LMFDB - Embedded newform 6025.2.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61751 q^{2} -2.91594 q^{3} +4.85138 q^{4} +7.63252 q^{6} +2.00988 q^{7} -7.46353 q^{8} +5.50273 q^{9} +O(q^{10})$	\(q-2.61751 q^{2} -2.91594 q^{3} +4.85138 q^{4} +7.63252 q^{6} +2.00988 q^{7} -7.46353 q^{8} +5.50273 q^{9} -1.47720 q^{11} -14.1463 q^{12} -0.967484 q^{13} -5.26090 q^{14} +9.83313 q^{16} -6.02295 q^{17} -14.4035 q^{18} +0.541650 q^{19} -5.86070 q^{21} +3.86660 q^{22} +1.49200 q^{23} +21.7632 q^{24} +2.53240 q^{26} -7.29781 q^{27} +9.75070 q^{28} -6.69224 q^{29} +6.96085 q^{31} -10.8113 q^{32} +4.30744 q^{33} +15.7652 q^{34} +26.6958 q^{36} +7.43384 q^{37} -1.41778 q^{38} +2.82113 q^{39} +6.91426 q^{41} +15.3405 q^{42} +8.06903 q^{43} -7.16647 q^{44} -3.90534 q^{46} -4.13499 q^{47} -28.6728 q^{48} -2.96037 q^{49} +17.5626 q^{51} -4.69363 q^{52} -5.72513 q^{53} +19.1021 q^{54} -15.0008 q^{56} -1.57942 q^{57} +17.5170 q^{58} -4.68972 q^{59} -3.80442 q^{61} -18.2201 q^{62} +11.0598 q^{63} +8.63246 q^{64} -11.2748 q^{66} -2.54318 q^{67} -29.2196 q^{68} -4.35060 q^{69} +2.73886 q^{71} -41.0697 q^{72} -4.42334 q^{73} -19.4582 q^{74} +2.62775 q^{76} -2.96900 q^{77} -7.38435 q^{78} -4.05640 q^{79} +4.77182 q^{81} -18.0982 q^{82} +1.66433 q^{83} -28.4325 q^{84} -21.1208 q^{86} +19.5142 q^{87} +11.0251 q^{88} -2.78206 q^{89} -1.94453 q^{91} +7.23828 q^{92} -20.2974 q^{93} +10.8234 q^{94} +31.5251 q^{96} +14.3639 q^{97} +7.74882 q^{98} -8.12864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * 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 $

$2$	−2.61751	−1.85086	−0.925431	−	0.378916i	$-0.876297\pi$
$2$	−2.61751	−1.85086	−0.925431	+	0.378916i	$0.876297\pi$
$3$	−2.91594	−1.68352	−0.841760	−	0.539851i	$-0.818480\pi$
$3$	−2.91594	−1.68352	−0.841760	+	0.539851i	$0.818480\pi$
$4$	4.85138	2.42569
$5$	0	0
$5$	0	0
$6$	7.63252	3.11596
$7$	2.00988	0.759664	0.379832	−	0.925055i	$-0.375982\pi$
$7$	2.00988	0.759664	0.379832	+	0.925055i	$0.375982\pi$
$8$	−7.46353	−2.63876
$9$	5.50273	1.83424
$10$	0	0
$11$	−1.47720	−0.445393	−0.222697	−	0.974888i	$-0.571486\pi$
$11$	−1.47720	−0.445393	−0.222697	+	0.974888i	$0.571486\pi$
$12$	−14.1463	−4.08370
$13$	−0.967484	−0.268332	−0.134166	−	0.990959i	$-0.542836\pi$
$13$	−0.967484	−0.268332	−0.134166	+	0.990959i	$0.542836\pi$
$14$	−5.26090	−1.40603
$15$	0	0
$16$	9.83313	2.45828
$17$	−6.02295	−1.46078	−0.730391	−	0.683030i	$-0.760662\pi$
$17$	−6.02295	−1.46078	−0.730391	+	0.683030i	$0.760662\pi$
$18$	−14.4035	−3.39493
$19$	0.541650	0.124263	0.0621315	−	0.998068i	$-0.480210\pi$
$19$	0.541650	0.124263	0.0621315	+	0.998068i	$0.480210\pi$
$20$	0	0
$21$	−5.86070	−1.27891
$22$	3.86660	0.824362
$23$	1.49200	0.311104	0.155552	−	0.987828i	$-0.450284\pi$
$23$	1.49200	0.311104	0.155552	+	0.987828i	$0.450284\pi$
$24$	21.7632	4.44240
$25$	0	0
$26$	2.53240	0.496645
$27$	−7.29781	−1.40446
$28$	9.75070	1.84271
$29$	−6.69224	−1.24272	−0.621359	−	0.783526i	$-0.713419\pi$
$29$	−6.69224	−1.24272	−0.621359	+	0.783526i	$0.713419\pi$
$30$	0	0
$31$	6.96085	1.25021	0.625103	−	0.780542i	$-0.285057\pi$
$31$	6.96085	1.25021	0.625103	+	0.780542i	$0.285057\pi$
$32$	−10.8113	−1.91119
$33$	4.30744	0.749829
$34$	15.7652	2.70370
$35$	0	0
$36$	26.6958	4.44930
$37$	7.43384	1.22212	0.611058	−	0.791586i	$-0.290744\pi$
$37$	7.43384	1.22212	0.611058	+	0.791586i	$0.290744\pi$
$38$	−1.41778	−0.229994
$39$	2.82113	0.451742
$40$	0	0
$41$	6.91426	1.07983	0.539913	−	0.841721i	$-0.318457\pi$
$41$	6.91426	1.07983	0.539913	+	0.841721i	$0.318457\pi$
$42$	15.3405	2.36709
$43$	8.06903	1.23052	0.615258	−	0.788326i	$-0.289052\pi$
$43$	8.06903	1.23052	0.615258	+	0.788326i	$0.289052\pi$
$44$	−7.16647	−1.08039
$45$	0	0
$46$	−3.90534	−0.575811
$47$	−4.13499	−0.603150	−0.301575	−	0.953442i	$-0.597512\pi$
$47$	−4.13499	−0.603150	−0.301575	+	0.953442i	$0.597512\pi$
$48$	−28.6728	−4.13857
$49$	−2.96037	−0.422910
$50$	0	0
$51$	17.5626	2.45926
$52$	−4.69363	−0.650890
$53$	−5.72513	−0.786407	−0.393203	−	0.919452i	$-0.628633\pi$
$53$	−5.72513	−0.786407	−0.393203	+	0.919452i	$0.628633\pi$
$54$	19.1021	2.59947
$55$	0	0
$56$	−15.0008	−2.00457
$57$	−1.57942	−0.209199
$58$	17.5170	2.30010
$59$	−4.68972	−0.610550	−0.305275	−	0.952264i	$-0.598748\pi$
$59$	−4.68972	−0.610550	−0.305275	+	0.952264i	$0.598748\pi$
$60$	0	0
$61$	−3.80442	−0.487106	−0.243553	−	0.969888i	$-0.578313\pi$
$61$	−3.80442	−0.487106	−0.243553	+	0.969888i	$0.578313\pi$
$62$	−18.2201	−2.31396
$63$	11.0598	1.39341
$64$	8.63246	1.07906
$65$	0	0
$66$	−11.2748	−1.38783
$67$	−2.54318	−0.310698	−0.155349	−	0.987860i	$-0.549650\pi$
$67$	−2.54318	−0.310698	−0.155349	+	0.987860i	$0.549650\pi$
$68$	−29.2196	−3.54340
$69$	−4.35060	−0.523751
$70$	0	0
$71$	2.73886	0.325043	0.162522	−	0.986705i	$-0.448037\pi$
$71$	2.73886	0.325043	0.162522	+	0.986705i	$0.448037\pi$
$72$	−41.0697	−4.84012
$73$	−4.42334	−0.517712	−0.258856	−	0.965916i	$-0.583346\pi$
$73$	−4.42334	−0.517712	−0.258856	+	0.965916i	$0.583346\pi$
$74$	−19.4582	−2.26197
$75$	0	0
$76$	2.62775	0.301424
$77$	−2.96900	−0.338349
$78$	−7.38435	−0.836113
$79$	−4.05640	−0.456381	−0.228190	−	0.973617i	$-0.573281\pi$
$79$	−4.05640	−0.456381	−0.228190	+	0.973617i	$0.573281\pi$
$80$	0	0
$81$	4.77182	0.530202
$82$	−18.0982	−1.99861
$83$	1.66433	0.182684	0.0913419	−	0.995820i	$-0.470884\pi$
$83$	1.66433	0.182684	0.0913419	+	0.995820i	$0.470884\pi$
$84$	−28.4325	−3.10224
$85$	0	0
$86$	−21.1208	−2.27751
$87$	19.5142	2.09214
$88$	11.0251	1.17528
$89$	−2.78206	−0.294898	−0.147449	−	0.989070i	$-0.547106\pi$
$89$	−2.78206	−0.294898	−0.147449	+	0.989070i	$0.547106\pi$
$90$	0	0
$91$	−1.94453	−0.203842
$92$	7.23828	0.754643
$93$	−20.2974	−2.10475
$94$	10.8234	1.11635
$95$	0	0
$96$	31.5251	3.21752
$97$	14.3639	1.45843	0.729214	−	0.684285i	$-0.239886\pi$
$97$	14.3639	1.45843	0.729214	+	0.684285i	$0.239886\pi$
$98$	7.74882	0.782749
$99$	−8.12864	−0.816959
$100$	0	0
$101$	6.14294	0.611245	0.305623	−	0.952153i	$-0.401135\pi$
$101$	6.14294	0.611245	0.305623	+	0.952153i	$0.401135\pi$
$102$	−45.9703	−4.55174
$103$	−18.4803	−1.82092	−0.910461	−	0.413595i	$-0.864273\pi$
$103$	−18.4803	−1.82092	−0.910461	+	0.413595i	$0.864273\pi$
$104$	7.22085	0.708062
$105$	0	0
$106$	14.9856	1.45553
$107$	17.5663	1.69820	0.849100	−	0.528231i	$-0.177145\pi$
$107$	17.5663	1.69820	0.849100	+	0.528231i	$0.177145\pi$
$108$	−35.4044	−3.40679
$109$	6.62056	0.634134	0.317067	−	0.948403i	$-0.397302\pi$
$109$	6.62056	0.634134	0.317067	+	0.948403i	$0.397302\pi$
$110$	0	0
$111$	−21.6767	−2.05746
$112$	19.7634	1.86747
$113$	9.32887	0.877587	0.438793	−	0.898588i	$-0.355406\pi$
$113$	9.32887	0.877587	0.438793	+	0.898588i	$0.355406\pi$
$114$	4.13416	0.387199
$115$	0	0
$116$	−32.4666	−3.01445
$117$	−5.32380	−0.492186
$118$	12.2754	1.13004
$119$	−12.1054	−1.10970
$120$	0	0
$121$	−8.81787	−0.801625
$122$	9.95813	0.901567
$123$	−20.1616	−1.81791
$124$	33.7697	3.03261
$125$	0	0
$126$	−28.9493	−2.57901
$127$	−16.3798	−1.45347	−0.726735	−	0.686918i	$-0.758963\pi$
$127$	−16.3798	−1.45347	−0.726735	+	0.686918i	$0.758963\pi$
$128$	−0.973005	−0.0860023
$129$	−23.5288	−2.07160
$130$	0	0
$131$	−15.4491	−1.34980	−0.674899	−	0.737910i	$-0.735813\pi$
$131$	−15.4491	−1.34980	−0.674899	+	0.737910i	$0.735813\pi$
$132$	20.8970	1.81885
$133$	1.08865	0.0943982
$134$	6.65680	0.575060
$135$	0	0
$136$	44.9525	3.85464
$137$	13.4896	1.15250	0.576249	−	0.817274i	$-0.304516\pi$
$137$	13.4896	1.15250	0.576249	+	0.817274i	$0.304516\pi$
$138$	11.3878	0.969391
$139$	21.9276	1.85988	0.929939	−	0.367714i	$-0.119860\pi$
$139$	21.9276	1.85988	0.929939	+	0.367714i	$0.119860\pi$
$140$	0	0
$141$	12.0574	1.01542
$142$	−7.16901	−0.601610
$143$	1.42917	0.119513
$144$	54.1090	4.50908
$145$	0	0
$146$	11.5781	0.958214
$147$	8.63228	0.711978
$148$	36.0644	2.96447
$149$	4.70327	0.385307	0.192653	−	0.981267i	$-0.438291\pi$
$149$	4.70327	0.385307	0.192653	+	0.981267i	$0.438291\pi$
$150$	0	0
$151$	−18.9686	−1.54364	−0.771822	−	0.635839i	$-0.780654\pi$
$151$	−18.9686	−1.54364	−0.771822	+	0.635839i	$0.780654\pi$
$152$	−4.04262	−0.327900
$153$	−33.1427	−2.67943
$154$	7.77141	0.626238
$155$	0	0
$156$	13.6864	1.09579
$157$	5.58592	0.445805	0.222902	−	0.974841i	$-0.428447\pi$
$157$	5.58592	0.445805	0.222902	+	0.974841i	$0.428447\pi$
$158$	10.6177	0.844698
$159$	16.6941	1.32393
$160$	0	0
$161$	2.99875	0.236335
$162$	−12.4903	−0.981330
$163$	3.66298	0.286907	0.143453	−	0.989657i	$-0.454179\pi$
$163$	3.66298	0.286907	0.143453	+	0.989657i	$0.454179\pi$
$164$	33.5437	2.61932
$165$	0	0
$166$	−4.35640	−0.338123
$167$	1.70255	0.131748	0.0658738	−	0.997828i	$-0.479017\pi$
$167$	1.70255	0.131748	0.0658738	+	0.997828i	$0.479017\pi$
$168$	43.7415	3.37473
$169$	−12.0640	−0.927998
$170$	0	0
$171$	2.98055	0.227929
$172$	39.1459	2.98485
$173$	−10.3525	−0.787086	−0.393543	−	0.919306i	$-0.628751\pi$
$173$	−10.3525	−0.787086	−0.393543	+	0.919306i	$0.628751\pi$
$174$	−51.0787	−3.87227
$175$	0	0
$176$	−14.5255	−1.09490
$177$	13.6750	1.02787
$178$	7.28208	0.545815
$179$	1.43819	0.107495	0.0537477	−	0.998555i	$-0.482883\pi$
$179$	1.43819	0.107495	0.0537477	+	0.998555i	$0.482883\pi$
$180$	0	0
$181$	6.65171	0.494418	0.247209	−	0.968962i	$-0.420487\pi$
$181$	6.65171	0.494418	0.247209	+	0.968962i	$0.420487\pi$
$182$	5.08983	0.377284
$183$	11.0935	0.820054
$184$	−11.1356	−0.820929
$185$	0	0
$186$	53.1288	3.89560
$187$	8.89712	0.650622
$188$	−20.0604	−1.46306
$189$	−14.6677	−1.06692
$190$	0	0
$191$	−21.4229	−1.55011	−0.775054	−	0.631896i	$-0.782277\pi$
$191$	−21.4229	−1.55011	−0.775054	+	0.631896i	$0.782277\pi$
$192$	−25.1718	−1.81662
$193$	−9.46494	−0.681302	−0.340651	−	0.940190i	$-0.610647\pi$
$193$	−9.46494	−0.681302	−0.340651	+	0.940190i	$0.610647\pi$
$194$	−37.5976	−2.69935
$195$	0	0
$196$	−14.3619	−1.02585
$197$	−10.8006	−0.769513	−0.384757	−	0.923018i	$-0.625715\pi$
$197$	−10.8006	−0.769513	−0.384757	+	0.923018i	$0.625715\pi$
$198$	21.2768	1.51208
$199$	−11.5501	−0.818768	−0.409384	−	0.912362i	$-0.634256\pi$
$199$	−11.5501	−0.818768	−0.409384	+	0.912362i	$0.634256\pi$
$200$	0	0
$201$	7.41576	0.523067
$202$	−16.0792	−1.13133
$203$	−13.4506	−0.944048
$204$	85.2028	5.96539
$205$	0	0
$206$	48.3725	3.37027
$207$	8.21009	0.570641
$208$	−9.51340	−0.659635
$209$	−0.800127	−0.0553460
$210$	0	0
$211$	17.7769	1.22381	0.611907	−	0.790930i	$-0.290403\pi$
$211$	17.7769	1.22381	0.611907	+	0.790930i	$0.290403\pi$
$212$	−27.7748	−1.90758
$213$	−7.98637	−0.547217
$214$	−45.9801	−3.14314
$215$	0	0
$216$	54.4674	3.70604
$217$	13.9905	0.949736
$218$	−17.3294	−1.17370
$219$	12.8982	0.871579
$220$	0	0
$221$	5.82711	0.391974
$222$	56.7390	3.80807
$223$	−6.39477	−0.428226	−0.214113	−	0.976809i	$-0.568686\pi$
$223$	−6.39477	−0.428226	−0.214113	+	0.976809i	$0.568686\pi$
$224$	−21.7294	−1.45186
$225$	0	0
$226$	−24.4185	−1.62429
$227$	28.9636	1.92238	0.961190	−	0.275888i	$-0.0889720\pi$
$227$	28.9636	1.92238	0.961190	+	0.275888i	$0.0889720\pi$
$228$	−7.66237	−0.507453
$229$	14.0844	0.930727	0.465363	−	0.885120i	$-0.345924\pi$
$229$	14.0844	0.930727	0.465363	+	0.885120i	$0.345924\pi$
$230$	0	0
$231$	8.65745	0.569618
$232$	49.9477	3.27923
$233$	−2.80871	−0.184005	−0.0920024	−	0.995759i	$-0.529327\pi$
$233$	−2.80871	−0.184005	−0.0920024	+	0.995759i	$0.529327\pi$
$234$	13.9351	0.910968
$235$	0	0
$236$	−22.7516	−1.48101
$237$	11.8282	0.768326
$238$	31.6861	2.05391
$239$	−14.0335	−0.907754	−0.453877	−	0.891064i	$-0.649960\pi$
$239$	−14.0335	−0.907754	−0.453877	+	0.891064i	$0.649960\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	23.0809	1.48370
$243$	7.97908	0.511858
$244$	−18.4567	−1.18157
$245$	0	0
$246$	52.7732	3.36470
$247$	−0.524038	−0.0333437
$248$	−51.9525	−3.29899
$249$	−4.85309	−0.307552
$250$	0	0
$251$	19.2508	1.21510	0.607550	−	0.794282i	$-0.292152\pi$
$251$	19.2508	1.21510	0.607550	+	0.794282i	$0.292152\pi$
$252$	53.6554	3.37998
$253$	−2.20399	−0.138564
$254$	42.8743	2.69017
$255$	0	0
$256$	−14.7181	−0.919880
$257$	3.03581	0.189369	0.0946843	−	0.995507i	$-0.469816\pi$
$257$	3.03581	0.189369	0.0946843	+	0.995507i	$0.469816\pi$
$258$	61.5870	3.83424
$259$	14.9411	0.928398
$260$	0	0
$261$	−36.8256	−2.27945
$262$	40.4383	2.49829
$263$	0.703973	0.0434089	0.0217044	−	0.999764i	$-0.493091\pi$
$263$	0.703973	0.0434089	0.0217044	+	0.999764i	$0.493091\pi$
$264$	−32.1487	−1.97862
$265$	0	0
$266$	−2.84957	−0.174718
$267$	8.11232	0.496466
$268$	−12.3379	−0.753658
$269$	30.7423	1.87439	0.937195	−	0.348807i	$-0.113413\pi$
$269$	30.7423	1.87439	0.937195	+	0.348807i	$0.113413\pi$
$270$	0	0
$271$	20.2233	1.22848	0.614238	−	0.789121i	$-0.289463\pi$
$271$	20.2233	1.22848	0.614238	+	0.789121i	$0.289463\pi$
$272$	−59.2245	−3.59101
$273$	5.67014	0.343172
$274$	−35.3093	−2.13312
$275$	0	0
$276$	−21.1064	−1.27046
$277$	2.84379	0.170867	0.0854335	−	0.996344i	$-0.472772\pi$
$277$	2.84379	0.170867	0.0854335	+	0.996344i	$0.472772\pi$
$278$	−57.3959	−3.44238
$279$	38.3036	2.29318
$280$	0	0
$281$	9.30607	0.555154	0.277577	−	0.960703i	$-0.410469\pi$
$281$	9.30607	0.555154	0.277577	+	0.960703i	$0.410469\pi$
$282$	−31.5604	−1.87940
$283$	−19.9804	−1.18771	−0.593856	−	0.804571i	$-0.702395\pi$
$283$	−19.9804	−1.18771	−0.593856	+	0.804571i	$0.702395\pi$
$284$	13.2873	0.788454
$285$	0	0
$286$	−3.74087	−0.221203
$287$	13.8968	0.820305
$288$	−59.4916	−3.50558
$289$	19.2760	1.13388
$290$	0	0
$291$	−41.8842	−2.45530
$292$	−21.4593	−1.25581
$293$	10.9840	0.641691	0.320845	−	0.947132i	$-0.396033\pi$
$293$	10.9840	0.641691	0.320845	+	0.947132i	$0.396033\pi$
$294$	−22.5951	−1.31777
$295$	0	0
$296$	−55.4827	−3.22487
$297$	10.7803	0.625539
$298$	−12.3109	−0.713150
$299$	−1.44349	−0.0834793
$300$	0	0
$301$	16.2178	0.934778
$302$	49.6506	2.85707
$303$	−17.9125	−1.02904
$304$	5.32612	0.305474
$305$	0	0
$306$	86.7514	4.95925
$307$	33.8904	1.93423	0.967114	−	0.254343i	$-0.0818593\pi$
$307$	33.8904	1.93423	0.967114	+	0.254343i	$0.0818593\pi$
$308$	−14.4038	−0.820731
$309$	53.8876	3.06556
$310$	0	0
$311$	7.38229	0.418611	0.209306	−	0.977850i	$-0.432880\pi$
$311$	7.38229	0.418611	0.209306	+	0.977850i	$0.432880\pi$
$312$	−21.0556	−1.19204
$313$	17.8476	1.00880	0.504402	−	0.863469i	$-0.331713\pi$
$313$	17.8476	1.00880	0.504402	+	0.863469i	$0.331713\pi$
$314$	−14.6212	−0.825123
$315$	0	0
$316$	−19.6791	−1.10704
$317$	−12.6525	−0.710634	−0.355317	−	0.934746i	$-0.615627\pi$
$317$	−12.6525	−0.710634	−0.355317	+	0.934746i	$0.615627\pi$
$318$	−43.6972	−2.45041
$319$	9.88580	0.553498
$320$	0	0
$321$	−51.2224	−2.85896
$322$	−7.84928	−0.437423
$323$	−3.26233	−0.181521
$324$	23.1499	1.28611
$325$	0	0
$326$	−9.58790	−0.531024
$327$	−19.3052	−1.06758
$328$	−51.6047	−2.84940
$329$	−8.31085	−0.458192
$330$	0	0
$331$	−18.7774	−1.03210	−0.516049	−	0.856559i	$-0.672598\pi$
$331$	−18.7774	−1.03210	−0.516049	+	0.856559i	$0.672598\pi$
$332$	8.07429	0.443134
$333$	40.9064	2.24166
$334$	−4.45646	−0.243847
$335$	0	0
$336$	−57.6290	−3.14392
$337$	11.1758	0.608787	0.304394	−	0.952546i	$-0.401546\pi$
$337$	11.1758	0.608787	0.304394	+	0.952546i	$0.401546\pi$
$338$	31.5776	1.71760
$339$	−27.2025	−1.47744
$340$	0	0
$341$	−10.2826	−0.556833
$342$	−7.80164	−0.421864
$343$	−20.0192	−1.08093
$344$	−60.2234	−3.24703
$345$	0	0
$346$	27.0978	1.45679
$347$	7.56445	0.406081	0.203040	−	0.979170i	$-0.434918\pi$
$347$	7.56445	0.406081	0.203040	+	0.979170i	$0.434918\pi$
$348$	94.6708	5.07489
$349$	−22.5350	−1.20627	−0.603135	−	0.797639i	$-0.706082\pi$
$349$	−22.5350	−1.20627	−0.603135	+	0.797639i	$0.706082\pi$
$350$	0	0
$351$	7.06052	0.376862
$352$	15.9705	0.851229
$353$	17.3041	0.921002	0.460501	−	0.887659i	$-0.347670\pi$
$353$	17.3041	0.921002	0.460501	+	0.887659i	$0.347670\pi$
$354$	−35.7944	−1.90245
$355$	0	0
$356$	−13.4968	−0.715330
$357$	35.2987	1.86821
$358$	−3.76449	−0.198959
$359$	−8.06827	−0.425827	−0.212914	−	0.977071i	$-0.568295\pi$
$359$	−8.06827	−0.425827	−0.212914	+	0.977071i	$0.568295\pi$
$360$	0	0
$361$	−18.7066	−0.984559
$362$	−17.4109	−0.915099
$363$	25.7124	1.34955
$364$	−9.43365	−0.494458
$365$	0	0
$366$	−29.0373	−1.51781
$367$	−30.8104	−1.60829	−0.804144	−	0.594435i	$-0.797376\pi$
$367$	−30.8104	−1.60829	−0.804144	+	0.594435i	$0.797376\pi$
$368$	14.6711	0.764783
$369$	38.0473	1.98066
$370$	0	0
$371$	−11.5068	−0.597405
$372$	−98.4706	−5.10546
$373$	10.1247	0.524237	0.262118	−	0.965036i	$-0.415579\pi$
$373$	10.1247	0.524237	0.262118	+	0.965036i	$0.415579\pi$
$374$	−23.2883	−1.20421
$375$	0	0
$376$	30.8616	1.59157
$377$	6.47464	0.333461
$378$	38.3930	1.97472
$379$	19.5232	1.00284	0.501419	−	0.865205i	$-0.332812\pi$
$379$	19.5232	1.00284	0.501419	+	0.865205i	$0.332812\pi$
$380$	0	0
$381$	47.7625	2.44695
$382$	56.0748	2.86903
$383$	−31.0185	−1.58497	−0.792484	−	0.609892i	$-0.791213\pi$
$383$	−31.0185	−1.58497	−0.792484	+	0.609892i	$0.791213\pi$
$384$	2.83723	0.144787
$385$	0	0
$386$	24.7746	1.26100
$387$	44.4017	2.25706
$388$	69.6845	3.53770
$389$	−26.0860	−1.32261	−0.661307	−	0.750115i	$-0.729998\pi$
$389$	−26.0860	−1.32261	−0.661307	+	0.750115i	$0.729998\pi$
$390$	0	0
$391$	−8.98628	−0.454456
$392$	22.0948	1.11596
$393$	45.0488	2.27241
$394$	28.2708	1.42426
$395$	0	0
$396$	−39.4351	−1.98169
$397$	7.96047	0.399524	0.199762	−	0.979844i	$-0.435983\pi$
$397$	7.96047	0.399524	0.199762	+	0.979844i	$0.435983\pi$
$398$	30.2326	1.51543
$399$	−3.17445	−0.158921
$400$	0	0
$401$	21.0082	1.04910	0.524551	−	0.851379i	$-0.324233\pi$
$401$	21.0082	1.04910	0.524551	+	0.851379i	$0.324233\pi$
$402$	−19.4108	−0.968125
$403$	−6.73451	−0.335470
$404$	29.8017	1.48269
$405$	0	0
$406$	35.2072	1.74730
$407$	−10.9813	−0.544322
$408$	−131.079	−6.48937
$409$	11.2395	0.555757	0.277878	−	0.960616i	$-0.410369\pi$
$409$	11.2395	0.555757	0.277878	+	0.960616i	$0.410369\pi$
$410$	0	0
$411$	−39.3351	−1.94026
$412$	−89.6551	−4.41699
$413$	−9.42579	−0.463813
$414$	−21.4900	−1.05618
$415$	0	0
$416$	10.4598	0.512832
$417$	−63.9397	−3.13114
$418$	2.09434	0.102438
$419$	−39.6052	−1.93484	−0.967420	−	0.253178i	$-0.918524\pi$
$419$	−39.6052	−1.93484	−0.967420	+	0.253178i	$0.918524\pi$
$420$	0	0
$421$	−6.34705	−0.309337	−0.154668	−	0.987966i	$-0.549431\pi$
$421$	−6.34705	−0.309337	−0.154668	+	0.987966i	$0.549431\pi$
$422$	−46.5313	−2.26511
$423$	−22.7537	−1.10632
$424$	42.7296	2.07513
$425$	0	0
$426$	20.9044	1.01282
$427$	−7.64644	−0.370037
$428$	85.2209	4.11931
$429$	−4.16738	−0.201203
$430$	0	0
$431$	16.5452	0.796954	0.398477	−	0.917178i	$-0.369539\pi$
$431$	16.5452	0.796954	0.398477	+	0.917178i	$0.369539\pi$
$432$	−71.7603	−3.45257
$433$	−12.7015	−0.610397	−0.305199	−	0.952289i	$-0.598723\pi$
$433$	−12.7015	−0.610397	−0.305199	+	0.952289i	$0.598723\pi$
$434$	−36.6203	−1.75783
$435$	0	0
$436$	32.1188	1.53821
$437$	0.808145	0.0386588
$438$	−33.7612	−1.61317
$439$	−16.4422	−0.784742	−0.392371	−	0.919807i	$-0.628345\pi$
$439$	−16.4422	−0.784742	−0.392371	+	0.919807i	$0.628345\pi$
$440$	0	0
$441$	−16.2901	−0.775720
$442$	−15.2526	−0.725490
$443$	−38.2619	−1.81788	−0.908940	−	0.416927i	$-0.863107\pi$
$443$	−38.2619	−1.81788	−0.908940	+	0.416927i	$0.863107\pi$
$444$	−105.162	−4.99075
$445$	0	0
$446$	16.7384	0.792587
$447$	−13.7145	−0.648672
$448$	17.3502	0.819722
$449$	−21.0276	−0.992355	−0.496178	−	0.868221i	$-0.665263\pi$
$449$	−21.0276	−0.992355	−0.496178	+	0.868221i	$0.665263\pi$
$450$	0	0
$451$	−10.2138	−0.480947
$452$	45.2579	2.12875
$453$	55.3114	2.59876
$454$	−75.8125	−3.55806
$455$	0	0
$456$	11.7881	0.552026
$457$	28.5200	1.33411	0.667055	−	0.745008i	$-0.267554\pi$
$457$	28.5200	1.33411	0.667055	+	0.745008i	$0.267554\pi$
$458$	−36.8662	−1.72265
$459$	43.9544	2.05161
$460$	0	0
$461$	34.4782	1.60581	0.802905	−	0.596107i	$-0.203286\pi$
$461$	34.4782	1.60581	0.802905	+	0.596107i	$0.203286\pi$
$462$	−22.6610	−1.05428
$463$	−9.61723	−0.446951	−0.223475	−	0.974710i	$-0.571740\pi$
$463$	−9.61723	−0.446951	−0.223475	+	0.974710i	$0.571740\pi$
$464$	−65.8057	−3.05495
$465$	0	0
$466$	7.35184	0.340568
$467$	−36.4956	−1.68882	−0.844408	−	0.535701i	$-0.820047\pi$
$467$	−36.4956	−1.68882	−0.844408	+	0.535701i	$0.820047\pi$
$468$	−25.8278	−1.19389
$469$	−5.11148	−0.236026
$470$	0	0
$471$	−16.2882	−0.750521
$472$	35.0019	1.61109
$473$	−11.9196	−0.548063
$474$	−30.9606	−1.42207
$475$	0	0
$476$	−58.7280	−2.69180
$477$	−31.5038	−1.44246
$478$	36.7330	1.68013
$479$	14.4680	0.661058	0.330529	−	0.943796i	$-0.392773\pi$
$479$	14.4680	0.661058	0.330529	+	0.943796i	$0.392773\pi$
$480$	0	0
$481$	−7.19213	−0.327933
$482$	−2.61751	−0.119224
$483$	−8.74420	−0.397875
$484$	−42.7789	−1.94449
$485$	0	0
$486$	−20.8853	−0.947379
$487$	−1.90549	−0.0863461	−0.0431730	−	0.999068i	$-0.513747\pi$
$487$	−1.90549	−0.0863461	−0.0431730	+	0.999068i	$0.513747\pi$
$488$	28.3944	1.28535
$489$	−10.6810	−0.483013
$490$	0	0
$491$	−10.0041	−0.451480	−0.225740	−	0.974188i	$-0.572480\pi$
$491$	−10.0041	−0.451480	−0.225740	+	0.974188i	$0.572480\pi$
$492$	−97.8115	−4.40968
$493$	40.3071	1.81534
$494$	1.37168	0.0617147
$495$	0	0
$496$	68.4469	3.07336
$497$	5.50479	0.246924
$498$	12.7030	0.569236
$499$	15.8138	0.707921	0.353961	−	0.935260i	$-0.384835\pi$
$499$	15.8138	0.707921	0.353961	+	0.935260i	$0.384835\pi$
$500$	0	0
$501$	−4.96455	−0.221800
$502$	−50.3892	−2.24898
$503$	−22.2704	−0.992989	−0.496495	−	0.868040i	$-0.665380\pi$
$503$	−22.2704	−0.992989	−0.496495	+	0.868040i	$0.665380\pi$
$504$	−82.5454	−3.67686
$505$	0	0
$506$	5.76898	0.256463
$507$	35.1779	1.56230
$508$	−79.4645	−3.52567
$509$	−4.30285	−0.190721	−0.0953603	−	0.995443i	$-0.530400\pi$
$509$	−4.30285	−0.190721	−0.0953603	+	0.995443i	$0.530400\pi$
$510$	0	0
$511$	−8.89038	−0.393287
$512$	40.4708	1.78857
$513$	−3.95286	−0.174523
$514$	−7.94627	−0.350495
$515$	0	0
$516$	−114.147	−5.02505
$517$	6.10822	0.268639
$518$	−39.1087	−1.71834
$519$	30.1873	1.32508
$520$	0	0
$521$	36.0258	1.57832	0.789160	−	0.614187i	$-0.210516\pi$
$521$	36.0258	1.57832	0.789160	+	0.614187i	$0.210516\pi$
$522$	96.3915	4.21894
$523$	26.7740	1.17074	0.585372	−	0.810764i	$-0.300948\pi$
$523$	26.7740	1.17074	0.585372	+	0.810764i	$0.300948\pi$
$524$	−74.9496	−3.27419
$525$	0	0
$526$	−1.84266	−0.0803438
$527$	−41.9249	−1.82628
$528$	42.3556	1.84329
$529$	−20.7739	−0.903214
$530$	0	0
$531$	−25.8063	−1.11990
$532$	5.28147	0.228981
$533$	−6.68944	−0.289752
$534$	−21.2341	−0.918890
$535$	0	0
$536$	18.9811	0.819857
$537$	−4.19368	−0.180971
$538$	−80.4683	−3.46924
$539$	4.37307	0.188361
$540$	0	0
$541$	−1.20360	−0.0517468	−0.0258734	−	0.999665i	$-0.508237\pi$
$541$	−1.20360	−0.0517468	−0.0258734	+	0.999665i	$0.508237\pi$
$542$	−52.9347	−2.27374
$543$	−19.3960	−0.832362
$544$	65.1159	2.79182
$545$	0	0
$546$	−14.8417	−0.635165
$547$	−11.1103	−0.475043	−0.237522	−	0.971382i	$-0.576335\pi$
$547$	−11.1103	−0.475043	−0.237522	+	0.971382i	$0.576335\pi$
$548$	65.4434	2.79560
$549$	−20.9347	−0.893471
$550$	0	0
$551$	−3.62485	−0.154424
$552$	32.4708	1.38205
$553$	−8.15289	−0.346696
$554$	−7.44367	−0.316251
$555$	0	0
$556$	106.379	4.51149
$557$	−41.9026	−1.77547	−0.887735	−	0.460354i	$-0.847722\pi$
$557$	−41.9026	−1.77547	−0.887735	+	0.460354i	$0.847722\pi$
$558$	−100.260	−4.24436
$559$	−7.80666	−0.330187
$560$	0	0
$561$	−25.9435	−1.09534
$562$	−24.3588	−1.02751
$563$	−20.0207	−0.843771	−0.421886	−	0.906649i	$-0.638632\pi$
$563$	−20.0207	−0.843771	−0.421886	+	0.906649i	$0.638632\pi$
$564$	58.4950	2.46309
$565$	0	0
$566$	52.2990	2.19829
$567$	9.59079	0.402775
$568$	−20.4416	−0.857709
$569$	−40.1123	−1.68159	−0.840797	−	0.541351i	$-0.817913\pi$
$569$	−40.1123	−1.68159	−0.840797	+	0.541351i	$0.817913\pi$
$570$	0	0
$571$	5.44389	0.227820	0.113910	−	0.993491i	$-0.463663\pi$
$571$	5.44389	0.227820	0.113910	+	0.993491i	$0.463663\pi$
$572$	6.93345	0.289902
$573$	62.4680	2.60964
$574$	−36.3752	−1.51827
$575$	0	0
$576$	47.5021	1.97925
$577$	−5.96992	−0.248531	−0.124266	−	0.992249i	$-0.539657\pi$
$577$	−5.96992	−0.248531	−0.124266	+	0.992249i	$0.539657\pi$
$578$	−50.4552	−2.09866
$579$	27.5992	1.14699
$580$	0	0
$581$	3.34511	0.138778
$582$	109.632	4.54441
$583$	8.45717	0.350260
$584$	33.0137	1.36612
$585$	0	0
$586$	−28.7507	−1.18768
$587$	46.9038	1.93593	0.967964	−	0.251091i	$-0.0807892\pi$
$587$	46.9038	1.93593	0.967964	+	0.251091i	$0.0807892\pi$
$588$	41.8785	1.72704
$589$	3.77035	0.155354
$590$	0	0
$591$	31.4940	1.29549
$592$	73.0979	3.00431
$593$	5.55227	0.228004	0.114002	−	0.993481i	$-0.463633\pi$
$593$	5.55227	0.228004	0.114002	+	0.993481i	$0.463633\pi$
$594$	−28.2177	−1.15779
$595$	0	0
$596$	22.8174	0.934635
$597$	33.6795	1.37841
$598$	3.77836	0.154509
$599$	−36.3540	−1.48538	−0.742691	−	0.669634i	$-0.766451\pi$
$599$	−36.3540	−1.48538	−0.742691	+	0.669634i	$0.766451\pi$
$600$	0	0
$601$	42.6980	1.74169	0.870844	−	0.491559i	$-0.163573\pi$
$601$	42.6980	1.74169	0.870844	+	0.491559i	$0.163573\pi$
$602$	−42.4503	−1.73015
$603$	−13.9944	−0.569896
$604$	−92.0239	−3.74440
$605$	0	0
$606$	46.8861	1.90462
$607$	−16.5312	−0.670981	−0.335490	−	0.942044i	$-0.608902\pi$
$607$	−16.5312	−0.670981	−0.335490	+	0.942044i	$0.608902\pi$
$608$	−5.85594	−0.237490
$609$	39.2212	1.58933
$610$	0	0
$611$	4.00054	0.161845
$612$	−160.788	−6.49946
$613$	17.8745	0.721945	0.360973	−	0.932576i	$-0.382445\pi$
$613$	17.8745	0.721945	0.360973	+	0.932576i	$0.382445\pi$
$614$	−88.7086	−3.57999
$615$	0	0
$616$	22.1592	0.892821
$617$	1.22431	0.0492888	0.0246444	−	0.999696i	$-0.492155\pi$
$617$	1.22431	0.0492888	0.0246444	+	0.999696i	$0.492155\pi$
$618$	−141.052	−5.67393
$619$	34.6297	1.39189	0.695943	−	0.718097i	$-0.254987\pi$
$619$	34.6297	1.39189	0.695943	+	0.718097i	$0.254987\pi$
$620$	0	0
$621$	−10.8884	−0.436935
$622$	−19.3233	−0.774792
$623$	−5.59161	−0.224023
$624$	27.7405	1.11051
$625$	0	0
$626$	−46.7163	−1.86716
$627$	2.33313	0.0931761
$628$	27.0994	1.08138
$629$	−44.7737	−1.78524
$630$	0	0
$631$	5.85881	0.233236	0.116618	−	0.993177i	$-0.462795\pi$
$631$	5.85881	0.233236	0.116618	+	0.993177i	$0.462795\pi$
$632$	30.2751	1.20428
$633$	−51.8365	−2.06032
$634$	33.1180	1.31528
$635$	0	0
$636$	80.9896	3.21145
$637$	2.86411	0.113480
$638$	−25.8762	−1.02445
$639$	15.0712	0.596208
$640$	0	0
$641$	−6.10916	−0.241297	−0.120649	−	0.992695i	$-0.538497\pi$
$641$	−6.10916	−0.241297	−0.120649	+	0.992695i	$0.538497\pi$
$642$	134.075	5.29153
$643$	−23.2044	−0.915092	−0.457546	−	0.889186i	$-0.651272\pi$
$643$	−23.2044	−0.915092	−0.457546	+	0.889186i	$0.651272\pi$
$644$	14.5481	0.573275
$645$	0	0
$646$	8.53921	0.335971
$647$	−38.1244	−1.49883	−0.749413	−	0.662103i	$-0.769664\pi$
$647$	−38.1244	−1.49883	−0.749413	+	0.662103i	$0.769664\pi$
$648$	−35.6146	−1.39907
$649$	6.92767	0.271935
$650$	0	0
$651$	−40.7955	−1.59890
$652$	17.7705	0.695946
$653$	14.8821	0.582383	0.291191	−	0.956665i	$-0.405948\pi$
$653$	14.8821	0.582383	0.291191	+	0.956665i	$0.405948\pi$
$654$	50.5316	1.97594
$655$	0	0
$656$	67.9888	2.65452
$657$	−24.3404	−0.949610
$658$	21.7538	0.848050
$659$	9.15991	0.356820	0.178410	−	0.983956i	$-0.442905\pi$
$659$	9.15991	0.356820	0.178410	+	0.983956i	$0.442905\pi$
$660$	0	0
$661$	9.23056	0.359027	0.179514	−	0.983755i	$-0.442548\pi$
$661$	9.23056	0.359027	0.179514	+	0.983755i	$0.442548\pi$
$662$	49.1500	1.91027
$663$	−16.9915	−0.659897
$664$	−12.4218	−0.482058
$665$	0	0
$666$	−107.073	−4.14900
$667$	−9.98486	−0.386615
$668$	8.25974	0.319579
$669$	18.6468	0.720927
$670$	0	0
$671$	5.61990	0.216954
$672$	63.3618	2.44423
$673$	16.0187	0.617476	0.308738	−	0.951147i	$-0.400093\pi$
$673$	16.0187	0.617476	0.308738	+	0.951147i	$0.400093\pi$
$674$	−29.2529	−1.12678
$675$	0	0
$676$	−58.5269	−2.25104
$677$	36.7022	1.41058	0.705290	−	0.708919i	$-0.250817\pi$
$677$	36.7022	1.41058	0.705290	+	0.708919i	$0.250817\pi$
$678$	71.2029	2.73453
$679$	28.8697	1.10792
$680$	0	0
$681$	−84.4561	−3.23637
$682$	26.9148	1.03062
$683$	−31.1207	−1.19080	−0.595400	−	0.803430i	$-0.703006\pi$
$683$	−31.1207	−1.19080	−0.595400	+	0.803430i	$0.703006\pi$
$684$	14.4598	0.552884
$685$	0	0
$686$	52.4005	2.00066
$687$	−41.0695	−1.56690
$688$	79.3438	3.02495
$689$	5.53897	0.211018
$690$	0	0
$691$	15.5540	0.591703	0.295852	−	0.955234i	$-0.404397\pi$
$691$	15.5540	0.591703	0.295852	+	0.955234i	$0.404397\pi$
$692$	−50.2239	−1.90923
$693$	−16.3376	−0.620615
$694$	−19.8000	−0.751599
$695$	0	0
$696$	−145.645	−5.52065
$697$	−41.6443	−1.57739
$698$	58.9856	2.23264
$699$	8.19004	0.309776
$700$	0	0
$701$	−41.2977	−1.55979	−0.779896	−	0.625909i	$-0.784728\pi$
$701$	−41.2977	−1.55979	−0.779896	+	0.625909i	$0.784728\pi$
$702$	−18.4810	−0.697520
$703$	4.02654	0.151864
$704$	−12.7519	−0.480605
$705$	0	0
$706$	−45.2936	−1.70465
$707$	12.3466	0.464341
$708$	66.3425	2.49330
$709$	−4.14082	−0.155512	−0.0777559	−	0.996972i	$-0.524775\pi$
$709$	−4.14082	−0.155512	−0.0777559	+	0.996972i	$0.524775\pi$
$710$	0	0
$711$	−22.3213	−0.837113
$712$	20.7640	0.778162
$713$	10.3856	0.388945
$714$	−92.3950	−3.45780
$715$	0	0
$716$	6.97721	0.260751
$717$	40.9210	1.52822
$718$	21.1188	0.788147
$719$	−7.26334	−0.270877	−0.135438	−	0.990786i	$-0.543244\pi$
$719$	−7.26334	−0.270877	−0.135438	+	0.990786i	$0.543244\pi$
$720$	0	0
$721$	−37.1433	−1.38329
$722$	48.9648	1.82228
$723$	−2.91594	−0.108445
$724$	32.2700	1.19930
$725$	0	0
$726$	−67.3026	−2.49783
$727$	−27.5563	−1.02201	−0.511004	−	0.859578i	$-0.670726\pi$
$727$	−27.5563	−1.02201	−0.511004	+	0.859578i	$0.670726\pi$
$728$	14.5131	0.537889
$729$	−37.5820	−1.39193
$730$	0	0
$731$	−48.5994	−1.79751
$732$	53.8187	1.98920
$733$	22.2034	0.820103	0.410051	−	0.912062i	$-0.365511\pi$
$733$	22.2034	0.820103	0.410051	+	0.912062i	$0.365511\pi$
$734$	80.6466	2.97672
$735$	0	0
$736$	−16.1305	−0.594578
$737$	3.75679	0.138383
$738$	−99.5892	−3.66593
$739$	17.1110	0.629440	0.314720	−	0.949185i	$-0.398089\pi$
$739$	17.1110	0.629440	0.314720	+	0.949185i	$0.398089\pi$
$740$	0	0
$741$	1.52807	0.0561349
$742$	30.1193	1.10571
$743$	−34.8194	−1.27740	−0.638700	−	0.769456i	$-0.720528\pi$
$743$	−34.8194	−1.27740	−0.638700	+	0.769456i	$0.720528\pi$
$744$	151.491	5.55391
$745$	0	0
$746$	−26.5015	−0.970290
$747$	9.15835	0.335086
$748$	43.1633	1.57821
$749$	35.3063	1.29006
$750$	0	0
$751$	−51.9686	−1.89636	−0.948180	−	0.317733i	$-0.897078\pi$
$751$	−51.9686	−1.89636	−0.948180	+	0.317733i	$0.897078\pi$
$752$	−40.6599	−1.48271
$753$	−56.1342	−2.04565
$754$	−16.9475	−0.617190
$755$	0	0
$756$	−71.1588	−2.58802
$757$	12.7291	0.462647	0.231323	−	0.972877i	$-0.425694\pi$
$757$	12.7291	0.462647	0.231323	+	0.972877i	$0.425694\pi$
$758$	−51.1021	−1.85611
$759$	6.42672	0.233275
$760$	0	0
$761$	0.108092	0.00391832	0.00195916	−	0.999998i	$-0.499376\pi$
$761$	0.108092	0.00391832	0.00195916	+	0.999998i	$0.499376\pi$
$762$	−125.019	−4.52896
$763$	13.3065	0.481729
$764$	−103.931	−3.76008
$765$	0	0
$766$	81.1912	2.93356
$767$	4.53723	0.163830
$768$	42.9171	1.54864
$769$	−36.3976	−1.31253	−0.656266	−	0.754530i	$-0.727865\pi$
$769$	−36.3976	−1.31253	−0.656266	+	0.754530i	$0.727865\pi$
$770$	0	0
$771$	−8.85224	−0.318806
$772$	−45.9180	−1.65263
$773$	−8.06503	−0.290079	−0.145039	−	0.989426i	$-0.546331\pi$
$773$	−8.06503	−0.290079	−0.145039	+	0.989426i	$0.546331\pi$
$774$	−116.222	−4.17751
$775$	0	0
$776$	−107.205	−3.84844
$777$	−43.5675	−1.56298
$778$	68.2805	2.44798
$779$	3.74511	0.134182
$780$	0	0
$781$	−4.04585	−0.144772
$782$	23.5217	0.841135
$783$	48.8387	1.74535
$784$	−29.1097	−1.03963
$785$	0	0
$786$	−117.916	−4.20592
$787$	−20.5415	−0.732226	−0.366113	−	0.930570i	$-0.619312\pi$
$787$	−20.5415	−0.732226	−0.366113	+	0.930570i	$0.619312\pi$
$788$	−52.3980	−1.86660
$789$	−2.05275	−0.0730797
$790$	0	0
$791$	18.7499	0.666671
$792$	60.6683	2.15576
$793$	3.68072	0.130706
$794$	−20.8366	−0.739465
$795$	0	0
$796$	−56.0341	−1.98608
$797$	2.56805	0.0909649	0.0454825	−	0.998965i	$-0.485517\pi$
$797$	2.56805	0.0909649	0.0454825	+	0.998965i	$0.485517\pi$
$798$	8.30917	0.294141
$799$	24.9049	0.881071
$800$	0	0
$801$	−15.3089	−0.540913
$802$	−54.9894	−1.94174
$803$	6.53416	0.230586
$804$	35.9767	1.26880
$805$	0	0
$806$	17.6277	0.620909
$807$	−89.6427	−3.15557
$808$	−45.8480	−1.61293
$809$	17.4707	0.614237	0.307119	−	0.951671i	$-0.400635\pi$
$809$	17.4707	0.614237	0.307119	+	0.951671i	$0.400635\pi$
$810$	0	0
$811$	−25.3292	−0.889427	−0.444713	−	0.895673i	$-0.646694\pi$
$811$	−25.3292	−0.889427	−0.444713	+	0.895673i	$0.646694\pi$
$812$	−65.2541	−2.28997
$813$	−58.9699	−2.06817
$814$	28.7437	1.00747
$815$	0	0
$816$	172.695	6.04554
$817$	4.37059	0.152908
$818$	−29.4195	−1.02863
$819$	−10.7002	−0.373896
$820$	0	0
$821$	0.554175	0.0193408	0.00967042	−	0.999953i	$-0.496922\pi$
$821$	0.554175	0.0193408	0.00967042	+	0.999953i	$0.496922\pi$
$822$	102.960	3.59114
$823$	−50.8525	−1.77261	−0.886304	−	0.463105i	$-0.846735\pi$
$823$	−50.8525	−1.77261	−0.886304	+	0.463105i	$0.846735\pi$
$824$	137.929	4.80497
$825$	0	0
$826$	24.6721	0.858454
$827$	52.2652	1.81744	0.908719	−	0.417409i	$-0.137062\pi$
$827$	52.2652	1.81744	0.908719	+	0.417409i	$0.137062\pi$
$828$	39.8303	1.38420
$829$	19.2786	0.669574	0.334787	−	0.942294i	$-0.391336\pi$
$829$	19.2786	0.669574	0.334787	+	0.942294i	$0.391336\pi$
$830$	0	0
$831$	−8.29234	−0.287658
$832$	−8.35177	−0.289546
$833$	17.8302	0.617780
$834$	167.363	5.79531
$835$	0	0
$836$	−3.88172	−0.134252
$837$	−50.7989	−1.75587
$838$	103.667	3.58112
$839$	52.3553	1.80751	0.903753	−	0.428055i	$-0.140801\pi$
$839$	52.3553	1.80751	0.903753	+	0.428055i	$0.140801\pi$
$840$	0	0
$841$	15.7861	0.544349
$842$	16.6135	0.572539
$843$	−27.1360	−0.934613
$844$	86.2426	2.96859
$845$	0	0
$846$	59.5582	2.04765
$847$	−17.7229	−0.608966
$848$	−56.2959	−1.93321
$849$	58.2617	1.99954
$850$	0	0
$851$	11.0913	0.380206
$852$	−38.7449	−1.32738
$853$	−46.7427	−1.60044	−0.800219	−	0.599708i	$-0.795284\pi$
$853$	−46.7427	−1.60044	−0.800219	+	0.599708i	$0.795284\pi$
$854$	20.0147	0.684888
$855$	0	0
$856$	−131.107	−4.48114
$857$	−32.2371	−1.10120	−0.550599	−	0.834770i	$-0.685601\pi$
$857$	−32.2371	−1.10120	−0.550599	+	0.834770i	$0.685601\pi$
$858$	10.9082	0.372399
$859$	−49.6830	−1.69516	−0.847581	−	0.530666i	$-0.821942\pi$
$859$	−49.6830	−1.69516	−0.847581	+	0.530666i	$0.821942\pi$
$860$	0	0
$861$	−40.5224	−1.38100
$862$	−43.3073	−1.47505
$863$	−19.4871	−0.663349	−0.331675	−	0.943394i	$-0.607614\pi$
$863$	−19.4871	−0.663349	−0.331675	+	0.943394i	$0.607614\pi$
$864$	78.8988	2.68419
$865$	0	0
$866$	33.2465	1.12976
$867$	−56.2077	−1.90891
$868$	67.8732	2.30377
$869$	5.99213	0.203269
$870$	0	0
$871$	2.46048	0.0833703
$872$	−49.4127	−1.67333
$873$	79.0404	2.67511
$874$	−2.11533	−0.0715521
$875$	0	0
$876$	62.5741	2.11418
$877$	−33.5686	−1.13353	−0.566766	−	0.823879i	$-0.691806\pi$
$877$	−33.5686	−1.13353	−0.566766	+	0.823879i	$0.691806\pi$
$878$	43.0376	1.45245
$879$	−32.0287	−1.08030
$880$	0	0
$881$	23.8009	0.801872	0.400936	−	0.916106i	$-0.368685\pi$
$881$	23.8009	0.801872	0.400936	+	0.916106i	$0.368685\pi$
$882$	42.6396	1.43575
$883$	−17.8466	−0.600585	−0.300293	−	0.953847i	$-0.597084\pi$
$883$	−17.8466	−0.600585	−0.300293	+	0.953847i	$0.597084\pi$
$884$	28.2695	0.950808
$885$	0	0
$886$	100.151	3.36464
$887$	47.4414	1.59292	0.796462	−	0.604688i	$-0.206702\pi$
$887$	47.4414	1.59292	0.796462	+	0.604688i	$0.206702\pi$
$888$	161.784	5.42913
$889$	−32.9214	−1.10415
$890$	0	0
$891$	−7.04894	−0.236148
$892$	−31.0235	−1.03874
$893$	−2.23972	−0.0749493
$894$	35.8978	1.20060
$895$	0	0
$896$	−1.95563	−0.0653329
$897$	4.20914	0.140539
$898$	55.0401	1.83671
$899$	−46.5837	−1.55365
$900$	0	0
$901$	34.4822	1.14877
$902$	26.7347	0.890167
$903$	−47.2902	−1.57372
$904$	−69.6263	−2.31574
$905$	0	0
$906$	−144.778	−4.80994
$907$	−2.24706	−0.0746123	−0.0373061	−	0.999304i	$-0.511878\pi$
$907$	−2.24706	−0.0746123	−0.0373061	+	0.999304i	$0.511878\pi$
$908$	140.513	4.66310
$909$	33.8029	1.12117
$910$	0	0
$911$	41.2694	1.36732	0.683658	−	0.729803i	$-0.260388\pi$
$911$	41.2694	1.36732	0.683658	+	0.729803i	$0.260388\pi$
$912$	−15.5307	−0.514271
$913$	−2.45855	−0.0813662
$914$	−74.6516	−2.46925
$915$	0	0
$916$	68.3290	2.25765
$917$	−31.0509	−1.02539
$918$	−115.051	−3.79725
$919$	50.0566	1.65121	0.825607	−	0.564246i	$-0.190833\pi$
$919$	50.0566	1.65121	0.825607	+	0.564246i	$0.190833\pi$
$920$	0	0
$921$	−98.8225	−3.25631
$922$	−90.2472	−2.97213
$923$	−2.64981	−0.0872195
$924$	42.0006	1.38172
$925$	0	0
$926$	25.1732	0.827244
$927$	−101.692	−3.34001
$928$	72.3518	2.37506
$929$	2.57944	0.0846288	0.0423144	−	0.999104i	$-0.486527\pi$
$929$	2.57944	0.0846288	0.0423144	+	0.999104i	$0.486527\pi$
$930$	0	0
$931$	−1.60349	−0.0525522
$932$	−13.6261	−0.446339
$933$	−21.5263	−0.704741
$934$	95.5278	3.12576
$935$	0	0
$936$	39.7343	1.29876
$937$	39.6842	1.29643	0.648213	−	0.761459i	$-0.275517\pi$
$937$	39.6842	1.29643	0.648213	+	0.761459i	$0.275517\pi$
$938$	13.3794	0.436852
$939$	−52.0425	−1.69834
$940$	0	0
$941$	−10.1641	−0.331339	−0.165669	−	0.986181i	$-0.552978\pi$
$941$	−10.1641	−0.331339	−0.165669	+	0.986181i	$0.552978\pi$
$942$	42.6346	1.38911
$943$	10.3161	0.335939
$944$	−46.1147	−1.50090
$945$	0	0
$946$	31.1997	1.01439
$947$	2.33651	0.0759263	0.0379631	−	0.999279i	$-0.487913\pi$
$947$	2.33651	0.0759263	0.0379631	+	0.999279i	$0.487913\pi$
$948$	57.3833	1.86372
$949$	4.27951	0.138919
$950$	0	0
$951$	36.8939	1.19637
$952$	90.3492	2.92823
$953$	6.62319	0.214546	0.107273	−	0.994230i	$-0.465788\pi$
$953$	6.62319	0.214546	0.107273	+	0.994230i	$0.465788\pi$
$954$	82.4616	2.66979
$955$	0	0
$956$	−68.0820	−2.20193
$957$	−28.8264	−0.931826
$958$	−37.8701	−1.22353
$959$	27.1126	0.875512
$960$	0	0
$961$	17.4534	0.563014
$962$	18.8255	0.606958
$963$	96.6627	3.11491
$964$	4.85138	0.156252
$965$	0	0
$966$	22.8881	0.736411
$967$	−27.1899	−0.874369	−0.437184	−	0.899372i	$-0.644024\pi$
$967$	−27.1899	−0.874369	−0.437184	+	0.899372i	$0.644024\pi$
$968$	65.8124	2.11529
$969$	9.51278	0.305595
$970$	0	0
$971$	17.9802	0.577011	0.288506	−	0.957478i	$-0.406842\pi$
$971$	17.9802	0.577011	0.288506	+	0.957478i	$0.406842\pi$
$972$	38.7095	1.24161
$973$	44.0720	1.41288
$974$	4.98765	0.159815
$975$	0	0
$976$	−37.4094	−1.19745
$977$	−11.9489	−0.382280	−0.191140	−	0.981563i	$-0.561218\pi$
$977$	−11.9489	−0.382280	−0.191140	+	0.981563i	$0.561218\pi$
$978$	27.9578	0.893991
$979$	4.10966	0.131345
$980$	0	0
$981$	36.4311	1.16316
$982$	26.1859	0.835626
$983$	−6.03967	−0.192636	−0.0963178	−	0.995351i	$-0.530707\pi$
$983$	−6.03967	−0.192636	−0.0963178	+	0.995351i	$0.530707\pi$
$984$	150.477	4.79702
$985$	0	0
$986$	−105.504	−3.35994
$987$	24.2340	0.771375
$988$	−2.54231	−0.0808816
$989$	12.0390	0.382819
$990$	0	0
$991$	39.2454	1.24667	0.623336	−	0.781954i	$-0.285777\pi$
$991$	39.2454	1.24667	0.623336	+	0.781954i	$0.285777\pi$
$992$	−75.2558	−2.38937
$993$	54.7538	1.73756
$994$	−14.4089	−0.457022
$995$	0	0
$996$	−23.5442	−0.746026
$997$	−45.7163	−1.44785	−0.723925	−	0.689878i	$-0.757664\pi$
$997$	−45.7163	−1.44785	−0.723925	+	0.689878i	$0.757664\pi$
$998$	−41.3927	−1.31026
$999$	−54.2507	−1.71642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.m.1.4	✓	40
5.4	even	2		6025.2.a.n.1.37	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.4	✓	40	1.1	even	1	trivial
6025.2.a.n.1.37	yes	40	5.4	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61751 q^{2} -2.91594 q^{3} +4.85138 q^{4} +7.63252 q^{6} +2.00988 q^{7} -7.46353 q^{8} +5.50273 q^{9} +O(q^{10})\)	\(q-2.61751 q^{2} -2.91594 q^{3} +4.85138 q^{4} +7.63252 q^{6} +2.00988 q^{7} -7.46353 q^{8} +5.50273 q^{9} -1.47720 q^{11} -14.1463 q^{12} -0.967484 q^{13} -5.26090 q^{14} +9.83313 q^{16} -6.02295 q^{17} -14.4035 q^{18} +0.541650 q^{19} -5.86070 q^{21} +3.86660 q^{22} +1.49200 q^{23} +21.7632 q^{24} +2.53240 q^{26} -7.29781 q^{27} +9.75070 q^{28} -6.69224 q^{29} +6.96085 q^{31} -10.8113 q^{32} +4.30744 q^{33} +15.7652 q^{34} +26.6958 q^{36} +7.43384 q^{37} -1.41778 q^{38} +2.82113 q^{39} +6.91426 q^{41} +15.3405 q^{42} +8.06903 q^{43} -7.16647 q^{44} -3.90534 q^{46} -4.13499 q^{47} -28.6728 q^{48} -2.96037 q^{49} +17.5626 q^{51} -4.69363 q^{52} -5.72513 q^{53} +19.1021 q^{54} -15.0008 q^{56} -1.57942 q^{57} +17.5170 q^{58} -4.68972 q^{59} -3.80442 q^{61} -18.2201 q^{62} +11.0598 q^{63} +8.63246 q^{64} -11.2748 q^{66} -2.54318 q^{67} -29.2196 q^{68} -4.35060 q^{69} +2.73886 q^{71} -41.0697 q^{72} -4.42334 q^{73} -19.4582 q^{74} +2.62775 q^{76} -2.96900 q^{77} -7.38435 q^{78} -4.05640 q^{79} +4.77182 q^{81} -18.0982 q^{82} +1.66433 q^{83} -28.4325 q^{84} -21.1208 q^{86} +19.5142 q^{87} +11.0251 q^{88} -2.78206 q^{89} -1.94453 q^{91} +7.23828 q^{92} -20.2974 q^{93} +10.8234 q^{94} +31.5251 q^{96} +14.3639 q^{97} +7.74882 q^{98} -8.12864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * q^99

Introduction

L-functions

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