LMFDB - Embedded newform 3525.2.a.z.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 10x^{4} + 16x^{3} - 15x^{2} - 6x + 5 $ x^7 - x^6 - 9x^5 + 10x^4 + 16x^3 - 15x^2 - 6*x + 5
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			1.4
Root			$0.608551$ 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)

$f(q)$	$=$	$q-0.608551 q^{2} +1.00000 q^{3} -1.62967 q^{4} -0.608551 q^{6} -3.83697 q^{7} +2.20884 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.608551 q^{2} +1.00000 q^{3} -1.62967 q^{4} -0.608551 q^{6} -3.83697 q^{7} +2.20884 q^{8} +1.00000 q^{9} -0.466507 q^{11} -1.62967 q^{12} +1.86947 q^{13} +2.33499 q^{14} +1.91514 q^{16} +0.268198 q^{17} -0.608551 q^{18} -5.20479 q^{19} -3.83697 q^{21} +0.283893 q^{22} -0.943541 q^{23} +2.20884 q^{24} -1.13767 q^{26} +1.00000 q^{27} +6.25298 q^{28} -5.99947 q^{29} +3.89535 q^{31} -5.58313 q^{32} -0.466507 q^{33} -0.163212 q^{34} -1.62967 q^{36} -4.18329 q^{37} +3.16738 q^{38} +1.86947 q^{39} +2.27006 q^{41} +2.33499 q^{42} +10.7877 q^{43} +0.760251 q^{44} +0.574192 q^{46} +1.00000 q^{47} +1.91514 q^{48} +7.72234 q^{49} +0.268198 q^{51} -3.04661 q^{52} -4.42746 q^{53} -0.608551 q^{54} -8.47523 q^{56} -5.20479 q^{57} +3.65098 q^{58} +6.97557 q^{59} -8.00205 q^{61} -2.37052 q^{62} -3.83697 q^{63} -0.432670 q^{64} +0.283893 q^{66} +2.37722 q^{67} -0.437073 q^{68} -0.943541 q^{69} -6.83440 q^{71} +2.20884 q^{72} +7.07956 q^{73} +2.54574 q^{74} +8.48206 q^{76} +1.78998 q^{77} -1.13767 q^{78} +1.79135 q^{79} +1.00000 q^{81} -1.38145 q^{82} -9.36113 q^{83} +6.25298 q^{84} -6.56488 q^{86} -5.99947 q^{87} -1.03044 q^{88} +5.44520 q^{89} -7.17309 q^{91} +1.53766 q^{92} +3.89535 q^{93} -0.608551 q^{94} -5.58313 q^{96} +15.2257 q^{97} -4.69943 q^{98} -0.466507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9} + 5 q^{12} + 5 q^{13} + 7 q^{14} + 9 q^{16} + 2 q^{17} - q^{18} - 13 q^{19} + 7 q^{21} - 14 q^{22} + 6 q^{23} + 6 q^{24} + 7 q^{27} + 30 q^{28} + 9 q^{29} + 5 q^{31} + 26 q^{32} - 8 q^{34} + 5 q^{36} - 5 q^{37} - 2 q^{38} + 5 q^{39} + 18 q^{41} + 7 q^{42} + 14 q^{43} + 17 q^{44} - 27 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} + 2 q^{51} - 3 q^{52} + 20 q^{53} - q^{54} + 17 q^{56} - 13 q^{57} + 37 q^{58} + 10 q^{59} - 8 q^{61} - 6 q^{62} + 7 q^{63} + 18 q^{64} - 14 q^{66} + 4 q^{67} + 10 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} + 4 q^{73} - 25 q^{74} - 66 q^{76} + 6 q^{77} - 5 q^{79} + 7 q^{81} - 29 q^{82} + 52 q^{83} + 30 q^{84} - 17 q^{86} + 9 q^{87} + 26 q^{88} + 32 q^{89} - 26 q^{91} - 17 q^{92} + 5 q^{93} - q^{94} + 26 q^{96} - 12 q^{97} + 40 q^{98}+O(q^{100}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9 + 5 * q^12 + 5 * q^13 + 7 * q^14 + 9 * q^16 + 2 * q^17 - q^18 - 13 * q^19 + 7 * q^21 - 14 * q^22 + 6 * q^23 + 6 * q^24 + 7 * q^27 + 30 * q^28 + 9 * q^29 + 5 * q^31 + 26 * q^32 - 8 * q^34 + 5 * q^36 - 5 * q^37 - 2 * q^38 + 5 * q^39 + 18 * q^41 + 7 * q^42 + 14 * q^43 + 17 * q^44 - 27 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 + 2 * q^51 - 3 * q^52 + 20 * q^53 - q^54 + 17 * q^56 - 13 * q^57 + 37 * q^58 + 10 * q^59 - 8 * q^61 - 6 * q^62 + 7 * q^63 + 18 * q^64 - 14 * q^66 + 4 * q^67 + 10 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 + 4 * q^73 - 25 * q^74 - 66 * q^76 + 6 * q^77 - 5 * q^79 + 7 * q^81 - 29 * q^82 + 52 * q^83 + 30 * q^84 - 17 * q^86 + 9 * q^87 + 26 * q^88 + 32 * q^89 - 26 * q^91 - 17 * q^92 + 5 * q^93 - q^94 + 26 * q^96 - 12 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.608551	−0.430310	−0.215155	−	0.976580i	$-0.569026\pi$
$2$	−0.608551	−0.430310	−0.215155	+	0.976580i	$0.569026\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.62967	−0.814833
$5$	0	0
$5$	0	0
$6$	−0.608551	−0.248440
$7$	−3.83697	−1.45024	−0.725119	−	0.688623i	$-0.758215\pi$
$7$	−3.83697	−1.45024	−0.725119	+	0.688623i	$0.758215\pi$
$8$	2.20884	0.780941
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.466507	−0.140657	−0.0703286	−	0.997524i	$-0.522405\pi$
$11$	−0.466507	−0.140657	−0.0703286	+	0.997524i	$0.522405\pi$
$12$	−1.62967	−0.470444
$13$	1.86947	0.518497	0.259249	−	0.965811i	$-0.416525\pi$
$13$	1.86947	0.518497	0.259249	+	0.965811i	$0.416525\pi$
$14$	2.33499	0.624052
$15$	0	0
$16$	1.91514	0.478786
$17$	0.268198	0.0650475	0.0325238	−	0.999471i	$-0.489646\pi$
$17$	0.268198	0.0650475	0.0325238	+	0.999471i	$0.489646\pi$
$18$	−0.608551	−0.143437
$19$	−5.20479	−1.19406	−0.597030	−	0.802219i	$-0.703653\pi$
$19$	−5.20479	−1.19406	−0.597030	+	0.802219i	$0.703653\pi$
$20$	0	0
$21$	−3.83697	−0.837295
$22$	0.283893	0.0605263
$23$	−0.943541	−0.196742	−0.0983709	−	0.995150i	$-0.531363\pi$
$23$	−0.943541	−0.196742	−0.0983709	+	0.995150i	$0.531363\pi$
$24$	2.20884	0.450877
$25$	0	0
$26$	−1.13767	−0.223115
$27$	1.00000	0.192450
$28$	6.25298	1.18170
$29$	−5.99947	−1.11407	−0.557037	−	0.830488i	$-0.688062\pi$
$29$	−5.99947	−1.11407	−0.557037	+	0.830488i	$0.688062\pi$
$30$	0	0
$31$	3.89535	0.699625	0.349812	−	0.936820i	$-0.386245\pi$
$31$	3.89535	0.699625	0.349812	+	0.936820i	$0.386245\pi$
$32$	−5.58313	−0.986968
$33$	−0.466507	−0.0812085
$34$	−0.163212	−0.0279906
$35$	0	0
$36$	−1.62967	−0.271611
$37$	−4.18329	−0.687729	−0.343864	−	0.939019i	$-0.611736\pi$
$37$	−4.18329	−0.687729	−0.343864	+	0.939019i	$0.611736\pi$
$38$	3.16738	0.513816
$39$	1.86947	0.299354
$40$	0	0
$41$	2.27006	0.354524	0.177262	−	0.984164i	$-0.443276\pi$
$41$	2.27006	0.354524	0.177262	+	0.984164i	$0.443276\pi$
$42$	2.33499	0.360297
$43$	10.7877	1.64511	0.822557	−	0.568682i	$-0.192547\pi$
$43$	10.7877	1.64511	0.822557	+	0.568682i	$0.192547\pi$
$44$	0.760251	0.114612
$45$	0	0
$46$	0.574192	0.0846600
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	1.91514	0.276427
$49$	7.72234	1.10319
$50$	0	0
$51$	0.268198	0.0375552
$52$	−3.04661	−0.422489
$53$	−4.42746	−0.608158	−0.304079	−	0.952647i	$-0.598349\pi$
$53$	−4.42746	−0.608158	−0.304079	+	0.952647i	$0.598349\pi$
$54$	−0.608551	−0.0828132
$55$	0	0
$56$	−8.47523	−1.13255
$57$	−5.20479	−0.689391
$58$	3.65098	0.479397
$59$	6.97557	0.908142	0.454071	−	0.890965i	$-0.349971\pi$
$59$	6.97557	0.908142	0.454071	+	0.890965i	$0.349971\pi$
$60$	0	0
$61$	−8.00205	−1.02456	−0.512279	−	0.858819i	$-0.671198\pi$
$61$	−8.00205	−1.02456	−0.512279	+	0.858819i	$0.671198\pi$
$62$	−2.37052	−0.301056
$63$	−3.83697	−0.483413
$64$	−0.432670	−0.0540838
$65$	0	0
$66$	0.283893	0.0349449
$67$	2.37722	0.290423	0.145212	−	0.989401i	$-0.453614\pi$
$67$	2.37722	0.290423	0.145212	+	0.989401i	$0.453614\pi$
$68$	−0.437073	−0.0530029
$69$	−0.943541	−0.113589
$70$	0	0
$71$	−6.83440	−0.811094	−0.405547	−	0.914074i	$-0.632919\pi$
$71$	−6.83440	−0.811094	−0.405547	+	0.914074i	$0.632919\pi$
$72$	2.20884	0.260314
$73$	7.07956	0.828600	0.414300	−	0.910140i	$-0.364026\pi$
$73$	7.07956	0.828600	0.414300	+	0.910140i	$0.364026\pi$
$74$	2.54574	0.295937
$75$	0	0
$76$	8.48206	0.972960
$77$	1.78998	0.203987
$78$	−1.13767	−0.128815
$79$	1.79135	0.201542	0.100771	−	0.994910i	$-0.467869\pi$
$79$	1.79135	0.201542	0.100771	+	0.994910i	$0.467869\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.38145	−0.152555
$83$	−9.36113	−1.02752	−0.513759	−	0.857935i	$-0.671747\pi$
$83$	−9.36113	−1.02752	−0.513759	+	0.857935i	$0.671747\pi$
$84$	6.25298	0.682256
$85$	0	0
$86$	−6.56488	−0.707910
$87$	−5.99947	−0.643211
$88$	−1.03044	−0.109845
$89$	5.44520	0.577190	0.288595	−	0.957451i	$-0.406812\pi$
$89$	5.44520	0.577190	0.288595	+	0.957451i	$0.406812\pi$
$90$	0	0
$91$	−7.17309	−0.751944
$92$	1.53766	0.160312
$93$	3.89535	0.403929
$94$	−0.608551	−0.0627672
$95$	0	0
$96$	−5.58313	−0.569826
$97$	15.2257	1.54594	0.772969	−	0.634444i	$-0.218771\pi$
$97$	15.2257	1.54594	0.772969	+	0.634444i	$0.218771\pi$
$98$	−4.69943	−0.474714
$99$	−0.466507	−0.0468858
$100$	0	0
$101$	5.22414	0.519821	0.259910	−	0.965633i	$-0.416307\pi$
$101$	5.22414	0.519821	0.259910	+	0.965633i	$0.416307\pi$
$102$	−0.163212	−0.0161604
$103$	−0.627482	−0.0618276	−0.0309138	−	0.999522i	$-0.509842\pi$
$103$	−0.627482	−0.0618276	−0.0309138	+	0.999522i	$0.509842\pi$
$104$	4.12935	0.404916
$105$	0	0
$106$	2.69433	0.261697
$107$	15.4462	1.49324	0.746619	−	0.665251i	$-0.231676\pi$
$107$	15.4462	1.49324	0.746619	+	0.665251i	$0.231676\pi$
$108$	−1.62967	−0.156815
$109$	1.17182	0.112240	0.0561202	−	0.998424i	$-0.482127\pi$
$109$	1.17182	0.112240	0.0561202	+	0.998424i	$0.482127\pi$
$110$	0	0
$111$	−4.18329	−0.397060
$112$	−7.34835	−0.694354
$113$	16.8560	1.58568	0.792838	−	0.609432i	$-0.208603\pi$
$113$	16.8560	1.58568	0.792838	+	0.609432i	$0.208603\pi$
$114$	3.16738	0.296652
$115$	0	0
$116$	9.77714	0.907784
$117$	1.86947	0.172832
$118$	−4.24499	−0.390783
$119$	−1.02907	−0.0943344
$120$	0	0
$121$	−10.7824	−0.980216
$122$	4.86965	0.440877
$123$	2.27006	0.204684
$124$	−6.34812	−0.570078
$125$	0	0
$126$	2.33499	0.208017
$127$	14.5547	1.29152	0.645761	−	0.763540i	$-0.276540\pi$
$127$	14.5547	1.29152	0.645761	+	0.763540i	$0.276540\pi$
$128$	11.4296	1.01024
$129$	10.7877	0.949807
$130$	0	0
$131$	−2.30939	−0.201772	−0.100886	−	0.994898i	$-0.532168\pi$
$131$	−2.30939	−0.201772	−0.100886	+	0.994898i	$0.532168\pi$
$132$	0.760251	0.0661714
$133$	19.9706	1.73167
$134$	−1.44666	−0.124972
$135$	0	0
$136$	0.592405	0.0507983
$137$	−6.14269	−0.524806	−0.262403	−	0.964958i	$-0.584515\pi$
$137$	−6.14269	−0.524806	−0.262403	+	0.964958i	$0.584515\pi$
$138$	0.574192	0.0488785
$139$	9.81672	0.832643	0.416322	−	0.909217i	$-0.363319\pi$
$139$	9.81672	0.832643	0.416322	+	0.909217i	$0.363319\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	4.15908	0.349022
$143$	−0.872121	−0.0729304
$144$	1.91514	0.159595
$145$	0	0
$146$	−4.30827	−0.356555
$147$	7.72234	0.636928
$148$	6.81737	0.560384
$149$	2.86596	0.234789	0.117394	−	0.993085i	$-0.462546\pi$
$149$	2.86596	0.234789	0.117394	+	0.993085i	$0.462546\pi$
$150$	0	0
$151$	−2.02137	−0.164496	−0.0822482	−	0.996612i	$-0.526210\pi$
$151$	−2.02137	−0.164496	−0.0822482	+	0.996612i	$0.526210\pi$
$152$	−11.4965	−0.932491
$153$	0.268198	0.0216825
$154$	−1.08929	−0.0877775
$155$	0	0
$156$	−3.04661	−0.243924
$157$	3.50949	0.280087	0.140044	−	0.990145i	$-0.455276\pi$
$157$	3.50949	0.280087	0.140044	+	0.990145i	$0.455276\pi$
$158$	−1.09012	−0.0867257
$159$	−4.42746	−0.351120
$160$	0	0
$161$	3.62034	0.285323
$162$	−0.608551	−0.0478122
$163$	21.0120	1.64578	0.822892	−	0.568198i	$-0.192359\pi$
$163$	21.0120	1.64578	0.822892	+	0.568198i	$0.192359\pi$
$164$	−3.69944	−0.288878
$165$	0	0
$166$	5.69672	0.442151
$167$	17.9635	1.39006	0.695028	−	0.718983i	$-0.255392\pi$
$167$	17.9635	1.39006	0.695028	+	0.718983i	$0.255392\pi$
$168$	−8.47523	−0.653879
$169$	−9.50509	−0.731161
$170$	0	0
$171$	−5.20479	−0.398020
$172$	−17.5804	−1.34049
$173$	18.3759	1.39709	0.698546	−	0.715565i	$-0.253831\pi$
$173$	18.3759	1.39709	0.698546	+	0.715565i	$0.253831\pi$
$174$	3.65098	0.276780
$175$	0	0
$176$	−0.893429	−0.0673448
$177$	6.97557	0.524316
$178$	−3.31368	−0.248371
$179$	1.86613	0.139481	0.0697406	−	0.997565i	$-0.477783\pi$
$179$	1.86613	0.139481	0.0697406	+	0.997565i	$0.477783\pi$
$180$	0	0
$181$	−11.7363	−0.872352	−0.436176	−	0.899861i	$-0.643668\pi$
$181$	−11.7363	−0.872352	−0.436176	+	0.899861i	$0.643668\pi$
$182$	4.36519	0.323569
$183$	−8.00205	−0.591528
$184$	−2.08413	−0.153644
$185$	0	0
$186$	−2.37052	−0.173815
$187$	−0.125116	−0.00914941
$188$	−1.62967	−0.118856
$189$	−3.83697	−0.279098
$190$	0	0
$191$	17.5402	1.26916	0.634581	−	0.772856i	$-0.281173\pi$
$191$	17.5402	1.26916	0.634581	+	0.772856i	$0.281173\pi$
$192$	−0.432670	−0.0312253
$193$	−11.5905	−0.834304	−0.417152	−	0.908837i	$-0.636972\pi$
$193$	−11.5905	−0.834304	−0.417152	+	0.908837i	$0.636972\pi$
$194$	−9.26562	−0.665233
$195$	0	0
$196$	−12.5848	−0.898917
$197$	15.4629	1.10168	0.550842	−	0.834609i	$-0.314307\pi$
$197$	15.4629	1.10168	0.550842	+	0.834609i	$0.314307\pi$
$198$	0.283893	0.0201754
$199$	−15.1873	−1.07660	−0.538300	−	0.842753i	$-0.680933\pi$
$199$	−15.1873	−1.07660	−0.538300	+	0.842753i	$0.680933\pi$
$200$	0	0
$201$	2.37722	0.167676
$202$	−3.17915	−0.223684
$203$	23.0198	1.61567
$204$	−0.437073	−0.0306012
$205$	0	0
$206$	0.381855	0.0266051
$207$	−0.943541	−0.0655806
$208$	3.58030	0.248249
$209$	2.42807	0.167953
$210$	0	0
$211$	14.8266	1.02070	0.510352	−	0.859965i	$-0.329515\pi$
$211$	14.8266	1.02070	0.510352	+	0.859965i	$0.329515\pi$
$212$	7.21528	0.495547
$213$	−6.83440	−0.468285
$214$	−9.39978	−0.642556
$215$	0	0
$216$	2.20884	0.150292
$217$	−14.9463	−1.01462
$218$	−0.713114	−0.0482982
$219$	7.07956	0.478393
$220$	0	0
$221$	0.501387	0.0337270
$222$	2.54574	0.170859
$223$	16.2253	1.08653	0.543263	−	0.839563i	$-0.317189\pi$
$223$	16.2253	1.08653	0.543263	+	0.839563i	$0.317189\pi$
$224$	21.4223	1.43134
$225$	0	0
$226$	−10.2577	−0.682333
$227$	24.8152	1.64704	0.823521	−	0.567286i	$-0.192007\pi$
$227$	24.8152	1.64704	0.823521	+	0.567286i	$0.192007\pi$
$228$	8.48206	0.561738
$229$	−3.34506	−0.221048	−0.110524	−	0.993873i	$-0.535253\pi$
$229$	−3.34506	−0.221048	−0.110524	+	0.993873i	$0.535253\pi$
$230$	0	0
$231$	1.78998	0.117772
$232$	−13.2518	−0.870026
$233$	−12.1364	−0.795083	−0.397541	−	0.917584i	$-0.630137\pi$
$233$	−12.1364	−0.795083	−0.397541	+	0.917584i	$0.630137\pi$
$234$	−1.13767	−0.0743715
$235$	0	0
$236$	−11.3679	−0.739985
$237$	1.79135	0.116360
$238$	0.626239	0.0405931
$239$	8.62595	0.557966	0.278983	−	0.960296i	$-0.410003\pi$
$239$	8.62595	0.557966	0.278983	+	0.960296i	$0.410003\pi$
$240$	0	0
$241$	1.89750	0.122228	0.0611142	−	0.998131i	$-0.480535\pi$
$241$	1.89750	0.122228	0.0611142	+	0.998131i	$0.480535\pi$
$242$	6.56162	0.421797
$243$	1.00000	0.0641500
$244$	13.0407	0.834843
$245$	0	0
$246$	−1.38145	−0.0880777
$247$	−9.73018	−0.619117
$248$	8.60418	0.546366
$249$	−9.36113	−0.593237
$250$	0	0
$251$	12.1643	0.767806	0.383903	−	0.923373i	$-0.374580\pi$
$251$	12.1643	0.767806	0.383903	+	0.923373i	$0.374580\pi$
$252$	6.25298	0.393901
$253$	0.440169	0.0276732
$254$	−8.85728	−0.555755
$255$	0	0
$256$	−6.09013	−0.380633
$257$	−6.55174	−0.408686	−0.204343	−	0.978899i	$-0.565506\pi$
$257$	−6.55174	−0.408686	−0.204343	+	0.978899i	$0.565506\pi$
$258$	−6.56488	−0.408712
$259$	16.0512	0.997370
$260$	0	0
$261$	−5.99947	−0.371358
$262$	1.40538	0.0868246
$263$	−12.6698	−0.781252	−0.390626	−	0.920550i	$-0.627741\pi$
$263$	−12.6698	−0.781252	−0.390626	+	0.920550i	$0.627741\pi$
$264$	−1.03044	−0.0634191
$265$	0	0
$266$	−12.1531	−0.745156
$267$	5.44520	0.333241
$268$	−3.87407	−0.236647
$269$	−25.8223	−1.57442	−0.787208	−	0.616688i	$-0.788474\pi$
$269$	−25.8223	−1.57442	−0.787208	+	0.616688i	$0.788474\pi$
$270$	0	0
$271$	5.47377	0.332508	0.166254	−	0.986083i	$-0.446833\pi$
$271$	5.47377	0.332508	0.166254	+	0.986083i	$0.446833\pi$
$272$	0.513638	0.0311439
$273$	−7.17309	−0.434135
$274$	3.73814	0.225829
$275$	0	0
$276$	1.53766	0.0925560
$277$	3.97637	0.238917	0.119459	−	0.992839i	$-0.461884\pi$
$277$	3.97637	0.238917	0.119459	+	0.992839i	$0.461884\pi$
$278$	−5.97397	−0.358295
$279$	3.89535	0.233208
$280$	0	0
$281$	3.44181	0.205321	0.102661	−	0.994716i	$-0.467264\pi$
$281$	3.44181	0.205321	0.102661	+	0.994716i	$0.467264\pi$
$282$	−0.608551	−0.0362387
$283$	8.49732	0.505113	0.252557	−	0.967582i	$-0.418729\pi$
$283$	8.49732	0.505113	0.252557	+	0.967582i	$0.418729\pi$
$284$	11.1378	0.660906
$285$	0	0
$286$	0.530730	0.0313827
$287$	−8.71014	−0.514144
$288$	−5.58313	−0.328989
$289$	−16.9281	−0.995769
$290$	0	0
$291$	15.2257	0.892548
$292$	−11.5373	−0.675171
$293$	4.15414	0.242688	0.121344	−	0.992611i	$-0.461280\pi$
$293$	4.15414	0.242688	0.121344	+	0.992611i	$0.461280\pi$
$294$	−4.69943	−0.274076
$295$	0	0
$296$	−9.24020	−0.537076
$297$	−0.466507	−0.0270695
$298$	−1.74408	−0.101032
$299$	−1.76392	−0.102010
$300$	0	0
$301$	−41.3922	−2.38581
$302$	1.23010	0.0707845
$303$	5.22414	0.300119
$304$	−9.96792	−0.571699
$305$	0	0
$306$	−0.163212	−0.00933020
$307$	−11.9138	−0.679958	−0.339979	−	0.940433i	$-0.610420\pi$
$307$	−11.9138	−0.679958	−0.339979	+	0.940433i	$0.610420\pi$
$308$	−2.91706	−0.166215
$309$	−0.627482	−0.0356962
$310$	0	0
$311$	−27.9286	−1.58369	−0.791843	−	0.610725i	$-0.790878\pi$
$311$	−27.9286	−1.58369	−0.791843	+	0.610725i	$0.790878\pi$
$312$	4.12935	0.233778
$313$	−2.90432	−0.164162	−0.0820809	−	0.996626i	$-0.526157\pi$
$313$	−2.90432	−0.164162	−0.0820809	+	0.996626i	$0.526157\pi$
$314$	−2.13570	−0.120524
$315$	0	0
$316$	−2.91930	−0.164223
$317$	−3.00003	−0.168498	−0.0842492	−	0.996445i	$-0.526849\pi$
$317$	−3.00003	−0.168498	−0.0842492	+	0.996445i	$0.526849\pi$
$318$	2.69433	0.151091
$319$	2.79880	0.156703
$320$	0	0
$321$	15.4462	0.862122
$322$	−2.20316	−0.122777
$323$	−1.39591	−0.0776706
$324$	−1.62967	−0.0905370
$325$	0	0
$326$	−12.7868	−0.708198
$327$	1.17182	0.0648020
$328$	5.01418	0.276862
$329$	−3.83697	−0.211539
$330$	0	0
$331$	5.74085	0.315546	0.157773	−	0.987475i	$-0.449569\pi$
$331$	5.74085	0.315546	0.157773	+	0.987475i	$0.449569\pi$
$332$	15.2555	0.837255
$333$	−4.18329	−0.229243
$334$	−10.9317	−0.598155
$335$	0	0
$336$	−7.34835	−0.400885
$337$	−16.3374	−0.889956	−0.444978	−	0.895542i	$-0.646789\pi$
$337$	−16.3374	−0.889956	−0.444978	+	0.895542i	$0.646789\pi$
$338$	5.78433	0.314626
$339$	16.8560	0.915491
$340$	0	0
$341$	−1.81721	−0.0984074
$342$	3.16738	0.171272
$343$	−2.77159	−0.149652
$344$	23.8283	1.28474
$345$	0	0
$346$	−11.1827	−0.601183
$347$	31.0241	1.66546	0.832731	−	0.553678i	$-0.186776\pi$
$347$	31.0241	1.66546	0.832731	+	0.553678i	$0.186776\pi$
$348$	9.77714	0.524110
$349$	−8.85299	−0.473890	−0.236945	−	0.971523i	$-0.576146\pi$
$349$	−8.85299	−0.473890	−0.236945	+	0.971523i	$0.576146\pi$
$350$	0	0
$351$	1.86947	0.0997848
$352$	2.60457	0.138824
$353$	18.3089	0.974485	0.487242	−	0.873267i	$-0.338003\pi$
$353$	18.3089	0.974485	0.487242	+	0.873267i	$0.338003\pi$
$354$	−4.24499	−0.225619
$355$	0	0
$356$	−8.87386	−0.470313
$357$	−1.02907	−0.0544640
$358$	−1.13563	−0.0600202
$359$	25.3963	1.34036	0.670182	−	0.742197i	$-0.266216\pi$
$359$	25.3963	1.34036	0.670182	+	0.742197i	$0.266216\pi$
$360$	0	0
$361$	8.08980	0.425779
$362$	7.14213	0.375382
$363$	−10.7824	−0.565928
$364$	11.6897	0.612709
$365$	0	0
$366$	4.86965	0.254541
$367$	−4.34902	−0.227017	−0.113509	−	0.993537i	$-0.536209\pi$
$367$	−4.34902	−0.227017	−0.113509	+	0.993537i	$0.536209\pi$
$368$	−1.80702	−0.0941973
$369$	2.27006	0.118175
$370$	0	0
$371$	16.9880	0.881974
$372$	−6.34812	−0.329134
$373$	6.98837	0.361844	0.180922	−	0.983497i	$-0.442092\pi$
$373$	6.98837	0.361844	0.180922	+	0.983497i	$0.442092\pi$
$374$	0.0761396	0.00393708
$375$	0	0
$376$	2.20884	0.113912
$377$	−11.2158	−0.577644
$378$	2.33499	0.120099
$379$	22.6938	1.16570	0.582852	−	0.812578i	$-0.301937\pi$
$379$	22.6938	1.16570	0.582852	+	0.812578i	$0.301937\pi$
$380$	0	0
$381$	14.5547	0.745660
$382$	−10.6741	−0.546134
$383$	−11.0200	−0.563098	−0.281549	−	0.959547i	$-0.590848\pi$
$383$	−11.0200	−0.563098	−0.281549	+	0.959547i	$0.590848\pi$
$384$	11.4296	0.583263
$385$	0	0
$386$	7.05342	0.359010
$387$	10.7877	0.548372
$388$	−24.8128	−1.25968
$389$	23.0574	1.16906	0.584529	−	0.811373i	$-0.301279\pi$
$389$	23.0574	1.16906	0.584529	+	0.811373i	$0.301279\pi$
$390$	0	0
$391$	−0.253056	−0.0127976
$392$	17.0574	0.861527
$393$	−2.30939	−0.116493
$394$	−9.40994	−0.474066
$395$	0	0
$396$	0.760251	0.0382041
$397$	−26.8820	−1.34917	−0.674584	−	0.738198i	$-0.735677\pi$
$397$	−26.8820	−1.34917	−0.674584	+	0.738198i	$0.735677\pi$
$398$	9.24225	0.463272
$399$	19.9706	0.999781
$400$	0	0
$401$	33.8428	1.69003	0.845015	−	0.534742i	$-0.179591\pi$
$401$	33.8428	1.69003	0.845015	+	0.534742i	$0.179591\pi$
$402$	−1.44666	−0.0721527
$403$	7.28223	0.362754
$404$	−8.51360	−0.423567
$405$	0	0
$406$	−14.0087	−0.695240
$407$	1.95154	0.0967340
$408$	0.592405	0.0293284
$409$	−1.37498	−0.0679882	−0.0339941	−	0.999422i	$-0.510823\pi$
$409$	−1.37498	−0.0679882	−0.0339941	+	0.999422i	$0.510823\pi$
$410$	0	0
$411$	−6.14269	−0.302997
$412$	1.02259	0.0503792
$413$	−26.7651	−1.31702
$414$	0.574192	0.0282200
$415$	0	0
$416$	−10.4375	−0.511740
$417$	9.81672	0.480727
$418$	−1.47760	−0.0722720
$419$	−32.6146	−1.59333	−0.796663	−	0.604424i	$-0.793403\pi$
$419$	−32.6146	−1.59333	−0.796663	+	0.604424i	$0.793403\pi$
$420$	0	0
$421$	0.0868444	0.00423254	0.00211627	−	0.999998i	$-0.499326\pi$
$421$	0.0868444	0.00423254	0.00211627	+	0.999998i	$0.499326\pi$
$422$	−9.02273	−0.439220
$423$	1.00000	0.0486217
$424$	−9.77952	−0.474936
$425$	0	0
$426$	4.15908	0.201508
$427$	30.7036	1.48585
$428$	−25.1721	−1.21674
$429$	−0.872121	−0.0421064
$430$	0	0
$431$	31.5118	1.51787	0.758936	−	0.651166i	$-0.225720\pi$
$431$	31.5118	1.51787	0.758936	+	0.651166i	$0.225720\pi$
$432$	1.91514	0.0921424
$433$	−9.50105	−0.456591	−0.228296	−	0.973592i	$-0.573315\pi$
$433$	−9.50105	−0.456591	−0.228296	+	0.973592i	$0.573315\pi$
$434$	9.09560	0.436603
$435$	0	0
$436$	−1.90968	−0.0914572
$437$	4.91093	0.234922
$438$	−4.30827	−0.205857
$439$	−15.0973	−0.720553	−0.360276	−	0.932846i	$-0.617318\pi$
$439$	−15.0973	−0.720553	−0.360276	+	0.932846i	$0.617318\pi$
$440$	0	0
$441$	7.72234	0.367730
$442$	−0.305119	−0.0145131
$443$	0.346829	0.0164784	0.00823918	−	0.999966i	$-0.497377\pi$
$443$	0.346829	0.0164784	0.00823918	+	0.999966i	$0.497377\pi$
$444$	6.81737	0.323538
$445$	0	0
$446$	−9.87391	−0.467543
$447$	2.86596	0.135555
$448$	1.66014	0.0784344
$449$	1.56835	0.0740151	0.0370075	−	0.999315i	$-0.488217\pi$
$449$	1.56835	0.0740151	0.0370075	+	0.999315i	$0.488217\pi$
$450$	0	0
$451$	−1.05900	−0.0498663
$452$	−27.4696	−1.29206
$453$	−2.02137	−0.0949721
$454$	−15.1013	−0.708739
$455$	0	0
$456$	−11.4965	−0.538374
$457$	−9.47826	−0.443374	−0.221687	−	0.975118i	$-0.571156\pi$
$457$	−9.47826	−0.443374	−0.221687	+	0.975118i	$0.571156\pi$
$458$	2.03564	0.0951191
$459$	0.268198	0.0125184
$460$	0	0
$461$	23.2316	1.08200	0.541002	−	0.841021i	$-0.318045\pi$
$461$	23.2316	1.08200	0.541002	+	0.841021i	$0.318045\pi$
$462$	−1.08929	−0.0506784
$463$	−0.197246	−0.00916680	−0.00458340	−	0.999989i	$-0.501459\pi$
$463$	−0.197246	−0.00916680	−0.00458340	+	0.999989i	$0.501459\pi$
$464$	−11.4899	−0.533403
$465$	0	0
$466$	7.38562	0.342132
$467$	9.91511	0.458816	0.229408	−	0.973330i	$-0.426321\pi$
$467$	9.91511	0.458816	0.229408	+	0.973330i	$0.426321\pi$
$468$	−3.04661	−0.140830
$469$	−9.12131	−0.421183
$470$	0	0
$471$	3.50949	0.161709
$472$	15.4079	0.709206
$473$	−5.03256	−0.231397
$474$	−1.09012	−0.0500711
$475$	0	0
$476$	1.67704	0.0768668
$477$	−4.42746	−0.202719
$478$	−5.24933	−0.240099
$479$	34.5951	1.58069	0.790346	−	0.612660i	$-0.209901\pi$
$479$	34.5951	1.58069	0.790346	+	0.612660i	$0.209901\pi$
$480$	0	0
$481$	−7.82052	−0.356585
$482$	−1.15472	−0.0525962
$483$	3.62034	0.164731
$484$	17.5717	0.798712
$485$	0	0
$486$	−0.608551	−0.0276044
$487$	−10.0686	−0.456253	−0.228126	−	0.973632i	$-0.573260\pi$
$487$	−10.0686	−0.456253	−0.228126	+	0.973632i	$0.573260\pi$
$488$	−17.6752	−0.800119
$489$	21.0120	0.950194
$490$	0	0
$491$	−26.9368	−1.21564	−0.607820	−	0.794075i	$-0.707956\pi$
$491$	−26.9368	−1.21564	−0.607820	+	0.794075i	$0.707956\pi$
$492$	−3.69944	−0.166784
$493$	−1.60905	−0.0724677
$494$	5.92131	0.266412
$495$	0	0
$496$	7.46015	0.334971
$497$	26.2234	1.17628
$498$	5.69672	0.255276
$499$	−13.7263	−0.614474	−0.307237	−	0.951633i	$-0.599404\pi$
$499$	−13.7263	−0.614474	−0.307237	+	0.951633i	$0.599404\pi$
$500$	0	0
$501$	17.9635	0.802549
$502$	−7.40261	−0.330395
$503$	−34.7797	−1.55075	−0.775375	−	0.631500i	$-0.782439\pi$
$503$	−34.7797	−1.55075	−0.775375	+	0.631500i	$0.782439\pi$
$504$	−8.47523	−0.377517
$505$	0	0
$506$	−0.267865	−0.0119080
$507$	−9.50509	−0.422136
$508$	−23.7193	−1.05237
$509$	−10.3711	−0.459690	−0.229845	−	0.973227i	$-0.573822\pi$
$509$	−10.3711	−0.459690	−0.229845	+	0.973227i	$0.573822\pi$
$510$	0	0
$511$	−27.1641	−1.20167
$512$	−19.1530	−0.846450
$513$	−5.20479	−0.229797
$514$	3.98706	0.175862
$515$	0	0
$516$	−17.5804	−0.773934
$517$	−0.466507	−0.0205170
$518$	−9.76794	−0.429179
$519$	18.3759	0.806612
$520$	0	0
$521$	22.1897	0.972149	0.486074	−	0.873917i	$-0.338428\pi$
$521$	22.1897	0.972149	0.486074	+	0.873917i	$0.338428\pi$
$522$	3.65098	0.159799
$523$	−28.7034	−1.25511	−0.627556	−	0.778571i	$-0.715945\pi$
$523$	−28.7034	−1.25511	−0.627556	+	0.778571i	$0.715945\pi$
$524$	3.76353	0.164411
$525$	0	0
$526$	7.71020	0.336181
$527$	1.04472	0.0455089
$528$	−0.893429	−0.0388815
$529$	−22.1097	−0.961293
$530$	0	0
$531$	6.97557	0.302714
$532$	−32.5454	−1.41102
$533$	4.24380	0.183819
$534$	−3.31368	−0.143397
$535$	0	0
$536$	5.25088	0.226804
$537$	1.86613	0.0805295
$538$	15.7142	0.677487
$539$	−3.60253	−0.155172
$540$	0	0
$541$	−24.7243	−1.06298	−0.531490	−	0.847065i	$-0.678368\pi$
$541$	−24.7243	−1.06298	−0.531490	+	0.847065i	$0.678368\pi$
$542$	−3.33107	−0.143082
$543$	−11.7363	−0.503653
$544$	−1.49738	−0.0641998
$545$	0	0
$546$	4.36519	0.186813
$547$	3.61379	0.154515	0.0772573	−	0.997011i	$-0.475384\pi$
$547$	3.61379	0.154515	0.0772573	+	0.997011i	$0.475384\pi$
$548$	10.0105	0.427629
$549$	−8.00205	−0.341519
$550$	0	0
$551$	31.2260	1.33027
$552$	−2.08413	−0.0887063
$553$	−6.87334	−0.292284
$554$	−2.41982	−0.102808
$555$	0	0
$556$	−15.9980	−0.678465
$557$	−2.55809	−0.108390	−0.0541949	−	0.998530i	$-0.517259\pi$
$557$	−2.55809	−0.108390	−0.0541949	+	0.998530i	$0.517259\pi$
$558$	−2.37052	−0.100352
$559$	20.1673	0.852987
$560$	0	0
$561$	−0.125116	−0.00528241
$562$	−2.09452	−0.0883519
$563$	40.5998	1.71108	0.855539	−	0.517738i	$-0.173226\pi$
$563$	40.5998	1.71108	0.855539	+	0.517738i	$0.173226\pi$
$564$	−1.62967	−0.0686213
$565$	0	0
$566$	−5.17105	−0.217355
$567$	−3.83697	−0.161138
$568$	−15.0961	−0.633417
$569$	31.1824	1.30724	0.653618	−	0.756825i	$-0.273250\pi$
$569$	31.1824	1.30724	0.653618	+	0.756825i	$0.273250\pi$
$570$	0	0
$571$	−24.7803	−1.03702	−0.518511	−	0.855071i	$-0.673513\pi$
$571$	−24.7803	−1.03702	−0.518511	+	0.855071i	$0.673513\pi$
$572$	1.42127	0.0594261
$573$	17.5402	0.732752
$574$	5.30056	0.221241
$575$	0	0
$576$	−0.432670	−0.0180279
$577$	−16.5930	−0.690777	−0.345388	−	0.938460i	$-0.612253\pi$
$577$	−16.5930	−0.690777	−0.345388	+	0.938460i	$0.612253\pi$
$578$	10.3016	0.428489
$579$	−11.5905	−0.481686
$580$	0	0
$581$	35.9184	1.49014
$582$	−9.26562	−0.384072
$583$	2.06544	0.0855419
$584$	15.6376	0.647088
$585$	0	0
$586$	−2.52801	−0.104431
$587$	−33.2266	−1.37141	−0.685703	−	0.727881i	$-0.740505\pi$
$587$	−33.2266	−1.37141	−0.685703	+	0.727881i	$0.740505\pi$
$588$	−12.5848	−0.518990
$589$	−20.2744	−0.835394
$590$	0	0
$591$	15.4629	0.636058
$592$	−8.01160	−0.329275
$593$	−41.8039	−1.71668	−0.858340	−	0.513082i	$-0.828504\pi$
$593$	−41.8039	−1.71668	−0.858340	+	0.513082i	$0.828504\pi$
$594$	0.283893	0.0116483
$595$	0	0
$596$	−4.67056	−0.191314
$597$	−15.1873	−0.621575
$598$	1.07343	0.0438960
$599$	18.7833	0.767465	0.383732	−	0.923444i	$-0.374639\pi$
$599$	18.7833	0.767465	0.383732	+	0.923444i	$0.374639\pi$
$600$	0	0
$601$	33.7501	1.37669	0.688347	−	0.725381i	$-0.258337\pi$
$601$	33.7501	1.37669	0.688347	+	0.725381i	$0.258337\pi$
$602$	25.1893	1.02664
$603$	2.37722	0.0968078
$604$	3.29415	0.134037
$605$	0	0
$606$	−3.17915	−0.129144
$607$	40.6335	1.64926	0.824632	−	0.565670i	$-0.191382\pi$
$607$	40.6335	1.64926	0.824632	+	0.565670i	$0.191382\pi$
$608$	29.0590	1.17850
$609$	23.0198	0.932809
$610$	0	0
$611$	1.86947	0.0756306
$612$	−0.437073	−0.0176676
$613$	5.63103	0.227435	0.113717	−	0.993513i	$-0.463724\pi$
$613$	5.63103	0.227435	0.113717	+	0.993513i	$0.463724\pi$
$614$	7.25017	0.292593
$615$	0	0
$616$	3.95376	0.159302
$617$	−43.4092	−1.74759	−0.873794	−	0.486296i	$-0.838348\pi$
$617$	−43.4092	−1.74759	−0.873794	+	0.486296i	$0.838348\pi$
$618$	0.381855	0.0153604
$619$	−13.6522	−0.548726	−0.274363	−	0.961626i	$-0.588467\pi$
$619$	−13.6522	−0.548726	−0.274363	+	0.961626i	$0.588467\pi$
$620$	0	0
$621$	−0.943541	−0.0378630
$622$	16.9960	0.681476
$623$	−20.8931	−0.837063
$624$	3.58030	0.143327
$625$	0	0
$626$	1.76743	0.0706405
$627$	2.42807	0.0969678
$628$	−5.71929	−0.228225
$629$	−1.12195	−0.0447350
$630$	0	0
$631$	−4.24102	−0.168832	−0.0844162	−	0.996431i	$-0.526903\pi$
$631$	−4.24102	−0.168832	−0.0844162	+	0.996431i	$0.526903\pi$
$632$	3.95679	0.157393
$633$	14.8266	0.589304
$634$	1.82567	0.0725066
$635$	0	0
$636$	7.21528	0.286104
$637$	14.4367	0.572001
$638$	−1.70321	−0.0674307
$639$	−6.83440	−0.270365
$640$	0	0
$641$	14.3381	0.566320	0.283160	−	0.959073i	$-0.408617\pi$
$641$	14.3381	0.566320	0.283160	+	0.959073i	$0.408617\pi$
$642$	−9.39978	−0.370980
$643$	26.2885	1.03672	0.518359	−	0.855163i	$-0.326543\pi$
$643$	26.2885	1.03672	0.518359	+	0.855163i	$0.326543\pi$
$644$	−5.89994	−0.232490
$645$	0	0
$646$	0.849483	0.0334225
$647$	−26.9918	−1.06116	−0.530579	−	0.847635i	$-0.678025\pi$
$647$	−26.9918	−1.06116	−0.530579	+	0.847635i	$0.678025\pi$
$648$	2.20884	0.0867712
$649$	−3.25416	−0.127737
$650$	0	0
$651$	−14.9463	−0.585793
$652$	−34.2425	−1.34104
$653$	20.7266	0.811093	0.405547	−	0.914074i	$-0.367081\pi$
$653$	20.7266	0.811093	0.405547	+	0.914074i	$0.367081\pi$
$654$	−0.713114	−0.0278850
$655$	0	0
$656$	4.34749	0.169741
$657$	7.07956	0.276200
$658$	2.33499	0.0910274
$659$	6.10303	0.237740	0.118870	−	0.992910i	$-0.462073\pi$
$659$	6.10303	0.237740	0.118870	+	0.992910i	$0.462073\pi$
$660$	0	0
$661$	45.4978	1.76966	0.884829	−	0.465915i	$-0.154275\pi$
$661$	45.4978	1.76966	0.884829	+	0.465915i	$0.154275\pi$
$662$	−3.49360	−0.135783
$663$	0.501387	0.0194723
$664$	−20.6772	−0.802430
$665$	0	0
$666$	2.54574	0.0986455
$667$	5.66075	0.219185
$668$	−29.2745	−1.13266
$669$	16.2253	0.627306
$670$	0	0
$671$	3.73301	0.144111
$672$	21.4223	0.826384
$673$	−5.72927	−0.220847	−0.110424	−	0.993885i	$-0.535221\pi$
$673$	−5.72927	−0.220847	−0.110424	+	0.993885i	$0.535221\pi$
$674$	9.94215	0.382957
$675$	0	0
$676$	15.4901	0.595774
$677$	12.5775	0.483392	0.241696	−	0.970352i	$-0.422296\pi$
$677$	12.5775	0.483392	0.241696	+	0.970352i	$0.422296\pi$
$678$	−10.2577	−0.393945
$679$	−58.4206	−2.24198
$680$	0	0
$681$	24.8152	0.950920
$682$	1.10586	0.0423457
$683$	−7.58765	−0.290333	−0.145167	−	0.989407i	$-0.546372\pi$
$683$	−7.58765	−0.290333	−0.145167	+	0.989407i	$0.546372\pi$
$684$	8.48206	0.324320
$685$	0	0
$686$	1.68665	0.0643966
$687$	−3.34506	−0.127622
$688$	20.6601	0.787658
$689$	−8.27699	−0.315328
$690$	0	0
$691$	16.0841	0.611867	0.305934	−	0.952053i	$-0.401031\pi$
$691$	16.0841	0.611867	0.305934	+	0.952053i	$0.401031\pi$
$692$	−29.9466	−1.13840
$693$	1.78998	0.0679955
$694$	−18.8797	−0.716665
$695$	0	0
$696$	−13.2518	−0.502310
$697$	0.608825	0.0230609
$698$	5.38749	0.203920
$699$	−12.1364	−0.459041
$700$	0	0
$701$	24.7566	0.935042	0.467521	−	0.883982i	$-0.345147\pi$
$701$	24.7566	0.935042	0.467521	+	0.883982i	$0.345147\pi$
$702$	−1.13767	−0.0429384
$703$	21.7731	0.821189
$704$	0.201844	0.00760728
$705$	0	0
$706$	−11.1419	−0.419331
$707$	−20.0449	−0.753864
$708$	−11.3679	−0.427230
$709$	−39.3908	−1.47935	−0.739677	−	0.672962i	$-0.765022\pi$
$709$	−39.3908	−1.47935	−0.739677	+	0.672962i	$0.765022\pi$
$710$	0	0
$711$	1.79135	0.0671807
$712$	12.0275	0.450751
$713$	−3.67542	−0.137645
$714$	0.626239	0.0234364
$715$	0	0
$716$	−3.04117	−0.113654
$717$	8.62595	0.322142
$718$	−15.4549	−0.576772
$719$	−42.7340	−1.59371	−0.796854	−	0.604172i	$-0.793504\pi$
$719$	−42.7340	−1.59371	−0.796854	+	0.604172i	$0.793504\pi$
$720$	0	0
$721$	2.40763	0.0896648
$722$	−4.92305	−0.183217
$723$	1.89750	0.0705686
$724$	19.1262	0.710821
$725$	0	0
$726$	6.56162	0.243524
$727$	51.9627	1.92719	0.963595	−	0.267365i	$-0.0861530\pi$
$727$	51.9627	1.92719	0.963595	+	0.267365i	$0.0861530\pi$
$728$	−15.8442	−0.587224
$729$	1.00000	0.0370370
$730$	0	0
$731$	2.89325	0.107011
$732$	13.0407	0.481997
$733$	35.8960	1.32585	0.662924	−	0.748687i	$-0.269315\pi$
$733$	35.8960	1.32585	0.662924	+	0.748687i	$0.269315\pi$
$734$	2.64660	0.0976878
$735$	0	0
$736$	5.26791	0.194178
$737$	−1.10899	−0.0408502
$738$	−1.38145	−0.0508517
$739$	−52.5195	−1.93196	−0.965981	−	0.258613i	$-0.916735\pi$
$739$	−52.5195	−1.93196	−0.965981	+	0.258613i	$0.916735\pi$
$740$	0	0
$741$	−9.73018	−0.357447
$742$	−10.3381	−0.379522
$743$	33.1153	1.21488	0.607442	−	0.794364i	$-0.292196\pi$
$743$	33.1153	1.21488	0.607442	+	0.794364i	$0.292196\pi$
$744$	8.60418	0.315445
$745$	0	0
$746$	−4.25278	−0.155705
$747$	−9.36113	−0.342506
$748$	0.203898	0.00745524
$749$	−59.2665	−2.16555
$750$	0	0
$751$	−28.5790	−1.04286	−0.521431	−	0.853293i	$-0.674602\pi$
$751$	−28.5790	−1.04286	−0.521431	+	0.853293i	$0.674602\pi$
$752$	1.91514	0.0698381
$753$	12.1643	0.443293
$754$	6.82539	0.248566
$755$	0	0
$756$	6.25298	0.227419
$757$	6.27587	0.228100	0.114050	−	0.993475i	$-0.463618\pi$
$757$	6.27587	0.228100	0.114050	+	0.993475i	$0.463618\pi$
$758$	−13.8104	−0.501615
$759$	0.440169	0.0159771
$760$	0	0
$761$	20.8050	0.754182	0.377091	−	0.926176i	$-0.376924\pi$
$761$	20.8050	0.754182	0.377091	+	0.926176i	$0.376924\pi$
$762$	−8.85728	−0.320865
$763$	−4.49625	−0.162775
$764$	−28.5846	−1.03416
$765$	0	0
$766$	6.70625	0.242307
$767$	13.0406	0.470869
$768$	−6.09013	−0.219759
$769$	−22.8019	−0.822258	−0.411129	−	0.911577i	$-0.634865\pi$
$769$	−22.8019	−0.822258	−0.411129	+	0.911577i	$0.634865\pi$
$770$	0	0
$771$	−6.55174	−0.235955
$772$	18.8887	0.679819
$773$	−16.3450	−0.587888	−0.293944	−	0.955823i	$-0.594968\pi$
$773$	−16.3450	−0.587888	−0.293944	+	0.955823i	$0.594968\pi$
$774$	−6.56488	−0.235970
$775$	0	0
$776$	33.6311	1.20729
$777$	16.0512	0.575832
$778$	−14.0316	−0.503057
$779$	−11.8152	−0.423322
$780$	0	0
$781$	3.18830	0.114086
$782$	0.153997	0.00550692
$783$	−5.99947	−0.214404
$784$	14.7894	0.528193
$785$	0	0
$786$	1.40538	0.0501282
$787$	13.7167	0.488947	0.244474	−	0.969656i	$-0.421385\pi$
$787$	13.7167	0.488947	0.244474	+	0.969656i	$0.421385\pi$
$788$	−25.1993	−0.897689
$789$	−12.6698	−0.451056
$790$	0	0
$791$	−64.6759	−2.29961
$792$	−1.03044	−0.0366150
$793$	−14.9596	−0.531230
$794$	16.3590	0.580561
$795$	0	0
$796$	24.7502	0.877249
$797$	21.5580	0.763624	0.381812	−	0.924240i	$-0.375300\pi$
$797$	21.5580	0.763624	0.381812	+	0.924240i	$0.375300\pi$
$798$	−12.1531	−0.430216
$799$	0.268198	0.00948816
$800$	0	0
$801$	5.44520	0.192397
$802$	−20.5951	−0.727237
$803$	−3.30267	−0.116549
$804$	−3.87407	−0.136628
$805$	0	0
$806$	−4.43160	−0.156097
$807$	−25.8223	−0.908989
$808$	11.5393	0.405950
$809$	−44.3785	−1.56026	−0.780132	−	0.625614i	$-0.784848\pi$
$809$	−44.3785	−1.56026	−0.780132	+	0.625614i	$0.784848\pi$
$810$	0	0
$811$	16.2341	0.570055	0.285028	−	0.958519i	$-0.407997\pi$
$811$	16.2341	0.570055	0.285028	+	0.958519i	$0.407997\pi$
$812$	−37.5146	−1.31650
$813$	5.47377	0.191974
$814$	−1.18761	−0.0416256
$815$	0	0
$816$	0.513638	0.0179809
$817$	−56.1479	−1.96437
$818$	0.836742	0.0292560
$819$	−7.17309	−0.250648
$820$	0	0
$821$	−14.9198	−0.520703	−0.260352	−	0.965514i	$-0.583838\pi$
$821$	−14.9198	−0.520703	−0.260352	+	0.965514i	$0.583838\pi$
$822$	3.73814	0.130383
$823$	39.6884	1.38345	0.691725	−	0.722161i	$-0.256851\pi$
$823$	39.6884	1.38345	0.691725	+	0.722161i	$0.256851\pi$
$824$	−1.38600	−0.0482838
$825$	0	0
$826$	16.2879	0.566728
$827$	−2.12751	−0.0739807	−0.0369903	−	0.999316i	$-0.511777\pi$
$827$	−2.12751	−0.0739807	−0.0369903	+	0.999316i	$0.511777\pi$
$828$	1.53766	0.0534373
$829$	10.0350	0.348529	0.174265	−	0.984699i	$-0.444245\pi$
$829$	10.0350	0.348529	0.174265	+	0.984699i	$0.444245\pi$
$830$	0	0
$831$	3.97637	0.137939
$832$	−0.808863	−0.0280423
$833$	2.07111	0.0717598
$834$	−5.97397	−0.206862
$835$	0	0
$836$	−3.95695	−0.136854
$837$	3.89535	0.134643
$838$	19.8476	0.685625
$839$	22.6245	0.781086	0.390543	−	0.920585i	$-0.372287\pi$
$839$	22.6245	0.781086	0.390543	+	0.920585i	$0.372287\pi$
$840$	0	0
$841$	6.99366	0.241161
$842$	−0.0528492	−0.00182130
$843$	3.44181	0.118542
$844$	−24.1624	−0.831704
$845$	0	0
$846$	−0.608551	−0.0209224
$847$	41.3716	1.42155
$848$	−8.47922	−0.291178
$849$	8.49732	0.291627
$850$	0	0
$851$	3.94710	0.135305
$852$	11.1378	0.381574
$853$	−13.8042	−0.472646	−0.236323	−	0.971674i	$-0.575942\pi$
$853$	−13.8042	−0.472646	−0.236323	+	0.971674i	$0.575942\pi$
$854$	−18.6847	−0.639377
$855$	0	0
$856$	34.1181	1.16613
$857$	−30.9407	−1.05692	−0.528458	−	0.848960i	$-0.677230\pi$
$857$	−30.9407	−1.05692	−0.528458	+	0.848960i	$0.677230\pi$
$858$	0.530730	0.0181188
$859$	15.0356	0.513008	0.256504	−	0.966543i	$-0.417429\pi$
$859$	15.0356	0.513008	0.256504	+	0.966543i	$0.417429\pi$
$860$	0	0
$861$	−8.71014	−0.296841
$862$	−19.1765	−0.653156
$863$	−42.0639	−1.43187	−0.715935	−	0.698167i	$-0.753999\pi$
$863$	−42.0639	−1.43187	−0.715935	+	0.698167i	$0.753999\pi$
$864$	−5.58313	−0.189942
$865$	0	0
$866$	5.78187	0.196476
$867$	−16.9281	−0.574907
$868$	24.3575	0.826748
$869$	−0.835676	−0.0283484
$870$	0	0
$871$	4.44413	0.150584
$872$	2.58837	0.0876532
$873$	15.2257	0.515313
$874$	−2.98855	−0.101089
$875$	0	0
$876$	−11.5373	−0.389810
$877$	−42.8035	−1.44537	−0.722685	−	0.691177i	$-0.757092\pi$
$877$	−42.8035	−1.44537	−0.722685	+	0.691177i	$0.757092\pi$
$878$	9.18744	0.310061
$879$	4.15414	0.140116
$880$	0	0
$881$	25.2644	0.851181	0.425590	−	0.904916i	$-0.360066\pi$
$881$	25.2644	0.851181	0.425590	+	0.904916i	$0.360066\pi$
$882$	−4.69943	−0.158238
$883$	−29.7374	−1.00074	−0.500372	−	0.865811i	$-0.666803\pi$
$883$	−29.7374	−1.00074	−0.500372	+	0.865811i	$0.666803\pi$
$884$	−0.817094	−0.0274818
$885$	0	0
$886$	−0.211063	−0.00709080
$887$	−47.6589	−1.60023	−0.800115	−	0.599846i	$-0.795228\pi$
$887$	−47.6589	−1.60023	−0.800115	+	0.599846i	$0.795228\pi$
$888$	−9.24020	−0.310081
$889$	−55.8460	−1.87301
$890$	0	0
$891$	−0.466507	−0.0156286
$892$	−26.4418	−0.885337
$893$	−5.20479	−0.174172
$894$	−1.74408	−0.0583308
$895$	0	0
$896$	−43.8549	−1.46509
$897$	−1.76392	−0.0588955
$898$	−0.954421	−0.0318494
$899$	−23.3700	−0.779434
$900$	0	0
$901$	−1.18743	−0.0395592
$902$	0.644454	0.0214580
$903$	−41.3922	−1.37745
$904$	37.2321	1.23832
$905$	0	0
$906$	1.23010	0.0408674
$907$	29.0517	0.964645	0.482322	−	0.875994i	$-0.339793\pi$
$907$	29.0517	0.964645	0.482322	+	0.875994i	$0.339793\pi$
$908$	−40.4405	−1.34206
$909$	5.22414	0.173274
$910$	0	0
$911$	50.8722	1.68547	0.842736	−	0.538327i	$-0.180944\pi$
$911$	50.8722	1.68547	0.842736	+	0.538327i	$0.180944\pi$
$912$	−9.96792	−0.330071
$913$	4.36704	0.144528
$914$	5.76800	0.190788
$915$	0	0
$916$	5.45133	0.180117
$917$	8.86105	0.292618
$918$	−0.163212	−0.00538680
$919$	4.08686	0.134813	0.0674065	−	0.997726i	$-0.478528\pi$
$919$	4.08686	0.134813	0.0674065	+	0.997726i	$0.478528\pi$
$920$	0	0
$921$	−11.9138	−0.392574
$922$	−14.1376	−0.465597
$923$	−12.7767	−0.420550
$924$	−2.91706	−0.0959643
$925$	0	0
$926$	0.120034	0.00394457
$927$	−0.627482	−0.0206092
$928$	33.4958	1.09956
$929$	0.777492	0.0255087	0.0127543	−	0.999919i	$-0.495940\pi$
$929$	0.777492	0.0255087	0.0127543	+	0.999919i	$0.495940\pi$
$930$	0	0
$931$	−40.1931	−1.31728
$932$	19.7783	0.647860
$933$	−27.9286	−0.914341
$934$	−6.03384	−0.197433
$935$	0	0
$936$	4.12935	0.134972
$937$	20.5608	0.671691	0.335846	−	0.941917i	$-0.390978\pi$
$937$	20.5608	0.671691	0.335846	+	0.941917i	$0.390978\pi$
$938$	5.55078	0.181239
$939$	−2.90432	−0.0947789
$940$	0	0
$941$	−34.5193	−1.12530	−0.562648	−	0.826697i	$-0.690217\pi$
$941$	−34.5193	−1.12530	−0.562648	+	0.826697i	$0.690217\pi$
$942$	−2.13570	−0.0695848
$943$	−2.14189	−0.0697496
$944$	13.3592	0.434806
$945$	0	0
$946$	3.06257	0.0995727
$947$	0.533102	0.0173235	0.00866175	−	0.999962i	$-0.497243\pi$
$947$	0.533102	0.0173235	0.00866175	+	0.999962i	$0.497243\pi$
$948$	−2.91930	−0.0948144
$949$	13.2350	0.429627
$950$	0	0
$951$	−3.00003	−0.0972826
$952$	−2.27304	−0.0736696
$953$	−20.2379	−0.655571	−0.327785	−	0.944752i	$-0.606302\pi$
$953$	−20.2379	−0.655571	−0.327785	+	0.944752i	$0.606302\pi$
$954$	2.69433	0.0872322
$955$	0	0
$956$	−14.0574	−0.454649
$957$	2.79880	0.0904723
$958$	−21.0529	−0.680188
$959$	23.5693	0.761093
$960$	0	0
$961$	−15.8263	−0.510525
$962$	4.75918	0.153442
$963$	15.4462	0.497746
$964$	−3.09229	−0.0995958
$965$	0	0
$966$	−2.20316	−0.0708854
$967$	38.1283	1.22612	0.613062	−	0.790034i	$-0.289937\pi$
$967$	38.1283	1.22612	0.613062	+	0.790034i	$0.289937\pi$
$968$	−23.8165	−0.765491
$969$	−1.39591	−0.0448432
$970$	0	0
$971$	−47.4486	−1.52270	−0.761350	−	0.648341i	$-0.775463\pi$
$971$	−47.4486	−1.52270	−0.761350	+	0.648341i	$0.775463\pi$
$972$	−1.62967	−0.0522716
$973$	−37.6665	−1.20753
$974$	6.12726	0.196330
$975$	0	0
$976$	−15.3251	−0.490544
$977$	5.98436	0.191457	0.0957284	−	0.995407i	$-0.469482\pi$
$977$	5.98436	0.191457	0.0957284	+	0.995407i	$0.469482\pi$
$978$	−12.7868	−0.408878
$979$	−2.54023	−0.0811860
$980$	0	0
$981$	1.17182	0.0374135
$982$	16.3924	0.523102
$983$	8.11340	0.258777	0.129389	−	0.991594i	$-0.458699\pi$
$983$	8.11340	0.258777	0.129389	+	0.991594i	$0.458699\pi$
$984$	5.01418	0.159846
$985$	0	0
$986$	0.979185	0.0311836
$987$	−3.83697	−0.122132
$988$	15.8569	0.504477
$989$	−10.1787	−0.323663
$990$	0	0
$991$	−39.6442	−1.25934	−0.629669	−	0.776864i	$-0.716809\pi$
$991$	−39.6442	−1.25934	−0.629669	+	0.776864i	$0.716809\pi$
$992$	−21.7482	−0.690507
$993$	5.74085	0.182180
$994$	−15.9583	−0.506165
$995$	0	0
$996$	15.2555	0.483389
$997$	7.99566	0.253225	0.126612	−	0.991952i	$-0.459590\pi$
$997$	7.99566	0.253225	0.126612	+	0.991952i	$0.459590\pi$
$998$	8.35316	0.264415
$999$	−4.18329	−0.132353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.z.1.4	✓	7
5.4	even	2		3525.2.a.ba.1.4	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.z.1.4	✓	7	1.1	even	1	trivial
3525.2.a.ba.1.4	yes	7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.608551 q^{2} +1.00000 q^{3} -1.62967 q^{4} -0.608551 q^{6} -3.83697 q^{7} +2.20884 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.608551 q^{2} +1.00000 q^{3} -1.62967 q^{4} -0.608551 q^{6} -3.83697 q^{7} +2.20884 q^{8} +1.00000 q^{9} -0.466507 q^{11} -1.62967 q^{12} +1.86947 q^{13} +2.33499 q^{14} +1.91514 q^{16} +0.268198 q^{17} -0.608551 q^{18} -5.20479 q^{19} -3.83697 q^{21} +0.283893 q^{22} -0.943541 q^{23} +2.20884 q^{24} -1.13767 q^{26} +1.00000 q^{27} +6.25298 q^{28} -5.99947 q^{29} +3.89535 q^{31} -5.58313 q^{32} -0.466507 q^{33} -0.163212 q^{34} -1.62967 q^{36} -4.18329 q^{37} +3.16738 q^{38} +1.86947 q^{39} +2.27006 q^{41} +2.33499 q^{42} +10.7877 q^{43} +0.760251 q^{44} +0.574192 q^{46} +1.00000 q^{47} +1.91514 q^{48} +7.72234 q^{49} +0.268198 q^{51} -3.04661 q^{52} -4.42746 q^{53} -0.608551 q^{54} -8.47523 q^{56} -5.20479 q^{57} +3.65098 q^{58} +6.97557 q^{59} -8.00205 q^{61} -2.37052 q^{62} -3.83697 q^{63} -0.432670 q^{64} +0.283893 q^{66} +2.37722 q^{67} -0.437073 q^{68} -0.943541 q^{69} -6.83440 q^{71} +2.20884 q^{72} +7.07956 q^{73} +2.54574 q^{74} +8.48206 q^{76} +1.78998 q^{77} -1.13767 q^{78} +1.79135 q^{79} +1.00000 q^{81} -1.38145 q^{82} -9.36113 q^{83} +6.25298 q^{84} -6.56488 q^{86} -5.99947 q^{87} -1.03044 q^{88} +5.44520 q^{89} -7.17309 q^{91} +1.53766 q^{92} +3.89535 q^{93} -0.608551 q^{94} -5.58313 q^{96} +15.2257 q^{97} -4.69943 q^{98} -0.466507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9} + 5 q^{12} + 5 q^{13} + 7 q^{14} + 9 q^{16} + 2 q^{17} - q^{18} - 13 q^{19} + 7 q^{21} - 14 q^{22} + 6 q^{23} + 6 q^{24} + 7 q^{27} + 30 q^{28} + 9 q^{29} + 5 q^{31} + 26 q^{32} - 8 q^{34} + 5 q^{36} - 5 q^{37} - 2 q^{38} + 5 q^{39} + 18 q^{41} + 7 q^{42} + 14 q^{43} + 17 q^{44} - 27 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} + 2 q^{51} - 3 q^{52} + 20 q^{53} - q^{54} + 17 q^{56} - 13 q^{57} + 37 q^{58} + 10 q^{59} - 8 q^{61} - 6 q^{62} + 7 q^{63} + 18 q^{64} - 14 q^{66} + 4 q^{67} + 10 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} + 4 q^{73} - 25 q^{74} - 66 q^{76} + 6 q^{77} - 5 q^{79} + 7 q^{81} - 29 q^{82} + 52 q^{83} + 30 q^{84} - 17 q^{86} + 9 q^{87} + 26 q^{88} + 32 q^{89} - 26 q^{91} - 17 q^{92} + 5 q^{93} - q^{94} + 26 q^{96} - 12 q^{97} + 40 q^{98}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9 + 5 * q^12 + 5 * q^13 + 7 * q^14 + 9 * q^16 + 2 * q^17 - q^18 - 13 * q^19 + 7 * q^21 - 14 * q^22 + 6 * q^23 + 6 * q^24 + 7 * q^27 + 30 * q^28 + 9 * q^29 + 5 * q^31 + 26 * q^32 - 8 * q^34 + 5 * q^36 - 5 * q^37 - 2 * q^38 + 5 * q^39 + 18 * q^41 + 7 * q^42 + 14 * q^43 + 17 * q^44 - 27 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 + 2 * q^51 - 3 * q^52 + 20 * q^53 - q^54 + 17 * q^56 - 13 * q^57 + 37 * q^58 + 10 * q^59 - 8 * q^61 - 6 * q^62 + 7 * q^63 + 18 * q^64 - 14 * q^66 + 4 * q^67 + 10 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 + 4 * q^73 - 25 * q^74 - 66 * q^76 + 6 * q^77 - 5 * q^79 + 7 * q^81 - 29 * q^82 + 52 * q^83 + 30 * q^84 - 17 * q^86 + 9 * q^87 + 26 * q^88 + 32 * q^89 - 26 * q^91 - 17 * q^92 + 5 * q^93 - q^94 + 26 * q^96 - 12 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more