LMFDB - Embedded newform 1150.4.a.bb.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 179x^{7} + 380x^{6} + 10197x^{5} - 8259x^{4} - 205207x^{3} - 105750x^{2} + 525560x + 178000 $ x^9 - 3x^8 - 179x^7 + 380x^6 + 10197x^5 - 8259x^4 - 205207x^3 - 105750x^2 + 525560x + 178000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.10900$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -2.10900 q^{3} +4.00000 q^{4} -4.21800 q^{6} +35.7485 q^{7} +8.00000 q^{8} -22.5521 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -2.10900 q^{3} +4.00000 q^{4} -4.21800 q^{6} +35.7485 q^{7} +8.00000 q^{8} -22.5521 q^{9} +55.0544 q^{11} -8.43600 q^{12} +59.6405 q^{13} +71.4970 q^{14} +16.0000 q^{16} +32.6105 q^{17} -45.1042 q^{18} +86.8067 q^{19} -75.3937 q^{21} +110.109 q^{22} -23.0000 q^{23} -16.8720 q^{24} +119.281 q^{26} +104.505 q^{27} +142.994 q^{28} -183.224 q^{29} -310.306 q^{31} +32.0000 q^{32} -116.110 q^{33} +65.2209 q^{34} -90.2085 q^{36} -172.616 q^{37} +173.613 q^{38} -125.782 q^{39} -116.035 q^{41} -150.787 q^{42} +23.6571 q^{43} +220.218 q^{44} -46.0000 q^{46} +91.5129 q^{47} -33.7440 q^{48} +934.957 q^{49} -68.7755 q^{51} +238.562 q^{52} +678.422 q^{53} +209.011 q^{54} +285.988 q^{56} -183.075 q^{57} -366.448 q^{58} -295.609 q^{59} +336.571 q^{61} -620.612 q^{62} -806.205 q^{63} +64.0000 q^{64} -232.220 q^{66} -915.837 q^{67} +130.442 q^{68} +48.5070 q^{69} +753.919 q^{71} -180.417 q^{72} -52.3219 q^{73} -345.231 q^{74} +347.227 q^{76} +1968.11 q^{77} -251.564 q^{78} +483.025 q^{79} +388.505 q^{81} -232.069 q^{82} -364.554 q^{83} -301.575 q^{84} +47.3141 q^{86} +386.420 q^{87} +440.435 q^{88} +451.047 q^{89} +2132.06 q^{91} -92.0000 q^{92} +654.435 q^{93} +183.026 q^{94} -67.4880 q^{96} +145.870 q^{97} +1869.91 q^{98} -1241.59 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9}+O(q^{10}) $ 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22} - 207 q^{23} + 24 q^{24} + 118 q^{26} + 336 q^{27} + 176 q^{28} + 205 q^{29} + 336 q^{31} + 288 q^{32} + 437 q^{33} + 220 q^{34} + 496 q^{36} - 5 q^{37} + 442 q^{38} - 44 q^{39} + 360 q^{41} + 284 q^{42} + 366 q^{43} + 324 q^{44} - 414 q^{46} - 122 q^{47} + 48 q^{48} + 457 q^{49} + 1025 q^{51} + 236 q^{52} + 631 q^{53} + 672 q^{54} + 352 q^{56} - 384 q^{57} + 410 q^{58} + 797 q^{59} + 211 q^{61} + 672 q^{62} + 2447 q^{63} + 576 q^{64} + 874 q^{66} + 111 q^{67} + 440 q^{68} - 69 q^{69} + 2912 q^{71} + 992 q^{72} + 98 q^{73} - 10 q^{74} + 884 q^{76} + 942 q^{77} - 88 q^{78} + 1184 q^{79} + 2093 q^{81} + 720 q^{82} + 2375 q^{83} + 568 q^{84} + 732 q^{86} - 1534 q^{87} + 648 q^{88} + 2588 q^{89} + 2677 q^{91} - 828 q^{92} + 1402 q^{93} - 244 q^{94} + 96 q^{96} - 593 q^{97} + 914 q^{98} - 1753 q^{99}+O(q^{100}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * 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
$3$	−2.10900	−0.405877	−0.202939	−	0.979191i	$-0.565049\pi$
$3$	−2.10900	−0.405877	−0.202939	+	0.979191i	$0.565049\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−4.21800	−0.286999
$7$	35.7485	1.93024	0.965119	−	0.261810i	$-0.0843195\pi$
$7$	35.7485	1.93024	0.965119	+	0.261810i	$0.0843195\pi$
$8$	8.00000	0.353553
$9$	−22.5521	−0.835264
$10$	0	0
$11$	55.0544	1.50905	0.754524	−	0.656273i	$-0.227868\pi$
$11$	55.0544	1.50905	0.754524	+	0.656273i	$0.227868\pi$
$12$	−8.43600	−0.202939
$13$	59.6405	1.27241	0.636204	−	0.771521i	$-0.280504\pi$
$13$	59.6405	1.27241	0.636204	+	0.771521i	$0.280504\pi$
$14$	71.4970	1.36488
$15$	0	0
$16$	16.0000	0.250000
$17$	32.6105	0.465247	0.232624	−	0.972567i	$-0.425269\pi$
$17$	32.6105	0.465247	0.232624	+	0.972567i	$0.425269\pi$
$18$	−45.1042	−0.590621
$19$	86.8067	1.04815	0.524074	−	0.851673i	$-0.324411\pi$
$19$	86.8067	1.04815	0.524074	+	0.851673i	$0.324411\pi$
$20$	0	0
$21$	−75.3937	−0.783440
$22$	110.109	1.06706
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−16.8720	−0.143499
$25$	0	0
$26$	119.281	0.899728
$27$	104.505	0.744892
$28$	142.994	0.965119
$29$	−183.224	−1.17324	−0.586618	−	0.809864i	$-0.699541\pi$
$29$	−183.224	−1.17324	−0.586618	+	0.809864i	$0.699541\pi$
$30$	0	0
$31$	−310.306	−1.79783	−0.898913	−	0.438128i	$-0.855642\pi$
$31$	−310.306	−1.79783	−0.898913	+	0.438128i	$0.855642\pi$
$32$	32.0000	0.176777
$33$	−116.110	−0.612488
$34$	65.2209	0.328979
$35$	0	0
$36$	−90.2085	−0.417632
$37$	−172.616	−0.766969	−0.383484	−	0.923547i	$-0.625276\pi$
$37$	−172.616	−0.766969	−0.383484	+	0.923547i	$0.625276\pi$
$38$	173.613	0.741153
$39$	−125.782	−0.516441
$40$	0	0
$41$	−116.035	−0.441989	−0.220995	−	0.975275i	$-0.570930\pi$
$41$	−116.035	−0.441989	−0.220995	+	0.975275i	$0.570930\pi$
$42$	−150.787	−0.553976
$43$	23.6571	0.0838993	0.0419496	−	0.999120i	$-0.486643\pi$
$43$	23.6571	0.0838993	0.0419496	+	0.999120i	$0.486643\pi$
$44$	220.218	0.754524
$45$	0	0
$46$	−46.0000	−0.147442
$47$	91.5129	0.284011	0.142006	−	0.989866i	$-0.454645\pi$
$47$	91.5129	0.284011	0.142006	+	0.989866i	$0.454645\pi$
$48$	−33.7440	−0.101469
$49$	934.957	2.72582
$50$	0	0
$51$	−68.7755	−0.188833
$52$	238.562	0.636204
$53$	678.422	1.75827	0.879136	−	0.476572i	$-0.158121\pi$
$53$	678.422	1.75827	0.879136	+	0.476572i	$0.158121\pi$
$54$	209.011	0.526718
$55$	0	0
$56$	285.988	0.682442
$57$	−183.075	−0.425420
$58$	−366.448	−0.829604
$59$	−295.609	−0.652288	−0.326144	−	0.945320i	$-0.605749\pi$
$59$	−295.609	−0.652288	−0.326144	+	0.945320i	$0.605749\pi$
$60$	0	0
$61$	336.571	0.706451	0.353225	−	0.935538i	$-0.385085\pi$
$61$	336.571	0.706451	0.353225	+	0.935538i	$0.385085\pi$
$62$	−620.612	−1.27125
$63$	−806.205	−1.61226
$64$	64.0000	0.125000
$65$	0	0
$66$	−232.220	−0.433095
$67$	−915.837	−1.66996	−0.834980	−	0.550281i	$-0.814521\pi$
$67$	−915.837	−1.66996	−0.834980	+	0.550281i	$0.814521\pi$
$68$	130.442	0.232624
$69$	48.5070	0.0846313
$70$	0	0
$71$	753.919	1.26019	0.630097	−	0.776517i	$-0.283015\pi$
$71$	753.919	1.26019	0.630097	+	0.776517i	$0.283015\pi$
$72$	−180.417	−0.295310
$73$	−52.3219	−0.0838878	−0.0419439	−	0.999120i	$-0.513355\pi$
$73$	−52.3219	−0.0838878	−0.0419439	+	0.999120i	$0.513355\pi$
$74$	−345.231	−0.542329
$75$	0	0
$76$	347.227	0.524074
$77$	1968.11	2.91282
$78$	−251.564	−0.365179
$79$	483.025	0.687906	0.343953	−	0.938987i	$-0.388234\pi$
$79$	483.025	0.687906	0.343953	+	0.938987i	$0.388234\pi$
$80$	0	0
$81$	388.505	0.532929
$82$	−232.069	−0.312534
$83$	−364.554	−0.482109	−0.241054	−	0.970512i	$-0.577493\pi$
$83$	−364.554	−0.482109	−0.241054	+	0.970512i	$0.577493\pi$
$84$	−301.575	−0.391720
$85$	0	0
$86$	47.3141	0.0593257
$87$	386.420	0.476190
$88$	440.435	0.533529
$89$	451.047	0.537201	0.268601	−	0.963252i	$-0.413439\pi$
$89$	451.047	0.537201	0.268601	+	0.963252i	$0.413439\pi$
$90$	0	0
$91$	2132.06	2.45605
$92$	−92.0000	−0.104257
$93$	654.435	0.729697
$94$	183.026	0.200826
$95$	0	0
$96$	−67.4880	−0.0717497
$97$	145.870	0.152689	0.0763446	−	0.997081i	$-0.475675\pi$
$97$	145.870	0.152689	0.0763446	+	0.997081i	$0.475675\pi$
$98$	1869.91	1.92745
$99$	−1241.59	−1.26045
$100$	0	0
$101$	−444.096	−0.437517	−0.218758	−	0.975779i	$-0.570201\pi$
$101$	−444.096	−0.437517	−0.218758	+	0.975779i	$0.570201\pi$
$102$	−137.551	−0.133525
$103$	−1724.93	−1.65012	−0.825062	−	0.565043i	$-0.808860\pi$
$103$	−1724.93	−1.65012	−0.825062	+	0.565043i	$0.808860\pi$
$104$	477.124	0.449864
$105$	0	0
$106$	1356.84	1.24329
$107$	−1536.14	−1.38789	−0.693945	−	0.720028i	$-0.744129\pi$
$107$	−1536.14	−1.38789	−0.693945	+	0.720028i	$0.744129\pi$
$108$	418.022	0.372446
$109$	−1945.69	−1.70975	−0.854876	−	0.518832i	$-0.826367\pi$
$109$	−1945.69	−1.70975	−0.854876	+	0.518832i	$0.826367\pi$
$110$	0	0
$111$	364.047	0.311295
$112$	571.976	0.482560
$113$	713.834	0.594264	0.297132	−	0.954836i	$-0.403970\pi$
$113$	713.834	0.594264	0.297132	+	0.954836i	$0.403970\pi$
$114$	−366.151	−0.300817
$115$	0	0
$116$	−732.896	−0.586618
$117$	−1345.02	−1.06280
$118$	−591.218	−0.461237
$119$	1165.78	0.898038
$120$	0	0
$121$	1699.99	1.27722
$122$	673.142	0.499536
$123$	244.717	0.179394
$124$	−1241.22	−0.898913
$125$	0	0
$126$	−1612.41	−1.14004
$127$	1283.46	0.896763	0.448382	−	0.893842i	$-0.352001\pi$
$127$	1283.46	0.896763	0.448382	+	0.893842i	$0.352001\pi$
$128$	128.000	0.0883883
$129$	−49.8928	−0.0340528
$130$	0	0
$131$	1556.38	1.03803	0.519013	−	0.854766i	$-0.326299\pi$
$131$	1556.38	1.03803	0.519013	+	0.854766i	$0.326299\pi$
$132$	−464.439	−0.306244
$133$	3103.21	2.02318
$134$	−1831.67	−1.18084
$135$	0	0
$136$	260.884	0.164490
$137$	390.204	0.243338	0.121669	−	0.992571i	$-0.461175\pi$
$137$	390.204	0.243338	0.121669	+	0.992571i	$0.461175\pi$
$138$	97.0140	0.0598434
$139$	−747.948	−0.456404	−0.228202	−	0.973614i	$-0.573285\pi$
$139$	−747.948	−0.456404	−0.228202	+	0.973614i	$0.573285\pi$
$140$	0	0
$141$	−193.001	−0.115274
$142$	1507.84	0.891091
$143$	3283.47	1.92012
$144$	−360.834	−0.208816
$145$	0	0
$146$	−104.644	−0.0593177
$147$	−1971.82	−1.10635
$148$	−690.463	−0.383484
$149$	2890.00	1.58898	0.794490	−	0.607277i	$-0.207738\pi$
$149$	2890.00	1.58898	0.794490	+	0.607277i	$0.207738\pi$
$150$	0	0
$151$	1416.66	0.763486	0.381743	−	0.924268i	$-0.375324\pi$
$151$	1416.66	0.763486	0.381743	+	0.924268i	$0.375324\pi$
$152$	694.453	0.370576
$153$	−735.435	−0.388604
$154$	3936.23	2.05968
$155$	0	0
$156$	−503.127	−0.258221
$157$	−1627.56	−0.827346	−0.413673	−	0.910425i	$-0.635754\pi$
$157$	−1627.56	−0.827346	−0.413673	+	0.910425i	$0.635754\pi$
$158$	966.050	0.486423
$159$	−1430.79	−0.713643
$160$	0	0
$161$	−822.216	−0.402483
$162$	777.010	0.376837
$163$	−150.872	−0.0724984	−0.0362492	−	0.999343i	$-0.511541\pi$
$163$	−150.872	−0.0724984	−0.0362492	+	0.999343i	$0.511541\pi$
$164$	−464.139	−0.220995
$165$	0	0
$166$	−729.109	−0.340902
$167$	2006.50	0.929746	0.464873	−	0.885377i	$-0.346100\pi$
$167$	2006.50	0.929746	0.464873	+	0.885377i	$0.346100\pi$
$168$	−603.149	−0.276988
$169$	1359.99	0.619020
$170$	0	0
$171$	−1957.67	−0.875480
$172$	94.6283	0.0419496
$173$	−1439.78	−0.632740	−0.316370	−	0.948636i	$-0.602464\pi$
$173$	−1439.78	−0.632740	−0.316370	+	0.948636i	$0.602464\pi$
$174$	772.840	0.336717
$175$	0	0
$176$	880.870	0.377262
$177$	623.439	0.264749
$178$	902.095	0.379859
$179$	2327.38	0.971824	0.485912	−	0.874008i	$-0.338488\pi$
$179$	2327.38	0.971824	0.485912	+	0.874008i	$0.338488\pi$
$180$	0	0
$181$	1306.98	0.536724	0.268362	−	0.963318i	$-0.413518\pi$
$181$	1306.98	0.536724	0.268362	+	0.963318i	$0.413518\pi$
$182$	4264.12	1.73669
$183$	−709.829	−0.286732
$184$	−184.000	−0.0737210
$185$	0	0
$186$	1308.87	0.515974
$187$	1795.35	0.702080
$188$	366.052	0.142006
$189$	3735.92	1.43782
$190$	0	0
$191$	2146.88	0.813313	0.406657	−	0.913581i	$-0.366695\pi$
$191$	2146.88	0.813313	0.406657	+	0.913581i	$0.366695\pi$
$192$	−134.976	−0.0507347
$193$	1251.33	0.466696	0.233348	−	0.972393i	$-0.425032\pi$
$193$	1251.33	0.466696	0.233348	+	0.972393i	$0.425032\pi$
$194$	291.740	0.107968
$195$	0	0
$196$	3739.83	1.36291
$197$	1063.45	0.384606	0.192303	−	0.981336i	$-0.438404\pi$
$197$	1063.45	0.384606	0.192303	+	0.981336i	$0.438404\pi$
$198$	−2483.19	−0.891274
$199$	−624.156	−0.222338	−0.111169	−	0.993802i	$-0.535460\pi$
$199$	−624.156	−0.222338	−0.111169	+	0.993802i	$0.535460\pi$
$200$	0	0
$201$	1931.50	0.677799
$202$	−888.191	−0.309371
$203$	−6549.99	−2.26463
$204$	−275.102	−0.0944166
$205$	0	0
$206$	−3449.87	−1.16681
$207$	518.699	0.174164
$208$	954.248	0.318102
$209$	4779.09	1.58171
$210$	0	0
$211$	−441.618	−0.144086	−0.0720432	−	0.997402i	$-0.522952\pi$
$211$	−441.618	−0.144086	−0.0720432	+	0.997402i	$0.522952\pi$
$212$	2713.69	0.879136
$213$	−1590.02	−0.511484
$214$	−3072.28	−0.981387
$215$	0	0
$216$	836.044	0.263359
$217$	−11093.0	−3.47023
$218$	−3891.37	−1.20898
$219$	110.347	0.0340482
$220$	0	0
$221$	1944.90	0.591984
$222$	728.093	0.220119
$223$	−504.361	−0.151455	−0.0757276	−	0.997129i	$-0.524128\pi$
$223$	−504.361	−0.151455	−0.0757276	+	0.997129i	$0.524128\pi$
$224$	1143.95	0.341221
$225$	0	0
$226$	1427.67	0.420208
$227$	−5315.31	−1.55414	−0.777069	−	0.629415i	$-0.783295\pi$
$227$	−5315.31	−1.55414	−0.777069	+	0.629415i	$0.783295\pi$
$228$	−732.301	−0.212710
$229$	4687.07	1.35253	0.676266	−	0.736657i	$-0.263597\pi$
$229$	4687.07	1.35253	0.676266	+	0.736657i	$0.263597\pi$
$230$	0	0
$231$	−4150.75	−1.18225
$232$	−1465.79	−0.414802
$233$	881.725	0.247913	0.123957	−	0.992288i	$-0.460442\pi$
$233$	881.725	0.247913	0.123957	+	0.992288i	$0.460442\pi$
$234$	−2690.04	−0.751510
$235$	0	0
$236$	−1182.44	−0.326144
$237$	−1018.70	−0.279206
$238$	2331.55	0.635009
$239$	−4216.85	−1.14128	−0.570639	−	0.821201i	$-0.693304\pi$
$239$	−4216.85	−1.14128	−0.570639	+	0.821201i	$0.693304\pi$
$240$	0	0
$241$	310.863	0.0830889	0.0415445	−	0.999137i	$-0.486772\pi$
$241$	310.863	0.0830889	0.0415445	+	0.999137i	$0.486772\pi$
$242$	3399.97	0.903134
$243$	−3641.00	−0.961196
$244$	1346.28	0.353225
$245$	0	0
$246$	489.434	0.126850
$247$	5177.19	1.33367
$248$	−2482.45	−0.635627
$249$	768.845	0.195677
$250$	0	0
$251$	5056.73	1.27162	0.635812	−	0.771844i	$-0.280665\pi$
$251$	5056.73	1.27162	0.635812	+	0.771844i	$0.280665\pi$
$252$	−3224.82	−0.806129
$253$	−1266.25	−0.314658
$254$	2566.93	0.634108
$255$	0	0
$256$	256.000	0.0625000
$257$	−247.756	−0.0601347	−0.0300673	−	0.999548i	$-0.509572\pi$
$257$	−247.756	−0.0601347	−0.0300673	+	0.999548i	$0.509572\pi$
$258$	−99.7855	−0.0240790
$259$	−6170.76	−1.48043
$260$	0	0
$261$	4132.09	0.979962
$262$	3112.76	0.733996
$263$	−630.260	−0.147770	−0.0738850	−	0.997267i	$-0.523540\pi$
$263$	−630.260	−0.147770	−0.0738850	+	0.997267i	$0.523540\pi$
$264$	−928.878	−0.216547
$265$	0	0
$266$	6206.42	1.43060
$267$	−951.259	−0.218038
$268$	−3663.35	−0.834980
$269$	−1151.78	−0.261060	−0.130530	−	0.991444i	$-0.541668\pi$
$269$	−1151.78	−0.261060	−0.130530	+	0.991444i	$0.541668\pi$
$270$	0	0
$271$	−1923.32	−0.431119	−0.215559	−	0.976491i	$-0.569157\pi$
$271$	−1923.32	−0.431119	−0.215559	+	0.976491i	$0.569157\pi$
$272$	521.767	0.116312
$273$	−4496.51	−0.996855
$274$	780.407	0.172066
$275$	0	0
$276$	194.028	0.0423156
$277$	−2860.64	−0.620503	−0.310251	−	0.950655i	$-0.600413\pi$
$277$	−2860.64	−0.620503	−0.310251	+	0.950655i	$0.600413\pi$
$278$	−1495.90	−0.322726
$279$	6998.06	1.50166
$280$	0	0
$281$	−6296.68	−1.33676	−0.668378	−	0.743822i	$-0.733011\pi$
$281$	−6296.68	−1.33676	−0.668378	+	0.743822i	$0.733011\pi$
$282$	−386.001	−0.0815108
$283$	−71.1347	−0.0149418	−0.00747088	−	0.999972i	$-0.502378\pi$
$283$	−71.1347	−0.0149418	−0.00747088	+	0.999972i	$0.502378\pi$
$284$	3015.68	0.630097
$285$	0	0
$286$	6566.94	1.35773
$287$	−4148.07	−0.853145
$288$	−721.668	−0.147655
$289$	−3849.56	−0.783545
$290$	0	0
$291$	−307.640	−0.0619731
$292$	−209.287	−0.0419439
$293$	−2398.86	−0.478304	−0.239152	−	0.970982i	$-0.576869\pi$
$293$	−2398.86	−0.478304	−0.239152	+	0.970982i	$0.576869\pi$
$294$	−3943.65	−0.782307
$295$	0	0
$296$	−1380.93	−0.271164
$297$	5753.48	1.12408
$298$	5780.00	1.12358
$299$	−1371.73	−0.265315
$300$	0	0
$301$	845.705	0.161946
$302$	2833.33	0.539866
$303$	936.598	0.177578
$304$	1388.91	0.262037
$305$	0	0
$306$	−1470.87	−0.274784
$307$	−6124.47	−1.13857	−0.569286	−	0.822139i	$-0.692780\pi$
$307$	−6124.47	−1.13857	−0.569286	+	0.822139i	$0.692780\pi$
$308$	7872.45	1.45641
$309$	3637.89	0.669748
$310$	0	0
$311$	−1879.27	−0.342648	−0.171324	−	0.985215i	$-0.554805\pi$
$311$	−1879.27	−0.342648	−0.171324	+	0.985215i	$0.554805\pi$
$312$	−1006.25	−0.182590
$313$	−868.530	−0.156844	−0.0784221	−	0.996920i	$-0.524988\pi$
$313$	−868.530	−0.156844	−0.0784221	+	0.996920i	$0.524988\pi$
$314$	−3255.12	−0.585022
$315$	0	0
$316$	1932.10	0.343953
$317$	1608.28	0.284953	0.142476	−	0.989798i	$-0.454493\pi$
$317$	1608.28	0.284953	0.142476	+	0.989798i	$0.454493\pi$
$318$	−2861.58	−0.504622
$319$	−10087.3	−1.77047
$320$	0	0
$321$	3239.72	0.563314
$322$	−1644.43	−0.284598
$323$	2830.81	0.487648
$324$	1554.02	0.266464
$325$	0	0
$326$	−301.745	−0.0512641
$327$	4103.46	0.693950
$328$	−928.277	−0.156267
$329$	3271.45	0.548209
$330$	0	0
$331$	−6916.60	−1.14855	−0.574276	−	0.818662i	$-0.694716\pi$
$331$	−6916.60	−1.14855	−0.574276	+	0.818662i	$0.694716\pi$
$332$	−1458.22	−0.241054
$333$	3892.85	0.640621
$334$	4013.00	0.657430
$335$	0	0
$336$	−1206.30	−0.195860
$337$	−10023.0	−1.62014	−0.810068	−	0.586336i	$-0.800570\pi$
$337$	−10023.0	−1.62014	−0.810068	+	0.586336i	$0.800570\pi$
$338$	2719.97	0.437713
$339$	−1505.48	−0.241198
$340$	0	0
$341$	−17083.7	−2.71300
$342$	−3915.35	−0.619058
$343$	21161.6	3.33125
$344$	189.257	0.0296629
$345$	0	0
$346$	−2879.55	−0.447415
$347$	3305.87	0.511437	0.255718	−	0.966751i	$-0.417688\pi$
$347$	3305.87	0.511437	0.255718	+	0.966751i	$0.417688\pi$
$348$	1545.68	0.238095
$349$	−8691.72	−1.33312	−0.666558	−	0.745454i	$-0.732233\pi$
$349$	−8691.72	−1.33312	−0.666558	+	0.745454i	$0.732233\pi$
$350$	0	0
$351$	6232.76	0.947806
$352$	1761.74	0.266764
$353$	8092.47	1.22017	0.610083	−	0.792337i	$-0.291136\pi$
$353$	8092.47	1.22017	0.610083	+	0.792337i	$0.291136\pi$
$354$	1246.88	0.187206
$355$	0	0
$356$	1804.19	0.268601
$357$	−2458.62	−0.364493
$358$	4654.76	0.687183
$359$	−6566.92	−0.965429	−0.482714	−	0.875778i	$-0.660349\pi$
$359$	−6566.92	−0.965429	−0.482714	+	0.875778i	$0.660349\pi$
$360$	0	0
$361$	676.398	0.0986146
$362$	2613.96	0.379521
$363$	−3585.27	−0.518397
$364$	8528.24	1.22802
$365$	0	0
$366$	−1419.66	−0.202750
$367$	3010.77	0.428231	0.214116	−	0.976808i	$-0.431313\pi$
$367$	3010.77	0.428231	0.214116	+	0.976808i	$0.431313\pi$
$368$	−368.000	−0.0521286
$369$	2616.83	0.369178
$370$	0	0
$371$	24252.6	3.39388
$372$	2617.74	0.364848
$373$	−10874.3	−1.50952	−0.754762	−	0.655999i	$-0.772248\pi$
$373$	−10874.3	−1.50952	−0.754762	+	0.655999i	$0.772248\pi$
$374$	3590.70	0.496445
$375$	0	0
$376$	732.103	0.100413
$377$	−10927.6	−1.49283
$378$	7471.83	1.01669
$379$	−10481.3	−1.42055	−0.710274	−	0.703926i	$-0.751429\pi$
$379$	−10481.3	−1.42055	−0.710274	+	0.703926i	$0.751429\pi$
$380$	0	0
$381$	−2706.83	−0.363976
$382$	4293.76	0.575099
$383$	−3588.96	−0.478818	−0.239409	−	0.970919i	$-0.576954\pi$
$383$	−3588.96	−0.478818	−0.239409	+	0.970919i	$0.576954\pi$
$384$	−269.952	−0.0358748
$385$	0	0
$386$	2502.65	0.330004
$387$	−533.517	−0.0700780
$388$	583.480	0.0763446
$389$	10904.2	1.42124	0.710620	−	0.703576i	$-0.248415\pi$
$389$	10904.2	1.42124	0.710620	+	0.703576i	$0.248415\pi$
$390$	0	0
$391$	−750.041	−0.0970107
$392$	7479.65	0.963723
$393$	−3282.41	−0.421312
$394$	2126.89	0.271958
$395$	0	0
$396$	−4966.37	−0.630226
$397$	−250.278	−0.0316400	−0.0158200	−	0.999875i	$-0.505036\pi$
$397$	−250.278	−0.0316400	−0.0158200	+	0.999875i	$0.505036\pi$
$398$	−1248.31	−0.157217
$399$	−6544.67	−0.821162
$400$	0	0
$401$	11553.7	1.43882	0.719408	−	0.694587i	$-0.244413\pi$
$401$	11553.7	1.43882	0.719408	+	0.694587i	$0.244413\pi$
$402$	3863.00	0.479276
$403$	−18506.8	−2.28757
$404$	−1776.38	−0.218758
$405$	0	0
$406$	−13100.0	−1.60133
$407$	−9503.25	−1.15739
$408$	−550.204	−0.0667626
$409$	−10348.3	−1.25107	−0.625536	−	0.780196i	$-0.715119\pi$
$409$	−10348.3	−1.25107	−0.625536	+	0.780196i	$0.715119\pi$
$410$	0	0
$411$	−822.940	−0.0987655
$412$	−6899.73	−0.825062
$413$	−10567.6	−1.25907
$414$	1037.40	0.123153
$415$	0	0
$416$	1908.50	0.224932
$417$	1577.42	0.185244
$418$	9558.18	1.11843
$419$	14790.6	1.72451	0.862253	−	0.506478i	$-0.169053\pi$
$419$	14790.6	1.72451	0.862253	+	0.506478i	$0.169053\pi$
$420$	0	0
$421$	−5755.67	−0.666305	−0.333152	−	0.942873i	$-0.608112\pi$
$421$	−5755.67	−0.666305	−0.333152	+	0.942873i	$0.608112\pi$
$422$	−883.236	−0.101885
$423$	−2063.81	−0.237224
$424$	5427.37	0.621643
$425$	0	0
$426$	−3180.03	−0.361674
$427$	12031.9	1.36362
$428$	−6144.56	−0.693945
$429$	−6924.84	−0.779335
$430$	0	0
$431$	−6334.05	−0.707889	−0.353945	−	0.935266i	$-0.615160\pi$
$431$	−6334.05	−0.707889	−0.353945	+	0.935266i	$0.615160\pi$
$432$	1672.09	0.186223
$433$	731.975	0.0812389	0.0406195	−	0.999175i	$-0.487067\pi$
$433$	731.975	0.0812389	0.0406195	+	0.999175i	$0.487067\pi$
$434$	−22186.0	−2.45382
$435$	0	0
$436$	−7782.75	−0.854876
$437$	−1996.55	−0.218554
$438$	220.694	0.0240757
$439$	2590.81	0.281669	0.140834	−	0.990033i	$-0.455022\pi$
$439$	2590.81	0.281669	0.140834	+	0.990033i	$0.455022\pi$
$440$	0	0
$441$	−21085.3	−2.27678
$442$	3889.81	0.418596
$443$	5781.25	0.620035	0.310018	−	0.950731i	$-0.399665\pi$
$443$	5781.25	0.620035	0.310018	+	0.950731i	$0.399665\pi$
$444$	1456.19	0.155648
$445$	0	0
$446$	−1008.72	−0.107095
$447$	−6095.01	−0.644931
$448$	2287.91	0.241280
$449$	16356.3	1.71915	0.859577	−	0.511006i	$-0.170727\pi$
$449$	16356.3	1.71915	0.859577	+	0.511006i	$0.170727\pi$
$450$	0	0
$451$	−6388.22	−0.666983
$452$	2855.34	0.297132
$453$	−2987.74	−0.309882
$454$	−10630.6	−1.09894
$455$	0	0
$456$	−1464.60	−0.150409
$457$	−2818.78	−0.288527	−0.144264	−	0.989539i	$-0.546081\pi$
$457$	−2818.78	−0.288527	−0.144264	+	0.989539i	$0.546081\pi$
$458$	9374.13	0.956385
$459$	3407.97	0.346559
$460$	0	0
$461$	5270.82	0.532508	0.266254	−	0.963903i	$-0.414214\pi$
$461$	5270.82	0.532508	0.266254	+	0.963903i	$0.414214\pi$
$462$	−8301.50	−0.835976
$463$	41.7995	0.00419566	0.00209783	−	0.999998i	$-0.499332\pi$
$463$	41.7995	0.00419566	0.00209783	+	0.999998i	$0.499332\pi$
$464$	−2931.59	−0.293309
$465$	0	0
$466$	1763.45	0.175301
$467$	4030.98	0.399425	0.199713	−	0.979854i	$-0.435999\pi$
$467$	4030.98	0.399425	0.199713	+	0.979854i	$0.435999\pi$
$468$	−5380.08	−0.531398
$469$	−32739.8	−3.22342
$470$	0	0
$471$	3432.52	0.335801
$472$	−2364.87	−0.230619
$473$	1302.43	0.126608
$474$	−2037.40	−0.197428
$475$	0	0
$476$	4663.10	0.449019
$477$	−15299.8	−1.46862
$478$	−8433.70	−0.807005
$479$	−3961.41	−0.377874	−0.188937	−	0.981989i	$-0.560504\pi$
$479$	−3961.41	−0.377874	−0.188937	+	0.981989i	$0.560504\pi$
$480$	0	0
$481$	−10294.9	−0.975897
$482$	621.726	0.0587528
$483$	1734.05	0.163359
$484$	6799.94	0.638612
$485$	0	0
$486$	−7282.01	−0.679668
$487$	18784.3	1.74784	0.873921	−	0.486067i	$-0.161569\pi$
$487$	18784.3	1.74784	0.873921	+	0.486067i	$0.161569\pi$
$488$	2692.57	0.249768
$489$	318.190	0.0294255
$490$	0	0
$491$	−19198.7	−1.76461	−0.882307	−	0.470675i	$-0.844010\pi$
$491$	−19198.7	−1.76461	−0.882307	+	0.470675i	$0.844010\pi$
$492$	978.869	0.0896968
$493$	−5975.02	−0.545845
$494$	10354.4	0.943048
$495$	0	0
$496$	−4964.89	−0.449456
$497$	26951.5	2.43247
$498$	1537.69	0.138365
$499$	13879.1	1.24512	0.622558	−	0.782573i	$-0.286093\pi$
$499$	13879.1	1.24512	0.622558	+	0.782573i	$0.286093\pi$
$500$	0	0
$501$	−4231.71	−0.377363
$502$	10113.5	0.899174
$503$	−17210.5	−1.52561	−0.762803	−	0.646631i	$-0.776177\pi$
$503$	−17210.5	−1.52561	−0.762803	+	0.646631i	$0.776177\pi$
$504$	−6449.64	−0.570019
$505$	0	0
$506$	−2532.50	−0.222497
$507$	−2868.21	−0.251246
$508$	5133.85	0.448382
$509$	−6209.17	−0.540701	−0.270350	−	0.962762i	$-0.587140\pi$
$509$	−6209.17	−0.540701	−0.270350	+	0.962762i	$0.587140\pi$
$510$	0	0
$511$	−1870.43	−0.161924
$512$	512.000	0.0441942
$513$	9071.77	0.780757
$514$	−495.513	−0.0425216
$515$	0	0
$516$	−199.571	−0.0170264
$517$	5038.19	0.428586
$518$	−12341.5	−1.04682
$519$	3036.49	0.256815
$520$	0	0
$521$	4664.01	0.392196	0.196098	−	0.980584i	$-0.437173\pi$
$521$	4664.01	0.392196	0.196098	+	0.980584i	$0.437173\pi$
$522$	8264.18	0.692938
$523$	13769.8	1.15126	0.575632	−	0.817709i	$-0.304756\pi$
$523$	13769.8	1.15126	0.575632	+	0.817709i	$0.304756\pi$
$524$	6225.52	0.519013
$525$	0	0
$526$	−1260.52	−0.104489
$527$	−10119.2	−0.836433
$528$	−1857.76	−0.153122
$529$	529.000	0.0434783
$530$	0	0
$531$	6666.61	0.544832
$532$	12412.8	1.01159
$533$	−6920.36	−0.562391
$534$	−1902.52	−0.154176
$535$	0	0
$536$	−7326.70	−0.590420
$537$	−4908.44	−0.394441
$538$	−2303.55	−0.184597
$539$	51473.5	4.11339
$540$	0	0
$541$	9475.09	0.752987	0.376494	−	0.926419i	$-0.377130\pi$
$541$	9475.09	0.752987	0.376494	+	0.926419i	$0.377130\pi$
$542$	−3846.63	−0.304847
$543$	−2756.42	−0.217844
$544$	1043.53	0.0822448
$545$	0	0
$546$	−8993.03	−0.704883
$547$	12848.9	1.00435	0.502177	−	0.864765i	$-0.332533\pi$
$547$	12848.9	1.00435	0.502177	+	0.864765i	$0.332533\pi$
$548$	1560.81	0.121669
$549$	−7590.39	−0.590073
$550$	0	0
$551$	−15905.1	−1.22973
$552$	388.056	0.0299217
$553$	17267.4	1.32782
$554$	−5721.28	−0.438762
$555$	0	0
$556$	−2991.79	−0.228202
$557$	−21148.0	−1.60874	−0.804370	−	0.594128i	$-0.797497\pi$
$557$	−21148.0	−1.60874	−0.804370	+	0.594128i	$0.797497\pi$
$558$	13996.1	1.06183
$559$	1410.92	0.106754
$560$	0	0
$561$	−3786.39	−0.284958
$562$	−12593.4	−0.945229
$563$	−1412.13	−0.105709	−0.0528544	−	0.998602i	$-0.516832\pi$
$563$	−1412.13	−0.105709	−0.0528544	+	0.998602i	$0.516832\pi$
$564$	−772.003	−0.0576369
$565$	0	0
$566$	−142.269	−0.0105654
$567$	13888.5	1.02868
$568$	6031.35	0.445546
$569$	−14127.9	−1.04090	−0.520450	−	0.853892i	$-0.674236\pi$
$569$	−14127.9	−1.04090	−0.520450	+	0.853892i	$0.674236\pi$
$570$	0	0
$571$	6208.53	0.455024	0.227512	−	0.973775i	$-0.426941\pi$
$571$	6208.53	0.455024	0.227512	+	0.973775i	$0.426941\pi$
$572$	13133.9	0.960062
$573$	−4527.77	−0.330106
$574$	−8296.13	−0.603265
$575$	0	0
$576$	−1443.34	−0.104408
$577$	−10994.5	−0.793253	−0.396626	−	0.917980i	$-0.629819\pi$
$577$	−10994.5	−0.793253	−0.396626	+	0.917980i	$0.629819\pi$
$578$	−7699.12	−0.554050
$579$	−2639.05	−0.189421
$580$	0	0
$581$	−13032.3	−0.930585
$582$	−615.280	−0.0438216
$583$	37350.1	2.65332
$584$	−418.575	−0.0296588
$585$	0	0
$586$	−4797.72	−0.338212
$587$	−10576.1	−0.743647	−0.371823	−	0.928304i	$-0.621267\pi$
$587$	−10576.1	−0.743647	−0.371823	+	0.928304i	$0.621267\pi$
$588$	−7887.30	−0.553175
$589$	−26936.6	−1.88439
$590$	0	0
$591$	−2242.81	−0.156103
$592$	−2761.85	−0.191742
$593$	859.214	0.0595003	0.0297501	−	0.999557i	$-0.490529\pi$
$593$	859.214	0.0595003	0.0297501	+	0.999557i	$0.490529\pi$
$594$	11507.0	0.794843
$595$	0	0
$596$	11560.0	0.794490
$597$	1316.35	0.0902420
$598$	−2743.46	−0.187606
$599$	2355.05	0.160642	0.0803212	−	0.996769i	$-0.474405\pi$
$599$	2355.05	0.160642	0.0803212	+	0.996769i	$0.474405\pi$
$600$	0	0
$601$	837.301	0.0568290	0.0284145	−	0.999596i	$-0.490954\pi$
$601$	837.301	0.0568290	0.0284145	+	0.999596i	$0.490954\pi$
$602$	1691.41	0.114513
$603$	20654.1	1.39486
$604$	5666.65	0.381743
$605$	0	0
$606$	1873.20	0.125567
$607$	−2630.59	−0.175902	−0.0879508	−	0.996125i	$-0.528032\pi$
$607$	−2630.59	−0.175902	−0.0879508	+	0.996125i	$0.528032\pi$
$608$	2777.81	0.185288
$609$	13813.9	0.919161
$610$	0	0
$611$	5457.87	0.361378
$612$	−2941.74	−0.194302
$613$	7679.98	0.506022	0.253011	−	0.967463i	$-0.418579\pi$
$613$	7679.98	0.506022	0.253011	+	0.967463i	$0.418579\pi$
$614$	−12248.9	−0.805093
$615$	0	0
$616$	15744.9	1.02984
$617$	−12107.2	−0.789982	−0.394991	−	0.918685i	$-0.629252\pi$
$617$	−12107.2	−0.789982	−0.394991	+	0.918685i	$0.629252\pi$
$618$	7275.77	0.473583
$619$	22830.8	1.48247	0.741233	−	0.671248i	$-0.234241\pi$
$619$	22830.8	1.48247	0.741233	+	0.671248i	$0.234241\pi$
$620$	0	0
$621$	−2403.63	−0.155321
$622$	−3758.54	−0.242289
$623$	16124.3	1.03693
$624$	−2012.51	−0.129110
$625$	0	0
$626$	−1737.06	−0.110906
$627$	−10079.1	−0.641979
$628$	−6510.24	−0.413673
$629$	−5629.08	−0.356830
$630$	0	0
$631$	−26642.4	−1.68085	−0.840427	−	0.541925i	$-0.817696\pi$
$631$	−26642.4	−1.68085	−0.840427	+	0.541925i	$0.817696\pi$
$632$	3864.20	0.243212
$633$	931.373	0.0584814
$634$	3216.56	0.201492
$635$	0	0
$636$	−5723.17	−0.356821
$637$	55761.3	3.46836
$638$	−20174.6	−1.25191
$639$	−17002.5	−1.05259
$640$	0	0
$641$	−15308.8	−0.943308	−0.471654	−	0.881784i	$-0.656343\pi$
$641$	−15308.8	−0.943308	−0.471654	+	0.881784i	$0.656343\pi$
$642$	6479.44	0.398323
$643$	19410.9	1.19050	0.595250	−	0.803541i	$-0.297053\pi$
$643$	19410.9	1.19050	0.595250	+	0.803541i	$0.297053\pi$
$644$	−3288.86	−0.201241
$645$	0	0
$646$	5661.61	0.344819
$647$	12579.4	0.764372	0.382186	−	0.924085i	$-0.375171\pi$
$647$	12579.4	0.764372	0.382186	+	0.924085i	$0.375171\pi$
$648$	3108.04	0.188419
$649$	−16274.6	−0.984334
$650$	0	0
$651$	23395.1	1.40849
$652$	−603.489	−0.0362492
$653$	6465.96	0.387493	0.193746	−	0.981052i	$-0.437936\pi$
$653$	6465.96	0.387493	0.193746	+	0.981052i	$0.437936\pi$
$654$	8206.91	0.490697
$655$	0	0
$656$	−1856.55	−0.110497
$657$	1179.97	0.0700684
$658$	6542.90	0.387643
$659$	−32362.3	−1.91298	−0.956491	−	0.291761i	$-0.905759\pi$
$659$	−32362.3	−1.91298	−0.956491	+	0.291761i	$0.905759\pi$
$660$	0	0
$661$	25956.4	1.52736	0.763680	−	0.645594i	$-0.223390\pi$
$661$	25956.4	1.52736	0.763680	+	0.645594i	$0.223390\pi$
$662$	−13833.2	−0.812149
$663$	−4101.80	−0.240273
$664$	−2916.43	−0.170451
$665$	0	0
$666$	7785.70	0.452987
$667$	4214.15	0.244637
$668$	8026.00	0.464873
$669$	1063.70	0.0614723
$670$	0	0
$671$	18529.7	1.06607
$672$	−2412.60	−0.138494
$673$	−19251.4	−1.10266	−0.551328	−	0.834289i	$-0.685879\pi$
$673$	−19251.4	−1.10266	−0.551328	+	0.834289i	$0.685879\pi$
$674$	−20045.9	−1.14561
$675$	0	0
$676$	5439.95	0.309510
$677$	−8020.10	−0.455299	−0.227650	−	0.973743i	$-0.573104\pi$
$677$	−8020.10	−0.455299	−0.227650	+	0.973743i	$0.573104\pi$
$678$	−3010.95	−0.170553
$679$	5214.64	0.294727
$680$	0	0
$681$	11210.0	0.630790
$682$	−34167.4	−1.91838
$683$	32490.2	1.82021	0.910105	−	0.414377i	$-0.136000\pi$
$683$	32490.2	1.82021	0.910105	+	0.414377i	$0.136000\pi$
$684$	−7830.70	−0.437740
$685$	0	0
$686$	42323.2	2.35555
$687$	−9885.03	−0.548962
$688$	378.513	0.0209748
$689$	40461.4	2.23724
$690$	0	0
$691$	12974.2	0.714273	0.357137	−	0.934052i	$-0.383753\pi$
$691$	12974.2	0.714273	0.357137	+	0.934052i	$0.383753\pi$
$692$	−5759.10	−0.316370
$693$	−44385.1	−2.43297
$694$	6611.75	0.361640
$695$	0	0
$696$	3091.36	0.168359
$697$	−3783.94	−0.205634
$698$	−17383.4	−0.942655
$699$	−1859.56	−0.100622
$700$	0	0
$701$	−13250.5	−0.713931	−0.356966	−	0.934117i	$-0.616189\pi$
$701$	−13250.5	−0.713931	−0.356966	+	0.934117i	$0.616189\pi$
$702$	12465.5	0.670200
$703$	−14984.2	−0.803897
$704$	3523.48	0.188631
$705$	0	0
$706$	16184.9	0.862788
$707$	−15875.8	−0.844511
$708$	2493.76	0.132375
$709$	7702.31	0.407992	0.203996	−	0.978972i	$-0.434607\pi$
$709$	7702.31	0.407992	0.203996	+	0.978972i	$0.434607\pi$
$710$	0	0
$711$	−10893.2	−0.574583
$712$	3608.38	0.189929
$713$	7137.04	0.374873
$714$	−4917.24	−0.257736
$715$	0	0
$716$	9309.51	0.485912
$717$	8893.34	0.463219
$718$	−13133.8	−0.682661
$719$	8627.22	0.447484	0.223742	−	0.974648i	$-0.428173\pi$
$719$	8627.22	0.447484	0.223742	+	0.974648i	$0.428173\pi$
$720$	0	0
$721$	−61663.8	−3.18513
$722$	1352.80	0.0697311
$723$	−655.610	−0.0337239
$724$	5227.91	0.268362
$725$	0	0
$726$	−7170.54	−0.366562
$727$	−18258.1	−0.931440	−0.465720	−	0.884932i	$-0.654205\pi$
$727$	−18258.1	−0.931440	−0.465720	+	0.884932i	$0.654205\pi$
$728$	17056.5	0.868345
$729$	−2810.75	−0.142801
$730$	0	0
$731$	771.468	0.0390339
$732$	−2839.31	−0.143366
$733$	−9740.02	−0.490799	−0.245400	−	0.969422i	$-0.578919\pi$
$733$	−9740.02	−0.490799	−0.245400	+	0.969422i	$0.578919\pi$
$734$	6021.54	0.302805
$735$	0	0
$736$	−736.000	−0.0368605
$737$	−50420.8	−2.52005
$738$	5233.65	0.261048
$739$	25667.2	1.27765	0.638825	−	0.769352i	$-0.279421\pi$
$739$	25667.2	1.27765	0.638825	+	0.769352i	$0.279421\pi$
$740$	0	0
$741$	−10918.7	−0.541307
$742$	48505.1	2.39984
$743$	20607.0	1.01749	0.508747	−	0.860916i	$-0.330109\pi$
$743$	20607.0	1.01749	0.508747	+	0.860916i	$0.330109\pi$
$744$	5235.48	0.257987
$745$	0	0
$746$	−21748.7	−1.06739
$747$	8221.47	0.402688
$748$	7181.40	0.351040
$749$	−54914.8	−2.67896
$750$	0	0
$751$	−34527.3	−1.67765	−0.838827	−	0.544398i	$-0.816758\pi$
$751$	−34527.3	−1.67765	−0.838827	+	0.544398i	$0.816758\pi$
$752$	1464.21	0.0710028
$753$	−10664.6	−0.516124
$754$	−21855.1	−1.05559
$755$	0	0
$756$	14943.7	0.718910
$757$	9130.46	0.438378	0.219189	−	0.975682i	$-0.429659\pi$
$757$	9130.46	0.438378	0.219189	+	0.975682i	$0.429659\pi$
$758$	−20962.6	−1.00448
$759$	2670.52	0.127713
$760$	0	0
$761$	−23815.6	−1.13445	−0.567224	−	0.823563i	$-0.691983\pi$
$761$	−23815.6	−1.13445	−0.567224	+	0.823563i	$0.691983\pi$
$762$	−5413.65	−0.257370
$763$	−69555.4	−3.30023
$764$	8587.52	0.406657
$765$	0	0
$766$	−7177.91	−0.338575
$767$	−17630.3	−0.829976
$768$	−539.904	−0.0253673
$769$	−8634.29	−0.404890	−0.202445	−	0.979294i	$-0.564889\pi$
$769$	−8634.29	−0.404890	−0.202445	+	0.979294i	$0.564889\pi$
$770$	0	0
$771$	522.518	0.0244073
$772$	5005.30	0.233348
$773$	−31031.4	−1.44388	−0.721942	−	0.691954i	$-0.756750\pi$
$773$	−31031.4	−1.44388	−0.721942	+	0.691954i	$0.756750\pi$
$774$	−1067.03	−0.0495526
$775$	0	0
$776$	1166.96	0.0539838
$777$	13014.1	0.600874
$778$	21808.3	1.00497
$779$	−10072.6	−0.463270
$780$	0	0
$781$	41506.5	1.90169
$782$	−1500.08	−0.0685969
$783$	−19147.9	−0.873935
$784$	14959.3	0.681455
$785$	0	0
$786$	−6564.81	−0.297912
$787$	−33638.4	−1.52361	−0.761805	−	0.647807i	$-0.775686\pi$
$787$	−33638.4	−1.52361	−0.761805	+	0.647807i	$0.775686\pi$
$788$	4253.79	0.192303
$789$	1329.22	0.0599765
$790$	0	0
$791$	25518.5	1.14707
$792$	−9932.74	−0.445637
$793$	20073.3	0.898893
$794$	−500.555	−0.0223728
$795$	0	0
$796$	−2496.63	−0.111169
$797$	16577.6	0.736773	0.368386	−	0.929673i	$-0.379910\pi$
$797$	16577.6	0.736773	0.368386	+	0.929673i	$0.379910\pi$
$798$	−13089.3	−0.580649
$799$	2984.28	0.132135
$800$	0	0
$801$	−10172.1	−0.448705
$802$	23107.5	1.01740
$803$	−2880.55	−0.126591
$804$	7726.00	0.338899
$805$	0	0
$806$	−37013.6	−1.61755
$807$	2429.10	0.105958
$808$	−3552.77	−0.154685
$809$	−18593.5	−0.808052	−0.404026	−	0.914747i	$-0.632389\pi$
$809$	−18593.5	−0.808052	−0.404026	+	0.914747i	$0.632389\pi$
$810$	0	0
$811$	27990.1	1.21192	0.605959	−	0.795495i	$-0.292789\pi$
$811$	27990.1	1.21192	0.605959	+	0.795495i	$0.292789\pi$
$812$	−26200.0	−1.13231
$813$	4056.28	0.174981
$814$	−19006.5	−0.818400
$815$	0	0
$816$	−1100.41	−0.0472083
$817$	2053.59	0.0879389
$818$	−20696.5	−0.884641
$819$	−48082.4	−2.05145
$820$	0	0
$821$	−768.013	−0.0326478	−0.0163239	−	0.999867i	$-0.505196\pi$
$821$	−768.013	−0.0326478	−0.0163239	+	0.999867i	$0.505196\pi$
$822$	−1645.88	−0.0698378
$823$	−14831.1	−0.628166	−0.314083	−	0.949396i	$-0.601697\pi$
$823$	−14831.1	−0.628166	−0.314083	+	0.949396i	$0.601697\pi$
$824$	−13799.5	−0.583407
$825$	0	0
$826$	−21135.2	−0.890298
$827$	−216.173	−0.00908955	−0.00454478	−	0.999990i	$-0.501447\pi$
$827$	−216.173	−0.00908955	−0.00454478	+	0.999990i	$0.501447\pi$
$828$	2074.79	0.0870822
$829$	42971.1	1.80030	0.900149	−	0.435583i	$-0.143458\pi$
$829$	42971.1	1.80030	0.900149	+	0.435583i	$0.143458\pi$
$830$	0	0
$831$	6033.10	0.251848
$832$	3816.99	0.159051
$833$	30489.4	1.26818
$834$	3154.85	0.130987
$835$	0	0
$836$	19116.4	0.790853
$837$	−32428.7	−1.33919
$838$	29581.2	1.21941
$839$	7089.70	0.291732	0.145866	−	0.989304i	$-0.453403\pi$
$839$	7089.70	0.291732	0.145866	+	0.989304i	$0.453403\pi$
$840$	0	0
$841$	9182.07	0.376484
$842$	−11511.3	−0.471149
$843$	13279.7	0.542559
$844$	−1766.47	−0.0720432
$845$	0	0
$846$	−4127.62	−0.167743
$847$	60772.0	2.46535
$848$	10854.7	0.439568
$849$	150.023	0.00606453
$850$	0	0
$851$	3970.16	0.159924
$852$	−6360.06	−0.255742
$853$	−36963.9	−1.48373	−0.741864	−	0.670550i	$-0.766058\pi$
$853$	−36963.9	−1.48373	−0.741864	+	0.670550i	$0.766058\pi$
$854$	24063.8	0.964224
$855$	0	0
$856$	−12289.1	−0.490694
$857$	15188.9	0.605418	0.302709	−	0.953083i	$-0.402109\pi$
$857$	15188.9	0.605418	0.302709	+	0.953083i	$0.402109\pi$
$858$	−13849.7	−0.551073
$859$	−7552.53	−0.299987	−0.149994	−	0.988687i	$-0.547925\pi$
$859$	−7552.53	−0.299987	−0.149994	+	0.988687i	$0.547925\pi$
$860$	0	0
$861$	8748.28	0.346272
$862$	−12668.1	−0.500553
$863$	2963.64	0.116898	0.0584492	−	0.998290i	$-0.481384\pi$
$863$	2963.64	0.116898	0.0584492	+	0.998290i	$0.481384\pi$
$864$	3344.17	0.131680
$865$	0	0
$866$	1463.95	0.0574446
$867$	8118.72	0.318023
$868$	−44371.9	−1.73512
$869$	26592.7	1.03808
$870$	0	0
$871$	−54621.0	−2.12487
$872$	−15565.5	−0.604489
$873$	−3289.68	−0.127536
$874$	−3993.11	−0.154541
$875$	0	0
$876$	441.387	0.0170241
$877$	7360.03	0.283387	0.141694	−	0.989911i	$-0.454745\pi$
$877$	7360.03	0.283387	0.141694	+	0.989911i	$0.454745\pi$
$878$	5181.62	0.199170
$879$	5059.20	0.194133
$880$	0	0
$881$	17605.6	0.673267	0.336633	−	0.941636i	$-0.390712\pi$
$881$	17605.6	0.673267	0.336633	+	0.941636i	$0.390712\pi$
$882$	−42170.5	−1.60993
$883$	−35640.2	−1.35831	−0.679155	−	0.733995i	$-0.737654\pi$
$883$	−35640.2	−1.35831	−0.679155	+	0.733995i	$0.737654\pi$
$884$	7779.62	0.295992
$885$	0	0
$886$	11562.5	0.438431
$887$	−38229.4	−1.44715	−0.723573	−	0.690248i	$-0.757502\pi$
$887$	−38229.4	−1.44715	−0.723573	+	0.690248i	$0.757502\pi$
$888$	2912.37	0.110059
$889$	45881.9	1.73097
$890$	0	0
$891$	21388.9	0.804215
$892$	−2017.45	−0.0757276
$893$	7943.93	0.297686
$894$	−12190.0	−0.456035
$895$	0	0
$896$	4575.81	0.170611
$897$	2892.98	0.107685
$898$	32712.5	1.21563
$899$	56855.5	2.10927
$900$	0	0
$901$	22123.6	0.818031
$902$	−12776.4	−0.471628
$903$	−1783.59	−0.0657301
$904$	5710.67	0.210104
$905$	0	0
$906$	−5975.49	−0.219120
$907$	−13033.9	−0.477159	−0.238579	−	0.971123i	$-0.576682\pi$
$907$	−13033.9	−0.477159	−0.238579	+	0.971123i	$0.576682\pi$
$908$	−21261.2	−0.777069
$909$	10015.3	0.365442
$910$	0	0
$911$	−24294.5	−0.883550	−0.441775	−	0.897126i	$-0.645651\pi$
$911$	−24294.5	−0.883550	−0.441775	+	0.897126i	$0.645651\pi$
$912$	−2929.21	−0.106355
$913$	−20070.3	−0.727525
$914$	−5637.56	−0.204020
$915$	0	0
$916$	18748.3	0.676266
$917$	55638.3	2.00364
$918$	6815.94	0.245054
$919$	−29920.0	−1.07396	−0.536981	−	0.843595i	$-0.680435\pi$
$919$	−29920.0	−1.07396	−0.536981	+	0.843595i	$0.680435\pi$
$920$	0	0
$921$	12916.5	0.462121
$922$	10541.6	0.376540
$923$	44964.1	1.60348
$924$	−16603.0	−0.591124
$925$	0	0
$926$	83.5991	0.00296678
$927$	38900.9	1.37829
$928$	−5863.17	−0.207401
$929$	31352.3	1.10725	0.553626	−	0.832766i	$-0.313244\pi$
$929$	31352.3	1.10725	0.553626	+	0.832766i	$0.313244\pi$
$930$	0	0
$931$	81160.5	2.85706
$932$	3526.90	0.123957
$933$	3963.38	0.139073
$934$	8061.97	0.282436
$935$	0	0
$936$	−10760.2	−0.375755
$937$	45716.4	1.59390	0.796952	−	0.604042i	$-0.206444\pi$
$937$	45716.4	1.59390	0.796952	+	0.604042i	$0.206444\pi$
$938$	−65479.6	−2.27930
$939$	1831.73	0.0636595
$940$	0	0
$941$	6473.51	0.224262	0.112131	−	0.993693i	$-0.464232\pi$
$941$	6473.51	0.224262	0.112131	+	0.993693i	$0.464232\pi$
$942$	6865.05	0.237447
$943$	2668.80	0.0921612
$944$	−4729.74	−0.163072
$945$	0	0
$946$	2604.85	0.0895254
$947$	−35651.5	−1.22336	−0.611678	−	0.791107i	$-0.709505\pi$
$947$	−35651.5	−1.22336	−0.611678	+	0.791107i	$0.709505\pi$
$948$	−4074.80	−0.139603
$949$	−3120.50	−0.106739
$950$	0	0
$951$	−3391.87	−0.115656
$952$	9326.21	0.317504
$953$	−23327.9	−0.792933	−0.396466	−	0.918049i	$-0.629764\pi$
$953$	−23327.9	−0.792933	−0.396466	+	0.918049i	$0.629764\pi$
$954$	−30599.7	−1.03847
$955$	0	0
$956$	−16867.4	−0.570639
$957$	21274.1	0.718594
$958$	−7922.83	−0.267197
$959$	13949.2	0.469701
$960$	0	0
$961$	66498.8	2.23218
$962$	−20589.8	−0.690063
$963$	34643.2	1.15925
$964$	1243.45	0.0415445
$965$	0	0
$966$	3468.11	0.115512
$967$	−6222.19	−0.206920	−0.103460	−	0.994634i	$-0.532991\pi$
$967$	−6222.19	−0.206920	−0.103460	+	0.994634i	$0.532991\pi$
$968$	13599.9	0.451567
$969$	−5970.17	−0.197925
$970$	0	0
$971$	−5022.99	−0.166010	−0.0830048	−	0.996549i	$-0.526452\pi$
$971$	−5022.99	−0.166010	−0.0830048	+	0.996549i	$0.526452\pi$
$972$	−14564.0	−0.480598
$973$	−26738.0	−0.880968
$974$	37568.7	1.23591
$975$	0	0
$976$	5385.14	0.176613
$977$	12388.5	0.405673	0.202837	−	0.979213i	$-0.434984\pi$
$977$	12388.5	0.405673	0.202837	+	0.979213i	$0.434984\pi$
$978$	636.380	0.0208069
$979$	24832.1	0.810662
$980$	0	0
$981$	43879.4	1.42809
$982$	−38397.4	−1.24777
$983$	18218.2	0.591120	0.295560	−	0.955324i	$-0.404494\pi$
$983$	18218.2	0.591120	0.295560	+	0.955324i	$0.404494\pi$
$984$	1957.74	0.0634252
$985$	0	0
$986$	−11950.0	−0.385971
$987$	−6899.49	−0.222506
$988$	20708.8	0.666836
$989$	−544.113	−0.0174942
$990$	0	0
$991$	−40116.2	−1.28591	−0.642954	−	0.765905i	$-0.722291\pi$
$991$	−40116.2	−1.28591	−0.642954	+	0.765905i	$0.722291\pi$
$992$	−9929.79	−0.317814
$993$	14587.1	0.466171
$994$	53903.0	1.72002
$995$	0	0
$996$	3075.38	0.0978385
$997$	11591.6	0.368214	0.184107	−	0.982906i	$-0.441061\pi$
$997$	11591.6	0.368214	0.184107	+	0.982906i	$0.441061\pi$
$998$	27758.2	0.880431
$999$	−18039.3	−0.571309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.bb.1.4		9
5.2	odd	4		230.4.b.b.139.15	yes	18
5.3	odd	4		230.4.b.b.139.4	✓	18
5.4	even	2		1150.4.a.ba.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.b.b.139.4	✓	18	5.3	odd	4
230.4.b.b.139.15	yes	18	5.2	odd	4
1150.4.a.ba.1.6		9	5.4	even	2
1150.4.a.bb.1.4		9	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -2.10900 q^{3} +4.00000 q^{4} -4.21800 q^{6} +35.7485 q^{7} +8.00000 q^{8} -22.5521 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -2.10900 q^{3} +4.00000 q^{4} -4.21800 q^{6} +35.7485 q^{7} +8.00000 q^{8} -22.5521 q^{9} +55.0544 q^{11} -8.43600 q^{12} +59.6405 q^{13} +71.4970 q^{14} +16.0000 q^{16} +32.6105 q^{17} -45.1042 q^{18} +86.8067 q^{19} -75.3937 q^{21} +110.109 q^{22} -23.0000 q^{23} -16.8720 q^{24} +119.281 q^{26} +104.505 q^{27} +142.994 q^{28} -183.224 q^{29} -310.306 q^{31} +32.0000 q^{32} -116.110 q^{33} +65.2209 q^{34} -90.2085 q^{36} -172.616 q^{37} +173.613 q^{38} -125.782 q^{39} -116.035 q^{41} -150.787 q^{42} +23.6571 q^{43} +220.218 q^{44} -46.0000 q^{46} +91.5129 q^{47} -33.7440 q^{48} +934.957 q^{49} -68.7755 q^{51} +238.562 q^{52} +678.422 q^{53} +209.011 q^{54} +285.988 q^{56} -183.075 q^{57} -366.448 q^{58} -295.609 q^{59} +336.571 q^{61} -620.612 q^{62} -806.205 q^{63} +64.0000 q^{64} -232.220 q^{66} -915.837 q^{67} +130.442 q^{68} +48.5070 q^{69} +753.919 q^{71} -180.417 q^{72} -52.3219 q^{73} -345.231 q^{74} +347.227 q^{76} +1968.11 q^{77} -251.564 q^{78} +483.025 q^{79} +388.505 q^{81} -232.069 q^{82} -364.554 q^{83} -301.575 q^{84} +47.3141 q^{86} +386.420 q^{87} +440.435 q^{88} +451.047 q^{89} +2132.06 q^{91} -92.0000 q^{92} +654.435 q^{93} +183.026 q^{94} -67.4880 q^{96} +145.870 q^{97} +1869.91 q^{98} -1241.59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9}+O(q^{10}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22} - 207 q^{23} + 24 q^{24} + 118 q^{26} + 336 q^{27} + 176 q^{28} + 205 q^{29} + 336 q^{31} + 288 q^{32} + 437 q^{33} + 220 q^{34} + 496 q^{36} - 5 q^{37} + 442 q^{38} - 44 q^{39} + 360 q^{41} + 284 q^{42} + 366 q^{43} + 324 q^{44} - 414 q^{46} - 122 q^{47} + 48 q^{48} + 457 q^{49} + 1025 q^{51} + 236 q^{52} + 631 q^{53} + 672 q^{54} + 352 q^{56} - 384 q^{57} + 410 q^{58} + 797 q^{59} + 211 q^{61} + 672 q^{62} + 2447 q^{63} + 576 q^{64} + 874 q^{66} + 111 q^{67} + 440 q^{68} - 69 q^{69} + 2912 q^{71} + 992 q^{72} + 98 q^{73} - 10 q^{74} + 884 q^{76} + 942 q^{77} - 88 q^{78} + 1184 q^{79} + 2093 q^{81} + 720 q^{82} + 2375 q^{83} + 568 q^{84} + 732 q^{86} - 1534 q^{87} + 648 q^{88} + 2588 q^{89} + 2677 q^{91} - 828 q^{92} + 1402 q^{93} - 244 q^{94} + 96 q^{96} - 593 q^{97} + 914 q^{98} - 1753 q^{99}+O(q^{100}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * q^99

Introduction

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