LMFDB - Embedded newform 177.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.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:	$10.4433380710$
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} - x^{6} - 34x^{5} + 25x^{4} + 315x^{3} - 146x^{2} - 736x + 512 $ x^7 - x^6 - 34x^5 + 25x^4 + 315x^3 - 146x^2 - 736*x + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.60512$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.60512 q^{2} +3.00000 q^{3} +23.4174 q^{4} +12.9748 q^{5} -16.8154 q^{6} -18.2988 q^{7} -86.4162 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.60512 q^{2} +3.00000 q^{3} +23.4174 q^{4} +12.9748 q^{5} -16.8154 q^{6} -18.2988 q^{7} -86.4162 q^{8} +9.00000 q^{9} -72.7251 q^{10} -71.8350 q^{11} +70.2521 q^{12} +31.4840 q^{13} +102.567 q^{14} +38.9243 q^{15} +297.034 q^{16} -94.8120 q^{17} -50.4461 q^{18} -53.7002 q^{19} +303.835 q^{20} -54.8965 q^{21} +402.644 q^{22} -70.2521 q^{23} -259.249 q^{24} +43.3445 q^{25} -176.472 q^{26} +27.0000 q^{27} -428.510 q^{28} +20.2046 q^{29} -218.175 q^{30} -5.95239 q^{31} -973.582 q^{32} -215.505 q^{33} +531.432 q^{34} -237.423 q^{35} +210.756 q^{36} +167.214 q^{37} +300.996 q^{38} +94.4520 q^{39} -1121.23 q^{40} +248.975 q^{41} +307.701 q^{42} -472.012 q^{43} -1682.19 q^{44} +116.773 q^{45} +393.771 q^{46} -140.560 q^{47} +891.102 q^{48} -8.15281 q^{49} -242.951 q^{50} -284.436 q^{51} +737.272 q^{52} -21.3540 q^{53} -151.338 q^{54} -932.042 q^{55} +1581.32 q^{56} -161.100 q^{57} -113.249 q^{58} -59.0000 q^{59} +911.504 q^{60} +375.516 q^{61} +33.3639 q^{62} -164.689 q^{63} +3080.77 q^{64} +408.497 q^{65} +1207.93 q^{66} -410.115 q^{67} -2220.25 q^{68} -210.756 q^{69} +1330.78 q^{70} +420.452 q^{71} -777.746 q^{72} -865.694 q^{73} -937.256 q^{74} +130.033 q^{75} -1257.52 q^{76} +1314.50 q^{77} -529.415 q^{78} -53.7139 q^{79} +3853.95 q^{80} +81.0000 q^{81} -1395.54 q^{82} +39.4923 q^{83} -1285.53 q^{84} -1230.16 q^{85} +2645.68 q^{86} +60.6137 q^{87} +6207.70 q^{88} -354.864 q^{89} -654.526 q^{90} -576.120 q^{91} -1645.12 q^{92} -17.8572 q^{93} +787.856 q^{94} -696.747 q^{95} -2920.75 q^{96} -1419.08 q^{97} +45.6975 q^{98} -646.515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 8 q^{2} + 21 q^{3} + 22 q^{4} - 28 q^{5} - 24 q^{6} - 59 q^{7} - 117 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 8 * q^2 + 21 * q^3 + 22 * q^4 - 28 * q^5 - 24 * q^6 - 59 * q^7 - 117 * q^8 + 63 * q^9	\( 7 q - 8 q^{2} + 21 q^{3} + 22 q^{4} - 28 q^{5} - 24 q^{6} - 59 q^{7} - 117 q^{8} + 63 q^{9} - 79 q^{10} - 131 q^{11} + 66 q^{12} - 123 q^{13} - 117 q^{14} - 84 q^{15} + 202 q^{16} - 235 q^{17} - 72 q^{18} - 80 q^{19} + 61 q^{20} - 177 q^{21} + 688 q^{22} - 274 q^{23} - 351 q^{24} + 193 q^{25} - 180 q^{26} + 189 q^{27} - 118 q^{28} - 406 q^{29} - 237 q^{30} - 346 q^{31} - 854 q^{32} - 393 q^{33} + 178 q^{34} - 424 q^{35} + 198 q^{36} - 157 q^{37} - 129 q^{38} - 369 q^{39} - 590 q^{40} - 825 q^{41} - 351 q^{42} - 815 q^{43} - 1690 q^{44} - 252 q^{45} + 1457 q^{46} - 1196 q^{47} + 606 q^{48} + 914 q^{49} + 713 q^{50} - 705 q^{51} + 1030 q^{52} - 900 q^{53} - 216 q^{54} - 1044 q^{55} + 2172 q^{56} - 240 q^{57} + 1242 q^{58} - 413 q^{59} + 183 q^{60} + 420 q^{61} + 646 q^{62} - 531 q^{63} + 3541 q^{64} + 190 q^{65} + 2064 q^{66} + 1316 q^{67} - 611 q^{68} - 822 q^{69} + 4658 q^{70} - 173 q^{71} - 1053 q^{72} - 418 q^{73} + 660 q^{74} + 579 q^{75} + 1540 q^{76} - 753 q^{77} - 540 q^{78} + 2635 q^{79} + 6155 q^{80} + 567 q^{81} - 125 q^{82} + 457 q^{83} - 354 q^{84} + 1270 q^{85} + 3482 q^{86} - 1218 q^{87} + 7685 q^{88} + 592 q^{89} - 711 q^{90} + 3179 q^{91} - 3500 q^{92} - 1038 q^{93} + 2064 q^{94} - 2250 q^{95} - 2562 q^{96} - 1906 q^{97} + 2994 q^{98} - 1179 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 + 21 * q^3 + 22 * q^4 - 28 * q^5 - 24 * q^6 - 59 * q^7 - 117 * q^8 + 63 * q^9 - 79 * q^10 - 131 * q^11 + 66 * q^12 - 123 * q^13 - 117 * q^14 - 84 * q^15 + 202 * q^16 - 235 * q^17 - 72 * q^18 - 80 * q^19 + 61 * q^20 - 177 * q^21 + 688 * q^22 - 274 * q^23 - 351 * q^24 + 193 * q^25 - 180 * q^26 + 189 * q^27 - 118 * q^28 - 406 * q^29 - 237 * q^30 - 346 * q^31 - 854 * q^32 - 393 * q^33 + 178 * q^34 - 424 * q^35 + 198 * q^36 - 157 * q^37 - 129 * q^38 - 369 * q^39 - 590 * q^40 - 825 * q^41 - 351 * q^42 - 815 * q^43 - 1690 * q^44 - 252 * q^45 + 1457 * q^46 - 1196 * q^47 + 606 * q^48 + 914 * q^49 + 713 * q^50 - 705 * q^51 + 1030 * q^52 - 900 * q^53 - 216 * q^54 - 1044 * q^55 + 2172 * q^56 - 240 * q^57 + 1242 * q^58 - 413 * q^59 + 183 * q^60 + 420 * q^61 + 646 * q^62 - 531 * q^63 + 3541 * q^64 + 190 * q^65 + 2064 * q^66 + 1316 * q^67 - 611 * q^68 - 822 * q^69 + 4658 * q^70 - 173 * q^71 - 1053 * q^72 - 418 * q^73 + 660 * q^74 + 579 * q^75 + 1540 * q^76 - 753 * q^77 - 540 * q^78 + 2635 * q^79 + 6155 * q^80 + 567 * q^81 - 125 * q^82 + 457 * q^83 - 354 * q^84 + 1270 * q^85 + 3482 * q^86 - 1218 * q^87 + 7685 * q^88 + 592 * q^89 - 711 * q^90 + 3179 * q^91 - 3500 * q^92 - 1038 * q^93 + 2064 * q^94 - 2250 * q^95 - 2562 * q^96 - 1906 * q^97 + 2994 * q^98 - 1179 * 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 $

$2$	−5.60512	−1.98171	−0.990855	−	0.134934i	$-0.956918\pi$
$2$	−5.60512	−1.98171	−0.990855	+	0.134934i	$0.956918\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	23.4174	2.92717
$5$	12.9748	1.16050	0.580249	−	0.814439i	$-0.302955\pi$
$5$	12.9748	1.16050	0.580249	+	0.814439i	$0.302955\pi$
$6$	−16.8154	−1.14414
$7$	−18.2988	−0.988044	−0.494022	−	0.869449i	$-0.664474\pi$
$7$	−18.2988	−0.988044	−0.494022	+	0.869449i	$0.664474\pi$
$8$	−86.4162	−3.81909
$9$	9.00000	0.333333
$10$	−72.7251	−2.29977
$11$	−71.8350	−1.96901	−0.984503	−	0.175370i	$-0.943888\pi$
$11$	−71.8350	−1.96901	−0.984503	+	0.175370i	$0.943888\pi$
$12$	70.2521	1.69000
$13$	31.4840	0.671699	0.335850	−	0.941916i	$-0.390977\pi$
$13$	31.4840	0.671699	0.335850	+	0.941916i	$0.390977\pi$
$14$	102.567	1.95802
$15$	38.9243	0.670014
$16$	297.034	4.64116
$17$	−94.8120	−1.35266	−0.676332	−	0.736597i	$-0.736431\pi$
$17$	−94.8120	−1.35266	−0.676332	+	0.736597i	$0.736431\pi$
$18$	−50.4461	−0.660570
$19$	−53.7002	−0.648403	−0.324202	−	0.945988i	$-0.605096\pi$
$19$	−53.7002	−0.648403	−0.324202	+	0.945988i	$0.605096\pi$
$20$	303.835	3.39698
$21$	−54.8965	−0.570447
$22$	402.644	3.90200
$23$	−70.2521	−0.636894	−0.318447	−	0.947941i	$-0.603161\pi$
$23$	−70.2521	−0.636894	−0.318447	+	0.947941i	$0.603161\pi$
$24$	−259.249	−2.20495
$25$	43.3445	0.346756
$26$	−176.472	−1.33111
$27$	27.0000	0.192450
$28$	−428.510	−2.89217
$29$	20.2046	0.129376	0.0646879	−	0.997906i	$-0.479395\pi$
$29$	20.2046	0.129376	0.0646879	+	0.997906i	$0.479395\pi$
$30$	−218.175	−1.32777
$31$	−5.95239	−0.0344865	−0.0172433	−	0.999851i	$-0.505489\pi$
$31$	−5.95239	−0.0344865	−0.0172433	+	0.999851i	$0.505489\pi$
$32$	−973.582	−5.37833
$33$	−215.505	−1.13681
$34$	531.432	2.68059
$35$	−237.423	−1.14662
$36$	210.756	0.975724
$37$	167.214	0.742969	0.371484	−	0.928439i	$-0.378849\pi$
$37$	167.214	0.742969	0.371484	+	0.928439i	$0.378849\pi$
$38$	300.996	1.28495
$39$	94.4520	0.387806
$40$	−1121.23	−4.43205
$41$	248.975	0.948376	0.474188	−	0.880424i	$-0.342742\pi$
$41$	248.975	0.948376	0.474188	+	0.880424i	$0.342742\pi$
$42$	307.701	1.13046
$43$	−472.012	−1.67398	−0.836990	−	0.547218i	$-0.815687\pi$
$43$	−472.012	−1.67398	−0.836990	+	0.547218i	$0.815687\pi$
$44$	−1682.19	−5.76361
$45$	116.773	0.386833
$46$	393.771	1.26214
$47$	−140.560	−0.436230	−0.218115	−	0.975923i	$-0.569991\pi$
$47$	−140.560	−0.436230	−0.218115	+	0.975923i	$0.569991\pi$
$48$	891.102	2.67957
$49$	−8.15281	−0.0237691
$50$	−242.951	−0.687169
$51$	−284.436	−0.780961
$52$	737.272	1.96618
$53$	−21.3540	−0.0553434	−0.0276717	−	0.999617i	$-0.508809\pi$
$53$	−21.3540	−0.0553434	−0.0276717	+	0.999617i	$0.508809\pi$
$54$	−151.338	−0.381380
$55$	−932.042	−2.28503
$56$	1581.32	3.77343
$57$	−161.100	−0.374356
$58$	−113.249	−0.256385
$59$	−59.0000	−0.130189
$59$	−59.0000	−0.130189
$60$	911.504	1.96125
$61$	375.516	0.788196	0.394098	−	0.919068i	$-0.371057\pi$
$61$	375.516	0.788196	0.394098	+	0.919068i	$0.371057\pi$
$62$	33.3639	0.0683422
$63$	−164.689	−0.329348
$64$	3080.77	6.01713
$65$	408.497	0.779505
$66$	1207.93	2.25282
$67$	−410.115	−0.747814	−0.373907	−	0.927466i	$-0.621982\pi$
$67$	−410.115	−0.747814	−0.373907	+	0.927466i	$0.621982\pi$
$68$	−2220.25	−3.95948
$69$	−210.756	−0.367711
$70$	1330.78	2.27227
$71$	420.452	0.702796	0.351398	−	0.936226i	$-0.385706\pi$
$71$	420.452	0.702796	0.351398	+	0.936226i	$0.385706\pi$
$72$	−777.746	−1.27303
$73$	−865.694	−1.38797	−0.693985	−	0.719990i	$-0.744147\pi$
$73$	−865.694	−1.38797	−0.693985	+	0.719990i	$0.744147\pi$
$74$	−937.256	−1.47235
$75$	130.033	0.200200
$76$	−1257.52	−1.89799
$77$	1314.50	1.94546
$78$	−529.415	−0.768518
$79$	−53.7139	−0.0764973	−0.0382486	−	0.999268i	$-0.512178\pi$
$79$	−53.7139	−0.0764973	−0.0382486	+	0.999268i	$0.512178\pi$
$80$	3853.95	5.38606
$81$	81.0000	0.111111
$82$	−1395.54	−1.87940
$83$	39.4923	0.0522270	0.0261135	−	0.999659i	$-0.491687\pi$
$83$	39.4923	0.0522270	0.0261135	+	0.999659i	$0.491687\pi$
$84$	−1285.53	−1.66980
$85$	−1230.16	−1.56976
$86$	2645.68	3.31734
$87$	60.6137	0.0746951
$88$	6207.70	7.51981
$89$	−354.864	−0.422646	−0.211323	−	0.977416i	$-0.567777\pi$
$89$	−354.864	−0.422646	−0.211323	+	0.977416i	$0.567777\pi$
$90$	−654.526	−0.766590
$91$	−576.120	−0.663668
$92$	−1645.12	−1.86430
$93$	−17.8572	−0.0199108
$94$	787.856	0.864480
$95$	−696.747	−0.752471
$96$	−2920.75	−3.10518
$97$	−1419.08	−1.48542	−0.742709	−	0.669614i	$-0.766460\pi$
$97$	−1419.08	−1.48542	−0.742709	+	0.669614i	$0.766460\pi$
$98$	45.6975	0.0471035
$99$	−646.515	−0.656335
$100$	1015.01	1.01501
$101$	1095.50	1.07927	0.539635	−	0.841899i	$-0.318562\pi$
$101$	1095.50	1.07927	0.539635	+	0.841899i	$0.318562\pi$
$102$	1594.30	1.54764
$103$	−240.220	−0.229802	−0.114901	−	0.993377i	$-0.536655\pi$
$103$	−240.220	−0.229802	−0.114901	+	0.993377i	$0.536655\pi$
$104$	−2720.73	−2.56528
$105$	−712.269	−0.662003
$106$	119.692	0.109675
$107$	−313.972	−0.283671	−0.141835	−	0.989890i	$-0.545300\pi$
$107$	−313.972	−0.283671	−0.141835	+	0.989890i	$0.545300\pi$
$108$	632.269	0.563334
$109$	−624.891	−0.549117	−0.274558	−	0.961570i	$-0.588532\pi$
$109$	−624.891	−0.549117	−0.274558	+	0.961570i	$0.588532\pi$
$110$	5224.20	4.52826
$111$	501.643	0.428953
$112$	−5435.38	−4.58567
$113$	201.896	0.168078	0.0840388	−	0.996462i	$-0.473218\pi$
$113$	201.896	0.168078	0.0840388	+	0.996462i	$0.473218\pi$
$114$	902.987	0.741864
$115$	−911.504	−0.739114
$116$	473.138	0.378705
$117$	283.356	0.223900
$118$	330.702	0.257997
$119$	1734.95	1.33649
$120$	−3363.69	−2.55884
$121$	3829.26	2.87698
$122$	−2104.81	−1.56197
$123$	746.926	0.547545
$124$	−139.389	−0.100948
$125$	−1059.46	−0.758089
$126$	923.104	0.652672
$127$	2526.09	1.76499	0.882496	−	0.470321i	$-0.155862\pi$
$127$	2526.09	1.76499	0.882496	+	0.470321i	$0.155862\pi$
$128$	−9479.44	−6.54588
$129$	−1416.04	−0.966473
$130$	−2289.68	−1.54475
$131$	1418.96	0.946373	0.473186	−	0.880962i	$-0.343104\pi$
$131$	1418.96	0.946373	0.473186	+	0.880962i	$0.343104\pi$
$132$	−5046.56	−3.32762
$133$	982.650	0.640651
$134$	2298.74	1.48195
$135$	350.319	0.223338
$136$	8193.29	5.16595
$137$	−1921.39	−1.19821	−0.599106	−	0.800670i	$-0.704477\pi$
$137$	−1921.39	−1.19821	−0.599106	+	0.800670i	$0.704477\pi$
$138$	1181.31	0.728696
$139$	−331.294	−0.202158	−0.101079	−	0.994878i	$-0.532229\pi$
$139$	−331.294	−0.202158	−0.101079	+	0.994878i	$0.532229\pi$
$140$	−5559.82	−3.35636
$141$	−421.680	−0.251857
$142$	−2356.69	−1.39274
$143$	−2261.65	−1.32258
$144$	2673.31	1.54705
$145$	262.150	0.150140
$146$	4852.32	2.75055
$147$	−24.4584	−0.0137231
$148$	3915.72	2.17480
$149$	−2319.61	−1.27537	−0.637683	−	0.770299i	$-0.720107\pi$
$149$	−2319.61	−1.27537	−0.637683	+	0.770299i	$0.720107\pi$
$150$	−728.853	−0.396737
$151$	1007.48	0.542962	0.271481	−	0.962444i	$-0.412487\pi$
$151$	1007.48	0.542962	0.271481	+	0.962444i	$0.412487\pi$
$152$	4640.56	2.47631
$153$	−853.308	−0.450888
$154$	−7367.91	−3.85534
$155$	−77.2309	−0.0400215
$156$	2211.82	1.13517
$157$	1583.56	0.804982	0.402491	−	0.915424i	$-0.368144\pi$
$157$	1583.56	0.804982	0.402491	+	0.915424i	$0.368144\pi$
$158$	301.073	0.151595
$159$	−64.0621	−0.0319525
$160$	−12632.0	−6.24155
$161$	1285.53	0.629279
$162$	−454.015	−0.220190
$163$	−801.561	−0.385172	−0.192586	−	0.981280i	$-0.561687\pi$
$163$	−801.561	−0.385172	−0.192586	+	0.981280i	$0.561687\pi$
$164$	5830.34	2.77606
$165$	−2796.12	−1.31926
$166$	−221.359	−0.103499
$167$	848.880	0.393343	0.196672	−	0.980469i	$-0.436987\pi$
$167$	848.880	0.393343	0.196672	+	0.980469i	$0.436987\pi$
$168$	4743.95	2.17859
$169$	−1205.76	−0.548820
$170$	6895.21	3.11081
$171$	−483.301	−0.216134
$172$	−11053.3	−4.90002
$173$	3645.72	1.60219	0.801095	−	0.598537i	$-0.204251\pi$
$173$	3645.72	1.60219	0.801095	+	0.598537i	$0.204251\pi$
$174$	−339.747	−0.148024
$175$	−793.153	−0.342610
$176$	−21337.4	−9.13846
$177$	−177.000	−0.0751646
$178$	1989.05	0.837562
$179$	−1134.73	−0.473818	−0.236909	−	0.971532i	$-0.576134\pi$
$179$	−1134.73	−0.473818	−0.236909	+	0.971532i	$0.576134\pi$
$180$	2734.51	1.13233
$181$	−2351.48	−0.965656	−0.482828	−	0.875715i	$-0.660390\pi$
$181$	−2351.48	−0.965656	−0.482828	+	0.875715i	$0.660390\pi$
$182$	3229.22	1.31520
$183$	1126.55	0.455065
$184$	6070.91	2.43236
$185$	2169.56	0.862214
$186$	100.092	0.0394574
$187$	6810.81	2.66340
$188$	−3291.55	−1.27692
$189$	−494.068	−0.190149
$190$	3905.35	1.49118
$191$	2659.35	1.00745	0.503727	−	0.863863i	$-0.331962\pi$
$191$	2659.35	1.00745	0.503727	+	0.863863i	$0.331962\pi$
$192$	9242.32	3.47399
$193$	191.102	0.0712735	0.0356368	−	0.999365i	$-0.488654\pi$
$193$	191.102	0.0712735	0.0356368	+	0.999365i	$0.488654\pi$
$194$	7954.11	2.94367
$195$	1225.49	0.450048
$196$	−190.917	−0.0695763
$197$	4448.69	1.60891	0.804456	−	0.594012i	$-0.202457\pi$
$197$	4448.69	1.60891	0.804456	+	0.594012i	$0.202457\pi$
$198$	3623.79	1.30067
$199$	2989.63	1.06497	0.532485	−	0.846439i	$-0.321258\pi$
$199$	2989.63	1.06497	0.532485	+	0.846439i	$0.321258\pi$
$200$	−3745.66	−1.32429
$201$	−1230.35	−0.431750
$202$	−6140.41	−2.13880
$203$	−369.720	−0.127829
$204$	−6660.74	−2.28601
$205$	3230.39	1.10059
$206$	1346.46	0.455400
$207$	−632.268	−0.212298
$208$	9351.82	3.11746
$209$	3857.55	1.27671
$210$	3992.35	1.31190
$211$	−1312.96	−0.428379	−0.214189	−	0.976792i	$-0.568711\pi$
$211$	−1312.96	−0.428379	−0.214189	+	0.976792i	$0.568711\pi$
$212$	−500.055	−0.162000
$213$	1261.36	0.405759
$214$	1759.85	0.562153
$215$	−6124.24	−1.94265
$216$	−2333.24	−0.734985
$217$	108.922	0.0340742
$218$	3502.59	1.08819
$219$	−2597.08	−0.801345
$220$	−21826.0	−6.68866
$221$	−2985.06	−0.908583
$222$	−2811.77	−0.850060
$223$	−1272.27	−0.382052	−0.191026	−	0.981585i	$-0.561181\pi$
$223$	−1272.27	−0.382052	−0.191026	+	0.981585i	$0.561181\pi$
$224$	17815.4	5.31403
$225$	390.100	0.115585
$226$	−1131.65	−0.333081
$227$	−1528.48	−0.446910	−0.223455	−	0.974714i	$-0.571734\pi$
$227$	−1528.48	−0.446910	−0.223455	+	0.974714i	$0.571734\pi$
$228$	−3772.55	−1.09580
$229$	−210.914	−0.0608629	−0.0304314	−	0.999537i	$-0.509688\pi$
$229$	−210.914	−0.0608629	−0.0304314	+	0.999537i	$0.509688\pi$
$230$	5109.09	1.46471
$231$	3943.49	1.12321
$232$	−1746.00	−0.494098
$233$	−2452.82	−0.689655	−0.344827	−	0.938666i	$-0.612063\pi$
$233$	−2452.82	−0.689655	−0.344827	+	0.938666i	$0.612063\pi$
$234$	−1588.24	−0.443704
$235$	−1823.73	−0.506244
$236$	−1381.62	−0.381085
$237$	−161.142	−0.0441657
$238$	−9724.59	−2.64854
$239$	1180.65	0.319540	0.159770	−	0.987154i	$-0.448925\pi$
$239$	1180.65	0.319540	0.159770	+	0.987154i	$0.448925\pi$
$240$	11561.8	3.10964
$241$	−2161.44	−0.577719	−0.288860	−	0.957371i	$-0.593276\pi$
$241$	−2161.44	−0.577719	−0.288860	+	0.957371i	$0.593276\pi$
$242$	−21463.5	−5.70134
$243$	243.000	0.0641500
$244$	8793.60	2.30718
$245$	−105.781	−0.0275840
$246$	−4186.61	−1.08507
$247$	−1690.70	−0.435532
$248$	514.383	0.131707
$249$	118.477	0.0301533
$250$	5938.41	1.50231
$251$	−2174.07	−0.546718	−0.273359	−	0.961912i	$-0.588135\pi$
$251$	−2174.07	−0.546718	−0.273359	+	0.961912i	$0.588135\pi$
$252$	−3856.59	−0.964058
$253$	5046.55	1.25405
$254$	−14159.0	−3.49770
$255$	−3690.49	−0.906303
$256$	28487.2	6.95489
$257$	6563.41	1.59305	0.796526	−	0.604604i	$-0.206669\pi$
$257$	6563.41	1.59305	0.796526	+	0.604604i	$0.206669\pi$
$258$	7937.05	1.91527
$259$	−3059.82	−0.734086
$260$	9565.93	2.28175
$261$	181.841	0.0431252
$262$	−7953.42	−1.87544
$263$	−1733.36	−0.406401	−0.203201	−	0.979137i	$-0.565134\pi$
$263$	−1733.36	−0.406401	−0.203201	+	0.979137i	$0.565134\pi$
$264$	18623.1	4.34157
$265$	−277.063	−0.0642259
$266$	−5507.87	−1.26958
$267$	−1064.59	−0.244015
$268$	−9603.81	−2.18898
$269$	1240.79	0.281235	0.140618	−	0.990064i	$-0.455091\pi$
$269$	1240.79	0.281235	0.140618	+	0.990064i	$0.455091\pi$
$270$	−1963.58	−0.442591
$271$	−1238.86	−0.277695	−0.138848	−	0.990314i	$-0.544340\pi$
$271$	−1238.86	−0.277695	−0.138848	+	0.990314i	$0.544340\pi$
$272$	−28162.4	−6.27793
$273$	−1728.36	−0.383169
$274$	10769.6	2.37451
$275$	−3113.65	−0.682764
$276$	−4935.35	−1.07635
$277$	−5349.92	−1.16045	−0.580226	−	0.814455i	$-0.697036\pi$
$277$	−5349.92	−1.16045	−0.580226	+	0.814455i	$0.697036\pi$
$278$	1856.94	0.400619
$279$	−53.5716	−0.0114955
$280$	20517.2	4.37906
$281$	−1010.45	−0.214514	−0.107257	−	0.994231i	$-0.534207\pi$
$281$	−1010.45	−0.214514	−0.107257	+	0.994231i	$0.534207\pi$
$282$	2363.57	0.499108
$283$	−1311.57	−0.275493	−0.137746	−	0.990468i	$-0.543986\pi$
$283$	−1311.57	−0.275493	−0.137746	+	0.990468i	$0.543986\pi$
$284$	9845.88	2.05720
$285$	−2090.24	−0.434439
$286$	12676.8	2.62097
$287$	−4555.96	−0.937037
$288$	−8762.24	−1.79278
$289$	4076.31	0.829699
$290$	−1469.38	−0.297534
$291$	−4257.24	−0.857607
$292$	−20272.3	−4.06282
$293$	−6982.71	−1.39227	−0.696134	−	0.717912i	$-0.745098\pi$
$293$	−6982.71	−1.39227	−0.696134	+	0.717912i	$0.745098\pi$
$294$	137.092	0.0271952
$295$	−765.511	−0.151084
$296$	−14450.0	−2.83747
$297$	−1939.54	−0.378935
$298$	13001.7	2.52741
$299$	−2211.81	−0.427801
$300$	3045.04	0.586018
$301$	8637.26	1.65397
$302$	−5647.03	−1.07599
$303$	3286.50	0.623117
$304$	−15950.8	−3.00934
$305$	4872.23	0.914700
$306$	4782.89	0.893529
$307$	2577.38	0.479148	0.239574	−	0.970878i	$-0.422992\pi$
$307$	2577.38	0.479148	0.239574	+	0.970878i	$0.422992\pi$
$308$	30782.0	5.69470
$309$	−720.659	−0.132676
$310$	432.888	0.0793110
$311$	6320.88	1.15249	0.576244	−	0.817277i	$-0.304518\pi$
$311$	6320.88	1.15249	0.576244	+	0.817277i	$0.304518\pi$
$312$	−8162.18	−1.48107
$313$	−2703.12	−0.488145	−0.244073	−	0.969757i	$-0.578483\pi$
$313$	−2703.12	−0.488145	−0.244073	+	0.969757i	$0.578483\pi$
$314$	−8876.07	−1.59524
$315$	−2136.81	−0.382208
$316$	−1257.84	−0.223921
$317$	−8918.51	−1.58017	−0.790084	−	0.612999i	$-0.789963\pi$
$317$	−8918.51	−1.58017	−0.790084	+	0.612999i	$0.789963\pi$
$318$	359.076	0.0633206
$319$	−1451.40	−0.254741
$320$	39972.3	6.98287
$321$	−941.915	−0.163777
$322$	−7205.55	−1.24705
$323$	5091.42	0.877071
$324$	1896.81	0.325241
$325$	1364.66	0.232915
$326$	4492.84	0.763299
$327$	−1874.67	−0.317033
$328$	−21515.5	−3.62193
$329$	2572.08	0.431014
$330$	15672.6	2.61439
$331$	−8555.58	−1.42072	−0.710358	−	0.703841i	$-0.751467\pi$
$331$	−8555.58	−1.42072	−0.710358	+	0.703841i	$0.751467\pi$
$332$	924.805	0.152877
$333$	1504.93	0.247656
$334$	−4758.07	−0.779491
$335$	−5321.15	−0.867836
$336$	−16306.1	−2.64754
$337$	6636.10	1.07268	0.536338	−	0.844003i	$-0.319807\pi$
$337$	6636.10	1.07268	0.536338	+	0.844003i	$0.319807\pi$
$338$	6758.42	1.08760
$339$	605.688	0.0970397
$340$	−28807.2	−4.59497
$341$	427.590	0.0679041
$342$	2708.96	0.428315
$343$	6425.69	1.01153
$344$	40789.5	6.39308
$345$	−2734.51	−0.426728
$346$	−20434.7	−3.17507
$347$	10375.1	1.60508	0.802539	−	0.596599i	$-0.203482\pi$
$347$	10375.1	1.60508	0.802539	+	0.596599i	$0.203482\pi$
$348$	1419.41	0.218645
$349$	−1257.24	−0.192832	−0.0964160	−	0.995341i	$-0.530738\pi$
$349$	−1257.24	−0.192832	−0.0964160	+	0.995341i	$0.530738\pi$
$350$	4445.72	0.678953
$351$	850.068	0.129269
$352$	69937.3	10.5900
$353$	10418.3	1.57085	0.785426	−	0.618955i	$-0.212444\pi$
$353$	10418.3	1.57085	0.785426	+	0.618955i	$0.212444\pi$
$354$	992.106	0.148954
$355$	5455.27	0.815593
$356$	−8309.98	−1.23716
$357$	5204.84	0.771623
$358$	6360.27	0.938969
$359$	3999.50	0.587983	0.293991	−	0.955808i	$-0.405016\pi$
$359$	3999.50	0.587983	0.293991	+	0.955808i	$0.405016\pi$
$360$	−10091.1	−1.47735
$361$	−3975.29	−0.579573
$362$	13180.3	1.91365
$363$	11487.8	1.66103
$364$	−13491.2	−1.94267
$365$	−11232.2	−1.61074
$366$	−6314.44	−0.901806
$367$	−171.633	−0.0244119	−0.0122060	−	0.999926i	$-0.503885\pi$
$367$	−171.633	−0.0244119	−0.0122060	+	0.999926i	$0.503885\pi$
$368$	−20867.3	−2.95593
$369$	2240.78	0.316125
$370$	−12160.7	−1.70866
$371$	390.754	0.0546817
$372$	−418.168	−0.0582823
$373$	−10286.9	−1.42798	−0.713990	−	0.700156i	$-0.753114\pi$
$373$	−10286.9	−1.42798	−0.713990	+	0.700156i	$0.753114\pi$
$374$	−38175.4	−5.27809
$375$	−3178.38	−0.437683
$376$	12146.7	1.66600
$377$	636.121	0.0869015
$378$	2769.31	0.376820
$379$	−4410.20	−0.597722	−0.298861	−	0.954297i	$-0.596607\pi$
$379$	−4410.20	−0.597722	−0.298861	+	0.954297i	$0.596607\pi$
$380$	−16316.0	−2.20261
$381$	7578.26	1.01902
$382$	−14906.0	−1.99648
$383$	−3877.45	−0.517307	−0.258654	−	0.965970i	$-0.583279\pi$
$383$	−3877.45	−0.517307	−0.258654	+	0.965970i	$0.583279\pi$
$384$	−28438.3	−3.77926
$385$	17055.3	2.25771
$386$	−1071.15	−0.141243
$387$	−4248.11	−0.557993
$388$	−33231.1	−4.34807
$389$	−8465.37	−1.10337	−0.551686	−	0.834052i	$-0.686015\pi$
$389$	−8465.37	−1.10337	−0.551686	+	0.834052i	$0.686015\pi$
$390$	−6869.03	−0.891864
$391$	6660.74	0.861503
$392$	704.534	0.0907764
$393$	4256.87	0.546389
$394$	−24935.4	−3.18840
$395$	−696.925	−0.0887749
$396$	−15139.7	−1.92120
$397$	13428.9	1.69768	0.848839	−	0.528652i	$-0.177302\pi$
$397$	13428.9	1.69768	0.848839	+	0.528652i	$0.177302\pi$
$398$	−16757.2	−2.11046
$399$	2947.95	0.369880
$400$	12874.8	1.60935
$401$	12373.5	1.54091	0.770455	−	0.637494i	$-0.220029\pi$
$401$	12373.5	1.54091	0.770455	+	0.637494i	$0.220029\pi$
$402$	6896.23	0.855604
$403$	−187.405	−0.0231646
$404$	25653.7	3.15921
$405$	1050.96	0.128944
$406$	2072.33	0.253320
$407$	−12011.8	−1.46291
$408$	24579.9	2.98256
$409$	11757.4	1.42143	0.710717	−	0.703478i	$-0.248371\pi$
$409$	11757.4	1.42143	0.710717	+	0.703478i	$0.248371\pi$
$410$	−18106.7	−2.18105
$411$	−5764.16	−0.691788
$412$	−5625.31	−0.672668
$413$	1079.63	0.128632
$414$	3543.94	0.420713
$415$	512.403	0.0606093
$416$	−30652.3	−3.61262
$417$	−993.881	−0.116716
$418$	−21622.0	−2.53007
$419$	3644.71	0.424954	0.212477	−	0.977166i	$-0.431847\pi$
$419$	3644.71	0.424954	0.212477	+	0.977166i	$0.431847\pi$
$420$	−16679.5	−1.93780
$421$	−5025.23	−0.581745	−0.290873	−	0.956762i	$-0.593946\pi$
$421$	−5025.23	−0.581745	−0.290873	+	0.956762i	$0.593946\pi$
$422$	7359.30	0.848922
$423$	−1265.04	−0.145410
$424$	1845.33	0.211362
$425$	−4109.57	−0.469044
$426$	−7070.06	−0.804097
$427$	−6871.51	−0.778772
$428$	−7352.39	−0.830353
$429$	−6784.95	−0.763591
$430$	34327.1	3.84977
$431$	−5974.34	−0.667688	−0.333844	−	0.942628i	$-0.608346\pi$
$431$	−5974.34	−0.667688	−0.333844	+	0.942628i	$0.608346\pi$
$432$	8019.92	0.893191
$433$	9508.16	1.05527	0.527636	−	0.849471i	$-0.323079\pi$
$433$	9508.16	1.05527	0.527636	+	0.849471i	$0.323079\pi$
$434$	−610.520	−0.0675251
$435$	786.449	0.0866835
$436$	−14633.3	−1.60736
$437$	3772.55	0.412964
$438$	14556.9	1.58803
$439$	9345.33	1.01601	0.508005	−	0.861354i	$-0.330383\pi$
$439$	9345.33	1.01601	0.508005	+	0.861354i	$0.330383\pi$
$440$	80543.5	8.72673
$441$	−73.3753	−0.00792304
$442$	16731.6	1.80055
$443$	10777.7	1.15590	0.577952	−	0.816071i	$-0.303852\pi$
$443$	10777.7	1.15590	0.577952	+	0.816071i	$0.303852\pi$
$444$	11747.1	1.25562
$445$	−4604.28	−0.490480
$446$	7131.23	0.757116
$447$	−6958.82	−0.736333
$448$	−56374.5	−5.94519
$449$	−10690.1	−1.12360	−0.561801	−	0.827272i	$-0.689891\pi$
$449$	−10690.1	−1.12360	−0.561801	+	0.827272i	$0.689891\pi$
$450$	−2186.56	−0.229056
$451$	−17885.1	−1.86736
$452$	4727.87	0.491992
$453$	3022.43	0.313479
$454$	8567.29	0.885645
$455$	−7475.02	−0.770186
$456$	13921.7	1.42970
$457$	14441.5	1.47822	0.739108	−	0.673587i	$-0.235247\pi$
$457$	14441.5	1.47822	0.739108	+	0.673587i	$0.235247\pi$
$458$	1182.20	0.120613
$459$	−2559.92	−0.260320
$460$	−21345.0	−2.16351
$461$	−7427.54	−0.750402	−0.375201	−	0.926944i	$-0.622426\pi$
$461$	−7427.54	−0.750402	−0.375201	+	0.926944i	$0.622426\pi$
$462$	−22103.7	−2.22588
$463$	−16270.9	−1.63320	−0.816602	−	0.577201i	$-0.804145\pi$
$463$	−16270.9	−1.63320	−0.816602	+	0.577201i	$0.804145\pi$
$464$	6001.45	0.600453
$465$	−231.693	−0.0231064
$466$	13748.3	1.36670
$467$	−15580.7	−1.54387	−0.771935	−	0.635702i	$-0.780711\pi$
$467$	−15580.7	−1.54387	−0.771935	+	0.635702i	$0.780711\pi$
$468$	6635.45	0.655393
$469$	7504.63	0.738873
$470$	10222.2	1.00323
$471$	4750.69	0.464757
$472$	5098.55	0.497203
$473$	33907.0	3.29608
$474$	903.218	0.0875236
$475$	−2327.60	−0.224838
$476$	40627.9	3.91214
$477$	−192.186	−0.0184478
$478$	−6617.69	−0.633235
$479$	−10461.9	−0.997951	−0.498976	−	0.866616i	$-0.666290\pi$
$479$	−10461.9	−0.997951	−0.498976	+	0.866616i	$0.666290\pi$
$480$	−37896.0	−3.60356
$481$	5264.57	0.499051
$482$	12115.1	1.14487
$483$	3856.59	0.363315
$484$	89671.2	8.42142
$485$	−18412.2	−1.72383
$486$	−1362.04	−0.127127
$487$	−905.076	−0.0842154	−0.0421077	−	0.999113i	$-0.513407\pi$
$487$	−905.076	−0.0842154	−0.0421077	+	0.999113i	$0.513407\pi$
$488$	−32450.7	−3.01019
$489$	−2404.68	−0.222379
$490$	592.914	0.0546635
$491$	−10221.5	−0.939491	−0.469746	−	0.882802i	$-0.655654\pi$
$491$	−10221.5	−0.939491	−0.469746	+	0.882802i	$0.655654\pi$
$492$	17491.0	1.60276
$493$	−1915.64	−0.175002
$494$	9476.55	0.863097
$495$	−8388.37	−0.761676
$496$	−1768.06	−0.160057
$497$	−7693.78	−0.694393
$498$	−664.077	−0.0597550
$499$	16843.7	1.51108	0.755538	−	0.655104i	$-0.227375\pi$
$499$	16843.7	1.51108	0.755538	+	0.655104i	$0.227375\pi$
$500$	−24809.8	−2.21906
$501$	2546.64	0.227097
$502$	12185.9	1.08344
$503$	−8181.54	−0.725243	−0.362621	−	0.931937i	$-0.618118\pi$
$503$	−8181.54	−0.725243	−0.362621	+	0.931937i	$0.618118\pi$
$504$	14231.8	1.25781
$505$	14213.9	1.25249
$506$	−28286.5	−2.48516
$507$	−3617.28	−0.316862
$508$	59154.3	5.16643
$509$	5119.71	0.445830	0.222915	−	0.974838i	$-0.428443\pi$
$509$	5119.71	0.445830	0.222915	+	0.974838i	$0.428443\pi$
$510$	20685.6	1.79603
$511$	15841.2	1.37137
$512$	−83838.7	−7.23669
$513$	−1449.90	−0.124785
$514$	−36788.7	−3.15697
$515$	−3116.79	−0.266684
$516$	−33159.8	−2.82903
$517$	10097.1	0.858938
$518$	17150.7	1.45474
$519$	10937.2	0.925025
$520$	−35300.8	−2.97700
$521$	8611.23	0.724117	0.362058	−	0.932155i	$-0.382074\pi$
$521$	8611.23	0.724117	0.362058	+	0.932155i	$0.382074\pi$
$522$	−1019.24	−0.0854617
$523$	1314.45	0.109899	0.0549493	−	0.998489i	$-0.482500\pi$
$523$	1314.45	0.109899	0.0549493	+	0.998489i	$0.482500\pi$
$524$	33228.2	2.77019
$525$	−2379.46	−0.197806
$526$	9715.69	0.805369
$527$	564.358	0.0466486
$528$	−64012.3	−5.27610
$529$	−7231.65	−0.594366
$530$	1552.97	0.127277
$531$	−531.000	−0.0433963
$532$	23011.1	1.87529
$533$	7838.73	0.637023
$534$	5967.16	0.483566
$535$	−4073.71	−0.329199
$536$	35440.6	2.85597
$537$	−3404.18	−0.273559
$538$	−6954.77	−0.557326
$539$	585.657	0.0468015
$540$	8203.54	0.653748
$541$	6075.96	0.482858	0.241429	−	0.970419i	$-0.422384\pi$
$541$	6075.96	0.482858	0.241429	+	0.970419i	$0.422384\pi$
$542$	6943.96	0.550311
$543$	−7054.43	−0.557522
$544$	92307.3	7.27508
$545$	−8107.82	−0.637249
$546$	9687.67	0.759330
$547$	−25132.5	−1.96451	−0.982256	−	0.187547i	$-0.939946\pi$
$547$	−25132.5	−1.96451	−0.982256	+	0.187547i	$0.939946\pi$
$548$	−44993.8	−3.50737
$549$	3379.65	0.262732
$550$	17452.4	1.35304
$551$	−1084.99	−0.0838876
$552$	18212.7	1.40432
$553$	982.901	0.0755827
$554$	29986.9	2.29968
$555$	6508.69	0.497799
$556$	−7758.03	−0.591751
$557$	7094.80	0.539706	0.269853	−	0.962901i	$-0.413025\pi$
$557$	7094.80	0.539706	0.269853	+	0.962901i	$0.413025\pi$
$558$	300.275	0.0227807
$559$	−14860.8	−1.12441
$560$	−70522.7	−5.32166
$561$	20432.4	1.53772
$562$	5663.69	0.425104
$563$	13314.5	0.996695	0.498348	−	0.866977i	$-0.333940\pi$
$563$	13314.5	0.996695	0.498348	+	0.866977i	$0.333940\pi$
$564$	−9874.64	−0.737229
$565$	2619.55	0.195054
$566$	7351.48	0.545947
$567$	−1482.21	−0.109783
$568$	−36333.9	−2.68404
$569$	−10321.3	−0.760445	−0.380223	−	0.924895i	$-0.624153\pi$
$569$	−10321.3	−0.760445	−0.380223	+	0.924895i	$0.624153\pi$
$570$	11716.0	0.860932
$571$	−17232.9	−1.26301	−0.631503	−	0.775374i	$-0.717562\pi$
$571$	−17232.9	−1.26301	−0.631503	+	0.775374i	$0.717562\pi$
$572$	−52961.9	−3.87141
$573$	7978.04	0.581653
$574$	25536.7	1.85693
$575$	−3045.04	−0.220847
$576$	27727.0	2.00571
$577$	−14043.3	−1.01322	−0.506612	−	0.862174i	$-0.669102\pi$
$577$	−14043.3	−1.01322	−0.506612	+	0.862174i	$0.669102\pi$
$578$	−22848.2	−1.64422
$579$	573.305	0.0411498
$580$	6138.85	0.439486
$581$	−722.662	−0.0516026
$582$	23862.3	1.69953
$583$	1533.97	0.108971
$584$	74809.9	5.30078
$585$	3676.48	0.259835
$586$	39138.9	2.75907
$587$	−3955.35	−0.278117	−0.139058	−	0.990284i	$-0.544408\pi$
$587$	−3955.35	−0.278117	−0.139058	+	0.990284i	$0.544408\pi$
$588$	−572.752	−0.0401699
$589$	319.645	0.0223612
$590$	4290.78	0.299404
$591$	13346.1	0.928906
$592$	49668.3	3.44824
$593$	−26744.5	−1.85205	−0.926026	−	0.377461i	$-0.876797\pi$
$593$	−26744.5	−1.85205	−0.926026	+	0.377461i	$0.876797\pi$
$594$	10871.4	0.750939
$595$	22510.5	1.55100
$596$	−54319.1	−3.73322
$597$	8968.89	0.614861
$598$	12397.5	0.847778
$599$	−23788.0	−1.62262	−0.811310	−	0.584616i	$-0.801245\pi$
$599$	−23788.0	−1.62262	−0.811310	+	0.584616i	$0.801245\pi$
$600$	−11237.0	−0.764580
$601$	1191.30	0.0808552	0.0404276	−	0.999182i	$-0.487128\pi$
$601$	1191.30	0.0808552	0.0404276	+	0.999182i	$0.487128\pi$
$602$	−48412.9	−3.27768
$603$	−3691.04	−0.249271
$604$	23592.4	1.58934
$605$	49683.8	3.33873
$606$	−18421.2	−1.23484
$607$	−24740.6	−1.65435	−0.827176	−	0.561943i	$-0.810054\pi$
$607$	−24740.6	−1.65435	−0.827176	+	0.561943i	$0.810054\pi$
$608$	52281.5	3.48733
$609$	−1109.16	−0.0738020
$610$	−27309.5	−1.81267
$611$	−4425.39	−0.293015
$612$	−19982.2	−1.31983
$613$	−1524.99	−0.100479	−0.0502395	−	0.998737i	$-0.515998\pi$
$613$	−1524.99	−0.100479	−0.0502395	+	0.998737i	$0.515998\pi$
$614$	−14446.5	−0.949533
$615$	9691.18	0.635425
$616$	−113594.	−7.42990
$617$	8382.64	0.546957	0.273479	−	0.961878i	$-0.411826\pi$
$617$	8382.64	0.546957	0.273479	+	0.961878i	$0.411826\pi$
$618$	4039.38	0.262925
$619$	−14268.7	−0.926505	−0.463252	−	0.886226i	$-0.653318\pi$
$619$	−14268.7	−0.926505	−0.463252	+	0.886226i	$0.653318\pi$
$620$	−1808.54	−0.117150
$621$	−1896.81	−0.122570
$622$	−35429.3	−2.28390
$623$	6493.60	0.417593
$624$	28055.5	1.79987
$625$	−19164.3	−1.22652
$626$	15151.3	0.967361
$627$	11572.6	0.737108
$628$	37082.9	2.35632
$629$	−15853.9	−1.00499
$630$	11977.1	0.757424
$631$	24816.1	1.56563	0.782816	−	0.622253i	$-0.213782\pi$
$631$	24816.1	1.56563	0.782816	+	0.622253i	$0.213782\pi$
$632$	4641.75	0.292150
$633$	−3938.88	−0.247324
$634$	49989.3	3.13143
$635$	32775.4	2.04827
$636$	−1500.16	−0.0935305
$637$	−256.683	−0.0159657
$638$	8135.24	0.504823
$639$	3784.07	0.234265
$640$	−122993.	−7.59648
$641$	−21073.3	−1.29851	−0.649256	−	0.760570i	$-0.724920\pi$
$641$	−21073.3	−1.29851	−0.649256	+	0.760570i	$0.724920\pi$
$642$	5279.55	0.324559
$643$	−26526.1	−1.62688	−0.813442	−	0.581645i	$-0.802409\pi$
$643$	−26526.1	−1.62688	−0.813442	+	0.581645i	$0.802409\pi$
$644$	30103.7	1.84201
$645$	−18372.7	−1.12159
$646$	−28538.0	−1.73810
$647$	30487.8	1.85255	0.926274	−	0.376851i	$-0.122993\pi$
$647$	30487.8	1.85255	0.926274	+	0.376851i	$0.122993\pi$
$648$	−6999.71	−0.424344
$649$	4238.26	0.256343
$650$	−7649.06	−0.461571
$651$	326.766	0.0196727
$652$	−18770.4	−1.12747
$653$	−18787.9	−1.12592	−0.562962	−	0.826483i	$-0.690338\pi$
$653$	−18787.9	−1.12592	−0.562962	+	0.826483i	$0.690338\pi$
$654$	10507.8	0.628267
$655$	18410.6	1.09826
$656$	73954.1	4.40156
$657$	−7791.24	−0.462657
$658$	−14416.8	−0.854144
$659$	−8131.03	−0.480637	−0.240319	−	0.970694i	$-0.577252\pi$
$659$	−8131.03	−0.480637	−0.240319	+	0.970694i	$0.577252\pi$
$660$	−65477.9	−3.86170
$661$	28408.2	1.67164	0.835819	−	0.549005i	$-0.184993\pi$
$661$	28408.2	1.67164	0.835819	+	0.549005i	$0.184993\pi$
$662$	47955.0	2.81545
$663$	−8955.18	−0.524571
$664$	−3412.77	−0.199460
$665$	12749.7	0.743474
$666$	−8435.30	−0.490783
$667$	−1419.41	−0.0823986
$668$	19878.5	1.15138
$669$	−3816.81	−0.220578
$670$	29825.7	1.71980
$671$	−26975.2	−1.55196
$672$	53446.3	3.06806
$673$	−10582.7	−0.606143	−0.303072	−	0.952968i	$-0.598012\pi$
$673$	−10582.7	−0.606143	−0.303072	+	0.952968i	$0.598012\pi$
$674$	−37196.2	−2.12573
$675$	1170.30	0.0667332
$676$	−28235.7	−1.60649
$677$	−3227.86	−0.183245	−0.0916223	−	0.995794i	$-0.529205\pi$
$677$	−3227.86	−0.183245	−0.0916223	+	0.995794i	$0.529205\pi$
$678$	−3394.95	−0.192304
$679$	25967.5	1.46766
$680$	106306.	5.99507
$681$	−4585.43	−0.258023
$682$	−2396.69	−0.134566
$683$	−27107.0	−1.51863	−0.759313	−	0.650726i	$-0.774465\pi$
$683$	−27107.0	−1.51863	−0.759313	+	0.650726i	$0.774465\pi$
$684$	−11317.6	−0.632662
$685$	−24929.5	−1.39052
$686$	−36016.7	−2.00456
$687$	−632.743	−0.0351392
$688$	−140204.	−7.76921
$689$	−672.310	−0.0371741
$690$	15327.3	0.845651
$691$	17579.1	0.967785	0.483893	−	0.875127i	$-0.339223\pi$
$691$	17579.1	0.967785	0.483893	+	0.875127i	$0.339223\pi$
$692$	85373.1	4.68988
$693$	11830.5	0.648488
$694$	−58153.4	−3.18080
$695$	−4298.46	−0.234604
$696$	−5238.01	−0.285267
$697$	−23605.8	−1.28283
$698$	7046.96	0.382137
$699$	−7358.46	−0.398172
$700$	−18573.6	−1.00288
$701$	−26746.3	−1.44107	−0.720537	−	0.693416i	$-0.756105\pi$
$701$	−26746.3	−1.44107	−0.720537	+	0.693416i	$0.756105\pi$
$702$	−4764.73	−0.256173
$703$	−8979.43	−0.481743
$704$	−221307.	−11.8478
$705$	−5471.20	−0.292280
$706$	−58395.9	−3.11297
$707$	−20046.4	−1.06637
$708$	−4144.87	−0.220020
$709$	−6249.37	−0.331029	−0.165515	−	0.986207i	$-0.552929\pi$
$709$	−6249.37	−0.331029	−0.165515	+	0.986207i	$0.552929\pi$
$710$	−30577.4	−1.61627
$711$	−483.425	−0.0254991
$712$	30666.0	1.61412
$713$	418.168	0.0219643
$714$	−29173.8	−1.52913
$715$	−29344.4	−1.53485
$716$	−26572.3	−1.38695
$717$	3541.95	0.184486
$718$	−22417.7	−1.16521
$719$	−22521.4	−1.16816	−0.584079	−	0.811697i	$-0.698544\pi$
$719$	−22521.4	−1.16816	−0.584079	+	0.811697i	$0.698544\pi$
$720$	34685.5	1.79535
$721$	4395.74	0.227054
$722$	22282.0	1.14855
$723$	−6484.31	−0.333546
$724$	−55065.4	−2.82664
$725$	875.757	0.0448618
$726$	−64390.4	−3.29167
$727$	31439.8	1.60390	0.801950	−	0.597391i	$-0.203796\pi$
$727$	31439.8	1.60390	0.801950	+	0.597391i	$0.203796\pi$
$728$	49786.1	2.53461
$729$	729.000	0.0370370
$730$	62957.7	3.19201
$731$	44752.4	2.26433
$732$	26380.8	1.33205
$733$	9684.11	0.487982	0.243991	−	0.969778i	$-0.421543\pi$
$733$	9684.11	0.487982	0.243991	+	0.969778i	$0.421543\pi$
$734$	962.024	0.0483773
$735$	−317.342	−0.0159256
$736$	68396.2	3.42543
$737$	29460.6	1.47245
$738$	−12559.8	−0.626468
$739$	2170.31	0.108033	0.0540164	−	0.998540i	$-0.482798\pi$
$739$	2170.31	0.108033	0.0540164	+	0.998540i	$0.482798\pi$
$740$	50805.5	2.52385
$741$	−5072.09	−0.251454
$742$	−2190.22	−0.108363
$743$	16314.2	0.805532	0.402766	−	0.915303i	$-0.368049\pi$
$743$	16314.2	0.805532	0.402766	+	0.915303i	$0.368049\pi$
$744$	1543.15	0.0760411
$745$	−30096.4	−1.48006
$746$	57659.4	2.82984
$747$	355.430	0.0174090
$748$	159491.	7.79623
$749$	5745.31	0.280279
$750$	17815.2	0.867360
$751$	−20763.2	−1.00887	−0.504433	−	0.863451i	$-0.668299\pi$
$751$	−20763.2	−1.00887	−0.504433	+	0.863451i	$0.668299\pi$
$752$	−41751.1	−2.02461
$753$	−6522.21	−0.315648
$754$	−3565.53	−0.172214
$755$	13071.8	0.630106
$756$	−11569.8	−0.556599
$757$	−4504.44	−0.216270	−0.108135	−	0.994136i	$-0.534488\pi$
$757$	−4504.44	−0.216270	−0.108135	+	0.994136i	$0.534488\pi$
$758$	24719.7	1.18451
$759$	15139.7	0.724025
$760$	60210.2	2.87375
$761$	−24834.5	−1.18298	−0.591492	−	0.806311i	$-0.701461\pi$
$761$	−24834.5	−1.18298	−0.591492	+	0.806311i	$0.701461\pi$
$762$	−42477.0	−2.01940
$763$	11434.8	0.542552
$764$	62274.9	2.94899
$765$	−11071.5	−0.523254
$766$	21733.6	1.02515
$767$	−1857.56	−0.0874478
$768$	85461.6	4.01541
$769$	8928.62	0.418692	0.209346	−	0.977842i	$-0.432866\pi$
$769$	8928.62	0.418692	0.209346	+	0.977842i	$0.432866\pi$
$770$	−95596.8	−4.47412
$771$	19690.2	0.919749
$772$	4475.09	0.208630
$773$	25882.5	1.20431	0.602154	−	0.798380i	$-0.294309\pi$
$773$	25882.5	1.20431	0.602154	+	0.798380i	$0.294309\pi$
$774$	23811.1	1.10578
$775$	−258.003	−0.0119584
$776$	122631.	5.67295
$777$	−9179.47	−0.423825
$778$	47449.4	2.18656
$779$	−13370.0	−0.614930
$780$	28697.8	1.31737
$781$	−30203.2	−1.38381
$782$	−37334.2	−1.70725
$783$	545.524	0.0248984
$784$	−2421.66	−0.110316
$785$	20546.4	0.934180
$786$	−23860.3	−1.08278
$787$	−19011.5	−0.861101	−0.430550	−	0.902567i	$-0.641680\pi$
$787$	−19011.5	−0.861101	−0.430550	+	0.902567i	$0.641680\pi$
$788$	104177.	4.70956
$789$	−5200.08	−0.234636
$790$	3906.35	0.175926
$791$	−3694.46	−0.166068
$792$	55869.3	2.50660
$793$	11822.8	0.529430
$794$	−75270.7	−3.36430
$795$	−831.190	−0.0370809
$796$	70009.2	3.11735
$797$	−37188.2	−1.65279	−0.826395	−	0.563090i	$-0.809612\pi$
$797$	−37188.2	−1.65279	−0.826395	+	0.563090i	$0.809612\pi$
$798$	−16523.6	−0.732994
$799$	13326.8	0.590072
$800$	−42199.4	−1.86497
$801$	−3193.78	−0.140882
$802$	−69355.2	−3.05364
$803$	62187.1	2.73292
$804$	−28811.4	−1.26381
$805$	16679.5	0.730278
$806$	1050.43	0.0459054
$807$	3722.37	0.162371
$808$	−94668.9	−4.12183
$809$	−42199.6	−1.83394	−0.916971	−	0.398955i	$-0.869373\pi$
$809$	−42199.6	−1.83394	−0.916971	+	0.398955i	$0.869373\pi$
$810$	−5890.73	−0.255530
$811$	17958.8	0.777580	0.388790	−	0.921326i	$-0.372893\pi$
$811$	17958.8	0.777580	0.388790	+	0.921326i	$0.372893\pi$
$812$	−8657.87	−0.374177
$813$	−3716.58	−0.160327
$814$	67327.7	2.89906
$815$	−10400.1	−0.446992
$816$	−84487.2	−3.62456
$817$	25347.1	1.08541
$818$	−65901.7	−2.81687
$819$	−5185.08	−0.221223
$820$	75647.3	3.22161
$821$	12021.1	0.511009	0.255505	−	0.966808i	$-0.417758\pi$
$821$	12021.1	0.511009	0.255505	+	0.966808i	$0.417758\pi$
$822$	32308.8	1.37092
$823$	−28070.3	−1.18891	−0.594453	−	0.804130i	$-0.702632\pi$
$823$	−28070.3	−1.18891	−0.594453	+	0.804130i	$0.702632\pi$
$824$	20758.9	0.877633
$825$	−9340.94	−0.394194
$826$	−6051.46	−0.254912
$827$	14096.2	0.592714	0.296357	−	0.955077i	$-0.404228\pi$
$827$	14096.2	0.592714	0.296357	+	0.955077i	$0.404228\pi$
$828$	−14806.1	−0.621433
$829$	4924.66	0.206322	0.103161	−	0.994665i	$-0.467104\pi$
$829$	4924.66	0.206322	0.103161	+	0.994665i	$0.467104\pi$
$830$	−2872.08	−0.120110
$831$	−16049.8	−0.669988
$832$	96995.0	4.04170
$833$	772.984	0.0321516
$834$	5570.82	0.231297
$835$	11014.0	0.456474
$836$	90333.6	3.73715
$837$	−160.715	−0.00663693
$838$	−20429.0	−0.842135
$839$	−9277.77	−0.381769	−0.190884	−	0.981613i	$-0.561136\pi$
$839$	−9277.77	−0.381769	−0.190884	+	0.981613i	$0.561136\pi$
$840$	61551.6	2.52825
$841$	−23980.8	−0.983262
$842$	28167.0	1.15285
$843$	−3031.35	−0.123850
$844$	−30746.1	−1.25394
$845$	−15644.4	−0.636905
$846$	7090.70	0.288160
$847$	−70071.0	−2.84258
$848$	−6342.87	−0.256858
$849$	−3934.70	−0.159056
$850$	23034.7	0.929508
$851$	−11747.1	−0.473192
$852$	29537.7	1.18773
$853$	20411.8	0.819329	0.409664	−	0.912236i	$-0.365646\pi$
$853$	20411.8	0.819329	0.409664	+	0.912236i	$0.365646\pi$
$854$	38515.6	1.54330
$855$	−6270.72	−0.250824
$856$	27132.2	1.08337
$857$	−27431.5	−1.09340	−0.546698	−	0.837330i	$-0.684116\pi$
$857$	−27431.5	−1.09340	−0.546698	+	0.837330i	$0.684116\pi$
$858$	38030.5	1.51322
$859$	−11503.0	−0.456900	−0.228450	−	0.973556i	$-0.573366\pi$
$859$	−11503.0	−0.456900	−0.228450	+	0.973556i	$0.573366\pi$
$860$	−143414.	−5.68647
$861$	−13667.9	−0.540998
$862$	33486.9	1.32316
$863$	15844.5	0.624973	0.312486	−	0.949922i	$-0.398838\pi$
$863$	15844.5	0.624973	0.312486	+	0.949922i	$0.398838\pi$
$864$	−26286.7	−1.03506
$865$	47302.3	1.85934
$866$	−53294.3	−2.09124
$867$	12228.9	0.479027
$868$	2550.66	0.0997410
$869$	3858.54	0.150624
$870$	−4408.14	−0.171782
$871$	−12912.1	−0.502306
$872$	54000.7	2.09713
$873$	−12771.7	−0.495140
$874$	−21145.6	−0.818375
$875$	19386.9	0.749025
$876$	−60816.8	−2.34567
$877$	15555.2	0.598931	0.299465	−	0.954107i	$-0.403192\pi$
$877$	15555.2	0.598931	0.299465	+	0.954107i	$0.403192\pi$
$878$	−52381.7	−2.01344
$879$	−20948.1	−0.803826
$880$	−276848.	−10.6052
$881$	43893.6	1.67856	0.839281	−	0.543697i	$-0.182976\pi$
$881$	43893.6	1.67856	0.839281	+	0.543697i	$0.182976\pi$
$882$	411.277	0.0157012
$883$	−10548.9	−0.402035	−0.201018	−	0.979588i	$-0.564425\pi$
$883$	−10548.9	−0.402035	−0.201018	+	0.979588i	$0.564425\pi$
$884$	−69902.2	−2.65958
$885$	−2296.53	−0.0872284
$886$	−60410.5	−2.29067
$887$	−15354.2	−0.581221	−0.290610	−	0.956841i	$-0.593858\pi$
$887$	−15354.2	−0.581221	−0.290610	+	0.956841i	$0.593858\pi$
$888$	−43350.0	−1.63821
$889$	−46224.4	−1.74389
$890$	25807.5	0.971989
$891$	−5818.63	−0.218778
$892$	−29793.2	−1.11833
$893$	7548.10	0.282853
$894$	39005.0	1.45920
$895$	−14722.8	−0.549865
$896$	173463.	6.46761
$897$	−6635.44	−0.246991
$898$	59919.3	2.22665
$899$	−120.266	−0.00446172
$900$	9135.12	0.338338
$901$	2024.62	0.0748610
$902$	100248.	3.70056
$903$	25911.8	0.954918
$904$	−17447.1	−0.641904
$905$	−30509.8	−1.12064
$906$	−16941.1	−0.621225
$907$	−1432.55	−0.0524443	−0.0262222	−	0.999656i	$-0.508348\pi$
$907$	−1432.55	−0.0524443	−0.0262222	+	0.999656i	$0.508348\pi$
$908$	−35792.9	−1.30818
$909$	9859.50	0.359757
$910$	41898.4	1.52628
$911$	−11210.0	−0.407688	−0.203844	−	0.979003i	$-0.565343\pi$
$911$	−11210.0	−0.407688	−0.203844	+	0.979003i	$0.565343\pi$
$912$	−47852.3	−1.73744
$913$	−2836.93	−0.102835
$914$	−80946.3	−2.92939
$915$	14616.7	0.528102
$916$	−4939.06	−0.178156
$917$	−25965.2	−0.935058
$918$	14348.7	0.515879
$919$	−6525.78	−0.234239	−0.117119	−	0.993118i	$-0.537366\pi$
$919$	−6525.78	−0.234239	−0.117119	+	0.993118i	$0.537366\pi$
$920$	78768.7	2.82275
$921$	7732.13	0.276636
$922$	41632.3	1.48708
$923$	13237.5	0.472067
$924$	92346.1	3.28784
$925$	7247.81	0.257629
$926$	91200.4	3.23654
$927$	−2161.98	−0.0766005
$928$	−19670.8	−0.695826
$929$	24465.6	0.864039	0.432019	−	0.901864i	$-0.357801\pi$
$929$	24465.6	0.864039	0.432019	+	0.901864i	$0.357801\pi$
$930$	1298.67	0.0457902
$931$	437.807	0.0154120
$932$	−57438.6	−2.01874
$933$	18962.6	0.665390
$934$	87331.5	3.05950
$935$	88368.7	3.09087
$936$	−24486.5	−0.855093
$937$	13782.7	0.480535	0.240268	−	0.970707i	$-0.422765\pi$
$937$	13782.7	0.480535	0.240268	+	0.970707i	$0.422765\pi$
$938$	−42064.3	−1.46423
$939$	−8109.36	−0.281831
$940$	−42707.0	−1.48186
$941$	20827.9	0.721542	0.360771	−	0.932654i	$-0.382514\pi$
$941$	20827.9	0.721542	0.360771	+	0.932654i	$0.382514\pi$
$942$	−26628.2	−0.921012
$943$	−17491.0	−0.604015
$944$	−17525.0	−0.604227
$945$	−6410.42	−0.220668
$946$	−190053.	−6.53186
$947$	42181.4	1.44743	0.723713	−	0.690102i	$-0.242434\pi$
$947$	42181.4	1.44743	0.723713	+	0.690102i	$0.242434\pi$
$948$	−3773.51	−0.129281
$949$	−27255.5	−0.932298
$950$	13046.5	0.445563
$951$	−26755.5	−0.912310
$952$	−149928.	−5.10418
$953$	13696.3	0.465548	0.232774	−	0.972531i	$-0.425220\pi$
$953$	13696.3	0.465548	0.232774	+	0.972531i	$0.425220\pi$
$954$	1077.23	0.0365582
$955$	34504.4	1.16915
$956$	27647.7	0.935347
$957$	−4354.19	−0.147075
$958$	58640.5	1.97765
$959$	35159.1	1.18389
$960$	119917.	4.03156
$961$	−29755.6	−0.998811
$962$	−29508.5	−0.988975
$963$	−2825.74	−0.0945570
$964$	−50615.1	−1.69108
$965$	2479.50	0.0827128
$966$	−21616.7	−0.719984
$967$	−44658.0	−1.48511	−0.742557	−	0.669782i	$-0.766387\pi$
$967$	−44658.0	−1.48511	−0.742557	+	0.669782i	$0.766387\pi$
$968$	−330910.	−10.9875
$969$	15274.3	0.506377
$970$	103203.	3.41612
$971$	21045.1	0.695539	0.347770	−	0.937580i	$-0.386939\pi$
$971$	21045.1	0.695539	0.347770	+	0.937580i	$0.386939\pi$
$972$	5690.42	0.187778
$973$	6062.29	0.199741
$974$	5073.06	0.166890
$975$	4093.97	0.134474
$976$	111541.	3.65814
$977$	7509.77	0.245915	0.122957	−	0.992412i	$-0.460762\pi$
$977$	7509.77	0.245915	0.122957	+	0.992412i	$0.460762\pi$
$978$	13478.5	0.440691
$979$	25491.6	0.832192
$980$	−2477.11	−0.0807431
$981$	−5624.02	−0.183039
$982$	57292.8	1.86180
$983$	−13912.8	−0.451424	−0.225712	−	0.974194i	$-0.572471\pi$
$983$	−13912.8	−0.451424	−0.225712	+	0.974194i	$0.572471\pi$
$984$	−64546.5	−2.09112
$985$	57720.6	1.86714
$986$	10737.4	0.346803
$987$	7716.25	0.248846
$988$	−39591.6	−1.27488
$989$	33159.8	1.06615
$990$	47017.8	1.50942
$991$	16460.0	0.527619	0.263810	−	0.964575i	$-0.415021\pi$
$991$	16460.0	0.527619	0.263810	+	0.964575i	$0.415021\pi$
$992$	5795.15	0.185480
$993$	−25666.7	−0.820251
$994$	43124.6	1.37609
$995$	38789.7	1.23590
$996$	2774.42	0.0882638
$997$	24297.4	0.771823	0.385912	−	0.922536i	$-0.373887\pi$
$997$	24297.4	0.771823	0.385912	+	0.922536i	$0.373887\pi$
$998$	−94410.9	−2.99451
$999$	4514.78	0.142984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.a.a.1.1	✓	7
3.2	odd	2		531.4.a.d.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.a.a.1.1	✓	7	1.1	even	1	trivial
531.4.a.d.1.7		7	3.2	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-5.60512 q^{2} +3.00000 q^{3} +23.4174 q^{4} +12.9748 q^{5} -16.8154 q^{6} -18.2988 q^{7} -86.4162 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.60512 q^{2} +3.00000 q^{3} +23.4174 q^{4} +12.9748 q^{5} -16.8154 q^{6} -18.2988 q^{7} -86.4162 q^{8} +9.00000 q^{9} -72.7251 q^{10} -71.8350 q^{11} +70.2521 q^{12} +31.4840 q^{13} +102.567 q^{14} +38.9243 q^{15} +297.034 q^{16} -94.8120 q^{17} -50.4461 q^{18} -53.7002 q^{19} +303.835 q^{20} -54.8965 q^{21} +402.644 q^{22} -70.2521 q^{23} -259.249 q^{24} +43.3445 q^{25} -176.472 q^{26} +27.0000 q^{27} -428.510 q^{28} +20.2046 q^{29} -218.175 q^{30} -5.95239 q^{31} -973.582 q^{32} -215.505 q^{33} +531.432 q^{34} -237.423 q^{35} +210.756 q^{36} +167.214 q^{37} +300.996 q^{38} +94.4520 q^{39} -1121.23 q^{40} +248.975 q^{41} +307.701 q^{42} -472.012 q^{43} -1682.19 q^{44} +116.773 q^{45} +393.771 q^{46} -140.560 q^{47} +891.102 q^{48} -8.15281 q^{49} -242.951 q^{50} -284.436 q^{51} +737.272 q^{52} -21.3540 q^{53} -151.338 q^{54} -932.042 q^{55} +1581.32 q^{56} -161.100 q^{57} -113.249 q^{58} -59.0000 q^{59} +911.504 q^{60} +375.516 q^{61} +33.3639 q^{62} -164.689 q^{63} +3080.77 q^{64} +408.497 q^{65} +1207.93 q^{66} -410.115 q^{67} -2220.25 q^{68} -210.756 q^{69} +1330.78 q^{70} +420.452 q^{71} -777.746 q^{72} -865.694 q^{73} -937.256 q^{74} +130.033 q^{75} -1257.52 q^{76} +1314.50 q^{77} -529.415 q^{78} -53.7139 q^{79} +3853.95 q^{80} +81.0000 q^{81} -1395.54 q^{82} +39.4923 q^{83} -1285.53 q^{84} -1230.16 q^{85} +2645.68 q^{86} +60.6137 q^{87} +6207.70 q^{88} -354.864 q^{89} -654.526 q^{90} -576.120 q^{91} -1645.12 q^{92} -17.8572 q^{93} +787.856 q^{94} -696.747 q^{95} -2920.75 q^{96} -1419.08 q^{97} +45.6975 q^{98} -646.515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 8 q^{2} + 21 q^{3} + 22 q^{4} - 28 q^{5} - 24 q^{6} - 59 q^{7} - 117 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 8 * q^2 + 21 * q^3 + 22 * q^4 - 28 * q^5 - 24 * q^6 - 59 * q^7 - 117 * q^8 + 63 * q^9	\( 7 q - 8 q^{2} + 21 q^{3} + 22 q^{4} - 28 q^{5} - 24 q^{6} - 59 q^{7} - 117 q^{8} + 63 q^{9} - 79 q^{10} - 131 q^{11} + 66 q^{12} - 123 q^{13} - 117 q^{14} - 84 q^{15} + 202 q^{16} - 235 q^{17} - 72 q^{18} - 80 q^{19} + 61 q^{20} - 177 q^{21} + 688 q^{22} - 274 q^{23} - 351 q^{24} + 193 q^{25} - 180 q^{26} + 189 q^{27} - 118 q^{28} - 406 q^{29} - 237 q^{30} - 346 q^{31} - 854 q^{32} - 393 q^{33} + 178 q^{34} - 424 q^{35} + 198 q^{36} - 157 q^{37} - 129 q^{38} - 369 q^{39} - 590 q^{40} - 825 q^{41} - 351 q^{42} - 815 q^{43} - 1690 q^{44} - 252 q^{45} + 1457 q^{46} - 1196 q^{47} + 606 q^{48} + 914 q^{49} + 713 q^{50} - 705 q^{51} + 1030 q^{52} - 900 q^{53} - 216 q^{54} - 1044 q^{55} + 2172 q^{56} - 240 q^{57} + 1242 q^{58} - 413 q^{59} + 183 q^{60} + 420 q^{61} + 646 q^{62} - 531 q^{63} + 3541 q^{64} + 190 q^{65} + 2064 q^{66} + 1316 q^{67} - 611 q^{68} - 822 q^{69} + 4658 q^{70} - 173 q^{71} - 1053 q^{72} - 418 q^{73} + 660 q^{74} + 579 q^{75} + 1540 q^{76} - 753 q^{77} - 540 q^{78} + 2635 q^{79} + 6155 q^{80} + 567 q^{81} - 125 q^{82} + 457 q^{83} - 354 q^{84} + 1270 q^{85} + 3482 q^{86} - 1218 q^{87} + 7685 q^{88} + 592 q^{89} - 711 q^{90} + 3179 q^{91} - 3500 q^{92} - 1038 q^{93} + 2064 q^{94} - 2250 q^{95} - 2562 q^{96} - 1906 q^{97} + 2994 q^{98} - 1179 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 + 21 * q^3 + 22 * q^4 - 28 * q^5 - 24 * q^6 - 59 * q^7 - 117 * q^8 + 63 * q^9 - 79 * q^10 - 131 * q^11 + 66 * q^12 - 123 * q^13 - 117 * q^14 - 84 * q^15 + 202 * q^16 - 235 * q^17 - 72 * q^18 - 80 * q^19 + 61 * q^20 - 177 * q^21 + 688 * q^22 - 274 * q^23 - 351 * q^24 + 193 * q^25 - 180 * q^26 + 189 * q^27 - 118 * q^28 - 406 * q^29 - 237 * q^30 - 346 * q^31 - 854 * q^32 - 393 * q^33 + 178 * q^34 - 424 * q^35 + 198 * q^36 - 157 * q^37 - 129 * q^38 - 369 * q^39 - 590 * q^40 - 825 * q^41 - 351 * q^42 - 815 * q^43 - 1690 * q^44 - 252 * q^45 + 1457 * q^46 - 1196 * q^47 + 606 * q^48 + 914 * q^49 + 713 * q^50 - 705 * q^51 + 1030 * q^52 - 900 * q^53 - 216 * q^54 - 1044 * q^55 + 2172 * q^56 - 240 * q^57 + 1242 * q^58 - 413 * q^59 + 183 * q^60 + 420 * q^61 + 646 * q^62 - 531 * q^63 + 3541 * q^64 + 190 * q^65 + 2064 * q^66 + 1316 * q^67 - 611 * q^68 - 822 * q^69 + 4658 * q^70 - 173 * q^71 - 1053 * q^72 - 418 * q^73 + 660 * q^74 + 579 * q^75 + 1540 * q^76 - 753 * q^77 - 540 * q^78 + 2635 * q^79 + 6155 * q^80 + 567 * q^81 - 125 * q^82 + 457 * q^83 - 354 * q^84 + 1270 * q^85 + 3482 * q^86 - 1218 * q^87 + 7685 * q^88 + 592 * q^89 - 711 * q^90 + 3179 * q^91 - 3500 * q^92 - 1038 * q^93 + 2064 * q^94 - 2250 * q^95 - 2562 * q^96 - 1906 * q^97 + 2994 * q^98 - 1179 * q^99

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