LMFDB - Embedded newform 7225.2.a.bx.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7225,2,Mod(1,7225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7225, 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("7225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.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:	$57.6919154604$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 425)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	7225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88586 q^{2} +1.88942 q^{3} +1.55648 q^{4} +3.56320 q^{6} +0.335329 q^{7} -0.836409 q^{8} +0.569922 q^{9} +O(q^{10})$	\(q+1.88586 q^{2} +1.88942 q^{3} +1.55648 q^{4} +3.56320 q^{6} +0.335329 q^{7} -0.836409 q^{8} +0.569922 q^{9} -3.80730 q^{11} +2.94086 q^{12} +0.558802 q^{13} +0.632385 q^{14} -4.69032 q^{16} +1.07480 q^{18} -3.73466 q^{19} +0.633578 q^{21} -7.18005 q^{22} +1.24609 q^{23} -1.58033 q^{24} +1.05382 q^{26} -4.59145 q^{27} +0.521934 q^{28} -3.98616 q^{29} -9.36293 q^{31} -7.17250 q^{32} -7.19360 q^{33} +0.887075 q^{36} +6.77191 q^{37} -7.04307 q^{38} +1.05581 q^{39} +1.68051 q^{41} +1.19484 q^{42} -5.66804 q^{43} -5.92600 q^{44} +2.34995 q^{46} +9.50560 q^{47} -8.86201 q^{48} -6.88755 q^{49} +0.869767 q^{52} +7.30416 q^{53} -8.65885 q^{54} -0.280472 q^{56} -7.05636 q^{57} -7.51736 q^{58} -9.33504 q^{59} -0.743895 q^{61} -17.6572 q^{62} +0.191111 q^{63} -4.14571 q^{64} -13.5662 q^{66} -7.29434 q^{67} +2.35438 q^{69} -15.5616 q^{71} -0.476688 q^{72} +11.1511 q^{73} +12.7709 q^{74} -5.81295 q^{76} -1.27670 q^{77} +1.99112 q^{78} +11.9882 q^{79} -10.3850 q^{81} +3.16922 q^{82} -11.7265 q^{83} +0.986155 q^{84} -10.6892 q^{86} -7.53155 q^{87} +3.18446 q^{88} +13.1316 q^{89} +0.187382 q^{91} +1.93951 q^{92} -17.6905 q^{93} +17.9263 q^{94} -13.5519 q^{96} +10.6199 q^{97} -12.9890 q^{98} -2.16986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9} - 16 q^{13} + 24 q^{16} - 40 q^{18} - 16 q^{21} - 16 q^{26} - 56 q^{32} - 48 q^{33} + 24 q^{36} - 48 q^{38} - 32 q^{43} - 88 q^{47} + 16 q^{49} - 48 q^{52} - 48 q^{53} - 8 q^{59} + 72 q^{64} + 32 q^{66} - 40 q^{67} - 48 q^{69} - 120 q^{72} + 32 q^{76} - 120 q^{77} - 24 q^{81} - 104 q^{83} + 40 q^{84} - 16 q^{86} - 64 q^{87} + 16 q^{89} + 72 q^{93} + 112 q^{94} - 48 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9 - 16 * q^13 + 24 * q^16 - 40 * q^18 - 16 * q^21 - 16 * q^26 - 56 * q^32 - 48 * q^33 + 24 * q^36 - 48 * q^38 - 32 * q^43 - 88 * q^47 + 16 * q^49 - 48 * q^52 - 48 * q^53 - 8 * q^59 + 72 * q^64 + 32 * q^66 - 40 * q^67 - 48 * q^69 - 120 * q^72 + 32 * q^76 - 120 * q^77 - 24 * q^81 - 104 * q^83 + 40 * q^84 - 16 * q^86 - 64 * q^87 + 16 * q^89 + 72 * q^93 + 112 * q^94 - 48 * 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 $

$2$	1.88586	1.33351	0.666754	−	0.745278i	$-0.267683\pi$
$2$	1.88586	1.33351	0.666754	+	0.745278i	$0.267683\pi$
$3$	1.88942	1.09086	0.545430	−	0.838157i	$-0.316367\pi$
$3$	1.88942	1.09086	0.545430	+	0.838157i	$0.316367\pi$
$4$	1.55648	0.778242
$5$	0	0
$5$	0	0
$6$	3.56320	1.45467
$7$	0.335329	0.126742	0.0633712	−	0.997990i	$-0.479815\pi$
$7$	0.335329	0.126742	0.0633712	+	0.997990i	$0.479815\pi$
$8$	−0.836409	−0.295715
$9$	0.569922	0.189974
$10$	0	0
$11$	−3.80730	−1.14794	−0.573972	−	0.818875i	$-0.694598\pi$
$11$	−3.80730	−1.14794	−0.573972	+	0.818875i	$0.694598\pi$
$12$	2.94086	0.848953
$13$	0.558802	0.154984	0.0774919	−	0.996993i	$-0.475309\pi$
$13$	0.558802	0.154984	0.0774919	+	0.996993i	$0.475309\pi$
$14$	0.632385	0.169012
$15$	0	0
$16$	−4.69032	−1.17258
$17$	0	0
$17$	0	0
$18$	1.07480	0.253332
$19$	−3.73466	−0.856791	−0.428395	−	0.903591i	$-0.640921\pi$
$19$	−3.73466	−0.856791	−0.428395	+	0.903591i	$0.640921\pi$
$20$	0	0
$21$	0.633578	0.138258
$22$	−7.18005	−1.53079
$23$	1.24609	0.259827	0.129913	−	0.991525i	$-0.458530\pi$
$23$	1.24609	0.259827	0.129913	+	0.991525i	$0.458530\pi$
$24$	−1.58033	−0.322584
$25$	0	0
$26$	1.05382	0.206672
$27$	−4.59145	−0.883624
$28$	0.521934	0.0986363
$29$	−3.98616	−0.740212	−0.370106	−	0.928990i	$-0.620679\pi$
$29$	−3.98616	−0.740212	−0.370106	+	0.928990i	$0.620679\pi$
$30$	0	0
$31$	−9.36293	−1.68163	−0.840816	−	0.541322i	$-0.817924\pi$
$31$	−9.36293	−1.68163	−0.840816	+	0.541322i	$0.817924\pi$
$32$	−7.17250	−1.26793
$33$	−7.19360	−1.25225
$34$	0	0
$35$	0	0
$36$	0.887075	0.147846
$37$	6.77191	1.11329	0.556647	−	0.830749i	$-0.312087\pi$
$37$	6.77191	1.11329	0.556647	+	0.830749i	$0.312087\pi$
$38$	−7.04307	−1.14254
$39$	1.05581	0.169065
$40$	0	0
$41$	1.68051	0.262452	0.131226	−	0.991352i	$-0.458109\pi$
$41$	1.68051	0.262452	0.131226	+	0.991352i	$0.458109\pi$
$42$	1.19484	0.184368
$43$	−5.66804	−0.864368	−0.432184	−	0.901786i	$-0.642257\pi$
$43$	−5.66804	−0.864368	−0.432184	+	0.901786i	$0.642257\pi$
$44$	−5.92600	−0.893379
$45$	0	0
$46$	2.34995	0.346481
$47$	9.50560	1.38653	0.693267	−	0.720680i	$-0.256170\pi$
$47$	9.50560	1.38653	0.693267	+	0.720680i	$0.256170\pi$
$48$	−8.86201	−1.27912
$49$	−6.88755	−0.983936
$50$	0	0
$51$	0	0
$52$	0.869767	0.120615
$53$	7.30416	1.00330	0.501652	−	0.865070i	$-0.332726\pi$
$53$	7.30416	1.00330	0.501652	+	0.865070i	$0.332726\pi$
$54$	−8.65885	−1.17832
$55$	0	0
$56$	−0.280472	−0.0374797
$57$	−7.05636	−0.934638
$58$	−7.51736	−0.987078
$59$	−9.33504	−1.21532	−0.607659	−	0.794198i	$-0.707891\pi$
$59$	−9.33504	−1.21532	−0.607659	+	0.794198i	$0.707891\pi$
$60$	0	0
$61$	−0.743895	−0.0952460	−0.0476230	−	0.998865i	$-0.515165\pi$
$61$	−0.743895	−0.0952460	−0.0476230	+	0.998865i	$0.515165\pi$
$62$	−17.6572	−2.24247
$63$	0.191111	0.0240778
$64$	−4.14571	−0.518214
$65$	0	0
$66$	−13.5662	−1.66988
$67$	−7.29434	−0.891146	−0.445573	−	0.895246i	$-0.647000\pi$
$67$	−7.29434	−0.891146	−0.445573	+	0.895246i	$0.647000\pi$
$68$	0	0
$69$	2.35438	0.283434
$70$	0	0
$71$	−15.5616	−1.84682	−0.923412	−	0.383811i	$-0.874611\pi$
$71$	−15.5616	−1.84682	−0.923412	+	0.383811i	$0.874611\pi$
$72$	−0.476688	−0.0561782
$73$	11.1511	1.30513	0.652567	−	0.757731i	$-0.273692\pi$
$73$	11.1511	1.30513	0.652567	+	0.757731i	$0.273692\pi$
$74$	12.7709	1.48459
$75$	0	0
$76$	−5.81295	−0.666791
$77$	−1.27670	−0.145493
$78$	1.99112	0.225450
$79$	11.9882	1.34878	0.674389	−	0.738376i	$-0.264407\pi$
$79$	11.9882	1.34878	0.674389	+	0.738376i	$0.264407\pi$
$80$	0	0
$81$	−10.3850	−1.15388
$82$	3.16922	0.349982
$83$	−11.7265	−1.28715	−0.643576	−	0.765382i	$-0.722550\pi$
$83$	−11.7265	−1.28715	−0.643576	+	0.765382i	$0.722550\pi$
$84$	0.986155	0.107598
$85$	0	0
$86$	−10.6892	−1.15264
$87$	−7.53155	−0.807467
$88$	3.18446	0.339465
$89$	13.1316	1.39195	0.695975	−	0.718066i	$-0.254972\pi$
$89$	13.1316	1.39195	0.695975	+	0.718066i	$0.254972\pi$
$90$	0	0
$91$	0.187382	0.0196430
$92$	1.93951	0.202208
$93$	−17.6905	−1.83442
$94$	17.9263	1.84895
$95$	0	0
$96$	−13.5519	−1.38313
$97$	10.6199	1.07829	0.539145	−	0.842213i	$-0.318748\pi$
$97$	10.6199	1.07829	0.539145	+	0.842213i	$0.318748\pi$
$98$	−12.9890	−1.31209
$99$	−2.16986	−0.218079
$100$	0	0
$101$	−12.6689	−1.26060	−0.630300	−	0.776352i	$-0.717068\pi$
$101$	−12.6689	−1.26060	−0.630300	+	0.776352i	$0.717068\pi$
$102$	0	0
$103$	−13.2397	−1.30455	−0.652273	−	0.757985i	$-0.726184\pi$
$103$	−13.2397	−1.30455	−0.652273	+	0.757985i	$0.726184\pi$
$104$	−0.467387	−0.0458311
$105$	0	0
$106$	13.7747	1.33791
$107$	−8.86472	−0.856985	−0.428492	−	0.903545i	$-0.640955\pi$
$107$	−8.86472	−0.856985	−0.428492	+	0.903545i	$0.640955\pi$
$108$	−7.14652	−0.687674
$109$	−2.56079	−0.245279	−0.122639	−	0.992451i	$-0.539136\pi$
$109$	−2.56079	−0.245279	−0.122639	+	0.992451i	$0.539136\pi$
$110$	0	0
$111$	12.7950	1.21445
$112$	−1.57280	−0.148616
$113$	7.08235	0.666252	0.333126	−	0.942882i	$-0.391897\pi$
$113$	7.08235	0.666252	0.333126	+	0.942882i	$0.391897\pi$
$114$	−13.3073	−1.24635
$115$	0	0
$116$	−6.20440	−0.576064
$117$	0.318473	0.0294429
$118$	−17.6046	−1.62064
$119$	0	0
$120$	0	0
$121$	3.49553	0.317775
$122$	−1.40289	−0.127011
$123$	3.17520	0.286298
$124$	−14.5733	−1.30872
$125$	0	0
$126$	0.360410	0.0321079
$127$	−0.438427	−0.0389041	−0.0194521	−	0.999811i	$-0.506192\pi$
$127$	−0.438427	−0.0389041	−0.0194521	+	0.999811i	$0.506192\pi$
$128$	6.52675	0.576888
$129$	−10.7093	−0.942904
$130$	0	0
$131$	−3.96922	−0.346792	−0.173396	−	0.984852i	$-0.555474\pi$
$131$	−3.96922	−0.346792	−0.173396	+	0.984852i	$0.555474\pi$
$132$	−11.1967	−0.974550
$133$	−1.25234	−0.108592
$134$	−13.7561	−1.18835
$135$	0	0
$136$	0	0
$137$	4.65140	0.397396	0.198698	−	0.980061i	$-0.436329\pi$
$137$	4.65140	0.397396	0.198698	+	0.980061i	$0.436329\pi$
$138$	4.44005	0.377962
$139$	−4.35127	−0.369069	−0.184535	−	0.982826i	$-0.559078\pi$
$139$	−4.35127	−0.369069	−0.184535	+	0.982826i	$0.559078\pi$
$140$	0	0
$141$	17.9601	1.51251
$142$	−29.3471	−2.46275
$143$	−2.12753	−0.177913
$144$	−2.67312	−0.222760
$145$	0	0
$146$	21.0294	1.74041
$147$	−13.0135	−1.07334
$148$	10.5404	0.866413
$149$	15.0861	1.23590	0.617950	−	0.786217i	$-0.287963\pi$
$149$	15.0861	1.23590	0.617950	+	0.786217i	$0.287963\pi$
$150$	0	0
$151$	−20.2249	−1.64588	−0.822938	−	0.568131i	$-0.807667\pi$
$151$	−20.2249	−1.64588	−0.822938	+	0.568131i	$0.807667\pi$
$152$	3.12371	0.253366
$153$	0	0
$154$	−2.40768	−0.194016
$155$	0	0
$156$	1.64336	0.131574
$157$	11.6845	0.932525	0.466263	−	0.884646i	$-0.345600\pi$
$157$	11.6845	0.932525	0.466263	+	0.884646i	$0.345600\pi$
$158$	22.6081	1.79861
$159$	13.8006	1.09446
$160$	0	0
$161$	0.417848	0.0329311
$162$	−19.5846	−1.53871
$163$	11.5868	0.907546	0.453773	−	0.891117i	$-0.350078\pi$
$163$	11.5868	0.907546	0.453773	+	0.891117i	$0.350078\pi$
$164$	2.61569	0.204251
$165$	0	0
$166$	−22.1146	−1.71643
$167$	18.5332	1.43414	0.717072	−	0.696999i	$-0.245482\pi$
$167$	18.5332	1.43414	0.717072	+	0.696999i	$0.245482\pi$
$168$	−0.529931	−0.0408850
$169$	−12.6877	−0.975980
$170$	0	0
$171$	−2.12847	−0.162768
$172$	−8.82222	−0.672688
$173$	1.34905	0.102566	0.0512831	−	0.998684i	$-0.483669\pi$
$173$	1.34905	0.102566	0.0512831	+	0.998684i	$0.483669\pi$
$174$	−14.2035	−1.07676
$175$	0	0
$176$	17.8575	1.34606
$177$	−17.6378	−1.32574
$178$	24.7645	1.85618
$179$	8.91105	0.666043	0.333021	−	0.942919i	$-0.391932\pi$
$179$	8.91105	0.666043	0.333021	+	0.942919i	$0.391932\pi$
$180$	0	0
$181$	7.78970	0.579004	0.289502	−	0.957177i	$-0.406510\pi$
$181$	7.78970	0.579004	0.289502	+	0.957177i	$0.406510\pi$
$182$	0.353378	0.0261941
$183$	−1.40553	−0.103900
$184$	−1.04224	−0.0768347
$185$	0	0
$186$	−33.3619	−2.44622
$187$	0	0
$188$	14.7953	1.07906
$189$	−1.53964	−0.111993
$190$	0	0
$191$	2.88897	0.209038	0.104519	−	0.994523i	$-0.466670\pi$
$191$	2.88897	0.209038	0.104519	+	0.994523i	$0.466670\pi$
$192$	−7.83300	−0.565298
$193$	17.6043	1.26719	0.633593	−	0.773667i	$-0.281580\pi$
$193$	17.6043	1.26719	0.633593	+	0.773667i	$0.281580\pi$
$194$	20.0277	1.43791
$195$	0	0
$196$	−10.7204	−0.765741
$197$	24.7556	1.76377	0.881883	−	0.471468i	$-0.156276\pi$
$197$	24.7556	1.76377	0.881883	+	0.471468i	$0.156276\pi$
$198$	−4.09207	−0.290811
$199$	2.38522	0.169083	0.0845417	−	0.996420i	$-0.473057\pi$
$199$	2.38522	0.169083	0.0845417	+	0.996420i	$0.473057\pi$
$200$	0	0
$201$	−13.7821	−0.972115
$202$	−23.8918	−1.68102
$203$	−1.33668	−0.0938162
$204$	0	0
$205$	0	0
$206$	−24.9683	−1.73962
$207$	0.710171	0.0493603
$208$	−2.62096	−0.181731
$209$	14.2190	0.983548
$210$	0	0
$211$	−9.93134	−0.683702	−0.341851	−	0.939754i	$-0.611054\pi$
$211$	−9.93134	−0.683702	−0.341851	+	0.939754i	$0.611054\pi$
$212$	11.3688	0.780813
$213$	−29.4025	−2.01462
$214$	−16.7177	−1.14280
$215$	0	0
$216$	3.84033	0.261301
$217$	−3.13966	−0.213134
$218$	−4.82930	−0.327081
$219$	21.0691	1.42372
$220$	0	0
$221$	0	0
$222$	24.1296	1.61948
$223$	−11.4203	−0.764758	−0.382379	−	0.924006i	$-0.624895\pi$
$223$	−11.4203	−0.764758	−0.382379	+	0.924006i	$0.624895\pi$
$224$	−2.40515	−0.160701
$225$	0	0
$226$	13.3564	0.888452
$227$	0.951424	0.0631482	0.0315741	−	0.999501i	$-0.489948\pi$
$227$	0.951424	0.0631482	0.0315741	+	0.999501i	$0.489948\pi$
$228$	−10.9831	−0.727375
$229$	−17.3031	−1.14342	−0.571710	−	0.820456i	$-0.693720\pi$
$229$	−17.3031	−1.14342	−0.571710	+	0.820456i	$0.693720\pi$
$230$	0	0
$231$	−2.41222	−0.158713
$232$	3.33406	0.218892
$233$	−15.9364	−1.04403	−0.522014	−	0.852937i	$-0.674819\pi$
$233$	−15.9364	−1.04403	−0.522014	+	0.852937i	$0.674819\pi$
$234$	0.600598	0.0392623
$235$	0	0
$236$	−14.5298	−0.945813
$237$	22.6508	1.47133
$238$	0	0
$239$	−9.77203	−0.632100	−0.316050	−	0.948743i	$-0.602357\pi$
$239$	−9.77203	−0.632100	−0.316050	+	0.948743i	$0.602357\pi$
$240$	0	0
$241$	−26.1915	−1.68714	−0.843571	−	0.537018i	$-0.819551\pi$
$241$	−26.1915	−1.68714	−0.843571	+	0.537018i	$0.819551\pi$
$242$	6.59209	0.423756
$243$	−5.84724	−0.375100
$244$	−1.15786	−0.0741245
$245$	0	0
$246$	5.98800	0.381781
$247$	−2.08694	−0.132789
$248$	7.83124	0.497284
$249$	−22.1564	−1.40410
$250$	0	0
$251$	−18.3573	−1.15870	−0.579351	−	0.815078i	$-0.696694\pi$
$251$	−18.3573	−1.15870	−0.579351	+	0.815078i	$0.696694\pi$
$252$	0.297462	0.0187383
$253$	−4.74422	−0.298266
$254$	−0.826814	−0.0518789
$255$	0	0
$256$	20.6000	1.28750
$257$	−20.2863	−1.26542	−0.632712	−	0.774387i	$-0.718058\pi$
$257$	−20.2863	−1.26542	−0.632712	+	0.774387i	$0.718058\pi$
$258$	−20.1963	−1.25737
$259$	2.27082	0.141102
$260$	0	0
$261$	−2.27180	−0.140621
$262$	−7.48541	−0.462450
$263$	−11.3513	−0.699949	−0.349974	−	0.936759i	$-0.613810\pi$
$263$	−11.3513	−0.699949	−0.349974	+	0.936759i	$0.613810\pi$
$264$	6.01679	0.370308
$265$	0	0
$266$	−2.36174	−0.144808
$267$	24.8112	1.51842
$268$	−11.3535	−0.693527
$269$	−1.40090	−0.0854146	−0.0427073	−	0.999088i	$-0.513598\pi$
$269$	−1.40090	−0.0854146	−0.0427073	+	0.999088i	$0.513598\pi$
$270$	0	0
$271$	3.64441	0.221382	0.110691	−	0.993855i	$-0.464694\pi$
$271$	3.64441	0.221382	0.110691	+	0.993855i	$0.464694\pi$
$272$	0	0
$273$	0.354045	0.0214278
$274$	8.77191	0.529931
$275$	0	0
$276$	3.66456	0.220581
$277$	12.8413	0.771560	0.385780	−	0.922591i	$-0.373932\pi$
$277$	12.8413	0.771560	0.385780	+	0.922591i	$0.373932\pi$
$278$	−8.20590	−0.492157
$279$	−5.33614	−0.319466
$280$	0	0
$281$	−21.4368	−1.27881	−0.639405	−	0.768870i	$-0.720819\pi$
$281$	−21.4368	−1.27881	−0.639405	+	0.768870i	$0.720819\pi$
$282$	33.8703	2.01695
$283$	−9.38050	−0.557613	−0.278807	−	0.960347i	$-0.589939\pi$
$283$	−9.38050	−0.557613	−0.278807	+	0.960347i	$0.589939\pi$
$284$	−24.2214	−1.43728
$285$	0	0
$286$	−4.01222	−0.237248
$287$	0.563525	0.0332638
$288$	−4.08776	−0.240874
$289$	0	0
$290$	0	0
$291$	20.0655	1.17626
$292$	17.3565	1.01571
$293$	22.0519	1.28828	0.644142	−	0.764906i	$-0.277214\pi$
$293$	22.0519	1.28828	0.644142	+	0.764906i	$0.277214\pi$
$294$	−24.5417	−1.43130
$295$	0	0
$296$	−5.66409	−0.329218
$297$	17.4810	1.01435
$298$	28.4503	1.64808
$299$	0.696314	0.0402689
$300$	0	0
$301$	−1.90066	−0.109552
$302$	−38.1414	−2.19479
$303$	−23.9369	−1.37514
$304$	17.5168	1.00466
$305$	0	0
$306$	0	0
$307$	4.89164	0.279181	0.139590	−	0.990209i	$-0.455421\pi$
$307$	4.89164	0.279181	0.139590	+	0.990209i	$0.455421\pi$
$308$	−1.98716	−0.113229
$309$	−25.0154	−1.42308
$310$	0	0
$311$	4.85994	0.275582	0.137791	−	0.990461i	$-0.456000\pi$
$311$	4.85994	0.275582	0.137791	+	0.990461i	$0.456000\pi$
$312$	−0.883092	−0.0499952
$313$	22.6039	1.27765	0.638824	−	0.769353i	$-0.279421\pi$
$313$	22.6039	1.27765	0.638824	+	0.769353i	$0.279421\pi$
$314$	22.0354	1.24353
$315$	0	0
$316$	18.6595	1.04968
$317$	5.09825	0.286346	0.143173	−	0.989698i	$-0.454269\pi$
$317$	5.09825	0.286346	0.143173	+	0.989698i	$0.454269\pi$
$318$	26.0262	1.45947
$319$	15.1765	0.849722
$320$	0	0
$321$	−16.7492	−0.934850
$322$	0.788005	0.0439138
$323$	0	0
$324$	−16.1640	−0.898001
$325$	0	0
$326$	21.8511	1.21022
$327$	−4.83841	−0.267565
$328$	−1.40560	−0.0776111
$329$	3.18750	0.175733
$330$	0	0
$331$	−34.0780	−1.87310	−0.936548	−	0.350539i	$-0.885998\pi$
$331$	−34.0780	−1.87310	−0.936548	+	0.350539i	$0.885998\pi$
$332$	−18.2522	−1.00172
$333$	3.85946	0.211497
$334$	34.9511	1.91244
$335$	0	0
$336$	−2.97169	−0.162119
$337$	11.2373	0.612135	0.306067	−	0.952010i	$-0.400987\pi$
$337$	11.2373	0.612135	0.306067	+	0.952010i	$0.400987\pi$
$338$	−23.9274	−1.30148
$339$	13.3816	0.726787
$340$	0	0
$341$	35.6475	1.93042
$342$	−4.01400	−0.217052
$343$	−4.65690	−0.251449
$344$	4.74080	0.255607
$345$	0	0
$346$	2.54412	0.136773
$347$	15.8735	0.852137	0.426068	−	0.904691i	$-0.359898\pi$
$347$	15.8735	0.852137	0.426068	+	0.904691i	$0.359898\pi$
$348$	−11.7227	−0.628405
$349$	−3.17213	−0.169800	−0.0849002	−	0.996389i	$-0.527057\pi$
$349$	−3.17213	−0.169800	−0.0849002	+	0.996389i	$0.527057\pi$
$350$	0	0
$351$	−2.56571	−0.136947
$352$	27.3078	1.45551
$353$	−34.6534	−1.84441	−0.922207	−	0.386696i	$-0.873616\pi$
$353$	−34.6534	−1.84441	−0.922207	+	0.386696i	$0.873616\pi$
$354$	−33.2626	−1.76789
$355$	0	0
$356$	20.4392	1.08327
$357$	0	0
$358$	16.8050	0.888173
$359$	21.9157	1.15667	0.578334	−	0.815800i	$-0.303703\pi$
$359$	21.9157	1.15667	0.578334	+	0.815800i	$0.303703\pi$
$360$	0	0
$361$	−5.05229	−0.265910
$362$	14.6903	0.772106
$363$	6.60453	0.346648
$364$	0.291658	0.0152870
$365$	0	0
$366$	−2.65065	−0.138551
$367$	−6.87049	−0.358637	−0.179318	−	0.983791i	$-0.557389\pi$
$367$	−6.87049	−0.358637	−0.179318	+	0.983791i	$0.557389\pi$
$368$	−5.84454	−0.304668
$369$	0.957761	0.0498591
$370$	0	0
$371$	2.44930	0.127161
$372$	−27.5350	−1.42763
$373$	34.8389	1.80389	0.901946	−	0.431850i	$-0.142139\pi$
$373$	34.8389	1.80389	0.901946	+	0.431850i	$0.142139\pi$
$374$	0	0
$375$	0	0
$376$	−7.95058	−0.410020
$377$	−2.22747	−0.114721
$378$	−2.90356	−0.149343
$379$	23.7553	1.22023	0.610114	−	0.792314i	$-0.291124\pi$
$379$	23.7553	1.22023	0.610114	+	0.792314i	$0.291124\pi$
$380$	0	0
$381$	−0.828374	−0.0424389
$382$	5.44820	0.278754
$383$	−5.33128	−0.272416	−0.136208	−	0.990680i	$-0.543491\pi$
$383$	−5.33128	−0.272416	−0.136208	+	0.990680i	$0.543491\pi$
$384$	12.3318	0.629304
$385$	0	0
$386$	33.1993	1.68980
$387$	−3.23034	−0.164207
$388$	16.5298	0.839171
$389$	20.5515	1.04200	0.521002	−	0.853555i	$-0.325558\pi$
$389$	20.5515	1.04200	0.521002	+	0.853555i	$0.325558\pi$
$390$	0	0
$391$	0	0
$392$	5.76081	0.290965
$393$	−7.49954	−0.378302
$394$	46.6858	2.35200
$395$	0	0
$396$	−3.37736	−0.169719
$397$	8.05574	0.404306	0.202153	−	0.979354i	$-0.435206\pi$
$397$	8.05574	0.404306	0.202153	+	0.979354i	$0.435206\pi$
$398$	4.49819	0.225474
$399$	−2.36620	−0.118458
$400$	0	0
$401$	13.4709	0.672703	0.336352	−	0.941737i	$-0.390807\pi$
$401$	13.4709	0.672703	0.336352	+	0.941737i	$0.390807\pi$
$402$	−25.9912	−1.29632
$403$	−5.23202	−0.260625
$404$	−19.7189	−0.981053
$405$	0	0
$406$	−2.52079	−0.125105
$407$	−25.7827	−1.27800
$408$	0	0
$409$	−7.88198	−0.389739	−0.194869	−	0.980829i	$-0.562428\pi$
$409$	−7.88198	−0.389739	−0.194869	+	0.980829i	$0.562428\pi$
$410$	0	0
$411$	8.78847	0.433503
$412$	−20.6074	−1.01525
$413$	−3.13031	−0.154032
$414$	1.33929	0.0658223
$415$	0	0
$416$	−4.00800	−0.196509
$417$	−8.22138	−0.402603
$418$	26.8151	1.31157
$419$	5.48112	0.267770	0.133885	−	0.990997i	$-0.457255\pi$
$419$	5.48112	0.267770	0.133885	+	0.990997i	$0.457255\pi$
$420$	0	0
$421$	13.5189	0.658873	0.329437	−	0.944178i	$-0.393141\pi$
$421$	13.5189	0.658873	0.329437	+	0.944178i	$0.393141\pi$
$422$	−18.7292	−0.911721
$423$	5.41745	0.263406
$424$	−6.10927	−0.296692
$425$	0	0
$426$	−55.4491	−2.68652
$427$	−0.249450	−0.0120717
$428$	−13.7978	−0.666942
$429$	−4.01980	−0.194078
$430$	0	0
$431$	−40.6698	−1.95899	−0.979497	−	0.201460i	$-0.935431\pi$
$431$	−40.6698	−1.95899	−0.979497	+	0.201460i	$0.935431\pi$
$432$	21.5354	1.03612
$433$	32.1863	1.54678	0.773388	−	0.633934i	$-0.218561\pi$
$433$	32.1863	1.54678	0.773388	+	0.633934i	$0.218561\pi$
$434$	−5.92097	−0.284216
$435$	0	0
$436$	−3.98583	−0.190886
$437$	−4.65371	−0.222617
$438$	39.7335	1.89854
$439$	38.2133	1.82382	0.911910	−	0.410389i	$-0.134607\pi$
$439$	38.2133	1.82382	0.911910	+	0.410389i	$0.134607\pi$
$440$	0	0
$441$	−3.92537	−0.186922
$442$	0	0
$443$	−39.5730	−1.88017	−0.940086	−	0.340938i	$-0.889255\pi$
$443$	−39.5730	−1.88017	−0.940086	+	0.340938i	$0.889255\pi$
$444$	19.9152	0.945135
$445$	0	0
$446$	−21.5371	−1.01981
$447$	28.5040	1.34819
$448$	−1.39018	−0.0656797
$449$	−11.3373	−0.535039	−0.267519	−	0.963552i	$-0.586204\pi$
$449$	−11.3373	−0.535039	−0.267519	+	0.963552i	$0.586204\pi$
$450$	0	0
$451$	−6.39822	−0.301280
$452$	11.0236	0.518505
$453$	−38.2134	−1.79542
$454$	1.79426	0.0842086
$455$	0	0
$456$	5.90201	0.276387
$457$	−3.93986	−0.184299	−0.0921495	−	0.995745i	$-0.529374\pi$
$457$	−3.93986	−0.184299	−0.0921495	+	0.995745i	$0.529374\pi$
$458$	−32.6313	−1.52476
$459$	0	0
$460$	0	0
$461$	−10.3897	−0.483895	−0.241947	−	0.970289i	$-0.577786\pi$
$461$	−10.3897	−0.483895	−0.241947	+	0.970289i	$0.577786\pi$
$462$	−4.54912	−0.211644
$463$	9.30604	0.432488	0.216244	−	0.976339i	$-0.430619\pi$
$463$	9.30604	0.432488	0.216244	+	0.976339i	$0.430619\pi$
$464$	18.6964	0.867958
$465$	0	0
$466$	−30.0539	−1.39222
$467$	−8.77654	−0.406130	−0.203065	−	0.979165i	$-0.565090\pi$
$467$	−8.77654	−0.406130	−0.203065	+	0.979165i	$0.565090\pi$
$468$	0.495699	0.0229137
$469$	−2.44600	−0.112946
$470$	0	0
$471$	22.0770	1.01725
$472$	7.80791	0.359388
$473$	21.5799	0.992246
$474$	42.7163	1.96203
$475$	0	0
$476$	0	0
$477$	4.16280	0.190601
$478$	−18.4287	−0.842910
$479$	−31.6313	−1.44527	−0.722635	−	0.691230i	$-0.757069\pi$
$479$	−31.6313	−1.44527	−0.722635	+	0.691230i	$0.757069\pi$
$480$	0	0
$481$	3.78415	0.172543
$482$	−49.3936	−2.24982
$483$	0.789492	0.0359232
$484$	5.44074	0.247306
$485$	0	0
$486$	−11.0271	−0.500199
$487$	−35.7485	−1.61992	−0.809959	−	0.586487i	$-0.800511\pi$
$487$	−35.7485	−1.61992	−0.809959	+	0.586487i	$0.800511\pi$
$488$	0.622201	0.0281657
$489$	21.8923	0.990005
$490$	0	0
$491$	15.3966	0.694838	0.347419	−	0.937710i	$-0.387058\pi$
$491$	15.3966	0.694838	0.347419	+	0.937710i	$0.387058\pi$
$492$	4.94215	0.222810
$493$	0	0
$494$	−3.93568	−0.177075
$495$	0	0
$496$	43.9152	1.97185
$497$	−5.21826	−0.234071
$498$	−41.7839	−1.87238
$499$	11.1782	0.500404	0.250202	−	0.968194i	$-0.419503\pi$
$499$	11.1782	0.500404	0.250202	+	0.968194i	$0.419503\pi$
$500$	0	0
$501$	35.0171	1.56445
$502$	−34.6193	−1.54514
$503$	−19.4872	−0.868891	−0.434445	−	0.900698i	$-0.643056\pi$
$503$	−19.4872	−0.868891	−0.434445	+	0.900698i	$0.643056\pi$
$504$	−0.159847	−0.00712016
$505$	0	0
$506$	−8.94695	−0.397741
$507$	−23.9725	−1.06466
$508$	−0.682405	−0.0302768
$509$	38.3851	1.70139	0.850695	−	0.525660i	$-0.176182\pi$
$509$	38.3851	1.70139	0.850695	+	0.525660i	$0.176182\pi$
$510$	0	0
$511$	3.73928	0.165416
$512$	25.7953	1.14000
$513$	17.1475	0.757081
$514$	−38.2572	−1.68745
$515$	0	0
$516$	−16.6689	−0.733808
$517$	−36.1907	−1.59166
$518$	4.28245	0.188160
$519$	2.54892	0.111885
$520$	0	0
$521$	6.10576	0.267498	0.133749	−	0.991015i	$-0.457298\pi$
$521$	6.10576	0.267498	0.133749	+	0.991015i	$0.457298\pi$
$522$	−4.28431	−0.187519
$523$	−16.2004	−0.708392	−0.354196	−	0.935171i	$-0.615245\pi$
$523$	−16.2004	−0.708392	−0.354196	+	0.935171i	$0.615245\pi$
$524$	−6.17803	−0.269889
$525$	0	0
$526$	−21.4069	−0.933387
$527$	0	0
$528$	33.7403	1.46836
$529$	−21.4473	−0.932490
$530$	0	0
$531$	−5.32024	−0.230879
$532$	−1.94925	−0.0845107
$533$	0.939074	0.0406758
$534$	46.7906	2.02483
$535$	0	0
$536$	6.10105	0.263525
$537$	16.8367	0.726559
$538$	−2.64191	−0.113901
$539$	26.2230	1.12950
$540$	0	0
$541$	3.90043	0.167692	0.0838462	−	0.996479i	$-0.473280\pi$
$541$	3.90043	0.167692	0.0838462	+	0.996479i	$0.473280\pi$
$542$	6.87286	0.295215
$543$	14.7180	0.631612
$544$	0	0
$545$	0	0
$546$	0.667680	0.0285741
$547$	15.7506	0.673448	0.336724	−	0.941603i	$-0.390681\pi$
$547$	15.7506	0.673448	0.336724	+	0.941603i	$0.390681\pi$
$548$	7.23984	0.309270
$549$	−0.423962	−0.0180943
$550$	0	0
$551$	14.8870	0.634207
$552$	−1.96923	−0.0838159
$553$	4.01999	0.170947
$554$	24.2170	1.02888
$555$	0	0
$556$	−6.77268	−0.287226
$557$	4.05067	0.171632	0.0858161	−	0.996311i	$-0.472650\pi$
$557$	4.05067	0.171632	0.0858161	+	0.996311i	$0.472650\pi$
$558$	−10.0632	−0.426010
$559$	−3.16731	−0.133963
$560$	0	0
$561$	0	0
$562$	−40.4268	−1.70530
$563$	−4.82184	−0.203216	−0.101608	−	0.994825i	$-0.532399\pi$
$563$	−4.82184	−0.203216	−0.101608	+	0.994825i	$0.532399\pi$
$564$	27.9546	1.17710
$565$	0	0
$566$	−17.6904	−0.743581
$567$	−3.48238	−0.146246
$568$	13.0159	0.546134
$569$	43.4098	1.81983	0.909916	−	0.414792i	$-0.136146\pi$
$569$	43.4098	1.81983	0.909916	+	0.414792i	$0.136146\pi$
$570$	0	0
$571$	−11.4842	−0.480599	−0.240299	−	0.970699i	$-0.577246\pi$
$571$	−11.4842	−0.480599	−0.240299	+	0.970699i	$0.577246\pi$
$572$	−3.31146	−0.138459
$573$	5.45849	0.228032
$574$	1.06273	0.0443575
$575$	0	0
$576$	−2.36273	−0.0984471
$577$	−36.7718	−1.53083	−0.765415	−	0.643537i	$-0.777466\pi$
$577$	−36.7718	−1.53083	−0.765415	+	0.643537i	$0.777466\pi$
$578$	0	0
$579$	33.2620	1.38232
$580$	0	0
$581$	−3.93224	−0.163137
$582$	37.8409	1.56855
$583$	−27.8091	−1.15174
$584$	−9.32686	−0.385948
$585$	0	0
$586$	41.5869	1.71794
$587$	18.8183	0.776713	0.388356	−	0.921509i	$-0.373043\pi$
$587$	18.8183	0.776713	0.388356	+	0.921509i	$0.373043\pi$
$588$	−20.2553	−0.835316
$589$	34.9674	1.44081
$590$	0	0
$591$	46.7739	1.92402
$592$	−31.7624	−1.30543
$593$	0.518978	0.0213119	0.0106559	−	0.999943i	$-0.496608\pi$
$593$	0.518978	0.0213119	0.0106559	+	0.999943i	$0.496608\pi$
$594$	32.9668	1.35265
$595$	0	0
$596$	23.4813	0.961830
$597$	4.50668	0.184446
$598$	1.31315	0.0536989
$599$	5.36433	0.219180	0.109590	−	0.993977i	$-0.465046\pi$
$599$	5.36433	0.219180	0.109590	+	0.993977i	$0.465046\pi$
$600$	0	0
$601$	−16.8095	−0.685675	−0.342837	−	0.939395i	$-0.611388\pi$
$601$	−16.8095	−0.685675	−0.342837	+	0.939395i	$0.611388\pi$
$602$	−3.58438	−0.146088
$603$	−4.15720	−0.169294
$604$	−31.4797	−1.28089
$605$	0	0
$606$	−45.1417	−1.83376
$607$	24.7361	1.00401	0.502004	−	0.864865i	$-0.332596\pi$
$607$	24.7361	1.00401	0.502004	+	0.864865i	$0.332596\pi$
$608$	26.7869	1.08635
$609$	−2.52555	−0.102340
$610$	0	0
$611$	5.31175	0.214890
$612$	0	0
$613$	−5.46570	−0.220757	−0.110379	−	0.993890i	$-0.535206\pi$
$613$	−5.46570	−0.220757	−0.110379	+	0.993890i	$0.535206\pi$
$614$	9.22497	0.372290
$615$	0	0
$616$	1.06784	0.0430246
$617$	−20.4021	−0.821358	−0.410679	−	0.911780i	$-0.634708\pi$
$617$	−20.4021	−0.821358	−0.410679	+	0.911780i	$0.634708\pi$
$618$	−47.1756	−1.89768
$619$	−38.0512	−1.52941	−0.764704	−	0.644382i	$-0.777115\pi$
$619$	−38.0512	−1.52941	−0.764704	+	0.644382i	$0.777115\pi$
$620$	0	0
$621$	−5.72133	−0.229589
$622$	9.16519	0.367491
$623$	4.40341	0.176419
$624$	−4.95211	−0.198243
$625$	0	0
$626$	42.6279	1.70375
$627$	26.8657	1.07291
$628$	18.1868	0.725731
$629$	0	0
$630$	0	0
$631$	36.8856	1.46839	0.734195	−	0.678938i	$-0.237560\pi$
$631$	36.8856	1.46839	0.734195	+	0.678938i	$0.237560\pi$
$632$	−10.0270	−0.398854
$633$	−18.7645	−0.745822
$634$	9.61461	0.381845
$635$	0	0
$636$	21.4805	0.851757
$637$	−3.84878	−0.152494
$638$	28.6208	1.13311
$639$	−8.86890	−0.350848
$640$	0	0
$641$	−30.8623	−1.21899	−0.609494	−	0.792791i	$-0.708627\pi$
$641$	−30.8623	−1.21899	−0.609494	+	0.792791i	$0.708627\pi$
$642$	−31.5867	−1.24663
$643$	38.9031	1.53419	0.767095	−	0.641533i	$-0.221701\pi$
$643$	38.9031	1.53419	0.767095	+	0.641533i	$0.221701\pi$
$644$	0.650375	0.0256283
$645$	0	0
$646$	0	0
$647$	−24.3986	−0.959209	−0.479605	−	0.877485i	$-0.659220\pi$
$647$	−24.3986	−0.959209	−0.479605	+	0.877485i	$0.659220\pi$
$648$	8.68607	0.341221
$649$	35.5413	1.39512
$650$	0	0
$651$	−5.93215	−0.232499
$652$	18.0346	0.706291
$653$	−15.8980	−0.622138	−0.311069	−	0.950387i	$-0.600687\pi$
$653$	−15.8980	−0.622138	−0.311069	+	0.950387i	$0.600687\pi$
$654$	−9.12459	−0.356800
$655$	0	0
$656$	−7.88215	−0.307746
$657$	6.35524	0.247942
$658$	6.01120	0.234341
$659$	−31.1072	−1.21176	−0.605882	−	0.795554i	$-0.707180\pi$
$659$	−31.1072	−1.21176	−0.605882	+	0.795554i	$0.707180\pi$
$660$	0	0
$661$	20.3734	0.792434	0.396217	−	0.918157i	$-0.370323\pi$
$661$	20.3734	0.792434	0.396217	+	0.918157i	$0.370323\pi$
$662$	−64.2665	−2.49779
$663$	0	0
$664$	9.80817	0.380631
$665$	0	0
$666$	7.27842	0.282033
$667$	−4.96710	−0.192327
$668$	28.8467	1.11611
$669$	−21.5777	−0.834243
$670$	0	0
$671$	2.83223	0.109337
$672$	−4.54434	−0.175302
$673$	−43.2460	−1.66701	−0.833506	−	0.552510i	$-0.813670\pi$
$673$	−43.2460	−1.66701	−0.833506	+	0.552510i	$0.813670\pi$
$674$	21.1920	0.816286
$675$	0	0
$676$	−19.7483	−0.759549
$677$	−3.60364	−0.138499	−0.0692496	−	0.997599i	$-0.522060\pi$
$677$	−3.60364	−0.138499	−0.0692496	+	0.997599i	$0.522060\pi$
$678$	25.2358	0.969176
$679$	3.56117	0.136665
$680$	0	0
$681$	1.79764	0.0688858
$682$	67.2263	2.57423
$683$	−0.227025	−0.00868687	−0.00434344	−	0.999991i	$-0.501383\pi$
$683$	−0.227025	−0.00868687	−0.00434344	+	0.999991i	$0.501383\pi$
$684$	−3.31293	−0.126673
$685$	0	0
$686$	−8.78228	−0.335309
$687$	−32.6929	−1.24731
$688$	26.5849	1.01354
$689$	4.08158	0.155496
$690$	0	0
$691$	−2.07037	−0.0787606	−0.0393803	−	0.999224i	$-0.512538\pi$
$691$	−2.07037	−0.0787606	−0.0393803	+	0.999224i	$0.512538\pi$
$692$	2.09977	0.0798214
$693$	−0.727618	−0.0276399
$694$	29.9354	1.13633
$695$	0	0
$696$	6.29946	0.238780
$697$	0	0
$698$	−5.98222	−0.226430
$699$	−30.1106	−1.13889
$700$	0	0
$701$	8.10138	0.305985	0.152992	−	0.988227i	$-0.451109\pi$
$701$	8.10138	0.305985	0.152992	+	0.988227i	$0.451109\pi$
$702$	−4.83858	−0.182620
$703$	−25.2908	−0.953861
$704$	15.7840	0.594880
$705$	0	0
$706$	−65.3516	−2.45954
$707$	−4.24824	−0.159771
$708$	−27.4530	−1.03175
$709$	−33.1207	−1.24388	−0.621938	−	0.783067i	$-0.713654\pi$
$709$	−33.1207	−1.24388	−0.621938	+	0.783067i	$0.713654\pi$
$710$	0	0
$711$	6.83234	0.256233
$712$	−10.9834	−0.411621
$713$	−11.6670	−0.436933
$714$	0	0
$715$	0	0
$716$	13.8699	0.518343
$717$	−18.4635	−0.689532
$718$	41.3301	1.54243
$719$	27.5667	1.02806	0.514032	−	0.857771i	$-0.328151\pi$
$719$	27.5667	1.02806	0.514032	+	0.857771i	$0.328151\pi$
$720$	0	0
$721$	−4.43965	−0.165341
$722$	−9.52793	−0.354593
$723$	−49.4868	−1.84043
$724$	12.1246	0.450605
$725$	0	0
$726$	12.4553	0.462258
$727$	7.87140	0.291934	0.145967	−	0.989289i	$-0.453371\pi$
$727$	7.87140	0.291934	0.145967	+	0.989289i	$0.453371\pi$
$728$	−0.156728	−0.00580874
$729$	20.1070	0.744702
$730$	0	0
$731$	0	0
$732$	−2.18769	−0.0808594
$733$	24.2951	0.897359	0.448680	−	0.893693i	$-0.351894\pi$
$733$	24.2951	0.897359	0.448680	+	0.893693i	$0.351894\pi$
$734$	−12.9568	−0.478245
$735$	0	0
$736$	−8.93754	−0.329442
$737$	27.7717	1.02299
$738$	1.80621	0.0664874
$739$	−36.3406	−1.33681	−0.668406	−	0.743797i	$-0.733023\pi$
$739$	−36.3406	−1.33681	−0.668406	+	0.743797i	$0.733023\pi$
$740$	0	0
$741$	−3.94311	−0.144854
$742$	4.61904	0.169570
$743$	−25.0596	−0.919347	−0.459673	−	0.888088i	$-0.652034\pi$
$743$	−25.0596	−0.919347	−0.459673	+	0.888088i	$0.652034\pi$
$744$	14.7965	0.542467
$745$	0	0
$746$	65.7015	2.40550
$747$	−6.68320	−0.244526
$748$	0	0
$749$	−2.97260	−0.108616
$750$	0	0
$751$	10.9728	0.400404	0.200202	−	0.979755i	$-0.435840\pi$
$751$	10.9728	0.400404	0.200202	+	0.979755i	$0.435840\pi$
$752$	−44.5844	−1.62582
$753$	−34.6847	−1.26398
$754$	−4.20072	−0.152981
$755$	0	0
$756$	−2.39643	−0.0871575
$757$	21.2184	0.771195	0.385598	−	0.922667i	$-0.373995\pi$
$757$	21.2184	0.771195	0.385598	+	0.922667i	$0.373995\pi$
$758$	44.7993	1.62718
$759$	−8.96384	−0.325367
$760$	0	0
$761$	37.2293	1.34956	0.674780	−	0.738019i	$-0.264238\pi$
$761$	37.2293	1.34956	0.674780	+	0.738019i	$0.264238\pi$
$762$	−1.56220	−0.0565926
$763$	−0.858706	−0.0310872
$764$	4.49664	0.162683
$765$	0	0
$766$	−10.0541	−0.363268
$767$	−5.21644	−0.188355
$768$	38.9221	1.40448
$769$	−28.9604	−1.04434	−0.522169	−	0.852842i	$-0.674877\pi$
$769$	−28.9604	−1.04434	−0.522169	+	0.852842i	$0.674877\pi$
$770$	0	0
$771$	−38.3294	−1.38040
$772$	27.4008	0.986177
$773$	−29.2595	−1.05239	−0.526195	−	0.850364i	$-0.676382\pi$
$773$	−29.2595	−1.05239	−0.526195	+	0.850364i	$0.676382\pi$
$774$	−6.09198	−0.218972
$775$	0	0
$776$	−8.88260	−0.318867
$777$	4.29053	0.153922
$778$	38.7574	1.38952
$779$	−6.27615	−0.224867
$780$	0	0
$781$	59.2477	2.12005
$782$	0	0
$783$	18.3023	0.654069
$784$	32.3049	1.15375
$785$	0	0
$786$	−14.1431	−0.504468
$787$	41.1670	1.46744	0.733722	−	0.679450i	$-0.237781\pi$
$787$	41.1670	1.46744	0.733722	+	0.679450i	$0.237781\pi$
$788$	38.5318	1.37264
$789$	−21.4473	−0.763545
$790$	0	0
$791$	2.37492	0.0844423
$792$	1.81489	0.0644894
$793$	−0.415690	−0.0147616
$794$	15.1920	0.539145
$795$	0	0
$796$	3.71255	0.131588
$797$	−28.1841	−0.998333	−0.499167	−	0.866506i	$-0.666360\pi$
$797$	−28.1841	−0.998333	−0.499167	+	0.866506i	$0.666360\pi$
$798$	−4.46234	−0.157965
$799$	0	0
$800$	0	0
$801$	7.48400	0.264434
$802$	25.4042	0.897055
$803$	−42.4555	−1.49822
$804$	−21.4516	−0.756541
$805$	0	0
$806$	−9.86688	−0.347546
$807$	−2.64690	−0.0931753
$808$	10.5964	0.372779
$809$	−36.4543	−1.28166	−0.640832	−	0.767681i	$-0.721410\pi$
$809$	−36.4543	−1.28166	−0.640832	+	0.767681i	$0.721410\pi$
$810$	0	0
$811$	39.5946	1.39036	0.695178	−	0.718838i	$-0.255326\pi$
$811$	39.5946	1.39036	0.695178	+	0.718838i	$0.255326\pi$
$812$	−2.08052	−0.0730118
$813$	6.88583	0.241497
$814$	−48.6226	−1.70422
$815$	0	0
$816$	0	0
$817$	21.1682	0.740582
$818$	−14.8643	−0.519720
$819$	0.106793	0.00373166
$820$	0	0
$821$	−51.9541	−1.81321	−0.906606	−	0.421978i	$-0.861336\pi$
$821$	−51.9541	−1.81321	−0.906606	+	0.421978i	$0.861336\pi$
$822$	16.5739	0.578080
$823$	−13.3704	−0.466064	−0.233032	−	0.972469i	$-0.574865\pi$
$823$	−13.3704	−0.466064	−0.233032	+	0.972469i	$0.574865\pi$
$824$	11.0738	0.385774
$825$	0	0
$826$	−5.90334	−0.205403
$827$	−8.23696	−0.286427	−0.143214	−	0.989692i	$-0.545744\pi$
$827$	−8.23696	−0.286427	−0.143214	+	0.989692i	$0.545744\pi$
$828$	1.10537	0.0384143
$829$	45.0159	1.56347	0.781734	−	0.623612i	$-0.214335\pi$
$829$	45.0159	1.56347	0.781734	+	0.623612i	$0.214335\pi$
$830$	0	0
$831$	24.2627	0.841664
$832$	−2.31663	−0.0803147
$833$	0	0
$834$	−15.5044	−0.536874
$835$	0	0
$836$	22.1316	0.765439
$837$	42.9894	1.48593
$838$	10.3366	0.357073
$839$	2.77923	0.0959498	0.0479749	−	0.998849i	$-0.484723\pi$
$839$	2.77923	0.0959498	0.0479749	+	0.998849i	$0.484723\pi$
$840$	0	0
$841$	−13.1105	−0.452086
$842$	25.4949	0.878612
$843$	−40.5031	−1.39500
$844$	−15.4580	−0.532086
$845$	0	0
$846$	10.2166	0.351253
$847$	1.17215	0.0402756
$848$	−34.2589	−1.17645
$849$	−17.7237	−0.608277
$850$	0	0
$851$	8.43837	0.289264
$852$	−45.7645	−1.56787
$853$	−5.49877	−0.188274	−0.0941371	−	0.995559i	$-0.530009\pi$
$853$	−5.49877	−0.188274	−0.0941371	+	0.995559i	$0.530009\pi$
$854$	−0.470428	−0.0160977
$855$	0	0
$856$	7.41453	0.253423
$857$	−11.2605	−0.384651	−0.192326	−	0.981331i	$-0.561603\pi$
$857$	−11.2605	−0.384651	−0.192326	+	0.981331i	$0.561603\pi$
$858$	−7.58079	−0.258804
$859$	−29.0155	−0.989996	−0.494998	−	0.868894i	$-0.664831\pi$
$859$	−29.0155	−0.989996	−0.494998	+	0.868894i	$0.664831\pi$
$860$	0	0
$861$	1.06474	0.0362861
$862$	−76.6977	−2.61233
$863$	2.49653	0.0849829	0.0424914	−	0.999097i	$-0.486470\pi$
$863$	2.49653	0.0849829	0.0424914	+	0.999097i	$0.486470\pi$
$864$	32.9321	1.12037
$865$	0	0
$866$	60.6990	2.06264
$867$	0	0
$868$	−4.88683	−0.165870
$869$	−45.6427	−1.54832
$870$	0	0
$871$	−4.07609	−0.138113
$872$	2.14187	0.0725327
$873$	6.05253	0.204847
$874$	−8.77626	−0.296862
$875$	0	0
$876$	32.7937	1.10800
$877$	−56.4739	−1.90699	−0.953495	−	0.301410i	$-0.902543\pi$
$877$	−56.4739	−1.90699	−0.953495	+	0.301410i	$0.902543\pi$
$878$	72.0651	2.43208
$879$	41.6653	1.40534
$880$	0	0
$881$	18.4671	0.622173	0.311087	−	0.950382i	$-0.399307\pi$
$881$	18.4671	0.622173	0.311087	+	0.950382i	$0.399307\pi$
$882$	−7.40271	−0.249262
$883$	38.2887	1.28852	0.644259	−	0.764808i	$-0.277166\pi$
$883$	38.2887	1.28852	0.644259	+	0.764808i	$0.277166\pi$
$884$	0	0
$885$	0	0
$886$	−74.6294	−2.50722
$887$	−32.3142	−1.08500	−0.542502	−	0.840055i	$-0.682523\pi$
$887$	−32.3142	−1.08500	−0.542502	+	0.840055i	$0.682523\pi$
$888$	−10.7019	−0.359131
$889$	−0.147017	−0.00493080
$890$	0	0
$891$	39.5386	1.32459
$892$	−17.7755	−0.595167
$893$	−35.5002	−1.18797
$894$	53.7547	1.79783
$895$	0	0
$896$	2.18861	0.0731162
$897$	1.31563	0.0439277
$898$	−21.3806	−0.713478
$899$	37.3221	1.24476
$900$	0	0
$901$	0	0
$902$	−12.0662	−0.401760
$903$	−3.59115	−0.119506
$904$	−5.92375	−0.197021
$905$	0	0
$906$	−72.0652	−2.39421
$907$	−20.8375	−0.691896	−0.345948	−	0.938254i	$-0.612443\pi$
$907$	−20.8375	−0.691896	−0.345948	+	0.938254i	$0.612443\pi$
$908$	1.48088	0.0491446
$909$	−7.22027	−0.239481
$910$	0	0
$911$	47.4734	1.57286	0.786431	−	0.617678i	$-0.211926\pi$
$911$	47.4734	1.57286	0.786431	+	0.617678i	$0.211926\pi$
$912$	33.0966	1.09594
$913$	44.6464	1.47758
$914$	−7.43005	−0.245764
$915$	0	0
$916$	−26.9320	−0.889858
$917$	−1.33099	−0.0439533
$918$	0	0
$919$	28.1486	0.928538	0.464269	−	0.885694i	$-0.346317\pi$
$919$	28.1486	0.928538	0.464269	+	0.885694i	$0.346317\pi$
$920$	0	0
$921$	9.24238	0.304547
$922$	−19.5935	−0.645277
$923$	−8.69585	−0.286228
$924$	−3.75459	−0.123517
$925$	0	0
$926$	17.5499	0.576727
$927$	−7.54559	−0.247830
$928$	28.5907	0.938537
$929$	−4.22573	−0.138642	−0.0693209	−	0.997594i	$-0.522083\pi$
$929$	−4.22573	−0.138642	−0.0693209	+	0.997594i	$0.522083\pi$
$930$	0	0
$931$	25.7227	0.843027
$932$	−24.8048	−0.812507
$933$	9.18248	0.300621
$934$	−16.5514	−0.541577
$935$	0	0
$936$	−0.266374	−0.00870671
$937$	−24.6846	−0.806412	−0.403206	−	0.915109i	$-0.632104\pi$
$937$	−24.6846	−0.806412	−0.403206	+	0.915109i	$0.632104\pi$
$938$	−4.61283	−0.150614
$939$	42.7083	1.39373
$940$	0	0
$941$	−22.7836	−0.742723	−0.371362	−	0.928488i	$-0.621109\pi$
$941$	−22.7836	−0.742723	−0.371362	+	0.928488i	$0.621109\pi$
$942$	41.6342	1.35652
$943$	2.09406	0.0681921
$944$	43.7844	1.42506
$945$	0	0
$946$	40.6968	1.32317
$947$	−9.48915	−0.308356	−0.154178	−	0.988043i	$-0.549273\pi$
$947$	−9.48915	−0.308356	−0.154178	+	0.988043i	$0.549273\pi$
$948$	35.2556	1.14505
$949$	6.23124	0.202275
$950$	0	0
$951$	9.63275	0.312363
$952$	0	0
$953$	15.0041	0.486031	0.243016	−	0.970022i	$-0.421863\pi$
$953$	15.0041	0.486031	0.243016	+	0.970022i	$0.421863\pi$
$954$	7.85048	0.254169
$955$	0	0
$956$	−15.2100	−0.491927
$957$	28.6749	0.926927
$958$	−59.6523	−1.92728
$959$	1.55975	0.0503669
$960$	0	0
$961$	56.6644	1.82788
$962$	7.13640	0.230087
$963$	−5.05220	−0.162805
$964$	−40.7667	−1.31301
$965$	0	0
$966$	1.48888	0.0479038
$967$	−28.2169	−0.907395	−0.453697	−	0.891156i	$-0.649895\pi$
$967$	−28.2169	−0.907395	−0.453697	+	0.891156i	$0.649895\pi$
$968$	−2.92369	−0.0939710
$969$	0	0
$970$	0	0
$971$	−49.9354	−1.60250	−0.801251	−	0.598328i	$-0.795832\pi$
$971$	−49.9354	−1.60250	−0.801251	+	0.598328i	$0.795832\pi$
$972$	−9.10114	−0.291919
$973$	−1.45910	−0.0467768
$974$	−67.4168	−2.16017
$975$	0	0
$976$	3.48911	0.111684
$977$	−8.77720	−0.280807	−0.140404	−	0.990094i	$-0.544840\pi$
$977$	−8.77720	−0.280807	−0.140404	+	0.990094i	$0.544840\pi$
$978$	41.2860	1.32018
$979$	−49.9960	−1.59788
$980$	0	0
$981$	−1.45945	−0.0465966
$982$	29.0358	0.926571
$983$	8.55577	0.272887	0.136443	−	0.990648i	$-0.456433\pi$
$983$	8.55577	0.272887	0.136443	+	0.990648i	$0.456433\pi$
$984$	−2.65577	−0.0846628
$985$	0	0
$986$	0	0
$987$	6.02254	0.191700
$988$	−3.24829	−0.103342
$989$	−7.06286	−0.224586
$990$	0	0
$991$	36.9477	1.17368	0.586841	−	0.809702i	$-0.300371\pi$
$991$	36.9477	1.17368	0.586841	+	0.809702i	$0.300371\pi$
$992$	67.1556	2.13219
$993$	−64.3878	−2.04328
$994$	−9.84092	−0.312135
$995$	0	0
$996$	−34.4861	−1.09273
$997$	54.7222	1.73307	0.866535	−	0.499116i	$-0.166342\pi$
$997$	54.7222	1.73307	0.866535	+	0.499116i	$0.166342\pi$
$998$	21.0805	0.667293
$999$	−31.0929	−0.983735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bx.1.22		24
5.4	even	2		7225.2.a.cb.1.3		24
17.10	odd	16		425.2.m.c.151.1	yes	24
17.12	odd	16		425.2.m.c.76.1	✓	24
17.16	even	2	inner	7225.2.a.bx.1.21		24
85.12	even	16		425.2.n.d.399.1		24
85.27	even	16		425.2.n.e.49.6		24
85.29	odd	16		425.2.m.d.76.6	yes	24
85.44	odd	16		425.2.m.d.151.6	yes	24
85.63	even	16		425.2.n.e.399.6		24
85.78	even	16		425.2.n.d.49.1		24
85.84	even	2		7225.2.a.cb.1.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.1	✓	24	17.12	odd	16
425.2.m.c.151.1	yes	24	17.10	odd	16
425.2.m.d.76.6	yes	24	85.29	odd	16
425.2.m.d.151.6	yes	24	85.44	odd	16
425.2.n.d.49.1		24	85.78	even	16
425.2.n.d.399.1		24	85.12	even	16
425.2.n.e.49.6		24	85.27	even	16
425.2.n.e.399.6		24	85.63	even	16
7225.2.a.bx.1.21		24	17.16	even	2	inner
7225.2.a.bx.1.22		24	1.1	even	1	trivial
7225.2.a.cb.1.3		24	5.4	even	2
7225.2.a.cb.1.4		24	85.84	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:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q+1.88586 q^{2} +1.88942 q^{3} +1.55648 q^{4} +3.56320 q^{6} +0.335329 q^{7} -0.836409 q^{8} +0.569922 q^{9} +O(q^{10})\)	\(q+1.88586 q^{2} +1.88942 q^{3} +1.55648 q^{4} +3.56320 q^{6} +0.335329 q^{7} -0.836409 q^{8} +0.569922 q^{9} -3.80730 q^{11} +2.94086 q^{12} +0.558802 q^{13} +0.632385 q^{14} -4.69032 q^{16} +1.07480 q^{18} -3.73466 q^{19} +0.633578 q^{21} -7.18005 q^{22} +1.24609 q^{23} -1.58033 q^{24} +1.05382 q^{26} -4.59145 q^{27} +0.521934 q^{28} -3.98616 q^{29} -9.36293 q^{31} -7.17250 q^{32} -7.19360 q^{33} +0.887075 q^{36} +6.77191 q^{37} -7.04307 q^{38} +1.05581 q^{39} +1.68051 q^{41} +1.19484 q^{42} -5.66804 q^{43} -5.92600 q^{44} +2.34995 q^{46} +9.50560 q^{47} -8.86201 q^{48} -6.88755 q^{49} +0.869767 q^{52} +7.30416 q^{53} -8.65885 q^{54} -0.280472 q^{56} -7.05636 q^{57} -7.51736 q^{58} -9.33504 q^{59} -0.743895 q^{61} -17.6572 q^{62} +0.191111 q^{63} -4.14571 q^{64} -13.5662 q^{66} -7.29434 q^{67} +2.35438 q^{69} -15.5616 q^{71} -0.476688 q^{72} +11.1511 q^{73} +12.7709 q^{74} -5.81295 q^{76} -1.27670 q^{77} +1.99112 q^{78} +11.9882 q^{79} -10.3850 q^{81} +3.16922 q^{82} -11.7265 q^{83} +0.986155 q^{84} -10.6892 q^{86} -7.53155 q^{87} +3.18446 q^{88} +13.1316 q^{89} +0.187382 q^{91} +1.93951 q^{92} -17.6905 q^{93} +17.9263 q^{94} -13.5519 q^{96} +10.6199 q^{97} -12.9890 q^{98} -2.16986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9} - 16 q^{13} + 24 q^{16} - 40 q^{18} - 16 q^{21} - 16 q^{26} - 56 q^{32} - 48 q^{33} + 24 q^{36} - 48 q^{38} - 32 q^{43} - 88 q^{47} + 16 q^{49} - 48 q^{52} - 48 q^{53} - 8 q^{59} + 72 q^{64} + 32 q^{66} - 40 q^{67} - 48 q^{69} - 120 q^{72} + 32 q^{76} - 120 q^{77} - 24 q^{81} - 104 q^{83} + 40 q^{84} - 16 q^{86} - 64 q^{87} + 16 q^{89} + 72 q^{93} + 112 q^{94} - 48 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9 - 16 * q^13 + 24 * q^16 - 40 * q^18 - 16 * q^21 - 16 * q^26 - 56 * q^32 - 48 * q^33 + 24 * q^36 - 48 * q^38 - 32 * q^43 - 88 * q^47 + 16 * q^49 - 48 * q^52 - 48 * q^53 - 8 * q^59 + 72 * q^64 + 32 * q^66 - 40 * q^67 - 48 * q^69 - 120 * q^72 + 32 * q^76 - 120 * q^77 - 24 * q^81 - 104 * q^83 + 40 * q^84 - 16 * q^86 - 64 * q^87 + 16 * q^89 + 72 * q^93 + 112 * q^94 - 48 * q^98

Introduction

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