LMFDB - Embedded newform 75.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,4,Mod(1,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, 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("75.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	75.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:	$4.42514325043$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{19}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 19 $ x^2 - 19
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.35890$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.35890 q^{2} +3.00000 q^{3} +20.7178 q^{4} -16.0767 q^{6} -4.43560 q^{7} -68.1534 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.35890 q^{2} +3.00000 q^{3} +20.7178 q^{4} -16.0767 q^{6} -4.43560 q^{7} -68.1534 q^{8} +9.00000 q^{9} -3.43560 q^{11} +62.1534 q^{12} +78.7424 q^{13} +23.7699 q^{14} +199.485 q^{16} +53.1780 q^{17} -48.2301 q^{18} +20.4356 q^{19} -13.3068 q^{21} +18.4110 q^{22} +118.307 q^{23} -204.460 q^{24} -421.972 q^{26} +27.0000 q^{27} -91.8958 q^{28} +168.049 q^{29} -61.0492 q^{31} -523.792 q^{32} -10.3068 q^{33} -284.975 q^{34} +186.460 q^{36} -246.614 q^{37} -109.512 q^{38} +236.227 q^{39} +422.663 q^{41} +71.3097 q^{42} +362.436 q^{43} -71.1780 q^{44} -633.994 q^{46} -170.515 q^{47} +598.454 q^{48} -323.325 q^{49} +159.534 q^{51} +1631.37 q^{52} -546.049 q^{53} -144.690 q^{54} +302.301 q^{56} +61.3068 q^{57} -900.559 q^{58} -216.970 q^{59} +130.902 q^{61} +327.156 q^{62} -39.9204 q^{63} +1211.07 q^{64} +55.2330 q^{66} -614.890 q^{67} +1101.73 q^{68} +354.920 q^{69} +324.822 q^{71} -613.381 q^{72} -88.8712 q^{73} +1321.58 q^{74} +423.381 q^{76} +15.2389 q^{77} -1265.92 q^{78} -1137.42 q^{79} +81.0000 q^{81} -2265.01 q^{82} -758.909 q^{83} -275.687 q^{84} -1942.26 q^{86} +504.148 q^{87} +234.148 q^{88} +195.681 q^{89} -349.269 q^{91} +2451.06 q^{92} -183.148 q^{93} +913.774 q^{94} -1571.37 q^{96} +521.000 q^{97} +1732.67 q^{98} -30.9204 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 6 q^{3} + 24 q^{4} - 6 q^{6} + 26 q^{7} - 84 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 6 * q^3 + 24 * q^4 - 6 * q^6 + 26 * q^7 - 84 * q^8 + 18 * q^9	$ 2 q - 2 q^{2} + 6 q^{3} + 24 q^{4} - 6 q^{6} + 26 q^{7} - 84 q^{8} + 18 q^{9} + 28 q^{11} + 72 q^{12} + 18 q^{13} + 126 q^{14} + 120 q^{16} - 68 q^{17} - 18 q^{18} + 6 q^{19} + 78 q^{21} + 124 q^{22} + 132 q^{23} - 252 q^{24} - 626 q^{26} + 54 q^{27} + 8 q^{28} + 92 q^{29} + 122 q^{31} - 664 q^{32} + 84 q^{33} - 692 q^{34} + 216 q^{36} - 284 q^{37} - 158 q^{38} + 54 q^{39} + 392 q^{41} + 378 q^{42} + 690 q^{43} + 32 q^{44} - 588 q^{46} - 620 q^{47} + 360 q^{48} + 260 q^{49} - 204 q^{51} + 1432 q^{52} - 848 q^{53} - 54 q^{54} - 180 q^{56} + 18 q^{57} - 1156 q^{58} + 124 q^{59} + 750 q^{61} + 942 q^{62} + 234 q^{63} + 1376 q^{64} + 372 q^{66} - 358 q^{67} + 704 q^{68} + 396 q^{69} + 824 q^{71} - 756 q^{72} - 108 q^{73} + 1196 q^{74} + 376 q^{76} + 972 q^{77} - 1878 q^{78} - 880 q^{79} + 162 q^{81} - 2368 q^{82} + 156 q^{83} + 24 q^{84} - 842 q^{86} + 276 q^{87} - 264 q^{88} - 864 q^{89} - 2198 q^{91} + 2496 q^{92} + 366 q^{93} - 596 q^{94} - 1992 q^{96} + 1042 q^{97} + 3692 q^{98} + 252 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 6 * q^3 + 24 * q^4 - 6 * q^6 + 26 * q^7 - 84 * q^8 + 18 * q^9 + 28 * q^11 + 72 * q^12 + 18 * q^13 + 126 * q^14 + 120 * q^16 - 68 * q^17 - 18 * q^18 + 6 * q^19 + 78 * q^21 + 124 * q^22 + 132 * q^23 - 252 * q^24 - 626 * q^26 + 54 * q^27 + 8 * q^28 + 92 * q^29 + 122 * q^31 - 664 * q^32 + 84 * q^33 - 692 * q^34 + 216 * q^36 - 284 * q^37 - 158 * q^38 + 54 * q^39 + 392 * q^41 + 378 * q^42 + 690 * q^43 + 32 * q^44 - 588 * q^46 - 620 * q^47 + 360 * q^48 + 260 * q^49 - 204 * q^51 + 1432 * q^52 - 848 * q^53 - 54 * q^54 - 180 * q^56 + 18 * q^57 - 1156 * q^58 + 124 * q^59 + 750 * q^61 + 942 * q^62 + 234 * q^63 + 1376 * q^64 + 372 * q^66 - 358 * q^67 + 704 * q^68 + 396 * q^69 + 824 * q^71 - 756 * q^72 - 108 * q^73 + 1196 * q^74 + 376 * q^76 + 972 * q^77 - 1878 * q^78 - 880 * q^79 + 162 * q^81 - 2368 * q^82 + 156 * q^83 + 24 * q^84 - 842 * q^86 + 276 * q^87 - 264 * q^88 - 864 * q^89 - 2198 * q^91 + 2496 * q^92 + 366 * q^93 - 596 * q^94 - 1992 * q^96 + 1042 * q^97 + 3692 * q^98 + 252 * 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 $

$2$	−5.35890	−1.89466	−0.947328	−	0.320264i	$-0.896228\pi$
$2$	−5.35890	−1.89466	−0.947328	+	0.320264i	$0.896228\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	20.7178	2.58972
$5$	0	0
$5$	0	0
$6$	−16.0767	−1.09388
$7$	−4.43560	−0.239500	−0.119750	−	0.992804i	$-0.538209\pi$
$7$	−4.43560	−0.239500	−0.119750	+	0.992804i	$0.538209\pi$
$8$	−68.1534	−3.01198
$9$	9.00000	0.333333
$10$	0	0
$11$	−3.43560	−0.0941701	−0.0470851	−	0.998891i	$-0.514993\pi$
$11$	−3.43560	−0.0941701	−0.0470851	+	0.998891i	$0.514993\pi$
$12$	62.1534	1.49518
$13$	78.7424	1.67994	0.839970	−	0.542634i	$-0.182573\pi$
$13$	78.7424	1.67994	0.839970	+	0.542634i	$0.182573\pi$
$14$	23.7699	0.453770
$15$	0	0
$16$	199.485	3.11695
$17$	53.1780	0.758680	0.379340	−	0.925257i	$-0.376151\pi$
$17$	53.1780	0.758680	0.379340	+	0.925257i	$0.376151\pi$
$18$	−48.2301	−0.631552
$19$	20.4356	0.246750	0.123375	−	0.992360i	$-0.460628\pi$
$19$	20.4356	0.246750	0.123375	+	0.992360i	$0.460628\pi$
$20$	0	0
$21$	−13.3068	−0.138275
$22$	18.4110	0.178420
$23$	118.307	1.07255	0.536275	−	0.844043i	$-0.319831\pi$
$23$	118.307	1.07255	0.536275	+	0.844043i	$0.319831\pi$
$24$	−204.460	−1.73897
$25$	0	0
$26$	−421.972	−3.18291
$27$	27.0000	0.192450
$28$	−91.8958	−0.620238
$29$	168.049	1.07607	0.538034	−	0.842923i	$-0.319167\pi$
$29$	168.049	1.07607	0.538034	+	0.842923i	$0.319167\pi$
$30$	0	0
$31$	−61.0492	−0.353702	−0.176851	−	0.984238i	$-0.556591\pi$
$31$	−61.0492	−0.353702	−0.176851	+	0.984238i	$0.556591\pi$
$32$	−523.792	−2.89357
$33$	−10.3068	−0.0543691
$34$	−284.975	−1.43744
$35$	0	0
$36$	186.460	0.863242
$37$	−246.614	−1.09576	−0.547879	−	0.836558i	$-0.684564\pi$
$37$	−246.614	−1.09576	−0.547879	+	0.836558i	$0.684564\pi$
$38$	−109.512	−0.467506
$39$	236.227	0.969913
$40$	0	0
$41$	422.663	1.60997	0.804986	−	0.593294i	$-0.202173\pi$
$41$	422.663	1.60997	0.804986	+	0.593294i	$0.202173\pi$
$42$	71.3097	0.261984
$43$	362.436	1.28537	0.642685	−	0.766131i	$-0.277820\pi$
$43$	362.436	1.28537	0.642685	+	0.766131i	$0.277820\pi$
$44$	−71.1780	−0.243875
$45$	0	0
$46$	−633.994	−2.03212
$47$	−170.515	−0.529196	−0.264598	−	0.964359i	$-0.585239\pi$
$47$	−170.515	−0.529196	−0.264598	+	0.964359i	$0.585239\pi$
$48$	598.454	1.79957
$49$	−323.325	−0.942640
$50$	0	0
$51$	159.534	0.438024
$52$	1631.37	4.35058
$53$	−546.049	−1.41520	−0.707600	−	0.706613i	$-0.750222\pi$
$53$	−546.049	−1.41520	−0.707600	+	0.706613i	$0.750222\pi$
$54$	−144.690	−0.364627
$55$	0	0
$56$	302.301	0.721369
$57$	61.3068	0.142461
$58$	−900.559	−2.03878
$59$	−216.970	−0.478763	−0.239382	−	0.970926i	$-0.576945\pi$
$59$	−216.970	−0.478763	−0.239382	+	0.970926i	$0.576945\pi$
$60$	0	0
$61$	130.902	0.274758	0.137379	−	0.990519i	$-0.456132\pi$
$61$	130.902	0.274758	0.137379	+	0.990519i	$0.456132\pi$
$62$	327.156	0.670143
$63$	−39.9204	−0.0798332
$64$	1211.07	2.36537
$65$	0	0
$66$	55.2330	0.103011
$67$	−614.890	−1.12121	−0.560603	−	0.828085i	$-0.689430\pi$
$67$	−614.890	−1.12121	−0.560603	+	0.828085i	$0.689430\pi$
$68$	1101.73	1.96477
$69$	354.920	0.619238
$70$	0	0
$71$	324.822	0.542948	0.271474	−	0.962446i	$-0.412489\pi$
$71$	324.822	0.542948	0.271474	+	0.962446i	$0.412489\pi$
$72$	−613.381	−1.00399
$73$	−88.8712	−0.142487	−0.0712437	−	0.997459i	$-0.522697\pi$
$73$	−88.8712	−0.142487	−0.0712437	+	0.997459i	$0.522697\pi$
$74$	1321.58	2.07608
$75$	0	0
$76$	423.381	0.639014
$77$	15.2389	0.0225537
$78$	−1265.92	−1.83765
$79$	−1137.42	−1.61988	−0.809938	−	0.586516i	$-0.800499\pi$
$79$	−1137.42	−1.61988	−0.809938	+	0.586516i	$0.800499\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−2265.01	−3.05034
$83$	−758.909	−1.00363	−0.501813	−	0.864976i	$-0.667334\pi$
$83$	−758.909	−1.00363	−0.501813	+	0.864976i	$0.667334\pi$
$84$	−275.687	−0.358095
$85$	0	0
$86$	−1942.26	−2.43534
$87$	504.148	0.621268
$88$	234.148	0.283639
$89$	195.681	0.233058	0.116529	−	0.993187i	$-0.462823\pi$
$89$	195.681	0.233058	0.116529	+	0.993187i	$0.462823\pi$
$90$	0	0
$91$	−349.269	−0.402345
$92$	2451.06	2.77761
$93$	−183.148	−0.204210
$94$	913.774	1.00264
$95$	0	0
$96$	−1571.37	−1.67060
$97$	521.000	0.545356	0.272678	−	0.962105i	$-0.412091\pi$
$97$	521.000	0.545356	0.272678	+	0.962105i	$0.412091\pi$
$98$	1732.67	1.78598
$99$	−30.9204	−0.0313900
$100$	0	0
$101$	660.920	0.651129	0.325565	−	0.945520i	$-0.394446\pi$
$101$	660.920	0.651129	0.325565	+	0.945520i	$0.394446\pi$
$102$	−854.926	−0.829905
$103$	1530.75	1.46436	0.732181	−	0.681110i	$-0.238503\pi$
$103$	1530.75	1.46436	0.732181	+	0.681110i	$0.238503\pi$
$104$	−5366.56	−5.05995
$105$	0	0
$106$	2926.22	2.68132
$107$	−264.625	−0.239087	−0.119543	−	0.992829i	$-0.538143\pi$
$107$	−264.625	−0.239087	−0.119543	+	0.992829i	$0.538143\pi$
$108$	559.381	0.498393
$109$	1117.61	0.982091	0.491046	−	0.871134i	$-0.336615\pi$
$109$	1117.61	0.982091	0.491046	+	0.871134i	$0.336615\pi$
$110$	0	0
$111$	−739.841	−0.632636
$112$	−884.834	−0.746508
$113$	−934.061	−0.777602	−0.388801	−	0.921322i	$-0.627111\pi$
$113$	−934.061	−0.777602	−0.388801	+	0.921322i	$0.627111\pi$
$114$	−328.537	−0.269915
$115$	0	0
$116$	3481.61	2.78672
$117$	708.681	0.559980
$118$	1162.72	0.907092
$119$	−235.876	−0.181704
$120$	0	0
$121$	−1319.20	−0.991132
$122$	−701.489	−0.520572
$123$	1267.99	0.929517
$124$	−1264.80	−0.915990
$125$	0	0
$126$	213.929	0.151257
$127$	630.356	0.440433	0.220217	−	0.975451i	$-0.429324\pi$
$127$	630.356	0.440433	0.220217	+	0.975451i	$0.429324\pi$
$128$	−2299.66	−1.58799
$129$	1087.31	0.742109
$130$	0	0
$131$	−2163.06	−1.44265	−0.721325	−	0.692597i	$-0.756466\pi$
$131$	−2163.06	−1.44265	−0.721325	+	0.692597i	$0.756466\pi$
$132$	−213.534	−0.140801
$133$	−90.6440	−0.0590965
$134$	3295.13	2.12430
$135$	0	0
$136$	−3624.26	−2.28513
$137$	1118.61	0.697588	0.348794	−	0.937199i	$-0.386591\pi$
$137$	1118.61	0.697588	0.348794	+	0.937199i	$0.386591\pi$
$138$	−1901.98	−1.17324
$139$	−166.478	−0.101586	−0.0507930	−	0.998709i	$-0.516175\pi$
$139$	−166.478	−0.101586	−0.0507930	+	0.998709i	$0.516175\pi$
$140$	0	0
$141$	−511.546	−0.305531
$142$	−1740.69	−1.02870
$143$	−270.527	−0.158200
$144$	1795.36	1.03898
$145$	0	0
$146$	476.252	0.269965
$147$	−969.976	−0.544233
$148$	−5109.29	−2.83771
$149$	−653.143	−0.359111	−0.179555	−	0.983748i	$-0.557466\pi$
$149$	−653.143	−0.359111	−0.179555	+	0.983748i	$0.557466\pi$
$150$	0	0
$151$	−1929.38	−1.03981	−0.519903	−	0.854225i	$-0.674032\pi$
$151$	−1929.38	−1.03981	−0.519903	+	0.854225i	$0.674032\pi$
$152$	−1392.76	−0.743206
$153$	478.602	0.252893
$154$	−81.6638	−0.0427315
$155$	0	0
$156$	4894.11	2.51181
$157$	2169.75	1.10296	0.551480	−	0.834188i	$-0.314063\pi$
$157$	2169.75	1.10296	0.551480	+	0.834188i	$0.314063\pi$
$158$	6095.34	3.06911
$159$	−1638.15	−0.817066
$160$	0	0
$161$	−524.761	−0.256876
$162$	−434.071	−0.210517
$163$	−763.738	−0.366997	−0.183499	−	0.983020i	$-0.558742\pi$
$163$	−763.738	−0.366997	−0.183499	+	0.983020i	$0.558742\pi$
$164$	8756.64	4.16938
$165$	0	0
$166$	4066.91	1.90153
$167$	−2564.28	−1.18820	−0.594102	−	0.804389i	$-0.702493\pi$
$167$	−2564.28	−1.18820	−0.594102	+	0.804389i	$0.702493\pi$
$168$	906.903	0.416483
$169$	4003.36	1.82220
$170$	0	0
$171$	183.920	0.0822500
$172$	7508.87	3.32875
$173$	51.8290	0.0227774	0.0113887	−	0.999935i	$-0.496375\pi$
$173$	51.8290	0.0227774	0.0113887	+	0.999935i	$0.496375\pi$
$174$	−2701.68	−1.17709
$175$	0	0
$176$	−685.349	−0.293523
$177$	−650.909	−0.276414
$178$	−1048.64	−0.441566
$179$	−3956.63	−1.65214	−0.826068	−	0.563571i	$-0.809427\pi$
$179$	−3956.63	−1.65214	−0.826068	+	0.563571i	$0.809427\pi$
$180$	0	0
$181$	1804.04	0.740848	0.370424	−	0.928863i	$-0.379212\pi$
$181$	1804.04	0.740848	0.370424	+	0.928863i	$0.379212\pi$
$182$	1871.70	0.762305
$183$	392.705	0.158632
$184$	−8063.01	−3.23050
$185$	0	0
$186$	981.469	0.386908
$187$	−182.698	−0.0714449
$188$	−3532.70	−1.37047
$189$	−119.761	−0.0460917
$190$	0	0
$191$	3666.75	1.38909	0.694547	−	0.719448i	$-0.255605\pi$
$191$	3666.75	1.38909	0.694547	+	0.719448i	$0.255605\pi$
$192$	3633.20	1.36565
$193$	−2716.98	−1.01333	−0.506664	−	0.862144i	$-0.669121\pi$
$193$	−2716.98	−1.01333	−0.506664	+	0.862144i	$0.669121\pi$
$194$	−2791.99	−1.03326
$195$	0	0
$196$	−6698.59	−2.44118
$197$	2034.30	0.735723	0.367862	−	0.929881i	$-0.380090\pi$
$197$	2034.30	0.735723	0.367862	+	0.929881i	$0.380090\pi$
$198$	165.699	0.0594733
$199$	−1551.27	−0.552596	−0.276298	−	0.961072i	$-0.589108\pi$
$199$	−1551.27	−0.552596	−0.276298	+	0.961072i	$0.589108\pi$
$200$	0	0
$201$	−1844.67	−0.647328
$202$	−3541.81	−1.23367
$203$	−745.398	−0.257718
$204$	3305.19	1.13436
$205$	0	0
$206$	−8203.13	−2.77446
$207$	1064.76	0.357517
$208$	15707.9	5.23629
$209$	−70.2084	−0.0232365
$210$	0	0
$211$	3192.51	1.04162	0.520809	−	0.853673i	$-0.325630\pi$
$211$	3192.51	1.04162	0.520809	+	0.853673i	$0.325630\pi$
$212$	−11312.9	−3.66498
$213$	974.466	0.313471
$214$	1418.10	0.452988
$215$	0	0
$216$	−1840.14	−0.579656
$217$	270.789	0.0847115
$218$	−5989.18	−1.86073
$219$	−266.614	−0.0822652
$220$	0	0
$221$	4187.36	1.27454
$222$	3964.73	1.19863
$223$	−1555.55	−0.467120	−0.233560	−	0.972342i	$-0.575037\pi$
$223$	−1555.55	−0.467120	−0.233560	+	0.972342i	$0.575037\pi$
$224$	2323.33	0.693008
$225$	0	0
$226$	5005.54	1.47329
$227$	−6206.86	−1.81482	−0.907409	−	0.420248i	$-0.861943\pi$
$227$	−6206.86	−1.81482	−0.907409	+	0.420248i	$0.861943\pi$
$228$	1270.14	0.368935
$229$	4679.51	1.35035	0.675176	−	0.737657i	$-0.264068\pi$
$229$	4679.51	1.35035	0.675176	+	0.737657i	$0.264068\pi$
$230$	0	0
$231$	45.7167	0.0130214
$232$	−11453.1	−3.24110
$233$	−3244.53	−0.912259	−0.456129	−	0.889913i	$-0.650765\pi$
$233$	−3244.53	−0.912259	−0.456129	+	0.889913i	$0.650765\pi$
$234$	−3797.75	−1.06097
$235$	0	0
$236$	−4495.13	−1.23986
$237$	−3412.27	−0.935236
$238$	1264.04	0.344266
$239$	−3658.62	−0.990193	−0.495097	−	0.868838i	$-0.664867\pi$
$239$	−3658.62	−0.990193	−0.495097	+	0.868838i	$0.664867\pi$
$240$	0	0
$241$	1931.01	0.516131	0.258065	−	0.966127i	$-0.416915\pi$
$241$	1931.01	0.516131	0.258065	+	0.966127i	$0.416915\pi$
$242$	7069.44	1.87786
$243$	243.000	0.0641500
$244$	2711.99	0.711548
$245$	0	0
$246$	−6795.02	−1.76112
$247$	1609.15	0.414525
$248$	4160.71	1.06534
$249$	−2276.73	−0.579444
$250$	0	0
$251$	−5843.34	−1.46944	−0.734718	−	0.678373i	$-0.762685\pi$
$251$	−5843.34	−1.46944	−0.734718	+	0.678373i	$0.762685\pi$
$252$	−827.062	−0.206746
$253$	−406.454	−0.101002
$254$	−3378.01	−0.834470
$255$	0	0
$256$	2635.09	0.643333
$257$	4506.11	1.09371	0.546855	−	0.837227i	$-0.315825\pi$
$257$	4506.11	1.09371	0.546855	+	0.837227i	$0.315825\pi$
$258$	−5826.77	−1.40604
$259$	1093.88	0.262434
$260$	0	0
$261$	1512.44	0.358689
$262$	11591.6	2.73333
$263$	5340.16	1.25205	0.626024	−	0.779804i	$-0.284681\pi$
$263$	5340.16	1.25205	0.626024	+	0.779804i	$0.284681\pi$
$264$	702.443	0.163759
$265$	0	0
$266$	485.752	0.111968
$267$	587.044	0.134556
$268$	−12739.2	−2.90361
$269$	2809.79	0.636863	0.318431	−	0.947946i	$-0.396844\pi$
$269$	2809.79	0.636863	0.318431	+	0.947946i	$0.396844\pi$
$270$	0	0
$271$	3102.95	0.695537	0.347769	−	0.937580i	$-0.386940\pi$
$271$	3102.95	0.695537	0.347769	+	0.937580i	$0.386940\pi$
$272$	10608.2	2.36477
$273$	−1047.81	−0.232294
$274$	−5994.54	−1.32169
$275$	0	0
$276$	7353.17	1.60365
$277$	−4598.93	−0.997555	−0.498777	−	0.866730i	$-0.666217\pi$
$277$	−4598.93	−0.997555	−0.498777	+	0.866730i	$0.666217\pi$
$278$	892.138	0.192471
$279$	−549.443	−0.117901
$280$	0	0
$281$	2571.83	0.545987	0.272994	−	0.962016i	$-0.411986\pi$
$281$	2571.83	0.545987	0.272994	+	0.962016i	$0.411986\pi$
$282$	2741.32	0.578877
$283$	5575.31	1.17109	0.585544	−	0.810641i	$-0.300881\pi$
$283$	5575.31	1.17109	0.585544	+	0.810641i	$0.300881\pi$
$284$	6729.60	1.40608
$285$	0	0
$286$	1449.73	0.299735
$287$	−1874.76	−0.385588
$288$	−4714.12	−0.964522
$289$	−2085.10	−0.424405
$290$	0	0
$291$	1563.00	0.314861
$292$	−1841.22	−0.369003
$293$	5794.27	1.15531	0.577654	−	0.816282i	$-0.303968\pi$
$293$	5794.27	1.15531	0.577654	+	0.816282i	$0.303968\pi$
$294$	5198.01	1.03114
$295$	0	0
$296$	16807.6	3.30040
$297$	−92.7611	−0.0181230
$298$	3500.13	0.680392
$299$	9315.76	1.80182
$300$	0	0
$301$	−1607.62	−0.307846
$302$	10339.4	1.97008
$303$	1982.76	0.375930
$304$	4076.59	0.769107
$305$	0	0
$306$	−2564.78	−0.479146
$307$	−1404.47	−0.261099	−0.130550	−	0.991442i	$-0.541674\pi$
$307$	−1404.47	−0.261099	−0.130550	+	0.991442i	$0.541674\pi$
$308$	315.717	0.0584079
$309$	4592.25	0.845449
$310$	0	0
$311$	−4096.75	−0.746963	−0.373481	−	0.927638i	$-0.621836\pi$
$311$	−4096.75	−0.746963	−0.373481	+	0.927638i	$0.621836\pi$
$312$	−16099.7	−2.92136
$313$	974.611	0.176001	0.0880004	−	0.996120i	$-0.471952\pi$
$313$	974.611	0.176001	0.0880004	+	0.996120i	$0.471952\pi$
$314$	−11627.5	−2.08973
$315$	0	0
$316$	−23564.9	−4.19503
$317$	−2071.69	−0.367058	−0.183529	−	0.983014i	$-0.558752\pi$
$317$	−2071.69	−0.367058	−0.183529	+	0.983014i	$0.558752\pi$
$318$	8778.67	1.54806
$319$	−577.349	−0.101333
$320$	0	0
$321$	−793.876	−0.138037
$322$	2812.14	0.486691
$323$	1086.72	0.187204
$324$	1678.14	0.287747
$325$	0	0
$326$	4092.79	0.695334
$327$	3352.84	0.567011
$328$	−28805.9	−4.84921
$329$	756.337	0.126742
$330$	0	0
$331$	−6159.17	−1.02278	−0.511388	−	0.859350i	$-0.670868\pi$
$331$	−6159.17	−1.02278	−0.511388	+	0.859350i	$0.670868\pi$
$332$	−15722.9	−2.59912
$333$	−2219.52	−0.365252
$334$	13741.7	2.25124
$335$	0	0
$336$	−2654.50	−0.430997
$337$	2791.26	0.451186	0.225593	−	0.974222i	$-0.427568\pi$
$337$	2791.26	0.451186	0.225593	+	0.974222i	$0.427568\pi$
$338$	−21453.6	−3.45243
$339$	−2802.18	−0.448949
$340$	0	0
$341$	209.740	0.0333081
$342$	−985.611	−0.155835
$343$	2955.55	0.465262
$344$	−24701.2	−3.87151
$345$	0	0
$346$	−277.746	−0.0431553
$347$	940.848	0.145554	0.0727772	−	0.997348i	$-0.476814\pi$
$347$	940.848	0.145554	0.0727772	+	0.997348i	$0.476814\pi$
$348$	10444.8	1.60891
$349$	−3519.62	−0.539831	−0.269915	−	0.962884i	$-0.586996\pi$
$349$	−3519.62	−0.539831	−0.269915	+	0.962884i	$0.586996\pi$
$350$	0	0
$351$	2126.04	0.323304
$352$	1799.54	0.272487
$353$	5021.60	0.757147	0.378573	−	0.925571i	$-0.376415\pi$
$353$	5021.60	0.757147	0.378573	+	0.925571i	$0.376415\pi$
$354$	3488.15	0.523710
$355$	0	0
$356$	4054.09	0.603557
$357$	−707.628	−0.104907
$358$	21203.2	3.13023
$359$	6811.99	1.00146	0.500728	−	0.865604i	$-0.333066\pi$
$359$	6811.99	1.00146	0.500728	+	0.865604i	$0.333066\pi$
$360$	0	0
$361$	−6441.39	−0.939115
$362$	−9667.69	−1.40365
$363$	−3957.59	−0.572230
$364$	−7236.09	−1.04196
$365$	0	0
$366$	−2104.47	−0.300553
$367$	3748.07	0.533099	0.266550	−	0.963821i	$-0.414116\pi$
$367$	3748.07	0.533099	0.266550	+	0.963821i	$0.414116\pi$
$368$	23600.4	3.34309
$369$	3803.96	0.536657
$370$	0	0
$371$	2422.05	0.338940
$372$	−3794.41	−0.528847
$373$	−898.302	−0.124698	−0.0623489	−	0.998054i	$-0.519859\pi$
$373$	−898.302	−0.124698	−0.0623489	+	0.998054i	$0.519859\pi$
$374$	979.060	0.135364
$375$	0	0
$376$	11621.2	1.59393
$377$	13232.6	1.80773
$378$	641.788	0.0873280
$379$	−9378.99	−1.27115	−0.635576	−	0.772038i	$-0.719237\pi$
$379$	−9378.99	−1.27115	−0.635576	+	0.772038i	$0.719237\pi$
$380$	0	0
$381$	1891.07	0.254284
$382$	−19649.8	−2.63186
$383$	−9446.29	−1.26027	−0.630134	−	0.776486i	$-0.717000\pi$
$383$	−9446.29	−1.26027	−0.630134	+	0.776486i	$0.717000\pi$
$384$	−6898.97	−0.916828
$385$	0	0
$386$	14560.0	1.91991
$387$	3261.92	0.428457
$388$	10794.0	1.41232
$389$	−7643.23	−0.996214	−0.498107	−	0.867116i	$-0.665971\pi$
$389$	−7643.23	−0.996214	−0.498107	+	0.867116i	$0.665971\pi$
$390$	0	0
$391$	6291.32	0.813723
$392$	22035.7	2.83922
$393$	−6489.17	−0.832914
$394$	−10901.6	−1.39394
$395$	0	0
$396$	−640.602	−0.0812915
$397$	−12013.6	−1.51876	−0.759378	−	0.650650i	$-0.774497\pi$
$397$	−12013.6	−1.51876	−0.759378	+	0.650650i	$0.774497\pi$
$398$	8313.10	1.04698
$399$	−271.932	−0.0341194
$400$	0	0
$401$	−8538.51	−1.06332	−0.531662	−	0.846957i	$-0.678432\pi$
$401$	−8538.51	−1.06332	−0.531662	+	0.846957i	$0.678432\pi$
$402$	9885.40	1.22646
$403$	−4807.16	−0.594197
$404$	13692.8	1.68625
$405$	0	0
$406$	3994.51	0.488287
$407$	847.265	0.103188
$408$	−10872.8	−1.31932
$409$	−12267.6	−1.48312	−0.741558	−	0.670889i	$-0.765913\pi$
$409$	−12267.6	−1.48312	−0.741558	+	0.670889i	$0.765913\pi$
$410$	0	0
$411$	3355.84	0.402753
$412$	31713.8	3.79229
$413$	962.389	0.114664
$414$	−5705.95	−0.677372
$415$	0	0
$416$	−41244.6	−4.86102
$417$	−499.433	−0.0586508
$418$	376.240	0.0440251
$419$	15493.0	1.80641	0.903204	−	0.429212i	$-0.141209\pi$
$419$	15493.0	1.80641	0.903204	+	0.429212i	$0.141209\pi$
$420$	0	0
$421$	7510.67	0.869472	0.434736	−	0.900558i	$-0.356842\pi$
$421$	7510.67	0.869472	0.434736	+	0.900558i	$0.356842\pi$
$422$	−17108.3	−1.97351
$423$	−1534.64	−0.176399
$424$	37215.1	4.26256
$425$	0	0
$426$	−5222.07	−0.593920
$427$	−580.627	−0.0658045
$428$	−5482.45	−0.619169
$429$	−811.581	−0.0913368
$430$	0	0
$431$	−15675.3	−1.75186	−0.875932	−	0.482434i	$-0.839753\pi$
$431$	−15675.3	−1.75186	−0.875932	+	0.482434i	$0.839753\pi$
$432$	5386.09	0.599857
$433$	−9604.78	−1.06600	−0.532998	−	0.846117i	$-0.678935\pi$
$433$	−9604.78	−1.06600	−0.532998	+	0.846117i	$0.678935\pi$
$434$	−1451.13	−0.160499
$435$	0	0
$436$	23154.5	2.54335
$437$	2417.67	0.264652
$438$	1428.76	0.155864
$439$	−6362.06	−0.691673	−0.345837	−	0.938295i	$-0.612405\pi$
$439$	−6362.06	−0.691673	−0.345837	+	0.938295i	$0.612405\pi$
$440$	0	0
$441$	−2909.93	−0.314213
$442$	−22439.6	−2.41481
$443$	931.658	0.0999196	0.0499598	−	0.998751i	$-0.484091\pi$
$443$	931.658	0.0999196	0.0499598	+	0.998751i	$0.484091\pi$
$444$	−15327.9	−1.63835
$445$	0	0
$446$	8336.06	0.885031
$447$	−1959.43	−0.207333
$448$	−5371.81	−0.566505
$449$	−18684.1	−1.96383	−0.981914	−	0.189329i	$-0.939369\pi$
$449$	−18684.1	−1.96383	−0.981914	+	0.189329i	$0.939369\pi$
$450$	0	0
$451$	−1452.10	−0.151611
$452$	−19351.7	−2.01378
$453$	−5788.14	−0.600333
$454$	33261.9	3.43846
$455$	0	0
$456$	−4178.27	−0.429090
$457$	−11565.9	−1.18387	−0.591936	−	0.805985i	$-0.701636\pi$
$457$	−11565.9	−1.18387	−0.591936	+	0.805985i	$0.701636\pi$
$458$	−25077.0	−2.55845
$459$	1435.81	0.146008
$460$	0	0
$461$	19401.0	1.96008	0.980039	−	0.198806i	$-0.0637062\pi$
$461$	19401.0	1.96008	0.980039	+	0.198806i	$0.0637062\pi$
$462$	−244.991	−0.0246711
$463$	1576.28	0.158220	0.0791099	−	0.996866i	$-0.474792\pi$
$463$	1576.28	0.158220	0.0791099	+	0.996866i	$0.474792\pi$
$464$	33523.2	3.35405
$465$	0	0
$466$	17387.1	1.72842
$467$	3256.55	0.322687	0.161344	−	0.986898i	$-0.448417\pi$
$467$	3256.55	0.322687	0.161344	+	0.986898i	$0.448417\pi$
$468$	14682.3	1.45019
$469$	2727.40	0.268528
$470$	0	0
$471$	6509.25	0.636795
$472$	14787.2	1.44203
$473$	−1245.18	−0.121043
$474$	18286.0	1.77195
$475$	0	0
$476$	−4886.83	−0.470562
$477$	−4914.44	−0.471733
$478$	19606.2	1.87608
$479$	8291.59	0.790924	0.395462	−	0.918482i	$-0.370585\pi$
$479$	8291.59	0.790924	0.395462	+	0.918482i	$0.370585\pi$
$480$	0	0
$481$	−19418.9	−1.84081
$482$	−10348.1	−0.977891
$483$	−1574.28	−0.148307
$484$	−27330.9	−2.56676
$485$	0	0
$486$	−1302.21	−0.121542
$487$	4758.55	0.442773	0.221387	−	0.975186i	$-0.428942\pi$
$487$	4758.55	0.442773	0.221387	+	0.975186i	$0.428942\pi$
$488$	−8921.39	−0.827567
$489$	−2291.21	−0.211886
$490$	0	0
$491$	3906.46	0.359055	0.179528	−	0.983753i	$-0.442543\pi$
$491$	3906.46	0.359055	0.179528	+	0.983753i	$0.442543\pi$
$492$	26269.9	2.40719
$493$	8936.52	0.816390
$494$	−8623.26	−0.785382
$495$	0	0
$496$	−12178.4	−1.10247
$497$	−1440.78	−0.130036
$498$	12200.7	1.09785
$499$	−3093.31	−0.277506	−0.138753	−	0.990327i	$-0.544309\pi$
$499$	−3093.31	−0.277506	−0.138753	+	0.990327i	$0.544309\pi$
$500$	0	0
$501$	−7692.85	−0.686010
$502$	31313.9	2.78408
$503$	−18153.9	−1.60923	−0.804616	−	0.593796i	$-0.797629\pi$
$503$	−18153.9	−1.60923	−0.804616	+	0.593796i	$0.797629\pi$
$504$	2720.71	0.240456
$505$	0	0
$506$	2178.15	0.191365
$507$	12010.1	1.05204
$508$	13059.6	1.14060
$509$	2281.32	0.198660	0.0993298	−	0.995055i	$-0.468330\pi$
$509$	2281.32	0.198660	0.0993298	+	0.995055i	$0.468330\pi$
$510$	0	0
$511$	394.197	0.0341257
$512$	4276.07	0.369097
$513$	551.761	0.0474870
$514$	−24147.8	−2.07221
$515$	0	0
$516$	22526.6	1.92186
$517$	585.821	0.0498344
$518$	−5861.98	−0.497221
$519$	155.487	0.0131505
$520$	0	0
$521$	−16691.9	−1.40362	−0.701809	−	0.712366i	$-0.747624\pi$
$521$	−16691.9	−1.40362	−0.701809	+	0.712366i	$0.747624\pi$
$522$	−8105.03	−0.679593
$523$	−17090.4	−1.42889	−0.714446	−	0.699690i	$-0.753321\pi$
$523$	−17090.4	−1.42889	−0.714446	+	0.699690i	$0.753321\pi$
$524$	−44813.8	−3.73607
$525$	0	0
$526$	−28617.4	−2.37220
$527$	−3246.47	−0.268346
$528$	−2056.05	−0.169466
$529$	1829.50	0.150365
$530$	0	0
$531$	−1952.73	−0.159588
$532$	−1877.94	−0.153044
$533$	33281.5	2.70465
$534$	−3145.91	−0.254938
$535$	0	0
$536$	41906.8	3.37705
$537$	−11869.9	−0.953861
$538$	−15057.4	−1.20664
$539$	1110.82	0.0887685
$540$	0	0
$541$	5271.40	0.418919	0.209459	−	0.977817i	$-0.432830\pi$
$541$	5271.40	0.418919	0.209459	+	0.977817i	$0.432830\pi$
$542$	−16628.4	−1.31780
$543$	5412.13	0.427729
$544$	−27854.2	−2.19529
$545$	0	0
$546$	5615.10	0.440117
$547$	15182.2	1.18673	0.593366	−	0.804933i	$-0.297799\pi$
$547$	15182.2	1.18673	0.593366	+	0.804933i	$0.297799\pi$
$548$	23175.2	1.80656
$549$	1178.11	0.0915860
$550$	0	0
$551$	3434.18	0.265519
$552$	−24189.0	−1.86513
$553$	5045.15	0.387960
$554$	24645.2	1.89002
$555$	0	0
$556$	−3449.05	−0.263080
$557$	12241.2	0.931198	0.465599	−	0.884996i	$-0.345839\pi$
$557$	12241.2	0.931198	0.465599	+	0.884996i	$0.345839\pi$
$558$	2944.41	0.223381
$559$	28539.0	2.15934
$560$	0	0
$561$	−548.094	−0.0412488
$562$	−13782.2	−1.03446
$563$	14196.4	1.06271	0.531355	−	0.847149i	$-0.321683\pi$
$563$	14196.4	1.06271	0.531355	+	0.847149i	$0.321683\pi$
$564$	−10598.1	−0.791242
$565$	0	0
$566$	−29877.5	−2.21881
$567$	−359.283	−0.0266111
$568$	−22137.7	−1.63535
$569$	9150.05	0.674148	0.337074	−	0.941478i	$-0.390563\pi$
$569$	9150.05	0.674148	0.337074	+	0.941478i	$0.390563\pi$
$570$	0	0
$571$	23582.1	1.72833	0.864167	−	0.503206i	$-0.167846\pi$
$571$	23582.1	1.72833	0.864167	+	0.503206i	$0.167846\pi$
$572$	−5604.72	−0.409695
$573$	11000.3	0.801993
$574$	10046.7	0.730556
$575$	0	0
$576$	10899.6	0.788456
$577$	3906.22	0.281834	0.140917	−	0.990021i	$-0.454995\pi$
$577$	3906.22	0.281834	0.140917	+	0.990021i	$0.454995\pi$
$578$	11173.9	0.804102
$579$	−8150.93	−0.585045
$580$	0	0
$581$	3366.21	0.240368
$582$	−8375.96	−0.596554
$583$	1876.00	0.133270
$584$	6056.87	0.429170
$585$	0	0
$586$	−31050.9	−2.18891
$587$	−25938.0	−1.82381	−0.911905	−	0.410401i	$-0.865389\pi$
$587$	−25938.0	−1.82381	−0.911905	+	0.410401i	$0.865389\pi$
$588$	−20095.8	−1.40941
$589$	−1247.58	−0.0872759
$590$	0	0
$591$	6102.89	0.424770
$592$	−49195.7	−3.41542
$593$	1908.23	0.132145	0.0660723	−	0.997815i	$-0.478953\pi$
$593$	1908.23	0.132145	0.0660723	+	0.997815i	$0.478953\pi$
$594$	497.097	0.0343370
$595$	0	0
$596$	−13531.7	−0.929999
$597$	−4653.81	−0.319041
$598$	−49922.2	−3.41383
$599$	−3495.41	−0.238429	−0.119214	−	0.992869i	$-0.538038\pi$
$599$	−3495.41	−0.238429	−0.119214	+	0.992869i	$0.538038\pi$
$600$	0	0
$601$	−18267.2	−1.23983	−0.619913	−	0.784671i	$-0.712832\pi$
$601$	−18267.2	−1.23983	−0.619913	+	0.784671i	$0.712832\pi$
$602$	8615.06	0.583262
$603$	−5534.01	−0.373735
$604$	−39972.5	−2.69281
$605$	0	0
$606$	−10625.4	−0.712257
$607$	11538.2	0.771534	0.385767	−	0.922596i	$-0.373937\pi$
$607$	11538.2	0.771534	0.385767	+	0.922596i	$0.373937\pi$
$608$	−10704.0	−0.713987
$609$	−2236.19	−0.148793
$610$	0	0
$611$	−13426.8	−0.889017
$612$	9915.58	0.654924
$613$	21136.9	1.39268	0.696340	−	0.717713i	$-0.254811\pi$
$613$	21136.9	1.39268	0.696340	+	0.717713i	$0.254811\pi$
$614$	7526.43	0.494694
$615$	0	0
$616$	−1038.58	−0.0679314
$617$	15673.2	1.02266	0.511329	−	0.859385i	$-0.329153\pi$
$617$	15673.2	1.02266	0.511329	+	0.859385i	$0.329153\pi$
$618$	−24609.4	−1.60184
$619$	22923.7	1.48850	0.744249	−	0.667902i	$-0.232807\pi$
$619$	22923.7	1.48850	0.744249	+	0.667902i	$0.232807\pi$
$620$	0	0
$621$	3194.28	0.206413
$622$	21954.1	1.41524
$623$	−867.964	−0.0558174
$624$	47123.7	3.02317
$625$	0	0
$626$	−5222.84	−0.333461
$627$	−210.625	−0.0134156
$628$	44952.4	2.85636
$629$	−13114.4	−0.831329
$630$	0	0
$631$	9108.23	0.574632	0.287316	−	0.957836i	$-0.407237\pi$
$631$	9108.23	0.574632	0.287316	+	0.957836i	$0.407237\pi$
$632$	77519.3	4.87904
$633$	9577.53	0.601379
$634$	11102.0	0.695449
$635$	0	0
$636$	−33938.8	−2.11598
$637$	−25459.4	−1.58358
$638$	3093.96	0.191992
$639$	2923.40	0.180983
$640$	0	0
$641$	20103.5	1.23875	0.619375	−	0.785095i	$-0.287386\pi$
$641$	20103.5	1.23875	0.619375	+	0.785095i	$0.287386\pi$
$642$	4254.30	0.261533
$643$	5934.92	0.363997	0.181999	−	0.983299i	$-0.441743\pi$
$643$	5934.92	0.363997	0.181999	+	0.983299i	$0.441743\pi$
$644$	−10871.9	−0.665237
$645$	0	0
$646$	−5823.64	−0.354688
$647$	−14193.7	−0.862460	−0.431230	−	0.902242i	$-0.641920\pi$
$647$	−14193.7	−0.862460	−0.431230	+	0.902242i	$0.641920\pi$
$648$	−5520.42	−0.334665
$649$	745.420	0.0450852
$650$	0	0
$651$	812.368	0.0489082
$652$	−15823.0	−0.950422
$653$	−4795.80	−0.287403	−0.143701	−	0.989621i	$-0.545900\pi$
$653$	−4795.80	−0.287403	−0.143701	+	0.989621i	$0.545900\pi$
$654$	−17967.5	−1.07429
$655$	0	0
$656$	84314.8	5.01820
$657$	−799.841	−0.0474958
$658$	−4053.13	−0.240133
$659$	4399.57	0.260065	0.130032	−	0.991510i	$-0.458492\pi$
$659$	4399.57	0.260065	0.130032	+	0.991510i	$0.458492\pi$
$660$	0	0
$661$	24096.0	1.41789	0.708945	−	0.705263i	$-0.249171\pi$
$661$	24096.0	1.41789	0.708945	+	0.705263i	$0.249171\pi$
$662$	33006.4	1.93781
$663$	12562.1	0.735853
$664$	51722.2	3.02291
$665$	0	0
$666$	11894.2	0.692028
$667$	19881.4	1.15414
$668$	−53126.3	−3.07712
$669$	−4666.66	−0.269692
$670$	0	0
$671$	−449.725	−0.0258740
$672$	6969.98	0.400109
$673$	−27648.3	−1.58360	−0.791800	−	0.610781i	$-0.790856\pi$
$673$	−27648.3	−1.58360	−0.791800	+	0.610781i	$0.790856\pi$
$674$	−14958.1	−0.854843
$675$	0	0
$676$	82940.9	4.71898
$677$	−27605.5	−1.56716	−0.783580	−	0.621292i	$-0.786608\pi$
$677$	−27605.5	−1.56716	−0.783580	+	0.621292i	$0.786608\pi$
$678$	15016.6	0.850604
$679$	−2310.95	−0.130613
$680$	0	0
$681$	−18620.6	−1.04779
$682$	−1123.98	−0.0631075
$683$	−14949.4	−0.837513	−0.418756	−	0.908099i	$-0.637534\pi$
$683$	−14949.4	−0.837513	−0.418756	+	0.908099i	$0.637534\pi$
$684$	3810.42	0.213005
$685$	0	0
$686$	−15838.5	−0.881511
$687$	14038.5	0.779626
$688$	72300.4	4.00643
$689$	−42997.2	−2.37745
$690$	0	0
$691$	8884.30	0.489110	0.244555	−	0.969635i	$-0.421358\pi$
$691$	8884.30	0.489110	0.244555	+	0.969635i	$0.421358\pi$
$692$	1073.78	0.0589871
$693$	137.150	0.00751790
$694$	−5041.91	−0.275775
$695$	0	0
$696$	−34359.4	−1.87125
$697$	22476.4	1.22145
$698$	18861.3	1.02279
$699$	−9733.59	−0.526693
$700$	0	0
$701$	10556.9	0.568798	0.284399	−	0.958706i	$-0.408206\pi$
$701$	10556.9	0.568798	0.284399	+	0.958706i	$0.408206\pi$
$702$	−11393.3	−0.612551
$703$	−5039.70	−0.270378
$704$	−4160.74	−0.222747
$705$	0	0
$706$	−26910.2	−1.43453
$707$	−2931.58	−0.155945
$708$	−13485.4	−0.715836
$709$	25351.9	1.34289	0.671445	−	0.741055i	$-0.265674\pi$
$709$	25351.9	1.34289	0.671445	+	0.741055i	$0.265674\pi$
$710$	0	0
$711$	−10236.8	−0.539959
$712$	−13336.4	−0.701968
$713$	−7222.53	−0.379363
$714$	3792.11	0.198762
$715$	0	0
$716$	−81972.6	−4.27858
$717$	−10975.8	−0.571688
$718$	−36504.8	−1.89742
$719$	9719.94	0.504162	0.252081	−	0.967706i	$-0.418885\pi$
$719$	9719.94	0.504162	0.252081	+	0.967706i	$0.418885\pi$
$720$	0	0
$721$	−6789.79	−0.350714
$722$	34518.7	1.77930
$723$	5793.04	0.297988
$724$	37375.8	1.91859
$725$	0	0
$726$	21208.3	1.08418
$727$	−27509.3	−1.40339	−0.701694	−	0.712479i	$-0.747572\pi$
$727$	−27509.3	−1.40339	−0.701694	+	0.712479i	$0.747572\pi$
$728$	23803.9	1.21186
$729$	729.000	0.0370370
$730$	0	0
$731$	19273.6	0.975184
$732$	8135.98	0.410812
$733$	−7240.49	−0.364848	−0.182424	−	0.983220i	$-0.558394\pi$
$733$	−7240.49	−0.364848	−0.182424	+	0.983220i	$0.558394\pi$
$734$	−20085.5	−1.01004
$735$	0	0
$736$	−61968.1	−3.10350
$737$	2112.51	0.105584
$738$	−20385.1	−1.01678
$739$	−15875.3	−0.790234	−0.395117	−	0.918631i	$-0.629296\pi$
$739$	−15875.3	−0.790234	−0.395117	+	0.918631i	$0.629296\pi$
$740$	0	0
$741$	4827.44	0.239326
$742$	−12979.5	−0.642175
$743$	−25714.3	−1.26967	−0.634836	−	0.772647i	$-0.718932\pi$
$743$	−25714.3	−1.26967	−0.634836	+	0.772647i	$0.718932\pi$
$744$	12482.1	0.615076
$745$	0	0
$746$	4813.91	0.236260
$747$	−6830.18	−0.334542
$748$	−3785.10	−0.185023
$749$	1173.77	0.0572612
$750$	0	0
$751$	−9709.09	−0.471757	−0.235879	−	0.971783i	$-0.575797\pi$
$751$	−9709.09	−0.471757	−0.235879	+	0.971783i	$0.575797\pi$
$752$	−34015.2	−1.64948
$753$	−17530.0	−0.848379
$754$	−70912.1	−3.42502
$755$	0	0
$756$	−2481.19	−0.119365
$757$	−9567.13	−0.459344	−0.229672	−	0.973268i	$-0.573765\pi$
$757$	−9567.13	−0.459344	−0.229672	+	0.973268i	$0.573765\pi$
$758$	50261.1	2.40840
$759$	−1219.36	−0.0583137
$760$	0	0
$761$	−12322.5	−0.586980	−0.293490	−	0.955962i	$-0.594817\pi$
$761$	−12322.5	−0.586980	−0.293490	+	0.955962i	$0.594817\pi$
$762$	−10134.0	−0.481782
$763$	−4957.28	−0.235211
$764$	75967.0	3.59737
$765$	0	0
$766$	50621.7	2.38778
$767$	−17084.7	−0.804293
$768$	7905.27	0.371428
$769$	2575.56	0.120776	0.0603881	−	0.998175i	$-0.480766\pi$
$769$	2575.56	0.120776	0.0603881	+	0.998175i	$0.480766\pi$
$770$	0	0
$771$	13518.3	0.631454
$772$	−56289.8	−2.62424
$773$	−6606.23	−0.307386	−0.153693	−	0.988119i	$-0.549117\pi$
$773$	−6606.23	−0.307386	−0.153693	+	0.988119i	$0.549117\pi$
$774$	−17480.3	−0.811778
$775$	0	0
$776$	−35507.9	−1.64260
$777$	3281.63	0.151516
$778$	40959.3	1.88748
$779$	8637.37	0.397260
$780$	0	0
$781$	−1115.96	−0.0511294
$782$	−33714.5	−1.54173
$783$	4537.33	0.207089
$784$	−64498.5	−2.93816
$785$	0	0
$786$	34774.8	1.57809
$787$	16417.0	0.743587	0.371793	−	0.928315i	$-0.378743\pi$
$787$	16417.0	0.743587	0.371793	+	0.928315i	$0.378743\pi$
$788$	42146.1	1.90532
$789$	16020.5	0.722870
$790$	0	0
$791$	4143.12	0.186235
$792$	2107.33	0.0945462
$793$	10307.5	0.461577
$794$	64379.8	2.87752
$795$	0	0
$796$	−32138.9	−1.43107
$797$	−3944.19	−0.175295	−0.0876477	−	0.996152i	$-0.527935\pi$
$797$	−3944.19	−0.175295	−0.0876477	+	0.996152i	$0.527935\pi$
$798$	1457.26	0.0646445
$799$	−9067.66	−0.401490
$800$	0	0
$801$	1761.13	0.0776861
$802$	45757.0	2.01463
$803$	305.325	0.0134181
$804$	−38217.5	−1.67640
$805$	0	0
$806$	25761.1	1.12580
$807$	8429.37	0.367693
$808$	−45044.0	−1.96119
$809$	−17960.7	−0.780549	−0.390275	−	0.920699i	$-0.627620\pi$
$809$	−17960.7	−0.780549	−0.390275	+	0.920699i	$0.627620\pi$
$810$	0	0
$811$	−13162.5	−0.569912	−0.284956	−	0.958541i	$-0.591979\pi$
$811$	−13162.5	−0.569912	−0.284956	+	0.958541i	$0.591979\pi$
$812$	−15443.0	−0.667418
$813$	9308.84	0.401569
$814$	−4540.41	−0.195505
$815$	0	0
$816$	31824.6	1.36530
$817$	7406.59	0.317165
$818$	65740.9	2.81000
$819$	−3143.42	−0.134115
$820$	0	0
$821$	26502.4	1.12660	0.563302	−	0.826251i	$-0.309531\pi$
$821$	26502.4	1.12660	0.563302	+	0.826251i	$0.309531\pi$
$822$	−17983.6	−0.763078
$823$	6937.86	0.293850	0.146925	−	0.989148i	$-0.453062\pi$
$823$	6937.86	0.293850	0.146925	+	0.989148i	$0.453062\pi$
$824$	−104326.	−4.41063
$825$	0	0
$826$	−5157.35	−0.217248
$827$	41197.9	1.73228	0.866138	−	0.499805i	$-0.166595\pi$
$827$	41197.9	1.73228	0.866138	+	0.499805i	$0.166595\pi$
$828$	22059.5	0.925871
$829$	−693.324	−0.0290472	−0.0145236	−	0.999895i	$-0.504623\pi$
$829$	−693.324	−0.0290472	−0.0145236	+	0.999895i	$0.504623\pi$
$830$	0	0
$831$	−13796.8	−0.575938
$832$	95362.4	3.97367
$833$	−17193.8	−0.715162
$834$	2676.41	0.111123
$835$	0	0
$836$	−1454.56	−0.0601760
$837$	−1648.33	−0.0680699
$838$	−83025.7	−3.42252
$839$	−6491.28	−0.267108	−0.133554	−	0.991042i	$-0.542639\pi$
$839$	−6491.28	−0.267108	−0.133554	+	0.991042i	$0.542639\pi$
$840$	0	0
$841$	3851.52	0.157921
$842$	−40248.9	−1.64735
$843$	7715.49	0.315226
$844$	66141.8	2.69750
$845$	0	0
$846$	8223.97	0.334215
$847$	5851.42	0.237376
$848$	−108928.	−4.41111
$849$	16725.9	0.676128
$850$	0	0
$851$	−29176.1	−1.17526
$852$	20188.8	0.811803
$853$	−1116.68	−0.0448233	−0.0224117	−	0.999749i	$-0.507134\pi$
$853$	−1116.68	−0.0448233	−0.0224117	+	0.999749i	$0.507134\pi$
$854$	3111.52	0.124677
$855$	0	0
$856$	18035.1	0.720126
$857$	44383.9	1.76911	0.884554	−	0.466438i	$-0.154463\pi$
$857$	44383.9	1.76911	0.884554	+	0.466438i	$0.154463\pi$
$858$	4349.18	0.173052
$859$	−25579.3	−1.01601	−0.508006	−	0.861354i	$-0.669617\pi$
$859$	−25579.3	−1.01601	−0.508006	+	0.861354i	$0.669617\pi$
$860$	0	0
$861$	−5624.28	−0.222619
$862$	84002.5	3.31918
$863$	−11194.8	−0.441570	−0.220785	−	0.975323i	$-0.570862\pi$
$863$	−11194.8	−0.441570	−0.220785	+	0.975323i	$0.570862\pi$
$864$	−14142.4	−0.556867
$865$	0	0
$866$	51471.0	2.01970
$867$	−6255.31	−0.245030
$868$	5610.16	0.219379
$869$	3907.73	0.152544
$870$	0	0
$871$	−48417.9	−1.88356
$872$	−76169.2	−2.95804
$873$	4689.00	0.181785
$874$	−12956.0	−0.501424
$875$	0	0
$876$	−5523.65	−0.213044
$877$	−5721.75	−0.220308	−0.110154	−	0.993915i	$-0.535134\pi$
$877$	−5721.75	−0.220308	−0.110154	+	0.993915i	$0.535134\pi$
$878$	34093.6	1.31048
$879$	17382.8	0.667017
$880$	0	0
$881$	−34682.8	−1.32633	−0.663163	−	0.748475i	$-0.730786\pi$
$881$	−34682.8	−1.32633	−0.663163	+	0.748475i	$0.730786\pi$
$882$	15594.0	0.595326
$883$	37990.4	1.44788	0.723941	−	0.689862i	$-0.242329\pi$
$883$	37990.4	1.44788	0.723941	+	0.689862i	$0.242329\pi$
$884$	86752.9	3.30070
$885$	0	0
$886$	−4992.66	−0.189313
$887$	−28299.0	−1.07124	−0.535618	−	0.844460i	$-0.679921\pi$
$887$	−28299.0	−1.07124	−0.535618	+	0.844460i	$0.679921\pi$
$888$	50422.7	1.90549
$889$	−2796.00	−0.105484
$890$	0	0
$891$	−278.283	−0.0104633
$892$	−32227.7	−1.20971
$893$	−3484.58	−0.130579
$894$	10500.4	0.392825
$895$	0	0
$896$	10200.4	0.380324
$897$	27947.3	1.04028
$898$	100126.	3.72078
$899$	−10259.3	−0.380607
$900$	0	0
$901$	−29037.8	−1.07368
$902$	7781.65	0.287251
$903$	−4822.85	−0.177735
$904$	63659.4	2.34212
$905$	0	0
$906$	31018.1	1.13742
$907$	−17388.0	−0.636559	−0.318280	−	0.947997i	$-0.603105\pi$
$907$	−17388.0	−0.636559	−0.318280	+	0.947997i	$0.603105\pi$
$908$	−128592.	−4.69988
$909$	5948.28	0.217043
$910$	0	0
$911$	23555.3	0.856663	0.428332	−	0.903622i	$-0.359101\pi$
$911$	23555.3	0.856663	0.428332	+	0.903622i	$0.359101\pi$
$912$	12229.8	0.444044
$913$	2607.30	0.0945117
$914$	61980.4	2.24303
$915$	0	0
$916$	96949.1	3.49704
$917$	9594.44	0.345514
$918$	−7694.34	−0.276635
$919$	−5983.09	−0.214760	−0.107380	−	0.994218i	$-0.534246\pi$
$919$	−5983.09	−0.214760	−0.107380	+	0.994218i	$0.534246\pi$
$920$	0	0
$921$	−4213.42	−0.150746
$922$	−103968.	−3.71368
$923$	25577.3	0.912119
$924$	947.150	0.0337218
$925$	0	0
$926$	−8447.10	−0.299772
$927$	13776.7	0.488120
$928$	−88022.7	−3.11367
$929$	20576.7	0.726694	0.363347	−	0.931654i	$-0.381634\pi$
$929$	20576.7	0.726694	0.363347	+	0.931654i	$0.381634\pi$
$930$	0	0
$931$	−6607.35	−0.232596
$932$	−67219.5	−2.36250
$933$	−12290.2	−0.431259
$934$	−17451.5	−0.611382
$935$	0	0
$936$	−48299.0	−1.68665
$937$	−11228.6	−0.391485	−0.195743	−	0.980655i	$-0.562712\pi$
$937$	−11228.6	−0.391485	−0.195743	+	0.980655i	$0.562712\pi$
$938$	−14615.9	−0.508769
$939$	2923.83	0.101614
$940$	0	0
$941$	38567.6	1.33610	0.668049	−	0.744118i	$-0.267130\pi$
$941$	38567.6	1.33610	0.668049	+	0.744118i	$0.267130\pi$
$942$	−34882.4	−1.20651
$943$	50003.9	1.72678
$944$	−43282.1	−1.49228
$945$	0	0
$946$	6672.81	0.229336
$947$	4606.17	0.158057	0.0790287	−	0.996872i	$-0.474818\pi$
$947$	4606.17	0.158057	0.0790287	+	0.996872i	$0.474818\pi$
$948$	−70694.8	−2.42200
$949$	−6997.93	−0.239370
$950$	0	0
$951$	−6215.06	−0.211921
$952$	16075.8	0.547288
$953$	−25559.7	−0.868795	−0.434397	−	0.900721i	$-0.643039\pi$
$953$	−25559.7	−0.868795	−0.434397	+	0.900721i	$0.643039\pi$
$954$	26336.0	0.893773
$955$	0	0
$956$	−75798.5	−2.56433
$957$	−1732.05	−0.0585048
$958$	−44433.8	−1.49853
$959$	−4961.72	−0.167072
$960$	0	0
$961$	−26064.0	−0.874895
$962$	104064.	3.48769
$963$	−2381.63	−0.0796956
$964$	40006.4	1.33664
$965$	0	0
$966$	8436.42	0.280991
$967$	37895.8	1.26023	0.630117	−	0.776500i	$-0.283007\pi$
$967$	37895.8	1.26023	0.630117	+	0.776500i	$0.283007\pi$
$968$	89907.7	2.98527
$969$	3260.17	0.108082
$970$	0	0
$971$	−46761.0	−1.54545	−0.772726	−	0.634740i	$-0.781107\pi$
$971$	−46761.0	−1.54545	−0.772726	+	0.634740i	$0.781107\pi$
$972$	5034.42	0.166131
$973$	738.428	0.0243298
$974$	−25500.6	−0.838903
$975$	0	0
$976$	26112.9	0.856407
$977$	3070.29	0.100540	0.0502698	−	0.998736i	$-0.483992\pi$
$977$	3070.29	0.100540	0.0502698	+	0.998736i	$0.483992\pi$
$978$	12278.4	0.401451
$979$	−672.282	−0.0219471
$980$	0	0
$981$	10058.5	0.327364
$982$	−20934.3	−0.680287
$983$	16319.0	0.529498	0.264749	−	0.964317i	$-0.414711\pi$
$983$	16319.0	0.529498	0.264749	+	0.964317i	$0.414711\pi$
$984$	−86417.7	−2.79969
$985$	0	0
$986$	−47889.9	−1.54678
$987$	2269.01	0.0731747
$988$	33338.0	1.07350
$989$	42878.6	1.37862
$990$	0	0
$991$	5105.79	0.163664	0.0818319	−	0.996646i	$-0.473923\pi$
$991$	5105.79	0.163664	0.0818319	+	0.996646i	$0.473923\pi$
$992$	31977.0	1.02346
$993$	−18477.5	−0.590500
$994$	7720.99	0.246373
$995$	0	0
$996$	−47168.7	−1.50060
$997$	7206.97	0.228934	0.114467	−	0.993427i	$-0.463484\pi$
$997$	7206.97	0.228934	0.114467	+	0.993427i	$0.463484\pi$
$998$	16576.7	0.525779
$999$	−6658.57	−0.210879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.4.a.d.1.1	✓	2
3.2	odd	2		225.4.a.n.1.2		2
4.3	odd	2		1200.4.a.bl.1.2		2
5.2	odd	4		75.4.b.c.49.1		4
5.3	odd	4		75.4.b.c.49.4		4
5.4	even	2		75.4.a.e.1.2	yes	2
15.2	even	4		225.4.b.h.199.4		4
15.8	even	4		225.4.b.h.199.1		4
15.14	odd	2		225.4.a.j.1.1		2
20.3	even	4		1200.4.f.v.49.1		4
20.7	even	4		1200.4.f.v.49.4		4
20.19	odd	2		1200.4.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.a.d.1.1	✓	2	1.1	even	1	trivial
75.4.a.e.1.2	yes	2	5.4	even	2
75.4.b.c.49.1		4	5.2	odd	4
75.4.b.c.49.4		4	5.3	odd	4
225.4.a.j.1.1		2	15.14	odd	2
225.4.a.n.1.2		2	3.2	odd	2
225.4.b.h.199.1		4	15.8	even	4
225.4.b.h.199.4		4	15.2	even	4
1200.4.a.bl.1.2		2	4.3	odd	2
1200.4.a.bu.1.1		2	20.19	odd	2
1200.4.f.v.49.1		4	20.3	even	4
1200.4.f.v.49.4		4	20.7	even	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q-5.35890 q^{2} +3.00000 q^{3} +20.7178 q^{4} -16.0767 q^{6} -4.43560 q^{7} -68.1534 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.35890 q^{2} +3.00000 q^{3} +20.7178 q^{4} -16.0767 q^{6} -4.43560 q^{7} -68.1534 q^{8} +9.00000 q^{9} -3.43560 q^{11} +62.1534 q^{12} +78.7424 q^{13} +23.7699 q^{14} +199.485 q^{16} +53.1780 q^{17} -48.2301 q^{18} +20.4356 q^{19} -13.3068 q^{21} +18.4110 q^{22} +118.307 q^{23} -204.460 q^{24} -421.972 q^{26} +27.0000 q^{27} -91.8958 q^{28} +168.049 q^{29} -61.0492 q^{31} -523.792 q^{32} -10.3068 q^{33} -284.975 q^{34} +186.460 q^{36} -246.614 q^{37} -109.512 q^{38} +236.227 q^{39} +422.663 q^{41} +71.3097 q^{42} +362.436 q^{43} -71.1780 q^{44} -633.994 q^{46} -170.515 q^{47} +598.454 q^{48} -323.325 q^{49} +159.534 q^{51} +1631.37 q^{52} -546.049 q^{53} -144.690 q^{54} +302.301 q^{56} +61.3068 q^{57} -900.559 q^{58} -216.970 q^{59} +130.902 q^{61} +327.156 q^{62} -39.9204 q^{63} +1211.07 q^{64} +55.2330 q^{66} -614.890 q^{67} +1101.73 q^{68} +354.920 q^{69} +324.822 q^{71} -613.381 q^{72} -88.8712 q^{73} +1321.58 q^{74} +423.381 q^{76} +15.2389 q^{77} -1265.92 q^{78} -1137.42 q^{79} +81.0000 q^{81} -2265.01 q^{82} -758.909 q^{83} -275.687 q^{84} -1942.26 q^{86} +504.148 q^{87} +234.148 q^{88} +195.681 q^{89} -349.269 q^{91} +2451.06 q^{92} -183.148 q^{93} +913.774 q^{94} -1571.37 q^{96} +521.000 q^{97} +1732.67 q^{98} -30.9204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 6 q^{3} + 24 q^{4} - 6 q^{6} + 26 q^{7} - 84 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 6 * q^3 + 24 * q^4 - 6 * q^6 + 26 * q^7 - 84 * q^8 + 18 * q^9	\( 2 q - 2 q^{2} + 6 q^{3} + 24 q^{4} - 6 q^{6} + 26 q^{7} - 84 q^{8} + 18 q^{9} + 28 q^{11} + 72 q^{12} + 18 q^{13} + 126 q^{14} + 120 q^{16} - 68 q^{17} - 18 q^{18} + 6 q^{19} + 78 q^{21} + 124 q^{22} + 132 q^{23} - 252 q^{24} - 626 q^{26} + 54 q^{27} + 8 q^{28} + 92 q^{29} + 122 q^{31} - 664 q^{32} + 84 q^{33} - 692 q^{34} + 216 q^{36} - 284 q^{37} - 158 q^{38} + 54 q^{39} + 392 q^{41} + 378 q^{42} + 690 q^{43} + 32 q^{44} - 588 q^{46} - 620 q^{47} + 360 q^{48} + 260 q^{49} - 204 q^{51} + 1432 q^{52} - 848 q^{53} - 54 q^{54} - 180 q^{56} + 18 q^{57} - 1156 q^{58} + 124 q^{59} + 750 q^{61} + 942 q^{62} + 234 q^{63} + 1376 q^{64} + 372 q^{66} - 358 q^{67} + 704 q^{68} + 396 q^{69} + 824 q^{71} - 756 q^{72} - 108 q^{73} + 1196 q^{74} + 376 q^{76} + 972 q^{77} - 1878 q^{78} - 880 q^{79} + 162 q^{81} - 2368 q^{82} + 156 q^{83} + 24 q^{84} - 842 q^{86} + 276 q^{87} - 264 q^{88} - 864 q^{89} - 2198 q^{91} + 2496 q^{92} + 366 q^{93} - 596 q^{94} - 1992 q^{96} + 1042 q^{97} + 3692 q^{98} + 252 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 6 * q^3 + 24 * q^4 - 6 * q^6 + 26 * q^7 - 84 * q^8 + 18 * q^9 + 28 * q^11 + 72 * q^12 + 18 * q^13 + 126 * q^14 + 120 * q^16 - 68 * q^17 - 18 * q^18 + 6 * q^19 + 78 * q^21 + 124 * q^22 + 132 * q^23 - 252 * q^24 - 626 * q^26 + 54 * q^27 + 8 * q^28 + 92 * q^29 + 122 * q^31 - 664 * q^32 + 84 * q^33 - 692 * q^34 + 216 * q^36 - 284 * q^37 - 158 * q^38 + 54 * q^39 + 392 * q^41 + 378 * q^42 + 690 * q^43 + 32 * q^44 - 588 * q^46 - 620 * q^47 + 360 * q^48 + 260 * q^49 - 204 * q^51 + 1432 * q^52 - 848 * q^53 - 54 * q^54 - 180 * q^56 + 18 * q^57 - 1156 * q^58 + 124 * q^59 + 750 * q^61 + 942 * q^62 + 234 * q^63 + 1376 * q^64 + 372 * q^66 - 358 * q^67 + 704 * q^68 + 396 * q^69 + 824 * q^71 - 756 * q^72 - 108 * q^73 + 1196 * q^74 + 376 * q^76 + 972 * q^77 - 1878 * q^78 - 880 * q^79 + 162 * q^81 - 2368 * q^82 + 156 * q^83 + 24 * q^84 - 842 * q^86 + 276 * q^87 - 264 * q^88 - 864 * q^89 - 2198 * q^91 + 2496 * q^92 + 366 * q^93 - 596 * q^94 - 1992 * q^96 + 1042 * q^97 + 3692 * q^98 + 252 * q^99

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