LMFDB - Embedded newform 1205.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39470 q^{2} -0.828213 q^{3} +3.73459 q^{4} -1.00000 q^{5} +1.98332 q^{6} -3.81161 q^{7} -4.15383 q^{8} -2.31406 q^{9} +O(q^{10})$	\(q-2.39470 q^{2} -0.828213 q^{3} +3.73459 q^{4} -1.00000 q^{5} +1.98332 q^{6} -3.81161 q^{7} -4.15383 q^{8} -2.31406 q^{9} +2.39470 q^{10} -0.175189 q^{11} -3.09304 q^{12} -3.64865 q^{13} +9.12767 q^{14} +0.828213 q^{15} +2.47800 q^{16} -4.10583 q^{17} +5.54149 q^{18} -3.33729 q^{19} -3.73459 q^{20} +3.15683 q^{21} +0.419526 q^{22} -3.44573 q^{23} +3.44026 q^{24} +1.00000 q^{25} +8.73742 q^{26} +4.40118 q^{27} -14.2348 q^{28} -8.69227 q^{29} -1.98332 q^{30} +7.44619 q^{31} +2.37359 q^{32} +0.145094 q^{33} +9.83223 q^{34} +3.81161 q^{35} -8.64209 q^{36} +4.45207 q^{37} +7.99181 q^{38} +3.02186 q^{39} +4.15383 q^{40} +3.61214 q^{41} -7.55966 q^{42} -8.99939 q^{43} -0.654261 q^{44} +2.31406 q^{45} +8.25148 q^{46} -13.5834 q^{47} -2.05231 q^{48} +7.52839 q^{49} -2.39470 q^{50} +3.40050 q^{51} -13.6262 q^{52} -6.28654 q^{53} -10.5395 q^{54} +0.175189 q^{55} +15.8328 q^{56} +2.76399 q^{57} +20.8154 q^{58} +0.276203 q^{59} +3.09304 q^{60} +8.13784 q^{61} -17.8314 q^{62} +8.82031 q^{63} -10.6400 q^{64} +3.64865 q^{65} -0.347457 q^{66} +8.85841 q^{67} -15.3336 q^{68} +2.85379 q^{69} -9.12767 q^{70} -13.1485 q^{71} +9.61223 q^{72} -8.63206 q^{73} -10.6614 q^{74} -0.828213 q^{75} -12.4634 q^{76} +0.667754 q^{77} -7.23645 q^{78} -4.87251 q^{79} -2.47800 q^{80} +3.29708 q^{81} -8.65001 q^{82} -7.62252 q^{83} +11.7895 q^{84} +4.10583 q^{85} +21.5509 q^{86} +7.19905 q^{87} +0.727708 q^{88} -4.38040 q^{89} -5.54149 q^{90} +13.9072 q^{91} -12.8684 q^{92} -6.16703 q^{93} +32.5282 q^{94} +3.33729 q^{95} -1.96584 q^{96} +10.5134 q^{97} -18.0283 q^{98} +0.405399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * 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 $

$2$	−2.39470	−1.69331	−0.846655	−	0.532143i	$-0.821387\pi$
$2$	−2.39470	−1.69331	−0.846655	+	0.532143i	$0.821387\pi$
$3$	−0.828213	−0.478169	−0.239084	−	0.970999i	$-0.576847\pi$
$3$	−0.828213	−0.478169	−0.239084	+	0.970999i	$0.576847\pi$
$4$	3.73459	1.86730
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.98332	0.809688
$7$	−3.81161	−1.44065	−0.720327	−	0.693634i	$-0.756008\pi$
$7$	−3.81161	−1.44065	−0.720327	+	0.693634i	$0.756008\pi$
$8$	−4.15383	−1.46860
$9$	−2.31406	−0.771354
$10$	2.39470	0.757271
$11$	−0.175189	−0.0528216	−0.0264108	−	0.999651i	$-0.508408\pi$
$11$	−0.175189	−0.0528216	−0.0264108	+	0.999651i	$0.508408\pi$
$12$	−3.09304	−0.892883
$13$	−3.64865	−1.01195	−0.505976	−	0.862547i	$-0.668868\pi$
$13$	−3.64865	−1.01195	−0.505976	+	0.862547i	$0.668868\pi$
$14$	9.12767	2.43947
$15$	0.828213	0.213844
$16$	2.47800	0.619500
$17$	−4.10583	−0.995809	−0.497905	−	0.867232i	$-0.665897\pi$
$17$	−4.10583	−0.995809	−0.497905	+	0.867232i	$0.665897\pi$
$18$	5.54149	1.30614
$19$	−3.33729	−0.765627	−0.382814	−	0.923826i	$-0.625045\pi$
$19$	−3.33729	−0.765627	−0.382814	+	0.923826i	$0.625045\pi$
$20$	−3.73459	−0.835080
$21$	3.15683	0.688876
$22$	0.419526	0.0894433
$23$	−3.44573	−0.718484	−0.359242	−	0.933245i	$-0.616965\pi$
$23$	−3.44573	−0.718484	−0.359242	+	0.933245i	$0.616965\pi$
$24$	3.44026	0.702240
$25$	1.00000	0.200000
$26$	8.73742	1.71355
$27$	4.40118	0.847007
$28$	−14.2348	−2.69013
$29$	−8.69227	−1.61411	−0.807057	−	0.590473i	$-0.798941\pi$
$29$	−8.69227	−1.61411	−0.807057	+	0.590473i	$0.798941\pi$
$30$	−1.98332	−0.362103
$31$	7.44619	1.33738	0.668688	−	0.743543i	$-0.266856\pi$
$31$	7.44619	1.33738	0.668688	+	0.743543i	$0.266856\pi$
$32$	2.37359	0.419596
$33$	0.145094	0.0252576
$34$	9.83223	1.68621
$35$	3.81161	0.644280
$36$	−8.64209	−1.44035
$37$	4.45207	0.731916	0.365958	−	0.930631i	$-0.380741\pi$
$37$	4.45207	0.731916	0.365958	+	0.930631i	$0.380741\pi$
$38$	7.99181	1.29644
$39$	3.02186	0.483884
$40$	4.15383	0.656779
$41$	3.61214	0.564122	0.282061	−	0.959396i	$-0.408982\pi$
$41$	3.61214	0.564122	0.282061	+	0.959396i	$0.408982\pi$
$42$	−7.55966	−1.16648
$43$	−8.99939	−1.37239	−0.686197	−	0.727416i	$-0.740721\pi$
$43$	−8.99939	−1.37239	−0.686197	+	0.727416i	$0.740721\pi$
$44$	−0.654261	−0.0986336
$45$	2.31406	0.344960
$46$	8.25148	1.21661
$47$	−13.5834	−1.98135	−0.990673	−	0.136262i	$-0.956491\pi$
$47$	−13.5834	−1.98135	−0.990673	+	0.136262i	$0.956491\pi$
$48$	−2.05231	−0.296226
$49$	7.52839	1.07548
$50$	−2.39470	−0.338662
$51$	3.40050	0.476165
$52$	−13.6262	−1.88962
$53$	−6.28654	−0.863522	−0.431761	−	0.901988i	$-0.642108\pi$
$53$	−6.28654	−0.863522	−0.431761	+	0.901988i	$0.642108\pi$
$54$	−10.5395	−1.43424
$55$	0.175189	0.0236225
$56$	15.8328	2.11575
$57$	2.76399	0.366099
$58$	20.8154	2.73320
$59$	0.276203	0.0359586	0.0179793	−	0.999838i	$-0.494277\pi$
$59$	0.276203	0.0359586	0.0179793	+	0.999838i	$0.494277\pi$
$60$	3.09304	0.399310
$61$	8.13784	1.04194	0.520972	−	0.853574i	$-0.325570\pi$
$61$	8.13784	1.04194	0.520972	+	0.853574i	$0.325570\pi$
$62$	−17.8314	−2.26459
$63$	8.82031	1.11126
$64$	−10.6400	−1.33001
$65$	3.64865	0.452559
$66$	−0.347457	−0.0427690
$67$	8.85841	1.08223	0.541114	−	0.840950i	$-0.318003\pi$
$67$	8.85841	1.08223	0.541114	+	0.840950i	$0.318003\pi$
$68$	−15.3336	−1.85947
$69$	2.85379	0.343556
$70$	−9.12767	−1.09097
$71$	−13.1485	−1.56044	−0.780221	−	0.625504i	$-0.784894\pi$
$71$	−13.1485	−1.56044	−0.780221	+	0.625504i	$0.784894\pi$
$72$	9.61223	1.13281
$73$	−8.63206	−1.01031	−0.505153	−	0.863030i	$-0.668564\pi$
$73$	−8.63206	−1.01031	−0.505153	+	0.863030i	$0.668564\pi$
$74$	−10.6614	−1.23936
$75$	−0.828213	−0.0956338
$76$	−12.4634	−1.42965
$77$	0.667754	0.0760977
$78$	−7.23645	−0.819366
$79$	−4.87251	−0.548201	−0.274100	−	0.961701i	$-0.588380\pi$
$79$	−4.87251	−0.548201	−0.274100	+	0.961701i	$0.588380\pi$
$80$	−2.47800	−0.277049
$81$	3.29708	0.366342
$82$	−8.65001	−0.955233
$83$	−7.62252	−0.836680	−0.418340	−	0.908291i	$-0.637388\pi$
$83$	−7.62252	−0.836680	−0.418340	+	0.908291i	$0.637388\pi$
$84$	11.7895	1.28634
$85$	4.10583	0.445340
$86$	21.5509	2.32389
$87$	7.19905	0.771819
$88$	0.727708	0.0775739
$89$	−4.38040	−0.464322	−0.232161	−	0.972677i	$-0.574580\pi$
$89$	−4.38040	−0.464322	−0.232161	+	0.972677i	$0.574580\pi$
$90$	−5.54149	−0.584124
$91$	13.9072	1.45787
$92$	−12.8684	−1.34162
$93$	−6.16703	−0.639492
$94$	32.5282	3.35503
$95$	3.33729	0.342399
$96$	−1.96584	−0.200638
$97$	10.5134	1.06748	0.533738	−	0.845650i	$-0.320787\pi$
$97$	10.5134	1.06748	0.533738	+	0.845650i	$0.320787\pi$
$98$	−18.0283	−1.82113
$99$	0.405399	0.0407442
$100$	3.73459	0.373459
$101$	5.06602	0.504088	0.252044	−	0.967716i	$-0.418897\pi$
$101$	5.06602	0.504088	0.252044	+	0.967716i	$0.418897\pi$
$102$	−8.14318	−0.806295
$103$	14.3337	1.41234	0.706169	−	0.708043i	$-0.250422\pi$
$103$	14.3337	1.41234	0.706169	+	0.708043i	$0.250422\pi$
$104$	15.1559	1.48616
$105$	−3.15683	−0.308075
$106$	15.0544	1.46221
$107$	14.5344	1.40509	0.702546	−	0.711639i	$-0.252047\pi$
$107$	14.5344	1.40509	0.702546	+	0.711639i	$0.252047\pi$
$108$	16.4366	1.58161
$109$	3.63563	0.348230	0.174115	−	0.984725i	$-0.444294\pi$
$109$	3.63563	0.348230	0.174115	+	0.984725i	$0.444294\pi$
$110$	−0.419526	−0.0400003
$111$	−3.68726	−0.349979
$112$	−9.44518	−0.892486
$113$	14.6917	1.38208	0.691039	−	0.722818i	$-0.257153\pi$
$113$	14.6917	1.38208	0.691039	+	0.722818i	$0.257153\pi$
$114$	−6.61892	−0.619919
$115$	3.44573	0.321316
$116$	−32.4621	−3.01403
$117$	8.44320	0.780574
$118$	−0.661424	−0.0608890
$119$	15.6498	1.43462
$120$	−3.44026	−0.314051
$121$	−10.9693	−0.997210
$122$	−19.4877	−1.76433
$123$	−2.99162	−0.269746
$124$	27.8085	2.49728
$125$	−1.00000	−0.0894427
$126$	−21.1220	−1.88170
$127$	17.6933	1.57003	0.785013	−	0.619479i	$-0.212656\pi$
$127$	17.6933	1.57003	0.785013	+	0.619479i	$0.212656\pi$
$128$	20.7326	1.83252
$129$	7.45341	0.656236
$130$	−8.73742	−0.766323
$131$	6.13908	0.536374	0.268187	−	0.963367i	$-0.413575\pi$
$131$	6.13908	0.536374	0.268187	+	0.963367i	$0.413575\pi$
$132$	0.541868	0.0471635
$133$	12.7205	1.10300
$134$	−21.2132	−1.83255
$135$	−4.40118	−0.378793
$136$	17.0549	1.46245
$137$	−3.17542	−0.271295	−0.135647	−	0.990757i	$-0.543311\pi$
$137$	−3.17542	−0.271295	−0.135647	+	0.990757i	$0.543311\pi$
$138$	−6.83398	−0.581747
$139$	−7.80006	−0.661592	−0.330796	−	0.943702i	$-0.607317\pi$
$139$	−7.80006	−0.661592	−0.330796	+	0.943702i	$0.607317\pi$
$140$	14.2348	1.20306
$141$	11.2500	0.947418
$142$	31.4868	2.64231
$143$	0.639205	0.0534530
$144$	−5.73425	−0.477854
$145$	8.69227	0.721854
$146$	20.6712	1.71076
$147$	−6.23511	−0.514263
$148$	16.6267	1.36670
$149$	−19.5961	−1.60537	−0.802687	−	0.596400i	$-0.796597\pi$
$149$	−19.5961	−1.60537	−0.802687	+	0.596400i	$0.796597\pi$
$150$	1.98332	0.161938
$151$	8.22208	0.669103	0.334552	−	0.942377i	$-0.391415\pi$
$151$	8.22208	0.669103	0.334552	+	0.942377i	$0.391415\pi$
$152$	13.8625	1.12440
$153$	9.50115	0.768122
$154$	−1.59907	−0.128857
$155$	−7.44619	−0.598093
$156$	11.2854	0.903556
$157$	−15.0190	−1.19865	−0.599325	−	0.800506i	$-0.704564\pi$
$157$	−15.0190	−1.19865	−0.599325	+	0.800506i	$0.704564\pi$
$158$	11.6682	0.928273
$159$	5.20659	0.412910
$160$	−2.37359	−0.187649
$161$	13.1338	1.03509
$162$	−7.89552	−0.620331
$163$	24.0898	1.88686	0.943428	−	0.331576i	$-0.107580\pi$
$163$	24.0898	1.88686	0.943428	+	0.331576i	$0.107580\pi$
$164$	13.4899	1.05338
$165$	−0.145094	−0.0112956
$166$	18.2537	1.41676
$167$	−15.7573	−1.21933	−0.609667	−	0.792658i	$-0.708697\pi$
$167$	−15.7573	−1.21933	−0.609667	+	0.792658i	$0.708697\pi$
$168$	−13.1129	−1.01168
$169$	0.312634	0.0240488
$170$	−9.83223	−0.754098
$171$	7.72270	0.590570
$172$	−33.6091	−2.56267
$173$	−9.76384	−0.742331	−0.371166	−	0.928567i	$-0.621042\pi$
$173$	−9.76384	−0.742331	−0.371166	+	0.928567i	$0.621042\pi$
$174$	−17.2396	−1.30693
$175$	−3.81161	−0.288131
$176$	−0.434120	−0.0327230
$177$	−0.228755	−0.0171943
$178$	10.4898	0.786241
$179$	14.8190	1.10762	0.553812	−	0.832642i	$-0.313173\pi$
$179$	14.8190	1.10762	0.553812	+	0.832642i	$0.313173\pi$
$180$	8.64209	0.644143
$181$	−11.0597	−0.822060	−0.411030	−	0.911622i	$-0.634831\pi$
$181$	−11.0597	−0.822060	−0.411030	+	0.911622i	$0.634831\pi$
$182$	−33.3037	−2.46863
$183$	−6.73986	−0.498225
$184$	14.3130	1.05517
$185$	−4.45207	−0.327323
$186$	14.7682	1.08286
$187$	0.719298	0.0526003
$188$	−50.7286	−3.69976
$189$	−16.7756	−1.22024
$190$	−7.99181	−0.579787
$191$	18.7058	1.35351	0.676754	−	0.736209i	$-0.263386\pi$
$191$	18.7058	1.35351	0.676754	+	0.736209i	$0.263386\pi$
$192$	8.81222	0.635968
$193$	−8.29892	−0.597369	−0.298685	−	0.954352i	$-0.596548\pi$
$193$	−8.29892	−0.597369	−0.298685	+	0.954352i	$0.596548\pi$
$194$	−25.1765	−1.80757
$195$	−3.02186	−0.216400
$196$	28.1155	2.00825
$197$	7.52960	0.536462	0.268231	−	0.963355i	$-0.413561\pi$
$197$	7.52960	0.536462	0.268231	+	0.963355i	$0.413561\pi$
$198$	−0.970811	−0.0689925
$199$	4.96620	0.352044	0.176022	−	0.984386i	$-0.443677\pi$
$199$	4.96620	0.352044	0.176022	+	0.984386i	$0.443677\pi$
$200$	−4.15383	−0.293720
$201$	−7.33665	−0.517487
$202$	−12.1316	−0.853577
$203$	33.1316	2.32538
$204$	12.6995	0.889142
$205$	−3.61214	−0.252283
$206$	−34.3248	−2.39153
$207$	7.97363	0.554205
$208$	−9.04136	−0.626905
$209$	0.584658	0.0404416
$210$	7.55966	0.521666
$211$	10.8907	0.749746	0.374873	−	0.927076i	$-0.377686\pi$
$211$	10.8907	0.749746	0.374873	+	0.927076i	$0.377686\pi$
$212$	−23.4777	−1.61245
$213$	10.8898	0.746155
$214$	−34.8055	−2.37925
$215$	8.99939	0.613753
$216$	−18.2817	−1.24392
$217$	−28.3820	−1.92670
$218$	−8.70624	−0.589661
$219$	7.14918	0.483097
$220$	0.654261	0.0441103
$221$	14.9807	1.00771
$222$	8.82989	0.592623
$223$	10.3966	0.696210	0.348105	−	0.937456i	$-0.386825\pi$
$223$	10.3966	0.696210	0.348105	+	0.937456i	$0.386825\pi$
$224$	−9.04722	−0.604493
$225$	−2.31406	−0.154271
$226$	−35.1822	−2.34029
$227$	−23.8830	−1.58517	−0.792585	−	0.609761i	$-0.791265\pi$
$227$	−23.8830	−1.58517	−0.792585	+	0.609761i	$0.791265\pi$
$228$	10.3224	0.683616
$229$	−11.2661	−0.744486	−0.372243	−	0.928135i	$-0.621411\pi$
$229$	−11.2661	−0.744486	−0.372243	+	0.928135i	$0.621411\pi$
$230$	−8.25148	−0.544087
$231$	−0.553043	−0.0363875
$232$	36.1063	2.37049
$233$	−18.4577	−1.20921	−0.604603	−	0.796527i	$-0.706668\pi$
$233$	−18.4577	−1.20921	−0.604603	+	0.796527i	$0.706668\pi$
$234$	−20.2189	−1.32175
$235$	13.5834	0.886085
$236$	1.03151	0.0671454
$237$	4.03548	0.262132
$238$	−37.4767	−2.42925
$239$	2.55433	0.165226	0.0826130	−	0.996582i	$-0.473673\pi$
$239$	2.55433	0.165226	0.0826130	+	0.996582i	$0.473673\pi$
$240$	2.05231	0.132476
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	26.2682	1.68858
$243$	−15.9342	−1.02218
$244$	30.3915	1.94562
$245$	−7.52839	−0.480971
$246$	7.16405	0.456763
$247$	12.1766	0.774779
$248$	−30.9302	−1.96407
$249$	6.31307	0.400074
$250$	2.39470	0.151454
$251$	−7.29749	−0.460613	−0.230307	−	0.973118i	$-0.573973\pi$
$251$	−7.29749	−0.460613	−0.230307	+	0.973118i	$0.573973\pi$
$252$	32.9403	2.07504
$253$	0.603655	0.0379515
$254$	−42.3702	−2.65854
$255$	−3.40050	−0.212948
$256$	−28.3682	−1.77301
$257$	16.2119	1.01127	0.505635	−	0.862748i	$-0.331258\pi$
$257$	16.2119	1.01127	0.505635	+	0.862748i	$0.331258\pi$
$258$	−17.8487	−1.11121
$259$	−16.9696	−1.05444
$260$	13.6262	0.845062
$261$	20.1145	1.24505
$262$	−14.7013	−0.908248
$263$	0.0327695	0.00202065	0.00101033	−	0.999999i	$-0.499678\pi$
$263$	0.0327695	0.00202065	0.00101033	+	0.999999i	$0.499678\pi$
$264$	−0.602697	−0.0370934
$265$	6.28654	0.386179
$266$	−30.4617	−1.86773
$267$	3.62791	0.222024
$268$	33.0826	2.02084
$269$	17.0253	1.03805	0.519025	−	0.854759i	$-0.326295\pi$
$269$	17.0253	1.03805	0.519025	+	0.854759i	$0.326295\pi$
$270$	10.5395	0.641414
$271$	−22.1498	−1.34551	−0.672753	−	0.739868i	$-0.734888\pi$
$271$	−22.1498	−1.34551	−0.672753	+	0.739868i	$0.734888\pi$
$272$	−10.1742	−0.616904
$273$	−11.5182	−0.697110
$274$	7.60419	0.459386
$275$	−0.175189	−0.0105643
$276$	10.6578	0.641522
$277$	−30.6653	−1.84250	−0.921249	−	0.388973i	$-0.872830\pi$
$277$	−30.6653	−1.84250	−0.921249	+	0.388973i	$0.872830\pi$
$278$	18.6788	1.12028
$279$	−17.2310	−1.03159
$280$	−15.8328	−0.946191
$281$	−18.3942	−1.09731	−0.548654	−	0.836050i	$-0.684859\pi$
$281$	−18.3942	−1.09731	−0.548654	+	0.836050i	$0.684859\pi$
$282$	−26.9403	−1.60427
$283$	16.9510	1.00763	0.503816	−	0.863811i	$-0.331929\pi$
$283$	16.9510	1.00763	0.503816	+	0.863811i	$0.331929\pi$
$284$	−49.1044	−2.91381
$285$	−2.76399	−0.163724
$286$	−1.53070	−0.0905124
$287$	−13.7681	−0.812705
$288$	−5.49264	−0.323657
$289$	−0.142180	−0.00836353
$290$	−20.8154	−1.22232
$291$	−8.70735	−0.510434
$292$	−32.2372	−1.88654
$293$	1.45778	0.0851643	0.0425821	−	0.999093i	$-0.486442\pi$
$293$	1.45778	0.0851643	0.0425821	+	0.999093i	$0.486442\pi$
$294$	14.9312	0.870807
$295$	−0.276203	−0.0160812
$296$	−18.4932	−1.07489
$297$	−0.771040	−0.0447403
$298$	46.9268	2.71840
$299$	12.5722	0.727072
$300$	−3.09304	−0.178577
$301$	34.3022	1.97715
$302$	−19.6894	−1.13300
$303$	−4.19575	−0.241039
$304$	−8.26981	−0.474306
$305$	−8.13784	−0.465971
$306$	−22.7524	−1.30067
$307$	2.38102	0.135892	0.0679459	−	0.997689i	$-0.478355\pi$
$307$	2.38102	0.135892	0.0679459	+	0.997689i	$0.478355\pi$
$308$	2.49379	0.142097
$309$	−11.8713	−0.675336
$310$	17.8314	1.01276
$311$	−16.1504	−0.915804	−0.457902	−	0.889003i	$-0.651399\pi$
$311$	−16.1504	−0.915804	−0.457902	+	0.889003i	$0.651399\pi$
$312$	−12.5523	−0.710634
$313$	−10.8326	−0.612295	−0.306148	−	0.951984i	$-0.599040\pi$
$313$	−10.8326	−0.612295	−0.306148	+	0.951984i	$0.599040\pi$
$314$	35.9661	2.02968
$315$	−8.82031	−0.496968
$316$	−18.1969	−1.02365
$317$	−5.93060	−0.333095	−0.166548	−	0.986033i	$-0.553262\pi$
$317$	−5.93060	−0.333095	−0.166548	+	0.986033i	$0.553262\pi$
$318$	−12.4682	−0.699184
$319$	1.52279	0.0852601
$320$	10.6400	0.594797
$321$	−12.0376	−0.671871
$322$	−31.4515	−1.75272
$323$	13.7023	0.762419
$324$	12.3133	0.684070
$325$	−3.64865	−0.202391
$326$	−57.6878	−3.19503
$327$	−3.01107	−0.166513
$328$	−15.0042	−0.828471
$329$	51.7747	2.85443
$330$	0.347457	0.0191269
$331$	−1.53979	−0.0846348	−0.0423174	−	0.999104i	$-0.513474\pi$
$331$	−1.53979	−0.0846348	−0.0423174	+	0.999104i	$0.513474\pi$
$332$	−28.4670	−1.56233
$333$	−10.3024	−0.564566
$334$	37.7339	2.06471
$335$	−8.85841	−0.483987
$336$	7.82262	0.426759
$337$	−16.4203	−0.894470	−0.447235	−	0.894417i	$-0.647591\pi$
$337$	−16.4203	−0.894470	−0.447235	+	0.894417i	$0.647591\pi$
$338$	−0.748665	−0.0407220
$339$	−12.1678	−0.660867
$340$	15.3336	0.831581
$341$	−1.30449	−0.0706423
$342$	−18.4936	−1.00002
$343$	−2.01403	−0.108748
$344$	37.3820	2.01550
$345$	−2.85379	−0.153643
$346$	23.3815	1.25700
$347$	−1.62520	−0.0872454	−0.0436227	−	0.999048i	$-0.513890\pi$
$347$	−1.62520	−0.0872454	−0.0436227	+	0.999048i	$0.513890\pi$
$348$	26.8855	1.44122
$349$	−17.1092	−0.915833	−0.457916	−	0.888995i	$-0.651404\pi$
$349$	−17.1092	−0.915833	−0.457916	+	0.888995i	$0.651404\pi$
$350$	9.12767	0.487895
$351$	−16.0583	−0.857131
$352$	−0.415828	−0.0221637
$353$	13.3946	0.712925	0.356463	−	0.934310i	$-0.383983\pi$
$353$	13.3946	0.712925	0.356463	+	0.934310i	$0.383983\pi$
$354$	0.547800	0.0291152
$355$	13.1485	0.697851
$356$	−16.3590	−0.867027
$357$	−12.9614	−0.685989
$358$	−35.4871	−1.87555
$359$	20.1919	1.06569	0.532844	−	0.846213i	$-0.321123\pi$
$359$	20.1919	1.06569	0.532844	+	0.846213i	$0.321123\pi$
$360$	−9.61223	−0.506609
$361$	−7.86249	−0.413815
$362$	26.4846	1.39200
$363$	9.08492	0.476835
$364$	51.9379	2.72228
$365$	8.63206	0.451823
$366$	16.1399	0.843649
$367$	28.7886	1.50275	0.751375	−	0.659875i	$-0.229391\pi$
$367$	28.7886	1.50275	0.751375	+	0.659875i	$0.229391\pi$
$368$	−8.53851	−0.445101
$369$	−8.35873	−0.435138
$370$	10.6614	0.554259
$371$	23.9619	1.24404
$372$	−23.0314	−1.19412
$373$	26.8363	1.38953	0.694765	−	0.719237i	$-0.255508\pi$
$373$	26.8363	1.38953	0.694765	+	0.719237i	$0.255508\pi$
$374$	−1.72250	−0.0890685
$375$	0.828213	0.0427687
$376$	56.4233	2.90981
$377$	31.7150	1.63341
$378$	40.1725	2.06625
$379$	−20.4446	−1.05017	−0.525083	−	0.851051i	$-0.675966\pi$
$379$	−20.4446	−1.05017	−0.525083	+	0.851051i	$0.675966\pi$
$380$	12.4634	0.639360
$381$	−14.6538	−0.750738
$382$	−44.7949	−2.29191
$383$	16.3210	0.833965	0.416983	−	0.908914i	$-0.363088\pi$
$383$	16.3210	0.833965	0.416983	+	0.908914i	$0.363088\pi$
$384$	−17.1710	−0.876252
$385$	−0.667754	−0.0340319
$386$	19.8734	1.01153
$387$	20.8252	1.05860
$388$	39.2634	1.99329
$389$	−31.6845	−1.60647	−0.803234	−	0.595663i	$-0.796889\pi$
$389$	−31.6845	−1.60647	−0.803234	+	0.595663i	$0.796889\pi$
$390$	7.23645	0.366432
$391$	14.1476	0.715473
$392$	−31.2717	−1.57946
$393$	−5.08447	−0.256478
$394$	−18.0311	−0.908396
$395$	4.87251	0.245163
$396$	1.51400	0.0760815
$397$	8.37582	0.420370	0.210185	−	0.977662i	$-0.432593\pi$
$397$	8.37582	0.420370	0.210185	+	0.977662i	$0.432593\pi$
$398$	−11.8926	−0.596120
$399$	−10.5352	−0.527422
$400$	2.47800	0.123900
$401$	−21.5614	−1.07672	−0.538362	−	0.842714i	$-0.680957\pi$
$401$	−21.5614	−1.07672	−0.538362	+	0.842714i	$0.680957\pi$
$402$	17.5691	0.876266
$403$	−27.1685	−1.35336
$404$	18.9195	0.941282
$405$	−3.29708	−0.163833
$406$	−79.3402	−3.93759
$407$	−0.779956	−0.0386610
$408$	−14.1251	−0.699297
$409$	20.2492	1.00126	0.500630	−	0.865661i	$-0.333102\pi$
$409$	20.2492	1.00126	0.500630	+	0.865661i	$0.333102\pi$
$410$	8.65001	0.427193
$411$	2.62993	0.129725
$412$	53.5304	2.63725
$413$	−1.05278	−0.0518039
$414$	−19.0945	−0.938441
$415$	7.62252	0.374175
$416$	−8.66040	−0.424611
$417$	6.46011	0.316353
$418$	−1.40008	−0.0684802
$419$	−34.0429	−1.66310	−0.831551	−	0.555448i	$-0.812547\pi$
$419$	−34.0429	−1.66310	−0.831551	+	0.555448i	$0.812547\pi$
$420$	−11.7895	−0.575267
$421$	−15.2826	−0.744829	−0.372414	−	0.928067i	$-0.621470\pi$
$421$	−15.2826	−0.744829	−0.372414	+	0.928067i	$0.621470\pi$
$422$	−26.0800	−1.26955
$423$	31.4329	1.52832
$424$	26.1132	1.26817
$425$	−4.10583	−0.199162
$426$	−26.0778	−1.26347
$427$	−31.0183	−1.50108
$428$	54.2800	2.62372
$429$	−0.529398	−0.0255596
$430$	−21.5509	−1.03927
$431$	−11.9870	−0.577393	−0.288697	−	0.957421i	$-0.593222\pi$
$431$	−11.9870	−0.577393	−0.288697	+	0.957421i	$0.593222\pi$
$432$	10.9061	0.524721
$433$	−18.1458	−0.872029	−0.436015	−	0.899940i	$-0.643610\pi$
$433$	−18.1458	−0.872029	−0.436015	+	0.899940i	$0.643610\pi$
$434$	67.9664	3.26249
$435$	−7.19905	−0.345168
$436$	13.5776	0.650249
$437$	11.4994	0.550090
$438$	−17.1202	−0.818033
$439$	−2.29402	−0.109488	−0.0547438	−	0.998500i	$-0.517434\pi$
$439$	−2.29402	−0.109488	−0.0547438	+	0.998500i	$0.517434\pi$
$440$	−0.727708	−0.0346921
$441$	−17.4212	−0.829580
$442$	−35.8743	−1.70637
$443$	22.3902	1.06379	0.531894	−	0.846811i	$-0.321480\pi$
$443$	22.3902	1.06379	0.531894	+	0.846811i	$0.321480\pi$
$444$	−13.7704	−0.653515
$445$	4.38040	0.207651
$446$	−24.8968	−1.17890
$447$	16.2297	0.767640
$448$	40.5557	1.91608
$449$	−3.56571	−0.168276	−0.0841382	−	0.996454i	$-0.526814\pi$
$449$	−3.56571	−0.168276	−0.0841382	+	0.996454i	$0.526814\pi$
$450$	5.54149	0.261228
$451$	−0.632810	−0.0297978
$452$	54.8675	2.58075
$453$	−6.80963	−0.319944
$454$	57.1926	2.68418
$455$	−13.9072	−0.651981
$456$	−11.4811	−0.537654
$457$	−24.5077	−1.14642	−0.573210	−	0.819409i	$-0.694302\pi$
$457$	−24.5077	−1.14642	−0.573210	+	0.819409i	$0.694302\pi$
$458$	26.9790	1.26065
$459$	−18.0705	−0.843457
$460$	12.8684	0.599992
$461$	−9.52557	−0.443650	−0.221825	−	0.975086i	$-0.571201\pi$
$461$	−9.52557	−0.443650	−0.221825	+	0.975086i	$0.571201\pi$
$462$	1.32437	0.0616154
$463$	−32.8372	−1.52607	−0.763036	−	0.646356i	$-0.776292\pi$
$463$	−32.8372	−1.52607	−0.763036	+	0.646356i	$0.776292\pi$
$464$	−21.5395	−0.999945
$465$	6.16703	0.285989
$466$	44.2008	2.04756
$467$	−13.5647	−0.627699	−0.313849	−	0.949473i	$-0.601619\pi$
$467$	−13.5647	−0.627699	−0.313849	+	0.949473i	$0.601619\pi$
$468$	31.5319	1.45756
$469$	−33.7648	−1.55912
$470$	−32.5282	−1.50042
$471$	12.4390	0.573157
$472$	−1.14730	−0.0528089
$473$	1.57660	0.0724921
$474$	−9.66376	−0.443871
$475$	−3.33729	−0.153125
$476$	58.4457	2.67886
$477$	14.5474	0.666082
$478$	−6.11686	−0.279779
$479$	30.8573	1.40990	0.704952	−	0.709255i	$-0.250968\pi$
$479$	30.8573	1.40990	0.704952	+	0.709255i	$0.250968\pi$
$480$	1.96584	0.0897279
$481$	−16.2440	−0.740664
$482$	−2.39470	−0.109076
$483$	−10.8776	−0.494946
$484$	−40.9659	−1.86209
$485$	−10.5134	−0.477390
$486$	38.1577	1.73087
$487$	−29.0601	−1.31684	−0.658419	−	0.752651i	$-0.728775\pi$
$487$	−29.0601	−1.31684	−0.658419	+	0.752651i	$0.728775\pi$
$488$	−33.8032	−1.53020
$489$	−19.9515	−0.902236
$490$	18.0283	0.814433
$491$	−10.6545	−0.480831	−0.240416	−	0.970670i	$-0.577284\pi$
$491$	−10.6545	−0.480831	−0.240416	+	0.970670i	$0.577284\pi$
$492$	−11.1725	−0.503695
$493$	35.6890	1.60735
$494$	−29.1593	−1.31194
$495$	−0.405399	−0.0182214
$496$	18.4517	0.828505
$497$	50.1171	2.24806
$498$	−15.1179	−0.677450
$499$	30.4355	1.36248	0.681241	−	0.732059i	$-0.261441\pi$
$499$	30.4355	1.36248	0.681241	+	0.732059i	$0.261441\pi$
$500$	−3.73459	−0.167016
$501$	13.0504	0.583048
$502$	17.4753	0.779961
$503$	10.9745	0.489329	0.244664	−	0.969608i	$-0.421322\pi$
$503$	10.9745	0.489329	0.244664	+	0.969608i	$0.421322\pi$
$504$	−36.6381	−1.63199
$505$	−5.06602	−0.225435
$506$	−1.44557	−0.0642636
$507$	−0.258928	−0.0114994
$508$	66.0773	2.93171
$509$	−5.50658	−0.244075	−0.122037	−	0.992525i	$-0.538943\pi$
$509$	−5.50658	−0.244075	−0.122037	+	0.992525i	$0.538943\pi$
$510$	8.14318	0.360586
$511$	32.9021	1.45550
$512$	26.4682	1.16974
$513$	−14.6880	−0.648491
$514$	−38.8226	−1.71239
$515$	−14.3337	−0.631617
$516$	27.8355	1.22539
$517$	2.37967	0.104658
$518$	40.6370	1.78549
$519$	8.08654	0.354960
$520$	−15.1559	−0.664629
$521$	23.2864	1.02020	0.510098	−	0.860116i	$-0.329609\pi$
$521$	23.2864	1.02020	0.510098	+	0.860116i	$0.329609\pi$
$522$	−48.1681	−2.10826
$523$	10.1583	0.444190	0.222095	−	0.975025i	$-0.428711\pi$
$523$	10.1583	0.444190	0.222095	+	0.975025i	$0.428711\pi$
$524$	22.9270	1.00157
$525$	3.15683	0.137775
$526$	−0.0784731	−0.00342159
$527$	−30.5728	−1.33177
$528$	0.359544	0.0156471
$529$	−11.1270	−0.483781
$530$	−15.0544	−0.653921
$531$	−0.639152	−0.0277368
$532$	47.5058	2.05964
$533$	−13.1794	−0.570865
$534$	−8.68775	−0.375956
$535$	−14.5344	−0.628376
$536$	−36.7964	−1.58936
$537$	−12.2733	−0.529632
$538$	−40.7705	−1.75774
$539$	−1.31890	−0.0568088
$540$	−16.4366	−0.707319
$541$	−19.7119	−0.847483	−0.423741	−	0.905783i	$-0.639283\pi$
$541$	−19.7119	−0.847483	−0.423741	+	0.905783i	$0.639283\pi$
$542$	53.0422	2.27836
$543$	9.15978	0.393084
$544$	−9.74556	−0.417838
$545$	−3.63563	−0.155733
$546$	27.5825	1.18042
$547$	33.7148	1.44154	0.720770	−	0.693174i	$-0.243788\pi$
$547$	33.7148	1.44154	0.720770	+	0.693174i	$0.243788\pi$
$548$	−11.8589	−0.506588
$549$	−18.8315	−0.803707
$550$	0.419526	0.0178887
$551$	29.0086	1.23581
$552$	−11.8542	−0.504548
$553$	18.5721	0.789767
$554$	73.4342	3.11992
$555$	3.68726	0.156516
$556$	−29.1300	−1.23539
$557$	−0.706757	−0.0299462	−0.0149731	−	0.999888i	$-0.504766\pi$
$557$	−0.706757	−0.0299462	−0.0149731	+	0.999888i	$0.504766\pi$
$558$	41.2630	1.74680
$559$	32.8356	1.38880
$560$	9.44518	0.399132
$561$	−0.595732	−0.0251518
$562$	44.0487	1.85808
$563$	9.74040	0.410509	0.205254	−	0.978709i	$-0.434198\pi$
$563$	9.74040	0.410509	0.205254	+	0.978709i	$0.434198\pi$
$564$	42.0140	1.76911
$565$	−14.6917	−0.618084
$566$	−40.5926	−1.70623
$567$	−12.5672	−0.527773
$568$	54.6168	2.29167
$569$	23.5609	0.987725	0.493862	−	0.869540i	$-0.335585\pi$
$569$	23.5609	0.987725	0.493862	+	0.869540i	$0.335585\pi$
$570$	6.61892	0.277236
$571$	−15.7877	−0.660696	−0.330348	−	0.943859i	$-0.607166\pi$
$571$	−15.7877	−0.660696	−0.330348	+	0.943859i	$0.607166\pi$
$572$	2.38717	0.0998126
$573$	−15.4924	−0.647205
$574$	32.9705	1.37616
$575$	−3.44573	−0.143697
$576$	24.6217	1.02591
$577$	−22.8586	−0.951617	−0.475809	−	0.879549i	$-0.657845\pi$
$577$	−22.8586	−0.951617	−0.475809	+	0.879549i	$0.657845\pi$
$578$	0.340479	0.0141620
$579$	6.87327	0.285643
$580$	32.4621	1.34792
$581$	29.0541	1.20537
$582$	20.8515	0.864323
$583$	1.10134	0.0456126
$584$	35.8561	1.48374
$585$	−8.44320	−0.349084
$586$	−3.49094	−0.144209
$587$	6.37904	0.263291	0.131645	−	0.991297i	$-0.457974\pi$
$587$	6.37904	0.263291	0.131645	+	0.991297i	$0.457974\pi$
$588$	−23.2856	−0.960282
$589$	−24.8501	−1.02393
$590$	0.661424	0.0272304
$591$	−6.23611	−0.256519
$592$	11.0322	0.453422
$593$	−5.56948	−0.228711	−0.114356	−	0.993440i	$-0.536480\pi$
$593$	−5.56948	−0.228711	−0.114356	+	0.993440i	$0.536480\pi$
$594$	1.84641	0.0757591
$595$	−15.6498	−0.641580
$596$	−73.1835	−2.99771
$597$	−4.11307	−0.168337
$598$	−30.1068	−1.23116
$599$	−33.7714	−1.37986	−0.689932	−	0.723875i	$-0.742359\pi$
$599$	−33.7714	−1.37986	−0.689932	+	0.723875i	$0.742359\pi$
$600$	3.44026	0.140448
$601$	35.2957	1.43974	0.719870	−	0.694108i	$-0.244201\pi$
$601$	35.2957	1.43974	0.719870	+	0.694108i	$0.244201\pi$
$602$	−82.1435	−3.34792
$603$	−20.4989	−0.834781
$604$	30.7061	1.24941
$605$	10.9693	0.445966
$606$	10.0476	0.408154
$607$	34.5971	1.40425	0.702125	−	0.712053i	$-0.252235\pi$
$607$	34.5971	1.40425	0.702125	+	0.712053i	$0.252235\pi$
$608$	−7.92137	−0.321254
$609$	−27.4400	−1.11192
$610$	19.4877	0.789033
$611$	49.5611	2.00503
$612$	35.4829	1.43431
$613$	−18.4107	−0.743599	−0.371800	−	0.928313i	$-0.621259\pi$
$613$	−18.4107	−0.743599	−0.371800	+	0.928313i	$0.621259\pi$
$614$	−5.70182	−0.230107
$615$	2.99162	0.120634
$616$	−2.77374	−0.111757
$617$	−19.4380	−0.782543	−0.391272	−	0.920275i	$-0.627965\pi$
$617$	−19.4380	−0.782543	−0.391272	+	0.920275i	$0.627965\pi$
$618$	28.4283	1.14355
$619$	45.5653	1.83142	0.915711	−	0.401837i	$-0.131628\pi$
$619$	45.5653	1.83142	0.915711	+	0.401837i	$0.131628\pi$
$620$	−27.8085	−1.11682
$621$	−15.1652	−0.608560
$622$	38.6753	1.55074
$623$	16.6964	0.668927
$624$	7.48817	0.299767
$625$	1.00000	0.0400000
$626$	25.9409	1.03681
$627$	−0.484221	−0.0193379
$628$	−56.0900	−2.23823
$629$	−18.2794	−0.728849
$630$	21.1220	0.841521
$631$	−46.3440	−1.84493	−0.922463	−	0.386087i	$-0.873827\pi$
$631$	−46.3440	−1.84493	−0.922463	+	0.386087i	$0.873827\pi$
$632$	20.2396	0.805088
$633$	−9.01981	−0.358505
$634$	14.2020	0.564034
$635$	−17.6933	−0.702137
$636$	19.4445	0.771025
$637$	−27.4685	−1.08834
$638$	−3.64664	−0.144372
$639$	30.4265	1.20365
$640$	−20.7326	−0.819526
$641$	39.3877	1.55572	0.777861	−	0.628436i	$-0.216305\pi$
$641$	39.3877	1.55572	0.777861	+	0.628436i	$0.216305\pi$
$642$	28.8263	1.13769
$643$	−4.33163	−0.170823	−0.0854114	−	0.996346i	$-0.527220\pi$
$643$	−4.33163	−0.170823	−0.0854114	+	0.996346i	$0.527220\pi$
$644$	49.0493	1.93281
$645$	−7.45341	−0.293478
$646$	−32.8130	−1.29101
$647$	−11.9525	−0.469903	−0.234951	−	0.972007i	$-0.575493\pi$
$647$	−11.9525	−0.469903	−0.234951	+	0.972007i	$0.575493\pi$
$648$	−13.6955	−0.538011
$649$	−0.0483879	−0.00189939
$650$	8.73742	0.342710
$651$	23.5063	0.921286
$652$	89.9655	3.52332
$653$	34.3615	1.34467	0.672334	−	0.740248i	$-0.265292\pi$
$653$	34.3615	1.34467	0.672334	+	0.740248i	$0.265292\pi$
$654$	7.21062	0.281958
$655$	−6.13908	−0.239874
$656$	8.95090	0.349474
$657$	19.9751	0.779304
$658$	−123.985	−4.83344
$659$	39.2676	1.52965	0.764824	−	0.644239i	$-0.222826\pi$
$659$	39.2676	1.52965	0.764824	+	0.644239i	$0.222826\pi$
$660$	−0.541868	−0.0210922
$661$	−10.0322	−0.390207	−0.195103	−	0.980783i	$-0.562504\pi$
$661$	−10.0322	−0.390207	−0.195103	+	0.980783i	$0.562504\pi$
$662$	3.68735	0.143313
$663$	−12.4072	−0.481857
$664$	31.6627	1.22875
$665$	−12.7205	−0.493278
$666$	24.6711	0.955986
$667$	29.9512	1.15971
$668$	−58.8470	−2.27686
$669$	−8.61062	−0.332906
$670$	21.2132	0.819539
$671$	−1.42566	−0.0550371
$672$	7.49302	0.289050
$673$	21.3844	0.824307	0.412154	−	0.911114i	$-0.364777\pi$
$673$	21.3844	0.824307	0.412154	+	0.911114i	$0.364777\pi$
$674$	39.3217	1.51461
$675$	4.40118	0.169401
$676$	1.16756	0.0449062
$677$	−19.3687	−0.744400	−0.372200	−	0.928153i	$-0.621396\pi$
$677$	−19.3687	−0.744400	−0.372200	+	0.928153i	$0.621396\pi$
$678$	29.1384	1.11905
$679$	−40.0731	−1.53786
$680$	−17.0549	−0.654026
$681$	19.7802	0.757979
$682$	3.12387	0.119619
$683$	7.62162	0.291633	0.145817	−	0.989312i	$-0.453419\pi$
$683$	7.62162	0.291633	0.145817	+	0.989312i	$0.453419\pi$
$684$	28.8412	1.10277
$685$	3.17542	0.121327
$686$	4.82301	0.184143
$687$	9.33075	0.355990
$688$	−22.3005	−0.850199
$689$	22.9374	0.873844
$690$	6.83398	0.260165
$691$	−11.6518	−0.443254	−0.221627	−	0.975131i	$-0.571137\pi$
$691$	−11.6518	−0.443254	−0.221627	+	0.975131i	$0.571137\pi$
$692$	−36.4640	−1.38615
$693$	−1.54523	−0.0586983
$694$	3.89187	0.147733
$695$	7.80006	0.295873
$696$	−29.9037	−1.13350
$697$	−14.8308	−0.561758
$698$	40.9713	1.55079
$699$	15.2869	0.578205
$700$	−14.2348	−0.538026
$701$	23.3914	0.883482	0.441741	−	0.897143i	$-0.354361\pi$
$701$	23.3914	0.883482	0.441741	+	0.897143i	$0.354361\pi$
$702$	38.4549	1.45139
$703$	−14.8579	−0.560374
$704$	1.86402	0.0702531
$705$	−11.2500	−0.423698
$706$	−32.0762	−1.20720
$707$	−19.3097	−0.726217
$708$	−0.854307	−0.0321068
$709$	−29.5694	−1.11050	−0.555251	−	0.831683i	$-0.687378\pi$
$709$	−29.5694	−1.11050	−0.555251	+	0.831683i	$0.687378\pi$
$710$	−31.4868	−1.18168
$711$	11.2753	0.422857
$712$	18.1955	0.681904
$713$	−25.6575	−0.960883
$714$	31.0386	1.16159
$715$	−0.639205	−0.0239049
$716$	55.3430	2.06826
$717$	−2.11553	−0.0790059
$718$	−48.3536	−1.80454
$719$	−27.8388	−1.03821	−0.519106	−	0.854710i	$-0.673735\pi$
$719$	−27.8388	−1.03821	−0.519106	+	0.854710i	$0.673735\pi$
$720$	5.73425	0.213703
$721$	−54.6344	−2.03469
$722$	18.8283	0.700717
$723$	−0.828213	−0.0308016
$724$	−41.3034	−1.53503
$725$	−8.69227	−0.322823
$726$	−21.7557	−0.807429
$727$	−18.8571	−0.699373	−0.349686	−	0.936867i	$-0.613712\pi$
$727$	−18.8571	−0.699373	−0.349686	+	0.936867i	$0.613712\pi$
$728$	−57.7683	−2.14104
$729$	3.30568	0.122433
$730$	−20.6712	−0.765076
$731$	36.9499	1.36664
$732$	−25.1706	−0.930333
$733$	2.02012	0.0746147	0.0373074	−	0.999304i	$-0.488122\pi$
$733$	2.02012	0.0746147	0.0373074	+	0.999304i	$0.488122\pi$
$734$	−68.9400	−2.54462
$735$	6.23511	0.229986
$736$	−8.17875	−0.301473
$737$	−1.55190	−0.0571650
$738$	20.0167	0.736824
$739$	−36.2906	−1.33497	−0.667486	−	0.744622i	$-0.732630\pi$
$739$	−36.2906	−1.33497	−0.667486	+	0.744622i	$0.732630\pi$
$740$	−16.6267	−0.611209
$741$	−10.0848	−0.370475
$742$	−57.3815	−2.10654
$743$	−52.4368	−1.92372	−0.961860	−	0.273543i	$-0.911805\pi$
$743$	−52.4368	−1.92372	−0.961860	+	0.273543i	$0.911805\pi$
$744$	25.6168	0.939158
$745$	19.5961	0.717945
$746$	−64.2649	−2.35290
$747$	17.6390	0.645377
$748$	2.68628	0.0982203
$749$	−55.3994	−2.02425
$750$	−1.98332	−0.0724207
$751$	2.02838	0.0740167	0.0370084	−	0.999315i	$-0.488217\pi$
$751$	2.02838	0.0740167	0.0370084	+	0.999315i	$0.488217\pi$
$752$	−33.6597	−1.22744
$753$	6.04387	0.220251
$754$	−75.9481	−2.76587
$755$	−8.22208	−0.299232
$756$	−62.6500	−2.27856
$757$	43.4023	1.57748	0.788741	−	0.614725i	$-0.210733\pi$
$757$	43.4023	1.57748	0.788741	+	0.614725i	$0.210733\pi$
$758$	48.9586	1.77826
$759$	−0.499955	−0.0181472
$760$	−13.8625	−0.502847
$761$	38.1340	1.38236	0.691179	−	0.722684i	$-0.257092\pi$
$761$	38.1340	1.38236	0.691179	+	0.722684i	$0.257092\pi$
$762$	35.0915	1.27123
$763$	−13.8576	−0.501679
$764$	69.8587	2.52740
$765$	−9.50115	−0.343515
$766$	−39.0840	−1.41216
$767$	−1.00777	−0.0363884
$768$	23.4949	0.847798
$769$	−0.195552	−0.00705179	−0.00352589	−	0.999994i	$-0.501122\pi$
$769$	−0.195552	−0.00705179	−0.00352589	+	0.999994i	$0.501122\pi$
$770$	1.59907	0.0576266
$771$	−13.4269	−0.483558
$772$	−30.9931	−1.11547
$773$	−53.9810	−1.94156	−0.970781	−	0.239969i	$-0.922863\pi$
$773$	−53.9810	−1.94156	−0.970781	+	0.239969i	$0.922863\pi$
$774$	−49.8700	−1.79254
$775$	7.44619	0.267475
$776$	−43.6710	−1.56770
$777$	14.0544	0.504199
$778$	75.8749	2.72025
$779$	−12.0548	−0.431907
$780$	−11.2854	−0.404082
$781$	2.30348	0.0824251
$782$	−33.8792	−1.21152
$783$	−38.2562	−1.36717
$784$	18.6554	0.666263
$785$	15.0190	0.536052
$786$	12.1758	0.434296
$787$	42.3231	1.50866	0.754329	−	0.656497i	$-0.227963\pi$
$787$	42.3231	1.50866	0.754329	+	0.656497i	$0.227963\pi$
$788$	28.1200	1.00173
$789$	−0.0271401	−0.000966213 0
$790$	−11.6682	−0.415136
$791$	−55.9990	−1.99110
$792$	−1.68396	−0.0598370
$793$	−29.6921	−1.05440
$794$	−20.0576	−0.711817
$795$	−5.20659	−0.184659
$796$	18.5467	0.657371
$797$	−19.5428	−0.692243	−0.346122	−	0.938190i	$-0.612502\pi$
$797$	−19.5428	−0.692243	−0.346122	+	0.938190i	$0.612502\pi$
$798$	25.2288	0.893089
$799$	55.7712	1.97304
$800$	2.37359	0.0839192
$801$	10.1365	0.358157
$802$	51.6331	1.82323
$803$	1.51225	0.0533660
$804$	−27.3994	−0.966302
$805$	−13.1338	−0.462905
$806$	65.0605	2.29166
$807$	−14.1006	−0.496363
$808$	−21.0434	−0.740305
$809$	−31.0039	−1.09004	−0.545019	−	0.838424i	$-0.683478\pi$
$809$	−31.0039	−1.09004	−0.545019	+	0.838424i	$0.683478\pi$
$810$	7.89552	0.277420
$811$	23.8923	0.838971	0.419485	−	0.907762i	$-0.362211\pi$
$811$	23.8923	0.838971	0.419485	+	0.907762i	$0.362211\pi$
$812$	123.733	4.34218
$813$	18.3448	0.643379
$814$	1.86776	0.0654650
$815$	−24.0898	−0.843828
$816$	8.42644	0.294984
$817$	30.0336	1.05074
$818$	−48.4909	−1.69544
$819$	−32.1822	−1.12454
$820$	−13.4899	−0.471087
$821$	19.1195	0.667275	0.333637	−	0.942702i	$-0.391724\pi$
$821$	19.1195	0.667275	0.333637	+	0.942702i	$0.391724\pi$
$822$	−6.29789	−0.219664
$823$	44.1353	1.53846	0.769229	−	0.638973i	$-0.220640\pi$
$823$	44.1353	1.53846	0.769229	+	0.638973i	$0.220640\pi$
$824$	−59.5397	−2.07416
$825$	0.145094	0.00505153
$826$	2.52109	0.0877200
$827$	−33.0643	−1.14976	−0.574880	−	0.818238i	$-0.694951\pi$
$827$	−33.0643	−1.14976	−0.574880	+	0.818238i	$0.694951\pi$
$828$	29.7783	1.03487
$829$	36.4003	1.26423	0.632117	−	0.774873i	$-0.282186\pi$
$829$	36.4003	1.26423	0.632117	+	0.774873i	$0.282186\pi$
$830$	−18.2537	−0.633593
$831$	25.3974	0.881025
$832$	38.8218	1.34590
$833$	−30.9103	−1.07098
$834$	−15.4700	−0.535683
$835$	15.7573	0.545303
$836$	2.18346	0.0755166
$837$	32.7720	1.13277
$838$	81.5225	2.81615
$839$	19.8056	0.683764	0.341882	−	0.939743i	$-0.388936\pi$
$839$	19.8056	0.683764	0.341882	+	0.939743i	$0.388936\pi$
$840$	13.1129	0.452439
$841$	46.5556	1.60537
$842$	36.5973	1.26123
$843$	15.2343	0.524698
$844$	40.6723	1.40000
$845$	−0.312634	−0.0107549
$846$	−75.2724	−2.58792
$847$	41.8108	1.43663
$848$	−15.5781	−0.534953
$849$	−14.0390	−0.481818
$850$	9.83223	0.337243
$851$	−15.3406	−0.525869
$852$	40.6689	1.39329
$853$	−2.00537	−0.0686626	−0.0343313	−	0.999411i	$-0.510930\pi$
$853$	−2.00537	−0.0686626	−0.0343313	+	0.999411i	$0.510930\pi$
$854$	74.2795	2.54179
$855$	−7.72270	−0.264111
$856$	−60.3734	−2.06352
$857$	−7.77080	−0.265446	−0.132723	−	0.991153i	$-0.542372\pi$
$857$	−7.77080	−0.265446	−0.132723	+	0.991153i	$0.542372\pi$
$858$	1.26775	0.0432802
$859$	21.5640	0.735754	0.367877	−	0.929874i	$-0.380085\pi$
$859$	21.5640	0.735754	0.367877	+	0.929874i	$0.380085\pi$
$860$	33.6091	1.14606
$861$	11.4029	0.388610
$862$	28.7053	0.977705
$863$	−39.9369	−1.35947	−0.679735	−	0.733458i	$-0.737905\pi$
$863$	−39.9369	−1.35947	−0.679735	+	0.733458i	$0.737905\pi$
$864$	10.4466	0.355400
$865$	9.76384	0.331981
$866$	43.4537	1.47662
$867$	0.117755	0.00399918
$868$	−105.995	−3.59771
$869$	0.853613	0.0289568
$870$	17.2396	0.584476
$871$	−32.3212	−1.09516
$872$	−15.1018	−0.511411
$873$	−24.3287	−0.823403
$874$	−27.5376	−0.931473
$875$	3.81161	0.128856
$876$	26.6993	0.902086
$877$	58.5884	1.97839	0.989195	−	0.146607i	$-0.0468352\pi$
$877$	58.5884	1.97839	0.989195	+	0.146607i	$0.0468352\pi$
$878$	5.49350	0.185397
$879$	−1.20735	−0.0407229
$880$	0.434120	0.0146342
$881$	40.0778	1.35026	0.675128	−	0.737701i	$-0.264088\pi$
$881$	40.0778	1.35026	0.675128	+	0.737701i	$0.264088\pi$
$882$	41.7185	1.40474
$883$	−29.2335	−0.983786	−0.491893	−	0.870656i	$-0.663695\pi$
$883$	−29.2335	−0.983786	−0.491893	+	0.870656i	$0.663695\pi$
$884$	55.9469	1.88170
$885$	0.228755	0.00768952
$886$	−53.6177	−1.80132
$887$	−5.95385	−0.199911	−0.0999553	−	0.994992i	$-0.531870\pi$
$887$	−5.95385	−0.199911	−0.0999553	+	0.994992i	$0.531870\pi$
$888$	15.3163	0.513980
$889$	−67.4400	−2.26187
$890$	−10.4898	−0.351618
$891$	−0.577614	−0.0193508
$892$	38.8272	1.30003
$893$	45.3318	1.51697
$894$	−38.8654	−1.29985
$895$	−14.8190	−0.495345
$896$	−79.0245	−2.64002
$897$	−10.4125	−0.347663
$898$	8.53882	0.284944
$899$	−64.7244	−2.15868
$900$	−8.64209	−0.288070
$901$	25.8114	0.859904
$902$	1.51539	0.0504570
$903$	−28.4095	−0.945410
$904$	−61.0268	−2.02972
$905$	11.0597	0.367636
$906$	16.3070	0.541765
$907$	23.5785	0.782912	0.391456	−	0.920197i	$-0.371972\pi$
$907$	23.5785	0.782912	0.391456	+	0.920197i	$0.371972\pi$
$908$	−89.1933	−2.95998
$909$	−11.7231	−0.388831
$910$	33.3037	1.10401
$911$	−26.0178	−0.862010	−0.431005	−	0.902350i	$-0.641841\pi$
$911$	−26.0178	−0.862010	−0.431005	+	0.902350i	$0.641841\pi$
$912$	6.84916	0.226799
$913$	1.33538	0.0441948
$914$	58.6885	1.94124
$915$	6.73986	0.222813
$916$	−42.0744	−1.39018
$917$	−23.3998	−0.772730
$918$	43.2734	1.42823
$919$	−30.2712	−0.998555	−0.499277	−	0.866442i	$-0.666401\pi$
$919$	−30.2712	−0.998555	−0.499277	+	0.866442i	$0.666401\pi$
$920$	−14.3130	−0.471885
$921$	−1.97199	−0.0649792
$922$	22.8109	0.751237
$923$	47.9743	1.57909
$924$	−2.06539	−0.0679463
$925$	4.45207	0.146383
$926$	78.6352	2.58411
$927$	−33.1690	−1.08941
$928$	−20.6319	−0.677276
$929$	4.55862	0.149563	0.0747817	−	0.997200i	$-0.476174\pi$
$929$	4.55862	0.149563	0.0747817	+	0.997200i	$0.476174\pi$
$930$	−14.7682	−0.484268
$931$	−25.1244	−0.823420
$932$	−68.9321	−2.25795
$933$	13.3760	0.437909
$934$	32.4834	1.06289
$935$	−0.719298	−0.0235235
$936$	−35.0717	−1.14635
$937$	7.77766	0.254085	0.127043	−	0.991897i	$-0.459452\pi$
$937$	7.77766	0.254085	0.127043	+	0.991897i	$0.459452\pi$
$938$	80.8567	2.64006
$939$	8.97171	0.292781
$940$	50.7286	1.65458
$941$	−27.9599	−0.911467	−0.455733	−	0.890116i	$-0.650623\pi$
$941$	−27.9599	−0.911467	−0.455733	+	0.890116i	$0.650623\pi$
$942$	−29.7876	−0.970532
$943$	−12.4465	−0.405312
$944$	0.684432	0.0222764
$945$	16.7756	0.545710
$946$	−3.77548	−0.122751
$947$	31.1304	1.01160	0.505801	−	0.862650i	$-0.331197\pi$
$947$	31.1304	1.01160	0.505801	+	0.862650i	$0.331197\pi$
$948$	15.0709	0.489479
$949$	31.4954	1.02238
$950$	7.99181	0.259289
$951$	4.91180	0.159276
$952$	−65.0068	−2.10688
$953$	−19.2098	−0.622266	−0.311133	−	0.950366i	$-0.600708\pi$
$953$	−19.2098	−0.622266	−0.311133	+	0.950366i	$0.600708\pi$
$954$	−34.8368	−1.12788
$955$	−18.7058	−0.605307
$956$	9.53939	0.308526
$957$	−1.26120	−0.0407687
$958$	−73.8940	−2.38741
$959$	12.1035	0.390842
$960$	−8.81222	−0.284413
$961$	24.4458	0.788574
$962$	38.8996	1.25417
$963$	−33.6335	−1.08382
$964$	3.73459	0.120283
$965$	8.29892	0.267152
$966$	26.0485	0.838097
$967$	−32.3268	−1.03956	−0.519780	−	0.854300i	$-0.673986\pi$
$967$	−32.3268	−1.03956	−0.519780	+	0.854300i	$0.673986\pi$
$968$	45.5647	1.46450
$969$	−11.3485	−0.364565
$970$	25.1765	0.808369
$971$	−4.12897	−0.132505	−0.0662525	−	0.997803i	$-0.521104\pi$
$971$	−4.12897	−0.132505	−0.0662525	+	0.997803i	$0.521104\pi$
$972$	−59.5078	−1.90871
$973$	29.7308	0.953126
$974$	69.5902	2.22981
$975$	3.02186	0.0967769
$976$	20.1656	0.645484
$977$	16.7056	0.534460	0.267230	−	0.963633i	$-0.413892\pi$
$977$	16.7056	0.534460	0.267230	+	0.963633i	$0.413892\pi$
$978$	47.7778	1.52777
$979$	0.767401	0.0245262
$980$	−28.1155	−0.898116
$981$	−8.41307	−0.268609
$982$	25.5144	0.814196
$983$	45.8244	1.46157	0.730786	−	0.682606i	$-0.239154\pi$
$983$	45.8244	1.46157	0.730786	+	0.682606i	$0.239154\pi$
$984$	12.4267	0.396149
$985$	−7.52960	−0.239913
$986$	−85.4644	−2.72174
$987$	−42.8805	−1.36490
$988$	45.4747	1.44674
$989$	31.0094	0.986043
$990$	0.970811	0.0308544
$991$	12.4118	0.394274	0.197137	−	0.980376i	$-0.436836\pi$
$991$	12.4118	0.394274	0.197137	+	0.980376i	$0.436836\pi$
$992$	17.6742	0.561157
$993$	1.27528	0.0404697
$994$	−120.015	−3.80666
$995$	−4.96620	−0.157439
$996$	23.5767	0.747058
$997$	18.7109	0.592581	0.296291	−	0.955098i	$-0.404250\pi$
$997$	18.7109	0.592581	0.296291	+	0.955098i	$0.404250\pi$
$998$	−72.8840	−2.30710
$999$	19.5943	0.619937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.4	✓	25
5.4	even	2		6025.2.a.k.1.22		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.4	✓	25	1.1	even	1	trivial
6025.2.a.k.1.22		25	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39470 q^{2} -0.828213 q^{3} +3.73459 q^{4} -1.00000 q^{5} +1.98332 q^{6} -3.81161 q^{7} -4.15383 q^{8} -2.31406 q^{9} +O(q^{10})\)	\(q-2.39470 q^{2} -0.828213 q^{3} +3.73459 q^{4} -1.00000 q^{5} +1.98332 q^{6} -3.81161 q^{7} -4.15383 q^{8} -2.31406 q^{9} +2.39470 q^{10} -0.175189 q^{11} -3.09304 q^{12} -3.64865 q^{13} +9.12767 q^{14} +0.828213 q^{15} +2.47800 q^{16} -4.10583 q^{17} +5.54149 q^{18} -3.33729 q^{19} -3.73459 q^{20} +3.15683 q^{21} +0.419526 q^{22} -3.44573 q^{23} +3.44026 q^{24} +1.00000 q^{25} +8.73742 q^{26} +4.40118 q^{27} -14.2348 q^{28} -8.69227 q^{29} -1.98332 q^{30} +7.44619 q^{31} +2.37359 q^{32} +0.145094 q^{33} +9.83223 q^{34} +3.81161 q^{35} -8.64209 q^{36} +4.45207 q^{37} +7.99181 q^{38} +3.02186 q^{39} +4.15383 q^{40} +3.61214 q^{41} -7.55966 q^{42} -8.99939 q^{43} -0.654261 q^{44} +2.31406 q^{45} +8.25148 q^{46} -13.5834 q^{47} -2.05231 q^{48} +7.52839 q^{49} -2.39470 q^{50} +3.40050 q^{51} -13.6262 q^{52} -6.28654 q^{53} -10.5395 q^{54} +0.175189 q^{55} +15.8328 q^{56} +2.76399 q^{57} +20.8154 q^{58} +0.276203 q^{59} +3.09304 q^{60} +8.13784 q^{61} -17.8314 q^{62} +8.82031 q^{63} -10.6400 q^{64} +3.64865 q^{65} -0.347457 q^{66} +8.85841 q^{67} -15.3336 q^{68} +2.85379 q^{69} -9.12767 q^{70} -13.1485 q^{71} +9.61223 q^{72} -8.63206 q^{73} -10.6614 q^{74} -0.828213 q^{75} -12.4634 q^{76} +0.667754 q^{77} -7.23645 q^{78} -4.87251 q^{79} -2.47800 q^{80} +3.29708 q^{81} -8.65001 q^{82} -7.62252 q^{83} +11.7895 q^{84} +4.10583 q^{85} +21.5509 q^{86} +7.19905 q^{87} +0.727708 q^{88} -4.38040 q^{89} -5.54149 q^{90} +13.9072 q^{91} -12.8684 q^{92} -6.16703 q^{93} +32.5282 q^{94} +3.33729 q^{95} -1.96584 q^{96} +10.5134 q^{97} -18.0283 q^{98} +0.405399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

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