LMFDB - Embedded newform 6223.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6223,2,Mod(1,6223)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6223, 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("6223.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6223 = 7^{2} \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6223.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:	$49.6909051778$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 8x^{5} + 15x^{4} + 17x^{3} - 28x^{2} - 11x + 15 $ x^7 - 2x^6 - 8x^5 + 15x^4 + 17x^3 - 28x^2 - 11x + 15
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 127)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.818322$ of defining polynomial
Character	$\chi$	$=$	6223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.818322 q^{2} -1.12872 q^{3} -1.33035 q^{4} -2.74338 q^{5} -0.923656 q^{6} -2.72530 q^{8} -1.72599 q^{9} +O(q^{10})$	\(q+0.818322 q^{2} -1.12872 q^{3} -1.33035 q^{4} -2.74338 q^{5} -0.923656 q^{6} -2.72530 q^{8} -1.72599 q^{9} -2.24497 q^{10} -0.266231 q^{11} +1.50159 q^{12} -3.28557 q^{13} +3.09650 q^{15} +0.430525 q^{16} +4.65292 q^{17} -1.41242 q^{18} +3.29662 q^{19} +3.64965 q^{20} -0.217863 q^{22} -1.80234 q^{23} +3.07609 q^{24} +2.52613 q^{25} -2.68866 q^{26} +5.33432 q^{27} +3.76272 q^{29} +2.53394 q^{30} +2.53611 q^{31} +5.80291 q^{32} +0.300500 q^{33} +3.80759 q^{34} +2.29617 q^{36} +0.0550810 q^{37} +2.69770 q^{38} +3.70849 q^{39} +7.47653 q^{40} -7.78083 q^{41} +3.55180 q^{43} +0.354180 q^{44} +4.73506 q^{45} -1.47489 q^{46} +6.62310 q^{47} -0.485941 q^{48} +2.06718 q^{50} -5.25184 q^{51} +4.37096 q^{52} +13.7361 q^{53} +4.36519 q^{54} +0.730373 q^{55} -3.72096 q^{57} +3.07912 q^{58} -13.5354 q^{59} -4.11943 q^{60} -9.30061 q^{61} +2.07535 q^{62} +3.88760 q^{64} +9.01357 q^{65} +0.245906 q^{66} +6.45752 q^{67} -6.19001 q^{68} +2.03433 q^{69} +2.95281 q^{71} +4.70385 q^{72} +11.8165 q^{73} +0.0450740 q^{74} -2.85129 q^{75} -4.38566 q^{76} +3.03474 q^{78} -11.4993 q^{79} -1.18109 q^{80} -0.842960 q^{81} -6.36722 q^{82} +0.0301401 q^{83} -12.7647 q^{85} +2.90652 q^{86} -4.24705 q^{87} +0.725560 q^{88} -2.02198 q^{89} +3.87480 q^{90} +2.39774 q^{92} -2.86255 q^{93} +5.41983 q^{94} -9.04388 q^{95} -6.54985 q^{96} -14.6568 q^{97} +0.459514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} + 3 q^{8} + 12 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 + 3 * q^8 + 12 * q^9	$ 7 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} + 3 q^{8} + 12 q^{9} + 5 q^{10} + q^{12} + q^{13} - 9 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 5 q^{19} - 11 q^{20} - 9 q^{22} - q^{23} + 24 q^{24} + 7 q^{25} + 4 q^{26} - 7 q^{29} - 43 q^{30} + 8 q^{31} - 2 q^{32} - 10 q^{33} + q^{34} + 10 q^{36} - 6 q^{37} - 29 q^{38} - 15 q^{39} + 3 q^{40} - 14 q^{41} - q^{43} - 21 q^{44} - 16 q^{45} - 3 q^{46} - 25 q^{47} - 2 q^{48} + 10 q^{50} + 17 q^{51} - 6 q^{52} + 29 q^{53} - q^{54} + 23 q^{55} + 4 q^{57} - 22 q^{58} + 12 q^{59} + 6 q^{60} - 7 q^{61} - 4 q^{62} - 3 q^{64} + 3 q^{65} - 36 q^{66} - 25 q^{67} - 53 q^{68} - 6 q^{69} + 7 q^{71} - 28 q^{72} - 13 q^{73} + 11 q^{74} - 12 q^{76} + 38 q^{78} - 23 q^{79} + 14 q^{80} - 5 q^{81} - 26 q^{82} - 26 q^{83} + 15 q^{85} + 5 q^{86} + 20 q^{87} + 25 q^{88} - 13 q^{89} + 24 q^{90} - 32 q^{92} - 7 q^{93} + 19 q^{94} - 40 q^{95} - 55 q^{96} + 5 q^{97} - 29 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 + 3 * q^8 + 12 * q^9 + 5 * q^10 + q^12 + q^13 - 9 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 5 * q^19 - 11 * q^20 - 9 * q^22 - q^23 + 24 * q^24 + 7 * q^25 + 4 * q^26 - 7 * q^29 - 43 * q^30 + 8 * q^31 - 2 * q^32 - 10 * q^33 + q^34 + 10 * q^36 - 6 * q^37 - 29 * q^38 - 15 * q^39 + 3 * q^40 - 14 * q^41 - q^43 - 21 * q^44 - 16 * q^45 - 3 * q^46 - 25 * q^47 - 2 * q^48 + 10 * q^50 + 17 * q^51 - 6 * q^52 + 29 * q^53 - q^54 + 23 * q^55 + 4 * q^57 - 22 * q^58 + 12 * q^59 + 6 * q^60 - 7 * q^61 - 4 * q^62 - 3 * q^64 + 3 * q^65 - 36 * q^66 - 25 * q^67 - 53 * q^68 - 6 * q^69 + 7 * q^71 - 28 * q^72 - 13 * q^73 + 11 * q^74 - 12 * q^76 + 38 * q^78 - 23 * q^79 + 14 * q^80 - 5 * q^81 - 26 * q^82 - 26 * q^83 + 15 * q^85 + 5 * q^86 + 20 * q^87 + 25 * q^88 - 13 * q^89 + 24 * q^90 - 32 * q^92 - 7 * q^93 + 19 * q^94 - 40 * q^95 - 55 * q^96 + 5 * q^97 - 29 * 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 $

$2$	0.818322	0.578641	0.289321	−	0.957232i	$-0.406571\pi$
$2$	0.818322	0.578641	0.289321	+	0.957232i	$0.406571\pi$
$3$	−1.12872	−0.651666	−0.325833	−	0.945427i	$-0.605645\pi$
$3$	−1.12872	−0.651666	−0.325833	+	0.945427i	$0.605645\pi$
$4$	−1.33035	−0.665174
$5$	−2.74338	−1.22688	−0.613438	−	0.789743i	$-0.710214\pi$
$5$	−2.74338	−1.22688	−0.613438	+	0.789743i	$0.710214\pi$
$6$	−0.923656	−0.377081
$7$	0	0
$7$	0	0
$8$	−2.72530	−0.963539
$9$	−1.72599	−0.575331
$10$	−2.24497	−0.709921
$11$	−0.266231	−0.0802717	−0.0401359	−	0.999194i	$-0.512779\pi$
$11$	−0.266231	−0.0802717	−0.0401359	+	0.999194i	$0.512779\pi$
$12$	1.50159	0.433471
$13$	−3.28557	−0.911254	−0.455627	−	0.890171i	$-0.650585\pi$
$13$	−3.28557	−0.911254	−0.455627	+	0.890171i	$0.650585\pi$
$14$	0	0
$15$	3.09650	0.799513
$16$	0.430525	0.107631
$17$	4.65292	1.12850	0.564250	−	0.825604i	$-0.309165\pi$
$17$	4.65292	1.12850	0.564250	+	0.825604i	$0.309165\pi$
$18$	−1.41242	−0.332911
$19$	3.29662	0.756297	0.378148	−	0.925745i	$-0.376561\pi$
$19$	3.29662	0.756297	0.378148	+	0.925745i	$0.376561\pi$
$20$	3.64965	0.816087
$21$	0	0
$22$	−0.217863	−0.0464485
$23$	−1.80234	−0.375814	−0.187907	−	0.982187i	$-0.560170\pi$
$23$	−1.80234	−0.375814	−0.187907	+	0.982187i	$0.560170\pi$
$24$	3.07609	0.627905
$25$	2.52613	0.505225
$26$	−2.68866	−0.527289
$27$	5.33432	1.02659
$28$	0	0
$29$	3.76272	0.698720	0.349360	−	0.936989i	$-0.386399\pi$
$29$	3.76272	0.698720	0.349360	+	0.936989i	$0.386399\pi$
$30$	2.53394	0.462631
$31$	2.53611	0.455498	0.227749	−	0.973720i	$-0.426863\pi$
$31$	2.53611	0.455498	0.227749	+	0.973720i	$0.426863\pi$
$32$	5.80291	1.02582
$33$	0.300500	0.0523104
$34$	3.80759	0.652996
$35$	0	0
$36$	2.29617	0.382696
$37$	0.0550810	0.00905525	0.00452763	−	0.999990i	$-0.498559\pi$
$37$	0.0550810	0.00905525	0.00452763	+	0.999990i	$0.498559\pi$
$38$	2.69770	0.437624
$39$	3.70849	0.593833
$40$	7.47653	1.18214
$41$	−7.78083	−1.21516	−0.607580	−	0.794258i	$-0.707860\pi$
$41$	−7.78083	−1.21516	−0.607580	+	0.794258i	$0.707860\pi$
$42$	0	0
$43$	3.55180	0.541645	0.270823	−	0.962629i	$-0.412704\pi$
$43$	3.55180	0.541645	0.270823	+	0.962629i	$0.412704\pi$
$44$	0.354180	0.0533947
$45$	4.73506	0.705860
$46$	−1.47489	−0.217461
$47$	6.62310	0.966078	0.483039	−	0.875599i	$-0.339533\pi$
$47$	6.62310	0.966078	0.483039	+	0.875599i	$0.339533\pi$
$48$	−0.485941	−0.0701396
$49$	0	0
$50$	2.06718	0.292344
$51$	−5.25184	−0.735405
$52$	4.37096	0.606143
$53$	13.7361	1.88680	0.943398	−	0.331664i	$-0.107610\pi$
$53$	13.7361	1.88680	0.943398	+	0.331664i	$0.107610\pi$
$54$	4.36519	0.594027
$55$	0.730373	0.0984835
$56$	0	0
$57$	−3.72096	−0.492853
$58$	3.07912	0.404308
$59$	−13.5354	−1.76216	−0.881082	−	0.472963i	$-0.843185\pi$
$59$	−13.5354	−1.76216	−0.881082	+	0.472963i	$0.843185\pi$
$60$	−4.11943	−0.531816
$61$	−9.30061	−1.19082	−0.595411	−	0.803421i	$-0.703011\pi$
$61$	−9.30061	−1.19082	−0.595411	+	0.803421i	$0.703011\pi$
$62$	2.07535	0.263570
$63$	0	0
$64$	3.88760	0.485950
$65$	9.01357	1.11800
$66$	0.245906	0.0302689
$67$	6.45752	0.788911	0.394456	−	0.918915i	$-0.370933\pi$
$67$	6.45752	0.788911	0.394456	+	0.918915i	$0.370933\pi$
$68$	−6.19001	−0.750649
$69$	2.03433	0.244905
$70$	0	0
$71$	2.95281	0.350434	0.175217	−	0.984530i	$-0.443937\pi$
$71$	2.95281	0.350434	0.175217	+	0.984530i	$0.443937\pi$
$72$	4.70385	0.554354
$73$	11.8165	1.38302	0.691509	−	0.722368i	$-0.256946\pi$
$73$	11.8165	1.38302	0.691509	+	0.722368i	$0.256946\pi$
$74$	0.0450740	0.00523974
$75$	−2.85129	−0.329238
$76$	−4.38566	−0.503069
$77$	0	0
$78$	3.03474	0.343616
$79$	−11.4993	−1.29378	−0.646888	−	0.762585i	$-0.723930\pi$
$79$	−11.4993	−1.29378	−0.646888	+	0.762585i	$0.723930\pi$
$80$	−1.18109	−0.132050
$81$	−0.842960	−0.0936622
$82$	−6.36722	−0.703142
$83$	0.0301401	0.00330830	0.00165415	−	0.999999i	$-0.499473\pi$
$83$	0.0301401	0.00330830	0.00165415	+	0.999999i	$0.499473\pi$
$84$	0	0
$85$	−12.7647	−1.38453
$86$	2.90652	0.313418
$87$	−4.24705	−0.455332
$88$	0.725560	0.0773449
$89$	−2.02198	−0.214330	−0.107165	−	0.994241i	$-0.534177\pi$
$89$	−2.02198	−0.214330	−0.107165	+	0.994241i	$0.534177\pi$
$90$	3.87480	0.408440
$91$	0	0
$92$	2.39774	0.249982
$93$	−2.86255	−0.296833
$94$	5.41983	0.559013
$95$	−9.04388	−0.927882
$96$	−6.54985	−0.668491
$97$	−14.6568	−1.48817	−0.744084	−	0.668086i	$-0.767114\pi$
$97$	−14.6568	−1.48817	−0.744084	+	0.668086i	$0.767114\pi$
$98$	0	0
$99$	0.459514	0.0461829
$100$	−3.36063	−0.336063
$101$	1.54470	0.153703	0.0768516	−	0.997043i	$-0.475513\pi$
$101$	1.54470	0.153703	0.0768516	+	0.997043i	$0.475513\pi$
$102$	−4.29770	−0.425536
$103$	14.2915	1.40819	0.704093	−	0.710108i	$-0.251354\pi$
$103$	14.2915	1.40819	0.704093	+	0.710108i	$0.251354\pi$
$104$	8.95417	0.878028
$105$	0	0
$106$	11.2405	1.09178
$107$	−19.6847	−1.90299	−0.951494	−	0.307667i	$-0.900452\pi$
$107$	−19.6847	−1.90299	−0.951494	+	0.307667i	$0.900452\pi$
$108$	−7.09650	−0.682861
$109$	3.84703	0.368479	0.184239	−	0.982881i	$-0.441018\pi$
$109$	3.84703	0.368479	0.184239	+	0.982881i	$0.441018\pi$
$110$	0.597681	0.0569866
$111$	−0.0621709	−0.00590100
$112$	0	0
$113$	11.2267	1.05612	0.528058	−	0.849208i	$-0.322920\pi$
$113$	11.2267	1.05612	0.528058	+	0.849208i	$0.322920\pi$
$114$	−3.04494	−0.285185
$115$	4.94450	0.461077
$116$	−5.00573	−0.464770
$117$	5.67088	0.524273
$118$	−11.0764	−1.01966
$119$	0	0
$120$	−8.43889	−0.770362
$121$	−10.9291	−0.993556
$122$	−7.61090	−0.689059
$123$	8.78236	0.791879
$124$	−3.37391	−0.302986
$125$	6.78677	0.607027
$126$	0	0
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−8.42450	−0.744628
$129$	−4.00899	−0.352972
$130$	7.37601	0.646919
$131$	−5.32947	−0.465638	−0.232819	−	0.972520i	$-0.574795\pi$
$131$	−5.32947	−0.465638	−0.232819	+	0.972520i	$0.574795\pi$
$132$	−0.399770	−0.0347955
$133$	0	0
$134$	5.28433	0.456496
$135$	−14.6341	−1.25950
$136$	−12.6806	−1.08735
$137$	7.84540	0.670278	0.335139	−	0.942169i	$-0.391217\pi$
$137$	7.84540	0.670278	0.335139	+	0.942169i	$0.391217\pi$
$138$	1.66474	0.141712
$139$	12.4749	1.05810	0.529052	−	0.848590i	$-0.322548\pi$
$139$	12.4749	1.05810	0.529052	+	0.848590i	$0.322548\pi$
$140$	0	0
$141$	−7.47562	−0.629560
$142$	2.41635	0.202775
$143$	0.874722	0.0731480
$144$	−0.743084	−0.0619236
$145$	−10.3226	−0.857243
$146$	9.66971	0.800271
$147$	0	0
$148$	−0.0732769	−0.00602332
$149$	−17.3556	−1.42183	−0.710913	−	0.703279i	$-0.751718\pi$
$149$	−17.3556	−1.42183	−0.710913	+	0.703279i	$0.751718\pi$
$150$	−2.33327	−0.190511
$151$	−21.4400	−1.74476	−0.872380	−	0.488828i	$-0.837425\pi$
$151$	−21.4400	−1.74476	−0.872380	+	0.488828i	$0.837425\pi$
$152$	−8.98428	−0.728721
$153$	−8.03092	−0.649261
$154$	0	0
$155$	−6.95750	−0.558840
$156$	−4.93358	−0.395003
$157$	18.0373	1.43953	0.719765	−	0.694217i	$-0.244249\pi$
$157$	18.0373	1.43953	0.719765	+	0.694217i	$0.244249\pi$
$158$	−9.41017	−0.748633
$159$	−15.5042	−1.22956
$160$	−15.9196	−1.25855
$161$	0	0
$162$	−0.689813	−0.0541968
$163$	11.3953	0.892552	0.446276	−	0.894895i	$-0.352750\pi$
$163$	11.3953	0.892552	0.446276	+	0.894895i	$0.352750\pi$
$164$	10.3512	0.808294
$165$	−0.824386	−0.0641783
$166$	0.0246643	0.00191432
$167$	−7.23205	−0.559633	−0.279816	−	0.960054i	$-0.590274\pi$
$167$	−7.23205	−0.559633	−0.279816	+	0.960054i	$0.590274\pi$
$168$	0	0
$169$	−2.20501	−0.169616
$170$	−10.4457	−0.801146
$171$	−5.68995	−0.435121
$172$	−4.72514	−0.360288
$173$	−8.65578	−0.658087	−0.329043	−	0.944315i	$-0.606726\pi$
$173$	−8.65578	−0.658087	−0.329043	+	0.944315i	$0.606726\pi$
$174$	−3.47546	−0.263474
$175$	0	0
$176$	−0.114619	−0.00863975
$177$	15.2777	1.14834
$178$	−1.65464	−0.124020
$179$	8.38070	0.626403	0.313201	−	0.949687i	$-0.398598\pi$
$179$	8.38070	0.626403	0.313201	+	0.949687i	$0.398598\pi$
$180$	−6.29928	−0.469520
$181$	−19.8253	−1.47360	−0.736802	−	0.676108i	$-0.763665\pi$
$181$	−19.8253	−1.47360	−0.736802	+	0.676108i	$0.763665\pi$
$182$	0	0
$183$	10.4978	0.776018
$184$	4.91191	0.362111
$185$	−0.151108	−0.0111097
$186$	−2.34249	−0.171760
$187$	−1.23875	−0.0905866
$188$	−8.81103	−0.642611
$189$	0	0
$190$	−7.40081	−0.536911
$191$	2.78774	0.201714	0.100857	−	0.994901i	$-0.467842\pi$
$191$	2.78774	0.201714	0.100857	+	0.994901i	$0.467842\pi$
$192$	−4.38800	−0.316677
$193$	5.12334	0.368786	0.184393	−	0.982853i	$-0.440968\pi$
$193$	5.12334	0.368786	0.184393	+	0.982853i	$0.440968\pi$
$194$	−11.9940	−0.861116
$195$	−10.1738	−0.728560
$196$	0	0
$197$	14.0543	1.00133	0.500665	−	0.865641i	$-0.333089\pi$
$197$	14.0543	1.00133	0.500665	+	0.865641i	$0.333089\pi$
$198$	0.376030	0.0267233
$199$	24.5793	1.74238	0.871191	−	0.490944i	$-0.163348\pi$
$199$	24.5793	1.74238	0.871191	+	0.490944i	$0.163348\pi$
$200$	−6.88445	−0.486804
$201$	−7.28872	−0.514106
$202$	1.26406	0.0889390
$203$	0	0
$204$	6.98678	0.489172
$205$	21.3458	1.49085
$206$	11.6951	0.814834
$207$	3.11083	0.216217
$208$	−1.41452	−0.0980794
$209$	−0.877664	−0.0607093
$210$	0	0
$211$	−11.8022	−0.812494	−0.406247	−	0.913763i	$-0.633163\pi$
$211$	−11.8022	−0.812494	−0.406247	+	0.913763i	$0.633163\pi$
$212$	−18.2738	−1.25505
$213$	−3.33289	−0.228366
$214$	−16.1084	−1.10115
$215$	−9.74394	−0.664532
$216$	−14.5376	−0.989159
$217$	0	0
$218$	3.14811	0.213217
$219$	−13.3375	−0.901266
$220$	−0.971651	−0.0655087
$221$	−15.2875	−1.02835
$222$	−0.0508758	−0.00341456
$223$	−20.6060	−1.37988	−0.689940	−	0.723867i	$-0.742363\pi$
$223$	−20.6060	−1.37988	−0.689940	+	0.723867i	$0.742363\pi$
$224$	0	0
$225$	−4.36008	−0.290672
$226$	9.18704	0.611113
$227$	−9.78820	−0.649665	−0.324833	−	0.945772i	$-0.605308\pi$
$227$	−9.78820	−0.649665	−0.324833	+	0.945772i	$0.605308\pi$
$228$	4.95017	0.327833
$229$	−5.51529	−0.364460	−0.182230	−	0.983256i	$-0.558332\pi$
$229$	−5.51529	−0.364460	−0.182230	+	0.983256i	$0.558332\pi$
$230$	4.04619	0.266798
$231$	0	0
$232$	−10.2545	−0.673243
$233$	16.5524	1.08438	0.542192	−	0.840255i	$-0.317595\pi$
$233$	16.5524	1.08438	0.542192	+	0.840255i	$0.317595\pi$
$234$	4.64061	0.303366
$235$	−18.1697	−1.18526
$236$	18.0069	1.17215
$237$	12.9795	0.843110
$238$	0	0
$239$	−18.7871	−1.21524	−0.607618	−	0.794229i	$-0.707875\pi$
$239$	−18.7871	−1.21524	−0.607618	+	0.794229i	$0.707875\pi$
$240$	1.33312	0.0860526
$241$	17.9210	1.15439	0.577196	−	0.816605i	$-0.304147\pi$
$241$	17.9210	1.15439	0.577196	+	0.816605i	$0.304147\pi$
$242$	−8.94354	−0.574913
$243$	−15.0515	−0.965553
$244$	12.3731	0.792104
$245$	0	0
$246$	7.18680	0.458214
$247$	−10.8313	−0.689178
$248$	−6.91165	−0.438890
$249$	−0.0340196	−0.00215591
$250$	5.55377	0.351251
$251$	8.22074	0.518888	0.259444	−	0.965758i	$-0.416461\pi$
$251$	8.22074	0.518888	0.259444	+	0.965758i	$0.416461\pi$
$252$	0	0
$253$	0.479839	0.0301672
$254$	0.818322	0.0513461
$255$	14.4078	0.902251
$256$	−14.6692	−0.916822
$257$	−18.7527	−1.16976	−0.584880	−	0.811120i	$-0.698859\pi$
$257$	−18.7527	−1.16976	−0.584880	+	0.811120i	$0.698859\pi$
$258$	−3.28064	−0.204244
$259$	0	0
$260$	−11.9912	−0.743662
$261$	−6.49443	−0.401995
$262$	−4.36122	−0.269437
$263$	6.97068	0.429831	0.214915	−	0.976633i	$-0.431052\pi$
$263$	6.97068	0.429831	0.214915	+	0.976633i	$0.431052\pi$
$264$	−0.818953	−0.0504031
$265$	−37.6833	−2.31486
$266$	0	0
$267$	2.28225	0.139672
$268$	−8.59075	−0.524763
$269$	0.735286	0.0448312	0.0224156	−	0.999749i	$-0.492864\pi$
$269$	0.735286	0.0448312	0.0224156	+	0.999749i	$0.492864\pi$
$270$	−11.9754	−0.728798
$271$	−20.6629	−1.25518	−0.627591	−	0.778543i	$-0.715959\pi$
$271$	−20.6629	−1.25518	−0.627591	+	0.778543i	$0.715959\pi$
$272$	2.00320	0.121462
$273$	0	0
$274$	6.42007	0.387850
$275$	−0.672534	−0.0405553
$276$	−2.70637	−0.162904
$277$	−0.175839	−0.0105652	−0.00528258	−	0.999986i	$-0.501682\pi$
$277$	−0.175839	−0.0105652	−0.00528258	+	0.999986i	$0.501682\pi$
$278$	10.2085	0.612262
$279$	−4.37731	−0.262063
$280$	0	0
$281$	−20.2767	−1.20961	−0.604804	−	0.796374i	$-0.706749\pi$
$281$	−20.2767	−1.20961	−0.604804	+	0.796374i	$0.706749\pi$
$282$	−6.11746	−0.364290
$283$	16.4628	0.978610	0.489305	−	0.872113i	$-0.337251\pi$
$283$	16.4628	0.978610	0.489305	+	0.872113i	$0.337251\pi$
$284$	−3.92826	−0.233100
$285$	10.2080	0.604669
$286$	0.715805	0.0423264
$287$	0	0
$288$	−10.0158	−0.590186
$289$	4.64969	0.273511
$290$	−8.44719	−0.496036
$291$	16.5434	0.969789
$292$	−15.7201	−0.919948
$293$	25.7168	1.50239	0.751196	−	0.660080i	$-0.229477\pi$
$293$	25.7168	1.50239	0.751196	+	0.660080i	$0.229477\pi$
$294$	0	0
$295$	37.1329	2.16196
$296$	−0.150112	−0.00872508
$297$	−1.42016	−0.0824062
$298$	−14.2025	−0.822728
$299$	5.92172	0.342462
$300$	3.79320	0.219001
$301$	0	0
$302$	−17.5448	−1.00959
$303$	−1.74353	−0.100163
$304$	1.41928	0.0814011
$305$	25.5151	1.46099
$306$	−6.57188	−0.375689
$307$	−23.8011	−1.35840	−0.679201	−	0.733952i	$-0.737674\pi$
$307$	−23.8011	−1.35840	−0.679201	+	0.733952i	$0.737674\pi$
$308$	0	0
$309$	−16.1311	−0.917667
$310$	−5.69348	−0.323368
$311$	7.55647	0.428488	0.214244	−	0.976780i	$-0.431271\pi$
$311$	7.55647	0.428488	0.214244	+	0.976780i	$0.431271\pi$
$312$	−10.1067	−0.572181
$313$	0.126520	0.00715132	0.00357566	−	0.999994i	$-0.498862\pi$
$313$	0.126520	0.00715132	0.00357566	+	0.999994i	$0.498862\pi$
$314$	14.7603	0.832972
$315$	0	0
$316$	15.2981	0.860587
$317$	0.143760	0.00807437	0.00403718	−	0.999992i	$-0.498715\pi$
$317$	0.143760	0.00807437	0.00403718	+	0.999992i	$0.498715\pi$
$318$	−12.6874	−0.711474
$319$	−1.00175	−0.0560874
$320$	−10.6651	−0.596200
$321$	22.2184	1.24011
$322$	0	0
$323$	15.3389	0.853480
$324$	1.12143	0.0623017
$325$	−8.29977	−0.460388
$326$	9.32507	0.516468
$327$	−4.34222	−0.240125
$328$	21.2051	1.17085
$329$	0	0
$330$	−0.674613	−0.0371362
$331$	10.1633	0.558626	0.279313	−	0.960200i	$-0.409893\pi$
$331$	10.1633	0.558626	0.279313	+	0.960200i	$0.409893\pi$
$332$	−0.0400968	−0.00220060
$333$	−0.0950694	−0.00520977
$334$	−5.91815	−0.323827
$335$	−17.7154	−0.967896
$336$	0	0
$337$	−2.83802	−0.154597	−0.0772983	−	0.997008i	$-0.524629\pi$
$337$	−2.83802	−0.154597	−0.0772983	+	0.997008i	$0.524629\pi$
$338$	−1.80441	−0.0981468
$339$	−12.6718	−0.688235
$340$	16.9815	0.920953
$341$	−0.675191	−0.0365636
$342$	−4.65621	−0.251779
$343$	0	0
$344$	−9.67973	−0.521896
$345$	−5.58095	−0.300468
$346$	−7.08322	−0.380796
$347$	−5.51387	−0.296000	−0.148000	−	0.988987i	$-0.547284\pi$
$347$	−5.51387	−0.296000	−0.148000	+	0.988987i	$0.547284\pi$
$348$	5.65006	0.302875
$349$	23.3543	1.25013	0.625065	−	0.780573i	$-0.285073\pi$
$349$	23.3543	1.25013	0.625065	+	0.780573i	$0.285073\pi$
$350$	0	0
$351$	−17.5263	−0.935484
$352$	−1.54491	−0.0823442
$353$	2.00940	0.106949	0.0534747	−	0.998569i	$-0.482970\pi$
$353$	2.00940	0.106949	0.0534747	+	0.998569i	$0.482970\pi$
$354$	12.5021	0.664479
$355$	−8.10067	−0.429939
$356$	2.68994	0.142567
$357$	0	0
$358$	6.85811	0.362463
$359$	28.7692	1.51838	0.759189	−	0.650870i	$-0.225596\pi$
$359$	28.7692	1.51838	0.759189	+	0.650870i	$0.225596\pi$
$360$	−12.9044	−0.680124
$361$	−8.13229	−0.428015
$362$	−16.2235	−0.852688
$363$	12.3359	0.647467
$364$	0	0
$365$	−32.4172	−1.69679
$366$	8.59056	0.449036
$367$	−35.8154	−1.86955	−0.934774	−	0.355243i	$-0.884398\pi$
$367$	−35.8154	−1.86955	−0.934774	+	0.355243i	$0.884398\pi$
$368$	−0.775952	−0.0404493
$369$	13.4297	0.699120
$370$	−0.123655	−0.00642852
$371$	0	0
$372$	3.80819	0.197446
$373$	−2.54824	−0.131943	−0.0659714	−	0.997822i	$-0.521015\pi$
$373$	−2.54824	−0.131943	−0.0659714	+	0.997822i	$0.521015\pi$
$374$	−1.01370	−0.0524172
$375$	−7.66036	−0.395579
$376$	−18.0499	−0.930854
$377$	−12.3627	−0.636711
$378$	0	0
$379$	28.6007	1.46912	0.734561	−	0.678543i	$-0.237388\pi$
$379$	28.6007	1.46912	0.734561	+	0.678543i	$0.237388\pi$
$380$	12.0315	0.617204
$381$	−1.12872	−0.0578260
$382$	2.28127	0.116720
$383$	12.0698	0.616736	0.308368	−	0.951267i	$-0.400217\pi$
$383$	12.0698	0.616736	0.308368	+	0.951267i	$0.400217\pi$
$384$	9.50889	0.485249
$385$	0	0
$386$	4.19254	0.213395
$387$	−6.13040	−0.311625
$388$	19.4986	0.989892
$389$	−22.4001	−1.13573	−0.567865	−	0.823122i	$-0.692230\pi$
$389$	−22.4001	−1.13573	−0.567865	+	0.823122i	$0.692230\pi$
$390$	−8.32544	−0.421575
$391$	−8.38614	−0.424106
$392$	0	0
$393$	6.01547	0.303440
$394$	11.5010	0.579410
$395$	31.5470	1.58730
$396$	−0.611313	−0.0307197
$397$	31.3195	1.57188	0.785940	−	0.618303i	$-0.212180\pi$
$397$	31.3195	1.57188	0.785940	+	0.618303i	$0.212180\pi$
$398$	20.1138	1.00821
$399$	0	0
$400$	1.08756	0.0543780
$401$	4.25162	0.212316	0.106158	−	0.994349i	$-0.466145\pi$
$401$	4.25162	0.212316	0.106158	+	0.994349i	$0.466145\pi$
$402$	−5.96452	−0.297483
$403$	−8.33257	−0.415075
$404$	−2.05499	−0.102239
$405$	2.31256	0.114912
$406$	0	0
$407$	−0.0146643	−0.000726881 0
$408$	14.3128	0.708591
$409$	25.0374	1.23802	0.619010	−	0.785383i	$-0.287534\pi$
$409$	25.0374	1.23802	0.619010	+	0.785383i	$0.287534\pi$
$410$	17.4677	0.862668
$411$	−8.85525	−0.436797
$412$	−19.0127	−0.936689
$413$	0	0
$414$	2.54566	0.125112
$415$	−0.0826856	−0.00405888
$416$	−19.0659	−0.934781
$417$	−14.0806	−0.689530
$418$	−0.718212	−0.0351289
$419$	−19.2538	−0.940612	−0.470306	−	0.882503i	$-0.655856\pi$
$419$	−19.2538	−0.940612	−0.470306	+	0.882503i	$0.655856\pi$
$420$	0	0
$421$	−5.07775	−0.247474	−0.123737	−	0.992315i	$-0.539488\pi$
$421$	−5.07775	−0.247474	−0.123737	+	0.992315i	$0.539488\pi$
$422$	−9.65797	−0.470142
$423$	−11.4314	−0.555815
$424$	−37.4349	−1.81800
$425$	11.7539	0.570146
$426$	−2.72738	−0.132142
$427$	0	0
$428$	26.1875	1.26582
$429$	−0.987315	−0.0476680
$430$	−7.97369	−0.384525
$431$	−23.7235	−1.14272	−0.571360	−	0.820699i	$-0.693584\pi$
$431$	−23.7235	−1.14272	−0.571360	+	0.820699i	$0.693584\pi$
$432$	2.29656	0.110493
$433$	1.24058	0.0596187	0.0298093	−	0.999556i	$-0.490510\pi$
$433$	1.24058	0.0596187	0.0298093	+	0.999556i	$0.490510\pi$
$434$	0	0
$435$	11.6513	0.558636
$436$	−5.11790	−0.245103
$437$	−5.94163	−0.284227
$438$	−10.9144	−0.521509
$439$	−16.1814	−0.772294	−0.386147	−	0.922437i	$-0.626194\pi$
$439$	−16.1814	−0.772294	−0.386147	+	0.922437i	$0.626194\pi$
$440$	−1.99048	−0.0948926
$441$	0	0
$442$	−12.5101	−0.595046
$443$	−17.0999	−0.812441	−0.406220	−	0.913775i	$-0.633153\pi$
$443$	−17.0999	−0.812441	−0.406220	+	0.913775i	$0.633153\pi$
$444$	0.0827090	0.00392519
$445$	5.54707	0.262956
$446$	−16.8624	−0.798455
$447$	19.5896	0.926556
$448$	0	0
$449$	36.9220	1.74246	0.871228	−	0.490879i	$-0.163324\pi$
$449$	36.9220	1.74246	0.871228	+	0.490879i	$0.163324\pi$
$450$	−3.56795	−0.168195
$451$	2.07150	0.0975431
$452$	−14.9354	−0.702502
$453$	24.1997	1.13700
$454$	−8.00990	−0.375923
$455$	0	0
$456$	10.1407	0.474883
$457$	−13.2331	−0.619017	−0.309508	−	0.950897i	$-0.600164\pi$
$457$	−13.2331	−0.619017	−0.309508	+	0.950897i	$0.600164\pi$
$458$	−4.51328	−0.210892
$459$	24.8202	1.15851
$460$	−6.57791	−0.306696
$461$	−17.0587	−0.794503	−0.397251	−	0.917710i	$-0.630036\pi$
$461$	−17.0587	−0.794503	−0.397251	+	0.917710i	$0.630036\pi$
$462$	0	0
$463$	−18.1318	−0.842657	−0.421328	−	0.906908i	$-0.638436\pi$
$463$	−18.1318	−0.842657	−0.421328	+	0.906908i	$0.638436\pi$
$464$	1.61994	0.0752040
$465$	7.85306	0.364177
$466$	13.5452	0.627469
$467$	−32.6217	−1.50955	−0.754776	−	0.655982i	$-0.772255\pi$
$467$	−32.6217	−1.50955	−0.754776	+	0.655982i	$0.772255\pi$
$468$	−7.54425	−0.348733
$469$	0	0
$470$	−14.8686	−0.685839
$471$	−20.3590	−0.938093
$472$	36.8881	1.69791
$473$	−0.945601	−0.0434788
$474$	10.6214	0.487858
$475$	8.32768	0.382100
$476$	0	0
$477$	−23.7084	−1.08553
$478$	−15.3739	−0.703186
$479$	−30.5570	−1.39619	−0.698093	−	0.716007i	$-0.745968\pi$
$479$	−30.5570	−1.39619	−0.698093	+	0.716007i	$0.745968\pi$
$480$	17.9687	0.820156
$481$	−0.180973	−0.00825164
$482$	14.6651	0.667979
$483$	0	0
$484$	14.5395	0.660888
$485$	40.2090	1.82580
$486$	−12.3170	−0.558709
$487$	20.5767	0.932419	0.466209	−	0.884674i	$-0.345619\pi$
$487$	20.5767	0.932419	0.466209	+	0.884674i	$0.345619\pi$
$488$	25.3470	1.14740
$489$	−12.8621	−0.581646
$490$	0	0
$491$	−26.3733	−1.19021	−0.595105	−	0.803648i	$-0.702889\pi$
$491$	−26.3733	−1.19021	−0.595105	+	0.803648i	$0.702889\pi$
$492$	−11.6836	−0.526738
$493$	17.5076	0.788505
$494$	−8.86349	−0.398787
$495$	−1.26062	−0.0566607
$496$	1.09186	0.0490258
$497$	0	0
$498$	−0.0278390	−0.00124750
$499$	5.20889	0.233182	0.116591	−	0.993180i	$-0.462803\pi$
$499$	5.20889	0.233182	0.116591	+	0.993180i	$0.462803\pi$
$500$	−9.02877	−0.403779
$501$	8.16295	0.364694
$502$	6.72721	0.300250
$503$	9.38865	0.418619	0.209310	−	0.977849i	$-0.432878\pi$
$503$	9.38865	0.418619	0.209310	+	0.977849i	$0.432878\pi$
$504$	0	0
$505$	−4.23769	−0.188575
$506$	0.392663	0.0174560
$507$	2.48883	0.110533
$508$	−1.33035	−0.0590247
$509$	31.6611	1.40335	0.701676	−	0.712496i	$-0.252435\pi$
$509$	31.6611	1.40335	0.701676	+	0.712496i	$0.252435\pi$
$510$	11.7902	0.522079
$511$	0	0
$512$	4.84491	0.214117
$513$	17.5852	0.776407
$514$	−15.3457	−0.676872
$515$	−39.2071	−1.72767
$516$	5.33335	0.234788
$517$	−1.76328	−0.0775488
$518$	0	0
$519$	9.76994	0.428853
$520$	−24.5647	−1.07723
$521$	−6.22207	−0.272594	−0.136297	−	0.990668i	$-0.543520\pi$
$521$	−6.22207	−0.272594	−0.136297	+	0.990668i	$0.543520\pi$
$522$	−5.31454	−0.232611
$523$	38.3006	1.67477	0.837385	−	0.546614i	$-0.184084\pi$
$523$	38.3006	1.67477	0.837385	+	0.546614i	$0.184084\pi$
$524$	7.09005	0.309730
$525$	0	0
$526$	5.70426	0.248718
$527$	11.8003	0.514030
$528$	0.129373	0.00563023
$529$	−19.7516	−0.858764
$530$	−30.8370	−1.33948
$531$	23.3621	1.01383
$532$	0	0
$533$	25.5645	1.10732
$534$	1.86762	0.0808197
$535$	54.0025	2.33473
$536$	−17.5987	−0.760146
$537$	−9.45945	−0.408205
$538$	0.601701	0.0259412
$539$	0	0
$540$	19.4684	0.837786
$541$	−41.0790	−1.76612	−0.883061	−	0.469258i	$-0.844522\pi$
$541$	−41.0790	−1.76612	−0.883061	+	0.469258i	$0.844522\pi$
$542$	−16.9089	−0.726300
$543$	22.3772	0.960298
$544$	27.0005	1.15764
$545$	−10.5539	−0.452078
$546$	0	0
$547$	8.06670	0.344907	0.172454	−	0.985018i	$-0.444830\pi$
$547$	8.06670	0.344907	0.172454	+	0.985018i	$0.444830\pi$
$548$	−10.4371	−0.445852
$549$	16.0528	0.685117
$550$	−0.550349	−0.0234670
$551$	12.4043	0.528439
$552$	−5.54417	−0.235975
$553$	0	0
$554$	−0.143893	−0.00611344
$555$	0.170558	0.00723980
$556$	−16.5959	−0.703823
$557$	−3.87559	−0.164214	−0.0821071	−	0.996624i	$-0.526165\pi$
$557$	−3.87559	−0.164214	−0.0821071	+	0.996624i	$0.526165\pi$
$558$	−3.58205	−0.151640
$559$	−11.6697	−0.493576
$560$	0	0
$561$	1.39820	0.0590322
$562$	−16.5929	−0.699930
$563$	−16.5843	−0.698945	−0.349472	−	0.936947i	$-0.613639\pi$
$563$	−16.5843	−0.698945	−0.349472	+	0.936947i	$0.613639\pi$
$564$	9.94518	0.418767
$565$	−30.7990	−1.29572
$566$	13.4718	0.566264
$567$	0	0
$568$	−8.04728	−0.337657
$569$	39.5356	1.65742	0.828710	−	0.559678i	$-0.189075\pi$
$569$	39.5356	1.65742	0.828710	+	0.559678i	$0.189075\pi$
$570$	8.35343	0.349887
$571$	17.7137	0.741293	0.370647	−	0.928774i	$-0.379136\pi$
$571$	17.7137	0.741293	0.370647	+	0.928774i	$0.379136\pi$
$572$	−1.16369	−0.0486561
$573$	−3.14657	−0.131450
$574$	0	0
$575$	−4.55293	−0.189871
$576$	−6.70997	−0.279582
$577$	−40.1099	−1.66980	−0.834898	−	0.550405i	$-0.814473\pi$
$577$	−40.1099	−1.66980	−0.834898	+	0.550405i	$0.814473\pi$
$578$	3.80495	0.158265
$579$	−5.78281	−0.240325
$580$	13.7326	0.570216
$581$	0	0
$582$	13.5378	0.561160
$583$	−3.65697	−0.151456
$584$	−32.2035	−1.33259
$585$	−15.5574	−0.643218
$586$	21.0446	0.869345
$587$	−24.7808	−1.02281	−0.511406	−	0.859339i	$-0.670875\pi$
$587$	−24.7808	−1.02281	−0.511406	+	0.859339i	$0.670875\pi$
$588$	0	0
$589$	8.36059	0.344492
$590$	30.3866	1.25100
$591$	−15.8634	−0.652532
$592$	0.0237137	0.000974628 0
$593$	−34.3299	−1.40976	−0.704880	−	0.709327i	$-0.748999\pi$
$593$	−34.3299	−1.40976	−0.704880	+	0.709327i	$0.748999\pi$
$594$	−1.16215	−0.0476836
$595$	0	0
$596$	23.0890	0.945763
$597$	−27.7431	−1.13545
$598$	4.84587	0.198162
$599$	−45.8613	−1.87384	−0.936921	−	0.349541i	$-0.886337\pi$
$599$	−45.8613	−1.87384	−0.936921	+	0.349541i	$0.886337\pi$
$600$	7.77060	0.317234
$601$	−11.0494	−0.450715	−0.225358	−	0.974276i	$-0.572355\pi$
$601$	−11.0494	−0.450715	−0.225358	+	0.974276i	$0.572355\pi$
$602$	0	0
$603$	−11.1456	−0.453885
$604$	28.5226	1.16057
$605$	29.9827	1.21897
$606$	−1.42677	−0.0579585
$607$	−4.91310	−0.199416	−0.0997082	−	0.995017i	$-0.531791\pi$
$607$	−4.91310	−0.199416	−0.0997082	+	0.995017i	$0.531791\pi$
$608$	19.1300	0.775823
$609$	0	0
$610$	20.8796	0.845390
$611$	−21.7607	−0.880343
$612$	10.6839	0.431872
$613$	−30.9734	−1.25101	−0.625503	−	0.780222i	$-0.715106\pi$
$613$	−30.9734	−1.25101	−0.625503	+	0.780222i	$0.715106\pi$
$614$	−19.4770	−0.786027
$615$	−24.0933	−0.971537
$616$	0	0
$617$	−12.3335	−0.496530	−0.248265	−	0.968692i	$-0.579860\pi$
$617$	−12.3335	−0.496530	−0.248265	+	0.968692i	$0.579860\pi$
$618$	−13.2004	−0.531000
$619$	−4.48347	−0.180206	−0.0901030	−	0.995932i	$-0.528720\pi$
$619$	−4.48347	−0.180206	−0.0901030	+	0.995932i	$0.528720\pi$
$620$	9.25590	0.371726
$621$	−9.61425	−0.385806
$622$	6.18363	0.247941
$623$	0	0
$624$	1.59660	0.0639150
$625$	−31.2493	−1.24997
$626$	0.103534	0.00413805
$627$	0.990635	0.0395622
$628$	−23.9959	−0.957539
$629$	0.256287	0.0102188
$630$	0	0
$631$	47.1030	1.87514	0.937570	−	0.347798i	$-0.113070\pi$
$631$	47.1030	1.87514	0.937570	+	0.347798i	$0.113070\pi$
$632$	31.3391	1.24660
$633$	13.3213	0.529475
$634$	0.117642	0.00467216
$635$	−2.74338	−0.108868
$636$	20.6259	0.817872
$637$	0	0
$638$	−0.819758	−0.0324545
$639$	−5.09653	−0.201616
$640$	23.1116	0.913566
$641$	−25.8930	−1.02271	−0.511357	−	0.859369i	$-0.670857\pi$
$641$	−25.8930	−1.02271	−0.511357	+	0.859369i	$0.670857\pi$
$642$	18.1818	0.717580
$643$	−22.4912	−0.886965	−0.443483	−	0.896283i	$-0.646257\pi$
$643$	−22.4912	−0.886965	−0.443483	+	0.896283i	$0.646257\pi$
$644$	0	0
$645$	10.9982	0.433053
$646$	12.5522	0.493859
$647$	−29.3863	−1.15530	−0.577648	−	0.816286i	$-0.696029\pi$
$647$	−29.3863	−1.15530	−0.577648	+	0.816286i	$0.696029\pi$
$648$	2.29732	0.0902472
$649$	3.60356	0.141452
$650$	−6.79189	−0.266400
$651$	0	0
$652$	−15.1598	−0.593703
$653$	15.8265	0.619338	0.309669	−	0.950844i	$-0.399782\pi$
$653$	15.8265	0.619338	0.309669	+	0.950844i	$0.399782\pi$
$654$	−3.55333	−0.138946
$655$	14.6207	0.571280
$656$	−3.34984	−0.130789
$657$	−20.3952	−0.795694
$658$	0	0
$659$	39.9760	1.55724	0.778622	−	0.627493i	$-0.215919\pi$
$659$	39.9760	1.55724	0.778622	+	0.627493i	$0.215919\pi$
$660$	1.09672	0.0426898
$661$	−12.3341	−0.479741	−0.239870	−	0.970805i	$-0.577105\pi$
$661$	−12.3341	−0.479741	−0.239870	+	0.970805i	$0.577105\pi$
$662$	8.31686	0.323244
$663$	17.2553	0.670141
$664$	−0.0821406	−0.00318768
$665$	0	0
$666$	−0.0777974	−0.00301459
$667$	−6.78170	−0.262588
$668$	9.62115	0.372253
$669$	23.2584	0.899221
$670$	−14.4969	−0.560065
$671$	2.47611	0.0955893
$672$	0	0
$673$	12.2289	0.471390	0.235695	−	0.971827i	$-0.424263\pi$
$673$	12.2289	0.471390	0.235695	+	0.971827i	$0.424263\pi$
$674$	−2.32241	−0.0894560
$675$	13.4752	0.518659
$676$	2.93343	0.112824
$677$	−23.6394	−0.908534	−0.454267	−	0.890865i	$-0.650099\pi$
$677$	−23.6394	−0.908534	−0.454267	+	0.890865i	$0.650099\pi$
$678$	−10.3696	−0.398241
$679$	0	0
$680$	34.7877	1.33405
$681$	11.0481	0.423365
$682$	−0.552524	−0.0211572
$683$	−34.0115	−1.30142	−0.650708	−	0.759328i	$-0.725528\pi$
$683$	−34.0115	−1.30142	−0.650708	+	0.759328i	$0.725528\pi$
$684$	7.56962	0.289432
$685$	−21.5229	−0.822348
$686$	0	0
$687$	6.22521	0.237506
$688$	1.52914	0.0582979
$689$	−45.1309	−1.71935
$690$	−4.56701	−0.173863
$691$	45.9774	1.74906	0.874531	−	0.484971i	$-0.161170\pi$
$691$	45.9774	1.74906	0.874531	+	0.484971i	$0.161170\pi$
$692$	11.5152	0.437743
$693$	0	0
$694$	−4.51213	−0.171278
$695$	−34.2232	−1.29816
$696$	11.5745	0.438730
$697$	−36.2036	−1.37131
$698$	19.1114	0.723376
$699$	−18.6830	−0.706656
$700$	0	0
$701$	19.5014	0.736557	0.368279	−	0.929715i	$-0.379947\pi$
$701$	19.5014	0.736557	0.368279	+	0.929715i	$0.379947\pi$
$702$	−14.3422	−0.541310
$703$	0.181581	0.00684846
$704$	−1.03500	−0.0390080
$705$	20.5084	0.772393
$706$	1.64434	0.0618854
$707$	0	0
$708$	−20.3247	−0.763848
$709$	16.1356	0.605984	0.302992	−	0.952993i	$-0.402015\pi$
$709$	16.1356	0.605984	0.302992	+	0.952993i	$0.402015\pi$
$710$	−6.62896	−0.248780
$711$	19.8478	0.744351
$712$	5.51051	0.206515
$713$	−4.57093	−0.171182
$714$	0	0
$715$	−2.39969	−0.0897435
$716$	−11.1493	−0.416667
$717$	21.2054	0.791929
$718$	23.5425	0.878597
$719$	16.7165	0.623419	0.311710	−	0.950177i	$-0.399098\pi$
$719$	16.7165	0.623419	0.311710	+	0.950177i	$0.399098\pi$
$720$	2.03856	0.0759726
$721$	0	0
$722$	−6.65484	−0.247667
$723$	−20.2278	−0.752278
$724$	26.3746	0.980204
$725$	9.50511	0.353011
$726$	10.0947	0.374651
$727$	22.7271	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$727$	22.7271	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$728$	0	0
$729$	19.5178	0.722881
$730$	−26.5277	−0.981834
$731$	16.5263	0.611246
$732$	−13.9657	−0.516187
$733$	−26.4585	−0.977266	−0.488633	−	0.872490i	$-0.662504\pi$
$733$	−26.4585	−0.977266	−0.488633	+	0.872490i	$0.662504\pi$
$734$	−29.3085	−1.08180
$735$	0	0
$736$	−10.4588	−0.385517
$737$	−1.71919	−0.0633273
$738$	10.9898	0.404540
$739$	50.7663	1.86747	0.933733	−	0.357969i	$-0.116531\pi$
$739$	50.7663	1.86747	0.933733	+	0.357969i	$0.116531\pi$
$740$	0.201026	0.00738987
$741$	12.2255	0.449114
$742$	0	0
$743$	−10.2193	−0.374910	−0.187455	−	0.982273i	$-0.560024\pi$
$743$	−10.2193	−0.374910	−0.187455	+	0.982273i	$0.560024\pi$
$744$	7.80131	0.286010
$745$	47.6130	1.74441
$746$	−2.08528	−0.0763475
$747$	−0.0520216	−0.00190337
$748$	1.64797	0.0602559
$749$	0	0
$750$	−6.26864	−0.228898
$751$	41.4093	1.51105	0.755524	−	0.655121i	$-0.227382\pi$
$751$	41.4093	1.51105	0.755524	+	0.655121i	$0.227382\pi$
$752$	2.85141	0.103980
$753$	−9.27890	−0.338142
$754$	−10.1167	−0.368427
$755$	58.8180	2.14061
$756$	0	0
$757$	23.1449	0.841214	0.420607	−	0.907243i	$-0.361817\pi$
$757$	23.1449	0.841214	0.420607	+	0.907243i	$0.361817\pi$
$758$	23.4046	0.850094
$759$	−0.541603	−0.0196589
$760$	24.6473	0.894050
$761$	39.4782	1.43108	0.715541	−	0.698571i	$-0.246180\pi$
$761$	39.4782	1.43108	0.715541	+	0.698571i	$0.246180\pi$
$762$	−0.923656	−0.0334605
$763$	0	0
$764$	−3.70867	−0.134175
$765$	22.0319	0.796563
$766$	9.87696	0.356869
$767$	44.4717	1.60578
$768$	16.5573	0.597462
$769$	4.81634	0.173682	0.0868408	−	0.996222i	$-0.472323\pi$
$769$	4.81634	0.173682	0.0868408	+	0.996222i	$0.472323\pi$
$770$	0	0
$771$	21.1665	0.762293
$772$	−6.81582	−0.245307
$773$	10.4872	0.377198	0.188599	−	0.982054i	$-0.439605\pi$
$773$	10.4872	0.377198	0.188599	+	0.982054i	$0.439605\pi$
$774$	−5.01664	−0.180319
$775$	6.40653	0.230129
$776$	39.9441	1.43391
$777$	0	0
$778$	−18.3305	−0.657180
$779$	−25.6504	−0.919022
$780$	13.5347	0.484619
$781$	−0.786130	−0.0281299
$782$	−6.86257	−0.245405
$783$	20.0715	0.717299
$784$	0	0
$785$	−49.4831	−1.76613
$786$	4.92259	0.175583
$787$	4.39250	0.156576	0.0782879	−	0.996931i	$-0.475055\pi$
$787$	4.39250	0.156576	0.0782879	+	0.996931i	$0.475055\pi$
$788$	−18.6972	−0.666058
$789$	−7.86794	−0.280106
$790$	25.8157	0.918480
$791$	0	0
$792$	−1.25231	−0.0444990
$793$	30.5579	1.08514
$794$	25.6294	0.909554
$795$	42.5338	1.50852
$796$	−32.6991	−1.15899
$797$	−39.2121	−1.38896	−0.694481	−	0.719511i	$-0.744366\pi$
$797$	−39.2121	−1.38896	−0.694481	+	0.719511i	$0.744366\pi$
$798$	0	0
$799$	30.8168	1.09022
$800$	14.6589	0.518269
$801$	3.48993	0.123311
$802$	3.47920	0.122855
$803$	−3.14592	−0.111017
$804$	9.69654	0.341970
$805$	0	0
$806$	−6.81873	−0.240179
$807$	−0.829931	−0.0292149
$808$	−4.20976	−0.148099
$809$	−0.316252	−0.0111188	−0.00555942	−	0.999985i	$-0.501770\pi$
$809$	−0.316252	−0.0111188	−0.00555942	+	0.999985i	$0.501770\pi$
$810$	1.89242	0.0664928
$811$	50.8916	1.78705	0.893524	−	0.449016i	$-0.148226\pi$
$811$	50.8916	1.78705	0.893524	+	0.449016i	$0.148226\pi$
$812$	0	0
$813$	23.3226	0.817960
$814$	−0.0120001	−0.000420603 0
$815$	−31.2617	−1.09505
$816$	−2.26105	−0.0791525
$817$	11.7090	0.409644
$818$	20.4887	0.716369
$819$	0	0
$820$	−28.3973	−0.991676
$821$	−15.4178	−0.538085	−0.269043	−	0.963128i	$-0.586707\pi$
$821$	−15.4178	−0.538085	−0.269043	+	0.963128i	$0.586707\pi$
$822$	−7.24645	−0.252749
$823$	−48.8660	−1.70336	−0.851680	−	0.524062i	$-0.824416\pi$
$823$	−48.8660	−1.70336	−0.851680	+	0.524062i	$0.824416\pi$
$824$	−38.9487	−1.35684
$825$	0.759101	0.0264285
$826$	0	0
$827$	−42.1609	−1.46608	−0.733039	−	0.680186i	$-0.761899\pi$
$827$	−42.1609	−1.46608	−0.733039	+	0.680186i	$0.761899\pi$
$828$	−4.13848	−0.143822
$829$	−28.4114	−0.986769	−0.493385	−	0.869811i	$-0.664240\pi$
$829$	−28.4114	−0.986769	−0.493385	+	0.869811i	$0.664240\pi$
$830$	−0.0676635	−0.00234863
$831$	0.198473	0.00688495
$832$	−12.7730	−0.442824
$833$	0	0
$834$	−11.5225	−0.398990
$835$	19.8402	0.686600
$836$	1.16760	0.0403822
$837$	13.5284	0.467610
$838$	−15.7558	−0.544277
$839$	10.9648	0.378546	0.189273	−	0.981924i	$-0.439387\pi$
$839$	10.9648	0.378546	0.189273	+	0.981924i	$0.439387\pi$
$840$	0	0
$841$	−14.8419	−0.511791
$842$	−4.15524	−0.143199
$843$	22.8867	0.788261
$844$	15.7010	0.540450
$845$	6.04917	0.208098
$846$	−9.35460	−0.321618
$847$	0	0
$848$	5.91372	0.203078
$849$	−18.5818	−0.637727
$850$	9.61845	0.329910
$851$	−0.0992745	−0.00340309
$852$	4.43390	0.151903
$853$	8.12843	0.278312	0.139156	−	0.990270i	$-0.455561\pi$
$853$	8.12843	0.278312	0.139156	+	0.990270i	$0.455561\pi$
$854$	0	0
$855$	15.6097	0.533840
$856$	53.6466	1.83360
$857$	−4.51225	−0.154135	−0.0770677	−	0.997026i	$-0.524556\pi$
$857$	−4.51225	−0.154135	−0.0770677	+	0.997026i	$0.524556\pi$
$858$	−0.807942	−0.0275827
$859$	−26.8887	−0.917431	−0.458716	−	0.888583i	$-0.651690\pi$
$859$	−26.8887	−0.917431	−0.458716	+	0.888583i	$0.651690\pi$
$860$	12.9628	0.442029
$861$	0	0
$862$	−19.4135	−0.661225
$863$	−47.8004	−1.62715	−0.813573	−	0.581463i	$-0.802481\pi$
$863$	−47.8004	−1.62715	−0.813573	+	0.581463i	$0.802481\pi$
$864$	30.9545	1.05309
$865$	23.7461	0.807391
$866$	1.01520	0.0344978
$867$	−5.24819	−0.178238
$868$	0	0
$869$	3.06148	0.103854
$870$	9.53450	0.323250
$871$	−21.2166	−0.718898
$872$	−10.4843	−0.355044
$873$	25.2975	0.856190
$874$	−4.86217	−0.164465
$875$	0	0
$876$	17.7435	0.599499
$877$	−3.96696	−0.133955	−0.0669774	−	0.997754i	$-0.521336\pi$
$877$	−3.96696	−0.133955	−0.0669774	+	0.997754i	$0.521336\pi$
$878$	−13.2416	−0.446881
$879$	−29.0270	−0.979057
$880$	0.314444	0.0105999
$881$	−0.114398	−0.00385416	−0.00192708	−	0.999998i	$-0.500613\pi$
$881$	−0.114398	−0.00385416	−0.00192708	+	0.999998i	$0.500613\pi$
$882$	0	0
$883$	12.1141	0.407672	0.203836	−	0.979005i	$-0.434659\pi$
$883$	12.1141	0.407672	0.203836	+	0.979005i	$0.434659\pi$
$884$	20.3377	0.684032
$885$	−41.9125	−1.40887
$886$	−13.9932	−0.470112
$887$	−11.0340	−0.370484	−0.185242	−	0.982693i	$-0.559307\pi$
$887$	−11.0340	−0.370484	−0.185242	+	0.982693i	$0.559307\pi$
$888$	0.169434	0.00568584
$889$	0	0
$890$	4.53929	0.152157
$891$	0.224422	0.00751843
$892$	27.4132	0.917861
$893$	21.8338	0.730642
$894$	16.0306	0.536144
$895$	−22.9914	−0.768519
$896$	0	0
$897$	−6.68395	−0.223171
$898$	30.2141	1.00826
$899$	9.54266	0.318266
$900$	5.80043	0.193348
$901$	63.9129	2.12925
$902$	1.69515	0.0564424
$903$	0	0
$904$	−30.5960	−1.01761
$905$	54.3884	1.80793
$906$	19.8032	0.657916
$907$	44.1494	1.46596	0.732979	−	0.680251i	$-0.238129\pi$
$907$	44.1494	1.46596	0.732979	+	0.680251i	$0.238129\pi$
$908$	13.0217	0.432141
$909$	−2.66614	−0.0884303
$910$	0	0
$911$	3.45436	0.114448	0.0572241	−	0.998361i	$-0.481775\pi$
$911$	3.45436	0.114448	0.0572241	+	0.998361i	$0.481775\pi$
$912$	−1.60196	−0.0530463
$913$	−0.00802423	−0.000265563 0
$914$	−10.8289	−0.358189
$915$	−28.7994	−0.952078
$916$	7.33726	0.242430
$917$	0	0
$918$	20.3109	0.670359
$919$	6.38517	0.210627	0.105314	−	0.994439i	$-0.466415\pi$
$919$	6.38517	0.210627	0.105314	+	0.994439i	$0.466415\pi$
$920$	−13.4752	−0.444265
$921$	26.8648	0.885224
$922$	−13.9595	−0.459732
$923$	−9.70167	−0.319334
$924$	0	0
$925$	0.139141	0.00457494
$926$	−14.8377	−0.487596
$927$	−24.6671	−0.810174
$928$	21.8347	0.716760
$929$	−5.06890	−0.166305	−0.0831525	−	0.996537i	$-0.526499\pi$
$929$	−5.06890	−0.166305	−0.0831525	+	0.996537i	$0.526499\pi$
$930$	6.42634	0.210728
$931$	0	0
$932$	−22.0205	−0.721304
$933$	−8.52913	−0.279231
$934$	−26.6951	−0.873489
$935$	3.39837	0.111139
$936$	−15.4548	−0.505157
$937$	16.2537	0.530984	0.265492	−	0.964113i	$-0.414466\pi$
$937$	16.2537	0.530984	0.265492	+	0.964113i	$0.414466\pi$
$938$	0	0
$939$	−0.142805	−0.00466027
$940$	24.1720	0.788404
$941$	37.5175	1.22304	0.611518	−	0.791230i	$-0.290559\pi$
$941$	37.5175	1.22304	0.611518	+	0.791230i	$0.290559\pi$
$942$	−16.6602	−0.542819
$943$	14.0237	0.456674
$944$	−5.82735	−0.189664
$945$	0	0
$946$	−0.773807	−0.0251586
$947$	−15.0972	−0.490592	−0.245296	−	0.969448i	$-0.578885\pi$
$947$	−15.0972	−0.490592	−0.245296	+	0.969448i	$0.578885\pi$
$948$	−17.2673	−0.560815
$949$	−38.8240	−1.26028
$950$	6.81472	0.221099
$951$	−0.162265	−0.00526179
$952$	0	0
$953$	−35.0151	−1.13425	−0.567125	−	0.823632i	$-0.691944\pi$
$953$	−35.0151	−1.13425	−0.567125	+	0.823632i	$0.691944\pi$
$954$	−19.4011	−0.628134
$955$	−7.64782	−0.247478
$956$	24.9934	0.808344
$957$	1.13070	0.0365503
$958$	−25.0055	−0.807891
$959$	0	0
$960$	12.0380	0.388523
$961$	−24.5682	−0.792521
$962$	−0.148094	−0.00477474
$963$	33.9756	1.09485
$964$	−23.8412	−0.767872
$965$	−14.0553	−0.452455
$966$	0	0
$967$	24.4686	0.786856	0.393428	−	0.919355i	$-0.371289\pi$
$967$	24.4686	0.786856	0.393428	+	0.919355i	$0.371289\pi$
$968$	29.7851	0.957330
$969$	−17.3133	−0.556184
$970$	32.9040	1.05648
$971$	−18.9699	−0.608773	−0.304387	−	0.952549i	$-0.598451\pi$
$971$	−18.9699	−0.608773	−0.304387	+	0.952549i	$0.598451\pi$
$972$	20.0237	0.642261
$973$	0	0
$974$	16.8384	0.539536
$975$	9.36811	0.300020
$976$	−4.00415	−0.128170
$977$	38.3716	1.22762	0.613809	−	0.789455i	$-0.289637\pi$
$977$	38.3716	1.22762	0.613809	+	0.789455i	$0.289637\pi$
$978$	−10.5254	−0.336564
$979$	0.538316	0.0172046
$980$	0	0
$981$	−6.63996	−0.211998
$982$	−21.5818	−0.688704
$983$	−15.5044	−0.494514	−0.247257	−	0.968950i	$-0.579529\pi$
$983$	−15.5044	−0.494514	−0.247257	+	0.968950i	$0.579529\pi$
$984$	−23.9346	−0.763006
$985$	−38.5563	−1.22851
$986$	14.3269	0.456261
$987$	0	0
$988$	14.4094	0.458424
$989$	−6.40156	−0.203558
$990$	−1.03159	−0.0327862
$991$	13.0862	0.415698	0.207849	−	0.978161i	$-0.433354\pi$
$991$	13.0862	0.415698	0.207849	+	0.978161i	$0.433354\pi$
$992$	14.7168	0.467259
$993$	−11.4715	−0.364037
$994$	0	0
$995$	−67.4304	−2.13769
$996$	0.0452580	0.00143405
$997$	3.78357	0.119827	0.0599135	−	0.998204i	$-0.480918\pi$
$997$	3.78357	0.119827	0.0599135	+	0.998204i	$0.480918\pi$
$998$	4.26255	0.134929
$999$	0.293819	0.00929603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6223.2.a.h.1.4		7
7.6	odd	2		127.2.a.b.1.4	✓	7
21.20	even	2		1143.2.a.i.1.4		7
28.27	even	2		2032.2.a.p.1.4		7
35.34	odd	2		3175.2.a.j.1.4		7
56.13	odd	2		8128.2.a.bi.1.4		7
56.27	even	2		8128.2.a.bj.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.a.b.1.4	✓	7	7.6	odd	2
1143.2.a.i.1.4		7	21.20	even	2
2032.2.a.p.1.4		7	28.27	even	2
3175.2.a.j.1.4		7	35.34	odd	2
6223.2.a.h.1.4		7	1.1	even	1	trivial
8128.2.a.bi.1.4		7	56.13	odd	2
8128.2.a.bj.1.4		7	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6223 = 7^{2} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6223.a (trivial)

\(f(q)\)	\(=\)	\(q+0.818322 q^{2} -1.12872 q^{3} -1.33035 q^{4} -2.74338 q^{5} -0.923656 q^{6} -2.72530 q^{8} -1.72599 q^{9} +O(q^{10})\)	\(q+0.818322 q^{2} -1.12872 q^{3} -1.33035 q^{4} -2.74338 q^{5} -0.923656 q^{6} -2.72530 q^{8} -1.72599 q^{9} -2.24497 q^{10} -0.266231 q^{11} +1.50159 q^{12} -3.28557 q^{13} +3.09650 q^{15} +0.430525 q^{16} +4.65292 q^{17} -1.41242 q^{18} +3.29662 q^{19} +3.64965 q^{20} -0.217863 q^{22} -1.80234 q^{23} +3.07609 q^{24} +2.52613 q^{25} -2.68866 q^{26} +5.33432 q^{27} +3.76272 q^{29} +2.53394 q^{30} +2.53611 q^{31} +5.80291 q^{32} +0.300500 q^{33} +3.80759 q^{34} +2.29617 q^{36} +0.0550810 q^{37} +2.69770 q^{38} +3.70849 q^{39} +7.47653 q^{40} -7.78083 q^{41} +3.55180 q^{43} +0.354180 q^{44} +4.73506 q^{45} -1.47489 q^{46} +6.62310 q^{47} -0.485941 q^{48} +2.06718 q^{50} -5.25184 q^{51} +4.37096 q^{52} +13.7361 q^{53} +4.36519 q^{54} +0.730373 q^{55} -3.72096 q^{57} +3.07912 q^{58} -13.5354 q^{59} -4.11943 q^{60} -9.30061 q^{61} +2.07535 q^{62} +3.88760 q^{64} +9.01357 q^{65} +0.245906 q^{66} +6.45752 q^{67} -6.19001 q^{68} +2.03433 q^{69} +2.95281 q^{71} +4.70385 q^{72} +11.8165 q^{73} +0.0450740 q^{74} -2.85129 q^{75} -4.38566 q^{76} +3.03474 q^{78} -11.4993 q^{79} -1.18109 q^{80} -0.842960 q^{81} -6.36722 q^{82} +0.0301401 q^{83} -12.7647 q^{85} +2.90652 q^{86} -4.24705 q^{87} +0.725560 q^{88} -2.02198 q^{89} +3.87480 q^{90} +2.39774 q^{92} -2.86255 q^{93} +5.41983 q^{94} -9.04388 q^{95} -6.54985 q^{96} -14.6568 q^{97} +0.459514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} + 3 q^{8} + 12 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 + 3 * q^8 + 12 * q^9	\( 7 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} + 3 q^{8} + 12 q^{9} + 5 q^{10} + q^{12} + q^{13} - 9 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 5 q^{19} - 11 q^{20} - 9 q^{22} - q^{23} + 24 q^{24} + 7 q^{25} + 4 q^{26} - 7 q^{29} - 43 q^{30} + 8 q^{31} - 2 q^{32} - 10 q^{33} + q^{34} + 10 q^{36} - 6 q^{37} - 29 q^{38} - 15 q^{39} + 3 q^{40} - 14 q^{41} - q^{43} - 21 q^{44} - 16 q^{45} - 3 q^{46} - 25 q^{47} - 2 q^{48} + 10 q^{50} + 17 q^{51} - 6 q^{52} + 29 q^{53} - q^{54} + 23 q^{55} + 4 q^{57} - 22 q^{58} + 12 q^{59} + 6 q^{60} - 7 q^{61} - 4 q^{62} - 3 q^{64} + 3 q^{65} - 36 q^{66} - 25 q^{67} - 53 q^{68} - 6 q^{69} + 7 q^{71} - 28 q^{72} - 13 q^{73} + 11 q^{74} - 12 q^{76} + 38 q^{78} - 23 q^{79} + 14 q^{80} - 5 q^{81} - 26 q^{82} - 26 q^{83} + 15 q^{85} + 5 q^{86} + 20 q^{87} + 25 q^{88} - 13 q^{89} + 24 q^{90} - 32 q^{92} - 7 q^{93} + 19 q^{94} - 40 q^{95} - 55 q^{96} + 5 q^{97} - 29 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 + 3 * q^8 + 12 * q^9 + 5 * q^10 + q^12 + q^13 - 9 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 5 * q^19 - 11 * q^20 - 9 * q^22 - q^23 + 24 * q^24 + 7 * q^25 + 4 * q^26 - 7 * q^29 - 43 * q^30 + 8 * q^31 - 2 * q^32 - 10 * q^33 + q^34 + 10 * q^36 - 6 * q^37 - 29 * q^38 - 15 * q^39 + 3 * q^40 - 14 * q^41 - q^43 - 21 * q^44 - 16 * q^45 - 3 * q^46 - 25 * q^47 - 2 * q^48 + 10 * q^50 + 17 * q^51 - 6 * q^52 + 29 * q^53 - q^54 + 23 * q^55 + 4 * q^57 - 22 * q^58 + 12 * q^59 + 6 * q^60 - 7 * q^61 - 4 * q^62 - 3 * q^64 + 3 * q^65 - 36 * q^66 - 25 * q^67 - 53 * q^68 - 6 * q^69 + 7 * q^71 - 28 * q^72 - 13 * q^73 + 11 * q^74 - 12 * q^76 + 38 * q^78 - 23 * q^79 + 14 * q^80 - 5 * q^81 - 26 * q^82 - 26 * q^83 + 15 * q^85 + 5 * q^86 + 20 * q^87 + 25 * q^88 - 13 * q^89 + 24 * q^90 - 32 * q^92 - 7 * q^93 + 19 * q^94 - 40 * q^95 - 55 * q^96 + 5 * q^97 - 29 * q^99

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