LMFDB - Embedded newform 8015.2.a.k.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.570951 q^{2} +0.725358 q^{3} -1.67401 q^{4} -1.00000 q^{5} -0.414144 q^{6} -1.00000 q^{7} +2.09768 q^{8} -2.47386 q^{9} +O(q^{10})$	\(q-0.570951 q^{2} +0.725358 q^{3} -1.67401 q^{4} -1.00000 q^{5} -0.414144 q^{6} -1.00000 q^{7} +2.09768 q^{8} -2.47386 q^{9} +0.570951 q^{10} -4.87523 q^{11} -1.21426 q^{12} -2.95851 q^{13} +0.570951 q^{14} -0.725358 q^{15} +2.15035 q^{16} +1.20883 q^{17} +1.41245 q^{18} +8.00582 q^{19} +1.67401 q^{20} -0.725358 q^{21} +2.78352 q^{22} -1.22483 q^{23} +1.52157 q^{24} +1.00000 q^{25} +1.68917 q^{26} -3.97050 q^{27} +1.67401 q^{28} +8.16889 q^{29} +0.414144 q^{30} -1.32122 q^{31} -5.42311 q^{32} -3.53629 q^{33} -0.690182 q^{34} +1.00000 q^{35} +4.14127 q^{36} -1.47400 q^{37} -4.57093 q^{38} -2.14598 q^{39} -2.09768 q^{40} +4.34893 q^{41} +0.414144 q^{42} +2.89777 q^{43} +8.16121 q^{44} +2.47386 q^{45} +0.699316 q^{46} +3.81530 q^{47} +1.55978 q^{48} +1.00000 q^{49} -0.570951 q^{50} +0.876833 q^{51} +4.95260 q^{52} +3.83302 q^{53} +2.26696 q^{54} +4.87523 q^{55} -2.09768 q^{56} +5.80708 q^{57} -4.66404 q^{58} -14.5590 q^{59} +1.21426 q^{60} +5.02829 q^{61} +0.754349 q^{62} +2.47386 q^{63} -1.20438 q^{64} +2.95851 q^{65} +2.01905 q^{66} +9.73662 q^{67} -2.02360 q^{68} -0.888437 q^{69} -0.570951 q^{70} -4.33142 q^{71} -5.18937 q^{72} -4.95608 q^{73} +0.841581 q^{74} +0.725358 q^{75} -13.4019 q^{76} +4.87523 q^{77} +1.22525 q^{78} +11.8609 q^{79} -2.15035 q^{80} +4.54153 q^{81} -2.48303 q^{82} +2.98097 q^{83} +1.21426 q^{84} -1.20883 q^{85} -1.65448 q^{86} +5.92537 q^{87} -10.2267 q^{88} +15.5552 q^{89} -1.41245 q^{90} +2.95851 q^{91} +2.05038 q^{92} -0.958354 q^{93} -2.17835 q^{94} -8.00582 q^{95} -3.93370 q^{96} -17.7625 q^{97} -0.570951 q^{98} +12.0606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−0.570951	−0.403723	−0.201862	−	0.979414i	$-0.564699\pi$
$2$	−0.570951	−0.403723	−0.201862	+	0.979414i	$0.564699\pi$
$3$	0.725358	0.418786	0.209393	−	0.977832i	$-0.432851\pi$
$3$	0.725358	0.418786	0.209393	+	0.977832i	$0.432851\pi$
$4$	−1.67401	−0.837007
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.414144	−0.169074
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.09768	0.741643
$9$	−2.47386	−0.824619
$10$	0.570951	0.180551
$11$	−4.87523	−1.46994	−0.734969	−	0.678100i	$-0.762803\pi$
$11$	−4.87523	−1.46994	−0.734969	+	0.678100i	$0.762803\pi$
$12$	−1.21426	−0.350527
$13$	−2.95851	−0.820544	−0.410272	−	0.911963i	$-0.634566\pi$
$13$	−2.95851	−0.820544	−0.410272	+	0.911963i	$0.634566\pi$
$14$	0.570951	0.152593
$15$	−0.725358	−0.187287
$16$	2.15035	0.537589
$17$	1.20883	0.293184	0.146592	−	0.989197i	$-0.453170\pi$
$17$	1.20883	0.293184	0.146592	+	0.989197i	$0.453170\pi$
$18$	1.41245	0.332918
$19$	8.00582	1.83666	0.918330	−	0.395815i	$-0.129538\pi$
$19$	8.00582	1.83666	0.918330	+	0.395815i	$0.129538\pi$
$20$	1.67401	0.374321
$21$	−0.725358	−0.158286
$22$	2.78352	0.593449
$23$	−1.22483	−0.255394	−0.127697	−	0.991813i	$-0.540758\pi$
$23$	−1.22483	−0.255394	−0.127697	+	0.991813i	$0.540758\pi$
$24$	1.52157	0.310589
$25$	1.00000	0.200000
$26$	1.68917	0.331273
$27$	−3.97050	−0.764124
$28$	1.67401	0.316359
$29$	8.16889	1.51693	0.758463	−	0.651717i	$-0.225951\pi$
$29$	8.16889	1.51693	0.758463	+	0.651717i	$0.225951\pi$
$30$	0.414144	0.0756120
$31$	−1.32122	−0.237297	−0.118649	−	0.992936i	$-0.537856\pi$
$31$	−1.32122	−0.237297	−0.118649	+	0.992936i	$0.537856\pi$
$32$	−5.42311	−0.958680
$33$	−3.53629	−0.615589
$34$	−0.690182	−0.118365
$35$	1.00000	0.169031
$36$	4.14127	0.690212
$37$	−1.47400	−0.242324	−0.121162	−	0.992633i	$-0.538662\pi$
$37$	−1.47400	−0.242324	−0.121162	+	0.992633i	$0.538662\pi$
$38$	−4.57093	−0.741503
$39$	−2.14598	−0.343632
$40$	−2.09768	−0.331673
$41$	4.34893	0.679189	0.339594	−	0.940572i	$-0.389710\pi$
$41$	4.34893	0.679189	0.339594	+	0.940572i	$0.389710\pi$
$42$	0.414144	0.0639038
$43$	2.89777	0.441905	0.220953	−	0.975285i	$-0.429083\pi$
$43$	2.89777	0.441905	0.220953	+	0.975285i	$0.429083\pi$
$44$	8.16121	1.23035
$45$	2.47386	0.368781
$46$	0.699316	0.103108
$47$	3.81530	0.556518	0.278259	−	0.960506i	$-0.410243\pi$
$47$	3.81530	0.556518	0.278259	+	0.960506i	$0.410243\pi$
$48$	1.55978	0.225134
$49$	1.00000	0.142857
$50$	−0.570951	−0.0807447
$51$	0.876833	0.122781
$52$	4.95260	0.686802
$53$	3.83302	0.526505	0.263253	−	0.964727i	$-0.415205\pi$
$53$	3.83302	0.526505	0.263253	+	0.964727i	$0.415205\pi$
$54$	2.26696	0.308495
$55$	4.87523	0.657376
$56$	−2.09768	−0.280315
$57$	5.80708	0.769167
$58$	−4.66404	−0.612418
$59$	−14.5590	−1.89543	−0.947713	−	0.319123i	$-0.896612\pi$
$59$	−14.5590	−1.89543	−0.947713	+	0.319123i	$0.896612\pi$
$60$	1.21426	0.156760
$61$	5.02829	0.643806	0.321903	−	0.946773i	$-0.395677\pi$
$61$	5.02829	0.643806	0.321903	+	0.946773i	$0.395677\pi$
$62$	0.754349	0.0958025
$63$	2.47386	0.311677
$64$	−1.20438	−0.150547
$65$	2.95851	0.366959
$66$	2.01905	0.248528
$67$	9.73662	1.18952	0.594759	−	0.803904i	$-0.297248\pi$
$67$	9.73662	1.18952	0.594759	+	0.803904i	$0.297248\pi$
$68$	−2.02360	−0.245397
$69$	−0.888437	−0.106955
$70$	−0.570951	−0.0682417
$71$	−4.33142	−0.514046	−0.257023	−	0.966405i	$-0.582742\pi$
$71$	−4.33142	−0.514046	−0.257023	+	0.966405i	$0.582742\pi$
$72$	−5.18937	−0.611573
$73$	−4.95608	−0.580065	−0.290032	−	0.957017i	$-0.593666\pi$
$73$	−4.95608	−0.580065	−0.290032	+	0.957017i	$0.593666\pi$
$74$	0.841581	0.0978318
$75$	0.725358	0.0837571
$76$	−13.4019	−1.53730
$77$	4.87523	0.555585
$78$	1.22525	0.138732
$79$	11.8609	1.33445	0.667226	−	0.744855i	$-0.267482\pi$
$79$	11.8609	1.33445	0.667226	+	0.744855i	$0.267482\pi$
$80$	−2.15035	−0.240417
$81$	4.54153	0.504615
$82$	−2.48303	−0.274205
$83$	2.98097	0.327204	0.163602	−	0.986526i	$-0.447689\pi$
$83$	2.98097	0.327204	0.163602	+	0.986526i	$0.447689\pi$
$84$	1.21426	0.132487
$85$	−1.20883	−0.131116
$86$	−1.65448	−0.178408
$87$	5.92537	0.635266
$88$	−10.2267	−1.09017
$89$	15.5552	1.64885	0.824423	−	0.565975i	$-0.191500\pi$
$89$	15.5552	1.64885	0.824423	+	0.565975i	$0.191500\pi$
$90$	−1.41245	−0.148885
$91$	2.95851	0.310137
$92$	2.05038	0.213767
$93$	−0.958354	−0.0993766
$94$	−2.17835	−0.224679
$95$	−8.00582	−0.821380
$96$	−3.93370	−0.401481
$97$	−17.7625	−1.80351	−0.901753	−	0.432251i	$-0.857720\pi$
$97$	−17.7625	−1.80351	−0.901753	+	0.432251i	$0.857720\pi$
$98$	−0.570951	−0.0576748
$99$	12.0606	1.21214
$100$	−1.67401	−0.167401
$101$	15.3699	1.52936	0.764680	−	0.644411i	$-0.222897\pi$
$101$	15.3699	1.52936	0.764680	+	0.644411i	$0.222897\pi$
$102$	−0.500629	−0.0495696
$103$	−11.5759	−1.14061	−0.570304	−	0.821434i	$-0.693175\pi$
$103$	−11.5759	−1.14061	−0.570304	+	0.821434i	$0.693175\pi$
$104$	−6.20603	−0.608551
$105$	0.725358	0.0707877
$106$	−2.18847	−0.212563
$107$	3.51413	0.339724	0.169862	−	0.985468i	$-0.445668\pi$
$107$	3.51413	0.339724	0.169862	+	0.985468i	$0.445668\pi$
$108$	6.64668	0.639577
$109$	−11.9841	−1.14787	−0.573936	−	0.818900i	$-0.694584\pi$
$109$	−11.9841	−1.14787	−0.573936	+	0.818900i	$0.694584\pi$
$110$	−2.78352	−0.265398
$111$	−1.06918	−0.101482
$112$	−2.15035	−0.203189
$113$	−10.2251	−0.961897	−0.480949	−	0.876749i	$-0.659708\pi$
$113$	−10.2251	−0.961897	−0.480949	+	0.876749i	$0.659708\pi$
$114$	−3.31556	−0.310531
$115$	1.22483	0.114216
$116$	−13.6748	−1.26968
$117$	7.31894	0.676636
$118$	8.31251	0.765228
$119$	−1.20883	−0.110813
$120$	−1.52157	−0.138900
$121$	12.7679	1.16072
$122$	−2.87091	−0.259920
$123$	3.15453	0.284434
$124$	2.21173	0.198620
$125$	−1.00000	−0.0894427
$126$	−1.41245	−0.125831
$127$	14.8940	1.32163	0.660813	−	0.750551i	$-0.270212\pi$
$127$	14.8940	1.32163	0.660813	+	0.750551i	$0.270212\pi$
$128$	11.5339	1.01946
$129$	2.10192	0.185064
$130$	−1.68917	−0.148150
$131$	18.7245	1.63597	0.817984	−	0.575242i	$-0.195092\pi$
$131$	18.7245	1.63597	0.817984	+	0.575242i	$0.195092\pi$
$132$	5.91980	0.515252
$133$	−8.00582	−0.694193
$134$	−5.55913	−0.480236
$135$	3.97050	0.341727
$136$	2.53574	0.217438
$137$	−14.7726	−1.26211	−0.631055	−	0.775738i	$-0.717378\pi$
$137$	−14.7726	−1.26211	−0.631055	+	0.775738i	$0.717378\pi$
$138$	0.507254	0.0431803
$139$	−15.3766	−1.30423	−0.652114	−	0.758121i	$-0.726118\pi$
$139$	−15.3766	−1.30423	−0.652114	+	0.758121i	$0.726118\pi$
$140$	−1.67401	−0.141480
$141$	2.76746	0.233062
$142$	2.47303	0.207532
$143$	14.4235	1.20615
$144$	−5.31967	−0.443306
$145$	−8.16889	−0.678390
$146$	2.82968	0.234186
$147$	0.725358	0.0598265
$148$	2.46749	0.202827
$149$	−10.2059	−0.836102	−0.418051	−	0.908424i	$-0.637287\pi$
$149$	−10.2059	−0.836102	−0.418051	+	0.908424i	$0.637287\pi$
$150$	−0.414144	−0.0338147
$151$	−12.6835	−1.03217	−0.516083	−	0.856539i	$-0.672610\pi$
$151$	−12.6835	−1.03217	−0.516083	+	0.856539i	$0.672610\pi$
$152$	16.7937	1.36215
$153$	−2.99047	−0.241765
$154$	−2.78352	−0.224303
$155$	1.32122	0.106123
$156$	3.59240	0.287623
$157$	1.08084	0.0862601	0.0431300	−	0.999069i	$-0.486267\pi$
$157$	1.08084	0.0862601	0.0431300	+	0.999069i	$0.486267\pi$
$158$	−6.77198	−0.538749
$159$	2.78031	0.220493
$160$	5.42311	0.428735
$161$	1.22483	0.0965298
$162$	−2.59299	−0.203725
$163$	−20.4214	−1.59952	−0.799762	−	0.600317i	$-0.795041\pi$
$163$	−20.4214	−1.59952	−0.799762	+	0.600317i	$0.795041\pi$
$164$	−7.28017	−0.568486
$165$	3.53629	0.275300
$166$	−1.70199	−0.132100
$167$	8.55450	0.661967	0.330984	−	0.943637i	$-0.392620\pi$
$167$	8.55450	0.661967	0.330984	+	0.943637i	$0.392620\pi$
$168$	−1.52157	−0.117392
$169$	−4.24719	−0.326707
$170$	0.690182	0.0529345
$171$	−19.8052	−1.51454
$172$	−4.85090	−0.369878
$173$	−17.4846	−1.32933	−0.664666	−	0.747141i	$-0.731426\pi$
$173$	−17.4846	−1.32933	−0.664666	+	0.747141i	$0.731426\pi$
$174$	−3.38310	−0.256472
$175$	−1.00000	−0.0755929
$176$	−10.4835	−0.790222
$177$	−10.5605	−0.793777
$178$	−8.88125	−0.665678
$179$	8.47957	0.633793	0.316896	−	0.948460i	$-0.397359\pi$
$179$	8.47957	0.633793	0.316896	+	0.948460i	$0.397359\pi$
$180$	−4.14127	−0.308672
$181$	−9.57017	−0.711345	−0.355673	−	0.934611i	$-0.615748\pi$
$181$	−9.57017	−0.711345	−0.355673	+	0.934611i	$0.615748\pi$
$182$	−1.68917	−0.125209
$183$	3.64731	0.269617
$184$	−2.56930	−0.189411
$185$	1.47400	0.108370
$186$	0.547173	0.0401207
$187$	−5.89332	−0.430962
$188$	−6.38686	−0.465810
$189$	3.97050	0.288812
$190$	4.57093	0.331610
$191$	−4.98887	−0.360982	−0.180491	−	0.983577i	$-0.557769\pi$
$191$	−4.98887	−0.360982	−0.180491	+	0.983577i	$0.557769\pi$
$192$	−0.873603	−0.0630469
$193$	24.6174	1.77200	0.885999	−	0.463686i	$-0.153474\pi$
$193$	24.6174	1.77200	0.885999	+	0.463686i	$0.153474\pi$
$194$	10.1415	0.728118
$195$	2.14598	0.153677
$196$	−1.67401	−0.119572
$197$	−18.3147	−1.30487	−0.652435	−	0.757844i	$-0.726253\pi$
$197$	−18.3147	−1.30487	−0.652435	+	0.757844i	$0.726253\pi$
$198$	−6.88603	−0.489369
$199$	−7.05924	−0.500417	−0.250208	−	0.968192i	$-0.580499\pi$
$199$	−7.05924	−0.500417	−0.250208	+	0.968192i	$0.580499\pi$
$200$	2.09768	0.148329
$201$	7.06253	0.498153
$202$	−8.77545	−0.617438
$203$	−8.16889	−0.573344
$204$	−1.46783	−0.102769
$205$	−4.34893	−0.303743
$206$	6.60928	0.460490
$207$	3.03004	0.210603
$208$	−6.36186	−0.441115
$209$	−39.0302	−2.69978
$210$	−0.414144	−0.0285786
$211$	−3.90363	−0.268737	−0.134369	−	0.990931i	$-0.542901\pi$
$211$	−3.90363	−0.268737	−0.134369	+	0.990931i	$0.542901\pi$
$212$	−6.41653	−0.440689
$213$	−3.14183	−0.215275
$214$	−2.00640	−0.137154
$215$	−2.89777	−0.197626
$216$	−8.32886	−0.566707
$217$	1.32122	0.0896899
$218$	6.84236	0.463423
$219$	−3.59493	−0.242923
$220$	−8.16121	−0.550229
$221$	−3.57634	−0.240570
$222$	0.610447	0.0409705
$223$	25.5769	1.71275	0.856377	−	0.516352i	$-0.172710\pi$
$223$	25.5769	1.71275	0.856377	+	0.516352i	$0.172710\pi$
$224$	5.42311	0.362347
$225$	−2.47386	−0.164924
$226$	5.83804	0.388340
$227$	13.3860	0.888462	0.444231	−	0.895912i	$-0.353477\pi$
$227$	13.3860	0.888462	0.444231	+	0.895912i	$0.353477\pi$
$228$	−9.72114	−0.643798
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−0.699316	−0.0461115
$231$	3.53629	0.232671
$232$	17.1357	1.12502
$233$	−23.4693	−1.53753	−0.768763	−	0.639534i	$-0.779127\pi$
$233$	−23.4693	−1.53753	−0.768763	+	0.639534i	$0.779127\pi$
$234$	−4.17876	−0.273174
$235$	−3.81530	−0.248883
$236$	24.3721	1.58649
$237$	8.60337	0.558849
$238$	0.690182	0.0447379
$239$	−4.78427	−0.309469	−0.154734	−	0.987956i	$-0.549452\pi$
$239$	−4.78427	−0.309469	−0.154734	+	0.987956i	$0.549452\pi$
$240$	−1.55978	−0.100683
$241$	−9.86392	−0.635391	−0.317695	−	0.948193i	$-0.602909\pi$
$241$	−9.86392	−0.635391	−0.317695	+	0.948193i	$0.602909\pi$
$242$	−7.28985	−0.468610
$243$	15.2057	0.975449
$244$	−8.41743	−0.538871
$245$	−1.00000	−0.0638877
$246$	−1.80108	−0.114833
$247$	−23.6853	−1.50706
$248$	−2.77149	−0.175990
$249$	2.16227	0.137028
$250$	0.570951	0.0361101
$251$	−12.2997	−0.776351	−0.388175	−	0.921586i	$-0.626895\pi$
$251$	−12.2997	−0.776351	−0.388175	+	0.921586i	$0.626895\pi$
$252$	−4.14127	−0.260876
$253$	5.97131	0.375413
$254$	−8.50373	−0.533572
$255$	−0.876833	−0.0549094
$256$	−4.17652	−0.261033
$257$	29.7544	1.85603	0.928015	−	0.372543i	$-0.121514\pi$
$257$	29.7544	1.85603	0.928015	+	0.372543i	$0.121514\pi$
$258$	−1.20009	−0.0747145
$259$	1.47400	0.0915898
$260$	−4.95260	−0.307147
$261$	−20.2087	−1.25088
$262$	−10.6908	−0.660478
$263$	−21.0826	−1.30001	−0.650005	−	0.759930i	$-0.725233\pi$
$263$	−21.0826	−1.30001	−0.650005	+	0.759930i	$0.725233\pi$
$264$	−7.41801	−0.456547
$265$	−3.83302	−0.235460
$266$	4.57093	0.280262
$267$	11.2831	0.690513
$268$	−16.2992	−0.995635
$269$	−4.09921	−0.249933	−0.124967	−	0.992161i	$-0.539882\pi$
$269$	−4.09921	−0.249933	−0.124967	+	0.992161i	$0.539882\pi$
$270$	−2.26696	−0.137963
$271$	−18.1403	−1.10194	−0.550971	−	0.834524i	$-0.685743\pi$
$271$	−18.1403	−1.10194	−0.550971	+	0.834524i	$0.685743\pi$
$272$	2.59941	0.157612
$273$	2.14598	0.129881
$274$	8.43444	0.509543
$275$	−4.87523	−0.293988
$276$	1.48726	0.0895223
$277$	−19.8601	−1.19328	−0.596638	−	0.802511i	$-0.703497\pi$
$277$	−19.8601	−1.19328	−0.596638	+	0.802511i	$0.703497\pi$
$278$	8.77930	0.526547
$279$	3.26850	0.195680
$280$	2.09768	0.125361
$281$	9.67507	0.577166	0.288583	−	0.957455i	$-0.406816\pi$
$281$	9.67507	0.577166	0.288583	+	0.957455i	$0.406816\pi$
$282$	−1.58008	−0.0940925
$283$	−2.69837	−0.160401	−0.0802007	−	0.996779i	$-0.525556\pi$
$283$	−2.69837	−0.160401	−0.0802007	+	0.996779i	$0.525556\pi$
$284$	7.25087	0.430260
$285$	−5.80708	−0.343982
$286$	−8.23509	−0.486951
$287$	−4.34893	−0.256709
$288$	13.4160	0.790546
$289$	−15.5387	−0.914043
$290$	4.66404	0.273882
$291$	−12.8842	−0.755283
$292$	8.29654	0.485519
$293$	−11.2837	−0.659202	−0.329601	−	0.944120i	$-0.606914\pi$
$293$	−11.2837	−0.659202	−0.329601	+	0.944120i	$0.606914\pi$
$294$	−0.414144	−0.0241534
$295$	14.5590	0.847660
$296$	−3.09198	−0.179718
$297$	19.3571	1.12322
$298$	5.82709	0.337554
$299$	3.62367	0.209562
$300$	−1.21426	−0.0701053
$301$	−2.89777	−0.167025
$302$	7.24164	0.416710
$303$	11.1487	0.640473
$304$	17.2153	0.987368
$305$	−5.02829	−0.287919
$306$	1.70741	0.0976062
$307$	−17.5107	−0.999389	−0.499694	−	0.866202i	$-0.666554\pi$
$307$	−17.5107	−0.999389	−0.499694	+	0.866202i	$0.666554\pi$
$308$	−8.16121	−0.465028
$309$	−8.39667	−0.477670
$310$	−0.754349	−0.0428442
$311$	17.5764	0.996669	0.498334	−	0.866985i	$-0.333945\pi$
$311$	17.5764	0.996669	0.498334	+	0.866985i	$0.333945\pi$
$312$	−4.50159	−0.254852
$313$	33.0606	1.86869	0.934347	−	0.356363i	$-0.115983\pi$
$313$	33.0606	1.86869	0.934347	+	0.356363i	$0.115983\pi$
$314$	−0.617105	−0.0348252
$315$	−2.47386	−0.139386
$316$	−19.8553	−1.11695
$317$	7.28292	0.409050	0.204525	−	0.978861i	$-0.434435\pi$
$317$	7.28292	0.409050	0.204525	+	0.978861i	$0.434435\pi$
$318$	−1.58742	−0.0890181
$319$	−39.8253	−2.22979
$320$	1.20438	0.0673267
$321$	2.54900	0.142271
$322$	−0.699316	−0.0389713
$323$	9.67766	0.538479
$324$	−7.60259	−0.422366
$325$	−2.95851	−0.164109
$326$	11.6596	0.645766
$327$	−8.69279	−0.480712
$328$	9.12268	0.503716
$329$	−3.81530	−0.210344
$330$	−2.01905	−0.111145
$331$	29.3797	1.61486	0.807428	−	0.589966i	$-0.200859\pi$
$331$	29.3797	1.61486	0.807428	+	0.589966i	$0.200859\pi$
$332$	−4.99019	−0.273872
$333$	3.64646	0.199825
$334$	−4.88420	−0.267252
$335$	−9.73662	−0.531968
$336$	−1.55978	−0.0850928
$337$	−12.4898	−0.680363	−0.340182	−	0.940360i	$-0.610489\pi$
$337$	−12.4898	−0.680363	−0.340182	+	0.940360i	$0.610489\pi$
$338$	2.42494	0.131899
$339$	−7.41686	−0.402829
$340$	2.02360	0.109745
$341$	6.44123	0.348812
$342$	11.3078	0.611457
$343$	−1.00000	−0.0539949
$344$	6.07860	0.327736
$345$	0.888437	0.0478318
$346$	9.98287	0.536683
$347$	35.0769	1.88303	0.941515	−	0.336972i	$-0.109403\pi$
$347$	35.0769	1.88303	0.941515	+	0.336972i	$0.109403\pi$
$348$	−9.91916	−0.531723
$349$	26.6816	1.42823	0.714116	−	0.700027i	$-0.246829\pi$
$349$	26.6816	1.42823	0.714116	+	0.700027i	$0.246829\pi$
$350$	0.570951	0.0305186
$351$	11.7468	0.626998
$352$	26.4390	1.40920
$353$	10.4436	0.555858	0.277929	−	0.960602i	$-0.410352\pi$
$353$	10.4436	0.555858	0.277929	+	0.960602i	$0.410352\pi$
$354$	6.02954	0.320466
$355$	4.33142	0.229888
$356$	−26.0396	−1.38010
$357$	−0.876833	−0.0464069
$358$	−4.84142	−0.255877
$359$	−30.8997	−1.63082	−0.815411	−	0.578883i	$-0.803489\pi$
$359$	−30.8997	−1.63082	−0.815411	+	0.578883i	$0.803489\pi$
$360$	5.18937	0.273504
$361$	45.0931	2.37332
$362$	5.46410	0.287187
$363$	9.26130	0.486092
$364$	−4.95260	−0.259587
$365$	4.95608	0.259413
$366$	−2.08244	−0.108851
$367$	23.4135	1.22217	0.611086	−	0.791564i	$-0.290733\pi$
$367$	23.4135	1.22217	0.611086	+	0.791564i	$0.290733\pi$
$368$	−2.63381	−0.137297
$369$	−10.7586	−0.560072
$370$	−0.841581	−0.0437517
$371$	−3.83302	−0.199000
$372$	1.60430	0.0831790
$373$	22.2993	1.15461	0.577306	−	0.816528i	$-0.304104\pi$
$373$	22.2993	1.15461	0.577306	+	0.816528i	$0.304104\pi$
$374$	3.36480	0.173990
$375$	−0.725358	−0.0374573
$376$	8.00328	0.412738
$377$	−24.1678	−1.24470
$378$	−2.26696	−0.116600
$379$	−27.4284	−1.40890	−0.704451	−	0.709753i	$-0.748807\pi$
$379$	−27.4284	−1.40890	−0.704451	+	0.709753i	$0.748807\pi$
$380$	13.4019	0.687501
$381$	10.8035	0.553478
$382$	2.84840	0.145737
$383$	5.27997	0.269794	0.134897	−	0.990860i	$-0.456930\pi$
$383$	5.27997	0.269794	0.134897	+	0.990860i	$0.456930\pi$
$384$	8.36618	0.426935
$385$	−4.87523	−0.248465
$386$	−14.0553	−0.715398
$387$	−7.16866	−0.364403
$388$	29.7347	1.50955
$389$	9.49592	0.481462	0.240731	−	0.970592i	$-0.422613\pi$
$389$	9.49592	0.481462	0.240731	+	0.970592i	$0.422613\pi$
$390$	−1.22525	−0.0620430
$391$	−1.48060	−0.0748774
$392$	2.09768	0.105949
$393$	13.5820	0.685119
$394$	10.4568	0.526807
$395$	−11.8609	−0.596785
$396$	−20.1897	−1.01457
$397$	−7.38419	−0.370602	−0.185301	−	0.982682i	$-0.559326\pi$
$397$	−7.38419	−0.370602	−0.185301	+	0.982682i	$0.559326\pi$
$398$	4.03048	0.202030
$399$	−5.80708	−0.290718
$400$	2.15035	0.107518
$401$	11.1001	0.554312	0.277156	−	0.960825i	$-0.410608\pi$
$401$	11.1001	0.554312	0.277156	+	0.960825i	$0.410608\pi$
$402$	−4.03236	−0.201116
$403$	3.90883	0.194713
$404$	−25.7294	−1.28008
$405$	−4.54153	−0.225671
$406$	4.66404	0.231472
$407$	7.18609	0.356201
$408$	1.83932	0.0910598
$409$	−34.4658	−1.70422	−0.852112	−	0.523360i	$-0.824678\pi$
$409$	−34.4658	−1.70422	−0.852112	+	0.523360i	$0.824678\pi$
$410$	2.48303	0.122628
$411$	−10.7154	−0.528553
$412$	19.3782	0.954697
$413$	14.5590	0.716404
$414$	−1.73001	−0.0850252
$415$	−2.98097	−0.146330
$416$	16.0444	0.786640
$417$	−11.1535	−0.546192
$418$	22.2844	1.08996
$419$	−7.29969	−0.356613	−0.178307	−	0.983975i	$-0.557062\pi$
$419$	−7.29969	−0.356613	−0.178307	+	0.983975i	$0.557062\pi$
$420$	−1.21426	−0.0592498
$421$	20.7937	1.01342	0.506712	−	0.862116i	$-0.330861\pi$
$421$	20.7937	1.01342	0.506712	+	0.862116i	$0.330861\pi$
$422$	2.22878	0.108496
$423$	−9.43849	−0.458915
$424$	8.04046	0.390479
$425$	1.20883	0.0586368
$426$	1.79383	0.0869115
$427$	−5.02829	−0.243336
$428$	−5.88271	−0.284351
$429$	10.4622	0.505118
$430$	1.65448	0.0797863
$431$	7.63496	0.367763	0.183882	−	0.982948i	$-0.441134\pi$
$431$	7.63496	0.367763	0.183882	+	0.982948i	$0.441134\pi$
$432$	−8.53799	−0.410784
$433$	3.79798	0.182519	0.0912596	−	0.995827i	$-0.470911\pi$
$433$	3.79798	0.182519	0.0912596	+	0.995827i	$0.470911\pi$
$434$	−0.754349	−0.0362099
$435$	−5.92537	−0.284100
$436$	20.0616	0.960778
$437$	−9.80573	−0.469072
$438$	2.05253	0.0980736
$439$	−20.9809	−1.00136	−0.500681	−	0.865632i	$-0.666917\pi$
$439$	−20.9809	−1.00136	−0.500681	+	0.865632i	$0.666917\pi$
$440$	10.2267	0.487539
$441$	−2.47386	−0.117803
$442$	2.04191	0.0971239
$443$	−7.83814	−0.372401	−0.186201	−	0.982512i	$-0.559617\pi$
$443$	−7.83814	−0.372401	−0.186201	+	0.982512i	$0.559617\pi$
$444$	1.78982	0.0849409
$445$	−15.5552	−0.737386
$446$	−14.6031	−0.691479
$447$	−7.40295	−0.350147
$448$	1.20438	0.0569014
$449$	−21.8261	−1.03004	−0.515019	−	0.857179i	$-0.672215\pi$
$449$	−21.8261	−1.03004	−0.515019	+	0.857179i	$0.672215\pi$
$450$	1.41245	0.0665836
$451$	−21.2021	−0.998366
$452$	17.1170	0.805115
$453$	−9.20005	−0.432256
$454$	−7.64277	−0.358693
$455$	−2.95851	−0.138697
$456$	12.1814	0.570447
$457$	2.83767	0.132741	0.0663704	−	0.997795i	$-0.478858\pi$
$457$	2.83767	0.132741	0.0663704	+	0.997795i	$0.478858\pi$
$458$	0.570951	0.0266788
$459$	−4.79966	−0.224029
$460$	−2.05038	−0.0955993
$461$	−22.8725	−1.06528	−0.532639	−	0.846343i	$-0.678799\pi$
$461$	−22.8725	−1.06528	−0.532639	+	0.846343i	$0.678799\pi$
$462$	−2.01905	−0.0939346
$463$	−27.5610	−1.28087	−0.640433	−	0.768014i	$-0.721245\pi$
$463$	−27.5610	−1.28087	−0.640433	+	0.768014i	$0.721245\pi$
$464$	17.5660	0.815482
$465$	0.958354	0.0444426
$466$	13.3998	0.620735
$467$	−9.80095	−0.453534	−0.226767	−	0.973949i	$-0.572816\pi$
$467$	−9.80095	−0.453534	−0.226767	+	0.973949i	$0.572816\pi$
$468$	−12.2520	−0.566349
$469$	−9.73662	−0.449595
$470$	2.17835	0.100480
$471$	0.783993	0.0361245
$472$	−30.5403	−1.40573
$473$	−14.1273	−0.649574
$474$	−4.91211	−0.225620
$475$	8.00582	0.367332
$476$	2.02360	0.0927514
$477$	−9.48233	−0.434166
$478$	2.73158	0.124940
$479$	−1.52086	−0.0694899	−0.0347450	−	0.999396i	$-0.511062\pi$
$479$	−1.52086	−0.0694899	−0.0347450	+	0.999396i	$0.511062\pi$
$480$	3.93370	0.179548
$481$	4.36084	0.198837
$482$	5.63182	0.256522
$483$	0.888437	0.0404253
$484$	−21.3737	−0.971530
$485$	17.7625	0.806553
$486$	−8.68174	−0.393812
$487$	6.03503	0.273473	0.136737	−	0.990607i	$-0.456339\pi$
$487$	6.03503	0.273473	0.136737	+	0.990607i	$0.456339\pi$
$488$	10.5478	0.477475
$489$	−14.8128	−0.669858
$490$	0.570951	0.0257929
$491$	−29.4396	−1.32859	−0.664295	−	0.747471i	$-0.731268\pi$
$491$	−29.4396	−1.32859	−0.664295	+	0.747471i	$0.731268\pi$
$492$	−5.28073	−0.238074
$493$	9.87479	0.444738
$494$	13.5232	0.608436
$495$	−12.0606	−0.542085
$496$	−2.84108	−0.127568
$497$	4.33142	0.194291
$498$	−1.23455	−0.0553215
$499$	−26.7198	−1.19614	−0.598070	−	0.801444i	$-0.704066\pi$
$499$	−26.7198	−1.19614	−0.598070	+	0.801444i	$0.704066\pi$
$500$	1.67401	0.0748642
$501$	6.20507	0.277222
$502$	7.02253	0.313431
$503$	5.93880	0.264798	0.132399	−	0.991197i	$-0.457732\pi$
$503$	5.93880	0.264798	0.132399	+	0.991197i	$0.457732\pi$
$504$	5.18937	0.231153
$505$	−15.3699	−0.683950
$506$	−3.40933	−0.151563
$507$	−3.08073	−0.136820
$508$	−24.9327	−1.10621
$509$	−13.1821	−0.584285	−0.292142	−	0.956375i	$-0.594368\pi$
$509$	−13.1821	−0.584285	−0.292142	+	0.956375i	$0.594368\pi$
$510$	0.500629	0.0221682
$511$	4.95608	0.219244
$512$	−20.6831	−0.914074
$513$	−31.7871	−1.40344
$514$	−16.9883	−0.749323
$515$	11.5759	0.510095
$516$	−3.51864	−0.154900
$517$	−18.6005	−0.818047
$518$	−0.841581	−0.0369769
$519$	−12.6826	−0.556705
$520$	6.20603	0.272152
$521$	42.4277	1.85879	0.929395	−	0.369087i	$-0.120329\pi$
$521$	42.4277	1.85879	0.929395	+	0.369087i	$0.120329\pi$
$522$	11.5382	0.505012
$523$	2.16737	0.0947725	0.0473862	−	0.998877i	$-0.484911\pi$
$523$	2.16737	0.0947725	0.0473862	+	0.998877i	$0.484911\pi$
$524$	−31.3451	−1.36932
$525$	−0.725358	−0.0316572
$526$	12.0371	0.524844
$527$	−1.59712	−0.0695717
$528$	−7.60428	−0.330934
$529$	−21.4998	−0.934774
$530$	2.18847	0.0950609
$531$	36.0170	1.56300
$532$	13.4019	0.581044
$533$	−12.8664	−0.557305
$534$	−6.44208	−0.278776
$535$	−3.51413	−0.151929
$536$	20.4243	0.882197
$537$	6.15072	0.265423
$538$	2.34045	0.100904
$539$	−4.87523	−0.209991
$540$	−6.64668	−0.286028
$541$	3.60192	0.154859	0.0774293	−	0.996998i	$-0.475329\pi$
$541$	3.60192	0.154859	0.0774293	+	0.996998i	$0.475329\pi$
$542$	10.3572	0.444880
$543$	−6.94180	−0.297901
$544$	−6.55561	−0.281070
$545$	11.9841	0.513344
$546$	−1.22525	−0.0524359
$547$	20.1213	0.860325	0.430162	−	0.902752i	$-0.358456\pi$
$547$	20.1213	0.860325	0.430162	+	0.902752i	$0.358456\pi$
$548$	24.7296	1.05640
$549$	−12.4393	−0.530895
$550$	2.78352	0.118690
$551$	65.3987	2.78608
$552$	−1.86366	−0.0793226
$553$	−11.8609	−0.504375
$554$	11.3391	0.481753
$555$	1.06918	0.0453840
$556$	25.7407	1.09165
$557$	−37.2638	−1.57892	−0.789459	−	0.613804i	$-0.789639\pi$
$557$	−37.2638	−1.57892	−0.789459	+	0.613804i	$0.789639\pi$
$558$	−1.86615	−0.0790005
$559$	−8.57309	−0.362603
$560$	2.15035	0.0908691
$561$	−4.27477	−0.180481
$562$	−5.52399	−0.233015
$563$	−6.41262	−0.270260	−0.135130	−	0.990828i	$-0.543145\pi$
$563$	−6.41262	−0.270260	−0.135130	+	0.990828i	$0.543145\pi$
$564$	−4.63276	−0.195074
$565$	10.2251	0.430174
$566$	1.54064	0.0647578
$567$	−4.54153	−0.190726
$568$	−9.08596	−0.381238
$569$	10.9692	0.459852	0.229926	−	0.973208i	$-0.426152\pi$
$569$	10.9692	0.459852	0.229926	+	0.973208i	$0.426152\pi$
$570$	3.31556	0.138874
$571$	−45.2405	−1.89325	−0.946627	−	0.322331i	$-0.895534\pi$
$571$	−45.2405	−1.89325	−0.946627	+	0.322331i	$0.895534\pi$
$572$	−24.1451	−1.00956
$573$	−3.61871	−0.151174
$574$	2.48303	0.103640
$575$	−1.22483	−0.0510788
$576$	2.97945	0.124144
$577$	−42.8670	−1.78458	−0.892289	−	0.451464i	$-0.850902\pi$
$577$	−42.8670	−1.78458	−0.892289	+	0.451464i	$0.850902\pi$
$578$	8.87186	0.369021
$579$	17.8564	0.742087
$580$	13.6748	0.567817
$581$	−2.98097	−0.123671
$582$	7.35622	0.304925
$583$	−18.6869	−0.773931
$584$	−10.3963	−0.430201
$585$	−7.31894	−0.302601
$586$	6.44246	0.266135
$587$	−5.81349	−0.239948	−0.119974	−	0.992777i	$-0.538281\pi$
$587$	−5.81349	−0.239948	−0.119974	+	0.992777i	$0.538281\pi$
$588$	−1.21426	−0.0500752
$589$	−10.5774	−0.435835
$590$	−8.31251	−0.342220
$591$	−13.2847	−0.546461
$592$	−3.16962	−0.130271
$593$	16.9113	0.694463	0.347231	−	0.937779i	$-0.387122\pi$
$593$	16.9113	0.694463	0.347231	+	0.937779i	$0.387122\pi$
$594$	−11.0520	−0.453468
$595$	1.20883	0.0495571
$596$	17.0849	0.699824
$597$	−5.12048	−0.209567
$598$	−2.06894	−0.0846051
$599$	39.6842	1.62145	0.810726	−	0.585426i	$-0.199073\pi$
$599$	39.6842	1.62145	0.810726	+	0.585426i	$0.199073\pi$
$600$	1.52157	0.0621179
$601$	23.7279	0.967880	0.483940	−	0.875101i	$-0.339205\pi$
$601$	23.7279	0.967880	0.483940	+	0.875101i	$0.339205\pi$
$602$	1.65448	0.0674317
$603$	−24.0870	−0.980898
$604$	21.2323	0.863930
$605$	−12.7679	−0.519089
$606$	−6.36534	−0.258574
$607$	−9.33262	−0.378799	−0.189400	−	0.981900i	$-0.560654\pi$
$607$	−9.33262	−0.378799	−0.189400	+	0.981900i	$0.560654\pi$
$608$	−43.4165	−1.76077
$609$	−5.92537	−0.240108
$610$	2.87091	0.116240
$611$	−11.2876	−0.456648
$612$	5.00609	0.202359
$613$	−36.2045	−1.46229	−0.731143	−	0.682224i	$-0.761013\pi$
$613$	−36.2045	−1.46229	−0.731143	+	0.682224i	$0.761013\pi$
$614$	9.99776	0.403477
$615$	−3.15453	−0.127203
$616$	10.2267	0.412045
$617$	4.83513	0.194655	0.0973274	−	0.995252i	$-0.468971\pi$
$617$	4.83513	0.194655	0.0973274	+	0.995252i	$0.468971\pi$
$618$	4.79409	0.192847
$619$	−14.6994	−0.590821	−0.295410	−	0.955370i	$-0.595456\pi$
$619$	−14.6994	−0.590821	−0.295410	+	0.955370i	$0.595456\pi$
$620$	−2.21173	−0.0888254
$621$	4.86318	0.195153
$622$	−10.0353	−0.402379
$623$	−15.5552	−0.623205
$624$	−4.61462	−0.184733
$625$	1.00000	0.0400000
$626$	−18.8760	−0.754436
$627$	−28.3109	−1.13063
$628$	−1.80934	−0.0722003
$629$	−1.78181	−0.0710454
$630$	1.41245	0.0562734
$631$	7.29817	0.290536	0.145268	−	0.989392i	$-0.453596\pi$
$631$	7.29817	0.290536	0.145268	+	0.989392i	$0.453596\pi$
$632$	24.8803	0.989687
$633$	−2.83153	−0.112543
$634$	−4.15819	−0.165143
$635$	−14.8940	−0.591049
$636$	−4.65428	−0.184554
$637$	−2.95851	−0.117221
$638$	22.7383	0.900217
$639$	10.7153	0.423892
$640$	−11.5339	−0.455916
$641$	−9.11505	−0.360023	−0.180011	−	0.983665i	$-0.557613\pi$
$641$	−9.11505	−0.360023	−0.180011	+	0.983665i	$0.557613\pi$
$642$	−1.45536	−0.0574383
$643$	−25.1838	−0.993151	−0.496576	−	0.867993i	$-0.665409\pi$
$643$	−25.1838	−0.993151	−0.496576	+	0.867993i	$0.665409\pi$
$644$	−2.05038	−0.0807962
$645$	−2.10192	−0.0827629
$646$	−5.52547	−0.217397
$647$	−8.67750	−0.341148	−0.170574	−	0.985345i	$-0.554562\pi$
$647$	−8.67750	−0.341148	−0.170574	+	0.985345i	$0.554562\pi$
$648$	9.52670	0.374244
$649$	70.9788	2.78616
$650$	1.68917	0.0662546
$651$	0.958354	0.0375608
$652$	34.1857	1.33881
$653$	−35.1511	−1.37557	−0.687785	−	0.725914i	$-0.741417\pi$
$653$	−35.1511	−1.37557	−0.687785	+	0.725914i	$0.741417\pi$
$654$	4.96316	0.194075
$655$	−18.7245	−0.731627
$656$	9.35174	0.365124
$657$	12.2606	0.478332
$658$	2.17835	0.0849209
$659$	10.2812	0.400497	0.200248	−	0.979745i	$-0.435825\pi$
$659$	10.2812	0.400497	0.200248	+	0.979745i	$0.435825\pi$
$660$	−5.91980	−0.230428
$661$	−22.3985	−0.871202	−0.435601	−	0.900140i	$-0.643464\pi$
$661$	−22.3985	−0.871202	−0.435601	+	0.900140i	$0.643464\pi$
$662$	−16.7744	−0.651955
$663$	−2.59412	−0.100747
$664$	6.25313	0.242668
$665$	8.00582	0.310452
$666$	−2.08195	−0.0806739
$667$	−10.0055	−0.387413
$668$	−14.3204	−0.554071
$669$	18.5524	0.717276
$670$	5.55913	0.214768
$671$	−24.5141	−0.946356
$672$	3.93370	0.151746
$673$	−47.0967	−1.81544	−0.907721	−	0.419574i	$-0.862180\pi$
$673$	−47.0967	−1.81544	−0.907721	+	0.419574i	$0.862180\pi$
$674$	7.13107	0.274679
$675$	−3.97050	−0.152825
$676$	7.10986	0.273456
$677$	10.2123	0.392492	0.196246	−	0.980555i	$-0.437125\pi$
$677$	10.2123	0.392492	0.196246	+	0.980555i	$0.437125\pi$
$678$	4.23467	0.162631
$679$	17.7625	0.681662
$680$	−2.53574	−0.0972411
$681$	9.70966	0.372075
$682$	−3.67763	−0.140824
$683$	−30.9861	−1.18565	−0.592825	−	0.805331i	$-0.701987\pi$
$683$	−30.9861	−1.18565	−0.592825	+	0.805331i	$0.701987\pi$
$684$	33.1543	1.26769
$685$	14.7726	0.564433
$686$	0.570951	0.0217990
$687$	−0.725358	−0.0276741
$688$	6.23123	0.237563
$689$	−11.3400	−0.432021
$690$	−0.507254	−0.0193108
$691$	35.8305	1.36306	0.681529	−	0.731791i	$-0.261315\pi$
$691$	35.8305	1.36306	0.681529	+	0.731791i	$0.261315\pi$
$692$	29.2695	1.11266
$693$	−12.0606	−0.458145
$694$	−20.0272	−0.760223
$695$	15.3766	0.583268
$696$	12.4295	0.471141
$697$	5.25711	0.199127
$698$	−15.2339	−0.576611
$699$	−17.0237	−0.643894
$700$	1.67401	0.0632718
$701$	34.5254	1.30401	0.652003	−	0.758217i	$-0.273929\pi$
$701$	34.5254	1.30401	0.652003	+	0.758217i	$0.273929\pi$
$702$	−6.70685	−0.253134
$703$	−11.8006	−0.445067
$704$	5.87161	0.221295
$705$	−2.76746	−0.104228
$706$	−5.96280	−0.224413
$707$	−15.3699	−0.578043
$708$	17.6785	0.664397
$709$	47.9497	1.80079	0.900394	−	0.435076i	$-0.143278\pi$
$709$	47.9497	1.80079	0.900394	+	0.435076i	$0.143278\pi$
$710$	−2.47303	−0.0928112
$711$	−29.3421	−1.10041
$712$	32.6298	1.22285
$713$	1.61826	0.0606043
$714$	0.500629	0.0187356
$715$	−14.4235	−0.539407
$716$	−14.1949	−0.530489
$717$	−3.47031	−0.129601
$718$	17.6422	0.658401
$719$	−23.1665	−0.863965	−0.431983	−	0.901882i	$-0.642186\pi$
$719$	−23.1665	−0.863965	−0.431983	+	0.901882i	$0.642186\pi$
$720$	5.31967	0.198252
$721$	11.5759	0.431109
$722$	−25.7460	−0.958166
$723$	−7.15487	−0.266092
$724$	16.0206	0.595401
$725$	8.16889	0.303385
$726$	−5.28775	−0.196247
$727$	−48.2233	−1.78851	−0.894253	−	0.447563i	$-0.852292\pi$
$727$	−48.2233	−1.78851	−0.894253	+	0.447563i	$0.852292\pi$
$728$	6.20603	0.230011
$729$	−2.59499	−0.0961107
$730$	−2.82968	−0.104731
$731$	3.50290	0.129560
$732$	−6.10565	−0.225671
$733$	−12.5010	−0.461735	−0.230867	−	0.972985i	$-0.574156\pi$
$733$	−12.5010	−0.461735	−0.230867	+	0.972985i	$0.574156\pi$
$734$	−13.3679	−0.493420
$735$	−0.725358	−0.0267552
$736$	6.64237	0.244841
$737$	−47.4683	−1.74852
$738$	6.14265	0.226114
$739$	−13.2738	−0.488285	−0.244143	−	0.969739i	$-0.578507\pi$
$739$	−13.2738	−0.488285	−0.244143	+	0.969739i	$0.578507\pi$
$740$	−2.46749	−0.0907069
$741$	−17.1803	−0.631136
$742$	2.18847	0.0803411
$743$	−27.1614	−0.996456	−0.498228	−	0.867046i	$-0.666016\pi$
$743$	−27.1614	−0.996456	−0.498228	+	0.867046i	$0.666016\pi$
$744$	−2.01032	−0.0737020
$745$	10.2059	0.373916
$746$	−12.7318	−0.466144
$747$	−7.37449	−0.269818
$748$	9.86551	0.360719
$749$	−3.51413	−0.128404
$750$	0.414144	0.0151224
$751$	−6.22739	−0.227241	−0.113620	−	0.993524i	$-0.536245\pi$
$751$	−6.22739	−0.227241	−0.113620	+	0.993524i	$0.536245\pi$
$752$	8.20424	0.299178
$753$	−8.92169	−0.325124
$754$	13.7986	0.502516
$755$	12.6835	0.461599
$756$	−6.64668	−0.241738
$757$	18.6547	0.678016	0.339008	−	0.940783i	$-0.389909\pi$
$757$	18.6547	0.678016	0.339008	+	0.940783i	$0.389909\pi$
$758$	15.6603	0.568807
$759$	4.33134	0.157218
$760$	−16.7937	−0.609170
$761$	25.1139	0.910378	0.455189	−	0.890395i	$-0.349572\pi$
$761$	25.1139	0.910378	0.455189	+	0.890395i	$0.349572\pi$
$762$	−6.16825	−0.223452
$763$	11.9841	0.433855
$764$	8.35143	0.302144
$765$	2.99047	0.108121
$766$	−3.01461	−0.108922
$767$	43.0732	1.55528
$768$	−3.02947	−0.109317
$769$	−13.8362	−0.498946	−0.249473	−	0.968382i	$-0.580257\pi$
$769$	−13.8362	−0.498946	−0.249473	+	0.968382i	$0.580257\pi$
$770$	2.78352	0.100311
$771$	21.5826	0.777279
$772$	−41.2099	−1.48318
$773$	−14.9909	−0.539185	−0.269592	−	0.962975i	$-0.586889\pi$
$773$	−14.9909	−0.539185	−0.269592	+	0.962975i	$0.586889\pi$
$774$	4.09295	0.147118
$775$	−1.32122	−0.0474594
$776$	−37.2601	−1.33756
$777$	1.06918	0.0383565
$778$	−5.42171	−0.194378
$779$	34.8168	1.24744
$780$	−3.59240	−0.128629
$781$	21.1167	0.755615
$782$	0.845353	0.0302298
$783$	−32.4346	−1.15912
$784$	2.15035	0.0767984
$785$	−1.08084	−0.0385767
$786$	−7.75464	−0.276599
$787$	8.77558	0.312816	0.156408	−	0.987693i	$-0.450009\pi$
$787$	8.77558	0.312816	0.156408	+	0.987693i	$0.450009\pi$
$788$	30.6591	1.09219
$789$	−15.2924	−0.544425
$790$	6.77198	0.240936
$791$	10.2251	0.363563
$792$	25.2994	0.898974
$793$	−14.8763	−0.528272
$794$	4.21601	0.149621
$795$	−2.78031	−0.0986074
$796$	11.8173	0.418852
$797$	−13.0377	−0.461821	−0.230910	−	0.972975i	$-0.574170\pi$
$797$	−13.0377	−0.461821	−0.230910	+	0.972975i	$0.574170\pi$
$798$	3.31556	0.117370
$799$	4.61204	0.163162
$800$	−5.42311	−0.191736
$801$	−38.4813	−1.35967
$802$	−6.33761	−0.223789
$803$	24.1620	0.852660
$804$	−11.8228	−0.416957
$805$	−1.22483	−0.0431694
$806$	−2.23175	−0.0786102
$807$	−2.97340	−0.104669
$808$	32.2411	1.13424
$809$	39.3623	1.38390	0.691952	−	0.721943i	$-0.256751\pi$
$809$	39.3623	1.38390	0.691952	+	0.721943i	$0.256751\pi$
$810$	2.59299	0.0911085
$811$	26.9531	0.946452	0.473226	−	0.880941i	$-0.343089\pi$
$811$	26.9531	0.946452	0.473226	+	0.880941i	$0.343089\pi$
$812$	13.6748	0.479893
$813$	−13.1582	−0.461478
$814$	−4.10290	−0.143807
$815$	20.4214	0.715329
$816$	1.88550	0.0660058
$817$	23.1990	0.811630
$818$	19.6783	0.688035
$819$	−7.31894	−0.255744
$820$	7.28017	0.254235
$821$	9.70017	0.338538	0.169269	−	0.985570i	$-0.445859\pi$
$821$	9.70017	0.338538	0.169269	+	0.985570i	$0.445859\pi$
$822$	6.11799	0.213389
$823$	52.3995	1.82653	0.913266	−	0.407365i	$-0.133552\pi$
$823$	52.3995	1.82653	0.913266	+	0.407365i	$0.133552\pi$
$824$	−24.2826	−0.845924
$825$	−3.53629	−0.123118
$826$	−8.31251	−0.289229
$827$	−6.65367	−0.231371	−0.115685	−	0.993286i	$-0.536906\pi$
$827$	−6.65367	−0.231371	−0.115685	+	0.993286i	$0.536906\pi$
$828$	−5.07234	−0.176276
$829$	−19.7400	−0.685598	−0.342799	−	0.939409i	$-0.611375\pi$
$829$	−19.7400	−0.685598	−0.342799	+	0.939409i	$0.611375\pi$
$830$	1.70199	0.0590769
$831$	−14.4056	−0.499726
$832$	3.56316	0.123530
$833$	1.20883	0.0418834
$834$	6.36813	0.220510
$835$	−8.55450	−0.296041
$836$	65.3372	2.25973
$837$	5.24589	0.181324
$838$	4.16777	0.143973
$839$	2.32508	0.0802708	0.0401354	−	0.999194i	$-0.487221\pi$
$839$	2.32508	0.0802708	0.0401354	+	0.999194i	$0.487221\pi$
$840$	1.52157	0.0524992
$841$	37.7308	1.30106
$842$	−11.8722	−0.409143
$843$	7.01788	0.241709
$844$	6.53474	0.224935
$845$	4.24719	0.146108
$846$	5.38892	0.185275
$847$	−12.7679	−0.438711
$848$	8.24235	0.283043
$849$	−1.95728	−0.0671738
$850$	−0.690182	−0.0236730
$851$	1.80539	0.0618880
$852$	5.25947	0.180187
$853$	−2.47928	−0.0848889	−0.0424444	−	0.999099i	$-0.513515\pi$
$853$	−2.47928	−0.0848889	−0.0424444	+	0.999099i	$0.513515\pi$
$854$	2.87091	0.0982404
$855$	19.8052	0.677325
$856$	7.37153	0.251954
$857$	−52.1068	−1.77993	−0.889967	−	0.456024i	$-0.849273\pi$
$857$	−52.1068	−1.77993	−0.889967	+	0.456024i	$0.849273\pi$
$858$	−5.97338	−0.203928
$859$	−28.4280	−0.969951	−0.484976	−	0.874528i	$-0.661172\pi$
$859$	−28.4280	−0.969951	−0.484976	+	0.874528i	$0.661172\pi$
$860$	4.85090	0.165414
$861$	−3.15453	−0.107506
$862$	−4.35919	−0.148475
$863$	11.2647	0.383455	0.191727	−	0.981448i	$-0.438591\pi$
$863$	11.2647	0.383455	0.191727	+	0.981448i	$0.438591\pi$
$864$	21.5325	0.732550
$865$	17.4846	0.594495
$866$	−2.16846	−0.0736873
$867$	−11.2711	−0.382788
$868$	−2.21173	−0.0750711
$869$	−57.8245	−1.96156
$870$	3.38310	0.114698
$871$	−28.8059	−0.976052
$872$	−25.1389	−0.851312
$873$	43.9418	1.48721
$874$	5.59860	0.189375
$875$	1.00000	0.0338062
$876$	6.01796	0.203328
$877$	30.1573	1.01834	0.509171	−	0.860666i	$-0.329952\pi$
$877$	30.1573	1.01834	0.509171	+	0.860666i	$0.329952\pi$
$878$	11.9791	0.404273
$879$	−8.18474	−0.276064
$880$	10.4835	0.353398
$881$	−37.2020	−1.25337	−0.626683	−	0.779274i	$-0.715588\pi$
$881$	−37.2020	−1.25337	−0.626683	+	0.779274i	$0.715588\pi$
$882$	1.41245	0.0475597
$883$	−41.0904	−1.38280	−0.691401	−	0.722471i	$-0.743006\pi$
$883$	−41.0904	−1.38280	−0.691401	+	0.722471i	$0.743006\pi$
$884$	5.98684	0.201359
$885$	10.5605	0.354988
$886$	4.47519	0.150347
$887$	−37.1130	−1.24613	−0.623067	−	0.782169i	$-0.714114\pi$
$887$	−37.1130	−1.24613	−0.623067	+	0.782169i	$0.714114\pi$
$888$	−2.24279	−0.0752632
$889$	−14.8940	−0.499528
$890$	8.88125	0.297700
$891$	−22.1410	−0.741753
$892$	−42.8160	−1.43359
$893$	30.5446	1.02214
$894$	4.22672	0.141363
$895$	−8.47957	−0.283441
$896$	−11.5339	−0.385319
$897$	2.62845	0.0877615
$898$	12.4616	0.415850
$899$	−10.7929	−0.359962
$900$	4.14127	0.138042
$901$	4.63346	0.154363
$902$	12.1053	0.403064
$903$	−2.10192	−0.0699474
$904$	−21.4490	−0.713384
$905$	9.57017	0.318123
$906$	5.25278	0.174512
$907$	−9.37948	−0.311441	−0.155720	−	0.987801i	$-0.549770\pi$
$907$	−9.37948	−0.311441	−0.155720	+	0.987801i	$0.549770\pi$
$908$	−22.4084	−0.743649
$909$	−38.0228	−1.26114
$910$	1.68917	0.0559954
$911$	54.7669	1.81451	0.907254	−	0.420582i	$-0.138174\pi$
$911$	54.7669	1.81451	0.907254	+	0.420582i	$0.138174\pi$
$912$	12.4873	0.413495
$913$	−14.5329	−0.480970
$914$	−1.62017	−0.0535905
$915$	−3.64731	−0.120576
$916$	1.67401	0.0553110
$917$	−18.7245	−0.618337
$918$	2.74037	0.0904457
$919$	−0.707406	−0.0233352	−0.0116676	−	0.999932i	$-0.503714\pi$
$919$	−0.707406	−0.0233352	−0.0116676	+	0.999932i	$0.503714\pi$
$920$	2.56930	0.0847072
$921$	−12.7015	−0.418530
$922$	13.0591	0.430077
$923$	12.8146	0.421797
$924$	−5.91980	−0.194747
$925$	−1.47400	−0.0484648
$926$	15.7360	0.517116
$927$	28.6371	0.940566
$928$	−44.3008	−1.45425
$929$	34.9753	1.14750	0.573751	−	0.819030i	$-0.305488\pi$
$929$	34.9753	1.14750	0.573751	+	0.819030i	$0.305488\pi$
$930$	−0.547173	−0.0179425
$931$	8.00582	0.262380
$932$	39.2880	1.28692
$933$	12.7492	0.417390
$934$	5.59586	0.183102
$935$	5.89332	0.192732
$936$	15.3528	0.501823
$937$	36.8705	1.20451	0.602254	−	0.798304i	$-0.294269\pi$
$937$	36.8705	1.20451	0.602254	+	0.798304i	$0.294269\pi$
$938$	5.55913	0.181512
$939$	23.9808	0.782582
$940$	6.38686	0.208316
$941$	−24.8044	−0.808601	−0.404300	−	0.914626i	$-0.632485\pi$
$941$	−24.8044	−0.808601	−0.404300	+	0.914626i	$0.632485\pi$
$942$	−0.447622	−0.0145843
$943$	−5.32668	−0.173461
$944$	−31.3071	−1.01896
$945$	−3.97050	−0.129161
$946$	8.06599	0.262248
$947$	28.6802	0.931980	0.465990	−	0.884790i	$-0.345698\pi$
$947$	28.6802	0.931980	0.465990	+	0.884790i	$0.345698\pi$
$948$	−14.4022	−0.467761
$949$	14.6626	0.475969
$950$	−4.57093	−0.148301
$951$	5.28272	0.171304
$952$	−2.53574	−0.0821838
$953$	−29.1836	−0.945349	−0.472674	−	0.881237i	$-0.656711\pi$
$953$	−29.1836	−0.945349	−0.472674	+	0.881237i	$0.656711\pi$
$954$	5.41395	0.175283
$955$	4.98887	0.161436
$956$	8.00894	0.259028
$957$	−28.8876	−0.933802
$958$	0.868338	0.0280547
$959$	14.7726	0.477033
$960$	0.873603	0.0281954
$961$	−29.2544	−0.943690
$962$	−2.48983	−0.0802753
$963$	−8.69345	−0.280143
$964$	16.5123	0.531827
$965$	−24.6174	−0.792462
$966$	−0.507254	−0.0163206
$967$	13.5394	0.435399	0.217699	−	0.976016i	$-0.430145\pi$
$967$	13.5394	0.435399	0.217699	+	0.976016i	$0.430145\pi$
$968$	26.7830	0.860839
$969$	7.01977	0.225507
$970$	−10.1415	−0.325624
$971$	19.6864	0.631768	0.315884	−	0.948798i	$-0.397699\pi$
$971$	19.6864	0.631768	0.315884	+	0.948798i	$0.397699\pi$
$972$	−25.4546	−0.816458
$973$	15.3766	0.492952
$974$	−3.44571	−0.110408
$975$	−2.14598	−0.0687264
$976$	10.8126	0.346103
$977$	−32.8274	−1.05024	−0.525121	−	0.851027i	$-0.675980\pi$
$977$	−32.8274	−1.05024	−0.525121	+	0.851027i	$0.675980\pi$
$978$	8.45738	0.270437
$979$	−75.8351	−2.42370
$980$	1.67401	0.0534744
$981$	29.6470	0.946557
$982$	16.8086	0.536383
$983$	1.81265	0.0578145	0.0289073	−	0.999582i	$-0.490797\pi$
$983$	1.81265	0.0578145	0.0289073	+	0.999582i	$0.490797\pi$
$984$	6.61721	0.210949
$985$	18.3147	0.583556
$986$	−5.63802	−0.179551
$987$	−2.76746	−0.0880891
$988$	39.6496	1.26142
$989$	−3.54926	−0.112860
$990$	6.88603	0.218852
$991$	61.8137	1.96358	0.981788	−	0.189979i	$-0.0608421\pi$
$991$	61.8137	1.96358	0.981788	+	0.189979i	$0.0608421\pi$
$992$	7.16510	0.227492
$993$	21.3108	0.676278
$994$	−2.47303	−0.0784398
$995$	7.05924	0.223793
$996$	−3.61967	−0.114694
$997$	40.6997	1.28897	0.644487	−	0.764616i	$-0.277071\pi$
$997$	40.6997	1.28897	0.644487	+	0.764616i	$0.277071\pi$
$998$	15.2557	0.482910
$999$	5.85251	0.185165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.22	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.22	✓	49	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.570951 q^{2} +0.725358 q^{3} -1.67401 q^{4} -1.00000 q^{5} -0.414144 q^{6} -1.00000 q^{7} +2.09768 q^{8} -2.47386 q^{9} +O(q^{10})\)	\(q-0.570951 q^{2} +0.725358 q^{3} -1.67401 q^{4} -1.00000 q^{5} -0.414144 q^{6} -1.00000 q^{7} +2.09768 q^{8} -2.47386 q^{9} +0.570951 q^{10} -4.87523 q^{11} -1.21426 q^{12} -2.95851 q^{13} +0.570951 q^{14} -0.725358 q^{15} +2.15035 q^{16} +1.20883 q^{17} +1.41245 q^{18} +8.00582 q^{19} +1.67401 q^{20} -0.725358 q^{21} +2.78352 q^{22} -1.22483 q^{23} +1.52157 q^{24} +1.00000 q^{25} +1.68917 q^{26} -3.97050 q^{27} +1.67401 q^{28} +8.16889 q^{29} +0.414144 q^{30} -1.32122 q^{31} -5.42311 q^{32} -3.53629 q^{33} -0.690182 q^{34} +1.00000 q^{35} +4.14127 q^{36} -1.47400 q^{37} -4.57093 q^{38} -2.14598 q^{39} -2.09768 q^{40} +4.34893 q^{41} +0.414144 q^{42} +2.89777 q^{43} +8.16121 q^{44} +2.47386 q^{45} +0.699316 q^{46} +3.81530 q^{47} +1.55978 q^{48} +1.00000 q^{49} -0.570951 q^{50} +0.876833 q^{51} +4.95260 q^{52} +3.83302 q^{53} +2.26696 q^{54} +4.87523 q^{55} -2.09768 q^{56} +5.80708 q^{57} -4.66404 q^{58} -14.5590 q^{59} +1.21426 q^{60} +5.02829 q^{61} +0.754349 q^{62} +2.47386 q^{63} -1.20438 q^{64} +2.95851 q^{65} +2.01905 q^{66} +9.73662 q^{67} -2.02360 q^{68} -0.888437 q^{69} -0.570951 q^{70} -4.33142 q^{71} -5.18937 q^{72} -4.95608 q^{73} +0.841581 q^{74} +0.725358 q^{75} -13.4019 q^{76} +4.87523 q^{77} +1.22525 q^{78} +11.8609 q^{79} -2.15035 q^{80} +4.54153 q^{81} -2.48303 q^{82} +2.98097 q^{83} +1.21426 q^{84} -1.20883 q^{85} -1.65448 q^{86} +5.92537 q^{87} -10.2267 q^{88} +15.5552 q^{89} -1.41245 q^{90} +2.95851 q^{91} +2.05038 q^{92} -0.958354 q^{93} -2.17835 q^{94} -8.00582 q^{95} -3.93370 q^{96} -17.7625 q^{97} -0.570951 q^{98} +12.0606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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