LMFDB - Embedded newform 6013.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31949 q^{2} +1.94621 q^{3} +3.38001 q^{4} +1.57325 q^{5} -4.51421 q^{6} +1.00000 q^{7} -3.20092 q^{8} +0.787746 q^{9} +O(q^{10})$	\(q-2.31949 q^{2} +1.94621 q^{3} +3.38001 q^{4} +1.57325 q^{5} -4.51421 q^{6} +1.00000 q^{7} -3.20092 q^{8} +0.787746 q^{9} -3.64913 q^{10} +0.174490 q^{11} +6.57822 q^{12} +2.79309 q^{13} -2.31949 q^{14} +3.06188 q^{15} +0.664454 q^{16} -5.90456 q^{17} -1.82717 q^{18} -5.02898 q^{19} +5.31760 q^{20} +1.94621 q^{21} -0.404728 q^{22} -1.47034 q^{23} -6.22966 q^{24} -2.52488 q^{25} -6.47854 q^{26} -4.30552 q^{27} +3.38001 q^{28} -1.87647 q^{29} -7.10199 q^{30} +5.69038 q^{31} +4.86064 q^{32} +0.339595 q^{33} +13.6955 q^{34} +1.57325 q^{35} +2.66259 q^{36} -0.939008 q^{37} +11.6646 q^{38} +5.43596 q^{39} -5.03584 q^{40} -7.94705 q^{41} -4.51421 q^{42} +10.6609 q^{43} +0.589779 q^{44} +1.23932 q^{45} +3.41043 q^{46} -5.99122 q^{47} +1.29317 q^{48} +1.00000 q^{49} +5.85643 q^{50} -11.4915 q^{51} +9.44069 q^{52} -10.2331 q^{53} +9.98658 q^{54} +0.274517 q^{55} -3.20092 q^{56} -9.78746 q^{57} +4.35245 q^{58} +5.26747 q^{59} +10.3492 q^{60} -5.80744 q^{61} -13.1988 q^{62} +0.787746 q^{63} -12.6031 q^{64} +4.39424 q^{65} -0.787687 q^{66} -3.73040 q^{67} -19.9575 q^{68} -2.86160 q^{69} -3.64913 q^{70} +2.63368 q^{71} -2.52151 q^{72} -10.9223 q^{73} +2.17801 q^{74} -4.91396 q^{75} -16.9980 q^{76} +0.174490 q^{77} -12.6086 q^{78} +4.70189 q^{79} +1.04535 q^{80} -10.7427 q^{81} +18.4331 q^{82} -2.15183 q^{83} +6.57822 q^{84} -9.28935 q^{85} -24.7278 q^{86} -3.65202 q^{87} -0.558529 q^{88} +8.20986 q^{89} -2.87459 q^{90} +2.79309 q^{91} -4.96977 q^{92} +11.0747 q^{93} +13.8966 q^{94} -7.91184 q^{95} +9.45984 q^{96} -7.19899 q^{97} -2.31949 q^{98} +0.137454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.31949	−1.64012	−0.820062	−	0.572275i	$-0.806061\pi$
$2$	−2.31949	−1.64012	−0.820062	+	0.572275i	$0.806061\pi$
$3$	1.94621	1.12365	0.561823	−	0.827257i	$-0.310100\pi$
$3$	1.94621	1.12365	0.561823	+	0.827257i	$0.310100\pi$
$4$	3.38001	1.69001
$5$	1.57325	0.703579	0.351789	−	0.936079i	$-0.385573\pi$
$5$	1.57325	0.703579	0.351789	+	0.936079i	$0.385573\pi$
$6$	−4.51421	−1.84292
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.20092	−1.13169
$9$	0.787746	0.262582
$10$	−3.64913	−1.15396
$11$	0.174490	0.0526108	0.0263054	−	0.999654i	$-0.491626\pi$
$11$	0.174490	0.0526108	0.0263054	+	0.999654i	$0.491626\pi$
$12$	6.57822	1.89897
$13$	2.79309	0.774665	0.387332	−	0.921940i	$-0.373397\pi$
$13$	2.79309	0.774665	0.387332	+	0.921940i	$0.373397\pi$
$14$	−2.31949	−0.619908
$15$	3.06188	0.790574
$16$	0.664454	0.166113
$17$	−5.90456	−1.43207	−0.716033	−	0.698067i	$-0.754044\pi$
$17$	−5.90456	−1.43207	−0.716033	+	0.698067i	$0.754044\pi$
$18$	−1.82717	−0.430667
$19$	−5.02898	−1.15373	−0.576863	−	0.816841i	$-0.695723\pi$
$19$	−5.02898	−1.15373	−0.576863	+	0.816841i	$0.695723\pi$
$20$	5.31760	1.18905
$21$	1.94621	0.424699
$22$	−0.404728	−0.0862883
$23$	−1.47034	−0.306587	−0.153294	−	0.988181i	$-0.548988\pi$
$23$	−1.47034	−0.306587	−0.153294	+	0.988181i	$0.548988\pi$
$24$	−6.22966	−1.27162
$25$	−2.52488	−0.504977
$26$	−6.47854	−1.27055
$27$	−4.30552	−0.828597
$28$	3.38001	0.638762
$29$	−1.87647	−0.348452	−0.174226	−	0.984706i	$-0.555742\pi$
$29$	−1.87647	−0.348452	−0.174226	+	0.984706i	$0.555742\pi$
$30$	−7.10199	−1.29664
$31$	5.69038	1.02202	0.511011	−	0.859574i	$-0.329271\pi$
$31$	5.69038	1.02202	0.511011	+	0.859574i	$0.329271\pi$
$32$	4.86064	0.859248
$33$	0.339595	0.0591160
$34$	13.6955	2.34877
$35$	1.57325	0.265928
$36$	2.66259	0.443765
$37$	−0.939008	−0.154372	−0.0771860	−	0.997017i	$-0.524594\pi$
$37$	−0.939008	−0.154372	−0.0771860	+	0.997017i	$0.524594\pi$
$38$	11.6646	1.89225
$39$	5.43596	0.870449
$40$	−5.03584	−0.796236
$41$	−7.94705	−1.24112	−0.620561	−	0.784159i	$-0.713095\pi$
$41$	−7.94705	−1.24112	−0.620561	+	0.784159i	$0.713095\pi$
$42$	−4.51421	−0.696558
$43$	10.6609	1.62577	0.812887	−	0.582421i	$-0.197895\pi$
$43$	10.6609	1.62577	0.812887	+	0.582421i	$0.197895\pi$
$44$	0.589779	0.0889126
$45$	1.23932	0.184747
$46$	3.41043	0.502841
$47$	−5.99122	−0.873910	−0.436955	−	0.899483i	$-0.643943\pi$
$47$	−5.99122	−0.873910	−0.436955	+	0.899483i	$0.643943\pi$
$48$	1.29317	0.186653
$49$	1.00000	0.142857
$50$	5.85643	0.828224
$51$	−11.4915	−1.60914
$52$	9.44069	1.30919
$53$	−10.2331	−1.40563	−0.702815	−	0.711372i	$-0.748074\pi$
$53$	−10.2331	−1.40563	−0.702815	+	0.711372i	$0.748074\pi$
$54$	9.98658	1.35900
$55$	0.274517	0.0370159
$56$	−3.20092	−0.427740
$57$	−9.78746	−1.29638
$58$	4.35245	0.571505
$59$	5.26747	0.685766	0.342883	−	0.939378i	$-0.388597\pi$
$59$	5.26747	0.685766	0.342883	+	0.939378i	$0.388597\pi$
$60$	10.3492	1.33607
$61$	−5.80744	−0.743566	−0.371783	−	0.928320i	$-0.621254\pi$
$61$	−5.80744	−0.743566	−0.371783	+	0.928320i	$0.621254\pi$
$62$	−13.1988	−1.67624
$63$	0.787746	0.0992467
$64$	−12.6031	−1.57539
$65$	4.39424	0.545038
$66$	−0.787687	−0.0969575
$67$	−3.73040	−0.455741	−0.227871	−	0.973691i	$-0.573176\pi$
$67$	−3.73040	−0.455741	−0.227871	+	0.973691i	$0.573176\pi$
$68$	−19.9575	−2.42020
$69$	−2.86160	−0.344496
$70$	−3.64913	−0.436155
$71$	2.63368	0.312560	0.156280	−	0.987713i	$-0.450050\pi$
$71$	2.63368	0.312560	0.156280	+	0.987713i	$0.450050\pi$
$72$	−2.52151	−0.297163
$73$	−10.9223	−1.27836	−0.639180	−	0.769057i	$-0.720726\pi$
$73$	−10.9223	−1.27836	−0.639180	+	0.769057i	$0.720726\pi$
$74$	2.17801	0.253189
$75$	−4.91396	−0.567415
$76$	−16.9980	−1.94980
$77$	0.174490	0.0198850
$78$	−12.6086	−1.42764
$79$	4.70189	0.529004	0.264502	−	0.964385i	$-0.414792\pi$
$79$	4.70189	0.529004	0.264502	+	0.964385i	$0.414792\pi$
$80$	1.04535	0.116874
$81$	−10.7427	−1.19363
$82$	18.4331	2.03559
$83$	−2.15183	−0.236194	−0.118097	−	0.993002i	$-0.537679\pi$
$83$	−2.15183	−0.236194	−0.118097	+	0.993002i	$0.537679\pi$
$84$	6.57822	0.717743
$85$	−9.28935	−1.00757
$86$	−24.7278	−2.66647
$87$	−3.65202	−0.391537
$88$	−0.558529	−0.0595394
$89$	8.20986	0.870244	0.435122	−	0.900372i	$-0.356705\pi$
$89$	8.20986	0.870244	0.435122	+	0.900372i	$0.356705\pi$
$90$	−2.87459	−0.303008
$91$	2.79309	0.292796
$92$	−4.96977	−0.518134
$93$	11.0747	1.14839
$94$	13.8966	1.43332
$95$	−7.91184	−0.811738
$96$	9.45984	0.965491
$97$	−7.19899	−0.730947	−0.365473	−	0.930822i	$-0.619093\pi$
$97$	−7.19899	−0.730947	−0.365473	+	0.930822i	$0.619093\pi$
$98$	−2.31949	−0.234303
$99$	0.137454	0.0138147
$100$	−8.53413	−0.853413
$101$	−5.37880	−0.535210	−0.267605	−	0.963529i	$-0.586232\pi$
$101$	−5.37880	−0.535210	−0.267605	+	0.963529i	$0.586232\pi$
$102$	26.6544	2.63918
$103$	5.78397	0.569912	0.284956	−	0.958541i	$-0.408021\pi$
$103$	5.78397	0.569912	0.284956	+	0.958541i	$0.408021\pi$
$104$	−8.94046	−0.876684
$105$	3.06188	0.298809
$106$	23.7356	2.30541
$107$	−1.11350	−0.107646	−0.0538232	−	0.998550i	$-0.517141\pi$
$107$	−1.11350	−0.107646	−0.0538232	+	0.998550i	$0.517141\pi$
$108$	−14.5527	−1.40033
$109$	−1.28304	−0.122893	−0.0614463	−	0.998110i	$-0.519571\pi$
$109$	−1.28304	−0.122893	−0.0614463	+	0.998110i	$0.519571\pi$
$110$	−0.636738	−0.0607106
$111$	−1.82751	−0.173460
$112$	0.664454	0.0627850
$113$	14.9590	1.40722	0.703612	−	0.710584i	$-0.251569\pi$
$113$	14.9590	1.40722	0.703612	+	0.710584i	$0.251569\pi$
$114$	22.7019	2.12623
$115$	−2.31321	−0.215708
$116$	−6.34250	−0.588887
$117$	2.20025	0.203413
$118$	−12.2178	−1.12474
$119$	−5.90456	−0.541270
$120$	−9.80082	−0.894689
$121$	−10.9696	−0.997232
$122$	13.4703	1.21954
$123$	−15.4667	−1.39458
$124$	19.2336	1.72722
$125$	−11.8385	−1.05887
$126$	−1.82717	−0.162777
$127$	15.7816	1.40039	0.700194	−	0.713953i	$-0.253097\pi$
$127$	15.7816	1.40039	0.700194	+	0.713953i	$0.253097\pi$
$128$	19.5114	1.72458
$129$	20.7484	1.82680
$130$	−10.1924	−0.893929
$131$	−7.36864	−0.643801	−0.321901	−	0.946773i	$-0.604322\pi$
$131$	−7.36864	−0.643801	−0.321901	+	0.946773i	$0.604322\pi$
$132$	1.14784	0.0999063
$133$	−5.02898	−0.436068
$134$	8.65262	0.747472
$135$	−6.77366	−0.582984
$136$	18.9000	1.62066
$137$	−8.12319	−0.694011	−0.347006	−	0.937863i	$-0.612802\pi$
$137$	−8.12319	−0.694011	−0.347006	+	0.937863i	$0.612802\pi$
$138$	6.63743	0.565015
$139$	−5.37804	−0.456159	−0.228080	−	0.973642i	$-0.573245\pi$
$139$	−5.37804	−0.456159	−0.228080	+	0.973642i	$0.573245\pi$
$140$	5.31760	0.449420
$141$	−11.6602	−0.981966
$142$	−6.10877	−0.512637
$143$	0.487368	0.0407557
$144$	0.523421	0.0436184
$145$	−2.95216	−0.245164
$146$	25.3341	2.09667
$147$	1.94621	0.160521
$148$	−3.17386	−0.260889
$149$	2.62368	0.214941	0.107470	−	0.994208i	$-0.465725\pi$
$149$	2.62368	0.214941	0.107470	+	0.994208i	$0.465725\pi$
$150$	11.3979	0.930631
$151$	4.09278	0.333065	0.166533	−	0.986036i	$-0.446743\pi$
$151$	4.09278	0.333065	0.166533	+	0.986036i	$0.446743\pi$
$152$	16.0973	1.30567
$153$	−4.65129	−0.376035
$154$	−0.404728	−0.0326139
$155$	8.95240	0.719074
$156$	18.3736	1.47106
$157$	−20.4226	−1.62990	−0.814952	−	0.579528i	$-0.803237\pi$
$157$	−20.4226	−1.62990	−0.814952	+	0.579528i	$0.803237\pi$
$158$	−10.9060	−0.867632
$159$	−19.9159	−1.57943
$160$	7.64700	0.604549
$161$	−1.47034	−0.115879
$162$	24.9175	1.95771
$163$	−14.7938	−1.15874	−0.579369	−	0.815066i	$-0.696701\pi$
$163$	−14.7938	−1.15874	−0.579369	+	0.815066i	$0.696701\pi$
$164$	−26.8611	−2.09750
$165$	0.534269	0.0415928
$166$	4.99113	0.387387
$167$	3.95613	0.306135	0.153067	−	0.988216i	$-0.451085\pi$
$167$	3.95613	0.306135	0.153067	+	0.988216i	$0.451085\pi$
$168$	−6.22966	−0.480629
$169$	−5.19863	−0.399895
$170$	21.5465	1.65254
$171$	−3.96156	−0.302948
$172$	36.0340	2.74757
$173$	−25.8760	−1.96732	−0.983658	−	0.180045i	$-0.942376\pi$
$173$	−25.8760	−1.96732	−0.983658	+	0.180045i	$0.942376\pi$
$174$	8.47080	0.642170
$175$	−2.52488	−0.190863
$176$	0.115941	0.00873936
$177$	10.2516	0.770559
$178$	−19.0427	−1.42731
$179$	−24.6106	−1.83948	−0.919742	−	0.392524i	$-0.871602\pi$
$179$	−24.6106	−1.83948	−0.919742	+	0.392524i	$0.871602\pi$
$180$	4.18892	0.312224
$181$	−15.9964	−1.18900	−0.594502	−	0.804094i	$-0.702651\pi$
$181$	−15.9964	−1.18900	−0.594502	+	0.804094i	$0.702651\pi$
$182$	−6.47854	−0.480221
$183$	−11.3025	−0.835506
$184$	4.70643	0.346963
$185$	−1.47729	−0.108613
$186$	−25.6876	−1.88351
$187$	−1.03029	−0.0753422
$188$	−20.2504	−1.47691
$189$	−4.30552	−0.313180
$190$	18.3514	1.33135
$191$	−6.85096	−0.495718	−0.247859	−	0.968796i	$-0.579727\pi$
$191$	−6.85096	−0.495718	−0.247859	+	0.968796i	$0.579727\pi$
$192$	−24.5283	−1.77018
$193$	26.0308	1.87374	0.936870	−	0.349677i	$-0.113709\pi$
$193$	26.0308	1.87374	0.936870	+	0.349677i	$0.113709\pi$
$194$	16.6980	1.19884
$195$	8.55212	0.612430
$196$	3.38001	0.241429
$197$	−15.7349	−1.12106	−0.560531	−	0.828133i	$-0.689403\pi$
$197$	−15.7349	−1.12106	−0.560531	+	0.828133i	$0.689403\pi$
$198$	−0.318823	−0.0226577
$199$	−15.8013	−1.12012	−0.560061	−	0.828451i	$-0.689222\pi$
$199$	−15.8013	−1.12012	−0.560061	+	0.828451i	$0.689222\pi$
$200$	8.08194	0.571479
$201$	−7.26016	−0.512092
$202$	12.4760	0.877811
$203$	−1.87647	−0.131703
$204$	−38.8415	−2.71945
$205$	−12.5027	−0.873227
$206$	−13.4158	−0.934726
$207$	−1.15825	−0.0805043
$208$	1.85588	0.128682
$209$	−0.877508	−0.0606985
$210$	−7.10199	−0.490084
$211$	28.2122	1.94221	0.971105	−	0.238654i	$-0.0767061\pi$
$211$	28.2122	1.94221	0.971105	+	0.238654i	$0.0767061\pi$
$212$	−34.5882	−2.37552
$213$	5.12570	0.351207
$214$	2.58276	0.176554
$215$	16.7723	1.14386
$216$	13.7816	0.937719
$217$	5.69038	0.386288
$218$	2.97598	0.201559
$219$	−21.2572	−1.43643
$220$	0.927871	0.0625570
$221$	−16.4920	−1.10937
$222$	4.23888	0.284495
$223$	23.4115	1.56775	0.783875	−	0.620919i	$-0.213240\pi$
$223$	23.4115	1.56775	0.783875	+	0.620919i	$0.213240\pi$
$224$	4.86064	0.324765
$225$	−1.98897	−0.132598
$226$	−34.6972	−2.30802
$227$	23.0625	1.53071	0.765357	−	0.643606i	$-0.222562\pi$
$227$	23.0625	1.53071	0.765357	+	0.643606i	$0.222562\pi$
$228$	−33.0817	−2.19089
$229$	13.4501	0.888809	0.444404	−	0.895826i	$-0.353415\pi$
$229$	13.4501	0.888809	0.444404	+	0.895826i	$0.353415\pi$
$230$	5.36546	0.353788
$231$	0.339595	0.0223437
$232$	6.00643	0.394342
$233$	−5.53924	−0.362888	−0.181444	−	0.983401i	$-0.558077\pi$
$233$	−5.53924	−0.362888	−0.181444	+	0.983401i	$0.558077\pi$
$234$	−5.10344	−0.333623
$235$	−9.42569	−0.614865
$236$	17.8041	1.15895
$237$	9.15089	0.594414
$238$	13.6955	0.887750
$239$	23.0875	1.49341	0.746704	−	0.665156i	$-0.231635\pi$
$239$	23.0875	1.49341	0.746704	+	0.665156i	$0.231635\pi$
$240$	2.03448	0.131325
$241$	−0.829714	−0.0534466	−0.0267233	−	0.999643i	$-0.508507\pi$
$241$	−0.829714	−0.0534466	−0.0267233	+	0.999643i	$0.508507\pi$
$242$	25.4437	1.63558
$243$	−7.99102	−0.512624
$244$	−19.6292	−1.25663
$245$	1.57325	0.100511
$246$	35.8747	2.28729
$247$	−14.0464	−0.893751
$248$	−18.2144	−1.15662
$249$	−4.18791	−0.265398
$250$	27.4593	1.73668
$251$	−4.88817	−0.308538	−0.154269	−	0.988029i	$-0.549302\pi$
$251$	−4.88817	−0.308538	−0.154269	+	0.988029i	$0.549302\pi$
$252$	2.66259	0.167727
$253$	−0.256560	−0.0161298
$254$	−36.6051	−2.29681
$255$	−18.0791	−1.13215
$256$	−20.0502	−1.25314
$257$	9.86260	0.615212	0.307606	−	0.951514i	$-0.400472\pi$
$257$	9.86260	0.615212	0.307606	+	0.951514i	$0.400472\pi$
$258$	−48.1256	−2.99617
$259$	−0.939008	−0.0583471
$260$	14.8526	0.921117
$261$	−1.47818	−0.0914973
$262$	17.0915	1.05591
$263$	6.38902	0.393964	0.196982	−	0.980407i	$-0.436886\pi$
$263$	6.38902	0.393964	0.196982	+	0.980407i	$0.436886\pi$
$264$	−1.08702	−0.0669012
$265$	−16.0993	−0.988972
$266$	11.6646	0.715205
$267$	15.9781	0.977847
$268$	−12.6088	−0.770205
$269$	−32.0521	−1.95425	−0.977127	−	0.212659i	$-0.931788\pi$
$269$	−32.0521	−1.95425	−0.977127	+	0.212659i	$0.931788\pi$
$270$	15.7114	0.956165
$271$	−17.9419	−1.08989	−0.544946	−	0.838471i	$-0.683450\pi$
$271$	−17.9419	−1.08989	−0.544946	+	0.838471i	$0.683450\pi$
$272$	−3.92331	−0.237885
$273$	5.43596	0.328999
$274$	18.8416	1.13826
$275$	−0.440568	−0.0265672
$276$	−9.67222	−0.582200
$277$	14.9294	0.897023	0.448511	−	0.893777i	$-0.351954\pi$
$277$	14.9294	0.897023	0.448511	+	0.893777i	$0.351954\pi$
$278$	12.4743	0.748158
$279$	4.48258	0.268365
$280$	−5.03584	−0.300949
$281$	7.40977	0.442030	0.221015	−	0.975270i	$-0.429063\pi$
$281$	7.40977	0.442030	0.221015	+	0.975270i	$0.429063\pi$
$282$	27.0457	1.61055
$283$	−12.3670	−0.735143	−0.367572	−	0.929995i	$-0.619811\pi$
$283$	−12.3670	−0.735143	−0.367572	+	0.929995i	$0.619811\pi$
$284$	8.90186	0.528228
$285$	−15.3981	−0.912107
$286$	−1.13044	−0.0668445
$287$	−7.94705	−0.469100
$288$	3.82895	0.225623
$289$	17.8638	1.05081
$290$	6.84750	0.402099
$291$	−14.0108	−0.821326
$292$	−36.9175	−2.16044
$293$	9.21103	0.538114	0.269057	−	0.963124i	$-0.413288\pi$
$293$	9.21103	0.538114	0.269057	+	0.963124i	$0.413288\pi$
$294$	−4.51421	−0.263274
$295$	8.28705	0.482491
$296$	3.00568	0.174702
$297$	−0.751271	−0.0435932
$298$	−6.08559	−0.352529
$299$	−4.10680	−0.237502
$300$	−16.6092	−0.958935
$301$	10.6609	0.614485
$302$	−9.49314	−0.546269
$303$	−10.4683	−0.601387
$304$	−3.34152	−0.191649
$305$	−9.13656	−0.523158
$306$	10.7886	0.616744
$307$	−8.89821	−0.507848	−0.253924	−	0.967224i	$-0.581721\pi$
$307$	−8.89821	−0.507848	−0.253924	+	0.967224i	$0.581721\pi$
$308$	0.589779	0.0336058
$309$	11.2568	0.640379
$310$	−20.7650	−1.17937
$311$	−13.7742	−0.781065	−0.390533	−	0.920589i	$-0.627709\pi$
$311$	−13.7742	−0.781065	−0.390533	+	0.920589i	$0.627709\pi$
$312$	−17.4000	−0.985083
$313$	21.4099	1.21016	0.605080	−	0.796165i	$-0.293141\pi$
$313$	21.4099	1.21016	0.605080	+	0.796165i	$0.293141\pi$
$314$	47.3700	2.67324
$315$	1.23932	0.0698279
$316$	15.8925	0.894020
$317$	−20.3991	−1.14573	−0.572864	−	0.819650i	$-0.694168\pi$
$317$	−20.3991	−1.14573	−0.572864	+	0.819650i	$0.694168\pi$
$318$	46.1946	2.59046
$319$	−0.327427	−0.0183324
$320$	−19.8278	−1.10841
$321$	−2.16712	−0.120957
$322$	3.41043	0.190056
$323$	29.6939	1.65221
$324$	−36.3104	−2.01725
$325$	−7.05223	−0.391188
$326$	34.3139	1.90047
$327$	−2.49706	−0.138088
$328$	25.4378	1.40457
$329$	−5.99122	−0.330307
$330$	−1.23923	−0.0682173
$331$	2.11984	0.116517	0.0582584	−	0.998302i	$-0.481445\pi$
$331$	2.11984	0.116517	0.0582584	+	0.998302i	$0.481445\pi$
$332$	−7.27320	−0.399169
$333$	−0.739700	−0.0405353
$334$	−9.17619	−0.502099
$335$	−5.86886	−0.320650
$336$	1.29317	0.0705481
$337$	2.13924	0.116532	0.0582660	−	0.998301i	$-0.481443\pi$
$337$	2.13924	0.116532	0.0582660	+	0.998301i	$0.481443\pi$
$338$	12.0581	0.655877
$339$	29.1134	1.58122
$340$	−31.3981	−1.70280
$341$	0.992917	0.0537695
$342$	9.18877	0.496872
$343$	1.00000	0.0539949
$344$	−34.1247	−1.83988
$345$	−4.50201	−0.242380
$346$	60.0190	3.22664
$347$	25.6242	1.37558	0.687789	−	0.725911i	$-0.258581\pi$
$347$	25.6242	1.37558	0.687789	+	0.725911i	$0.258581\pi$
$348$	−12.3439	−0.661700
$349$	27.5242	1.47334	0.736669	−	0.676254i	$-0.236398\pi$
$349$	27.5242	1.47334	0.736669	+	0.676254i	$0.236398\pi$
$350$	5.85643	0.313039
$351$	−12.0257	−0.641885
$352$	0.848135	0.0452057
$353$	10.4489	0.556140	0.278070	−	0.960561i	$-0.410305\pi$
$353$	10.4489	0.556140	0.278070	+	0.960561i	$0.410305\pi$
$354$	−23.7785	−1.26381
$355$	4.14343	0.219911
$356$	27.7494	1.47072
$357$	−11.4915	−0.608196
$358$	57.0840	3.01698
$359$	−16.1289	−0.851253	−0.425626	−	0.904899i	$-0.639946\pi$
$359$	−16.1289	−0.851253	−0.425626	+	0.904899i	$0.639946\pi$
$360$	−3.96696	−0.209077
$361$	6.29062	0.331085
$362$	37.1034	1.95011
$363$	−21.3491	−1.12054
$364$	9.44069	0.494826
$365$	−17.1835	−0.899427
$366$	26.2160	1.37033
$367$	−13.9018	−0.725666	−0.362833	−	0.931854i	$-0.618190\pi$
$367$	−13.9018	−0.725666	−0.362833	+	0.931854i	$0.618190\pi$
$368$	−0.976973	−0.0509282
$369$	−6.26026	−0.325896
$370$	3.42656	0.178138
$371$	−10.2331	−0.531278
$372$	37.4326	1.94079
$373$	22.5766	1.16897	0.584487	−	0.811403i	$-0.301296\pi$
$373$	22.5766	1.16897	0.584487	+	0.811403i	$0.301296\pi$
$374$	2.38974	0.123570
$375$	−23.0403	−1.18980
$376$	19.1774	0.988999
$377$	−5.24117	−0.269934
$378$	9.98658	0.513654
$379$	2.60243	0.133678	0.0668390	−	0.997764i	$-0.478709\pi$
$379$	2.60243	0.133678	0.0668390	+	0.997764i	$0.478709\pi$
$380$	−26.7421	−1.37184
$381$	30.7143	1.57354
$382$	15.8907	0.813039
$383$	−32.1427	−1.64241	−0.821206	−	0.570631i	$-0.806699\pi$
$383$	−32.1427	−1.64241	−0.821206	+	0.570631i	$0.806699\pi$
$384$	37.9733	1.93782
$385$	0.274517	0.0139907
$386$	−60.3781	−3.07317
$387$	8.39809	0.426899
$388$	−24.3327	−1.23530
$389$	25.8998	1.31317	0.656587	−	0.754251i	$-0.272000\pi$
$389$	25.8998	1.31317	0.656587	+	0.754251i	$0.272000\pi$
$390$	−19.8365	−1.00446
$391$	8.68171	0.439053
$392$	−3.20092	−0.161671
$393$	−14.3410	−0.723405
$394$	36.4968	1.83868
$395$	7.39725	0.372196
$396$	0.464596	0.0233468
$397$	22.8061	1.14461	0.572304	−	0.820042i	$-0.306050\pi$
$397$	22.8061	1.14461	0.572304	+	0.820042i	$0.306050\pi$
$398$	36.6508	1.83714
$399$	−9.78746	−0.489986
$400$	−1.67767	−0.0838834
$401$	10.2567	0.512194	0.256097	−	0.966651i	$-0.417563\pi$
$401$	10.2567	0.512194	0.256097	+	0.966651i	$0.417563\pi$
$402$	16.8398	0.839895
$403$	15.8938	0.791725
$404$	−18.1804	−0.904509
$405$	−16.9009	−0.839815
$406$	4.35245	0.216009
$407$	−0.163848	−0.00812164
$408$	36.7834	1.82105
$409$	−6.38293	−0.315615	−0.157808	−	0.987470i	$-0.550443\pi$
$409$	−6.38293	−0.315615	−0.157808	+	0.987470i	$0.550443\pi$
$410$	28.9998	1.43220
$411$	−15.8095	−0.779824
$412$	19.5499	0.963154
$413$	5.26747	0.259195
$414$	2.68655	0.132037
$415$	−3.38536	−0.166181
$416$	13.5762	0.665629
$417$	−10.4668	−0.512562
$418$	2.03537	0.0995531
$419$	−6.04354	−0.295246	−0.147623	−	0.989044i	$-0.547162\pi$
$419$	−6.04354	−0.295246	−0.147623	+	0.989044i	$0.547162\pi$
$420$	10.3492	0.504989
$421$	25.3174	1.23389	0.616947	−	0.787004i	$-0.288369\pi$
$421$	25.3174	1.23389	0.616947	+	0.787004i	$0.288369\pi$
$422$	−65.4378	−3.18546
$423$	−4.71956	−0.229473
$424$	32.7554	1.59074
$425$	14.9083	0.723160
$426$	−11.8890	−0.576023
$427$	−5.80744	−0.281042
$428$	−3.76366	−0.181923
$429$	0.948522	0.0457951
$430$	−38.9031	−1.87607
$431$	2.67488	0.128845	0.0644223	−	0.997923i	$-0.479480\pi$
$431$	2.67488	0.128845	0.0644223	+	0.997923i	$0.479480\pi$
$432$	−2.86082	−0.137641
$433$	39.5057	1.89852	0.949261	−	0.314489i	$-0.101833\pi$
$433$	39.5057	1.89852	0.949261	+	0.314489i	$0.101833\pi$
$434$	−13.1988	−0.633561
$435$	−5.74554	−0.275477
$436$	−4.33667	−0.207689
$437$	7.39431	0.353718
$438$	49.3056	2.35591
$439$	12.8342	0.612543	0.306272	−	0.951944i	$-0.400918\pi$
$439$	12.8342	0.612543	0.306272	+	0.951944i	$0.400918\pi$
$440$	−0.878706	−0.0418907
$441$	0.787746	0.0375117
$442$	38.2529	1.81951
$443$	−2.81298	−0.133649	−0.0668244	−	0.997765i	$-0.521287\pi$
$443$	−2.81298	−0.133649	−0.0668244	+	0.997765i	$0.521287\pi$
$444$	−6.17700	−0.293148
$445$	12.9162	0.612285
$446$	−54.3026	−2.57130
$447$	5.10625	0.241517
$448$	−12.6031	−0.595440
$449$	4.33335	0.204503	0.102252	−	0.994759i	$-0.467395\pi$
$449$	4.33335	0.204503	0.102252	+	0.994759i	$0.467395\pi$
$450$	4.61338	0.217477
$451$	−1.38668	−0.0652964
$452$	50.5616	2.37822
$453$	7.96542	0.374248
$454$	−53.4932	−2.51056
$455$	4.39424	0.206005
$456$	31.3288	1.46711
$457$	−31.3400	−1.46602	−0.733011	−	0.680217i	$-0.761886\pi$
$457$	−31.3400	−1.46602	−0.733011	+	0.680217i	$0.761886\pi$
$458$	−31.1973	−1.45776
$459$	25.4222	1.18661
$460$	−7.81869	−0.364548
$461$	−18.5719	−0.864978	−0.432489	−	0.901639i	$-0.642365\pi$
$461$	−18.5719	−0.864978	−0.432489	+	0.901639i	$0.642365\pi$
$462$	−0.787687	−0.0366465
$463$	−18.9721	−0.881710	−0.440855	−	0.897578i	$-0.645325\pi$
$463$	−18.9721	−0.881710	−0.440855	+	0.897578i	$0.645325\pi$
$464$	−1.24683	−0.0578826
$465$	17.4233	0.807985
$466$	12.8482	0.595181
$467$	−25.5930	−1.18430	−0.592151	−	0.805827i	$-0.701721\pi$
$467$	−25.5930	−1.18430	−0.592151	+	0.805827i	$0.701721\pi$
$468$	7.43686	0.343769
$469$	−3.73040	−0.172254
$470$	21.8628	1.00845
$471$	−39.7468	−1.83144
$472$	−16.8607	−0.776078
$473$	1.86023	0.0855333
$474$	−21.2253	−0.974912
$475$	12.6976	0.582605
$476$	−19.9575	−0.914749
$477$	−8.06112	−0.369093
$478$	−53.5512	−2.44937
$479$	9.82226	0.448790	0.224395	−	0.974498i	$-0.427959\pi$
$479$	9.82226	0.448790	0.224395	+	0.974498i	$0.427959\pi$
$480$	14.8827	0.679299
$481$	−2.62274	−0.119586
$482$	1.92451	0.0876590
$483$	−2.86160	−0.130207
$484$	−37.0772	−1.68533
$485$	−11.3258	−0.514279
$486$	18.5351	0.840767
$487$	15.2901	0.692859	0.346430	−	0.938076i	$-0.387394\pi$
$487$	15.2901	0.692859	0.346430	+	0.938076i	$0.387394\pi$
$488$	18.5891	0.841490
$489$	−28.7918	−1.30201
$490$	−3.64913	−0.164851
$491$	22.8291	1.03026	0.515132	−	0.857111i	$-0.327743\pi$
$491$	22.8291	1.03026	0.515132	+	0.857111i	$0.327743\pi$
$492$	−52.2775	−2.35685
$493$	11.0797	0.499007
$494$	32.5804	1.46586
$495$	0.216250	0.00971970
$496$	3.78100	0.169772
$497$	2.63368	0.118137
$498$	9.71380	0.435286
$499$	37.7079	1.68804	0.844018	−	0.536315i	$-0.180184\pi$
$499$	37.7079	1.68804	0.844018	+	0.536315i	$0.180184\pi$
$500$	−40.0143	−1.78950
$501$	7.69947	0.343987
$502$	11.3380	0.506041
$503$	−39.4653	−1.75967	−0.879836	−	0.475278i	$-0.842347\pi$
$503$	−39.4653	−1.75967	−0.879836	+	0.475278i	$0.842347\pi$
$504$	−2.52151	−0.112317
$505$	−8.46220	−0.376563
$506$	0.595088	0.0264549
$507$	−10.1176	−0.449340
$508$	53.3419	2.36666
$509$	−23.8370	−1.05656	−0.528278	−	0.849072i	$-0.677162\pi$
$509$	−23.8370	−1.05656	−0.528278	+	0.849072i	$0.677162\pi$
$510$	41.9341	1.85687
$511$	−10.9223	−0.483175
$512$	7.48339	0.330722
$513$	21.6524	0.955975
$514$	−22.8762	−1.00902
$515$	9.09963	0.400978
$516$	70.1299	3.08730
$517$	−1.04541	−0.0459771
$518$	2.17801	0.0956965
$519$	−50.3602	−2.21057
$520$	−14.0656	−0.616816
$521$	−0.267637	−0.0117254	−0.00586270	−	0.999983i	$-0.501866\pi$
$521$	−0.267637	−0.0117254	−0.00586270	+	0.999983i	$0.501866\pi$
$522$	3.42863	0.150067
$523$	21.2991	0.931344	0.465672	−	0.884957i	$-0.345813\pi$
$523$	21.2991	0.931344	0.465672	+	0.884957i	$0.345813\pi$
$524$	−24.9061	−1.08803
$525$	−4.91396	−0.214463
$526$	−14.8192	−0.646150
$527$	−33.5992	−1.46360
$528$	0.225645	0.00981996
$529$	−20.8381	−0.906004
$530$	37.3421	1.62204
$531$	4.14943	0.180070
$532$	−16.9980	−0.736957
$533$	−22.1969	−0.961453
$534$	−37.0611	−1.60379
$535$	−1.75182	−0.0757378
$536$	11.9407	0.515760
$537$	−47.8975	−2.06693
$538$	74.3444	3.20522
$539$	0.174490	0.00751583
$540$	−22.8950	−0.985246
$541$	−9.07881	−0.390329	−0.195164	−	0.980771i	$-0.562524\pi$
$541$	−9.07881	−0.390329	−0.195164	+	0.980771i	$0.562524\pi$
$542$	41.6159	1.78756
$543$	−31.1324	−1.33602
$544$	−28.6999	−1.23050
$545$	−2.01854	−0.0864646
$546$	−12.6086	−0.539599
$547$	−40.8101	−1.74491	−0.872456	−	0.488692i	$-0.837474\pi$
$547$	−40.8101	−1.74491	−0.872456	+	0.488692i	$0.837474\pi$
$548$	−27.4565	−1.17288
$549$	−4.57479	−0.195247
$550$	1.02189	0.0435736
$551$	9.43674	0.402019
$552$	9.15973	0.389864
$553$	4.70189	0.199945
$554$	−34.6286	−1.47123
$555$	−2.87513	−0.122042
$556$	−18.1778	−0.770912
$557$	37.2574	1.57865	0.789324	−	0.613977i	$-0.210431\pi$
$557$	37.2574	1.57865	0.789324	+	0.613977i	$0.210431\pi$
$558$	−10.3973	−0.440152
$559$	29.7769	1.25943
$560$	1.04535	0.0441742
$561$	−2.00516	−0.0846580
$562$	−17.1869	−0.724984
$563$	7.94804	0.334970	0.167485	−	0.985875i	$-0.446435\pi$
$563$	7.94804	0.334970	0.167485	+	0.985875i	$0.446435\pi$
$564$	−39.4116	−1.65953
$565$	23.5342	0.990093
$566$	28.6851	1.20573
$567$	−10.7427	−0.451151
$568$	−8.43018	−0.353722
$569$	−23.4833	−0.984471	−0.492235	−	0.870462i	$-0.663820\pi$
$569$	−23.4833	−0.984471	−0.492235	+	0.870462i	$0.663820\pi$
$570$	35.7157	1.49597
$571$	−35.7436	−1.49582	−0.747911	−	0.663799i	$-0.768943\pi$
$571$	−35.7436	−1.49582	−0.747911	+	0.663799i	$0.768943\pi$
$572$	1.64731	0.0688774
$573$	−13.3334	−0.557012
$574$	18.4331	0.769382
$575$	3.71244	0.154819
$576$	−9.92804	−0.413668
$577$	20.7906	0.865522	0.432761	−	0.901509i	$-0.357539\pi$
$577$	20.7906	0.865522	0.432761	+	0.901509i	$0.357539\pi$
$578$	−41.4348	−1.72346
$579$	50.6616	2.10542
$580$	−9.97834	−0.414328
$581$	−2.15183	−0.0892728
$582$	32.4978	1.34708
$583$	−1.78559	−0.0739514
$584$	34.9614	1.44671
$585$	3.46154	0.143117
$586$	−21.3649	−0.882574
$587$	−4.10492	−0.169428	−0.0847142	−	0.996405i	$-0.526998\pi$
$587$	−4.10492	−0.169428	−0.0847142	+	0.996405i	$0.526998\pi$
$588$	6.57822	0.271281
$589$	−28.6168	−1.17914
$590$	−19.2217	−0.791344
$591$	−30.6234	−1.25968
$592$	−0.623927	−0.0256433
$593$	−6.03541	−0.247844	−0.123922	−	0.992292i	$-0.539547\pi$
$593$	−6.03541	−0.247844	−0.123922	+	0.992292i	$0.539547\pi$
$594$	1.74256	0.0714982
$595$	−9.28935	−0.380826
$596$	8.86808	0.363251
$597$	−30.7526	−1.25862
$598$	9.52566	0.389533
$599$	25.0471	1.02339	0.511697	−	0.859166i	$-0.329017\pi$
$599$	25.0471	1.02339	0.511697	+	0.859166i	$0.329017\pi$
$600$	15.7292	0.642141
$601$	−5.75378	−0.234702	−0.117351	−	0.993091i	$-0.537440\pi$
$601$	−5.75378	−0.234702	−0.117351	+	0.993091i	$0.537440\pi$
$602$	−24.7278	−1.00783
$603$	−2.93861	−0.119669
$604$	13.8336	0.562883
$605$	−17.2579	−0.701632
$606$	24.2810	0.986350
$607$	1.91667	0.0777952	0.0388976	−	0.999243i	$-0.487615\pi$
$607$	1.91667	0.0777952	0.0388976	+	0.999243i	$0.487615\pi$
$608$	−24.4441	−0.991337
$609$	−3.65202	−0.147987
$610$	21.1921	0.858043
$611$	−16.7340	−0.676987
$612$	−15.7214	−0.635501
$613$	−47.4769	−1.91757	−0.958787	−	0.284127i	$-0.908296\pi$
$613$	−47.4769	−1.91757	−0.958787	+	0.284127i	$0.908296\pi$
$614$	20.6393	0.832933
$615$	−24.3329	−0.981198
$616$	−0.558529	−0.0225038
$617$	−47.4534	−1.91040	−0.955202	−	0.295956i	$-0.904362\pi$
$617$	−47.4534	−1.91040	−0.955202	+	0.295956i	$0.904362\pi$
$618$	−26.1101	−1.05030
$619$	35.2675	1.41752	0.708760	−	0.705450i	$-0.249255\pi$
$619$	35.2675	1.41752	0.708760	+	0.705450i	$0.249255\pi$
$620$	30.2592	1.21524
$621$	6.33058	0.254037
$622$	31.9491	1.28104
$623$	8.20986	0.328921
$624$	3.61194	0.144593
$625$	−6.00055	−0.240022
$626$	−49.6600	−1.98481
$627$	−1.70782	−0.0682037
$628$	−69.0288	−2.75455
$629$	5.54443	0.221071
$630$	−2.87459	−0.114526
$631$	32.9181	1.31045	0.655224	−	0.755435i	$-0.272574\pi$
$631$	32.9181	1.31045	0.655224	+	0.755435i	$0.272574\pi$
$632$	−15.0504	−0.598671
$633$	54.9070	2.18236
$634$	47.3154	1.87914
$635$	24.8284	0.985283
$636$	−67.3159	−2.66925
$637$	2.79309	0.110666
$638$	0.759461	0.0300674
$639$	2.07467	0.0820726
$640$	30.6963	1.21338
$641$	42.8334	1.69182	0.845910	−	0.533326i	$-0.179058\pi$
$641$	42.8334	1.69182	0.845910	+	0.533326i	$0.179058\pi$
$642$	5.02659	0.198384
$643$	−13.9839	−0.551473	−0.275737	−	0.961233i	$-0.588922\pi$
$643$	−13.9839	−0.551473	−0.275737	+	0.961233i	$0.588922\pi$
$644$	−4.96977	−0.195836
$645$	32.6424	1.28530
$646$	−68.8745	−2.70983
$647$	0.578414	0.0227398	0.0113699	−	0.999935i	$-0.496381\pi$
$647$	0.578414	0.0227398	0.0113699	+	0.999935i	$0.496381\pi$
$648$	34.3865	1.35083
$649$	0.919123	0.0360787
$650$	16.3576	0.641596
$651$	11.0747	0.434052
$652$	−50.0031	−1.95827
$653$	−16.8242	−0.658380	−0.329190	−	0.944264i	$-0.606776\pi$
$653$	−16.8242	−0.658380	−0.329190	+	0.944264i	$0.606776\pi$
$654$	5.79190	0.226481
$655$	−11.5927	−0.452965
$656$	−5.28045	−0.206167
$657$	−8.60401	−0.335674
$658$	13.8966	0.541744
$659$	36.6236	1.42665	0.713326	−	0.700833i	$-0.247188\pi$
$659$	36.6236	1.42665	0.713326	+	0.700833i	$0.247188\pi$
$660$	1.80583	0.0702920
$661$	2.52318	0.0981405	0.0490702	−	0.998795i	$-0.484374\pi$
$661$	2.52318	0.0981405	0.0490702	+	0.998795i	$0.484374\pi$
$662$	−4.91693	−0.191102
$663$	−32.0969	−1.24654
$664$	6.88782	0.267299
$665$	−7.91184	−0.306808
$666$	1.71572	0.0664829
$667$	2.75905	0.106831
$668$	13.3718	0.517369
$669$	45.5637	1.76160
$670$	13.6127	0.525906
$671$	−1.01334	−0.0391196
$672$	9.45984	0.364921
$673$	25.7471	0.992476	0.496238	−	0.868186i	$-0.334714\pi$
$673$	25.7471	0.992476	0.496238	+	0.868186i	$0.334714\pi$
$674$	−4.96194	−0.191127
$675$	10.8709	0.418422
$676$	−17.5714	−0.675824
$677$	−26.6008	−1.02235	−0.511175	−	0.859477i	$-0.670790\pi$
$677$	−26.6008	−1.02235	−0.511175	+	0.859477i	$0.670790\pi$
$678$	−67.5281	−2.59340
$679$	−7.19899	−0.276272
$680$	29.7344	1.14026
$681$	44.8846	1.71998
$682$	−2.30306	−0.0881886
$683$	0.0476454	0.00182310	0.000911550	−	1.00000i	$-0.499710\pi$
$683$	0.0476454	0.00182310	0.000911550		1.00000i	$0.499710\pi$
$684$	−13.3901	−0.511984
$685$	−12.7798	−0.488292
$686$	−2.31949	−0.0885584
$687$	26.1768	0.998707
$688$	7.08368	0.270063
$689$	−28.5821	−1.08889
$690$	10.4423	0.397533
$691$	−9.69399	−0.368777	−0.184388	−	0.982853i	$-0.559030\pi$
$691$	−9.69399	−0.368777	−0.184388	+	0.982853i	$0.559030\pi$
$692$	−87.4612	−3.32478
$693$	0.137454	0.00522145
$694$	−59.4349	−2.25612
$695$	−8.46100	−0.320944
$696$	11.6898	0.443101
$697$	46.9238	1.77737
$698$	−63.8420	−2.41646
$699$	−10.7805	−0.407758
$700$	−8.53413	−0.322560
$701$	−9.13640	−0.345077	−0.172539	−	0.985003i	$-0.555197\pi$
$701$	−9.13640	−0.345077	−0.172539	+	0.985003i	$0.555197\pi$
$702$	27.8935	1.05277
$703$	4.72225	0.178103
$704$	−2.19912	−0.0828824
$705$	−18.3444	−0.690891
$706$	−24.2361	−0.912138
$707$	−5.37880	−0.202291
$708$	34.6506	1.30225
$709$	6.22777	0.233889	0.116944	−	0.993138i	$-0.462690\pi$
$709$	6.22777	0.233889	0.116944	+	0.993138i	$0.462690\pi$
$710$	−9.61063	−0.360681
$711$	3.70390	0.138907
$712$	−26.2791	−0.984850
$713$	−8.36680	−0.313339
$714$	26.6544	0.997517
$715$	0.766752	0.0286749
$716$	−83.1842	−3.10874
$717$	44.9333	1.67806
$718$	37.4108	1.39616
$719$	−31.5956	−1.17832	−0.589158	−	0.808018i	$-0.700541\pi$
$719$	−31.5956	−1.17832	−0.589158	+	0.808018i	$0.700541\pi$
$720$	0.823472	0.0306890
$721$	5.78397	0.215406
$722$	−14.5910	−0.543021
$723$	−1.61480	−0.0600551
$724$	−54.0680	−2.00942
$725$	4.73788	0.175960
$726$	49.5189	1.83782
$727$	32.2267	1.19522	0.597610	−	0.801787i	$-0.296117\pi$
$727$	32.2267	1.19522	0.597610	+	0.801787i	$0.296117\pi$
$728$	−8.94046	−0.331355
$729$	16.6759	0.617624
$730$	39.8569	1.47517
$731$	−62.9480	−2.32822
$732$	−38.2026	−1.41201
$733$	38.1310	1.40840	0.704200	−	0.710001i	$-0.251306\pi$
$733$	38.1310	1.40840	0.704200	+	0.710001i	$0.251306\pi$
$734$	32.2449	1.19018
$735$	3.06188	0.112939
$736$	−7.14680	−0.263434
$737$	−0.650920	−0.0239769
$738$	14.5206	0.534510
$739$	−28.6262	−1.05303	−0.526516	−	0.850165i	$-0.676502\pi$
$739$	−28.6262	−1.05303	−0.526516	+	0.850165i	$0.676502\pi$
$740$	−4.99327	−0.183556
$741$	−27.3373	−1.00426
$742$	23.7356	0.871362
$743$	−37.9201	−1.39115	−0.695577	−	0.718451i	$-0.744851\pi$
$743$	−37.9201	−1.39115	−0.695577	+	0.718451i	$0.744851\pi$
$744$	−35.4492	−1.29963
$745$	4.12771	0.151228
$746$	−52.3661	−1.91726
$747$	−1.69509	−0.0620202
$748$	−3.48239	−0.127329
$749$	−1.11350	−0.0406866
$750$	53.4416	1.95141
$751$	1.53996	0.0561938	0.0280969	−	0.999605i	$-0.491055\pi$
$751$	1.53996	0.0561938	0.0280969	+	0.999605i	$0.491055\pi$
$752$	−3.98089	−0.145168
$753$	−9.51342	−0.346688
$754$	12.1568	0.442725
$755$	6.43896	0.234338
$756$	−14.5527	−0.529277
$757$	−17.1491	−0.623296	−0.311648	−	0.950198i	$-0.600881\pi$
$757$	−17.1491	−0.623296	−0.311648	+	0.950198i	$0.600881\pi$
$758$	−6.03631	−0.219249
$759$	−0.499321	−0.0181242
$760$	25.3251	0.918639
$761$	−10.0945	−0.365927	−0.182963	−	0.983120i	$-0.558569\pi$
$761$	−10.0945	−0.365927	−0.182963	+	0.983120i	$0.558569\pi$
$762$	−71.2413	−2.58080
$763$	−1.28304	−0.0464490
$764$	−23.1563	−0.837766
$765$	−7.31765	−0.264570
$766$	74.5544	2.69376
$767$	14.7125	0.531239
$768$	−39.0220	−1.40809
$769$	21.9948	0.793152	0.396576	−	0.918002i	$-0.370198\pi$
$769$	21.9948	0.793152	0.396576	+	0.918002i	$0.370198\pi$
$770$	−0.636738	−0.0229465
$771$	19.1947	0.691281
$772$	87.9845	3.16663
$773$	−43.8189	−1.57606	−0.788029	−	0.615638i	$-0.788898\pi$
$773$	−43.8189	−1.57606	−0.788029	+	0.615638i	$0.788898\pi$
$774$	−19.4793	−0.700167
$775$	−14.3676	−0.516098
$776$	23.0434	0.827208
$777$	−1.82751	−0.0655615
$778$	−60.0743	−2.15377
$779$	39.9656	1.43191
$780$	28.9063	1.03501
$781$	0.459551	0.0164440
$782$	−20.1371	−0.720101
$783$	8.07919	0.288727
$784$	0.664454	0.0237305
$785$	−32.1299	−1.14677
$786$	33.2636	1.18647
$787$	−14.0925	−0.502345	−0.251172	−	0.967942i	$-0.580816\pi$
$787$	−14.0925	−0.502345	−0.251172	+	0.967942i	$0.580816\pi$
$788$	−53.1840	−1.89460
$789$	12.4344	0.442676
$790$	−17.1578	−0.610448
$791$	14.9590	0.531881
$792$	−0.439979	−0.0156340
$793$	−16.2207	−0.576015
$794$	−52.8985	−1.87730
$795$	−31.3327	−1.11126
$796$	−53.4084	−1.89301
$797$	−37.4351	−1.32602	−0.663009	−	0.748611i	$-0.730721\pi$
$797$	−37.4351	−1.32602	−0.663009	+	0.748611i	$0.730721\pi$
$798$	22.7019	0.803638
$799$	35.3755	1.25150
$800$	−12.2726	−0.433900
$801$	6.46729	0.228510
$802$	−23.7902	−0.840062
$803$	−1.90584	−0.0672556
$804$	−24.5394	−0.865439
$805$	−2.31321	−0.0815300
$806$	−36.8654	−1.29853
$807$	−62.3803	−2.19589
$808$	17.2171	0.605695
$809$	9.61925	0.338195	0.169097	−	0.985599i	$-0.445915\pi$
$809$	9.61925	0.338195	0.169097	+	0.985599i	$0.445915\pi$
$810$	39.2015	1.37740
$811$	−1.60824	−0.0564731	−0.0282366	−	0.999601i	$-0.508989\pi$
$811$	−1.60824	−0.0564731	−0.0282366	+	0.999601i	$0.508989\pi$
$812$	−6.34250	−0.222578
$813$	−34.9187	−1.22465
$814$	0.380043	0.0133205
$815$	−23.2743	−0.815263
$816$	−7.63559	−0.267299
$817$	−53.6135	−1.87570
$818$	14.8051	0.517648
$819$	2.20025	0.0768829
$820$	−42.2593	−1.47576
$821$	−47.0046	−1.64047	−0.820236	−	0.572026i	$-0.806158\pi$
$821$	−47.0046	−1.64047	−0.820236	+	0.572026i	$0.806158\pi$
$822$	36.6698	1.27901
$823$	−10.5337	−0.367183	−0.183591	−	0.983003i	$-0.558772\pi$
$823$	−10.5337	−0.367183	−0.183591	+	0.983003i	$0.558772\pi$
$824$	−18.5140	−0.644966
$825$	−0.857439	−0.0298522
$826$	−12.2178	−0.425112
$827$	32.2459	1.12130	0.560650	−	0.828053i	$-0.310551\pi$
$827$	32.2459	1.12130	0.560650	+	0.828053i	$0.310551\pi$
$828$	−3.91491	−0.136053
$829$	−8.45711	−0.293727	−0.146864	−	0.989157i	$-0.546918\pi$
$829$	−8.45711	−0.293727	−0.146864	+	0.989157i	$0.546918\pi$
$830$	7.85230	0.272557
$831$	29.0559	1.00794
$832$	−35.2016	−1.22040
$833$	−5.90456	−0.204581
$834$	24.2776	0.840665
$835$	6.22398	0.215390
$836$	−2.96599	−0.102581
$837$	−24.5000	−0.846845
$838$	14.0179	0.484240
$839$	−16.6498	−0.574815	−0.287407	−	0.957808i	$-0.592793\pi$
$839$	−16.6498	−0.574815	−0.287407	+	0.957808i	$0.592793\pi$
$840$	−9.80082	−0.338160
$841$	−25.4788	−0.878581
$842$	−58.7233	−2.02374
$843$	14.4210	0.496686
$844$	95.3576	3.28234
$845$	−8.17875	−0.281357
$846$	10.9470	0.376364
$847$	−10.9696	−0.376918
$848$	−6.79945	−0.233494
$849$	−24.0689	−0.826041
$850$	−34.5796	−1.18607
$851$	1.38066	0.0473284
$852$	17.3249	0.593542
$853$	13.7746	0.471633	0.235817	−	0.971798i	$-0.424224\pi$
$853$	13.7746	0.471633	0.235817	+	0.971798i	$0.424224\pi$
$854$	13.4703	0.460943
$855$	−6.23252	−0.213148
$856$	3.56423	0.121823
$857$	30.3579	1.03701	0.518503	−	0.855076i	$-0.326490\pi$
$857$	30.3579	1.03701	0.518503	+	0.855076i	$0.326490\pi$
$858$	−2.20008	−0.0751096
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	56.6905	1.93313
$861$	−15.4667	−0.527102
$862$	−6.20435	−0.211321
$863$	23.5508	0.801677	0.400839	−	0.916149i	$-0.368719\pi$
$863$	23.5508	0.801677	0.400839	+	0.916149i	$0.368719\pi$
$864$	−20.9276	−0.711971
$865$	−40.7094	−1.38416
$866$	−91.6329	−3.11381
$867$	34.7668	1.18074
$868$	19.2336	0.652830
$869$	0.820435	0.0278314
$870$	13.3267	0.451817
$871$	−10.4194	−0.353047
$872$	4.10689	0.139077
$873$	−5.67098	−0.191933
$874$	−17.1510	−0.580141
$875$	−11.8385	−0.400215
$876$	−71.8494	−2.42757
$877$	−18.3087	−0.618241	−0.309120	−	0.951023i	$-0.600035\pi$
$877$	−18.3087	−0.618241	−0.309120	+	0.951023i	$0.600035\pi$
$878$	−29.7687	−1.00465
$879$	17.9266	0.604650
$880$	0.182404	0.00614883
$881$	−20.3483	−0.685550	−0.342775	−	0.939418i	$-0.611367\pi$
$881$	−20.3483	−0.685550	−0.342775	+	0.939418i	$0.611367\pi$
$882$	−1.82717	−0.0615239
$883$	18.2537	0.614287	0.307143	−	0.951663i	$-0.400627\pi$
$883$	18.2537	0.614287	0.307143	+	0.951663i	$0.400627\pi$
$884$	−55.7431	−1.87484
$885$	16.1284	0.542149
$886$	6.52467	0.219201
$887$	2.00884	0.0674501	0.0337250	−	0.999431i	$-0.489263\pi$
$887$	2.00884	0.0674501	0.0337250	+	0.999431i	$0.489263\pi$
$888$	5.84970	0.196303
$889$	15.7816	0.529297
$890$	−29.9589	−1.00422
$891$	−1.87450	−0.0627980
$892$	79.1311	2.64950
$893$	30.1297	1.00825
$894$	−11.8439	−0.396118
$895$	−38.7187	−1.29422
$896$	19.5114	0.651830
$897$	−7.99270	−0.266869
$898$	−10.0511	−0.335411
$899$	−10.6779	−0.356126
$900$	−6.72273	−0.224091
$901$	60.4222	2.01296
$902$	3.21639	0.107094
$903$	20.7484	0.690464
$904$	−47.8825	−1.59255
$905$	−25.1664	−0.836558
$906$	−18.4757	−0.613813
$907$	−48.1496	−1.59878	−0.799391	−	0.600811i	$-0.794845\pi$
$907$	−48.1496	−1.59878	−0.799391	+	0.600811i	$0.794845\pi$
$908$	77.9516	2.58692
$909$	−4.23713	−0.140537
$910$	−10.1924	−0.337874
$911$	26.3638	0.873470	0.436735	−	0.899590i	$-0.356135\pi$
$911$	26.3638	0.873470	0.436735	+	0.899590i	$0.356135\pi$
$912$	−6.50332	−0.215346
$913$	−0.375473	−0.0124263
$914$	72.6926	2.40446
$915$	−17.7817	−0.587844
$916$	45.4615	1.50209
$917$	−7.36864	−0.243334
$918$	−58.9664	−1.94618
$919$	27.9681	0.922582	0.461291	−	0.887249i	$-0.347386\pi$
$919$	27.9681	0.922582	0.461291	+	0.887249i	$0.347386\pi$
$920$	7.40440	0.244116
$921$	−17.3178	−0.570642
$922$	43.0772	1.41867
$923$	7.35610	0.242129
$924$	1.14784	0.0377610
$925$	2.37089	0.0779542
$926$	44.0056	1.44611
$927$	4.55630	0.149649
$928$	−9.12086	−0.299407
$929$	−37.0537	−1.21569	−0.607846	−	0.794055i	$-0.707966\pi$
$929$	−37.0537	−1.21569	−0.607846	+	0.794055i	$0.707966\pi$
$930$	−40.4130	−1.32520
$931$	−5.02898	−0.164818
$932$	−18.7227	−0.613282
$933$	−26.8076	−0.877641
$934$	59.3625	1.94240
$935$	−1.62090	−0.0530092
$936$	−7.04281	−0.230201
$937$	19.4512	0.635443	0.317722	−	0.948184i	$-0.397082\pi$
$937$	19.4512	0.635443	0.317722	+	0.948184i	$0.397082\pi$
$938$	8.65262	0.282518
$939$	41.6682	1.35979
$940$	−31.8590	−1.03912
$941$	16.6963	0.544284	0.272142	−	0.962257i	$-0.412268\pi$
$941$	16.6963	0.544284	0.272142	+	0.962257i	$0.412268\pi$
$942$	92.1922	3.00378
$943$	11.6849	0.380512
$944$	3.49999	0.113915
$945$	−6.77366	−0.220347
$946$	−4.31477	−0.140285
$947$	−27.1552	−0.882425	−0.441213	−	0.897403i	$-0.645452\pi$
$947$	−27.1552	−0.882425	−0.441213	+	0.897403i	$0.645452\pi$
$948$	30.9301	1.00456
$949$	−30.5070	−0.990300
$950$	−29.4519	−0.955544
$951$	−39.7010	−1.28739
$952$	18.9000	0.612552
$953$	−22.8322	−0.739606	−0.369803	−	0.929110i	$-0.620575\pi$
$953$	−22.8322	−0.739606	−0.369803	+	0.929110i	$0.620575\pi$
$954$	18.6977	0.605359
$955$	−10.7783	−0.348777
$956$	78.0361	2.52387
$957$	−0.637242	−0.0205991
$958$	−22.7826	−0.736072
$959$	−8.12319	−0.262312
$960$	−38.5892	−1.24546
$961$	1.38046	0.0445310
$962$	6.08340	0.196137
$963$	−0.877159	−0.0282660
$964$	−2.80444	−0.0903250
$965$	40.9530	1.31832
$966$	6.63743	0.213556
$967$	2.07167	0.0666205	0.0333103	−	0.999445i	$-0.489395\pi$
$967$	2.07167	0.0666205	0.0333103	+	0.999445i	$0.489395\pi$
$968$	35.1126	1.12856
$969$	57.7907	1.85650
$970$	26.2701	0.843481
$971$	−43.2494	−1.38794	−0.693969	−	0.720005i	$-0.744140\pi$
$971$	−43.2494	−1.38794	−0.693969	+	0.720005i	$0.744140\pi$
$972$	−27.0097	−0.866338
$973$	−5.37804	−0.172412
$974$	−35.4651	−1.13637
$975$	−13.7252	−0.439557
$976$	−3.85877	−0.123516
$977$	−14.4682	−0.462879	−0.231440	−	0.972849i	$-0.574344\pi$
$977$	−14.4682	−0.462879	−0.231440	+	0.972849i	$0.574344\pi$
$978$	66.7822	2.13546
$979$	1.43254	0.0457842
$980$	5.31760	0.169865
$981$	−1.01071	−0.0322694
$982$	−52.9518	−1.68976
$983$	−33.5992	−1.07165	−0.535824	−	0.844330i	$-0.679999\pi$
$983$	−33.5992	−1.07165	−0.535824	+	0.844330i	$0.679999\pi$
$984$	49.5075	1.57824
$985$	−24.7549	−0.788756
$986$	−25.6993	−0.818433
$987$	−11.6602	−0.371148
$988$	−47.4770	−1.51044
$989$	−15.6752	−0.498441
$990$	−0.501588	−0.0159415
$991$	2.31703	0.0736029	0.0368015	−	0.999323i	$-0.488283\pi$
$991$	2.31703	0.0736029	0.0368015	+	0.999323i	$0.488283\pi$
$992$	27.6589	0.878171
$993$	4.12565	0.130924
$994$	−6.10877	−0.193759
$995$	−24.8593	−0.788094
$996$	−14.1552	−0.448525
$997$	35.2006	1.11481	0.557407	−	0.830239i	$-0.311796\pi$
$997$	35.2006	1.11481	0.557407	+	0.830239i	$0.311796\pi$
$998$	−87.4628	−2.76859
$999$	4.04292	0.127912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.14	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.14	✓	104	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31949 q^{2} +1.94621 q^{3} +3.38001 q^{4} +1.57325 q^{5} -4.51421 q^{6} +1.00000 q^{7} -3.20092 q^{8} +0.787746 q^{9} +O(q^{10})\)	\(q-2.31949 q^{2} +1.94621 q^{3} +3.38001 q^{4} +1.57325 q^{5} -4.51421 q^{6} +1.00000 q^{7} -3.20092 q^{8} +0.787746 q^{9} -3.64913 q^{10} +0.174490 q^{11} +6.57822 q^{12} +2.79309 q^{13} -2.31949 q^{14} +3.06188 q^{15} +0.664454 q^{16} -5.90456 q^{17} -1.82717 q^{18} -5.02898 q^{19} +5.31760 q^{20} +1.94621 q^{21} -0.404728 q^{22} -1.47034 q^{23} -6.22966 q^{24} -2.52488 q^{25} -6.47854 q^{26} -4.30552 q^{27} +3.38001 q^{28} -1.87647 q^{29} -7.10199 q^{30} +5.69038 q^{31} +4.86064 q^{32} +0.339595 q^{33} +13.6955 q^{34} +1.57325 q^{35} +2.66259 q^{36} -0.939008 q^{37} +11.6646 q^{38} +5.43596 q^{39} -5.03584 q^{40} -7.94705 q^{41} -4.51421 q^{42} +10.6609 q^{43} +0.589779 q^{44} +1.23932 q^{45} +3.41043 q^{46} -5.99122 q^{47} +1.29317 q^{48} +1.00000 q^{49} +5.85643 q^{50} -11.4915 q^{51} +9.44069 q^{52} -10.2331 q^{53} +9.98658 q^{54} +0.274517 q^{55} -3.20092 q^{56} -9.78746 q^{57} +4.35245 q^{58} +5.26747 q^{59} +10.3492 q^{60} -5.80744 q^{61} -13.1988 q^{62} +0.787746 q^{63} -12.6031 q^{64} +4.39424 q^{65} -0.787687 q^{66} -3.73040 q^{67} -19.9575 q^{68} -2.86160 q^{69} -3.64913 q^{70} +2.63368 q^{71} -2.52151 q^{72} -10.9223 q^{73} +2.17801 q^{74} -4.91396 q^{75} -16.9980 q^{76} +0.174490 q^{77} -12.6086 q^{78} +4.70189 q^{79} +1.04535 q^{80} -10.7427 q^{81} +18.4331 q^{82} -2.15183 q^{83} +6.57822 q^{84} -9.28935 q^{85} -24.7278 q^{86} -3.65202 q^{87} -0.558529 q^{88} +8.20986 q^{89} -2.87459 q^{90} +2.79309 q^{91} -4.96977 q^{92} +11.0747 q^{93} +13.8966 q^{94} -7.91184 q^{95} +9.45984 q^{96} -7.19899 q^{97} -2.31949 q^{98} +0.137454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more