LMFDB - Embedded newform 2695.2.a.y.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 51x^{6} - 184x^{5} - 45x^{4} + 297x^{3} - 59x^{2} - 109x + 21 $ x^10 - 3x^9 - 13x^8 + 41x^7 + 51x^6 - 184x^5 - 45x^4 + 297x^3 - 59x^2 - 109*x + 21
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.78109$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.78109 q^{2} -1.53729 q^{3} +5.73447 q^{4} -1.00000 q^{5} -4.27536 q^{6} +10.3859 q^{8} -0.636727 q^{9} +O(q^{10})$	\(q+2.78109 q^{2} -1.53729 q^{3} +5.73447 q^{4} -1.00000 q^{5} -4.27536 q^{6} +10.3859 q^{8} -0.636727 q^{9} -2.78109 q^{10} +1.00000 q^{11} -8.81557 q^{12} +3.09211 q^{13} +1.53729 q^{15} +17.4152 q^{16} -1.94078 q^{17} -1.77079 q^{18} +4.26368 q^{19} -5.73447 q^{20} +2.78109 q^{22} -7.85660 q^{23} -15.9662 q^{24} +1.00000 q^{25} +8.59943 q^{26} +5.59072 q^{27} +9.28995 q^{29} +4.27536 q^{30} +6.13436 q^{31} +27.6614 q^{32} -1.53729 q^{33} -5.39749 q^{34} -3.65129 q^{36} +1.94000 q^{37} +11.8577 q^{38} -4.75348 q^{39} -10.3859 q^{40} -1.46532 q^{41} +0.414699 q^{43} +5.73447 q^{44} +0.636727 q^{45} -21.8499 q^{46} -0.697848 q^{47} -26.7723 q^{48} +2.78109 q^{50} +2.98355 q^{51} +17.7316 q^{52} +0.314954 q^{53} +15.5483 q^{54} -1.00000 q^{55} -6.55453 q^{57} +25.8362 q^{58} +6.38408 q^{59} +8.81557 q^{60} +0.578079 q^{61} +17.0602 q^{62} +42.0986 q^{64} -3.09211 q^{65} -4.27536 q^{66} -4.08268 q^{67} -11.1293 q^{68} +12.0779 q^{69} -7.27272 q^{71} -6.61298 q^{72} -11.5011 q^{73} +5.39533 q^{74} -1.53729 q^{75} +24.4499 q^{76} -13.2199 q^{78} -6.97918 q^{79} -17.4152 q^{80} -6.68440 q^{81} -4.07519 q^{82} +16.3778 q^{83} +1.94078 q^{85} +1.15332 q^{86} -14.2814 q^{87} +10.3859 q^{88} +8.87704 q^{89} +1.77079 q^{90} -45.0534 q^{92} -9.43032 q^{93} -1.94078 q^{94} -4.26368 q^{95} -42.5238 q^{96} -11.6545 q^{97} -0.636727 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9	$ 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9 - 3 * q^10 + 10 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^15 + 21 * q^16 - 5 * q^17 + q^18 + q^19 - 15 * q^20 + 3 * q^22 + 18 * q^23 + 10 * q^24 + 10 * q^25 + 13 * q^26 - 15 * q^27 + 14 * q^29 - 5 * q^30 + 10 * q^31 + 46 * q^32 - 3 * q^33 - 2 * q^34 + 26 * q^36 + 13 * q^37 + 9 * q^38 + 3 * q^39 - 9 * q^40 - 7 * q^41 + 6 * q^43 + 15 * q^44 - 19 * q^45 + 10 * q^46 + q^47 - 35 * q^48 + 3 * q^50 + 9 * q^51 - 17 * q^52 + 16 * q^53 + 73 * q^54 - 10 * q^55 + 12 * q^57 - 9 * q^58 + 13 * q^59 + 3 * q^60 + 18 * q^61 + 14 * q^62 + 43 * q^64 + 6 * q^65 + 5 * q^66 + 29 * q^67 + 13 * q^68 + 19 * q^71 - 48 * q^72 - 31 * q^73 - 8 * q^74 - 3 * q^75 - 8 * q^76 + 3 * q^78 - 21 * q^80 + 42 * q^81 + q^82 - 2 * q^83 + 5 * q^85 + 10 * q^86 - 50 * q^87 + 9 * q^88 + 23 * q^89 - q^90 + 14 * q^92 + 4 * q^93 - 5 * q^94 - q^95 + 39 * q^96 - 43 * q^97 + 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.78109	1.96653	0.983264	−	0.182185i	$-0.0583170\pi$
$2$	2.78109	1.96653	0.983264	+	0.182185i	$0.0583170\pi$
$3$	−1.53729	−0.887557	−0.443779	−	0.896136i	$-0.646362\pi$
$3$	−1.53729	−0.887557	−0.443779	+	0.896136i	$0.646362\pi$
$4$	5.73447	2.86723
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.27536	−1.74541
$7$	0	0
$7$	0	0
$8$	10.3859	3.67197
$9$	−0.636727	−0.212242
$10$	−2.78109	−0.879458
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−8.81557	−2.54483
$13$	3.09211	0.857596	0.428798	−	0.903400i	$-0.358937\pi$
$13$	3.09211	0.857596	0.428798	+	0.903400i	$0.358937\pi$
$14$	0	0
$15$	1.53729	0.396928
$16$	17.4152	4.35380
$17$	−1.94078	−0.470708	−0.235354	−	0.971910i	$-0.575625\pi$
$17$	−1.94078	−0.470708	−0.235354	+	0.971910i	$0.575625\pi$
$18$	−1.77079	−0.417380
$19$	4.26368	0.978155	0.489077	−	0.872240i	$-0.337334\pi$
$19$	4.26368	0.978155	0.489077	+	0.872240i	$0.337334\pi$
$20$	−5.73447	−1.28227
$21$	0	0
$22$	2.78109	0.592931
$23$	−7.85660	−1.63821	−0.819107	−	0.573640i	$-0.805531\pi$
$23$	−7.85660	−1.63821	−0.819107	+	0.573640i	$0.805531\pi$
$24$	−15.9662	−3.25908
$25$	1.00000	0.200000
$26$	8.59943	1.68649
$27$	5.59072	1.07593
$28$	0	0
$29$	9.28995	1.72510	0.862550	−	0.505972i	$-0.168866\pi$
$29$	9.28995	1.72510	0.862550	+	0.505972i	$0.168866\pi$
$30$	4.27536	0.780570
$31$	6.13436	1.10176	0.550882	−	0.834583i	$-0.314291\pi$
$31$	6.13436	1.10176	0.550882	+	0.834583i	$0.314291\pi$
$32$	27.6614	4.88990
$33$	−1.53729	−0.267609
$34$	−5.39749	−0.925661
$35$	0	0
$36$	−3.65129	−0.608548
$37$	1.94000	0.318935	0.159467	−	0.987203i	$-0.449022\pi$
$37$	1.94000	0.318935	0.159467	+	0.987203i	$0.449022\pi$
$38$	11.8577	1.92357
$39$	−4.75348	−0.761166
$40$	−10.3859	−1.64215
$41$	−1.46532	−0.228845	−0.114422	−	0.993432i	$-0.536502\pi$
$41$	−1.46532	−0.228845	−0.114422	+	0.993432i	$0.536502\pi$
$42$	0	0
$43$	0.414699	0.0632410	0.0316205	−	0.999500i	$-0.489933\pi$
$43$	0.414699	0.0632410	0.0316205	+	0.999500i	$0.489933\pi$
$44$	5.73447	0.864504
$45$	0.636727	0.0949176
$46$	−21.8499	−3.22160
$47$	−0.697848	−0.101792	−0.0508958	−	0.998704i	$-0.516208\pi$
$47$	−0.697848	−0.101792	−0.0508958	+	0.998704i	$0.516208\pi$
$48$	−26.7723	−3.86424
$49$	0	0
$50$	2.78109	0.393306
$51$	2.98355	0.417781
$52$	17.7316	2.45893
$53$	0.314954	0.0432622	0.0216311	−	0.999766i	$-0.493114\pi$
$53$	0.314954	0.0432622	0.0216311	+	0.999766i	$0.493114\pi$
$54$	15.5483	2.11586
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−6.55453	−0.868169
$58$	25.8362	3.39246
$59$	6.38408	0.831136	0.415568	−	0.909562i	$-0.363583\pi$
$59$	6.38408	0.831136	0.415568	+	0.909562i	$0.363583\pi$
$60$	8.81557	1.13808
$61$	0.578079	0.0740154	0.0370077	−	0.999315i	$-0.488217\pi$
$61$	0.578079	0.0740154	0.0370077	+	0.999315i	$0.488217\pi$
$62$	17.0602	2.16665
$63$	0	0
$64$	42.0986	5.26233
$65$	−3.09211	−0.383529
$66$	−4.27536	−0.526260
$67$	−4.08268	−0.498778	−0.249389	−	0.968403i	$-0.580230\pi$
$67$	−4.08268	−0.498778	−0.249389	+	0.968403i	$0.580230\pi$
$68$	−11.1293	−1.34963
$69$	12.0779	1.45401
$70$	0	0
$71$	−7.27272	−0.863113	−0.431557	−	0.902086i	$-0.642035\pi$
$71$	−7.27272	−0.863113	−0.431557	+	0.902086i	$0.642035\pi$
$72$	−6.61298	−0.779347
$73$	−11.5011	−1.34610	−0.673052	−	0.739595i	$-0.735017\pi$
$73$	−11.5011	−1.34610	−0.673052	+	0.739595i	$0.735017\pi$
$74$	5.39533	0.627194
$75$	−1.53729	−0.177511
$76$	24.4499	2.80460
$77$	0	0
$78$	−13.2199	−1.49685
$79$	−6.97918	−0.785220	−0.392610	−	0.919705i	$-0.628428\pi$
$79$	−6.97918	−0.785220	−0.392610	+	0.919705i	$0.628428\pi$
$80$	−17.4152	−1.94708
$81$	−6.68440	−0.742711
$82$	−4.07519	−0.450030
$83$	16.3778	1.79770	0.898851	−	0.438255i	$-0.144403\pi$
$83$	16.3778	1.79770	0.898851	+	0.438255i	$0.144403\pi$
$84$	0	0
$85$	1.94078	0.210507
$86$	1.15332	0.124365
$87$	−14.2814	−1.53112
$88$	10.3859	1.10714
$89$	8.87704	0.940965	0.470482	−	0.882409i	$-0.344080\pi$
$89$	8.87704	0.940965	0.470482	+	0.882409i	$0.344080\pi$
$90$	1.77079	0.186658
$91$	0	0
$92$	−45.0534	−4.69715
$93$	−9.43032	−0.977879
$94$	−1.94078	−0.200176
$95$	−4.26368	−0.437444
$96$	−42.5238	−4.34006
$97$	−11.6545	−1.18333	−0.591665	−	0.806184i	$-0.701529\pi$
$97$	−11.6545	−1.18333	−0.591665	+	0.806184i	$0.701529\pi$
$98$	0	0
$99$	−0.636727	−0.0639934
$100$	5.73447	0.573447
$101$	−3.61930	−0.360134	−0.180067	−	0.983654i	$-0.557631\pi$
$101$	−3.61930	−0.360134	−0.180067	+	0.983654i	$0.557631\pi$
$102$	8.29753	0.821577
$103$	−8.90605	−0.877539	−0.438769	−	0.898600i	$-0.644586\pi$
$103$	−8.90605	−0.877539	−0.438769	+	0.898600i	$0.644586\pi$
$104$	32.1143	3.14907
$105$	0	0
$106$	0.875915	0.0850764
$107$	11.4809	1.10990	0.554949	−	0.831884i	$-0.312738\pi$
$107$	11.4809	1.10990	0.554949	+	0.831884i	$0.312738\pi$
$108$	32.0598	3.08496
$109$	4.38621	0.420123	0.210061	−	0.977688i	$-0.432634\pi$
$109$	4.38621	0.420123	0.210061	+	0.977688i	$0.432634\pi$
$110$	−2.78109	−0.265167
$111$	−2.98236	−0.283073
$112$	0	0
$113$	7.89458	0.742660	0.371330	−	0.928501i	$-0.378902\pi$
$113$	7.89458	0.742660	0.371330	+	0.928501i	$0.378902\pi$
$114$	−18.2287	−1.70728
$115$	7.85660	0.732632
$116$	53.2729	4.94627
$117$	−1.96883	−0.182018
$118$	17.7547	1.63445
$119$	0	0
$120$	15.9662	1.45751
$121$	1.00000	0.0909091
$122$	1.60769	0.145553
$123$	2.25263	0.203113
$124$	35.1773	3.15902
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−12.8091	−1.13662	−0.568310	−	0.822814i	$-0.692403\pi$
$127$	−12.8091	−1.13662	−0.568310	+	0.822814i	$0.692403\pi$
$128$	61.7572	5.45862
$129$	−0.637514	−0.0561300
$130$	−8.59943	−0.754220
$131$	−2.11967	−0.185196	−0.0925981	−	0.995704i	$-0.529517\pi$
$131$	−2.11967	−0.185196	−0.0925981	+	0.995704i	$0.529517\pi$
$132$	−8.81557	−0.767296
$133$	0	0
$134$	−11.3543	−0.980862
$135$	−5.59072	−0.481172
$136$	−20.1567	−1.72843
$137$	2.28653	0.195351	0.0976757	−	0.995218i	$-0.468859\pi$
$137$	2.28653	0.195351	0.0976757	+	0.995218i	$0.468859\pi$
$138$	33.5898	2.85935
$139$	−17.4014	−1.47597	−0.737984	−	0.674818i	$-0.764222\pi$
$139$	−17.4014	−1.47597	−0.737984	+	0.674818i	$0.764222\pi$
$140$	0	0
$141$	1.07280	0.0903459
$142$	−20.2261	−1.69734
$143$	3.09211	0.258575
$144$	−11.0887	−0.924060
$145$	−9.28995	−0.771488
$146$	−31.9857	−2.64715
$147$	0	0
$148$	11.1249	0.914460
$149$	6.50471	0.532886	0.266443	−	0.963851i	$-0.414152\pi$
$149$	6.50471	0.532886	0.266443	+	0.963851i	$0.414152\pi$
$150$	−4.27536	−0.349081
$151$	−4.01761	−0.326948	−0.163474	−	0.986548i	$-0.552270\pi$
$151$	−4.01761	−0.326948	−0.163474	+	0.986548i	$0.552270\pi$
$152$	44.2821	3.59176
$153$	1.23575	0.0999042
$154$	0	0
$155$	−6.13436	−0.492724
$156$	−27.2587	−2.18244
$157$	−17.8604	−1.42542	−0.712709	−	0.701460i	$-0.752532\pi$
$157$	−17.8604	−1.42542	−0.712709	+	0.701460i	$0.752532\pi$
$158$	−19.4097	−1.54416
$159$	−0.484176	−0.0383977
$160$	−27.6614	−2.18683
$161$	0	0
$162$	−18.5899	−1.46056
$163$	−9.49491	−0.743699	−0.371849	−	0.928293i	$-0.621276\pi$
$163$	−9.49491	−0.743699	−0.371849	+	0.928293i	$0.621276\pi$
$164$	−8.40284	−0.656151
$165$	1.53729	0.119678
$166$	45.5483	3.53523
$167$	12.7426	0.986048	0.493024	−	0.870016i	$-0.335891\pi$
$167$	12.7426	0.986048	0.493024	+	0.870016i	$0.335891\pi$
$168$	0	0
$169$	−3.43887	−0.264529
$170$	5.39749	0.413968
$171$	−2.71480	−0.207606
$172$	2.37808	0.181327
$173$	20.3324	1.54584	0.772922	−	0.634501i	$-0.218794\pi$
$173$	20.3324	1.54584	0.772922	+	0.634501i	$0.218794\pi$
$174$	−39.7178	−3.01100
$175$	0	0
$176$	17.4152	1.31272
$177$	−9.81421	−0.737681
$178$	24.6879	1.85043
$179$	12.1370	0.907164	0.453582	−	0.891214i	$-0.350146\pi$
$179$	12.1370	0.907164	0.453582	+	0.891214i	$0.350146\pi$
$180$	3.65129	0.272151
$181$	−5.39053	−0.400675	−0.200338	−	0.979727i	$-0.564204\pi$
$181$	−5.39053	−0.400675	−0.200338	+	0.979727i	$0.564204\pi$
$182$	0	0
$183$	−0.888677	−0.0656929
$184$	−81.5979	−6.01547
$185$	−1.94000	−0.142632
$186$	−26.2266	−1.92303
$187$	−1.94078	−0.141924
$188$	−4.00179	−0.291861
$189$	0	0
$190$	−11.8577	−0.860247
$191$	−8.15526	−0.590094	−0.295047	−	0.955483i	$-0.595335\pi$
$191$	−8.15526	−0.590094	−0.295047	+	0.955483i	$0.595335\pi$
$192$	−64.7180	−4.67062
$193$	0.141539	0.0101882	0.00509409	−	0.999987i	$-0.498378\pi$
$193$	0.141539	0.0101882	0.00509409	+	0.999987i	$0.498378\pi$
$194$	−32.4121	−2.32705
$195$	4.75348	0.340404
$196$	0	0
$197$	−6.53406	−0.465533	−0.232766	−	0.972533i	$-0.574778\pi$
$197$	−6.53406	−0.465533	−0.232766	+	0.972533i	$0.574778\pi$
$198$	−1.77079	−0.125845
$199$	−16.6729	−1.18191	−0.590955	−	0.806705i	$-0.701249\pi$
$199$	−16.6729	−1.18191	−0.590955	+	0.806705i	$0.701249\pi$
$200$	10.3859	0.734394
$201$	6.27628	0.442694
$202$	−10.0656	−0.708213
$203$	0	0
$204$	17.1091	1.19787
$205$	1.46532	0.102342
$206$	−24.7685	−1.72571
$207$	5.00251	0.347698
$208$	53.8496	3.73380
$209$	4.26368	0.294925
$210$	0	0
$211$	−11.2302	−0.773117	−0.386559	−	0.922265i	$-0.626336\pi$
$211$	−11.2302	−0.773117	−0.386559	+	0.922265i	$0.626336\pi$
$212$	1.80609	0.124043
$213$	11.1803	0.766062
$214$	31.9294	2.18265
$215$	−0.414699	−0.0282822
$216$	58.0646	3.95080
$217$	0	0
$218$	12.1985	0.826184
$219$	17.6806	1.19474
$220$	−5.73447	−0.386618
$221$	−6.00110	−0.403678
$222$	−8.29421	−0.556671
$223$	−25.9761	−1.73949	−0.869744	−	0.493502i	$-0.835716\pi$
$223$	−25.9761	−1.73949	−0.869744	+	0.493502i	$0.835716\pi$
$224$	0	0
$225$	−0.636727	−0.0424484
$226$	21.9556	1.46046
$227$	−4.04553	−0.268511	−0.134256	−	0.990947i	$-0.542864\pi$
$227$	−4.04553	−0.268511	−0.134256	+	0.990947i	$0.542864\pi$
$228$	−37.5867	−2.48924
$229$	−2.24518	−0.148366	−0.0741828	−	0.997245i	$-0.523635\pi$
$229$	−2.24518	−0.148366	−0.0741828	+	0.997245i	$0.523635\pi$
$230$	21.8499	1.44074
$231$	0	0
$232$	96.4844	6.33451
$233$	−3.98145	−0.260833	−0.130417	−	0.991459i	$-0.541631\pi$
$233$	−3.98145	−0.260833	−0.130417	+	0.991459i	$0.541631\pi$
$234$	−5.47549	−0.357944
$235$	0.697848	0.0455226
$236$	36.6093	2.38306
$237$	10.7291	0.696927
$238$	0	0
$239$	−21.2060	−1.37170	−0.685850	−	0.727743i	$-0.740569\pi$
$239$	−21.2060	−1.37170	−0.685850	+	0.727743i	$0.740569\pi$
$240$	26.7723	1.72814
$241$	3.24544	0.209057	0.104529	−	0.994522i	$-0.466667\pi$
$241$	3.24544	0.209057	0.104529	+	0.994522i	$0.466667\pi$
$242$	2.78109	0.178775
$243$	−6.49627	−0.416736
$244$	3.31497	0.212219
$245$	0	0
$246$	6.26477	0.399427
$247$	13.1838	0.838862
$248$	63.7109	4.04564
$249$	−25.1776	−1.59556
$250$	−2.78109	−0.175892
$251$	9.96799	0.629174	0.314587	−	0.949229i	$-0.398134\pi$
$251$	9.96799	0.629174	0.314587	+	0.949229i	$0.398134\pi$
$252$	0	0
$253$	−7.85660	−0.493940
$254$	−35.6232	−2.23520
$255$	−2.98355	−0.186837
$256$	87.5552	5.47220
$257$	−20.6945	−1.29089	−0.645443	−	0.763809i	$-0.723327\pi$
$257$	−20.6945	−1.29089	−0.645443	+	0.763809i	$0.723327\pi$
$258$	−1.77299	−0.110381
$259$	0	0
$260$	−17.7316	−1.09967
$261$	−5.91516	−0.366139
$262$	−5.89499	−0.364194
$263$	18.1504	1.11920	0.559602	−	0.828762i	$-0.310954\pi$
$263$	18.1504	1.11920	0.559602	+	0.828762i	$0.310954\pi$
$264$	−15.9662	−0.982650
$265$	−0.314954	−0.0193475
$266$	0	0
$267$	−13.6466	−0.835160
$268$	−23.4120	−1.43011
$269$	−23.6512	−1.44204	−0.721019	−	0.692915i	$-0.756326\pi$
$269$	−23.6512	−1.44204	−0.721019	+	0.692915i	$0.756326\pi$
$270$	−15.5483	−0.946239
$271$	25.8588	1.57081	0.785406	−	0.618981i	$-0.212454\pi$
$271$	25.8588	1.57081	0.785406	+	0.618981i	$0.212454\pi$
$272$	−33.7991	−2.04937
$273$	0	0
$274$	6.35905	0.384164
$275$	1.00000	0.0603023
$276$	69.2604	4.16899
$277$	3.42418	0.205739	0.102869	−	0.994695i	$-0.467198\pi$
$277$	3.42418	0.205739	0.102869	+	0.994695i	$0.467198\pi$
$278$	−48.3949	−2.90253
$279$	−3.90591	−0.233841
$280$	0	0
$281$	−3.86399	−0.230506	−0.115253	−	0.993336i	$-0.536768\pi$
$281$	−3.86399	−0.230506	−0.115253	+	0.993336i	$0.536768\pi$
$282$	2.98355	0.177668
$283$	−0.640788	−0.0380909	−0.0190454	−	0.999819i	$-0.506063\pi$
$283$	−0.640788	−0.0380909	−0.0190454	+	0.999819i	$0.506063\pi$
$284$	−41.7052	−2.47475
$285$	6.55453	0.388257
$286$	8.59943	0.508495
$287$	0	0
$288$	−17.6128	−1.03784
$289$	−13.2334	−0.778434
$290$	−25.8362	−1.51715
$291$	17.9163	1.05027
$292$	−65.9528	−3.85960
$293$	28.1336	1.64358	0.821790	−	0.569790i	$-0.192976\pi$
$293$	28.1336	1.64358	0.821790	+	0.569790i	$0.192976\pi$
$294$	0	0
$295$	−6.38408	−0.371695
$296$	20.1487	1.17112
$297$	5.59072	0.324406
$298$	18.0902	1.04794
$299$	−24.2935	−1.40493
$300$	−8.81557	−0.508967
$301$	0	0
$302$	−11.1733	−0.642953
$303$	5.56393	0.319639
$304$	74.2528	4.25869
$305$	−0.578079	−0.0331007
$306$	3.43672	0.196464
$307$	−27.9718	−1.59644	−0.798218	−	0.602369i	$-0.794224\pi$
$307$	−27.9718	−1.59644	−0.798218	+	0.602369i	$0.794224\pi$
$308$	0	0
$309$	13.6912	0.778866
$310$	−17.0602	−0.968955
$311$	−28.0045	−1.58799	−0.793996	−	0.607923i	$-0.792003\pi$
$311$	−28.0045	−1.58799	−0.793996	+	0.607923i	$0.792003\pi$
$312$	−49.3691	−2.79498
$313$	6.86186	0.387855	0.193928	−	0.981016i	$-0.437877\pi$
$313$	6.86186	0.387855	0.193928	+	0.981016i	$0.437877\pi$
$314$	−49.6715	−2.80313
$315$	0	0
$316$	−40.0219	−2.25141
$317$	−6.09328	−0.342233	−0.171116	−	0.985251i	$-0.554737\pi$
$317$	−6.09328	−0.342233	−0.171116	+	0.985251i	$0.554737\pi$
$318$	−1.34654	−0.0755101
$319$	9.28995	0.520137
$320$	−42.0986	−2.35338
$321$	−17.6495	−0.985098
$322$	0	0
$323$	−8.27486	−0.460426
$324$	−38.3315	−2.12953
$325$	3.09211	0.171519
$326$	−26.4062	−1.46250
$327$	−6.74290	−0.372883
$328$	−15.2187	−0.840311
$329$	0	0
$330$	4.27536	0.235351
$331$	11.3548	0.624119	0.312059	−	0.950063i	$-0.398981\pi$
$331$	11.3548	0.624119	0.312059	+	0.950063i	$0.398981\pi$
$332$	93.9182	5.15443
$333$	−1.23525	−0.0676914
$334$	35.4382	1.93909
$335$	4.08268	0.223060
$336$	0	0
$337$	−10.6182	−0.578411	−0.289206	−	0.957267i	$-0.593391\pi$
$337$	−10.6182	−0.578411	−0.289206	+	0.957267i	$0.593391\pi$
$338$	−9.56382	−0.520203
$339$	−12.1363	−0.659153
$340$	11.1293	0.603573
$341$	6.13436	0.332194
$342$	−7.55010	−0.408263
$343$	0	0
$344$	4.30702	0.232219
$345$	−12.0779	−0.650253
$346$	56.5463	3.03995
$347$	−32.1388	−1.72530	−0.862651	−	0.505800i	$-0.831197\pi$
$347$	−32.1388	−1.72530	−0.862651	+	0.505800i	$0.831197\pi$
$348$	−81.8961	−4.39009
$349$	14.6781	0.785702	0.392851	−	0.919602i	$-0.371489\pi$
$349$	14.6781	0.785702	0.392851	+	0.919602i	$0.371489\pi$
$350$	0	0
$351$	17.2871	0.922717
$352$	27.6614	1.47436
$353$	−25.1054	−1.33622	−0.668112	−	0.744061i	$-0.732897\pi$
$353$	−25.1054	−1.33622	−0.668112	+	0.744061i	$0.732897\pi$
$354$	−27.2942	−1.45067
$355$	7.27272	0.385996
$356$	50.9051	2.69797
$357$	0	0
$358$	33.7542	1.78396
$359$	14.4784	0.764143	0.382071	−	0.924133i	$-0.375211\pi$
$359$	14.4784	0.764143	0.382071	+	0.924133i	$0.375211\pi$
$360$	6.61298	0.348535
$361$	−0.821043	−0.0432128
$362$	−14.9916	−0.787939
$363$	−1.53729	−0.0806870
$364$	0	0
$365$	11.5011	0.601996
$366$	−2.47149	−0.129187
$367$	−16.7252	−0.873050	−0.436525	−	0.899692i	$-0.643791\pi$
$367$	−16.7252	−0.873050	−0.436525	+	0.899692i	$0.643791\pi$
$368$	−136.824	−7.13246
$369$	0.933009	0.0485705
$370$	−5.39533	−0.280490
$371$	0	0
$372$	−54.0779	−2.80381
$373$	16.1801	0.837773	0.418887	−	0.908039i	$-0.362420\pi$
$373$	16.1801	0.837773	0.418887	+	0.908039i	$0.362420\pi$
$374$	−5.39749	−0.279097
$375$	1.53729	0.0793855
$376$	−7.24778	−0.373776
$377$	28.7255	1.47944
$378$	0	0
$379$	6.03417	0.309954	0.154977	−	0.987918i	$-0.450470\pi$
$379$	6.03417	0.309954	0.154977	+	0.987918i	$0.450470\pi$
$380$	−24.4499	−1.25426
$381$	19.6913	1.00882
$382$	−22.6805	−1.16044
$383$	6.82104	0.348539	0.174270	−	0.984698i	$-0.444244\pi$
$383$	6.82104	0.348539	0.174270	+	0.984698i	$0.444244\pi$
$384$	−94.9390	−4.84483
$385$	0	0
$386$	0.393632	0.0200354
$387$	−0.264050	−0.0134224
$388$	−66.8321	−3.39289
$389$	10.3169	0.523086	0.261543	−	0.965192i	$-0.415769\pi$
$389$	10.3169	0.523086	0.261543	+	0.965192i	$0.415769\pi$
$390$	13.2199	0.669413
$391$	15.2479	0.771121
$392$	0	0
$393$	3.25855	0.164372
$394$	−18.1718	−0.915483
$395$	6.97918	0.351161
$396$	−3.65129	−0.183484
$397$	−15.5451	−0.780186	−0.390093	−	0.920776i	$-0.627557\pi$
$397$	−15.5451	−0.780186	−0.390093	+	0.920776i	$0.627557\pi$
$398$	−46.3688	−2.32426
$399$	0	0
$400$	17.4152	0.870760
$401$	−16.1387	−0.805930	−0.402965	−	0.915215i	$-0.632020\pi$
$401$	−16.1387	−0.805930	−0.402965	+	0.915215i	$0.632020\pi$
$402$	17.4549	0.870571
$403$	18.9681	0.944869
$404$	−20.7548	−1.03259
$405$	6.68440	0.332150
$406$	0	0
$407$	1.94000	0.0961624
$408$	30.9868	1.53408
$409$	15.6615	0.774412	0.387206	−	0.921993i	$-0.373440\pi$
$409$	15.6615	0.774412	0.387206	+	0.921993i	$0.373440\pi$
$410$	4.07519	0.201259
$411$	−3.51507	−0.173386
$412$	−51.0715	−2.51611
$413$	0	0
$414$	13.9124	0.683759
$415$	−16.3778	−0.803956
$416$	85.5321	4.19356
$417$	26.7511	1.31001
$418$	11.8577	0.579978
$419$	−4.99479	−0.244012	−0.122006	−	0.992529i	$-0.538933\pi$
$419$	−4.99479	−0.244012	−0.122006	+	0.992529i	$0.538933\pi$
$420$	0	0
$421$	18.8075	0.916621	0.458310	−	0.888792i	$-0.348455\pi$
$421$	18.8075	0.916621	0.458310	+	0.888792i	$0.348455\pi$
$422$	−31.2321	−1.52036
$423$	0.444339	0.0216045
$424$	3.27108	0.158858
$425$	−1.94078	−0.0941417
$426$	31.0935	1.50648
$427$	0	0
$428$	65.8367	3.18234
$429$	−4.75348	−0.229500
$430$	−1.15332	−0.0556178
$431$	34.1022	1.64265	0.821324	−	0.570462i	$-0.193236\pi$
$431$	34.1022	1.64265	0.821324	+	0.570462i	$0.193236\pi$
$432$	97.3634	4.68440
$433$	8.47305	0.407189	0.203594	−	0.979055i	$-0.434738\pi$
$433$	8.47305	0.407189	0.203594	+	0.979055i	$0.434738\pi$
$434$	0	0
$435$	14.2814	0.684740
$436$	25.1526	1.20459
$437$	−33.4980	−1.60243
$438$	49.1714	2.34950
$439$	19.5942	0.935182	0.467591	−	0.883945i	$-0.345122\pi$
$439$	19.5942	0.935182	0.467591	+	0.883945i	$0.345122\pi$
$440$	−10.3859	−0.495128
$441$	0	0
$442$	−16.6896	−0.793844
$443$	7.18266	0.341258	0.170629	−	0.985335i	$-0.445420\pi$
$443$	7.18266	0.341258	0.170629	+	0.985335i	$0.445420\pi$
$444$	−17.1022	−0.811636
$445$	−8.87704	−0.420812
$446$	−72.2419	−3.42075
$447$	−9.99965	−0.472967
$448$	0	0
$449$	7.38032	0.348299	0.174150	−	0.984719i	$-0.444282\pi$
$449$	7.38032	0.348299	0.174150	+	0.984719i	$0.444282\pi$
$450$	−1.77079	−0.0834761
$451$	−1.46532	−0.0689993
$452$	45.2712	2.12938
$453$	6.17625	0.290185
$454$	−11.2510	−0.528035
$455$	0	0
$456$	−68.0747	−3.18789
$457$	29.0202	1.35751	0.678753	−	0.734366i	$-0.262521\pi$
$457$	29.0202	1.35751	0.678753	+	0.734366i	$0.262521\pi$
$458$	−6.24405	−0.291765
$459$	−10.8504	−0.506451
$460$	45.0534	2.10063
$461$	16.7934	0.782145	0.391072	−	0.920360i	$-0.372104\pi$
$461$	16.7934	0.782145	0.391072	+	0.920360i	$0.372104\pi$
$462$	0	0
$463$	−25.2990	−1.17574	−0.587872	−	0.808954i	$-0.700034\pi$
$463$	−25.2990	−1.17574	−0.587872	+	0.808954i	$0.700034\pi$
$464$	161.786	7.51074
$465$	9.43032	0.437321
$466$	−11.0728	−0.512936
$467$	−6.88135	−0.318431	−0.159215	−	0.987244i	$-0.550896\pi$
$467$	−6.88135	−0.318431	−0.159215	+	0.987244i	$0.550896\pi$
$468$	−11.2902	−0.521889
$469$	0	0
$470$	1.94078	0.0895215
$471$	27.4568	1.26514
$472$	66.3044	3.05191
$473$	0.414699	0.0190679
$474$	29.8385	1.37053
$475$	4.26368	0.195631
$476$	0	0
$477$	−0.200539	−0.00918207
$478$	−58.9757	−2.69749
$479$	−4.36583	−0.199480	−0.0997399	−	0.995014i	$-0.531801\pi$
$479$	−4.36583	−0.199480	−0.0997399	+	0.995014i	$0.531801\pi$
$480$	42.5238	1.94094
$481$	5.99870	0.273517
$482$	9.02586	0.411117
$483$	0	0
$484$	5.73447	0.260658
$485$	11.6545	0.529202
$486$	−18.0667	−0.819523
$487$	−42.1756	−1.91116	−0.955580	−	0.294733i	$-0.904769\pi$
$487$	−42.1756	−1.91116	−0.955580	+	0.294733i	$0.904769\pi$
$488$	6.00386	0.271782
$489$	14.5965	0.660075
$490$	0	0
$491$	0.399532	0.0180306	0.00901532	−	0.999959i	$-0.497130\pi$
$491$	0.399532	0.0180306	0.00901532	+	0.999959i	$0.497130\pi$
$492$	12.9176	0.582372
$493$	−18.0297	−0.812019
$494$	36.6652	1.64965
$495$	0.636727	0.0286187
$496$	106.831	4.79686
$497$	0	0
$498$	−70.0211	−3.13772
$499$	34.2938	1.53520	0.767600	−	0.640929i	$-0.221451\pi$
$499$	34.2938	1.53520	0.767600	+	0.640929i	$0.221451\pi$
$500$	−5.73447	−0.256453
$501$	−19.5891	−0.875174
$502$	27.7219	1.23729
$503$	40.7509	1.81699	0.908496	−	0.417893i	$-0.137231\pi$
$503$	40.7509	1.81699	0.908496	+	0.417893i	$0.137231\pi$
$504$	0	0
$505$	3.61930	0.161057
$506$	−21.8499	−0.971348
$507$	5.28656	0.234784
$508$	−73.4532	−3.25896
$509$	−0.923802	−0.0409468	−0.0204734	−	0.999790i	$-0.506517\pi$
$509$	−0.923802	−0.0409468	−0.0204734	+	0.999790i	$0.506517\pi$
$510$	−8.29753	−0.367421
$511$	0	0
$512$	119.985	5.30262
$513$	23.8370	1.05243
$514$	−57.5532	−2.53856
$515$	8.90605	0.392447
$516$	−3.65580	−0.160938
$517$	−0.697848	−0.0306913
$518$	0	0
$519$	−31.2569	−1.37202
$520$	−32.1143	−1.40831
$521$	24.8744	1.08977	0.544884	−	0.838511i	$-0.316574\pi$
$521$	24.8744	1.08977	0.544884	+	0.838511i	$0.316574\pi$
$522$	−16.4506	−0.720023
$523$	−9.31821	−0.407457	−0.203728	−	0.979027i	$-0.565306\pi$
$523$	−9.31821	−0.407457	−0.203728	+	0.979027i	$0.565306\pi$
$524$	−12.1552	−0.531001
$525$	0	0
$526$	50.4780	2.20095
$527$	−11.9054	−0.518609
$528$	−26.7723	−1.16511
$529$	38.7262	1.68375
$530$	−0.875915	−0.0380473
$531$	−4.06491	−0.176402
$532$	0	0
$533$	−4.53093	−0.196256
$534$	−37.9525	−1.64237
$535$	−11.4809	−0.496362
$536$	−42.4023	−1.83150
$537$	−18.6582	−0.805160
$538$	−65.7761	−2.83581
$539$	0	0
$540$	−32.0598	−1.37963
$541$	−43.5036	−1.87037	−0.935183	−	0.354165i	$-0.884765\pi$
$541$	−43.5036	−1.87037	−0.935183	+	0.354165i	$0.884765\pi$
$542$	71.9158	3.08905
$543$	8.28683	0.355622
$544$	−53.6848	−2.30172
$545$	−4.38621	−0.187885
$546$	0	0
$547$	−26.3787	−1.12787	−0.563936	−	0.825819i	$-0.690713\pi$
$547$	−26.3787	−1.12787	−0.563936	+	0.825819i	$0.690713\pi$
$548$	13.1120	0.560118
$549$	−0.368078	−0.0157092
$550$	2.78109	0.118586
$551$	39.6094	1.68742
$552$	125.440	5.33908
$553$	0	0
$554$	9.52294	0.404591
$555$	2.98236	0.126594
$556$	−99.7878	−4.23195
$557$	−34.2885	−1.45285	−0.726425	−	0.687246i	$-0.758820\pi$
$557$	−34.2885	−1.45285	−0.726425	+	0.687246i	$0.758820\pi$
$558$	−10.8627	−0.459855
$559$	1.28229	0.0542352
$560$	0	0
$561$	2.98355	0.125966
$562$	−10.7461	−0.453297
$563$	−16.2925	−0.686646	−0.343323	−	0.939217i	$-0.611553\pi$
$563$	−16.2925	−0.686646	−0.343323	+	0.939217i	$0.611553\pi$
$564$	6.15193	0.259043
$565$	−7.89458	−0.332128
$566$	−1.78209	−0.0749068
$567$	0	0
$568$	−75.5337	−3.16933
$569$	31.2099	1.30839	0.654194	−	0.756327i	$-0.273008\pi$
$569$	31.2099	1.30839	0.654194	+	0.756327i	$0.273008\pi$
$570$	18.2287	0.763518
$571$	24.9674	1.04485	0.522426	−	0.852684i	$-0.325027\pi$
$571$	24.9674	1.04485	0.522426	+	0.852684i	$0.325027\pi$
$572$	17.7316	0.741395
$573$	12.5370	0.523742
$574$	0	0
$575$	−7.85660	−0.327643
$576$	−26.8053	−1.11689
$577$	12.6735	0.527606	0.263803	−	0.964577i	$-0.415023\pi$
$577$	12.6735	0.527606	0.263803	+	0.964577i	$0.415023\pi$
$578$	−36.8032	−1.53081
$579$	−0.217587	−0.00904260
$580$	−53.2729	−2.21204
$581$	0	0
$582$	49.8269	2.06539
$583$	0.314954	0.0130440
$584$	−119.449	−4.94286
$585$	1.96883	0.0814010
$586$	78.2420	3.23215
$587$	−33.6437	−1.38863	−0.694313	−	0.719674i	$-0.744291\pi$
$587$	−33.6437	−1.38863	−0.694313	+	0.719674i	$0.744291\pi$
$588$	0	0
$589$	26.1549	1.07770
$590$	−17.7547	−0.730950
$591$	10.0448	0.413187
$592$	33.7855	1.38858
$593$	35.7996	1.47011	0.735056	−	0.678007i	$-0.237156\pi$
$593$	35.7996	1.47011	0.735056	+	0.678007i	$0.237156\pi$
$594$	15.5483	0.637954
$595$	0	0
$596$	37.3010	1.52791
$597$	25.6311	1.04901
$598$	−67.5623	−2.76283
$599$	33.1360	1.35390	0.676949	−	0.736030i	$-0.263302\pi$
$599$	33.1360	1.35390	0.676949	+	0.736030i	$0.263302\pi$
$600$	−15.9662	−0.651817
$601$	−17.4979	−0.713753	−0.356877	−	0.934152i	$-0.616158\pi$
$601$	−17.4979	−0.713753	−0.356877	+	0.934152i	$0.616158\pi$
$602$	0	0
$603$	2.59955	0.105862
$604$	−23.0389	−0.937438
$605$	−1.00000	−0.0406558
$606$	15.4738	0.628580
$607$	−15.8892	−0.644923	−0.322462	−	0.946582i	$-0.604510\pi$
$607$	−15.8892	−0.644923	−0.322462	+	0.946582i	$0.604510\pi$
$608$	117.940	4.78308
$609$	0	0
$610$	−1.60769	−0.0650934
$611$	−2.15782	−0.0872961
$612$	7.08635	0.286449
$613$	−3.12140	−0.126072	−0.0630360	−	0.998011i	$-0.520078\pi$
$613$	−3.12140	−0.126072	−0.0630360	+	0.998011i	$0.520078\pi$
$614$	−77.7922	−3.13944
$615$	−2.25263	−0.0908348
$616$	0	0
$617$	36.9003	1.48555	0.742775	−	0.669542i	$-0.233509\pi$
$617$	36.9003	1.48555	0.742775	+	0.669542i	$0.233509\pi$
$618$	38.0765	1.53166
$619$	3.29227	0.132328	0.0661638	−	0.997809i	$-0.478924\pi$
$619$	3.29227	0.132328	0.0661638	+	0.997809i	$0.478924\pi$
$620$	−35.1773	−1.41275
$621$	−43.9241	−1.76261
$622$	−77.8832	−3.12283
$623$	0	0
$624$	−82.7827	−3.31396
$625$	1.00000	0.0400000
$626$	19.0834	0.762728
$627$	−6.55453	−0.261763
$628$	−102.420	−4.08701
$629$	−3.76512	−0.150125
$630$	0	0
$631$	−34.0214	−1.35437	−0.677185	−	0.735812i	$-0.736800\pi$
$631$	−34.0214	−1.35437	−0.677185	+	0.735812i	$0.736800\pi$
$632$	−72.4851	−2.88330
$633$	17.2641	0.686186
$634$	−16.9460	−0.673010
$635$	12.8091	0.508312
$636$	−2.77649	−0.110095
$637$	0	0
$638$	25.8362	1.02286
$639$	4.63074	0.183189
$640$	−61.7572	−2.44117
$641$	−47.3317	−1.86949	−0.934745	−	0.355318i	$-0.884372\pi$
$641$	−47.3317	−1.86949	−0.934745	+	0.355318i	$0.884372\pi$
$642$	−49.0848	−1.93722
$643$	12.0870	0.476666	0.238333	−	0.971184i	$-0.423399\pi$
$643$	12.0870	0.476666	0.238333	+	0.971184i	$0.423399\pi$
$644$	0	0
$645$	0.637514	0.0251021
$646$	−23.0132	−0.905440
$647$	−37.8383	−1.48758	−0.743789	−	0.668414i	$-0.766973\pi$
$647$	−37.8383	−1.48758	−0.743789	+	0.668414i	$0.766973\pi$
$648$	−69.4235	−2.72721
$649$	6.38408	0.250597
$650$	8.59943	0.337297
$651$	0	0
$652$	−54.4482	−2.13236
$653$	15.3862	0.602109	0.301055	−	0.953607i	$-0.402661\pi$
$653$	15.3862	0.602109	0.301055	+	0.953607i	$0.402661\pi$
$654$	−18.7526	−0.733285
$655$	2.11967	0.0828222
$656$	−25.5188	−0.996343
$657$	7.32307	0.285700
$658$	0	0
$659$	−25.3699	−0.988270	−0.494135	−	0.869385i	$-0.664515\pi$
$659$	−25.3699	−0.988270	−0.494135	+	0.869385i	$0.664515\pi$
$660$	8.81557	0.343145
$661$	42.7996	1.66471	0.832356	−	0.554242i	$-0.186992\pi$
$661$	42.7996	1.66471	0.832356	+	0.554242i	$0.186992\pi$
$662$	31.5789	1.22735
$663$	9.22546	0.358287
$664$	170.099	6.60110
$665$	0	0
$666$	−3.43535	−0.133117
$667$	−72.9874	−2.82608
$668$	73.0718	2.82723
$669$	39.9329	1.54390
$670$	11.3543	0.438655
$671$	0.578079	0.0223165
$672$	0	0
$673$	−19.9025	−0.767184	−0.383592	−	0.923503i	$-0.625313\pi$
$673$	−19.9025	−0.767184	−0.383592	+	0.923503i	$0.625313\pi$
$674$	−29.5302	−1.13746
$675$	5.59072	0.215187
$676$	−19.7201	−0.758466
$677$	16.6946	0.641624	0.320812	−	0.947143i	$-0.396044\pi$
$677$	16.6946	0.641624	0.320812	+	0.947143i	$0.396044\pi$
$678$	−33.7521	−1.29624
$679$	0	0
$680$	20.1567	0.772976
$681$	6.21917	0.238319
$682$	17.0602	0.653270
$683$	31.2785	1.19684	0.598419	−	0.801183i	$-0.295796\pi$
$683$	31.2785	1.19684	0.598419	+	0.801183i	$0.295796\pi$
$684$	−15.5679	−0.595254
$685$	−2.28653	−0.0873638
$686$	0	0
$687$	3.45150	0.131683
$688$	7.22206	0.275338
$689$	0.973870	0.0371015
$690$	−33.5898	−1.27874
$691$	−0.704289	−0.0267924	−0.0133962	−	0.999910i	$-0.504264\pi$
$691$	−0.704289	−0.0267924	−0.0133962	+	0.999910i	$0.504264\pi$
$692$	116.596	4.43230
$693$	0	0
$694$	−89.3810	−3.39285
$695$	17.4014	0.660073
$696$	−148.325	−5.62224
$697$	2.84387	0.107719
$698$	40.8212	1.54511
$699$	6.12065	0.231504
$700$	0	0
$701$	9.46422	0.357459	0.178729	−	0.983898i	$-0.442801\pi$
$701$	9.46422	0.357459	0.178729	+	0.983898i	$0.442801\pi$
$702$	48.0770	1.81455
$703$	8.27155	0.311968
$704$	42.0986	1.58665
$705$	−1.07280	−0.0404039
$706$	−69.8203	−2.62772
$707$	0	0
$708$	−56.2793	−2.11510
$709$	30.5199	1.14620	0.573100	−	0.819486i	$-0.305741\pi$
$709$	30.5199	1.14620	0.573100	+	0.819486i	$0.305741\pi$
$710$	20.2261	0.759072
$711$	4.44383	0.166657
$712$	92.1961	3.45519
$713$	−48.1952	−1.80493
$714$	0	0
$715$	−3.09211	−0.115638
$716$	69.5994	2.60105
$717$	32.5998	1.21746
$718$	40.2659	1.50271
$719$	−19.5944	−0.730748	−0.365374	−	0.930861i	$-0.619059\pi$
$719$	−19.5944	−0.730748	−0.365374	+	0.930861i	$0.619059\pi$
$720$	11.0887	0.413252
$721$	0	0
$722$	−2.28340	−0.0849792
$723$	−4.98919	−0.185550
$724$	−30.9118	−1.14883
$725$	9.28995	0.345020
$726$	−4.27536	−0.158673
$727$	32.8408	1.21800	0.608999	−	0.793171i	$-0.291571\pi$
$727$	32.8408	1.21800	0.608999	+	0.793171i	$0.291571\pi$
$728$	0	0
$729$	30.0399	1.11259
$730$	31.9857	1.18384
$731$	−0.804839	−0.0297681
$732$	−5.09609	−0.188357
$733$	−7.69491	−0.284218	−0.142109	−	0.989851i	$-0.545388\pi$
$733$	−7.69491	−0.284218	−0.142109	+	0.989851i	$0.545388\pi$
$734$	−46.5144	−1.71688
$735$	0	0
$736$	−217.325	−8.01070
$737$	−4.08268	−0.150387
$738$	2.59478	0.0955153
$739$	−16.5378	−0.608354	−0.304177	−	0.952615i	$-0.598382\pi$
$739$	−16.5378	−0.608354	−0.304177	+	0.952615i	$0.598382\pi$
$740$	−11.1249	−0.408959
$741$	−20.2673	−0.744538
$742$	0	0
$743$	−5.29600	−0.194292	−0.0971458	−	0.995270i	$-0.530971\pi$
$743$	−5.29600	−0.194292	−0.0971458	+	0.995270i	$0.530971\pi$
$744$	−97.9423	−3.59074
$745$	−6.50471	−0.238314
$746$	44.9983	1.64751
$747$	−10.4282	−0.381548
$748$	−11.1293	−0.406929
$749$	0	0
$750$	4.27536	0.156114
$751$	−46.6636	−1.70278	−0.851389	−	0.524535i	$-0.824239\pi$
$751$	−46.6636	−1.70278	−0.851389	+	0.524535i	$0.824239\pi$
$752$	−12.1532	−0.443180
$753$	−15.3237	−0.558428
$754$	79.8883	2.90936
$755$	4.01761	0.146216
$756$	0	0
$757$	20.9004	0.759636	0.379818	−	0.925061i	$-0.375987\pi$
$757$	20.9004	0.759636	0.379818	+	0.925061i	$0.375987\pi$
$758$	16.7816	0.609534
$759$	12.0779	0.438400
$760$	−44.2821	−1.60628
$761$	4.98748	0.180796	0.0903980	−	0.995906i	$-0.471186\pi$
$761$	4.98748	0.180796	0.0903980	+	0.995906i	$0.471186\pi$
$762$	54.7633	1.98386
$763$	0	0
$764$	−46.7661	−1.69194
$765$	−1.23575	−0.0446785
$766$	18.9699	0.685412
$767$	19.7403	0.712779
$768$	−134.598	−4.85689
$769$	−12.8949	−0.465004	−0.232502	−	0.972596i	$-0.574691\pi$
$769$	−12.8949	−0.465004	−0.232502	+	0.972596i	$0.574691\pi$
$770$	0	0
$771$	31.8135	1.14573
$772$	0.811650	0.0292119
$773$	26.2186	0.943018	0.471509	−	0.881861i	$-0.343709\pi$
$773$	26.2186	0.943018	0.471509	+	0.881861i	$0.343709\pi$
$774$	−0.734347	−0.0263955
$775$	6.13436	0.220353
$776$	−121.042	−4.34515
$777$	0	0
$778$	28.6922	1.02866
$779$	−6.24766	−0.223846
$780$	27.2587	0.976017
$781$	−7.27272	−0.260238
$782$	42.4059	1.51643
$783$	51.9375	1.85609
$784$	0	0
$785$	17.8604	0.637466
$786$	9.06233	0.323243
$787$	−5.35201	−0.190779	−0.0953894	−	0.995440i	$-0.530410\pi$
$787$	−5.35201	−0.190779	−0.0953894	+	0.995440i	$0.530410\pi$
$788$	−37.4694	−1.33479
$789$	−27.9026	−0.993357
$790$	19.4097	0.690568
$791$	0	0
$792$	−6.61298	−0.234982
$793$	1.78748	0.0634753
$794$	−43.2323	−1.53426
$795$	0.484176	0.0171720
$796$	−95.6101	−3.38881
$797$	−32.5894	−1.15437	−0.577187	−	0.816612i	$-0.695850\pi$
$797$	−32.5894	−1.15437	−0.577187	+	0.816612i	$0.695850\pi$
$798$	0	0
$799$	1.35437	0.0479142
$800$	27.6614	0.977980
$801$	−5.65225	−0.199712
$802$	−44.8833	−1.58488
$803$	−11.5011	−0.405866
$804$	35.9911	1.26931
$805$	0	0
$806$	52.7520	1.85811
$807$	36.3588	1.27989
$808$	−37.5897	−1.32240
$809$	41.8669	1.47196	0.735981	−	0.677002i	$-0.236721\pi$
$809$	41.8669	1.47196	0.735981	+	0.677002i	$0.236721\pi$
$810$	18.5899	0.653183
$811$	41.2465	1.44836	0.724180	−	0.689611i	$-0.242218\pi$
$811$	41.2465	1.44836	0.724180	+	0.689611i	$0.242218\pi$
$812$	0	0
$813$	−39.7526	−1.39419
$814$	5.39533	0.189106
$815$	9.49491	0.332592
$816$	51.9591	1.81893
$817$	1.76814	0.0618595
$818$	43.5561	1.52290
$819$	0	0
$820$	8.40284	0.293440
$821$	19.9318	0.695625	0.347813	−	0.937564i	$-0.386925\pi$
$821$	19.9318	0.695625	0.347813	+	0.937564i	$0.386925\pi$
$822$	−9.77572	−0.340968
$823$	−34.4733	−1.20167	−0.600833	−	0.799375i	$-0.705164\pi$
$823$	−34.4733	−1.20167	−0.600833	+	0.799375i	$0.705164\pi$
$824$	−92.4973	−3.22230
$825$	−1.53729	−0.0535217
$826$	0	0
$827$	−43.6872	−1.51915	−0.759576	−	0.650419i	$-0.774593\pi$
$827$	−43.6872	−1.51915	−0.759576	+	0.650419i	$0.774593\pi$
$828$	28.6867	0.996933
$829$	17.6908	0.614429	0.307214	−	0.951640i	$-0.400603\pi$
$829$	17.6908	0.614429	0.307214	+	0.951640i	$0.400603\pi$
$830$	−45.5483	−1.58100
$831$	−5.26396	−0.182605
$832$	130.173	4.51295
$833$	0	0
$834$	74.3972	2.57616
$835$	−12.7426	−0.440974
$836$	24.4499	0.845619
$837$	34.2955	1.18543
$838$	−13.8910	−0.479856
$839$	−8.35823	−0.288558	−0.144279	−	0.989537i	$-0.546086\pi$
$839$	−8.35823	−0.288558	−0.144279	+	0.989537i	$0.546086\pi$
$840$	0	0
$841$	57.3031	1.97597
$842$	52.3053	1.80256
$843$	5.94009	0.204588
$844$	−64.3991	−2.21671
$845$	3.43887	0.118301
$846$	1.23575	0.0424858
$847$	0	0
$848$	5.48498	0.188355
$849$	0.985080	0.0338078
$850$	−5.39749	−0.185132
$851$	−15.2418	−0.522484
$852$	64.1131	2.19648
$853$	−21.0748	−0.721586	−0.360793	−	0.932646i	$-0.617494\pi$
$853$	−21.0748	−0.721586	−0.360793	+	0.932646i	$0.617494\pi$
$854$	0	0
$855$	2.71480	0.0928441
$856$	119.239	4.07551
$857$	−48.3096	−1.65022	−0.825112	−	0.564969i	$-0.808888\pi$
$857$	−48.3096	−1.65022	−0.825112	+	0.564969i	$0.808888\pi$
$858$	−13.2199	−0.451318
$859$	1.65371	0.0564237	0.0282119	−	0.999602i	$-0.491019\pi$
$859$	1.65371	0.0564237	0.0282119	+	0.999602i	$0.491019\pi$
$860$	−2.37808	−0.0810918
$861$	0	0
$862$	94.8415	3.23031
$863$	−18.0794	−0.615430	−0.307715	−	0.951479i	$-0.599564\pi$
$863$	−18.0794	−0.615430	−0.307715	+	0.951479i	$0.599564\pi$
$864$	154.647	5.26121
$865$	−20.3324	−0.691322
$866$	23.5643	0.800749
$867$	20.3436	0.690904
$868$	0	0
$869$	−6.97918	−0.236753
$870$	39.7178	1.34656
$871$	−12.6241	−0.427750
$872$	45.5547	1.54268
$873$	7.42070	0.251153
$874$	−93.1611	−3.15122
$875$	0	0
$876$	101.389	3.42561
$877$	6.52548	0.220350	0.110175	−	0.993912i	$-0.464859\pi$
$877$	6.52548	0.220350	0.110175	+	0.993912i	$0.464859\pi$
$878$	54.4934	1.83906
$879$	−43.2496	−1.45877
$880$	−17.4152	−0.587066
$881$	2.84709	0.0959208	0.0479604	−	0.998849i	$-0.484728\pi$
$881$	2.84709	0.0959208	0.0479604	+	0.998849i	$0.484728\pi$
$882$	0	0
$883$	−13.9412	−0.469159	−0.234579	−	0.972097i	$-0.575371\pi$
$883$	−13.9412	−0.469159	−0.234579	+	0.972097i	$0.575371\pi$
$884$	−34.4131	−1.15744
$885$	9.81421	0.329901
$886$	19.9756	0.671094
$887$	−12.2053	−0.409813	−0.204907	−	0.978782i	$-0.565689\pi$
$887$	−12.2053	−0.409813	−0.204907	+	0.978782i	$0.565689\pi$
$888$	−30.9744	−1.03943
$889$	0	0
$890$	−24.6879	−0.827539
$891$	−6.68440	−0.223936
$892$	−148.959	−4.98752
$893$	−2.97540	−0.0995680
$894$	−27.8099	−0.930103
$895$	−12.1370	−0.405696
$896$	0	0
$897$	37.3462	1.24695
$898$	20.5254	0.684940
$899$	56.9879	1.90065
$900$	−3.65129	−0.121710
$901$	−0.611256	−0.0203639
$902$	−4.07519	−0.135689
$903$	0	0
$904$	81.9923	2.72702
$905$	5.39053	0.179187
$906$	17.1767	0.570658
$907$	43.6733	1.45015	0.725075	−	0.688670i	$-0.241805\pi$
$907$	43.6733	1.45015	0.725075	+	0.688670i	$0.241805\pi$
$908$	−23.1990	−0.769885
$909$	2.30450	0.0764356
$910$	0	0
$911$	24.2984	0.805041	0.402520	−	0.915411i	$-0.368134\pi$
$911$	24.2984	0.805041	0.402520	+	0.915411i	$0.368134\pi$
$912$	−114.148	−3.77983
$913$	16.3778	0.542027
$914$	80.7078	2.66958
$915$	0.888677	0.0293787
$916$	−12.8749	−0.425399
$917$	0	0
$918$	−30.1758	−0.995951
$919$	8.34764	0.275363	0.137682	−	0.990477i	$-0.456035\pi$
$919$	8.34764	0.275363	0.137682	+	0.990477i	$0.456035\pi$
$920$	81.5979	2.69020
$921$	43.0009	1.41693
$922$	46.7039	1.53811
$923$	−22.4880	−0.740203
$924$	0	0
$925$	1.94000	0.0637869
$926$	−70.3588	−2.31213
$927$	5.67072	0.186251
$928$	256.973	8.43556
$929$	−0.466316	−0.0152993	−0.00764966	−	0.999971i	$-0.502435\pi$
$929$	−0.466316	−0.0152993	−0.00764966	+	0.999971i	$0.502435\pi$
$930$	26.2266	0.860003
$931$	0	0
$932$	−22.8315	−0.747870
$933$	43.0512	1.40943
$934$	−19.1377	−0.626203
$935$	1.94078	0.0634703
$936$	−20.4480	−0.668365
$937$	40.2058	1.31347	0.656734	−	0.754123i	$-0.271938\pi$
$937$	40.2058	1.31347	0.656734	+	0.754123i	$0.271938\pi$
$938$	0	0
$939$	−10.5487	−0.344244
$940$	4.00179	0.130524
$941$	6.60752	0.215399	0.107699	−	0.994183i	$-0.465652\pi$
$941$	6.60752	0.215399	0.107699	+	0.994183i	$0.465652\pi$
$942$	76.3597	2.48793
$943$	11.5124	0.374897
$944$	111.180	3.61860
$945$	0	0
$946$	1.15332	0.0374975
$947$	−14.5784	−0.473736	−0.236868	−	0.971542i	$-0.576121\pi$
$947$	−14.5784	−0.473736	−0.236868	+	0.971542i	$0.576121\pi$
$948$	61.5254	1.99825
$949$	−35.5627	−1.15441
$950$	11.8577	0.384714
$951$	9.36716	0.303751
$952$	0	0
$953$	41.4296	1.34204	0.671018	−	0.741441i	$-0.265857\pi$
$953$	41.4296	1.34204	0.671018	+	0.741441i	$0.265857\pi$
$954$	−0.557718	−0.0180568
$955$	8.15526	0.263898
$956$	−121.605	−3.93298
$957$	−14.2814	−0.461652
$958$	−12.1418	−0.392283
$959$	0	0
$960$	64.7180	2.08876
$961$	6.63040	0.213884
$962$	16.6829	0.537879
$963$	−7.31018	−0.235567
$964$	18.6109	0.599416
$965$	−0.141539	−0.00455630
$966$	0	0
$967$	18.6861	0.600905	0.300453	−	0.953797i	$-0.402862\pi$
$967$	18.6861	0.600905	0.300453	+	0.953797i	$0.402862\pi$
$968$	10.3859	0.333815
$969$	12.7209	0.408654
$970$	32.4121	1.04069
$971$	−53.7928	−1.72629	−0.863147	−	0.504953i	$-0.831510\pi$
$971$	−53.7928	−1.72629	−0.863147	+	0.504953i	$0.831510\pi$
$972$	−37.2526	−1.19488
$973$	0	0
$974$	−117.294	−3.75835
$975$	−4.75348	−0.152233
$976$	10.0673	0.322248
$977$	41.9693	1.34272	0.671358	−	0.741134i	$-0.265711\pi$
$977$	41.9693	1.34272	0.671358	+	0.741134i	$0.265711\pi$
$978$	40.5941	1.29806
$979$	8.87704	0.283712
$980$	0	0
$981$	−2.79282	−0.0891678
$982$	1.11114	0.0354578
$983$	−10.1449	−0.323573	−0.161786	−	0.986826i	$-0.551726\pi$
$983$	−10.1449	−0.323573	−0.161786	+	0.986826i	$0.551726\pi$
$984$	23.3956	0.745824
$985$	6.53406	0.208192
$986$	−50.1424	−1.59686
$987$	0	0
$988$	75.6018	2.40521
$989$	−3.25812	−0.103602
$990$	1.77079	0.0562796
$991$	−36.4438	−1.15768	−0.578838	−	0.815443i	$-0.696494\pi$
$991$	−36.4438	−1.15768	−0.578838	+	0.815443i	$0.696494\pi$
$992$	169.685	5.38751
$993$	−17.4557	−0.553941
$994$	0	0
$995$	16.6729	0.528566
$996$	−144.380	−4.57485
$997$	42.2055	1.33666	0.668331	−	0.743864i	$-0.267009\pi$
$997$	42.2055	1.33666	0.668331	+	0.743864i	$0.267009\pi$
$998$	95.3741	3.01902
$999$	10.8460	0.343153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.y.1.10		10
7.2	even	3		385.2.i.d.221.1	✓	20
7.4	even	3		385.2.i.d.331.1	yes	20
7.6	odd	2		2695.2.a.z.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.d.221.1	✓	20	7.2	even	3
385.2.i.d.331.1	yes	20	7.4	even	3
2695.2.a.y.1.10		10	1.1	even	1	trivial
2695.2.a.z.1.10		10	7.6	odd	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q+2.78109 q^{2} -1.53729 q^{3} +5.73447 q^{4} -1.00000 q^{5} -4.27536 q^{6} +10.3859 q^{8} -0.636727 q^{9} +O(q^{10})\)	\(q+2.78109 q^{2} -1.53729 q^{3} +5.73447 q^{4} -1.00000 q^{5} -4.27536 q^{6} +10.3859 q^{8} -0.636727 q^{9} -2.78109 q^{10} +1.00000 q^{11} -8.81557 q^{12} +3.09211 q^{13} +1.53729 q^{15} +17.4152 q^{16} -1.94078 q^{17} -1.77079 q^{18} +4.26368 q^{19} -5.73447 q^{20} +2.78109 q^{22} -7.85660 q^{23} -15.9662 q^{24} +1.00000 q^{25} +8.59943 q^{26} +5.59072 q^{27} +9.28995 q^{29} +4.27536 q^{30} +6.13436 q^{31} +27.6614 q^{32} -1.53729 q^{33} -5.39749 q^{34} -3.65129 q^{36} +1.94000 q^{37} +11.8577 q^{38} -4.75348 q^{39} -10.3859 q^{40} -1.46532 q^{41} +0.414699 q^{43} +5.73447 q^{44} +0.636727 q^{45} -21.8499 q^{46} -0.697848 q^{47} -26.7723 q^{48} +2.78109 q^{50} +2.98355 q^{51} +17.7316 q^{52} +0.314954 q^{53} +15.5483 q^{54} -1.00000 q^{55} -6.55453 q^{57} +25.8362 q^{58} +6.38408 q^{59} +8.81557 q^{60} +0.578079 q^{61} +17.0602 q^{62} +42.0986 q^{64} -3.09211 q^{65} -4.27536 q^{66} -4.08268 q^{67} -11.1293 q^{68} +12.0779 q^{69} -7.27272 q^{71} -6.61298 q^{72} -11.5011 q^{73} +5.39533 q^{74} -1.53729 q^{75} +24.4499 q^{76} -13.2199 q^{78} -6.97918 q^{79} -17.4152 q^{80} -6.68440 q^{81} -4.07519 q^{82} +16.3778 q^{83} +1.94078 q^{85} +1.15332 q^{86} -14.2814 q^{87} +10.3859 q^{88} +8.87704 q^{89} +1.77079 q^{90} -45.0534 q^{92} -9.43032 q^{93} -1.94078 q^{94} -4.26368 q^{95} -42.5238 q^{96} -11.6545 q^{97} -0.636727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9	\( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9 - 3 * q^10 + 10 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^15 + 21 * q^16 - 5 * q^17 + q^18 + q^19 - 15 * q^20 + 3 * q^22 + 18 * q^23 + 10 * q^24 + 10 * q^25 + 13 * q^26 - 15 * q^27 + 14 * q^29 - 5 * q^30 + 10 * q^31 + 46 * q^32 - 3 * q^33 - 2 * q^34 + 26 * q^36 + 13 * q^37 + 9 * q^38 + 3 * q^39 - 9 * q^40 - 7 * q^41 + 6 * q^43 + 15 * q^44 - 19 * q^45 + 10 * q^46 + q^47 - 35 * q^48 + 3 * q^50 + 9 * q^51 - 17 * q^52 + 16 * q^53 + 73 * q^54 - 10 * q^55 + 12 * q^57 - 9 * q^58 + 13 * q^59 + 3 * q^60 + 18 * q^61 + 14 * q^62 + 43 * q^64 + 6 * q^65 + 5 * q^66 + 29 * q^67 + 13 * q^68 + 19 * q^71 - 48 * q^72 - 31 * q^73 - 8 * q^74 - 3 * q^75 - 8 * q^76 + 3 * q^78 - 21 * q^80 + 42 * q^81 + q^82 - 2 * q^83 + 5 * q^85 + 10 * q^86 - 50 * q^87 + 9 * q^88 + 23 * q^89 - q^90 + 14 * q^92 + 4 * q^93 - 5 * q^94 - q^95 + 39 * q^96 - 43 * q^97 + 19 * q^99

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