LMFDB - Embedded newform 1075.2.a.j.1.1

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:	$1$
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			1.1
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)

$f(q)$	$=$	$q-2.65109 q^{2} +1.37720 q^{3} +5.02830 q^{4} -3.65109 q^{6} -2.65109 q^{7} -8.02830 q^{8} -1.10331 q^{9} +O(q^{10})$	\(q-2.65109 q^{2} +1.37720 q^{3} +5.02830 q^{4} -3.65109 q^{6} -2.65109 q^{7} -8.02830 q^{8} -1.10331 q^{9} +0.273891 q^{11} +6.92498 q^{12} +0.547781 q^{13} +7.02830 q^{14} +11.2272 q^{16} -2.00000 q^{17} +2.92498 q^{18} +7.84997 q^{19} -3.65109 q^{21} -0.726109 q^{22} +2.20662 q^{23} -11.0566 q^{24} -1.45222 q^{26} -5.65109 q^{27} -13.3305 q^{28} -7.84997 q^{29} -8.15990 q^{31} -13.7077 q^{32} +0.377203 q^{33} +5.30219 q^{34} -5.54778 q^{36} +1.02830 q^{37} -20.8110 q^{38} +0.754406 q^{39} +7.58383 q^{41} +9.67939 q^{42} +1.00000 q^{43} +1.37720 q^{44} -5.84997 q^{46} -13.3022 q^{47} +15.4621 q^{48} +0.0282963 q^{49} -2.75441 q^{51} +2.75441 q^{52} -7.30219 q^{53} +14.9816 q^{54} +21.2838 q^{56} +10.8110 q^{57} +20.8110 q^{58} -12.1316 q^{59} -4.54778 q^{61} +21.6327 q^{62} +2.92498 q^{63} +13.8860 q^{64} -1.00000 q^{66} +4.05659 q^{67} -10.0566 q^{68} +3.03897 q^{69} -2.75441 q^{71} +8.85772 q^{72} +15.2838 q^{73} -2.72611 q^{74} +39.4720 q^{76} -0.726109 q^{77} -2.00000 q^{78} -10.8783 q^{79} -4.47277 q^{81} -20.1054 q^{82} -1.11106 q^{83} -18.3588 q^{84} -2.65109 q^{86} -10.8110 q^{87} -2.19887 q^{88} -9.15215 q^{89} -1.45222 q^{91} +11.0956 q^{92} -11.2378 q^{93} +35.2653 q^{94} -18.8783 q^{96} -0.206625 q^{97} -0.0750160 q^{98} -0.302187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65109	−1.87461	−0.937303	−	0.348515i	$-0.886686\pi$
$2$	−2.65109	−1.87461	−0.937303	+	0.348515i	$0.886686\pi$
$3$	1.37720	0.795128	0.397564	−	0.917574i	$-0.369856\pi$
$3$	1.37720	0.795128	0.397564	+	0.917574i	$0.369856\pi$
$4$	5.02830	2.51415
$5$	0	0
$5$	0	0
$6$	−3.65109	−1.49055
$7$	−2.65109	−1.00202	−0.501010	−	0.865442i	$-0.667038\pi$
$7$	−2.65109	−1.00202	−0.501010	+	0.865442i	$0.667038\pi$
$8$	−8.02830	−2.83843
$9$	−1.10331	−0.367771
$10$	0	0
$11$	0.273891	0.0825811	0.0412906	−	0.999147i	$-0.486853\pi$
$11$	0.273891	0.0825811	0.0412906	+	0.999147i	$0.486853\pi$
$12$	6.92498	1.99907
$13$	0.547781	0.151927	0.0759636	−	0.997111i	$-0.475797\pi$
$13$	0.547781	0.151927	0.0759636	+	0.997111i	$0.475797\pi$
$14$	7.02830	1.87839
$15$	0	0
$16$	11.2272	2.80679
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	2.92498	0.689425
$19$	7.84997	1.80091	0.900453	−	0.434953i	$-0.143235\pi$
$19$	7.84997	1.80091	0.900453	+	0.434953i	$0.143235\pi$
$20$	0	0
$21$	−3.65109	−0.796734
$22$	−0.726109	−0.154807
$23$	2.20662	0.460113	0.230057	−	0.973177i	$-0.426109\pi$
$23$	2.20662	0.460113	0.230057	+	0.973177i	$0.426109\pi$
$24$	−11.0566	−2.25692
$25$	0	0
$26$	−1.45222	−0.284804
$27$	−5.65109	−1.08755
$28$	−13.3305	−2.51922
$29$	−7.84997	−1.45770	−0.728851	−	0.684672i	$-0.759945\pi$
$29$	−7.84997	−1.45770	−0.728851	+	0.684672i	$0.759945\pi$
$30$	0	0
$31$	−8.15990	−1.46556	−0.732781	−	0.680464i	$-0.761778\pi$
$31$	−8.15990	−1.46556	−0.732781	+	0.680464i	$0.761778\pi$
$32$	−13.7077	−2.42320
$33$	0.377203	0.0656626
$34$	5.30219	0.909318
$35$	0	0
$36$	−5.54778	−0.924630
$37$	1.02830	0.169051	0.0845254	−	0.996421i	$-0.473063\pi$
$37$	1.02830	0.169051	0.0845254	+	0.996421i	$0.473063\pi$
$38$	−20.8110	−3.37599
$39$	0.754406	0.120802
$40$	0	0
$41$	7.58383	1.18439	0.592197	−	0.805793i	$-0.298261\pi$
$41$	7.58383	1.18439	0.592197	+	0.805793i	$0.298261\pi$
$42$	9.67939	1.49356
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.37720	0.207621
$45$	0	0
$46$	−5.84997	−0.862531
$47$	−13.3022	−1.94032	−0.970162	−	0.242459i	$-0.922046\pi$
$47$	−13.3022	−1.94032	−0.970162	+	0.242459i	$0.922046\pi$
$48$	15.4621	2.23176
$49$	0.0282963	0.00404232
$50$	0	0
$51$	−2.75441	−0.385694
$52$	2.75441	0.381967
$53$	−7.30219	−1.00303	−0.501516	−	0.865148i	$-0.667224\pi$
$53$	−7.30219	−1.00303	−0.501516	+	0.865148i	$0.667224\pi$
$54$	14.9816	2.03873
$55$	0	0
$56$	21.2838	2.84416
$57$	10.8110	1.43195
$58$	20.8110	2.73262
$59$	−12.1316	−1.57940	−0.789700	−	0.613493i	$-0.789764\pi$
$59$	−12.1316	−1.57940	−0.789700	+	0.613493i	$0.789764\pi$
$60$	0	0
$61$	−4.54778	−0.582284	−0.291142	−	0.956680i	$-0.594035\pi$
$61$	−4.54778	−0.582284	−0.291142	+	0.956680i	$0.594035\pi$
$62$	21.6327	2.74735
$63$	2.92498	0.368513
$64$	13.8860	1.73575
$65$	0	0
$66$	−1.00000	−0.123091
$67$	4.05659	0.495592	0.247796	−	0.968812i	$-0.420294\pi$
$67$	4.05659	0.495592	0.247796	+	0.968812i	$0.420294\pi$
$68$	−10.0566	−1.21954
$69$	3.03897	0.365849
$70$	0	0
$71$	−2.75441	−0.326888	−0.163444	−	0.986553i	$-0.552260\pi$
$71$	−2.75441	−0.326888	−0.163444	+	0.986553i	$0.552260\pi$
$72$	8.85772	1.04389
$73$	15.2838	1.78883	0.894415	−	0.447239i	$-0.147593\pi$
$73$	15.2838	1.78883	0.894415	+	0.447239i	$0.147593\pi$
$74$	−2.72611	−0.316904
$75$	0	0
$76$	39.4720	4.52774
$77$	−0.726109	−0.0827479
$78$	−2.00000	−0.226455
$79$	−10.8783	−1.22390	−0.611950	−	0.790896i	$-0.709615\pi$
$79$	−10.8783	−1.22390	−0.611950	+	0.790896i	$0.709615\pi$
$80$	0	0
$81$	−4.47277	−0.496974
$82$	−20.1054	−2.22027
$83$	−1.11106	−0.121955	−0.0609775	−	0.998139i	$-0.519422\pi$
$83$	−1.11106	−0.121955	−0.0609775	+	0.998139i	$0.519422\pi$
$84$	−18.3588	−2.00311
$85$	0	0
$86$	−2.65109	−0.285875
$87$	−10.8110	−1.15906
$88$	−2.19887	−0.234401
$89$	−9.15215	−0.970126	−0.485063	−	0.874479i	$-0.661203\pi$
$89$	−9.15215	−0.970126	−0.485063	+	0.874479i	$0.661203\pi$
$90$	0	0
$91$	−1.45222	−0.152234
$92$	11.0956	1.15679
$93$	−11.2378	−1.16531
$94$	35.2653	3.63734
$95$	0	0
$96$	−18.8783	−1.92675
$97$	−0.206625	−0.0209795	−0.0104898	−	0.999945i	$-0.503339\pi$
$97$	−0.206625	−0.0209795	−0.0104898	+	0.999945i	$0.503339\pi$
$98$	−0.0750160	−0.00757776
$99$	−0.302187	−0.0303709
$100$	0	0
$101$	−2.59450	−0.258162	−0.129081	−	0.991634i	$-0.541203\pi$
$101$	−2.59450	−0.258162	−0.129081	+	0.991634i	$0.541203\pi$
$102$	7.30219	0.723024
$103$	−11.6999	−1.15283	−0.576414	−	0.817157i	$-0.695549\pi$
$103$	−11.6999	−1.15283	−0.576414	+	0.817157i	$0.695549\pi$
$104$	−4.39775	−0.431235
$105$	0	0
$106$	19.3588	1.88029
$107$	0.604374	0.0584270	0.0292135	−	0.999573i	$-0.490700\pi$
$107$	0.604374	0.0584270	0.0292135	+	0.999573i	$0.490700\pi$
$108$	−28.4154	−2.73427
$109$	2.80113	0.268299	0.134150	−	0.990961i	$-0.457170\pi$
$109$	2.80113	0.268299	0.134150	+	0.990961i	$0.457170\pi$
$110$	0	0
$111$	1.41617	0.134417
$112$	−29.7643	−2.81246
$113$	−8.30994	−0.781733	−0.390867	−	0.920447i	$-0.627825\pi$
$113$	−8.30994	−0.781733	−0.390867	+	0.920447i	$0.627825\pi$
$114$	−28.6610	−2.68435
$115$	0	0
$116$	−39.4720	−3.66488
$117$	−0.604374	−0.0558744
$118$	32.1620	2.96075
$119$	5.30219	0.486051
$120$	0	0
$121$	−10.9250	−0.993180
$122$	12.0566	1.09155
$123$	10.4445	0.941746
$124$	−41.0304	−3.68464
$125$	0	0
$126$	−7.75441	−0.690817
$127$	18.9455	1.68114	0.840572	−	0.541700i	$-0.182219\pi$
$127$	18.9455	1.68114	0.840572	+	0.541700i	$0.182219\pi$
$128$	−9.39775	−0.830652
$129$	1.37720	0.121256
$130$	0	0
$131$	8.41325	0.735069	0.367534	−	0.930010i	$-0.380202\pi$
$131$	8.41325	0.735069	0.367534	+	0.930010i	$0.380202\pi$
$132$	1.89669	0.165085
$133$	−20.8110	−1.80454
$134$	−10.7544	−0.929039
$135$	0	0
$136$	16.0566	1.37684
$137$	−5.92498	−0.506206	−0.253103	−	0.967439i	$-0.581451\pi$
$137$	−5.92498	−0.506206	−0.253103	+	0.967439i	$0.581451\pi$
$138$	−8.05659	−0.685823
$139$	−14.7360	−1.24989	−0.624945	−	0.780669i	$-0.714879\pi$
$139$	−14.7360	−1.24989	−0.624945	+	0.780669i	$0.714879\pi$
$140$	0	0
$141$	−18.3198	−1.54281
$142$	7.30219	0.612786
$143$	0.150032	0.0125463
$144$	−12.3871	−1.03226
$145$	0	0
$146$	−40.5187	−3.35335
$147$	0.0389697	0.00321417
$148$	5.17058	0.425019
$149$	3.09556	0.253598	0.126799	−	0.991928i	$-0.459530\pi$
$149$	3.09556	0.253598	0.126799	+	0.991928i	$0.459530\pi$
$150$	0	0
$151$	−2.88894	−0.235098	−0.117549	−	0.993067i	$-0.537504\pi$
$151$	−2.88894	−0.235098	−0.117549	+	0.993067i	$0.537504\pi$
$152$	−63.0219	−5.11175
$153$	2.20662	0.178395
$154$	1.92498	0.155120
$155$	0	0
$156$	3.79338	0.303713
$157$	−12.1161	−0.966971	−0.483485	−	0.875352i	$-0.660629\pi$
$157$	−12.1161	−0.966971	−0.483485	+	0.875352i	$0.660629\pi$
$158$	28.8393	2.29433
$159$	−10.0566	−0.797540
$160$	0	0
$161$	−5.84997	−0.461042
$162$	11.8577	0.931630
$163$	18.3305	1.43575	0.717877	−	0.696170i	$-0.245114\pi$
$163$	18.3305	1.43575	0.717877	+	0.696170i	$0.245114\pi$
$164$	38.1337	2.97774
$165$	0	0
$166$	2.94553	0.228617
$167$	−7.24559	−0.560681	−0.280340	−	0.959901i	$-0.590447\pi$
$167$	−7.24559	−0.560681	−0.280340	+	0.959901i	$0.590447\pi$
$168$	29.3121	2.26147
$169$	−12.6999	−0.976918
$170$	0	0
$171$	−8.66097	−0.662321
$172$	5.02830	0.383404
$173$	−9.94341	−0.755983	−0.377992	−	0.925809i	$-0.623385\pi$
$173$	−9.94341	−0.755983	−0.377992	+	0.925809i	$0.623385\pi$
$174$	28.6610	2.17278
$175$	0	0
$176$	3.07502	0.231788
$177$	−16.7077	−1.25583
$178$	24.2632	1.81861
$179$	6.05659	0.452691	0.226345	−	0.974047i	$-0.427322\pi$
$179$	6.05659	0.452691	0.226345	+	0.974047i	$0.427322\pi$
$180$	0	0
$181$	18.0382	1.34077	0.670383	−	0.742015i	$-0.266130\pi$
$181$	18.0382	1.34077	0.670383	+	0.742015i	$0.266130\pi$
$182$	3.84997	0.285379
$183$	−6.26322	−0.462990
$184$	−17.7154	−1.30600
$185$	0	0
$186$	29.7926	2.18450
$187$	−0.547781	−0.0400577
$188$	−66.8873	−4.87826
$189$	14.9816	1.08975
$190$	0	0
$191$	−7.01762	−0.507777	−0.253889	−	0.967233i	$-0.581710\pi$
$191$	−7.01762	−0.507777	−0.253889	+	0.967233i	$0.581710\pi$
$192$	19.1239	1.38015
$193$	−9.41537	−0.677733	−0.338867	−	0.940834i	$-0.610044\pi$
$193$	−9.41537	−0.677733	−0.338867	+	0.940834i	$0.610044\pi$
$194$	0.547781	0.0393284
$195$	0	0
$196$	0.142282	0.0101630
$197$	22.2632	1.58619	0.793094	−	0.609099i	$-0.208469\pi$
$197$	22.2632	1.58619	0.793094	+	0.609099i	$0.208469\pi$
$198$	0.801125	0.0569335
$199$	6.05659	0.429340	0.214670	−	0.976687i	$-0.431132\pi$
$199$	6.05659	0.429340	0.214670	+	0.976687i	$0.431132\pi$
$200$	0	0
$201$	5.58675	0.394059
$202$	6.87826	0.483953
$203$	20.8110	1.46065
$204$	−13.8500	−0.969692
$205$	0	0
$206$	31.0176	2.16110
$207$	−2.43460	−0.169216
$208$	6.15003	0.426428
$209$	2.15003	0.148721
$210$	0	0
$211$	−4.41325	−0.303821	−0.151910	−	0.988394i	$-0.548542\pi$
$211$	−4.41325	−0.303821	−0.151910	+	0.988394i	$0.548542\pi$
$212$	−36.7176	−2.52177
$213$	−3.79338	−0.259918
$214$	−1.60225	−0.109528
$215$	0	0
$216$	45.3687	3.08695
$217$	21.6327	1.46852
$218$	−7.42605	−0.502955
$219$	21.0488	1.42235
$220$	0	0
$221$	−1.09556	−0.0736955
$222$	−3.75441	−0.251979
$223$	13.5088	0.904617	0.452308	−	0.891862i	$-0.350601\pi$
$223$	13.5088	0.904617	0.452308	+	0.891862i	$0.350601\pi$
$224$	36.3404	2.42809
$225$	0	0
$226$	22.0304	1.46544
$227$	14.3510	0.952511	0.476256	−	0.879307i	$-0.341994\pi$
$227$	14.3510	0.952511	0.476256	+	0.879307i	$0.341994\pi$
$228$	54.3609	3.60014
$229$	18.2370	1.20514	0.602569	−	0.798067i	$-0.294144\pi$
$229$	18.2370	1.20514	0.602569	+	0.798067i	$0.294144\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	63.0219	4.13759
$233$	−7.99708	−0.523906	−0.261953	−	0.965081i	$-0.584367\pi$
$233$	−7.99708	−0.523906	−0.261953	+	0.965081i	$0.584367\pi$
$234$	1.60225	0.104742
$235$	0	0
$236$	−61.0013	−3.97085
$237$	−14.9816	−0.973158
$238$	−14.0566	−0.911154
$239$	8.36653	0.541186	0.270593	−	0.962694i	$-0.412780\pi$
$239$	8.36653	0.541186	0.270593	+	0.962694i	$0.412780\pi$
$240$	0	0
$241$	−8.35666	−0.538300	−0.269150	−	0.963098i	$-0.586743\pi$
$241$	−8.35666	−0.538300	−0.269150	+	0.963098i	$0.586743\pi$
$242$	28.9632	1.86182
$243$	10.7934	0.692395
$244$	−22.8676	−1.46395
$245$	0	0
$246$	−27.6893	−1.76540
$247$	4.30006	0.273607
$248$	65.5101	4.15990
$249$	−1.53016	−0.0969698
$250$	0	0
$251$	11.0176	0.695426	0.347713	−	0.937601i	$-0.386958\pi$
$251$	11.0176	0.695426	0.347713	+	0.937601i	$0.386958\pi$
$252$	14.7077	0.926497
$253$	0.604374	0.0379966
$254$	−50.2264	−3.15148
$255$	0	0
$256$	−2.85772	−0.178607
$257$	−11.9327	−0.744343	−0.372172	−	0.928164i	$-0.621387\pi$
$257$	−11.9327	−0.744343	−0.372172	+	0.928164i	$0.621387\pi$
$258$	−3.65109	−0.227307
$259$	−2.72611	−0.169392
$260$	0	0
$261$	8.66097	0.536100
$262$	−22.3043	−1.37796
$263$	1.78270	0.109926	0.0549631	−	0.998488i	$-0.482496\pi$
$263$	1.78270	0.109926	0.0549631	+	0.998488i	$0.482496\pi$
$264$	−3.02830	−0.186379
$265$	0	0
$266$	55.1719	3.38281
$267$	−12.6044	−0.771375
$268$	20.3977	1.24599
$269$	15.6327	0.953141	0.476570	−	0.879136i	$-0.341880\pi$
$269$	15.6327	0.953141	0.476570	+	0.879136i	$0.341880\pi$
$270$	0	0
$271$	−11.5683	−0.702726	−0.351363	−	0.936239i	$-0.614282\pi$
$271$	−11.5683	−0.702726	−0.351363	+	0.936239i	$0.614282\pi$
$272$	−22.4543	−1.36149
$273$	−2.00000	−0.121046
$274$	15.7077	0.948936
$275$	0	0
$276$	15.2808	0.919798
$277$	1.88119	0.113030	0.0565148	−	0.998402i	$-0.482001\pi$
$277$	1.88119	0.113030	0.0565148	+	0.998402i	$0.482001\pi$
$278$	39.0665	2.34305
$279$	9.00292	0.538991
$280$	0	0
$281$	−2.01067	−0.119947	−0.0599734	−	0.998200i	$-0.519102\pi$
$281$	−2.01067	−0.119947	−0.0599734	+	0.998200i	$0.519102\pi$
$282$	48.5675	2.89215
$283$	−10.8889	−0.647280	−0.323640	−	0.946180i	$-0.604907\pi$
$283$	−10.8889	−0.647280	−0.323640	+	0.946180i	$0.604907\pi$
$284$	−13.8500	−0.821844
$285$	0	0
$286$	−0.397749	−0.0235194
$287$	−20.1054	−1.18679
$288$	15.1239	0.891182
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−0.284564	−0.0166814
$292$	76.8513	4.49738
$293$	−27.3999	−1.60072	−0.800359	−	0.599521i	$-0.795358\pi$
$293$	−27.3999	−1.60072	−0.800359	+	0.599521i	$0.795358\pi$
$294$	−0.103312	−0.00602530
$295$	0	0
$296$	−8.25547	−0.479839
$297$	−1.54778	−0.0898114
$298$	−8.20662	−0.475397
$299$	1.20875	0.0699037
$300$	0	0
$301$	−2.65109	−0.152806
$302$	7.65884	0.440717
$303$	−3.57315	−0.205272
$304$	88.1329	5.05477
$305$	0	0
$306$	−5.84997	−0.334420
$307$	−4.24772	−0.242430	−0.121215	−	0.992626i	$-0.538679\pi$
$307$	−4.24772	−0.242430	−0.121215	+	0.992626i	$0.538679\pi$
$308$	−3.65109	−0.208040
$309$	−16.1132	−0.916647
$310$	0	0
$311$	6.05952	0.343604	0.171802	−	0.985132i	$-0.445041\pi$
$311$	6.05952	0.343604	0.171802	+	0.985132i	$0.445041\pi$
$312$	−6.05659	−0.342887
$313$	−15.8032	−0.893252	−0.446626	−	0.894721i	$-0.647375\pi$
$313$	−15.8032	−0.893252	−0.446626	+	0.894721i	$0.647375\pi$
$314$	32.1209	1.81269
$315$	0	0
$316$	−54.6991	−3.07707
$317$	−12.8110	−0.719537	−0.359769	−	0.933042i	$-0.617144\pi$
$317$	−12.8110	−0.719537	−0.359769	+	0.933042i	$0.617144\pi$
$318$	26.6610	1.49507
$319$	−2.15003	−0.120379
$320$	0	0
$321$	0.832345	0.0464570
$322$	15.5088	0.864272
$323$	−15.6999	−0.873568
$324$	−22.4904	−1.24947
$325$	0	0
$326$	−48.5958	−2.69147
$327$	3.85772	0.213332
$328$	−60.8852	−3.36182
$329$	35.2653	1.94424
$330$	0	0
$331$	21.1153	1.16060	0.580301	−	0.814402i	$-0.302935\pi$
$331$	21.1153	1.16060	0.580301	+	0.814402i	$0.302935\pi$
$332$	−5.58675	−0.306613
$333$	−1.13453	−0.0621720
$334$	19.2087	1.05106
$335$	0	0
$336$	−40.9914	−2.23627
$337$	−25.4154	−1.38446	−0.692232	−	0.721675i	$-0.743372\pi$
$337$	−25.4154	−1.38446	−0.692232	+	0.721675i	$0.743372\pi$
$338$	33.6687	1.83134
$339$	−11.4445	−0.621578
$340$	0	0
$341$	−2.23492	−0.121028
$342$	22.9610	1.24159
$343$	18.4826	0.997969
$344$	−8.02830	−0.432857
$345$	0	0
$346$	26.3609	1.41717
$347$	10.9914	0.590052	0.295026	−	0.955489i	$-0.404672\pi$
$347$	10.9914	0.590052	0.295026	+	0.955489i	$0.404672\pi$
$348$	−54.3609	−2.91405
$349$	20.4543	1.09490	0.547448	−	0.836840i	$-0.315599\pi$
$349$	20.4543	1.09490	0.547448	+	0.836840i	$0.315599\pi$
$350$	0	0
$351$	−3.09556	−0.165229
$352$	−3.75441	−0.200110
$353$	7.90656	0.420824	0.210412	−	0.977613i	$-0.432519\pi$
$353$	7.90656	0.420824	0.210412	+	0.977613i	$0.432519\pi$
$354$	44.2936	2.35418
$355$	0	0
$356$	−46.0197	−2.43904
$357$	7.30219	0.386473
$358$	−16.0566	−0.848617
$359$	4.30006	0.226949	0.113474	−	0.993541i	$-0.463802\pi$
$359$	4.30006	0.226949	0.113474	+	0.993541i	$0.463802\pi$
$360$	0	0
$361$	42.6220	2.24326
$362$	−47.8209	−2.51341
$363$	−15.0459	−0.789706
$364$	−7.30219	−0.382739
$365$	0	0
$366$	16.6044	0.867925
$367$	−20.1698	−1.05285	−0.526427	−	0.850220i	$-0.676469\pi$
$367$	−20.1698	−1.05285	−0.526427	+	0.850220i	$0.676469\pi$
$368$	24.7742	1.29144
$369$	−8.36733	−0.435586
$370$	0	0
$371$	19.3588	1.00506
$372$	−56.5072	−2.92976
$373$	0.216497	0.0112098	0.00560490	−	0.999984i	$-0.498216\pi$
$373$	0.216497	0.0112098	0.00560490	+	0.999984i	$0.498216\pi$
$374$	1.45222	0.0750925
$375$	0	0
$376$	106.794	5.50747
$377$	−4.30006	−0.221465
$378$	−39.7176	−2.04285
$379$	−10.0304	−0.515228	−0.257614	−	0.966248i	$-0.582936\pi$
$379$	−10.0304	−0.515228	−0.257614	+	0.966248i	$0.582936\pi$
$380$	0	0
$381$	26.0918	1.33673
$382$	18.6044	0.951883
$383$	−14.9992	−0.766423	−0.383212	−	0.923661i	$-0.625182\pi$
$383$	−14.9992	−0.766423	−0.383212	+	0.923661i	$0.625182\pi$
$384$	−12.9426	−0.660475
$385$	0	0
$386$	24.9610	1.27048
$387$	−1.10331	−0.0560845
$388$	−1.03897	−0.0527457
$389$	−10.9455	−0.554960	−0.277480	−	0.960731i	$-0.589499\pi$
$389$	−10.9455	−0.554960	−0.277480	+	0.960731i	$0.589499\pi$
$390$	0	0
$391$	−4.41325	−0.223188
$392$	−0.227171	−0.0114739
$393$	11.5868	0.584474
$394$	−59.0219	−2.97348
$395$	0	0
$396$	−1.51948	−0.0763570
$397$	−0.697813	−0.0350222	−0.0175111	−	0.999847i	$-0.505574\pi$
$397$	−0.697813	−0.0350222	−0.0175111	+	0.999847i	$0.505574\pi$
$398$	−16.0566	−0.804844
$399$	−28.6610	−1.43484
$400$	0	0
$401$	30.8209	1.53912	0.769560	−	0.638574i	$-0.220475\pi$
$401$	30.8209	1.53912	0.769560	+	0.638574i	$0.220475\pi$
$402$	−14.8110	−0.738705
$403$	−4.46984	−0.222659
$404$	−13.0459	−0.649059
$405$	0	0
$406$	−55.1719	−2.73814
$407$	0.281641	0.0139604
$408$	22.1132	1.09477
$409$	5.11106	0.252726	0.126363	−	0.991984i	$-0.459670\pi$
$409$	5.11106	0.252726	0.126363	+	0.991984i	$0.459670\pi$
$410$	0	0
$411$	−8.15990	−0.402498
$412$	−58.8307	−2.89838
$413$	32.1620	1.58259
$414$	6.45434	0.317214
$415$	0	0
$416$	−7.50881	−0.368150
$417$	−20.2944	−0.993823
$418$	−5.69994	−0.278793
$419$	16.0566	0.784416	0.392208	−	0.919877i	$-0.371711\pi$
$419$	16.0566	0.784416	0.392208	+	0.919877i	$0.371711\pi$
$420$	0	0
$421$	19.2242	0.936932	0.468466	−	0.883481i	$-0.344807\pi$
$421$	19.2242	0.936932	0.468466	+	0.883481i	$0.344807\pi$
$422$	11.6999	0.569544
$423$	14.6765	0.713594
$424$	58.6241	2.84704
$425$	0	0
$426$	10.0566	0.487243
$427$	12.0566	0.583459
$428$	3.03897	0.146894
$429$	0.206625	0.00997593
$430$	0	0
$431$	21.5272	1.03693	0.518465	−	0.855099i	$-0.326504\pi$
$431$	21.5272	1.03693	0.518465	+	0.855099i	$0.326504\pi$
$432$	−63.4458	−3.05254
$433$	4.06727	0.195460	0.0977302	−	0.995213i	$-0.468842\pi$
$433$	4.06727	0.195460	0.0977302	+	0.995213i	$0.468842\pi$
$434$	−57.3502	−2.75290
$435$	0	0
$436$	14.0849	0.674544
$437$	17.3219	0.828620
$438$	−55.8024	−2.66634
$439$	−3.97383	−0.189660	−0.0948302	−	0.995493i	$-0.530231\pi$
$439$	−3.97383	−0.189660	−0.0948302	+	0.995493i	$0.530231\pi$
$440$	0	0
$441$	−0.0312196	−0.00148665
$442$	2.90444	0.138150
$443$	11.7154	0.556617	0.278309	−	0.960492i	$-0.410226\pi$
$443$	11.7154	0.556617	0.278309	+	0.960492i	$0.410226\pi$
$444$	7.12094	0.337945
$445$	0	0
$446$	−35.8131	−1.69580
$447$	4.26322	0.201643
$448$	−36.8131	−1.73926
$449$	−28.0352	−1.32307	−0.661533	−	0.749916i	$-0.730094\pi$
$449$	−28.0352	−1.32307	−0.661533	+	0.749916i	$0.730094\pi$
$450$	0	0
$451$	2.07714	0.0978086
$452$	−41.7848	−1.96539
$453$	−3.97865	−0.186933
$454$	−38.0459	−1.78558
$455$	0	0
$456$	−86.7939	−4.06450
$457$	−30.8647	−1.44379	−0.721894	−	0.692004i	$-0.756728\pi$
$457$	−30.8647	−1.44379	−0.721894	+	0.692004i	$0.756728\pi$
$458$	−48.3481	−2.25916
$459$	11.3022	0.527541
$460$	0	0
$461$	14.6716	0.683326	0.341663	−	0.939822i	$-0.389010\pi$
$461$	14.6716	0.683326	0.341663	+	0.939822i	$0.389010\pi$
$462$	2.65109	0.123340
$463$	−2.20955	−0.102686	−0.0513432	−	0.998681i	$-0.516350\pi$
$463$	−2.20955	−0.102686	−0.0513432	+	0.998681i	$0.516350\pi$
$464$	−88.1329	−4.09147
$465$	0	0
$466$	21.2010	0.982117
$467$	15.8131	0.731744	0.365872	−	0.930665i	$-0.380771\pi$
$467$	15.8131	0.731744	0.365872	+	0.930665i	$0.380771\pi$
$468$	−3.03897	−0.140476
$469$	−10.7544	−0.496592
$470$	0	0
$471$	−16.6863	−0.768866
$472$	97.3961	4.48302
$473$	0.273891	0.0125935
$474$	39.7176	1.82429
$475$	0	0
$476$	26.6610	1.22200
$477$	8.05659	0.368886
$478$	−22.1805	−1.01451
$479$	−22.4445	−1.02551	−0.512757	−	0.858534i	$-0.671376\pi$
$479$	−22.4445	−1.02551	−0.512757	+	0.858534i	$0.671376\pi$
$480$	0	0
$481$	0.563281	0.0256834
$482$	22.1543	1.00910
$483$	−8.05659	−0.366588
$484$	−54.9341	−2.49700
$485$	0	0
$486$	−28.6142	−1.29797
$487$	0.284564	0.0128948	0.00644741	−	0.999979i	$-0.497948\pi$
$487$	0.284564	0.0128948	0.00644741	+	0.999979i	$0.497948\pi$
$488$	36.5109	1.65277
$489$	25.2448	1.14161
$490$	0	0
$491$	39.4565	1.78065	0.890323	−	0.455330i	$-0.150479\pi$
$491$	39.4565	1.78065	0.890323	+	0.455330i	$0.150479\pi$
$492$	52.5179	2.36769
$493$	15.6999	0.707090
$494$	−11.3999	−0.512904
$495$	0	0
$496$	−91.6126	−4.11353
$497$	7.30219	0.327548
$498$	4.05659	0.181780
$499$	16.0566	0.718792	0.359396	−	0.933185i	$-0.382983\pi$
$499$	16.0566	0.718792	0.359396	+	0.933185i	$0.382983\pi$
$500$	0	0
$501$	−9.97865	−0.445813
$502$	−29.2087	−1.30365
$503$	23.1775	1.03343	0.516717	−	0.856156i	$-0.327154\pi$
$503$	23.1775	1.03343	0.516717	+	0.856156i	$0.327154\pi$
$504$	−23.4826	−1.04600
$505$	0	0
$506$	−1.60225	−0.0712287
$507$	−17.4904	−0.776775
$508$	95.2637	4.22664
$509$	24.4231	1.08254	0.541268	−	0.840850i	$-0.317944\pi$
$509$	24.4231	1.08254	0.541268	+	0.840850i	$0.317944\pi$
$510$	0	0
$511$	−40.5187	−1.79244
$512$	26.3716	1.16547
$513$	−44.3609	−1.95858
$514$	31.6348	1.39535
$515$	0	0
$516$	6.92498	0.304855
$517$	−3.64334	−0.160234
$518$	7.22717	0.317544
$519$	−13.6941	−0.601104
$520$	0	0
$521$	16.0411	0.702773	0.351387	−	0.936230i	$-0.385710\pi$
$521$	16.0411	0.702773	0.351387	+	0.936230i	$0.385710\pi$
$522$	−22.9610	−1.00498
$523$	−20.5526	−0.898703	−0.449351	−	0.893355i	$-0.648345\pi$
$523$	−20.5526	−0.898703	−0.449351	+	0.893355i	$0.648345\pi$
$524$	42.3043	1.84807
$525$	0	0
$526$	−4.72611	−0.206068
$527$	16.3198	0.710902
$528$	4.23492	0.184301
$529$	−18.1308	−0.788296
$530$	0	0
$531$	13.3850	0.580857
$532$	−104.644	−4.53689
$533$	4.15428	0.179942
$534$	33.4154	1.44602
$535$	0	0
$536$	−32.5675	−1.40670
$537$	8.34116	0.359947
$538$	−41.4437	−1.78676
$539$	0.00775008	0.000333820 0
$540$	0	0
$541$	−28.8414	−1.23999	−0.619995	−	0.784606i	$-0.712865\pi$
$541$	−28.8414	−1.23999	−0.619995	+	0.784606i	$0.712865\pi$
$542$	30.6687	1.31733
$543$	24.8422	1.06608
$544$	27.4154	1.17542
$545$	0	0
$546$	5.30219	0.226913
$547$	−36.6807	−1.56835	−0.784177	−	0.620537i	$-0.786915\pi$
$547$	−36.6807	−1.56835	−0.784177	+	0.620537i	$0.786915\pi$
$548$	−29.7926	−1.27268
$549$	5.01762	0.214147
$550$	0	0
$551$	−61.6220	−2.62519
$552$	−24.3977	−1.03844
$553$	28.8393	1.22637
$554$	−4.98720	−0.211886
$555$	0	0
$556$	−74.0969	−3.14241
$557$	−1.54566	−0.0654916	−0.0327458	−	0.999464i	$-0.510425\pi$
$557$	−1.54566	−0.0654916	−0.0327458	+	0.999464i	$0.510425\pi$
$558$	−23.8676	−1.01040
$559$	0.547781	0.0231687
$560$	0	0
$561$	−0.754406	−0.0318510
$562$	5.33048	0.224853
$563$	45.1308	1.90204	0.951018	−	0.309134i	$-0.100039\pi$
$563$	45.1308	1.90204	0.951018	+	0.309134i	$0.100039\pi$
$564$	−92.1174	−3.87884
$565$	0	0
$566$	28.8676	1.21340
$567$	11.8577	0.497977
$568$	22.1132	0.927849
$569$	31.5966	1.32460	0.662300	−	0.749239i	$-0.269581\pi$
$569$	31.5966	1.32460	0.662300	+	0.749239i	$0.269581\pi$
$570$	0	0
$571$	−9.26534	−0.387742	−0.193871	−	0.981027i	$-0.562104\pi$
$571$	−9.26534	−0.387742	−0.193871	+	0.981027i	$0.562104\pi$
$572$	0.754406	0.0315433
$573$	−9.66469	−0.403748
$574$	53.3014	2.22476
$575$	0	0
$576$	−15.3206	−0.638359
$577$	36.0352	1.50017	0.750083	−	0.661343i	$-0.230013\pi$
$577$	36.0352	1.50017	0.750083	+	0.661343i	$0.230013\pi$
$578$	34.4642	1.43352
$579$	−12.9669	−0.538885
$580$	0	0
$581$	2.94553	0.122201
$582$	0.754406	0.0312711
$583$	−2.00000	−0.0828315
$584$	−122.703	−5.07747
$585$	0	0
$586$	72.6396	3.00072
$587$	25.5555	1.05479	0.527395	−	0.849620i	$-0.323169\pi$
$587$	25.5555	1.05479	0.527395	+	0.849620i	$0.323169\pi$
$588$	0.195951	0.00808089
$589$	−64.0550	−2.63934
$590$	0	0
$591$	30.6610	1.26122
$592$	11.5449	0.474491
$593$	9.27601	0.380920	0.190460	−	0.981695i	$-0.439002\pi$
$593$	9.27601	0.380920	0.190460	+	0.981695i	$0.439002\pi$
$594$	4.10331	0.168361
$595$	0	0
$596$	15.5654	0.637584
$597$	8.34116	0.341381
$598$	−3.20450	−0.131042
$599$	11.2400	0.459253	0.229626	−	0.973279i	$-0.426250\pi$
$599$	11.2400	0.459253	0.229626	+	0.973279i	$0.426250\pi$
$600$	0	0
$601$	−18.3198	−0.747281	−0.373640	−	0.927574i	$-0.621891\pi$
$601$	−18.3198	−0.747281	−0.373640	+	0.927574i	$0.621891\pi$
$602$	7.02830	0.286452
$603$	−4.47569	−0.182264
$604$	−14.5264	−0.591072
$605$	0	0
$606$	9.47277	0.384805
$607$	40.7712	1.65485	0.827427	−	0.561574i	$-0.189804\pi$
$607$	40.7712	1.65485	0.827427	+	0.561574i	$0.189804\pi$
$608$	−107.605	−4.36395
$609$	28.6610	1.16140
$610$	0	0
$611$	−7.28669	−0.294788
$612$	11.0956	0.448512
$613$	−18.1132	−0.731585	−0.365792	−	0.930696i	$-0.619202\pi$
$613$	−18.1132	−0.731585	−0.365792	+	0.930696i	$0.619202\pi$
$614$	11.2611	0.454461
$615$	0	0
$616$	5.82942	0.234874
$617$	13.0742	0.526348	0.263174	−	0.964748i	$-0.415231\pi$
$617$	13.0742	0.526348	0.263174	+	0.964748i	$0.415231\pi$
$618$	42.7176	1.71835
$619$	−1.14228	−0.0459122	−0.0229561	−	0.999736i	$-0.507308\pi$
$619$	−1.14228	−0.0459122	−0.0229561	+	0.999736i	$0.507308\pi$
$620$	0	0
$621$	−12.4698	−0.500398
$622$	−16.0643	−0.644121
$623$	24.2632	0.972085
$624$	8.46984	0.339065
$625$	0	0
$626$	41.8959	1.67450
$627$	2.96103	0.118252
$628$	−60.9234	−2.43111
$629$	−2.05659	−0.0820017
$630$	0	0
$631$	−25.3588	−1.00952	−0.504759	−	0.863261i	$-0.668418\pi$
$631$	−25.3588	−1.00952	−0.504759	+	0.863261i	$0.668418\pi$
$632$	87.3339	3.47396
$633$	−6.07794	−0.241576
$634$	33.9632	1.34885
$635$	0	0
$636$	−50.5675	−2.00513
$637$	0.0155002	0.000614139 0
$638$	5.69994	0.225663
$639$	3.03897	0.120220
$640$	0	0
$641$	−14.6823	−0.579916	−0.289958	−	0.957039i	$-0.593641\pi$
$641$	−14.6823	−0.579916	−0.289958	+	0.957039i	$0.593641\pi$
$642$	−2.20662	−0.0870885
$643$	−5.05447	−0.199329	−0.0996644	−	0.995021i	$-0.531777\pi$
$643$	−5.05447	−0.199329	−0.0996644	+	0.995021i	$0.531777\pi$
$644$	−29.4154	−1.15913
$645$	0	0
$646$	41.6220	1.63760
$647$	5.82460	0.228988	0.114494	−	0.993424i	$-0.463475\pi$
$647$	5.82460	0.228988	0.114494	+	0.993424i	$0.463475\pi$
$648$	35.9087	1.41063
$649$	−3.32273	−0.130429
$650$	0	0
$651$	29.7926	1.16766
$652$	92.1711	3.60970
$653$	−20.1033	−0.786703	−0.393352	−	0.919388i	$-0.628685\pi$
$653$	−20.1033	−0.786703	−0.393352	+	0.919388i	$0.628685\pi$
$654$	−10.2272	−0.399914
$655$	0	0
$656$	85.1449	3.32435
$657$	−16.8628	−0.657879
$658$	−93.4917	−3.64469
$659$	20.9640	0.816640	0.408320	−	0.912839i	$-0.366115\pi$
$659$	20.9640	0.816640	0.408320	+	0.912839i	$0.366115\pi$
$660$	0	0
$661$	36.2936	1.41166	0.705829	−	0.708382i	$-0.250574\pi$
$661$	36.2936	1.41166	0.705829	+	0.708382i	$0.250574\pi$
$662$	−55.9787	−2.17567
$663$	−1.50881	−0.0585974
$664$	8.91994	0.346161
$665$	0	0
$666$	3.00775	0.116548
$667$	−17.3219	−0.670708
$668$	−36.4330	−1.40963
$669$	18.6044	0.719287
$670$	0	0
$671$	−1.24559	−0.0480856
$672$	50.0480	1.93065
$673$	1.46289	0.0563904	0.0281952	−	0.999602i	$-0.491024\pi$
$673$	1.46289	0.0563904	0.0281952	+	0.999602i	$0.491024\pi$
$674$	67.3785	2.59532
$675$	0	0
$676$	−63.8590	−2.45612
$677$	−33.8238	−1.29995	−0.649977	−	0.759954i	$-0.725221\pi$
$677$	−33.8238	−1.29995	−0.649977	+	0.759954i	$0.725221\pi$
$678$	30.3404	1.16521
$679$	0.547781	0.0210219
$680$	0	0
$681$	19.7643	0.757369
$682$	5.92498	0.226879
$683$	19.4309	0.743502	0.371751	−	0.928333i	$-0.378758\pi$
$683$	19.4309	0.743502	0.371751	+	0.928333i	$0.378758\pi$
$684$	−43.5499	−1.66517
$685$	0	0
$686$	−48.9992	−1.87080
$687$	25.1161	0.958239
$688$	11.2272	0.428032
$689$	−4.00000	−0.152388
$690$	0	0
$691$	20.7955	0.791098	0.395549	−	0.918445i	$-0.370554\pi$
$691$	20.7955	0.791098	0.395549	+	0.918445i	$0.370554\pi$
$692$	−49.9984	−1.90065
$693$	0.801125	0.0304322
$694$	−29.1394	−1.10611
$695$	0	0
$696$	86.7939	3.28991
$697$	−15.1677	−0.574516
$698$	−54.2264	−2.05250
$699$	−11.0136	−0.416572
$700$	0	0
$701$	−20.0459	−0.757124	−0.378562	−	0.925576i	$-0.623581\pi$
$701$	−20.0459	−0.757124	−0.378562	+	0.925576i	$0.623581\pi$
$702$	8.20662	0.309739
$703$	8.07209	0.304445
$704$	3.80325	0.143340
$705$	0	0
$706$	−20.9610	−0.788879
$707$	6.87826	0.258684
$708$	−84.0112	−3.15733
$709$	17.5117	0.657667	0.328834	−	0.944388i	$-0.393345\pi$
$709$	17.5117	0.657667	0.328834	+	0.944388i	$0.393345\pi$
$710$	0	0
$711$	12.0021	0.450115
$712$	73.4762	2.75364
$713$	−18.0058	−0.674324
$714$	−19.3588	−0.724484
$715$	0	0
$716$	30.4543	1.13813
$717$	11.5224	0.430312
$718$	−11.3999	−0.425439
$719$	−28.0048	−1.04440	−0.522202	−	0.852822i	$-0.674889\pi$
$719$	−28.0048	−1.04440	−0.522202	+	0.852822i	$0.674889\pi$
$720$	0	0
$721$	31.0176	1.15516
$722$	−112.995	−4.20523
$723$	−11.5088	−0.428017
$724$	90.7013	3.37089
$725$	0	0
$726$	39.8881	1.48039
$727$	44.2215	1.64009	0.820043	−	0.572302i	$-0.193949\pi$
$727$	44.2215	1.64009	0.820043	+	0.572302i	$0.193949\pi$
$728$	11.6588	0.432105
$729$	28.2830	1.04752
$730$	0	0
$731$	−2.00000	−0.0739727
$732$	−31.4933	−1.16403
$733$	−20.7176	−0.765220	−0.382610	−	0.923910i	$-0.624975\pi$
$733$	−20.7176	−0.765220	−0.382610	+	0.923910i	$0.624975\pi$
$734$	53.4720	1.97369
$735$	0	0
$736$	−30.2477	−1.11495
$737$	1.11106	0.0409265
$738$	22.1826	0.816552
$739$	7.12656	0.262155	0.131077	−	0.991372i	$-0.458156\pi$
$739$	7.12656	0.262155	0.131077	+	0.991372i	$0.458156\pi$
$740$	0	0
$741$	5.92206	0.217552
$742$	−51.3219	−1.88409
$743$	−29.7536	−1.09155	−0.545777	−	0.837930i	$-0.683765\pi$
$743$	−29.7536	−1.09155	−0.545777	+	0.837930i	$0.683765\pi$
$744$	90.2207	3.30765
$745$	0	0
$746$	−0.573955	−0.0210140
$747$	1.22585	0.0448515
$748$	−2.75441	−0.100711
$749$	−1.60225	−0.0585450
$750$	0	0
$751$	−39.3999	−1.43772	−0.718861	−	0.695154i	$-0.755336\pi$
$751$	−39.3999	−1.43772	−0.718861	+	0.695154i	$0.755336\pi$
$752$	−149.346	−5.44609
$753$	15.1735	0.552953
$754$	11.3999	0.415159
$755$	0	0
$756$	75.3318	2.73979
$757$	−38.4386	−1.39708	−0.698538	−	0.715573i	$-0.746166\pi$
$757$	−38.4386	−1.39708	−0.698538	+	0.715573i	$0.746166\pi$
$758$	26.5916	0.965850
$759$	0.832345	0.0302122
$760$	0	0
$761$	−42.3241	−1.53425	−0.767123	−	0.641500i	$-0.778312\pi$
$761$	−42.3241	−1.53425	−0.767123	+	0.641500i	$0.778312\pi$
$762$	−69.1719	−2.50583
$763$	−7.42605	−0.268841
$764$	−35.2867	−1.27663
$765$	0	0
$766$	39.7643	1.43674
$767$	−6.64547	−0.239954
$768$	−3.93566	−0.142016
$769$	5.01200	0.180737	0.0903686	−	0.995908i	$-0.471195\pi$
$769$	5.01200	0.180737	0.0903686	+	0.995908i	$0.471195\pi$
$770$	0	0
$771$	−16.4338	−0.591849
$772$	−47.3433	−1.70392
$773$	35.2031	1.26617	0.633084	−	0.774083i	$-0.281789\pi$
$773$	35.2031	1.26617	0.633084	+	0.774083i	$0.281789\pi$
$774$	2.92498	0.105136
$775$	0	0
$776$	1.65884	0.0595490
$777$	−3.75441	−0.134689
$778$	29.0176	1.04033
$779$	59.5328	2.13298
$780$	0	0
$781$	−0.754406	−0.0269948
$782$	11.6999	0.418389
$783$	44.3609	1.58533
$784$	0.317687	0.0113460
$785$	0	0
$786$	−30.7176	−1.09566
$787$	25.5910	0.912220	0.456110	−	0.889923i	$-0.349242\pi$
$787$	25.5910	0.912220	0.456110	+	0.889923i	$0.349242\pi$
$788$	111.946	3.98791
$789$	2.45514	0.0874054
$790$	0	0
$791$	22.0304	0.783312
$792$	2.42605	0.0862058
$793$	−2.49119	−0.0884647
$794$	1.84997	0.0656529
$795$	0	0
$796$	30.4543	1.07943
$797$	−16.0411	−0.568205	−0.284102	−	0.958794i	$-0.591696\pi$
$797$	−16.0411	−0.568205	−0.284102	+	0.958794i	$0.591696\pi$
$798$	75.9829	2.68977
$799$	26.6044	0.941195
$800$	0	0
$801$	10.0977	0.356784
$802$	−81.7090	−2.88525
$803$	4.18608	0.147723
$804$	28.0918	0.990723
$805$	0	0
$806$	11.8500	0.417397
$807$	21.5294	0.757869
$808$	20.8294	0.732776
$809$	−39.8470	−1.40095	−0.700474	−	0.713678i	$-0.747028\pi$
$809$	−39.8470	−1.40095	−0.700474	+	0.713678i	$0.747028\pi$
$810$	0	0
$811$	−38.8110	−1.36284	−0.681419	−	0.731893i	$-0.738637\pi$
$811$	−38.8110	−1.36284	−0.681419	+	0.731893i	$0.738637\pi$
$812$	104.644	3.67228
$813$	−15.9319	−0.558757
$814$	−0.746656	−0.0261703
$815$	0	0
$816$	−30.9242	−1.08256
$817$	7.84997	0.274636
$818$	−13.5499	−0.473761
$819$	1.60225	0.0559872
$820$	0	0
$821$	−46.4204	−1.62008	−0.810042	−	0.586372i	$-0.800556\pi$
$821$	−46.4204	−1.62008	−0.810042	+	0.586372i	$0.800556\pi$
$822$	21.6327	0.754526
$823$	16.7021	0.582197	0.291099	−	0.956693i	$-0.405979\pi$
$823$	16.7021	0.582197	0.291099	+	0.956693i	$0.405979\pi$
$824$	93.9306	3.27223
$825$	0	0
$826$	−85.2645	−2.96673
$827$	−9.13665	−0.317713	−0.158856	−	0.987302i	$-0.550781\pi$
$827$	−9.13665	−0.317713	−0.158856	+	0.987302i	$0.550781\pi$
$828$	−12.2419	−0.425434
$829$	−38.3043	−1.33036	−0.665182	−	0.746681i	$-0.731646\pi$
$829$	−38.3043	−1.33036	−0.665182	+	0.746681i	$0.731646\pi$
$830$	0	0
$831$	2.59078	0.0898731
$832$	7.60650	0.263708
$833$	−0.0565925	−0.00196081
$834$	53.8024	1.86303
$835$	0	0
$836$	10.8110	0.373906
$837$	46.1124	1.59388
$838$	−42.5675	−1.47047
$839$	−40.1484	−1.38608	−0.693039	−	0.720900i	$-0.743729\pi$
$839$	−40.1484	−1.38608	−0.693039	+	0.720900i	$0.743729\pi$
$840$	0	0
$841$	32.6220	1.12490
$842$	−50.9653	−1.75638
$843$	−2.76911	−0.0953730
$844$	−22.1911	−0.763850
$845$	0	0
$846$	−38.9087	−1.33771
$847$	28.9632	0.995186
$848$	−81.9829	−2.81530
$849$	−14.9963	−0.514671
$850$	0	0
$851$	2.26906	0.0777825
$852$	−19.0742	−0.653472
$853$	−27.4875	−0.941153	−0.470576	−	0.882359i	$-0.655954\pi$
$853$	−27.4875	−0.941153	−0.470576	+	0.882359i	$0.655954\pi$
$854$	−31.9632	−1.09376
$855$	0	0
$856$	−4.85209	−0.165841
$857$	25.9477	0.886355	0.443177	−	0.896434i	$-0.353851\pi$
$857$	25.9477	0.886355	0.443177	+	0.896434i	$0.353851\pi$
$858$	−0.547781	−0.0187009
$859$	0.393504	0.0134262	0.00671309	−	0.999977i	$-0.497863\pi$
$859$	0.393504	0.0134262	0.00671309	+	0.999977i	$0.497863\pi$
$860$	0	0
$861$	−27.6893	−0.943648
$862$	−57.0707	−1.94384
$863$	16.5422	0.563101	0.281551	−	0.959546i	$-0.409151\pi$
$863$	16.5422	0.563101	0.281551	+	0.959546i	$0.409151\pi$
$864$	77.4634	2.63536
$865$	0	0
$866$	−10.7827	−0.366411
$867$	−17.9036	−0.608039
$868$	108.775	3.69208
$869$	−2.97945	−0.101071
$870$	0	0
$871$	2.22212	0.0752938
$872$	−22.4883	−0.761549
$873$	0.227971	0.00771566
$874$	−45.9221	−1.55334
$875$	0	0
$876$	105.840	3.57600
$877$	−3.57125	−0.120593	−0.0602963	−	0.998181i	$-0.519205\pi$
$877$	−3.57125	−0.120593	−0.0602963	+	0.998181i	$0.519205\pi$
$878$	10.5350	0.355539
$879$	−37.7352	−1.27278
$880$	0	0
$881$	−33.7253	−1.13623	−0.568117	−	0.822948i	$-0.692328\pi$
$881$	−33.7253	−1.13623	−0.568117	+	0.822948i	$0.692328\pi$
$882$	0.0827661	0.00278688
$883$	−36.4175	−1.22555	−0.612773	−	0.790259i	$-0.709946\pi$
$883$	−36.4175	−1.22555	−0.612773	+	0.790259i	$0.709946\pi$
$884$	−5.50881	−0.185281
$885$	0	0
$886$	−31.0587	−1.04344
$887$	−4.11319	−0.138107	−0.0690536	−	0.997613i	$-0.521998\pi$
$887$	−4.11319	−0.138107	−0.0690536	+	0.997613i	$0.521998\pi$
$888$	−11.3695	−0.381534
$889$	−50.2264	−1.68454
$890$	0	0
$891$	−1.22505	−0.0410407
$892$	67.9263	2.27434
$893$	−104.422	−3.49434
$894$	−11.3022	−0.378002
$895$	0	0
$896$	24.9143	0.832329
$897$	1.66469	0.0555824
$898$	74.3241	2.48023
$899$	64.0550	2.13635
$900$	0	0
$901$	14.6044	0.486542
$902$	−5.50669	−0.183353
$903$	−3.65109	−0.121501
$904$	66.7146	2.21890
$905$	0	0
$906$	10.5478	0.350427
$907$	47.8286	1.58812	0.794062	−	0.607837i	$-0.207963\pi$
$907$	47.8286	1.58812	0.794062	+	0.607837i	$0.207963\pi$
$908$	72.1612	2.39475
$909$	2.86254	0.0949446
$910$	0	0
$911$	50.9808	1.68907	0.844534	−	0.535502i	$-0.179877\pi$
$911$	50.9808	1.68907	0.844534	+	0.535502i	$0.179877\pi$
$912$	121.377	4.01919
$913$	−0.304309	−0.0100712
$914$	81.8251	2.70653
$915$	0	0
$916$	91.7013	3.02989
$917$	−22.3043	−0.736553
$918$	−29.9632	−0.988931
$919$	−35.6815	−1.17702	−0.588512	−	0.808488i	$-0.700286\pi$
$919$	−35.6815	−1.17702	−0.588512	+	0.808488i	$0.700286\pi$
$920$	0	0
$921$	−5.84997	−0.192763
$922$	−38.8959	−1.28097
$923$	−1.50881	−0.0496631
$924$	−5.02830	−0.165419
$925$	0	0
$926$	5.85772	0.192497
$927$	12.9087	0.423977
$928$	107.605	3.53230
$929$	−8.43884	−0.276869	−0.138435	−	0.990372i	$-0.544207\pi$
$929$	−8.43884	−0.276869	−0.138435	+	0.990372i	$0.544207\pi$
$930$	0	0
$931$	0.222125	0.00727984
$932$	−40.2117	−1.31718
$933$	8.34518	0.273209
$934$	−41.9221	−1.37173
$935$	0	0
$936$	4.85209	0.158596
$937$	37.6319	1.22938	0.614690	−	0.788769i	$-0.289281\pi$
$937$	37.6319	1.22938	0.614690	+	0.788769i	$0.289281\pi$
$938$	28.5109	0.930915
$939$	−21.7643	−0.710250
$940$	0	0
$941$	26.4954	0.863726	0.431863	−	0.901939i	$-0.357856\pi$
$941$	26.4954	0.863726	0.431863	+	0.901939i	$0.357856\pi$
$942$	44.2370	1.44132
$943$	16.7347	0.544956
$944$	−136.204	−4.43305
$945$	0	0
$946$	−0.726109	−0.0236079
$947$	20.0155	0.650416	0.325208	−	0.945642i	$-0.394566\pi$
$947$	20.0155	0.650416	0.325208	+	0.945642i	$0.394566\pi$
$948$	−75.3318	−2.44666
$949$	8.37216	0.271772
$950$	0	0
$951$	−17.6433	−0.572125
$952$	−42.5675	−1.37962
$953$	40.9298	1.32585	0.662923	−	0.748687i	$-0.269316\pi$
$953$	40.9298	1.32585	0.662923	+	0.748687i	$0.269316\pi$
$954$	−21.3588	−0.691516
$955$	0	0
$956$	42.0694	1.36062
$957$	−2.96103	−0.0957165
$958$	59.5024	1.92243
$959$	15.7077	0.507228
$960$	0	0
$961$	35.5840	1.14787
$962$	−1.49331	−0.0481463
$963$	−0.666813	−0.0214877
$964$	−42.0197	−1.35336
$965$	0	0
$966$	21.3588	0.687207
$967$	12.7913	0.411339	0.205669	−	0.978622i	$-0.434063\pi$
$967$	12.7913	0.411339	0.205669	+	0.978622i	$0.434063\pi$
$968$	87.7090	2.81907
$969$	−21.6220	−0.694599
$970$	0	0
$971$	0.366529	0.0117625	0.00588124	−	0.999983i	$-0.498128\pi$
$971$	0.366529	0.0117625	0.00588124	+	0.999983i	$0.498128\pi$
$972$	54.2723	1.74078
$973$	39.0665	1.25241
$974$	−0.754406	−0.0241727
$975$	0	0
$976$	−51.0587	−1.63435
$977$	−55.0219	−1.76031	−0.880153	−	0.474691i	$-0.842560\pi$
$977$	−55.0219	−1.76031	−0.880153	+	0.474691i	$0.842560\pi$
$978$	−66.9263	−2.14007
$979$	−2.50669	−0.0801141
$980$	0	0
$981$	−3.09052	−0.0986726
$982$	−104.603	−3.33801
$983$	−45.6268	−1.45527	−0.727635	−	0.685965i	$-0.759380\pi$
$983$	−45.6268	−1.45527	−0.727635	+	0.685965i	$0.759380\pi$
$984$	−83.8513	−2.67308
$985$	0	0
$986$	−41.6220	−1.32551
$987$	48.5675	1.54592
$988$	21.6220	0.687887
$989$	2.20662	0.0701666
$990$	0	0
$991$	7.24559	0.230164	0.115082	−	0.993356i	$-0.463287\pi$
$991$	7.24559	0.230164	0.115082	+	0.993356i	$0.463287\pi$
$992$	111.853	3.55135
$993$	29.0801	0.922828
$994$	−19.3588	−0.614023
$995$	0	0
$996$	−7.69409	−0.243797
$997$	17.7106	0.560901	0.280450	−	0.959869i	$-0.409516\pi$
$997$	17.7106	0.560901	0.280450	+	0.959869i	$0.409516\pi$
$998$	−42.5675	−1.34745
$999$	−5.81100	−0.183852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.j.1.1		3
3.2	odd	2		9675.2.a.bt.1.3		3
5.2	odd	4		215.2.b.a.44.1	✓	6
5.3	odd	4		215.2.b.a.44.6	yes	6
5.4	even	2		1075.2.a.k.1.3		3
15.2	even	4		1935.2.b.c.1549.6		6
15.8	even	4		1935.2.b.c.1549.1		6
15.14	odd	2		9675.2.a.br.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.b.a.44.1	✓	6	5.2	odd	4
215.2.b.a.44.6	yes	6	5.3	odd	4
1075.2.a.j.1.1		3	1.1	even	1	trivial
1075.2.a.k.1.3		3	5.4	even	2
1935.2.b.c.1549.1		6	15.8	even	4
1935.2.b.c.1549.6		6	15.2	even	4
9675.2.a.br.1.1		3	15.14	odd	2
9675.2.a.bt.1.3		3	3.2	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)

\(f(q)\)	\(=\)	\(q-2.65109 q^{2} +1.37720 q^{3} +5.02830 q^{4} -3.65109 q^{6} -2.65109 q^{7} -8.02830 q^{8} -1.10331 q^{9} +O(q^{10})\)	\(q-2.65109 q^{2} +1.37720 q^{3} +5.02830 q^{4} -3.65109 q^{6} -2.65109 q^{7} -8.02830 q^{8} -1.10331 q^{9} +0.273891 q^{11} +6.92498 q^{12} +0.547781 q^{13} +7.02830 q^{14} +11.2272 q^{16} -2.00000 q^{17} +2.92498 q^{18} +7.84997 q^{19} -3.65109 q^{21} -0.726109 q^{22} +2.20662 q^{23} -11.0566 q^{24} -1.45222 q^{26} -5.65109 q^{27} -13.3305 q^{28} -7.84997 q^{29} -8.15990 q^{31} -13.7077 q^{32} +0.377203 q^{33} +5.30219 q^{34} -5.54778 q^{36} +1.02830 q^{37} -20.8110 q^{38} +0.754406 q^{39} +7.58383 q^{41} +9.67939 q^{42} +1.00000 q^{43} +1.37720 q^{44} -5.84997 q^{46} -13.3022 q^{47} +15.4621 q^{48} +0.0282963 q^{49} -2.75441 q^{51} +2.75441 q^{52} -7.30219 q^{53} +14.9816 q^{54} +21.2838 q^{56} +10.8110 q^{57} +20.8110 q^{58} -12.1316 q^{59} -4.54778 q^{61} +21.6327 q^{62} +2.92498 q^{63} +13.8860 q^{64} -1.00000 q^{66} +4.05659 q^{67} -10.0566 q^{68} +3.03897 q^{69} -2.75441 q^{71} +8.85772 q^{72} +15.2838 q^{73} -2.72611 q^{74} +39.4720 q^{76} -0.726109 q^{77} -2.00000 q^{78} -10.8783 q^{79} -4.47277 q^{81} -20.1054 q^{82} -1.11106 q^{83} -18.3588 q^{84} -2.65109 q^{86} -10.8110 q^{87} -2.19887 q^{88} -9.15215 q^{89} -1.45222 q^{91} +11.0956 q^{92} -11.2378 q^{93} +35.2653 q^{94} -18.8783 q^{96} -0.206625 q^{97} -0.0750160 q^{98} -0.302187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - q^{3} + 3 q^{4} - 4 q^{6} - q^{7} - 12 q^{8}+O(q^{10}) \) 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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