LMFDB - Embedded newform 1690.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(1,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, 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("1690.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.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:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.20439713.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 15x^{4} + 22x^{3} + 70x^{2} - 56x - 91 $ x^6 - 2x^5 - 15x^4 + 22x^3 + 70x^2 - 56*x - 91
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			1.1
Root			$3.23543$ of defining polynomial
Character	$\chi$	$=$	1690.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.23543 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.23543 q^{6} +4.13802 q^{7} +1.00000 q^{8} +7.46801 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.23543 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.23543 q^{6} +4.13802 q^{7} +1.00000 q^{8} +7.46801 q^{9} +1.00000 q^{10} +3.69843 q^{11} -3.23543 q^{12} +4.13802 q^{14} -3.23543 q^{15} +1.00000 q^{16} +4.39940 q^{17} +7.46801 q^{18} -4.02938 q^{19} +1.00000 q^{20} -13.3883 q^{21} +3.69843 q^{22} -4.90379 q^{23} -3.23543 q^{24} +1.00000 q^{25} -14.4559 q^{27} +4.13802 q^{28} +5.10470 q^{29} -3.23543 q^{30} +0.517058 q^{31} +1.00000 q^{32} -11.9660 q^{33} +4.39940 q^{34} +4.13802 q^{35} +7.46801 q^{36} -4.07931 q^{37} -4.02938 q^{38} +1.00000 q^{40} -0.988450 q^{41} -13.3883 q^{42} +7.45593 q^{43} +3.69843 q^{44} +7.46801 q^{45} -4.90379 q^{46} -7.60730 q^{47} -3.23543 q^{48} +10.1232 q^{49} +1.00000 q^{50} -14.2340 q^{51} -2.73689 q^{53} -14.4559 q^{54} +3.69843 q^{55} +4.13802 q^{56} +13.0368 q^{57} +5.10470 q^{58} +4.96891 q^{59} -3.23543 q^{60} -5.09714 q^{61} +0.517058 q^{62} +30.9028 q^{63} +1.00000 q^{64} -11.9660 q^{66} +0.530276 q^{67} +4.39940 q^{68} +15.8659 q^{69} +4.13802 q^{70} +0.121998 q^{71} +7.46801 q^{72} +7.47315 q^{73} -4.07931 q^{74} -3.23543 q^{75} -4.02938 q^{76} +15.3042 q^{77} +12.2658 q^{79} +1.00000 q^{80} +24.3671 q^{81} -0.988450 q^{82} -13.5727 q^{83} -13.3883 q^{84} +4.39940 q^{85} +7.45593 q^{86} -16.5159 q^{87} +3.69843 q^{88} +13.3394 q^{89} +7.46801 q^{90} -4.90379 q^{92} -1.67291 q^{93} -7.60730 q^{94} -4.02938 q^{95} -3.23543 q^{96} -4.40968 q^{97} +10.1232 q^{98} +27.6199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 6 q^{8} + 16 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 6 * q^8 + 16 * q^9	$ 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 6 q^{8} + 16 q^{9} + 6 q^{10} + 15 q^{11} - 2 q^{12} + 3 q^{14} - 2 q^{15} + 6 q^{16} - 3 q^{17} + 16 q^{18} + q^{19} + 6 q^{20} - 2 q^{21} + 15 q^{22} - 3 q^{23} - 2 q^{24} + 6 q^{25} - 20 q^{27} + 3 q^{28} + 7 q^{29} - 2 q^{30} + 6 q^{32} + 4 q^{33} - 3 q^{34} + 3 q^{35} + 16 q^{36} + 6 q^{37} + q^{38} + 6 q^{40} + 2 q^{41} - 2 q^{42} - 22 q^{43} + 15 q^{44} + 16 q^{45} - 3 q^{46} + 7 q^{47} - 2 q^{48} + 31 q^{49} + 6 q^{50} - 22 q^{51} - 16 q^{53} - 20 q^{54} + 15 q^{55} + 3 q^{56} + 2 q^{57} + 7 q^{58} + 15 q^{59} - 2 q^{60} + 33 q^{61} + 25 q^{63} + 6 q^{64} + 4 q^{66} - 8 q^{67} - 3 q^{68} - 6 q^{69} + 3 q^{70} + 40 q^{71} + 16 q^{72} + 21 q^{73} + 6 q^{74} - 2 q^{75} + q^{76} - 34 q^{77} + 20 q^{79} + 6 q^{80} - 2 q^{81} + 2 q^{82} + 22 q^{83} - 2 q^{84} - 3 q^{85} - 22 q^{86} - 39 q^{87} + 15 q^{88} + 20 q^{89} + 16 q^{90} - 3 q^{92} + 48 q^{93} + 7 q^{94} + q^{95} - 2 q^{96} - 7 q^{97} + 31 q^{98} + 55 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 6 * q^8 + 16 * q^9 + 6 * q^10 + 15 * q^11 - 2 * q^12 + 3 * q^14 - 2 * q^15 + 6 * q^16 - 3 * q^17 + 16 * q^18 + q^19 + 6 * q^20 - 2 * q^21 + 15 * q^22 - 3 * q^23 - 2 * q^24 + 6 * q^25 - 20 * q^27 + 3 * q^28 + 7 * q^29 - 2 * q^30 + 6 * q^32 + 4 * q^33 - 3 * q^34 + 3 * q^35 + 16 * q^36 + 6 * q^37 + q^38 + 6 * q^40 + 2 * q^41 - 2 * q^42 - 22 * q^43 + 15 * q^44 + 16 * q^45 - 3 * q^46 + 7 * q^47 - 2 * q^48 + 31 * q^49 + 6 * q^50 - 22 * q^51 - 16 * q^53 - 20 * q^54 + 15 * q^55 + 3 * q^56 + 2 * q^57 + 7 * q^58 + 15 * q^59 - 2 * q^60 + 33 * q^61 + 25 * q^63 + 6 * q^64 + 4 * q^66 - 8 * q^67 - 3 * q^68 - 6 * q^69 + 3 * q^70 + 40 * q^71 + 16 * q^72 + 21 * q^73 + 6 * q^74 - 2 * q^75 + q^76 - 34 * q^77 + 20 * q^79 + 6 * q^80 - 2 * q^81 + 2 * q^82 + 22 * q^83 - 2 * q^84 - 3 * q^85 - 22 * q^86 - 39 * q^87 + 15 * q^88 + 20 * q^89 + 16 * q^90 - 3 * q^92 + 48 * q^93 + 7 * q^94 + q^95 - 2 * q^96 - 7 * q^97 + 31 * q^98 + 55 * 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
$3$	−3.23543	−1.86798	−0.933988	−	0.357304i	$-0.883696\pi$
$3$	−3.23543	−1.86798	−0.933988	+	0.357304i	$0.883696\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.23543	−1.32086
$7$	4.13802	1.56403	0.782013	−	0.623263i	$-0.214193\pi$
$7$	4.13802	1.56403	0.782013	+	0.623263i	$0.214193\pi$
$8$	1.00000	0.353553
$9$	7.46801	2.48934
$10$	1.00000	0.316228
$11$	3.69843	1.11512	0.557559	−	0.830137i	$-0.311738\pi$
$11$	3.69843	1.11512	0.557559	+	0.830137i	$0.311738\pi$
$12$	−3.23543	−0.933988
$13$	0	0
$13$	0	0
$14$	4.13802	1.10593
$15$	−3.23543	−0.835384
$16$	1.00000	0.250000
$17$	4.39940	1.06701	0.533506	−	0.845796i	$-0.320874\pi$
$17$	4.39940	1.06701	0.533506	+	0.845796i	$0.320874\pi$
$18$	7.46801	1.76023
$19$	−4.02938	−0.924402	−0.462201	−	0.886775i	$-0.652940\pi$
$19$	−4.02938	−0.924402	−0.462201	+	0.886775i	$0.652940\pi$
$20$	1.00000	0.223607
$21$	−13.3883	−2.92156
$22$	3.69843	0.788508
$23$	−4.90379	−1.02251	−0.511255	−	0.859429i	$-0.670819\pi$
$23$	−4.90379	−1.02251	−0.511255	+	0.859429i	$0.670819\pi$
$24$	−3.23543	−0.660429
$25$	1.00000	0.200000
$26$	0	0
$27$	−14.4559	−2.78204
$28$	4.13802	0.782013
$29$	5.10470	0.947919	0.473960	−	0.880547i	$-0.342824\pi$
$29$	5.10470	0.947919	0.473960	+	0.880547i	$0.342824\pi$
$30$	−3.23543	−0.590706
$31$	0.517058	0.0928664	0.0464332	−	0.998921i	$-0.485215\pi$
$31$	0.517058	0.0928664	0.0464332	+	0.998921i	$0.485215\pi$
$32$	1.00000	0.176777
$33$	−11.9660	−2.08302
$34$	4.39940	0.754492
$35$	4.13802	0.699453
$36$	7.46801	1.24467
$37$	−4.07931	−0.670635	−0.335317	−	0.942105i	$-0.608844\pi$
$37$	−4.07931	−0.670635	−0.335317	+	0.942105i	$0.608844\pi$
$38$	−4.02938	−0.653651
$39$	0	0
$40$	1.00000	0.158114
$41$	−0.988450	−0.154370	−0.0771850	−	0.997017i	$-0.524593\pi$
$41$	−0.988450	−0.154370	−0.0771850	+	0.997017i	$0.524593\pi$
$42$	−13.3883	−2.06586
$43$	7.45593	1.13702	0.568509	−	0.822677i	$-0.307520\pi$
$43$	7.45593	1.13702	0.568509	+	0.822677i	$0.307520\pi$
$44$	3.69843	0.557559
$45$	7.46801	1.11326
$46$	−4.90379	−0.723024
$47$	−7.60730	−1.10964	−0.554819	−	0.831971i	$-0.687213\pi$
$47$	−7.60730	−1.10964	−0.554819	+	0.831971i	$0.687213\pi$
$48$	−3.23543	−0.466994
$49$	10.1232	1.44618
$50$	1.00000	0.141421
$51$	−14.2340	−1.99315
$52$	0	0
$53$	−2.73689	−0.375941	−0.187970	−	0.982175i	$-0.560191\pi$
$53$	−2.73689	−0.375941	−0.187970	+	0.982175i	$0.560191\pi$
$54$	−14.4559	−1.96720
$55$	3.69843	0.498696
$56$	4.13802	0.552966
$57$	13.0368	1.72676
$58$	5.10470	0.670280
$59$	4.96891	0.646897	0.323448	−	0.946246i	$-0.395158\pi$
$59$	4.96891	0.646897	0.323448	+	0.946246i	$0.395158\pi$
$60$	−3.23543	−0.417692
$61$	−5.09714	−0.652621	−0.326311	−	0.945263i	$-0.605806\pi$
$61$	−5.09714	−0.652621	−0.326311	+	0.945263i	$0.605806\pi$
$62$	0.517058	0.0656665
$63$	30.9028	3.89338
$64$	1.00000	0.125000
$65$	0	0
$66$	−11.9660	−1.47291
$67$	0.530276	0.0647835	0.0323918	−	0.999475i	$-0.489688\pi$
$67$	0.530276	0.0647835	0.0323918	+	0.999475i	$0.489688\pi$
$68$	4.39940	0.533506
$69$	15.8659	1.91003
$70$	4.13802	0.494588
$71$	0.121998	0.0144785	0.00723924	−	0.999974i	$-0.497696\pi$
$71$	0.121998	0.0144785	0.00723924	+	0.999974i	$0.497696\pi$
$72$	7.46801	0.880113
$73$	7.47315	0.874666	0.437333	−	0.899300i	$-0.355923\pi$
$73$	7.47315	0.874666	0.437333	+	0.899300i	$0.355923\pi$
$74$	−4.07931	−0.474210
$75$	−3.23543	−0.373595
$76$	−4.02938	−0.462201
$77$	15.3042	1.74407
$78$	0	0
$79$	12.2658	1.38001	0.690003	−	0.723806i	$-0.257609\pi$
$79$	12.2658	1.38001	0.690003	+	0.723806i	$0.257609\pi$
$80$	1.00000	0.111803
$81$	24.3671	2.70746
$82$	−0.988450	−0.109156
$83$	−13.5727	−1.48980	−0.744898	−	0.667179i	$-0.767502\pi$
$83$	−13.5727	−1.48980	−0.744898	+	0.667179i	$0.767502\pi$
$84$	−13.3883	−1.46078
$85$	4.39940	0.477182
$86$	7.45593	0.803993
$87$	−16.5159	−1.77069
$88$	3.69843	0.394254
$89$	13.3394	1.41397	0.706985	−	0.707229i	$-0.250055\pi$
$89$	13.3394	1.41397	0.706985	+	0.707229i	$0.250055\pi$
$90$	7.46801	0.787197
$91$	0	0
$92$	−4.90379	−0.511255
$93$	−1.67291	−0.173472
$94$	−7.60730	−0.784633
$95$	−4.02938	−0.413405
$96$	−3.23543	−0.330215
$97$	−4.40968	−0.447736	−0.223868	−	0.974620i	$-0.571868\pi$
$97$	−4.40968	−0.447736	−0.223868	+	0.974620i	$0.571868\pi$
$98$	10.1232	1.02260
$99$	27.6199	2.77591
$100$	1.00000	0.100000
$101$	0.639941	0.0636765	0.0318382	−	0.999493i	$-0.489864\pi$
$101$	0.639941	0.0636765	0.0318382	+	0.999493i	$0.489864\pi$
$102$	−14.2340	−1.40937
$103$	6.40187	0.630795	0.315397	−	0.948960i	$-0.397862\pi$
$103$	6.40187	0.630795	0.315397	+	0.948960i	$0.397862\pi$
$104$	0	0
$105$	−13.3883	−1.30656
$106$	−2.73689	−0.265830
$107$	−17.0045	−1.64388	−0.821942	−	0.569571i	$-0.807109\pi$
$107$	−17.0045	−1.64388	−0.821942	+	0.569571i	$0.807109\pi$
$108$	−14.4559	−1.39102
$109$	12.6945	1.21591	0.607957	−	0.793970i	$-0.291989\pi$
$109$	12.6945	1.21591	0.607957	+	0.793970i	$0.291989\pi$
$110$	3.69843	0.352632
$111$	13.1983	1.25273
$112$	4.13802	0.391006
$113$	1.56177	0.146919	0.0734593	−	0.997298i	$-0.476596\pi$
$113$	1.56177	0.146919	0.0734593	+	0.997298i	$0.476596\pi$
$114$	13.0368	1.22100
$115$	−4.90379	−0.457281
$116$	5.10470	0.473960
$117$	0	0
$118$	4.96891	0.457425
$119$	18.2048	1.66883
$120$	−3.23543	−0.295353
$121$	2.67839	0.243490
$122$	−5.09714	−0.461473
$123$	3.19806	0.288360
$124$	0.517058	0.0464332
$125$	1.00000	0.0894427
$126$	30.9028	2.75304
$127$	1.53946	0.136605	0.0683025	−	0.997665i	$-0.478242\pi$
$127$	1.53946	0.136605	0.0683025	+	0.997665i	$0.478242\pi$
$128$	1.00000	0.0883883
$129$	−24.1231	−2.12392
$130$	0	0
$131$	2.87784	0.251438	0.125719	−	0.992066i	$-0.459876\pi$
$131$	2.87784	0.251438	0.125719	+	0.992066i	$0.459876\pi$
$132$	−11.9660	−1.04151
$133$	−16.6736	−1.44579
$134$	0.530276	0.0458089
$135$	−14.4559	−1.24417
$136$	4.39940	0.377246
$137$	17.0411	1.45592	0.727960	−	0.685620i	$-0.240469\pi$
$137$	17.0411	1.45592	0.727960	+	0.685620i	$0.240469\pi$
$138$	15.8659	1.35059
$139$	−16.4870	−1.39841	−0.699203	−	0.714923i	$-0.746462\pi$
$139$	−16.4870	−1.39841	−0.699203	+	0.714923i	$0.746462\pi$
$140$	4.13802	0.349727
$141$	24.6129	2.07278
$142$	0.121998	0.0102378
$143$	0	0
$144$	7.46801	0.622334
$145$	5.10470	0.423922
$146$	7.47315	0.618482
$147$	−32.7530	−2.70142
$148$	−4.07931	−0.335317
$149$	18.2731	1.49699	0.748495	−	0.663141i	$-0.230777\pi$
$149$	18.2731	1.49699	0.748495	+	0.663141i	$0.230777\pi$
$150$	−3.23543	−0.264172
$151$	−15.8124	−1.28679	−0.643396	−	0.765534i	$-0.722475\pi$
$151$	−15.8124	−1.28679	−0.643396	+	0.765534i	$0.722475\pi$
$152$	−4.02938	−0.326825
$153$	32.8548	2.65615
$154$	15.3042	1.23325
$155$	0.517058	0.0415311
$156$	0	0
$157$	−22.5961	−1.80337	−0.901683	−	0.432398i	$-0.857667\pi$
$157$	−22.5961	−1.80337	−0.901683	+	0.432398i	$0.857667\pi$
$158$	12.2658	0.975812
$159$	8.85502	0.702249
$160$	1.00000	0.0790569
$161$	−20.2920	−1.59923
$162$	24.3671	1.91446
$163$	4.47519	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$163$	4.47519	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$164$	−0.988450	−0.0771850
$165$	−11.9660	−0.931553
$166$	−13.5727	−1.05344
$167$	−8.83137	−0.683392	−0.341696	−	0.939811i	$-0.611001\pi$
$167$	−8.83137	−0.683392	−0.341696	+	0.939811i	$0.611001\pi$
$168$	−13.3883	−1.03293
$169$	0	0
$170$	4.39940	0.337419
$171$	−30.0914	−2.30115
$172$	7.45593	0.568509
$173$	−13.6889	−1.04075	−0.520374	−	0.853939i	$-0.674207\pi$
$173$	−13.6889	−1.04075	−0.520374	+	0.853939i	$0.674207\pi$
$174$	−16.5159	−1.25207
$175$	4.13802	0.312805
$176$	3.69843	0.278780
$177$	−16.0766	−1.20839
$178$	13.3394	0.999828
$179$	−18.1668	−1.35785	−0.678923	−	0.734209i	$-0.737553\pi$
$179$	−18.1668	−1.35785	−0.678923	+	0.734209i	$0.737553\pi$
$180$	7.46801	0.556632
$181$	16.5998	1.23385	0.616926	−	0.787021i	$-0.288378\pi$
$181$	16.5998	1.23385	0.616926	+	0.787021i	$0.288378\pi$
$182$	0	0
$183$	16.4914	1.21908
$184$	−4.90379	−0.361512
$185$	−4.07931	−0.299917
$186$	−1.67291	−0.122663
$187$	16.2709	1.18985
$188$	−7.60730	−0.554819
$189$	−59.8189	−4.35119
$190$	−4.02938	−0.292322
$191$	4.55032	0.329250	0.164625	−	0.986356i	$-0.447359\pi$
$191$	4.55032	0.329250	0.164625	+	0.986356i	$0.447359\pi$
$192$	−3.23543	−0.233497
$193$	−19.7745	−1.42340	−0.711699	−	0.702485i	$-0.752074\pi$
$193$	−19.7745	−1.42340	−0.711699	+	0.702485i	$0.752074\pi$
$194$	−4.40968	−0.316597
$195$	0	0
$196$	10.1232	0.723088
$197$	14.2131	1.01264	0.506319	−	0.862346i	$-0.331006\pi$
$197$	14.2131	1.01264	0.506319	+	0.862346i	$0.331006\pi$
$198$	27.6199	1.96286
$199$	20.8990	1.48149	0.740747	−	0.671785i	$-0.234472\pi$
$199$	20.8990	1.48149	0.740747	+	0.671785i	$0.234472\pi$
$200$	1.00000	0.0707107
$201$	−1.71567	−0.121014
$202$	0.639941	0.0450261
$203$	21.1234	1.48257
$204$	−14.2340	−0.996577
$205$	−0.988450	−0.0690364
$206$	6.40187	0.446039
$207$	−36.6215	−2.54537
$208$	0	0
$209$	−14.9024	−1.03082
$210$	−13.3883	−0.923879
$211$	−27.4802	−1.89182	−0.945909	−	0.324432i	$-0.894827\pi$
$211$	−27.4802	−1.89182	−0.945909	+	0.324432i	$0.894827\pi$
$212$	−2.73689	−0.187970
$213$	−0.394716	−0.0270455
$214$	−17.0045	−1.16240
$215$	7.45593	0.508490
$216$	−14.4559	−0.983601
$217$	2.13960	0.145245
$218$	12.6945	0.859781
$219$	−24.1788	−1.63386
$220$	3.69843	0.249348
$221$	0	0
$222$	13.1983	0.885814
$223$	−19.6984	−1.31910	−0.659552	−	0.751659i	$-0.729254\pi$
$223$	−19.6984	−1.31910	−0.659552	+	0.751659i	$0.729254\pi$
$224$	4.13802	0.276483
$225$	7.46801	0.497867
$226$	1.56177	0.103887
$227$	12.4168	0.824130	0.412065	−	0.911154i	$-0.364808\pi$
$227$	12.4168	0.824130	0.412065	+	0.911154i	$0.364808\pi$
$228$	13.0368	0.863381
$229$	−13.3509	−0.882251	−0.441125	−	0.897445i	$-0.645421\pi$
$229$	−13.3509	−0.882251	−0.441125	+	0.897445i	$0.645421\pi$
$230$	−4.90379	−0.323346
$231$	−49.5156	−3.25789
$232$	5.10470	0.335140
$233$	13.6551	0.894578	0.447289	−	0.894389i	$-0.352389\pi$
$233$	13.6551	0.894578	0.447289	+	0.894389i	$0.352389\pi$
$234$	0	0
$235$	−7.60730	−0.496245
$236$	4.96891	0.323448
$237$	−39.6850	−2.57782
$238$	18.2048	1.18004
$239$	7.83653	0.506903	0.253451	−	0.967348i	$-0.418434\pi$
$239$	7.83653	0.506903	0.253451	+	0.967348i	$0.418434\pi$
$240$	−3.23543	−0.208846
$241$	−1.24370	−0.0801138	−0.0400569	−	0.999197i	$-0.512754\pi$
$241$	−1.24370	−0.0801138	−0.0400569	+	0.999197i	$0.512754\pi$
$242$	2.67839	0.172174
$243$	−35.4703	−2.27542
$244$	−5.09714	−0.326311
$245$	10.1232	0.646749
$246$	3.19806	0.203901
$247$	0	0
$248$	0.517058	0.0328332
$249$	43.9135	2.78290
$250$	1.00000	0.0632456
$251$	23.5622	1.48723	0.743617	−	0.668606i	$-0.233109\pi$
$251$	23.5622	1.48723	0.743617	+	0.668606i	$0.233109\pi$
$252$	30.9028	1.94669
$253$	−18.1363	−1.14022
$254$	1.53946	0.0965943
$255$	−14.2340	−0.891365
$256$	1.00000	0.0625000
$257$	8.45894	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$257$	8.45894	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$258$	−24.1231	−1.50184
$259$	−16.8803	−1.04889
$260$	0	0
$261$	38.1220	2.35969
$262$	2.87784	0.177793
$263$	13.2054	0.814280	0.407140	−	0.913366i	$-0.366526\pi$
$263$	13.2054	0.814280	0.407140	+	0.913366i	$0.366526\pi$
$264$	−11.9660	−0.736457
$265$	−2.73689	−0.168126
$266$	−16.6736	−1.02233
$267$	−43.1586	−2.64126
$268$	0.530276	0.0323918
$269$	5.23846	0.319394	0.159697	−	0.987166i	$-0.448948\pi$
$269$	5.23846	0.319394	0.159697	+	0.987166i	$0.448948\pi$
$270$	−14.4559	−0.879760
$271$	−6.51186	−0.395567	−0.197784	−	0.980246i	$-0.563374\pi$
$271$	−6.51186	−0.395567	−0.197784	+	0.980246i	$0.563374\pi$
$272$	4.39940	0.266753
$273$	0	0
$274$	17.0411	1.02949
$275$	3.69843	0.223024
$276$	15.8659	0.955013
$277$	27.6378	1.66060	0.830298	−	0.557319i	$-0.188170\pi$
$277$	27.6378	1.66060	0.830298	+	0.557319i	$0.188170\pi$
$278$	−16.4870	−0.988822
$279$	3.86140	0.231176
$280$	4.13802	0.247294
$281$	18.7264	1.11713	0.558563	−	0.829462i	$-0.311353\pi$
$281$	18.7264	1.11713	0.558563	+	0.829462i	$0.311353\pi$
$282$	24.6129	1.46568
$283$	−25.1178	−1.49310	−0.746549	−	0.665330i	$-0.768291\pi$
$283$	−25.1178	−1.49310	−0.746549	+	0.665330i	$0.768291\pi$
$284$	0.121998	0.00723924
$285$	13.0368	0.772231
$286$	0	0
$287$	−4.09023	−0.241439
$288$	7.46801	0.440057
$289$	2.35475	0.138515
$290$	5.10470	0.299758
$291$	14.2672	0.836359
$292$	7.47315	0.437333
$293$	6.22680	0.363773	0.181887	−	0.983319i	$-0.441780\pi$
$293$	6.22680	0.363773	0.181887	+	0.983319i	$0.441780\pi$
$294$	−32.7530	−1.91019
$295$	4.96891	0.289301
$296$	−4.07931	−0.237105
$297$	−53.4642	−3.10231
$298$	18.2731	1.05853
$299$	0	0
$300$	−3.23543	−0.186798
$301$	30.8528	1.77833
$302$	−15.8124	−0.909899
$303$	−2.07048	−0.118946
$304$	−4.02938	−0.231101
$305$	−5.09714	−0.291861
$306$	32.8548	1.87818
$307$	−0.649087	−0.0370454	−0.0185227	−	0.999828i	$-0.505896\pi$
$307$	−0.649087	−0.0370454	−0.0185227	+	0.999828i	$0.505896\pi$
$308$	15.3042	0.872037
$309$	−20.7128	−1.17831
$310$	0.517058	0.0293669
$311$	2.97728	0.168826	0.0844131	−	0.996431i	$-0.473098\pi$
$311$	2.97728	0.168826	0.0844131	+	0.996431i	$0.473098\pi$
$312$	0	0
$313$	9.44206	0.533697	0.266848	−	0.963739i	$-0.414018\pi$
$313$	9.44206	0.533697	0.266848	+	0.963739i	$0.414018\pi$
$314$	−22.5961	−1.27517
$315$	30.9028	1.74117
$316$	12.2658	0.690003
$317$	−9.41701	−0.528912	−0.264456	−	0.964398i	$-0.585192\pi$
$317$	−9.41701	−0.528912	−0.264456	+	0.964398i	$0.585192\pi$
$318$	8.85502	0.496565
$319$	18.8794	1.05704
$320$	1.00000	0.0559017
$321$	55.0168	3.07074
$322$	−20.2920	−1.13083
$323$	−17.7268	−0.986348
$324$	24.3671	1.35373
$325$	0	0
$326$	4.47519	0.247858
$327$	−41.0722	−2.27130
$328$	−0.988450	−0.0545780
$329$	−31.4792	−1.73550
$330$	−11.9660	−0.658707
$331$	−1.35778	−0.0746302	−0.0373151	−	0.999304i	$-0.511881\pi$
$331$	−1.35778	−0.0746302	−0.0373151	+	0.999304i	$0.511881\pi$
$332$	−13.5727	−0.744898
$333$	−30.4643	−1.66943
$334$	−8.83137	−0.483231
$335$	0.530276	0.0289721
$336$	−13.3883	−0.730391
$337$	−10.2183	−0.556628	−0.278314	−	0.960490i	$-0.589776\pi$
$337$	−10.2183	−0.556628	−0.278314	+	0.960490i	$0.589776\pi$
$338$	0	0
$339$	−5.05299	−0.274441
$340$	4.39940	0.238591
$341$	1.91230	0.103557
$342$	−30.0914	−1.62716
$343$	12.9240	0.697829
$344$	7.45593	0.401997
$345$	15.8659	0.854189
$346$	−13.6889	−0.735919
$347$	−30.3022	−1.62671	−0.813353	−	0.581771i	$-0.802360\pi$
$347$	−30.3022	−1.62671	−0.813353	+	0.581771i	$0.802360\pi$
$348$	−16.5159	−0.885346
$349$	−6.99010	−0.374172	−0.187086	−	0.982344i	$-0.559904\pi$
$349$	−6.99010	−0.374172	−0.187086	+	0.982344i	$0.559904\pi$
$350$	4.13802	0.221187
$351$	0	0
$352$	3.69843	0.197127
$353$	−9.99539	−0.532001	−0.266000	−	0.963973i	$-0.585702\pi$
$353$	−9.99539	−0.532001	−0.266000	+	0.963973i	$0.585702\pi$
$354$	−16.0766	−0.854459
$355$	0.121998	0.00647497
$356$	13.3394	0.706985
$357$	−58.9005	−3.11734
$358$	−18.1668	−0.960143
$359$	32.7796	1.73004	0.865020	−	0.501738i	$-0.167306\pi$
$359$	32.7796	1.73004	0.865020	+	0.501738i	$0.167306\pi$
$360$	7.46801	0.393599
$361$	−2.76414	−0.145481
$362$	16.5998	0.872466
$363$	−8.66575	−0.454834
$364$	0	0
$365$	7.47315	0.391162
$366$	16.4914	0.862021
$367$	29.9518	1.56347	0.781736	−	0.623609i	$-0.214334\pi$
$367$	29.9518	1.56347	0.781736	+	0.623609i	$0.214334\pi$
$368$	−4.90379	−0.255628
$369$	−7.38176	−0.384279
$370$	−4.07931	−0.212073
$371$	−11.3253	−0.587981
$372$	−1.67291	−0.0867361
$373$	−14.3796	−0.744547	−0.372273	−	0.928123i	$-0.621422\pi$
$373$	−14.3796	−0.744547	−0.372273	+	0.928123i	$0.621422\pi$
$374$	16.2709	0.841348
$375$	−3.23543	−0.167077
$376$	−7.60730	−0.392316
$377$	0	0
$378$	−59.8189	−3.07675
$379$	−33.9184	−1.74227	−0.871137	−	0.491040i	$-0.836617\pi$
$379$	−33.9184	−1.74227	−0.871137	+	0.491040i	$0.836617\pi$
$380$	−4.02938	−0.206703
$381$	−4.98081	−0.255175
$382$	4.55032	0.232815
$383$	−19.6131	−1.00218	−0.501092	−	0.865394i	$-0.667068\pi$
$383$	−19.6131	−1.00218	−0.501092	+	0.865394i	$0.667068\pi$
$384$	−3.23543	−0.165107
$385$	15.3042	0.779974
$386$	−19.7745	−1.00649
$387$	55.6809	2.83042
$388$	−4.40968	−0.223868
$389$	−11.6768	−0.592039	−0.296020	−	0.955182i	$-0.595659\pi$
$389$	−11.6768	−0.592039	−0.296020	+	0.955182i	$0.595659\pi$
$390$	0	0
$391$	−21.5737	−1.09103
$392$	10.1232	0.511300
$393$	−9.31104	−0.469680
$394$	14.2131	0.716044
$395$	12.2658	0.617158
$396$	27.6199	1.38795
$397$	−27.7028	−1.39037	−0.695183	−	0.718833i	$-0.744677\pi$
$397$	−27.7028	−1.39037	−0.695183	+	0.718833i	$0.744677\pi$
$398$	20.8990	1.04757
$399$	53.9464	2.70070
$400$	1.00000	0.0500000
$401$	5.57831	0.278568	0.139284	−	0.990253i	$-0.455520\pi$
$401$	5.57831	0.278568	0.139284	+	0.990253i	$0.455520\pi$
$402$	−1.71567	−0.0855699
$403$	0	0
$404$	0.639941	0.0318382
$405$	24.3671	1.21081
$406$	21.1234	1.04834
$407$	−15.0870	−0.747837
$408$	−14.2340	−0.704686
$409$	−3.73914	−0.184889	−0.0924443	−	0.995718i	$-0.529468\pi$
$409$	−3.73914	−0.184889	−0.0924443	+	0.995718i	$0.529468\pi$
$410$	−0.988450	−0.0488161
$411$	−55.1353	−2.71962
$412$	6.40187	0.315397
$413$	20.5615	1.01176
$414$	−36.6215	−1.79985
$415$	−13.5727	−0.666257
$416$	0	0
$417$	53.3424	2.61219
$418$	−14.9024	−0.728899
$419$	−31.7645	−1.55180	−0.775898	−	0.630858i	$-0.782703\pi$
$419$	−31.7645	−1.55180	−0.775898	+	0.630858i	$0.782703\pi$
$420$	−13.3883	−0.653281
$421$	−23.4191	−1.14137	−0.570687	−	0.821167i	$-0.693323\pi$
$421$	−23.4191	−1.14137	−0.570687	+	0.821167i	$0.693323\pi$
$422$	−27.4802	−1.33772
$423$	−56.8114	−2.76226
$424$	−2.73689	−0.132915
$425$	4.39940	0.213402
$426$	−0.394716	−0.0191240
$427$	−21.0921	−1.02072
$428$	−17.0045	−0.821942
$429$	0	0
$430$	7.45593	0.359557
$431$	14.4701	0.696999	0.348500	−	0.937309i	$-0.386691\pi$
$431$	14.4701	0.696999	0.348500	+	0.937309i	$0.386691\pi$
$432$	−14.4559	−0.695511
$433$	−38.2377	−1.83758	−0.918792	−	0.394742i	$-0.870834\pi$
$433$	−38.2377	−1.83758	−0.918792	+	0.394742i	$0.870834\pi$
$434$	2.13960	0.102704
$435$	−16.5159	−0.791877
$436$	12.6945	0.607957
$437$	19.7592	0.945211
$438$	−24.1788	−1.15531
$439$	14.3819	0.686411	0.343206	−	0.939260i	$-0.388487\pi$
$439$	14.3819	0.686411	0.343206	+	0.939260i	$0.388487\pi$
$440$	3.69843	0.176316
$441$	75.6003	3.60002
$442$	0	0
$443$	10.1853	0.483916	0.241958	−	0.970287i	$-0.422210\pi$
$443$	10.1853	0.483916	0.241958	+	0.970287i	$0.422210\pi$
$444$	13.1983	0.626365
$445$	13.3394	0.632346
$446$	−19.6984	−0.932747
$447$	−59.1213	−2.79634
$448$	4.13802	0.195503
$449$	15.3798	0.725820	0.362910	−	0.931824i	$-0.381783\pi$
$449$	15.3798	0.725820	0.362910	+	0.931824i	$0.381783\pi$
$450$	7.46801	0.352045
$451$	−3.65572	−0.172141
$452$	1.56177	0.0734593
$453$	51.1598	2.40370
$454$	12.4168	0.582748
$455$	0	0
$456$	13.0368	0.610502
$457$	37.9943	1.77730	0.888650	−	0.458586i	$-0.151644\pi$
$457$	37.9943	1.77730	0.888650	+	0.458586i	$0.151644\pi$
$458$	−13.3509	−0.623846
$459$	−63.5975	−2.96847
$460$	−4.90379	−0.228640
$461$	10.4170	0.485168	0.242584	−	0.970130i	$-0.422005\pi$
$461$	10.4170	0.485168	0.242584	+	0.970130i	$0.422005\pi$
$462$	−49.5156	−2.30368
$463$	−13.3069	−0.618422	−0.309211	−	0.950993i	$-0.600065\pi$
$463$	−13.3069	−0.618422	−0.309211	+	0.950993i	$0.600065\pi$
$464$	5.10470	0.236980
$465$	−1.67291	−0.0775792
$466$	13.6551	0.632562
$467$	33.5745	1.55364	0.776821	−	0.629722i	$-0.216831\pi$
$467$	33.5745	1.55364	0.776821	+	0.629722i	$0.216831\pi$
$468$	0	0
$469$	2.19429	0.101323
$470$	−7.60730	−0.350899
$471$	73.1081	3.36864
$472$	4.96891	0.228713
$473$	27.5752	1.26791
$474$	−39.6850	−1.82279
$475$	−4.02938	−0.184880
$476$	18.2048	0.834417
$477$	−20.4391	−0.935843
$478$	7.83653	0.358434
$479$	4.25242	0.194298	0.0971491	−	0.995270i	$-0.469028\pi$
$479$	4.25242	0.194298	0.0971491	+	0.995270i	$0.469028\pi$
$480$	−3.23543	−0.147677
$481$	0	0
$482$	−1.24370	−0.0566490
$483$	65.6533	2.98733
$484$	2.67839	0.121745
$485$	−4.40968	−0.200233
$486$	−35.4703	−1.60897
$487$	28.4772	1.29042	0.645212	−	0.764003i	$-0.276769\pi$
$487$	28.4772	1.29042	0.645212	+	0.764003i	$0.276769\pi$
$488$	−5.09714	−0.230737
$489$	−14.4792	−0.654770
$490$	10.1232	0.457321
$491$	−24.4891	−1.10518	−0.552589	−	0.833454i	$-0.686360\pi$
$491$	−24.4891	−1.10518	−0.552589	+	0.833454i	$0.686360\pi$
$492$	3.19806	0.144180
$493$	22.4576	1.01144
$494$	0	0
$495$	27.6199	1.24142
$496$	0.517058	0.0232166
$497$	0.504830	0.0226447
$498$	43.9135	1.96781
$499$	18.2842	0.818512	0.409256	−	0.912420i	$-0.365788\pi$
$499$	18.2842	0.818512	0.409256	+	0.912420i	$0.365788\pi$
$500$	1.00000	0.0447214
$501$	28.5733	1.27656
$502$	23.5622	1.05163
$503$	−32.3462	−1.44225	−0.721124	−	0.692806i	$-0.756374\pi$
$503$	−32.3462	−1.44225	−0.721124	+	0.692806i	$0.756374\pi$
$504$	30.9028	1.37652
$505$	0.639941	0.0284770
$506$	−18.1363	−0.806258
$507$	0	0
$508$	1.53946	0.0683025
$509$	5.57001	0.246886	0.123443	−	0.992352i	$-0.460606\pi$
$509$	5.57001	0.246886	0.123443	+	0.992352i	$0.460606\pi$
$510$	−14.2340	−0.630290
$511$	30.9240	1.36800
$512$	1.00000	0.0441942
$513$	58.2484	2.57173
$514$	8.45894	0.373108
$515$	6.40187	0.282100
$516$	−24.1231	−1.06196
$517$	−28.1351	−1.23738
$518$	−16.8803	−0.741677
$519$	44.2894	1.94409
$520$	0	0
$521$	−35.7635	−1.56683	−0.783413	−	0.621501i	$-0.786523\pi$
$521$	−35.7635	−1.56683	−0.783413	+	0.621501i	$0.786523\pi$
$522$	38.1220	1.66855
$523$	−12.8088	−0.560088	−0.280044	−	0.959987i	$-0.590349\pi$
$523$	−12.8088	−0.560088	−0.280044	+	0.959987i	$0.590349\pi$
$524$	2.87784	0.125719
$525$	−13.3883	−0.584312
$526$	13.2054	0.575783
$527$	2.27475	0.0990896
$528$	−11.9660	−0.520754
$529$	1.04713	0.0455274
$530$	−2.73689	−0.118883
$531$	37.1078	1.61034
$532$	−16.6736	−0.722894
$533$	0	0
$534$	−43.1586	−1.86765
$535$	−17.0045	−0.735168
$536$	0.530276	0.0229044
$537$	58.7773	2.53643
$538$	5.23846	0.225846
$539$	37.4401	1.61266
$540$	−14.4559	−0.622084
$541$	−9.36713	−0.402724	−0.201362	−	0.979517i	$-0.564537\pi$
$541$	−9.36713	−0.402724	−0.201362	+	0.979517i	$0.564537\pi$
$542$	−6.51186	−0.279708
$543$	−53.7075	−2.30481
$544$	4.39940	0.188623
$545$	12.6945	0.543773
$546$	0	0
$547$	−12.4406	−0.531921	−0.265961	−	0.963984i	$-0.585689\pi$
$547$	−12.4406	−0.531921	−0.265961	+	0.963984i	$0.585689\pi$
$548$	17.0411	0.727960
$549$	−38.0655	−1.62459
$550$	3.69843	0.157702
$551$	−20.5688	−0.876259
$552$	15.8659	0.675296
$553$	50.7560	2.15836
$554$	27.6378	1.17422
$555$	13.1983	0.560238
$556$	−16.4870	−0.699203
$557$	25.3653	1.07476	0.537380	−	0.843340i	$-0.319414\pi$
$557$	25.3653	1.07476	0.537380	+	0.843340i	$0.319414\pi$
$558$	3.86140	0.163466
$559$	0	0
$560$	4.13802	0.174863
$561$	−52.6433	−2.22260
$562$	18.7264	0.789927
$563$	−22.2600	−0.938145	−0.469073	−	0.883160i	$-0.655412\pi$
$563$	−22.2600	−0.938145	−0.469073	+	0.883160i	$0.655412\pi$
$564$	24.6129	1.03639
$565$	1.56177	0.0657040
$566$	−25.1178	−1.05578
$567$	100.832	4.23453
$568$	0.121998	0.00511892
$569$	17.9559	0.752753	0.376376	−	0.926467i	$-0.377170\pi$
$569$	17.9559	0.752753	0.376376	+	0.926467i	$0.377170\pi$
$570$	13.0368	0.546050
$571$	22.7591	0.952441	0.476220	−	0.879326i	$-0.342006\pi$
$571$	22.7591	0.952441	0.476220	+	0.879326i	$0.342006\pi$
$572$	0	0
$573$	−14.7222	−0.615030
$574$	−4.09023	−0.170723
$575$	−4.90379	−0.204502
$576$	7.46801	0.311167
$577$	23.8510	0.992928	0.496464	−	0.868057i	$-0.334631\pi$
$577$	23.8510	0.992928	0.496464	+	0.868057i	$0.334631\pi$
$578$	2.35475	0.0979448
$579$	63.9789	2.65887
$580$	5.10470	0.211961
$581$	−56.1640	−2.33008
$582$	14.2672	0.591395
$583$	−10.1222	−0.419219
$584$	7.47315	0.309241
$585$	0	0
$586$	6.22680	0.257227
$587$	6.63880	0.274013	0.137006	−	0.990570i	$-0.456252\pi$
$587$	6.63880	0.274013	0.137006	+	0.990570i	$0.456252\pi$
$588$	−32.7530	−1.35071
$589$	−2.08342	−0.0858459
$590$	4.96891	0.204567
$591$	−45.9854	−1.89159
$592$	−4.07931	−0.167659
$593$	−11.1923	−0.459614	−0.229807	−	0.973236i	$-0.573810\pi$
$593$	−11.1923	−0.459614	−0.229807	+	0.973236i	$0.573810\pi$
$594$	−53.4642	−2.19366
$595$	18.2048	0.746325
$596$	18.2731	0.748495
$597$	−67.6174	−2.76739
$598$	0	0
$599$	−38.0249	−1.55366	−0.776829	−	0.629712i	$-0.783173\pi$
$599$	−38.0249	−1.55366	−0.776829	+	0.629712i	$0.783173\pi$
$600$	−3.23543	−0.132086
$601$	−6.79482	−0.277167	−0.138583	−	0.990351i	$-0.544255\pi$
$601$	−6.79482	−0.277167	−0.138583	+	0.990351i	$0.544255\pi$
$602$	30.8528	1.25747
$603$	3.96011	0.161268
$604$	−15.8124	−0.643396
$605$	2.67839	0.108892
$606$	−2.07048	−0.0841077
$607$	−8.18733	−0.332313	−0.166157	−	0.986099i	$-0.553136\pi$
$607$	−8.18733	−0.332313	−0.166157	+	0.986099i	$0.553136\pi$
$608$	−4.02938	−0.163413
$609$	−68.3432	−2.76941
$610$	−5.09714	−0.206377
$611$	0	0
$612$	32.8548	1.32808
$613$	−34.0275	−1.37436	−0.687178	−	0.726489i	$-0.741151\pi$
$613$	−34.0275	−1.37436	−0.687178	+	0.726489i	$0.741151\pi$
$614$	−0.649087	−0.0261950
$615$	3.19806	0.128958
$616$	15.3042	0.616623
$617$	−30.1844	−1.21518	−0.607588	−	0.794252i	$-0.707863\pi$
$617$	−30.1844	−1.21518	−0.607588	+	0.794252i	$0.707863\pi$
$618$	−20.7128	−0.833191
$619$	30.1783	1.21297	0.606484	−	0.795096i	$-0.292580\pi$
$619$	30.1783	1.21297	0.606484	+	0.795096i	$0.292580\pi$
$620$	0.517058	0.0207656
$621$	70.8888	2.84467
$622$	2.97728	0.119378
$623$	55.1986	2.21148
$624$	0	0
$625$	1.00000	0.0400000
$626$	9.44206	0.377381
$627$	48.2156	1.92554
$628$	−22.5961	−0.901683
$629$	−17.9465	−0.715575
$630$	30.9028	1.23120
$631$	−8.36219	−0.332894	−0.166447	−	0.986050i	$-0.553229\pi$
$631$	−8.36219	−0.332894	−0.166447	+	0.986050i	$0.553229\pi$
$632$	12.2658	0.487906
$633$	88.9104	3.53387
$634$	−9.41701	−0.373997
$635$	1.53946	0.0610916
$636$	8.85502	0.351124
$637$	0	0
$638$	18.8794	0.747442
$639$	0.911081	0.0360418
$640$	1.00000	0.0395285
$641$	−35.7120	−1.41054	−0.705270	−	0.708938i	$-0.749174\pi$
$641$	−35.7120	−1.41054	−0.705270	+	0.708938i	$0.749174\pi$
$642$	55.0168	2.17134
$643$	40.4090	1.59358	0.796788	−	0.604258i	$-0.206531\pi$
$643$	40.4090	1.59358	0.796788	+	0.604258i	$0.206531\pi$
$644$	−20.2920	−0.799616
$645$	−24.1231	−0.949847
$646$	−17.7268	−0.697454
$647$	7.97823	0.313656	0.156828	−	0.987626i	$-0.449873\pi$
$647$	7.97823	0.313656	0.156828	+	0.987626i	$0.449873\pi$
$648$	24.3671	0.957231
$649$	18.3772	0.721367
$650$	0	0
$651$	−6.92252	−0.271315
$652$	4.47519	0.175262
$653$	24.4915	0.958426	0.479213	−	0.877699i	$-0.340922\pi$
$653$	24.4915	0.958426	0.479213	+	0.877699i	$0.340922\pi$
$654$	−41.0722	−1.60605
$655$	2.87784	0.112446
$656$	−0.988450	−0.0385925
$657$	55.8095	2.17734
$658$	−31.4792	−1.22719
$659$	13.2692	0.516894	0.258447	−	0.966025i	$-0.416789\pi$
$659$	13.2692	0.516894	0.258447	+	0.966025i	$0.416789\pi$
$660$	−11.9660	−0.465776
$661$	−19.6284	−0.763455	−0.381727	−	0.924275i	$-0.624671\pi$
$661$	−19.6284	−0.763455	−0.381727	+	0.924275i	$0.624671\pi$
$662$	−1.35778	−0.0527715
$663$	0	0
$664$	−13.5727	−0.526722
$665$	−16.6736	−0.646576
$666$	−30.4643	−1.18047
$667$	−25.0324	−0.969257
$668$	−8.83137	−0.341696
$669$	63.7328	2.46405
$670$	0.530276	0.0204863
$671$	−18.8514	−0.727750
$672$	−13.3883	−0.516464
$673$	−11.8977	−0.458622	−0.229311	−	0.973353i	$-0.573647\pi$
$673$	−11.8977	−0.458622	−0.229311	+	0.973353i	$0.573647\pi$
$674$	−10.2183	−0.393596
$675$	−14.4559	−0.556409
$676$	0	0
$677$	32.1575	1.23591	0.617957	−	0.786212i	$-0.287961\pi$
$677$	32.1575	1.23591	0.617957	+	0.786212i	$0.287961\pi$
$678$	−5.05299	−0.194059
$679$	−18.2474	−0.700270
$680$	4.39940	0.168709
$681$	−40.1736	−1.53946
$682$	1.91230	0.0732259
$683$	11.9749	0.458207	0.229103	−	0.973402i	$-0.426421\pi$
$683$	11.9749	0.458207	0.229103	+	0.973402i	$0.426421\pi$
$684$	−30.0914	−1.15057
$685$	17.0411	0.651107
$686$	12.9240	0.493440
$687$	43.1958	1.64802
$688$	7.45593	0.284255
$689$	0	0
$690$	15.8659	0.604003
$691$	−35.2741	−1.34189	−0.670945	−	0.741507i	$-0.734111\pi$
$691$	−35.2741	−1.34189	−0.670945	+	0.741507i	$0.734111\pi$
$692$	−13.6889	−0.520374
$693$	114.292	4.34159
$694$	−30.3022	−1.15025
$695$	−16.4870	−0.625386
$696$	−16.5159	−0.626034
$697$	−4.34859	−0.164715
$698$	−6.99010	−0.264579
$699$	−44.1803	−1.67105
$700$	4.13802	0.156403
$701$	−2.05245	−0.0775200	−0.0387600	−	0.999249i	$-0.512341\pi$
$701$	−2.05245	−0.0775200	−0.0387600	+	0.999249i	$0.512341\pi$
$702$	0	0
$703$	16.4371	0.619936
$704$	3.69843	0.139390
$705$	24.6129	0.926975
$706$	−9.99539	−0.376181
$707$	2.64809	0.0995916
$708$	−16.0766	−0.604194
$709$	−36.1871	−1.35903	−0.679517	−	0.733660i	$-0.737811\pi$
$709$	−36.1871	−1.35903	−0.679517	+	0.733660i	$0.737811\pi$
$710$	0.121998	0.00457850
$711$	91.6008	3.43530
$712$	13.3394	0.499914
$713$	−2.53554	−0.0949569
$714$	−58.9005	−2.20429
$715$	0	0
$716$	−18.1668	−0.678923
$717$	−25.3545	−0.946882
$718$	32.7796	1.22332
$719$	−21.4993	−0.801788	−0.400894	−	0.916124i	$-0.631300\pi$
$719$	−21.4993	−0.801788	−0.400894	+	0.916124i	$0.631300\pi$
$720$	7.46801	0.278316
$721$	26.4911	0.986579
$722$	−2.76414	−0.102870
$723$	4.02391	0.149651
$724$	16.5998	0.616926
$725$	5.10470	0.189584
$726$	−8.66575	−0.321616
$727$	−47.5909	−1.76505	−0.882525	−	0.470265i	$-0.844158\pi$
$727$	−47.5909	−1.76505	−0.882525	+	0.470265i	$0.844158\pi$
$728$	0	0
$729$	41.6604	1.54298
$730$	7.47315	0.276594
$731$	32.8016	1.21321
$732$	16.4914	0.609541
$733$	0.731581	0.0270216	0.0135108	−	0.999909i	$-0.495699\pi$
$733$	0.731581	0.0270216	0.0135108	+	0.999909i	$0.495699\pi$
$734$	29.9518	1.10554
$735$	−32.7530	−1.20811
$736$	−4.90379	−0.180756
$737$	1.96119	0.0722413
$738$	−7.38176	−0.271726
$739$	37.3869	1.37530	0.687649	−	0.726043i	$-0.258643\pi$
$739$	37.3869	1.37530	0.687649	+	0.726043i	$0.258643\pi$
$740$	−4.07931	−0.149958
$741$	0	0
$742$	−11.3253	−0.415765
$743$	−43.3551	−1.59054	−0.795272	−	0.606253i	$-0.792672\pi$
$743$	−43.3551	−1.59054	−0.795272	+	0.606253i	$0.792672\pi$
$744$	−1.67291	−0.0613317
$745$	18.2731	0.669474
$746$	−14.3796	−0.526474
$747$	−101.361	−3.70860
$748$	16.2709	0.594923
$749$	−70.3649	−2.57108
$750$	−3.23543	−0.118141
$751$	2.48301	0.0906063	0.0453032	−	0.998973i	$-0.485575\pi$
$751$	2.48301	0.0906063	0.0453032	+	0.998973i	$0.485575\pi$
$752$	−7.60730	−0.277410
$753$	−76.2339	−2.77812
$754$	0	0
$755$	−15.8124	−0.575471
$756$	−59.8189	−2.17559
$757$	−12.8144	−0.465749	−0.232874	−	0.972507i	$-0.574813\pi$
$757$	−12.8144	−0.465749	−0.232874	+	0.972507i	$0.574813\pi$
$758$	−33.9184	−1.23197
$759$	58.6788	2.12991
$760$	−4.02938	−0.146161
$761$	−19.9840	−0.724419	−0.362210	−	0.932097i	$-0.617978\pi$
$761$	−19.9840	−0.724419	−0.362210	+	0.932097i	$0.617978\pi$
$762$	−4.98081	−0.180436
$763$	52.5302	1.90172
$764$	4.55032	0.164625
$765$	32.8548	1.18787
$766$	−19.6131	−0.708650
$767$	0	0
$768$	−3.23543	−0.116749
$769$	−33.2165	−1.19782	−0.598909	−	0.800817i	$-0.704399\pi$
$769$	−33.2165	−1.19782	−0.598909	+	0.800817i	$0.704399\pi$
$770$	15.3042	0.551525
$771$	−27.3683	−0.985646
$772$	−19.7745	−0.711699
$773$	47.0596	1.69262	0.846308	−	0.532695i	$-0.178821\pi$
$773$	47.0596	1.69262	0.846308	+	0.532695i	$0.178821\pi$
$774$	55.6809	2.00141
$775$	0.517058	0.0185733
$776$	−4.40968	−0.158298
$777$	54.6150	1.95930
$778$	−11.6768	−0.418635
$779$	3.98284	0.142700
$780$	0	0
$781$	0.451201	0.0161452
$782$	−21.5737	−0.771475
$783$	−73.7932	−2.63715
$784$	10.1232	0.361544
$785$	−22.5961	−0.806489
$786$	−9.31104	−0.332114
$787$	17.7155	0.631491	0.315746	−	0.948844i	$-0.397745\pi$
$787$	17.7155	0.631491	0.315746	+	0.948844i	$0.397745\pi$
$788$	14.2131	0.506319
$789$	−42.7251	−1.52106
$790$	12.2658	0.436396
$791$	6.46262	0.229784
$792$	27.6199	0.981431
$793$	0	0
$794$	−27.7028	−0.983137
$795$	8.85502	0.314055
$796$	20.8990	0.740747
$797$	−9.32326	−0.330247	−0.165123	−	0.986273i	$-0.552802\pi$
$797$	−9.32326	−0.330247	−0.165123	+	0.986273i	$0.552802\pi$
$798$	53.9464	1.90968
$799$	−33.4676	−1.18400
$800$	1.00000	0.0353553
$801$	99.6185	3.51985
$802$	5.57831	0.196977
$803$	27.6389	0.975356
$804$	−1.71567	−0.0605070
$805$	−20.2920	−0.715198
$806$	0	0
$807$	−16.9487	−0.596621
$808$	0.639941	0.0225130
$809$	−2.27797	−0.0800893	−0.0400446	−	0.999198i	$-0.512750\pi$
$809$	−2.27797	−0.0800893	−0.0400446	+	0.999198i	$0.512750\pi$
$810$	24.3671	0.856173
$811$	38.0410	1.33580	0.667901	−	0.744250i	$-0.267193\pi$
$811$	38.0410	1.33580	0.667901	+	0.744250i	$0.267193\pi$
$812$	21.1234	0.741285
$813$	21.0687	0.738911
$814$	−15.0870	−0.528801
$815$	4.47519	0.156759
$816$	−14.2340	−0.498288
$817$	−30.0427	−1.05106
$818$	−3.73914	−0.130736
$819$	0	0
$820$	−0.988450	−0.0345182
$821$	30.9508	1.08019	0.540095	−	0.841604i	$-0.318388\pi$
$821$	30.9508	1.08019	0.540095	+	0.841604i	$0.318388\pi$
$822$	−55.1353	−1.92306
$823$	−37.1944	−1.29651	−0.648257	−	0.761421i	$-0.724502\pi$
$823$	−37.1944	−1.29651	−0.648257	+	0.761421i	$0.724502\pi$
$824$	6.40187	0.223020
$825$	−11.9660	−0.416603
$826$	20.5615	0.715424
$827$	15.9518	0.554697	0.277349	−	0.960769i	$-0.410544\pi$
$827$	15.9518	0.554697	0.277349	+	0.960769i	$0.410544\pi$
$828$	−36.6215	−1.27269
$829$	−40.8906	−1.42019	−0.710095	−	0.704106i	$-0.751348\pi$
$829$	−40.8906	−1.42019	−0.710095	+	0.704106i	$0.751348\pi$
$830$	−13.5727	−0.471115
$831$	−89.4203	−3.10196
$832$	0	0
$833$	44.5362	1.54309
$834$	53.3424	1.84710
$835$	−8.83137	−0.305622
$836$	−14.9024	−0.515409
$837$	−7.47456	−0.258358
$838$	−31.7645	−1.09729
$839$	−21.1904	−0.731575	−0.365788	−	0.930698i	$-0.619200\pi$
$839$	−21.1904	−0.731575	−0.365788	+	0.930698i	$0.619200\pi$
$840$	−13.3883	−0.461940
$841$	−2.94202	−0.101449
$842$	−23.4191	−0.807074
$843$	−60.5881	−2.08677
$844$	−27.4802	−0.945909
$845$	0	0
$846$	−56.8114	−1.95322
$847$	11.0832	0.380825
$848$	−2.73689	−0.0939852
$849$	81.2669	2.78907
$850$	4.39940	0.150898
$851$	20.0041	0.685731
$852$	−0.394716	−0.0135227
$853$	−2.68792	−0.0920327	−0.0460163	−	0.998941i	$-0.514653\pi$
$853$	−2.68792	−0.0920327	−0.0460163	+	0.998941i	$0.514653\pi$
$854$	−21.0921	−0.721756
$855$	−30.0914	−1.02910
$856$	−17.0045	−0.581201
$857$	−22.3058	−0.761950	−0.380975	−	0.924585i	$-0.624412\pi$
$857$	−22.3058	−0.761950	−0.380975	+	0.924585i	$0.624412\pi$
$858$	0	0
$859$	3.38433	0.115472	0.0577360	−	0.998332i	$-0.481612\pi$
$859$	3.38433	0.115472	0.0577360	+	0.998332i	$0.481612\pi$
$860$	7.45593	0.254245
$861$	13.2337	0.451002
$862$	14.4701	0.492853
$863$	22.9470	0.781125	0.390563	−	0.920576i	$-0.372280\pi$
$863$	22.9470	0.781125	0.390563	+	0.920576i	$0.372280\pi$
$864$	−14.4559	−0.491801
$865$	−13.6889	−0.465436
$866$	−38.2377	−1.29937
$867$	−7.61864	−0.258743
$868$	2.13960	0.0726227
$869$	45.3641	1.53887
$870$	−16.5159	−0.559942
$871$	0	0
$872$	12.6945	0.429891
$873$	−32.9316	−1.11456
$874$	19.7592	0.668365
$875$	4.13802	0.139891
$876$	−24.1788	−0.816928
$877$	−38.6220	−1.30417	−0.652085	−	0.758146i	$-0.726106\pi$
$877$	−38.6220	−1.30417	−0.652085	+	0.758146i	$0.726106\pi$
$878$	14.3819	0.485366
$879$	−20.1464	−0.679520
$880$	3.69843	0.124674
$881$	−0.890768	−0.0300107	−0.0150054	−	0.999887i	$-0.504777\pi$
$881$	−0.890768	−0.0300107	−0.0150054	+	0.999887i	$0.504777\pi$
$882$	75.6003	2.54560
$883$	−51.6175	−1.73707	−0.868534	−	0.495630i	$-0.834937\pi$
$883$	−51.6175	−1.73707	−0.868534	+	0.495630i	$0.834937\pi$
$884$	0	0
$885$	−16.0766	−0.540407
$886$	10.1853	0.342180
$887$	0.367429	0.0123371	0.00616854	−	0.999981i	$-0.498036\pi$
$887$	0.367429	0.0123371	0.00616854	+	0.999981i	$0.498036\pi$
$888$	13.1983	0.442907
$889$	6.37032	0.213654
$890$	13.3394	0.447136
$891$	90.1201	3.01914
$892$	−19.6984	−0.659552
$893$	30.6527	1.02575
$894$	−59.1213	−1.97731
$895$	−18.1668	−0.607248
$896$	4.13802	0.138242
$897$	0	0
$898$	15.3798	0.513232
$899$	2.63943	0.0880299
$900$	7.46801	0.248934
$901$	−12.0407	−0.401133
$902$	−3.65572	−0.121722
$903$	−99.8220	−3.32187
$904$	1.56177	0.0519436
$905$	16.5998	0.551796
$906$	51.1598	1.69967
$907$	6.19041	0.205549	0.102775	−	0.994705i	$-0.467228\pi$
$907$	6.19041	0.205549	0.102775	+	0.994705i	$0.467228\pi$
$908$	12.4168	0.412065
$909$	4.77908	0.158512
$910$	0	0
$911$	−3.77931	−0.125214	−0.0626071	−	0.998038i	$-0.519942\pi$
$911$	−3.77931	−0.125214	−0.0626071	+	0.998038i	$0.519942\pi$
$912$	13.0368	0.431690
$913$	−50.1976	−1.66130
$914$	37.9943	1.25674
$915$	16.4914	0.545190
$916$	−13.3509	−0.441125
$917$	11.9085	0.393255
$918$	−63.5975	−2.09903
$919$	−33.8210	−1.11565	−0.557826	−	0.829958i	$-0.688364\pi$
$919$	−33.8210	−1.11565	−0.557826	+	0.829958i	$0.688364\pi$
$920$	−4.90379	−0.161673
$921$	2.10008	0.0691998
$922$	10.4170	0.343066
$923$	0	0
$924$	−49.5156	−1.62894
$925$	−4.07931	−0.134127
$926$	−13.3069	−0.437290
$927$	47.8092	1.57026
$928$	5.10470	0.167570
$929$	−4.86324	−0.159558	−0.0797789	−	0.996813i	$-0.525421\pi$
$929$	−4.86324	−0.159558	−0.0797789	+	0.996813i	$0.525421\pi$
$930$	−1.67291	−0.0548567
$931$	−40.7903	−1.33685
$932$	13.6551	0.447289
$933$	−9.63279	−0.315363
$934$	33.5745	1.09859
$935$	16.2709	0.532115
$936$	0	0
$937$	33.6300	1.09864	0.549322	−	0.835610i	$-0.314886\pi$
$937$	33.6300	1.09864	0.549322	+	0.835610i	$0.314886\pi$
$938$	2.19429	0.0716462
$939$	−30.5491	−0.996933
$940$	−7.60730	−0.248123
$941$	−12.1989	−0.397672	−0.198836	−	0.980033i	$-0.563716\pi$
$941$	−12.1989	−0.397672	−0.198836	+	0.980033i	$0.563716\pi$
$942$	73.1081	2.38199
$943$	4.84715	0.157845
$944$	4.96891	0.161724
$945$	−59.8189	−1.94591
$946$	27.5752	0.896548
$947$	54.6480	1.77582	0.887910	−	0.460016i	$-0.152156\pi$
$947$	54.6480	1.77582	0.887910	+	0.460016i	$0.152156\pi$
$948$	−39.6850	−1.28891
$949$	0	0
$950$	−4.02938	−0.130730
$951$	30.4681	0.987996
$952$	18.2048	0.590022
$953$	−17.5689	−0.569112	−0.284556	−	0.958659i	$-0.591846\pi$
$953$	−17.5689	−0.569112	−0.284556	+	0.958659i	$0.591846\pi$
$954$	−20.4391	−0.661741
$955$	4.55032	0.147245
$956$	7.83653	0.253451
$957$	−61.0829	−1.97453
$958$	4.25242	0.137390
$959$	70.5165	2.27710
$960$	−3.23543	−0.104423
$961$	−30.7327	−0.991376
$962$	0	0
$963$	−126.990	−4.09218
$964$	−1.24370	−0.0400569
$965$	−19.7745	−0.636563
$966$	65.6533	2.11236
$967$	31.9097	1.02615	0.513074	−	0.858345i	$-0.328507\pi$
$967$	31.9097	1.02615	0.513074	+	0.858345i	$0.328507\pi$
$968$	2.67839	0.0860868
$969$	57.3540	1.84248
$970$	−4.40968	−0.141586
$971$	20.8261	0.668341	0.334171	−	0.942513i	$-0.391544\pi$
$971$	20.8261	0.668341	0.334171	+	0.942513i	$0.391544\pi$
$972$	−35.4703	−1.13771
$973$	−68.2234	−2.18714
$974$	28.4772	0.912468
$975$	0	0
$976$	−5.09714	−0.163155
$977$	−25.2647	−0.808291	−0.404145	−	0.914695i	$-0.632431\pi$
$977$	−25.2647	−0.808291	−0.404145	+	0.914695i	$0.632431\pi$
$978$	−14.4792	−0.462992
$979$	49.3347	1.57674
$980$	10.1232	0.323375
$981$	94.8028	3.02682
$982$	−24.4891	−0.781478
$983$	22.6682	0.723002	0.361501	−	0.932372i	$-0.382264\pi$
$983$	22.6682	0.723002	0.361501	+	0.932372i	$0.382264\pi$
$984$	3.19806	0.101951
$985$	14.2131	0.452866
$986$	22.4576	0.715197
$987$	101.849	3.24188
$988$	0	0
$989$	−36.5623	−1.16261
$990$	27.6199	0.877818
$991$	−19.3395	−0.614339	−0.307170	−	0.951655i	$-0.599382\pi$
$991$	−19.3395	−0.614339	−0.307170	+	0.951655i	$0.599382\pi$
$992$	0.517058	0.0164166
$993$	4.39300	0.139407
$994$	0.504830	0.0160122
$995$	20.8990	0.662544
$996$	43.9135	1.39145
$997$	−5.96006	−0.188757	−0.0943785	−	0.995536i	$-0.530086\pi$
$997$	−5.96006	−0.188757	−0.0943785	+	0.995536i	$0.530086\pi$
$998$	18.2842	0.578775
$999$	58.9702	1.86573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.a.w.1.1	yes	6
5.4	even	2		8450.2.a.cp.1.6		6
13.2	odd	12		1690.2.l.n.1161.7		24
13.3	even	3		1690.2.e.u.191.6		12
13.4	even	6		1690.2.e.v.991.6		12
13.5	odd	4		1690.2.d.l.1351.1		12
13.6	odd	12		1690.2.l.n.361.2		24
13.7	odd	12		1690.2.l.n.361.7		24
13.8	odd	4		1690.2.d.l.1351.7		12
13.9	even	3		1690.2.e.u.991.6		12
13.10	even	6		1690.2.e.v.191.6		12
13.11	odd	12		1690.2.l.n.1161.2		24
13.12	even	2		1690.2.a.v.1.1	✓	6
65.64	even	2		8450.2.a.cq.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.v.1.1	✓	6	13.12	even	2
1690.2.a.w.1.1	yes	6	1.1	even	1	trivial
1690.2.d.l.1351.1		12	13.5	odd	4
1690.2.d.l.1351.7		12	13.8	odd	4
1690.2.e.u.191.6		12	13.3	even	3
1690.2.e.u.991.6		12	13.9	even	3
1690.2.e.v.191.6		12	13.10	even	6
1690.2.e.v.991.6		12	13.4	even	6
1690.2.l.n.361.2		24	13.6	odd	12
1690.2.l.n.361.7		24	13.7	odd	12
1690.2.l.n.1161.2		24	13.11	odd	12
1690.2.l.n.1161.7		24	13.2	odd	12
8450.2.a.cp.1.6		6	5.4	even	2
8450.2.a.cq.1.6		6	65.64	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.23543 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.23543 q^{6} +4.13802 q^{7} +1.00000 q^{8} +7.46801 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.23543 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.23543 q^{6} +4.13802 q^{7} +1.00000 q^{8} +7.46801 q^{9} +1.00000 q^{10} +3.69843 q^{11} -3.23543 q^{12} +4.13802 q^{14} -3.23543 q^{15} +1.00000 q^{16} +4.39940 q^{17} +7.46801 q^{18} -4.02938 q^{19} +1.00000 q^{20} -13.3883 q^{21} +3.69843 q^{22} -4.90379 q^{23} -3.23543 q^{24} +1.00000 q^{25} -14.4559 q^{27} +4.13802 q^{28} +5.10470 q^{29} -3.23543 q^{30} +0.517058 q^{31} +1.00000 q^{32} -11.9660 q^{33} +4.39940 q^{34} +4.13802 q^{35} +7.46801 q^{36} -4.07931 q^{37} -4.02938 q^{38} +1.00000 q^{40} -0.988450 q^{41} -13.3883 q^{42} +7.45593 q^{43} +3.69843 q^{44} +7.46801 q^{45} -4.90379 q^{46} -7.60730 q^{47} -3.23543 q^{48} +10.1232 q^{49} +1.00000 q^{50} -14.2340 q^{51} -2.73689 q^{53} -14.4559 q^{54} +3.69843 q^{55} +4.13802 q^{56} +13.0368 q^{57} +5.10470 q^{58} +4.96891 q^{59} -3.23543 q^{60} -5.09714 q^{61} +0.517058 q^{62} +30.9028 q^{63} +1.00000 q^{64} -11.9660 q^{66} +0.530276 q^{67} +4.39940 q^{68} +15.8659 q^{69} +4.13802 q^{70} +0.121998 q^{71} +7.46801 q^{72} +7.47315 q^{73} -4.07931 q^{74} -3.23543 q^{75} -4.02938 q^{76} +15.3042 q^{77} +12.2658 q^{79} +1.00000 q^{80} +24.3671 q^{81} -0.988450 q^{82} -13.5727 q^{83} -13.3883 q^{84} +4.39940 q^{85} +7.45593 q^{86} -16.5159 q^{87} +3.69843 q^{88} +13.3394 q^{89} +7.46801 q^{90} -4.90379 q^{92} -1.67291 q^{93} -7.60730 q^{94} -4.02938 q^{95} -3.23543 q^{96} -4.40968 q^{97} +10.1232 q^{98} +27.6199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 6 q^{8} + 16 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 6 * q^8 + 16 * q^9	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 6 q^{8} + 16 q^{9} + 6 q^{10} + 15 q^{11} - 2 q^{12} + 3 q^{14} - 2 q^{15} + 6 q^{16} - 3 q^{17} + 16 q^{18} + q^{19} + 6 q^{20} - 2 q^{21} + 15 q^{22} - 3 q^{23} - 2 q^{24} + 6 q^{25} - 20 q^{27} + 3 q^{28} + 7 q^{29} - 2 q^{30} + 6 q^{32} + 4 q^{33} - 3 q^{34} + 3 q^{35} + 16 q^{36} + 6 q^{37} + q^{38} + 6 q^{40} + 2 q^{41} - 2 q^{42} - 22 q^{43} + 15 q^{44} + 16 q^{45} - 3 q^{46} + 7 q^{47} - 2 q^{48} + 31 q^{49} + 6 q^{50} - 22 q^{51} - 16 q^{53} - 20 q^{54} + 15 q^{55} + 3 q^{56} + 2 q^{57} + 7 q^{58} + 15 q^{59} - 2 q^{60} + 33 q^{61} + 25 q^{63} + 6 q^{64} + 4 q^{66} - 8 q^{67} - 3 q^{68} - 6 q^{69} + 3 q^{70} + 40 q^{71} + 16 q^{72} + 21 q^{73} + 6 q^{74} - 2 q^{75} + q^{76} - 34 q^{77} + 20 q^{79} + 6 q^{80} - 2 q^{81} + 2 q^{82} + 22 q^{83} - 2 q^{84} - 3 q^{85} - 22 q^{86} - 39 q^{87} + 15 q^{88} + 20 q^{89} + 16 q^{90} - 3 q^{92} + 48 q^{93} + 7 q^{94} + q^{95} - 2 q^{96} - 7 q^{97} + 31 q^{98} + 55 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 6 * q^8 + 16 * q^9 + 6 * q^10 + 15 * q^11 - 2 * q^12 + 3 * q^14 - 2 * q^15 + 6 * q^16 - 3 * q^17 + 16 * q^18 + q^19 + 6 * q^20 - 2 * q^21 + 15 * q^22 - 3 * q^23 - 2 * q^24 + 6 * q^25 - 20 * q^27 + 3 * q^28 + 7 * q^29 - 2 * q^30 + 6 * q^32 + 4 * q^33 - 3 * q^34 + 3 * q^35 + 16 * q^36 + 6 * q^37 + q^38 + 6 * q^40 + 2 * q^41 - 2 * q^42 - 22 * q^43 + 15 * q^44 + 16 * q^45 - 3 * q^46 + 7 * q^47 - 2 * q^48 + 31 * q^49 + 6 * q^50 - 22 * q^51 - 16 * q^53 - 20 * q^54 + 15 * q^55 + 3 * q^56 + 2 * q^57 + 7 * q^58 + 15 * q^59 - 2 * q^60 + 33 * q^61 + 25 * q^63 + 6 * q^64 + 4 * q^66 - 8 * q^67 - 3 * q^68 - 6 * q^69 + 3 * q^70 + 40 * q^71 + 16 * q^72 + 21 * q^73 + 6 * q^74 - 2 * q^75 + q^76 - 34 * q^77 + 20 * q^79 + 6 * q^80 - 2 * q^81 + 2 * q^82 + 22 * q^83 - 2 * q^84 - 3 * q^85 - 22 * q^86 - 39 * q^87 + 15 * q^88 + 20 * q^89 + 16 * q^90 - 3 * q^92 + 48 * q^93 + 7 * q^94 + q^95 - 2 * q^96 - 7 * q^97 + 31 * q^98 + 55 * q^99

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