LMFDB - Embedded newform 3525.2.a.bc.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} - 15x^{2} + 1 $ x^7 - 3x^6 - 5x^5 + 18x^4 - 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.28015$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.28015 q^{2} +1.00000 q^{3} -0.361223 q^{4} +1.28015 q^{6} -3.00128 q^{7} -3.02271 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.28015 q^{2} +1.00000 q^{3} -0.361223 q^{4} +1.28015 q^{6} -3.00128 q^{7} -3.02271 q^{8} +1.00000 q^{9} +2.74632 q^{11} -0.361223 q^{12} +1.26074 q^{13} -3.84208 q^{14} -3.14707 q^{16} +0.0436434 q^{17} +1.28015 q^{18} +0.625373 q^{19} -3.00128 q^{21} +3.51570 q^{22} +5.48349 q^{23} -3.02271 q^{24} +1.61393 q^{26} +1.00000 q^{27} +1.08413 q^{28} -3.98787 q^{29} -1.30027 q^{31} +2.01671 q^{32} +2.74632 q^{33} +0.0558700 q^{34} -0.361223 q^{36} +5.54991 q^{37} +0.800569 q^{38} +1.26074 q^{39} +6.26096 q^{41} -3.84208 q^{42} +11.4265 q^{43} -0.992033 q^{44} +7.01968 q^{46} -1.00000 q^{47} -3.14707 q^{48} +2.00767 q^{49} +0.0436434 q^{51} -0.455407 q^{52} +5.93481 q^{53} +1.28015 q^{54} +9.07200 q^{56} +0.625373 q^{57} -5.10507 q^{58} -2.51829 q^{59} +0.757284 q^{61} -1.66453 q^{62} -3.00128 q^{63} +8.87583 q^{64} +3.51570 q^{66} +1.99624 q^{67} -0.0157650 q^{68} +5.48349 q^{69} -2.84526 q^{71} -3.02271 q^{72} +4.79041 q^{73} +7.10471 q^{74} -0.225899 q^{76} -8.24247 q^{77} +1.61393 q^{78} +7.03902 q^{79} +1.00000 q^{81} +8.01496 q^{82} +6.52979 q^{83} +1.08413 q^{84} +14.6276 q^{86} -3.98787 q^{87} -8.30134 q^{88} +2.62065 q^{89} -3.78383 q^{91} -1.98076 q^{92} -1.30027 q^{93} -1.28015 q^{94} +2.01671 q^{96} +1.36869 q^{97} +2.57012 q^{98} +2.74632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.28015	0.905201	0.452600	−	0.891713i	$-0.350496\pi$
$2$	1.28015	0.905201	0.452600	+	0.891713i	$0.350496\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.361223	−0.180611
$5$	0	0
$5$	0	0
$6$	1.28015	0.522618
$7$	−3.00128	−1.13438	−0.567188	−	0.823588i	$-0.691969\pi$
$7$	−3.00128	−1.13438	−0.567188	+	0.823588i	$0.691969\pi$
$8$	−3.02271	−1.06869
$9$	1.00000	0.333333
$10$	0	0
$11$	2.74632	0.828047	0.414023	−	0.910266i	$-0.364123\pi$
$11$	2.74632	0.828047	0.414023	+	0.910266i	$0.364123\pi$
$12$	−0.361223	−0.104276
$13$	1.26074	0.349666	0.174833	−	0.984598i	$-0.444061\pi$
$13$	1.26074	0.349666	0.174833	+	0.984598i	$0.444061\pi$
$14$	−3.84208	−1.02684
$15$	0	0
$16$	−3.14707	−0.786768
$17$	0.0436434	0.0105851	0.00529254	−	0.999986i	$-0.498315\pi$
$17$	0.0436434	0.0105851	0.00529254	+	0.999986i	$0.498315\pi$
$18$	1.28015	0.301734
$19$	0.625373	0.143470	0.0717352	−	0.997424i	$-0.477146\pi$
$19$	0.625373	0.143470	0.0717352	+	0.997424i	$0.477146\pi$
$20$	0	0
$21$	−3.00128	−0.654933
$22$	3.51570	0.749549
$23$	5.48349	1.14339	0.571694	−	0.820467i	$-0.306287\pi$
$23$	5.48349	1.14339	0.571694	+	0.820467i	$0.306287\pi$
$24$	−3.02271	−0.617009
$25$	0	0
$26$	1.61393	0.316518
$27$	1.00000	0.192450
$28$	1.08413	0.204881
$29$	−3.98787	−0.740530	−0.370265	−	0.928926i	$-0.620733\pi$
$29$	−3.98787	−0.740530	−0.370265	+	0.928926i	$0.620733\pi$
$30$	0	0
$31$	−1.30027	−0.233535	−0.116768	−	0.993159i	$-0.537253\pi$
$31$	−1.30027	−0.233535	−0.116768	+	0.993159i	$0.537253\pi$
$32$	2.01671	0.356507
$33$	2.74632	0.478073
$34$	0.0558700	0.00958162
$35$	0	0
$36$	−0.361223	−0.0602038
$37$	5.54991	0.912400	0.456200	−	0.889877i	$-0.349210\pi$
$37$	5.54991	0.912400	0.456200	+	0.889877i	$0.349210\pi$
$38$	0.800569	0.129870
$39$	1.26074	0.201880
$40$	0	0
$41$	6.26096	0.977798	0.488899	−	0.872340i	$-0.337399\pi$
$41$	6.26096	0.977798	0.488899	+	0.872340i	$0.337399\pi$
$42$	−3.84208	−0.592846
$43$	11.4265	1.74252	0.871260	−	0.490821i	$-0.163303\pi$
$43$	11.4265	1.74252	0.871260	+	0.490821i	$0.163303\pi$
$44$	−0.992033	−0.149555
$45$	0	0
$46$	7.01968	1.03500
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−3.14707	−0.454241
$49$	2.00767	0.286810
$50$	0	0
$51$	0.0436434	0.00611129
$52$	−0.455407	−0.0631536
$53$	5.93481	0.815209	0.407605	−	0.913159i	$-0.366364\pi$
$53$	5.93481	0.815209	0.407605	+	0.913159i	$0.366364\pi$
$54$	1.28015	0.174206
$55$	0	0
$56$	9.07200	1.21230
$57$	0.625373	0.0828327
$58$	−5.10507	−0.670328
$59$	−2.51829	−0.327853	−0.163927	−	0.986473i	$-0.552416\pi$
$59$	−2.51829	−0.327853	−0.163927	+	0.986473i	$0.552416\pi$
$60$	0	0
$61$	0.757284	0.0969603	0.0484802	−	0.998824i	$-0.484562\pi$
$61$	0.757284	0.0969603	0.0484802	+	0.998824i	$0.484562\pi$
$62$	−1.66453	−0.211396
$63$	−3.00128	−0.378126
$64$	8.87583	1.10948
$65$	0	0
$66$	3.51570	0.432752
$67$	1.99624	0.243880	0.121940	−	0.992537i	$-0.461088\pi$
$67$	1.99624	0.243880	0.121940	+	0.992537i	$0.461088\pi$
$68$	−0.0157650	−0.00191178
$69$	5.48349	0.660135
$70$	0	0
$71$	−2.84526	−0.337670	−0.168835	−	0.985644i	$-0.554001\pi$
$71$	−2.84526	−0.337670	−0.168835	+	0.985644i	$0.554001\pi$
$72$	−3.02271	−0.356230
$73$	4.79041	0.560675	0.280337	−	0.959902i	$-0.409554\pi$
$73$	4.79041	0.560675	0.280337	+	0.959902i	$0.409554\pi$
$74$	7.10471	0.825906
$75$	0	0
$76$	−0.225899	−0.0259124
$77$	−8.24247	−0.939317
$78$	1.61393	0.182742
$79$	7.03902	0.791951	0.395976	−	0.918261i	$-0.370406\pi$
$79$	7.03902	0.791951	0.395976	+	0.918261i	$0.370406\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	8.01496	0.885104
$83$	6.52979	0.716738	0.358369	−	0.933580i	$-0.383333\pi$
$83$	6.52979	0.716738	0.358369	+	0.933580i	$0.383333\pi$
$84$	1.08413	0.118288
$85$	0	0
$86$	14.6276	1.57733
$87$	−3.98787	−0.427545
$88$	−8.30134	−0.884926
$89$	2.62065	0.277788	0.138894	−	0.990307i	$-0.455645\pi$
$89$	2.62065	0.277788	0.138894	+	0.990307i	$0.455645\pi$
$90$	0	0
$91$	−3.78383	−0.396653
$92$	−1.98076	−0.206509
$93$	−1.30027	−0.134832
$94$	−1.28015	−0.132037
$95$	0	0
$96$	2.01671	0.205829
$97$	1.36869	0.138969	0.0694845	−	0.997583i	$-0.477865\pi$
$97$	1.36869	0.138969	0.0694845	+	0.997583i	$0.477865\pi$
$98$	2.57012	0.259621
$99$	2.74632	0.276016
$100$	0	0
$101$	9.70659	0.965842	0.482921	−	0.875664i	$-0.339576\pi$
$101$	9.70659	0.965842	0.482921	+	0.875664i	$0.339576\pi$
$102$	0.0558700	0.00553195
$103$	6.53582	0.643993	0.321997	−	0.946741i	$-0.395646\pi$
$103$	6.53582	0.643993	0.321997	+	0.946741i	$0.395646\pi$
$104$	−3.81085	−0.373684
$105$	0	0
$106$	7.59744	0.737928
$107$	−14.3818	−1.39034	−0.695170	−	0.718845i	$-0.744671\pi$
$107$	−14.3818	−1.39034	−0.695170	+	0.718845i	$0.744671\pi$
$108$	−0.361223	−0.0347587
$109$	−5.49097	−0.525940	−0.262970	−	0.964804i	$-0.584702\pi$
$109$	−5.49097	−0.525940	−0.262970	+	0.964804i	$0.584702\pi$
$110$	0	0
$111$	5.54991	0.526775
$112$	9.44524	0.892492
$113$	3.41501	0.321258	0.160629	−	0.987015i	$-0.448648\pi$
$113$	3.41501	0.321258	0.160629	+	0.987015i	$0.448648\pi$
$114$	0.800569	0.0749802
$115$	0	0
$116$	1.44051	0.133748
$117$	1.26074	0.116555
$118$	−3.22378	−0.296773
$119$	−0.130986	−0.0120075
$120$	0	0
$121$	−3.45772	−0.314338
$122$	0.969435	0.0877686
$123$	6.26096	0.564532
$124$	0.469686	0.0421791
$125$	0	0
$126$	−3.84208	−0.342280
$127$	8.82246	0.782867	0.391433	−	0.920206i	$-0.371979\pi$
$127$	8.82246	0.782867	0.391433	+	0.920206i	$0.371979\pi$
$128$	7.32896	0.647794
$129$	11.4265	1.00604
$130$	0	0
$131$	11.8906	1.03888	0.519441	−	0.854506i	$-0.326140\pi$
$131$	11.8906	1.03888	0.519441	+	0.854506i	$0.326140\pi$
$132$	−0.992033	−0.0863454
$133$	−1.87692	−0.162749
$134$	2.55549	0.220761
$135$	0	0
$136$	−0.131921	−0.0113122
$137$	0.799838	0.0683348	0.0341674	−	0.999416i	$-0.489122\pi$
$137$	0.799838	0.0683348	0.0341674	+	0.999416i	$0.489122\pi$
$138$	7.01968	0.597555
$139$	7.44116	0.631151	0.315575	−	0.948901i	$-0.397802\pi$
$139$	7.44116	0.631151	0.315575	+	0.948901i	$0.397802\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−3.64235	−0.305659
$143$	3.46239	0.289540
$144$	−3.14707	−0.262256
$145$	0	0
$146$	6.13243	0.507523
$147$	2.00767	0.165590
$148$	−2.00475	−0.164790
$149$	−8.99509	−0.736907	−0.368453	−	0.929646i	$-0.620113\pi$
$149$	−8.99509	−0.736907	−0.368453	+	0.929646i	$0.620113\pi$
$150$	0	0
$151$	−2.46804	−0.200846	−0.100423	−	0.994945i	$-0.532020\pi$
$151$	−2.46804	−0.200846	−0.100423	+	0.994945i	$0.532020\pi$
$152$	−1.89032	−0.153325
$153$	0.0436434	0.00352836
$154$	−10.5516	−0.850271
$155$	0	0
$156$	−0.455407	−0.0364617
$157$	11.1273	0.888055	0.444028	−	0.896013i	$-0.353549\pi$
$157$	11.1273	0.888055	0.444028	+	0.896013i	$0.353549\pi$
$158$	9.01098	0.716875
$159$	5.93481	0.470661
$160$	0	0
$161$	−16.4575	−1.29703
$162$	1.28015	0.100578
$163$	1.00895	0.0790267	0.0395134	−	0.999219i	$-0.487419\pi$
$163$	1.00895	0.0790267	0.0395134	+	0.999219i	$0.487419\pi$
$164$	−2.26160	−0.176601
$165$	0	0
$166$	8.35910	0.648792
$167$	−19.5523	−1.51300	−0.756500	−	0.653994i	$-0.773092\pi$
$167$	−19.5523	−1.51300	−0.756500	+	0.653994i	$0.773092\pi$
$168$	9.07200	0.699920
$169$	−11.4105	−0.877734
$170$	0	0
$171$	0.625373	0.0478235
$172$	−4.12750	−0.314719
$173$	10.5469	0.801867	0.400933	−	0.916107i	$-0.368686\pi$
$173$	10.5469	0.801867	0.400933	+	0.916107i	$0.368686\pi$
$174$	−5.10507	−0.387014
$175$	0	0
$176$	−8.64287	−0.651481
$177$	−2.51829	−0.189286
$178$	3.35481	0.251454
$179$	2.24430	0.167747	0.0838736	−	0.996476i	$-0.473271\pi$
$179$	2.24430	0.167747	0.0838736	+	0.996476i	$0.473271\pi$
$180$	0	0
$181$	5.09647	0.378818	0.189409	−	0.981898i	$-0.439343\pi$
$181$	5.09647	0.378818	0.189409	+	0.981898i	$0.439343\pi$
$182$	−4.84385	−0.359050
$183$	0.757284	0.0559801
$184$	−16.5750	−1.22193
$185$	0	0
$186$	−1.66453	−0.122050
$187$	0.119859	0.00876494
$188$	0.361223	0.0263449
$189$	−3.00128	−0.218311
$190$	0	0
$191$	2.97972	0.215605	0.107803	−	0.994172i	$-0.465619\pi$
$191$	2.97972	0.215605	0.107803	+	0.994172i	$0.465619\pi$
$192$	8.87583	0.640558
$193$	23.4268	1.68630	0.843150	−	0.537678i	$-0.180698\pi$
$193$	23.4268	1.68630	0.843150	+	0.537678i	$0.180698\pi$
$194$	1.75212	0.125795
$195$	0	0
$196$	−0.725216	−0.0518012
$197$	3.24107	0.230916	0.115458	−	0.993312i	$-0.463166\pi$
$197$	3.24107	0.230916	0.115458	+	0.993312i	$0.463166\pi$
$198$	3.51570	0.249850
$199$	−6.33165	−0.448839	−0.224419	−	0.974493i	$-0.572049\pi$
$199$	−6.33165	−0.448839	−0.224419	+	0.974493i	$0.572049\pi$
$200$	0	0
$201$	1.99624	0.140804
$202$	12.4259	0.874281
$203$	11.9687	0.840039
$204$	−0.0157650	−0.00110377
$205$	0	0
$206$	8.36681	0.582943
$207$	5.48349	0.381129
$208$	−3.96763	−0.275106
$209$	1.71747	0.118800
$210$	0	0
$211$	−24.1230	−1.66070	−0.830349	−	0.557244i	$-0.811859\pi$
$211$	−24.1230	−1.66070	−0.830349	+	0.557244i	$0.811859\pi$
$212$	−2.14379	−0.147236
$213$	−2.84526	−0.194954
$214$	−18.4108	−1.25854
$215$	0	0
$216$	−3.02271	−0.205670
$217$	3.90247	0.264917
$218$	−7.02926	−0.476081
$219$	4.79041	0.323706
$220$	0	0
$221$	0.0550229	0.00370124
$222$	7.10471	0.476837
$223$	4.36499	0.292302	0.146151	−	0.989262i	$-0.453312\pi$
$223$	4.36499	0.292302	0.146151	+	0.989262i	$0.453312\pi$
$224$	−6.05270	−0.404413
$225$	0	0
$226$	4.37172	0.290803
$227$	−9.58430	−0.636133	−0.318066	−	0.948068i	$-0.603033\pi$
$227$	−9.58430	−0.636133	−0.318066	+	0.948068i	$0.603033\pi$
$228$	−0.225899	−0.0149605
$229$	−17.8132	−1.17713	−0.588564	−	0.808451i	$-0.700306\pi$
$229$	−17.8132	−1.17713	−0.588564	+	0.808451i	$0.700306\pi$
$230$	0	0
$231$	−8.24247	−0.542315
$232$	12.0542	0.791397
$233$	−5.99617	−0.392822	−0.196411	−	0.980522i	$-0.562929\pi$
$233$	−5.99617	−0.392822	−0.196411	+	0.980522i	$0.562929\pi$
$234$	1.61393	0.105506
$235$	0	0
$236$	0.909662	0.0592140
$237$	7.03902	0.457233
$238$	−0.167681	−0.0108692
$239$	1.01926	0.0659307	0.0329653	−	0.999456i	$-0.489505\pi$
$239$	1.01926	0.0659307	0.0329653	+	0.999456i	$0.489505\pi$
$240$	0	0
$241$	18.5139	1.19258	0.596291	−	0.802768i	$-0.296640\pi$
$241$	18.5139	1.19258	0.596291	+	0.802768i	$0.296640\pi$
$242$	−4.42639	−0.284539
$243$	1.00000	0.0641500
$244$	−0.273548	−0.0175121
$245$	0	0
$246$	8.01496	0.511015
$247$	0.788431	0.0501667
$248$	3.93034	0.249577
$249$	6.52979	0.413809
$250$	0	0
$251$	−27.9665	−1.76523	−0.882614	−	0.470099i	$-0.844218\pi$
$251$	−27.9665	−1.76523	−0.882614	+	0.470099i	$0.844218\pi$
$252$	1.08413	0.0682937
$253$	15.0594	0.946779
$254$	11.2941	0.708652
$255$	0	0
$256$	−8.36952	−0.523095
$257$	24.6092	1.53508	0.767538	−	0.641003i	$-0.221481\pi$
$257$	24.6092	1.53508	0.767538	+	0.641003i	$0.221481\pi$
$258$	14.6276	0.910673
$259$	−16.6568	−1.03501
$260$	0	0
$261$	−3.98787	−0.246843
$262$	15.2217	0.940398
$263$	−27.2428	−1.67987	−0.839933	−	0.542691i	$-0.817406\pi$
$263$	−27.2428	−1.67987	−0.839933	+	0.542691i	$0.817406\pi$
$264$	−8.30134	−0.510912
$265$	0	0
$266$	−2.40273	−0.147321
$267$	2.62065	0.160381
$268$	−0.721089	−0.0440475
$269$	−10.7199	−0.653603	−0.326802	−	0.945093i	$-0.605971\pi$
$269$	−10.7199	−0.653603	−0.326802	+	0.945093i	$0.605971\pi$
$270$	0	0
$271$	−15.5861	−0.946787	−0.473393	−	0.880851i	$-0.656971\pi$
$271$	−15.5861	−0.946787	−0.473393	+	0.880851i	$0.656971\pi$
$272$	−0.137349	−0.00832800
$273$	−3.78383	−0.229008
$274$	1.02391	0.0618567
$275$	0	0
$276$	−1.98076	−0.119228
$277$	−14.7586	−0.886756	−0.443378	−	0.896335i	$-0.646220\pi$
$277$	−14.7586	−0.886756	−0.443378	+	0.896335i	$0.646220\pi$
$278$	9.52578	0.571318
$279$	−1.30027	−0.0778450
$280$	0	0
$281$	4.61694	0.275424	0.137712	−	0.990472i	$-0.456025\pi$
$281$	4.61694	0.275424	0.137712	+	0.990472i	$0.456025\pi$
$282$	−1.28015	−0.0762317
$283$	1.79804	0.106882	0.0534412	−	0.998571i	$-0.482981\pi$
$283$	1.79804	0.106882	0.0534412	+	0.998571i	$0.482981\pi$
$284$	1.02777	0.0609870
$285$	0	0
$286$	4.43237	0.262092
$287$	−18.7909	−1.10919
$288$	2.01671	0.118836
$289$	−16.9981	−0.999888
$290$	0	0
$291$	1.36869	0.0802337
$292$	−1.73040	−0.101264
$293$	1.62662	0.0950280	0.0475140	−	0.998871i	$-0.484870\pi$
$293$	1.62662	0.0950280	0.0475140	+	0.998871i	$0.484870\pi$
$294$	2.57012	0.149892
$295$	0	0
$296$	−16.7758	−0.975073
$297$	2.74632	0.159358
$298$	−11.5150	−0.667049
$299$	6.91325	0.399804
$300$	0	0
$301$	−34.2940	−1.97667
$302$	−3.15945	−0.181806
$303$	9.70659	0.557629
$304$	−1.96809	−0.112878
$305$	0	0
$306$	0.0558700	0.00319387
$307$	30.9040	1.76378	0.881892	−	0.471452i	$-0.156270\pi$
$307$	30.9040	1.76378	0.881892	+	0.471452i	$0.156270\pi$
$308$	2.97737	0.169651
$309$	6.53582	0.371810
$310$	0	0
$311$	16.6590	0.944648	0.472324	−	0.881425i	$-0.343415\pi$
$311$	16.6590	0.944648	0.472324	+	0.881425i	$0.343415\pi$
$312$	−3.81085	−0.215747
$313$	−22.1171	−1.25013	−0.625065	−	0.780572i	$-0.714928\pi$
$313$	−22.1171	−1.25013	−0.625065	+	0.780572i	$0.714928\pi$
$314$	14.2446	0.803868
$315$	0	0
$316$	−2.54265	−0.143035
$317$	−19.7631	−1.11001	−0.555004	−	0.831847i	$-0.687283\pi$
$317$	−19.7631	−1.11001	−0.555004	+	0.831847i	$0.687283\pi$
$318$	7.59744	0.426043
$319$	−10.9520	−0.613193
$320$	0	0
$321$	−14.3818	−0.802713
$322$	−21.0680	−1.17407
$323$	0.0272934	0.00151864
$324$	−0.361223	−0.0200679
$325$	0	0
$326$	1.29160	0.0715351
$327$	−5.49097	−0.303652
$328$	−18.9251	−1.04496
$329$	3.00128	0.165466
$330$	0	0
$331$	23.3167	1.28160	0.640801	−	0.767707i	$-0.278602\pi$
$331$	23.3167	1.28160	0.640801	+	0.767707i	$0.278602\pi$
$332$	−2.35871	−0.129451
$333$	5.54991	0.304133
$334$	−25.0298	−1.36957
$335$	0	0
$336$	9.44524	0.515280
$337$	0.425756	0.0231924	0.0115962	−	0.999933i	$-0.496309\pi$
$337$	0.425756	0.0231924	0.0115962	+	0.999933i	$0.496309\pi$
$338$	−14.6072	−0.794525
$339$	3.41501	0.185478
$340$	0	0
$341$	−3.57095	−0.193378
$342$	0.800569	0.0432898
$343$	14.9834	0.809026
$344$	−34.5390	−1.86222
$345$	0	0
$346$	13.5016	0.725850
$347$	32.3440	1.73632	0.868159	−	0.496286i	$-0.165303\pi$
$347$	32.3440	1.73632	0.868159	+	0.496286i	$0.165303\pi$
$348$	1.44051	0.0772194
$349$	−13.6558	−0.730979	−0.365490	−	0.930815i	$-0.619098\pi$
$349$	−13.6558	−0.730979	−0.365490	+	0.930815i	$0.619098\pi$
$350$	0	0
$351$	1.26074	0.0672932
$352$	5.53853	0.295205
$353$	−22.3747	−1.19089	−0.595444	−	0.803397i	$-0.703024\pi$
$353$	−22.3747	−1.19089	−0.595444	+	0.803397i	$0.703024\pi$
$354$	−3.22378	−0.171342
$355$	0	0
$356$	−0.946636	−0.0501716
$357$	−0.130986	−0.00693251
$358$	2.87304	0.151845
$359$	−9.45030	−0.498768	−0.249384	−	0.968405i	$-0.580228\pi$
$359$	−9.45030	−0.498768	−0.249384	+	0.968405i	$0.580228\pi$
$360$	0	0
$361$	−18.6089	−0.979416
$362$	6.52423	0.342906
$363$	−3.45772	−0.181483
$364$	1.36680	0.0716399
$365$	0	0
$366$	0.969435	0.0506732
$367$	−13.5022	−0.704810	−0.352405	−	0.935848i	$-0.614636\pi$
$367$	−13.5022	−0.704810	−0.352405	+	0.935848i	$0.614636\pi$
$368$	−17.2570	−0.899581
$369$	6.26096	0.325933
$370$	0	0
$371$	−17.8120	−0.924754
$372$	0.469686	0.0243521
$373$	−31.1481	−1.61279	−0.806394	−	0.591379i	$-0.798584\pi$
$373$	−31.1481	−1.61279	−0.806394	+	0.591379i	$0.798584\pi$
$374$	0.153437	0.00793403
$375$	0	0
$376$	3.02271	0.155885
$377$	−5.02766	−0.258938
$378$	−3.84208	−0.197615
$379$	18.1059	0.930038	0.465019	−	0.885301i	$-0.346047\pi$
$379$	18.1059	0.930038	0.465019	+	0.885301i	$0.346047\pi$
$380$	0	0
$381$	8.82246	0.451988
$382$	3.81448	0.195166
$383$	16.9924	0.868270	0.434135	−	0.900848i	$-0.357054\pi$
$383$	16.9924	0.868270	0.434135	+	0.900848i	$0.357054\pi$
$384$	7.32896	0.374004
$385$	0	0
$386$	29.9898	1.52644
$387$	11.4265	0.580840
$388$	−0.494400	−0.0250994
$389$	−6.98631	−0.354220	−0.177110	−	0.984191i	$-0.556675\pi$
$389$	−6.98631	−0.354220	−0.177110	+	0.984191i	$0.556675\pi$
$390$	0	0
$391$	0.239318	0.0121028
$392$	−6.06862	−0.306511
$393$	11.8906	0.599799
$394$	4.14904	0.209026
$395$	0	0
$396$	−0.992033	−0.0498515
$397$	−8.43657	−0.423420	−0.211710	−	0.977333i	$-0.567903\pi$
$397$	−8.43657	−0.423420	−0.211710	+	0.977333i	$0.567903\pi$
$398$	−8.10544	−0.406289
$399$	−1.87692	−0.0939634
$400$	0	0
$401$	27.1342	1.35502	0.677508	−	0.735515i	$-0.263060\pi$
$401$	27.1342	1.35502	0.677508	+	0.735515i	$0.263060\pi$
$402$	2.55549	0.127456
$403$	−1.63930	−0.0816592
$404$	−3.50624	−0.174442
$405$	0	0
$406$	15.3217	0.760404
$407$	15.2418	0.755510
$408$	−0.131921	−0.00653108
$409$	−13.9481	−0.689687	−0.344843	−	0.938660i	$-0.612068\pi$
$409$	−13.9481	−0.689687	−0.344843	+	0.938660i	$0.612068\pi$
$410$	0	0
$411$	0.799838	0.0394531
$412$	−2.36088	−0.116312
$413$	7.55808	0.371909
$414$	7.01968	0.344999
$415$	0	0
$416$	2.54254	0.124658
$417$	7.44116	0.364395
$418$	2.19862	0.107538
$419$	−23.1673	−1.13179	−0.565897	−	0.824476i	$-0.691470\pi$
$419$	−23.1673	−1.13179	−0.565897	+	0.824476i	$0.691470\pi$
$420$	0	0
$421$	−20.6977	−1.00874	−0.504372	−	0.863487i	$-0.668276\pi$
$421$	−20.6977	−1.00874	−0.504372	+	0.863487i	$0.668276\pi$
$422$	−30.8810	−1.50327
$423$	−1.00000	−0.0486217
$424$	−17.9392	−0.871206
$425$	0	0
$426$	−3.64235	−0.176472
$427$	−2.27282	−0.109990
$428$	5.19503	0.251111
$429$	3.46239	0.167166
$430$	0	0
$431$	20.4020	0.982732	0.491366	−	0.870953i	$-0.336498\pi$
$431$	20.4020	0.982732	0.491366	+	0.870953i	$0.336498\pi$
$432$	−3.14707	−0.151414
$433$	−19.7933	−0.951203	−0.475602	−	0.879661i	$-0.657770\pi$
$433$	−19.7933	−0.951203	−0.475602	+	0.879661i	$0.657770\pi$
$434$	4.99573	0.239803
$435$	0	0
$436$	1.98346	0.0949907
$437$	3.42923	0.164042
$438$	6.13243	0.293019
$439$	12.1111	0.578030	0.289015	−	0.957325i	$-0.406672\pi$
$439$	12.1111	0.578030	0.289015	+	0.957325i	$0.406672\pi$
$440$	0	0
$441$	2.00767	0.0956034
$442$	0.0704374	0.00335036
$443$	33.8626	1.60886	0.804430	−	0.594048i	$-0.202471\pi$
$443$	33.8626	1.60886	0.804430	+	0.594048i	$0.202471\pi$
$444$	−2.00475	−0.0951414
$445$	0	0
$446$	5.58783	0.264592
$447$	−8.99509	−0.425453
$448$	−26.6388	−1.25857
$449$	29.7807	1.40544	0.702720	−	0.711466i	$-0.251969\pi$
$449$	29.7807	1.40544	0.702720	+	0.711466i	$0.251969\pi$
$450$	0	0
$451$	17.1946	0.809663
$452$	−1.23358	−0.0580227
$453$	−2.46804	−0.115959
$454$	−12.2693	−0.575828
$455$	0	0
$456$	−1.89032	−0.0885225
$457$	16.1423	0.755104	0.377552	−	0.925988i	$-0.376766\pi$
$457$	16.1423	0.755104	0.377552	+	0.925988i	$0.376766\pi$
$458$	−22.8035	−1.06554
$459$	0.0436434	0.00203710
$460$	0	0
$461$	18.0452	0.840447	0.420224	−	0.907421i	$-0.361952\pi$
$461$	18.0452	0.840447	0.420224	+	0.907421i	$0.361952\pi$
$462$	−10.5516	−0.490904
$463$	−4.95570	−0.230311	−0.115155	−	0.993347i	$-0.536737\pi$
$463$	−4.95570	−0.230311	−0.115155	+	0.993347i	$0.536737\pi$
$464$	12.5501	0.582625
$465$	0	0
$466$	−7.67599	−0.355583
$467$	17.9884	0.832405	0.416203	−	0.909272i	$-0.363361\pi$
$467$	17.9884	0.832405	0.416203	+	0.909272i	$0.363361\pi$
$468$	−0.455407	−0.0210512
$469$	−5.99129	−0.276652
$470$	0	0
$471$	11.1273	0.512719
$472$	7.61206	0.350374
$473$	31.3808	1.44289
$474$	9.01098	0.413888
$475$	0	0
$476$	0.0473151	0.00216868
$477$	5.93481	0.271736
$478$	1.30481	0.0596805
$479$	15.0937	0.689651	0.344826	−	0.938667i	$-0.387938\pi$
$479$	15.0937	0.689651	0.344826	+	0.938667i	$0.387938\pi$
$480$	0	0
$481$	6.99699	0.319035
$482$	23.7005	1.07953
$483$	−16.4575	−0.748842
$484$	1.24901	0.0567730
$485$	0	0
$486$	1.28015	0.0580687
$487$	27.3152	1.23777	0.618886	−	0.785481i	$-0.287584\pi$
$487$	27.3152	1.23777	0.618886	+	0.785481i	$0.287584\pi$
$488$	−2.28905	−0.103621
$489$	1.00895	0.0456261
$490$	0	0
$491$	−22.0136	−0.993458	−0.496729	−	0.867906i	$-0.665466\pi$
$491$	−22.0136	−0.993458	−0.496729	+	0.867906i	$0.665466\pi$
$492$	−2.26160	−0.101961
$493$	−0.174044	−0.00783856
$494$	1.00931	0.0454109
$495$	0	0
$496$	4.09204	0.183738
$497$	8.53941	0.383045
$498$	8.35910	0.374580
$499$	10.1756	0.455521	0.227761	−	0.973717i	$-0.426860\pi$
$499$	10.1756	0.455521	0.227761	+	0.973717i	$0.426860\pi$
$500$	0	0
$501$	−19.5523	−0.873530
$502$	−35.8012	−1.59789
$503$	−40.2890	−1.79640	−0.898198	−	0.439591i	$-0.855123\pi$
$503$	−40.2890	−1.79640	−0.898198	+	0.439591i	$0.855123\pi$
$504$	9.07200	0.404099
$505$	0	0
$506$	19.2783	0.857025
$507$	−11.4105	−0.506760
$508$	−3.18687	−0.141395
$509$	26.6410	1.18084	0.590421	−	0.807095i	$-0.298962\pi$
$509$	26.6410	1.18084	0.590421	+	0.807095i	$0.298962\pi$
$510$	0	0
$511$	−14.3773	−0.636016
$512$	−25.3721	−1.12130
$513$	0.625373	0.0276109
$514$	31.5033	1.38955
$515$	0	0
$516$	−4.12750	−0.181703
$517$	−2.74632	−0.120783
$518$	−21.3232	−0.936888
$519$	10.5469	0.462958
$520$	0	0
$521$	−6.47355	−0.283611	−0.141806	−	0.989895i	$-0.545291\pi$
$521$	−6.47355	−0.283611	−0.141806	+	0.989895i	$0.545291\pi$
$522$	−5.10507	−0.223443
$523$	29.4372	1.28720	0.643600	−	0.765362i	$-0.277440\pi$
$523$	29.4372	1.28720	0.643600	+	0.765362i	$0.277440\pi$
$524$	−4.29514	−0.187634
$525$	0	0
$526$	−34.8748	−1.52062
$527$	−0.0567481	−0.00247199
$528$	−8.64287	−0.376133
$529$	7.06871	0.307335
$530$	0	0
$531$	−2.51829	−0.109284
$532$	0.677985	0.0293944
$533$	7.89343	0.341903
$534$	3.35481	0.145177
$535$	0	0
$536$	−6.03407	−0.260632
$537$	2.24430	0.0968489
$538$	−13.7230	−0.591642
$539$	5.51371	0.237492
$540$	0	0
$541$	−3.30807	−0.142225	−0.0711125	−	0.997468i	$-0.522655\pi$
$541$	−3.30807	−0.142225	−0.0711125	+	0.997468i	$0.522655\pi$
$542$	−19.9525	−0.857032
$543$	5.09647	0.218711
$544$	0.0880159	0.00377365
$545$	0	0
$546$	−4.84385	−0.207298
$547$	29.5399	1.26303	0.631517	−	0.775362i	$-0.282433\pi$
$547$	29.5399	1.26303	0.631517	+	0.775362i	$0.282433\pi$
$548$	−0.288919	−0.0123420
$549$	0.757284	0.0323201
$550$	0	0
$551$	−2.49391	−0.106244
$552$	−16.5750	−0.705480
$553$	−21.1261	−0.898371
$554$	−18.8931	−0.802692
$555$	0	0
$556$	−2.68791	−0.113993
$557$	16.0811	0.681379	0.340690	−	0.940176i	$-0.389339\pi$
$557$	16.0811	0.681379	0.340690	+	0.940176i	$0.389339\pi$
$558$	−1.66453	−0.0704654
$559$	14.4058	0.609300
$560$	0	0
$561$	0.119859	0.00506044
$562$	5.91037	0.249314
$563$	−6.01165	−0.253361	−0.126680	−	0.991944i	$-0.540432\pi$
$563$	−6.01165	−0.253361	−0.126680	+	0.991944i	$0.540432\pi$
$564$	0.361223	0.0152102
$565$	0	0
$566$	2.30176	0.0967500
$567$	−3.00128	−0.126042
$568$	8.60040	0.360865
$569$	−15.3523	−0.643603	−0.321802	−	0.946807i	$-0.604288\pi$
$569$	−15.3523	−0.643603	−0.321802	+	0.946807i	$0.604288\pi$
$570$	0	0
$571$	−38.4977	−1.61108	−0.805539	−	0.592543i	$-0.798124\pi$
$571$	−38.4977	−1.61108	−0.805539	+	0.592543i	$0.798124\pi$
$572$	−1.25069	−0.0522941
$573$	2.97972	0.124480
$574$	−24.0551	−1.00404
$575$	0	0
$576$	8.87583	0.369826
$577$	25.5609	1.06411	0.532057	−	0.846708i	$-0.321419\pi$
$577$	25.5609	1.06411	0.532057	+	0.846708i	$0.321419\pi$
$578$	−21.7601	−0.905100
$579$	23.4268	0.973586
$580$	0	0
$581$	−19.5977	−0.813051
$582$	1.75212	0.0726277
$583$	16.2989	0.675031
$584$	−14.4800	−0.599188
$585$	0	0
$586$	2.08231	0.0860194
$587$	26.5180	1.09452	0.547258	−	0.836964i	$-0.315672\pi$
$587$	26.5180	1.09452	0.547258	+	0.836964i	$0.315672\pi$
$588$	−0.725216	−0.0299074
$589$	−0.813152	−0.0335054
$590$	0	0
$591$	3.24107	0.133320
$592$	−17.4660	−0.717848
$593$	4.63271	0.190243	0.0951213	−	0.995466i	$-0.469676\pi$
$593$	4.63271	0.190243	0.0951213	+	0.995466i	$0.469676\pi$
$594$	3.51570	0.144251
$595$	0	0
$596$	3.24923	0.133094
$597$	−6.33165	−0.259137
$598$	8.84998	0.361903
$599$	0.439819	0.0179705	0.00898526	−	0.999960i	$-0.497140\pi$
$599$	0.439819	0.0179705	0.00898526	+	0.999960i	$0.497140\pi$
$600$	0	0
$601$	−6.75233	−0.275433	−0.137717	−	0.990472i	$-0.543976\pi$
$601$	−6.75233	−0.275433	−0.137717	+	0.990472i	$0.543976\pi$
$602$	−43.9014	−1.78929
$603$	1.99624	0.0812934
$604$	0.891511	0.0362751
$605$	0	0
$606$	12.4259	0.504767
$607$	5.22523	0.212086	0.106043	−	0.994362i	$-0.466182\pi$
$607$	5.22523	0.212086	0.106043	+	0.994362i	$0.466182\pi$
$608$	1.26119	0.0511482
$609$	11.9687	0.484997
$610$	0	0
$611$	−1.26074	−0.0510040
$612$	−0.0157650	−0.000637261 0
$613$	−32.9602	−1.33125	−0.665624	−	0.746287i	$-0.731835\pi$
$613$	−32.9602	−1.33125	−0.665624	+	0.746287i	$0.731835\pi$
$614$	39.5617	1.59658
$615$	0	0
$616$	24.9146	1.00384
$617$	−1.72235	−0.0693391	−0.0346695	−	0.999399i	$-0.511038\pi$
$617$	−1.72235	−0.0693391	−0.0346695	+	0.999399i	$0.511038\pi$
$618$	8.36681	0.336562
$619$	−2.34896	−0.0944127	−0.0472064	−	0.998885i	$-0.515032\pi$
$619$	−2.34896	−0.0944127	−0.0472064	+	0.998885i	$0.515032\pi$
$620$	0	0
$621$	5.48349	0.220045
$622$	21.3260	0.855096
$623$	−7.86529	−0.315116
$624$	−3.96763	−0.158833
$625$	0	0
$626$	−28.3131	−1.13162
$627$	1.71747	0.0685893
$628$	−4.01943	−0.160393
$629$	0.242217	0.00965782
$630$	0	0
$631$	−7.48159	−0.297837	−0.148919	−	0.988849i	$-0.547579\pi$
$631$	−7.48159	−0.297837	−0.148919	+	0.988849i	$0.547579\pi$
$632$	−21.2769	−0.846351
$633$	−24.1230	−0.958804
$634$	−25.2997	−1.00478
$635$	0	0
$636$	−2.14379	−0.0850067
$637$	2.53115	0.100288
$638$	−14.0202	−0.555063
$639$	−2.84526	−0.112557
$640$	0	0
$641$	−22.8289	−0.901689	−0.450845	−	0.892603i	$-0.648877\pi$
$641$	−22.8289	−0.901689	−0.450845	+	0.892603i	$0.648877\pi$
$642$	−18.4108	−0.726617
$643$	−25.8446	−1.01921	−0.509606	−	0.860408i	$-0.670209\pi$
$643$	−25.8446	−1.01921	−0.509606	+	0.860408i	$0.670209\pi$
$644$	5.94482	0.234259
$645$	0	0
$646$	0.0349396	0.00137468
$647$	0.601084	0.0236311	0.0118155	−	0.999930i	$-0.496239\pi$
$647$	0.601084	0.0236311	0.0118155	+	0.999930i	$0.496239\pi$
$648$	−3.02271	−0.118743
$649$	−6.91603	−0.271478
$650$	0	0
$651$	3.90247	0.152950
$652$	−0.364454	−0.0142731
$653$	−5.80060	−0.226995	−0.113497	−	0.993538i	$-0.536205\pi$
$653$	−5.80060	−0.226995	−0.113497	+	0.993538i	$0.536205\pi$
$654$	−7.02926	−0.274866
$655$	0	0
$656$	−19.7037	−0.769301
$657$	4.79041	0.186892
$658$	3.84208	0.149780
$659$	17.1755	0.669062	0.334531	−	0.942385i	$-0.391422\pi$
$659$	17.1755	0.669062	0.334531	+	0.942385i	$0.391422\pi$
$660$	0	0
$661$	−27.2153	−1.05855	−0.529277	−	0.848449i	$-0.677537\pi$
$661$	−27.2153	−1.05855	−0.529277	+	0.848449i	$0.677537\pi$
$662$	29.8488	1.16011
$663$	0.0550229	0.00213691
$664$	−19.7377	−0.765971
$665$	0	0
$666$	7.10471	0.275302
$667$	−21.8675	−0.846712
$668$	7.06272	0.273265
$669$	4.36499	0.168760
$670$	0	0
$671$	2.07975	0.0802877
$672$	−6.05270	−0.233488
$673$	−37.9955	−1.46462	−0.732309	−	0.680973i	$-0.761557\pi$
$673$	−37.9955	−1.46462	−0.732309	+	0.680973i	$0.761557\pi$
$674$	0.545030	0.0209938
$675$	0	0
$676$	4.12174	0.158529
$677$	−5.40023	−0.207548	−0.103774	−	0.994601i	$-0.533092\pi$
$677$	−5.40023	−0.207548	−0.103774	+	0.994601i	$0.533092\pi$
$678$	4.37172	0.167895
$679$	−4.10781	−0.157643
$680$	0	0
$681$	−9.58430	−0.367271
$682$	−4.57135	−0.175046
$683$	48.7695	1.86611	0.933056	−	0.359730i	$-0.117131\pi$
$683$	48.7695	1.86611	0.933056	+	0.359730i	$0.117131\pi$
$684$	−0.225899	−0.00863745
$685$	0	0
$686$	19.1809	0.732331
$687$	−17.8132	−0.679615
$688$	−35.9600	−1.37096
$689$	7.48224	0.285051
$690$	0	0
$691$	−1.86416	−0.0709161	−0.0354581	−	0.999371i	$-0.511289\pi$
$691$	−1.86416	−0.0709161	−0.0354581	+	0.999371i	$0.511289\pi$
$692$	−3.80978	−0.144826
$693$	−8.24247	−0.313106
$694$	41.4051	1.57172
$695$	0	0
$696$	12.0542	0.456913
$697$	0.273250	0.0103501
$698$	−17.4815	−0.661683
$699$	−5.99617	−0.226796
$700$	0	0
$701$	0.345089	0.0130338	0.00651691	−	0.999979i	$-0.497926\pi$
$701$	0.345089	0.0130338	0.00651691	+	0.999979i	$0.497926\pi$
$702$	1.61393	0.0609139
$703$	3.47077	0.130902
$704$	24.3759	0.918700
$705$	0	0
$706$	−28.6430	−1.07799
$707$	−29.1322	−1.09563
$708$	0.909662	0.0341872
$709$	18.3242	0.688181	0.344091	−	0.938936i	$-0.388187\pi$
$709$	18.3242	0.688181	0.344091	+	0.938936i	$0.388187\pi$
$710$	0	0
$711$	7.03902	0.263984
$712$	−7.92146	−0.296869
$713$	−7.13001	−0.267021
$714$	−0.167681	−0.00627531
$715$	0	0
$716$	−0.810693	−0.0302970
$717$	1.01926	0.0380651
$718$	−12.0978	−0.451485
$719$	−5.08045	−0.189469	−0.0947345	−	0.995503i	$-0.530200\pi$
$719$	−5.08045	−0.189469	−0.0947345	+	0.995503i	$0.530200\pi$
$720$	0	0
$721$	−19.6158	−0.730531
$722$	−23.8221	−0.886569
$723$	18.5139	0.688538
$724$	−1.84096	−0.0684187
$725$	0	0
$726$	−4.42639	−0.164279
$727$	36.2611	1.34485	0.672425	−	0.740166i	$-0.265253\pi$
$727$	36.2611	1.34485	0.672425	+	0.740166i	$0.265253\pi$
$728$	11.4374	0.423899
$729$	1.00000	0.0370370
$730$	0	0
$731$	0.498690	0.0184447
$732$	−0.273548	−0.0101106
$733$	−53.1357	−1.96261	−0.981306	−	0.192452i	$-0.938356\pi$
$733$	−53.1357	−1.96261	−0.981306	+	0.192452i	$0.938356\pi$
$734$	−17.2848	−0.637995
$735$	0	0
$736$	11.0586	0.407626
$737$	5.48233	0.201944
$738$	8.01496	0.295035
$739$	−33.4919	−1.23202	−0.616010	−	0.787738i	$-0.711252\pi$
$739$	−33.4919	−1.23202	−0.616010	+	0.787738i	$0.711252\pi$
$740$	0	0
$741$	0.788431	0.0289637
$742$	−22.8020	−0.837088
$743$	21.4912	0.788437	0.394218	−	0.919017i	$-0.371015\pi$
$743$	21.4912	0.788437	0.394218	+	0.919017i	$0.371015\pi$
$744$	3.93034	0.144093
$745$	0	0
$746$	−39.8742	−1.45990
$747$	6.52979	0.238913
$748$	−0.0432957	−0.00158305
$749$	43.1638	1.57717
$750$	0	0
$751$	−10.6321	−0.387971	−0.193985	−	0.981004i	$-0.562141\pi$
$751$	−10.6321	−0.387971	−0.193985	+	0.981004i	$0.562141\pi$
$752$	3.14707	0.114762
$753$	−27.9665	−1.01915
$754$	−6.43615	−0.234391
$755$	0	0
$756$	1.08413	0.0394294
$757$	−11.6197	−0.422325	−0.211163	−	0.977451i	$-0.567725\pi$
$757$	−11.6197	−0.422325	−0.211163	+	0.977451i	$0.567725\pi$
$758$	23.1782	0.841872
$759$	15.0594	0.546623
$760$	0	0
$761$	30.4374	1.10335	0.551677	−	0.834058i	$-0.313988\pi$
$761$	30.4374	1.10335	0.551677	+	0.834058i	$0.313988\pi$
$762$	11.2941	0.409140
$763$	16.4799	0.596614
$764$	−1.07634	−0.0389407
$765$	0	0
$766$	21.7527	0.785959
$767$	−3.17490	−0.114639
$768$	−8.36952	−0.302009
$769$	32.3872	1.16791	0.583956	−	0.811786i	$-0.301504\pi$
$769$	32.3872	1.16791	0.583956	+	0.811786i	$0.301504\pi$
$770$	0	0
$771$	24.6092	0.886277
$772$	−8.46230	−0.304565
$773$	−12.0546	−0.433572	−0.216786	−	0.976219i	$-0.569557\pi$
$773$	−12.0546	−0.433572	−0.216786	+	0.976219i	$0.569557\pi$
$774$	14.6276	0.525777
$775$	0	0
$776$	−4.13714	−0.148515
$777$	−16.6568	−0.597561
$778$	−8.94351	−0.320640
$779$	3.91544	0.140285
$780$	0	0
$781$	−7.81399	−0.279607
$782$	0.306363	0.0109555
$783$	−3.98787	−0.142515
$784$	−6.31829	−0.225653
$785$	0	0
$786$	15.2217	0.542939
$787$	−34.3220	−1.22345	−0.611723	−	0.791072i	$-0.709523\pi$
$787$	−34.3220	−1.22345	−0.611723	+	0.791072i	$0.709523\pi$
$788$	−1.17075	−0.0417061
$789$	−27.2428	−0.969871
$790$	0	0
$791$	−10.2494	−0.364427
$792$	−8.30134	−0.294975
$793$	0.954737	0.0339037
$794$	−10.8001	−0.383280
$795$	0	0
$796$	2.28713	0.0810653
$797$	2.20524	0.0781136	0.0390568	−	0.999237i	$-0.487565\pi$
$797$	2.20524	0.0781136	0.0390568	+	0.999237i	$0.487565\pi$
$798$	−2.40273	−0.0850558
$799$	−0.0436434	−0.00154399
$800$	0	0
$801$	2.62065	0.0925960
$802$	34.7358	1.22656
$803$	13.1560	0.464265
$804$	−0.721089	−0.0254308
$805$	0	0
$806$	−2.09854	−0.0739180
$807$	−10.7199	−0.377358
$808$	−29.3402	−1.03219
$809$	36.0940	1.26900	0.634499	−	0.772924i	$-0.281206\pi$
$809$	36.0940	1.26900	0.634499	+	0.772924i	$0.281206\pi$
$810$	0	0
$811$	−34.3505	−1.20621	−0.603104	−	0.797662i	$-0.706070\pi$
$811$	−34.3505	−1.20621	−0.603104	+	0.797662i	$0.706070\pi$
$812$	−4.32337	−0.151721
$813$	−15.5861	−0.546628
$814$	19.5118	0.683889
$815$	0	0
$816$	−0.137349	−0.00480817
$817$	7.14581	0.250000
$818$	−17.8556	−0.624305
$819$	−3.78383	−0.132218
$820$	0	0
$821$	39.7658	1.38783	0.693917	−	0.720055i	$-0.255883\pi$
$821$	39.7658	1.38783	0.693917	+	0.720055i	$0.255883\pi$
$822$	1.02391	0.0357130
$823$	7.96369	0.277597	0.138798	−	0.990321i	$-0.455676\pi$
$823$	7.96369	0.277597	0.138798	+	0.990321i	$0.455676\pi$
$824$	−19.7559	−0.688229
$825$	0	0
$826$	9.67546	0.336652
$827$	0.0730801	0.00254124	0.00127062	−	0.999999i	$-0.499596\pi$
$827$	0.0730801	0.00254124	0.00127062	+	0.999999i	$0.499596\pi$
$828$	−1.98076	−0.0688362
$829$	−2.64633	−0.0919107	−0.0459553	−	0.998943i	$-0.514633\pi$
$829$	−2.64633	−0.0919107	−0.0459553	+	0.998943i	$0.514633\pi$
$830$	0	0
$831$	−14.7586	−0.511969
$832$	11.1901	0.387947
$833$	0.0876216	0.00303591
$834$	9.52578	0.329851
$835$	0	0
$836$	−0.620390	−0.0214567
$837$	−1.30027	−0.0449438
$838$	−29.6575	−1.02450
$839$	−13.9464	−0.481484	−0.240742	−	0.970589i	$-0.577391\pi$
$839$	−13.9464	−0.481484	−0.240742	+	0.970589i	$0.577391\pi$
$840$	0	0
$841$	−13.0969	−0.451616
$842$	−26.4961	−0.913115
$843$	4.61694	0.159016
$844$	8.71378	0.299941
$845$	0	0
$846$	−1.28015	−0.0440124
$847$	10.3776	0.356578
$848$	−18.6773	−0.641381
$849$	1.79804	0.0617086
$850$	0	0
$851$	30.4329	1.04323
$852$	1.02777	0.0352109
$853$	30.3976	1.04079	0.520397	−	0.853924i	$-0.325784\pi$
$853$	30.3976	1.04079	0.520397	+	0.853924i	$0.325784\pi$
$854$	−2.90955	−0.0995626
$855$	0	0
$856$	43.4720	1.48584
$857$	39.8138	1.36001	0.680007	−	0.733206i	$-0.261977\pi$
$857$	39.8138	1.36001	0.680007	+	0.733206i	$0.261977\pi$
$858$	4.43237	0.151319
$859$	−4.16443	−0.142088	−0.0710442	−	0.997473i	$-0.522633\pi$
$859$	−4.16443	−0.142088	−0.0710442	+	0.997473i	$0.522633\pi$
$860$	0	0
$861$	−18.7909	−0.640392
$862$	26.1176	0.889570
$863$	−9.94406	−0.338500	−0.169250	−	0.985573i	$-0.554134\pi$
$863$	−9.94406	−0.338500	−0.169250	+	0.985573i	$0.554134\pi$
$864$	2.01671	0.0686098
$865$	0	0
$866$	−25.3383	−0.861030
$867$	−16.9981	−0.577286
$868$	−1.40966	−0.0478469
$869$	19.3314	0.655773
$870$	0	0
$871$	2.51674	0.0852765
$872$	16.5976	0.562067
$873$	1.36869	0.0463230
$874$	4.38992	0.148491
$875$	0	0
$876$	−1.73040	−0.0584649
$877$	−35.9092	−1.21257	−0.606284	−	0.795249i	$-0.707340\pi$
$877$	−35.9092	−1.21257	−0.606284	+	0.795249i	$0.707340\pi$
$878$	15.5040	0.523233
$879$	1.62662	0.0548644
$880$	0	0
$881$	−28.9158	−0.974197	−0.487098	−	0.873347i	$-0.661945\pi$
$881$	−28.9158	−0.974197	−0.487098	+	0.873347i	$0.661945\pi$
$882$	2.57012	0.0865403
$883$	44.1603	1.48611	0.743056	−	0.669229i	$-0.233375\pi$
$883$	44.1603	1.48611	0.743056	+	0.669229i	$0.233375\pi$
$884$	−0.0198755	−0.000668485 0
$885$	0	0
$886$	43.3491	1.45634
$887$	−20.6047	−0.691839	−0.345919	−	0.938264i	$-0.612433\pi$
$887$	−20.6047	−0.691839	−0.345919	+	0.938264i	$0.612433\pi$
$888$	−16.7758	−0.562959
$889$	−26.4787	−0.888066
$890$	0	0
$891$	2.74632	0.0920052
$892$	−1.57673	−0.0527930
$893$	−0.625373	−0.0209273
$894$	−11.5150	−0.385121
$895$	0	0
$896$	−21.9962	−0.734843
$897$	6.91325	0.230827
$898$	38.1237	1.27221
$899$	5.18530	0.172940
$900$	0	0
$901$	0.259015	0.00862905
$902$	22.0116	0.732907
$903$	−34.2940	−1.14123
$904$	−10.3226	−0.343325
$905$	0	0
$906$	−3.15945	−0.104966
$907$	−41.5017	−1.37804	−0.689021	−	0.724741i	$-0.741959\pi$
$907$	−41.5017	−1.37804	−0.689021	+	0.724741i	$0.741959\pi$
$908$	3.46207	0.114893
$909$	9.70659	0.321947
$910$	0	0
$911$	23.9189	0.792468	0.396234	−	0.918149i	$-0.370317\pi$
$911$	23.9189	0.792468	0.396234	+	0.918149i	$0.370317\pi$
$912$	−1.96809	−0.0651701
$913$	17.9329	0.593493
$914$	20.6645	0.683521
$915$	0	0
$916$	6.43452	0.212602
$917$	−35.6869	−1.17848
$918$	0.0558700	0.00184398
$919$	23.4374	0.773129	0.386564	−	0.922262i	$-0.373662\pi$
$919$	23.4374	0.773129	0.386564	+	0.922262i	$0.373662\pi$
$920$	0	0
$921$	30.9040	1.01832
$922$	23.1005	0.760774
$923$	−3.58713	−0.118072
$924$	2.97737	0.0979482
$925$	0	0
$926$	−6.34402	−0.208477
$927$	6.53582	0.214664
$928$	−8.04238	−0.264004
$929$	−2.60216	−0.0853742	−0.0426871	−	0.999088i	$-0.513592\pi$
$929$	−2.60216	−0.0853742	−0.0426871	+	0.999088i	$0.513592\pi$
$930$	0	0
$931$	1.25554	0.0411488
$932$	2.16595	0.0709481
$933$	16.6590	0.545393
$934$	23.0278	0.753494
$935$	0	0
$936$	−3.81085	−0.124561
$937$	46.9772	1.53468	0.767339	−	0.641242i	$-0.221580\pi$
$937$	46.9772	1.53468	0.767339	+	0.641242i	$0.221580\pi$
$938$	−7.66973	−0.250426
$939$	−22.1171	−0.721763
$940$	0	0
$941$	12.4382	0.405473	0.202736	−	0.979233i	$-0.435017\pi$
$941$	12.4382	0.405473	0.202736	+	0.979233i	$0.435017\pi$
$942$	14.2446	0.464114
$943$	34.3320	1.11800
$944$	7.92524	0.257944
$945$	0	0
$946$	40.1720	1.30610
$947$	45.2384	1.47005	0.735025	−	0.678040i	$-0.237171\pi$
$947$	45.2384	1.47005	0.735025	+	0.678040i	$0.237171\pi$
$948$	−2.54265	−0.0825815
$949$	6.03945	0.196049
$950$	0	0
$951$	−19.7631	−0.640864
$952$	0.395933	0.0128323
$953$	1.31316	0.0425375	0.0212688	−	0.999774i	$-0.493229\pi$
$953$	1.31316	0.0425375	0.0212688	+	0.999774i	$0.493229\pi$
$954$	7.59744	0.245976
$955$	0	0
$956$	−0.368181	−0.0119078
$957$	−10.9520	−0.354027
$958$	19.3222	0.624273
$959$	−2.40054	−0.0775174
$960$	0	0
$961$	−29.3093	−0.945461
$962$	8.95718	0.288791
$963$	−14.3818	−0.463447
$964$	−6.68763	−0.215394
$965$	0	0
$966$	−21.0680	−0.677852
$967$	−37.8507	−1.21720	−0.608598	−	0.793479i	$-0.708268\pi$
$967$	−37.8507	−1.21720	−0.608598	+	0.793479i	$0.708268\pi$
$968$	10.4517	0.335930
$969$	0.0272934	0.000876790 0
$970$	0	0
$971$	5.52714	0.177374	0.0886872	−	0.996060i	$-0.471733\pi$
$971$	5.52714	0.177374	0.0886872	+	0.996060i	$0.471733\pi$
$972$	−0.361223	−0.0115862
$973$	−22.3330	−0.715963
$974$	34.9675	1.12043
$975$	0	0
$976$	−2.38323	−0.0762853
$977$	−16.5771	−0.530348	−0.265174	−	0.964201i	$-0.585429\pi$
$977$	−16.5771	−0.530348	−0.265174	+	0.964201i	$0.585429\pi$
$978$	1.29160	0.0413008
$979$	7.19714	0.230021
$980$	0	0
$981$	−5.49097	−0.175313
$982$	−28.1806	−0.899279
$983$	38.2733	1.22073	0.610365	−	0.792121i	$-0.291023\pi$
$983$	38.2733	1.22073	0.610365	+	0.792121i	$0.291023\pi$
$984$	−18.9251	−0.603310
$985$	0	0
$986$	−0.222802	−0.00709547
$987$	3.00128	0.0955317
$988$	−0.284799	−0.00906067
$989$	62.6570	1.99238
$990$	0	0
$991$	3.07893	0.0978054	0.0489027	−	0.998804i	$-0.484428\pi$
$991$	3.07893	0.0978054	0.0489027	+	0.998804i	$0.484428\pi$
$992$	−2.62226	−0.0832569
$993$	23.3167	0.739933
$994$	10.9317	0.346733
$995$	0	0
$996$	−2.35871	−0.0747385
$997$	17.0094	0.538692	0.269346	−	0.963044i	$-0.413193\pi$
$997$	17.0094	0.538692	0.269346	+	0.963044i	$0.413193\pi$
$998$	13.0262	0.412338
$999$	5.54991	0.175592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bc.1.5	yes	7
5.4	even	2		3525.2.a.x.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.x.1.3	✓	7	5.4	even	2
3525.2.a.bc.1.5	yes	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+1.28015 q^{2} +1.00000 q^{3} -0.361223 q^{4} +1.28015 q^{6} -3.00128 q^{7} -3.02271 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.28015 q^{2} +1.00000 q^{3} -0.361223 q^{4} +1.28015 q^{6} -3.00128 q^{7} -3.02271 q^{8} +1.00000 q^{9} +2.74632 q^{11} -0.361223 q^{12} +1.26074 q^{13} -3.84208 q^{14} -3.14707 q^{16} +0.0436434 q^{17} +1.28015 q^{18} +0.625373 q^{19} -3.00128 q^{21} +3.51570 q^{22} +5.48349 q^{23} -3.02271 q^{24} +1.61393 q^{26} +1.00000 q^{27} +1.08413 q^{28} -3.98787 q^{29} -1.30027 q^{31} +2.01671 q^{32} +2.74632 q^{33} +0.0558700 q^{34} -0.361223 q^{36} +5.54991 q^{37} +0.800569 q^{38} +1.26074 q^{39} +6.26096 q^{41} -3.84208 q^{42} +11.4265 q^{43} -0.992033 q^{44} +7.01968 q^{46} -1.00000 q^{47} -3.14707 q^{48} +2.00767 q^{49} +0.0436434 q^{51} -0.455407 q^{52} +5.93481 q^{53} +1.28015 q^{54} +9.07200 q^{56} +0.625373 q^{57} -5.10507 q^{58} -2.51829 q^{59} +0.757284 q^{61} -1.66453 q^{62} -3.00128 q^{63} +8.87583 q^{64} +3.51570 q^{66} +1.99624 q^{67} -0.0157650 q^{68} +5.48349 q^{69} -2.84526 q^{71} -3.02271 q^{72} +4.79041 q^{73} +7.10471 q^{74} -0.225899 q^{76} -8.24247 q^{77} +1.61393 q^{78} +7.03902 q^{79} +1.00000 q^{81} +8.01496 q^{82} +6.52979 q^{83} +1.08413 q^{84} +14.6276 q^{86} -3.98787 q^{87} -8.30134 q^{88} +2.62065 q^{89} -3.78383 q^{91} -1.98076 q^{92} -1.30027 q^{93} -1.28015 q^{94} +2.01671 q^{96} +1.36869 q^{97} +2.57012 q^{98} +2.74632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * q^99

Introduction

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