LMFDB - Embedded newform 7225.2.a.z.1.5

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:	$6$
Coefficient field:	6.6.7718912.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 7x^{4} + 4x^{3} + 9x^{2} - 2x - 1 $ x^6 - 2x^5 - 7x^4 + 4x^3 + 9x^2 - 2*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.455023$ of defining polynomial
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)

$f(q)$	$=$	\(q+0.783476 q^{2} -0.544977 q^{3} -1.38617 q^{4} -0.426976 q^{6} -1.18848 q^{7} -2.65298 q^{8} -2.70300 q^{9} -2.55419 q^{11} +0.755428 q^{12} -0.368117 q^{13} -0.931143 q^{14} +0.693788 q^{16} -2.11773 q^{18} +6.61138 q^{19} +0.647692 q^{21} -2.00114 q^{22} +3.86343 q^{23} +1.44581 q^{24} -0.288411 q^{26} +3.10800 q^{27} +1.64743 q^{28} +2.31176 q^{29} +6.62531 q^{31} +5.84952 q^{32} +1.39197 q^{33} +3.74681 q^{36} -3.17659 q^{37} +5.17986 q^{38} +0.200615 q^{39} +7.30543 q^{41} +0.507451 q^{42} -6.82350 q^{43} +3.54053 q^{44} +3.02690 q^{46} +7.80793 q^{47} -0.378098 q^{48} -5.58752 q^{49} +0.510272 q^{52} -8.01219 q^{53} +2.43504 q^{54} +3.15300 q^{56} -3.60305 q^{57} +1.81121 q^{58} +5.22381 q^{59} -8.12136 q^{61} +5.19077 q^{62} +3.21245 q^{63} +3.19538 q^{64} +1.09058 q^{66} +7.94564 q^{67} -2.10548 q^{69} +11.8880 q^{71} +7.17100 q^{72} -14.7327 q^{73} -2.48878 q^{74} -9.16447 q^{76} +3.03559 q^{77} +0.157177 q^{78} +0.813189 q^{79} +6.41521 q^{81} +5.72362 q^{82} -3.99116 q^{83} -0.897809 q^{84} -5.34604 q^{86} -1.25986 q^{87} +6.77621 q^{88} -9.14311 q^{89} +0.437499 q^{91} -5.35536 q^{92} -3.61064 q^{93} +6.11732 q^{94} -3.18785 q^{96} -7.06440 q^{97} -4.37769 q^{98} +6.90397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 6 q^{4} + 4 q^{6} - 8 q^{7} - 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{14} + 2 q^{16} - 14 q^{18} - 12 q^{19} + 8 q^{21} - 16 q^{22} + 24 q^{24} - 12 q^{26} + 8 q^{27} + 8 q^{28} + 8 q^{29}+ \cdots + 20 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 + 4 * q^6 - 8 * q^7 - 6 * q^8 + 2 * q^9 - 8 * q^12 + 8 * q^14 + 2 * q^16 - 14 * q^18 - 12 * q^19 + 8 * q^21 - 16 * q^22 + 24 * q^24 - 12 * q^26 + 8 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^31 + 6 * q^32 + 8 * q^33 - 10 * q^36 - 16 * q^37 + 12 * q^38 + 28 * q^39 + 12 * q^41 + 8 * q^42 - 8 * q^43 - 4 * q^44 + 20 * q^46 - 24 * q^47 - 8 * q^48 - 10 * q^49 + 28 * q^52 - 12 * q^54 + 20 * q^56 + 16 * q^57 - 48 * q^58 - 16 * q^59 - 4 * q^61 + 40 * q^62 - 20 * q^63 - 14 * q^64 - 16 * q^66 + 4 * q^67 + 32 * q^71 + 10 * q^72 + 8 * q^73 - 8 * q^74 - 36 * q^76 - 24 * q^77 - 4 * q^78 + 36 * q^79 - 14 * q^81 + 28 * q^82 - 20 * q^83 - 48 * q^86 - 24 * q^87 - 12 * q^88 - 12 * q^89 + 12 * q^91 - 28 * q^92 - 36 * q^93 + 20 * q^94 - 44 * q^96 - 16 * q^97 + 22 * q^98 + 20 * q^99

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 $

$2$	0.783476	0.554001	0.277000	−	0.960870i	$-0.410660\pi$
$2$	0.783476	0.554001	0.277000	+	0.960870i	$0.410660\pi$
$3$	−0.544977	−0.314642	−0.157321	−	0.987547i	$-0.550286\pi$
$3$	−0.544977	−0.314642	−0.157321	+	0.987547i	$0.550286\pi$
$4$	−1.38617	−0.693083
$5$	0	0
$5$	0	0
$6$	−0.426976	−0.174312
$7$	−1.18848	−0.449202	−0.224601	−	0.974451i	$-0.572108\pi$
$7$	−1.18848	−0.449202	−0.224601	+	0.974451i	$0.572108\pi$
$8$	−2.65298	−0.937970
$9$	−2.70300	−0.901000
$10$	0	0
$11$	−2.55419	−0.770117	−0.385058	−	0.922892i	$-0.625819\pi$
$11$	−2.55419	−0.770117	−0.385058	+	0.922892i	$0.625819\pi$
$12$	0.755428	0.218073
$13$	−0.368117	−0.102097	−0.0510487	−	0.998696i	$-0.516256\pi$
$13$	−0.368117	−0.102097	−0.0510487	+	0.998696i	$0.516256\pi$
$14$	−0.931143	−0.248858
$15$	0	0
$16$	0.693788	0.173447
$17$	0	0
$17$	0	0
$18$	−2.11773	−0.499155
$19$	6.61138	1.51676	0.758378	−	0.651816i	$-0.225992\pi$
$19$	6.61138	1.51676	0.758378	+	0.651816i	$0.225992\pi$
$20$	0	0
$21$	0.647692	0.141338
$22$	−2.00114	−0.426645
$23$	3.86343	0.805581	0.402790	−	0.915292i	$-0.368040\pi$
$23$	3.86343	0.805581	0.402790	+	0.915292i	$0.368040\pi$
$24$	1.44581	0.295125
$25$	0	0
$26$	−0.288411	−0.0565621
$27$	3.10800	0.598135
$28$	1.64743	0.311334
$29$	2.31176	0.429284	0.214642	−	0.976693i	$-0.431142\pi$
$29$	2.31176	0.429284	0.214642	+	0.976693i	$0.431142\pi$
$30$	0	0
$31$	6.62531	1.18994	0.594970	−	0.803748i	$-0.297164\pi$
$31$	6.62531	1.18994	0.594970	+	0.803748i	$0.297164\pi$
$32$	5.84952	1.03406
$33$	1.39197	0.242311
$34$	0	0
$35$	0	0
$36$	3.74681	0.624468
$37$	−3.17659	−0.522229	−0.261114	−	0.965308i	$-0.584090\pi$
$37$	−3.17659	−0.522229	−0.261114	+	0.965308i	$0.584090\pi$
$38$	5.17986	0.840284
$39$	0.200615	0.0321242
$40$	0	0
$41$	7.30543	1.14092	0.570458	−	0.821327i	$-0.306766\pi$
$41$	7.30543	1.14092	0.570458	+	0.821327i	$0.306766\pi$
$42$	0.507451	0.0783014
$43$	−6.82350	−1.04057	−0.520287	−	0.853992i	$-0.674175\pi$
$43$	−6.82350	−1.04057	−0.520287	+	0.853992i	$0.674175\pi$
$44$	3.54053	0.533755
$45$	0	0
$46$	3.02690	0.446292
$47$	7.80793	1.13890	0.569452	−	0.822025i	$-0.307156\pi$
$47$	7.80793	1.13890	0.569452	+	0.822025i	$0.307156\pi$
$48$	−0.378098	−0.0545738
$49$	−5.58752	−0.798218
$50$	0	0
$51$	0	0
$52$	0.510272	0.0707620
$53$	−8.01219	−1.10056	−0.550280	−	0.834980i	$-0.685479\pi$
$53$	−8.01219	−1.10056	−0.550280	+	0.834980i	$0.685479\pi$
$54$	2.43504	0.331367
$55$	0	0
$56$	3.15300	0.421338
$57$	−3.60305	−0.477235
$58$	1.81121	0.237824
$59$	5.22381	0.680082	0.340041	−	0.940411i	$-0.389559\pi$
$59$	5.22381	0.680082	0.340041	+	0.940411i	$0.389559\pi$
$60$	0	0
$61$	−8.12136	−1.03983	−0.519917	−	0.854217i	$-0.674037\pi$
$61$	−8.12136	−1.03983	−0.519917	+	0.854217i	$0.674037\pi$
$62$	5.19077	0.659228
$63$	3.21245	0.404731
$64$	3.19538	0.399423
$65$	0	0
$66$	1.09058	0.134241
$67$	7.94564	0.970715	0.485357	−	0.874316i	$-0.338690\pi$
$67$	7.94564	0.970715	0.485357	+	0.874316i	$0.338690\pi$
$68$	0	0
$69$	−2.10548	−0.253470
$70$	0	0
$71$	11.8880	1.41085	0.705425	−	0.708785i	$-0.250756\pi$
$71$	11.8880	1.41085	0.705425	+	0.708785i	$0.250756\pi$
$72$	7.17100	0.845111
$73$	−14.7327	−1.72434	−0.862168	−	0.506622i	$-0.830894\pi$
$73$	−14.7327	−1.72434	−0.862168	+	0.506622i	$0.830894\pi$
$74$	−2.48878	−0.289315
$75$	0	0
$76$	−9.16447	−1.05124
$77$	3.03559	0.345938
$78$	0.157177	0.0177968
$79$	0.813189	0.0914909	0.0457454	−	0.998953i	$-0.485434\pi$
$79$	0.813189	0.0914909	0.0457454	+	0.998953i	$0.485434\pi$
$80$	0	0
$81$	6.41521	0.712801
$82$	5.72362	0.632068
$83$	−3.99116	−0.438087	−0.219044	−	0.975715i	$-0.570294\pi$
$83$	−3.99116	−0.438087	−0.219044	+	0.975715i	$0.570294\pi$
$84$	−0.897809	−0.0979590
$85$	0	0
$86$	−5.34604	−0.576479
$87$	−1.25986	−0.135071
$88$	6.77621	0.722346
$89$	−9.14311	−0.969168	−0.484584	−	0.874745i	$-0.661029\pi$
$89$	−9.14311	−0.969168	−0.484584	+	0.874745i	$0.661029\pi$
$90$	0	0
$91$	0.437499	0.0458624
$92$	−5.35536	−0.558334
$93$	−3.61064	−0.374406
$94$	6.11732	0.630953
$95$	0	0
$96$	−3.18785	−0.325359
$97$	−7.06440	−0.717281	−0.358641	−	0.933476i	$-0.616760\pi$
$97$	−7.06440	−0.717281	−0.358641	+	0.933476i	$0.616760\pi$
$98$	−4.37769	−0.442213
$99$	6.90397	0.693875
$100$	0	0
$101$	0.296263	0.0294793	0.0147396	−	0.999891i	$-0.495308\pi$
$101$	0.296263	0.0294793	0.0147396	+	0.999891i	$0.495308\pi$
$102$	0	0
$103$	−17.0372	−1.67873	−0.839363	−	0.543571i	$-0.817072\pi$
$103$	−17.0372	−1.67873	−0.839363	+	0.543571i	$0.817072\pi$
$104$	0.976608	0.0957642
$105$	0	0
$106$	−6.27736	−0.609711
$107$	−3.80874	−0.368205	−0.184102	−	0.982907i	$-0.558938\pi$
$107$	−3.80874	−0.368205	−0.184102	+	0.982907i	$0.558938\pi$
$108$	−4.30821	−0.414557
$109$	12.0374	1.15297	0.576486	−	0.817107i	$-0.304424\pi$
$109$	12.0374	1.15297	0.576486	+	0.817107i	$0.304424\pi$
$110$	0	0
$111$	1.73117	0.164315
$112$	−0.824551	−0.0779128
$113$	−16.4819	−1.55049	−0.775243	−	0.631664i	$-0.782372\pi$
$113$	−16.4819	−1.55049	−0.775243	+	0.631664i	$0.782372\pi$
$114$	−2.82290	−0.264389
$115$	0	0
$116$	−3.20449	−0.297529
$117$	0.995022	0.0919898
$118$	4.09272	0.376766
$119$	0	0
$120$	0	0
$121$	−4.47612	−0.406920
$122$	−6.36288	−0.576068
$123$	−3.98129	−0.358980
$124$	−9.18378	−0.824727
$125$	0	0
$126$	2.51688	0.224221
$127$	4.48798	0.398244	0.199122	−	0.979975i	$-0.436191\pi$
$127$	4.48798	0.398244	0.199122	+	0.979975i	$0.436191\pi$
$128$	−9.19554	−0.812779
$129$	3.71865	0.327409
$130$	0	0
$131$	9.34295	0.816297	0.408149	−	0.912915i	$-0.366174\pi$
$131$	9.34295	0.816297	0.408149	+	0.912915i	$0.366174\pi$
$132$	−1.92951	−0.167942
$133$	−7.85747	−0.681329
$134$	6.22522	0.537777
$135$	0	0
$136$	0	0
$137$	−8.47822	−0.724344	−0.362172	−	0.932111i	$-0.617965\pi$
$137$	−8.47822	−0.724344	−0.362172	+	0.932111i	$0.617965\pi$
$138$	−1.64959	−0.140423
$139$	−6.00703	−0.509509	−0.254755	−	0.967006i	$-0.581995\pi$
$139$	−6.00703	−0.509509	−0.254755	+	0.967006i	$0.581995\pi$
$140$	0	0
$141$	−4.25514	−0.358347
$142$	9.31398	0.781612
$143$	0.940241	0.0786269
$144$	−1.87531	−0.156276
$145$	0	0
$146$	−11.5427	−0.955284
$147$	3.04507	0.251153
$148$	4.40329	0.361948
$149$	−9.11821	−0.746993	−0.373497	−	0.927632i	$-0.621841\pi$
$149$	−9.11821	−0.746993	−0.373497	+	0.927632i	$0.621841\pi$
$150$	0	0
$151$	−13.1144	−1.06724	−0.533619	−	0.845725i	$-0.679168\pi$
$151$	−13.1144	−1.06724	−0.533619	+	0.845725i	$0.679168\pi$
$152$	−17.5399	−1.42267
$153$	0	0
$154$	2.37831	0.191650
$155$	0	0
$156$	−0.278086	−0.0222647
$157$	−20.0496	−1.60013	−0.800065	−	0.599913i	$-0.795202\pi$
$157$	−20.0496	−1.60013	−0.800065	+	0.599913i	$0.795202\pi$
$158$	0.637113	0.0506860
$159$	4.36646	0.346283
$160$	0	0
$161$	−4.59160	−0.361869
$162$	5.02616	0.394893
$163$	−14.2708	−1.11778	−0.558888	−	0.829243i	$-0.688772\pi$
$163$	−14.2708	−1.11778	−0.558888	+	0.829243i	$0.688772\pi$
$164$	−10.1265	−0.790749
$165$	0	0
$166$	−3.12698	−0.242701
$167$	0.222335	0.0172048	0.00860240	−	0.999963i	$-0.497262\pi$
$167$	0.222335	0.0172048	0.00860240	+	0.999963i	$0.497262\pi$
$168$	−1.71831	−0.132571
$169$	−12.8645	−0.989576
$170$	0	0
$171$	−17.8706	−1.36660
$172$	9.45850	0.721204
$173$	19.9946	1.52016	0.760080	−	0.649829i	$-0.225160\pi$
$173$	19.9946	1.52016	0.760080	+	0.649829i	$0.225160\pi$
$174$	−0.987067	−0.0748294
$175$	0	0
$176$	−1.77207	−0.133575
$177$	−2.84685	−0.213982
$178$	−7.16341	−0.536920
$179$	−24.3120	−1.81716	−0.908581	−	0.417708i	$-0.862834\pi$
$179$	−24.3120	−1.81716	−0.908581	+	0.417708i	$0.862834\pi$
$180$	0	0
$181$	11.8866	0.883522	0.441761	−	0.897133i	$-0.354354\pi$
$181$	11.8866	0.883522	0.441761	+	0.897133i	$0.354354\pi$
$182$	0.342770	0.0254078
$183$	4.42595	0.327176
$184$	−10.2496	−0.755610
$185$	0	0
$186$	−2.82885	−0.207421
$187$	0	0
$188$	−10.8231	−0.789354
$189$	−3.69379	−0.268684
$190$	0	0
$191$	17.2930	1.25128	0.625638	−	0.780114i	$-0.284839\pi$
$191$	17.2930	1.25128	0.625638	+	0.780114i	$0.284839\pi$
$192$	−1.74141	−0.125675
$193$	−1.80952	−0.130252	−0.0651261	−	0.997877i	$-0.520745\pi$
$193$	−1.80952	−0.130252	−0.0651261	+	0.997877i	$0.520745\pi$
$194$	−5.53479	−0.397375
$195$	0	0
$196$	7.74523	0.553231
$197$	16.5784	1.18116	0.590580	−	0.806979i	$-0.298899\pi$
$197$	16.5784	1.18116	0.590580	+	0.806979i	$0.298899\pi$
$198$	5.40909	0.384408
$199$	25.1610	1.78362	0.891808	−	0.452414i	$-0.149437\pi$
$199$	25.1610	1.78362	0.891808	+	0.452414i	$0.149437\pi$
$200$	0	0
$201$	−4.33019	−0.305428
$202$	0.232115	0.0163315
$203$	−2.74748	−0.192835
$204$	0	0
$205$	0	0
$206$	−13.3482	−0.930016
$207$	−10.4429	−0.725828
$208$	−0.255396	−0.0177085
$209$	−16.8867	−1.16808
$210$	0	0
$211$	−8.40826	−0.578849	−0.289424	−	0.957201i	$-0.593464\pi$
$211$	−8.40826	−0.578849	−0.289424	+	0.957201i	$0.593464\pi$
$212$	11.1062	0.762779
$213$	−6.47870	−0.443913
$214$	−2.98406	−0.203986
$215$	0	0
$216$	−8.24546	−0.561033
$217$	−7.87402	−0.534524
$218$	9.43099	0.638748
$219$	8.02900	0.542549
$220$	0	0
$221$	0	0
$222$	1.35633	0.0910308
$223$	16.5499	1.10826	0.554132	−	0.832429i	$-0.313050\pi$
$223$	16.5499	1.10826	0.554132	+	0.832429i	$0.313050\pi$
$224$	−6.95202	−0.464502
$225$	0	0
$226$	−12.9132	−0.858970
$227$	7.11700	0.472372	0.236186	−	0.971708i	$-0.424103\pi$
$227$	7.11700	0.472372	0.236186	+	0.971708i	$0.424103\pi$
$228$	4.99442	0.330764
$229$	−1.46774	−0.0969907	−0.0484953	−	0.998823i	$-0.515443\pi$
$229$	−1.46774	−0.0969907	−0.0484953	+	0.998823i	$0.515443\pi$
$230$	0	0
$231$	−1.65433	−0.108847
$232$	−6.13306	−0.402655
$233$	23.1663	1.51767	0.758837	−	0.651280i	$-0.225768\pi$
$233$	23.1663	1.51767	0.758837	+	0.651280i	$0.225768\pi$
$234$	0.779575	0.0509624
$235$	0	0
$236$	−7.24106	−0.471353
$237$	−0.443169	−0.0287869
$238$	0	0
$239$	−6.43252	−0.416085	−0.208042	−	0.978120i	$-0.566709\pi$
$239$	−6.43252	−0.416085	−0.208042	+	0.978120i	$0.566709\pi$
$240$	0	0
$241$	27.3959	1.76473	0.882364	−	0.470568i	$-0.155951\pi$
$241$	27.3959	1.76473	0.882364	+	0.470568i	$0.155951\pi$
$242$	−3.50693	−0.225434
$243$	−12.8201	−0.822413
$244$	11.2575	0.720691
$245$	0	0
$246$	−3.11924	−0.198875
$247$	−2.43376	−0.154857
$248$	−17.5768	−1.11613
$249$	2.17509	0.137841
$250$	0	0
$251$	−0.234413	−0.0147960	−0.00739800	−	0.999973i	$-0.502355\pi$
$251$	−0.234413	−0.0147960	−0.00739800	+	0.999973i	$0.502355\pi$
$252$	−4.45299	−0.280512
$253$	−9.86793	−0.620391
$254$	3.51623	0.220628
$255$	0	0
$256$	−13.5952	−0.849703
$257$	3.56040	0.222092	0.111046	−	0.993815i	$-0.464580\pi$
$257$	3.56040	0.222092	0.111046	+	0.993815i	$0.464580\pi$
$258$	2.91347	0.181385
$259$	3.77531	0.234586
$260$	0	0
$261$	−6.24870	−0.386785
$262$	7.31997	0.452229
$263$	−30.0000	−1.84988	−0.924940	−	0.380112i	$-0.875885\pi$
$263$	−30.0000	−1.84988	−0.924940	+	0.380112i	$0.875885\pi$
$264$	−3.69287	−0.227281
$265$	0	0
$266$	−6.15614	−0.377457
$267$	4.98278	0.304941
$268$	−11.0140	−0.672786
$269$	−0.379243	−0.0231229	−0.0115614	−	0.999933i	$-0.503680\pi$
$269$	−0.379243	−0.0231229	−0.0115614	+	0.999933i	$0.503680\pi$
$270$	0	0
$271$	10.6144	0.644780	0.322390	−	0.946607i	$-0.395514\pi$
$271$	10.6144	0.644780	0.322390	+	0.946607i	$0.395514\pi$
$272$	0	0
$273$	−0.238427	−0.0144302
$274$	−6.64248	−0.401287
$275$	0	0
$276$	2.91854	0.175676
$277$	30.4925	1.83211	0.916057	−	0.401048i	$-0.131354\pi$
$277$	30.4925	1.83211	0.916057	+	0.401048i	$0.131354\pi$
$278$	−4.70636	−0.282269
$279$	−17.9082	−1.07214
$280$	0	0
$281$	−26.4402	−1.57729	−0.788645	−	0.614849i	$-0.789217\pi$
$281$	−26.4402	−1.57729	−0.788645	+	0.614849i	$0.789217\pi$
$282$	−3.33380	−0.198525
$283$	−18.5761	−1.10424	−0.552118	−	0.833766i	$-0.686180\pi$
$283$	−18.5761	−1.10424	−0.552118	+	0.833766i	$0.686180\pi$
$284$	−16.4788	−0.977836
$285$	0	0
$286$	0.736656	0.0435594
$287$	−8.68233	−0.512502
$288$	−15.8113	−0.931688
$289$	0	0
$290$	0	0
$291$	3.84993	0.225687
$292$	20.4220	1.19511
$293$	3.59958	0.210289	0.105145	−	0.994457i	$-0.466469\pi$
$293$	3.59958	0.210289	0.105145	+	0.994457i	$0.466469\pi$
$294$	2.38574	0.139139
$295$	0	0
$296$	8.42743	0.489835
$297$	−7.93842	−0.460634
$298$	−7.14390	−0.413835
$299$	−1.42220	−0.0822477
$300$	0	0
$301$	8.10957	0.467428
$302$	−10.2748	−0.591251
$303$	−0.161456	−0.00927543
$304$	4.58690	0.263077
$305$	0	0
$306$	0	0
$307$	33.4128	1.90697	0.953486	−	0.301438i	$-0.0974668\pi$
$307$	33.4128	1.90697	0.953486	+	0.301438i	$0.0974668\pi$
$308$	−4.20784	−0.239764
$309$	9.28488	0.528199
$310$	0	0
$311$	−13.7961	−0.782303	−0.391152	−	0.920326i	$-0.627923\pi$
$311$	−13.7961	−0.782303	−0.391152	+	0.920326i	$0.627923\pi$
$312$	−0.532228	−0.0301315
$313$	30.5703	1.72793	0.863966	−	0.503550i	$-0.167973\pi$
$313$	30.5703	1.72793	0.863966	+	0.503550i	$0.167973\pi$
$314$	−15.7084	−0.886473
$315$	0	0
$316$	−1.12721	−0.0634108
$317$	3.21700	0.180685	0.0903424	−	0.995911i	$-0.471204\pi$
$317$	3.21700	0.180685	0.0903424	+	0.995911i	$0.471204\pi$
$318$	3.42101	0.191841
$319$	−5.90468	−0.330599
$320$	0	0
$321$	2.07568	0.115853
$322$	−3.59740	−0.200475
$323$	0	0
$324$	−8.89255	−0.494031
$325$	0	0
$326$	−11.1808	−0.619248
$327$	−6.56009	−0.362774
$328$	−19.3811	−1.07014
$329$	−9.27954	−0.511598
$330$	0	0
$331$	−29.7637	−1.63596	−0.817981	−	0.575246i	$-0.804906\pi$
$331$	−29.7637	−1.63596	−0.817981	+	0.575246i	$0.804906\pi$
$332$	5.53242	0.303631
$333$	8.58633	0.470528
$334$	0.174194	0.00953147
$335$	0	0
$336$	0.449361	0.0245147
$337$	−10.7314	−0.584578	−0.292289	−	0.956330i	$-0.594417\pi$
$337$	−10.7314	−0.584578	−0.292289	+	0.956330i	$0.594417\pi$
$338$	−10.0790	−0.548226
$339$	8.98224	0.487848
$340$	0	0
$341$	−16.9223	−0.916393
$342$	−14.0012	−0.757096
$343$	14.9600	0.807763
$344$	18.1026	0.976026
$345$	0	0
$346$	15.6653	0.842170
$347$	1.14416	0.0614219	0.0307109	−	0.999528i	$-0.490223\pi$
$347$	1.14416	0.0614219	0.0307109	+	0.999528i	$0.490223\pi$
$348$	1.74637	0.0936153
$349$	18.6531	0.998476	0.499238	−	0.866465i	$-0.333613\pi$
$349$	18.6531	0.998476	0.499238	+	0.866465i	$0.333613\pi$
$350$	0	0
$351$	−1.14411	−0.0610681
$352$	−14.9408	−0.796347
$353$	4.34305	0.231157	0.115579	−	0.993298i	$-0.463128\pi$
$353$	4.34305	0.231157	0.115579	+	0.993298i	$0.463128\pi$
$354$	−2.23044	−0.118546
$355$	0	0
$356$	12.6739	0.671714
$357$	0	0
$358$	−19.0478	−1.00671
$359$	−6.35821	−0.335573	−0.167787	−	0.985823i	$-0.553662\pi$
$359$	−6.35821	−0.335573	−0.167787	+	0.985823i	$0.553662\pi$
$360$	0	0
$361$	24.7104	1.30055
$362$	9.31284	0.489472
$363$	2.43938	0.128034
$364$	−0.606446	−0.0317864
$365$	0	0
$366$	3.46762	0.181256
$367$	−16.2147	−0.846401	−0.423200	−	0.906036i	$-0.639093\pi$
$367$	−16.2147	−0.846401	−0.423200	+	0.906036i	$0.639093\pi$
$368$	2.68040	0.139726
$369$	−19.7466	−1.02797
$370$	0	0
$371$	9.52230	0.494373
$372$	5.00494	0.259494
$373$	18.5947	0.962797	0.481398	−	0.876502i	$-0.340129\pi$
$373$	18.5947	0.962797	0.481398	+	0.876502i	$0.340129\pi$
$374$	0	0
$375$	0	0
$376$	−20.7143	−1.06826
$377$	−0.851001	−0.0438288
$378$	−2.89399	−0.148851
$379$	9.06118	0.465441	0.232721	−	0.972544i	$-0.425237\pi$
$379$	9.06118	0.465441	0.232721	+	0.972544i	$0.425237\pi$
$380$	0	0
$381$	−2.44585	−0.125305
$382$	13.5486	0.693208
$383$	2.75136	0.140588	0.0702941	−	0.997526i	$-0.477606\pi$
$383$	2.75136	0.140588	0.0702941	+	0.997526i	$0.477606\pi$
$384$	5.01136	0.255735
$385$	0	0
$386$	−1.41772	−0.0721598
$387$	18.4439	0.937557
$388$	9.79244	0.497136
$389$	−27.3962	−1.38904	−0.694521	−	0.719472i	$-0.744384\pi$
$389$	−27.3962	−1.38904	−0.694521	+	0.719472i	$0.744384\pi$
$390$	0	0
$391$	0	0
$392$	14.8236	0.748704
$393$	−5.09169	−0.256842
$394$	12.9888	0.654364
$395$	0	0
$396$	−9.57005	−0.480913
$397$	−24.9827	−1.25385	−0.626923	−	0.779081i	$-0.715686\pi$
$397$	−24.9827	−1.25385	−0.626923	+	0.779081i	$0.715686\pi$
$398$	19.7130	0.988125
$399$	4.28214	0.214375
$400$	0	0
$401$	−31.7357	−1.58480	−0.792402	−	0.610000i	$-0.791170\pi$
$401$	−31.7357	−1.58480	−0.792402	+	0.610000i	$0.791170\pi$
$402$	−3.39260	−0.169207
$403$	−2.43889	−0.121490
$404$	−0.410670	−0.0204316
$405$	0	0
$406$	−2.15258	−0.106831
$407$	8.11362	0.402177
$408$	0	0
$409$	0.721793	0.0356904	0.0178452	−	0.999841i	$-0.494319\pi$
$409$	0.721793	0.0356904	0.0178452	+	0.999841i	$0.494319\pi$
$410$	0	0
$411$	4.62043	0.227909
$412$	23.6164	1.16350
$413$	−6.20837	−0.305494
$414$	−8.18172	−0.402110
$415$	0	0
$416$	−2.15331	−0.105575
$417$	3.27369	0.160313
$418$	−13.2303	−0.647117
$419$	−14.3360	−0.700361	−0.350180	−	0.936682i	$-0.613880\pi$
$419$	−14.3360	−0.700361	−0.350180	+	0.936682i	$0.613880\pi$
$420$	0	0
$421$	−2.94304	−0.143435	−0.0717175	−	0.997425i	$-0.522848\pi$
$421$	−2.94304	−0.143435	−0.0717175	+	0.997425i	$0.522848\pi$
$422$	−6.58767	−0.320683
$423$	−21.1048	−1.02615
$424$	21.2562	1.03229
$425$	0	0
$426$	−5.07590	−0.245928
$427$	9.65204	0.467095
$428$	5.27955	0.255197
$429$	−0.512410	−0.0247394
$430$	0	0
$431$	−32.1754	−1.54983	−0.774917	−	0.632063i	$-0.782208\pi$
$431$	−32.1754	−1.54983	−0.774917	+	0.632063i	$0.782208\pi$
$432$	2.15630	0.103745
$433$	1.76074	0.0846158	0.0423079	−	0.999105i	$-0.486529\pi$
$433$	1.76074	0.0846158	0.0423079	+	0.999105i	$0.486529\pi$
$434$	−6.16911	−0.296127
$435$	0	0
$436$	−16.6858	−0.799105
$437$	25.5426	1.22187
$438$	6.29052	0.300573
$439$	0.551679	0.0263302	0.0131651	−	0.999913i	$-0.495809\pi$
$439$	0.551679	0.0263302	0.0131651	+	0.999913i	$0.495809\pi$
$440$	0	0
$441$	15.1031	0.719194
$442$	0	0
$443$	−2.19117	−0.104106	−0.0520528	−	0.998644i	$-0.516576\pi$
$443$	−2.19117	−0.104106	−0.0520528	+	0.998644i	$0.516576\pi$
$444$	−2.39969	−0.113884
$445$	0	0
$446$	12.9665	0.613980
$447$	4.96921	0.235036
$448$	−3.79764	−0.179422
$449$	−2.15978	−0.101926	−0.0509631	−	0.998701i	$-0.516229\pi$
$449$	−2.15978	−0.101926	−0.0509631	+	0.998701i	$0.516229\pi$
$450$	0	0
$451$	−18.6594	−0.878639
$452$	22.8466	1.07461
$453$	7.14706	0.335798
$454$	5.57599	0.261694
$455$	0	0
$456$	9.55881	0.447632
$457$	−9.46893	−0.442938	−0.221469	−	0.975167i	$-0.571085\pi$
$457$	−9.46893	−0.442938	−0.221469	+	0.975167i	$0.571085\pi$
$458$	−1.14993	−0.0537329
$459$	0	0
$460$	0	0
$461$	16.6646	0.776149	0.388075	−	0.921628i	$-0.373140\pi$
$461$	16.6646	0.776149	0.388075	+	0.921628i	$0.373140\pi$
$462$	−1.29613	−0.0603012
$463$	14.3738	0.668009	0.334005	−	0.942571i	$-0.391600\pi$
$463$	14.3738	0.668009	0.334005	+	0.942571i	$0.391600\pi$
$464$	1.60387	0.0744580
$465$	0	0
$466$	18.1502	0.840793
$467$	−12.9129	−0.597537	−0.298769	−	0.954326i	$-0.596576\pi$
$467$	−12.9129	−0.597537	−0.298769	+	0.954326i	$0.596576\pi$
$468$	−1.37927	−0.0637565
$469$	−9.44321	−0.436047
$470$	0	0
$471$	10.9265	0.503469
$472$	−13.8586	−0.637896
$473$	17.4285	0.801363
$474$	−0.347212	−0.0159480
$475$	0	0
$476$	0	0
$477$	21.6570	0.991604
$478$	−5.03972	−0.230511
$479$	6.01194	0.274692	0.137346	−	0.990523i	$-0.456143\pi$
$479$	6.01194	0.274692	0.137346	+	0.990523i	$0.456143\pi$
$480$	0	0
$481$	1.16936	0.0533182
$482$	21.4640	0.977661
$483$	2.50231	0.113859
$484$	6.20464	0.282029
$485$	0	0
$486$	−10.0443	−0.455617
$487$	−33.1010	−1.49995	−0.749975	−	0.661466i	$-0.769935\pi$
$487$	−33.1010	−1.49995	−0.749975	+	0.661466i	$0.769935\pi$
$488$	21.5458	0.975332
$489$	7.77725	0.351699
$490$	0	0
$491$	18.7705	0.847099	0.423549	−	0.905873i	$-0.360784\pi$
$491$	18.7705	0.847099	0.423549	+	0.905873i	$0.360784\pi$
$492$	5.51872	0.248803
$493$	0	0
$494$	−1.90680	−0.0857908
$495$	0	0
$496$	4.59656	0.206392
$497$	−14.1286	−0.633756
$498$	1.70413	0.0763639
$499$	−7.14440	−0.319827	−0.159914	−	0.987131i	$-0.551122\pi$
$499$	−7.14440	−0.319827	−0.159914	+	0.987131i	$0.551122\pi$
$500$	0	0
$501$	−0.121167	−0.00541336
$502$	−0.183657	−0.00819700
$503$	−29.3535	−1.30881	−0.654404	−	0.756145i	$-0.727080\pi$
$503$	−29.3535	−1.30881	−0.654404	+	0.756145i	$0.727080\pi$
$504$	−8.52257	−0.379625
$505$	0	0
$506$	−7.73128	−0.343697
$507$	7.01085	0.311363
$508$	−6.22109	−0.276016
$509$	−9.83824	−0.436072	−0.218036	−	0.975941i	$-0.569965\pi$
$509$	−9.83824	−0.436072	−0.218036	+	0.975941i	$0.569965\pi$
$510$	0	0
$511$	17.5095	0.774575
$512$	7.73954	0.342043
$513$	20.5482	0.907225
$514$	2.78949	0.123039
$515$	0	0
$516$	−5.15466	−0.226921
$517$	−19.9429	−0.877089
$518$	2.95786	0.129961
$519$	−10.8966	−0.478307
$520$	0	0
$521$	−6.82338	−0.298938	−0.149469	−	0.988766i	$-0.547756\pi$
$521$	−6.82338	−0.298938	−0.149469	+	0.988766i	$0.547756\pi$
$522$	−4.89570	−0.214279
$523$	−7.90422	−0.345628	−0.172814	−	0.984955i	$-0.555286\pi$
$523$	−7.90422	−0.345628	−0.172814	+	0.984955i	$0.555286\pi$
$524$	−12.9509	−0.565762
$525$	0	0
$526$	−23.5043	−1.02484
$527$	0	0
$528$	0.965735	0.0420282
$529$	−8.07391	−0.351040
$530$	0	0
$531$	−14.1199	−0.612754
$532$	10.8918	0.472218
$533$	−2.68925	−0.116485
$534$	3.90389	0.168938
$535$	0	0
$536$	−21.0796	−0.910501
$537$	13.2495	0.571756
$538$	−0.297128	−0.0128101
$539$	14.2716	0.614721
$540$	0	0
$541$	−36.2840	−1.55997	−0.779985	−	0.625798i	$-0.784774\pi$
$541$	−36.2840	−1.55997	−0.779985	+	0.625798i	$0.784774\pi$
$542$	8.31614	0.357209
$543$	−6.47790	−0.277993
$544$	0	0
$545$	0	0
$546$	−0.186802	−0.00799437
$547$	−28.2798	−1.20915	−0.604577	−	0.796546i	$-0.706658\pi$
$547$	−28.2798	−1.20915	−0.604577	+	0.796546i	$0.706658\pi$
$548$	11.7522	0.502030
$549$	21.9520	0.936890
$550$	0	0
$551$	15.2840	0.651118
$552$	5.58579	0.237747
$553$	−0.966456	−0.0410979
$554$	23.8901	1.01499
$555$	0	0
$556$	8.32674	0.353132
$557$	−15.4059	−0.652768	−0.326384	−	0.945237i	$-0.605830\pi$
$557$	−15.4059	−0.652768	−0.326384	+	0.945237i	$0.605830\pi$
$558$	−14.0306	−0.593964
$559$	2.51185	0.106240
$560$	0	0
$561$	0	0
$562$	−20.7153	−0.873820
$563$	−8.51617	−0.358914	−0.179457	−	0.983766i	$-0.557434\pi$
$563$	−8.51617	−0.358914	−0.179457	+	0.983766i	$0.557434\pi$
$564$	5.89833	0.248364
$565$	0	0
$566$	−14.5539	−0.611748
$567$	−7.62433	−0.320192
$568$	−31.5387	−1.32333
$569$	−10.0268	−0.420346	−0.210173	−	0.977664i	$-0.567403\pi$
$569$	−10.0268	−0.420346	−0.210173	+	0.977664i	$0.567403\pi$
$570$	0	0
$571$	13.8174	0.578242	0.289121	−	0.957293i	$-0.406637\pi$
$571$	13.8174	0.578242	0.289121	+	0.957293i	$0.406637\pi$
$572$	−1.30333	−0.0544950
$573$	−9.42427	−0.393704
$574$	−6.80239	−0.283926
$575$	0	0
$576$	−8.63712	−0.359880
$577$	13.6068	0.566457	0.283229	−	0.959052i	$-0.408594\pi$
$577$	13.6068	0.566457	0.283229	+	0.959052i	$0.408594\pi$
$578$	0	0
$579$	0.986147	0.0409829
$580$	0	0
$581$	4.74341	0.196790
$582$	3.01633	0.125031
$583$	20.4647	0.847559
$584$	39.0856	1.61738
$585$	0	0
$586$	2.82018	0.116501
$587$	−27.9191	−1.15234	−0.576172	−	0.817329i	$-0.695454\pi$
$587$	−27.9191	−1.15234	−0.576172	+	0.817329i	$0.695454\pi$
$588$	−4.22097	−0.174070
$589$	43.8024	1.80485
$590$	0	0
$591$	−9.03483	−0.371643
$592$	−2.20388	−0.0905790
$593$	40.0318	1.64391	0.821954	−	0.569554i	$-0.192884\pi$
$593$	40.0318	1.64391	0.821954	+	0.569554i	$0.192884\pi$
$594$	−6.21956	−0.255192
$595$	0	0
$596$	12.6394	0.517728
$597$	−13.7122	−0.561201
$598$	−1.11426	−0.0455653
$599$	−25.5481	−1.04387	−0.521934	−	0.852986i	$-0.674789\pi$
$599$	−25.5481	−1.04387	−0.521934	+	0.852986i	$0.674789\pi$
$600$	0	0
$601$	3.89097	0.158716	0.0793581	−	0.996846i	$-0.474713\pi$
$601$	3.89097	0.158716	0.0793581	+	0.996846i	$0.474713\pi$
$602$	6.35365	0.258955
$603$	−21.4771	−0.874614
$604$	18.1788	0.739684
$605$	0	0
$606$	−0.126497	−0.00513859
$607$	−9.82009	−0.398585	−0.199293	−	0.979940i	$-0.563864\pi$
$607$	−9.82009	−0.398585	−0.199293	+	0.979940i	$0.563864\pi$
$608$	38.6734	1.56841
$609$	1.49731	0.0606741
$610$	0	0
$611$	−2.87423	−0.116279
$612$	0	0
$613$	−44.6175	−1.80208	−0.901042	−	0.433733i	$-0.857196\pi$
$613$	−44.6175	−1.80208	−0.901042	+	0.433733i	$0.857196\pi$
$614$	26.1781	1.05646
$615$	0	0
$616$	−8.05337	−0.324479
$617$	−35.6864	−1.43668	−0.718341	−	0.695691i	$-0.755098\pi$
$617$	−35.6864	−1.43668	−0.718341	+	0.695691i	$0.755098\pi$
$618$	7.27448	0.292622
$619$	16.5853	0.666620	0.333310	−	0.942817i	$-0.391834\pi$
$619$	16.5853	0.666620	0.333310	+	0.942817i	$0.391834\pi$
$620$	0	0
$621$	12.0075	0.481846
$622$	−10.8089	−0.433397
$623$	10.8664	0.435352
$624$	0.139185	0.00557184
$625$	0	0
$626$	23.9510	0.957276
$627$	9.20287	0.367527
$628$	27.7920	1.10902
$629$	0	0
$630$	0	0
$631$	−38.0364	−1.51421	−0.757103	−	0.653295i	$-0.773386\pi$
$631$	−38.0364	−1.51421	−0.757103	+	0.653295i	$0.773386\pi$
$632$	−2.15737	−0.0858156
$633$	4.58231	0.182130
$634$	2.52044	0.100100
$635$	0	0
$636$	−6.05263	−0.240003
$637$	2.05686	0.0814959
$638$	−4.62617	−0.183152
$639$	−32.1333	−1.27118
$640$	0	0
$641$	−3.64035	−0.143785	−0.0718927	−	0.997412i	$-0.522904\pi$
$641$	−3.64035	−0.143785	−0.0718927	+	0.997412i	$0.522904\pi$
$642$	1.62624	0.0641826
$643$	−18.4030	−0.725743	−0.362871	−	0.931839i	$-0.618204\pi$
$643$	−18.4030	−0.725743	−0.362871	+	0.931839i	$0.618204\pi$
$644$	6.36472	0.250805
$645$	0	0
$646$	0	0
$647$	−3.12579	−0.122888	−0.0614438	−	0.998111i	$-0.519571\pi$
$647$	−3.12579	−0.122888	−0.0614438	+	0.998111i	$0.519571\pi$
$648$	−17.0194	−0.668586
$649$	−13.3426	−0.523742
$650$	0	0
$651$	4.29116	0.168184
$652$	19.7817	0.774711
$653$	14.0378	0.549341	0.274671	−	0.961538i	$-0.411431\pi$
$653$	14.0378	0.549341	0.274671	+	0.961538i	$0.411431\pi$
$654$	−5.13967	−0.200977
$655$	0	0
$656$	5.06842	0.197888
$657$	39.8226	1.55363
$658$	−7.27029	−0.283426
$659$	−4.52370	−0.176218	−0.0881092	−	0.996111i	$-0.528082\pi$
$659$	−4.52370	−0.176218	−0.0881092	+	0.996111i	$0.528082\pi$
$660$	0	0
$661$	−31.6484	−1.23098	−0.615490	−	0.788145i	$-0.711042\pi$
$661$	−31.6484	−1.23098	−0.615490	+	0.788145i	$0.711042\pi$
$662$	−23.3191	−0.906324
$663$	0	0
$664$	10.5885	0.410912
$665$	0	0
$666$	6.72718	0.260673
$667$	8.93134	0.345823
$668$	−0.308193	−0.0119244
$669$	−9.01932	−0.348707
$670$	0	0
$671$	20.7435	0.800793
$672$	3.78869	0.146152
$673$	−11.1926	−0.431443	−0.215721	−	0.976455i	$-0.569210\pi$
$673$	−11.1926	−0.431443	−0.215721	+	0.976455i	$0.569210\pi$
$674$	−8.40781	−0.323857
$675$	0	0
$676$	17.8323	0.685858
$677$	6.53326	0.251094	0.125547	−	0.992088i	$-0.459931\pi$
$677$	6.53326	0.251094	0.125547	+	0.992088i	$0.459931\pi$
$678$	7.03737	0.270268
$679$	8.39588	0.322204
$680$	0	0
$681$	−3.87860	−0.148628
$682$	−13.2582	−0.507683
$683$	−23.6629	−0.905434	−0.452717	−	0.891654i	$-0.649545\pi$
$683$	−23.6629	−0.905434	−0.452717	+	0.891654i	$0.649545\pi$
$684$	24.7716	0.947165
$685$	0	0
$686$	11.7208	0.447501
$687$	0.799882	0.0305174
$688$	−4.73406	−0.180484
$689$	2.94943	0.112364
$690$	0	0
$691$	−8.11102	−0.308558	−0.154279	−	0.988027i	$-0.549305\pi$
$691$	−8.11102	−0.308558	−0.154279	+	0.988027i	$0.549305\pi$
$692$	−27.7158	−1.05360
$693$	−8.20521	−0.311690
$694$	0.896423	0.0340278
$695$	0	0
$696$	3.34237	0.126692
$697$	0	0
$698$	14.6142	0.553157
$699$	−12.6251	−0.477525
$700$	0	0
$701$	−35.4115	−1.33748	−0.668738	−	0.743498i	$-0.733165\pi$
$701$	−35.4115	−1.33748	−0.668738	+	0.743498i	$0.733165\pi$
$702$	−0.896382	−0.0338318
$703$	−21.0017	−0.792093
$704$	−8.16161	−0.307602
$705$	0	0
$706$	3.40268	0.128061
$707$	−0.352102	−0.0132421
$708$	3.94621	0.148308
$709$	14.9400	0.561082	0.280541	−	0.959842i	$-0.409486\pi$
$709$	14.9400	0.561082	0.280541	+	0.959842i	$0.409486\pi$
$710$	0	0
$711$	−2.19805	−0.0824333
$712$	24.2565	0.909050
$713$	25.5964	0.958593
$714$	0	0
$715$	0	0
$716$	33.7004	1.25944
$717$	3.50557	0.130918
$718$	−4.98150	−0.185908
$719$	23.1554	0.863552	0.431776	−	0.901981i	$-0.357887\pi$
$719$	23.1554	0.863552	0.431776	+	0.901981i	$0.357887\pi$
$720$	0	0
$721$	20.2483	0.754087
$722$	19.3600	0.720504
$723$	−14.9301	−0.555258
$724$	−16.4768	−0.612354
$725$	0	0
$726$	1.91119	0.0709311
$727$	11.3367	0.420456	0.210228	−	0.977652i	$-0.432579\pi$
$727$	11.3367	0.420456	0.210228	+	0.977652i	$0.432579\pi$
$728$	−1.16068	−0.0430175
$729$	−12.2590	−0.454036
$730$	0	0
$731$	0	0
$732$	−6.13510	−0.226760
$733$	−3.32332	−0.122750	−0.0613748	−	0.998115i	$-0.519548\pi$
$733$	−3.32332	−0.122750	−0.0613748	+	0.998115i	$0.519548\pi$
$734$	−12.7038	−0.468907
$735$	0	0
$736$	22.5992	0.833018
$737$	−20.2947	−0.747564
$738$	−15.4710	−0.569494
$739$	−12.5661	−0.462253	−0.231127	−	0.972924i	$-0.574241\pi$
$739$	−12.5661	−0.462253	−0.231127	+	0.972924i	$0.574241\pi$
$740$	0	0
$741$	1.32634	0.0487245
$742$	7.46049	0.273883
$743$	−52.5812	−1.92902	−0.964508	−	0.264053i	$-0.914941\pi$
$743$	−52.5812	−1.92902	−0.964508	+	0.264053i	$0.914941\pi$
$744$	9.57894	0.351181
$745$	0	0
$746$	14.5685	0.533390
$747$	10.7881	0.394717
$748$	0	0
$749$	4.52660	0.165398
$750$	0	0
$751$	3.93922	0.143744	0.0718720	−	0.997414i	$-0.477103\pi$
$751$	3.93922	0.143744	0.0718720	+	0.997414i	$0.477103\pi$
$752$	5.41705	0.197539
$753$	0.127749	0.00465545
$754$	−0.666738	−0.0242812
$755$	0	0
$756$	5.12020	0.186220
$757$	6.38475	0.232058	0.116029	−	0.993246i	$-0.462984\pi$
$757$	6.38475	0.232058	0.116029	+	0.993246i	$0.462984\pi$
$758$	7.09921	0.257855
$759$	5.37779	0.195201
$760$	0	0
$761$	19.3638	0.701938	0.350969	−	0.936387i	$-0.385852\pi$
$761$	19.3638	0.701938	0.350969	+	0.936387i	$0.385852\pi$
$762$	−1.91626	−0.0694188
$763$	−14.3061	−0.517917
$764$	−23.9709	−0.867238
$765$	0	0
$766$	2.15563	0.0778860
$767$	−1.92297	−0.0694346
$768$	7.40909	0.267353
$769$	−5.10469	−0.184080	−0.0920398	−	0.995755i	$-0.529339\pi$
$769$	−5.10469	−0.184080	−0.0920398	+	0.995755i	$0.529339\pi$
$770$	0	0
$771$	−1.94034	−0.0698795
$772$	2.50830	0.0902756
$773$	3.00249	0.107992	0.0539961	−	0.998541i	$-0.482804\pi$
$773$	3.00249	0.107992	0.0539961	+	0.998541i	$0.482804\pi$
$774$	14.4504	0.519408
$775$	0	0
$776$	18.7417	0.672788
$777$	−2.05745	−0.0738108
$778$	−21.4642	−0.769531
$779$	48.2990	1.73049
$780$	0	0
$781$	−30.3643	−1.08652
$782$	0	0
$783$	7.18497	0.256770
$784$	−3.87656	−0.138448
$785$	0	0
$786$	−3.98921	−0.142291
$787$	−2.63458	−0.0939127	−0.0469564	−	0.998897i	$-0.514952\pi$
$787$	−2.63458	−0.0939127	−0.0469564	+	0.998897i	$0.514952\pi$
$788$	−22.9804	−0.818642
$789$	16.3493	0.582051
$790$	0	0
$791$	19.5883	0.696481
$792$	−18.3161	−0.650834
$793$	2.98961	0.106164
$794$	−19.5733	−0.694632
$795$	0	0
$796$	−34.8773	−1.23619
$797$	−27.2441	−0.965036	−0.482518	−	0.875886i	$-0.660278\pi$
$797$	−27.2441	−0.965036	−0.482518	+	0.875886i	$0.660278\pi$
$798$	3.35495	0.118764
$799$	0	0
$800$	0	0
$801$	24.7138	0.873221
$802$	−24.8641	−0.877982
$803$	37.6302	1.32794
$804$	6.00236	0.211687
$805$	0	0
$806$	−1.91081	−0.0673055
$807$	0.206679	0.00727543
$808$	−0.785979	−0.0276506
$809$	−36.9078	−1.29761	−0.648805	−	0.760954i	$-0.724731\pi$
$809$	−36.9078	−1.29761	−0.648805	+	0.760954i	$0.724731\pi$
$810$	0	0
$811$	16.8302	0.590987	0.295494	−	0.955345i	$-0.404516\pi$
$811$	16.8302	0.590987	0.295494	+	0.955345i	$0.404516\pi$
$812$	3.80846	0.133651
$813$	−5.78461	−0.202875
$814$	6.35682	0.222807
$815$	0	0
$816$	0	0
$817$	−45.1128	−1.57830
$818$	0.565507	0.0197725
$819$	−1.18256	−0.0413220
$820$	0	0
$821$	−17.6162	−0.614810	−0.307405	−	0.951579i	$-0.599461\pi$
$821$	−17.6162	−0.614810	−0.307405	+	0.951579i	$0.599461\pi$
$822$	3.62000	0.126262
$823$	−29.5332	−1.02946	−0.514732	−	0.857351i	$-0.672108\pi$
$823$	−29.5332	−1.02946	−0.514732	+	0.857351i	$0.672108\pi$
$824$	45.1994	1.57459
$825$	0	0
$826$	−4.86411	−0.169244
$827$	29.8319	1.03736	0.518678	−	0.854970i	$-0.326424\pi$
$827$	29.8319	1.03736	0.518678	+	0.854970i	$0.326424\pi$
$828$	14.4755	0.503059
$829$	53.2461	1.84931	0.924657	−	0.380802i	$-0.124352\pi$
$829$	53.2461	1.84931	0.924657	+	0.380802i	$0.124352\pi$
$830$	0	0
$831$	−16.6177	−0.576461
$832$	−1.17628	−0.0407800
$833$	0	0
$834$	2.56486	0.0888137
$835$	0	0
$836$	23.4078	0.809576
$837$	20.5915	0.711745
$838$	−11.2319	−0.388001
$839$	−38.2607	−1.32091	−0.660453	−	0.750867i	$-0.729636\pi$
$839$	−38.2607	−1.32091	−0.660453	+	0.750867i	$0.729636\pi$
$840$	0	0
$841$	−23.6557	−0.815715
$842$	−2.30580	−0.0794632
$843$	14.4093	0.496282
$844$	11.6552	0.401190
$845$	0	0
$846$	−16.5351	−0.568489
$847$	5.31976	0.182789
$848$	−5.55876	−0.190889
$849$	10.1236	0.347439
$850$	0	0
$851$	−12.2725	−0.420697
$852$	8.98055	0.307668
$853$	6.72263	0.230179	0.115089	−	0.993355i	$-0.463285\pi$
$853$	6.72263	0.230179	0.115089	+	0.993355i	$0.463285\pi$
$854$	7.56214	0.258771
$855$	0	0
$856$	10.1045	0.345365
$857$	−32.1865	−1.09947	−0.549735	−	0.835339i	$-0.685271\pi$
$857$	−32.1865	−1.09947	−0.549735	+	0.835339i	$0.685271\pi$
$858$	−0.401460	−0.0137056
$859$	46.6741	1.59250	0.796250	−	0.604968i	$-0.206814\pi$
$859$	46.6741	1.59250	0.796250	+	0.604968i	$0.206814\pi$
$860$	0	0
$861$	4.73167	0.161255
$862$	−25.2086	−0.858609
$863$	9.97544	0.339568	0.169784	−	0.985481i	$-0.445693\pi$
$863$	9.97544	0.339568	0.169784	+	0.985481i	$0.445693\pi$
$864$	18.1803	0.618507
$865$	0	0
$866$	1.37950	0.0468772
$867$	0	0
$868$	10.9147	0.370469
$869$	−2.07704	−0.0704587
$870$	0	0
$871$	−2.92493	−0.0991074
$872$	−31.9349	−1.08145
$873$	19.0951	0.646271
$874$	20.0120	0.676916
$875$	0	0
$876$	−11.1295	−0.376032
$877$	1.55373	0.0524659	0.0262329	−	0.999656i	$-0.491649\pi$
$877$	1.55373	0.0524659	0.0262329	+	0.999656i	$0.491649\pi$
$878$	0.432227	0.0145870
$879$	−1.96168	−0.0661660
$880$	0	0
$881$	27.2232	0.917174	0.458587	−	0.888649i	$-0.348356\pi$
$881$	27.2232	0.917174	0.458587	+	0.888649i	$0.348356\pi$
$882$	11.8329	0.398434
$883$	−41.7225	−1.40407	−0.702037	−	0.712140i	$-0.747726\pi$
$883$	−41.7225	−1.40407	−0.702037	+	0.712140i	$0.747726\pi$
$884$	0	0
$885$	0	0
$886$	−1.71673	−0.0576746
$887$	7.64625	0.256736	0.128368	−	0.991727i	$-0.459026\pi$
$887$	7.64625	0.256736	0.128368	+	0.991727i	$0.459026\pi$
$888$	−4.59275	−0.154123
$889$	−5.33387	−0.178892
$890$	0	0
$891$	−16.3857	−0.548940
$892$	−22.9409	−0.768120
$893$	51.6212	1.72744
$894$	3.89326	0.130210
$895$	0	0
$896$	10.9287	0.365102
$897$	0.775063	0.0258786
$898$	−1.69213	−0.0564672
$899$	15.3161	0.510822
$900$	0	0
$901$	0	0
$902$	−14.6192	−0.486767
$903$	−4.41953	−0.147073
$904$	43.7261	1.45431
$905$	0	0
$906$	5.59955	0.186033
$907$	−43.5561	−1.44626	−0.723129	−	0.690713i	$-0.757297\pi$
$907$	−43.5561	−1.44626	−0.723129	+	0.690713i	$0.757297\pi$
$908$	−9.86534	−0.327393
$909$	−0.800799	−0.0265608
$910$	0	0
$911$	33.1208	1.09734	0.548671	−	0.836039i	$-0.315134\pi$
$911$	33.1208	1.09734	0.548671	+	0.836039i	$0.315134\pi$
$912$	−2.49975	−0.0827751
$913$	10.1942	0.337378
$914$	−7.41867	−0.245388
$915$	0	0
$916$	2.03453	0.0672226
$917$	−11.1039	−0.366682
$918$	0	0
$919$	22.9512	0.757089	0.378545	−	0.925583i	$-0.376425\pi$
$919$	22.9512	0.757089	0.378545	+	0.925583i	$0.376425\pi$
$920$	0	0
$921$	−18.2092	−0.600014
$922$	13.0563	0.429987
$923$	−4.37619	−0.144044
$924$	2.29317	0.0754399
$925$	0	0
$926$	11.2616	0.370078
$927$	46.0516	1.51253
$928$	13.5227	0.443905
$929$	−19.2701	−0.632231	−0.316115	−	0.948721i	$-0.602379\pi$
$929$	−19.2701	−0.632231	−0.316115	+	0.948721i	$0.602379\pi$
$930$	0	0
$931$	−36.9412	−1.21070
$932$	−32.1123	−1.05187
$933$	7.51853	0.246146
$934$	−10.1169	−0.331036
$935$	0	0
$936$	−2.63977	−0.0862836
$937$	−23.6659	−0.773132	−0.386566	−	0.922262i	$-0.626339\pi$
$937$	−23.6659	−0.773132	−0.386566	+	0.922262i	$0.626339\pi$
$938$	−7.39853	−0.241570
$939$	−16.6601	−0.543681
$940$	0	0
$941$	3.14215	0.102431	0.0512156	−	0.998688i	$-0.483690\pi$
$941$	3.14215	0.102431	0.0512156	+	0.998688i	$0.483690\pi$
$942$	8.56068	0.278922
$943$	28.2240	0.919100
$944$	3.62421	0.117958
$945$	0	0
$946$	13.6548	0.443956
$947$	38.2986	1.24454	0.622268	−	0.782804i	$-0.286211\pi$
$947$	38.2986	1.24454	0.622268	+	0.782804i	$0.286211\pi$
$948$	0.614305	0.0199517
$949$	5.42338	0.176050
$950$	0	0
$951$	−1.75319	−0.0568511
$952$	0	0
$953$	34.0185	1.10197	0.550984	−	0.834516i	$-0.314253\pi$
$953$	34.0185	1.10197	0.550984	+	0.834516i	$0.314253\pi$
$954$	16.9677	0.549349
$955$	0	0
$956$	8.91654	0.288381
$957$	3.21791	0.104020
$958$	4.71020	0.152180
$959$	10.0762	0.325377
$960$	0	0
$961$	12.8947	0.415958
$962$	0.916164	0.0295383
$963$	10.2950	0.331753
$964$	−37.9753	−1.22310
$965$	0	0
$966$	1.96050	0.0630781
$967$	−33.0762	−1.06366	−0.531829	−	0.846852i	$-0.678495\pi$
$967$	−33.0762	−1.06366	−0.531829	+	0.846852i	$0.678495\pi$
$968$	11.8750	0.381678
$969$	0	0
$970$	0	0
$971$	22.1601	0.711152	0.355576	−	0.934647i	$-0.384285\pi$
$971$	22.1601	0.711152	0.355576	+	0.934647i	$0.384285\pi$
$972$	17.7709	0.570000
$973$	7.13921	0.228873
$974$	−25.9338	−0.830974
$975$	0	0
$976$	−5.63450	−0.180356
$977$	15.7856	0.505025	0.252513	−	0.967594i	$-0.418743\pi$
$977$	15.7856	0.505025	0.252513	+	0.967594i	$0.418743\pi$
$978$	6.09329	0.194842
$979$	23.3532	0.746373
$980$	0	0
$981$	−32.5370	−1.03883
$982$	14.7062	0.469293
$983$	38.7627	1.23634	0.618169	−	0.786045i	$-0.287875\pi$
$983$	38.7627	1.23634	0.618169	+	0.786045i	$0.287875\pi$
$984$	10.5623	0.336713
$985$	0	0
$986$	0	0
$987$	5.05713	0.160970
$988$	3.37360	0.107329
$989$	−26.3621	−0.838266
$990$	0	0
$991$	31.9997	1.01650	0.508252	−	0.861209i	$-0.330292\pi$
$991$	31.9997	1.01650	0.508252	+	0.861209i	$0.330292\pi$
$992$	38.7549	1.23047
$993$	16.2205	0.514743
$994$	−11.0694	−0.351102
$995$	0	0
$996$	−3.01504	−0.0955351
$997$	13.9386	0.441440	0.220720	−	0.975337i	$-0.429159\pi$
$997$	13.9386	0.441440	0.220720	+	0.975337i	$0.429159\pi$
$998$	−5.59746	−0.177184
$999$	−9.87286	−0.312363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.z.1.5		6
5.4	even	2		1445.2.a.o.1.2		6
17.2	even	8		425.2.e.f.276.5		12
17.9	even	8		425.2.e.f.251.2		12
17.16	even	2		7225.2.a.bb.1.5		6
85.2	odd	8		425.2.j.c.174.2		12
85.4	even	4		1445.2.d.g.866.9		12
85.9	even	8		85.2.e.a.81.5	yes	12
85.19	even	8		85.2.e.a.21.2	✓	12
85.43	odd	8		425.2.j.c.149.2		12
85.53	odd	8		425.2.j.b.174.5		12
85.64	even	4		1445.2.d.g.866.10		12
85.77	odd	8		425.2.j.b.149.5		12
85.84	even	2		1445.2.a.n.1.2		6
255.104	odd	8		765.2.k.b.361.5		12
255.179	odd	8		765.2.k.b.676.2		12
340.19	odd	8		1360.2.bt.d.1041.2		12
340.179	odd	8		1360.2.bt.d.81.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.2	✓	12	85.19	even	8
85.2.e.a.81.5	yes	12	85.9	even	8
425.2.e.f.251.2		12	17.9	even	8
425.2.e.f.276.5		12	17.2	even	8
425.2.j.b.149.5		12	85.77	odd	8
425.2.j.b.174.5		12	85.53	odd	8
425.2.j.c.149.2		12	85.43	odd	8
425.2.j.c.174.2		12	85.2	odd	8
765.2.k.b.361.5		12	255.104	odd	8
765.2.k.b.676.2		12	255.179	odd	8
1360.2.bt.d.81.2		12	340.179	odd	8
1360.2.bt.d.1041.2		12	340.19	odd	8
1445.2.a.n.1.2		6	85.84	even	2
1445.2.a.o.1.2		6	5.4	even	2
1445.2.d.g.866.9		12	85.4	even	4
1445.2.d.g.866.10		12	85.64	even	4
7225.2.a.z.1.5		6	1.1	even	1	trivial
7225.2.a.bb.1.5		6	17.16	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)

\(f(q)\)	\(=\)	\(q+0.783476 q^{2} -0.544977 q^{3} -1.38617 q^{4} -0.426976 q^{6} -1.18848 q^{7} -2.65298 q^{8} -2.70300 q^{9} -2.55419 q^{11} +0.755428 q^{12} -0.368117 q^{13} -0.931143 q^{14} +0.693788 q^{16} -2.11773 q^{18} +6.61138 q^{19} +0.647692 q^{21} -2.00114 q^{22} +3.86343 q^{23} +1.44581 q^{24} -0.288411 q^{26} +3.10800 q^{27} +1.64743 q^{28} +2.31176 q^{29} +6.62531 q^{31} +5.84952 q^{32} +1.39197 q^{33} +3.74681 q^{36} -3.17659 q^{37} +5.17986 q^{38} +0.200615 q^{39} +7.30543 q^{41} +0.507451 q^{42} -6.82350 q^{43} +3.54053 q^{44} +3.02690 q^{46} +7.80793 q^{47} -0.378098 q^{48} -5.58752 q^{49} +0.510272 q^{52} -8.01219 q^{53} +2.43504 q^{54} +3.15300 q^{56} -3.60305 q^{57} +1.81121 q^{58} +5.22381 q^{59} -8.12136 q^{61} +5.19077 q^{62} +3.21245 q^{63} +3.19538 q^{64} +1.09058 q^{66} +7.94564 q^{67} -2.10548 q^{69} +11.8880 q^{71} +7.17100 q^{72} -14.7327 q^{73} -2.48878 q^{74} -9.16447 q^{76} +3.03559 q^{77} +0.157177 q^{78} +0.813189 q^{79} +6.41521 q^{81} +5.72362 q^{82} -3.99116 q^{83} -0.897809 q^{84} -5.34604 q^{86} -1.25986 q^{87} +6.77621 q^{88} -9.14311 q^{89} +0.437499 q^{91} -5.35536 q^{92} -3.61064 q^{93} +6.11732 q^{94} -3.18785 q^{96} -7.06440 q^{97} -4.37769 q^{98} +6.90397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 6 q^{4} + 4 q^{6} - 8 q^{7} - 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{14} + 2 q^{16} - 14 q^{18} - 12 q^{19} + 8 q^{21} - 16 q^{22} + 24 q^{24} - 12 q^{26} + 8 q^{27} + 8 q^{28} + 8 q^{29}+ \cdots + 20 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 + 4 * q^6 - 8 * q^7 - 6 * q^8 + 2 * q^9 - 8 * q^12 + 8 * q^14 + 2 * q^16 - 14 * q^18 - 12 * q^19 + 8 * q^21 - 16 * q^22 + 24 * q^24 - 12 * q^26 + 8 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^31 + 6 * q^32 + 8 * q^33 - 10 * q^36 - 16 * q^37 + 12 * q^38 + 28 * q^39 + 12 * q^41 + 8 * q^42 - 8 * q^43 - 4 * q^44 + 20 * q^46 - 24 * q^47 - 8 * q^48 - 10 * q^49 + 28 * q^52 - 12 * q^54 + 20 * q^56 + 16 * q^57 - 48 * q^58 - 16 * q^59 - 4 * q^61 + 40 * q^62 - 20 * q^63 - 14 * q^64 - 16 * q^66 + 4 * q^67 + 32 * q^71 + 10 * q^72 + 8 * q^73 - 8 * q^74 - 36 * q^76 - 24 * q^77 - 4 * q^78 + 36 * q^79 - 14 * q^81 + 28 * q^82 - 20 * q^83 - 48 * q^86 - 24 * q^87 - 12 * q^88 - 12 * q^89 + 12 * q^91 - 28 * q^92 - 36 * q^93 + 20 * q^94 - 44 * q^96 - 16 * q^97 + 22 * q^98 + 20 * q^99

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