LMFDB - Embedded newform 4013.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79865 q^{2} +3.21303 q^{3} +5.83245 q^{4} +0.484406 q^{5} -8.99216 q^{6} +2.55250 q^{7} -10.7257 q^{8} +7.32359 q^{9} +O(q^{10})$	\(q-2.79865 q^{2} +3.21303 q^{3} +5.83245 q^{4} +0.484406 q^{5} -8.99216 q^{6} +2.55250 q^{7} -10.7257 q^{8} +7.32359 q^{9} -1.35568 q^{10} -1.90936 q^{11} +18.7398 q^{12} +6.50595 q^{13} -7.14354 q^{14} +1.55641 q^{15} +18.3525 q^{16} -0.494095 q^{17} -20.4962 q^{18} -4.44873 q^{19} +2.82527 q^{20} +8.20125 q^{21} +5.34363 q^{22} +1.77065 q^{23} -34.4620 q^{24} -4.76535 q^{25} -18.2079 q^{26} +13.8918 q^{27} +14.8873 q^{28} +6.55412 q^{29} -4.35586 q^{30} +2.27872 q^{31} -29.9110 q^{32} -6.13483 q^{33} +1.38280 q^{34} +1.23644 q^{35} +42.7144 q^{36} -2.96860 q^{37} +12.4505 q^{38} +20.9038 q^{39} -5.19559 q^{40} +10.2218 q^{41} -22.9524 q^{42} +7.42382 q^{43} -11.1362 q^{44} +3.54759 q^{45} -4.95542 q^{46} -1.06490 q^{47} +58.9674 q^{48} -0.484766 q^{49} +13.3366 q^{50} -1.58754 q^{51} +37.9456 q^{52} -7.01832 q^{53} -38.8784 q^{54} -0.924905 q^{55} -27.3773 q^{56} -14.2939 q^{57} -18.3427 q^{58} -8.54717 q^{59} +9.07770 q^{60} -1.54454 q^{61} -6.37734 q^{62} +18.6934 q^{63} +47.0054 q^{64} +3.15152 q^{65} +17.1693 q^{66} -6.76345 q^{67} -2.88178 q^{68} +5.68914 q^{69} -3.46038 q^{70} -5.54528 q^{71} -78.5505 q^{72} +12.7695 q^{73} +8.30807 q^{74} -15.3112 q^{75} -25.9470 q^{76} -4.87363 q^{77} -58.5026 q^{78} -2.08141 q^{79} +8.89009 q^{80} +22.6641 q^{81} -28.6072 q^{82} -15.4551 q^{83} +47.8334 q^{84} -0.239342 q^{85} -20.7767 q^{86} +21.0586 q^{87} +20.4792 q^{88} +11.1723 q^{89} -9.92846 q^{90} +16.6064 q^{91} +10.3272 q^{92} +7.32160 q^{93} +2.98027 q^{94} -2.15499 q^{95} -96.1051 q^{96} -1.22651 q^{97} +1.35669 q^{98} -13.9833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.79865	−1.97895	−0.989473	−	0.144721i	$-0.953772\pi$
$2$	−2.79865	−1.97895	−0.989473	+	0.144721i	$0.953772\pi$
$3$	3.21303	1.85505	0.927523	−	0.373766i	$-0.121934\pi$
$3$	3.21303	1.85505	0.927523	+	0.373766i	$0.121934\pi$
$4$	5.83245	2.91622
$5$	0.484406	0.216633	0.108316	−	0.994116i	$-0.465454\pi$
$5$	0.484406	0.216633	0.108316	+	0.994116i	$0.465454\pi$
$6$	−8.99216	−3.67103
$7$	2.55250	0.964753	0.482376	−	0.875964i	$-0.339774\pi$
$7$	2.55250	0.964753	0.482376	+	0.875964i	$0.339774\pi$
$8$	−10.7257	−3.79210
$9$	7.32359	2.44120
$10$	−1.35568	−0.428705
$11$	−1.90936	−0.575693	−0.287847	−	0.957677i	$-0.592939\pi$
$11$	−1.90936	−0.575693	−0.287847	+	0.957677i	$0.592939\pi$
$12$	18.7398	5.40973
$13$	6.50595	1.80443	0.902213	−	0.431290i	$-0.141941\pi$
$13$	6.50595	1.80443	0.902213	+	0.431290i	$0.141941\pi$
$14$	−7.14354	−1.90919
$15$	1.55641	0.401864
$16$	18.3525	4.58814
$17$	−0.494095	−0.119836	−0.0599178	−	0.998203i	$-0.519084\pi$
$17$	−0.494095	−0.119836	−0.0599178	+	0.998203i	$0.519084\pi$
$18$	−20.4962	−4.83099
$19$	−4.44873	−1.02061	−0.510305	−	0.859994i	$-0.670467\pi$
$19$	−4.44873	−1.02061	−0.510305	+	0.859994i	$0.670467\pi$
$20$	2.82527	0.631750
$21$	8.20125	1.78966
$22$	5.34363	1.13927
$23$	1.77065	0.369205	0.184603	−	0.982813i	$-0.440900\pi$
$23$	1.77065	0.369205	0.184603	+	0.982813i	$0.440900\pi$
$24$	−34.4620	−7.03452
$25$	−4.76535	−0.953070
$26$	−18.2079	−3.57086
$27$	13.8918	2.67348
$28$	14.8873	2.81343
$29$	6.55412	1.21707	0.608534	−	0.793527i	$-0.291758\pi$
$29$	6.55412	1.21707	0.608534	+	0.793527i	$0.291758\pi$
$30$	−4.35586	−0.795267
$31$	2.27872	0.409270	0.204635	−	0.978838i	$-0.434399\pi$
$31$	2.27872	0.409270	0.204635	+	0.978838i	$0.434399\pi$
$32$	−29.9110	−5.28757
$33$	−6.13483	−1.06794
$34$	1.38280	0.237148
$35$	1.23644	0.208997
$36$	42.7144	7.11907
$37$	−2.96860	−0.488035	−0.244017	−	0.969771i	$-0.578465\pi$
$37$	−2.96860	−0.488035	−0.244017	+	0.969771i	$0.578465\pi$
$38$	12.4505	2.01973
$39$	20.9038	3.34729
$40$	−5.19559	−0.821494
$41$	10.2218	1.59637	0.798187	−	0.602410i	$-0.205793\pi$
$41$	10.2218	1.59637	0.798187	+	0.602410i	$0.205793\pi$
$42$	−22.9524	−3.54164
$43$	7.42382	1.13212	0.566061	−	0.824363i	$-0.308467\pi$
$43$	7.42382	1.13212	0.566061	+	0.824363i	$0.308467\pi$
$44$	−11.1362	−1.67885
$45$	3.54759	0.528843
$46$	−4.95542	−0.730637
$47$	−1.06490	−0.155331	−0.0776655	−	0.996979i	$-0.524747\pi$
$47$	−1.06490	−0.155331	−0.0776655	+	0.996979i	$0.524747\pi$
$48$	58.9674	8.51120
$49$	−0.484766	−0.0692522
$50$	13.3366	1.88607
$51$	−1.58754	−0.222300
$52$	37.9456	5.26211
$53$	−7.01832	−0.964041	−0.482020	−	0.876160i	$-0.660097\pi$
$53$	−7.01832	−0.964041	−0.482020	+	0.876160i	$0.660097\pi$
$54$	−38.8784	−5.29068
$55$	−0.924905	−0.124714
$56$	−27.3773	−3.65844
$57$	−14.2939	−1.89328
$58$	−18.3427	−2.40851
$59$	−8.54717	−1.11275	−0.556374	−	0.830932i	$-0.687808\pi$
$59$	−8.54717	−1.11275	−0.556374	+	0.830932i	$0.687808\pi$
$60$	9.07770	1.17193
$61$	−1.54454	−0.197758	−0.0988791	−	0.995099i	$-0.531526\pi$
$61$	−1.54454	−0.197758	−0.0988791	+	0.995099i	$0.531526\pi$
$62$	−6.37734	−0.809923
$63$	18.6934	2.35515
$64$	47.0054	5.87567
$65$	3.15152	0.390898
$66$	17.1693	2.11339
$67$	−6.76345	−0.826287	−0.413144	−	0.910666i	$-0.635569\pi$
$67$	−6.76345	−0.826287	−0.413144	+	0.910666i	$0.635569\pi$
$68$	−2.88178	−0.349467
$69$	5.68914	0.684892
$70$	−3.46038	−0.413594
$71$	−5.54528	−0.658103	−0.329052	−	0.944312i	$-0.606729\pi$
$71$	−5.54528	−0.658103	−0.329052	+	0.944312i	$0.606729\pi$
$72$	−78.5505	−9.25726
$73$	12.7695	1.49456	0.747280	−	0.664509i	$-0.231359\pi$
$73$	12.7695	1.49456	0.747280	+	0.664509i	$0.231359\pi$
$74$	8.30807	0.965794
$75$	−15.3112	−1.76799
$76$	−25.9470	−2.97633
$77$	−4.87363	−0.555402
$78$	−58.5026	−6.62411
$79$	−2.08141	−0.234177	−0.117088	−	0.993122i	$-0.537356\pi$
$79$	−2.08141	−0.234177	−0.117088	+	0.993122i	$0.537356\pi$
$80$	8.89009	0.993942
$81$	22.6641	2.51824
$82$	−28.6072	−3.15914
$83$	−15.4551	−1.69642	−0.848211	−	0.529658i	$-0.822320\pi$
$83$	−15.4551	−1.69642	−0.848211	+	0.529658i	$0.822320\pi$
$84$	47.8334	5.21905
$85$	−0.239342	−0.0259603
$86$	−20.7767	−2.24041
$87$	21.0586	2.25772
$88$	20.4792	2.18309
$89$	11.1723	1.18426	0.592131	−	0.805842i	$-0.298287\pi$
$89$	11.1723	1.18426	0.592131	+	0.805842i	$0.298287\pi$
$90$	−9.92846	−1.04655
$91$	16.6064	1.74083
$92$	10.3272	1.07668
$93$	7.32160	0.759215
$94$	2.98027	0.307392
$95$	−2.15499	−0.221098
$96$	−96.1051	−9.80868
$97$	−1.22651	−0.124533	−0.0622667	−	0.998060i	$-0.519833\pi$
$97$	−1.22651	−0.124533	−0.0622667	+	0.998060i	$0.519833\pi$
$98$	1.35669	0.137046
$99$	−13.9833	−1.40538
$100$	−27.7937	−2.77937
$101$	5.73401	0.570556	0.285278	−	0.958445i	$-0.407914\pi$
$101$	5.73401	0.570556	0.285278	+	0.958445i	$0.407914\pi$
$102$	4.44298	0.439920
$103$	20.0744	1.97799	0.988994	−	0.147954i	$-0.0472688\pi$
$103$	20.0744	1.97799	0.988994	+	0.147954i	$0.0472688\pi$
$104$	−69.7808	−6.84257
$105$	3.97274	0.387699
$106$	19.6418	1.90778
$107$	3.20158	0.309509	0.154754	−	0.987953i	$-0.450541\pi$
$107$	3.20158	0.309509	0.154754	+	0.987953i	$0.450541\pi$
$108$	81.0233	7.79647
$109$	0.756379	0.0724480	0.0362240	−	0.999344i	$-0.488467\pi$
$109$	0.756379	0.0724480	0.0362240	+	0.999344i	$0.488467\pi$
$110$	2.58849	0.246802
$111$	−9.53821	−0.905327
$112$	46.8448	4.42642
$113$	−19.8856	−1.87068	−0.935339	−	0.353754i	$-0.884905\pi$
$113$	−19.8856	−1.87068	−0.935339	+	0.353754i	$0.884905\pi$
$114$	40.0037	3.74669
$115$	0.857711	0.0799820
$116$	38.2265	3.54925
$117$	47.6469	4.40496
$118$	23.9206	2.20207
$119$	−1.26117	−0.115612
$120$	−16.6936	−1.52391
$121$	−7.35435	−0.668577
$122$	4.32263	0.391353
$123$	32.8429	2.96135
$124$	13.2905	1.19352
$125$	−4.73040	−0.423099
$126$	−52.3164	−4.66071
$127$	18.3122	1.62495	0.812474	−	0.582997i	$-0.198120\pi$
$127$	18.3122	1.62495	0.812474	+	0.582997i	$0.198120\pi$
$128$	−71.7296	−6.34006
$129$	23.8530	2.10014
$130$	−8.82001	−0.773566
$131$	7.00937	0.612411	0.306206	−	0.951965i	$-0.400940\pi$
$131$	7.00937	0.612411	0.306206	+	0.951965i	$0.400940\pi$
$132$	−35.7811	−3.11434
$133$	−11.3554	−0.984636
$134$	18.9285	1.63518
$135$	6.72928	0.579165
$136$	5.29950	0.454429
$137$	−22.3348	−1.90819	−0.954094	−	0.299508i	$-0.903177\pi$
$137$	−22.3348	−1.90819	−0.954094	+	0.299508i	$0.903177\pi$
$138$	−15.9219	−1.35536
$139$	−13.4348	−1.13953	−0.569763	−	0.821809i	$-0.692965\pi$
$139$	−13.4348	−1.13953	−0.569763	+	0.821809i	$0.692965\pi$
$140$	7.21150	0.609483
$141$	−3.42155	−0.288146
$142$	15.5193	1.30235
$143$	−12.4222	−1.03880
$144$	134.406	11.2005
$145$	3.17485	0.263657
$146$	−35.7375	−2.95765
$147$	−1.55757	−0.128466
$148$	−17.3142	−1.42322
$149$	5.51126	0.451500	0.225750	−	0.974185i	$-0.427517\pi$
$149$	5.51126	0.451500	0.225750	+	0.974185i	$0.427517\pi$
$150$	42.8508	3.49875
$151$	0.963613	0.0784177	0.0392088	−	0.999231i	$-0.487516\pi$
$151$	0.963613	0.0784177	0.0392088	+	0.999231i	$0.487516\pi$
$152$	47.7157	3.87026
$153$	−3.61854	−0.292542
$154$	13.6396	1.09911
$155$	1.10383	0.0886614
$156$	121.921	9.76146
$157$	16.3695	1.30643	0.653215	−	0.757172i	$-0.273420\pi$
$157$	16.3695	1.30643	0.653215	+	0.757172i	$0.273420\pi$
$158$	5.82514	0.463423
$159$	−22.5501	−1.78834
$160$	−14.4891	−1.14546
$161$	4.51956	0.356192
$162$	−63.4290	−4.98346
$163$	3.55785	0.278672	0.139336	−	0.990245i	$-0.455503\pi$
$163$	3.55785	0.278672	0.139336	+	0.990245i	$0.455503\pi$
$164$	59.6180	4.65538
$165$	−2.97175	−0.231350
$166$	43.2536	3.35713
$167$	12.4014	0.959652	0.479826	−	0.877364i	$-0.340700\pi$
$167$	12.4014	0.959652	0.479826	+	0.877364i	$0.340700\pi$
$168$	−87.9641	−6.78657
$169$	29.3274	2.25596
$170$	0.669836	0.0513741
$171$	−32.5807	−2.49151
$172$	43.2991	3.30152
$173$	−5.67628	−0.431560	−0.215780	−	0.976442i	$-0.569229\pi$
$173$	−5.67628	−0.431560	−0.215780	+	0.976442i	$0.569229\pi$
$174$	−58.9357	−4.46790
$175$	−12.1635	−0.919477
$176$	−35.0416	−2.64136
$177$	−27.4624	−2.06420
$178$	−31.2674	−2.34359
$179$	3.40454	0.254467	0.127234	−	0.991873i	$-0.459390\pi$
$179$	3.40454	0.254467	0.127234	+	0.991873i	$0.459390\pi$
$180$	20.6911	1.54223
$181$	2.18334	0.162287	0.0811434	−	0.996702i	$-0.474143\pi$
$181$	2.18334	0.162287	0.0811434	+	0.996702i	$0.474143\pi$
$182$	−46.4756	−3.44500
$183$	−4.96266	−0.366851
$184$	−18.9914	−1.40006
$185$	−1.43801	−0.105724
$186$	−20.4906	−1.50244
$187$	0.943404	0.0689885
$188$	−6.21095	−0.452980
$189$	35.4588	2.57925
$190$	6.03108	0.437540
$191$	−5.38261	−0.389472	−0.194736	−	0.980856i	$-0.562385\pi$
$191$	−5.38261	−0.389472	−0.194736	+	0.980856i	$0.562385\pi$
$192$	151.030	10.8996
$193$	−23.9893	−1.72679	−0.863393	−	0.504533i	$-0.831665\pi$
$193$	−23.9893	−1.72679	−0.863393	+	0.504533i	$0.831665\pi$
$194$	3.43258	0.246445
$195$	10.1259	0.725134
$196$	−2.82737	−0.201955
$197$	15.9060	1.13326	0.566629	−	0.823973i	$-0.308247\pi$
$197$	15.9060	1.13326	0.566629	+	0.823973i	$0.308247\pi$
$198$	39.1345	2.78117
$199$	−6.26694	−0.444252	−0.222126	−	0.975018i	$-0.571300\pi$
$199$	−6.26694	−0.444252	−0.222126	+	0.975018i	$0.571300\pi$
$200$	51.1116	3.61414
$201$	−21.7312	−1.53280
$202$	−16.0475	−1.12910
$203$	16.7294	1.17417
$204$	−9.25926	−0.648278
$205$	4.95149	0.345827
$206$	−56.1812	−3.91433
$207$	12.9675	0.901302
$208$	119.401	8.27896
$209$	8.49423	0.587558
$210$	−11.1183	−0.767236
$211$	−0.548383	−0.0377522	−0.0188761	−	0.999822i	$-0.506009\pi$
$211$	−0.548383	−0.0377522	−0.0188761	+	0.999822i	$0.506009\pi$
$212$	−40.9340	−2.81136
$213$	−17.8172	−1.22081
$214$	−8.96011	−0.612501
$215$	3.59615	0.245255
$216$	−148.999	−10.1381
$217$	5.81642	0.394844
$218$	−2.11684	−0.143371
$219$	41.0289	2.77248
$220$	−5.39446	−0.363694
$221$	−3.21456	−0.216234
$222$	26.6941	1.79159
$223$	−0.965604	−0.0646616	−0.0323308	−	0.999477i	$-0.510293\pi$
$223$	−0.965604	−0.0646616	−0.0323308	+	0.999477i	$0.510293\pi$
$224$	−76.3477	−5.10120
$225$	−34.8995	−2.32663
$226$	55.6528	3.70197
$227$	6.01791	0.399423	0.199711	−	0.979855i	$-0.436000\pi$
$227$	6.01791	0.399423	0.199711	+	0.979855i	$0.436000\pi$
$228$	−83.3686	−5.52122
$229$	4.64644	0.307046	0.153523	−	0.988145i	$-0.450938\pi$
$229$	4.64644	0.307046	0.153523	+	0.988145i	$0.450938\pi$
$230$	−2.40043	−0.158280
$231$	−15.6591	−1.03030
$232$	−70.2974	−4.61525
$233$	−3.34712	−0.219277	−0.109638	−	0.993972i	$-0.534969\pi$
$233$	−3.34712	−0.219277	−0.109638	+	0.993972i	$0.534969\pi$
$234$	−133.347	−8.71717
$235$	−0.515842	−0.0336498
$236$	−49.8509	−3.24502
$237$	−6.68764	−0.434409
$238$	3.52959	0.228789
$239$	18.7680	1.21400	0.607000	−	0.794702i	$-0.292373\pi$
$239$	18.7680	1.21400	0.607000	+	0.794702i	$0.292373\pi$
$240$	28.5641	1.84381
$241$	−17.6507	−1.13698	−0.568489	−	0.822691i	$-0.692472\pi$
$241$	−17.6507	−1.13698	−0.568489	+	0.822691i	$0.692472\pi$
$242$	20.5823	1.32308
$243$	31.1452	1.99796
$244$	−9.00845	−0.576707
$245$	−0.234823	−0.0150023
$246$	−91.9159	−5.86034
$247$	−28.9433	−1.84162
$248$	−24.4408	−1.55199
$249$	−49.6579	−3.14694
$250$	13.2387	0.837290
$251$	6.22809	0.393113	0.196557	−	0.980492i	$-0.437024\pi$
$251$	6.22809	0.393113	0.196557	+	0.980492i	$0.437024\pi$
$252$	109.028	6.86814
$253$	−3.38080	−0.212549
$254$	−51.2496	−3.21568
$255$	−0.769015	−0.0481576
$256$	106.735	6.67097
$257$	−15.7295	−0.981181	−0.490590	−	0.871390i	$-0.663219\pi$
$257$	−15.7295	−0.981181	−0.490590	+	0.871390i	$0.663219\pi$
$258$	−66.7562	−4.15606
$259$	−7.57734	−0.470833
$260$	18.3811	1.13995
$261$	47.9996	2.97110
$262$	−19.6168	−1.21193
$263$	4.04112	0.249186	0.124593	−	0.992208i	$-0.460237\pi$
$263$	4.04112	0.249186	0.124593	+	0.992208i	$0.460237\pi$
$264$	65.8003	4.04973
$265$	−3.39972	−0.208843
$266$	31.7797	1.94854
$267$	35.8970	2.19686
$268$	−39.4475	−2.40964
$269$	−3.01183	−0.183634	−0.0918172	−	0.995776i	$-0.529268\pi$
$269$	−3.01183	−0.183634	−0.0918172	+	0.995776i	$0.529268\pi$
$270$	−18.8329	−1.14613
$271$	−19.6193	−1.19179	−0.595893	−	0.803064i	$-0.703202\pi$
$271$	−19.6193	−1.19179	−0.595893	+	0.803064i	$0.703202\pi$
$272$	−9.06790	−0.549822
$273$	53.3570	3.22931
$274$	62.5072	3.77620
$275$	9.09876	0.548676
$276$	33.1816	1.99730
$277$	−26.9573	−1.61971	−0.809853	−	0.586633i	$-0.800453\pi$
$277$	−26.9573	−1.61971	−0.809853	+	0.586633i	$0.800453\pi$
$278$	37.5994	2.25506
$279$	16.6884	0.999108
$280$	−13.2617	−0.792539
$281$	−4.02133	−0.239893	−0.119946	−	0.992780i	$-0.538272\pi$
$281$	−4.02133	−0.239893	−0.119946	+	0.992780i	$0.538272\pi$
$282$	9.57572	0.570226
$283$	9.85733	0.585957	0.292979	−	0.956119i	$-0.405354\pi$
$283$	9.85733	0.585957	0.292979	+	0.956119i	$0.405354\pi$
$284$	−32.3425	−1.91918
$285$	−6.92407	−0.410146
$286$	34.7654	2.05572
$287$	26.0911	1.54011
$288$	−219.056	−12.9080
$289$	−16.7559	−0.985639
$290$	−8.88531	−0.521763
$291$	−3.94082	−0.231015
$292$	74.4776	4.35847
$293$	−26.9952	−1.57708	−0.788539	−	0.614984i	$-0.789162\pi$
$293$	−26.9952	−1.57708	−0.788539	+	0.614984i	$0.789162\pi$
$294$	4.35909	0.254227
$295$	−4.14030	−0.241058
$296$	31.8403	1.85068
$297$	−26.5245	−1.53911
$298$	−15.4241	−0.893494
$299$	11.5197	0.666204
$300$	−89.3020	−5.15585
$301$	18.9493	1.09222
$302$	−2.69682	−0.155184
$303$	18.4236	1.05841
$304$	−81.6456	−4.68270
$305$	−0.748185	−0.0428410
$306$	10.1270	0.578925
$307$	−15.1976	−0.867375	−0.433688	−	0.901063i	$-0.642788\pi$
$307$	−15.1976	−0.867375	−0.433688	+	0.901063i	$0.642788\pi$
$308$	−28.4252	−1.61968
$309$	64.4997	3.66926
$310$	−3.08922	−0.175456
$311$	24.6464	1.39757	0.698785	−	0.715332i	$-0.253725\pi$
$311$	24.6464	1.39757	0.698785	+	0.715332i	$0.253725\pi$
$312$	−224.208	−12.6933
$313$	−31.7088	−1.79229	−0.896143	−	0.443764i	$-0.853643\pi$
$313$	−31.7088	−1.79229	−0.896143	+	0.443764i	$0.853643\pi$
$314$	−45.8126	−2.58535
$315$	9.05521	0.510203
$316$	−12.1397	−0.682912
$317$	0.802946	0.0450979	0.0225490	−	0.999746i	$-0.492822\pi$
$317$	0.802946	0.0450979	0.0225490	+	0.999746i	$0.492822\pi$
$318$	63.1099	3.53903
$319$	−12.5142	−0.700658
$320$	22.7697	1.27286
$321$	10.2868	0.574153
$322$	−12.6487	−0.704884
$323$	2.19810	0.122305
$324$	132.187	7.34375
$325$	−31.0031	−1.71975
$326$	−9.95718	−0.551477
$327$	2.43027	0.134394
$328$	−109.636	−6.05361
$329$	−2.71814	−0.149856
$330$	8.31689	0.457830
$331$	26.2278	1.44161	0.720805	−	0.693138i	$-0.243772\pi$
$331$	26.2278	1.44161	0.720805	+	0.693138i	$0.243772\pi$
$332$	−90.1413	−4.94715
$333$	−21.7408	−1.19139
$334$	−34.7073	−1.89910
$335$	−3.27626	−0.179001
$336$	150.514	8.21121
$337$	−4.79315	−0.261099	−0.130550	−	0.991442i	$-0.541674\pi$
$337$	−4.79315	−0.261099	−0.130550	+	0.991442i	$0.541674\pi$
$338$	−82.0772	−4.46441
$339$	−63.8930	−3.47019
$340$	−1.39595	−0.0757061
$341$	−4.35089	−0.235614
$342$	91.1820	4.93056
$343$	−19.1048	−1.03156
$344$	−79.6256	−4.29312
$345$	2.75586	0.148370
$346$	15.8859	0.854033
$347$	31.2655	1.67842	0.839211	−	0.543806i	$-0.183017\pi$
$347$	31.2655	1.67842	0.839211	+	0.543806i	$0.183017\pi$
$348$	122.823	6.58401
$349$	−13.1490	−0.703849	−0.351925	−	0.936028i	$-0.614473\pi$
$349$	−13.1490	−0.703849	−0.351925	+	0.936028i	$0.614473\pi$
$350$	34.0415	1.81959
$351$	90.3796	4.82410
$352$	57.1108	3.04402
$353$	−13.0834	−0.696361	−0.348180	−	0.937428i	$-0.613200\pi$
$353$	−13.0834	−0.696361	−0.348180	+	0.937428i	$0.613200\pi$
$354$	76.8575	4.08493
$355$	−2.68617	−0.142567
$356$	65.1619	3.45357
$357$	−4.05220	−0.214465
$358$	−9.52812	−0.503577
$359$	18.8621	0.995501	0.497751	−	0.867320i	$-0.334159\pi$
$359$	18.8621	0.995501	0.497751	+	0.867320i	$0.334159\pi$
$360$	−38.0503	−2.00543
$361$	0.791241	0.0416443
$362$	−6.11042	−0.321156
$363$	−23.6298	−1.24024
$364$	96.8561	5.07664
$365$	6.18564	0.323771
$366$	13.8888	0.725977
$367$	−7.73078	−0.403544	−0.201772	−	0.979433i	$-0.564670\pi$
$367$	−7.73078	−0.403544	−0.201772	+	0.979433i	$0.564670\pi$
$368$	32.4959	1.69396
$369$	74.8601	3.89706
$370$	4.02448	0.209223
$371$	−17.9142	−0.930061
$372$	42.7029	2.21404
$373$	3.40056	0.176074	0.0880371	−	0.996117i	$-0.471941\pi$
$373$	3.40056	0.176074	0.0880371	+	0.996117i	$0.471941\pi$
$374$	−2.64026	−0.136524
$375$	−15.1989	−0.784869
$376$	11.4217	0.589031
$377$	42.6408	2.19611
$378$	−99.2369	−5.10419
$379$	−22.9861	−1.18072	−0.590358	−	0.807142i	$-0.701013\pi$
$379$	−22.9861	−1.18072	−0.590358	+	0.807142i	$0.701013\pi$
$380$	−12.5689	−0.644770
$381$	58.8378	3.01435
$382$	15.0640	0.770744
$383$	−20.9855	−1.07231	−0.536155	−	0.844119i	$-0.680124\pi$
$383$	−20.9855	−1.07231	−0.536155	+	0.844119i	$0.680124\pi$
$384$	−230.470	−11.7611
$385$	−2.36082	−0.120318
$386$	67.1376	3.41721
$387$	54.3690	2.76373
$388$	−7.15356	−0.363167
$389$	−35.5701	−1.80348	−0.901739	−	0.432282i	$-0.857709\pi$
$389$	−35.5701	−1.80348	−0.901739	+	0.432282i	$0.857709\pi$
$390$	−28.3390	−1.43500
$391$	−0.874866	−0.0442439
$392$	5.19944	0.262612
$393$	22.5213	1.13605
$394$	−44.5154	−2.24266
$395$	−1.00825	−0.0507304
$396$	−81.5572	−4.09840
$397$	30.7259	1.54209	0.771044	−	0.636782i	$-0.219735\pi$
$397$	30.7259	1.54209	0.771044	+	0.636782i	$0.219735\pi$
$398$	17.5390	0.879150
$399$	−36.4852	−1.82654
$400$	−87.4563	−4.37282
$401$	−14.3758	−0.717895	−0.358947	−	0.933358i	$-0.616864\pi$
$401$	−14.3758	−0.717895	−0.358947	+	0.933358i	$0.616864\pi$
$402$	60.8181	3.03333
$403$	14.8252	0.738498
$404$	33.4433	1.66387
$405$	10.9787	0.545534
$406$	−46.8196	−2.32362
$407$	5.66812	0.280958
$408$	17.0275	0.842986
$409$	13.2979	0.657536	0.328768	−	0.944411i	$-0.393367\pi$
$409$	13.2979	0.657536	0.328768	+	0.944411i	$0.393367\pi$
$410$	−13.8575	−0.684373
$411$	−71.7623	−3.53978
$412$	117.083	5.76826
$413$	−21.8166	−1.07353
$414$	−36.2914	−1.78363
$415$	−7.48657	−0.367501
$416$	−194.600	−9.54103
$417$	−43.1665	−2.11387
$418$	−23.7724	−1.16275
$419$	−24.1691	−1.18074	−0.590368	−	0.807134i	$-0.701017\pi$
$419$	−24.1691	−1.18074	−0.590368	+	0.807134i	$0.701017\pi$
$420$	23.1708	1.13062
$421$	−17.7549	−0.865319	−0.432659	−	0.901557i	$-0.642425\pi$
$421$	−17.7549	−0.865319	−0.432659	+	0.901557i	$0.642425\pi$
$422$	1.53473	0.0747096
$423$	−7.79886	−0.379193
$424$	75.2763	3.65574
$425$	2.35453	0.114212
$426$	49.8640	2.41592
$427$	−3.94243	−0.190788
$428$	18.6731	0.902596
$429$	−39.9129	−1.92701
$430$	−10.0644	−0.485346
$431$	32.8702	1.58330	0.791651	−	0.610973i	$-0.209222\pi$
$431$	32.8702	1.58330	0.791651	+	0.610973i	$0.209222\pi$
$432$	254.950	12.2663
$433$	6.18392	0.297180	0.148590	−	0.988899i	$-0.452526\pi$
$433$	6.18392	0.297180	0.148590	+	0.988899i	$0.452526\pi$
$434$	−16.2781	−0.781375
$435$	10.2009	0.489096
$436$	4.41154	0.211274
$437$	−7.87713	−0.376814
$438$	−114.826	−5.48658
$439$	7.50917	0.358393	0.179197	−	0.983813i	$-0.442650\pi$
$439$	7.50917	0.358393	0.179197	+	0.983813i	$0.442650\pi$
$440$	9.92024	0.472929
$441$	−3.55022	−0.169058
$442$	8.99642	0.427916
$443$	30.7323	1.46014	0.730068	−	0.683375i	$-0.239489\pi$
$443$	30.7323	1.46014	0.730068	+	0.683375i	$0.239489\pi$
$444$	−55.6311	−2.64014
$445$	5.41193	0.256550
$446$	2.70239	0.127962
$447$	17.7079	0.837554
$448$	119.981	5.66857
$449$	−12.5273	−0.591200	−0.295600	−	0.955312i	$-0.595520\pi$
$449$	−12.5273	−0.591200	−0.295600	+	0.955312i	$0.595520\pi$
$450$	97.6714	4.60427
$451$	−19.5170	−0.919022
$452$	−115.982	−5.45531
$453$	3.09612	0.145468
$454$	−16.8420	−0.790435
$455$	8.04425	0.377120
$456$	153.312	7.17950
$457$	15.6076	0.730094	0.365047	−	0.930989i	$-0.381053\pi$
$457$	15.6076	0.730094	0.365047	+	0.930989i	$0.381053\pi$
$458$	−13.0038	−0.607626
$459$	−6.86388	−0.320378
$460$	5.00256	0.233245
$461$	15.0910	0.702856	0.351428	−	0.936215i	$-0.385696\pi$
$461$	15.0910	0.702856	0.351428	+	0.936215i	$0.385696\pi$
$462$	43.8245	2.03890
$463$	25.2266	1.17238	0.586189	−	0.810174i	$-0.300628\pi$
$463$	25.2266	1.17238	0.586189	+	0.810174i	$0.300628\pi$
$464$	120.285	5.58408
$465$	3.54663	0.164471
$466$	9.36741	0.433937
$467$	30.6972	1.42050	0.710249	−	0.703951i	$-0.248582\pi$
$467$	30.6972	1.42050	0.710249	+	0.703951i	$0.248582\pi$
$468$	277.898	12.8458
$469$	−17.2637	−0.797163
$470$	1.44366	0.0665912
$471$	52.5958	2.42349
$472$	91.6743	4.21965
$473$	−14.1747	−0.651755
$474$	18.7164	0.859671
$475$	21.1998	0.972713
$476$	−7.35573	−0.337150
$477$	−51.3993	−2.35341
$478$	−52.5251	−2.40244
$479$	−19.4508	−0.888732	−0.444366	−	0.895845i	$-0.646571\pi$
$479$	−19.4508	−0.888732	−0.444366	+	0.895845i	$0.646571\pi$
$480$	−46.5539	−2.12488
$481$	−19.3136	−0.880623
$482$	49.3980	2.25002
$483$	14.5215	0.660752
$484$	−42.8939	−1.94972
$485$	−0.594129	−0.0269780
$486$	−87.1645	−3.95386
$487$	−18.6571	−0.845432	−0.422716	−	0.906262i	$-0.638923\pi$
$487$	−18.6571	−0.845432	−0.422716	+	0.906262i	$0.638923\pi$
$488$	16.5663	0.749919
$489$	11.4315	0.516950
$490$	0.657189	0.0296888
$491$	25.5725	1.15407	0.577036	−	0.816719i	$-0.304209\pi$
$491$	25.5725	1.15407	0.577036	+	0.816719i	$0.304209\pi$
$492$	191.555	8.63595
$493$	−3.23835	−0.145848
$494$	81.0021	3.64446
$495$	−6.77362	−0.304452
$496$	41.8203	1.87779
$497$	−14.1543	−0.634907
$498$	138.975	6.22762
$499$	21.5189	0.963319	0.481659	−	0.876359i	$-0.340034\pi$
$499$	21.5189	0.963319	0.481659	+	0.876359i	$0.340034\pi$
$500$	−27.5898	−1.23385
$501$	39.8462	1.78020
$502$	−17.4302	−0.777950
$503$	−9.97793	−0.444894	−0.222447	−	0.974945i	$-0.571404\pi$
$503$	−9.97793	−0.444894	−0.222447	+	0.974945i	$0.571404\pi$
$504$	−200.500	−8.93097
$505$	2.77759	0.123601
$506$	9.46167	0.420623
$507$	94.2300	4.18490
$508$	106.805	4.73871
$509$	−41.1926	−1.82583	−0.912915	−	0.408150i	$-0.866174\pi$
$509$	−41.1926	−1.82583	−0.912915	+	0.408150i	$0.866174\pi$
$510$	2.15221	0.0953013
$511$	32.5942	1.44188
$512$	−155.256	−6.86141
$513$	−61.8010	−2.72858
$514$	44.0214	1.94170
$515$	9.72416	0.428498
$516$	139.121	6.12448
$517$	2.03327	0.0894230
$518$	21.2063	0.931752
$519$	−18.2381	−0.800563
$520$	−33.8022	−1.48233
$521$	−1.76996	−0.0775434	−0.0387717	−	0.999248i	$-0.512345\pi$
$521$	−1.76996	−0.0775434	−0.0387717	+	0.999248i	$0.512345\pi$
$522$	−134.334	−5.87965
$523$	15.0747	0.659170	0.329585	−	0.944126i	$-0.393091\pi$
$523$	15.0747	0.659170	0.329585	+	0.944126i	$0.393091\pi$
$524$	40.8818	1.78593
$525$	−39.0819	−1.70567
$526$	−11.3097	−0.493126
$527$	−1.12590	−0.0490451
$528$	−112.590	−4.89984
$529$	−19.8648	−0.863688
$530$	9.51462	0.413289
$531$	−62.5960	−2.71643
$532$	−66.2296	−2.87142
$533$	66.5024	2.88054
$534$	−100.463	−4.34747
$535$	1.55087	0.0670498
$536$	72.5427	3.13337
$537$	10.9389	0.472048
$538$	8.42905	0.363402
$539$	0.925591	0.0398680
$540$	39.2482	1.68897
$541$	9.73961	0.418738	0.209369	−	0.977837i	$-0.432859\pi$
$541$	9.73961	0.418738	0.209369	+	0.977837i	$0.432859\pi$
$542$	54.9075	2.35848
$543$	7.01516	0.301049
$544$	14.7789	0.633639
$545$	0.366395	0.0156946
$546$	−149.328	−6.39063
$547$	−28.2570	−1.20818	−0.604092	−	0.796915i	$-0.706464\pi$
$547$	−28.2570	−1.20818	−0.604092	+	0.796915i	$0.706464\pi$
$548$	−130.266	−5.56470
$549$	−11.3116	−0.482766
$550$	−25.4643	−1.08580
$551$	−29.1575	−1.24215
$552$	−61.0199	−2.59718
$553$	−5.31279	−0.225923
$554$	75.4440	3.20531
$555$	−4.62037	−0.196124
$556$	−78.3579	−3.32311
$557$	36.9751	1.56668	0.783342	−	0.621591i	$-0.213513\pi$
$557$	36.9751	1.56668	0.783342	+	0.621591i	$0.213513\pi$
$558$	−46.7050	−1.97718
$559$	48.2990	2.04283
$560$	22.6919	0.958908
$561$	3.03119	0.127977
$562$	11.2543	0.474734
$563$	14.4789	0.610211	0.305105	−	0.952319i	$-0.401308\pi$
$563$	14.4789	0.610211	0.305105	+	0.952319i	$0.401308\pi$
$564$	−19.9560	−0.840299
$565$	−9.63269	−0.405250
$566$	−27.5872	−1.15958
$567$	57.8501	2.42948
$568$	59.4769	2.49559
$569$	−0.635945	−0.0266602	−0.0133301	−	0.999911i	$-0.504243\pi$
$569$	−0.635945	−0.0266602	−0.0133301	+	0.999911i	$0.504243\pi$
$570$	19.3781	0.811657
$571$	−9.83739	−0.411682	−0.205841	−	0.978585i	$-0.565993\pi$
$571$	−9.83739	−0.411682	−0.205841	+	0.978585i	$0.565993\pi$
$572$	−72.4518	−3.02936
$573$	−17.2945	−0.722489
$574$	−73.0198	−3.04779
$575$	−8.43775	−0.351878
$576$	344.248	14.3437
$577$	43.1784	1.79754	0.898770	−	0.438421i	$-0.144462\pi$
$577$	43.1784	1.79754	0.898770	+	0.438421i	$0.144462\pi$
$578$	46.8938	1.95053
$579$	−77.0783	−3.20327
$580$	18.5172	0.768884
$581$	−39.4492	−1.63663
$582$	11.0290	0.457166
$583$	13.4005	0.554992
$584$	−136.962	−5.66753
$585$	23.0804	0.954259
$586$	75.5503	3.12095
$587$	36.6368	1.51216	0.756082	−	0.654477i	$-0.227111\pi$
$587$	36.6368	1.51216	0.756082	+	0.654477i	$0.227111\pi$
$588$	−9.08444	−0.374636
$589$	−10.1374	−0.417705
$590$	11.5873	0.477040
$591$	51.1066	2.10225
$592$	−54.4814	−2.23917
$593$	−3.62672	−0.148932	−0.0744658	−	0.997224i	$-0.523725\pi$
$593$	−3.62672	−0.148932	−0.0744658	+	0.997224i	$0.523725\pi$
$594$	74.2327	3.04581
$595$	−0.610921	−0.0250453
$596$	32.1442	1.31668
$597$	−20.1359	−0.824108
$598$	−32.2397	−1.31838
$599$	−1.07418	−0.0438896	−0.0219448	−	0.999759i	$-0.506986\pi$
$599$	−1.07418	−0.0438896	−0.0219448	+	0.999759i	$0.506986\pi$
$600$	164.223	6.70439
$601$	40.5980	1.65603	0.828013	−	0.560709i	$-0.189471\pi$
$601$	40.5980	1.65603	0.828013	+	0.560709i	$0.189471\pi$
$602$	−53.0324	−2.16144
$603$	−49.5327	−2.01713
$604$	5.62022	0.228684
$605$	−3.56249	−0.144836
$606$	−51.5612	−2.09453
$607$	−25.7197	−1.04393	−0.521964	−	0.852967i	$-0.674801\pi$
$607$	−25.7197	−1.04393	−0.521964	+	0.852967i	$0.674801\pi$
$608$	133.066	5.39655
$609$	53.7520	2.17814
$610$	2.09391	0.0847799
$611$	−6.92816	−0.280284
$612$	−21.1050	−0.853118
$613$	12.6948	0.512737	0.256368	−	0.966579i	$-0.417474\pi$
$613$	12.6948	0.512737	0.256368	+	0.966579i	$0.417474\pi$
$614$	42.5329	1.71649
$615$	15.9093	0.641525
$616$	52.2730	2.10614
$617$	10.3183	0.415398	0.207699	−	0.978193i	$-0.433403\pi$
$617$	10.3183	0.415398	0.207699	+	0.978193i	$0.433403\pi$
$618$	−180.512	−7.26126
$619$	−30.2421	−1.21553	−0.607767	−	0.794115i	$-0.707935\pi$
$619$	−30.2421	−1.21553	−0.607767	+	0.794115i	$0.707935\pi$
$620$	6.43800	0.258556
$621$	24.5975	0.987064
$622$	−68.9767	−2.76571
$623$	28.5173	1.14252
$624$	383.639	15.3578
$625$	21.5353	0.861413
$626$	88.7418	3.54684
$627$	27.2922	1.08995
$628$	95.4744	3.80984
$629$	1.46677	0.0584839
$630$	−25.3424	−1.00966
$631$	−30.9248	−1.23110	−0.615548	−	0.788100i	$-0.711065\pi$
$631$	−30.9248	−1.23110	−0.615548	+	0.788100i	$0.711065\pi$
$632$	22.3245	0.888022
$633$	−1.76197	−0.0700321
$634$	−2.24717	−0.0892463
$635$	8.87056	0.352017
$636$	−131.522	−5.21520
$637$	−3.15386	−0.124961
$638$	35.0228	1.38656
$639$	−40.6113	−1.60656
$640$	−34.7463	−1.37347
$641$	37.8972	1.49685	0.748424	−	0.663220i	$-0.230811\pi$
$641$	37.8972	1.49685	0.748424	+	0.663220i	$0.230811\pi$
$642$	−28.7891	−1.13622
$643$	−44.6682	−1.76154	−0.880771	−	0.473543i	$-0.842975\pi$
$643$	−44.6682	−1.76154	−0.880771	+	0.473543i	$0.842975\pi$
$644$	26.3601	1.03873
$645$	11.5545	0.454959
$646$	−6.15170	−0.242036
$647$	20.7353	0.815189	0.407595	−	0.913163i	$-0.366368\pi$
$647$	20.7353	0.815189	0.407595	+	0.913163i	$0.366368\pi$
$648$	−243.088	−9.54942
$649$	16.3196	0.640601
$650$	86.7670	3.40328
$651$	18.6884	0.732455
$652$	20.7510	0.812671
$653$	29.1888	1.14224	0.571122	−	0.820865i	$-0.306508\pi$
$653$	29.1888	1.14224	0.571122	+	0.820865i	$0.306508\pi$
$654$	−6.80148	−0.265959
$655$	3.39538	0.132668
$656$	187.596	7.32438
$657$	93.5187	3.64851
$658$	7.60713	0.296557
$659$	−33.5443	−1.30670	−0.653350	−	0.757056i	$-0.726637\pi$
$659$	−33.5443	−1.30670	−0.653350	+	0.757056i	$0.726637\pi$
$660$	−17.3326	−0.674670
$661$	24.8798	0.967710	0.483855	−	0.875148i	$-0.339236\pi$
$661$	24.8798	0.967710	0.483855	+	0.875148i	$0.339236\pi$
$662$	−73.4025	−2.85287
$663$	−10.3285	−0.401125
$664$	165.767	6.43301
$665$	−5.50061	−0.213305
$666$	60.8449	2.35769
$667$	11.6050	0.449348
$668$	72.3307	2.79856
$669$	−3.10252	−0.119950
$670$	9.16910	0.354233
$671$	2.94908	0.113848
$672$	−245.308	−9.46295
$673$	−51.5072	−1.98546	−0.992729	−	0.120370i	$-0.961592\pi$
$673$	−51.5072	−1.98546	−0.992729	+	0.120370i	$0.961592\pi$
$674$	13.4144	0.516702
$675$	−66.1994	−2.54802
$676$	171.051	6.57887
$677$	−8.02777	−0.308532	−0.154266	−	0.988029i	$-0.549301\pi$
$677$	−8.02777	−0.308532	−0.154266	+	0.988029i	$0.549301\pi$
$678$	178.814	6.86732
$679$	−3.13066	−0.120144
$680$	2.56711	0.0984442
$681$	19.3357	0.740947
$682$	12.1766	0.466267
$683$	−12.9914	−0.497101	−0.248550	−	0.968619i	$-0.579954\pi$
$683$	−12.9914	−0.497101	−0.248550	+	0.968619i	$0.579954\pi$
$684$	−190.025	−7.26579
$685$	−10.8191	−0.413376
$686$	53.4678	2.04141
$687$	14.9292	0.569584
$688$	136.246	5.19433
$689$	−45.6609	−1.73954
$690$	−7.71268	−0.293617
$691$	−20.8972	−0.794968	−0.397484	−	0.917609i	$-0.630117\pi$
$691$	−20.8972	−0.794968	−0.397484	+	0.917609i	$0.630117\pi$
$692$	−33.1066	−1.25852
$693$	−35.6924	−1.35584
$694$	−87.5013	−3.32151
$695$	−6.50791	−0.246859
$696$	−225.868	−8.56150
$697$	−5.05053	−0.191302
$698$	36.7994	1.39288
$699$	−10.7544	−0.406769
$700$	−70.9432	−2.68140
$701$	−38.3708	−1.44924	−0.724622	−	0.689146i	$-0.757986\pi$
$701$	−38.3708	−1.44924	−0.724622	+	0.689146i	$0.757986\pi$
$702$	−252.941	−9.54664
$703$	13.2065	0.498093
$704$	−89.7501	−3.38259
$705$	−1.65742	−0.0624220
$706$	36.6159	1.37806
$707$	14.6360	0.550445
$708$	−160.173	−6.01966
$709$	−13.5503	−0.508893	−0.254446	−	0.967087i	$-0.581893\pi$
$709$	−13.5503	−0.508893	−0.254446	+	0.967087i	$0.581893\pi$
$710$	7.51764	0.282132
$711$	−15.2434	−0.571671
$712$	−119.831	−4.49084
$713$	4.03480	0.151105
$714$	11.3407	0.424414
$715$	−6.01739	−0.225038
$716$	19.8568	0.742083
$717$	60.3022	2.25203
$718$	−52.7883	−1.97004
$719$	−27.6956	−1.03287	−0.516435	−	0.856326i	$-0.672741\pi$
$719$	−27.6956	−1.03287	−0.516435	+	0.856326i	$0.672741\pi$
$720$	65.1073	2.42641
$721$	51.2398	1.90827
$722$	−2.21441	−0.0824117
$723$	−56.7121	−2.10915
$724$	12.7342	0.473264
$725$	−31.2327	−1.15995
$726$	66.1315	2.45437
$727$	−33.3256	−1.23598	−0.617988	−	0.786187i	$-0.712052\pi$
$727$	−33.3256	−1.23598	−0.617988	+	0.786187i	$0.712052\pi$
$728$	−178.115	−6.60139
$729$	32.0781	1.18808
$730$	−17.3114	−0.640725
$731$	−3.66807	−0.135669
$732$	−28.9445	−1.06982
$733$	−29.1060	−1.07506	−0.537528	−	0.843246i	$-0.680642\pi$
$733$	−29.1060	−1.07506	−0.537528	+	0.843246i	$0.680642\pi$
$734$	21.6358	0.798591
$735$	−0.754496	−0.0278300
$736$	−52.9618	−1.95220
$737$	12.9139	0.475688
$738$	−209.507	−7.71207
$739$	−16.1557	−0.594297	−0.297149	−	0.954831i	$-0.596036\pi$
$739$	−16.1557	−0.594297	−0.297149	+	0.954831i	$0.596036\pi$
$740$	−8.38710	−0.308316
$741$	−92.9957	−3.41628
$742$	50.1357	1.84054
$743$	11.1036	0.407353	0.203676	−	0.979038i	$-0.434711\pi$
$743$	11.1036	0.407353	0.203676	+	0.979038i	$0.434711\pi$
$744$	−78.5292	−2.87902
$745$	2.66969	0.0978099
$746$	−9.51697	−0.348441
$747$	−113.187	−4.14130
$748$	5.50235	0.201186
$749$	8.17202	0.298599
$750$	42.5365	1.55321
$751$	−15.1944	−0.554453	−0.277226	−	0.960805i	$-0.589415\pi$
$751$	−15.1944	−0.554453	−0.277226	+	0.960805i	$0.589415\pi$
$752$	−19.5436	−0.712680
$753$	20.0110	0.729243
$754$	−119.337	−4.34598
$755$	0.466780	0.0169879
$756$	206.812	7.52167
$757$	14.1482	0.514225	0.257112	−	0.966381i	$-0.417229\pi$
$757$	14.1482	0.514225	0.257112	+	0.966381i	$0.417229\pi$
$758$	64.3300	2.33657
$759$	−10.8626	−0.394288
$760$	23.1138	0.838425
$761$	−19.6746	−0.713205	−0.356602	−	0.934256i	$-0.616065\pi$
$761$	−19.6746	−0.713205	−0.356602	+	0.934256i	$0.616065\pi$
$762$	−164.667	−5.96524
$763$	1.93065	0.0698944
$764$	−31.3938	−1.13579
$765$	−1.75284	−0.0633742
$766$	58.7312	2.12204
$767$	−55.6075	−2.00787
$768$	342.945	12.3750
$769$	−22.4289	−0.808807	−0.404403	−	0.914581i	$-0.632521\pi$
$769$	−22.4289	−0.808807	−0.404403	+	0.914581i	$0.632521\pi$
$770$	6.60710	0.238103
$771$	−50.5395	−1.82014
$772$	−139.916	−5.03569
$773$	3.10760	0.111773	0.0558863	−	0.998437i	$-0.482202\pi$
$773$	3.10760	0.111773	0.0558863	+	0.998437i	$0.482202\pi$
$774$	−152.160	−5.46927
$775$	−10.8589	−0.390063
$776$	13.1552	0.472243
$777$	−24.3462	−0.873417
$778$	99.5484	3.56898
$779$	−45.4740	−1.62928
$780$	59.0591	2.11465
$781$	10.5879	0.378866
$782$	2.44845	0.0875562
$783$	91.0486	3.25381
$784$	−8.89669	−0.317739
$785$	7.92950	0.283016
$786$	−63.0294	−2.24818
$787$	5.77866	0.205987	0.102994	−	0.994682i	$-0.467158\pi$
$787$	5.77866	0.205987	0.102994	+	0.994682i	$0.467158\pi$
$788$	92.7711	3.30483
$789$	12.9843	0.462252
$790$	2.82173	0.100393
$791$	−50.7578	−1.80474
$792$	149.981	5.32934
$793$	−10.0487	−0.356840
$794$	−85.9910	−3.05171
$795$	−10.9234	−0.387413
$796$	−36.5516	−1.29554
$797$	26.5487	0.940405	0.470202	−	0.882559i	$-0.344181\pi$
$797$	26.5487	0.940405	0.470202	+	0.882559i	$0.344181\pi$
$798$	102.109	3.61463
$799$	0.526160	0.0186142
$800$	142.536	5.03942
$801$	81.8213	2.89102
$802$	40.2329	1.42067
$803$	−24.3816	−0.860408
$804$	−126.746	−4.46999
$805$	2.18930	0.0771628
$806$	−41.4907	−1.46145
$807$	−9.67710	−0.340650
$808$	−61.5012	−2.16361
$809$	−6.92345	−0.243415	−0.121708	−	0.992566i	$-0.538837\pi$
$809$	−6.92345	−0.243415	−0.121708	+	0.992566i	$0.538837\pi$
$810$	−30.7254	−1.07958
$811$	28.9204	1.01553	0.507766	−	0.861495i	$-0.330471\pi$
$811$	28.9204	1.01553	0.507766	+	0.861495i	$0.330471\pi$
$812$	97.5731	3.42414
$813$	−63.0374	−2.21082
$814$	−15.8631	−0.556001
$815$	1.72344	0.0603696
$816$	−29.1355	−1.01994
$817$	−33.0266	−1.15546
$818$	−37.2160	−1.30123
$819$	121.619	4.24969
$820$	28.8793	1.00851
$821$	−38.6770	−1.34984	−0.674918	−	0.737893i	$-0.735821\pi$
$821$	−38.6770	−1.34984	−0.674918	+	0.737893i	$0.735821\pi$
$822$	200.838	7.00502
$823$	−34.8223	−1.21383	−0.606914	−	0.794768i	$-0.707593\pi$
$823$	−34.8223	−1.21383	−0.606914	+	0.794768i	$0.707593\pi$
$824$	−215.312	−7.50073
$825$	29.2346	1.01782
$826$	61.0571	2.12445
$827$	35.3473	1.22914	0.614572	−	0.788860i	$-0.289329\pi$
$827$	35.3473	1.22914	0.614572	+	0.788860i	$0.289329\pi$
$828$	75.6321	2.62840
$829$	28.3103	0.983258	0.491629	−	0.870805i	$-0.336402\pi$
$829$	28.3103	0.983258	0.491629	+	0.870805i	$0.336402\pi$
$830$	20.9523	0.727264
$831$	−86.6146	−3.00463
$832$	305.815	10.6022
$833$	0.239520	0.00829888
$834$	120.808	4.18324
$835$	6.00733	0.207892
$836$	49.5421	1.71345
$837$	31.6556	1.09418
$838$	67.6407	2.33661
$839$	35.1300	1.21282	0.606412	−	0.795151i	$-0.292608\pi$
$839$	35.1300	1.21282	0.606412	+	0.795151i	$0.292608\pi$
$840$	−42.6103	−1.47020
$841$	13.9564	0.481257
$842$	49.6897	1.71242
$843$	−12.9207	−0.445012
$844$	−3.19841	−0.110094
$845$	14.2064	0.488714
$846$	21.8263	0.750403
$847$	−18.7719	−0.645012
$848$	−128.804	−4.42315
$849$	31.6719	1.08698
$850$	−6.58952	−0.226019
$851$	−5.25634	−0.180185
$852$	−103.918	−3.56016
$853$	9.01275	0.308591	0.154295	−	0.988025i	$-0.450689\pi$
$853$	9.01275	0.308591	0.154295	+	0.988025i	$0.450689\pi$
$854$	11.0335	0.377559
$855$	−15.7823	−0.539743
$856$	−34.3392	−1.17369
$857$	−28.2069	−0.963528	−0.481764	−	0.876301i	$-0.660004\pi$
$857$	−28.2069	−0.963528	−0.481764	+	0.876301i	$0.660004\pi$
$858$	111.702	3.81346
$859$	36.4180	1.24257	0.621283	−	0.783586i	$-0.286612\pi$
$859$	36.4180	1.24257	0.621283	+	0.783586i	$0.286612\pi$
$860$	20.9743	0.715219
$861$	83.8314	2.85697
$862$	−91.9922	−3.13327
$863$	28.0016	0.953186	0.476593	−	0.879124i	$-0.341872\pi$
$863$	28.0016	0.953186	0.476593	+	0.879124i	$0.341872\pi$
$864$	−415.519	−14.1362
$865$	−2.74963	−0.0934901
$866$	−17.3066	−0.588103
$867$	−53.8372	−1.82841
$868$	33.9240	1.15145
$869$	3.97415	0.134814
$870$	−28.5488	−0.967895
$871$	−44.0027	−1.49097
$872$	−8.11268	−0.274730
$873$	−8.98246	−0.304010
$874$	22.0453	0.745695
$875$	−12.0743	−0.408186
$876$	239.299	8.08517
$877$	−22.4255	−0.757255	−0.378627	−	0.925549i	$-0.623604\pi$
$877$	−22.4255	−0.757255	−0.378627	+	0.925549i	$0.623604\pi$
$878$	−21.0155	−0.709240
$879$	−86.7366	−2.92555
$880$	−16.9744	−0.572206
$881$	−5.61190	−0.189070	−0.0945348	−	0.995522i	$-0.530136\pi$
$881$	−5.61190	−0.189070	−0.0945348	+	0.995522i	$0.530136\pi$
$882$	9.93583	0.334557
$883$	4.27924	0.144008	0.0720040	−	0.997404i	$-0.477061\pi$
$883$	4.27924	0.144008	0.0720040	+	0.997404i	$0.477061\pi$
$884$	−18.7487	−0.630588
$885$	−13.3029	−0.447173
$886$	−86.0089	−2.88953
$887$	38.9816	1.30887	0.654437	−	0.756117i	$-0.272906\pi$
$887$	38.9816	1.30887	0.654437	+	0.756117i	$0.272906\pi$
$888$	102.304	3.43309
$889$	46.7419	1.56767
$890$	−15.1461	−0.507699
$891$	−43.2740	−1.44973
$892$	−5.63183	−0.188568
$893$	4.73744	0.158532
$894$	−49.5582	−1.65747
$895$	1.64918	0.0551260
$896$	−183.090	−6.11659
$897$	37.0133	1.23584
$898$	35.0595	1.16995
$899$	14.9350	0.498110
$900$	−203.549	−6.78497
$901$	3.46772	0.115526
$902$	54.6214	1.81869
$903$	60.8847	2.02611
$904$	213.286	7.09380
$905$	1.05763	0.0351567
$906$	−8.66496	−0.287874
$907$	38.0504	1.26344	0.631721	−	0.775196i	$-0.282349\pi$
$907$	38.0504	1.26344	0.631721	+	0.775196i	$0.282349\pi$
$908$	35.0991	1.16481
$909$	41.9935	1.39284
$910$	−22.5130	−0.746300
$911$	−40.4400	−1.33984	−0.669918	−	0.742435i	$-0.733671\pi$
$911$	−40.4400	−1.33984	−0.669918	+	0.742435i	$0.733671\pi$
$912$	−262.330	−8.68662
$913$	29.5094	0.976619
$914$	−43.6803	−1.44482
$915$	−2.40394	−0.0794719
$916$	27.1001	0.895414
$917$	17.8914	0.590825
$918$	19.2096	0.634011
$919$	20.9374	0.690661	0.345331	−	0.938481i	$-0.387767\pi$
$919$	20.9374	0.690661	0.345331	+	0.938481i	$0.387767\pi$
$920$	−9.19954	−0.303300
$921$	−48.8305	−1.60902
$922$	−42.2343	−1.39091
$923$	−36.0773	−1.18750
$924$	−91.3311	−3.00457
$925$	14.1464	0.465131
$926$	−70.6004	−2.32007
$927$	147.017	4.82866
$928$	−196.040	−6.43534
$929$	20.1717	0.661811	0.330906	−	0.943664i	$-0.392646\pi$
$929$	20.1717	0.661811	0.330906	+	0.943664i	$0.392646\pi$
$930$	−9.92578	−0.325479
$931$	2.15659	0.0706795
$932$	−19.5219	−0.639461
$933$	79.1897	2.59255
$934$	−85.9108	−2.81109
$935$	0.456991	0.0149452
$936$	−511.046	−16.7040
$937$	60.3308	1.97092	0.985461	−	0.169901i	$-0.0543448\pi$
$937$	60.3308	1.97092	0.985461	+	0.169901i	$0.0543448\pi$
$938$	48.3150	1.57754
$939$	−101.881	−3.32477
$940$	−3.00862	−0.0981304
$941$	−33.8742	−1.10427	−0.552134	−	0.833755i	$-0.686186\pi$
$941$	−33.8742	−1.10427	−0.552134	+	0.833755i	$0.686186\pi$
$942$	−147.197	−4.79595
$943$	18.0992	0.589389
$944$	−156.862	−5.10544
$945$	17.1765	0.558751
$946$	39.6702	1.28979
$947$	−3.75087	−0.121887	−0.0609435	−	0.998141i	$-0.519411\pi$
$947$	−3.75087	−0.121887	−0.0609435	+	0.998141i	$0.519411\pi$
$948$	−39.0053	−1.26683
$949$	83.0780	2.69682
$950$	−59.3308	−1.92495
$951$	2.57989	0.0836587
$952$	13.5270	0.438411
$953$	57.5442	1.86404	0.932019	−	0.362409i	$-0.118046\pi$
$953$	57.5442	1.86404	0.932019	+	0.362409i	$0.118046\pi$
$954$	143.849	4.65727
$955$	−2.60737	−0.0843725
$956$	109.463	3.54030
$957$	−40.2084	−1.29975
$958$	54.4361	1.75875
$959$	−57.0094	−1.84093
$960$	73.1598	2.36122
$961$	−25.8074	−0.832498
$962$	54.0519	1.74270
$963$	23.4471	0.755571
$964$	−102.947	−3.31568
$965$	−11.6205	−0.374079
$966$	−40.6407	−1.30759
$967$	54.6546	1.75757	0.878786	−	0.477216i	$-0.158354\pi$
$967$	54.6546	1.75757	0.878786	+	0.477216i	$0.158354\pi$
$968$	78.8804	2.53531
$969$	7.06256	0.226882
$970$	1.66276	0.0533880
$971$	21.4099	0.687078	0.343539	−	0.939138i	$-0.388374\pi$
$971$	21.4099	0.687078	0.343539	+	0.939138i	$0.388374\pi$
$972$	181.653	5.82651
$973$	−34.2923	−1.09936
$974$	52.2146	1.67306
$975$	−99.6142	−3.19021
$976$	−28.3463	−0.907342
$977$	54.2363	1.73517	0.867587	−	0.497286i	$-0.165670\pi$
$977$	54.2363	1.73517	0.867587	+	0.497286i	$0.165670\pi$
$978$	−31.9928	−1.02302
$979$	−21.3319	−0.681772
$980$	−1.36960	−0.0437501
$981$	5.53941	0.176860
$982$	−71.5686	−2.28385
$983$	−29.5257	−0.941725	−0.470862	−	0.882207i	$-0.656057\pi$
$983$	−29.5257	−0.941725	−0.470862	+	0.882207i	$0.656057\pi$
$984$	−352.263	−11.2297
$985$	7.70498	0.245501
$986$	9.06302	0.288625
$987$	−8.73348	−0.277990
$988$	−168.810	−5.37056
$989$	13.1450	0.417985
$990$	18.9570	0.602493
$991$	21.3208	0.677276	0.338638	−	0.940917i	$-0.390034\pi$
$991$	21.3208	0.677276	0.338638	+	0.940917i	$0.390034\pi$
$992$	−68.1588	−2.16404
$993$	84.2708	2.67425
$994$	39.6129	1.25645
$995$	−3.03575	−0.0962396
$996$	−289.627	−9.17719
$997$	−19.3789	−0.613736	−0.306868	−	0.951752i	$-0.599281\pi$
$997$	−19.3789	−0.613736	−0.306868	+	0.951752i	$0.599281\pi$
$998$	−60.2239	−1.90635
$999$	−41.2393	−1.30475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.1	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.1	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79865 q^{2} +3.21303 q^{3} +5.83245 q^{4} +0.484406 q^{5} -8.99216 q^{6} +2.55250 q^{7} -10.7257 q^{8} +7.32359 q^{9} +O(q^{10})\)	\(q-2.79865 q^{2} +3.21303 q^{3} +5.83245 q^{4} +0.484406 q^{5} -8.99216 q^{6} +2.55250 q^{7} -10.7257 q^{8} +7.32359 q^{9} -1.35568 q^{10} -1.90936 q^{11} +18.7398 q^{12} +6.50595 q^{13} -7.14354 q^{14} +1.55641 q^{15} +18.3525 q^{16} -0.494095 q^{17} -20.4962 q^{18} -4.44873 q^{19} +2.82527 q^{20} +8.20125 q^{21} +5.34363 q^{22} +1.77065 q^{23} -34.4620 q^{24} -4.76535 q^{25} -18.2079 q^{26} +13.8918 q^{27} +14.8873 q^{28} +6.55412 q^{29} -4.35586 q^{30} +2.27872 q^{31} -29.9110 q^{32} -6.13483 q^{33} +1.38280 q^{34} +1.23644 q^{35} +42.7144 q^{36} -2.96860 q^{37} +12.4505 q^{38} +20.9038 q^{39} -5.19559 q^{40} +10.2218 q^{41} -22.9524 q^{42} +7.42382 q^{43} -11.1362 q^{44} +3.54759 q^{45} -4.95542 q^{46} -1.06490 q^{47} +58.9674 q^{48} -0.484766 q^{49} +13.3366 q^{50} -1.58754 q^{51} +37.9456 q^{52} -7.01832 q^{53} -38.8784 q^{54} -0.924905 q^{55} -27.3773 q^{56} -14.2939 q^{57} -18.3427 q^{58} -8.54717 q^{59} +9.07770 q^{60} -1.54454 q^{61} -6.37734 q^{62} +18.6934 q^{63} +47.0054 q^{64} +3.15152 q^{65} +17.1693 q^{66} -6.76345 q^{67} -2.88178 q^{68} +5.68914 q^{69} -3.46038 q^{70} -5.54528 q^{71} -78.5505 q^{72} +12.7695 q^{73} +8.30807 q^{74} -15.3112 q^{75} -25.9470 q^{76} -4.87363 q^{77} -58.5026 q^{78} -2.08141 q^{79} +8.89009 q^{80} +22.6641 q^{81} -28.6072 q^{82} -15.4551 q^{83} +47.8334 q^{84} -0.239342 q^{85} -20.7767 q^{86} +21.0586 q^{87} +20.4792 q^{88} +11.1723 q^{89} -9.92846 q^{90} +16.6064 q^{91} +10.3272 q^{92} +7.32160 q^{93} +2.98027 q^{94} -2.15499 q^{95} -96.1051 q^{96} -1.22651 q^{97} +1.35669 q^{98} -13.9833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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