LMFDB - Embedded newform 1175.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, 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("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 47)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.396339$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.283841 q^{2} -2.23925 q^{3} -1.91943 q^{4} +0.635593 q^{6} -2.44658 q^{7} +1.11250 q^{8} +2.01426 q^{9} +O(q^{10})$	\(q-0.283841 q^{2} -2.23925 q^{3} -1.91943 q^{4} +0.635593 q^{6} -2.44658 q^{7} +1.11250 q^{8} +2.01426 q^{9} +3.04619 q^{11} +4.29810 q^{12} +1.68583 q^{13} +0.694440 q^{14} +3.52310 q^{16} +1.59961 q^{17} -0.571730 q^{18} +0.792677 q^{19} +5.47851 q^{21} -0.864635 q^{22} +0.639640 q^{23} -2.49116 q^{24} -0.478509 q^{26} +2.20732 q^{27} +4.69604 q^{28} -7.04619 q^{29} +1.68583 q^{31} -3.22499 q^{32} -6.82120 q^{33} -0.454036 q^{34} -3.86624 q^{36} -4.01426 q^{37} -0.224994 q^{38} -3.77501 q^{39} +1.43232 q^{41} -1.55503 q^{42} +3.91083 q^{43} -5.84696 q^{44} -0.181556 q^{46} -1.00000 q^{47} -7.88911 q^{48} -1.01426 q^{49} -3.58194 q^{51} -3.23584 q^{52} -4.35740 q^{53} -0.626529 q^{54} -2.72181 q^{56} -1.77501 q^{57} +2.00000 q^{58} +0.861223 q^{59} -11.9713 q^{61} -0.478509 q^{62} -4.92804 q^{63} -6.13080 q^{64} +1.93614 q^{66} +8.76054 q^{67} -3.07035 q^{68} -1.43232 q^{69} +2.26777 q^{71} +2.24086 q^{72} -10.7035 q^{73} +1.13941 q^{74} -1.52149 q^{76} -7.45274 q^{77} +1.07150 q^{78} +10.2678 q^{79} -10.9855 q^{81} -0.406551 q^{82} -12.5070 q^{83} -10.5156 q^{84} -1.11005 q^{86} +15.7782 q^{87} +3.38888 q^{88} -6.18497 q^{89} -4.12452 q^{91} -1.22775 q^{92} -3.77501 q^{93} +0.283841 q^{94} +7.22158 q^{96} +7.58515 q^{97} +0.287889 q^{98} +6.13582 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9	$ 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9} - 6 q^{11} + 11 q^{12} - 8 q^{13} - 5 q^{14} + 5 q^{16} - 6 q^{17} - 16 q^{18} + 4 q^{21} - 4 q^{22} + 6 q^{23} - 13 q^{24} + 16 q^{26} + 12 q^{27} - 16 q^{28} - 10 q^{29} - 8 q^{31} - 10 q^{32} - 12 q^{33} - 10 q^{34} + 11 q^{36} - 10 q^{37} + 2 q^{38} - 18 q^{39} + 6 q^{41} + 15 q^{42} - 2 q^{43} - 30 q^{44} + 18 q^{46} - 4 q^{47} - 6 q^{48} + 2 q^{49} - 8 q^{51} - 4 q^{52} + 6 q^{53} - 5 q^{54} + 2 q^{56} - 10 q^{57} + 8 q^{58} + 4 q^{59} - 6 q^{61} + 16 q^{62} - 16 q^{63} - 31 q^{64} + 32 q^{66} - 10 q^{67} - 43 q^{68} - 6 q^{69} - 12 q^{71} - 27 q^{72} - 22 q^{73} + 18 q^{74} - 24 q^{76} + 10 q^{77} + 28 q^{78} + 20 q^{79} + 4 q^{81} + 20 q^{82} - 20 q^{83} - 19 q^{84} + 38 q^{86} + 12 q^{87} - 2 q^{88} - 6 q^{89} - 22 q^{91} + 32 q^{92} - 18 q^{93} + q^{94} + 26 q^{96} - 30 q^{97} + 15 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9 - 6 * q^11 + 11 * q^12 - 8 * q^13 - 5 * q^14 + 5 * q^16 - 6 * q^17 - 16 * q^18 + 4 * q^21 - 4 * q^22 + 6 * q^23 - 13 * q^24 + 16 * q^26 + 12 * q^27 - 16 * q^28 - 10 * q^29 - 8 * q^31 - 10 * q^32 - 12 * q^33 - 10 * q^34 + 11 * q^36 - 10 * q^37 + 2 * q^38 - 18 * q^39 + 6 * q^41 + 15 * q^42 - 2 * q^43 - 30 * q^44 + 18 * q^46 - 4 * q^47 - 6 * q^48 + 2 * q^49 - 8 * q^51 - 4 * q^52 + 6 * q^53 - 5 * q^54 + 2 * q^56 - 10 * q^57 + 8 * q^58 + 4 * q^59 - 6 * q^61 + 16 * q^62 - 16 * q^63 - 31 * q^64 + 32 * q^66 - 10 * q^67 - 43 * q^68 - 6 * q^69 - 12 * q^71 - 27 * q^72 - 22 * q^73 + 18 * q^74 - 24 * q^76 + 10 * q^77 + 28 * q^78 + 20 * q^79 + 4 * q^81 + 20 * q^82 - 20 * q^83 - 19 * q^84 + 38 * q^86 + 12 * q^87 - 2 * q^88 - 6 * q^89 - 22 * q^91 + 32 * q^92 - 18 * q^93 + q^94 + 26 * q^96 - 30 * q^97 + 15 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.283841	−0.200706	−0.100353	−	0.994952i	$-0.531997\pi$
$2$	−0.283841	−0.200706	−0.100353	+	0.994952i	$0.531997\pi$
$3$	−2.23925	−1.29283	−0.646417	−	0.762984i	$-0.723733\pi$
$3$	−2.23925	−1.29283	−0.646417	+	0.762984i	$0.723733\pi$
$4$	−1.91943	−0.959717
$5$	0	0
$5$	0	0
$6$	0.635593	0.259480
$7$	−2.44658	−0.924719	−0.462360	−	0.886692i	$-0.652997\pi$
$7$	−2.44658	−0.924719	−0.462360	+	0.886692i	$0.652997\pi$
$8$	1.11250	0.393327
$9$	2.01426	0.671420
$10$	0	0
$11$	3.04619	0.918461	0.459231	−	0.888317i	$-0.348125\pi$
$11$	3.04619	0.918461	0.459231	+	0.888317i	$0.348125\pi$
$12$	4.29810	1.24075
$13$	1.68583	0.467566	0.233783	−	0.972289i	$-0.424890\pi$
$13$	1.68583	0.467566	0.233783	+	0.972289i	$0.424890\pi$
$14$	0.694440	0.185597
$15$	0	0
$16$	3.52310	0.880774
$17$	1.59961	0.387963	0.193982	−	0.981005i	$-0.437860\pi$
$17$	1.59961	0.387963	0.193982	+	0.981005i	$0.437860\pi$
$18$	−0.571730	−0.134758
$19$	0.792677	0.181853	0.0909263	−	0.995858i	$-0.471017\pi$
$19$	0.792677	0.181853	0.0909263	+	0.995858i	$0.471017\pi$
$20$	0	0
$21$	5.47851	1.19551
$22$	−0.864635	−0.184341
$23$	0.639640	0.133374	0.0666871	−	0.997774i	$-0.478757\pi$
$23$	0.639640	0.133374	0.0666871	+	0.997774i	$0.478757\pi$
$24$	−2.49116	−0.508507
$25$	0	0
$26$	−0.478509	−0.0938433
$27$	2.20732	0.424799
$28$	4.69604	0.887469
$29$	−7.04619	−1.30844	−0.654222	−	0.756302i	$-0.727004\pi$
$29$	−7.04619	−1.30844	−0.654222	+	0.756302i	$0.727004\pi$
$30$	0	0
$31$	1.68583	0.302784	0.151392	−	0.988474i	$-0.451624\pi$
$31$	1.68583	0.302784	0.151392	+	0.988474i	$0.451624\pi$
$32$	−3.22499	−0.570104
$33$	−6.82120	−1.18742
$34$	−0.454036	−0.0778666
$35$	0	0
$36$	−3.86624	−0.644373
$37$	−4.01426	−0.659940	−0.329970	−	0.943991i	$-0.607039\pi$
$37$	−4.01426	−0.659940	−0.329970	+	0.943991i	$0.607039\pi$
$38$	−0.224994	−0.0364989
$39$	−3.77501	−0.604485
$40$	0	0
$41$	1.43232	0.223690	0.111845	−	0.993726i	$-0.464324\pi$
$41$	1.43232	0.223690	0.111845	+	0.993726i	$0.464324\pi$
$42$	−1.55503	−0.239946
$43$	3.91083	0.596395	0.298198	−	0.954504i	$-0.403615\pi$
$43$	3.91083	0.596395	0.298198	+	0.954504i	$0.403615\pi$
$44$	−5.84696	−0.881463
$45$	0	0
$46$	−0.181556	−0.0267690
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−7.88911	−1.13869
$49$	−1.01426	−0.144894
$50$	0	0
$51$	−3.58194	−0.501572
$52$	−3.23584	−0.448731
$53$	−4.35740	−0.598535	−0.299268	−	0.954169i	$-0.596742\pi$
$53$	−4.35740	−0.598535	−0.299268	+	0.954169i	$0.596742\pi$
$54$	−0.626529	−0.0852599
$55$	0	0
$56$	−2.72181	−0.363717
$57$	−1.77501	−0.235105
$58$	2.00000	0.262613
$59$	0.861223	0.112122	0.0560608	−	0.998427i	$-0.482146\pi$
$59$	0.861223	0.112122	0.0560608	+	0.998427i	$0.482146\pi$
$60$	0	0
$61$	−11.9713	−1.53276	−0.766382	−	0.642385i	$-0.777945\pi$
$61$	−11.9713	−1.53276	−0.766382	+	0.642385i	$0.777945\pi$
$62$	−0.478509	−0.0607707
$63$	−4.92804	−0.620875
$64$	−6.13080	−0.766351
$65$	0	0
$66$	1.93614	0.238322
$67$	8.76054	1.07027	0.535135	−	0.844766i	$-0.320261\pi$
$67$	8.76054	1.07027	0.535135	+	0.844766i	$0.320261\pi$
$68$	−3.07035	−0.372335
$69$	−1.43232	−0.172431
$70$	0	0
$71$	2.26777	0.269135	0.134568	−	0.990904i	$-0.457035\pi$
$71$	2.26777	0.269135	0.134568	+	0.990904i	$0.457035\pi$
$72$	2.24086	0.264088
$73$	−10.7035	−1.25275	−0.626375	−	0.779522i	$-0.715462\pi$
$73$	−10.7035	−1.25275	−0.626375	+	0.779522i	$0.715462\pi$
$74$	1.13941	0.132454
$75$	0	0
$76$	−1.52149	−0.174527
$77$	−7.45274	−0.849319
$78$	1.07150	0.121324
$79$	10.2678	1.15521	0.577607	−	0.816315i	$-0.303986\pi$
$79$	10.2678	1.15521	0.577607	+	0.816315i	$0.303986\pi$
$80$	0	0
$81$	−10.9855	−1.22062
$82$	−0.406551	−0.0448960
$83$	−12.5070	−1.37282	−0.686412	−	0.727213i	$-0.740815\pi$
$83$	−12.5070	−1.37282	−0.686412	+	0.727213i	$0.740815\pi$
$84$	−10.5156	−1.14735
$85$	0	0
$86$	−1.11005	−0.119700
$87$	15.7782	1.69160
$88$	3.38888	0.361256
$89$	−6.18497	−0.655605	−0.327803	−	0.944746i	$-0.606308\pi$
$89$	−6.18497	−0.655605	−0.327803	+	0.944746i	$0.606308\pi$
$90$	0	0
$91$	−4.12452	−0.432367
$92$	−1.22775	−0.128002
$93$	−3.77501	−0.391450
$94$	0.283841	0.0292760
$95$	0	0
$96$	7.22158	0.737050
$97$	7.58515	0.770155	0.385078	−	0.922884i	$-0.374175\pi$
$97$	7.58515	0.770155	0.385078	+	0.922884i	$0.374175\pi$
$98$	0.287889	0.0290812
$99$	6.13582	0.616673
$100$	0	0
$101$	−5.29354	−0.526727	−0.263363	−	0.964697i	$-0.584832\pi$
$101$	−5.29354	−0.526727	−0.263363	+	0.964697i	$0.584832\pi$
$102$	1.01670	0.100669
$103$	10.2678	1.01171	0.505857	−	0.862617i	$-0.331176\pi$
$103$	10.2678	1.01171	0.505857	+	0.862617i	$0.331176\pi$
$104$	1.87548	0.183906
$105$	0	0
$106$	1.23681	0.120130
$107$	−9.19923	−0.889323	−0.444661	−	0.895699i	$-0.646676\pi$
$107$	−9.19923	−0.889323	−0.444661	+	0.895699i	$0.646676\pi$
$108$	−4.23681	−0.407687
$109$	15.1671	1.45274	0.726372	−	0.687302i	$-0.241205\pi$
$109$	15.1671	1.45274	0.726372	+	0.687302i	$0.241205\pi$
$110$	0	0
$111$	8.98895	0.853193
$112$	−8.61953	−0.814469
$113$	−16.2567	−1.52930	−0.764652	−	0.644444i	$-0.777089\pi$
$113$	−16.2567	−1.52930	−0.764652	+	0.644444i	$0.777089\pi$
$114$	0.503820	0.0471871
$115$	0	0
$116$	13.5247	1.25574
$117$	3.39570	0.313933
$118$	−0.244451	−0.0225035
$119$	−3.91358	−0.358757
$120$	0	0
$121$	−1.72072	−0.156429
$122$	3.39794	0.307635
$123$	−3.20732	−0.289195
$124$	−3.23584	−0.290587
$125$	0	0
$126$	1.39878	0.124613
$127$	−15.1820	−1.34719	−0.673593	−	0.739103i	$-0.735250\pi$
$127$	−15.1820	−1.34719	−0.673593	+	0.739103i	$0.735250\pi$
$128$	8.19016	0.723915
$129$	−8.75733	−0.771040
$130$	0	0
$131$	7.13878	0.623718	0.311859	−	0.950128i	$-0.399048\pi$
$131$	7.13878	0.623718	0.311859	+	0.950128i	$0.399048\pi$
$132$	13.0928	1.13959
$133$	−1.93935	−0.168163
$134$	−2.48660	−0.214810
$135$	0	0
$136$	1.77957	0.152597
$137$	−8.34269	−0.712764	−0.356382	−	0.934340i	$-0.615990\pi$
$137$	−8.34269	−0.712764	−0.356382	+	0.934340i	$0.615990\pi$
$138$	0.406551	0.0346079
$139$	−20.0489	−1.70053	−0.850265	−	0.526355i	$-0.823558\pi$
$139$	−20.0489	−1.70053	−0.850265	+	0.526355i	$0.823558\pi$
$140$	0	0
$141$	2.23925	0.188579
$142$	−0.643688	−0.0540171
$143$	5.13537	0.429441
$144$	7.09643	0.591369
$145$	0	0
$146$	3.03810	0.251435
$147$	2.27119	0.187324
$148$	7.70511	0.633356
$149$	13.4498	1.10185	0.550925	−	0.834555i	$-0.314275\pi$
$149$	13.4498	1.10185	0.550925	+	0.834555i	$0.314275\pi$
$150$	0	0
$151$	−11.3282	−0.921878	−0.460939	−	0.887432i	$-0.652487\pi$
$151$	−11.3282	−0.921878	−0.460939	+	0.887432i	$0.652487\pi$
$152$	0.881851	0.0715276
$153$	3.22204	0.260486
$154$	2.11540	0.170463
$155$	0	0
$156$	7.24587	0.580134
$157$	−5.49277	−0.438371	−0.219185	−	0.975683i	$-0.570340\pi$
$157$	−5.49277	−0.438371	−0.219185	+	0.975683i	$0.570340\pi$
$158$	−2.91442	−0.231859
$159$	9.75733	0.773807
$160$	0	0
$161$	−1.56493	−0.123334
$162$	3.11815	0.244985
$163$	7.52470	0.589380	0.294690	−	0.955593i	$-0.404784\pi$
$163$	7.52470	0.589380	0.294690	+	0.955593i	$0.404784\pi$
$164$	−2.74924	−0.214679
$165$	0	0
$166$	3.55001	0.275534
$167$	−5.11815	−0.396054	−0.198027	−	0.980197i	$-0.563453\pi$
$167$	−5.11815	−0.396054	−0.198027	+	0.980197i	$0.563453\pi$
$168$	6.09483	0.470226
$169$	−10.1580	−0.781382
$170$	0	0
$171$	1.59666	0.122099
$172$	−7.50657	−0.572371
$173$	19.5213	1.48418	0.742088	−	0.670302i	$-0.233836\pi$
$173$	19.5213	1.48418	0.742088	+	0.670302i	$0.233836\pi$
$174$	−4.47851	−0.339515
$175$	0	0
$176$	10.7320	0.808957
$177$	−1.92850	−0.144955
$178$	1.75555	0.131584
$179$	−0.236298	−0.0176617	−0.00883087	−	0.999961i	$-0.502811\pi$
$179$	−0.236298	−0.0176617	−0.00883087	+	0.999961i	$0.502811\pi$
$180$	0	0
$181$	−14.4066	−1.07083	−0.535415	−	0.844589i	$-0.679845\pi$
$181$	−14.4066	−1.07083	−0.535415	+	0.844589i	$0.679845\pi$
$182$	1.17071	0.0867787
$183$	26.8067	1.98161
$184$	0.711598	0.0524597
$185$	0	0
$186$	1.07150	0.0785664
$187$	4.87273	0.356329
$188$	1.91943	0.139989
$189$	−5.40039	−0.392820
$190$	0	0
$191$	21.4640	1.55308	0.776542	−	0.630066i	$-0.216972\pi$
$191$	21.4640	1.55308	0.776542	+	0.630066i	$0.216972\pi$
$192$	13.7284	0.990764
$193$	−5.93614	−0.427293	−0.213646	−	0.976911i	$-0.568534\pi$
$193$	−5.93614	−0.427293	−0.213646	+	0.976911i	$0.568534\pi$
$194$	−2.15298	−0.154575
$195$	0	0
$196$	1.94680	0.139057
$197$	−2.65094	−0.188872	−0.0944360	−	0.995531i	$-0.530105\pi$
$197$	−2.65094	−0.188872	−0.0944360	+	0.995531i	$0.530105\pi$
$198$	−1.74160	−0.123770
$199$	20.5102	1.45393	0.726966	−	0.686673i	$-0.240930\pi$
$199$	20.5102	1.45393	0.726966	+	0.686673i	$0.240930\pi$
$200$	0	0
$201$	−19.6171	−1.38368
$202$	1.50253	0.105717
$203$	17.2391	1.20994
$204$	6.87530	0.481367
$205$	0	0
$206$	−2.91442	−0.203057
$207$	1.28840	0.0895501
$208$	5.93935	0.411820
$209$	2.41465	0.167025
$210$	0	0
$211$	−27.0892	−1.86490	−0.932449	−	0.361300i	$-0.882333\pi$
$211$	−27.0892	−1.86490	−0.932449	+	0.361300i	$0.882333\pi$
$212$	8.36375	0.574425
$213$	−5.07812	−0.347947
$214$	2.61112	0.178493
$215$	0	0
$216$	2.45564	0.167085
$217$	−4.12452	−0.279990
$218$	−4.30505	−0.291575
$219$	23.9679	1.61960
$220$	0	0
$221$	2.69668	0.181398
$222$	−2.55143	−0.171241
$223$	−6.55276	−0.438806	−0.219403	−	0.975634i	$-0.570411\pi$
$223$	−6.55276	−0.438806	−0.219403	+	0.975634i	$0.570411\pi$
$224$	7.89020	0.527186
$225$	0	0
$226$	4.61433	0.306941
$227$	16.0752	1.06695	0.533473	−	0.845817i	$-0.320887\pi$
$227$	16.0752	1.06695	0.533473	+	0.845817i	$0.320887\pi$
$228$	3.40701	0.225634
$229$	11.2803	0.745424	0.372712	−	0.927947i	$-0.378428\pi$
$229$	11.2803	0.745424	0.372712	+	0.927947i	$0.378428\pi$
$230$	0	0
$231$	16.6886	1.09803
$232$	−7.83887	−0.514647
$233$	5.49618	0.360067	0.180033	−	0.983661i	$-0.442379\pi$
$233$	5.49618	0.360067	0.180033	+	0.983661i	$0.442379\pi$
$234$	−0.963841	−0.0630082
$235$	0	0
$236$	−1.65306	−0.107605
$237$	−22.9922	−1.49350
$238$	1.11084	0.0720048
$239$	−18.1465	−1.17380	−0.586899	−	0.809660i	$-0.699651\pi$
$239$	−18.1465	−1.17380	−0.586899	+	0.809660i	$0.699651\pi$
$240$	0	0
$241$	7.32888	0.472095	0.236047	−	0.971742i	$-0.424148\pi$
$241$	7.32888	0.472095	0.236047	+	0.971742i	$0.424148\pi$
$242$	0.488411	0.0313963
$243$	17.9774	1.15325
$244$	22.9781	1.47102
$245$	0	0
$246$	0.910371	0.0580431
$247$	1.33632	0.0850280
$248$	1.87548	0.119093
$249$	28.0064	1.77483
$250$	0	0
$251$	−28.6603	−1.80902	−0.904512	−	0.426449i	$-0.859764\pi$
$251$	−28.6603	−1.80902	−0.904512	+	0.426449i	$0.859764\pi$
$252$	9.45905	0.595864
$253$	1.94847	0.122499
$254$	4.30928	0.270388
$255$	0	0
$256$	9.93690	0.621056
$257$	9.41510	0.587298	0.293649	−	0.955913i	$-0.405130\pi$
$257$	9.41510	0.587298	0.293649	+	0.955913i	$0.405130\pi$
$258$	2.48569	0.154752
$259$	9.82120	0.610259
$260$	0	0
$261$	−14.1929	−0.878516
$262$	−2.02628	−0.125184
$263$	14.8165	0.913625	0.456813	−	0.889563i	$-0.348991\pi$
$263$	14.8165	0.913625	0.456813	+	0.889563i	$0.348991\pi$
$264$	−7.58856	−0.467044
$265$	0	0
$266$	0.550466	0.0337513
$267$	13.8497	0.847589
$268$	−16.8153	−1.02716
$269$	−8.59941	−0.524315	−0.262158	−	0.965025i	$-0.584434\pi$
$269$	−8.59941	−0.524315	−0.262158	+	0.965025i	$0.584434\pi$
$270$	0	0
$271$	−19.7092	−1.19725	−0.598625	−	0.801030i	$-0.704286\pi$
$271$	−19.7092	−1.19725	−0.598625	+	0.801030i	$0.704286\pi$
$272$	5.63559	0.341708
$273$	9.23584	0.558979
$274$	2.36800	0.143056
$275$	0	0
$276$	2.74924	0.165485
$277$	−20.6775	−1.24239	−0.621196	−	0.783655i	$-0.713353\pi$
$277$	−20.6775	−1.24239	−0.621196	+	0.783655i	$0.713353\pi$
$278$	5.69072	0.341307
$279$	3.39570	0.203295
$280$	0	0
$281$	22.3744	1.33475	0.667373	−	0.744724i	$-0.267419\pi$
$281$	22.3744	1.33475	0.667373	+	0.744724i	$0.267419\pi$
$282$	−0.635593	−0.0378490
$283$	−5.04599	−0.299953	−0.149976	−	0.988690i	$-0.547920\pi$
$283$	−5.04599	−0.299953	−0.149976	+	0.988690i	$0.547920\pi$
$284$	−4.35284	−0.258294
$285$	0	0
$286$	−1.45763	−0.0861914
$287$	−3.50428	−0.206851
$288$	−6.49598	−0.382779
$289$	−14.4412	−0.849484
$290$	0	0
$291$	−16.9851	−0.995683
$292$	20.5447	1.20229
$293$	−21.9951	−1.28497	−0.642484	−	0.766299i	$-0.722096\pi$
$293$	−21.9951	−1.28497	−0.642484	+	0.766299i	$0.722096\pi$
$294$	−0.644656	−0.0375971
$295$	0	0
$296$	−4.46585	−0.259572
$297$	6.72393	0.390162
$298$	−3.81760	−0.221148
$299$	1.07833	0.0623612
$300$	0	0
$301$	−9.56814	−0.551498
$302$	3.21542	0.185027
$303$	11.8536	0.680971
$304$	2.79268	0.160171
$305$	0	0
$306$	−0.914547	−0.0522812
$307$	−23.1963	−1.32388	−0.661941	−	0.749556i	$-0.730267\pi$
$307$	−23.1963	−1.32388	−0.661941	+	0.749556i	$0.730267\pi$
$308$	14.3050	0.815106
$309$	−22.9922	−1.30798
$310$	0	0
$311$	−6.57451	−0.372806	−0.186403	−	0.982473i	$-0.559683\pi$
$311$	−6.57451	−0.372806	−0.186403	+	0.982473i	$0.559683\pi$
$312$	−4.19968	−0.237760
$313$	−1.73839	−0.0982597	−0.0491298	−	0.998792i	$-0.515645\pi$
$313$	−1.73839	−0.0982597	−0.0491298	+	0.998792i	$0.515645\pi$
$314$	1.55907	0.0879837
$315$	0	0
$316$	−19.7083	−1.10868
$317$	23.0698	1.29573	0.647865	−	0.761755i	$-0.275662\pi$
$317$	23.0698	1.29573	0.647865	+	0.761755i	$0.275662\pi$
$318$	−2.76953	−0.155308
$319$	−21.4640	−1.20176
$320$	0	0
$321$	20.5994	1.14975
$322$	0.444192	0.0247538
$323$	1.26798	0.0705521
$324$	21.0860	1.17145
$325$	0	0
$326$	−2.13582	−0.118292
$327$	−33.9630	−1.87816
$328$	1.59345	0.0879835
$329$	2.44658	0.134884
$330$	0	0
$331$	−14.0034	−0.769697	−0.384849	−	0.922980i	$-0.625746\pi$
$331$	−14.0034	−0.769697	−0.384849	+	0.922980i	$0.625746\pi$
$332$	24.0064	1.31752
$333$	−8.08576	−0.443097
$334$	1.45274	0.0794905
$335$	0	0
$336$	19.3013	1.05297
$337$	−19.4004	−1.05681	−0.528403	−	0.848994i	$-0.677209\pi$
$337$	−19.4004	−1.05681	−0.528403	+	0.848994i	$0.677209\pi$
$338$	2.88325	0.156828
$339$	36.4029	1.97714
$340$	0	0
$341$	5.13537	0.278096
$342$	−0.453197	−0.0245061
$343$	19.6075	1.05871
$344$	4.35078	0.234579
$345$	0	0
$346$	−5.54095	−0.297883
$347$	−25.3742	−1.36216	−0.681080	−	0.732209i	$-0.738489\pi$
$347$	−25.3742	−1.36216	−0.681080	+	0.732209i	$0.738489\pi$
$348$	−30.2852	−1.62346
$349$	13.5179	0.723595	0.361798	−	0.932257i	$-0.382163\pi$
$349$	13.5179	0.723595	0.361798	+	0.932257i	$0.382163\pi$
$350$	0	0
$351$	3.72117	0.198622
$352$	−9.82395	−0.523618
$353$	−23.9138	−1.27280	−0.636402	−	0.771357i	$-0.719578\pi$
$353$	−23.9138	−1.27280	−0.636402	+	0.771357i	$0.719578\pi$
$354$	0.547387	0.0290933
$355$	0	0
$356$	11.8716	0.629196
$357$	8.76350	0.463814
$358$	0.0670711	0.00354482
$359$	−4.99363	−0.263554	−0.131777	−	0.991279i	$-0.542068\pi$
$359$	−4.99363	−0.263554	−0.131777	+	0.991279i	$0.542068\pi$
$360$	0	0
$361$	−18.3717	−0.966930
$362$	4.08917	0.214922
$363$	3.85313	0.202237
$364$	7.91674	0.414950
$365$	0	0
$366$	−7.60886	−0.397721
$367$	4.30607	0.224775	0.112388	−	0.993664i	$-0.464150\pi$
$367$	4.30607	0.224775	0.112388	+	0.993664i	$0.464150\pi$
$368$	2.25351	0.117473
$369$	2.88506	0.150190
$370$	0	0
$371$	10.6607	0.553477
$372$	7.24587	0.375681
$373$	−26.2921	−1.36135	−0.680676	−	0.732585i	$-0.738314\pi$
$373$	−26.2921	−1.36135	−0.680676	+	0.732585i	$0.738314\pi$
$374$	−1.38308	−0.0715175
$375$	0	0
$376$	−1.11250	−0.0573727
$377$	−11.8787	−0.611784
$378$	1.53285	0.0788414
$379$	−4.41806	−0.226940	−0.113470	−	0.993541i	$-0.536197\pi$
$379$	−4.41806	−0.226940	−0.113470	+	0.993541i	$0.536197\pi$
$380$	0	0
$381$	33.9964	1.74169
$382$	−6.09238	−0.311713
$383$	10.0894	0.515546	0.257773	−	0.966206i	$-0.417011\pi$
$383$	10.0894	0.515546	0.257773	+	0.966206i	$0.417011\pi$
$384$	−18.3399	−0.935902
$385$	0	0
$386$	1.68492	0.0857602
$387$	7.87742	0.400432
$388$	−14.5592	−0.739131
$389$	−0.824812	−0.0418196	−0.0209098	−	0.999781i	$-0.506656\pi$
$389$	−0.824812	−0.0418196	−0.0209098	+	0.999781i	$0.506656\pi$
$390$	0	0
$391$	1.02318	0.0517443
$392$	−1.12836	−0.0569908
$393$	−15.9855	−0.806364
$394$	0.752447	0.0379077
$395$	0	0
$396$	−11.7773	−0.591832
$397$	24.4928	1.22926	0.614628	−	0.788817i	$-0.289306\pi$
$397$	24.4928	1.22926	0.614628	+	0.788817i	$0.289306\pi$
$398$	−5.82165	−0.291813
$399$	4.34269	0.217406
$400$	0	0
$401$	−28.6205	−1.42924	−0.714620	−	0.699513i	$-0.753400\pi$
$401$	−28.6205	−1.42924	−0.714620	+	0.699513i	$0.753400\pi$
$402$	5.56814	0.277713
$403$	2.84203	0.141571
$404$	10.1606	0.505509
$405$	0	0
$406$	−4.89315	−0.242843
$407$	−12.2282	−0.606130
$408$	−3.98490	−0.197282
$409$	−13.1580	−0.650620	−0.325310	−	0.945607i	$-0.605469\pi$
$409$	−13.1580	−0.650620	−0.325310	+	0.945607i	$0.605469\pi$
$410$	0	0
$411$	18.6814	0.921486
$412$	−19.7083	−0.970959
$413$	−2.10705	−0.103681
$414$	−0.365702	−0.0179733
$415$	0	0
$416$	−5.43680	−0.266561
$417$	44.8947	2.19850
$418$	−0.685376	−0.0335228
$419$	9.57944	0.467986	0.233993	−	0.972238i	$-0.424821\pi$
$419$	9.57944	0.467986	0.233993	+	0.972238i	$0.424821\pi$
$420$	0	0
$421$	6.63155	0.323202	0.161601	−	0.986856i	$-0.448334\pi$
$421$	6.63155	0.323202	0.161601	+	0.986856i	$0.448334\pi$
$422$	7.68904	0.374297
$423$	−2.01426	−0.0979367
$424$	−4.84760	−0.235420
$425$	0	0
$426$	1.44138	0.0698351
$427$	29.2887	1.41738
$428$	17.6573	0.853498
$429$	−11.4994	−0.555196
$430$	0	0
$431$	−20.4977	−0.987340	−0.493670	−	0.869649i	$-0.664345\pi$
$431$	−20.4977	−0.987340	−0.493670	+	0.869649i	$0.664345\pi$
$432$	7.77661	0.374152
$433$	−15.6252	−0.750898	−0.375449	−	0.926843i	$-0.622511\pi$
$433$	−15.6252	−0.750898	−0.375449	+	0.926843i	$0.622511\pi$
$434$	1.17071	0.0561958
$435$	0	0
$436$	−29.1122	−1.39422
$437$	0.507028	0.0242544
$438$	−6.80307	−0.325063
$439$	16.7080	0.797429	0.398714	−	0.917075i	$-0.369457\pi$
$439$	16.7080	0.797429	0.398714	+	0.917075i	$0.369457\pi$
$440$	0	0
$441$	−2.04298	−0.0972849
$442$	−0.765429	−0.0364077
$443$	9.34544	0.444015	0.222008	−	0.975045i	$-0.428739\pi$
$443$	9.34544	0.444015	0.222008	+	0.975045i	$0.428739\pi$
$444$	−17.2537	−0.818824
$445$	0	0
$446$	1.85995	0.0880709
$447$	−30.1175	−1.42451
$448$	14.9995	0.708659
$449$	−13.6950	−0.646305	−0.323152	−	0.946347i	$-0.604743\pi$
$449$	−13.6950	−0.646305	−0.323152	+	0.946347i	$0.604743\pi$
$450$	0	0
$451$	4.36311	0.205451
$452$	31.2037	1.46770
$453$	25.3668	1.19184
$454$	−4.56280	−0.214143
$455$	0	0
$456$	−1.97469	−0.0924733
$457$	−21.9057	−1.02470	−0.512352	−	0.858775i	$-0.671226\pi$
$457$	−21.9057	−1.02470	−0.512352	+	0.858775i	$0.671226\pi$
$458$	−3.20182	−0.149611
$459$	3.53086	0.164807
$460$	0	0
$461$	24.2716	1.13044	0.565222	−	0.824939i	$-0.308791\pi$
$461$	24.2716	1.13044	0.565222	+	0.824939i	$0.308791\pi$
$462$	−4.73691	−0.220381
$463$	−17.0449	−0.792145	−0.396072	−	0.918219i	$-0.629627\pi$
$463$	−17.0449	−0.792145	−0.396072	+	0.918219i	$0.629627\pi$
$464$	−24.8244	−1.15244
$465$	0	0
$466$	−1.56004	−0.0722676
$467$	7.71308	0.356919	0.178459	−	0.983947i	$-0.442889\pi$
$467$	7.71308	0.356919	0.178459	+	0.983947i	$0.442889\pi$
$468$	−6.51783	−0.301287
$469$	−21.4333	−0.989700
$470$	0	0
$471$	12.2997	0.566741
$472$	0.958108	0.0441005
$473$	11.9131	0.547766
$474$	6.52612	0.299755
$475$	0	0
$476$	7.51186	0.344305
$477$	−8.77694	−0.401869
$478$	5.15072	0.235588
$479$	21.3521	0.975601	0.487800	−	0.872955i	$-0.337799\pi$
$479$	21.3521	0.975601	0.487800	+	0.872955i	$0.337799\pi$
$480$	0	0
$481$	−6.76737	−0.308565
$482$	−2.08024	−0.0947523
$483$	3.50428	0.159450
$484$	3.30281	0.150128
$485$	0	0
$486$	−5.10274	−0.231465
$487$	−1.96466	−0.0890271	−0.0445136	−	0.999009i	$-0.514174\pi$
$487$	−1.96466	−0.0890271	−0.0445136	+	0.999009i	$0.514174\pi$
$488$	−13.3180	−0.602878
$489$	−16.8497	−0.761971
$490$	0	0
$491$	−10.5036	−0.474022	−0.237011	−	0.971507i	$-0.576168\pi$
$491$	−10.5036	−0.474022	−0.237011	+	0.971507i	$0.576168\pi$
$492$	6.15625	0.277545
$493$	−11.2712	−0.507629
$494$	−0.379303	−0.0170656
$495$	0	0
$496$	5.93935	0.266684
$497$	−5.54828	−0.248875
$498$	−7.94938	−0.356220
$499$	−3.77821	−0.169136	−0.0845680	−	0.996418i	$-0.526951\pi$
$499$	−3.77821	−0.169136	−0.0845680	+	0.996418i	$0.526951\pi$
$500$	0	0
$501$	11.4608	0.512032
$502$	8.13498	0.363082
$503$	18.7126	0.834355	0.417177	−	0.908825i	$-0.363019\pi$
$503$	18.7126	0.834355	0.417177	+	0.908825i	$0.363019\pi$
$504$	−5.48243	−0.244207
$505$	0	0
$506$	−0.553055	−0.0245863
$507$	22.7463	1.01020
$508$	29.1409	1.29292
$509$	14.1848	0.628729	0.314364	−	0.949302i	$-0.398209\pi$
$509$	14.1848	0.628729	0.314364	+	0.949302i	$0.398209\pi$
$510$	0	0
$511$	26.1869	1.15844
$512$	−19.2008	−0.848565
$513$	1.74969	0.0772509
$514$	−2.67239	−0.117874
$515$	0	0
$516$	16.8091	0.739980
$517$	−3.04619	−0.133971
$518$	−2.78766	−0.122483
$519$	−43.7131	−1.91879
$520$	0	0
$521$	36.6861	1.60725	0.803623	−	0.595138i	$-0.202903\pi$
$521$	36.6861	1.60725	0.803623	+	0.595138i	$0.202903\pi$
$522$	4.02852	0.176324
$523$	−4.59390	−0.200877	−0.100439	−	0.994943i	$-0.532025\pi$
$523$	−4.59390	−0.200877	−0.100439	+	0.994943i	$0.532025\pi$
$524$	−13.7024	−0.598593
$525$	0	0
$526$	−4.20554	−0.183370
$527$	2.69668	0.117469
$528$	−24.0317	−1.04585
$529$	−22.5909	−0.982211
$530$	0	0
$531$	1.73473	0.0752807
$532$	3.72245	0.161389
$533$	2.41465	0.104590
$534$	−3.93112	−0.170116
$535$	0	0
$536$	9.74608	0.420967
$537$	0.529131	0.0228337
$538$	2.44087	0.105233
$539$	−3.08963	−0.133080
$540$	0	0
$541$	−14.9730	−0.643740	−0.321870	−	0.946784i	$-0.604311\pi$
$541$	−14.9730	−0.643740	−0.321870	+	0.946784i	$0.604311\pi$
$542$	5.59429	0.240295
$543$	32.2599	1.38441
$544$	−5.15875	−0.221179
$545$	0	0
$546$	−2.62151	−0.112190
$547$	−25.3233	−1.08275	−0.541374	−	0.840782i	$-0.682096\pi$
$547$	−25.3233	−1.08275	−0.541374	+	0.840782i	$0.682096\pi$
$548$	16.0132	0.684052
$549$	−24.1133	−1.02913
$550$	0	0
$551$	−5.58535	−0.237944
$552$	−1.59345	−0.0678217
$553$	−25.1209	−1.06825
$554$	5.86914	0.249356
$555$	0	0
$556$	38.4826	1.63203
$557$	1.19693	0.0507156	0.0253578	−	0.999678i	$-0.491928\pi$
$557$	1.19693	0.0507156	0.0253578	+	0.999678i	$0.491928\pi$
$558$	−0.963841	−0.0408026
$559$	6.59299	0.278854
$560$	0	0
$561$	−10.9113	−0.460675
$562$	−6.35078	−0.267892
$563$	−8.99363	−0.379036	−0.189518	−	0.981877i	$-0.560693\pi$
$563$	−8.99363	−0.379036	−0.189518	+	0.981877i	$0.560693\pi$
$564$	−4.29810	−0.180983
$565$	0	0
$566$	1.43226	0.0602024
$567$	26.8770	1.12873
$568$	2.52289	0.105858
$569$	−8.55047	−0.358454	−0.179227	−	0.983808i	$-0.557360\pi$
$569$	−8.55047	−0.358454	−0.179227	+	0.983808i	$0.557360\pi$
$570$	0	0
$571$	14.7178	0.615919	0.307960	−	0.951399i	$-0.400354\pi$
$571$	14.7178	0.615919	0.307960	+	0.951399i	$0.400354\pi$
$572$	−9.85700	−0.412142
$573$	−48.0635	−2.00788
$574$	0.994658	0.0415162
$575$	0	0
$576$	−12.3490	−0.514543
$577$	−2.66006	−0.110740	−0.0553700	−	0.998466i	$-0.517634\pi$
$577$	−2.66006	−0.110740	−0.0553700	+	0.998466i	$0.517634\pi$
$578$	4.09902	0.170497
$579$	13.2925	0.552418
$580$	0	0
$581$	30.5994	1.26948
$582$	4.82107	0.199840
$583$	−13.2735	−0.549732
$584$	−11.9076	−0.492741
$585$	0	0
$586$	6.24312	0.257901
$587$	−5.85058	−0.241479	−0.120740	−	0.992684i	$-0.538527\pi$
$587$	−5.85058	−0.241479	−0.120740	+	0.992684i	$0.538527\pi$
$588$	−4.35939	−0.179778
$589$	1.33632	0.0550621
$590$	0	0
$591$	5.93614	0.244180
$592$	−14.1426	−0.581258
$593$	−3.95426	−0.162382	−0.0811911	−	0.996699i	$-0.525872\pi$
$593$	−3.95426	−0.162382	−0.0811911	+	0.996699i	$0.525872\pi$
$594$	−1.90853	−0.0783079
$595$	0	0
$596$	−25.8160	−1.05746
$597$	−45.9276	−1.87969
$598$	−0.306073	−0.0125163
$599$	14.2418	0.581904	0.290952	−	0.956738i	$-0.406028\pi$
$599$	14.2418	0.581904	0.290952	+	0.956738i	$0.406028\pi$
$600$	0	0
$601$	−7.52811	−0.307078	−0.153539	−	0.988143i	$-0.549067\pi$
$601$	−7.52811	−0.307078	−0.153539	+	0.988143i	$0.549067\pi$
$602$	2.71583	0.110689
$603$	17.6460	0.718601
$604$	21.7438	0.884742
$605$	0	0
$606$	−3.36454	−0.136675
$607$	−35.5596	−1.44332	−0.721661	−	0.692247i	$-0.756621\pi$
$607$	−35.5596	−1.44332	−0.721661	+	0.692247i	$0.756621\pi$
$608$	−2.55638	−0.103675
$609$	−38.6026	−1.56426
$610$	0	0
$611$	−1.68583	−0.0682014
$612$	−6.18449	−0.249993
$613$	−32.6222	−1.31760	−0.658800	−	0.752319i	$-0.728935\pi$
$613$	−32.6222	−1.31760	−0.658800	+	0.752319i	$0.728935\pi$
$614$	6.58406	0.265711
$615$	0	0
$616$	−8.29115	−0.334060
$617$	22.9015	0.921980	0.460990	−	0.887405i	$-0.347494\pi$
$617$	22.9015	0.921980	0.460990	+	0.887405i	$0.347494\pi$
$618$	6.52612	0.262519
$619$	25.1418	1.01053	0.505267	−	0.862963i	$-0.331394\pi$
$619$	25.1418	1.01053	0.505267	+	0.862963i	$0.331394\pi$
$620$	0	0
$621$	1.41189	0.0566573
$622$	1.86612	0.0748244
$623$	15.1320	0.606251
$624$	−13.2997	−0.532414
$625$	0	0
$626$	0.493427	0.0197213
$627$	−5.40701	−0.215935
$628$	10.5430	0.420712
$629$	−6.42127	−0.256033
$630$	0	0
$631$	36.2885	1.44462	0.722310	−	0.691569i	$-0.243080\pi$
$631$	36.2885	1.44462	0.722310	+	0.691569i	$0.243080\pi$
$632$	11.4229	0.454377
$633$	60.6597	2.41100
$634$	−6.54817	−0.260061
$635$	0	0
$636$	−18.7286	−0.742636
$637$	−1.70987	−0.0677476
$638$	6.09238	0.241200
$639$	4.56789	0.180703
$640$	0	0
$641$	−41.0652	−1.62198	−0.810989	−	0.585062i	$-0.801070\pi$
$641$	−41.0652	−1.62198	−0.810989	+	0.585062i	$0.801070\pi$
$642$	−5.84696	−0.230761
$643$	5.36143	0.211434	0.105717	−	0.994396i	$-0.466286\pi$
$643$	5.36143	0.211434	0.105717	+	0.994396i	$0.466286\pi$
$644$	3.00378	0.118365
$645$	0	0
$646$	−0.359904	−0.0141602
$647$	−39.5653	−1.55547	−0.777737	−	0.628590i	$-0.783633\pi$
$647$	−39.5653	−1.55547	−0.777737	+	0.628590i	$0.783633\pi$
$648$	−12.2214	−0.480101
$649$	2.62345	0.102979
$650$	0	0
$651$	9.23584	0.361981
$652$	−14.4432	−0.565638
$653$	−0.342940	−0.0134203	−0.00671014	−	0.999977i	$-0.502136\pi$
$653$	−0.342940	−0.0134203	−0.00671014	+	0.999977i	$0.502136\pi$
$654$	9.64010	0.376958
$655$	0	0
$656$	5.04619	0.197021
$657$	−21.5596	−0.841122
$658$	−0.694440	−0.0270721
$659$	31.2248	1.21635	0.608173	−	0.793805i	$-0.291903\pi$
$659$	31.2248	1.21635	0.608173	+	0.793805i	$0.291903\pi$
$660$	0	0
$661$	8.52720	0.331670	0.165835	−	0.986154i	$-0.446968\pi$
$661$	8.52720	0.331670	0.165835	+	0.986154i	$0.446968\pi$
$662$	3.97475	0.154483
$663$	−6.03855	−0.234518
$664$	−13.9140	−0.539969
$665$	0	0
$666$	2.29507	0.0889323
$667$	−4.50703	−0.174513
$668$	9.82395	0.380100
$669$	14.6733	0.567303
$670$	0	0
$671$	−36.4668	−1.40779
$672$	−17.6682	−0.681564
$673$	−19.2041	−0.740264	−0.370132	−	0.928979i	$-0.620688\pi$
$673$	−19.2041	−0.740264	−0.370132	+	0.928979i	$0.620688\pi$
$674$	5.50663	0.212107
$675$	0	0
$676$	19.4976	0.749906
$677$	47.2980	1.81781	0.908905	−	0.417002i	$-0.136919\pi$
$677$	47.2980	1.81781	0.908905	+	0.417002i	$0.136919\pi$
$678$	−10.3327	−0.396823
$679$	−18.5577	−0.712178
$680$	0	0
$681$	−35.9964	−1.37938
$682$	−1.45763	−0.0558155
$683$	−19.1384	−0.732309	−0.366155	−	0.930554i	$-0.619326\pi$
$683$	−19.1384	−0.732309	−0.366155	+	0.930554i	$0.619326\pi$
$684$	−3.06468	−0.117181
$685$	0	0
$686$	−5.56542	−0.212489
$687$	−25.2595	−0.963709
$688$	13.7782	0.525289
$689$	−7.34585	−0.279855
$690$	0	0
$691$	−23.2867	−0.885869	−0.442934	−	0.896554i	$-0.646063\pi$
$691$	−23.2867	−0.885869	−0.442934	+	0.896554i	$0.646063\pi$
$692$	−37.4698	−1.42439
$693$	−15.0118	−0.570250
$694$	7.20225	0.273394
$695$	0	0
$696$	17.5532	0.665353
$697$	2.29115	0.0867837
$698$	−3.83693	−0.145230
$699$	−12.3073	−0.465507
$700$	0	0
$701$	45.5247	1.71944	0.859722	−	0.510762i	$-0.170637\pi$
$701$	45.5247	1.71944	0.859722	+	0.510762i	$0.170637\pi$
$702$	−1.05622	−0.0398646
$703$	−3.18201	−0.120012
$704$	−18.6756	−0.703863
$705$	0	0
$706$	6.78773	0.255460
$707$	12.9511	0.487075
$708$	3.70162	0.139116
$709$	−24.4144	−0.916904	−0.458452	−	0.888719i	$-0.651596\pi$
$709$	−24.4144	−0.916904	−0.458452	+	0.888719i	$0.651596\pi$
$710$	0	0
$711$	20.6820	0.775634
$712$	−6.88076	−0.257867
$713$	1.07833	0.0403836
$714$	−2.48744	−0.0930902
$715$	0	0
$716$	0.453558	0.0169503
$717$	40.6346	1.51753
$718$	1.41740	0.0528969
$719$	−20.3312	−0.758225	−0.379113	−	0.925351i	$-0.623771\pi$
$719$	−20.3312	−0.758225	−0.379113	+	0.925351i	$0.623771\pi$
$720$	0	0
$721$	−25.1209	−0.935551
$722$	5.21464	0.194069
$723$	−16.4112	−0.610340
$724$	27.6524	1.02769
$725$	0	0
$726$	−1.09368	−0.0405902
$727$	35.0743	1.30083	0.650417	−	0.759577i	$-0.274594\pi$
$727$	35.0743	1.30083	0.650417	+	0.759577i	$0.274594\pi$
$728$	−4.58851	−0.170062
$729$	−7.29945	−0.270350
$730$	0	0
$731$	6.25581	0.231380
$732$	−51.4538	−1.90179
$733$	−15.1084	−0.558040	−0.279020	−	0.960285i	$-0.590010\pi$
$733$	−15.1084	−0.558040	−0.279020	+	0.960285i	$0.590010\pi$
$734$	−1.22224	−0.0451138
$735$	0	0
$736$	−2.06284	−0.0760372
$737$	26.6863	0.983002
$738$	−0.818899	−0.0301441
$739$	−2.82588	−0.103952	−0.0519758	−	0.998648i	$-0.516552\pi$
$739$	−2.82588	−0.103952	−0.0519758	+	0.998648i	$0.516552\pi$
$740$	0	0
$741$	−2.99236	−0.109927
$742$	−3.02595	−0.111086
$743$	−32.9485	−1.20876	−0.604382	−	0.796695i	$-0.706580\pi$
$743$	−32.9485	−1.20876	−0.604382	+	0.796695i	$0.706580\pi$
$744$	−4.19968	−0.153968
$745$	0	0
$746$	7.46277	0.273232
$747$	−25.1924	−0.921742
$748$	−9.35288	−0.341975
$749$	22.5066	0.822374
$750$	0	0
$751$	4.95110	0.180668	0.0903342	−	0.995912i	$-0.471206\pi$
$751$	4.95110	0.180668	0.0903342	+	0.995912i	$0.471206\pi$
$752$	−3.52310	−0.128474
$753$	64.1777	2.33877
$754$	3.37166	0.122789
$755$	0	0
$756$	10.3657	0.376996
$757$	23.8932	0.868413	0.434207	−	0.900813i	$-0.357029\pi$
$757$	23.8932	0.868413	0.434207	+	0.900813i	$0.357029\pi$
$758$	1.25403	0.0455483
$759$	−4.36311	−0.158371
$760$	0	0
$761$	−34.0064	−1.23273	−0.616366	−	0.787460i	$-0.711396\pi$
$761$	−34.0064	−1.23273	−0.616366	+	0.787460i	$0.711396\pi$
$762$	−9.64958	−0.349567
$763$	−37.1075	−1.34338
$764$	−41.1988	−1.49052
$765$	0	0
$766$	−2.86380	−0.103473
$767$	1.45188	0.0524242
$768$	−22.2513	−0.802923
$769$	−5.02963	−0.181373	−0.0906866	−	0.995879i	$-0.528906\pi$
$769$	−5.02963	−0.181373	−0.0906866	+	0.995879i	$0.528906\pi$
$770$	0	0
$771$	−21.0828	−0.759279
$772$	11.3940	0.410080
$773$	−29.3118	−1.05427	−0.527136	−	0.849781i	$-0.676734\pi$
$773$	−29.3118	−1.05427	−0.527136	+	0.849781i	$0.676734\pi$
$774$	−2.23594	−0.0803691
$775$	0	0
$776$	8.43846	0.302923
$777$	−21.9922	−0.788964
$778$	0.234116	0.00839345
$779$	1.13537	0.0406787
$780$	0	0
$781$	6.90807	0.247190
$782$	−0.290420	−0.0103854
$783$	−15.5532	−0.555827
$784$	−3.57333	−0.127619
$785$	0	0
$786$	4.53736	0.161842
$787$	41.7046	1.48661	0.743304	−	0.668954i	$-0.233258\pi$
$787$	41.7046	1.48661	0.743304	+	0.668954i	$0.233258\pi$
$788$	5.08831	0.181264
$789$	−33.1779	−1.18117
$790$	0	0
$791$	39.7733	1.41418
$792$	6.82608	0.242554
$793$	−20.1816	−0.716668
$794$	−6.95206	−0.246719
$795$	0	0
$796$	−39.3680	−1.39536
$797$	25.0448	0.887131	0.443565	−	0.896242i	$-0.353713\pi$
$797$	25.0448	0.887131	0.443565	+	0.896242i	$0.353713\pi$
$798$	−1.23263	−0.0436348
$799$	−1.59961	−0.0565903
$800$	0	0
$801$	−12.4581	−0.440186
$802$	8.12368	0.286857
$803$	−32.6049	−1.15060
$804$	37.6537	1.32794
$805$	0	0
$806$	−0.806685	−0.0284143
$807$	19.2563	0.677853
$808$	−5.88905	−0.207176
$809$	−9.29186	−0.326684	−0.163342	−	0.986569i	$-0.552227\pi$
$809$	−9.29186	−0.326684	−0.163342	+	0.986569i	$0.552227\pi$
$810$	0	0
$811$	24.2836	0.852711	0.426356	−	0.904556i	$-0.359797\pi$
$811$	24.2836	0.852711	0.426356	+	0.904556i	$0.359797\pi$
$812$	−33.0892	−1.16120
$813$	44.1339	1.54784
$814$	3.47087	0.121654
$815$	0	0
$816$	−12.6195	−0.441772
$817$	3.10002	0.108456
$818$	3.73478	0.130583
$819$	−8.30785	−0.290300
$820$	0	0
$821$	26.7981	0.935259	0.467630	−	0.883925i	$-0.345108\pi$
$821$	26.7981	0.935259	0.467630	+	0.883925i	$0.345108\pi$
$822$	−5.30255	−0.184948
$823$	34.7497	1.21130	0.605650	−	0.795731i	$-0.292913\pi$
$823$	34.7497	1.21130	0.605650	+	0.795731i	$0.292913\pi$
$824$	11.4229	0.397935
$825$	0	0
$826$	0.598067	0.0208094
$827$	25.0804	0.872132	0.436066	−	0.899915i	$-0.356371\pi$
$827$	25.0804	0.872132	0.436066	+	0.899915i	$0.356371\pi$
$828$	−2.47300	−0.0859428
$829$	15.3680	0.533754	0.266877	−	0.963731i	$-0.414008\pi$
$829$	15.3680	0.533754	0.266877	+	0.963731i	$0.414008\pi$
$830$	0	0
$831$	46.3023	1.60621
$832$	−10.3355	−0.358319
$833$	−1.62242	−0.0562137
$834$	−12.7430	−0.441253
$835$	0	0
$836$	−4.63475	−0.160296
$837$	3.72117	0.128623
$838$	−2.71904	−0.0939277
$839$	−6.97383	−0.240763	−0.120382	−	0.992728i	$-0.538412\pi$
$839$	−6.97383	−0.240763	−0.120382	+	0.992728i	$0.538412\pi$
$840$	0	0
$841$	20.6488	0.712028
$842$	−1.88231	−0.0648686
$843$	−50.1020	−1.72560
$844$	51.9960	1.78978
$845$	0	0
$846$	0.571730	0.0196565
$847$	4.20987	0.144653
$848$	−15.3515	−0.527174
$849$	11.2992	0.387789
$850$	0	0
$851$	−2.56768	−0.0880190
$852$	9.74712	0.333931
$853$	9.20798	0.315275	0.157638	−	0.987497i	$-0.449612\pi$
$853$	9.20798	0.315275	0.157638	+	0.987497i	$0.449612\pi$
$854$	−8.31333	−0.284476
$855$	0	0
$856$	−10.2341	−0.349795
$857$	41.4329	1.41532	0.707661	−	0.706552i	$-0.249750\pi$
$857$	41.4329	1.41532	0.707661	+	0.706552i	$0.249750\pi$
$858$	3.26400	0.111431
$859$	27.9941	0.955146	0.477573	−	0.878592i	$-0.341517\pi$
$859$	27.9941	0.955146	0.477573	+	0.878592i	$0.341517\pi$
$860$	0	0
$861$	7.84696	0.267424
$862$	5.81809	0.198165
$863$	−17.5539	−0.597541	−0.298770	−	0.954325i	$-0.596577\pi$
$863$	−17.5539	−0.597541	−0.298770	+	0.954325i	$0.596577\pi$
$864$	−7.11860	−0.242180
$865$	0	0
$866$	4.43507	0.150710
$867$	32.3376	1.09824
$868$	7.91674	0.268712
$869$	31.2776	1.06102
$870$	0	0
$871$	14.7688	0.500422
$872$	16.8733	0.571404
$873$	15.2785	0.517098
$874$	−0.143916	−0.00486802
$875$	0	0
$876$	−46.0047	−1.55436
$877$	51.8738	1.75165	0.875827	−	0.482625i	$-0.160317\pi$
$877$	51.8738	1.75165	0.875827	+	0.482625i	$0.160317\pi$
$878$	−4.74242	−0.160049
$879$	49.2527	1.66125
$880$	0	0
$881$	−18.4545	−0.621747	−0.310873	−	0.950451i	$-0.600622\pi$
$881$	−18.4545	−0.621747	−0.310873	+	0.950451i	$0.600622\pi$
$882$	0.579883	0.0195257
$883$	42.4462	1.42843	0.714214	−	0.699928i	$-0.246784\pi$
$883$	42.4462	1.42843	0.714214	+	0.699928i	$0.246784\pi$
$884$	−5.17610	−0.174091
$885$	0	0
$886$	−2.65262	−0.0891166
$887$	38.9089	1.30643	0.653217	−	0.757171i	$-0.273419\pi$
$887$	38.9089	1.30643	0.653217	+	0.757171i	$0.273419\pi$
$888$	10.0002	0.335584
$889$	37.1440	1.24577
$890$	0	0
$891$	−33.4640	−1.12109
$892$	12.5776	0.421129
$893$	−0.792677	−0.0265259
$894$	8.54859	0.285908
$895$	0	0
$896$	−20.0379	−0.669418
$897$	−2.41465	−0.0806227
$898$	3.88719	0.129717
$899$	−11.8787	−0.396177
$900$	0	0
$901$	−6.97016	−0.232210
$902$	−1.23843	−0.0412353
$903$	21.4255	0.712996
$904$	−18.0856	−0.601517
$905$	0	0
$906$	−7.20014	−0.239209
$907$	−23.4857	−0.779831	−0.389916	−	0.920851i	$-0.627496\pi$
$907$	−23.4857	−0.779831	−0.389916	+	0.920851i	$0.627496\pi$
$908$	−30.8552	−1.02397
$909$	−10.6626	−0.353655
$910$	0	0
$911$	−53.2077	−1.76285	−0.881426	−	0.472323i	$-0.843416\pi$
$911$	−53.2077	−1.76285	−0.881426	+	0.472323i	$0.843416\pi$
$912$	−6.25351	−0.207075
$913$	−38.0988	−1.26089
$914$	6.21774	0.205665
$915$	0	0
$916$	−21.6518	−0.715396
$917$	−17.4656	−0.576764
$918$	−1.00221	−0.0330777
$919$	−27.6080	−0.910703	−0.455351	−	0.890312i	$-0.650486\pi$
$919$	−27.6080	−0.910703	−0.455351	+	0.890312i	$0.650486\pi$
$920$	0	0
$921$	51.9424	1.71156
$922$	−6.88929	−0.226887
$923$	3.82308	0.125838
$924$	−32.0326	−1.05380
$925$	0	0
$926$	4.83805	0.158988
$927$	20.6820	0.679285
$928$	22.7239	0.745949
$929$	19.7652	0.648476	0.324238	−	0.945976i	$-0.394892\pi$
$929$	19.7652	0.648476	0.324238	+	0.945976i	$0.394892\pi$
$930$	0	0
$931$	−0.803980	−0.0263494
$932$	−10.5496	−0.345562
$933$	14.7220	0.481976
$934$	−2.18929	−0.0716358
$935$	0	0
$936$	3.77771	0.123478
$937$	−33.7940	−1.10400	−0.552001	−	0.833844i	$-0.686136\pi$
$937$	−33.7940	−1.10400	−0.552001	+	0.833844i	$0.686136\pi$
$938$	6.08367	0.198639
$939$	3.89270	0.127033
$940$	0	0
$941$	24.7205	0.805866	0.402933	−	0.915230i	$-0.367991\pi$
$941$	24.7205	0.805866	0.402933	+	0.915230i	$0.367991\pi$
$942$	−3.49116	−0.113748
$943$	0.916168	0.0298345
$944$	3.03417	0.0987539
$945$	0	0
$946$	−3.38144	−0.109940
$947$	19.4351	0.631557	0.315778	−	0.948833i	$-0.397734\pi$
$947$	19.4351	0.631557	0.315778	+	0.948833i	$0.397734\pi$
$948$	44.1319	1.43334
$949$	−18.0443	−0.585743
$950$	0	0
$951$	−51.6592	−1.67516
$952$	−4.35385	−0.141109
$953$	−10.7976	−0.349767	−0.174884	−	0.984589i	$-0.555955\pi$
$953$	−10.7976	−0.349767	−0.174884	+	0.984589i	$0.555955\pi$
$954$	2.49126	0.0806575
$955$	0	0
$956$	34.8309	1.12651
$957$	48.0635	1.55367
$958$	−6.06060	−0.195809
$959$	20.4110	0.659107
$960$	0	0
$961$	−28.1580	−0.908322
$962$	1.92086	0.0619309
$963$	−18.5296	−0.597109
$964$	−14.0673	−0.453078
$965$	0	0
$966$	−0.994658	−0.0320026
$967$	−17.2538	−0.554844	−0.277422	−	0.960748i	$-0.589480\pi$
$967$	−17.2538	−0.554844	−0.277422	+	0.960748i	$0.589480\pi$
$968$	−1.91430	−0.0615278
$969$	−2.83932	−0.0912122
$970$	0	0
$971$	45.5769	1.46263	0.731315	−	0.682039i	$-0.238907\pi$
$971$	45.5769	1.46263	0.731315	+	0.682039i	$0.238907\pi$
$972$	−34.5065	−1.10680
$973$	49.0513	1.57251
$974$	0.557651	0.0178683
$975$	0	0
$976$	−42.1760	−1.35002
$977$	7.34274	0.234915	0.117457	−	0.993078i	$-0.462526\pi$
$977$	7.34274	0.234915	0.117457	+	0.993078i	$0.462526\pi$
$978$	4.78265	0.152932
$979$	−18.8406	−0.602148
$980$	0	0
$981$	30.5505	0.975401
$982$	2.98136	0.0951390
$983$	59.9413	1.91183	0.955915	−	0.293644i	$-0.0948679\pi$
$983$	59.9413	1.91183	0.955915	+	0.293644i	$0.0948679\pi$
$984$	−3.56814	−0.113748
$985$	0	0
$986$	3.19923	0.101884
$987$	−5.47851	−0.174383
$988$	−2.56498	−0.0816028
$989$	2.50152	0.0795438
$990$	0	0
$991$	−1.82506	−0.0579751	−0.0289875	−	0.999580i	$-0.509228\pi$
$991$	−1.82506	−0.0579751	−0.0289875	+	0.999580i	$0.509228\pi$
$992$	−5.43680	−0.172618
$993$	31.3572	0.995091
$994$	1.57483	0.0499506
$995$	0	0
$996$	−53.7565	−1.70334
$997$	−31.1359	−0.986083	−0.493041	−	0.870006i	$-0.664115\pi$
$997$	−31.1359	−0.986083	−0.493041	+	0.870006i	$0.664115\pi$
$998$	1.07241	0.0339466
$999$	−8.86077	−0.280342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.f.1.3		4
5.2	odd	4		1175.2.c.e.424.4		8
5.3	odd	4		1175.2.c.e.424.5		8
5.4	even	2		47.2.a.a.1.2	✓	4
15.14	odd	2		423.2.a.k.1.3		4
20.19	odd	2		752.2.a.h.1.1		4
35.34	odd	2		2303.2.a.h.1.2		4
40.19	odd	2		3008.2.a.p.1.4		4
40.29	even	2		3008.2.a.q.1.1		4
55.54	odd	2		5687.2.a.s.1.3		4
60.59	even	2		6768.2.a.bv.1.4		4
65.64	even	2		7943.2.a.h.1.3		4
235.234	odd	2		2209.2.a.e.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.2.a.a.1.2	✓	4	5.4	even	2
423.2.a.k.1.3		4	15.14	odd	2
752.2.a.h.1.1		4	20.19	odd	2
1175.2.a.f.1.3		4	1.1	even	1	trivial
1175.2.c.e.424.4		8	5.2	odd	4
1175.2.c.e.424.5		8	5.3	odd	4
2209.2.a.e.1.2		4	235.234	odd	2
2303.2.a.h.1.2		4	35.34	odd	2
3008.2.a.p.1.4		4	40.19	odd	2
3008.2.a.q.1.1		4	40.29	even	2
5687.2.a.s.1.3		4	55.54	odd	2
6768.2.a.bv.1.4		4	60.59	even	2
7943.2.a.h.1.3		4	65.64	even	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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-0.283841 q^{2} -2.23925 q^{3} -1.91943 q^{4} +0.635593 q^{6} -2.44658 q^{7} +1.11250 q^{8} +2.01426 q^{9} +O(q^{10})\)	\(q-0.283841 q^{2} -2.23925 q^{3} -1.91943 q^{4} +0.635593 q^{6} -2.44658 q^{7} +1.11250 q^{8} +2.01426 q^{9} +3.04619 q^{11} +4.29810 q^{12} +1.68583 q^{13} +0.694440 q^{14} +3.52310 q^{16} +1.59961 q^{17} -0.571730 q^{18} +0.792677 q^{19} +5.47851 q^{21} -0.864635 q^{22} +0.639640 q^{23} -2.49116 q^{24} -0.478509 q^{26} +2.20732 q^{27} +4.69604 q^{28} -7.04619 q^{29} +1.68583 q^{31} -3.22499 q^{32} -6.82120 q^{33} -0.454036 q^{34} -3.86624 q^{36} -4.01426 q^{37} -0.224994 q^{38} -3.77501 q^{39} +1.43232 q^{41} -1.55503 q^{42} +3.91083 q^{43} -5.84696 q^{44} -0.181556 q^{46} -1.00000 q^{47} -7.88911 q^{48} -1.01426 q^{49} -3.58194 q^{51} -3.23584 q^{52} -4.35740 q^{53} -0.626529 q^{54} -2.72181 q^{56} -1.77501 q^{57} +2.00000 q^{58} +0.861223 q^{59} -11.9713 q^{61} -0.478509 q^{62} -4.92804 q^{63} -6.13080 q^{64} +1.93614 q^{66} +8.76054 q^{67} -3.07035 q^{68} -1.43232 q^{69} +2.26777 q^{71} +2.24086 q^{72} -10.7035 q^{73} +1.13941 q^{74} -1.52149 q^{76} -7.45274 q^{77} +1.07150 q^{78} +10.2678 q^{79} -10.9855 q^{81} -0.406551 q^{82} -12.5070 q^{83} -10.5156 q^{84} -1.11005 q^{86} +15.7782 q^{87} +3.38888 q^{88} -6.18497 q^{89} -4.12452 q^{91} -1.22775 q^{92} -3.77501 q^{93} +0.283841 q^{94} +7.22158 q^{96} +7.58515 q^{97} +0.287889 q^{98} +6.13582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9	\( 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9} - 6 q^{11} + 11 q^{12} - 8 q^{13} - 5 q^{14} + 5 q^{16} - 6 q^{17} - 16 q^{18} + 4 q^{21} - 4 q^{22} + 6 q^{23} - 13 q^{24} + 16 q^{26} + 12 q^{27} - 16 q^{28} - 10 q^{29} - 8 q^{31} - 10 q^{32} - 12 q^{33} - 10 q^{34} + 11 q^{36} - 10 q^{37} + 2 q^{38} - 18 q^{39} + 6 q^{41} + 15 q^{42} - 2 q^{43} - 30 q^{44} + 18 q^{46} - 4 q^{47} - 6 q^{48} + 2 q^{49} - 8 q^{51} - 4 q^{52} + 6 q^{53} - 5 q^{54} + 2 q^{56} - 10 q^{57} + 8 q^{58} + 4 q^{59} - 6 q^{61} + 16 q^{62} - 16 q^{63} - 31 q^{64} + 32 q^{66} - 10 q^{67} - 43 q^{68} - 6 q^{69} - 12 q^{71} - 27 q^{72} - 22 q^{73} + 18 q^{74} - 24 q^{76} + 10 q^{77} + 28 q^{78} + 20 q^{79} + 4 q^{81} + 20 q^{82} - 20 q^{83} - 19 q^{84} + 38 q^{86} + 12 q^{87} - 2 q^{88} - 6 q^{89} - 22 q^{91} + 32 q^{92} - 18 q^{93} + q^{94} + 26 q^{96} - 30 q^{97} + 15 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9 - 6 * q^11 + 11 * q^12 - 8 * q^13 - 5 * q^14 + 5 * q^16 - 6 * q^17 - 16 * q^18 + 4 * q^21 - 4 * q^22 + 6 * q^23 - 13 * q^24 + 16 * q^26 + 12 * q^27 - 16 * q^28 - 10 * q^29 - 8 * q^31 - 10 * q^32 - 12 * q^33 - 10 * q^34 + 11 * q^36 - 10 * q^37 + 2 * q^38 - 18 * q^39 + 6 * q^41 + 15 * q^42 - 2 * q^43 - 30 * q^44 + 18 * q^46 - 4 * q^47 - 6 * q^48 + 2 * q^49 - 8 * q^51 - 4 * q^52 + 6 * q^53 - 5 * q^54 + 2 * q^56 - 10 * q^57 + 8 * q^58 + 4 * q^59 - 6 * q^61 + 16 * q^62 - 16 * q^63 - 31 * q^64 + 32 * q^66 - 10 * q^67 - 43 * q^68 - 6 * q^69 - 12 * q^71 - 27 * q^72 - 22 * q^73 + 18 * q^74 - 24 * q^76 + 10 * q^77 + 28 * q^78 + 20 * q^79 + 4 * q^81 + 20 * q^82 - 20 * q^83 - 19 * q^84 + 38 * q^86 + 12 * q^87 - 2 * q^88 - 6 * q^89 - 22 * q^91 + 32 * q^92 - 18 * q^93 + q^94 + 26 * q^96 - 30 * q^97 + 15 * q^98 + 4 * q^99

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