LMFDB - Embedded newform 1875.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.44400625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 $ x^6 - 11x^4 - x^3 + 29x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.246759$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.246759 q^{2} +1.00000 q^{3} -1.93911 q^{4} -0.246759 q^{6} +1.24676 q^{7} +0.972011 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.246759 q^{2} +1.00000 q^{3} -1.93911 q^{4} -0.246759 q^{6} +1.24676 q^{7} +0.972011 q^{8} +1.00000 q^{9} +2.56971 q^{11} -1.93911 q^{12} +4.68126 q^{13} -0.307649 q^{14} +3.63837 q^{16} -5.83914 q^{17} -0.246759 q^{18} +4.16857 q^{19} +1.24676 q^{21} -0.634099 q^{22} -1.60547 q^{23} +0.972011 q^{24} -1.15514 q^{26} +1.00000 q^{27} -2.41760 q^{28} -3.21573 q^{29} -9.19312 q^{31} -2.84182 q^{32} +2.56971 q^{33} +1.44086 q^{34} -1.93911 q^{36} +1.27778 q^{37} -1.02863 q^{38} +4.68126 q^{39} +8.69592 q^{41} -0.307649 q^{42} +3.88086 q^{43} -4.98295 q^{44} +0.396163 q^{46} +3.20952 q^{47} +3.63837 q^{48} -5.44559 q^{49} -5.83914 q^{51} -9.07748 q^{52} +13.3343 q^{53} -0.246759 q^{54} +1.21186 q^{56} +4.16857 q^{57} +0.793511 q^{58} -6.39279 q^{59} +3.82692 q^{61} +2.26848 q^{62} +1.24676 q^{63} -6.57549 q^{64} -0.634099 q^{66} +10.1238 q^{67} +11.3227 q^{68} -1.60547 q^{69} +13.8791 q^{71} +0.972011 q^{72} +11.3814 q^{73} -0.315305 q^{74} -8.08332 q^{76} +3.20381 q^{77} -1.15514 q^{78} +11.4832 q^{79} +1.00000 q^{81} -2.14580 q^{82} +2.83229 q^{83} -2.41760 q^{84} -0.957636 q^{86} -3.21573 q^{87} +2.49779 q^{88} -1.38077 q^{89} +5.83641 q^{91} +3.11318 q^{92} -9.19312 q^{93} -0.791979 q^{94} -2.84182 q^{96} -0.0305081 q^{97} +1.34375 q^{98} +2.56971 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9	$ 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 10 q^{12} + 6 q^{13} - 22 q^{14} + 18 q^{16} + 13 q^{17} + 11 q^{19} + 6 q^{21} + 16 q^{22} + 13 q^{23} + 3 q^{24} - 28 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} - 11 q^{31} + 16 q^{32} + 3 q^{33} + 15 q^{34} + 10 q^{36} + 21 q^{37} - 9 q^{38} + 6 q^{39} - q^{41} - 22 q^{42} + 2 q^{43} + 9 q^{44} + 19 q^{46} + 14 q^{47} + 18 q^{48} - 14 q^{49} + 13 q^{51} + 13 q^{52} + 23 q^{53} - 35 q^{56} + 11 q^{57} + 22 q^{58} + 9 q^{59} + 11 q^{61} - 23 q^{62} + 6 q^{63} - 23 q^{64} + 16 q^{66} + 8 q^{67} + 50 q^{68} + 13 q^{69} - 8 q^{71} + 3 q^{72} + 13 q^{73} - 22 q^{74} - 26 q^{76} - 13 q^{77} - 28 q^{78} - 5 q^{79} + 6 q^{81} - 13 q^{82} - 20 q^{83} + 7 q^{84} - 37 q^{86} - 3 q^{87} + 28 q^{88} - 4 q^{89} + 34 q^{91} + 61 q^{92} - 11 q^{93} + 41 q^{94} + 16 q^{96} - 7 q^{97} - 41 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 10 * q^12 + 6 * q^13 - 22 * q^14 + 18 * q^16 + 13 * q^17 + 11 * q^19 + 6 * q^21 + 16 * q^22 + 13 * q^23 + 3 * q^24 - 28 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 - 11 * q^31 + 16 * q^32 + 3 * q^33 + 15 * q^34 + 10 * q^36 + 21 * q^37 - 9 * q^38 + 6 * q^39 - q^41 - 22 * q^42 + 2 * q^43 + 9 * q^44 + 19 * q^46 + 14 * q^47 + 18 * q^48 - 14 * q^49 + 13 * q^51 + 13 * q^52 + 23 * q^53 - 35 * q^56 + 11 * q^57 + 22 * q^58 + 9 * q^59 + 11 * q^61 - 23 * q^62 + 6 * q^63 - 23 * q^64 + 16 * q^66 + 8 * q^67 + 50 * q^68 + 13 * q^69 - 8 * q^71 + 3 * q^72 + 13 * q^73 - 22 * q^74 - 26 * q^76 - 13 * q^77 - 28 * q^78 - 5 * q^79 + 6 * q^81 - 13 * q^82 - 20 * q^83 + 7 * q^84 - 37 * q^86 - 3 * q^87 + 28 * q^88 - 4 * q^89 + 34 * q^91 + 61 * q^92 - 11 * q^93 + 41 * q^94 + 16 * q^96 - 7 * q^97 - 41 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.246759	−0.174485	−0.0872425	−	0.996187i	$-0.527805\pi$
$2$	−0.246759	−0.174485	−0.0872425	+	0.996187i	$0.527805\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.93911	−0.969555
$5$	0	0
$5$	0	0
$6$	−0.246759	−0.100739
$7$	1.24676	0.471231	0.235615	−	0.971846i	$-0.424289\pi$
$7$	1.24676	0.471231	0.235615	+	0.971846i	$0.424289\pi$
$8$	0.972011	0.343658
$9$	1.00000	0.333333
$10$	0	0
$11$	2.56971	0.774797	0.387398	−	0.921912i	$-0.373374\pi$
$11$	2.56971	0.774797	0.387398	+	0.921912i	$0.373374\pi$
$12$	−1.93911	−0.559773
$13$	4.68126	1.29835	0.649174	−	0.760640i	$-0.275115\pi$
$13$	4.68126	1.29835	0.649174	+	0.760640i	$0.275115\pi$
$14$	−0.307649	−0.0822226
$15$	0	0
$16$	3.63837	0.909592
$17$	−5.83914	−1.41620	−0.708100	−	0.706112i	$-0.750447\pi$
$17$	−5.83914	−1.41620	−0.708100	+	0.706112i	$0.750447\pi$
$18$	−0.246759	−0.0581616
$19$	4.16857	0.956336	0.478168	−	0.878268i	$-0.341301\pi$
$19$	4.16857	0.956336	0.478168	+	0.878268i	$0.341301\pi$
$20$	0	0
$21$	1.24676	0.272065
$22$	−0.634099	−0.135190
$23$	−1.60547	−0.334763	−0.167382	−	0.985892i	$-0.553531\pi$
$23$	−1.60547	−0.334763	−0.167382	+	0.985892i	$0.553531\pi$
$24$	0.972011	0.198411
$25$	0	0
$26$	−1.15514	−0.226542
$27$	1.00000	0.192450
$28$	−2.41760	−0.456884
$29$	−3.21573	−0.597147	−0.298573	−	0.954387i	$-0.596511\pi$
$29$	−3.21573	−0.597147	−0.298573	+	0.954387i	$0.596511\pi$
$30$	0	0
$31$	−9.19312	−1.65113	−0.825566	−	0.564305i	$-0.809144\pi$
$31$	−9.19312	−1.65113	−0.825566	+	0.564305i	$0.809144\pi$
$32$	−2.84182	−0.502368
$33$	2.56971	0.447329
$34$	1.44086	0.247106
$35$	0	0
$36$	−1.93911	−0.323185
$37$	1.27778	0.210066	0.105033	−	0.994469i	$-0.466505\pi$
$37$	1.27778	0.210066	0.105033	+	0.994469i	$0.466505\pi$
$38$	−1.02863	−0.166866
$39$	4.68126	0.749602
$40$	0	0
$41$	8.69592	1.35808	0.679038	−	0.734104i	$-0.262397\pi$
$41$	8.69592	1.35808	0.679038	+	0.734104i	$0.262397\pi$
$42$	−0.307649	−0.0474713
$43$	3.88086	0.591825	0.295913	−	0.955215i	$-0.404376\pi$
$43$	3.88086	0.591825	0.295913	+	0.955215i	$0.404376\pi$
$44$	−4.98295	−0.751208
$45$	0	0
$46$	0.396163	0.0584111
$47$	3.20952	0.468157	0.234079	−	0.972218i	$-0.424793\pi$
$47$	3.20952	0.468157	0.234079	+	0.972218i	$0.424793\pi$
$48$	3.63837	0.525153
$49$	−5.44559	−0.777942
$50$	0	0
$51$	−5.83914	−0.817643
$52$	−9.07748	−1.25882
$53$	13.3343	1.83161	0.915803	−	0.401628i	$-0.131556\pi$
$53$	13.3343	1.83161	0.915803	+	0.401628i	$0.131556\pi$
$54$	−0.246759	−0.0335796
$55$	0	0
$56$	1.21186	0.161942
$57$	4.16857	0.552141
$58$	0.793511	0.104193
$59$	−6.39279	−0.832270	−0.416135	−	0.909303i	$-0.636616\pi$
$59$	−6.39279	−0.832270	−0.416135	+	0.909303i	$0.636616\pi$
$60$	0	0
$61$	3.82692	0.489986	0.244993	−	0.969525i	$-0.421214\pi$
$61$	3.82692	0.489986	0.244993	+	0.969525i	$0.421214\pi$
$62$	2.26848	0.288098
$63$	1.24676	0.157077
$64$	−6.57549	−0.821936
$65$	0	0
$66$	−0.634099	−0.0780522
$67$	10.1238	1.23682	0.618411	−	0.785855i	$-0.287777\pi$
$67$	10.1238	1.23682	0.618411	+	0.785855i	$0.287777\pi$
$68$	11.3227	1.37308
$69$	−1.60547	−0.193276
$70$	0	0
$71$	13.8791	1.64715	0.823574	−	0.567209i	$-0.191977\pi$
$71$	13.8791	1.64715	0.823574	+	0.567209i	$0.191977\pi$
$72$	0.972011	0.114553
$73$	11.3814	1.33209	0.666045	−	0.745912i	$-0.267986\pi$
$73$	11.3814	1.33209	0.666045	+	0.745912i	$0.267986\pi$
$74$	−0.315305	−0.0366534
$75$	0	0
$76$	−8.08332	−0.927220
$77$	3.20381	0.365108
$78$	−1.15514	−0.130794
$79$	11.4832	1.29196	0.645979	−	0.763355i	$-0.276449\pi$
$79$	11.4832	1.29196	0.645979	+	0.763355i	$0.276449\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.14580	−0.236964
$83$	2.83229	0.310884	0.155442	−	0.987845i	$-0.450320\pi$
$83$	2.83229	0.310884	0.155442	+	0.987845i	$0.450320\pi$
$84$	−2.41760	−0.263782
$85$	0	0
$86$	−0.957636	−0.103265
$87$	−3.21573	−0.344763
$88$	2.49779	0.266265
$89$	−1.38077	−0.146362	−0.0731808	−	0.997319i	$-0.523315\pi$
$89$	−1.38077	−0.146362	−0.0731808	+	0.997319i	$0.523315\pi$
$90$	0	0
$91$	5.83641	0.611822
$92$	3.11318	0.324571
$93$	−9.19312	−0.953282
$94$	−0.791979	−0.0816864
$95$	0	0
$96$	−2.84182	−0.290042
$97$	−0.0305081	−0.00309763	−0.00154881	−	0.999999i	$-0.500493\pi$
$97$	−0.0305081	−0.00309763	−0.00154881	+	0.999999i	$0.500493\pi$
$98$	1.34375	0.135739
$99$	2.56971	0.258266
$100$	0	0
$101$	−11.2308	−1.11750	−0.558751	−	0.829336i	$-0.688719\pi$
$101$	−11.2308	−1.11750	−0.558751	+	0.829336i	$0.688719\pi$
$102$	1.44086	0.142666
$103$	0.720983	0.0710406	0.0355203	−	0.999369i	$-0.488691\pi$
$103$	0.720983	0.0710406	0.0355203	+	0.999369i	$0.488691\pi$
$104$	4.55024	0.446187
$105$	0	0
$106$	−3.29036	−0.319588
$107$	−2.11668	−0.204627	−0.102313	−	0.994752i	$-0.532624\pi$
$107$	−2.11668	−0.204627	−0.102313	+	0.994752i	$0.532624\pi$
$108$	−1.93911	−0.186591
$109$	2.23483	0.214058	0.107029	−	0.994256i	$-0.465866\pi$
$109$	2.23483	0.214058	0.107029	+	0.994256i	$0.465866\pi$
$110$	0	0
$111$	1.27778	0.121282
$112$	4.53617	0.428628
$113$	3.14940	0.296270	0.148135	−	0.988967i	$-0.452673\pi$
$113$	3.14940	0.296270	0.148135	+	0.988967i	$0.452673\pi$
$114$	−1.02863	−0.0963402
$115$	0	0
$116$	6.23566	0.578967
$117$	4.68126	0.432783
$118$	1.57748	0.145219
$119$	−7.28000	−0.667357
$120$	0	0
$121$	−4.39659	−0.399690
$122$	−0.944326	−0.0854952
$123$	8.69592	0.784085
$124$	17.8265	1.60086
$125$	0	0
$126$	−0.307649	−0.0274075
$127$	15.6603	1.38962	0.694812	−	0.719191i	$-0.255487\pi$
$127$	15.6603	1.38962	0.694812	+	0.719191i	$0.255487\pi$
$128$	7.30620	0.645783
$129$	3.88086	0.341691
$130$	0	0
$131$	−14.9564	−1.30675	−0.653374	−	0.757036i	$-0.726647\pi$
$131$	−14.9564	−1.30675	−0.653374	+	0.757036i	$0.726647\pi$
$132$	−4.98295	−0.433710
$133$	5.19720	0.450655
$134$	−2.49814	−0.215807
$135$	0	0
$136$	−5.67571	−0.486688
$137$	10.4946	0.896611	0.448305	−	0.893881i	$-0.352028\pi$
$137$	10.4946	0.896611	0.448305	+	0.893881i	$0.352028\pi$
$138$	0.396163	0.0337237
$139$	12.4508	1.05606	0.528030	−	0.849226i	$-0.322931\pi$
$139$	12.4508	1.05606	0.528030	+	0.849226i	$0.322931\pi$
$140$	0	0
$141$	3.20952	0.270291
$142$	−3.42480	−0.287402
$143$	12.0295	1.00596
$144$	3.63837	0.303197
$145$	0	0
$146$	−2.80846	−0.232430
$147$	−5.44559	−0.449145
$148$	−2.47776	−0.203671
$149$	−17.0680	−1.39826	−0.699131	−	0.714994i	$-0.746430\pi$
$149$	−17.0680	−1.39826	−0.699131	+	0.714994i	$0.746430\pi$
$150$	0	0
$151$	−1.57516	−0.128185	−0.0640923	−	0.997944i	$-0.520415\pi$
$151$	−1.57516	−0.128185	−0.0640923	+	0.997944i	$0.520415\pi$
$152$	4.05190	0.328652
$153$	−5.83914	−0.472067
$154$	−0.790569	−0.0637059
$155$	0	0
$156$	−9.07748	−0.726780
$157$	9.20058	0.734286	0.367143	−	0.930164i	$-0.380336\pi$
$157$	9.20058	0.734286	0.367143	+	0.930164i	$0.380336\pi$
$158$	−2.83358	−0.225427
$159$	13.3343	1.05748
$160$	0	0
$161$	−2.00163	−0.157751
$162$	−0.246759	−0.0193872
$163$	4.58076	0.358793	0.179396	−	0.983777i	$-0.442586\pi$
$163$	4.58076	0.358793	0.179396	+	0.983777i	$0.442586\pi$
$164$	−16.8624	−1.31673
$165$	0	0
$166$	−0.698893	−0.0542446
$167$	−0.142531	−0.0110294	−0.00551469	−	0.999985i	$-0.501755\pi$
$167$	−0.142531	−0.0110294	−0.00551469	+	0.999985i	$0.501755\pi$
$168$	1.21186	0.0934973
$169$	8.91422	0.685709
$170$	0	0
$171$	4.16857	0.318779
$172$	−7.52541	−0.573807
$173$	−24.6228	−1.87203	−0.936017	−	0.351954i	$-0.885517\pi$
$173$	−24.6228	−1.87203	−0.936017	+	0.351954i	$0.885517\pi$
$174$	0.793511	0.0601559
$175$	0	0
$176$	9.34955	0.704749
$177$	−6.39279	−0.480511
$178$	0.340718	0.0255379
$179$	−24.1553	−1.80545	−0.902726	−	0.430216i	$-0.858437\pi$
$179$	−24.1553	−1.80545	−0.902726	+	0.430216i	$0.858437\pi$
$180$	0	0
$181$	1.96805	0.146284	0.0731419	−	0.997322i	$-0.476697\pi$
$181$	1.96805	0.146284	0.0731419	+	0.997322i	$0.476697\pi$
$182$	−1.44019	−0.106754
$183$	3.82692	0.282894
$184$	−1.56053	−0.115044
$185$	0	0
$186$	2.26848	0.166333
$187$	−15.0049	−1.09727
$188$	−6.22362	−0.453904
$189$	1.24676	0.0906884
$190$	0	0
$191$	−7.76854	−0.562112	−0.281056	−	0.959691i	$-0.590685\pi$
$191$	−7.76854	−0.562112	−0.281056	+	0.959691i	$0.590685\pi$
$192$	−6.57549	−0.474545
$193$	−14.3458	−1.03264	−0.516318	−	0.856397i	$-0.672698\pi$
$193$	−14.3458	−1.03264	−0.516318	+	0.856397i	$0.672698\pi$
$194$	0.00752814	0.000540489 0
$195$	0	0
$196$	10.5596	0.754257
$197$	−0.163540	−0.0116517	−0.00582587	−	0.999983i	$-0.501854\pi$
$197$	−0.163540	−0.0116517	−0.00582587	+	0.999983i	$0.501854\pi$
$198$	−0.634099	−0.0450635
$199$	4.96974	0.352295	0.176148	−	0.984364i	$-0.443636\pi$
$199$	4.96974	0.352295	0.176148	+	0.984364i	$0.443636\pi$
$200$	0	0
$201$	10.1238	0.714079
$202$	2.77129	0.194987
$203$	−4.00925	−0.281394
$204$	11.3227	0.792750
$205$	0	0
$206$	−0.177909	−0.0123955
$207$	−1.60547	−0.111588
$208$	17.0322	1.18097
$209$	10.7120	0.740966
$210$	0	0
$211$	3.29381	0.226755	0.113378	−	0.993552i	$-0.463833\pi$
$211$	3.29381	0.226755	0.113378	+	0.993552i	$0.463833\pi$
$212$	−25.8567	−1.77584
$213$	13.8791	0.950981
$214$	0.522309	0.0357043
$215$	0	0
$216$	0.972011	0.0661369
$217$	−11.4616	−0.778064
$218$	−0.551465	−0.0373500
$219$	11.3814	0.769082
$220$	0	0
$221$	−27.3346	−1.83872
$222$	−0.315305	−0.0211619
$223$	15.7732	1.05625	0.528127	−	0.849166i	$-0.322895\pi$
$223$	15.7732	1.05625	0.528127	+	0.849166i	$0.322895\pi$
$224$	−3.54307	−0.236731
$225$	0	0
$226$	−0.777142	−0.0516947
$227$	−13.5406	−0.898721	−0.449360	−	0.893351i	$-0.648348\pi$
$227$	−13.5406	−0.898721	−0.449360	+	0.893351i	$0.648348\pi$
$228$	−8.08332	−0.535331
$229$	−14.7829	−0.976879	−0.488440	−	0.872598i	$-0.662434\pi$
$229$	−14.7829	−0.976879	−0.488440	+	0.872598i	$0.662434\pi$
$230$	0	0
$231$	3.20381	0.210795
$232$	−3.12573	−0.205214
$233$	−0.518980	−0.0339995	−0.0169998	−	0.999855i	$-0.505411\pi$
$233$	−0.518980	−0.0339995	−0.0169998	+	0.999855i	$0.505411\pi$
$234$	−1.15514	−0.0755141
$235$	0	0
$236$	12.3963	0.806932
$237$	11.4832	0.745912
$238$	1.79641	0.116444
$239$	8.23032	0.532375	0.266188	−	0.963921i	$-0.414236\pi$
$239$	8.23032	0.532375	0.266188	+	0.963921i	$0.414236\pi$
$240$	0	0
$241$	−1.28118	−0.0825280	−0.0412640	−	0.999148i	$-0.513138\pi$
$241$	−1.28118	−0.0825280	−0.0412640	+	0.999148i	$0.513138\pi$
$242$	1.08490	0.0697398
$243$	1.00000	0.0641500
$244$	−7.42081	−0.475069
$245$	0	0
$246$	−2.14580	−0.136811
$247$	19.5142	1.24166
$248$	−8.93581	−0.567424
$249$	2.83229	0.179489
$250$	0	0
$251$	4.63494	0.292555	0.146277	−	0.989244i	$-0.453271\pi$
$251$	4.63494	0.292555	0.146277	+	0.989244i	$0.453271\pi$
$252$	−2.41760	−0.152295
$253$	−4.12559	−0.259373
$254$	−3.86431	−0.242469
$255$	0	0
$256$	11.3481	0.709257
$257$	18.3001	1.14153	0.570766	−	0.821113i	$-0.306647\pi$
$257$	18.3001	1.14153	0.570766	+	0.821113i	$0.306647\pi$
$258$	−0.957636	−0.0596198
$259$	1.59309	0.0989897
$260$	0	0
$261$	−3.21573	−0.199049
$262$	3.69063	0.228008
$263$	−16.6666	−1.02771	−0.513854	−	0.857877i	$-0.671783\pi$
$263$	−16.6666	−1.02771	−0.513854	+	0.857877i	$0.671783\pi$
$264$	2.49779	0.153728
$265$	0	0
$266$	−1.28246	−0.0786324
$267$	−1.38077	−0.0845020
$268$	−19.6312	−1.19917
$269$	2.63211	0.160483	0.0802414	−	0.996775i	$-0.474431\pi$
$269$	2.63211	0.160483	0.0802414	+	0.996775i	$0.474431\pi$
$270$	0	0
$271$	4.56346	0.277210	0.138605	−	0.990348i	$-0.455738\pi$
$271$	4.56346	0.277210	0.138605	+	0.990348i	$0.455738\pi$
$272$	−21.2449	−1.28816
$273$	5.83641	0.353235
$274$	−2.58963	−0.156445
$275$	0	0
$276$	3.11318	0.187391
$277$	−1.25926	−0.0756614	−0.0378307	−	0.999284i	$-0.512045\pi$
$277$	−1.25926	−0.0756614	−0.0378307	+	0.999284i	$0.512045\pi$
$278$	−3.07234	−0.184266
$279$	−9.19312	−0.550378
$280$	0	0
$281$	13.4167	0.800370	0.400185	−	0.916434i	$-0.368946\pi$
$281$	13.4167	0.800370	0.400185	+	0.916434i	$0.368946\pi$
$282$	−0.791979	−0.0471617
$283$	−24.0890	−1.43194	−0.715971	−	0.698130i	$-0.754016\pi$
$283$	−24.0890	−1.43194	−0.715971	+	0.698130i	$0.754016\pi$
$284$	−26.9131	−1.59700
$285$	0	0
$286$	−2.96838	−0.175524
$287$	10.8417	0.639966
$288$	−2.84182	−0.167456
$289$	17.0956	1.00562
$290$	0	0
$291$	−0.0305081	−0.00178841
$292$	−22.0697	−1.29153
$293$	32.1727	1.87955	0.939776	−	0.341792i	$-0.111034\pi$
$293$	32.1727	1.87955	0.939776	+	0.341792i	$0.111034\pi$
$294$	1.34375	0.0783690
$295$	0	0
$296$	1.24202	0.0721909
$297$	2.56971	0.149110
$298$	4.21167	0.243976
$299$	−7.51561	−0.434639
$300$	0	0
$301$	4.83849	0.278886
$302$	0.388685	0.0223663
$303$	−11.2308	−0.645190
$304$	15.1668	0.869875
$305$	0	0
$306$	1.44086	0.0823685
$307$	−20.2962	−1.15837	−0.579183	−	0.815198i	$-0.696628\pi$
$307$	−20.2962	−1.15837	−0.579183	+	0.815198i	$0.696628\pi$
$308$	−6.21254	−0.353992
$309$	0.720983	0.0410153
$310$	0	0
$311$	−18.7224	−1.06165	−0.530825	−	0.847481i	$-0.678118\pi$
$311$	−18.7224	−1.06165	−0.530825	+	0.847481i	$0.678118\pi$
$312$	4.55024	0.257606
$313$	−24.8839	−1.40652	−0.703261	−	0.710932i	$-0.748274\pi$
$313$	−24.8839	−1.40652	−0.703261	+	0.710932i	$0.748274\pi$
$314$	−2.27033	−0.128122
$315$	0	0
$316$	−22.2671	−1.25262
$317$	25.1880	1.41470	0.707350	−	0.706863i	$-0.249890\pi$
$317$	25.1880	1.41470	0.707350	+	0.706863i	$0.249890\pi$
$318$	−3.29036	−0.184514
$319$	−8.26351	−0.462668
$320$	0	0
$321$	−2.11668	−0.118141
$322$	0.493920	0.0275251
$323$	−24.3409	−1.35436
$324$	−1.93911	−0.107728
$325$	0	0
$326$	−1.13034	−0.0626039
$327$	2.23483	0.123587
$328$	8.45253	0.466713
$329$	4.00150	0.220610
$330$	0	0
$331$	30.4193	1.67199	0.835997	−	0.548735i	$-0.184890\pi$
$331$	30.4193	1.67199	0.835997	+	0.548735i	$0.184890\pi$
$332$	−5.49212	−0.301419
$333$	1.27778	0.0700221
$334$	0.0351708	0.00192446
$335$	0	0
$336$	4.53617	0.247468
$337$	4.57455	0.249192	0.124596	−	0.992208i	$-0.460237\pi$
$337$	4.57455	0.249192	0.124596	+	0.992208i	$0.460237\pi$
$338$	−2.19966	−0.119646
$339$	3.14940	0.171052
$340$	0	0
$341$	−23.6237	−1.27929
$342$	−1.02863	−0.0556221
$343$	−15.5167	−0.837821
$344$	3.77224	0.203385
$345$	0	0
$346$	6.07589	0.326642
$347$	16.8153	0.902691	0.451346	−	0.892349i	$-0.350944\pi$
$347$	16.8153	0.902691	0.451346	+	0.892349i	$0.350944\pi$
$348$	6.23566	0.334267
$349$	0.373581	0.0199973	0.00999866	−	0.999950i	$-0.496817\pi$
$349$	0.373581	0.0199973	0.00999866	+	0.999950i	$0.496817\pi$
$350$	0	0
$351$	4.68126	0.249867
$352$	−7.30266	−0.389233
$353$	23.9685	1.27572	0.637858	−	0.770154i	$-0.279821\pi$
$353$	23.9685	1.27572	0.637858	+	0.770154i	$0.279821\pi$
$354$	1.57748	0.0838420
$355$	0	0
$356$	2.67747	0.141906
$357$	−7.28000	−0.385299
$358$	5.96054	0.315024
$359$	−4.75020	−0.250706	−0.125353	−	0.992112i	$-0.540006\pi$
$359$	−4.75020	−0.250706	−0.125353	+	0.992112i	$0.540006\pi$
$360$	0	0
$361$	−1.62302	−0.0854221
$362$	−0.485633	−0.0255243
$363$	−4.39659	−0.230761
$364$	−11.3174	−0.593195
$365$	0	0
$366$	−0.944326	−0.0493607
$367$	17.3700	0.906706	0.453353	−	0.891331i	$-0.350228\pi$
$367$	17.3700	0.906706	0.453353	+	0.891331i	$0.350228\pi$
$368$	−5.84128	−0.304498
$369$	8.69592	0.452692
$370$	0	0
$371$	16.6246	0.863109
$372$	17.8265	0.924259
$373$	−2.10877	−0.109188	−0.0545939	−	0.998509i	$-0.517386\pi$
$373$	−2.10877	−0.109188	−0.0545939	+	0.998509i	$0.517386\pi$
$374$	3.70260	0.191457
$375$	0	0
$376$	3.11969	0.160886
$377$	−15.0537	−0.775305
$378$	−0.307649	−0.0158238
$379$	12.4090	0.637405	0.318703	−	0.947855i	$-0.396753\pi$
$379$	12.4090	0.637405	0.318703	+	0.947855i	$0.396753\pi$
$380$	0	0
$381$	15.6603	0.802300
$382$	1.91696	0.0980801
$383$	−33.3056	−1.70184	−0.850919	−	0.525297i	$-0.823954\pi$
$383$	−33.3056	−1.70184	−0.850919	+	0.525297i	$0.823954\pi$
$384$	7.30620	0.372843
$385$	0	0
$386$	3.53996	0.180179
$387$	3.88086	0.197275
$388$	0.0591585	0.00300332
$389$	−16.9777	−0.860802	−0.430401	−	0.902638i	$-0.641628\pi$
$389$	−16.9777	−0.860802	−0.430401	+	0.902638i	$0.641628\pi$
$390$	0	0
$391$	9.37455	0.474091
$392$	−5.29317	−0.267346
$393$	−14.9564	−0.754451
$394$	0.0403549	0.00203305
$395$	0	0
$396$	−4.98295	−0.250403
$397$	0.866570	0.0434919	0.0217460	−	0.999764i	$-0.493078\pi$
$397$	0.866570	0.0434919	0.0217460	+	0.999764i	$0.493078\pi$
$398$	−1.22633	−0.0614702
$399$	5.19720	0.260186
$400$	0	0
$401$	9.68680	0.483736	0.241868	−	0.970309i	$-0.422240\pi$
$401$	9.68680	0.483736	0.241868	+	0.970309i	$0.422240\pi$
$402$	−2.49814	−0.124596
$403$	−43.0354	−2.14375
$404$	21.7777	1.08348
$405$	0	0
$406$	0.989317	0.0490990
$407$	3.28353	0.162759
$408$	−5.67571	−0.280989
$409$	1.51785	0.0750531	0.0375265	−	0.999296i	$-0.488052\pi$
$409$	1.51785	0.0750531	0.0375265	+	0.999296i	$0.488052\pi$
$410$	0	0
$411$	10.4946	0.517658
$412$	−1.39807	−0.0688778
$413$	−7.97027	−0.392191
$414$	0.396163	0.0194704
$415$	0	0
$416$	−13.3033	−0.652249
$417$	12.4508	0.609716
$418$	−2.64329	−0.129287
$419$	−30.5620	−1.49305	−0.746526	−	0.665356i	$-0.768280\pi$
$419$	−30.5620	−1.49305	−0.746526	+	0.665356i	$0.768280\pi$
$420$	0	0
$421$	−6.97162	−0.339776	−0.169888	−	0.985463i	$-0.554341\pi$
$421$	−6.97162	−0.339776	−0.169888	+	0.985463i	$0.554341\pi$
$422$	−0.812777	−0.0395654
$423$	3.20952	0.156052
$424$	12.9611	0.629445
$425$	0	0
$426$	−3.42480	−0.165932
$427$	4.77124	0.230897
$428$	4.10447	0.198397
$429$	12.0295	0.580789
$430$	0	0
$431$	10.9472	0.527310	0.263655	−	0.964617i	$-0.415072\pi$
$431$	10.9472	0.527310	0.263655	+	0.964617i	$0.415072\pi$
$432$	3.63837	0.175051
$433$	−10.4393	−0.501683	−0.250841	−	0.968028i	$-0.580707\pi$
$433$	−10.4393	−0.501683	−0.250841	+	0.968028i	$0.580707\pi$
$434$	2.82825	0.135761
$435$	0	0
$436$	−4.33359	−0.207541
$437$	−6.69250	−0.320146
$438$	−2.80846	−0.134193
$439$	15.4334	0.736594	0.368297	−	0.929708i	$-0.379941\pi$
$439$	15.4334	0.736594	0.368297	+	0.929708i	$0.379941\pi$
$440$	0	0
$441$	−5.44559	−0.259314
$442$	6.74505	0.320829
$443$	−18.9105	−0.898463	−0.449231	−	0.893415i	$-0.648302\pi$
$443$	−18.9105	−0.898463	−0.449231	+	0.893415i	$0.648302\pi$
$444$	−2.47776	−0.117589
$445$	0	0
$446$	−3.89218	−0.184300
$447$	−17.0680	−0.807287
$448$	−8.19805	−0.387322
$449$	−11.4152	−0.538714	−0.269357	−	0.963040i	$-0.586811\pi$
$449$	−11.4152	−0.538714	−0.269357	+	0.963040i	$0.586811\pi$
$450$	0	0
$451$	22.3460	1.05223
$452$	−6.10703	−0.287250
$453$	−1.57516	−0.0740074
$454$	3.34126	0.156813
$455$	0	0
$456$	4.05190	0.189747
$457$	33.9739	1.58923	0.794616	−	0.607112i	$-0.207672\pi$
$457$	33.9739	1.58923	0.794616	+	0.607112i	$0.207672\pi$
$458$	3.64780	0.170451
$459$	−5.83914	−0.272548
$460$	0	0
$461$	−24.6907	−1.14996	−0.574981	−	0.818167i	$-0.694991\pi$
$461$	−24.6907	−1.14996	−0.574981	+	0.818167i	$0.694991\pi$
$462$	−0.790569	−0.0367806
$463$	13.6315	0.633510	0.316755	−	0.948507i	$-0.397407\pi$
$463$	13.6315	0.633510	0.316755	+	0.948507i	$0.397407\pi$
$464$	−11.7000	−0.543160
$465$	0	0
$466$	0.128063	0.00593241
$467$	−9.47115	−0.438272	−0.219136	−	0.975694i	$-0.570324\pi$
$467$	−9.47115	−0.438272	−0.219136	+	0.975694i	$0.570324\pi$
$468$	−9.07748	−0.419607
$469$	12.6220	0.582828
$470$	0	0
$471$	9.20058	0.423940
$472$	−6.21386	−0.286016
$473$	9.97268	0.458544
$474$	−2.83358	−0.130150
$475$	0	0
$476$	14.1167	0.647039
$477$	13.3343	0.610535
$478$	−2.03091	−0.0928914
$479$	−25.7286	−1.17557	−0.587784	−	0.809018i	$-0.700000\pi$
$479$	−25.7286	−1.17557	−0.587784	+	0.809018i	$0.700000\pi$
$480$	0	0
$481$	5.98164	0.272739
$482$	0.316142	0.0143999
$483$	−2.00163	−0.0910773
$484$	8.52546	0.387521
$485$	0	0
$486$	−0.246759	−0.0111932
$487$	28.4046	1.28714	0.643568	−	0.765389i	$-0.277453\pi$
$487$	28.4046	1.28714	0.643568	+	0.765389i	$0.277453\pi$
$488$	3.71980	0.168388
$489$	4.58076	0.207149
$490$	0	0
$491$	−6.10299	−0.275424	−0.137712	−	0.990472i	$-0.543975\pi$
$491$	−6.10299	−0.275424	−0.137712	+	0.990472i	$0.543975\pi$
$492$	−16.8624	−0.760214
$493$	18.7771	0.845679
$494$	−4.81530	−0.216650
$495$	0	0
$496$	−33.4479	−1.50186
$497$	17.3039	0.776186
$498$	−0.698893	−0.0313181
$499$	−20.3163	−0.909481	−0.454740	−	0.890624i	$-0.650268\pi$
$499$	−20.3163	−0.909481	−0.454740	+	0.890624i	$0.650268\pi$
$500$	0	0
$501$	−0.142531	−0.00636782
$502$	−1.14371	−0.0510464
$503$	−14.6267	−0.652171	−0.326085	−	0.945340i	$-0.605730\pi$
$503$	−14.6267	−0.652171	−0.326085	+	0.945340i	$0.605730\pi$
$504$	1.21186	0.0539807
$505$	0	0
$506$	1.01803	0.0452567
$507$	8.91422	0.395894
$508$	−30.3670	−1.34732
$509$	−4.30584	−0.190853	−0.0954265	−	0.995436i	$-0.530422\pi$
$509$	−4.30584	−0.190853	−0.0954265	+	0.995436i	$0.530422\pi$
$510$	0	0
$511$	14.1898	0.627721
$512$	−17.4127	−0.769538
$513$	4.16857	0.184047
$514$	−4.51572	−0.199180
$515$	0	0
$516$	−7.52541	−0.331288
$517$	8.24755	0.362727
$518$	−0.393109	−0.0172722
$519$	−24.6228	−1.08082
$520$	0	0
$521$	−39.6413	−1.73672	−0.868358	−	0.495938i	$-0.834824\pi$
$521$	−39.6413	−1.73672	−0.868358	+	0.495938i	$0.834824\pi$
$522$	0.793511	0.0347310
$523$	−36.2874	−1.58674	−0.793369	−	0.608741i	$-0.791675\pi$
$523$	−36.2874	−1.58674	−0.793369	+	0.608741i	$0.791675\pi$
$524$	29.0021	1.26696
$525$	0	0
$526$	4.11264	0.179320
$527$	53.6799	2.33833
$528$	9.34955	0.406887
$529$	−20.4225	−0.887934
$530$	0	0
$531$	−6.39279	−0.277423
$532$	−10.0779	−0.436934
$533$	40.7079	1.76325
$534$	0.340718	0.0147443
$535$	0	0
$536$	9.84046	0.425043
$537$	−24.1553	−1.04238
$538$	−0.649497	−0.0280018
$539$	−13.9936	−0.602747
$540$	0	0
$541$	−38.6044	−1.65973	−0.829866	−	0.557962i	$-0.811583\pi$
$541$	−38.6044	−1.65973	−0.829866	+	0.557962i	$0.811583\pi$
$542$	−1.12607	−0.0483690
$543$	1.96805	0.0844570
$544$	16.5938	0.711453
$545$	0	0
$546$	−1.44019	−0.0616343
$547$	−10.3620	−0.443047	−0.221524	−	0.975155i	$-0.571103\pi$
$547$	−10.3620	−0.443047	−0.221524	+	0.975155i	$0.571103\pi$
$548$	−20.3501	−0.869313
$549$	3.82692	0.163329
$550$	0	0
$551$	−13.4050	−0.571073
$552$	−1.56053	−0.0664206
$553$	14.3167	0.608810
$554$	0.310733	0.0132018
$555$	0	0
$556$	−24.1434	−1.02391
$557$	−12.6830	−0.537398	−0.268699	−	0.963224i	$-0.586594\pi$
$557$	−12.6830	−0.537398	−0.268699	+	0.963224i	$0.586594\pi$
$558$	2.26848	0.0960326
$559$	18.1673	0.768396
$560$	0	0
$561$	−15.0049	−0.633508
$562$	−3.31068	−0.139653
$563$	−13.0892	−0.551645	−0.275823	−	0.961209i	$-0.588950\pi$
$563$	−13.0892	−0.551645	−0.275823	+	0.961209i	$0.588950\pi$
$564$	−6.22362	−0.262062
$565$	0	0
$566$	5.94417	0.249852
$567$	1.24676	0.0523590
$568$	13.4906	0.566055
$569$	−2.58803	−0.108496	−0.0542478	−	0.998528i	$-0.517276\pi$
$569$	−2.58803	−0.108496	−0.0542478	+	0.998528i	$0.517276\pi$
$570$	0	0
$571$	−10.5754	−0.442568	−0.221284	−	0.975209i	$-0.571025\pi$
$571$	−10.5754	−0.442568	−0.221284	+	0.975209i	$0.571025\pi$
$572$	−23.3265	−0.975330
$573$	−7.76854	−0.324536
$574$	−2.67529	−0.111665
$575$	0	0
$576$	−6.57549	−0.273979
$577$	0.0142904	0.000594917 0	0.000297458	−	1.00000i	$-0.499905\pi$
$577$	0.0142904	0.000594917 0	0.000297458		1.00000i	$0.499905\pi$
$578$	−4.21849	−0.175466
$579$	−14.3458	−0.596193
$580$	0	0
$581$	3.53118	0.146498
$582$	0.00752814	0.000312051 0
$583$	34.2653	1.41912
$584$	11.0628	0.457783
$585$	0	0
$586$	−7.93891	−0.327953
$587$	22.6389	0.934408	0.467204	−	0.884149i	$-0.345261\pi$
$587$	22.6389	0.934408	0.467204	+	0.884149i	$0.345261\pi$
$588$	10.5596	0.435471
$589$	−38.3222	−1.57904
$590$	0	0
$591$	−0.163540	−0.00672713
$592$	4.64905	0.191075
$593$	−12.7423	−0.523264	−0.261632	−	0.965168i	$-0.584261\pi$
$593$	−12.7423	−0.523264	−0.261632	+	0.965168i	$0.584261\pi$
$594$	−0.634099	−0.0260174
$595$	0	0
$596$	33.0967	1.35569
$597$	4.96974	0.203398
$598$	1.85454	0.0758380
$599$	−6.83599	−0.279311	−0.139656	−	0.990200i	$-0.544600\pi$
$599$	−6.83599	−0.279311	−0.139656	+	0.990200i	$0.544600\pi$
$600$	0	0
$601$	31.8422	1.29887	0.649435	−	0.760417i	$-0.275005\pi$
$601$	31.8422	1.29887	0.649435	+	0.760417i	$0.275005\pi$
$602$	−1.19394	−0.0486614
$603$	10.1238	0.412274
$604$	3.05441	0.124282
$605$	0	0
$606$	2.77129	0.112576
$607$	−27.7763	−1.12741	−0.563703	−	0.825977i	$-0.690624\pi$
$607$	−27.7763	−1.12741	−0.563703	+	0.825977i	$0.690624\pi$
$608$	−11.8463	−0.480432
$609$	−4.00925	−0.162463
$610$	0	0
$611$	15.0246	0.607831
$612$	11.3227	0.457695
$613$	3.61694	0.146087	0.0730433	−	0.997329i	$-0.476729\pi$
$613$	3.61694	0.146087	0.0730433	+	0.997329i	$0.476729\pi$
$614$	5.00827	0.202117
$615$	0	0
$616$	3.11414	0.125472
$617$	−44.6425	−1.79724	−0.898621	−	0.438727i	$-0.855430\pi$
$617$	−44.6425	−1.79724	−0.898621	+	0.438727i	$0.855430\pi$
$618$	−0.177909	−0.00715655
$619$	20.5085	0.824307	0.412153	−	0.911115i	$-0.364777\pi$
$619$	20.5085	0.824307	0.412153	+	0.911115i	$0.364777\pi$
$620$	0	0
$621$	−1.60547	−0.0644252
$622$	4.61992	0.185242
$623$	−1.72149	−0.0689701
$624$	17.0322	0.681832
$625$	0	0
$626$	6.14033	0.245417
$627$	10.7120	0.427797
$628$	−17.8409	−0.711931
$629$	−7.46116	−0.297496
$630$	0	0
$631$	−37.7357	−1.50223	−0.751117	−	0.660169i	$-0.770485\pi$
$631$	−37.7357	−1.50223	−0.751117	+	0.660169i	$0.770485\pi$
$632$	11.1618	0.443991
$633$	3.29381	0.130917
$634$	−6.21537	−0.246844
$635$	0	0
$636$	−25.8567	−1.02528
$637$	−25.4922	−1.01004
$638$	2.03909	0.0807285
$639$	13.8791	0.549049
$640$	0	0
$641$	−9.18606	−0.362828	−0.181414	−	0.983407i	$-0.558067\pi$
$641$	−9.18606	−0.362828	−0.181414	+	0.983407i	$0.558067\pi$
$642$	0.522309	0.0206139
$643$	−3.42111	−0.134915	−0.0674577	−	0.997722i	$-0.521489\pi$
$643$	−3.42111	−0.134915	−0.0674577	+	0.997722i	$0.521489\pi$
$644$	3.88138	0.152948
$645$	0	0
$646$	6.00633	0.236316
$647$	−3.26735	−0.128453	−0.0642264	−	0.997935i	$-0.520458\pi$
$647$	−3.26735	−0.128453	−0.0642264	+	0.997935i	$0.520458\pi$
$648$	0.972011	0.0381842
$649$	−16.4276	−0.644840
$650$	0	0
$651$	−11.4616	−0.449216
$652$	−8.88259	−0.347869
$653$	−12.6362	−0.494494	−0.247247	−	0.968952i	$-0.579526\pi$
$653$	−12.6362	−0.494494	−0.247247	+	0.968952i	$0.579526\pi$
$654$	−0.551465	−0.0215640
$655$	0	0
$656$	31.6390	1.23529
$657$	11.3814	0.444030
$658$	−0.987407	−0.0384931
$659$	−9.14896	−0.356393	−0.178197	−	0.983995i	$-0.557026\pi$
$659$	−9.14896	−0.356393	−0.178197	+	0.983995i	$0.557026\pi$
$660$	0	0
$661$	6.39083	0.248574	0.124287	−	0.992246i	$-0.460336\pi$
$661$	6.39083	0.248574	0.124287	+	0.992246i	$0.460336\pi$
$662$	−7.50622	−0.291738
$663$	−27.3346	−1.06159
$664$	2.75302	0.106838
$665$	0	0
$666$	−0.315305	−0.0122178
$667$	5.16276	0.199903
$668$	0.276383	0.0106936
$669$	15.7732	0.609828
$670$	0	0
$671$	9.83407	0.379640
$672$	−3.54307	−0.136677
$673$	33.7063	1.29928	0.649641	−	0.760241i	$-0.274919\pi$
$673$	33.7063	1.29928	0.649641	+	0.760241i	$0.274919\pi$
$674$	−1.12881	−0.0434802
$675$	0	0
$676$	−17.2857	−0.664833
$677$	−9.20340	−0.353715	−0.176858	−	0.984236i	$-0.556593\pi$
$677$	−9.20340	−0.353715	−0.176858	+	0.984236i	$0.556593\pi$
$678$	−0.777142	−0.0298459
$679$	−0.0380362	−0.00145970
$680$	0	0
$681$	−13.5406	−0.518877
$682$	5.82935	0.223217
$683$	−27.2216	−1.04161	−0.520803	−	0.853677i	$-0.674367\pi$
$683$	−27.2216	−1.04161	−0.520803	+	0.853677i	$0.674367\pi$
$684$	−8.08332	−0.309073
$685$	0	0
$686$	3.82887	0.146187
$687$	−14.7829	−0.564001
$688$	14.1200	0.538320
$689$	62.4213	2.37806
$690$	0	0
$691$	29.8238	1.13455	0.567276	−	0.823528i	$-0.307997\pi$
$691$	29.8238	1.13455	0.567276	+	0.823528i	$0.307997\pi$
$692$	47.7463	1.81504
$693$	3.20381	0.121703
$694$	−4.14932	−0.157506
$695$	0	0
$696$	−3.12573	−0.118480
$697$	−50.7767	−1.92331
$698$	−0.0921844	−0.00348923
$699$	−0.518980	−0.0196296
$700$	0	0
$701$	−19.1081	−0.721704	−0.360852	−	0.932623i	$-0.617514\pi$
$701$	−19.1081	−0.721704	−0.360852	+	0.932623i	$0.617514\pi$
$702$	−1.15514	−0.0435981
$703$	5.32653	0.200894
$704$	−16.8971	−0.636834
$705$	0	0
$706$	−5.91445	−0.222593
$707$	−14.0020	−0.526601
$708$	12.3963	0.465882
$709$	14.5146	0.545107	0.272553	−	0.962141i	$-0.412132\pi$
$709$	14.5146	0.545107	0.272553	+	0.962141i	$0.412132\pi$
$710$	0	0
$711$	11.4832	0.430653
$712$	−1.34213	−0.0502983
$713$	14.7592	0.552738
$714$	1.79641	0.0672288
$715$	0	0
$716$	46.8398	1.75048
$717$	8.23032	0.307367
$718$	1.17215	0.0437444
$719$	34.7507	1.29598	0.647992	−	0.761647i	$-0.275609\pi$
$719$	34.7507	1.29598	0.647992	+	0.761647i	$0.275609\pi$
$720$	0	0
$721$	0.898892	0.0334765
$722$	0.400494	0.0149049
$723$	−1.28118	−0.0476476
$724$	−3.81626	−0.141830
$725$	0	0
$726$	1.08490	0.0402643
$727$	−42.6279	−1.58098	−0.790490	−	0.612475i	$-0.790174\pi$
$727$	−42.6279	−1.58098	−0.790490	+	0.612475i	$0.790174\pi$
$728$	5.67305	0.210257
$729$	1.00000	0.0370370
$730$	0	0
$731$	−22.6609	−0.838143
$732$	−7.42081	−0.274281
$733$	−1.96230	−0.0724793	−0.0362397	−	0.999343i	$-0.511538\pi$
$733$	−1.96230	−0.0724793	−0.0362397	+	0.999343i	$0.511538\pi$
$734$	−4.28620	−0.158207
$735$	0	0
$736$	4.56245	0.168174
$737$	26.0153	0.958286
$738$	−2.14580	−0.0789879
$739$	12.3601	0.454672	0.227336	−	0.973816i	$-0.426998\pi$
$739$	12.3601	0.454672	0.227336	+	0.973816i	$0.426998\pi$
$740$	0	0
$741$	19.5142	0.716871
$742$	−4.10228	−0.150599
$743$	−8.63742	−0.316876	−0.158438	−	0.987369i	$-0.550646\pi$
$743$	−8.63742	−0.316876	−0.158438	+	0.987369i	$0.550646\pi$
$744$	−8.93581	−0.327603
$745$	0	0
$746$	0.520357	0.0190516
$747$	2.83229	0.103628
$748$	29.0962	1.06386
$749$	−2.63898	−0.0964264
$750$	0	0
$751$	−24.3654	−0.889105	−0.444552	−	0.895753i	$-0.646637\pi$
$751$	−24.3654	−0.889105	−0.444552	+	0.895753i	$0.646637\pi$
$752$	11.6774	0.425832
$753$	4.63494	0.168906
$754$	3.71463	0.135279
$755$	0	0
$756$	−2.41760	−0.0879274
$757$	5.18352	0.188398	0.0941991	−	0.995553i	$-0.469971\pi$
$757$	5.18352	0.188398	0.0941991	+	0.995553i	$0.469971\pi$
$758$	−3.06202	−0.111218
$759$	−4.12559	−0.149749
$760$	0	0
$761$	31.2636	1.13331	0.566653	−	0.823957i	$-0.308238\pi$
$761$	31.2636	1.13331	0.566653	+	0.823957i	$0.308238\pi$
$762$	−3.86431	−0.139989
$763$	2.78630	0.100871
$764$	15.0641	0.544999
$765$	0	0
$766$	8.21846	0.296945
$767$	−29.9263	−1.08058
$768$	11.3481	0.409490
$769$	−44.1891	−1.59350	−0.796750	−	0.604309i	$-0.793449\pi$
$769$	−44.1891	−1.59350	−0.796750	+	0.604309i	$0.793449\pi$
$770$	0	0
$771$	18.3001	0.659063
$772$	27.8182	1.00120
$773$	21.5881	0.776471	0.388236	−	0.921560i	$-0.373085\pi$
$773$	21.5881	0.776471	0.388236	+	0.921560i	$0.373085\pi$
$774$	−0.957636	−0.0344215
$775$	0	0
$776$	−0.0296542	−0.00106452
$777$	1.59309	0.0571517
$778$	4.18939	0.150197
$779$	36.2496	1.29878
$780$	0	0
$781$	35.6653	1.27621
$782$	−2.31325	−0.0827218
$783$	−3.21573	−0.114921
$784$	−19.8131	−0.707610
$785$	0	0
$786$	3.69063	0.131640
$787$	−14.4212	−0.514059	−0.257029	−	0.966404i	$-0.582744\pi$
$787$	−14.4212	−0.514059	−0.257029	+	0.966404i	$0.582744\pi$
$788$	0.317122	0.0112970
$789$	−16.6666	−0.593348
$790$	0	0
$791$	3.92654	0.139612
$792$	2.49779	0.0887550
$793$	17.9148	0.636173
$794$	−0.213834	−0.00758868
$795$	0	0
$796$	−9.63687	−0.341570
$797$	39.4567	1.39763	0.698814	−	0.715304i	$-0.253712\pi$
$797$	39.4567	1.39763	0.698814	+	0.715304i	$0.253712\pi$
$798$	−1.28246	−0.0453985
$799$	−18.7409	−0.663004
$800$	0	0
$801$	−1.38077	−0.0487872
$802$	−2.39031	−0.0844046
$803$	29.2469	1.03210
$804$	−19.6312	−0.692339
$805$	0	0
$806$	10.6194	0.374051
$807$	2.63211	0.0926547
$808$	−10.9164	−0.384038
$809$	−5.96204	−0.209614	−0.104807	−	0.994493i	$-0.533423\pi$
$809$	−5.96204	−0.209614	−0.104807	+	0.994493i	$0.533423\pi$
$810$	0	0
$811$	−39.1764	−1.37567	−0.687835	−	0.725867i	$-0.741439\pi$
$811$	−39.1764	−1.37567	−0.687835	+	0.725867i	$0.741439\pi$
$812$	7.77437	0.272827
$813$	4.56346	0.160048
$814$	−0.810242	−0.0283990
$815$	0	0
$816$	−21.2449	−0.743722
$817$	16.1776	0.565984
$818$	−0.374544	−0.0130956
$819$	5.83641	0.203941
$820$	0	0
$821$	20.6329	0.720092	0.360046	−	0.932934i	$-0.382761\pi$
$821$	20.6329	0.720092	0.360046	+	0.932934i	$0.382761\pi$
$822$	−2.58963	−0.0903236
$823$	−39.0162	−1.36002	−0.680009	−	0.733203i	$-0.738024\pi$
$823$	−39.0162	−1.36002	−0.680009	+	0.733203i	$0.738024\pi$
$824$	0.700803	0.0244136
$825$	0	0
$826$	1.96673	0.0684314
$827$	−19.5976	−0.681474	−0.340737	−	0.940159i	$-0.610677\pi$
$827$	−19.5976	−0.681474	−0.340737	+	0.940159i	$0.610677\pi$
$828$	3.11318	0.108190
$829$	−8.67511	−0.301299	−0.150650	−	0.988587i	$-0.548136\pi$
$829$	−8.67511	−0.301299	−0.150650	+	0.988587i	$0.548136\pi$
$830$	0	0
$831$	−1.25926	−0.0436831
$832$	−30.7816	−1.06716
$833$	31.7976	1.10172
$834$	−3.07234	−0.106386
$835$	0	0
$836$	−20.7718	−0.718407
$837$	−9.19312	−0.317761
$838$	7.54145	0.260515
$839$	−3.85921	−0.133235	−0.0666173	−	0.997779i	$-0.521221\pi$
$839$	−3.85921	−0.133235	−0.0666173	+	0.997779i	$0.521221\pi$
$840$	0	0
$841$	−18.6591	−0.643416
$842$	1.72031	0.0592858
$843$	13.4167	0.462094
$844$	−6.38706	−0.219852
$845$	0	0
$846$	−0.791979	−0.0272288
$847$	−5.48148	−0.188346
$848$	48.5151	1.66601
$849$	−24.0890	−0.826732
$850$	0	0
$851$	−2.05144	−0.0703224
$852$	−26.9131	−0.922029
$853$	29.7898	1.01998	0.509991	−	0.860180i	$-0.329649\pi$
$853$	29.7898	1.01998	0.509991	+	0.860180i	$0.329649\pi$
$854$	−1.17735	−0.0402880
$855$	0	0
$856$	−2.05743	−0.0703216
$857$	−36.2041	−1.23671	−0.618354	−	0.785899i	$-0.712200\pi$
$857$	−36.2041	−1.23671	−0.618354	+	0.785899i	$0.712200\pi$
$858$	−2.96838	−0.101339
$859$	−37.6533	−1.28471	−0.642357	−	0.766406i	$-0.722043\pi$
$859$	−37.6533	−1.28471	−0.642357	+	0.766406i	$0.722043\pi$
$860$	0	0
$861$	10.8417	0.369485
$862$	−2.70133	−0.0920077
$863$	2.49913	0.0850715	0.0425357	−	0.999095i	$-0.486456\pi$
$863$	2.49913	0.0850715	0.0425357	+	0.999095i	$0.486456\pi$
$864$	−2.84182	−0.0966807
$865$	0	0
$866$	2.57600	0.0875361
$867$	17.0956	0.580596
$868$	22.2253	0.754376
$869$	29.5084	1.00100
$870$	0	0
$871$	47.3923	1.60583
$872$	2.17228	0.0735628
$873$	−0.0305081	−0.00103254
$874$	1.65143	0.0558606
$875$	0	0
$876$	−22.0697	−0.745668
$877$	32.4491	1.09573	0.547864	−	0.836567i	$-0.315441\pi$
$877$	32.4491	1.09573	0.547864	+	0.836567i	$0.315441\pi$
$878$	−3.80832	−0.128525
$879$	32.1727	1.08516
$880$	0	0
$881$	−33.2625	−1.12064	−0.560321	−	0.828275i	$-0.689322\pi$
$881$	−33.2625	−1.12064	−0.560321	+	0.828275i	$0.689322\pi$
$882$	1.34375	0.0452464
$883$	10.9730	0.369269	0.184635	−	0.982807i	$-0.440890\pi$
$883$	10.9730	0.369269	0.184635	+	0.982807i	$0.440890\pi$
$884$	53.0047	1.78274
$885$	0	0
$886$	4.66632	0.156768
$887$	26.0052	0.873168	0.436584	−	0.899664i	$-0.356188\pi$
$887$	26.0052	0.873168	0.436584	+	0.899664i	$0.356188\pi$
$888$	1.24202	0.0416794
$889$	19.5246	0.654834
$890$	0	0
$891$	2.56971	0.0860886
$892$	−30.5860	−1.02410
$893$	13.3791	0.447715
$894$	4.21167	0.140859
$895$	0	0
$896$	9.10907	0.304313
$897$	−7.51561	−0.250939
$898$	2.81679	0.0939975
$899$	29.5626	0.985969
$900$	0	0
$901$	−77.8608	−2.59392
$902$	−5.51408	−0.183599
$903$	4.83849	0.161015
$904$	3.06125	0.101816
$905$	0	0
$906$	0.388685	0.0129132
$907$	55.0108	1.82660	0.913302	−	0.407283i	$-0.133524\pi$
$907$	55.0108	1.82660	0.913302	+	0.407283i	$0.133524\pi$
$908$	26.2567	0.871359
$909$	−11.2308	−0.372501
$910$	0	0
$911$	−12.1075	−0.401139	−0.200569	−	0.979679i	$-0.564279\pi$
$911$	−12.1075	−0.401139	−0.200569	+	0.979679i	$0.564279\pi$
$912$	15.1668	0.502223
$913$	7.27817	0.240872
$914$	−8.38337	−0.277297
$915$	0	0
$916$	28.6656	0.947138
$917$	−18.6470	−0.615779
$918$	1.44086	0.0475555
$919$	5.97191	0.196995	0.0984975	−	0.995137i	$-0.468596\pi$
$919$	5.97191	0.196995	0.0984975	+	0.995137i	$0.468596\pi$
$920$	0	0
$921$	−20.2962	−0.668783
$922$	6.09266	0.200651
$923$	64.9718	2.13857
$924$	−6.21254	−0.204378
$925$	0	0
$926$	−3.36370	−0.110538
$927$	0.720983	0.0236802
$928$	9.13854	0.299987
$929$	46.8756	1.53794	0.768970	−	0.639285i	$-0.220770\pi$
$929$	46.8756	1.53794	0.768970	+	0.639285i	$0.220770\pi$
$930$	0	0
$931$	−22.7003	−0.743973
$932$	1.00636	0.0329644
$933$	−18.7224	−0.612944
$934$	2.33709	0.0764719
$935$	0	0
$936$	4.55024	0.148729
$937$	19.4335	0.634864	0.317432	−	0.948281i	$-0.397179\pi$
$937$	19.4335	0.634864	0.317432	+	0.948281i	$0.397179\pi$
$938$	−3.11458	−0.101695
$939$	−24.8839	−0.812056
$940$	0	0
$941$	21.7097	0.707717	0.353858	−	0.935299i	$-0.384870\pi$
$941$	21.7097	0.707717	0.353858	+	0.935299i	$0.384870\pi$
$942$	−2.27033	−0.0739712
$943$	−13.9610	−0.454633
$944$	−23.2593	−0.757026
$945$	0	0
$946$	−2.46085	−0.0800091
$947$	6.31560	0.205229	0.102615	−	0.994721i	$-0.467279\pi$
$947$	6.31560	0.205229	0.102615	+	0.994721i	$0.467279\pi$
$948$	−22.2671	−0.723203
$949$	53.2792	1.72952
$950$	0	0
$951$	25.1880	0.816778
$952$	−7.07624	−0.229342
$953$	−21.8017	−0.706227	−0.353114	−	0.935580i	$-0.614877\pi$
$953$	−21.8017	−0.706227	−0.353114	+	0.935580i	$0.614877\pi$
$954$	−3.29036	−0.106529
$955$	0	0
$956$	−15.9595	−0.516167
$957$	−8.26351	−0.267121
$958$	6.34876	0.205119
$959$	13.0842	0.422510
$960$	0	0
$961$	53.5134	1.72624
$962$	−1.47602	−0.0475889
$963$	−2.11668	−0.0682089
$964$	2.48435	0.0800154
$965$	0	0
$966$	0.493920	0.0158916
$967$	7.01268	0.225513	0.112756	−	0.993623i	$-0.464032\pi$
$967$	7.01268	0.225513	0.112756	+	0.993623i	$0.464032\pi$
$968$	−4.27353	−0.137356
$969$	−24.3409	−0.781942
$970$	0	0
$971$	7.41028	0.237807	0.118904	−	0.992906i	$-0.462062\pi$
$971$	7.41028	0.237807	0.118904	+	0.992906i	$0.462062\pi$
$972$	−1.93911	−0.0621970
$973$	15.5231	0.497647
$974$	−7.00909	−0.224586
$975$	0	0
$976$	13.9237	0.445688
$977$	−39.2585	−1.25599	−0.627995	−	0.778217i	$-0.716124\pi$
$977$	−39.2585	−1.25599	−0.627995	+	0.778217i	$0.716124\pi$
$978$	−1.13034	−0.0361444
$979$	−3.54819	−0.113401
$980$	0	0
$981$	2.23483	0.0713528
$982$	1.50597	0.0480573
$983$	18.3827	0.586317	0.293159	−	0.956064i	$-0.405294\pi$
$983$	18.3827	0.586317	0.293159	+	0.956064i	$0.405294\pi$
$984$	8.45253	0.269457
$985$	0	0
$986$	−4.63343	−0.147558
$987$	4.00150	0.127369
$988$	−37.8401	−1.20385
$989$	−6.23059	−0.198121
$990$	0	0
$991$	52.4658	1.66663	0.833316	−	0.552797i	$-0.186440\pi$
$991$	52.4658	1.66663	0.833316	+	0.552797i	$0.186440\pi$
$992$	26.1252	0.829476
$993$	30.4193	0.965326
$994$	−4.26989	−0.135433
$995$	0	0
$996$	−5.49212	−0.174025
$997$	36.3720	1.15191	0.575956	−	0.817480i	$-0.304630\pi$
$997$	36.3720	1.15191	0.575956	+	0.817480i	$0.304630\pi$
$998$	5.01322	0.158691
$999$	1.27778	0.0404273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.k.1.3		6
3.2	odd	2		5625.2.a.q.1.4		6
5.2	odd	4		1875.2.b.f.1249.5		12
5.3	odd	4		1875.2.b.f.1249.8		12
5.4	even	2		1875.2.a.j.1.4		6
15.14	odd	2		5625.2.a.p.1.3		6
25.2	odd	20		375.2.i.d.274.3		24
25.9	even	10		75.2.g.c.31.2	✓	12
25.11	even	5		375.2.g.c.226.2		12
25.12	odd	20		375.2.i.d.349.4		24
25.13	odd	20		375.2.i.d.349.3		24
25.14	even	10		75.2.g.c.46.2	yes	12
25.16	even	5		375.2.g.c.151.2		12
25.23	odd	20		375.2.i.d.274.4		24
75.14	odd	10		225.2.h.d.46.2		12
75.59	odd	10		225.2.h.d.181.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.2	✓	12	25.9	even	10
75.2.g.c.46.2	yes	12	25.14	even	10
225.2.h.d.46.2		12	75.14	odd	10
225.2.h.d.181.2		12	75.59	odd	10
375.2.g.c.151.2		12	25.16	even	5
375.2.g.c.226.2		12	25.11	even	5
375.2.i.d.274.3		24	25.2	odd	20
375.2.i.d.274.4		24	25.23	odd	20
375.2.i.d.349.3		24	25.13	odd	20
375.2.i.d.349.4		24	25.12	odd	20
1875.2.a.j.1.4		6	5.4	even	2
1875.2.a.k.1.3		6	1.1	even	1	trivial
1875.2.b.f.1249.5		12	5.2	odd	4
1875.2.b.f.1249.8		12	5.3	odd	4
5625.2.a.p.1.3		6	15.14	odd	2
5625.2.a.q.1.4		6	3.2	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-0.246759 q^{2} +1.00000 q^{3} -1.93911 q^{4} -0.246759 q^{6} +1.24676 q^{7} +0.972011 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.246759 q^{2} +1.00000 q^{3} -1.93911 q^{4} -0.246759 q^{6} +1.24676 q^{7} +0.972011 q^{8} +1.00000 q^{9} +2.56971 q^{11} -1.93911 q^{12} +4.68126 q^{13} -0.307649 q^{14} +3.63837 q^{16} -5.83914 q^{17} -0.246759 q^{18} +4.16857 q^{19} +1.24676 q^{21} -0.634099 q^{22} -1.60547 q^{23} +0.972011 q^{24} -1.15514 q^{26} +1.00000 q^{27} -2.41760 q^{28} -3.21573 q^{29} -9.19312 q^{31} -2.84182 q^{32} +2.56971 q^{33} +1.44086 q^{34} -1.93911 q^{36} +1.27778 q^{37} -1.02863 q^{38} +4.68126 q^{39} +8.69592 q^{41} -0.307649 q^{42} +3.88086 q^{43} -4.98295 q^{44} +0.396163 q^{46} +3.20952 q^{47} +3.63837 q^{48} -5.44559 q^{49} -5.83914 q^{51} -9.07748 q^{52} +13.3343 q^{53} -0.246759 q^{54} +1.21186 q^{56} +4.16857 q^{57} +0.793511 q^{58} -6.39279 q^{59} +3.82692 q^{61} +2.26848 q^{62} +1.24676 q^{63} -6.57549 q^{64} -0.634099 q^{66} +10.1238 q^{67} +11.3227 q^{68} -1.60547 q^{69} +13.8791 q^{71} +0.972011 q^{72} +11.3814 q^{73} -0.315305 q^{74} -8.08332 q^{76} +3.20381 q^{77} -1.15514 q^{78} +11.4832 q^{79} +1.00000 q^{81} -2.14580 q^{82} +2.83229 q^{83} -2.41760 q^{84} -0.957636 q^{86} -3.21573 q^{87} +2.49779 q^{88} -1.38077 q^{89} +5.83641 q^{91} +3.11318 q^{92} -9.19312 q^{93} -0.791979 q^{94} -2.84182 q^{96} -0.0305081 q^{97} +1.34375 q^{98} +2.56971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 10 q^{12} + 6 q^{13} - 22 q^{14} + 18 q^{16} + 13 q^{17} + 11 q^{19} + 6 q^{21} + 16 q^{22} + 13 q^{23} + 3 q^{24} - 28 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} - 11 q^{31} + 16 q^{32} + 3 q^{33} + 15 q^{34} + 10 q^{36} + 21 q^{37} - 9 q^{38} + 6 q^{39} - q^{41} - 22 q^{42} + 2 q^{43} + 9 q^{44} + 19 q^{46} + 14 q^{47} + 18 q^{48} - 14 q^{49} + 13 q^{51} + 13 q^{52} + 23 q^{53} - 35 q^{56} + 11 q^{57} + 22 q^{58} + 9 q^{59} + 11 q^{61} - 23 q^{62} + 6 q^{63} - 23 q^{64} + 16 q^{66} + 8 q^{67} + 50 q^{68} + 13 q^{69} - 8 q^{71} + 3 q^{72} + 13 q^{73} - 22 q^{74} - 26 q^{76} - 13 q^{77} - 28 q^{78} - 5 q^{79} + 6 q^{81} - 13 q^{82} - 20 q^{83} + 7 q^{84} - 37 q^{86} - 3 q^{87} + 28 q^{88} - 4 q^{89} + 34 q^{91} + 61 q^{92} - 11 q^{93} + 41 q^{94} + 16 q^{96} - 7 q^{97} - 41 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 10 * q^12 + 6 * q^13 - 22 * q^14 + 18 * q^16 + 13 * q^17 + 11 * q^19 + 6 * q^21 + 16 * q^22 + 13 * q^23 + 3 * q^24 - 28 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 - 11 * q^31 + 16 * q^32 + 3 * q^33 + 15 * q^34 + 10 * q^36 + 21 * q^37 - 9 * q^38 + 6 * q^39 - q^41 - 22 * q^42 + 2 * q^43 + 9 * q^44 + 19 * q^46 + 14 * q^47 + 18 * q^48 - 14 * q^49 + 13 * q^51 + 13 * q^52 + 23 * q^53 - 35 * q^56 + 11 * q^57 + 22 * q^58 + 9 * q^59 + 11 * q^61 - 23 * q^62 + 6 * q^63 - 23 * q^64 + 16 * q^66 + 8 * q^67 + 50 * q^68 + 13 * q^69 - 8 * q^71 + 3 * q^72 + 13 * q^73 - 22 * q^74 - 26 * q^76 - 13 * q^77 - 28 * q^78 - 5 * q^79 + 6 * q^81 - 13 * q^82 - 20 * q^83 + 7 * q^84 - 37 * q^86 - 3 * q^87 + 28 * q^88 - 4 * q^89 + 34 * q^91 + 61 * q^92 - 11 * q^93 + 41 * q^94 + 16 * q^96 - 7 * q^97 - 41 * q^98 + 3 * q^99

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