LMFDB - Embedded newform 3025.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3025,2,Mod(1,3025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3025 = 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3025.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:	$24.1547466114$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 275)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -4.23607 q^{6} +2.85410 q^{7} +2.23607 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -4.23607 q^{6} +2.85410 q^{7} +2.23607 q^{8} +3.85410 q^{9} +1.61803 q^{12} -6.23607 q^{13} -4.61803 q^{14} -4.85410 q^{16} +0.618034 q^{17} -6.23607 q^{18} +6.70820 q^{19} +7.47214 q^{21} -4.09017 q^{23} +5.85410 q^{24} +10.0902 q^{26} +2.23607 q^{27} +1.76393 q^{28} +1.38197 q^{29} -3.00000 q^{31} +3.38197 q^{32} -1.00000 q^{34} +2.38197 q^{36} +10.2361 q^{37} -10.8541 q^{38} -16.3262 q^{39} +3.00000 q^{41} -12.0902 q^{42} +6.00000 q^{43} +6.61803 q^{46} +11.9443 q^{47} -12.7082 q^{48} +1.14590 q^{49} +1.61803 q^{51} -3.85410 q^{52} +9.32624 q^{53} -3.61803 q^{54} +6.38197 q^{56} +17.5623 q^{57} -2.23607 q^{58} +0.527864 q^{59} -0.0901699 q^{61} +4.85410 q^{62} +11.0000 q^{63} +4.23607 q^{64} +8.00000 q^{67} +0.381966 q^{68} -10.7082 q^{69} +8.18034 q^{71} +8.61803 q^{72} -10.3820 q^{73} -16.5623 q^{74} +4.14590 q^{76} +26.4164 q^{78} -5.85410 q^{79} -5.70820 q^{81} -4.85410 q^{82} +10.1459 q^{83} +4.61803 q^{84} -9.70820 q^{86} +3.61803 q^{87} -6.90983 q^{89} -17.7984 q^{91} -2.52786 q^{92} -7.85410 q^{93} -19.3262 q^{94} +8.85410 q^{96} +1.61803 q^{97} -1.85410 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{6} - q^{7} + q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^6 - q^7 + q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{6} - q^{7} + q^{9} + q^{12} - 8 q^{13} - 7 q^{14} - 3 q^{16} - q^{17} - 8 q^{18} + 6 q^{21} + 3 q^{23} + 5 q^{24} + 9 q^{26} + 8 q^{28} + 5 q^{29} - 6 q^{31} + 9 q^{32} - 2 q^{34} + 7 q^{36} + 16 q^{37} - 15 q^{38} - 17 q^{39} + 6 q^{41} - 13 q^{42} + 12 q^{43} + 11 q^{46} + 6 q^{47} - 12 q^{48} + 9 q^{49} + q^{51} - q^{52} + 3 q^{53} - 5 q^{54} + 15 q^{56} + 15 q^{57} + 10 q^{59} + 11 q^{61} + 3 q^{62} + 22 q^{63} + 4 q^{64} + 16 q^{67} + 3 q^{68} - 8 q^{69} - 6 q^{71} + 15 q^{72} - 23 q^{73} - 13 q^{74} + 15 q^{76} + 26 q^{78} - 5 q^{79} + 2 q^{81} - 3 q^{82} + 27 q^{83} + 7 q^{84} - 6 q^{86} + 5 q^{87} - 25 q^{89} - 11 q^{91} - 14 q^{92} - 9 q^{93} - 23 q^{94} + 11 q^{96} + q^{97} + 3 q^{98}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^6 - q^7 + q^9 + q^12 - 8 * q^13 - 7 * q^14 - 3 * q^16 - q^17 - 8 * q^18 + 6 * q^21 + 3 * q^23 + 5 * q^24 + 9 * q^26 + 8 * q^28 + 5 * q^29 - 6 * q^31 + 9 * q^32 - 2 * q^34 + 7 * q^36 + 16 * q^37 - 15 * q^38 - 17 * q^39 + 6 * q^41 - 13 * q^42 + 12 * q^43 + 11 * q^46 + 6 * q^47 - 12 * q^48 + 9 * q^49 + q^51 - q^52 + 3 * q^53 - 5 * q^54 + 15 * q^56 + 15 * q^57 + 10 * q^59 + 11 * q^61 + 3 * q^62 + 22 * q^63 + 4 * q^64 + 16 * q^67 + 3 * q^68 - 8 * q^69 - 6 * q^71 + 15 * q^72 - 23 * q^73 - 13 * q^74 + 15 * q^76 + 26 * q^78 - 5 * q^79 + 2 * q^81 - 3 * q^82 + 27 * q^83 + 7 * q^84 - 6 * q^86 + 5 * q^87 - 25 * q^89 - 11 * q^91 - 14 * q^92 - 9 * q^93 - 23 * q^94 + 11 * q^96 + q^97 + 3 * 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 $

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	0.618034	0.309017
$5$	0	0
$5$	0	0
$6$	−4.23607	−1.72937
$7$	2.85410	1.07875	0.539375	−	0.842066i	$-0.318661\pi$
$7$	2.85410	1.07875	0.539375	+	0.842066i	$0.318661\pi$
$8$	2.23607	0.790569
$9$	3.85410	1.28470
$10$	0	0
$11$	0	0
$11$	0	0
$12$	1.61803	0.467086
$13$	−6.23607	−1.72957	−0.864787	−	0.502139i	$-0.832547\pi$
$13$	−6.23607	−1.72957	−0.864787	+	0.502139i	$0.832547\pi$
$14$	−4.61803	−1.23422
$15$	0	0
$16$	−4.85410	−1.21353
$17$	0.618034	0.149895	0.0749476	−	0.997187i	$-0.476121\pi$
$17$	0.618034	0.149895	0.0749476	+	0.997187i	$0.476121\pi$
$18$	−6.23607	−1.46986
$19$	6.70820	1.53897	0.769484	−	0.638666i	$-0.220514\pi$
$19$	6.70820	1.53897	0.769484	+	0.638666i	$0.220514\pi$
$20$	0	0
$21$	7.47214	1.63055
$22$	0	0
$23$	−4.09017	−0.852859	−0.426430	−	0.904521i	$-0.640229\pi$
$23$	−4.09017	−0.852859	−0.426430	+	0.904521i	$0.640229\pi$
$24$	5.85410	1.19496
$25$	0	0
$26$	10.0902	1.97885
$27$	2.23607	0.430331
$28$	1.76393	0.333352
$29$	1.38197	0.256625	0.128312	−	0.991734i	$-0.459044\pi$
$29$	1.38197	0.256625	0.128312	+	0.991734i	$0.459044\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	3.38197	0.597853
$33$	0	0
$34$	−1.00000	−0.171499
$35$	0	0
$36$	2.38197	0.396994
$37$	10.2361	1.68280	0.841400	−	0.540413i	$-0.181732\pi$
$37$	10.2361	1.68280	0.841400	+	0.540413i	$0.181732\pi$
$38$	−10.8541	−1.76077
$39$	−16.3262	−2.61429
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	−12.0902	−1.86555
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	0	0
$45$	0	0
$46$	6.61803	0.975776
$47$	11.9443	1.74225	0.871126	−	0.491060i	$-0.163391\pi$
$47$	11.9443	1.74225	0.871126	+	0.491060i	$0.163391\pi$
$48$	−12.7082	−1.83427
$49$	1.14590	0.163700
$50$	0	0
$51$	1.61803	0.226570
$52$	−3.85410	−0.534468
$53$	9.32624	1.28106	0.640529	−	0.767934i	$-0.278715\pi$
$53$	9.32624	1.28106	0.640529	+	0.767934i	$0.278715\pi$
$54$	−3.61803	−0.492352
$55$	0	0
$56$	6.38197	0.852826
$57$	17.5623	2.32618
$58$	−2.23607	−0.293610
$59$	0.527864	0.0687220	0.0343610	−	0.999409i	$-0.489060\pi$
$59$	0.527864	0.0687220	0.0343610	+	0.999409i	$0.489060\pi$
$60$	0	0
$61$	−0.0901699	−0.0115451	−0.00577254	−	0.999983i	$-0.501837\pi$
$61$	−0.0901699	−0.0115451	−0.00577254	+	0.999983i	$0.501837\pi$
$62$	4.85410	0.616472
$63$	11.0000	1.38587
$64$	4.23607	0.529508
$65$	0	0
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	0.381966	0.0463202
$69$	−10.7082	−1.28912
$70$	0	0
$71$	8.18034	0.970828	0.485414	−	0.874284i	$-0.338669\pi$
$71$	8.18034	0.970828	0.485414	+	0.874284i	$0.338669\pi$
$72$	8.61803	1.01565
$73$	−10.3820	−1.21512	−0.607559	−	0.794275i	$-0.707851\pi$
$73$	−10.3820	−1.21512	−0.607559	+	0.794275i	$0.707851\pi$
$74$	−16.5623	−1.92533
$75$	0	0
$76$	4.14590	0.475567
$77$	0	0
$78$	26.4164	2.99107
$79$	−5.85410	−0.658638	−0.329319	−	0.944219i	$-0.606819\pi$
$79$	−5.85410	−0.658638	−0.329319	+	0.944219i	$0.606819\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	−4.85410	−0.536046
$83$	10.1459	1.11366	0.556828	−	0.830627i	$-0.312018\pi$
$83$	10.1459	1.11366	0.556828	+	0.830627i	$0.312018\pi$
$84$	4.61803	0.503869
$85$	0	0
$86$	−9.70820	−1.04686
$87$	3.61803	0.387894
$88$	0	0
$89$	−6.90983	−0.732441	−0.366220	−	0.930528i	$-0.619348\pi$
$89$	−6.90983	−0.732441	−0.366220	+	0.930528i	$0.619348\pi$
$90$	0	0
$91$	−17.7984	−1.86578
$92$	−2.52786	−0.263548
$93$	−7.85410	−0.814432
$94$	−19.3262	−1.99335
$95$	0	0
$96$	8.85410	0.903668
$97$	1.61803	0.164286	0.0821432	−	0.996621i	$-0.473824\pi$
$97$	1.61803	0.164286	0.0821432	+	0.996621i	$0.473824\pi$
$98$	−1.85410	−0.187293
$99$	0	0
$100$	0	0
$101$	6.09017	0.605995	0.302997	−	0.952991i	$-0.402013\pi$
$101$	6.09017	0.605995	0.302997	+	0.952991i	$0.402013\pi$
$102$	−2.61803	−0.259224
$103$	5.38197	0.530301	0.265150	−	0.964207i	$-0.414578\pi$
$103$	5.38197	0.530301	0.265150	+	0.964207i	$0.414578\pi$
$104$	−13.9443	−1.36735
$105$	0	0
$106$	−15.0902	−1.46569
$107$	4.23607	0.409516	0.204758	−	0.978813i	$-0.434359\pi$
$107$	4.23607	0.409516	0.204758	+	0.978813i	$0.434359\pi$
$108$	1.38197	0.132980
$109$	3.09017	0.295985	0.147992	−	0.988989i	$-0.452719\pi$
$109$	3.09017	0.295985	0.147992	+	0.988989i	$0.452719\pi$
$110$	0	0
$111$	26.7984	2.54359
$112$	−13.8541	−1.30909
$113$	−11.6525	−1.09617	−0.548086	−	0.836422i	$-0.684643\pi$
$113$	−11.6525	−1.09617	−0.548086	+	0.836422i	$0.684643\pi$
$114$	−28.4164	−2.66144
$115$	0	0
$116$	0.854102	0.0793014
$117$	−24.0344	−2.22198
$118$	−0.854102	−0.0786265
$119$	1.76393	0.161699
$120$	0	0
$121$	0	0
$122$	0.145898	0.0132090
$123$	7.85410	0.708181
$124$	−1.85410	−0.166503
$125$	0	0
$126$	−17.7984	−1.58561
$127$	0.618034	0.0548416	0.0274208	−	0.999624i	$-0.491271\pi$
$127$	0.618034	0.0548416	0.0274208	+	0.999624i	$0.491271\pi$
$128$	−13.6180	−1.20368
$129$	15.7082	1.38303
$130$	0	0
$131$	−10.0902	−0.881582	−0.440791	−	0.897610i	$-0.645302\pi$
$131$	−10.0902	−0.881582	−0.440791	+	0.897610i	$0.645302\pi$
$132$	0	0
$133$	19.1459	1.66016
$134$	−12.9443	−1.11821
$135$	0	0
$136$	1.38197	0.118503
$137$	5.56231	0.475220	0.237610	−	0.971361i	$-0.423636\pi$
$137$	5.56231	0.475220	0.237610	+	0.971361i	$0.423636\pi$
$138$	17.3262	1.47491
$139$	3.29180	0.279206	0.139603	−	0.990208i	$-0.455417\pi$
$139$	3.29180	0.279206	0.139603	+	0.990208i	$0.455417\pi$
$140$	0	0
$141$	31.2705	2.63345
$142$	−13.2361	−1.11075
$143$	0	0
$144$	−18.7082	−1.55902
$145$	0	0
$146$	16.7984	1.39024
$147$	3.00000	0.247436
$148$	6.32624	0.520014
$149$	8.94427	0.732743	0.366372	−	0.930469i	$-0.380600\pi$
$149$	8.94427	0.732743	0.366372	+	0.930469i	$0.380600\pi$
$150$	0	0
$151$	3.00000	0.244137	0.122068	−	0.992522i	$-0.461047\pi$
$151$	3.00000	0.244137	0.122068	+	0.992522i	$0.461047\pi$
$152$	15.0000	1.21666
$153$	2.38197	0.192571
$154$	0	0
$155$	0	0
$156$	−10.0902	−0.807860
$157$	−5.41641	−0.432276	−0.216138	−	0.976363i	$-0.569346\pi$
$157$	−5.41641	−0.432276	−0.216138	+	0.976363i	$0.569346\pi$
$158$	9.47214	0.753563
$159$	24.4164	1.93635
$160$	0	0
$161$	−11.6738	−0.920021
$162$	9.23607	0.725654
$163$	−6.85410	−0.536855	−0.268427	−	0.963300i	$-0.586504\pi$
$163$	−6.85410	−0.536855	−0.268427	+	0.963300i	$0.586504\pi$
$164$	1.85410	0.144781
$165$	0	0
$166$	−16.4164	−1.27416
$167$	5.29180	0.409491	0.204746	−	0.978815i	$-0.434363\pi$
$167$	5.29180	0.409491	0.204746	+	0.978815i	$0.434363\pi$
$168$	16.7082	1.28907
$169$	25.8885	1.99143
$170$	0	0
$171$	25.8541	1.97711
$172$	3.70820	0.282748
$173$	5.47214	0.416039	0.208019	−	0.978125i	$-0.433298\pi$
$173$	5.47214	0.416039	0.208019	+	0.978125i	$0.433298\pi$
$174$	−5.85410	−0.443798
$175$	0	0
$176$	0	0
$177$	1.38197	0.103875
$178$	11.1803	0.838002
$179$	−13.6180	−1.01786	−0.508930	−	0.860808i	$-0.669959\pi$
$179$	−13.6180	−1.01786	−0.508930	+	0.860808i	$0.669959\pi$
$180$	0	0
$181$	−6.09017	−0.452679	−0.226339	−	0.974049i	$-0.572676\pi$
$181$	−6.09017	−0.452679	−0.226339	+	0.974049i	$0.572676\pi$
$182$	28.7984	2.13468
$183$	−0.236068	−0.0174506
$184$	−9.14590	−0.674245
$185$	0	0
$186$	12.7082	0.931811
$187$	0	0
$188$	7.38197	0.538385
$189$	6.38197	0.464220
$190$	0	0
$191$	−21.0902	−1.52603	−0.763016	−	0.646380i	$-0.776282\pi$
$191$	−21.0902	−1.52603	−0.763016	+	0.646380i	$0.776282\pi$
$192$	11.0902	0.800364
$193$	−12.9443	−0.931749	−0.465875	−	0.884851i	$-0.654260\pi$
$193$	−12.9443	−0.931749	−0.465875	+	0.884851i	$0.654260\pi$
$194$	−2.61803	−0.187964
$195$	0	0
$196$	0.708204	0.0505860
$197$	20.0902	1.43137	0.715683	−	0.698426i	$-0.246116\pi$
$197$	20.0902	1.43137	0.715683	+	0.698426i	$0.246116\pi$
$198$	0	0
$199$	−3.09017	−0.219056	−0.109528	−	0.993984i	$-0.534934\pi$
$199$	−3.09017	−0.219056	−0.109528	+	0.993984i	$0.534934\pi$
$200$	0	0
$201$	20.9443	1.47730
$202$	−9.85410	−0.693332
$203$	3.94427	0.276834
$204$	1.00000	0.0700140
$205$	0	0
$206$	−8.70820	−0.606729
$207$	−15.7639	−1.09567
$208$	30.2705	2.09888
$209$	0	0
$210$	0	0
$211$	−17.0000	−1.17033	−0.585164	−	0.810915i	$-0.698970\pi$
$211$	−17.0000	−1.17033	−0.585164	+	0.810915i	$0.698970\pi$
$212$	5.76393	0.395868
$213$	21.4164	1.46743
$214$	−6.85410	−0.468537
$215$	0	0
$216$	5.00000	0.340207
$217$	−8.56231	−0.581247
$218$	−5.00000	−0.338643
$219$	−27.1803	−1.83668
$220$	0	0
$221$	−3.85410	−0.259255
$222$	−43.3607	−2.91018
$223$	16.8885	1.13094	0.565470	−	0.824769i	$-0.308695\pi$
$223$	16.8885	1.13094	0.565470	+	0.824769i	$0.308695\pi$
$224$	9.65248	0.644933
$225$	0	0
$226$	18.8541	1.25416
$227$	24.0344	1.59522	0.797611	−	0.603172i	$-0.206097\pi$
$227$	24.0344	1.59522	0.797611	+	0.603172i	$0.206097\pi$
$228$	10.8541	0.718830
$229$	12.0344	0.795258	0.397629	−	0.917546i	$-0.369833\pi$
$229$	12.0344	0.795258	0.397629	+	0.917546i	$0.369833\pi$
$230$	0	0
$231$	0	0
$232$	3.09017	0.202880
$233$	−15.5066	−1.01587	−0.507935	−	0.861395i	$-0.669591\pi$
$233$	−15.5066	−1.01587	−0.507935	+	0.861395i	$0.669591\pi$
$234$	38.8885	2.54222
$235$	0	0
$236$	0.326238	0.0212363
$237$	−15.3262	−0.995546
$238$	−2.85410	−0.185004
$239$	−6.38197	−0.412815	−0.206408	−	0.978466i	$-0.566177\pi$
$239$	−6.38197	−0.412815	−0.206408	+	0.978466i	$0.566177\pi$
$240$	0	0
$241$	−21.2705	−1.37015	−0.685077	−	0.728471i	$-0.740231\pi$
$241$	−21.2705	−1.37015	−0.685077	+	0.728471i	$0.740231\pi$
$242$	0	0
$243$	−21.6525	−1.38901
$244$	−0.0557281	−0.00356763
$245$	0	0
$246$	−12.7082	−0.810245
$247$	−41.8328	−2.66176
$248$	−6.70820	−0.425971
$249$	26.5623	1.68332
$250$	0	0
$251$	−27.2705	−1.72130	−0.860650	−	0.509198i	$-0.829942\pi$
$251$	−27.2705	−1.72130	−0.860650	+	0.509198i	$0.829942\pi$
$252$	6.79837	0.428257
$253$	0	0
$254$	−1.00000	−0.0627456
$255$	0	0
$256$	13.5623	0.847644
$257$	−10.9443	−0.682685	−0.341342	−	0.939939i	$-0.610882\pi$
$257$	−10.9443	−0.682685	−0.341342	+	0.939939i	$0.610882\pi$
$258$	−25.4164	−1.58236
$259$	29.2148	1.81532
$260$	0	0
$261$	5.32624	0.329686
$262$	16.3262	1.00864
$263$	21.0000	1.29492	0.647458	−	0.762101i	$-0.275832\pi$
$263$	21.0000	1.29492	0.647458	+	0.762101i	$0.275832\pi$
$264$	0	0
$265$	0	0
$266$	−30.9787	−1.89943
$267$	−18.0902	−1.10710
$268$	4.94427	0.302019
$269$	30.3262	1.84902	0.924512	−	0.381154i	$-0.124473\pi$
$269$	30.3262	1.84902	0.924512	+	0.381154i	$0.124473\pi$
$270$	0	0
$271$	−13.1803	−0.800649	−0.400324	−	0.916374i	$-0.631103\pi$
$271$	−13.1803	−0.800649	−0.400324	+	0.916374i	$0.631103\pi$
$272$	−3.00000	−0.181902
$273$	−46.5967	−2.82016
$274$	−9.00000	−0.543710
$275$	0	0
$276$	−6.61803	−0.398359
$277$	11.4721	0.689294	0.344647	−	0.938732i	$-0.387999\pi$
$277$	11.4721	0.689294	0.344647	+	0.938732i	$0.387999\pi$
$278$	−5.32624	−0.319447
$279$	−11.5623	−0.692217
$280$	0	0
$281$	25.3607	1.51289	0.756446	−	0.654057i	$-0.226934\pi$
$281$	25.3607	1.51289	0.756446	+	0.654057i	$0.226934\pi$
$282$	−50.5967	−3.01299
$283$	7.38197	0.438812	0.219406	−	0.975634i	$-0.429588\pi$
$283$	7.38197	0.438812	0.219406	+	0.975634i	$0.429588\pi$
$284$	5.05573	0.300002
$285$	0	0
$286$	0	0
$287$	8.56231	0.505417
$288$	13.0344	0.768062
$289$	−16.6180	−0.977531
$290$	0	0
$291$	4.23607	0.248323
$292$	−6.41641	−0.375492
$293$	23.8885	1.39558	0.697792	−	0.716301i	$-0.254166\pi$
$293$	23.8885	1.39558	0.697792	+	0.716301i	$0.254166\pi$
$294$	−4.85410	−0.283097
$295$	0	0
$296$	22.8885	1.33037
$297$	0	0
$298$	−14.4721	−0.838348
$299$	25.5066	1.47508
$300$	0	0
$301$	17.1246	0.987046
$302$	−4.85410	−0.279322
$303$	15.9443	0.915974
$304$	−32.5623	−1.86758
$305$	0	0
$306$	−3.85410	−0.220324
$307$	−33.4508	−1.90914	−0.954570	−	0.297985i	$-0.903685\pi$
$307$	−33.4508	−1.90914	−0.954570	+	0.297985i	$0.903685\pi$
$308$	0	0
$309$	14.0902	0.801562
$310$	0	0
$311$	−19.1803	−1.08762	−0.543809	−	0.839209i	$-0.683018\pi$
$311$	−19.1803	−1.08762	−0.543809	+	0.839209i	$0.683018\pi$
$312$	−36.5066	−2.06678
$313$	−3.23607	−0.182913	−0.0914567	−	0.995809i	$-0.529152\pi$
$313$	−3.23607	−0.182913	−0.0914567	+	0.995809i	$0.529152\pi$
$314$	8.76393	0.494577
$315$	0	0
$316$	−3.61803	−0.203530
$317$	16.6180	0.933362	0.466681	−	0.884426i	$-0.345450\pi$
$317$	16.6180	0.933362	0.466681	+	0.884426i	$0.345450\pi$
$318$	−39.5066	−2.21542
$319$	0	0
$320$	0	0
$321$	11.0902	0.618993
$322$	18.8885	1.05262
$323$	4.14590	0.230684
$324$	−3.52786	−0.195992
$325$	0	0
$326$	11.0902	0.614228
$327$	8.09017	0.447387
$328$	6.70820	0.370399
$329$	34.0902	1.87945
$330$	0	0
$331$	−19.1803	−1.05425	−0.527123	−	0.849789i	$-0.676729\pi$
$331$	−19.1803	−1.05425	−0.527123	+	0.849789i	$0.676729\pi$
$332$	6.27051	0.344139
$333$	39.4508	2.16189
$334$	−8.56231	−0.468509
$335$	0	0
$336$	−36.2705	−1.97872
$337$	−1.41641	−0.0771567	−0.0385783	−	0.999256i	$-0.512283\pi$
$337$	−1.41641	−0.0771567	−0.0385783	+	0.999256i	$0.512283\pi$
$338$	−41.8885	−2.27844
$339$	−30.5066	−1.65689
$340$	0	0
$341$	0	0
$342$	−41.8328	−2.26206
$343$	−16.7082	−0.902158
$344$	13.4164	0.723364
$345$	0	0
$346$	−8.85410	−0.475999
$347$	−20.5623	−1.10384	−0.551921	−	0.833896i	$-0.686105\pi$
$347$	−20.5623	−1.10384	−0.551921	+	0.833896i	$0.686105\pi$
$348$	2.23607	0.119866
$349$	−21.8328	−1.16868	−0.584342	−	0.811508i	$-0.698647\pi$
$349$	−21.8328	−1.16868	−0.584342	+	0.811508i	$0.698647\pi$
$350$	0	0
$351$	−13.9443	−0.744290
$352$	0	0
$353$	21.3607	1.13691	0.568457	−	0.822713i	$-0.307541\pi$
$353$	21.3607	1.13691	0.568457	+	0.822713i	$0.307541\pi$
$354$	−2.23607	−0.118846
$355$	0	0
$356$	−4.27051	−0.226337
$357$	4.61803	0.244412
$358$	22.0344	1.16456
$359$	4.47214	0.236030	0.118015	−	0.993012i	$-0.462347\pi$
$359$	4.47214	0.236030	0.118015	+	0.993012i	$0.462347\pi$
$360$	0	0
$361$	26.0000	1.36842
$362$	9.85410	0.517920
$363$	0	0
$364$	−11.0000	−0.576557
$365$	0	0
$366$	0.381966	0.0199657
$367$	7.14590	0.373013	0.186506	−	0.982454i	$-0.440283\pi$
$367$	7.14590	0.373013	0.186506	+	0.982454i	$0.440283\pi$
$368$	19.8541	1.03497
$369$	11.5623	0.601910
$370$	0	0
$371$	26.6180	1.38194
$372$	−4.85410	−0.251673
$373$	−2.81966	−0.145996	−0.0729982	−	0.997332i	$-0.523257\pi$
$373$	−2.81966	−0.145996	−0.0729982	+	0.997332i	$0.523257\pi$
$374$	0	0
$375$	0	0
$376$	26.7082	1.37737
$377$	−8.61803	−0.443851
$378$	−10.3262	−0.531124
$379$	−17.7639	−0.912472	−0.456236	−	0.889859i	$-0.650803\pi$
$379$	−17.7639	−0.912472	−0.456236	+	0.889859i	$0.650803\pi$
$380$	0	0
$381$	1.61803	0.0828944
$382$	34.1246	1.74597
$383$	5.05573	0.258336	0.129168	−	0.991623i	$-0.458769\pi$
$383$	5.05573	0.258336	0.129168	+	0.991623i	$0.458769\pi$
$384$	−35.6525	−1.81938
$385$	0	0
$386$	20.9443	1.06604
$387$	23.1246	1.17549
$388$	1.00000	0.0507673
$389$	5.52786	0.280274	0.140137	−	0.990132i	$-0.455246\pi$
$389$	5.52786	0.280274	0.140137	+	0.990132i	$0.455246\pi$
$390$	0	0
$391$	−2.52786	−0.127840
$392$	2.56231	0.129416
$393$	−26.4164	−1.33253
$394$	−32.5066	−1.63766
$395$	0	0
$396$	0	0
$397$	14.9098	0.748303	0.374151	−	0.927368i	$-0.377934\pi$
$397$	14.9098	0.748303	0.374151	+	0.927368i	$0.377934\pi$
$398$	5.00000	0.250627
$399$	50.1246	2.50937
$400$	0	0
$401$	34.3607	1.71589	0.857945	−	0.513741i	$-0.171741\pi$
$401$	34.3607	1.71589	0.857945	+	0.513741i	$0.171741\pi$
$402$	−33.8885	−1.69021
$403$	18.7082	0.931922
$404$	3.76393	0.187263
$405$	0	0
$406$	−6.38197	−0.316732
$407$	0	0
$408$	3.61803	0.179119
$409$	−20.1246	−0.995098	−0.497549	−	0.867436i	$-0.665767\pi$
$409$	−20.1246	−0.995098	−0.497549	+	0.867436i	$0.665767\pi$
$410$	0	0
$411$	14.5623	0.718306
$412$	3.32624	0.163872
$413$	1.50658	0.0741338
$414$	25.5066	1.25358
$415$	0	0
$416$	−21.0902	−1.03403
$417$	8.61803	0.422027
$418$	0	0
$419$	21.1803	1.03473	0.517364	−	0.855766i	$-0.326913\pi$
$419$	21.1803	1.03473	0.517364	+	0.855766i	$0.326913\pi$
$420$	0	0
$421$	−12.2705	−0.598028	−0.299014	−	0.954249i	$-0.596658\pi$
$421$	−12.2705	−0.598028	−0.299014	+	0.954249i	$0.596658\pi$
$422$	27.5066	1.33900
$423$	46.0344	2.23827
$424$	20.8541	1.01276
$425$	0	0
$426$	−34.6525	−1.67892
$427$	−0.257354	−0.0124542
$428$	2.61803	0.126547
$429$	0	0
$430$	0	0
$431$	−0.819660	−0.0394816	−0.0197408	−	0.999805i	$-0.506284\pi$
$431$	−0.819660	−0.0394816	−0.0197408	+	0.999805i	$0.506284\pi$
$432$	−10.8541	−0.522218
$433$	−18.8885	−0.907725	−0.453863	−	0.891072i	$-0.649954\pi$
$433$	−18.8885	−0.907725	−0.453863	+	0.891072i	$0.649954\pi$
$434$	13.8541	0.665018
$435$	0	0
$436$	1.90983	0.0914643
$437$	−27.4377	−1.31252
$438$	43.9787	2.10138
$439$	0.729490	0.0348167	0.0174083	−	0.999848i	$-0.494458\pi$
$439$	0.729490	0.0348167	0.0174083	+	0.999848i	$0.494458\pi$
$440$	0	0
$441$	4.41641	0.210305
$442$	6.23607	0.296620
$443$	−36.6525	−1.74141	−0.870706	−	0.491804i	$-0.836338\pi$
$443$	−36.6525	−1.74141	−0.870706	+	0.491804i	$0.836338\pi$
$444$	16.5623	0.786012
$445$	0	0
$446$	−27.3262	−1.29393
$447$	23.4164	1.10756
$448$	12.0902	0.571207
$449$	−15.3262	−0.723290	−0.361645	−	0.932316i	$-0.617785\pi$
$449$	−15.3262	−0.723290	−0.361645	+	0.932316i	$0.617785\pi$
$450$	0	0
$451$	0	0
$452$	−7.20163	−0.338736
$453$	7.85410	0.369018
$454$	−38.8885	−1.82513
$455$	0	0
$456$	39.2705	1.83901
$457$	7.97871	0.373228	0.186614	−	0.982433i	$-0.440249\pi$
$457$	7.97871	0.373228	0.186614	+	0.982433i	$0.440249\pi$
$458$	−19.4721	−0.909873
$459$	1.38197	0.0645046
$460$	0	0
$461$	9.18034	0.427571	0.213786	−	0.976881i	$-0.431421\pi$
$461$	9.18034	0.427571	0.213786	+	0.976881i	$0.431421\pi$
$462$	0	0
$463$	11.3607	0.527976	0.263988	−	0.964526i	$-0.414962\pi$
$463$	11.3607	0.527976	0.263988	+	0.964526i	$0.414962\pi$
$464$	−6.70820	−0.311421
$465$	0	0
$466$	25.0902	1.16228
$467$	37.4721	1.73400	0.867002	−	0.498305i	$-0.166044\pi$
$467$	37.4721	1.73400	0.867002	+	0.498305i	$0.166044\pi$
$468$	−14.8541	−0.686631
$469$	22.8328	1.05432
$470$	0	0
$471$	−14.1803	−0.653396
$472$	1.18034	0.0543295
$473$	0	0
$474$	24.7984	1.13903
$475$	0	0
$476$	1.09017	0.0499679
$477$	35.9443	1.64578
$478$	10.3262	0.472311
$479$	−28.4164	−1.29838	−0.649189	−	0.760627i	$-0.724892\pi$
$479$	−28.4164	−1.29838	−0.649189	+	0.760627i	$0.724892\pi$
$480$	0	0
$481$	−63.8328	−2.91053
$482$	34.4164	1.56762
$483$	−30.5623	−1.39063
$484$	0	0
$485$	0	0
$486$	35.0344	1.58919
$487$	−30.4164	−1.37830	−0.689150	−	0.724619i	$-0.742016\pi$
$487$	−30.4164	−1.37830	−0.689150	+	0.724619i	$0.742016\pi$
$488$	−0.201626	−0.00912719
$489$	−17.9443	−0.811468
$490$	0	0
$491$	6.81966	0.307767	0.153883	−	0.988089i	$-0.450822\pi$
$491$	6.81966	0.307767	0.153883	+	0.988089i	$0.450822\pi$
$492$	4.85410	0.218840
$493$	0.854102	0.0384668
$494$	67.6869	3.04538
$495$	0	0
$496$	14.5623	0.653867
$497$	23.3475	1.04728
$498$	−42.9787	−1.92592
$499$	29.7984	1.33396	0.666979	−	0.745076i	$-0.267587\pi$
$499$	29.7984	1.33396	0.666979	+	0.745076i	$0.267587\pi$
$500$	0	0
$501$	13.8541	0.618956
$502$	44.1246	1.96938
$503$	6.65248	0.296619	0.148310	−	0.988941i	$-0.452617\pi$
$503$	6.65248	0.296619	0.148310	+	0.988941i	$0.452617\pi$
$504$	24.5967	1.09563
$505$	0	0
$506$	0	0
$507$	67.7771	3.01009
$508$	0.381966	0.0169470
$509$	16.3820	0.726118	0.363059	−	0.931766i	$-0.381732\pi$
$509$	16.3820	0.726118	0.363059	+	0.931766i	$0.381732\pi$
$510$	0	0
$511$	−29.6312	−1.31081
$512$	5.29180	0.233867
$513$	15.0000	0.662266
$514$	17.7082	0.781075
$515$	0	0
$516$	9.70820	0.427380
$517$	0	0
$518$	−47.2705	−2.07695
$519$	14.3262	0.628852
$520$	0	0
$521$	−1.81966	−0.0797208	−0.0398604	−	0.999205i	$-0.512691\pi$
$521$	−1.81966	−0.0797208	−0.0398604	+	0.999205i	$0.512691\pi$
$522$	−8.61803	−0.377201
$523$	−22.9443	−1.00328	−0.501641	−	0.865076i	$-0.667270\pi$
$523$	−22.9443	−1.00328	−0.501641	+	0.865076i	$0.667270\pi$
$524$	−6.23607	−0.272424
$525$	0	0
$526$	−33.9787	−1.48154
$527$	−1.85410	−0.0807660
$528$	0	0
$529$	−6.27051	−0.272631
$530$	0	0
$531$	2.03444	0.0882873
$532$	11.8328	0.513018
$533$	−18.7082	−0.810342
$534$	29.2705	1.26666
$535$	0	0
$536$	17.8885	0.772667
$537$	−35.6525	−1.53852
$538$	−49.0689	−2.11551
$539$	0	0
$540$	0	0
$541$	42.2705	1.81735	0.908676	−	0.417503i	$-0.137095\pi$
$541$	42.2705	1.81735	0.908676	+	0.417503i	$0.137095\pi$
$542$	21.3262	0.916040
$543$	−15.9443	−0.684234
$544$	2.09017	0.0896153
$545$	0	0
$546$	75.3951	3.22661
$547$	21.1459	0.904133	0.452067	−	0.891984i	$-0.350687\pi$
$547$	21.1459	0.904133	0.452067	+	0.891984i	$0.350687\pi$
$548$	3.43769	0.146851
$549$	−0.347524	−0.0148320
$550$	0	0
$551$	9.27051	0.394937
$552$	−23.9443	−1.01914
$553$	−16.7082	−0.710505
$554$	−18.5623	−0.788637
$555$	0	0
$556$	2.03444	0.0862796
$557$	9.76393	0.413711	0.206856	−	0.978371i	$-0.433677\pi$
$557$	9.76393	0.413711	0.206856	+	0.978371i	$0.433677\pi$
$558$	18.7082	0.791981
$559$	−37.4164	−1.58255
$560$	0	0
$561$	0	0
$562$	−41.0344	−1.73093
$563$	13.0344	0.549336	0.274668	−	0.961539i	$-0.411432\pi$
$563$	13.0344	0.549336	0.274668	+	0.961539i	$0.411432\pi$
$564$	19.3262	0.813781
$565$	0	0
$566$	−11.9443	−0.502055
$567$	−16.2918	−0.684191
$568$	18.2918	0.767507
$569$	−26.3820	−1.10599	−0.552995	−	0.833185i	$-0.686515\pi$
$569$	−26.3820	−1.10599	−0.552995	+	0.833185i	$0.686515\pi$
$570$	0	0
$571$	−36.2705	−1.51787	−0.758937	−	0.651164i	$-0.774281\pi$
$571$	−36.2705	−1.51787	−0.758937	+	0.651164i	$0.774281\pi$
$572$	0	0
$573$	−55.2148	−2.30663
$574$	−13.8541	−0.578259
$575$	0	0
$576$	16.3262	0.680260
$577$	15.5623	0.647867	0.323934	−	0.946080i	$-0.394995\pi$
$577$	15.5623	0.647867	0.323934	+	0.946080i	$0.394995\pi$
$578$	26.8885	1.11842
$579$	−33.8885	−1.40836
$580$	0	0
$581$	28.9574	1.20136
$582$	−6.85410	−0.284112
$583$	0	0
$584$	−23.2148	−0.960635
$585$	0	0
$586$	−38.6525	−1.59672
$587$	−4.03444	−0.166519	−0.0832596	−	0.996528i	$-0.526533\pi$
$587$	−4.03444	−0.166519	−0.0832596	+	0.996528i	$0.526533\pi$
$588$	1.85410	0.0764619
$589$	−20.1246	−0.829220
$590$	0	0
$591$	52.5967	2.16354
$592$	−49.6869	−2.04212
$593$	−9.00000	−0.369586	−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000	−0.369586	−0.184793	+	0.982777i	$0.559161\pi$
$594$	0	0
$595$	0	0
$596$	5.52786	0.226430
$597$	−8.09017	−0.331109
$598$	−41.2705	−1.68768
$599$	0.326238	0.0133297	0.00666486	−	0.999978i	$-0.497878\pi$
$599$	0.326238	0.0133297	0.00666486	+	0.999978i	$0.497878\pi$
$600$	0	0
$601$	22.2705	0.908433	0.454217	−	0.890891i	$-0.349919\pi$
$601$	22.2705	0.908433	0.454217	+	0.890891i	$0.349919\pi$
$602$	−27.7082	−1.12930
$603$	30.8328	1.25561
$604$	1.85410	0.0754423
$605$	0	0
$606$	−25.7984	−1.04799
$607$	−3.52786	−0.143192	−0.0715958	−	0.997434i	$-0.522809\pi$
$607$	−3.52786	−0.143192	−0.0715958	+	0.997434i	$0.522809\pi$
$608$	22.6869	0.920076
$609$	10.3262	0.418440
$610$	0	0
$611$	−74.4853	−3.01335
$612$	1.47214	0.0595076
$613$	−6.43769	−0.260016	−0.130008	−	0.991513i	$-0.541500\pi$
$613$	−6.43769	−0.260016	−0.130008	+	0.991513i	$0.541500\pi$
$614$	54.1246	2.18429
$615$	0	0
$616$	0	0
$617$	−38.1803	−1.53708	−0.768541	−	0.639800i	$-0.779017\pi$
$617$	−38.1803	−1.53708	−0.768541	+	0.639800i	$0.779017\pi$
$618$	−22.7984	−0.917085
$619$	−22.8885	−0.919968	−0.459984	−	0.887927i	$-0.652145\pi$
$619$	−22.8885	−0.919968	−0.459984	+	0.887927i	$0.652145\pi$
$620$	0	0
$621$	−9.14590	−0.367012
$622$	31.0344	1.24437
$623$	−19.7214	−0.790120
$624$	79.2492	3.17251
$625$	0	0
$626$	5.23607	0.209275
$627$	0	0
$628$	−3.34752	−0.133581
$629$	6.32624	0.252244
$630$	0	0
$631$	36.2705	1.44391	0.721953	−	0.691942i	$-0.243245\pi$
$631$	36.2705	1.44391	0.721953	+	0.691942i	$0.243245\pi$
$632$	−13.0902	−0.520699
$633$	−44.5066	−1.76898
$634$	−26.8885	−1.06788
$635$	0	0
$636$	15.0902	0.598364
$637$	−7.14590	−0.283131
$638$	0	0
$639$	31.5279	1.24722
$640$	0	0
$641$	−3.00000	−0.118493	−0.0592464	−	0.998243i	$-0.518870\pi$
$641$	−3.00000	−0.118493	−0.0592464	+	0.998243i	$0.518870\pi$
$642$	−17.9443	−0.708204
$643$	10.5836	0.417376	0.208688	−	0.977982i	$-0.433081\pi$
$643$	10.5836	0.417376	0.208688	+	0.977982i	$0.433081\pi$
$644$	−7.21478	−0.284302
$645$	0	0
$646$	−6.70820	−0.263931
$647$	12.3475	0.485431	0.242716	−	0.970097i	$-0.421962\pi$
$647$	12.3475	0.485431	0.242716	+	0.970097i	$0.421962\pi$
$648$	−12.7639	−0.501415
$649$	0	0
$650$	0	0
$651$	−22.4164	−0.878568
$652$	−4.23607	−0.165897
$653$	7.74265	0.302993	0.151497	−	0.988458i	$-0.451591\pi$
$653$	7.74265	0.302993	0.151497	+	0.988458i	$0.451591\pi$
$654$	−13.0902	−0.511866
$655$	0	0
$656$	−14.5623	−0.568563
$657$	−40.0132	−1.56106
$658$	−55.1591	−2.15032
$659$	−9.27051	−0.361128	−0.180564	−	0.983563i	$-0.557792\pi$
$659$	−9.27051	−0.361128	−0.180564	+	0.983563i	$0.557792\pi$
$660$	0	0
$661$	−49.1803	−1.91289	−0.956447	−	0.291907i	$-0.905710\pi$
$661$	−49.1803	−1.91289	−0.956447	+	0.291907i	$0.905710\pi$
$662$	31.0344	1.20619
$663$	−10.0902	−0.391870
$664$	22.6869	0.880423
$665$	0	0
$666$	−63.8328	−2.47347
$667$	−5.65248	−0.218865
$668$	3.27051	0.126540
$669$	44.2148	1.70944
$670$	0	0
$671$	0	0
$672$	25.2705	0.974831
$673$	−2.41641	−0.0931457	−0.0465728	−	0.998915i	$-0.514830\pi$
$673$	−2.41641	−0.0931457	−0.0465728	+	0.998915i	$0.514830\pi$
$674$	2.29180	0.0882767
$675$	0	0
$676$	16.0000	0.615385
$677$	−28.6525	−1.10120	−0.550602	−	0.834768i	$-0.685602\pi$
$677$	−28.6525	−1.10120	−0.550602	+	0.834768i	$0.685602\pi$
$678$	49.3607	1.89569
$679$	4.61803	0.177224
$680$	0	0
$681$	62.9230	2.41121
$682$	0	0
$683$	−43.3607	−1.65915	−0.829575	−	0.558395i	$-0.811417\pi$
$683$	−43.3607	−1.65915	−0.829575	+	0.558395i	$0.811417\pi$
$684$	15.9787	0.610961
$685$	0	0
$686$	27.0344	1.03218
$687$	31.5066	1.20205
$688$	−29.1246	−1.11037
$689$	−58.1591	−2.21568
$690$	0	0
$691$	30.0902	1.14468	0.572342	−	0.820015i	$-0.306035\pi$
$691$	30.0902	1.14468	0.572342	+	0.820015i	$0.306035\pi$
$692$	3.38197	0.128563
$693$	0	0
$694$	33.2705	1.26293
$695$	0	0
$696$	8.09017	0.306657
$697$	1.85410	0.0702291
$698$	35.3262	1.33712
$699$	−40.5967	−1.53551
$700$	0	0
$701$	0.360680	0.0136227	0.00681134	−	0.999977i	$-0.497832\pi$
$701$	0.360680	0.0136227	0.00681134	+	0.999977i	$0.497832\pi$
$702$	22.5623	0.851559
$703$	68.6656	2.58977
$704$	0	0
$705$	0	0
$706$	−34.5623	−1.30077
$707$	17.3820	0.653716
$708$	0.854102	0.0320991
$709$	−41.3050	−1.55124	−0.775620	−	0.631200i	$-0.782563\pi$
$709$	−41.3050	−1.55124	−0.775620	+	0.631200i	$0.782563\pi$
$710$	0	0
$711$	−22.5623	−0.846153
$712$	−15.4508	−0.579045
$713$	12.2705	0.459534
$714$	−7.47214	−0.279638
$715$	0	0
$716$	−8.41641	−0.314536
$717$	−16.7082	−0.623979
$718$	−7.23607	−0.270048
$719$	−15.6525	−0.583739	−0.291869	−	0.956458i	$-0.594277\pi$
$719$	−15.6525	−0.583739	−0.291869	+	0.956458i	$0.594277\pi$
$720$	0	0
$721$	15.3607	0.572062
$722$	−42.0689	−1.56564
$723$	−55.6869	−2.07102
$724$	−3.76393	−0.139885
$725$	0	0
$726$	0	0
$727$	−41.2705	−1.53064	−0.765319	−	0.643651i	$-0.777419\pi$
$727$	−41.2705	−1.53064	−0.765319	+	0.643651i	$0.777419\pi$
$728$	−39.7984	−1.47503
$729$	−39.5623	−1.46527
$730$	0	0
$731$	3.70820	0.137153
$732$	−0.145898	−0.00539255
$733$	−45.8328	−1.69287	−0.846437	−	0.532489i	$-0.821257\pi$
$733$	−45.8328	−1.69287	−0.846437	+	0.532489i	$0.821257\pi$
$734$	−11.5623	−0.426772
$735$	0	0
$736$	−13.8328	−0.509884
$737$	0	0
$738$	−18.7082	−0.688659
$739$	29.1459	1.07215	0.536075	−	0.844171i	$-0.319907\pi$
$739$	29.1459	1.07215	0.536075	+	0.844171i	$0.319907\pi$
$740$	0	0
$741$	−109.520	−4.02331
$742$	−43.0689	−1.58111
$743$	−18.6738	−0.685074	−0.342537	−	0.939504i	$-0.611286\pi$
$743$	−18.6738	−0.685074	−0.342537	+	0.939504i	$0.611286\pi$
$744$	−17.5623	−0.643865
$745$	0	0
$746$	4.56231	0.167038
$747$	39.1033	1.43072
$748$	0	0
$749$	12.0902	0.441765
$750$	0	0
$751$	11.2705	0.411267	0.205633	−	0.978629i	$-0.434075\pi$
$751$	11.2705	0.411267	0.205633	+	0.978629i	$0.434075\pi$
$752$	−57.9787	−2.11427
$753$	−71.3951	−2.60178
$754$	13.9443	0.507820
$755$	0	0
$756$	3.94427	0.143452
$757$	−21.4721	−0.780418	−0.390209	−	0.920726i	$-0.627597\pi$
$757$	−21.4721	−0.780418	−0.390209	+	0.920726i	$0.627597\pi$
$758$	28.7426	1.04398
$759$	0	0
$760$	0	0
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	−2.61803	−0.0948414
$763$	8.81966	0.319293
$764$	−13.0344	−0.471570
$765$	0	0
$766$	−8.18034	−0.295568
$767$	−3.29180	−0.118860
$768$	35.5066	1.28123
$769$	5.00000	0.180305	0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000	0.180305	0.0901523	+	0.995928i	$0.471265\pi$
$770$	0	0
$771$	−28.6525	−1.03189
$772$	−8.00000	−0.287926
$773$	33.7984	1.21564	0.607822	−	0.794074i	$-0.292044\pi$
$773$	33.7984	1.21564	0.607822	+	0.794074i	$0.292044\pi$
$774$	−37.4164	−1.34491
$775$	0	0
$776$	3.61803	0.129880
$777$	76.4853	2.74389
$778$	−8.94427	−0.320668
$779$	20.1246	0.721039
$780$	0	0
$781$	0	0
$782$	4.09017	0.146264
$783$	3.09017	0.110434
$784$	−5.56231	−0.198654
$785$	0	0
$786$	42.7426	1.52458
$787$	−21.2918	−0.758971	−0.379485	−	0.925198i	$-0.623899\pi$
$787$	−21.2918	−0.758971	−0.379485	+	0.925198i	$0.623899\pi$
$788$	12.4164	0.442316
$789$	54.9787	1.95729
$790$	0	0
$791$	−33.2574	−1.18250
$792$	0	0
$793$	0.562306	0.0199681
$794$	−24.1246	−0.856150
$795$	0	0
$796$	−1.90983	−0.0676921
$797$	3.20163	0.113407	0.0567037	−	0.998391i	$-0.481941\pi$
$797$	3.20163	0.113407	0.0567037	+	0.998391i	$0.481941\pi$
$798$	−81.1033	−2.87103
$799$	7.38197	0.261155
$800$	0	0
$801$	−26.6312	−0.940967
$802$	−55.5967	−1.96319
$803$	0	0
$804$	12.9443	0.456509
$805$	0	0
$806$	−30.2705	−1.06623
$807$	79.3951	2.79484
$808$	13.6180	0.479081
$809$	16.5836	0.583048	0.291524	−	0.956564i	$-0.405838\pi$
$809$	16.5836	0.583048	0.291524	+	0.956564i	$0.405838\pi$
$810$	0	0
$811$	−17.0000	−0.596951	−0.298475	−	0.954417i	$-0.596478\pi$
$811$	−17.0000	−0.596951	−0.298475	+	0.954417i	$0.596478\pi$
$812$	2.43769	0.0855463
$813$	−34.5066	−1.21020
$814$	0	0
$815$	0	0
$816$	−7.85410	−0.274949
$817$	40.2492	1.40814
$818$	32.5623	1.13851
$819$	−68.5967	−2.39696
$820$	0	0
$821$	−4.36068	−0.152189	−0.0760944	−	0.997101i	$-0.524245\pi$
$821$	−4.36068	−0.152189	−0.0760944	+	0.997101i	$0.524245\pi$
$822$	−23.5623	−0.821830
$823$	27.4164	0.955676	0.477838	−	0.878448i	$-0.341421\pi$
$823$	27.4164	0.955676	0.477838	+	0.878448i	$0.341421\pi$
$824$	12.0344	0.419240
$825$	0	0
$826$	−2.43769	−0.0848182
$827$	−32.0689	−1.11514	−0.557572	−	0.830128i	$-0.688267\pi$
$827$	−32.0689	−1.11514	−0.557572	+	0.830128i	$0.688267\pi$
$828$	−9.74265	−0.338580
$829$	−36.1033	−1.25392	−0.626960	−	0.779051i	$-0.715701\pi$
$829$	−36.1033	−1.25392	−0.626960	+	0.779051i	$0.715701\pi$
$830$	0	0
$831$	30.0344	1.04188
$832$	−26.4164	−0.915824
$833$	0.708204	0.0245378
$834$	−13.9443	−0.482851
$835$	0	0
$836$	0	0
$837$	−6.70820	−0.231869
$838$	−34.2705	−1.18386
$839$	−48.3394	−1.66886	−0.834431	−	0.551113i	$-0.814203\pi$
$839$	−48.3394	−1.66886	−0.834431	+	0.551113i	$0.814203\pi$
$840$	0	0
$841$	−27.0902	−0.934144
$842$	19.8541	0.684218
$843$	66.3951	2.28677
$844$	−10.5066	−0.361651
$845$	0	0
$846$	−74.4853	−2.56086
$847$	0	0
$848$	−45.2705	−1.55460
$849$	19.3262	0.663275
$850$	0	0
$851$	−41.8673	−1.43519
$852$	13.2361	0.453460
$853$	−49.8541	−1.70697	−0.853486	−	0.521116i	$-0.825516\pi$
$853$	−49.8541	−1.70697	−0.853486	+	0.521116i	$0.825516\pi$
$854$	0.416408	0.0142492
$855$	0	0
$856$	9.47214	0.323751
$857$	53.1803	1.81661	0.908303	−	0.418313i	$-0.137379\pi$
$857$	53.1803	1.81661	0.908303	+	0.418313i	$0.137379\pi$
$858$	0	0
$859$	16.1803	0.552066	0.276033	−	0.961148i	$-0.410980\pi$
$859$	16.1803	0.552066	0.276033	+	0.961148i	$0.410980\pi$
$860$	0	0
$861$	22.4164	0.763949
$862$	1.32624	0.0451718
$863$	−0.596748	−0.0203135	−0.0101568	−	0.999948i	$-0.503233\pi$
$863$	−0.596748	−0.0203135	−0.0101568	+	0.999948i	$0.503233\pi$
$864$	7.56231	0.257275
$865$	0	0
$866$	30.5623	1.03855
$867$	−43.5066	−1.47756
$868$	−5.29180	−0.179615
$869$	0	0
$870$	0	0
$871$	−49.8885	−1.69041
$872$	6.90983	0.233996
$873$	6.23607	0.211059
$874$	44.3951	1.50169
$875$	0	0
$876$	−16.7984	−0.567564
$877$	−4.58359	−0.154777	−0.0773885	−	0.997001i	$-0.524658\pi$
$877$	−4.58359	−0.154777	−0.0773885	+	0.997001i	$0.524658\pi$
$878$	−1.18034	−0.0398345
$879$	62.5410	2.10946
$880$	0	0
$881$	10.0902	0.339946	0.169973	−	0.985449i	$-0.445632\pi$
$881$	10.0902	0.339946	0.169973	+	0.985449i	$0.445632\pi$
$882$	−7.14590	−0.240615
$883$	−31.6525	−1.06519	−0.532595	−	0.846370i	$-0.678783\pi$
$883$	−31.6525	−1.06519	−0.532595	+	0.846370i	$0.678783\pi$
$884$	−2.38197	−0.0801142
$885$	0	0
$886$	59.3050	1.99239
$887$	−28.7771	−0.966240	−0.483120	−	0.875554i	$-0.660497\pi$
$887$	−28.7771	−0.966240	−0.483120	+	0.875554i	$0.660497\pi$
$888$	59.9230	2.01088
$889$	1.76393	0.0591604
$890$	0	0
$891$	0	0
$892$	10.4377	0.349480
$893$	80.1246	2.68127
$894$	−37.8885	−1.26718
$895$	0	0
$896$	−38.8673	−1.29846
$897$	66.7771	2.22962
$898$	24.7984	0.827532
$899$	−4.14590	−0.138273
$900$	0	0
$901$	5.76393	0.192024
$902$	0	0
$903$	44.8328	1.49194
$904$	−26.0557	−0.866601
$905$	0	0
$906$	−12.7082	−0.422202
$907$	14.8328	0.492516	0.246258	−	0.969204i	$-0.420799\pi$
$907$	14.8328	0.492516	0.246258	+	0.969204i	$0.420799\pi$
$908$	14.8541	0.492951
$909$	23.4721	0.778522
$910$	0	0
$911$	−18.0000	−0.596367	−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000	−0.596367	−0.298183	+	0.954509i	$0.596381\pi$
$912$	−85.2492	−2.82288
$913$	0	0
$914$	−12.9098	−0.427019
$915$	0	0
$916$	7.43769	0.245748
$917$	−28.7984	−0.951006
$918$	−2.23607	−0.0738012
$919$	−23.4164	−0.772436	−0.386218	−	0.922408i	$-0.626219\pi$
$919$	−23.4164	−0.772436	−0.386218	+	0.922408i	$0.626219\pi$
$920$	0	0
$921$	−87.5755	−2.88571
$922$	−14.8541	−0.489194
$923$	−51.0132	−1.67912
$924$	0	0
$925$	0	0
$926$	−18.3820	−0.604069
$927$	20.7426	0.681278
$928$	4.67376	0.153424
$929$	54.5967	1.79126	0.895631	−	0.444799i	$-0.146725\pi$
$929$	54.5967	1.79126	0.895631	+	0.444799i	$0.146725\pi$
$930$	0	0
$931$	7.68692	0.251929
$932$	−9.58359	−0.313921
$933$	−50.2148	−1.64396
$934$	−60.6312	−1.98391
$935$	0	0
$936$	−53.7426	−1.75663
$937$	38.8328	1.26861	0.634306	−	0.773082i	$-0.281286\pi$
$937$	38.8328	1.26861	0.634306	+	0.773082i	$0.281286\pi$
$938$	−36.9443	−1.20627
$939$	−8.47214	−0.276478
$940$	0	0
$941$	−41.7214	−1.36008	−0.680039	−	0.733176i	$-0.738037\pi$
$941$	−41.7214	−1.36008	−0.680039	+	0.733176i	$0.738037\pi$
$942$	22.9443	0.747565
$943$	−12.2705	−0.399583
$944$	−2.56231	−0.0833960
$945$	0	0
$946$	0	0
$947$	−39.3607	−1.27905	−0.639525	−	0.768770i	$-0.720869\pi$
$947$	−39.3607	−1.27905	−0.639525	+	0.768770i	$0.720869\pi$
$948$	−9.47214	−0.307641
$949$	64.7426	2.10164
$950$	0	0
$951$	43.5066	1.41080
$952$	3.94427	0.127835
$953$	−8.47214	−0.274439	−0.137220	−	0.990541i	$-0.543817\pi$
$953$	−8.47214	−0.274439	−0.137220	+	0.990541i	$0.543817\pi$
$954$	−58.1591	−1.88297
$955$	0	0
$956$	−3.94427	−0.127567
$957$	0	0
$958$	45.9787	1.48550
$959$	15.8754	0.512643
$960$	0	0
$961$	−22.0000	−0.709677
$962$	103.284	3.33000
$963$	16.3262	0.526106
$964$	−13.1459	−0.423401
$965$	0	0
$966$	49.4508	1.59106
$967$	−37.2705	−1.19854	−0.599269	−	0.800547i	$-0.704542\pi$
$967$	−37.2705	−1.19854	−0.599269	+	0.800547i	$0.704542\pi$
$968$	0	0
$969$	10.8541	0.348684
$970$	0	0
$971$	23.9098	0.767303	0.383651	−	0.923478i	$-0.374666\pi$
$971$	23.9098	0.767303	0.383651	+	0.923478i	$0.374666\pi$
$972$	−13.3820	−0.429227
$973$	9.39512	0.301194
$974$	49.2148	1.57694
$975$	0	0
$976$	0.437694	0.0140102
$977$	57.0689	1.82580	0.912898	−	0.408188i	$-0.133839\pi$
$977$	57.0689	1.82580	0.912898	+	0.408188i	$0.133839\pi$
$978$	29.0344	0.928419
$979$	0	0
$980$	0	0
$981$	11.9098	0.380252
$982$	−11.0344	−0.352123
$983$	−1.52786	−0.0487313	−0.0243656	−	0.999703i	$-0.507757\pi$
$983$	−1.52786	−0.0487313	−0.0243656	+	0.999703i	$0.507757\pi$
$984$	17.5623	0.559866
$985$	0	0
$986$	−1.38197	−0.0440108
$987$	89.2492	2.84083
$988$	−25.8541	−0.822529
$989$	−24.5410	−0.780359
$990$	0	0
$991$	21.2705	0.675680	0.337840	−	0.941204i	$-0.390304\pi$
$991$	21.2705	0.675680	0.337840	+	0.941204i	$0.390304\pi$
$992$	−10.1459	−0.322133
$993$	−50.2148	−1.59352
$994$	−37.7771	−1.19822
$995$	0	0
$996$	16.4164	0.520174
$997$	−32.1459	−1.01807	−0.509035	−	0.860746i	$-0.669998\pi$
$997$	−32.1459	−1.01807	−0.509035	+	0.860746i	$0.669998\pi$
$998$	−48.2148	−1.52621
$999$	22.8885	0.724161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3025.2.a.i.1.1		2
5.4	even	2		3025.2.a.m.1.2		2
11.10	odd	2		275.2.a.g.1.2	yes	2
33.32	even	2		2475.2.a.n.1.1		2
44.43	even	2		4400.2.a.bg.1.1		2
55.32	even	4		275.2.b.e.199.4		4
55.43	even	4		275.2.b.e.199.1		4
55.54	odd	2		275.2.a.d.1.1	✓	2
165.32	odd	4		2475.2.c.p.199.1		4
165.98	odd	4		2475.2.c.p.199.4		4
165.164	even	2		2475.2.a.s.1.2		2
220.43	odd	4		4400.2.b.x.4049.1		4
220.87	odd	4		4400.2.b.x.4049.4		4
220.219	even	2		4400.2.a.bv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.a.d.1.1	✓	2	55.54	odd	2
275.2.a.g.1.2	yes	2	11.10	odd	2
275.2.b.e.199.1		4	55.43	even	4
275.2.b.e.199.4		4	55.32	even	4
2475.2.a.n.1.1		2	33.32	even	2
2475.2.a.s.1.2		2	165.164	even	2
2475.2.c.p.199.1		4	165.32	odd	4
2475.2.c.p.199.4		4	165.98	odd	4
3025.2.a.i.1.1		2	1.1	even	1	trivial
3025.2.a.m.1.2		2	5.4	even	2
4400.2.a.bg.1.1		2	44.43	even	2
4400.2.a.bv.1.2		2	220.219	even	2
4400.2.b.x.4049.1		4	220.43	odd	4
4400.2.b.x.4049.4		4	220.87	odd	4

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:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -4.23607 q^{6} +2.85410 q^{7} +2.23607 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -4.23607 q^{6} +2.85410 q^{7} +2.23607 q^{8} +3.85410 q^{9} +1.61803 q^{12} -6.23607 q^{13} -4.61803 q^{14} -4.85410 q^{16} +0.618034 q^{17} -6.23607 q^{18} +6.70820 q^{19} +7.47214 q^{21} -4.09017 q^{23} +5.85410 q^{24} +10.0902 q^{26} +2.23607 q^{27} +1.76393 q^{28} +1.38197 q^{29} -3.00000 q^{31} +3.38197 q^{32} -1.00000 q^{34} +2.38197 q^{36} +10.2361 q^{37} -10.8541 q^{38} -16.3262 q^{39} +3.00000 q^{41} -12.0902 q^{42} +6.00000 q^{43} +6.61803 q^{46} +11.9443 q^{47} -12.7082 q^{48} +1.14590 q^{49} +1.61803 q^{51} -3.85410 q^{52} +9.32624 q^{53} -3.61803 q^{54} +6.38197 q^{56} +17.5623 q^{57} -2.23607 q^{58} +0.527864 q^{59} -0.0901699 q^{61} +4.85410 q^{62} +11.0000 q^{63} +4.23607 q^{64} +8.00000 q^{67} +0.381966 q^{68} -10.7082 q^{69} +8.18034 q^{71} +8.61803 q^{72} -10.3820 q^{73} -16.5623 q^{74} +4.14590 q^{76} +26.4164 q^{78} -5.85410 q^{79} -5.70820 q^{81} -4.85410 q^{82} +10.1459 q^{83} +4.61803 q^{84} -9.70820 q^{86} +3.61803 q^{87} -6.90983 q^{89} -17.7984 q^{91} -2.52786 q^{92} -7.85410 q^{93} -19.3262 q^{94} +8.85410 q^{96} +1.61803 q^{97} -1.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{6} - q^{7} + q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^6 - q^7 + q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{6} - q^{7} + q^{9} + q^{12} - 8 q^{13} - 7 q^{14} - 3 q^{16} - q^{17} - 8 q^{18} + 6 q^{21} + 3 q^{23} + 5 q^{24} + 9 q^{26} + 8 q^{28} + 5 q^{29} - 6 q^{31} + 9 q^{32} - 2 q^{34} + 7 q^{36} + 16 q^{37} - 15 q^{38} - 17 q^{39} + 6 q^{41} - 13 q^{42} + 12 q^{43} + 11 q^{46} + 6 q^{47} - 12 q^{48} + 9 q^{49} + q^{51} - q^{52} + 3 q^{53} - 5 q^{54} + 15 q^{56} + 15 q^{57} + 10 q^{59} + 11 q^{61} + 3 q^{62} + 22 q^{63} + 4 q^{64} + 16 q^{67} + 3 q^{68} - 8 q^{69} - 6 q^{71} + 15 q^{72} - 23 q^{73} - 13 q^{74} + 15 q^{76} + 26 q^{78} - 5 q^{79} + 2 q^{81} - 3 q^{82} + 27 q^{83} + 7 q^{84} - 6 q^{86} + 5 q^{87} - 25 q^{89} - 11 q^{91} - 14 q^{92} - 9 q^{93} - 23 q^{94} + 11 q^{96} + q^{97} + 3 q^{98}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^6 - q^7 + q^9 + q^12 - 8 * q^13 - 7 * q^14 - 3 * q^16 - q^17 - 8 * q^18 + 6 * q^21 + 3 * q^23 + 5 * q^24 + 9 * q^26 + 8 * q^28 + 5 * q^29 - 6 * q^31 + 9 * q^32 - 2 * q^34 + 7 * q^36 + 16 * q^37 - 15 * q^38 - 17 * q^39 + 6 * q^41 - 13 * q^42 + 12 * q^43 + 11 * q^46 + 6 * q^47 - 12 * q^48 + 9 * q^49 + q^51 - q^52 + 3 * q^53 - 5 * q^54 + 15 * q^56 + 15 * q^57 + 10 * q^59 + 11 * q^61 + 3 * q^62 + 22 * q^63 + 4 * q^64 + 16 * q^67 + 3 * q^68 - 8 * q^69 - 6 * q^71 + 15 * q^72 - 23 * q^73 - 13 * q^74 + 15 * q^76 + 26 * q^78 - 5 * q^79 + 2 * q^81 - 3 * q^82 + 27 * q^83 + 7 * q^84 - 6 * q^86 + 5 * q^87 - 25 * q^89 - 11 * q^91 - 14 * q^92 - 9 * q^93 - 23 * q^94 + 11 * q^96 + q^97 + 3 * q^98

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