LMFDB - Embedded newform 4730.2.a.z.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 21x^{7} + 107x^{6} - 45x^{5} - 262x^{4} - 47x^{3} + 120x^{2} - 2x - 6 $ x^10 - 2x^9 - 17x^8 + 21x^7 + 107x^6 - 45x^5 - 262x^4 - 47x^3 + 120x^2 - 2*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.88983$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.88983 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.88983 q^{6} -3.45622 q^{7} -1.00000 q^{8} +0.571445 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.88983 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.88983 q^{6} -3.45622 q^{7} -1.00000 q^{8} +0.571445 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.88983 q^{12} -1.07751 q^{13} +3.45622 q^{14} -1.88983 q^{15} +1.00000 q^{16} +4.59357 q^{17} -0.571445 q^{18} -6.77604 q^{19} +1.00000 q^{20} +6.53165 q^{21} -1.00000 q^{22} +8.70472 q^{23} +1.88983 q^{24} +1.00000 q^{25} +1.07751 q^{26} +4.58955 q^{27} -3.45622 q^{28} -5.36254 q^{29} +1.88983 q^{30} -4.60842 q^{31} -1.00000 q^{32} -1.88983 q^{33} -4.59357 q^{34} -3.45622 q^{35} +0.571445 q^{36} -7.21267 q^{37} +6.77604 q^{38} +2.03630 q^{39} -1.00000 q^{40} -7.42557 q^{41} -6.53165 q^{42} +1.00000 q^{43} +1.00000 q^{44} +0.571445 q^{45} -8.70472 q^{46} +11.0724 q^{47} -1.88983 q^{48} +4.94542 q^{49} -1.00000 q^{50} -8.68106 q^{51} -1.07751 q^{52} -11.2984 q^{53} -4.58955 q^{54} +1.00000 q^{55} +3.45622 q^{56} +12.8055 q^{57} +5.36254 q^{58} +12.0322 q^{59} -1.88983 q^{60} -7.57534 q^{61} +4.60842 q^{62} -1.97504 q^{63} +1.00000 q^{64} -1.07751 q^{65} +1.88983 q^{66} +6.54539 q^{67} +4.59357 q^{68} -16.4504 q^{69} +3.45622 q^{70} -9.42496 q^{71} -0.571445 q^{72} -15.2890 q^{73} +7.21267 q^{74} -1.88983 q^{75} -6.77604 q^{76} -3.45622 q^{77} -2.03630 q^{78} -17.5153 q^{79} +1.00000 q^{80} -10.3878 q^{81} +7.42557 q^{82} +11.9844 q^{83} +6.53165 q^{84} +4.59357 q^{85} -1.00000 q^{86} +10.1343 q^{87} -1.00000 q^{88} +2.04961 q^{89} -0.571445 q^{90} +3.72409 q^{91} +8.70472 q^{92} +8.70912 q^{93} -11.0724 q^{94} -6.77604 q^{95} +1.88983 q^{96} +17.4928 q^{97} -4.94542 q^{98} +0.571445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.88983	−1.09109	−0.545546	−	0.838081i	$-0.683678\pi$
$3$	−1.88983	−1.09109	−0.545546	+	0.838081i	$0.683678\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.88983	0.771518
$7$	−3.45622	−1.30633	−0.653163	−	0.757217i	$-0.726558\pi$
$7$	−3.45622	−1.30633	−0.653163	+	0.757217i	$0.726558\pi$
$8$	−1.00000	−0.353553
$9$	0.571445	0.190482
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.88983	−0.545546
$13$	−1.07751	−0.298846	−0.149423	−	0.988773i	$-0.547742\pi$
$13$	−1.07751	−0.298846	−0.149423	+	0.988773i	$0.547742\pi$
$14$	3.45622	0.923712
$15$	−1.88983	−0.487951
$16$	1.00000	0.250000
$17$	4.59357	1.11410	0.557052	−	0.830477i	$-0.311932\pi$
$17$	4.59357	1.11410	0.557052	+	0.830477i	$0.311932\pi$
$18$	−0.571445	−0.134691
$19$	−6.77604	−1.55453	−0.777265	−	0.629174i	$-0.783393\pi$
$19$	−6.77604	−1.55453	−0.777265	+	0.629174i	$0.783393\pi$
$20$	1.00000	0.223607
$21$	6.53165	1.42532
$22$	−1.00000	−0.213201
$23$	8.70472	1.81506	0.907529	−	0.419989i	$-0.137966\pi$
$23$	8.70472	1.81506	0.907529	+	0.419989i	$0.137966\pi$
$24$	1.88983	0.385759
$25$	1.00000	0.200000
$26$	1.07751	0.211316
$27$	4.58955	0.883259
$28$	−3.45622	−0.653163
$29$	−5.36254	−0.995798	−0.497899	−	0.867235i	$-0.665895\pi$
$29$	−5.36254	−0.995798	−0.497899	+	0.867235i	$0.665895\pi$
$30$	1.88983	0.345034
$31$	−4.60842	−0.827698	−0.413849	−	0.910346i	$-0.635816\pi$
$31$	−4.60842	−0.827698	−0.413849	+	0.910346i	$0.635816\pi$
$32$	−1.00000	−0.176777
$33$	−1.88983	−0.328977
$34$	−4.59357	−0.787791
$35$	−3.45622	−0.584207
$36$	0.571445	0.0952408
$37$	−7.21267	−1.18576	−0.592878	−	0.805293i	$-0.702008\pi$
$37$	−7.21267	−1.18576	−0.592878	+	0.805293i	$0.702008\pi$
$38$	6.77604	1.09922
$39$	2.03630	0.326069
$40$	−1.00000	−0.158114
$41$	−7.42557	−1.15968	−0.579839	−	0.814731i	$-0.696885\pi$
$41$	−7.42557	−1.15968	−0.579839	+	0.814731i	$0.696885\pi$
$42$	−6.53165	−1.00786
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	0.571445	0.0851859
$46$	−8.70472	−1.28344
$47$	11.0724	1.61507	0.807534	−	0.589820i	$-0.200801\pi$
$47$	11.0724	1.61507	0.807534	+	0.589820i	$0.200801\pi$
$48$	−1.88983	−0.272773
$49$	4.94542	0.706489
$50$	−1.00000	−0.141421
$51$	−8.68106	−1.21559
$52$	−1.07751	−0.149423
$53$	−11.2984	−1.55196	−0.775980	−	0.630757i	$-0.782744\pi$
$53$	−11.2984	−1.55196	−0.775980	+	0.630757i	$0.782744\pi$
$54$	−4.58955	−0.624558
$55$	1.00000	0.134840
$56$	3.45622	0.461856
$57$	12.8055	1.69613
$58$	5.36254	0.704135
$59$	12.0322	1.56646	0.783231	−	0.621731i	$-0.213570\pi$
$59$	12.0322	1.56646	0.783231	+	0.621731i	$0.213570\pi$
$60$	−1.88983	−0.243976
$61$	−7.57534	−0.969923	−0.484962	−	0.874535i	$-0.661166\pi$
$61$	−7.57534	−0.969923	−0.484962	+	0.874535i	$0.661166\pi$
$62$	4.60842	0.585271
$63$	−1.97504	−0.248831
$64$	1.00000	0.125000
$65$	−1.07751	−0.133648
$66$	1.88983	0.232622
$67$	6.54539	0.799647	0.399824	−	0.916592i	$-0.369071\pi$
$67$	6.54539	0.799647	0.399824	+	0.916592i	$0.369071\pi$
$68$	4.59357	0.557052
$69$	−16.4504	−1.98040
$70$	3.45622	0.413097
$71$	−9.42496	−1.11854	−0.559268	−	0.828987i	$-0.688918\pi$
$71$	−9.42496	−1.11854	−0.559268	+	0.828987i	$0.688918\pi$
$72$	−0.571445	−0.0673454
$73$	−15.2890	−1.78944	−0.894720	−	0.446628i	$-0.852625\pi$
$73$	−15.2890	−1.78944	−0.894720	+	0.446628i	$0.852625\pi$
$74$	7.21267	0.838455
$75$	−1.88983	−0.218218
$76$	−6.77604	−0.777265
$77$	−3.45622	−0.393872
$78$	−2.03630	−0.230565
$79$	−17.5153	−1.97063	−0.985313	−	0.170759i	$-0.945378\pi$
$79$	−17.5153	−1.97063	−0.985313	+	0.170759i	$0.945378\pi$
$80$	1.00000	0.111803
$81$	−10.3878	−1.15420
$82$	7.42557	0.820017
$83$	11.9844	1.31546	0.657731	−	0.753253i	$-0.271516\pi$
$83$	11.9844	1.31546	0.657731	+	0.753253i	$0.271516\pi$
$84$	6.53165	0.712661
$85$	4.59357	0.498243
$86$	−1.00000	−0.107833
$87$	10.1343	1.08651
$88$	−1.00000	−0.106600
$89$	2.04961	0.217258	0.108629	−	0.994082i	$-0.465354\pi$
$89$	2.04961	0.217258	0.108629	+	0.994082i	$0.465354\pi$
$90$	−0.571445	−0.0602356
$91$	3.72409	0.390391
$92$	8.70472	0.907529
$93$	8.70912	0.903094
$94$	−11.0724	−1.14203
$95$	−6.77604	−0.695207
$96$	1.88983	0.192880
$97$	17.4928	1.77612	0.888062	−	0.459725i	$-0.152052\pi$
$97$	17.4928	1.77612	0.888062	+	0.459725i	$0.152052\pi$
$98$	−4.94542	−0.499563
$99$	0.571445	0.0574323
$100$	1.00000	0.100000
$101$	6.35009	0.631857	0.315929	−	0.948783i	$-0.397684\pi$
$101$	6.35009	0.631857	0.315929	+	0.948783i	$0.397684\pi$
$102$	8.68106	0.859553
$103$	−16.4883	−1.62464	−0.812321	−	0.583211i	$-0.801796\pi$
$103$	−16.4883	−1.62464	−0.812321	+	0.583211i	$0.801796\pi$
$104$	1.07751	0.105658
$105$	6.53165	0.637423
$106$	11.2984	1.09740
$107$	8.99548	0.869626	0.434813	−	0.900521i	$-0.356814\pi$
$107$	8.99548	0.869626	0.434813	+	0.900521i	$0.356814\pi$
$108$	4.58955	0.441630
$109$	−3.22082	−0.308499	−0.154249	−	0.988032i	$-0.549296\pi$
$109$	−3.22082	−0.308499	−0.154249	+	0.988032i	$0.549296\pi$
$110$	−1.00000	−0.0953463
$111$	13.6307	1.29377
$112$	−3.45622	−0.326582
$113$	1.08010	0.101607	0.0508036	−	0.998709i	$-0.483822\pi$
$113$	1.08010	0.101607	0.0508036	+	0.998709i	$0.483822\pi$
$114$	−12.8055	−1.19935
$115$	8.70472	0.811719
$116$	−5.36254	−0.497899
$117$	−0.615734	−0.0569247
$118$	−12.0322	−1.10766
$119$	−15.8764	−1.45538
$120$	1.88983	0.172517
$121$	1.00000	0.0909091
$122$	7.57534	0.685839
$123$	14.0330	1.26532
$124$	−4.60842	−0.413849
$125$	1.00000	0.0894427
$126$	1.97504	0.175950
$127$	−9.67459	−0.858481	−0.429240	−	0.903190i	$-0.641219\pi$
$127$	−9.67459	−0.858481	−0.429240	+	0.903190i	$0.641219\pi$
$128$	−1.00000	−0.0883883
$129$	−1.88983	−0.166390
$130$	1.07751	0.0945034
$131$	16.5621	1.44704	0.723518	−	0.690305i	$-0.242524\pi$
$131$	16.5621	1.44704	0.723518	+	0.690305i	$0.242524\pi$
$132$	−1.88983	−0.164488
$133$	23.4194	2.03072
$134$	−6.54539	−0.565436
$135$	4.58955	0.395005
$136$	−4.59357	−0.393896
$137$	10.1048	0.863310	0.431655	−	0.902039i	$-0.357930\pi$
$137$	10.1048	0.863310	0.431655	+	0.902039i	$0.357930\pi$
$138$	16.4504	1.40035
$139$	16.7883	1.42396	0.711980	−	0.702199i	$-0.247798\pi$
$139$	16.7883	1.42396	0.711980	+	0.702199i	$0.247798\pi$
$140$	−3.45622	−0.292103
$141$	−20.9248	−1.76219
$142$	9.42496	0.790925
$143$	−1.07751	−0.0901055
$144$	0.571445	0.0476204
$145$	−5.36254	−0.445334
$146$	15.2890	1.26533
$147$	−9.34599	−0.770844
$148$	−7.21267	−0.592878
$149$	−8.89973	−0.729094	−0.364547	−	0.931185i	$-0.618776\pi$
$149$	−8.89973	−0.729094	−0.364547	+	0.931185i	$0.618776\pi$
$150$	1.88983	0.154304
$151$	12.7841	1.04036	0.520178	−	0.854058i	$-0.325866\pi$
$151$	12.7841	1.04036	0.520178	+	0.854058i	$0.325866\pi$
$152$	6.77604	0.549609
$153$	2.62497	0.212216
$154$	3.45622	0.278510
$155$	−4.60842	−0.370158
$156$	2.03630	0.163034
$157$	1.70031	0.135699	0.0678496	−	0.997696i	$-0.478386\pi$
$157$	1.70031	0.135699	0.0678496	+	0.997696i	$0.478386\pi$
$158$	17.5153	1.39344
$159$	21.3521	1.69333
$160$	−1.00000	−0.0790569
$161$	−30.0854	−2.37106
$162$	10.3878	0.816141
$163$	10.3010	0.806835	0.403418	−	0.915016i	$-0.367822\pi$
$163$	10.3010	0.806835	0.403418	+	0.915016i	$0.367822\pi$
$164$	−7.42557	−0.579839
$165$	−1.88983	−0.147123
$166$	−11.9844	−0.930172
$167$	9.69317	0.750080	0.375040	−	0.927009i	$-0.377629\pi$
$167$	9.69317	0.750080	0.375040	+	0.927009i	$0.377629\pi$
$168$	−6.53165	−0.503928
$169$	−11.8390	−0.910691
$170$	−4.59357	−0.352311
$171$	−3.87213	−0.296109
$172$	1.00000	0.0762493
$173$	−15.4912	−1.17778	−0.588889	−	0.808214i	$-0.700434\pi$
$173$	−15.4912	−1.17778	−0.588889	+	0.808214i	$0.700434\pi$
$174$	−10.1343	−0.768277
$175$	−3.45622	−0.261265
$176$	1.00000	0.0753778
$177$	−22.7388	−1.70915
$178$	−2.04961	−0.153625
$179$	19.4443	1.45333	0.726667	−	0.686989i	$-0.241068\pi$
$179$	19.4443	1.45333	0.726667	+	0.686989i	$0.241068\pi$
$180$	0.571445	0.0425930
$181$	−6.81662	−0.506675	−0.253338	−	0.967378i	$-0.581528\pi$
$181$	−6.81662	−0.506675	−0.253338	+	0.967378i	$0.581528\pi$
$182$	−3.72409	−0.276048
$183$	14.3161	1.05828
$184$	−8.70472	−0.641720
$185$	−7.21267	−0.530286
$186$	−8.70912	−0.638584
$187$	4.59357	0.335915
$188$	11.0724	0.807534
$189$	−15.8625	−1.15382
$190$	6.77604	0.491585
$191$	−8.02035	−0.580332	−0.290166	−	0.956976i	$-0.593711\pi$
$191$	−8.02035	−0.580332	−0.290166	+	0.956976i	$0.593711\pi$
$192$	−1.88983	−0.136386
$193$	−9.01693	−0.649053	−0.324526	−	0.945877i	$-0.605205\pi$
$193$	−9.01693	−0.649053	−0.324526	+	0.945877i	$0.605205\pi$
$194$	−17.4928	−1.25591
$195$	2.03630	0.145822
$196$	4.94542	0.353244
$197$	−25.1470	−1.79165	−0.895825	−	0.444408i	$-0.853414\pi$
$197$	−25.1470	−1.79165	−0.895825	+	0.444408i	$0.853414\pi$
$198$	−0.571445	−0.0406108
$199$	−5.50392	−0.390163	−0.195081	−	0.980787i	$-0.562497\pi$
$199$	−5.50392	−0.390163	−0.195081	+	0.980787i	$0.562497\pi$
$200$	−1.00000	−0.0707107
$201$	−12.3697	−0.872489
$202$	−6.35009	−0.446791
$203$	18.5341	1.30084
$204$	−8.68106	−0.607795
$205$	−7.42557	−0.518624
$206$	16.4883	1.14880
$207$	4.97426	0.345735
$208$	−1.07751	−0.0747115
$209$	−6.77604	−0.468708
$210$	−6.53165	−0.450726
$211$	−10.3421	−0.711982	−0.355991	−	0.934489i	$-0.615857\pi$
$211$	−10.3421	−0.711982	−0.355991	+	0.934489i	$0.615857\pi$
$212$	−11.2984	−0.775980
$213$	17.8115	1.22043
$214$	−8.99548	−0.614919
$215$	1.00000	0.0681994
$216$	−4.58955	−0.312279
$217$	15.9277	1.08124
$218$	3.22082	0.218142
$219$	28.8935	1.95244
$220$	1.00000	0.0674200
$221$	−4.94960	−0.332946
$222$	−13.6307	−0.914832
$223$	−14.5630	−0.975209	−0.487605	−	0.873065i	$-0.662129\pi$
$223$	−14.5630	−0.975209	−0.487605	+	0.873065i	$0.662129\pi$
$224$	3.45622	0.230928
$225$	0.571445	0.0380963
$226$	−1.08010	−0.0718471
$227$	−17.2021	−1.14174	−0.570872	−	0.821039i	$-0.693395\pi$
$227$	−17.2021	−1.14174	−0.570872	+	0.821039i	$0.693395\pi$
$228$	12.8055	0.848067
$229$	13.8155	0.912954	0.456477	−	0.889735i	$-0.349111\pi$
$229$	13.8155	0.912954	0.456477	+	0.889735i	$0.349111\pi$
$230$	−8.70472	−0.573972
$231$	6.53165	0.429751
$232$	5.36254	0.352068
$233$	9.04894	0.592816	0.296408	−	0.955061i	$-0.404211\pi$
$233$	9.04894	0.592816	0.296408	+	0.955061i	$0.404211\pi$
$234$	0.615734	0.0402518
$235$	11.0724	0.722281
$236$	12.0322	0.783231
$237$	33.1009	2.15013
$238$	15.8764	1.02911
$239$	22.8641	1.47896	0.739479	−	0.673180i	$-0.235072\pi$
$239$	22.8641	1.47896	0.739479	+	0.673180i	$0.235072\pi$
$240$	−1.88983	−0.121988
$241$	−4.14263	−0.266850	−0.133425	−	0.991059i	$-0.542598\pi$
$241$	−4.14263	−0.266850	−0.133425	+	0.991059i	$0.542598\pi$
$242$	−1.00000	−0.0642824
$243$	5.86247	0.376077
$244$	−7.57534	−0.484962
$245$	4.94542	0.315951
$246$	−14.0330	−0.894714
$247$	7.30121	0.464565
$248$	4.60842	0.292635
$249$	−22.6485	−1.43529
$250$	−1.00000	−0.0632456
$251$	−2.52626	−0.159456	−0.0797281	−	0.996817i	$-0.525405\pi$
$251$	−2.52626	−0.159456	−0.0797281	+	0.996817i	$0.525405\pi$
$252$	−1.97504	−0.124416
$253$	8.70472	0.547261
$254$	9.67459	0.607038
$255$	−8.68106	−0.543629
$256$	1.00000	0.0625000
$257$	10.6223	0.662599	0.331300	−	0.943526i	$-0.392513\pi$
$257$	10.6223	0.662599	0.331300	+	0.943526i	$0.392513\pi$
$258$	1.88983	0.117655
$259$	24.9285	1.54898
$260$	−1.07751	−0.0668240
$261$	−3.06439	−0.189681
$262$	−16.5621	−1.02321
$263$	21.1937	1.30686	0.653431	−	0.756986i	$-0.273329\pi$
$263$	21.1937	1.30686	0.653431	+	0.756986i	$0.273329\pi$
$264$	1.88983	0.116311
$265$	−11.2984	−0.694058
$266$	−23.4194	−1.43594
$267$	−3.87341	−0.237049
$268$	6.54539	0.399824
$269$	−4.15461	−0.253311	−0.126655	−	0.991947i	$-0.540424\pi$
$269$	−4.15461	−0.253311	−0.126655	+	0.991947i	$0.540424\pi$
$270$	−4.58955	−0.279311
$271$	18.9427	1.15069	0.575343	−	0.817912i	$-0.304868\pi$
$271$	18.9427	1.15069	0.575343	+	0.817912i	$0.304868\pi$
$272$	4.59357	0.278526
$273$	−7.03788	−0.425952
$274$	−10.1048	−0.610452
$275$	1.00000	0.0603023
$276$	−16.4504	−0.990198
$277$	17.5473	1.05432	0.527158	−	0.849767i	$-0.323258\pi$
$277$	17.5473	1.05432	0.527158	+	0.849767i	$0.323258\pi$
$278$	−16.7883	−1.00689
$279$	−2.63346	−0.157661
$280$	3.45622	0.206548
$281$	13.4738	0.803780	0.401890	−	0.915688i	$-0.368353\pi$
$281$	13.4738	0.803780	0.401890	+	0.915688i	$0.368353\pi$
$282$	20.9248	1.24606
$283$	12.9479	0.769670	0.384835	−	0.922985i	$-0.374258\pi$
$283$	12.9479	0.769670	0.384835	+	0.922985i	$0.374258\pi$
$284$	−9.42496	−0.559268
$285$	12.8055	0.758534
$286$	1.07751	0.0637142
$287$	25.6644	1.51492
$288$	−0.571445	−0.0336727
$289$	4.10091	0.241230
$290$	5.36254	0.314899
$291$	−33.0583	−1.93791
$292$	−15.2890	−0.894720
$293$	24.7492	1.44586	0.722932	−	0.690919i	$-0.242794\pi$
$293$	24.7492	1.44586	0.722932	+	0.690919i	$0.242794\pi$
$294$	9.34599	0.545069
$295$	12.0322	0.700543
$296$	7.21267	0.419228
$297$	4.58955	0.266313
$298$	8.89973	0.515548
$299$	−9.37938	−0.542423
$300$	−1.88983	−0.109109
$301$	−3.45622	−0.199213
$302$	−12.7841	−0.735643
$303$	−12.0006	−0.689415
$304$	−6.77604	−0.388632
$305$	−7.57534	−0.433763
$306$	−2.62497	−0.150060
$307$	−19.0895	−1.08949	−0.544747	−	0.838601i	$-0.683374\pi$
$307$	−19.0895	−1.08949	−0.544747	+	0.838601i	$0.683374\pi$
$308$	−3.45622	−0.196936
$309$	31.1601	1.77263
$310$	4.60842	0.261741
$311$	12.7689	0.724057	0.362029	−	0.932167i	$-0.382084\pi$
$311$	12.7689	0.724057	0.362029	+	0.932167i	$0.382084\pi$
$312$	−2.03630	−0.115283
$313$	−14.5767	−0.823926	−0.411963	−	0.911201i	$-0.635157\pi$
$313$	−14.5767	−0.823926	−0.411963	+	0.911201i	$0.635157\pi$
$314$	−1.70031	−0.0959539
$315$	−1.97504	−0.111281
$316$	−17.5153	−0.985313
$317$	26.4861	1.48761	0.743805	−	0.668397i	$-0.233019\pi$
$317$	26.4861	1.48761	0.743805	+	0.668397i	$0.233019\pi$
$318$	−21.3521	−1.19737
$319$	−5.36254	−0.300244
$320$	1.00000	0.0559017
$321$	−16.9999	−0.948842
$322$	30.0854	1.67659
$323$	−31.1262	−1.73191
$324$	−10.3878	−0.577099
$325$	−1.07751	−0.0597692
$326$	−10.3010	−0.570519
$327$	6.08680	0.336601
$328$	7.42557	0.410008
$329$	−38.2684	−2.10981
$330$	1.88983	0.104032
$331$	25.6588	1.41033	0.705166	−	0.709042i	$-0.250872\pi$
$331$	25.6588	1.41033	0.705166	+	0.709042i	$0.250872\pi$
$332$	11.9844	0.657731
$333$	−4.12164	−0.225864
$334$	−9.69317	−0.530387
$335$	6.54539	0.357613
$336$	6.53165	0.356331
$337$	26.1800	1.42612	0.713059	−	0.701104i	$-0.247309\pi$
$337$	26.1800	1.42612	0.713059	+	0.701104i	$0.247309\pi$
$338$	11.8390	0.643956
$339$	−2.04120	−0.110863
$340$	4.59357	0.249121
$341$	−4.60842	−0.249560
$342$	3.87213	0.209381
$343$	7.10106	0.383421
$344$	−1.00000	−0.0539164
$345$	−16.4504	−0.885660
$346$	15.4912	0.832814
$347$	0.381914	0.0205022	0.0102511	−	0.999947i	$-0.496737\pi$
$347$	0.381914	0.0205022	0.0102511	+	0.999947i	$0.496737\pi$
$348$	10.1343	0.543254
$349$	36.1193	1.93342	0.966710	−	0.255875i	$-0.0823636\pi$
$349$	36.1193	1.93342	0.966710	+	0.255875i	$0.0823636\pi$
$350$	3.45622	0.184742
$351$	−4.94526	−0.263959
$352$	−1.00000	−0.0533002
$353$	13.8626	0.737833	0.368917	−	0.929463i	$-0.379729\pi$
$353$	13.8626	0.737833	0.368917	+	0.929463i	$0.379729\pi$
$354$	22.7388	1.20855
$355$	−9.42496	−0.500225
$356$	2.04961	0.108629
$357$	30.0036	1.58796
$358$	−19.4443	−1.02766
$359$	−6.72567	−0.354967	−0.177484	−	0.984124i	$-0.556796\pi$
$359$	−6.72567	−0.354967	−0.177484	+	0.984124i	$0.556796\pi$
$360$	−0.571445	−0.0301178
$361$	26.9147	1.41656
$362$	6.81662	0.358273
$363$	−1.88983	−0.0991902
$364$	3.72409	0.195195
$365$	−15.2890	−0.800262
$366$	−14.3161	−0.748314
$367$	−18.1752	−0.948737	−0.474368	−	0.880326i	$-0.657323\pi$
$367$	−18.1752	−0.948737	−0.474368	+	0.880326i	$0.657323\pi$
$368$	8.70472	0.453765
$369$	−4.24330	−0.220897
$370$	7.21267	0.374969
$371$	39.0498	2.02737
$372$	8.70912	0.451547
$373$	10.2057	0.528429	0.264214	−	0.964464i	$-0.414887\pi$
$373$	10.2057	0.528429	0.264214	+	0.964464i	$0.414887\pi$
$374$	−4.59357	−0.237528
$375$	−1.88983	−0.0975902
$376$	−11.0724	−0.571013
$377$	5.77816	0.297590
$378$	15.8625	0.815877
$379$	−15.2049	−0.781023	−0.390512	−	0.920598i	$-0.627702\pi$
$379$	−15.2049	−0.781023	−0.390512	+	0.920598i	$0.627702\pi$
$380$	−6.77604	−0.347603
$381$	18.2833	0.936681
$382$	8.02035	0.410357
$383$	3.18647	0.162821	0.0814106	−	0.996681i	$-0.474058\pi$
$383$	3.18647	0.162821	0.0814106	+	0.996681i	$0.474058\pi$
$384$	1.88983	0.0964398
$385$	−3.45622	−0.176145
$386$	9.01693	0.458950
$387$	0.571445	0.0290482
$388$	17.4928	0.888062
$389$	6.25531	0.317157	0.158578	−	0.987346i	$-0.449309\pi$
$389$	6.25531	0.317157	0.158578	+	0.987346i	$0.449309\pi$
$390$	−2.03630	−0.103112
$391$	39.9857	2.02217
$392$	−4.94542	−0.249782
$393$	−31.2995	−1.57885
$394$	25.1470	1.26689
$395$	−17.5153	−0.881291
$396$	0.571445	0.0287162
$397$	16.0927	0.807668	0.403834	−	0.914832i	$-0.367677\pi$
$397$	16.0927	0.807668	0.403834	+	0.914832i	$0.367677\pi$
$398$	5.50392	0.275887
$399$	−44.2587	−2.21571
$400$	1.00000	0.0500000
$401$	−22.0145	−1.09935	−0.549675	−	0.835379i	$-0.685248\pi$
$401$	−22.0145	−1.09935	−0.549675	+	0.835379i	$0.685248\pi$
$402$	12.3697	0.616943
$403$	4.96560	0.247354
$404$	6.35009	0.315929
$405$	−10.3878	−0.516173
$406$	−18.5341	−0.919831
$407$	−7.21267	−0.357519
$408$	8.68106	0.429776
$409$	16.4582	0.813806	0.406903	−	0.913471i	$-0.366609\pi$
$409$	16.4582	0.813806	0.406903	+	0.913471i	$0.366609\pi$
$410$	7.42557	0.366723
$411$	−19.0963	−0.941950
$412$	−16.4883	−0.812321
$413$	−41.5860	−2.04631
$414$	−4.97426	−0.244472
$415$	11.9844	0.588293
$416$	1.07751	0.0528290
$417$	−31.7269	−1.55367
$418$	6.77604	0.331427
$419$	19.9866	0.976409	0.488204	−	0.872729i	$-0.337652\pi$
$419$	19.9866	0.976409	0.488204	+	0.872729i	$0.337652\pi$
$420$	6.53165	0.318712
$421$	28.4459	1.38637	0.693185	−	0.720760i	$-0.256207\pi$
$421$	28.4459	1.38637	0.693185	+	0.720760i	$0.256207\pi$
$422$	10.3421	0.503447
$423$	6.32724	0.307641
$424$	11.2984	0.548701
$425$	4.59357	0.222821
$426$	−17.8115	−0.862972
$427$	26.1820	1.26704
$428$	8.99548	0.434813
$429$	2.03630	0.0983134
$430$	−1.00000	−0.0482243
$431$	−4.26692	−0.205530	−0.102765	−	0.994706i	$-0.532769\pi$
$431$	−4.26692	−0.205530	−0.102765	+	0.994706i	$0.532769\pi$
$432$	4.58955	0.220815
$433$	2.49978	0.120132	0.0600659	−	0.998194i	$-0.480869\pi$
$433$	2.49978	0.120132	0.0600659	+	0.998194i	$0.480869\pi$
$434$	−15.9277	−0.764554
$435$	10.1343	0.485901
$436$	−3.22082	−0.154249
$437$	−58.9835	−2.82156
$438$	−28.8935	−1.38059
$439$	−20.6046	−0.983403	−0.491702	−	0.870764i	$-0.663625\pi$
$439$	−20.6046	−0.983403	−0.491702	+	0.870764i	$0.663625\pi$
$440$	−1.00000	−0.0476731
$441$	2.82604	0.134573
$442$	4.94960	0.235428
$443$	21.0118	0.998302	0.499151	−	0.866515i	$-0.333645\pi$
$443$	21.0118	0.998302	0.499151	+	0.866515i	$0.333645\pi$
$444$	13.6307	0.646884
$445$	2.04961	0.0971608
$446$	14.5630	0.689577
$447$	16.8189	0.795509
$448$	−3.45622	−0.163291
$449$	37.0426	1.74815	0.874075	−	0.485792i	$-0.161469\pi$
$449$	37.0426	1.74815	0.874075	+	0.485792i	$0.161469\pi$
$450$	−0.571445	−0.0269382
$451$	−7.42557	−0.349656
$452$	1.08010	0.0508036
$453$	−24.1598	−1.13512
$454$	17.2021	0.807336
$455$	3.72409	0.174588
$456$	−12.8055	−0.599674
$457$	23.7135	1.10927	0.554636	−	0.832093i	$-0.312858\pi$
$457$	23.7135	1.10927	0.554636	+	0.832093i	$0.312858\pi$
$458$	−13.8155	−0.645556
$459$	21.0824	0.984043
$460$	8.70472	0.405859
$461$	18.1272	0.844269	0.422135	−	0.906533i	$-0.361281\pi$
$461$	18.1272	0.844269	0.422135	+	0.906533i	$0.361281\pi$
$462$	−6.53165	−0.303880
$463$	−1.95012	−0.0906296	−0.0453148	−	0.998973i	$-0.514429\pi$
$463$	−1.95012	−0.0906296	−0.0453148	+	0.998973i	$0.514429\pi$
$464$	−5.36254	−0.248949
$465$	8.70912	0.403876
$466$	−9.04894	−0.419184
$467$	−10.8915	−0.503999	−0.252000	−	0.967727i	$-0.581088\pi$
$467$	−10.8915	−0.503999	−0.252000	+	0.967727i	$0.581088\pi$
$468$	−0.615734	−0.0284623
$469$	−22.6223	−1.04460
$470$	−11.0724	−0.510730
$471$	−3.21329	−0.148060
$472$	−12.0322	−0.553828
$473$	1.00000	0.0459800
$474$	−33.1009	−1.52037
$475$	−6.77604	−0.310906
$476$	−15.8764	−0.727692
$477$	−6.45643	−0.295620
$478$	−22.8641	−1.04578
$479$	−20.1081	−0.918763	−0.459381	−	0.888239i	$-0.651929\pi$
$479$	−20.1081	−0.918763	−0.459381	+	0.888239i	$0.651929\pi$
$480$	1.88983	0.0862584
$481$	7.77168	0.354358
$482$	4.14263	0.188692
$483$	56.8561	2.58704
$484$	1.00000	0.0454545
$485$	17.4928	0.794306
$486$	−5.86247	−0.265927
$487$	0.0886944	0.00401913	0.00200956	−	0.999998i	$-0.499360\pi$
$487$	0.0886944	0.00401913	0.00200956	+	0.999998i	$0.499360\pi$
$488$	7.57534	0.342920
$489$	−19.4671	−0.880331
$490$	−4.94542	−0.223411
$491$	17.0693	0.770328	0.385164	−	0.922848i	$-0.374145\pi$
$491$	17.0693	0.770328	0.385164	+	0.922848i	$0.374145\pi$
$492$	14.0330	0.632658
$493$	−24.6332	−1.10942
$494$	−7.30121	−0.328497
$495$	0.571445	0.0256845
$496$	−4.60842	−0.206924
$497$	32.5747	1.46117
$498$	22.6485	1.01490
$499$	19.6472	0.879530	0.439765	−	0.898113i	$-0.355062\pi$
$499$	19.6472	0.879530	0.439765	+	0.898113i	$0.355062\pi$
$500$	1.00000	0.0447214
$501$	−18.3184	−0.818406
$502$	2.52626	0.112753
$503$	−30.5714	−1.36311	−0.681555	−	0.731767i	$-0.738696\pi$
$503$	−30.5714	−1.36311	−0.681555	+	0.731767i	$0.738696\pi$
$504$	1.97504	0.0879751
$505$	6.35009	0.282575
$506$	−8.70472	−0.386972
$507$	22.3736	0.993648
$508$	−9.67459	−0.429240
$509$	−41.9122	−1.85773	−0.928863	−	0.370424i	$-0.879212\pi$
$509$	−41.9122	−1.85773	−0.928863	+	0.370424i	$0.879212\pi$
$510$	8.68106	0.384404
$511$	52.8420	2.33759
$512$	−1.00000	−0.0441942
$513$	−31.0989	−1.37305
$514$	−10.6223	−0.468528
$515$	−16.4883	−0.726562
$516$	−1.88983	−0.0831950
$517$	11.0724	0.486962
$518$	−24.9285	−1.09530
$519$	29.2758	1.28506
$520$	1.07751	0.0472517
$521$	24.5762	1.07670	0.538351	−	0.842721i	$-0.319047\pi$
$521$	24.5762	1.07670	0.538351	+	0.842721i	$0.319047\pi$
$522$	3.06439	0.134125
$523$	−8.55331	−0.374010	−0.187005	−	0.982359i	$-0.559878\pi$
$523$	−8.55331	−0.374010	−0.187005	+	0.982359i	$0.559878\pi$
$524$	16.5621	0.723518
$525$	6.53165	0.285064
$526$	−21.1937	−0.924091
$527$	−21.1691	−0.922142
$528$	−1.88983	−0.0822441
$529$	52.7721	2.29444
$530$	11.2984	0.490773
$531$	6.87575	0.298382
$532$	23.4194	1.01536
$533$	8.00109	0.346565
$534$	3.87341	0.167619
$535$	8.99548	0.388909
$536$	−6.54539	−0.282718
$537$	−36.7463	−1.58572
$538$	4.15461	0.179118
$539$	4.94542	0.213014
$540$	4.58955	0.197503
$541$	43.8421	1.88492	0.942459	−	0.334321i	$-0.108507\pi$
$541$	43.8421	1.88492	0.942459	+	0.334321i	$0.108507\pi$
$542$	−18.9427	−0.813658
$543$	12.8822	0.552829
$544$	−4.59357	−0.196948
$545$	−3.22082	−0.137965
$546$	7.03788	0.301194
$547$	30.2464	1.29324	0.646620	−	0.762812i	$-0.276182\pi$
$547$	30.2464	1.29324	0.646620	+	0.762812i	$0.276182\pi$
$548$	10.1048	0.431655
$549$	−4.32889	−0.184752
$550$	−1.00000	−0.0426401
$551$	36.3367	1.54800
$552$	16.4504	0.700176
$553$	60.5367	2.57428
$554$	−17.5473	−0.745514
$555$	13.6307	0.578591
$556$	16.7883	0.711980
$557$	26.2412	1.11188	0.555938	−	0.831224i	$-0.312359\pi$
$557$	26.2412	1.11188	0.555938	+	0.831224i	$0.312359\pi$
$558$	2.63346	0.111483
$559$	−1.07751	−0.0455736
$560$	−3.45622	−0.146052
$561$	−8.68106	−0.366514
$562$	−13.4738	−0.568358
$563$	−22.3309	−0.941135	−0.470567	−	0.882364i	$-0.655951\pi$
$563$	−22.3309	−0.941135	−0.470567	+	0.882364i	$0.655951\pi$
$564$	−20.9248	−0.881094
$565$	1.08010	0.0454401
$566$	−12.9479	−0.544239
$567$	35.9024	1.50776
$568$	9.42496	0.395462
$569$	−19.1033	−0.800853	−0.400427	−	0.916329i	$-0.631138\pi$
$569$	−19.1033	−0.800853	−0.400427	+	0.916329i	$0.631138\pi$
$570$	−12.8055	−0.536365
$571$	16.3831	0.685612	0.342806	−	0.939406i	$-0.388623\pi$
$571$	16.3831	0.685612	0.342806	+	0.939406i	$0.388623\pi$
$572$	−1.07751	−0.0450527
$573$	15.1571	0.633196
$574$	−25.6644	−1.07121
$575$	8.70472	0.363012
$576$	0.571445	0.0238102
$577$	−7.26312	−0.302368	−0.151184	−	0.988506i	$-0.548309\pi$
$577$	−7.26312	−0.302368	−0.151184	+	0.988506i	$0.548309\pi$
$578$	−4.10091	−0.170575
$579$	17.0404	0.708176
$580$	−5.36254	−0.222667
$581$	−41.4208	−1.71842
$582$	33.0583	1.37031
$583$	−11.2984	−0.467934
$584$	15.2890	0.632663
$585$	−0.615734	−0.0254575
$586$	−24.7492	−1.02238
$587$	14.7950	0.610657	0.305328	−	0.952247i	$-0.401234\pi$
$587$	14.7950	0.610657	0.305328	+	0.952247i	$0.401234\pi$
$588$	−9.34599	−0.385422
$589$	31.2269	1.28668
$590$	−12.0322	−0.495359
$591$	47.5235	1.95485
$592$	−7.21267	−0.296439
$593$	14.6562	0.601859	0.300929	−	0.953646i	$-0.402703\pi$
$593$	14.6562	0.601859	0.300929	+	0.953646i	$0.402703\pi$
$594$	−4.58955	−0.188311
$595$	−15.8764	−0.650868
$596$	−8.89973	−0.364547
$597$	10.4015	0.425703
$598$	9.37938	0.383551
$599$	2.16647	0.0885196	0.0442598	−	0.999020i	$-0.485907\pi$
$599$	2.16647	0.0885196	0.0442598	+	0.999020i	$0.485907\pi$
$600$	1.88983	0.0771518
$601$	0.578261	0.0235878	0.0117939	−	0.999930i	$-0.496246\pi$
$601$	0.578261	0.0235878	0.0117939	+	0.999930i	$0.496246\pi$
$602$	3.45622	0.140865
$603$	3.74033	0.152318
$604$	12.7841	0.520178
$605$	1.00000	0.0406558
$606$	12.0006	0.487490
$607$	10.8521	0.440472	0.220236	−	0.975447i	$-0.429317\pi$
$607$	10.8521	0.440472	0.220236	+	0.975447i	$0.429317\pi$
$608$	6.77604	0.274805
$609$	−35.0262	−1.41933
$610$	7.57534	0.306717
$611$	−11.9305	−0.482657
$612$	2.62497	0.106108
$613$	−46.8590	−1.89262	−0.946309	−	0.323262i	$-0.895220\pi$
$613$	−46.8590	−1.89262	−0.946309	+	0.323262i	$0.895220\pi$
$614$	19.0895	0.770388
$615$	14.0330	0.565867
$616$	3.45622	0.139255
$617$	21.8229	0.878556	0.439278	−	0.898351i	$-0.355234\pi$
$617$	21.8229	0.878556	0.439278	+	0.898351i	$0.355234\pi$
$618$	−31.1601	−1.25344
$619$	9.61180	0.386331	0.193165	−	0.981166i	$-0.438125\pi$
$619$	9.61180	0.386331	0.193165	+	0.981166i	$0.438125\pi$
$620$	−4.60842	−0.185079
$621$	39.9507	1.60317
$622$	−12.7689	−0.511986
$623$	−7.08389	−0.283810
$624$	2.03630	0.0815171
$625$	1.00000	0.0400000
$626$	14.5767	0.582603
$627$	12.8055	0.511404
$628$	1.70031	0.0678496
$629$	−33.1319	−1.32106
$630$	1.97504	0.0786873
$631$	−5.74932	−0.228877	−0.114438	−	0.993430i	$-0.536507\pi$
$631$	−5.74932	−0.228877	−0.114438	+	0.993430i	$0.536507\pi$
$632$	17.5153	0.696721
$633$	19.5448	0.776838
$634$	−26.4861	−1.05190
$635$	−9.67459	−0.383924
$636$	21.3521	0.846666
$637$	−5.32872	−0.211131
$638$	5.36254	0.212305
$639$	−5.38584	−0.213061
$640$	−1.00000	−0.0395285
$641$	−5.71092	−0.225568	−0.112784	−	0.993620i	$-0.535977\pi$
$641$	−5.71092	−0.225568	−0.112784	+	0.993620i	$0.535977\pi$
$642$	16.9999	0.670933
$643$	−39.1330	−1.54325	−0.771627	−	0.636075i	$-0.780557\pi$
$643$	−39.1330	−1.54325	−0.771627	+	0.636075i	$0.780557\pi$
$644$	−30.0854	−1.18553
$645$	−1.88983	−0.0744119
$646$	31.1262	1.22464
$647$	−1.14254	−0.0449179	−0.0224589	−	0.999748i	$-0.507149\pi$
$647$	−1.14254	−0.0449179	−0.0224589	+	0.999748i	$0.507149\pi$
$648$	10.3878	0.408071
$649$	12.0322	0.472306
$650$	1.07751	0.0422632
$651$	−30.1006	−1.17974
$652$	10.3010	0.403418
$653$	−12.3063	−0.481582	−0.240791	−	0.970577i	$-0.577407\pi$
$653$	−12.3063	−0.481582	−0.240791	+	0.970577i	$0.577407\pi$
$654$	−6.08680	−0.238013
$655$	16.5621	0.647134
$656$	−7.42557	−0.289920
$657$	−8.73681	−0.340855
$658$	38.2684	1.49186
$659$	−34.7802	−1.35484	−0.677422	−	0.735595i	$-0.736903\pi$
$659$	−34.7802	−1.35484	−0.677422	+	0.735595i	$0.736903\pi$
$660$	−1.88983	−0.0735614
$661$	29.2294	1.13689	0.568446	−	0.822720i	$-0.307545\pi$
$661$	29.2294	1.13689	0.568446	+	0.822720i	$0.307545\pi$
$662$	−25.6588	−0.997256
$663$	9.35388	0.363275
$664$	−11.9844	−0.465086
$665$	23.4194	0.908167
$666$	4.12164	0.159710
$667$	−46.6794	−1.80743
$668$	9.69317	0.375040
$669$	27.5215	1.06404
$670$	−6.54539	−0.252871
$671$	−7.57534	−0.292443
$672$	−6.53165	−0.251964
$673$	−24.2715	−0.935597	−0.467799	−	0.883835i	$-0.654953\pi$
$673$	−24.2715	−0.935597	−0.467799	+	0.883835i	$0.654953\pi$
$674$	−26.1800	−1.00842
$675$	4.58955	0.176652
$676$	−11.8390	−0.455345
$677$	3.54176	0.136121	0.0680605	−	0.997681i	$-0.478319\pi$
$677$	3.54176	0.136121	0.0680605	+	0.997681i	$0.478319\pi$
$678$	2.04120	0.0783918
$679$	−60.4588	−2.32020
$680$	−4.59357	−0.176155
$681$	32.5090	1.24575
$682$	4.60842	0.176466
$683$	−25.3591	−0.970338	−0.485169	−	0.874420i	$-0.661242\pi$
$683$	−25.3591	−0.970338	−0.485169	+	0.874420i	$0.661242\pi$
$684$	−3.87213	−0.148055
$685$	10.1048	0.386084
$686$	−7.10106	−0.271120
$687$	−26.1089	−0.996117
$688$	1.00000	0.0381246
$689$	12.1741	0.463797
$690$	16.4504	0.626256
$691$	−46.6313	−1.77394	−0.886968	−	0.461830i	$-0.847193\pi$
$691$	−46.6313	−1.77394	−0.886968	+	0.461830i	$0.847193\pi$
$692$	−15.4912	−0.588889
$693$	−1.97504	−0.0750254
$694$	−0.381914	−0.0144973
$695$	16.7883	0.636815
$696$	−10.1343	−0.384138
$697$	−34.1099	−1.29200
$698$	−36.1193	−1.36713
$699$	−17.1009	−0.646817
$700$	−3.45622	−0.130633
$701$	−4.84094	−0.182840	−0.0914198	−	0.995812i	$-0.529141\pi$
$701$	−4.84094	−0.182840	−0.0914198	+	0.995812i	$0.529141\pi$
$702$	4.94526	0.186647
$703$	48.8733	1.84329
$704$	1.00000	0.0376889
$705$	−20.9248	−0.788075
$706$	−13.8626	−0.521727
$707$	−21.9473	−0.825412
$708$	−22.7388	−0.854577
$709$	−31.1161	−1.16859	−0.584295	−	0.811541i	$-0.698629\pi$
$709$	−31.1161	−1.16859	−0.584295	+	0.811541i	$0.698629\pi$
$710$	9.42496	0.353712
$711$	−10.0090	−0.375368
$712$	−2.04961	−0.0768124
$713$	−40.1150	−1.50232
$714$	−30.0036	−1.12286
$715$	−1.07751	−0.0402964
$716$	19.4443	0.726667
$717$	−43.2092	−1.61368
$718$	6.72567	0.251000
$719$	4.25998	0.158870	0.0794352	−	0.996840i	$-0.474688\pi$
$719$	4.25998	0.158870	0.0794352	+	0.996840i	$0.474688\pi$
$720$	0.571445	0.0212965
$721$	56.9872	2.12231
$722$	−26.9147	−1.00166
$723$	7.82886	0.291158
$724$	−6.81662	−0.253338
$725$	−5.36254	−0.199160
$726$	1.88983	0.0701380
$727$	11.4378	0.424203	0.212101	−	0.977248i	$-0.431969\pi$
$727$	11.4378	0.424203	0.212101	+	0.977248i	$0.431969\pi$
$728$	−3.72409	−0.138024
$729$	20.0843	0.743863
$730$	15.2890	0.565871
$731$	4.59357	0.169899
$732$	14.3161	0.529138
$733$	−2.21227	−0.0817121	−0.0408560	−	0.999165i	$-0.513009\pi$
$733$	−2.21227	−0.0817121	−0.0408560	+	0.999165i	$0.513009\pi$
$734$	18.1752	0.670858
$735$	−9.34599	−0.344732
$736$	−8.70472	−0.320860
$737$	6.54539	0.241103
$738$	4.24330	0.156198
$739$	33.0428	1.21550	0.607749	−	0.794129i	$-0.292073\pi$
$739$	33.0428	1.21550	0.607749	+	0.794129i	$0.292073\pi$
$740$	−7.21267	−0.265143
$741$	−13.7980	−0.506883
$742$	−39.0498	−1.43356
$743$	32.8702	1.20589	0.602945	−	0.797783i	$-0.293994\pi$
$743$	32.8702	1.20589	0.602945	+	0.797783i	$0.293994\pi$
$744$	−8.70912	−0.319292
$745$	−8.89973	−0.326061
$746$	−10.2057	−0.373656
$747$	6.84844	0.250571
$748$	4.59357	0.167958
$749$	−31.0903	−1.13602
$750$	1.88983	0.0690067
$751$	−31.8864	−1.16355	−0.581777	−	0.813349i	$-0.697642\pi$
$751$	−31.8864	−1.16355	−0.581777	+	0.813349i	$0.697642\pi$
$752$	11.0724	0.403767
$753$	4.77420	0.173981
$754$	−5.77816	−0.210428
$755$	12.7841	0.465261
$756$	−15.8625	−0.576912
$757$	41.6726	1.51462	0.757308	−	0.653058i	$-0.226514\pi$
$757$	41.6726	1.51462	0.757308	+	0.653058i	$0.226514\pi$
$758$	15.2049	0.552267
$759$	−16.4504	−0.597112
$760$	6.77604	0.245793
$761$	−22.7206	−0.823620	−0.411810	−	0.911270i	$-0.635103\pi$
$761$	−22.7206	−0.823620	−0.411810	+	0.911270i	$0.635103\pi$
$762$	−18.2833	−0.662334
$763$	11.1319	0.403000
$764$	−8.02035	−0.290166
$765$	2.62497	0.0949061
$766$	−3.18647	−0.115132
$767$	−12.9648	−0.468131
$768$	−1.88983	−0.0681932
$769$	−49.3991	−1.78138	−0.890689	−	0.454613i	$-0.849778\pi$
$769$	−49.3991	−1.78138	−0.890689	+	0.454613i	$0.849778\pi$
$770$	3.45622	0.124553
$771$	−20.0743	−0.722957
$772$	−9.01693	−0.324526
$773$	52.5239	1.88916	0.944578	−	0.328288i	$-0.106472\pi$
$773$	52.5239	1.88916	0.944578	+	0.328288i	$0.106472\pi$
$774$	−0.571445	−0.0205402
$775$	−4.60842	−0.165540
$776$	−17.4928	−0.627954
$777$	−47.1106	−1.69008
$778$	−6.25531	−0.224264
$779$	50.3159	1.80275
$780$	2.03630	0.0729112
$781$	−9.42496	−0.337251
$782$	−39.9857	−1.42989
$783$	−24.6116	−0.879548
$784$	4.94542	0.176622
$785$	1.70031	0.0606866
$786$	31.2995	1.11642
$787$	−6.04865	−0.215611	−0.107806	−	0.994172i	$-0.534382\pi$
$787$	−6.04865	−0.215611	−0.107806	+	0.994172i	$0.534382\pi$
$788$	−25.1470	−0.895825
$789$	−40.0525	−1.42591
$790$	17.5153	0.623167
$791$	−3.73305	−0.132732
$792$	−0.571445	−0.0203054
$793$	8.16247	0.289858
$794$	−16.0927	−0.571108
$795$	21.3521	0.757281
$796$	−5.50392	−0.195081
$797$	15.7906	0.559333	0.279666	−	0.960097i	$-0.409776\pi$
$797$	15.7906	0.559333	0.279666	+	0.960097i	$0.409776\pi$
$798$	44.2587	1.56674
$799$	50.8617	1.79936
$800$	−1.00000	−0.0353553
$801$	1.17124	0.0413837
$802$	22.0145	0.777358
$803$	−15.2890	−0.539536
$804$	−12.3697	−0.436244
$805$	−30.0854	−1.06037
$806$	−4.96560	−0.174906
$807$	7.85149	0.276385
$808$	−6.35009	−0.223395
$809$	−7.73591	−0.271980	−0.135990	−	0.990710i	$-0.543422\pi$
$809$	−7.73591	−0.271980	−0.135990	+	0.990710i	$0.543422\pi$
$810$	10.3878	0.364990
$811$	−1.69537	−0.0595327	−0.0297663	−	0.999557i	$-0.509476\pi$
$811$	−1.69537	−0.0595327	−0.0297663	+	0.999557i	$0.509476\pi$
$812$	18.5341	0.650419
$813$	−35.7984	−1.25550
$814$	7.21267	0.252804
$815$	10.3010	0.360828
$816$	−8.68106	−0.303898
$817$	−6.77604	−0.237063
$818$	−16.4582	−0.575448
$819$	2.12811	0.0743622
$820$	−7.42557	−0.259312
$821$	14.2645	0.497836	0.248918	−	0.968525i	$-0.419925\pi$
$821$	14.2645	0.497836	0.248918	+	0.968525i	$0.419925\pi$
$822$	19.0963	0.666059
$823$	11.4395	0.398757	0.199379	−	0.979923i	$-0.436108\pi$
$823$	11.4395	0.398757	0.199379	+	0.979923i	$0.436108\pi$
$824$	16.4883	0.574398
$825$	−1.88983	−0.0657953
$826$	41.5860	1.44696
$827$	6.31733	0.219675	0.109837	−	0.993950i	$-0.464967\pi$
$827$	6.31733	0.219675	0.109837	+	0.993950i	$0.464967\pi$
$828$	4.97426	0.172868
$829$	41.6164	1.44540	0.722699	−	0.691163i	$-0.242901\pi$
$829$	41.6164	1.44540	0.722699	+	0.691163i	$0.242901\pi$
$830$	−11.9844	−0.415986
$831$	−33.1614	−1.15036
$832$	−1.07751	−0.0373558
$833$	22.7172	0.787103
$834$	31.7269	1.09861
$835$	9.69317	0.335446
$836$	−6.77604	−0.234354
$837$	−21.1506	−0.731071
$838$	−19.9866	−0.690425
$839$	−12.8606	−0.443999	−0.221999	−	0.975047i	$-0.571258\pi$
$839$	−12.8606	−0.443999	−0.221999	+	0.975047i	$0.571258\pi$
$840$	−6.53165	−0.225363
$841$	−0.243206	−0.00838642
$842$	−28.4459	−0.980311
$843$	−25.4632	−0.876998
$844$	−10.3421	−0.355991
$845$	−11.8390	−0.407273
$846$	−6.32724	−0.217535
$847$	−3.45622	−0.118757
$848$	−11.2984	−0.387990
$849$	−24.4692	−0.839781
$850$	−4.59357	−0.157558
$851$	−62.7842	−2.15222
$852$	17.8115	0.610213
$853$	−41.6895	−1.42742	−0.713710	−	0.700441i	$-0.752986\pi$
$853$	−41.6895	−1.42742	−0.713710	+	0.700441i	$0.752986\pi$
$854$	−26.1820	−0.895930
$855$	−3.87213	−0.132424
$856$	−8.99548	−0.307459
$857$	−14.9183	−0.509599	−0.254800	−	0.966994i	$-0.582009\pi$
$857$	−14.9183	−0.509599	−0.254800	+	0.966994i	$0.582009\pi$
$858$	−2.03630	−0.0695181
$859$	16.9198	0.577296	0.288648	−	0.957435i	$-0.406794\pi$
$859$	16.9198	0.577296	0.288648	+	0.957435i	$0.406794\pi$
$860$	1.00000	0.0340997
$861$	−48.5012	−1.65292
$862$	4.26692	0.145332
$863$	7.18409	0.244549	0.122275	−	0.992496i	$-0.460981\pi$
$863$	7.18409	0.244549	0.122275	+	0.992496i	$0.460981\pi$
$864$	−4.58955	−0.156140
$865$	−15.4912	−0.526718
$866$	−2.49978	−0.0849461
$867$	−7.75001	−0.263204
$868$	15.9277	0.540622
$869$	−17.5153	−0.594166
$870$	−10.1343	−0.343584
$871$	−7.05269	−0.238971
$872$	3.22082	0.109071
$873$	9.99616	0.338319
$874$	58.9835	1.99515
$875$	−3.45622	−0.116841
$876$	28.8935	0.976222
$877$	20.6988	0.698947	0.349474	−	0.936946i	$-0.386360\pi$
$877$	20.6988	0.698947	0.349474	+	0.936946i	$0.386360\pi$
$878$	20.6046	0.695371
$879$	−46.7717	−1.57757
$880$	1.00000	0.0337100
$881$	−16.8633	−0.568140	−0.284070	−	0.958804i	$-0.591685\pi$
$881$	−16.8633	−0.568140	−0.284070	+	0.958804i	$0.591685\pi$
$882$	−2.82604	−0.0951576
$883$	−50.7983	−1.70950	−0.854749	−	0.519042i	$-0.826289\pi$
$883$	−50.7983	−1.70950	−0.854749	+	0.519042i	$0.826289\pi$
$884$	−4.94960	−0.166473
$885$	−22.7388	−0.764357
$886$	−21.0118	−0.705906
$887$	38.9950	1.30932	0.654662	−	0.755921i	$-0.272811\pi$
$887$	38.9950	1.30932	0.654662	+	0.755921i	$0.272811\pi$
$888$	−13.6307	−0.457416
$889$	33.4375	1.12146
$890$	−2.04961	−0.0687031
$891$	−10.3878	−0.348004
$892$	−14.5630	−0.487605
$893$	−75.0267	−2.51067
$894$	−16.8189	−0.562510
$895$	19.4443	0.649951
$896$	3.45622	0.115464
$897$	17.7254	0.591834
$898$	−37.0426	−1.23613
$899$	24.7128	0.824220
$900$	0.571445	0.0190482
$901$	−51.9002	−1.72905
$902$	7.42557	0.247244
$903$	6.53165	0.217360
$904$	−1.08010	−0.0359236
$905$	−6.81662	−0.226592
$906$	24.1598	0.802654
$907$	−26.9022	−0.893271	−0.446636	−	0.894716i	$-0.647378\pi$
$907$	−26.9022	−0.893271	−0.446636	+	0.894716i	$0.647378\pi$
$908$	−17.2021	−0.570872
$909$	3.62872	0.120357
$910$	−3.72409	−0.123452
$911$	−35.0920	−1.16265	−0.581325	−	0.813671i	$-0.697466\pi$
$911$	−35.0920	−1.16265	−0.581325	+	0.813671i	$0.697466\pi$
$912$	12.8055	0.424034
$913$	11.9844	0.396627
$914$	−23.7135	−0.784374
$915$	14.3161	0.473275
$916$	13.8155	0.456477
$917$	−57.2421	−1.89030
$918$	−21.0824	−0.695824
$919$	9.80966	0.323591	0.161795	−	0.986824i	$-0.448272\pi$
$919$	9.80966	0.323591	0.161795	+	0.986824i	$0.448272\pi$
$920$	−8.70472	−0.286986
$921$	36.0758	1.18874
$922$	−18.1272	−0.596988
$923$	10.1554	0.334270
$924$	6.53165	0.214875
$925$	−7.21267	−0.237151
$926$	1.95012	0.0640848
$927$	−9.42216	−0.309464
$928$	5.36254	0.176034
$929$	−5.90224	−0.193646	−0.0968230	−	0.995302i	$-0.530868\pi$
$929$	−5.90224	−0.193646	−0.0968230	+	0.995302i	$0.530868\pi$
$930$	−8.70912	−0.285583
$931$	−33.5104	−1.09826
$932$	9.04894	0.296408
$933$	−24.1310	−0.790013
$934$	10.8915	0.356381
$935$	4.59357	0.150226
$936$	0.615734	0.0201259
$937$	−11.8302	−0.386477	−0.193238	−	0.981152i	$-0.561899\pi$
$937$	−11.8302	−0.386477	−0.193238	+	0.981152i	$0.561899\pi$
$938$	22.6223	0.738644
$939$	27.5475	0.898979
$940$	11.0724	0.361140
$941$	22.5149	0.733966	0.366983	−	0.930228i	$-0.380391\pi$
$941$	22.5149	0.733966	0.366983	+	0.930228i	$0.380391\pi$
$942$	3.21329	0.104694
$943$	−64.6375	−2.10489
$944$	12.0322	0.391616
$945$	−15.8625	−0.516006
$946$	−1.00000	−0.0325128
$947$	7.12502	0.231532	0.115766	−	0.993277i	$-0.463068\pi$
$947$	7.12502	0.231532	0.115766	+	0.993277i	$0.463068\pi$
$948$	33.1009	1.07507
$949$	16.4740	0.534767
$950$	6.77604	0.219844
$951$	−50.0542	−1.62312
$952$	15.8764	0.514556
$953$	41.5431	1.34571	0.672857	−	0.739773i	$-0.265067\pi$
$953$	41.5431	1.34571	0.672857	+	0.739773i	$0.265067\pi$
$954$	6.45643	0.209035
$955$	−8.02035	−0.259533
$956$	22.8641	0.739479
$957$	10.1343	0.327594
$958$	20.1081	0.649663
$959$	−34.9243	−1.12776
$960$	−1.88983	−0.0609939
$961$	−9.76242	−0.314917
$962$	−7.77168	−0.250569
$963$	5.14042	0.165648
$964$	−4.14263	−0.133425
$965$	−9.01693	−0.290265
$966$	−56.8561	−1.82932
$967$	54.8016	1.76230	0.881150	−	0.472837i	$-0.156770\pi$
$967$	54.8016	1.76230	0.881150	+	0.472837i	$0.156770\pi$
$968$	−1.00000	−0.0321412
$969$	58.8231	1.88967
$970$	−17.4928	−0.561659
$971$	38.1471	1.22420	0.612100	−	0.790781i	$-0.290325\pi$
$971$	38.1471	1.22420	0.612100	+	0.790781i	$0.290325\pi$
$972$	5.86247	0.188039
$973$	−58.0238	−1.86016
$974$	−0.0886944	−0.00284195
$975$	2.03630	0.0652137
$976$	−7.57534	−0.242481
$977$	−37.0437	−1.18513	−0.592567	−	0.805521i	$-0.701885\pi$
$977$	−37.0437	−1.18513	−0.592567	+	0.805521i	$0.701885\pi$
$978$	19.4671	0.622488
$979$	2.04961	0.0655058
$980$	4.94542	0.157976
$981$	−1.84052	−0.0587634
$982$	−17.0693	−0.544704
$983$	2.73678	0.0872899	0.0436449	−	0.999047i	$-0.486103\pi$
$983$	2.73678	0.0872899	0.0436449	+	0.999047i	$0.486103\pi$
$984$	−14.0330	−0.447357
$985$	−25.1470	−0.801250
$986$	24.6332	0.784481
$987$	72.3207	2.30199
$988$	7.30121	0.232283
$989$	8.70472	0.276794
$990$	−0.571445	−0.0181617
$991$	29.5784	0.939589	0.469794	−	0.882776i	$-0.344328\pi$
$991$	29.5784	0.939589	0.469794	+	0.882776i	$0.344328\pi$
$992$	4.60842	0.146318
$993$	−48.4906	−1.53880
$994$	−32.5747	−1.03321
$995$	−5.50392	−0.174486
$996$	−22.6485	−0.717645
$997$	44.8319	1.41984	0.709920	−	0.704283i	$-0.248731\pi$
$997$	44.8319	1.41984	0.709920	+	0.704283i	$0.248731\pi$
$998$	−19.6472	−0.621921
$999$	−33.1029	−1.04733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.z.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.z.1.2	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.88983 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.88983 q^{6} -3.45622 q^{7} -1.00000 q^{8} +0.571445 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.88983 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.88983 q^{6} -3.45622 q^{7} -1.00000 q^{8} +0.571445 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.88983 q^{12} -1.07751 q^{13} +3.45622 q^{14} -1.88983 q^{15} +1.00000 q^{16} +4.59357 q^{17} -0.571445 q^{18} -6.77604 q^{19} +1.00000 q^{20} +6.53165 q^{21} -1.00000 q^{22} +8.70472 q^{23} +1.88983 q^{24} +1.00000 q^{25} +1.07751 q^{26} +4.58955 q^{27} -3.45622 q^{28} -5.36254 q^{29} +1.88983 q^{30} -4.60842 q^{31} -1.00000 q^{32} -1.88983 q^{33} -4.59357 q^{34} -3.45622 q^{35} +0.571445 q^{36} -7.21267 q^{37} +6.77604 q^{38} +2.03630 q^{39} -1.00000 q^{40} -7.42557 q^{41} -6.53165 q^{42} +1.00000 q^{43} +1.00000 q^{44} +0.571445 q^{45} -8.70472 q^{46} +11.0724 q^{47} -1.88983 q^{48} +4.94542 q^{49} -1.00000 q^{50} -8.68106 q^{51} -1.07751 q^{52} -11.2984 q^{53} -4.58955 q^{54} +1.00000 q^{55} +3.45622 q^{56} +12.8055 q^{57} +5.36254 q^{58} +12.0322 q^{59} -1.88983 q^{60} -7.57534 q^{61} +4.60842 q^{62} -1.97504 q^{63} +1.00000 q^{64} -1.07751 q^{65} +1.88983 q^{66} +6.54539 q^{67} +4.59357 q^{68} -16.4504 q^{69} +3.45622 q^{70} -9.42496 q^{71} -0.571445 q^{72} -15.2890 q^{73} +7.21267 q^{74} -1.88983 q^{75} -6.77604 q^{76} -3.45622 q^{77} -2.03630 q^{78} -17.5153 q^{79} +1.00000 q^{80} -10.3878 q^{81} +7.42557 q^{82} +11.9844 q^{83} +6.53165 q^{84} +4.59357 q^{85} -1.00000 q^{86} +10.1343 q^{87} -1.00000 q^{88} +2.04961 q^{89} -0.571445 q^{90} +3.72409 q^{91} +8.70472 q^{92} +8.70912 q^{93} -11.0724 q^{94} -6.77604 q^{95} +1.88983 q^{96} +17.4928 q^{97} -4.94542 q^{98} +0.571445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * q^99

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