LMFDB - Embedded newform 8025.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1605)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.396339$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52310 q^{2} -1.00000 q^{3} +0.319820 q^{4} +1.52310 q^{6} +4.23925 q^{7} +2.55907 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.52310 q^{2} -1.00000 q^{3} +0.319820 q^{4} +1.52310 q^{6} +4.23925 q^{7} +2.55907 q^{8} +1.00000 q^{9} -0.603661 q^{11} -0.319820 q^{12} +3.73042 q^{13} -6.45679 q^{14} -4.53736 q^{16} +4.59961 q^{17} -1.52310 q^{18} -0.665920 q^{19} -4.23925 q^{21} +0.919434 q^{22} +2.15708 q^{23} -2.55907 q^{24} -5.68178 q^{26} -1.00000 q^{27} +1.35580 q^{28} +2.38773 q^{29} -2.61792 q^{31} +1.79268 q^{32} +0.603661 q^{33} -7.00565 q^{34} +0.319820 q^{36} -3.40655 q^{37} +1.01426 q^{38} -3.73042 q^{39} +2.23360 q^{41} +6.45679 q^{42} +0.243302 q^{43} -0.193063 q^{44} -3.28545 q^{46} +11.8228 q^{47} +4.53736 q^{48} +10.9713 q^{49} -4.59961 q^{51} +1.19306 q^{52} -3.72296 q^{53} +1.52310 q^{54} +10.8486 q^{56} +0.665920 q^{57} -3.63674 q^{58} +2.94795 q^{59} +9.98958 q^{61} +3.98734 q^{62} +4.23925 q^{63} +6.34429 q^{64} -0.919434 q^{66} +6.11089 q^{67} +1.47105 q^{68} -2.15708 q^{69} -7.63720 q^{71} +2.55907 q^{72} +6.34429 q^{73} +5.18850 q^{74} -0.212975 q^{76} -2.55907 q^{77} +5.68178 q^{78} +15.4235 q^{79} +1.00000 q^{81} -3.40199 q^{82} -3.38027 q^{83} -1.35580 q^{84} -0.370572 q^{86} -2.38773 q^{87} -1.54481 q^{88} -13.3642 q^{89} +15.8142 q^{91} +0.689879 q^{92} +2.61792 q^{93} -18.0073 q^{94} -1.79268 q^{96} +17.4407 q^{97} -16.7103 q^{98} -0.603661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9	$ 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9} - 4 q^{11} - 3 q^{12} + 9 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{18} - 7 q^{19} - 8 q^{21} - 7 q^{22} + 16 q^{23} - 3 q^{24} + 6 q^{26} - 4 q^{27} + 9 q^{28} + q^{29} - 6 q^{31} + 4 q^{32} + 4 q^{33} - 15 q^{34} + 3 q^{36} + 8 q^{37} - 2 q^{38} - 9 q^{39} + 13 q^{41} + 6 q^{43} - 10 q^{44} + 14 q^{46} + 5 q^{47} + 3 q^{48} + 2 q^{49} - 6 q^{51} + 14 q^{52} + 5 q^{53} - 3 q^{54} + 23 q^{56} + 7 q^{57} + 3 q^{58} - 11 q^{59} + 6 q^{61} - 5 q^{62} + 8 q^{63} + q^{64} + 7 q^{66} + 50 q^{67} - 26 q^{68} - 16 q^{69} + 7 q^{71} + 3 q^{72} + q^{73} + 37 q^{74} + 9 q^{76} - 3 q^{77} - 6 q^{78} + q^{79} + 4 q^{81} + q^{82} + 9 q^{83} - 9 q^{84} + 22 q^{86} - q^{87} - 5 q^{88} - 10 q^{89} + 14 q^{91} + 2 q^{92} + 6 q^{93} - 32 q^{94} - 4 q^{96} + 23 q^{97} - 26 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9 - 4 * q^11 - 3 * q^12 + 9 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^18 - 7 * q^19 - 8 * q^21 - 7 * q^22 + 16 * q^23 - 3 * q^24 + 6 * q^26 - 4 * q^27 + 9 * q^28 + q^29 - 6 * q^31 + 4 * q^32 + 4 * q^33 - 15 * q^34 + 3 * q^36 + 8 * q^37 - 2 * q^38 - 9 * q^39 + 13 * q^41 + 6 * q^43 - 10 * q^44 + 14 * q^46 + 5 * q^47 + 3 * q^48 + 2 * q^49 - 6 * q^51 + 14 * q^52 + 5 * q^53 - 3 * q^54 + 23 * q^56 + 7 * q^57 + 3 * q^58 - 11 * q^59 + 6 * q^61 - 5 * q^62 + 8 * q^63 + q^64 + 7 * q^66 + 50 * q^67 - 26 * q^68 - 16 * q^69 + 7 * q^71 + 3 * q^72 + q^73 + 37 * q^74 + 9 * q^76 - 3 * q^77 - 6 * q^78 + q^79 + 4 * q^81 + q^82 + 9 * q^83 - 9 * q^84 + 22 * q^86 - q^87 - 5 * q^88 - 10 * q^89 + 14 * q^91 + 2 * q^92 + 6 * q^93 - 32 * q^94 - 4 * q^96 + 23 * q^97 - 26 * q^98 - 4 * 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 $

$2$	−1.52310	−1.07699	−0.538496	−	0.842628i	$-0.681007\pi$
$2$	−1.52310	−1.07699	−0.538496	+	0.842628i	$0.681007\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.319820	0.159910
$5$	0	0
$5$	0	0
$6$	1.52310	0.621801
$7$	4.23925	1.60229	0.801144	−	0.598472i	$-0.204225\pi$
$7$	4.23925	1.60229	0.801144	+	0.598472i	$0.204225\pi$
$8$	2.55907	0.904769
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.603661	−0.182011	−0.0910054	−	0.995850i	$-0.529008\pi$
$11$	−0.603661	−0.182011	−0.0910054	+	0.995850i	$0.529008\pi$
$12$	−0.319820	−0.0923241
$13$	3.73042	1.03463	0.517316	−	0.855794i	$-0.326931\pi$
$13$	3.73042	1.03463	0.517316	+	0.855794i	$0.326931\pi$
$14$	−6.45679	−1.72565
$15$	0	0
$16$	−4.53736	−1.13434
$17$	4.59961	1.11557	0.557785	−	0.829985i	$-0.311651\pi$
$17$	4.59961	1.11557	0.557785	+	0.829985i	$0.311651\pi$
$18$	−1.52310	−0.358997
$19$	−0.665920	−0.152773	−0.0763863	−	0.997078i	$-0.524338\pi$
$19$	−0.665920	−0.152773	−0.0763863	+	0.997078i	$0.524338\pi$
$20$	0	0
$21$	−4.23925	−0.925081
$22$	0.919434	0.196024
$23$	2.15708	0.449783	0.224892	−	0.974384i	$-0.427797\pi$
$23$	2.15708	0.449783	0.224892	+	0.974384i	$0.427797\pi$
$24$	−2.55907	−0.522369
$25$	0	0
$26$	−5.68178	−1.11429
$27$	−1.00000	−0.192450
$28$	1.35580	0.256222
$29$	2.38773	0.443390	0.221695	−	0.975116i	$-0.428841\pi$
$29$	2.38773	0.443390	0.221695	+	0.975116i	$0.428841\pi$
$30$	0	0
$31$	−2.61792	−0.470193	−0.235096	−	0.971972i	$-0.575541\pi$
$31$	−2.61792	−0.470193	−0.235096	+	0.971972i	$0.575541\pi$
$32$	1.79268	0.316904
$33$	0.603661	0.105084
$34$	−7.00565	−1.20146
$35$	0	0
$36$	0.319820	0.0533034
$37$	−3.40655	−0.560034	−0.280017	−	0.959995i	$-0.590340\pi$
$37$	−3.40655	−0.560034	−0.280017	+	0.959995i	$0.590340\pi$
$38$	1.01426	0.164535
$39$	−3.73042	−0.597345
$40$	0	0
$41$	2.23360	0.348830	0.174415	−	0.984672i	$-0.444197\pi$
$41$	2.23360	0.348830	0.174415	+	0.984672i	$0.444197\pi$
$42$	6.45679	0.996304
$43$	0.243302	0.0371032	0.0185516	−	0.999828i	$-0.494095\pi$
$43$	0.243302	0.0371032	0.0185516	+	0.999828i	$0.494095\pi$
$44$	−0.193063	−0.0291054
$45$	0	0
$46$	−3.28545	−0.484413
$47$	11.8228	1.72453	0.862266	−	0.506455i	$-0.169044\pi$
$47$	11.8228	1.72453	0.862266	+	0.506455i	$0.169044\pi$
$48$	4.53736	0.654911
$49$	10.9713	1.56733
$50$	0	0
$51$	−4.59961	−0.644075
$52$	1.19306	0.165448
$53$	−3.72296	−0.511388	−0.255694	−	0.966758i	$-0.582304\pi$
$53$	−3.72296	−0.511388	−0.255694	+	0.966758i	$0.582304\pi$
$54$	1.52310	0.207267
$55$	0	0
$56$	10.8486	1.44970
$57$	0.665920	0.0882033
$58$	−3.63674	−0.477528
$59$	2.94795	0.383791	0.191895	−	0.981415i	$-0.438537\pi$
$59$	2.94795	0.383791	0.191895	+	0.981415i	$0.438537\pi$
$60$	0	0
$61$	9.98958	1.27904	0.639518	−	0.768776i	$-0.279134\pi$
$61$	9.98958	1.27904	0.639518	+	0.768776i	$0.279134\pi$
$62$	3.98734	0.506393
$63$	4.23925	0.534096
$64$	6.34429	0.793037
$65$	0	0
$66$	−0.919434	−0.113175
$67$	6.11089	0.746564	0.373282	−	0.927718i	$-0.378232\pi$
$67$	6.11089	0.746564	0.373282	+	0.927718i	$0.378232\pi$
$68$	1.47105	0.178391
$69$	−2.15708	−0.259682
$70$	0	0
$71$	−7.63720	−0.906369	−0.453184	−	0.891417i	$-0.649712\pi$
$71$	−7.63720	−0.906369	−0.453184	+	0.891417i	$0.649712\pi$
$72$	2.55907	0.301590
$73$	6.34429	0.742543	0.371272	−	0.928524i	$-0.378922\pi$
$73$	6.34429	0.742543	0.371272	+	0.928524i	$0.378922\pi$
$74$	5.18850	0.603151
$75$	0	0
$76$	−0.212975	−0.0244299
$77$	−2.55907	−0.291634
$78$	5.68178	0.643335
$79$	15.4235	1.73528	0.867640	−	0.497193i	$-0.165636\pi$
$79$	15.4235	1.73528	0.867640	+	0.497193i	$0.165636\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.40199	−0.375687
$83$	−3.38027	−0.371033	−0.185516	−	0.982641i	$-0.559396\pi$
$83$	−3.38027	−0.371033	−0.185516	+	0.982641i	$0.559396\pi$
$84$	−1.35580	−0.147930
$85$	0	0
$86$	−0.370572	−0.0399598
$87$	−2.38773	−0.255992
$88$	−1.54481	−0.164678
$89$	−13.3642	−1.41660	−0.708301	−	0.705910i	$-0.750538\pi$
$89$	−13.3642	−1.41660	−0.708301	+	0.705910i	$0.750538\pi$
$90$	0	0
$91$	15.8142	1.65778
$92$	0.689879	0.0719249
$93$	2.61792	0.271466
$94$	−18.0073	−1.85731
$95$	0	0
$96$	−1.79268	−0.182964
$97$	17.4407	1.77084	0.885419	−	0.464795i	$-0.153872\pi$
$97$	17.4407	1.77084	0.885419	+	0.464795i	$0.153872\pi$
$98$	−16.7103	−1.68800
$99$	−0.603661	−0.0606703
$100$	0	0
$101$	−7.63720	−0.759930	−0.379965	−	0.925001i	$-0.624064\pi$
$101$	−7.63720	−0.759930	−0.379965	+	0.925001i	$0.624064\pi$
$102$	7.00565	0.693663
$103$	5.00906	0.493558	0.246779	−	0.969072i	$-0.420628\pi$
$103$	5.00906	0.493558	0.246779	+	0.969072i	$0.420628\pi$
$104$	9.54642	0.936103
$105$	0	0
$106$	5.67042	0.550760
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	−0.319820	−0.0307747
$109$	12.2391	1.17229	0.586144	−	0.810207i	$-0.300645\pi$
$109$	12.2391	1.17229	0.586144	+	0.810207i	$0.300645\pi$
$110$	0	0
$111$	3.40655	0.323335
$112$	−19.2350	−1.81754
$113$	−7.89476	−0.742676	−0.371338	−	0.928498i	$-0.621101\pi$
$113$	−7.89476	−0.742676	−0.371338	+	0.928498i	$0.621101\pi$
$114$	−1.01426	−0.0949941
$115$	0	0
$116$	0.763644	0.0709026
$117$	3.73042	0.344877
$118$	−4.49002	−0.413339
$119$	19.4989	1.78746
$120$	0	0
$121$	−10.6356	−0.966872
$122$	−15.2151	−1.37751
$123$	−2.23360	−0.201397
$124$	−0.837264	−0.0751885
$125$	0	0
$126$	−6.45679	−0.575217
$127$	−7.28705	−0.646621	−0.323311	−	0.946293i	$-0.604796\pi$
$127$	−7.28705	−0.646621	−0.323311	+	0.946293i	$0.604796\pi$
$128$	−13.2483	−1.17100
$129$	−0.243302	−0.0214215
$130$	0	0
$131$	−8.76691	−0.765969	−0.382984	−	0.923755i	$-0.625104\pi$
$131$	−8.76691	−0.765969	−0.382984	+	0.923755i	$0.625104\pi$
$132$	0.193063	0.0168040
$133$	−2.82300	−0.244786
$134$	−9.30747	−0.804043
$135$	0	0
$136$	11.7708	1.00933
$137$	8.84452	0.755638	0.377819	−	0.925879i	$-0.376674\pi$
$137$	8.84452	0.755638	0.377819	+	0.925879i	$0.376674\pi$
$138$	3.28545	0.279676
$139$	1.14738	0.0973199	0.0486600	−	0.998815i	$-0.484505\pi$
$139$	1.14738	0.0973199	0.0486600	+	0.998815i	$0.484505\pi$
$140$	0	0
$141$	−11.8228	−0.995659
$142$	11.6322	0.976151
$143$	−2.25191	−0.188314
$144$	−4.53736	−0.378113
$145$	0	0
$146$	−9.66296	−0.799713
$147$	−10.9713	−0.904896
$148$	−1.08948	−0.0895550
$149$	4.35066	0.356420	0.178210	−	0.983992i	$-0.442969\pi$
$149$	4.35066	0.356420	0.178210	+	0.983992i	$0.442969\pi$
$150$	0	0
$151$	−3.48981	−0.283997	−0.141998	−	0.989867i	$-0.545353\pi$
$151$	−3.48981	−0.283997	−0.141998	+	0.989867i	$0.545353\pi$
$152$	−1.70414	−0.138224
$153$	4.59961	0.371857
$154$	3.89772	0.314087
$155$	0	0
$156$	−1.19306	−0.0955215
$157$	−12.2825	−0.980249	−0.490125	−	0.871652i	$-0.663049\pi$
$157$	−12.2825	−0.980249	−0.490125	+	0.871652i	$0.663049\pi$
$158$	−23.4915	−1.86888
$159$	3.72296	0.295250
$160$	0	0
$161$	9.14443	0.720682
$162$	−1.52310	−0.119666
$163$	17.3056	1.35548	0.677738	−	0.735303i	$-0.262960\pi$
$163$	17.3056	1.35548	0.677738	+	0.735303i	$0.262960\pi$
$164$	0.714351	0.0557815
$165$	0	0
$166$	5.14848	0.399599
$167$	−9.62294	−0.744645	−0.372323	−	0.928103i	$-0.621439\pi$
$167$	−9.62294	−0.744645	−0.372323	+	0.928103i	$0.621439\pi$
$168$	−10.8486	−0.836985
$169$	0.916022	0.0704633
$170$	0	0
$171$	−0.665920	−0.0509242
$172$	0.0778128	0.00593317
$173$	−20.1739	−1.53379	−0.766897	−	0.641770i	$-0.778200\pi$
$173$	−20.1739	−1.53379	−0.766897	+	0.641770i	$0.778200\pi$
$174$	3.63674	0.275701
$175$	0	0
$176$	2.73903	0.206462
$177$	−2.94795	−0.221582
$178$	20.3550	1.52567
$179$	8.94551	0.668619	0.334309	−	0.942463i	$-0.391497\pi$
$179$	8.94551	0.668619	0.334309	+	0.942463i	$0.391497\pi$
$180$	0	0
$181$	4.48775	0.333572	0.166786	−	0.985993i	$-0.446661\pi$
$181$	4.48775	0.333572	0.166786	+	0.985993i	$0.446661\pi$
$182$	−24.0865	−1.78541
$183$	−9.98958	−0.738451
$184$	5.52014	0.406950
$185$	0	0
$186$	−3.98734	−0.292366
$187$	−2.77661	−0.203046
$188$	3.78117	0.275770
$189$	−4.23925	−0.308360
$190$	0	0
$191$	−16.0204	−1.15920	−0.579599	−	0.814902i	$-0.696791\pi$
$191$	−16.0204	−1.15920	−0.579599	+	0.814902i	$0.696791\pi$
$192$	−6.34429	−0.457860
$193$	14.4373	1.03922	0.519610	−	0.854403i	$-0.326077\pi$
$193$	14.4373	1.03922	0.519610	+	0.854403i	$0.326077\pi$
$194$	−26.5639	−1.90718
$195$	0	0
$196$	3.50884	0.250631
$197$	6.74918	0.480859	0.240430	−	0.970667i	$-0.422712\pi$
$197$	6.74918	0.480859	0.240430	+	0.970667i	$0.422712\pi$
$198$	0.919434	0.0653413
$199$	5.69670	0.403829	0.201914	−	0.979403i	$-0.435284\pi$
$199$	5.69670	0.403829	0.201914	+	0.979403i	$0.435284\pi$
$200$	0	0
$201$	−6.11089	−0.431029
$202$	11.6322	0.818437
$203$	10.1222	0.710439
$204$	−1.47105	−0.102994
$205$	0	0
$206$	−7.62928	−0.531557
$207$	2.15708	0.149928
$208$	−16.9262	−1.17362
$209$	0.401990	0.0278062
$210$	0	0
$211$	−6.89315	−0.474544	−0.237272	−	0.971443i	$-0.576253\pi$
$211$	−6.89315	−0.474544	−0.237272	+	0.971443i	$0.576253\pi$
$212$	−1.19068	−0.0817761
$213$	7.63720	0.523292
$214$	−1.52310	−0.104117
$215$	0	0
$216$	−2.55907	−0.174123
$217$	−11.0980	−0.753384
$218$	−18.6412	−1.26254
$219$	−6.34429	−0.428708
$220$	0	0
$221$	17.1585	1.15420
$222$	−5.18850	−0.348229
$223$	28.6474	1.91837	0.959186	−	0.282775i	$-0.0912550\pi$
$223$	28.6474	1.91837	0.959186	+	0.282775i	$0.0912550\pi$
$224$	7.59961	0.507771
$225$	0	0
$226$	12.0245	0.799856
$227$	25.8330	1.71460	0.857299	−	0.514819i	$-0.172141\pi$
$227$	25.8330	1.71460	0.857299	+	0.514819i	$0.172141\pi$
$228$	0.212975	0.0141046
$229$	−5.08943	−0.336319	−0.168159	−	0.985760i	$-0.553782\pi$
$229$	−5.08943	−0.336319	−0.168159	+	0.985760i	$0.553782\pi$
$230$	0	0
$231$	2.55907	0.168375
$232$	6.11038	0.401166
$233$	−16.1318	−1.05683	−0.528414	−	0.848987i	$-0.677213\pi$
$233$	−16.1318	−1.05683	−0.528414	+	0.848987i	$0.677213\pi$
$234$	−5.68178	−0.371430
$235$	0	0
$236$	0.942815	0.0613720
$237$	−15.4235	−1.00186
$238$	−29.6987	−1.92508
$239$	6.21644	0.402108	0.201054	−	0.979580i	$-0.435563\pi$
$239$	6.21644	0.402108	0.201054	+	0.979580i	$0.435563\pi$
$240$	0	0
$241$	−15.8541	−1.02125	−0.510626	−	0.859803i	$-0.670586\pi$
$241$	−15.8541	−1.02125	−0.510626	+	0.859803i	$0.670586\pi$
$242$	16.1990	1.04131
$243$	−1.00000	−0.0641500
$244$	3.19487	0.204531
$245$	0	0
$246$	3.40199	0.216903
$247$	−2.48416	−0.158063
$248$	−6.69946	−0.425416
$249$	3.38027	0.214216
$250$	0	0
$251$	−19.8169	−1.25083	−0.625415	−	0.780292i	$-0.715070\pi$
$251$	−19.8169	−1.25083	−0.625415	+	0.780292i	$0.715070\pi$
$252$	1.35580	0.0854073
$253$	−1.30215	−0.0818654
$254$	11.0989	0.696405
$255$	0	0
$256$	7.48987	0.468117
$257$	−8.39634	−0.523749	−0.261875	−	0.965102i	$-0.584341\pi$
$257$	−8.39634	−0.523749	−0.261875	+	0.965102i	$0.584341\pi$
$258$	0.370572	0.0230708
$259$	−14.4412	−0.897335
$260$	0	0
$261$	2.38773	0.147797
$262$	13.3528	0.824941
$263$	−1.76479	−0.108822	−0.0544109	−	0.998519i	$-0.517328\pi$
$263$	−1.76479	−0.108822	−0.0544109	+	0.998519i	$0.517328\pi$
$264$	1.54481	0.0950768
$265$	0	0
$266$	4.29971	0.263632
$267$	13.3642	0.817876
$268$	1.95439	0.119383
$269$	10.8668	0.662558	0.331279	−	0.943533i	$-0.392520\pi$
$269$	10.8668	0.662558	0.331279	+	0.943533i	$0.392520\pi$
$270$	0	0
$271$	−16.6850	−1.01354	−0.506771	−	0.862081i	$-0.669161\pi$
$271$	−16.6850	−1.01354	−0.506771	+	0.862081i	$0.669161\pi$
$272$	−20.8701	−1.26543
$273$	−15.8142	−0.957118
$274$	−13.4710	−0.813816
$275$	0	0
$276$	−0.689879	−0.0415258
$277$	0.297010	0.0178456	0.00892280	−	0.999960i	$-0.497160\pi$
$277$	0.297010	0.0178456	0.00892280	+	0.999960i	$0.497160\pi$
$278$	−1.74758	−0.104813
$279$	−2.61792	−0.156731
$280$	0	0
$281$	−3.41444	−0.203689	−0.101844	−	0.994800i	$-0.532474\pi$
$281$	−3.41444	−0.203689	−0.101844	+	0.994800i	$0.532474\pi$
$282$	18.0073	1.07232
$283$	−3.47787	−0.206738	−0.103369	−	0.994643i	$-0.532962\pi$
$283$	−3.47787	−0.206738	−0.103369	+	0.994643i	$0.532962\pi$
$284$	−2.44253	−0.144937
$285$	0	0
$286$	3.42987	0.202813
$287$	9.46881	0.558926
$288$	1.79268	0.105635
$289$	4.15645	0.244497
$290$	0	0
$291$	−17.4407	−1.02239
$292$	2.02903	0.118740
$293$	−8.37846	−0.489475	−0.244738	−	0.969589i	$-0.578702\pi$
$293$	−8.37846	−0.489475	−0.244738	+	0.969589i	$0.578702\pi$
$294$	16.7103	0.974565
$295$	0	0
$296$	−8.71762	−0.506701
$297$	0.603661	0.0350280
$298$	−6.62647	−0.383861
$299$	8.04683	0.465360
$300$	0	0
$301$	1.03142	0.0594500
$302$	5.31532	0.305862
$303$	7.63720	0.438746
$304$	3.02152	0.173296
$305$	0	0
$306$	−7.00565	−0.400486
$307$	−32.1361	−1.83411	−0.917053	−	0.398766i	$-0.869439\pi$
$307$	−32.1361	−1.83411	−0.917053	+	0.398766i	$0.869439\pi$
$308$	−0.818444	−0.0466352
$309$	−5.00906	−0.284956
$310$	0	0
$311$	7.81483	0.443138	0.221569	−	0.975145i	$-0.428882\pi$
$311$	7.81483	0.443138	0.221569	+	0.975145i	$0.428882\pi$
$312$	−9.54642	−0.540460
$313$	−19.8135	−1.11993	−0.559964	−	0.828517i	$-0.689185\pi$
$313$	−19.8135	−1.11993	−0.559964	+	0.828517i	$0.689185\pi$
$314$	18.7074	1.05572
$315$	0	0
$316$	4.93275	0.277489
$317$	−27.1363	−1.52412	−0.762062	−	0.647504i	$-0.775813\pi$
$317$	−27.1363	−1.52412	−0.762062	+	0.647504i	$0.775813\pi$
$318$	−5.67042	−0.317982
$319$	−1.44138	−0.0807018
$320$	0	0
$321$	−1.00000	−0.0558146
$322$	−13.9278	−0.776168
$323$	−3.06297	−0.170428
$324$	0.319820	0.0177678
$325$	0	0
$326$	−26.3580	−1.45984
$327$	−12.2391	−0.676821
$328$	5.71596	0.315611
$329$	50.1199	2.76320
$330$	0	0
$331$	−20.4070	−1.12167	−0.560835	−	0.827928i	$-0.689520\pi$
$331$	−20.4070	−1.12167	−0.560835	+	0.827928i	$0.689520\pi$
$332$	−1.08108	−0.0593319
$333$	−3.40655	−0.186678
$334$	14.6567	0.801976
$335$	0	0
$336$	19.2350	1.04936
$337$	15.4835	0.843441	0.421721	−	0.906726i	$-0.361426\pi$
$337$	15.4835	0.843441	0.421721	+	0.906726i	$0.361426\pi$
$338$	−1.39519	−0.0758883
$339$	7.89476	0.428784
$340$	0	0
$341$	1.58034	0.0855801
$342$	1.01426	0.0548449
$343$	16.8353	0.909018
$344$	0.622627	0.0335698
$345$	0	0
$346$	30.7268	1.65188
$347$	−3.14962	−0.169081	−0.0845404	−	0.996420i	$-0.526942\pi$
$347$	−3.14962	−0.169081	−0.0845404	+	0.996420i	$0.526942\pi$
$348$	−0.763644	−0.0409356
$349$	−9.83006	−0.526191	−0.263095	−	0.964770i	$-0.584743\pi$
$349$	−9.83006	−0.526191	−0.263095	+	0.964770i	$0.584743\pi$
$350$	0	0
$351$	−3.73042	−0.199115
$352$	−1.08217	−0.0576799
$353$	−13.4710	−0.716992	−0.358496	−	0.933531i	$-0.616710\pi$
$353$	−13.4710	−0.716992	−0.358496	+	0.933531i	$0.616710\pi$
$354$	4.49002	0.238642
$355$	0	0
$356$	−4.27414	−0.226529
$357$	−19.4989	−1.03199
$358$	−13.6249	−0.720097
$359$	22.2112	1.17226	0.586130	−	0.810217i	$-0.300651\pi$
$359$	22.2112	1.17226	0.586130	+	0.810217i	$0.300651\pi$
$360$	0	0
$361$	−18.5566	−0.976661
$362$	−6.83528	−0.359254
$363$	10.6356	0.558224
$364$	5.05770	0.265095
$365$	0	0
$366$	15.2151	0.795306
$367$	4.78349	0.249696	0.124848	−	0.992176i	$-0.460156\pi$
$367$	4.78349	0.249696	0.124848	+	0.992176i	$0.460156\pi$
$368$	−9.78746	−0.510207
$369$	2.23360	0.116277
$370$	0	0
$371$	−15.7826	−0.819390
$372$	0.837264	0.0434101
$373$	−12.7589	−0.660633	−0.330316	−	0.943870i	$-0.607155\pi$
$373$	−12.7589	−0.660633	−0.330316	+	0.943870i	$0.607155\pi$
$374$	4.22904	0.218679
$375$	0	0
$376$	30.2554	1.56030
$377$	8.90723	0.458746
$378$	6.45679	0.332101
$379$	15.0397	0.772538	0.386269	−	0.922386i	$-0.373764\pi$
$379$	15.0397	0.772538	0.386269	+	0.922386i	$0.373764\pi$
$380$	0	0
$381$	7.28705	0.373327
$382$	24.4006	1.24845
$383$	13.8047	0.705387	0.352694	−	0.935739i	$-0.385266\pi$
$383$	13.8047	0.705387	0.352694	+	0.935739i	$0.385266\pi$
$384$	13.2483	0.676075
$385$	0	0
$386$	−21.9894	−1.11923
$387$	0.243302	0.0123677
$388$	5.57789	0.283175
$389$	−20.0265	−1.01538	−0.507692	−	0.861539i	$-0.669501\pi$
$389$	−20.0265	−1.01538	−0.507692	+	0.861539i	$0.669501\pi$
$390$	0	0
$391$	9.92175	0.501765
$392$	28.0763	1.41807
$393$	8.76691	0.442232
$394$	−10.2796	−0.517881
$395$	0	0
$396$	−0.193063	−0.00970179
$397$	24.6832	1.23881	0.619407	−	0.785070i	$-0.287373\pi$
$397$	24.6832	1.23881	0.619407	+	0.785070i	$0.287373\pi$
$398$	−8.67662	−0.434920
$399$	2.82300	0.141327
$400$	0	0
$401$	−36.2176	−1.80862	−0.904310	−	0.426877i	$-0.859614\pi$
$401$	−36.2176	−1.80862	−0.904310	+	0.426877i	$0.859614\pi$
$402$	9.30747	0.464215
$403$	−9.76594	−0.486476
$404$	−2.44253	−0.121520
$405$	0	0
$406$	−15.4171	−0.765136
$407$	2.05640	0.101932
$408$	−11.7708	−0.582739
$409$	13.2809	0.656697	0.328349	−	0.944557i	$-0.393508\pi$
$409$	13.2809	0.656697	0.328349	+	0.944557i	$0.393508\pi$
$410$	0	0
$411$	−8.84452	−0.436268
$412$	1.60200	0.0789249
$413$	12.4971	0.614943
$414$	−3.28545	−0.161471
$415$	0	0
$416$	6.68744	0.327879
$417$	−1.14738	−0.0561877
$418$	−0.612270	−0.0299471
$419$	6.77365	0.330915	0.165457	−	0.986217i	$-0.447090\pi$
$419$	6.77365	0.330915	0.165457	+	0.986217i	$0.447090\pi$
$420$	0	0
$421$	29.1897	1.42262	0.711309	−	0.702879i	$-0.248102\pi$
$421$	29.1897	1.42262	0.711309	+	0.702879i	$0.248102\pi$
$422$	10.4989	0.511080
$423$	11.8228	0.574844
$424$	−9.52733	−0.462688
$425$	0	0
$426$	−11.6322	−0.563581
$427$	42.3484	2.04938
$428$	0.319820	0.0154591
$429$	2.25191	0.108723
$430$	0	0
$431$	10.7334	0.517008	0.258504	−	0.966010i	$-0.416770\pi$
$431$	10.7334	0.517008	0.258504	+	0.966010i	$0.416770\pi$
$432$	4.53736	0.218304
$433$	13.2561	0.637047	0.318523	−	0.947915i	$-0.396813\pi$
$433$	13.2561	0.637047	0.318523	+	0.947915i	$0.396813\pi$
$434$	16.9034	0.811388
$435$	0	0
$436$	3.91430	0.187461
$437$	−1.43645	−0.0687145
$438$	9.66296	0.461714
$439$	−8.14996	−0.388976	−0.194488	−	0.980905i	$-0.562305\pi$
$439$	−8.14996	−0.388976	−0.194488	+	0.980905i	$0.562305\pi$
$440$	0	0
$441$	10.9713	0.522442
$442$	−26.1340	−1.24307
$443$	−28.0933	−1.33475	−0.667376	−	0.744721i	$-0.732582\pi$
$443$	−28.0933	−1.33475	−0.667376	+	0.744721i	$0.732582\pi$
$444$	1.08948	0.0517046
$445$	0	0
$446$	−43.6327	−2.06607
$447$	−4.35066	−0.205779
$448$	26.8951	1.27067
$449$	−1.53458	−0.0724213	−0.0362106	−	0.999344i	$-0.511529\pi$
$449$	−1.53458	−0.0724213	−0.0362106	+	0.999344i	$0.511529\pi$
$450$	0	0
$451$	−1.34834	−0.0634908
$452$	−2.52490	−0.118761
$453$	3.48981	0.163966
$454$	−39.3461	−1.84661
$455$	0	0
$456$	1.70414	0.0798036
$457$	30.1084	1.40841	0.704207	−	0.709995i	$-0.251303\pi$
$457$	30.1084	1.40841	0.704207	+	0.709995i	$0.251303\pi$
$458$	7.75168	0.362212
$459$	−4.59961	−0.214692
$460$	0	0
$461$	−21.9792	−1.02367	−0.511836	−	0.859083i	$-0.671034\pi$
$461$	−21.9792	−1.02367	−0.511836	+	0.859083i	$0.671034\pi$
$462$	−3.89772	−0.181338
$463$	29.5110	1.37149	0.685745	−	0.727842i	$-0.259476\pi$
$463$	29.5110	1.37149	0.685745	+	0.727842i	$0.259476\pi$
$464$	−10.8340	−0.502955
$465$	0	0
$466$	24.5702	1.13819
$467$	−0.549831	−0.0254431	−0.0127216	−	0.999919i	$-0.504050\pi$
$467$	−0.549831	−0.0254431	−0.0127216	+	0.999919i	$0.504050\pi$
$468$	1.19306	0.0551494
$469$	25.9056	1.19621
$470$	0	0
$471$	12.2825	0.565947
$472$	7.54403	0.347242
$473$	−0.146872	−0.00675318
$474$	23.4915	1.07900
$475$	0	0
$476$	6.23615	0.285834
$477$	−3.72296	−0.170463
$478$	−9.46824	−0.433067
$479$	7.62024	0.348178	0.174089	−	0.984730i	$-0.444302\pi$
$479$	7.62024	0.348178	0.174089	+	0.984730i	$0.444302\pi$
$480$	0	0
$481$	−12.7079	−0.579429
$482$	24.1473	1.09988
$483$	−9.14443	−0.416086
$484$	−3.40148	−0.154613
$485$	0	0
$486$	1.52310	0.0690890
$487$	−25.7090	−1.16499	−0.582493	−	0.812836i	$-0.697923\pi$
$487$	−25.7090	−1.16499	−0.582493	+	0.812836i	$0.697923\pi$
$488$	25.5641	1.15723
$489$	−17.3056	−0.782584
$490$	0	0
$491$	4.59760	0.207487	0.103743	−	0.994604i	$-0.466918\pi$
$491$	4.59760	0.207487	0.103743	+	0.994604i	$0.466918\pi$
$492$	−0.714351	−0.0322054
$493$	10.9826	0.494633
$494$	3.78361	0.170233
$495$	0	0
$496$	11.8784	0.533358
$497$	−32.3760	−1.45226
$498$	−5.14848	−0.230709
$499$	−3.69997	−0.165633	−0.0828167	−	0.996565i	$-0.526392\pi$
$499$	−3.69997	−0.165633	−0.0828167	+	0.996565i	$0.526392\pi$
$500$	0	0
$501$	9.62294	0.429921
$502$	30.1830	1.34713
$503$	30.4896	1.35946	0.679732	−	0.733460i	$-0.262096\pi$
$503$	30.4896	1.35946	0.679732	+	0.733460i	$0.262096\pi$
$504$	10.8486	0.483234
$505$	0	0
$506$	1.98330	0.0881683
$507$	−0.916022	−0.0406820
$508$	−2.33055	−0.103401
$509$	34.2583	1.51847	0.759237	−	0.650814i	$-0.225572\pi$
$509$	34.2583	1.51847	0.759237	+	0.650814i	$0.225572\pi$
$510$	0	0
$511$	26.8951	1.18977
$512$	15.0888	0.666839
$513$	0.665920	0.0294011
$514$	12.7884	0.564073
$515$	0	0
$516$	−0.0778128	−0.00342552
$517$	−7.13697	−0.313884
$518$	21.9954	0.966422
$519$	20.1739	0.885537
$520$	0	0
$521$	42.0539	1.84241	0.921207	−	0.389073i	$-0.127205\pi$
$521$	42.0539	1.84241	0.921207	+	0.389073i	$0.127205\pi$
$522$	−3.63674	−0.159176
$523$	28.9419	1.26554	0.632770	−	0.774340i	$-0.281918\pi$
$523$	28.9419	1.26554	0.632770	+	0.774340i	$0.281918\pi$
$524$	−2.80383	−0.122486
$525$	0	0
$526$	2.68795	0.117200
$527$	−12.0414	−0.524533
$528$	−2.73903	−0.119201
$529$	−18.3470	−0.797695
$530$	0	0
$531$	2.94795	0.127930
$532$	−0.902854	−0.0391437
$533$	8.33227	0.360911
$534$	−20.3550	−0.880845
$535$	0	0
$536$	15.6382	0.675469
$537$	−8.94551	−0.386027
$538$	−16.5511	−0.713569
$539$	−6.62294	−0.285270
$540$	0	0
$541$	−20.3280	−0.873970	−0.436985	−	0.899469i	$-0.643954\pi$
$541$	−20.3280	−0.873970	−0.436985	+	0.899469i	$0.643954\pi$
$542$	25.4128	1.09157
$543$	−4.48775	−0.192588
$544$	8.24562	0.353528
$545$	0	0
$546$	24.0865	1.03081
$547$	3.83591	0.164012	0.0820059	−	0.996632i	$-0.473867\pi$
$547$	3.83591	0.164012	0.0820059	+	0.996632i	$0.473867\pi$
$548$	2.82866	0.120834
$549$	9.98958	0.426345
$550$	0	0
$551$	−1.59004	−0.0677379
$552$	−5.52014	−0.234953
$553$	65.3842	2.78042
$554$	−0.452375	−0.0192196
$555$	0	0
$556$	0.366957	0.0155624
$557$	−11.0778	−0.469382	−0.234691	−	0.972070i	$-0.575408\pi$
$557$	−11.0778	−0.469382	−0.234691	+	0.972070i	$0.575408\pi$
$558$	3.98734	0.168798
$559$	0.907618	0.0383881
$560$	0	0
$561$	2.77661	0.117229
$562$	5.20052	0.219371
$563$	−0.497784	−0.0209791	−0.0104896	−	0.999945i	$-0.503339\pi$
$563$	−0.497784	−0.0209791	−0.0104896	+	0.999945i	$0.503339\pi$
$564$	−3.78117	−0.159216
$565$	0	0
$566$	5.29713	0.222655
$567$	4.23925	0.178032
$568$	−19.5442	−0.820055
$569$	11.4602	0.480436	0.240218	−	0.970719i	$-0.422781\pi$
$569$	11.4602	0.480436	0.240218	+	0.970719i	$0.422781\pi$
$570$	0	0
$571$	35.1264	1.47000	0.734998	−	0.678070i	$-0.237183\pi$
$571$	35.1264	1.47000	0.734998	+	0.678070i	$0.237183\pi$
$572$	−0.720206	−0.0301133
$573$	16.0204	0.669263
$574$	−14.4219	−0.601959
$575$	0	0
$576$	6.34429	0.264346
$577$	30.1716	1.25606	0.628030	−	0.778189i	$-0.283862\pi$
$577$	30.1716	1.25606	0.628030	+	0.778189i	$0.283862\pi$
$578$	−6.33067	−0.263321
$579$	−14.4373	−0.599994
$580$	0	0
$581$	−14.3298	−0.594501
$582$	26.5639	1.10111
$583$	2.24741	0.0930781
$584$	16.2355	0.671830
$585$	0	0
$586$	12.7612	0.527160
$587$	−1.33838	−0.0552408	−0.0276204	−	0.999618i	$-0.508793\pi$
$587$	−1.33838	−0.0552408	−0.0276204	+	0.999618i	$0.508793\pi$
$588$	−3.50884	−0.144702
$589$	1.74333	0.0718325
$590$	0	0
$591$	−6.74918	−0.277624
$592$	15.4567	0.635268
$593$	−33.5238	−1.37666	−0.688328	−	0.725399i	$-0.741655\pi$
$593$	−33.5238	−1.37666	−0.688328	+	0.725399i	$0.741655\pi$
$594$	−0.919434	−0.0377248
$595$	0	0
$596$	1.39143	0.0569952
$597$	−5.69670	−0.233151
$598$	−12.2561	−0.501189
$599$	−22.6056	−0.923641	−0.461821	−	0.886973i	$-0.652804\pi$
$599$	−22.6056	−0.923641	−0.461821	+	0.886973i	$0.652804\pi$
$600$	0	0
$601$	25.3543	1.03422	0.517112	−	0.855918i	$-0.327007\pi$
$601$	25.3543	1.03422	0.517112	+	0.855918i	$0.327007\pi$
$602$	−1.57095	−0.0640271
$603$	6.11089	0.248855
$604$	−1.11611	−0.0454140
$605$	0	0
$606$	−11.6322	−0.472525
$607$	38.2108	1.55093	0.775465	−	0.631391i	$-0.217516\pi$
$607$	38.2108	1.55093	0.775465	+	0.631391i	$0.217516\pi$
$608$	−1.19378	−0.0484142
$609$	−10.1222	−0.410172
$610$	0	0
$611$	44.1040	1.78426
$612$	1.47105	0.0594636
$613$	−42.3838	−1.71187	−0.855933	−	0.517087i	$-0.827016\pi$
$613$	−42.3838	−1.71187	−0.855933	+	0.517087i	$0.827016\pi$
$614$	48.9464	1.97532
$615$	0	0
$616$	−6.54886	−0.263861
$617$	13.3921	0.539145	0.269573	−	0.962980i	$-0.413118\pi$
$617$	13.3921	0.539145	0.269573	+	0.962980i	$0.413118\pi$
$618$	7.62928	0.306895
$619$	−16.3233	−0.656088	−0.328044	−	0.944662i	$-0.606389\pi$
$619$	−16.3233	−0.656088	−0.328044	+	0.944662i	$0.606389\pi$
$620$	0	0
$621$	−2.15708	−0.0865608
$622$	−11.9027	−0.477256
$623$	−56.6543	−2.26980
$624$	16.9262	0.677592
$625$	0	0
$626$	30.1779	1.20615
$627$	−0.401990	−0.0160539
$628$	−3.92819	−0.156752
$629$	−15.6688	−0.624757
$630$	0	0
$631$	−34.2834	−1.36480	−0.682401	−	0.730978i	$-0.739064\pi$
$631$	−34.2834	−1.36480	−0.682401	+	0.730978i	$0.739064\pi$
$632$	39.4699	1.57003
$633$	6.89315	0.273978
$634$	41.3311	1.64147
$635$	0	0
$636$	1.19068	0.0472134
$637$	40.9275	1.62160
$638$	2.19536	0.0869152
$639$	−7.63720	−0.302123
$640$	0	0
$641$	31.4389	1.24176	0.620882	−	0.783904i	$-0.286775\pi$
$641$	31.4389	1.24176	0.620882	+	0.783904i	$0.286775\pi$
$642$	1.52310	0.0601118
$643$	8.11975	0.320212	0.160106	−	0.987100i	$-0.448816\pi$
$643$	8.11975	0.320212	0.160106	+	0.987100i	$0.448816\pi$
$644$	2.92457	0.115244
$645$	0	0
$646$	4.66520	0.183550
$647$	−0.796292	−0.0313055	−0.0156527	−	0.999877i	$-0.504983\pi$
$647$	−0.796292	−0.0313055	−0.0156527	+	0.999877i	$0.504983\pi$
$648$	2.55907	0.100530
$649$	−1.77957	−0.0698541
$650$	0	0
$651$	11.0980	0.434966
$652$	5.53467	0.216754
$653$	−36.9218	−1.44486	−0.722431	−	0.691443i	$-0.756975\pi$
$653$	−36.9218	−1.44486	−0.722431	+	0.691443i	$0.756975\pi$
$654$	18.6412	0.728930
$655$	0	0
$656$	−10.1346	−0.395692
$657$	6.34429	0.247514
$658$	−76.3373	−2.97594
$659$	−21.2941	−0.829500	−0.414750	−	0.909935i	$-0.636131\pi$
$659$	−21.2941	−0.829500	−0.414750	+	0.909935i	$0.636131\pi$
$660$	0	0
$661$	29.7884	1.15864	0.579318	−	0.815102i	$-0.303319\pi$
$661$	29.7884	1.15864	0.579318	+	0.815102i	$0.303319\pi$
$662$	31.0818	1.20803
$663$	−17.1585	−0.666380
$664$	−8.65037	−0.335699
$665$	0	0
$666$	5.18850	0.201050
$667$	5.15054	0.199430
$668$	−3.07761	−0.119076
$669$	−28.6474	−1.10757
$670$	0	0
$671$	−6.03033	−0.232798
$672$	−7.59961	−0.293161
$673$	45.0929	1.73821	0.869103	−	0.494632i	$-0.164697\pi$
$673$	45.0929	1.73821	0.869103	+	0.494632i	$0.164697\pi$
$674$	−23.5829	−0.908379
$675$	0	0
$676$	0.292962	0.0112678
$677$	−9.05492	−0.348009	−0.174004	−	0.984745i	$-0.555671\pi$
$677$	−9.05492	−0.348009	−0.174004	+	0.984745i	$0.555671\pi$
$678$	−12.0245	−0.461797
$679$	73.9357	2.83739
$680$	0	0
$681$	−25.8330	−0.989923
$682$	−2.40701	−0.0921690
$683$	−7.40996	−0.283534	−0.141767	−	0.989900i	$-0.545278\pi$
$683$	−7.40996	−0.283534	−0.141767	+	0.989900i	$0.545278\pi$
$684$	−0.212975	−0.00814329
$685$	0	0
$686$	−25.6417	−0.979005
$687$	5.08943	0.194174
$688$	−1.10395	−0.0420876
$689$	−13.8882	−0.529098
$690$	0	0
$691$	−10.7105	−0.407447	−0.203723	−	0.979028i	$-0.565304\pi$
$691$	−10.7105	−0.407447	−0.203723	+	0.979028i	$0.565304\pi$
$692$	−6.45203	−0.245269
$693$	−2.55907	−0.0972112
$694$	4.79718	0.182098
$695$	0	0
$696$	−6.11038	−0.231613
$697$	10.2737	0.389144
$698$	14.9721	0.566703
$699$	16.1318	0.610160
$700$	0	0
$701$	−18.1375	−0.685043	−0.342522	−	0.939510i	$-0.611281\pi$
$701$	−18.1375	−0.685043	−0.342522	+	0.939510i	$0.611281\pi$
$702$	5.68178	0.214445
$703$	2.26849	0.0855577
$704$	−3.82980	−0.144341
$705$	0	0
$706$	20.5177	0.772194
$707$	−32.3760	−1.21763
$708$	−0.942815	−0.0354332
$709$	−13.7406	−0.516038	−0.258019	−	0.966140i	$-0.583070\pi$
$709$	−13.7406	−0.516038	−0.258019	+	0.966140i	$0.583070\pi$
$710$	0	0
$711$	15.4235	0.578427
$712$	−34.2000	−1.28170
$713$	−5.64708	−0.211485
$714$	29.6987	1.11145
$715$	0	0
$716$	2.86095	0.106919
$717$	−6.21644	−0.232157
$718$	−33.8297	−1.26251
$719$	−16.8272	−0.627547	−0.313774	−	0.949498i	$-0.601593\pi$
$719$	−16.8272	−0.627547	−0.313774	+	0.949498i	$0.601593\pi$
$720$	0	0
$721$	21.2347	0.790821
$722$	28.2634	1.05185
$723$	15.8541	0.589620
$724$	1.43527	0.0533415
$725$	0	0
$726$	−16.1990	−0.601202
$727$	30.8820	1.14535	0.572675	−	0.819783i	$-0.305906\pi$
$727$	30.8820	1.14535	0.572675	+	0.819783i	$0.305906\pi$
$728$	40.4697	1.49991
$729$	1.00000	0.0370370
$730$	0	0
$731$	1.11909	0.0413912
$732$	−3.19487	−0.118086
$733$	−40.4153	−1.49277	−0.746386	−	0.665513i	$-0.768213\pi$
$733$	−40.4153	−1.49277	−0.746386	+	0.665513i	$0.768213\pi$
$734$	−7.28571	−0.268921
$735$	0	0
$736$	3.86696	0.142538
$737$	−3.68891	−0.135883
$738$	−3.40199	−0.125229
$739$	−36.2153	−1.33220	−0.666101	−	0.745861i	$-0.732038\pi$
$739$	−36.2153	−1.33220	−0.666101	+	0.745861i	$0.732038\pi$
$740$	0	0
$741$	2.48416	0.0912579
$742$	24.0384	0.882476
$743$	51.5884	1.89260	0.946298	−	0.323296i	$-0.104791\pi$
$743$	51.5884	1.89260	0.946298	+	0.323296i	$0.104791\pi$
$744$	6.69946	0.245614
$745$	0	0
$746$	19.4331	0.711496
$747$	−3.38027	−0.123678
$748$	−0.888016	−0.0324691
$749$	4.23925	0.154899
$750$	0	0
$751$	−31.0207	−1.13196	−0.565980	−	0.824419i	$-0.691502\pi$
$751$	−31.0207	−1.13196	−0.565980	+	0.824419i	$0.691502\pi$
$752$	−53.6442	−1.95620
$753$	19.8169	0.722168
$754$	−13.5666	−0.494065
$755$	0	0
$756$	−1.35580	−0.0493099
$757$	42.7642	1.55429	0.777146	−	0.629321i	$-0.216667\pi$
$757$	42.7642	1.55429	0.777146	+	0.629321i	$0.216667\pi$
$758$	−22.9069	−0.832016
$759$	1.30215	0.0472650
$760$	0	0
$761$	35.7684	1.29660	0.648302	−	0.761383i	$-0.275479\pi$
$761$	35.7684	1.29660	0.648302	+	0.761383i	$0.275479\pi$
$762$	−11.0989	−0.402070
$763$	51.8844	1.87834
$764$	−5.12366	−0.185367
$765$	0	0
$766$	−21.0259	−0.759696
$767$	10.9971	0.397082
$768$	−7.48987	−0.270267
$769$	10.5780	0.381451	0.190725	−	0.981643i	$-0.438916\pi$
$769$	10.5780	0.381451	0.190725	+	0.981643i	$0.438916\pi$
$770$	0	0
$771$	8.39634	0.302387
$772$	4.61734	0.166182
$773$	22.2386	0.799868	0.399934	−	0.916544i	$-0.369033\pi$
$773$	22.2386	0.799868	0.399934	+	0.916544i	$0.369033\pi$
$774$	−0.370572	−0.0133199
$775$	0	0
$776$	44.6321	1.60220
$777$	14.4412	0.518076
$778$	30.5023	1.09356
$779$	−1.48740	−0.0532917
$780$	0	0
$781$	4.61028	0.164969
$782$	−15.1118	−0.540396
$783$	−2.38773	−0.0853305
$784$	−49.7806	−1.77788
$785$	0	0
$786$	−13.3528	−0.476280
$787$	−8.84785	−0.315392	−0.157696	−	0.987488i	$-0.550407\pi$
$787$	−8.84785	−0.315392	−0.157696	+	0.987488i	$0.550407\pi$
$788$	2.15852	0.0768942
$789$	1.76479	0.0628283
$790$	0	0
$791$	−33.4679	−1.18998
$792$	−1.54481	−0.0548926
$793$	37.2653	1.32333
$794$	−37.5949	−1.33419
$795$	0	0
$796$	1.82192	0.0645763
$797$	−8.95312	−0.317136	−0.158568	−	0.987348i	$-0.550688\pi$
$797$	−8.95312	−0.317136	−0.158568	+	0.987348i	$0.550688\pi$
$798$	−4.29971	−0.152208
$799$	54.3803	1.92384
$800$	0	0
$801$	−13.3642	−0.472201
$802$	55.1628	1.94787
$803$	−3.82980	−0.135151
$804$	−1.95439	−0.0689259
$805$	0	0
$806$	14.8745	0.523931
$807$	−10.8668	−0.382528
$808$	−19.5442	−0.687561
$809$	−49.0035	−1.72287	−0.861436	−	0.507866i	$-0.830434\pi$
$809$	−49.0035	−1.72287	−0.861436	+	0.507866i	$0.830434\pi$
$810$	0	0
$811$	−2.90441	−0.101988	−0.0509938	−	0.998699i	$-0.516239\pi$
$811$	−2.90441	−0.101988	−0.0509938	+	0.998699i	$0.516239\pi$
$812$	3.23728	0.113606
$813$	16.6850	0.585168
$814$	−3.13210	−0.109780
$815$	0	0
$816$	20.8701	0.730599
$817$	−0.162020	−0.00566835
$818$	−20.2281	−0.707257
$819$	15.8142	0.552593
$820$	0	0
$821$	50.5326	1.76360	0.881801	−	0.471622i	$-0.156331\pi$
$821$	50.5326	1.76360	0.881801	+	0.471622i	$0.156331\pi$
$822$	13.4710	0.469857
$823$	14.7569	0.514394	0.257197	−	0.966359i	$-0.417201\pi$
$823$	14.7569	0.514394	0.257197	+	0.966359i	$0.417201\pi$
$824$	12.8186	0.446556
$825$	0	0
$826$	−19.0343	−0.662289
$827$	51.0534	1.77530	0.887650	−	0.460519i	$-0.152337\pi$
$827$	51.0534	1.77530	0.887650	+	0.460519i	$0.152337\pi$
$828$	0.689879	0.0239750
$829$	−11.1704	−0.387964	−0.193982	−	0.981005i	$-0.562140\pi$
$829$	−11.1704	−0.387964	−0.193982	+	0.981005i	$0.562140\pi$
$830$	0	0
$831$	−0.297010	−0.0103032
$832$	23.6669	0.820501
$833$	50.4636	1.74846
$834$	1.74758	0.0605136
$835$	0	0
$836$	0.128565	0.00444650
$837$	2.61792	0.0904886
$838$	−10.3169	−0.356392
$839$	−6.90413	−0.238357	−0.119178	−	0.992873i	$-0.538026\pi$
$839$	−6.90413	−0.238357	−0.119178	+	0.992873i	$0.538026\pi$
$840$	0	0
$841$	−23.2987	−0.803405
$842$	−44.4587	−1.53215
$843$	3.41444	0.117600
$844$	−2.20457	−0.0758844
$845$	0	0
$846$	−18.0073	−0.619102
$847$	−45.0870	−1.54921
$848$	16.8924	0.580087
$849$	3.47787	0.119360
$850$	0	0
$851$	−7.34822	−0.251894
$852$	2.44253	0.0836797
$853$	−11.2289	−0.384469	−0.192234	−	0.981349i	$-0.561573\pi$
$853$	−11.2289	−0.384469	−0.192234	+	0.981349i	$0.561573\pi$
$854$	−64.5006	−2.20717
$855$	0	0
$856$	2.55907	0.0874674
$857$	33.8349	1.15578	0.577890	−	0.816115i	$-0.303876\pi$
$857$	33.8349	1.15578	0.577890	+	0.816115i	$0.303876\pi$
$858$	−3.42987	−0.117094
$859$	6.09913	0.208099	0.104050	−	0.994572i	$-0.466820\pi$
$859$	6.09913	0.208099	0.104050	+	0.994572i	$0.466820\pi$
$860$	0	0
$861$	−9.46881	−0.322696
$862$	−16.3480	−0.556814
$863$	−43.9182	−1.49499	−0.747496	−	0.664266i	$-0.768744\pi$
$863$	−43.9182	−1.49499	−0.747496	+	0.664266i	$0.768744\pi$
$864$	−1.79268	−0.0609881
$865$	0	0
$866$	−20.1903	−0.686094
$867$	−4.15645	−0.141160
$868$	−3.54938	−0.120474
$869$	−9.31058	−0.315840
$870$	0	0
$871$	22.7962	0.772419
$872$	31.3206	1.06065
$873$	17.4407	0.590279
$874$	2.18784	0.0740049
$875$	0	0
$876$	−2.02903	−0.0685547
$877$	−6.86741	−0.231896	−0.115948	−	0.993255i	$-0.536991\pi$
$877$	−6.86741	−0.231896	−0.115948	+	0.993255i	$0.536991\pi$
$878$	12.4132	0.418924
$879$	8.37846	0.282599
$880$	0	0
$881$	36.4455	1.22788	0.613940	−	0.789353i	$-0.289584\pi$
$881$	36.4455	1.22788	0.613940	+	0.789353i	$0.289584\pi$
$882$	−16.7103	−0.562665
$883$	−31.3965	−1.05658	−0.528288	−	0.849065i	$-0.677166\pi$
$883$	−31.3965	−1.05658	−0.528288	+	0.849065i	$0.677166\pi$
$884$	5.48763	0.184569
$885$	0	0
$886$	42.7887	1.43752
$887$	53.9146	1.81027	0.905137	−	0.425120i	$-0.139768\pi$
$887$	53.9146	1.81027	0.905137	+	0.425120i	$0.139768\pi$
$888$	8.71762	0.292544
$889$	−30.8917	−1.03607
$890$	0	0
$891$	−0.603661	−0.0202234
$892$	9.16202	0.306767
$893$	−7.87304	−0.263461
$894$	6.62647	0.221622
$895$	0	0
$896$	−56.1630	−1.87627
$897$	−8.04683	−0.268676
$898$	2.33731	0.0779971
$899$	−6.25089	−0.208479
$900$	0	0
$901$	−17.1242	−0.570489
$902$	2.05365	0.0683791
$903$	−1.03142	−0.0343235
$904$	−20.2033	−0.671951
$905$	0	0
$906$	−5.31532	−0.176590
$907$	−26.5585	−0.881860	−0.440930	−	0.897541i	$-0.645351\pi$
$907$	−26.5585	−0.881860	−0.440930	+	0.897541i	$0.645351\pi$
$908$	8.26192	0.274181
$909$	−7.63720	−0.253310
$910$	0	0
$911$	−53.2230	−1.76336	−0.881678	−	0.471851i	$-0.843586\pi$
$911$	−53.2230	−1.76336	−0.881678	+	0.471851i	$0.843586\pi$
$912$	−3.02152	−0.100052
$913$	2.04054	0.0675320
$914$	−45.8580	−1.51685
$915$	0	0
$916$	−1.62770	−0.0537808
$917$	−37.1652	−1.22730
$918$	7.00565	0.231221
$919$	18.0164	0.594305	0.297152	−	0.954830i	$-0.403963\pi$
$919$	18.0164	0.594305	0.297152	+	0.954830i	$0.403963\pi$
$920$	0	0
$921$	32.1361	1.05892
$922$	33.4764	1.10249
$923$	−28.4899	−0.937758
$924$	0.818444	0.0269248
$925$	0	0
$926$	−44.9480	−1.47708
$927$	5.00906	0.164519
$928$	4.28043	0.140512
$929$	−15.5423	−0.509927	−0.254963	−	0.966951i	$-0.582063\pi$
$929$	−15.5423	−0.509927	−0.254963	+	0.966951i	$0.582063\pi$
$930$	0	0
$931$	−7.30599	−0.239444
$932$	−5.15927	−0.168997
$933$	−7.81483	−0.255846
$934$	0.837445	0.0274020
$935$	0	0
$936$	9.54642	0.312034
$937$	25.0351	0.817862	0.408931	−	0.912565i	$-0.365902\pi$
$937$	25.0351	0.817862	0.408931	+	0.912565i	$0.365902\pi$
$938$	−39.4568	−1.28831
$939$	19.8135	0.646590
$940$	0	0
$941$	−13.0085	−0.424066	−0.212033	−	0.977263i	$-0.568008\pi$
$941$	−13.0085	−0.424066	−0.212033	+	0.977263i	$0.568008\pi$
$942$	−18.7074	−0.609520
$943$	4.81807	0.156898
$944$	−13.3759	−0.435349
$945$	0	0
$946$	0.223700	0.00727311
$947$	17.1323	0.556724	0.278362	−	0.960476i	$-0.410209\pi$
$947$	17.1323	0.556724	0.278362	+	0.960476i	$0.410209\pi$
$948$	−4.93275	−0.160208
$949$	23.6669	0.768259
$950$	0	0
$951$	27.1363	0.879953
$952$	49.8992	1.61724
$953$	58.1880	1.88489	0.942447	−	0.334354i	$-0.108518\pi$
$953$	58.1880	1.88489	0.942447	+	0.334354i	$0.108518\pi$
$954$	5.67042	0.183587
$955$	0	0
$956$	1.98814	0.0643012
$957$	1.44138	0.0465932
$958$	−11.6064	−0.374984
$959$	37.4942	1.21075
$960$	0	0
$961$	−24.1465	−0.778919
$962$	19.3553	0.624039
$963$	1.00000	0.0322245
$964$	−5.07046	−0.163309
$965$	0	0
$966$	13.9278	0.448121
$967$	−25.2689	−0.812592	−0.406296	−	0.913742i	$-0.633180\pi$
$967$	−25.2689	−0.812592	−0.406296	+	0.913742i	$0.633180\pi$
$968$	−27.2173	−0.874796
$969$	3.06297	0.0983969
$970$	0	0
$971$	−42.0748	−1.35025	−0.675123	−	0.737706i	$-0.735909\pi$
$971$	−42.0748	−1.35025	−0.675123	+	0.737706i	$0.735909\pi$
$972$	−0.319820	−0.0102582
$973$	4.86406	0.155935
$974$	39.1573	1.25468
$975$	0	0
$976$	−45.3263	−1.45086
$977$	−43.7172	−1.39864	−0.699318	−	0.714811i	$-0.746513\pi$
$977$	−43.7172	−1.39864	−0.699318	+	0.714811i	$0.746513\pi$
$978$	26.3580	0.842837
$979$	8.06745	0.257837
$980$	0	0
$981$	12.2391	0.390763
$982$	−7.00259	−0.223462
$983$	−31.9579	−1.01930	−0.509649	−	0.860382i	$-0.670225\pi$
$983$	−31.9579	−1.01930	−0.509649	+	0.860382i	$0.670225\pi$
$984$	−5.71596	−0.182218
$985$	0	0
$986$	−16.7276	−0.532716
$987$	−50.1199	−1.59533
$988$	−0.794485	−0.0252759
$989$	0.524823	0.0166884
$990$	0	0
$991$	−6.09027	−0.193464	−0.0967318	−	0.995310i	$-0.530839\pi$
$991$	−6.09027	−0.193464	−0.0967318	+	0.995310i	$0.530839\pi$
$992$	−4.69309	−0.149006
$993$	20.4070	0.647596
$994$	49.3118	1.56407
$995$	0	0
$996$	1.08108	0.0342553
$997$	18.2020	0.576465	0.288232	−	0.957561i	$-0.406932\pi$
$997$	18.2020	0.576465	0.288232	+	0.957561i	$0.406932\pi$
$998$	5.63541	0.178386
$999$	3.40655	0.107778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.w.1.1		4
5.4	even	2		1605.2.a.g.1.4	✓	4
15.14	odd	2		4815.2.a.j.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1605.2.a.g.1.4	✓	4	5.4	even	2
4815.2.a.j.1.1		4	15.14	odd	2
8025.2.a.w.1.1		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52310 q^{2} -1.00000 q^{3} +0.319820 q^{4} +1.52310 q^{6} +4.23925 q^{7} +2.55907 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.52310 q^{2} -1.00000 q^{3} +0.319820 q^{4} +1.52310 q^{6} +4.23925 q^{7} +2.55907 q^{8} +1.00000 q^{9} -0.603661 q^{11} -0.319820 q^{12} +3.73042 q^{13} -6.45679 q^{14} -4.53736 q^{16} +4.59961 q^{17} -1.52310 q^{18} -0.665920 q^{19} -4.23925 q^{21} +0.919434 q^{22} +2.15708 q^{23} -2.55907 q^{24} -5.68178 q^{26} -1.00000 q^{27} +1.35580 q^{28} +2.38773 q^{29} -2.61792 q^{31} +1.79268 q^{32} +0.603661 q^{33} -7.00565 q^{34} +0.319820 q^{36} -3.40655 q^{37} +1.01426 q^{38} -3.73042 q^{39} +2.23360 q^{41} +6.45679 q^{42} +0.243302 q^{43} -0.193063 q^{44} -3.28545 q^{46} +11.8228 q^{47} +4.53736 q^{48} +10.9713 q^{49} -4.59961 q^{51} +1.19306 q^{52} -3.72296 q^{53} +1.52310 q^{54} +10.8486 q^{56} +0.665920 q^{57} -3.63674 q^{58} +2.94795 q^{59} +9.98958 q^{61} +3.98734 q^{62} +4.23925 q^{63} +6.34429 q^{64} -0.919434 q^{66} +6.11089 q^{67} +1.47105 q^{68} -2.15708 q^{69} -7.63720 q^{71} +2.55907 q^{72} +6.34429 q^{73} +5.18850 q^{74} -0.212975 q^{76} -2.55907 q^{77} +5.68178 q^{78} +15.4235 q^{79} +1.00000 q^{81} -3.40199 q^{82} -3.38027 q^{83} -1.35580 q^{84} -0.370572 q^{86} -2.38773 q^{87} -1.54481 q^{88} -13.3642 q^{89} +15.8142 q^{91} +0.689879 q^{92} +2.61792 q^{93} -18.0073 q^{94} -1.79268 q^{96} +17.4407 q^{97} -16.7103 q^{98} -0.603661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9} - 4 q^{11} - 3 q^{12} + 9 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{18} - 7 q^{19} - 8 q^{21} - 7 q^{22} + 16 q^{23} - 3 q^{24} + 6 q^{26} - 4 q^{27} + 9 q^{28} + q^{29} - 6 q^{31} + 4 q^{32} + 4 q^{33} - 15 q^{34} + 3 q^{36} + 8 q^{37} - 2 q^{38} - 9 q^{39} + 13 q^{41} + 6 q^{43} - 10 q^{44} + 14 q^{46} + 5 q^{47} + 3 q^{48} + 2 q^{49} - 6 q^{51} + 14 q^{52} + 5 q^{53} - 3 q^{54} + 23 q^{56} + 7 q^{57} + 3 q^{58} - 11 q^{59} + 6 q^{61} - 5 q^{62} + 8 q^{63} + q^{64} + 7 q^{66} + 50 q^{67} - 26 q^{68} - 16 q^{69} + 7 q^{71} + 3 q^{72} + q^{73} + 37 q^{74} + 9 q^{76} - 3 q^{77} - 6 q^{78} + q^{79} + 4 q^{81} + q^{82} + 9 q^{83} - 9 q^{84} + 22 q^{86} - q^{87} - 5 q^{88} - 10 q^{89} + 14 q^{91} + 2 q^{92} + 6 q^{93} - 32 q^{94} - 4 q^{96} + 23 q^{97} - 26 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9 - 4 * q^11 - 3 * q^12 + 9 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^18 - 7 * q^19 - 8 * q^21 - 7 * q^22 + 16 * q^23 - 3 * q^24 + 6 * q^26 - 4 * q^27 + 9 * q^28 + q^29 - 6 * q^31 + 4 * q^32 + 4 * q^33 - 15 * q^34 + 3 * q^36 + 8 * q^37 - 2 * q^38 - 9 * q^39 + 13 * q^41 + 6 * q^43 - 10 * q^44 + 14 * q^46 + 5 * q^47 + 3 * q^48 + 2 * q^49 - 6 * q^51 + 14 * q^52 + 5 * q^53 - 3 * q^54 + 23 * q^56 + 7 * q^57 + 3 * q^58 - 11 * q^59 + 6 * q^61 - 5 * q^62 + 8 * q^63 + q^64 + 7 * q^66 + 50 * q^67 - 26 * q^68 - 16 * q^69 + 7 * q^71 + 3 * q^72 + q^73 + 37 * q^74 + 9 * q^76 - 3 * q^77 - 6 * q^78 + q^79 + 4 * q^81 + q^82 + 9 * q^83 - 9 * q^84 + 22 * q^86 - q^87 - 5 * q^88 - 10 * q^89 + 14 * q^91 + 2 * q^92 + 6 * q^93 - 32 * q^94 - 4 * q^96 + 23 * q^97 - 26 * q^98 - 4 * q^99

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