LMFDB - Embedded newform 507.4.a.r.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,4,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, 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("507.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	507.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:	$29.9139683729$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 $ x^10 - 70x^8 + 1645x^6 - 14700x^4 + 44100x^2 - 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.27897$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.27897 q^{2} +3.00000 q^{3} +2.75167 q^{4} -17.5414 q^{5} +9.83692 q^{6} +26.6999 q^{7} -17.2091 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.27897 q^{2} +3.00000 q^{3} +2.75167 q^{4} -17.5414 q^{5} +9.83692 q^{6} +26.6999 q^{7} -17.2091 q^{8} +9.00000 q^{9} -57.5178 q^{10} +21.4026 q^{11} +8.25501 q^{12} +87.5483 q^{14} -52.6242 q^{15} -78.4417 q^{16} +83.9630 q^{17} +29.5108 q^{18} +77.1142 q^{19} -48.2682 q^{20} +80.0997 q^{21} +70.1785 q^{22} +142.119 q^{23} -51.6274 q^{24} +182.701 q^{25} +27.0000 q^{27} +73.4693 q^{28} +134.223 q^{29} -172.553 q^{30} -122.559 q^{31} -119.535 q^{32} +64.2077 q^{33} +275.312 q^{34} -468.354 q^{35} +24.7650 q^{36} +222.587 q^{37} +252.855 q^{38} +301.873 q^{40} -198.321 q^{41} +262.645 q^{42} +154.656 q^{43} +58.8928 q^{44} -157.873 q^{45} +466.006 q^{46} +78.7956 q^{47} -235.325 q^{48} +369.884 q^{49} +599.072 q^{50} +251.889 q^{51} -477.088 q^{53} +88.5323 q^{54} -375.431 q^{55} -459.482 q^{56} +231.342 q^{57} +440.114 q^{58} +42.9282 q^{59} -144.804 q^{60} +496.539 q^{61} -401.869 q^{62} +240.299 q^{63} +235.581 q^{64} +210.535 q^{66} +484.659 q^{67} +231.038 q^{68} +426.358 q^{69} -1535.72 q^{70} -382.432 q^{71} -154.882 q^{72} -193.622 q^{73} +729.858 q^{74} +548.103 q^{75} +212.193 q^{76} +571.447 q^{77} +1049.60 q^{79} +1375.98 q^{80} +81.0000 q^{81} -650.289 q^{82} -861.900 q^{83} +220.408 q^{84} -1472.83 q^{85} +507.112 q^{86} +402.669 q^{87} -368.320 q^{88} -967.645 q^{89} -517.660 q^{90} +391.065 q^{92} -367.678 q^{93} +258.369 q^{94} -1352.69 q^{95} -358.605 q^{96} -591.470 q^{97} +1212.84 q^{98} +192.623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9}+O(q^{10}) $ 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9	$ 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9} + 80 q^{10} + 180 q^{12} - 60 q^{14} + 500 q^{16} + 210 q^{17} + 580 q^{22} - 120 q^{23} + 960 q^{25} + 270 q^{27} + 990 q^{29} + 240 q^{30} - 120 q^{35} + 540 q^{36} + 1380 q^{38} + 2000 q^{40} - 180 q^{42} - 740 q^{43} + 1500 q^{48} + 1550 q^{49} + 630 q^{51} + 330 q^{53} + 520 q^{55} - 5340 q^{56} + 2750 q^{61} - 1560 q^{62} + 3140 q^{64} + 1740 q^{66} + 1200 q^{68} - 360 q^{69} - 4380 q^{74} + 2880 q^{75} + 4320 q^{77} + 1100 q^{79} + 810 q^{81} - 4780 q^{82} + 2970 q^{87} + 6340 q^{88} + 720 q^{90} - 1740 q^{92} + 6460 q^{94} - 2760 q^{95}+O(q^{100}) $ 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9 + 80 * q^10 + 180 * q^12 - 60 * q^14 + 500 * q^16 + 210 * q^17 + 580 * q^22 - 120 * q^23 + 960 * q^25 + 270 * q^27 + 990 * q^29 + 240 * q^30 - 120 * q^35 + 540 * q^36 + 1380 * q^38 + 2000 * q^40 - 180 * q^42 - 740 * q^43 + 1500 * q^48 + 1550 * q^49 + 630 * q^51 + 330 * q^53 + 520 * q^55 - 5340 * q^56 + 2750 * q^61 - 1560 * q^62 + 3140 * q^64 + 1740 * q^66 + 1200 * q^68 - 360 * q^69 - 4380 * q^74 + 2880 * q^75 + 4320 * q^77 + 1100 * q^79 + 810 * q^81 - 4780 * q^82 + 2970 * q^87 + 6340 * q^88 + 720 * q^90 - 1740 * q^92 + 6460 * q^94 - 2760 * q^95

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 $

$2$	3.27897	1.15929	0.579646	−	0.814868i	$-0.303191\pi$
$2$	3.27897	1.15929	0.579646	+	0.814868i	$0.303191\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	2.75167	0.343959
$5$	−17.5414	−1.56895	−0.784476	−	0.620160i	$-0.787068\pi$
$5$	−17.5414	−1.56895	−0.784476	+	0.620160i	$0.787068\pi$
$6$	9.83692	0.669318
$7$	26.6999	1.44166	0.720829	−	0.693112i	$-0.243761\pi$
$7$	26.6999	1.44166	0.720829	+	0.693112i	$0.243761\pi$
$8$	−17.2091	−0.760544
$9$	9.00000	0.333333
$10$	−57.5178	−1.81887
$11$	21.4026	0.586647	0.293324	−	0.956013i	$-0.405239\pi$
$11$	21.4026	0.586647	0.293324	+	0.956013i	$0.405239\pi$
$12$	8.25501	0.198585
$13$	0	0
$13$	0	0
$14$	87.5483	1.67130
$15$	−52.6242	−0.905834
$16$	−78.4417	−1.22565
$17$	83.9630	1.19788	0.598942	−	0.800793i	$-0.295588\pi$
$17$	83.9630	1.19788	0.598942	+	0.800793i	$0.295588\pi$
$18$	29.5108	0.386431
$19$	77.1142	0.931116	0.465558	−	0.885017i	$-0.345854\pi$
$19$	77.1142	0.931116	0.465558	+	0.885017i	$0.345854\pi$
$20$	−48.2682	−0.539654
$21$	80.0997	0.832342
$22$	70.1785	0.680096
$23$	142.119	1.28843	0.644216	−	0.764844i	$-0.277184\pi$
$23$	142.119	1.28843	0.644216	+	0.764844i	$0.277184\pi$
$24$	−51.6274	−0.439100
$25$	182.701	1.46161
$26$	0	0
$27$	27.0000	0.192450
$28$	73.4693	0.495871
$29$	134.223	0.859469	0.429734	−	0.902955i	$-0.358607\pi$
$29$	134.223	0.859469	0.429734	+	0.902955i	$0.358607\pi$
$30$	−172.553	−1.05013
$31$	−122.559	−0.710074	−0.355037	−	0.934852i	$-0.615532\pi$
$31$	−122.559	−0.710074	−0.355037	+	0.934852i	$0.615532\pi$
$32$	−119.535	−0.660344
$33$	64.2077	0.338701
$34$	275.312	1.38870
$35$	−468.354	−2.26189
$36$	24.7650	0.114653
$37$	222.587	0.989003	0.494502	−	0.869177i	$-0.335351\pi$
$37$	222.587	0.989003	0.494502	+	0.869177i	$0.335351\pi$
$38$	252.855	1.07944
$39$	0	0
$40$	301.873	1.19326
$41$	−198.321	−0.755427	−0.377713	−	0.925923i	$-0.623290\pi$
$41$	−198.321	−0.755427	−0.377713	+	0.925923i	$0.623290\pi$
$42$	262.645	0.964928
$43$	154.656	0.548483	0.274242	−	0.961661i	$-0.411573\pi$
$43$	154.656	0.548483	0.274242	+	0.961661i	$0.411573\pi$
$44$	58.8928	0.201782
$45$	−157.873	−0.522984
$46$	466.006	1.49367
$47$	78.7956	0.244543	0.122271	−	0.992497i	$-0.460982\pi$
$47$	78.7956	0.244543	0.122271	+	0.992497i	$0.460982\pi$
$48$	−235.325	−0.707630
$49$	369.884	1.07838
$50$	599.072	1.69443
$51$	251.889	0.691598
$52$	0	0
$53$	−477.088	−1.23647	−0.618237	−	0.785992i	$-0.712153\pi$
$53$	−477.088	−1.23647	−0.618237	+	0.785992i	$0.712153\pi$
$54$	88.5323	0.223106
$55$	−375.431	−0.920421
$56$	−459.482	−1.09644
$57$	231.342	0.537580
$58$	440.114	0.996376
$59$	42.9282	0.0947249	0.0473625	−	0.998878i	$-0.484918\pi$
$59$	42.9282	0.0947249	0.0473625	+	0.998878i	$0.484918\pi$
$60$	−144.804	−0.311570
$61$	496.539	1.04222	0.521109	−	0.853490i	$-0.325519\pi$
$61$	496.539	1.04222	0.521109	+	0.853490i	$0.325519\pi$
$62$	−401.869	−0.823183
$63$	240.299	0.480553
$64$	235.581	0.460119
$65$	0	0
$66$	210.535	0.392653
$67$	484.659	0.883739	0.441869	−	0.897079i	$-0.354315\pi$
$67$	484.659	0.883739	0.441869	+	0.897079i	$0.354315\pi$
$68$	231.038	0.412022
$69$	426.358	0.743876
$70$	−1535.72	−2.62219
$71$	−382.432	−0.639245	−0.319622	−	0.947545i	$-0.603556\pi$
$71$	−382.432	−0.639245	−0.319622	+	0.947545i	$0.603556\pi$
$72$	−154.882	−0.253515
$73$	−193.622	−0.310435	−0.155217	−	0.987880i	$-0.549608\pi$
$73$	−193.622	−0.310435	−0.155217	+	0.987880i	$0.549608\pi$
$74$	729.858	1.14654
$75$	548.103	0.843860
$76$	212.193	0.320265
$77$	571.447	0.845745
$78$	0	0
$79$	1049.60	1.49480	0.747399	−	0.664375i	$-0.231302\pi$
$79$	1049.60	1.49480	0.747399	+	0.664375i	$0.231302\pi$
$80$	1375.98	1.92299
$81$	81.0000	0.111111
$82$	−650.289	−0.875761
$83$	−861.900	−1.13983	−0.569914	−	0.821704i	$-0.693024\pi$
$83$	−861.900	−1.13983	−0.569914	+	0.821704i	$0.693024\pi$
$84$	220.408	0.286291
$85$	−1472.83	−1.87942
$86$	507.112	0.635853
$87$	402.669	0.496215
$88$	−368.320	−0.446171
$89$	−967.645	−1.15247	−0.576237	−	0.817283i	$-0.695479\pi$
$89$	−967.645	−1.15247	−0.576237	+	0.817283i	$0.695479\pi$
$90$	−517.660	−0.606291
$91$	0	0
$92$	391.065	0.443167
$93$	−367.678	−0.409961
$94$	258.369	0.283497
$95$	−1352.69	−1.46088
$96$	−358.605	−0.381250
$97$	−591.470	−0.619120	−0.309560	−	0.950880i	$-0.600182\pi$
$97$	−591.470	−0.619120	−0.309560	+	0.950880i	$0.600182\pi$
$98$	1212.84	1.25016
$99$	192.623	0.195549
$100$	502.733	0.502733
$101$	255.110	0.251331	0.125665	−	0.992073i	$-0.459893\pi$
$101$	255.110	0.251331	0.125665	+	0.992073i	$0.459893\pi$
$102$	825.937	0.801764
$103$	−247.355	−0.236627	−0.118313	−	0.992976i	$-0.537749\pi$
$103$	−247.355	−0.236627	−0.118313	+	0.992976i	$0.537749\pi$
$104$	0	0
$105$	−1405.06	−1.30590
$106$	−1564.36	−1.43343
$107$	683.484	0.617522	0.308761	−	0.951140i	$-0.400086\pi$
$107$	683.484	0.617522	0.308761	+	0.951140i	$0.400086\pi$
$108$	74.2951	0.0661949
$109$	−1697.76	−1.49189	−0.745946	−	0.666006i	$-0.768002\pi$
$109$	−1697.76	−1.49189	−0.745946	+	0.666006i	$0.768002\pi$
$110$	−1231.03	−1.06704
$111$	667.762	0.571001
$112$	−2094.38	−1.76697
$113$	−380.709	−0.316939	−0.158469	−	0.987364i	$-0.550656\pi$
$113$	−380.709	−0.316939	−0.158469	+	0.987364i	$0.550656\pi$
$114$	758.566	0.623212
$115$	−2492.97	−2.02149
$116$	369.337	0.295622
$117$	0	0
$118$	140.760	0.109814
$119$	2241.80	1.72694
$120$	905.618	0.688927
$121$	−872.930	−0.655845
$122$	1628.14	1.20824
$123$	−594.962	−0.436146
$124$	−337.243	−0.244236
$125$	−1012.16	−0.724241
$126$	787.934	0.557101
$127$	123.231	0.0861025	0.0430513	−	0.999073i	$-0.486292\pi$
$127$	123.231	0.0861025	0.0430513	+	0.999073i	$0.486292\pi$
$128$	1728.74	1.19376
$129$	463.967	0.316667
$130$	0	0
$131$	−1218.41	−0.812616	−0.406308	−	0.913736i	$-0.633184\pi$
$131$	−1218.41	−0.812616	−0.406308	+	0.913736i	$0.633184\pi$
$132$	176.678	0.116499
$133$	2058.94	1.34235
$134$	1589.18	1.02451
$135$	−473.618	−0.301945
$136$	−1444.93	−0.911042
$137$	−2728.83	−1.70175	−0.850875	−	0.525369i	$-0.823927\pi$
$137$	−2728.83	−1.70175	−0.850875	+	0.525369i	$0.823927\pi$
$138$	1398.02	0.862370
$139$	3112.78	1.89944	0.949722	−	0.313094i	$-0.101366\pi$
$139$	3112.78	1.89944	0.949722	+	0.313094i	$0.101366\pi$
$140$	−1288.75	−0.777998
$141$	236.387	0.141187
$142$	−1253.99	−0.741071
$143$	0	0
$144$	−705.975	−0.408550
$145$	−2354.46	−1.34846
$146$	−634.881	−0.359885
$147$	1109.65	0.622603
$148$	612.487	0.340176
$149$	−1370.57	−0.753567	−0.376784	−	0.926301i	$-0.622970\pi$
$149$	−1370.57	−0.753567	−0.376784	+	0.926301i	$0.622970\pi$
$150$	1797.22	0.978280
$151$	2847.56	1.53464	0.767321	−	0.641263i	$-0.221589\pi$
$151$	2847.56	1.53464	0.767321	+	0.641263i	$0.221589\pi$
$152$	−1327.07	−0.708154
$153$	755.667	0.399294
$154$	1873.76	0.980466
$155$	2149.86	1.11407
$156$	0	0
$157$	3354.00	1.70496	0.852479	−	0.522761i	$-0.175098\pi$
$157$	3354.00	1.70496	0.852479	+	0.522761i	$0.175098\pi$
$158$	3441.61	1.73291
$159$	−1431.26	−0.713878
$160$	2096.81	1.03605
$161$	3794.57	1.85748
$162$	265.597	0.128810
$163$	2196.18	1.05533	0.527664	−	0.849453i	$-0.323068\pi$
$163$	2196.18	1.05533	0.527664	+	0.849453i	$0.323068\pi$
$164$	−545.713	−0.259836
$165$	−1126.29	−0.531405
$166$	−2826.15	−1.32139
$167$	−912.535	−0.422839	−0.211419	−	0.977395i	$-0.567809\pi$
$167$	−912.535	−0.422839	−0.211419	+	0.977395i	$0.567809\pi$
$168$	−1378.45	−0.633033
$169$	0	0
$170$	−4829.37	−2.17880
$171$	694.027	0.310372
$172$	425.562	0.188656
$173$	899.636	0.395364	0.197682	−	0.980266i	$-0.436659\pi$
$173$	899.636	0.395364	0.197682	+	0.980266i	$0.436659\pi$
$174$	1320.34	0.575258
$175$	4878.10	2.10714
$176$	−1678.85	−0.719025
$177$	128.784	0.0546895
$178$	−3172.88	−1.33605
$179$	313.278	0.130813	0.0654064	−	0.997859i	$-0.479166\pi$
$179$	313.278	0.130813	0.0654064	+	0.997859i	$0.479166\pi$
$180$	−434.413	−0.179885
$181$	−2745.06	−1.12728	−0.563642	−	0.826019i	$-0.690600\pi$
$181$	−2745.06	−1.12728	−0.563642	+	0.826019i	$0.690600\pi$
$182$	0	0
$183$	1489.62	0.601725
$184$	−2445.75	−0.979909
$185$	−3904.50	−1.55170
$186$	−1205.61	−0.475265
$187$	1797.02	0.702735
$188$	216.819	0.0841126
$189$	720.897	0.277447
$190$	−4435.44	−1.69358
$191$	89.8679	0.0340451	0.0170226	−	0.999855i	$-0.494581\pi$
$191$	89.8679	0.0340451	0.0170226	+	0.999855i	$0.494581\pi$
$192$	706.743	0.265650
$193$	−848.954	−0.316627	−0.158314	−	0.987389i	$-0.550606\pi$
$193$	−848.954	−0.316627	−0.158314	+	0.987389i	$0.550606\pi$
$194$	−1939.41	−0.717741
$195$	0	0
$196$	1017.80	0.370918
$197$	−4343.86	−1.57100	−0.785501	−	0.618860i	$-0.787595\pi$
$197$	−4343.86	−1.57100	−0.785501	+	0.618860i	$0.787595\pi$
$198$	631.606	0.226699
$199$	−3328.41	−1.18565	−0.592825	−	0.805331i	$-0.701988\pi$
$199$	−3328.41	−1.18565	−0.592825	+	0.805331i	$0.701988\pi$
$200$	−3144.13	−1.11162
$201$	1453.98	0.510227
$202$	836.499	0.291366
$203$	3583.74	1.23906
$204$	693.115	0.237881
$205$	3478.83	1.18523
$206$	−811.069	−0.274320
$207$	1279.07	0.429477
$208$	0	0
$209$	1650.44	0.546236
$210$	−4607.16	−1.51392
$211$	−4599.88	−1.50080	−0.750401	−	0.660983i	$-0.770139\pi$
$211$	−4599.88	−1.50080	−0.750401	+	0.660983i	$0.770139\pi$
$212$	−1312.79	−0.425296
$213$	−1147.30	−0.369068
$214$	2241.13	0.715889
$215$	−2712.88	−0.860544
$216$	−464.647	−0.146367
$217$	−3272.32	−1.02368
$218$	−5566.92	−1.72954
$219$	−580.866	−0.179230
$220$	−1033.06	−0.316587
$221$	0	0
$222$	2189.57	0.661958
$223$	2529.58	0.759611	0.379806	−	0.925066i	$-0.375991\pi$
$223$	2529.58	0.759611	0.379806	+	0.925066i	$0.375991\pi$
$224$	−3191.57	−0.951991
$225$	1644.31	0.487203
$226$	−1248.33	−0.367425
$227$	−37.2670	−0.0108965	−0.00544823	−	0.999985i	$-0.501734\pi$
$227$	−37.2670	−0.0108965	−0.00544823	+	0.999985i	$0.501734\pi$
$228$	636.578	0.184905
$229$	4094.45	1.18152	0.590762	−	0.806846i	$-0.298827\pi$
$229$	4094.45	1.18152	0.590762	+	0.806846i	$0.298827\pi$
$230$	−8174.40	−2.34349
$231$	1714.34	0.488291
$232$	−2309.86	−0.653664
$233$	1466.04	0.412205	0.206103	−	0.978530i	$-0.433922\pi$
$233$	1466.04	0.412205	0.206103	+	0.978530i	$0.433922\pi$
$234$	0	0
$235$	−1382.19	−0.383676
$236$	118.124	0.0325815
$237$	3148.80	0.863023
$238$	7350.81	2.00203
$239$	5520.53	1.49412	0.747058	−	0.664759i	$-0.231466\pi$
$239$	5520.53	1.49412	0.747058	+	0.664759i	$0.231466\pi$
$240$	4127.93	1.11024
$241$	−2665.63	−0.712483	−0.356241	−	0.934394i	$-0.615942\pi$
$241$	−2665.63	−0.712483	−0.356241	+	0.934394i	$0.615942\pi$
$242$	−2862.31	−0.760316
$243$	243.000	0.0641500
$244$	1366.31	0.358480
$245$	−6488.30	−1.69193
$246$	−1950.87	−0.505621
$247$	0	0
$248$	2109.14	0.540042
$249$	−2585.70	−0.658080
$250$	−3318.84	−0.839607
$251$	1579.21	0.397127	0.198564	−	0.980088i	$-0.436372\pi$
$251$	1579.21	0.397127	0.198564	+	0.980088i	$0.436372\pi$
$252$	661.224	0.165290
$253$	3041.72	0.755855
$254$	404.073	0.0998180
$255$	−4418.49	−1.08508
$256$	3783.86	0.923794
$257$	−2663.91	−0.646577	−0.323288	−	0.946300i	$-0.604788\pi$
$257$	−2663.91	−0.646577	−0.323288	+	0.946300i	$0.604788\pi$
$258$	1521.34	0.367110
$259$	5943.06	1.42581
$260$	0	0
$261$	1208.01	0.286490
$262$	−3995.12	−0.942059
$263$	−2436.93	−0.571360	−0.285680	−	0.958325i	$-0.592219\pi$
$263$	−2436.93	−0.571360	−0.285680	+	0.958325i	$0.592219\pi$
$264$	−1104.96	−0.257597
$265$	8368.80	1.93997
$266$	6751.21	1.55618
$267$	−2902.94	−0.665381
$268$	1333.62	0.303970
$269$	−2683.18	−0.608165	−0.304083	−	0.952646i	$-0.598350\pi$
$269$	−2683.18	−0.608165	−0.304083	+	0.952646i	$0.598350\pi$
$270$	−1552.98	−0.350042
$271$	3857.14	0.864592	0.432296	−	0.901732i	$-0.357704\pi$
$271$	3857.14	0.864592	0.432296	+	0.901732i	$0.357704\pi$
$272$	−6586.20	−1.46819
$273$	0	0
$274$	−8947.76	−1.97282
$275$	3910.27	0.857448
$276$	1173.20	0.255863
$277$	1104.91	0.239666	0.119833	−	0.992794i	$-0.461764\pi$
$277$	1104.91	0.239666	0.119833	+	0.992794i	$0.461764\pi$
$278$	10206.7	2.20201
$279$	−1103.03	−0.236691
$280$	8059.97	1.72027
$281$	−4982.58	−1.05778	−0.528890	−	0.848691i	$-0.677391\pi$
$281$	−4982.58	−1.05778	−0.528890	+	0.848691i	$0.677391\pi$
$282$	775.106	0.163677
$283$	2584.86	0.542947	0.271473	−	0.962446i	$-0.412489\pi$
$283$	2584.86	0.542947	0.271473	+	0.962446i	$0.412489\pi$
$284$	−1052.33	−0.219874
$285$	−4058.07	−0.843437
$286$	0	0
$287$	−5295.14	−1.08907
$288$	−1075.82	−0.220115
$289$	2136.78	0.434924
$290$	−7720.22	−1.56326
$291$	−1774.41	−0.357449
$292$	−532.784	−0.106777
$293$	92.5482	0.0184530	0.00922649	−	0.999957i	$-0.497063\pi$
$293$	92.5482	0.0184530	0.00922649	+	0.999957i	$0.497063\pi$
$294$	3638.52	0.721779
$295$	−753.020	−0.148619
$296$	−3830.54	−0.752180
$297$	577.870	0.112900
$298$	−4494.07	−0.873605
$299$	0	0
$300$	1508.20	0.290253
$301$	4129.29	0.790726
$302$	9337.07	1.77910
$303$	765.330	0.145106
$304$	−6048.96	−1.14122
$305$	−8709.99	−1.63519
$306$	2477.81	0.462899
$307$	3979.46	0.739803	0.369901	−	0.929071i	$-0.379391\pi$
$307$	3979.46	0.739803	0.369901	+	0.929071i	$0.379391\pi$
$308$	1572.43	0.290901
$309$	−742.064	−0.136617
$310$	7049.34	1.29153
$311$	3450.91	0.629207	0.314604	−	0.949223i	$-0.398128\pi$
$311$	3450.91	0.629207	0.314604	+	0.949223i	$0.398128\pi$
$312$	0	0
$313$	−6189.03	−1.11765	−0.558825	−	0.829285i	$-0.688748\pi$
$313$	−6189.03	−1.11765	−0.558825	+	0.829285i	$0.688748\pi$
$314$	10997.7	1.97654
$315$	−4215.18	−0.753964
$316$	2888.15	0.514149
$317$	−5437.78	−0.963459	−0.481729	−	0.876320i	$-0.659991\pi$
$317$	−5437.78	−0.963459	−0.481729	+	0.876320i	$0.659991\pi$
$318$	−4693.08	−0.827593
$319$	2872.72	0.504205
$320$	−4132.42	−0.721904
$321$	2050.45	0.356527
$322$	12442.3	2.15336
$323$	6474.73	1.11537
$324$	222.885	0.0382176
$325$	0	0
$326$	7201.23	1.22343
$327$	−5093.29	−0.861344
$328$	3412.93	0.574535
$329$	2103.83	0.352547
$330$	−3693.09	−0.616054
$331$	−6626.64	−1.10040	−0.550201	−	0.835032i	$-0.685449\pi$
$331$	−6626.64	−1.10040	−0.550201	+	0.835032i	$0.685449\pi$
$332$	−2371.66	−0.392054
$333$	2003.29	0.329668
$334$	−2992.18	−0.490194
$335$	−8501.60	−1.38654
$336$	−6283.15	−1.02016
$337$	−5538.63	−0.895277	−0.447638	−	0.894215i	$-0.647735\pi$
$337$	−5538.63	−0.895277	−0.447638	+	0.894215i	$0.647735\pi$
$338$	0	0
$339$	−1142.13	−0.182985
$340$	−4052.74	−0.646443
$341$	−2623.08	−0.416563
$342$	2275.70	0.359812
$343$	717.813	0.112998
$344$	−2661.49	−0.417146
$345$	−7478.92	−1.16711
$346$	2949.88	0.458343
$347$	9398.94	1.45407	0.727034	−	0.686602i	$-0.240898\pi$
$347$	9398.94	1.45407	0.727034	+	0.686602i	$0.240898\pi$
$348$	1108.01	0.170677
$349$	−5757.33	−0.883045	−0.441522	−	0.897250i	$-0.645561\pi$
$349$	−5757.33	−0.883045	−0.441522	+	0.897250i	$0.645561\pi$
$350$	15995.2	2.44279
$351$	0	0
$352$	−2558.36	−0.387389
$353$	−3457.82	−0.521364	−0.260682	−	0.965425i	$-0.583947\pi$
$353$	−3457.82	−0.521364	−0.260682	+	0.965425i	$0.583947\pi$
$354$	422.281	0.0634011
$355$	6708.40	1.00294
$356$	−2662.64	−0.396403
$357$	6725.41	0.997049
$358$	1027.23	0.151650
$359$	7168.96	1.05394	0.526968	−	0.849885i	$-0.323329\pi$
$359$	7168.96	1.05394	0.526968	+	0.849885i	$0.323329\pi$
$360$	2716.85	0.397752
$361$	−912.407	−0.133023
$362$	−9000.97	−1.30685
$363$	−2618.79	−0.378652
$364$	0	0
$365$	3396.40	0.487057
$366$	4884.41	0.697575
$367$	3910.11	0.556147	0.278073	−	0.960560i	$-0.410304\pi$
$367$	3910.11	0.556147	0.278073	+	0.960560i	$0.410304\pi$
$368$	−11148.1	−1.57917
$369$	−1784.89	−0.251809
$370$	−12802.7	−1.79887
$371$	−12738.2	−1.78257
$372$	−1011.73	−0.141010
$373$	11377.6	1.57938	0.789691	−	0.613505i	$-0.210241\pi$
$373$	11377.6	1.57938	0.789691	+	0.613505i	$0.210241\pi$
$374$	5892.39	0.814675
$375$	−3036.47	−0.418141
$376$	−1356.00	−0.185986
$377$	0	0
$378$	2363.80	0.321643
$379$	4032.22	0.546494	0.273247	−	0.961944i	$-0.411902\pi$
$379$	4032.22	0.546494	0.273247	+	0.961944i	$0.411902\pi$
$380$	−3722.16	−0.502481
$381$	369.694	0.0497113
$382$	294.675	0.0394682
$383$	1990.96	0.265622	0.132811	−	0.991141i	$-0.457600\pi$
$383$	1990.96	0.265622	0.132811	+	0.991141i	$0.457600\pi$
$384$	5186.23	0.689216
$385$	−10024.0	−1.32693
$386$	−2783.70	−0.367063
$387$	1391.90	0.182828
$388$	−1627.53	−0.212952
$389$	−11122.4	−1.44969	−0.724846	−	0.688911i	$-0.758089\pi$
$389$	−11122.4	−1.44969	−0.724846	+	0.688911i	$0.758089\pi$
$390$	0	0
$391$	11932.8	1.54339
$392$	−6365.39	−0.820155
$393$	−3655.22	−0.469164
$394$	−14243.4	−1.82125
$395$	−18411.4	−2.34527
$396$	530.035	0.0672608
$397$	−10778.1	−1.36256	−0.681282	−	0.732021i	$-0.738577\pi$
$397$	−10778.1	−1.36256	−0.681282	+	0.732021i	$0.738577\pi$
$398$	−10913.8	−1.37452
$399$	6176.82	0.775007
$400$	−14331.4	−1.79142
$401$	4711.58	0.586746	0.293373	−	0.955998i	$-0.405222\pi$
$401$	4711.58	0.586746	0.293373	+	0.955998i	$0.405222\pi$
$402$	4767.55	0.591502
$403$	0	0
$404$	701.978	0.0864473
$405$	−1420.85	−0.174328
$406$	11751.0	1.43643
$407$	4763.94	0.580196
$408$	−4334.79	−0.525991
$409$	−1184.78	−0.143236	−0.0716179	−	0.997432i	$-0.522816\pi$
$409$	−1184.78	−0.143236	−0.0716179	+	0.997432i	$0.522816\pi$
$410$	11407.0	1.37403
$411$	−8186.49	−0.982505
$412$	−680.638	−0.0813899
$413$	1146.18	0.136561
$414$	4194.05	0.497890
$415$	15118.9	1.78834
$416$	0	0
$417$	9338.35	1.09664
$418$	5411.75	0.633248
$419$	−6168.30	−0.719191	−0.359596	−	0.933108i	$-0.617085\pi$
$419$	−6168.30	−0.719191	−0.359596	+	0.933108i	$0.617085\pi$
$420$	−3866.26	−0.449177
$421$	10328.8	1.19571	0.597857	−	0.801603i	$-0.296019\pi$
$421$	10328.8	1.19571	0.597857	+	0.801603i	$0.296019\pi$
$422$	−15082.9	−1.73987
$423$	709.160	0.0815143
$424$	8210.27	0.940392
$425$	15340.1	1.75084
$426$	−3761.96	−0.427858
$427$	13257.5	1.50252
$428$	1880.72	0.212402
$429$	0	0
$430$	−8895.46	−0.997622
$431$	11312.5	1.26427	0.632137	−	0.774857i	$-0.282178\pi$
$431$	11312.5	1.26427	0.632137	+	0.774857i	$0.282178\pi$
$432$	−2117.93	−0.235877
$433$	−10475.7	−1.16266	−0.581331	−	0.813667i	$-0.697468\pi$
$433$	−10475.7	−1.16266	−0.581331	+	0.813667i	$0.697468\pi$
$434$	−10729.8	−1.18675
$435$	−7063.38	−0.778536
$436$	−4671.68	−0.513149
$437$	10959.4	1.19968
$438$	−1904.64	−0.207779
$439$	−2040.62	−0.221853	−0.110926	−	0.993829i	$-0.535382\pi$
$439$	−2040.62	−0.221853	−0.110926	+	0.993829i	$0.535382\pi$
$440$	6460.85	0.700020
$441$	3328.96	0.359460
$442$	0	0
$443$	−4089.28	−0.438572	−0.219286	−	0.975661i	$-0.570373\pi$
$443$	−4089.28	−0.438572	−0.219286	+	0.975661i	$0.570373\pi$
$444$	1837.46	0.196401
$445$	16973.9	1.80818
$446$	8294.43	0.880611
$447$	−4111.71	−0.435072
$448$	6289.99	0.663335
$449$	15217.9	1.59951	0.799753	−	0.600330i	$-0.204964\pi$
$449$	15217.9	1.59951	0.799753	+	0.600330i	$0.204964\pi$
$450$	5391.65	0.564810
$451$	−4244.58	−0.443169
$452$	−1047.58	−0.109014
$453$	8542.67	0.886026
$454$	−122.197	−0.0126322
$455$	0	0
$456$	−3981.20	−0.408853
$457$	−876.316	−0.0896988	−0.0448494	−	0.998994i	$-0.514281\pi$
$457$	−876.316	−0.0896988	−0.0448494	+	0.998994i	$0.514281\pi$
$458$	13425.6	1.36973
$459$	2267.00	0.230533
$460$	−6859.84	−0.695308
$461$	16293.4	1.64611	0.823057	−	0.567959i	$-0.192267\pi$
$461$	16293.4	1.64611	0.823057	+	0.567959i	$0.192267\pi$
$462$	5621.27	0.566072
$463$	−11704.8	−1.17488	−0.587438	−	0.809269i	$-0.699863\pi$
$463$	−11704.8	−1.17488	−0.587438	+	0.809269i	$0.699863\pi$
$464$	−10528.7	−1.05341
$465$	6449.59	0.643209
$466$	4807.12	0.477866
$467$	−15616.1	−1.54738	−0.773688	−	0.633567i	$-0.781590\pi$
$467$	−15616.1	−1.54738	−0.773688	+	0.633567i	$0.781590\pi$
$468$	0	0
$469$	12940.3	1.27405
$470$	−4532.15	−0.444792
$471$	10062.0	0.984358
$472$	−738.757	−0.0720424
$473$	3310.03	0.321766
$474$	10324.8	1.00050
$475$	14088.8	1.36093
$476$	6168.70	0.593996
$477$	−4293.79	−0.412158
$478$	18101.7	1.73212
$479$	−10376.0	−0.989755	−0.494877	−	0.868963i	$-0.664787\pi$
$479$	−10376.0	−0.989755	−0.494877	+	0.868963i	$0.664787\pi$
$480$	6290.44	0.598163
$481$	0	0
$482$	−8740.53	−0.825976
$483$	11383.7	1.07242
$484$	−2402.01	−0.225584
$485$	10375.2	0.971369
$486$	796.791	0.0743686
$487$	3994.27	0.371658	0.185829	−	0.982582i	$-0.440503\pi$
$487$	3994.27	0.371658	0.185829	+	0.982582i	$0.440503\pi$
$488$	−8545.01	−0.792652
$489$	6588.55	0.609294
$490$	−21275.0	−1.96144
$491$	12267.3	1.12753	0.563763	−	0.825936i	$-0.309353\pi$
$491$	12267.3	1.12753	0.563763	+	0.825936i	$0.309353\pi$
$492$	−1637.14	−0.150016
$493$	11269.8	1.02954
$494$	0	0
$495$	−3378.88	−0.306807
$496$	9613.75	0.870303
$497$	−10210.9	−0.921573
$498$	−8478.44	−0.762907
$499$	3578.76	0.321056	0.160528	−	0.987031i	$-0.448680\pi$
$499$	3578.76	0.321056	0.160528	+	0.987031i	$0.448680\pi$
$500$	−2785.12	−0.249109
$501$	−2737.61	−0.244126
$502$	5178.19	0.460386
$503$	−1296.82	−0.114955	−0.0574774	−	0.998347i	$-0.518306\pi$
$503$	−1296.82	−0.114955	−0.0574774	+	0.998347i	$0.518306\pi$
$504$	−4135.34	−0.365482
$505$	−4474.99	−0.394325
$506$	9973.72	0.876257
$507$	0	0
$508$	339.092	0.0296157
$509$	−4728.60	−0.411771	−0.205886	−	0.978576i	$-0.566007\pi$
$509$	−4728.60	−0.411771	−0.205886	+	0.978576i	$0.566007\pi$
$510$	−14488.1	−1.25793
$511$	−5169.69	−0.447541
$512$	−1422.78	−0.122810
$513$	2082.08	0.179193
$514$	−8734.90	−0.749571
$515$	4338.95	0.371256
$516$	1276.68	0.108920
$517$	1686.43	0.143460
$518$	19487.1	1.65293
$519$	2698.91	0.228264
$520$	0	0
$521$	−9220.74	−0.775370	−0.387685	−	0.921792i	$-0.626725\pi$
$521$	−9220.74	−0.775370	−0.387685	+	0.921792i	$0.626725\pi$
$522$	3961.03	0.332125
$523$	−12102.7	−1.01188	−0.505939	−	0.862569i	$-0.668854\pi$
$523$	−12102.7	−1.01188	−0.505939	+	0.862569i	$0.668854\pi$
$524$	−3352.65	−0.279506
$525$	14634.3	1.21656
$526$	−7990.64	−0.662373
$527$	−10290.4	−0.850585
$528$	−5036.56	−0.415129
$529$	8030.91	0.660057
$530$	27441.1	2.24899
$531$	386.353	0.0315750
$532$	5665.52	0.461713
$533$	0	0
$534$	−9518.65	−0.771371
$535$	−11989.3	−0.968862
$536$	−8340.56	−0.672122
$537$	939.833	0.0755248
$538$	−8798.08	−0.705041
$539$	7916.48	0.632629
$540$	−1303.24	−0.103857
$541$	12801.3	1.01732	0.508659	−	0.860968i	$-0.330141\pi$
$541$	12801.3	1.01732	0.508659	+	0.860968i	$0.330141\pi$
$542$	12647.5	1.00231
$543$	−8235.17	−0.650838
$544$	−10036.5	−0.791015
$545$	29781.2	2.34071
$546$	0	0
$547$	400.693	0.0313207	0.0156603	−	0.999877i	$-0.495015\pi$
$547$	400.693	0.0313207	0.0156603	+	0.999877i	$0.495015\pi$
$548$	−7508.84	−0.585331
$549$	4468.85	0.347406
$550$	12821.7	0.994033
$551$	10350.5	0.800265
$552$	−7337.25	−0.565751
$553$	28024.2	2.15499
$554$	3622.96	0.277843
$555$	−11713.5	−0.895873
$556$	8565.35	0.653330
$557$	14475.5	1.10116	0.550582	−	0.834781i	$-0.314406\pi$
$557$	14475.5	1.10116	0.550582	+	0.834781i	$0.314406\pi$
$558$	−3616.82	−0.274394
$559$	0	0
$560$	36738.5	2.77229
$561$	5391.07	0.405724
$562$	−16337.8	−1.22628
$563$	−14776.4	−1.10613	−0.553063	−	0.833139i	$-0.686541\pi$
$563$	−14776.4	−1.10613	−0.553063	+	0.833139i	$0.686541\pi$
$564$	650.458	0.0485625
$565$	6678.17	0.497261
$566$	8475.68	0.629434
$567$	2162.69	0.160184
$568$	6581.33	0.486173
$569$	−6868.88	−0.506078	−0.253039	−	0.967456i	$-0.581430\pi$
$569$	−6868.88	−0.506078	−0.253039	+	0.967456i	$0.581430\pi$
$570$	−13306.3	−0.977790
$571$	3011.00	0.220677	0.110338	−	0.993894i	$-0.464807\pi$
$571$	3011.00	0.220677	0.110338	+	0.993894i	$0.464807\pi$
$572$	0	0
$573$	269.604	0.0196559
$574$	−17362.6	−1.26255
$575$	25965.4	1.88318
$576$	2120.23	0.153373
$577$	−23106.6	−1.66714	−0.833572	−	0.552411i	$-0.813708\pi$
$577$	−23106.6	−1.66714	−0.833572	+	0.552411i	$0.813708\pi$
$578$	7006.45	0.504204
$579$	−2546.86	−0.182805
$580$	−6478.70	−0.463816
$581$	−23012.6	−1.64324
$582$	−5818.24	−0.414388
$583$	−10210.9	−0.725374
$584$	3332.07	0.236099
$585$	0	0
$586$	303.463	0.0213924
$587$	3024.81	0.212687	0.106343	−	0.994329i	$-0.466086\pi$
$587$	3024.81	0.212687	0.106343	+	0.994329i	$0.466086\pi$
$588$	3053.40	0.214150
$589$	−9451.05	−0.661161
$590$	−2469.13	−0.172293
$591$	−13031.6	−0.907019
$592$	−17460.1	−1.21217
$593$	−6396.07	−0.442926	−0.221463	−	0.975169i	$-0.571083\pi$
$593$	−6396.07	−0.442926	−0.221463	+	0.975169i	$0.571083\pi$
$594$	1894.82	0.130884
$595$	−39324.4	−2.70948
$596$	−3771.36	−0.259196
$597$	−9985.22	−0.684536
$598$	0	0
$599$	12095.9	0.825084	0.412542	−	0.910939i	$-0.364641\pi$
$599$	12095.9	0.825084	0.412542	+	0.910939i	$0.364641\pi$
$600$	−9432.38	−0.641792
$601$	−11816.5	−0.802005	−0.401003	−	0.916077i	$-0.631338\pi$
$601$	−11816.5	−0.802005	−0.401003	+	0.916077i	$0.631338\pi$
$602$	13539.8	0.916682
$603$	4361.93	0.294580
$604$	7835.54	0.527853
$605$	15312.4	1.02899
$606$	2509.50	0.168220
$607$	−25164.0	−1.68266	−0.841329	−	0.540523i	$-0.818226\pi$
$607$	−25164.0	−1.68266	−0.841329	+	0.540523i	$0.818226\pi$
$608$	−9217.85	−0.614857
$609$	10751.2	0.715372
$610$	−28559.8	−1.89566
$611$	0	0
$612$	2079.35	0.137341
$613$	19583.0	1.29030	0.645148	−	0.764058i	$-0.276796\pi$
$613$	19583.0	1.29030	0.645148	+	0.764058i	$0.276796\pi$
$614$	13048.5	0.857648
$615$	10436.5	0.684292
$616$	−9834.10	−0.643226
$617$	19677.1	1.28390	0.641952	−	0.766745i	$-0.278125\pi$
$617$	19677.1	1.28390	0.641952	+	0.766745i	$0.278125\pi$
$618$	−2433.21	−0.158379
$619$	−4394.05	−0.285318	−0.142659	−	0.989772i	$-0.545565\pi$
$619$	−4394.05	−0.285318	−0.142659	+	0.989772i	$0.545565\pi$
$620$	5915.71	0.383194
$621$	3837.22	0.247959
$622$	11315.5	0.729435
$623$	−25836.0	−1.66147
$624$	0	0
$625$	−5082.96	−0.325310
$626$	−20293.7	−1.29568
$627$	4951.32	0.315370
$628$	9229.10	0.586435
$629$	18689.1	1.18471
$630$	−13821.5	−0.874065
$631$	−23887.7	−1.50706	−0.753529	−	0.657415i	$-0.771650\pi$
$631$	−23887.7	−1.50706	−0.753529	+	0.657415i	$0.771650\pi$
$632$	−18062.7	−1.13686
$633$	−13799.7	−0.866488
$634$	−17830.4	−1.11693
$635$	−2161.65	−0.135091
$636$	−3938.37	−0.245545
$637$	0	0
$638$	9419.57	0.584521
$639$	−3441.89	−0.213082
$640$	−30324.6	−1.87295
$641$	−5443.62	−0.335429	−0.167714	−	0.985836i	$-0.553639\pi$
$641$	−5443.62	−0.335429	−0.167714	+	0.985836i	$0.553639\pi$
$642$	6723.38	0.413318
$643$	5839.00	0.358115	0.179057	−	0.983839i	$-0.442695\pi$
$643$	5839.00	0.358115	0.179057	+	0.983839i	$0.442695\pi$
$644$	10441.4	0.638896
$645$	−8138.64	−0.496835
$646$	21230.5	1.29304
$647$	8708.86	0.529182	0.264591	−	0.964361i	$-0.414763\pi$
$647$	8708.86	0.529182	0.264591	+	0.964361i	$0.414763\pi$
$648$	−1393.94	−0.0845049
$649$	918.773	0.0555701
$650$	0	0
$651$	−9816.96	−0.591024
$652$	6043.17	0.362989
$653$	2794.93	0.167495	0.0837475	−	0.996487i	$-0.473311\pi$
$653$	2794.93	0.167495	0.0837475	+	0.996487i	$0.473311\pi$
$654$	−16700.8	−0.998550
$655$	21372.6	1.27495
$656$	15556.6	0.925890
$657$	−1742.60	−0.103478
$658$	6898.41	0.408705
$659$	31389.9	1.85550	0.927752	−	0.373197i	$-0.121738\pi$
$659$	31389.9	1.85550	0.927752	+	0.373197i	$0.121738\pi$
$660$	−3099.19	−0.182781
$661$	−20597.2	−1.21201	−0.606005	−	0.795461i	$-0.707229\pi$
$661$	−20597.2	−1.21201	−0.606005	+	0.795461i	$0.707229\pi$
$662$	−21728.6	−1.27569
$663$	0	0
$664$	14832.5	0.866889
$665$	−36116.7	−2.10608
$666$	6568.72	0.382181
$667$	19075.7	1.10737
$668$	−2511.00	−0.145439
$669$	7588.74	0.438562
$670$	−27876.5	−1.60741
$671$	10627.2	0.611414
$672$	−9574.72	−0.549632
$673$	−17935.8	−1.02730	−0.513651	−	0.857999i	$-0.671707\pi$
$673$	−17935.8	−1.02730	−0.513651	+	0.857999i	$0.671707\pi$
$674$	−18161.0	−1.03789
$675$	4932.93	0.281287
$676$	0	0
$677$	−24104.0	−1.36838	−0.684188	−	0.729305i	$-0.739843\pi$
$677$	−24104.0	−1.36838	−0.684188	+	0.729305i	$0.739843\pi$
$678$	−3745.00	−0.212133
$679$	−15792.2	−0.892560
$680$	25346.1	1.42938
$681$	−111.801	−0.00629107
$682$	−8601.02	−0.482918
$683$	6744.25	0.377835	0.188918	−	0.981993i	$-0.439502\pi$
$683$	6744.25	0.377835	0.188918	+	0.981993i	$0.439502\pi$
$684$	1909.73	0.106755
$685$	47867.5	2.66996
$686$	2353.69	0.130998
$687$	12283.3	0.682153
$688$	−12131.5	−0.672249
$689$	0	0
$690$	−24523.2	−1.35302
$691$	30844.4	1.69809	0.849043	−	0.528323i	$-0.177179\pi$
$691$	30844.4	1.69809	0.849043	+	0.528323i	$0.177179\pi$
$692$	2475.50	0.135989
$693$	5143.02	0.281915
$694$	30818.9	1.68569
$695$	−54602.6	−2.98014
$696$	−6929.59	−0.377393
$697$	−16651.6	−0.904913
$698$	−18878.1	−1.02371
$699$	4398.13	0.237987
$700$	13422.9	0.724769
$701$	−21007.6	−1.13188	−0.565940	−	0.824447i	$-0.691486\pi$
$701$	−21007.6	−1.13188	−0.565940	+	0.824447i	$0.691486\pi$
$702$	0	0
$703$	17164.6	0.920877
$704$	5042.04	0.269928
$705$	−4146.56	−0.221515
$706$	−11338.1	−0.604413
$707$	6811.41	0.362333
$708$	354.372	0.0188109
$709$	14763.4	0.782017	0.391008	−	0.920387i	$-0.372126\pi$
$709$	14763.4	0.782017	0.391008	+	0.920387i	$0.372126\pi$
$710$	21996.7	1.16271
$711$	9446.39	0.498266
$712$	16652.3	0.876507
$713$	−17418.0	−0.914882
$714$	22052.4	1.15587
$715$	0	0
$716$	862.037	0.0449942
$717$	16561.6	0.862628
$718$	23506.8	1.22182
$719$	−26186.3	−1.35825	−0.679126	−	0.734022i	$-0.737641\pi$
$719$	−26186.3	−1.35825	−0.679126	+	0.734022i	$0.737641\pi$
$720$	12383.8	0.640996
$721$	−6604.34	−0.341135
$722$	−2991.76	−0.154213
$723$	−7996.89	−0.411352
$724$	−7553.49	−0.387739
$725$	24522.7	1.25621
$726$	−8586.94	−0.438969
$727$	20044.0	1.02254	0.511272	−	0.859419i	$-0.329175\pi$
$727$	20044.0	1.02254	0.511272	+	0.859419i	$0.329175\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	11136.7	0.564641
$731$	12985.4	0.657019
$732$	4098.93	0.206968
$733$	−25555.5	−1.28774	−0.643871	−	0.765134i	$-0.722673\pi$
$733$	−25555.5	−1.28774	−0.643871	+	0.765134i	$0.722673\pi$
$734$	12821.1	0.644737
$735$	−19464.9	−0.976834
$736$	−16988.2	−0.850809
$737$	10372.9	0.518443
$738$	−5852.60	−0.291920
$739$	−11108.5	−0.552953	−0.276477	−	0.961021i	$-0.589167\pi$
$739$	−11108.5	−0.552953	−0.276477	+	0.961021i	$0.589167\pi$
$740$	−10743.9	−0.533720
$741$	0	0
$742$	−41768.2	−2.06652
$743$	−28188.2	−1.39182	−0.695911	−	0.718128i	$-0.744999\pi$
$743$	−28188.2	−1.39182	−0.695911	+	0.718128i	$0.744999\pi$
$744$	6327.42	0.311793
$745$	24041.7	1.18231
$746$	37306.8	1.83096
$747$	−7757.10	−0.379943
$748$	4944.82	0.241712
$749$	18248.9	0.890256
$750$	−9956.51	−0.484747
$751$	17176.6	0.834596	0.417298	−	0.908770i	$-0.362977\pi$
$751$	17176.6	0.834596	0.417298	+	0.908770i	$0.362977\pi$
$752$	−6180.86	−0.299724
$753$	4737.63	0.229281
$754$	0	0
$755$	−49950.2	−2.40778
$756$	1983.67	0.0954304
$757$	−4409.96	−0.211734	−0.105867	−	0.994380i	$-0.533762\pi$
$757$	−4409.96	−0.211734	−0.105867	+	0.994380i	$0.533762\pi$
$758$	13221.5	0.633546
$759$	9125.16	0.436393
$760$	23278.6	1.11106
$761$	32443.6	1.54544	0.772721	−	0.634746i	$-0.218895\pi$
$761$	32443.6	1.54544	0.772721	+	0.634746i	$0.218895\pi$
$762$	1212.22	0.0576300
$763$	−45330.1	−2.15080
$764$	247.287	0.0117101
$765$	−13255.5	−0.626473
$766$	6528.30	0.307934
$767$	0	0
$768$	11351.6	0.533353
$769$	−31994.1	−1.50031	−0.750155	−	0.661263i	$-0.770021\pi$
$769$	−31994.1	−1.50031	−0.750155	+	0.661263i	$0.770021\pi$
$770$	−32868.4	−1.53830
$771$	−7991.73	−0.373301
$772$	−2336.04	−0.108907
$773$	−8979.39	−0.417809	−0.208904	−	0.977936i	$-0.566990\pi$
$773$	−8979.39	−0.417809	−0.208904	+	0.977936i	$0.566990\pi$
$774$	4564.01	0.211951
$775$	−22391.7	−1.03785
$776$	10178.7	0.470868
$777$	17829.2	0.823189
$778$	−36470.2	−1.68062
$779$	−15293.3	−0.703390
$780$	0	0
$781$	−8185.04	−0.375011
$782$	39127.2	1.78924
$783$	3624.02	0.165405
$784$	−29014.4	−1.32172
$785$	−58833.9	−2.67500
$786$	−11985.4	−0.543898
$787$	−12570.5	−0.569366	−0.284683	−	0.958622i	$-0.591888\pi$
$787$	−12570.5	−0.569366	−0.284683	+	0.958622i	$0.591888\pi$
$788$	−11952.9	−0.540360
$789$	−7310.80	−0.329875
$790$	−60370.6	−2.71885
$791$	−10164.9	−0.456917
$792$	−3314.88	−0.148724
$793$	0	0
$794$	−35341.2	−1.57961
$795$	25106.4	1.12004
$796$	−9158.67	−0.407815
$797$	37863.3	1.68280	0.841398	−	0.540416i	$-0.181733\pi$
$797$	37863.3	1.68280	0.841398	+	0.540416i	$0.181733\pi$
$798$	20253.6	0.898460
$799$	6615.91	0.292934
$800$	−21839.2	−0.965165
$801$	−8708.81	−0.384158
$802$	15449.2	0.680210
$803$	−4144.01	−0.182116
$804$	4000.86	0.175497
$805$	−66562.1	−2.91429
$806$	0	0
$807$	−8049.54	−0.351124
$808$	−4390.22	−0.191148
$809$	2503.79	0.108812	0.0544058	−	0.998519i	$-0.482674\pi$
$809$	2503.79	0.108812	0.0544058	+	0.998519i	$0.482674\pi$
$810$	−4658.94	−0.202097
$811$	−5409.55	−0.234223	−0.117112	−	0.993119i	$-0.537364\pi$
$811$	−5409.55	−0.234223	−0.117112	+	0.993119i	$0.537364\pi$
$812$	9861.27	0.426186
$813$	11571.4	0.499172
$814$	15620.8	0.672617
$815$	−38524.2	−1.65576
$816$	−19758.6	−0.847658
$817$	11926.1	0.510702
$818$	−3884.85	−0.166052
$819$	0	0
$820$	9572.58	0.407669
$821$	−31381.6	−1.33401	−0.667007	−	0.745051i	$-0.732425\pi$
$821$	−31381.6	−1.33401	−0.667007	+	0.745051i	$0.732425\pi$
$822$	−26843.3	−1.13901
$823$	−33046.1	−1.39965	−0.699827	−	0.714312i	$-0.746740\pi$
$823$	−33046.1	−1.39965	−0.699827	+	0.714312i	$0.746740\pi$
$824$	4256.76	0.179965
$825$	11730.8	0.495048
$826$	3758.29	0.158314
$827$	−33653.7	−1.41506	−0.707529	−	0.706684i	$-0.750190\pi$
$827$	−33653.7	−1.41506	−0.707529	+	0.706684i	$0.750190\pi$
$828$	3519.59	0.147722
$829$	12898.5	0.540390	0.270195	−	0.962806i	$-0.412912\pi$
$829$	12898.5	0.540390	0.270195	+	0.962806i	$0.412912\pi$
$830$	49574.6	2.07320
$831$	3314.72	0.138371
$832$	0	0
$833$	31056.6	1.29177
$834$	30620.2	1.27133
$835$	16007.2	0.663414
$836$	4541.47	0.187883
$837$	−3309.10	−0.136654
$838$	−20225.7	−0.833753
$839$	−395.829	−0.0162879	−0.00814395	−	0.999967i	$-0.502592\pi$
$839$	−395.829	−0.0162879	−0.00814395	+	0.999967i	$0.502592\pi$
$840$	24179.9	0.993197
$841$	−6373.17	−0.261313
$842$	33867.9	1.38618
$843$	−14947.7	−0.610709
$844$	−12657.4	−0.516214
$845$	0	0
$846$	2325.32	0.0944989
$847$	−23307.1	−0.945505
$848$	37423.6	1.51548
$849$	7754.57	0.313470
$850$	50299.9	2.02973
$851$	31634.0	1.27426
$852$	−3156.98	−0.126944
$853$	−21248.9	−0.852930	−0.426465	−	0.904504i	$-0.640241\pi$
$853$	−21248.9	−0.852930	−0.426465	+	0.904504i	$0.640241\pi$
$854$	43471.1	1.74186
$855$	−12174.2	−0.486958
$856$	−11762.2	−0.469653
$857$	−9920.37	−0.395418	−0.197709	−	0.980261i	$-0.563350\pi$
$857$	−9920.37	−0.395418	−0.197709	+	0.980261i	$0.563350\pi$
$858$	0	0
$859$	20946.3	0.831990	0.415995	−	0.909367i	$-0.363433\pi$
$859$	20946.3	0.831990	0.415995	+	0.909367i	$0.363433\pi$
$860$	−7464.95	−0.295991
$861$	−15885.4	−0.628774
$862$	37093.2	1.46566
$863$	−11271.4	−0.444594	−0.222297	−	0.974979i	$-0.571355\pi$
$863$	−11271.4	−0.444594	−0.222297	+	0.974979i	$0.571355\pi$
$864$	−3227.45	−0.127083
$865$	−15780.9	−0.620308
$866$	−34349.7	−1.34786
$867$	6410.34	0.251103
$868$	−9004.34	−0.352105
$869$	22464.1	0.876920
$870$	−23160.7	−0.902551
$871$	0	0
$872$	29217.0	1.13465
$873$	−5323.23	−0.206373
$874$	35935.6	1.39078
$875$	−27024.5	−1.04411
$876$	−1598.35	−0.0616476
$877$	−9436.36	−0.363333	−0.181667	−	0.983360i	$-0.558149\pi$
$877$	−9436.36	−0.363333	−0.181667	+	0.983360i	$0.558149\pi$
$878$	−6691.13	−0.257192
$879$	277.645	0.0106538
$880$	29449.5	1.12811
$881$	−20343.0	−0.777949	−0.388974	−	0.921249i	$-0.627171\pi$
$881$	−20343.0	−0.777949	−0.388974	+	0.921249i	$0.627171\pi$
$882$	10915.6	0.416719
$883$	46521.9	1.77303	0.886515	−	0.462699i	$-0.153119\pi$
$883$	46521.9	1.77303	0.886515	+	0.462699i	$0.153119\pi$
$884$	0	0
$885$	−2259.06	−0.0858051
$886$	−13408.6	−0.508433
$887$	−19955.1	−0.755384	−0.377692	−	0.925931i	$-0.623282\pi$
$887$	−19955.1	−0.755384	−0.377692	+	0.925931i	$0.623282\pi$
$888$	−11491.6	−0.434272
$889$	3290.27	0.124130
$890$	55656.8	2.09620
$891$	1733.61	0.0651830
$892$	6960.57	0.261275
$893$	6076.25	0.227698
$894$	−13482.2	−0.504376
$895$	−5495.33	−0.205239
$896$	46157.3	1.72099
$897$	0	0
$898$	49899.1	1.85429
$899$	−16450.3	−0.610286
$900$	4524.60	0.167578
$901$	−40057.7	−1.48115
$902$	−13917.9	−0.513762
$903$	12387.9	0.456526
$904$	6551.67	0.241046
$905$	48152.2	1.76866
$906$	28011.2	1.02716
$907$	−2653.95	−0.0971587	−0.0485793	−	0.998819i	$-0.515469\pi$
$907$	−2653.95	−0.0971587	−0.0485793	+	0.998819i	$0.515469\pi$
$908$	−102.546	−0.00374793
$909$	2295.99	0.0837769
$910$	0	0
$911$	1797.50	0.0653720	0.0326860	−	0.999466i	$-0.489594\pi$
$911$	1797.50	0.0653720	0.0326860	+	0.999466i	$0.489594\pi$
$912$	−18146.9	−0.658885
$913$	−18446.9	−0.668677
$914$	−2873.42	−0.103987
$915$	−26130.0	−0.944077
$916$	11266.6	0.406395
$917$	−32531.3	−1.17151
$918$	7433.43	0.267255
$919$	−48642.0	−1.74597	−0.872987	−	0.487743i	$-0.837820\pi$
$919$	−48642.0	−1.74597	−0.872987	+	0.487743i	$0.837820\pi$
$920$	42901.9	1.53743
$921$	11938.4	0.427125
$922$	53425.6	1.90833
$923$	0	0
$924$	4717.30	0.167952
$925$	40666.9	1.44554
$926$	−38379.7	−1.36202
$927$	−2226.19	−0.0788756
$928$	−16044.4	−0.567545
$929$	−37745.3	−1.33303	−0.666513	−	0.745493i	$-0.732214\pi$
$929$	−37745.3	−1.33303	−0.666513	+	0.745493i	$0.732214\pi$
$930$	21148.0	0.745668
$931$	28523.3	1.00410
$932$	4034.07	0.141782
$933$	10352.7	0.363273
$934$	−51204.6	−1.79386
$935$	−31522.3	−1.10256
$936$	0	0
$937$	2705.50	0.0943273	0.0471637	−	0.998887i	$-0.484982\pi$
$937$	2705.50	0.0943273	0.0471637	+	0.998887i	$0.484982\pi$
$938$	42431.0	1.47700
$939$	−18567.1	−0.645276
$940$	−3803.32	−0.131969
$941$	−5189.27	−0.179772	−0.0898860	−	0.995952i	$-0.528650\pi$
$941$	−5189.27	−0.179772	−0.0898860	+	0.995952i	$0.528650\pi$
$942$	32993.0	1.14116
$943$	−28185.2	−0.973316
$944$	−3367.36	−0.116100
$945$	−12645.6	−0.435301
$946$	10853.5	0.373021
$947$	72.2711	0.00247993	0.00123997	−	0.999999i	$-0.499605\pi$
$947$	72.2711	0.00247993	0.00123997	+	0.999999i	$0.499605\pi$
$948$	8664.45	0.296844
$949$	0	0
$950$	46196.9	1.57771
$951$	−16313.4	−0.556253
$952$	−38579.5	−1.31341
$953$	44695.1	1.51922	0.759609	−	0.650380i	$-0.225390\pi$
$953$	44695.1	1.51922	0.759609	+	0.650380i	$0.225390\pi$
$954$	−14079.2	−0.477811
$955$	−1576.41	−0.0534151
$956$	15190.7	0.513914
$957$	8618.16	0.291103
$958$	−34022.7	−1.14742
$959$	−72859.5	−2.45334
$960$	−12397.3	−0.416792
$961$	−14770.2	−0.495795
$962$	0	0
$963$	6151.35	0.205841
$964$	−7334.93	−0.245065
$965$	14891.8	0.496772
$966$	37326.9	1.24324
$967$	17936.9	0.596496	0.298248	−	0.954488i	$-0.403598\pi$
$967$	17936.9	0.596496	0.298248	+	0.954488i	$0.403598\pi$
$968$	15022.4	0.498799
$969$	19424.2	0.643958
$970$	34020.1	1.12610
$971$	−40914.6	−1.35223	−0.676113	−	0.736798i	$-0.736337\pi$
$971$	−40914.6	−1.35223	−0.676113	+	0.736798i	$0.736337\pi$
$972$	668.656	0.0220650
$973$	83111.0	2.73835
$974$	13097.1	0.430860
$975$	0	0
$976$	−38949.3	−1.27740
$977$	−24118.1	−0.789770	−0.394885	−	0.918731i	$-0.629216\pi$
$977$	−24118.1	−0.789770	−0.394885	+	0.918731i	$0.629216\pi$
$978$	21603.7	0.706350
$979$	−20710.1	−0.676096
$980$	−17853.6	−0.581953
$981$	−15279.9	−0.497297
$982$	40224.2	1.30713
$983$	2928.61	0.0950235	0.0475118	−	0.998871i	$-0.484871\pi$
$983$	2928.61	0.0950235	0.0475118	+	0.998871i	$0.484871\pi$
$984$	10238.8	0.331708
$985$	76197.5	2.46483
$986$	36953.3	1.19354
$987$	6311.50	0.203543
$988$	0	0
$989$	21979.6	0.706683
$990$	−11079.3	−0.355679
$991$	49809.9	1.59663	0.798317	−	0.602238i	$-0.205724\pi$
$991$	49809.9	1.59663	0.798317	+	0.602238i	$0.205724\pi$
$992$	14650.1	0.468893
$993$	−19879.9	−0.635318
$994$	−33481.3	−1.06837
$995$	58384.9	1.86023
$996$	−7114.99	−0.226352
$997$	−41151.7	−1.30721	−0.653604	−	0.756837i	$-0.726744\pi$
$997$	−41151.7	−1.30721	−0.653604	+	0.756837i	$0.726744\pi$
$998$	11734.7	0.372198
$999$	6009.86	0.190334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.r.1.8		10
3.2	odd	2		1521.4.a.bk.1.3		10
13.2	odd	12		39.4.j.c.4.4	✓	10
13.5	odd	4		507.4.b.i.337.3		10
13.7	odd	12		39.4.j.c.10.4	yes	10
13.8	odd	4		507.4.b.i.337.8		10
13.12	even	2	inner	507.4.a.r.1.3		10
39.2	even	12		117.4.q.e.82.2		10
39.20	even	12		117.4.q.e.10.2		10
39.38	odd	2		1521.4.a.bk.1.8		10
52.7	even	12		624.4.bv.h.49.1		10
52.15	even	12		624.4.bv.h.433.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.4	✓	10	13.2	odd	12
39.4.j.c.10.4	yes	10	13.7	odd	12
117.4.q.e.10.2		10	39.20	even	12
117.4.q.e.82.2		10	39.2	even	12
507.4.a.r.1.3		10	13.12	even	2	inner
507.4.a.r.1.8		10	1.1	even	1	trivial
507.4.b.i.337.3		10	13.5	odd	4
507.4.b.i.337.8		10	13.8	odd	4
624.4.bv.h.49.1		10	52.7	even	12
624.4.bv.h.433.5		10	52.15	even	12
1521.4.a.bk.1.3		10	3.2	odd	2
1521.4.a.bk.1.8		10	39.38	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q+3.27897 q^{2} +3.00000 q^{3} +2.75167 q^{4} -17.5414 q^{5} +9.83692 q^{6} +26.6999 q^{7} -17.2091 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.27897 q^{2} +3.00000 q^{3} +2.75167 q^{4} -17.5414 q^{5} +9.83692 q^{6} +26.6999 q^{7} -17.2091 q^{8} +9.00000 q^{9} -57.5178 q^{10} +21.4026 q^{11} +8.25501 q^{12} +87.5483 q^{14} -52.6242 q^{15} -78.4417 q^{16} +83.9630 q^{17} +29.5108 q^{18} +77.1142 q^{19} -48.2682 q^{20} +80.0997 q^{21} +70.1785 q^{22} +142.119 q^{23} -51.6274 q^{24} +182.701 q^{25} +27.0000 q^{27} +73.4693 q^{28} +134.223 q^{29} -172.553 q^{30} -122.559 q^{31} -119.535 q^{32} +64.2077 q^{33} +275.312 q^{34} -468.354 q^{35} +24.7650 q^{36} +222.587 q^{37} +252.855 q^{38} +301.873 q^{40} -198.321 q^{41} +262.645 q^{42} +154.656 q^{43} +58.8928 q^{44} -157.873 q^{45} +466.006 q^{46} +78.7956 q^{47} -235.325 q^{48} +369.884 q^{49} +599.072 q^{50} +251.889 q^{51} -477.088 q^{53} +88.5323 q^{54} -375.431 q^{55} -459.482 q^{56} +231.342 q^{57} +440.114 q^{58} +42.9282 q^{59} -144.804 q^{60} +496.539 q^{61} -401.869 q^{62} +240.299 q^{63} +235.581 q^{64} +210.535 q^{66} +484.659 q^{67} +231.038 q^{68} +426.358 q^{69} -1535.72 q^{70} -382.432 q^{71} -154.882 q^{72} -193.622 q^{73} +729.858 q^{74} +548.103 q^{75} +212.193 q^{76} +571.447 q^{77} +1049.60 q^{79} +1375.98 q^{80} +81.0000 q^{81} -650.289 q^{82} -861.900 q^{83} +220.408 q^{84} -1472.83 q^{85} +507.112 q^{86} +402.669 q^{87} -368.320 q^{88} -967.645 q^{89} -517.660 q^{90} +391.065 q^{92} -367.678 q^{93} +258.369 q^{94} -1352.69 q^{95} -358.605 q^{96} -591.470 q^{97} +1212.84 q^{98} +192.623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9}+O(q^{10}) \) 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9	\( 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9} + 80 q^{10} + 180 q^{12} - 60 q^{14} + 500 q^{16} + 210 q^{17} + 580 q^{22} - 120 q^{23} + 960 q^{25} + 270 q^{27} + 990 q^{29} + 240 q^{30} - 120 q^{35} + 540 q^{36} + 1380 q^{38} + 2000 q^{40} - 180 q^{42} - 740 q^{43} + 1500 q^{48} + 1550 q^{49} + 630 q^{51} + 330 q^{53} + 520 q^{55} - 5340 q^{56} + 2750 q^{61} - 1560 q^{62} + 3140 q^{64} + 1740 q^{66} + 1200 q^{68} - 360 q^{69} - 4380 q^{74} + 2880 q^{75} + 4320 q^{77} + 1100 q^{79} + 810 q^{81} - 4780 q^{82} + 2970 q^{87} + 6340 q^{88} + 720 q^{90} - 1740 q^{92} + 6460 q^{94} - 2760 q^{95}+O(q^{100}) \) 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9 + 80 * q^10 + 180 * q^12 - 60 * q^14 + 500 * q^16 + 210 * q^17 + 580 * q^22 - 120 * q^23 + 960 * q^25 + 270 * q^27 + 990 * q^29 + 240 * q^30 - 120 * q^35 + 540 * q^36 + 1380 * q^38 + 2000 * q^40 - 180 * q^42 - 740 * q^43 + 1500 * q^48 + 1550 * q^49 + 630 * q^51 + 330 * q^53 + 520 * q^55 - 5340 * q^56 + 2750 * q^61 - 1560 * q^62 + 3140 * q^64 + 1740 * q^66 + 1200 * q^68 - 360 * q^69 - 4380 * q^74 + 2880 * q^75 + 4320 * q^77 + 1100 * q^79 + 810 * q^81 - 4780 * q^82 + 2970 * q^87 + 6340 * q^88 + 720 * q^90 - 1740 * q^92 + 6460 * q^94 - 2760 * q^95

Introduction

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