LMFDB - Embedded newform 1450.2.a.t.1.4

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:	$5$
Coefficient field:	5.5.3661564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 10x^{3} + 3x^{2} + 20x + 8 $ x^5 - 2x^4 - 10x^3 + 3x^2 + 20x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
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			1.4
Root			$1.68193$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.681929 q^{3} +1.00000 q^{4} -0.681929 q^{6} -0.936197 q^{7} -1.00000 q^{8} -2.53497 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.681929 q^{3} +1.00000 q^{4} -0.681929 q^{6} -0.936197 q^{7} -1.00000 q^{8} -2.53497 q^{9} +0.0929484 q^{11} +0.681929 q^{12} +1.69629 q^{13} +0.936197 q^{14} +1.00000 q^{16} -4.42766 q^{17} +2.53497 q^{18} +5.52019 q^{19} -0.638420 q^{21} -0.0929484 q^{22} -5.73095 q^{23} -0.681929 q^{24} -1.69629 q^{26} -3.77446 q^{27} -0.936197 q^{28} +1.00000 q^{29} +0.970854 q^{31} -1.00000 q^{32} +0.0633842 q^{33} +4.42766 q^{34} -2.53497 q^{36} -1.49146 q^{37} -5.52019 q^{38} +1.15675 q^{39} -3.54975 q^{41} +0.638420 q^{42} -10.9276 q^{43} +0.0929484 q^{44} +5.73095 q^{46} -0.950979 q^{47} +0.681929 q^{48} -6.12353 q^{49} -3.01935 q^{51} +1.69629 q^{52} -9.91319 q^{53} +3.77446 q^{54} +0.936197 q^{56} +3.76438 q^{57} -1.00000 q^{58} -2.36709 q^{59} +3.12437 q^{61} -0.970854 q^{62} +2.37323 q^{63} +1.00000 q^{64} -0.0633842 q^{66} +9.54892 q^{67} -4.42766 q^{68} -3.90810 q^{69} -7.64780 q^{71} +2.53497 q^{72} -13.5559 q^{73} +1.49146 q^{74} +5.52019 q^{76} -0.0870180 q^{77} -1.15675 q^{78} -9.18776 q^{79} +5.03101 q^{81} +3.54975 q^{82} +11.9540 q^{83} -0.638420 q^{84} +10.9276 q^{86} +0.681929 q^{87} -0.0929484 q^{88} +10.7564 q^{89} -1.58806 q^{91} -5.73095 q^{92} +0.662054 q^{93} +0.950979 q^{94} -0.681929 q^{96} +5.18266 q^{97} +6.12353 q^{98} -0.235622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9} - 3 q^{12} - 7 q^{13} + 5 q^{14} + 5 q^{16} - 9 q^{17} - 10 q^{18} - 4 q^{19} - 6 q^{21} - 13 q^{23} + 3 q^{24} + 7 q^{26} + 6 q^{27} - 5 q^{28} + 5 q^{29} + 5 q^{31} - 5 q^{32} - 18 q^{33} + 9 q^{34} + 10 q^{36} + 6 q^{37} + 4 q^{38} + 5 q^{39} - 4 q^{41} + 6 q^{42} - q^{43} + 13 q^{46} - 14 q^{47} - 3 q^{48} + 16 q^{49} - 32 q^{51} - 7 q^{52} - 5 q^{53} - 6 q^{54} + 5 q^{56} - 14 q^{57} - 5 q^{58} - 9 q^{59} + 5 q^{61} - 5 q^{62} - 36 q^{63} + 5 q^{64} + 18 q^{66} - 2 q^{67} - 9 q^{68} + 7 q^{69} - 6 q^{71} - 10 q^{72} - 9 q^{73} - 6 q^{74} - 4 q^{76} + 18 q^{77} - 5 q^{78} - 17 q^{79} - 3 q^{81} + 4 q^{82} - 30 q^{83} - 6 q^{84} + q^{86} - 3 q^{87} + 10 q^{89} - 22 q^{91} - 13 q^{92} + 6 q^{93} + 14 q^{94} + 3 q^{96} + 15 q^{97} - 16 q^{98} - 34 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9 - 3 * q^12 - 7 * q^13 + 5 * q^14 + 5 * q^16 - 9 * q^17 - 10 * q^18 - 4 * q^19 - 6 * q^21 - 13 * q^23 + 3 * q^24 + 7 * q^26 + 6 * q^27 - 5 * q^28 + 5 * q^29 + 5 * q^31 - 5 * q^32 - 18 * q^33 + 9 * q^34 + 10 * q^36 + 6 * q^37 + 4 * q^38 + 5 * q^39 - 4 * q^41 + 6 * q^42 - q^43 + 13 * q^46 - 14 * q^47 - 3 * q^48 + 16 * q^49 - 32 * q^51 - 7 * q^52 - 5 * q^53 - 6 * q^54 + 5 * q^56 - 14 * q^57 - 5 * q^58 - 9 * q^59 + 5 * q^61 - 5 * q^62 - 36 * q^63 + 5 * q^64 + 18 * q^66 - 2 * q^67 - 9 * q^68 + 7 * q^69 - 6 * q^71 - 10 * q^72 - 9 * q^73 - 6 * q^74 - 4 * q^76 + 18 * q^77 - 5 * q^78 - 17 * q^79 - 3 * q^81 + 4 * q^82 - 30 * q^83 - 6 * q^84 + q^86 - 3 * q^87 + 10 * q^89 - 22 * q^91 - 13 * q^92 + 6 * q^93 + 14 * q^94 + 3 * q^96 + 15 * q^97 - 16 * q^98 - 34 * 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
$3$	0.681929	0.393712	0.196856	−	0.980432i	$-0.436927\pi$
$3$	0.681929	0.393712	0.196856	+	0.980432i	$0.436927\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−0.681929	−0.278396
$7$	−0.936197	−0.353849	−0.176925	−	0.984224i	$-0.556615\pi$
$7$	−0.936197	−0.353849	−0.176925	+	0.984224i	$0.556615\pi$
$8$	−1.00000	−0.353553
$9$	−2.53497	−0.844991
$10$	0	0
$11$	0.0929484	0.0280250	0.0140125	−	0.999902i	$-0.495540\pi$
$11$	0.0929484	0.0280250	0.0140125	+	0.999902i	$0.495540\pi$
$12$	0.681929	0.196856
$13$	1.69629	0.470467	0.235233	−	0.971939i	$-0.424415\pi$
$13$	1.69629	0.470467	0.235233	+	0.971939i	$0.424415\pi$
$14$	0.936197	0.250209
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.42766	−1.07387	−0.536933	−	0.843625i	$-0.680417\pi$
$17$	−4.42766	−1.07387	−0.536933	+	0.843625i	$0.680417\pi$
$18$	2.53497	0.597499
$19$	5.52019	1.26642	0.633209	−	0.773981i	$-0.281737\pi$
$19$	5.52019	1.26642	0.633209	+	0.773981i	$0.281737\pi$
$20$	0	0
$21$	−0.638420	−0.139315
$22$	−0.0929484	−0.0198167
$23$	−5.73095	−1.19499	−0.597493	−	0.801874i	$-0.703836\pi$
$23$	−5.73095	−1.19499	−0.597493	+	0.801874i	$0.703836\pi$
$24$	−0.681929	−0.139198
$25$	0	0
$26$	−1.69629	−0.332670
$27$	−3.77446	−0.726395
$28$	−0.936197	−0.176925
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	0.970854	0.174371	0.0871853	−	0.996192i	$-0.472213\pi$
$31$	0.970854	0.174371	0.0871853	+	0.996192i	$0.472213\pi$
$32$	−1.00000	−0.176777
$33$	0.0633842	0.0110338
$34$	4.42766	0.759338
$35$	0	0
$36$	−2.53497	−0.422495
$37$	−1.49146	−0.245195	−0.122598	−	0.992456i	$-0.539122\pi$
$37$	−1.49146	−0.245195	−0.122598	+	0.992456i	$0.539122\pi$
$38$	−5.52019	−0.895493
$39$	1.15675	0.185228
$40$	0	0
$41$	−3.54975	−0.554379	−0.277189	−	0.960815i	$-0.589403\pi$
$41$	−3.54975	−0.554379	−0.277189	+	0.960815i	$0.589403\pi$
$42$	0.638420	0.0985104
$43$	−10.9276	−1.66644	−0.833218	−	0.552944i	$-0.813504\pi$
$43$	−10.9276	−1.66644	−0.833218	+	0.552944i	$0.813504\pi$
$44$	0.0929484	0.0140125
$45$	0	0
$46$	5.73095	0.844982
$47$	−0.950979	−0.138715	−0.0693573	−	0.997592i	$-0.522095\pi$
$47$	−0.950979	−0.138715	−0.0693573	+	0.997592i	$0.522095\pi$
$48$	0.681929	0.0984280
$49$	−6.12353	−0.874791
$50$	0	0
$51$	−3.01935	−0.422794
$52$	1.69629	0.235233
$53$	−9.91319	−1.36168	−0.680841	−	0.732431i	$-0.738386\pi$
$53$	−9.91319	−1.36168	−0.680841	+	0.732431i	$0.738386\pi$
$54$	3.77446	0.513639
$55$	0	0
$56$	0.936197	0.125105
$57$	3.76438	0.498604
$58$	−1.00000	−0.131306
$59$	−2.36709	−0.308169	−0.154085	−	0.988058i	$-0.549243\pi$
$59$	−2.36709	−0.308169	−0.154085	+	0.988058i	$0.549243\pi$
$60$	0	0
$61$	3.12437	0.400035	0.200017	−	0.979792i	$-0.435900\pi$
$61$	3.12437	0.400035	0.200017	+	0.979792i	$0.435900\pi$
$62$	−0.970854	−0.123299
$63$	2.37323	0.298999
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.0633842	−0.00780205
$67$	9.54892	1.16659	0.583293	−	0.812262i	$-0.301764\pi$
$67$	9.54892	1.16659	0.583293	+	0.812262i	$0.301764\pi$
$68$	−4.42766	−0.536933
$69$	−3.90810	−0.470480
$70$	0	0
$71$	−7.64780	−0.907626	−0.453813	−	0.891097i	$-0.649937\pi$
$71$	−7.64780	−0.907626	−0.453813	+	0.891097i	$0.649937\pi$
$72$	2.53497	0.298749
$73$	−13.5559	−1.58660	−0.793299	−	0.608832i	$-0.791638\pi$
$73$	−13.5559	−1.58660	−0.793299	+	0.608832i	$0.791638\pi$
$74$	1.49146	0.173379
$75$	0	0
$76$	5.52019	0.633209
$77$	−0.0870180	−0.00991662
$78$	−1.15675	−0.130976
$79$	−9.18776	−1.03370	−0.516852	−	0.856075i	$-0.672896\pi$
$79$	−9.18776	−1.03370	−0.516852	+	0.856075i	$0.672896\pi$
$80$	0	0
$81$	5.03101	0.559001
$82$	3.54975	0.392005
$83$	11.9540	1.31212	0.656061	−	0.754708i	$-0.272222\pi$
$83$	11.9540	1.31212	0.656061	+	0.754708i	$0.272222\pi$
$84$	−0.638420	−0.0696573
$85$	0	0
$86$	10.9276	1.17835
$87$	0.681929	0.0731105
$88$	−0.0929484	−0.00990833
$89$	10.7564	1.14018	0.570090	−	0.821582i	$-0.306908\pi$
$89$	10.7564	1.14018	0.570090	+	0.821582i	$0.306908\pi$
$90$	0	0
$91$	−1.58806	−0.166474
$92$	−5.73095	−0.597493
$93$	0.662054	0.0686518
$94$	0.950979	0.0980860
$95$	0	0
$96$	−0.681929	−0.0695991
$97$	5.18266	0.526220	0.263110	−	0.964766i	$-0.415252\pi$
$97$	5.18266	0.526220	0.263110	+	0.964766i	$0.415252\pi$
$98$	6.12353	0.618570
$99$	−0.235622	−0.0236809
$100$	0	0
$101$	−2.42538	−0.241335	−0.120667	−	0.992693i	$-0.538503\pi$
$101$	−2.42538	−0.241335	−0.120667	+	0.992693i	$0.538503\pi$
$102$	3.01935	0.298960
$103$	−7.45088	−0.734157	−0.367078	−	0.930190i	$-0.619642\pi$
$103$	−7.45088	−0.734157	−0.367078	+	0.930190i	$0.619642\pi$
$104$	−1.69629	−0.166335
$105$	0	0
$106$	9.91319	0.962855
$107$	−4.82204	−0.466164	−0.233082	−	0.972457i	$-0.574881\pi$
$107$	−4.82204	−0.466164	−0.233082	+	0.972457i	$0.574881\pi$
$108$	−3.77446	−0.363197
$109$	7.19889	0.689528	0.344764	−	0.938689i	$-0.387959\pi$
$109$	7.19889	0.689528	0.344764	+	0.938689i	$0.387959\pi$
$110$	0	0
$111$	−1.01707	−0.0965362
$112$	−0.936197	−0.0884623
$113$	−0.533399	−0.0501779	−0.0250890	−	0.999685i	$-0.507987\pi$
$113$	−0.533399	−0.0501779	−0.0250890	+	0.999685i	$0.507987\pi$
$114$	−3.76438	−0.352566
$115$	0	0
$116$	1.00000	0.0928477
$117$	−4.30006	−0.397540
$118$	2.36709	0.217908
$119$	4.14516	0.379987
$120$	0	0
$121$	−10.9914	−0.999215
$122$	−3.12437	−0.282867
$123$	−2.42068	−0.218265
$124$	0.970854	0.0871853
$125$	0	0
$126$	−2.37323	−0.211425
$127$	−4.91278	−0.435938	−0.217969	−	0.975956i	$-0.569943\pi$
$127$	−4.91278	−0.435938	−0.217969	+	0.975956i	$0.569943\pi$
$128$	−1.00000	−0.0883883
$129$	−7.45182	−0.656096
$130$	0	0
$131$	−13.5202	−1.18126	−0.590632	−	0.806941i	$-0.701122\pi$
$131$	−13.5202	−1.18126	−0.590632	+	0.806941i	$0.701122\pi$
$132$	0.0633842	0.00551689
$133$	−5.16799	−0.448121
$134$	−9.54892	−0.824901
$135$	0	0
$136$	4.42766	0.379669
$137$	−21.5869	−1.84429	−0.922147	−	0.386840i	$-0.873567\pi$
$137$	−21.5869	−1.84429	−0.922147	+	0.386840i	$0.873567\pi$
$138$	3.90810	0.332680
$139$	10.9485	0.928638	0.464319	−	0.885668i	$-0.346299\pi$
$139$	10.9485	0.928638	0.464319	+	0.885668i	$0.346299\pi$
$140$	0	0
$141$	−0.648500	−0.0546136
$142$	7.64780	0.641789
$143$	0.157668	0.0131848
$144$	−2.53497	−0.211248
$145$	0	0
$146$	13.5559	1.12189
$147$	−4.17582	−0.344416
$148$	−1.49146	−0.122598
$149$	−0.922252	−0.0755539	−0.0377769	−	0.999286i	$-0.512028\pi$
$149$	−0.922252	−0.0755539	−0.0377769	+	0.999286i	$0.512028\pi$
$150$	0	0
$151$	−10.8147	−0.880091	−0.440045	−	0.897976i	$-0.645038\pi$
$151$	−10.8147	−0.880091	−0.440045	+	0.897976i	$0.645038\pi$
$152$	−5.52019	−0.447747
$153$	11.2240	0.907407
$154$	0.0870180	0.00701211
$155$	0	0
$156$	1.15675	0.0926142
$157$	17.6405	1.40786	0.703932	−	0.710267i	$-0.251426\pi$
$157$	17.6405	1.40786	0.703932	+	0.710267i	$0.251426\pi$
$158$	9.18776	0.730939
$159$	−6.76010	−0.536110
$160$	0	0
$161$	5.36530	0.422845
$162$	−5.03101	−0.395273
$163$	14.9050	1.16745	0.583724	−	0.811952i	$-0.301595\pi$
$163$	14.9050	1.16745	0.583724	+	0.811952i	$0.301595\pi$
$164$	−3.54975	−0.277189
$165$	0	0
$166$	−11.9540	−0.927810
$167$	−21.6926	−1.67863	−0.839313	−	0.543648i	$-0.817043\pi$
$167$	−21.6926	−1.67863	−0.839313	+	0.543648i	$0.817043\pi$
$168$	0.638420	0.0492552
$169$	−10.1226	−0.778661
$170$	0	0
$171$	−13.9935	−1.07011
$172$	−10.9276	−0.833218
$173$	6.70202	0.509545	0.254772	−	0.967001i	$-0.417999\pi$
$173$	6.70202	0.509545	0.254772	+	0.967001i	$0.417999\pi$
$174$	−0.681929	−0.0516969
$175$	0	0
$176$	0.0929484	0.00700625
$177$	−1.61419	−0.121330
$178$	−10.7564	−0.806230
$179$	−0.690568	−0.0516155	−0.0258078	−	0.999667i	$-0.508216\pi$
$179$	−0.690568	−0.0516155	−0.0258078	+	0.999667i	$0.508216\pi$
$180$	0	0
$181$	13.9220	1.03482	0.517409	−	0.855738i	$-0.326897\pi$
$181$	13.9220	1.03482	0.517409	+	0.855738i	$0.326897\pi$
$182$	1.58806	0.117715
$183$	2.13060	0.157498
$184$	5.73095	0.422491
$185$	0	0
$186$	−0.662054	−0.0485441
$187$	−0.411544	−0.0300951
$188$	−0.950979	−0.0693573
$189$	3.53364	0.257034
$190$	0	0
$191$	−0.300055	−0.0217112	−0.0108556	−	0.999941i	$-0.503456\pi$
$191$	−0.300055	−0.0217112	−0.0108556	+	0.999941i	$0.503456\pi$
$192$	0.681929	0.0492140
$193$	13.9168	1.00176	0.500878	−	0.865518i	$-0.333010\pi$
$193$	13.9168	1.00176	0.500878	+	0.865518i	$0.333010\pi$
$194$	−5.18266	−0.372094
$195$	0	0
$196$	−6.12353	−0.437395
$197$	16.1264	1.14896	0.574481	−	0.818518i	$-0.305204\pi$
$197$	16.1264	1.14896	0.574481	+	0.818518i	$0.305204\pi$
$198$	0.235622	0.0167449
$199$	−24.9546	−1.76899	−0.884493	−	0.466553i	$-0.845496\pi$
$199$	−24.9546	−1.76899	−0.884493	+	0.466553i	$0.845496\pi$
$200$	0	0
$201$	6.51168	0.459299
$202$	2.42538	0.170649
$203$	−0.936197	−0.0657082
$204$	−3.01935	−0.211397
$205$	0	0
$206$	7.45088	0.519127
$207$	14.5278	1.00975
$208$	1.69629	0.117617
$209$	0.513093	0.0354914
$210$	0	0
$211$	−9.54382	−0.657024	−0.328512	−	0.944500i	$-0.606547\pi$
$211$	−9.54382	−0.657024	−0.328512	+	0.944500i	$0.606547\pi$
$212$	−9.91319	−0.680841
$213$	−5.21525	−0.357343
$214$	4.82204	0.329628
$215$	0	0
$216$	3.77446	0.256819
$217$	−0.908911	−0.0617009
$218$	−7.19889	−0.487570
$219$	−9.24416	−0.624662
$220$	0	0
$221$	−7.51061	−0.505218
$222$	1.01707	0.0682614
$223$	−3.18913	−0.213560	−0.106780	−	0.994283i	$-0.534054\pi$
$223$	−3.18913	−0.213560	−0.106780	+	0.994283i	$0.534054\pi$
$224$	0.936197	0.0625523
$225$	0	0
$226$	0.533399	0.0354812
$227$	15.8847	1.05430	0.527152	−	0.849771i	$-0.323260\pi$
$227$	15.8847	1.05430	0.527152	+	0.849771i	$0.323260\pi$
$228$	3.76438	0.249302
$229$	−4.51924	−0.298639	−0.149320	−	0.988789i	$-0.547708\pi$
$229$	−4.51924	−0.298639	−0.149320	+	0.988789i	$0.547708\pi$
$230$	0	0
$231$	−0.0593401	−0.00390429
$232$	−1.00000	−0.0656532
$233$	−20.8617	−1.36669	−0.683347	−	0.730094i	$-0.739476\pi$
$233$	−20.8617	−1.36669	−0.683347	+	0.730094i	$0.739476\pi$
$234$	4.30006	0.281103
$235$	0	0
$236$	−2.36709	−0.154085
$237$	−6.26540	−0.406981
$238$	−4.14516	−0.268691
$239$	−4.27747	−0.276687	−0.138343	−	0.990384i	$-0.544178\pi$
$239$	−4.27747	−0.276687	−0.138343	+	0.990384i	$0.544178\pi$
$240$	0	0
$241$	5.18963	0.334293	0.167147	−	0.985932i	$-0.446545\pi$
$241$	5.18963	0.334293	0.167147	+	0.985932i	$0.446545\pi$
$242$	10.9914	0.706551
$243$	14.7542	0.946480
$244$	3.12437	0.200017
$245$	0	0
$246$	2.42068	0.154337
$247$	9.36386	0.595808
$248$	−0.970854	−0.0616493
$249$	8.15178	0.516598
$250$	0	0
$251$	−23.8028	−1.50242	−0.751208	−	0.660065i	$-0.770529\pi$
$251$	−23.8028	−1.50242	−0.751208	+	0.660065i	$0.770529\pi$
$252$	2.37323	0.149500
$253$	−0.532682	−0.0334895
$254$	4.91278	0.308255
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.80817	−0.487060	−0.243530	−	0.969893i	$-0.578306\pi$
$257$	−7.80817	−0.487060	−0.243530	+	0.969893i	$0.578306\pi$
$258$	7.45182	0.463930
$259$	1.39630	0.0867621
$260$	0	0
$261$	−2.53497	−0.156911
$262$	13.5202	0.835280
$263$	5.92288	0.365221	0.182610	−	0.983185i	$-0.441545\pi$
$263$	5.92288	0.365221	0.182610	+	0.983185i	$0.441545\pi$
$264$	−0.0633842	−0.00390103
$265$	0	0
$266$	5.16799	0.316870
$267$	7.33513	0.448903
$268$	9.54892	0.583293
$269$	20.9780	1.27905	0.639527	−	0.768769i	$-0.279130\pi$
$269$	20.9780	1.27905	0.639527	+	0.768769i	$0.279130\pi$
$270$	0	0
$271$	30.4270	1.84831	0.924155	−	0.382017i	$-0.124770\pi$
$271$	30.4270	1.84831	0.924155	+	0.382017i	$0.124770\pi$
$272$	−4.42766	−0.268466
$273$	−1.08295	−0.0655429
$274$	21.5869	1.30411
$275$	0	0
$276$	−3.90810	−0.235240
$277$	27.5908	1.65777	0.828884	−	0.559420i	$-0.188976\pi$
$277$	27.5908	1.65777	0.828884	+	0.559420i	$0.188976\pi$
$278$	−10.9485	−0.656646
$279$	−2.46109	−0.147342
$280$	0	0
$281$	−1.19274	−0.0711531	−0.0355766	−	0.999367i	$-0.511327\pi$
$281$	−1.19274	−0.0711531	−0.0355766	+	0.999367i	$0.511327\pi$
$282$	0.648500	0.0386176
$283$	20.8048	1.23671	0.618357	−	0.785897i	$-0.287798\pi$
$283$	20.8048	1.23671	0.618357	+	0.785897i	$0.287798\pi$
$284$	−7.64780	−0.453813
$285$	0	0
$286$	−0.157668	−0.00932308
$287$	3.32327	0.196166
$288$	2.53497	0.149375
$289$	2.60418	0.153187
$290$	0	0
$291$	3.53421	0.207179
$292$	−13.5559	−0.793299
$293$	19.5620	1.14283	0.571413	−	0.820662i	$-0.306395\pi$
$293$	19.5620	1.14283	0.571413	+	0.820662i	$0.306395\pi$
$294$	4.17582	0.243539
$295$	0	0
$296$	1.49146	0.0866896
$297$	−0.350830	−0.0203572
$298$	0.922252	0.0534246
$299$	−9.72137	−0.562201
$300$	0	0
$301$	10.2303	0.589668
$302$	10.8147	0.622318
$303$	−1.65394	−0.0950163
$304$	5.52019	0.316605
$305$	0	0
$306$	−11.2240	−0.641633
$307$	13.9035	0.793515	0.396757	−	0.917923i	$-0.370135\pi$
$307$	13.9035	0.793515	0.396757	+	0.917923i	$0.370135\pi$
$308$	−0.0870180	−0.00495831
$309$	−5.08097	−0.289046
$310$	0	0
$311$	15.8598	0.899328	0.449664	−	0.893198i	$-0.351544\pi$
$311$	15.8598	0.899328	0.449664	+	0.893198i	$0.351544\pi$
$312$	−1.15675	−0.0654881
$313$	11.0463	0.624374	0.312187	−	0.950021i	$-0.398938\pi$
$313$	11.0463	0.624374	0.312187	+	0.950021i	$0.398938\pi$
$314$	−17.6405	−0.995511
$315$	0	0
$316$	−9.18776	−0.516852
$317$	−8.31350	−0.466933	−0.233466	−	0.972365i	$-0.575007\pi$
$317$	−8.31350	−0.466933	−0.233466	+	0.972365i	$0.575007\pi$
$318$	6.76010	0.379087
$319$	0.0929484	0.00520411
$320$	0	0
$321$	−3.28829	−0.183534
$322$	−5.36530	−0.298996
$323$	−24.4415	−1.35996
$324$	5.03101	0.279500
$325$	0	0
$326$	−14.9050	−0.825510
$327$	4.90913	0.271475
$328$	3.54975	0.196002
$329$	0.890304	0.0490841
$330$	0	0
$331$	−11.5430	−0.634460	−0.317230	−	0.948349i	$-0.602753\pi$
$331$	−11.5430	−0.634460	−0.317230	+	0.948349i	$0.602753\pi$
$332$	11.9540	0.656061
$333$	3.78082	0.207188
$334$	21.6926	1.18697
$335$	0	0
$336$	−0.638420	−0.0348287
$337$	8.42766	0.459084	0.229542	−	0.973299i	$-0.426277\pi$
$337$	8.42766	0.459084	0.229542	+	0.973299i	$0.426277\pi$
$338$	10.1226	0.550596
$339$	−0.363740	−0.0197556
$340$	0	0
$341$	0.0902393	0.00488673
$342$	13.9935	0.756684
$343$	12.2862	0.663393
$344$	10.9276	0.589174
$345$	0	0
$346$	−6.70202	−0.360303
$347$	−23.6295	−1.26850	−0.634248	−	0.773130i	$-0.718690\pi$
$347$	−23.6295	−1.26850	−0.634248	+	0.773130i	$0.718690\pi$
$348$	0.681929	0.0365552
$349$	19.5908	1.04867	0.524337	−	0.851511i	$-0.324313\pi$
$349$	19.5908	1.04867	0.524337	+	0.851511i	$0.324313\pi$
$350$	0	0
$351$	−6.40259	−0.341745
$352$	−0.0929484	−0.00495416
$353$	−21.3963	−1.13881	−0.569405	−	0.822057i	$-0.692826\pi$
$353$	−21.3963	−1.13881	−0.569405	+	0.822057i	$0.692826\pi$
$354$	1.61419	0.0857932
$355$	0	0
$356$	10.7564	0.570090
$357$	2.82671	0.149605
$358$	0.690568	0.0364977
$359$	−19.3081	−1.01904	−0.509520	−	0.860459i	$-0.670177\pi$
$359$	−19.3081	−1.01904	−0.509520	+	0.860459i	$0.670177\pi$
$360$	0	0
$361$	11.4725	0.603816
$362$	−13.9220	−0.731726
$363$	−7.49533	−0.393403
$364$	−1.58806	−0.0832372
$365$	0	0
$366$	−2.13060	−0.111368
$367$	−3.64049	−0.190032	−0.0950161	−	0.995476i	$-0.530290\pi$
$367$	−3.64049	−0.190032	−0.0950161	+	0.995476i	$0.530290\pi$
$368$	−5.73095	−0.298746
$369$	8.99853	0.468445
$370$	0	0
$371$	9.28070	0.481830
$372$	0.662054	0.0343259
$373$	36.2814	1.87858	0.939290	−	0.343125i	$-0.111485\pi$
$373$	36.2814	1.87858	0.939290	+	0.343125i	$0.111485\pi$
$374$	0.411544	0.0212804
$375$	0	0
$376$	0.950979	0.0490430
$377$	1.69629	0.0873635
$378$	−3.53364	−0.181751
$379$	4.24791	0.218200	0.109100	−	0.994031i	$-0.465203\pi$
$379$	4.24791	0.218200	0.109100	+	0.994031i	$0.465203\pi$
$380$	0	0
$381$	−3.35016	−0.171634
$382$	0.300055	0.0153522
$383$	20.4601	1.04546	0.522731	−	0.852497i	$-0.324913\pi$
$383$	20.4601	1.04546	0.522731	+	0.852497i	$0.324913\pi$
$384$	−0.681929	−0.0347995
$385$	0	0
$386$	−13.9168	−0.708349
$387$	27.7011	1.40812
$388$	5.18266	0.263110
$389$	5.42945	0.275284	0.137642	−	0.990482i	$-0.456048\pi$
$389$	5.42945	0.275284	0.137642	+	0.990482i	$0.456048\pi$
$390$	0	0
$391$	25.3747	1.28325
$392$	6.12353	0.309285
$393$	−9.21981	−0.465078
$394$	−16.1264	−0.812439
$395$	0	0
$396$	−0.235622	−0.0118404
$397$	−35.2671	−1.77000	−0.885002	−	0.465587i	$-0.845843\pi$
$397$	−35.2671	−1.77000	−0.885002	+	0.465587i	$0.845843\pi$
$398$	24.9546	1.25086
$399$	−3.52420	−0.176431
$400$	0	0
$401$	−28.6951	−1.43296	−0.716481	−	0.697606i	$-0.754248\pi$
$401$	−28.6951	−1.43296	−0.716481	+	0.697606i	$0.754248\pi$
$402$	−6.51168	−0.324773
$403$	1.64685	0.0820356
$404$	−2.42538	−0.120667
$405$	0	0
$406$	0.936197	0.0464627
$407$	−0.138629	−0.00687159
$408$	3.01935	0.149480
$409$	24.8020	1.22638	0.613190	−	0.789935i	$-0.289886\pi$
$409$	24.8020	1.22638	0.613190	+	0.789935i	$0.289886\pi$
$410$	0	0
$411$	−14.7207	−0.726120
$412$	−7.45088	−0.367078
$413$	2.21606	0.109045
$414$	−14.5278	−0.714002
$415$	0	0
$416$	−1.69629	−0.0831676
$417$	7.46609	0.365616
$418$	−0.513093	−0.0250962
$419$	13.2174	0.645712	0.322856	−	0.946448i	$-0.395357\pi$
$419$	13.2174	0.645712	0.322856	+	0.946448i	$0.395357\pi$
$420$	0	0
$421$	23.8374	1.16176	0.580882	−	0.813988i	$-0.302708\pi$
$421$	23.8374	1.16176	0.580882	+	0.813988i	$0.302708\pi$
$422$	9.54382	0.464586
$423$	2.41071	0.117213
$424$	9.91319	0.481427
$425$	0	0
$426$	5.21525	0.252680
$427$	−2.92503	−0.141552
$428$	−4.82204	−0.233082
$429$	0.107518	0.00519102
$430$	0	0
$431$	30.3459	1.46171	0.730856	−	0.682531i	$-0.239121\pi$
$431$	30.3459	1.46171	0.730856	+	0.682531i	$0.239121\pi$
$432$	−3.77446	−0.181599
$433$	35.5547	1.70865	0.854326	−	0.519738i	$-0.173970\pi$
$433$	35.5547	1.70865	0.854326	+	0.519738i	$0.173970\pi$
$434$	0.908911	0.0436291
$435$	0	0
$436$	7.19889	0.344764
$437$	−31.6359	−1.51335
$438$	9.24416	0.441703
$439$	−33.9864	−1.62208	−0.811042	−	0.584988i	$-0.801099\pi$
$439$	−33.9864	−1.62208	−0.811042	+	0.584988i	$0.801099\pi$
$440$	0	0
$441$	15.5230	0.739190
$442$	7.51061	0.357243
$443$	19.1827	0.911396	0.455698	−	0.890134i	$-0.349390\pi$
$443$	19.1827	0.911396	0.455698	+	0.890134i	$0.349390\pi$
$444$	−1.01707	−0.0482681
$445$	0	0
$446$	3.18913	0.151010
$447$	−0.628911	−0.0297465
$448$	−0.936197	−0.0442312
$449$	39.5566	1.86679	0.933396	−	0.358847i	$-0.116830\pi$
$449$	39.5566	1.86679	0.933396	+	0.358847i	$0.116830\pi$
$450$	0	0
$451$	−0.329944	−0.0155365
$452$	−0.533399	−0.0250890
$453$	−7.37488	−0.346502
$454$	−15.8847	−0.745505
$455$	0	0
$456$	−3.76438	−0.176283
$457$	−29.4632	−1.37823	−0.689114	−	0.724653i	$-0.742000\pi$
$457$	−29.4632	−1.37823	−0.689114	+	0.724653i	$0.742000\pi$
$458$	4.51924	0.211170
$459$	16.7120	0.780050
$460$	0	0
$461$	−1.20911	−0.0563140	−0.0281570	−	0.999604i	$-0.508964\pi$
$461$	−1.20911	−0.0563140	−0.0281570	+	0.999604i	$0.508964\pi$
$462$	0.0593401	0.00276075
$463$	−11.2059	−0.520780	−0.260390	−	0.965504i	$-0.583851\pi$
$463$	−11.2059	−0.520780	−0.260390	+	0.965504i	$0.583851\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	20.8617	0.966399
$467$	−16.7129	−0.773382	−0.386691	−	0.922209i	$-0.626382\pi$
$467$	−16.7129	−0.773382	−0.386691	+	0.922209i	$0.626382\pi$
$468$	−4.30006	−0.198770
$469$	−8.93967	−0.412796
$470$	0	0
$471$	12.0296	0.554293
$472$	2.36709	0.108954
$473$	−1.01570	−0.0467019
$474$	6.26540	0.287779
$475$	0	0
$476$	4.14516	0.189993
$477$	25.1297	1.15061
$478$	4.27747	0.195647
$479$	−41.5241	−1.89729	−0.948643	−	0.316349i	$-0.897543\pi$
$479$	−41.5241	−1.89729	−0.948643	+	0.316349i	$0.897543\pi$
$480$	0	0
$481$	−2.52996	−0.115356
$482$	−5.18963	−0.236381
$483$	3.65875	0.166479
$484$	−10.9914	−0.499607
$485$	0	0
$486$	−14.7542	−0.669263
$487$	33.5396	1.51983	0.759913	−	0.650025i	$-0.225242\pi$
$487$	33.5396	1.51983	0.759913	+	0.650025i	$0.225242\pi$
$488$	−3.12437	−0.141434
$489$	10.1641	0.459638
$490$	0	0
$491$	−0.0688022	−0.00310500	−0.00155250	−	0.999999i	$-0.500494\pi$
$491$	−0.0688022	−0.00310500	−0.00155250	+	0.999999i	$0.500494\pi$
$492$	−2.42068	−0.109133
$493$	−4.42766	−0.199412
$494$	−9.36386	−0.421300
$495$	0	0
$496$	0.970854	0.0435927
$497$	7.15985	0.321163
$498$	−8.15178	−0.365290
$499$	3.93911	0.176339	0.0881693	−	0.996106i	$-0.471898\pi$
$499$	3.93911	0.176339	0.0881693	+	0.996106i	$0.471898\pi$
$500$	0	0
$501$	−14.7928	−0.660895
$502$	23.8028	1.06237
$503$	5.89332	0.262770	0.131385	−	0.991331i	$-0.458058\pi$
$503$	5.89332	0.262770	0.131385	+	0.991331i	$0.458058\pi$
$504$	−2.37323	−0.105712
$505$	0	0
$506$	0.532682	0.0236806
$507$	−6.90289	−0.306568
$508$	−4.91278	−0.217969
$509$	31.5284	1.39747	0.698736	−	0.715380i	$-0.253746\pi$
$509$	31.5284	1.39747	0.698736	+	0.715380i	$0.253746\pi$
$510$	0	0
$511$	12.6910	0.561416
$512$	−1.00000	−0.0441942
$513$	−20.8357	−0.919920
$514$	7.80817	0.344404
$515$	0	0
$516$	−7.45182	−0.328048
$517$	−0.0883920	−0.00388747
$518$	−1.39630	−0.0613501
$519$	4.57030	0.200614
$520$	0	0
$521$	17.4758	0.765631	0.382815	−	0.923825i	$-0.374955\pi$
$521$	17.4758	0.765631	0.382815	+	0.923825i	$0.374955\pi$
$522$	2.53497	0.110953
$523$	−20.8193	−0.910364	−0.455182	−	0.890398i	$-0.650426\pi$
$523$	−20.8193	−0.910364	−0.455182	+	0.890398i	$0.650426\pi$
$524$	−13.5202	−0.590632
$525$	0	0
$526$	−5.92288	−0.258250
$527$	−4.29861	−0.187251
$528$	0.0633842	0.00275844
$529$	9.84379	0.427991
$530$	0	0
$531$	6.00051	0.260400
$532$	−5.16799	−0.224061
$533$	−6.02142	−0.260817
$534$	−7.33513	−0.317422
$535$	0	0
$536$	−9.54892	−0.412450
$537$	−0.470919	−0.0203216
$538$	−20.9780	−0.904428
$539$	−0.569172	−0.0245160
$540$	0	0
$541$	−31.4903	−1.35387	−0.676937	−	0.736041i	$-0.736693\pi$
$541$	−31.4903	−1.35387	−0.676937	+	0.736041i	$0.736693\pi$
$542$	−30.4270	−1.30695
$543$	9.49385	0.407420
$544$	4.42766	0.189834
$545$	0	0
$546$	1.08295	0.0463459
$547$	−12.2073	−0.521947	−0.260974	−	0.965346i	$-0.584044\pi$
$547$	−12.2073	−0.521947	−0.260974	+	0.965346i	$0.584044\pi$
$548$	−21.5869	−0.922147
$549$	−7.92020	−0.338026
$550$	0	0
$551$	5.52019	0.235168
$552$	3.90810	0.166340
$553$	8.60155	0.365775
$554$	−27.5908	−1.17222
$555$	0	0
$556$	10.9485	0.464319
$557$	3.40642	0.144335	0.0721674	−	0.997393i	$-0.477008\pi$
$557$	3.40642	0.144335	0.0721674	+	0.997393i	$0.477008\pi$
$558$	2.46109	0.104186
$559$	−18.5363	−0.784003
$560$	0	0
$561$	−0.280644	−0.0118488
$562$	1.19274	0.0503128
$563$	−32.5575	−1.37213	−0.686067	−	0.727538i	$-0.740664\pi$
$563$	−32.5575	−1.37213	−0.686067	+	0.727538i	$0.740664\pi$
$564$	−0.648500	−0.0273068
$565$	0	0
$566$	−20.8048	−0.874489
$567$	−4.71001	−0.197802
$568$	7.64780	0.320894
$569$	44.2594	1.85545	0.927724	−	0.373266i	$-0.121762\pi$
$569$	44.2594	1.85545	0.927724	+	0.373266i	$0.121762\pi$
$570$	0	0
$571$	−45.2803	−1.89492	−0.947460	−	0.319874i	$-0.896359\pi$
$571$	−45.2803	−1.89492	−0.947460	+	0.319874i	$0.896359\pi$
$572$	0.157668	0.00659241
$573$	−0.204616	−0.00854797
$574$	−3.32327	−0.138711
$575$	0	0
$576$	−2.53497	−0.105624
$577$	26.6718	1.11036	0.555182	−	0.831729i	$-0.312649\pi$
$577$	26.6718	1.11036	0.555182	+	0.831729i	$0.312649\pi$
$578$	−2.60418	−0.108320
$579$	9.49030	0.394403
$580$	0	0
$581$	−11.1913	−0.464293
$582$	−3.53421	−0.146498
$583$	−0.921415	−0.0381611
$584$	13.5559	0.560947
$585$	0	0
$586$	−19.5620	−0.808100
$587$	−21.7053	−0.895872	−0.447936	−	0.894066i	$-0.647841\pi$
$587$	−21.7053	−0.895872	−0.447936	+	0.894066i	$0.647841\pi$
$588$	−4.17582	−0.172208
$589$	5.35930	0.220826
$590$	0	0
$591$	10.9971	0.452360
$592$	−1.49146	−0.0612988
$593$	2.06422	0.0847674	0.0423837	−	0.999101i	$-0.486505\pi$
$593$	2.06422	0.0847674	0.0423837	+	0.999101i	$0.486505\pi$
$594$	0.350830	0.0143947
$595$	0	0
$596$	−0.922252	−0.0377769
$597$	−17.0173	−0.696471
$598$	9.72137	0.397536
$599$	−26.5670	−1.08550	−0.542749	−	0.839895i	$-0.682617\pi$
$599$	−26.5670	−1.08550	−0.542749	+	0.839895i	$0.682617\pi$
$600$	0	0
$601$	26.7113	1.08958	0.544788	−	0.838574i	$-0.316610\pi$
$601$	26.7113	1.08958	0.544788	+	0.838574i	$0.316610\pi$
$602$	−10.2303	−0.416958
$603$	−24.2062	−0.985755
$604$	−10.8147	−0.440045
$605$	0	0
$606$	1.65394	0.0671867
$607$	−28.8840	−1.17236	−0.586182	−	0.810179i	$-0.699370\pi$
$607$	−28.8840	−1.17236	−0.586182	+	0.810179i	$0.699370\pi$
$608$	−5.52019	−0.223873
$609$	−0.638420	−0.0258701
$610$	0	0
$611$	−1.61314	−0.0652606
$612$	11.2240	0.453703
$613$	−37.0803	−1.49766	−0.748830	−	0.662762i	$-0.769384\pi$
$613$	−37.0803	−1.49766	−0.748830	+	0.662762i	$0.769384\pi$
$614$	−13.9035	−0.561100
$615$	0	0
$616$	0.0870180	0.00350605
$617$	−0.643122	−0.0258911	−0.0129456	−	0.999916i	$-0.504121\pi$
$617$	−0.643122	−0.0258911	−0.0129456	+	0.999916i	$0.504121\pi$
$618$	5.08097	0.204387
$619$	7.82234	0.314407	0.157203	−	0.987566i	$-0.449752\pi$
$619$	7.82234	0.314407	0.157203	+	0.987566i	$0.449752\pi$
$620$	0	0
$621$	21.6312	0.868032
$622$	−15.8598	−0.635921
$623$	−10.0702	−0.403452
$624$	1.15675	0.0463071
$625$	0	0
$626$	−11.0463	−0.441499
$627$	0.349893	0.0139734
$628$	17.6405	0.703932
$629$	6.60370	0.263307
$630$	0	0
$631$	9.69878	0.386102	0.193051	−	0.981189i	$-0.438162\pi$
$631$	9.69878	0.386102	0.193051	+	0.981189i	$0.438162\pi$
$632$	9.18776	0.365469
$633$	−6.50821	−0.258678
$634$	8.31350	0.330171
$635$	0	0
$636$	−6.76010	−0.268055
$637$	−10.3873	−0.411560
$638$	−0.0929484	−0.00367986
$639$	19.3870	0.766936
$640$	0	0
$641$	−23.2181	−0.917061	−0.458531	−	0.888679i	$-0.651624\pi$
$641$	−23.2181	−0.917061	−0.458531	+	0.888679i	$0.651624\pi$
$642$	3.28829	0.129778
$643$	−12.9730	−0.511603	−0.255802	−	0.966729i	$-0.582339\pi$
$643$	−12.9730	−0.511603	−0.255802	+	0.966729i	$0.582339\pi$
$644$	5.36530	0.211422
$645$	0	0
$646$	24.4415	0.961639
$647$	30.9915	1.21840	0.609201	−	0.793016i	$-0.291490\pi$
$647$	30.9915	1.21840	0.609201	+	0.793016i	$0.291490\pi$
$648$	−5.03101	−0.197637
$649$	−0.220017	−0.00863643
$650$	0	0
$651$	−0.619813	−0.0242924
$652$	14.9050	0.583724
$653$	−9.99544	−0.391152	−0.195576	−	0.980689i	$-0.562658\pi$
$653$	−9.99544	−0.391152	−0.195576	+	0.980689i	$0.562658\pi$
$654$	−4.90913	−0.191962
$655$	0	0
$656$	−3.54975	−0.138595
$657$	34.3638	1.34066
$658$	−0.890304	−0.0347077
$659$	−21.1916	−0.825508	−0.412754	−	0.910842i	$-0.635433\pi$
$659$	−21.1916	−0.825508	−0.412754	+	0.910842i	$0.635433\pi$
$660$	0	0
$661$	13.7448	0.534610	0.267305	−	0.963612i	$-0.413867\pi$
$661$	13.7448	0.534610	0.267305	+	0.963612i	$0.413867\pi$
$662$	11.5430	0.448631
$663$	−5.12170	−0.198910
$664$	−11.9540	−0.463905
$665$	0	0
$666$	−3.78082	−0.146504
$667$	−5.73095	−0.221903
$668$	−21.6926	−0.839313
$669$	−2.17476	−0.0840811
$670$	0	0
$671$	0.290405	0.0112110
$672$	0.638420	0.0246276
$673$	−11.3365	−0.436990	−0.218495	−	0.975838i	$-0.570115\pi$
$673$	−11.3365	−0.436990	−0.218495	+	0.975838i	$0.570115\pi$
$674$	−8.42766	−0.324621
$675$	0	0
$676$	−10.1226	−0.389330
$677$	8.60116	0.330569	0.165285	−	0.986246i	$-0.447146\pi$
$677$	8.60116	0.330569	0.165285	+	0.986246i	$0.447146\pi$
$678$	0.363740	0.0139694
$679$	−4.85199	−0.186202
$680$	0	0
$681$	10.8322	0.415092
$682$	−0.0902393	−0.00345544
$683$	−7.96397	−0.304733	−0.152366	−	0.988324i	$-0.548689\pi$
$683$	−7.96397	−0.304733	−0.152366	+	0.988324i	$0.548689\pi$
$684$	−13.9935	−0.535056
$685$	0	0
$686$	−12.2862	−0.469090
$687$	−3.08180	−0.117578
$688$	−10.9276	−0.416609
$689$	−16.8157	−0.640626
$690$	0	0
$691$	−41.5199	−1.57949	−0.789745	−	0.613435i	$-0.789787\pi$
$691$	−41.5199	−1.57949	−0.789745	+	0.613435i	$0.789787\pi$
$692$	6.70202	0.254772
$693$	0.220588	0.00837945
$694$	23.6295	0.896962
$695$	0	0
$696$	−0.681929	−0.0258485
$697$	15.7171	0.595328
$698$	−19.5908	−0.741524
$699$	−14.2262	−0.538084
$700$	0	0
$701$	−10.5786	−0.399549	−0.199774	−	0.979842i	$-0.564021\pi$
$701$	−10.5786	−0.399549	−0.199774	+	0.979842i	$0.564021\pi$
$702$	6.40259	0.241650
$703$	−8.23316	−0.310520
$704$	0.0929484	0.00350312
$705$	0	0
$706$	21.3963	0.805261
$707$	2.27064	0.0853961
$708$	−1.61419	−0.0606649
$709$	−37.1287	−1.39440	−0.697199	−	0.716877i	$-0.745571\pi$
$709$	−37.1287	−1.39440	−0.697199	+	0.716877i	$0.745571\pi$
$710$	0	0
$711$	23.2907	0.873470
$712$	−10.7564	−0.403115
$713$	−5.56392	−0.208370
$714$	−2.82671	−0.105787
$715$	0	0
$716$	−0.690568	−0.0258078
$717$	−2.91693	−0.108935
$718$	19.3081	0.720570
$719$	14.3710	0.535946	0.267973	−	0.963426i	$-0.413646\pi$
$719$	14.3710	0.535946	0.267973	+	0.963426i	$0.413646\pi$
$720$	0	0
$721$	6.97549	0.259781
$722$	−11.4725	−0.426962
$723$	3.53896	0.131615
$724$	13.9220	0.517409
$725$	0	0
$726$	7.49533	0.278178
$727$	−22.6111	−0.838601	−0.419300	−	0.907848i	$-0.637725\pi$
$727$	−22.6111	−0.838601	−0.419300	+	0.907848i	$0.637725\pi$
$728$	1.58806	0.0588576
$729$	−5.03172	−0.186360
$730$	0	0
$731$	48.3835	1.78953
$732$	2.13060	0.0787492
$733$	−12.5893	−0.464996	−0.232498	−	0.972597i	$-0.574690\pi$
$733$	−12.5893	−0.464996	−0.232498	+	0.972597i	$0.574690\pi$
$734$	3.64049	0.134373
$735$	0	0
$736$	5.73095	0.211246
$737$	0.887556	0.0326936
$738$	−8.99853	−0.331241
$739$	−48.8490	−1.79694	−0.898469	−	0.439037i	$-0.855320\pi$
$739$	−48.8490	−1.79694	−0.898469	+	0.439037i	$0.855320\pi$
$740$	0	0
$741$	6.38549	0.234577
$742$	−9.28070	−0.340705
$743$	3.19440	0.117191	0.0585956	−	0.998282i	$-0.481338\pi$
$743$	3.19440	0.117191	0.0585956	+	0.998282i	$0.481338\pi$
$744$	−0.662054	−0.0242721
$745$	0	0
$746$	−36.2814	−1.32836
$747$	−30.3030	−1.10873
$748$	−0.411544	−0.0150475
$749$	4.51438	0.164952
$750$	0	0
$751$	−20.0102	−0.730182	−0.365091	−	0.930972i	$-0.618962\pi$
$751$	−20.0102	−0.730182	−0.365091	+	0.930972i	$0.618962\pi$
$752$	−0.950979	−0.0346786
$753$	−16.2318	−0.591519
$754$	−1.69629	−0.0617753
$755$	0	0
$756$	3.53364	0.128517
$757$	39.0441	1.41908	0.709541	−	0.704664i	$-0.248902\pi$
$757$	39.0441	1.41908	0.709541	+	0.704664i	$0.248902\pi$
$758$	−4.24791	−0.154291
$759$	−0.363252	−0.0131852
$760$	0	0
$761$	12.1423	0.440159	0.220079	−	0.975482i	$-0.429368\pi$
$761$	12.1423	0.440159	0.220079	+	0.975482i	$0.429368\pi$
$762$	3.35016	0.121364
$763$	−6.73958	−0.243989
$764$	−0.300055	−0.0108556
$765$	0	0
$766$	−20.4601	−0.739254
$767$	−4.01528	−0.144983
$768$	0.681929	0.0246070
$769$	−13.7367	−0.495358	−0.247679	−	0.968842i	$-0.579668\pi$
$769$	−13.7367	−0.495358	−0.247679	+	0.968842i	$0.579668\pi$
$770$	0	0
$771$	−5.32462	−0.191762
$772$	13.9168	0.500878
$773$	40.0976	1.44221	0.721105	−	0.692825i	$-0.243634\pi$
$773$	40.0976	1.44221	0.721105	+	0.692825i	$0.243634\pi$
$774$	−27.7011	−0.995694
$775$	0	0
$776$	−5.18266	−0.186047
$777$	0.952180	0.0341593
$778$	−5.42945	−0.194655
$779$	−19.5953	−0.702075
$780$	0	0
$781$	−0.710850	−0.0254362
$782$	−25.3747	−0.907398
$783$	−3.77446	−0.134888
$784$	−6.12353	−0.218698
$785$	0	0
$786$	9.21981	0.328860
$787$	−47.0637	−1.67764	−0.838820	−	0.544409i	$-0.816754\pi$
$787$	−47.0637	−1.67764	−0.838820	+	0.544409i	$0.816754\pi$
$788$	16.1264	0.574481
$789$	4.03899	0.143792
$790$	0	0
$791$	0.499366	0.0177554
$792$	0.235622	0.00837245
$793$	5.29985	0.188203
$794$	35.2671	1.25158
$795$	0	0
$796$	−24.9546	−0.884493
$797$	7.86965	0.278757	0.139379	−	0.990239i	$-0.455490\pi$
$797$	7.86965	0.278757	0.139379	+	0.990239i	$0.455490\pi$
$798$	3.52420	0.124755
$799$	4.21061	0.148961
$800$	0	0
$801$	−27.2673	−0.963442
$802$	28.6951	1.01326
$803$	−1.26000	−0.0444644
$804$	6.51168	0.229649
$805$	0	0
$806$	−1.64685	−0.0580079
$807$	14.3055	0.503579
$808$	2.42538	0.0853247
$809$	−42.7737	−1.50384	−0.751922	−	0.659252i	$-0.770873\pi$
$809$	−42.7737	−1.50384	−0.751922	+	0.659252i	$0.770873\pi$
$810$	0	0
$811$	−26.2522	−0.921838	−0.460919	−	0.887442i	$-0.652480\pi$
$811$	−26.2522	−0.921838	−0.460919	+	0.887442i	$0.652480\pi$
$812$	−0.936197	−0.0328541
$813$	20.7491	0.727702
$814$	0.138629	0.00485895
$815$	0	0
$816$	−3.01935	−0.105698
$817$	−60.3222	−2.11041
$818$	−24.8020	−0.867182
$819$	4.02570	0.140669
$820$	0	0
$821$	−26.2393	−0.915757	−0.457878	−	0.889015i	$-0.651390\pi$
$821$	−26.2393	−0.915757	−0.457878	+	0.889015i	$0.651390\pi$
$822$	14.7207	0.513445
$823$	−1.93896	−0.0675879	−0.0337940	−	0.999429i	$-0.510759\pi$
$823$	−1.93896	−0.0675879	−0.0337940	+	0.999429i	$0.510759\pi$
$824$	7.45088	0.259564
$825$	0	0
$826$	−2.21606	−0.0771067
$827$	44.3474	1.54211	0.771056	−	0.636768i	$-0.219729\pi$
$827$	44.3474	1.54211	0.771056	+	0.636768i	$0.219729\pi$
$828$	14.5278	0.504876
$829$	26.3298	0.914473	0.457236	−	0.889345i	$-0.348839\pi$
$829$	26.3298	0.914473	0.457236	+	0.889345i	$0.348839\pi$
$830$	0	0
$831$	18.8149	0.652683
$832$	1.69629	0.0588084
$833$	27.1129	0.939408
$834$	−7.46609	−0.258529
$835$	0	0
$836$	0.513093	0.0177457
$837$	−3.66445	−0.126662
$838$	−13.2174	−0.456587
$839$	37.1337	1.28200	0.640999	−	0.767541i	$-0.278520\pi$
$839$	37.1337	1.28200	0.640999	+	0.767541i	$0.278520\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−23.8374	−0.821491
$843$	−0.813366	−0.0280138
$844$	−9.54382	−0.328512
$845$	0	0
$846$	−2.41071	−0.0828818
$847$	10.2901	0.353571
$848$	−9.91319	−0.340420
$849$	14.1874	0.486909
$850$	0	0
$851$	8.54750	0.293005
$852$	−5.21525	−0.178672
$853$	15.8793	0.543696	0.271848	−	0.962340i	$-0.412365\pi$
$853$	15.8793	0.543696	0.271848	+	0.962340i	$0.412365\pi$
$854$	2.92503	0.100092
$855$	0	0
$856$	4.82204	0.164814
$857$	−28.4262	−0.971020	−0.485510	−	0.874231i	$-0.661366\pi$
$857$	−28.4262	−0.971020	−0.485510	+	0.874231i	$0.661366\pi$
$858$	−0.107518	−0.00367061
$859$	−33.9381	−1.15795	−0.578976	−	0.815344i	$-0.696548\pi$
$859$	−33.9381	−1.15795	−0.578976	+	0.815344i	$0.696548\pi$
$860$	0	0
$861$	2.26623	0.0772331
$862$	−30.3459	−1.03359
$863$	−56.0515	−1.90802	−0.954008	−	0.299781i	$-0.903087\pi$
$863$	−56.0515	−1.90802	−0.954008	+	0.299781i	$0.903087\pi$
$864$	3.77446	0.128410
$865$	0	0
$866$	−35.5547	−1.20820
$867$	1.77587	0.0603116
$868$	−0.908911	−0.0308505
$869$	−0.853987	−0.0289695
$870$	0	0
$871$	16.1978	0.548840
$872$	−7.19889	−0.243785
$873$	−13.1379	−0.444651
$874$	31.6359	1.07010
$875$	0	0
$876$	−9.24416	−0.312331
$877$	6.06036	0.204644	0.102322	−	0.994751i	$-0.467373\pi$
$877$	6.06036	0.204644	0.102322	+	0.994751i	$0.467373\pi$
$878$	33.9864	1.14699
$879$	13.3399	0.449944
$880$	0	0
$881$	29.6282	0.998200	0.499100	−	0.866544i	$-0.333664\pi$
$881$	29.6282	0.998200	0.499100	+	0.866544i	$0.333664\pi$
$882$	−15.5230	−0.522686
$883$	33.1967	1.11716	0.558579	−	0.829451i	$-0.311347\pi$
$883$	33.1967	1.11716	0.558579	+	0.829451i	$0.311347\pi$
$884$	−7.51061	−0.252609
$885$	0	0
$886$	−19.1827	−0.644454
$887$	−44.8762	−1.50680	−0.753398	−	0.657564i	$-0.771587\pi$
$887$	−44.8762	−1.50680	−0.753398	+	0.657564i	$0.771587\pi$
$888$	1.01707	0.0341307
$889$	4.59933	0.154256
$890$	0	0
$891$	0.467624	0.0156660
$892$	−3.18913	−0.106780
$893$	−5.24959	−0.175671
$894$	0.628911	0.0210339
$895$	0	0
$896$	0.936197	0.0312762
$897$	−6.62928	−0.221345
$898$	−39.5566	−1.32002
$899$	0.970854	0.0323798
$900$	0	0
$901$	43.8923	1.46226
$902$	0.329944	0.0109859
$903$	6.97637	0.232159
$904$	0.533399	0.0177406
$905$	0	0
$906$	7.37488	0.245014
$907$	47.3600	1.57256	0.786282	−	0.617868i	$-0.212003\pi$
$907$	47.3600	1.57256	0.786282	+	0.617868i	$0.212003\pi$
$908$	15.8847	0.527152
$909$	6.14828	0.203926
$910$	0	0
$911$	58.1573	1.92684	0.963419	−	0.267999i	$-0.0863623\pi$
$911$	58.1573	1.92684	0.963419	+	0.267999i	$0.0863623\pi$
$912$	3.76438	0.124651
$913$	1.11110	0.0367722
$914$	29.4632	0.974555
$915$	0	0
$916$	−4.51924	−0.149320
$917$	12.6576	0.417990
$918$	−16.7120	−0.551579
$919$	41.6474	1.37382	0.686910	−	0.726742i	$-0.258967\pi$
$919$	41.6474	1.37382	0.686910	+	0.726742i	$0.258967\pi$
$920$	0	0
$921$	9.48120	0.312416
$922$	1.20911	0.0398200
$923$	−12.9729	−0.427008
$924$	−0.0593401	−0.00195215
$925$	0	0
$926$	11.2059	0.368247
$927$	18.8878	0.620356
$928$	−1.00000	−0.0328266
$929$	8.98368	0.294745	0.147372	−	0.989081i	$-0.452918\pi$
$929$	8.98368	0.294745	0.147372	+	0.989081i	$0.452918\pi$
$930$	0	0
$931$	−33.8031	−1.10785
$932$	−20.8617	−0.683347
$933$	10.8153	0.354076
$934$	16.7129	0.546864
$935$	0	0
$936$	4.30006	0.140552
$937$	28.1272	0.918875	0.459438	−	0.888210i	$-0.348051\pi$
$937$	28.1272	0.918875	0.459438	+	0.888210i	$0.348051\pi$
$938$	8.93967	0.291891
$939$	7.53280	0.245824
$940$	0	0
$941$	10.2487	0.334097	0.167049	−	0.985949i	$-0.446576\pi$
$941$	10.2487	0.334097	0.167049	+	0.985949i	$0.446576\pi$
$942$	−12.0296	−0.391944
$943$	20.3435	0.662474
$944$	−2.36709	−0.0770423
$945$	0	0
$946$	1.01570	0.0330232
$947$	5.85491	0.190259	0.0951295	−	0.995465i	$-0.469673\pi$
$947$	5.85491	0.190259	0.0951295	+	0.995465i	$0.469673\pi$
$948$	−6.26540	−0.203491
$949$	−22.9948	−0.746442
$950$	0	0
$951$	−5.66922	−0.183837
$952$	−4.14516	−0.134346
$953$	−47.6766	−1.54440	−0.772199	−	0.635381i	$-0.780843\pi$
$953$	−47.6766	−1.54440	−0.772199	+	0.635381i	$0.780843\pi$
$954$	−25.1297	−0.813603
$955$	0	0
$956$	−4.27747	−0.138343
$957$	0.0633842	0.00204892
$958$	41.5241	1.34158
$959$	20.2096	0.652602
$960$	0	0
$961$	−30.0574	−0.969595
$962$	2.52996	0.0815691
$963$	12.2237	0.393904
$964$	5.18963	0.167147
$965$	0	0
$966$	−3.65875	−0.117718
$967$	6.75969	0.217377	0.108688	−	0.994076i	$-0.465335\pi$
$967$	6.75969	0.217377	0.108688	+	0.994076i	$0.465335\pi$
$968$	10.9914	0.353276
$969$	−16.6674	−0.535434
$970$	0	0
$971$	15.1374	0.485781	0.242891	−	0.970054i	$-0.421904\pi$
$971$	15.1374	0.485781	0.242891	+	0.970054i	$0.421904\pi$
$972$	14.7542	0.473240
$973$	−10.2499	−0.328598
$974$	−33.5396	−1.07468
$975$	0	0
$976$	3.12437	0.100009
$977$	−38.7459	−1.23959	−0.619796	−	0.784763i	$-0.712785\pi$
$977$	−38.7459	−1.23959	−0.619796	+	0.784763i	$0.712785\pi$
$978$	−10.1641	−0.325013
$979$	0.999794	0.0319535
$980$	0	0
$981$	−18.2490	−0.582645
$982$	0.0688022	0.00219557
$983$	−23.0659	−0.735687	−0.367843	−	0.929888i	$-0.619904\pi$
$983$	−23.0659	−0.735687	−0.367843	+	0.929888i	$0.619904\pi$
$984$	2.42068	0.0771685
$985$	0	0
$986$	4.42766	0.141005
$987$	0.607124	0.0193250
$988$	9.36386	0.297904
$989$	62.6253	1.99137
$990$	0	0
$991$	21.3315	0.677619	0.338809	−	0.940855i	$-0.389976\pi$
$991$	21.3315	0.677619	0.338809	+	0.940855i	$0.389976\pi$
$992$	−0.970854	−0.0308247
$993$	−7.87150	−0.249794
$994$	−7.15985	−0.227097
$995$	0	0
$996$	8.15178	0.258299
$997$	−6.77148	−0.214455	−0.107227	−	0.994235i	$-0.534197\pi$
$997$	−6.77148	−0.214455	−0.107227	+	0.994235i	$0.534197\pi$
$998$	−3.93911	−0.124690
$999$	5.62947	0.178109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.t.1.4		5
5.2	odd	4		290.2.b.b.59.2	✓	10
5.3	odd	4		290.2.b.b.59.9	yes	10
5.4	even	2		1450.2.a.u.1.2		5
15.2	even	4		2610.2.e.i.2089.6		10
15.8	even	4		2610.2.e.i.2089.1		10
20.3	even	4		2320.2.d.h.929.5		10
20.7	even	4		2320.2.d.h.929.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.b.b.59.2	✓	10	5.2	odd	4
290.2.b.b.59.9	yes	10	5.3	odd	4
1450.2.a.t.1.4		5	1.1	even	1	trivial
1450.2.a.u.1.2		5	5.4	even	2
2320.2.d.h.929.5		10	20.3	even	4
2320.2.d.h.929.6		10	20.7	even	4
2610.2.e.i.2089.1		10	15.8	even	4
2610.2.e.i.2089.6		10	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.681929 q^{3} +1.00000 q^{4} -0.681929 q^{6} -0.936197 q^{7} -1.00000 q^{8} -2.53497 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.681929 q^{3} +1.00000 q^{4} -0.681929 q^{6} -0.936197 q^{7} -1.00000 q^{8} -2.53497 q^{9} +0.0929484 q^{11} +0.681929 q^{12} +1.69629 q^{13} +0.936197 q^{14} +1.00000 q^{16} -4.42766 q^{17} +2.53497 q^{18} +5.52019 q^{19} -0.638420 q^{21} -0.0929484 q^{22} -5.73095 q^{23} -0.681929 q^{24} -1.69629 q^{26} -3.77446 q^{27} -0.936197 q^{28} +1.00000 q^{29} +0.970854 q^{31} -1.00000 q^{32} +0.0633842 q^{33} +4.42766 q^{34} -2.53497 q^{36} -1.49146 q^{37} -5.52019 q^{38} +1.15675 q^{39} -3.54975 q^{41} +0.638420 q^{42} -10.9276 q^{43} +0.0929484 q^{44} +5.73095 q^{46} -0.950979 q^{47} +0.681929 q^{48} -6.12353 q^{49} -3.01935 q^{51} +1.69629 q^{52} -9.91319 q^{53} +3.77446 q^{54} +0.936197 q^{56} +3.76438 q^{57} -1.00000 q^{58} -2.36709 q^{59} +3.12437 q^{61} -0.970854 q^{62} +2.37323 q^{63} +1.00000 q^{64} -0.0633842 q^{66} +9.54892 q^{67} -4.42766 q^{68} -3.90810 q^{69} -7.64780 q^{71} +2.53497 q^{72} -13.5559 q^{73} +1.49146 q^{74} +5.52019 q^{76} -0.0870180 q^{77} -1.15675 q^{78} -9.18776 q^{79} +5.03101 q^{81} +3.54975 q^{82} +11.9540 q^{83} -0.638420 q^{84} +10.9276 q^{86} +0.681929 q^{87} -0.0929484 q^{88} +10.7564 q^{89} -1.58806 q^{91} -5.73095 q^{92} +0.662054 q^{93} +0.950979 q^{94} -0.681929 q^{96} +5.18266 q^{97} +6.12353 q^{98} -0.235622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9} - 3 q^{12} - 7 q^{13} + 5 q^{14} + 5 q^{16} - 9 q^{17} - 10 q^{18} - 4 q^{19} - 6 q^{21} - 13 q^{23} + 3 q^{24} + 7 q^{26} + 6 q^{27} - 5 q^{28} + 5 q^{29} + 5 q^{31} - 5 q^{32} - 18 q^{33} + 9 q^{34} + 10 q^{36} + 6 q^{37} + 4 q^{38} + 5 q^{39} - 4 q^{41} + 6 q^{42} - q^{43} + 13 q^{46} - 14 q^{47} - 3 q^{48} + 16 q^{49} - 32 q^{51} - 7 q^{52} - 5 q^{53} - 6 q^{54} + 5 q^{56} - 14 q^{57} - 5 q^{58} - 9 q^{59} + 5 q^{61} - 5 q^{62} - 36 q^{63} + 5 q^{64} + 18 q^{66} - 2 q^{67} - 9 q^{68} + 7 q^{69} - 6 q^{71} - 10 q^{72} - 9 q^{73} - 6 q^{74} - 4 q^{76} + 18 q^{77} - 5 q^{78} - 17 q^{79} - 3 q^{81} + 4 q^{82} - 30 q^{83} - 6 q^{84} + q^{86} - 3 q^{87} + 10 q^{89} - 22 q^{91} - 13 q^{92} + 6 q^{93} + 14 q^{94} + 3 q^{96} + 15 q^{97} - 16 q^{98} - 34 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9 - 3 * q^12 - 7 * q^13 + 5 * q^14 + 5 * q^16 - 9 * q^17 - 10 * q^18 - 4 * q^19 - 6 * q^21 - 13 * q^23 + 3 * q^24 + 7 * q^26 + 6 * q^27 - 5 * q^28 + 5 * q^29 + 5 * q^31 - 5 * q^32 - 18 * q^33 + 9 * q^34 + 10 * q^36 + 6 * q^37 + 4 * q^38 + 5 * q^39 - 4 * q^41 + 6 * q^42 - q^43 + 13 * q^46 - 14 * q^47 - 3 * q^48 + 16 * q^49 - 32 * q^51 - 7 * q^52 - 5 * q^53 - 6 * q^54 + 5 * q^56 - 14 * q^57 - 5 * q^58 - 9 * q^59 + 5 * q^61 - 5 * q^62 - 36 * q^63 + 5 * q^64 + 18 * q^66 - 2 * q^67 - 9 * q^68 + 7 * q^69 - 6 * q^71 - 10 * q^72 - 9 * q^73 - 6 * q^74 - 4 * q^76 + 18 * q^77 - 5 * q^78 - 17 * q^79 - 3 * q^81 + 4 * q^82 - 30 * q^83 - 6 * q^84 + q^86 - 3 * q^87 + 10 * q^89 - 22 * q^91 - 13 * q^92 + 6 * q^93 + 14 * q^94 + 3 * q^96 + 15 * q^97 - 16 * q^98 - 34 * q^99

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