LMFDB - Embedded newform 4030.2.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 8x^{5} + 24x^{4} + 18x^{3} - 48x^{2} - 9x + 4 $ x^7 - 3x^6 - 8x^5 + 24x^4 + 18x^3 - 48x^2 - 9x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.217747$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.217747 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217747 q^{6} +2.27131 q^{7} -1.00000 q^{8} -2.95259 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.217747 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217747 q^{6} +2.27131 q^{7} -1.00000 q^{8} -2.95259 q^{9} +1.00000 q^{10} +0.616883 q^{11} +0.217747 q^{12} -1.00000 q^{13} -2.27131 q^{14} -0.217747 q^{15} +1.00000 q^{16} +0.807095 q^{17} +2.95259 q^{18} +4.82221 q^{19} -1.00000 q^{20} +0.494571 q^{21} -0.616883 q^{22} -3.56747 q^{23} -0.217747 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.29616 q^{27} +2.27131 q^{28} -9.62389 q^{29} +0.217747 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.134324 q^{33} -0.807095 q^{34} -2.27131 q^{35} -2.95259 q^{36} +7.18731 q^{37} -4.82221 q^{38} -0.217747 q^{39} +1.00000 q^{40} +1.90011 q^{41} -0.494571 q^{42} -4.97757 q^{43} +0.616883 q^{44} +2.95259 q^{45} +3.56747 q^{46} -3.73815 q^{47} +0.217747 q^{48} -1.84113 q^{49} -1.00000 q^{50} +0.175742 q^{51} -1.00000 q^{52} +0.258285 q^{53} +1.29616 q^{54} -0.616883 q^{55} -2.27131 q^{56} +1.05002 q^{57} +9.62389 q^{58} +10.8579 q^{59} -0.217747 q^{60} +4.92319 q^{61} +1.00000 q^{62} -6.70625 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.134324 q^{66} -0.173645 q^{67} +0.807095 q^{68} -0.776805 q^{69} +2.27131 q^{70} -7.42422 q^{71} +2.95259 q^{72} -0.318728 q^{73} -7.18731 q^{74} +0.217747 q^{75} +4.82221 q^{76} +1.40114 q^{77} +0.217747 q^{78} -0.818845 q^{79} -1.00000 q^{80} +8.57553 q^{81} -1.90011 q^{82} -13.7043 q^{83} +0.494571 q^{84} -0.807095 q^{85} +4.97757 q^{86} -2.09557 q^{87} -0.616883 q^{88} -7.46724 q^{89} -2.95259 q^{90} -2.27131 q^{91} -3.56747 q^{92} -0.217747 q^{93} +3.73815 q^{94} -4.82221 q^{95} -0.217747 q^{96} -8.95472 q^{97} +1.84113 q^{98} -1.82140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.217747	0.125716	0.0628581	−	0.998022i	$-0.479978\pi$
$3$	0.217747	0.125716	0.0628581	+	0.998022i	$0.479978\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.217747	−0.0888947
$7$	2.27131	0.858476	0.429238	−	0.903191i	$-0.358782\pi$
$7$	2.27131	0.858476	0.429238	+	0.903191i	$0.358782\pi$
$8$	−1.00000	−0.353553
$9$	−2.95259	−0.984195
$10$	1.00000	0.316228
$11$	0.616883	0.185997	0.0929986	−	0.995666i	$-0.470355\pi$
$11$	0.616883	0.185997	0.0929986	+	0.995666i	$0.470355\pi$
$12$	0.217747	0.0628581
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.27131	−0.607034
$15$	−0.217747	−0.0562220
$16$	1.00000	0.250000
$17$	0.807095	0.195749	0.0978747	−	0.995199i	$-0.468796\pi$
$17$	0.807095	0.195749	0.0978747	+	0.995199i	$0.468796\pi$
$18$	2.95259	0.695931
$19$	4.82221	1.10629	0.553145	−	0.833085i	$-0.313427\pi$
$19$	4.82221	1.10629	0.553145	+	0.833085i	$0.313427\pi$
$20$	−1.00000	−0.223607
$21$	0.494571	0.107924
$22$	−0.616883	−0.131520
$23$	−3.56747	−0.743869	−0.371935	−	0.928259i	$-0.621305\pi$
$23$	−3.56747	−0.743869	−0.371935	+	0.928259i	$0.621305\pi$
$24$	−0.217747	−0.0444474
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−1.29616	−0.249445
$28$	2.27131	0.429238
$29$	−9.62389	−1.78711	−0.893556	−	0.448951i	$-0.851798\pi$
$29$	−9.62389	−1.78711	−0.893556	+	0.448951i	$0.851798\pi$
$30$	0.217747	0.0397549
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	0.134324	0.0233829
$34$	−0.807095	−0.138416
$35$	−2.27131	−0.383922
$36$	−2.95259	−0.492098
$37$	7.18731	1.18159	0.590793	−	0.806823i	$-0.298815\pi$
$37$	7.18731	1.18159	0.590793	+	0.806823i	$0.298815\pi$
$38$	−4.82221	−0.782266
$39$	−0.217747	−0.0348674
$40$	1.00000	0.158114
$41$	1.90011	0.296748	0.148374	−	0.988931i	$-0.452596\pi$
$41$	1.90011	0.296748	0.148374	+	0.988931i	$0.452596\pi$
$42$	−0.494571	−0.0763140
$43$	−4.97757	−0.759072	−0.379536	−	0.925177i	$-0.623916\pi$
$43$	−4.97757	−0.759072	−0.379536	+	0.925177i	$0.623916\pi$
$44$	0.616883	0.0929986
$45$	2.95259	0.440146
$46$	3.56747	0.525995
$47$	−3.73815	−0.545265	−0.272633	−	0.962118i	$-0.587894\pi$
$47$	−3.73815	−0.545265	−0.272633	+	0.962118i	$0.587894\pi$
$48$	0.217747	0.0314290
$49$	−1.84113	−0.263019
$50$	−1.00000	−0.141421
$51$	0.175742	0.0246089
$52$	−1.00000	−0.138675
$53$	0.258285	0.0354782	0.0177391	−	0.999843i	$-0.494353\pi$
$53$	0.258285	0.0354782	0.0177391	+	0.999843i	$0.494353\pi$
$54$	1.29616	0.176385
$55$	−0.616883	−0.0831805
$56$	−2.27131	−0.303517
$57$	1.05002	0.139079
$58$	9.62389	1.26368
$59$	10.8579	1.41358	0.706791	−	0.707423i	$-0.250142\pi$
$59$	10.8579	1.41358	0.706791	+	0.707423i	$0.250142\pi$
$60$	−0.217747	−0.0281110
$61$	4.92319	0.630350	0.315175	−	0.949034i	$-0.397937\pi$
$61$	4.92319	0.630350	0.315175	+	0.949034i	$0.397937\pi$
$62$	1.00000	0.127000
$63$	−6.70625	−0.844908
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−0.134324	−0.0165342
$67$	−0.173645	−0.0212142	−0.0106071	−	0.999944i	$-0.503376\pi$
$67$	−0.173645	−0.0212142	−0.0106071	+	0.999944i	$0.503376\pi$
$68$	0.807095	0.0978747
$69$	−0.776805	−0.0935163
$70$	2.27131	0.271474
$71$	−7.42422	−0.881092	−0.440546	−	0.897730i	$-0.645215\pi$
$71$	−7.42422	−0.881092	−0.440546	+	0.897730i	$0.645215\pi$
$72$	2.95259	0.347966
$73$	−0.318728	−0.0373043	−0.0186521	−	0.999826i	$-0.505938\pi$
$73$	−0.318728	−0.0373043	−0.0186521	+	0.999826i	$0.505938\pi$
$74$	−7.18731	−0.835508
$75$	0.217747	0.0251432
$76$	4.82221	0.553145
$77$	1.40114	0.159674
$78$	0.217747	0.0246550
$79$	−0.818845	−0.0921273	−0.0460636	−	0.998939i	$-0.514668\pi$
$79$	−0.818845	−0.0921273	−0.0460636	+	0.998939i	$0.514668\pi$
$80$	−1.00000	−0.111803
$81$	8.57553	0.952836
$82$	−1.90011	−0.209832
$83$	−13.7043	−1.50424	−0.752121	−	0.659025i	$-0.770969\pi$
$83$	−13.7043	−1.50424	−0.752121	+	0.659025i	$0.770969\pi$
$84$	0.494571	0.0539621
$85$	−0.807095	−0.0875418
$86$	4.97757	0.536745
$87$	−2.09557	−0.224669
$88$	−0.616883	−0.0657600
$89$	−7.46724	−0.791526	−0.395763	−	0.918353i	$-0.629520\pi$
$89$	−7.46724	−0.791526	−0.395763	+	0.918353i	$0.629520\pi$
$90$	−2.95259	−0.311230
$91$	−2.27131	−0.238098
$92$	−3.56747	−0.371935
$93$	−0.217747	−0.0225793
$94$	3.73815	0.385561
$95$	−4.82221	−0.494748
$96$	−0.217747	−0.0222237
$97$	−8.95472	−0.909214	−0.454607	−	0.890692i	$-0.650220\pi$
$97$	−8.95472	−0.909214	−0.454607	+	0.890692i	$0.650220\pi$
$98$	1.84113	0.185982
$99$	−1.82140	−0.183058
$100$	1.00000	0.100000
$101$	−4.57833	−0.455561	−0.227780	−	0.973713i	$-0.573147\pi$
$101$	−4.57833	−0.455561	−0.227780	+	0.973713i	$0.573147\pi$
$102$	−0.175742	−0.0174011
$103$	3.16717	0.312071	0.156035	−	0.987751i	$-0.450129\pi$
$103$	3.16717	0.312071	0.156035	+	0.987751i	$0.450129\pi$
$104$	1.00000	0.0980581
$105$	−0.494571	−0.0482652
$106$	−0.258285	−0.0250869
$107$	−3.57251	−0.345368	−0.172684	−	0.984977i	$-0.555244\pi$
$107$	−3.57251	−0.345368	−0.172684	+	0.984977i	$0.555244\pi$
$108$	−1.29616	−0.124723
$109$	−4.91695	−0.470958	−0.235479	−	0.971879i	$-0.575666\pi$
$109$	−4.91695	−0.470958	−0.235479	+	0.971879i	$0.575666\pi$
$110$	0.616883	0.0588175
$111$	1.56501	0.148544
$112$	2.27131	0.214619
$113$	−2.30426	−0.216766	−0.108383	−	0.994109i	$-0.534567\pi$
$113$	−2.30426	−0.216766	−0.108383	+	0.994109i	$0.534567\pi$
$114$	−1.05002	−0.0983434
$115$	3.56747	0.332668
$116$	−9.62389	−0.893556
$117$	2.95259	0.272967
$118$	−10.8579	−0.999553
$119$	1.83317	0.168046
$120$	0.217747	0.0198775
$121$	−10.6195	−0.965405
$122$	−4.92319	−0.445725
$123$	0.413743	0.0373060
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	6.70625	0.597440
$127$	7.62325	0.676454	0.338227	−	0.941065i	$-0.390173\pi$
$127$	7.62325	0.676454	0.338227	+	0.941065i	$0.390173\pi$
$128$	−1.00000	−0.0883883
$129$	−1.08385	−0.0954276
$130$	−1.00000	−0.0877058
$131$	−20.0225	−1.74937	−0.874687	−	0.484687i	$-0.838933\pi$
$131$	−20.0225	−1.74937	−0.874687	+	0.484687i	$0.838933\pi$
$132$	0.134324	0.0116914
$133$	10.9528	0.949724
$134$	0.173645	0.0150007
$135$	1.29616	0.111555
$136$	−0.807095	−0.0692079
$137$	23.3343	1.99358	0.996790	−	0.0800631i	$-0.0255122\pi$
$137$	23.3343	1.99358	0.996790	+	0.0800631i	$0.0255122\pi$
$138$	0.776805	0.0661260
$139$	−15.0857	−1.27955	−0.639775	−	0.768562i	$-0.720973\pi$
$139$	−15.0857	−1.27955	−0.639775	+	0.768562i	$0.720973\pi$
$140$	−2.27131	−0.191961
$141$	−0.813970	−0.0685487
$142$	7.42422	0.623026
$143$	−0.616883	−0.0515864
$144$	−2.95259	−0.246049
$145$	9.62389	0.799221
$146$	0.318728	0.0263781
$147$	−0.400900	−0.0330657
$148$	7.18731	0.590793
$149$	−6.25487	−0.512419	−0.256210	−	0.966621i	$-0.582474\pi$
$149$	−6.25487	−0.512419	−0.256210	+	0.966621i	$0.582474\pi$
$150$	−0.217747	−0.0177789
$151$	2.62675	0.213762	0.106881	−	0.994272i	$-0.465914\pi$
$151$	2.62675	0.213762	0.106881	+	0.994272i	$0.465914\pi$
$152$	−4.82221	−0.391133
$153$	−2.38302	−0.192656
$154$	−1.40114	−0.112907
$155$	1.00000	0.0803219
$156$	−0.217747	−0.0174337
$157$	3.79151	0.302596	0.151298	−	0.988488i	$-0.451655\pi$
$157$	3.79151	0.302596	0.151298	+	0.988488i	$0.451655\pi$
$158$	0.818845	0.0651438
$159$	0.0562408	0.00446019
$160$	1.00000	0.0790569
$161$	−8.10285	−0.638594
$162$	−8.57553	−0.673757
$163$	−16.7772	−1.31409	−0.657047	−	0.753849i	$-0.728195\pi$
$163$	−16.7772	−1.31409	−0.657047	+	0.753849i	$0.728195\pi$
$164$	1.90011	0.148374
$165$	−0.134324	−0.0104571
$166$	13.7043	1.06366
$167$	−5.78515	−0.447668	−0.223834	−	0.974627i	$-0.571857\pi$
$167$	−5.78515	−0.447668	−0.223834	+	0.974627i	$0.571857\pi$
$168$	−0.494571	−0.0381570
$169$	1.00000	0.0769231
$170$	0.807095	0.0619014
$171$	−14.2380	−1.08881
$172$	−4.97757	−0.379536
$173$	17.9557	1.36514	0.682572	−	0.730818i	$-0.260861\pi$
$173$	17.9557	1.36514	0.682572	+	0.730818i	$0.260861\pi$
$174$	2.09557	0.158865
$175$	2.27131	0.171695
$176$	0.616883	0.0464993
$177$	2.36428	0.177710
$178$	7.46724	0.559693
$179$	−9.72955	−0.727220	−0.363610	−	0.931551i	$-0.618456\pi$
$179$	−9.72955	−0.727220	−0.363610	+	0.931551i	$0.618456\pi$
$180$	2.95259	0.220073
$181$	8.06159	0.599213	0.299606	−	0.954063i	$-0.403145\pi$
$181$	8.06159	0.599213	0.299606	+	0.954063i	$0.403145\pi$
$182$	2.27131	0.168361
$183$	1.07201	0.0792452
$184$	3.56747	0.262997
$185$	−7.18731	−0.528421
$186$	0.217747	0.0159660
$187$	0.497884	0.0364088
$188$	−3.73815	−0.272633
$189$	−2.94398	−0.214143
$190$	4.82221	0.349840
$191$	15.2326	1.10219	0.551096	−	0.834442i	$-0.314210\pi$
$191$	15.2326	1.10219	0.551096	+	0.834442i	$0.314210\pi$
$192$	0.217747	0.0157145
$193$	14.9464	1.07587	0.537933	−	0.842988i	$-0.319206\pi$
$193$	14.9464	1.07587	0.537933	+	0.842988i	$0.319206\pi$
$194$	8.95472	0.642912
$195$	0.217747	0.0155932
$196$	−1.84113	−0.131509
$197$	−10.2147	−0.727768	−0.363884	−	0.931444i	$-0.618550\pi$
$197$	−10.2147	−0.727768	−0.363884	+	0.931444i	$0.618550\pi$
$198$	1.82140	0.129441
$199$	10.2163	0.724215	0.362107	−	0.932136i	$-0.382057\pi$
$199$	10.2163	0.724215	0.362107	+	0.932136i	$0.382057\pi$
$200$	−1.00000	−0.0707107
$201$	−0.0378107	−0.00266696
$202$	4.57833	0.322130
$203$	−21.8589	−1.53419
$204$	0.175742	0.0123044
$205$	−1.90011	−0.132710
$206$	−3.16717	−0.220667
$207$	10.5333	0.732113
$208$	−1.00000	−0.0693375
$209$	2.97474	0.205767
$210$	0.494571	0.0341287
$211$	−26.0863	−1.79586	−0.897928	−	0.440142i	$-0.854928\pi$
$211$	−26.0863	−1.79586	−0.897928	+	0.440142i	$0.854928\pi$
$212$	0.258285	0.0177391
$213$	−1.61660	−0.110768
$214$	3.57251	0.244212
$215$	4.97757	0.339467
$216$	1.29616	0.0881923
$217$	−2.27131	−0.154187
$218$	4.91695	0.333018
$219$	−0.0694019	−0.00468975
$220$	−0.616883	−0.0415903
$221$	−0.807095	−0.0542911
$222$	−1.56501	−0.105037
$223$	−20.9825	−1.40509	−0.702546	−	0.711639i	$-0.747953\pi$
$223$	−20.9825	−1.40509	−0.702546	+	0.711639i	$0.747953\pi$
$224$	−2.27131	−0.151759
$225$	−2.95259	−0.196839
$226$	2.30426	0.153277
$227$	−6.80193	−0.451460	−0.225730	−	0.974190i	$-0.572477\pi$
$227$	−6.80193	−0.451460	−0.225730	+	0.974190i	$0.572477\pi$
$228$	1.05002	0.0695393
$229$	−12.2294	−0.808140	−0.404070	−	0.914728i	$-0.632405\pi$
$229$	−12.2294	−0.808140	−0.404070	+	0.914728i	$0.632405\pi$
$230$	−3.56747	−0.235232
$231$	0.305093	0.0200736
$232$	9.62389	0.631840
$233$	4.36276	0.285814	0.142907	−	0.989736i	$-0.454355\pi$
$233$	4.36276	0.285814	0.142907	+	0.989736i	$0.454355\pi$
$234$	−2.95259	−0.193017
$235$	3.73815	0.243850
$236$	10.8579	0.706791
$237$	−0.178301	−0.0115819
$238$	−1.83317	−0.118827
$239$	9.74993	0.630671	0.315335	−	0.948980i	$-0.397883\pi$
$239$	9.74993	0.630671	0.315335	+	0.948980i	$0.397883\pi$
$240$	−0.217747	−0.0140555
$241$	2.77084	0.178485	0.0892427	−	0.996010i	$-0.471555\pi$
$241$	2.77084	0.178485	0.0892427	+	0.996010i	$0.471555\pi$
$242$	10.6195	0.682644
$243$	5.75576	0.369232
$244$	4.92319	0.315175
$245$	1.84113	0.117626
$246$	−0.413743	−0.0263793
$247$	−4.82221	−0.306830
$248$	1.00000	0.0635001
$249$	−2.98407	−0.189108
$250$	1.00000	0.0632456
$251$	6.99951	0.441805	0.220902	−	0.975296i	$-0.429100\pi$
$251$	6.99951	0.441805	0.220902	+	0.975296i	$0.429100\pi$
$252$	−6.70625	−0.422454
$253$	−2.20071	−0.138358
$254$	−7.62325	−0.478325
$255$	−0.175742	−0.0110054
$256$	1.00000	0.0625000
$257$	−25.7830	−1.60830	−0.804148	−	0.594429i	$-0.797378\pi$
$257$	−25.7830	−1.60830	−0.804148	+	0.594429i	$0.797378\pi$
$258$	1.08385	0.0674775
$259$	16.3246	1.01436
$260$	1.00000	0.0620174
$261$	28.4154	1.75887
$262$	20.0225	1.23699
$263$	9.11720	0.562191	0.281095	−	0.959680i	$-0.409302\pi$
$263$	9.11720	0.562191	0.281095	+	0.959680i	$0.409302\pi$
$264$	−0.134324	−0.00826709
$265$	−0.258285	−0.0158663
$266$	−10.9528	−0.671556
$267$	−1.62597	−0.0995075
$268$	−0.173645	−0.0106071
$269$	−11.9678	−0.729687	−0.364843	−	0.931069i	$-0.618877\pi$
$269$	−11.9678	−0.729687	−0.364843	+	0.931069i	$0.618877\pi$
$270$	−1.29616	−0.0788816
$271$	−8.26870	−0.502287	−0.251144	−	0.967950i	$-0.580807\pi$
$271$	−8.26870	−0.502287	−0.251144	+	0.967950i	$0.580807\pi$
$272$	0.807095	0.0489373
$273$	−0.494571	−0.0299328
$274$	−23.3343	−1.40967
$275$	0.616883	0.0371995
$276$	−0.776805	−0.0467582
$277$	−2.34880	−0.141125	−0.0705627	−	0.997507i	$-0.522479\pi$
$277$	−2.34880	−0.141125	−0.0705627	+	0.997507i	$0.522479\pi$
$278$	15.0857	0.904779
$279$	2.95259	0.176767
$280$	2.27131	0.135737
$281$	−33.1764	−1.97914	−0.989569	−	0.144057i	$-0.953985\pi$
$281$	−33.1764	−1.97914	−0.989569	+	0.144057i	$0.953985\pi$
$282$	0.813970	0.0484712
$283$	2.77662	0.165053	0.0825265	−	0.996589i	$-0.473701\pi$
$283$	2.77662	0.165053	0.0825265	+	0.996589i	$0.473701\pi$
$284$	−7.42422	−0.440546
$285$	−1.05002	−0.0621978
$286$	0.616883	0.0364771
$287$	4.31575	0.254751
$288$	2.95259	0.173983
$289$	−16.3486	−0.961682
$290$	−9.62389	−0.565135
$291$	−1.94986	−0.114303
$292$	−0.318728	−0.0186521
$293$	−16.0276	−0.936342	−0.468171	−	0.883638i	$-0.655087\pi$
$293$	−16.0276	−0.936342	−0.468171	+	0.883638i	$0.655087\pi$
$294$	0.400900	0.0233810
$295$	−10.8579	−0.632173
$296$	−7.18731	−0.417754
$297$	−0.799577	−0.0463962
$298$	6.25487	0.362335
$299$	3.56747	0.206312
$300$	0.217747	0.0125716
$301$	−11.3056	−0.651645
$302$	−2.62675	−0.151152
$303$	−0.996916	−0.0572713
$304$	4.82221	0.276573
$305$	−4.92319	−0.281901
$306$	2.38302	0.136228
$307$	4.68218	0.267226	0.133613	−	0.991034i	$-0.457342\pi$
$307$	4.68218	0.267226	0.133613	+	0.991034i	$0.457342\pi$
$308$	1.40114	0.0798371
$309$	0.689641	0.0392323
$310$	−1.00000	−0.0567962
$311$	−30.6974	−1.74069	−0.870345	−	0.492442i	$-0.836104\pi$
$311$	−30.6974	−1.74069	−0.870345	+	0.492442i	$0.836104\pi$
$312$	0.217747	0.0123275
$313$	−16.0187	−0.905429	−0.452714	−	0.891656i	$-0.649544\pi$
$313$	−16.0187	−0.905429	−0.452714	+	0.891656i	$0.649544\pi$
$314$	−3.79151	−0.213967
$315$	6.70625	0.377854
$316$	−0.818845	−0.0460636
$317$	1.77383	0.0996281	0.0498140	−	0.998759i	$-0.484137\pi$
$317$	1.77383	0.0996281	0.0498140	+	0.998759i	$0.484137\pi$
$318$	−0.0562408	−0.00315383
$319$	−5.93682	−0.332398
$320$	−1.00000	−0.0559017
$321$	−0.777902	−0.0434183
$322$	8.10285	0.451554
$323$	3.89198	0.216556
$324$	8.57553	0.476418
$325$	−1.00000	−0.0554700
$326$	16.7772	0.929205
$327$	−1.07065	−0.0592071
$328$	−1.90011	−0.104916
$329$	−8.49052	−0.468097
$330$	0.134324	0.00739431
$331$	−9.37314	−0.515194	−0.257597	−	0.966252i	$-0.582931\pi$
$331$	−9.37314	−0.515194	−0.257597	+	0.966252i	$0.582931\pi$
$332$	−13.7043	−0.752121
$333$	−21.2211	−1.16291
$334$	5.78515	0.316549
$335$	0.173645	0.00948726
$336$	0.494571	0.0269811
$337$	30.4501	1.65872	0.829361	−	0.558714i	$-0.188705\pi$
$337$	30.4501	1.65872	0.829361	+	0.558714i	$0.188705\pi$
$338$	−1.00000	−0.0543928
$339$	−0.501745	−0.0272510
$340$	−0.807095	−0.0437709
$341$	−0.616883	−0.0334061
$342$	14.2380	0.769902
$343$	−20.0810	−1.08427
$344$	4.97757	0.268372
$345$	0.776805	0.0418218
$346$	−17.9557	−0.965303
$347$	14.7937	0.794170	0.397085	−	0.917782i	$-0.370022\pi$
$347$	14.7937	0.794170	0.397085	+	0.917782i	$0.370022\pi$
$348$	−2.09557	−0.112334
$349$	−7.09326	−0.379694	−0.189847	−	0.981814i	$-0.560799\pi$
$349$	−7.09326	−0.379694	−0.189847	+	0.981814i	$0.560799\pi$
$350$	−2.27131	−0.121407
$351$	1.29616	0.0691837
$352$	−0.616883	−0.0328800
$353$	6.60257	0.351420	0.175710	−	0.984442i	$-0.443778\pi$
$353$	6.60257	0.351420	0.175710	+	0.984442i	$0.443778\pi$
$354$	−2.36428	−0.125660
$355$	7.42422	0.394036
$356$	−7.46724	−0.395763
$357$	0.399166	0.0211261
$358$	9.72955	0.514222
$359$	−29.7487	−1.57008	−0.785039	−	0.619446i	$-0.787357\pi$
$359$	−29.7487	−1.57008	−0.785039	+	0.619446i	$0.787357\pi$
$360$	−2.95259	−0.155615
$361$	4.25370	0.223879
$362$	−8.06159	−0.423708
$363$	−2.31235	−0.121367
$364$	−2.27131	−0.119049
$365$	0.318728	0.0166830
$366$	−1.07201	−0.0560348
$367$	−8.16884	−0.426410	−0.213205	−	0.977007i	$-0.568390\pi$
$367$	−8.16884	−0.426410	−0.213205	+	0.977007i	$0.568390\pi$
$368$	−3.56747	−0.185967
$369$	−5.61024	−0.292058
$370$	7.18731	0.373650
$371$	0.586647	0.0304572
$372$	−0.217747	−0.0112896
$373$	−0.434696	−0.0225077	−0.0112538	−	0.999937i	$-0.503582\pi$
$373$	−0.434696	−0.0225077	−0.0112538	+	0.999937i	$0.503582\pi$
$374$	−0.497884	−0.0257449
$375$	−0.217747	−0.0112444
$376$	3.73815	0.192780
$377$	9.62389	0.495656
$378$	2.94398	0.151422
$379$	15.0865	0.774943	0.387472	−	0.921882i	$-0.373349\pi$
$379$	15.0865	0.774943	0.387472	+	0.921882i	$0.373349\pi$
$380$	−4.82221	−0.247374
$381$	1.65994	0.0850412
$382$	−15.2326	−0.779367
$383$	−28.9851	−1.48107	−0.740534	−	0.672018i	$-0.765428\pi$
$383$	−28.9851	−1.48107	−0.740534	+	0.672018i	$0.765428\pi$
$384$	−0.217747	−0.0111118
$385$	−1.40114	−0.0714085
$386$	−14.9464	−0.760751
$387$	14.6967	0.747075
$388$	−8.95472	−0.454607
$389$	30.6505	1.55404	0.777021	−	0.629475i	$-0.216730\pi$
$389$	30.6505	1.55404	0.777021	+	0.629475i	$0.216730\pi$
$390$	−0.217747	−0.0110260
$391$	−2.87929	−0.145612
$392$	1.84113	0.0929912
$393$	−4.35984	−0.219925
$394$	10.2147	0.514610
$395$	0.818845	0.0412006
$396$	−1.82140	−0.0915288
$397$	13.3863	0.671840	0.335920	−	0.941890i	$-0.390953\pi$
$397$	13.3863	0.671840	0.335920	+	0.941890i	$0.390953\pi$
$398$	−10.2163	−0.512097
$399$	2.38493	0.119396
$400$	1.00000	0.0500000
$401$	−17.4946	−0.873637	−0.436819	−	0.899550i	$-0.643895\pi$
$401$	−17.4946	−0.873637	−0.436819	+	0.899550i	$0.643895\pi$
$402$	0.0378107	0.00188583
$403$	1.00000	0.0498135
$404$	−4.57833	−0.227780
$405$	−8.57553	−0.426121
$406$	21.8589	1.08484
$407$	4.43373	0.219772
$408$	−0.175742	−0.00870055
$409$	−26.8159	−1.32596	−0.662981	−	0.748636i	$-0.730709\pi$
$409$	−26.8159	−1.32596	−0.662981	+	0.748636i	$0.730709\pi$
$410$	1.90011	0.0938398
$411$	5.08096	0.250625
$412$	3.16717	0.156035
$413$	24.6618	1.21353
$414$	−10.5333	−0.517682
$415$	13.7043	0.672718
$416$	1.00000	0.0490290
$417$	−3.28486	−0.160860
$418$	−2.97474	−0.145499
$419$	−2.09786	−0.102487	−0.0512436	−	0.998686i	$-0.516318\pi$
$419$	−2.09786	−0.102487	−0.0512436	+	0.998686i	$0.516318\pi$
$420$	−0.494571	−0.0241326
$421$	−26.6920	−1.30089	−0.650445	−	0.759554i	$-0.725417\pi$
$421$	−26.6920	−1.30089	−0.650445	+	0.759554i	$0.725417\pi$
$422$	26.0863	1.26986
$423$	11.0372	0.536648
$424$	−0.258285	−0.0125434
$425$	0.807095	0.0391499
$426$	1.61660	0.0783245
$427$	11.1821	0.541140
$428$	−3.57251	−0.172684
$429$	−0.134324	−0.00648524
$430$	−4.97757	−0.240040
$431$	−7.29510	−0.351393	−0.175696	−	0.984444i	$-0.556218\pi$
$431$	−7.29510	−0.351393	−0.175696	+	0.984444i	$0.556218\pi$
$432$	−1.29616	−0.0623613
$433$	4.59415	0.220781	0.110390	−	0.993888i	$-0.464790\pi$
$433$	4.59415	0.220781	0.110390	+	0.993888i	$0.464790\pi$
$434$	2.27131	0.109027
$435$	2.09557	0.100475
$436$	−4.91695	−0.235479
$437$	−17.2031	−0.822935
$438$	0.0694019	0.00331615
$439$	16.7417	0.799038	0.399519	−	0.916725i	$-0.369177\pi$
$439$	16.7417	0.799038	0.399519	+	0.916725i	$0.369177\pi$
$440$	0.616883	0.0294087
$441$	5.43610	0.258862
$442$	0.807095	0.0383896
$443$	34.5935	1.64359	0.821794	−	0.569785i	$-0.192973\pi$
$443$	34.5935	1.64359	0.821794	+	0.569785i	$0.192973\pi$
$444$	1.56501	0.0742722
$445$	7.46724	0.353981
$446$	20.9825	0.993550
$447$	−1.36198	−0.0644194
$448$	2.27131	0.107310
$449$	−15.3441	−0.724134	−0.362067	−	0.932152i	$-0.617929\pi$
$449$	−15.3441	−0.724134	−0.362067	+	0.932152i	$0.617929\pi$
$450$	2.95259	0.139186
$451$	1.17215	0.0551942
$452$	−2.30426	−0.108383
$453$	0.571966	0.0268733
$454$	6.80193	0.319230
$455$	2.27131	0.106481
$456$	−1.05002	−0.0491717
$457$	35.1199	1.64284	0.821419	−	0.570326i	$-0.193183\pi$
$457$	35.1199	1.64284	0.821419	+	0.570326i	$0.193183\pi$
$458$	12.2294	0.571442
$459$	−1.04612	−0.0488288
$460$	3.56747	0.166334
$461$	0.963200	0.0448607	0.0224303	−	0.999748i	$-0.492860\pi$
$461$	0.963200	0.0448607	0.0224303	+	0.999748i	$0.492860\pi$
$462$	−0.305093	−0.0141942
$463$	−14.8842	−0.691727	−0.345863	−	0.938285i	$-0.612414\pi$
$463$	−14.8842	−0.691727	−0.345863	+	0.938285i	$0.612414\pi$
$464$	−9.62389	−0.446778
$465$	0.217747	0.0100978
$466$	−4.36276	−0.202101
$467$	−26.4855	−1.22560	−0.612800	−	0.790238i	$-0.709957\pi$
$467$	−26.4855	−1.22560	−0.612800	+	0.790238i	$0.709957\pi$
$468$	2.95259	0.136483
$469$	−0.394403	−0.0182118
$470$	−3.73815	−0.172428
$471$	0.825589	0.0380411
$472$	−10.8579	−0.499776
$473$	−3.07058	−0.141185
$474$	0.178301	0.00818963
$475$	4.82221	0.221258
$476$	1.83317	0.0840231
$477$	−0.762610	−0.0349175
$478$	−9.74993	−0.445951
$479$	4.22844	0.193203	0.0966013	−	0.995323i	$-0.469203\pi$
$479$	4.22844	0.193203	0.0966013	+	0.995323i	$0.469203\pi$
$480$	0.217747	0.00993873
$481$	−7.18731	−0.327713
$482$	−2.77084	−0.126208
$483$	−1.76437	−0.0802815
$484$	−10.6195	−0.482703
$485$	8.95472	0.406613
$486$	−5.75576	−0.261087
$487$	−1.17430	−0.0532124	−0.0266062	−	0.999646i	$-0.508470\pi$
$487$	−1.17430	−0.0532124	−0.0266062	+	0.999646i	$0.508470\pi$
$488$	−4.92319	−0.222862
$489$	−3.65319	−0.165203
$490$	−1.84113	−0.0831739
$491$	−25.3137	−1.14239	−0.571195	−	0.820815i	$-0.693520\pi$
$491$	−25.3137	−1.14239	−0.571195	+	0.820815i	$0.693520\pi$
$492$	0.413743	0.0186530
$493$	−7.76740	−0.349826
$494$	4.82221	0.216961
$495$	1.82140	0.0818659
$496$	−1.00000	−0.0449013
$497$	−16.8627	−0.756397
$498$	2.98407	0.133719
$499$	28.0108	1.25393	0.626967	−	0.779045i	$-0.284296\pi$
$499$	28.0108	1.25393	0.626967	+	0.779045i	$0.284296\pi$
$500$	−1.00000	−0.0447214
$501$	−1.25970	−0.0562791
$502$	−6.99951	−0.312403
$503$	26.6975	1.19038	0.595190	−	0.803585i	$-0.297077\pi$
$503$	26.6975	1.19038	0.595190	+	0.803585i	$0.297077\pi$
$504$	6.70625	0.298720
$505$	4.57833	0.203733
$506$	2.20071	0.0978336
$507$	0.217747	0.00967047
$508$	7.62325	0.338227
$509$	26.9464	1.19438	0.597188	−	0.802101i	$-0.296285\pi$
$509$	26.9464	1.19438	0.597188	+	0.802101i	$0.296285\pi$
$510$	0.175742	0.00778200
$511$	−0.723931	−0.0320248
$512$	−1.00000	−0.0441942
$513$	−6.25034	−0.275959
$514$	25.7830	1.13724
$515$	−3.16717	−0.139562
$516$	−1.08385	−0.0477138
$517$	−2.30600	−0.101418
$518$	−16.3246	−0.717263
$519$	3.90979	0.171621
$520$	−1.00000	−0.0438529
$521$	−21.0898	−0.923963	−0.461981	−	0.886890i	$-0.652861\pi$
$521$	−21.0898	−0.923963	−0.461981	+	0.886890i	$0.652861\pi$
$522$	−28.4154	−1.24371
$523$	3.39631	0.148510	0.0742552	−	0.997239i	$-0.476342\pi$
$523$	3.39631	0.148510	0.0742552	+	0.997239i	$0.476342\pi$
$524$	−20.0225	−0.874687
$525$	0.494571	0.0215849
$526$	−9.11720	−0.397529
$527$	−0.807095	−0.0351576
$528$	0.134324	0.00584571
$529$	−10.2732	−0.446659
$530$	0.258285	0.0112192
$531$	−32.0590	−1.39124
$532$	10.9528	0.474862
$533$	−1.90011	−0.0823030
$534$	1.62597	0.0703625
$535$	3.57251	0.154453
$536$	0.173645	0.00750034
$537$	−2.11858	−0.0914233
$538$	11.9678	0.515966
$539$	−1.13576	−0.0489208
$540$	1.29616	0.0557777
$541$	−28.9690	−1.24548	−0.622738	−	0.782431i	$-0.713980\pi$
$541$	−28.9690	−1.24548	−0.622738	+	0.782431i	$0.713980\pi$
$542$	8.26870	0.355171
$543$	1.75538	0.0753307
$544$	−0.807095	−0.0346039
$545$	4.91695	0.210619
$546$	0.494571	0.0211657
$547$	25.2920	1.08141	0.540704	−	0.841213i	$-0.318158\pi$
$547$	25.2920	1.08141	0.540704	+	0.841213i	$0.318158\pi$
$548$	23.3343	0.996790
$549$	−14.5361	−0.620387
$550$	−0.616883	−0.0263040
$551$	−46.4084	−1.97707
$552$	0.776805	0.0330630
$553$	−1.85985	−0.0790891
$554$	2.34880	0.0997908
$555$	−1.56501	−0.0664311
$556$	−15.0857	−0.639775
$557$	20.1245	0.852701	0.426351	−	0.904558i	$-0.359799\pi$
$557$	20.1245	0.852701	0.426351	+	0.904558i	$0.359799\pi$
$558$	−2.95259	−0.124993
$559$	4.97757	0.210529
$560$	−2.27131	−0.0959805
$561$	0.108413	0.00457718
$562$	33.1764	1.39946
$563$	−7.13044	−0.300512	−0.150256	−	0.988647i	$-0.548010\pi$
$563$	−7.13044	−0.300512	−0.150256	+	0.988647i	$0.548010\pi$
$564$	−0.813970	−0.0342743
$565$	2.30426	0.0969409
$566$	−2.77662	−0.116710
$567$	19.4777	0.817987
$568$	7.42422	0.311513
$569$	7.33193	0.307370	0.153685	−	0.988120i	$-0.450886\pi$
$569$	7.33193	0.307370	0.153685	+	0.988120i	$0.450886\pi$
$570$	1.05002	0.0439805
$571$	1.74616	0.0730747	0.0365373	−	0.999332i	$-0.488367\pi$
$571$	1.74616	0.0730747	0.0365373	+	0.999332i	$0.488367\pi$
$572$	−0.616883	−0.0257932
$573$	3.31685	0.138563
$574$	−4.31575	−0.180136
$575$	−3.56747	−0.148774
$576$	−2.95259	−0.123024
$577$	35.7732	1.48926	0.744630	−	0.667478i	$-0.232626\pi$
$577$	35.7732	1.48926	0.744630	+	0.667478i	$0.232626\pi$
$578$	16.3486	0.680012
$579$	3.25453	0.135254
$580$	9.62389	0.399610
$581$	−31.1268	−1.29136
$582$	1.94986	0.0808244
$583$	0.159332	0.00659885
$584$	0.318728	0.0131891
$585$	−2.95259	−0.122074
$586$	16.0276	0.662094
$587$	18.8215	0.776846	0.388423	−	0.921481i	$-0.373020\pi$
$587$	18.8215	0.776846	0.388423	+	0.921481i	$0.373020\pi$
$588$	−0.400900	−0.0165329
$589$	−4.82221	−0.198696
$590$	10.8579	0.447014
$591$	−2.22422	−0.0914922
$592$	7.18731	0.295397
$593$	−16.2712	−0.668179	−0.334090	−	0.942541i	$-0.608429\pi$
$593$	−16.2712	−0.668179	−0.334090	+	0.942541i	$0.608429\pi$
$594$	0.799577	0.0328070
$595$	−1.83317	−0.0751525
$596$	−6.25487	−0.256210
$597$	2.22457	0.0910455
$598$	−3.56747	−0.145885
$599$	−11.1623	−0.456077	−0.228039	−	0.973652i	$-0.573231\pi$
$599$	−11.1623	−0.456077	−0.228039	+	0.973652i	$0.573231\pi$
$600$	−0.217747	−0.00888947
$601$	−27.9095	−1.13845	−0.569226	−	0.822181i	$-0.692757\pi$
$601$	−27.9095	−1.13845	−0.569226	+	0.822181i	$0.692757\pi$
$602$	11.3056	0.460782
$603$	0.512703	0.0208789
$604$	2.62675	0.106881
$605$	10.6195	0.431742
$606$	0.996916	0.0404969
$607$	14.9970	0.608711	0.304355	−	0.952559i	$-0.401559\pi$
$607$	14.9970	0.608711	0.304355	+	0.952559i	$0.401559\pi$
$608$	−4.82221	−0.195566
$609$	−4.75970	−0.192873
$610$	4.92319	0.199334
$611$	3.73815	0.151229
$612$	−2.38302	−0.0963278
$613$	9.54902	0.385681	0.192841	−	0.981230i	$-0.438230\pi$
$613$	9.54902	0.385681	0.192841	+	0.981230i	$0.438230\pi$
$614$	−4.68218	−0.188957
$615$	−0.413743	−0.0166837
$616$	−1.40114	−0.0564534
$617$	−20.0040	−0.805330	−0.402665	−	0.915347i	$-0.631916\pi$
$617$	−20.0040	−0.805330	−0.402665	+	0.915347i	$0.631916\pi$
$618$	−0.689641	−0.0277414
$619$	−14.3035	−0.574906	−0.287453	−	0.957795i	$-0.592808\pi$
$619$	−14.3035	−0.574906	−0.287453	+	0.957795i	$0.592808\pi$
$620$	1.00000	0.0401610
$621$	4.62400	0.185555
$622$	30.6974	1.23085
$623$	−16.9604	−0.679506
$624$	−0.217747	−0.00871685
$625$	1.00000	0.0400000
$626$	16.0187	0.640235
$627$	0.647740	0.0258682
$628$	3.79151	0.151298
$629$	5.80084	0.231295
$630$	−6.70625	−0.267183
$631$	28.2572	1.12490	0.562450	−	0.826831i	$-0.309859\pi$
$631$	28.2572	1.12490	0.562450	+	0.826831i	$0.309859\pi$
$632$	0.818845	0.0325719
$633$	−5.68021	−0.225768
$634$	−1.77383	−0.0704477
$635$	−7.62325	−0.302520
$636$	0.0562408	0.00223009
$637$	1.84113	0.0729483
$638$	5.93682	0.235041
$639$	21.9206	0.867167
$640$	1.00000	0.0395285
$641$	−21.4620	−0.847699	−0.423850	−	0.905733i	$-0.639321\pi$
$641$	−21.4620	−0.847699	−0.423850	+	0.905733i	$0.639321\pi$
$642$	0.777902	0.0307014
$643$	36.4080	1.43579	0.717896	−	0.696150i	$-0.245105\pi$
$643$	36.4080	1.43579	0.717896	+	0.696150i	$0.245105\pi$
$644$	−8.10285	−0.319297
$645$	1.08385	0.0426765
$646$	−3.89198	−0.153128
$647$	20.0012	0.786328	0.393164	−	0.919468i	$-0.371380\pi$
$647$	20.0012	0.786328	0.393164	+	0.919468i	$0.371380\pi$
$648$	−8.57553	−0.336878
$649$	6.69807	0.262922
$650$	1.00000	0.0392232
$651$	−0.494571	−0.0193838
$652$	−16.7772	−0.657047
$653$	−26.1070	−1.02164	−0.510822	−	0.859686i	$-0.670659\pi$
$653$	−26.1070	−1.02164	−0.510822	+	0.859686i	$0.670659\pi$
$654$	1.07065	0.0418657
$655$	20.0225	0.782344
$656$	1.90011	0.0741869
$657$	0.941071	0.0367147
$658$	8.49052	0.330995
$659$	−20.2430	−0.788556	−0.394278	−	0.918991i	$-0.629005\pi$
$659$	−20.2430	−0.788556	−0.394278	+	0.918991i	$0.629005\pi$
$660$	−0.134324	−0.00522857
$661$	−40.1221	−1.56057	−0.780285	−	0.625424i	$-0.784926\pi$
$661$	−40.1221	−1.56057	−0.780285	+	0.625424i	$0.784926\pi$
$662$	9.37314	0.364297
$663$	−0.175742	−0.00682527
$664$	13.7043	0.531830
$665$	−10.9528	−0.424729
$666$	21.2211	0.822303
$667$	34.3330	1.32938
$668$	−5.78515	−0.223834
$669$	−4.56887	−0.176643
$670$	−0.173645	−0.00670851
$671$	3.03703	0.117243
$672$	−0.494571	−0.0190785
$673$	0.280391	0.0108083	0.00540415	−	0.999985i	$-0.498280\pi$
$673$	0.280391	0.0108083	0.00540415	+	0.999985i	$0.498280\pi$
$674$	−30.4501	−1.17289
$675$	−1.29616	−0.0498891
$676$	1.00000	0.0384615
$677$	−25.7464	−0.989515	−0.494757	−	0.869031i	$-0.664743\pi$
$677$	−25.7464	−0.989515	−0.494757	+	0.869031i	$0.664743\pi$
$678$	0.501745	0.0192694
$679$	−20.3390	−0.780539
$680$	0.807095	0.0309507
$681$	−1.48110	−0.0567558
$682$	0.616883	0.0236217
$683$	−27.5293	−1.05338	−0.526690	−	0.850057i	$-0.676567\pi$
$683$	−27.5293	−1.05338	−0.526690	+	0.850057i	$0.676567\pi$
$684$	−14.2380	−0.544403
$685$	−23.3343	−0.891556
$686$	20.0810	0.766696
$687$	−2.66291	−0.101596
$688$	−4.97757	−0.189768
$689$	−0.258285	−0.00983989
$690$	−0.776805	−0.0295725
$691$	−5.93006	−0.225590	−0.112795	−	0.993618i	$-0.535980\pi$
$691$	−5.93006	−0.225590	−0.112795	+	0.993618i	$0.535980\pi$
$692$	17.9557	0.682572
$693$	−4.13697	−0.157151
$694$	−14.7937	−0.561563
$695$	15.0857	0.572233
$696$	2.09557	0.0794324
$697$	1.53357	0.0580882
$698$	7.09326	0.268484
$699$	0.949977	0.0359314
$700$	2.27131	0.0858476
$701$	18.1122	0.684089	0.342045	−	0.939684i	$-0.388881\pi$
$701$	18.1122	0.684089	0.342045	+	0.939684i	$0.388881\pi$
$702$	−1.29616	−0.0489203
$703$	34.6587	1.30718
$704$	0.616883	0.0232497
$705$	0.813970	0.0306559
$706$	−6.60257	−0.248491
$707$	−10.3988	−0.391088
$708$	2.36428	0.0888550
$709$	20.4818	0.769212	0.384606	−	0.923081i	$-0.374337\pi$
$709$	20.4818	0.769212	0.384606	+	0.923081i	$0.374337\pi$
$710$	−7.42422	−0.278626
$711$	2.41771	0.0906713
$712$	7.46724	0.279847
$713$	3.56747	0.133603
$714$	−0.399166	−0.0149384
$715$	0.616883	0.0230701
$716$	−9.72955	−0.363610
$717$	2.12302	0.0792855
$718$	29.7487	1.11021
$719$	−0.726758	−0.0271035	−0.0135517	−	0.999908i	$-0.504314\pi$
$719$	−0.726758	−0.0271035	−0.0135517	+	0.999908i	$0.504314\pi$
$720$	2.95259	0.110036
$721$	7.19364	0.267905
$722$	−4.25370	−0.158306
$723$	0.603341	0.0224385
$724$	8.06159	0.299606
$725$	−9.62389	−0.357422
$726$	2.31235	0.0858194
$727$	−32.2624	−1.19655	−0.598273	−	0.801292i	$-0.704146\pi$
$727$	−32.2624	−1.19655	−0.598273	+	0.801292i	$0.704146\pi$
$728$	2.27131	0.0841805
$729$	−24.4733	−0.906418
$730$	−0.318728	−0.0117966
$731$	−4.01737	−0.148588
$732$	1.07201	0.0396226
$733$	−34.2316	−1.26437	−0.632186	−	0.774816i	$-0.717842\pi$
$733$	−34.2316	−1.26437	−0.632186	+	0.774816i	$0.717842\pi$
$734$	8.16884	0.301517
$735$	0.400900	0.0147874
$736$	3.56747	0.131499
$737$	−0.107119	−0.00394578
$738$	5.61024	0.206516
$739$	−28.5468	−1.05011	−0.525056	−	0.851068i	$-0.675956\pi$
$739$	−28.5468	−1.05011	−0.525056	+	0.851068i	$0.675956\pi$
$740$	−7.18731	−0.264211
$741$	−1.05002	−0.0385735
$742$	−0.586647	−0.0215365
$743$	8.84982	0.324668	0.162334	−	0.986736i	$-0.448098\pi$
$743$	8.84982	0.324668	0.162334	+	0.986736i	$0.448098\pi$
$744$	0.217747	0.00798298
$745$	6.25487	0.229161
$746$	0.434696	0.0159153
$747$	40.4631	1.48047
$748$	0.497884	0.0182044
$749$	−8.11429	−0.296490
$750$	0.217747	0.00795099
$751$	51.9618	1.89611	0.948056	−	0.318105i	$-0.103046\pi$
$751$	51.9618	1.89611	0.948056	+	0.318105i	$0.103046\pi$
$752$	−3.73815	−0.136316
$753$	1.52412	0.0555420
$754$	−9.62389	−0.350482
$755$	−2.62675	−0.0955972
$756$	−2.94398	−0.107071
$757$	26.9711	0.980281	0.490140	−	0.871643i	$-0.336945\pi$
$757$	26.9711	0.980281	0.490140	+	0.871643i	$0.336945\pi$
$758$	−15.0865	−0.547968
$759$	−0.479198	−0.0173938
$760$	4.82221	0.174920
$761$	0.655355	0.0237566	0.0118783	−	0.999929i	$-0.496219\pi$
$761$	0.655355	0.0237566	0.0118783	+	0.999929i	$0.496219\pi$
$762$	−1.65994	−0.0601332
$763$	−11.1679	−0.404307
$764$	15.2326	0.551096
$765$	2.38302	0.0861582
$766$	28.9851	1.04727
$767$	−10.8579	−0.392057
$768$	0.217747	0.00785726
$769$	30.9327	1.11546	0.557730	−	0.830022i	$-0.311672\pi$
$769$	30.9327	1.11546	0.557730	+	0.830022i	$0.311672\pi$
$770$	1.40114	0.0504934
$771$	−5.61415	−0.202189
$772$	14.9464	0.537933
$773$	−10.1363	−0.364577	−0.182288	−	0.983245i	$-0.558350\pi$
$773$	−10.1363	−0.364577	−0.182288	+	0.983245i	$0.558350\pi$
$774$	−14.6967	−0.528262
$775$	−1.00000	−0.0359211
$776$	8.95472	0.321456
$777$	3.55464	0.127522
$778$	−30.6505	−1.09887
$779$	9.16274	0.328289
$780$	0.217747	0.00779658
$781$	−4.57987	−0.163881
$782$	2.87929	0.102963
$783$	12.4741	0.445787
$784$	−1.84113	−0.0657547
$785$	−3.79151	−0.135325
$786$	4.35984	0.155510
$787$	26.8360	0.956601	0.478300	−	0.878196i	$-0.341253\pi$
$787$	26.8360	0.956601	0.478300	+	0.878196i	$0.341253\pi$
$788$	−10.2147	−0.363884
$789$	1.98524	0.0706764
$790$	−0.818845	−0.0291332
$791$	−5.23369	−0.186089
$792$	1.82140	0.0647207
$793$	−4.92319	−0.174828
$794$	−13.3863	−0.475063
$795$	−0.0562408	−0.00199466
$796$	10.2163	0.362107
$797$	24.8474	0.880140	0.440070	−	0.897964i	$-0.354954\pi$
$797$	24.8474	0.880140	0.440070	+	0.897964i	$0.354954\pi$
$798$	−2.38493	−0.0844255
$799$	−3.01705	−0.106735
$800$	−1.00000	−0.0353553
$801$	22.0477	0.779016
$802$	17.4946	0.617755
$803$	−0.196618	−0.00693849
$804$	−0.0378107	−0.00133348
$805$	8.10285	0.285588
$806$	−1.00000	−0.0352235
$807$	−2.60594	−0.0917334
$808$	4.57833	0.161065
$809$	16.8770	0.593364	0.296682	−	0.954976i	$-0.404120\pi$
$809$	16.8770	0.593364	0.296682	+	0.954976i	$0.404120\pi$
$810$	8.57553	0.301313
$811$	30.6868	1.07756	0.538780	−	0.842446i	$-0.318885\pi$
$811$	30.6868	1.07756	0.538780	+	0.842446i	$0.318885\pi$
$812$	−21.8589	−0.767097
$813$	−1.80048	−0.0631456
$814$	−4.43373	−0.155402
$815$	16.7772	0.587681
$816$	0.175742	0.00615221
$817$	−24.0029	−0.839754
$818$	26.8159	0.937597
$819$	6.70625	0.234335
$820$	−1.90011	−0.0663548
$821$	52.7478	1.84091	0.920456	−	0.390846i	$-0.127817\pi$
$821$	52.7478	1.84091	0.920456	+	0.390846i	$0.127817\pi$
$822$	−5.08096	−0.177219
$823$	−37.8896	−1.32075	−0.660375	−	0.750936i	$-0.729603\pi$
$823$	−37.8896	−1.32075	−0.660375	+	0.750936i	$0.729603\pi$
$824$	−3.16717	−0.110334
$825$	0.134324	0.00467657
$826$	−24.6618	−0.858092
$827$	56.6408	1.96959	0.984796	−	0.173713i	$-0.0555764\pi$
$827$	56.6408	1.96959	0.984796	+	0.173713i	$0.0555764\pi$
$828$	10.5333	0.366056
$829$	7.70117	0.267473	0.133736	−	0.991017i	$-0.457302\pi$
$829$	7.70117	0.267473	0.133736	+	0.991017i	$0.457302\pi$
$830$	−13.7043	−0.475683
$831$	−0.511443	−0.0177417
$832$	−1.00000	−0.0346688
$833$	−1.48597	−0.0514858
$834$	3.28486	0.113745
$835$	5.78515	0.200203
$836$	2.97474	0.102884
$837$	1.29616	0.0448017
$838$	2.09786	0.0724694
$839$	29.9906	1.03539	0.517695	−	0.855565i	$-0.326790\pi$
$839$	29.9906	1.03539	0.517695	+	0.855565i	$0.326790\pi$
$840$	0.494571	0.0170643
$841$	63.6194	2.19377
$842$	26.6920	0.919868
$843$	−7.22406	−0.248810
$844$	−26.0863	−0.897928
$845$	−1.00000	−0.0344010
$846$	−11.0372	−0.379467
$847$	−24.1201	−0.828777
$848$	0.258285	0.00886956
$849$	0.604601	0.0207498
$850$	−0.807095	−0.0276831
$851$	−25.6405	−0.878945
$852$	−1.61660	−0.0553838
$853$	14.3004	0.489635	0.244818	−	0.969569i	$-0.421272\pi$
$853$	14.3004	0.489635	0.244818	+	0.969569i	$0.421272\pi$
$854$	−11.1821	−0.382644
$855$	14.2380	0.486929
$856$	3.57251	0.122106
$857$	−11.1442	−0.380678	−0.190339	−	0.981718i	$-0.560959\pi$
$857$	−11.1442	−0.380678	−0.190339	+	0.981718i	$0.560959\pi$
$858$	0.134324	0.00458576
$859$	−14.5869	−0.497700	−0.248850	−	0.968542i	$-0.580053\pi$
$859$	−14.5869	−0.497700	−0.248850	+	0.968542i	$0.580053\pi$
$860$	4.97757	0.169734
$861$	0.939741	0.0320263
$862$	7.29510	0.248472
$863$	−8.06764	−0.274626	−0.137313	−	0.990528i	$-0.543847\pi$
$863$	−8.06764	−0.274626	−0.137313	+	0.990528i	$0.543847\pi$
$864$	1.29616	0.0440961
$865$	−17.9557	−0.610511
$866$	−4.59415	−0.156116
$867$	−3.55985	−0.120899
$868$	−2.27131	−0.0770934
$869$	−0.505132	−0.0171354
$870$	−2.09557	−0.0710465
$871$	0.173645	0.00588375
$872$	4.91695	0.166509
$873$	26.4396	0.894845
$874$	17.2031	0.581903
$875$	−2.27131	−0.0767844
$876$	−0.0694019	−0.00234487
$877$	41.7487	1.40975	0.704876	−	0.709330i	$-0.251003\pi$
$877$	41.7487	1.40975	0.704876	+	0.709330i	$0.251003\pi$
$878$	−16.7417	−0.565005
$879$	−3.48996	−0.117713
$880$	−0.616883	−0.0207951
$881$	51.0292	1.71922	0.859609	−	0.510953i	$-0.170707\pi$
$881$	51.0292	1.71922	0.859609	+	0.510953i	$0.170707\pi$
$882$	−5.43610	−0.183043
$883$	40.1933	1.35261	0.676306	−	0.736621i	$-0.263580\pi$
$883$	40.1933	1.35261	0.676306	+	0.736621i	$0.263580\pi$
$884$	−0.807095	−0.0271456
$885$	−2.36428	−0.0794743
$886$	−34.5935	−1.16219
$887$	48.2660	1.62061	0.810307	−	0.586006i	$-0.199300\pi$
$887$	48.2660	1.62061	0.810307	+	0.586006i	$0.199300\pi$
$888$	−1.56501	−0.0525184
$889$	17.3148	0.580720
$890$	−7.46724	−0.250302
$891$	5.29010	0.177225
$892$	−20.9825	−0.702546
$893$	−18.0261	−0.603222
$894$	1.36198	0.0455514
$895$	9.72955	0.325223
$896$	−2.27131	−0.0758793
$897$	0.776805	0.0259368
$898$	15.3441	0.512040
$899$	9.62389	0.320975
$900$	−2.95259	−0.0984195
$901$	0.208461	0.00694484
$902$	−1.17215	−0.0390282
$903$	−2.46176	−0.0819223
$904$	2.30426	0.0766385
$905$	−8.06159	−0.267976
$906$	−0.571966	−0.0190023
$907$	41.9915	1.39430	0.697152	−	0.716923i	$-0.254450\pi$
$907$	41.9915	1.39430	0.697152	+	0.716923i	$0.254450\pi$
$908$	−6.80193	−0.225730
$909$	13.5179	0.448361
$910$	−2.27131	−0.0752933
$911$	−37.3230	−1.23657	−0.618283	−	0.785955i	$-0.712172\pi$
$911$	−37.3230	−1.23657	−0.618283	+	0.785955i	$0.712172\pi$
$912$	1.05002	0.0347696
$913$	−8.45395	−0.279785
$914$	−35.1199	−1.16166
$915$	−1.07201	−0.0354395
$916$	−12.2294	−0.404070
$917$	−45.4774	−1.50180
$918$	1.04612	0.0345272
$919$	11.2599	0.371430	0.185715	−	0.982604i	$-0.440540\pi$
$919$	11.2599	0.371430	0.185715	+	0.982604i	$0.440540\pi$
$920$	−3.56747	−0.117616
$921$	1.01953	0.0335946
$922$	−0.963200	−0.0317213
$923$	7.42422	0.244371
$924$	0.305093	0.0100368
$925$	7.18731	0.236317
$926$	14.8842	0.489125
$927$	−9.35134	−0.307138
$928$	9.62389	0.315920
$929$	−59.7572	−1.96057	−0.980286	−	0.197586i	$-0.936690\pi$
$929$	−59.7572	−1.96057	−0.980286	+	0.197586i	$0.936690\pi$
$930$	−0.217747	−0.00714020
$931$	−8.87832	−0.290975
$932$	4.36276	0.142907
$933$	−6.68426	−0.218833
$934$	26.4855	0.866631
$935$	−0.497884	−0.0162825
$936$	−2.95259	−0.0965083
$937$	28.4447	0.929247	0.464623	−	0.885508i	$-0.346190\pi$
$937$	28.4447	0.929247	0.464623	+	0.885508i	$0.346190\pi$
$938$	0.394403	0.0128777
$939$	−3.48801	−0.113827
$940$	3.73815	0.121925
$941$	50.2401	1.63778	0.818890	−	0.573951i	$-0.194590\pi$
$941$	50.2401	1.63778	0.818890	+	0.573951i	$0.194590\pi$
$942$	−0.825589	−0.0268992
$943$	−6.77859	−0.220741
$944$	10.8579	0.353395
$945$	2.94398	0.0957676
$946$	3.07058	0.0998330
$947$	28.3474	0.921168	0.460584	−	0.887616i	$-0.347640\pi$
$947$	28.3474	0.921168	0.460584	+	0.887616i	$0.347640\pi$
$948$	−0.178301	−0.00579094
$949$	0.318728	0.0103463
$950$	−4.82221	−0.156453
$951$	0.386245	0.0125249
$952$	−1.83317	−0.0594133
$953$	−11.8602	−0.384190	−0.192095	−	0.981376i	$-0.561528\pi$
$953$	−11.8602	−0.384190	−0.192095	+	0.981376i	$0.561528\pi$
$954$	0.762610	0.0246904
$955$	−15.2326	−0.492915
$956$	9.74993	0.315335
$957$	−1.29272	−0.0417878
$958$	−4.22844	−0.136615
$959$	52.9994	1.71144
$960$	−0.217747	−0.00702775
$961$	1.00000	0.0322581
$962$	7.18731	0.231728
$963$	10.5481	0.339909
$964$	2.77084	0.0892427
$965$	−14.9464	−0.481141
$966$	1.76437	0.0567676
$967$	−8.00303	−0.257360	−0.128680	−	0.991686i	$-0.541074\pi$
$967$	−8.00303	−0.257360	−0.128680	+	0.991686i	$0.541074\pi$
$968$	10.6195	0.341322
$969$	0.847467	0.0272245
$970$	−8.95472	−0.287519
$971$	31.9454	1.02518	0.512588	−	0.858635i	$-0.328687\pi$
$971$	31.9454	1.02518	0.512588	+	0.858635i	$0.328687\pi$
$972$	5.75576	0.184616
$973$	−34.2643	−1.09846
$974$	1.17430	0.0376268
$975$	−0.217747	−0.00697348
$976$	4.92319	0.157587
$977$	−18.7800	−0.600825	−0.300412	−	0.953809i	$-0.597124\pi$
$977$	−18.7800	−0.600825	−0.300412	+	0.953809i	$0.597124\pi$
$978$	3.65319	0.116816
$979$	−4.60641	−0.147222
$980$	1.84113	0.0588128
$981$	14.5177	0.463515
$982$	25.3137	0.807791
$983$	−6.93601	−0.221224	−0.110612	−	0.993864i	$-0.535281\pi$
$983$	−6.93601	−0.221224	−0.110612	+	0.993864i	$0.535281\pi$
$984$	−0.413743	−0.0131896
$985$	10.2147	0.325468
$986$	7.76740	0.247364
$987$	−1.84878	−0.0588474
$988$	−4.82221	−0.153415
$989$	17.7573	0.564650
$990$	−1.82140	−0.0578879
$991$	9.84775	0.312824	0.156412	−	0.987692i	$-0.450007\pi$
$991$	9.84775	0.312824	0.156412	+	0.987692i	$0.450007\pi$
$992$	1.00000	0.0317500
$993$	−2.04097	−0.0647682
$994$	16.8627	0.534853
$995$	−10.2163	−0.323879
$996$	−2.98407	−0.0945538
$997$	−29.5378	−0.935472	−0.467736	−	0.883868i	$-0.654930\pi$
$997$	−29.5378	−0.935472	−0.467736	+	0.883868i	$0.654930\pi$
$998$	−28.0108	−0.886666
$999$	−9.31588	−0.294741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.i.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.i.1.4	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.217747 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217747 q^{6} +2.27131 q^{7} -1.00000 q^{8} -2.95259 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.217747 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217747 q^{6} +2.27131 q^{7} -1.00000 q^{8} -2.95259 q^{9} +1.00000 q^{10} +0.616883 q^{11} +0.217747 q^{12} -1.00000 q^{13} -2.27131 q^{14} -0.217747 q^{15} +1.00000 q^{16} +0.807095 q^{17} +2.95259 q^{18} +4.82221 q^{19} -1.00000 q^{20} +0.494571 q^{21} -0.616883 q^{22} -3.56747 q^{23} -0.217747 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.29616 q^{27} +2.27131 q^{28} -9.62389 q^{29} +0.217747 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.134324 q^{33} -0.807095 q^{34} -2.27131 q^{35} -2.95259 q^{36} +7.18731 q^{37} -4.82221 q^{38} -0.217747 q^{39} +1.00000 q^{40} +1.90011 q^{41} -0.494571 q^{42} -4.97757 q^{43} +0.616883 q^{44} +2.95259 q^{45} +3.56747 q^{46} -3.73815 q^{47} +0.217747 q^{48} -1.84113 q^{49} -1.00000 q^{50} +0.175742 q^{51} -1.00000 q^{52} +0.258285 q^{53} +1.29616 q^{54} -0.616883 q^{55} -2.27131 q^{56} +1.05002 q^{57} +9.62389 q^{58} +10.8579 q^{59} -0.217747 q^{60} +4.92319 q^{61} +1.00000 q^{62} -6.70625 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.134324 q^{66} -0.173645 q^{67} +0.807095 q^{68} -0.776805 q^{69} +2.27131 q^{70} -7.42422 q^{71} +2.95259 q^{72} -0.318728 q^{73} -7.18731 q^{74} +0.217747 q^{75} +4.82221 q^{76} +1.40114 q^{77} +0.217747 q^{78} -0.818845 q^{79} -1.00000 q^{80} +8.57553 q^{81} -1.90011 q^{82} -13.7043 q^{83} +0.494571 q^{84} -0.807095 q^{85} +4.97757 q^{86} -2.09557 q^{87} -0.616883 q^{88} -7.46724 q^{89} -2.95259 q^{90} -2.27131 q^{91} -3.56747 q^{92} -0.217747 q^{93} +3.73815 q^{94} -4.82221 q^{95} -0.217747 q^{96} -8.95472 q^{97} +1.84113 q^{98} -1.82140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * q^99

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