	−0.644198
$512$	1.00000	0.0441942
$513$	−4.47214	−0.197450
$514$	−2.29180	−0.101087
$515$	0	0
$516$	1.29180	0.0568682
$517$	−3.05573	−0.134391
$518$	23.4164	1.02886
$519$	6.68692	0.293523
$520$	0	0
$521$	−36.3951	−1.59450	−0.797250	−	0.603650i	$-0.793713\pi$
$521$	−36.3951	−1.59450	−0.797250	+	0.603650i	$0.793713\pi$
$522$	2.85410	0.124921
$523$	11.1246	0.486445	0.243223	−	0.969970i	$-0.421795\pi$
$523$	11.1246	0.486445	0.243223	+	0.969970i	$0.421795\pi$
$524$	21.4164	0.935580
$525$	0	0
$526$	21.5967	0.941663
$527$	13.0344	0.567789
$528$	−0.763932	−0.0332459
$529$	0.562306	0.0244481
$530$	0	0
$531$	−8.14590	−0.353502
$532$	5.23607	0.227012
$533$	−2.94427	−0.127531
$534$	−0.763932	−0.0330586
$535$	0	0
$536$	8.94427	0.386334
$537$	−3.49342	−0.150752
$538$	3.27051	0.141002
$539$	−0.291796	−0.0125685
$540$	0	0
$541$	−27.5623	−1.18500	−0.592498	−	0.805572i	$-0.701858\pi$
$541$	−27.5623	−1.18500	−0.592498	+	0.805572i	$0.701858\pi$
$542$	23.4164	1.00582
$543$	3.81966	0.163917
$544$	−3.38197	−0.145001
$545$	0	0
$546$	−0.381966	−0.0163466
$547$	14.8328	0.634205	0.317103	−	0.948391i	$-0.397290\pi$
$547$	14.8328	0.634205	0.317103	+	0.948391i	$0.397290\pi$
$548$	4.85410	0.207357
$549$	30.9787	1.32214
$550$	0	0
$551$	2.00000	0.0852029
$552$	1.85410	0.0789158
$553$	−17.1803	−0.730582
$554$	30.0000	1.27458
$555$	0	0
$556$	−5.56231	−0.235894
$557$	7.79837	0.330428	0.165214	−	0.986258i	$-0.447169\pi$
$557$	7.79837	0.330428	0.165214	+	0.986258i	$0.447169\pi$
$558$	11.0000	0.465667
$559$	1.29180	0.0546372
$560$	0	0
$561$	2.58359	0.109079
$562$	−17.5623	−0.740821
$563$	−33.3262	−1.40453	−0.702267	−	0.711914i	$-0.747829\pi$
$563$	−33.3262	−1.40453	−0.702267	+	0.711914i	$0.747829\pi$
$564$	0.583592	0.0245737
$565$	0	0
$566$	6.76393	0.284309
$567$	−20.1803	−0.847495
$568$	−5.70820	−0.239511
$569$	12.0000	0.503066	0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000	0.503066	0.251533	+	0.967849i	$0.419065\pi$
$570$	0	0
$571$	−6.85410	−0.286835	−0.143418	−	0.989662i	$-0.545809\pi$
$571$	−6.85410	−0.286835	−0.143418	+	0.989662i	$0.545809\pi$
$572$	−0.763932	−0.0319416
$573$	−8.88854	−0.371324
$574$	−20.1803	−0.842311
$575$	0	0
$576$	−2.85410	−0.118921
$577$	28.0344	1.16709	0.583545	−	0.812081i	$-0.301665\pi$
$577$	28.0344	1.16709	0.583545	+	0.812081i	$0.301665\pi$
$578$	−5.56231	−0.231361
$579$	−0.978714	−0.0406740
$580$	0	0
$581$	39.1246	1.62316
$582$	2.72949	0.113141
$583$	−18.7639	−0.777123
$584$	5.56231	0.230170
$585$	0	0
$586$	19.4164	0.802084
$587$	−12.6525	−0.522224	−0.261112	−	0.965309i	$-0.584089\pi$
$587$	−12.6525	−0.522224	−0.261112	+	0.965309i	$0.584089\pi$
$588$	0.0557281	0.00229819
$589$	7.70820	0.317611
$590$	0	0
$591$	3.58359	0.147409
$592$	−8.94427	−0.367607
$593$	−43.3050	−1.77832	−0.889161	−	0.457595i	$-0.848711\pi$
$593$	−43.3050	−1.77832	−0.889161	+	0.457595i	$0.848711\pi$
$594$	4.47214	0.183494
$595$	0	0
$596$	−21.4164	−0.877250
$597$	−7.30495	−0.298972
$598$	1.85410	0.0758199
$599$	23.5623	0.962730	0.481365	−	0.876520i	$-0.340141\pi$
$599$	23.5623	0.962730	0.481365	+	0.876520i	$0.340141\pi$
$600$	0	0
$601$	5.70820	0.232842	0.116421	−	0.993200i	$-0.462858\pi$
$601$	5.70820	0.232842	0.116421	+	0.993200i	$0.462858\pi$
$602$	8.85410	0.360866
$603$	−25.5279	−1.03957
$604$	4.29180	0.174631
$605$	0	0
$606$	−4.14590	−0.168416
$607$	−0.763932	−0.0310070	−0.0155035	−	0.999880i	$-0.504935\pi$
$607$	−0.763932	−0.0310070	−0.0155035	+	0.999880i	$0.504935\pi$
$608$	−2.00000	−0.0811107
$609$	−1.00000	−0.0405220
$610$	0	0
$611$	0.583592	0.0236096
$612$	9.65248	0.390178
$613$	−13.7426	−0.555060	−0.277530	−	0.960717i	$-0.589516\pi$
$613$	−13.7426	−0.555060	−0.277530	+	0.960717i	$0.589516\pi$
$614$	24.0000	0.968561
$615$	0	0
$616$	−5.23607	−0.210967
$617$	−32.6180	−1.31315	−0.656576	−	0.754260i	$-0.727996\pi$
$617$	−32.6180	−1.31315	−0.656576	+	0.754260i	$0.727996\pi$
$618$	2.83282	0.113953
$619$	−7.41641	−0.298091	−0.149045	−	0.988830i	$-0.547620\pi$
$619$	−7.41641	−0.298091	−0.149045	+	0.988830i	$0.547620\pi$
$620$	0	0
$621$	−10.8541	−0.435560
$622$	−34.5623	−1.38582
$623$	−5.23607	−0.209779
$624$	0.145898	0.00584060
$625$	0	0
$626$	12.7639	0.510149
$627$	1.52786	0.0610170
$628$	−9.70820	−0.387400
$629$	30.2492	1.20612
$630$	0	0
$631$	−34.8328	−1.38667	−0.693336	−	0.720614i	$-0.743860\pi$
$631$	−34.8328	−1.38667	−0.693336	+	0.720614i	$0.743860\pi$
$632$	6.56231	0.261035
$633$	4.36068	0.173321
$634$	20.1803	0.801464
$635$	0	0
$636$	3.58359	0.142099
$637$	0.0557281	0.00220803
$638$	−2.00000	−0.0791808
$639$	16.2918	0.644493
$640$	0	0
$641$	0.291796	0.0115253	0.00576263	−	0.999983i	$-0.498166\pi$
$641$	0.291796	0.0115253	0.00576263	+	0.999983i	$0.498166\pi$
$642$	−5.41641	−0.213769
$643$	16.5836	0.653993	0.326997	−	0.945026i	$-0.393963\pi$
$643$	16.5836	0.653993	0.326997	+	0.945026i	$0.393963\pi$
$644$	12.7082	0.500773
$645$	0	0
$646$	6.76393	0.266123
$647$	−13.5279	−0.531835	−0.265918	−	0.963996i	$-0.585675\pi$
$647$	−13.5279	−0.531835	−0.265918	+	0.963996i	$0.585675\pi$
$648$	7.70820	0.302807
$649$	5.70820	0.224067
$650$	0	0
$651$	−3.85410	−0.151054
$652$	−7.41641	−0.290449
$653$	−37.3050	−1.45986	−0.729928	−	0.683524i	$-0.760446\pi$
$653$	−37.3050	−1.45986	−0.729928	+	0.683524i	$0.760446\pi$
$654$	−7.41641	−0.290004
$655$	0	0
$656$	7.70820	0.300955
$657$	−15.8754	−0.619358
$658$	4.00000	0.155936
$659$	40.5410	1.57925	0.789627	−	0.613587i	$-0.210274\pi$
$659$	40.5410	1.57925	0.789627	+	0.613587i	$0.210274\pi$
$660$	0	0
$661$	28.8328	1.12147	0.560733	−	0.827996i	$-0.310519\pi$
$661$	28.8328	1.12147	0.560733	+	0.827996i	$0.310519\pi$
$662$	27.1246	1.05423
$663$	−0.493422	−0.0191629
$664$	−14.9443	−0.579950
$665$	0	0
$666$	25.5279	0.989185
$667$	4.85410	0.187952
$668$	−2.61803	−0.101295
$669$	−10.1459	−0.392263
$670$	0	0
$671$	−21.7082	−0.838036
$672$	1.00000	0.0385758
$673$	−26.9443	−1.03863	−0.519313	−	0.854584i	$-0.673812\pi$
$673$	−26.9443	−1.03863	−0.519313	+	0.854584i	$0.673812\pi$
$674$	−8.61803	−0.331954
$675$	0	0
$676$	−12.8541	−0.494389
$677$	−32.9443	−1.26615	−0.633076	−	0.774090i	$-0.718208\pi$
$677$	−32.9443	−1.26615	−0.633076	+	0.774090i	$0.718208\pi$
$678$	1.56231	0.0600000
$679$	18.7082	0.717955
$680$	0	0
$681$	6.29180	0.241102
$682$	−7.70820	−0.295162
$683$	23.7771	0.909805	0.454902	−	0.890541i	$-0.349674\pi$
$683$	23.7771	0.909805	0.454902	+	0.890541i	$0.349674\pi$
$684$	5.70820	0.218259
$685$	0	0
$686$	18.7082	0.714283
$687$	3.11146	0.118709
$688$	−3.38197	−0.128936
$689$	3.58359	0.136524
$690$	0	0
$691$	−13.5623	−0.515934	−0.257967	−	0.966154i	$-0.583053\pi$
$691$	−13.5623	−0.515934	−0.257967	+	0.966154i	$0.583053\pi$
$692$	−17.5066	−0.665500
$693$	14.9443	0.567686
$694$	6.00000	0.227757
$695$	0	0
$696$	0.381966	0.0144784
$697$	−26.0689	−0.987429
$698$	−24.8328	−0.939936
$699$	−4.29180	−0.162331
$700$	0	0
$701$	−9.12461	−0.344632	−0.172316	−	0.985042i	$-0.555125\pi$
$701$	−9.12461	−0.344632	−0.172316	+	0.985042i	$0.555125\pi$
$702$	−0.854102	−0.0322360
$703$	17.8885	0.674679
$704$	2.00000	0.0753778
$705$	0	0
$706$	3.05573	0.115004
$707$	−28.4164	−1.06871
$708$	−1.09017	−0.0409711
$709$	12.2918	0.461628	0.230814	−	0.972998i	$-0.425861\pi$
$709$	12.2918	0.461628	0.230814	+	0.972998i	$0.425861\pi$
$710$	0	0
$711$	−18.7295	−0.702411
$712$	2.00000	0.0749532
$713$	18.7082	0.700628
$714$	−3.38197	−0.126567
$715$	0	0
$716$	9.14590	0.341798
$717$	−2.18034	−0.0814263
$718$	0.270510	0.0100953
$719$	8.29180	0.309232	0.154616	−	0.987975i	$-0.450586\pi$
$719$	8.29180	0.309232	0.154616	+	0.987975i	$0.450586\pi$
$720$	0	0
$721$	19.4164	0.723105
$722$	−15.0000	−0.558242
$723$	3.38197	0.125777
$724$	−10.0000	−0.371647
$725$	0	0
$726$	2.67376	0.0992326
$727$	32.9443	1.22184	0.610918	−	0.791694i	$-0.290801\pi$
$727$	32.9443	1.22184	0.610918	+	0.791694i	$0.290801\pi$
$728$	1.00000	0.0370625
$729$	−19.4377	−0.719915
$730$	0	0
$731$	11.4377	0.423038
$732$	4.14590	0.153237
$733$	−12.0000	−0.443230	−0.221615	−	0.975134i	$-0.571133\pi$
$733$	−12.0000	−0.443230	−0.221615	+	0.975134i	$0.571133\pi$
$734$	−35.1246	−1.29647
$735$	0	0
$736$	−4.85410	−0.178925
$737$	17.8885	0.658933
$738$	−22.0000	−0.809831
$739$	28.2918	1.04073	0.520365	−	0.853944i	$-0.325796\pi$
$739$	28.2918	1.04073	0.520365	+	0.853944i	$0.325796\pi$
$740$	0	0
$741$	−0.291796	−0.0107194
$742$	24.5623	0.901711
$743$	25.4164	0.932438	0.466219	−	0.884669i	$-0.345616\pi$
$743$	25.4164	0.932438	0.466219	+	0.884669i	$0.345616\pi$
$744$	1.47214	0.0539711
$745$	0	0
$746$	−15.2705	−0.559093
$747$	42.6525	1.56057
$748$	−6.76393	−0.247314
$749$	−37.1246	−1.35650
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	−1.52786	−0.0557155
$753$	11.1246	0.405403
$754$	0.381966	0.0139104
$755$	0	0
$756$	−5.85410	−0.212912
$757$	−32.0689	−1.16556	−0.582782	−	0.812629i	$-0.698036\pi$
$757$	−32.0689	−1.16556	−0.582782	+	0.812629i	$0.698036\pi$
$758$	26.0000	0.944363
$759$	3.70820	0.134599
$760$	0	0
$761$	−9.85410	−0.357211	−0.178605	−	0.983921i	$-0.557159\pi$
$761$	−9.85410	−0.357211	−0.178605	+	0.983921i	$0.557159\pi$
$762$	−3.16718	−0.114735
$763$	−50.8328	−1.84027
$764$	23.2705	0.841897
$765$	0	0
$766$	7.85410	0.283780
$767$	−1.09017	−0.0393638
$768$	−0.381966	−0.0137830
$769$	−18.5836	−0.670141	−0.335071	−	0.942193i	$-0.608760\pi$
$769$	−18.5836	−0.670141	−0.335071	+	0.942193i	$0.608760\pi$
$770$	0	0
$771$	0.875388	0.0315263
$772$	2.56231	0.0922194
$773$	−6.76393	−0.243282	−0.121641	−	0.992574i	$-0.538816\pi$
$773$	−6.76393	−0.243282	−0.121641	+	0.992574i	$0.538816\pi$
$774$	9.65248	0.346951
$775$	0	0
$776$	−7.14590	−0.256523
$777$	−8.94427	−0.320874
$778$	−20.8328	−0.746893
$779$	−15.4164	−0.552350
$780$	0	0
$781$	−11.4164	−0.408511
$782$	16.4164	0.587050
$783$	−2.23607	−0.0799106
$784$	−0.145898	−0.00521064
$785$	0	0
$786$	−8.18034	−0.291783
$787$	41.7771	1.48919	0.744596	−	0.667515i	$-0.232642\pi$
$787$	41.7771	1.48919	0.744596	+	0.667515i	$0.232642\pi$
$788$	−9.38197	−0.334219
$789$	−8.24922	−0.293680
$790$	0	0
$791$	10.7082	0.380740
$792$	−5.70820	−0.202832
$793$	4.14590	0.147225
$794$	1.96556	0.0697550
$795$	0	0
$796$	19.1246	0.677854
$797$	35.2361	1.24813	0.624063	−	0.781374i	$-0.285481\pi$
$797$	35.2361	1.24813	0.624063	+	0.781374i	$0.285481\pi$
$798$	−2.00000	−0.0707992
$799$	5.16718	0.182802
$800$	0	0
$801$	−5.70820	−0.201689
$802$	21.9787	0.776095
$803$	11.1246	0.392579
$804$	−3.41641	−0.120487
$805$	0	0
$806$	1.47214	0.0518538
$807$	−1.24922	−0.0439748
$808$	10.8541	0.381846
$809$	−39.4164	−1.38581	−0.692904	−	0.721030i	$-0.743669\pi$
$809$	−39.4164	−1.38581	−0.692904	+	0.721030i	$0.743669\pi$
$810$	0	0
$811$	48.3951	1.69938	0.849691	−	0.527280i	$-0.176788\pi$
$811$	48.3951	1.69938	0.849691	+	0.527280i	$0.176788\pi$
$812$	2.61803	0.0918750
$813$	−8.94427	−0.313689
$814$	−17.8885	−0.626993
$815$	0	0
$816$	1.29180	0.0452219
$817$	6.76393	0.236640
$818$	−7.12461	−0.249106
$819$	−2.85410	−0.0997304
$820$	0	0
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	−1.85410	−0.0646692
$823$	−5.23607	−0.182518	−0.0912589	−	0.995827i	$-0.529089\pi$
$823$	−5.23607	−0.182518	−0.0912589	+	0.995827i	$0.529089\pi$
$824$	−7.41641	−0.258363
$825$	0	0
$826$	−7.47214	−0.259989
$827$	−25.2016	−0.876346	−0.438173	−	0.898891i	$-0.644374\pi$
$827$	−25.2016	−0.876346	−0.438173	+	0.898891i	$0.644374\pi$
$828$	13.8541	0.481463
$829$	−0.729490	−0.0253362	−0.0126681	−	0.999920i	$-0.504032\pi$
$829$	−0.729490	−0.0253362	−0.0126681	+	0.999920i	$0.504032\pi$
$830$	0	0
$831$	−11.4590	−0.397508
$832$	−0.381966	−0.0132423
$833$	0.493422	0.0170961
$834$	2.12461	0.0735693
$835$	0	0
$836$	−4.00000	−0.138343
$837$	−8.61803	−0.297883
$838$	−21.8541	−0.754937
$839$	−38.8328	−1.34066	−0.670329	−	0.742064i	$-0.733847\pi$
$839$	−38.8328	−1.34066	−0.670329	+	0.742064i	$0.733847\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−10.0000	−0.344623
$843$	6.70820	0.231043
$844$	−11.4164	−0.392969
$845$	0	0
$846$	4.36068	0.149923
$847$	18.3262	0.629697
$848$	−9.38197	−0.322178
$849$	−2.58359	−0.0886687
$850$	0	0
$851$	43.4164	1.48830
$852$	2.18034	0.0746972
$853$	8.83282	0.302430	0.151215	−	0.988501i	$-0.451681\pi$
$853$	8.83282	0.302430	0.151215	+	0.988501i	$0.451681\pi$
$854$	28.4164	0.972389
$855$	0	0
$856$	14.1803	0.484674
$857$	−21.8197	−0.745345	−0.372673	−	0.927963i	$-0.621559\pi$
$857$	−21.8197	−0.745345	−0.372673	+	0.927963i	$0.621559\pi$
$858$	0.291796	0.00996175
$859$	27.7082	0.945392	0.472696	−	0.881226i	$-0.343281\pi$
$859$	27.7082	0.945392	0.472696	+	0.881226i	$0.343281\pi$
$860$	0	0
$861$	7.70820	0.262695
$862$	−33.4164	−1.13817
$863$	−30.9230	−1.05263	−0.526315	−	0.850289i	$-0.676427\pi$
$863$	−30.9230	−1.05263	−0.526315	+	0.850289i	$0.676427\pi$
$864$	2.23607	0.0760726
$865$	0	0
$866$	16.4721	0.559746
$867$	2.12461	0.0721556
$868$	10.0902	0.342483
$869$	13.1246	0.445222
$870$	0	0
$871$	−3.41641	−0.115761
$872$	19.4164	0.657523
$873$	20.3951	0.690270
$874$	9.70820	0.328385
$875$	0	0
$876$	−2.12461	−0.0717840
$877$	42.2705	1.42737	0.713687	−	0.700465i	$-0.247024\pi$
$877$	42.2705	1.42737	0.713687	+	0.700465i	$0.247024\pi$
$878$	−37.1246	−1.25289
$879$	−7.41641	−0.250149
$880$	0	0
$881$	−14.5836	−0.491334	−0.245667	−	0.969354i	$-0.579007\pi$
$881$	−14.5836	−0.491334	−0.245667	+	0.969354i	$0.579007\pi$
$882$	0.416408	0.0140212
$883$	33.7082	1.13437	0.567186	−	0.823590i	$-0.308032\pi$
$883$	33.7082	1.13437	0.567186	+	0.823590i	$0.308032\pi$
$884$	1.29180	0.0434478
$885$	0	0
$886$	1.90983	0.0641620
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	3.41641	0.114647
$889$	−21.7082	−0.728070
$890$	0	0
$891$	15.4164	0.516469
$892$	26.5623	0.889372
$893$	3.05573	0.102256
$894$	8.18034	0.273591
$895$	0	0
$896$	−2.61803	−0.0874624
$897$	−0.708204	−0.0236462
$898$	−4.58359	−0.152956
$899$	3.85410	0.128541
$900$	0	0
$901$	31.7295	1.05706
$902$	15.4164	0.513310
$903$	−3.38197	−0.112545
$904$	−4.09017	−0.136037
$905$	0	0
$906$	−1.63932	−0.0544628
$907$	7.74265	0.257090	0.128545	−	0.991704i	$-0.458969\pi$
$907$	7.74265	0.257090	0.128545	+	0.991704i	$0.458969\pi$
$908$	−16.4721	−0.546647
$909$	−30.9787	−1.02750
$910$	0	0
$911$	12.8541	0.425875	0.212938	−	0.977066i	$-0.431697\pi$
$911$	12.8541	0.425875	0.212938	+	0.977066i	$0.431697\pi$
$912$	0.763932	0.0252963
$913$	−29.8885	−0.989166
$914$	14.2918	0.472731
$915$	0	0
$916$	−8.14590	−0.269148
$917$	−56.0689	−1.85156
$918$	−7.56231	−0.249593
$919$	−52.5410	−1.73317	−0.866584	−	0.499031i	$-0.833689\pi$
$919$	−52.5410	−1.73317	−0.866584	+	0.499031i	$0.833689\pi$
$920$	0	0
$921$	−9.16718	−0.302069
$922$	−24.1459	−0.795203
$923$	2.18034	0.0717668
$924$	2.00000	0.0657952
$925$	0	0
$926$	17.8885	0.587854
$927$	21.1672	0.695222
$928$	−1.00000	−0.0328266
$929$	34.1459	1.12029	0.560145	−	0.828394i	$-0.310745\pi$
$929$	34.1459	1.12029	0.560145	+	0.828394i	$0.310745\pi$
$930$	0	0
$931$	0.291796	0.00956323
$932$	11.2361	0.368050
$933$	13.2016	0.432202
$934$	−34.7984	−1.13864
$935$	0	0
$936$	1.09017	0.0356333
$937$	−44.0689	−1.43967	−0.719834	−	0.694146i	$-0.755782\pi$
$937$	−44.0689	−1.43967	−0.719834	+	0.694146i	$0.755782\pi$
$938$	−23.4164	−0.764573
$939$	−4.87539	−0.159102
$940$	0	0
$941$	−21.7082	−0.707667	−0.353834	−	0.935308i	$-0.615122\pi$
$941$	−21.7082	−0.707667	−0.353834	+	0.935308i	$0.615122\pi$
$942$	3.70820	0.120820
$943$	−37.4164	−1.21845
$944$	2.85410	0.0928931
$945$	0	0
$946$	−6.76393	−0.219914
$947$	−60.1591	−1.95491	−0.977453	−	0.211152i	$-0.932279\pi$
$947$	−60.1591	−1.95491	−0.977453	+	0.211152i	$0.932279\pi$
$948$	−2.50658	−0.0814099
$949$	−2.12461	−0.0689678
$950$	0	0
$951$	−7.70820	−0.249956
$952$	8.85410	0.286963
$953$	2.83282	0.0917639	0.0458820	−	0.998947i	$-0.485390\pi$
$953$	2.83282	0.0917639	0.0458820	+	0.998947i	$0.485390\pi$
$954$	26.7771	0.866940
$955$	0	0
$956$	5.70820	0.184617
$957$	0.763932	0.0246944
$958$	−18.9787	−0.613174
$959$	−12.7082	−0.410369
$960$	0	0
$961$	−16.1459	−0.520835
$962$	3.41641	0.110149
$963$	−40.4721	−1.30420
$964$	−8.85410	−0.285171
$965$	0	0
$966$	−4.85410	−0.156178
$967$	−33.7082	−1.08398	−0.541991	−	0.840384i	$-0.682329\pi$
$967$	−33.7082	−1.08398	−0.541991	+	0.840384i	$0.682329\pi$
$968$	−7.00000	−0.224989
$969$	−2.58359	−0.0829969
$970$	0	0
$971$	1.70820	0.0548189	0.0274094	−	0.999624i	$-0.491274\pi$
$971$	1.70820	0.0548189	0.0274094	+	0.999624i	$0.491274\pi$
$972$	−9.65248	−0.309603
$973$	14.5623	0.466846
$974$	−38.5623	−1.23562
$975$	0	0
$976$	−10.8541	−0.347431
$977$	33.0557	1.05755	0.528773	−	0.848763i	$-0.322652\pi$
$977$	33.0557	1.05755	0.528773	+	0.848763i	$0.322652\pi$
$978$	2.83282	0.0905835
$979$	4.00000	0.127841
$980$	0	0
$981$	−55.4164	−1.76931
$982$	−6.29180	−0.200779
$983$	3.59675	0.114718	0.0573592	−	0.998354i	$-0.481732\pi$
$983$	3.59675	0.114718	0.0573592	+	0.998354i	$0.481732\pi$
$984$	−2.94427	−0.0938600
$985$	0	0
$986$	3.38197	0.107704
$987$	−1.52786	−0.0486324
$988$	0.763932	0.0243039
$989$	16.4164	0.522011
$990$	0	0
$991$	−41.4164	−1.31564	−0.657818	−	0.753177i	$-0.728520\pi$
$991$	−41.4164	−1.31564	−0.657818	+	0.753177i	$0.728520\pi$
$992$	−3.85410	−0.122368
$993$	−10.3607	−0.328786
$994$	14.9443	0.474004
$995$	0	0
$996$	5.70820	0.180871
$997$	−17.1246	−0.542342	−0.271171	−	0.962531i	$-0.587411\pi$
$997$	−17.1246	−0.542342	−0.271171	+	0.962531i	$0.587411\pi$
$998$	28.5623	0.904124
$999$	−20.0000	−0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.l.1.2		2
5.2	odd	4		290.2.b.a.59.3	yes	4
5.3	odd	4		290.2.b.a.59.2	✓	4
5.4	even	2		1450.2.a.k.1.1		2
15.2	even	4		2610.2.e.e.2089.2		4
15.8	even	4		2610.2.e.e.2089.3		4
20.3	even	4		2320.2.d.d.929.3		4
20.7	even	4		2320.2.d.d.929.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.b.a.59.2	✓	4	5.3	odd	4
290.2.b.a.59.3	yes	4	5.2	odd	4
1450.2.a.k.1.1		2	5.4	even	2
1450.2.a.l.1.2		2	1.1	even	1	trivial
2320.2.d.d.929.2		4	20.7	even	4
2320.2.d.d.929.3		4	20.3	even	4
2610.2.e.e.2089.2		4	15.2	even	4
2610.2.e.e.2089.3		4	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.381966 q^{3} +1.00000 q^{4} -0.381966 q^{6} -2.61803 q^{7} +1.00000 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.381966 q^{3} +1.00000 q^{4} -0.381966 q^{6} -2.61803 q^{7} +1.00000 q^{8} -2.85410 q^{9} +2.00000 q^{11} -0.381966 q^{12} -0.381966 q^{13} -2.61803 q^{14} +1.00000 q^{16} -3.38197 q^{17} -2.85410 q^{18} -2.00000 q^{19} +1.00000 q^{21} +2.00000 q^{22} -4.85410 q^{23} -0.381966 q^{24} -0.381966 q^{26} +2.23607 q^{27} -2.61803 q^{28} -1.00000 q^{29} -3.85410 q^{31} +1.00000 q^{32} -0.763932 q^{33} -3.38197 q^{34} -2.85410 q^{36} -8.94427 q^{37} -2.00000 q^{38} +0.145898 q^{39} +7.70820 q^{41} +1.00000 q^{42} -3.38197 q^{43} +2.00000 q^{44} -4.85410 q^{46} -1.52786 q^{47} -0.381966 q^{48} -0.145898 q^{49} +1.29180 q^{51} -0.381966 q^{52} -9.38197 q^{53} +2.23607 q^{54} -2.61803 q^{56} +0.763932 q^{57} -1.00000 q^{58} +2.85410 q^{59} -10.8541 q^{61} -3.85410 q^{62} +7.47214 q^{63} +1.00000 q^{64} -0.763932 q^{66} +8.94427 q^{67} -3.38197 q^{68} +1.85410 q^{69} -5.70820 q^{71} -2.85410 q^{72} +5.56231 q^{73} -8.94427 q^{74} -2.00000 q^{76} -5.23607 q^{77} +0.145898 q^{78} +6.56231 q^{79} +7.70820 q^{81} +7.70820 q^{82} -14.9443 q^{83} +1.00000 q^{84} -3.38197 q^{86} +0.381966 q^{87} +2.00000 q^{88} +2.00000 q^{89} +1.00000 q^{91} -4.85410 q^{92} +1.47214 q^{93} -1.52786 q^{94} -0.381966 q^{96} -7.14590 q^{97} -0.145898 q^{98} -5.70820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + q^{9} + 4 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} + 2 q^{16} - 9 q^{17} + q^{18} - 4 q^{19} + 2 q^{21} + 4 q^{22} - 3 q^{23} - 3 q^{24} - 3 q^{26} - 3 q^{28} - 2 q^{29} - q^{31} + 2 q^{32} - 6 q^{33} - 9 q^{34} + q^{36} - 4 q^{38} + 7 q^{39} + 2 q^{41} + 2 q^{42} - 9 q^{43} + 4 q^{44} - 3 q^{46} - 12 q^{47} - 3 q^{48} - 7 q^{49} + 16 q^{51} - 3 q^{52} - 21 q^{53} - 3 q^{56} + 6 q^{57} - 2 q^{58} - q^{59} - 15 q^{61} - q^{62} + 6 q^{63} + 2 q^{64} - 6 q^{66} - 9 q^{68} - 3 q^{69} + 2 q^{71} + q^{72} - 9 q^{73} - 4 q^{76} - 6 q^{77} + 7 q^{78} - 7 q^{79} + 2 q^{81} + 2 q^{82} - 12 q^{83} + 2 q^{84} - 9 q^{86} + 3 q^{87} + 4 q^{88} + 4 q^{89} + 2 q^{91} - 3 q^{92} - 6 q^{93} - 12 q^{94} - 3 q^{96} - 21 q^{97} - 7 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + q^9 + 4 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 + 2 * q^16 - 9 * q^17 + q^18 - 4 * q^19 + 2 * q^21 + 4 * q^22 - 3 * q^23 - 3 * q^24 - 3 * q^26 - 3 * q^28 - 2 * q^29 - q^31 + 2 * q^32 - 6 * q^33 - 9 * q^34 + q^36 - 4 * q^38 + 7 * q^39 + 2 * q^41 + 2 * q^42 - 9 * q^43 + 4 * q^44 - 3 * q^46 - 12 * q^47 - 3 * q^48 - 7 * q^49 + 16 * q^51 - 3 * q^52 - 21 * q^53 - 3 * q^56 + 6 * q^57 - 2 * q^58 - q^59 - 15 * q^61 - q^62 + 6 * q^63 + 2 * q^64 - 6 * q^66 - 9 * q^68 - 3 * q^69 + 2 * q^71 + q^72 - 9 * q^73 - 4 * q^76 - 6 * q^77 + 7 * q^78 - 7 * q^79 + 2 * q^81 + 2 * q^82 - 12 * q^83 + 2 * q^84 - 9 * q^86 + 3 * q^87 + 4 * q^88 + 4 * q^89 + 2 * q^91 - 3 * q^92 - 6 * q^93 - 12 * q^94 - 3 * q^96 - 21 * q^97 - 7 * q^98 + 2 * q^99

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