LMFDB - Embedded newform 6025.2.a.m.1.20

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			1.20
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)

$f(q)$	$=$	$q-0.333070 q^{2} -1.03111 q^{3} -1.88906 q^{4} +0.343432 q^{6} +2.91492 q^{7} +1.29533 q^{8} -1.93681 q^{9} +O(q^{10})$	\(q-0.333070 q^{2} -1.03111 q^{3} -1.88906 q^{4} +0.343432 q^{6} +2.91492 q^{7} +1.29533 q^{8} -1.93681 q^{9} -5.85066 q^{11} +1.94783 q^{12} +5.25897 q^{13} -0.970871 q^{14} +3.34669 q^{16} +1.44402 q^{17} +0.645094 q^{18} -4.06597 q^{19} -3.00560 q^{21} +1.94868 q^{22} +1.01807 q^{23} -1.33563 q^{24} -1.75160 q^{26} +5.09040 q^{27} -5.50646 q^{28} -7.18385 q^{29} +6.93668 q^{31} -3.70534 q^{32} +6.03267 q^{33} -0.480959 q^{34} +3.65876 q^{36} -5.29003 q^{37} +1.35425 q^{38} -5.42257 q^{39} -4.45798 q^{41} +1.00107 q^{42} +3.29679 q^{43} +11.0523 q^{44} -0.339090 q^{46} +1.96909 q^{47} -3.45081 q^{48} +1.49673 q^{49} -1.48894 q^{51} -9.93453 q^{52} +0.430807 q^{53} -1.69546 q^{54} +3.77578 q^{56} +4.19246 q^{57} +2.39272 q^{58} +8.44640 q^{59} +3.27665 q^{61} -2.31040 q^{62} -5.64565 q^{63} -5.45925 q^{64} -2.00930 q^{66} +13.7065 q^{67} -2.72784 q^{68} -1.04974 q^{69} +4.02073 q^{71} -2.50881 q^{72} -3.64203 q^{73} +1.76195 q^{74} +7.68088 q^{76} -17.0542 q^{77} +1.80610 q^{78} -8.06707 q^{79} +0.561685 q^{81} +1.48482 q^{82} -9.94154 q^{83} +5.67777 q^{84} -1.09806 q^{86} +7.40733 q^{87} -7.57853 q^{88} -7.05272 q^{89} +15.3294 q^{91} -1.92321 q^{92} -7.15248 q^{93} -0.655845 q^{94} +3.82062 q^{96} -3.07235 q^{97} -0.498517 q^{98} +11.3316 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.333070	−0.235516	−0.117758	−	0.993042i	$-0.537571\pi$
$2$	−0.333070	−0.235516	−0.117758	+	0.993042i	$0.537571\pi$
$3$	−1.03111	−0.595311	−0.297656	−	0.954673i	$-0.596205\pi$
$3$	−1.03111	−0.595311	−0.297656	+	0.954673i	$0.596205\pi$
$4$	−1.88906	−0.944532
$5$	0	0
$5$	0	0
$6$	0.343432	0.140205
$7$	2.91492	1.10173	0.550867	−	0.834593i	$-0.314297\pi$
$7$	2.91492	1.10173	0.550867	+	0.834593i	$0.314297\pi$
$8$	1.29533	0.457969
$9$	−1.93681	−0.645604
$10$	0	0
$11$	−5.85066	−1.76404	−0.882020	−	0.471213i	$-0.843816\pi$
$11$	−5.85066	−1.76404	−0.882020	+	0.471213i	$0.843816\pi$
$12$	1.94783	0.562291
$13$	5.25897	1.45858	0.729288	−	0.684207i	$-0.239852\pi$
$13$	5.25897	1.45858	0.729288	+	0.684207i	$0.239852\pi$
$14$	−0.970871	−0.259476
$15$	0	0
$16$	3.34669	0.836673
$17$	1.44402	0.350226	0.175113	−	0.984548i	$-0.443971\pi$
$17$	1.44402	0.350226	0.175113	+	0.984548i	$0.443971\pi$
$18$	0.645094	0.152050
$19$	−4.06597	−0.932798	−0.466399	−	0.884574i	$-0.654449\pi$
$19$	−4.06597	−0.932798	−0.466399	+	0.884574i	$0.654449\pi$
$20$	0	0
$21$	−3.00560	−0.655875
$22$	1.94868	0.415460
$23$	1.01807	0.212283	0.106141	−	0.994351i	$-0.466150\pi$
$23$	1.01807	0.212283	0.106141	+	0.994351i	$0.466150\pi$
$24$	−1.33563	−0.272634
$25$	0	0
$26$	−1.75160	−0.343518
$27$	5.09040	0.979647
$28$	−5.50646	−1.04062
$29$	−7.18385	−1.33401	−0.667004	−	0.745055i	$-0.732423\pi$
$29$	−7.18385	−1.33401	−0.667004	+	0.745055i	$0.732423\pi$
$30$	0	0
$31$	6.93668	1.24587	0.622933	−	0.782276i	$-0.285941\pi$
$31$	6.93668	1.24587	0.622933	+	0.782276i	$0.285941\pi$
$32$	−3.70534	−0.655019
$33$	6.03267	1.05015
$34$	−0.480959	−0.0824838
$35$	0	0
$36$	3.65876	0.609794
$37$	−5.29003	−0.869675	−0.434838	−	0.900509i	$-0.643194\pi$
$37$	−5.29003	−0.869675	−0.434838	+	0.900509i	$0.643194\pi$
$38$	1.35425	0.219689
$39$	−5.42257	−0.868306
$40$	0	0
$41$	−4.45798	−0.696220	−0.348110	−	0.937454i	$-0.613176\pi$
$41$	−4.45798	−0.696220	−0.348110	+	0.937454i	$0.613176\pi$
$42$	1.00107	0.154469
$43$	3.29679	0.502756	0.251378	−	0.967889i	$-0.419116\pi$
$43$	3.29679	0.502756	0.251378	+	0.967889i	$0.419116\pi$
$44$	11.0523	1.66619
$45$	0	0
$46$	−0.339090	−0.0499960
$47$	1.96909	0.287221	0.143611	−	0.989634i	$-0.454129\pi$
$47$	1.96909	0.287221	0.143611	+	0.989634i	$0.454129\pi$
$48$	−3.45081	−0.498081
$49$	1.49673	0.213819
$50$	0	0
$51$	−1.48894	−0.208493
$52$	−9.93453	−1.37767
$53$	0.430807	0.0591759	0.0295879	−	0.999562i	$-0.490580\pi$
$53$	0.430807	0.0591759	0.0295879	+	0.999562i	$0.490580\pi$
$54$	−1.69546	−0.230723
$55$	0	0
$56$	3.77578	0.504560
$57$	4.19246	0.555305
$58$	2.39272	0.314180
$59$	8.44640	1.09963	0.549814	−	0.835287i	$-0.314699\pi$
$59$	8.44640	1.09963	0.549814	+	0.835287i	$0.314699\pi$
$60$	0	0
$61$	3.27665	0.419532	0.209766	−	0.977752i	$-0.432730\pi$
$61$	3.27665	0.419532	0.209766	+	0.977752i	$0.432730\pi$
$62$	−2.31040	−0.293421
$63$	−5.64565	−0.711285
$64$	−5.45925	−0.682406
$65$	0	0
$66$	−2.00930	−0.247328
$67$	13.7065	1.67451	0.837256	−	0.546812i	$-0.184159\pi$
$67$	13.7065	1.67451	0.837256	+	0.546812i	$0.184159\pi$
$68$	−2.72784	−0.330800
$69$	−1.04974	−0.126374
$70$	0	0
$71$	4.02073	0.477173	0.238586	−	0.971121i	$-0.423316\pi$
$71$	4.02073	0.477173	0.238586	+	0.971121i	$0.423316\pi$
$72$	−2.50881	−0.295666
$73$	−3.64203	−0.426267	−0.213134	−	0.977023i	$-0.568367\pi$
$73$	−3.64203	−0.426267	−0.213134	+	0.977023i	$0.568367\pi$
$74$	1.76195	0.204822
$75$	0	0
$76$	7.68088	0.881058
$77$	−17.0542	−1.94350
$78$	1.80610	0.204500
$79$	−8.06707	−0.907616	−0.453808	−	0.891100i	$-0.649935\pi$
$79$	−8.06707	−0.907616	−0.453808	+	0.891100i	$0.649935\pi$
$80$	0	0
$81$	0.561685	0.0624094
$82$	1.48482	0.163971
$83$	−9.94154	−1.09123	−0.545613	−	0.838037i	$-0.683703\pi$
$83$	−9.94154	−1.09123	−0.545613	+	0.838037i	$0.683703\pi$
$84$	5.67777	0.619495
$85$	0	0
$86$	−1.09806	−0.118407
$87$	7.40733	0.794150
$88$	−7.57853	−0.807874
$89$	−7.05272	−0.747586	−0.373793	−	0.927512i	$-0.621943\pi$
$89$	−7.05272	−0.747586	−0.373793	+	0.927512i	$0.621943\pi$
$90$	0	0
$91$	15.3294	1.60696
$92$	−1.92321	−0.200508
$93$	−7.15248	−0.741678
$94$	−0.655845	−0.0676453
$95$	0	0
$96$	3.82062	0.389940
$97$	−3.07235	−0.311950	−0.155975	−	0.987761i	$-0.549852\pi$
$97$	−3.07235	−0.311950	−0.155975	+	0.987761i	$0.549852\pi$
$98$	−0.498517	−0.0503578
$99$	11.3316	1.13887
$100$	0	0
$101$	7.95908	0.791958	0.395979	−	0.918260i	$-0.370405\pi$
$101$	7.95908	0.791958	0.395979	+	0.918260i	$0.370405\pi$
$102$	0.495921	0.0491035
$103$	6.26170	0.616983	0.308492	−	0.951227i	$-0.400176\pi$
$103$	6.26170	0.616983	0.308492	+	0.951227i	$0.400176\pi$
$104$	6.81210	0.667981
$105$	0	0
$106$	−0.143489	−0.0139369
$107$	−4.96053	−0.479553	−0.239776	−	0.970828i	$-0.577074\pi$
$107$	−4.96053	−0.479553	−0.239776	+	0.970828i	$0.577074\pi$
$108$	−9.61608	−0.925308
$109$	−11.4289	−1.09469	−0.547344	−	0.836907i	$-0.684361\pi$
$109$	−11.4289	−1.09469	−0.547344	+	0.836907i	$0.684361\pi$
$110$	0	0
$111$	5.45460	0.517727
$112$	9.75533	0.921792
$113$	14.5891	1.37242	0.686212	−	0.727402i	$-0.259272\pi$
$113$	14.5891	1.37242	0.686212	+	0.727402i	$0.259272\pi$
$114$	−1.39638	−0.130783
$115$	0	0
$116$	13.5708	1.26001
$117$	−10.1856	−0.941662
$118$	−2.81324	−0.258980
$119$	4.20919	0.385856
$120$	0	0
$121$	23.2302	2.11183
$122$	−1.09135	−0.0988065
$123$	4.59667	0.414467
$124$	−13.1038	−1.17676
$125$	0	0
$126$	1.88040	0.167519
$127$	10.6738	0.947146	0.473573	−	0.880754i	$-0.342964\pi$
$127$	10.6738	0.947146	0.473573	+	0.880754i	$0.342964\pi$
$128$	9.22900	0.815736
$129$	−3.39935	−0.299296
$130$	0	0
$131$	5.69054	0.497185	0.248592	−	0.968608i	$-0.420032\pi$
$131$	5.69054	0.497185	0.248592	+	0.968608i	$0.420032\pi$
$132$	−11.3961	−0.991903
$133$	−11.8520	−1.02770
$134$	−4.56521	−0.394374
$135$	0	0
$136$	1.87048	0.160392
$137$	−2.39550	−0.204661	−0.102331	−	0.994750i	$-0.532630\pi$
$137$	−2.39550	−0.204661	−0.102331	+	0.994750i	$0.532630\pi$
$138$	0.349638	0.0297632
$139$	15.8916	1.34791	0.673956	−	0.738772i	$-0.264594\pi$
$139$	15.8916	1.34791	0.673956	+	0.738772i	$0.264594\pi$
$140$	0	0
$141$	−2.03035	−0.170986
$142$	−1.33918	−0.112382
$143$	−30.7684	−2.57298
$144$	−6.48192	−0.540160
$145$	0	0
$146$	1.21305	0.100393
$147$	−1.54330	−0.127289
$148$	9.99320	0.821436
$149$	−23.4096	−1.91779	−0.958893	−	0.283767i	$-0.908416\pi$
$149$	−23.4096	−1.91779	−0.958893	+	0.283767i	$0.908416\pi$
$150$	0	0
$151$	−22.0186	−1.79185	−0.895925	−	0.444206i	$-0.853486\pi$
$151$	−22.0186	−1.79185	−0.895925	+	0.444206i	$0.853486\pi$
$152$	−5.26678	−0.427192
$153$	−2.79679	−0.226107
$154$	5.68023	0.457726
$155$	0	0
$156$	10.2436	0.820143
$157$	15.2432	1.21654	0.608271	−	0.793729i	$-0.291863\pi$
$157$	15.2432	1.21654	0.608271	+	0.793729i	$0.291863\pi$
$158$	2.68690	0.213758
$159$	−0.444209	−0.0352281
$160$	0	0
$161$	2.96760	0.233879
$162$	−0.187080	−0.0146984
$163$	1.04988	0.0822332	0.0411166	−	0.999154i	$-0.486908\pi$
$163$	1.04988	0.0822332	0.0411166	+	0.999154i	$0.486908\pi$
$164$	8.42141	0.657602
$165$	0	0
$166$	3.31123	0.257001
$167$	−10.7693	−0.833353	−0.416676	−	0.909055i	$-0.636805\pi$
$167$	−10.7693	−0.833353	−0.416676	+	0.909055i	$0.636805\pi$
$168$	−3.89324	−0.300370
$169$	14.6567	1.12744
$170$	0	0
$171$	7.87503	0.602219
$172$	−6.22785	−0.474869
$173$	−15.6941	−1.19320	−0.596598	−	0.802540i	$-0.703481\pi$
$173$	−15.6941	−1.19320	−0.596598	+	0.802540i	$0.703481\pi$
$174$	−2.46716	−0.187035
$175$	0	0
$176$	−19.5803	−1.47592
$177$	−8.70916	−0.654621
$178$	2.34905	0.176069
$179$	3.10495	0.232075	0.116038	−	0.993245i	$-0.462981\pi$
$179$	3.10495	0.232075	0.116038	+	0.993245i	$0.462981\pi$
$180$	0	0
$181$	20.2216	1.50306	0.751528	−	0.659701i	$-0.229317\pi$
$181$	20.2216	1.50306	0.751528	+	0.659701i	$0.229317\pi$
$182$	−5.10578	−0.378465
$183$	−3.37858	−0.249752
$184$	1.31874	0.0972189
$185$	0	0
$186$	2.38228	0.174677
$187$	−8.44845	−0.617812
$188$	−3.71974	−0.271290
$189$	14.8381	1.07931
$190$	0	0
$191$	−22.2015	−1.60644	−0.803221	−	0.595681i	$-0.796882\pi$
$191$	−22.2015	−1.60644	−0.803221	+	0.595681i	$0.796882\pi$
$192$	5.62908	0.406244
$193$	−2.27894	−0.164041	−0.0820207	−	0.996631i	$-0.526137\pi$
$193$	−2.27894	−0.164041	−0.0820207	+	0.996631i	$0.526137\pi$
$194$	1.02331	0.0734692
$195$	0	0
$196$	−2.82743	−0.201959
$197$	3.93329	0.280236	0.140118	−	0.990135i	$-0.455252\pi$
$197$	3.93329	0.280236	0.140118	+	0.990135i	$0.455252\pi$
$198$	−3.77423	−0.268222
$199$	−23.7466	−1.68335	−0.841677	−	0.539981i	$-0.818431\pi$
$199$	−23.7466	−1.68335	−0.841677	+	0.539981i	$0.818431\pi$
$200$	0	0
$201$	−14.1329	−0.996855
$202$	−2.65093	−0.186519
$203$	−20.9403	−1.46972
$204$	2.81270	0.196929
$205$	0	0
$206$	−2.08558	−0.145309
$207$	−1.97182	−0.137051
$208$	17.6001	1.22035
$209$	23.7886	1.64549
$210$	0	0
$211$	6.51792	0.448712	0.224356	−	0.974507i	$-0.427972\pi$
$211$	6.51792	0.448712	0.224356	+	0.974507i	$0.427972\pi$
$212$	−0.813822	−0.0558935
$213$	−4.14581	−0.284066
$214$	1.65220	0.112942
$215$	0	0
$216$	6.59374	0.448647
$217$	20.2198	1.37261
$218$	3.80662	0.257817
$219$	3.75533	0.253762
$220$	0	0
$221$	7.59404	0.510831
$222$	−1.81676	−0.121933
$223$	−16.5368	−1.10739	−0.553693	−	0.832721i	$-0.686782\pi$
$223$	−16.5368	−1.10739	−0.553693	+	0.832721i	$0.686782\pi$
$224$	−10.8008	−0.721657
$225$	0	0
$226$	−4.85918	−0.323228
$227$	18.2508	1.21135	0.605674	−	0.795713i	$-0.292904\pi$
$227$	18.2508	1.21135	0.605674	+	0.795713i	$0.292904\pi$
$228$	−7.91983	−0.524504
$229$	11.8502	0.783086	0.391543	−	0.920160i	$-0.371941\pi$
$229$	11.8502	0.783086	0.391543	+	0.920160i	$0.371941\pi$
$230$	0	0
$231$	17.5847	1.15699
$232$	−9.30546	−0.610933
$233$	4.45651	0.291955	0.145978	−	0.989288i	$-0.453367\pi$
$233$	4.45651	0.291955	0.145978	+	0.989288i	$0.453367\pi$
$234$	3.39253	0.221777
$235$	0	0
$236$	−15.9558	−1.03863
$237$	8.31803	0.540314
$238$	−1.40196	−0.0908753
$239$	−17.5740	−1.13676	−0.568382	−	0.822765i	$-0.692431\pi$
$239$	−17.5740	−1.13676	−0.568382	+	0.822765i	$0.692431\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−7.73727	−0.497371
$243$	−15.8503	−1.01680
$244$	−6.18980	−0.396261
$245$	0	0
$246$	−1.53101	−0.0976137
$247$	−21.3828	−1.36056
$248$	8.98530	0.570567
$249$	10.2508	0.649619
$250$	0	0
$251$	−17.0655	−1.07717	−0.538583	−	0.842572i	$-0.681040\pi$
$251$	−17.0655	−1.07717	−0.538583	+	0.842572i	$0.681040\pi$
$252$	10.6650	0.671831
$253$	−5.95639	−0.374475
$254$	−3.55512	−0.223068
$255$	0	0
$256$	7.84459	0.490287
$257$	7.84310	0.489239	0.244620	−	0.969619i	$-0.421337\pi$
$257$	7.84310	0.489239	0.244620	+	0.969619i	$0.421337\pi$
$258$	1.13222	0.0704891
$259$	−15.4200	−0.958151
$260$	0	0
$261$	13.9138	0.861241
$262$	−1.89535	−0.117095
$263$	−30.1496	−1.85911	−0.929553	−	0.368688i	$-0.879807\pi$
$263$	−30.1496	−1.85911	−0.929553	+	0.368688i	$0.879807\pi$
$264$	7.81430	0.480937
$265$	0	0
$266$	3.94753	0.242039
$267$	7.27212	0.445047
$268$	−25.8924	−1.58163
$269$	2.40509	0.146641	0.0733204	−	0.997308i	$-0.476640\pi$
$269$	2.40509	0.146641	0.0733204	+	0.997308i	$0.476640\pi$
$270$	0	0
$271$	−30.9386	−1.87938	−0.939692	−	0.342022i	$-0.888888\pi$
$271$	−30.9386	−1.87938	−0.939692	+	0.342022i	$0.888888\pi$
$272$	4.83269	0.293025
$273$	−15.8063	−0.956643
$274$	0.797869	0.0482010
$275$	0	0
$276$	1.98304	0.119365
$277$	19.3911	1.16510	0.582550	−	0.812795i	$-0.302055\pi$
$277$	19.3911	1.16510	0.582550	+	0.812795i	$0.302055\pi$
$278$	−5.29303	−0.317455
$279$	−13.4351	−0.804336
$280$	0	0
$281$	−26.2129	−1.56373	−0.781864	−	0.623448i	$-0.785731\pi$
$281$	−26.2129	−1.56373	−0.781864	+	0.623448i	$0.785731\pi$
$282$	0.676248	0.0402700
$283$	20.3156	1.20764	0.603819	−	0.797121i	$-0.293645\pi$
$283$	20.3156	1.20764	0.603819	+	0.797121i	$0.293645\pi$
$284$	−7.59542	−0.450705
$285$	0	0
$286$	10.2480	0.605979
$287$	−12.9946	−0.767049
$288$	7.17656	0.422883
$289$	−14.9148	−0.877342
$290$	0	0
$291$	3.16793	0.185707
$292$	6.88003	0.402623
$293$	−0.889038	−0.0519382	−0.0259691	−	0.999663i	$-0.508267\pi$
$293$	−0.889038	−0.0519382	−0.0259691	+	0.999663i	$0.508267\pi$
$294$	0.514026	0.0299786
$295$	0	0
$296$	−6.85233	−0.398284
$297$	−29.7822	−1.72814
$298$	7.79702	0.451669
$299$	5.35401	0.309631
$300$	0	0
$301$	9.60986	0.553903
$302$	7.33374	0.422009
$303$	−8.20669	−0.471462
$304$	−13.6076	−0.780447
$305$	0	0
$306$	0.931528	0.0532519
$307$	−29.1697	−1.66480	−0.832401	−	0.554173i	$-0.813035\pi$
$307$	−29.1697	−1.66480	−0.832401	+	0.554173i	$0.813035\pi$
$308$	32.2164	1.83570
$309$	−6.45650	−0.367297
$310$	0	0
$311$	0.909742	0.0515867	0.0257934	−	0.999667i	$-0.491789\pi$
$311$	0.909742	0.0515867	0.0257934	+	0.999667i	$0.491789\pi$
$312$	−7.02402	−0.397657
$313$	23.8202	1.34640	0.673198	−	0.739463i	$-0.264920\pi$
$313$	23.8202	1.34640	0.673198	+	0.739463i	$0.264920\pi$
$314$	−5.07706	−0.286515
$315$	0	0
$316$	15.2392	0.857272
$317$	3.49764	0.196447	0.0982236	−	0.995164i	$-0.468684\pi$
$317$	3.49764	0.196447	0.0982236	+	0.995164i	$0.468684\pi$
$318$	0.147953	0.00829678
$319$	42.0302	2.35324
$320$	0	0
$321$	5.11485	0.285483
$322$	−0.988417	−0.0550823
$323$	−5.87134	−0.326690
$324$	−1.06106	−0.0589477
$325$	0	0
$326$	−0.349685	−0.0193672
$327$	11.7844	0.651681
$328$	−5.77456	−0.318847
$329$	5.73973	0.316442
$330$	0	0
$331$	−2.41133	−0.132539	−0.0662693	−	0.997802i	$-0.521110\pi$
$331$	−2.41133	−0.132539	−0.0662693	+	0.997802i	$0.521110\pi$
$332$	18.7802	1.03070
$333$	10.2458	0.561466
$334$	3.58693	0.196268
$335$	0	0
$336$	−10.0588	−0.548753
$337$	−18.3801	−1.00123	−0.500615	−	0.865670i	$-0.666893\pi$
$337$	−18.3801	−1.00123	−0.500615	+	0.865670i	$0.666893\pi$
$338$	−4.88172	−0.265530
$339$	−15.0429	−0.817019
$340$	0	0
$341$	−40.5842	−2.19775
$342$	−2.62294	−0.141832
$343$	−16.0416	−0.866163
$344$	4.27043	0.230246
$345$	0	0
$346$	5.22722	0.281017
$347$	−22.1659	−1.18993	−0.594963	−	0.803753i	$-0.702833\pi$
$347$	−22.1659	−1.18993	−0.594963	+	0.803753i	$0.702833\pi$
$348$	−13.9929	−0.750100
$349$	−8.81153	−0.471670	−0.235835	−	0.971793i	$-0.575783\pi$
$349$	−8.81153	−0.471670	−0.235835	+	0.971793i	$0.575783\pi$
$350$	0	0
$351$	26.7702	1.42889
$352$	21.6787	1.15548
$353$	20.1876	1.07448	0.537238	−	0.843431i	$-0.319468\pi$
$353$	20.1876	1.07448	0.537238	+	0.843431i	$0.319468\pi$
$354$	2.90076	0.154174
$355$	0	0
$356$	13.3230	0.706119
$357$	−4.34014	−0.229704
$358$	−1.03417	−0.0546574
$359$	21.3173	1.12508	0.562541	−	0.826769i	$-0.309824\pi$
$359$	21.3173	1.12508	0.562541	+	0.826769i	$0.309824\pi$
$360$	0	0
$361$	−2.46787	−0.129888
$362$	−6.73519	−0.353994
$363$	−23.9529	−1.25720
$364$	−28.9583	−1.51783
$365$	0	0
$366$	1.12530	0.0588206
$367$	9.10147	0.475093	0.237546	−	0.971376i	$-0.423657\pi$
$367$	9.10147	0.475093	0.237546	+	0.971376i	$0.423657\pi$
$368$	3.40718	0.177611
$369$	8.63427	0.449482
$370$	0	0
$371$	1.25577	0.0651961
$372$	13.5115	0.700538
$373$	−6.33715	−0.328125	−0.164063	−	0.986450i	$-0.552460\pi$
$373$	−6.33715	−0.328125	−0.164063	+	0.986450i	$0.552460\pi$
$374$	2.81393	0.145505
$375$	0	0
$376$	2.55062	0.131538
$377$	−37.7796	−1.94575
$378$	−4.94212	−0.254195
$379$	−20.7733	−1.06705	−0.533526	−	0.845784i	$-0.679133\pi$
$379$	−20.7733	−1.06705	−0.533526	+	0.845784i	$0.679133\pi$
$380$	0	0
$381$	−11.0059	−0.563847
$382$	7.39464	0.378343
$383$	7.29626	0.372822	0.186411	−	0.982472i	$-0.440314\pi$
$383$	7.29626	0.372822	0.186411	+	0.982472i	$0.440314\pi$
$384$	−9.51611	−0.485617
$385$	0	0
$386$	0.759045	0.0386344
$387$	−6.38527	−0.324581
$388$	5.80387	0.294647
$389$	−0.402390	−0.0204020	−0.0102010	−	0.999948i	$-0.503247\pi$
$389$	−0.402390	−0.0204020	−0.0102010	+	0.999948i	$0.503247\pi$
$390$	0	0
$391$	1.47012	0.0743469
$392$	1.93876	0.0979224
$393$	−5.86757	−0.295980
$394$	−1.31006	−0.0660000
$395$	0	0
$396$	−21.4062	−1.07570
$397$	−32.2805	−1.62011	−0.810057	−	0.586351i	$-0.800564\pi$
$397$	−32.2805	−1.62011	−0.810057	+	0.586351i	$0.800564\pi$
$398$	7.90929	0.396457
$399$	12.2207	0.611799
$400$	0	0
$401$	−25.2445	−1.26065	−0.630324	−	0.776332i	$-0.717078\pi$
$401$	−25.2445	−1.26065	−0.630324	+	0.776332i	$0.717078\pi$
$402$	4.70723	0.234775
$403$	36.4798	1.81719
$404$	−15.0352	−0.748030
$405$	0	0
$406$	6.97459	0.346143
$407$	30.9501	1.53414
$408$	−1.92867	−0.0954834
$409$	15.2153	0.752348	0.376174	−	0.926549i	$-0.377239\pi$
$409$	15.2153	0.752348	0.376174	+	0.926549i	$0.377239\pi$
$410$	0	0
$411$	2.47002	0.121837
$412$	−11.8287	−0.582761
$413$	24.6205	1.21150
$414$	0.656753	0.0322777
$415$	0	0
$416$	−19.4863	−0.955394
$417$	−16.3860	−0.802427
$418$	−7.92327	−0.387540
$419$	−24.2883	−1.18656	−0.593280	−	0.804996i	$-0.702167\pi$
$419$	−24.2883	−1.18656	−0.593280	+	0.804996i	$0.702167\pi$
$420$	0	0
$421$	1.24005	0.0604366	0.0302183	−	0.999543i	$-0.490380\pi$
$421$	1.24005	0.0604366	0.0302183	+	0.999543i	$0.490380\pi$
$422$	−2.17092	−0.105679
$423$	−3.81376	−0.185431
$424$	0.558037	0.0271007
$425$	0	0
$426$	1.38085	0.0669022
$427$	9.55115	0.462213
$428$	9.37076	0.452953
$429$	31.7256	1.53173
$430$	0	0
$431$	−25.7031	−1.23807	−0.619036	−	0.785362i	$-0.712477\pi$
$431$	−25.7031	−1.23807	−0.619036	+	0.785362i	$0.712477\pi$
$432$	17.0360	0.819644
$433$	−21.4579	−1.03120	−0.515601	−	0.856829i	$-0.672431\pi$
$433$	−21.4579	−1.03120	−0.515601	+	0.856829i	$0.672431\pi$
$434$	−6.73462	−0.323272
$435$	0	0
$436$	21.5899	1.03397
$437$	−4.13946	−0.198017
$438$	−1.25079	−0.0597649
$439$	−17.7057	−0.845048	−0.422524	−	0.906352i	$-0.638856\pi$
$439$	−17.7057	−0.845048	−0.422524	+	0.906352i	$0.638856\pi$
$440$	0	0
$441$	−2.89889	−0.138043
$442$	−2.52935	−0.120309
$443$	−14.5582	−0.691682	−0.345841	−	0.938293i	$-0.612406\pi$
$443$	−14.5582	−0.691682	−0.345841	+	0.938293i	$0.612406\pi$
$444$	−10.3041	−0.489010
$445$	0	0
$446$	5.50791	0.260807
$447$	24.1378	1.14168
$448$	−15.9132	−0.751830
$449$	16.8552	0.795446	0.397723	−	0.917505i	$-0.369800\pi$
$449$	16.8552	0.795446	0.397723	+	0.917505i	$0.369800\pi$
$450$	0	0
$451$	26.0821	1.22816
$452$	−27.5597	−1.29630
$453$	22.7036	1.06671
$454$	−6.07879	−0.285292
$455$	0	0
$456$	5.43063	0.254312
$457$	−21.9145	−1.02512	−0.512558	−	0.858653i	$-0.671302\pi$
$457$	−21.9145	−1.02512	−0.512558	+	0.858653i	$0.671302\pi$
$458$	−3.94696	−0.184429
$459$	7.35062	0.343098
$460$	0	0
$461$	6.72445	0.313189	0.156594	−	0.987663i	$-0.449948\pi$
$461$	6.72445	0.313189	0.156594	+	0.987663i	$0.449948\pi$
$462$	−5.85694	−0.272490
$463$	−26.5995	−1.23618	−0.618092	−	0.786106i	$-0.712094\pi$
$463$	−26.5995	−1.23618	−0.618092	+	0.786106i	$0.712094\pi$
$464$	−24.0421	−1.11613
$465$	0	0
$466$	−1.48433	−0.0687602
$467$	−7.75161	−0.358702	−0.179351	−	0.983785i	$-0.557400\pi$
$467$	−7.75161	−0.358702	−0.179351	+	0.983785i	$0.557400\pi$
$468$	19.2413	0.889431
$469$	39.9532	1.84487
$470$	0	0
$471$	−15.7174	−0.724221
$472$	10.9409	0.503595
$473$	−19.2884	−0.886881
$474$	−2.77049	−0.127253
$475$	0	0
$476$	−7.95143	−0.364453
$477$	−0.834393	−0.0382042
$478$	5.85336	0.267726
$479$	−40.0472	−1.82980	−0.914901	−	0.403679i	$-0.867731\pi$
$479$	−40.0472	−1.82980	−0.914901	+	0.403679i	$0.867731\pi$
$480$	0	0
$481$	−27.8201	−1.26849
$482$	−0.333070	−0.0151709
$483$	−3.05992	−0.139231
$484$	−43.8833	−1.99470
$485$	0	0
$486$	5.27927	0.239473
$487$	−10.4935	−0.475504	−0.237752	−	0.971326i	$-0.576411\pi$
$487$	−10.4935	−0.475504	−0.237752	+	0.971326i	$0.576411\pi$
$488$	4.24434	0.192132
$489$	−1.08255	−0.0489544
$490$	0	0
$491$	29.0414	1.31062	0.655311	−	0.755359i	$-0.272538\pi$
$491$	29.0414	1.31062	0.655311	+	0.755359i	$0.272538\pi$
$492$	−8.68340	−0.391478
$493$	−10.3736	−0.467204
$494$	7.12197	0.320433
$495$	0	0
$496$	23.2150	1.04238
$497$	11.7201	0.525718
$498$	−3.41424	−0.152996
$499$	−9.82170	−0.439679	−0.219840	−	0.975536i	$-0.570553\pi$
$499$	−9.82170	−0.439679	−0.219840	+	0.975536i	$0.570553\pi$
$500$	0	0
$501$	11.1043	0.496104
$502$	5.68402	0.253690
$503$	−32.6913	−1.45763	−0.728817	−	0.684709i	$-0.759929\pi$
$503$	−32.6913	−1.45763	−0.728817	+	0.684709i	$0.759929\pi$
$504$	−7.31298	−0.325746
$505$	0	0
$506$	1.98390	0.0881949
$507$	−15.1127	−0.671179
$508$	−20.1635	−0.894610
$509$	−16.3559	−0.724962	−0.362481	−	0.931991i	$-0.618070\pi$
$509$	−16.3559	−0.724962	−0.362481	+	0.931991i	$0.618070\pi$
$510$	0	0
$511$	−10.6162	−0.469633
$512$	−21.0708	−0.931206
$513$	−20.6974	−0.913813
$514$	−2.61230	−0.115224
$515$	0	0
$516$	6.42159	0.282695
$517$	−11.5205	−0.506670
$518$	5.13593	0.225660
$519$	16.1823	0.710324
$520$	0	0
$521$	−10.8661	−0.476052	−0.238026	−	0.971259i	$-0.576500\pi$
$521$	−10.8661	−0.476052	−0.238026	+	0.971259i	$0.576500\pi$
$522$	−4.63426	−0.202836
$523$	−30.9516	−1.35342	−0.676710	−	0.736250i	$-0.736595\pi$
$523$	−30.9516	−1.35342	−0.676710	+	0.736250i	$0.736595\pi$
$524$	−10.7498	−0.469607
$525$	0	0
$526$	10.0419	0.437849
$527$	10.0167	0.436334
$528$	20.1895	0.878635
$529$	−21.9635	−0.954936
$530$	0	0
$531$	−16.3591	−0.709924
$532$	22.3891	0.970692
$533$	−23.4444	−1.01549
$534$	−2.42213	−0.104816
$535$	0	0
$536$	17.7544	0.766873
$537$	−3.20155	−0.138157
$538$	−0.801063	−0.0345363
$539$	−8.75687	−0.377185
$540$	0	0
$541$	31.3353	1.34721	0.673606	−	0.739091i	$-0.264745\pi$
$541$	31.3353	1.34721	0.673606	+	0.739091i	$0.264745\pi$
$542$	10.3047	0.442625
$543$	−20.8506	−0.894786
$544$	−5.35058	−0.229404
$545$	0	0
$546$	5.26462	0.225305
$547$	37.6463	1.60964	0.804821	−	0.593518i	$-0.202261\pi$
$547$	37.6463	1.60964	0.804821	+	0.593518i	$0.202261\pi$
$548$	4.52525	0.193309
$549$	−6.34626	−0.270852
$550$	0	0
$551$	29.2093	1.24436
$552$	−1.35977	−0.0578755
$553$	−23.5148	−0.999952
$554$	−6.45860	−0.274400
$555$	0	0
$556$	−30.0203	−1.27315
$557$	23.6732	1.00307	0.501534	−	0.865138i	$-0.332769\pi$
$557$	23.6732	1.00307	0.501534	+	0.865138i	$0.332769\pi$
$558$	4.47482	0.189434
$559$	17.3377	0.733307
$560$	0	0
$561$	8.71128	0.367791
$562$	8.73072	0.368283
$563$	−17.4383	−0.734935	−0.367468	−	0.930036i	$-0.619775\pi$
$563$	−17.4383	−0.734935	−0.367468	+	0.930036i	$0.619775\pi$
$564$	3.83546	0.161502
$565$	0	0
$566$	−6.76652	−0.284418
$567$	1.63726	0.0687586
$568$	5.20817	0.218530
$569$	−1.59178	−0.0667309	−0.0333654	−	0.999443i	$-0.510623\pi$
$569$	−1.59178	−0.0667309	−0.0333654	+	0.999443i	$0.510623\pi$
$570$	0	0
$571$	8.95835	0.374895	0.187448	−	0.982275i	$-0.439978\pi$
$571$	8.95835	0.374895	0.187448	+	0.982275i	$0.439978\pi$
$572$	58.1235	2.43027
$573$	22.8921	0.956333
$574$	4.32812	0.180652
$575$	0	0
$576$	10.5735	0.440564
$577$	−35.6551	−1.48434	−0.742171	−	0.670211i	$-0.766204\pi$
$577$	−35.6551	−1.48434	−0.742171	+	0.670211i	$0.766204\pi$
$578$	4.96768	0.206628
$579$	2.34983	0.0976557
$580$	0	0
$581$	−28.9788	−1.20224
$582$	−1.05514	−0.0437371
$583$	−2.52050	−0.104389
$584$	−4.71763	−0.195217
$585$	0	0
$586$	0.296112	0.0122323
$587$	−44.6462	−1.84275	−0.921374	−	0.388678i	$-0.872932\pi$
$587$	−44.6462	−1.84275	−0.921374	+	0.388678i	$0.872932\pi$
$588$	2.91539	0.120228
$589$	−28.2044	−1.16214
$590$	0	0
$591$	−4.05566	−0.166827
$592$	−17.7041	−0.727634
$593$	−15.0888	−0.619622	−0.309811	−	0.950798i	$-0.600266\pi$
$593$	−15.0888	−0.619622	−0.309811	+	0.950798i	$0.600266\pi$
$594$	9.91954	0.407004
$595$	0	0
$596$	44.2222	1.81141
$597$	24.4854	1.00212
$598$	−1.78326	−0.0729230
$599$	5.24328	0.214234	0.107117	−	0.994246i	$-0.465838\pi$
$599$	5.24328	0.214234	0.107117	+	0.994246i	$0.465838\pi$
$600$	0	0
$601$	−6.89463	−0.281238	−0.140619	−	0.990064i	$-0.544909\pi$
$601$	−6.89463	−0.281238	−0.140619	+	0.990064i	$0.544909\pi$
$602$	−3.20076	−0.130453
$603$	−26.5469	−1.08107
$604$	41.5946	1.69246
$605$	0	0
$606$	2.73340	0.111037
$607$	−34.0874	−1.38356	−0.691782	−	0.722106i	$-0.743174\pi$
$607$	−34.0874	−1.38356	−0.691782	+	0.722106i	$0.743174\pi$
$608$	15.0658	0.611000
$609$	21.5918	0.874942
$610$	0	0
$611$	10.3554	0.418934
$612$	5.28332	0.213566
$613$	46.7467	1.88808	0.944040	−	0.329831i	$-0.106992\pi$
$613$	46.7467	1.88808	0.944040	+	0.329831i	$0.106992\pi$
$614$	9.71555	0.392088
$615$	0	0
$616$	−22.0908	−0.890063
$617$	−3.53207	−0.142196	−0.0710979	−	0.997469i	$-0.522650\pi$
$617$	−3.53207	−0.142196	−0.0710979	+	0.997469i	$0.522650\pi$
$618$	2.15046	0.0865044
$619$	−5.50908	−0.221428	−0.110714	−	0.993852i	$-0.535314\pi$
$619$	−5.50908	−0.221428	−0.110714	+	0.993852i	$0.535314\pi$
$620$	0	0
$621$	5.18239	0.207962
$622$	−0.303008	−0.0121495
$623$	−20.5581	−0.823642
$624$	−18.1477	−0.726489
$625$	0	0
$626$	−7.93378	−0.317098
$627$	−24.5287	−0.979580
$628$	−28.7954	−1.14906
$629$	−7.63889	−0.304583
$630$	0	0
$631$	8.40113	0.334444	0.167222	−	0.985919i	$-0.446520\pi$
$631$	8.40113	0.334444	0.167222	+	0.985919i	$0.446520\pi$
$632$	−10.4495	−0.415660
$633$	−6.72068	−0.267123
$634$	−1.16496	−0.0462664
$635$	0	0
$636$	0.839140	0.0332741
$637$	7.87127	0.311871
$638$	−13.9990	−0.554226
$639$	−7.78740	−0.308065
$640$	0	0
$641$	28.6572	1.13189	0.565945	−	0.824443i	$-0.308511\pi$
$641$	28.6572	1.13189	0.565945	+	0.824443i	$0.308511\pi$
$642$	−1.70360	−0.0672359
$643$	−12.2879	−0.484588	−0.242294	−	0.970203i	$-0.577900\pi$
$643$	−12.2879	−0.484588	−0.242294	+	0.970203i	$0.577900\pi$
$644$	−5.60598	−0.220907
$645$	0	0
$646$	1.95557	0.0769407
$647$	−28.5820	−1.12367	−0.561837	−	0.827248i	$-0.689905\pi$
$647$	−28.5820	−1.12367	−0.561837	+	0.827248i	$0.689905\pi$
$648$	0.727568	0.0285816
$649$	−49.4170	−1.93979
$650$	0	0
$651$	−20.8489	−0.817132
$652$	−1.98330	−0.0776719
$653$	37.3291	1.46080	0.730400	−	0.683019i	$-0.239334\pi$
$653$	37.3291	1.46080	0.730400	+	0.683019i	$0.239334\pi$
$654$	−3.92504	−0.153481
$655$	0	0
$656$	−14.9195	−0.582508
$657$	7.05393	0.275200
$658$	−1.91173	−0.0745271
$659$	26.9165	1.04852	0.524258	−	0.851559i	$-0.324343\pi$
$659$	26.9165	1.04852	0.524258	+	0.851559i	$0.324343\pi$
$660$	0	0
$661$	5.47194	0.212834	0.106417	−	0.994322i	$-0.466062\pi$
$661$	5.47194	0.212834	0.106417	+	0.994322i	$0.466062\pi$
$662$	0.803141	0.0312150
$663$	−7.83029	−0.304103
$664$	−12.8776	−0.499747
$665$	0	0
$666$	−3.41257	−0.132234
$667$	−7.31368	−0.283187
$668$	20.3439	0.787128
$669$	17.0512	0.659239
$670$	0	0
$671$	−19.1705	−0.740071
$672$	11.1368	0.429610
$673$	23.1664	0.892997	0.446499	−	0.894784i	$-0.352671\pi$
$673$	23.1664	0.892997	0.446499	+	0.894784i	$0.352671\pi$
$674$	6.12187	0.235806
$675$	0	0
$676$	−27.6875	−1.06490
$677$	25.7492	0.989620	0.494810	−	0.869001i	$-0.335238\pi$
$677$	25.7492	0.989620	0.494810	+	0.869001i	$0.335238\pi$
$678$	5.01035	0.192421
$679$	−8.95565	−0.343686
$680$	0	0
$681$	−18.8186	−0.721129
$682$	13.5174	0.517607
$683$	16.8086	0.643163	0.321581	−	0.946882i	$-0.395786\pi$
$683$	16.8086	0.643163	0.321581	+	0.946882i	$0.395786\pi$
$684$	−14.8764	−0.568815
$685$	0	0
$686$	5.34296	0.203995
$687$	−12.2189	−0.466180
$688$	11.0333	0.420642
$689$	2.26560	0.0863125
$690$	0	0
$691$	−27.0705	−1.02981	−0.514905	−	0.857247i	$-0.672173\pi$
$691$	−27.0705	−1.02981	−0.514905	+	0.857247i	$0.672173\pi$
$692$	29.6471	1.12701
$693$	33.0307	1.25473
$694$	7.38278	0.280247
$695$	0	0
$696$	9.59495	0.363695
$697$	−6.43740	−0.243834
$698$	2.93486	0.111086
$699$	−4.59515	−0.173804
$700$	0	0
$701$	−5.70437	−0.215451	−0.107726	−	0.994181i	$-0.534357\pi$
$701$	−5.70437	−0.215451	−0.107726	+	0.994181i	$0.534357\pi$
$702$	−8.91636	−0.336526
$703$	21.5091	0.811231
$704$	31.9402	1.20379
$705$	0	0
$706$	−6.72387	−0.253056
$707$	23.2001	0.872528
$708$	16.4522	0.618310
$709$	−47.1794	−1.77186	−0.885929	−	0.463821i	$-0.846478\pi$
$709$	−47.1794	−1.77186	−0.885929	+	0.463821i	$0.846478\pi$
$710$	0	0
$711$	15.6244	0.585961
$712$	−9.13560	−0.342371
$713$	7.06205	0.264476
$714$	1.44557	0.0540991
$715$	0	0
$716$	−5.86545	−0.219202
$717$	18.1207	0.676729
$718$	−7.10014	−0.264975
$719$	8.68947	0.324063	0.162031	−	0.986786i	$-0.448195\pi$
$719$	8.68947	0.324063	0.162031	+	0.986786i	$0.448195\pi$
$720$	0	0
$721$	18.2523	0.679752
$722$	0.821973	0.0305907
$723$	−1.03111	−0.0383474
$724$	−38.1998	−1.41968
$725$	0	0
$726$	7.97798	0.296091
$727$	−28.3067	−1.04984	−0.524919	−	0.851152i	$-0.675905\pi$
$727$	−28.3067	−1.04984	−0.524919	+	0.851152i	$0.675905\pi$
$728$	19.8567	0.735938
$729$	14.6584	0.542903
$730$	0	0
$731$	4.76062	0.176078
$732$	6.38236	0.235899
$733$	35.7145	1.31914	0.659572	−	0.751641i	$-0.270737\pi$
$733$	35.7145	1.31914	0.659572	+	0.751641i	$0.270737\pi$
$734$	−3.03143	−0.111892
$735$	0	0
$736$	−3.77231	−0.139049
$737$	−80.1918	−2.95390
$738$	−2.87582	−0.105860
$739$	23.3411	0.858617	0.429309	−	0.903158i	$-0.358757\pi$
$739$	23.3411	0.858617	0.429309	+	0.903158i	$0.358757\pi$
$740$	0	0
$741$	22.0480	0.809954
$742$	−0.418258	−0.0153547
$743$	48.4819	1.77863	0.889313	−	0.457298i	$-0.151183\pi$
$743$	48.4819	1.77863	0.889313	+	0.457298i	$0.151183\pi$
$744$	−9.26483	−0.339665
$745$	0	0
$746$	2.11072	0.0772788
$747$	19.2549	0.704500
$748$	15.9597	0.583543
$749$	−14.4595	−0.528340
$750$	0	0
$751$	−27.2145	−0.993071	−0.496535	−	0.868016i	$-0.665395\pi$
$751$	−27.2145	−0.993071	−0.496535	+	0.868016i	$0.665395\pi$
$752$	6.58994	0.240311
$753$	17.5964	0.641250
$754$	12.5833	0.458255
$755$	0	0
$756$	−28.0301	−1.01944
$757$	34.2995	1.24664	0.623318	−	0.781968i	$-0.285784\pi$
$757$	34.2995	1.24664	0.623318	+	0.781968i	$0.285784\pi$
$758$	6.91896	0.251308
$759$	6.14169	0.222929
$760$	0	0
$761$	−36.8695	−1.33652	−0.668260	−	0.743928i	$-0.732961\pi$
$761$	−36.8695	−1.33652	−0.668260	+	0.743928i	$0.732961\pi$
$762$	3.66572	0.132795
$763$	−33.3142	−1.20606
$764$	41.9400	1.51734
$765$	0	0
$766$	−2.43017	−0.0878055
$767$	44.4193	1.60389
$768$	−8.08863	−0.291873
$769$	38.5560	1.39036	0.695182	−	0.718834i	$-0.255324\pi$
$769$	38.5560	1.39036	0.695182	+	0.718834i	$0.255324\pi$
$770$	0	0
$771$	−8.08710	−0.291250
$772$	4.30506	0.154942
$773$	−31.5788	−1.13581	−0.567905	−	0.823094i	$-0.692246\pi$
$773$	−31.5788	−1.13581	−0.567905	+	0.823094i	$0.692246\pi$
$774$	2.12674	0.0764441
$775$	0	0
$776$	−3.97971	−0.142863
$777$	15.8997	0.570398
$778$	0.134024	0.00480499
$779$	18.1260	0.649432
$780$	0	0
$781$	−23.5239	−0.841752
$782$	−0.489651	−0.0175099
$783$	−36.5686	−1.30686
$784$	5.00911	0.178897
$785$	0	0
$786$	1.95431	0.0697080
$787$	9.97778	0.355669	0.177835	−	0.984060i	$-0.443091\pi$
$787$	9.97778	0.355669	0.177835	+	0.984060i	$0.443091\pi$
$788$	−7.43024	−0.264691
$789$	31.0876	1.10675
$790$	0	0
$791$	42.5259	1.51205
$792$	14.6782	0.521567
$793$	17.2318	0.611919
$794$	10.7517	0.381563
$795$	0	0
$796$	44.8589	1.58998
$797$	34.8558	1.23466	0.617329	−	0.786705i	$-0.288215\pi$
$797$	34.8558	1.23466	0.617329	+	0.786705i	$0.288215\pi$
$798$	−4.07034	−0.144088
$799$	2.84340	0.100592
$800$	0	0
$801$	13.6598	0.482645
$802$	8.40817	0.296903
$803$	21.3083	0.751952
$804$	26.6979	0.941562
$805$	0	0
$806$	−12.1503	−0.427977
$807$	−2.47991	−0.0872970
$808$	10.3096	0.362692
$809$	51.0838	1.79601	0.898006	−	0.439984i	$-0.145016\pi$
$809$	51.0838	1.79601	0.898006	+	0.439984i	$0.145016\pi$
$810$	0	0
$811$	−19.5274	−0.685699	−0.342849	−	0.939390i	$-0.611392\pi$
$811$	−19.5274	−0.685699	−0.342849	+	0.939390i	$0.611392\pi$
$812$	39.5576	1.38820
$813$	31.9011	1.11882
$814$	−10.3086	−0.361315
$815$	0	0
$816$	−4.98303	−0.174441
$817$	−13.4047	−0.468970
$818$	−5.06776	−0.177190
$819$	−29.6903	−1.03746
$820$	0	0
$821$	−25.3733	−0.885536	−0.442768	−	0.896636i	$-0.646003\pi$
$821$	−25.3733	−0.885536	−0.442768	+	0.896636i	$0.646003\pi$
$822$	−0.822690	−0.0286946
$823$	22.3168	0.777913	0.388957	−	0.921256i	$-0.372836\pi$
$823$	22.3168	0.777913	0.388957	+	0.921256i	$0.372836\pi$
$824$	8.11097	0.282559
$825$	0	0
$826$	−8.20036	−0.285327
$827$	4.78461	0.166377	0.0831887	−	0.996534i	$-0.473490\pi$
$827$	4.78461	0.166377	0.0831887	+	0.996534i	$0.473490\pi$
$828$	3.72489	0.129449
$829$	7.61397	0.264444	0.132222	−	0.991220i	$-0.457789\pi$
$829$	7.61397	0.264444	0.132222	+	0.991220i	$0.457789\pi$
$830$	0	0
$831$	−19.9944	−0.693597
$832$	−28.7100	−0.995340
$833$	2.16131	0.0748850
$834$	5.45769	0.188984
$835$	0	0
$836$	−44.9382	−1.55422
$837$	35.3105	1.22051
$838$	8.08969	0.279454
$839$	33.0206	1.14000	0.569999	−	0.821646i	$-0.306944\pi$
$839$	33.0206	1.14000	0.569999	+	0.821646i	$0.306944\pi$
$840$	0	0
$841$	22.6077	0.779575
$842$	−0.413025	−0.0142338
$843$	27.0283	0.930906
$844$	−12.3128	−0.423823
$845$	0	0
$846$	1.27025	0.0436721
$847$	67.7140	2.32668
$848$	1.44178	0.0495109
$849$	−20.9476	−0.718921
$850$	0	0
$851$	−5.38563	−0.184617
$852$	7.83171	0.268310
$853$	−26.1191	−0.894301	−0.447151	−	0.894459i	$-0.647561\pi$
$853$	−26.1191	−0.894301	−0.447151	+	0.894459i	$0.647561\pi$
$854$	−3.18120	−0.108859
$855$	0	0
$856$	−6.42553	−0.219620
$857$	−12.0143	−0.410400	−0.205200	−	0.978720i	$-0.565785\pi$
$857$	−12.0143	−0.410400	−0.205200	+	0.978720i	$0.565785\pi$
$858$	−10.5668	−0.360746
$859$	−16.9150	−0.577132	−0.288566	−	0.957460i	$-0.593179\pi$
$859$	−16.9150	−0.577132	−0.288566	+	0.957460i	$0.593179\pi$
$860$	0	0
$861$	13.3989	0.456633
$862$	8.56092	0.291586
$863$	−15.6125	−0.531456	−0.265728	−	0.964048i	$-0.585612\pi$
$863$	−15.6125	−0.531456	−0.265728	+	0.964048i	$0.585612\pi$
$864$	−18.8617	−0.641687
$865$	0	0
$866$	7.14699	0.242865
$867$	15.3788	0.522292
$868$	−38.1966	−1.29648
$869$	47.1976	1.60107
$870$	0	0
$871$	72.0818	2.44240
$872$	−14.8042	−0.501333
$873$	5.95057	0.201396
$874$	1.37873	0.0466362
$875$	0	0
$876$	−7.09406	−0.239686
$877$	−10.0352	−0.338863	−0.169432	−	0.985542i	$-0.554193\pi$
$877$	−10.0352	−0.338863	−0.169432	+	0.985542i	$0.554193\pi$
$878$	5.89724	0.199022
$879$	0.916696	0.0309194
$880$	0	0
$881$	−30.4908	−1.02726	−0.513630	−	0.858012i	$-0.671700\pi$
$881$	−30.4908	−1.02726	−0.513630	+	0.858012i	$0.671700\pi$
$882$	0.965534	0.0325112
$883$	45.8663	1.54352	0.771762	−	0.635912i	$-0.219376\pi$
$883$	45.8663	1.54352	0.771762	+	0.635912i	$0.219376\pi$
$884$	−14.3456	−0.482496
$885$	0	0
$886$	4.84890	0.162902
$887$	−19.4561	−0.653272	−0.326636	−	0.945150i	$-0.605915\pi$
$887$	−19.4561	−0.653272	−0.326636	+	0.945150i	$0.605915\pi$
$888$	7.06551	0.237103
$889$	31.1132	1.04350
$890$	0	0
$891$	−3.28622	−0.110093
$892$	31.2391	1.04596
$893$	−8.00627	−0.267920
$894$	−8.03959	−0.268884
$895$	0	0
$896$	26.9018	0.898725
$897$	−5.52057	−0.184327
$898$	−5.61396	−0.187340
$899$	−49.8321	−1.66199
$900$	0	0
$901$	0.622093	0.0207249
$902$	−8.68717	−0.289251
$903$	−9.90882	−0.329745
$904$	18.8977	0.628527
$905$	0	0
$906$	−7.56189	−0.251227
$907$	18.5957	0.617460	0.308730	−	0.951150i	$-0.400096\pi$
$907$	18.5957	0.617460	0.308730	+	0.951150i	$0.400096\pi$
$908$	−34.4769	−1.14416
$909$	−15.4153	−0.511292
$910$	0	0
$911$	60.0890	1.99084	0.995419	−	0.0956059i	$-0.0304788\pi$
$911$	60.0890	1.99084	0.995419	+	0.0956059i	$0.0304788\pi$
$912$	14.0309	0.464609
$913$	58.1645	1.92496
$914$	7.29905	0.241431
$915$	0	0
$916$	−22.3859	−0.739650
$917$	16.5874	0.547765
$918$	−2.44827	−0.0808050
$919$	54.4741	1.79693	0.898467	−	0.439040i	$-0.144682\pi$
$919$	54.4741	1.79693	0.898467	+	0.439040i	$0.144682\pi$
$920$	0	0
$921$	30.0772	0.991076
$922$	−2.23971	−0.0737610
$923$	21.1449	0.695992
$924$	−33.2187	−1.09281
$925$	0	0
$926$	8.85950	0.291141
$927$	−12.1277	−0.398327
$928$	26.6186	0.873799
$929$	16.3989	0.538030	0.269015	−	0.963136i	$-0.413302\pi$
$929$	16.3989	0.538030	0.269015	+	0.963136i	$0.413302\pi$
$930$	0	0
$931$	−6.08568	−0.199450
$932$	−8.41863	−0.275761
$933$	−0.938043	−0.0307102
$934$	2.58183	0.0844800
$935$	0	0
$936$	−13.1938	−0.431252
$937$	37.0074	1.20898	0.604490	−	0.796613i	$-0.293377\pi$
$937$	37.0074	1.20898	0.604490	+	0.796613i	$0.293377\pi$
$938$	−13.3072	−0.434496
$939$	−24.5612	−0.801524
$940$	0	0
$941$	−21.6164	−0.704674	−0.352337	−	0.935873i	$-0.614613\pi$
$941$	−21.6164	−0.704674	−0.352337	+	0.935873i	$0.614613\pi$
$942$	5.23501	0.170566
$943$	−4.53855	−0.147795
$944$	28.2675	0.920029
$945$	0	0
$946$	6.42438	0.208875
$947$	−42.1072	−1.36830	−0.684151	−	0.729341i	$-0.739827\pi$
$947$	−42.1072	−1.36830	−0.684151	+	0.729341i	$0.739827\pi$
$948$	−15.7133	−0.510344
$949$	−19.1533	−0.621743
$950$	0	0
$951$	−3.60645	−0.116947
$952$	5.45229	0.176710
$953$	46.7030	1.51286	0.756429	−	0.654075i	$-0.226942\pi$
$953$	46.7030	1.51286	0.756429	+	0.654075i	$0.226942\pi$
$954$	0.277911	0.00899770
$955$	0	0
$956$	33.1983	1.07371
$957$	−43.3378	−1.40091
$958$	13.3385	0.430948
$959$	−6.98268	−0.225482
$960$	0	0
$961$	17.1176	0.552180
$962$	9.26603	0.298749
$963$	9.60762	0.309601
$964$	−1.88906	−0.0608427
$965$	0	0
$966$	1.01917	0.0327911
$967$	6.24268	0.200751	0.100376	−	0.994950i	$-0.467996\pi$
$967$	6.24268	0.200751	0.100376	+	0.994950i	$0.467996\pi$
$968$	30.0908	0.967154
$969$	6.05399	0.194482
$970$	0	0
$971$	30.7115	0.985579	0.492789	−	0.870149i	$-0.335977\pi$
$971$	30.7115	0.985579	0.492789	+	0.870149i	$0.335977\pi$
$972$	29.9423	0.960400
$973$	46.3228	1.48504
$974$	3.49506	0.111989
$975$	0	0
$976$	10.9659	0.351011
$977$	0.0525151	0.00168011	0.000840054	−	1.00000i	$-0.499733\pi$
$977$	0.0525151	0.00168011	0.000840054		1.00000i	$0.499733\pi$
$978$	0.360563	0.0115295
$979$	41.2630	1.31877
$980$	0	0
$981$	22.1356	0.706736
$982$	−9.67283	−0.308672
$983$	4.00915	0.127872	0.0639360	−	0.997954i	$-0.479635\pi$
$983$	4.00915	0.127872	0.0639360	+	0.997954i	$0.479635\pi$
$984$	5.95420	0.189813
$985$	0	0
$986$	3.45514	0.110034
$987$	−5.91829	−0.188381
$988$	40.3935	1.28509
$989$	3.35637	0.106726
$990$	0	0
$991$	−21.5335	−0.684035	−0.342017	−	0.939694i	$-0.611110\pi$
$991$	−21.5335	−0.684035	−0.342017	+	0.939694i	$0.611110\pi$
$992$	−25.7028	−0.816065
$993$	2.48634	0.0789017
$994$	−3.90361	−0.123815
$995$	0	0
$996$	−19.3645	−0.613586
$997$	−29.3420	−0.929271	−0.464635	−	0.885502i	$-0.653815\pi$
$997$	−29.3420	−0.929271	−0.464635	+	0.885502i	$0.653815\pi$
$998$	3.27131	0.103552
$999$	−26.9283	−0.851975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.m.1.20	✓	40
5.4	even	2		6025.2.a.n.1.21	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.20	✓	40	1.1	even	1	trivial
6025.2.a.n.1.21	yes	40	5.4	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.333070 q^{2} -1.03111 q^{3} -1.88906 q^{4} +0.343432 q^{6} +2.91492 q^{7} +1.29533 q^{8} -1.93681 q^{9} +O(q^{10})\)	\(q-0.333070 q^{2} -1.03111 q^{3} -1.88906 q^{4} +0.343432 q^{6} +2.91492 q^{7} +1.29533 q^{8} -1.93681 q^{9} -5.85066 q^{11} +1.94783 q^{12} +5.25897 q^{13} -0.970871 q^{14} +3.34669 q^{16} +1.44402 q^{17} +0.645094 q^{18} -4.06597 q^{19} -3.00560 q^{21} +1.94868 q^{22} +1.01807 q^{23} -1.33563 q^{24} -1.75160 q^{26} +5.09040 q^{27} -5.50646 q^{28} -7.18385 q^{29} +6.93668 q^{31} -3.70534 q^{32} +6.03267 q^{33} -0.480959 q^{34} +3.65876 q^{36} -5.29003 q^{37} +1.35425 q^{38} -5.42257 q^{39} -4.45798 q^{41} +1.00107 q^{42} +3.29679 q^{43} +11.0523 q^{44} -0.339090 q^{46} +1.96909 q^{47} -3.45081 q^{48} +1.49673 q^{49} -1.48894 q^{51} -9.93453 q^{52} +0.430807 q^{53} -1.69546 q^{54} +3.77578 q^{56} +4.19246 q^{57} +2.39272 q^{58} +8.44640 q^{59} +3.27665 q^{61} -2.31040 q^{62} -5.64565 q^{63} -5.45925 q^{64} -2.00930 q^{66} +13.7065 q^{67} -2.72784 q^{68} -1.04974 q^{69} +4.02073 q^{71} -2.50881 q^{72} -3.64203 q^{73} +1.76195 q^{74} +7.68088 q^{76} -17.0542 q^{77} +1.80610 q^{78} -8.06707 q^{79} +0.561685 q^{81} +1.48482 q^{82} -9.94154 q^{83} +5.67777 q^{84} -1.09806 q^{86} +7.40733 q^{87} -7.57853 q^{88} -7.05272 q^{89} +15.3294 q^{91} -1.92321 q^{92} -7.15248 q^{93} -0.655845 q^{94} +3.82062 q^{96} -3.07235 q^{97} -0.498517 q^{98} +11.3316 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

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Database

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