LMFDB - Embedded newform 1250.4.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1250,4,Mod(1,1250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1250, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1250.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1250 = 2 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1250.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:	$73.7523875072$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2140313125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 36x^{4} + 44x^{3} + 334x^{2} - 172x - 349 $ x^6 - 2x^5 - 36x^4 + 44x^3 + 334x^2 - 172*x - 349
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-4.28390$ of defining polynomial
Character	$\chi$	$=$	1250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +4.32700 q^{3} +4.00000 q^{4} +8.65399 q^{6} -17.3088 q^{7} +8.00000 q^{8} -8.27710 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +4.32700 q^{3} +4.00000 q^{4} +8.65399 q^{6} -17.3088 q^{7} +8.00000 q^{8} -8.27710 q^{9} +26.0182 q^{11} +17.3080 q^{12} -66.9252 q^{13} -34.6177 q^{14} +16.0000 q^{16} +65.2420 q^{17} -16.5542 q^{18} -9.59086 q^{19} -74.8953 q^{21} +52.0364 q^{22} -110.200 q^{23} +34.6160 q^{24} -133.850 q^{26} -152.644 q^{27} -69.2353 q^{28} +238.034 q^{29} +2.98408 q^{31} +32.0000 q^{32} +112.581 q^{33} +130.484 q^{34} -33.1084 q^{36} -315.961 q^{37} -19.1817 q^{38} -289.585 q^{39} -439.530 q^{41} -149.791 q^{42} -132.682 q^{43} +104.073 q^{44} -220.401 q^{46} +158.109 q^{47} +69.2319 q^{48} -43.4043 q^{49} +282.302 q^{51} -267.701 q^{52} -381.485 q^{53} -305.288 q^{54} -138.471 q^{56} -41.4996 q^{57} +476.068 q^{58} -536.027 q^{59} +125.932 q^{61} +5.96816 q^{62} +143.267 q^{63} +64.0000 q^{64} +225.161 q^{66} +871.688 q^{67} +260.968 q^{68} -476.836 q^{69} -766.732 q^{71} -66.2168 q^{72} -871.343 q^{73} -631.922 q^{74} -38.3634 q^{76} -450.345 q^{77} -579.170 q^{78} -289.677 q^{79} -437.008 q^{81} -879.060 q^{82} -1167.33 q^{83} -299.581 q^{84} -265.364 q^{86} +1029.97 q^{87} +208.146 q^{88} -270.769 q^{89} +1158.40 q^{91} -440.801 q^{92} +12.9121 q^{93} +316.217 q^{94} +138.464 q^{96} -206.315 q^{97} -86.8085 q^{98} -215.355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 8 q^{3} + 24 q^{4} - 16 q^{6} - 29 q^{7} + 48 q^{8} - 18 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 8 * q^3 + 24 * q^4 - 16 * q^6 - 29 * q^7 + 48 * q^8 - 18 * q^9	\( 6 q + 12 q^{2} - 8 q^{3} + 24 q^{4} - 16 q^{6} - 29 q^{7} + 48 q^{8} - 18 q^{9} - 33 q^{11} - 32 q^{12} + 32 q^{13} - 58 q^{14} + 96 q^{16} + 26 q^{17} - 36 q^{18} - 75 q^{19} - 88 q^{21} - 66 q^{22} - 113 q^{23} - 64 q^{24} + 64 q^{26} + 40 q^{27} - 116 q^{28} + 230 q^{29} - 13 q^{31} + 192 q^{32} - 101 q^{33} + 52 q^{34} - 72 q^{36} - 664 q^{37} - 150 q^{38} - 826 q^{39} - 253 q^{41} - 176 q^{42} - 373 q^{43} - 132 q^{44} - 226 q^{46} - 1534 q^{47} - 128 q^{48} - 417 q^{49} + 1362 q^{51} + 128 q^{52} - 1233 q^{53} + 80 q^{54} - 232 q^{56} - 640 q^{57} + 460 q^{58} + 220 q^{59} - 588 q^{61} - 26 q^{62} + 447 q^{63} + 384 q^{64} - 202 q^{66} - 739 q^{67} + 104 q^{68} - 511 q^{69} - 1628 q^{71} - 144 q^{72} - 3283 q^{73} - 1328 q^{74} - 300 q^{76} - 248 q^{77} - 1652 q^{78} + 1220 q^{79} - 1754 q^{81} - 506 q^{82} - 893 q^{83} - 352 q^{84} - 746 q^{86} - 725 q^{87} - 264 q^{88} - 2305 q^{89} + 1127 q^{91} - 452 q^{92} - 2276 q^{93} - 3068 q^{94} - 256 q^{96} - 4369 q^{97} - 834 q^{98} - 601 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 8 * q^3 + 24 * q^4 - 16 * q^6 - 29 * q^7 + 48 * q^8 - 18 * q^9 - 33 * q^11 - 32 * q^12 + 32 * q^13 - 58 * q^14 + 96 * q^16 + 26 * q^17 - 36 * q^18 - 75 * q^19 - 88 * q^21 - 66 * q^22 - 113 * q^23 - 64 * q^24 + 64 * q^26 + 40 * q^27 - 116 * q^28 + 230 * q^29 - 13 * q^31 + 192 * q^32 - 101 * q^33 + 52 * q^34 - 72 * q^36 - 664 * q^37 - 150 * q^38 - 826 * q^39 - 253 * q^41 - 176 * q^42 - 373 * q^43 - 132 * q^44 - 226 * q^46 - 1534 * q^47 - 128 * q^48 - 417 * q^49 + 1362 * q^51 + 128 * q^52 - 1233 * q^53 + 80 * q^54 - 232 * q^56 - 640 * q^57 + 460 * q^58 + 220 * q^59 - 588 * q^61 - 26 * q^62 + 447 * q^63 + 384 * q^64 - 202 * q^66 - 739 * q^67 + 104 * q^68 - 511 * q^69 - 1628 * q^71 - 144 * q^72 - 3283 * q^73 - 1328 * q^74 - 300 * q^76 - 248 * q^77 - 1652 * q^78 + 1220 * q^79 - 1754 * q^81 - 506 * q^82 - 893 * q^83 - 352 * q^84 - 746 * q^86 - 725 * q^87 - 264 * q^88 - 2305 * q^89 + 1127 * q^91 - 452 * q^92 - 2276 * q^93 - 3068 * q^94 - 256 * q^96 - 4369 * q^97 - 834 * q^98 - 601 * 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
$3$	4.32700	0.832731	0.416365	−	0.909197i	$-0.363304\pi$
$3$	4.32700	0.832731	0.416365	+	0.909197i	$0.363304\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	8.65399	0.588830
$7$	−17.3088	−0.934589	−0.467295	−	0.884102i	$-0.654771\pi$
$7$	−17.3088	−0.934589	−0.467295	+	0.884102i	$0.654771\pi$
$8$	8.00000	0.353553
$9$	−8.27710	−0.306559
$10$	0	0
$11$	26.0182	0.713162	0.356581	−	0.934264i	$-0.383942\pi$
$11$	26.0182	0.713162	0.356581	+	0.934264i	$0.383942\pi$
$12$	17.3080	0.416365
$13$	−66.9252	−1.42782	−0.713912	−	0.700235i	$-0.753078\pi$
$13$	−66.9252	−1.42782	−0.713912	+	0.700235i	$0.753078\pi$
$14$	−34.6177	−0.660854
$15$	0	0
$16$	16.0000	0.250000
$17$	65.2420	0.930794	0.465397	−	0.885102i	$-0.345912\pi$
$17$	65.2420	0.930794	0.465397	+	0.885102i	$0.345912\pi$
$18$	−16.5542	−0.216770
$19$	−9.59086	−0.115805	−0.0579025	−	0.998322i	$-0.518441\pi$
$19$	−9.59086	−0.115805	−0.0579025	+	0.998322i	$0.518441\pi$
$20$	0	0
$21$	−74.8953	−0.778261
$22$	52.0364	0.504282
$23$	−110.200	−0.999058	−0.499529	−	0.866297i	$-0.666494\pi$
$23$	−110.200	−0.999058	−0.499529	+	0.866297i	$0.666494\pi$
$24$	34.6160	0.294415
$25$	0	0
$26$	−133.850	−1.00962
$27$	−152.644	−1.08801
$28$	−69.2353	−0.467295
$29$	238.034	1.52420	0.762101	−	0.647459i	$-0.224168\pi$
$29$	238.034	1.52420	0.762101	+	0.647459i	$0.224168\pi$
$30$	0	0
$31$	2.98408	0.0172889	0.00864447	−	0.999963i	$-0.497248\pi$
$31$	2.98408	0.0172889	0.00864447	+	0.999963i	$0.497248\pi$
$32$	32.0000	0.176777
$33$	112.581	0.593872
$34$	130.484	0.658171
$35$	0	0
$36$	−33.1084	−0.153280
$37$	−315.961	−1.40388	−0.701942	−	0.712234i	$-0.747683\pi$
$37$	−315.961	−1.40388	−0.701942	+	0.712234i	$0.747683\pi$
$38$	−19.1817	−0.0818864
$39$	−289.585	−1.18899
$40$	0	0
$41$	−439.530	−1.67422	−0.837111	−	0.547034i	$-0.815757\pi$
$41$	−439.530	−1.67422	−0.837111	+	0.547034i	$0.815757\pi$
$42$	−149.791	−0.550314
$43$	−132.682	−0.470554	−0.235277	−	0.971928i	$-0.575600\pi$
$43$	−132.682	−0.470554	−0.235277	+	0.971928i	$0.575600\pi$
$44$	104.073	0.356581
$45$	0	0
$46$	−220.401	−0.706441
$47$	158.109	0.490692	0.245346	−	0.969436i	$-0.421098\pi$
$47$	158.109	0.490692	0.245346	+	0.969436i	$0.421098\pi$
$48$	69.2319	0.208183
$49$	−43.4043	−0.126543
$50$	0	0
$51$	282.302	0.775101
$52$	−267.701	−0.713912
$53$	−381.485	−0.988697	−0.494349	−	0.869264i	$-0.664593\pi$
$53$	−381.485	−0.988697	−0.494349	+	0.869264i	$0.664593\pi$
$54$	−305.288	−0.769341
$55$	0	0
$56$	−138.471	−0.330427
$57$	−41.4996	−0.0964343
$58$	476.068	1.07777
$59$	−536.027	−1.18279	−0.591396	−	0.806381i	$-0.701423\pi$
$59$	−536.027	−1.18279	−0.591396	+	0.806381i	$0.701423\pi$
$60$	0	0
$61$	125.932	0.264328	0.132164	−	0.991228i	$-0.457808\pi$
$61$	125.932	0.264328	0.132164	+	0.991228i	$0.457808\pi$
$62$	5.96816	0.0122251
$63$	143.267	0.286507
$64$	64.0000	0.125000
$65$	0	0
$66$	225.161	0.419931
$67$	871.688	1.58946	0.794729	−	0.606965i	$-0.207613\pi$
$67$	871.688	1.58946	0.794729	+	0.606965i	$0.207613\pi$
$68$	260.968	0.465397
$69$	−476.836	−0.831947
$70$	0	0
$71$	−766.732	−1.28161	−0.640805	−	0.767704i	$-0.721399\pi$
$71$	−766.732	−1.28161	−0.640805	+	0.767704i	$0.721399\pi$
$72$	−66.2168	−0.108385
$73$	−871.343	−1.39703	−0.698514	−	0.715596i	$-0.746155\pi$
$73$	−871.343	−1.39703	−0.698514	+	0.715596i	$0.746155\pi$
$74$	−631.922	−0.992695
$75$	0	0
$76$	−38.3634	−0.0579025
$77$	−450.345	−0.666513
$78$	−579.170	−0.840745
$79$	−289.677	−0.412547	−0.206274	−	0.978494i	$-0.566134\pi$
$79$	−289.677	−0.412547	−0.206274	+	0.978494i	$0.566134\pi$
$80$	0	0
$81$	−437.008	−0.599462
$82$	−879.060	−1.18385
$83$	−1167.33	−1.54374	−0.771872	−	0.635778i	$-0.780680\pi$
$83$	−1167.33	−1.54374	−0.771872	+	0.635778i	$0.780680\pi$
$84$	−299.581	−0.389131
$85$	0	0
$86$	−265.364	−0.332732
$87$	1029.97	1.26925
$88$	208.146	0.252141
$89$	−270.769	−0.322488	−0.161244	−	0.986915i	$-0.551551\pi$
$89$	−270.769	−0.322488	−0.161244	+	0.986915i	$0.551551\pi$
$90$	0	0
$91$	1158.40	1.33443
$92$	−440.801	−0.499529
$93$	12.9121	0.0143970
$94$	316.217	0.346972
$95$	0	0
$96$	138.464	0.147207
$97$	−206.315	−0.215960	−0.107980	−	0.994153i	$-0.534438\pi$
$97$	−206.315	−0.215960	−0.107980	+	0.994153i	$0.534438\pi$
$98$	−86.8085	−0.0894795
$99$	−215.355	−0.218626
$100$	0	0
$101$	1436.09	1.41481	0.707406	−	0.706807i	$-0.249865\pi$
$101$	1436.09	1.41481	0.707406	+	0.706807i	$0.249865\pi$
$102$	564.604	0.548079
$103$	−141.197	−0.135073	−0.0675365	−	0.997717i	$-0.521514\pi$
$103$	−141.197	−0.135073	−0.0675365	+	0.997717i	$0.521514\pi$
$104$	−535.402	−0.504812
$105$	0	0
$106$	−762.969	−0.699115
$107$	−427.679	−0.386404	−0.193202	−	0.981159i	$-0.561887\pi$
$107$	−427.679	−0.386404	−0.193202	+	0.981159i	$0.561887\pi$
$108$	−610.576	−0.544006
$109$	−3.59755	−0.00316131	−0.00158066	−	0.999999i	$-0.500503\pi$
$109$	−3.59755	−0.00316131	−0.00158066	+	0.999999i	$0.500503\pi$
$110$	0	0
$111$	−1367.16	−1.16906
$112$	−276.941	−0.233647
$113$	1899.49	1.58132	0.790661	−	0.612254i	$-0.209737\pi$
$113$	1899.49	1.58132	0.790661	+	0.612254i	$0.209737\pi$
$114$	−82.9992	−0.0681894
$115$	0	0
$116$	952.137	0.762101
$117$	553.947	0.437713
$118$	−1072.05	−0.836361
$119$	−1129.26	−0.869910
$120$	0	0
$121$	−654.053	−0.491400
$122$	251.865	0.186908
$123$	−1901.85	−1.39418
$124$	11.9363	0.00864447
$125$	0	0
$126$	286.534	0.202591
$127$	2447.08	1.70979	0.854894	−	0.518803i	$-0.173622\pi$
$127$	2447.08	1.70979	0.854894	+	0.518803i	$0.173622\pi$
$128$	128.000	0.0883883
$129$	−574.114	−0.391845
$130$	0	0
$131$	−2289.05	−1.52668	−0.763340	−	0.645997i	$-0.776442\pi$
$131$	−2289.05	−1.52668	−0.763340	+	0.645997i	$0.776442\pi$
$132$	450.323	0.296936
$133$	166.007	0.108230
$134$	1743.38	1.12392
$135$	0	0
$136$	521.936	0.329085
$137$	51.8673	0.0323454	0.0161727	−	0.999869i	$-0.494852\pi$
$137$	51.8673	0.0323454	0.0161727	+	0.999869i	$0.494852\pi$
$138$	−953.672	−0.588275
$139$	1886.14	1.15094	0.575468	−	0.817824i	$-0.304820\pi$
$139$	1886.14	1.15094	0.575468	+	0.817824i	$0.304820\pi$
$140$	0	0
$141$	684.136	0.408614
$142$	−1533.46	−0.906235
$143$	−1741.27	−1.01827
$144$	−132.434	−0.0766398
$145$	0	0
$146$	−1742.69	−0.987848
$147$	−187.810	−0.105376
$148$	−1263.84	−0.701942
$149$	−712.590	−0.391796	−0.195898	−	0.980624i	$-0.562762\pi$
$149$	−712.590	−0.391796	−0.195898	+	0.980624i	$0.562762\pi$
$150$	0	0
$151$	2245.13	1.20998	0.604988	−	0.796235i	$-0.293178\pi$
$151$	2245.13	1.20998	0.604988	+	0.796235i	$0.293178\pi$
$152$	−76.7268	−0.0409432
$153$	−540.014	−0.285344
$154$	−900.689	−0.471296
$155$	0	0
$156$	−1158.34	−0.594497
$157$	1018.81	0.517895	0.258948	−	0.965891i	$-0.416624\pi$
$157$	1018.81	0.517895	0.258948	+	0.965891i	$0.416624\pi$
$158$	−579.355	−0.291715
$159$	−1650.68	−0.823319
$160$	0	0
$161$	1907.44	0.933709
$162$	−874.016	−0.423884
$163$	−3985.00	−1.91490	−0.957452	−	0.288594i	$-0.906812\pi$
$163$	−3985.00	−1.91490	−0.957452	+	0.288594i	$0.906812\pi$
$164$	−1758.12	−0.837111
$165$	0	0
$166$	−2334.65	−1.09159
$167$	−458.200	−0.212315	−0.106157	−	0.994349i	$-0.533855\pi$
$167$	−458.200	−0.212315	−0.106157	+	0.994349i	$0.533855\pi$
$168$	−599.162	−0.275157
$169$	2281.98	1.03868
$170$	0	0
$171$	79.3845	0.0355011
$172$	−530.728	−0.235277
$173$	1297.31	0.570129	0.285064	−	0.958508i	$-0.407985\pi$
$173$	1297.31	0.570129	0.285064	+	0.958508i	$0.407985\pi$
$174$	2059.95	0.897495
$175$	0	0
$176$	416.291	0.178290
$177$	−2319.39	−0.984948
$178$	−541.537	−0.228033
$179$	1892.83	0.790372	0.395186	−	0.918601i	$-0.370680\pi$
$179$	1892.83	0.790372	0.395186	+	0.918601i	$0.370680\pi$
$180$	0	0
$181$	3996.83	1.64134	0.820668	−	0.571406i	$-0.193602\pi$
$181$	3996.83	1.64134	0.820668	+	0.571406i	$0.193602\pi$
$182$	2316.79	0.943584
$183$	544.909	0.220114
$184$	−881.602	−0.353220
$185$	0	0
$186$	25.8242	0.0101802
$187$	1697.48	0.663807
$188$	632.435	0.245346
$189$	2642.09	1.01684
$190$	0	0
$191$	4079.64	1.54551	0.772755	−	0.634705i	$-0.218878\pi$
$191$	4079.64	1.54551	0.772755	+	0.634705i	$0.218878\pi$
$192$	276.928	0.104091
$193$	−1635.27	−0.609891	−0.304946	−	0.952370i	$-0.598638\pi$
$193$	−1635.27	−0.609891	−0.304946	+	0.952370i	$0.598638\pi$
$194$	−412.631	−0.152707
$195$	0	0
$196$	−173.617	−0.0632715
$197$	1342.62	0.485574	0.242787	−	0.970080i	$-0.421938\pi$
$197$	1342.62	0.485574	0.242787	+	0.970080i	$0.421938\pi$
$198$	−430.710	−0.154592
$199$	2884.91	1.02767	0.513833	−	0.857890i	$-0.328225\pi$
$199$	2884.91	1.02767	0.513833	+	0.857890i	$0.328225\pi$
$200$	0	0
$201$	3771.79	1.32359
$202$	2872.18	1.00042
$203$	−4120.09	−1.42450
$204$	1129.21	0.387551
$205$	0	0
$206$	−282.393	−0.0955111
$207$	912.139	0.306271
$208$	−1070.80	−0.356956
$209$	−249.537	−0.0825877
$210$	0	0
$211$	5116.09	1.66922	0.834611	−	0.550840i	$-0.185692\pi$
$211$	5116.09	1.66922	0.834611	+	0.550840i	$0.185692\pi$
$212$	−1525.94	−0.494349
$213$	−3317.65	−1.06724
$214$	−855.357	−0.273229
$215$	0	0
$216$	−1221.15	−0.384670
$217$	−51.6510	−0.0161580
$218$	−7.19510	−0.00223538
$219$	−3770.30	−1.16335
$220$	0	0
$221$	−4366.33	−1.32901
$222$	−2734.33	−0.826648
$223$	−1892.52	−0.568309	−0.284154	−	0.958779i	$-0.591713\pi$
$223$	−1892.52	−0.568309	−0.284154	+	0.958779i	$0.591713\pi$
$224$	−553.883	−0.165214
$225$	0	0
$226$	3798.99	1.11816
$227$	−5882.14	−1.71987	−0.859936	−	0.510401i	$-0.829497\pi$
$227$	−5882.14	−1.71987	−0.859936	+	0.510401i	$0.829497\pi$
$228$	−165.998	−0.0482172
$229$	−361.549	−0.104331	−0.0521655	−	0.998638i	$-0.516612\pi$
$229$	−361.549	−0.104331	−0.0521655	+	0.998638i	$0.516612\pi$
$230$	0	0
$231$	−1948.64	−0.555026
$232$	1904.27	0.538887
$233$	−2457.78	−0.691048	−0.345524	−	0.938410i	$-0.612299\pi$
$233$	−2457.78	−0.691048	−0.345524	+	0.938410i	$0.612299\pi$
$234$	1107.89	0.309510
$235$	0	0
$236$	−2144.11	−0.591396
$237$	−1253.43	−0.343541
$238$	−2258.53	−0.615119
$239$	−5951.73	−1.61082	−0.805409	−	0.592720i	$-0.798054\pi$
$239$	−5951.73	−1.61082	−0.805409	+	0.592720i	$0.798054\pi$
$240$	0	0
$241$	4839.08	1.29341	0.646706	−	0.762739i	$-0.276146\pi$
$241$	4839.08	1.29341	0.646706	+	0.762739i	$0.276146\pi$
$242$	−1308.11	−0.347472
$243$	2230.45	0.588822
$244$	503.729	0.132164
$245$	0	0
$246$	−3803.69	−0.985831
$247$	641.870	0.165349
$248$	23.8727	0.00611256
$249$	−5051.02	−1.28552
$250$	0	0
$251$	−101.973	−0.0256434	−0.0128217	−	0.999918i	$-0.504081\pi$
$251$	−101.973	−0.0256434	−0.0128217	+	0.999918i	$0.504081\pi$
$252$	573.068	0.143253
$253$	−2867.21	−0.712490
$254$	4894.16	1.20900
$255$	0	0
$256$	256.000	0.0625000
$257$	−697.647	−0.169331	−0.0846655	−	0.996409i	$-0.526982\pi$
$257$	−697.647	−0.169331	−0.0846655	+	0.996409i	$0.526982\pi$
$258$	−1148.23	−0.277076
$259$	5468.92	1.31205
$260$	0	0
$261$	−1970.23	−0.467258
$262$	−4578.10	−1.07953
$263$	−3657.98	−0.857646	−0.428823	−	0.903389i	$-0.641072\pi$
$263$	−3657.98	−0.857646	−0.428823	+	0.903389i	$0.641072\pi$
$264$	900.645	0.209965
$265$	0	0
$266$	332.013	0.0765302
$267$	−1171.62	−0.268546
$268$	3486.75	0.794729
$269$	4304.69	0.975694	0.487847	−	0.872929i	$-0.337782\pi$
$269$	4304.69	0.975694	0.487847	+	0.872929i	$0.337782\pi$
$270$	0	0
$271$	429.990	0.0963838	0.0481919	−	0.998838i	$-0.484654\pi$
$271$	429.990	0.0963838	0.0481919	+	0.998838i	$0.484654\pi$
$272$	1043.87	0.232699
$273$	5012.38	1.11122
$274$	103.735	0.0228716
$275$	0	0
$276$	−1907.34	−0.415973
$277$	1718.92	0.372852	0.186426	−	0.982469i	$-0.440310\pi$
$277$	1718.92	0.372852	0.186426	+	0.982469i	$0.440310\pi$
$278$	3772.28	0.813835
$279$	−24.6995	−0.00530008
$280$	0	0
$281$	−2716.32	−0.576663	−0.288331	−	0.957531i	$-0.593100\pi$
$281$	−2716.32	−0.576663	−0.288331	+	0.957531i	$0.593100\pi$
$282$	1368.27	0.288934
$283$	−3231.35	−0.678741	−0.339370	−	0.940653i	$-0.610214\pi$
$283$	−3231.35	−0.678741	−0.339370	+	0.940653i	$0.610214\pi$
$284$	−3066.93	−0.640805
$285$	0	0
$286$	−3482.55	−0.720026
$287$	7607.75	1.56471
$288$	−264.867	−0.0541925
$289$	−656.485	−0.133622
$290$	0	0
$291$	−892.726	−0.179837
$292$	−3485.37	−0.698514
$293$	−6070.89	−1.21046	−0.605231	−	0.796050i	$-0.706919\pi$
$293$	−6070.89	−1.21046	−0.605231	+	0.796050i	$0.706919\pi$
$294$	−375.620	−0.0745123
$295$	0	0
$296$	−2527.69	−0.496348
$297$	−3971.52	−0.775929
$298$	−1425.18	−0.277042
$299$	7375.18	1.42648
$300$	0	0
$301$	2296.57	0.439774
$302$	4490.27	0.855582
$303$	6213.95	1.17816
$304$	−153.454	−0.0289512
$305$	0	0
$306$	−1080.03	−0.201768
$307$	−8228.56	−1.52973	−0.764867	−	0.644188i	$-0.777196\pi$
$307$	−8228.56	−1.52973	−0.764867	+	0.644188i	$0.777196\pi$
$308$	−1801.38	−0.333257
$309$	−610.958	−0.112479
$310$	0	0
$311$	4529.81	0.825923	0.412961	−	0.910749i	$-0.364494\pi$
$311$	4529.81	0.825923	0.412961	+	0.910749i	$0.364494\pi$
$312$	−2316.68	−0.420373
$313$	1426.25	0.257561	0.128780	−	0.991673i	$-0.458894\pi$
$313$	1426.25	0.257561	0.128780	+	0.991673i	$0.458894\pi$
$314$	2037.61	0.366207
$315$	0	0
$316$	−1158.71	−0.206274
$317$	6847.03	1.21315	0.606574	−	0.795027i	$-0.292544\pi$
$317$	6847.03	1.21315	0.606574	+	0.795027i	$0.292544\pi$
$318$	−3301.37	−0.582174
$319$	6193.22	1.08700
$320$	0	0
$321$	−1850.56	−0.321771
$322$	3814.88	0.660232
$323$	−625.726	−0.107791
$324$	−1748.03	−0.299731
$325$	0	0
$326$	−7970.00	−1.35404
$327$	−15.5666	−0.00263252
$328$	−3516.24	−0.591927
$329$	−2736.68	−0.458595
$330$	0	0
$331$	−7877.38	−1.30810	−0.654048	−	0.756453i	$-0.726931\pi$
$331$	−7877.38	−1.30810	−0.654048	+	0.756453i	$0.726931\pi$
$332$	−4669.31	−0.771872
$333$	2615.24	0.430374
$334$	−916.399	−0.150129
$335$	0	0
$336$	−1198.32	−0.194565
$337$	−3416.52	−0.552255	−0.276127	−	0.961121i	$-0.589051\pi$
$337$	−3416.52	−0.552255	−0.276127	+	0.961121i	$0.589051\pi$
$338$	4563.97	0.734459
$339$	8219.10	1.31682
$340$	0	0
$341$	77.6404	0.0123298
$342$	158.769	0.0251030
$343$	6688.21	1.05285
$344$	−1061.46	−0.166366
$345$	0	0
$346$	2594.61	0.403142
$347$	4585.50	0.709403	0.354701	−	0.934980i	$-0.384583\pi$
$347$	4585.50	0.709403	0.354701	+	0.934980i	$0.384583\pi$
$348$	4119.89	0.634625
$349$	−7646.87	−1.17286	−0.586429	−	0.810001i	$-0.699467\pi$
$349$	−7646.87	−1.17286	−0.586429	+	0.810001i	$0.699467\pi$
$350$	0	0
$351$	10215.7	1.55349
$352$	832.582	0.126070
$353$	3824.50	0.576651	0.288325	−	0.957532i	$-0.406902\pi$
$353$	3824.50	0.576651	0.288325	+	0.957532i	$0.406902\pi$
$354$	−4638.77	−0.696463
$355$	0	0
$356$	−1083.07	−0.161244
$357$	−4886.31	−0.724401
$358$	3785.65	0.558877
$359$	3649.18	0.536480	0.268240	−	0.963352i	$-0.413558\pi$
$359$	3649.18	0.536480	0.268240	+	0.963352i	$0.413558\pi$
$360$	0	0
$361$	−6767.02	−0.986589
$362$	7993.65	1.16060
$363$	−2830.09	−0.409204
$364$	4633.59	0.667214
$365$	0	0
$366$	1089.82	0.155644
$367$	7646.22	1.08755	0.543773	−	0.839232i	$-0.316995\pi$
$367$	7646.22	1.08755	0.543773	+	0.839232i	$0.316995\pi$
$368$	−1763.20	−0.249765
$369$	3638.04	0.513248
$370$	0	0
$371$	6603.06	0.924026
$372$	51.6484	0.00719851
$373$	−967.962	−0.134368	−0.0671839	−	0.997741i	$-0.521401\pi$
$373$	−967.962	−0.134368	−0.0671839	+	0.997741i	$0.521401\pi$
$374$	3394.96	0.469383
$375$	0	0
$376$	1264.87	0.173486
$377$	−15930.5	−2.17629
$378$	5284.18	0.719018
$379$	2207.34	0.299164	0.149582	−	0.988749i	$-0.452207\pi$
$379$	2207.34	0.299164	0.149582	+	0.988749i	$0.452207\pi$
$380$	0	0
$381$	10588.5	1.42379
$382$	8159.28	1.09284
$383$	−6477.43	−0.864181	−0.432091	−	0.901830i	$-0.642224\pi$
$383$	−6477.43	−0.864181	−0.432091	+	0.901830i	$0.642224\pi$
$384$	553.856	0.0736037
$385$	0	0
$386$	−3270.53	−0.431258
$387$	1098.22	0.144253
$388$	−825.262	−0.107980
$389$	4781.55	0.623225	0.311612	−	0.950209i	$-0.399131\pi$
$389$	4781.55	0.623225	0.311612	+	0.950209i	$0.399131\pi$
$390$	0	0
$391$	−7189.68	−0.929918
$392$	−347.234	−0.0447397
$393$	−9904.71	−1.27131
$394$	2685.25	0.343352
$395$	0	0
$396$	−861.421	−0.109313
$397$	−8914.30	−1.12694	−0.563471	−	0.826136i	$-0.690534\pi$
$397$	−8914.30	−1.12694	−0.563471	+	0.826136i	$0.690534\pi$
$398$	5769.81	0.726670
$399$	718.310	0.0901265
$400$	0	0
$401$	−9368.71	−1.16671	−0.583356	−	0.812217i	$-0.698261\pi$
$401$	−9368.71	−1.16671	−0.583356	+	0.812217i	$0.698261\pi$
$402$	7543.58	0.935920
$403$	−199.710	−0.0246856
$404$	5744.35	0.707406
$405$	0	0
$406$	−8240.19	−1.00728
$407$	−8220.74	−1.00120
$408$	2258.41	0.274040
$409$	4390.06	0.530745	0.265372	−	0.964146i	$-0.414505\pi$
$409$	4390.06	0.530745	0.265372	+	0.964146i	$0.414505\pi$
$410$	0	0
$411$	224.429	0.0269350
$412$	−564.787	−0.0675365
$413$	9278.00	1.10543
$414$	1824.28	0.216566
$415$	0	0
$416$	−2141.61	−0.252406
$417$	8161.32	0.958420
$418$	−499.074	−0.0583983
$419$	−6522.08	−0.760440	−0.380220	−	0.924896i	$-0.624152\pi$
$419$	−6522.08	−0.760440	−0.380220	+	0.924896i	$0.624152\pi$
$420$	0	0
$421$	14097.3	1.63197	0.815985	−	0.578073i	$-0.196195\pi$
$421$	14097.3	1.63197	0.815985	+	0.578073i	$0.196195\pi$
$422$	10232.2	1.18032
$423$	−1308.68	−0.150426
$424$	−3051.88	−0.349557
$425$	0	0
$426$	−6635.29	−0.754650
$427$	−2179.74	−0.247038
$428$	−1710.71	−0.193202
$429$	−7534.48	−0.847945
$430$	0	0
$431$	4075.03	0.455423	0.227711	−	0.973729i	$-0.426876\pi$
$431$	4075.03	0.455423	0.227711	+	0.973729i	$0.426876\pi$
$432$	−2442.30	−0.272003
$433$	−1866.55	−0.207161	−0.103581	−	0.994621i	$-0.533030\pi$
$433$	−1866.55	−0.207161	−0.103581	+	0.994621i	$0.533030\pi$
$434$	−103.302	−0.0114255
$435$	0	0
$436$	−14.3902	−0.00158066
$437$	1056.91	0.115696
$438$	−7540.60	−0.822611
$439$	−13623.3	−1.48110	−0.740550	−	0.672002i	$-0.765435\pi$
$439$	−13623.3	−1.48110	−0.740550	+	0.672002i	$0.765435\pi$
$440$	0	0
$441$	359.261	0.0387929
$442$	−8732.67	−0.939752
$443$	3798.21	0.407356	0.203678	−	0.979038i	$-0.434710\pi$
$443$	3798.21	0.407356	0.203678	+	0.979038i	$0.434710\pi$
$444$	−5468.65	−0.584529
$445$	0	0
$446$	−3785.05	−0.401855
$447$	−3083.37	−0.326261
$448$	−1107.77	−0.116824
$449$	14616.5	1.53629	0.768145	−	0.640276i	$-0.221180\pi$
$449$	14616.5	1.53629	0.768145	+	0.640276i	$0.221180\pi$
$450$	0	0
$451$	−11435.8	−1.19399
$452$	7597.98	0.790661
$453$	9714.68	1.00758
$454$	−11764.3	−1.21613
$455$	0	0
$456$	−331.997	−0.0340947
$457$	2485.82	0.254446	0.127223	−	0.991874i	$-0.459394\pi$
$457$	2485.82	0.254446	0.127223	+	0.991874i	$0.459394\pi$
$458$	−723.097	−0.0737732
$459$	−9958.79	−1.01272
$460$	0	0
$461$	−2883.55	−0.291324	−0.145662	−	0.989334i	$-0.546531\pi$
$461$	−2883.55	−0.291324	−0.145662	+	0.989334i	$0.546531\pi$
$462$	−3897.28	−0.392463
$463$	8314.62	0.834585	0.417293	−	0.908772i	$-0.362979\pi$
$463$	8314.62	0.834585	0.417293	+	0.908772i	$0.362979\pi$
$464$	3808.55	0.381050
$465$	0	0
$466$	−4915.55	−0.488645
$467$	−3404.83	−0.337380	−0.168690	−	0.985669i	$-0.553954\pi$
$467$	−3404.83	−0.337380	−0.168690	+	0.985669i	$0.553954\pi$
$468$	2215.79	0.218856
$469$	−15087.9	−1.48549
$470$	0	0
$471$	4408.37	0.431268
$472$	−4288.22	−0.418180
$473$	−3452.15	−0.335581
$474$	−2506.87	−0.242920
$475$	0	0
$476$	−4517.05	−0.434955
$477$	3157.59	0.303094
$478$	−11903.5	−1.13902
$479$	13614.6	1.29868	0.649338	−	0.760500i	$-0.275046\pi$
$479$	13614.6	1.29868	0.649338	+	0.760500i	$0.275046\pi$
$480$	0	0
$481$	21145.8	2.00450
$482$	9678.15	0.914581
$483$	8253.48	0.777528
$484$	−2616.21	−0.245700
$485$	0	0
$486$	4460.91	0.416360
$487$	−3229.42	−0.300490	−0.150245	−	0.988649i	$-0.548006\pi$
$487$	−3229.42	−0.300490	−0.150245	+	0.988649i	$0.548006\pi$
$488$	1007.46	0.0934539
$489$	−17243.1	−1.59460
$490$	0	0
$491$	−629.891	−0.0578953	−0.0289476	−	0.999581i	$-0.509216\pi$
$491$	−629.891	−0.0578953	−0.0289476	+	0.999581i	$0.509216\pi$
$492$	−7607.38	−0.697088
$493$	15529.8	1.41872
$494$	1283.74	0.116919
$495$	0	0
$496$	47.7453	0.00432223
$497$	13271.2	1.19778
$498$	−10102.0	−0.909003
$499$	−4951.62	−0.444218	−0.222109	−	0.975022i	$-0.571294\pi$
$499$	−4951.62	−0.444218	−0.222109	+	0.975022i	$0.571294\pi$
$500$	0	0
$501$	−1982.63	−0.176801
$502$	−203.947	−0.0181326
$503$	−10254.6	−0.909009	−0.454505	−	0.890744i	$-0.650184\pi$
$503$	−10254.6	−0.909009	−0.454505	+	0.890744i	$0.650184\pi$
$504$	1146.14	0.101296
$505$	0	0
$506$	−5734.42	−0.503807
$507$	9874.13	0.864942
$508$	9788.31	0.854894
$509$	−3069.96	−0.267335	−0.133668	−	0.991026i	$-0.542675\pi$
$509$	−3069.96	−0.267335	−0.133668	+	0.991026i	$0.542675\pi$
$510$	0	0
$511$	15081.9	1.30565
$512$	512.000	0.0441942
$513$	1463.99	0.125997
$514$	−1395.29	−0.119735
$515$	0	0
$516$	−2296.46	−0.195922
$517$	4113.70	0.349943
$518$	10937.8	0.927762
$519$	5613.44	0.474764
$520$	0	0
$521$	−8294.68	−0.697498	−0.348749	−	0.937216i	$-0.613393\pi$
$521$	−8294.68	−0.697498	−0.348749	+	0.937216i	$0.613393\pi$
$522$	−3940.47	−0.330401
$523$	−427.593	−0.0357502	−0.0178751	−	0.999840i	$-0.505690\pi$
$523$	−427.593	−0.0357502	−0.0178751	+	0.999840i	$0.505690\pi$
$524$	−9156.20	−0.763340
$525$	0	0
$526$	−7315.96	−0.606447
$527$	194.687	0.0160924
$528$	1801.29	0.148468
$529$	−22.9015	−0.00188227
$530$	0	0
$531$	4436.75	0.362596
$532$	664.026	0.0541150
$533$	29415.6	2.39049
$534$	−2343.23	−0.189890
$535$	0	0
$536$	6973.50	0.561958
$537$	8190.25	0.658167
$538$	8609.38	0.689920
$539$	−1129.30	−0.0902457
$540$	0	0
$541$	−8016.89	−0.637103	−0.318552	−	0.947905i	$-0.603196\pi$
$541$	−8016.89	−0.637103	−0.318552	+	0.947905i	$0.603196\pi$
$542$	859.979	0.0681537
$543$	17294.2	1.36679
$544$	2087.74	0.164543
$545$	0	0
$546$	10024.8	0.785751
$547$	−9345.56	−0.730507	−0.365253	−	0.930908i	$-0.619018\pi$
$547$	−9345.56	−0.730507	−0.365253	+	0.930908i	$0.619018\pi$
$548$	207.469	0.0161727
$549$	−1042.35	−0.0810321
$550$	0	0
$551$	−2282.95	−0.176510
$552$	−3814.69	−0.294138
$553$	5013.98	0.385562
$554$	3437.84	0.263646
$555$	0	0
$556$	7544.55	0.575468
$557$	8146.38	0.619700	0.309850	−	0.950785i	$-0.399721\pi$
$557$	8146.38	0.619700	0.309850	+	0.950785i	$0.399721\pi$
$558$	−49.3991	−0.00374772
$559$	8879.77	0.671868
$560$	0	0
$561$	7344.98	0.552773
$562$	−5432.64	−0.407762
$563$	15577.1	1.16607	0.583034	−	0.812447i	$-0.301865\pi$
$563$	15577.1	1.16607	0.583034	+	0.812447i	$0.301865\pi$
$564$	2736.54	0.204307
$565$	0	0
$566$	−6462.69	−0.479942
$567$	7564.10	0.560251
$568$	−6133.85	−0.453118
$569$	−11618.0	−0.855976	−0.427988	−	0.903784i	$-0.640777\pi$
$569$	−11618.0	−0.855976	−0.427988	+	0.903784i	$0.640777\pi$
$570$	0	0
$571$	21631.2	1.58535	0.792677	−	0.609642i	$-0.208687\pi$
$571$	21631.2	1.58535	0.792677	+	0.609642i	$0.208687\pi$
$572$	−6965.09	−0.509135
$573$	17652.6	1.28699
$574$	15215.5	1.10642
$575$	0	0
$576$	−529.734	−0.0383199
$577$	−10060.7	−0.725879	−0.362939	−	0.931813i	$-0.618227\pi$
$577$	−10060.7	−0.725879	−0.362939	+	0.931813i	$0.618227\pi$
$578$	−1312.97	−0.0944850
$579$	−7075.79	−0.507875
$580$	0	0
$581$	20205.1	1.44277
$582$	−1785.45	−0.127164
$583$	−9925.54	−0.705101
$584$	−6970.75	−0.493924
$585$	0	0
$586$	−12141.8	−0.855926
$587$	−6930.11	−0.487285	−0.243642	−	0.969865i	$-0.578342\pi$
$587$	−6930.11	−0.487285	−0.243642	+	0.969865i	$0.578342\pi$
$588$	−751.240	−0.0526882
$589$	−28.6199	−0.00200214
$590$	0	0
$591$	5809.53	0.404352
$592$	−5055.38	−0.350971
$593$	8835.99	0.611890	0.305945	−	0.952049i	$-0.401028\pi$
$593$	8835.99	0.611890	0.305945	+	0.952049i	$0.401028\pi$
$594$	−7943.04	−0.548665
$595$	0	0
$596$	−2850.36	−0.195898
$597$	12483.0	0.855770
$598$	14750.4	1.00867
$599$	−6416.69	−0.437694	−0.218847	−	0.975759i	$-0.570230\pi$
$599$	−6416.69	−0.437694	−0.218847	+	0.975759i	$0.570230\pi$
$600$	0	0
$601$	−104.752	−0.00710971	−0.00355486	−	0.999994i	$-0.501132\pi$
$601$	−104.752	−0.00710971	−0.00355486	+	0.999994i	$0.501132\pi$
$602$	4593.14	0.310967
$603$	−7215.05	−0.487263
$604$	8980.53	0.604988
$605$	0	0
$606$	12427.9	0.833084
$607$	5057.18	0.338163	0.169081	−	0.985602i	$-0.445920\pi$
$607$	5057.18	0.338163	0.169081	+	0.985602i	$0.445920\pi$
$608$	−306.907	−0.0204716
$609$	−17827.6	−1.18623
$610$	0	0
$611$	−10581.5	−0.700622
$612$	−2160.06	−0.142672
$613$	16262.7	1.07152	0.535761	−	0.844370i	$-0.320025\pi$
$613$	16262.7	1.07152	0.535761	+	0.844370i	$0.320025\pi$
$614$	−16457.1	−1.08169
$615$	0	0
$616$	−3602.76	−0.235648
$617$	−4678.16	−0.305244	−0.152622	−	0.988285i	$-0.548772\pi$
$617$	−4678.16	−0.305244	−0.152622	+	0.988285i	$0.548772\pi$
$618$	−1221.92	−0.0795350
$619$	14569.2	0.946016	0.473008	−	0.881058i	$-0.343168\pi$
$619$	14569.2	0.946016	0.473008	+	0.881058i	$0.343168\pi$
$620$	0	0
$621$	16821.4	1.08699
$622$	9059.62	0.584016
$623$	4686.69	0.301394
$624$	−4633.36	−0.297248
$625$	0	0
$626$	2852.50	0.182123
$627$	−1079.74	−0.0687733
$628$	4075.22	0.258948
$629$	−20613.9	−1.30673
$630$	0	0
$631$	6690.99	0.422130	0.211065	−	0.977472i	$-0.432307\pi$
$631$	6690.99	0.422130	0.211065	+	0.977472i	$0.432307\pi$
$632$	−2317.42	−0.145858
$633$	22137.3	1.39001
$634$	13694.1	0.857825
$635$	0	0
$636$	−6602.73	−0.411659
$637$	2904.84	0.180681
$638$	12386.4	0.768627
$639$	6346.32	0.392890
$640$	0	0
$641$	−620.964	−0.0382631	−0.0191315	−	0.999817i	$-0.506090\pi$
$641$	−620.964	−0.0382631	−0.0191315	+	0.999817i	$0.506090\pi$
$642$	−3701.13	−0.227526
$643$	−27013.5	−1.65678	−0.828388	−	0.560155i	$-0.810742\pi$
$643$	−27013.5	−1.65678	−0.828388	+	0.560155i	$0.810742\pi$
$644$	7629.75	0.466855
$645$	0	0
$646$	−1251.45	−0.0762194
$647$	−6508.88	−0.395503	−0.197752	−	0.980252i	$-0.563364\pi$
$647$	−6508.88	−0.395503	−0.197752	+	0.980252i	$0.563364\pi$
$648$	−3496.06	−0.211942
$649$	−13946.5	−0.843523
$650$	0	0
$651$	−223.494	−0.0134553
$652$	−15940.0	−0.957452
$653$	18620.8	1.11591	0.557954	−	0.829872i	$-0.311587\pi$
$653$	18620.8	1.11591	0.557954	+	0.829872i	$0.311587\pi$
$654$	−31.1332	−0.00186147
$655$	0	0
$656$	−7032.48	−0.418555
$657$	7212.20	0.428272
$658$	−5473.35	−0.324276
$659$	1222.49	0.0722631	0.0361315	−	0.999347i	$-0.488496\pi$
$659$	1222.49	0.0722631	0.0361315	+	0.999347i	$0.488496\pi$
$660$	0	0
$661$	−3928.53	−0.231168	−0.115584	−	0.993298i	$-0.536874\pi$
$661$	−3928.53	−0.231168	−0.115584	+	0.993298i	$0.536874\pi$
$662$	−15754.8	−0.924964
$663$	−18893.1	−1.10671
$664$	−9338.62	−0.545796
$665$	0	0
$666$	5230.48	0.304320
$667$	−26231.4	−1.52277
$668$	−1832.80	−0.106157
$669$	−8188.95	−0.473248
$670$	0	0
$671$	3276.53	0.188508
$672$	−2396.65	−0.137578
$673$	−17721.4	−1.01502	−0.507510	−	0.861646i	$-0.669434\pi$
$673$	−17721.4	−1.01502	−0.507510	+	0.861646i	$0.669434\pi$
$674$	−6833.05	−0.390503
$675$	0	0
$676$	9127.93	0.519341
$677$	18266.9	1.03701	0.518503	−	0.855076i	$-0.326490\pi$
$677$	18266.9	1.03701	0.518503	+	0.855076i	$0.326490\pi$
$678$	16438.2	0.931129
$679$	3571.08	0.201834
$680$	0	0
$681$	−25452.0	−1.43219
$682$	155.281	0.00871849
$683$	−531.830	−0.0297949	−0.0148974	−	0.999889i	$-0.504742\pi$
$683$	−531.830	−0.0297949	−0.0148974	+	0.999889i	$0.504742\pi$
$684$	317.538	0.0177505
$685$	0	0
$686$	13376.4	0.744481
$687$	−1564.42	−0.0868797
$688$	−2122.91	−0.117638
$689$	25530.9	1.41169
$690$	0	0
$691$	6815.57	0.375219	0.187610	−	0.982244i	$-0.439926\pi$
$691$	6815.57	0.375219	0.187610	+	0.982244i	$0.439926\pi$
$692$	5189.22	0.285064
$693$	3727.55	0.204326
$694$	9171.01	0.501623
$695$	0	0
$696$	8239.78	0.448747
$697$	−28675.8	−1.55836
$698$	−15293.7	−0.829336
$699$	−10634.8	−0.575457
$700$	0	0
$701$	−26578.4	−1.43203	−0.716015	−	0.698085i	$-0.754036\pi$
$701$	−26578.4	−1.43203	−0.716015	+	0.698085i	$0.754036\pi$
$702$	20431.4	1.09848
$703$	3030.34	0.162577
$704$	1665.16	0.0891452
$705$	0	0
$706$	7649.01	0.407754
$707$	−24857.0	−1.32227
$708$	−9277.55	−0.492474
$709$	9552.18	0.505980	0.252990	−	0.967469i	$-0.418586\pi$
$709$	9552.18	0.505980	0.252990	+	0.967469i	$0.418586\pi$
$710$	0	0
$711$	2397.69	0.126470
$712$	−2166.15	−0.114017
$713$	−328.847	−0.0172727
$714$	−9772.63	−0.512229
$715$	0	0
$716$	7571.31	0.395186
$717$	−25753.1	−1.34138
$718$	7298.36	0.379349
$719$	25422.7	1.31865	0.659323	−	0.751860i	$-0.270843\pi$
$719$	25422.7	1.31865	0.659323	+	0.751860i	$0.270843\pi$
$720$	0	0
$721$	2443.95	0.126238
$722$	−13534.0	−0.697624
$723$	20938.7	1.07706
$724$	15987.3	0.820668
$725$	0	0
$726$	−5660.17	−0.289351
$727$	10343.9	0.527696	0.263848	−	0.964564i	$-0.415008\pi$
$727$	10343.9	0.527696	0.263848	+	0.964564i	$0.415008\pi$
$728$	9267.18	0.471792
$729$	21450.4	1.08979
$730$	0	0
$731$	−8656.43	−0.437989
$732$	2179.63	0.110057
$733$	−1237.78	−0.0623715	−0.0311858	−	0.999514i	$-0.509928\pi$
$733$	−1237.78	−0.0623715	−0.0311858	+	0.999514i	$0.509928\pi$
$734$	15292.4	0.769011
$735$	0	0
$736$	−3526.41	−0.176610
$737$	22679.8	1.13354
$738$	7276.07	0.362921
$739$	32907.1	1.63803	0.819017	−	0.573769i	$-0.194519\pi$
$739$	32907.1	1.63803	0.819017	+	0.573769i	$0.194519\pi$
$740$	0	0
$741$	2777.37	0.137691
$742$	13206.1	0.653385
$743$	2700.91	0.133360	0.0666802	−	0.997774i	$-0.478759\pi$
$743$	2700.91	0.133360	0.0666802	+	0.997774i	$0.478759\pi$
$744$	103.297	0.00509012
$745$	0	0
$746$	−1935.92	−0.0950123
$747$	9662.08	0.473249
$748$	6789.91	0.331904
$749$	7402.62	0.361129
$750$	0	0
$751$	−20058.0	−0.974603	−0.487302	−	0.873234i	$-0.662019\pi$
$751$	−20058.0	−0.974603	−0.487302	+	0.873234i	$0.662019\pi$
$752$	2529.74	0.122673
$753$	−441.238	−0.0213541
$754$	−31861.0	−1.53887
$755$	0	0
$756$	10568.4	0.508422
$757$	−23344.1	−1.12081	−0.560406	−	0.828218i	$-0.689355\pi$
$757$	−23344.1	−1.12081	−0.560406	+	0.828218i	$0.689355\pi$
$758$	4414.67	0.211541
$759$	−12406.4	−0.593313
$760$	0	0
$761$	−16265.8	−0.774815	−0.387408	−	0.921908i	$-0.626629\pi$
$761$	−16265.8	−0.774815	−0.387408	+	0.921908i	$0.626629\pi$
$762$	21177.0	1.00677
$763$	62.2694	0.00295453
$764$	16318.6	0.772755
$765$	0	0
$766$	−12954.9	−0.611068
$767$	35873.7	1.68882
$768$	1107.71	0.0520457
$769$	−471.765	−0.0221226	−0.0110613	−	0.999939i	$-0.503521\pi$
$769$	−471.765	−0.0221226	−0.0110613	+	0.999939i	$0.503521\pi$
$770$	0	0
$771$	−3018.72	−0.141007
$772$	−6541.06	−0.304946
$773$	−6557.31	−0.305110	−0.152555	−	0.988295i	$-0.548750\pi$
$773$	−6557.31	−0.305110	−0.152555	+	0.988295i	$0.548750\pi$
$774$	2196.44	0.102002
$775$	0	0
$776$	−1650.52	−0.0763535
$777$	23664.0	1.09259
$778$	9563.11	0.440686
$779$	4215.47	0.193883
$780$	0	0
$781$	−19949.0	−0.913996
$782$	−14379.4	−0.657551
$783$	−36334.5	−1.65835
$784$	−694.468	−0.0316358
$785$	0	0
$786$	−19809.4	−0.898955
$787$	23740.4	1.07529	0.537645	−	0.843172i	$-0.319314\pi$
$787$	23740.4	1.07529	0.537645	+	0.843172i	$0.319314\pi$
$788$	5370.50	0.242787
$789$	−15828.1	−0.714188
$790$	0	0
$791$	−32878.0	−1.47789
$792$	−1722.84	−0.0772961
$793$	−8428.05	−0.377413
$794$	−17828.6	−0.796868
$795$	0	0
$796$	11539.6	0.513833
$797$	25328.7	1.12571	0.562854	−	0.826557i	$-0.309703\pi$
$797$	25328.7	1.12571	0.562854	+	0.826557i	$0.309703\pi$
$798$	1436.62	0.0637290
$799$	10315.3	0.456733
$800$	0	0
$801$	2241.18	0.0988617
$802$	−18737.4	−0.824989
$803$	−22670.8	−0.996307
$804$	15087.2	0.661795
$805$	0	0
$806$	−399.421	−0.0174553
$807$	18626.4	0.812490
$808$	11488.7	0.500212
$809$	−19994.0	−0.868913	−0.434456	−	0.900693i	$-0.643060\pi$
$809$	−19994.0	−0.868913	−0.434456	+	0.900693i	$0.643060\pi$
$810$	0	0
$811$	23436.5	1.01475	0.507377	−	0.861724i	$-0.330615\pi$
$811$	23436.5	1.01475	0.507377	+	0.861724i	$0.330615\pi$
$812$	−16480.4	−0.712251
$813$	1860.56	0.0802618
$814$	−16441.5	−0.707953
$815$	0	0
$816$	4516.83	0.193775
$817$	1272.53	0.0544924
$818$	8780.13	0.375293
$819$	−9588.17	−0.409082
$820$	0	0
$821$	39360.3	1.67318	0.836592	−	0.547827i	$-0.184545\pi$
$821$	39360.3	1.67318	0.836592	+	0.547827i	$0.184545\pi$
$822$	448.859	0.0190459
$823$	−3488.52	−0.147755	−0.0738773	−	0.997267i	$-0.523537\pi$
$823$	−3488.52	−0.147755	−0.0738773	+	0.997267i	$0.523537\pi$
$824$	−1129.57	−0.0477555
$825$	0	0
$826$	18556.0	0.781654
$827$	−31041.3	−1.30522	−0.652608	−	0.757696i	$-0.726325\pi$
$827$	−31041.3	−1.30522	−0.652608	+	0.757696i	$0.726325\pi$
$828$	3648.55	0.153135
$829$	14017.3	0.587264	0.293632	−	0.955919i	$-0.405136\pi$
$829$	14017.3	0.587264	0.293632	+	0.955919i	$0.405136\pi$
$830$	0	0
$831$	7437.77	0.310485
$832$	−4283.21	−0.178478
$833$	−2831.78	−0.117786
$834$	16322.6	0.677706
$835$	0	0
$836$	−998.147	−0.0412938
$837$	−455.502	−0.0188106
$838$	−13044.2	−0.537712
$839$	23478.8	0.966125	0.483063	−	0.875586i	$-0.339524\pi$
$839$	23478.8	0.966125	0.483063	+	0.875586i	$0.339524\pi$
$840$	0	0
$841$	32271.3	1.32319
$842$	28194.6	1.15398
$843$	−11753.5	−0.480205
$844$	20464.3	0.834611
$845$	0	0
$846$	−2617.36	−0.106367
$847$	11320.9	0.459257
$848$	−6103.76	−0.247174
$849$	−13982.0	−0.565208
$850$	0	0
$851$	34819.0	1.40256
$852$	−13270.6	−0.533618
$853$	5036.65	0.202171	0.101085	−	0.994878i	$-0.467769\pi$
$853$	5036.65	0.202171	0.101085	+	0.994878i	$0.467769\pi$
$854$	−4359.48	−0.174682
$855$	0	0
$856$	−3421.43	−0.136615
$857$	−8927.91	−0.355860	−0.177930	−	0.984043i	$-0.556940\pi$
$857$	−8927.91	−0.355860	−0.177930	+	0.984043i	$0.556940\pi$
$858$	−15069.0	−0.599587
$859$	39224.1	1.55799	0.778993	−	0.627033i	$-0.215731\pi$
$859$	39224.1	1.55799	0.778993	+	0.627033i	$0.215731\pi$
$860$	0	0
$861$	32918.7	1.30298
$862$	8150.06	0.322033
$863$	−14370.6	−0.566839	−0.283419	−	0.958996i	$-0.591469\pi$
$863$	−14370.6	−0.566839	−0.283419	+	0.958996i	$0.591469\pi$
$864$	−4884.60	−0.192335
$865$	0	0
$866$	−3733.10	−0.146485
$867$	−2840.61	−0.111271
$868$	−206.604	−0.00807902
$869$	−7536.88	−0.294213
$870$	0	0
$871$	−58337.9	−2.26947
$872$	−28.7804	−0.00111769
$873$	1707.69	0.0662047
$874$	2113.83	0.0818093
$875$	0	0
$876$	−15081.2	−0.581674
$877$	−11388.8	−0.438507	−0.219254	−	0.975668i	$-0.570362\pi$
$877$	−11388.8	−0.438507	−0.219254	+	0.975668i	$0.570362\pi$
$878$	−27246.5	−1.04730
$879$	−26268.7	−1.00799
$880$	0	0
$881$	−25241.3	−0.965267	−0.482634	−	0.875822i	$-0.660320\pi$
$881$	−25241.3	−0.965267	−0.482634	+	0.875822i	$0.660320\pi$
$882$	718.523	0.0274308
$883$	−12038.3	−0.458802	−0.229401	−	0.973332i	$-0.573677\pi$
$883$	−12038.3	−0.458802	−0.229401	+	0.973332i	$0.573677\pi$
$884$	−17465.3	−0.664505
$885$	0	0
$886$	7596.43	0.288044
$887$	−47282.2	−1.78983	−0.894917	−	0.446233i	$-0.852765\pi$
$887$	−47282.2	−1.78983	−0.894917	+	0.446233i	$0.852765\pi$
$888$	−10937.3	−0.413324
$889$	−42356.1	−1.59795
$890$	0	0
$891$	−11370.2	−0.427514
$892$	−7570.10	−0.284154
$893$	−1516.40	−0.0568245
$894$	−6166.75	−0.230701
$895$	0	0
$896$	−2215.53	−0.0826068
$897$	31912.4	1.18787
$898$	29232.9	1.08632
$899$	710.313	0.0263518
$900$	0	0
$901$	−24888.8	−0.920274
$902$	−22871.6	−0.844279
$903$	9937.25	0.366214
$904$	15196.0	0.559082
$905$	0	0
$906$	19429.4	0.712470
$907$	27755.0	1.01608	0.508042	−	0.861332i	$-0.330369\pi$
$907$	27755.0	1.01608	0.508042	+	0.861332i	$0.330369\pi$
$908$	−23528.5	−0.859936
$909$	−11886.6	−0.433724
$910$	0	0
$911$	−40062.2	−1.45699	−0.728497	−	0.685049i	$-0.759781\pi$
$911$	−40062.2	−1.45699	−0.728497	+	0.685049i	$0.759781\pi$
$912$	−663.994	−0.0241086
$913$	−30371.7	−1.10094
$914$	4971.63	0.179920
$915$	0	0
$916$	−1446.19	−0.0521655
$917$	39620.8	1.42682
$918$	−19917.6	−0.716098
$919$	−15590.7	−0.559619	−0.279809	−	0.960056i	$-0.590271\pi$
$919$	−15590.7	−0.559619	−0.279809	+	0.960056i	$0.590271\pi$
$920$	0	0
$921$	−35604.9	−1.27386
$922$	−5767.10	−0.205997
$923$	51313.7	1.82991
$924$	−7794.56	−0.277513
$925$	0	0
$926$	16629.2	0.590141
$927$	1168.70	0.0414079
$928$	7617.09	0.269443
$929$	624.811	0.0220661	0.0110330	−	0.999939i	$-0.496488\pi$
$929$	624.811	0.0220661	0.0110330	+	0.999939i	$0.496488\pi$
$930$	0	0
$931$	416.284	0.0146543
$932$	−9831.10	−0.345524
$933$	19600.5	0.687771
$934$	−6809.66	−0.238564
$935$	0	0
$936$	4431.57	0.154755
$937$	−24449.6	−0.852438	−0.426219	−	0.904620i	$-0.640155\pi$
$937$	−24449.6	−0.852438	−0.426219	+	0.904620i	$0.640155\pi$
$938$	−30175.8	−1.05040
$939$	6171.39	0.214479
$940$	0	0
$941$	−21899.2	−0.758655	−0.379327	−	0.925262i	$-0.623845\pi$
$941$	−21899.2	−0.758655	−0.379327	+	0.925262i	$0.623845\pi$
$942$	8816.74	0.304952
$943$	48436.3	1.67264
$944$	−8576.43	−0.295698
$945$	0	0
$946$	−6904.29	−0.237292
$947$	13006.2	0.446298	0.223149	−	0.974784i	$-0.428366\pi$
$947$	13006.2	0.446298	0.223149	+	0.974784i	$0.428366\pi$
$948$	−5013.73	−0.171771
$949$	58314.8	1.99471
$950$	0	0
$951$	29627.1	1.01023
$952$	−9034.10	−0.307560
$953$	−10041.6	−0.341322	−0.170661	−	0.985330i	$-0.554590\pi$
$953$	−10041.6	−0.341322	−0.170661	+	0.985330i	$0.554590\pi$
$954$	6315.17	0.214320
$955$	0	0
$956$	−23806.9	−0.805409
$957$	26798.0	0.905180
$958$	27229.2	0.918303
$959$	−897.762	−0.0302297
$960$	0	0
$961$	−29782.1	−0.999701
$962$	42291.5	1.41739
$963$	3539.94	0.118456
$964$	19356.3	0.646706
$965$	0	0
$966$	16507.0	0.549796
$967$	−22247.5	−0.739848	−0.369924	−	0.929062i	$-0.620616\pi$
$967$	−22247.5	−0.739848	−0.369924	+	0.929062i	$0.620616\pi$
$968$	−5232.43	−0.173736
$969$	−2707.52	−0.0897605
$970$	0	0
$971$	−60454.3	−1.99801	−0.999007	−	0.0445630i	$-0.985810\pi$
$971$	−60454.3	−1.99801	−0.999007	+	0.0445630i	$0.985810\pi$
$972$	8921.81	0.294411
$973$	−32646.9	−1.07565
$974$	−6458.83	−0.212479
$975$	0	0
$976$	2014.92	0.0660819
$977$	32272.9	1.05681	0.528403	−	0.848993i	$-0.322791\pi$
$977$	32272.9	1.05681	0.528403	+	0.848993i	$0.322791\pi$
$978$	−34486.2	−1.12755
$979$	−7044.91	−0.229986
$980$	0	0
$981$	29.7773	0.000969129 0
$982$	−1259.78	−0.0409381
$983$	−4015.66	−0.130295	−0.0651474	−	0.997876i	$-0.520752\pi$
$983$	−4015.66	−0.130295	−0.0651474	+	0.997876i	$0.520752\pi$
$984$	−15214.8	−0.492916
$985$	0	0
$986$	31059.6	1.00319
$987$	−11841.6	−0.381886
$988$	2567.48	0.0826745
$989$	14621.6	0.470111
$990$	0	0
$991$	−30680.4	−0.983446	−0.491723	−	0.870752i	$-0.663633\pi$
$991$	−30680.4	−0.983446	−0.491723	+	0.870752i	$0.663633\pi$
$992$	95.4906	0.00305628
$993$	−34085.4	−1.08929
$994$	26542.5	0.846958
$995$	0	0
$996$	−20204.1	−0.642762
$997$	−23669.9	−0.751889	−0.375944	−	0.926642i	$-0.622682\pi$
$997$	−23669.9	−0.751889	−0.375944	+	0.926642i	$0.622682\pi$
$998$	−9903.24	−0.314110
$999$	48229.5	1.52744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.4.a.e.1.5		6
5.4	even	2		1250.4.a.d.1.2		6
25.3	odd	20		250.4.e.a.49.1		24
25.4	even	10		50.4.d.a.41.1	yes	12
25.6	even	5		250.4.d.a.51.3		12
25.8	odd	20		250.4.e.a.199.6		24
25.17	odd	20		250.4.e.a.199.1		24
25.19	even	10		50.4.d.a.11.1	✓	12
25.21	even	5		250.4.d.a.201.3		12
25.22	odd	20		250.4.e.a.49.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.d.a.11.1	✓	12	25.19	even	10
50.4.d.a.41.1	yes	12	25.4	even	10
250.4.d.a.51.3		12	25.6	even	5
250.4.d.a.201.3		12	25.21	even	5
250.4.e.a.49.1		24	25.3	odd	20
250.4.e.a.49.6		24	25.22	odd	20
250.4.e.a.199.1		24	25.17	odd	20
250.4.e.a.199.6		24	25.8	odd	20
1250.4.a.d.1.2		6	5.4	even	2
1250.4.a.e.1.5		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1250.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +4.32700 q^{3} +4.00000 q^{4} +8.65399 q^{6} -17.3088 q^{7} +8.00000 q^{8} -8.27710 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +4.32700 q^{3} +4.00000 q^{4} +8.65399 q^{6} -17.3088 q^{7} +8.00000 q^{8} -8.27710 q^{9} +26.0182 q^{11} +17.3080 q^{12} -66.9252 q^{13} -34.6177 q^{14} +16.0000 q^{16} +65.2420 q^{17} -16.5542 q^{18} -9.59086 q^{19} -74.8953 q^{21} +52.0364 q^{22} -110.200 q^{23} +34.6160 q^{24} -133.850 q^{26} -152.644 q^{27} -69.2353 q^{28} +238.034 q^{29} +2.98408 q^{31} +32.0000 q^{32} +112.581 q^{33} +130.484 q^{34} -33.1084 q^{36} -315.961 q^{37} -19.1817 q^{38} -289.585 q^{39} -439.530 q^{41} -149.791 q^{42} -132.682 q^{43} +104.073 q^{44} -220.401 q^{46} +158.109 q^{47} +69.2319 q^{48} -43.4043 q^{49} +282.302 q^{51} -267.701 q^{52} -381.485 q^{53} -305.288 q^{54} -138.471 q^{56} -41.4996 q^{57} +476.068 q^{58} -536.027 q^{59} +125.932 q^{61} +5.96816 q^{62} +143.267 q^{63} +64.0000 q^{64} +225.161 q^{66} +871.688 q^{67} +260.968 q^{68} -476.836 q^{69} -766.732 q^{71} -66.2168 q^{72} -871.343 q^{73} -631.922 q^{74} -38.3634 q^{76} -450.345 q^{77} -579.170 q^{78} -289.677 q^{79} -437.008 q^{81} -879.060 q^{82} -1167.33 q^{83} -299.581 q^{84} -265.364 q^{86} +1029.97 q^{87} +208.146 q^{88} -270.769 q^{89} +1158.40 q^{91} -440.801 q^{92} +12.9121 q^{93} +316.217 q^{94} +138.464 q^{96} -206.315 q^{97} -86.8085 q^{98} -215.355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 8 q^{3} + 24 q^{4} - 16 q^{6} - 29 q^{7} + 48 q^{8} - 18 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 8 * q^3 + 24 * q^4 - 16 * q^6 - 29 * q^7 + 48 * q^8 - 18 * q^9	\( 6 q + 12 q^{2} - 8 q^{3} + 24 q^{4} - 16 q^{6} - 29 q^{7} + 48 q^{8} - 18 q^{9} - 33 q^{11} - 32 q^{12} + 32 q^{13} - 58 q^{14} + 96 q^{16} + 26 q^{17} - 36 q^{18} - 75 q^{19} - 88 q^{21} - 66 q^{22} - 113 q^{23} - 64 q^{24} + 64 q^{26} + 40 q^{27} - 116 q^{28} + 230 q^{29} - 13 q^{31} + 192 q^{32} - 101 q^{33} + 52 q^{34} - 72 q^{36} - 664 q^{37} - 150 q^{38} - 826 q^{39} - 253 q^{41} - 176 q^{42} - 373 q^{43} - 132 q^{44} - 226 q^{46} - 1534 q^{47} - 128 q^{48} - 417 q^{49} + 1362 q^{51} + 128 q^{52} - 1233 q^{53} + 80 q^{54} - 232 q^{56} - 640 q^{57} + 460 q^{58} + 220 q^{59} - 588 q^{61} - 26 q^{62} + 447 q^{63} + 384 q^{64} - 202 q^{66} - 739 q^{67} + 104 q^{68} - 511 q^{69} - 1628 q^{71} - 144 q^{72} - 3283 q^{73} - 1328 q^{74} - 300 q^{76} - 248 q^{77} - 1652 q^{78} + 1220 q^{79} - 1754 q^{81} - 506 q^{82} - 893 q^{83} - 352 q^{84} - 746 q^{86} - 725 q^{87} - 264 q^{88} - 2305 q^{89} + 1127 q^{91} - 452 q^{92} - 2276 q^{93} - 3068 q^{94} - 256 q^{96} - 4369 q^{97} - 834 q^{98} - 601 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 8 * q^3 + 24 * q^4 - 16 * q^6 - 29 * q^7 + 48 * q^8 - 18 * q^9 - 33 * q^11 - 32 * q^12 + 32 * q^13 - 58 * q^14 + 96 * q^16 + 26 * q^17 - 36 * q^18 - 75 * q^19 - 88 * q^21 - 66 * q^22 - 113 * q^23 - 64 * q^24 + 64 * q^26 + 40 * q^27 - 116 * q^28 + 230 * q^29 - 13 * q^31 + 192 * q^32 - 101 * q^33 + 52 * q^34 - 72 * q^36 - 664 * q^37 - 150 * q^38 - 826 * q^39 - 253 * q^41 - 176 * q^42 - 373 * q^43 - 132 * q^44 - 226 * q^46 - 1534 * q^47 - 128 * q^48 - 417 * q^49 + 1362 * q^51 + 128 * q^52 - 1233 * q^53 + 80 * q^54 - 232 * q^56 - 640 * q^57 + 460 * q^58 + 220 * q^59 - 588 * q^61 - 26 * q^62 + 447 * q^63 + 384 * q^64 - 202 * q^66 - 739 * q^67 + 104 * q^68 - 511 * q^69 - 1628 * q^71 - 144 * q^72 - 3283 * q^73 - 1328 * q^74 - 300 * q^76 - 248 * q^77 - 1652 * q^78 + 1220 * q^79 - 1754 * q^81 - 506 * q^82 - 893 * q^83 - 352 * q^84 - 746 * q^86 - 725 * q^87 - 264 * q^88 - 2305 * q^89 + 1127 * q^91 - 452 * q^92 - 2276 * q^93 - 3068 * q^94 - 256 * q^96 - 4369 * q^97 - 834 * q^98 - 601 * q^99

Introduction

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