LMFDB - Embedded newform 3525.2.a.x.1.7

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:	$1$
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			1.7
Root			$-2.23799$ 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)

$f(q)$	$=$	$q+2.23799 q^{2} -1.00000 q^{3} +3.00859 q^{4} -2.23799 q^{6} +0.583922 q^{7} +2.25722 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.23799 q^{2} -1.00000 q^{3} +3.00859 q^{4} -2.23799 q^{6} +0.583922 q^{7} +2.25722 q^{8} +1.00000 q^{9} -2.62923 q^{11} -3.00859 q^{12} -0.671031 q^{13} +1.30681 q^{14} -0.965554 q^{16} -6.30217 q^{17} +2.23799 q^{18} +1.49949 q^{19} -0.583922 q^{21} -5.88418 q^{22} -5.58326 q^{23} -2.25722 q^{24} -1.50176 q^{26} -1.00000 q^{27} +1.75678 q^{28} +0.925178 q^{29} -7.27441 q^{31} -6.67534 q^{32} +2.62923 q^{33} -14.1042 q^{34} +3.00859 q^{36} -1.67682 q^{37} +3.35585 q^{38} +0.671031 q^{39} +3.79503 q^{41} -1.30681 q^{42} +1.27083 q^{43} -7.91027 q^{44} -12.4953 q^{46} +1.00000 q^{47} +0.965554 q^{48} -6.65904 q^{49} +6.30217 q^{51} -2.01886 q^{52} +4.64629 q^{53} -2.23799 q^{54} +1.31804 q^{56} -1.49949 q^{57} +2.07054 q^{58} +5.37099 q^{59} -1.83479 q^{61} -16.2800 q^{62} +0.583922 q^{63} -13.0082 q^{64} +5.88418 q^{66} -10.1244 q^{67} -18.9607 q^{68} +5.58326 q^{69} +8.68435 q^{71} +2.25722 q^{72} +5.77318 q^{73} -3.75270 q^{74} +4.51137 q^{76} -1.53526 q^{77} +1.50176 q^{78} -9.02733 q^{79} +1.00000 q^{81} +8.49323 q^{82} +6.83558 q^{83} -1.75678 q^{84} +2.84410 q^{86} -0.925178 q^{87} -5.93474 q^{88} +6.50153 q^{89} -0.391830 q^{91} -16.7978 q^{92} +7.27441 q^{93} +2.23799 q^{94} +6.67534 q^{96} -11.9931 q^{97} -14.9028 q^{98} -2.62923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.23799	1.58250	0.791248	−	0.611495i	$-0.209431\pi$
$2$	2.23799	1.58250	0.791248	+	0.611495i	$0.209431\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.00859	1.50430
$5$	0	0
$5$	0	0
$6$	−2.23799	−0.913655
$7$	0.583922	0.220702	0.110351	−	0.993893i	$-0.464803\pi$
$7$	0.583922	0.220702	0.110351	+	0.993893i	$0.464803\pi$
$8$	2.25722	0.798048
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.62923	−0.792742	−0.396371	−	0.918090i	$-0.629731\pi$
$11$	−2.62923	−0.792742	−0.396371	+	0.918090i	$0.629731\pi$
$12$	−3.00859	−0.868506
$13$	−0.671031	−0.186111	−0.0930553	−	0.995661i	$-0.529663\pi$
$13$	−0.671031	−0.186111	−0.0930553	+	0.995661i	$0.529663\pi$
$14$	1.30681	0.349260
$15$	0	0
$16$	−0.965554	−0.241389
$17$	−6.30217	−1.52850	−0.764251	−	0.644919i	$-0.776891\pi$
$17$	−6.30217	−1.52850	−0.764251	+	0.644919i	$0.776891\pi$
$18$	2.23799	0.527499
$19$	1.49949	0.344007	0.172004	−	0.985096i	$-0.444976\pi$
$19$	1.49949	0.344007	0.172004	+	0.985096i	$0.444976\pi$
$20$	0	0
$21$	−0.583922	−0.127422
$22$	−5.88418	−1.25451
$23$	−5.58326	−1.16419	−0.582095	−	0.813121i	$-0.697767\pi$
$23$	−5.58326	−1.16419	−0.582095	+	0.813121i	$0.697767\pi$
$24$	−2.25722	−0.460753
$25$	0	0
$26$	−1.50176	−0.294519
$27$	−1.00000	−0.192450
$28$	1.75678	0.332001
$29$	0.925178	0.171801	0.0859006	−	0.996304i	$-0.472623\pi$
$29$	0.925178	0.171801	0.0859006	+	0.996304i	$0.472623\pi$
$30$	0	0
$31$	−7.27441	−1.30652	−0.653261	−	0.757133i	$-0.726600\pi$
$31$	−7.27441	−1.30652	−0.653261	+	0.757133i	$0.726600\pi$
$32$	−6.67534	−1.18004
$33$	2.62923	0.457690
$34$	−14.1042	−2.41885
$35$	0	0
$36$	3.00859	0.501432
$37$	−1.67682	−0.275667	−0.137833	−	0.990455i	$-0.544014\pi$
$37$	−1.67682	−0.275667	−0.137833	+	0.990455i	$0.544014\pi$
$38$	3.35585	0.544391
$39$	0.671031	0.107451
$40$	0	0
$41$	3.79503	0.592684	0.296342	−	0.955082i	$-0.404233\pi$
$41$	3.79503	0.592684	0.296342	+	0.955082i	$0.404233\pi$
$42$	−1.30681	−0.201645
$43$	1.27083	0.193800	0.0968999	−	0.995294i	$-0.469107\pi$
$43$	1.27083	0.193800	0.0968999	+	0.995294i	$0.469107\pi$
$44$	−7.91027	−1.19252
$45$	0	0
$46$	−12.4953	−1.84233
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	0.965554	0.139366
$49$	−6.65904	−0.951291
$50$	0	0
$51$	6.30217	0.882481
$52$	−2.01886	−0.279965
$53$	4.64629	0.638217	0.319108	−	0.947718i	$-0.396617\pi$
$53$	4.64629	0.638217	0.319108	+	0.947718i	$0.396617\pi$
$54$	−2.23799	−0.304552
$55$	0	0
$56$	1.31804	0.176130
$57$	−1.49949	−0.198613
$58$	2.07054	0.271875
$59$	5.37099	0.699244	0.349622	−	0.936891i	$-0.386310\pi$
$59$	5.37099	0.699244	0.349622	+	0.936891i	$0.386310\pi$
$60$	0	0
$61$	−1.83479	−0.234921	−0.117460	−	0.993078i	$-0.537475\pi$
$61$	−1.83479	−0.234921	−0.117460	+	0.993078i	$0.537475\pi$
$62$	−16.2800	−2.06757
$63$	0.583922	0.0735672
$64$	−13.0082	−1.62603
$65$	0	0
$66$	5.88418	0.724292
$67$	−10.1244	−1.23690	−0.618448	−	0.785825i	$-0.712238\pi$
$67$	−10.1244	−1.23690	−0.618448	+	0.785825i	$0.712238\pi$
$68$	−18.9607	−2.29932
$69$	5.58326	0.672146
$70$	0	0
$71$	8.68435	1.03064	0.515322	−	0.856997i	$-0.327673\pi$
$71$	8.68435	1.03064	0.515322	+	0.856997i	$0.327673\pi$
$72$	2.25722	0.266016
$73$	5.77318	0.675700	0.337850	−	0.941200i	$-0.390300\pi$
$73$	5.77318	0.675700	0.337850	+	0.941200i	$0.390300\pi$
$74$	−3.75270	−0.436242
$75$	0	0
$76$	4.51137	0.517489
$77$	−1.53526	−0.174959
$78$	1.50176	0.170041
$79$	−9.02733	−1.01565	−0.507827	−	0.861459i	$-0.669551\pi$
$79$	−9.02733	−1.01565	−0.507827	+	0.861459i	$0.669551\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	8.49323	0.937921
$83$	6.83558	0.750302	0.375151	−	0.926964i	$-0.377591\pi$
$83$	6.83558	0.750302	0.375151	+	0.926964i	$0.377591\pi$
$84$	−1.75678	−0.191681
$85$	0	0
$86$	2.84410	0.306688
$87$	−0.925178	−0.0991894
$88$	−5.93474	−0.632646
$89$	6.50153	0.689161	0.344581	−	0.938757i	$-0.388021\pi$
$89$	6.50153	0.689161	0.344581	+	0.938757i	$0.388021\pi$
$90$	0	0
$91$	−0.391830	−0.0410749
$92$	−16.7978	−1.75129
$93$	7.27441	0.754321
$94$	2.23799	0.230831
$95$	0	0
$96$	6.67534	0.681299
$97$	−11.9931	−1.21771	−0.608857	−	0.793280i	$-0.708372\pi$
$97$	−11.9931	−1.21771	−0.608857	+	0.793280i	$0.708372\pi$
$98$	−14.9028	−1.50541
$99$	−2.62923	−0.264247
$100$	0	0
$101$	−2.46600	−0.245376	−0.122688	−	0.992445i	$-0.539151\pi$
$101$	−2.46600	−0.245376	−0.122688	+	0.992445i	$0.539151\pi$
$102$	14.1042	1.39652
$103$	−18.3966	−1.81267	−0.906334	−	0.422562i	$-0.861131\pi$
$103$	−18.3966	−1.81267	−0.906334	+	0.422562i	$0.861131\pi$
$104$	−1.51466	−0.148525
$105$	0	0
$106$	10.3983	1.00998
$107$	−13.3202	−1.28771	−0.643854	−	0.765148i	$-0.722666\pi$
$107$	−13.3202	−1.28771	−0.643854	+	0.765148i	$0.722666\pi$
$108$	−3.00859	−0.289502
$109$	2.01754	0.193245	0.0966225	−	0.995321i	$-0.469196\pi$
$109$	2.01754	0.193245	0.0966225	+	0.995321i	$0.469196\pi$
$110$	0	0
$111$	1.67682	0.159156
$112$	−0.563808	−0.0532749
$113$	8.07381	0.759520	0.379760	−	0.925085i	$-0.376007\pi$
$113$	8.07381	0.759520	0.379760	+	0.925085i	$0.376007\pi$
$114$	−3.35585	−0.314304
$115$	0	0
$116$	2.78348	0.258440
$117$	−0.671031	−0.0620369
$118$	12.0202	1.10655
$119$	−3.67998	−0.337343
$120$	0	0
$121$	−4.08717	−0.371561
$122$	−4.10624	−0.371761
$123$	−3.79503	−0.342186
$124$	−21.8857	−1.96540
$125$	0	0
$126$	1.30681	0.116420
$127$	11.1909	0.993028	0.496514	−	0.868029i	$-0.334613\pi$
$127$	11.1909	0.993028	0.496514	+	0.868029i	$0.334613\pi$
$128$	−15.7616	−1.39314
$129$	−1.27083	−0.111890
$130$	0	0
$131$	2.22145	0.194089	0.0970445	−	0.995280i	$-0.469061\pi$
$131$	2.22145	0.194089	0.0970445	+	0.995280i	$0.469061\pi$
$132$	7.91027	0.688501
$133$	0.875587	0.0759230
$134$	−22.6584	−1.95739
$135$	0	0
$136$	−14.2254	−1.21982
$137$	−10.4305	−0.891136	−0.445568	−	0.895248i	$-0.646998\pi$
$137$	−10.4305	−0.891136	−0.445568	+	0.895248i	$0.646998\pi$
$138$	12.4953	1.06367
$139$	−5.17781	−0.439176	−0.219588	−	0.975593i	$-0.570471\pi$
$139$	−5.17781	−0.439176	−0.219588	+	0.975593i	$0.570471\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	19.4355	1.63099
$143$	1.76429	0.147538
$144$	−0.965554	−0.0804629
$145$	0	0
$146$	12.9203	1.06929
$147$	6.65904	0.549228
$148$	−5.04486	−0.414685
$149$	9.83385	0.805620	0.402810	−	0.915284i	$-0.368034\pi$
$149$	9.83385	0.805620	0.402810	+	0.915284i	$0.368034\pi$
$150$	0	0
$151$	16.0056	1.30252	0.651261	−	0.758854i	$-0.274241\pi$
$151$	16.0056	1.30252	0.651261	+	0.758854i	$0.274241\pi$
$152$	3.38469	0.274534
$153$	−6.30217	−0.509500
$154$	−3.43590	−0.276873
$155$	0	0
$156$	2.01886	0.161638
$157$	−6.12094	−0.488504	−0.244252	−	0.969712i	$-0.578542\pi$
$157$	−6.12094	−0.488504	−0.244252	+	0.969712i	$0.578542\pi$
$158$	−20.2031	−1.60727
$159$	−4.64629	−0.368475
$160$	0	0
$161$	−3.26019	−0.256939
$162$	2.23799	0.175833
$163$	−12.3027	−0.963623	−0.481812	−	0.876275i	$-0.660021\pi$
$163$	−12.3027	−0.963623	−0.481812	+	0.876275i	$0.660021\pi$
$164$	11.4177	0.891573
$165$	0	0
$166$	15.2979	1.18735
$167$	−10.1735	−0.787246	−0.393623	−	0.919272i	$-0.628778\pi$
$167$	−10.1735	−0.787246	−0.393623	+	0.919272i	$0.628778\pi$
$168$	−1.31804	−0.101689
$169$	−12.5497	−0.965363
$170$	0	0
$171$	1.49949	0.114669
$172$	3.82341	0.291532
$173$	5.04726	0.383736	0.191868	−	0.981421i	$-0.438545\pi$
$173$	5.04726	0.383736	0.191868	+	0.981421i	$0.438545\pi$
$174$	−2.07054	−0.156967
$175$	0	0
$176$	2.53866	0.191359
$177$	−5.37099	−0.403709
$178$	14.5504	1.09060
$179$	24.9522	1.86501	0.932507	−	0.361151i	$-0.117616\pi$
$179$	24.9522	1.86501	0.932507	+	0.361151i	$0.117616\pi$
$180$	0	0
$181$	−9.10307	−0.676626	−0.338313	−	0.941034i	$-0.609856\pi$
$181$	−9.10307	−0.676626	−0.338313	+	0.941034i	$0.609856\pi$
$182$	−0.876910	−0.0650009
$183$	1.83479	0.135631
$184$	−12.6026	−0.929079
$185$	0	0
$186$	16.2800	1.19371
$187$	16.5698	1.21171
$188$	3.00859	0.219424
$189$	−0.583922	−0.0424741
$190$	0	0
$191$	−9.63316	−0.697031	−0.348515	−	0.937303i	$-0.613314\pi$
$191$	−9.63316	−0.697031	−0.348515	+	0.937303i	$0.613314\pi$
$192$	13.0082	0.938788
$193$	3.82543	0.275360	0.137680	−	0.990477i	$-0.456035\pi$
$193$	3.82543	0.275360	0.137680	+	0.990477i	$0.456035\pi$
$194$	−26.8404	−1.92703
$195$	0	0
$196$	−20.0343	−1.43102
$197$	10.5934	0.754746	0.377373	−	0.926061i	$-0.376827\pi$
$197$	10.5934	0.754746	0.377373	+	0.926061i	$0.376827\pi$
$198$	−5.88418	−0.418170
$199$	0.516905	0.0366424	0.0183212	−	0.999832i	$-0.494168\pi$
$199$	0.516905	0.0366424	0.0183212	+	0.999832i	$0.494168\pi$
$200$	0	0
$201$	10.1244	0.714123
$202$	−5.51888	−0.388307
$203$	0.540231	0.0379168
$204$	18.9607	1.32751
$205$	0	0
$206$	−41.1713	−2.86854
$207$	−5.58326	−0.388063
$208$	0.647917	0.0449250
$209$	−3.94251	−0.272709
$210$	0	0
$211$	10.5455	0.725984	0.362992	−	0.931792i	$-0.381755\pi$
$211$	10.5455	0.725984	0.362992	+	0.931792i	$0.381755\pi$
$212$	13.9788	0.960067
$213$	−8.68435	−0.595042
$214$	−29.8104	−2.03779
$215$	0	0
$216$	−2.25722	−0.153584
$217$	−4.24768	−0.288352
$218$	4.51523	0.305810
$219$	−5.77318	−0.390115
$220$	0	0
$221$	4.22895	0.284470
$222$	3.75270	0.251865
$223$	−13.6517	−0.914185	−0.457093	−	0.889419i	$-0.651109\pi$
$223$	−13.6517	−0.914185	−0.457093	+	0.889419i	$0.651109\pi$
$224$	−3.89788	−0.260438
$225$	0	0
$226$	18.0691	1.20194
$227$	−6.69702	−0.444497	−0.222248	−	0.974990i	$-0.571340\pi$
$227$	−6.69702	−0.444497	−0.222248	+	0.974990i	$0.571340\pi$
$228$	−4.51137	−0.298773
$229$	−13.9387	−0.921096	−0.460548	−	0.887635i	$-0.652347\pi$
$229$	−13.9387	−0.921096	−0.460548	+	0.887635i	$0.652347\pi$
$230$	0	0
$231$	1.53526	0.101013
$232$	2.08833	0.137106
$233$	24.9705	1.63587	0.817935	−	0.575311i	$-0.195119\pi$
$233$	24.9705	1.63587	0.817935	+	0.575311i	$0.195119\pi$
$234$	−1.50176	−0.0981731
$235$	0	0
$236$	16.1591	1.05187
$237$	9.02733	0.586388
$238$	−8.23574	−0.533844
$239$	26.8262	1.73524	0.867621	−	0.497227i	$-0.165648\pi$
$239$	26.8262	1.73524	0.867621	+	0.497227i	$0.165648\pi$
$240$	0	0
$241$	12.6312	0.813650	0.406825	−	0.913506i	$-0.366636\pi$
$241$	12.6312	0.813650	0.406825	+	0.913506i	$0.366636\pi$
$242$	−9.14703	−0.587993
$243$	−1.00000	−0.0641500
$244$	−5.52013	−0.353390
$245$	0	0
$246$	−8.49323	−0.541509
$247$	−1.00621	−0.0640234
$248$	−16.4199	−1.04267
$249$	−6.83558	−0.433187
$250$	0	0
$251$	−4.89666	−0.309074	−0.154537	−	0.987987i	$-0.549389\pi$
$251$	−4.89666	−0.309074	−0.154537	+	0.987987i	$0.549389\pi$
$252$	1.75678	0.110667
$253$	14.6797	0.922902
$254$	25.0450	1.57146
$255$	0	0
$256$	−9.25778	−0.578612
$257$	−4.37065	−0.272634	−0.136317	−	0.990665i	$-0.543527\pi$
$257$	−4.37065	−0.272634	−0.136317	+	0.990665i	$0.543527\pi$
$258$	−2.84410	−0.177066
$259$	−0.979130	−0.0608402
$260$	0	0
$261$	0.925178	0.0572671
$262$	4.97158	0.307145
$263$	−7.53255	−0.464477	−0.232238	−	0.972659i	$-0.574605\pi$
$263$	−7.53255	−0.464477	−0.232238	+	0.972659i	$0.574605\pi$
$264$	5.93474	0.365258
$265$	0	0
$266$	1.95955	0.120148
$267$	−6.50153	−0.397887
$268$	−30.4603	−1.86066
$269$	−0.907936	−0.0553578	−0.0276789	−	0.999617i	$-0.508812\pi$
$269$	−0.907936	−0.0553578	−0.0276789	+	0.999617i	$0.508812\pi$
$270$	0	0
$271$	1.26712	0.0769718	0.0384859	−	0.999259i	$-0.487747\pi$
$271$	1.26712	0.0769718	0.0384859	+	0.999259i	$0.487747\pi$
$272$	6.08509	0.368963
$273$	0.391830	0.0237146
$274$	−23.3433	−1.41022
$275$	0	0
$276$	16.7978	1.01111
$277$	26.6696	1.60242	0.801212	−	0.598381i	$-0.204189\pi$
$277$	26.6696	1.60242	0.801212	+	0.598381i	$0.204189\pi$
$278$	−11.5879	−0.694995
$279$	−7.27441	−0.435507
$280$	0	0
$281$	5.14077	0.306673	0.153336	−	0.988174i	$-0.450998\pi$
$281$	5.14077	0.306673	0.153336	+	0.988174i	$0.450998\pi$
$282$	−2.23799	−0.133270
$283$	−13.9738	−0.830656	−0.415328	−	0.909672i	$-0.636333\pi$
$283$	−13.9738	−0.830656	−0.415328	+	0.909672i	$0.636333\pi$
$284$	26.1277	1.55039
$285$	0	0
$286$	3.94847	0.233478
$287$	2.21600	0.130806
$288$	−6.67534	−0.393348
$289$	22.7174	1.33632
$290$	0	0
$291$	11.9931	0.703048
$292$	17.3692	1.01645
$293$	−12.2078	−0.713186	−0.356593	−	0.934260i	$-0.616062\pi$
$293$	−12.2078	−0.713186	−0.356593	+	0.934260i	$0.616062\pi$
$294$	14.9028	0.869152
$295$	0	0
$296$	−3.78494	−0.219995
$297$	2.62923	0.152563
$298$	22.0080	1.27489
$299$	3.74654	0.216668
$300$	0	0
$301$	0.742065	0.0427719
$302$	35.8205	2.06124
$303$	2.46600	0.141668
$304$	−1.44784	−0.0830395
$305$	0	0
$306$	−14.1042	−0.806283
$307$	−7.22568	−0.412391	−0.206196	−	0.978511i	$-0.566108\pi$
$307$	−7.22568	−0.412391	−0.206196	+	0.978511i	$0.566108\pi$
$308$	−4.61898	−0.263191
$309$	18.3966	1.04654
$310$	0	0
$311$	−19.5224	−1.10702	−0.553508	−	0.832844i	$-0.686711\pi$
$311$	−19.5224	−1.10702	−0.553508	+	0.832844i	$0.686711\pi$
$312$	1.51466	0.0857510
$313$	−9.90251	−0.559723	−0.279862	−	0.960040i	$-0.590289\pi$
$313$	−9.90251	−0.559723	−0.279862	+	0.960040i	$0.590289\pi$
$314$	−13.6986	−0.773056
$315$	0	0
$316$	−27.1596	−1.52784
$317$	−12.3476	−0.693511	−0.346755	−	0.937956i	$-0.612717\pi$
$317$	−12.3476	−0.693511	−0.346755	+	0.937956i	$0.612717\pi$
$318$	−10.3983	−0.583110
$319$	−2.43250	−0.136194
$320$	0	0
$321$	13.3202	0.743459
$322$	−7.29626	−0.406605
$323$	−9.45007	−0.525816
$324$	3.00859	0.167144
$325$	0	0
$326$	−27.5333	−1.52493
$327$	−2.01754	−0.111570
$328$	8.56621	0.472990
$329$	0.583922	0.0321926
$330$	0	0
$331$	−18.9970	−1.04417	−0.522084	−	0.852894i	$-0.674845\pi$
$331$	−18.9970	−1.04417	−0.522084	+	0.852894i	$0.674845\pi$
$332$	20.5655	1.12868
$333$	−1.67682	−0.0918890
$334$	−22.7681	−1.24581
$335$	0	0
$336$	0.563808	0.0307583
$337$	1.93430	0.105368	0.0526841	−	0.998611i	$-0.483222\pi$
$337$	1.93430	0.105368	0.0526841	+	0.998611i	$0.483222\pi$
$338$	−28.0861	−1.52768
$339$	−8.07381	−0.438509
$340$	0	0
$341$	19.1261	1.03573
$342$	3.35585	0.181464
$343$	−7.97581	−0.430653
$344$	2.86854	0.154661
$345$	0	0
$346$	11.2957	0.607261
$347$	−29.5871	−1.58832	−0.794159	−	0.607710i	$-0.792088\pi$
$347$	−29.5871	−1.58832	−0.794159	+	0.607710i	$0.792088\pi$
$348$	−2.78348	−0.149210
$349$	19.2799	1.03203	0.516015	−	0.856579i	$-0.327415\pi$
$349$	19.2799	1.03203	0.516015	+	0.856579i	$0.327415\pi$
$350$	0	0
$351$	0.671031	0.0358170
$352$	17.5510	0.935470
$353$	−0.818892	−0.0435852	−0.0217926	−	0.999763i	$-0.506937\pi$
$353$	−0.818892	−0.0435852	−0.0217926	+	0.999763i	$0.506937\pi$
$354$	−12.0202	−0.638868
$355$	0	0
$356$	19.5605	1.03670
$357$	3.67998	0.194765
$358$	55.8427	2.95138
$359$	28.4903	1.50366	0.751831	−	0.659356i	$-0.229171\pi$
$359$	28.4903	1.50366	0.751831	+	0.659356i	$0.229171\pi$
$360$	0	0
$361$	−16.7515	−0.881659
$362$	−20.3726	−1.07076
$363$	4.08717	0.214521
$364$	−1.17886	−0.0617888
$365$	0	0
$366$	4.10624	0.214636
$367$	16.1396	0.842479	0.421239	−	0.906949i	$-0.361595\pi$
$367$	16.1396	0.842479	0.421239	+	0.906949i	$0.361595\pi$
$368$	5.39094	0.281022
$369$	3.79503	0.197561
$370$	0	0
$371$	2.71307	0.140855
$372$	21.8857	1.13472
$373$	11.4707	0.593928	0.296964	−	0.954889i	$-0.404026\pi$
$373$	11.4707	0.593928	0.296964	+	0.954889i	$0.404026\pi$
$374$	37.0831	1.91752
$375$	0	0
$376$	2.25722	0.116407
$377$	−0.620823	−0.0319740
$378$	−1.30681	−0.0672151
$379$	26.7485	1.37398	0.686989	−	0.726668i	$-0.258932\pi$
$379$	26.7485	1.37398	0.686989	+	0.726668i	$0.258932\pi$
$380$	0	0
$381$	−11.1909	−0.573325
$382$	−21.5589	−1.10305
$383$	15.0342	0.768212	0.384106	−	0.923289i	$-0.374510\pi$
$383$	15.0342	0.768212	0.384106	+	0.923289i	$0.374510\pi$
$384$	15.7616	0.804330
$385$	0	0
$386$	8.56127	0.435757
$387$	1.27083	0.0645999
$388$	−36.0823	−1.83180
$389$	10.1503	0.514638	0.257319	−	0.966326i	$-0.417161\pi$
$389$	10.1503	0.514638	0.257319	+	0.966326i	$0.417161\pi$
$390$	0	0
$391$	35.1867	1.77947
$392$	−15.0309	−0.759175
$393$	−2.22145	−0.112057
$394$	23.7078	1.19438
$395$	0	0
$396$	−7.91027	−0.397506
$397$	−24.2362	−1.21638	−0.608190	−	0.793791i	$-0.708104\pi$
$397$	−24.2362	−1.21638	−0.608190	+	0.793791i	$0.708104\pi$
$398$	1.15683	0.0579865
$399$	−0.875587	−0.0438342
$400$	0	0
$401$	3.11558	0.155585	0.0777924	−	0.996970i	$-0.475213\pi$
$401$	3.11558	0.155585	0.0777924	+	0.996970i	$0.475213\pi$
$402$	22.6584	1.13010
$403$	4.88135	0.243158
$404$	−7.41919	−0.369119
$405$	0	0
$406$	1.20903	0.0600032
$407$	4.40873	0.218533
$408$	14.2254	0.704262
$409$	31.9008	1.57739	0.788697	−	0.614783i	$-0.210756\pi$
$409$	31.9008	1.57739	0.788697	+	0.614783i	$0.210756\pi$
$410$	0	0
$411$	10.4305	0.514498
$412$	−55.3478	−2.72679
$413$	3.13624	0.154324
$414$	−12.4953	−0.614109
$415$	0	0
$416$	4.47936	0.219619
$417$	5.17781	0.253558
$418$	−8.82329	−0.431561
$419$	16.2775	0.795207	0.397603	−	0.917557i	$-0.369842\pi$
$419$	16.2775	0.795207	0.397603	+	0.917557i	$0.369842\pi$
$420$	0	0
$421$	15.0220	0.732125	0.366063	−	0.930590i	$-0.380706\pi$
$421$	15.0220	0.732125	0.366063	+	0.930590i	$0.380706\pi$
$422$	23.6008	1.14887
$423$	1.00000	0.0486217
$424$	10.4877	0.509327
$425$	0	0
$426$	−19.4355	−0.941652
$427$	−1.07137	−0.0518474
$428$	−40.0749	−1.93710
$429$	−1.76429	−0.0851809
$430$	0	0
$431$	−12.8858	−0.620689	−0.310344	−	0.950624i	$-0.600444\pi$
$431$	−12.8858	−0.620689	−0.310344	+	0.950624i	$0.600444\pi$
$432$	0.965554	0.0464553
$433$	7.21293	0.346631	0.173316	−	0.984866i	$-0.444552\pi$
$433$	7.21293	0.346631	0.173316	+	0.984866i	$0.444552\pi$
$434$	−9.50627	−0.456315
$435$	0	0
$436$	6.06995	0.290698
$437$	−8.37206	−0.400490
$438$	−12.9203	−0.617357
$439$	0.427364	0.0203970	0.0101985	−	0.999948i	$-0.496754\pi$
$439$	0.427364	0.0203970	0.0101985	+	0.999948i	$0.496754\pi$
$440$	0	0
$441$	−6.65904	−0.317097
$442$	9.46435	0.450173
$443$	22.0011	1.04530	0.522652	−	0.852546i	$-0.324943\pi$
$443$	22.0011	1.04530	0.522652	+	0.852546i	$0.324943\pi$
$444$	5.04486	0.239418
$445$	0	0
$446$	−30.5523	−1.44670
$447$	−9.83385	−0.465125
$448$	−7.59578	−0.358867
$449$	30.1190	1.42141	0.710703	−	0.703492i	$-0.248377\pi$
$449$	30.1190	1.42141	0.710703	+	0.703492i	$0.248377\pi$
$450$	0	0
$451$	−9.97799	−0.469845
$452$	24.2908	1.14254
$453$	−16.0056	−0.752011
$454$	−14.9878	−0.703414
$455$	0	0
$456$	−3.38469	−0.158502
$457$	−28.9691	−1.35512	−0.677558	−	0.735469i	$-0.736962\pi$
$457$	−28.9691	−1.35512	−0.677558	+	0.735469i	$0.736962\pi$
$458$	−31.1947	−1.45763
$459$	6.30217	0.294160
$460$	0	0
$461$	−1.48014	−0.0689368	−0.0344684	−	0.999406i	$-0.510974\pi$
$461$	−1.48014	−0.0689368	−0.0344684	+	0.999406i	$0.510974\pi$
$462$	3.43590	0.159853
$463$	18.0423	0.838498	0.419249	−	0.907871i	$-0.362293\pi$
$463$	18.0423	0.838498	0.419249	+	0.907871i	$0.362293\pi$
$464$	−0.893309	−0.0414708
$465$	0	0
$466$	55.8836	2.58876
$467$	−37.9158	−1.75453	−0.877267	−	0.480004i	$-0.840635\pi$
$467$	−37.9158	−1.75453	−0.877267	+	0.480004i	$0.840635\pi$
$468$	−2.01886	−0.0933218
$469$	−5.91188	−0.272985
$470$	0	0
$471$	6.12094	0.282038
$472$	12.1235	0.558030
$473$	−3.34130	−0.153633
$474$	20.2031	0.927957
$475$	0	0
$476$	−11.0715	−0.507464
$477$	4.64629	0.212739
$478$	60.0367	2.74601
$479$	5.54183	0.253213	0.126606	−	0.991953i	$-0.459592\pi$
$479$	5.54183	0.253213	0.126606	+	0.991953i	$0.459592\pi$
$480$	0	0
$481$	1.12520	0.0513045
$482$	28.2686	1.28760
$483$	3.26019	0.148344
$484$	−12.2966	−0.558937
$485$	0	0
$486$	−2.23799	−0.101517
$487$	−39.5746	−1.79330	−0.896649	−	0.442742i	$-0.854006\pi$
$487$	−39.5746	−1.79330	−0.896649	+	0.442742i	$0.854006\pi$
$488$	−4.14152	−0.187478
$489$	12.3027	0.556348
$490$	0	0
$491$	24.8199	1.12011	0.560054	−	0.828456i	$-0.310780\pi$
$491$	24.8199	1.12011	0.560054	+	0.828456i	$0.310780\pi$
$492$	−11.4177	−0.514750
$493$	−5.83063	−0.262598
$494$	−2.25188	−0.101317
$495$	0	0
$496$	7.02383	0.315379
$497$	5.07098	0.227465
$498$	−15.2979	−0.685517
$499$	5.70002	0.255168	0.127584	−	0.991828i	$-0.459278\pi$
$499$	5.70002	0.255168	0.127584	+	0.991828i	$0.459278\pi$
$500$	0	0
$501$	10.1735	0.454517
$502$	−10.9587	−0.489109
$503$	−32.3229	−1.44121	−0.720604	−	0.693347i	$-0.756135\pi$
$503$	−32.3229	−1.44121	−0.720604	+	0.693347i	$0.756135\pi$
$504$	1.31804	0.0587101
$505$	0	0
$506$	32.8529	1.46049
$507$	12.5497	0.557353
$508$	33.6687	1.49381
$509$	6.09275	0.270056	0.135028	−	0.990842i	$-0.456887\pi$
$509$	6.09275	0.270056	0.135028	+	0.990842i	$0.456887\pi$
$510$	0	0
$511$	3.37109	0.149128
$512$	10.8043	0.477489
$513$	−1.49949	−0.0662043
$514$	−9.78146	−0.431442
$515$	0	0
$516$	−3.82341	−0.168316
$517$	−2.62923	−0.115633
$518$	−2.19128	−0.0962794
$519$	−5.04726	−0.221550
$520$	0	0
$521$	−21.0479	−0.922124	−0.461062	−	0.887368i	$-0.652531\pi$
$521$	−21.0479	−0.922124	−0.461062	+	0.887368i	$0.652531\pi$
$522$	2.07054	0.0906249
$523$	−2.47158	−0.108074	−0.0540372	−	0.998539i	$-0.517209\pi$
$523$	−2.47158	−0.108074	−0.0540372	+	0.998539i	$0.517209\pi$
$524$	6.68344	0.291967
$525$	0	0
$526$	−16.8578	−0.735033
$527$	45.8446	1.99702
$528$	−2.53866	−0.110481
$529$	8.17280	0.355339
$530$	0	0
$531$	5.37099	0.233081
$532$	2.63428	0.114211
$533$	−2.54658	−0.110305
$534$	−14.5504	−0.629656
$535$	0	0
$536$	−22.8531	−0.987102
$537$	−24.9522	−1.07677
$538$	−2.03195	−0.0876036
$539$	17.5081	0.754128
$540$	0	0
$541$	3.15610	0.135691	0.0678457	−	0.997696i	$-0.478387\pi$
$541$	3.15610	0.135691	0.0678457	+	0.997696i	$0.478387\pi$
$542$	2.83579	0.121808
$543$	9.10307	0.390650
$544$	42.0691	1.80370
$545$	0	0
$546$	0.876910	0.0375283
$547$	−18.5160	−0.791688	−0.395844	−	0.918318i	$-0.629548\pi$
$547$	−18.5160	−0.791688	−0.395844	+	0.918318i	$0.629548\pi$
$548$	−31.3811	−1.34053
$549$	−1.83479	−0.0783069
$550$	0	0
$551$	1.38730	0.0591009
$552$	12.6026	0.536404
$553$	−5.27125	−0.224156
$554$	59.6864	2.53583
$555$	0	0
$556$	−15.5779	−0.660651
$557$	−8.14376	−0.345062	−0.172531	−	0.985004i	$-0.555195\pi$
$557$	−8.14376	−0.345062	−0.172531	+	0.985004i	$0.555195\pi$
$558$	−16.2800	−0.689189
$559$	−0.852767	−0.0360682
$560$	0	0
$561$	−16.5698	−0.699579
$562$	11.5050	0.485309
$563$	17.3516	0.731284	0.365642	−	0.930756i	$-0.380849\pi$
$563$	17.3516	0.731284	0.365642	+	0.930756i	$0.380849\pi$
$564$	−3.00859	−0.126685
$565$	0	0
$566$	−31.2732	−1.31451
$567$	0.583922	0.0245224
$568$	19.6025	0.822502
$569$	−34.4131	−1.44267	−0.721337	−	0.692585i	$-0.756472\pi$
$569$	−34.4131	−1.44267	−0.721337	+	0.692585i	$0.756472\pi$
$570$	0	0
$571$	0.595471	0.0249197	0.0124599	−	0.999922i	$-0.496034\pi$
$571$	0.595471	0.0249197	0.0124599	+	0.999922i	$0.496034\pi$
$572$	5.30804	0.221940
$573$	9.63316	0.402431
$574$	4.95938	0.207001
$575$	0	0
$576$	−13.0082	−0.542009
$577$	39.6546	1.65084	0.825422	−	0.564516i	$-0.190937\pi$
$577$	39.6546	1.65084	0.825422	+	0.564516i	$0.190937\pi$
$578$	50.8412	2.11472
$579$	−3.82543	−0.158979
$580$	0	0
$581$	3.99144	0.165593
$582$	26.8404	1.11257
$583$	−12.2161	−0.505941
$584$	13.0313	0.539241
$585$	0	0
$586$	−27.3209	−1.12861
$587$	−12.8374	−0.529857	−0.264929	−	0.964268i	$-0.585348\pi$
$587$	−12.8374	−0.529857	−0.264929	+	0.964268i	$0.585348\pi$
$588$	20.0343	0.826202
$589$	−10.9079	−0.449453
$590$	0	0
$591$	−10.5934	−0.435753
$592$	1.61906	0.0665429
$593$	−22.8925	−0.940084	−0.470042	−	0.882644i	$-0.655761\pi$
$593$	−22.8925	−0.940084	−0.470042	+	0.882644i	$0.655761\pi$
$594$	5.88418	0.241431
$595$	0	0
$596$	29.5860	1.21189
$597$	−0.516905	−0.0211555
$598$	8.38472	0.342877
$599$	−21.3054	−0.870514	−0.435257	−	0.900306i	$-0.643342\pi$
$599$	−21.3054	−0.870514	−0.435257	+	0.900306i	$0.643342\pi$
$600$	0	0
$601$	25.0568	1.02209	0.511044	−	0.859554i	$-0.329259\pi$
$601$	25.0568	1.02209	0.511044	+	0.859554i	$0.329259\pi$
$602$	1.66073	0.0676865
$603$	−10.1244	−0.412299
$604$	48.1545	1.95938
$605$	0	0
$606$	5.51888	0.224189
$607$	−21.2133	−0.861023	−0.430512	−	0.902585i	$-0.641667\pi$
$607$	−21.2133	−0.861023	−0.430512	+	0.902585i	$0.641667\pi$
$608$	−10.0096	−0.405944
$609$	−0.540231	−0.0218913
$610$	0	0
$611$	−0.671031	−0.0271470
$612$	−18.9607	−0.766440
$613$	47.0375	1.89983	0.949914	−	0.312511i	$-0.101170\pi$
$613$	47.0375	1.89983	0.949914	+	0.312511i	$0.101170\pi$
$614$	−16.1710	−0.652608
$615$	0	0
$616$	−3.46543	−0.139626
$617$	9.00776	0.362639	0.181319	−	0.983424i	$-0.441963\pi$
$617$	9.00776	0.362639	0.181319	+	0.983424i	$0.441963\pi$
$618$	41.1713	1.65615
$619$	−47.0624	−1.89160	−0.945800	−	0.324751i	$-0.894720\pi$
$619$	−47.0624	−1.89160	−0.945800	+	0.324751i	$0.894720\pi$
$620$	0	0
$621$	5.58326	0.224049
$622$	−43.6910	−1.75185
$623$	3.79639	0.152099
$624$	−0.647917	−0.0259374
$625$	0	0
$626$	−22.1617	−0.885760
$627$	3.94251	0.157449
$628$	−18.4154	−0.734855
$629$	10.5676	0.421357
$630$	0	0
$631$	−15.2861	−0.608529	−0.304264	−	0.952588i	$-0.598411\pi$
$631$	−15.2861	−0.608529	−0.304264	+	0.952588i	$0.598411\pi$
$632$	−20.3767	−0.810540
$633$	−10.5455	−0.419147
$634$	−27.6338	−1.09748
$635$	0	0
$636$	−13.9788	−0.554295
$637$	4.46842	0.177045
$638$	−5.44391	−0.215527
$639$	8.68435	0.343548
$640$	0	0
$641$	−35.1476	−1.38825	−0.694124	−	0.719856i	$-0.744208\pi$
$641$	−35.1476	−1.38825	−0.694124	+	0.719856i	$0.744208\pi$
$642$	29.8104	1.17652
$643$	−3.20318	−0.126321	−0.0631606	−	0.998003i	$-0.520118\pi$
$643$	−3.20318	−0.126321	−0.0631606	+	0.998003i	$0.520118\pi$
$644$	−9.80858	−0.386512
$645$	0	0
$646$	−21.1491	−0.832102
$647$	15.1664	0.596252	0.298126	−	0.954527i	$-0.403639\pi$
$647$	15.1664	0.596252	0.298126	+	0.954527i	$0.403639\pi$
$648$	2.25722	0.0886720
$649$	−14.1216	−0.554320
$650$	0	0
$651$	4.24768	0.166480
$652$	−37.0139	−1.44958
$653$	−11.4730	−0.448973	−0.224486	−	0.974477i	$-0.572070\pi$
$653$	−11.4730	−0.448973	−0.224486	+	0.974477i	$0.572070\pi$
$654$	−4.51523	−0.176559
$655$	0	0
$656$	−3.66431	−0.143067
$657$	5.77318	0.225233
$658$	1.30681	0.0509448
$659$	−13.7288	−0.534799	−0.267400	−	0.963586i	$-0.586164\pi$
$659$	−13.7288	−0.534799	−0.267400	+	0.963586i	$0.586164\pi$
$660$	0	0
$661$	16.5027	0.641880	0.320940	−	0.947099i	$-0.396001\pi$
$661$	16.5027	0.641880	0.320940	+	0.947099i	$0.396001\pi$
$662$	−42.5150	−1.65239
$663$	−4.22895	−0.164239
$664$	15.4294	0.598777
$665$	0	0
$666$	−3.75270	−0.145414
$667$	−5.16551	−0.200009
$668$	−30.6078	−1.18425
$669$	13.6517	0.527805
$670$	0	0
$671$	4.82408	0.186231
$672$	3.89788	0.150364
$673$	−2.60608	−0.100457	−0.0502285	−	0.998738i	$-0.515995\pi$
$673$	−2.60608	−0.100457	−0.0502285	+	0.998738i	$0.515995\pi$
$674$	4.32895	0.166745
$675$	0	0
$676$	−37.7570	−1.45219
$677$	−22.5213	−0.865563	−0.432781	−	0.901499i	$-0.642468\pi$
$677$	−22.5213	−0.865563	−0.432781	+	0.901499i	$0.642468\pi$
$678$	−18.0691	−0.693940
$679$	−7.00303	−0.268752
$680$	0	0
$681$	6.69702	0.256630
$682$	42.8039	1.63905
$683$	−6.91938	−0.264763	−0.132381	−	0.991199i	$-0.542262\pi$
$683$	−6.91938	−0.264763	−0.132381	+	0.991199i	$0.542262\pi$
$684$	4.51137	0.172496
$685$	0	0
$686$	−17.8498	−0.681507
$687$	13.9387	0.531795
$688$	−1.22706	−0.0467811
$689$	−3.11780	−0.118779
$690$	0	0
$691$	22.9974	0.874862	0.437431	−	0.899252i	$-0.355888\pi$
$691$	22.9974	0.874862	0.437431	+	0.899252i	$0.355888\pi$
$692$	15.1851	0.577252
$693$	−1.53526	−0.0583198
$694$	−66.2155	−2.51351
$695$	0	0
$696$	−2.08833	−0.0791579
$697$	−23.9169	−0.905918
$698$	43.1482	1.63318
$699$	−24.9705	−0.944470
$700$	0	0
$701$	−0.356500	−0.0134648	−0.00673241	−	0.999977i	$-0.502143\pi$
$701$	−0.356500	−0.0134648	−0.00673241	+	0.999977i	$0.502143\pi$
$702$	1.50176	0.0566803
$703$	−2.51438	−0.0948315
$704$	34.2016	1.28902
$705$	0	0
$706$	−1.83267	−0.0689735
$707$	−1.43995	−0.0541549
$708$	−16.1591	−0.607298
$709$	−13.2761	−0.498593	−0.249297	−	0.968427i	$-0.580199\pi$
$709$	−13.2761	−0.498593	−0.249297	+	0.968427i	$0.580199\pi$
$710$	0	0
$711$	−9.02733	−0.338551
$712$	14.6754	0.549984
$713$	40.6149	1.52104
$714$	8.23574	0.308215
$715$	0	0
$716$	75.0710	2.80554
$717$	−26.8262	−1.00184
$718$	63.7610	2.37954
$719$	−31.5521	−1.17669	−0.588347	−	0.808608i	$-0.700221\pi$
$719$	−31.5521	−1.17669	−0.588347	+	0.808608i	$0.700221\pi$
$720$	0	0
$721$	−10.7422	−0.400059
$722$	−37.4897	−1.39522
$723$	−12.6312	−0.469761
$724$	−27.3874	−1.01785
$725$	0	0
$726$	9.14703	0.339478
$727$	30.4192	1.12819	0.564093	−	0.825711i	$-0.309226\pi$
$727$	30.4192	1.12819	0.564093	+	0.825711i	$0.309226\pi$
$728$	−0.884446	−0.0327797
$729$	1.00000	0.0370370
$730$	0	0
$731$	−8.00899	−0.296223
$732$	5.52013	0.204030
$733$	−13.0709	−0.482786	−0.241393	−	0.970427i	$-0.577604\pi$
$733$	−13.0709	−0.482786	−0.241393	+	0.970427i	$0.577604\pi$
$734$	36.1202	1.33322
$735$	0	0
$736$	37.2702	1.37380
$737$	26.6194	0.980540
$738$	8.49323	0.312640
$739$	−14.8645	−0.546801	−0.273400	−	0.961900i	$-0.588148\pi$
$739$	−14.8645	−0.546801	−0.273400	+	0.961900i	$0.588148\pi$
$740$	0	0
$741$	1.00621	0.0369639
$742$	6.07182	0.222903
$743$	7.67370	0.281521	0.140760	−	0.990044i	$-0.455045\pi$
$743$	7.67370	0.281521	0.140760	+	0.990044i	$0.455045\pi$
$744$	16.4199	0.601984
$745$	0	0
$746$	25.6712	0.939890
$747$	6.83558	0.250101
$748$	49.8519	1.82277
$749$	−7.77793	−0.284199
$750$	0	0
$751$	−10.6566	−0.388865	−0.194433	−	0.980916i	$-0.562287\pi$
$751$	−10.6566	−0.388865	−0.194433	+	0.980916i	$0.562287\pi$
$752$	−0.965554	−0.0352101
$753$	4.89666	0.178444
$754$	−1.38939	−0.0505988
$755$	0	0
$756$	−1.75678	−0.0638936
$757$	8.95914	0.325625	0.162813	−	0.986657i	$-0.447943\pi$
$757$	8.95914	0.325625	0.162813	+	0.986657i	$0.447943\pi$
$758$	59.8628	2.17432
$759$	−14.6797	−0.532838
$760$	0	0
$761$	36.4170	1.32012	0.660058	−	0.751215i	$-0.270532\pi$
$761$	36.4170	1.32012	0.660058	+	0.751215i	$0.270532\pi$
$762$	−25.0450	−0.907285
$763$	1.17808	0.0426495
$764$	−28.9823	−1.04854
$765$	0	0
$766$	33.6464	1.21569
$767$	−3.60411	−0.130137
$768$	9.25778	0.334062
$769$	−10.8796	−0.392328	−0.196164	−	0.980571i	$-0.562849\pi$
$769$	−10.8796	−0.392328	−0.196164	+	0.980571i	$0.562849\pi$
$770$	0	0
$771$	4.37065	0.157405
$772$	11.5092	0.414224
$773$	52.5912	1.89157	0.945787	−	0.324788i	$-0.105293\pi$
$773$	52.5912	1.89157	0.945787	+	0.324788i	$0.105293\pi$
$774$	2.84410	0.102229
$775$	0	0
$776$	−27.0711	−0.971794
$777$	0.979130	0.0351261
$778$	22.7162	0.814414
$779$	5.69062	0.203888
$780$	0	0
$781$	−22.8331	−0.817034
$782$	78.7474	2.81600
$783$	−0.925178	−0.0330631
$784$	6.42966	0.229631
$785$	0	0
$786$	−4.97158	−0.177330
$787$	−7.45907	−0.265887	−0.132944	−	0.991124i	$-0.542443\pi$
$787$	−7.45907	−0.265887	−0.132944	+	0.991124i	$0.542443\pi$
$788$	31.8711	1.13536
$789$	7.53255	0.268166
$790$	0	0
$791$	4.71447	0.167627
$792$	−5.93474	−0.210882
$793$	1.23120	0.0437212
$794$	−54.2403	−1.92492
$795$	0	0
$796$	1.55516	0.0551211
$797$	10.4052	0.368572	0.184286	−	0.982873i	$-0.441003\pi$
$797$	10.4052	0.368572	0.184286	+	0.982873i	$0.441003\pi$
$798$	−1.95955	−0.0693674
$799$	−6.30217	−0.222955
$800$	0	0
$801$	6.50153	0.229720
$802$	6.97264	0.246213
$803$	−15.1790	−0.535655
$804$	30.4603	1.07425
$805$	0	0
$806$	10.9244	0.384796
$807$	0.907936	0.0319609
$808$	−5.56630	−0.195822
$809$	12.5071	0.439726	0.219863	−	0.975531i	$-0.429439\pi$
$809$	12.5071	0.439726	0.219863	+	0.975531i	$0.429439\pi$
$810$	0	0
$811$	−32.4187	−1.13837	−0.569187	−	0.822208i	$-0.692742\pi$
$811$	−32.4187	−1.13837	−0.569187	+	0.822208i	$0.692742\pi$
$812$	1.62534	0.0570381
$813$	−1.26712	−0.0444397
$814$	9.86669	0.345827
$815$	0	0
$816$	−6.08509	−0.213021
$817$	1.90560	0.0666686
$818$	71.3936	2.49622
$819$	−0.391830	−0.0136916
$820$	0	0
$821$	−41.9011	−1.46236	−0.731180	−	0.682185i	$-0.761030\pi$
$821$	−41.9011	−1.46236	−0.731180	+	0.682185i	$0.761030\pi$
$822$	23.3433	0.814191
$823$	13.0163	0.453720	0.226860	−	0.973927i	$-0.427154\pi$
$823$	13.0163	0.453720	0.226860	+	0.973927i	$0.427154\pi$
$824$	−41.5251	−1.44660
$825$	0	0
$826$	7.01887	0.244218
$827$	45.5010	1.58223	0.791113	−	0.611670i	$-0.209502\pi$
$827$	45.5010	1.58223	0.791113	+	0.611670i	$0.209502\pi$
$828$	−16.7978	−0.583762
$829$	36.3516	1.26254	0.631272	−	0.775561i	$-0.282533\pi$
$829$	36.3516	1.26254	0.631272	+	0.775561i	$0.282533\pi$
$830$	0	0
$831$	−26.6696	−0.925160
$832$	8.72892	0.302621
$833$	41.9664	1.45405
$834$	11.5879	0.401255
$835$	0	0
$836$	−11.8614	−0.410235
$837$	7.27441	0.251440
$838$	36.4288	1.25841
$839$	−49.3747	−1.70461	−0.852303	−	0.523049i	$-0.824795\pi$
$839$	−49.3747	−1.70461	−0.852303	+	0.523049i	$0.824795\pi$
$840$	0	0
$841$	−28.1440	−0.970484
$842$	33.6190	1.15859
$843$	−5.14077	−0.177058
$844$	31.7272	1.09210
$845$	0	0
$846$	2.23799	0.0769436
$847$	−2.38658	−0.0820040
$848$	−4.48624	−0.154058
$849$	13.9738	0.479579
$850$	0	0
$851$	9.36211	0.320929
$852$	−26.1277	−0.895120
$853$	29.6507	1.01522	0.507610	−	0.861587i	$-0.330529\pi$
$853$	29.6507	1.01522	0.507610	+	0.861587i	$0.330529\pi$
$854$	−2.39772	−0.0820483
$855$	0	0
$856$	−30.0665	−1.02765
$857$	53.4437	1.82560	0.912800	−	0.408406i	$-0.133915\pi$
$857$	53.4437	1.82560	0.912800	+	0.408406i	$0.133915\pi$
$858$	−3.94847	−0.134798
$859$	−7.65486	−0.261180	−0.130590	−	0.991436i	$-0.541687\pi$
$859$	−7.65486	−0.261180	−0.130590	+	0.991436i	$0.541687\pi$
$860$	0	0
$861$	−2.21600	−0.0755211
$862$	−28.8384	−0.982238
$863$	−37.5089	−1.27682	−0.638410	−	0.769697i	$-0.720407\pi$
$863$	−37.5089	−1.27682	−0.638410	+	0.769697i	$0.720407\pi$
$864$	6.67534	0.227100
$865$	0	0
$866$	16.1425	0.548543
$867$	−22.7174	−0.771523
$868$	−12.7796	−0.433766
$869$	23.7349	0.805151
$870$	0	0
$871$	6.79381	0.230200
$872$	4.55403	0.154219
$873$	−11.9931	−0.405905
$874$	−18.7366	−0.633774
$875$	0	0
$876$	−17.3692	−0.586849
$877$	−31.9568	−1.07910	−0.539551	−	0.841953i	$-0.681406\pi$
$877$	−31.9568	−1.07910	−0.539551	+	0.841953i	$0.681406\pi$
$878$	0.956436	0.0322781
$879$	12.2078	0.411758
$880$	0	0
$881$	−4.92413	−0.165898	−0.0829491	−	0.996554i	$-0.526434\pi$
$881$	−4.92413	−0.165898	−0.0829491	+	0.996554i	$0.526434\pi$
$882$	−14.9028	−0.501805
$883$	20.4618	0.688593	0.344297	−	0.938861i	$-0.388117\pi$
$883$	20.4618	0.688593	0.344297	+	0.938861i	$0.388117\pi$
$884$	12.7232	0.427928
$885$	0	0
$886$	49.2382	1.65419
$887$	−20.4206	−0.685656	−0.342828	−	0.939398i	$-0.611385\pi$
$887$	−20.4206	−0.685656	−0.342828	+	0.939398i	$0.611385\pi$
$888$	3.78494	0.127014
$889$	6.53459	0.219163
$890$	0	0
$891$	−2.62923	−0.0880824
$892$	−41.0724	−1.37521
$893$	1.49949	0.0501786
$894$	−22.0080	−0.736059
$895$	0	0
$896$	−9.20353	−0.307468
$897$	−3.74654	−0.125093
$898$	67.4061	2.24937
$899$	−6.73012	−0.224462
$900$	0	0
$901$	−29.2817	−0.975515
$902$	−22.3306	−0.743529
$903$	−0.742065	−0.0246944
$904$	18.2244	0.606133
$905$	0	0
$906$	−35.8205	−1.19005
$907$	−25.4242	−0.844197	−0.422099	−	0.906550i	$-0.638706\pi$
$907$	−25.4242	−0.844197	−0.422099	+	0.906550i	$0.638706\pi$
$908$	−20.1486	−0.668655
$909$	−2.46600	−0.0817921
$910$	0	0
$911$	−38.1071	−1.26254	−0.631272	−	0.775562i	$-0.717467\pi$
$911$	−38.1071	−1.26254	−0.631272	+	0.775562i	$0.717467\pi$
$912$	1.44784	0.0479429
$913$	−17.9723	−0.594796
$914$	−64.8325	−2.14447
$915$	0	0
$916$	−41.9359	−1.38560
$917$	1.29715	0.0428358
$918$	14.1042	0.465508
$919$	56.5157	1.86428	0.932140	−	0.362098i	$-0.117939\pi$
$919$	56.5157	1.86428	0.932140	+	0.362098i	$0.117939\pi$
$920$	0	0
$921$	7.22568	0.238094
$922$	−3.31253	−0.109092
$923$	−5.82747	−0.191814
$924$	4.61898	0.151953
$925$	0	0
$926$	40.3785	1.32692
$927$	−18.3966	−0.604223
$928$	−6.17587	−0.202733
$929$	−13.5059	−0.443113	−0.221556	−	0.975148i	$-0.571114\pi$
$929$	−13.5059	−0.443113	−0.221556	+	0.975148i	$0.571114\pi$
$930$	0	0
$931$	−9.98518	−0.327251
$932$	75.1260	2.46083
$933$	19.5224	0.639136
$934$	−84.8551	−2.77654
$935$	0	0
$936$	−1.51466	−0.0495084
$937$	−27.8881	−0.911066	−0.455533	−	0.890219i	$-0.650551\pi$
$937$	−27.8881	−0.911066	−0.455533	+	0.890219i	$0.650551\pi$
$938$	−13.2307	−0.431998
$939$	9.90251	0.323156
$940$	0	0
$941$	−11.2627	−0.367154	−0.183577	−	0.983005i	$-0.558768\pi$
$941$	−11.2627	−0.367154	−0.183577	+	0.983005i	$0.558768\pi$
$942$	13.6986	0.446324
$943$	−21.1886	−0.689997
$944$	−5.18599	−0.168790
$945$	0	0
$946$	−7.47779	−0.243124
$947$	−48.0045	−1.55994	−0.779968	−	0.625820i	$-0.784765\pi$
$947$	−48.0045	−1.55994	−0.779968	+	0.625820i	$0.784765\pi$
$948$	27.1596	0.882101
$949$	−3.87399	−0.125755
$950$	0	0
$951$	12.3476	0.400399
$952$	−8.30651	−0.269216
$953$	38.3892	1.24355	0.621775	−	0.783196i	$-0.286412\pi$
$953$	38.3892	1.24355	0.621775	+	0.783196i	$0.286412\pi$
$954$	10.3983	0.336659
$955$	0	0
$956$	80.7091	2.61032
$957$	2.43250	0.0786316
$958$	12.4025	0.400708
$959$	−6.09058	−0.196675
$960$	0	0
$961$	21.9170	0.706999
$962$	2.51818	0.0811893
$963$	−13.3202	−0.429236
$964$	38.0023	1.22397
$965$	0	0
$966$	7.29626	0.234753
$967$	−31.2048	−1.00348	−0.501739	−	0.865019i	$-0.667306\pi$
$967$	−31.2048	−1.00348	−0.501739	+	0.865019i	$0.667306\pi$
$968$	−9.22563	−0.296523
$969$	9.45007	0.303580
$970$	0	0
$971$	−36.4754	−1.17055	−0.585276	−	0.810834i	$-0.699014\pi$
$971$	−36.4754	−1.17055	−0.585276	+	0.810834i	$0.699014\pi$
$972$	−3.00859	−0.0965007
$973$	−3.02344	−0.0969269
$974$	−88.5676	−2.83789
$975$	0	0
$976$	1.77159	0.0567072
$977$	40.4655	1.29461	0.647304	−	0.762232i	$-0.275897\pi$
$977$	40.4655	1.29461	0.647304	+	0.762232i	$0.275897\pi$
$978$	27.5333	0.880419
$979$	−17.0940	−0.546327
$980$	0	0
$981$	2.01754	0.0644150
$982$	55.5467	1.77257
$983$	50.8952	1.62330	0.811652	−	0.584141i	$-0.198569\pi$
$983$	50.8952	1.62330	0.811652	+	0.584141i	$0.198569\pi$
$984$	−8.56621	−0.273081
$985$	0	0
$986$	−13.0489	−0.415561
$987$	−0.583922	−0.0185864
$988$	−3.02727	−0.0963102
$989$	−7.09538	−0.225620
$990$	0	0
$991$	−22.2728	−0.707519	−0.353760	−	0.935336i	$-0.615097\pi$
$991$	−22.2728	−0.707519	−0.353760	+	0.935336i	$0.615097\pi$
$992$	48.5591	1.54175
$993$	18.9970	0.602851
$994$	11.3488	0.359962
$995$	0	0
$996$	−20.5655	−0.651642
$997$	−7.80881	−0.247308	−0.123654	−	0.992325i	$-0.539461\pi$
$997$	−7.80881	−0.247308	−0.123654	+	0.992325i	$0.539461\pi$
$998$	12.7566	0.403802
$999$	1.67682	0.0530521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.x.1.7	✓	7
5.4	even	2		3525.2.a.bc.1.1	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.x.1.7	✓	7	1.1	even	1	trivial
3525.2.a.bc.1.1	yes	7	5.4	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+2.23799 q^{2} -1.00000 q^{3} +3.00859 q^{4} -2.23799 q^{6} +0.583922 q^{7} +2.25722 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.23799 q^{2} -1.00000 q^{3} +3.00859 q^{4} -2.23799 q^{6} +0.583922 q^{7} +2.25722 q^{8} +1.00000 q^{9} -2.62923 q^{11} -3.00859 q^{12} -0.671031 q^{13} +1.30681 q^{14} -0.965554 q^{16} -6.30217 q^{17} +2.23799 q^{18} +1.49949 q^{19} -0.583922 q^{21} -5.88418 q^{22} -5.58326 q^{23} -2.25722 q^{24} -1.50176 q^{26} -1.00000 q^{27} +1.75678 q^{28} +0.925178 q^{29} -7.27441 q^{31} -6.67534 q^{32} +2.62923 q^{33} -14.1042 q^{34} +3.00859 q^{36} -1.67682 q^{37} +3.35585 q^{38} +0.671031 q^{39} +3.79503 q^{41} -1.30681 q^{42} +1.27083 q^{43} -7.91027 q^{44} -12.4953 q^{46} +1.00000 q^{47} +0.965554 q^{48} -6.65904 q^{49} +6.30217 q^{51} -2.01886 q^{52} +4.64629 q^{53} -2.23799 q^{54} +1.31804 q^{56} -1.49949 q^{57} +2.07054 q^{58} +5.37099 q^{59} -1.83479 q^{61} -16.2800 q^{62} +0.583922 q^{63} -13.0082 q^{64} +5.88418 q^{66} -10.1244 q^{67} -18.9607 q^{68} +5.58326 q^{69} +8.68435 q^{71} +2.25722 q^{72} +5.77318 q^{73} -3.75270 q^{74} +4.51137 q^{76} -1.53526 q^{77} +1.50176 q^{78} -9.02733 q^{79} +1.00000 q^{81} +8.49323 q^{82} +6.83558 q^{83} -1.75678 q^{84} +2.84410 q^{86} -0.925178 q^{87} -5.93474 q^{88} +6.50153 q^{89} -0.391830 q^{91} -16.7978 q^{92} +7.27441 q^{93} +2.23799 q^{94} +6.67534 q^{96} -11.9931 q^{97} -14.9028 q^{98} -2.62923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 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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