LMFDB - Embedded newform 7935.2.a.bu.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.98465 q^{2} -1.00000 q^{3} +1.93882 q^{4} +1.00000 q^{5} -1.98465 q^{6} +1.53611 q^{7} -0.121418 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.98465 q^{2} -1.00000 q^{3} +1.93882 q^{4} +1.00000 q^{5} -1.98465 q^{6} +1.53611 q^{7} -0.121418 q^{8} +1.00000 q^{9} +1.98465 q^{10} +3.86345 q^{11} -1.93882 q^{12} -3.56879 q^{13} +3.04863 q^{14} -1.00000 q^{15} -4.11861 q^{16} -6.61188 q^{17} +1.98465 q^{18} +5.57556 q^{19} +1.93882 q^{20} -1.53611 q^{21} +7.66759 q^{22} +0.121418 q^{24} +1.00000 q^{25} -7.08279 q^{26} -1.00000 q^{27} +2.97823 q^{28} +7.13122 q^{29} -1.98465 q^{30} -4.49394 q^{31} -7.93116 q^{32} -3.86345 q^{33} -13.1222 q^{34} +1.53611 q^{35} +1.93882 q^{36} -1.90863 q^{37} +11.0655 q^{38} +3.56879 q^{39} -0.121418 q^{40} +7.16094 q^{41} -3.04863 q^{42} +7.25092 q^{43} +7.49054 q^{44} +1.00000 q^{45} +13.4619 q^{47} +4.11861 q^{48} -4.64038 q^{49} +1.98465 q^{50} +6.61188 q^{51} -6.91925 q^{52} +5.03082 q^{53} -1.98465 q^{54} +3.86345 q^{55} -0.186511 q^{56} -5.57556 q^{57} +14.1529 q^{58} -1.15296 q^{59} -1.93882 q^{60} +11.0198 q^{61} -8.91887 q^{62} +1.53611 q^{63} -7.50331 q^{64} -3.56879 q^{65} -7.66759 q^{66} +5.66412 q^{67} -12.8192 q^{68} +3.04863 q^{70} +9.38923 q^{71} -0.121418 q^{72} +3.40026 q^{73} -3.78796 q^{74} -1.00000 q^{75} +10.8100 q^{76} +5.93467 q^{77} +7.08279 q^{78} -4.05656 q^{79} -4.11861 q^{80} +1.00000 q^{81} +14.2119 q^{82} +9.56105 q^{83} -2.97823 q^{84} -6.61188 q^{85} +14.3905 q^{86} -7.13122 q^{87} -0.469092 q^{88} -11.6302 q^{89} +1.98465 q^{90} -5.48204 q^{91} +4.49394 q^{93} +26.7171 q^{94} +5.57556 q^{95} +7.93116 q^{96} -6.28649 q^{97} -9.20951 q^{98} +3.86345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * 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 $

$2$	1.98465	1.40336	0.701678	−	0.712494i	$-0.252434\pi$
$2$	1.98465	1.40336	0.701678	+	0.712494i	$0.252434\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.93882	0.969411
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.98465	−0.810229
$7$	1.53611	0.580593	0.290297	−	0.956937i	$-0.406246\pi$
$7$	1.53611	0.580593	0.290297	+	0.956937i	$0.406246\pi$
$8$	−0.121418	−0.0429277
$9$	1.00000	0.333333
$10$	1.98465	0.627600
$11$	3.86345	1.16487	0.582437	−	0.812876i	$-0.302099\pi$
$11$	3.86345	1.16487	0.582437	+	0.812876i	$0.302099\pi$
$12$	−1.93882	−0.559690
$13$	−3.56879	−0.989804	−0.494902	−	0.868949i	$-0.664796\pi$
$13$	−3.56879	−0.989804	−0.494902	+	0.868949i	$0.664796\pi$
$14$	3.04863	0.814780
$15$	−1.00000	−0.258199
$16$	−4.11861	−1.02965
$17$	−6.61188	−1.60362	−0.801808	−	0.597582i	$-0.796128\pi$
$17$	−6.61188	−1.60362	−0.801808	+	0.597582i	$0.796128\pi$
$18$	1.98465	0.467786
$19$	5.57556	1.27912	0.639561	−	0.768741i	$-0.279116\pi$
$19$	5.57556	1.27912	0.639561	+	0.768741i	$0.279116\pi$
$20$	1.93882	0.433534
$21$	−1.53611	−0.335206
$22$	7.66759	1.63473
$23$	0	0
$23$	0	0
$24$	0.121418	0.0247843
$25$	1.00000	0.200000
$26$	−7.08279	−1.38905
$27$	−1.00000	−0.192450
$28$	2.97823	0.562833
$29$	7.13122	1.32423	0.662117	−	0.749401i	$-0.269658\pi$
$29$	7.13122	1.32423	0.662117	+	0.749401i	$0.269658\pi$
$30$	−1.98465	−0.362345
$31$	−4.49394	−0.807135	−0.403567	−	0.914950i	$-0.632230\pi$
$31$	−4.49394	−0.807135	−0.403567	+	0.914950i	$0.632230\pi$
$32$	−7.93116	−1.40204
$33$	−3.86345	−0.672541
$34$	−13.1222	−2.25044
$35$	1.53611	0.259649
$36$	1.93882	0.323137
$37$	−1.90863	−0.313777	−0.156888	−	0.987616i	$-0.550146\pi$
$37$	−1.90863	−0.313777	−0.156888	+	0.987616i	$0.550146\pi$
$38$	11.0655	1.79506
$39$	3.56879	0.571464
$40$	−0.121418	−0.0191979
$41$	7.16094	1.11835	0.559175	−	0.829049i	$-0.311118\pi$
$41$	7.16094	1.11835	0.559175	+	0.829049i	$0.311118\pi$
$42$	−3.04863	−0.470413
$43$	7.25092	1.10575	0.552877	−	0.833263i	$-0.313530\pi$
$43$	7.25092	1.10575	0.552877	+	0.833263i	$0.313530\pi$
$44$	7.49054	1.12924
$45$	1.00000	0.149071
$46$	0	0
$47$	13.4619	1.96362	0.981809	−	0.189873i	$-0.0608077\pi$
$47$	13.4619	1.96362	0.981809	+	0.189873i	$0.0608077\pi$
$48$	4.11861	0.594471
$49$	−4.64038	−0.662911
$50$	1.98465	0.280671
$51$	6.61188	0.925848
$52$	−6.91925	−0.959527
$53$	5.03082	0.691036	0.345518	−	0.938412i	$-0.387703\pi$
$53$	5.03082	0.691036	0.345518	+	0.938412i	$0.387703\pi$
$54$	−1.98465	−0.270076
$55$	3.86345	0.520948
$56$	−0.186511	−0.0249235
$57$	−5.57556	−0.738501
$58$	14.1529	1.85837
$59$	−1.15296	−0.150102	−0.0750510	−	0.997180i	$-0.523912\pi$
$59$	−1.15296	−0.150102	−0.0750510	+	0.997180i	$0.523912\pi$
$60$	−1.93882	−0.250301
$61$	11.0198	1.41095	0.705473	−	0.708736i	$-0.250734\pi$
$61$	11.0198	1.41095	0.705473	+	0.708736i	$0.250734\pi$
$62$	−8.91887	−1.13270
$63$	1.53611	0.193531
$64$	−7.50331	−0.937914
$65$	−3.56879	−0.442654
$66$	−7.66759	−0.943815
$67$	5.66412	0.691983	0.345991	−	0.938238i	$-0.387543\pi$
$67$	5.66412	0.691983	0.345991	+	0.938238i	$0.387543\pi$
$68$	−12.8192	−1.55456
$69$	0	0
$70$	3.04863	0.364381
$71$	9.38923	1.11430	0.557148	−	0.830413i	$-0.311895\pi$
$71$	9.38923	1.11430	0.557148	+	0.830413i	$0.311895\pi$
$72$	−0.121418	−0.0143092
$73$	3.40026	0.397970	0.198985	−	0.980002i	$-0.436235\pi$
$73$	3.40026	0.397970	0.198985	+	0.980002i	$0.436235\pi$
$74$	−3.78796	−0.440341
$75$	−1.00000	−0.115470
$76$	10.8100	1.23999
$77$	5.93467	0.676319
$78$	7.08279	0.801968
$79$	−4.05656	−0.456399	−0.228199	−	0.973614i	$-0.573284\pi$
$79$	−4.05656	−0.456399	−0.228199	+	0.973614i	$0.573284\pi$
$80$	−4.11861	−0.460475
$81$	1.00000	0.111111
$82$	14.2119	1.56945
$83$	9.56105	1.04946	0.524731	−	0.851268i	$-0.324166\pi$
$83$	9.56105	1.04946	0.524731	+	0.851268i	$0.324166\pi$
$84$	−2.97823	−0.324952
$85$	−6.61188	−0.717159
$86$	14.3905	1.55177
$87$	−7.13122	−0.764547
$88$	−0.469092	−0.0500054
$89$	−11.6302	−1.23280	−0.616398	−	0.787434i	$-0.711409\pi$
$89$	−11.6302	−1.23280	−0.616398	+	0.787434i	$0.711409\pi$
$90$	1.98465	0.209200
$91$	−5.48204	−0.574674
$92$	0	0
$93$	4.49394	0.465999
$94$	26.7171	2.75566
$95$	5.57556	0.572040
$96$	7.93116	0.809470
$97$	−6.28649	−0.638296	−0.319148	−	0.947705i	$-0.603397\pi$
$97$	−6.28649	−0.638296	−0.319148	+	0.947705i	$0.603397\pi$
$98$	−9.20951	−0.930301
$99$	3.86345	0.388292
$100$	1.93882	0.193882
$101$	11.4449	1.13881	0.569404	−	0.822058i	$-0.307174\pi$
$101$	11.4449	1.13881	0.569404	+	0.822058i	$0.307174\pi$
$102$	13.1222	1.29929
$103$	6.86891	0.676814	0.338407	−	0.941000i	$-0.390112\pi$
$103$	6.86891	0.676814	0.338407	+	0.941000i	$0.390112\pi$
$104$	0.433315	0.0424900
$105$	−1.53611	−0.149909
$106$	9.98439	0.969770
$107$	−13.8710	−1.34096	−0.670481	−	0.741927i	$-0.733912\pi$
$107$	−13.8710	−1.34096	−0.670481	+	0.741927i	$0.733912\pi$
$108$	−1.93882	−0.186563
$109$	−13.2023	−1.26455	−0.632276	−	0.774743i	$-0.717879\pi$
$109$	−13.2023	−1.26455	−0.632276	+	0.774743i	$0.717879\pi$
$110$	7.66759	0.731076
$111$	1.90863	0.181159
$112$	−6.32663	−0.597810
$113$	−5.68903	−0.535179	−0.267590	−	0.963533i	$-0.586227\pi$
$113$	−5.68903	−0.535179	−0.267590	+	0.963533i	$0.586227\pi$
$114$	−11.0655	−1.03638
$115$	0	0
$116$	13.8262	1.28373
$117$	−3.56879	−0.329935
$118$	−2.28821	−0.210647
$119$	−10.1565	−0.931049
$120$	0.121418	0.0110839
$121$	3.92626	0.356933
$122$	21.8705	1.98006
$123$	−7.16094	−0.645680
$124$	−8.71294	−0.782445
$125$	1.00000	0.0894427
$126$	3.04863	0.271593
$127$	7.14351	0.633884	0.316942	−	0.948445i	$-0.397344\pi$
$127$	7.14351	0.633884	0.316942	+	0.948445i	$0.397344\pi$
$128$	0.970889	0.0858153
$129$	−7.25092	−0.638408
$130$	−7.08279	−0.621201
$131$	21.9253	1.91562	0.957811	−	0.287398i	$-0.0927903\pi$
$131$	21.9253	1.91562	0.957811	+	0.287398i	$0.0927903\pi$
$132$	−7.49054	−0.651968
$133$	8.56465	0.742649
$134$	11.2413	0.971099
$135$	−1.00000	−0.0860663
$136$	0.802800	0.0688395
$137$	−11.0331	−0.942620	−0.471310	−	0.881968i	$-0.656219\pi$
$137$	−11.0331	−0.942620	−0.471310	+	0.881968i	$0.656219\pi$
$138$	0	0
$139$	18.8770	1.60113	0.800563	−	0.599249i	$-0.204534\pi$
$139$	18.8770	1.60113	0.800563	+	0.599249i	$0.204534\pi$
$140$	2.97823	0.251707
$141$	−13.4619	−1.13369
$142$	18.6343	1.56376
$143$	−13.7879	−1.15300
$144$	−4.11861	−0.343218
$145$	7.13122	0.592215
$146$	6.74831	0.558494
$147$	4.64038	0.382732
$148$	−3.70049	−0.304179
$149$	−6.92293	−0.567149	−0.283574	−	0.958950i	$-0.591520\pi$
$149$	−6.92293	−0.567149	−0.283574	+	0.958950i	$0.591520\pi$
$150$	−1.98465	−0.162046
$151$	−2.55747	−0.208124	−0.104062	−	0.994571i	$-0.533184\pi$
$151$	−2.55747	−0.208124	−0.104062	+	0.994571i	$0.533184\pi$
$152$	−0.676973	−0.0549097
$153$	−6.61188	−0.534538
$154$	11.7782	0.949116
$155$	−4.49394	−0.360962
$156$	6.91925	0.553983
$157$	−6.00810	−0.479499	−0.239749	−	0.970835i	$-0.577065\pi$
$157$	−6.00810	−0.479499	−0.239749	+	0.970835i	$0.577065\pi$
$158$	−8.05084	−0.640490
$159$	−5.03082	−0.398970
$160$	−7.93116	−0.627013
$161$	0	0
$162$	1.98465	0.155929
$163$	−1.45197	−0.113727	−0.0568637	−	0.998382i	$-0.518110\pi$
$163$	−1.45197	−0.113727	−0.0568637	+	0.998382i	$0.518110\pi$
$164$	13.8838	1.08414
$165$	−3.86345	−0.300769
$166$	18.9753	1.47277
$167$	−11.5902	−0.896874	−0.448437	−	0.893814i	$-0.648019\pi$
$167$	−11.5902	−0.896874	−0.448437	+	0.893814i	$0.648019\pi$
$168$	0.186511	0.0143896
$169$	−0.263737	−0.0202874
$170$	−13.1222	−1.00643
$171$	5.57556	0.426374
$172$	14.0582	1.07193
$173$	−17.5416	−1.33366	−0.666830	−	0.745210i	$-0.732349\pi$
$173$	−17.5416	−1.33366	−0.666830	+	0.745210i	$0.732349\pi$
$174$	−14.1529	−1.07293
$175$	1.53611	0.116119
$176$	−15.9121	−1.19942
$177$	1.15296	0.0866614
$178$	−23.0818	−1.73005
$179$	−1.47309	−0.110104	−0.0550521	−	0.998483i	$-0.517532\pi$
$179$	−1.47309	−0.110104	−0.0550521	+	0.998483i	$0.517532\pi$
$180$	1.93882	0.144511
$181$	3.39108	0.252057	0.126028	−	0.992027i	$-0.459777\pi$
$181$	3.39108	0.252057	0.126028	+	0.992027i	$0.459777\pi$
$182$	−10.8799	−0.806473
$183$	−11.0198	−0.814610
$184$	0	0
$185$	−1.90863	−0.140325
$186$	8.91887	0.653964
$187$	−25.5447	−1.86801
$188$	26.1002	1.90355
$189$	−1.53611	−0.111735
$190$	11.0655	0.802777
$191$	13.1408	0.950837	0.475418	−	0.879760i	$-0.342297\pi$
$191$	13.1408	0.950837	0.475418	+	0.879760i	$0.342297\pi$
$192$	7.50331	0.541505
$193$	9.42258	0.678252	0.339126	−	0.940741i	$-0.389869\pi$
$193$	9.42258	0.678252	0.339126	+	0.940741i	$0.389869\pi$
$194$	−12.4765	−0.895757
$195$	3.56879	0.255566
$196$	−8.99687	−0.642633
$197$	13.9220	0.991904	0.495952	−	0.868350i	$-0.334819\pi$
$197$	13.9220	0.991904	0.495952	+	0.868350i	$0.334819\pi$
$198$	7.66759	0.544912
$199$	18.8217	1.33424	0.667118	−	0.744952i	$-0.267528\pi$
$199$	18.8217	1.33424	0.667118	+	0.744952i	$0.267528\pi$
$200$	−0.121418	−0.00858554
$201$	−5.66412	−0.399516
$202$	22.7140	1.59815
$203$	10.9543	0.768841
$204$	12.8192	0.897527
$205$	7.16094	0.500142
$206$	13.6324	0.949812
$207$	0	0
$208$	14.6985	1.01916
$209$	21.5409	1.49002
$210$	−3.04863	−0.210375
$211$	10.1186	0.696593	0.348296	−	0.937384i	$-0.386760\pi$
$211$	10.1186	0.696593	0.348296	+	0.937384i	$0.386760\pi$
$212$	9.75385	0.669897
$213$	−9.38923	−0.643339
$214$	−27.5291	−1.88185
$215$	7.25092	0.494509
$216$	0.121418	0.00826144
$217$	−6.90316	−0.468617
$218$	−26.2019	−1.77462
$219$	−3.40026	−0.229768
$220$	7.49054	0.505012
$221$	23.5964	1.58727
$222$	3.78796	0.254231
$223$	−8.18749	−0.548275	−0.274138	−	0.961690i	$-0.588392\pi$
$223$	−8.18749	−0.548275	−0.274138	+	0.961690i	$0.588392\pi$
$224$	−12.1831	−0.814017
$225$	1.00000	0.0666667
$226$	−11.2907	−0.751048
$227$	15.2588	1.01276	0.506382	−	0.862309i	$-0.330983\pi$
$227$	15.2588	1.01276	0.506382	+	0.862309i	$0.330983\pi$
$228$	−10.8100	−0.715911
$229$	17.1997	1.13659	0.568295	−	0.822825i	$-0.307603\pi$
$229$	17.1997	1.13659	0.568295	+	0.822825i	$0.307603\pi$
$230$	0	0
$231$	−5.93467	−0.390473
$232$	−0.865858	−0.0568463
$233$	−12.0815	−0.791486	−0.395743	−	0.918361i	$-0.629513\pi$
$233$	−12.0815	−0.791486	−0.395743	+	0.918361i	$0.629513\pi$
$234$	−7.08279	−0.463016
$235$	13.4619	0.878156
$236$	−2.23537	−0.145510
$237$	4.05656	0.263502
$238$	−20.1571	−1.30659
$239$	−12.7006	−0.821533	−0.410767	−	0.911741i	$-0.634739\pi$
$239$	−12.7006	−0.821533	−0.410767	+	0.911741i	$0.634739\pi$
$240$	4.11861	0.265855
$241$	−16.7092	−1.07633	−0.538166	−	0.842839i	$-0.680883\pi$
$241$	−16.7092	−1.07633	−0.538166	+	0.842839i	$0.680883\pi$
$242$	7.79224	0.500904
$243$	−1.00000	−0.0641500
$244$	21.3655	1.36779
$245$	−4.64038	−0.296463
$246$	−14.2119	−0.906120
$247$	−19.8980	−1.26608
$248$	0.545644	0.0346485
$249$	−9.56105	−0.605907
$250$	1.98465	0.125520
$251$	19.1037	1.20582	0.602909	−	0.797810i	$-0.294008\pi$
$251$	19.1037	1.20582	0.602909	+	0.797810i	$0.294008\pi$
$252$	2.97823	0.187611
$253$	0	0
$254$	14.1773	0.889565
$255$	6.61188	0.414052
$256$	16.9335	1.05834
$257$	−0.248305	−0.0154888	−0.00774442	−	0.999970i	$-0.502465\pi$
$257$	−0.248305	−0.0154888	−0.00774442	+	0.999970i	$0.502465\pi$
$258$	−14.3905	−0.895914
$259$	−2.93186	−0.182177
$260$	−6.91925	−0.429113
$261$	7.13122	0.441411
$262$	43.5140	2.68830
$263$	9.77667	0.602855	0.301428	−	0.953489i	$-0.402537\pi$
$263$	9.77667	0.602855	0.301428	+	0.953489i	$0.402537\pi$
$264$	0.469092	0.0288706
$265$	5.03082	0.309041
$266$	16.9978	1.04220
$267$	11.6302	0.711756
$268$	10.9817	0.670815
$269$	23.4266	1.42834	0.714172	−	0.699970i	$-0.246804\pi$
$269$	23.4266	1.42834	0.714172	+	0.699970i	$0.246804\pi$
$270$	−1.98465	−0.120782
$271$	−2.36483	−0.143653	−0.0718266	−	0.997417i	$-0.522883\pi$
$271$	−2.36483	−0.143653	−0.0718266	+	0.997417i	$0.522883\pi$
$272$	27.2318	1.65117
$273$	5.48204	0.331788
$274$	−21.8968	−1.32283
$275$	3.86345	0.232975
$276$	0	0
$277$	11.3097	0.679533	0.339767	−	0.940510i	$-0.389652\pi$
$277$	11.3097	0.679533	0.339767	+	0.940510i	$0.389652\pi$
$278$	37.4641	2.24695
$279$	−4.49394	−0.269045
$280$	−0.186511	−0.0111461
$281$	−13.6857	−0.816418	−0.408209	−	0.912889i	$-0.633847\pi$
$281$	−13.6857	−0.816418	−0.408209	+	0.912889i	$0.633847\pi$
$282$	−26.7171	−1.59098
$283$	12.2261	0.726768	0.363384	−	0.931639i	$-0.381621\pi$
$283$	12.2261	0.726768	0.363384	+	0.931639i	$0.381621\pi$
$284$	18.2040	1.08021
$285$	−5.57556	−0.330268
$286$	−27.3640	−1.61807
$287$	11.0000	0.649307
$288$	−7.93116	−0.467348
$289$	26.7169	1.57158
$290$	14.1529	0.831090
$291$	6.28649	0.368520
$292$	6.59250	0.385797
$293$	21.1747	1.23704	0.618519	−	0.785770i	$-0.287733\pi$
$293$	21.1747	1.23704	0.618519	+	0.785770i	$0.287733\pi$
$294$	9.20951	0.537110
$295$	−1.15296	−0.0671276
$296$	0.231742	0.0134697
$297$	−3.86345	−0.224180
$298$	−13.7396	−0.795912
$299$	0	0
$300$	−1.93882	−0.111938
$301$	11.1382	0.641994
$302$	−5.07567	−0.292072
$303$	−11.4449	−0.657491
$304$	−22.9636	−1.31705
$305$	11.0198	0.630995
$306$	−13.1222	−0.750148
$307$	10.8568	0.619633	0.309817	−	0.950796i	$-0.399732\pi$
$307$	10.8568	0.619633	0.309817	+	0.950796i	$0.399732\pi$
$308$	11.5063	0.655630
$309$	−6.86891	−0.390759
$310$	−8.91887	−0.506558
$311$	32.2095	1.82644	0.913218	−	0.407472i	$-0.133590\pi$
$311$	32.2095	1.82644	0.913218	+	0.407472i	$0.133590\pi$
$312$	−0.433315	−0.0245316
$313$	−12.6901	−0.717288	−0.358644	−	0.933474i	$-0.616761\pi$
$313$	−12.6901	−0.717288	−0.358644	+	0.933474i	$0.616761\pi$
$314$	−11.9240	−0.672908
$315$	1.53611	0.0865498
$316$	−7.86494	−0.442438
$317$	−30.6393	−1.72087	−0.860436	−	0.509558i	$-0.829809\pi$
$317$	−30.6393	−1.72087	−0.860436	+	0.509558i	$0.829809\pi$
$318$	−9.98439	−0.559897
$319$	27.5511	1.54257
$320$	−7.50331	−0.419448
$321$	13.8710	0.774204
$322$	0	0
$323$	−36.8649	−2.05122
$324$	1.93882	0.107712
$325$	−3.56879	−0.197961
$326$	−2.88166	−0.159600
$327$	13.2023	0.730089
$328$	−0.869466	−0.0480082
$329$	20.6789	1.14006
$330$	−7.66759	−0.422087
$331$	−18.6065	−1.02271	−0.511354	−	0.859370i	$-0.670856\pi$
$331$	−18.6065	−1.02271	−0.511354	+	0.859370i	$0.670856\pi$
$332$	18.5372	1.01736
$333$	−1.90863	−0.104592
$334$	−23.0024	−1.25863
$335$	5.66412	0.309464
$336$	6.32663	0.345146
$337$	−33.7923	−1.84078	−0.920392	−	0.390997i	$-0.872130\pi$
$337$	−33.7923	−1.84078	−0.920392	+	0.390997i	$0.872130\pi$
$338$	−0.523424	−0.0284705
$339$	5.68903	0.308986
$340$	−12.8192	−0.695221
$341$	−17.3621	−0.940211
$342$	11.0655	0.598355
$343$	−17.8809	−0.965475
$344$	−0.880392	−0.0474675
$345$	0	0
$346$	−34.8138	−1.87160
$347$	−9.57075	−0.513785	−0.256892	−	0.966440i	$-0.582699\pi$
$347$	−9.57075	−0.513785	−0.256892	+	0.966440i	$0.582699\pi$
$348$	−13.8262	−0.741160
$349$	6.80727	0.364385	0.182192	−	0.983263i	$-0.441681\pi$
$349$	6.80727	0.364385	0.182192	+	0.983263i	$0.441681\pi$
$350$	3.04863	0.162956
$351$	3.56879	0.190488
$352$	−30.6416	−1.63321
$353$	5.47606	0.291461	0.145731	−	0.989324i	$-0.453447\pi$
$353$	5.47606	0.291461	0.145731	+	0.989324i	$0.453447\pi$
$354$	2.28821	0.121617
$355$	9.38923	0.498329
$356$	−22.5488	−1.19509
$357$	10.1565	0.537541
$358$	−2.92357	−0.154516
$359$	−10.4885	−0.553563	−0.276782	−	0.960933i	$-0.589268\pi$
$359$	−10.4885	−0.553563	−0.276782	+	0.960933i	$0.589268\pi$
$360$	−0.121418	−0.00639929
$361$	12.0869	0.636151
$362$	6.73009	0.353726
$363$	−3.92626	−0.206075
$364$	−10.6287	−0.557095
$365$	3.40026	0.177978
$366$	−21.8705	−1.14319
$367$	−27.4581	−1.43330	−0.716651	−	0.697432i	$-0.754326\pi$
$367$	−27.4581	−1.43330	−0.716651	+	0.697432i	$0.754326\pi$
$368$	0	0
$369$	7.16094	0.372784
$370$	−3.78796	−0.196927
$371$	7.72787	0.401211
$372$	8.71294	0.451745
$373$	−12.3444	−0.639171	−0.319585	−	0.947558i	$-0.603544\pi$
$373$	−12.3444	−0.639171	−0.319585	+	0.947558i	$0.603544\pi$
$374$	−50.6971	−2.62149
$375$	−1.00000	−0.0516398
$376$	−1.63451	−0.0842936
$377$	−25.4498	−1.31073
$378$	−3.04863	−0.156804
$379$	−9.35895	−0.480737	−0.240368	−	0.970682i	$-0.577268\pi$
$379$	−9.35895	−0.480737	−0.240368	+	0.970682i	$0.577268\pi$
$380$	10.8100	0.554542
$381$	−7.14351	−0.365973
$382$	26.0799	1.33436
$383$	−23.9981	−1.22625	−0.613124	−	0.789987i	$-0.710087\pi$
$383$	−23.9981	−1.22625	−0.613124	+	0.789987i	$0.710087\pi$
$384$	−0.970889	−0.0495455
$385$	5.93467	0.302459
$386$	18.7005	0.951830
$387$	7.25092	0.368585
$388$	−12.1884	−0.618771
$389$	10.2502	0.519707	0.259854	−	0.965648i	$-0.416326\pi$
$389$	10.2502	0.519707	0.259854	+	0.965648i	$0.416326\pi$
$390$	7.08279	0.358651
$391$	0	0
$392$	0.563425	0.0284573
$393$	−21.9253	−1.10599
$394$	27.6303	1.39200
$395$	−4.05656	−0.204108
$396$	7.49054	0.376414
$397$	20.4026	1.02398	0.511990	−	0.858992i	$-0.328909\pi$
$397$	20.4026	1.02398	0.511990	+	0.858992i	$0.328909\pi$
$398$	37.3544	1.87241
$399$	−8.56465	−0.428769
$400$	−4.11861	−0.205931
$401$	−9.32379	−0.465608	−0.232804	−	0.972524i	$-0.574790\pi$
$401$	−9.32379	−0.465608	−0.232804	+	0.972524i	$0.574790\pi$
$402$	−11.2413	−0.560664
$403$	16.0379	0.798905
$404$	22.1896	1.10397
$405$	1.00000	0.0496904
$406$	21.7404	1.07896
$407$	−7.37390	−0.365511
$408$	−0.802800	−0.0397445
$409$	9.34806	0.462232	0.231116	−	0.972926i	$-0.425762\pi$
$409$	9.34806	0.462232	0.231116	+	0.972926i	$0.425762\pi$
$410$	14.2119	0.701877
$411$	11.0331	0.544222
$412$	13.3176	0.656111
$413$	−1.77106	−0.0871482
$414$	0	0
$415$	9.56105	0.469334
$416$	28.3046	1.38775
$417$	−18.8770	−0.924410
$418$	42.7511	2.09102
$419$	−13.4735	−0.658226	−0.329113	−	0.944291i	$-0.606750\pi$
$419$	−13.4735	−0.658226	−0.329113	+	0.944291i	$0.606750\pi$
$420$	−2.97823	−0.145323
$421$	18.1401	0.884095	0.442047	−	0.896992i	$-0.354252\pi$
$421$	18.1401	0.884095	0.442047	+	0.896992i	$0.354252\pi$
$422$	20.0818	0.977568
$423$	13.4619	0.654539
$424$	−0.610831	−0.0296646
$425$	−6.61188	−0.320723
$426$	−18.6343	−0.902835
$427$	16.9276	0.819186
$428$	−26.8934	−1.29994
$429$	13.7879	0.665684
$430$	14.3905	0.693972
$431$	−10.3611	−0.499079	−0.249539	−	0.968365i	$-0.580279\pi$
$431$	−10.3611	−0.499079	−0.249539	+	0.968365i	$0.580279\pi$
$432$	4.11861	0.198157
$433$	−10.7908	−0.518575	−0.259287	−	0.965800i	$-0.583488\pi$
$433$	−10.7908	−0.518575	−0.259287	+	0.965800i	$0.583488\pi$
$434$	−13.7003	−0.657637
$435$	−7.13122	−0.341916
$436$	−25.5969	−1.22587
$437$	0	0
$438$	−6.74831	−0.322447
$439$	−5.05177	−0.241108	−0.120554	−	0.992707i	$-0.538467\pi$
$439$	−5.05177	−0.241108	−0.120554	+	0.992707i	$0.538467\pi$
$440$	−0.469092	−0.0223631
$441$	−4.64038	−0.220970
$442$	46.8305	2.22750
$443$	21.1043	1.00269	0.501347	−	0.865246i	$-0.332838\pi$
$443$	21.1043	1.00269	0.501347	+	0.865246i	$0.332838\pi$
$444$	3.70049	0.175618
$445$	−11.6302	−0.551323
$446$	−16.2493	−0.769426
$447$	6.92293	0.327443
$448$	−11.5259	−0.544547
$449$	−39.6128	−1.86944	−0.934721	−	0.355383i	$-0.884351\pi$
$449$	−39.6128	−1.86944	−0.934721	+	0.355383i	$0.884351\pi$
$450$	1.98465	0.0935571
$451$	27.6659	1.30274
$452$	−11.0300	−0.518809
$453$	2.55747	0.120160
$454$	30.2834	1.42127
$455$	−5.48204	−0.257002
$456$	0.676973	0.0317022
$457$	37.0098	1.73125	0.865624	−	0.500695i	$-0.166922\pi$
$457$	37.0098	1.73125	0.865624	+	0.500695i	$0.166922\pi$
$458$	34.1354	1.59504
$459$	6.61188	0.308616
$460$	0	0
$461$	−24.4177	−1.13725	−0.568623	−	0.822599i	$-0.692524\pi$
$461$	−24.4177	−1.13725	−0.568623	+	0.822599i	$0.692524\pi$
$462$	−11.7782	−0.547973
$463$	20.4467	0.950239	0.475120	−	0.879921i	$-0.342405\pi$
$463$	20.4467	0.950239	0.475120	+	0.879921i	$0.342405\pi$
$464$	−29.3707	−1.36350
$465$	4.49394	0.208401
$466$	−23.9775	−1.11074
$467$	−12.7258	−0.588881	−0.294441	−	0.955670i	$-0.595133\pi$
$467$	−12.7258	−0.588881	−0.294441	+	0.955670i	$0.595133\pi$
$468$	−6.91925	−0.319842
$469$	8.70069	0.401761
$470$	26.7171	1.23237
$471$	6.00810	0.276839
$472$	0.139989	0.00644353
$473$	28.0136	1.28807
$474$	8.05084	0.369787
$475$	5.57556	0.255824
$476$	−19.6917	−0.902568
$477$	5.03082	0.230345
$478$	−25.2062	−1.15290
$479$	26.9629	1.23197	0.615984	−	0.787759i	$-0.288759\pi$
$479$	26.9629	1.23197	0.615984	+	0.787759i	$0.288759\pi$
$480$	7.93116	0.362006
$481$	6.81150	0.310578
$482$	−33.1618	−1.51048
$483$	0	0
$484$	7.61232	0.346015
$485$	−6.28649	−0.285455
$486$	−1.98465	−0.0900254
$487$	19.6341	0.889705	0.444852	−	0.895604i	$-0.353256\pi$
$487$	19.6341	0.889705	0.444852	+	0.895604i	$0.353256\pi$
$488$	−1.33801	−0.0605687
$489$	1.45197	0.0656606
$490$	−9.20951	−0.416043
$491$	−42.2596	−1.90715	−0.953574	−	0.301160i	$-0.902626\pi$
$491$	−42.2596	−1.90715	−0.953574	+	0.301160i	$0.902626\pi$
$492$	−13.8838	−0.625929
$493$	−47.1507	−2.12356
$494$	−39.4905	−1.77676
$495$	3.86345	0.173649
$496$	18.5088	0.831069
$497$	14.4229	0.646953
$498$	−18.9753	−0.850304
$499$	−4.78134	−0.214042	−0.107021	−	0.994257i	$-0.534131\pi$
$499$	−4.78134	−0.214042	−0.107021	+	0.994257i	$0.534131\pi$
$500$	1.93882	0.0867067
$501$	11.5902	0.517810
$502$	37.9142	1.69219
$503$	22.1187	0.986225	0.493113	−	0.869966i	$-0.335859\pi$
$503$	22.1187	0.986225	0.493113	+	0.869966i	$0.335859\pi$
$504$	−0.186511	−0.00830785
$505$	11.4449	0.509291
$506$	0	0
$507$	0.263737	0.0117130
$508$	13.8500	0.614494
$509$	27.9891	1.24059	0.620297	−	0.784367i	$-0.287012\pi$
$509$	27.9891	1.24059	0.620297	+	0.784367i	$0.287012\pi$
$510$	13.1222	0.581062
$511$	5.22316	0.231059
$512$	31.6652	1.39942
$513$	−5.57556	−0.246167
$514$	−0.492798	−0.0217364
$515$	6.86891	0.302681
$516$	−14.0582	−0.618879
$517$	52.0093	2.28737
$518$	−5.81870	−0.255659
$519$	17.5416	0.769989
$520$	0.433315	0.0190021
$521$	−20.1378	−0.882254	−0.441127	−	0.897445i	$-0.645421\pi$
$521$	−20.1378	−0.882254	−0.441127	+	0.897445i	$0.645421\pi$
$522$	14.1529	0.619458
$523$	−0.721760	−0.0315604	−0.0157802	−	0.999875i	$-0.505023\pi$
$523$	−0.721760	−0.0315604	−0.0157802	+	0.999875i	$0.505023\pi$
$524$	42.5092	1.85702
$525$	−1.53611	−0.0670412
$526$	19.4032	0.846021
$527$	29.7133	1.29433
$528$	15.9121	0.692484
$529$	0	0
$530$	9.98439	0.433694
$531$	−1.15296	−0.0500340
$532$	16.6053	0.719932
$533$	−25.5559	−1.10695
$534$	23.0818	0.998847
$535$	−13.8710	−0.599696
$536$	−0.687726	−0.0297052
$537$	1.47309	0.0635687
$538$	46.4935	2.00448
$539$	−17.9279	−0.772209
$540$	−1.93882	−0.0834336
$541$	12.3817	0.532329	0.266164	−	0.963928i	$-0.414244\pi$
$541$	12.3817	0.532329	0.266164	+	0.963928i	$0.414244\pi$
$542$	−4.69335	−0.201597
$543$	−3.39108	−0.145525
$544$	52.4398	2.24834
$545$	−13.2023	−0.565525
$546$	10.8799	0.465617
$547$	−34.4156	−1.47150	−0.735752	−	0.677251i	$-0.763171\pi$
$547$	−34.4156	−1.47150	−0.735752	+	0.677251i	$0.763171\pi$
$548$	−21.3912	−0.913786
$549$	11.0198	0.470316
$550$	7.66759	0.326947
$551$	39.7605	1.69386
$552$	0	0
$553$	−6.23130	−0.264982
$554$	22.4457	0.953628
$555$	1.90863	0.0810169
$556$	36.5991	1.55215
$557$	−37.9913	−1.60974	−0.804872	−	0.593449i	$-0.797766\pi$
$557$	−37.9913	−1.60974	−0.804872	+	0.593449i	$0.797766\pi$
$558$	−8.91887	−0.377566
$559$	−25.8770	−1.09448
$560$	−6.32663	−0.267349
$561$	25.5447	1.07850
$562$	−27.1612	−1.14573
$563$	−33.9766	−1.43194	−0.715971	−	0.698130i	$-0.754016\pi$
$563$	−33.9766	−1.43194	−0.715971	+	0.698130i	$0.754016\pi$
$564$	−26.1002	−1.09902
$565$	−5.68903	−0.239339
$566$	24.2645	1.01992
$567$	1.53611	0.0645104
$568$	−1.14002	−0.0478342
$569$	15.0862	0.632448	0.316224	−	0.948684i	$-0.397585\pi$
$569$	15.0862	0.632448	0.316224	+	0.948684i	$0.397585\pi$
$570$	−11.0655	−0.463483
$571$	11.7087	0.489992	0.244996	−	0.969524i	$-0.421213\pi$
$571$	11.7087	0.489992	0.244996	+	0.969524i	$0.421213\pi$
$572$	−26.7322	−1.11773
$573$	−13.1408	−0.548966
$574$	21.8310	0.911210
$575$	0	0
$576$	−7.50331	−0.312638
$577$	14.4751	0.602607	0.301304	−	0.953528i	$-0.402578\pi$
$577$	14.4751	0.602607	0.301304	+	0.953528i	$0.402578\pi$
$578$	53.0236	2.20549
$579$	−9.42258	−0.391589
$580$	13.8262	0.574100
$581$	14.6868	0.609311
$582$	12.4765	0.517166
$583$	19.4363	0.804970
$584$	−0.412852	−0.0170840
$585$	−3.56879	−0.147551
$586$	42.0243	1.73601
$587$	0.611111	0.0252232	0.0126116	−	0.999920i	$-0.495985\pi$
$587$	0.611111	0.0252232	0.0126116	+	0.999920i	$0.495985\pi$
$588$	8.99687	0.371025
$589$	−25.0562	−1.03242
$590$	−2.28821	−0.0942040
$591$	−13.9220	−0.572676
$592$	7.86091	0.323082
$593$	27.9553	1.14799	0.573993	−	0.818860i	$-0.305394\pi$
$593$	27.9553	1.14799	0.573993	+	0.818860i	$0.305394\pi$
$594$	−7.66759	−0.314605
$595$	−10.1565	−0.416378
$596$	−13.4223	−0.549800
$597$	−18.8217	−0.770321
$598$	0	0
$599$	−27.8666	−1.13860	−0.569299	−	0.822131i	$-0.692785\pi$
$599$	−27.8666	−1.13860	−0.569299	+	0.822131i	$0.692785\pi$
$600$	0.121418	0.00495687
$601$	−42.9543	−1.75214	−0.876071	−	0.482182i	$-0.839844\pi$
$601$	−42.9543	−1.75214	−0.876071	+	0.482182i	$0.839844\pi$
$602$	22.1053	0.900947
$603$	5.66412	0.230661
$604$	−4.95847	−0.201757
$605$	3.92626	0.159625
$606$	−22.7140	−0.922695
$607$	−4.73120	−0.192034	−0.0960168	−	0.995380i	$-0.530610\pi$
$607$	−4.73120	−0.192034	−0.0960168	+	0.995380i	$0.530610\pi$
$608$	−44.2206	−1.79338
$609$	−10.9543	−0.443891
$610$	21.8705	0.885511
$611$	−48.0426	−1.94360
$612$	−12.8192	−0.518187
$613$	−24.1321	−0.974686	−0.487343	−	0.873211i	$-0.662034\pi$
$613$	−24.1321	−0.974686	−0.487343	+	0.873211i	$0.662034\pi$
$614$	21.5470	0.869566
$615$	−7.16094	−0.288757
$616$	−0.720575	−0.0290328
$617$	−11.0054	−0.443061	−0.221530	−	0.975153i	$-0.571105\pi$
$617$	−11.0054	−0.443061	−0.221530	+	0.975153i	$0.571105\pi$
$618$	−13.6324	−0.548374
$619$	−29.2546	−1.17584	−0.587921	−	0.808918i	$-0.700054\pi$
$619$	−29.2546	−1.17584	−0.587921	+	0.808918i	$0.700054\pi$
$620$	−8.71294	−0.349920
$621$	0	0
$622$	63.9246	2.56314
$623$	−17.8652	−0.715754
$624$	−14.6985	−0.588410
$625$	1.00000	0.0400000
$626$	−25.1854	−1.00661
$627$	−21.5409	−0.860261
$628$	−11.6486	−0.464831
$629$	12.6196	0.503178
$630$	3.04863	0.121460
$631$	1.19061	0.0473973	0.0236987	−	0.999719i	$-0.492456\pi$
$631$	1.19061	0.0473973	0.0236987	+	0.999719i	$0.492456\pi$
$632$	0.492539	0.0195921
$633$	−10.1186	−0.402178
$634$	−60.8081	−2.41500
$635$	7.14351	0.283481
$636$	−9.75385	−0.386765
$637$	16.5605	0.656152
$638$	54.6792	2.16477
$639$	9.38923	0.371432
$640$	0.970889	0.0383777
$641$	10.4909	0.414364	0.207182	−	0.978302i	$-0.433571\pi$
$641$	10.4909	0.414364	0.207182	+	0.978302i	$0.433571\pi$
$642$	27.5291	1.08649
$643$	25.5492	1.00756	0.503782	−	0.863831i	$-0.331942\pi$
$643$	25.5492	1.00756	0.503782	+	0.863831i	$0.331942\pi$
$644$	0	0
$645$	−7.25092	−0.285505
$646$	−73.1638	−2.87859
$647$	38.6250	1.51850	0.759252	−	0.650796i	$-0.225565\pi$
$647$	38.6250	1.51850	0.759252	+	0.650796i	$0.225565\pi$
$648$	−0.121418	−0.00476975
$649$	−4.45439	−0.174850
$650$	−7.08279	−0.277810
$651$	6.90316	0.270556
$652$	−2.81512	−0.110249
$653$	19.8355	0.776223	0.388111	−	0.921612i	$-0.373128\pi$
$653$	19.8355	0.776223	0.388111	+	0.921612i	$0.373128\pi$
$654$	26.2019	1.02458
$655$	21.9253	0.856692
$656$	−29.4931	−1.15151
$657$	3.40026	0.132657
$658$	41.0403	1.59992
$659$	−20.4504	−0.796636	−0.398318	−	0.917247i	$-0.630406\pi$
$659$	−20.4504	−0.796636	−0.398318	+	0.917247i	$0.630406\pi$
$660$	−7.49054	−0.291569
$661$	42.3193	1.64603	0.823014	−	0.568021i	$-0.192291\pi$
$661$	42.3193	1.64603	0.823014	+	0.568021i	$0.192291\pi$
$662$	−36.9274	−1.43522
$663$	−23.5964	−0.916408
$664$	−1.16088	−0.0450510
$665$	8.56465	0.332123
$666$	−3.78796	−0.146780
$667$	0	0
$668$	−22.4713	−0.869439
$669$	8.18749	0.316547
$670$	11.2413	0.434289
$671$	42.5746	1.64358
$672$	12.1831	0.469973
$673$	−36.3040	−1.39942	−0.699708	−	0.714429i	$-0.746686\pi$
$673$	−36.3040	−1.39942	−0.699708	+	0.714429i	$0.746686\pi$
$674$	−67.0658	−2.58328
$675$	−1.00000	−0.0384900
$676$	−0.511338	−0.0196669
$677$	−0.147292	−0.00566090	−0.00283045	−	0.999996i	$-0.500901\pi$
$677$	−0.147292	−0.00566090	−0.00283045	+	0.999996i	$0.500901\pi$
$678$	11.2907	0.433618
$679$	−9.65671	−0.370591
$680$	0.802800	0.0307860
$681$	−15.2588	−0.584720
$682$	−34.4576	−1.31945
$683$	3.04863	0.116653	0.0583263	−	0.998298i	$-0.481424\pi$
$683$	3.04863	0.116653	0.0583263	+	0.998298i	$0.481424\pi$
$684$	10.8100	0.413331
$685$	−11.0331	−0.421552
$686$	−35.4872	−1.35491
$687$	−17.1997	−0.656211
$688$	−29.8637	−1.13854
$689$	−17.9539	−0.683990
$690$	0	0
$691$	13.3515	0.507915	0.253958	−	0.967215i	$-0.418268\pi$
$691$	13.3515	0.507915	0.253958	+	0.967215i	$0.418268\pi$
$692$	−34.0099	−1.29286
$693$	5.93467	0.225440
$694$	−18.9945	−0.721023
$695$	18.8770	0.716045
$696$	0.865858	0.0328202
$697$	−47.3472	−1.79340
$698$	13.5100	0.511362
$699$	12.0815	0.456965
$700$	2.97823	0.112567
$701$	15.6159	0.589803	0.294901	−	0.955528i	$-0.404713\pi$
$701$	15.6159	0.589803	0.294901	+	0.955528i	$0.404713\pi$
$702$	7.08279	0.267323
$703$	−10.6417	−0.401359
$704$	−28.9887	−1.09255
$705$	−13.4619	−0.507004
$706$	10.8680	0.409024
$707$	17.5806	0.661185
$708$	2.23537	0.0840105
$709$	24.4290	0.917451	0.458726	−	0.888578i	$-0.348306\pi$
$709$	24.4290	0.917451	0.458726	+	0.888578i	$0.348306\pi$
$710$	18.6343	0.699333
$711$	−4.05656	−0.152133
$712$	1.41211	0.0529211
$713$	0	0
$714$	20.1571	0.754362
$715$	−13.7879	−0.515636
$716$	−2.85607	−0.106736
$717$	12.7006	0.474312
$718$	−20.8160	−0.776847
$719$	−22.7657	−0.849016	−0.424508	−	0.905424i	$-0.639553\pi$
$719$	−22.7657	−0.849016	−0.424508	+	0.905424i	$0.639553\pi$
$720$	−4.11861	−0.153492
$721$	10.5514	0.392954
$722$	23.9882	0.892747
$723$	16.7092	0.621420
$724$	6.57470	0.244347
$725$	7.13122	0.264847
$726$	−7.79224	−0.289197
$727$	−46.6668	−1.73078	−0.865388	−	0.501103i	$-0.832928\pi$
$727$	−46.6668	−1.73078	−0.865388	+	0.501103i	$0.832928\pi$
$728$	0.665618	0.0246694
$729$	1.00000	0.0370370
$730$	6.74831	0.249766
$731$	−47.9422	−1.77321
$732$	−21.3655	−0.789692
$733$	−40.8013	−1.50703	−0.753516	−	0.657430i	$-0.771644\pi$
$733$	−40.8013	−1.50703	−0.753516	+	0.657430i	$0.771644\pi$
$734$	−54.4946	−2.01143
$735$	4.64038	0.171163
$736$	0	0
$737$	21.8831	0.806073
$738$	14.2119	0.523148
$739$	−1.11537	−0.0410296	−0.0205148	−	0.999790i	$-0.506531\pi$
$739$	−1.11537	−0.0410296	−0.0205148	+	0.999790i	$0.506531\pi$
$740$	−3.70049	−0.136033
$741$	19.8980	0.730971
$742$	15.3371	0.563042
$743$	−26.9780	−0.989728	−0.494864	−	0.868970i	$-0.664782\pi$
$743$	−26.9780	−0.989728	−0.494864	+	0.868970i	$0.664782\pi$
$744$	−0.545644	−0.0200043
$745$	−6.92293	−0.253637
$746$	−24.4993	−0.896985
$747$	9.56105	0.349821
$748$	−49.5265	−1.81087
$749$	−21.3073	−0.778553
$750$	−1.98465	−0.0724690
$751$	29.0150	1.05877	0.529385	−	0.848381i	$-0.322423\pi$
$751$	29.0150	1.05877	0.529385	+	0.848381i	$0.322423\pi$
$752$	−55.4443	−2.02185
$753$	−19.1037	−0.696179
$754$	−50.5089	−1.83943
$755$	−2.55747	−0.0930758
$756$	−2.97823	−0.108317
$757$	4.13084	0.150138	0.0750689	−	0.997178i	$-0.476082\pi$
$757$	4.13084	0.150138	0.0750689	+	0.997178i	$0.476082\pi$
$758$	−18.5742	−0.674645
$759$	0	0
$760$	−0.676973	−0.0245564
$761$	30.0873	1.09066	0.545332	−	0.838220i	$-0.316404\pi$
$761$	30.0873	1.09066	0.545332	+	0.838220i	$0.316404\pi$
$762$	−14.1773	−0.513591
$763$	−20.2801	−0.734190
$764$	25.4777	0.921751
$765$	−6.61188	−0.239053
$766$	−47.6278	−1.72086
$767$	4.11466	0.148572
$768$	−16.9335	−0.611035
$769$	8.55429	0.308475	0.154238	−	0.988034i	$-0.450708\pi$
$769$	8.55429	0.308475	0.154238	+	0.988034i	$0.450708\pi$
$770$	11.7782	0.424458
$771$	0.248305	0.00894249
$772$	18.2687	0.657505
$773$	−24.8005	−0.892011	−0.446005	−	0.895030i	$-0.647154\pi$
$773$	−24.8005	−0.892011	−0.446005	+	0.895030i	$0.647154\pi$
$774$	14.3905	0.517256
$775$	−4.49394	−0.161427
$776$	0.763292	0.0274006
$777$	2.93186	0.105180
$778$	20.3431	0.729335
$779$	39.9262	1.43051
$780$	6.91925	0.247749
$781$	36.2748	1.29802
$782$	0	0
$783$	−7.13122	−0.254849
$784$	19.1119	0.682569
$785$	−6.00810	−0.214438
$786$	−43.5140	−1.55209
$787$	32.3684	1.15381	0.576904	−	0.816812i	$-0.304261\pi$
$787$	32.3684	1.15381	0.576904	+	0.816812i	$0.304261\pi$
$788$	26.9924	0.961563
$789$	−9.77667	−0.348059
$790$	−8.05084	−0.286436
$791$	−8.73896	−0.310722
$792$	−0.469092	−0.0166685
$793$	−39.3275	−1.39656
$794$	40.4920	1.43701
$795$	−5.03082	−0.178425
$796$	36.4919	1.29342
$797$	−12.5840	−0.445746	−0.222873	−	0.974847i	$-0.571544\pi$
$797$	−12.5840	−0.445746	−0.222873	+	0.974847i	$0.571544\pi$
$798$	−16.9978	−0.601716
$799$	−89.0083	−3.14889
$800$	−7.93116	−0.280409
$801$	−11.6302	−0.410932
$802$	−18.5044	−0.653414
$803$	13.1367	0.463586
$804$	−10.9817	−0.387295
$805$	0	0
$806$	31.8296	1.12115
$807$	−23.4266	−0.824655
$808$	−1.38961	−0.0488864
$809$	−49.8687	−1.75329	−0.876645	−	0.481138i	$-0.840224\pi$
$809$	−49.8687	−1.75329	−0.876645	+	0.481138i	$0.840224\pi$
$810$	1.98465	0.0697334
$811$	15.0210	0.527459	0.263730	−	0.964597i	$-0.415047\pi$
$811$	15.0210	0.527459	0.263730	+	0.964597i	$0.415047\pi$
$812$	21.2384	0.745323
$813$	2.36483	0.0829382
$814$	−14.6346	−0.512942
$815$	−1.45197	−0.0508605
$816$	−27.2318	−0.953303
$817$	40.4279	1.41439
$818$	18.5526	0.648676
$819$	−5.48204	−0.191558
$820$	13.8838	0.484843
$821$	−20.1794	−0.704266	−0.352133	−	0.935950i	$-0.614544\pi$
$821$	−20.1794	−0.704266	−0.352133	+	0.935950i	$0.614544\pi$
$822$	21.8968	0.763737
$823$	−42.2677	−1.47336	−0.736680	−	0.676242i	$-0.763607\pi$
$823$	−42.2677	−1.47336	−0.736680	+	0.676242i	$0.763607\pi$
$824$	−0.834009	−0.0290541
$825$	−3.86345	−0.134508
$826$	−3.51493	−0.122300
$827$	50.5615	1.75819	0.879097	−	0.476643i	$-0.158147\pi$
$827$	50.5615	1.75819	0.879097	+	0.476643i	$0.158147\pi$
$828$	0	0
$829$	−44.8210	−1.55670	−0.778349	−	0.627832i	$-0.783942\pi$
$829$	−44.8210	−1.55670	−0.778349	+	0.627832i	$0.783942\pi$
$830$	18.9753	0.658643
$831$	−11.3097	−0.392329
$832$	26.7778	0.928352
$833$	30.6816	1.06305
$834$	−37.4641	−1.29728
$835$	−11.5902	−0.401094
$836$	41.7640	1.44444
$837$	4.49394	0.155333
$838$	−26.7402	−0.923726
$839$	−32.1321	−1.10932	−0.554661	−	0.832076i	$-0.687152\pi$
$839$	−32.1321	−1.10932	−0.554661	+	0.832076i	$0.687152\pi$
$840$	0.186511	0.00643523
$841$	21.8543	0.753596
$842$	36.0017	1.24070
$843$	13.6857	0.471359
$844$	19.6181	0.675284
$845$	−0.263737	−0.00907282
$846$	26.7171	0.918552
$847$	6.03116	0.207233
$848$	−20.7200	−0.711527
$849$	−12.2261	−0.419600
$850$	−13.1222	−0.450089
$851$	0	0
$852$	−18.2040	−0.623660
$853$	16.5678	0.567269	0.283635	−	0.958932i	$-0.408460\pi$
$853$	16.5678	0.567269	0.283635	+	0.958932i	$0.408460\pi$
$854$	33.5954	1.14961
$855$	5.57556	0.190680
$856$	1.68419	0.0575644
$857$	−4.62567	−0.158010	−0.0790049	−	0.996874i	$-0.525174\pi$
$857$	−4.62567	−0.158010	−0.0790049	+	0.996874i	$0.525174\pi$
$858$	27.3640	0.934192
$859$	0.144134	0.00491780	0.00245890	−	0.999997i	$-0.499217\pi$
$859$	0.144134	0.00491780	0.00245890	+	0.999997i	$0.499217\pi$
$860$	14.0582	0.479382
$861$	−11.0000	−0.374878
$862$	−20.5632	−0.700386
$863$	7.86532	0.267739	0.133869	−	0.990999i	$-0.457260\pi$
$863$	7.86532	0.267739	0.133869	+	0.990999i	$0.457260\pi$
$864$	7.93116	0.269823
$865$	−17.5416	−0.596431
$866$	−21.4160	−0.727746
$867$	−26.7169	−0.907354
$868$	−13.3840	−0.454282
$869$	−15.6723	−0.531647
$870$	−14.1529	−0.479830
$871$	−20.2141	−0.684927
$872$	1.60300	0.0542843
$873$	−6.28649	−0.212765
$874$	0	0
$875$	1.53611	0.0519299
$876$	−6.59250	−0.222740
$877$	−38.8569	−1.31211	−0.656053	−	0.754715i	$-0.727775\pi$
$877$	−38.8569	−1.31211	−0.656053	+	0.754715i	$0.727775\pi$
$878$	−10.0260	−0.338360
$879$	−21.1747	−0.714204
$880$	−15.9121	−0.536396
$881$	47.7332	1.60817	0.804086	−	0.594513i	$-0.202655\pi$
$881$	47.7332	1.60817	0.804086	+	0.594513i	$0.202655\pi$
$882$	−9.20951	−0.310100
$883$	14.8650	0.500246	0.250123	−	0.968214i	$-0.419529\pi$
$883$	14.8650	0.500246	0.250123	+	0.968214i	$0.419529\pi$
$884$	45.7492	1.53871
$885$	1.15296	0.0387562
$886$	41.8845	1.40714
$887$	50.7868	1.70525	0.852627	−	0.522519i	$-0.175008\pi$
$887$	50.7868	1.70525	0.852627	+	0.522519i	$0.175008\pi$
$888$	−0.231742	−0.00777675
$889$	10.9732	0.368029
$890$	−23.0818	−0.773704
$891$	3.86345	0.129431
$892$	−15.8741	−0.531504
$893$	75.0575	2.51170
$894$	13.7396	0.459520
$895$	−1.47309	−0.0492401
$896$	1.49139	0.0498238
$897$	0	0
$898$	−78.6173	−2.62349
$899$	−32.0472	−1.06884
$900$	1.93882	0.0646274
$901$	−33.2631	−1.10816
$902$	54.9071	1.82821
$903$	−11.1382	−0.370655
$904$	0.690751	0.0229740
$905$	3.39108	0.112723
$906$	5.07567	0.168628
$907$	56.9105	1.88968	0.944842	−	0.327528i	$-0.106215\pi$
$907$	56.9105	1.88968	0.944842	+	0.327528i	$0.106215\pi$
$908$	29.5841	0.981784
$909$	11.4449	0.379603
$910$	−10.8799	−0.360665
$911$	−56.2949	−1.86513	−0.932566	−	0.360999i	$-0.882436\pi$
$911$	−56.2949	−1.86513	−0.932566	+	0.360999i	$0.882436\pi$
$912$	22.9636	0.760400
$913$	36.9387	1.22249
$914$	73.4514	2.42956
$915$	−11.0198	−0.364305
$916$	33.3472	1.10182
$917$	33.6796	1.11220
$918$	13.1222	0.433098
$919$	−30.2566	−0.998074	−0.499037	−	0.866581i	$-0.666313\pi$
$919$	−30.2566	−0.998074	−0.499037	+	0.866581i	$0.666313\pi$
$920$	0	0
$921$	−10.8568	−0.357745
$922$	−48.4605	−1.59596
$923$	−33.5082	−1.10294
$924$	−11.5063	−0.378528
$925$	−1.90863	−0.0627554
$926$	40.5795	1.33352
$927$	6.86891	0.225605
$928$	−56.5588	−1.85663
$929$	−54.8350	−1.79908	−0.899539	−	0.436840i	$-0.856098\pi$
$929$	−54.8350	−1.79908	−0.899539	+	0.436840i	$0.856098\pi$
$930$	8.91887	0.292461
$931$	−25.8727	−0.847944
$932$	−23.4239	−0.767275
$933$	−32.2095	−1.05449
$934$	−25.2563	−0.826410
$935$	−25.5447	−0.835400
$936$	0.433315	0.0141633
$937$	−43.9292	−1.43511	−0.717553	−	0.696504i	$-0.754738\pi$
$937$	−43.9292	−1.43511	−0.717553	+	0.696504i	$0.754738\pi$
$938$	17.2678	0.563814
$939$	12.6901	0.414126
$940$	26.1002	0.851294
$941$	−18.2036	−0.593422	−0.296711	−	0.954967i	$-0.595890\pi$
$941$	−18.2036	−0.593422	−0.296711	+	0.954967i	$0.595890\pi$
$942$	11.9240	0.388503
$943$	0	0
$944$	4.74858	0.154553
$945$	−1.53611	−0.0499695
$946$	55.5971	1.80762
$947$	46.7414	1.51889	0.759446	−	0.650570i	$-0.225470\pi$
$947$	46.7414	1.51889	0.759446	+	0.650570i	$0.225470\pi$
$948$	7.86494	0.255442
$949$	−12.1348	−0.393913
$950$	11.0655	0.359013
$951$	30.6393	0.993546
$952$	1.23319	0.0399678
$953$	−30.5781	−0.990522	−0.495261	−	0.868744i	$-0.664928\pi$
$953$	−30.5781	−0.990522	−0.495261	+	0.868744i	$0.664928\pi$
$954$	9.98439	0.323257
$955$	13.1408	0.425227
$956$	−24.6242	−0.796403
$957$	−27.5511	−0.890601
$958$	53.5119	1.72889
$959$	−16.9480	−0.547279
$960$	7.50331	0.242168
$961$	−10.8045	−0.348533
$962$	13.5184	0.435852
$963$	−13.8710	−0.446987
$964$	−32.3961	−1.04341
$965$	9.42258	0.303324
$966$	0	0
$967$	−12.4368	−0.399942	−0.199971	−	0.979802i	$-0.564085\pi$
$967$	−12.4368	−0.399942	−0.199971	+	0.979802i	$0.564085\pi$
$968$	−0.476719	−0.0153223
$969$	36.8649	1.18427
$970$	−12.4765	−0.400595
$971$	−23.5044	−0.754292	−0.377146	−	0.926154i	$-0.623095\pi$
$971$	−23.5044	−0.754292	−0.377146	+	0.926154i	$0.623095\pi$
$972$	−1.93882	−0.0621877
$973$	28.9971	0.929603
$974$	38.9667	1.24857
$975$	3.56879	0.114293
$976$	−45.3865	−1.45279
$977$	18.3924	0.588424	0.294212	−	0.955740i	$-0.404943\pi$
$977$	18.3924	0.588424	0.294212	+	0.955740i	$0.404943\pi$
$978$	2.88166	0.0921452
$979$	−44.9326	−1.43605
$980$	−8.99687	−0.287394
$981$	−13.2023	−0.421517
$982$	−83.8703	−2.67641
$983$	−49.0284	−1.56376	−0.781882	−	0.623427i	$-0.785740\pi$
$983$	−49.0284	−1.56376	−0.781882	+	0.623427i	$0.785740\pi$
$984$	0.869466	0.0277176
$985$	13.9220	0.443593
$986$	−93.5775	−2.98012
$987$	−20.6789	−0.658216
$988$	−38.5787	−1.22735
$989$	0	0
$990$	7.66759	0.243692
$991$	−52.1834	−1.65766	−0.828831	−	0.559500i	$-0.810993\pi$
$991$	−52.1834	−1.65766	−0.828831	+	0.559500i	$0.810993\pi$
$992$	35.6421	1.13164
$993$	18.6065	0.590460
$994$	28.6243	0.907906
$995$	18.8217	0.596688
$996$	−18.5372	−0.587373
$997$	−10.9206	−0.345857	−0.172929	−	0.984934i	$-0.555323\pi$
$997$	−10.9206	−0.345857	−0.172929	+	0.984934i	$0.555323\pi$
$998$	−9.48927	−0.300378
$999$	1.90863	0.0603864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bu.1.21		25
23.3	even	11		345.2.m.d.331.1	yes	50
23.8	even	11		345.2.m.d.271.1	✓	50
23.22	odd	2		7935.2.a.bt.1.21		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.271.1	✓	50	23.8	even	11
345.2.m.d.331.1	yes	50	23.3	even	11
7935.2.a.bt.1.21		25	23.22	odd	2
7935.2.a.bu.1.21		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+1.98465 q^{2} -1.00000 q^{3} +1.93882 q^{4} +1.00000 q^{5} -1.98465 q^{6} +1.53611 q^{7} -0.121418 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.98465 q^{2} -1.00000 q^{3} +1.93882 q^{4} +1.00000 q^{5} -1.98465 q^{6} +1.53611 q^{7} -0.121418 q^{8} +1.00000 q^{9} +1.98465 q^{10} +3.86345 q^{11} -1.93882 q^{12} -3.56879 q^{13} +3.04863 q^{14} -1.00000 q^{15} -4.11861 q^{16} -6.61188 q^{17} +1.98465 q^{18} +5.57556 q^{19} +1.93882 q^{20} -1.53611 q^{21} +7.66759 q^{22} +0.121418 q^{24} +1.00000 q^{25} -7.08279 q^{26} -1.00000 q^{27} +2.97823 q^{28} +7.13122 q^{29} -1.98465 q^{30} -4.49394 q^{31} -7.93116 q^{32} -3.86345 q^{33} -13.1222 q^{34} +1.53611 q^{35} +1.93882 q^{36} -1.90863 q^{37} +11.0655 q^{38} +3.56879 q^{39} -0.121418 q^{40} +7.16094 q^{41} -3.04863 q^{42} +7.25092 q^{43} +7.49054 q^{44} +1.00000 q^{45} +13.4619 q^{47} +4.11861 q^{48} -4.64038 q^{49} +1.98465 q^{50} +6.61188 q^{51} -6.91925 q^{52} +5.03082 q^{53} -1.98465 q^{54} +3.86345 q^{55} -0.186511 q^{56} -5.57556 q^{57} +14.1529 q^{58} -1.15296 q^{59} -1.93882 q^{60} +11.0198 q^{61} -8.91887 q^{62} +1.53611 q^{63} -7.50331 q^{64} -3.56879 q^{65} -7.66759 q^{66} +5.66412 q^{67} -12.8192 q^{68} +3.04863 q^{70} +9.38923 q^{71} -0.121418 q^{72} +3.40026 q^{73} -3.78796 q^{74} -1.00000 q^{75} +10.8100 q^{76} +5.93467 q^{77} +7.08279 q^{78} -4.05656 q^{79} -4.11861 q^{80} +1.00000 q^{81} +14.2119 q^{82} +9.56105 q^{83} -2.97823 q^{84} -6.61188 q^{85} +14.3905 q^{86} -7.13122 q^{87} -0.469092 q^{88} -11.6302 q^{89} +1.98465 q^{90} -5.48204 q^{91} +4.49394 q^{93} +26.7171 q^{94} +5.57556 q^{95} +7.93116 q^{96} -6.28649 q^{97} -9.20951 q^{98} +3.86345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * q^99

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