LMFDB - Embedded newform 1075.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x - 1 $ x^3 - x^2 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.65109$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.273891 q^{2} +2.65109 q^{3} -1.92498 q^{4} -0.726109 q^{6} -0.273891 q^{7} +1.07502 q^{8} +4.02830 q^{9} +O(q^{10})$	\(q-0.273891 q^{2} +2.65109 q^{3} -1.92498 q^{4} -0.726109 q^{6} -0.273891 q^{7} +1.07502 q^{8} +4.02830 q^{9} +1.37720 q^{11} -5.10331 q^{12} -2.75441 q^{13} +0.0750160 q^{14} +3.55553 q^{16} +2.00000 q^{17} -1.10331 q^{18} +4.20662 q^{19} -0.726109 q^{21} -0.377203 q^{22} +8.05659 q^{23} +2.84997 q^{24} +0.754406 q^{26} +2.72611 q^{27} +0.527235 q^{28} -4.20662 q^{29} +10.8783 q^{31} -3.12386 q^{32} +3.65109 q^{33} -0.547781 q^{34} -7.75441 q^{36} +5.92498 q^{37} -1.15215 q^{38} -7.30219 q^{39} -6.70769 q^{41} +0.198875 q^{42} -1.00000 q^{43} -2.65109 q^{44} -2.20662 q^{46} +7.45222 q^{47} +9.42605 q^{48} -6.92498 q^{49} +5.30219 q^{51} +5.30219 q^{52} +1.45222 q^{53} -0.746656 q^{54} -0.294437 q^{56} +11.1522 q^{57} +1.15215 q^{58} -0.0467198 q^{59} -6.75441 q^{61} -2.97945 q^{62} -1.10331 q^{63} -6.25547 q^{64} -1.00000 q^{66} +9.84997 q^{67} -3.84997 q^{68} +21.3588 q^{69} +5.30219 q^{71} +4.33048 q^{72} +6.29444 q^{73} -1.62280 q^{74} -8.09768 q^{76} -0.377203 q^{77} +2.00000 q^{78} -0.281641 q^{79} -4.85772 q^{81} +1.83717 q^{82} -13.5654 q^{83} +1.39775 q^{84} +0.273891 q^{86} -11.1522 q^{87} +1.48052 q^{88} +0.341157 q^{89} +0.754406 q^{91} -15.5088 q^{92} +28.8393 q^{93} -2.04109 q^{94} -8.28164 q^{96} -10.0566 q^{97} +1.89669 q^{98} +5.54778 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{3} + 3 q^{4} - 4 q^{6} + q^{7} + 12 q^{8}+O(q^{10}) $ 3 * q + q^2 + q^3 + 3 * q^4 - 4 * q^6 + q^7 + 12 * q^8	$ 3 q + q^{2} + q^{3} + 3 q^{4} - 4 q^{6} + q^{7} + 12 q^{8} - q^{11} - 12 q^{12} + 2 q^{13} + 9 q^{14} + 11 q^{16} + 6 q^{17} + 6 q^{19} - 4 q^{21} + 4 q^{22} - 9 q^{24} - 8 q^{26} + 10 q^{27} + 14 q^{28} - 6 q^{29} + 3 q^{31} + 10 q^{32} + 4 q^{33} + 2 q^{34} - 13 q^{36} + 9 q^{37} + 28 q^{38} - 8 q^{39} + 11 q^{41} - 10 q^{42} - 3 q^{43} - q^{44} + 26 q^{47} - 5 q^{48} - 12 q^{49} + 2 q^{51} + 2 q^{52} + 8 q^{53} + 12 q^{54} + 17 q^{56} + 2 q^{57} - 28 q^{58} - 21 q^{59} - 10 q^{61} - 25 q^{62} + 16 q^{64} - 3 q^{66} + 12 q^{67} + 6 q^{68} + 26 q^{69} + 2 q^{71} - 13 q^{72} + q^{73} - 10 q^{74} + 32 q^{76} + 4 q^{77} + 6 q^{78} - 3 q^{79} - q^{81} + 8 q^{82} + 4 q^{83} - 17 q^{84} - q^{86} - 2 q^{87} - 4 q^{88} + 4 q^{89} - 8 q^{91} - 26 q^{92} + 40 q^{93} + 26 q^{94} - 27 q^{96} - 6 q^{97} + 9 q^{98} + 13 q^{99}+O(q^{100}) $ 3 * q + q^2 + q^3 + 3 * q^4 - 4 * q^6 + q^7 + 12 * q^8 - q^11 - 12 * q^12 + 2 * q^13 + 9 * q^14 + 11 * q^16 + 6 * q^17 + 6 * q^19 - 4 * q^21 + 4 * q^22 - 9 * q^24 - 8 * q^26 + 10 * q^27 + 14 * q^28 - 6 * q^29 + 3 * q^31 + 10 * q^32 + 4 * q^33 + 2 * q^34 - 13 * q^36 + 9 * q^37 + 28 * q^38 - 8 * q^39 + 11 * q^41 - 10 * q^42 - 3 * q^43 - q^44 + 26 * q^47 - 5 * q^48 - 12 * q^49 + 2 * q^51 + 2 * q^52 + 8 * q^53 + 12 * q^54 + 17 * q^56 + 2 * q^57 - 28 * q^58 - 21 * q^59 - 10 * q^61 - 25 * q^62 + 16 * q^64 - 3 * q^66 + 12 * q^67 + 6 * q^68 + 26 * q^69 + 2 * q^71 - 13 * q^72 + q^73 - 10 * q^74 + 32 * q^76 + 4 * q^77 + 6 * q^78 - 3 * q^79 - q^81 + 8 * q^82 + 4 * q^83 - 17 * q^84 - q^86 - 2 * q^87 - 4 * q^88 + 4 * q^89 - 8 * q^91 - 26 * q^92 + 40 * q^93 + 26 * q^94 - 27 * q^96 - 6 * q^97 + 9 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.273891	−0.193670	−0.0968349	−	0.995300i	$-0.530872\pi$
$2$	−0.273891	−0.193670	−0.0968349	+	0.995300i	$0.530872\pi$
$3$	2.65109	1.53061	0.765305	−	0.643668i	$-0.222588\pi$
$3$	2.65109	1.53061	0.765305	+	0.643668i	$0.222588\pi$
$4$	−1.92498	−0.962492
$5$	0	0
$5$	0	0
$6$	−0.726109	−0.296433
$7$	−0.273891	−0.103521	−0.0517604	−	0.998660i	$-0.516483\pi$
$7$	−0.273891	−0.103521	−0.0517604	+	0.998660i	$0.516483\pi$
$8$	1.07502	0.380076
$9$	4.02830	1.34277
$10$	0	0
$11$	1.37720	0.415242	0.207621	−	0.978209i	$-0.433428\pi$
$11$	1.37720	0.415242	0.207621	+	0.978209i	$0.433428\pi$
$12$	−5.10331	−1.47320
$13$	−2.75441	−0.763935	−0.381967	−	0.924176i	$-0.624753\pi$
$13$	−2.75441	−0.763935	−0.381967	+	0.924176i	$0.624753\pi$
$14$	0.0750160	0.0200489
$15$	0	0
$16$	3.55553	0.888883
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.10331	−0.260053
$19$	4.20662	0.965066	0.482533	−	0.875878i	$-0.339717\pi$
$19$	4.20662	0.965066	0.482533	+	0.875878i	$0.339717\pi$
$20$	0	0
$21$	−0.726109	−0.158450
$22$	−0.377203	−0.0804199
$23$	8.05659	1.67992	0.839958	−	0.542652i	$-0.182580\pi$
$23$	8.05659	1.67992	0.839958	+	0.542652i	$0.182580\pi$
$24$	2.84997	0.581747
$25$	0	0
$26$	0.754406	0.147951
$27$	2.72611	0.524640
$28$	0.527235	0.0996380
$29$	−4.20662	−0.781151	−0.390575	−	0.920571i	$-0.627724\pi$
$29$	−4.20662	−0.781151	−0.390575	+	0.920571i	$0.627724\pi$
$30$	0	0
$31$	10.8783	1.95379	0.976897	−	0.213711i	$-0.0685550\pi$
$31$	10.8783	1.95379	0.976897	+	0.213711i	$0.0685550\pi$
$32$	−3.12386	−0.552225
$33$	3.65109	0.635574
$34$	−0.547781	−0.0939437
$35$	0	0
$36$	−7.75441	−1.29240
$37$	5.92498	0.974061	0.487031	−	0.873385i	$-0.338080\pi$
$37$	5.92498	0.974061	0.487031	+	0.873385i	$0.338080\pi$
$38$	−1.15215	−0.186904
$39$	−7.30219	−1.16929
$40$	0	0
$41$	−6.70769	−1.04756	−0.523782	−	0.851852i	$-0.675479\pi$
$41$	−6.70769	−1.04756	−0.523782	+	0.851852i	$0.675479\pi$
$42$	0.198875	0.0306870
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−2.65109	−0.399667
$45$	0	0
$46$	−2.20662	−0.325349
$47$	7.45222	1.08702	0.543509	−	0.839403i	$-0.317095\pi$
$47$	7.45222	1.08702	0.543509	+	0.839403i	$0.317095\pi$
$48$	9.42605	1.36053
$49$	−6.92498	−0.989283
$50$	0	0
$51$	5.30219	0.742455
$52$	5.30219	0.735281
$53$	1.45222	0.199478	0.0997388	−	0.995014i	$-0.468199\pi$
$53$	1.45222	0.199478	0.0997388	+	0.995014i	$0.468199\pi$
$54$	−0.746656	−0.101607
$55$	0	0
$56$	−0.294437	−0.0393458
$57$	11.1522	1.47714
$58$	1.15215	0.151285
$59$	−0.0467198	−0.00608240	−0.00304120	−	0.999995i	$-0.500968\pi$
$59$	−0.0467198	−0.00608240	−0.00304120	+	0.999995i	$0.500968\pi$
$60$	0	0
$61$	−6.75441	−0.864813	−0.432407	−	0.901679i	$-0.642335\pi$
$61$	−6.75441	−0.864813	−0.432407	+	0.901679i	$0.642335\pi$
$62$	−2.97945	−0.378391
$63$	−1.10331	−0.139004
$64$	−6.25547	−0.781933
$65$	0	0
$66$	−1.00000	−0.123091
$67$	9.84997	1.20337	0.601683	−	0.798735i	$-0.294497\pi$
$67$	9.84997	1.20337	0.601683	+	0.798735i	$0.294497\pi$
$68$	−3.84997	−0.466877
$69$	21.3588	2.57129
$70$	0	0
$71$	5.30219	0.629254	0.314627	−	0.949215i	$-0.398121\pi$
$71$	5.30219	0.629254	0.314627	+	0.949215i	$0.398121\pi$
$72$	4.33048	0.510352
$73$	6.29444	0.736708	0.368354	−	0.929686i	$-0.379921\pi$
$73$	6.29444	0.736708	0.368354	+	0.929686i	$0.379921\pi$
$74$	−1.62280	−0.188646
$75$	0	0
$76$	−8.09768	−0.928868
$77$	−0.377203	−0.0429863
$78$	2.00000	0.226455
$79$	−0.281641	−0.0316870	−0.0158435	−	0.999874i	$-0.505043\pi$
$79$	−0.281641	−0.0316870	−0.0158435	+	0.999874i	$0.505043\pi$
$80$	0	0
$81$	−4.85772	−0.539746
$82$	1.83717	0.202882
$83$	−13.5654	−1.48900	−0.744498	−	0.667624i	$-0.767311\pi$
$83$	−13.5654	−1.48900	−0.744498	+	0.667624i	$0.767311\pi$
$84$	1.39775	0.152507
$85$	0	0
$86$	0.273891	0.0295344
$87$	−11.1522	−1.19564
$88$	1.48052	0.157823
$89$	0.341157	0.0361625	0.0180813	−	0.999837i	$-0.494244\pi$
$89$	0.341157	0.0361625	0.0180813	+	0.999837i	$0.494244\pi$
$90$	0	0
$91$	0.754406	0.0790832
$92$	−15.5088	−1.61691
$93$	28.8393	2.99050
$94$	−2.04109	−0.210523
$95$	0	0
$96$	−8.28164	−0.845241
$97$	−10.0566	−1.02109	−0.510546	−	0.859850i	$-0.670557\pi$
$97$	−10.0566	−1.02109	−0.510546	+	0.859850i	$0.670557\pi$
$98$	1.89669	0.191594
$99$	5.54778	0.557573
$100$	0	0
$101$	−13.5761	−1.35087	−0.675435	−	0.737419i	$-0.736044\pi$
$101$	−13.5761	−1.35087	−0.675435	+	0.737419i	$0.736044\pi$
$102$	−1.45222	−0.143791
$103$	4.41325	0.434850	0.217425	−	0.976077i	$-0.430234\pi$
$103$	4.41325	0.434850	0.217425	+	0.976077i	$0.430234\pi$
$104$	−2.96103	−0.290353
$105$	0	0
$106$	−0.397749	−0.0386328
$107$	11.0956	1.07265	0.536324	−	0.844012i	$-0.319812\pi$
$107$	11.0956	1.07265	0.536324	+	0.844012i	$0.319812\pi$
$108$	−5.24772	−0.504962
$109$	3.51948	0.337106	0.168553	−	0.985693i	$-0.446091\pi$
$109$	3.51948	0.337106	0.168553	+	0.985693i	$0.446091\pi$
$110$	0	0
$111$	15.7077	1.49091
$112$	−0.973826	−0.0920179
$113$	−7.08489	−0.666490	−0.333245	−	0.942840i	$-0.608144\pi$
$113$	−7.08489	−0.666490	−0.333245	+	0.942840i	$0.608144\pi$
$114$	−3.05447	−0.286077
$115$	0	0
$116$	8.09768	0.751851
$117$	−11.0956	−1.02579
$118$	0.0127961	0.00117798
$119$	−0.547781	−0.0502150
$120$	0	0
$121$	−9.10331	−0.827574
$122$	1.84997	0.167488
$123$	−17.7827	−1.60341
$124$	−20.9405	−1.88051
$125$	0	0
$126$	0.302187	0.0269209
$127$	−19.7154	−1.74946	−0.874731	−	0.484609i	$-0.838962\pi$
$127$	−19.7154	−1.74946	−0.874731	+	0.484609i	$0.838962\pi$
$128$	7.96103	0.703662
$129$	−2.65109	−0.233416
$130$	0	0
$131$	−12.1132	−1.05833	−0.529167	−	0.848518i	$-0.677495\pi$
$131$	−12.1132	−1.05833	−0.529167	+	0.848518i	$0.677495\pi$
$132$	−7.02830	−0.611735
$133$	−1.15215	−0.0999045
$134$	−2.69781	−0.233056
$135$	0	0
$136$	2.15003	0.184364
$137$	4.10331	0.350570	0.175285	−	0.984518i	$-0.443915\pi$
$137$	4.10331	0.350570	0.175285	+	0.984518i	$0.443915\pi$
$138$	−5.84997	−0.497982
$139$	9.04884	0.767513	0.383756	−	0.923434i	$-0.374630\pi$
$139$	9.04884	0.767513	0.383756	+	0.923434i	$0.374630\pi$
$140$	0	0
$141$	19.7565	1.66380
$142$	−1.45222	−0.121868
$143$	−3.79338	−0.317218
$144$	14.3227	1.19356
$145$	0	0
$146$	−1.72399	−0.142678
$147$	−18.3588	−1.51421
$148$	−11.4055	−0.937526
$149$	7.50881	0.615146	0.307573	−	0.951525i	$-0.400483\pi$
$149$	7.50881	0.615146	0.307573	+	0.951525i	$0.400483\pi$
$150$	0	0
$151$	−17.5654	−1.42945	−0.714726	−	0.699404i	$-0.753449\pi$
$151$	−17.5654	−1.42945	−0.714726	+	0.699404i	$0.753449\pi$
$152$	4.52219	0.366798
$153$	8.05659	0.651337
$154$	0.103312	0.00832514
$155$	0	0
$156$	14.0566	1.12543
$157$	19.1209	1.52602	0.763008	−	0.646389i	$-0.223721\pi$
$157$	19.1209	1.52602	0.763008	+	0.646389i	$0.223721\pi$
$158$	0.0771387	0.00613683
$159$	3.84997	0.305322
$160$	0	0
$161$	−2.20662	−0.173906
$162$	1.33048	0.104533
$163$	−5.52723	−0.432926	−0.216463	−	0.976291i	$-0.569452\pi$
$163$	−5.52723	−0.432926	−0.216463	+	0.976291i	$0.569452\pi$
$164$	12.9122	1.00827
$165$	0	0
$166$	3.71544	0.288374
$167$	15.3022	1.18412	0.592059	−	0.805894i	$-0.298315\pi$
$167$	15.3022	1.18412	0.592059	+	0.805894i	$0.298315\pi$
$168$	−0.780579	−0.0602230
$169$	−5.41325	−0.416404
$170$	0	0
$171$	16.9455	1.29586
$172$	1.92498	0.146779
$173$	23.8500	1.81328	0.906640	−	0.421906i	$-0.138639\pi$
$173$	23.8500	1.81328	0.906640	+	0.421906i	$0.138639\pi$
$174$	3.05447	0.231559
$175$	0	0
$176$	4.89669	0.369102
$177$	−0.123858	−0.00930977
$178$	−0.0934395	−0.00700359
$179$	−7.84997	−0.586734	−0.293367	−	0.956000i	$-0.594776\pi$
$179$	−7.84997	−0.586734	−0.293367	+	0.956000i	$0.594776\pi$
$180$	0	0
$181$	−11.5966	−0.861970	−0.430985	−	0.902359i	$-0.641834\pi$
$181$	−11.5966	−0.861970	−0.430985	+	0.902359i	$0.641834\pi$
$182$	−0.206625	−0.0153160
$183$	−17.9066	−1.32369
$184$	8.66097	0.638495
$185$	0	0
$186$	−7.89881	−0.579169
$187$	2.75441	0.201422
$188$	−14.3454	−1.04625
$189$	−0.746656	−0.0543112
$190$	0	0
$191$	25.2087	1.82404	0.912020	−	0.410145i	$-0.134522\pi$
$191$	25.2087	1.82404	0.912020	+	0.410145i	$0.134522\pi$
$192$	−16.5838	−1.19683
$193$	−24.2477	−1.74539	−0.872694	−	0.488267i	$-0.837629\pi$
$193$	−24.2477	−1.74539	−0.872694	+	0.488267i	$0.837629\pi$
$194$	2.75441	0.197755
$195$	0	0
$196$	13.3305	0.952177
$197$	1.90656	0.135837	0.0679184	−	0.997691i	$-0.478364\pi$
$197$	1.90656	0.135837	0.0679184	+	0.997691i	$0.478364\pi$
$198$	−1.51948	−0.107985
$199$	−7.84997	−0.556469	−0.278235	−	0.960513i	$-0.589749\pi$
$199$	−7.84997	−0.556469	−0.278235	+	0.960513i	$0.589749\pi$
$200$	0	0
$201$	26.1132	1.84188
$202$	3.71836	0.261623
$203$	1.15215	0.0808654
$204$	−10.2066	−0.714607
$205$	0	0
$206$	−1.20875	−0.0842174
$207$	32.4543	2.25573
$208$	−9.79338	−0.679048
$209$	5.79338	0.400736
$210$	0	0
$211$	16.1132	1.10928	0.554639	−	0.832091i	$-0.312856\pi$
$211$	16.1132	1.10928	0.554639	+	0.832091i	$0.312856\pi$
$212$	−2.79550	−0.191996
$213$	14.0566	0.963142
$214$	−3.03897	−0.207740
$215$	0	0
$216$	2.93061	0.199403
$217$	−2.97945	−0.202259
$218$	−0.963954	−0.0652872
$219$	16.6871	1.12761
$220$	0	0
$221$	−5.50881	−0.370563
$222$	−4.30219	−0.288744
$223$	2.60437	0.174402	0.0872009	−	0.996191i	$-0.472208\pi$
$223$	2.60437	0.174402	0.0872009	+	0.996191i	$0.472208\pi$
$224$	0.855595	0.0571669
$225$	0	0
$226$	1.94048	0.129079
$227$	−4.13936	−0.274739	−0.137369	−	0.990520i	$-0.543865\pi$
$227$	−4.13936	−0.274739	−0.137369	+	0.990520i	$0.543865\pi$
$228$	−21.4677	−1.42173
$229$	−12.1161	−0.800655	−0.400327	−	0.916372i	$-0.631104\pi$
$229$	−12.1161	−0.800655	−0.400327	+	0.916372i	$0.631104\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	−4.52219	−0.296896
$233$	−26.8209	−1.75709	−0.878547	−	0.477656i	$-0.841486\pi$
$233$	−26.8209	−1.75709	−0.878547	+	0.477656i	$0.841486\pi$
$234$	3.03897	0.198664
$235$	0	0
$236$	0.0899348	0.00585426
$237$	−0.746656	−0.0485005
$238$	0.150032	0.00972513
$239$	−20.9349	−1.35416	−0.677082	−	0.735908i	$-0.736756\pi$
$239$	−20.9349	−1.35416	−0.677082	+	0.735908i	$0.736756\pi$
$240$	0	0
$241$	−1.73678	−0.111876	−0.0559380	−	0.998434i	$-0.517815\pi$
$241$	−1.73678	−0.111876	−0.0559380	+	0.998434i	$0.517815\pi$
$242$	2.49331	0.160276
$243$	−21.0566	−1.35078
$244$	13.0021	0.832376
$245$	0	0
$246$	4.87051	0.310533
$247$	−11.5868	−0.737247
$248$	11.6943	0.742589
$249$	−35.9632	−2.27907
$250$	0	0
$251$	−21.2087	−1.33868	−0.669342	−	0.742954i	$-0.733424\pi$
$251$	−21.2087	−1.33868	−0.669342	+	0.742954i	$0.733424\pi$
$252$	2.12386	0.133791
$253$	11.0956	0.697572
$254$	5.39987	0.338818
$255$	0	0
$256$	10.3305	0.645655
$257$	0.566205	0.0353189	0.0176594	−	0.999844i	$-0.494379\pi$
$257$	0.566205	0.0353189	0.0176594	+	0.999844i	$0.494379\pi$
$258$	0.726109	0.0452056
$259$	−1.62280	−0.100836
$260$	0	0
$261$	−16.9455	−1.04890
$262$	3.31769	0.204967
$263$	13.2272	0.815622	0.407811	−	0.913066i	$-0.366292\pi$
$263$	13.2272	0.815622	0.407811	+	0.913066i	$0.366292\pi$
$264$	3.92498	0.241566
$265$	0	0
$266$	0.315564	0.0193485
$267$	0.904438	0.0553507
$268$	−18.9610	−1.15823
$269$	−3.02055	−0.184166	−0.0920830	−	0.995751i	$-0.529353\pi$
$269$	−3.02055	−0.184166	−0.0920830	+	0.995751i	$0.529353\pi$
$270$	0	0
$271$	−16.3665	−0.994196	−0.497098	−	0.867694i	$-0.665601\pi$
$271$	−16.3665	−0.994196	−0.497098	+	0.867694i	$0.665601\pi$
$272$	7.11106	0.431171
$273$	2.00000	0.121046
$274$	−1.12386	−0.0678948
$275$	0	0
$276$	−41.1153	−2.47485
$277$	−26.1025	−1.56835	−0.784174	−	0.620541i	$-0.786913\pi$
$277$	−26.1025	−1.56835	−0.784174	+	0.620541i	$0.786913\pi$
$278$	−2.47839	−0.148644
$279$	43.8209	2.62349
$280$	0	0
$281$	−27.2838	−1.62761	−0.813806	−	0.581136i	$-0.802608\pi$
$281$	−27.2838	−1.62761	−0.813806	+	0.581136i	$0.802608\pi$
$282$	−5.41113	−0.322228
$283$	25.5654	1.51971	0.759853	−	0.650095i	$-0.225271\pi$
$283$	25.5654	1.51971	0.759853	+	0.650095i	$0.225271\pi$
$284$	−10.2066	−0.605652
$285$	0	0
$286$	1.03897	0.0614356
$287$	1.83717	0.108445
$288$	−12.5838	−0.741509
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−26.6610	−1.56289
$292$	−12.1167	−0.709076
$293$	12.8265	0.749332	0.374666	−	0.927160i	$-0.377757\pi$
$293$	12.8265	0.749332	0.374666	+	0.927160i	$0.377757\pi$
$294$	5.02830	0.293256
$295$	0	0
$296$	6.36945	0.370217
$297$	3.75441	0.217853
$298$	−2.05659	−0.119135
$299$	−22.1911	−1.28335
$300$	0	0
$301$	0.273891	0.0157868
$302$	4.81100	0.276842
$303$	−35.9914	−2.06765
$304$	14.9568	0.857830
$305$	0	0
$306$	−2.20662	−0.126144
$307$	−0.832345	−0.0475044	−0.0237522	−	0.999718i	$-0.507561\pi$
$307$	−0.832345	−0.0475044	−0.0237522	+	0.999718i	$0.507561\pi$
$308$	0.726109	0.0413739
$309$	11.6999	0.665586
$310$	0	0
$311$	26.9709	1.52938	0.764690	−	0.644399i	$-0.222892\pi$
$311$	26.9709	1.52938	0.764690	+	0.644399i	$0.222892\pi$
$312$	−7.84997	−0.444417
$313$	3.38495	0.191329	0.0956644	−	0.995414i	$-0.469502\pi$
$313$	3.38495	0.191329	0.0956644	+	0.995414i	$0.469502\pi$
$314$	−5.23704	−0.295543
$315$	0	0
$316$	0.542154	0.0304985
$317$	−9.15215	−0.514036	−0.257018	−	0.966407i	$-0.582740\pi$
$317$	−9.15215	−0.514036	−0.257018	+	0.966407i	$0.582740\pi$
$318$	−1.05447	−0.0591317
$319$	−5.79338	−0.324367
$320$	0	0
$321$	29.4154	1.64181
$322$	0.604374	0.0336804
$323$	8.41325	0.468126
$324$	9.35103	0.519502
$325$	0	0
$326$	1.51386	0.0838448
$327$	9.33048	0.515977
$328$	−7.21087	−0.398154
$329$	−2.04109	−0.112529
$330$	0	0
$331$	−19.8345	−1.09020	−0.545100	−	0.838371i	$-0.683508\pi$
$331$	−19.8345	−1.09020	−0.545100	+	0.838371i	$0.683508\pi$
$332$	26.1132	1.43315
$333$	23.8676	1.30794
$334$	−4.19112	−0.229328
$335$	0	0
$336$	−2.58170	−0.140844
$337$	−8.24772	−0.449282	−0.224641	−	0.974442i	$-0.572121\pi$
$337$	−8.24772	−0.449282	−0.224641	+	0.974442i	$0.572121\pi$
$338$	1.48264	0.0806449
$339$	−18.7827	−1.02014
$340$	0	0
$341$	14.9816	0.811298
$342$	−4.64122	−0.250968
$343$	3.81392	0.205932
$344$	−1.07502	−0.0579610
$345$	0	0
$346$	−6.53228	−0.351178
$347$	27.4183	1.47189	0.735946	−	0.677041i	$-0.236738\pi$
$347$	27.4183	1.47189	0.735946	+	0.677041i	$0.236738\pi$
$348$	21.4677	1.15079
$349$	5.11106	0.273589	0.136794	−	0.990599i	$-0.456320\pi$
$349$	5.11106	0.273589	0.136794	+	0.990599i	$0.456320\pi$
$350$	0	0
$351$	−7.50881	−0.400791
$352$	−4.30219	−0.229307
$353$	9.64334	0.513263	0.256632	−	0.966509i	$-0.417387\pi$
$353$	9.64334	0.513263	0.256632	+	0.966509i	$0.417387\pi$
$354$	0.0339237	0.00180302
$355$	0	0
$356$	−0.656721	−0.0348061
$357$	−1.45222	−0.0768596
$358$	2.15003	0.113633
$359$	11.5868	0.611525	0.305763	−	0.952108i	$-0.401089\pi$
$359$	11.5868	0.611525	0.305763	+	0.952108i	$0.401089\pi$
$360$	0	0
$361$	−1.30431	−0.0686479
$362$	3.17621	0.166938
$363$	−24.1337	−1.26669
$364$	−1.45222	−0.0761170
$365$	0	0
$366$	4.90444	0.256359
$367$	−21.5499	−1.12490	−0.562448	−	0.826833i	$-0.690140\pi$
$367$	−21.5499	−1.12490	−0.562448	+	0.826833i	$0.690140\pi$
$368$	28.6455	1.49325
$369$	−27.0205	−1.40663
$370$	0	0
$371$	−0.397749	−0.0206501
$372$	−55.5152	−2.87833
$373$	32.7282	1.69460	0.847302	−	0.531112i	$-0.178226\pi$
$373$	32.7282	1.69460	0.847302	+	0.531112i	$0.178226\pi$
$374$	−0.754406	−0.0390094
$375$	0	0
$376$	8.01125	0.413149
$377$	11.5868	0.596748
$378$	0.204502	0.0105184
$379$	10.0595	0.516723	0.258361	−	0.966048i	$-0.416817\pi$
$379$	10.0595	0.516723	0.258361	+	0.966048i	$0.416817\pi$
$380$	0	0
$381$	−52.2675	−2.67774
$382$	−6.90444	−0.353262
$383$	−32.9554	−1.68394	−0.841971	−	0.539522i	$-0.818605\pi$
$383$	−32.9554	−1.68394	−0.841971	+	0.539522i	$0.818605\pi$
$384$	21.1054	1.07703
$385$	0	0
$386$	6.64122	0.338029
$387$	−4.02830	−0.204770
$388$	19.3588	0.982793
$389$	−11.7154	−0.593996	−0.296998	−	0.954878i	$-0.595986\pi$
$389$	−11.7154	−0.593996	−0.296998	+	0.954878i	$0.595986\pi$
$390$	0	0
$391$	16.1132	0.814879
$392$	−7.44447	−0.376002
$393$	−32.1132	−1.61990
$394$	−0.522189	−0.0263075
$395$	0	0
$396$	−10.6794	−0.536660
$397$	6.54778	0.328624	0.164312	−	0.986408i	$-0.447460\pi$
$397$	6.54778	0.328624	0.164312	+	0.986408i	$0.447460\pi$
$398$	2.15003	0.107771
$399$	−3.05447	−0.152915
$400$	0	0
$401$	−13.8238	−0.690327	−0.345164	−	0.938543i	$-0.612177\pi$
$401$	−13.8238	−0.690327	−0.345164	+	0.938543i	$0.612177\pi$
$402$	−7.15215	−0.356717
$403$	−29.9632	−1.49257
$404$	26.1337	1.30020
$405$	0	0
$406$	−0.315564	−0.0156612
$407$	8.15990	0.404471
$408$	5.69994	0.282189
$409$	−9.56540	−0.472979	−0.236489	−	0.971634i	$-0.575997\pi$
$409$	−9.56540	−0.472979	−0.236489	+	0.971634i	$0.575997\pi$
$410$	0	0
$411$	10.8783	0.536585
$412$	−8.49543	−0.418540
$413$	0.0127961	0.000629655 0
$414$	−8.88894	−0.436867
$415$	0	0
$416$	8.60437	0.421864
$417$	23.9893	1.17476
$418$	−1.58675	−0.0776105
$419$	2.15003	0.105036	0.0525180	−	0.998620i	$-0.483275\pi$
$419$	2.15003	0.105036	0.0525180	+	0.998620i	$0.483275\pi$
$420$	0	0
$421$	−23.2653	−1.13388	−0.566942	−	0.823758i	$-0.691874\pi$
$421$	−23.2653	−1.13388	−0.566942	+	0.823758i	$0.691874\pi$
$422$	−4.41325	−0.214834
$423$	30.0197	1.45961
$424$	1.56116	0.0758166
$425$	0	0
$426$	−3.84997	−0.186532
$427$	1.84997	0.0895262
$428$	−21.3588	−1.03242
$429$	−10.0566	−0.485537
$430$	0	0
$431$	21.1423	1.01839	0.509194	−	0.860652i	$-0.329944\pi$
$431$	21.1423	1.01839	0.509194	+	0.860652i	$0.329944\pi$
$432$	9.69277	0.466343
$433$	−15.4338	−0.741701	−0.370850	−	0.928693i	$-0.620934\pi$
$433$	−15.4338	−0.741701	−0.370850	+	0.928693i	$0.620934\pi$
$434$	0.816044	0.0391714
$435$	0	0
$436$	−6.77495	−0.324461
$437$	33.8911	1.62123
$438$	−4.57045	−0.218385
$439$	2.20955	0.105456	0.0527280	−	0.998609i	$-0.483208\pi$
$439$	2.20955	0.105456	0.0527280	+	0.998609i	$0.483208\pi$
$440$	0	0
$441$	−27.8959	−1.32838
$442$	1.50881	0.0717668
$443$	14.6610	0.696564	0.348282	−	0.937390i	$-0.386765\pi$
$443$	14.6610	0.696564	0.348282	+	0.937390i	$0.386765\pi$
$444$	−30.2370	−1.43499
$445$	0	0
$446$	−0.713313	−0.0337764
$447$	19.9066	0.941548
$448$	1.71331	0.0809464
$449$	36.4175	1.71865	0.859324	−	0.511432i	$-0.170885\pi$
$449$	36.4175	1.71865	0.859324	+	0.511432i	$0.170885\pi$
$450$	0	0
$451$	−9.23784	−0.434993
$452$	13.6383	0.641492
$453$	−46.5675	−2.18793
$454$	1.13373	0.0532086
$455$	0	0
$456$	11.9887	0.561424
$457$	−39.8230	−1.86284	−0.931421	−	0.363945i	$-0.881430\pi$
$457$	−39.8230	−1.86284	−0.931421	+	0.363945i	$0.881430\pi$
$458$	3.31849	0.155063
$459$	5.45222	0.254488
$460$	0	0
$461$	14.3382	0.667798	0.333899	−	0.942609i	$-0.391636\pi$
$461$	14.3382	0.667798	0.333899	+	0.942609i	$0.391636\pi$
$462$	0.273891	0.0127425
$463$	26.7643	1.24384	0.621921	−	0.783080i	$-0.286353\pi$
$463$	26.7643	1.24384	0.621921	+	0.783080i	$0.286353\pi$
$464$	−14.9568	−0.694351
$465$	0	0
$466$	7.34598	0.340296
$467$	19.2867	0.892481	0.446241	−	0.894913i	$-0.352763\pi$
$467$	19.2867	0.892481	0.446241	+	0.894913i	$0.352763\pi$
$468$	21.3588	0.987310
$469$	−2.69781	−0.124573
$470$	0	0
$471$	50.6914	2.33574
$472$	−0.0502245	−0.00231177
$473$	−1.37720	−0.0633239
$474$	0.204502	0.00939308
$475$	0	0
$476$	1.05447	0.0483315
$477$	5.84997	0.267852
$478$	5.73386	0.262261
$479$	−29.7827	−1.36081	−0.680403	−	0.732838i	$-0.738195\pi$
$479$	−29.7827	−1.36081	−0.680403	+	0.732838i	$0.738195\pi$
$480$	0	0
$481$	−16.3198	−0.744119
$482$	0.475688	0.0216670
$483$	−5.84997	−0.266183
$484$	17.5237	0.796533
$485$	0	0
$486$	5.76720	0.261606
$487$	−26.6610	−1.20812	−0.604062	−	0.796937i	$-0.706452\pi$
$487$	−26.6610	−1.20812	−0.604062	+	0.796937i	$0.706452\pi$
$488$	−7.26109	−0.328694
$489$	−14.6532	−0.662641
$490$	0	0
$491$	10.9765	0.495364	0.247682	−	0.968841i	$-0.420331\pi$
$491$	10.9765	0.495364	0.247682	+	0.968841i	$0.420331\pi$
$492$	34.2314	1.54327
$493$	−8.41325	−0.378914
$494$	3.17350	0.142783
$495$	0	0
$496$	38.6780	1.73669
$497$	−1.45222	−0.0651409
$498$	9.84997	0.441388
$499$	2.15003	0.0962487	0.0481243	−	0.998841i	$-0.484676\pi$
$499$	2.15003	0.0962487	0.0481243	+	0.998841i	$0.484676\pi$
$500$	0	0
$501$	40.5675	1.81242
$502$	5.80888	0.259263
$503$	28.0870	1.25234	0.626169	−	0.779687i	$-0.284622\pi$
$503$	28.0870	1.25234	0.626169	+	0.779687i	$0.284622\pi$
$504$	−1.18608	−0.0528321
$505$	0	0
$506$	−3.03897	−0.135099
$507$	−14.3510	−0.637352
$508$	37.9519	1.68384
$509$	−18.7848	−0.832623	−0.416311	−	0.909222i	$-0.636677\pi$
$509$	−18.7848	−0.832623	−0.416311	+	0.909222i	$0.636677\pi$
$510$	0	0
$511$	−1.72399	−0.0762647
$512$	−18.7515	−0.828706
$513$	11.4677	0.506312
$514$	−0.155078	−0.00684020
$515$	0	0
$516$	5.10331	0.224661
$517$	10.2632	0.451376
$518$	0.444469	0.0195288
$519$	63.2285	2.77542
$520$	0	0
$521$	21.2242	0.929851	0.464926	−	0.885350i	$-0.346081\pi$
$521$	21.2242	0.929851	0.464926	+	0.885350i	$0.346081\pi$
$522$	4.64122	0.203141
$523$	−21.6036	−0.944658	−0.472329	−	0.881422i	$-0.656587\pi$
$523$	−21.6036	−0.944658	−0.472329	+	0.881422i	$0.656587\pi$
$524$	23.3177	1.01864
$525$	0	0
$526$	−3.62280	−0.157961
$527$	21.7565	0.947729
$528$	12.9816	0.564951
$529$	41.9087	1.82212
$530$	0	0
$531$	−0.188201	−0.00816723
$532$	2.21788	0.0961573
$533$	18.4757	0.800271
$534$	−0.247717	−0.0107198
$535$	0	0
$536$	10.5889	0.457370
$537$	−20.8110	−0.898061
$538$	0.827299	0.0356674
$539$	−9.53711	−0.410792
$540$	0	0
$541$	13.2117	0.568014	0.284007	−	0.958822i	$-0.408336\pi$
$541$	13.2117	0.568014	0.284007	+	0.958822i	$0.408336\pi$
$542$	4.48264	0.192546
$543$	−30.7437	−1.31934
$544$	−6.24772	−0.267869
$545$	0	0
$546$	−0.547781	−0.0234429
$547$	−34.2888	−1.46608	−0.733042	−	0.680184i	$-0.761900\pi$
$547$	−34.2888	−1.46608	−0.733042	+	0.680184i	$0.761900\pi$
$548$	−7.89881	−0.337420
$549$	−27.2087	−1.16124
$550$	0	0
$551$	−17.6957	−0.753862
$552$	22.9610	0.977286
$553$	0.0771387	0.00328027
$554$	7.14923	0.303742
$555$	0	0
$556$	−17.4189	−0.738725
$557$	16.8889	0.715607	0.357804	−	0.933797i	$-0.383526\pi$
$557$	16.8889	0.715607	0.357804	+	0.933797i	$0.383526\pi$
$558$	−12.0021	−0.508090
$559$	2.75441	0.116499
$560$	0	0
$561$	7.30219	0.308299
$562$	7.47277	0.315220
$563$	14.9087	0.628326	0.314163	−	0.949369i	$-0.398276\pi$
$563$	14.9087	0.628326	0.314163	+	0.949369i	$0.398276\pi$
$564$	−38.0310	−1.60139
$565$	0	0
$566$	−7.00212	−0.294321
$567$	1.33048	0.0558750
$568$	5.69994	0.239164
$569$	29.4415	1.23425	0.617127	−	0.786864i	$-0.288297\pi$
$569$	29.4415	1.23425	0.617127	+	0.786864i	$0.288297\pi$
$570$	0	0
$571$	28.0411	1.17348	0.586742	−	0.809774i	$-0.300410\pi$
$571$	28.0411	1.17348	0.586742	+	0.809774i	$0.300410\pi$
$572$	7.30219	0.305320
$573$	66.8307	2.79189
$574$	−0.503184	−0.0210025
$575$	0	0
$576$	−25.1989	−1.04995
$577$	28.4175	1.18304	0.591518	−	0.806292i	$-0.298529\pi$
$577$	28.4175	1.18304	0.591518	+	0.806292i	$0.298529\pi$
$578$	3.56058	0.148100
$579$	−64.2830	−2.67151
$580$	0	0
$581$	3.71544	0.154142
$582$	7.30219	0.302685
$583$	2.00000	0.0828315
$584$	6.76662	0.280005
$585$	0	0
$586$	−3.51306	−0.145123
$587$	−18.2173	−0.751908	−0.375954	−	0.926638i	$-0.622685\pi$
$587$	−18.2173	−0.751908	−0.375954	+	0.926638i	$0.622685\pi$
$588$	35.3404	1.45741
$589$	45.7608	1.88554
$590$	0	0
$591$	5.05447	0.207913
$592$	21.0665	0.865826
$593$	2.75733	0.113230	0.0566150	−	0.998396i	$-0.481969\pi$
$593$	2.75733	0.113230	0.0566150	+	0.998396i	$0.481969\pi$
$594$	−1.02830	−0.0421915
$595$	0	0
$596$	−14.4543	−0.592073
$597$	−20.8110	−0.851737
$598$	6.07794	0.248545
$599$	15.7048	0.641679	0.320840	−	0.947134i	$-0.396035\pi$
$599$	15.7048	0.641679	0.320840	+	0.947134i	$0.396035\pi$
$600$	0	0
$601$	19.7565	0.805886	0.402943	−	0.915225i	$-0.367987\pi$
$601$	19.7565	0.805886	0.402943	+	0.915225i	$0.367987\pi$
$602$	−0.0750160	−0.00305743
$603$	39.6786	1.61584
$604$	33.8131	1.37584
$605$	0	0
$606$	9.85772	0.400442
$607$	47.4663	1.92660	0.963300	−	0.268429i	$-0.0865043\pi$
$607$	47.4663	1.92660	0.963300	+	0.268429i	$0.0865043\pi$
$608$	−13.1409	−0.532934
$609$	3.05447	0.123773
$610$	0	0
$611$	−20.5264	−0.830411
$612$	−15.5088	−0.626907
$613$	−9.69994	−0.391777	−0.195888	−	0.980626i	$-0.562759\pi$
$613$	−9.69994	−0.391777	−0.195888	+	0.980626i	$0.562759\pi$
$614$	0.227971	0.00920018
$615$	0	0
$616$	−0.405499	−0.0163380
$617$	33.0587	1.33089	0.665447	−	0.746445i	$-0.268241\pi$
$617$	33.0587	1.33089	0.665447	+	0.746445i	$0.268241\pi$
$618$	−3.20450	−0.128904
$619$	−14.3305	−0.575991	−0.287995	−	0.957632i	$-0.592989\pi$
$619$	−14.3305	−0.575991	−0.287995	+	0.957632i	$0.592989\pi$
$620$	0	0
$621$	21.9632	0.881351
$622$	−7.38708	−0.296195
$623$	−0.0934395	−0.00374358
$624$	−25.9632	−1.03936
$625$	0	0
$626$	−0.927107	−0.0370546
$627$	15.3588	0.613371
$628$	−36.8075	−1.46878
$629$	11.8500	0.472489
$630$	0	0
$631$	−5.60225	−0.223022	−0.111511	−	0.993763i	$-0.535569\pi$
$631$	−5.60225	−0.223022	−0.111511	+	0.993763i	$0.535569\pi$
$632$	−0.302768	−0.0120435
$633$	42.7176	1.69787
$634$	2.50669	0.0995533
$635$	0	0
$636$	−7.41113	−0.293870
$637$	19.0742	0.755748
$638$	1.58675	0.0628201
$639$	21.3588	0.844940
$640$	0	0
$641$	−39.6220	−1.56497	−0.782487	−	0.622666i	$-0.786049\pi$
$641$	−39.6220	−1.56497	−0.782487	+	0.622666i	$0.786049\pi$
$642$	−8.05659	−0.317968
$643$	4.28456	0.168967	0.0844834	−	0.996425i	$-0.473076\pi$
$643$	4.28456	0.168967	0.0844834	+	0.996425i	$0.473076\pi$
$644$	4.24772	0.167383
$645$	0	0
$646$	−2.30431	−0.0906618
$647$	−43.9525	−1.72795	−0.863975	−	0.503534i	$-0.832033\pi$
$647$	−43.9525	−1.72795	−0.863975	+	0.503534i	$0.832033\pi$
$648$	−5.22212	−0.205144
$649$	−0.0643426	−0.00252567
$650$	0	0
$651$	−7.89881	−0.309579
$652$	10.6398	0.416688
$653$	14.9717	0.585888	0.292944	−	0.956130i	$-0.405365\pi$
$653$	14.9717	0.585888	0.292944	+	0.956130i	$0.405365\pi$
$654$	−2.55553	−0.0999292
$655$	0	0
$656$	−23.8494	−0.931162
$657$	25.3559	0.989226
$658$	0.559036	0.0217935
$659$	37.4621	1.45932	0.729658	−	0.683812i	$-0.239679\pi$
$659$	37.4621	1.45932	0.729658	+	0.683812i	$0.239679\pi$
$660$	0	0
$661$	−7.96608	−0.309844	−0.154922	−	0.987927i	$-0.549513\pi$
$661$	−7.96608	−0.309844	−0.154922	+	0.987927i	$0.549513\pi$
$662$	5.43247	0.211139
$663$	−14.6044	−0.567187
$664$	−14.5830	−0.565931
$665$	0	0
$666$	−6.53711	−0.253308
$667$	−33.8911	−1.31227
$668$	−29.4565	−1.13970
$669$	6.90444	0.266941
$670$	0	0
$671$	−9.30219	−0.359107
$672$	2.26826	0.0875002
$673$	−24.5294	−0.945537	−0.472769	−	0.881187i	$-0.656745\pi$
$673$	−24.5294	−0.945537	−0.472769	+	0.881187i	$0.656745\pi$
$674$	2.25897	0.0870123
$675$	0	0
$676$	10.4204	0.400785
$677$	23.9971	0.922283	0.461141	−	0.887327i	$-0.347440\pi$
$677$	23.9971	0.922283	0.461141	+	0.887327i	$0.347440\pi$
$678$	5.14440	0.197570
$679$	2.75441	0.105704
$680$	0	0
$681$	−10.9738	−0.420518
$682$	−4.10331	−0.157124
$683$	33.3219	1.27503	0.637514	−	0.770439i	$-0.279963\pi$
$683$	33.3219	1.27503	0.637514	+	0.770439i	$0.279963\pi$
$684$	−32.6199	−1.24725
$685$	0	0
$686$	−1.04460	−0.0398829
$687$	−32.1209	−1.22549
$688$	−3.55553	−0.135553
$689$	−4.00000	−0.152388
$690$	0	0
$691$	17.9221	0.681787	0.340894	−	0.940102i	$-0.389270\pi$
$691$	17.9221	0.681787	0.340894	+	0.940102i	$0.389270\pi$
$692$	−45.9108	−1.74527
$693$	−1.51948	−0.0577205
$694$	−7.50961	−0.285061
$695$	0	0
$696$	−11.9887	−0.454432
$697$	−13.4154	−0.508143
$698$	−1.39987	−0.0529859
$699$	−71.1046	−2.68942
$700$	0	0
$701$	19.1337	0.722671	0.361336	−	0.932436i	$-0.382321\pi$
$701$	19.1337	0.722671	0.361336	+	0.932436i	$0.382321\pi$
$702$	2.05659	0.0776211
$703$	24.9242	0.940033
$704$	−8.61505	−0.324692
$705$	0	0
$706$	−2.64122	−0.0994037
$707$	3.71836	0.139843
$708$	0.238426	0.00896058
$709$	36.2165	1.36014	0.680070	−	0.733148i	$-0.261950\pi$
$709$	36.2165	1.36014	0.680070	+	0.733148i	$0.261950\pi$
$710$	0	0
$711$	−1.13453	−0.0425483
$712$	0.366749	0.0137445
$713$	87.6417	3.28221
$714$	0.397749	0.0148854
$715$	0	0
$716$	15.1111	0.564727
$717$	−55.5003	−2.07270
$718$	−3.17350	−0.118434
$719$	16.3580	0.610050	0.305025	−	0.952344i	$-0.401335\pi$
$719$	16.3580	0.610050	0.305025	+	0.952344i	$0.401335\pi$
$720$	0	0
$721$	−1.20875	−0.0450161
$722$	0.357238	0.0132950
$723$	−4.60437	−0.171238
$724$	22.3233	0.829639
$725$	0	0
$726$	6.61000	0.245320
$727$	−32.9581	−1.22235	−0.611174	−	0.791496i	$-0.709303\pi$
$727$	−32.9581	−1.22235	−0.611174	+	0.791496i	$0.709303\pi$
$728$	0.810998	0.0300576
$729$	−41.2498	−1.52777
$730$	0	0
$731$	−2.00000	−0.0739727
$732$	34.4698	1.27404
$733$	−18.7955	−0.694228	−0.347114	−	0.937823i	$-0.612838\pi$
$733$	−18.7955	−0.694228	−0.347114	+	0.937823i	$0.612838\pi$
$734$	5.90232	0.217858
$735$	0	0
$736$	−25.1677	−0.927692
$737$	13.5654	0.499688
$738$	7.40067	0.272423
$739$	−26.6396	−0.979954	−0.489977	−	0.871735i	$-0.662995\pi$
$739$	−26.6396	−0.979954	−0.489977	+	0.871735i	$0.662995\pi$
$740$	0	0
$741$	−30.7176	−1.12844
$742$	0.108940	0.00399930
$743$	−26.2576	−0.963298	−0.481649	−	0.876364i	$-0.659962\pi$
$743$	−26.2576	−0.963298	−0.481649	+	0.876364i	$0.659962\pi$
$744$	31.0027	1.13661
$745$	0	0
$746$	−8.96395	−0.328194
$747$	−54.6455	−1.99937
$748$	−5.30219	−0.193867
$749$	−3.03897	−0.111042
$750$	0	0
$751$	−24.8265	−0.905932	−0.452966	−	0.891528i	$-0.649634\pi$
$751$	−24.8265	−0.905932	−0.452966	+	0.891528i	$0.649634\pi$
$752$	26.4966	0.966231
$753$	−56.2264	−2.04900
$754$	−3.17350	−0.115572
$755$	0	0
$756$	1.43730	0.0522741
$757$	−23.8590	−0.867172	−0.433586	−	0.901112i	$-0.642752\pi$
$757$	−23.8590	−0.867172	−0.433586	+	0.901112i	$0.642752\pi$
$758$	−2.75521	−0.100074
$759$	29.4154	1.06771
$760$	0	0
$761$	22.0256	0.798427	0.399214	−	0.916858i	$-0.369283\pi$
$761$	22.0256	0.798427	0.399214	+	0.916858i	$0.369283\pi$
$762$	14.3156	0.518598
$763$	−0.963954	−0.0348975
$764$	−48.5264	−1.75562
$765$	0	0
$766$	9.02617	0.326129
$767$	0.128685	0.00464655
$768$	27.3871	0.988246
$769$	−30.8062	−1.11090	−0.555449	−	0.831550i	$-0.687454\pi$
$769$	−30.8062	−1.11090	−0.555449	+	0.831550i	$0.687454\pi$
$770$	0	0
$771$	1.50106	0.0540594
$772$	46.6765	1.67992
$773$	−8.21145	−0.295345	−0.147673	−	0.989036i	$-0.547178\pi$
$773$	−8.21145	−0.295345	−0.147673	+	0.989036i	$0.547178\pi$
$774$	1.10331	0.0396577
$775$	0	0
$776$	−10.8110	−0.388092
$777$	−4.30219	−0.154340
$778$	3.20875	0.115039
$779$	−28.2167	−1.01097
$780$	0	0
$781$	7.30219	0.261293
$782$	−4.41325	−0.157817
$783$	−11.4677	−0.409823
$784$	−24.6220	−0.879357
$785$	0	0
$786$	8.79550	0.313725
$787$	−19.8441	−0.707367	−0.353683	−	0.935365i	$-0.615071\pi$
$787$	−19.8441	−0.707367	−0.353683	+	0.935365i	$0.615071\pi$
$788$	−3.67010	−0.130742
$789$	35.0665	1.24840
$790$	0	0
$791$	1.94048	0.0689957
$792$	5.96395	0.211920
$793$	18.6044	0.660661
$794$	−1.79338	−0.0636445
$795$	0	0
$796$	15.1111	0.535597
$797$	21.2242	0.751801	0.375901	−	0.926660i	$-0.377333\pi$
$797$	21.2242	0.751801	0.375901	+	0.926660i	$0.377333\pi$
$798$	0.836590	0.0296150
$799$	14.9044	0.527281
$800$	0	0
$801$	1.37428	0.0485578
$802$	3.78621	0.133696
$803$	8.66872	0.305912
$804$	−50.2675	−1.77280
$805$	0	0
$806$	8.20662	0.289066
$807$	−8.00775	−0.281886
$808$	−14.5945	−0.513433
$809$	−1.38575	−0.0487205	−0.0243603	−	0.999703i	$-0.507755\pi$
$809$	−1.38575	−0.0487205	−0.0243603	+	0.999703i	$0.507755\pi$
$810$	0	0
$811$	−16.8478	−0.591608	−0.295804	−	0.955249i	$-0.595588\pi$
$811$	−16.8478	−0.591608	−0.295804	+	0.955249i	$0.595588\pi$
$812$	−2.21788	−0.0778323
$813$	−43.3892	−1.52173
$814$	−2.23492	−0.0783339
$815$	0	0
$816$	18.8521	0.659955
$817$	−4.20662	−0.147171
$818$	2.61987	0.0916017
$819$	3.03897	0.106190
$820$	0	0
$821$	−34.4386	−1.20192	−0.600958	−	0.799281i	$-0.705214\pi$
$821$	−34.4386	−1.20192	−0.600958	+	0.799281i	$0.705214\pi$
$822$	−2.97945	−0.103920
$823$	3.72128	0.129716	0.0648579	−	0.997895i	$-0.479341\pi$
$823$	3.72128	0.129716	0.0648579	+	0.997895i	$0.479341\pi$
$824$	4.74431	0.165276
$825$	0	0
$826$	−0.00350473	−0.000121945 0
$827$	18.7331	0.651412	0.325706	−	0.945471i	$-0.394398\pi$
$827$	18.7331	0.651412	0.325706	+	0.945471i	$0.394398\pi$
$828$	−62.4741	−2.17112
$829$	−19.3177	−0.670931	−0.335466	−	0.942052i	$-0.608894\pi$
$829$	−19.3177	−0.670931	−0.335466	+	0.942052i	$0.608894\pi$
$830$	0	0
$831$	−69.2002	−2.40053
$832$	17.2301	0.597346
$833$	−13.8500	−0.479873
$834$	−6.57045	−0.227516
$835$	0	0
$836$	−11.1522	−0.385705
$837$	29.6553	1.02504
$838$	−0.588873	−0.0203423
$839$	52.1174	1.79929	0.899647	−	0.436618i	$-0.143824\pi$
$839$	52.1174	1.79929	0.899647	+	0.436618i	$0.143824\pi$
$840$	0	0
$841$	−11.3043	−0.389804
$842$	6.37216	0.219599
$843$	−72.3318	−2.49124
$844$	−31.0176	−1.06767
$845$	0	0
$846$	−8.22212	−0.282682
$847$	2.49331	0.0856712
$848$	5.16341	0.177312
$849$	67.7763	2.32608
$850$	0	0
$851$	47.7352	1.63634
$852$	−27.0587	−0.927016
$853$	−39.1719	−1.34122	−0.670610	−	0.741810i	$-0.733968\pi$
$853$	−39.1719	−1.34122	−0.670610	+	0.741810i	$0.733968\pi$
$854$	−0.506689	−0.0173385
$855$	0	0
$856$	11.9279	0.407687
$857$	−13.5809	−0.463915	−0.231957	−	0.972726i	$-0.574513\pi$
$857$	−13.5809	−0.463915	−0.231957	+	0.972726i	$0.574513\pi$
$858$	2.75441	0.0940339
$859$	25.2301	0.860840	0.430420	−	0.902629i	$-0.358366\pi$
$859$	25.2301	0.860840	0.430420	+	0.902629i	$0.358366\pi$
$860$	0	0
$861$	4.87051	0.165987
$862$	−5.79067	−0.197231
$863$	−15.1570	−0.515950	−0.257975	−	0.966152i	$-0.583055\pi$
$863$	−15.1570	−0.515950	−0.257975	+	0.966152i	$0.583055\pi$
$864$	−8.51598	−0.289720
$865$	0	0
$866$	4.22717	0.143645
$867$	−34.4642	−1.17047
$868$	5.73540	0.194672
$869$	−0.387876	−0.0131578
$870$	0	0
$871$	−27.1308	−0.919292
$872$	3.78350	0.128126
$873$	−40.5109	−1.37109
$874$	−9.28244	−0.313983
$875$	0	0
$876$	−32.1225	−1.08532
$877$	43.1874	1.45833	0.729167	−	0.684335i	$-0.239908\pi$
$877$	43.1874	1.45833	0.729167	+	0.684335i	$0.239908\pi$
$878$	−0.605174	−0.0204236
$879$	34.0042	1.14693
$880$	0	0
$881$	15.3326	0.516569	0.258284	−	0.966069i	$-0.416843\pi$
$881$	15.3326	0.516569	0.258284	+	0.966069i	$0.416843\pi$
$882$	7.64042	0.257266
$883$	−10.3822	−0.349390	−0.174695	−	0.984623i	$-0.555894\pi$
$883$	−10.3822	−0.349390	−0.174695	+	0.984623i	$0.555894\pi$
$884$	10.6044	0.356664
$885$	0	0
$886$	−4.01550	−0.134903
$887$	−23.6999	−0.795766	−0.397883	−	0.917436i	$-0.630255\pi$
$887$	−23.6999	−0.795766	−0.397883	+	0.917436i	$0.630255\pi$
$888$	16.8860	0.566658
$889$	5.39987	0.181106
$890$	0	0
$891$	−6.69006	−0.224126
$892$	−5.01338	−0.167860
$893$	31.3487	1.04904
$894$	−5.45222	−0.182349
$895$	0	0
$896$	−2.18045	−0.0728438
$897$	−58.8307	−1.96430
$898$	−9.97441	−0.332850
$899$	−45.7608	−1.52621
$900$	0	0
$901$	2.90444	0.0967609
$902$	2.53016	0.0842451
$903$	0.726109	0.0241634
$904$	−7.61637	−0.253317
$905$	0	0
$906$	12.7544	0.423737
$907$	6.36090	0.211210	0.105605	−	0.994408i	$-0.466322\pi$
$907$	6.36090	0.211210	0.105605	+	0.994408i	$0.466322\pi$
$908$	7.96820	0.264434
$909$	−54.6885	−1.81390
$910$	0	0
$911$	−12.7021	−0.420838	−0.210419	−	0.977611i	$-0.567483\pi$
$911$	−12.7021	−0.420838	−0.210419	+	0.977611i	$0.567483\pi$
$912$	39.6518	1.31300
$913$	−18.6823	−0.618294
$914$	10.9071	0.360776
$915$	0	0
$916$	23.3233	0.770624
$917$	3.31769	0.109560
$918$	−1.49331	−0.0492866
$919$	−12.6666	−0.417832	−0.208916	−	0.977934i	$-0.566994\pi$
$919$	−12.6666	−0.417832	−0.208916	+	0.977934i	$0.566994\pi$
$920$	0	0
$921$	−2.20662	−0.0727108
$922$	−3.92711	−0.129332
$923$	−14.6044	−0.480709
$924$	1.92498	0.0633273
$925$	0	0
$926$	−7.33048	−0.240895
$927$	17.7779	0.583902
$928$	13.1409	0.431371
$929$	−12.1853	−0.399786	−0.199893	−	0.979818i	$-0.564059\pi$
$929$	−12.1853	−0.399786	−0.199893	+	0.979818i	$0.564059\pi$
$930$	0	0
$931$	−29.1308	−0.954724
$932$	51.6297	1.69119
$933$	71.5024	2.34088
$934$	−5.28244	−0.172847
$935$	0	0
$936$	−11.9279	−0.389876
$937$	28.9759	0.946603	0.473301	−	0.880901i	$-0.343062\pi$
$937$	28.9759	0.946603	0.473301	+	0.880901i	$0.343062\pi$
$938$	0.738906	0.0241261
$939$	8.97383	0.292850
$940$	0	0
$941$	16.3353	0.532516	0.266258	−	0.963902i	$-0.414213\pi$
$941$	16.3353	0.532516	0.266258	+	0.963902i	$0.414213\pi$
$942$	−13.8839	−0.452362
$943$	−54.0411	−1.75982
$944$	−0.166114	−0.00540654
$945$	0	0
$946$	0.377203	0.0122639
$947$	−0.925785	−0.0300840	−0.0150420	−	0.999887i	$-0.504788\pi$
$947$	−0.925785	−0.0300840	−0.0150420	+	0.999887i	$0.504788\pi$
$948$	1.43730	0.0466813
$949$	−17.3374	−0.562797
$950$	0	0
$951$	−24.2632	−0.786789
$952$	−0.588873	−0.0190855
$953$	5.25467	0.170215	0.0851077	−	0.996372i	$-0.472877\pi$
$953$	5.25467	0.170215	0.0851077	+	0.996372i	$0.472877\pi$
$954$	−1.60225	−0.0518748
$955$	0	0
$956$	40.2993	1.30337
$957$	−15.3588	−0.496479
$958$	8.15720	0.263547
$959$	−1.12386	−0.0362913
$960$	0	0
$961$	87.3366	2.81731
$962$	4.46984	0.144113
$963$	44.6962	1.44032
$964$	3.34328	0.107680
$965$	0	0
$966$	1.60225	0.0515516
$967$	−36.1911	−1.16383	−0.581914	−	0.813250i	$-0.697696\pi$
$967$	−36.1911	−1.16383	−0.581914	+	0.813250i	$0.697696\pi$
$968$	−9.78621	−0.314541
$969$	22.3043	0.716518
$970$	0	0
$971$	−28.9349	−0.928564	−0.464282	−	0.885687i	$-0.653688\pi$
$971$	−28.9349	−0.928564	−0.464282	+	0.885687i	$0.653688\pi$
$972$	40.5336	1.30012
$973$	−2.47839	−0.0794536
$974$	7.30219	0.233977
$975$	0	0
$976$	−24.0155	−0.768717
$977$	−3.47781	−0.111265	−0.0556325	−	0.998451i	$-0.517718\pi$
$977$	−3.47781	−0.111265	−0.0556325	+	0.998451i	$0.517718\pi$
$978$	4.01338	0.128334
$979$	0.469842	0.0150162
$980$	0	0
$981$	14.1775	0.452654
$982$	−3.00637	−0.0959371
$983$	−42.6623	−1.36072	−0.680358	−	0.732880i	$-0.738176\pi$
$983$	−42.6623	−1.36072	−0.680358	+	0.732880i	$0.738176\pi$
$984$	−19.1167	−0.609418
$985$	0	0
$986$	2.30431	0.0733842
$987$	−5.41113	−0.172238
$988$	22.3043	0.709595
$989$	−8.05659	−0.256185
$990$	0	0
$991$	15.3022	0.486090	0.243045	−	0.970015i	$-0.421854\pi$
$991$	15.3022	0.486090	0.243045	+	0.970015i	$0.421854\pi$
$992$	−33.9822	−1.07893
$993$	−52.5830	−1.66867
$994$	0.397749	0.0126158
$995$	0	0
$996$	69.2285	2.19359
$997$	−35.6970	−1.13054	−0.565268	−	0.824907i	$-0.691227\pi$
$997$	−35.6970	−1.13054	−0.565268	+	0.824907i	$0.691227\pi$
$998$	−0.588873	−0.0186405
$999$	16.1522	0.511032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.k.1.2		3
3.2	odd	2		9675.2.a.br.1.2		3
5.2	odd	4		215.2.b.a.44.3	✓	6
5.3	odd	4		215.2.b.a.44.4	yes	6
5.4	even	2		1075.2.a.j.1.2		3
15.2	even	4		1935.2.b.c.1549.4		6
15.8	even	4		1935.2.b.c.1549.3		6
15.14	odd	2		9675.2.a.bt.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.b.a.44.3	✓	6	5.2	odd	4
215.2.b.a.44.4	yes	6	5.3	odd	4
1075.2.a.j.1.2		3	5.4	even	2
1075.2.a.k.1.2		3	1.1	even	1	trivial
1935.2.b.c.1549.3		6	15.8	even	4
1935.2.b.c.1549.4		6	15.2	even	4
9675.2.a.br.1.2		3	3.2	odd	2
9675.2.a.bt.1.2		3	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-0.273891 q^{2} +2.65109 q^{3} -1.92498 q^{4} -0.726109 q^{6} -0.273891 q^{7} +1.07502 q^{8} +4.02830 q^{9} +O(q^{10})\)	\(q-0.273891 q^{2} +2.65109 q^{3} -1.92498 q^{4} -0.726109 q^{6} -0.273891 q^{7} +1.07502 q^{8} +4.02830 q^{9} +1.37720 q^{11} -5.10331 q^{12} -2.75441 q^{13} +0.0750160 q^{14} +3.55553 q^{16} +2.00000 q^{17} -1.10331 q^{18} +4.20662 q^{19} -0.726109 q^{21} -0.377203 q^{22} +8.05659 q^{23} +2.84997 q^{24} +0.754406 q^{26} +2.72611 q^{27} +0.527235 q^{28} -4.20662 q^{29} +10.8783 q^{31} -3.12386 q^{32} +3.65109 q^{33} -0.547781 q^{34} -7.75441 q^{36} +5.92498 q^{37} -1.15215 q^{38} -7.30219 q^{39} -6.70769 q^{41} +0.198875 q^{42} -1.00000 q^{43} -2.65109 q^{44} -2.20662 q^{46} +7.45222 q^{47} +9.42605 q^{48} -6.92498 q^{49} +5.30219 q^{51} +5.30219 q^{52} +1.45222 q^{53} -0.746656 q^{54} -0.294437 q^{56} +11.1522 q^{57} +1.15215 q^{58} -0.0467198 q^{59} -6.75441 q^{61} -2.97945 q^{62} -1.10331 q^{63} -6.25547 q^{64} -1.00000 q^{66} +9.84997 q^{67} -3.84997 q^{68} +21.3588 q^{69} +5.30219 q^{71} +4.33048 q^{72} +6.29444 q^{73} -1.62280 q^{74} -8.09768 q^{76} -0.377203 q^{77} +2.00000 q^{78} -0.281641 q^{79} -4.85772 q^{81} +1.83717 q^{82} -13.5654 q^{83} +1.39775 q^{84} +0.273891 q^{86} -11.1522 q^{87} +1.48052 q^{88} +0.341157 q^{89} +0.754406 q^{91} -15.5088 q^{92} +28.8393 q^{93} -2.04109 q^{94} -8.28164 q^{96} -10.0566 q^{97} +1.89669 q^{98} +5.54778 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 3 q^{4} - 4 q^{6} + q^{7} + 12 q^{8}+O(q^{10}) \) 3 * q + q^2 + q^3 + 3 * q^4 - 4 * q^6 + q^7 + 12 * q^8	\( 3 q + q^{2} + q^{3} + 3 q^{4} - 4 q^{6} + q^{7} + 12 q^{8} - q^{11} - 12 q^{12} + 2 q^{13} + 9 q^{14} + 11 q^{16} + 6 q^{17} + 6 q^{19} - 4 q^{21} + 4 q^{22} - 9 q^{24} - 8 q^{26} + 10 q^{27} + 14 q^{28} - 6 q^{29} + 3 q^{31} + 10 q^{32} + 4 q^{33} + 2 q^{34} - 13 q^{36} + 9 q^{37} + 28 q^{38} - 8 q^{39} + 11 q^{41} - 10 q^{42} - 3 q^{43} - q^{44} + 26 q^{47} - 5 q^{48} - 12 q^{49} + 2 q^{51} + 2 q^{52} + 8 q^{53} + 12 q^{54} + 17 q^{56} + 2 q^{57} - 28 q^{58} - 21 q^{59} - 10 q^{61} - 25 q^{62} + 16 q^{64} - 3 q^{66} + 12 q^{67} + 6 q^{68} + 26 q^{69} + 2 q^{71} - 13 q^{72} + q^{73} - 10 q^{74} + 32 q^{76} + 4 q^{77} + 6 q^{78} - 3 q^{79} - q^{81} + 8 q^{82} + 4 q^{83} - 17 q^{84} - q^{86} - 2 q^{87} - 4 q^{88} + 4 q^{89} - 8 q^{91} - 26 q^{92} + 40 q^{93} + 26 q^{94} - 27 q^{96} - 6 q^{97} + 9 q^{98} + 13 q^{99}+O(q^{100}) \) 3 * q + q^2 + q^3 + 3 * q^4 - 4 * q^6 + q^7 + 12 * q^8 - q^11 - 12 * q^12 + 2 * q^13 + 9 * q^14 + 11 * q^16 + 6 * q^17 + 6 * q^19 - 4 * q^21 + 4 * q^22 - 9 * q^24 - 8 * q^26 + 10 * q^27 + 14 * q^28 - 6 * q^29 + 3 * q^31 + 10 * q^32 + 4 * q^33 + 2 * q^34 - 13 * q^36 + 9 * q^37 + 28 * q^38 - 8 * q^39 + 11 * q^41 - 10 * q^42 - 3 * q^43 - q^44 + 26 * q^47 - 5 * q^48 - 12 * q^49 + 2 * q^51 + 2 * q^52 + 8 * q^53 + 12 * q^54 + 17 * q^56 + 2 * q^57 - 28 * q^58 - 21 * q^59 - 10 * q^61 - 25 * q^62 + 16 * q^64 - 3 * q^66 + 12 * q^67 + 6 * q^68 + 26 * q^69 + 2 * q^71 - 13 * q^72 + q^73 - 10 * q^74 + 32 * q^76 + 4 * q^77 + 6 * q^78 - 3 * q^79 - q^81 + 8 * q^82 + 4 * q^83 - 17 * q^84 - q^86 - 2 * q^87 - 4 * q^88 + 4 * q^89 - 8 * q^91 - 26 * q^92 + 40 * q^93 + 26 * q^94 - 27 * q^96 - 6 * q^97 + 9 * q^98 + 13 * q^99

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