LMFDB - Embedded newform 2645.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, 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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.679643$ of defining polynomial
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.679643 q^{2} +0.178799 q^{3} -1.53809 q^{4} +1.00000 q^{5} +0.121519 q^{6} +1.84651 q^{7} -2.40464 q^{8} -2.96803 q^{9} +O(q^{10})$	\(q+0.679643 q^{2} +0.178799 q^{3} -1.53809 q^{4} +1.00000 q^{5} +0.121519 q^{6} +1.84651 q^{7} -2.40464 q^{8} -2.96803 q^{9} +0.679643 q^{10} -0.320357 q^{11} -0.275008 q^{12} +0.954651 q^{13} +1.25497 q^{14} +0.178799 q^{15} +1.44188 q^{16} -5.78112 q^{17} -2.01720 q^{18} +6.14852 q^{19} -1.53809 q^{20} +0.330154 q^{21} -0.217728 q^{22} -0.429946 q^{24} +1.00000 q^{25} +0.648822 q^{26} -1.06708 q^{27} -2.84009 q^{28} -7.37649 q^{29} +0.121519 q^{30} -4.03724 q^{31} +5.78923 q^{32} -0.0572794 q^{33} -3.92910 q^{34} +1.84651 q^{35} +4.56508 q^{36} -6.16045 q^{37} +4.17880 q^{38} +0.170690 q^{39} -2.40464 q^{40} -4.23777 q^{41} +0.224387 q^{42} +1.48081 q^{43} +0.492736 q^{44} -2.96803 q^{45} +9.26193 q^{47} +0.257806 q^{48} -3.59039 q^{49} +0.679643 q^{50} -1.03366 q^{51} -1.46833 q^{52} -11.8535 q^{53} -0.725231 q^{54} -0.320357 q^{55} -4.44019 q^{56} +1.09935 q^{57} -5.01338 q^{58} +3.57701 q^{59} -0.275008 q^{60} -1.28312 q^{61} -2.74388 q^{62} -5.48050 q^{63} +1.05086 q^{64} +0.954651 q^{65} -0.0389296 q^{66} -8.07235 q^{67} +8.89186 q^{68} +1.25497 q^{70} +13.6477 q^{71} +7.13703 q^{72} -11.3581 q^{73} -4.18691 q^{74} +0.178799 q^{75} -9.45695 q^{76} -0.591543 q^{77} +0.116009 q^{78} -14.7709 q^{79} +1.44188 q^{80} +8.71330 q^{81} -2.88017 q^{82} -2.66244 q^{83} -0.507805 q^{84} -5.78112 q^{85} +1.00642 q^{86} -1.31891 q^{87} +0.770341 q^{88} -7.64125 q^{89} -2.01720 q^{90} +1.76277 q^{91} -0.721854 q^{93} +6.29481 q^{94} +6.14852 q^{95} +1.03511 q^{96} -10.4872 q^{97} -2.44019 q^{98} +0.950829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9	$ 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9} - q^{10} - 5 q^{11} - q^{12} - 9 q^{14} + q^{15} - q^{16} + 5 q^{17} + 9 q^{18} - 4 q^{19} + q^{20} + 4 q^{21} + 10 q^{22} + 12 q^{24} + 4 q^{25} + 17 q^{26} - 14 q^{27} + 14 q^{28} - 5 q^{29} - 10 q^{30} - 13 q^{31} + 2 q^{32} - 11 q^{33} - 6 q^{34} - 3 q^{35} - 7 q^{36} - 3 q^{37} + 17 q^{38} - 6 q^{39} - 6 q^{40} - 20 q^{41} + 21 q^{42} - 12 q^{43} - 9 q^{44} + 9 q^{45} - 9 q^{47} + 18 q^{48} + 21 q^{49} - q^{50} - 17 q^{51} - 28 q^{52} - 5 q^{53} - 19 q^{54} - 5 q^{55} - 19 q^{56} - 28 q^{57} - 3 q^{58} - 4 q^{59} - q^{60} - 12 q^{61} + 14 q^{62} - 67 q^{63} + 11 q^{66} - 18 q^{67} + 29 q^{68} - 9 q^{70} + 30 q^{71} + 9 q^{72} + q^{73} - 24 q^{74} + q^{75} - 6 q^{76} - 6 q^{77} - 2 q^{78} - 16 q^{79} - q^{80} + 44 q^{81} - 14 q^{82} - 24 q^{83} + 34 q^{84} + 5 q^{85} + 19 q^{86} - 33 q^{87} + 7 q^{88} + 9 q^{89} + 9 q^{90} - 43 q^{91} - 35 q^{93} + 23 q^{94} - 4 q^{95} - 7 q^{96} - 39 q^{97} - 11 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9 - q^10 - 5 * q^11 - q^12 - 9 * q^14 + q^15 - q^16 + 5 * q^17 + 9 * q^18 - 4 * q^19 + q^20 + 4 * q^21 + 10 * q^22 + 12 * q^24 + 4 * q^25 + 17 * q^26 - 14 * q^27 + 14 * q^28 - 5 * q^29 - 10 * q^30 - 13 * q^31 + 2 * q^32 - 11 * q^33 - 6 * q^34 - 3 * q^35 - 7 * q^36 - 3 * q^37 + 17 * q^38 - 6 * q^39 - 6 * q^40 - 20 * q^41 + 21 * q^42 - 12 * q^43 - 9 * q^44 + 9 * q^45 - 9 * q^47 + 18 * q^48 + 21 * q^49 - q^50 - 17 * q^51 - 28 * q^52 - 5 * q^53 - 19 * q^54 - 5 * q^55 - 19 * q^56 - 28 * q^57 - 3 * q^58 - 4 * q^59 - q^60 - 12 * q^61 + 14 * q^62 - 67 * q^63 + 11 * q^66 - 18 * q^67 + 29 * q^68 - 9 * q^70 + 30 * q^71 + 9 * q^72 + q^73 - 24 * q^74 + q^75 - 6 * q^76 - 6 * q^77 - 2 * q^78 - 16 * q^79 - q^80 + 44 * q^81 - 14 * q^82 - 24 * q^83 + 34 * q^84 + 5 * q^85 + 19 * q^86 - 33 * q^87 + 7 * q^88 + 9 * q^89 + 9 * q^90 - 43 * q^91 - 35 * q^93 + 23 * q^94 - 4 * q^95 - 7 * q^96 - 39 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.679643	0.480580	0.240290	−	0.970701i	$-0.422757\pi$
$2$	0.679643	0.480580	0.240290	+	0.970701i	$0.422757\pi$
$3$	0.178799	0.103230	0.0516148	−	0.998667i	$-0.483563\pi$
$3$	0.178799	0.103230	0.0516148	+	0.998667i	$0.483563\pi$
$4$	−1.53809	−0.769043
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.121519	0.0496101
$7$	1.84651	0.697916	0.348958	−	0.937138i	$-0.386536\pi$
$7$	1.84651	0.697916	0.348958	+	0.937138i	$0.386536\pi$
$8$	−2.40464	−0.850167
$9$	−2.96803	−0.989344
$10$	0.679643	0.214922
$11$	−0.320357	−0.0965912	−0.0482956	−	0.998833i	$-0.515379\pi$
$11$	−0.320357	−0.0965912	−0.0482956	+	0.998833i	$0.515379\pi$
$12$	−0.275008	−0.0793879
$13$	0.954651	0.264773	0.132386	−	0.991198i	$-0.457736\pi$
$13$	0.954651	0.264773	0.132386	+	0.991198i	$0.457736\pi$
$14$	1.25497	0.335405
$15$	0.178799	0.0461656
$16$	1.44188	0.360469
$17$	−5.78112	−1.40213	−0.701064	−	0.713098i	$-0.747291\pi$
$17$	−5.78112	−1.40213	−0.701064	+	0.713098i	$0.747291\pi$
$18$	−2.01720	−0.475459
$19$	6.14852	1.41057	0.705283	−	0.708925i	$-0.250820\pi$
$19$	6.14852	1.41057	0.705283	+	0.708925i	$0.250820\pi$
$20$	−1.53809	−0.343926
$21$	0.330154	0.0720455
$22$	−0.217728	−0.0464198
$23$	0	0
$23$	0	0
$24$	−0.429946	−0.0877623
$25$	1.00000	0.200000
$26$	0.648822	0.127244
$27$	−1.06708	−0.205359
$28$	−2.84009	−0.536727
$29$	−7.37649	−1.36978	−0.684890	−	0.728647i	$-0.740150\pi$
$29$	−7.37649	−1.36978	−0.684890	+	0.728647i	$0.740150\pi$
$30$	0.121519	0.0221863
$31$	−4.03724	−0.725110	−0.362555	−	0.931962i	$-0.618095\pi$
$31$	−4.03724	−0.725110	−0.362555	+	0.931962i	$0.618095\pi$
$32$	5.78923	1.02340
$33$	−0.0572794	−0.00997106
$34$	−3.92910	−0.673835
$35$	1.84651	0.312117
$36$	4.56508	0.760847
$37$	−6.16045	−1.01277	−0.506386	−	0.862307i	$-0.669019\pi$
$37$	−6.16045	−1.01277	−0.506386	+	0.862307i	$0.669019\pi$
$38$	4.17880	0.677891
$39$	0.170690	0.0273323
$40$	−2.40464	−0.380206
$41$	−4.23777	−0.661828	−0.330914	−	0.943661i	$-0.607357\pi$
$41$	−4.23777	−0.661828	−0.330914	+	0.943661i	$0.607357\pi$
$42$	0.224387	0.0346237
$43$	1.48081	0.225821	0.112910	−	0.993605i	$-0.463983\pi$
$43$	1.48081	0.225821	0.112910	+	0.993605i	$0.463983\pi$
$44$	0.492736	0.0742828
$45$	−2.96803	−0.442448
$46$	0	0
$47$	9.26193	1.35099	0.675496	−	0.737364i	$-0.263930\pi$
$47$	9.26193	1.35099	0.675496	+	0.737364i	$0.263930\pi$
$48$	0.257806	0.0372110
$49$	−3.59039	−0.512914
$50$	0.679643	0.0961161
$51$	−1.03366	−0.144741
$52$	−1.46833	−0.203621
$53$	−11.8535	−1.62820	−0.814100	−	0.580725i	$-0.802769\pi$
$53$	−11.8535	−1.62820	−0.814100	+	0.580725i	$0.802769\pi$
$54$	−0.725231	−0.0986915
$55$	−0.320357	−0.0431969
$56$	−4.44019	−0.593345
$57$	1.09935	0.145612
$58$	−5.01338	−0.658289
$59$	3.57701	0.465688	0.232844	−	0.972514i	$-0.425197\pi$
$59$	3.57701	0.465688	0.232844	+	0.972514i	$0.425197\pi$
$60$	−0.275008	−0.0355033
$61$	−1.28312	−0.164286	−0.0821431	−	0.996621i	$-0.526176\pi$
$61$	−1.28312	−0.164286	−0.0821431	+	0.996621i	$0.526176\pi$
$62$	−2.74388	−0.348474
$63$	−5.48050	−0.690479
$64$	1.05086	0.131357
$65$	0.954651	0.118410
$66$	−0.0389296	−0.00479190
$67$	−8.07235	−0.986194	−0.493097	−	0.869974i	$-0.664135\pi$
$67$	−8.07235	−0.986194	−0.493097	+	0.869974i	$0.664135\pi$
$68$	8.89186	1.07830
$69$	0	0
$70$	1.25497	0.149997
$71$	13.6477	1.61968	0.809840	−	0.586650i	$-0.199554\pi$
$71$	13.6477	1.61968	0.809840	+	0.586650i	$0.199554\pi$
$72$	7.13703	0.841107
$73$	−11.3581	−1.32937	−0.664685	−	0.747124i	$-0.731434\pi$
$73$	−11.3581	−1.32937	−0.664685	+	0.747124i	$0.731434\pi$
$74$	−4.18691	−0.486718
$75$	0.178799	0.0206459
$76$	−9.45695	−1.08479
$77$	−0.591543	−0.0674125
$78$	0.116009	0.0131354
$79$	−14.7709	−1.66185	−0.830927	−	0.556381i	$-0.812189\pi$
$79$	−14.7709	−1.66185	−0.830927	+	0.556381i	$0.812189\pi$
$80$	1.44188	0.161207
$81$	8.71330	0.968145
$82$	−2.88017	−0.318062
$83$	−2.66244	−0.292241	−0.146120	−	0.989267i	$-0.546679\pi$
$83$	−2.66244	−0.292241	−0.146120	+	0.989267i	$0.546679\pi$
$84$	−0.507805	−0.0554061
$85$	−5.78112	−0.627051
$86$	1.00642	0.108525
$87$	−1.31891	−0.141402
$88$	0.770341	0.0821187
$89$	−7.64125	−0.809971	−0.404986	−	0.914323i	$-0.632724\pi$
$89$	−7.64125	−0.809971	−0.404986	+	0.914323i	$0.632724\pi$
$90$	−2.01720	−0.212632
$91$	1.76277	0.184789
$92$	0	0
$93$	−0.721854	−0.0748527
$94$	6.29481	0.649260
$95$	6.14852	0.630825
$96$	1.03511	0.105645
$97$	−10.4872	−1.06482	−0.532408	−	0.846488i	$-0.678713\pi$
$97$	−10.4872	−1.06482	−0.532408	+	0.846488i	$0.678713\pi$
$98$	−2.44019	−0.246496
$99$	0.950829	0.0955619
$100$	−1.53809	−0.153809
$101$	2.13132	0.212074	0.106037	−	0.994362i	$-0.466184\pi$
$101$	2.13132	0.212074	0.106037	+	0.994362i	$0.466184\pi$
$102$	−0.702519	−0.0695597
$103$	−9.76750	−0.962421	−0.481210	−	0.876605i	$-0.659803\pi$
$103$	−9.76750	−0.962421	−0.481210	+	0.876605i	$0.659803\pi$
$104$	−2.29559	−0.225101
$105$	0.330154	0.0322197
$106$	−8.05613	−0.782481
$107$	1.87993	0.181740	0.0908699	−	0.995863i	$-0.471035\pi$
$107$	1.87993	0.181740	0.0908699	+	0.995863i	$0.471035\pi$
$108$	1.64125	0.157930
$109$	−11.9881	−1.14825	−0.574124	−	0.818768i	$-0.694657\pi$
$109$	−11.9881	−1.14825	−0.574124	+	0.818768i	$0.694657\pi$
$110$	−0.217728	−0.0207596
$111$	−1.10148	−0.104548
$112$	2.66244	0.251577
$113$	3.85347	0.362504	0.181252	−	0.983437i	$-0.441985\pi$
$113$	3.85347	0.362504	0.181252	+	0.983437i	$0.441985\pi$
$114$	0.747164	0.0699783
$115$	0	0
$116$	11.3457	1.05342
$117$	−2.83343	−0.261951
$118$	2.43109	0.223800
$119$	−10.6749	−0.978568
$120$	−0.429946	−0.0392485
$121$	−10.8974	−0.990670
$122$	−0.872061	−0.0789527
$123$	−0.757708	−0.0683202
$124$	6.20962	0.557640
$125$	1.00000	0.0894427
$126$	−3.72479	−0.331830
$127$	17.1242	1.51953	0.759763	−	0.650200i	$-0.225315\pi$
$127$	17.1242	1.51953	0.759763	+	0.650200i	$0.225315\pi$
$128$	−10.8643	−0.960274
$129$	0.264766	0.0233114
$130$	0.648822	0.0569055
$131$	12.3560	1.07955	0.539775	−	0.841810i	$-0.318509\pi$
$131$	12.3560	1.07955	0.539775	+	0.841810i	$0.318509\pi$
$132$	0.0881006	0.00766817
$133$	11.3533	0.984457
$134$	−5.48632	−0.473946
$135$	−1.06708	−0.0918393
$136$	13.9015	1.19204
$137$	7.90264	0.675168	0.337584	−	0.941295i	$-0.390390\pi$
$137$	7.90264	0.675168	0.337584	+	0.941295i	$0.390390\pi$
$138$	0	0
$139$	−18.1646	−1.54070	−0.770349	−	0.637622i	$-0.779918\pi$
$139$	−18.1646	−1.54070	−0.770349	+	0.637622i	$0.779918\pi$
$140$	−2.84009	−0.240032
$141$	1.65602	0.139462
$142$	9.27555	0.778387
$143$	−0.305829	−0.0255747
$144$	−4.27953	−0.356628
$145$	−7.37649	−0.612584
$146$	−7.71948	−0.638869
$147$	−0.641958	−0.0529478
$148$	9.47529	0.778864
$149$	−3.72881	−0.305476	−0.152738	−	0.988267i	$-0.548809\pi$
$149$	−3.72881	−0.305476	−0.152738	+	0.988267i	$0.548809\pi$
$150$	0.121519	0.00992201
$151$	−11.7394	−0.955335	−0.477668	−	0.878541i	$-0.658518\pi$
$151$	−11.7394	−0.955335	−0.477668	+	0.878541i	$0.658518\pi$
$152$	−14.7849	−1.19922
$153$	17.1586	1.38719
$154$	−0.402038	−0.0323971
$155$	−4.03724	−0.324279
$156$	−0.262536	−0.0210197
$157$	21.4260	1.70998	0.854989	−	0.518646i	$-0.173564\pi$
$157$	21.4260	1.70998	0.854989	+	0.518646i	$0.173564\pi$
$158$	−10.0389	−0.798654
$159$	−2.11939	−0.168078
$160$	5.78923	0.457679
$161$	0	0
$162$	5.92194	0.465271
$163$	12.8573	1.00706	0.503531	−	0.863977i	$-0.332034\pi$
$163$	12.8573	1.00706	0.503531	+	0.863977i	$0.332034\pi$
$164$	6.51805	0.508974
$165$	−0.0572794	−0.00445920
$166$	−1.80951	−0.140445
$167$	−6.03197	−0.466768	−0.233384	−	0.972385i	$-0.574980\pi$
$167$	−6.03197	−0.466768	−0.233384	+	0.972385i	$0.574980\pi$
$168$	−0.793900	−0.0612507
$169$	−12.0886	−0.929896
$170$	−3.92910	−0.301348
$171$	−18.2490	−1.39554
$172$	−2.27761	−0.173666
$173$	9.14737	0.695462	0.347731	−	0.937594i	$-0.386952\pi$
$173$	9.14737	0.695462	0.347731	+	0.937594i	$0.386952\pi$
$174$	−0.896386	−0.0679549
$175$	1.84651	0.139583
$176$	−0.461915	−0.0348181
$177$	0.639566	0.0480727
$178$	−5.19333	−0.389256
$179$	−8.96330	−0.669949	−0.334974	−	0.942227i	$-0.608728\pi$
$179$	−8.96330	−0.669949	−0.334974	+	0.942227i	$0.608728\pi$
$180$	4.56508	0.340261
$181$	10.7088	0.795977	0.397989	−	0.917390i	$-0.369708\pi$
$181$	10.7088	0.795977	0.397989	+	0.917390i	$0.369708\pi$
$182$	1.19806	0.0888059
$183$	−0.229420	−0.0169592
$184$	0	0
$185$	−6.16045	−0.452925
$186$	−0.490603	−0.0359728
$187$	1.85202	0.135433
$188$	−14.2456	−1.03897
$189$	−1.97037	−0.143323
$190$	4.17880	0.303162
$191$	21.7253	1.57199	0.785994	−	0.618235i	$-0.212152\pi$
$191$	21.7253	1.57199	0.785994	+	0.618235i	$0.212152\pi$
$192$	0.187892	0.0135600
$193$	−20.0793	−1.44534	−0.722670	−	0.691193i	$-0.757085\pi$
$193$	−20.0793	−1.44534	−0.722670	+	0.691193i	$0.757085\pi$
$194$	−7.12757	−0.511730
$195$	0.170690	0.0122234
$196$	5.52233	0.394452
$197$	0.701576	0.0499852	0.0249926	−	0.999688i	$-0.492044\pi$
$197$	0.701576	0.0499852	0.0249926	+	0.999688i	$0.492044\pi$
$198$	0.646224	0.0459252
$199$	−13.0779	−0.927065	−0.463532	−	0.886080i	$-0.653418\pi$
$199$	−13.0779	−0.927065	−0.463532	+	0.886080i	$0.653418\pi$
$200$	−2.40464	−0.170033
$201$	−1.44333	−0.101804
$202$	1.44853	0.101919
$203$	−13.6208	−0.955991
$204$	1.58985	0.111312
$205$	−4.23777	−0.295978
$206$	−6.63842	−0.462520
$207$	0	0
$208$	1.37649	0.0954423
$209$	−1.96972	−0.136248
$210$	0.224387	0.0154842
$211$	5.10983	0.351775	0.175888	−	0.984410i	$-0.443720\pi$
$211$	5.10983	0.351775	0.175888	+	0.984410i	$0.443720\pi$
$212$	18.2316	1.25215
$213$	2.44019	0.167199
$214$	1.27768	0.0873405
$215$	1.48081	0.100990
$216$	2.56593	0.174589
$217$	−7.45481	−0.506066
$218$	−8.14761	−0.551826
$219$	−2.03082	−0.137230
$220$	0.492736	0.0332203
$221$	−5.51896	−0.371245
$222$	−0.748614	−0.0502437
$223$	−21.0786	−1.41153	−0.705764	−	0.708447i	$-0.749396\pi$
$223$	−21.0786	−1.41153	−0.705764	+	0.708447i	$0.749396\pi$
$224$	10.6899	0.714248
$225$	−2.96803	−0.197869
$226$	2.61899	0.174212
$227$	9.27700	0.615736	0.307868	−	0.951429i	$-0.400384\pi$
$227$	9.27700	0.615736	0.307868	+	0.951429i	$0.400384\pi$
$228$	−1.69089	−0.111982
$229$	−2.89568	−0.191352	−0.0956760	−	0.995413i	$-0.530501\pi$
$229$	−2.89568	−0.191352	−0.0956760	+	0.995413i	$0.530501\pi$
$230$	0	0
$231$	−0.105767	−0.00695896
$232$	17.7378	1.16454
$233$	15.6768	1.02702	0.513511	−	0.858083i	$-0.328345\pi$
$233$	15.6768	1.02702	0.513511	+	0.858083i	$0.328345\pi$
$234$	−1.92572	−0.125889
$235$	9.26193	0.604182
$236$	−5.50175	−0.358134
$237$	−2.64102	−0.171552
$238$	−7.25513	−0.470280
$239$	10.2462	0.662770	0.331385	−	0.943496i	$-0.392484\pi$
$239$	10.2462	0.662770	0.331385	+	0.943496i	$0.392484\pi$
$240$	0.257806	0.0166413
$241$	−0.958937	−0.0617706	−0.0308853	−	0.999523i	$-0.509833\pi$
$241$	−0.958937	−0.0617706	−0.0308853	+	0.999523i	$0.509833\pi$
$242$	−7.40632	−0.476097
$243$	4.75916	0.305300
$244$	1.97354	0.126343
$245$	−3.59039	−0.229382
$246$	−0.514971	−0.0328333
$247$	5.86969	0.373479
$248$	9.70809	0.616464
$249$	−0.476041	−0.0301679
$250$	0.679643	0.0429844
$251$	−18.9521	−1.19625	−0.598123	−	0.801404i	$-0.704087\pi$
$251$	−18.9521	−1.19625	−0.598123	+	0.801404i	$0.704087\pi$
$252$	8.42948	0.531007
$253$	0	0
$254$	11.6383	0.730254
$255$	−1.03366	−0.0647302
$256$	−9.48554	−0.592846
$257$	9.46833	0.590618	0.295309	−	0.955402i	$-0.404577\pi$
$257$	9.46833	0.590618	0.295309	+	0.955402i	$0.404577\pi$
$258$	0.179947	0.0112030
$259$	−11.3753	−0.706829
$260$	−1.46833	−0.0910622
$261$	21.8936	1.35518
$262$	8.39767	0.518810
$263$	22.2966	1.37487	0.687433	−	0.726248i	$-0.258738\pi$
$263$	22.2966	1.37487	0.687433	+	0.726248i	$0.258738\pi$
$264$	0.137736	0.00847707
$265$	−11.8535	−0.728153
$266$	7.71620	0.473111
$267$	−1.36625	−0.0836130
$268$	12.4160	0.758425
$269$	−8.69998	−0.530447	−0.265224	−	0.964187i	$-0.585446\pi$
$269$	−8.69998	−0.530447	−0.265224	+	0.964187i	$0.585446\pi$
$270$	−0.725231	−0.0441362
$271$	0.786094	0.0477518	0.0238759	−	0.999715i	$-0.492399\pi$
$271$	0.786094	0.0477518	0.0238759	+	0.999715i	$0.492399\pi$
$272$	−8.33566	−0.505424
$273$	0.315182	0.0190757
$274$	5.37098	0.324473
$275$	−0.320357	−0.0193182
$276$	0	0
$277$	−11.7709	−0.707244	−0.353622	−	0.935388i	$-0.615050\pi$
$277$	−11.7709	−0.707244	−0.353622	+	0.935388i	$0.615050\pi$
$278$	−12.3454	−0.740430
$279$	11.9827	0.717383
$280$	−4.44019	−0.265352
$281$	−13.7043	−0.817528	−0.408764	−	0.912640i	$-0.634040\pi$
$281$	−13.7043	−0.817528	−0.408764	+	0.912640i	$0.634040\pi$
$282$	1.12550	0.0670228
$283$	−26.5148	−1.57614	−0.788070	−	0.615586i	$-0.788919\pi$
$283$	−26.5148	−1.57614	−0.788070	+	0.615586i	$0.788919\pi$
$284$	−20.9913	−1.24560
$285$	1.09935	0.0651197
$286$	−0.207855	−0.0122907
$287$	−7.82509	−0.461900
$288$	−17.1826	−1.01250
$289$	16.4214	0.965964
$290$	−5.01338	−0.294396
$291$	−1.87510	−0.109920
$292$	17.4698	1.02234
$293$	−21.8032	−1.27375	−0.636877	−	0.770966i	$-0.719774\pi$
$293$	−21.8032	−1.27375	−0.636877	+	0.770966i	$0.719774\pi$
$294$	−0.436302	−0.0254457
$295$	3.57701	0.208262
$296$	14.8136	0.861025
$297$	0.341845	0.0198359
$298$	−2.53426	−0.146806
$299$	0	0
$300$	−0.275008	−0.0158776
$301$	2.73433	0.157604
$302$	−7.97857	−0.459115
$303$	0.381077	0.0218923
$304$	8.86540	0.508466
$305$	−1.28312	−0.0734710
$306$	11.6617	0.666655
$307$	11.7425	0.670180	0.335090	−	0.942186i	$-0.391233\pi$
$307$	11.7425	0.670180	0.335090	+	0.942186i	$0.391233\pi$
$308$	0.909843	0.0518431
$309$	−1.74642	−0.0993502
$310$	−2.74388	−0.155842
$311$	−1.29987	−0.0737091	−0.0368545	−	0.999321i	$-0.511734\pi$
$311$	−1.29987	−0.0737091	−0.0368545	+	0.999321i	$0.511734\pi$
$312$	−0.410448	−0.0232371
$313$	27.8260	1.57282	0.786410	−	0.617705i	$-0.211937\pi$
$313$	27.8260	1.57282	0.786410	+	0.617705i	$0.211937\pi$
$314$	14.5620	0.821782
$315$	−5.48050	−0.308791
$316$	22.7189	1.27804
$317$	−32.6260	−1.83246	−0.916231	−	0.400651i	$-0.868784\pi$
$317$	−32.6260	−1.83246	−0.916231	+	0.400651i	$0.868784\pi$
$318$	−1.44043	−0.0807751
$319$	2.36311	0.132309
$320$	1.05086	0.0587449
$321$	0.336129	0.0187609
$322$	0	0
$323$	−35.5453	−1.97780
$324$	−13.4018	−0.744544
$325$	0.954651	0.0529545
$326$	8.73837	0.483974
$327$	−2.14345	−0.118533
$328$	10.1903	0.562664
$329$	17.1023	0.942878
$330$	−0.0389296	−0.00214300
$331$	30.6922	1.68699	0.843497	−	0.537133i	$-0.180493\pi$
$331$	30.6922	1.68699	0.843497	+	0.537133i	$0.180493\pi$
$332$	4.09506	0.224746
$333$	18.2844	1.00198
$334$	−4.09959	−0.224319
$335$	−8.07235	−0.441040
$336$	0.476041	0.0259702
$337$	−28.0681	−1.52897	−0.764484	−	0.644643i	$-0.777006\pi$
$337$	−28.0681	−1.52897	−0.764484	+	0.644643i	$0.777006\pi$
$338$	−8.21596	−0.446889
$339$	0.688996	0.0374211
$340$	8.89186	0.482229
$341$	1.29336	0.0700392
$342$	−12.4028	−0.670667
$343$	−19.5553	−1.05589
$344$	−3.56080	−0.191985
$345$	0	0
$346$	6.21695	0.334225
$347$	11.5646	0.620822	0.310411	−	0.950602i	$-0.399533\pi$
$347$	11.5646	0.620822	0.310411	+	0.950602i	$0.399533\pi$
$348$	2.02859	0.108744
$349$	33.3698	1.78625	0.893123	−	0.449812i	$-0.148509\pi$
$349$	33.3698	1.78625	0.893123	+	0.449812i	$0.148509\pi$
$350$	1.25497	0.0670809
$351$	−1.01869	−0.0543734
$352$	−1.85462	−0.0988516
$353$	29.9232	1.59265	0.796326	−	0.604867i	$-0.206774\pi$
$353$	29.9232	1.59265	0.796326	+	0.604867i	$0.206774\pi$
$354$	0.434677	0.0231028
$355$	13.6477	0.724343
$356$	11.7529	0.622902
$357$	−1.90866	−0.101017
$358$	−6.09185	−0.321964
$359$	14.0814	0.743190	0.371595	−	0.928395i	$-0.378811\pi$
$359$	14.0814	0.743190	0.371595	+	0.928395i	$0.378811\pi$
$360$	7.13703	0.376155
$361$	18.8043	0.989699
$362$	7.27815	0.382531
$363$	−1.94844	−0.102266
$364$	−2.71130	−0.142111
$365$	−11.3581	−0.594512
$366$	−0.155923	−0.00815025
$367$	−33.1140	−1.72853	−0.864267	−	0.503033i	$-0.832217\pi$
$367$	−33.1140	−1.72853	−0.864267	+	0.503033i	$0.832217\pi$
$368$	0	0
$369$	12.5778	0.654775
$370$	−4.18691	−0.217667
$371$	−21.8876	−1.13635
$372$	1.11027	0.0575649
$373$	−9.76294	−0.505506	−0.252753	−	0.967531i	$-0.581336\pi$
$373$	−9.76294	−0.505506	−0.252753	+	0.967531i	$0.581336\pi$
$374$	1.25871	0.0650866
$375$	0.178799	0.00923313
$376$	−22.2716	−1.14857
$377$	−7.04197	−0.362680
$378$	−1.33915	−0.0688783
$379$	23.2520	1.19437	0.597187	−	0.802102i	$-0.296285\pi$
$379$	23.2520	1.19437	0.597187	+	0.802102i	$0.296285\pi$
$380$	−9.45695	−0.485131
$381$	3.06178	0.156860
$382$	14.7654	0.755466
$383$	23.6723	1.20960	0.604799	−	0.796379i	$-0.293254\pi$
$383$	23.6723	1.20960	0.604799	+	0.796379i	$0.293254\pi$
$384$	−1.94252	−0.0991286
$385$	−0.591543	−0.0301478
$386$	−13.6468	−0.694602
$387$	−4.39508	−0.223414
$388$	16.1302	0.818889
$389$	6.51781	0.330466	0.165233	−	0.986255i	$-0.447162\pi$
$389$	6.51781	0.330466	0.165233	+	0.986255i	$0.447162\pi$
$390$	0.116009	0.00587432
$391$	0	0
$392$	8.63359	0.436062
$393$	2.20924	0.111441
$394$	0.476821	0.0240219
$395$	−14.7709	−0.743204
$396$	−1.46246	−0.0734912
$397$	1.47608	0.0740821	0.0370410	−	0.999314i	$-0.488207\pi$
$397$	1.47608	0.0740821	0.0370410	+	0.999314i	$0.488207\pi$
$398$	−8.88828	−0.445529
$399$	2.02996	0.101625
$400$	1.44188	0.0720938
$401$	−23.3884	−1.16796	−0.583981	−	0.811767i	$-0.698506\pi$
$401$	−23.3884	−1.16796	−0.583981	+	0.811767i	$0.698506\pi$
$402$	−0.980947	−0.0489252
$403$	−3.85416	−0.191989
$404$	−3.27815	−0.163094
$405$	8.71330	0.432967
$406$	−9.25726	−0.459430
$407$	1.97354	0.0978248
$408$	2.48557	0.123054
$409$	36.6979	1.81459	0.907296	−	0.420493i	$-0.138143\pi$
$409$	36.6979	1.81459	0.907296	+	0.420493i	$0.138143\pi$
$410$	−2.88017	−0.142241
$411$	1.41298	0.0696973
$412$	15.0233	0.740143
$413$	6.60500	0.325011
$414$	0	0
$415$	−2.66244	−0.130694
$416$	5.52670	0.270969
$417$	−3.24780	−0.159046
$418$	−1.33871	−0.0654783
$419$	36.5772	1.78691	0.893455	−	0.449152i	$-0.148274\pi$
$419$	36.5772	1.78691	0.893455	+	0.449152i	$0.148274\pi$
$420$	−0.507805	−0.0247783
$421$	29.1908	1.42267	0.711336	−	0.702852i	$-0.248090\pi$
$421$	29.1908	1.42267	0.711336	+	0.702852i	$0.248090\pi$
$422$	3.47286	0.169056
$423$	−27.4897	−1.33659
$424$	28.5033	1.38424
$425$	−5.78112	−0.280426
$426$	1.65846	0.0803525
$427$	−2.36929	−0.114658
$428$	−2.89149	−0.139766
$429$	−0.0546818	−0.00264006
$430$	1.00642	0.0485339
$431$	13.7231	0.661020	0.330510	−	0.943802i	$-0.392779\pi$
$431$	13.7231	0.661020	0.330510	+	0.943802i	$0.392779\pi$
$432$	−1.53859	−0.0740256
$433$	−1.38558	−0.0665868	−0.0332934	−	0.999446i	$-0.510600\pi$
$433$	−1.38558	−0.0665868	−0.0332934	+	0.999446i	$0.510600\pi$
$434$	−5.06661	−0.243205
$435$	−1.31891	−0.0632368
$436$	18.4387	0.883052
$437$	0	0
$438$	−1.38023	−0.0659501
$439$	−11.5200	−0.549821	−0.274911	−	0.961470i	$-0.588648\pi$
$439$	−11.5200	−0.549821	−0.274911	+	0.961470i	$0.588648\pi$
$440$	0.770341	0.0367246
$441$	10.6564	0.507448
$442$	−3.75092	−0.178413
$443$	38.4160	1.82520	0.912599	−	0.408857i	$-0.134072\pi$
$443$	38.4160	1.82520	0.912599	+	0.408857i	$0.134072\pi$
$444$	1.69417	0.0804018
$445$	−7.64125	−0.362230
$446$	−14.3259	−0.678352
$447$	−0.666707	−0.0315342
$448$	1.94042	0.0916765
$449$	6.08955	0.287384	0.143692	−	0.989622i	$-0.454103\pi$
$449$	6.08955	0.287384	0.143692	+	0.989622i	$0.454103\pi$
$450$	−2.01720	−0.0950918
$451$	1.35760	0.0639268
$452$	−5.92697	−0.278781
$453$	−2.09898	−0.0986188
$454$	6.30505	0.295911
$455$	1.76277	0.0826401
$456$	−2.64353	−0.123795
$457$	17.5048	0.818838	0.409419	−	0.912346i	$-0.365731\pi$
$457$	17.5048	0.818838	0.409419	+	0.912346i	$0.365731\pi$
$458$	−1.96803	−0.0919600
$459$	6.16890	0.287940
$460$	0	0
$461$	12.7363	0.593189	0.296595	−	0.955003i	$-0.404149\pi$
$461$	12.7363	0.593189	0.296595	+	0.955003i	$0.404149\pi$
$462$	−0.0718839	−0.00334434
$463$	−10.4801	−0.487052	−0.243526	−	0.969894i	$-0.578304\pi$
$463$	−10.4801	−0.487052	−0.243526	+	0.969894i	$0.578304\pi$
$464$	−10.6360	−0.493763
$465$	−0.721854	−0.0334752
$466$	10.6546	0.493566
$467$	26.6840	1.23479	0.617394	−	0.786654i	$-0.288188\pi$
$467$	26.6840	1.23479	0.617394	+	0.786654i	$0.288188\pi$
$468$	4.35806	0.201451
$469$	−14.9057	−0.688281
$470$	6.29481	0.290358
$471$	3.83094	0.176520
$472$	−8.60142	−0.395912
$473$	−0.474386	−0.0218123
$474$	−1.79495	−0.0824447
$475$	6.14852	0.282113
$476$	16.4189	0.752560
$477$	35.1815	1.61085
$478$	6.96374	0.318514
$479$	8.98310	0.410448	0.205224	−	0.978715i	$-0.434208\pi$
$479$	8.98310	0.410448	0.205224	+	0.978715i	$0.434208\pi$
$480$	1.03511	0.0472460
$481$	−5.88108	−0.268154
$482$	−0.651735	−0.0296857
$483$	0	0
$484$	16.7611	0.761868
$485$	−10.4872	−0.476200
$486$	3.23453	0.146721
$487$	7.48195	0.339040	0.169520	−	0.985527i	$-0.445778\pi$
$487$	7.48195	0.339040	0.169520	+	0.985527i	$0.445778\pi$
$488$	3.08543	0.139671
$489$	2.29887	0.103958
$490$	−2.44019	−0.110236
$491$	43.4477	1.96077	0.980383	−	0.197100i	$-0.0631524\pi$
$491$	43.4477	1.96077	0.980383	+	0.197100i	$0.0631524\pi$
$492$	1.16542	0.0525411
$493$	42.6444	1.92061
$494$	3.98929	0.179487
$495$	0.950829	0.0427366
$496$	−5.82120	−0.261380
$497$	25.2006	1.13040
$498$	−0.323538	−0.0144981
$499$	18.8205	0.842522	0.421261	−	0.906939i	$-0.361588\pi$
$499$	18.8205	0.842522	0.421261	+	0.906939i	$0.361588\pi$
$500$	−1.53809	−0.0687853
$501$	−1.07851	−0.0481842
$502$	−12.8807	−0.574893
$503$	−44.3064	−1.97553	−0.987763	−	0.155962i	$-0.950152\pi$
$503$	−44.3064	−1.97553	−0.987763	+	0.155962i	$0.950152\pi$
$504$	13.1786	0.587022
$505$	2.13132	0.0948423
$506$	0	0
$507$	−2.16143	−0.0959927
$508$	−26.3385	−1.16858
$509$	−13.2106	−0.585551	−0.292775	−	0.956181i	$-0.594579\pi$
$509$	−13.2106	−0.585551	−0.292775	+	0.956181i	$0.594579\pi$
$510$	−0.702519	−0.0311080
$511$	−20.9729	−0.927788
$512$	15.2817	0.675363
$513$	−6.56094	−0.289673
$514$	6.43509	0.283840
$515$	−9.76750	−0.430408
$516$	−0.407233	−0.0179274
$517$	−2.96712	−0.130494
$518$	−7.73117	−0.339688
$519$	1.63554	0.0717922
$520$	−2.29559	−0.100668
$521$	−28.6702	−1.25607	−0.628033	−	0.778187i	$-0.716140\pi$
$521$	−28.6702	−1.25607	−0.628033	+	0.778187i	$0.716140\pi$
$522$	14.8799	0.651274
$523$	−22.3061	−0.975379	−0.487690	−	0.873017i	$-0.662160\pi$
$523$	−22.3061	−0.975379	−0.487690	+	0.873017i	$0.662160\pi$
$524$	−19.0046	−0.830219
$525$	0.330154	0.0144091
$526$	15.1537	0.660733
$527$	23.3398	1.01670
$528$	−0.0825898	−0.00359426
$529$	0	0
$530$	−8.05613	−0.349936
$531$	−10.6167	−0.460725
$532$	−17.4624	−0.757089
$533$	−4.04559	−0.175234
$534$	−0.928560	−0.0401827
$535$	1.87993	0.0812765
$536$	19.4111	0.838430
$537$	−1.60263	−0.0691585
$538$	−5.91288	−0.254923
$539$	1.15021	0.0495429
$540$	1.64125	0.0706284
$541$	27.6098	1.18704	0.593520	−	0.804820i	$-0.297738\pi$
$541$	27.6098	1.18704	0.593520	+	0.804820i	$0.297738\pi$
$542$	0.534263	0.0229486
$543$	1.91472	0.0821683
$544$	−33.4683	−1.43494
$545$	−11.9881	−0.513512
$546$	0.214211	0.00916739
$547$	29.2427	1.25033	0.625165	−	0.780493i	$-0.285032\pi$
$547$	29.2427	1.25033	0.625165	+	0.780493i	$0.285032\pi$
$548$	−12.1549	−0.519233
$549$	3.80833	0.162535
$550$	−0.217728	−0.00928397
$551$	−45.3545	−1.93217
$552$	0	0
$553$	−27.2746	−1.15983
$554$	−8.00000	−0.339887
$555$	−1.10148	−0.0467553
$556$	27.9387	1.18486
$557$	−12.5383	−0.531266	−0.265633	−	0.964074i	$-0.585581\pi$
$557$	−12.5383	−0.531266	−0.265633	+	0.964074i	$0.585581\pi$
$558$	8.14393	0.344760
$559$	1.41365	0.0597911
$560$	2.66244	0.112509
$561$	0.331139	0.0139807
$562$	−9.31401	−0.392888
$563$	−3.73622	−0.157463	−0.0787314	−	0.996896i	$-0.525087\pi$
$563$	−3.73622	−0.157463	−0.0787314	+	0.996896i	$0.525087\pi$
$564$	−2.54710	−0.107252
$565$	3.85347	0.162117
$566$	−18.0206	−0.757461
$567$	16.0892	0.675683
$568$	−32.8177	−1.37700
$569$	19.2951	0.808893	0.404447	−	0.914562i	$-0.367464\pi$
$569$	19.2951	0.808893	0.404447	+	0.914562i	$0.367464\pi$
$570$	0.747164	0.0312953
$571$	−7.20312	−0.301441	−0.150721	−	0.988576i	$-0.548159\pi$
$571$	−7.20312	−0.301441	−0.150721	+	0.988576i	$0.548159\pi$
$572$	0.470391	0.0196680
$573$	3.88446	0.162275
$574$	−5.31827	−0.221980
$575$	0	0
$576$	−3.11898	−0.129958
$577$	−38.4187	−1.59939	−0.799695	−	0.600407i	$-0.795005\pi$
$577$	−38.4187	−1.59939	−0.799695	+	0.600407i	$0.795005\pi$
$578$	11.1607	0.464223
$579$	−3.59016	−0.149202
$580$	11.3457	0.471103
$581$	−4.91623	−0.203960
$582$	−1.27440	−0.0528256
$583$	3.79734	0.157270
$584$	27.3122	1.13019
$585$	−2.83343	−0.117148
$586$	−14.8184	−0.612141
$587$	20.9142	0.863221	0.431611	−	0.902060i	$-0.357945\pi$
$587$	20.9142	0.863221	0.431611	+	0.902060i	$0.357945\pi$
$588$	0.987386	0.0407191
$589$	−24.8230	−1.02282
$590$	2.43109	0.100087
$591$	0.125441	0.00515995
$592$	−8.88260	−0.365073
$593$	17.7894	0.730525	0.365262	−	0.930905i	$-0.380979\pi$
$593$	17.7894	0.730525	0.365262	+	0.930905i	$0.380979\pi$
$594$	0.232333	0.00953273
$595$	−10.6749	−0.437629
$596$	5.73523	0.234924
$597$	−2.33831	−0.0957005
$598$	0	0
$599$	−19.6642	−0.803457	−0.401729	−	0.915759i	$-0.631590\pi$
$599$	−19.6642	−0.803457	−0.401729	+	0.915759i	$0.631590\pi$
$600$	−0.429946	−0.0175525
$601$	−42.4614	−1.73204	−0.866018	−	0.500012i	$-0.833329\pi$
$601$	−42.4614	−1.73204	−0.866018	+	0.500012i	$0.833329\pi$
$602$	1.85837	0.0757413
$603$	23.9590	0.975685
$604$	18.0561	0.734694
$605$	−10.8974	−0.443041
$606$	0.258996	0.0105210
$607$	−6.53197	−0.265124	−0.132562	−	0.991175i	$-0.542320\pi$
$607$	−6.53197	−0.265124	−0.132562	+	0.991175i	$0.542320\pi$
$608$	35.5952	1.44358
$609$	−2.43538	−0.0986865
$610$	−0.872061	−0.0353087
$611$	8.84191	0.357705
$612$	−26.3913	−1.06681
$613$	6.73385	0.271978	0.135989	−	0.990710i	$-0.456579\pi$
$613$	6.73385	0.271978	0.135989	+	0.990710i	$0.456579\pi$
$614$	7.98071	0.322075
$615$	−0.757708	−0.0305537
$616$	1.42244	0.0573119
$617$	−15.4771	−0.623083	−0.311541	−	0.950233i	$-0.600845\pi$
$617$	−15.4771	−0.623083	−0.311541	+	0.950233i	$0.600845\pi$
$618$	−1.18694	−0.0477458
$619$	−16.4420	−0.660859	−0.330429	−	0.943831i	$-0.607194\pi$
$619$	−16.4420	−0.660859	−0.330429	+	0.943831i	$0.607194\pi$
$620$	6.20962	0.249384
$621$	0	0
$622$	−0.883450	−0.0354231
$623$	−14.1097	−0.565292
$624$	0.246114	0.00985246
$625$	1.00000	0.0400000
$626$	18.9118	0.755866
$627$	−0.352183	−0.0140649
$628$	−32.9550	−1.31505
$629$	35.6143	1.42004
$630$	−3.72479	−0.148399
$631$	0.125341	0.00498976	0.00249488	−	0.999997i	$-0.499206\pi$
$631$	0.125341	0.00498976	0.00249488	+	0.999997i	$0.499206\pi$
$632$	35.5186	1.41285
$633$	0.913631	0.0363136
$634$	−22.1741	−0.880645
$635$	17.1242	0.679553
$636$	3.25980	0.129259
$637$	−3.42757	−0.135805
$638$	1.60607	0.0635849
$639$	−40.5067	−1.60242
$640$	−10.8643	−0.429447
$641$	−9.55339	−0.377336	−0.188668	−	0.982041i	$-0.560417\pi$
$641$	−9.55339	−0.377336	−0.188668	+	0.982041i	$0.560417\pi$
$642$	0.228448	0.00901612
$643$	−21.4245	−0.844900	−0.422450	−	0.906386i	$-0.638830\pi$
$643$	−21.4245	−0.844900	−0.422450	+	0.906386i	$0.638830\pi$
$644$	0	0
$645$	0.264766	0.0104252
$646$	−24.1582	−0.950490
$647$	−25.5429	−1.00420	−0.502098	−	0.864811i	$-0.667438\pi$
$647$	−25.5429	−1.00420	−0.502098	+	0.864811i	$0.667438\pi$
$648$	−20.9523	−0.823085
$649$	−1.14592	−0.0449813
$650$	0.648822	0.0254489
$651$	−1.33291	−0.0522409
$652$	−19.7756	−0.774473
$653$	−27.8857	−1.09125	−0.545627	−	0.838028i	$-0.683708\pi$
$653$	−27.8857	−1.09125	−0.545627	+	0.838028i	$0.683708\pi$
$654$	−1.45678	−0.0569647
$655$	12.3560	0.482789
$656$	−6.11034	−0.238569
$657$	33.7113	1.31520
$658$	11.6234	0.453129
$659$	−34.4447	−1.34178	−0.670888	−	0.741559i	$-0.734087\pi$
$659$	−34.4447	−1.34178	−0.670888	+	0.741559i	$0.734087\pi$
$660$	0.0881006	0.00342931
$661$	29.5592	1.14972	0.574860	−	0.818252i	$-0.305057\pi$
$661$	29.5592	1.14972	0.574860	+	0.818252i	$0.305057\pi$
$662$	20.8597	0.810736
$663$	−0.986782	−0.0383235
$664$	6.40220	0.248454
$665$	11.3533	0.440263
$666$	12.4269	0.481531
$667$	0	0
$668$	9.27768	0.358964
$669$	−3.76883	−0.145711
$670$	−5.48632	−0.211955
$671$	0.411055	0.0158686
$672$	1.91134	0.0737315
$673$	20.6087	0.794409	0.397204	−	0.917730i	$-0.369980\pi$
$673$	20.6087	0.794409	0.397204	+	0.917730i	$0.369980\pi$
$674$	−19.0763	−0.734792
$675$	−1.06708	−0.0410718
$676$	18.5934	0.715129
$677$	−40.6629	−1.56280	−0.781401	−	0.624030i	$-0.785494\pi$
$677$	−40.6629	−1.56280	−0.781401	+	0.624030i	$0.785494\pi$
$678$	0.468271	0.0179839
$679$	−19.3648	−0.743152
$680$	13.9015	0.533098
$681$	1.65872	0.0635621
$682$	0.879022	0.0336595
$683$	−17.1969	−0.658021	−0.329011	−	0.944326i	$-0.606715\pi$
$683$	−17.1969	−0.658021	−0.329011	+	0.944326i	$0.606715\pi$
$684$	28.0685	1.07323
$685$	7.90264	0.301944
$686$	−13.2906	−0.507438
$687$	−0.517744	−0.0197532
$688$	2.13514	0.0814014
$689$	−11.3159	−0.431103
$690$	0	0
$691$	27.3432	1.04019	0.520093	−	0.854110i	$-0.325897\pi$
$691$	27.3432	1.04019	0.520093	+	0.854110i	$0.325897\pi$
$692$	−14.0694	−0.534840
$693$	1.75572	0.0666942
$694$	7.85983	0.298355
$695$	−18.1646	−0.689022
$696$	3.17149	0.120215
$697$	24.4991	0.927968
$698$	22.6796	0.858435
$699$	2.80299	0.106019
$700$	−2.84009	−0.107345
$701$	42.7510	1.61468	0.807341	−	0.590085i	$-0.200906\pi$
$701$	42.7510	1.61468	0.807341	+	0.590085i	$0.200906\pi$
$702$	−0.692343	−0.0261308
$703$	−37.8776	−1.42858
$704$	−0.336650	−0.0126880
$705$	1.65602	0.0623694
$706$	20.3371	0.765397
$707$	3.93550	0.148010
$708$	−0.983707	−0.0369700
$709$	2.64409	0.0993009	0.0496505	−	0.998767i	$-0.484189\pi$
$709$	2.64409	0.0993009	0.0496505	+	0.998767i	$0.484189\pi$
$710$	9.27555	0.348105
$711$	43.8404	1.64414
$712$	18.3744	0.688611
$713$	0	0
$714$	−1.29721	−0.0485468
$715$	−0.305829	−0.0114374
$716$	13.7863	0.515219
$717$	1.83200	0.0684174
$718$	9.57036	0.357163
$719$	46.3337	1.72795	0.863977	−	0.503531i	$-0.167966\pi$
$719$	46.3337	1.72795	0.863977	+	0.503531i	$0.167966\pi$
$720$	−4.27953	−0.159489
$721$	−18.0358	−0.671689
$722$	12.7802	0.475630
$723$	−0.171457	−0.00637655
$724$	−16.4710	−0.612140
$725$	−7.37649	−0.273956
$726$	−1.32424	−0.0491472
$727$	13.7305	0.509236	0.254618	−	0.967042i	$-0.418050\pi$
$727$	13.7305	0.509236	0.254618	+	0.967042i	$0.418050\pi$
$728$	−4.23883	−0.157101
$729$	−25.2890	−0.936629
$730$	−7.71948	−0.285711
$731$	−8.56072	−0.316630
$732$	0.352867	0.0130423
$733$	−4.41258	−0.162982	−0.0814912	−	0.996674i	$-0.525968\pi$
$733$	−4.41258	−0.162982	−0.0814912	+	0.996674i	$0.525968\pi$
$734$	−22.5057	−0.830700
$735$	−0.641958	−0.0236790
$736$	0	0
$737$	2.58603	0.0952577
$738$	8.54843	0.314672
$739$	−17.6822	−0.650452	−0.325226	−	0.945636i	$-0.605440\pi$
$739$	−17.6822	−0.650452	−0.325226	+	0.945636i	$0.605440\pi$
$740$	9.47529	0.348319
$741$	1.04949	0.0385541
$742$	−14.8757	−0.546106
$743$	0.705637	0.0258873	0.0129437	−	0.999916i	$-0.495880\pi$
$743$	0.705637	0.0258873	0.0129437	+	0.999916i	$0.495880\pi$
$744$	1.73579	0.0636373
$745$	−3.72881	−0.136613
$746$	−6.63531	−0.242936
$747$	7.90221	0.289127
$748$	−2.84857	−0.104154
$749$	3.47131	0.126839
$750$	0.121519	0.00443726
$751$	−53.1367	−1.93898	−0.969492	−	0.245122i	$-0.921172\pi$
$751$	−53.1367	−1.93898	−0.969492	+	0.245122i	$0.921172\pi$
$752$	13.3546	0.486991
$753$	−3.38862	−0.123488
$754$	−4.78603	−0.174297
$755$	−11.7394	−0.427239
$756$	3.03060	0.110222
$757$	−37.0595	−1.34695	−0.673475	−	0.739210i	$-0.735199\pi$
$757$	−37.0595	−1.34695	−0.673475	+	0.739210i	$0.735199\pi$
$758$	15.8031	0.573993
$759$	0	0
$760$	−14.7849	−0.536306
$761$	27.3682	0.992098	0.496049	−	0.868295i	$-0.334784\pi$
$761$	27.3682	0.992098	0.496049	+	0.868295i	$0.334784\pi$
$762$	2.08092	0.0753838
$763$	−22.1361	−0.801381
$764$	−33.4154	−1.20893
$765$	17.1586	0.620369
$766$	16.0887	0.581309
$767$	3.41480	0.123301
$768$	−1.69600	−0.0611992
$769$	−14.6783	−0.529311	−0.264656	−	0.964343i	$-0.585258\pi$
$769$	−14.6783	−0.529311	−0.264656	+	0.964343i	$0.585258\pi$
$770$	−0.402038	−0.0144884
$771$	1.69293	0.0609693
$772$	30.8837	1.11153
$773$	11.5338	0.414843	0.207421	−	0.978252i	$-0.433493\pi$
$773$	11.5338	0.414843	0.207421	+	0.978252i	$0.433493\pi$
$774$	−2.98708	−0.107369
$775$	−4.03724	−0.145022
$776$	25.2180	0.905272
$777$	−2.03390	−0.0729656
$778$	4.42978	0.158815
$779$	−26.0560	−0.933553
$780$	−0.262536	−0.00940031
$781$	−4.37213	−0.156447
$782$	0	0
$783$	7.87128	0.281297
$784$	−5.17690	−0.184889
$785$	21.4260	0.764725
$786$	1.50149	0.0535565
$787$	−27.1882	−0.969155	−0.484578	−	0.874748i	$-0.661027\pi$
$787$	−27.1882	−0.969155	−0.484578	+	0.874748i	$0.661027\pi$
$788$	−1.07908	−0.0384408
$789$	3.98660	0.141927
$790$	−10.0389	−0.357169
$791$	7.11548	0.252997
$792$	−2.28640	−0.0812436
$793$	−1.22493	−0.0434985
$794$	1.00320	0.0356024
$795$	−2.11939	−0.0751669
$796$	20.1149	0.712952
$797$	0.549030	0.0194476	0.00972382	−	0.999953i	$-0.496905\pi$
$797$	0.549030	0.0194476	0.00972382	+	0.999953i	$0.496905\pi$
$798$	1.37965	0.0488390
$799$	−53.5444	−1.89426
$800$	5.78923	0.204680
$801$	22.6795	0.801340
$802$	−15.8958	−0.561299
$803$	3.63866	0.128405
$804$	2.21996	0.0782919
$805$	0	0
$806$	−2.61945	−0.0922662
$807$	−1.55555	−0.0547578
$808$	−5.12504	−0.180298
$809$	18.4568	0.648906	0.324453	−	0.945902i	$-0.394820\pi$
$809$	18.4568	0.648906	0.324453	+	0.945902i	$0.394820\pi$
$810$	5.92194	0.208076
$811$	−10.0693	−0.353581	−0.176791	−	0.984248i	$-0.556572\pi$
$811$	−10.0693	−0.353581	−0.176791	+	0.984248i	$0.556572\pi$
$812$	20.9499	0.735198
$813$	0.140553	0.00492939
$814$	1.34130	0.0470127
$815$	12.8573	0.450371
$816$	−1.49041	−0.0521747
$817$	9.10476	0.318535
$818$	24.9414	0.872057
$819$	−5.23197	−0.182820
$820$	6.51805	0.227620
$821$	17.5224	0.611536	0.305768	−	0.952106i	$-0.401087\pi$
$821$	17.5224	0.611536	0.305768	+	0.952106i	$0.401087\pi$
$822$	0.960324	0.0334952
$823$	21.5694	0.751861	0.375931	−	0.926648i	$-0.377323\pi$
$823$	21.5694	0.751861	0.375931	+	0.926648i	$0.377323\pi$
$824$	23.4873	0.818218
$825$	−0.0572794	−0.00199421
$826$	4.48904	0.156194
$827$	−17.8553	−0.620890	−0.310445	−	0.950591i	$-0.600478\pi$
$827$	−17.8553	−0.620890	−0.310445	+	0.950591i	$0.600478\pi$
$828$	0	0
$829$	−4.83221	−0.167830	−0.0839148	−	0.996473i	$-0.526742\pi$
$829$	−4.83221	−0.167830	−0.0839148	+	0.996473i	$0.526742\pi$
$830$	−1.80951	−0.0628090
$831$	−2.10462	−0.0730084
$832$	1.00320	0.0347799
$833$	20.7565	0.719171
$834$	−2.20735	−0.0764342
$835$	−6.03197	−0.208745
$836$	3.02960	0.104781
$837$	4.30805	0.148908
$838$	24.8594	0.858754
$839$	12.6381	0.436315	0.218158	−	0.975914i	$-0.429995\pi$
$839$	12.6381	0.436315	0.218158	+	0.975914i	$0.429995\pi$
$840$	−0.793900	−0.0273922
$841$	25.4126	0.876296
$842$	19.8393	0.683708
$843$	−2.45031	−0.0843930
$844$	−7.85935	−0.270530
$845$	−12.0886	−0.415862
$846$	−18.6832	−0.642341
$847$	−20.1221	−0.691404
$848$	−17.0912	−0.586916
$849$	−4.74081	−0.162704
$850$	−3.92910	−0.134767
$851$	0	0
$852$	−3.75322	−0.128583
$853$	−41.1227	−1.40801	−0.704007	−	0.710193i	$-0.748607\pi$
$853$	−41.1227	−1.40801	−0.704007	+	0.710193i	$0.748607\pi$
$854$	−1.61027	−0.0551023
$855$	−18.2490	−0.624102
$856$	−4.52055	−0.154509
$857$	−30.8021	−1.05218	−0.526091	−	0.850428i	$-0.676343\pi$
$857$	−30.8021	−1.05218	−0.526091	+	0.850428i	$0.676343\pi$
$858$	−0.0371641	−0.00126876
$859$	6.50942	0.222098	0.111049	−	0.993815i	$-0.464579\pi$
$859$	6.50942	0.222098	0.111049	+	0.993815i	$0.464579\pi$
$860$	−2.27761	−0.0776657
$861$	−1.39912	−0.0476817
$862$	9.32684	0.317673
$863$	−56.6195	−1.92735	−0.963676	−	0.267076i	$-0.913943\pi$
$863$	−56.6195	−1.92735	−0.963676	+	0.267076i	$0.913943\pi$
$864$	−6.17755	−0.210165
$865$	9.14737	0.311020
$866$	−0.941701	−0.0320003
$867$	2.93612	0.0997160
$868$	11.4661	0.389186
$869$	4.73195	0.160521
$870$	−0.896386	−0.0303903
$871$	−7.70627	−0.261117
$872$	28.8269	0.976203
$873$	31.1264	1.05347
$874$	0	0
$875$	1.84651	0.0624235
$876$	3.12358	0.105536
$877$	7.38895	0.249507	0.124753	−	0.992188i	$-0.460186\pi$
$877$	7.38895	0.249507	0.124753	+	0.992188i	$0.460186\pi$
$878$	−7.82951	−0.264233
$879$	−3.89838	−0.131489
$880$	−0.461915	−0.0155711
$881$	−16.1904	−0.545469	−0.272735	−	0.962089i	$-0.587928\pi$
$881$	−16.1904	−0.545469	−0.272735	+	0.962089i	$0.587928\pi$
$882$	7.24255	0.243869
$883$	0.137941	0.00464209	0.00232105	−	0.999997i	$-0.499261\pi$
$883$	0.137941	0.00464209	0.00232105	+	0.999997i	$0.499261\pi$
$884$	8.48862	0.285503
$885$	0.639566	0.0214988
$886$	26.1091	0.877154
$887$	−52.5723	−1.76520	−0.882602	−	0.470122i	$-0.844210\pi$
$887$	−52.5723	−1.76520	−0.882602	+	0.470122i	$0.844210\pi$
$888$	2.64866	0.0888832
$889$	31.6200	1.06050
$890$	−5.19333	−0.174081
$891$	−2.79137	−0.0935143
$892$	32.4207	1.08552
$893$	56.9471	1.90566
$894$	−0.453123	−0.0151547
$895$	−8.96330	−0.299610
$896$	−20.0610	−0.670190
$897$	0	0
$898$	4.13872	0.138111
$899$	29.7807	0.993241
$900$	4.56508	0.152169
$901$	68.5264	2.28295
$902$	0.922682	0.0307219
$903$	0.488894	0.0162694
$904$	−9.26620	−0.308189
$905$	10.7088	0.355972
$906$	−1.42656	−0.0473943
$907$	33.2186	1.10300	0.551502	−	0.834173i	$-0.314055\pi$
$907$	33.2186	1.10300	0.551502	+	0.834173i	$0.314055\pi$
$908$	−14.2688	−0.473527
$909$	−6.32581	−0.209814
$910$	1.19806	0.0397152
$911$	−21.4750	−0.711498	−0.355749	−	0.934582i	$-0.615774\pi$
$911$	−21.4750	−0.711498	−0.355749	+	0.934582i	$0.615774\pi$
$912$	1.58512	0.0524887
$913$	0.852931	0.0282279
$914$	11.8970	0.393518
$915$	−0.229420	−0.00758438
$916$	4.45381	0.147158
$917$	22.8155	0.753434
$918$	4.19265	0.138378
$919$	12.9420	0.426918	0.213459	−	0.976952i	$-0.431527\pi$
$919$	12.9420	0.426918	0.213459	+	0.976952i	$0.431527\pi$
$920$	0	0
$921$	2.09954	0.0691823
$922$	8.65615	0.285075
$923$	13.0288	0.428847
$924$	0.162679	0.00535174
$925$	−6.16045	−0.202554
$926$	−7.12273	−0.234067
$927$	28.9903	0.952165
$928$	−42.7042	−1.40183
$929$	−20.2173	−0.663309	−0.331654	−	0.943401i	$-0.607607\pi$
$929$	−20.2173	−0.663309	−0.331654	+	0.943401i	$0.607607\pi$
$930$	−0.490603	−0.0160875
$931$	−22.0756	−0.723499
$932$	−24.1123	−0.789823
$933$	−0.232416	−0.00760895
$934$	18.1356	0.593415
$935$	1.85202	0.0605676
$936$	6.81337	0.222702
$937$	18.3659	0.599988	0.299994	−	0.953941i	$-0.403015\pi$
$937$	18.3659	0.599988	0.299994	+	0.953941i	$0.403015\pi$
$938$	−10.1305	−0.330774
$939$	4.97526	0.162361
$940$	−14.2456	−0.464641
$941$	13.0688	0.426030	0.213015	−	0.977049i	$-0.431672\pi$
$941$	13.0688	0.426030	0.213015	+	0.977049i	$0.431672\pi$
$942$	2.60367	0.0848321
$943$	0	0
$944$	5.15761	0.167866
$945$	−1.97037	−0.0640961
$946$	−0.322413	−0.0104826
$947$	−47.6188	−1.54740	−0.773702	−	0.633549i	$-0.781597\pi$
$947$	−47.6188	−1.54740	−0.773702	+	0.633549i	$0.781597\pi$
$948$	4.06211	0.131931
$949$	−10.8431	−0.351981
$950$	4.17880	0.135578
$951$	−5.83350	−0.189164
$952$	25.6693	0.831946
$953$	12.3969	0.401576	0.200788	−	0.979635i	$-0.435650\pi$
$953$	12.3969	0.401576	0.200788	+	0.979635i	$0.435650\pi$
$954$	23.9108	0.774142
$955$	21.7253	0.703014
$956$	−15.7595	−0.509698
$957$	0.422521	0.0136582
$958$	6.10530	0.197253
$959$	14.5923	0.471211
$960$	0.187892	0.00606420
$961$	−14.7007	−0.474216
$962$	−3.99703	−0.128870
$963$	−5.57969	−0.179803
$964$	1.47493	0.0475042
$965$	−20.0793	−0.646376
$966$	0	0
$967$	19.3988	0.623824	0.311912	−	0.950111i	$-0.399031\pi$
$967$	19.3988	0.623824	0.311912	+	0.950111i	$0.399031\pi$
$968$	26.2042	0.842235
$969$	−6.35546	−0.204167
$970$	−7.12757	−0.228853
$971$	27.6016	0.885779	0.442889	−	0.896576i	$-0.353953\pi$
$971$	27.6016	0.885779	0.442889	+	0.896576i	$0.353953\pi$
$972$	−7.31999	−0.234789
$973$	−33.5411	−1.07528
$974$	5.08506	0.162936
$975$	0.170690	0.00546647
$976$	−1.85009	−0.0592201
$977$	−3.91574	−0.125276	−0.0626378	−	0.998036i	$-0.519951\pi$
$977$	−3.91574	−0.125276	−0.0626378	+	0.998036i	$0.519951\pi$
$978$	1.56241	0.0499604
$979$	2.44793	0.0782361
$980$	5.52233	0.176404
$981$	35.5810	1.13601
$982$	29.5289	0.942306
$983$	−27.7398	−0.884761	−0.442380	−	0.896827i	$-0.645866\pi$
$983$	−27.7398	−0.884761	−0.442380	+	0.896827i	$0.645866\pi$
$984$	1.82201	0.0580836
$985$	0.701576	0.0223541
$986$	28.9830	0.923006
$987$	3.05786	0.0973329
$988$	−9.02808	−0.287222
$989$	0	0
$990$	0.646224	0.0205384
$991$	41.1418	1.30691	0.653456	−	0.756964i	$-0.273318\pi$
$991$	41.1418	1.30691	0.653456	+	0.756964i	$0.273318\pi$
$992$	−23.3725	−0.742078
$993$	5.48772	0.174148
$994$	17.1274	0.543248
$995$	−13.0779	−0.414596
$996$	0.732192	0.0232004
$997$	−52.6344	−1.66695	−0.833473	−	0.552560i	$-0.813651\pi$
$997$	−52.6344	−1.66695	−0.833473	+	0.552560i	$0.813651\pi$
$998$	12.7912	0.404900
$999$	6.57367	0.207982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.l.1.3	yes	4
23.22	odd	2		2645.2.a.k.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2645.2.a.k.1.3	✓	4	23.22	odd	2
2645.2.a.l.1.3	yes	4	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:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q+0.679643 q^{2} +0.178799 q^{3} -1.53809 q^{4} +1.00000 q^{5} +0.121519 q^{6} +1.84651 q^{7} -2.40464 q^{8} -2.96803 q^{9} +O(q^{10})\)	\(q+0.679643 q^{2} +0.178799 q^{3} -1.53809 q^{4} +1.00000 q^{5} +0.121519 q^{6} +1.84651 q^{7} -2.40464 q^{8} -2.96803 q^{9} +0.679643 q^{10} -0.320357 q^{11} -0.275008 q^{12} +0.954651 q^{13} +1.25497 q^{14} +0.178799 q^{15} +1.44188 q^{16} -5.78112 q^{17} -2.01720 q^{18} +6.14852 q^{19} -1.53809 q^{20} +0.330154 q^{21} -0.217728 q^{22} -0.429946 q^{24} +1.00000 q^{25} +0.648822 q^{26} -1.06708 q^{27} -2.84009 q^{28} -7.37649 q^{29} +0.121519 q^{30} -4.03724 q^{31} +5.78923 q^{32} -0.0572794 q^{33} -3.92910 q^{34} +1.84651 q^{35} +4.56508 q^{36} -6.16045 q^{37} +4.17880 q^{38} +0.170690 q^{39} -2.40464 q^{40} -4.23777 q^{41} +0.224387 q^{42} +1.48081 q^{43} +0.492736 q^{44} -2.96803 q^{45} +9.26193 q^{47} +0.257806 q^{48} -3.59039 q^{49} +0.679643 q^{50} -1.03366 q^{51} -1.46833 q^{52} -11.8535 q^{53} -0.725231 q^{54} -0.320357 q^{55} -4.44019 q^{56} +1.09935 q^{57} -5.01338 q^{58} +3.57701 q^{59} -0.275008 q^{60} -1.28312 q^{61} -2.74388 q^{62} -5.48050 q^{63} +1.05086 q^{64} +0.954651 q^{65} -0.0389296 q^{66} -8.07235 q^{67} +8.89186 q^{68} +1.25497 q^{70} +13.6477 q^{71} +7.13703 q^{72} -11.3581 q^{73} -4.18691 q^{74} +0.178799 q^{75} -9.45695 q^{76} -0.591543 q^{77} +0.116009 q^{78} -14.7709 q^{79} +1.44188 q^{80} +8.71330 q^{81} -2.88017 q^{82} -2.66244 q^{83} -0.507805 q^{84} -5.78112 q^{85} +1.00642 q^{86} -1.31891 q^{87} +0.770341 q^{88} -7.64125 q^{89} -2.01720 q^{90} +1.76277 q^{91} -0.721854 q^{93} +6.29481 q^{94} +6.14852 q^{95} +1.03511 q^{96} -10.4872 q^{97} -2.44019 q^{98} +0.950829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9	\( 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9} - q^{10} - 5 q^{11} - q^{12} - 9 q^{14} + q^{15} - q^{16} + 5 q^{17} + 9 q^{18} - 4 q^{19} + q^{20} + 4 q^{21} + 10 q^{22} + 12 q^{24} + 4 q^{25} + 17 q^{26} - 14 q^{27} + 14 q^{28} - 5 q^{29} - 10 q^{30} - 13 q^{31} + 2 q^{32} - 11 q^{33} - 6 q^{34} - 3 q^{35} - 7 q^{36} - 3 q^{37} + 17 q^{38} - 6 q^{39} - 6 q^{40} - 20 q^{41} + 21 q^{42} - 12 q^{43} - 9 q^{44} + 9 q^{45} - 9 q^{47} + 18 q^{48} + 21 q^{49} - q^{50} - 17 q^{51} - 28 q^{52} - 5 q^{53} - 19 q^{54} - 5 q^{55} - 19 q^{56} - 28 q^{57} - 3 q^{58} - 4 q^{59} - q^{60} - 12 q^{61} + 14 q^{62} - 67 q^{63} + 11 q^{66} - 18 q^{67} + 29 q^{68} - 9 q^{70} + 30 q^{71} + 9 q^{72} + q^{73} - 24 q^{74} + q^{75} - 6 q^{76} - 6 q^{77} - 2 q^{78} - 16 q^{79} - q^{80} + 44 q^{81} - 14 q^{82} - 24 q^{83} + 34 q^{84} + 5 q^{85} + 19 q^{86} - 33 q^{87} + 7 q^{88} + 9 q^{89} + 9 q^{90} - 43 q^{91} - 35 q^{93} + 23 q^{94} - 4 q^{95} - 7 q^{96} - 39 q^{97} - 11 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9 - q^10 - 5 * q^11 - q^12 - 9 * q^14 + q^15 - q^16 + 5 * q^17 + 9 * q^18 - 4 * q^19 + q^20 + 4 * q^21 + 10 * q^22 + 12 * q^24 + 4 * q^25 + 17 * q^26 - 14 * q^27 + 14 * q^28 - 5 * q^29 - 10 * q^30 - 13 * q^31 + 2 * q^32 - 11 * q^33 - 6 * q^34 - 3 * q^35 - 7 * q^36 - 3 * q^37 + 17 * q^38 - 6 * q^39 - 6 * q^40 - 20 * q^41 + 21 * q^42 - 12 * q^43 - 9 * q^44 + 9 * q^45 - 9 * q^47 + 18 * q^48 + 21 * q^49 - q^50 - 17 * q^51 - 28 * q^52 - 5 * q^53 - 19 * q^54 - 5 * q^55 - 19 * q^56 - 28 * q^57 - 3 * q^58 - 4 * q^59 - q^60 - 12 * q^61 + 14 * q^62 - 67 * q^63 + 11 * q^66 - 18 * q^67 + 29 * q^68 - 9 * q^70 + 30 * q^71 + 9 * q^72 + q^73 - 24 * q^74 + q^75 - 6 * q^76 - 6 * q^77 - 2 * q^78 - 16 * q^79 - q^80 + 44 * q^81 - 14 * q^82 - 24 * q^83 + 34 * q^84 + 5 * q^85 + 19 * q^86 - 33 * q^87 + 7 * q^88 + 9 * q^89 + 9 * q^90 - 43 * q^91 - 35 * q^93 + 23 * q^94 - 4 * q^95 - 7 * q^96 - 39 * q^97 - 11 * q^98

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