LMFDB - Embedded newform 4033.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75248 q^{2} +1.04725 q^{3} +5.57617 q^{4} -2.70262 q^{5} -2.88255 q^{6} +3.33593 q^{7} -9.84336 q^{8} -1.90326 q^{9} +O(q^{10})$	\(q-2.75248 q^{2} +1.04725 q^{3} +5.57617 q^{4} -2.70262 q^{5} -2.88255 q^{6} +3.33593 q^{7} -9.84336 q^{8} -1.90326 q^{9} +7.43892 q^{10} -0.447139 q^{11} +5.83967 q^{12} +4.89893 q^{13} -9.18210 q^{14} -2.83033 q^{15} +15.9414 q^{16} +3.35196 q^{17} +5.23869 q^{18} +1.23881 q^{19} -15.0703 q^{20} +3.49357 q^{21} +1.23074 q^{22} +0.723127 q^{23} -10.3085 q^{24} +2.30415 q^{25} -13.4842 q^{26} -5.13496 q^{27} +18.6017 q^{28} -9.97154 q^{29} +7.79044 q^{30} -7.53893 q^{31} -24.1916 q^{32} -0.468269 q^{33} -9.22623 q^{34} -9.01575 q^{35} -10.6129 q^{36} -1.00000 q^{37} -3.40981 q^{38} +5.13042 q^{39} +26.6029 q^{40} -2.21063 q^{41} -9.61599 q^{42} -3.86519 q^{43} -2.49333 q^{44} +5.14378 q^{45} -1.99040 q^{46} +3.74690 q^{47} +16.6947 q^{48} +4.12843 q^{49} -6.34214 q^{50} +3.51036 q^{51} +27.3173 q^{52} +2.44279 q^{53} +14.1339 q^{54} +1.20845 q^{55} -32.8368 q^{56} +1.29735 q^{57} +27.4465 q^{58} +0.178316 q^{59} -15.7824 q^{60} -8.99074 q^{61} +20.7508 q^{62} -6.34914 q^{63} +34.7044 q^{64} -13.2399 q^{65} +1.28890 q^{66} -3.84687 q^{67} +18.6911 q^{68} +0.757298 q^{69} +24.8157 q^{70} -3.69396 q^{71} +18.7345 q^{72} +10.8238 q^{73} +2.75248 q^{74} +2.41303 q^{75} +6.90783 q^{76} -1.49163 q^{77} -14.1214 q^{78} -10.2525 q^{79} -43.0834 q^{80} +0.332168 q^{81} +6.08472 q^{82} -9.10878 q^{83} +19.4807 q^{84} -9.05908 q^{85} +10.6389 q^{86} -10.4427 q^{87} +4.40135 q^{88} +14.8130 q^{89} -14.1582 q^{90} +16.3425 q^{91} +4.03228 q^{92} -7.89518 q^{93} -10.3133 q^{94} -3.34804 q^{95} -25.3348 q^{96} -0.00498767 q^{97} -11.3634 q^{98} +0.851022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−2.75248	−1.94630	−0.973150	−	0.230170i	$-0.926072\pi$
$2$	−2.75248	−1.94630	−0.973150	+	0.230170i	$0.926072\pi$
$3$	1.04725	0.604633	0.302316	−	0.953208i	$-0.402240\pi$
$3$	1.04725	0.604633	0.302316	+	0.953208i	$0.402240\pi$
$4$	5.57617	2.78809
$5$	−2.70262	−1.20865	−0.604324	−	0.796739i	$-0.706557\pi$
$5$	−2.70262	−1.20865	−0.604324	+	0.796739i	$0.706557\pi$
$6$	−2.88255	−1.17680
$7$	3.33593	1.26086	0.630432	−	0.776245i	$-0.282878\pi$
$7$	3.33593	1.26086	0.630432	+	0.776245i	$0.282878\pi$
$8$	−9.84336	−3.48015
$9$	−1.90326	−0.634420
$10$	7.43892	2.35239
$11$	−0.447139	−0.134818	−0.0674088	−	0.997725i	$-0.521473\pi$
$11$	−0.447139	−0.134818	−0.0674088	+	0.997725i	$0.521473\pi$
$12$	5.83967	1.68577
$13$	4.89893	1.35872	0.679359	−	0.733806i	$-0.262258\pi$
$13$	4.89893	1.35872	0.679359	+	0.733806i	$0.262258\pi$
$14$	−9.18210	−2.45402
$15$	−2.83033	−0.730788
$16$	15.9414	3.98534
$17$	3.35196	0.812971	0.406485	−	0.913657i	$-0.366754\pi$
$17$	3.35196	0.812971	0.406485	+	0.913657i	$0.366754\pi$
$18$	5.23869	1.23477
$19$	1.23881	0.284203	0.142102	−	0.989852i	$-0.454614\pi$
$19$	1.23881	0.284203	0.142102	+	0.989852i	$0.454614\pi$
$20$	−15.0703	−3.36982
$21$	3.49357	0.762359
$22$	1.23074	0.262396
$23$	0.723127	0.150782	0.0753912	−	0.997154i	$-0.475979\pi$
$23$	0.723127	0.150782	0.0753912	+	0.997154i	$0.475979\pi$
$24$	−10.3085	−2.10421
$25$	2.30415	0.460830
$26$	−13.4842	−2.64447
$27$	−5.13496	−0.988223
$28$	18.6017	3.51540
$29$	−9.97154	−1.85167	−0.925834	−	0.377931i	$-0.876636\pi$
$29$	−9.97154	−1.85167	−0.925834	+	0.377931i	$0.876636\pi$
$30$	7.79044	1.42233
$31$	−7.53893	−1.35403	−0.677016	−	0.735968i	$-0.736727\pi$
$31$	−7.53893	−1.35403	−0.677016	+	0.735968i	$0.736727\pi$
$32$	−24.1916	−4.27652
$33$	−0.468269	−0.0815151
$34$	−9.22623	−1.58229
$35$	−9.01575	−1.52394
$36$	−10.6129	−1.76882
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−3.40981	−0.553145
$39$	5.13042	0.821525
$40$	26.6029	4.20628
$41$	−2.21063	−0.345242	−0.172621	−	0.984988i	$-0.555224\pi$
$41$	−2.21063	−0.345242	−0.172621	+	0.984988i	$0.555224\pi$
$42$	−9.61599	−1.48378
$43$	−3.86519	−0.589437	−0.294718	−	0.955584i	$-0.595226\pi$
$43$	−3.86519	−0.589437	−0.294718	+	0.955584i	$0.595226\pi$
$44$	−2.49333	−0.375883
$45$	5.14378	0.766790
$46$	−1.99040	−0.293468
$47$	3.74690	0.546541	0.273270	−	0.961937i	$-0.411895\pi$
$47$	3.74690	0.546541	0.273270	+	0.961937i	$0.411895\pi$
$48$	16.6947	2.40967
$49$	4.12843	0.589776
$50$	−6.34214	−0.896915
$51$	3.51036	0.491549
$52$	27.3173	3.78822
$53$	2.44279	0.335544	0.167772	−	0.985826i	$-0.446343\pi$
$53$	2.44279	0.335544	0.167772	+	0.985826i	$0.446343\pi$
$54$	14.1339	1.92338
$55$	1.20845	0.162947
$56$	−32.8368	−4.38800
$57$	1.29735	0.171838
$58$	27.4465	3.60390
$59$	0.178316	0.0232147	0.0116074	−	0.999933i	$-0.496305\pi$
$59$	0.178316	0.0232147	0.0116074	+	0.999933i	$0.496305\pi$
$60$	−15.7824	−2.03750
$61$	−8.99074	−1.15115	−0.575573	−	0.817750i	$-0.695221\pi$
$61$	−8.99074	−1.15115	−0.575573	+	0.817750i	$0.695221\pi$
$62$	20.7508	2.63535
$63$	−6.34914	−0.799916
$64$	34.7044	4.33805
$65$	−13.2399	−1.64221
$66$	1.28890	0.158653
$67$	−3.84687	−0.469970	−0.234985	−	0.971999i	$-0.575504\pi$
$67$	−3.84687	−0.469970	−0.234985	+	0.971999i	$0.575504\pi$
$68$	18.6911	2.26663
$69$	0.757298	0.0911680
$70$	24.8157	2.96605
$71$	−3.69396	−0.438392	−0.219196	−	0.975681i	$-0.570343\pi$
$71$	−3.69396	−0.438392	−0.219196	+	0.975681i	$0.570343\pi$
$72$	18.7345	2.20788
$73$	10.8238	1.26683	0.633413	−	0.773814i	$-0.281653\pi$
$73$	10.8238	1.26683	0.633413	+	0.773814i	$0.281653\pi$
$74$	2.75248	0.319970
$75$	2.41303	0.278633
$76$	6.90783	0.792383
$77$	−1.49163	−0.169986
$78$	−14.1214	−1.59893
$79$	−10.2525	−1.15349	−0.576747	−	0.816923i	$-0.695678\pi$
$79$	−10.2525	−1.15349	−0.576747	+	0.816923i	$0.695678\pi$
$80$	−43.0834	−4.81687
$81$	0.332168	0.0369076
$82$	6.08472	0.671945
$83$	−9.10878	−0.999819	−0.499909	−	0.866078i	$-0.666633\pi$
$83$	−9.10878	−0.999819	−0.499909	+	0.866078i	$0.666633\pi$
$84$	19.4807	2.12552
$85$	−9.05908	−0.982596
$86$	10.6389	1.14722
$87$	−10.4427	−1.11958
$88$	4.40135	0.469186
$89$	14.8130	1.57017	0.785086	−	0.619387i	$-0.212619\pi$
$89$	14.8130	1.57017	0.785086	+	0.619387i	$0.212619\pi$
$90$	−14.1582	−1.49240
$91$	16.3425	1.71316
$92$	4.03228	0.420395
$93$	−7.89518	−0.818692
$94$	−10.3133	−1.06373
$95$	−3.34804	−0.343502
$96$	−25.3348	−2.58572
$97$	−0.00498767	−0.000506421 0	−0.000253210	−	1.00000i	$-0.500081\pi$
$97$	−0.00498767	−0.000506421 0	−0.000253210		1.00000i	$0.500081\pi$
$98$	−11.3634	−1.14788
$99$	0.851022	0.0855309
$100$	12.8484	1.28484
$101$	15.0443	1.49697	0.748483	−	0.663154i	$-0.230783\pi$
$101$	15.0443	1.49697	0.748483	+	0.663154i	$0.230783\pi$
$102$	−9.66221	−0.956701
$103$	−2.86587	−0.282382	−0.141191	−	0.989982i	$-0.545093\pi$
$103$	−2.86587	−0.282382	−0.141191	+	0.989982i	$0.545093\pi$
$104$	−48.2219	−4.72855
$105$	−9.44178	−0.921424
$106$	−6.72375	−0.653069
$107$	18.1977	1.75924	0.879618	−	0.475681i	$-0.157798\pi$
$107$	18.1977	1.75924	0.879618	+	0.475681i	$0.157798\pi$
$108$	−28.6334	−2.75525
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−3.32623	−0.317144
$111$	−1.04725	−0.0994010
$112$	53.1793	5.02497
$113$	−13.0088	−1.22376	−0.611881	−	0.790950i	$-0.709587\pi$
$113$	−13.0088	−1.22376	−0.611881	+	0.790950i	$0.709587\pi$
$114$	−3.57094	−0.334449
$115$	−1.95434	−0.182243
$116$	−55.6030	−5.16261
$117$	−9.32393	−0.861997
$118$	−0.490811	−0.0451828
$119$	11.1819	1.02504
$120$	27.8600	2.54325
$121$	−10.8001	−0.981824
$122$	24.7469	2.24048
$123$	−2.31509	−0.208745
$124$	−42.0384	−3.77516
$125$	7.28585	0.651666
$126$	17.4759	1.55688
$127$	−4.46844	−0.396510	−0.198255	−	0.980151i	$-0.563527\pi$
$127$	−4.46844	−0.396510	−0.198255	+	0.980151i	$0.563527\pi$
$128$	−47.1400	−4.16663
$129$	−4.04784	−0.356393
$130$	36.4427	3.19624
$131$	9.17000	0.801186	0.400593	−	0.916256i	$-0.368804\pi$
$131$	9.17000	0.801186	0.400593	+	0.916256i	$0.368804\pi$
$132$	−2.61115	−0.227271
$133$	4.13259	0.358341
$134$	10.5884	0.914702
$135$	13.8778	1.19441
$136$	−32.9946	−2.82926
$137$	8.12235	0.693939	0.346969	−	0.937876i	$-0.387211\pi$
$137$	8.12235	0.693939	0.346969	+	0.937876i	$0.387211\pi$
$138$	−2.08445	−0.177440
$139$	−18.6683	−1.58343	−0.791714	−	0.610892i	$-0.790811\pi$
$139$	−18.6683	−1.58343	−0.791714	+	0.610892i	$0.790811\pi$
$140$	−50.2734	−4.24888
$141$	3.92395	0.330456
$142$	10.1676	0.853243
$143$	−2.19050	−0.183179
$144$	−30.3405	−2.52838
$145$	26.9493	2.23801
$146$	−29.7923	−2.46563
$147$	4.32351	0.356597
$148$	−5.57617	−0.458359
$149$	0.899330	0.0736760	0.0368380	−	0.999321i	$-0.488271\pi$
$149$	0.899330	0.0736760	0.0368380	+	0.999321i	$0.488271\pi$
$150$	−6.64184	−0.542304
$151$	−20.2811	−1.65045	−0.825226	−	0.564803i	$-0.808952\pi$
$151$	−20.2811	−1.65045	−0.825226	+	0.564803i	$0.808952\pi$
$152$	−12.1941	−0.989070
$153$	−6.37965	−0.515764
$154$	4.10568	0.330845
$155$	20.3749	1.63655
$156$	28.6081	2.29048
$157$	−6.52191	−0.520505	−0.260252	−	0.965541i	$-0.583806\pi$
$157$	−6.52191	−0.520505	−0.260252	+	0.965541i	$0.583806\pi$
$158$	28.2198	2.24504
$159$	2.55823	0.202881
$160$	65.3808	5.16880
$161$	2.41230	0.190116
$162$	−0.914289	−0.0718333
$163$	−12.9035	−1.01068	−0.505340	−	0.862921i	$-0.668633\pi$
$163$	−12.9035	−1.01068	−0.505340	+	0.862921i	$0.668633\pi$
$164$	−12.3268	−0.962565
$165$	1.26555	0.0985231
$166$	25.0718	1.94595
$167$	−21.0968	−1.63252	−0.816261	−	0.577683i	$-0.803957\pi$
$167$	−21.0968	−1.63252	−0.816261	+	0.577683i	$0.803957\pi$
$168$	−34.3884	−2.65313
$169$	10.9995	0.846115
$170$	24.9350	1.91243
$171$	−2.35778	−0.180304
$172$	−21.5530	−1.64340
$173$	−7.50058	−0.570259	−0.285129	−	0.958489i	$-0.592037\pi$
$173$	−7.50058	−0.570259	−0.285129	+	0.958489i	$0.592037\pi$
$174$	28.7435	2.17904
$175$	7.68649	0.581044
$176$	−7.12801	−0.537294
$177$	0.186742	0.0140364
$178$	−40.7725	−3.05603
$179$	−5.53584	−0.413768	−0.206884	−	0.978365i	$-0.566332\pi$
$179$	−5.53584	−0.413768	−0.206884	+	0.978365i	$0.566332\pi$
$180$	28.6826	2.13788
$181$	2.33748	0.173744	0.0868718	−	0.996219i	$-0.472313\pi$
$181$	2.33748	0.173744	0.0868718	+	0.996219i	$0.472313\pi$
$182$	−44.9824	−3.33432
$183$	−9.41560	−0.696021
$184$	−7.11801	−0.524746
$185$	2.70262	0.198701
$186$	21.7314	1.59342
$187$	−1.49879	−0.109603
$188$	20.8933	1.52380
$189$	−17.1299	−1.24601
$190$	9.21543	0.668557
$191$	5.22039	0.377734	0.188867	−	0.982003i	$-0.439518\pi$
$191$	5.22039	0.377734	0.188867	+	0.982003i	$0.439518\pi$
$192$	36.3443	2.62292
$193$	−0.253889	−0.0182753	−0.00913766	−	0.999958i	$-0.502909\pi$
$193$	−0.253889	−0.0182753	−0.00913766	+	0.999958i	$0.502909\pi$
$194$	0.0137285	0.000985647 0
$195$	−13.8656	−0.992935
$196$	23.0208	1.64435
$197$	16.4830	1.17437	0.587184	−	0.809454i	$-0.300237\pi$
$197$	16.4830	1.17437	0.587184	+	0.809454i	$0.300237\pi$
$198$	−2.34242	−0.166469
$199$	7.17168	0.508387	0.254193	−	0.967153i	$-0.418190\pi$
$199$	7.17168	0.508387	0.254193	+	0.967153i	$0.418190\pi$
$200$	−22.6806	−1.60376
$201$	−4.02865	−0.284159
$202$	−41.4093	−2.91354
$203$	−33.2643	−2.33470
$204$	19.5744	1.37048
$205$	5.97449	0.417276
$206$	7.88825	0.549601
$207$	−1.37630	−0.0956594
$208$	78.0956	5.41495
$209$	−0.553922	−0.0383156
$210$	25.9884	1.79337
$211$	14.5563	1.00209	0.501047	−	0.865420i	$-0.332948\pi$
$211$	14.5563	1.00209	0.501047	+	0.865420i	$0.332948\pi$
$212$	13.6214	0.935525
$213$	−3.86851	−0.265066
$214$	−50.0888	−3.42400
$215$	10.4461	0.712421
$216$	50.5453	3.43917
$217$	−25.1493	−1.70725
$218$	2.75248	0.186422
$219$	11.3352	0.765965
$220$	6.73851	0.454310
$221$	16.4210	1.10460
$222$	2.88255	0.193464
$223$	21.1098	1.41362	0.706810	−	0.707404i	$-0.250134\pi$
$223$	21.1098	1.41362	0.706810	+	0.707404i	$0.250134\pi$
$224$	−80.7016	−5.39210
$225$	−4.38540	−0.292360
$226$	35.8064	2.38181
$227$	13.3012	0.882834	0.441417	−	0.897302i	$-0.354476\pi$
$227$	13.3012	0.882834	0.441417	+	0.897302i	$0.354476\pi$
$228$	7.23426	0.479100
$229$	2.14342	0.141641	0.0708206	−	0.997489i	$-0.477438\pi$
$229$	2.14342	0.141641	0.0708206	+	0.997489i	$0.477438\pi$
$230$	5.37929	0.354700
$231$	−1.56211	−0.102779
$232$	98.1534	6.44409
$233$	4.39981	0.288241	0.144121	−	0.989560i	$-0.453965\pi$
$233$	4.39981	0.288241	0.144121	+	0.989560i	$0.453965\pi$
$234$	25.6640	1.67771
$235$	−10.1264	−0.660576
$236$	0.994319	0.0647247
$237$	−10.7369	−0.697440
$238$	−30.7781	−1.99505
$239$	−26.7078	−1.72758	−0.863791	−	0.503850i	$-0.831916\pi$
$239$	−26.7078	−1.72758	−0.863791	+	0.503850i	$0.831916\pi$
$240$	−45.1193	−2.91244
$241$	−9.83072	−0.633252	−0.316626	−	0.948550i	$-0.602550\pi$
$241$	−9.83072	−0.633252	−0.316626	+	0.948550i	$0.602550\pi$
$242$	29.7270	1.91093
$243$	15.7527	1.01054
$244$	−50.1339	−3.20950
$245$	−11.1576	−0.712831
$246$	6.37225	0.406280
$247$	6.06885	0.386152
$248$	74.2084	4.71224
$249$	−9.53921	−0.604523
$250$	−20.0542	−1.26834
$251$	−18.3964	−1.16117	−0.580585	−	0.814199i	$-0.697176\pi$
$251$	−18.3964	−1.16117	−0.580585	+	0.814199i	$0.697176\pi$
$252$	−35.4039	−2.23024
$253$	−0.323339	−0.0203281
$254$	12.2993	0.771727
$255$	−9.48716	−0.594109
$256$	60.3434	3.77146
$257$	−24.9057	−1.55358	−0.776789	−	0.629761i	$-0.783153\pi$
$257$	−24.9057	−1.55358	−0.776789	+	0.629761i	$0.783153\pi$
$258$	11.1416	0.693647
$259$	−3.33593	−0.207285
$260$	−73.8282	−4.57863
$261$	18.9784	1.17473
$262$	−25.2403	−1.55935
$263$	−24.2552	−1.49564	−0.747819	−	0.663903i	$-0.768899\pi$
$263$	−24.2552	−1.49564	−0.747819	+	0.663903i	$0.768899\pi$
$264$	4.60934	0.283685
$265$	−6.60194	−0.405554
$266$	−11.3749	−0.697440
$267$	15.5129	0.949377
$268$	−21.4508	−1.31032
$269$	−3.54338	−0.216044	−0.108022	−	0.994149i	$-0.534452\pi$
$269$	−3.54338	−0.216044	−0.108022	+	0.994149i	$0.534452\pi$
$270$	−38.1985	−2.32469
$271$	15.2758	0.927937	0.463969	−	0.885852i	$-0.346425\pi$
$271$	15.2758	0.927937	0.463969	+	0.885852i	$0.346425\pi$
$272$	53.4349	3.23996
$273$	17.1147	1.03583
$274$	−22.3566	−1.35061
$275$	−1.03028	−0.0621280
$276$	4.22283	0.254184
$277$	−21.9736	−1.32027	−0.660133	−	0.751149i	$-0.729500\pi$
$277$	−21.9736	−1.32027	−0.660133	+	0.751149i	$0.729500\pi$
$278$	51.3843	3.08183
$279$	14.3485	0.859024
$280$	88.7453	5.30355
$281$	−23.8190	−1.42092	−0.710461	−	0.703736i	$-0.751514\pi$
$281$	−23.8190	−1.42092	−0.710461	+	0.703736i	$0.751514\pi$
$282$	−10.8006	−0.643168
$283$	1.30054	0.0773089	0.0386545	−	0.999253i	$-0.487693\pi$
$283$	1.30054	0.0773089	0.0386545	+	0.999253i	$0.487693\pi$
$284$	−20.5981	−1.22227
$285$	−3.50625	−0.207692
$286$	6.02933	0.356522
$287$	−7.37450	−0.435303
$288$	46.0429	2.71310
$289$	−5.76434	−0.339079
$290$	−74.1775	−4.35585
$291$	−0.00522335	−0.000306198 0
$292$	60.3552	3.53202
$293$	2.98604	0.174446	0.0872232	−	0.996189i	$-0.472201\pi$
$293$	2.98604	0.174446	0.0872232	+	0.996189i	$0.472201\pi$
$294$	−11.9004	−0.694046
$295$	−0.481919	−0.0280584
$296$	9.84336	0.572134
$297$	2.29604	0.133230
$298$	−2.47539	−0.143396
$299$	3.54255	0.204871
$300$	13.4555	0.776853
$301$	−12.8940	−0.743199
$302$	55.8234	3.21227
$303$	15.7552	0.905114
$304$	19.7484	1.13265
$305$	24.2986	1.39133
$306$	17.5599	1.00383
$307$	−0.413311	−0.0235889	−0.0117945	−	0.999930i	$-0.503754\pi$
$307$	−0.413311	−0.0235889	−0.0117945	+	0.999930i	$0.503754\pi$
$308$	−8.31756	−0.473937
$309$	−3.00129	−0.170737
$310$	−56.0815	−3.18522
$311$	4.85348	0.275216	0.137608	−	0.990487i	$-0.456059\pi$
$311$	4.85348	0.275216	0.137608	+	0.990487i	$0.456059\pi$
$312$	−50.5006	−2.85903
$313$	3.56845	0.201701	0.100850	−	0.994902i	$-0.467844\pi$
$313$	3.56845	0.201701	0.100850	+	0.994902i	$0.467844\pi$
$314$	17.9514	1.01306
$315$	17.1593	0.966817
$316$	−57.1696	−3.21604
$317$	−0.620200	−0.0348339	−0.0174170	−	0.999848i	$-0.505544\pi$
$317$	−0.620200	−0.0348339	−0.0174170	+	0.999848i	$0.505544\pi$
$318$	−7.04148	−0.394867
$319$	4.45867	0.249637
$320$	−93.7927	−5.24317
$321$	19.0576	1.06369
$322$	−6.63983	−0.370023
$323$	4.15245	0.231049
$324$	1.85223	0.102902
$325$	11.2879	0.626139
$326$	35.5167	1.96709
$327$	−1.04725	−0.0579133
$328$	21.7600	1.20150
$329$	12.4994	0.689113
$330$	−3.48341	−0.191756
$331$	16.0189	0.880481	0.440240	−	0.897880i	$-0.354893\pi$
$331$	16.0189	0.880481	0.440240	+	0.897880i	$0.354893\pi$
$332$	−50.7921	−2.78758
$333$	1.90326	0.104298
$334$	58.0687	3.17738
$335$	10.3966	0.568028
$336$	55.6922	3.03826
$337$	−8.77114	−0.477794	−0.238897	−	0.971045i	$-0.576786\pi$
$337$	−8.77114	−0.477794	−0.238897	+	0.971045i	$0.576786\pi$
$338$	−30.2759	−1.64679
$339$	−13.6235	−0.739926
$340$	−50.5150	−2.73956
$341$	3.37095	0.182547
$342$	6.48975	0.350926
$343$	−9.57936	−0.517237
$344$	38.0465	2.05133
$345$	−2.04669	−0.110190
$346$	20.6452	1.10989
$347$	−1.92975	−0.103594	−0.0517971	−	0.998658i	$-0.516495\pi$
$347$	−1.92975	−0.103594	−0.0517971	+	0.998658i	$0.516495\pi$
$348$	−58.2305	−3.12148
$349$	26.2258	1.40384	0.701918	−	0.712258i	$-0.252327\pi$
$349$	26.2258	1.40384	0.701918	+	0.712258i	$0.252327\pi$
$350$	−21.1569	−1.13089
$351$	−25.1558	−1.34272
$352$	10.8170	0.576549
$353$	2.23569	0.118994	0.0594969	−	0.998228i	$-0.481050\pi$
$353$	2.23569	0.118994	0.0594969	+	0.998228i	$0.481050\pi$
$354$	−0.514004	−0.0273190
$355$	9.98336	0.529862
$356$	82.5997	4.37777
$357$	11.7103	0.619775
$358$	15.2373	0.805318
$359$	−19.5995	−1.03442	−0.517210	−	0.855858i	$-0.673029\pi$
$359$	−19.5995	−1.03442	−0.517210	+	0.855858i	$0.673029\pi$
$360$	−50.6321	−2.66855
$361$	−17.4653	−0.919229
$362$	−6.43388	−0.338157
$363$	−11.3104	−0.593643
$364$	91.1285	4.77643
$365$	−29.2525	−1.53115
$366$	25.9163	1.35467
$367$	31.0498	1.62079	0.810393	−	0.585887i	$-0.199254\pi$
$367$	31.0498	1.62079	0.810393	+	0.585887i	$0.199254\pi$
$368$	11.5276	0.600919
$369$	4.20740	0.219028
$370$	−7.43892	−0.386731
$371$	8.14899	0.423074
$372$	−44.0249	−2.28258
$373$	−31.7553	−1.64423	−0.822114	−	0.569323i	$-0.807206\pi$
$373$	−31.7553	−1.64423	−0.822114	+	0.569323i	$0.807206\pi$
$374$	4.12541	0.213320
$375$	7.63014	0.394019
$376$	−36.8821	−1.90205
$377$	−48.8498	−2.51589
$378$	47.1497	2.42512
$379$	18.8937	0.970506	0.485253	−	0.874374i	$-0.338728\pi$
$379$	18.8937	0.970506	0.485253	+	0.874374i	$0.338728\pi$
$380$	−18.6692	−0.957712
$381$	−4.67959	−0.239743
$382$	−14.3690	−0.735184
$383$	−8.58405	−0.438625	−0.219312	−	0.975655i	$-0.570381\pi$
$383$	−8.58405	−0.438625	−0.219312	+	0.975655i	$0.570381\pi$
$384$	−49.3676	−2.51928
$385$	4.03130	0.205454
$386$	0.698825	0.0355693
$387$	7.35646	0.373950
$388$	−0.0278121	−0.00141194
$389$	30.8780	1.56558	0.782789	−	0.622287i	$-0.213796\pi$
$389$	30.8780	1.56558	0.782789	+	0.622287i	$0.213796\pi$
$390$	38.1648	1.93255
$391$	2.42390	0.122582
$392$	−40.6376	−2.05251
$393$	9.60332	0.484423
$394$	−45.3693	−2.28567
$395$	27.7085	1.39417
$396$	4.74544	0.238468
$397$	−35.1300	−1.76313	−0.881563	−	0.472066i	$-0.843508\pi$
$397$	−35.1300	−1.76313	−0.881563	+	0.472066i	$0.843508\pi$
$398$	−19.7399	−0.989473
$399$	4.32787	0.216665
$400$	36.7313	1.83657
$401$	5.18820	0.259086	0.129543	−	0.991574i	$-0.458649\pi$
$401$	5.18820	0.259086	0.129543	+	0.991574i	$0.458649\pi$
$402$	11.0888	0.553059
$403$	−36.9327	−1.83975
$404$	83.8897	4.17367
$405$	−0.897725	−0.0446083
$406$	91.5596	4.54403
$407$	0.447139	0.0221639
$408$	−34.5537	−1.71066
$409$	−22.0305	−1.08934	−0.544669	−	0.838651i	$-0.683345\pi$
$409$	−22.0305	−1.08934	−0.544669	+	0.838651i	$0.683345\pi$
$410$	−16.4447	−0.812145
$411$	8.50616	0.419578
$412$	−15.9806	−0.787306
$413$	0.594849	0.0292706
$414$	3.78824	0.186182
$415$	24.6176	1.20843
$416$	−118.513	−5.81058
$417$	−19.5505	−0.957392
$418$	1.52466	0.0745736
$419$	20.5617	1.00450	0.502251	−	0.864722i	$-0.332505\pi$
$419$	20.5617	1.00450	0.502251	+	0.864722i	$0.332505\pi$
$420$	−52.6490	−2.56901
$421$	−13.5982	−0.662735	−0.331367	−	0.943502i	$-0.607510\pi$
$421$	−13.5982	−0.662735	−0.331367	+	0.943502i	$0.607510\pi$
$422$	−40.0659	−1.95038
$423$	−7.13131	−0.346736
$424$	−24.0453	−1.16774
$425$	7.72343	0.374642
$426$	10.6480	0.515898
$427$	−29.9925	−1.45144
$428$	101.473	4.90490
$429$	−2.29401	−0.110756
$430$	−28.7529	−1.38659
$431$	−29.4436	−1.41825	−0.709123	−	0.705084i	$-0.750909\pi$
$431$	−29.4436	−1.41825	−0.709123	+	0.705084i	$0.750909\pi$
$432$	−81.8582	−3.93841
$433$	−10.7005	−0.514234	−0.257117	−	0.966380i	$-0.582773\pi$
$433$	−10.7005	−0.514234	−0.257117	+	0.966380i	$0.582773\pi$
$434$	69.2232	3.32282
$435$	28.2227	1.35318
$436$	−5.57617	−0.267050
$437$	0.895819	0.0428528
$438$	−31.2001	−1.49080
$439$	5.86555	0.279948	0.139974	−	0.990155i	$-0.455298\pi$
$439$	5.86555	0.279948	0.139974	+	0.990155i	$0.455298\pi$
$440$	−11.8952	−0.567081
$441$	−7.85747	−0.374165
$442$	−45.1986	−2.14988
$443$	−38.2169	−1.81574	−0.907869	−	0.419254i	$-0.862292\pi$
$443$	−38.2169	−1.81574	−0.907869	+	0.419254i	$0.862292\pi$
$444$	−5.83967	−0.277139
$445$	−40.0338	−1.89779
$446$	−58.1045	−2.75133
$447$	0.941827	0.0445469
$448$	115.771	5.46968
$449$	−17.5524	−0.828349	−0.414174	−	0.910198i	$-0.635930\pi$
$449$	−17.5524	−0.828349	−0.414174	+	0.910198i	$0.635930\pi$
$450$	12.0707	0.569020
$451$	0.988459	0.0465447
$452$	−72.5391	−3.41195
$453$	−21.2395	−0.997917
$454$	−36.6114	−1.71826
$455$	−44.1675	−2.07060
$456$	−12.7703	−0.598024
$457$	−3.41998	−0.159980	−0.0799899	−	0.996796i	$-0.525489\pi$
$457$	−3.41998	−0.159980	−0.0799899	+	0.996796i	$0.525489\pi$
$458$	−5.89974	−0.275677
$459$	−17.2122	−0.803397
$460$	−10.8977	−0.508109
$461$	12.7712	0.594814	0.297407	−	0.954751i	$-0.403878\pi$
$461$	12.7712	0.594814	0.297407	+	0.954751i	$0.403878\pi$
$462$	4.29969	0.200040
$463$	7.98062	0.370891	0.185445	−	0.982655i	$-0.440627\pi$
$463$	7.98062	0.370891	0.185445	+	0.982655i	$0.440627\pi$
$464$	−158.960	−7.37953
$465$	21.3377	0.989510
$466$	−12.1104	−0.561004
$467$	−31.0775	−1.43809	−0.719047	−	0.694961i	$-0.755421\pi$
$467$	−31.0775	−1.43809	−0.719047	+	0.694961i	$0.755421\pi$
$468$	−51.9918	−2.40332
$469$	−12.8329	−0.592567
$470$	27.8729	1.28568
$471$	−6.83009	−0.314714
$472$	−1.75523	−0.0807908
$473$	1.72828	0.0794664
$474$	29.5533	1.35743
$475$	2.85441	0.130969
$476$	62.3523	2.85791
$477$	−4.64927	−0.212875
$478$	73.5127	3.36239
$479$	17.6207	0.805110	0.402555	−	0.915396i	$-0.368122\pi$
$479$	17.6207	0.805110	0.402555	+	0.915396i	$0.368122\pi$
$480$	68.4703	3.12523
$481$	−4.89893	−0.223372
$482$	27.0589	1.23250
$483$	2.52629	0.114950
$484$	−60.2230	−2.73741
$485$	0.0134798	0.000612085 0
$486$	−43.3592	−1.96681
$487$	−38.3287	−1.73684	−0.868420	−	0.495829i	$-0.834864\pi$
$487$	−38.3287	−1.73684	−0.868420	+	0.495829i	$0.834864\pi$
$488$	88.4992	4.00617
$489$	−13.5132	−0.611089
$490$	30.7110	1.38738
$491$	4.93566	0.222743	0.111372	−	0.993779i	$-0.464476\pi$
$491$	4.93566	0.222743	0.111372	+	0.993779i	$0.464476\pi$
$492$	−12.9093	−0.581998
$493$	−33.4242	−1.50535
$494$	−16.7044	−0.751568
$495$	−2.29999	−0.103377
$496$	−120.181	−5.39628
$497$	−12.3228	−0.552752
$498$	26.2565	1.17658
$499$	36.8248	1.64850	0.824252	−	0.566223i	$-0.191596\pi$
$499$	36.8248	1.64850	0.824252	+	0.566223i	$0.191596\pi$
$500$	40.6272	1.81690
$501$	−22.0938	−0.987076
$502$	50.6358	2.25999
$503$	−12.4470	−0.554983	−0.277491	−	0.960728i	$-0.589503\pi$
$503$	−12.4470	−0.554983	−0.277491	+	0.960728i	$0.589503\pi$
$504$	62.4969	2.78383
$505$	−40.6591	−1.80930
$506$	0.889985	0.0395647
$507$	11.5193	0.511588
$508$	−24.9168	−1.10550
$509$	29.5028	1.30769	0.653845	−	0.756629i	$-0.273155\pi$
$509$	29.5028	1.30769	0.653845	+	0.756629i	$0.273155\pi$
$510$	26.1133	1.15632
$511$	36.1073	1.59729
$512$	−71.8143	−3.17377
$513$	−6.36125	−0.280856
$514$	68.5527	3.02373
$515$	7.74535	0.341301
$516$	−22.5715	−0.993653
$517$	−1.67538	−0.0736833
$518$	9.18210	0.403438
$519$	−7.85501	−0.344797
$520$	130.325	5.71515
$521$	−32.5553	−1.42627	−0.713136	−	0.701026i	$-0.752726\pi$
$521$	−32.5553	−1.42627	−0.713136	+	0.701026i	$0.752726\pi$
$522$	−52.2378	−2.28639
$523$	−0.443058	−0.0193736	−0.00968680	−	0.999953i	$-0.503083\pi$
$523$	−0.443058	−0.0193736	−0.00968680	+	0.999953i	$0.503083\pi$
$524$	51.1335	2.23378
$525$	8.04971	0.351318
$526$	66.7620	2.91096
$527$	−25.2702	−1.10079
$528$	−7.46484	−0.324865
$529$	−22.4771	−0.977265
$530$	18.1717	0.789330
$531$	−0.339381	−0.0147279
$532$	23.0440	0.999086
$533$	−10.8297	−0.469087
$534$	−42.6992	−1.84777
$535$	−49.1814	−2.12630
$536$	37.8661	1.63557
$537$	−5.79744	−0.250178
$538$	9.75310	0.420486
$539$	−1.84598	−0.0795121
$540$	77.3852	3.33013
$541$	18.4273	0.792252	0.396126	−	0.918196i	$-0.370354\pi$
$541$	18.4273	0.792252	0.396126	+	0.918196i	$0.370354\pi$
$542$	−42.0463	−1.80604
$543$	2.44794	0.105051
$544$	−81.0895	−3.47668
$545$	2.70262	0.115767
$546$	−47.1080	−2.01604
$547$	−41.4134	−1.77071	−0.885355	−	0.464917i	$-0.846084\pi$
$547$	−41.4134	−1.77071	−0.885355	+	0.464917i	$0.846084\pi$
$548$	45.2916	1.93476
$549$	17.1117	0.730310
$550$	2.83582	0.120920
$551$	−12.3529	−0.526250
$552$	−7.45436	−0.317279
$553$	−34.2015	−1.45440
$554$	60.4820	2.56963
$555$	2.83033	0.120141
$556$	−104.098	−4.41473
$557$	39.0199	1.65333	0.826663	−	0.562697i	$-0.190236\pi$
$557$	39.0199	1.65333	0.826663	+	0.562697i	$0.190236\pi$
$558$	−39.4941	−1.67192
$559$	−18.9353	−0.800878
$560$	−143.723	−6.07342
$561$	−1.56962	−0.0662694
$562$	65.5614	2.76554
$563$	−4.12232	−0.173735	−0.0868676	−	0.996220i	$-0.527686\pi$
$563$	−4.12232	−0.173735	−0.0868676	+	0.996220i	$0.527686\pi$
$564$	21.8806	0.921341
$565$	35.1578	1.47910
$566$	−3.57971	−0.150466
$567$	1.10809	0.0465354
$568$	36.3610	1.52567
$569$	7.97922	0.334506	0.167253	−	0.985914i	$-0.446510\pi$
$569$	7.97922	0.334506	0.167253	+	0.985914i	$0.446510\pi$
$570$	9.65089	0.404231
$571$	−29.9634	−1.25393	−0.626965	−	0.779047i	$-0.715703\pi$
$571$	−29.9634	−1.25393	−0.626965	+	0.779047i	$0.715703\pi$
$572$	−12.2146	−0.510719
$573$	5.46707	0.228390
$574$	20.2982	0.847231
$575$	1.66620	0.0694852
$576$	−66.0514	−2.75214
$577$	−7.09252	−0.295265	−0.147633	−	0.989042i	$-0.547165\pi$
$577$	−7.09252	−0.295265	−0.147633	+	0.989042i	$0.547165\pi$
$578$	15.8662	0.659949
$579$	−0.265886	−0.0110499
$580$	150.274	6.23978
$581$	−30.3863	−1.26063
$582$	0.0143772	0.000595954 0
$583$	−1.09227	−0.0452372
$584$	−106.542	−4.40875
$585$	25.1990	1.04185
$586$	−8.21903	−0.339525
$587$	−19.0066	−0.784486	−0.392243	−	0.919862i	$-0.628301\pi$
$587$	−19.0066	−0.784486	−0.392243	+	0.919862i	$0.628301\pi$
$588$	24.1087	0.994225
$589$	−9.33932	−0.384820
$590$	1.32648	0.0546101
$591$	17.2619	0.710061
$592$	−15.9414	−0.655186
$593$	7.50231	0.308083	0.154041	−	0.988064i	$-0.450771\pi$
$593$	7.50231	0.308083	0.154041	+	0.988064i	$0.450771\pi$
$594$	−6.31982	−0.259305
$595$	−30.2205	−1.23892
$596$	5.01482	0.205415
$597$	7.51057	0.307387
$598$	−9.75081	−0.398740
$599$	−42.1320	−1.72147	−0.860734	−	0.509054i	$-0.829995\pi$
$599$	−42.1320	−1.72147	−0.860734	+	0.509054i	$0.829995\pi$
$600$	−23.7524	−0.969686
$601$	0.300303	0.0122496	0.00612480	−	0.999981i	$-0.498050\pi$
$601$	0.300303	0.0122496	0.00612480	+	0.999981i	$0.498050\pi$
$602$	35.4906	1.44649
$603$	7.32158	0.298158
$604$	−113.091	−4.60160
$605$	29.1885	1.18668
$606$	−43.3660	−1.76162
$607$	23.3212	0.946578	0.473289	−	0.880907i	$-0.343067\pi$
$607$	23.3212	0.946578	0.473289	+	0.880907i	$0.343067\pi$
$608$	−29.9689	−1.21540
$609$	−34.8362	−1.41164
$610$	−66.8814	−2.70795
$611$	18.3558	0.742595
$612$	−35.5741	−1.43800
$613$	−2.00742	−0.0810787	−0.0405394	−	0.999178i	$-0.512908\pi$
$613$	−2.00742	−0.0810787	−0.0405394	+	0.999178i	$0.512908\pi$
$614$	1.13763	0.0459111
$615$	6.25681	0.252299
$616$	14.6826	0.591579
$617$	−15.4738	−0.622951	−0.311476	−	0.950254i	$-0.600823\pi$
$617$	−15.4738	−0.622951	−0.311476	+	0.950254i	$0.600823\pi$
$618$	8.26101	0.332306
$619$	−45.3020	−1.82084	−0.910420	−	0.413686i	$-0.864241\pi$
$619$	−45.3020	−1.82084	−0.910420	+	0.413686i	$0.864241\pi$
$620$	113.614	4.56284
$621$	−3.71323	−0.149007
$622$	−13.3591	−0.535652
$623$	49.4150	1.97977
$624$	81.7859	3.27406
$625$	−31.2116	−1.24847
$626$	−9.82212	−0.392571
$627$	−0.580097	−0.0231668
$628$	−36.3673	−1.45121
$629$	−3.35196	−0.133652
$630$	−47.2307	−1.88172
$631$	34.3793	1.36862	0.684309	−	0.729192i	$-0.260104\pi$
$631$	34.3793	1.36862	0.684309	+	0.729192i	$0.260104\pi$
$632$	100.919	4.01433
$633$	15.2441	0.605899
$634$	1.70709	0.0677972
$635$	12.0765	0.479241
$636$	14.2651	0.565649
$637$	20.2249	0.801339
$638$	−12.2724	−0.485869
$639$	7.03055	0.278124
$640$	127.401	5.03598
$641$	−37.8024	−1.49311	−0.746553	−	0.665326i	$-0.768293\pi$
$641$	−37.8024	−1.49311	−0.746553	+	0.665326i	$0.768293\pi$
$642$	−52.4557	−2.07026
$643$	10.7348	0.423338	0.211669	−	0.977341i	$-0.432110\pi$
$643$	10.7348	0.423338	0.211669	+	0.977341i	$0.432110\pi$
$644$	13.4514	0.530060
$645$	10.9398	0.430753
$646$	−11.4296	−0.449690
$647$	42.5228	1.67174	0.835872	−	0.548925i	$-0.184963\pi$
$647$	42.5228	1.67174	0.835872	+	0.548925i	$0.184963\pi$
$648$	−3.26965	−0.128444
$649$	−0.0797319	−0.00312975
$650$	−31.0697	−1.21865
$651$	−26.3378	−1.03226
$652$	−71.9521	−2.81786
$653$	5.20122	0.203539	0.101770	−	0.994808i	$-0.467550\pi$
$653$	5.20122	0.203539	0.101770	+	0.994808i	$0.467550\pi$
$654$	2.88255	0.112717
$655$	−24.7830	−0.968353
$656$	−35.2404	−1.37591
$657$	−20.6004	−0.803700
$658$	−34.4044	−1.34122
$659$	−23.3092	−0.907998	−0.453999	−	0.891002i	$-0.650003\pi$
$659$	−23.3092	−0.907998	−0.453999	+	0.891002i	$0.650003\pi$
$660$	7.05693	0.274691
$661$	17.1593	0.667421	0.333711	−	0.942676i	$-0.391699\pi$
$661$	17.1593	0.667421	0.333711	+	0.942676i	$0.391699\pi$
$662$	−44.0919	−1.71368
$663$	17.1970	0.667876
$664$	89.6610	3.47952
$665$	−11.1688	−0.433108
$666$	−5.23869	−0.202995
$667$	−7.21069	−0.279199
$668$	−117.640	−4.55161
$669$	22.1074	0.854721
$670$	−28.6165	−1.10555
$671$	4.02012	0.155195
$672$	−84.5151	−3.26024
$673$	21.4583	0.827158	0.413579	−	0.910468i	$-0.364279\pi$
$673$	21.4583	0.827158	0.413579	+	0.910468i	$0.364279\pi$
$674$	24.1424	0.929931
$675$	−11.8317	−0.455403
$676$	61.3351	2.35904
$677$	−33.1920	−1.27567	−0.637836	−	0.770172i	$-0.720170\pi$
$677$	−33.1920	−1.27567	−0.637836	+	0.770172i	$0.720170\pi$
$678$	37.4984	1.44012
$679$	−0.0166385	−0.000638527 0
$680$	89.1718	3.41958
$681$	13.9298	0.533790
$682$	−9.27850	−0.355292
$683$	32.8804	1.25813	0.629066	−	0.777352i	$-0.283438\pi$
$683$	32.8804	1.25813	0.629066	+	0.777352i	$0.283438\pi$
$684$	−13.1474	−0.502703
$685$	−21.9516	−0.838728
$686$	26.3670	1.00670
$687$	2.24471	0.0856409
$688$	−61.6164	−2.34910
$689$	11.9671	0.455909
$690$	5.63348	0.214463
$691$	28.6210	1.08879	0.544396	−	0.838828i	$-0.316759\pi$
$691$	28.6210	1.08879	0.544396	+	0.838828i	$0.316759\pi$
$692$	−41.8245	−1.58993
$693$	2.83895	0.107843
$694$	5.31160	0.201625
$695$	50.4534	1.91381
$696$	102.792	3.89631
$697$	−7.40995	−0.280672
$698$	−72.1862	−2.73229
$699$	4.60772	0.174280
$700$	42.8612	1.62000
$701$	2.29515	0.0866868	0.0433434	−	0.999060i	$-0.486199\pi$
$701$	2.29515	0.0866868	0.0433434	+	0.999060i	$0.486199\pi$
$702$	69.2409	2.61333
$703$	−1.23881	−0.0467227
$704$	−15.5177	−0.584845
$705$	−10.6050	−0.399406
$706$	−6.15370	−0.231598
$707$	50.1868	1.88747
$708$	1.04130	0.0391346
$709$	−4.33283	−0.162723	−0.0813614	−	0.996685i	$-0.525927\pi$
$709$	−4.33283	−0.162723	−0.0813614	+	0.996685i	$0.525927\pi$
$710$	−27.4790	−1.03127
$711$	19.5131	0.731799
$712$	−145.809	−5.46444
$713$	−5.45161	−0.204164
$714$	−32.2325	−1.20627
$715$	5.92010	0.221399
$716$	−30.8688	−1.15362
$717$	−27.9698	−1.04455
$718$	53.9472	2.01329
$719$	29.5785	1.10309	0.551546	−	0.834145i	$-0.314038\pi$
$719$	29.5785	1.10309	0.551546	+	0.834145i	$0.314038\pi$
$720$	81.9989	3.05592
$721$	−9.56033	−0.356045
$722$	48.0731	1.78910
$723$	−10.2953	−0.382885
$724$	13.0342	0.484412
$725$	−22.9759	−0.853305
$726$	31.1317	1.15541
$727$	30.4695	1.13005	0.565026	−	0.825073i	$-0.308866\pi$
$727$	30.4695	1.13005	0.565026	+	0.825073i	$0.308866\pi$
$728$	−160.865	−5.96205
$729$	15.5006	0.574097
$730$	80.5172	2.98007
$731$	−12.9560	−0.479195
$732$	−52.5030	−1.94057
$733$	10.9215	0.403395	0.201698	−	0.979448i	$-0.435354\pi$
$733$	10.9215	0.403395	0.201698	+	0.979448i	$0.435354\pi$
$734$	−85.4641	−3.15454
$735$	−11.6848	−0.431001
$736$	−17.4936	−0.644824
$737$	1.72009	0.0633601
$738$	−11.5808	−0.426295
$739$	−20.1716	−0.742023	−0.371011	−	0.928628i	$-0.620989\pi$
$739$	−20.1716	−0.742023	−0.371011	+	0.928628i	$0.620989\pi$
$740$	15.0703	0.553994
$741$	6.35563	0.233480
$742$	−22.4300	−0.823430
$743$	23.3945	0.858262	0.429131	−	0.903242i	$-0.358820\pi$
$743$	23.3945	0.858262	0.429131	+	0.903242i	$0.358820\pi$
$744$	77.7151	2.84917
$745$	−2.43055	−0.0890483
$746$	87.4060	3.20016
$747$	17.3364	0.634304
$748$	−8.35754	−0.305582
$749$	60.7062	2.21815
$750$	−21.0018	−0.766879
$751$	−5.63299	−0.205551	−0.102775	−	0.994705i	$-0.532772\pi$
$751$	−5.63299	−0.205551	−0.102775	+	0.994705i	$0.532772\pi$
$752$	59.7306	2.17815
$753$	−19.2657	−0.702081
$754$	134.458	4.89669
$755$	54.8121	1.99482
$756$	−95.5191	−3.47400
$757$	−10.4411	−0.379487	−0.189743	−	0.981834i	$-0.560766\pi$
$757$	−10.4411	−0.379487	−0.189743	+	0.981834i	$0.560766\pi$
$758$	−52.0047	−1.88890
$759$	−0.338618	−0.0122910
$760$	32.9560	1.19544
$761$	−5.59752	−0.202910	−0.101455	−	0.994840i	$-0.532350\pi$
$761$	−5.59752	−0.202910	−0.101455	+	0.994840i	$0.532350\pi$
$762$	12.8805	0.466611
$763$	−3.33593	−0.120769
$764$	29.1098	1.05316
$765$	17.2418	0.623378
$766$	23.6275	0.853695
$767$	0.873556	0.0315423
$768$	63.1949	2.28035
$769$	50.1109	1.80704	0.903522	−	0.428542i	$-0.140973\pi$
$769$	50.1109	1.80704	0.903522	+	0.428542i	$0.140973\pi$
$770$	−11.0961	−0.399875
$771$	−26.0826	−0.939344
$772$	−1.41573	−0.0509532
$773$	−38.8668	−1.39794	−0.698970	−	0.715151i	$-0.746358\pi$
$773$	−38.8668	−1.39794	−0.698970	+	0.715151i	$0.746358\pi$
$774$	−20.2486	−0.727819
$775$	−17.3708	−0.623979
$776$	0.0490954	0.00176242
$777$	−3.49357	−0.125331
$778$	−84.9913	−3.04709
$779$	−2.73855	−0.0981189
$780$	−77.3169	−2.76839
$781$	1.65171	0.0591029
$782$	−6.67174	−0.238581
$783$	51.2034	1.82986
$784$	65.8128	2.35046
$785$	17.6262	0.629107
$786$	−26.4330	−0.942834
$787$	52.5476	1.87312	0.936559	−	0.350510i	$-0.113992\pi$
$787$	52.5476	1.87312	0.936559	+	0.350510i	$0.113992\pi$
$788$	91.9122	3.27424
$789$	−25.4013	−0.904311
$790$	−76.2673	−2.71347
$791$	−43.3963	−1.54300
$792$	−8.37691	−0.297661
$793$	−44.0450	−1.56408
$794$	96.6949	3.43157
$795$	−6.91391	−0.245211
$796$	39.9905	1.41743
$797$	−23.5460	−0.834043	−0.417021	−	0.908897i	$-0.636926\pi$
$797$	−23.5460	−0.834043	−0.417021	+	0.908897i	$0.636926\pi$
$798$	−11.9124	−0.421695
$799$	12.5595	0.444322
$800$	−55.7412	−1.97075
$801$	−28.1929	−0.996148
$802$	−14.2804	−0.504260
$803$	−4.83973	−0.170790
$804$	−22.4644	−0.792259
$805$	−6.51954	−0.229783
$806$	101.657	3.58070
$807$	−3.71082	−0.130627
$808$	−148.087	−5.20967
$809$	−24.4445	−0.859425	−0.429712	−	0.902966i	$-0.641385\pi$
$809$	−24.4445	−0.859425	−0.429712	+	0.902966i	$0.641385\pi$
$810$	2.47097	0.0868212
$811$	47.6556	1.67341	0.836707	−	0.547652i	$-0.184478\pi$
$811$	47.6556	1.67341	0.836707	+	0.547652i	$0.184478\pi$
$812$	−185.488	−6.50934
$813$	15.9976	0.561061
$814$	−1.23074	−0.0431376
$815$	34.8732	1.22156
$816$	55.9599	1.95899
$817$	−4.78825	−0.167520
$818$	60.6386	2.12018
$819$	−31.1040	−1.08686
$820$	33.3148	1.16340
$821$	−52.3103	−1.82564	−0.912821	−	0.408360i	$-0.866101\pi$
$821$	−52.3103	−1.82564	−0.912821	+	0.408360i	$0.866101\pi$
$822$	−23.4131	−0.816625
$823$	−12.4650	−0.434504	−0.217252	−	0.976116i	$-0.569709\pi$
$823$	−12.4650	−0.434504	−0.217252	+	0.976116i	$0.569709\pi$
$824$	28.2098	0.982734
$825$	−1.07896	−0.0375646
$826$	−1.63731	−0.0569694
$827$	−22.9820	−0.799161	−0.399580	−	0.916698i	$-0.630844\pi$
$827$	−22.9820	−0.799161	−0.399580	+	0.916698i	$0.630844\pi$
$828$	−7.67448	−0.266707
$829$	1.90556	0.0661829	0.0330915	−	0.999452i	$-0.489465\pi$
$829$	1.90556	0.0661829	0.0330915	+	0.999452i	$0.489465\pi$
$830$	−67.7595	−2.35197
$831$	−23.0119	−0.798275
$832$	170.014	5.89418
$833$	13.8383	0.479470
$834$	53.8125	1.86337
$835$	57.0167	1.97315
$836$	−3.08876	−0.106827
$837$	38.7121	1.33809
$838$	−56.5956	−1.95506
$839$	−14.4469	−0.498762	−0.249381	−	0.968405i	$-0.580227\pi$
$839$	−14.4469	−0.498762	−0.249381	+	0.968405i	$0.580227\pi$
$840$	92.9389	3.20670
$841$	70.4315	2.42867
$842$	37.4288	1.28988
$843$	−24.9445	−0.859136
$844$	81.1682	2.79393
$845$	−29.7274	−1.02265
$846$	19.6288	0.674853
$847$	−36.0283	−1.23795
$848$	38.9415	1.33726
$849$	1.36199	0.0467435
$850$	−21.2586	−0.729165
$851$	−0.723127	−0.0247885
$852$	−21.5715	−0.739027
$853$	8.07892	0.276617	0.138308	−	0.990389i	$-0.455833\pi$
$853$	8.07892	0.276617	0.138308	+	0.990389i	$0.455833\pi$
$854$	82.5539	2.82494
$855$	6.37218	0.217924
$856$	−179.126	−6.12241
$857$	9.09217	0.310583	0.155291	−	0.987869i	$-0.450368\pi$
$857$	9.09217	0.310583	0.155291	+	0.987869i	$0.450368\pi$
$858$	6.31424	0.215565
$859$	26.4213	0.901484	0.450742	−	0.892654i	$-0.351159\pi$
$859$	26.4213	0.901484	0.450742	+	0.892654i	$0.351159\pi$
$860$	58.2495	1.98629
$861$	−7.72298	−0.263198
$862$	81.0430	2.76034
$863$	−10.3828	−0.353434	−0.176717	−	0.984262i	$-0.556548\pi$
$863$	−10.3828	−0.353434	−0.176717	+	0.984262i	$0.556548\pi$
$864$	124.223	4.22615
$865$	20.2712	0.689242
$866$	29.4530	1.00085
$867$	−6.03673	−0.205018
$868$	−140.237	−4.75996
$869$	4.58428	0.155511
$870$	−77.6827	−2.63369
$871$	−18.8455	−0.638556
$872$	9.84336	0.333338
$873$	0.00949282	0.000321283 0
$874$	−2.46573	−0.0834045
$875$	24.3051	0.821662
$876$	63.2073	2.13558
$877$	0.126829	0.00428271	0.00214136	−	0.999998i	$-0.499318\pi$
$877$	0.126829	0.00428271	0.00214136	+	0.999998i	$0.499318\pi$
$878$	−16.1448	−0.544862
$879$	3.12714	0.105476
$880$	19.2643	0.649399
$881$	−31.3266	−1.05542	−0.527710	−	0.849425i	$-0.676949\pi$
$881$	−31.3266	−1.05542	−0.527710	+	0.849425i	$0.676949\pi$
$882$	21.6276	0.728238
$883$	50.9822	1.71569	0.857843	−	0.513912i	$-0.171804\pi$
$883$	50.9822	1.71569	0.857843	+	0.513912i	$0.171804\pi$
$884$	91.5665	3.07971
$885$	−0.504692	−0.0169650
$886$	105.191	3.53397
$887$	−0.347598	−0.0116712	−0.00583560	−	0.999983i	$-0.501858\pi$
$887$	−0.347598	−0.0116712	−0.00583560	+	0.999983i	$0.501858\pi$
$888$	10.3085	0.345931
$889$	−14.9064	−0.499944
$890$	110.192	3.69366
$891$	−0.148526	−0.00497579
$892$	117.712	3.94129
$893$	4.64170	0.155329
$894$	−2.59236	−0.0867016
$895$	14.9613	0.500100
$896$	−157.256	−5.25354
$897$	3.70995	0.123872
$898$	48.3127	1.61222
$899$	75.1747	2.50722
$900$	−24.4537	−0.815124
$901$	8.18816	0.272787
$902$	−2.72072	−0.0905900
$903$	−13.5033	−0.449362
$904$	128.050	4.25888
$905$	−6.31732	−0.209995
$906$	58.4613	1.94225
$907$	44.2098	1.46796	0.733982	−	0.679169i	$-0.237660\pi$
$907$	44.2098	1.46796	0.733982	+	0.679169i	$0.237660\pi$
$908$	74.1700	2.46142
$909$	−28.6332	−0.949704
$910$	121.570	4.03002
$911$	18.2971	0.606210	0.303105	−	0.952957i	$-0.401977\pi$
$911$	18.2971	0.606210	0.303105	+	0.952957i	$0.401977\pi$
$912$	20.6815	0.684834
$913$	4.07289	0.134793
$914$	9.41344	0.311369
$915$	25.4468	0.841244
$916$	11.9521	0.394908
$917$	30.5905	1.01019
$918$	47.3763	1.56365
$919$	22.8623	0.754156	0.377078	−	0.926181i	$-0.376929\pi$
$919$	22.8623	0.754156	0.377078	+	0.926181i	$0.376929\pi$
$920$	19.2373	0.634234
$921$	−0.432842	−0.0142626
$922$	−35.1525	−1.15769
$923$	−18.0964	−0.595651
$924$	−8.71060	−0.286558
$925$	−2.30415	−0.0757601
$926$	−21.9665	−0.721865
$927$	5.45448	0.179149
$928$	241.228	7.91869
$929$	17.8539	0.585767	0.292884	−	0.956148i	$-0.405385\pi$
$929$	17.8539	0.585767	0.292884	+	0.956148i	$0.405385\pi$
$930$	−58.7316	−1.92588
$931$	5.11435	0.167616
$932$	24.5341	0.803641
$933$	5.08283	0.166404
$934$	85.5403	2.79896
$935$	4.05067	0.132471
$936$	91.7788	2.99988
$937$	−1.84611	−0.0603099	−0.0301549	−	0.999545i	$-0.509600\pi$
$937$	−1.84611	−0.0603099	−0.0301549	+	0.999545i	$0.509600\pi$
$938$	35.3223	1.15331
$939$	3.73708	0.121955
$940$	−56.4667	−1.84174
$941$	3.09992	0.101055	0.0505273	−	0.998723i	$-0.483910\pi$
$941$	3.09992	0.101055	0.0505273	+	0.998723i	$0.483910\pi$
$942$	18.7997	0.612528
$943$	−1.59857	−0.0520565
$944$	2.84259	0.0925186
$945$	46.2955	1.50599
$946$	−4.75706	−0.154666
$947$	2.27193	0.0738278	0.0369139	−	0.999318i	$-0.488247\pi$
$947$	2.27193	0.0738278	0.0369139	+	0.999318i	$0.488247\pi$
$948$	−59.8711	−1.94452
$949$	53.0249	1.72126
$950$	−7.85673	−0.254906
$951$	−0.649507	−0.0210617
$952$	−110.068	−3.56731
$953$	−42.9917	−1.39264	−0.696319	−	0.717732i	$-0.745180\pi$
$953$	−42.9917	−1.39264	−0.696319	+	0.717732i	$0.745180\pi$
$954$	12.7970	0.414320
$955$	−14.1087	−0.456548
$956$	−148.927	−4.81665
$957$	4.66936	0.150939
$958$	−48.5007	−1.56699
$959$	27.0956	0.874962
$960$	−98.2248	−3.17019
$961$	25.8355	0.833403
$962$	13.4842	0.434749
$963$	−34.6349	−1.11609
$964$	−54.8178	−1.76556
$965$	0.686165	0.0220884
$966$	−6.95359	−0.223728
$967$	−47.2081	−1.51811	−0.759055	−	0.651027i	$-0.774339\pi$
$967$	−47.2081	−1.51811	−0.759055	+	0.651027i	$0.774339\pi$
$968$	106.309	3.41690
$969$	4.34868	0.139700
$970$	−0.0371028	−0.00119130
$971$	−3.38992	−0.108788	−0.0543939	−	0.998520i	$-0.517323\pi$
$971$	−3.38992	−0.108788	−0.0543939	+	0.998520i	$0.517323\pi$
$972$	87.8400	2.81747
$973$	−62.2763	−1.99649
$974$	105.499	3.38041
$975$	11.8213	0.378584
$976$	−143.325	−4.58771
$977$	51.0116	1.63200	0.816002	−	0.578049i	$-0.196186\pi$
$977$	51.0116	1.63200	0.816002	+	0.578049i	$0.196186\pi$
$978$	37.1950	1.18936
$979$	−6.62346	−0.211687
$980$	−62.2166	−1.98743
$981$	1.90326	0.0607664
$982$	−13.5853	−0.433525
$983$	−41.2820	−1.31669	−0.658346	−	0.752716i	$-0.728744\pi$
$983$	−41.2820	−1.31669	−0.658346	+	0.752716i	$0.728744\pi$
$984$	22.7883	0.726464
$985$	−44.5474	−1.41940
$986$	91.9997	2.92987
$987$	13.0900	0.416660
$988$	33.8410	1.07662
$989$	−2.79503	−0.0888767
$990$	6.33068	0.201202
$991$	15.7928	0.501676	0.250838	−	0.968029i	$-0.419294\pi$
$991$	15.7928	0.501676	0.250838	+	0.968029i	$0.419294\pi$
$992$	182.379	5.79054
$993$	16.7759	0.532367
$994$	33.9183	1.07582
$995$	−19.3823	−0.614461
$996$	−53.1923	−1.68546
$997$	−2.21630	−0.0701908	−0.0350954	−	0.999384i	$-0.511174\pi$
$997$	−2.21630	−0.0701908	−0.0350954	+	0.999384i	$0.511174\pi$
$998$	−101.360	−3.20849
$999$	5.13496	0.162463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.4	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.4	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75248 q^{2} +1.04725 q^{3} +5.57617 q^{4} -2.70262 q^{5} -2.88255 q^{6} +3.33593 q^{7} -9.84336 q^{8} -1.90326 q^{9} +O(q^{10})\)	\(q-2.75248 q^{2} +1.04725 q^{3} +5.57617 q^{4} -2.70262 q^{5} -2.88255 q^{6} +3.33593 q^{7} -9.84336 q^{8} -1.90326 q^{9} +7.43892 q^{10} -0.447139 q^{11} +5.83967 q^{12} +4.89893 q^{13} -9.18210 q^{14} -2.83033 q^{15} +15.9414 q^{16} +3.35196 q^{17} +5.23869 q^{18} +1.23881 q^{19} -15.0703 q^{20} +3.49357 q^{21} +1.23074 q^{22} +0.723127 q^{23} -10.3085 q^{24} +2.30415 q^{25} -13.4842 q^{26} -5.13496 q^{27} +18.6017 q^{28} -9.97154 q^{29} +7.79044 q^{30} -7.53893 q^{31} -24.1916 q^{32} -0.468269 q^{33} -9.22623 q^{34} -9.01575 q^{35} -10.6129 q^{36} -1.00000 q^{37} -3.40981 q^{38} +5.13042 q^{39} +26.6029 q^{40} -2.21063 q^{41} -9.61599 q^{42} -3.86519 q^{43} -2.49333 q^{44} +5.14378 q^{45} -1.99040 q^{46} +3.74690 q^{47} +16.6947 q^{48} +4.12843 q^{49} -6.34214 q^{50} +3.51036 q^{51} +27.3173 q^{52} +2.44279 q^{53} +14.1339 q^{54} +1.20845 q^{55} -32.8368 q^{56} +1.29735 q^{57} +27.4465 q^{58} +0.178316 q^{59} -15.7824 q^{60} -8.99074 q^{61} +20.7508 q^{62} -6.34914 q^{63} +34.7044 q^{64} -13.2399 q^{65} +1.28890 q^{66} -3.84687 q^{67} +18.6911 q^{68} +0.757298 q^{69} +24.8157 q^{70} -3.69396 q^{71} +18.7345 q^{72} +10.8238 q^{73} +2.75248 q^{74} +2.41303 q^{75} +6.90783 q^{76} -1.49163 q^{77} -14.1214 q^{78} -10.2525 q^{79} -43.0834 q^{80} +0.332168 q^{81} +6.08472 q^{82} -9.10878 q^{83} +19.4807 q^{84} -9.05908 q^{85} +10.6389 q^{86} -10.4427 q^{87} +4.40135 q^{88} +14.8130 q^{89} -14.1582 q^{90} +16.3425 q^{91} +4.03228 q^{92} -7.89518 q^{93} -10.3133 q^{94} -3.34804 q^{95} -25.3348 q^{96} -0.00498767 q^{97} -11.3634 q^{98} +0.851022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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