LMFDB - Embedded newform 294.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("294.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.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:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1345}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 336 $ x^2 - x - 336
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$18.8371$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.8371 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.8371 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -31.6742 q^{10} +51.8371 q^{11} +12.0000 q^{12} +38.8371 q^{13} -47.5114 q^{15} +16.0000 q^{16} +27.3485 q^{17} +18.0000 q^{18} +76.5114 q^{19} -63.3485 q^{20} +103.674 q^{22} +147.348 q^{23} +24.0000 q^{24} +125.814 q^{25} +77.6742 q^{26} +27.0000 q^{27} +240.208 q^{29} -95.0227 q^{30} -296.674 q^{31} +32.0000 q^{32} +155.511 q^{33} +54.6970 q^{34} +36.0000 q^{36} -161.534 q^{37} +153.023 q^{38} +116.511 q^{39} -126.697 q^{40} -102.977 q^{41} -328.557 q^{43} +207.348 q^{44} -142.534 q^{45} +294.697 q^{46} +67.9546 q^{47} +48.0000 q^{48} +251.629 q^{50} +82.0454 q^{51} +155.348 q^{52} -66.4886 q^{53} +54.0000 q^{54} -820.951 q^{55} +229.534 q^{57} +480.417 q^{58} -461.928 q^{59} -190.045 q^{60} +185.348 q^{61} -593.348 q^{62} +64.0000 q^{64} -615.068 q^{65} +311.023 q^{66} +545.208 q^{67} +109.394 q^{68} +442.045 q^{69} -130.742 q^{71} +72.0000 q^{72} +181.299 q^{73} -323.068 q^{74} +377.443 q^{75} +306.045 q^{76} +233.023 q^{78} -409.697 q^{79} -253.394 q^{80} +81.0000 q^{81} -205.955 q^{82} +347.928 q^{83} -433.121 q^{85} -657.114 q^{86} +720.625 q^{87} +414.697 q^{88} +1157.16 q^{89} -285.068 q^{90} +589.394 q^{92} -890.023 q^{93} +135.909 q^{94} -1211.72 q^{95} +96.0000 q^{96} +1618.30 q^{97} +466.534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 5 q^{5} + 12 q^{6} + 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 5 * q^5 + 12 * q^6 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 5 q^{5} + 12 q^{6} + 16 q^{8} + 18 q^{9} + 10 q^{10} + 67 q^{11} + 24 q^{12} + 41 q^{13} + 15 q^{15} + 32 q^{16} - 92 q^{17} + 36 q^{18} + 43 q^{19} + 20 q^{20} + 134 q^{22} + 148 q^{23} + 48 q^{24} + 435 q^{25} + 82 q^{26} + 54 q^{27} + 77 q^{29} + 30 q^{30} - 520 q^{31} + 64 q^{32} + 201 q^{33} - 184 q^{34} + 72 q^{36} + 7 q^{37} + 86 q^{38} + 123 q^{39} + 40 q^{40} - 426 q^{41} - 107 q^{43} + 268 q^{44} + 45 q^{45} + 296 q^{46} + 576 q^{47} + 96 q^{48} + 870 q^{50} - 276 q^{51} + 164 q^{52} - 243 q^{53} + 108 q^{54} - 505 q^{55} + 129 q^{57} + 154 q^{58} - 7 q^{59} + 60 q^{60} + 224 q^{61} - 1040 q^{62} + 128 q^{64} - 570 q^{65} + 402 q^{66} + 687 q^{67} - 368 q^{68} + 444 q^{69} + 472 q^{71} + 144 q^{72} - 921 q^{73} + 14 q^{74} + 1305 q^{75} + 172 q^{76} + 246 q^{78} - 526 q^{79} + 80 q^{80} + 162 q^{81} - 852 q^{82} - 221 q^{83} - 2920 q^{85} - 214 q^{86} + 231 q^{87} + 536 q^{88} + 774 q^{89} + 90 q^{90} + 592 q^{92} - 1560 q^{93} + 1152 q^{94} - 1910 q^{95} + 192 q^{96} + 1953 q^{97} + 603 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 5 * q^5 + 12 * q^6 + 16 * q^8 + 18 * q^9 + 10 * q^10 + 67 * q^11 + 24 * q^12 + 41 * q^13 + 15 * q^15 + 32 * q^16 - 92 * q^17 + 36 * q^18 + 43 * q^19 + 20 * q^20 + 134 * q^22 + 148 * q^23 + 48 * q^24 + 435 * q^25 + 82 * q^26 + 54 * q^27 + 77 * q^29 + 30 * q^30 - 520 * q^31 + 64 * q^32 + 201 * q^33 - 184 * q^34 + 72 * q^36 + 7 * q^37 + 86 * q^38 + 123 * q^39 + 40 * q^40 - 426 * q^41 - 107 * q^43 + 268 * q^44 + 45 * q^45 + 296 * q^46 + 576 * q^47 + 96 * q^48 + 870 * q^50 - 276 * q^51 + 164 * q^52 - 243 * q^53 + 108 * q^54 - 505 * q^55 + 129 * q^57 + 154 * q^58 - 7 * q^59 + 60 * q^60 + 224 * q^61 - 1040 * q^62 + 128 * q^64 - 570 * q^65 + 402 * q^66 + 687 * q^67 - 368 * q^68 + 444 * q^69 + 472 * q^71 + 144 * q^72 - 921 * q^73 + 14 * q^74 + 1305 * q^75 + 172 * q^76 + 246 * q^78 - 526 * q^79 + 80 * q^80 + 162 * q^81 - 852 * q^82 - 221 * q^83 - 2920 * q^85 - 214 * q^86 + 231 * q^87 + 536 * q^88 + 774 * q^89 + 90 * q^90 + 592 * q^92 - 1560 * q^93 + 1152 * q^94 - 1910 * q^95 + 192 * q^96 + 1953 * q^97 + 603 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−15.8371	−1.41652	−0.708258	−	0.705954i	$-0.750518\pi$
$5$	−15.8371	−1.41652	−0.708258	+	0.705954i	$0.750518\pi$
$6$	6.00000	0.408248
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−31.6742	−1.00163
$11$	51.8371	1.42086	0.710431	−	0.703767i	$-0.248500\pi$
$11$	51.8371	1.42086	0.710431	+	0.703767i	$0.248500\pi$
$12$	12.0000	0.288675
$13$	38.8371	0.828575	0.414288	−	0.910146i	$-0.364031\pi$
$13$	38.8371	0.828575	0.414288	+	0.910146i	$0.364031\pi$
$14$	0	0
$15$	−47.5114	−0.817825
$16$	16.0000	0.250000
$17$	27.3485	0.390175	0.195088	−	0.980786i	$-0.437501\pi$
$17$	27.3485	0.390175	0.195088	+	0.980786i	$0.437501\pi$
$18$	18.0000	0.235702
$19$	76.5114	0.923837	0.461919	−	0.886922i	$-0.347161\pi$
$19$	76.5114	0.923837	0.461919	+	0.886922i	$0.347161\pi$
$20$	−63.3485	−0.708258
$21$	0	0
$22$	103.674	1.00470
$23$	147.348	1.33584	0.667919	−	0.744234i	$-0.267185\pi$
$23$	147.348	1.33584	0.667919	+	0.744234i	$0.267185\pi$
$24$	24.0000	0.204124
$25$	125.814	1.00652
$26$	77.6742	0.585891
$27$	27.0000	0.192450
$28$	0	0
$29$	240.208	1.53812	0.769061	−	0.639175i	$-0.220724\pi$
$29$	240.208	1.53812	0.769061	+	0.639175i	$0.220724\pi$
$30$	−95.0227	−0.578290
$31$	−296.674	−1.71885	−0.859424	−	0.511264i	$-0.829177\pi$
$31$	−296.674	−1.71885	−0.859424	+	0.511264i	$0.829177\pi$
$32$	32.0000	0.176777
$33$	155.511	0.820335
$34$	54.6970	0.275896
$35$	0	0
$36$	36.0000	0.166667
$37$	−161.534	−0.717731	−0.358865	−	0.933389i	$-0.616836\pi$
$37$	−161.534	−0.717731	−0.358865	+	0.933389i	$0.616836\pi$
$38$	153.023	0.653252
$39$	116.511	0.478378
$40$	−126.697	−0.500814
$41$	−102.977	−0.392252	−0.196126	−	0.980579i	$-0.562836\pi$
$41$	−102.977	−0.392252	−0.196126	+	0.980579i	$0.562836\pi$
$42$	0	0
$43$	−328.557	−1.16522	−0.582610	−	0.812752i	$-0.697968\pi$
$43$	−328.557	−1.16522	−0.582610	+	0.812752i	$0.697968\pi$
$44$	207.348	0.710431
$45$	−142.534	−0.472172
$46$	294.697	0.944580
$47$	67.9546	0.210898	0.105449	−	0.994425i	$-0.466372\pi$
$47$	67.9546	0.210898	0.105449	+	0.994425i	$0.466372\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	251.629	0.711714
$51$	82.0454	0.225268
$52$	155.348	0.414288
$53$	−66.4886	−0.172319	−0.0861596	−	0.996281i	$-0.527459\pi$
$53$	−66.4886	−0.172319	−0.0861596	+	0.996281i	$0.527459\pi$
$54$	54.0000	0.136083
$55$	−820.951	−2.01267
$56$	0	0
$57$	229.534	0.533378
$58$	480.417	1.08762
$59$	−461.928	−1.01929	−0.509643	−	0.860386i	$-0.670223\pi$
$59$	−461.928	−1.01929	−0.509643	+	0.860386i	$0.670223\pi$
$60$	−190.045	−0.408913
$61$	185.348	0.389040	0.194520	−	0.980899i	$-0.437685\pi$
$61$	185.348	0.389040	0.194520	+	0.980899i	$0.437685\pi$
$62$	−593.348	−1.21541
$63$	0	0
$64$	64.0000	0.125000
$65$	−615.068	−1.17369
$66$	311.023	0.580064
$67$	545.208	0.994146	0.497073	−	0.867709i	$-0.334408\pi$
$67$	545.208	0.994146	0.497073	+	0.867709i	$0.334408\pi$
$68$	109.394	0.195088
$69$	442.045	0.771247
$70$	0	0
$71$	−130.742	−0.218539	−0.109270	−	0.994012i	$-0.534851\pi$
$71$	−130.742	−0.218539	−0.109270	+	0.994012i	$0.534851\pi$
$72$	72.0000	0.117851
$73$	181.299	0.290678	0.145339	−	0.989382i	$-0.453573\pi$
$73$	181.299	0.290678	0.145339	+	0.989382i	$0.453573\pi$
$74$	−323.068	−0.507512
$75$	377.443	0.581112
$76$	306.045	0.461919
$77$	0	0
$78$	233.023	0.338264
$79$	−409.697	−0.583475	−0.291737	−	0.956498i	$-0.594233\pi$
$79$	−409.697	−0.583475	−0.291737	+	0.956498i	$0.594233\pi$
$80$	−253.394	−0.354129
$81$	81.0000	0.111111
$82$	−205.955	−0.277364
$83$	347.928	0.460121	0.230061	−	0.973176i	$-0.426108\pi$
$83$	347.928	0.460121	0.230061	+	0.973176i	$0.426108\pi$
$84$	0	0
$85$	−433.121	−0.552689
$86$	−657.114	−0.823935
$87$	720.625	0.888036
$88$	414.697	0.502351
$89$	1157.16	1.37819	0.689093	−	0.724673i	$-0.258009\pi$
$89$	1157.16	1.37819	0.689093	+	0.724673i	$0.258009\pi$
$90$	−285.068	−0.333876
$91$	0	0
$92$	589.394	0.667919
$93$	−890.023	−0.992377
$94$	135.909	0.149127
$95$	−1211.72	−1.30863
$96$	96.0000	0.102062
$97$	1618.30	1.69395	0.846976	−	0.531631i	$-0.178421\pi$
$97$	1618.30	1.69395	0.846976	+	0.531631i	$0.178421\pi$
$98$	0	0
$99$	466.534	0.473621
$100$	503.258	0.503258
$101$	718.742	0.708094	0.354047	−	0.935228i	$-0.384805\pi$
$101$	718.742	0.708094	0.354047	+	0.935228i	$0.384805\pi$
$102$	164.091	0.159288
$103$	−1611.58	−1.54169	−0.770843	−	0.637025i	$-0.780165\pi$
$103$	−1611.58	−1.54169	−0.770843	+	0.637025i	$0.780165\pi$
$104$	310.697	0.292946
$105$	0	0
$106$	−132.977	−0.121848
$107$	934.670	0.844467	0.422234	−	0.906487i	$-0.361246\pi$
$107$	934.670	0.844467	0.422234	+	0.906487i	$0.361246\pi$
$108$	108.000	0.0962250
$109$	−1197.02	−1.05187	−0.525934	−	0.850525i	$-0.676284\pi$
$109$	−1197.02	−1.05187	−0.525934	+	0.850525i	$0.676284\pi$
$110$	−1641.90	−1.42317
$111$	−484.602	−0.414382
$112$	0	0
$113$	−2384.64	−1.98521	−0.992604	−	0.121400i	$-0.961262\pi$
$113$	−2384.64	−1.98521	−0.992604	+	0.121400i	$0.961262\pi$
$114$	459.068	0.377155
$115$	−2333.58	−1.89224
$116$	960.833	0.769061
$117$	349.534	0.276192
$118$	−923.856	−0.720744
$119$	0	0
$120$	−380.091	−0.289145
$121$	1356.09	1.01885
$122$	370.697	0.275093
$123$	−308.932	−0.226467
$124$	−1186.70	−0.859424
$125$	−12.8977	−0.00922883
$126$	0	0
$127$	−2673.92	−1.86829	−0.934143	−	0.356898i	$-0.883834\pi$
$127$	−2673.92	−1.86829	−0.934143	+	0.356898i	$0.883834\pi$
$128$	128.000	0.0883883
$129$	−985.670	−0.672740
$130$	−1230.14	−0.829924
$131$	−38.8598	−0.0259176	−0.0129588	−	0.999916i	$-0.504125\pi$
$131$	−38.8598	−0.0259176	−0.0129588	+	0.999916i	$0.504125\pi$
$132$	622.045	0.410167
$133$	0	0
$134$	1090.42	0.702968
$135$	−427.602	−0.272608
$136$	218.788	0.137948
$137$	−768.144	−0.479029	−0.239514	−	0.970893i	$-0.576988\pi$
$137$	−768.144	−0.479029	−0.239514	+	0.970893i	$0.576988\pi$
$138$	884.091	0.545354
$139$	1052.55	0.642274	0.321137	−	0.947033i	$-0.395935\pi$
$139$	1052.55	0.642274	0.321137	+	0.947033i	$0.395935\pi$
$140$	0	0
$141$	203.864	0.121762
$142$	−261.485	−0.154530
$143$	2013.20	1.17729
$144$	144.000	0.0833333
$145$	−3804.21	−2.17877
$146$	362.598	0.205540
$147$	0	0
$148$	−646.136	−0.358865
$149$	360.977	0.198473	0.0992363	−	0.995064i	$-0.468360\pi$
$149$	360.977	0.198473	0.0992363	+	0.995064i	$0.468360\pi$
$150$	754.886	0.410908
$151$	1548.39	0.834478	0.417239	−	0.908797i	$-0.362998\pi$
$151$	1548.39	0.834478	0.417239	+	0.908797i	$0.362998\pi$
$152$	612.091	0.326626
$153$	246.136	0.130058
$154$	0	0
$155$	4698.47	2.43477
$156$	466.045	0.239189
$157$	−967.068	−0.491595	−0.245798	−	0.969321i	$-0.579050\pi$
$157$	−967.068	−0.491595	−0.245798	+	0.969321i	$0.579050\pi$
$158$	−819.394	−0.412579
$159$	−199.466	−0.0994885
$160$	−506.788	−0.250407
$161$	0	0
$162$	162.000	0.0785674
$163$	−1326.50	−0.637420	−0.318710	−	0.947852i	$-0.603250\pi$
$163$	−1326.50	−0.637420	−0.318710	+	0.947852i	$0.603250\pi$
$164$	−411.909	−0.196126
$165$	−2462.85	−1.16202
$166$	695.856	0.325355
$167$	1416.70	0.656451	0.328225	−	0.944599i	$-0.393549\pi$
$167$	1416.70	0.656451	0.328225	+	0.944599i	$0.393549\pi$
$168$	0	0
$169$	−688.678	−0.313463
$170$	−866.242	−0.390810
$171$	688.602	0.307946
$172$	−1314.23	−0.582610
$173$	−1036.60	−0.455556	−0.227778	−	0.973713i	$-0.573146\pi$
$173$	−1036.60	−0.455556	−0.227778	+	0.973713i	$0.573146\pi$
$174$	1441.25	0.627936
$175$	0	0
$176$	829.394	0.355215
$177$	−1385.78	−0.588485
$178$	2314.32	0.974525
$179$	−767.432	−0.320450	−0.160225	−	0.987081i	$-0.551222\pi$
$179$	−767.432	−0.320450	−0.160225	+	0.987081i	$0.551222\pi$
$180$	−570.136	−0.236086
$181$	−3957.71	−1.62527	−0.812636	−	0.582772i	$-0.801968\pi$
$181$	−3957.71	−1.62527	−0.812636	+	0.582772i	$0.801968\pi$
$182$	0	0
$183$	556.045	0.224612
$184$	1178.79	0.472290
$185$	2558.23	1.01668
$186$	−1780.05	−0.701716
$187$	1417.67	0.554385
$188$	271.818	0.105449
$189$	0	0
$190$	−2423.44	−0.925341
$191$	−1805.30	−0.683909	−0.341954	−	0.939717i	$-0.611089\pi$
$191$	−1805.30	−0.683909	−0.341954	+	0.939717i	$0.611089\pi$
$192$	192.000	0.0721688
$193$	3370.84	1.25719	0.628597	−	0.777731i	$-0.283630\pi$
$193$	3370.84	1.25719	0.628597	+	0.777731i	$0.283630\pi$
$194$	3236.60	1.19781
$195$	−1845.20	−0.677630
$196$	0	0
$197$	−4612.31	−1.66809	−0.834044	−	0.551697i	$-0.813980\pi$
$197$	−4612.31	−1.66809	−0.834044	+	0.551697i	$0.813980\pi$
$198$	933.068	0.334900
$199$	−2229.86	−0.794326	−0.397163	−	0.917748i	$-0.630005\pi$
$199$	−2229.86	−0.794326	−0.397163	+	0.917748i	$0.630005\pi$
$200$	1006.52	0.355857
$201$	1635.62	0.573971
$202$	1437.48	0.500698
$203$	0	0
$204$	328.182	0.112634
$205$	1630.86	0.555631
$206$	−3223.16	−1.09014
$207$	1326.14	0.445279
$208$	621.394	0.207144
$209$	3966.13	1.31265
$210$	0	0
$211$	912.614	0.297758	0.148879	−	0.988855i	$-0.452434\pi$
$211$	912.614	0.297758	0.148879	+	0.988855i	$0.452434\pi$
$212$	−265.955	−0.0861596
$213$	−392.227	−0.126174
$214$	1869.34	0.597129
$215$	5203.39	1.65055
$216$	216.000	0.0680414
$217$	0	0
$218$	−2394.04	−0.743783
$219$	543.898	0.167823
$220$	−3283.80	−1.00634
$221$	1062.14	0.323290
$222$	−969.205	−0.293012
$223$	−4319.47	−1.29710	−0.648549	−	0.761173i	$-0.724624\pi$
$223$	−4319.47	−1.29710	−0.648549	+	0.761173i	$0.724624\pi$
$224$	0	0
$225$	1132.33	0.335505
$226$	−4769.29	−1.40375
$227$	2061.28	0.602697	0.301349	−	0.953514i	$-0.402563\pi$
$227$	2061.28	0.602697	0.301349	+	0.953514i	$0.402563\pi$
$228$	918.136	0.266689
$229$	−3474.63	−1.00266	−0.501332	−	0.865255i	$-0.667157\pi$
$229$	−3474.63	−1.00266	−0.501332	+	0.865255i	$0.667157\pi$
$230$	−4667.15	−1.33801
$231$	0	0
$232$	1921.67	0.543809
$233$	776.099	0.218214	0.109107	−	0.994030i	$-0.465201\pi$
$233$	776.099	0.218214	0.109107	+	0.994030i	$0.465201\pi$
$234$	699.068	0.195297
$235$	−1076.20	−0.298740
$236$	−1847.71	−0.509643
$237$	−1229.09	−0.336869
$238$	0	0
$239$	2006.80	0.543133	0.271567	−	0.962420i	$-0.412458\pi$
$239$	2006.80	0.543133	0.271567	+	0.962420i	$0.412458\pi$
$240$	−760.182	−0.204456
$241$	805.648	0.215337	0.107669	−	0.994187i	$-0.465661\pi$
$241$	805.648	0.215337	0.107669	+	0.994187i	$0.465661\pi$
$242$	2712.17	0.720435
$243$	243.000	0.0641500
$244$	741.394	0.194520
$245$	0	0
$246$	−617.864	−0.160136
$247$	2971.48	0.765469
$248$	−2373.39	−0.607704
$249$	1043.78	0.265651
$250$	−25.7954	−0.00652577
$251$	1421.78	0.357539	0.178769	−	0.983891i	$-0.442788\pi$
$251$	1421.78	0.357539	0.178769	+	0.983891i	$0.442788\pi$
$252$	0	0
$253$	7638.12	1.89804
$254$	−5347.85	−1.32108
$255$	−1299.36	−0.319095
$256$	256.000	0.0625000
$257$	−1465.82	−0.355779	−0.177890	−	0.984050i	$-0.556927\pi$
$257$	−1465.82	−0.355779	−0.177890	+	0.984050i	$0.556927\pi$
$258$	−1971.34	−0.475699
$259$	0	0
$260$	−2460.27	−0.586845
$261$	2161.87	0.512708
$262$	−77.7197	−0.0183265
$263$	6991.39	1.63919	0.819596	−	0.572942i	$-0.194198\pi$
$263$	6991.39	1.63919	0.819596	+	0.572942i	$0.194198\pi$
$264$	1244.09	0.290032
$265$	1052.99	0.244093
$266$	0	0
$267$	3471.48	0.795696
$268$	2180.83	0.497073
$269$	808.958	0.183357	0.0916786	−	0.995789i	$-0.470777\pi$
$269$	808.958	0.183357	0.0916786	+	0.995789i	$0.470777\pi$
$270$	−855.205	−0.192763
$271$	6661.77	1.49326	0.746630	−	0.665239i	$-0.231670\pi$
$271$	6661.77	1.49326	0.746630	+	0.665239i	$0.231670\pi$
$272$	437.576	0.0975438
$273$	0	0
$274$	−1536.29	−0.338725
$275$	6521.86	1.43012
$276$	1768.18	0.385623
$277$	−7531.47	−1.63365	−0.816827	−	0.576883i	$-0.804269\pi$
$277$	−7531.47	−1.63365	−0.816827	+	0.576883i	$0.804269\pi$
$278$	2105.10	0.454156
$279$	−2670.07	−0.572949
$280$	0	0
$281$	1690.19	0.358819	0.179410	−	0.983774i	$-0.442581\pi$
$281$	1690.19	0.358819	0.179410	+	0.983774i	$0.442581\pi$
$282$	407.727	0.0860986
$283$	3178.23	0.667584	0.333792	−	0.942647i	$-0.391672\pi$
$283$	3178.23	0.667584	0.333792	+	0.942647i	$0.391672\pi$
$284$	−522.970	−0.109270
$285$	−3635.16	−0.755538
$286$	4026.41	0.832470
$287$	0	0
$288$	288.000	0.0589256
$289$	−4165.06	−0.847763
$290$	−7608.42	−1.54063
$291$	4854.90	0.978004
$292$	725.197	0.145339
$293$	−2176.53	−0.433974	−0.216987	−	0.976174i	$-0.569623\pi$
$293$	−2176.53	−0.433974	−0.216987	+	0.976174i	$0.569623\pi$
$294$	0	0
$295$	7315.61	1.44383
$296$	−1292.27	−0.253756
$297$	1399.60	0.273445
$298$	721.955	0.140341
$299$	5722.59	1.10684
$300$	1509.77	0.290556
$301$	0	0
$302$	3096.78	0.590065
$303$	2156.23	0.408819
$304$	1224.18	0.230959
$305$	−2935.39	−0.551081
$306$	492.273	0.0919652
$307$	623.504	0.115913	0.0579564	−	0.998319i	$-0.481542\pi$
$307$	623.504	0.115913	0.0579564	+	0.998319i	$0.481542\pi$
$308$	0	0
$309$	−4834.74	−0.890093
$310$	9396.93	1.72164
$311$	467.992	0.0853293	0.0426647	−	0.999089i	$-0.486415\pi$
$311$	467.992	0.0853293	0.0426647	+	0.999089i	$0.486415\pi$
$312$	932.091	0.169132
$313$	3612.81	0.652422	0.326211	−	0.945297i	$-0.394228\pi$
$313$	3612.81	0.652422	0.326211	+	0.945297i	$0.394228\pi$
$314$	−1934.14	−0.347610
$315$	0	0
$316$	−1638.79	−0.291737
$317$	4531.74	0.802927	0.401463	−	0.915875i	$-0.368502\pi$
$317$	4531.74	0.802927	0.401463	+	0.915875i	$0.368502\pi$
$318$	−398.932	−0.0703490
$319$	12451.7	2.18546
$320$	−1013.58	−0.177064
$321$	2804.01	0.487553
$322$	0	0
$323$	2092.47	0.360459
$324$	324.000	0.0555556
$325$	4886.27	0.833974
$326$	−2653.00	−0.450724
$327$	−3591.06	−0.607296
$328$	−823.818	−0.138682
$329$	0	0
$330$	−4925.70	−0.821670
$331$	−1237.06	−0.205422	−0.102711	−	0.994711i	$-0.532752\pi$
$331$	−1237.06	−0.205422	−0.102711	+	0.994711i	$0.532752\pi$
$332$	1391.71	0.230061
$333$	−1453.81	−0.239244
$334$	2833.39	0.464181
$335$	−8634.53	−1.40822
$336$	0	0
$337$	−1867.83	−0.301921	−0.150960	−	0.988540i	$-0.548237\pi$
$337$	−1867.83	−0.301921	−0.150960	+	0.988540i	$0.548237\pi$
$338$	−1377.36	−0.221652
$339$	−7153.93	−1.14616
$340$	−1732.48	−0.276345
$341$	−15378.7	−2.44224
$342$	1377.20	0.217751
$343$	0	0
$344$	−2628.45	−0.411967
$345$	−7000.73	−1.09248
$346$	−2073.20	−0.322126
$347$	−63.3637	−0.00980271	−0.00490136	−	0.999988i	$-0.501560\pi$
$347$	−63.3637	−0.00980271	−0.00490136	+	0.999988i	$0.501560\pi$
$348$	2882.50	0.444018
$349$	1223.79	0.187702	0.0938508	−	0.995586i	$-0.470082\pi$
$349$	1223.79	0.187702	0.0938508	+	0.995586i	$0.470082\pi$
$350$	0	0
$351$	1048.60	0.159459
$352$	1658.79	0.251175
$353$	−4515.61	−0.680855	−0.340428	−	0.940271i	$-0.610572\pi$
$353$	−4515.61	−0.680855	−0.340428	+	0.940271i	$0.610572\pi$
$354$	−2771.57	−0.416122
$355$	2070.58	0.309564
$356$	4628.64	0.689093
$357$	0	0
$358$	−1534.86	−0.226592
$359$	2228.49	0.327619	0.163810	−	0.986492i	$-0.447622\pi$
$359$	2228.49	0.327619	0.163810	+	0.986492i	$0.447622\pi$
$360$	−1140.27	−0.166938
$361$	−1005.01	−0.146524
$362$	−7915.42	−1.14924
$363$	4068.26	0.588232
$364$	0	0
$365$	−2871.26	−0.411749
$366$	1112.09	0.158825
$367$	−1437.34	−0.204438	−0.102219	−	0.994762i	$-0.532594\pi$
$367$	−1437.34	−0.204438	−0.102219	+	0.994762i	$0.532594\pi$
$368$	2357.58	0.333960
$369$	−926.795	−0.130751
$370$	5116.47	0.718899
$371$	0	0
$372$	−3560.09	−0.496188
$373$	−12237.4	−1.69874	−0.849370	−	0.527798i	$-0.823018\pi$
$373$	−12237.4	−1.69874	−0.849370	+	0.527798i	$0.823018\pi$
$374$	2835.33	0.392010
$375$	−38.6931	−0.00532827
$376$	543.636	0.0745636
$377$	9329.00	1.27445
$378$	0	0
$379$	−10647.0	−1.44301	−0.721503	−	0.692411i	$-0.756549\pi$
$379$	−10647.0	−1.44301	−0.721503	+	0.692411i	$0.756549\pi$
$380$	−4846.88	−0.654315
$381$	−8021.77	−1.07866
$382$	−3610.59	−0.483597
$383$	−6714.81	−0.895851	−0.447925	−	0.894071i	$-0.647837\pi$
$383$	−6714.81	−0.895851	−0.447925	+	0.894071i	$0.647837\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	6741.68	0.888970
$387$	−2957.01	−0.388407
$388$	6473.20	0.846976
$389$	−10653.1	−1.38852	−0.694258	−	0.719727i	$-0.744267\pi$
$389$	−10653.1	−1.38852	−0.694258	+	0.719727i	$0.744267\pi$
$390$	−3690.41	−0.479157
$391$	4029.76	0.521211
$392$	0	0
$393$	−116.580	−0.0149635
$394$	−9224.62	−1.17952
$395$	6488.42	0.826501
$396$	1866.14	0.236810
$397$	3221.04	0.407203	0.203601	−	0.979054i	$-0.434735\pi$
$397$	3221.04	0.407203	0.203601	+	0.979054i	$0.434735\pi$
$398$	−4459.73	−0.561673
$399$	0	0
$400$	2013.03	0.251629
$401$	12485.0	1.55479	0.777395	−	0.629012i	$-0.216540\pi$
$401$	12485.0	1.55479	0.777395	+	0.629012i	$0.216540\pi$
$402$	3271.25	0.405859
$403$	−11522.0	−1.42419
$404$	2874.97	0.354047
$405$	−1282.81	−0.157391
$406$	0	0
$407$	−8373.46	−1.01980
$408$	656.364	0.0796442
$409$	7037.39	0.850798	0.425399	−	0.905006i	$-0.360134\pi$
$409$	7037.39	0.850798	0.425399	+	0.905006i	$0.360134\pi$
$410$	3261.73	0.392891
$411$	−2304.43	−0.276567
$412$	−6446.32	−0.770843
$413$	0	0
$414$	2652.27	0.314860
$415$	−5510.18	−0.651769
$416$	1242.79	0.146473
$417$	3157.65	0.370817
$418$	7932.26	0.928180
$419$	−1549.66	−0.180682	−0.0903410	−	0.995911i	$-0.528796\pi$
$419$	−1549.66	−0.180682	−0.0903410	+	0.995911i	$0.528796\pi$
$420$	0	0
$421$	5531.63	0.640369	0.320184	−	0.947355i	$-0.396255\pi$
$421$	5531.63	0.640369	0.320184	+	0.947355i	$0.396255\pi$
$422$	1825.23	0.210547
$423$	611.591	0.0702992
$424$	−531.909	−0.0609240
$425$	3440.83	0.392717
$426$	−784.454	−0.0892182
$427$	0	0
$428$	3738.68	0.422234
$429$	6039.61	0.679709
$430$	10406.8	1.16712
$431$	−2029.93	−0.226864	−0.113432	−	0.993546i	$-0.536184\pi$
$431$	−2029.93	−0.226864	−0.113432	+	0.993546i	$0.536184\pi$
$432$	432.000	0.0481125
$433$	−327.739	−0.0363744	−0.0181872	−	0.999835i	$-0.505789\pi$
$433$	−327.739	−0.0363744	−0.0181872	+	0.999835i	$0.505789\pi$
$434$	0	0
$435$	−11412.6	−1.25792
$436$	−4788.08	−0.525934
$437$	11273.8	1.23410
$438$	1087.80	0.118669
$439$	7908.68	0.859819	0.429910	−	0.902872i	$-0.358545\pi$
$439$	7908.68	0.859819	0.429910	+	0.902872i	$0.358545\pi$
$440$	−6567.61	−0.711587
$441$	0	0
$442$	2124.27	0.228600
$443$	−2920.82	−0.313256	−0.156628	−	0.987658i	$-0.550062\pi$
$443$	−2920.82	−0.313256	−0.156628	+	0.987658i	$0.550062\pi$
$444$	−1938.41	−0.207191
$445$	−18326.1	−1.95222
$446$	−8638.93	−0.917187
$447$	1082.93	0.114588
$448$	0	0
$449$	−10240.2	−1.07631	−0.538156	−	0.842845i	$-0.680879\pi$
$449$	−10240.2	−1.07631	−0.538156	+	0.842845i	$0.680879\pi$
$450$	2264.66	0.237238
$451$	−5338.05	−0.557336
$452$	−9538.58	−0.992604
$453$	4645.17	0.481786
$454$	4122.57	0.426171
$455$	0	0
$456$	1836.27	0.188578
$457$	5892.63	0.603163	0.301582	−	0.953440i	$-0.402485\pi$
$457$	5892.63	0.603163	0.301582	+	0.953440i	$0.402485\pi$
$458$	−6949.26	−0.708991
$459$	738.409	0.0750893
$460$	−9334.30	−0.946118
$461$	−12643.4	−1.27735	−0.638677	−	0.769475i	$-0.720518\pi$
$461$	−12643.4	−1.27735	−0.638677	+	0.769475i	$0.720518\pi$
$462$	0	0
$463$	15093.2	1.51499	0.757494	−	0.652842i	$-0.226423\pi$
$463$	15093.2	1.51499	0.757494	+	0.652842i	$0.226423\pi$
$464$	3843.33	0.384531
$465$	14095.4	1.40572
$466$	1552.20	0.154301
$467$	−2820.23	−0.279454	−0.139727	−	0.990190i	$-0.544622\pi$
$467$	−2820.23	−0.279454	−0.139727	+	0.990190i	$0.544622\pi$
$468$	1398.14	0.138096
$469$	0	0
$470$	−2152.41	−0.211241
$471$	−2901.20	−0.283823
$472$	−3695.42	−0.360372
$473$	−17031.4	−1.65562
$474$	−2458.18	−0.238203
$475$	9626.23	0.929856
$476$	0	0
$477$	−598.398	−0.0574397
$478$	4013.59	0.384053
$479$	−16448.5	−1.56900	−0.784500	−	0.620129i	$-0.787080\pi$
$479$	−16448.5	−1.56900	−0.784500	+	0.620129i	$0.787080\pi$
$480$	−1520.36	−0.144572
$481$	−6273.52	−0.594694
$482$	1611.30	0.152267
$483$	0	0
$484$	5424.35	0.509424
$485$	−25629.2	−2.39951
$486$	486.000	0.0453609
$487$	6331.07	0.589093	0.294546	−	0.955637i	$-0.404831\pi$
$487$	6331.07	0.589093	0.294546	+	0.955637i	$0.404831\pi$
$488$	1482.79	0.137546
$489$	−3979.50	−0.368015
$490$	0	0
$491$	−9286.90	−0.853588	−0.426794	−	0.904349i	$-0.640357\pi$
$491$	−9286.90	−0.853588	−0.426794	+	0.904349i	$0.640357\pi$
$492$	−1235.73	−0.113234
$493$	6569.33	0.600138
$494$	5942.96	0.541268
$495$	−7388.56	−0.670891
$496$	−4746.79	−0.429712
$497$	0	0
$498$	2087.57	0.187844
$499$	−243.451	−0.0218404	−0.0109202	−	0.999940i	$-0.503476\pi$
$499$	−243.451	−0.0218404	−0.0109202	+	0.999940i	$0.503476\pi$
$500$	−51.5907	−0.00461442
$501$	4250.09	0.379002
$502$	2843.57	0.252818
$503$	8499.30	0.753409	0.376705	−	0.926333i	$-0.377057\pi$
$503$	8499.30	0.753409	0.376705	+	0.926333i	$0.377057\pi$
$504$	0	0
$505$	−11382.8	−1.00303
$506$	15276.2	1.34212
$507$	−2066.03	−0.180978
$508$	−10695.7	−0.934143
$509$	−7683.10	−0.669052	−0.334526	−	0.942387i	$-0.608576\pi$
$509$	−7683.10	−0.669052	−0.334526	+	0.942387i	$0.608576\pi$
$510$	−2598.73	−0.225634
$511$	0	0
$512$	512.000	0.0441942
$513$	2065.81	0.177793
$514$	−2931.64	−0.251574
$515$	25522.8	2.18382
$516$	−3942.68	−0.336370
$517$	3522.57	0.299656
$518$	0	0
$519$	−3109.80	−0.263015
$520$	−4920.55	−0.414962
$521$	−21530.6	−1.81051	−0.905253	−	0.424874i	$-0.860319\pi$
$521$	−21530.6	−1.81051	−0.905253	+	0.424874i	$0.860319\pi$
$522$	4323.75	0.362539
$523$	−16847.1	−1.40855	−0.704274	−	0.709929i	$-0.748727\pi$
$523$	−16847.1	−1.40855	−0.704274	+	0.709929i	$0.748727\pi$
$524$	−155.439	−0.0129588
$525$	0	0
$526$	13982.8	1.15908
$527$	−8113.59	−0.670652
$528$	2488.18	0.205084
$529$	9544.58	0.784464
$530$	2105.98	0.172600
$531$	−4157.35	−0.339762
$532$	0	0
$533$	−3999.34	−0.325011
$534$	6942.95	0.562642
$535$	−14802.5	−1.19620
$536$	4361.67	0.351484
$537$	−2302.30	−0.185012
$538$	1617.92	0.129653
$539$	0	0
$540$	−1710.41	−0.136304
$541$	17440.0	1.38596	0.692981	−	0.720955i	$-0.256297\pi$
$541$	17440.0	1.38596	0.692981	+	0.720955i	$0.256297\pi$
$542$	13323.5	1.05589
$543$	−11873.1	−0.938351
$544$	875.151	0.0689739
$545$	18957.3	1.48999
$546$	0	0
$547$	11520.7	0.900530	0.450265	−	0.892895i	$-0.351329\pi$
$547$	11520.7	0.900530	0.450265	+	0.892895i	$0.351329\pi$
$548$	−3072.58	−0.239514
$549$	1668.14	0.129680
$550$	13043.7	1.01125
$551$	18378.7	1.42098
$552$	3536.36	0.272677
$553$	0	0
$554$	−15062.9	−1.15517
$555$	7674.70	0.586978
$556$	4210.20	0.321137
$557$	11493.0	0.874282	0.437141	−	0.899393i	$-0.355991\pi$
$557$	11493.0	0.874282	0.437141	+	0.899393i	$0.355991\pi$
$558$	−5340.14	−0.405136
$559$	−12760.2	−0.965472
$560$	0	0
$561$	4253.00	0.320075
$562$	3380.38	0.253724
$563$	18111.3	1.35577	0.677886	−	0.735167i	$-0.262896\pi$
$563$	18111.3	1.35577	0.677886	+	0.735167i	$0.262896\pi$
$564$	815.455	0.0608809
$565$	37765.9	2.81208
$566$	6356.46	0.472053
$567$	0	0
$568$	−1045.94	−0.0772652
$569$	4417.61	0.325476	0.162738	−	0.986669i	$-0.447967\pi$
$569$	4417.61	0.325476	0.162738	+	0.986669i	$0.447967\pi$
$570$	−7270.32	−0.534246
$571$	13219.7	0.968878	0.484439	−	0.874825i	$-0.339024\pi$
$571$	13219.7	0.968878	0.484439	+	0.874825i	$0.339024\pi$
$572$	8052.82	0.588646
$573$	−5415.89	−0.394855
$574$	0	0
$575$	18538.6	1.34454
$576$	576.000	0.0416667
$577$	−17496.4	−1.26236	−0.631182	−	0.775634i	$-0.717430\pi$
$577$	−17496.4	−1.26236	−0.631182	+	0.775634i	$0.717430\pi$
$578$	−8330.12	−0.599459
$579$	10112.5	0.725841
$580$	−15216.8	−1.08939
$581$	0	0
$582$	9709.80	0.691553
$583$	−3446.58	−0.244842
$584$	1450.39	0.102770
$585$	−5535.61	−0.391230
$586$	−4353.07	−0.306866
$587$	−4280.53	−0.300982	−0.150491	−	0.988611i	$-0.548085\pi$
$587$	−4280.53	−0.300982	−0.150491	+	0.988611i	$0.548085\pi$
$588$	0	0
$589$	−22699.0	−1.58794
$590$	14631.2	1.02095
$591$	−13836.9	−0.963072
$592$	−2584.55	−0.179433
$593$	−1590.93	−0.110172	−0.0550858	−	0.998482i	$-0.517543\pi$
$593$	−1590.93	−0.110172	−0.0550858	+	0.998482i	$0.517543\pi$
$594$	2799.20	0.193355
$595$	0	0
$596$	1443.91	0.0992363
$597$	−6689.59	−0.458604
$598$	11445.2	0.782656
$599$	−13922.8	−0.949703	−0.474851	−	0.880066i	$-0.657498\pi$
$599$	−13922.8	−0.949703	−0.474851	+	0.880066i	$0.657498\pi$
$600$	3019.55	0.205454
$601$	12559.7	0.852446	0.426223	−	0.904618i	$-0.359844\pi$
$601$	12559.7	0.852446	0.426223	+	0.904618i	$0.359844\pi$
$602$	0	0
$603$	4906.87	0.331382
$604$	6193.56	0.417239
$605$	−21476.5	−1.44321
$606$	4312.45	0.289078
$607$	7678.37	0.513436	0.256718	−	0.966486i	$-0.417359\pi$
$607$	7678.37	0.513436	0.256718	+	0.966486i	$0.417359\pi$
$608$	2448.36	0.163313
$609$	0	0
$610$	−5870.77	−0.389673
$611$	2639.16	0.174745
$612$	984.545	0.0650292
$613$	6158.37	0.405766	0.202883	−	0.979203i	$-0.434969\pi$
$613$	6158.37	0.405766	0.202883	+	0.979203i	$0.434969\pi$
$614$	1247.01	0.0819628
$615$	4892.59	0.320794
$616$	0	0
$617$	8813.12	0.575045	0.287523	−	0.957774i	$-0.407168\pi$
$617$	8813.12	0.575045	0.287523	+	0.957774i	$0.407168\pi$
$618$	−9669.48	−0.629391
$619$	23189.9	1.50579	0.752894	−	0.658142i	$-0.228658\pi$
$619$	23189.9	1.50579	0.752894	+	0.658142i	$0.228658\pi$
$620$	18793.9	1.21739
$621$	3978.41	0.257082
$622$	935.985	0.0603369
$623$	0	0
$624$	1864.18	0.119595
$625$	−15522.5	−0.993442
$626$	7225.62	0.461332
$627$	11898.4	0.757856
$628$	−3868.27	−0.245798
$629$	−4417.71	−0.280041
$630$	0	0
$631$	7936.94	0.500736	0.250368	−	0.968151i	$-0.419448\pi$
$631$	7936.94	0.500736	0.250368	+	0.968151i	$0.419448\pi$
$632$	−3277.58	−0.206289
$633$	2737.84	0.171911
$634$	9063.48	0.567755
$635$	42347.3	2.64646
$636$	−797.864	−0.0497443
$637$	0	0
$638$	24903.4	1.54535
$639$	−1176.68	−0.0728463
$640$	−2027.15	−0.125203
$641$	32114.6	1.97886	0.989432	−	0.144996i	$-0.0463169\pi$
$641$	32114.6	1.97886	0.989432	+	0.144996i	$0.0463169\pi$
$642$	5608.02	0.344752
$643$	−24786.7	−1.52021	−0.760104	−	0.649802i	$-0.774852\pi$
$643$	−24786.7	−1.52021	−0.760104	+	0.649802i	$0.774852\pi$
$644$	0	0
$645$	15610.2	0.952946
$646$	4184.94	0.254883
$647$	7545.59	0.458497	0.229249	−	0.973368i	$-0.426373\pi$
$647$	7545.59	0.458497	0.229249	+	0.973368i	$0.426373\pi$
$648$	648.000	0.0392837
$649$	−23945.0	−1.44827
$650$	9772.54	0.589708
$651$	0	0
$652$	−5306.00	−0.318710
$653$	−4888.99	−0.292988	−0.146494	−	0.989212i	$-0.546799\pi$
$653$	−4888.99	−0.292988	−0.146494	+	0.989212i	$0.546799\pi$
$654$	−7182.11	−0.429423
$655$	615.428	0.0367126
$656$	−1647.64	−0.0980631
$657$	1631.69	0.0968926
$658$	0	0
$659$	25895.9	1.53075	0.765374	−	0.643586i	$-0.222554\pi$
$659$	25895.9	1.53075	0.765374	+	0.643586i	$0.222554\pi$
$660$	−9851.41	−0.581008
$661$	8183.37	0.481537	0.240769	−	0.970583i	$-0.422601\pi$
$661$	8183.37	0.481537	0.240769	+	0.970583i	$0.422601\pi$
$662$	−2474.11	−0.145256
$663$	3186.41	0.186651
$664$	2783.42	0.162677
$665$	0	0
$666$	−2907.61	−0.169171
$667$	35394.3	2.05468
$668$	5666.79	0.328225
$669$	−12958.4	−0.748880
$670$	−17269.1	−0.995764
$671$	9607.93	0.552772
$672$	0	0
$673$	−4635.02	−0.265478	−0.132739	−	0.991151i	$-0.542377\pi$
$673$	−4635.02	−0.265478	−0.132739	+	0.991151i	$0.542377\pi$
$674$	−3735.67	−0.213490
$675$	3396.99	0.193704
$676$	−2754.71	−0.156731
$677$	−24385.8	−1.38437	−0.692187	−	0.721718i	$-0.743353\pi$
$677$	−24385.8	−1.38437	−0.692187	+	0.721718i	$0.743353\pi$
$678$	−14307.9	−0.810458
$679$	0	0
$680$	−3464.97	−0.195405
$681$	6183.85	0.347967
$682$	−30757.5	−1.72693
$683$	−18393.4	−1.03046	−0.515230	−	0.857052i	$-0.672294\pi$
$683$	−18393.4	−1.03046	−0.515230	+	0.857052i	$0.672294\pi$
$684$	2754.41	0.153973
$685$	12165.2	0.678552
$686$	0	0
$687$	−10423.9	−0.578889
$688$	−5256.91	−0.291305
$689$	−2582.23	−0.142779
$690$	−14001.5	−0.772502
$691$	−14898.9	−0.820231	−0.410116	−	0.912034i	$-0.634512\pi$
$691$	−14898.9	−0.820231	−0.410116	+	0.912034i	$0.634512\pi$
$692$	−4146.39	−0.227778
$693$	0	0
$694$	−126.727	−0.00693157
$695$	−16669.3	−0.909791
$696$	5765.00	0.313968
$697$	−2816.27	−0.153047
$698$	2447.58	0.132725
$699$	2328.30	0.125986
$700$	0	0
$701$	−5725.70	−0.308497	−0.154249	−	0.988032i	$-0.549296\pi$
$701$	−5725.70	−0.308497	−0.154249	+	0.988032i	$0.549296\pi$
$702$	2097.20	0.112755
$703$	−12359.2	−0.663067
$704$	3317.58	0.177608
$705$	−3228.61	−0.172477
$706$	−9031.23	−0.481437
$707$	0	0
$708$	−5543.14	−0.294243
$709$	−23456.8	−1.24251	−0.621255	−	0.783609i	$-0.713377\pi$
$709$	−23456.8	−1.24251	−0.621255	+	0.783609i	$0.713377\pi$
$710$	4141.17	0.218895
$711$	−3687.27	−0.194492
$712$	9257.27	0.487263
$713$	−43714.5	−2.29610
$714$	0	0
$715$	−31883.4	−1.66765
$716$	−3069.73	−0.160225
$717$	6020.39	0.313578
$718$	4456.98	0.231662
$719$	−8459.00	−0.438759	−0.219379	−	0.975640i	$-0.570403\pi$
$719$	−8459.00	−0.438759	−0.219379	+	0.975640i	$0.570403\pi$
$720$	−2280.55	−0.118043
$721$	0	0
$722$	−2010.02	−0.103608
$723$	2416.94	0.124325
$724$	−15830.8	−0.812636
$725$	30221.7	1.54814
$726$	8136.52	0.415943
$727$	−11822.2	−0.603111	−0.301555	−	0.953449i	$-0.597506\pi$
$727$	−11822.2	−0.603111	−0.301555	+	0.953449i	$0.597506\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−5742.52	−0.291151
$731$	−8985.53	−0.454640
$732$	2224.18	0.112306
$733$	5028.95	0.253409	0.126704	−	0.991941i	$-0.459560\pi$
$733$	5028.95	0.253409	0.126704	+	0.991941i	$0.459560\pi$
$734$	−2874.68	−0.144559
$735$	0	0
$736$	4715.15	0.236145
$737$	28262.0	1.41254
$738$	−1853.59	−0.0924548
$739$	−17743.9	−0.883247	−0.441624	−	0.897200i	$-0.645597\pi$
$739$	−17743.9	−0.883247	−0.441624	+	0.897200i	$0.645597\pi$
$740$	10232.9	0.508338
$741$	8914.44	0.441944
$742$	0	0
$743$	−13202.3	−0.651877	−0.325938	−	0.945391i	$-0.605680\pi$
$743$	−13202.3	−0.651877	−0.325938	+	0.945391i	$0.605680\pi$
$744$	−7120.18	−0.350858
$745$	−5716.84	−0.281139
$746$	−24474.9	−1.20119
$747$	3131.35	0.153374
$748$	5670.67	0.277193
$749$	0	0
$750$	−77.3861	−0.00376766
$751$	15601.0	0.758040	0.379020	−	0.925388i	$-0.376261\pi$
$751$	15601.0	0.758040	0.379020	+	0.925388i	$0.376261\pi$
$752$	1087.27	0.0527244
$753$	4265.35	0.206425
$754$	18658.0	0.901173
$755$	−24522.0	−1.18205
$756$	0	0
$757$	2948.08	0.141545	0.0707725	−	0.997492i	$-0.477454\pi$
$757$	2948.08	0.141545	0.0707725	+	0.997492i	$0.477454\pi$
$758$	−21294.0	−1.02036
$759$	22914.4	1.09583
$760$	−9693.76	−0.462670
$761$	1697.03	0.0808375	0.0404187	−	0.999183i	$-0.487131\pi$
$761$	1697.03	0.0808375	0.0404187	+	0.999183i	$0.487131\pi$
$762$	−16043.5	−0.762725
$763$	0	0
$764$	−7221.18	−0.341954
$765$	−3898.09	−0.184230
$766$	−13429.6	−0.633462
$767$	−17940.0	−0.844556
$768$	768.000	0.0360844
$769$	−96.7799	−0.00453833	−0.00226916	−	0.999997i	$-0.500722\pi$
$769$	−96.7799	−0.00453833	−0.00226916	+	0.999997i	$0.500722\pi$
$770$	0	0
$771$	−4397.45	−0.205409
$772$	13483.4	0.628597
$773$	36326.8	1.69028	0.845138	−	0.534548i	$-0.179518\pi$
$773$	36326.8	1.69028	0.845138	+	0.534548i	$0.179518\pi$
$774$	−5914.02	−0.274645
$775$	−37325.9	−1.73005
$776$	12946.4	0.598903
$777$	0	0
$778$	−21306.2	−0.981828
$779$	−7878.93	−0.362377
$780$	−7380.82	−0.338815
$781$	−6777.31	−0.310514
$782$	8059.52	0.368552
$783$	6485.62	0.296012
$784$	0	0
$785$	15315.6	0.696352
$786$	−233.159	−0.0105808
$787$	7096.46	0.321425	0.160713	−	0.987001i	$-0.448621\pi$
$787$	7096.46	0.321425	0.160713	+	0.987001i	$0.448621\pi$
$788$	−18449.2	−0.834044
$789$	20974.2	0.946388
$790$	12976.8	0.584424
$791$	0	0
$792$	3732.27	0.167450
$793$	7198.40	0.322349
$794$	6442.08	0.287936
$795$	3158.97	0.140927
$796$	−8919.45	−0.397163
$797$	40289.6	1.79063	0.895314	−	0.445436i	$-0.146951\pi$
$797$	40289.6	1.79063	0.895314	+	0.445436i	$0.146951\pi$
$798$	0	0
$799$	1858.45	0.0822871
$800$	4026.06	0.177928
$801$	10414.4	0.459396
$802$	24970.0	1.09940
$803$	9398.03	0.413013
$804$	6542.50	0.286985
$805$	0	0
$806$	−23043.9	−1.00706
$807$	2426.88	0.105861
$808$	5749.94	0.250349
$809$	−11566.0	−0.502642	−0.251321	−	0.967904i	$-0.580865\pi$
$809$	−11566.0	−0.502642	−0.251321	+	0.967904i	$0.580865\pi$
$810$	−2565.61	−0.111292
$811$	18014.2	0.779981	0.389991	−	0.920819i	$-0.372478\pi$
$811$	18014.2	0.779981	0.389991	+	0.920819i	$0.372478\pi$
$812$	0	0
$813$	19985.3	0.862134
$814$	−16746.9	−0.721105
$815$	21007.9	0.902915
$816$	1312.73	0.0563170
$817$	−25138.3	−1.07647
$818$	14074.8	0.601605
$819$	0	0
$820$	6523.45	0.277816
$821$	−16792.4	−0.713837	−0.356918	−	0.934136i	$-0.616173\pi$
$821$	−16792.4	−0.713837	−0.356918	+	0.934136i	$0.616173\pi$
$822$	−4608.86	−0.195563
$823$	−8819.03	−0.373526	−0.186763	−	0.982405i	$-0.559800\pi$
$823$	−8819.03	−0.373526	−0.186763	+	0.982405i	$0.559800\pi$
$824$	−12892.6	−0.545068
$825$	19565.6	0.825680
$826$	0	0
$827$	8250.13	0.346898	0.173449	−	0.984843i	$-0.444509\pi$
$827$	8250.13	0.346898	0.173449	+	0.984843i	$0.444509\pi$
$828$	5304.55	0.222640
$829$	−21550.5	−0.902871	−0.451435	−	0.892304i	$-0.649088\pi$
$829$	−21550.5	−0.902871	−0.451435	+	0.892304i	$0.649088\pi$
$830$	−11020.4	−0.460870
$831$	−22594.4	−0.943190
$832$	2485.58	0.103572
$833$	0	0
$834$	6315.30	0.262207
$835$	−22436.4	−0.929873
$836$	15864.5	0.656323
$837$	−8010.20	−0.330792
$838$	−3099.32	−0.127762
$839$	30130.4	1.23983	0.619916	−	0.784669i	$-0.287167\pi$
$839$	30130.4	1.23983	0.619916	+	0.784669i	$0.287167\pi$
$840$	0	0
$841$	33311.0	1.36582
$842$	11063.3	0.452809
$843$	5070.57	0.207164
$844$	3650.45	0.148879
$845$	10906.7	0.444025
$846$	1223.18	0.0497091
$847$	0	0
$848$	−1063.82	−0.0430798
$849$	9534.69	0.385430
$850$	6881.67	0.277693
$851$	−23801.8	−0.958772
$852$	−1568.91	−0.0630868
$853$	−40738.6	−1.63525	−0.817623	−	0.575754i	$-0.804709\pi$
$853$	−40738.6	−1.63525	−0.817623	+	0.575754i	$0.804709\pi$
$854$	0	0
$855$	−10905.5	−0.436210
$856$	7477.36	0.298564
$857$	−36508.2	−1.45519	−0.727594	−	0.686008i	$-0.759362\pi$
$857$	−36508.2	−1.45519	−0.727594	+	0.686008i	$0.759362\pi$
$858$	12079.2	0.480627
$859$	−21980.8	−0.873081	−0.436541	−	0.899685i	$-0.643796\pi$
$859$	−21980.8	−0.873081	−0.436541	+	0.899685i	$0.643796\pi$
$860$	20813.6	0.825276
$861$	0	0
$862$	−4059.86	−0.160417
$863$	−23426.1	−0.924024	−0.462012	−	0.886874i	$-0.652872\pi$
$863$	−23426.1	−0.924024	−0.462012	+	0.886874i	$0.652872\pi$
$864$	864.000	0.0340207
$865$	16416.7	0.645301
$866$	−655.477	−0.0257206
$867$	−12495.2	−0.489456
$868$	0	0
$869$	−21237.5	−0.829037
$870$	−22825.2	−0.889481
$871$	21174.3	0.823725
$872$	−9576.15	−0.371892
$873$	14564.7	0.564651
$874$	22547.7	0.872639
$875$	0	0
$876$	2175.59	0.0839114
$877$	307.401	0.0118360	0.00591802	−	0.999982i	$-0.498116\pi$
$877$	307.401	0.0118360	0.00591802	+	0.999982i	$0.498116\pi$
$878$	15817.4	0.607984
$879$	−6529.60	−0.250555
$880$	−13135.2	−0.503168
$881$	−19941.7	−0.762605	−0.381302	−	0.924450i	$-0.624524\pi$
$881$	−19941.7	−0.762605	−0.381302	+	0.924450i	$0.624524\pi$
$882$	0	0
$883$	−37524.1	−1.43011	−0.715056	−	0.699068i	$-0.753599\pi$
$883$	−37524.1	−1.43011	−0.715056	+	0.699068i	$0.753599\pi$
$884$	4248.55	0.161645
$885$	21946.8	0.833598
$886$	−5841.64	−0.221505
$887$	−2880.20	−0.109028	−0.0545140	−	0.998513i	$-0.517361\pi$
$887$	−2880.20	−0.109028	−0.0545140	+	0.998513i	$0.517361\pi$
$888$	−3876.82	−0.146506
$889$	0	0
$890$	−36652.1	−1.38043
$891$	4198.81	0.157874
$892$	−17277.9	−0.648549
$893$	5199.30	0.194835
$894$	2165.86	0.0810261
$895$	12153.9	0.453922
$896$	0	0
$897$	17167.8	0.639036
$898$	−20480.4	−0.761068
$899$	−71263.6	−2.64380
$900$	4529.32	0.167753
$901$	−1818.36	−0.0672347
$902$	−10676.1	−0.394096
$903$	0	0
$904$	−19077.2	−0.701877
$905$	62678.7	2.30222
$906$	9290.34	0.340674
$907$	18319.2	0.670651	0.335326	−	0.942102i	$-0.391154\pi$
$907$	18319.2	0.670651	0.335326	+	0.942102i	$0.391154\pi$
$908$	8245.14	0.301349
$909$	6468.68	0.236031
$910$	0	0
$911$	46150.7	1.67842	0.839210	−	0.543807i	$-0.183018\pi$
$911$	46150.7	1.67842	0.839210	+	0.543807i	$0.183018\pi$
$912$	3672.55	0.133344
$913$	18035.6	0.653769
$914$	11785.3	0.426501
$915$	−8806.16	−0.318167
$916$	−13898.5	−0.501332
$917$	0	0
$918$	1476.82	0.0530961
$919$	47264.3	1.69652	0.848261	−	0.529578i	$-0.177650\pi$
$919$	47264.3	1.69652	0.848261	+	0.529578i	$0.177650\pi$
$920$	−18668.6	−0.669006
$921$	1870.51	0.0669223
$922$	−25286.7	−0.903226
$923$	−5077.66	−0.181076
$924$	0	0
$925$	−20323.3	−0.722407
$926$	30186.4	1.07126
$927$	−14504.2	−0.513895
$928$	7686.67	0.271904
$929$	−53271.5	−1.88136	−0.940678	−	0.339301i	$-0.889810\pi$
$929$	−53271.5	−1.88136	−0.940678	+	0.339301i	$0.889810\pi$
$930$	28190.8	0.993992
$931$	0	0
$932$	3104.39	0.109107
$933$	1403.98	0.0492649
$934$	−5640.47	−0.197604
$935$	−22451.8	−0.785295
$936$	2796.27	0.0976485
$937$	17197.8	0.599602	0.299801	−	0.954002i	$-0.403080\pi$
$937$	17197.8	0.599602	0.299801	+	0.954002i	$0.403080\pi$
$938$	0	0
$939$	10838.4	0.376676
$940$	−4304.82	−0.149370
$941$	28834.9	0.998926	0.499463	−	0.866335i	$-0.333531\pi$
$941$	28834.9	0.998926	0.499463	+	0.866335i	$0.333531\pi$
$942$	−5802.41	−0.200693
$943$	−15173.5	−0.523986
$944$	−7390.85	−0.254822
$945$	0	0
$946$	−34062.9	−1.17070
$947$	−51841.2	−1.77890	−0.889448	−	0.457037i	$-0.848911\pi$
$947$	−51841.2	−1.77890	−0.889448	+	0.457037i	$0.848911\pi$
$948$	−4916.36	−0.168435
$949$	7041.14	0.240848
$950$	19252.5	0.657508
$951$	13595.2	0.463570
$952$	0	0
$953$	−5887.31	−0.200114	−0.100057	−	0.994982i	$-0.531903\pi$
$953$	−5887.31	−0.200114	−0.100057	+	0.994982i	$0.531903\pi$
$954$	−1196.80	−0.0406160
$955$	28590.7	0.968767
$956$	8027.18	0.271567
$957$	37355.1	1.26178
$958$	−32897.0	−1.10945
$959$	0	0
$960$	−3040.73	−0.102228
$961$	58224.6	1.95444
$962$	−12547.0	−0.420512
$963$	8412.03	0.281489
$964$	3222.59	0.107669
$965$	−53384.4	−1.78083
$966$	0	0
$967$	−36620.0	−1.21781	−0.608904	−	0.793244i	$-0.708391\pi$
$967$	−36620.0	−1.21781	−0.608904	+	0.793244i	$0.708391\pi$
$968$	10848.7	0.360217
$969$	6277.41	0.208111
$970$	−51258.4	−1.69671
$971$	−42364.9	−1.40016	−0.700079	−	0.714065i	$-0.746852\pi$
$971$	−42364.9	−1.40016	−0.700079	+	0.714065i	$0.746852\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	12662.1	0.416551
$975$	14658.8	0.481495
$976$	2965.58	0.0972600
$977$	5022.32	0.164461	0.0822304	−	0.996613i	$-0.473796\pi$
$977$	5022.32	0.164461	0.0822304	+	0.996613i	$0.473796\pi$
$978$	−7959.00	−0.260226
$979$	59983.8	1.95821
$980$	0	0
$981$	−10773.2	−0.350623
$982$	−18573.8	−0.603578
$983$	28292.8	0.918005	0.459003	−	0.888435i	$-0.348207\pi$
$983$	28292.8	0.918005	0.459003	+	0.888435i	$0.348207\pi$
$984$	−2471.45	−0.0800682
$985$	73045.7	2.36287
$986$	13138.7	0.424361
$987$	0	0
$988$	11885.9	0.382734
$989$	−48412.3	−1.55655
$990$	−14777.1	−0.474391
$991$	36401.1	1.16682	0.583410	−	0.812178i	$-0.301718\pi$
$991$	36401.1	1.16682	0.583410	+	0.812178i	$0.301718\pi$
$992$	−9493.58	−0.303852
$993$	−3711.17	−0.118601
$994$	0	0
$995$	35314.6	1.12517
$996$	4175.14	0.132826
$997$	−2357.19	−0.0748777	−0.0374389	−	0.999299i	$-0.511920\pi$
$997$	−2357.19	−0.0748777	−0.0374389	+	0.999299i	$0.511920\pi$
$998$	−486.902	−0.0154435
$999$	−4361.42	−0.138127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.a.n.1.1		2
3.2	odd	2		882.4.a.v.1.2		2
4.3	odd	2		2352.4.a.bq.1.1		2
7.2	even	3		42.4.e.c.25.2	✓	4
7.3	odd	6		294.4.e.l.79.1		4
7.4	even	3		42.4.e.c.37.2	yes	4
7.5	odd	6		294.4.e.l.67.1		4
7.6	odd	2		294.4.a.m.1.2		2
21.2	odd	6		126.4.g.g.109.1		4
21.5	even	6		882.4.g.bf.361.2		4
21.11	odd	6		126.4.g.g.37.1		4
21.17	even	6		882.4.g.bf.667.2		4
21.20	even	2		882.4.a.z.1.1		2
28.11	odd	6		336.4.q.j.289.2		4
28.23	odd	6		336.4.q.j.193.2		4
28.27	even	2		2352.4.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.c.25.2	✓	4	7.2	even	3
42.4.e.c.37.2	yes	4	7.4	even	3
126.4.g.g.37.1		4	21.11	odd	6
126.4.g.g.109.1		4	21.2	odd	6
294.4.a.m.1.2		2	7.6	odd	2
294.4.a.n.1.1		2	1.1	even	1	trivial
294.4.e.l.67.1		4	7.5	odd	6
294.4.e.l.79.1		4	7.3	odd	6
336.4.q.j.193.2		4	28.23	odd	6
336.4.q.j.289.2		4	28.11	odd	6
882.4.a.v.1.2		2	3.2	odd	2
882.4.a.z.1.1		2	21.20	even	2
882.4.g.bf.361.2		4	21.5	even	6
882.4.g.bf.667.2		4	21.17	even	6
2352.4.a.bq.1.1		2	4.3	odd	2
2352.4.a.ca.1.2		2	28.27	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.8371 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.8371 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -31.6742 q^{10} +51.8371 q^{11} +12.0000 q^{12} +38.8371 q^{13} -47.5114 q^{15} +16.0000 q^{16} +27.3485 q^{17} +18.0000 q^{18} +76.5114 q^{19} -63.3485 q^{20} +103.674 q^{22} +147.348 q^{23} +24.0000 q^{24} +125.814 q^{25} +77.6742 q^{26} +27.0000 q^{27} +240.208 q^{29} -95.0227 q^{30} -296.674 q^{31} +32.0000 q^{32} +155.511 q^{33} +54.6970 q^{34} +36.0000 q^{36} -161.534 q^{37} +153.023 q^{38} +116.511 q^{39} -126.697 q^{40} -102.977 q^{41} -328.557 q^{43} +207.348 q^{44} -142.534 q^{45} +294.697 q^{46} +67.9546 q^{47} +48.0000 q^{48} +251.629 q^{50} +82.0454 q^{51} +155.348 q^{52} -66.4886 q^{53} +54.0000 q^{54} -820.951 q^{55} +229.534 q^{57} +480.417 q^{58} -461.928 q^{59} -190.045 q^{60} +185.348 q^{61} -593.348 q^{62} +64.0000 q^{64} -615.068 q^{65} +311.023 q^{66} +545.208 q^{67} +109.394 q^{68} +442.045 q^{69} -130.742 q^{71} +72.0000 q^{72} +181.299 q^{73} -323.068 q^{74} +377.443 q^{75} +306.045 q^{76} +233.023 q^{78} -409.697 q^{79} -253.394 q^{80} +81.0000 q^{81} -205.955 q^{82} +347.928 q^{83} -433.121 q^{85} -657.114 q^{86} +720.625 q^{87} +414.697 q^{88} +1157.16 q^{89} -285.068 q^{90} +589.394 q^{92} -890.023 q^{93} +135.909 q^{94} -1211.72 q^{95} +96.0000 q^{96} +1618.30 q^{97} +466.534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 5 q^{5} + 12 q^{6} + 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 5 * q^5 + 12 * q^6 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 5 q^{5} + 12 q^{6} + 16 q^{8} + 18 q^{9} + 10 q^{10} + 67 q^{11} + 24 q^{12} + 41 q^{13} + 15 q^{15} + 32 q^{16} - 92 q^{17} + 36 q^{18} + 43 q^{19} + 20 q^{20} + 134 q^{22} + 148 q^{23} + 48 q^{24} + 435 q^{25} + 82 q^{26} + 54 q^{27} + 77 q^{29} + 30 q^{30} - 520 q^{31} + 64 q^{32} + 201 q^{33} - 184 q^{34} + 72 q^{36} + 7 q^{37} + 86 q^{38} + 123 q^{39} + 40 q^{40} - 426 q^{41} - 107 q^{43} + 268 q^{44} + 45 q^{45} + 296 q^{46} + 576 q^{47} + 96 q^{48} + 870 q^{50} - 276 q^{51} + 164 q^{52} - 243 q^{53} + 108 q^{54} - 505 q^{55} + 129 q^{57} + 154 q^{58} - 7 q^{59} + 60 q^{60} + 224 q^{61} - 1040 q^{62} + 128 q^{64} - 570 q^{65} + 402 q^{66} + 687 q^{67} - 368 q^{68} + 444 q^{69} + 472 q^{71} + 144 q^{72} - 921 q^{73} + 14 q^{74} + 1305 q^{75} + 172 q^{76} + 246 q^{78} - 526 q^{79} + 80 q^{80} + 162 q^{81} - 852 q^{82} - 221 q^{83} - 2920 q^{85} - 214 q^{86} + 231 q^{87} + 536 q^{88} + 774 q^{89} + 90 q^{90} + 592 q^{92} - 1560 q^{93} + 1152 q^{94} - 1910 q^{95} + 192 q^{96} + 1953 q^{97} + 603 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 5 * q^5 + 12 * q^6 + 16 * q^8 + 18 * q^9 + 10 * q^10 + 67 * q^11 + 24 * q^12 + 41 * q^13 + 15 * q^15 + 32 * q^16 - 92 * q^17 + 36 * q^18 + 43 * q^19 + 20 * q^20 + 134 * q^22 + 148 * q^23 + 48 * q^24 + 435 * q^25 + 82 * q^26 + 54 * q^27 + 77 * q^29 + 30 * q^30 - 520 * q^31 + 64 * q^32 + 201 * q^33 - 184 * q^34 + 72 * q^36 + 7 * q^37 + 86 * q^38 + 123 * q^39 + 40 * q^40 - 426 * q^41 - 107 * q^43 + 268 * q^44 + 45 * q^45 + 296 * q^46 + 576 * q^47 + 96 * q^48 + 870 * q^50 - 276 * q^51 + 164 * q^52 - 243 * q^53 + 108 * q^54 - 505 * q^55 + 129 * q^57 + 154 * q^58 - 7 * q^59 + 60 * q^60 + 224 * q^61 - 1040 * q^62 + 128 * q^64 - 570 * q^65 + 402 * q^66 + 687 * q^67 - 368 * q^68 + 444 * q^69 + 472 * q^71 + 144 * q^72 - 921 * q^73 + 14 * q^74 + 1305 * q^75 + 172 * q^76 + 246 * q^78 - 526 * q^79 + 80 * q^80 + 162 * q^81 - 852 * q^82 - 221 * q^83 - 2920 * q^85 - 214 * q^86 + 231 * q^87 + 536 * q^88 + 774 * q^89 + 90 * q^90 + 592 * q^92 - 1560 * q^93 + 1152 * q^94 - 1910 * q^95 + 192 * q^96 + 1953 * q^97 + 603 * q^99

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