LMFDB - Embedded newform 6015.2.a.i.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41364 q^{2} +1.00000 q^{3} -0.00162729 q^{4} +1.00000 q^{5} -1.41364 q^{6} -1.83352 q^{7} +2.82958 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.41364 q^{2} +1.00000 q^{3} -0.00162729 q^{4} +1.00000 q^{5} -1.41364 q^{6} -1.83352 q^{7} +2.82958 q^{8} +1.00000 q^{9} -1.41364 q^{10} +4.77336 q^{11} -0.00162729 q^{12} +0.778033 q^{13} +2.59193 q^{14} +1.00000 q^{15} -3.99674 q^{16} +7.82338 q^{17} -1.41364 q^{18} +5.72551 q^{19} -0.00162729 q^{20} -1.83352 q^{21} -6.74781 q^{22} +7.45683 q^{23} +2.82958 q^{24} +1.00000 q^{25} -1.09986 q^{26} +1.00000 q^{27} +0.00298366 q^{28} +10.3578 q^{29} -1.41364 q^{30} +0.923725 q^{31} -0.00920532 q^{32} +4.77336 q^{33} -11.0594 q^{34} -1.83352 q^{35} -0.00162729 q^{36} +2.81750 q^{37} -8.09380 q^{38} +0.778033 q^{39} +2.82958 q^{40} -1.14906 q^{41} +2.59193 q^{42} -2.94769 q^{43} -0.00776763 q^{44} +1.00000 q^{45} -10.5413 q^{46} +10.3529 q^{47} -3.99674 q^{48} -3.63822 q^{49} -1.41364 q^{50} +7.82338 q^{51} -0.00126608 q^{52} -8.82047 q^{53} -1.41364 q^{54} +4.77336 q^{55} -5.18808 q^{56} +5.72551 q^{57} -14.6422 q^{58} +11.2471 q^{59} -0.00162729 q^{60} -11.1616 q^{61} -1.30581 q^{62} -1.83352 q^{63} +8.00650 q^{64} +0.778033 q^{65} -6.74781 q^{66} -0.706618 q^{67} -0.0127309 q^{68} +7.45683 q^{69} +2.59193 q^{70} -5.40502 q^{71} +2.82958 q^{72} -13.6039 q^{73} -3.98292 q^{74} +1.00000 q^{75} -0.00931704 q^{76} -8.75204 q^{77} -1.09986 q^{78} -2.65239 q^{79} -3.99674 q^{80} +1.00000 q^{81} +1.62436 q^{82} +8.65714 q^{83} +0.00298366 q^{84} +7.82338 q^{85} +4.16697 q^{86} +10.3578 q^{87} +13.5066 q^{88} -15.3576 q^{89} -1.41364 q^{90} -1.42654 q^{91} -0.0121344 q^{92} +0.923725 q^{93} -14.6352 q^{94} +5.72551 q^{95} -0.00920532 q^{96} -6.38282 q^{97} +5.14312 q^{98} +4.77336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * 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 $

$2$	−1.41364	−0.999593	−0.499797	−	0.866143i	$-0.666592\pi$
$2$	−1.41364	−0.999593	−0.499797	+	0.866143i	$0.666592\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.00162729	−0.000813643 0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.41364	−0.577115
$7$	−1.83352	−0.693004	−0.346502	−	0.938049i	$-0.612631\pi$
$7$	−1.83352	−0.693004	−0.346502	+	0.938049i	$0.612631\pi$
$8$	2.82958	1.00041
$9$	1.00000	0.333333
$10$	−1.41364	−0.447032
$11$	4.77336	1.43922	0.719612	−	0.694377i	$-0.244320\pi$
$11$	4.77336	1.43922	0.719612	+	0.694377i	$0.244320\pi$
$12$	−0.00162729	−0.000469757 0
$13$	0.778033	0.215788	0.107894	−	0.994162i	$-0.465589\pi$
$13$	0.778033	0.215788	0.107894	+	0.994162i	$0.465589\pi$
$14$	2.59193	0.692722
$15$	1.00000	0.258199
$16$	−3.99674	−0.999186
$17$	7.82338	1.89745	0.948724	−	0.316106i	$-0.102376\pi$
$17$	7.82338	1.89745	0.948724	+	0.316106i	$0.102376\pi$
$18$	−1.41364	−0.333198
$19$	5.72551	1.31352	0.656761	−	0.754099i	$-0.271926\pi$
$19$	5.72551	1.31352	0.656761	+	0.754099i	$0.271926\pi$
$20$	−0.00162729	−0.000363872 0
$21$	−1.83352	−0.400106
$22$	−6.74781	−1.43864
$23$	7.45683	1.55486	0.777428	−	0.628972i	$-0.216524\pi$
$23$	7.45683	1.55486	0.777428	+	0.628972i	$0.216524\pi$
$24$	2.82958	0.577585
$25$	1.00000	0.200000
$26$	−1.09986	−0.215700
$27$	1.00000	0.192450
$28$	0.00298366	0.000563858 0
$29$	10.3578	1.92340	0.961701	−	0.274099i	$-0.0883796\pi$
$29$	10.3578	1.92340	0.961701	+	0.274099i	$0.0883796\pi$
$30$	−1.41364	−0.258094
$31$	0.923725	0.165906	0.0829529	−	0.996553i	$-0.473565\pi$
$31$	0.923725	0.165906	0.0829529	+	0.996553i	$0.473565\pi$
$32$	−0.00920532	−0.00162729
$33$	4.77336	0.830936
$34$	−11.0594	−1.89668
$35$	−1.83352	−0.309921
$36$	−0.00162729	−0.000271214 0
$37$	2.81750	0.463194	0.231597	−	0.972812i	$-0.425605\pi$
$37$	2.81750	0.463194	0.231597	+	0.972812i	$0.425605\pi$
$38$	−8.09380	−1.31299
$39$	0.778033	0.124585
$40$	2.82958	0.447395
$41$	−1.14906	−0.179454	−0.0897268	−	0.995966i	$-0.528599\pi$
$41$	−1.14906	−0.179454	−0.0897268	+	0.995966i	$0.528599\pi$
$42$	2.59193	0.399943
$43$	−2.94769	−0.449519	−0.224759	−	0.974414i	$-0.572160\pi$
$43$	−2.94769	−0.449519	−0.224759	+	0.974414i	$0.572160\pi$
$44$	−0.00776763	−0.00117101
$45$	1.00000	0.149071
$46$	−10.5413	−1.55422
$47$	10.3529	1.51012	0.755062	−	0.655653i	$-0.227607\pi$
$47$	10.3529	1.51012	0.755062	+	0.655653i	$0.227607\pi$
$48$	−3.99674	−0.576880
$49$	−3.63822	−0.519745
$50$	−1.41364	−0.199919
$51$	7.82338	1.09549
$52$	−0.00126608	−0.000175574 0
$53$	−8.82047	−1.21158	−0.605792	−	0.795623i	$-0.707144\pi$
$53$	−8.82047	−1.21158	−0.605792	+	0.795623i	$0.707144\pi$
$54$	−1.41364	−0.192372
$55$	4.77336	0.643640
$56$	−5.18808	−0.693286
$57$	5.72551	0.758362
$58$	−14.6422	−1.92262
$59$	11.2471	1.46424	0.732122	−	0.681173i	$-0.238530\pi$
$59$	11.2471	1.46424	0.732122	+	0.681173i	$0.238530\pi$
$60$	−0.00162729	−0.000210082 0
$61$	−11.1616	−1.42910	−0.714550	−	0.699584i	$-0.753368\pi$
$61$	−11.1616	−1.42910	−0.714550	+	0.699584i	$0.753368\pi$
$62$	−1.30581	−0.165838
$63$	−1.83352	−0.231001
$64$	8.00650	1.00081
$65$	0.778033	0.0965031
$66$	−6.74781	−0.830598
$67$	−0.706618	−0.0863271	−0.0431636	−	0.999068i	$-0.513744\pi$
$67$	−0.706618	−0.0863271	−0.0431636	+	0.999068i	$0.513744\pi$
$68$	−0.0127309	−0.00154385
$69$	7.45683	0.897696
$70$	2.59193	0.309795
$71$	−5.40502	−0.641458	−0.320729	−	0.947171i	$-0.603928\pi$
$71$	−5.40502	−0.641458	−0.320729	+	0.947171i	$0.603928\pi$
$72$	2.82958	0.333469
$73$	−13.6039	−1.59222	−0.796109	−	0.605153i	$-0.793112\pi$
$73$	−13.6039	−1.59222	−0.796109	+	0.605153i	$0.793112\pi$
$74$	−3.98292	−0.463005
$75$	1.00000	0.115470
$76$	−0.00931704	−0.00106874
$77$	−8.75204	−0.997388
$78$	−1.09986	−0.124534
$79$	−2.65239	−0.298417	−0.149209	−	0.988806i	$-0.547673\pi$
$79$	−2.65239	−0.298417	−0.149209	+	0.988806i	$0.547673\pi$
$80$	−3.99674	−0.446849
$81$	1.00000	0.111111
$82$	1.62436	0.179381
$83$	8.65714	0.950244	0.475122	−	0.879920i	$-0.342404\pi$
$83$	8.65714	0.950244	0.475122	+	0.879920i	$0.342404\pi$
$84$	0.00298366	0.000325544 0
$85$	7.82338	0.848564
$86$	4.16697	0.449336
$87$	10.3578	1.11048
$88$	13.5066	1.43981
$89$	−15.3576	−1.62790	−0.813952	−	0.580932i	$-0.802688\pi$
$89$	−15.3576	−1.62790	−0.813952	+	0.580932i	$0.802688\pi$
$90$	−1.41364	−0.149011
$91$	−1.42654	−0.149542
$92$	−0.0121344	−0.00126510
$93$	0.923725	0.0957858
$94$	−14.6352	−1.50951
$95$	5.72551	0.587425
$96$	−0.00920532	−0.000939514 0
$97$	−6.38282	−0.648077	−0.324038	−	0.946044i	$-0.605041\pi$
$97$	−6.38282	−0.648077	−0.324038	+	0.946044i	$0.605041\pi$
$98$	5.14312	0.519534
$99$	4.77336	0.479741
$100$	−0.00162729	−0.000162729 0
$101$	12.0913	1.20313	0.601567	−	0.798822i	$-0.294543\pi$
$101$	12.0913	1.20313	0.601567	+	0.798822i	$0.294543\pi$
$102$	−11.0594	−1.09505
$103$	−10.8074	−1.06489	−0.532443	−	0.846466i	$-0.678726\pi$
$103$	−10.8074	−1.06489	−0.532443	+	0.846466i	$0.678726\pi$
$104$	2.20150	0.215875
$105$	−1.83352	−0.178933
$106$	12.4690	1.21109
$107$	−7.19730	−0.695790	−0.347895	−	0.937534i	$-0.613103\pi$
$107$	−7.19730	−0.695790	−0.347895	+	0.937534i	$0.613103\pi$
$108$	−0.00162729	−0.000156586 0
$109$	−2.34630	−0.224735	−0.112367	−	0.993667i	$-0.535843\pi$
$109$	−2.34630	−0.224735	−0.112367	+	0.993667i	$0.535843\pi$
$110$	−6.74781	−0.643378
$111$	2.81750	0.267425
$112$	7.32809	0.692440
$113$	0.306579	0.0288405	0.0144203	−	0.999896i	$-0.495410\pi$
$113$	0.306579	0.0288405	0.0144203	+	0.999896i	$0.495410\pi$
$114$	−8.09380	−0.758054
$115$	7.45683	0.695353
$116$	−0.0168552	−0.00156496
$117$	0.778033	0.0719292
$118$	−15.8993	−1.46365
$119$	−14.3443	−1.31494
$120$	2.82958	0.258304
$121$	11.7850	1.07136
$122$	15.7785	1.42852
$123$	−1.14906	−0.103608
$124$	−0.00150316	−0.000134988 0
$125$	1.00000	0.0894427
$126$	2.59193	0.230907
$127$	4.40128	0.390550	0.195275	−	0.980748i	$-0.437440\pi$
$127$	4.40128	0.390550	0.195275	+	0.980748i	$0.437440\pi$
$128$	−11.2999	−0.998778
$129$	−2.94769	−0.259530
$130$	−1.09986	−0.0964639
$131$	8.80009	0.768867	0.384434	−	0.923153i	$-0.374397\pi$
$131$	8.80009	0.768867	0.384434	+	0.923153i	$0.374397\pi$
$132$	−0.00776763	−0.000676085 0
$133$	−10.4978	−0.910276
$134$	0.998902	0.0862920
$135$	1.00000	0.0860663
$136$	22.1368	1.89822
$137$	−1.00799	−0.0861185	−0.0430592	−	0.999073i	$-0.513710\pi$
$137$	−1.00799	−0.0861185	−0.0430592	+	0.999073i	$0.513710\pi$
$138$	−10.5413	−0.897331
$139$	6.16439	0.522856	0.261428	−	0.965223i	$-0.415807\pi$
$139$	6.16439	0.522856	0.261428	+	0.965223i	$0.415807\pi$
$140$	0.00298366	0.000252165 0
$141$	10.3529	0.871871
$142$	7.64074	0.641197
$143$	3.71384	0.310567
$144$	−3.99674	−0.333062
$145$	10.3578	0.860172
$146$	19.2310	1.59157
$147$	−3.63822	−0.300075
$148$	−0.00458487	−0.000376874 0
$149$	−7.29305	−0.597470	−0.298735	−	0.954336i	$-0.596565\pi$
$149$	−7.29305	−0.597470	−0.298735	+	0.954336i	$0.596565\pi$
$150$	−1.41364	−0.115423
$151$	−7.78403	−0.633456	−0.316728	−	0.948516i	$-0.602584\pi$
$151$	−7.78403	−0.633456	−0.316728	+	0.948516i	$0.602584\pi$
$152$	16.2008	1.31406
$153$	7.82338	0.632483
$154$	12.3722	0.996982
$155$	0.923725	0.0741954
$156$	−0.00126608	−0.000101368 0
$157$	−6.13735	−0.489814	−0.244907	−	0.969547i	$-0.578757\pi$
$157$	−6.13735	−0.489814	−0.244907	+	0.969547i	$0.578757\pi$
$158$	3.74952	0.298296
$159$	−8.82047	−0.699509
$160$	−0.00920532	−0.000727744 0
$161$	−13.6722	−1.07752
$162$	−1.41364	−0.111066
$163$	0.315606	0.0247202	0.0123601	−	0.999924i	$-0.496066\pi$
$163$	0.315606	0.0247202	0.0123601	+	0.999924i	$0.496066\pi$
$164$	0.00186986	0.000146011 0
$165$	4.77336	0.371606
$166$	−12.2381	−0.949858
$167$	−19.0190	−1.47174	−0.735869	−	0.677124i	$-0.763226\pi$
$167$	−19.0190	−1.47174	−0.735869	+	0.677124i	$0.763226\pi$
$168$	−5.18808	−0.400269
$169$	−12.3947	−0.953436
$170$	−11.0594	−0.848219
$171$	5.72551	0.437841
$172$	0.00479674	0.000365748 0
$173$	−17.9952	−1.36815	−0.684076	−	0.729411i	$-0.739794\pi$
$173$	−17.9952	−1.36815	−0.684076	+	0.729411i	$0.739794\pi$
$174$	−14.6422	−1.11003
$175$	−1.83352	−0.138601
$176$	−19.0779	−1.43805
$177$	11.2471	0.845382
$178$	21.7101	1.62724
$179$	−7.54868	−0.564215	−0.282108	−	0.959383i	$-0.591034\pi$
$179$	−7.54868	−0.564215	−0.282108	+	0.959383i	$0.591034\pi$
$180$	−0.00162729	−0.000121291 0
$181$	8.22845	0.611616	0.305808	−	0.952093i	$-0.401073\pi$
$181$	8.22845	0.611616	0.305808	+	0.952093i	$0.401073\pi$
$182$	2.01661	0.149481
$183$	−11.1616	−0.825091
$184$	21.0997	1.55549
$185$	2.81750	0.207146
$186$	−1.30581	−0.0957468
$187$	37.3438	2.73085
$188$	−0.0168471	−0.00122870
$189$	−1.83352	−0.133369
$190$	−8.09380	−0.587186
$191$	26.7633	1.93652	0.968261	−	0.249942i	$-0.0804116\pi$
$191$	26.7633	1.93652	0.968261	+	0.249942i	$0.0804116\pi$
$192$	8.00650	0.577819
$193$	7.84613	0.564777	0.282388	−	0.959300i	$-0.408873\pi$
$193$	7.84613	0.564777	0.282388	+	0.959300i	$0.408873\pi$
$194$	9.02299	0.647813
$195$	0.778033	0.0557161
$196$	0.00592042	0.000422887 0
$197$	3.75233	0.267342	0.133671	−	0.991026i	$-0.457323\pi$
$197$	3.75233	0.267342	0.133671	+	0.991026i	$0.457323\pi$
$198$	−6.74781	−0.479546
$199$	10.5149	0.745385	0.372692	−	0.927955i	$-0.378435\pi$
$199$	10.5149	0.745385	0.372692	+	0.927955i	$0.378435\pi$
$200$	2.82958	0.200081
$201$	−0.706618	−0.0498410
$202$	−17.0928	−1.20264
$203$	−18.9913	−1.33293
$204$	−0.0127309	−0.000891339 0
$205$	−1.14906	−0.0802541
$206$	15.2778	1.06445
$207$	7.45683	0.518285
$208$	−3.10960	−0.215612
$209$	27.3299	1.89045
$210$	2.59193	0.178860
$211$	−18.3009	−1.25989	−0.629944	−	0.776641i	$-0.716922\pi$
$211$	−18.3009	−1.25989	−0.629944	+	0.776641i	$0.716922\pi$
$212$	0.0143534	0.000985798 0
$213$	−5.40502	−0.370346
$214$	10.1744	0.695506
$215$	−2.94769	−0.201031
$216$	2.82958	0.192528
$217$	−1.69367	−0.114973
$218$	3.31682	0.224643
$219$	−13.6039	−0.919268
$220$	−0.00776763	−0.000523693 0
$221$	6.08685	0.409446
$222$	−3.98292	−0.267316
$223$	−8.42216	−0.563990	−0.281995	−	0.959416i	$-0.590996\pi$
$223$	−8.42216	−0.563990	−0.281995	+	0.959416i	$0.590996\pi$
$224$	0.0168781	0.00112772
$225$	1.00000	0.0666667
$226$	−0.433392	−0.0288288
$227$	−0.857378	−0.0569062	−0.0284531	−	0.999595i	$-0.509058\pi$
$227$	−0.857378	−0.0569062	−0.0284531	+	0.999595i	$0.509058\pi$
$228$	−0.00931704	−0.000617036 0
$229$	−11.0002	−0.726913	−0.363457	−	0.931611i	$-0.618403\pi$
$229$	−11.0002	−0.726913	−0.363457	+	0.931611i	$0.618403\pi$
$230$	−10.5413	−0.695070
$231$	−8.75204	−0.575842
$232$	29.3083	1.92418
$233$	10.6777	0.699518	0.349759	−	0.936840i	$-0.386263\pi$
$233$	10.6777	0.699518	0.349759	+	0.936840i	$0.386263\pi$
$234$	−1.09986	−0.0718999
$235$	10.3529	0.675348
$236$	−0.0183022	−0.00119137
$237$	−2.65239	−0.172291
$238$	20.2776	1.31440
$239$	−22.4151	−1.44991	−0.724956	−	0.688795i	$-0.758140\pi$
$239$	−22.4151	−1.44991	−0.724956	+	0.688795i	$0.758140\pi$
$240$	−3.99674	−0.257989
$241$	23.1582	1.49175	0.745875	−	0.666086i	$-0.232032\pi$
$241$	23.1582	1.49175	0.745875	+	0.666086i	$0.232032\pi$
$242$	−16.6597	−1.07093
$243$	1.00000	0.0641500
$244$	0.0181632	0.00116278
$245$	−3.63822	−0.232437
$246$	1.62436	0.103565
$247$	4.45464	0.283442
$248$	2.61375	0.165973
$249$	8.65714	0.548624
$250$	−1.41364	−0.0894063
$251$	−19.9209	−1.25740	−0.628698	−	0.777650i	$-0.716412\pi$
$251$	−19.9209	−1.25740	−0.628698	+	0.777650i	$0.716412\pi$
$252$	0.00298366	0.000187953 0
$253$	35.5941	2.23778
$254$	−6.22182	−0.390391
$255$	7.82338	0.489919
$256$	−0.0390548	−0.00244093
$257$	9.91977	0.618778	0.309389	−	0.950935i	$-0.399875\pi$
$257$	9.91977	0.618778	0.309389	+	0.950935i	$0.399875\pi$
$258$	4.16697	0.259424
$259$	−5.16593	−0.320995
$260$	−0.00126608	−7.85191e−5 0
$261$	10.3578	0.641134
$262$	−12.4401	−0.768554
$263$	−29.8458	−1.84037	−0.920187	−	0.391480i	$-0.871963\pi$
$263$	−29.8458	−1.84037	−0.920187	+	0.391480i	$0.871963\pi$
$264$	13.5066	0.831274
$265$	−8.82047	−0.541837
$266$	14.8401	0.909906
$267$	−15.3576	−0.939871
$268$	0.00114987	7.02395e−5 0
$269$	8.96915	0.546859	0.273429	−	0.961892i	$-0.411842\pi$
$269$	8.96915	0.546859	0.273429	+	0.961892i	$0.411842\pi$
$270$	−1.41364	−0.0860313
$271$	−14.9350	−0.907238	−0.453619	−	0.891196i	$-0.649867\pi$
$271$	−14.9350	−0.907238	−0.453619	+	0.891196i	$0.649867\pi$
$272$	−31.2680	−1.89590
$273$	−1.42654	−0.0863379
$274$	1.42493	0.0860835
$275$	4.77336	0.287845
$276$	−0.0121344	−0.000730404 0
$277$	4.87004	0.292612	0.146306	−	0.989239i	$-0.453262\pi$
$277$	4.87004	0.292612	0.146306	+	0.989239i	$0.453262\pi$
$278$	−8.71421	−0.522644
$279$	0.923725	0.0553020
$280$	−5.18808	−0.310047
$281$	−3.80017	−0.226699	−0.113350	−	0.993555i	$-0.536158\pi$
$281$	−3.80017	−0.226699	−0.113350	+	0.993555i	$0.536158\pi$
$282$	−14.6352	−0.871516
$283$	−31.6749	−1.88288	−0.941439	−	0.337184i	$-0.890525\pi$
$283$	−31.6749	−1.88288	−0.941439	+	0.337184i	$0.890525\pi$
$284$	0.00879551	0.000521918 0
$285$	5.72551	0.339150
$286$	−5.25002	−0.310440
$287$	2.10683	0.124362
$288$	−0.00920532	−0.000542429 0
$289$	44.2052	2.60031
$290$	−14.6422	−0.859822
$291$	−6.38282	−0.374167
$292$	0.0221375	0.00129550
$293$	9.57604	0.559438	0.279719	−	0.960082i	$-0.409759\pi$
$293$	9.57604	0.559438	0.279719	+	0.960082i	$0.409759\pi$
$294$	5.14312	0.299953
$295$	11.2471	0.654830
$296$	7.97232	0.463382
$297$	4.77336	0.276979
$298$	10.3097	0.597227
$299$	5.80166	0.335519
$300$	−0.00162729	−9.39514e−5 0
$301$	5.40464	0.311518
$302$	11.0038	0.633198
$303$	12.0913	0.694630
$304$	−22.8834	−1.31245
$305$	−11.1616	−0.639113
$306$	−11.0594	−0.632225
$307$	27.1010	1.54674	0.773369	−	0.633957i	$-0.218570\pi$
$307$	27.1010	1.54674	0.773369	+	0.633957i	$0.218570\pi$
$308$	0.0142421	0.000811518 0
$309$	−10.8074	−0.614812
$310$	−1.30581	−0.0741652
$311$	−16.3500	−0.927123	−0.463561	−	0.886065i	$-0.653429\pi$
$311$	−16.3500	−0.927123	−0.463561	+	0.886065i	$0.653429\pi$
$312$	2.20150	0.124636
$313$	−22.9659	−1.29811	−0.649055	−	0.760741i	$-0.724836\pi$
$313$	−22.9659	−1.29811	−0.649055	+	0.760741i	$0.724836\pi$
$314$	8.67599	0.489615
$315$	−1.83352	−0.103307
$316$	0.00431620	0.000242805 0
$317$	25.2680	1.41919	0.709596	−	0.704609i	$-0.248878\pi$
$317$	25.2680	1.41919	0.709596	+	0.704609i	$0.248878\pi$
$318$	12.4690	0.699224
$319$	49.4417	2.76821
$320$	8.00650	0.447577
$321$	−7.19730	−0.401714
$322$	19.3276	1.07708
$323$	44.7928	2.49234
$324$	−0.00162729	−9.04048e−5 0
$325$	0.778033	0.0431575
$326$	−0.446153	−0.0247101
$327$	−2.34630	−0.129751
$328$	−3.25137	−0.179527
$329$	−18.9822	−1.04652
$330$	−6.74781	−0.371455
$331$	25.6893	1.41201	0.706007	−	0.708205i	$-0.250495\pi$
$331$	25.6893	1.41201	0.706007	+	0.708205i	$0.250495\pi$
$332$	−0.0140876	−0.000773160 0
$333$	2.81750	0.154398
$334$	26.8861	1.47114
$335$	−0.706618	−0.0386067
$336$	7.32809	0.399780
$337$	−25.1613	−1.37063	−0.685313	−	0.728249i	$-0.740334\pi$
$337$	−25.1613	−1.37063	−0.685313	+	0.728249i	$0.740334\pi$
$338$	17.5216	0.953048
$339$	0.306579	0.0166511
$340$	−0.0127309	−0.000690429 0
$341$	4.40927	0.238776
$342$	−8.09380	−0.437663
$343$	19.5053	1.05319
$344$	−8.34072	−0.449701
$345$	7.45683	0.401462
$346$	25.4387	1.36759
$347$	−19.8841	−1.06743	−0.533717	−	0.845663i	$-0.679205\pi$
$347$	−19.8841	−1.06743	−0.533717	+	0.845663i	$0.679205\pi$
$348$	−0.0168552	−0.000903532 0
$349$	18.4338	0.986739	0.493370	−	0.869820i	$-0.335765\pi$
$349$	18.4338	0.986739	0.493370	+	0.869820i	$0.335765\pi$
$350$	2.59193	0.138544
$351$	0.778033	0.0415283
$352$	−0.0439403	−0.00234203
$353$	−7.36231	−0.391856	−0.195928	−	0.980618i	$-0.562772\pi$
$353$	−7.36231	−0.391856	−0.195928	+	0.980618i	$0.562772\pi$
$354$	−15.8993	−0.845038
$355$	−5.40502	−0.286869
$356$	0.0249912	0.00132453
$357$	−14.3443	−0.759181
$358$	10.6711	0.563986
$359$	−30.6076	−1.61541	−0.807704	−	0.589588i	$-0.799290\pi$
$359$	−30.6076	−1.61541	−0.807704	+	0.589588i	$0.799290\pi$
$360$	2.82958	0.149132
$361$	13.7815	0.725341
$362$	−11.6321	−0.611367
$363$	11.7850	0.618552
$364$	0.00232138	0.000121674 0
$365$	−13.6039	−0.712062
$366$	15.7785	0.824755
$367$	−27.8719	−1.45490	−0.727450	−	0.686161i	$-0.759295\pi$
$367$	−27.8719	−1.45490	−0.727450	+	0.686161i	$0.759295\pi$
$368$	−29.8030	−1.55359
$369$	−1.14906	−0.0598179
$370$	−3.98292	−0.207062
$371$	16.1725	0.839633
$372$	−0.00150316	−7.79354e−5 0
$373$	1.50273	0.0778085	0.0389043	−	0.999243i	$-0.487613\pi$
$373$	1.50273	0.0778085	0.0389043	+	0.999243i	$0.487613\pi$
$374$	−52.7907	−2.72974
$375$	1.00000	0.0516398
$376$	29.2943	1.51074
$377$	8.05875	0.415047
$378$	2.59193	0.133314
$379$	−9.43682	−0.484737	−0.242368	−	0.970184i	$-0.577924\pi$
$379$	−9.43682	−0.484737	−0.242368	+	0.970184i	$0.577924\pi$
$380$	−0.00931704	−0.000477954 0
$381$	4.40128	0.225484
$382$	−37.8336	−1.93573
$383$	−1.04809	−0.0535549	−0.0267775	−	0.999641i	$-0.508525\pi$
$383$	−1.04809	−0.0535549	−0.0267775	+	0.999641i	$0.508525\pi$
$384$	−11.2999	−0.576645
$385$	−8.75204	−0.446045
$386$	−11.0916	−0.564547
$387$	−2.94769	−0.149840
$388$	0.0103867	0.000527303 0
$389$	−5.64210	−0.286066	−0.143033	−	0.989718i	$-0.545685\pi$
$389$	−5.64210	−0.286066	−0.143033	+	0.989718i	$0.545685\pi$
$390$	−1.09986	−0.0556934
$391$	58.3376	2.95026
$392$	−10.2946	−0.519956
$393$	8.80009	0.443906
$394$	−5.30443	−0.267234
$395$	−2.65239	−0.133456
$396$	−0.00776763	−0.000390338 0
$397$	−6.76095	−0.339323	−0.169661	−	0.985502i	$-0.554267\pi$
$397$	−6.76095	−0.339323	−0.169661	+	0.985502i	$0.554267\pi$
$398$	−14.8643	−0.745081
$399$	−10.4978	−0.525548
$400$	−3.99674	−0.199837
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	0.998902	0.0498207
$403$	0.718689	0.0358004
$404$	−0.0196761	−0.000978922 0
$405$	1.00000	0.0496904
$406$	26.8468	1.33238
$407$	13.4489	0.666639
$408$	22.1368	1.09594
$409$	−25.7316	−1.27235	−0.636174	−	0.771546i	$-0.719484\pi$
$409$	−25.7316	−1.27235	−0.636174	+	0.771546i	$0.719484\pi$
$410$	1.62436	0.0802215
$411$	−1.00799	−0.0497205
$412$	0.0175868	0.000866437 0
$413$	−20.6217	−1.01473
$414$	−10.5413	−0.518074
$415$	8.65714	0.424962
$416$	−0.00716204	−0.000351148 0
$417$	6.16439	0.301871
$418$	−38.6347	−1.88968
$419$	19.5708	0.956095	0.478047	−	0.878334i	$-0.341345\pi$
$419$	19.5708	0.956095	0.478047	+	0.878334i	$0.341345\pi$
$420$	0.00298366	0.000145588 0
$421$	−7.08450	−0.345278	−0.172639	−	0.984985i	$-0.555229\pi$
$421$	−7.08450	−0.345278	−0.172639	+	0.984985i	$0.555229\pi$
$422$	25.8709	1.25937
$423$	10.3529	0.503375
$424$	−24.9582	−1.21208
$425$	7.82338	0.379490
$426$	7.64074	0.370195
$427$	20.4650	0.990372
$428$	0.0117121	0.000566124 0
$429$	3.71384	0.179306
$430$	4.16697	0.200949
$431$	15.9715	0.769318	0.384659	−	0.923059i	$-0.374319\pi$
$431$	15.9715	0.769318	0.384659	+	0.923059i	$0.374319\pi$
$432$	−3.99674	−0.192293
$433$	14.7328	0.708013	0.354007	−	0.935243i	$-0.384819\pi$
$433$	14.7328	0.708013	0.354007	+	0.935243i	$0.384819\pi$
$434$	2.39423	0.114927
$435$	10.3578	0.496621
$436$	0.00381810	0.000182854 0
$437$	42.6941	2.04234
$438$	19.2310	0.918894
$439$	−10.6909	−0.510247	−0.255123	−	0.966909i	$-0.582116\pi$
$439$	−10.6909	−0.510247	−0.255123	+	0.966909i	$0.582116\pi$
$440$	13.5066	0.643902
$441$	−3.63822	−0.173248
$442$	−8.60460	−0.409279
$443$	−24.0839	−1.14426	−0.572131	−	0.820162i	$-0.693883\pi$
$443$	−24.0839	−1.14426	−0.572131	+	0.820162i	$0.693883\pi$
$444$	−0.00458487	−0.000217588 0
$445$	−15.3576	−0.728021
$446$	11.9059	0.563760
$447$	−7.29305	−0.344949
$448$	−14.6800	−0.693567
$449$	20.3110	0.958537	0.479268	−	0.877668i	$-0.340902\pi$
$449$	20.3110	0.958537	0.479268	+	0.877668i	$0.340902\pi$
$450$	−1.41364	−0.0666395
$451$	−5.48490	−0.258274
$452$	−0.000498891 0	−2.34659e−5 0
$453$	−7.78403	−0.365726
$454$	1.21202	0.0568831
$455$	−1.42654	−0.0668771
$456$	16.2008	0.758671
$457$	−21.1565	−0.989660	−0.494830	−	0.868990i	$-0.664770\pi$
$457$	−21.1565	−0.989660	−0.494830	+	0.868990i	$0.664770\pi$
$458$	15.5503	0.726617
$459$	7.82338	0.365164
$460$	−0.0121344	−0.000565769 0
$461$	−29.0613	−1.35352	−0.676759	−	0.736205i	$-0.736616\pi$
$461$	−29.0613	−1.35352	−0.676759	+	0.736205i	$0.736616\pi$
$462$	12.3722	0.575608
$463$	−36.4687	−1.69484	−0.847422	−	0.530919i	$-0.821847\pi$
$463$	−36.4687	−1.69484	−0.847422	+	0.530919i	$0.821847\pi$
$464$	−41.3976	−1.92184
$465$	0.923725	0.0428367
$466$	−15.0944	−0.699234
$467$	31.2421	1.44571	0.722855	−	0.690999i	$-0.242829\pi$
$467$	31.2421	1.44571	0.722855	+	0.690999i	$0.242829\pi$
$468$	−0.00126608	−5.85247e−5 0
$469$	1.29560	0.0598251
$470$	−14.6352	−0.675073
$471$	−6.13735	−0.282794
$472$	31.8245	1.46484
$473$	−14.0704	−0.646958
$474$	3.74952	0.172221
$475$	5.72551	0.262704
$476$	0.0233423	0.00106989
$477$	−8.82047	−0.403862
$478$	31.6868	1.44932
$479$	9.95571	0.454888	0.227444	−	0.973791i	$-0.426963\pi$
$479$	9.95571	0.454888	0.227444	+	0.973791i	$0.426963\pi$
$480$	−0.00920532	−0.000420163 0
$481$	2.19211	0.0999514
$482$	−32.7373	−1.49114
$483$	−13.6722	−0.622107
$484$	−0.0191776	−0.000871707 0
$485$	−6.38282	−0.289829
$486$	−1.41364	−0.0641239
$487$	−24.0858	−1.09143	−0.545717	−	0.837970i	$-0.683742\pi$
$487$	−24.0858	−1.09143	−0.545717	+	0.837970i	$0.683742\pi$
$488$	−31.5827	−1.42968
$489$	0.315606	0.0142722
$490$	5.14312	0.232343
$491$	−9.06322	−0.409017	−0.204509	−	0.978865i	$-0.565560\pi$
$491$	−9.06322	−0.409017	−0.204509	+	0.978865i	$0.565560\pi$
$492$	0.00186986	8.42996e−5 0
$493$	81.0333	3.64956
$494$	−6.29725	−0.283326
$495$	4.77336	0.214547
$496$	−3.69189	−0.165771
$497$	9.91020	0.444533
$498$	−12.2381	−0.548401
$499$	−31.7777	−1.42257	−0.711283	−	0.702906i	$-0.751886\pi$
$499$	−31.7777	−1.42257	−0.711283	+	0.702906i	$0.751886\pi$
$500$	−0.00162729	−7.27744e−5 0
$501$	−19.0190	−0.849708
$502$	28.1609	1.25688
$503$	−30.3024	−1.35112	−0.675559	−	0.737306i	$-0.736098\pi$
$503$	−30.3024	−1.35112	−0.675559	+	0.737306i	$0.736098\pi$
$504$	−5.18808	−0.231095
$505$	12.0913	0.538058
$506$	−50.3172	−2.23687
$507$	−12.3947	−0.550466
$508$	−0.00716214	−0.000317769 0
$509$	−4.39346	−0.194737	−0.0973684	−	0.995248i	$-0.531043\pi$
$509$	−4.39346	−0.194737	−0.0973684	+	0.995248i	$0.531043\pi$
$510$	−11.0594	−0.489720
$511$	24.9430	1.10341
$512$	22.6550	1.00122
$513$	5.72551	0.252787
$514$	−14.0230	−0.618527
$515$	−10.8074	−0.476232
$516$	0.00479674	0.000211165 0
$517$	49.4181	2.17341
$518$	7.30275	0.320864
$519$	−17.9952	−0.789902
$520$	2.20150	0.0965424
$521$	−34.2767	−1.50169	−0.750844	−	0.660480i	$-0.770353\pi$
$521$	−34.2767	−1.50169	−0.750844	+	0.660480i	$0.770353\pi$
$522$	−14.6422	−0.640873
$523$	−40.8147	−1.78470	−0.892350	−	0.451343i	$-0.850945\pi$
$523$	−40.8147	−1.78470	−0.892350	+	0.451343i	$0.850945\pi$
$524$	−0.0143203	−0.000625583 0
$525$	−1.83352	−0.0800212
$526$	42.1912	1.83962
$527$	7.22665	0.314798
$528$	−19.0779	−0.830259
$529$	32.6043	1.41758
$530$	12.4690	0.541617
$531$	11.2471	0.488081
$532$	0.0170830	0.000740640 0
$533$	−0.894010	−0.0387239
$534$	21.7101	0.939489
$535$	−7.19730	−0.311167
$536$	−1.99943	−0.0863622
$537$	−7.54868	−0.325750
$538$	−12.6791	−0.546636
$539$	−17.3665	−0.748029
$540$	−0.00162729	−7.00272e−5 0
$541$	−15.6032	−0.670835	−0.335418	−	0.942070i	$-0.608877\pi$
$541$	−15.6032	−0.670835	−0.335418	+	0.942070i	$0.608877\pi$
$542$	21.1127	0.906869
$543$	8.22845	0.353117
$544$	−0.0720167	−0.00308769
$545$	−2.34630	−0.100504
$546$	2.01661	0.0863028
$547$	−7.89452	−0.337545	−0.168773	−	0.985655i	$-0.553980\pi$
$547$	−7.89452	−0.337545	−0.168773	+	0.985655i	$0.553980\pi$
$548$	0.00164029	7.00697e−5 0
$549$	−11.1616	−0.476367
$550$	−6.74781	−0.287728
$551$	59.3039	2.52643
$552$	21.0997	0.898061
$553$	4.86320	0.206804
$554$	−6.88448	−0.292493
$555$	2.81750	0.119596
$556$	−0.0100312	−0.000425419 0
$557$	16.3058	0.690899	0.345450	−	0.938437i	$-0.387726\pi$
$557$	16.3058	0.690899	0.345450	+	0.938437i	$0.387726\pi$
$558$	−1.30581	−0.0552795
$559$	−2.29340	−0.0970005
$560$	7.32809	0.309669
$561$	37.3438	1.57666
$562$	5.37206	0.226607
$563$	−6.23532	−0.262787	−0.131394	−	0.991330i	$-0.541945\pi$
$563$	−6.23532	−0.262787	−0.131394	+	0.991330i	$0.541945\pi$
$564$	−0.0168471	−0.000709392 0
$565$	0.306579	0.0128979
$566$	44.7768	1.88211
$567$	−1.83352	−0.0770005
$568$	−15.2939	−0.641719
$569$	41.7271	1.74929	0.874646	−	0.484762i	$-0.161094\pi$
$569$	41.7271	1.74929	0.874646	+	0.484762i	$0.161094\pi$
$570$	−8.09380	−0.339012
$571$	32.8723	1.37566	0.687831	−	0.725871i	$-0.258563\pi$
$571$	32.8723	1.37566	0.687831	+	0.725871i	$0.258563\pi$
$572$	−0.00604347	−0.000252690 0
$573$	26.7633	1.11805
$574$	−2.97829	−0.124312
$575$	7.45683	0.310971
$576$	8.00650	0.333604
$577$	43.4076	1.80708	0.903541	−	0.428502i	$-0.140959\pi$
$577$	43.4076	1.80708	0.903541	+	0.428502i	$0.140959\pi$
$578$	−62.4902	−2.59925
$579$	7.84613	0.326074
$580$	−0.0168552	−0.000699873 0
$581$	−15.8730	−0.658523
$582$	9.02299	0.374015
$583$	−42.1033	−1.74374
$584$	−38.4933	−1.59287
$585$	0.778033	0.0321677
$586$	−13.5371	−0.559211
$587$	−12.9790	−0.535700	−0.267850	−	0.963461i	$-0.586313\pi$
$587$	−12.9790	−0.535700	−0.267850	+	0.963461i	$0.586313\pi$
$588$	0.00592042	0.000244154 0
$589$	5.28880	0.217921
$590$	−15.8993	−0.654563
$591$	3.75233	0.154350
$592$	−11.2608	−0.462816
$593$	19.8788	0.816324	0.408162	−	0.912910i	$-0.366170\pi$
$593$	19.8788	0.816324	0.408162	+	0.912910i	$0.366170\pi$
$594$	−6.74781	−0.276866
$595$	−14.3443	−0.588059
$596$	0.0118679	0.000486127 0
$597$	10.5149	0.430348
$598$	−8.20145	−0.335382
$599$	25.2633	1.03223	0.516114	−	0.856520i	$-0.327378\pi$
$599$	25.2633	1.03223	0.516114	+	0.856520i	$0.327378\pi$
$600$	2.82958	0.115517
$601$	34.3552	1.40138	0.700689	−	0.713467i	$-0.252876\pi$
$601$	34.3552	1.40138	0.700689	+	0.713467i	$0.252876\pi$
$602$	−7.64021	−0.311392
$603$	−0.706618	−0.0287757
$604$	0.0126668	0.000515407 0
$605$	11.7850	0.479128
$606$	−17.0928	−0.694347
$607$	−21.8149	−0.885438	−0.442719	−	0.896661i	$-0.645986\pi$
$607$	−21.8149	−0.885438	−0.442719	+	0.896661i	$0.645986\pi$
$608$	−0.0527051	−0.00213748
$609$	−18.9913	−0.769565
$610$	15.7785	0.638853
$611$	8.05489	0.325866
$612$	−0.0127309	−0.000514615 0
$613$	−10.0349	−0.405307	−0.202653	−	0.979251i	$-0.564956\pi$
$613$	−10.0349	−0.405307	−0.202653	+	0.979251i	$0.564956\pi$
$614$	−38.3110	−1.54611
$615$	−1.14906	−0.0463347
$616$	−24.7646	−0.997793
$617$	−23.5419	−0.947759	−0.473880	−	0.880590i	$-0.657147\pi$
$617$	−23.5419	−0.947759	−0.473880	+	0.880590i	$0.657147\pi$
$618$	15.2778	0.614562
$619$	−22.1368	−0.889754	−0.444877	−	0.895592i	$-0.646753\pi$
$619$	−22.1368	−0.889754	−0.444877	+	0.895592i	$0.646753\pi$
$620$	−0.00150316	−6.03685e−5 0
$621$	7.45683	0.299232
$622$	23.1130	0.926746
$623$	28.1585	1.12814
$624$	−3.10960	−0.124484
$625$	1.00000	0.0400000
$626$	32.4655	1.29758
$627$	27.3299	1.09145
$628$	0.00998723	0.000398534 0
$629$	22.0423	0.878886
$630$	2.59193	0.103265
$631$	22.9158	0.912263	0.456132	−	0.889912i	$-0.349235\pi$
$631$	22.9158	0.912263	0.456132	+	0.889912i	$0.349235\pi$
$632$	−7.50514	−0.298538
$633$	−18.3009	−0.727396
$634$	−35.7198	−1.41861
$635$	4.40128	0.174659
$636$	0.0143534	0.000569151 0
$637$	−2.83065	−0.112155
$638$	−69.8927	−2.76708
$639$	−5.40502	−0.213819
$640$	−11.2999	−0.446667
$641$	−9.48451	−0.374616	−0.187308	−	0.982301i	$-0.559976\pi$
$641$	−9.48451	−0.374616	−0.187308	+	0.982301i	$0.559976\pi$
$642$	10.1744	0.401551
$643$	22.4651	0.885936	0.442968	−	0.896537i	$-0.353926\pi$
$643$	22.4651	0.885936	0.442968	+	0.896537i	$0.353926\pi$
$644$	0.0222486	0.000876718 0
$645$	−2.94769	−0.116065
$646$	−63.3209	−2.49133
$647$	29.2050	1.14817	0.574084	−	0.818797i	$-0.305358\pi$
$647$	29.2050	1.14817	0.574084	+	0.818797i	$0.305358\pi$
$648$	2.82958	0.111156
$649$	53.6864	2.10737
$650$	−1.09986	−0.0431400
$651$	−1.69367	−0.0663800
$652$	−0.000513582 0	−2.01134e−5 0
$653$	−23.2166	−0.908538	−0.454269	−	0.890865i	$-0.650099\pi$
$653$	−23.2166	−0.908538	−0.454269	+	0.890865i	$0.650099\pi$
$654$	3.31682	0.129698
$655$	8.80009	0.343848
$656$	4.59251	0.179308
$657$	−13.6039	−0.530740
$658$	26.8340	1.04610
$659$	47.3914	1.84611	0.923054	−	0.384670i	$-0.125685\pi$
$659$	47.3914	1.84611	0.923054	+	0.384670i	$0.125685\pi$
$660$	−0.00776763	−0.000302354 0
$661$	−38.4596	−1.49591	−0.747953	−	0.663752i	$-0.768963\pi$
$661$	−38.4596	−1.49591	−0.747953	+	0.663752i	$0.768963\pi$
$662$	−36.3154	−1.41144
$663$	6.08685	0.236394
$664$	24.4960	0.950630
$665$	−10.4978	−0.407088
$666$	−3.98292	−0.154335
$667$	77.2366	2.99061
$668$	0.0309494	0.00119747
$669$	−8.42216	−0.325620
$670$	0.998902	0.0385910
$671$	−53.2785	−2.05679
$672$	0.0168781	0.000651087 0
$673$	−12.5916	−0.485370	−0.242685	−	0.970105i	$-0.578028\pi$
$673$	−12.5916	−0.485370	−0.242685	+	0.970105i	$0.578028\pi$
$674$	35.5690	1.37007
$675$	1.00000	0.0384900
$676$	0.0201697	0.000775756 0
$677$	21.0329	0.808360	0.404180	−	0.914679i	$-0.367557\pi$
$677$	21.0329	0.808360	0.404180	+	0.914679i	$0.367557\pi$
$678$	−0.433392	−0.0166443
$679$	11.7030	0.449120
$680$	22.1368	0.848909
$681$	−0.857378	−0.0328548
$682$	−6.23312	−0.238678
$683$	−22.9288	−0.877348	−0.438674	−	0.898646i	$-0.644552\pi$
$683$	−22.9288	−0.877348	−0.438674	+	0.898646i	$0.644552\pi$
$684$	−0.00931704	−0.000356246 0
$685$	−1.00799	−0.0385134
$686$	−27.5735	−1.05276
$687$	−11.0002	−0.419684
$688$	11.7812	0.449153
$689$	−6.86262	−0.261445
$690$	−10.5413	−0.401299
$691$	44.2023	1.68153	0.840767	−	0.541397i	$-0.182105\pi$
$691$	44.2023	1.68153	0.840767	+	0.541397i	$0.182105\pi$
$692$	0.0292834	0.00111319
$693$	−8.75204	−0.332463
$694$	28.1089	1.06700
$695$	6.16439	0.233829
$696$	29.3083	1.11093
$697$	−8.98956	−0.340504
$698$	−26.0587	−0.986338
$699$	10.6777	0.403867
$700$	0.00298366	0.000112772 0
$701$	47.7390	1.80308	0.901538	−	0.432699i	$-0.142439\pi$
$701$	47.7390	1.80308	0.901538	+	0.432699i	$0.142439\pi$
$702$	−1.09986	−0.0415114
$703$	16.1316	0.608415
$704$	38.2179	1.44039
$705$	10.3529	0.389912
$706$	10.4076	0.391697
$707$	−22.1697	−0.833777
$708$	−0.0183022	−0.000687839 0
$709$	36.2259	1.36049	0.680246	−	0.732984i	$-0.261873\pi$
$709$	36.2259	1.36049	0.680246	+	0.732984i	$0.261873\pi$
$710$	7.64074	0.286752
$711$	−2.65239	−0.0994724
$712$	−43.4556	−1.62857
$713$	6.88806	0.257960
$714$	20.2776	0.758872
$715$	3.71384	0.138890
$716$	0.0122839	0.000459070 0
$717$	−22.4151	−0.837107
$718$	43.2681	1.61475
$719$	−27.4180	−1.02252	−0.511259	−	0.859427i	$-0.670821\pi$
$719$	−27.4180	−1.02252	−0.511259	+	0.859427i	$0.670821\pi$
$720$	−3.99674	−0.148950
$721$	19.8156	0.737971
$722$	−19.4820	−0.725046
$723$	23.1582	0.861262
$724$	−0.0133900	−0.000497637 0
$725$	10.3578	0.384681
$726$	−16.6597	−0.618300
$727$	11.6709	0.432851	0.216426	−	0.976299i	$-0.430560\pi$
$727$	11.6709	0.432851	0.216426	+	0.976299i	$0.430560\pi$
$728$	−4.03650	−0.149602
$729$	1.00000	0.0370370
$730$	19.2310	0.711772
$731$	−23.0609	−0.852938
$732$	0.0181632	0.000671330 0
$733$	−11.3373	−0.418754	−0.209377	−	0.977835i	$-0.567144\pi$
$733$	−11.3373	−0.418754	−0.209377	+	0.977835i	$0.567144\pi$
$734$	39.4007	1.45431
$735$	−3.63822	−0.134198
$736$	−0.0686425	−0.00253019
$737$	−3.37295	−0.124244
$738$	1.62436	0.0597936
$739$	29.6901	1.09217	0.546085	−	0.837730i	$-0.316118\pi$
$739$	29.6901	1.09217	0.546085	+	0.837730i	$0.316118\pi$
$740$	−0.00458487	−0.000168543 0
$741$	4.45464	0.163645
$742$	−22.8620	−0.839292
$743$	16.9946	0.623472	0.311736	−	0.950169i	$-0.399090\pi$
$743$	16.9946	0.623472	0.311736	+	0.950169i	$0.399090\pi$
$744$	2.61375	0.0958247
$745$	−7.29305	−0.267197
$746$	−2.12432	−0.0777769
$747$	8.65714	0.316748
$748$	−0.0607691	−0.00222194
$749$	13.1964	0.482185
$750$	−1.41364	−0.0516188
$751$	28.0557	1.02377	0.511884	−	0.859055i	$-0.328948\pi$
$751$	28.0557	1.02377	0.511884	+	0.859055i	$0.328948\pi$
$752$	−41.3778	−1.50889
$753$	−19.9209	−0.725958
$754$	−11.3921	−0.414878
$755$	−7.78403	−0.283290
$756$	0.00298366	0.000108515 0
$757$	−32.7055	−1.18870	−0.594351	−	0.804206i	$-0.702591\pi$
$757$	−32.7055	−1.18870	−0.594351	+	0.804206i	$0.702591\pi$
$758$	13.3402	0.484539
$759$	35.5941	1.29199
$760$	16.2008	0.587664
$761$	−34.4995	−1.25060	−0.625302	−	0.780383i	$-0.715024\pi$
$761$	−34.4995	−1.25060	−0.625302	+	0.780383i	$0.715024\pi$
$762$	−6.22182	−0.225393
$763$	4.30198	0.155742
$764$	−0.0435515	−0.00157564
$765$	7.82338	0.282855
$766$	1.48162	0.0535331
$767$	8.75060	0.315966
$768$	−0.0390548	−0.00140927
$769$	0.793454	0.0286127	0.0143063	−	0.999898i	$-0.495446\pi$
$769$	0.793454	0.0286127	0.0143063	+	0.999898i	$0.495446\pi$
$770$	12.3722	0.445864
$771$	9.91977	0.357252
$772$	−0.0127679	−0.000459527 0
$773$	−23.6730	−0.851457	−0.425729	−	0.904851i	$-0.639982\pi$
$773$	−23.6730	−0.851457	−0.425729	+	0.904851i	$0.639982\pi$
$774$	4.16697	0.149779
$775$	0.923725	0.0331812
$776$	−18.0607	−0.648340
$777$	−5.16593	−0.185327
$778$	7.97589	0.285949
$779$	−6.57898	−0.235716
$780$	−0.00126608	−4.53330e−5 0
$781$	−25.8001	−0.923201
$782$	−82.4682	−2.94906
$783$	10.3578	0.370159
$784$	14.5410	0.519322
$785$	−6.13735	−0.219051
$786$	−12.4401	−0.443725
$787$	−45.8278	−1.63358	−0.816792	−	0.576933i	$-0.804249\pi$
$787$	−45.8278	−1.63358	−0.816792	+	0.576933i	$0.804249\pi$
$788$	−0.00610611	−0.000217521 0
$789$	−29.8458	−1.06254
$790$	3.74952	0.133402
$791$	−0.562117	−0.0199866
$792$	13.5066	0.479936
$793$	−8.68412	−0.308382
$794$	9.55754	0.339184
$795$	−8.82047	−0.312830
$796$	−0.0171108	−0.000606477 0
$797$	14.7497	0.522459	0.261230	−	0.965277i	$-0.415872\pi$
$797$	14.7497	0.522459	0.261230	+	0.965277i	$0.415872\pi$
$798$	14.8401	0.525335
$799$	80.9946	2.86538
$800$	−0.00920532	−0.000325457 0
$801$	−15.3576	−0.542635
$802$	−1.41364	−0.0499173
$803$	−64.9365	−2.29156
$804$	0.00114987	4.05528e−5 0
$805$	−13.6722	−0.481882
$806$	−1.01597	−0.0357859
$807$	8.96915	0.315729
$808$	34.2134	1.20362
$809$	1.68781	0.0593402	0.0296701	−	0.999560i	$-0.490554\pi$
$809$	1.68781	0.0593402	0.0296701	+	0.999560i	$0.490554\pi$
$810$	−1.41364	−0.0496702
$811$	−1.60907	−0.0565020	−0.0282510	−	0.999601i	$-0.508994\pi$
$811$	−1.60907	−0.0565020	−0.0282510	+	0.999601i	$0.508994\pi$
$812$	0.0309042	0.00108453
$813$	−14.9350	−0.523794
$814$	−19.0119	−0.666368
$815$	0.315606	0.0110552
$816$	−31.2680	−1.09460
$817$	−16.8770	−0.590453
$818$	36.3752	1.27183
$819$	−1.42654	−0.0498472
$820$	0.00186986	6.52982e−5 0
$821$	−16.9076	−0.590078	−0.295039	−	0.955485i	$-0.595333\pi$
$821$	−16.9076	−0.590078	−0.295039	+	0.955485i	$0.595333\pi$
$822$	1.42493	0.0497003
$823$	−28.8858	−1.00690	−0.503449	−	0.864025i	$-0.667936\pi$
$823$	−28.8858	−1.00690	−0.503449	+	0.864025i	$0.667936\pi$
$824$	−30.5804	−1.06532
$825$	4.77336	0.166187
$826$	29.1516	1.01431
$827$	53.7282	1.86831	0.934156	−	0.356866i	$-0.116155\pi$
$827$	53.7282	1.86831	0.934156	+	0.356866i	$0.116155\pi$
$828$	−0.0121344	−0.000421699 0
$829$	24.7745	0.860454	0.430227	−	0.902721i	$-0.358434\pi$
$829$	24.7745	0.860454	0.430227	+	0.902721i	$0.358434\pi$
$830$	−12.2381	−0.424789
$831$	4.87004	0.168940
$832$	6.22932	0.215963
$833$	−28.4631	−0.986189
$834$	−8.71421	−0.301749
$835$	−19.0190	−0.658181
$836$	−0.0444736	−0.00153815
$837$	0.923725	0.0319286
$838$	−27.6660	−0.955706
$839$	28.8029	0.994385	0.497193	−	0.867640i	$-0.334364\pi$
$839$	28.8029	0.994385	0.497193	+	0.867640i	$0.334364\pi$
$840$	−5.18808	−0.179006
$841$	78.2849	2.69948
$842$	10.0149	0.345137
$843$	−3.80017	−0.130885
$844$	0.0297808	0.00102510
$845$	−12.3947	−0.426389
$846$	−14.6352	−0.503170
$847$	−21.6080	−0.742459
$848$	35.2532	1.21060
$849$	−31.6749	−1.08708
$850$	−11.0594	−0.379335
$851$	21.0096	0.720199
$852$	0.00879551	0.000301329 0
$853$	−15.4749	−0.529849	−0.264925	−	0.964269i	$-0.585347\pi$
$853$	−15.4749	−0.529849	−0.264925	+	0.964269i	$0.585347\pi$
$854$	−28.9301	−0.989969
$855$	5.72551	0.195808
$856$	−20.3653	−0.696072
$857$	48.9217	1.67113	0.835566	−	0.549390i	$-0.185140\pi$
$857$	48.9217	1.67113	0.835566	+	0.549390i	$0.185140\pi$
$858$	−5.25002	−0.179233
$859$	−22.7889	−0.777549	−0.388774	−	0.921333i	$-0.627101\pi$
$859$	−22.7889	−0.777549	−0.388774	+	0.921333i	$0.627101\pi$
$860$	0.00479674	0.000163567 0
$861$	2.10683	0.0718005
$862$	−22.5779	−0.769005
$863$	−8.07855	−0.274997	−0.137498	−	0.990502i	$-0.543906\pi$
$863$	−8.07855	−0.274997	−0.137498	+	0.990502i	$0.543906\pi$
$864$	−0.00920532	−0.000313171 0
$865$	−17.9952	−0.611856
$866$	−20.8269	−0.707725
$867$	44.2052	1.50129
$868$	0.00275608	9.35474e−5 0
$869$	−12.6608	−0.429489
$870$	−14.6422	−0.496418
$871$	−0.549772	−0.0186283
$872$	−6.63904	−0.224826
$873$	−6.38282	−0.216026
$874$	−60.3541	−2.04151
$875$	−1.83352	−0.0619842
$876$	0.0221375	0.000747956 0
$877$	−26.4773	−0.894074	−0.447037	−	0.894515i	$-0.647521\pi$
$877$	−26.4773	−0.894074	−0.447037	+	0.894515i	$0.647521\pi$
$878$	15.1130	0.510039
$879$	9.57604	0.322992
$880$	−19.0779	−0.643116
$881$	21.1890	0.713875	0.356937	−	0.934128i	$-0.383821\pi$
$881$	21.1890	0.713875	0.356937	+	0.934128i	$0.383821\pi$
$882$	5.14312	0.173178
$883$	20.1332	0.677537	0.338768	−	0.940870i	$-0.389990\pi$
$883$	20.1332	0.677537	0.338768	+	0.940870i	$0.389990\pi$
$884$	−0.00990504	−0.000333143 0
$885$	11.2471	0.378066
$886$	34.0459	1.14380
$887$	−28.7651	−0.965837	−0.482919	−	0.875665i	$-0.660423\pi$
$887$	−28.7651	−0.965837	−0.482919	+	0.875665i	$0.660423\pi$
$888$	7.97232	0.267534
$889$	−8.06982	−0.270653
$890$	21.7101	0.727725
$891$	4.77336	0.159914
$892$	0.0137053	0.000458886 0
$893$	59.2756	1.98358
$894$	10.3097	0.344809
$895$	−7.54868	−0.252325
$896$	20.7185	0.692157
$897$	5.80166	0.193712
$898$	−28.7125	−0.958147
$899$	9.56780	0.319104
$900$	−0.00162729	−5.42429e−5 0
$901$	−69.0059	−2.29892
$902$	7.75367	0.258169
$903$	5.40464	0.179855
$904$	0.867488	0.0288522
$905$	8.22845	0.273523
$906$	11.0038	0.365577
$907$	54.1275	1.79727	0.898637	−	0.438692i	$-0.144558\pi$
$907$	54.1275	1.79727	0.898637	+	0.438692i	$0.144558\pi$
$908$	0.00139520	4.63013e−5 0
$909$	12.0913	0.401045
$910$	2.01661	0.0668499
$911$	34.6365	1.14756	0.573779	−	0.819010i	$-0.305477\pi$
$911$	34.6365	1.14756	0.573779	+	0.819010i	$0.305477\pi$
$912$	−22.8834	−0.757745
$913$	41.3237	1.36761
$914$	29.9077	0.989257
$915$	−11.1616	−0.368992
$916$	0.0179005	0.000591448 0
$917$	−16.1351	−0.532828
$918$	−11.0594	−0.365015
$919$	−42.3803	−1.39800	−0.698999	−	0.715123i	$-0.746371\pi$
$919$	−42.3803	−1.39800	−0.698999	+	0.715123i	$0.746371\pi$
$920$	21.0997	0.695635
$921$	27.1010	0.893009
$922$	41.0821	1.35297
$923$	−4.20529	−0.138419
$924$	0.0142421	0.000468530 0
$925$	2.81750	0.0926387
$926$	51.5536	1.69416
$927$	−10.8074	−0.354962
$928$	−0.0953472	−0.00312993
$929$	14.8906	0.488544	0.244272	−	0.969707i	$-0.421451\pi$
$929$	14.8906	0.488544	0.244272	+	0.969707i	$0.421451\pi$
$930$	−1.30581	−0.0428193
$931$	−20.8306	−0.682697
$932$	−0.0173756	−0.000569158 0
$933$	−16.3500	−0.535275
$934$	−44.1650	−1.44512
$935$	37.3438	1.22127
$936$	2.20150	0.0719584
$937$	3.40984	0.111395	0.0556973	−	0.998448i	$-0.482262\pi$
$937$	3.40984	0.111395	0.0556973	+	0.998448i	$0.482262\pi$
$938$	−1.83150	−0.0598007
$939$	−22.9659	−0.749465
$940$	−0.0168471	−0.000549492 0
$941$	0.578740	0.0188664	0.00943319	−	0.999956i	$-0.496997\pi$
$941$	0.578740	0.0188664	0.00943319	+	0.999956i	$0.496997\pi$
$942$	8.67599	0.282679
$943$	−8.56837	−0.279025
$944$	−44.9517	−1.46305
$945$	−1.83352	−0.0596443
$946$	19.8905	0.646694
$947$	25.3002	0.822147	0.411074	−	0.911602i	$-0.365154\pi$
$947$	25.3002	0.822147	0.411074	+	0.911602i	$0.365154\pi$
$948$	0.00431620	0.000140184 0
$949$	−10.5843	−0.343581
$950$	−8.09380	−0.262598
$951$	25.2680	0.819370
$952$	−40.5883	−1.31547
$953$	−0.0379478	−0.00122925	−0.000614625	−	1.00000i	$-0.500196\pi$
$953$	−0.0379478	−0.00122925	−0.000614625		1.00000i	$0.500196\pi$
$954$	12.4690	0.403697
$955$	26.7633	0.866039
$956$	0.0364758	0.00117971
$957$	49.4417	1.59822
$958$	−14.0738	−0.454703
$959$	1.84817	0.0596805
$960$	8.00650	0.258409
$961$	−30.1467	−0.972475
$962$	−3.09884	−0.0999108
$963$	−7.19730	−0.231930
$964$	−0.0376850	−0.00121375
$965$	7.84613	0.252576
$966$	19.3276	0.621854
$967$	3.34486	0.107563	0.0537817	−	0.998553i	$-0.482873\pi$
$967$	3.34486	0.107563	0.0537817	+	0.998553i	$0.482873\pi$
$968$	33.3466	1.07180
$969$	44.7928	1.43895
$970$	9.02299	0.289711
$971$	−21.7703	−0.698644	−0.349322	−	0.937003i	$-0.613588\pi$
$971$	−21.7703	−0.698644	−0.349322	+	0.937003i	$0.613588\pi$
$972$	−0.00162729	−5.21952e−5 0
$973$	−11.3025	−0.362342
$974$	34.0486	1.09099
$975$	0.778033	0.0249170
$976$	44.6101	1.42794
$977$	−57.4293	−1.83733	−0.918663	−	0.395042i	$-0.870730\pi$
$977$	−57.4293	−1.83733	−0.918663	+	0.395042i	$0.870730\pi$
$978$	−0.446153	−0.0142664
$979$	−73.3075	−2.34292
$980$	0.00592042	0.000189121 0
$981$	−2.34630	−0.0749116
$982$	12.8121	0.408851
$983$	−32.8384	−1.04738	−0.523692	−	0.851908i	$-0.675446\pi$
$983$	−32.8384	−1.04738	−0.523692	+	0.851908i	$0.675446\pi$
$984$	−3.25137	−0.103650
$985$	3.75233	0.119559
$986$	−114.552	−3.64807
$987$	−18.9822	−0.604210
$988$	−0.00724897	−0.000230620 0
$989$	−21.9804	−0.698937
$990$	−6.74781	−0.214459
$991$	−45.0791	−1.43199	−0.715993	−	0.698108i	$-0.754026\pi$
$991$	−45.0791	−1.43199	−0.715993	+	0.698108i	$0.754026\pi$
$992$	−0.00850318	−0.000269976 0
$993$	25.6893	0.815226
$994$	−14.0094	−0.444352
$995$	10.5149	0.333346
$996$	−0.0140876	−0.000446384 0
$997$	20.2057	0.639922	0.319961	−	0.947431i	$-0.396330\pi$
$997$	20.2057	0.639922	0.319961	+	0.947431i	$0.396330\pi$
$998$	44.9222	1.42199
$999$	2.81750	0.0891416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.13	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.13	✓	43	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41364 q^{2} +1.00000 q^{3} -0.00162729 q^{4} +1.00000 q^{5} -1.41364 q^{6} -1.83352 q^{7} +2.82958 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.41364 q^{2} +1.00000 q^{3} -0.00162729 q^{4} +1.00000 q^{5} -1.41364 q^{6} -1.83352 q^{7} +2.82958 q^{8} +1.00000 q^{9} -1.41364 q^{10} +4.77336 q^{11} -0.00162729 q^{12} +0.778033 q^{13} +2.59193 q^{14} +1.00000 q^{15} -3.99674 q^{16} +7.82338 q^{17} -1.41364 q^{18} +5.72551 q^{19} -0.00162729 q^{20} -1.83352 q^{21} -6.74781 q^{22} +7.45683 q^{23} +2.82958 q^{24} +1.00000 q^{25} -1.09986 q^{26} +1.00000 q^{27} +0.00298366 q^{28} +10.3578 q^{29} -1.41364 q^{30} +0.923725 q^{31} -0.00920532 q^{32} +4.77336 q^{33} -11.0594 q^{34} -1.83352 q^{35} -0.00162729 q^{36} +2.81750 q^{37} -8.09380 q^{38} +0.778033 q^{39} +2.82958 q^{40} -1.14906 q^{41} +2.59193 q^{42} -2.94769 q^{43} -0.00776763 q^{44} +1.00000 q^{45} -10.5413 q^{46} +10.3529 q^{47} -3.99674 q^{48} -3.63822 q^{49} -1.41364 q^{50} +7.82338 q^{51} -0.00126608 q^{52} -8.82047 q^{53} -1.41364 q^{54} +4.77336 q^{55} -5.18808 q^{56} +5.72551 q^{57} -14.6422 q^{58} +11.2471 q^{59} -0.00162729 q^{60} -11.1616 q^{61} -1.30581 q^{62} -1.83352 q^{63} +8.00650 q^{64} +0.778033 q^{65} -6.74781 q^{66} -0.706618 q^{67} -0.0127309 q^{68} +7.45683 q^{69} +2.59193 q^{70} -5.40502 q^{71} +2.82958 q^{72} -13.6039 q^{73} -3.98292 q^{74} +1.00000 q^{75} -0.00931704 q^{76} -8.75204 q^{77} -1.09986 q^{78} -2.65239 q^{79} -3.99674 q^{80} +1.00000 q^{81} +1.62436 q^{82} +8.65714 q^{83} +0.00298366 q^{84} +7.82338 q^{85} +4.16697 q^{86} +10.3578 q^{87} +13.5066 q^{88} -15.3576 q^{89} -1.41364 q^{90} -1.42654 q^{91} -0.0121344 q^{92} +0.923725 q^{93} -14.6352 q^{94} +5.72551 q^{95} -0.00920532 q^{96} -6.38282 q^{97} +5.14312 q^{98} +4.77336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more