LMFDB - Embedded newform 3525.2.a.bg.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.49126$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.49126 q^{2} -1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} -1.33606 q^{7} -2.64869 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.49126 q^{2} -1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} -1.33606 q^{7} -2.64869 q^{8} +1.00000 q^{9} +3.95638 q^{11} -0.223857 q^{12} -0.0410899 q^{13} -1.99241 q^{14} -4.39760 q^{16} +6.69389 q^{17} +1.49126 q^{18} -5.69401 q^{19} +1.33606 q^{21} +5.90000 q^{22} -4.16638 q^{23} +2.64869 q^{24} -0.0612758 q^{26} -1.00000 q^{27} -0.299086 q^{28} -7.48398 q^{29} +0.727923 q^{31} -1.26059 q^{32} -3.95638 q^{33} +9.98233 q^{34} +0.223857 q^{36} +5.03176 q^{37} -8.49126 q^{38} +0.0410899 q^{39} -2.90659 q^{41} +1.99241 q^{42} +5.70025 q^{43} +0.885665 q^{44} -6.21316 q^{46} +1.00000 q^{47} +4.39760 q^{48} -5.21495 q^{49} -6.69389 q^{51} -0.00919828 q^{52} +5.79623 q^{53} -1.49126 q^{54} +3.53881 q^{56} +5.69401 q^{57} -11.1606 q^{58} -13.3302 q^{59} -4.38784 q^{61} +1.08552 q^{62} -1.33606 q^{63} +6.91534 q^{64} -5.90000 q^{66} -14.9200 q^{67} +1.49847 q^{68} +4.16638 q^{69} -15.2350 q^{71} -2.64869 q^{72} +12.9221 q^{73} +7.50366 q^{74} -1.27465 q^{76} -5.28596 q^{77} +0.0612758 q^{78} +15.3290 q^{79} +1.00000 q^{81} -4.33448 q^{82} -13.7297 q^{83} +0.299086 q^{84} +8.50056 q^{86} +7.48398 q^{87} -10.4792 q^{88} -4.68480 q^{89} +0.0548986 q^{91} -0.932675 q^{92} -0.727923 q^{93} +1.49126 q^{94} +1.26059 q^{96} -8.64892 q^{97} -7.77684 q^{98} +3.95638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.49126	1.05448	0.527240	−	0.849716i	$-0.323227\pi$
$2$	1.49126	1.05448	0.527240	+	0.849716i	$0.323227\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.223857	0.111929
$5$	0	0
$5$	0	0
$6$	−1.49126	−0.608804
$7$	−1.33606	−0.504983	−0.252491	−	0.967599i	$-0.581250\pi$
$7$	−1.33606	−0.504983	−0.252491	+	0.967599i	$0.581250\pi$
$8$	−2.64869	−0.936454
$9$	1.00000	0.333333
$10$	0	0
$11$	3.95638	1.19289	0.596447	−	0.802652i	$-0.296578\pi$
$11$	3.95638	1.19289	0.596447	+	0.802652i	$0.296578\pi$
$12$	−0.223857	−0.0646220
$13$	−0.0410899	−0.0113963	−0.00569815	−	0.999984i	$-0.501814\pi$
$13$	−0.0410899	−0.0113963	−0.00569815	+	0.999984i	$0.501814\pi$
$14$	−1.99241	−0.532494
$15$	0	0
$16$	−4.39760	−1.09940
$17$	6.69389	1.62351	0.811753	−	0.584001i	$-0.198514\pi$
$17$	6.69389	1.62351	0.811753	+	0.584001i	$0.198514\pi$
$18$	1.49126	0.351493
$19$	−5.69401	−1.30630	−0.653148	−	0.757230i	$-0.726552\pi$
$19$	−5.69401	−1.30630	−0.653148	+	0.757230i	$0.726552\pi$
$20$	0	0
$21$	1.33606	0.291552
$22$	5.90000	1.25788
$23$	−4.16638	−0.868751	−0.434375	−	0.900732i	$-0.643031\pi$
$23$	−4.16638	−0.868751	−0.434375	+	0.900732i	$0.643031\pi$
$24$	2.64869	0.540662
$25$	0	0
$26$	−0.0612758	−0.0120172
$27$	−1.00000	−0.192450
$28$	−0.299086	−0.0565220
$29$	−7.48398	−1.38974	−0.694870	−	0.719136i	$-0.744538\pi$
$29$	−7.48398	−1.38974	−0.694870	+	0.719136i	$0.744538\pi$
$30$	0	0
$31$	0.727923	0.130739	0.0653694	−	0.997861i	$-0.479177\pi$
$31$	0.727923	0.130739	0.0653694	+	0.997861i	$0.479177\pi$
$32$	−1.26059	−0.222843
$33$	−3.95638	−0.688718
$34$	9.98233	1.71195
$35$	0	0
$36$	0.223857	0.0373095
$37$	5.03176	0.827216	0.413608	−	0.910455i	$-0.364268\pi$
$37$	5.03176	0.827216	0.413608	+	0.910455i	$0.364268\pi$
$38$	−8.49126	−1.37746
$39$	0.0410899	0.00657966
$40$	0	0
$41$	−2.90659	−0.453932	−0.226966	−	0.973903i	$-0.572881\pi$
$41$	−2.90659	−0.453932	−0.226966	+	0.973903i	$0.572881\pi$
$42$	1.99241	0.307436
$43$	5.70025	0.869280	0.434640	−	0.900604i	$-0.356876\pi$
$43$	5.70025	0.869280	0.434640	+	0.900604i	$0.356876\pi$
$44$	0.885665	0.133519
$45$	0	0
$46$	−6.21316	−0.916081
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	4.39760	0.634739
$49$	−5.21495	−0.744993
$50$	0	0
$51$	−6.69389	−0.937331
$52$	−0.00919828	−0.00127557
$53$	5.79623	0.796174	0.398087	−	0.917348i	$-0.369674\pi$
$53$	5.79623	0.796174	0.398087	+	0.917348i	$0.369674\pi$
$54$	−1.49126	−0.202935
$55$	0	0
$56$	3.53881	0.472893
$57$	5.69401	0.754190
$58$	−11.1606	−1.46545
$59$	−13.3302	−1.73544	−0.867719	−	0.497055i	$-0.834415\pi$
$59$	−13.3302	−1.73544	−0.867719	+	0.497055i	$0.834415\pi$
$60$	0	0
$61$	−4.38784	−0.561805	−0.280902	−	0.959736i	$-0.590634\pi$
$61$	−4.38784	−0.561805	−0.280902	+	0.959736i	$0.590634\pi$
$62$	1.08552	0.137861
$63$	−1.33606	−0.168328
$64$	6.91534	0.864418
$65$	0	0
$66$	−5.90000	−0.726240
$67$	−14.9200	−1.82277	−0.911383	−	0.411560i	$-0.864984\pi$
$67$	−14.9200	−1.82277	−0.911383	+	0.411560i	$0.864984\pi$
$68$	1.49847	0.181717
$69$	4.16638	0.501574
$70$	0	0
$71$	−15.2350	−1.80806	−0.904031	−	0.427466i	$-0.859406\pi$
$71$	−15.2350	−1.80806	−0.904031	+	0.427466i	$0.859406\pi$
$72$	−2.64869	−0.312151
$73$	12.9221	1.51242	0.756210	−	0.654329i	$-0.227049\pi$
$73$	12.9221	1.51242	0.756210	+	0.654329i	$0.227049\pi$
$74$	7.50366	0.872283
$75$	0	0
$76$	−1.27465	−0.146212
$77$	−5.28596	−0.602391
$78$	0.0612758	0.00693812
$79$	15.3290	1.72464	0.862322	−	0.506360i	$-0.169009\pi$
$79$	15.3290	1.72464	0.862322	+	0.506360i	$0.169009\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−4.33448	−0.478663
$83$	−13.7297	−1.50703	−0.753514	−	0.657431i	$-0.771643\pi$
$83$	−13.7297	−1.50703	−0.753514	+	0.657431i	$0.771643\pi$
$84$	0.299086	0.0326330
$85$	0	0
$86$	8.50056	0.916639
$87$	7.48398	0.802366
$88$	−10.4792	−1.11709
$89$	−4.68480	−0.496588	−0.248294	−	0.968685i	$-0.579870\pi$
$89$	−4.68480	−0.496588	−0.248294	+	0.968685i	$0.579870\pi$
$90$	0	0
$91$	0.0548986	0.00575493
$92$	−0.932675	−0.0972381
$93$	−0.727923	−0.0754821
$94$	1.49126	0.153812
$95$	0	0
$96$	1.26059	0.128658
$97$	−8.64892	−0.878164	−0.439082	−	0.898447i	$-0.644696\pi$
$97$	−8.64892	−0.878164	−0.439082	+	0.898447i	$0.644696\pi$
$98$	−7.77684	−0.785580
$99$	3.95638	0.397632
$100$	0	0
$101$	−11.0905	−1.10355	−0.551774	−	0.833994i	$-0.686049\pi$
$101$	−11.0905	−1.10355	−0.551774	+	0.833994i	$0.686049\pi$
$102$	−9.98233	−0.988398
$103$	−7.30204	−0.719492	−0.359746	−	0.933050i	$-0.617137\pi$
$103$	−7.30204	−0.719492	−0.359746	+	0.933050i	$0.617137\pi$
$104$	0.108835	0.0106721
$105$	0	0
$106$	8.64369	0.839549
$107$	−1.65045	−0.159555	−0.0797776	−	0.996813i	$-0.525421\pi$
$107$	−1.65045	−0.159555	−0.0797776	+	0.996813i	$0.525421\pi$
$108$	−0.223857	−0.0215407
$109$	−0.956668	−0.0916321	−0.0458161	−	0.998950i	$-0.514589\pi$
$109$	−0.956668	−0.0916321	−0.0458161	+	0.998950i	$0.514589\pi$
$110$	0	0
$111$	−5.03176	−0.477593
$112$	5.87545	0.555178
$113$	−9.62581	−0.905520	−0.452760	−	0.891632i	$-0.649561\pi$
$113$	−9.62581	−0.905520	−0.452760	+	0.891632i	$0.649561\pi$
$114$	8.49126	0.795279
$115$	0	0
$116$	−1.67534	−0.155552
$117$	−0.0410899	−0.00379877
$118$	−19.8787	−1.82999
$119$	−8.94342	−0.819842
$120$	0	0
$121$	4.65298	0.422998
$122$	−6.54341	−0.592412
$123$	2.90659	0.262078
$124$	0.162951	0.0146334
$125$	0	0
$126$	−1.99241	−0.177498
$127$	−9.80920	−0.870426	−0.435213	−	0.900328i	$-0.643327\pi$
$127$	−9.80920	−0.870426	−0.435213	+	0.900328i	$0.643327\pi$
$128$	12.8337	1.13435
$129$	−5.70025	−0.501879
$130$	0	0
$131$	6.95672	0.607812	0.303906	−	0.952702i	$-0.401709\pi$
$131$	6.95672	0.607812	0.303906	+	0.952702i	$0.401709\pi$
$132$	−0.885665	−0.0770873
$133$	7.60753	0.659657
$134$	−22.2496	−1.92207
$135$	0	0
$136$	−17.7300	−1.52034
$137$	−1.76638	−0.150912	−0.0754560	−	0.997149i	$-0.524041\pi$
$137$	−1.76638	−0.150912	−0.0754560	+	0.997149i	$0.524041\pi$
$138$	6.21316	0.528899
$139$	−14.5812	−1.23676	−0.618380	−	0.785879i	$-0.712211\pi$
$139$	−14.5812	−1.23676	−0.618380	+	0.785879i	$0.712211\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−22.7194	−1.90657
$143$	−0.162568	−0.0135946
$144$	−4.39760	−0.366467
$145$	0	0
$146$	19.2702	1.59482
$147$	5.21495	0.430122
$148$	1.12640	0.0925891
$149$	−10.2641	−0.840865	−0.420433	−	0.907324i	$-0.638122\pi$
$149$	−10.2641	−0.840865	−0.420433	+	0.907324i	$0.638122\pi$
$150$	0	0
$151$	−6.37876	−0.519096	−0.259548	−	0.965730i	$-0.583574\pi$
$151$	−6.37876	−0.519096	−0.259548	+	0.965730i	$0.583574\pi$
$152$	15.0817	1.22329
$153$	6.69389	0.541169
$154$	−7.88274	−0.635209
$155$	0	0
$156$	0.00919828	0.000736452 0
$157$	−11.3052	−0.902250	−0.451125	−	0.892461i	$-0.648977\pi$
$157$	−11.3052	−0.902250	−0.451125	+	0.892461i	$0.648977\pi$
$158$	22.8595	1.81860
$159$	−5.79623	−0.459671
$160$	0	0
$161$	5.56653	0.438704
$162$	1.49126	0.117164
$163$	−10.5829	−0.828918	−0.414459	−	0.910068i	$-0.636029\pi$
$163$	−10.5829	−0.828918	−0.414459	+	0.910068i	$0.636029\pi$
$164$	−0.650660	−0.0508080
$165$	0	0
$166$	−20.4745	−1.58913
$167$	8.53831	0.660714	0.330357	−	0.943856i	$-0.392831\pi$
$167$	8.53831	0.660714	0.330357	+	0.943856i	$0.392831\pi$
$168$	−3.53881	−0.273025
$169$	−12.9983	−0.999870
$170$	0	0
$171$	−5.69401	−0.435432
$172$	1.27604	0.0972974
$173$	20.2593	1.54028	0.770141	−	0.637873i	$-0.220186\pi$
$173$	20.2593	1.54028	0.770141	+	0.637873i	$0.220186\pi$
$174$	11.1606	0.846080
$175$	0	0
$176$	−17.3986	−1.31147
$177$	13.3302	1.00196
$178$	−6.98625	−0.523642
$179$	20.1939	1.50937	0.754683	−	0.656090i	$-0.227791\pi$
$179$	20.1939	1.50937	0.754683	+	0.656090i	$0.227791\pi$
$180$	0	0
$181$	−7.00047	−0.520341	−0.260170	−	0.965563i	$-0.583779\pi$
$181$	−7.00047	−0.520341	−0.260170	+	0.965563i	$0.583779\pi$
$182$	0.0818680	0.00606846
$183$	4.38784	0.324358
$184$	11.0355	0.813545
$185$	0	0
$186$	−1.08552	−0.0795943
$187$	26.4836	1.93667
$188$	0.223857	0.0163265
$189$	1.33606	0.0971839
$190$	0	0
$191$	−17.9866	−1.30146	−0.650731	−	0.759309i	$-0.725537\pi$
$191$	−17.9866	−1.30146	−0.650731	+	0.759309i	$0.725537\pi$
$192$	−6.91534	−0.499072
$193$	−5.45134	−0.392396	−0.196198	−	0.980564i	$-0.562860\pi$
$193$	−5.45134	−0.392396	−0.196198	+	0.980564i	$0.562860\pi$
$194$	−12.8978	−0.926007
$195$	0	0
$196$	−1.16740	−0.0833860
$197$	−10.7734	−0.767576	−0.383788	−	0.923421i	$-0.625381\pi$
$197$	−10.7734	−0.767576	−0.383788	+	0.923421i	$0.625381\pi$
$198$	5.90000	0.419295
$199$	9.32085	0.660737	0.330369	−	0.943852i	$-0.392827\pi$
$199$	9.32085	0.660737	0.330369	+	0.943852i	$0.392827\pi$
$200$	0	0
$201$	14.9200	1.05237
$202$	−16.5389	−1.16367
$203$	9.99903	0.701794
$204$	−1.49847	−0.104914
$205$	0	0
$206$	−10.8892	−0.758690
$207$	−4.16638	−0.289584
$208$	0.180697	0.0125291
$209$	−22.5277	−1.55827
$210$	0	0
$211$	2.63574	0.181452	0.0907258	−	0.995876i	$-0.471081\pi$
$211$	2.63574	0.181452	0.0907258	+	0.995876i	$0.471081\pi$
$212$	1.29753	0.0891146
$213$	15.2350	1.04389
$214$	−2.46125	−0.168248
$215$	0	0
$216$	2.64869	0.180221
$217$	−0.972547	−0.0660208
$218$	−1.42664	−0.0966243
$219$	−12.9221	−0.873196
$220$	0	0
$221$	−0.275051	−0.0185020
$222$	−7.50366	−0.503613
$223$	−10.6703	−0.714536	−0.357268	−	0.934002i	$-0.616292\pi$
$223$	−10.6703	−0.714536	−0.357268	+	0.934002i	$0.616292\pi$
$224$	1.68422	0.112532
$225$	0	0
$226$	−14.3546	−0.954853
$227$	−14.4678	−0.960265	−0.480132	−	0.877196i	$-0.659411\pi$
$227$	−14.4678	−0.960265	−0.480132	+	0.877196i	$0.659411\pi$
$228$	1.27465	0.0844155
$229$	2.42710	0.160387	0.0801935	−	0.996779i	$-0.474446\pi$
$229$	2.42710	0.160387	0.0801935	+	0.996779i	$0.474446\pi$
$230$	0	0
$231$	5.28596	0.347791
$232$	19.8227	1.30143
$233$	26.8074	1.75621	0.878105	−	0.478468i	$-0.158808\pi$
$233$	26.8074	1.75621	0.878105	+	0.478468i	$0.158808\pi$
$234$	−0.0612758	−0.00400572
$235$	0	0
$236$	−2.98405	−0.194245
$237$	−15.3290	−0.995724
$238$	−13.3370	−0.864507
$239$	9.26735	0.599455	0.299728	−	0.954025i	$-0.403104\pi$
$239$	9.26735	0.599455	0.299728	+	0.954025i	$0.403104\pi$
$240$	0	0
$241$	13.0989	0.843772	0.421886	−	0.906649i	$-0.361368\pi$
$241$	13.0989	0.843772	0.421886	+	0.906649i	$0.361368\pi$
$242$	6.93880	0.446043
$243$	−1.00000	−0.0641500
$244$	−0.982249	−0.0628821
$245$	0	0
$246$	4.33448	0.276356
$247$	0.233967	0.0148869
$248$	−1.92804	−0.122431
$249$	13.7297	0.870083
$250$	0	0
$251$	−19.7237	−1.24495	−0.622475	−	0.782640i	$-0.713873\pi$
$251$	−19.7237	−1.24495	−0.622475	+	0.782640i	$0.713873\pi$
$252$	−0.299086	−0.0188407
$253$	−16.4838	−1.03633
$254$	−14.6281	−0.917847
$255$	0	0
$256$	5.30778	0.331736
$257$	24.1225	1.50472	0.752360	−	0.658752i	$-0.228915\pi$
$257$	24.1225	1.50472	0.752360	+	0.658752i	$0.228915\pi$
$258$	−8.50056	−0.529222
$259$	−6.72272	−0.417730
$260$	0	0
$261$	−7.48398	−0.463247
$262$	10.3743	0.640926
$263$	23.2111	1.43126	0.715630	−	0.698480i	$-0.246140\pi$
$263$	23.2111	1.43126	0.715630	+	0.698480i	$0.246140\pi$
$264$	10.4792	0.644953
$265$	0	0
$266$	11.3448	0.695595
$267$	4.68480	0.286705
$268$	−3.33995	−0.204020
$269$	−2.70597	−0.164986	−0.0824928	−	0.996592i	$-0.526288\pi$
$269$	−2.70597	−0.164986	−0.0824928	+	0.996592i	$0.526288\pi$
$270$	0	0
$271$	26.3044	1.59788	0.798938	−	0.601413i	$-0.205395\pi$
$271$	26.3044	1.59788	0.798938	+	0.601413i	$0.205395\pi$
$272$	−29.4370	−1.78488
$273$	−0.0548986	−0.00332261
$274$	−2.63413	−0.159134
$275$	0	0
$276$	0.932675	0.0561404
$277$	16.1779	0.972035	0.486017	−	0.873949i	$-0.338449\pi$
$277$	16.1779	0.972035	0.486017	+	0.873949i	$0.338449\pi$
$278$	−21.7443	−1.30414
$279$	0.727923	0.0435796
$280$	0	0
$281$	−15.5980	−0.930499	−0.465250	−	0.885180i	$-0.654035\pi$
$281$	−15.5980	−0.930499	−0.465250	+	0.885180i	$0.654035\pi$
$282$	−1.49126	−0.0888033
$283$	5.10329	0.303359	0.151680	−	0.988430i	$-0.451532\pi$
$283$	5.10329	0.303359	0.151680	+	0.988430i	$0.451532\pi$
$284$	−3.41047	−0.202374
$285$	0	0
$286$	−0.242431	−0.0143352
$287$	3.88337	0.229228
$288$	−1.26059	−0.0742808
$289$	27.8081	1.63577
$290$	0	0
$291$	8.64892	0.507008
$292$	2.89271	0.169283
$293$	33.6381	1.96516	0.982578	−	0.185849i	$-0.0595035\pi$
$293$	33.6381	1.96516	0.982578	+	0.185849i	$0.0595035\pi$
$294$	7.77684	0.453555
$295$	0	0
$296$	−13.3276	−0.774649
$297$	−3.95638	−0.229573
$298$	−15.3064	−0.886676
$299$	0.171196	0.00990054
$300$	0	0
$301$	−7.61587	−0.438971
$302$	−9.51239	−0.547377
$303$	11.0905	0.637134
$304$	25.0400	1.43614
$305$	0	0
$306$	9.98233	0.570652
$307$	29.1813	1.66546	0.832731	−	0.553677i	$-0.186776\pi$
$307$	29.1813	1.66546	0.832731	+	0.553677i	$0.186776\pi$
$308$	−1.18330	−0.0674248
$309$	7.30204	0.415399
$310$	0	0
$311$	15.0237	0.851914	0.425957	−	0.904743i	$-0.359937\pi$
$311$	15.0237	0.851914	0.425957	+	0.904743i	$0.359937\pi$
$312$	−0.108835	−0.00616154
$313$	−5.65747	−0.319779	−0.159890	−	0.987135i	$-0.551114\pi$
$313$	−5.65747	−0.319779	−0.159890	+	0.987135i	$0.551114\pi$
$314$	−16.8589	−0.951404
$315$	0	0
$316$	3.43150	0.193037
$317$	7.18475	0.403536	0.201768	−	0.979433i	$-0.435331\pi$
$317$	7.18475	0.403536	0.201768	+	0.979433i	$0.435331\pi$
$318$	−8.64369	−0.484714
$319$	−29.6095	−1.65781
$320$	0	0
$321$	1.65045	0.0921192
$322$	8.30115	0.462605
$323$	−38.1151	−2.12078
$324$	0.223857	0.0124365
$325$	0	0
$326$	−15.7819	−0.874077
$327$	0.956668	0.0529038
$328$	7.69865	0.425087
$329$	−1.33606	−0.0736593
$330$	0	0
$331$	−6.33141	−0.348006	−0.174003	−	0.984745i	$-0.555670\pi$
$331$	−6.33141	−0.348006	−0.174003	+	0.984745i	$0.555670\pi$
$332$	−3.07349	−0.168680
$333$	5.03176	0.275739
$334$	12.7328	0.696710
$335$	0	0
$336$	−5.87545	−0.320532
$337$	10.7733	0.586859	0.293429	−	0.955981i	$-0.405203\pi$
$337$	10.7733	0.586859	0.293429	+	0.955981i	$0.405203\pi$
$338$	−19.3839	−1.05434
$339$	9.62581	0.522802
$340$	0	0
$341$	2.87994	0.155958
$342$	−8.49126	−0.459155
$343$	16.3199	0.881191
$344$	−15.0982	−0.814041
$345$	0	0
$346$	30.2118	1.62420
$347$	−5.31635	−0.285397	−0.142698	−	0.989766i	$-0.545578\pi$
$347$	−5.31635	−0.285397	−0.142698	+	0.989766i	$0.545578\pi$
$348$	1.67534	0.0898078
$349$	13.4716	0.721118	0.360559	−	0.932736i	$-0.382586\pi$
$349$	13.4716	0.721118	0.360559	+	0.932736i	$0.382586\pi$
$350$	0	0
$351$	0.0410899	0.00219322
$352$	−4.98737	−0.265828
$353$	−11.5955	−0.617167	−0.308584	−	0.951197i	$-0.599855\pi$
$353$	−11.5955	−0.617167	−0.308584	+	0.951197i	$0.599855\pi$
$354$	19.8787	1.05654
$355$	0	0
$356$	−1.04873	−0.0555824
$357$	8.94342	0.473336
$358$	30.1144	1.59160
$359$	31.8068	1.67870	0.839349	−	0.543594i	$-0.182937\pi$
$359$	31.8068	1.67870	0.839349	+	0.543594i	$0.182937\pi$
$360$	0	0
$361$	13.4218	0.706410
$362$	−10.4395	−0.548689
$363$	−4.65298	−0.244218
$364$	0.0122894	0.000644142 0
$365$	0	0
$366$	6.54341	0.342029
$367$	−29.5268	−1.54129	−0.770643	−	0.637267i	$-0.780065\pi$
$367$	−29.5268	−1.54129	−0.770643	+	0.637267i	$0.780065\pi$
$368$	18.3221	0.955105
$369$	−2.90659	−0.151311
$370$	0	0
$371$	−7.74410	−0.402054
$372$	−0.162951	−0.00844860
$373$	15.7126	0.813567	0.406784	−	0.913525i	$-0.366650\pi$
$373$	15.7126	0.813567	0.406784	+	0.913525i	$0.366650\pi$
$374$	39.4939	2.04218
$375$	0	0
$376$	−2.64869	−0.136596
$377$	0.307516	0.0158379
$378$	1.99241	0.102479
$379$	11.7012	0.601048	0.300524	−	0.953774i	$-0.402838\pi$
$379$	11.7012	0.601048	0.300524	+	0.953774i	$0.402838\pi$
$380$	0	0
$381$	9.80920	0.502541
$382$	−26.8226	−1.37237
$383$	−10.9122	−0.557587	−0.278794	−	0.960351i	$-0.589935\pi$
$383$	−10.9122	−0.557587	−0.278794	+	0.960351i	$0.589935\pi$
$384$	−12.8337	−0.654919
$385$	0	0
$386$	−8.12937	−0.413774
$387$	5.70025	0.289760
$388$	−1.93612	−0.0982917
$389$	0.756182	0.0383399	0.0191700	−	0.999816i	$-0.493898\pi$
$389$	0.756182	0.0383399	0.0191700	+	0.999816i	$0.493898\pi$
$390$	0	0
$391$	−27.8893	−1.41042
$392$	13.8128	0.697651
$393$	−6.95672	−0.350920
$394$	−16.0660	−0.809394
$395$	0	0
$396$	0.885665	0.0445064
$397$	−13.3378	−0.669406	−0.334703	−	0.942324i	$-0.608636\pi$
$397$	−13.3378	−0.669406	−0.334703	+	0.942324i	$0.608636\pi$
$398$	13.8998	0.696735
$399$	−7.60753	−0.380853
$400$	0	0
$401$	21.2304	1.06020	0.530098	−	0.847936i	$-0.322155\pi$
$401$	21.2304	1.06020	0.530098	+	0.847936i	$0.322155\pi$
$402$	22.2496	1.10971
$403$	−0.0299103	−0.00148994
$404$	−2.48269	−0.123519
$405$	0	0
$406$	14.9112	0.740028
$407$	19.9076	0.986782
$408$	17.7300	0.877768
$409$	−1.86339	−0.0921385	−0.0460693	−	0.998938i	$-0.514669\pi$
$409$	−1.86339	−0.0921385	−0.0460693	+	0.998938i	$0.514669\pi$
$410$	0	0
$411$	1.76638	0.0871291
$412$	−1.63462	−0.0805317
$413$	17.8099	0.876366
$414$	−6.21316	−0.305360
$415$	0	0
$416$	0.0517975	0.00253958
$417$	14.5812	0.714044
$418$	−33.5947	−1.64317
$419$	2.40878	0.117677	0.0588383	−	0.998268i	$-0.481260\pi$
$419$	2.40878	0.117677	0.0588383	+	0.998268i	$0.481260\pi$
$420$	0	0
$421$	−23.2256	−1.13195	−0.565974	−	0.824423i	$-0.691500\pi$
$421$	−23.2256	−1.13195	−0.565974	+	0.824423i	$0.691500\pi$
$422$	3.93057	0.191337
$423$	1.00000	0.0486217
$424$	−15.3524	−0.745580
$425$	0	0
$426$	22.7194	1.10076
$427$	5.86241	0.283702
$428$	−0.369466	−0.0178588
$429$	0.162568	0.00784884
$430$	0	0
$431$	−15.8418	−0.763075	−0.381537	−	0.924353i	$-0.624605\pi$
$431$	−15.8418	−0.763075	−0.381537	+	0.924353i	$0.624605\pi$
$432$	4.39760	0.211580
$433$	17.2105	0.827086	0.413543	−	0.910485i	$-0.364291\pi$
$433$	17.2105	0.827086	0.413543	+	0.910485i	$0.364291\pi$
$434$	−1.45032	−0.0696176
$435$	0	0
$436$	−0.214157	−0.0102563
$437$	23.7234	1.13485
$438$	−19.2702	−0.920768
$439$	−28.1289	−1.34252	−0.671259	−	0.741223i	$-0.734246\pi$
$439$	−28.1289	−1.34252	−0.671259	+	0.741223i	$0.734246\pi$
$440$	0	0
$441$	−5.21495	−0.248331
$442$	−0.410173	−0.0195099
$443$	2.41901	0.114930	0.0574652	−	0.998348i	$-0.481698\pi$
$443$	2.41901	0.114930	0.0574652	+	0.998348i	$0.481698\pi$
$444$	−1.12640	−0.0534564
$445$	0	0
$446$	−15.9122	−0.753464
$447$	10.2641	0.485474
$448$	−9.23930	−0.436516
$449$	−17.6406	−0.832512	−0.416256	−	0.909248i	$-0.636658\pi$
$449$	−17.6406	−0.832512	−0.416256	+	0.909248i	$0.636658\pi$
$450$	0	0
$451$	−11.4996	−0.541494
$452$	−2.15481	−0.101354
$453$	6.37876	0.299700
$454$	−21.5753	−1.01258
$455$	0	0
$456$	−15.0817	−0.706264
$457$	−37.6972	−1.76340	−0.881699	−	0.471812i	$-0.843600\pi$
$457$	−37.6972	−1.76340	−0.881699	+	0.471812i	$0.843600\pi$
$458$	3.61943	0.169125
$459$	−6.69389	−0.312444
$460$	0	0
$461$	−29.9929	−1.39691	−0.698454	−	0.715655i	$-0.746128\pi$
$461$	−29.9929	−1.39691	−0.698454	+	0.715655i	$0.746128\pi$
$462$	7.88274	0.366738
$463$	−8.99642	−0.418099	−0.209050	−	0.977905i	$-0.567037\pi$
$463$	−8.99642	−0.418099	−0.209050	+	0.977905i	$0.567037\pi$
$464$	32.9116	1.52788
$465$	0	0
$466$	39.9768	1.85189
$467$	−12.1293	−0.561279	−0.280640	−	0.959813i	$-0.590547\pi$
$467$	−12.1293	−0.561279	−0.280640	+	0.959813i	$0.590547\pi$
$468$	−0.00919828	−0.000425191 0
$469$	19.9340	0.920465
$470$	0	0
$471$	11.3052	0.520914
$472$	35.3075	1.62516
$473$	22.5524	1.03696
$474$	−22.8595	−1.04997
$475$	0	0
$476$	−2.00205	−0.0917638
$477$	5.79623	0.265391
$478$	13.8200	0.632114
$479$	−2.08391	−0.0952161	−0.0476081	−	0.998866i	$-0.515160\pi$
$479$	−2.08391	−0.0952161	−0.0476081	+	0.998866i	$0.515160\pi$
$480$	0	0
$481$	−0.206755	−0.00942720
$482$	19.5338	0.889740
$483$	−5.56653	−0.253286
$484$	1.04160	0.0473456
$485$	0	0
$486$	−1.49126	−0.0676449
$487$	−6.70756	−0.303949	−0.151974	−	0.988384i	$-0.548563\pi$
$487$	−6.70756	−0.303949	−0.151974	+	0.988384i	$0.548563\pi$
$488$	11.6220	0.526104
$489$	10.5829	0.478576
$490$	0	0
$491$	−31.4777	−1.42057	−0.710285	−	0.703914i	$-0.751434\pi$
$491$	−31.4777	−1.42057	−0.710285	+	0.703914i	$0.751434\pi$
$492$	0.650660	0.0293340
$493$	−50.0969	−2.25625
$494$	0.348905	0.0156980
$495$	0	0
$496$	−3.20111	−0.143734
$497$	20.3549	0.913040
$498$	20.4745	0.917486
$499$	−20.0811	−0.898955	−0.449478	−	0.893292i	$-0.648390\pi$
$499$	−20.0811	−0.898955	−0.449478	+	0.893292i	$0.648390\pi$
$500$	0	0
$501$	−8.53831	−0.381464
$502$	−29.4132	−1.31277
$503$	−14.6931	−0.655135	−0.327567	−	0.944828i	$-0.606229\pi$
$503$	−14.6931	−0.655135	−0.327567	+	0.944828i	$0.606229\pi$
$504$	3.53881	0.157631
$505$	0	0
$506$	−24.5817	−1.09279
$507$	12.9983	0.577275
$508$	−2.19586	−0.0974256
$509$	−27.1134	−1.20178	−0.600890	−	0.799332i	$-0.705187\pi$
$509$	−27.1134	−1.20178	−0.600890	+	0.799332i	$0.705187\pi$
$510$	0	0
$511$	−17.2647	−0.763746
$512$	−17.7522	−0.784545
$513$	5.69401	0.251397
$514$	35.9729	1.58670
$515$	0	0
$516$	−1.27604	−0.0561747
$517$	3.95638	0.174002
$518$	−10.0253	−0.440488
$519$	−20.2593	−0.889282
$520$	0	0
$521$	9.80741	0.429670	0.214835	−	0.976650i	$-0.431079\pi$
$521$	9.80741	0.429670	0.214835	+	0.976650i	$0.431079\pi$
$522$	−11.1606	−0.488484
$523$	−9.32826	−0.407896	−0.203948	−	0.978982i	$-0.565377\pi$
$523$	−9.32826	−0.407896	−0.203948	+	0.978982i	$0.565377\pi$
$524$	1.55731	0.0680315
$525$	0	0
$526$	34.6138	1.50923
$527$	4.87263	0.212255
$528$	17.3986	0.757177
$529$	−5.64125	−0.245272
$530$	0	0
$531$	−13.3302	−0.578479
$532$	1.70300	0.0738345
$533$	0.119431	0.00517315
$534$	6.98625	0.302325
$535$	0	0
$536$	39.5184	1.70694
$537$	−20.1939	−0.871432
$538$	−4.03530	−0.173974
$539$	−20.6323	−0.888698
$540$	0	0
$541$	−0.416268	−0.0178967	−0.00894837	−	0.999960i	$-0.502848\pi$
$541$	−0.416268	−0.0178967	−0.00894837	+	0.999960i	$0.502848\pi$
$542$	39.2267	1.68493
$543$	7.00047	0.300419
$544$	−8.43823	−0.361786
$545$	0	0
$546$	−0.0818680	−0.00350363
$547$	−0.189446	−0.00810013	−0.00405007	−	0.999992i	$-0.501289\pi$
$547$	−0.189446	−0.00810013	−0.00405007	+	0.999992i	$0.501289\pi$
$548$	−0.395417	−0.0168914
$549$	−4.38784	−0.187268
$550$	0	0
$551$	42.6139	1.81541
$552$	−11.0355	−0.469700
$553$	−20.4804	−0.870915
$554$	24.1254	1.02499
$555$	0	0
$556$	−3.26410	−0.138429
$557$	25.8465	1.09515	0.547576	−	0.836756i	$-0.315551\pi$
$557$	25.8465	1.09515	0.547576	+	0.836756i	$0.315551\pi$
$558$	1.08552	0.0459538
$559$	−0.234223	−0.00990658
$560$	0	0
$561$	−26.4836	−1.11814
$562$	−23.2607	−0.981193
$563$	−24.1557	−1.01804	−0.509021	−	0.860754i	$-0.669993\pi$
$563$	−24.1557	−1.01804	−0.509021	+	0.860754i	$0.669993\pi$
$564$	−0.223857	−0.00942609
$565$	0	0
$566$	7.61033	0.319886
$567$	−1.33606	−0.0561092
$568$	40.3528	1.69317
$569$	24.1361	1.01184	0.505919	−	0.862581i	$-0.331153\pi$
$569$	24.1361	1.01184	0.505919	+	0.862581i	$0.331153\pi$
$570$	0	0
$571$	5.80442	0.242907	0.121454	−	0.992597i	$-0.461244\pi$
$571$	5.80442	0.242907	0.121454	+	0.992597i	$0.461244\pi$
$572$	−0.0363919	−0.00152162
$573$	17.9866	0.751399
$574$	5.79111	0.241716
$575$	0	0
$576$	6.91534	0.288139
$577$	−22.8280	−0.950344	−0.475172	−	0.879893i	$-0.657614\pi$
$577$	−22.8280	−0.950344	−0.475172	+	0.879893i	$0.657614\pi$
$578$	41.4691	1.72489
$579$	5.45134	0.226550
$580$	0	0
$581$	18.3437	0.761023
$582$	12.8978	0.534630
$583$	22.9321	0.949751
$584$	−34.2267	−1.41631
$585$	0	0
$586$	50.1631	2.07222
$587$	−28.4503	−1.17427	−0.587135	−	0.809489i	$-0.699744\pi$
$587$	−28.4503	−1.17427	−0.587135	+	0.809489i	$0.699744\pi$
$588$	1.16740	0.0481429
$589$	−4.14480	−0.170784
$590$	0	0
$591$	10.7734	0.443160
$592$	−22.1277	−0.909442
$593$	8.26303	0.339322	0.169661	−	0.985503i	$-0.445733\pi$
$593$	8.26303	0.339322	0.169661	+	0.985503i	$0.445733\pi$
$594$	−5.90000	−0.242080
$595$	0	0
$596$	−2.29769	−0.0941169
$597$	−9.32085	−0.381477
$598$	0.255298	0.0104399
$599$	−0.574161	−0.0234596	−0.0117298	−	0.999931i	$-0.503734\pi$
$599$	−0.574161	−0.0234596	−0.0117298	+	0.999931i	$0.503734\pi$
$600$	0	0
$601$	17.0446	0.695262	0.347631	−	0.937631i	$-0.386986\pi$
$601$	17.0446	0.695262	0.347631	+	0.937631i	$0.386986\pi$
$602$	−11.3572	−0.462887
$603$	−14.9200	−0.607588
$604$	−1.42793	−0.0581017
$605$	0	0
$606$	16.5389	0.671845
$607$	22.8467	0.927321	0.463660	−	0.886013i	$-0.346536\pi$
$607$	22.8467	0.927321	0.463660	+	0.886013i	$0.346536\pi$
$608$	7.17780	0.291098
$609$	−9.99903	−0.405181
$610$	0	0
$611$	−0.0410899	−0.00166232
$612$	1.49847	0.0605723
$613$	−15.5322	−0.627338	−0.313669	−	0.949532i	$-0.601558\pi$
$613$	−15.5322	−0.627338	−0.313669	+	0.949532i	$0.601558\pi$
$614$	43.5169	1.75620
$615$	0	0
$616$	14.0009	0.564111
$617$	−29.3687	−1.18234	−0.591169	−	0.806548i	$-0.701333\pi$
$617$	−29.3687	−1.18234	−0.591169	+	0.806548i	$0.701333\pi$
$618$	10.8892	0.438030
$619$	−17.7422	−0.713117	−0.356559	−	0.934273i	$-0.616050\pi$
$619$	−17.7422	−0.713117	−0.356559	+	0.934273i	$0.616050\pi$
$620$	0	0
$621$	4.16638	0.167191
$622$	22.4042	0.898326
$623$	6.25916	0.250768
$624$	−0.180697	−0.00723368
$625$	0	0
$626$	−8.43677	−0.337201
$627$	22.5277	0.899670
$628$	−2.53074	−0.100988
$629$	33.6820	1.34299
$630$	0	0
$631$	24.7735	0.986219	0.493109	−	0.869967i	$-0.335860\pi$
$631$	24.7735	0.986219	0.493109	+	0.869967i	$0.335860\pi$
$632$	−40.6017	−1.61505
$633$	−2.63574	−0.104761
$634$	10.7143	0.425520
$635$	0	0
$636$	−1.29753	−0.0514503
$637$	0.214282	0.00849016
$638$	−44.1554	−1.74813
$639$	−15.2350	−0.602687
$640$	0	0
$641$	36.8836	1.45682	0.728408	−	0.685144i	$-0.240261\pi$
$641$	36.8836	1.45682	0.728408	+	0.685144i	$0.240261\pi$
$642$	2.46125	0.0971379
$643$	12.9077	0.509030	0.254515	−	0.967069i	$-0.418084\pi$
$643$	12.9077	0.509030	0.254515	+	0.967069i	$0.418084\pi$
$644$	1.24611	0.0491035
$645$	0	0
$646$	−56.8395	−2.23632
$647$	11.0990	0.436348	0.218174	−	0.975910i	$-0.429990\pi$
$647$	11.0990	0.436348	0.218174	+	0.975910i	$0.429990\pi$
$648$	−2.64869	−0.104050
$649$	−52.7392	−2.07019
$650$	0	0
$651$	0.972547	0.0381171
$652$	−2.36906	−0.0927796
$653$	39.9476	1.56327	0.781635	−	0.623736i	$-0.214386\pi$
$653$	39.9476	1.56327	0.781635	+	0.623736i	$0.214386\pi$
$654$	1.42664	0.0557861
$655$	0	0
$656$	12.7820	0.499054
$657$	12.9221	0.504140
$658$	−1.99241	−0.0776723
$659$	27.1718	1.05846	0.529231	−	0.848478i	$-0.322480\pi$
$659$	27.1718	1.05846	0.529231	+	0.848478i	$0.322480\pi$
$660$	0	0
$661$	25.9254	1.00838	0.504191	−	0.863592i	$-0.331791\pi$
$661$	25.9254	1.00838	0.504191	+	0.863592i	$0.331791\pi$
$662$	−9.44178	−0.366965
$663$	0.275051	0.0106821
$664$	36.3657	1.41126
$665$	0	0
$666$	7.50366	0.290761
$667$	31.1811	1.20734
$668$	1.91136	0.0739529
$669$	10.6703	0.412538
$670$	0	0
$671$	−17.3600	−0.670174
$672$	−1.68422	−0.0649701
$673$	−7.12018	−0.274463	−0.137231	−	0.990539i	$-0.543820\pi$
$673$	−7.12018	−0.274463	−0.137231	+	0.990539i	$0.543820\pi$
$674$	16.0658	0.618831
$675$	0	0
$676$	−2.90977	−0.111914
$677$	16.1591	0.621046	0.310523	−	0.950566i	$-0.399496\pi$
$677$	16.1591	0.621046	0.310523	+	0.950566i	$0.399496\pi$
$678$	14.3546	0.551285
$679$	11.5555	0.443458
$680$	0	0
$681$	14.4678	0.554409
$682$	4.29474	0.164454
$683$	−22.3426	−0.854915	−0.427457	−	0.904036i	$-0.640591\pi$
$683$	−22.3426	−0.854915	−0.427457	+	0.904036i	$0.640591\pi$
$684$	−1.27465	−0.0487373
$685$	0	0
$686$	24.3372	0.929198
$687$	−2.42710	−0.0925995
$688$	−25.0674	−0.955687
$689$	−0.238167	−0.00907343
$690$	0	0
$691$	−19.3114	−0.734642	−0.367321	−	0.930094i	$-0.619725\pi$
$691$	−19.3114	−0.734642	−0.367321	+	0.930094i	$0.619725\pi$
$692$	4.53518	0.172402
$693$	−5.28596	−0.200797
$694$	−7.92806	−0.300945
$695$	0	0
$696$	−19.8227	−0.751379
$697$	−19.4563	−0.736962
$698$	20.0897	0.760405
$699$	−26.8074	−1.01395
$700$	0	0
$701$	48.3676	1.82682	0.913409	−	0.407042i	$-0.133440\pi$
$701$	48.3676	1.82682	0.913409	+	0.407042i	$0.133440\pi$
$702$	0.0612758	0.00231271
$703$	−28.6509	−1.08059
$704$	27.3597	1.03116
$705$	0	0
$706$	−17.2919	−0.650791
$707$	14.8176	0.557273
$708$	2.98405	0.112148
$709$	4.64215	0.174340	0.0871698	−	0.996193i	$-0.472218\pi$
$709$	4.64215	0.174340	0.0871698	+	0.996193i	$0.472218\pi$
$710$	0	0
$711$	15.3290	0.574881
$712$	12.4086	0.465031
$713$	−3.03280	−0.113579
$714$	13.3370	0.499124
$715$	0	0
$716$	4.52056	0.168941
$717$	−9.26735	−0.346096
$718$	47.4322	1.77015
$719$	5.80041	0.216319	0.108159	−	0.994134i	$-0.465504\pi$
$719$	5.80041	0.216319	0.108159	+	0.994134i	$0.465504\pi$
$720$	0	0
$721$	9.75595	0.363331
$722$	20.0154	0.744895
$723$	−13.0989	−0.487152
$724$	−1.56711	−0.0582410
$725$	0	0
$726$	−6.93880	−0.257523
$727$	41.5541	1.54116	0.770579	−	0.637345i	$-0.219967\pi$
$727$	41.5541	1.54116	0.770579	+	0.637345i	$0.219967\pi$
$728$	−0.145409	−0.00538923
$729$	1.00000	0.0370370
$730$	0	0
$731$	38.1568	1.41128
$732$	0.982249	0.0363050
$733$	−34.6874	−1.28121	−0.640605	−	0.767871i	$-0.721316\pi$
$733$	−34.6874	−1.28121	−0.640605	+	0.767871i	$0.721316\pi$
$734$	−44.0322	−1.62526
$735$	0	0
$736$	5.25209	0.193595
$737$	−59.0292	−2.17437
$738$	−4.33448	−0.159554
$739$	17.3473	0.638130	0.319065	−	0.947733i	$-0.396631\pi$
$739$	17.3473	0.638130	0.319065	+	0.947733i	$0.396631\pi$
$740$	0	0
$741$	−0.233967	−0.00859498
$742$	−11.5485	−0.423958
$743$	15.6303	0.573421	0.286710	−	0.958017i	$-0.407438\pi$
$743$	15.6303	0.573421	0.286710	+	0.958017i	$0.407438\pi$
$744$	1.92804	0.0706854
$745$	0	0
$746$	23.4316	0.857891
$747$	−13.7297	−0.502343
$748$	5.92854	0.216769
$749$	2.20510	0.0805726
$750$	0	0
$751$	−14.6908	−0.536075	−0.268038	−	0.963408i	$-0.586375\pi$
$751$	−14.6908	−0.536075	−0.268038	+	0.963408i	$0.586375\pi$
$752$	−4.39760	−0.160364
$753$	19.7237	0.718772
$754$	0.458587	0.0167007
$755$	0	0
$756$	0.299086	0.0108777
$757$	16.5774	0.602515	0.301258	−	0.953543i	$-0.402594\pi$
$757$	16.5774	0.602515	0.301258	+	0.953543i	$0.402594\pi$
$758$	17.4495	0.633794
$759$	16.4838	0.598324
$760$	0	0
$761$	−35.7483	−1.29587	−0.647937	−	0.761694i	$-0.724368\pi$
$761$	−35.7483	−1.29587	−0.647937	+	0.761694i	$0.724368\pi$
$762$	14.6281	0.529919
$763$	1.27816	0.0462726
$764$	−4.02642	−0.145671
$765$	0	0
$766$	−16.2729	−0.587965
$767$	0.547735	0.0197776
$768$	−5.30778	−0.191528
$769$	−46.2771	−1.66879	−0.834397	−	0.551164i	$-0.814184\pi$
$769$	−46.2771	−1.66879	−0.834397	+	0.551164i	$0.814184\pi$
$770$	0	0
$771$	−24.1225	−0.868751
$772$	−1.22032	−0.0439204
$773$	40.3104	1.44986	0.724932	−	0.688820i	$-0.241871\pi$
$773$	40.3104	1.44986	0.724932	+	0.688820i	$0.241871\pi$
$774$	8.50056	0.305546
$775$	0	0
$776$	22.9083	0.822360
$777$	6.72272	0.241176
$778$	1.12766	0.0404287
$779$	16.5501	0.592970
$780$	0	0
$781$	−60.2755	−2.15683
$782$	−41.5902	−1.48726
$783$	7.48398	0.267455
$784$	22.9333	0.819045
$785$	0	0
$786$	−10.3743	−0.370039
$787$	−33.1243	−1.18076	−0.590378	−	0.807127i	$-0.701021\pi$
$787$	−33.1243	−1.18076	−0.590378	+	0.807127i	$0.701021\pi$
$788$	−2.41171	−0.0859137
$789$	−23.2111	−0.826338
$790$	0	0
$791$	12.8606	0.457272
$792$	−10.4792	−0.372364
$793$	0.180296	0.00640250
$794$	−19.8902	−0.705876
$795$	0	0
$796$	2.08654	0.0739554
$797$	22.7431	0.805601	0.402800	−	0.915288i	$-0.368037\pi$
$797$	22.7431	0.805601	0.402800	+	0.915288i	$0.368037\pi$
$798$	−11.3448	−0.401602
$799$	6.69389	0.236813
$800$	0	0
$801$	−4.68480	−0.165529
$802$	31.6601	1.11796
$803$	51.1249	1.80416
$804$	3.33995	0.117791
$805$	0	0
$806$	−0.0446040	−0.00157111
$807$	2.70597	0.0952545
$808$	29.3754	1.03342
$809$	−10.6421	−0.374156	−0.187078	−	0.982345i	$-0.559902\pi$
$809$	−10.6421	−0.374156	−0.187078	+	0.982345i	$0.559902\pi$
$810$	0	0
$811$	20.4955	0.719696	0.359848	−	0.933011i	$-0.382829\pi$
$811$	20.4955	0.719696	0.359848	+	0.933011i	$0.382829\pi$
$812$	2.23836	0.0785509
$813$	−26.3044	−0.922535
$814$	29.6874	1.04054
$815$	0	0
$816$	29.4370	1.03050
$817$	−32.4573	−1.13554
$818$	−2.77879	−0.0971582
$819$	0.0548986	0.00191831
$820$	0	0
$821$	29.9290	1.04453	0.522265	−	0.852783i	$-0.325087\pi$
$821$	29.9290	1.04453	0.522265	+	0.852783i	$0.325087\pi$
$822$	2.63413	0.0918759
$823$	−4.74742	−0.165485	−0.0827423	−	0.996571i	$-0.526368\pi$
$823$	−4.74742	−0.165485	−0.0827423	+	0.996571i	$0.526368\pi$
$824$	19.3409	0.673771
$825$	0	0
$826$	26.5591	0.924111
$827$	26.6718	0.927469	0.463735	−	0.885974i	$-0.346509\pi$
$827$	26.6718	0.927469	0.463735	+	0.885974i	$0.346509\pi$
$828$	−0.932675	−0.0324127
$829$	17.3861	0.603845	0.301922	−	0.953333i	$-0.402372\pi$
$829$	17.3861	0.603845	0.301922	+	0.953333i	$0.402372\pi$
$830$	0	0
$831$	−16.1779	−0.561204
$832$	−0.284151	−0.00985116
$833$	−34.9083	−1.20950
$834$	21.7443	0.752945
$835$	0	0
$836$	−5.04299	−0.174415
$837$	−0.727923	−0.0251607
$838$	3.59212	0.124088
$839$	25.9446	0.895707	0.447854	−	0.894107i	$-0.352189\pi$
$839$	25.9446	0.895707	0.447854	+	0.894107i	$0.352189\pi$
$840$	0	0
$841$	27.0099	0.931376
$842$	−34.6354	−1.19362
$843$	15.5980	0.537224
$844$	0.590029	0.0203096
$845$	0	0
$846$	1.49126	0.0512706
$847$	−6.21665	−0.213607
$848$	−25.4895	−0.875314
$849$	−5.10329	−0.175144
$850$	0	0
$851$	−20.9642	−0.718645
$852$	3.41047	0.116841
$853$	−38.1799	−1.30725	−0.653627	−	0.756817i	$-0.726753\pi$
$853$	−38.1799	−1.30725	−0.653627	+	0.756817i	$0.726753\pi$
$854$	8.74237	0.299158
$855$	0	0
$856$	4.37154	0.149416
$857$	40.2741	1.37574	0.687869	−	0.725835i	$-0.258546\pi$
$857$	40.2741	1.37574	0.687869	+	0.725835i	$0.258546\pi$
$858$	0.242431	0.00827644
$859$	−42.0209	−1.43373	−0.716867	−	0.697210i	$-0.754424\pi$
$859$	−42.0209	−1.43373	−0.716867	+	0.697210i	$0.754424\pi$
$860$	0	0
$861$	−3.88337	−0.132345
$862$	−23.6243	−0.804647
$863$	−49.1260	−1.67227	−0.836134	−	0.548525i	$-0.815190\pi$
$863$	−49.1260	−1.67227	−0.836134	+	0.548525i	$0.815190\pi$
$864$	1.26059	0.0428861
$865$	0	0
$866$	25.6654	0.872146
$867$	−27.8081	−0.944413
$868$	−0.217712	−0.00738962
$869$	60.6473	2.05732
$870$	0	0
$871$	0.613061	0.0207728
$872$	2.53392	0.0858093
$873$	−8.64892	−0.292721
$874$	35.3778	1.19667
$875$	0	0
$876$	−2.89271	−0.0977356
$877$	−12.7166	−0.429408	−0.214704	−	0.976679i	$-0.568879\pi$
$877$	−12.7166	−0.429408	−0.214704	+	0.976679i	$0.568879\pi$
$878$	−41.9475	−1.41566
$879$	−33.6381	−1.13458
$880$	0	0
$881$	−43.3268	−1.45972	−0.729859	−	0.683598i	$-0.760414\pi$
$881$	−43.3268	−1.45972	−0.729859	+	0.683598i	$0.760414\pi$
$882$	−7.77684	−0.261860
$883$	1.27229	0.0428160	0.0214080	−	0.999771i	$-0.493185\pi$
$883$	1.27229	0.0428160	0.0214080	+	0.999771i	$0.493185\pi$
$884$	−0.0615722	−0.00207090
$885$	0	0
$886$	3.60737	0.121192
$887$	−8.80233	−0.295553	−0.147777	−	0.989021i	$-0.547212\pi$
$887$	−8.80233	−0.295553	−0.147777	+	0.989021i	$0.547212\pi$
$888$	13.3276	0.447244
$889$	13.1057	0.439550
$890$	0	0
$891$	3.95638	0.132544
$892$	−2.38862	−0.0799770
$893$	−5.69401	−0.190543
$894$	15.3064	0.511922
$895$	0	0
$896$	−17.1466	−0.572829
$897$	−0.171196	−0.00571608
$898$	−26.3067	−0.877867
$899$	−5.44776	−0.181693
$900$	0	0
$901$	38.7993	1.29259
$902$	−17.1488	−0.570994
$903$	7.61587	0.253440
$904$	25.4958	0.847978
$905$	0	0
$906$	9.51239	0.316028
$907$	17.5566	0.582957	0.291479	−	0.956577i	$-0.405853\pi$
$907$	17.5566	0.582957	0.291479	+	0.956577i	$0.405853\pi$
$908$	−3.23873	−0.107481
$909$	−11.0905	−0.367849
$910$	0	0
$911$	36.0055	1.19292	0.596458	−	0.802645i	$-0.296574\pi$
$911$	36.0055	1.19292	0.596458	+	0.802645i	$0.296574\pi$
$912$	−25.0400	−0.829157
$913$	−54.3199	−1.79773
$914$	−56.2163	−1.85947
$915$	0	0
$916$	0.543323	0.0179519
$917$	−9.29459	−0.306934
$918$	−9.98233	−0.329466
$919$	39.3778	1.29895	0.649477	−	0.760381i	$-0.274988\pi$
$919$	39.3778	1.29895	0.649477	+	0.760381i	$0.274988\pi$
$920$	0	0
$921$	−29.1813	−0.961555
$922$	−44.7272	−1.47301
$923$	0.626005	0.0206052
$924$	1.18330	0.0389277
$925$	0	0
$926$	−13.4160	−0.440877
$927$	−7.30204	−0.239831
$928$	9.43421	0.309693
$929$	−58.8640	−1.93126	−0.965632	−	0.259913i	$-0.916306\pi$
$929$	−58.8640	−1.93126	−0.965632	+	0.259913i	$0.916306\pi$
$930$	0	0
$931$	29.6940	0.973181
$932$	6.00103	0.196570
$933$	−15.0237	−0.491853
$934$	−18.0880	−0.591858
$935$	0	0
$936$	0.108835	0.00355737
$937$	−12.2677	−0.400767	−0.200384	−	0.979718i	$-0.564219\pi$
$937$	−12.2677	−0.400767	−0.200384	+	0.979718i	$0.564219\pi$
$938$	29.7267	0.970612
$939$	5.65747	0.184625
$940$	0	0
$941$	51.9936	1.69494	0.847471	−	0.530842i	$-0.178124\pi$
$941$	51.9936	1.69494	0.847471	+	0.530842i	$0.178124\pi$
$942$	16.8589	0.549294
$943$	12.1099	0.394354
$944$	58.6207	1.90794
$945$	0	0
$946$	33.6315	1.09345
$947$	52.0168	1.69032	0.845159	−	0.534514i	$-0.179505\pi$
$947$	52.0168	1.69032	0.845159	+	0.534514i	$0.179505\pi$
$948$	−3.43150	−0.111450
$949$	−0.530969	−0.0172360
$950$	0	0
$951$	−7.18475	−0.232981
$952$	23.6884	0.767744
$953$	1.76284	0.0571041	0.0285520	−	0.999592i	$-0.490910\pi$
$953$	1.76284	0.0571041	0.0285520	+	0.999592i	$0.490910\pi$
$954$	8.64369	0.279850
$955$	0	0
$956$	2.07456	0.0670962
$957$	29.6095	0.957139
$958$	−3.10765	−0.100404
$959$	2.35999	0.0762079
$960$	0	0
$961$	−30.4701	−0.982907
$962$	−0.308325	−0.00994080
$963$	−1.65045	−0.0531851
$964$	2.93227	0.0944422
$965$	0	0
$966$	−8.30115	−0.267085
$967$	23.6228	0.759657	0.379828	−	0.925057i	$-0.375983\pi$
$967$	23.6228	0.759657	0.379828	+	0.925057i	$0.375983\pi$
$968$	−12.3243	−0.396118
$969$	38.1151	1.22443
$970$	0	0
$971$	11.1293	0.357156	0.178578	−	0.983926i	$-0.442850\pi$
$971$	11.1293	0.357156	0.178578	+	0.983926i	$0.442850\pi$
$972$	−0.223857	−0.00718022
$973$	19.4813	0.624542
$974$	−10.0027	−0.320508
$975$	0	0
$976$	19.2960	0.617649
$977$	31.9269	1.02143	0.510717	−	0.859749i	$-0.329380\pi$
$977$	31.9269	1.02143	0.510717	+	0.859749i	$0.329380\pi$
$978$	15.7819	0.504649
$979$	−18.5349	−0.592377
$980$	0	0
$981$	−0.956668	−0.0305440
$982$	−46.9415	−1.49796
$983$	0.0136206	0.000434430 0	0.000217215	−	1.00000i	$-0.499931\pi$
$983$	0.0136206	0.000434430 0	0.000217215		1.00000i	$0.499931\pi$
$984$	−7.69865	−0.245424
$985$	0	0
$986$	−74.7075	−2.37917
$987$	1.33606	0.0425272
$988$	0.0523751	0.00166628
$989$	−23.7494	−0.755188
$990$	0	0
$991$	14.6375	0.464975	0.232487	−	0.972599i	$-0.425314\pi$
$991$	14.6375	0.464975	0.232487	+	0.972599i	$0.425314\pi$
$992$	−0.917610	−0.0291342
$993$	6.33141	0.200921
$994$	30.3544	0.962783
$995$	0	0
$996$	3.07349	0.0973873
$997$	−10.9289	−0.346122	−0.173061	−	0.984911i	$-0.555366\pi$
$997$	−10.9289	−0.346122	−0.173061	+	0.984911i	$0.555366\pi$
$998$	−29.9462	−0.947931
$999$	−5.03176	−0.159198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bg.1.7		10
5.2	odd	4		705.2.c.b.424.15	yes	20
5.3	odd	4		705.2.c.b.424.6	✓	20
5.4	even	2		3525.2.a.bf.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.6	✓	20	5.3	odd	4
705.2.c.b.424.15	yes	20	5.2	odd	4
3525.2.a.bf.1.4		10	5.4	even	2
3525.2.a.bg.1.7		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.49126 q^{2} -1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} -1.33606 q^{7} -2.64869 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.49126 q^{2} -1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} -1.33606 q^{7} -2.64869 q^{8} +1.00000 q^{9} +3.95638 q^{11} -0.223857 q^{12} -0.0410899 q^{13} -1.99241 q^{14} -4.39760 q^{16} +6.69389 q^{17} +1.49126 q^{18} -5.69401 q^{19} +1.33606 q^{21} +5.90000 q^{22} -4.16638 q^{23} +2.64869 q^{24} -0.0612758 q^{26} -1.00000 q^{27} -0.299086 q^{28} -7.48398 q^{29} +0.727923 q^{31} -1.26059 q^{32} -3.95638 q^{33} +9.98233 q^{34} +0.223857 q^{36} +5.03176 q^{37} -8.49126 q^{38} +0.0410899 q^{39} -2.90659 q^{41} +1.99241 q^{42} +5.70025 q^{43} +0.885665 q^{44} -6.21316 q^{46} +1.00000 q^{47} +4.39760 q^{48} -5.21495 q^{49} -6.69389 q^{51} -0.00919828 q^{52} +5.79623 q^{53} -1.49126 q^{54} +3.53881 q^{56} +5.69401 q^{57} -11.1606 q^{58} -13.3302 q^{59} -4.38784 q^{61} +1.08552 q^{62} -1.33606 q^{63} +6.91534 q^{64} -5.90000 q^{66} -14.9200 q^{67} +1.49847 q^{68} +4.16638 q^{69} -15.2350 q^{71} -2.64869 q^{72} +12.9221 q^{73} +7.50366 q^{74} -1.27465 q^{76} -5.28596 q^{77} +0.0612758 q^{78} +15.3290 q^{79} +1.00000 q^{81} -4.33448 q^{82} -13.7297 q^{83} +0.299086 q^{84} +8.50056 q^{86} +7.48398 q^{87} -10.4792 q^{88} -4.68480 q^{89} +0.0548986 q^{91} -0.932675 q^{92} -0.727923 q^{93} +1.49126 q^{94} +1.26059 q^{96} -8.64892 q^{97} -7.77684 q^{98} +3.95638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more