LMFDB - Embedded newform 4025.2.a.z.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.744662$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.744662 q^{2} +1.85918 q^{3} -1.44548 q^{4} -1.38446 q^{6} -1.00000 q^{7} +2.56572 q^{8} +0.456544 q^{9} +O(q^{10})$	\(q-0.744662 q^{2} +1.85918 q^{3} -1.44548 q^{4} -1.38446 q^{6} -1.00000 q^{7} +2.56572 q^{8} +0.456544 q^{9} -4.15056 q^{11} -2.68740 q^{12} +4.70829 q^{13} +0.744662 q^{14} +0.980365 q^{16} +7.26493 q^{17} -0.339971 q^{18} -7.26457 q^{19} -1.85918 q^{21} +3.09076 q^{22} -1.00000 q^{23} +4.77013 q^{24} -3.50609 q^{26} -4.72874 q^{27} +1.44548 q^{28} +6.03544 q^{29} -6.07044 q^{31} -5.86147 q^{32} -7.71663 q^{33} -5.40992 q^{34} -0.659924 q^{36} -2.81843 q^{37} +5.40965 q^{38} +8.75355 q^{39} -9.74872 q^{41} +1.38446 q^{42} +10.7560 q^{43} +5.99954 q^{44} +0.744662 q^{46} -9.52192 q^{47} +1.82267 q^{48} +1.00000 q^{49} +13.5068 q^{51} -6.80573 q^{52} +2.72336 q^{53} +3.52131 q^{54} -2.56572 q^{56} -13.5061 q^{57} -4.49436 q^{58} +0.216254 q^{59} -5.26318 q^{61} +4.52042 q^{62} -0.456544 q^{63} +2.40409 q^{64} +5.74628 q^{66} +12.6060 q^{67} -10.5013 q^{68} -1.85918 q^{69} +1.44888 q^{71} +1.17136 q^{72} +11.1840 q^{73} +2.09877 q^{74} +10.5008 q^{76} +4.15056 q^{77} -6.51844 q^{78} -3.55944 q^{79} -10.1612 q^{81} +7.25950 q^{82} -10.0255 q^{83} +2.68740 q^{84} -8.00961 q^{86} +11.2210 q^{87} -10.6492 q^{88} +2.63238 q^{89} -4.70829 q^{91} +1.44548 q^{92} -11.2860 q^{93} +7.09061 q^{94} -10.8975 q^{96} -10.8731 q^{97} -0.744662 q^{98} -1.89491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * 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 $

$2$	−0.744662	−0.526556	−0.263278	−	0.964720i	$-0.584804\pi$
$2$	−0.744662	−0.526556	−0.263278	+	0.964720i	$0.584804\pi$
$3$	1.85918	1.07340	0.536699	−	0.843774i	$-0.319671\pi$
$3$	1.85918	1.07340	0.536699	+	0.843774i	$0.319671\pi$
$4$	−1.44548	−0.722739
$5$	0	0
$5$	0	0
$6$	−1.38446	−0.565203
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.56572	0.907118
$9$	0.456544	0.152181
$10$	0	0
$11$	−4.15056	−1.25144	−0.625720	−	0.780048i	$-0.715195\pi$
$11$	−4.15056	−1.25144	−0.625720	+	0.780048i	$0.715195\pi$
$12$	−2.68740	−0.775786
$13$	4.70829	1.30584	0.652922	−	0.757425i	$-0.273543\pi$
$13$	4.70829	1.30584	0.652922	+	0.757425i	$0.273543\pi$
$14$	0.744662	0.199019
$15$	0	0
$16$	0.980365	0.245091
$17$	7.26493	1.76201	0.881003	−	0.473111i	$-0.156869\pi$
$17$	7.26493	1.76201	0.881003	+	0.473111i	$0.156869\pi$
$18$	−0.339971	−0.0801319
$19$	−7.26457	−1.66661	−0.833303	−	0.552816i	$-0.813553\pi$
$19$	−7.26457	−1.66661	−0.833303	+	0.552816i	$0.813553\pi$
$20$	0	0
$21$	−1.85918	−0.405706
$22$	3.09076	0.658953
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	4.77013	0.973698
$25$	0	0
$26$	−3.50609	−0.687600
$27$	−4.72874	−0.910046
$28$	1.44548	0.273170
$29$	6.03544	1.12075	0.560377	−	0.828238i	$-0.310656\pi$
$29$	6.03544	1.12075	0.560377	+	0.828238i	$0.310656\pi$
$30$	0	0
$31$	−6.07044	−1.09028	−0.545141	−	0.838344i	$-0.683524\pi$
$31$	−6.07044	−1.09028	−0.545141	+	0.838344i	$0.683524\pi$
$32$	−5.86147	−1.03617
$33$	−7.71663	−1.34329
$34$	−5.40992	−0.927794
$35$	0	0
$36$	−0.659924	−0.109987
$37$	−2.81843	−0.463346	−0.231673	−	0.972794i	$-0.574420\pi$
$37$	−2.81843	−0.463346	−0.231673	+	0.972794i	$0.574420\pi$
$38$	5.40965	0.877561
$39$	8.75355	1.40169
$40$	0	0
$41$	−9.74872	−1.52249	−0.761247	−	0.648462i	$-0.775413\pi$
$41$	−9.74872	−1.52249	−0.761247	+	0.648462i	$0.775413\pi$
$42$	1.38446	0.213627
$43$	10.7560	1.64028	0.820140	−	0.572163i	$-0.193896\pi$
$43$	10.7560	1.64028	0.820140	+	0.572163i	$0.193896\pi$
$44$	5.99954	0.904465
$45$	0	0
$46$	0.744662	0.109794
$47$	−9.52192	−1.38892	−0.694458	−	0.719534i	$-0.744356\pi$
$47$	−9.52192	−1.38892	−0.694458	+	0.719534i	$0.744356\pi$
$48$	1.82267	0.263080
$49$	1.00000	0.142857
$50$	0	0
$51$	13.5068	1.89133
$52$	−6.80573	−0.943785
$53$	2.72336	0.374082	0.187041	−	0.982352i	$-0.440110\pi$
$53$	2.72336	0.374082	0.187041	+	0.982352i	$0.440110\pi$
$54$	3.52131	0.479190
$55$	0	0
$56$	−2.56572	−0.342858
$57$	−13.5061	−1.78893
$58$	−4.49436	−0.590139
$59$	0.216254	0.0281539	0.0140770	−	0.999901i	$-0.495519\pi$
$59$	0.216254	0.0281539	0.0140770	+	0.999901i	$0.495519\pi$
$60$	0	0
$61$	−5.26318	−0.673881	−0.336941	−	0.941526i	$-0.609392\pi$
$61$	−5.26318	−0.673881	−0.336941	+	0.941526i	$0.609392\pi$
$62$	4.52042	0.574095
$63$	−0.456544	−0.0575191
$64$	2.40409	0.300511
$65$	0	0
$66$	5.74628	0.707318
$67$	12.6060	1.54007	0.770034	−	0.638003i	$-0.220239\pi$
$67$	12.6060	1.54007	0.770034	+	0.638003i	$0.220239\pi$
$68$	−10.5013	−1.27347
$69$	−1.85918	−0.223819
$70$	0	0
$71$	1.44888	0.171950	0.0859751	−	0.996297i	$-0.472599\pi$
$71$	1.44888	0.171950	0.0859751	+	0.996297i	$0.472599\pi$
$72$	1.17136	0.138046
$73$	11.1840	1.30899	0.654494	−	0.756067i	$-0.272882\pi$
$73$	11.1840	1.30899	0.654494	+	0.756067i	$0.272882\pi$
$74$	2.09877	0.243978
$75$	0	0
$76$	10.5008	1.20452
$77$	4.15056	0.473000
$78$	−6.51844	−0.738068
$79$	−3.55944	−0.400469	−0.200234	−	0.979748i	$-0.564170\pi$
$79$	−3.55944	−0.400469	−0.200234	+	0.979748i	$0.564170\pi$
$80$	0	0
$81$	−10.1612	−1.12902
$82$	7.25950	0.801678
$83$	−10.0255	−1.10045	−0.550223	−	0.835018i	$-0.685457\pi$
$83$	−10.0255	−1.10045	−0.550223	+	0.835018i	$0.685457\pi$
$84$	2.68740	0.293220
$85$	0	0
$86$	−8.00961	−0.863698
$87$	11.2210	1.20301
$88$	−10.6492	−1.13520
$89$	2.63238	0.279031	0.139516	−	0.990220i	$-0.455445\pi$
$89$	2.63238	0.279031	0.139516	+	0.990220i	$0.455445\pi$
$90$	0	0
$91$	−4.70829	−0.493563
$92$	1.44548	0.150702
$93$	−11.2860	−1.17031
$94$	7.09061	0.731341
$95$	0	0
$96$	−10.8975	−1.11222
$97$	−10.8731	−1.10400	−0.552000	−	0.833844i	$-0.686135\pi$
$97$	−10.8731	−1.10400	−0.552000	+	0.833844i	$0.686135\pi$
$98$	−0.744662	−0.0752222
$99$	−1.89491	−0.190446
$100$	0	0
$101$	1.05038	0.104516	0.0522582	−	0.998634i	$-0.483358\pi$
$101$	1.05038	0.104516	0.0522582	+	0.998634i	$0.483358\pi$
$102$	−10.0580	−0.995891
$103$	−9.97214	−0.982584	−0.491292	−	0.870995i	$-0.663475\pi$
$103$	−9.97214	−0.982584	−0.491292	+	0.870995i	$0.663475\pi$
$104$	12.0801	1.18456
$105$	0	0
$106$	−2.02798	−0.196975
$107$	−1.57397	−0.152161	−0.0760806	−	0.997102i	$-0.524241\pi$
$107$	−1.57397	−0.152161	−0.0760806	+	0.997102i	$0.524241\pi$
$108$	6.83529	0.657726
$109$	−6.36653	−0.609803	−0.304902	−	0.952384i	$-0.598624\pi$
$109$	−6.36653	−0.609803	−0.304902	+	0.952384i	$0.598624\pi$
$110$	0	0
$111$	−5.23996	−0.497355
$112$	−0.980365	−0.0926358
$113$	−4.95842	−0.466449	−0.233225	−	0.972423i	$-0.574928\pi$
$113$	−4.95842	−0.466449	−0.233225	+	0.972423i	$0.574928\pi$
$114$	10.0575	0.941972
$115$	0	0
$116$	−8.72410	−0.810013
$117$	2.14954	0.198725
$118$	−0.161036	−0.0148246
$119$	−7.26493	−0.665975
$120$	0	0
$121$	6.22713	0.566102
$122$	3.91929	0.354836
$123$	−18.1246	−1.63424
$124$	8.77469	0.787990
$125$	0	0
$126$	0.339971	0.0302870
$127$	−12.3438	−1.09534	−0.547669	−	0.836695i	$-0.684484\pi$
$127$	−12.3438	−1.09534	−0.547669	+	0.836695i	$0.684484\pi$
$128$	9.93272	0.877936
$129$	19.9974	1.76067
$130$	0	0
$131$	−16.2576	−1.42043	−0.710215	−	0.703985i	$-0.751402\pi$
$131$	−16.2576	−1.42043	−0.710215	+	0.703985i	$0.751402\pi$
$132$	11.1542	0.970850
$133$	7.26457	0.629918
$134$	−9.38721	−0.810931
$135$	0	0
$136$	18.6398	1.59835
$137$	−4.78624	−0.408916	−0.204458	−	0.978875i	$-0.565543\pi$
$137$	−4.78624	−0.408916	−0.204458	+	0.978875i	$0.565543\pi$
$138$	1.38446	0.117853
$139$	−22.1041	−1.87484	−0.937421	−	0.348199i	$-0.886793\pi$
$139$	−22.1041	−1.87484	−0.937421	+	0.348199i	$0.886793\pi$
$140$	0	0
$141$	−17.7030	−1.49086
$142$	−1.07892	−0.0905413
$143$	−19.5420	−1.63419
$144$	0.447579	0.0372983
$145$	0	0
$146$	−8.32829	−0.689255
$147$	1.85918	0.153342
$148$	4.07397	0.334879
$149$	−7.94083	−0.650538	−0.325269	−	0.945622i	$-0.605455\pi$
$149$	−7.94083	−0.650538	−0.325269	+	0.945622i	$0.605455\pi$
$150$	0	0
$151$	0.143654	0.0116904	0.00584519	−	0.999983i	$-0.498139\pi$
$151$	0.143654	0.0116904	0.00584519	+	0.999983i	$0.498139\pi$
$152$	−18.6388	−1.51181
$153$	3.31676	0.268144
$154$	−3.09076	−0.249061
$155$	0	0
$156$	−12.6531	−1.01306
$157$	−0.540011	−0.0430976	−0.0215488	−	0.999768i	$-0.506860\pi$
$157$	−0.540011	−0.0430976	−0.0215488	+	0.999768i	$0.506860\pi$
$158$	2.65058	0.210869
$159$	5.06321	0.401539
$160$	0	0
$161$	1.00000	0.0788110
$162$	7.56666	0.594493
$163$	−23.4716	−1.83844	−0.919219	−	0.393746i	$-0.871179\pi$
$163$	−23.4716	−1.83844	−0.919219	+	0.393746i	$0.871179\pi$
$164$	14.0916	1.10037
$165$	0	0
$166$	7.46564	0.579446
$167$	11.9329	0.923398	0.461699	−	0.887037i	$-0.347240\pi$
$167$	11.9329	0.923398	0.461699	+	0.887037i	$0.347240\pi$
$168$	−4.77013	−0.368023
$169$	9.16800	0.705231
$170$	0	0
$171$	−3.31659	−0.253626
$172$	−15.5476	−1.18549
$173$	18.5314	1.40891	0.704457	−	0.709747i	$-0.251191\pi$
$173$	18.5314	1.40891	0.704457	+	0.709747i	$0.251191\pi$
$174$	−8.35583	−0.633453
$175$	0	0
$176$	−4.06906	−0.306717
$177$	0.402055	0.0302203
$178$	−1.96023	−0.146925
$179$	−6.83115	−0.510584	−0.255292	−	0.966864i	$-0.582172\pi$
$179$	−6.83115	−0.510584	−0.255292	+	0.966864i	$0.582172\pi$
$180$	0	0
$181$	16.3130	1.21254	0.606269	−	0.795260i	$-0.292665\pi$
$181$	16.3130	1.21254	0.606269	+	0.795260i	$0.292665\pi$
$182$	3.50609	0.259888
$183$	−9.78519	−0.723342
$184$	−2.56572	−0.189147
$185$	0	0
$186$	8.40428	0.616231
$187$	−30.1535	−2.20504
$188$	13.7637	1.00382
$189$	4.72874	0.343965
$190$	0	0
$191$	10.7658	0.778987	0.389494	−	0.921029i	$-0.372650\pi$
$191$	10.7658	0.778987	0.389494	+	0.921029i	$0.372650\pi$
$192$	4.46963	0.322568
$193$	−1.35105	−0.0972508	−0.0486254	−	0.998817i	$-0.515484\pi$
$193$	−1.35105	−0.0972508	−0.0486254	+	0.998817i	$0.515484\pi$
$194$	8.09682	0.581318
$195$	0	0
$196$	−1.44548	−0.103248
$197$	−14.2786	−1.01730	−0.508652	−	0.860972i	$-0.669856\pi$
$197$	−14.2786	−1.01730	−0.508652	+	0.860972i	$0.669856\pi$
$198$	1.41107	0.100280
$199$	15.7839	1.11889	0.559444	−	0.828868i	$-0.311015\pi$
$199$	15.7839	1.11889	0.559444	+	0.828868i	$0.311015\pi$
$200$	0	0
$201$	23.4368	1.65310
$202$	−0.782176	−0.0550337
$203$	−6.03544	−0.423605
$204$	−19.5238	−1.36694
$205$	0	0
$206$	7.42587	0.517385
$207$	−0.456544	−0.0317320
$208$	4.61584	0.320051
$209$	30.1520	2.08566
$210$	0	0
$211$	−5.30381	−0.365129	−0.182565	−	0.983194i	$-0.558440\pi$
$211$	−5.30381	−0.365129	−0.182565	+	0.983194i	$0.558440\pi$
$212$	−3.93656	−0.270364
$213$	2.69372	0.184571
$214$	1.17207	0.0801214
$215$	0	0
$216$	−12.1326	−0.825519
$217$	6.07044	0.412088
$218$	4.74091	0.321095
$219$	20.7930	1.40506
$220$	0	0
$221$	34.2054	2.30091
$222$	3.90200	0.261885
$223$	−13.0993	−0.877194	−0.438597	−	0.898684i	$-0.644524\pi$
$223$	−13.0993	−0.877194	−0.438597	+	0.898684i	$0.644524\pi$
$224$	5.86147	0.391636
$225$	0	0
$226$	3.69235	0.245611
$227$	−26.6193	−1.76679	−0.883393	−	0.468633i	$-0.844747\pi$
$227$	−26.6193	−1.76679	−0.883393	+	0.468633i	$0.844747\pi$
$228$	19.5228	1.29293
$229$	−1.24875	−0.0825198	−0.0412599	−	0.999148i	$-0.513137\pi$
$229$	−1.24875	−0.0825198	−0.0412599	+	0.999148i	$0.513137\pi$
$230$	0	0
$231$	7.71663	0.507717
$232$	15.4852	1.01666
$233$	−22.3736	−1.46574	−0.732870	−	0.680368i	$-0.761820\pi$
$233$	−22.3736	−1.46574	−0.732870	+	0.680368i	$0.761820\pi$
$234$	−1.60068	−0.104640
$235$	0	0
$236$	−0.312591	−0.0203479
$237$	−6.61764	−0.429862
$238$	5.40992	0.350673
$239$	−18.5309	−1.19866	−0.599331	−	0.800501i	$-0.704567\pi$
$239$	−18.5309	−1.19866	−0.599331	+	0.800501i	$0.704567\pi$
$240$	0	0
$241$	−15.6764	−1.00980	−0.504902	−	0.863177i	$-0.668471\pi$
$241$	−15.6764	−1.00980	−0.504902	+	0.863177i	$0.668471\pi$
$242$	−4.63710	−0.298084
$243$	−4.70526	−0.301843
$244$	7.60781	0.487040
$245$	0	0
$246$	13.4967	0.860519
$247$	−34.2037	−2.17633
$248$	−15.5750	−0.989015
$249$	−18.6393	−1.18122
$250$	0	0
$251$	−14.5092	−0.915811	−0.457905	−	0.889001i	$-0.651400\pi$
$251$	−14.5092	−0.915811	−0.457905	+	0.889001i	$0.651400\pi$
$252$	0.659924	0.0415713
$253$	4.15056	0.260943
$254$	9.19198	0.576756
$255$	0	0
$256$	−12.2047	−0.762793
$257$	−1.30270	−0.0812601	−0.0406301	−	0.999174i	$-0.512937\pi$
$257$	−1.30270	−0.0812601	−0.0406301	+	0.999174i	$0.512937\pi$
$258$	−14.8913	−0.927091
$259$	2.81843	0.175128
$260$	0	0
$261$	2.75544	0.170558
$262$	12.1064	0.747935
$263$	−1.74599	−0.107662	−0.0538311	−	0.998550i	$-0.517143\pi$
$263$	−1.74599	−0.107662	−0.0538311	+	0.998550i	$0.517143\pi$
$264$	−19.7987	−1.21852
$265$	0	0
$266$	−5.40965	−0.331687
$267$	4.89406	0.299511
$268$	−18.2217	−1.11307
$269$	−17.1334	−1.04464	−0.522320	−	0.852750i	$-0.674933\pi$
$269$	−17.1334	−1.04464	−0.522320	+	0.852750i	$0.674933\pi$
$270$	0	0
$271$	−0.408764	−0.0248307	−0.0124153	−	0.999923i	$-0.503952\pi$
$271$	−0.408764	−0.0248307	−0.0124153	+	0.999923i	$0.503952\pi$
$272$	7.12229	0.431852
$273$	−8.75355	−0.529789
$274$	3.56413	0.215317
$275$	0	0
$276$	2.68740	0.161763
$277$	0.0866959	0.00520905	0.00260453	−	0.999997i	$-0.499171\pi$
$277$	0.0866959	0.00520905	0.00260453	+	0.999997i	$0.499171\pi$
$278$	16.4601	0.987208
$279$	−2.77142	−0.165921
$280$	0	0
$281$	−3.08401	−0.183977	−0.0919883	−	0.995760i	$-0.529322\pi$
$281$	−3.08401	−0.183977	−0.0919883	+	0.995760i	$0.529322\pi$
$282$	13.1827	0.785019
$283$	−15.3040	−0.909727	−0.454863	−	0.890561i	$-0.650312\pi$
$283$	−15.3040	−0.909727	−0.454863	+	0.890561i	$0.650312\pi$
$284$	−2.09432	−0.124275
$285$	0	0
$286$	14.5522	0.860490
$287$	9.74872	0.575449
$288$	−2.67602	−0.157686
$289$	35.7793	2.10466
$290$	0	0
$291$	−20.2151	−1.18503
$292$	−16.1662	−0.946057
$293$	10.4407	0.609952	0.304976	−	0.952360i	$-0.401352\pi$
$293$	10.4407	0.609952	0.304976	+	0.952360i	$0.401352\pi$
$294$	−1.38446	−0.0807433
$295$	0	0
$296$	−7.23128	−0.420310
$297$	19.6269	1.13887
$298$	5.91323	0.342544
$299$	−4.70829	−0.272287
$300$	0	0
$301$	−10.7560	−0.619967
$302$	−0.106974	−0.00615564
$303$	1.95284	0.112188
$304$	−7.12193	−0.408471
$305$	0	0
$306$	−2.46986	−0.141193
$307$	−3.04115	−0.173568	−0.0867839	−	0.996227i	$-0.527659\pi$
$307$	−3.04115	−0.173568	−0.0867839	+	0.996227i	$0.527659\pi$
$308$	−5.99954	−0.341856
$309$	−18.5400	−1.05470
$310$	0	0
$311$	−14.1387	−0.801730	−0.400865	−	0.916137i	$-0.631290\pi$
$311$	−14.1387	−0.801730	−0.400865	+	0.916137i	$0.631290\pi$
$312$	22.4591	1.27150
$313$	17.7801	1.00499	0.502494	−	0.864581i	$-0.332416\pi$
$313$	17.7801	1.00499	0.502494	+	0.864581i	$0.332416\pi$
$314$	0.402126	0.0226933
$315$	0	0
$316$	5.14510	0.289434
$317$	32.2109	1.80914	0.904571	−	0.426322i	$-0.140191\pi$
$317$	32.2109	1.80914	0.904571	+	0.426322i	$0.140191\pi$
$318$	−3.77038	−0.211432
$319$	−25.0505	−1.40256
$320$	0	0
$321$	−2.92629	−0.163329
$322$	−0.744662	−0.0414984
$323$	−52.7766	−2.93657
$324$	14.6878	0.815989
$325$	0	0
$326$	17.4784	0.968040
$327$	−11.8365	−0.654561
$328$	−25.0125	−1.38108
$329$	9.52192	0.524961
$330$	0	0
$331$	30.1088	1.65493	0.827466	−	0.561516i	$-0.189782\pi$
$331$	30.1088	1.65493	0.827466	+	0.561516i	$0.189782\pi$
$332$	14.4917	0.795336
$333$	−1.28673	−0.0705126
$334$	−8.88601	−0.486221
$335$	0	0
$336$	−1.82267	−0.0994350
$337$	20.7204	1.12871	0.564357	−	0.825531i	$-0.309124\pi$
$337$	20.7204	1.12871	0.564357	+	0.825531i	$0.309124\pi$
$338$	−6.82706	−0.371343
$339$	−9.21859	−0.500685
$340$	0	0
$341$	25.1957	1.36442
$342$	2.46974	0.133548
$343$	−1.00000	−0.0539949
$344$	27.5969	1.48793
$345$	0	0
$346$	−13.7996	−0.741872
$347$	23.1732	1.24400	0.622000	−	0.783017i	$-0.286320\pi$
$347$	23.1732	1.24400	0.622000	+	0.783017i	$0.286320\pi$
$348$	−16.2197	−0.869465
$349$	−18.1475	−0.971412	−0.485706	−	0.874122i	$-0.661437\pi$
$349$	−18.1475	−0.971412	−0.485706	+	0.874122i	$0.661437\pi$
$350$	0	0
$351$	−22.2643	−1.18838
$352$	24.3284	1.29671
$353$	18.6617	0.993262	0.496631	−	0.867962i	$-0.334570\pi$
$353$	18.6617	0.993262	0.496631	+	0.867962i	$0.334570\pi$
$354$	−0.299395	−0.0159127
$355$	0	0
$356$	−3.80504	−0.201667
$357$	−13.5068	−0.714856
$358$	5.08690	0.268851
$359$	−0.543738	−0.0286974	−0.0143487	−	0.999897i	$-0.504567\pi$
$359$	−0.543738	−0.0286974	−0.0143487	+	0.999897i	$0.504567\pi$
$360$	0	0
$361$	33.7740	1.77758
$362$	−12.1477	−0.638469
$363$	11.5773	0.607653
$364$	6.80573	0.356717
$365$	0	0
$366$	7.28666	0.380880
$367$	−9.03587	−0.471668	−0.235834	−	0.971793i	$-0.575782\pi$
$367$	−9.03587	−0.471668	−0.235834	+	0.971793i	$0.575782\pi$
$368$	−0.980365	−0.0511051
$369$	−4.45072	−0.231695
$370$	0	0
$371$	−2.72336	−0.141390
$372$	16.3137	0.845826
$373$	−22.3806	−1.15883	−0.579413	−	0.815034i	$-0.696718\pi$
$373$	−22.3806	−1.15883	−0.579413	+	0.815034i	$0.696718\pi$
$374$	22.4542	1.16108
$375$	0	0
$376$	−24.4306	−1.25991
$377$	28.4166	1.46353
$378$	−3.52131	−0.181117
$379$	37.1718	1.90939	0.954695	−	0.297587i	$-0.0961818\pi$
$379$	37.1718	1.90939	0.954695	+	0.297587i	$0.0961818\pi$
$380$	0	0
$381$	−22.9494	−1.17573
$382$	−8.01690	−0.410180
$383$	26.3267	1.34523	0.672615	−	0.739992i	$-0.265171\pi$
$383$	26.3267	1.34523	0.672615	+	0.739992i	$0.265171\pi$
$384$	18.4667	0.942374
$385$	0	0
$386$	1.00608	0.0512079
$387$	4.91060	0.249620
$388$	15.7169	0.797904
$389$	−3.91335	−0.198415	−0.0992075	−	0.995067i	$-0.531631\pi$
$389$	−3.91335	−0.198415	−0.0992075	+	0.995067i	$0.531631\pi$
$390$	0	0
$391$	−7.26493	−0.367403
$392$	2.56572	0.129588
$393$	−30.2257	−1.52468
$394$	10.6327	0.535667
$395$	0	0
$396$	2.73905	0.137643
$397$	−33.9665	−1.70473	−0.852364	−	0.522949i	$-0.824832\pi$
$397$	−33.9665	−1.70473	−0.852364	+	0.522949i	$0.824832\pi$
$398$	−11.7536	−0.589157
$399$	13.5061	0.676152
$400$	0	0
$401$	11.1790	0.558250	0.279125	−	0.960255i	$-0.409956\pi$
$401$	11.1790	0.558250	0.279125	+	0.960255i	$0.409956\pi$
$402$	−17.4525	−0.870451
$403$	−28.5814	−1.42374
$404$	−1.51830	−0.0755382
$405$	0	0
$406$	4.49436	0.223052
$407$	11.6980	0.579850
$408$	34.6546	1.71566
$409$	−15.9818	−0.790251	−0.395125	−	0.918627i	$-0.629299\pi$
$409$	−15.9818	−0.790251	−0.395125	+	0.918627i	$0.629299\pi$
$410$	0	0
$411$	−8.89847	−0.438929
$412$	14.4145	0.710152
$413$	−0.216254	−0.0106412
$414$	0.339971	0.0167087
$415$	0	0
$416$	−27.5975	−1.35308
$417$	−41.0954	−2.01245
$418$	−22.4531	−1.09822
$419$	−5.15949	−0.252058	−0.126029	−	0.992027i	$-0.540223\pi$
$419$	−5.15949	−0.252058	−0.126029	+	0.992027i	$0.540223\pi$
$420$	0	0
$421$	−27.9670	−1.36303	−0.681515	−	0.731804i	$-0.738679\pi$
$421$	−27.9670	−1.36303	−0.681515	+	0.731804i	$0.738679\pi$
$422$	3.94954	0.192261
$423$	−4.34717	−0.211367
$424$	6.98737	0.339337
$425$	0	0
$426$	−2.00591	−0.0971868
$427$	5.26318	0.254703
$428$	2.27514	0.109973
$429$	−36.3321	−1.75413
$430$	0	0
$431$	34.2057	1.64763	0.823814	−	0.566860i	$-0.191842\pi$
$431$	34.2057	1.64763	0.823814	+	0.566860i	$0.191842\pi$
$432$	−4.63589	−0.223044
$433$	36.1568	1.73758	0.868792	−	0.495178i	$-0.164897\pi$
$433$	36.1568	1.73758	0.868792	+	0.495178i	$0.164897\pi$
$434$	−4.52042	−0.216987
$435$	0	0
$436$	9.20268	0.440729
$437$	7.26457	0.347512
$438$	−15.4838	−0.739844
$439$	−9.87260	−0.471193	−0.235597	−	0.971851i	$-0.575704\pi$
$439$	−9.87260	−0.471193	−0.235597	+	0.971851i	$0.575704\pi$
$440$	0	0
$441$	0.456544	0.0217402
$442$	−25.4715	−1.21155
$443$	20.8167	0.989029	0.494514	−	0.869169i	$-0.335346\pi$
$443$	20.8167	0.989029	0.494514	+	0.869169i	$0.335346\pi$
$444$	7.57424	0.359458
$445$	0	0
$446$	9.75455	0.461892
$447$	−14.7634	−0.698286
$448$	−2.40409	−0.113582
$449$	−35.5720	−1.67875	−0.839374	−	0.543555i	$-0.817078\pi$
$449$	−35.5720	−1.67875	−0.839374	+	0.543555i	$0.817078\pi$
$450$	0	0
$451$	40.4626	1.90531
$452$	7.16729	0.337121
$453$	0.267078	0.0125484
$454$	19.8224	0.930311
$455$	0	0
$456$	−34.6529	−1.62277
$457$	−19.8689	−0.929428	−0.464714	−	0.885461i	$-0.653843\pi$
$457$	−19.8689	−0.929428	−0.464714	+	0.885461i	$0.653843\pi$
$458$	0.929898	0.0434513
$459$	−34.3540	−1.60351
$460$	0	0
$461$	17.5290	0.816407	0.408203	−	0.912891i	$-0.366155\pi$
$461$	17.5290	0.816407	0.408203	+	0.912891i	$0.366155\pi$
$462$	−5.74628	−0.267341
$463$	28.4419	1.32181	0.660903	−	0.750471i	$-0.270173\pi$
$463$	28.4419	1.32181	0.660903	+	0.750471i	$0.270173\pi$
$464$	5.91694	0.274687
$465$	0	0
$466$	16.6607	0.771794
$467$	1.22851	0.0568485	0.0284242	−	0.999596i	$-0.490951\pi$
$467$	1.22851	0.0568485	0.0284242	+	0.999596i	$0.490951\pi$
$468$	−3.10711	−0.143626
$469$	−12.6060	−0.582091
$470$	0	0
$471$	−1.00398	−0.0462608
$472$	0.554847	0.0255389
$473$	−44.6435	−2.05271
$474$	4.92790	0.226346
$475$	0	0
$476$	10.5013	0.481327
$477$	1.24333	0.0569283
$478$	13.7992	0.631162
$479$	−2.74343	−0.125351	−0.0626753	−	0.998034i	$-0.519963\pi$
$479$	−2.74343	−0.125351	−0.0626753	+	0.998034i	$0.519963\pi$
$480$	0	0
$481$	−13.2700	−0.605058
$482$	11.6736	0.531718
$483$	1.85918	0.0845955
$484$	−9.00118	−0.409144
$485$	0	0
$486$	3.50383	0.158937
$487$	5.70954	0.258724	0.129362	−	0.991597i	$-0.458707\pi$
$487$	5.70954	0.258724	0.129362	+	0.991597i	$0.458707\pi$
$488$	−13.5038	−0.611290
$489$	−43.6379	−1.97337
$490$	0	0
$491$	−7.15811	−0.323041	−0.161521	−	0.986869i	$-0.551640\pi$
$491$	−7.15811	−0.323041	−0.161521	+	0.986869i	$0.551640\pi$
$492$	26.1987	1.18113
$493$	43.8471	1.97477
$494$	25.4702	1.14596
$495$	0	0
$496$	−5.95124	−0.267219
$497$	−1.44888	−0.0649910
$498$	13.8800	0.621976
$499$	−25.0333	−1.12065	−0.560323	−	0.828274i	$-0.689323\pi$
$499$	−25.0333	−1.12065	−0.560323	+	0.828274i	$0.689323\pi$
$500$	0	0
$501$	22.1855	0.991173
$502$	10.8044	0.482225
$503$	35.6434	1.58926	0.794631	−	0.607093i	$-0.207664\pi$
$503$	35.6434	1.58926	0.794631	+	0.607093i	$0.207664\pi$
$504$	−1.17136	−0.0521766
$505$	0	0
$506$	−3.09076	−0.137401
$507$	17.0449	0.756993
$508$	17.8427	0.791643
$509$	−26.8573	−1.19043	−0.595215	−	0.803566i	$-0.702933\pi$
$509$	−26.8573	−1.19043	−0.595215	+	0.803566i	$0.702933\pi$
$510$	0	0
$511$	−11.1840	−0.494751
$512$	−10.7771	−0.476283
$513$	34.3523	1.51669
$514$	0.970070	0.0427880
$515$	0	0
$516$	−28.9058	−1.27251
$517$	39.5213	1.73814
$518$	−2.09877	−0.0922148
$519$	34.4531	1.51232
$520$	0	0
$521$	21.6994	0.950667	0.475333	−	0.879806i	$-0.342327\pi$
$521$	21.6994	0.950667	0.475333	+	0.879806i	$0.342327\pi$
$522$	−2.05187	−0.0898081
$523$	0.827420	0.0361805	0.0180903	−	0.999836i	$-0.494241\pi$
$523$	0.827420	0.0361805	0.0180903	+	0.999836i	$0.494241\pi$
$524$	23.4999	1.02660
$525$	0	0
$526$	1.30017	0.0566901
$527$	−44.1013	−1.92108
$528$	−7.56511	−0.329229
$529$	1.00000	0.0434783
$530$	0	0
$531$	0.0987295	0.00428450
$532$	−10.5008	−0.455267
$533$	−45.8998	−1.98814
$534$	−3.64442	−0.157709
$535$	0	0
$536$	32.3434	1.39702
$537$	−12.7003	−0.548059
$538$	12.7586	0.550061
$539$	−4.15056	−0.178777
$540$	0	0
$541$	−17.2428	−0.741326	−0.370663	−	0.928767i	$-0.620870\pi$
$541$	−17.2428	−0.741326	−0.370663	+	0.928767i	$0.620870\pi$
$542$	0.304391	0.0130747
$543$	30.3288	1.30154
$544$	−42.5832	−1.82574
$545$	0	0
$546$	6.51844	0.278963
$547$	7.51138	0.321163	0.160582	−	0.987023i	$-0.448663\pi$
$547$	7.51138	0.321163	0.160582	+	0.987023i	$0.448663\pi$
$548$	6.91840	0.295540
$549$	−2.40287	−0.102552
$550$	0	0
$551$	−43.8449	−1.86786
$552$	−4.77013	−0.203030
$553$	3.55944	0.151363
$554$	−0.0645592	−0.00274286
$555$	0	0
$556$	31.9509	1.35502
$557$	2.11176	0.0894783	0.0447391	−	0.998999i	$-0.485754\pi$
$557$	2.11176	0.0894783	0.0447391	+	0.998999i	$0.485754\pi$
$558$	2.06377	0.0873664
$559$	50.6425	2.14195
$560$	0	0
$561$	−56.0608	−2.36689
$562$	2.29655	0.0968739
$563$	−19.6348	−0.827507	−0.413753	−	0.910389i	$-0.635782\pi$
$563$	−19.6348	−0.827507	−0.413753	+	0.910389i	$0.635782\pi$
$564$	25.5892	1.07750
$565$	0	0
$566$	11.3963	0.479022
$567$	10.1612	0.426730
$568$	3.71741	0.155979
$569$	23.8823	1.00120	0.500599	−	0.865680i	$-0.333113\pi$
$569$	23.8823	1.00120	0.500599	+	0.865680i	$0.333113\pi$
$570$	0	0
$571$	22.2413	0.930768	0.465384	−	0.885109i	$-0.345916\pi$
$571$	22.2413	0.930768	0.465384	+	0.885109i	$0.345916\pi$
$572$	28.2476	1.18109
$573$	20.0156	0.836163
$574$	−7.25950	−0.303006
$575$	0	0
$576$	1.09757	0.0457321
$577$	−28.6886	−1.19432	−0.597161	−	0.802121i	$-0.703705\pi$
$577$	−28.6886	−1.19432	−0.597161	+	0.802121i	$0.703705\pi$
$578$	−26.6435	−1.10822
$579$	−2.51184	−0.104389
$580$	0	0
$581$	10.0255	0.415930
$582$	15.0534	0.623985
$583$	−11.3035	−0.468141
$584$	28.6950	1.18741
$585$	0	0
$586$	−7.77479	−0.321173
$587$	17.8802	0.737996	0.368998	−	0.929430i	$-0.379701\pi$
$587$	17.8802	0.737996	0.368998	+	0.929430i	$0.379701\pi$
$588$	−2.68740	−0.110827
$589$	44.0991	1.81707
$590$	0	0
$591$	−26.5464	−1.09197
$592$	−2.76309	−0.113562
$593$	−3.81144	−0.156517	−0.0782585	−	0.996933i	$-0.524936\pi$
$593$	−3.81144	−0.156517	−0.0782585	+	0.996933i	$0.524936\pi$
$594$	−14.6154	−0.599677
$595$	0	0
$596$	11.4783	0.470169
$597$	29.3450	1.20101
$598$	3.50609	0.143374
$599$	−39.2548	−1.60391	−0.801953	−	0.597387i	$-0.796206\pi$
$599$	−39.2548	−1.60391	−0.801953	+	0.597387i	$0.796206\pi$
$600$	0	0
$601$	−3.53493	−0.144193	−0.0720963	−	0.997398i	$-0.522969\pi$
$601$	−3.53493	−0.144193	−0.0720963	+	0.997398i	$0.522969\pi$
$602$	8.00961	0.326447
$603$	5.75519	0.234369
$604$	−0.207649	−0.00844910
$605$	0	0
$606$	−1.45421	−0.0590731
$607$	−10.2624	−0.416537	−0.208269	−	0.978072i	$-0.566783\pi$
$607$	−10.2624	−0.416537	−0.208269	+	0.978072i	$0.566783\pi$
$608$	42.5811	1.72689
$609$	−11.2210	−0.454696
$610$	0	0
$611$	−44.8320	−1.81371
$612$	−4.79430	−0.193798
$613$	−8.56724	−0.346027	−0.173014	−	0.984919i	$-0.555351\pi$
$613$	−8.56724	−0.346027	−0.173014	+	0.984919i	$0.555351\pi$
$614$	2.26463	0.0913930
$615$	0	0
$616$	10.6492	0.429067
$617$	29.3206	1.18040	0.590202	−	0.807256i	$-0.299048\pi$
$617$	29.3206	1.18040	0.590202	+	0.807256i	$0.299048\pi$
$618$	13.8060	0.555360
$619$	14.7925	0.594562	0.297281	−	0.954790i	$-0.403920\pi$
$619$	14.7925	0.594562	0.297281	+	0.954790i	$0.403920\pi$
$620$	0	0
$621$	4.72874	0.189758
$622$	10.5285	0.422155
$623$	−2.63238	−0.105464
$624$	8.58167	0.343542
$625$	0	0
$626$	−13.2401	−0.529182
$627$	56.0580	2.23874
$628$	0.780575	0.0311483
$629$	−20.4757	−0.816419
$630$	0	0
$631$	13.0046	0.517705	0.258853	−	0.965917i	$-0.416656\pi$
$631$	13.0046	0.517705	0.258853	+	0.965917i	$0.416656\pi$
$632$	−9.13252	−0.363272
$633$	−9.86072	−0.391928
$634$	−23.9862	−0.952614
$635$	0	0
$636$	−7.31876	−0.290208
$637$	4.70829	0.186549
$638$	18.6541	0.738524
$639$	0.661476	0.0261676
$640$	0	0
$641$	−1.01387	−0.0400454	−0.0200227	−	0.999800i	$-0.506374\pi$
$641$	−1.01387	−0.0400454	−0.0200227	+	0.999800i	$0.506374\pi$
$642$	2.17910	0.0860020
$643$	−20.3706	−0.803338	−0.401669	−	0.915785i	$-0.631570\pi$
$643$	−20.3706	−0.803338	−0.401669	+	0.915785i	$0.631570\pi$
$644$	−1.44548	−0.0569598
$645$	0	0
$646$	39.3007	1.54627
$647$	19.5011	0.766669	0.383334	−	0.923610i	$-0.374776\pi$
$647$	19.5011	0.766669	0.383334	+	0.923610i	$0.374776\pi$
$648$	−26.0708	−1.02416
$649$	−0.897576	−0.0352329
$650$	0	0
$651$	11.2860	0.442334
$652$	33.9277	1.32871
$653$	−29.1199	−1.13955	−0.569774	−	0.821801i	$-0.692969\pi$
$653$	−29.1199	−1.13955	−0.569774	+	0.821801i	$0.692969\pi$
$654$	8.81421	0.344663
$655$	0	0
$656$	−9.55730	−0.373150
$657$	5.10598	0.199203
$658$	−7.09061	−0.276421
$659$	−19.8486	−0.773190	−0.386595	−	0.922250i	$-0.626349\pi$
$659$	−19.8486	−0.773190	−0.386595	+	0.922250i	$0.626349\pi$
$660$	0	0
$661$	−36.3458	−1.41369	−0.706844	−	0.707370i	$-0.749882\pi$
$661$	−36.3458	−1.41369	−0.706844	+	0.707370i	$0.749882\pi$
$662$	−22.4209	−0.871413
$663$	63.5940	2.46979
$664$	−25.7227	−0.998235
$665$	0	0
$666$	0.958182	0.0371288
$667$	−6.03544	−0.233693
$668$	−17.2488	−0.667376
$669$	−24.3539	−0.941578
$670$	0	0
$671$	21.8451	0.843322
$672$	10.8975	0.420381
$673$	19.2700	0.742803	0.371402	−	0.928472i	$-0.378877\pi$
$673$	19.2700	0.742803	0.371402	+	0.928472i	$0.378877\pi$
$674$	−15.4297	−0.594331
$675$	0	0
$676$	−13.2521	−0.509698
$677$	34.8178	1.33816	0.669078	−	0.743192i	$-0.266689\pi$
$677$	34.8178	1.33816	0.669078	+	0.743192i	$0.266689\pi$
$678$	6.86474	0.263639
$679$	10.8731	0.417273
$680$	0	0
$681$	−49.4901	−1.89646
$682$	−18.7623	−0.718445
$683$	12.3598	0.472935	0.236467	−	0.971639i	$-0.424010\pi$
$683$	12.3598	0.472935	0.236467	+	0.971639i	$0.424010\pi$
$684$	4.79407	0.183306
$685$	0	0
$686$	0.744662	0.0284313
$687$	−2.32165	−0.0885765
$688$	10.5448	0.402018
$689$	12.8224	0.488493
$690$	0	0
$691$	−24.1431	−0.918446	−0.459223	−	0.888321i	$-0.651872\pi$
$691$	−24.1431	−0.918446	−0.459223	+	0.888321i	$0.651872\pi$
$692$	−26.7867	−1.01828
$693$	1.89491	0.0719817
$694$	−17.2562	−0.655035
$695$	0	0
$696$	28.7898	1.09128
$697$	−70.8238	−2.68264
$698$	13.5137	0.511503
$699$	−41.5964	−1.57332
$700$	0	0
$701$	16.1833	0.611235	0.305617	−	0.952154i	$-0.401137\pi$
$701$	16.1833	0.611235	0.305617	+	0.952154i	$0.401137\pi$
$702$	16.5794	0.625748
$703$	20.4747	0.772216
$704$	−9.97830	−0.376071
$705$	0	0
$706$	−13.8967	−0.523008
$707$	−1.05038	−0.0395035
$708$	−0.581162	−0.0218414
$709$	−46.4071	−1.74285	−0.871427	−	0.490525i	$-0.836805\pi$
$709$	−46.4071	−1.74285	−0.871427	+	0.490525i	$0.836805\pi$
$710$	0	0
$711$	−1.62504	−0.0609438
$712$	6.75393	0.253114
$713$	6.07044	0.227340
$714$	10.0580	0.376411
$715$	0	0
$716$	9.87428	0.369019
$717$	−34.4522	−1.28664
$718$	0.404901	0.0151108
$719$	24.7503	0.923031	0.461515	−	0.887132i	$-0.347306\pi$
$719$	24.7503	0.923031	0.461515	+	0.887132i	$0.347306\pi$
$720$	0	0
$721$	9.97214	0.371382
$722$	−25.1502	−0.935994
$723$	−29.1452	−1.08392
$724$	−23.5801	−0.876349
$725$	0	0
$726$	−8.62120	−0.319963
$727$	−16.5578	−0.614093	−0.307047	−	0.951694i	$-0.599341\pi$
$727$	−16.5578	−0.614093	−0.307047	+	0.951694i	$0.599341\pi$
$728$	−12.0801	−0.447720
$729$	21.7357	0.805025
$730$	0	0
$731$	78.1418	2.89018
$732$	14.1443	0.522788
$733$	51.1234	1.88828	0.944142	−	0.329538i	$-0.106893\pi$
$733$	51.1234	1.88828	0.944142	+	0.329538i	$0.106893\pi$
$734$	6.72867	0.248360
$735$	0	0
$736$	5.86147	0.216057
$737$	−52.3219	−1.92730
$738$	3.31428	0.122000
$739$	26.3896	0.970756	0.485378	−	0.874304i	$-0.338682\pi$
$739$	26.3896	0.970756	0.485378	+	0.874304i	$0.338682\pi$
$740$	0	0
$741$	−63.5908	−2.33607
$742$	2.02798	0.0744496
$743$	30.3572	1.11370	0.556849	−	0.830614i	$-0.312010\pi$
$743$	30.3572	1.11370	0.556849	+	0.830614i	$0.312010\pi$
$744$	−28.9567	−1.06161
$745$	0	0
$746$	16.6660	0.610186
$747$	−4.57710	−0.167467
$748$	43.5863	1.59367
$749$	1.57397	0.0575116
$750$	0	0
$751$	−9.53932	−0.348095	−0.174047	−	0.984737i	$-0.555685\pi$
$751$	−9.53932	−0.348095	−0.174047	+	0.984737i	$0.555685\pi$
$752$	−9.33496	−0.340411
$753$	−26.9751	−0.983029
$754$	−21.1608	−0.770630
$755$	0	0
$756$	−6.83529	−0.248597
$757$	−26.3487	−0.957660	−0.478830	−	0.877908i	$-0.658939\pi$
$757$	−26.3487	−0.957660	−0.478830	+	0.877908i	$0.658939\pi$
$758$	−27.6805	−1.00540
$759$	7.71663	0.280096
$760$	0	0
$761$	−29.3251	−1.06303	−0.531516	−	0.847048i	$-0.678378\pi$
$761$	−29.3251	−1.06303	−0.531516	+	0.847048i	$0.678378\pi$
$762$	17.0895	0.619088
$763$	6.36653	0.230484
$764$	−15.5618	−0.563005
$765$	0	0
$766$	−19.6045	−0.708339
$767$	1.01819	0.0367646
$768$	−22.6907	−0.818780
$769$	−33.7359	−1.21655	−0.608274	−	0.793727i	$-0.708138\pi$
$769$	−33.7359	−1.21655	−0.608274	+	0.793727i	$0.708138\pi$
$770$	0	0
$771$	−2.42195	−0.0872244
$772$	1.95291	0.0702869
$773$	54.5812	1.96315	0.981574	−	0.191083i	$-0.0612000\pi$
$773$	54.5812	1.96315	0.981574	+	0.191083i	$0.0612000\pi$
$774$	−3.65674	−0.131439
$775$	0	0
$776$	−27.8974	−1.00146
$777$	5.23996	0.187982
$778$	2.91413	0.104476
$779$	70.8203	2.53740
$780$	0	0
$781$	−6.01365	−0.215185
$782$	5.40992	0.193458
$783$	−28.5400	−1.01994
$784$	0.980365	0.0350130
$785$	0	0
$786$	22.5079	0.802831
$787$	33.8886	1.20800	0.604000	−	0.796985i	$-0.293573\pi$
$787$	33.8886	1.20800	0.604000	+	0.796985i	$0.293573\pi$
$788$	20.6393	0.735246
$789$	−3.24610	−0.115564
$790$	0	0
$791$	4.95842	0.176301
$792$	−4.86180	−0.172757
$793$	−24.7806	−0.879984
$794$	25.2935	0.897634
$795$	0	0
$796$	−22.8152	−0.808665
$797$	−17.4865	−0.619405	−0.309703	−	0.950833i	$-0.600230\pi$
$797$	−17.4865	−0.619405	−0.309703	+	0.950833i	$0.600230\pi$
$798$	−10.0575	−0.356032
$799$	−69.1761	−2.44728
$800$	0	0
$801$	1.20179	0.0424633
$802$	−8.32454	−0.293950
$803$	−46.4198	−1.63812
$804$	−33.8774	−1.19476
$805$	0	0
$806$	21.2835	0.749678
$807$	−31.8540	−1.12131
$808$	2.69497	0.0948088
$809$	5.80563	0.204115	0.102057	−	0.994779i	$-0.467457\pi$
$809$	5.80563	0.204115	0.102057	+	0.994779i	$0.467457\pi$
$810$	0	0
$811$	−4.97160	−0.174576	−0.0872882	−	0.996183i	$-0.527820\pi$
$811$	−4.97160	−0.174576	−0.0872882	+	0.996183i	$0.527820\pi$
$812$	8.72410	0.306156
$813$	−0.759966	−0.0266532
$814$	−8.71108	−0.305323
$815$	0	0
$816$	13.2416	0.463549
$817$	−78.1379	−2.73370
$818$	11.9011	0.416111
$819$	−2.14954	−0.0751110
$820$	0	0
$821$	33.0977	1.15512	0.577558	−	0.816350i	$-0.304006\pi$
$821$	33.0977	1.15512	0.577558	+	0.816350i	$0.304006\pi$
$822$	6.62635	0.231121
$823$	−31.4657	−1.09683	−0.548413	−	0.836208i	$-0.684768\pi$
$823$	−31.4657	−1.09683	−0.548413	+	0.836208i	$0.684768\pi$
$824$	−25.5857	−0.891320
$825$	0	0
$826$	0.161036	0.00560317
$827$	−45.8645	−1.59486	−0.797432	−	0.603409i	$-0.793809\pi$
$827$	−45.8645	−1.59486	−0.797432	+	0.603409i	$0.793809\pi$
$828$	0.659924	0.0229339
$829$	−32.0454	−1.11298	−0.556491	−	0.830854i	$-0.687853\pi$
$829$	−32.0454	−1.11298	−0.556491	+	0.830854i	$0.687853\pi$
$830$	0	0
$831$	0.161183	0.00559138
$832$	11.3191	0.392421
$833$	7.26493	0.251715
$834$	30.6022	1.05967
$835$	0	0
$836$	−43.5841	−1.50739
$837$	28.7055	0.992208
$838$	3.84208	0.132722
$839$	48.1771	1.66326	0.831630	−	0.555330i	$-0.187408\pi$
$839$	48.1771	1.66326	0.831630	+	0.555330i	$0.187408\pi$
$840$	0	0
$841$	7.42657	0.256089
$842$	20.8260	0.717711
$843$	−5.73373	−0.197480
$844$	7.66654	0.263893
$845$	0	0
$846$	3.23718	0.111296
$847$	−6.22713	−0.213967
$848$	2.66989	0.0916843
$849$	−28.4528	−0.976498
$850$	0	0
$851$	2.81843	0.0966144
$852$	−3.89372	−0.133397
$853$	37.4187	1.28119	0.640596	−	0.767878i	$-0.278687\pi$
$853$	37.4187	1.28119	0.640596	+	0.767878i	$0.278687\pi$
$854$	−3.91929	−0.134115
$855$	0	0
$856$	−4.03836	−0.138028
$857$	−52.9863	−1.80998	−0.904988	−	0.425436i	$-0.860121\pi$
$857$	−52.9863	−1.80998	−0.904988	+	0.425436i	$0.860121\pi$
$858$	27.0551	0.923647
$859$	48.6517	1.65997	0.829987	−	0.557783i	$-0.188348\pi$
$859$	48.6517	1.65997	0.829987	+	0.557783i	$0.188348\pi$
$860$	0	0
$861$	18.1246	0.617685
$862$	−25.4717	−0.867568
$863$	−13.1761	−0.448519	−0.224260	−	0.974529i	$-0.571996\pi$
$863$	−13.1761	−0.448519	−0.224260	+	0.974529i	$0.571996\pi$
$864$	27.7174	0.942964
$865$	0	0
$866$	−26.9246	−0.914934
$867$	66.5200	2.25914
$868$	−8.77469	−0.297832
$869$	14.7737	0.501162
$870$	0	0
$871$	59.3527	2.01109
$872$	−16.3347	−0.553163
$873$	−4.96406	−0.168008
$874$	−5.40965	−0.182984
$875$	0	0
$876$	−30.0559	−1.01549
$877$	22.9134	0.773729	0.386865	−	0.922136i	$-0.373558\pi$
$877$	22.9134	0.773729	0.386865	+	0.922136i	$0.373558\pi$
$878$	7.35175	0.248110
$879$	19.4111	0.654720
$880$	0	0
$881$	19.6240	0.661149	0.330574	−	0.943780i	$-0.392758\pi$
$881$	19.6240	0.661149	0.330574	+	0.943780i	$0.392758\pi$
$882$	−0.339971	−0.0114474
$883$	−10.3377	−0.347892	−0.173946	−	0.984755i	$-0.555652\pi$
$883$	−10.3377	−0.347892	−0.173946	+	0.984755i	$0.555652\pi$
$884$	−49.4432	−1.66295
$885$	0	0
$886$	−15.5014	−0.520779
$887$	13.5341	0.454432	0.227216	−	0.973844i	$-0.427038\pi$
$887$	13.5341	0.454432	0.227216	+	0.973844i	$0.427038\pi$
$888$	−13.4442	−0.451159
$889$	12.3438	0.413998
$890$	0	0
$891$	42.1746	1.41290
$892$	18.9348	0.633983
$893$	69.1727	2.31478
$894$	10.9938	0.367686
$895$	0	0
$896$	−9.93272	−0.331829
$897$	−8.75355	−0.292273
$898$	26.4891	0.883954
$899$	−36.6378	−1.22194
$900$	0	0
$901$	19.7850	0.659135
$902$	−30.1310	−1.00325
$903$	−19.9974	−0.665471
$904$	−12.7219	−0.423124
$905$	0	0
$906$	−0.198883	−0.00660744
$907$	34.7281	1.15313	0.576564	−	0.817052i	$-0.304393\pi$
$907$	34.7281	1.15313	0.576564	+	0.817052i	$0.304393\pi$
$908$	38.4776	1.27693
$909$	0.479543	0.0159054
$910$	0	0
$911$	41.1587	1.36365	0.681824	−	0.731516i	$-0.261187\pi$
$911$	41.1587	1.36365	0.681824	+	0.731516i	$0.261187\pi$
$912$	−13.2409	−0.438451
$913$	41.6116	1.37714
$914$	14.7956	0.489395
$915$	0	0
$916$	1.80504	0.0596403
$917$	16.2576	0.536872
$918$	25.5821	0.844335
$919$	34.9914	1.15426	0.577130	−	0.816652i	$-0.304173\pi$
$919$	34.9914	1.15426	0.577130	+	0.816652i	$0.304173\pi$
$920$	0	0
$921$	−5.65404	−0.186307
$922$	−13.0532	−0.429884
$923$	6.82174	0.224540
$924$	−11.1542	−0.366947
$925$	0	0
$926$	−21.1796	−0.696005
$927$	−4.55272	−0.149531
$928$	−35.3766	−1.16129
$929$	15.9236	0.522437	0.261218	−	0.965280i	$-0.415876\pi$
$929$	15.9236	0.522437	0.261218	+	0.965280i	$0.415876\pi$
$930$	0	0
$931$	−7.26457	−0.238087
$932$	32.3405	1.05935
$933$	−26.2863	−0.860574
$934$	−0.914822	−0.0299339
$935$	0	0
$936$	5.51511	0.180267
$937$	−19.7404	−0.644892	−0.322446	−	0.946588i	$-0.604505\pi$
$937$	−19.7404	−0.644892	−0.322446	+	0.946588i	$0.604505\pi$
$938$	9.38721	0.306503
$939$	33.0563	1.07875
$940$	0	0
$941$	24.2745	0.791326	0.395663	−	0.918396i	$-0.370515\pi$
$941$	24.2745	0.791326	0.395663	+	0.918396i	$0.370515\pi$
$942$	0.747624	0.0243589
$943$	9.74872	0.317462
$944$	0.212008	0.00690028
$945$	0	0
$946$	33.2443	1.08087
$947$	33.9454	1.10308	0.551539	−	0.834149i	$-0.314041\pi$
$947$	33.9454	1.10308	0.551539	+	0.834149i	$0.314041\pi$
$948$	9.56565	0.310678
$949$	52.6575	1.70933
$950$	0	0
$951$	59.8858	1.94193
$952$	−18.6398	−0.604118
$953$	46.2066	1.49678	0.748390	−	0.663259i	$-0.230827\pi$
$953$	46.2066	1.49678	0.748390	+	0.663259i	$0.230827\pi$
$954$	−0.925863	−0.0299759
$955$	0	0
$956$	26.7860	0.866320
$957$	−46.5733	−1.50550
$958$	2.04293	0.0660041
$959$	4.78624	0.154556
$960$	0	0
$961$	5.85022	0.188717
$962$	9.88164	0.318597
$963$	−0.718585	−0.0231561
$964$	22.6599	0.729825
$965$	0	0
$966$	−1.38446	−0.0445443
$967$	−51.9127	−1.66940	−0.834699	−	0.550706i	$-0.814359\pi$
$967$	−51.9127	−1.66940	−0.834699	+	0.550706i	$0.814359\pi$
$968$	15.9770	0.513522
$969$	−98.1211	−3.15211
$970$	0	0
$971$	−49.5691	−1.59075	−0.795375	−	0.606118i	$-0.792726\pi$
$971$	−49.5691	−1.59075	−0.795375	+	0.606118i	$0.792726\pi$
$972$	6.80136	0.218154
$973$	22.1041	0.708623
$974$	−4.25168	−0.136233
$975$	0	0
$976$	−5.15984	−0.165162
$977$	−17.9111	−0.573026	−0.286513	−	0.958076i	$-0.592496\pi$
$977$	−17.9111	−0.573026	−0.286513	+	0.958076i	$0.592496\pi$
$978$	32.4955	1.03909
$979$	−10.9258	−0.349191
$980$	0	0
$981$	−2.90660	−0.0928006
$982$	5.33037	0.170099
$983$	−25.3176	−0.807506	−0.403753	−	0.914868i	$-0.632295\pi$
$983$	−25.3176	−0.807506	−0.403753	+	0.914868i	$0.632295\pi$
$984$	−46.5026	−1.48245
$985$	0	0
$986$	−32.6513	−1.03983
$987$	17.7030	0.563491
$988$	49.4407	1.57292
$989$	−10.7560	−0.342022
$990$	0	0
$991$	42.4764	1.34931	0.674653	−	0.738135i	$-0.264293\pi$
$991$	42.4764	1.34931	0.674653	+	0.738135i	$0.264293\pi$
$992$	35.5817	1.12972
$993$	55.9777	1.77640
$994$	1.07892	0.0342214
$995$	0	0
$996$	26.9427	0.853711
$997$	61.5691	1.94991	0.974957	−	0.222393i	$-0.0713868\pi$
$997$	61.5691	1.94991	0.974957	+	0.222393i	$0.0713868\pi$
$998$	18.6414	0.590083
$999$	13.3276	0.421667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.z.1.7	✓	14
5.4	even	2		4025.2.a.bc.1.8	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.7	✓	14	1.1	even	1	trivial
4025.2.a.bc.1.8	yes	14	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.744662 q^{2} +1.85918 q^{3} -1.44548 q^{4} -1.38446 q^{6} -1.00000 q^{7} +2.56572 q^{8} +0.456544 q^{9} +O(q^{10})\)	\(q-0.744662 q^{2} +1.85918 q^{3} -1.44548 q^{4} -1.38446 q^{6} -1.00000 q^{7} +2.56572 q^{8} +0.456544 q^{9} -4.15056 q^{11} -2.68740 q^{12} +4.70829 q^{13} +0.744662 q^{14} +0.980365 q^{16} +7.26493 q^{17} -0.339971 q^{18} -7.26457 q^{19} -1.85918 q^{21} +3.09076 q^{22} -1.00000 q^{23} +4.77013 q^{24} -3.50609 q^{26} -4.72874 q^{27} +1.44548 q^{28} +6.03544 q^{29} -6.07044 q^{31} -5.86147 q^{32} -7.71663 q^{33} -5.40992 q^{34} -0.659924 q^{36} -2.81843 q^{37} +5.40965 q^{38} +8.75355 q^{39} -9.74872 q^{41} +1.38446 q^{42} +10.7560 q^{43} +5.99954 q^{44} +0.744662 q^{46} -9.52192 q^{47} +1.82267 q^{48} +1.00000 q^{49} +13.5068 q^{51} -6.80573 q^{52} +2.72336 q^{53} +3.52131 q^{54} -2.56572 q^{56} -13.5061 q^{57} -4.49436 q^{58} +0.216254 q^{59} -5.26318 q^{61} +4.52042 q^{62} -0.456544 q^{63} +2.40409 q^{64} +5.74628 q^{66} +12.6060 q^{67} -10.5013 q^{68} -1.85918 q^{69} +1.44888 q^{71} +1.17136 q^{72} +11.1840 q^{73} +2.09877 q^{74} +10.5008 q^{76} +4.15056 q^{77} -6.51844 q^{78} -3.55944 q^{79} -10.1612 q^{81} +7.25950 q^{82} -10.0255 q^{83} +2.68740 q^{84} -8.00961 q^{86} +11.2210 q^{87} -10.6492 q^{88} +2.63238 q^{89} -4.70829 q^{91} +1.44548 q^{92} -11.2860 q^{93} +7.09061 q^{94} -10.8975 q^{96} -10.8731 q^{97} -0.744662 q^{98} -1.89491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more