LMFDB - Embedded newform 1205.2.a.e.1.13

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			1.13
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)

$f(q)$	$=$	$q+0.362712 q^{2} +3.41577 q^{3} -1.86844 q^{4} +1.00000 q^{5} +1.23894 q^{6} +3.34046 q^{7} -1.40313 q^{8} +8.66752 q^{9} +O(q^{10})$	\(q+0.362712 q^{2} +3.41577 q^{3} -1.86844 q^{4} +1.00000 q^{5} +1.23894 q^{6} +3.34046 q^{7} -1.40313 q^{8} +8.66752 q^{9} +0.362712 q^{10} -2.67832 q^{11} -6.38217 q^{12} +0.591068 q^{13} +1.21163 q^{14} +3.41577 q^{15} +3.22795 q^{16} -1.07744 q^{17} +3.14382 q^{18} -5.88556 q^{19} -1.86844 q^{20} +11.4103 q^{21} -0.971461 q^{22} +2.98266 q^{23} -4.79278 q^{24} +1.00000 q^{25} +0.214388 q^{26} +19.3590 q^{27} -6.24145 q^{28} +3.96926 q^{29} +1.23894 q^{30} -4.71138 q^{31} +3.97708 q^{32} -9.14854 q^{33} -0.390800 q^{34} +3.34046 q^{35} -16.1947 q^{36} +8.86039 q^{37} -2.13477 q^{38} +2.01895 q^{39} -1.40313 q^{40} -9.79063 q^{41} +4.13864 q^{42} -2.42881 q^{43} +5.00428 q^{44} +8.66752 q^{45} +1.08185 q^{46} -9.02079 q^{47} +11.0259 q^{48} +4.15867 q^{49} +0.362712 q^{50} -3.68028 q^{51} -1.10437 q^{52} -14.0701 q^{53} +7.02174 q^{54} -2.67832 q^{55} -4.68710 q^{56} -20.1037 q^{57} +1.43970 q^{58} +9.68407 q^{59} -6.38217 q^{60} -0.830604 q^{61} -1.70887 q^{62} +28.9535 q^{63} -5.01336 q^{64} +0.591068 q^{65} -3.31829 q^{66} +10.9586 q^{67} +2.01313 q^{68} +10.1881 q^{69} +1.21163 q^{70} +0.250176 q^{71} -12.1617 q^{72} -10.3124 q^{73} +3.21377 q^{74} +3.41577 q^{75} +10.9968 q^{76} -8.94682 q^{77} +0.732300 q^{78} +10.1480 q^{79} +3.22795 q^{80} +40.1233 q^{81} -3.55119 q^{82} -7.04557 q^{83} -21.3194 q^{84} -1.07744 q^{85} -0.880961 q^{86} +13.5581 q^{87} +3.75804 q^{88} +6.66265 q^{89} +3.14382 q^{90} +1.97444 q^{91} -5.57292 q^{92} -16.0930 q^{93} -3.27195 q^{94} -5.88556 q^{95} +13.5848 q^{96} +0.0770398 q^{97} +1.50840 q^{98} -23.2144 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.362712	0.256476	0.128238	−	0.991743i	$-0.459068\pi$
$2$	0.362712	0.256476	0.128238	+	0.991743i	$0.459068\pi$
$3$	3.41577	1.97210	0.986049	−	0.166454i	$-0.0532318\pi$
$3$	3.41577	1.97210	0.986049	+	0.166454i	$0.0532318\pi$
$4$	−1.86844	−0.934220
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.23894	0.505797
$7$	3.34046	1.26257	0.631287	−	0.775549i	$-0.282527\pi$
$7$	3.34046	1.26257	0.631287	+	0.775549i	$0.282527\pi$
$8$	−1.40313	−0.496082
$9$	8.66752	2.88917
$10$	0.362712	0.114700
$11$	−2.67832	−0.807544	−0.403772	−	0.914860i	$-0.632301\pi$
$11$	−2.67832	−0.807544	−0.403772	+	0.914860i	$0.632301\pi$
$12$	−6.38217	−1.84237
$13$	0.591068	0.163933	0.0819663	−	0.996635i	$-0.473880\pi$
$13$	0.591068	0.163933	0.0819663	+	0.996635i	$0.473880\pi$
$14$	1.21163	0.323821
$15$	3.41577	0.881949
$16$	3.22795	0.806987
$17$	−1.07744	−0.261317	−0.130658	−	0.991427i	$-0.541709\pi$
$17$	−1.07744	−0.261317	−0.130658	+	0.991427i	$0.541709\pi$
$18$	3.14382	0.741005
$19$	−5.88556	−1.35024	−0.675120	−	0.737708i	$-0.735908\pi$
$19$	−5.88556	−1.35024	−0.675120	+	0.737708i	$0.735908\pi$
$20$	−1.86844	−0.417796
$21$	11.4103	2.48992
$22$	−0.971461	−0.207116
$23$	2.98266	0.621928	0.310964	−	0.950422i	$-0.399348\pi$
$23$	2.98266	0.621928	0.310964	+	0.950422i	$0.399348\pi$
$24$	−4.79278	−0.978322
$25$	1.00000	0.200000
$26$	0.214388	0.0420449
$27$	19.3590	3.72563
$28$	−6.24145	−1.17952
$29$	3.96926	0.737073	0.368536	−	0.929613i	$-0.379859\pi$
$29$	3.96926	0.737073	0.368536	+	0.929613i	$0.379859\pi$
$30$	1.23894	0.226199
$31$	−4.71138	−0.846188	−0.423094	−	0.906086i	$-0.639056\pi$
$31$	−4.71138	−0.846188	−0.423094	+	0.906086i	$0.639056\pi$
$32$	3.97708	0.703055
$33$	−9.14854	−1.59256
$34$	−0.390800	−0.0670216
$35$	3.34046	0.564641
$36$	−16.1947	−2.69912
$37$	8.86039	1.45664	0.728319	−	0.685238i	$-0.240302\pi$
$37$	8.86039	1.45664	0.728319	+	0.685238i	$0.240302\pi$
$38$	−2.13477	−0.346305
$39$	2.01895	0.323291
$40$	−1.40313	−0.221855
$41$	−9.79063	−1.52904	−0.764520	−	0.644600i	$-0.777024\pi$
$41$	−9.79063	−1.52904	−0.764520	+	0.644600i	$0.777024\pi$
$42$	4.13864	0.638606
$43$	−2.42881	−0.370391	−0.185195	−	0.982702i	$-0.559292\pi$
$43$	−2.42881	−0.370391	−0.185195	+	0.982702i	$0.559292\pi$
$44$	5.00428	0.754424
$45$	8.66752	1.29208
$46$	1.08185	0.159510
$47$	−9.02079	−1.31582	−0.657909	−	0.753098i	$-0.728559\pi$
$47$	−9.02079	−1.31582	−0.657909	+	0.753098i	$0.728559\pi$
$48$	11.0259	1.59146
$49$	4.15867	0.594095
$50$	0.362712	0.0512953
$51$	−3.68028	−0.515342
$52$	−1.10437	−0.153149
$53$	−14.0701	−1.93268	−0.966340	−	0.257270i	$-0.917177\pi$
$53$	−14.0701	−1.93268	−0.966340	+	0.257270i	$0.917177\pi$
$54$	7.02174	0.955537
$55$	−2.67832	−0.361145
$56$	−4.68710	−0.626341
$57$	−20.1037	−2.66281
$58$	1.43970	0.189042
$59$	9.68407	1.26076	0.630379	−	0.776287i	$-0.282899\pi$
$59$	9.68407	1.26076	0.630379	+	0.776287i	$0.282899\pi$
$60$	−6.38217	−0.823934
$61$	−0.830604	−0.106348	−0.0531740	−	0.998585i	$-0.516934\pi$
$61$	−0.830604	−0.106348	−0.0531740	+	0.998585i	$0.516934\pi$
$62$	−1.70887	−0.217027
$63$	28.9535	3.64780
$64$	−5.01336	−0.626669
$65$	0.591068	0.0733129
$66$	−3.31829	−0.408453
$67$	10.9586	1.33881	0.669403	−	0.742899i	$-0.266550\pi$
$67$	10.9586	1.33881	0.669403	+	0.742899i	$0.266550\pi$
$68$	2.01313	0.244127
$69$	10.1881	1.22650
$70$	1.21163	0.144817
$71$	0.250176	0.0296904	0.0148452	−	0.999890i	$-0.495274\pi$
$71$	0.250176	0.0296904	0.0148452	+	0.999890i	$0.495274\pi$
$72$	−12.1617	−1.43327
$73$	−10.3124	−1.20697	−0.603486	−	0.797373i	$-0.706222\pi$
$73$	−10.3124	−1.20697	−0.603486	+	0.797373i	$0.706222\pi$
$74$	3.21377	0.373594
$75$	3.41577	0.394420
$76$	10.9968	1.26142
$77$	−8.94682	−1.01959
$78$	0.732300	0.0829166
$79$	10.1480	1.14174	0.570871	−	0.821040i	$-0.306606\pi$
$79$	10.1480	1.14174	0.570871	+	0.821040i	$0.306606\pi$
$80$	3.22795	0.360895
$81$	40.1233	4.45814
$82$	−3.55119	−0.392163
$83$	−7.04557	−0.773351	−0.386676	−	0.922216i	$-0.626377\pi$
$83$	−7.04557	−0.773351	−0.386676	+	0.922216i	$0.626377\pi$
$84$	−21.3194	−2.32613
$85$	−1.07744	−0.116864
$86$	−0.880961	−0.0949965
$87$	13.5581	1.45358
$88$	3.75804	0.400608
$89$	6.66265	0.706240	0.353120	−	0.935578i	$-0.385121\pi$
$89$	6.66265	0.706240	0.353120	+	0.935578i	$0.385121\pi$
$90$	3.14382	0.331387
$91$	1.97444	0.206977
$92$	−5.57292	−0.581017
$93$	−16.0930	−1.66877
$94$	−3.27195	−0.337476
$95$	−5.88556	−0.603846
$96$	13.5848	1.38649
$97$	0.0770398	0.00782221	0.00391110	−	0.999992i	$-0.498755\pi$
$97$	0.0770398	0.00782221	0.00391110	+	0.999992i	$0.498755\pi$
$98$	1.50840	0.152372
$99$	−23.2144	−2.33313
$100$	−1.86844	−0.186844
$101$	4.48262	0.446038	0.223019	−	0.974814i	$-0.428409\pi$
$101$	4.48262	0.446038	0.223019	+	0.974814i	$0.428409\pi$
$102$	−1.33488	−0.132173
$103$	−3.98186	−0.392345	−0.196172	−	0.980569i	$-0.562851\pi$
$103$	−3.98186	−0.392345	−0.196172	+	0.980569i	$0.562851\pi$
$104$	−0.829345	−0.0813240
$105$	11.4103	1.11353
$106$	−5.10341	−0.495687
$107$	−10.2751	−0.993335	−0.496668	−	0.867941i	$-0.665443\pi$
$107$	−10.2751	−0.993335	−0.496668	+	0.867941i	$0.665443\pi$
$108$	−36.1710	−3.48056
$109$	−3.79466	−0.363463	−0.181731	−	0.983348i	$-0.558170\pi$
$109$	−3.79466	−0.363463	−0.181731	+	0.983348i	$0.558170\pi$
$110$	−0.971461	−0.0926251
$111$	30.2651	2.87263
$112$	10.7828	1.01888
$113$	10.3798	0.976448	0.488224	−	0.872718i	$-0.337645\pi$
$113$	10.3798	0.976448	0.488224	+	0.872718i	$0.337645\pi$
$114$	−7.29188	−0.682947
$115$	2.98266	0.278135
$116$	−7.41632	−0.688588
$117$	5.12309	0.473630
$118$	3.51253	0.323355
$119$	−3.59913	−0.329932
$120$	−4.79278	−0.437519
$121$	−3.82659	−0.347872
$122$	−0.301270	−0.0272757
$123$	−33.4426	−3.01542
$124$	8.80292	0.790526
$125$	1.00000	0.0894427
$126$	10.5018	0.935574
$127$	8.55650	0.759267	0.379633	−	0.925137i	$-0.376050\pi$
$127$	8.55650	0.759267	0.379633	+	0.925137i	$0.376050\pi$
$128$	−9.77257	−0.863781
$129$	−8.29628	−0.730447
$130$	0.214388	0.0188030
$131$	−0.367465	−0.0321055	−0.0160528	−	0.999871i	$-0.505110\pi$
$131$	−0.367465	−0.0321055	−0.0160528	+	0.999871i	$0.505110\pi$
$132$	17.0935	1.48780
$133$	−19.6605	−1.70478
$134$	3.97482	0.343372
$135$	19.3590	1.66615
$136$	1.51179	0.129635
$137$	−8.68523	−0.742029	−0.371015	−	0.928627i	$-0.620990\pi$
$137$	−8.68523	−0.742029	−0.371015	+	0.928627i	$0.620990\pi$
$138$	3.69535	0.314569
$139$	13.2597	1.12468	0.562338	−	0.826907i	$-0.309902\pi$
$139$	13.2597	1.12468	0.562338	+	0.826907i	$0.309902\pi$
$140$	−6.24145	−0.527499
$141$	−30.8130	−2.59492
$142$	0.0907418	0.00761489
$143$	−1.58307	−0.132383
$144$	27.9783	2.33152
$145$	3.96926	0.329629
$146$	−3.74043	−0.309560
$147$	14.2051	1.17161
$148$	−16.5551	−1.36082
$149$	−13.5526	−1.11028	−0.555138	−	0.831759i	$-0.687334\pi$
$149$	−13.5526	−1.11028	−0.555138	+	0.831759i	$0.687334\pi$
$150$	1.23894	0.101159
$151$	−5.83929	−0.475195	−0.237597	−	0.971364i	$-0.576360\pi$
$151$	−5.83929	−0.475195	−0.237597	+	0.971364i	$0.576360\pi$
$152$	8.25821	0.669830
$153$	−9.33870	−0.754989
$154$	−3.24512	−0.261500
$155$	−4.71138	−0.378427
$156$	−3.77229	−0.302025
$157$	−13.2138	−1.05457	−0.527286	−	0.849688i	$-0.676790\pi$
$157$	−13.2138	−1.05457	−0.527286	+	0.849688i	$0.676790\pi$
$158$	3.68082	0.292830
$159$	−48.0604	−3.81143
$160$	3.97708	0.314416
$161$	9.96346	0.785230
$162$	14.5532	1.14341
$163$	−24.5109	−1.91984	−0.959921	−	0.280272i	$-0.909575\pi$
$163$	−24.5109	−1.91984	−0.959921	+	0.280272i	$0.909575\pi$
$164$	18.2932	1.42846
$165$	−9.14854	−0.712213
$166$	−2.55551	−0.198346
$167$	16.9393	1.31080	0.655400	−	0.755282i	$-0.272500\pi$
$167$	16.9393	1.31080	0.655400	+	0.755282i	$0.272500\pi$
$168$	−16.0101	−1.23521
$169$	−12.6506	−0.973126
$170$	−0.390800	−0.0299730
$171$	−51.0132	−3.90108
$172$	4.53809	0.346026
$173$	−22.5016	−1.71077	−0.855383	−	0.517996i	$-0.826678\pi$
$173$	−22.5016	−1.71077	−0.855383	+	0.517996i	$0.826678\pi$
$174$	4.91769	0.372809
$175$	3.34046	0.252515
$176$	−8.64548	−0.651677
$177$	33.0786	2.48634
$178$	2.41663	0.181134
$179$	−3.45024	−0.257883	−0.128941	−	0.991652i	$-0.541158\pi$
$179$	−3.45024	−0.257883	−0.128941	+	0.991652i	$0.541158\pi$
$180$	−16.1947	−1.20708
$181$	15.2794	1.13571	0.567853	−	0.823130i	$-0.307774\pi$
$181$	15.2794	1.13571	0.567853	+	0.823130i	$0.307774\pi$
$182$	0.716153	0.0530848
$183$	−2.83716	−0.209729
$184$	−4.18506	−0.308527
$185$	8.86039	0.651429
$186$	−5.83713	−0.427999
$187$	2.88572	0.211025
$188$	16.8548	1.22926
$189$	64.6678	4.70389
$190$	−2.13477	−0.154872
$191$	3.66386	0.265107	0.132554	−	0.991176i	$-0.457682\pi$
$191$	3.66386	0.265107	0.132554	+	0.991176i	$0.457682\pi$
$192$	−17.1245	−1.23585
$193$	−4.66451	−0.335759	−0.167880	−	0.985808i	$-0.553692\pi$
$193$	−4.66451	−0.335759	−0.167880	+	0.985808i	$0.553692\pi$
$194$	0.0279433	0.00200621
$195$	2.01895	0.144580
$196$	−7.77022	−0.555016
$197$	15.4498	1.10075	0.550377	−	0.834916i	$-0.314484\pi$
$197$	15.4498	1.10075	0.550377	+	0.834916i	$0.314484\pi$
$198$	−8.42015	−0.598394
$199$	−5.40435	−0.383104	−0.191552	−	0.981482i	$-0.561352\pi$
$199$	−5.40435	−0.383104	−0.191552	+	0.981482i	$0.561352\pi$
$200$	−1.40313	−0.0992164
$201$	37.4321	2.64026
$202$	1.62590	0.114398
$203$	13.2591	0.930609
$204$	6.87638	0.481443
$205$	−9.79063	−0.683808
$206$	−1.44427	−0.100627
$207$	25.8523	1.79686
$208$	1.90793	0.132291
$209$	15.7634	1.09038
$210$	4.13864	0.285593
$211$	1.59042	0.109489	0.0547446	−	0.998500i	$-0.482566\pi$
$211$	1.59042	0.109489	0.0547446	+	0.998500i	$0.482566\pi$
$212$	26.2892	1.80555
$213$	0.854544	0.0585524
$214$	−3.72692	−0.254767
$215$	−2.42881	−0.165644
$216$	−27.1632	−1.84822
$217$	−15.7382	−1.06838
$218$	−1.37637	−0.0932197
$219$	−35.2248	−2.38027
$220$	5.00428	0.337389
$221$	−0.636838	−0.0428384
$222$	10.9775	0.736763
$223$	22.8974	1.53333	0.766663	−	0.642049i	$-0.221916\pi$
$223$	22.8974	1.53333	0.766663	+	0.642049i	$0.221916\pi$
$224$	13.2853	0.887660
$225$	8.66752	0.577834
$226$	3.76488	0.250436
$227$	−20.7584	−1.37779	−0.688893	−	0.724863i	$-0.741903\pi$
$227$	−20.7584	−1.37779	−0.688893	+	0.724863i	$0.741903\pi$
$228$	37.5626	2.48765
$229$	−2.70281	−0.178607	−0.0893033	−	0.996004i	$-0.528464\pi$
$229$	−2.70281	−0.178607	−0.0893033	+	0.996004i	$0.528464\pi$
$230$	1.08185	0.0713350
$231$	−30.5603	−2.01072
$232$	−5.56939	−0.365648
$233$	−4.42131	−0.289650	−0.144825	−	0.989457i	$-0.546262\pi$
$233$	−4.42131	−0.289650	−0.144825	+	0.989457i	$0.546262\pi$
$234$	1.85821	0.121475
$235$	−9.02079	−0.588452
$236$	−18.0941	−1.17783
$237$	34.6634	2.25163
$238$	−1.30545	−0.0846198
$239$	−15.5478	−1.00570	−0.502851	−	0.864373i	$-0.667715\pi$
$239$	−15.5478	−1.00570	−0.502851	+	0.864373i	$0.667715\pi$
$240$	11.0259	0.711721
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−1.38795	−0.0892210
$243$	78.9752	5.06626
$244$	1.55193	0.0993523
$245$	4.15867	0.265688
$246$	−12.1300	−0.773384
$247$	−3.47876	−0.221348
$248$	6.61068	0.419778
$249$	−24.0661	−1.52512
$250$	0.362712	0.0229400
$251$	25.2828	1.59584	0.797920	−	0.602764i	$-0.205934\pi$
$251$	25.2828	1.59584	0.797920	+	0.602764i	$0.205934\pi$
$252$	−54.0978	−3.40784
$253$	−7.98852	−0.502234
$254$	3.10355	0.194734
$255$	−3.68028	−0.230468
$256$	6.48208	0.405130
$257$	−18.6057	−1.16059	−0.580296	−	0.814405i	$-0.697063\pi$
$257$	−18.6057	−1.16059	−0.580296	+	0.814405i	$0.697063\pi$
$258$	−3.00917	−0.187342
$259$	29.5978	1.83912
$260$	−1.10437	−0.0684904
$261$	34.4036	2.12953
$262$	−0.133284	−0.00823431
$263$	−7.45593	−0.459753	−0.229876	−	0.973220i	$-0.573832\pi$
$263$	−7.45593	−0.459753	−0.229876	+	0.973220i	$0.573832\pi$
$264$	12.8366	0.790039
$265$	−14.0701	−0.864320
$266$	−7.13110	−0.437236
$267$	22.7581	1.39277
$268$	−20.4755	−1.25074
$269$	31.0344	1.89220	0.946101	−	0.323871i	$-0.104984\pi$
$269$	31.0344	1.89220	0.946101	+	0.323871i	$0.104984\pi$
$270$	7.02174	0.427329
$271$	−13.0676	−0.793802	−0.396901	−	0.917861i	$-0.629914\pi$
$271$	−13.0676	−0.793802	−0.396901	+	0.917861i	$0.629914\pi$
$272$	−3.47791	−0.210879
$273$	6.74423	0.408179
$274$	−3.15024	−0.190313
$275$	−2.67832	−0.161509
$276$	−19.0358	−1.14582
$277$	−16.4559	−0.988740	−0.494370	−	0.869252i	$-0.664601\pi$
$277$	−16.4559	−0.988740	−0.494370	+	0.869252i	$0.664601\pi$
$278$	4.80947	0.288453
$279$	−40.8359	−2.44478
$280$	−4.68710	−0.280108
$281$	15.2677	0.910793	0.455397	−	0.890289i	$-0.349497\pi$
$281$	15.2677	0.910793	0.455397	+	0.890289i	$0.349497\pi$
$282$	−11.1763	−0.665536
$283$	15.0853	0.896726	0.448363	−	0.893852i	$-0.352007\pi$
$283$	15.0853	0.896726	0.448363	+	0.893852i	$0.352007\pi$
$284$	−0.467438	−0.0277374
$285$	−20.1037	−1.19084
$286$	−0.574199	−0.0339531
$287$	−32.7052	−1.93053
$288$	34.4714	2.03125
$289$	−15.8391	−0.931714
$290$	1.43970	0.0845420
$291$	0.263151	0.0154262
$292$	19.2681	1.12758
$293$	−26.1109	−1.52541	−0.762706	−	0.646745i	$-0.776130\pi$
$293$	−26.1109	−1.52541	−0.762706	+	0.646745i	$0.776130\pi$
$294$	5.15236	0.300492
$295$	9.68407	0.563828
$296$	−12.4323	−0.722612
$297$	−51.8495	−3.00861
$298$	−4.91571	−0.284759
$299$	1.76295	0.101954
$300$	−6.38217	−0.368475
$301$	−8.11336	−0.467646
$302$	−2.11798	−0.121876
$303$	15.3116	0.879630
$304$	−18.9983	−1.08963
$305$	−0.830604	−0.0475602
$306$	−3.38726	−0.193637
$307$	0.0551646	0.00314841	0.00157421	−	0.999999i	$-0.499499\pi$
$307$	0.0551646	0.00314841	0.00157421	+	0.999999i	$0.499499\pi$
$308$	16.7166	0.952517
$309$	−13.6011	−0.773742
$310$	−1.70887	−0.0970576
$311$	−20.8676	−1.18330	−0.591648	−	0.806197i	$-0.701522\pi$
$311$	−20.8676	−1.18330	−0.591648	+	0.806197i	$0.701522\pi$
$312$	−2.83286	−0.160379
$313$	25.7693	1.45657	0.728283	−	0.685276i	$-0.240318\pi$
$313$	25.7693	1.45657	0.728283	+	0.685276i	$0.240318\pi$
$314$	−4.79279	−0.270473
$315$	28.9535	1.63134
$316$	−18.9610	−1.06664
$317$	2.63788	0.148158	0.0740792	−	0.997252i	$-0.476398\pi$
$317$	2.63788	0.148158	0.0740792	+	0.997252i	$0.476398\pi$
$318$	−17.4321	−0.977543
$319$	−10.6309	−0.595219
$320$	−5.01336	−0.280255
$321$	−35.0976	−1.95895
$322$	3.61387	0.201393
$323$	6.34132	0.352840
$324$	−74.9679	−4.16489
$325$	0.591068	0.0327865
$326$	−8.89041	−0.492394
$327$	−12.9617	−0.716785
$328$	13.7375	0.758529
$329$	−30.1336	−1.66132
$330$	−3.31829	−0.182666
$331$	−2.00015	−0.109938	−0.0549691	−	0.998488i	$-0.517506\pi$
$331$	−2.00015	−0.109938	−0.0549691	+	0.998488i	$0.517506\pi$
$332$	13.1642	0.722480
$333$	76.7975	4.20848
$334$	6.14408	0.336189
$335$	10.9586	0.598732
$336$	36.8317	2.00933
$337$	31.5650	1.71945	0.859727	−	0.510754i	$-0.170634\pi$
$337$	31.5650	1.71945	0.859727	+	0.510754i	$0.170634\pi$
$338$	−4.58854	−0.249584
$339$	35.4550	1.92565
$340$	2.01313	0.109177
$341$	12.6186	0.683334
$342$	−18.5031	−1.00053
$343$	−9.49135	−0.512485
$344$	3.40795	0.183744
$345$	10.1881	0.548509
$346$	−8.16162	−0.438771
$347$	−11.1162	−0.596747	−0.298373	−	0.954449i	$-0.596444\pi$
$347$	−11.1162	−0.596747	−0.298373	+	0.954449i	$0.596444\pi$
$348$	−25.3325	−1.35796
$349$	2.19652	0.117577	0.0587884	−	0.998270i	$-0.481276\pi$
$349$	2.19652	0.117577	0.0587884	+	0.998270i	$0.481276\pi$
$350$	1.21163	0.0647642
$351$	11.4425	0.610753
$352$	−10.6519	−0.567748
$353$	−1.90559	−0.101424	−0.0507122	−	0.998713i	$-0.516149\pi$
$353$	−1.90559	−0.101424	−0.0507122	+	0.998713i	$0.516149\pi$
$354$	11.9980	0.637688
$355$	0.250176	0.0132779
$356$	−12.4488	−0.659783
$357$	−12.2938	−0.650659
$358$	−1.25144	−0.0661409
$359$	−8.45511	−0.446244	−0.223122	−	0.974791i	$-0.571625\pi$
$359$	−8.45511	−0.446244	−0.223122	+	0.974791i	$0.571625\pi$
$360$	−12.1617	−0.640976
$361$	15.6398	0.823149
$362$	5.54201	0.291282
$363$	−13.0708	−0.686038
$364$	−3.68912	−0.193362
$365$	−10.3124	−0.539775
$366$	−1.02907	−0.0537904
$367$	30.7371	1.60446	0.802232	−	0.597013i	$-0.203646\pi$
$367$	30.7371	1.60446	0.802232	+	0.597013i	$0.203646\pi$
$368$	9.62787	0.501887
$369$	−84.8605	−4.41766
$370$	3.21377	0.167076
$371$	−47.0007	−2.44015
$372$	30.0688	1.55899
$373$	7.23017	0.374364	0.187182	−	0.982325i	$-0.440065\pi$
$373$	7.23017	0.374364	0.187182	+	0.982325i	$0.440065\pi$
$374$	1.04669	0.0541229
$375$	3.41577	0.176390
$376$	12.6574	0.652753
$377$	2.34610	0.120830
$378$	23.4558	1.20644
$379$	−16.3620	−0.840459	−0.420229	−	0.907418i	$-0.638050\pi$
$379$	−16.3620	−0.840459	−0.420229	+	0.907418i	$0.638050\pi$
$380$	10.9968	0.564125
$381$	29.2271	1.49735
$382$	1.32893	0.0679938
$383$	−17.0940	−0.873462	−0.436731	−	0.899592i	$-0.643864\pi$
$383$	−17.0940	−0.873462	−0.436731	+	0.899592i	$0.643864\pi$
$384$	−33.3809	−1.70346
$385$	−8.94682	−0.455972
$386$	−1.69188	−0.0861143
$387$	−21.0518	−1.07012
$388$	−0.143944	−0.00730766
$389$	−18.4363	−0.934760	−0.467380	−	0.884057i	$-0.654802\pi$
$389$	−18.4363	−0.934760	−0.467380	+	0.884057i	$0.654802\pi$
$390$	0.732300	0.0370814
$391$	−3.21363	−0.162520
$392$	−5.83516	−0.294720
$393$	−1.25518	−0.0633153
$394$	5.60384	0.282317
$395$	10.1480	0.510603
$396$	43.3747	2.17966
$397$	34.6231	1.73769	0.868843	−	0.495088i	$-0.164864\pi$
$397$	34.6231	1.73769	0.868843	+	0.495088i	$0.164864\pi$
$398$	−1.96023	−0.0982573
$399$	−67.1558	−3.36199
$400$	3.22795	0.161397
$401$	18.7453	0.936094	0.468047	−	0.883703i	$-0.344958\pi$
$401$	18.7453	0.936094	0.468047	+	0.883703i	$0.344958\pi$
$402$	13.5771	0.677164
$403$	−2.78474	−0.138718
$404$	−8.37551	−0.416697
$405$	40.1233	1.99374
$406$	4.80926	0.238679
$407$	−23.7310	−1.17630
$408$	5.16392	0.255652
$409$	36.1825	1.78911	0.894554	−	0.446960i	$-0.147493\pi$
$409$	36.1825	1.78911	0.894554	+	0.446960i	$0.147493\pi$
$410$	−3.55119	−0.175381
$411$	−29.6668	−1.46335
$412$	7.43987	0.366536
$413$	32.3492	1.59180
$414$	9.37694	0.460851
$415$	−7.04557	−0.345853
$416$	2.35072	0.115254
$417$	45.2923	2.21797
$418$	5.71759	0.279657
$419$	27.8441	1.36027	0.680137	−	0.733085i	$-0.261920\pi$
$419$	27.8441	1.36027	0.680137	+	0.733085i	$0.261920\pi$
$420$	−21.3194	−1.04028
$421$	−31.4544	−1.53299	−0.766497	−	0.642248i	$-0.778002\pi$
$421$	−31.4544	−1.53299	−0.766497	+	0.642248i	$0.778002\pi$
$422$	0.576866	0.0280814
$423$	−78.1879	−3.80162
$424$	19.7422	0.958767
$425$	−1.07744	−0.0522634
$426$	0.309954	0.0150173
$427$	−2.77460	−0.134272
$428$	19.1985	0.927993
$429$	−5.40741	−0.261072
$430$	−0.880961	−0.0424837
$431$	−31.3748	−1.51127	−0.755635	−	0.654993i	$-0.772672\pi$
$431$	−31.3748	−1.51127	−0.755635	+	0.654993i	$0.772672\pi$
$432$	62.4897	3.00654
$433$	27.6739	1.32992	0.664962	−	0.746877i	$-0.268448\pi$
$433$	27.6739	1.32992	0.664962	+	0.746877i	$0.268448\pi$
$434$	−5.70843	−0.274013
$435$	13.5581	0.650061
$436$	7.09010	0.339554
$437$	−17.5546	−0.839752
$438$	−12.7765	−0.610483
$439$	35.9019	1.71350	0.856752	−	0.515729i	$-0.172479\pi$
$439$	35.9019	1.71350	0.856752	+	0.515729i	$0.172479\pi$
$440$	3.75804	0.179157
$441$	36.0453	1.71644
$442$	−0.230989	−0.0109870
$443$	6.70280	0.318460	0.159230	−	0.987242i	$-0.449099\pi$
$443$	6.70280	0.318460	0.159230	+	0.987242i	$0.449099\pi$
$444$	−56.5485	−2.68367
$445$	6.66265	0.315840
$446$	8.30519	0.393262
$447$	−46.2927	−2.18957
$448$	−16.7469	−0.791217
$449$	4.17189	0.196884	0.0984418	−	0.995143i	$-0.468614\pi$
$449$	4.17189	0.196884	0.0984418	+	0.995143i	$0.468614\pi$
$450$	3.14382	0.148201
$451$	26.2225	1.23477
$452$	−19.3940	−0.912217
$453$	−19.9457	−0.937131
$454$	−7.52935	−0.353370
$455$	1.97444	0.0925630
$456$	28.2082	1.32097
$457$	13.4988	0.631448	0.315724	−	0.948851i	$-0.397753\pi$
$457$	13.4988	0.631448	0.315724	+	0.948851i	$0.397753\pi$
$458$	−0.980342	−0.0458084
$459$	−20.8581	−0.973571
$460$	−5.57292	−0.259839
$461$	−36.6435	−1.70666	−0.853328	−	0.521374i	$-0.825420\pi$
$461$	−36.6435	−1.70666	−0.853328	+	0.521374i	$0.825420\pi$
$462$	−11.0846	−0.515703
$463$	2.14127	0.0995130	0.0497565	−	0.998761i	$-0.484155\pi$
$463$	2.14127	0.0995130	0.0497565	+	0.998761i	$0.484155\pi$
$464$	12.8125	0.594808
$465$	−16.0930	−0.746295
$466$	−1.60367	−0.0742884
$467$	−0.514805	−0.0238223	−0.0119112	−	0.999929i	$-0.503792\pi$
$467$	−0.514805	−0.0238223	−0.0119112	+	0.999929i	$0.503792\pi$
$468$	−9.57218	−0.442474
$469$	36.6068	1.69034
$470$	−3.27195	−0.150924
$471$	−45.1352	−2.07972
$472$	−13.5880	−0.625439
$473$	6.50515	0.299107
$474$	12.5728	0.577490
$475$	−5.88556	−0.270048
$476$	6.72476	0.308229
$477$	−121.953	−5.58384
$478$	−5.63937	−0.257939
$479$	28.0468	1.28149	0.640745	−	0.767754i	$-0.278626\pi$
$479$	28.0468	1.28149	0.640745	+	0.767754i	$0.278626\pi$
$480$	13.5848	0.620059
$481$	5.23709	0.238791
$482$	−0.362712	−0.0165211
$483$	34.0329	1.54855
$484$	7.14976	0.324989
$485$	0.0770398	0.00349820
$486$	28.6453	1.29938
$487$	22.7761	1.03208	0.516041	−	0.856564i	$-0.327405\pi$
$487$	22.7761	1.03208	0.516041	+	0.856564i	$0.327405\pi$
$488$	1.16545	0.0527573
$489$	−83.7237	−3.78612
$490$	1.50840	0.0681426
$491$	25.8901	1.16840	0.584201	−	0.811609i	$-0.301408\pi$
$491$	25.8901	1.16840	0.584201	+	0.811609i	$0.301408\pi$
$492$	62.4855	2.81706
$493$	−4.27662	−0.192609
$494$	−1.26179	−0.0567707
$495$	−23.2144	−1.04341
$496$	−15.2081	−0.682862
$497$	0.835702	0.0374863
$498$	−8.72906	−0.391159
$499$	−1.54718	−0.0692611	−0.0346306	−	0.999400i	$-0.511025\pi$
$499$	−1.54718	−0.0692611	−0.0346306	+	0.999400i	$0.511025\pi$
$500$	−1.86844	−0.0835592
$501$	57.8607	2.58503
$502$	9.17040	0.409295
$503$	−6.37809	−0.284385	−0.142192	−	0.989839i	$-0.545415\pi$
$503$	−6.37809	−0.284385	−0.142192	+	0.989839i	$0.545415\pi$
$504$	−40.6255	−1.80961
$505$	4.48262	0.199474
$506$	−2.89754	−0.128811
$507$	−43.2117	−1.91910
$508$	−15.9873	−0.709322
$509$	26.8650	1.19077	0.595386	−	0.803440i	$-0.296999\pi$
$509$	26.8650	1.19077	0.595386	+	0.803440i	$0.296999\pi$
$510$	−1.33488	−0.0591097
$511$	−34.4481	−1.52389
$512$	21.8963	0.967687
$513$	−113.938	−5.03050
$514$	−6.74853	−0.297665
$515$	−3.98186	−0.175462
$516$	15.5011	0.682398
$517$	24.1606	1.06258
$518$	10.7355	0.471690
$519$	−76.8604	−3.37380
$520$	−0.829345	−0.0363692
$521$	7.51004	0.329021	0.164511	−	0.986375i	$-0.447396\pi$
$521$	7.51004	0.329021	0.164511	+	0.986375i	$0.447396\pi$
$522$	12.4786	0.546174
$523$	33.2991	1.45607	0.728034	−	0.685542i	$-0.240435\pi$
$523$	33.2991	1.45607	0.728034	+	0.685542i	$0.240435\pi$
$524$	0.686585	0.0299936
$525$	11.4103	0.497984
$526$	−2.70436	−0.117916
$527$	5.07621	0.221123
$528$	−29.5310	−1.28517
$529$	−14.1037	−0.613206
$530$	−5.10341	−0.221678
$531$	83.9368	3.64255
$532$	36.7344	1.59264
$533$	−5.78693	−0.250660
$534$	8.25465	0.357214
$535$	−10.2751	−0.444233
$536$	−15.3764	−0.664157
$537$	−11.7852	−0.508571
$538$	11.2566	0.485305
$539$	−11.1383	−0.479758
$540$	−36.1710	−1.55655
$541$	−21.8383	−0.938900	−0.469450	−	0.882959i	$-0.655548\pi$
$541$	−21.8383	−0.938900	−0.469450	+	0.882959i	$0.655548\pi$
$542$	−4.73979	−0.203592
$543$	52.1908	2.23972
$544$	−4.28505	−0.183720
$545$	−3.79466	−0.162546
$546$	2.44622	0.104688
$547$	−14.9034	−0.637223	−0.318612	−	0.947885i	$-0.603217\pi$
$547$	−14.9034	−0.637223	−0.318612	+	0.947885i	$0.603217\pi$
$548$	16.2278	0.693218
$549$	−7.19927	−0.307257
$550$	−0.971461	−0.0414232
$551$	−23.3613	−0.995225
$552$	−14.2952	−0.608446
$553$	33.8991	1.44154
$554$	−5.96876	−0.253589
$555$	30.2651	1.28468
$556$	−24.7750	−1.05069
$557$	37.2999	1.58045	0.790224	−	0.612819i	$-0.209964\pi$
$557$	37.2999	1.58045	0.790224	+	0.612819i	$0.209964\pi$
$558$	−14.8117	−0.627029
$559$	−1.43559	−0.0607191
$560$	10.7828	0.455657
$561$	9.85698	0.416162
$562$	5.53778	0.233597
$563$	15.4464	0.650989	0.325494	−	0.945544i	$-0.394469\pi$
$563$	15.4464	0.650989	0.325494	+	0.945544i	$0.394469\pi$
$564$	57.5722	2.42423
$565$	10.3798	0.436681
$566$	5.47161	0.229989
$567$	134.030	5.62874
$568$	−0.351029	−0.0147289
$569$	29.8232	1.25025	0.625127	−	0.780523i	$-0.285047\pi$
$569$	29.8232	1.25025	0.625127	+	0.780523i	$0.285047\pi$
$570$	−7.29188	−0.305423
$571$	35.6202	1.49066	0.745329	−	0.666697i	$-0.232292\pi$
$571$	35.6202	1.49066	0.745329	+	0.666697i	$0.232292\pi$
$572$	2.95787	0.123675
$573$	12.5149	0.522818
$574$	−11.8626	−0.495135
$575$	2.98266	0.124386
$576$	−43.4533	−1.81056
$577$	−21.9411	−0.913419	−0.456709	−	0.889616i	$-0.650972\pi$
$577$	−21.9411	−0.913419	−0.456709	+	0.889616i	$0.650972\pi$
$578$	−5.74505	−0.238963
$579$	−15.9329	−0.662150
$580$	−7.41632	−0.307946
$581$	−23.5354	−0.976414
$582$	0.0954480	0.00395645
$583$	37.6843	1.56072
$584$	14.4696	0.598757
$585$	5.12309	0.211814
$586$	−9.47073	−0.391232
$587$	7.00544	0.289146	0.144573	−	0.989494i	$-0.453819\pi$
$587$	7.00544	0.289146	0.144573	+	0.989494i	$0.453819\pi$
$588$	−26.5413	−1.09455
$589$	27.7291	1.14256
$590$	3.51253	0.144609
$591$	52.7731	2.17079
$592$	28.6009	1.17549
$593$	15.1748	0.623155	0.311577	−	0.950221i	$-0.399143\pi$
$593$	15.1748	0.623155	0.311577	+	0.950221i	$0.399143\pi$
$594$	−18.8065	−0.771639
$595$	−3.59913	−0.147550
$596$	25.3223	1.03724
$597$	−18.4601	−0.755520
$598$	0.639445	0.0261489
$599$	−13.0172	−0.531870	−0.265935	−	0.963991i	$-0.585681\pi$
$599$	−13.0172	−0.531870	−0.265935	+	0.963991i	$0.585681\pi$
$600$	−4.79278	−0.195664
$601$	36.1757	1.47564	0.737818	−	0.674999i	$-0.235856\pi$
$601$	36.1757	1.47564	0.737818	+	0.674999i	$0.235856\pi$
$602$	−2.94282	−0.119940
$603$	94.9838	3.86804
$604$	10.9104	0.443936
$605$	−3.82659	−0.155573
$606$	5.55372	0.225604
$607$	−4.90393	−0.199044	−0.0995221	−	0.995035i	$-0.531731\pi$
$607$	−4.90393	−0.199044	−0.0995221	+	0.995035i	$0.531731\pi$
$608$	−23.4073	−0.949293
$609$	45.2902	1.83525
$610$	−0.301270	−0.0121981
$611$	−5.33190	−0.215705
$612$	17.4488	0.705326
$613$	5.66442	0.228784	0.114392	−	0.993436i	$-0.463508\pi$
$613$	5.66442	0.228784	0.114392	+	0.993436i	$0.463508\pi$
$614$	0.0200089	0.000807494 0
$615$	−33.4426	−1.34854
$616$	12.5536	0.505798
$617$	26.7780	1.07804	0.539020	−	0.842293i	$-0.318795\pi$
$617$	26.7780	1.07804	0.539020	+	0.842293i	$0.318795\pi$
$618$	−4.93331	−0.198447
$619$	39.9899	1.60733	0.803665	−	0.595082i	$-0.202880\pi$
$619$	39.9899	1.60733	0.803665	+	0.595082i	$0.202880\pi$
$620$	8.80292	0.353534
$621$	57.7412	2.31707
$622$	−7.56895	−0.303487
$623$	22.2563	0.891680
$624$	6.51707	0.260892
$625$	1.00000	0.0400000
$626$	9.34685	0.373575
$627$	53.8443	2.15033
$628$	24.6891	0.985202
$629$	−9.54651	−0.380644
$630$	10.5018	0.418401
$631$	32.9213	1.31058	0.655288	−	0.755379i	$-0.272547\pi$
$631$	32.9213	1.31058	0.655288	+	0.755379i	$0.272547\pi$
$632$	−14.2390	−0.566398
$633$	5.43252	0.215923
$634$	0.956793	0.0379991
$635$	8.55650	0.339555
$636$	89.7979	3.56072
$637$	2.45805	0.0973916
$638$	−3.85598	−0.152660
$639$	2.16840	0.0857806
$640$	−9.77257	−0.386295
$641$	−19.2412	−0.759983	−0.379991	−	0.924990i	$-0.624073\pi$
$641$	−19.2412	−0.759983	−0.379991	+	0.924990i	$0.624073\pi$
$642$	−12.7303	−0.502426
$643$	37.4059	1.47514	0.737572	−	0.675268i	$-0.235972\pi$
$643$	37.4059	1.47514	0.737572	+	0.675268i	$0.235972\pi$
$644$	−18.6161	−0.733578
$645$	−8.29628	−0.326666
$646$	2.30008	0.0904953
$647$	−38.1467	−1.49970	−0.749851	−	0.661607i	$-0.769875\pi$
$647$	−38.1467	−1.49970	−0.749851	+	0.661607i	$0.769875\pi$
$648$	−56.2982	−2.21160
$649$	−25.9371	−1.01812
$650$	0.214388	0.00840897
$651$	−53.7580	−2.10694
$652$	45.7971	1.79355
$653$	−26.3157	−1.02981	−0.514906	−	0.857247i	$-0.672173\pi$
$653$	−26.3157	−1.02981	−0.514906	+	0.857247i	$0.672173\pi$
$654$	−4.70138	−0.183838
$655$	−0.367465	−0.0143580
$656$	−31.6036	−1.23391
$657$	−89.3827	−3.48715
$658$	−10.9298	−0.426089
$659$	−25.5777	−0.996366	−0.498183	−	0.867072i	$-0.665999\pi$
$659$	−25.5777	−0.996366	−0.498183	+	0.867072i	$0.665999\pi$
$660$	17.0935	0.665364
$661$	16.8601	0.655781	0.327890	−	0.944716i	$-0.393662\pi$
$661$	16.8601	0.655781	0.327890	+	0.944716i	$0.393662\pi$
$662$	−0.725479	−0.0281966
$663$	−2.17529	−0.0844815
$664$	9.88585	0.383646
$665$	−19.6605	−0.762401
$666$	27.8554	1.07938
$667$	11.8389	0.458406
$668$	−31.6500	−1.22458
$669$	78.2125	3.02387
$670$	3.97482	0.153561
$671$	2.22462	0.0858807
$672$	45.3795	1.75055
$673$	13.1203	0.505751	0.252875	−	0.967499i	$-0.418624\pi$
$673$	13.1203	0.505751	0.252875	+	0.967499i	$0.418624\pi$
$674$	11.4490	0.440999
$675$	19.3590	0.745127
$676$	23.6370	0.909114
$677$	−4.07063	−0.156447	−0.0782236	−	0.996936i	$-0.524925\pi$
$677$	−4.07063	−0.156447	−0.0782236	+	0.996936i	$0.524925\pi$
$678$	12.8600	0.493884
$679$	0.257348	0.00987612
$680$	1.51179	0.0579743
$681$	−70.9062	−2.71713
$682$	4.57692	0.175259
$683$	24.7733	0.947924	0.473962	−	0.880545i	$-0.342823\pi$
$683$	24.7733	0.947924	0.473962	+	0.880545i	$0.342823\pi$
$684$	95.3151	3.64446
$685$	−8.68523	−0.331846
$686$	−3.44263	−0.131440
$687$	−9.23218	−0.352230
$688$	−7.84008	−0.298900
$689$	−8.31639	−0.316829
$690$	3.69535	0.140680
$691$	−15.7267	−0.598270	−0.299135	−	0.954211i	$-0.596698\pi$
$691$	−15.7267	−0.598270	−0.299135	+	0.954211i	$0.596698\pi$
$692$	42.0429	1.59823
$693$	−77.5467	−2.94576
$694$	−4.03197	−0.153051
$695$	13.2597	0.502971
$696$	−19.0238	−0.721094
$697$	10.5488	0.399564
$698$	0.796704	0.0301557
$699$	−15.1022	−0.571218
$700$	−6.24145	−0.235905
$701$	23.0979	0.872397	0.436199	−	0.899850i	$-0.356325\pi$
$701$	23.0979	0.872397	0.436199	+	0.899850i	$0.356325\pi$
$702$	4.15032	0.156644
$703$	−52.1483	−1.96681
$704$	13.4274	0.506063
$705$	−30.8130	−1.16048
$706$	−0.691182	−0.0260130
$707$	14.9740	0.563156
$708$	−61.8054	−2.32279
$709$	1.65188	0.0620376	0.0310188	−	0.999519i	$-0.490125\pi$
$709$	1.65188	0.0620376	0.0310188	+	0.999519i	$0.490125\pi$
$710$	0.0907418	0.00340548
$711$	87.9582	3.29869
$712$	−9.34858	−0.350353
$713$	−14.0524	−0.526268
$714$	−4.45913	−0.166879
$715$	−1.58307	−0.0592034
$716$	6.44656	0.240919
$717$	−53.1077	−1.98334
$718$	−3.06677	−0.114451
$719$	−30.6145	−1.14173	−0.570865	−	0.821044i	$-0.693392\pi$
$719$	−30.6145	−1.14173	−0.570865	+	0.821044i	$0.693392\pi$
$720$	27.9783	1.04269
$721$	−13.3013	−0.495365
$722$	5.67276	0.211118
$723$	−3.41577	−0.127034
$724$	−28.5485	−1.06100
$725$	3.96926	0.147415
$726$	−4.74094	−0.175953
$727$	−20.1615	−0.747750	−0.373875	−	0.927479i	$-0.621971\pi$
$727$	−20.1615	−0.747750	−0.373875	+	0.927479i	$0.621971\pi$
$728$	−2.77039	−0.102678
$729$	149.392	5.53303
$730$	−3.74043	−0.138440
$731$	2.61689	0.0967893
$732$	5.30105	0.195933
$733$	16.5899	0.612762	0.306381	−	0.951909i	$-0.400882\pi$
$733$	16.5899	0.612762	0.306381	+	0.951909i	$0.400882\pi$
$734$	11.1487	0.411507
$735$	14.2051	0.523962
$736$	11.8623	0.437249
$737$	−29.3507	−1.08115
$738$	−30.7800	−1.13303
$739$	44.8663	1.65043	0.825217	−	0.564816i	$-0.191053\pi$
$739$	44.8663	1.65043	0.825217	+	0.564816i	$0.191053\pi$
$740$	−16.5551	−0.608578
$741$	−11.8827	−0.436521
$742$	−17.0477	−0.625842
$743$	−15.0186	−0.550978	−0.275489	−	0.961304i	$-0.588840\pi$
$743$	−15.0186	−0.550978	−0.275489	+	0.961304i	$0.588840\pi$
$744$	22.5806	0.827844
$745$	−13.5526	−0.496530
$746$	2.62247	0.0960156
$747$	−61.0676	−2.23434
$748$	−5.39180	−0.197144
$749$	−34.3237	−1.25416
$750$	1.23894	0.0452398
$751$	−15.0984	−0.550948	−0.275474	−	0.961309i	$-0.588835\pi$
$751$	−15.0984	−0.550948	−0.275474	+	0.961309i	$0.588835\pi$
$752$	−29.1186	−1.06185
$753$	86.3605	3.14715
$754$	0.850959	0.0309901
$755$	−5.83929	−0.212514
$756$	−120.828	−4.39447
$757$	−12.1390	−0.441198	−0.220599	−	0.975365i	$-0.570801\pi$
$757$	−12.1390	−0.441198	−0.220599	+	0.975365i	$0.570801\pi$
$758$	−5.93470	−0.215558
$759$	−27.2870	−0.990455
$760$	8.25821	0.299557
$761$	−26.6306	−0.965358	−0.482679	−	0.875797i	$-0.660336\pi$
$761$	−26.6306	−0.965358	−0.482679	+	0.875797i	$0.660336\pi$
$762$	10.6010	0.384035
$763$	−12.6759	−0.458899
$764$	−6.84570	−0.247669
$765$	−9.33870	−0.337641
$766$	−6.20020	−0.224022
$767$	5.72394	0.206679
$768$	22.1413	0.798956
$769$	−19.3398	−0.697411	−0.348705	−	0.937232i	$-0.613379\pi$
$769$	−19.3398	−0.697411	−0.348705	+	0.937232i	$0.613379\pi$
$770$	−3.24512	−0.116946
$771$	−63.5529	−2.28880
$772$	8.71536	0.313673
$773$	−35.1241	−1.26333	−0.631663	−	0.775243i	$-0.717627\pi$
$773$	−35.1241	−1.26333	−0.631663	+	0.775243i	$0.717627\pi$
$774$	−7.63575	−0.274461
$775$	−4.71138	−0.169238
$776$	−0.108097	−0.00388046
$777$	101.099	3.62692
$778$	−6.68709	−0.239744
$779$	57.6234	2.06457
$780$	−3.77229	−0.135070
$781$	−0.670051	−0.0239763
$782$	−1.16562	−0.0416826
$783$	76.8407	2.74606
$784$	13.4240	0.479427
$785$	−13.2138	−0.471619
$786$	−0.455268	−0.0162389
$787$	33.6906	1.20094	0.600469	−	0.799648i	$-0.294980\pi$
$787$	33.6906	1.20094	0.600469	+	0.799648i	$0.294980\pi$
$788$	−28.8671	−1.02835
$789$	−25.4678	−0.906677
$790$	3.68082	0.130958
$791$	34.6733	1.23284
$792$	32.5728	1.15743
$793$	−0.490943	−0.0174339
$794$	12.5582	0.445675
$795$	−48.0604	−1.70453
$796$	10.0977	0.357904
$797$	−44.2786	−1.56843	−0.784215	−	0.620489i	$-0.786934\pi$
$797$	−44.2786	−1.56843	−0.784215	+	0.620489i	$0.786934\pi$
$798$	−24.3582	−0.862272
$799$	9.71933	0.343845
$800$	3.97708	0.140611
$801$	57.7486	2.04045
$802$	6.79915	0.240086
$803$	27.6199	0.974684
$804$	−69.9396	−2.46658
$805$	9.96346	0.351166
$806$	−1.01006	−0.0355779
$807$	106.007	3.73161
$808$	−6.28971	−0.221271
$809$	−40.3465	−1.41851	−0.709253	−	0.704954i	$-0.750968\pi$
$809$	−40.3465	−1.41851	−0.709253	+	0.704954i	$0.750968\pi$
$810$	14.5532	0.511348
$811$	−5.93409	−0.208374	−0.104187	−	0.994558i	$-0.533224\pi$
$811$	−5.93409	−0.208374	−0.104187	+	0.994558i	$0.533224\pi$
$812$	−24.7739	−0.869394
$813$	−44.6361	−1.56546
$814$	−8.60752	−0.301693
$815$	−24.5109	−0.858579
$816$	−11.8798	−0.415874
$817$	14.2949	0.500117
$818$	13.1238	0.458864
$819$	17.1135	0.597993
$820$	18.2932	0.638827
$821$	−34.3672	−1.19942	−0.599711	−	0.800217i	$-0.704718\pi$
$821$	−34.3672	−1.19942	−0.599711	+	0.800217i	$0.704718\pi$
$822$	−10.7605	−0.375316
$823$	−36.1276	−1.25933	−0.629665	−	0.776867i	$-0.716808\pi$
$823$	−36.1276	−1.25933	−0.629665	+	0.776867i	$0.716808\pi$
$824$	5.58708	0.194635
$825$	−9.14854	−0.318511
$826$	11.7335	0.408260
$827$	27.2587	0.947877	0.473938	−	0.880558i	$-0.342832\pi$
$827$	27.2587	0.947877	0.473938	+	0.880558i	$0.342832\pi$
$828$	−48.3034	−1.67866
$829$	31.7188	1.10164	0.550819	−	0.834625i	$-0.314315\pi$
$829$	31.7188	1.10164	0.550819	+	0.834625i	$0.314315\pi$
$830$	−2.55551	−0.0887032
$831$	−56.2097	−1.94989
$832$	−2.96323	−0.102732
$833$	−4.48070	−0.155247
$834$	16.4281	0.568858
$835$	16.9393	0.586207
$836$	−29.4530	−1.01865
$837$	−91.2073	−3.15259
$838$	10.0994	0.348878
$839$	19.0221	0.656715	0.328357	−	0.944554i	$-0.393505\pi$
$839$	19.0221	0.656715	0.328357	+	0.944554i	$0.393505\pi$
$840$	−16.0101	−0.552401
$841$	−13.2450	−0.456724
$842$	−11.4089	−0.393177
$843$	52.1510	1.79617
$844$	−2.97161	−0.102287
$845$	−12.6506	−0.435195
$846$	−28.3597	−0.975027
$847$	−12.7826	−0.439215
$848$	−45.4176	−1.55965
$849$	51.5279	1.76843
$850$	−0.390800	−0.0134043
$851$	26.4275	0.905924
$852$	−1.59666	−0.0547008
$853$	−44.3027	−1.51690	−0.758448	−	0.651733i	$-0.774042\pi$
$853$	−44.3027	−1.51690	−0.758448	+	0.651733i	$0.774042\pi$
$854$	−1.00638	−0.0344377
$855$	−51.0132	−1.74461
$856$	14.4174	0.492776
$857$	−4.65097	−0.158874	−0.0794371	−	0.996840i	$-0.525312\pi$
$857$	−4.65097	−0.158874	−0.0794371	+	0.996840i	$0.525312\pi$
$858$	−1.96133	−0.0669588
$859$	−19.3303	−0.659540	−0.329770	−	0.944061i	$-0.606971\pi$
$859$	−19.3303	−0.659540	−0.329770	+	0.944061i	$0.606971\pi$
$860$	4.53809	0.154748
$861$	−111.714	−3.80719
$862$	−11.3800	−0.387605
$863$	22.7992	0.776094	0.388047	−	0.921640i	$-0.373150\pi$
$863$	22.7992	0.776094	0.388047	+	0.921640i	$0.373150\pi$
$864$	76.9921	2.61932
$865$	−22.5016	−0.765078
$866$	10.0377	0.341094
$867$	−54.1029	−1.83743
$868$	29.4058	0.998098
$869$	−27.1797	−0.922007
$870$	4.91769	0.166725
$871$	6.47727	0.219474
$872$	5.32441	0.180307
$873$	0.667744	0.0225997
$874$	−6.36728	−0.215377
$875$	3.34046	0.112928
$876$	65.8154	2.22369
$877$	52.0581	1.75788	0.878939	−	0.476934i	$-0.158252\pi$
$877$	52.0581	1.75788	0.878939	+	0.476934i	$0.158252\pi$
$878$	13.0221	0.439473
$879$	−89.1888	−3.00826
$880$	−8.64548	−0.291439
$881$	−30.1695	−1.01644	−0.508218	−	0.861229i	$-0.669695\pi$
$881$	−30.1695	−1.01644	−0.508218	+	0.861229i	$0.669695\pi$
$882$	13.0741	0.440228
$883$	33.7863	1.13700	0.568500	−	0.822683i	$-0.307524\pi$
$883$	33.7863	1.13700	0.568500	+	0.822683i	$0.307524\pi$
$884$	1.18989	0.0400204
$885$	33.0786	1.11192
$886$	2.43119	0.0816774
$887$	35.3082	1.18553	0.592767	−	0.805374i	$-0.298036\pi$
$887$	35.3082	1.18553	0.592767	+	0.805374i	$0.298036\pi$
$888$	−42.4659	−1.42506
$889$	28.5827	0.958631
$890$	2.41663	0.0810055
$891$	−107.463	−3.60015
$892$	−42.7825	−1.43246
$893$	53.0924	1.77667
$894$	−16.7910	−0.561574
$895$	−3.45024	−0.115329
$896$	−32.6449	−1.09059
$897$	6.02185	0.201064
$898$	1.51320	0.0504960
$899$	−18.7007	−0.623702
$900$	−16.1947	−0.539824
$901$	15.1597	0.505042
$902$	9.51122	0.316689
$903$	−27.7134	−0.922244
$904$	−14.5642	−0.484398
$905$	15.2794	0.507903
$906$	−7.23456	−0.240352
$907$	−13.2957	−0.441476	−0.220738	−	0.975333i	$-0.570847\pi$
$907$	−13.2957	−0.441476	−0.220738	+	0.975333i	$0.570847\pi$
$908$	38.7859	1.28716
$909$	38.8532	1.28868
$910$	0.716153	0.0237402
$911$	32.8035	1.08683	0.543415	−	0.839464i	$-0.317131\pi$
$911$	32.8035	1.08683	0.543415	+	0.839464i	$0.317131\pi$
$912$	−64.8938	−2.14885
$913$	18.8703	0.624515
$914$	4.89619	0.161951
$915$	−2.83716	−0.0937935
$916$	5.05003	0.166858
$917$	−1.22750	−0.0405356
$918$	−7.56548	−0.249698
$919$	4.52202	0.149168	0.0745838	−	0.997215i	$-0.476237\pi$
$919$	4.52202	0.149168	0.0745838	+	0.997215i	$0.476237\pi$
$920$	−4.18506	−0.137978
$921$	0.188430	0.00620898
$922$	−13.2910	−0.437717
$923$	0.147871	0.00486722
$924$	57.1001	1.87846
$925$	8.86039	0.291328
$926$	0.776664	0.0255227
$927$	−34.5129	−1.13355
$928$	15.7860	0.518202
$929$	40.2300	1.31990	0.659952	−	0.751308i	$-0.270577\pi$
$929$	40.2300	1.31990	0.659952	+	0.751308i	$0.270577\pi$
$930$	−5.83713	−0.191407
$931$	−24.4761	−0.802172
$932$	8.26096	0.270597
$933$	−71.2792	−2.33357
$934$	−0.186726	−0.00610987
$935$	2.88572	0.0943732
$936$	−7.18836	−0.234959
$937$	34.8986	1.14009	0.570044	−	0.821614i	$-0.306926\pi$
$937$	34.8986	1.14009	0.570044	+	0.821614i	$0.306926\pi$
$938$	13.2777	0.433533
$939$	88.0221	2.87249
$940$	16.8548	0.549743
$941$	−19.4140	−0.632879	−0.316439	−	0.948613i	$-0.602487\pi$
$941$	−19.4140	−0.632879	−0.316439	+	0.948613i	$0.602487\pi$
$942$	−16.3711	−0.533399
$943$	−29.2021	−0.950953
$944$	31.2597	1.01742
$945$	64.6678	2.10364
$946$	2.35950	0.0767139
$947$	19.3006	0.627184	0.313592	−	0.949558i	$-0.398468\pi$
$947$	19.3006	0.627184	0.313592	+	0.949558i	$0.398468\pi$
$948$	−64.7664	−2.10352
$949$	−6.09531	−0.197862
$950$	−2.13477	−0.0692610
$951$	9.01042	0.292183
$952$	5.05006	0.163673
$953$	6.26171	0.202837	0.101418	−	0.994844i	$-0.467662\pi$
$953$	6.26171	0.202837	0.101418	+	0.994844i	$0.467662\pi$
$954$	−44.2339	−1.43212
$955$	3.66386	0.118560
$956$	29.0501	0.939546
$957$	−36.3129	−1.17383
$958$	10.1729	0.328672
$959$	−29.0127	−0.936867
$960$	−17.1245	−0.552691
$961$	−8.80294	−0.283966
$962$	1.89956	0.0612442
$963$	−89.0599	−2.86992
$964$	1.86844	0.0601784
$965$	−4.66451	−0.150156
$966$	12.3442	0.397167
$967$	−16.5403	−0.531899	−0.265950	−	0.963987i	$-0.585685\pi$
$967$	−16.5403	−0.531899	−0.265950	+	0.963987i	$0.585685\pi$
$968$	5.36921	0.172573
$969$	21.6605	0.695836
$970$	0.0279433	0.000897205 0
$971$	12.6336	0.405433	0.202717	−	0.979237i	$-0.435023\pi$
$971$	12.6336	0.405433	0.202717	+	0.979237i	$0.435023\pi$
$972$	−147.560	−4.73300
$973$	44.2936	1.41999
$974$	8.26116	0.264705
$975$	2.01895	0.0646583
$976$	−2.68114	−0.0858213
$977$	0.0361421	0.00115629	0.000578145	−	1.00000i	$-0.499816\pi$
$977$	0.0361421	0.00115629	0.000578145		1.00000i	$0.499816\pi$
$978$	−30.3676	−0.971050
$979$	−17.8447	−0.570320
$980$	−7.77022	−0.248211
$981$	−32.8903	−1.05011
$982$	9.39065	0.299668
$983$	21.7663	0.694236	0.347118	−	0.937821i	$-0.387160\pi$
$983$	21.7663	0.694236	0.347118	+	0.937821i	$0.387160\pi$
$984$	46.9244	1.49589
$985$	15.4498	0.492272
$986$	−1.55118	−0.0493998
$987$	−102.930	−3.27628
$988$	6.49986	0.206788
$989$	−7.24433	−0.230356
$990$	−8.42015	−0.267610
$991$	12.9908	0.412665	0.206332	−	0.978482i	$-0.433847\pi$
$991$	12.9908	0.412665	0.206332	+	0.978482i	$0.433847\pi$
$992$	−18.7375	−0.594917
$993$	−6.83206	−0.216809
$994$	0.303119	0.00961437
$995$	−5.40435	−0.171330
$996$	44.9660	1.42480
$997$	−2.82932	−0.0896055	−0.0448028	−	0.998996i	$-0.514266\pi$
$997$	−2.82932	−0.0896055	−0.0448028	+	0.998996i	$0.514266\pi$
$998$	−0.561180	−0.0177638
$999$	171.528	5.42690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.e.1.13	✓	25
5.4	even	2		6025.2.a.j.1.13		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.13	✓	25	1.1	even	1	trivial
6025.2.a.j.1.13		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)

\(f(q)\)	\(=\)	\(q+0.362712 q^{2} +3.41577 q^{3} -1.86844 q^{4} +1.00000 q^{5} +1.23894 q^{6} +3.34046 q^{7} -1.40313 q^{8} +8.66752 q^{9} +O(q^{10})\)	\(q+0.362712 q^{2} +3.41577 q^{3} -1.86844 q^{4} +1.00000 q^{5} +1.23894 q^{6} +3.34046 q^{7} -1.40313 q^{8} +8.66752 q^{9} +0.362712 q^{10} -2.67832 q^{11} -6.38217 q^{12} +0.591068 q^{13} +1.21163 q^{14} +3.41577 q^{15} +3.22795 q^{16} -1.07744 q^{17} +3.14382 q^{18} -5.88556 q^{19} -1.86844 q^{20} +11.4103 q^{21} -0.971461 q^{22} +2.98266 q^{23} -4.79278 q^{24} +1.00000 q^{25} +0.214388 q^{26} +19.3590 q^{27} -6.24145 q^{28} +3.96926 q^{29} +1.23894 q^{30} -4.71138 q^{31} +3.97708 q^{32} -9.14854 q^{33} -0.390800 q^{34} +3.34046 q^{35} -16.1947 q^{36} +8.86039 q^{37} -2.13477 q^{38} +2.01895 q^{39} -1.40313 q^{40} -9.79063 q^{41} +4.13864 q^{42} -2.42881 q^{43} +5.00428 q^{44} +8.66752 q^{45} +1.08185 q^{46} -9.02079 q^{47} +11.0259 q^{48} +4.15867 q^{49} +0.362712 q^{50} -3.68028 q^{51} -1.10437 q^{52} -14.0701 q^{53} +7.02174 q^{54} -2.67832 q^{55} -4.68710 q^{56} -20.1037 q^{57} +1.43970 q^{58} +9.68407 q^{59} -6.38217 q^{60} -0.830604 q^{61} -1.70887 q^{62} +28.9535 q^{63} -5.01336 q^{64} +0.591068 q^{65} -3.31829 q^{66} +10.9586 q^{67} +2.01313 q^{68} +10.1881 q^{69} +1.21163 q^{70} +0.250176 q^{71} -12.1617 q^{72} -10.3124 q^{73} +3.21377 q^{74} +3.41577 q^{75} +10.9968 q^{76} -8.94682 q^{77} +0.732300 q^{78} +10.1480 q^{79} +3.22795 q^{80} +40.1233 q^{81} -3.55119 q^{82} -7.04557 q^{83} -21.3194 q^{84} -1.07744 q^{85} -0.880961 q^{86} +13.5581 q^{87} +3.75804 q^{88} +6.66265 q^{89} +3.14382 q^{90} +1.97444 q^{91} -5.57292 q^{92} -16.0930 q^{93} -3.27195 q^{94} -5.88556 q^{95} +13.5848 q^{96} +0.0770398 q^{97} +1.50840 q^{98} -23.2144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

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