LMFDB - Embedded newform 407.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [407,2,Mod(1,407)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(407, 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("407.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 407 = 11 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	407.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:	$3.24991136227$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 16 x^{9} + 32 x^{8} + 89 x^{7} - 179 x^{6} - 201 x^{5} + 407 x^{4} + 168 x^{3} + \cdots + 75 $ x^11 - 2x^10 - 16x^9 + 32x^8 + 89x^7 - 179x^6 - 201x^5 + 407x^4 + 168x^3 - 333x^2 - 51x + 75
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.77363$ of defining polynomial
Character	$\chi$	$=$	407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77363 q^{2} +2.13379 q^{3} +1.14575 q^{4} +0.365878 q^{5} -3.78454 q^{6} +3.16809 q^{7} +1.51512 q^{8} +1.55305 q^{9} +O(q^{10})$	\(q-1.77363 q^{2} +2.13379 q^{3} +1.14575 q^{4} +0.365878 q^{5} -3.78454 q^{6} +3.16809 q^{7} +1.51512 q^{8} +1.55305 q^{9} -0.648930 q^{10} -1.00000 q^{11} +2.44479 q^{12} +0.746710 q^{13} -5.61900 q^{14} +0.780706 q^{15} -4.97876 q^{16} -1.19144 q^{17} -2.75454 q^{18} +7.87275 q^{19} +0.419205 q^{20} +6.76003 q^{21} +1.77363 q^{22} -0.823054 q^{23} +3.23294 q^{24} -4.86613 q^{25} -1.32438 q^{26} -3.08748 q^{27} +3.62984 q^{28} +0.0852041 q^{29} -1.38468 q^{30} +4.67963 q^{31} +5.80022 q^{32} -2.13379 q^{33} +2.11317 q^{34} +1.15913 q^{35} +1.77941 q^{36} +1.00000 q^{37} -13.9633 q^{38} +1.59332 q^{39} +0.554348 q^{40} +3.00659 q^{41} -11.9898 q^{42} +4.23694 q^{43} -1.14575 q^{44} +0.568228 q^{45} +1.45979 q^{46} +0.227652 q^{47} -10.6236 q^{48} +3.03677 q^{49} +8.63070 q^{50} -2.54229 q^{51} +0.855544 q^{52} -2.21852 q^{53} +5.47603 q^{54} -0.365878 q^{55} +4.80002 q^{56} +16.7988 q^{57} -0.151120 q^{58} +6.31092 q^{59} +0.894495 q^{60} +4.85841 q^{61} -8.29991 q^{62} +4.92021 q^{63} -0.329914 q^{64} +0.273204 q^{65} +3.78454 q^{66} +13.9582 q^{67} -1.36510 q^{68} -1.75622 q^{69} -2.05587 q^{70} -14.5753 q^{71} +2.35306 q^{72} -7.13033 q^{73} -1.77363 q^{74} -10.3833 q^{75} +9.02022 q^{76} -3.16809 q^{77} -2.82596 q^{78} +3.19565 q^{79} -1.82162 q^{80} -11.2472 q^{81} -5.33258 q^{82} -16.0225 q^{83} +7.74531 q^{84} -0.435922 q^{85} -7.51476 q^{86} +0.181808 q^{87} -1.51512 q^{88} -0.393159 q^{89} -1.00782 q^{90} +2.36564 q^{91} -0.943016 q^{92} +9.98533 q^{93} -0.403770 q^{94} +2.88046 q^{95} +12.3764 q^{96} -17.7126 q^{97} -5.38610 q^{98} -1.55305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9	\( 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9} + 5 q^{10} - 11 q^{11} + q^{12} + 22 q^{13} + 3 q^{14} - 10 q^{15} + 19 q^{17} + 18 q^{18} + 14 q^{19} + 6 q^{20} - 13 q^{21} - 2 q^{22} - 14 q^{23} - 11 q^{24} + 38 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 13 q^{29} + 19 q^{30} + 12 q^{31} - 3 q^{32} + q^{34} + 12 q^{35} + 18 q^{36} + 11 q^{37} - 31 q^{38} - 8 q^{39} + 22 q^{40} + 8 q^{41} + 15 q^{42} + 21 q^{43} - 14 q^{44} - 8 q^{45} - 45 q^{46} - 14 q^{47} - 37 q^{48} + 20 q^{49} - 41 q^{50} - 2 q^{51} + 51 q^{52} - 2 q^{53} + 6 q^{54} - q^{55} - 22 q^{56} - 3 q^{57} + 15 q^{58} - 30 q^{59} - 107 q^{60} + 20 q^{61} + 22 q^{62} + 31 q^{63} - 14 q^{64} - 4 q^{66} + 7 q^{67} + 24 q^{68} + 9 q^{69} - 86 q^{70} - 15 q^{71} - 7 q^{72} + 47 q^{73} + 2 q^{74} - 40 q^{75} + 6 q^{76} - 9 q^{77} - 42 q^{78} + 2 q^{79} + 3 q^{80} - 17 q^{81} - 54 q^{82} + 24 q^{83} - 33 q^{84} - 25 q^{85} - 13 q^{86} + 21 q^{87} + 4 q^{89} - 107 q^{90} + 21 q^{91} - 46 q^{92} - 37 q^{93} + 3 q^{94} - 36 q^{95} - 49 q^{96} + 25 q^{97} - 52 q^{98} - 15 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9 + 5 * q^10 - 11 * q^11 + q^12 + 22 * q^13 + 3 * q^14 - 10 * q^15 + 19 * q^17 + 18 * q^18 + 14 * q^19 + 6 * q^20 - 13 * q^21 - 2 * q^22 - 14 * q^23 - 11 * q^24 + 38 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 13 * q^29 + 19 * q^30 + 12 * q^31 - 3 * q^32 + q^34 + 12 * q^35 + 18 * q^36 + 11 * q^37 - 31 * q^38 - 8 * q^39 + 22 * q^40 + 8 * q^41 + 15 * q^42 + 21 * q^43 - 14 * q^44 - 8 * q^45 - 45 * q^46 - 14 * q^47 - 37 * q^48 + 20 * q^49 - 41 * q^50 - 2 * q^51 + 51 * q^52 - 2 * q^53 + 6 * q^54 - q^55 - 22 * q^56 - 3 * q^57 + 15 * q^58 - 30 * q^59 - 107 * q^60 + 20 * q^61 + 22 * q^62 + 31 * q^63 - 14 * q^64 - 4 * q^66 + 7 * q^67 + 24 * q^68 + 9 * q^69 - 86 * q^70 - 15 * q^71 - 7 * q^72 + 47 * q^73 + 2 * q^74 - 40 * q^75 + 6 * q^76 - 9 * q^77 - 42 * q^78 + 2 * q^79 + 3 * q^80 - 17 * q^81 - 54 * q^82 + 24 * q^83 - 33 * q^84 - 25 * q^85 - 13 * q^86 + 21 * q^87 + 4 * q^89 - 107 * q^90 + 21 * q^91 - 46 * q^92 - 37 * q^93 + 3 * q^94 - 36 * q^95 - 49 * q^96 + 25 * q^97 - 52 * q^98 - 15 * 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 $

$2$	−1.77363	−1.25414	−0.627072	−	0.778961i	$-0.715747\pi$
$2$	−1.77363	−1.25414	−0.627072	+	0.778961i	$0.715747\pi$
$3$	2.13379	1.23194	0.615972	−	0.787768i	$-0.288764\pi$
$3$	2.13379	1.23194	0.615972	+	0.787768i	$0.288764\pi$
$4$	1.14575	0.572876
$5$	0.365878	0.163625	0.0818127	−	0.996648i	$-0.473929\pi$
$5$	0.365878	0.163625	0.0818127	+	0.996648i	$0.473929\pi$
$6$	−3.78454	−1.54503
$7$	3.16809	1.19742	0.598712	−	0.800964i	$-0.295679\pi$
$7$	3.16809	1.19742	0.598712	+	0.800964i	$0.295679\pi$
$8$	1.51512	0.535675
$9$	1.55305	0.517685
$10$	−0.648930	−0.205210
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.44479	0.705751
$13$	0.746710	0.207100	0.103550	−	0.994624i	$-0.466980\pi$
$13$	0.746710	0.207100	0.103550	+	0.994624i	$0.466980\pi$
$14$	−5.61900	−1.50174
$15$	0.780706	0.201577
$16$	−4.97876	−1.24469
$17$	−1.19144	−0.288967	−0.144484	−	0.989507i	$-0.546152\pi$
$17$	−1.19144	−0.288967	−0.144484	+	0.989507i	$0.546152\pi$
$18$	−2.75454	−0.649251
$19$	7.87275	1.80613	0.903067	−	0.429500i	$-0.141310\pi$
$19$	7.87275	1.80613	0.903067	+	0.429500i	$0.141310\pi$
$20$	0.419205	0.0937371
$21$	6.76003	1.47516
$22$	1.77363	0.378138
$23$	−0.823054	−0.171619	−0.0858093	−	0.996312i	$-0.527348\pi$
$23$	−0.823054	−0.171619	−0.0858093	+	0.996312i	$0.527348\pi$
$24$	3.23294	0.659921
$25$	−4.86613	−0.973227
$26$	−1.32438	−0.259733
$27$	−3.08748	−0.594185
$28$	3.62984	0.685975
$29$	0.0852041	0.0158220	0.00791100	−	0.999969i	$-0.497482\pi$
$29$	0.0852041	0.0158220	0.00791100	+	0.999969i	$0.497482\pi$
$30$	−1.38468	−0.252807
$31$	4.67963	0.840485	0.420243	−	0.907412i	$-0.361945\pi$
$31$	4.67963	0.840485	0.420243	+	0.907412i	$0.361945\pi$
$32$	5.80022	1.02534
$33$	−2.13379	−0.371445
$34$	2.11317	0.362406
$35$	1.15913	0.195929
$36$	1.77941	0.296569
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−13.9633	−2.26515
$39$	1.59332	0.255135
$40$	0.554348	0.0876501
$41$	3.00659	0.469551	0.234776	−	0.972050i	$-0.424564\pi$
$41$	3.00659	0.469551	0.234776	+	0.972050i	$0.424564\pi$
$42$	−11.9898	−1.85006
$43$	4.23694	0.646128	0.323064	−	0.946377i	$-0.395287\pi$
$43$	4.23694	0.646128	0.323064	+	0.946377i	$0.395287\pi$
$44$	−1.14575	−0.172729
$45$	0.568228	0.0847064
$46$	1.45979	0.215234
$47$	0.227652	0.0332065	0.0166032	−	0.999862i	$-0.494715\pi$
$47$	0.227652	0.0332065	0.0166032	+	0.999862i	$0.494715\pi$
$48$	−10.6236	−1.53339
$49$	3.03677	0.433824
$50$	8.63070	1.22057
$51$	−2.54229	−0.355991
$52$	0.855544	0.118643
$53$	−2.21852	−0.304737	−0.152369	−	0.988324i	$-0.548690\pi$
$53$	−2.21852	−0.304737	−0.152369	+	0.988324i	$0.548690\pi$
$54$	5.47603	0.745194
$55$	−0.365878	−0.0493349
$56$	4.80002	0.641430
$57$	16.7988	2.22505
$58$	−0.151120	−0.0198431
$59$	6.31092	0.821611	0.410806	−	0.911723i	$-0.365247\pi$
$59$	6.31092	0.821611	0.410806	+	0.911723i	$0.365247\pi$
$60$	0.894495	0.115479
$61$	4.85841	0.622055	0.311028	−	0.950401i	$-0.399327\pi$
$61$	4.85841	0.622055	0.311028	+	0.950401i	$0.399327\pi$
$62$	−8.29991	−1.05409
$63$	4.92021	0.619888
$64$	−0.329914	−0.0412393
$65$	0.273204	0.0338868
$66$	3.78454	0.465845
$67$	13.9582	1.70527	0.852634	−	0.522508i	$-0.175004\pi$
$67$	13.9582	1.70527	0.852634	+	0.522508i	$0.175004\pi$
$68$	−1.36510	−0.165542
$69$	−1.75622	−0.211425
$70$	−2.05587	−0.245723
$71$	−14.5753	−1.72977	−0.864887	−	0.501966i	$-0.832610\pi$
$71$	−14.5753	−1.72977	−0.864887	+	0.501966i	$0.832610\pi$
$72$	2.35306	0.277311
$73$	−7.13033	−0.834543	−0.417271	−	0.908782i	$-0.637013\pi$
$73$	−7.13033	−0.834543	−0.417271	+	0.908782i	$0.637013\pi$
$74$	−1.77363	−0.206180
$75$	−10.3833	−1.19896
$76$	9.02022	1.03469
$77$	−3.16809	−0.361037
$78$	−2.82596	−0.319976
$79$	3.19565	0.359539	0.179769	−	0.983709i	$-0.442465\pi$
$79$	3.19565	0.359539	0.179769	+	0.983709i	$0.442465\pi$
$80$	−1.82162	−0.203663
$81$	−11.2472	−1.24969
$82$	−5.33258	−0.588885
$83$	−16.0225	−1.75870	−0.879348	−	0.476179i	$-0.842021\pi$
$83$	−16.0225	−1.75870	−0.879348	+	0.476179i	$0.842021\pi$
$84$	7.74531	0.845083
$85$	−0.435922	−0.0472824
$86$	−7.51476	−0.810337
$87$	0.181808	0.0194918
$88$	−1.51512	−0.161512
$89$	−0.393159	−0.0416748	−0.0208374	−	0.999783i	$-0.506633\pi$
$89$	−0.393159	−0.0416748	−0.0208374	+	0.999783i	$0.506633\pi$
$90$	−1.00782	−0.106234
$91$	2.36564	0.247986
$92$	−0.943016	−0.0983162
$93$	9.98533	1.03543
$94$	−0.403770	−0.0416457
$95$	2.88046	0.295529
$96$	12.3764	1.26317
$97$	−17.7126	−1.79844	−0.899220	−	0.437497i	$-0.855865\pi$
$97$	−17.7126	−1.79844	−0.899220	+	0.437497i	$0.855865\pi$
$98$	−5.38610	−0.544078
$99$	−1.55305	−0.156088
$100$	−5.57538	−0.557538
$101$	−10.7441	−1.06908	−0.534540	−	0.845143i	$-0.679515\pi$
$101$	−10.7441	−1.06908	−0.534540	+	0.845143i	$0.679515\pi$
$102$	4.50906	0.446464
$103$	−5.42658	−0.534697	−0.267348	−	0.963600i	$-0.586147\pi$
$103$	−5.42658	−0.534697	−0.267348	+	0.963600i	$0.586147\pi$
$104$	1.13135	0.110938
$105$	2.47334	0.241374
$106$	3.93483	0.382184
$107$	−1.93352	−0.186921	−0.0934604	−	0.995623i	$-0.529793\pi$
$107$	−1.93352	−0.186921	−0.0934604	+	0.995623i	$0.529793\pi$
$108$	−3.53748	−0.340395
$109$	−11.9480	−1.14441	−0.572204	−	0.820112i	$-0.693911\pi$
$109$	−11.9480	−1.14441	−0.572204	+	0.820112i	$0.693911\pi$
$110$	0.648930	0.0618731
$111$	2.13379	0.202530
$112$	−15.7731	−1.49042
$113$	−12.8704	−1.21074	−0.605370	−	0.795944i	$-0.706975\pi$
$113$	−12.8704	−1.21074	−0.605370	+	0.795944i	$0.706975\pi$
$114$	−29.7948	−2.79054
$115$	−0.301137	−0.0280812
$116$	0.0976227	0.00906404
$117$	1.15968	0.107212
$118$	−11.1932	−1.03042
$119$	−3.77459	−0.346016
$120$	1.18286	0.107980
$121$	1.00000	0.0909091
$122$	−8.61700	−0.780146
$123$	6.41544	0.578460
$124$	5.36169	0.481494
$125$	−3.60980	−0.322870
$126$	−8.72661	−0.777428
$127$	10.9804	0.974351	0.487175	−	0.873304i	$-0.338027\pi$
$127$	10.9804	0.974351	0.487175	+	0.873304i	$0.338027\pi$
$128$	−11.0153	−0.973624
$129$	9.04074	0.795993
$130$	−0.484563	−0.0424989
$131$	−10.7804	−0.941888	−0.470944	−	0.882163i	$-0.656087\pi$
$131$	−10.7804	−0.941888	−0.470944	+	0.882163i	$0.656087\pi$
$132$	−2.44479	−0.212792
$133$	24.9416	2.16271
$134$	−24.7567	−2.13865
$135$	−1.12964	−0.0972239
$136$	−1.80517	−0.154792
$137$	17.2946	1.47758	0.738789	−	0.673937i	$-0.235398\pi$
$137$	17.2946	1.47758	0.738789	+	0.673937i	$0.235398\pi$
$138$	3.11489	0.265157
$139$	−5.28772	−0.448498	−0.224249	−	0.974532i	$-0.571993\pi$
$139$	−5.28772	−0.448498	−0.224249	+	0.974532i	$0.571993\pi$
$140$	1.32808	0.112243
$141$	0.485761	0.0409085
$142$	25.8512	2.16939
$143$	−0.746710	−0.0624430
$144$	−7.73228	−0.644356
$145$	0.0311743	0.00258888
$146$	12.6466	1.04664
$147$	6.47983	0.534447
$148$	1.14575	0.0941802
$149$	−6.31538	−0.517376	−0.258688	−	0.965961i	$-0.583290\pi$
$149$	−6.31538	−0.517376	−0.258688	+	0.965961i	$0.583290\pi$
$150$	18.4161	1.50367
$151$	1.86028	0.151387	0.0756937	−	0.997131i	$-0.475883\pi$
$151$	1.86028	0.151387	0.0756937	+	0.997131i	$0.475883\pi$
$152$	11.9281	0.967500
$153$	−1.85037	−0.149594
$154$	5.61900	0.452792
$155$	1.71217	0.137525
$156$	1.82555	0.146161
$157$	8.75410	0.698653	0.349326	−	0.937001i	$-0.386410\pi$
$157$	8.75410	0.698653	0.349326	+	0.937001i	$0.386410\pi$
$158$	−5.66789	−0.450913
$159$	−4.73385	−0.375419
$160$	2.12217	0.167772
$161$	−2.60751	−0.205500
$162$	19.9483	1.56729
$163$	−8.83915	−0.692335	−0.346168	−	0.938173i	$-0.612517\pi$
$163$	−8.83915	−0.692335	−0.346168	+	0.938173i	$0.612517\pi$
$164$	3.44481	0.268995
$165$	−0.780706	−0.0607779
$166$	28.4179	2.20566
$167$	9.82258	0.760094	0.380047	−	0.924967i	$-0.375908\pi$
$167$	9.82258	0.760094	0.380047	+	0.924967i	$0.375908\pi$
$168$	10.2422	0.790205
$169$	−12.4424	−0.957110
$170$	0.773163	0.0592989
$171$	12.2268	0.935007
$172$	4.85449	0.370151
$173$	14.6677	1.11517	0.557584	−	0.830121i	$-0.311729\pi$
$173$	14.6677	1.11517	0.557584	+	0.830121i	$0.311729\pi$
$174$	−0.322459	−0.0244455
$175$	−15.4163	−1.16537
$176$	4.97876	0.375288
$177$	13.4662	1.01218
$178$	0.697317	0.0522661
$179$	6.51334	0.486830	0.243415	−	0.969922i	$-0.421732\pi$
$179$	6.51334	0.486830	0.243415	+	0.969922i	$0.421732\pi$
$180$	0.651048	0.0485262
$181$	−19.9316	−1.48151	−0.740754	−	0.671776i	$-0.765532\pi$
$181$	−19.9316	−1.48151	−0.740754	+	0.671776i	$0.765532\pi$
$182$	−4.19576	−0.311011
$183$	10.3668	0.766337
$184$	−1.24702	−0.0919318
$185$	0.365878	0.0268999
$186$	−17.7102	−1.29858
$187$	1.19144	0.0871269
$188$	0.260833	0.0190232
$189$	−9.78140	−0.711492
$190$	−5.10887	−0.370636
$191$	−10.6146	−0.768045	−0.384022	−	0.923324i	$-0.625461\pi$
$191$	−10.6146	−0.768045	−0.384022	+	0.923324i	$0.625461\pi$
$192$	−0.703968	−0.0508045
$193$	22.5264	1.62149	0.810743	−	0.585402i	$-0.199063\pi$
$193$	22.5264	1.62149	0.810743	+	0.585402i	$0.199063\pi$
$194$	31.4155	2.25550
$195$	0.582960	0.0417467
$196$	3.47939	0.248528
$197$	−8.52432	−0.607332	−0.303666	−	0.952778i	$-0.598211\pi$
$197$	−8.52432	−0.607332	−0.303666	+	0.952778i	$0.598211\pi$
$198$	2.75454	0.195756
$199$	−7.91560	−0.561122	−0.280561	−	0.959836i	$-0.590520\pi$
$199$	−7.91560	−0.561122	−0.280561	+	0.959836i	$0.590520\pi$
$200$	−7.37276	−0.521333
$201$	29.7839	2.10079
$202$	19.0561	1.34078
$203$	0.269934	0.0189456
$204$	−2.91283	−0.203939
$205$	1.10005	0.0768305
$206$	9.62473	0.670587
$207$	−1.27825	−0.0888443
$208$	−3.71768	−0.257775
$209$	−7.87275	−0.544570
$210$	−4.38679	−0.302717
$211$	0.698266	0.0480706	0.0240353	−	0.999711i	$-0.492349\pi$
$211$	0.698266	0.0480706	0.0240353	+	0.999711i	$0.492349\pi$
$212$	−2.54187	−0.174577
$213$	−31.1007	−2.13098
$214$	3.42935	0.234425
$215$	1.55020	0.105723
$216$	−4.67789	−0.318290
$217$	14.8255	1.00642
$218$	21.1912	1.43525
$219$	−15.2146	−1.02811
$220$	−0.419205	−0.0282628
$221$	−0.889661	−0.0598451
$222$	−3.78454	−0.254002
$223$	−25.4482	−1.70414	−0.852068	−	0.523432i	$-0.824652\pi$
$223$	−25.4482	−1.70414	−0.852068	+	0.523432i	$0.824652\pi$
$224$	18.3756	1.22777
$225$	−7.55737	−0.503824
$226$	22.8272	1.51844
$227$	1.54858	0.102783	0.0513914	−	0.998679i	$-0.483634\pi$
$227$	1.54858	0.102783	0.0513914	+	0.998679i	$0.483634\pi$
$228$	19.2472	1.27468
$229$	−1.31151	−0.0866669	−0.0433334	−	0.999061i	$-0.513798\pi$
$229$	−1.31151	−0.0866669	−0.0433334	+	0.999061i	$0.513798\pi$
$230$	0.534105	0.0352178
$231$	−6.76003	−0.444777
$232$	0.129094	0.00847545
$233$	26.1180	1.71105	0.855524	−	0.517763i	$-0.173235\pi$
$233$	26.1180	1.71105	0.855524	+	0.517763i	$0.173235\pi$
$234$	−2.05684	−0.134460
$235$	0.0832928	0.00543342
$236$	7.23074	0.470681
$237$	6.81885	0.442932
$238$	6.69472	0.433954
$239$	−7.98922	−0.516780	−0.258390	−	0.966041i	$-0.583192\pi$
$239$	−7.98922	−0.516780	−0.258390	+	0.966041i	$0.583192\pi$
$240$	−3.88694	−0.250901
$241$	7.64335	0.492351	0.246176	−	0.969225i	$-0.420826\pi$
$241$	7.64335	0.492351	0.246176	+	0.969225i	$0.420826\pi$
$242$	−1.77363	−0.114013
$243$	−14.7367	−0.945359
$244$	5.56653	0.356360
$245$	1.11109	0.0709847
$246$	−11.3786	−0.725472
$247$	5.87866	0.374050
$248$	7.09018	0.450227
$249$	−34.1886	−2.16662
$250$	6.40243	0.404926
$251$	6.63199	0.418607	0.209304	−	0.977851i	$-0.432880\pi$
$251$	6.63199	0.418607	0.209304	+	0.977851i	$0.432880\pi$
$252$	5.63734	0.355119
$253$	0.823054	0.0517450
$254$	−19.4751	−1.22198
$255$	−0.930165	−0.0582492
$256$	20.1969	1.26230
$257$	31.9252	1.99144	0.995720	−	0.0924213i	$-0.0294607\pi$
$257$	31.9252	1.99144	0.995720	+	0.0924213i	$0.0294607\pi$
$258$	−16.0349	−0.998289
$259$	3.16809	0.196855
$260$	0.313024	0.0194130
$261$	0.132327	0.00819081
$262$	19.1204	1.18126
$263$	−13.8295	−0.852766	−0.426383	−	0.904543i	$-0.640212\pi$
$263$	−13.8295	−0.852766	−0.426383	+	0.904543i	$0.640212\pi$
$264$	−3.23294	−0.198974
$265$	−0.811707	−0.0498628
$266$	−44.2370	−2.71235
$267$	−0.838918	−0.0513409
$268$	15.9927	0.976908
$269$	24.5273	1.49546	0.747728	−	0.664005i	$-0.231145\pi$
$269$	24.5273	1.49546	0.747728	+	0.664005i	$0.231145\pi$
$270$	2.00356	0.121933
$271$	18.2933	1.11124	0.555619	−	0.831437i	$-0.312482\pi$
$271$	18.2933	1.11124	0.555619	+	0.831437i	$0.312482\pi$
$272$	5.93190	0.359674
$273$	5.04778	0.305505
$274$	−30.6742	−1.85309
$275$	4.86613	0.293439
$276$	−2.01220	−0.121120
$277$	−28.6174	−1.71945	−0.859727	−	0.510755i	$-0.829366\pi$
$277$	−28.6174	−1.71945	−0.859727	+	0.510755i	$0.829366\pi$
$278$	9.37844	0.562481
$279$	7.26771	0.435106
$280$	1.75622	0.104954
$281$	9.92157	0.591871	0.295936	−	0.955208i	$-0.404369\pi$
$281$	9.92157	0.591871	0.295936	+	0.955208i	$0.404369\pi$
$282$	−0.861559	−0.0513051
$283$	3.08639	0.183467	0.0917333	−	0.995784i	$-0.470759\pi$
$283$	3.08639	0.183467	0.0917333	+	0.995784i	$0.470759\pi$
$284$	−16.6997	−0.990946
$285$	6.14630	0.364076
$286$	1.32438	0.0783125
$287$	9.52515	0.562252
$288$	9.00805	0.530805
$289$	−15.5805	−0.916498
$290$	−0.0552915	−0.00324683
$291$	−37.7949	−2.21558
$292$	−8.16959	−0.478089
$293$	−29.9275	−1.74838	−0.874191	−	0.485583i	$-0.838607\pi$
$293$	−29.9275	−1.74838	−0.874191	+	0.485583i	$0.838607\pi$
$294$	−11.4928	−0.670273
$295$	2.30902	0.134437
$296$	1.51512	0.0880644
$297$	3.08748	0.179154
$298$	11.2011	0.648864
$299$	−0.614582	−0.0355422
$300$	−11.8967	−0.686855
$301$	13.4230	0.773689
$302$	−3.29944	−0.189862
$303$	−22.9257	−1.31705
$304$	−39.1965	−2.24807
$305$	1.77758	0.101784
$306$	3.28187	0.187612
$307$	12.5774	0.717831	0.358916	−	0.933370i	$-0.383147\pi$
$307$	12.5774	0.717831	0.358916	+	0.933370i	$0.383147\pi$
$308$	−3.62984	−0.206829
$309$	−11.5792	−0.658716
$310$	−3.03675	−0.172476
$311$	−10.4206	−0.590896	−0.295448	−	0.955359i	$-0.595469\pi$
$311$	−10.4206	−0.590896	−0.295448	+	0.955359i	$0.595469\pi$
$312$	2.41407	0.136670
$313$	8.06183	0.455681	0.227841	−	0.973698i	$-0.426833\pi$
$313$	8.06183	0.455681	0.227841	+	0.973698i	$0.426833\pi$
$314$	−15.5265	−0.876211
$315$	1.80019	0.101429
$316$	3.66142	0.205971
$317$	4.45385	0.250153	0.125076	−	0.992147i	$-0.460082\pi$
$317$	4.45385	0.250153	0.125076	+	0.992147i	$0.460082\pi$
$318$	8.39609	0.470829
$319$	−0.0852041	−0.00477051
$320$	−0.120708	−0.00674780
$321$	−4.12573	−0.230276
$322$	4.62474	0.257727
$323$	−9.37993	−0.521913
$324$	−12.8865	−0.715916
$325$	−3.63359	−0.201555
$326$	15.6773	0.868288
$327$	−25.4944	−1.40984
$328$	4.55534	0.251527
$329$	0.721222	0.0397622
$330$	1.38468	0.0762241
$331$	5.20130	0.285889	0.142945	−	0.989731i	$-0.454343\pi$
$331$	5.20130	0.285889	0.142945	+	0.989731i	$0.454343\pi$
$332$	−18.3578	−1.00752
$333$	1.55305	0.0851068
$334$	−17.4216	−0.953267
$335$	5.10700	0.279025
$336$	−33.6565	−1.83611
$337$	14.1868	0.772806	0.386403	−	0.922330i	$-0.373717\pi$
$337$	14.1868	0.772806	0.386403	+	0.922330i	$0.373717\pi$
$338$	22.0682	1.20035
$339$	−27.4626	−1.49156
$340$	−0.499458	−0.0270869
$341$	−4.67963	−0.253416
$342$	−21.6858	−1.17263
$343$	−12.5559	−0.677952
$344$	6.41947	0.346114
$345$	−0.642563	−0.0345944
$346$	−26.0151	−1.39858
$347$	−2.81106	−0.150906	−0.0754528	−	0.997149i	$-0.524040\pi$
$347$	−2.81106	−0.150906	−0.0754528	+	0.997149i	$0.524040\pi$
$348$	0.208306	0.0111664
$349$	−17.3210	−0.927173	−0.463586	−	0.886052i	$-0.653438\pi$
$349$	−17.3210	−0.927173	−0.463586	+	0.886052i	$0.653438\pi$
$350$	27.3428	1.46154
$351$	−2.30545	−0.123056
$352$	−5.80022	−0.309153
$353$	22.1411	1.17845	0.589227	−	0.807968i	$-0.299432\pi$
$353$	22.1411	1.17845	0.589227	+	0.807968i	$0.299432\pi$
$354$	−23.8839	−1.26942
$355$	−5.33279	−0.283035
$356$	−0.450463	−0.0238745
$357$	−8.05418	−0.426272
$358$	−11.5522	−0.610554
$359$	15.4235	0.814022	0.407011	−	0.913423i	$-0.366571\pi$
$359$	15.4235	0.814022	0.407011	+	0.913423i	$0.366571\pi$
$360$	0.860932	0.0453751
$361$	42.9802	2.26212
$362$	35.3513	1.85802
$363$	2.13379	0.111995
$364$	2.71044	0.142065
$365$	−2.60883	−0.136552
$366$	−18.3869	−0.961096
$367$	−4.73070	−0.246940	−0.123470	−	0.992348i	$-0.539402\pi$
$367$	−4.73070	−0.246940	−0.123470	+	0.992348i	$0.539402\pi$
$368$	4.09779	0.213612
$369$	4.66940	0.243079
$370$	−0.648930	−0.0337363
$371$	−7.02847	−0.364900
$372$	11.4407	0.593173
$373$	20.0506	1.03818	0.519090	−	0.854720i	$-0.326271\pi$
$373$	20.0506	1.03818	0.519090	+	0.854720i	$0.326271\pi$
$374$	−2.11317	−0.109270
$375$	−7.70255	−0.397758
$376$	0.344920	0.0177879
$377$	0.0636227	0.00327674
$378$	17.3485	0.892313
$379$	−22.6858	−1.16529	−0.582645	−	0.812727i	$-0.697982\pi$
$379$	−22.6858	−1.16529	−0.582645	+	0.812727i	$0.697982\pi$
$380$	3.30030	0.169302
$381$	23.4298	1.20034
$382$	18.8263	0.963239
$383$	−36.7395	−1.87730	−0.938649	−	0.344873i	$-0.887922\pi$
$383$	−36.7395	−1.87730	−0.938649	+	0.344873i	$0.887922\pi$
$384$	−23.5043	−1.19945
$385$	−1.15913	−0.0590748
$386$	−39.9534	−2.03358
$387$	6.58020	0.334490
$388$	−20.2942	−1.03028
$389$	31.4471	1.59443	0.797216	−	0.603694i	$-0.206305\pi$
$389$	31.4471	1.59443	0.797216	+	0.603694i	$0.206305\pi$
$390$	−1.03395	−0.0523563
$391$	0.980621	0.0495922
$392$	4.60106	0.232389
$393$	−23.0031	−1.16035
$394$	15.1190	0.761682
$395$	1.16922	0.0588297
$396$	−1.77941	−0.0894189
$397$	5.69240	0.285693	0.142847	−	0.989745i	$-0.454374\pi$
$397$	5.69240	0.285693	0.142847	+	0.989745i	$0.454374\pi$
$398$	14.0393	0.703727
$399$	53.2200	2.66433
$400$	24.2273	1.21136
$401$	27.0625	1.35144	0.675718	−	0.737160i	$-0.263834\pi$
$401$	27.0625	1.35144	0.675718	+	0.737160i	$0.263834\pi$
$402$	−52.8255	−2.63470
$403$	3.49432	0.174065
$404$	−12.3101	−0.612450
$405$	−4.11509	−0.204481
$406$	−0.478762	−0.0237606
$407$	−1.00000	−0.0495682
$408$	−3.85186	−0.190695
$409$	3.46673	0.171419	0.0857094	−	0.996320i	$-0.472684\pi$
$409$	3.46673	0.171419	0.0857094	+	0.996320i	$0.472684\pi$
$410$	−1.95107	−0.0963565
$411$	36.9030	1.82029
$412$	−6.21752	−0.306315
$413$	19.9935	0.983817
$414$	2.26713	0.111424
$415$	−5.86227	−0.287768
$416$	4.33108	0.212349
$417$	−11.2829	−0.552524
$418$	13.9633	0.682969
$419$	−29.4521	−1.43883	−0.719415	−	0.694581i	$-0.755590\pi$
$419$	−29.4521	−1.43883	−0.719415	+	0.694581i	$0.755590\pi$
$420$	2.83384	0.138277
$421$	−22.5811	−1.10053	−0.550267	−	0.834989i	$-0.685474\pi$
$421$	−22.5811	−1.10053	−0.550267	+	0.834989i	$0.685474\pi$
$422$	−1.23846	−0.0602875
$423$	0.353556	0.0171905
$424$	−3.36132	−0.163240
$425$	5.79772	0.281231
$426$	55.1610	2.67256
$427$	15.3918	0.744864
$428$	−2.21534	−0.107082
$429$	−1.59332	−0.0769262
$430$	−2.74948	−0.132592
$431$	8.11365	0.390821	0.195410	−	0.980722i	$-0.437396\pi$
$431$	8.11365	0.390821	0.195410	+	0.980722i	$0.437396\pi$
$432$	15.3718	0.739576
$433$	−3.29511	−0.158353	−0.0791764	−	0.996861i	$-0.525229\pi$
$433$	−3.29511	−0.158353	−0.0791764	+	0.996861i	$0.525229\pi$
$434$	−26.2948	−1.26219
$435$	0.0665193	0.00318936
$436$	−13.6894	−0.655603
$437$	−6.47970	−0.309966
$438$	26.9851	1.28940
$439$	−32.6880	−1.56011	−0.780057	−	0.625709i	$-0.784810\pi$
$439$	−32.6880	−1.56011	−0.780057	+	0.625709i	$0.784810\pi$
$440$	−0.554348	−0.0264275
$441$	4.71627	0.224584
$442$	1.57793	0.0750543
$443$	27.4215	1.30283	0.651417	−	0.758720i	$-0.274175\pi$
$443$	27.4215	1.30283	0.651417	+	0.758720i	$0.274175\pi$
$444$	2.44479	0.116025
$445$	−0.143848	−0.00681905
$446$	45.1355	2.13723
$447$	−13.4757	−0.637378
$448$	−1.04520	−0.0493809
$449$	−10.0371	−0.473678	−0.236839	−	0.971549i	$-0.576111\pi$
$449$	−10.0371	−0.473678	−0.236839	+	0.971549i	$0.576111\pi$
$450$	13.4039	0.631868
$451$	−3.00659	−0.141575
$452$	−14.7462	−0.693604
$453$	3.96944	0.186501
$454$	−2.74660	−0.128904
$455$	0.865535	0.0405769
$456$	25.4521	1.19191
$457$	−1.43413	−0.0670857	−0.0335429	−	0.999437i	$-0.510679\pi$
$457$	−1.43413	−0.0670857	−0.0335429	+	0.999437i	$0.510679\pi$
$458$	2.32613	0.108693
$459$	3.67855	0.171700
$460$	−0.345029	−0.0160870
$461$	3.64734	0.169873	0.0849367	−	0.996386i	$-0.472931\pi$
$461$	3.64734	0.169873	0.0849367	+	0.996386i	$0.472931\pi$
$462$	11.9898	0.557814
$463$	23.1233	1.07463	0.537315	−	0.843381i	$-0.319439\pi$
$463$	23.1233	1.07463	0.537315	+	0.843381i	$0.319439\pi$
$464$	−0.424210	−0.0196935
$465$	3.65341	0.169423
$466$	−46.3236	−2.14590
$467$	15.5741	0.720686	0.360343	−	0.932820i	$-0.382660\pi$
$467$	15.5741	0.720686	0.360343	+	0.932820i	$0.382660\pi$
$468$	1.32871	0.0614194
$469$	44.2209	2.04193
$470$	−0.147730	−0.00681429
$471$	18.6794	0.860701
$472$	9.56178	0.440116
$473$	−4.23694	−0.194815
$474$	−12.0941	−0.555500
$475$	−38.3099	−1.75778
$476$	−4.32474	−0.198224
$477$	−3.44548	−0.157758
$478$	14.1699	0.648116
$479$	3.40934	0.155777	0.0778883	−	0.996962i	$-0.475182\pi$
$479$	3.40934	0.155777	0.0778883	+	0.996962i	$0.475182\pi$
$480$	4.52827	0.206686
$481$	0.746710	0.0340470
$482$	−13.5564	−0.617479
$483$	−5.56387	−0.253165
$484$	1.14575	0.0520796
$485$	−6.48064	−0.294271
$486$	26.1374	1.18562
$487$	−24.2220	−1.09760	−0.548802	−	0.835953i	$-0.684916\pi$
$487$	−24.2220	−1.09760	−0.548802	+	0.835953i	$0.684916\pi$
$488$	7.36105	0.333219
$489$	−18.8609	−0.852918
$490$	−1.97065	−0.0890251
$491$	12.1851	0.549906	0.274953	−	0.961458i	$-0.411338\pi$
$491$	12.1851	0.549906	0.274953	+	0.961458i	$0.411338\pi$
$492$	7.35050	0.331386
$493$	−0.101516	−0.00457204
$494$	−10.4265	−0.469113
$495$	−0.568228	−0.0255399
$496$	−23.2987	−1.04614
$497$	−46.1759	−2.07127
$498$	60.6378	2.71725
$499$	−5.12265	−0.229321	−0.114661	−	0.993405i	$-0.536578\pi$
$499$	−5.12265	−0.229321	−0.114661	+	0.993405i	$0.536578\pi$
$500$	−4.13593	−0.184965
$501$	20.9593	0.936392
$502$	−11.7627	−0.524994
$503$	−23.5969	−1.05214	−0.526068	−	0.850443i	$-0.676334\pi$
$503$	−23.5969	−1.05214	−0.526068	+	0.850443i	$0.676334\pi$
$504$	7.45469	0.332058
$505$	−3.93103	−0.174929
$506$	−1.45979	−0.0648956
$507$	−26.5495	−1.17910
$508$	12.5808	0.558182
$509$	10.5938	0.469562	0.234781	−	0.972048i	$-0.424563\pi$
$509$	10.5938	0.469562	0.234781	+	0.972048i	$0.424563\pi$
$510$	1.64977	0.0730529
$511$	−22.5895	−0.999301
$512$	−13.7911	−0.609486
$513$	−24.3070	−1.07318
$514$	−56.6234	−2.49755
$515$	−1.98547	−0.0874900
$516$	10.3584	0.456005
$517$	−0.227652	−0.0100121
$518$	−5.61900	−0.246885
$519$	31.2979	1.37382
$520$	0.413937	0.0181523
$521$	−16.3901	−0.718065	−0.359032	−	0.933325i	$-0.616893\pi$
$521$	−16.3901	−0.718065	−0.359032	+	0.933325i	$0.616893\pi$
$522$	−0.234698	−0.0102724
$523$	−7.37161	−0.322338	−0.161169	−	0.986927i	$-0.551526\pi$
$523$	−7.37161	−0.322338	−0.161169	+	0.986927i	$0.551526\pi$
$524$	−12.3517	−0.539585
$525$	−32.8952	−1.43566
$526$	24.5284	1.06949
$527$	−5.57550	−0.242873
$528$	10.6236	0.462333
$529$	−22.3226	−0.970547
$530$	1.43967	0.0625351
$531$	9.80119	0.425335
$532$	28.5768	1.23896
$533$	2.24505	0.0972440
$534$	1.48793	0.0643889
$535$	−0.707433	−0.0305850
$536$	21.1484	0.913470
$537$	13.8981	0.599747
$538$	−43.5023	−1.87552
$539$	−3.03677	−0.130803
$540$	−1.29429	−0.0556972
$541$	−6.55483	−0.281814	−0.140907	−	0.990023i	$-0.545002\pi$
$541$	−6.55483	−0.281814	−0.140907	+	0.990023i	$0.545002\pi$
$542$	−32.4454	−1.39365
$543$	−42.5299	−1.82513
$544$	−6.91063	−0.296291
$545$	−4.37149	−0.187254
$546$	−8.95287	−0.383148
$547$	22.4865	0.961453	0.480726	−	0.876871i	$-0.340373\pi$
$547$	22.4865	0.961453	0.480726	+	0.876871i	$0.340373\pi$
$548$	19.8153	0.846469
$549$	7.54536	0.322028
$550$	−8.63070	−0.368014
$551$	0.670791	0.0285766
$552$	−2.66089	−0.113255
$553$	10.1241	0.430521
$554$	50.7566	2.15644
$555$	0.780706	0.0331391
$556$	−6.05841	−0.256934
$557$	44.7280	1.89519	0.947593	−	0.319481i	$-0.103509\pi$
$557$	44.7280	1.89519	0.947593	+	0.319481i	$0.103509\pi$
$558$	−12.8902	−0.545686
$559$	3.16377	0.133813
$560$	−5.77104	−0.243871
$561$	2.54229	0.107335
$562$	−17.5972	−0.742292
$563$	29.6105	1.24793	0.623966	−	0.781451i	$-0.285520\pi$
$563$	29.6105	1.24793	0.623966	+	0.781451i	$0.285520\pi$
$564$	0.556562	0.0234355
$565$	−4.70897	−0.198108
$566$	−5.47410	−0.230093
$567$	−35.6321	−1.49641
$568$	−22.0833	−0.926597
$569$	−0.324144	−0.0135888	−0.00679440	−	0.999977i	$-0.502163\pi$
$569$	−0.324144	−0.0135888	−0.00679440	+	0.999977i	$0.502163\pi$
$570$	−10.9012	−0.456603
$571$	−8.54812	−0.357728	−0.178864	−	0.983874i	$-0.557242\pi$
$571$	−8.54812	−0.357728	−0.178864	+	0.983874i	$0.557242\pi$
$572$	−0.855544	−0.0357721
$573$	−22.6493	−0.946188
$574$	−16.8941	−0.705145
$575$	4.00509	0.167024
$576$	−0.512375	−0.0213490
$577$	20.1719	0.839768	0.419884	−	0.907578i	$-0.362071\pi$
$577$	20.1719	0.839768	0.419884	+	0.907578i	$0.362071\pi$
$578$	27.6339	1.14942
$579$	48.0666	1.99758
$580$	0.0357180	0.00148311
$581$	−50.7606	−2.10591
$582$	67.0341	2.77865
$583$	2.21852	0.0918818
$584$	−10.8033	−0.447043
$585$	0.424301	0.0175427
$586$	53.0802	2.19272
$587$	−2.92805	−0.120853	−0.0604267	−	0.998173i	$-0.519246\pi$
$587$	−2.92805	−0.120853	−0.0604267	+	0.998173i	$0.519246\pi$
$588$	7.42428	0.306172
$589$	36.8415	1.51803
$590$	−4.09535	−0.168603
$591$	−18.1891	−0.748199
$592$	−4.97876	−0.204626
$593$	27.3279	1.12222	0.561111	−	0.827740i	$-0.310374\pi$
$593$	27.3279	1.12222	0.561111	+	0.827740i	$0.310374\pi$
$594$	−5.47603	−0.224684
$595$	−1.38104	−0.0566171
$596$	−7.23586	−0.296393
$597$	−16.8902	−0.691270
$598$	1.09004	0.0445750
$599$	41.5454	1.69750	0.848750	−	0.528794i	$-0.177356\pi$
$599$	41.5454	1.69750	0.848750	+	0.528794i	$0.177356\pi$
$600$	−15.7319	−0.642253
$601$	15.8668	0.647219	0.323610	−	0.946191i	$-0.395104\pi$
$601$	15.8668	0.647219	0.323610	+	0.946191i	$0.395104\pi$
$602$	−23.8074	−0.970317
$603$	21.6779	0.882791
$604$	2.13142	0.0867262
$605$	0.365878	0.0148750
$606$	40.6616	1.65176
$607$	12.2585	0.497558	0.248779	−	0.968560i	$-0.419971\pi$
$607$	12.2585	0.497558	0.248779	+	0.968560i	$0.419971\pi$
$608$	45.6637	1.85191
$609$	0.575982	0.0233400
$610$	−3.15277	−0.127652
$611$	0.169990	0.00687706
$612$	−2.12007	−0.0856987
$613$	−47.6835	−1.92592	−0.962959	−	0.269646i	$-0.913093\pi$
$613$	−47.6835	−1.92592	−0.962959	+	0.269646i	$0.913093\pi$
$614$	−22.3076	−0.900263
$615$	2.34727	0.0946509
$616$	−4.80002	−0.193398
$617$	34.4418	1.38657	0.693287	−	0.720662i	$-0.256162\pi$
$617$	34.4418	1.38657	0.693287	+	0.720662i	$0.256162\pi$
$618$	20.5371	0.826125
$619$	−5.16751	−0.207700	−0.103850	−	0.994593i	$-0.533116\pi$
$619$	−5.16751	−0.207700	−0.103850	+	0.994593i	$0.533116\pi$
$620$	1.96172	0.0787847
$621$	2.54116	0.101973
$622$	18.4822	0.741068
$623$	−1.24556	−0.0499024
$624$	−7.93275	−0.317564
$625$	23.0099	0.920397
$626$	−14.2987	−0.571490
$627$	−16.7988	−0.670879
$628$	10.0300	0.400241
$629$	−1.19144	−0.0475059
$630$	−3.19287	−0.127207
$631$	−26.0934	−1.03876	−0.519382	−	0.854542i	$-0.673838\pi$
$631$	−26.0934	−1.03876	−0.519382	+	0.854542i	$0.673838\pi$
$632$	4.84179	0.192596
$633$	1.48995	0.0592203
$634$	−7.89946	−0.313728
$635$	4.01747	0.159429
$636$	−5.42382	−0.215069
$637$	2.26759	0.0898450
$638$	0.151120	0.00598291
$639$	−22.6363	−0.895477
$640$	−4.03025	−0.159310
$641$	−38.1079	−1.50517	−0.752586	−	0.658494i	$-0.771194\pi$
$641$	−38.1079	−1.50517	−0.752586	+	0.658494i	$0.771194\pi$
$642$	7.31751	0.288799
$643$	17.9660	0.708510	0.354255	−	0.935149i	$-0.384734\pi$
$643$	17.9660	0.708510	0.354255	+	0.935149i	$0.384734\pi$
$644$	−2.98756	−0.117726
$645$	3.30781	0.130245
$646$	16.6365	0.654554
$647$	−37.4720	−1.47318	−0.736589	−	0.676341i	$-0.763565\pi$
$647$	−37.4720	−1.47318	−0.736589	+	0.676341i	$0.763565\pi$
$648$	−17.0408	−0.669426
$649$	−6.31092	−0.247725
$650$	6.44463	0.252779
$651$	31.6344	1.23985
$652$	−10.1275	−0.396622
$653$	14.0047	0.548048	0.274024	−	0.961723i	$-0.411645\pi$
$653$	14.0047	0.548048	0.274024	+	0.961723i	$0.411645\pi$
$654$	45.2176	1.76815
$655$	−3.94431	−0.154117
$656$	−14.9691	−0.584445
$657$	−11.0738	−0.432030
$658$	−1.27918	−0.0498675
$659$	25.4552	0.991594	0.495797	−	0.868439i	$-0.334876\pi$
$659$	25.4552	0.991594	0.495797	+	0.868439i	$0.334876\pi$
$660$	−0.894495	−0.0348182
$661$	−23.7275	−0.922891	−0.461446	−	0.887169i	$-0.652669\pi$
$661$	−23.7275	−0.922891	−0.461446	+	0.887169i	$0.652669\pi$
$662$	−9.22516	−0.358546
$663$	−1.89835	−0.0737257
$664$	−24.2760	−0.942090
$665$	9.12556	0.353874
$666$	−2.75454	−0.106736
$667$	−0.0701276	−0.00271535
$668$	11.2542	0.435439
$669$	−54.3010	−2.09940
$670$	−9.05792	−0.349938
$671$	−4.85841	−0.187557
$672$	39.2096	1.51254
$673$	37.0634	1.42869	0.714344	−	0.699795i	$-0.246725\pi$
$673$	37.0634	1.42869	0.714344	+	0.699795i	$0.246725\pi$
$674$	−25.1622	−0.969210
$675$	15.0241	0.578277
$676$	−14.2559	−0.548305
$677$	12.2870	0.472229	0.236115	−	0.971725i	$-0.424126\pi$
$677$	12.2870	0.472229	0.236115	+	0.971725i	$0.424126\pi$
$678$	48.7084	1.87064
$679$	−56.1150	−2.15350
$680$	−0.660473	−0.0253280
$681$	3.30434	0.126623
$682$	8.29991	0.317820
$683$	5.92103	0.226562	0.113281	−	0.993563i	$-0.463864\pi$
$683$	5.92103	0.226562	0.113281	+	0.993563i	$0.463864\pi$
$684$	14.0089	0.535643
$685$	6.32771	0.241769
$686$	22.2694	0.850249
$687$	−2.79848	−0.106769
$688$	−21.0947	−0.804228
$689$	−1.65659	−0.0631111
$690$	1.13967	0.0433864
$691$	−42.3208	−1.60996	−0.804979	−	0.593303i	$-0.797823\pi$
$691$	−42.3208	−1.60996	−0.804979	+	0.593303i	$0.797823\pi$
$692$	16.8056	0.638853
$693$	−4.92021	−0.186903
$694$	4.98577	0.189257
$695$	−1.93466	−0.0733857
$696$	0.275460	0.0104413
$697$	−3.58218	−0.135685
$698$	30.7210	1.16281
$699$	55.7303	2.10791
$700$	−17.6633	−0.667610
$701$	12.6847	0.479095	0.239548	−	0.970885i	$-0.423001\pi$
$701$	12.6847	0.479095	0.239548	+	0.970885i	$0.423001\pi$
$702$	4.08901	0.154330
$703$	7.87275	0.296927
$704$	0.329914	0.0124341
$705$	0.177729	0.00669367
$706$	−39.2701	−1.47795
$707$	−34.0383	−1.28014
$708$	15.4289	0.579853
$709$	29.9368	1.12430	0.562149	−	0.827036i	$-0.309975\pi$
$709$	29.9368	1.12430	0.562149	+	0.827036i	$0.309975\pi$
$710$	9.45838	0.354967
$711$	4.96302	0.186128
$712$	−0.595682	−0.0223241
$713$	−3.85159	−0.144243
$714$	14.2851	0.534607
$715$	−0.273204	−0.0102173
$716$	7.46267	0.278893
$717$	−17.0473	−0.636643
$718$	−27.3556	−1.02090
$719$	−30.3440	−1.13164	−0.565820	−	0.824529i	$-0.691440\pi$
$719$	−30.3440	−1.13164	−0.565820	+	0.824529i	$0.691440\pi$
$720$	−2.82907	−0.105433
$721$	−17.1919	−0.640259
$722$	−76.2309	−2.83702
$723$	16.3093	0.606549
$724$	−22.8367	−0.848720
$725$	−0.414614	−0.0153984
$726$	−3.78454	−0.140458
$727$	38.0157	1.40992	0.704962	−	0.709245i	$-0.250964\pi$
$727$	38.0157	1.40992	0.704962	+	0.709245i	$0.250964\pi$
$728$	3.58422	0.132840
$729$	2.29659	0.0850590
$730$	4.62709	0.171256
$731$	−5.04807	−0.186710
$732$	11.8778	0.439016
$733$	−13.4001	−0.494945	−0.247473	−	0.968895i	$-0.579600\pi$
$733$	−13.4001	−0.494945	−0.247473	+	0.968895i	$0.579600\pi$
$734$	8.39049	0.309699
$735$	2.37082	0.0874492
$736$	−4.77390	−0.175968
$737$	−13.9582	−0.514158
$738$	−8.28178	−0.304856
$739$	43.0142	1.58230	0.791152	−	0.611619i	$-0.209482\pi$
$739$	43.0142	1.58230	0.791152	+	0.611619i	$0.209482\pi$
$740$	0.419205	0.0154103
$741$	12.5438	0.460809
$742$	12.4659	0.457637
$743$	39.6785	1.45566	0.727831	−	0.685757i	$-0.240529\pi$
$743$	39.6785	1.45566	0.727831	+	0.685757i	$0.240529\pi$
$744$	15.1289	0.554654
$745$	−2.31066	−0.0846560
$746$	−35.5622	−1.30203
$747$	−24.8838	−0.910450
$748$	1.36510	0.0499129
$749$	−6.12557	−0.223823
$750$	13.6614	0.498845
$751$	1.72854	0.0630752	0.0315376	−	0.999503i	$-0.489960\pi$
$751$	1.72854	0.0630752	0.0315376	+	0.999503i	$0.489960\pi$
$752$	−1.13342	−0.0413317
$753$	14.1513	0.515701
$754$	−0.112843	−0.00410950
$755$	0.680635	0.0247708
$756$	−11.2071	−0.407597
$757$	22.3680	0.812981	0.406490	−	0.913655i	$-0.366752\pi$
$757$	22.3680	0.812981	0.406490	+	0.913655i	$0.366752\pi$
$758$	40.2361	1.46144
$759$	1.75622	0.0637469
$760$	4.36424	0.158308
$761$	22.0349	0.798764	0.399382	−	0.916785i	$-0.369225\pi$
$761$	22.0349	0.798764	0.399382	+	0.916785i	$0.369225\pi$
$762$	−41.5557	−1.50540
$763$	−37.8522	−1.37034
$764$	−12.1617	−0.439994
$765$	−0.677010	−0.0244774
$766$	65.1621	2.35440
$767$	4.71242	0.170156
$768$	43.0958	1.55509
$769$	52.6410	1.89828	0.949142	−	0.314849i	$-0.101954\pi$
$769$	52.6410	1.89828	0.949142	+	0.314849i	$0.101954\pi$
$770$	2.05587	0.0740883
$771$	68.1217	2.45334
$772$	25.8097	0.928910
$773$	7.54837	0.271496	0.135748	−	0.990743i	$-0.456656\pi$
$773$	7.54837	0.271496	0.135748	+	0.990743i	$0.456656\pi$
$774$	−11.6708	−0.419499
$775$	−22.7717	−0.817983
$776$	−26.8366	−0.963379
$777$	6.76003	0.242515
$778$	−55.7755	−1.99965
$779$	23.6702	0.848072
$780$	0.667928	0.0239157
$781$	14.5753	0.521547
$782$	−1.73926	−0.0621957
$783$	−0.263066	−0.00940120
$784$	−15.1193	−0.539977
$785$	3.20293	0.114317
$786$	40.7989	1.45525
$787$	27.9979	0.998018	0.499009	−	0.866597i	$-0.333698\pi$
$787$	27.9979	0.998018	0.499009	+	0.866597i	$0.333698\pi$
$788$	−9.76675	−0.347926
$789$	−29.5093	−1.05056
$790$	−2.07376	−0.0737809
$791$	−40.7744	−1.44977
$792$	−2.35306	−0.0836123
$793$	3.62782	0.128828
$794$	−10.0962	−0.358301
$795$	−1.73201	−0.0614281
$796$	−9.06931	−0.321453
$797$	27.9468	0.989928	0.494964	−	0.868913i	$-0.335181\pi$
$797$	27.9468	0.989928	0.494964	+	0.868913i	$0.335181\pi$
$798$	−94.3925	−3.34146
$799$	−0.271234	−0.00959558
$800$	−28.2246	−0.997892
$801$	−0.610597	−0.0215744
$802$	−47.9988	−1.69489
$803$	7.13033	0.251624
$804$	34.1250	1.20349
$805$	−0.954029	−0.0336251
$806$	−6.19762	−0.218302
$807$	52.3361	1.84232
$808$	−16.2786	−0.572679
$809$	−3.09949	−0.108972	−0.0544862	−	0.998515i	$-0.517352\pi$
$809$	−3.09949	−0.108972	−0.0544862	+	0.998515i	$0.517352\pi$
$810$	7.29864	0.256448
$811$	−29.1041	−1.02198	−0.510992	−	0.859586i	$-0.670722\pi$
$811$	−29.1041	−1.02198	−0.510992	+	0.859586i	$0.670722\pi$
$812$	0.309277	0.0108535
$813$	39.0340	1.36898
$814$	1.77363	0.0621656
$815$	−3.23405	−0.113284
$816$	12.6574	0.443098
$817$	33.3564	1.16699
$818$	−6.14868	−0.214984
$819$	3.67397	0.128379
$820$	1.26038	0.0440144
$821$	−51.8546	−1.80974	−0.904870	−	0.425689i	$-0.860032\pi$
$821$	−51.8546	−1.80974	−0.904870	+	0.425689i	$0.860032\pi$
$822$	−65.4522	−2.28291
$823$	−20.2194	−0.704803	−0.352401	−	0.935849i	$-0.614635\pi$
$823$	−20.2194	−0.704803	−0.352401	+	0.935849i	$0.614635\pi$
$824$	−8.22191	−0.286424
$825$	10.3833	0.361500
$826$	−35.4611	−1.23385
$827$	2.68883	0.0934999	0.0467500	−	0.998907i	$-0.485114\pi$
$827$	2.68883	0.0934999	0.0467500	+	0.998907i	$0.485114\pi$
$828$	−1.46455	−0.0508968
$829$	19.0362	0.661154	0.330577	−	0.943779i	$-0.392757\pi$
$829$	19.0362	0.661154	0.330577	+	0.943779i	$0.392757\pi$
$830$	10.3975	0.360902
$831$	−61.0635	−2.11827
$832$	−0.246350	−0.00854066
$833$	−3.61814	−0.125361
$834$	20.0116	0.692945
$835$	3.59386	0.124371
$836$	−9.02022	−0.311971
$837$	−14.4482	−0.499404
$838$	52.2371	1.80450
$839$	29.9265	1.03318	0.516588	−	0.856234i	$-0.327202\pi$
$839$	29.9265	1.03318	0.516588	+	0.856234i	$0.327202\pi$
$840$	3.74740	0.129298
$841$	−28.9927	−0.999750
$842$	40.0504	1.38023
$843$	21.1705	0.729152
$844$	0.800040	0.0275385
$845$	−4.55241	−0.156608
$846$	−0.627076	−0.0215593
$847$	3.16809	0.108857
$848$	11.0455	0.379303
$849$	6.58570	0.226020
$850$	−10.2830	−0.352703
$851$	−0.823054	−0.0282139
$852$	−35.6337	−1.22079
$853$	31.9692	1.09460	0.547302	−	0.836935i	$-0.315655\pi$
$853$	31.9692	1.09460	0.547302	+	0.836935i	$0.315655\pi$
$854$	−27.2994	−0.934166
$855$	4.47352	0.152991
$856$	−2.92952	−0.100129
$857$	−2.18482	−0.0746319	−0.0373160	−	0.999304i	$-0.511881\pi$
$857$	−2.18482	−0.0746319	−0.0373160	+	0.999304i	$0.511881\pi$
$858$	2.82596	0.0964765
$859$	49.0759	1.67445	0.837224	−	0.546860i	$-0.184177\pi$
$859$	49.0759	1.67445	0.837224	+	0.546860i	$0.184177\pi$
$860$	1.77615	0.0605662
$861$	20.3247	0.692663
$862$	−14.3906	−0.490146
$863$	42.7019	1.45359	0.726794	−	0.686856i	$-0.241009\pi$
$863$	42.7019	1.45359	0.726794	+	0.686856i	$0.241009\pi$
$864$	−17.9081	−0.609244
$865$	5.36660	0.182470
$866$	5.84429	0.198597
$867$	−33.2454	−1.12907
$868$	16.9863	0.576552
$869$	−3.19565	−0.108405
$870$	−0.117980	−0.00399991
$871$	10.4227	0.353161
$872$	−18.1026	−0.613030
$873$	−27.5086	−0.931025
$874$	11.4926	0.388742
$875$	−11.4362	−0.386613
$876$	−17.4322	−0.588979
$877$	11.9608	0.403888	0.201944	−	0.979397i	$-0.435274\pi$
$877$	11.9608	0.403888	0.201944	+	0.979397i	$0.435274\pi$
$878$	57.9763	1.95661
$879$	−63.8589	−2.15391
$880$	1.82162	0.0614067
$881$	17.3717	0.585268	0.292634	−	0.956225i	$-0.405468\pi$
$881$	17.3717	0.585268	0.292634	+	0.956225i	$0.405468\pi$
$882$	−8.36490	−0.281661
$883$	−49.7231	−1.67332	−0.836658	−	0.547725i	$-0.815494\pi$
$883$	−49.7231	−1.67332	−0.836658	+	0.547725i	$0.815494\pi$
$884$	−1.01933	−0.0342838
$885$	4.92697	0.165618
$886$	−48.6355	−1.63394
$887$	−46.2787	−1.55389	−0.776944	−	0.629570i	$-0.783231\pi$
$887$	−46.2787	−1.55389	−0.776944	+	0.629570i	$0.783231\pi$
$888$	3.23294	0.108490
$889$	34.7868	1.16671
$890$	0.255133	0.00855207
$891$	11.2472	0.376795
$892$	−29.1573	−0.976258
$893$	1.79225	0.0599753
$894$	23.9009	0.799364
$895$	2.38309	0.0796578
$896$	−34.8974	−1.16584
$897$	−1.31139	−0.0437860
$898$	17.8020	0.594060
$899$	0.398723	0.0132982
$900$	−8.65887	−0.288629
$901$	2.64324	0.0880591
$902$	5.33258	0.177555
$903$	28.6419	0.953141
$904$	−19.5001	−0.648563
$905$	−7.29255	−0.242412
$906$	−7.04031	−0.233899
$907$	−50.0943	−1.66335	−0.831677	−	0.555259i	$-0.812619\pi$
$907$	−50.0943	−1.66335	−0.831677	+	0.555259i	$0.812619\pi$
$908$	1.77429	0.0588818
$909$	−16.6862	−0.553446
$910$	−1.53514	−0.0508893
$911$	−27.6733	−0.916857	−0.458428	−	0.888731i	$-0.651587\pi$
$911$	−27.6733	−0.916857	−0.458428	+	0.888731i	$0.651587\pi$
$912$	−83.6371	−2.76950
$913$	16.0225	0.530267
$914$	2.54361	0.0841351
$915$	3.79298	0.125392
$916$	−1.50266	−0.0496494
$917$	−34.1532	−1.12784
$918$	−6.52438	−0.215336
$919$	34.6759	1.14385	0.571926	−	0.820305i	$-0.306196\pi$
$919$	34.6759	1.14385	0.571926	+	0.820305i	$0.306196\pi$
$920$	−0.456258	−0.0150424
$921$	26.8376	0.884328
$922$	−6.46901	−0.213046
$923$	−10.8835	−0.358236
$924$	−7.74531	−0.254802
$925$	−4.86613	−0.159997
$926$	−41.0121	−1.34774
$927$	−8.42777	−0.276804
$928$	0.494203	0.0162230
$929$	−25.9610	−0.851754	−0.425877	−	0.904781i	$-0.640034\pi$
$929$	−25.9610	−0.851754	−0.425877	+	0.904781i	$0.640034\pi$
$930$	−6.47979	−0.212481
$931$	23.9078	0.783545
$932$	29.9248	0.980218
$933$	−22.2353	−0.727950
$934$	−27.6227	−0.903843
$935$	0.435922	0.0142562
$936$	1.75705	0.0574310
$937$	8.38853	0.274041	0.137021	−	0.990568i	$-0.456247\pi$
$937$	8.38853	0.274041	0.137021	+	0.990568i	$0.456247\pi$
$938$	−78.4313	−2.56087
$939$	17.2022	0.561374
$940$	0.0954329	0.00311268
$941$	−30.5845	−0.997028	−0.498514	−	0.866882i	$-0.666121\pi$
$941$	−30.5845	−0.997028	−0.498514	+	0.866882i	$0.666121\pi$
$942$	−33.1303	−1.07944
$943$	−2.47459	−0.0805838
$944$	−31.4205	−1.02265
$945$	−3.57879	−0.116418
$946$	7.51476	0.244326
$947$	−15.2375	−0.495153	−0.247577	−	0.968868i	$-0.579634\pi$
$947$	−15.2375	−0.495153	−0.247577	+	0.968868i	$0.579634\pi$
$948$	7.81271	0.253745
$949$	−5.32429	−0.172834
$950$	67.9474	2.20451
$951$	9.50356	0.308174
$952$	−5.71895	−0.185352
$953$	−53.1365	−1.72126	−0.860631	−	0.509230i	$-0.829930\pi$
$953$	−53.1365	−1.72126	−0.860631	+	0.509230i	$0.829930\pi$
$954$	6.11100	0.197851
$955$	−3.88364	−0.125672
$956$	−9.15367	−0.296051
$957$	−0.181808	−0.00587700
$958$	−6.04690	−0.195366
$959$	54.7908	1.76929
$960$	−0.257566	−0.00831291
$961$	−9.10111	−0.293584
$962$	−1.32438	−0.0426999
$963$	−3.00287	−0.0967660
$964$	8.75738	0.282056
$965$	8.24191	0.265316
$966$	9.86823	0.317505
$967$	42.3775	1.36277	0.681384	−	0.731926i	$-0.261378\pi$
$967$	42.3775	1.36277	0.681384	+	0.731926i	$0.261378\pi$
$968$	1.51512	0.0486977
$969$	−20.0148	−0.642967
$970$	11.4942	0.369058
$971$	−35.6629	−1.14448	−0.572239	−	0.820087i	$-0.693925\pi$
$971$	−35.6629	−1.14448	−0.572239	+	0.820087i	$0.693925\pi$
$972$	−16.8846	−0.541573
$973$	−16.7519	−0.537043
$974$	42.9608	1.37655
$975$	−7.75331	−0.248305
$976$	−24.1888	−0.774265
$977$	27.5346	0.880911	0.440455	−	0.897775i	$-0.354817\pi$
$977$	27.5346	0.880911	0.440455	+	0.897775i	$0.354817\pi$
$978$	33.4521	1.06968
$979$	0.393159	0.0125654
$980$	1.27303	0.0406655
$981$	−18.5558	−0.592442
$982$	−21.6118	−0.689661
$983$	−6.02146	−0.192055	−0.0960273	−	0.995379i	$-0.530614\pi$
$983$	−6.02146	−0.192055	−0.0960273	+	0.995379i	$0.530614\pi$
$984$	9.72014	0.309867
$985$	−3.11886	−0.0993750
$986$	0.180051	0.00573399
$987$	1.53893	0.0489848
$988$	6.73549	0.214284
$989$	−3.48724	−0.110888
$990$	1.00782	0.0320307
$991$	33.9691	1.07906	0.539532	−	0.841965i	$-0.318601\pi$
$991$	33.9691	1.07906	0.539532	+	0.841965i	$0.318601\pi$
$992$	27.1429	0.861787
$993$	11.0985	0.352199
$994$	81.8989	2.59767
$995$	−2.89614	−0.0918138
$996$	−39.1717	−1.24120
$997$	−60.0391	−1.90146	−0.950729	−	0.310022i	$-0.899664\pi$
$997$	−60.0391	−1.90146	−0.950729	+	0.310022i	$0.899664\pi$
$998$	9.08567	0.287602
$999$	−3.08748	−0.0976835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	407.2.a.c.1.3	✓	11
3.2	odd	2		3663.2.a.u.1.9		11
4.3	odd	2		6512.2.a.bb.1.3		11
11.10	odd	2		4477.2.a.k.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
407.2.a.c.1.3	✓	11	1.1	even	1	trivial
3663.2.a.u.1.9		11	3.2	odd	2
4477.2.a.k.1.9		11	11.10	odd	2
6512.2.a.bb.1.3		11	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 407 = 11 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	407.a (trivial)

\(f(q)\)	\(=\)	\(q-1.77363 q^{2} +2.13379 q^{3} +1.14575 q^{4} +0.365878 q^{5} -3.78454 q^{6} +3.16809 q^{7} +1.51512 q^{8} +1.55305 q^{9} +O(q^{10})\)	\(q-1.77363 q^{2} +2.13379 q^{3} +1.14575 q^{4} +0.365878 q^{5} -3.78454 q^{6} +3.16809 q^{7} +1.51512 q^{8} +1.55305 q^{9} -0.648930 q^{10} -1.00000 q^{11} +2.44479 q^{12} +0.746710 q^{13} -5.61900 q^{14} +0.780706 q^{15} -4.97876 q^{16} -1.19144 q^{17} -2.75454 q^{18} +7.87275 q^{19} +0.419205 q^{20} +6.76003 q^{21} +1.77363 q^{22} -0.823054 q^{23} +3.23294 q^{24} -4.86613 q^{25} -1.32438 q^{26} -3.08748 q^{27} +3.62984 q^{28} +0.0852041 q^{29} -1.38468 q^{30} +4.67963 q^{31} +5.80022 q^{32} -2.13379 q^{33} +2.11317 q^{34} +1.15913 q^{35} +1.77941 q^{36} +1.00000 q^{37} -13.9633 q^{38} +1.59332 q^{39} +0.554348 q^{40} +3.00659 q^{41} -11.9898 q^{42} +4.23694 q^{43} -1.14575 q^{44} +0.568228 q^{45} +1.45979 q^{46} +0.227652 q^{47} -10.6236 q^{48} +3.03677 q^{49} +8.63070 q^{50} -2.54229 q^{51} +0.855544 q^{52} -2.21852 q^{53} +5.47603 q^{54} -0.365878 q^{55} +4.80002 q^{56} +16.7988 q^{57} -0.151120 q^{58} +6.31092 q^{59} +0.894495 q^{60} +4.85841 q^{61} -8.29991 q^{62} +4.92021 q^{63} -0.329914 q^{64} +0.273204 q^{65} +3.78454 q^{66} +13.9582 q^{67} -1.36510 q^{68} -1.75622 q^{69} -2.05587 q^{70} -14.5753 q^{71} +2.35306 q^{72} -7.13033 q^{73} -1.77363 q^{74} -10.3833 q^{75} +9.02022 q^{76} -3.16809 q^{77} -2.82596 q^{78} +3.19565 q^{79} -1.82162 q^{80} -11.2472 q^{81} -5.33258 q^{82} -16.0225 q^{83} +7.74531 q^{84} -0.435922 q^{85} -7.51476 q^{86} +0.181808 q^{87} -1.51512 q^{88} -0.393159 q^{89} -1.00782 q^{90} +2.36564 q^{91} -0.943016 q^{92} +9.98533 q^{93} -0.403770 q^{94} +2.88046 q^{95} +12.3764 q^{96} -17.7126 q^{97} -5.38610 q^{98} -1.55305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9	\( 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9} + 5 q^{10} - 11 q^{11} + q^{12} + 22 q^{13} + 3 q^{14} - 10 q^{15} + 19 q^{17} + 18 q^{18} + 14 q^{19} + 6 q^{20} - 13 q^{21} - 2 q^{22} - 14 q^{23} - 11 q^{24} + 38 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 13 q^{29} + 19 q^{30} + 12 q^{31} - 3 q^{32} + q^{34} + 12 q^{35} + 18 q^{36} + 11 q^{37} - 31 q^{38} - 8 q^{39} + 22 q^{40} + 8 q^{41} + 15 q^{42} + 21 q^{43} - 14 q^{44} - 8 q^{45} - 45 q^{46} - 14 q^{47} - 37 q^{48} + 20 q^{49} - 41 q^{50} - 2 q^{51} + 51 q^{52} - 2 q^{53} + 6 q^{54} - q^{55} - 22 q^{56} - 3 q^{57} + 15 q^{58} - 30 q^{59} - 107 q^{60} + 20 q^{61} + 22 q^{62} + 31 q^{63} - 14 q^{64} - 4 q^{66} + 7 q^{67} + 24 q^{68} + 9 q^{69} - 86 q^{70} - 15 q^{71} - 7 q^{72} + 47 q^{73} + 2 q^{74} - 40 q^{75} + 6 q^{76} - 9 q^{77} - 42 q^{78} + 2 q^{79} + 3 q^{80} - 17 q^{81} - 54 q^{82} + 24 q^{83} - 33 q^{84} - 25 q^{85} - 13 q^{86} + 21 q^{87} + 4 q^{89} - 107 q^{90} + 21 q^{91} - 46 q^{92} - 37 q^{93} + 3 q^{94} - 36 q^{95} - 49 q^{96} + 25 q^{97} - 52 q^{98} - 15 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9 + 5 * q^10 - 11 * q^11 + q^12 + 22 * q^13 + 3 * q^14 - 10 * q^15 + 19 * q^17 + 18 * q^18 + 14 * q^19 + 6 * q^20 - 13 * q^21 - 2 * q^22 - 14 * q^23 - 11 * q^24 + 38 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 13 * q^29 + 19 * q^30 + 12 * q^31 - 3 * q^32 + q^34 + 12 * q^35 + 18 * q^36 + 11 * q^37 - 31 * q^38 - 8 * q^39 + 22 * q^40 + 8 * q^41 + 15 * q^42 + 21 * q^43 - 14 * q^44 - 8 * q^45 - 45 * q^46 - 14 * q^47 - 37 * q^48 + 20 * q^49 - 41 * q^50 - 2 * q^51 + 51 * q^52 - 2 * q^53 + 6 * q^54 - q^55 - 22 * q^56 - 3 * q^57 + 15 * q^58 - 30 * q^59 - 107 * q^60 + 20 * q^61 + 22 * q^62 + 31 * q^63 - 14 * q^64 - 4 * q^66 + 7 * q^67 + 24 * q^68 + 9 * q^69 - 86 * q^70 - 15 * q^71 - 7 * q^72 + 47 * q^73 + 2 * q^74 - 40 * q^75 + 6 * q^76 - 9 * q^77 - 42 * q^78 + 2 * q^79 + 3 * q^80 - 17 * q^81 - 54 * q^82 + 24 * q^83 - 33 * q^84 - 25 * q^85 - 13 * q^86 + 21 * q^87 + 4 * q^89 - 107 * q^90 + 21 * q^91 - 46 * q^92 - 37 * q^93 + 3 * q^94 - 36 * q^95 - 49 * q^96 + 25 * q^97 - 52 * q^98 - 15 * q^99

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