LMFDB - Embedded newform 4025.2.a.h.1.2

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:	$0$
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 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-0.381966 q^{2} -2.23607 q^{3} -1.85410 q^{4} +0.854102 q^{6} +1.00000 q^{7} +1.47214 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-0.381966 q^{2} -2.23607 q^{3} -1.85410 q^{4} +0.854102 q^{6} +1.00000 q^{7} +1.47214 q^{8} +2.00000 q^{9} +6.00000 q^{11} +4.14590 q^{12} -3.00000 q^{13} -0.381966 q^{14} +3.14590 q^{16} +1.23607 q^{17} -0.763932 q^{18} +8.47214 q^{19} -2.23607 q^{21} -2.29180 q^{22} -1.00000 q^{23} -3.29180 q^{24} +1.14590 q^{26} +2.23607 q^{27} -1.85410 q^{28} +7.47214 q^{29} -5.47214 q^{31} -4.14590 q^{32} -13.4164 q^{33} -0.472136 q^{34} -3.70820 q^{36} +7.23607 q^{37} -3.23607 q^{38} +6.70820 q^{39} +6.70820 q^{41} +0.854102 q^{42} -3.70820 q^{43} -11.1246 q^{44} +0.381966 q^{46} +4.23607 q^{47} -7.03444 q^{48} +1.00000 q^{49} -2.76393 q^{51} +5.56231 q^{52} +8.76393 q^{53} -0.854102 q^{54} +1.47214 q^{56} -18.9443 q^{57} -2.85410 q^{58} -6.47214 q^{59} -1.70820 q^{61} +2.09017 q^{62} +2.00000 q^{63} -4.70820 q^{64} +5.12461 q^{66} -3.23607 q^{67} -2.29180 q^{68} +2.23607 q^{69} -4.23607 q^{71} +2.94427 q^{72} -9.00000 q^{73} -2.76393 q^{74} -15.7082 q^{76} +6.00000 q^{77} -2.56231 q^{78} -13.4164 q^{79} -11.0000 q^{81} -2.56231 q^{82} -3.70820 q^{83} +4.14590 q^{84} +1.41641 q^{86} -16.7082 q^{87} +8.83282 q^{88} -9.23607 q^{89} -3.00000 q^{91} +1.85410 q^{92} +12.2361 q^{93} -1.61803 q^{94} +9.27051 q^{96} +0.291796 q^{97} -0.381966 q^{98} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 3 q^{4} - 5 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 3 * q^4 - 5 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9	$ 2 q - 3 q^{2} + 3 q^{4} - 5 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9} + 12 q^{11} + 15 q^{12} - 6 q^{13} - 3 q^{14} + 13 q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - 18 q^{22} - 2 q^{23} - 20 q^{24} + 9 q^{26} + 3 q^{28} + 6 q^{29} - 2 q^{31} - 15 q^{32} + 8 q^{34} + 6 q^{36} + 10 q^{37} - 2 q^{38} - 5 q^{42} + 6 q^{43} + 18 q^{44} + 3 q^{46} + 4 q^{47} + 15 q^{48} + 2 q^{49} - 10 q^{51} - 9 q^{52} + 22 q^{53} + 5 q^{54} - 6 q^{56} - 20 q^{57} + q^{58} - 4 q^{59} + 10 q^{61} - 7 q^{62} + 4 q^{63} + 4 q^{64} - 30 q^{66} - 2 q^{67} - 18 q^{68} - 4 q^{71} - 12 q^{72} - 18 q^{73} - 10 q^{74} - 18 q^{76} + 12 q^{77} + 15 q^{78} - 22 q^{81} + 15 q^{82} + 6 q^{83} + 15 q^{84} - 24 q^{86} - 20 q^{87} - 36 q^{88} - 14 q^{89} - 6 q^{91} - 3 q^{92} + 20 q^{93} - q^{94} - 15 q^{96} + 14 q^{97} - 3 q^{98} + 24 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 + 3 * q^4 - 5 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9 + 12 * q^11 + 15 * q^12 - 6 * q^13 - 3 * q^14 + 13 * q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - 18 * q^22 - 2 * q^23 - 20 * q^24 + 9 * q^26 + 3 * q^28 + 6 * q^29 - 2 * q^31 - 15 * q^32 + 8 * q^34 + 6 * q^36 + 10 * q^37 - 2 * q^38 - 5 * q^42 + 6 * q^43 + 18 * q^44 + 3 * q^46 + 4 * q^47 + 15 * q^48 + 2 * q^49 - 10 * q^51 - 9 * q^52 + 22 * q^53 + 5 * q^54 - 6 * q^56 - 20 * q^57 + q^58 - 4 * q^59 + 10 * q^61 - 7 * q^62 + 4 * q^63 + 4 * q^64 - 30 * q^66 - 2 * q^67 - 18 * q^68 - 4 * q^71 - 12 * q^72 - 18 * q^73 - 10 * q^74 - 18 * q^76 + 12 * q^77 + 15 * q^78 - 22 * q^81 + 15 * q^82 + 6 * q^83 + 15 * q^84 - 24 * q^86 - 20 * q^87 - 36 * q^88 - 14 * q^89 - 6 * q^91 - 3 * q^92 + 20 * q^93 - q^94 - 15 * q^96 + 14 * q^97 - 3 * q^98 + 24 * 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 $

$2$	−0.381966	−0.270091	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−0.381966	−0.270091	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−2.23607	−1.29099	−0.645497	−	0.763763i	$-0.723350\pi$
$3$	−2.23607	−1.29099	−0.645497	+	0.763763i	$0.723350\pi$
$4$	−1.85410	−0.927051
$5$	0	0
$5$	0	0
$6$	0.854102	0.348686
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.47214	0.520479
$9$	2.00000	0.666667
$10$	0	0
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	4.14590	1.19682
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−0.381966	−0.102085
$15$	0	0
$16$	3.14590	0.786475
$17$	1.23607	0.299791	0.149895	−	0.988702i	$-0.452106\pi$
$17$	1.23607	0.299791	0.149895	+	0.988702i	$0.452106\pi$
$18$	−0.763932	−0.180061
$19$	8.47214	1.94364	0.971821	−	0.235722i	$-0.0757453\pi$
$19$	8.47214	1.94364	0.971821	+	0.235722i	$0.0757453\pi$
$20$	0	0
$21$	−2.23607	−0.487950
$22$	−2.29180	−0.488613
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.29180	−0.671935
$25$	0	0
$26$	1.14590	0.224729
$27$	2.23607	0.430331
$28$	−1.85410	−0.350392
$29$	7.47214	1.38754	0.693770	−	0.720196i	$-0.255948\pi$
$29$	7.47214	1.38754	0.693770	+	0.720196i	$0.255948\pi$
$30$	0	0
$31$	−5.47214	−0.982825	−0.491412	−	0.870927i	$-0.663519\pi$
$31$	−5.47214	−0.982825	−0.491412	+	0.870927i	$0.663519\pi$
$32$	−4.14590	−0.732898
$33$	−13.4164	−2.33550
$34$	−0.472136	−0.0809706
$35$	0	0
$36$	−3.70820	−0.618034
$37$	7.23607	1.18960	0.594801	−	0.803873i	$-0.297231\pi$
$37$	7.23607	1.18960	0.594801	+	0.803873i	$0.297231\pi$
$38$	−3.23607	−0.524960
$39$	6.70820	1.07417
$40$	0	0
$41$	6.70820	1.04765	0.523823	−	0.851827i	$-0.324505\pi$
$41$	6.70820	1.04765	0.523823	+	0.851827i	$0.324505\pi$
$42$	0.854102	0.131791
$43$	−3.70820	−0.565496	−0.282748	−	0.959194i	$-0.591246\pi$
$43$	−3.70820	−0.565496	−0.282748	+	0.959194i	$0.591246\pi$
$44$	−11.1246	−1.67710
$45$	0	0
$46$	0.381966	0.0563178
$47$	4.23607	0.617894	0.308947	−	0.951079i	$-0.400023\pi$
$47$	4.23607	0.617894	0.308947	+	0.951079i	$0.400023\pi$
$48$	−7.03444	−1.01533
$49$	1.00000	0.142857
$50$	0	0
$51$	−2.76393	−0.387028
$52$	5.56231	0.771353
$53$	8.76393	1.20382	0.601909	−	0.798564i	$-0.294407\pi$
$53$	8.76393	1.20382	0.601909	+	0.798564i	$0.294407\pi$
$54$	−0.854102	−0.116229
$55$	0	0
$56$	1.47214	0.196722
$57$	−18.9443	−2.50923
$58$	−2.85410	−0.374762
$59$	−6.47214	−0.842600	−0.421300	−	0.906921i	$-0.638426\pi$
$59$	−6.47214	−0.842600	−0.421300	+	0.906921i	$0.638426\pi$
$60$	0	0
$61$	−1.70820	−0.218713	−0.109357	−	0.994003i	$-0.534879\pi$
$61$	−1.70820	−0.218713	−0.109357	+	0.994003i	$0.534879\pi$
$62$	2.09017	0.265452
$63$	2.00000	0.251976
$64$	−4.70820	−0.588525
$65$	0	0
$66$	5.12461	0.630796
$67$	−3.23607	−0.395349	−0.197674	−	0.980268i	$-0.563339\pi$
$67$	−3.23607	−0.395349	−0.197674	+	0.980268i	$0.563339\pi$
$68$	−2.29180	−0.277921
$69$	2.23607	0.269191
$70$	0	0
$71$	−4.23607	−0.502729	−0.251364	−	0.967893i	$-0.580879\pi$
$71$	−4.23607	−0.502729	−0.251364	+	0.967893i	$0.580879\pi$
$72$	2.94427	0.346986
$73$	−9.00000	−1.05337	−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000	−1.05337	−0.526685	+	0.850060i	$0.676565\pi$
$74$	−2.76393	−0.321301
$75$	0	0
$76$	−15.7082	−1.80185
$77$	6.00000	0.683763
$78$	−2.56231	−0.290124
$79$	−13.4164	−1.50946	−0.754732	−	0.656033i	$-0.772233\pi$
$79$	−13.4164	−1.50946	−0.754732	+	0.656033i	$0.772233\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	−2.56231	−0.282959
$83$	−3.70820	−0.407028	−0.203514	−	0.979072i	$-0.565236\pi$
$83$	−3.70820	−0.407028	−0.203514	+	0.979072i	$0.565236\pi$
$84$	4.14590	0.452355
$85$	0	0
$86$	1.41641	0.152735
$87$	−16.7082	−1.79131
$88$	8.83282	0.941581
$89$	−9.23607	−0.979021	−0.489511	−	0.871997i	$-0.662825\pi$
$89$	−9.23607	−0.979021	−0.489511	+	0.871997i	$0.662825\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	1.85410	0.193303
$93$	12.2361	1.26882
$94$	−1.61803	−0.166887
$95$	0	0
$96$	9.27051	0.946167
$97$	0.291796	0.0296274	0.0148137	−	0.999890i	$-0.495284\pi$
$97$	0.291796	0.0296274	0.0148137	+	0.999890i	$0.495284\pi$
$98$	−0.381966	−0.0385844
$99$	12.0000	1.20605
$100$	0	0
$101$	6.94427	0.690981	0.345490	−	0.938422i	$-0.387713\pi$
$101$	6.94427	0.690981	0.345490	+	0.938422i	$0.387713\pi$
$102$	1.05573	0.104533
$103$	−0.944272	−0.0930419	−0.0465209	−	0.998917i	$-0.514813\pi$
$103$	−0.944272	−0.0930419	−0.0465209	+	0.998917i	$0.514813\pi$
$104$	−4.41641	−0.433064
$105$	0	0
$106$	−3.34752	−0.325140
$107$	15.8885	1.53600	0.768002	−	0.640448i	$-0.221251\pi$
$107$	15.8885	1.53600	0.768002	+	0.640448i	$0.221251\pi$
$108$	−4.14590	−0.398939
$109$	11.7082	1.12144	0.560721	−	0.828005i	$-0.310524\pi$
$109$	11.7082	1.12144	0.560721	+	0.828005i	$0.310524\pi$
$110$	0	0
$111$	−16.1803	−1.53577
$112$	3.14590	0.297259
$113$	−7.41641	−0.697677	−0.348838	−	0.937183i	$-0.613424\pi$
$113$	−7.41641	−0.697677	−0.348838	+	0.937183i	$0.613424\pi$
$114$	7.23607	0.677720
$115$	0	0
$116$	−13.8541	−1.28632
$117$	−6.00000	−0.554700
$118$	2.47214	0.227579
$119$	1.23607	0.113310
$120$	0	0
$121$	25.0000	2.27273
$122$	0.652476	0.0590724
$123$	−15.0000	−1.35250
$124$	10.1459	0.911129
$125$	0	0
$126$	−0.763932	−0.0680565
$127$	−3.00000	−0.266207	−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000	−0.266207	−0.133103	+	0.991102i	$0.542494\pi$
$128$	10.0902	0.891853
$129$	8.29180	0.730052
$130$	0	0
$131$	10.5279	0.919824	0.459912	−	0.887965i	$-0.347881\pi$
$131$	10.5279	0.919824	0.459912	+	0.887965i	$0.347881\pi$
$132$	24.8754	2.16512
$133$	8.47214	0.734627
$134$	1.23607	0.106780
$135$	0	0
$136$	1.81966	0.156035
$137$	−1.23607	−0.105604	−0.0528022	−	0.998605i	$-0.516815\pi$
$137$	−1.23607	−0.105604	−0.0528022	+	0.998605i	$0.516815\pi$
$138$	−0.854102	−0.0727060
$139$	−11.4721	−0.973054	−0.486527	−	0.873666i	$-0.661736\pi$
$139$	−11.4721	−0.973054	−0.486527	+	0.873666i	$0.661736\pi$
$140$	0	0
$141$	−9.47214	−0.797698
$142$	1.61803	0.135782
$143$	−18.0000	−1.50524
$144$	6.29180	0.524316
$145$	0	0
$146$	3.43769	0.284506
$147$	−2.23607	−0.184428
$148$	−13.4164	−1.10282
$149$	4.76393	0.390277	0.195138	−	0.980776i	$-0.437484\pi$
$149$	4.76393	0.390277	0.195138	+	0.980776i	$0.437484\pi$
$150$	0	0
$151$	22.2361	1.80955	0.904773	−	0.425895i	$-0.140041\pi$
$151$	22.2361	1.80955	0.904773	+	0.425895i	$0.140041\pi$
$152$	12.4721	1.01162
$153$	2.47214	0.199860
$154$	−2.29180	−0.184678
$155$	0	0
$156$	−12.4377	−0.995812
$157$	14.7639	1.17829	0.589145	−	0.808027i	$-0.299465\pi$
$157$	14.7639	1.17829	0.589145	+	0.808027i	$0.299465\pi$
$158$	5.12461	0.407692
$159$	−19.5967	−1.55412
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	4.20163	0.330111
$163$	17.0000	1.33154	0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000	1.33154	0.665771	+	0.746156i	$0.268103\pi$
$164$	−12.4377	−0.971221
$165$	0	0
$166$	1.41641	0.109935
$167$	−16.9443	−1.31119	−0.655594	−	0.755114i	$-0.727582\pi$
$167$	−16.9443	−1.31119	−0.655594	+	0.755114i	$0.727582\pi$
$168$	−3.29180	−0.253968
$169$	−4.00000	−0.307692
$170$	0	0
$171$	16.9443	1.29576
$172$	6.87539	0.524243
$173$	2.94427	0.223849	0.111924	−	0.993717i	$-0.464299\pi$
$173$	2.94427	0.223849	0.111924	+	0.993717i	$0.464299\pi$
$174$	6.38197	0.483816
$175$	0	0
$176$	18.8754	1.42279
$177$	14.4721	1.08779
$178$	3.52786	0.264425
$179$	18.7082	1.39832	0.699158	−	0.714967i	$-0.253558\pi$
$179$	18.7082	1.39832	0.699158	+	0.714967i	$0.253558\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	1.14590	0.0849396
$183$	3.81966	0.282357
$184$	−1.47214	−0.108527
$185$	0	0
$186$	−4.67376	−0.342697
$187$	7.41641	0.542341
$188$	−7.85410	−0.572819
$189$	2.23607	0.162650
$190$	0	0
$191$	0.472136	0.0341626	0.0170813	−	0.999854i	$-0.494563\pi$
$191$	0.472136	0.0341626	0.0170813	+	0.999854i	$0.494563\pi$
$192$	10.5279	0.759783
$193$	1.76393	0.126971	0.0634853	−	0.997983i	$-0.479778\pi$
$193$	1.76393	0.126971	0.0634853	+	0.997983i	$0.479778\pi$
$194$	−0.111456	−0.00800209
$195$	0	0
$196$	−1.85410	−0.132436
$197$	−5.29180	−0.377025	−0.188512	−	0.982071i	$-0.560367\pi$
$197$	−5.29180	−0.377025	−0.188512	+	0.982071i	$0.560367\pi$
$198$	−4.58359	−0.325742
$199$	1.41641	0.100406	0.0502032	−	0.998739i	$-0.484013\pi$
$199$	1.41641	0.100406	0.0502032	+	0.998739i	$0.484013\pi$
$200$	0	0
$201$	7.23607	0.510393
$202$	−2.65248	−0.186628
$203$	7.47214	0.524441
$204$	5.12461	0.358795
$205$	0	0
$206$	0.360680	0.0251298
$207$	−2.00000	−0.139010
$208$	−9.43769	−0.654386
$209$	50.8328	3.51618
$210$	0	0
$211$	−16.9443	−1.16649	−0.583246	−	0.812296i	$-0.698218\pi$
$211$	−16.9443	−1.16649	−0.583246	+	0.812296i	$0.698218\pi$
$212$	−16.2492	−1.11600
$213$	9.47214	0.649020
$214$	−6.06888	−0.414860
$215$	0	0
$216$	3.29180	0.223978
$217$	−5.47214	−0.371473
$218$	−4.47214	−0.302891
$219$	20.1246	1.35990
$220$	0	0
$221$	−3.70820	−0.249441
$222$	6.18034	0.414797
$223$	12.9443	0.866813	0.433406	−	0.901199i	$-0.357312\pi$
$223$	12.9443	0.866813	0.433406	+	0.901199i	$0.357312\pi$
$224$	−4.14590	−0.277009
$225$	0	0
$226$	2.83282	0.188436
$227$	19.4164	1.28871	0.644356	−	0.764726i	$-0.277125\pi$
$227$	19.4164	1.28871	0.644356	+	0.764726i	$0.277125\pi$
$228$	35.1246	2.32618
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	0	0
$231$	−13.4164	−0.882735
$232$	11.0000	0.722185
$233$	−6.70820	−0.439469	−0.219735	−	0.975560i	$-0.570519\pi$
$233$	−6.70820	−0.439469	−0.219735	+	0.975560i	$0.570519\pi$
$234$	2.29180	0.149819
$235$	0	0
$236$	12.0000	0.781133
$237$	30.0000	1.94871
$238$	−0.472136	−0.0306040
$239$	17.6525	1.14184	0.570922	−	0.821004i	$-0.306586\pi$
$239$	17.6525	1.14184	0.570922	+	0.821004i	$0.306586\pi$
$240$	0	0
$241$	−29.1246	−1.87608	−0.938041	−	0.346525i	$-0.887361\pi$
$241$	−29.1246	−1.87608	−0.938041	+	0.346525i	$0.887361\pi$
$242$	−9.54915	−0.613843
$243$	17.8885	1.14755
$244$	3.16718	0.202758
$245$	0	0
$246$	5.72949	0.365299
$247$	−25.4164	−1.61721
$248$	−8.05573	−0.511539
$249$	8.29180	0.525471
$250$	0	0
$251$	−8.94427	−0.564557	−0.282279	−	0.959332i	$-0.591090\pi$
$251$	−8.94427	−0.564557	−0.282279	+	0.959332i	$0.591090\pi$
$252$	−3.70820	−0.233595
$253$	−6.00000	−0.377217
$254$	1.14590	0.0719000
$255$	0	0
$256$	5.56231	0.347644
$257$	17.3607	1.08293	0.541465	−	0.840723i	$-0.317870\pi$
$257$	17.3607	1.08293	0.541465	+	0.840723i	$0.317870\pi$
$258$	−3.16718	−0.197180
$259$	7.23607	0.449627
$260$	0	0
$261$	14.9443	0.925027
$262$	−4.02129	−0.248436
$263$	23.5967	1.45504	0.727519	−	0.686088i	$-0.240673\pi$
$263$	23.5967	1.45504	0.727519	+	0.686088i	$0.240673\pi$
$264$	−19.7508	−1.21558
$265$	0	0
$266$	−3.23607	−0.198416
$267$	20.6525	1.26391
$268$	6.00000	0.366508
$269$	−6.70820	−0.409006	−0.204503	−	0.978866i	$-0.565558\pi$
$269$	−6.70820	−0.409006	−0.204503	+	0.978866i	$0.565558\pi$
$270$	0	0
$271$	−17.5279	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$271$	−17.5279	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$272$	3.88854	0.235778
$273$	6.70820	0.405999
$274$	0.472136	0.0285228
$275$	0	0
$276$	−4.14590	−0.249554
$277$	−25.0689	−1.50624	−0.753122	−	0.657881i	$-0.771453\pi$
$277$	−25.0689	−1.50624	−0.753122	+	0.657881i	$0.771453\pi$
$278$	4.38197	0.262813
$279$	−10.9443	−0.655216
$280$	0	0
$281$	14.1803	0.845928	0.422964	−	0.906146i	$-0.360990\pi$
$281$	14.1803	0.845928	0.422964	+	0.906146i	$0.360990\pi$
$282$	3.61803	0.215451
$283$	29.1246	1.73128	0.865639	−	0.500668i	$-0.166912\pi$
$283$	29.1246	1.73128	0.865639	+	0.500668i	$0.166912\pi$
$284$	7.85410	0.466055
$285$	0	0
$286$	6.87539	0.406550
$287$	6.70820	0.395973
$288$	−8.29180	−0.488599
$289$	−15.4721	−0.910126
$290$	0	0
$291$	−0.652476	−0.0382488
$292$	16.6869	0.976528
$293$	9.81966	0.573671	0.286835	−	0.957980i	$-0.407397\pi$
$293$	9.81966	0.573671	0.286835	+	0.957980i	$0.407397\pi$
$294$	0.854102	0.0498122
$295$	0	0
$296$	10.6525	0.619163
$297$	13.4164	0.778499
$298$	−1.81966	−0.105410
$299$	3.00000	0.173494
$300$	0	0
$301$	−3.70820	−0.213737
$302$	−8.49342	−0.488742
$303$	−15.5279	−0.892052
$304$	26.6525	1.52862
$305$	0	0
$306$	−0.944272	−0.0539804
$307$	7.41641	0.423277	0.211638	−	0.977348i	$-0.432120\pi$
$307$	7.41641	0.423277	0.211638	+	0.977348i	$0.432120\pi$
$308$	−11.1246	−0.633884
$309$	2.11146	0.120117
$310$	0	0
$311$	16.4164	0.930889	0.465445	−	0.885077i	$-0.345894\pi$
$311$	16.4164	0.930889	0.465445	+	0.885077i	$0.345894\pi$
$312$	9.87539	0.559084
$313$	19.7082	1.11397	0.556987	−	0.830521i	$-0.311957\pi$
$313$	19.7082	1.11397	0.556987	+	0.830521i	$0.311957\pi$
$314$	−5.63932	−0.318245
$315$	0	0
$316$	24.8754	1.39935
$317$	12.4721	0.700505	0.350252	−	0.936655i	$-0.386096\pi$
$317$	12.4721	0.700505	0.350252	+	0.936655i	$0.386096\pi$
$318$	7.48529	0.419754
$319$	44.8328	2.51016
$320$	0	0
$321$	−35.5279	−1.98297
$322$	0.381966	0.0212861
$323$	10.4721	0.582685
$324$	20.3951	1.13306
$325$	0	0
$326$	−6.49342	−0.359637
$327$	−26.1803	−1.44778
$328$	9.87539	0.545277
$329$	4.23607	0.233542
$330$	0	0
$331$	−20.1246	−1.10615	−0.553074	−	0.833132i	$-0.686545\pi$
$331$	−20.1246	−1.10615	−0.553074	+	0.833132i	$0.686545\pi$
$332$	6.87539	0.377336
$333$	14.4721	0.793068
$334$	6.47214	0.354140
$335$	0	0
$336$	−7.03444	−0.383760
$337$	−19.4164	−1.05768	−0.528840	−	0.848722i	$-0.677373\pi$
$337$	−19.4164	−1.05768	−0.528840	+	0.848722i	$0.677373\pi$
$338$	1.52786	0.0831048
$339$	16.5836	0.900697
$340$	0	0
$341$	−32.8328	−1.77800
$342$	−6.47214	−0.349973
$343$	1.00000	0.0539949
$344$	−5.45898	−0.294328
$345$	0	0
$346$	−1.12461	−0.0604595
$347$	−21.5279	−1.15568	−0.577838	−	0.816151i	$-0.696104\pi$
$347$	−21.5279	−1.15568	−0.577838	+	0.816151i	$0.696104\pi$
$348$	30.9787	1.66063
$349$	−16.2361	−0.869097	−0.434548	−	0.900648i	$-0.643092\pi$
$349$	−16.2361	−0.869097	−0.434548	+	0.900648i	$0.643092\pi$
$350$	0	0
$351$	−6.70820	−0.358057
$352$	−24.8754	−1.32586
$353$	−29.9443	−1.59377	−0.796886	−	0.604129i	$-0.793521\pi$
$353$	−29.9443	−1.59377	−0.796886	+	0.604129i	$0.793521\pi$
$354$	−5.52786	−0.293803
$355$	0	0
$356$	17.1246	0.907603
$357$	−2.76393	−0.146283
$358$	−7.14590	−0.377672
$359$	−14.9443	−0.788729	−0.394364	−	0.918954i	$-0.629035\pi$
$359$	−14.9443	−0.788729	−0.394364	+	0.918954i	$0.629035\pi$
$360$	0	0
$361$	52.7771	2.77774
$362$	3.81966	0.200757
$363$	−55.9017	−2.93408
$364$	5.56231	0.291544
$365$	0	0
$366$	−1.45898	−0.0762621
$367$	9.23607	0.482119	0.241059	−	0.970510i	$-0.422505\pi$
$367$	9.23607	0.482119	0.241059	+	0.970510i	$0.422505\pi$
$368$	−3.14590	−0.163991
$369$	13.4164	0.698430
$370$	0	0
$371$	8.76393	0.455001
$372$	−22.6869	−1.17626
$373$	8.76393	0.453779	0.226890	−	0.973920i	$-0.427144\pi$
$373$	8.76393	0.453779	0.226890	+	0.973920i	$0.427144\pi$
$374$	−2.83282	−0.146481
$375$	0	0
$376$	6.23607	0.321601
$377$	−22.4164	−1.15450
$378$	−0.854102	−0.0439303
$379$	−17.5967	−0.903884	−0.451942	−	0.892047i	$-0.649269\pi$
$379$	−17.5967	−0.903884	−0.451942	+	0.892047i	$0.649269\pi$
$380$	0	0
$381$	6.70820	0.343672
$382$	−0.180340	−0.00922699
$383$	6.47214	0.330711	0.165355	−	0.986234i	$-0.447123\pi$
$383$	6.47214	0.330711	0.165355	+	0.986234i	$0.447123\pi$
$384$	−22.5623	−1.15138
$385$	0	0
$386$	−0.673762	−0.0342936
$387$	−7.41641	−0.376997
$388$	−0.541020	−0.0274661
$389$	−9.88854	−0.501369	−0.250685	−	0.968069i	$-0.580656\pi$
$389$	−9.88854	−0.501369	−0.250685	+	0.968069i	$0.580656\pi$
$390$	0	0
$391$	−1.23607	−0.0625106
$392$	1.47214	0.0743541
$393$	−23.5410	−1.18749
$394$	2.02129	0.101831
$395$	0	0
$396$	−22.2492	−1.11807
$397$	−26.4164	−1.32580	−0.662901	−	0.748707i	$-0.730675\pi$
$397$	−26.4164	−1.32580	−0.662901	+	0.748707i	$0.730675\pi$
$398$	−0.541020	−0.0271189
$399$	−18.9443	−0.948400
$400$	0	0
$401$	35.5967	1.77762	0.888808	−	0.458279i	$-0.151534\pi$
$401$	35.5967	1.77762	0.888808	+	0.458279i	$0.151534\pi$
$402$	−2.76393	−0.137852
$403$	16.4164	0.817760
$404$	−12.8754	−0.640575
$405$	0	0
$406$	−2.85410	−0.141647
$407$	43.4164	2.15207
$408$	−4.06888	−0.201440
$409$	14.8197	0.732785	0.366393	−	0.930460i	$-0.380593\pi$
$409$	14.8197	0.732785	0.366393	+	0.930460i	$0.380593\pi$
$410$	0	0
$411$	2.76393	0.136335
$412$	1.75078	0.0862546
$413$	−6.47214	−0.318473
$414$	0.763932	0.0375452
$415$	0	0
$416$	12.4377	0.609808
$417$	25.6525	1.25621
$418$	−19.4164	−0.949688
$419$	16.6525	0.813527	0.406763	−	0.913534i	$-0.366657\pi$
$419$	16.6525	0.813527	0.406763	+	0.913534i	$0.366657\pi$
$420$	0	0
$421$	32.0000	1.55958	0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000	1.55958	0.779792	+	0.626038i	$0.215325\pi$
$422$	6.47214	0.315059
$423$	8.47214	0.411929
$424$	12.9017	0.626562
$425$	0	0
$426$	−3.61803	−0.175294
$427$	−1.70820	−0.0826658
$428$	−29.4590	−1.42395
$429$	40.2492	1.94325
$430$	0	0
$431$	20.9443	1.00885	0.504425	−	0.863455i	$-0.331704\pi$
$431$	20.9443	1.00885	0.504425	+	0.863455i	$0.331704\pi$
$432$	7.03444	0.338445
$433$	−17.7082	−0.851002	−0.425501	−	0.904958i	$-0.639902\pi$
$433$	−17.7082	−0.851002	−0.425501	+	0.904958i	$0.639902\pi$
$434$	2.09017	0.100331
$435$	0	0
$436$	−21.7082	−1.03963
$437$	−8.47214	−0.405277
$438$	−7.68692	−0.367295
$439$	−9.00000	−0.429547	−0.214773	−	0.976664i	$-0.568901\pi$
$439$	−9.00000	−0.429547	−0.214773	+	0.976664i	$0.568901\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	1.41641	0.0673717
$443$	−37.3607	−1.77506	−0.887530	−	0.460750i	$-0.847580\pi$
$443$	−37.3607	−1.77506	−0.887530	+	0.460750i	$0.847580\pi$
$444$	30.0000	1.42374
$445$	0	0
$446$	−4.94427	−0.234118
$447$	−10.6525	−0.503845
$448$	−4.70820	−0.222442
$449$	1.41641	0.0668444	0.0334222	−	0.999441i	$-0.489359\pi$
$449$	1.41641	0.0668444	0.0334222	+	0.999441i	$0.489359\pi$
$450$	0	0
$451$	40.2492	1.89526
$452$	13.7508	0.646782
$453$	−49.7214	−2.33611
$454$	−7.41641	−0.348069
$455$	0	0
$456$	−27.8885	−1.30600
$457$	33.2361	1.55472	0.777359	−	0.629057i	$-0.216559\pi$
$457$	33.2361	1.55472	0.777359	+	0.629057i	$0.216559\pi$
$458$	4.58359	0.214177
$459$	2.76393	0.129009
$460$	0	0
$461$	−27.6525	−1.28790	−0.643952	−	0.765066i	$-0.722706\pi$
$461$	−27.6525	−1.28790	−0.643952	+	0.765066i	$0.722706\pi$
$462$	5.12461	0.238419
$463$	18.8328	0.875235	0.437618	−	0.899161i	$-0.355822\pi$
$463$	18.8328	0.875235	0.437618	+	0.899161i	$0.355822\pi$
$464$	23.5066	1.09127
$465$	0	0
$466$	2.56231	0.118697
$467$	−26.9443	−1.24683	−0.623416	−	0.781890i	$-0.714256\pi$
$467$	−26.9443	−1.24683	−0.623416	+	0.781890i	$0.714256\pi$
$468$	11.1246	0.514235
$469$	−3.23607	−0.149428
$470$	0	0
$471$	−33.0132	−1.52117
$472$	−9.52786	−0.438555
$473$	−22.2492	−1.02302
$474$	−11.4590	−0.526328
$475$	0	0
$476$	−2.29180	−0.105044
$477$	17.5279	0.802546
$478$	−6.74265	−0.308401
$479$	26.8328	1.22602	0.613011	−	0.790074i	$-0.289958\pi$
$479$	26.8328	1.22602	0.613011	+	0.790074i	$0.289958\pi$
$480$	0	0
$481$	−21.7082	−0.989809
$482$	11.1246	0.506712
$483$	2.23607	0.101745
$484$	−46.3525	−2.10693
$485$	0	0
$486$	−6.83282	−0.309943
$487$	13.5836	0.615531	0.307766	−	0.951462i	$-0.400419\pi$
$487$	13.5836	0.615531	0.307766	+	0.951462i	$0.400419\pi$
$488$	−2.51471	−0.113836
$489$	−38.0132	−1.71901
$490$	0	0
$491$	13.1803	0.594820	0.297410	−	0.954750i	$-0.403877\pi$
$491$	13.1803	0.594820	0.297410	+	0.954750i	$0.403877\pi$
$492$	27.8115	1.25384
$493$	9.23607	0.415972
$494$	9.70820	0.436793
$495$	0	0
$496$	−17.2148	−0.772967
$497$	−4.23607	−0.190014
$498$	−3.16718	−0.141925
$499$	4.70820	0.210768	0.105384	−	0.994432i	$-0.466393\pi$
$499$	4.70820	0.210768	0.105384	+	0.994432i	$0.466393\pi$
$500$	0	0
$501$	37.8885	1.69274
$502$	3.41641	0.152482
$503$	−31.2361	−1.39275	−0.696374	−	0.717679i	$-0.745204\pi$
$503$	−31.2361	−1.39275	−0.696374	+	0.717679i	$0.745204\pi$
$504$	2.94427	0.131148
$505$	0	0
$506$	2.29180	0.101883
$507$	8.94427	0.397229
$508$	5.56231	0.246787
$509$	−36.0132	−1.59626	−0.798128	−	0.602489i	$-0.794176\pi$
$509$	−36.0132	−1.59626	−0.798128	+	0.602489i	$0.794176\pi$
$510$	0	0
$511$	−9.00000	−0.398137
$512$	−22.3050	−0.985749
$513$	18.9443	0.836410
$514$	−6.63119	−0.292489
$515$	0	0
$516$	−15.3738	−0.676795
$517$	25.4164	1.11781
$518$	−2.76393	−0.121440
$519$	−6.58359	−0.288988
$520$	0	0
$521$	−29.8885	−1.30944	−0.654720	−	0.755871i	$-0.727214\pi$
$521$	−29.8885	−1.30944	−0.654720	+	0.755871i	$0.727214\pi$
$522$	−5.70820	−0.249841
$523$	34.5410	1.51037	0.755187	−	0.655510i	$-0.227546\pi$
$523$	34.5410	1.51037	0.755187	+	0.655510i	$0.227546\pi$
$524$	−19.5197	−0.852724
$525$	0	0
$526$	−9.01316	−0.392992
$527$	−6.76393	−0.294642
$528$	−42.2067	−1.83681
$529$	1.00000	0.0434783
$530$	0	0
$531$	−12.9443	−0.561734
$532$	−15.7082	−0.681037
$533$	−20.1246	−0.871694
$534$	−7.88854	−0.341371
$535$	0	0
$536$	−4.76393	−0.205771
$537$	−41.8328	−1.80522
$538$	2.56231	0.110469
$539$	6.00000	0.258438
$540$	0	0
$541$	13.0000	0.558914	0.279457	−	0.960158i	$-0.409846\pi$
$541$	13.0000	0.558914	0.279457	+	0.960158i	$0.409846\pi$
$542$	6.69505	0.287577
$543$	22.3607	0.959589
$544$	−5.12461	−0.219716
$545$	0	0
$546$	−2.56231	−0.109657
$547$	−24.5279	−1.04874	−0.524368	−	0.851492i	$-0.675698\pi$
$547$	−24.5279	−1.04874	−0.524368	+	0.851492i	$0.675698\pi$
$548$	2.29180	0.0979007
$549$	−3.41641	−0.145809
$550$	0	0
$551$	63.3050	2.69688
$552$	3.29180	0.140108
$553$	−13.4164	−0.570524
$554$	9.57546	0.406822
$555$	0	0
$556$	21.2705	0.902071
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	4.18034	0.176968
$559$	11.1246	0.470521
$560$	0	0
$561$	−16.5836	−0.700160
$562$	−5.41641	−0.228477
$563$	−9.81966	−0.413849	−0.206925	−	0.978357i	$-0.566346\pi$
$563$	−9.81966	−0.413849	−0.206925	+	0.978357i	$0.566346\pi$
$564$	17.5623	0.739506
$565$	0	0
$566$	−11.1246	−0.467602
$567$	−11.0000	−0.461957
$568$	−6.23607	−0.261660
$569$	−36.4721	−1.52899	−0.764496	−	0.644629i	$-0.777012\pi$
$569$	−36.4721	−1.52899	−0.764496	+	0.644629i	$0.777012\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	33.3738	1.39543
$573$	−1.05573	−0.0441037
$574$	−2.56231	−0.106949
$575$	0	0
$576$	−9.41641	−0.392350
$577$	40.8885	1.70221	0.851106	−	0.524994i	$-0.175932\pi$
$577$	40.8885	1.70221	0.851106	+	0.524994i	$0.175932\pi$
$578$	5.90983	0.245817
$579$	−3.94427	−0.163918
$580$	0	0
$581$	−3.70820	−0.153842
$582$	0.249224	0.0103307
$583$	52.5836	2.17779
$584$	−13.2492	−0.548257
$585$	0	0
$586$	−3.75078	−0.154943
$587$	−21.0689	−0.869606	−0.434803	−	0.900526i	$-0.643182\pi$
$587$	−21.0689	−0.869606	−0.434803	+	0.900526i	$0.643182\pi$
$588$	4.14590	0.170974
$589$	−46.3607	−1.91026
$590$	0	0
$591$	11.8328	0.486737
$592$	22.7639	0.935592
$593$	29.7771	1.22280	0.611399	−	0.791322i	$-0.290607\pi$
$593$	29.7771	1.22280	0.611399	+	0.791322i	$0.290607\pi$
$594$	−5.12461	−0.210265
$595$	0	0
$596$	−8.83282	−0.361806
$597$	−3.16718	−0.129624
$598$	−1.14590	−0.0468593
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	14.5967	0.595414	0.297707	−	0.954657i	$-0.403778\pi$
$601$	14.5967	0.595414	0.297707	+	0.954657i	$0.403778\pi$
$602$	1.41641	0.0577285
$603$	−6.47214	−0.263566
$604$	−41.2279	−1.67754
$605$	0	0
$606$	5.93112	0.240935
$607$	−3.41641	−0.138668	−0.0693339	−	0.997594i	$-0.522087\pi$
$607$	−3.41641	−0.138668	−0.0693339	+	0.997594i	$0.522087\pi$
$608$	−35.1246	−1.42449
$609$	−16.7082	−0.677051
$610$	0	0
$611$	−12.7082	−0.514119
$612$	−4.58359	−0.185281
$613$	42.4721	1.71543	0.857717	−	0.514123i	$-0.171882\pi$
$613$	42.4721	1.71543	0.857717	+	0.514123i	$0.171882\pi$
$614$	−2.83282	−0.114323
$615$	0	0
$616$	8.83282	0.355884
$617$	−7.52786	−0.303060	−0.151530	−	0.988453i	$-0.548420\pi$
$617$	−7.52786	−0.303060	−0.151530	+	0.988453i	$0.548420\pi$
$618$	−0.806504	−0.0324424
$619$	8.65248	0.347772	0.173886	−	0.984766i	$-0.444368\pi$
$619$	8.65248	0.347772	0.173886	+	0.984766i	$0.444368\pi$
$620$	0	0
$621$	−2.23607	−0.0897303
$622$	−6.27051	−0.251425
$623$	−9.23607	−0.370035
$624$	21.1033	0.844809
$625$	0	0
$626$	−7.52786	−0.300874
$627$	−113.666	−4.53937
$628$	−27.3738	−1.09233
$629$	8.94427	0.356631
$630$	0	0
$631$	−25.2361	−1.00463	−0.502316	−	0.864684i	$-0.667519\pi$
$631$	−25.2361	−1.00463	−0.502316	+	0.864684i	$0.667519\pi$
$632$	−19.7508	−0.785644
$633$	37.8885	1.50593
$634$	−4.76393	−0.189200
$635$	0	0
$636$	36.3344	1.44075
$637$	−3.00000	−0.118864
$638$	−17.1246	−0.677970
$639$	−8.47214	−0.335153
$640$	0	0
$641$	0.875388	0.0345758	0.0172879	−	0.999851i	$-0.494497\pi$
$641$	0.875388	0.0345758	0.0172879	+	0.999851i	$0.494497\pi$
$642$	13.5704	0.535582
$643$	8.11146	0.319885	0.159942	−	0.987126i	$-0.448869\pi$
$643$	8.11146	0.319885	0.159942	+	0.987126i	$0.448869\pi$
$644$	1.85410	0.0730619
$645$	0	0
$646$	−4.00000	−0.157378
$647$	4.81966	0.189480	0.0947402	−	0.995502i	$-0.469798\pi$
$647$	4.81966	0.189480	0.0947402	+	0.995502i	$0.469798\pi$
$648$	−16.1935	−0.636141
$649$	−38.8328	−1.52432
$650$	0	0
$651$	12.2361	0.479569
$652$	−31.5197	−1.23441
$653$	42.5967	1.66694	0.833470	−	0.552565i	$-0.186351\pi$
$653$	42.5967	1.66694	0.833470	+	0.552565i	$0.186351\pi$
$654$	10.0000	0.391031
$655$	0	0
$656$	21.1033	0.823946
$657$	−18.0000	−0.702247
$658$	−1.61803	−0.0630775
$659$	32.9443	1.28333	0.641663	−	0.766986i	$-0.278245\pi$
$659$	32.9443	1.28333	0.641663	+	0.766986i	$0.278245\pi$
$660$	0	0
$661$	−25.7082	−0.999933	−0.499967	−	0.866045i	$-0.666654\pi$
$661$	−25.7082	−0.999933	−0.499967	+	0.866045i	$0.666654\pi$
$662$	7.68692	0.298761
$663$	8.29180	0.322027
$664$	−5.45898	−0.211850
$665$	0	0
$666$	−5.52786	−0.214200
$667$	−7.47214	−0.289322
$668$	31.4164	1.21554
$669$	−28.9443	−1.11905
$670$	0	0
$671$	−10.2492	−0.395667
$672$	9.27051	0.357618
$673$	−27.2918	−1.05202	−0.526011	−	0.850478i	$-0.676313\pi$
$673$	−27.2918	−1.05202	−0.526011	+	0.850478i	$0.676313\pi$
$674$	7.41641	0.285669
$675$	0	0
$676$	7.41641	0.285246
$677$	36.1803	1.39052	0.695262	−	0.718757i	$-0.255288\pi$
$677$	36.1803	1.39052	0.695262	+	0.718757i	$0.255288\pi$
$678$	−6.33437	−0.243270
$679$	0.291796	0.0111981
$680$	0	0
$681$	−43.4164	−1.66372
$682$	12.5410	0.480220
$683$	−43.3607	−1.65915	−0.829575	−	0.558395i	$-0.811417\pi$
$683$	−43.3607	−1.65915	−0.829575	+	0.558395i	$0.811417\pi$
$684$	−31.4164	−1.20124
$685$	0	0
$686$	−0.381966	−0.0145835
$687$	26.8328	1.02374
$688$	−11.6656	−0.444748
$689$	−26.2918	−1.00164
$690$	0	0
$691$	46.8328	1.78160	0.890802	−	0.454391i	$-0.150143\pi$
$691$	46.8328	1.78160	0.890802	+	0.454391i	$0.150143\pi$
$692$	−5.45898	−0.207519
$693$	12.0000	0.455842
$694$	8.22291	0.312137
$695$	0	0
$696$	−24.5967	−0.932337
$697$	8.29180	0.314074
$698$	6.20163	0.234735
$699$	15.0000	0.567352
$700$	0	0
$701$	−3.70820	−0.140057	−0.0700285	−	0.997545i	$-0.522309\pi$
$701$	−3.70820	−0.140057	−0.0700285	+	0.997545i	$0.522309\pi$
$702$	2.56231	0.0967080
$703$	61.3050	2.31216
$704$	−28.2492	−1.06468
$705$	0	0
$706$	11.4377	0.430463
$707$	6.94427	0.261166
$708$	−26.8328	−1.00844
$709$	0.944272	0.0354629	0.0177314	−	0.999843i	$-0.494356\pi$
$709$	0.944272	0.0354629	0.0177314	+	0.999843i	$0.494356\pi$
$710$	0	0
$711$	−26.8328	−1.00631
$712$	−13.5967	−0.509560
$713$	5.47214	0.204933
$714$	1.05573	0.0395096
$715$	0	0
$716$	−34.6869	−1.29631
$717$	−39.4721	−1.47411
$718$	5.70820	0.213028
$719$	11.0557	0.412309	0.206155	−	0.978519i	$-0.433905\pi$
$719$	11.0557	0.412309	0.206155	+	0.978519i	$0.433905\pi$
$720$	0	0
$721$	−0.944272	−0.0351665
$722$	−20.1591	−0.750242
$723$	65.1246	2.42201
$724$	18.5410	0.689072
$725$	0	0
$726$	21.3525	0.792467
$727$	18.0000	0.667583	0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000	0.667583	0.333792	+	0.942647i	$0.391672\pi$
$728$	−4.41641	−0.163683
$729$	−7.00000	−0.259259
$730$	0	0
$731$	−4.58359	−0.169530
$732$	−7.08204	−0.261760
$733$	−3.70820	−0.136966	−0.0684828	−	0.997652i	$-0.521816\pi$
$733$	−3.70820	−0.136966	−0.0684828	+	0.997652i	$0.521816\pi$
$734$	−3.52786	−0.130216
$735$	0	0
$736$	4.14590	0.152820
$737$	−19.4164	−0.715213
$738$	−5.12461	−0.188640
$739$	−20.1246	−0.740296	−0.370148	−	0.928973i	$-0.620693\pi$
$739$	−20.1246	−0.740296	−0.370148	+	0.928973i	$0.620693\pi$
$740$	0	0
$741$	56.8328	2.08781
$742$	−3.34752	−0.122891
$743$	−20.0689	−0.736256	−0.368128	−	0.929775i	$-0.620001\pi$
$743$	−20.0689	−0.736256	−0.368128	+	0.929775i	$0.620001\pi$
$744$	18.0132	0.660394
$745$	0	0
$746$	−3.34752	−0.122562
$747$	−7.41641	−0.271352
$748$	−13.7508	−0.502778
$749$	15.8885	0.580555
$750$	0	0
$751$	47.1246	1.71960	0.859801	−	0.510630i	$-0.170588\pi$
$751$	47.1246	1.71960	0.859801	+	0.510630i	$0.170588\pi$
$752$	13.3262	0.485958
$753$	20.0000	0.728841
$754$	8.56231	0.311821
$755$	0	0
$756$	−4.14590	−0.150785
$757$	−35.3050	−1.28318	−0.641590	−	0.767048i	$-0.721725\pi$
$757$	−35.3050	−1.28318	−0.641590	+	0.767048i	$0.721725\pi$
$758$	6.72136	0.244131
$759$	13.4164	0.486985
$760$	0	0
$761$	2.23607	0.0810574	0.0405287	−	0.999178i	$-0.487096\pi$
$761$	2.23607	0.0810574	0.0405287	+	0.999178i	$0.487096\pi$
$762$	−2.56231	−0.0928225
$763$	11.7082	0.423865
$764$	−0.875388	−0.0316704
$765$	0	0
$766$	−2.47214	−0.0893219
$767$	19.4164	0.701086
$768$	−12.4377	−0.448807
$769$	−36.8328	−1.32823	−0.664113	−	0.747633i	$-0.731190\pi$
$769$	−36.8328	−1.32823	−0.664113	+	0.747633i	$0.731190\pi$
$770$	0	0
$771$	−38.8197	−1.39806
$772$	−3.27051	−0.117708
$773$	−50.8328	−1.82833	−0.914165	−	0.405343i	$-0.867152\pi$
$773$	−50.8328	−1.82833	−0.914165	+	0.405343i	$0.867152\pi$
$774$	2.83282	0.101823
$775$	0	0
$776$	0.429563	0.0154204
$777$	−16.1803	−0.580466
$778$	3.77709	0.135415
$779$	56.8328	2.03625
$780$	0	0
$781$	−25.4164	−0.909471
$782$	0.472136	0.0168835
$783$	16.7082	0.597102
$784$	3.14590	0.112354
$785$	0	0
$786$	8.99187	0.320729
$787$	−48.3607	−1.72387	−0.861936	−	0.507017i	$-0.830748\pi$
$787$	−48.3607	−1.72387	−0.861936	+	0.507017i	$0.830748\pi$
$788$	9.81153	0.349521
$789$	−52.7639	−1.87845
$790$	0	0
$791$	−7.41641	−0.263697
$792$	17.6656	0.627721
$793$	5.12461	0.181980
$794$	10.0902	0.358087
$795$	0	0
$796$	−2.62616	−0.0930819
$797$	6.94427	0.245979	0.122989	−	0.992408i	$-0.460752\pi$
$797$	6.94427	0.245979	0.122989	+	0.992408i	$0.460752\pi$
$798$	7.23607	0.256154
$799$	5.23607	0.185239
$800$	0	0
$801$	−18.4721	−0.652681
$802$	−13.5967	−0.480118
$803$	−54.0000	−1.90562
$804$	−13.4164	−0.473160
$805$	0	0
$806$	−6.27051	−0.220869
$807$	15.0000	0.528025
$808$	10.2229	0.359641
$809$	−35.8885	−1.26177	−0.630887	−	0.775875i	$-0.717309\pi$
$809$	−35.8885	−1.26177	−0.630887	+	0.775875i	$0.717309\pi$
$810$	0	0
$811$	9.00000	0.316033	0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000	0.316033	0.158016	+	0.987436i	$0.449490\pi$
$812$	−13.8541	−0.486184
$813$	39.1935	1.37458
$814$	−16.5836	−0.581255
$815$	0	0
$816$	−8.69505	−0.304388
$817$	−31.4164	−1.09912
$818$	−5.66061	−0.197918
$819$	−6.00000	−0.209657
$820$	0	0
$821$	34.3607	1.19920	0.599598	−	0.800301i	$-0.295327\pi$
$821$	34.3607	1.19920	0.599598	+	0.800301i	$0.295327\pi$
$822$	−1.05573	−0.0368227
$823$	33.8328	1.17934	0.589669	−	0.807645i	$-0.299258\pi$
$823$	33.8328	1.17934	0.589669	+	0.807645i	$0.299258\pi$
$824$	−1.39010	−0.0484263
$825$	0	0
$826$	2.47214	0.0860166
$827$	33.3050	1.15813	0.579063	−	0.815283i	$-0.303418\pi$
$827$	33.3050	1.15813	0.579063	+	0.815283i	$0.303418\pi$
$828$	3.70820	0.128869
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	0	0
$831$	56.0557	1.94455
$832$	14.1246	0.489683
$833$	1.23607	0.0428272
$834$	−9.79837	−0.339290
$835$	0	0
$836$	−94.2492	−3.25968
$837$	−12.2361	−0.422940
$838$	−6.36068	−0.219726
$839$	47.1246	1.62692	0.813461	−	0.581619i	$-0.197581\pi$
$839$	47.1246	1.62692	0.813461	+	0.581619i	$0.197581\pi$
$840$	0	0
$841$	26.8328	0.925270
$842$	−12.2229	−0.421229
$843$	−31.7082	−1.09209
$844$	31.4164	1.08140
$845$	0	0
$846$	−3.23607	−0.111258
$847$	25.0000	0.859010
$848$	27.5704	0.946773
$849$	−65.1246	−2.23507
$850$	0	0
$851$	−7.23607	−0.248049
$852$	−17.5623	−0.601675
$853$	39.3050	1.34578	0.672888	−	0.739744i	$-0.265054\pi$
$853$	39.3050	1.34578	0.672888	+	0.739744i	$0.265054\pi$
$854$	0.652476	0.0223273
$855$	0	0
$856$	23.3901	0.799457
$857$	0.0557281	0.00190364	0.000951818	−	1.00000i	$-0.499697\pi$
$857$	0.0557281	0.00190364	0.000951818		1.00000i	$0.499697\pi$
$858$	−15.3738	−0.524854
$859$	−20.5279	−0.700402	−0.350201	−	0.936675i	$-0.613887\pi$
$859$	−20.5279	−0.700402	−0.350201	+	0.936675i	$0.613887\pi$
$860$	0	0
$861$	−15.0000	−0.511199
$862$	−8.00000	−0.272481
$863$	−27.3607	−0.931368	−0.465684	−	0.884951i	$-0.654192\pi$
$863$	−27.3607	−0.931368	−0.465684	+	0.884951i	$0.654192\pi$
$864$	−9.27051	−0.315389
$865$	0	0
$866$	6.76393	0.229848
$867$	34.5967	1.17497
$868$	10.1459	0.344374
$869$	−80.4984	−2.73072
$870$	0	0
$871$	9.70820	0.328950
$872$	17.2361	0.583687
$873$	0.583592	0.0197516
$874$	3.23607	0.109462
$875$	0	0
$876$	−37.3131	−1.26069
$877$	−6.58359	−0.222312	−0.111156	−	0.993803i	$-0.535455\pi$
$877$	−6.58359	−0.222312	−0.111156	+	0.993803i	$0.535455\pi$
$878$	3.43769	0.116017
$879$	−21.9574	−0.740606
$880$	0	0
$881$	14.8328	0.499730	0.249865	−	0.968281i	$-0.419614\pi$
$881$	14.8328	0.499730	0.249865	+	0.968281i	$0.419614\pi$
$882$	−0.763932	−0.0257229
$883$	−37.8885	−1.27505	−0.637526	−	0.770429i	$-0.720042\pi$
$883$	−37.8885	−1.27505	−0.637526	+	0.770429i	$0.720042\pi$
$884$	6.87539	0.231244
$885$	0	0
$886$	14.2705	0.479427
$887$	−42.0132	−1.41066	−0.705332	−	0.708877i	$-0.749202\pi$
$887$	−42.0132	−1.41066	−0.705332	+	0.708877i	$0.749202\pi$
$888$	−23.8197	−0.799335
$889$	−3.00000	−0.100617
$890$	0	0
$891$	−66.0000	−2.21108
$892$	−24.0000	−0.803579
$893$	35.8885	1.20096
$894$	4.06888	0.136084
$895$	0	0
$896$	10.0902	0.337089
$897$	−6.70820	−0.223980
$898$	−0.541020	−0.0180541
$899$	−40.8885	−1.36371
$900$	0	0
$901$	10.8328	0.360893
$902$	−15.3738	−0.511893
$903$	8.29180	0.275934
$904$	−10.9180	−0.363126
$905$	0	0
$906$	18.9919	0.630963
$907$	44.2492	1.46927	0.734636	−	0.678462i	$-0.237353\pi$
$907$	44.2492	1.46927	0.734636	+	0.678462i	$0.237353\pi$
$908$	−36.0000	−1.19470
$909$	13.8885	0.460654
$910$	0	0
$911$	2.29180	0.0759306	0.0379653	−	0.999279i	$-0.487912\pi$
$911$	2.29180	0.0759306	0.0379653	+	0.999279i	$0.487912\pi$
$912$	−59.5967	−1.97345
$913$	−22.2492	−0.736342
$914$	−12.6950	−0.419915
$915$	0	0
$916$	22.2492	0.735135
$917$	10.5279	0.347661
$918$	−1.05573	−0.0348442
$919$	35.1246	1.15865	0.579327	−	0.815095i	$-0.303315\pi$
$919$	35.1246	1.15865	0.579327	+	0.815095i	$0.303315\pi$
$920$	0	0
$921$	−16.5836	−0.546448
$922$	10.5623	0.347851
$923$	12.7082	0.418296
$924$	24.8754	0.818340
$925$	0	0
$926$	−7.19350	−0.236393
$927$	−1.88854	−0.0620279
$928$	−30.9787	−1.01693
$929$	−46.9574	−1.54062	−0.770312	−	0.637668i	$-0.779899\pi$
$929$	−46.9574	−1.54062	−0.770312	+	0.637668i	$0.779899\pi$
$930$	0	0
$931$	8.47214	0.277663
$932$	12.4377	0.407410
$933$	−36.7082	−1.20177
$934$	10.2918	0.336758
$935$	0	0
$936$	−8.83282	−0.288710
$937$	2.65248	0.0866526	0.0433263	−	0.999061i	$-0.486204\pi$
$937$	2.65248	0.0866526	0.0433263	+	0.999061i	$0.486204\pi$
$938$	1.23607	0.0403591
$939$	−44.0689	−1.43813
$940$	0	0
$941$	−21.3050	−0.694522	−0.347261	−	0.937769i	$-0.612888\pi$
$941$	−21.3050	−0.694522	−0.347261	+	0.937769i	$0.612888\pi$
$942$	12.6099	0.410853
$943$	−6.70820	−0.218449
$944$	−20.3607	−0.662684
$945$	0	0
$946$	8.49845	0.276308
$947$	22.4164	0.728435	0.364218	−	0.931314i	$-0.381336\pi$
$947$	22.4164	0.728435	0.364218	+	0.931314i	$0.381336\pi$
$948$	−55.6231	−1.80655
$949$	27.0000	0.876457
$950$	0	0
$951$	−27.8885	−0.904348
$952$	1.81966	0.0589755
$953$	−2.94427	−0.0953743	−0.0476872	−	0.998862i	$-0.515185\pi$
$953$	−2.94427	−0.0953743	−0.0476872	+	0.998862i	$0.515185\pi$
$954$	−6.69505	−0.216760
$955$	0	0
$956$	−32.7295	−1.05855
$957$	−100.249	−3.24060
$958$	−10.2492	−0.331137
$959$	−1.23607	−0.0399147
$960$	0	0
$961$	−1.05573	−0.0340557
$962$	8.29180	0.267338
$963$	31.7771	1.02400
$964$	54.0000	1.73922
$965$	0	0
$966$	−0.854102	−0.0274803
$967$	−52.8885	−1.70078	−0.850390	−	0.526152i	$-0.823634\pi$
$967$	−52.8885	−1.70078	−0.850390	+	0.526152i	$0.823634\pi$
$968$	36.8034	1.18291
$969$	−23.4164	−0.752243
$970$	0	0
$971$	−20.1803	−0.647618	−0.323809	−	0.946122i	$-0.604964\pi$
$971$	−20.1803	−0.647618	−0.323809	+	0.946122i	$0.604964\pi$
$972$	−33.1672	−1.06384
$973$	−11.4721	−0.367780
$974$	−5.18847	−0.166249
$975$	0	0
$976$	−5.37384	−0.172012
$977$	−40.7639	−1.30415	−0.652077	−	0.758153i	$-0.726102\pi$
$977$	−40.7639	−1.30415	−0.652077	+	0.758153i	$0.726102\pi$
$978$	14.5197	0.464290
$979$	−55.4164	−1.77112
$980$	0	0
$981$	23.4164	0.747628
$982$	−5.03444	−0.160655
$983$	51.0132	1.62707	0.813533	−	0.581518i	$-0.197541\pi$
$983$	51.0132	1.62707	0.813533	+	0.581518i	$0.197541\pi$
$984$	−22.0820	−0.703950
$985$	0	0
$986$	−3.52786	−0.112350
$987$	−9.47214	−0.301501
$988$	47.1246	1.49923
$989$	3.70820	0.117914
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	22.6869	0.720310
$993$	45.0000	1.42803
$994$	1.61803	0.0513209
$995$	0	0
$996$	−15.3738	−0.487139
$997$	4.83282	0.153057	0.0765284	−	0.997067i	$-0.475616\pi$
$997$	4.83282	0.153057	0.0765284	+	0.997067i	$0.475616\pi$
$998$	−1.79837	−0.0569265
$999$	16.1803	0.511923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.h.1.2		2
5.4	even	2		805.2.a.e.1.1	✓	2
15.14	odd	2		7245.2.a.v.1.2		2
35.34	odd	2		5635.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.e.1.1	✓	2	5.4	even	2
4025.2.a.h.1.2		2	1.1	even	1	trivial
5635.2.a.q.1.1		2	35.34	odd	2
7245.2.a.v.1.2		2	15.14	odd	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)

\(f(q)\)	\(=\)	\(q-0.381966 q^{2} -2.23607 q^{3} -1.85410 q^{4} +0.854102 q^{6} +1.00000 q^{7} +1.47214 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-0.381966 q^{2} -2.23607 q^{3} -1.85410 q^{4} +0.854102 q^{6} +1.00000 q^{7} +1.47214 q^{8} +2.00000 q^{9} +6.00000 q^{11} +4.14590 q^{12} -3.00000 q^{13} -0.381966 q^{14} +3.14590 q^{16} +1.23607 q^{17} -0.763932 q^{18} +8.47214 q^{19} -2.23607 q^{21} -2.29180 q^{22} -1.00000 q^{23} -3.29180 q^{24} +1.14590 q^{26} +2.23607 q^{27} -1.85410 q^{28} +7.47214 q^{29} -5.47214 q^{31} -4.14590 q^{32} -13.4164 q^{33} -0.472136 q^{34} -3.70820 q^{36} +7.23607 q^{37} -3.23607 q^{38} +6.70820 q^{39} +6.70820 q^{41} +0.854102 q^{42} -3.70820 q^{43} -11.1246 q^{44} +0.381966 q^{46} +4.23607 q^{47} -7.03444 q^{48} +1.00000 q^{49} -2.76393 q^{51} +5.56231 q^{52} +8.76393 q^{53} -0.854102 q^{54} +1.47214 q^{56} -18.9443 q^{57} -2.85410 q^{58} -6.47214 q^{59} -1.70820 q^{61} +2.09017 q^{62} +2.00000 q^{63} -4.70820 q^{64} +5.12461 q^{66} -3.23607 q^{67} -2.29180 q^{68} +2.23607 q^{69} -4.23607 q^{71} +2.94427 q^{72} -9.00000 q^{73} -2.76393 q^{74} -15.7082 q^{76} +6.00000 q^{77} -2.56231 q^{78} -13.4164 q^{79} -11.0000 q^{81} -2.56231 q^{82} -3.70820 q^{83} +4.14590 q^{84} +1.41641 q^{86} -16.7082 q^{87} +8.83282 q^{88} -9.23607 q^{89} -3.00000 q^{91} +1.85410 q^{92} +12.2361 q^{93} -1.61803 q^{94} +9.27051 q^{96} +0.291796 q^{97} -0.381966 q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 3 q^{4} - 5 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 3 * q^4 - 5 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9	\( 2 q - 3 q^{2} + 3 q^{4} - 5 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9} + 12 q^{11} + 15 q^{12} - 6 q^{13} - 3 q^{14} + 13 q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - 18 q^{22} - 2 q^{23} - 20 q^{24} + 9 q^{26} + 3 q^{28} + 6 q^{29} - 2 q^{31} - 15 q^{32} + 8 q^{34} + 6 q^{36} + 10 q^{37} - 2 q^{38} - 5 q^{42} + 6 q^{43} + 18 q^{44} + 3 q^{46} + 4 q^{47} + 15 q^{48} + 2 q^{49} - 10 q^{51} - 9 q^{52} + 22 q^{53} + 5 q^{54} - 6 q^{56} - 20 q^{57} + q^{58} - 4 q^{59} + 10 q^{61} - 7 q^{62} + 4 q^{63} + 4 q^{64} - 30 q^{66} - 2 q^{67} - 18 q^{68} - 4 q^{71} - 12 q^{72} - 18 q^{73} - 10 q^{74} - 18 q^{76} + 12 q^{77} + 15 q^{78} - 22 q^{81} + 15 q^{82} + 6 q^{83} + 15 q^{84} - 24 q^{86} - 20 q^{87} - 36 q^{88} - 14 q^{89} - 6 q^{91} - 3 q^{92} + 20 q^{93} - q^{94} - 15 q^{96} + 14 q^{97} - 3 q^{98} + 24 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 3 * q^4 - 5 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9 + 12 * q^11 + 15 * q^12 - 6 * q^13 - 3 * q^14 + 13 * q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - 18 * q^22 - 2 * q^23 - 20 * q^24 + 9 * q^26 + 3 * q^28 + 6 * q^29 - 2 * q^31 - 15 * q^32 + 8 * q^34 + 6 * q^36 + 10 * q^37 - 2 * q^38 - 5 * q^42 + 6 * q^43 + 18 * q^44 + 3 * q^46 + 4 * q^47 + 15 * q^48 + 2 * q^49 - 10 * q^51 - 9 * q^52 + 22 * q^53 + 5 * q^54 - 6 * q^56 - 20 * q^57 + q^58 - 4 * q^59 + 10 * q^61 - 7 * q^62 + 4 * q^63 + 4 * q^64 - 30 * q^66 - 2 * q^67 - 18 * q^68 - 4 * q^71 - 12 * q^72 - 18 * q^73 - 10 * q^74 - 18 * q^76 + 12 * q^77 + 15 * q^78 - 22 * q^81 + 15 * q^82 + 6 * q^83 + 15 * q^84 - 24 * q^86 - 20 * q^87 - 36 * q^88 - 14 * q^89 - 6 * q^91 - 3 * q^92 + 20 * q^93 - q^94 - 15 * q^96 + 14 * q^97 - 3 * q^98 + 24 * q^99

Introduction

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