LMFDB - Embedded newform 3525.2.a.be.1.8

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 $ x^8 - 3x^7 - 7x^6 + 24x^5 + 8x^4 - 47x^3 + 8x^2 + 13*x + 2
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			1.8
Root			$2.62510$ 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)

$f(q)$	$=$	$q+2.62510 q^{2} -1.00000 q^{3} +4.89115 q^{4} -2.62510 q^{6} +5.24764 q^{7} +7.58955 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.62510 q^{2} -1.00000 q^{3} +4.89115 q^{4} -2.62510 q^{6} +5.24764 q^{7} +7.58955 q^{8} +1.00000 q^{9} +2.45327 q^{11} -4.89115 q^{12} -1.47869 q^{13} +13.7756 q^{14} +10.1410 q^{16} +4.14255 q^{17} +2.62510 q^{18} +4.25408 q^{19} -5.24764 q^{21} +6.44007 q^{22} -6.50248 q^{23} -7.58955 q^{24} -3.88171 q^{26} -1.00000 q^{27} +25.6670 q^{28} -8.17052 q^{29} -5.69350 q^{31} +11.4421 q^{32} -2.45327 q^{33} +10.8746 q^{34} +4.89115 q^{36} -1.84684 q^{37} +11.1674 q^{38} +1.47869 q^{39} -9.39994 q^{41} -13.7756 q^{42} -4.34441 q^{43} +11.9993 q^{44} -17.0697 q^{46} +1.00000 q^{47} -10.1410 q^{48} +20.5377 q^{49} -4.14255 q^{51} -7.23250 q^{52} -6.95955 q^{53} -2.62510 q^{54} +39.8272 q^{56} -4.25408 q^{57} -21.4484 q^{58} -7.70051 q^{59} +12.0670 q^{61} -14.9460 q^{62} +5.24764 q^{63} +9.75464 q^{64} -6.44007 q^{66} -5.84395 q^{67} +20.2618 q^{68} +6.50248 q^{69} -2.81951 q^{71} +7.58955 q^{72} +5.10213 q^{73} -4.84815 q^{74} +20.8074 q^{76} +12.8739 q^{77} +3.88171 q^{78} +5.56405 q^{79} +1.00000 q^{81} -24.6758 q^{82} +15.4973 q^{83} -25.6670 q^{84} -11.4045 q^{86} +8.17052 q^{87} +18.6192 q^{88} -3.59698 q^{89} -7.75963 q^{91} -31.8046 q^{92} +5.69350 q^{93} +2.62510 q^{94} -11.4421 q^{96} -3.34748 q^{97} +53.9135 q^{98} +2.45327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * 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 $

$2$	2.62510	1.85623	0.928113	−	0.372299i	$-0.121430\pi$
$2$	2.62510	1.85623	0.928113	+	0.372299i	$0.121430\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.89115	2.44557
$5$	0	0
$5$	0	0
$6$	−2.62510	−1.07169
$7$	5.24764	1.98342	0.991710	−	0.128494i	$-0.0410142\pi$
$7$	5.24764	1.98342	0.991710	+	0.128494i	$0.0410142\pi$
$8$	7.58955	2.68331
$9$	1.00000	0.333333
$10$	0	0
$11$	2.45327	0.739688	0.369844	−	0.929094i	$-0.379411\pi$
$11$	2.45327	0.739688	0.369844	+	0.929094i	$0.379411\pi$
$12$	−4.89115	−1.41195
$13$	−1.47869	−0.410115	−0.205058	−	0.978750i	$-0.565738\pi$
$13$	−1.47869	−0.410115	−0.205058	+	0.978750i	$0.565738\pi$
$14$	13.7756	3.68168
$15$	0	0
$16$	10.1410	2.53526
$17$	4.14255	1.00471	0.502357	−	0.864660i	$-0.332466\pi$
$17$	4.14255	1.00471	0.502357	+	0.864660i	$0.332466\pi$
$18$	2.62510	0.618742
$19$	4.25408	0.975954	0.487977	−	0.872857i	$-0.337735\pi$
$19$	4.25408	0.975954	0.487977	+	0.872857i	$0.337735\pi$
$20$	0	0
$21$	−5.24764	−1.14513
$22$	6.44007	1.37303
$23$	−6.50248	−1.35586	−0.677931	−	0.735126i	$-0.737123\pi$
$23$	−6.50248	−1.35586	−0.677931	+	0.735126i	$0.737123\pi$
$24$	−7.58955	−1.54921
$25$	0	0
$26$	−3.88171	−0.761266
$27$	−1.00000	−0.192450
$28$	25.6670	4.85060
$29$	−8.17052	−1.51723	−0.758614	−	0.651540i	$-0.774123\pi$
$29$	−8.17052	−1.51723	−0.758614	+	0.651540i	$0.774123\pi$
$30$	0	0
$31$	−5.69350	−1.02258	−0.511291	−	0.859407i	$-0.670833\pi$
$31$	−5.69350	−1.02258	−0.511291	+	0.859407i	$0.670833\pi$
$32$	11.4421	2.02270
$33$	−2.45327	−0.427059
$34$	10.8746	1.86498
$35$	0	0
$36$	4.89115	0.815191
$37$	−1.84684	−0.303619	−0.151810	−	0.988410i	$-0.548510\pi$
$37$	−1.84684	−0.303619	−0.151810	+	0.988410i	$0.548510\pi$
$38$	11.1674	1.81159
$39$	1.47869	0.236780
$40$	0	0
$41$	−9.39994	−1.46802	−0.734012	−	0.679137i	$-0.762354\pi$
$41$	−9.39994	−1.46802	−0.734012	+	0.679137i	$0.762354\pi$
$42$	−13.7756	−2.12562
$43$	−4.34441	−0.662517	−0.331259	−	0.943540i	$-0.607473\pi$
$43$	−4.34441	−0.662517	−0.331259	+	0.943540i	$0.607473\pi$
$44$	11.9993	1.80896
$45$	0	0
$46$	−17.0697	−2.51679
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−10.1410	−1.46373
$49$	20.5377	2.93396
$50$	0	0
$51$	−4.14255	−0.580072
$52$	−7.23250	−1.00297
$53$	−6.95955	−0.955967	−0.477984	−	0.878369i	$-0.658632\pi$
$53$	−6.95955	−0.955967	−0.477984	+	0.878369i	$0.658632\pi$
$54$	−2.62510	−0.357231
$55$	0	0
$56$	39.8272	5.32214
$57$	−4.25408	−0.563467
$58$	−21.4484	−2.81632
$59$	−7.70051	−1.00252	−0.501260	−	0.865297i	$-0.667130\pi$
$59$	−7.70051	−1.00252	−0.501260	+	0.865297i	$0.667130\pi$
$60$	0	0
$61$	12.0670	1.54501	0.772507	−	0.635006i	$-0.219002\pi$
$61$	12.0670	1.54501	0.772507	+	0.635006i	$0.219002\pi$
$62$	−14.9460	−1.89814
$63$	5.24764	0.661140
$64$	9.75464	1.21933
$65$	0	0
$66$	−6.44007	−0.792718
$67$	−5.84395	−0.713952	−0.356976	−	0.934113i	$-0.616192\pi$
$67$	−5.84395	−0.713952	−0.356976	+	0.934113i	$0.616192\pi$
$68$	20.2618	2.45710
$69$	6.50248	0.782807
$70$	0	0
$71$	−2.81951	−0.334614	−0.167307	−	0.985905i	$-0.553507\pi$
$71$	−2.81951	−0.334614	−0.167307	+	0.985905i	$0.553507\pi$
$72$	7.58955	0.894437
$73$	5.10213	0.597159	0.298579	−	0.954385i	$-0.403487\pi$
$73$	5.10213	0.597159	0.298579	+	0.954385i	$0.403487\pi$
$74$	−4.84815	−0.563586
$75$	0	0
$76$	20.8074	2.38677
$77$	12.8739	1.46711
$78$	3.88171	0.439517
$79$	5.56405	0.626005	0.313002	−	0.949752i	$-0.398665\pi$
$79$	5.56405	0.626005	0.313002	+	0.949752i	$0.398665\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−24.6758	−2.72498
$83$	15.4973	1.70105	0.850523	−	0.525937i	$-0.176285\pi$
$83$	15.4973	1.70105	0.850523	+	0.525937i	$0.176285\pi$
$84$	−25.6670	−2.80050
$85$	0	0
$86$	−11.4045	−1.22978
$87$	8.17052	0.875972
$88$	18.6192	1.98481
$89$	−3.59698	−0.381280	−0.190640	−	0.981660i	$-0.561056\pi$
$89$	−3.59698	−0.381280	−0.190640	+	0.981660i	$0.561056\pi$
$90$	0	0
$91$	−7.75963	−0.813431
$92$	−31.8046	−3.31586
$93$	5.69350	0.590388
$94$	2.62510	0.270758
$95$	0	0
$96$	−11.4421	−1.16781
$97$	−3.34748	−0.339886	−0.169943	−	0.985454i	$-0.554358\pi$
$97$	−3.34748	−0.339886	−0.169943	+	0.985454i	$0.554358\pi$
$98$	53.9135	5.44609
$99$	2.45327	0.246563
$100$	0	0
$101$	−1.29938	−0.129294	−0.0646468	−	0.997908i	$-0.520592\pi$
$101$	−1.29938	−0.129294	−0.0646468	+	0.997908i	$0.520592\pi$
$102$	−10.8746	−1.07675
$103$	−16.5846	−1.63413	−0.817065	−	0.576546i	$-0.804400\pi$
$103$	−16.5846	−1.63413	−0.817065	+	0.576546i	$0.804400\pi$
$104$	−11.2226	−1.10047
$105$	0	0
$106$	−18.2695	−1.77449
$107$	10.0354	0.970163	0.485081	−	0.874469i	$-0.338790\pi$
$107$	10.0354	0.970163	0.485081	+	0.874469i	$0.338790\pi$
$108$	−4.89115	−0.470651
$109$	−9.16258	−0.877616	−0.438808	−	0.898581i	$-0.644599\pi$
$109$	−9.16258	−0.877616	−0.438808	+	0.898581i	$0.644599\pi$
$110$	0	0
$111$	1.84684	0.175295
$112$	53.2165	5.02848
$113$	11.4553	1.07762	0.538810	−	0.842427i	$-0.318874\pi$
$113$	11.4553	1.07762	0.538810	+	0.842427i	$0.318874\pi$
$114$	−11.1674	−1.04592
$115$	0	0
$116$	−39.9632	−3.71049
$117$	−1.47869	−0.136705
$118$	−20.2146	−1.86090
$119$	21.7386	1.99277
$120$	0	0
$121$	−4.98148	−0.452862
$122$	31.6770	2.86790
$123$	9.39994	0.847564
$124$	−27.8477	−2.50080
$125$	0	0
$126$	13.7756	1.22723
$127$	7.50757	0.666189	0.333095	−	0.942893i	$-0.391907\pi$
$127$	7.50757	0.666189	0.333095	+	0.942893i	$0.391907\pi$
$128$	2.72267	0.240652
$129$	4.34441	0.382504
$130$	0	0
$131$	12.4292	1.08595	0.542974	−	0.839749i	$-0.317298\pi$
$131$	12.4292	1.08595	0.542974	+	0.839749i	$0.317298\pi$
$132$	−11.9993	−1.04440
$133$	22.3239	1.93573
$134$	−15.3410	−1.32526
$135$	0	0
$136$	31.4401	2.69596
$137$	−12.7385	−1.08832	−0.544162	−	0.838980i	$-0.683152\pi$
$137$	−12.7385	−1.08832	−0.544162	+	0.838980i	$0.683152\pi$
$138$	17.0697	1.45307
$139$	−13.7235	−1.16401	−0.582005	−	0.813185i	$-0.697732\pi$
$139$	−13.7235	−1.16401	−0.582005	+	0.813185i	$0.697732\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−7.40148	−0.621119
$143$	−3.62762	−0.303357
$144$	10.1410	0.845086
$145$	0	0
$146$	13.3936	1.10846
$147$	−20.5377	−1.69392
$148$	−9.03319	−0.742524
$149$	6.30968	0.516909	0.258455	−	0.966023i	$-0.416787\pi$
$149$	6.30968	0.516909	0.258455	+	0.966023i	$0.416787\pi$
$150$	0	0
$151$	7.80524	0.635182	0.317591	−	0.948228i	$-0.397126\pi$
$151$	7.80524	0.635182	0.317591	+	0.948228i	$0.397126\pi$
$152$	32.2866	2.61879
$153$	4.14255	0.334905
$154$	33.7952	2.72329
$155$	0	0
$156$	7.23250	0.579063
$157$	21.1234	1.68583	0.842914	−	0.538048i	$-0.180838\pi$
$157$	21.1234	1.68583	0.842914	+	0.538048i	$0.180838\pi$
$158$	14.6062	1.16201
$159$	6.95955	0.551928
$160$	0	0
$161$	−34.1227	−2.68924
$162$	2.62510	0.206247
$163$	19.5801	1.53363	0.766816	−	0.641867i	$-0.221840\pi$
$163$	19.5801	1.53363	0.766816	+	0.641867i	$0.221840\pi$
$164$	−45.9765	−3.59016
$165$	0	0
$166$	40.6819	3.15753
$167$	−2.84701	−0.220308	−0.110154	−	0.993915i	$-0.535134\pi$
$167$	−2.84701	−0.220308	−0.110154	+	0.993915i	$0.535134\pi$
$168$	−39.8272	−3.07274
$169$	−10.8135	−0.831806
$170$	0	0
$171$	4.25408	0.325318
$172$	−21.2492	−1.62023
$173$	−7.99152	−0.607584	−0.303792	−	0.952738i	$-0.598253\pi$
$173$	−7.99152	−0.607584	−0.303792	+	0.952738i	$0.598253\pi$
$174$	21.4484	1.62600
$175$	0	0
$176$	24.8787	1.87530
$177$	7.70051	0.578806
$178$	−9.44244	−0.707741
$179$	−11.6594	−0.871461	−0.435731	−	0.900077i	$-0.643510\pi$
$179$	−11.6594	−0.871461	−0.435731	+	0.900077i	$0.643510\pi$
$180$	0	0
$181$	19.5331	1.45188	0.725942	−	0.687756i	$-0.241404\pi$
$181$	19.5331	1.45188	0.725942	+	0.687756i	$0.241404\pi$
$182$	−20.3698	−1.50991
$183$	−12.0670	−0.892015
$184$	−49.3509	−3.63820
$185$	0	0
$186$	14.9460	1.09589
$187$	10.1628	0.743175
$188$	4.89115	0.356724
$189$	−5.24764	−0.381709
$190$	0	0
$191$	−23.1126	−1.67237	−0.836185	−	0.548447i	$-0.815219\pi$
$191$	−23.1126	−1.67237	−0.836185	+	0.548447i	$0.815219\pi$
$192$	−9.75464	−0.703981
$193$	17.2364	1.24070	0.620351	−	0.784324i	$-0.286990\pi$
$193$	17.2364	1.24070	0.620351	+	0.784324i	$0.286990\pi$
$194$	−8.78748	−0.630904
$195$	0	0
$196$	100.453	7.17521
$197$	11.1056	0.791240	0.395620	−	0.918414i	$-0.370530\pi$
$197$	11.1056	0.791240	0.395620	+	0.918414i	$0.370530\pi$
$198$	6.44007	0.457676
$199$	−23.0611	−1.63476	−0.817380	−	0.576098i	$-0.804575\pi$
$199$	−23.0611	−1.63476	−0.817380	+	0.576098i	$0.804575\pi$
$200$	0	0
$201$	5.84395	0.412201
$202$	−3.41101	−0.239998
$203$	−42.8759	−3.00930
$204$	−20.2618	−1.41861
$205$	0	0
$206$	−43.5362	−3.03331
$207$	−6.50248	−0.451954
$208$	−14.9955	−1.03975
$209$	10.4364	0.721901
$210$	0	0
$211$	4.09406	0.281847	0.140923	−	0.990021i	$-0.454993\pi$
$211$	4.09406	0.281847	0.140923	+	0.990021i	$0.454993\pi$
$212$	−34.0402	−2.33789
$213$	2.81951	0.193189
$214$	26.3440	1.80084
$215$	0	0
$216$	−7.58955	−0.516404
$217$	−29.8774	−2.02821
$218$	−24.0527	−1.62905
$219$	−5.10213	−0.344770
$220$	0	0
$221$	−6.12555	−0.412049
$222$	4.84815	0.325387
$223$	−21.0775	−1.41146	−0.705728	−	0.708483i	$-0.749380\pi$
$223$	−21.0775	−1.41146	−0.705728	+	0.708483i	$0.749380\pi$
$224$	60.0441	4.01187
$225$	0	0
$226$	30.0712	2.00031
$227$	−1.70842	−0.113392	−0.0566958	−	0.998391i	$-0.518057\pi$
$227$	−1.70842	−0.113392	−0.0566958	+	0.998391i	$0.518057\pi$
$228$	−20.8074	−1.37800
$229$	5.07837	0.335588	0.167794	−	0.985822i	$-0.446336\pi$
$229$	5.07837	0.335588	0.167794	+	0.985822i	$0.446336\pi$
$230$	0	0
$231$	−12.8739	−0.847037
$232$	−62.0106	−4.07120
$233$	0.738739	0.0483964	0.0241982	−	0.999707i	$-0.492297\pi$
$233$	0.738739	0.0483964	0.0241982	+	0.999707i	$0.492297\pi$
$234$	−3.88171	−0.253755
$235$	0	0
$236$	−37.6643	−2.45174
$237$	−5.56405	−0.361424
$238$	57.0659	3.69904
$239$	−3.36660	−0.217767	−0.108884	−	0.994055i	$-0.534728\pi$
$239$	−3.36660	−0.217767	−0.108884	+	0.994055i	$0.534728\pi$
$240$	0	0
$241$	6.51135	0.419433	0.209716	−	0.977762i	$-0.432746\pi$
$241$	6.51135	0.419433	0.209716	+	0.977762i	$0.432746\pi$
$242$	−13.0769	−0.840614
$243$	−1.00000	−0.0641500
$244$	59.0212	3.77845
$245$	0	0
$246$	24.6758	1.57327
$247$	−6.29048	−0.400253
$248$	−43.2111	−2.74391
$249$	−15.4973	−0.982100
$250$	0	0
$251$	11.7004	0.738524	0.369262	−	0.929325i	$-0.379611\pi$
$251$	11.7004	0.738524	0.369262	+	0.929325i	$0.379611\pi$
$252$	25.6670	1.61687
$253$	−15.9523	−1.00291
$254$	19.7081	1.23660
$255$	0	0
$256$	−12.3620	−0.772626
$257$	28.1645	1.75685	0.878427	−	0.477876i	$-0.158593\pi$
$257$	28.1645	1.75685	0.878427	+	0.477876i	$0.158593\pi$
$258$	11.4045	0.710015
$259$	−9.69157	−0.602205
$260$	0	0
$261$	−8.17052	−0.505743
$262$	32.6280	2.01577
$263$	−15.2487	−0.940276	−0.470138	−	0.882593i	$-0.655796\pi$
$263$	−15.2487	−0.940276	−0.470138	+	0.882593i	$0.655796\pi$
$264$	−18.6192	−1.14593
$265$	0	0
$266$	58.6024	3.59315
$267$	3.59698	0.220132
$268$	−28.5836	−1.74602
$269$	−7.75275	−0.472693	−0.236347	−	0.971669i	$-0.575950\pi$
$269$	−7.75275	−0.472693	−0.236347	+	0.971669i	$0.575950\pi$
$270$	0	0
$271$	−14.9314	−0.907020	−0.453510	−	0.891251i	$-0.649828\pi$
$271$	−14.9314	−0.907020	−0.453510	+	0.891251i	$0.649828\pi$
$272$	42.0097	2.54721
$273$	7.75963	0.469634
$274$	−33.4398	−2.02018
$275$	0	0
$276$	31.8046	1.91441
$277$	−19.0645	−1.14548	−0.572739	−	0.819738i	$-0.694119\pi$
$277$	−19.0645	−1.14548	−0.572739	+	0.819738i	$0.694119\pi$
$278$	−36.0255	−2.16067
$279$	−5.69350	−0.340861
$280$	0	0
$281$	−11.2828	−0.673076	−0.336538	−	0.941670i	$-0.609256\pi$
$281$	−11.2828	−0.673076	−0.336538	+	0.941670i	$0.609256\pi$
$282$	−2.62510	−0.156322
$283$	16.9950	1.01025	0.505124	−	0.863047i	$-0.331447\pi$
$283$	16.9950	1.01025	0.505124	+	0.863047i	$0.331447\pi$
$284$	−13.7906	−0.818323
$285$	0	0
$286$	−9.52287	−0.563099
$287$	−49.3275	−2.91171
$288$	11.4421	0.674234
$289$	0.160687	0.00945218
$290$	0	0
$291$	3.34748	0.196233
$292$	24.9553	1.46040
$293$	29.7556	1.73834	0.869170	−	0.494513i	$-0.164654\pi$
$293$	29.7556	1.73834	0.869170	+	0.494513i	$0.164654\pi$
$294$	−53.9135	−3.14430
$295$	0	0
$296$	−14.0167	−0.814705
$297$	−2.45327	−0.142353
$298$	16.5635	0.959500
$299$	9.61516	0.556059
$300$	0	0
$301$	−22.7979	−1.31405
$302$	20.4895	1.17904
$303$	1.29938	0.0746477
$304$	43.1408	2.47430
$305$	0	0
$306$	10.8746	0.621659
$307$	24.4730	1.39675	0.698373	−	0.715734i	$-0.253908\pi$
$307$	24.4730	1.39675	0.698373	+	0.715734i	$0.253908\pi$
$308$	62.9679	3.58793
$309$	16.5846	0.943465
$310$	0	0
$311$	−8.26842	−0.468859	−0.234430	−	0.972133i	$-0.575322\pi$
$311$	−8.26842	−0.468859	−0.234430	+	0.972133i	$0.575322\pi$
$312$	11.2226	0.635355
$313$	26.7049	1.50945	0.754724	−	0.656043i	$-0.227771\pi$
$313$	26.7049	1.50945	0.754724	+	0.656043i	$0.227771\pi$
$314$	55.4509	3.12928
$315$	0	0
$316$	27.2146	1.53094
$317$	−12.1898	−0.684649	−0.342325	−	0.939582i	$-0.611214\pi$
$317$	−12.1898	−0.684649	−0.342325	+	0.939582i	$0.611214\pi$
$318$	18.2695	1.02450
$319$	−20.0445	−1.12227
$320$	0	0
$321$	−10.0354	−0.560124
$322$	−89.5754	−4.99184
$323$	17.6227	0.980556
$324$	4.89115	0.271730
$325$	0	0
$326$	51.3997	2.84677
$327$	9.16258	0.506692
$328$	−71.3413	−3.93916
$329$	5.24764	0.289312
$330$	0	0
$331$	8.91572	0.490052	0.245026	−	0.969516i	$-0.421203\pi$
$331$	8.91572	0.490052	0.245026	+	0.969516i	$0.421203\pi$
$332$	75.7995	4.16004
$333$	−1.84684	−0.101206
$334$	−7.47368	−0.408942
$335$	0	0
$336$	−53.2165	−2.90320
$337$	0.427820	0.0233049	0.0116524	−	0.999932i	$-0.496291\pi$
$337$	0.427820	0.0233049	0.0116524	+	0.999932i	$0.496291\pi$
$338$	−28.3864	−1.54402
$339$	−11.4553	−0.622165
$340$	0	0
$341$	−13.9677	−0.756392
$342$	11.1674	0.603864
$343$	71.0410	3.83585
$344$	−32.9722	−1.77774
$345$	0	0
$346$	−20.9785	−1.12781
$347$	13.8379	0.742859	0.371430	−	0.928461i	$-0.378868\pi$
$347$	13.8379	0.742859	0.371430	+	0.928461i	$0.378868\pi$
$348$	39.9632	2.14225
$349$	22.3237	1.19496	0.597479	−	0.801884i	$-0.296169\pi$
$349$	22.3237	1.19496	0.597479	+	0.801884i	$0.296169\pi$
$350$	0	0
$351$	1.47869	0.0789267
$352$	28.0706	1.49617
$353$	20.0786	1.06868	0.534339	−	0.845270i	$-0.320561\pi$
$353$	20.0786	1.06868	0.534339	+	0.845270i	$0.320561\pi$
$354$	20.2146	1.07439
$355$	0	0
$356$	−17.5934	−0.932448
$357$	−21.7386	−1.15053
$358$	−30.6070	−1.61763
$359$	−18.8565	−0.995208	−0.497604	−	0.867404i	$-0.665787\pi$
$359$	−18.8565	−0.995208	−0.497604	+	0.867404i	$0.665787\pi$
$360$	0	0
$361$	−0.902764	−0.0475139
$362$	51.2763	2.69502
$363$	4.98148	0.261460
$364$	−37.9535	−1.98931
$365$	0	0
$366$	−31.6770	−1.65578
$367$	21.5685	1.12587	0.562934	−	0.826502i	$-0.309672\pi$
$367$	21.5685	1.12587	0.562934	+	0.826502i	$0.309672\pi$
$368$	−65.9419	−3.43746
$369$	−9.39994	−0.489341
$370$	0	0
$371$	−36.5212	−1.89609
$372$	27.8477	1.44384
$373$	−8.49759	−0.439988	−0.219994	−	0.975501i	$-0.570604\pi$
$373$	−8.49759	−0.439988	−0.219994	+	0.975501i	$0.570604\pi$
$374$	26.6783	1.37950
$375$	0	0
$376$	7.58955	0.391401
$377$	12.0817	0.622238
$378$	−13.7756	−0.708539
$379$	12.9777	0.666618	0.333309	−	0.942818i	$-0.391835\pi$
$379$	12.9777	0.666618	0.333309	+	0.942818i	$0.391835\pi$
$380$	0	0
$381$	−7.50757	−0.384624
$382$	−60.6729	−3.10430
$383$	−28.8351	−1.47340	−0.736701	−	0.676218i	$-0.763618\pi$
$383$	−28.8351	−1.47340	−0.736701	+	0.676218i	$0.763618\pi$
$384$	−2.72267	−0.138940
$385$	0	0
$386$	45.2472	2.30302
$387$	−4.34441	−0.220839
$388$	−16.3730	−0.831215
$389$	21.5803	1.09417	0.547084	−	0.837078i	$-0.315738\pi$
$389$	21.5803	1.09417	0.547084	+	0.837078i	$0.315738\pi$
$390$	0	0
$391$	−26.9368	−1.36225
$392$	155.872	7.87272
$393$	−12.4292	−0.626972
$394$	29.1533	1.46872
$395$	0	0
$396$	11.9993	0.602987
$397$	−16.6366	−0.834969	−0.417484	−	0.908684i	$-0.637088\pi$
$397$	−16.6366	−0.834969	−0.417484	+	0.908684i	$0.637088\pi$
$398$	−60.5378	−3.03449
$399$	−22.3239	−1.11759
$400$	0	0
$401$	−33.5127	−1.67354	−0.836772	−	0.547552i	$-0.815560\pi$
$401$	−33.5127	−1.67354	−0.836772	+	0.547552i	$0.815560\pi$
$402$	15.3410	0.765137
$403$	8.41892	0.419376
$404$	−6.35548	−0.316197
$405$	0	0
$406$	−112.554	−5.58594
$407$	−4.53080	−0.224583
$408$	−31.4401	−1.55652
$409$	−11.8817	−0.587512	−0.293756	−	0.955880i	$-0.594905\pi$
$409$	−11.8817	−0.587512	−0.293756	+	0.955880i	$0.594905\pi$
$410$	0	0
$411$	12.7385	0.628344
$412$	−81.1178	−3.99639
$413$	−40.4095	−1.98842
$414$	−17.0697	−0.838928
$415$	0	0
$416$	−16.9194	−0.829540
$417$	13.7235	0.672042
$418$	27.3966	1.34001
$419$	−2.52390	−0.123301	−0.0616503	−	0.998098i	$-0.519636\pi$
$419$	−2.52390	−0.123301	−0.0616503	+	0.998098i	$0.519636\pi$
$420$	0	0
$421$	14.7777	0.720220	0.360110	−	0.932910i	$-0.382739\pi$
$421$	14.7777	0.720220	0.360110	+	0.932910i	$0.382739\pi$
$422$	10.7473	0.523171
$423$	1.00000	0.0486217
$424$	−52.8198	−2.56516
$425$	0	0
$426$	7.40148	0.358603
$427$	63.3230	3.06441
$428$	49.0848	2.37260
$429$	3.62762	0.175143
$430$	0	0
$431$	−28.6446	−1.37976	−0.689880	−	0.723923i	$-0.742337\pi$
$431$	−28.6446	−1.37976	−0.689880	+	0.723923i	$0.742337\pi$
$432$	−10.1410	−0.487911
$433$	−14.0010	−0.672844	−0.336422	−	0.941711i	$-0.609217\pi$
$433$	−14.0010	−0.672844	−0.336422	+	0.941711i	$0.609217\pi$
$434$	−78.4312	−3.76482
$435$	0	0
$436$	−44.8155	−2.14627
$437$	−27.6621	−1.32326
$438$	−13.3936	−0.639971
$439$	−23.0784	−1.10147	−0.550735	−	0.834680i	$-0.685653\pi$
$439$	−23.0784	−1.10147	−0.550735	+	0.834680i	$0.685653\pi$
$440$	0	0
$441$	20.5377	0.977986
$442$	−16.0802	−0.764856
$443$	17.2342	0.818822	0.409411	−	0.912350i	$-0.365734\pi$
$443$	17.2342	0.818822	0.409411	+	0.912350i	$0.365734\pi$
$444$	9.03319	0.428696
$445$	0	0
$446$	−55.3306	−2.61998
$447$	−6.30968	−0.298438
$448$	51.1888	2.41845
$449$	−14.4444	−0.681673	−0.340837	−	0.940123i	$-0.610710\pi$
$449$	−14.4444	−0.681673	−0.340837	+	0.940123i	$0.610710\pi$
$450$	0	0
$451$	−23.0606	−1.08588
$452$	56.0294	2.63540
$453$	−7.80524	−0.366722
$454$	−4.48476	−0.210480
$455$	0	0
$456$	−32.2866	−1.51196
$457$	−29.3230	−1.37167	−0.685835	−	0.727757i	$-0.740563\pi$
$457$	−29.3230	−1.37167	−0.685835	+	0.727757i	$0.740563\pi$
$458$	13.3312	0.622928
$459$	−4.14255	−0.193357
$460$	0	0
$461$	−10.0074	−0.466091	−0.233045	−	0.972466i	$-0.574869\pi$
$461$	−10.0074	−0.466091	−0.233045	+	0.972466i	$0.574869\pi$
$462$	−33.7952	−1.57229
$463$	6.74306	0.313377	0.156688	−	0.987648i	$-0.449918\pi$
$463$	6.74306	0.313377	0.156688	+	0.987648i	$0.449918\pi$
$464$	−82.8576	−3.84657
$465$	0	0
$466$	1.93926	0.0898347
$467$	22.6006	1.04583	0.522915	−	0.852385i	$-0.324845\pi$
$467$	22.6006	1.04583	0.522915	+	0.852385i	$0.324845\pi$
$468$	−7.23250	−0.334322
$469$	−30.6669	−1.41607
$470$	0	0
$471$	−21.1234	−0.973313
$472$	−58.4434	−2.69008
$473$	−10.6580	−0.490056
$474$	−14.6062	−0.670885
$475$	0	0
$476$	106.327	4.87347
$477$	−6.95955	−0.318656
$478$	−8.83765	−0.404225
$479$	28.0031	1.27949	0.639747	−	0.768585i	$-0.279039\pi$
$479$	28.0031	1.27949	0.639747	+	0.768585i	$0.279039\pi$
$480$	0	0
$481$	2.73091	0.124519
$482$	17.0929	0.778562
$483$	34.1227	1.55264
$484$	−24.3652	−1.10751
$485$	0	0
$486$	−2.62510	−0.119077
$487$	29.5359	1.33840	0.669200	−	0.743082i	$-0.266637\pi$
$487$	29.5359	1.33840	0.669200	+	0.743082i	$0.266637\pi$
$488$	91.5828	4.14576
$489$	−19.5801	−0.885443
$490$	0	0
$491$	−10.1287	−0.457102	−0.228551	−	0.973532i	$-0.573399\pi$
$491$	−10.1287	−0.457102	−0.228551	+	0.973532i	$0.573399\pi$
$492$	45.9765	2.07278
$493$	−33.8468	−1.52438
$494$	−16.5131	−0.742961
$495$	0	0
$496$	−57.7380	−2.59251
$497$	−14.7957	−0.663680
$498$	−40.6819	−1.82300
$499$	−6.22375	−0.278613	−0.139307	−	0.990249i	$-0.544487\pi$
$499$	−6.22375	−0.278613	−0.139307	+	0.990249i	$0.544487\pi$
$500$	0	0
$501$	2.84701	0.127195
$502$	30.7148	1.37087
$503$	31.8043	1.41809	0.709043	−	0.705166i	$-0.249127\pi$
$503$	31.8043	1.41809	0.709043	+	0.705166i	$0.249127\pi$
$504$	39.8272	1.77405
$505$	0	0
$506$	−41.8765	−1.86164
$507$	10.8135	0.480243
$508$	36.7206	1.62921
$509$	13.5256	0.599513	0.299756	−	0.954016i	$-0.403095\pi$
$509$	13.5256	0.599513	0.299756	+	0.954016i	$0.403095\pi$
$510$	0	0
$511$	26.7741	1.18442
$512$	−37.8969	−1.67482
$513$	−4.25408	−0.187822
$514$	73.9347	3.26112
$515$	0	0
$516$	21.2492	0.935443
$517$	2.45327	0.107895
$518$	−25.4413	−1.11783
$519$	7.99152	0.350789
$520$	0	0
$521$	−6.89142	−0.301918	−0.150959	−	0.988540i	$-0.548236\pi$
$521$	−6.89142	−0.301918	−0.150959	+	0.988540i	$0.548236\pi$
$522$	−21.4484	−0.938773
$523$	−10.4160	−0.455461	−0.227730	−	0.973724i	$-0.573131\pi$
$523$	−10.4160	−0.455461	−0.227730	+	0.973724i	$0.573131\pi$
$524$	60.7933	2.65577
$525$	0	0
$526$	−40.0294	−1.74537
$527$	−23.5856	−1.02740
$528$	−24.8787	−1.08270
$529$	19.2823	0.838361
$530$	0	0
$531$	−7.70051	−0.334174
$532$	109.189	4.73396
$533$	13.8996	0.602059
$534$	9.44244	0.408615
$535$	0	0
$536$	−44.3530	−1.91576
$537$	11.6594	0.503138
$538$	−20.3517	−0.877426
$539$	50.3845	2.17021
$540$	0	0
$541$	−4.77543	−0.205312	−0.102656	−	0.994717i	$-0.532734\pi$
$541$	−4.77543	−0.205312	−0.102656	+	0.994717i	$0.532734\pi$
$542$	−39.1965	−1.68363
$543$	−19.5331	−0.838245
$544$	47.3995	2.03224
$545$	0	0
$546$	20.3698	0.871748
$547$	−35.1733	−1.50390	−0.751950	−	0.659220i	$-0.770887\pi$
$547$	−35.1733	−1.50390	−0.751950	+	0.659220i	$0.770887\pi$
$548$	−62.3059	−2.66158
$549$	12.0670	0.515005
$550$	0	0
$551$	−34.7581	−1.48074
$552$	49.3509	2.10052
$553$	29.1981	1.24163
$554$	−50.0463	−2.12626
$555$	0	0
$556$	−67.1236	−2.84667
$557$	−41.5731	−1.76151	−0.880755	−	0.473573i	$-0.842964\pi$
$557$	−41.5731	−1.76151	−0.880755	+	0.473573i	$0.842964\pi$
$558$	−14.9460	−0.632715
$559$	6.42405	0.271708
$560$	0	0
$561$	−10.1628	−0.429072
$562$	−29.6185	−1.24938
$563$	−20.6694	−0.871112	−0.435556	−	0.900162i	$-0.643448\pi$
$563$	−20.6694	−0.871112	−0.435556	+	0.900162i	$0.643448\pi$
$564$	−4.89115	−0.205954
$565$	0	0
$566$	44.6135	1.87525
$567$	5.24764	0.220380
$568$	−21.3988	−0.897873
$569$	33.7275	1.41393	0.706966	−	0.707248i	$-0.250063\pi$
$569$	33.7275	1.41393	0.706966	+	0.707248i	$0.250063\pi$
$570$	0	0
$571$	1.88647	0.0789464	0.0394732	−	0.999221i	$-0.487432\pi$
$571$	1.88647	0.0789464	0.0394732	+	0.999221i	$0.487432\pi$
$572$	−17.7432	−0.741882
$573$	23.1126	0.965544
$574$	−129.490	−5.40479
$575$	0	0
$576$	9.75464	0.406443
$577$	15.4800	0.644440	0.322220	−	0.946665i	$-0.395571\pi$
$577$	15.4800	0.644440	0.322220	+	0.946665i	$0.395571\pi$
$578$	0.421820	0.0175454
$579$	−17.2364	−0.716320
$580$	0	0
$581$	81.3241	3.37389
$582$	8.78748	0.364253
$583$	−17.0736	−0.707117
$584$	38.7229	1.60236
$585$	0	0
$586$	78.1114	3.22675
$587$	24.5995	1.01533	0.507665	−	0.861554i	$-0.330509\pi$
$587$	24.5995	1.01533	0.507665	+	0.861554i	$0.330509\pi$
$588$	−100.453	−4.14261
$589$	−24.2206	−0.997993
$590$	0	0
$591$	−11.1056	−0.456823
$592$	−18.7289	−0.769754
$593$	−5.36195	−0.220189	−0.110094	−	0.993921i	$-0.535115\pi$
$593$	−5.36195	−0.220189	−0.110094	+	0.993921i	$0.535115\pi$
$594$	−6.44007	−0.264239
$595$	0	0
$596$	30.8616	1.26414
$597$	23.0611	0.943830
$598$	25.2408	1.03217
$599$	32.0888	1.31111	0.655556	−	0.755147i	$-0.272434\pi$
$599$	32.0888	1.31111	0.655556	+	0.755147i	$0.272434\pi$
$600$	0	0
$601$	10.4599	0.426668	0.213334	−	0.976979i	$-0.431568\pi$
$601$	10.4599	0.426668	0.213334	+	0.976979i	$0.431568\pi$
$602$	−59.8468	−2.43917
$603$	−5.84395	−0.237984
$604$	38.1766	1.55338
$605$	0	0
$606$	3.41101	0.138563
$607$	37.0898	1.50543	0.752714	−	0.658347i	$-0.228744\pi$
$607$	37.0898	1.50543	0.752714	+	0.658347i	$0.228744\pi$
$608$	48.6758	1.97406
$609$	42.8759	1.73742
$610$	0	0
$611$	−1.47869	−0.0598214
$612$	20.2618	0.819035
$613$	−40.3328	−1.62903	−0.814513	−	0.580145i	$-0.802996\pi$
$613$	−40.3328	−1.62903	−0.814513	+	0.580145i	$0.802996\pi$
$614$	64.2440	2.59268
$615$	0	0
$616$	97.7068	3.93672
$617$	−5.61640	−0.226108	−0.113054	−	0.993589i	$-0.536063\pi$
$617$	−5.61640	−0.226108	−0.113054	+	0.993589i	$0.536063\pi$
$618$	43.5362	1.75128
$619$	−26.8598	−1.07959	−0.539794	−	0.841797i	$-0.681498\pi$
$619$	−26.8598	−1.07959	−0.539794	+	0.841797i	$0.681498\pi$
$620$	0	0
$621$	6.50248	0.260936
$622$	−21.7054	−0.870308
$623$	−18.8757	−0.756238
$624$	14.9955	0.600299
$625$	0	0
$626$	70.1029	2.80188
$627$	−10.4364	−0.416790
$628$	103.318	4.12282
$629$	−7.65064	−0.305051
$630$	0	0
$631$	−46.1673	−1.83789	−0.918946	−	0.394384i	$-0.870958\pi$
$631$	−46.1673	−1.83789	−0.918946	+	0.394384i	$0.870958\pi$
$632$	42.2287	1.67977
$633$	−4.09406	−0.162724
$634$	−31.9995	−1.27086
$635$	0	0
$636$	34.0402	1.34978
$637$	−30.3689	−1.20326
$638$	−52.6187	−2.08320
$639$	−2.81951	−0.111538
$640$	0	0
$641$	−18.1813	−0.718119	−0.359059	−	0.933315i	$-0.616902\pi$
$641$	−18.1813	−0.718119	−0.359059	+	0.933315i	$0.616902\pi$
$642$	−26.3440	−1.03972
$643$	23.3628	0.921338	0.460669	−	0.887572i	$-0.347609\pi$
$643$	23.3628	0.921338	0.460669	+	0.887572i	$0.347609\pi$
$644$	−166.899	−6.57675
$645$	0	0
$646$	46.2615	1.82013
$647$	−36.0372	−1.41677	−0.708383	−	0.705828i	$-0.750575\pi$
$647$	−36.0372	−1.41677	−0.708383	+	0.705828i	$0.750575\pi$
$648$	7.58955	0.298146
$649$	−18.8914	−0.741552
$650$	0	0
$651$	29.8774	1.17099
$652$	95.7692	3.75061
$653$	−39.5118	−1.54622	−0.773109	−	0.634274i	$-0.781299\pi$
$653$	−39.5118	−1.54622	−0.773109	+	0.634274i	$0.781299\pi$
$654$	24.0527	0.940534
$655$	0	0
$656$	−95.3251	−3.72182
$657$	5.10213	0.199053
$658$	13.7756	0.537028
$659$	2.13562	0.0831919	0.0415960	−	0.999135i	$-0.486756\pi$
$659$	2.13562	0.0831919	0.0415960	+	0.999135i	$0.486756\pi$
$660$	0	0
$661$	0.344591	0.0134030	0.00670151	−	0.999978i	$-0.497867\pi$
$661$	0.344591	0.0134030	0.00670151	+	0.999978i	$0.497867\pi$
$662$	23.4047	0.909648
$663$	6.12555	0.237896
$664$	117.617	4.56444
$665$	0	0
$666$	−4.84815	−0.187862
$667$	53.1287	2.05715
$668$	−13.9251	−0.538780
$669$	21.0775	0.814904
$670$	0	0
$671$	29.6034	1.14283
$672$	−60.0441	−2.31625
$673$	27.1613	1.04699	0.523495	−	0.852029i	$-0.324628\pi$
$673$	27.1613	1.04699	0.523495	+	0.852029i	$0.324628\pi$
$674$	1.12307	0.0432591
$675$	0	0
$676$	−52.8903	−2.03424
$677$	13.1729	0.506275	0.253137	−	0.967430i	$-0.418538\pi$
$677$	13.1729	0.506275	0.253137	+	0.967430i	$0.418538\pi$
$678$	−30.0712	−1.15488
$679$	−17.5664	−0.674136
$680$	0	0
$681$	1.70842	0.0654667
$682$	−36.6665	−1.40403
$683$	15.2104	0.582011	0.291006	−	0.956721i	$-0.406010\pi$
$683$	15.2104	0.582011	0.291006	+	0.956721i	$0.406010\pi$
$684$	20.8074	0.795589
$685$	0	0
$686$	186.490	7.12021
$687$	−5.07837	−0.193752
$688$	−44.0569	−1.67965
$689$	10.2910	0.392057
$690$	0	0
$691$	13.3184	0.506656	0.253328	−	0.967380i	$-0.418475\pi$
$691$	13.3184	0.506656	0.253328	+	0.967380i	$0.418475\pi$
$692$	−39.0877	−1.48589
$693$	12.8739	0.489037
$694$	36.3260	1.37891
$695$	0	0
$696$	62.0106	2.35051
$697$	−38.9397	−1.47495
$698$	58.6018	2.21811
$699$	−0.738739	−0.0279417
$700$	0	0
$701$	−24.9303	−0.941604	−0.470802	−	0.882239i	$-0.656035\pi$
$701$	−24.9303	−0.941604	−0.470802	+	0.882239i	$0.656035\pi$
$702$	3.88171	0.146506
$703$	−7.85663	−0.296318
$704$	23.9307	0.901924
$705$	0	0
$706$	52.7084	1.98371
$707$	−6.81870	−0.256444
$708$	37.6643	1.41551
$709$	17.1322	0.643414	0.321707	−	0.946839i	$-0.395743\pi$
$709$	17.1322	0.643414	0.321707	+	0.946839i	$0.395743\pi$
$710$	0	0
$711$	5.56405	0.208668
$712$	−27.2995	−1.02309
$713$	37.0219	1.38648
$714$	−57.0659	−2.13564
$715$	0	0
$716$	−57.0277	−2.13122
$717$	3.36660	0.125728
$718$	−49.5002	−1.84733
$719$	−36.7634	−1.37104	−0.685521	−	0.728053i	$-0.740426\pi$
$719$	−36.7634	−1.37104	−0.685521	+	0.728053i	$0.740426\pi$
$720$	0	0
$721$	−87.0300	−3.24117
$722$	−2.36985	−0.0881965
$723$	−6.51135	−0.242160
$724$	95.5392	3.55069
$725$	0	0
$726$	13.0769	0.485329
$727$	46.9974	1.74304	0.871519	−	0.490362i	$-0.163135\pi$
$727$	46.9974	1.74304	0.871519	+	0.490362i	$0.163135\pi$
$728$	−58.8922	−2.18269
$729$	1.00000	0.0370370
$730$	0	0
$731$	−17.9969	−0.665641
$732$	−59.0212	−2.18149
$733$	0.790148	0.0291848	0.0145924	−	0.999894i	$-0.495355\pi$
$733$	0.790148	0.0291848	0.0145924	+	0.999894i	$0.495355\pi$
$734$	56.6196	2.08987
$735$	0	0
$736$	−74.4022	−2.74250
$737$	−14.3368	−0.528102
$738$	−24.6758	−0.908328
$739$	34.4106	1.26581	0.632907	−	0.774228i	$-0.281861\pi$
$739$	34.4106	1.26581	0.632907	+	0.774228i	$0.281861\pi$
$740$	0	0
$741$	6.29048	0.231086
$742$	−95.8717	−3.51956
$743$	−26.4476	−0.970267	−0.485133	−	0.874440i	$-0.661229\pi$
$743$	−26.4476	−0.970267	−0.485133	+	0.874440i	$0.661229\pi$
$744$	43.2111	1.58420
$745$	0	0
$746$	−22.3070	−0.816718
$747$	15.4973	0.567016
$748$	49.7076	1.81749
$749$	52.6624	1.92424
$750$	0	0
$751$	47.6505	1.73879	0.869396	−	0.494117i	$-0.164508\pi$
$751$	47.6505	1.73879	0.869396	+	0.494117i	$0.164508\pi$
$752$	10.1410	0.369806
$753$	−11.7004	−0.426387
$754$	31.7156	1.15501
$755$	0	0
$756$	−25.6670	−0.933499
$757$	−32.3523	−1.17587	−0.587933	−	0.808910i	$-0.700058\pi$
$757$	−32.3523	−1.17587	−0.587933	+	0.808910i	$0.700058\pi$
$758$	34.0677	1.23739
$759$	15.9523	0.579033
$760$	0	0
$761$	−2.25280	−0.0816639	−0.0408319	−	0.999166i	$-0.513001\pi$
$761$	−2.25280	−0.0816639	−0.0408319	+	0.999166i	$0.513001\pi$
$762$	−19.7081	−0.713950
$763$	−48.0819	−1.74068
$764$	−113.047	−4.08991
$765$	0	0
$766$	−75.6949	−2.73497
$767$	11.3867	0.411149
$768$	12.3620	0.446076
$769$	2.40249	0.0866361	0.0433181	−	0.999061i	$-0.486207\pi$
$769$	2.40249	0.0866361	0.0433181	+	0.999061i	$0.486207\pi$
$770$	0	0
$771$	−28.1645	−1.01432
$772$	84.3057	3.03423
$773$	16.0770	0.578248	0.289124	−	0.957292i	$-0.406636\pi$
$773$	16.0770	0.578248	0.289124	+	0.957292i	$0.406636\pi$
$774$	−11.4045	−0.409927
$775$	0	0
$776$	−25.4059	−0.912019
$777$	9.69157	0.347683
$778$	56.6506	2.03102
$779$	−39.9881	−1.43272
$780$	0	0
$781$	−6.91700	−0.247510
$782$	−70.7119	−2.52865
$783$	8.17052	0.291991
$784$	208.274	7.43834
$785$	0	0
$786$	−32.6280	−1.16380
$787$	18.5923	0.662745	0.331372	−	0.943500i	$-0.392488\pi$
$787$	18.5923	0.662745	0.331372	+	0.943500i	$0.392488\pi$
$788$	54.3190	1.93504
$789$	15.2487	0.542869
$790$	0	0
$791$	60.1131	2.13738
$792$	18.6192	0.661604
$793$	−17.8433	−0.633634
$794$	−43.6728	−1.54989
$795$	0	0
$796$	−112.795	−3.99793
$797$	−19.2123	−0.680535	−0.340267	−	0.940329i	$-0.610518\pi$
$797$	−19.2123	−0.680535	−0.340267	+	0.940329i	$0.610518\pi$
$798$	−58.6024	−2.07450
$799$	4.14255	0.146553
$800$	0	0
$801$	−3.59698	−0.127093
$802$	−87.9741	−3.10647
$803$	12.5169	0.441711
$804$	28.5836	1.00807
$805$	0	0
$806$	22.1005	0.778457
$807$	7.75275	0.272910
$808$	−9.86175	−0.346935
$809$	15.4036	0.541561	0.270781	−	0.962641i	$-0.412718\pi$
$809$	15.4036	0.541561	0.270781	+	0.962641i	$0.412718\pi$
$810$	0	0
$811$	−16.0580	−0.563872	−0.281936	−	0.959433i	$-0.590977\pi$
$811$	−16.0580	−0.563872	−0.281936	+	0.959433i	$0.590977\pi$
$812$	−209.713	−7.35947
$813$	14.9314	0.523668
$814$	−11.8938	−0.416878
$815$	0	0
$816$	−42.0097	−1.47063
$817$	−18.4815	−0.646586
$818$	−31.1906	−1.09055
$819$	−7.75963	−0.271144
$820$	0	0
$821$	−24.4199	−0.852259	−0.426130	−	0.904662i	$-0.640123\pi$
$821$	−24.4199	−0.852259	−0.426130	+	0.904662i	$0.640123\pi$
$822$	33.4398	1.16635
$823$	36.9868	1.28928	0.644640	−	0.764486i	$-0.277007\pi$
$823$	36.9868	1.28928	0.644640	+	0.764486i	$0.277007\pi$
$824$	−125.870	−4.38488
$825$	0	0
$826$	−106.079	−3.69096
$827$	11.7608	0.408963	0.204481	−	0.978870i	$-0.434449\pi$
$827$	11.7608	0.408963	0.204481	+	0.978870i	$0.434449\pi$
$828$	−31.8046	−1.10529
$829$	1.09175	0.0379182	0.0189591	−	0.999820i	$-0.493965\pi$
$829$	1.09175	0.0379182	0.0189591	+	0.999820i	$0.493965\pi$
$830$	0	0
$831$	19.0645	0.661342
$832$	−14.4241	−0.500066
$833$	85.0784	2.94779
$834$	36.0255	1.24746
$835$	0	0
$836$	51.0460	1.76546
$837$	5.69350	0.196796
$838$	−6.62549	−0.228874
$839$	−9.05720	−0.312689	−0.156345	−	0.987703i	$-0.549971\pi$
$839$	−9.05720	−0.312689	−0.156345	+	0.987703i	$0.549971\pi$
$840$	0	0
$841$	37.7574	1.30198
$842$	38.7929	1.33689
$843$	11.2828	0.388601
$844$	20.0247	0.689277
$845$	0	0
$846$	2.62510	0.0902528
$847$	−26.1410	−0.898216
$848$	−70.5770	−2.42362
$849$	−16.9950	−0.583266
$850$	0	0
$851$	12.0091	0.411666
$852$	13.7906	0.472459
$853$	23.2497	0.796053	0.398027	−	0.917374i	$-0.369695\pi$
$853$	23.2497	0.796053	0.398027	+	0.917374i	$0.369695\pi$
$854$	166.229	5.68824
$855$	0	0
$856$	76.1645	2.60325
$857$	−22.9394	−0.783596	−0.391798	−	0.920051i	$-0.628147\pi$
$857$	−22.9394	−0.783596	−0.391798	+	0.920051i	$0.628147\pi$
$858$	9.52287	0.325105
$859$	−1.31714	−0.0449402	−0.0224701	−	0.999748i	$-0.507153\pi$
$859$	−1.31714	−0.0449402	−0.0224701	+	0.999748i	$0.507153\pi$
$860$	0	0
$861$	49.3275	1.68108
$862$	−75.1949	−2.56115
$863$	42.4780	1.44597	0.722983	−	0.690865i	$-0.242770\pi$
$863$	42.4780	1.44597	0.722983	+	0.690865i	$0.242770\pi$
$864$	−11.4421	−0.389269
$865$	0	0
$866$	−36.7539	−1.24895
$867$	−0.160687	−0.00545722
$868$	−146.135	−4.96014
$869$	13.6501	0.463048
$870$	0	0
$871$	8.64140	0.292803
$872$	−69.5399	−2.35492
$873$	−3.34748	−0.113295
$874$	−72.6158	−2.45627
$875$	0	0
$876$	−24.9553	−0.843160
$877$	50.9867	1.72170	0.860850	−	0.508859i	$-0.169932\pi$
$877$	50.9867	1.72170	0.860850	+	0.508859i	$0.169932\pi$
$878$	−60.5830	−2.04458
$879$	−29.7556	−1.00363
$880$	0	0
$881$	0.851944	0.0287027	0.0143514	−	0.999897i	$-0.495432\pi$
$881$	0.851944	0.0287027	0.0143514	+	0.999897i	$0.495432\pi$
$882$	53.9135	1.81536
$883$	−21.6486	−0.728532	−0.364266	−	0.931295i	$-0.618680\pi$
$883$	−21.6486	−0.728532	−0.364266	+	0.931295i	$0.618680\pi$
$884$	−29.9609	−1.00770
$885$	0	0
$886$	45.2415	1.51992
$887$	−20.7832	−0.697830	−0.348915	−	0.937154i	$-0.613450\pi$
$887$	−20.7832	−0.697830	−0.348915	+	0.937154i	$0.613450\pi$
$888$	14.0167	0.470370
$889$	39.3970	1.32133
$890$	0	0
$891$	2.45327	0.0821875
$892$	−103.093	−3.45182
$893$	4.25408	0.142358
$894$	−16.5635	−0.553968
$895$	0	0
$896$	14.2876	0.477314
$897$	−9.61516	−0.321041
$898$	−37.9180	−1.26534
$899$	46.5189	1.55149
$900$	0	0
$901$	−28.8302	−0.960475
$902$	−60.5362	−2.01564
$903$	22.7979	0.758667
$904$	86.9404	2.89159
$905$	0	0
$906$	−20.4895	−0.680719
$907$	−31.4193	−1.04326	−0.521631	−	0.853171i	$-0.674676\pi$
$907$	−31.4193	−1.04326	−0.521631	+	0.853171i	$0.674676\pi$
$908$	−8.35612	−0.277308
$909$	−1.29938	−0.0430979
$910$	0	0
$911$	53.0020	1.75603	0.878017	−	0.478630i	$-0.158867\pi$
$911$	53.0020	1.75603	0.878017	+	0.478630i	$0.158867\pi$
$912$	−43.1408	−1.42854
$913$	38.0189	1.25824
$914$	−76.9757	−2.54613
$915$	0	0
$916$	24.8391	0.820706
$917$	65.2242	2.15389
$918$	−10.8746	−0.358915
$919$	−29.1849	−0.962720	−0.481360	−	0.876523i	$-0.659857\pi$
$919$	−29.1849	−0.962720	−0.481360	+	0.876523i	$0.659857\pi$
$920$	0	0
$921$	−24.4730	−0.806412
$922$	−26.2704	−0.865170
$923$	4.16918	0.137230
$924$	−62.9679	−2.07149
$925$	0	0
$926$	17.7012	0.581698
$927$	−16.5846	−0.544710
$928$	−93.4881	−3.06890
$929$	3.60942	0.118421	0.0592106	−	0.998246i	$-0.481142\pi$
$929$	3.60942	0.118421	0.0592106	+	0.998246i	$0.481142\pi$
$930$	0	0
$931$	87.3691	2.86341
$932$	3.61328	0.118357
$933$	8.26842	0.270696
$934$	59.3287	1.94129
$935$	0	0
$936$	−11.2226	−0.366822
$937$	2.39765	0.0783279	0.0391640	−	0.999233i	$-0.487531\pi$
$937$	2.39765	0.0783279	0.0391640	+	0.999233i	$0.487531\pi$
$938$	−80.5038	−2.62854
$939$	−26.7049	−0.871480
$940$	0	0
$941$	−2.61594	−0.0852774	−0.0426387	−	0.999091i	$-0.513576\pi$
$941$	−2.61594	−0.0852774	−0.0426387	+	0.999091i	$0.513576\pi$
$942$	−55.4509	−1.80669
$943$	61.1229	1.99044
$944$	−78.0911	−2.54165
$945$	0	0
$946$	−27.9783	−0.909654
$947$	49.1337	1.59663	0.798316	−	0.602239i	$-0.205724\pi$
$947$	49.1337	1.59663	0.798316	+	0.602239i	$0.205724\pi$
$948$	−27.2146	−0.883889
$949$	−7.54447	−0.244904
$950$	0	0
$951$	12.1898	0.395283
$952$	164.986	5.34723
$953$	−52.3473	−1.69569	−0.847847	−	0.530240i	$-0.822102\pi$
$953$	−52.3473	−1.69569	−0.847847	+	0.530240i	$0.822102\pi$
$954$	−18.2695	−0.591497
$955$	0	0
$956$	−16.4665	−0.532565
$957$	20.0445	0.647946
$958$	73.5109	2.37503
$959$	−66.8471	−2.15860
$960$	0	0
$961$	1.41592	0.0456750
$962$	7.16892	0.231135
$963$	10.0354	0.323388
$964$	31.8480	1.02575
$965$	0	0
$966$	89.5754	2.88204
$967$	34.5982	1.11260	0.556301	−	0.830981i	$-0.312220\pi$
$967$	34.5982	1.11260	0.556301	+	0.830981i	$0.312220\pi$
$968$	−37.8072	−1.21517
$969$	−17.6227	−0.566124
$970$	0	0
$971$	18.0689	0.579857	0.289929	−	0.957048i	$-0.406368\pi$
$971$	18.0689	0.579857	0.289929	+	0.957048i	$0.406368\pi$
$972$	−4.89115	−0.156884
$973$	−72.0158	−2.30872
$974$	77.5348	2.48437
$975$	0	0
$976$	122.371	3.91701
$977$	−4.72708	−0.151233	−0.0756163	−	0.997137i	$-0.524092\pi$
$977$	−4.72708	−0.151233	−0.0756163	+	0.997137i	$0.524092\pi$
$978$	−51.3997	−1.64358
$979$	−8.82436	−0.282028
$980$	0	0
$981$	−9.16258	−0.292539
$982$	−26.5889	−0.848485
$983$	−53.3395	−1.70126	−0.850632	−	0.525761i	$-0.823781\pi$
$983$	−53.3395	−1.70126	−0.850632	+	0.525761i	$0.823781\pi$
$984$	71.3413	2.27428
$985$	0	0
$986$	−88.8511	−2.82960
$987$	−5.24764	−0.167034
$988$	−30.7677	−0.978849
$989$	28.2495	0.898282
$990$	0	0
$991$	−17.8741	−0.567791	−0.283895	−	0.958855i	$-0.591627\pi$
$991$	−17.8741	−0.567791	−0.283895	+	0.958855i	$0.591627\pi$
$992$	−65.1457	−2.06838
$993$	−8.91572	−0.282932
$994$	−38.8403	−1.23194
$995$	0	0
$996$	−75.7995	−2.40180
$997$	26.5743	0.841616	0.420808	−	0.907150i	$-0.361747\pi$
$997$	26.5743	0.841616	0.420808	+	0.907150i	$0.361747\pi$
$998$	−16.3380	−0.517169
$999$	1.84684	0.0584316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.be.1.8	yes	8
5.4	even	2		3525.2.a.bd.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.bd.1.1	✓	8	5.4	even	2
3525.2.a.be.1.8	yes	8	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)

\(f(q)\)	\(=\)	\(q+2.62510 q^{2} -1.00000 q^{3} +4.89115 q^{4} -2.62510 q^{6} +5.24764 q^{7} +7.58955 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.62510 q^{2} -1.00000 q^{3} +4.89115 q^{4} -2.62510 q^{6} +5.24764 q^{7} +7.58955 q^{8} +1.00000 q^{9} +2.45327 q^{11} -4.89115 q^{12} -1.47869 q^{13} +13.7756 q^{14} +10.1410 q^{16} +4.14255 q^{17} +2.62510 q^{18} +4.25408 q^{19} -5.24764 q^{21} +6.44007 q^{22} -6.50248 q^{23} -7.58955 q^{24} -3.88171 q^{26} -1.00000 q^{27} +25.6670 q^{28} -8.17052 q^{29} -5.69350 q^{31} +11.4421 q^{32} -2.45327 q^{33} +10.8746 q^{34} +4.89115 q^{36} -1.84684 q^{37} +11.1674 q^{38} +1.47869 q^{39} -9.39994 q^{41} -13.7756 q^{42} -4.34441 q^{43} +11.9993 q^{44} -17.0697 q^{46} +1.00000 q^{47} -10.1410 q^{48} +20.5377 q^{49} -4.14255 q^{51} -7.23250 q^{52} -6.95955 q^{53} -2.62510 q^{54} +39.8272 q^{56} -4.25408 q^{57} -21.4484 q^{58} -7.70051 q^{59} +12.0670 q^{61} -14.9460 q^{62} +5.24764 q^{63} +9.75464 q^{64} -6.44007 q^{66} -5.84395 q^{67} +20.2618 q^{68} +6.50248 q^{69} -2.81951 q^{71} +7.58955 q^{72} +5.10213 q^{73} -4.84815 q^{74} +20.8074 q^{76} +12.8739 q^{77} +3.88171 q^{78} +5.56405 q^{79} +1.00000 q^{81} -24.6758 q^{82} +15.4973 q^{83} -25.6670 q^{84} -11.4045 q^{86} +8.17052 q^{87} +18.6192 q^{88} -3.59698 q^{89} -7.75963 q^{91} -31.8046 q^{92} +5.69350 q^{93} +2.62510 q^{94} -11.4421 q^{96} -3.34748 q^{97} +53.9135 q^{98} +2.45327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * q^99

Introduction

L-functions

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