LMFDB - Embedded newform 2645.2.a.x.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, 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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.10124 q^{2} +3.19240 q^{3} +2.41520 q^{4} -1.00000 q^{5} +6.70798 q^{6} +3.48850 q^{7} +0.872423 q^{8} +7.19141 q^{9} +O(q^{10})$	\(q+2.10124 q^{2} +3.19240 q^{3} +2.41520 q^{4} -1.00000 q^{5} +6.70798 q^{6} +3.48850 q^{7} +0.872423 q^{8} +7.19141 q^{9} -2.10124 q^{10} -2.99007 q^{11} +7.71027 q^{12} +2.47871 q^{13} +7.33017 q^{14} -3.19240 q^{15} -2.99722 q^{16} -1.89724 q^{17} +15.1109 q^{18} +0.418318 q^{19} -2.41520 q^{20} +11.1367 q^{21} -6.28285 q^{22} +2.78512 q^{24} +1.00000 q^{25} +5.20836 q^{26} +13.3807 q^{27} +8.42541 q^{28} -7.10037 q^{29} -6.70798 q^{30} +4.36608 q^{31} -8.04272 q^{32} -9.54550 q^{33} -3.98656 q^{34} -3.48850 q^{35} +17.3687 q^{36} +2.54222 q^{37} +0.878985 q^{38} +7.91304 q^{39} -0.872423 q^{40} -1.87344 q^{41} +23.4008 q^{42} -7.26222 q^{43} -7.22161 q^{44} -7.19141 q^{45} -10.6829 q^{47} -9.56833 q^{48} +5.16965 q^{49} +2.10124 q^{50} -6.05675 q^{51} +5.98658 q^{52} +12.6830 q^{53} +28.1159 q^{54} +2.99007 q^{55} +3.04345 q^{56} +1.33544 q^{57} -14.9196 q^{58} +3.80365 q^{59} -7.71027 q^{60} -7.92539 q^{61} +9.17418 q^{62} +25.0872 q^{63} -10.9052 q^{64} -2.47871 q^{65} -20.0574 q^{66} +4.30802 q^{67} -4.58221 q^{68} -7.33017 q^{70} -8.22890 q^{71} +6.27395 q^{72} +8.64151 q^{73} +5.34181 q^{74} +3.19240 q^{75} +1.01032 q^{76} -10.4309 q^{77} +16.6272 q^{78} +7.77080 q^{79} +2.99722 q^{80} +21.1421 q^{81} -3.93654 q^{82} -7.60098 q^{83} +26.8973 q^{84} +1.89724 q^{85} -15.2597 q^{86} -22.6672 q^{87} -2.60861 q^{88} +4.62977 q^{89} -15.1109 q^{90} +8.64700 q^{91} +13.9383 q^{93} -22.4473 q^{94} -0.418318 q^{95} -25.6756 q^{96} -3.81498 q^{97} +10.8627 q^{98} -21.5028 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) $ 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9} - 3 q^{10} + 8 q^{11} + 34 q^{12} + 15 q^{13} + 6 q^{14} - 10 q^{15} + 41 q^{16} - 19 q^{17} + 23 q^{18} + 8 q^{19} - 33 q^{20} + 21 q^{21} - 3 q^{22} + 51 q^{24} + 25 q^{25} + 7 q^{26} + 64 q^{27} - 27 q^{28} + 3 q^{29} - 22 q^{30} + 34 q^{31} + 30 q^{32} + q^{33} + 21 q^{34} + 14 q^{35} + 31 q^{36} + q^{37} + 7 q^{38} + 49 q^{39} - 21 q^{40} + 29 q^{42} - 25 q^{43} + 33 q^{44} - 29 q^{45} - 5 q^{47} + 42 q^{48} + 33 q^{49} + 3 q^{50} - 23 q^{51} + 67 q^{52} - 24 q^{53} + 37 q^{54} - 8 q^{55} + 55 q^{56} + 19 q^{57} + 49 q^{58} + 41 q^{59} - 34 q^{60} + 31 q^{61} - 3 q^{62} - 37 q^{63} + 77 q^{64} - 15 q^{65} + 39 q^{66} + 5 q^{67} - 27 q^{68} - 6 q^{70} + 15 q^{71} + 48 q^{72} + 34 q^{73} + 29 q^{74} + 10 q^{75} + 24 q^{76} - 35 q^{77} - 45 q^{78} + 41 q^{79} - 41 q^{80} + 25 q^{81} + 33 q^{82} - 62 q^{83} + 126 q^{84} + 19 q^{85} + 10 q^{86} + 26 q^{87} + 50 q^{88} + 23 q^{89} - 23 q^{90} - 19 q^{91} + 50 q^{93} + 9 q^{94} - 8 q^{95} + 64 q^{96} - 37 q^{97} - 55 q^{98} + 48 q^{99}+O(q^{100}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9 - 3 * q^10 + 8 * q^11 + 34 * q^12 + 15 * q^13 + 6 * q^14 - 10 * q^15 + 41 * q^16 - 19 * q^17 + 23 * q^18 + 8 * q^19 - 33 * q^20 + 21 * q^21 - 3 * q^22 + 51 * q^24 + 25 * q^25 + 7 * q^26 + 64 * q^27 - 27 * q^28 + 3 * q^29 - 22 * q^30 + 34 * q^31 + 30 * q^32 + q^33 + 21 * q^34 + 14 * q^35 + 31 * q^36 + q^37 + 7 * q^38 + 49 * q^39 - 21 * q^40 + 29 * q^42 - 25 * q^43 + 33 * q^44 - 29 * q^45 - 5 * q^47 + 42 * q^48 + 33 * q^49 + 3 * q^50 - 23 * q^51 + 67 * q^52 - 24 * q^53 + 37 * q^54 - 8 * q^55 + 55 * q^56 + 19 * q^57 + 49 * q^58 + 41 * q^59 - 34 * q^60 + 31 * q^61 - 3 * q^62 - 37 * q^63 + 77 * q^64 - 15 * q^65 + 39 * q^66 + 5 * q^67 - 27 * q^68 - 6 * q^70 + 15 * q^71 + 48 * q^72 + 34 * q^73 + 29 * q^74 + 10 * q^75 + 24 * q^76 - 35 * q^77 - 45 * q^78 + 41 * q^79 - 41 * q^80 + 25 * q^81 + 33 * q^82 - 62 * q^83 + 126 * q^84 + 19 * q^85 + 10 * q^86 + 26 * q^87 + 50 * q^88 + 23 * q^89 - 23 * q^90 - 19 * q^91 + 50 * q^93 + 9 * q^94 - 8 * q^95 + 64 * q^96 - 37 * q^97 - 55 * q^98 + 48 * 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 $

$2$	2.10124	1.48580	0.742899	−	0.669403i	$-0.233450\pi$
$2$	2.10124	1.48580	0.742899	+	0.669403i	$0.233450\pi$
$3$	3.19240	1.84313	0.921566	−	0.388221i	$-0.126910\pi$
$3$	3.19240	1.84313	0.921566	+	0.388221i	$0.126910\pi$
$4$	2.41520	1.20760
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.70798	2.73852
$7$	3.48850	1.31853	0.659265	−	0.751911i	$-0.270868\pi$
$7$	3.48850	1.31853	0.659265	+	0.751911i	$0.270868\pi$
$8$	0.872423	0.308448
$9$	7.19141	2.39714
$10$	−2.10124	−0.664469
$11$	−2.99007	−0.901541	−0.450770	−	0.892640i	$-0.648851\pi$
$11$	−2.99007	−0.901541	−0.450770	+	0.892640i	$0.648851\pi$
$12$	7.71027	2.22576
$13$	2.47871	0.687472	0.343736	−	0.939066i	$-0.388308\pi$
$13$	2.47871	0.687472	0.343736	+	0.939066i	$0.388308\pi$
$14$	7.33017	1.95907
$15$	−3.19240	−0.824274
$16$	−2.99722	−0.749306
$17$	−1.89724	−0.460149	−0.230074	−	0.973173i	$-0.573897\pi$
$17$	−1.89724	−0.460149	−0.230074	+	0.973173i	$0.573897\pi$
$18$	15.1109	3.56166
$19$	0.418318	0.0959688	0.0479844	−	0.998848i	$-0.484720\pi$
$19$	0.418318	0.0959688	0.0479844	+	0.998848i	$0.484720\pi$
$20$	−2.41520	−0.540054
$21$	11.1367	2.43023
$22$	−6.28285	−1.33951
$23$	0	0
$23$	0	0
$24$	2.78512	0.568511
$25$	1.00000	0.200000
$26$	5.20836	1.02144
$27$	13.3807	2.57511
$28$	8.42541	1.59225
$29$	−7.10037	−1.31851	−0.659253	−	0.751922i	$-0.729127\pi$
$29$	−7.10037	−1.31851	−0.659253	+	0.751922i	$0.729127\pi$
$30$	−6.70798	−1.22470
$31$	4.36608	0.784172	0.392086	−	0.919929i	$-0.371754\pi$
$31$	4.36608	0.784172	0.392086	+	0.919929i	$0.371754\pi$
$32$	−8.04272	−1.42177
$33$	−9.54550	−1.66166
$34$	−3.98656	−0.683689
$35$	−3.48850	−0.589665
$36$	17.3687	2.89478
$37$	2.54222	0.417939	0.208969	−	0.977922i	$-0.432989\pi$
$37$	2.54222	0.417939	0.208969	+	0.977922i	$0.432989\pi$
$38$	0.878985	0.142590
$39$	7.91304	1.26710
$40$	−0.872423	−0.137942
$41$	−1.87344	−0.292582	−0.146291	−	0.989242i	$-0.546734\pi$
$41$	−1.87344	−0.292582	−0.146291	+	0.989242i	$0.546734\pi$
$42$	23.4008	3.61083
$43$	−7.26222	−1.10748	−0.553739	−	0.832690i	$-0.686800\pi$
$43$	−7.26222	−1.10748	−0.553739	+	0.832690i	$0.686800\pi$
$44$	−7.22161	−1.08870
$45$	−7.19141	−1.07203
$46$	0	0
$47$	−10.6829	−1.55826	−0.779132	−	0.626860i	$-0.784340\pi$
$47$	−10.6829	−1.55826	−0.779132	+	0.626860i	$0.784340\pi$
$48$	−9.56833	−1.38107
$49$	5.16965	0.738521
$50$	2.10124	0.297160
$51$	−6.05675	−0.848115
$52$	5.98658	0.830189
$53$	12.6830	1.74214	0.871071	−	0.491156i	$-0.163426\pi$
$53$	12.6830	1.74214	0.871071	+	0.491156i	$0.163426\pi$
$54$	28.1159	3.82609
$55$	2.99007	0.403181
$56$	3.04345	0.406698
$57$	1.33544	0.176883
$58$	−14.9196	−1.95903
$59$	3.80365	0.495193	0.247596	−	0.968863i	$-0.420359\pi$
$59$	3.80365	0.495193	0.247596	+	0.968863i	$0.420359\pi$
$60$	−7.71027	−0.995391
$61$	−7.92539	−1.01474	−0.507371	−	0.861728i	$-0.669383\pi$
$61$	−7.92539	−1.01474	−0.507371	+	0.861728i	$0.669383\pi$
$62$	9.17418	1.16512
$63$	25.0872	3.16070
$64$	−10.9052	−1.36315
$65$	−2.47871	−0.307447
$66$	−20.0574	−2.46889
$67$	4.30802	0.526308	0.263154	−	0.964754i	$-0.415237\pi$
$67$	4.30802	0.526308	0.263154	+	0.964754i	$0.415237\pi$
$68$	−4.58221	−0.555675
$69$	0	0
$70$	−7.33017	−0.876123
$71$	−8.22890	−0.976591	−0.488296	−	0.872678i	$-0.662381\pi$
$71$	−8.22890	−0.976591	−0.488296	+	0.872678i	$0.662381\pi$
$72$	6.27395	0.739392
$73$	8.64151	1.01141	0.505706	−	0.862706i	$-0.331232\pi$
$73$	8.64151	1.01141	0.505706	+	0.862706i	$0.331232\pi$
$74$	5.34181	0.620972
$75$	3.19240	0.368626
$76$	1.01032	0.115892
$77$	−10.4309	−1.18871
$78$	16.6272	1.88266
$79$	7.77080	0.874283	0.437142	−	0.899393i	$-0.355991\pi$
$79$	7.77080	0.874283	0.437142	+	0.899393i	$0.355991\pi$
$80$	2.99722	0.335100
$81$	21.1421	2.34913
$82$	−3.93654	−0.434718
$83$	−7.60098	−0.834316	−0.417158	−	0.908834i	$-0.636974\pi$
$83$	−7.60098	−0.834316	−0.417158	+	0.908834i	$0.636974\pi$
$84$	26.8973	2.93473
$85$	1.89724	0.205785
$86$	−15.2597	−1.64549
$87$	−22.6672	−2.43018
$88$	−2.60861	−0.278079
$89$	4.62977	0.490754	0.245377	−	0.969428i	$-0.421088\pi$
$89$	4.62977	0.490754	0.245377	+	0.969428i	$0.421088\pi$
$90$	−15.1109	−1.59282
$91$	8.64700	0.906452
$92$	0	0
$93$	13.9383	1.44533
$94$	−22.4473	−2.31527
$95$	−0.418318	−0.0429185
$96$	−25.6756	−2.62050
$97$	−3.81498	−0.387352	−0.193676	−	0.981066i	$-0.562041\pi$
$97$	−3.81498	−0.387352	−0.193676	+	0.981066i	$0.562041\pi$
$98$	10.8627	1.09729
$99$	−21.5028	−2.16112
$100$	2.41520	0.241520
$101$	−7.50606	−0.746881	−0.373441	−	0.927654i	$-0.621822\pi$
$101$	−7.50606	−0.746881	−0.373441	+	0.927654i	$0.621822\pi$
$102$	−12.7267	−1.26013
$103$	−2.11940	−0.208831	−0.104415	−	0.994534i	$-0.533297\pi$
$103$	−2.11940	−0.208831	−0.104415	+	0.994534i	$0.533297\pi$
$104$	2.16249	0.212049
$105$	−11.1367	−1.08683
$106$	26.6500	2.58847
$107$	10.0469	0.971274	0.485637	−	0.874161i	$-0.338588\pi$
$107$	10.0469	0.971274	0.485637	+	0.874161i	$0.338588\pi$
$108$	32.3169	3.10969
$109$	1.39107	0.133240	0.0666200	−	0.997778i	$-0.478778\pi$
$109$	1.39107	0.133240	0.0666200	+	0.997778i	$0.478778\pi$
$110$	6.28285	0.599046
$111$	8.11578	0.770316
$112$	−10.4558	−0.987982
$113$	−14.8705	−1.39890	−0.699449	−	0.714683i	$-0.746571\pi$
$113$	−14.8705	−1.39890	−0.699449	+	0.714683i	$0.746571\pi$
$114$	2.80607	0.262813
$115$	0	0
$116$	−17.1488	−1.59222
$117$	17.8254	1.64796
$118$	7.99236	0.735757
$119$	−6.61853	−0.606720
$120$	−2.78512	−0.254246
$121$	−2.05947	−0.187224
$122$	−16.6531	−1.50770
$123$	−5.98077	−0.539268
$124$	10.5449	0.946964
$125$	−1.00000	−0.0894427
$126$	52.7142	4.69616
$127$	−0.806016	−0.0715224	−0.0357612	−	0.999360i	$-0.511386\pi$
$127$	−0.806016	−0.0715224	−0.0357612	+	0.999360i	$0.511386\pi$
$128$	−6.82899	−0.603603
$129$	−23.1839	−2.04123
$130$	−5.20836	−0.456804
$131$	7.21953	0.630774	0.315387	−	0.948963i	$-0.397866\pi$
$131$	7.21953	0.630774	0.315387	+	0.948963i	$0.397866\pi$
$132$	−23.0543	−2.00662
$133$	1.45930	0.126538
$134$	9.05216	0.781988
$135$	−13.3807	−1.15162
$136$	−1.65520	−0.141932
$137$	−6.25223	−0.534164	−0.267082	−	0.963674i	$-0.586059\pi$
$137$	−6.25223	−0.534164	−0.267082	+	0.963674i	$0.586059\pi$
$138$	0	0
$139$	−3.99678	−0.339003	−0.169501	−	0.985530i	$-0.554216\pi$
$139$	−3.99678	−0.339003	−0.169501	+	0.985530i	$0.554216\pi$
$140$	−8.42541	−0.712077
$141$	−34.1041	−2.87209
$142$	−17.2909	−1.45102
$143$	−7.41154	−0.619784
$144$	−21.5543	−1.79619
$145$	7.10037	0.589653
$146$	18.1579	1.50275
$147$	16.5036	1.36119
$148$	6.13996	0.504702
$149$	−8.00659	−0.655926	−0.327963	−	0.944691i	$-0.606362\pi$
$149$	−8.00659	−0.655926	−0.327963	+	0.944691i	$0.606362\pi$
$150$	6.70798	0.547705
$151$	13.3089	1.08306	0.541530	−	0.840681i	$-0.317845\pi$
$151$	13.3089	1.08306	0.541530	+	0.840681i	$0.317845\pi$
$152$	0.364950	0.0296014
$153$	−13.6438	−1.10304
$154$	−21.9177	−1.76618
$155$	−4.36608	−0.350692
$156$	19.1115	1.53015
$157$	13.6457	1.08904	0.544522	−	0.838747i	$-0.316711\pi$
$157$	13.6457	1.08904	0.544522	+	0.838747i	$0.316711\pi$
$158$	16.3283	1.29901
$159$	40.4892	3.21100
$160$	8.04272	0.635833
$161$	0	0
$162$	44.4246	3.49033
$163$	−15.6108	−1.22273	−0.611367	−	0.791347i	$-0.709380\pi$
$163$	−15.6108	−1.22273	−0.611367	+	0.791347i	$0.709380\pi$
$164$	−4.52472	−0.353322
$165$	9.54550	0.743116
$166$	−15.9715	−1.23963
$167$	13.0258	1.00796	0.503982	−	0.863714i	$-0.331868\pi$
$167$	13.0258	1.00796	0.503982	+	0.863714i	$0.331868\pi$
$168$	9.71591	0.749599
$169$	−6.85598	−0.527383
$170$	3.98656	0.305755
$171$	3.00830	0.230050
$172$	−17.5397	−1.33739
$173$	19.2219	1.46141	0.730707	−	0.682691i	$-0.239190\pi$
$173$	19.2219	1.46141	0.730707	+	0.682691i	$0.239190\pi$
$174$	−47.6292	−3.61076
$175$	3.48850	0.263706
$176$	8.96191	0.675530
$177$	12.1428	0.912706
$178$	9.72823	0.729162
$179$	−1.95390	−0.146042	−0.0730208	−	0.997330i	$-0.523264\pi$
$179$	−1.95390	−0.146042	−0.0730208	+	0.997330i	$0.523264\pi$
$180$	−17.3687	−1.29458
$181$	10.3453	0.768963	0.384482	−	0.923133i	$-0.374380\pi$
$181$	10.3453	0.768963	0.384482	+	0.923133i	$0.374380\pi$
$182$	18.1694	1.34681
$183$	−25.3010	−1.87030
$184$	0	0
$185$	−2.54222	−0.186908
$186$	29.2876	2.14747
$187$	5.67289	0.414843
$188$	−25.8013	−1.88176
$189$	46.6784	3.39536
$190$	−0.878985	−0.0637683
$191$	22.7742	1.64788	0.823942	−	0.566674i	$-0.191770\pi$
$191$	22.7742	1.64788	0.823942	+	0.566674i	$0.191770\pi$
$192$	−34.8138	−2.51247
$193$	−19.1362	−1.37746	−0.688728	−	0.725020i	$-0.741831\pi$
$193$	−19.1362	−1.37746	−0.688728	+	0.725020i	$0.741831\pi$
$194$	−8.01617	−0.575527
$195$	−7.91304	−0.566665
$196$	12.4857	0.891836
$197$	−13.0466	−0.929528	−0.464764	−	0.885434i	$-0.653861\pi$
$197$	−13.0466	−0.929528	−0.464764	+	0.885434i	$0.653861\pi$
$198$	−45.1825	−3.21098
$199$	−18.0351	−1.27848	−0.639239	−	0.769009i	$-0.720750\pi$
$199$	−18.0351	−1.27848	−0.639239	+	0.769009i	$0.720750\pi$
$200$	0.872423	0.0616896
$201$	13.7529	0.970055
$202$	−15.7720	−1.10971
$203$	−24.7696	−1.73849
$204$	−14.6282	−1.02418
$205$	1.87344	0.130847
$206$	−4.45337	−0.310281
$207$	0	0
$208$	−7.42926	−0.515126
$209$	−1.25080	−0.0865198
$210$	−23.4008	−1.61481
$211$	2.73763	0.188466	0.0942332	−	0.995550i	$-0.469960\pi$
$211$	2.73763	0.188466	0.0942332	+	0.995550i	$0.469960\pi$
$212$	30.6319	2.10381
$213$	−26.2699	−1.79999
$214$	21.1110	1.44312
$215$	7.26222	0.495280
$216$	11.6736	0.794287
$217$	15.2311	1.03395
$218$	2.92296	0.197968
$219$	27.5871	1.86417
$220$	7.22161	0.486881
$221$	−4.70272	−0.316339
$222$	17.0532	1.14453
$223$	8.60787	0.576426	0.288213	−	0.957566i	$-0.406939\pi$
$223$	8.60787	0.576426	0.288213	+	0.957566i	$0.406939\pi$
$224$	−28.0570	−1.87464
$225$	7.19141	0.479427
$226$	−31.2464	−2.07848
$227$	16.6943	1.10804	0.554021	−	0.832503i	$-0.313093\pi$
$227$	16.6943	1.10804	0.554021	+	0.832503i	$0.313093\pi$
$228$	3.22534	0.213604
$229$	−3.79890	−0.251038	−0.125519	−	0.992091i	$-0.540060\pi$
$229$	−3.79890	−0.251038	−0.125519	+	0.992091i	$0.540060\pi$
$230$	0	0
$231$	−33.2995	−2.19095
$232$	−6.19452	−0.406690
$233$	9.88966	0.647893	0.323946	−	0.946075i	$-0.394990\pi$
$233$	9.88966	0.647893	0.323946	+	0.946075i	$0.394990\pi$
$234$	37.4555	2.44854
$235$	10.6829	0.696877
$236$	9.18655	0.597993
$237$	24.8075	1.61142
$238$	−13.9071	−0.901464
$239$	−20.9587	−1.35571	−0.677853	−	0.735197i	$-0.737090\pi$
$239$	−20.9587	−1.35571	−0.677853	+	0.735197i	$0.737090\pi$
$240$	9.56833	0.617633
$241$	13.7992	0.888884	0.444442	−	0.895808i	$-0.353402\pi$
$241$	13.7992	0.888884	0.444442	+	0.895808i	$0.353402\pi$
$242$	−4.32743	−0.278178
$243$	27.3522	1.75464
$244$	−19.1414	−1.22540
$245$	−5.16965	−0.330277
$246$	−12.5670	−0.801243
$247$	1.03689	0.0659758
$248$	3.80907	0.241876
$249$	−24.2654	−1.53775
$250$	−2.10124	−0.132894
$251$	−1.05989	−0.0668994	−0.0334497	−	0.999440i	$-0.510649\pi$
$251$	−1.05989	−0.0668994	−0.0334497	+	0.999440i	$0.510649\pi$
$252$	60.5906	3.81685
$253$	0	0
$254$	−1.69363	−0.106268
$255$	6.05675	0.379289
$256$	7.46110	0.466319
$257$	−0.332710	−0.0207539	−0.0103769	−	0.999946i	$-0.503303\pi$
$257$	−0.332710	−0.0207539	−0.0103769	+	0.999946i	$0.503303\pi$
$258$	−48.7149	−3.03286
$259$	8.86854	0.551064
$260$	−5.98658	−0.371272
$261$	−51.0616	−3.16064
$262$	15.1699	0.937203
$263$	−10.6432	−0.656291	−0.328145	−	0.944627i	$-0.606424\pi$
$263$	−10.6432	−0.656291	−0.328145	+	0.944627i	$0.606424\pi$
$264$	−8.32772	−0.512536
$265$	−12.6830	−0.779110
$266$	3.06634	0.188010
$267$	14.7801	0.904525
$268$	10.4047	0.635568
$269$	−22.4789	−1.37056	−0.685281	−	0.728278i	$-0.740321\pi$
$269$	−22.4789	−1.37056	−0.685281	+	0.728278i	$0.740321\pi$
$270$	−28.1159	−1.71108
$271$	6.61791	0.402010	0.201005	−	0.979590i	$-0.435579\pi$
$271$	6.61791	0.402010	0.201005	+	0.979590i	$0.435579\pi$
$272$	5.68646	0.344792
$273$	27.6047	1.67071
$274$	−13.1374	−0.793660
$275$	−2.99007	−0.180308
$276$	0	0
$277$	7.69277	0.462214	0.231107	−	0.972928i	$-0.425765\pi$
$277$	7.69277	0.462214	0.231107	+	0.972928i	$0.425765\pi$
$278$	−8.39819	−0.503690
$279$	31.3983	1.87977
$280$	−3.04345	−0.181881
$281$	8.50526	0.507381	0.253691	−	0.967285i	$-0.418356\pi$
$281$	8.50526	0.507381	0.253691	+	0.967285i	$0.418356\pi$
$282$	−71.6608	−4.26734
$283$	30.2763	1.79974	0.899871	−	0.436156i	$-0.143661\pi$
$283$	30.2763	1.79974	0.899871	+	0.436156i	$0.143661\pi$
$284$	−19.8744	−1.17933
$285$	−1.33544	−0.0791045
$286$	−15.5734	−0.920874
$287$	−6.53550	−0.385778
$288$	−57.8385	−3.40817
$289$	−13.4005	−0.788263
$290$	14.9196	0.876106
$291$	−12.1789	−0.713941
$292$	20.8709	1.22138
$293$	−23.6687	−1.38274	−0.691371	−	0.722500i	$-0.742993\pi$
$293$	−23.6687	−1.38274	−0.691371	+	0.722500i	$0.742993\pi$
$294$	34.6779	2.02246
$295$	−3.80365	−0.221457
$296$	2.21789	0.128912
$297$	−40.0091	−2.32156
$298$	−16.8237	−0.974574
$299$	0	0
$300$	7.71027	0.445152
$301$	−25.3343	−1.46024
$302$	27.9651	1.60921
$303$	−23.9623	−1.37660
$304$	−1.25379	−0.0719099
$305$	7.92539	0.453807
$306$	−28.6690	−1.63889
$307$	24.6042	1.40424	0.702119	−	0.712059i	$-0.252237\pi$
$307$	24.6042	1.40424	0.702119	+	0.712059i	$0.252237\pi$
$308$	−25.1926	−1.43548
$309$	−6.76598	−0.384903
$310$	−9.17418	−0.521058
$311$	−25.9787	−1.47312	−0.736559	−	0.676373i	$-0.763551\pi$
$311$	−25.9787	−1.47312	−0.736559	+	0.676373i	$0.763551\pi$
$312$	6.90352	0.390835
$313$	20.0173	1.13144	0.565722	−	0.824596i	$-0.308598\pi$
$313$	20.0173	1.13144	0.565722	+	0.824596i	$0.308598\pi$
$314$	28.6728	1.61810
$315$	−25.0872	−1.41351
$316$	18.7680	1.05578
$317$	4.23767	0.238011	0.119006	−	0.992894i	$-0.462029\pi$
$317$	4.23767	0.238011	0.119006	+	0.992894i	$0.462029\pi$
$318$	85.0773	4.77090
$319$	21.2306	1.18869
$320$	10.9052	0.609620
$321$	32.0738	1.79019
$322$	0	0
$323$	−0.793651	−0.0441599
$324$	51.0624	2.83680
$325$	2.47871	0.137494
$326$	−32.8021	−1.81674
$327$	4.44084	0.245579
$328$	−1.63443	−0.0902464
$329$	−37.2674	−2.05462
$330$	20.0574	1.10412
$331$	20.8293	1.14488	0.572442	−	0.819945i	$-0.305996\pi$
$331$	20.8293	1.14488	0.572442	+	0.819945i	$0.305996\pi$
$332$	−18.3579	−1.00752
$333$	18.2822	1.00186
$334$	27.3702	1.49763
$335$	−4.30802	−0.235372
$336$	−33.3791	−1.82098
$337$	−5.86295	−0.319375	−0.159688	−	0.987168i	$-0.551049\pi$
$337$	−5.86295	−0.319375	−0.159688	+	0.987168i	$0.551049\pi$
$338$	−14.4060	−0.783585
$339$	−47.4725	−2.57835
$340$	4.58221	0.248505
$341$	−13.0549	−0.706963
$342$	6.32114	0.341808
$343$	−6.38518	−0.344768
$344$	−6.33573	−0.341600
$345$	0	0
$346$	40.3898	2.17137
$347$	20.2697	1.08813	0.544066	−	0.839042i	$-0.316884\pi$
$347$	20.2697	1.08813	0.544066	+	0.839042i	$0.316884\pi$
$348$	−54.7457	−2.93468
$349$	20.8232	1.11464	0.557320	−	0.830298i	$-0.311830\pi$
$349$	20.8232	1.11464	0.557320	+	0.830298i	$0.311830\pi$
$350$	7.33017	0.391814
$351$	33.1668	1.77031
$352$	24.0483	1.28178
$353$	31.1051	1.65556	0.827778	−	0.561055i	$-0.189604\pi$
$353$	31.1051	1.65556	0.827778	+	0.561055i	$0.189604\pi$
$354$	25.5148	1.35610
$355$	8.22890	0.436745
$356$	11.1818	0.592633
$357$	−21.1290	−1.11827
$358$	−4.10562	−0.216989
$359$	−9.97720	−0.526577	−0.263288	−	0.964717i	$-0.584807\pi$
$359$	−9.97720	−0.526577	−0.263288	+	0.964717i	$0.584807\pi$
$360$	−6.27395	−0.330666
$361$	−18.8250	−0.990790
$362$	21.7380	1.14252
$363$	−6.57464	−0.345079
$364$	20.8842	1.09463
$365$	−8.64151	−0.452317
$366$	−53.1634	−2.77890
$367$	−32.8929	−1.71699	−0.858497	−	0.512818i	$-0.828602\pi$
$367$	−32.8929	−1.71699	−0.858497	+	0.512818i	$0.828602\pi$
$368$	0	0
$369$	−13.4727	−0.701359
$370$	−5.34181	−0.277707
$371$	44.2446	2.29707
$372$	33.6637	1.74538
$373$	−10.6368	−0.550753	−0.275376	−	0.961336i	$-0.588802\pi$
$373$	−10.6368	−0.550753	−0.275376	+	0.961336i	$0.588802\pi$
$374$	11.9201	0.616373
$375$	−3.19240	−0.164855
$376$	−9.32002	−0.480644
$377$	−17.5998	−0.906435
$378$	98.0824	5.04482
$379$	−29.5401	−1.51737	−0.758686	−	0.651456i	$-0.774158\pi$
$379$	−29.5401	−1.51737	−0.758686	+	0.651456i	$0.774158\pi$
$380$	−1.01032	−0.0518283
$381$	−2.57313	−0.131825
$382$	47.8540	2.44842
$383$	−9.29846	−0.475129	−0.237564	−	0.971372i	$-0.576349\pi$
$383$	−9.29846	−0.475129	−0.237564	+	0.971372i	$0.576349\pi$
$384$	−21.8009	−1.11252
$385$	10.4309	0.531607
$386$	−40.2098	−2.04662
$387$	−52.2256	−2.65478
$388$	−9.21391	−0.467765
$389$	−24.2330	−1.22866	−0.614330	−	0.789049i	$-0.710574\pi$
$389$	−24.2330	−1.22866	−0.614330	+	0.789049i	$0.710574\pi$
$390$	−16.6272	−0.841950
$391$	0	0
$392$	4.51012	0.227796
$393$	23.0476	1.16260
$394$	−27.4139	−1.38109
$395$	−7.77080	−0.390991
$396$	−51.9335	−2.60976
$397$	14.9309	0.749358	0.374679	−	0.927154i	$-0.377753\pi$
$397$	14.9309	0.749358	0.374679	+	0.927154i	$0.377753\pi$
$398$	−37.8961	−1.89956
$399$	4.65868	0.233226
$400$	−2.99722	−0.149861
$401$	−0.371881	−0.0185709	−0.00928543	−	0.999957i	$-0.502956\pi$
$401$	−0.371881	−0.0185709	−0.00928543	+	0.999957i	$0.502956\pi$
$402$	28.8981	1.44131
$403$	10.8223	0.539096
$404$	−18.1286	−0.901932
$405$	−21.1421	−1.05056
$406$	−52.0469	−2.58304
$407$	−7.60142	−0.376789
$408$	−5.28405	−0.261600
$409$	1.08535	0.0536673	0.0268337	−	0.999640i	$-0.491458\pi$
$409$	1.08535	0.0536673	0.0268337	+	0.999640i	$0.491458\pi$
$410$	3.93654	0.194412
$411$	−19.9596	−0.984535
$412$	−5.11877	−0.252184
$413$	13.2690	0.652926
$414$	0	0
$415$	7.60098	0.373117
$416$	−19.9356	−0.977423
$417$	−12.7593	−0.624827
$418$	−2.62823	−0.128551
$419$	−32.1159	−1.56896	−0.784482	−	0.620152i	$-0.787071\pi$
$419$	−32.1159	−1.56896	−0.784482	+	0.620152i	$0.787071\pi$
$420$	−26.8973	−1.31245
$421$	−22.2813	−1.08593	−0.542963	−	0.839756i	$-0.682698\pi$
$421$	−22.2813	−1.08593	−0.542963	+	0.839756i	$0.682698\pi$
$422$	5.75242	0.280023
$423$	−76.8252	−3.73537
$424$	11.0649	0.537361
$425$	−1.89724	−0.0920298
$426$	−55.1994	−2.67442
$427$	−27.6478	−1.33797
$428$	24.2653	1.17291
$429$	−23.6606	−1.14234
$430$	15.2597	0.735886
$431$	13.8497	0.667114	0.333557	−	0.942730i	$-0.391751\pi$
$431$	13.8497	0.667114	0.333557	+	0.942730i	$0.391751\pi$
$432$	−40.1048	−1.92954
$433$	38.5294	1.85160	0.925802	−	0.378009i	$-0.123391\pi$
$433$	38.5294	1.85160	0.925802	+	0.378009i	$0.123391\pi$
$434$	32.0041	1.53625
$435$	22.6672	1.08681
$436$	3.35970	0.160900
$437$	0	0
$438$	57.9671	2.76978
$439$	−4.41831	−0.210874	−0.105437	−	0.994426i	$-0.533624\pi$
$439$	−4.41831	−0.210874	−0.105437	+	0.994426i	$0.533624\pi$
$440$	2.60861	0.124361
$441$	37.1771	1.77034
$442$	−9.88153	−0.470016
$443$	13.8432	0.657712	0.328856	−	0.944380i	$-0.393337\pi$
$443$	13.8432	0.657712	0.328856	+	0.944380i	$0.393337\pi$
$444$	19.6012	0.930232
$445$	−4.62977	−0.219472
$446$	18.0872	0.856453
$447$	−25.5602	−1.20896
$448$	−38.0429	−1.79736
$449$	10.7835	0.508905	0.254452	−	0.967085i	$-0.418105\pi$
$449$	10.7835	0.508905	0.254452	+	0.967085i	$0.418105\pi$
$450$	15.1109	0.712332
$451$	5.60172	0.263775
$452$	−35.9151	−1.68931
$453$	42.4872	1.99622
$454$	35.0788	1.64633
$455$	−8.64700	−0.405378
$456$	1.16507	0.0545593
$457$	25.8663	1.20997	0.604986	−	0.796236i	$-0.293179\pi$
$457$	25.8663	1.20997	0.604986	+	0.796236i	$0.293179\pi$
$458$	−7.98238	−0.372992
$459$	−25.3863	−1.18493
$460$	0	0
$461$	11.7035	0.545085	0.272542	−	0.962144i	$-0.412136\pi$
$461$	11.7035	0.545085	0.272542	+	0.962144i	$0.412136\pi$
$462$	−69.9702	−3.25531
$463$	−1.88123	−0.0874282	−0.0437141	−	0.999044i	$-0.513919\pi$
$463$	−1.88123	−0.0874282	−0.0437141	+	0.999044i	$0.513919\pi$
$464$	21.2814	0.987963
$465$	−13.9383	−0.646372
$466$	20.7805	0.962638
$467$	−17.5221	−0.810828	−0.405414	−	0.914133i	$-0.632873\pi$
$467$	−17.5221	−0.810828	−0.405414	+	0.914133i	$0.632873\pi$
$468$	43.0519	1.99008
$469$	15.0285	0.693953
$470$	22.4473	1.03542
$471$	43.5624	2.00725
$472$	3.31839	0.152741
$473$	21.7146	0.998437
$474$	52.1264	2.39424
$475$	0.418318	0.0191938
$476$	−15.9851	−0.732674
$477$	91.2086	4.17615
$478$	−44.0392	−2.01431
$479$	−8.22909	−0.375997	−0.187998	−	0.982169i	$-0.560200\pi$
$479$	−8.22909	−0.375997	−0.187998	+	0.982169i	$0.560200\pi$
$480$	25.6756	1.17192
$481$	6.30144	0.287321
$482$	28.9954	1.32070
$483$	0	0
$484$	−4.97401	−0.226092
$485$	3.81498	0.173229
$486$	57.4734	2.60705
$487$	34.1695	1.54837	0.774184	−	0.632961i	$-0.218161\pi$
$487$	34.1695	1.54837	0.774184	+	0.632961i	$0.218161\pi$
$488$	−6.91430	−0.312996
$489$	−49.8360	−2.25366
$490$	−10.8627	−0.490725
$491$	2.21099	0.0997806	0.0498903	−	0.998755i	$-0.484113\pi$
$491$	2.21099	0.0997806	0.0498903	+	0.998755i	$0.484113\pi$
$492$	−14.4447	−0.651218
$493$	13.4711	0.606709
$494$	2.17875	0.0980268
$495$	21.5028	0.966481
$496$	−13.0861	−0.587584
$497$	−28.7065	−1.28766
$498$	−50.9873	−2.28479
$499$	−21.0952	−0.944351	−0.472175	−	0.881505i	$-0.656531\pi$
$499$	−21.0952	−0.944351	−0.472175	+	0.881505i	$0.656531\pi$
$500$	−2.41520	−0.108011
$501$	41.5835	1.85781
$502$	−2.22707	−0.0993991
$503$	−5.27945	−0.235399	−0.117699	−	0.993049i	$-0.537552\pi$
$503$	−5.27945	−0.235399	−0.117699	+	0.993049i	$0.537552\pi$
$504$	21.8867	0.974911
$505$	7.50606	0.334015
$506$	0	0
$507$	−21.8870	−0.972036
$508$	−1.94669	−0.0863702
$509$	4.15760	0.184283	0.0921413	−	0.995746i	$-0.470629\pi$
$509$	4.15760	0.184283	0.0921413	+	0.995746i	$0.470629\pi$
$510$	12.7267	0.563547
$511$	30.1459	1.33358
$512$	29.3355	1.29646
$513$	5.59737	0.247130
$514$	−0.699102	−0.0308361
$515$	2.11940	0.0933920
$516$	−55.9937	−2.46498
$517$	31.9427	1.40484
$518$	18.6349	0.818771
$519$	61.3640	2.69358
$520$	−2.16249	−0.0948314
$521$	39.2302	1.71871	0.859354	−	0.511381i	$-0.170866\pi$
$521$	39.2302	1.71871	0.859354	+	0.511381i	$0.170866\pi$
$522$	−107.293	−4.69607
$523$	−32.5277	−1.42234	−0.711168	−	0.703023i	$-0.751833\pi$
$523$	−32.5277	−1.42234	−0.711168	+	0.703023i	$0.751833\pi$
$524$	17.4366	0.761721
$525$	11.1367	0.486045
$526$	−22.3640	−0.975116
$527$	−8.28352	−0.360836
$528$	28.6100	1.24509
$529$	0	0
$530$	−26.6500	−1.15760
$531$	27.3536	1.18704
$532$	3.52450	0.152807
$533$	−4.64372	−0.201142
$534$	31.0564	1.34394
$535$	−10.0469	−0.434367
$536$	3.75841	0.162339
$537$	−6.23764	−0.269174
$538$	−47.2335	−2.03638
$539$	−15.4576	−0.665807
$540$	−32.3169	−1.39070
$541$	34.6576	1.49005	0.745023	−	0.667039i	$-0.232439\pi$
$541$	34.6576	1.49005	0.745023	+	0.667039i	$0.232439\pi$
$542$	13.9058	0.597305
$543$	33.0265	1.41730
$544$	15.2590	0.654224
$545$	−1.39107	−0.0595867
$546$	58.0039	2.48234
$547$	42.2398	1.80604	0.903021	−	0.429596i	$-0.141344\pi$
$547$	42.2398	1.80604	0.903021	+	0.429596i	$0.141344\pi$
$548$	−15.1004	−0.645055
$549$	−56.9948	−2.43248
$550$	−6.28285	−0.267902
$551$	−2.97021	−0.126535
$552$	0	0
$553$	27.1084	1.15277
$554$	16.1643	0.686757
$555$	−8.11578	−0.344496
$556$	−9.65301	−0.409379
$557$	38.0204	1.61098	0.805488	−	0.592612i	$-0.201903\pi$
$557$	38.0204	1.61098	0.805488	+	0.592612i	$0.201903\pi$
$558$	65.9753	2.79296
$559$	−18.0010	−0.761360
$560$	10.4558	0.441839
$561$	18.1101	0.764610
$562$	17.8716	0.753866
$563$	24.4565	1.03072	0.515360	−	0.856974i	$-0.327658\pi$
$563$	24.4565	1.03072	0.515360	+	0.856974i	$0.327658\pi$
$564$	−82.3681	−3.46832
$565$	14.8705	0.625606
$566$	63.6178	2.67405
$567$	73.7544	3.09739
$568$	−7.17909	−0.301228
$569$	−20.8830	−0.875461	−0.437731	−	0.899106i	$-0.644218\pi$
$569$	−20.8830	−0.875461	−0.437731	+	0.899106i	$0.644218\pi$
$570$	−2.80607	−0.117533
$571$	2.12473	0.0889170	0.0444585	−	0.999011i	$-0.485844\pi$
$571$	2.12473	0.0889170	0.0444585	+	0.999011i	$0.485844\pi$
$572$	−17.9003	−0.748449
$573$	72.7044	3.03727
$574$	−13.7326	−0.573189
$575$	0	0
$576$	−78.4239	−3.26766
$577$	39.7121	1.65324	0.826618	−	0.562763i	$-0.190262\pi$
$577$	39.7121	1.65324	0.826618	+	0.562763i	$0.190262\pi$
$578$	−28.1576	−1.17120
$579$	−61.0905	−2.53883
$580$	17.1488	0.712064
$581$	−26.5160	−1.10007
$582$	−25.5908	−1.06077
$583$	−37.9231	−1.57061
$584$	7.53905	0.311968
$585$	−17.8254	−0.736992
$586$	−49.7336	−2.05448
$587$	−32.4554	−1.33958	−0.669790	−	0.742551i	$-0.733616\pi$
$587$	−32.4554	−1.33958	−0.669790	+	0.742551i	$0.733616\pi$
$588$	39.8594	1.64377
$589$	1.82641	0.0752560
$590$	−7.99236	−0.329040
$591$	−41.6498	−1.71324
$592$	−7.61960	−0.313164
$593$	34.8428	1.43082	0.715412	−	0.698703i	$-0.246239\pi$
$593$	34.8428	1.43082	0.715412	+	0.698703i	$0.246239\pi$
$594$	−84.0686	−3.44938
$595$	6.61853	0.271333
$596$	−19.3375	−0.792094
$597$	−57.5754	−2.35640
$598$	0	0
$599$	6.38230	0.260774	0.130387	−	0.991463i	$-0.458378\pi$
$599$	6.38230	0.260774	0.130387	+	0.991463i	$0.458378\pi$
$600$	2.78512	0.113702
$601$	−35.8158	−1.46096	−0.730479	−	0.682935i	$-0.760703\pi$
$601$	−35.8158	−1.46096	−0.730479	+	0.682935i	$0.760703\pi$
$602$	−53.2333	−2.16963
$603$	30.9807	1.26163
$604$	32.1435	1.30790
$605$	2.05947	0.0837292
$606$	−50.3506	−2.04535
$607$	33.7535	1.37001	0.685006	−	0.728538i	$-0.259800\pi$
$607$	33.7535	1.37001	0.685006	+	0.728538i	$0.259800\pi$
$608$	−3.36442	−0.136445
$609$	−79.0746	−3.20426
$610$	16.6531	0.674265
$611$	−26.4799	−1.07126
$612$	−32.9526	−1.33203
$613$	−7.97066	−0.321932	−0.160966	−	0.986960i	$-0.551461\pi$
$613$	−7.97066	−0.321932	−0.160966	+	0.986960i	$0.551461\pi$
$614$	51.6993	2.08642
$615$	5.98077	0.241168
$616$	−9.10014	−0.366655
$617$	36.4209	1.46625	0.733124	−	0.680094i	$-0.238061\pi$
$617$	36.4209	1.46625	0.733124	+	0.680094i	$0.238061\pi$
$618$	−14.2169	−0.571888
$619$	−22.1664	−0.890941	−0.445471	−	0.895297i	$-0.646964\pi$
$619$	−22.1664	−0.890941	−0.445471	+	0.895297i	$0.646964\pi$
$620$	−10.5449	−0.423495
$621$	0	0
$622$	−54.5874	−2.18876
$623$	16.1509	0.647074
$624$	−23.7172	−0.949446
$625$	1.00000	0.0400000
$626$	42.0610	1.68110
$627$	−3.99306	−0.159467
$628$	32.9570	1.31513
$629$	−4.82321	−0.192314
$630$	−52.7142	−2.10019
$631$	−16.0406	−0.638566	−0.319283	−	0.947659i	$-0.603442\pi$
$631$	−16.0406	−0.638566	−0.319283	+	0.947659i	$0.603442\pi$
$632$	6.77942	0.269671
$633$	8.73962	0.347369
$634$	8.90435	0.353637
$635$	0.806016	0.0319858
$636$	97.7892	3.87760
$637$	12.8141	0.507712
$638$	44.6105	1.76615
$639$	−59.1774	−2.34102
$640$	6.82899	0.269940
$641$	4.01642	0.158639	0.0793195	−	0.996849i	$-0.474725\pi$
$641$	4.01642	0.158639	0.0793195	+	0.996849i	$0.474725\pi$
$642$	67.3947	2.65986
$643$	21.7802	0.858926	0.429463	−	0.903085i	$-0.358703\pi$
$643$	21.7802	0.858926	0.429463	+	0.903085i	$0.358703\pi$
$644$	0	0
$645$	23.1839	0.912866
$646$	−1.66765	−0.0656127
$647$	26.4335	1.03921	0.519604	−	0.854407i	$-0.326079\pi$
$647$	26.4335	1.03921	0.519604	+	0.854407i	$0.326079\pi$
$648$	18.4449	0.724584
$649$	−11.3732	−0.446436
$650$	5.20836	0.204289
$651$	48.6237	1.90571
$652$	−37.7032	−1.47657
$653$	8.71587	0.341078	0.170539	−	0.985351i	$-0.445449\pi$
$653$	8.71587	0.341078	0.170539	+	0.985351i	$0.445449\pi$
$654$	9.33125	0.364881
$655$	−7.21953	−0.282091
$656$	5.61512	0.219233
$657$	62.1446	2.42449
$658$	−78.3076	−3.05275
$659$	31.3617	1.22168	0.610839	−	0.791754i	$-0.290832\pi$
$659$	31.3617	1.22168	0.610839	+	0.791754i	$0.290832\pi$
$660$	23.0543	0.897386
$661$	9.13435	0.355285	0.177643	−	0.984095i	$-0.443153\pi$
$661$	9.13435	0.355285	0.177643	+	0.984095i	$0.443153\pi$
$662$	43.7673	1.70107
$663$	−15.0130	−0.583055
$664$	−6.63127	−0.257343
$665$	−1.45930	−0.0565894
$666$	38.4151	1.48856
$667$	0	0
$668$	31.4598	1.21722
$669$	27.4798	1.06243
$670$	−9.05216	−0.349716
$671$	23.6975	0.914832
$672$	−89.5693	−3.45521
$673$	−9.13180	−0.352005	−0.176003	−	0.984390i	$-0.556317\pi$
$673$	−9.13180	−0.352005	−0.176003	+	0.984390i	$0.556317\pi$
$674$	−12.3194	−0.474527
$675$	13.3807	0.515021
$676$	−16.5585	−0.636866
$677$	−21.9459	−0.843450	−0.421725	−	0.906724i	$-0.638575\pi$
$677$	−21.9459	−0.843450	−0.421725	+	0.906724i	$0.638575\pi$
$678$	−99.7510	−3.83091
$679$	−13.3086	−0.510735
$680$	1.65520	0.0634740
$681$	53.2950	2.04227
$682$	−27.4315	−1.05040
$683$	4.50628	0.172428	0.0862140	−	0.996277i	$-0.472523\pi$
$683$	4.50628	0.172428	0.0862140	+	0.996277i	$0.472523\pi$
$684$	7.26562	0.277808
$685$	6.25223	0.238885
$686$	−13.4168	−0.512255
$687$	−12.1276	−0.462696
$688$	21.7665	0.829840
$689$	31.4375	1.19767
$690$	0	0
$691$	−3.50040	−0.133162	−0.0665808	−	0.997781i	$-0.521209\pi$
$691$	−3.50040	−0.133162	−0.0665808	+	0.997781i	$0.521209\pi$
$692$	46.4247	1.76480
$693$	−75.0127	−2.84950
$694$	42.5913	1.61675
$695$	3.99678	0.151607
$696$	−19.7754	−0.749584
$697$	3.55437	0.134631
$698$	43.7544	1.65613
$699$	31.5717	1.19415
$700$	8.42541	0.318451
$701$	−10.9373	−0.413098	−0.206549	−	0.978436i	$-0.566223\pi$
$701$	−10.9373	−0.413098	−0.206549	+	0.978436i	$0.566223\pi$
$702$	69.6913	2.63033
$703$	1.06346	0.0401090
$704$	32.6074	1.22894
$705$	34.1041	1.28444
$706$	65.3591	2.45982
$707$	−26.1849	−0.984785
$708$	29.3271	1.10218
$709$	0.653580	0.0245457	0.0122729	−	0.999925i	$-0.496093\pi$
$709$	0.653580	0.0245457	0.0122729	+	0.999925i	$0.496093\pi$
$710$	17.2909	0.648915
$711$	55.8830	2.09578
$712$	4.03911	0.151372
$713$	0	0
$714$	−44.3970	−1.66152
$715$	7.41154	0.277176
$716$	−4.71906	−0.176360
$717$	−66.9086	−2.49875
$718$	−20.9645	−0.782387
$719$	34.3461	1.28089	0.640446	−	0.768003i	$-0.278750\pi$
$719$	34.3461	1.28089	0.640446	+	0.768003i	$0.278750\pi$
$720$	21.5543	0.803280
$721$	−7.39354	−0.275350
$722$	−39.5558	−1.47211
$723$	44.0525	1.63833
$724$	24.9860	0.928598
$725$	−7.10037	−0.263701
$726$	−13.8149	−0.512718
$727$	−33.6355	−1.24747	−0.623736	−	0.781635i	$-0.714386\pi$
$727$	−33.6355	−1.24747	−0.623736	+	0.781635i	$0.714386\pi$
$728$	7.54384	0.279593
$729$	23.8927	0.884915
$730$	−18.1579	−0.672052
$731$	13.7782	0.509605
$732$	−61.1069	−2.25858
$733$	−0.350071	−0.0129302	−0.00646509	−	0.999979i	$-0.502058\pi$
$733$	−0.350071	−0.0129302	−0.00646509	+	0.999979i	$0.502058\pi$
$734$	−69.1157	−2.55111
$735$	−16.5036	−0.608744
$736$	0	0
$737$	−12.8813	−0.474488
$738$	−28.3093	−1.04208
$739$	9.52188	0.350268	0.175134	−	0.984545i	$-0.443964\pi$
$739$	9.52188	0.350268	0.175134	+	0.984545i	$0.443964\pi$
$740$	−6.13996	−0.225709
$741$	3.31017	0.121602
$742$	92.9685	3.41298
$743$	0.566207	0.0207721	0.0103861	−	0.999946i	$-0.496694\pi$
$743$	0.566207	0.0207721	0.0103861	+	0.999946i	$0.496694\pi$
$744$	12.1601	0.445810
$745$	8.00659	0.293339
$746$	−22.3504	−0.818308
$747$	−54.6618	−1.99997
$748$	13.7011	0.500963
$749$	35.0488	1.28065
$750$	−6.70798	−0.244941
$751$	−51.8622	−1.89248	−0.946239	−	0.323470i	$-0.895151\pi$
$751$	−51.8622	−1.89248	−0.946239	+	0.323470i	$0.895151\pi$
$752$	32.0191	1.16762
$753$	−3.38358	−0.123304
$754$	−36.9813	−1.34678
$755$	−13.3089	−0.484359
$756$	112.738	4.10022
$757$	35.4668	1.28906	0.644531	−	0.764578i	$-0.277053\pi$
$757$	35.4668	1.28906	0.644531	+	0.764578i	$0.277053\pi$
$758$	−62.0707	−2.25451
$759$	0	0
$760$	−0.364950	−0.0132381
$761$	9.08375	0.329286	0.164643	−	0.986353i	$-0.447353\pi$
$761$	9.08375	0.329286	0.164643	+	0.986353i	$0.447353\pi$
$762$	−5.40674	−0.195866
$763$	4.85274	0.175681
$764$	55.0042	1.98998
$765$	13.6438	0.493294
$766$	−19.5383	−0.705946
$767$	9.42815	0.340431
$768$	23.8188	0.859487
$769$	−51.0516	−1.84097	−0.920483	−	0.390782i	$-0.872205\pi$
$769$	−51.0516	−1.84097	−0.920483	+	0.390782i	$0.872205\pi$
$770$	21.9177	0.789860
$771$	−1.06214	−0.0382521
$772$	−46.2178	−1.66341
$773$	10.9549	0.394022	0.197011	−	0.980401i	$-0.436877\pi$
$773$	10.9549	0.394022	0.197011	+	0.980401i	$0.436877\pi$
$774$	−109.738	−3.94447
$775$	4.36608	0.156834
$776$	−3.32827	−0.119478
$777$	28.3119	1.01568
$778$	−50.9192	−1.82554
$779$	−0.783694	−0.0280787
$780$	−19.1115	−0.684303
$781$	24.6050	0.880437
$782$	0	0
$783$	−95.0075	−3.39529
$784$	−15.4946	−0.553378
$785$	−13.6457	−0.487035
$786$	48.4285	1.72739
$787$	−25.5164	−0.909560	−0.454780	−	0.890604i	$-0.650282\pi$
$787$	−25.5164	−0.909560	−0.454780	+	0.890604i	$0.650282\pi$
$788$	−31.5100	−1.12250
$789$	−33.9775	−1.20963
$790$	−16.3283	−0.580934
$791$	−51.8757	−1.84449
$792$	−18.7596	−0.666592
$793$	−19.6448	−0.697607
$794$	31.3733	1.11340
$795$	−40.4892	−1.43600
$796$	−43.5584	−1.54389
$797$	−5.49330	−0.194583	−0.0972914	−	0.995256i	$-0.531018\pi$
$797$	−5.49330	−0.194583	−0.0972914	+	0.995256i	$0.531018\pi$
$798$	9.78899	0.346526
$799$	20.2681	0.717033
$800$	−8.04272	−0.284353
$801$	33.2945	1.17640
$802$	−0.781410	−0.0275926
$803$	−25.8387	−0.911829
$804$	33.2160	1.17144
$805$	0	0
$806$	22.7402	0.800988
$807$	−71.7616	−2.52613
$808$	−6.54846	−0.230374
$809$	20.9929	0.738072	0.369036	−	0.929415i	$-0.379688\pi$
$809$	20.9929	0.738072	0.369036	+	0.929415i	$0.379688\pi$
$810$	−44.4246	−1.56092
$811$	−41.2868	−1.44977	−0.724887	−	0.688868i	$-0.758108\pi$
$811$	−41.2868	−1.44977	−0.724887	+	0.688868i	$0.758108\pi$
$812$	−59.8235	−2.09939
$813$	21.1270	0.740957
$814$	−15.9724	−0.559832
$815$	15.6108	0.546824
$816$	18.1534	0.635498
$817$	−3.03792	−0.106283
$818$	2.28059	0.0797389
$819$	62.1841	2.17289
$820$	4.52472	0.158010
$821$	−0.977838	−0.0341268	−0.0170634	−	0.999854i	$-0.505432\pi$
$821$	−0.977838	−0.0341268	−0.0170634	+	0.999854i	$0.505432\pi$
$822$	−41.9399	−1.46282
$823$	−24.6107	−0.857876	−0.428938	−	0.903334i	$-0.641112\pi$
$823$	−24.6107	−0.857876	−0.428938	+	0.903334i	$0.641112\pi$
$824$	−1.84902	−0.0644135
$825$	−9.54550	−0.332332
$826$	27.8814	0.970117
$827$	−2.89984	−0.100837	−0.0504187	−	0.998728i	$-0.516056\pi$
$827$	−2.89984	−0.100837	−0.0504187	+	0.998728i	$0.516056\pi$
$828$	0	0
$829$	16.3337	0.567293	0.283647	−	0.958929i	$-0.408456\pi$
$829$	16.3337	0.567293	0.283647	+	0.958929i	$0.408456\pi$
$830$	15.9715	0.554377
$831$	24.5584	0.851922
$832$	−27.0309	−0.937128
$833$	−9.80808	−0.339830
$834$	−26.8104	−0.928367
$835$	−13.0258	−0.450776
$836$	−3.02093	−0.104481
$837$	58.4210	2.01933
$838$	−67.4831	−2.33116
$839$	11.7299	0.404963	0.202481	−	0.979286i	$-0.435099\pi$
$839$	11.7299	0.404963	0.202481	+	0.979286i	$0.435099\pi$
$840$	−9.71591	−0.335231
$841$	21.4152	0.738455
$842$	−46.8184	−1.61347
$843$	27.1522	0.935171
$844$	6.61192	0.227592
$845$	6.85598	0.235853
$846$	−161.428	−5.55001
$847$	−7.18445	−0.246861
$848$	−38.0138	−1.30540
$849$	96.6542	3.31716
$850$	−3.98656	−0.136738
$851$	0	0
$852$	−63.4470	−2.17366
$853$	26.9768	0.923668	0.461834	−	0.886966i	$-0.347192\pi$
$853$	26.9768	0.923668	0.461834	+	0.886966i	$0.347192\pi$
$854$	−58.0945	−1.98795
$855$	−3.00830	−0.102882
$856$	8.76518	0.299588
$857$	−31.6850	−1.08234	−0.541169	−	0.840914i	$-0.682018\pi$
$857$	−31.6850	−1.08234	−0.541169	+	0.840914i	$0.682018\pi$
$858$	−49.7165	−1.69729
$859$	−8.09415	−0.276169	−0.138084	−	0.990420i	$-0.544095\pi$
$859$	−8.09415	−0.276169	−0.138084	+	0.990420i	$0.544095\pi$
$860$	17.5397	0.598098
$861$	−20.8639	−0.711041
$862$	29.1014	0.991198
$863$	−49.7824	−1.69461	−0.847307	−	0.531103i	$-0.821778\pi$
$863$	−49.7824	−1.69461	−0.847307	+	0.531103i	$0.821778\pi$
$864$	−107.617	−3.66120
$865$	−19.2219	−0.653564
$866$	80.9593	2.75111
$867$	−42.7796	−1.45287
$868$	36.7861	1.24860
$869$	−23.2353	−0.788202
$870$	47.6292	1.61478
$871$	10.6783	0.361822
$872$	1.21360	0.0410976
$873$	−27.4351	−0.928536
$874$	0	0
$875$	−3.48850	−0.117933
$876$	66.6283	2.25116
$877$	−21.4451	−0.724148	−0.362074	−	0.932149i	$-0.617931\pi$
$877$	−21.4451	−0.724148	−0.362074	+	0.932149i	$0.617931\pi$
$878$	−9.28391	−0.313317
$879$	−75.5600	−2.54858
$880$	−8.96191	−0.302106
$881$	36.2899	1.22264	0.611318	−	0.791385i	$-0.290640\pi$
$881$	36.2899	1.22264	0.611318	+	0.791385i	$0.290640\pi$
$882$	78.1178	2.63036
$883$	23.8350	0.802111	0.401056	−	0.916054i	$-0.368643\pi$
$883$	23.8350	0.802111	0.401056	+	0.916054i	$0.368643\pi$
$884$	−11.3580	−0.382011
$885$	−12.1428	−0.408174
$886$	29.0879	0.977228
$887$	−14.6269	−0.491122	−0.245561	−	0.969381i	$-0.578972\pi$
$887$	−14.6269	−0.491122	−0.245561	+	0.969381i	$0.578972\pi$
$888$	7.08040	0.237603
$889$	−2.81179	−0.0943044
$890$	−9.72823	−0.326091
$891$	−63.2165	−2.11783
$892$	20.7897	0.696090
$893$	−4.46886	−0.149545
$894$	−53.7081	−1.79627
$895$	1.95390	0.0653118
$896$	−23.8230	−0.795869
$897$	0	0
$898$	22.6587	0.756130
$899$	−31.0008	−1.03393
$900$	17.3687	0.578955
$901$	−24.0627	−0.801645
$902$	11.7705	0.391916
$903$	−80.8772	−2.69142
$904$	−12.9734	−0.431487
$905$	−10.3453	−0.343891
$906$	89.2757	2.96599
$907$	50.7647	1.68561	0.842807	−	0.538216i	$-0.180901\pi$
$907$	50.7647	1.68561	0.842807	+	0.538216i	$0.180901\pi$
$908$	40.3201	1.33807
$909$	−53.9792	−1.79038
$910$	−18.1694	−0.602310
$911$	3.00241	0.0994742	0.0497371	−	0.998762i	$-0.484162\pi$
$911$	3.00241	0.0994742	0.0497371	+	0.998762i	$0.484162\pi$
$912$	−4.00261	−0.132540
$913$	22.7275	0.752170
$914$	54.3511	1.79778
$915$	25.3010	0.836426
$916$	−9.17507	−0.303153
$917$	25.1854	0.831694
$918$	−53.3427	−1.76057
$919$	43.3160	1.42886	0.714431	−	0.699706i	$-0.246686\pi$
$919$	43.3160	1.42886	0.714431	+	0.699706i	$0.246686\pi$
$920$	0	0
$921$	78.5466	2.58820
$922$	24.5917	0.809886
$923$	−20.3971	−0.671379
$924$	−80.4248	−2.64578
$925$	2.54222	0.0835877
$926$	−3.95291	−0.129901
$927$	−15.2415	−0.500596
$928$	57.1063	1.87460
$929$	−16.3574	−0.536670	−0.268335	−	0.963326i	$-0.586473\pi$
$929$	−16.3574	−0.536670	−0.268335	+	0.963326i	$0.586473\pi$
$930$	−29.2876	−0.960379
$931$	2.16256	0.0708750
$932$	23.8854	0.782394
$933$	−82.9344	−2.71515
$934$	−36.8182	−1.20473
$935$	−5.67289	−0.185523
$936$	15.5513	0.508311
$937$	36.0190	1.17669	0.588344	−	0.808611i	$-0.299780\pi$
$937$	36.0190	1.17669	0.588344	+	0.808611i	$0.299780\pi$
$938$	31.5785	1.03107
$939$	63.9031	2.08540
$940$	25.8013	0.841547
$941$	4.75452	0.154993	0.0774965	−	0.996993i	$-0.475307\pi$
$941$	4.75452	0.154993	0.0774965	+	0.996993i	$0.475307\pi$
$942$	91.5350	2.98237
$943$	0	0
$944$	−11.4004	−0.371051
$945$	−46.6784	−1.51845
$946$	45.6275	1.48348
$947$	−0.938126	−0.0304850	−0.0152425	−	0.999884i	$-0.504852\pi$
$947$	−0.938126	−0.0304850	−0.0152425	+	0.999884i	$0.504852\pi$
$948$	59.9149	1.94595
$949$	21.4198	0.695317
$950$	0.878985	0.0285181
$951$	13.5283	0.438687
$952$	−5.77416	−0.187142
$953$	−58.9402	−1.90926	−0.954630	−	0.297794i	$-0.903749\pi$
$953$	−58.9402	−1.90926	−0.954630	+	0.297794i	$0.903749\pi$
$954$	191.651	6.20492
$955$	−22.7742	−0.736956
$956$	−50.6194	−1.63715
$957$	67.7766	2.19091
$958$	−17.2913	−0.558656
$959$	−21.8109	−0.704311
$960$	34.8138	1.12361
$961$	−11.9373	−0.385074
$962$	13.2408	0.426901
$963$	72.2517	2.32828
$964$	33.3277	1.07341
$965$	19.1362	0.616017
$966$	0	0
$967$	−39.4846	−1.26974	−0.634869	−	0.772620i	$-0.718946\pi$
$967$	−39.4846	−1.26974	−0.634869	+	0.772620i	$0.718946\pi$
$968$	−1.79673	−0.0577490
$969$	−2.53365	−0.0813926
$970$	8.01617	0.257384
$971$	12.0164	0.385624	0.192812	−	0.981236i	$-0.438239\pi$
$971$	12.0164	0.385624	0.192812	+	0.981236i	$0.438239\pi$
$972$	66.0609	2.11890
$973$	−13.9428	−0.446985
$974$	71.7982	2.30056
$975$	7.91304	0.253420
$976$	23.7542	0.760352
$977$	44.1212	1.41156	0.705781	−	0.708430i	$-0.250596\pi$
$977$	44.1212	1.41156	0.705781	+	0.708430i	$0.250596\pi$
$978$	−104.717	−3.34849
$979$	−13.8433	−0.442435
$980$	−12.4857	−0.398841
$981$	10.0037	0.319395
$982$	4.64581	0.148254
$983$	−51.4846	−1.64211	−0.821053	−	0.570852i	$-0.806613\pi$
$983$	−51.4846	−1.64211	−0.821053	+	0.570852i	$0.806613\pi$
$984$	−5.21776	−0.166336
$985$	13.0466	0.415698
$986$	28.3060	0.901447
$987$	−118.972	−3.78693
$988$	2.50429	0.0796722
$989$	0	0
$990$	45.1825	1.43600
$991$	−2.62138	−0.0832709	−0.0416354	−	0.999133i	$-0.513257\pi$
$991$	−2.62138	−0.0832709	−0.0416354	+	0.999133i	$0.513257\pi$
$992$	−35.1152	−1.11491
$993$	66.4955	2.11017
$994$	−60.3192	−1.91321
$995$	18.0351	0.571752
$996$	−58.6056	−1.85699
$997$	−29.8046	−0.943922	−0.471961	−	0.881620i	$-0.656454\pi$
$997$	−29.8046	−0.943922	−0.471961	+	0.881620i	$0.656454\pi$
$998$	−44.3260	−1.40311
$999$	34.0166	1.07624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.x.1.20		25
23.15	odd	22		115.2.g.c.41.2	✓	50
23.20	odd	22		115.2.g.c.101.2	yes	50
23.22	odd	2		2645.2.a.y.1.20		25
115.38	even	44		575.2.p.d.524.2		100
115.43	even	44		575.2.p.d.124.9		100
115.84	odd	22		575.2.k.d.501.4		50
115.89	odd	22		575.2.k.d.101.4		50
115.107	even	44		575.2.p.d.524.9		100
115.112	even	44		575.2.p.d.124.2		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.41.2	✓	50	23.15	odd	22
115.2.g.c.101.2	yes	50	23.20	odd	22
575.2.k.d.101.4		50	115.89	odd	22
575.2.k.d.501.4		50	115.84	odd	22
575.2.p.d.124.2		100	115.112	even	44
575.2.p.d.124.9		100	115.43	even	44
575.2.p.d.524.2		100	115.38	even	44
575.2.p.d.524.9		100	115.107	even	44
2645.2.a.x.1.20		25	1.1	even	1	trivial
2645.2.a.y.1.20		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q+2.10124 q^{2} +3.19240 q^{3} +2.41520 q^{4} -1.00000 q^{5} +6.70798 q^{6} +3.48850 q^{7} +0.872423 q^{8} +7.19141 q^{9} +O(q^{10})\)	\(q+2.10124 q^{2} +3.19240 q^{3} +2.41520 q^{4} -1.00000 q^{5} +6.70798 q^{6} +3.48850 q^{7} +0.872423 q^{8} +7.19141 q^{9} -2.10124 q^{10} -2.99007 q^{11} +7.71027 q^{12} +2.47871 q^{13} +7.33017 q^{14} -3.19240 q^{15} -2.99722 q^{16} -1.89724 q^{17} +15.1109 q^{18} +0.418318 q^{19} -2.41520 q^{20} +11.1367 q^{21} -6.28285 q^{22} +2.78512 q^{24} +1.00000 q^{25} +5.20836 q^{26} +13.3807 q^{27} +8.42541 q^{28} -7.10037 q^{29} -6.70798 q^{30} +4.36608 q^{31} -8.04272 q^{32} -9.54550 q^{33} -3.98656 q^{34} -3.48850 q^{35} +17.3687 q^{36} +2.54222 q^{37} +0.878985 q^{38} +7.91304 q^{39} -0.872423 q^{40} -1.87344 q^{41} +23.4008 q^{42} -7.26222 q^{43} -7.22161 q^{44} -7.19141 q^{45} -10.6829 q^{47} -9.56833 q^{48} +5.16965 q^{49} +2.10124 q^{50} -6.05675 q^{51} +5.98658 q^{52} +12.6830 q^{53} +28.1159 q^{54} +2.99007 q^{55} +3.04345 q^{56} +1.33544 q^{57} -14.9196 q^{58} +3.80365 q^{59} -7.71027 q^{60} -7.92539 q^{61} +9.17418 q^{62} +25.0872 q^{63} -10.9052 q^{64} -2.47871 q^{65} -20.0574 q^{66} +4.30802 q^{67} -4.58221 q^{68} -7.33017 q^{70} -8.22890 q^{71} +6.27395 q^{72} +8.64151 q^{73} +5.34181 q^{74} +3.19240 q^{75} +1.01032 q^{76} -10.4309 q^{77} +16.6272 q^{78} +7.77080 q^{79} +2.99722 q^{80} +21.1421 q^{81} -3.93654 q^{82} -7.60098 q^{83} +26.8973 q^{84} +1.89724 q^{85} -15.2597 q^{86} -22.6672 q^{87} -2.60861 q^{88} +4.62977 q^{89} -15.1109 q^{90} +8.64700 q^{91} +13.9383 q^{93} -22.4473 q^{94} -0.418318 q^{95} -25.6756 q^{96} -3.81498 q^{97} +10.8627 q^{98} -21.5028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9} - 3 q^{10} + 8 q^{11} + 34 q^{12} + 15 q^{13} + 6 q^{14} - 10 q^{15} + 41 q^{16} - 19 q^{17} + 23 q^{18} + 8 q^{19} - 33 q^{20} + 21 q^{21} - 3 q^{22} + 51 q^{24} + 25 q^{25} + 7 q^{26} + 64 q^{27} - 27 q^{28} + 3 q^{29} - 22 q^{30} + 34 q^{31} + 30 q^{32} + q^{33} + 21 q^{34} + 14 q^{35} + 31 q^{36} + q^{37} + 7 q^{38} + 49 q^{39} - 21 q^{40} + 29 q^{42} - 25 q^{43} + 33 q^{44} - 29 q^{45} - 5 q^{47} + 42 q^{48} + 33 q^{49} + 3 q^{50} - 23 q^{51} + 67 q^{52} - 24 q^{53} + 37 q^{54} - 8 q^{55} + 55 q^{56} + 19 q^{57} + 49 q^{58} + 41 q^{59} - 34 q^{60} + 31 q^{61} - 3 q^{62} - 37 q^{63} + 77 q^{64} - 15 q^{65} + 39 q^{66} + 5 q^{67} - 27 q^{68} - 6 q^{70} + 15 q^{71} + 48 q^{72} + 34 q^{73} + 29 q^{74} + 10 q^{75} + 24 q^{76} - 35 q^{77} - 45 q^{78} + 41 q^{79} - 41 q^{80} + 25 q^{81} + 33 q^{82} - 62 q^{83} + 126 q^{84} + 19 q^{85} + 10 q^{86} + 26 q^{87} + 50 q^{88} + 23 q^{89} - 23 q^{90} - 19 q^{91} + 50 q^{93} + 9 q^{94} - 8 q^{95} + 64 q^{96} - 37 q^{97} - 55 q^{98} + 48 q^{99}+O(q^{100}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9 - 3 * q^10 + 8 * q^11 + 34 * q^12 + 15 * q^13 + 6 * q^14 - 10 * q^15 + 41 * q^16 - 19 * q^17 + 23 * q^18 + 8 * q^19 - 33 * q^20 + 21 * q^21 - 3 * q^22 + 51 * q^24 + 25 * q^25 + 7 * q^26 + 64 * q^27 - 27 * q^28 + 3 * q^29 - 22 * q^30 + 34 * q^31 + 30 * q^32 + q^33 + 21 * q^34 + 14 * q^35 + 31 * q^36 + q^37 + 7 * q^38 + 49 * q^39 - 21 * q^40 + 29 * q^42 - 25 * q^43 + 33 * q^44 - 29 * q^45 - 5 * q^47 + 42 * q^48 + 33 * q^49 + 3 * q^50 - 23 * q^51 + 67 * q^52 - 24 * q^53 + 37 * q^54 - 8 * q^55 + 55 * q^56 + 19 * q^57 + 49 * q^58 + 41 * q^59 - 34 * q^60 + 31 * q^61 - 3 * q^62 - 37 * q^63 + 77 * q^64 - 15 * q^65 + 39 * q^66 + 5 * q^67 - 27 * q^68 - 6 * q^70 + 15 * q^71 + 48 * q^72 + 34 * q^73 + 29 * q^74 + 10 * q^75 + 24 * q^76 - 35 * q^77 - 45 * q^78 + 41 * q^79 - 41 * q^80 + 25 * q^81 + 33 * q^82 - 62 * q^83 + 126 * q^84 + 19 * q^85 + 10 * q^86 + 26 * q^87 + 50 * q^88 + 23 * q^89 - 23 * q^90 - 19 * q^91 + 50 * q^93 + 9 * q^94 - 8 * q^95 + 64 * q^96 - 37 * q^97 - 55 * q^98 + 48 * q^99

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