LMFDB - Embedded newform 1205.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37469 q^{2} +1.45345 q^{3} +3.63916 q^{4} -1.00000 q^{5} -3.45148 q^{6} +1.94580 q^{7} -3.89249 q^{8} -0.887497 q^{9} +O(q^{10})$	\(q-2.37469 q^{2} +1.45345 q^{3} +3.63916 q^{4} -1.00000 q^{5} -3.45148 q^{6} +1.94580 q^{7} -3.89249 q^{8} -0.887497 q^{9} +2.37469 q^{10} -6.31948 q^{11} +5.28931 q^{12} -2.12627 q^{13} -4.62068 q^{14} -1.45345 q^{15} +1.96514 q^{16} -0.676897 q^{17} +2.10753 q^{18} +6.14644 q^{19} -3.63916 q^{20} +2.82812 q^{21} +15.0068 q^{22} +1.31595 q^{23} -5.65752 q^{24} +1.00000 q^{25} +5.04924 q^{26} -5.65026 q^{27} +7.08108 q^{28} +7.00174 q^{29} +3.45148 q^{30} +6.77673 q^{31} +3.11837 q^{32} -9.18502 q^{33} +1.60742 q^{34} -1.94580 q^{35} -3.22974 q^{36} +6.97024 q^{37} -14.5959 q^{38} -3.09042 q^{39} +3.89249 q^{40} +7.66596 q^{41} -6.71590 q^{42} +6.41837 q^{43} -22.9976 q^{44} +0.887497 q^{45} -3.12498 q^{46} +1.24652 q^{47} +2.85622 q^{48} -3.21385 q^{49} -2.37469 q^{50} -0.983833 q^{51} -7.73784 q^{52} -0.377822 q^{53} +13.4176 q^{54} +6.31948 q^{55} -7.57401 q^{56} +8.93351 q^{57} -16.6270 q^{58} +11.9093 q^{59} -5.28931 q^{60} +9.81677 q^{61} -16.0926 q^{62} -1.72689 q^{63} -11.3355 q^{64} +2.12627 q^{65} +21.8116 q^{66} -2.68659 q^{67} -2.46333 q^{68} +1.91267 q^{69} +4.62068 q^{70} +6.49279 q^{71} +3.45457 q^{72} -6.10212 q^{73} -16.5522 q^{74} +1.45345 q^{75} +22.3678 q^{76} -12.2965 q^{77} +7.33880 q^{78} +6.30483 q^{79} -1.96514 q^{80} -5.54986 q^{81} -18.2043 q^{82} -15.5091 q^{83} +10.2920 q^{84} +0.676897 q^{85} -15.2416 q^{86} +10.1766 q^{87} +24.5985 q^{88} -11.1197 q^{89} -2.10753 q^{90} -4.13731 q^{91} +4.78896 q^{92} +9.84960 q^{93} -2.96011 q^{94} -6.14644 q^{95} +4.53238 q^{96} +1.84760 q^{97} +7.63191 q^{98} +5.60852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.37469	−1.67916	−0.839580	−	0.543236i	$-0.817199\pi$
$2$	−2.37469	−1.67916	−0.839580	+	0.543236i	$0.817199\pi$
$3$	1.45345	0.839147	0.419573	−	0.907721i	$-0.362180\pi$
$3$	1.45345	0.839147	0.419573	+	0.907721i	$0.362180\pi$
$4$	3.63916	1.81958
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.45148	−1.40906
$7$	1.94580	0.735444	0.367722	−	0.929936i	$-0.380138\pi$
$7$	1.94580	0.735444	0.367722	+	0.929936i	$0.380138\pi$
$8$	−3.89249	−1.37620
$9$	−0.887497	−0.295832
$10$	2.37469	0.750943
$11$	−6.31948	−1.90539	−0.952697	−	0.303920i	$-0.901704\pi$
$11$	−6.31948	−1.90539	−0.952697	+	0.303920i	$0.901704\pi$
$12$	5.28931	1.52689
$13$	−2.12627	−0.589722	−0.294861	−	0.955540i	$-0.595273\pi$
$13$	−2.12627	−0.589722	−0.294861	+	0.955540i	$0.595273\pi$
$14$	−4.62068	−1.23493
$15$	−1.45345	−0.375278
$16$	1.96514	0.491285
$17$	−0.676897	−0.164172	−0.0820858	−	0.996625i	$-0.526158\pi$
$17$	−0.676897	−0.164172	−0.0820858	+	0.996625i	$0.526158\pi$
$18$	2.10753	0.496750
$19$	6.14644	1.41009	0.705045	−	0.709163i	$-0.250927\pi$
$19$	6.14644	1.41009	0.705045	+	0.709163i	$0.250927\pi$
$20$	−3.63916	−0.813740
$21$	2.82812	0.617146
$22$	15.0068	3.19946
$23$	1.31595	0.274395	0.137198	−	0.990544i	$-0.456190\pi$
$23$	1.31595	0.274395	0.137198	+	0.990544i	$0.456190\pi$
$24$	−5.65752	−1.15484
$25$	1.00000	0.200000
$26$	5.04924	0.990238
$27$	−5.65026	−1.08739
$28$	7.08108	1.33820
$29$	7.00174	1.30019	0.650095	−	0.759853i	$-0.274729\pi$
$29$	7.00174	1.30019	0.650095	+	0.759853i	$0.274729\pi$
$30$	3.45148	0.630152
$31$	6.77673	1.21714	0.608568	−	0.793502i	$-0.291744\pi$
$31$	6.77673	1.21714	0.608568	+	0.793502i	$0.291744\pi$
$32$	3.11837	0.551256
$33$	−9.18502	−1.59891
$34$	1.60742	0.275670
$35$	−1.94580	−0.328901
$36$	−3.22974	−0.538290
$37$	6.97024	1.14590	0.572950	−	0.819590i	$-0.305799\pi$
$37$	6.97024	1.14590	0.572950	+	0.819590i	$0.305799\pi$
$38$	−14.5959	−2.36777
$39$	−3.09042	−0.494864
$40$	3.89249	0.615456
$41$	7.66596	1.19722	0.598611	−	0.801040i	$-0.295720\pi$
$41$	7.66596	1.19722	0.598611	+	0.801040i	$0.295720\pi$
$42$	−6.71590	−1.03629
$43$	6.41837	0.978793	0.489396	−	0.872062i	$-0.337217\pi$
$43$	6.41837	0.978793	0.489396	+	0.872062i	$0.337217\pi$
$44$	−22.9976	−3.46701
$45$	0.887497	0.132300
$46$	−3.12498	−0.460754
$47$	1.24652	0.181824	0.0909120	−	0.995859i	$-0.471022\pi$
$47$	1.24652	0.181824	0.0909120	+	0.995859i	$0.471022\pi$
$48$	2.85622	0.412260
$49$	−3.21385	−0.459122
$50$	−2.37469	−0.335832
$51$	−0.983833	−0.137764
$52$	−7.73784	−1.07305
$53$	−0.377822	−0.0518978	−0.0259489	−	0.999663i	$-0.508261\pi$
$53$	−0.377822	−0.0518978	−0.0259489	+	0.999663i	$0.508261\pi$
$54$	13.4176	1.82591
$55$	6.31948	0.852119
$56$	−7.57401	−1.01212
$57$	8.93351	1.18327
$58$	−16.6270	−2.18323
$59$	11.9093	1.55047	0.775233	−	0.631676i	$-0.217633\pi$
$59$	11.9093	1.55047	0.775233	+	0.631676i	$0.217633\pi$
$60$	−5.28931	−0.682847
$61$	9.81677	1.25691	0.628454	−	0.777846i	$-0.283688\pi$
$61$	9.81677	1.25691	0.628454	+	0.777846i	$0.283688\pi$
$62$	−16.0926	−2.04377
$63$	−1.72689	−0.217568
$64$	−11.3355	−1.41693
$65$	2.12627	0.263732
$66$	21.8116	2.68482
$67$	−2.68659	−0.328219	−0.164109	−	0.986442i	$-0.552475\pi$
$67$	−2.68659	−0.328219	−0.164109	+	0.986442i	$0.552475\pi$
$68$	−2.46333	−0.298723
$69$	1.91267	0.230258
$70$	4.62068	0.552277
$71$	6.49279	0.770552	0.385276	−	0.922801i	$-0.374106\pi$
$71$	6.49279	0.770552	0.385276	+	0.922801i	$0.374106\pi$
$72$	3.45457	0.407125
$73$	−6.10212	−0.714199	−0.357099	−	0.934066i	$-0.616234\pi$
$73$	−6.10212	−0.714199	−0.357099	+	0.934066i	$0.616234\pi$
$74$	−16.5522	−1.92415
$75$	1.45345	0.167829
$76$	22.3678	2.56577
$77$	−12.2965	−1.40131
$78$	7.33880	0.830955
$79$	6.30483	0.709349	0.354675	−	0.934990i	$-0.384592\pi$
$79$	6.30483	0.709349	0.354675	+	0.934990i	$0.384592\pi$
$80$	−1.96514	−0.219709
$81$	−5.54986	−0.616651
$82$	−18.2043	−2.01033
$83$	−15.5091	−1.70235	−0.851173	−	0.524886i	$-0.824108\pi$
$83$	−15.5091	−1.70235	−0.851173	+	0.524886i	$0.824108\pi$
$84$	10.2920	1.12294
$85$	0.676897	0.0734198
$86$	−15.2416	−1.64355
$87$	10.1766	1.09105
$88$	24.5985	2.62221
$89$	−11.1197	−1.17869	−0.589344	−	0.807882i	$-0.700614\pi$
$89$	−11.1197	−1.17869	−0.589344	+	0.807882i	$0.700614\pi$
$90$	−2.10753	−0.222153
$91$	−4.13731	−0.433708
$92$	4.78896	0.499284
$93$	9.84960	1.02136
$94$	−2.96011	−0.305312
$95$	−6.14644	−0.630611
$96$	4.53238	0.462584
$97$	1.84760	0.187595	0.0937977	−	0.995591i	$-0.470099\pi$
$97$	1.84760	0.187595	0.0937977	+	0.995591i	$0.470099\pi$
$98$	7.63191	0.770939
$99$	5.60852	0.563678
$100$	3.63916	0.363916
$101$	4.53390	0.451140	0.225570	−	0.974227i	$-0.427576\pi$
$101$	4.53390	0.451140	0.225570	+	0.974227i	$0.427576\pi$
$102$	2.33630	0.231328
$103$	−5.68958	−0.560611	−0.280306	−	0.959911i	$-0.590436\pi$
$103$	−5.68958	−0.560611	−0.280306	+	0.959911i	$0.590436\pi$
$104$	8.27650	0.811577
$105$	−2.82812	−0.275996
$106$	0.897210	0.0871447
$107$	−3.08010	−0.297765	−0.148882	−	0.988855i	$-0.547568\pi$
$107$	−3.08010	−0.297765	−0.148882	+	0.988855i	$0.547568\pi$
$108$	−20.5622	−1.97860
$109$	−0.552152	−0.0528865	−0.0264433	−	0.999650i	$-0.508418\pi$
$109$	−0.552152	−0.0528865	−0.0264433	+	0.999650i	$0.508418\pi$
$110$	−15.0068	−1.43084
$111$	10.1309	0.961579
$112$	3.82377	0.361313
$113$	15.7844	1.48488	0.742438	−	0.669915i	$-0.233670\pi$
$113$	15.7844	1.48488	0.742438	+	0.669915i	$0.233670\pi$
$114$	−21.2143	−1.98690
$115$	−1.31595	−0.122713
$116$	25.4804	2.36580
$117$	1.88706	0.174459
$118$	−28.2810	−2.60348
$119$	−1.31711	−0.120739
$120$	5.65752	0.516458
$121$	28.9358	2.63053
$122$	−23.3118	−2.11055
$123$	11.1420	1.00464
$124$	24.6616	2.21467
$125$	−1.00000	−0.0894427
$126$	4.10084	0.365332
$127$	−16.7481	−1.48615	−0.743075	−	0.669208i	$-0.766633\pi$
$127$	−16.7481	−1.48615	−0.743075	+	0.669208i	$0.766633\pi$
$128$	20.6814	1.82800
$129$	9.32875	0.821351
$130$	−5.04924	−0.442848
$131$	18.4735	1.61404	0.807018	−	0.590527i	$-0.201080\pi$
$131$	18.4735	1.61404	0.807018	+	0.590527i	$0.201080\pi$
$132$	−33.4257	−2.90933
$133$	11.9597	1.03704
$134$	6.37981	0.551132
$135$	5.65026	0.486297
$136$	2.63481	0.225933
$137$	2.84423	0.242999	0.121499	−	0.992592i	$-0.461230\pi$
$137$	2.84423	0.242999	0.121499	+	0.992592i	$0.461230\pi$
$138$	−4.54199	−0.386640
$139$	−5.19758	−0.440853	−0.220426	−	0.975404i	$-0.570745\pi$
$139$	−5.19758	−0.440853	−0.220426	+	0.975404i	$0.570745\pi$
$140$	−7.08108	−0.598460
$141$	1.81175	0.152577
$142$	−15.4184	−1.29388
$143$	13.4370	1.12365
$144$	−1.74406	−0.145338
$145$	−7.00174	−0.581463
$146$	14.4906	1.19925
$147$	−4.67116	−0.385271
$148$	25.3658	2.08506
$149$	−11.4402	−0.937222	−0.468611	−	0.883405i	$-0.655245\pi$
$149$	−11.4402	−0.937222	−0.468611	+	0.883405i	$0.655245\pi$
$150$	−3.45148	−0.281812
$151$	2.21951	0.180621	0.0903106	−	0.995914i	$-0.471214\pi$
$151$	2.21951	0.180621	0.0903106	+	0.995914i	$0.471214\pi$
$152$	−23.9249	−1.94057
$153$	0.600744	0.0485673
$154$	29.2003	2.35303
$155$	−6.77673	−0.544320
$156$	−11.2465	−0.900443
$157$	16.6395	1.32797	0.663987	−	0.747744i	$-0.268863\pi$
$157$	16.6395	1.32797	0.663987	+	0.747744i	$0.268863\pi$
$158$	−14.9720	−1.19111
$159$	−0.549143	−0.0435499
$160$	−3.11837	−0.246529
$161$	2.56059	0.201802
$162$	13.1792	1.03546
$163$	−17.2008	−1.34727	−0.673634	−	0.739066i	$-0.735267\pi$
$163$	−17.2008	−1.34727	−0.673634	+	0.739066i	$0.735267\pi$
$164$	27.8976	2.17844
$165$	9.18502	0.715053
$166$	36.8293	2.85851
$167$	−1.40902	−0.109033	−0.0545165	−	0.998513i	$-0.517362\pi$
$167$	−1.40902	−0.109033	−0.0545165	+	0.998513i	$0.517362\pi$
$168$	−11.0084	−0.849317
$169$	−8.47896	−0.652227
$170$	−1.60742	−0.123284
$171$	−5.45494	−0.417150
$172$	23.3575	1.78099
$173$	21.7012	1.64991	0.824957	−	0.565195i	$-0.191199\pi$
$173$	21.7012	1.64991	0.824957	+	0.565195i	$0.191199\pi$
$174$	−24.1664	−1.83205
$175$	1.94580	0.147089
$176$	−12.4187	−0.936092
$177$	17.3096	1.30107
$178$	26.4059	1.97920
$179$	8.85585	0.661917	0.330959	−	0.943645i	$-0.392628\pi$
$179$	8.85585	0.661917	0.330959	+	0.943645i	$0.392628\pi$
$180$	3.22974	0.240731
$181$	12.2774	0.912575	0.456287	−	0.889832i	$-0.349179\pi$
$181$	12.2774	0.912575	0.456287	+	0.889832i	$0.349179\pi$
$182$	9.82483	0.728265
$183$	14.2681	1.05473
$184$	−5.12233	−0.377623
$185$	−6.97024	−0.512462
$186$	−23.3898	−1.71502
$187$	4.27764	0.312812
$188$	4.53629	0.330843
$189$	−10.9943	−0.799717
$190$	14.5959	1.05890
$191$	3.64730	0.263909	0.131955	−	0.991256i	$-0.457875\pi$
$191$	3.64730	0.263909	0.131955	+	0.991256i	$0.457875\pi$
$192$	−16.4755	−1.18901
$193$	19.8114	1.42605	0.713026	−	0.701137i	$-0.247324\pi$
$193$	19.8114	1.42605	0.713026	+	0.701137i	$0.247324\pi$
$194$	−4.38748	−0.315003
$195$	3.09042	0.221310
$196$	−11.6957	−0.835408
$197$	−25.4267	−1.81158	−0.905790	−	0.423728i	$-0.860721\pi$
$197$	−25.4267	−1.81158	−0.905790	+	0.423728i	$0.860721\pi$
$198$	−13.3185	−0.946505
$199$	24.6892	1.75017	0.875084	−	0.483970i	$-0.160806\pi$
$199$	24.6892	1.75017	0.875084	+	0.483970i	$0.160806\pi$
$200$	−3.89249	−0.275240
$201$	−3.90481	−0.275424
$202$	−10.7666	−0.757535
$203$	13.6240	0.956218
$204$	−3.58032	−0.250673
$205$	−7.66596	−0.535414
$206$	13.5110	0.941355
$207$	−1.16791	−0.0811750
$208$	−4.17843	−0.289722
$209$	−38.8423	−2.68678
$210$	6.71590	0.463441
$211$	−7.71155	−0.530885	−0.265443	−	0.964127i	$-0.585518\pi$
$211$	−7.71155	−0.530885	−0.265443	+	0.964127i	$0.585518\pi$
$212$	−1.37495	−0.0944321
$213$	9.43691	0.646606
$214$	7.31429	0.499995
$215$	−6.41837	−0.437729
$216$	21.9936	1.49647
$217$	13.1862	0.895135
$218$	1.31119	0.0888050
$219$	−8.86909	−0.599318
$220$	22.9976	1.55050
$221$	1.43927	0.0968157
$222$	−24.0577	−1.61464
$223$	−3.85783	−0.258339	−0.129170	−	0.991623i	$-0.541231\pi$
$223$	−3.85783	−0.258339	−0.129170	+	0.991623i	$0.541231\pi$
$224$	6.06774	0.405418
$225$	−0.887497	−0.0591665
$226$	−37.4832	−2.49334
$227$	7.77878	0.516296	0.258148	−	0.966105i	$-0.416888\pi$
$227$	7.77878	0.516296	0.258148	+	0.966105i	$0.416888\pi$
$228$	32.5104	2.15306
$229$	−21.5006	−1.42080	−0.710400	−	0.703799i	$-0.751486\pi$
$229$	−21.5006	−1.42080	−0.710400	+	0.703799i	$0.751486\pi$
$230$	3.12498	0.206055
$231$	−17.8722	−1.17591
$232$	−27.2542	−1.78933
$233$	−19.8180	−1.29832	−0.649159	−	0.760653i	$-0.724879\pi$
$233$	−19.8180	−1.29832	−0.649159	+	0.760653i	$0.724879\pi$
$234$	−4.48119	−0.292945
$235$	−1.24652	−0.0813142
$236$	43.3400	2.82119
$237$	9.16373	0.595248
$238$	3.12772	0.202740
$239$	−15.3987	−0.996062	−0.498031	−	0.867159i	$-0.665943\pi$
$239$	−15.3987	−0.996062	−0.498031	+	0.867159i	$0.665943\pi$
$240$	−2.85622	−0.184368
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−68.7136	−4.41708
$243$	8.88438	0.569933
$244$	35.7248	2.28704
$245$	3.21385	0.205326
$246$	−26.4589	−1.68696
$247$	−13.0690	−0.831561
$248$	−26.3783	−1.67502
$249$	−22.5416	−1.42852
$250$	2.37469	0.150189
$251$	−5.13124	−0.323881	−0.161940	−	0.986801i	$-0.551775\pi$
$251$	−5.13124	−0.323881	−0.161940	+	0.986801i	$0.551775\pi$
$252$	−6.28443	−0.395882
$253$	−8.31614	−0.522831
$254$	39.7714	2.49548
$255$	0.983833	0.0616100
$256$	−26.4411	−1.65257
$257$	−11.5216	−0.718698	−0.359349	−	0.933203i	$-0.617001\pi$
$257$	−11.5216	−0.718698	−0.359349	+	0.933203i	$0.617001\pi$
$258$	−22.1529	−1.37918
$259$	13.5627	0.842746
$260$	7.73784	0.479881
$261$	−6.21403	−0.384639
$262$	−43.8688	−2.71022
$263$	2.35498	0.145215	0.0726073	−	0.997361i	$-0.476868\pi$
$263$	2.35498	0.145215	0.0726073	+	0.997361i	$0.476868\pi$
$264$	35.7526	2.20042
$265$	0.377822	0.0232094
$266$	−28.4007	−1.74136
$267$	−16.1619	−0.989092
$268$	−9.77690	−0.597219
$269$	21.6050	1.31728	0.658641	−	0.752457i	$-0.271131\pi$
$269$	21.6050	1.31728	0.658641	+	0.752457i	$0.271131\pi$
$270$	−13.4176	−0.816571
$271$	−24.3395	−1.47852	−0.739260	−	0.673420i	$-0.764825\pi$
$271$	−24.3395	−1.47852	−0.739260	+	0.673420i	$0.764825\pi$
$272$	−1.33020	−0.0806551
$273$	−6.01335	−0.363945
$274$	−6.75416	−0.408034
$275$	−6.31948	−0.381079
$276$	6.96049	0.418972
$277$	17.1220	1.02876	0.514382	−	0.857561i	$-0.328021\pi$
$277$	17.1220	1.02876	0.514382	+	0.857561i	$0.328021\pi$
$278$	12.3426	0.740262
$279$	−6.01433	−0.360068
$280$	7.57401	0.452634
$281$	−4.64508	−0.277103	−0.138551	−	0.990355i	$-0.544245\pi$
$281$	−4.64508	−0.277103	−0.138551	+	0.990355i	$0.544245\pi$
$282$	−4.30235	−0.256201
$283$	−21.2889	−1.26549	−0.632746	−	0.774360i	$-0.718072\pi$
$283$	−21.2889	−1.26549	−0.632746	+	0.774360i	$0.718072\pi$
$284$	23.6283	1.40208
$285$	−8.93351	−0.529175
$286$	−31.9086	−1.88680
$287$	14.9164	0.880489
$288$	−2.76755	−0.163079
$289$	−16.5418	−0.973048
$290$	16.6270	0.976369
$291$	2.68539	0.157420
$292$	−22.2066	−1.29954
$293$	−20.1321	−1.17613	−0.588064	−	0.808815i	$-0.700110\pi$
$293$	−20.1321	−1.17613	−0.588064	+	0.808815i	$0.700110\pi$
$294$	11.0926	0.646931
$295$	−11.9093	−0.693389
$296$	−27.1316	−1.57699
$297$	35.7067	2.07191
$298$	27.1670	1.57374
$299$	−2.79808	−0.161817
$300$	5.28931	0.305379
$301$	12.4889	0.719847
$302$	−5.27065	−0.303292
$303$	6.58977	0.378572
$304$	12.0786	0.692756
$305$	−9.81677	−0.562107
$306$	−1.42658	−0.0815522
$307$	17.9777	1.02604	0.513021	−	0.858376i	$-0.328526\pi$
$307$	17.9777	1.02604	0.513021	+	0.858376i	$0.328526\pi$
$308$	−44.7487	−2.54979
$309$	−8.26949	−0.470435
$310$	16.0926	0.914000
$311$	4.33522	0.245828	0.122914	−	0.992417i	$-0.460776\pi$
$311$	4.33522	0.245828	0.122914	+	0.992417i	$0.460776\pi$
$312$	12.0294	0.681032
$313$	−0.444130	−0.0251037	−0.0125519	−	0.999921i	$-0.503995\pi$
$313$	−0.444130	−0.0251037	−0.0125519	+	0.999921i	$0.503995\pi$
$314$	−39.5136	−2.22988
$315$	1.72689	0.0972994
$316$	22.9443	1.29072
$317$	12.6255	0.709118	0.354559	−	0.935034i	$-0.384631\pi$
$317$	12.6255	0.709118	0.354559	+	0.935034i	$0.384631\pi$
$318$	1.30405	0.0731272
$319$	−44.2474	−2.47738
$320$	11.3355	0.633671
$321$	−4.47676	−0.249868
$322$	−6.08060	−0.338858
$323$	−4.16050	−0.231497
$324$	−20.1968	−1.12204
$325$	−2.12627	−0.117944
$326$	40.8465	2.26228
$327$	−0.802522	−0.0443796
$328$	−29.8396	−1.64762
$329$	2.42549	0.133721
$330$	−21.8116	−1.20069
$331$	20.6605	1.13561	0.567803	−	0.823165i	$-0.307794\pi$
$331$	20.6605	1.13561	0.567803	+	0.823165i	$0.307794\pi$
$332$	−56.4400	−3.09755
$333$	−6.18607	−0.338995
$334$	3.34598	0.183084
$335$	2.68659	0.146784
$336$	5.55765	0.303194
$337$	14.8894	0.811079	0.405540	−	0.914077i	$-0.367084\pi$
$337$	14.8894	0.811079	0.405540	+	0.914077i	$0.367084\pi$
$338$	20.1349	1.09519
$339$	22.9418	1.24603
$340$	2.46333	0.133593
$341$	−42.8254	−2.31912
$342$	12.9538	0.700462
$343$	−19.8741	−1.07310
$344$	−24.9834	−1.34702
$345$	−1.91267	−0.102975
$346$	−51.5337	−2.77047
$347$	2.47806	0.133029	0.0665147	−	0.997785i	$-0.478812\pi$
$347$	2.47806	0.133029	0.0665147	+	0.997785i	$0.478812\pi$
$348$	37.0344	1.98525
$349$	2.33925	0.125217	0.0626087	−	0.998038i	$-0.480058\pi$
$349$	2.33925	0.125217	0.0626087	+	0.998038i	$0.480058\pi$
$350$	−4.62068	−0.246986
$351$	12.0140	0.641261
$352$	−19.7065	−1.05036
$353$	−16.5361	−0.880126	−0.440063	−	0.897967i	$-0.645044\pi$
$353$	−16.5361	−0.880126	−0.440063	+	0.897967i	$0.645044\pi$
$354$	−41.1049	−2.18470
$355$	−6.49279	−0.344601
$356$	−40.4664	−2.14471
$357$	−1.91434	−0.101318
$358$	−21.0299	−1.11146
$359$	−0.520057	−0.0274475	−0.0137238	−	0.999906i	$-0.504369\pi$
$359$	−0.520057	−0.0274475	−0.0137238	+	0.999906i	$0.504369\pi$
$360$	−3.45457	−0.182072
$361$	18.7787	0.988351
$362$	−29.1551	−1.53236
$363$	42.0566	2.20740
$364$	−15.0563	−0.789165
$365$	6.10212	0.319399
$366$	−33.8824	−1.77106
$367$	22.3425	1.16627	0.583136	−	0.812375i	$-0.301826\pi$
$367$	22.3425	1.16627	0.583136	+	0.812375i	$0.301826\pi$
$368$	2.58603	0.134806
$369$	−6.80352	−0.354177
$370$	16.5522	0.860506
$371$	−0.735167	−0.0381679
$372$	35.8442	1.85844
$373$	19.8176	1.02612	0.513058	−	0.858354i	$-0.328513\pi$
$373$	19.8176	1.02612	0.513058	+	0.858354i	$0.328513\pi$
$374$	−10.1581	−0.525261
$375$	−1.45345	−0.0750556
$376$	−4.85207	−0.250227
$377$	−14.8876	−0.766752
$378$	26.1080	1.34285
$379$	−5.55700	−0.285444	−0.142722	−	0.989763i	$-0.545585\pi$
$379$	−5.55700	−0.285444	−0.142722	+	0.989763i	$0.545585\pi$
$380$	−22.3678	−1.14745
$381$	−24.3424	−1.24710
$382$	−8.66121	−0.443146
$383$	−17.1937	−0.878556	−0.439278	−	0.898351i	$-0.644766\pi$
$383$	−17.1937	−0.878556	−0.439278	+	0.898351i	$0.644766\pi$
$384$	30.0593	1.53396
$385$	12.2965	0.626685
$386$	−47.0458	−2.39457
$387$	−5.69629	−0.289559
$388$	6.72370	0.341344
$389$	27.8495	1.41202	0.706012	−	0.708199i	$-0.250492\pi$
$389$	27.8495	1.41202	0.706012	+	0.708199i	$0.250492\pi$
$390$	−7.33880	−0.371615
$391$	−0.890765	−0.0450479
$392$	12.5099	0.631845
$393$	26.8502	1.35441
$394$	60.3806	3.04193
$395$	−6.30483	−0.317231
$396$	20.4103	1.02566
$397$	−5.79577	−0.290881	−0.145441	−	0.989367i	$-0.546460\pi$
$397$	−5.79577	−0.290881	−0.145441	+	0.989367i	$0.546460\pi$
$398$	−58.6291	−2.93881
$399$	17.3828	0.870230
$400$	1.96514	0.0982570
$401$	36.2551	1.81049	0.905246	−	0.424889i	$-0.139687\pi$
$401$	36.2551	1.81049	0.905246	+	0.424889i	$0.139687\pi$
$402$	9.27270	0.462480
$403$	−14.4092	−0.717772
$404$	16.4996	0.820883
$405$	5.54986	0.275775
$406$	−32.3528	−1.60564
$407$	−44.0483	−2.18339
$408$	3.82956	0.189591
$409$	−2.83987	−0.140422	−0.0702112	−	0.997532i	$-0.522367\pi$
$409$	−2.83987	−0.140422	−0.0702112	+	0.997532i	$0.522367\pi$
$410$	18.2043	0.899045
$411$	4.13393	0.203912
$412$	−20.7053	−1.02008
$413$	23.1732	1.14028
$414$	2.77341	0.136306
$415$	15.5091	0.761312
$416$	−6.63052	−0.325088
$417$	−7.55439	−0.369940
$418$	92.2384	4.51153
$419$	22.7092	1.10942	0.554709	−	0.832045i	$-0.312830\pi$
$419$	22.7092	1.10942	0.554709	+	0.832045i	$0.312830\pi$
$420$	−10.2920	−0.502196
$421$	−10.9819	−0.535225	−0.267613	−	0.963527i	$-0.586235\pi$
$421$	−10.9819	−0.535225	−0.267613	+	0.963527i	$0.586235\pi$
$422$	18.3126	0.891441
$423$	−1.10629	−0.0537894
$424$	1.47067	0.0714219
$425$	−0.676897	−0.0328343
$426$	−22.4097	−1.08576
$427$	19.1015	0.924386
$428$	−11.2090	−0.541806
$429$	19.5299	0.942911
$430$	15.2416	0.735017
$431$	27.4307	1.32129	0.660646	−	0.750698i	$-0.270283\pi$
$431$	27.4307	1.32129	0.660646	+	0.750698i	$0.270283\pi$
$432$	−11.1036	−0.534220
$433$	−18.5951	−0.893623	−0.446812	−	0.894628i	$-0.647441\pi$
$433$	−18.5951	−0.893623	−0.446812	+	0.894628i	$0.647441\pi$
$434$	−31.3131	−1.50308
$435$	−10.1766	−0.487933
$436$	−2.00937	−0.0962312
$437$	8.08843	0.386922
$438$	21.0614	1.00635
$439$	9.72828	0.464305	0.232153	−	0.972679i	$-0.425423\pi$
$439$	9.72828	0.464305	0.232153	+	0.972679i	$0.425423\pi$
$440$	−24.5985	−1.17269
$441$	2.85229	0.135823
$442$	−3.41782	−0.162569
$443$	23.5808	1.12036	0.560178	−	0.828372i	$-0.310733\pi$
$443$	23.5808	1.12036	0.560178	+	0.828372i	$0.310733\pi$
$444$	36.8678	1.74967
$445$	11.1197	0.527125
$446$	9.16115	0.433793
$447$	−16.6278	−0.786467
$448$	−22.0565	−1.04207
$449$	17.4647	0.824209	0.412105	−	0.911137i	$-0.364794\pi$
$449$	17.4647	0.824209	0.412105	+	0.911137i	$0.364794\pi$
$450$	2.10753	0.0993500
$451$	−48.4449	−2.28118
$452$	57.4420	2.70185
$453$	3.22594	0.151568
$454$	−18.4722	−0.866943
$455$	4.13731	0.193960
$456$	−34.7736	−1.62842
$457$	19.8783	0.929867	0.464933	−	0.885346i	$-0.346078\pi$
$457$	19.8783	0.929867	0.464933	+	0.885346i	$0.346078\pi$
$458$	51.0573	2.38575
$459$	3.82465	0.178519
$460$	−4.78896	−0.223286
$461$	−25.6500	−1.19464	−0.597321	−	0.802002i	$-0.703768\pi$
$461$	−25.6500	−1.19464	−0.597321	+	0.802002i	$0.703768\pi$
$462$	42.4410	1.97453
$463$	−17.4651	−0.811672	−0.405836	−	0.913946i	$-0.633020\pi$
$463$	−17.4651	−0.811672	−0.405836	+	0.913946i	$0.633020\pi$
$464$	13.7594	0.638764
$465$	−9.84960	−0.456764
$466$	47.0615	2.18008
$467$	−2.44704	−0.113236	−0.0566178	−	0.998396i	$-0.518032\pi$
$467$	−2.44704	−0.113236	−0.0566178	+	0.998396i	$0.518032\pi$
$468$	6.86731	0.317442
$469$	−5.22756	−0.241386
$470$	2.96011	0.136540
$471$	24.1846	1.11437
$472$	−46.3570	−2.13375
$473$	−40.5608	−1.86499
$474$	−21.7610	−0.999517
$475$	6.14644	0.282018
$476$	−4.79316	−0.219694
$477$	0.335316	0.0153531
$478$	36.5673	1.67255
$479$	−37.4459	−1.71095	−0.855473	−	0.517847i	$-0.826734\pi$
$479$	−37.4459	−1.71095	−0.855473	+	0.517847i	$0.826734\pi$
$480$	−4.53238	−0.206874
$481$	−14.8206	−0.675763
$482$	−2.37469	−0.108164
$483$	3.72167	0.169342
$484$	105.302	4.78645
$485$	−1.84760	−0.0838952
$486$	−21.0977	−0.957009
$487$	30.6062	1.38690	0.693450	−	0.720505i	$-0.256090\pi$
$487$	30.6062	1.38690	0.693450	+	0.720505i	$0.256090\pi$
$488$	−38.2117	−1.72976
$489$	−25.0004	−1.13056
$490$	−7.63191	−0.344775
$491$	40.0423	1.80709	0.903543	−	0.428498i	$-0.140957\pi$
$491$	40.0423	1.80709	0.903543	+	0.428498i	$0.140957\pi$
$492$	40.5476	1.82803
$493$	−4.73946	−0.213454
$494$	31.0349	1.39632
$495$	−5.60852	−0.252084
$496$	13.3172	0.597961
$497$	12.6337	0.566698
$498$	53.5294	2.39871
$499$	−15.8608	−0.710025	−0.355012	−	0.934862i	$-0.615523\pi$
$499$	−15.8608	−0.710025	−0.355012	+	0.934862i	$0.615523\pi$
$500$	−3.63916	−0.162748
$501$	−2.04793	−0.0914948
$502$	12.1851	0.543848
$503$	−37.4314	−1.66899	−0.834493	−	0.551019i	$-0.814239\pi$
$503$	−37.4314	−1.66899	−0.834493	+	0.551019i	$0.814239\pi$
$504$	6.72191	0.299418
$505$	−4.53390	−0.201756
$506$	19.7483	0.877918
$507$	−12.3237	−0.547315
$508$	−60.9488	−2.70416
$509$	26.1850	1.16063	0.580315	−	0.814392i	$-0.302930\pi$
$509$	26.1850	1.16063	0.580315	+	0.814392i	$0.302930\pi$
$510$	−2.33630	−0.103453
$511$	−11.8735	−0.525253
$512$	21.4266	0.946931
$513$	−34.7290	−1.53332
$514$	27.3602	1.20681
$515$	5.68958	0.250713
$516$	33.9488	1.49451
$517$	−7.87738	−0.346447
$518$	−32.2072	−1.41510
$519$	31.5416	1.38452
$520$	−8.27650	−0.362948
$521$	27.9441	1.22425	0.612127	−	0.790759i	$-0.290314\pi$
$521$	27.9441	1.22425	0.612127	+	0.790759i	$0.290314\pi$
$522$	14.7564	0.645870
$523$	7.47199	0.326727	0.163364	−	0.986566i	$-0.447766\pi$
$523$	7.47199	0.326727	0.163364	+	0.986566i	$0.447766\pi$
$524$	67.2278	2.93686
$525$	2.82812	0.123429
$526$	−5.59236	−0.243838
$527$	−4.58715	−0.199819
$528$	−18.0498	−0.785519
$529$	−21.2683	−0.924707
$530$	−0.897210	−0.0389723
$531$	−10.5695	−0.458678
$532$	43.5234	1.88698
$533$	−16.2999	−0.706028
$534$	38.3795	1.66084
$535$	3.08010	0.133164
$536$	10.4575	0.451695
$537$	12.8715	0.555446
$538$	−51.3053	−2.21193
$539$	20.3099	0.874809
$540$	20.5622	0.884856
$541$	−0.108938	−0.00468363	−0.00234182	−	0.999997i	$-0.500745\pi$
$541$	−0.108938	−0.00468363	−0.00234182	+	0.999997i	$0.500745\pi$
$542$	57.7988	2.48267
$543$	17.8446	0.765785
$544$	−2.11082	−0.0905005
$545$	0.552152	0.0236516
$546$	14.2799	0.611121
$547$	−21.2574	−0.908901	−0.454450	−	0.890772i	$-0.650164\pi$
$547$	−21.2574	−0.908901	−0.454450	+	0.890772i	$0.650164\pi$
$548$	10.3506	0.442155
$549$	−8.71236	−0.371834
$550$	15.0068	0.639893
$551$	43.0358	1.83339
$552$	−7.44503	−0.316881
$553$	12.2680	0.521687
$554$	−40.6595	−1.72746
$555$	−10.1309	−0.430031
$556$	−18.9148	−0.802166
$557$	−16.5575	−0.701565	−0.350782	−	0.936457i	$-0.614084\pi$
$557$	−16.5575	−0.701565	−0.350782	+	0.936457i	$0.614084\pi$
$558$	14.2822	0.604612
$559$	−13.6472	−0.577216
$560$	−3.82377	−0.161584
$561$	6.21731	0.262495
$562$	11.0306	0.465299
$563$	45.1247	1.90178	0.950890	−	0.309529i	$-0.100171\pi$
$563$	45.1247	1.90178	0.950890	+	0.309529i	$0.100171\pi$
$564$	6.59325	0.277626
$565$	−15.7844	−0.664056
$566$	50.5545	2.12496
$567$	−10.7989	−0.453512
$568$	−25.2731	−1.06044
$569$	−15.3783	−0.644690	−0.322345	−	0.946622i	$-0.604471\pi$
$569$	−15.3783	−0.644690	−0.322345	+	0.946622i	$0.604471\pi$
$570$	21.2143	0.888570
$571$	36.9031	1.54435	0.772173	−	0.635412i	$-0.219170\pi$
$571$	36.9031	1.54435	0.772173	+	0.635412i	$0.219170\pi$
$572$	48.8991	2.04458
$573$	5.30115	0.221459
$574$	−35.4219	−1.47848
$575$	1.31595	0.0548791
$576$	10.0602	0.419174
$577$	5.07203	0.211151	0.105576	−	0.994411i	$-0.466331\pi$
$577$	5.07203	0.211151	0.105576	+	0.994411i	$0.466331\pi$
$578$	39.2817	1.63390
$579$	28.7947	1.19667
$580$	−25.4804	−1.05802
$581$	−30.1776	−1.25198
$582$	−6.37696	−0.264333
$583$	2.38764	0.0988859
$584$	23.7524	0.982882
$585$	−1.88706	−0.0780204
$586$	47.8074	1.97491
$587$	−17.2453	−0.711792	−0.355896	−	0.934526i	$-0.615824\pi$
$587$	−17.2453	−0.711792	−0.355896	+	0.934526i	$0.615824\pi$
$588$	−16.9991	−0.701030
$589$	41.6527	1.71627
$590$	28.2810	1.16431
$591$	−36.9563	−1.52018
$592$	13.6975	0.562964
$593$	−29.7137	−1.22020	−0.610098	−	0.792326i	$-0.708870\pi$
$593$	−29.7137	−1.22020	−0.610098	+	0.792326i	$0.708870\pi$
$594$	−84.7924	−3.47908
$595$	1.31711	0.0539961
$596$	−41.6328	−1.70535
$597$	35.8844	1.46865
$598$	6.64457	0.271717
$599$	28.6511	1.17065	0.585326	−	0.810798i	$-0.300966\pi$
$599$	28.6511	1.17065	0.585326	+	0.810798i	$0.300966\pi$
$600$	−5.65752	−0.230967
$601$	−7.82824	−0.319321	−0.159660	−	0.987172i	$-0.551040\pi$
$601$	−7.82824	−0.319321	−0.159660	+	0.987172i	$0.551040\pi$
$602$	−29.6572	−1.20874
$603$	2.38434	0.0970977
$604$	8.07715	0.328654
$605$	−28.9358	−1.17641
$606$	−15.6487	−0.635683
$607$	15.5685	0.631905	0.315952	−	0.948775i	$-0.397676\pi$
$607$	15.5685	0.631905	0.315952	+	0.948775i	$0.397676\pi$
$608$	19.1669	0.777320
$609$	19.8017	0.802407
$610$	23.3118	0.943867
$611$	−2.65045	−0.107226
$612$	2.18620	0.0883720
$613$	0.165594	0.00668828	0.00334414	−	0.999994i	$-0.498936\pi$
$613$	0.165594	0.00668828	0.00334414	+	0.999994i	$0.498936\pi$
$614$	−42.6915	−1.72289
$615$	−11.1420	−0.449291
$616$	47.8638	1.92849
$617$	40.5561	1.63273	0.816364	−	0.577537i	$-0.195986\pi$
$617$	40.5561	1.63273	0.816364	+	0.577537i	$0.195986\pi$
$618$	19.6375	0.789936
$619$	0.965977	0.0388259	0.0194129	−	0.999812i	$-0.493820\pi$
$619$	0.965977	0.0388259	0.0194129	+	0.999812i	$0.493820\pi$
$620$	−24.6616	−0.990432
$621$	−7.43549	−0.298376
$622$	−10.2948	−0.412784
$623$	−21.6368	−0.866859
$624$	−6.07312	−0.243119
$625$	1.00000	0.0400000
$626$	1.05467	0.0421531
$627$	−56.4551	−2.25460
$628$	60.5536	2.41635
$629$	−4.71814	−0.188124
$630$	−4.10084	−0.163381
$631$	−21.3544	−0.850104	−0.425052	−	0.905169i	$-0.639744\pi$
$631$	−21.3544	−0.850104	−0.425052	+	0.905169i	$0.639744\pi$
$632$	−24.5415	−0.976208
$633$	−11.2083	−0.445491
$634$	−29.9816	−1.19072
$635$	16.7481	0.664626
$636$	−1.99842	−0.0792424
$637$	6.83354	0.270755
$638$	105.074	4.15991
$639$	−5.76233	−0.227954
$640$	−20.6814	−0.817506
$641$	−45.5753	−1.80011	−0.900057	−	0.435772i	$-0.856475\pi$
$641$	−45.5753	−1.80011	−0.900057	+	0.435772i	$0.856475\pi$
$642$	10.6309	0.419569
$643$	−24.5050	−0.966382	−0.483191	−	0.875515i	$-0.660522\pi$
$643$	−24.5050	−0.966382	−0.483191	+	0.875515i	$0.660522\pi$
$644$	9.31837	0.367195
$645$	−9.32875	−0.367319
$646$	9.87991	0.388720
$647$	−16.2319	−0.638142	−0.319071	−	0.947731i	$-0.603371\pi$
$647$	−16.2319	−0.638142	−0.319071	+	0.947731i	$0.603371\pi$
$648$	21.6027	0.848636
$649$	−75.2609	−2.95425
$650$	5.04924	0.198048
$651$	19.1654	0.751150
$652$	−62.5962	−2.45146
$653$	−8.04806	−0.314945	−0.157472	−	0.987523i	$-0.550335\pi$
$653$	−8.04806	−0.314945	−0.157472	+	0.987523i	$0.550335\pi$
$654$	1.90574	0.0745204
$655$	−18.4735	−0.721818
$656$	15.0647	0.588177
$657$	5.41561	0.211283
$658$	−5.75978	−0.224540
$659$	−16.4056	−0.639072	−0.319536	−	0.947574i	$-0.603527\pi$
$659$	−16.4056	−0.639072	−0.319536	+	0.947574i	$0.603527\pi$
$660$	33.4257	1.30109
$661$	−4.17945	−0.162562	−0.0812810	−	0.996691i	$-0.525901\pi$
$661$	−4.17945	−0.162562	−0.0812810	+	0.996691i	$0.525901\pi$
$662$	−49.0624	−1.90686
$663$	2.09190	0.0812426
$664$	60.3690	2.34277
$665$	−11.9597	−0.463779
$666$	14.6900	0.569226
$667$	9.21397	0.356766
$668$	−5.12763	−0.198394
$669$	−5.60714	−0.216785
$670$	−6.37981	−0.246474
$671$	−62.0369	−2.39491
$672$	8.81912	0.340205
$673$	−40.9378	−1.57804	−0.789019	−	0.614369i	$-0.789411\pi$
$673$	−40.9378	−1.57804	−0.789019	+	0.614369i	$0.789411\pi$
$674$	−35.3578	−1.36193
$675$	−5.65026	−0.217479
$676$	−30.8562	−1.18678
$677$	−38.0437	−1.46214	−0.731069	−	0.682303i	$-0.760978\pi$
$677$	−38.0437	−1.46214	−0.731069	+	0.682303i	$0.760978\pi$
$678$	−54.4797	−2.09228
$679$	3.59506	0.137966
$680$	−2.63481	−0.101040
$681$	11.3060	0.433248
$682$	101.697	3.89418
$683$	30.4392	1.16472	0.582361	−	0.812930i	$-0.302129\pi$
$683$	30.4392	1.16472	0.582361	+	0.812930i	$0.302129\pi$
$684$	−19.8514	−0.759037
$685$	−2.84423	−0.108672
$686$	47.1949	1.80191
$687$	−31.2499	−1.19226
$688$	12.6130	0.480866
$689$	0.803353	0.0306053
$690$	4.54199	0.172911
$691$	42.7996	1.62817	0.814087	−	0.580743i	$-0.197238\pi$
$691$	42.7996	1.62817	0.814087	+	0.580743i	$0.197238\pi$
$692$	78.9742	3.00215
$693$	10.9131	0.414553
$694$	−5.88463	−0.223378
$695$	5.19758	0.197155
$696$	−39.6125	−1.50151
$697$	−5.18906	−0.196550
$698$	−5.55500	−0.210260
$699$	−28.8043	−1.08948
$700$	7.08108	0.267640
$701$	−8.57705	−0.323951	−0.161975	−	0.986795i	$-0.551787\pi$
$701$	−8.57705	−0.323951	−0.161975	+	0.986795i	$0.551787\pi$
$702$	−28.5296	−1.07678
$703$	42.8421	1.61582
$704$	71.6342	2.69981
$705$	−1.81175	−0.0682345
$706$	39.2681	1.47787
$707$	8.82206	0.331788
$708$	62.9923	2.36739
$709$	−6.62107	−0.248659	−0.124330	−	0.992241i	$-0.539678\pi$
$709$	−6.62107	−0.248659	−0.124330	+	0.992241i	$0.539678\pi$
$710$	15.4184	0.578641
$711$	−5.59552	−0.209848
$712$	43.2833	1.62211
$713$	8.91786	0.333976
$714$	4.54597	0.170129
$715$	−13.4370	−0.502513
$716$	32.2278	1.20441
$717$	−22.3812	−0.835842
$718$	1.23497	0.0460888
$719$	−45.9064	−1.71202	−0.856010	−	0.516959i	$-0.827064\pi$
$719$	−45.9064	−1.71202	−0.856010	+	0.516959i	$0.827064\pi$
$720$	1.74406	0.0649972
$721$	−11.0708	−0.412298
$722$	−44.5935	−1.65960
$723$	1.45345	0.0540542
$724$	44.6795	1.66050
$725$	7.00174	0.260038
$726$	−99.8715	−3.70658
$727$	−13.3964	−0.496847	−0.248423	−	0.968652i	$-0.579912\pi$
$727$	−13.3964	−0.496847	−0.248423	+	0.968652i	$0.579912\pi$
$728$	16.1044	0.596870
$729$	29.5625	1.09491
$730$	−14.4906	−0.536323
$731$	−4.34458	−0.160690
$732$	51.9240	1.91917
$733$	−26.9332	−0.994799	−0.497399	−	0.867522i	$-0.665712\pi$
$733$	−26.9332	−0.994799	−0.497399	+	0.867522i	$0.665712\pi$
$734$	−53.0566	−1.95836
$735$	4.67116	0.172298
$736$	4.10363	0.151262
$737$	16.9778	0.625386
$738$	16.1562	0.594720
$739$	−41.6860	−1.53345	−0.766723	−	0.641978i	$-0.778114\pi$
$739$	−41.6860	−1.53345	−0.766723	+	0.641978i	$0.778114\pi$
$740$	−25.3658	−0.932465
$741$	−18.9951	−0.697802
$742$	1.74579	0.0640901
$743$	30.6274	1.12361	0.561805	−	0.827270i	$-0.310107\pi$
$743$	30.6274	1.12361	0.561805	+	0.827270i	$0.310107\pi$
$744$	−38.3394	−1.40559
$745$	11.4402	0.419138
$746$	−47.0606	−1.72301
$747$	13.7643	0.503609
$748$	15.5670	0.569185
$749$	−5.99327	−0.218989
$750$	3.45148	0.126030
$751$	−13.6519	−0.498164	−0.249082	−	0.968482i	$-0.580129\pi$
$751$	−13.6519	−0.498164	−0.249082	+	0.968482i	$0.580129\pi$
$752$	2.44959	0.0893274
$753$	−7.45797	−0.271784
$754$	35.3535	1.28750
$755$	−2.21951	−0.0807763
$756$	−40.0099	−1.45515
$757$	48.5377	1.76413	0.882066	−	0.471126i	$-0.156152\pi$
$757$	48.5377	1.76413	0.882066	+	0.471126i	$0.156152\pi$
$758$	13.1962	0.479306
$759$	−12.0871	−0.438732
$760$	23.9249	0.867848
$761$	−11.2163	−0.406592	−0.203296	−	0.979117i	$-0.565165\pi$
$761$	−11.2163	−0.406592	−0.203296	+	0.979117i	$0.565165\pi$
$762$	57.8056	2.09408
$763$	−1.07438	−0.0388951
$764$	13.2731	0.480203
$765$	−0.600744	−0.0217200
$766$	40.8297	1.47524
$767$	−25.3225	−0.914344
$768$	−38.4307	−1.38675
$769$	7.95271	0.286782	0.143391	−	0.989666i	$-0.454199\pi$
$769$	7.95271	0.286782	0.143391	+	0.989666i	$0.454199\pi$
$770$	−29.2003	−1.05231
$771$	−16.7460	−0.603093
$772$	72.0966	2.59481
$773$	−6.04947	−0.217584	−0.108792	−	0.994065i	$-0.534698\pi$
$773$	−6.04947	−0.217584	−0.108792	+	0.994065i	$0.534698\pi$
$774$	13.5269	0.486215
$775$	6.77673	0.243427
$776$	−7.19176	−0.258169
$777$	19.7127	0.707188
$778$	−66.1339	−2.37102
$779$	47.1183	1.68819
$780$	11.2465	0.402690
$781$	−41.0310	−1.46821
$782$	2.11529	0.0756427
$783$	−39.5617	−1.41382
$784$	−6.31568	−0.225560
$785$	−16.6395	−0.593888
$786$	−63.7609	−2.27428
$787$	18.9656	0.676052	0.338026	−	0.941137i	$-0.390241\pi$
$787$	18.9656	0.676052	0.338026	+	0.941137i	$0.390241\pi$
$788$	−92.5318	−3.29631
$789$	3.42284	0.121856
$790$	14.9720	0.532681
$791$	30.7134	1.09204
$792$	−21.8311	−0.775734
$793$	−20.8732	−0.741227
$794$	13.7632	0.488436
$795$	0.549143	0.0194761
$796$	89.8477	3.18457
$797$	46.0565	1.63140	0.815702	−	0.578472i	$-0.196351\pi$
$797$	46.0565	1.63140	0.815702	+	0.578472i	$0.196351\pi$
$798$	−41.2789	−1.46126
$799$	−0.843768	−0.0298504
$800$	3.11837	0.110251
$801$	9.86872	0.348694
$802$	−86.0945	−3.04010
$803$	38.5622	1.36083
$804$	−14.2102	−0.501155
$805$	−2.56059	−0.0902488
$806$	34.2173	1.20525
$807$	31.4017	1.10539
$808$	−17.6481	−0.620859
$809$	−8.53648	−0.300127	−0.150063	−	0.988676i	$-0.547948\pi$
$809$	−8.53648	−0.300127	−0.150063	+	0.988676i	$0.547948\pi$
$810$	−13.1792	−0.463070
$811$	32.1898	1.13034	0.565168	−	0.824976i	$-0.308811\pi$
$811$	32.1898	1.13034	0.565168	+	0.824976i	$0.308811\pi$
$812$	49.5799	1.73991
$813$	−35.3762	−1.24070
$814$	104.601	3.66627
$815$	17.2008	0.602516
$816$	−1.93337	−0.0676815
$817$	39.4501	1.38018
$818$	6.74380	0.235792
$819$	3.67185	0.128305
$820$	−27.8976	−0.974227
$821$	37.5706	1.31122	0.655611	−	0.755099i	$-0.272411\pi$
$821$	37.5706	1.31122	0.655611	+	0.755099i	$0.272411\pi$
$822$	−9.81680	−0.342400
$823$	14.5713	0.507923	0.253962	−	0.967214i	$-0.418266\pi$
$823$	14.5713	0.507923	0.253962	+	0.967214i	$0.418266\pi$
$824$	22.1466	0.771514
$825$	−9.18502	−0.319781
$826$	−55.0293	−1.91471
$827$	18.6963	0.650133	0.325067	−	0.945691i	$-0.394613\pi$
$827$	18.6963	0.650133	0.325067	+	0.945691i	$0.394613\pi$
$828$	−4.25019	−0.147704
$829$	−42.5609	−1.47820	−0.739101	−	0.673594i	$-0.764750\pi$
$829$	−42.5609	−1.47820	−0.739101	+	0.673594i	$0.764750\pi$
$830$	−36.8293	−1.27836
$831$	24.8859	0.863284
$832$	24.1023	0.835596
$833$	2.17545	0.0753748
$834$	17.9393	0.621189
$835$	1.40902	0.0487611
$836$	−141.353	−4.88880
$837$	−38.2903	−1.32351
$838$	−53.9274	−1.86289
$839$	42.4447	1.46535	0.732677	−	0.680577i	$-0.238271\pi$
$839$	42.4447	1.46535	0.732677	+	0.680577i	$0.238271\pi$
$840$	11.0084	0.379826
$841$	20.0244	0.690496
$842$	26.0786	0.898729
$843$	−6.75138	−0.232530
$844$	−28.0635	−0.965987
$845$	8.47896	0.291685
$846$	2.62709	0.0903211
$847$	56.3034	1.93461
$848$	−0.742473	−0.0254966
$849$	−30.9422	−1.06193
$850$	1.60742	0.0551341
$851$	9.17252	0.314430
$852$	34.3424	1.17655
$853$	−49.6121	−1.69869	−0.849343	−	0.527841i	$-0.823002\pi$
$853$	−49.6121	−1.69869	−0.849343	+	0.527841i	$0.823002\pi$
$854$	−45.3601	−1.55219
$855$	5.45494	0.186555
$856$	11.9893	0.409784
$857$	−2.65236	−0.0906028	−0.0453014	−	0.998973i	$-0.514425\pi$
$857$	−2.65236	−0.0906028	−0.0453014	+	0.998973i	$0.514425\pi$
$858$	−46.3774	−1.58330
$859$	20.5315	0.700524	0.350262	−	0.936652i	$-0.386093\pi$
$859$	20.5315	0.700524	0.350262	+	0.936652i	$0.386093\pi$
$860$	−23.3575	−0.796482
$861$	21.6802	0.738860
$862$	−65.1395	−2.21866
$863$	−7.65713	−0.260652	−0.130326	−	0.991471i	$-0.541602\pi$
$863$	−7.65713	−0.260652	−0.130326	+	0.991471i	$0.541602\pi$
$864$	−17.6196	−0.599432
$865$	−21.7012	−0.737864
$866$	44.1576	1.50054
$867$	−24.0426	−0.816530
$868$	47.9865	1.62877
$869$	−39.8433	−1.35159
$870$	24.1664	0.819317
$871$	5.71242	0.193558
$872$	2.14924	0.0727826
$873$	−1.63974	−0.0554968
$874$	−19.2075	−0.649704
$875$	−1.94580	−0.0657801
$876$	−32.2760	−1.09051
$877$	−44.7683	−1.51172	−0.755859	−	0.654734i	$-0.772780\pi$
$877$	−44.7683	−1.51172	−0.755859	+	0.654734i	$0.772780\pi$
$878$	−23.1017	−0.779643
$879$	−29.2608	−0.986944
$880$	12.4187	0.418633
$881$	−33.5825	−1.13142	−0.565712	−	0.824603i	$-0.691399\pi$
$881$	−33.5825	−1.13142	−0.565712	+	0.824603i	$0.691399\pi$
$882$	−6.77330	−0.228069
$883$	1.03227	0.0347386	0.0173693	−	0.999849i	$-0.494471\pi$
$883$	1.03227	0.0347386	0.0173693	+	0.999849i	$0.494471\pi$
$884$	5.23772	0.176164
$885$	−17.3096	−0.581855
$886$	−55.9971	−1.88126
$887$	15.7545	0.528983	0.264491	−	0.964388i	$-0.414796\pi$
$887$	15.7545	0.528983	0.264491	+	0.964388i	$0.414796\pi$
$888$	−39.4342	−1.32333
$889$	−32.5884	−1.09298
$890$	−26.4059	−0.885127
$891$	35.0722	1.17496
$892$	−14.0392	−0.470068
$893$	7.66167	0.256388
$894$	39.4858	1.32060
$895$	−8.85585	−0.296018
$896$	40.2420	1.34439
$897$	−4.06685	−0.135788
$898$	−41.4732	−1.38398
$899$	47.4489	1.58251
$900$	−3.22974	−0.107658
$901$	0.255747	0.00852015
$902$	115.042	3.83046
$903$	18.1519	0.604058
$904$	−61.4407	−2.04349
$905$	−12.2774	−0.408116
$906$	−7.66060	−0.254507
$907$	35.3498	1.17377	0.586886	−	0.809670i	$-0.300354\pi$
$907$	35.3498	1.17377	0.586886	+	0.809670i	$0.300354\pi$
$908$	28.3082	0.939440
$909$	−4.02382	−0.133462
$910$	−9.82483	−0.325690
$911$	−25.0708	−0.830632	−0.415316	−	0.909677i	$-0.636329\pi$
$911$	−25.0708	−0.830632	−0.415316	+	0.909677i	$0.636329\pi$
$912$	17.5556	0.581324
$913$	98.0095	3.24364
$914$	−47.2048	−1.56140
$915$	−14.2681	−0.471690
$916$	−78.2440	−2.58525
$917$	35.9457	1.18703
$918$	−9.08235	−0.299762
$919$	39.3022	1.29646	0.648230	−	0.761445i	$-0.275510\pi$
$919$	39.3022	1.29646	0.648230	+	0.761445i	$0.275510\pi$
$920$	5.12233	0.168878
$921$	26.1296	0.860999
$922$	60.9109	2.00599
$923$	−13.8054	−0.454412
$924$	−65.0398	−2.13965
$925$	6.97024	0.229180
$926$	41.4742	1.36293
$927$	5.04949	0.165847
$928$	21.8340	0.716738
$929$	20.7712	0.681482	0.340741	−	0.940157i	$-0.389322\pi$
$929$	20.7712	0.681482	0.340741	+	0.940157i	$0.389322\pi$
$930$	23.3898	0.766980
$931$	−19.7538	−0.647403
$932$	−72.1207	−2.36239
$933$	6.30100	0.206285
$934$	5.81097	0.190141
$935$	−4.27764	−0.139894
$936$	−7.34537	−0.240091
$937$	−18.6411	−0.608978	−0.304489	−	0.952516i	$-0.598486\pi$
$937$	−18.6411	−0.608978	−0.304489	+	0.952516i	$0.598486\pi$
$938$	12.4138	0.405326
$939$	−0.645519	−0.0210657
$940$	−4.53629	−0.147957
$941$	12.8407	0.418596	0.209298	−	0.977852i	$-0.432882\pi$
$941$	12.8407	0.418596	0.209298	+	0.977852i	$0.432882\pi$
$942$	−57.4308	−1.87120
$943$	10.0880	0.328512
$944$	23.4035	0.761720
$945$	10.9943	0.357644
$946$	96.3193	3.13161
$947$	22.8067	0.741118	0.370559	−	0.928809i	$-0.379166\pi$
$947$	22.8067	0.741118	0.370559	+	0.928809i	$0.379166\pi$
$948$	33.3482	1.08310
$949$	12.9748	0.421179
$950$	−14.5959	−0.473553
$951$	18.3504	0.595054
$952$	5.12682	0.166161
$953$	−1.75269	−0.0567751	−0.0283875	−	0.999597i	$-0.509037\pi$
$953$	−1.75269	−0.0567751	−0.0283875	+	0.999597i	$0.509037\pi$
$954$	−0.796271	−0.0257802
$955$	−3.64730	−0.118024
$956$	−56.0384	−1.81241
$957$	−64.3111	−2.07888
$958$	88.9224	2.87295
$959$	5.53430	0.178712
$960$	16.4755	0.531743
$961$	14.9240	0.481420
$962$	35.1945	1.13471
$963$	2.73358	0.0880885
$964$	3.63916	0.117209
$965$	−19.8114	−0.637750
$966$	−8.83782	−0.284352
$967$	−39.6158	−1.27396	−0.636978	−	0.770882i	$-0.719816\pi$
$967$	−39.6158	−1.27396	−0.636978	+	0.770882i	$0.719816\pi$
$968$	−112.632	−3.62014
$969$	−6.04706	−0.194260
$970$	4.38748	0.140873
$971$	2.47682	0.0794850	0.0397425	−	0.999210i	$-0.487346\pi$
$971$	2.47682	0.0794850	0.0397425	+	0.999210i	$0.487346\pi$
$972$	32.3316	1.03704
$973$	−10.1135	−0.324222
$974$	−72.6803	−2.32883
$975$	−3.09042	−0.0989728
$976$	19.2913	0.617501
$977$	−47.3115	−1.51363	−0.756814	−	0.653630i	$-0.773245\pi$
$977$	−47.3115	−1.51363	−0.756814	+	0.653630i	$0.773245\pi$
$978$	59.3681	1.89838
$979$	70.2708	2.24587
$980$	11.6957	0.373606
$981$	0.490033	0.0156456
$982$	−95.0882	−3.03439
$983$	13.1579	0.419671	0.209835	−	0.977737i	$-0.432707\pi$
$983$	13.1579	0.419671	0.209835	+	0.977737i	$0.432707\pi$
$984$	−43.3703	−1.38259
$985$	25.4267	0.810163
$986$	11.2547	0.358424
$987$	3.52531	0.112212
$988$	−47.5602	−1.51309
$989$	8.44628	0.268576
$990$	13.3185	0.423290
$991$	4.15594	0.132018	0.0660089	−	0.997819i	$-0.478973\pi$
$991$	4.15594	0.132018	0.0660089	+	0.997819i	$0.478973\pi$
$992$	21.1324	0.670953
$993$	30.0289	0.952940
$994$	−30.0011	−0.951576
$995$	−24.6892	−0.782699
$996$	−82.0325	−2.59930
$997$	−19.3979	−0.614336	−0.307168	−	0.951655i	$-0.599381\pi$
$997$	−19.3979	−0.614336	−0.307168	+	0.951655i	$0.599381\pi$
$998$	37.6644	1.19225
$999$	−39.3837	−1.24605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.5	✓	25
5.4	even	2		6025.2.a.k.1.21		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.5	✓	25	1.1	even	1	trivial
6025.2.a.k.1.21		25	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.37469 q^{2} +1.45345 q^{3} +3.63916 q^{4} -1.00000 q^{5} -3.45148 q^{6} +1.94580 q^{7} -3.89249 q^{8} -0.887497 q^{9} +O(q^{10})\)	\(q-2.37469 q^{2} +1.45345 q^{3} +3.63916 q^{4} -1.00000 q^{5} -3.45148 q^{6} +1.94580 q^{7} -3.89249 q^{8} -0.887497 q^{9} +2.37469 q^{10} -6.31948 q^{11} +5.28931 q^{12} -2.12627 q^{13} -4.62068 q^{14} -1.45345 q^{15} +1.96514 q^{16} -0.676897 q^{17} +2.10753 q^{18} +6.14644 q^{19} -3.63916 q^{20} +2.82812 q^{21} +15.0068 q^{22} +1.31595 q^{23} -5.65752 q^{24} +1.00000 q^{25} +5.04924 q^{26} -5.65026 q^{27} +7.08108 q^{28} +7.00174 q^{29} +3.45148 q^{30} +6.77673 q^{31} +3.11837 q^{32} -9.18502 q^{33} +1.60742 q^{34} -1.94580 q^{35} -3.22974 q^{36} +6.97024 q^{37} -14.5959 q^{38} -3.09042 q^{39} +3.89249 q^{40} +7.66596 q^{41} -6.71590 q^{42} +6.41837 q^{43} -22.9976 q^{44} +0.887497 q^{45} -3.12498 q^{46} +1.24652 q^{47} +2.85622 q^{48} -3.21385 q^{49} -2.37469 q^{50} -0.983833 q^{51} -7.73784 q^{52} -0.377822 q^{53} +13.4176 q^{54} +6.31948 q^{55} -7.57401 q^{56} +8.93351 q^{57} -16.6270 q^{58} +11.9093 q^{59} -5.28931 q^{60} +9.81677 q^{61} -16.0926 q^{62} -1.72689 q^{63} -11.3355 q^{64} +2.12627 q^{65} +21.8116 q^{66} -2.68659 q^{67} -2.46333 q^{68} +1.91267 q^{69} +4.62068 q^{70} +6.49279 q^{71} +3.45457 q^{72} -6.10212 q^{73} -16.5522 q^{74} +1.45345 q^{75} +22.3678 q^{76} -12.2965 q^{77} +7.33880 q^{78} +6.30483 q^{79} -1.96514 q^{80} -5.54986 q^{81} -18.2043 q^{82} -15.5091 q^{83} +10.2920 q^{84} +0.676897 q^{85} -15.2416 q^{86} +10.1766 q^{87} +24.5985 q^{88} -11.1197 q^{89} -2.10753 q^{90} -4.13731 q^{91} +4.78896 q^{92} +9.84960 q^{93} -2.96011 q^{94} -6.14644 q^{95} +4.53238 q^{96} +1.84760 q^{97} +7.63191 q^{98} +5.60852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

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