LMFDB - Embedded newform 825.4.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.47528.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 26x - 22 $ x^3 - x^2 - 26*x - 22
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.97123$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.97123 q^{2} -3.00000 q^{3} +16.7131 q^{4} +14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.97123 q^{2} -3.00000 q^{3} +16.7131 q^{4} +14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +11.0000 q^{11} -50.1393 q^{12} -24.5738 q^{13} +27.2610 q^{14} +81.6231 q^{16} +59.3687 q^{17} -44.7411 q^{18} +5.89234 q^{19} +16.4513 q^{21} -54.6835 q^{22} +68.4570 q^{23} +129.945 q^{24} +122.162 q^{26} -27.0000 q^{27} -91.6506 q^{28} -265.022 q^{29} -196.554 q^{31} -59.2482 q^{32} -33.0000 q^{33} -295.135 q^{34} +150.418 q^{36} -166.575 q^{37} -29.2922 q^{38} +73.7214 q^{39} +424.101 q^{41} -81.7830 q^{42} +177.351 q^{43} +183.844 q^{44} -340.316 q^{46} -141.148 q^{47} -244.869 q^{48} -312.928 q^{49} -178.106 q^{51} -410.704 q^{52} +339.828 q^{53} +134.223 q^{54} +237.528 q^{56} -17.6770 q^{57} +1317.48 q^{58} +416.784 q^{59} +662.146 q^{61} +977.115 q^{62} -49.3538 q^{63} -358.448 q^{64} +164.051 q^{66} -313.713 q^{67} +992.235 q^{68} -205.371 q^{69} -153.693 q^{71} -389.834 q^{72} -153.866 q^{73} +828.084 q^{74} +98.4793 q^{76} -60.3213 q^{77} -366.486 q^{78} +403.000 q^{79} +81.0000 q^{81} -2108.30 q^{82} +652.313 q^{83} +274.952 q^{84} -881.650 q^{86} +795.065 q^{87} -476.463 q^{88} +1226.77 q^{89} +134.757 q^{91} +1144.13 q^{92} +589.662 q^{93} +701.677 q^{94} +177.745 q^{96} -959.746 q^{97} +1555.64 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	$ 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} + 33 q^{11} - 90 q^{12} - 114 q^{13} - 68 q^{14} + 178 q^{16} + 104 q^{17} + 18 q^{18} - 58 q^{19} + 30 q^{21} + 22 q^{22} - 120 q^{23} + 54 q^{24} - 120 q^{26} - 81 q^{27} - 676 q^{28} - 220 q^{29} + 248 q^{31} + 258 q^{32} - 99 q^{33} - 80 q^{34} + 270 q^{36} - 838 q^{37} - 600 q^{38} + 342 q^{39} + 156 q^{41} + 204 q^{42} - 122 q^{43} + 330 q^{44} - 1256 q^{46} - 504 q^{47} - 534 q^{48} + 279 q^{49} - 312 q^{51} - 520 q^{52} - 282 q^{53} - 54 q^{54} - 1644 q^{56} + 174 q^{57} + 1644 q^{58} + 548 q^{59} + 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} - 66 q^{66} + 428 q^{67} + 1704 q^{68} + 360 q^{69} - 912 q^{71} - 162 q^{72} - 618 q^{73} - 1612 q^{74} - 2752 q^{76} - 110 q^{77} + 360 q^{78} - 542 q^{79} + 243 q^{81} - 3372 q^{82} + 2028 q^{84} - 1548 q^{86} + 660 q^{87} - 198 q^{88} + 790 q^{89} - 772 q^{91} - 1912 q^{92} - 744 q^{93} - 424 q^{94} - 774 q^{96} - 2074 q^{97} + 3978 q^{98} + 297 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 + 33 * q^11 - 90 * q^12 - 114 * q^13 - 68 * q^14 + 178 * q^16 + 104 * q^17 + 18 * q^18 - 58 * q^19 + 30 * q^21 + 22 * q^22 - 120 * q^23 + 54 * q^24 - 120 * q^26 - 81 * q^27 - 676 * q^28 - 220 * q^29 + 248 * q^31 + 258 * q^32 - 99 * q^33 - 80 * q^34 + 270 * q^36 - 838 * q^37 - 600 * q^38 + 342 * q^39 + 156 * q^41 + 204 * q^42 - 122 * q^43 + 330 * q^44 - 1256 * q^46 - 504 * q^47 - 534 * q^48 + 279 * q^49 - 312 * q^51 - 520 * q^52 - 282 * q^53 - 54 * q^54 - 1644 * q^56 + 174 * q^57 + 1644 * q^58 + 548 * q^59 + 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 - 66 * q^66 + 428 * q^67 + 1704 * q^68 + 360 * q^69 - 912 * q^71 - 162 * q^72 - 618 * q^73 - 1612 * q^74 - 2752 * q^76 - 110 * q^77 + 360 * q^78 - 542 * q^79 + 243 * q^81 - 3372 * q^82 + 2028 * q^84 - 1548 * q^86 + 660 * q^87 - 198 * q^88 + 790 * q^89 - 772 * q^91 - 1912 * q^92 - 744 * q^93 - 424 * q^94 - 774 * q^96 - 2074 * q^97 + 3978 * q^98 + 297 * 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 $

$2$	−4.97123	−1.75759	−0.878797	−	0.477195i	$-0.841653\pi$
$2$	−4.97123	−1.75759	−0.878797	+	0.477195i	$0.841653\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	16.7131	2.08914
$5$	0	0
$5$	0	0
$6$	14.9137	1.01475
$7$	−5.48376	−0.296095	−0.148048	−	0.988980i	$-0.547299\pi$
$7$	−5.48376	−0.296095	−0.148048	+	0.988980i	$0.547299\pi$
$8$	−43.3148	−1.91426
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−50.1393	−1.20616
$13$	−24.5738	−0.524272	−0.262136	−	0.965031i	$-0.584427\pi$
$13$	−24.5738	−0.524272	−0.262136	+	0.965031i	$0.584427\pi$
$14$	27.2610	0.520415
$15$	0	0
$16$	81.6231	1.27536
$17$	59.3687	0.847001	0.423501	−	0.905896i	$-0.360801\pi$
$17$	59.3687	0.847001	0.423501	+	0.905896i	$0.360801\pi$
$18$	−44.7411	−0.585865
$19$	5.89234	0.0711471	0.0355736	−	0.999367i	$-0.488674\pi$
$19$	5.89234	0.0711471	0.0355736	+	0.999367i	$0.488674\pi$
$20$	0	0
$21$	16.4513	0.170951
$22$	−54.6835	−0.529935
$23$	68.4570	0.620621	0.310310	−	0.950635i	$-0.399567\pi$
$23$	68.4570	0.620621	0.310310	+	0.950635i	$0.399567\pi$
$24$	129.945	1.10520
$25$	0	0
$26$	122.162	0.921458
$27$	−27.0000	−0.192450
$28$	−91.6506	−0.618584
$29$	−265.022	−1.69701	−0.848505	−	0.529187i	$-0.822497\pi$
$29$	−265.022	−1.69701	−0.848505	+	0.529187i	$0.822497\pi$
$30$	0	0
$31$	−196.554	−1.13878	−0.569389	−	0.822068i	$-0.692820\pi$
$31$	−196.554	−1.13878	−0.569389	+	0.822068i	$0.692820\pi$
$32$	−59.2482	−0.327303
$33$	−33.0000	−0.174078
$34$	−295.135	−1.48868
$35$	0	0
$36$	150.418	0.696379
$37$	−166.575	−0.740131	−0.370065	−	0.929006i	$-0.620665\pi$
$37$	−166.575	−0.740131	−0.370065	+	0.929006i	$0.620665\pi$
$38$	−29.2922	−0.125048
$39$	73.7214	0.302689
$40$	0	0
$41$	424.101	1.61545	0.807725	−	0.589559i	$-0.200699\pi$
$41$	424.101	1.61545	0.807725	+	0.589559i	$0.200699\pi$
$42$	−81.7830	−0.300462
$43$	177.351	0.628970	0.314485	−	0.949262i	$-0.398168\pi$
$43$	177.351	0.628970	0.314485	+	0.949262i	$0.398168\pi$
$44$	183.844	0.629899
$45$	0	0
$46$	−340.316	−1.09080
$47$	−141.148	−0.438053	−0.219026	−	0.975719i	$-0.570288\pi$
$47$	−141.148	−0.438053	−0.219026	+	0.975719i	$0.570288\pi$
$48$	−244.869	−0.736330
$49$	−312.928	−0.912328
$50$	0	0
$51$	−178.106	−0.489016
$52$	−410.704	−1.09528
$53$	339.828	0.880736	0.440368	−	0.897817i	$-0.354848\pi$
$53$	339.828	0.880736	0.440368	+	0.897817i	$0.354848\pi$
$54$	134.223	0.338249
$55$	0	0
$56$	237.528	0.566804
$57$	−17.6770	−0.0410768
$58$	1317.48	2.98266
$59$	416.784	0.919672	0.459836	−	0.888004i	$-0.347908\pi$
$59$	416.784	0.919672	0.459836	+	0.888004i	$0.347908\pi$
$60$	0	0
$61$	662.146	1.38982	0.694911	−	0.719096i	$-0.255444\pi$
$61$	662.146	1.38982	0.694911	+	0.719096i	$0.255444\pi$
$62$	977.115	2.00151
$63$	−49.3538	−0.0986984
$64$	−358.448	−0.700094
$65$	0	0
$66$	164.051	0.305958
$67$	−313.713	−0.572032	−0.286016	−	0.958225i	$-0.592331\pi$
$67$	−313.713	−0.572032	−0.286016	+	0.958225i	$0.592331\pi$
$68$	992.235	1.76950
$69$	−205.371	−0.358316
$70$	0	0
$71$	−153.693	−0.256902	−0.128451	−	0.991716i	$-0.541000\pi$
$71$	−153.693	−0.256902	−0.128451	+	0.991716i	$0.541000\pi$
$72$	−389.834	−0.638088
$73$	−153.866	−0.246694	−0.123347	−	0.992364i	$-0.539363\pi$
$73$	−153.866	−0.246694	−0.123347	+	0.992364i	$0.539363\pi$
$74$	828.084	1.30085
$75$	0	0
$76$	98.4793	0.148636
$77$	−60.3213	−0.0892760
$78$	−366.486	−0.532004
$79$	403.000	0.573938	0.286969	−	0.957940i	$-0.407352\pi$
$79$	403.000	0.573938	0.286969	+	0.957940i	$0.407352\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−2108.30	−2.83931
$83$	652.313	0.862659	0.431329	−	0.902195i	$-0.358045\pi$
$83$	652.313	0.862659	0.431329	+	0.902195i	$0.358045\pi$
$84$	274.952	0.357139
$85$	0	0
$86$	−881.650	−1.10547
$87$	795.065	0.979769
$88$	−476.463	−0.577172
$89$	1226.77	1.46109	0.730545	−	0.682864i	$-0.239266\pi$
$89$	1226.77	1.46109	0.730545	+	0.682864i	$0.239266\pi$
$90$	0	0
$91$	134.757	0.155234
$92$	1144.13	1.29656
$93$	589.662	0.657474
$94$	701.677	0.769919
$95$	0	0
$96$	177.745	0.188969
$97$	−959.746	−1.00461	−0.502306	−	0.864690i	$-0.667515\pi$
$97$	−959.746	−1.00461	−0.502306	+	0.864690i	$0.667515\pi$
$98$	1555.64	1.60350
$99$	99.0000	0.100504
$100$	0	0
$101$	−1258.52	−1.23988	−0.619939	−	0.784650i	$-0.712843\pi$
$101$	−1258.52	−1.23988	−0.619939	+	0.784650i	$0.712843\pi$
$102$	885.406	0.859492
$103$	493.175	0.471786	0.235893	−	0.971779i	$-0.424198\pi$
$103$	493.175	0.471786	0.235893	+	0.971779i	$0.424198\pi$
$104$	1064.41	1.00360
$105$	0	0
$106$	−1689.36	−1.54798
$107$	1099.05	0.992983	0.496492	−	0.868042i	$-0.334621\pi$
$107$	1099.05	0.992983	0.496492	+	0.868042i	$0.334621\pi$
$108$	−451.254	−0.402055
$109$	1275.04	1.12043	0.560216	−	0.828347i	$-0.310718\pi$
$109$	1275.04	1.12043	0.560216	+	0.828347i	$0.310718\pi$
$110$	0	0
$111$	499.726	0.427315
$112$	−447.601	−0.377628
$113$	946.433	0.787902	0.393951	−	0.919131i	$-0.371108\pi$
$113$	946.433	0.787902	0.393951	+	0.919131i	$0.371108\pi$
$114$	87.8765	0.0721964
$115$	0	0
$116$	−4429.34	−3.54529
$117$	−221.164	−0.174757
$118$	−2071.93	−1.61641
$119$	−325.563	−0.250793
$120$	0	0
$121$	121.000	0.0909091
$122$	−3291.68	−2.44274
$123$	−1272.30	−0.932681
$124$	−3285.03	−2.37907
$125$	0	0
$126$	245.349	0.173472
$127$	−2260.77	−1.57962	−0.789808	−	0.613354i	$-0.789820\pi$
$127$	−2260.77	−1.57962	−0.789808	+	0.613354i	$0.789820\pi$
$128$	2255.91	1.55778
$129$	−532.052	−0.363136
$130$	0	0
$131$	−57.1277	−0.0381013	−0.0190507	−	0.999819i	$-0.506064\pi$
$131$	−57.1277	−0.0381013	−0.0190507	+	0.999819i	$0.506064\pi$
$132$	−551.533	−0.363672
$133$	−32.3122	−0.0210663
$134$	1559.54	1.00540
$135$	0	0
$136$	−2571.54	−1.62138
$137$	−1919.27	−1.19689	−0.598447	−	0.801162i	$-0.704215\pi$
$137$	−1919.27	−1.19689	−0.598447	+	0.801162i	$0.704215\pi$
$138$	1020.95	0.629774
$139$	−1690.46	−1.03153	−0.515766	−	0.856729i	$-0.672493\pi$
$139$	−1690.46	−1.03153	−0.515766	+	0.856729i	$0.672493\pi$
$140$	0	0
$141$	423.443	0.252910
$142$	764.044	0.451529
$143$	−270.312	−0.158074
$144$	734.608	0.425120
$145$	0	0
$146$	764.904	0.433588
$147$	938.785	0.526733
$148$	−2783.99	−1.54624
$149$	−2077.88	−1.14246	−0.571231	−	0.820789i	$-0.693534\pi$
$149$	−2077.88	−1.14246	−0.571231	+	0.820789i	$0.693534\pi$
$150$	0	0
$151$	2711.16	1.46113	0.730566	−	0.682842i	$-0.239256\pi$
$151$	2711.16	1.46113	0.730566	+	0.682842i	$0.239256\pi$
$152$	−255.226	−0.136194
$153$	534.318	0.282334
$154$	299.871	0.156911
$155$	0	0
$156$	1232.11	0.632359
$157$	−2341.23	−1.19013	−0.595066	−	0.803677i	$-0.702874\pi$
$157$	−2341.23	−1.19013	−0.595066	+	0.803677i	$0.702874\pi$
$158$	−2003.41	−1.00875
$159$	−1019.48	−0.508493
$160$	0	0
$161$	−375.402	−0.183763
$162$	−402.669	−0.195288
$163$	−3523.01	−1.69291	−0.846453	−	0.532464i	$-0.821266\pi$
$163$	−3523.01	−1.69291	−0.846453	+	0.532464i	$0.821266\pi$
$164$	7088.05	3.37490
$165$	0	0
$166$	−3242.80	−1.51620
$167$	−4011.90	−1.85898	−0.929492	−	0.368842i	$-0.879754\pi$
$167$	−4011.90	−1.85898	−0.929492	+	0.368842i	$0.879754\pi$
$168$	−712.584	−0.327244
$169$	−1593.13	−0.725138
$170$	0	0
$171$	53.0310	0.0237157
$172$	2964.08	1.31400
$173$	−3325.30	−1.46137	−0.730687	−	0.682713i	$-0.760800\pi$
$173$	−3325.30	−1.46137	−0.730687	+	0.682713i	$0.760800\pi$
$174$	−3952.45	−1.72204
$175$	0	0
$176$	897.854	0.384536
$177$	−1250.35	−0.530973
$178$	−6098.54	−2.56800
$179$	−26.6350	−0.0111217	−0.00556087	−	0.999985i	$-0.501770\pi$
$179$	−26.6350	−0.0111217	−0.00556087	+	0.999985i	$0.501770\pi$
$180$	0	0
$181$	1934.25	0.794320	0.397160	−	0.917749i	$-0.369996\pi$
$181$	1934.25	0.794320	0.397160	+	0.917749i	$0.369996\pi$
$182$	−669.906	−0.272839
$183$	−1986.44	−0.802414
$184$	−2965.21	−1.18803
$185$	0	0
$186$	−2931.34	−1.15557
$187$	653.055	0.255380
$188$	−2359.01	−0.915153
$189$	148.061	0.0569835
$190$	0	0
$191$	−3341.59	−1.26591	−0.632956	−	0.774188i	$-0.718158\pi$
$191$	−3341.59	−1.26591	−0.632956	+	0.774188i	$0.718158\pi$
$192$	1075.34	0.404200
$193$	1293.97	0.482600	0.241300	−	0.970451i	$-0.422426\pi$
$193$	1293.97	0.482600	0.241300	+	0.970451i	$0.422426\pi$
$194$	4771.12	1.76570
$195$	0	0
$196$	−5230.01	−1.90598
$197$	2301.17	0.832240	0.416120	−	0.909310i	$-0.363390\pi$
$197$	2301.17	0.832240	0.416120	+	0.909310i	$0.363390\pi$
$198$	−492.152	−0.176645
$199$	−3039.64	−1.08279	−0.541393	−	0.840770i	$-0.682103\pi$
$199$	−3039.64	−1.08279	−0.541393	+	0.840770i	$0.682103\pi$
$200$	0	0
$201$	941.139	0.330263
$202$	6256.40	2.17920
$203$	1453.31	0.502476
$204$	−2976.70	−1.02162
$205$	0	0
$206$	−2451.69	−0.829209
$207$	616.113	0.206874
$208$	−2005.79	−0.668636
$209$	64.8157	0.0214517
$210$	0	0
$211$	2807.86	0.916119	0.458060	−	0.888921i	$-0.348545\pi$
$211$	2807.86	0.916119	0.458060	+	0.888921i	$0.348545\pi$
$212$	5679.58	1.83998
$213$	461.080	0.148322
$214$	−5463.63	−1.74526
$215$	0	0
$216$	1169.50	0.368400
$217$	1077.85	0.337187
$218$	−6338.53	−1.96926
$219$	461.598	0.142429
$220$	0	0
$221$	−1458.91	−0.444059
$222$	−2484.25	−0.751046
$223$	−1443.09	−0.433348	−0.216674	−	0.976244i	$-0.569521\pi$
$223$	−1443.09	−0.433348	−0.216674	+	0.976244i	$0.569521\pi$
$224$	324.903	0.0969129
$225$	0	0
$226$	−4704.94	−1.38481
$227$	−3658.71	−1.06977	−0.534884	−	0.844926i	$-0.679645\pi$
$227$	−3658.71	−1.06977	−0.534884	+	0.844926i	$0.679645\pi$
$228$	−295.438	−0.0858151
$229$	−1695.50	−0.489265	−0.244632	−	0.969616i	$-0.578667\pi$
$229$	−1695.50	−0.489265	−0.244632	+	0.969616i	$0.578667\pi$
$230$	0	0
$231$	180.964	0.0515435
$232$	11479.4	3.24853
$233$	5782.24	1.62578	0.812890	−	0.582417i	$-0.197893\pi$
$233$	5782.24	1.62578	0.812890	+	0.582417i	$0.197893\pi$
$234$	1099.46	0.307153
$235$	0	0
$236$	6965.76	1.92132
$237$	−1209.00	−0.331363
$238$	1618.45	0.440792
$239$	−5836.16	−1.57954	−0.789770	−	0.613404i	$-0.789800\pi$
$239$	−5836.16	−1.57954	−0.789770	+	0.613404i	$0.789800\pi$
$240$	0	0
$241$	−982.308	−0.262556	−0.131278	−	0.991346i	$-0.541908\pi$
$241$	−982.308	−0.262556	−0.131278	+	0.991346i	$0.541908\pi$
$242$	−601.519	−0.159781
$243$	−243.000	−0.0641500
$244$	11066.5	2.90353
$245$	0	0
$246$	6324.91	1.63927
$247$	−144.797	−0.0373005
$248$	8513.70	2.17992
$249$	−1956.94	−0.498056
$250$	0	0
$251$	4320.23	1.08642	0.543209	−	0.839598i	$-0.317209\pi$
$251$	4320.23	1.08642	0.543209	+	0.839598i	$0.317209\pi$
$252$	−824.856	−0.206195
$253$	753.027	0.187124
$254$	11238.8	2.77633
$255$	0	0
$256$	−8347.07	−2.03786
$257$	6224.29	1.51074	0.755371	−	0.655298i	$-0.227457\pi$
$257$	6224.29	1.51074	0.755371	+	0.655298i	$0.227457\pi$
$258$	2644.95	0.638246
$259$	913.459	0.219149
$260$	0	0
$261$	−2385.20	−0.565670
$262$	283.995	0.0669666
$263$	2588.95	0.607002	0.303501	−	0.952831i	$-0.401844\pi$
$263$	2588.95	0.607002	0.303501	+	0.952831i	$0.401844\pi$
$264$	1429.39	0.333230
$265$	0	0
$266$	160.631	0.0370260
$267$	−3680.30	−0.843561
$268$	−5243.12	−1.19505
$269$	−5871.53	−1.33083	−0.665415	−	0.746473i	$-0.731746\pi$
$269$	−5871.53	−1.33083	−0.665415	+	0.746473i	$0.731746\pi$
$270$	0	0
$271$	−3306.93	−0.741261	−0.370630	−	0.928780i	$-0.620858\pi$
$271$	−3306.93	−0.741261	−0.370630	+	0.928780i	$0.620858\pi$
$272$	4845.85	1.08023
$273$	−404.270	−0.0896247
$274$	9541.14	2.10366
$275$	0	0
$276$	−3432.39	−0.748571
$277$	2861.37	0.620660	0.310330	−	0.950629i	$-0.399560\pi$
$277$	2861.37	0.620660	0.310330	+	0.950629i	$0.399560\pi$
$278$	8403.66	1.81302
$279$	−1768.99	−0.379593
$280$	0	0
$281$	−2988.05	−0.634349	−0.317174	−	0.948367i	$-0.602734\pi$
$281$	−2988.05	−0.634349	−0.317174	+	0.948367i	$0.602734\pi$
$282$	−2105.03	−0.444513
$283$	−1454.60	−0.305536	−0.152768	−	0.988262i	$-0.548819\pi$
$283$	−1454.60	−0.305536	−0.152768	+	0.988262i	$0.548819\pi$
$284$	−2568.69	−0.536704
$285$	0	0
$286$	1343.78	0.277830
$287$	−2325.67	−0.478327
$288$	−533.234	−0.109101
$289$	−1388.36	−0.282589
$290$	0	0
$291$	2879.24	0.580014
$292$	−2571.58	−0.515378
$293$	8586.52	1.71205	0.856023	−	0.516937i	$-0.172928\pi$
$293$	8586.52	1.71205	0.856023	+	0.516937i	$0.172928\pi$
$294$	−4666.92	−0.925782
$295$	0	0
$296$	7215.19	1.41681
$297$	−297.000	−0.0580259
$298$	10329.6	2.00798
$299$	−1682.25	−0.325374
$300$	0	0
$301$	−972.547	−0.186235
$302$	−13477.8	−2.56808
$303$	3775.57	0.715844
$304$	480.951	0.0907382
$305$	0	0
$306$	−2656.22	−0.496228
$307$	−529.029	−0.0983495	−0.0491748	−	0.998790i	$-0.515659\pi$
$307$	−529.029	−0.0983495	−0.0491748	+	0.998790i	$0.515659\pi$
$308$	−1008.16	−0.186510
$309$	−1479.53	−0.272386
$310$	0	0
$311$	−5008.00	−0.913111	−0.456555	−	0.889695i	$-0.650917\pi$
$311$	−5008.00	−0.913111	−0.456555	+	0.889695i	$0.650917\pi$
$312$	−3193.23	−0.579426
$313$	−7858.53	−1.41914	−0.709570	−	0.704635i	$-0.751111\pi$
$313$	−7858.53	−1.41914	−0.709570	+	0.704635i	$0.751111\pi$
$314$	11638.8	2.09177
$315$	0	0
$316$	6735.39	1.19904
$317$	−7747.04	−1.37261	−0.686304	−	0.727315i	$-0.740768\pi$
$317$	−7747.04	−1.37261	−0.686304	+	0.727315i	$0.740768\pi$
$318$	5068.09	0.893724
$319$	−2915.24	−0.511668
$320$	0	0
$321$	−3297.15	−0.573299
$322$	1866.21	0.322980
$323$	349.820	0.0602617
$324$	1353.76	0.232126
$325$	0	0
$326$	17513.7	2.97544
$327$	−3825.13	−0.646882
$328$	−18369.9	−3.09240
$329$	774.019	0.129705
$330$	0	0
$331$	1355.08	0.225022	0.112511	−	0.993650i	$-0.464111\pi$
$331$	1355.08	0.225022	0.112511	+	0.993650i	$0.464111\pi$
$332$	10902.2	1.80221
$333$	−1499.18	−0.246710
$334$	19944.1	3.26734
$335$	0	0
$336$	1342.80	0.218024
$337$	−2596.97	−0.419780	−0.209890	−	0.977725i	$-0.567311\pi$
$337$	−2596.97	−0.419780	−0.209890	+	0.977725i	$0.567311\pi$
$338$	7919.81	1.27450
$339$	−2839.30	−0.454896
$340$	0	0
$341$	−2162.09	−0.343355
$342$	−263.629	−0.0416826
$343$	3596.95	0.566231
$344$	−7681.91	−1.20401
$345$	0	0
$346$	16530.8	2.56850
$347$	−266.820	−0.0412785	−0.0206392	−	0.999787i	$-0.506570\pi$
$347$	−266.820	−0.0412785	−0.0206392	+	0.999787i	$0.506570\pi$
$348$	13288.0	2.04687
$349$	−10549.4	−1.61804	−0.809021	−	0.587780i	$-0.800002\pi$
$349$	−10549.4	−1.61804	−0.809021	+	0.587780i	$0.800002\pi$
$350$	0	0
$351$	663.492	0.100896
$352$	−651.730	−0.0986856
$353$	−7152.63	−1.07846	−0.539229	−	0.842159i	$-0.681284\pi$
$353$	−7152.63	−1.07846	−0.539229	+	0.842159i	$0.681284\pi$
$354$	6215.79	0.933235
$355$	0	0
$356$	20503.1	3.05242
$357$	976.690	0.144795
$358$	132.409	0.0195475
$359$	359.182	0.0528047	0.0264024	−	0.999651i	$-0.491595\pi$
$359$	359.182	0.0528047	0.0264024	+	0.999651i	$0.491595\pi$
$360$	0	0
$361$	−6824.28	−0.994938
$362$	−9615.62	−1.39609
$363$	−363.000	−0.0524864
$364$	2252.20	0.324306
$365$	0	0
$366$	9875.04	1.41032
$367$	−9042.47	−1.28614	−0.643070	−	0.765808i	$-0.722339\pi$
$367$	−9042.47	−1.28614	−0.643070	+	0.765808i	$0.722339\pi$
$368$	5587.67	0.791515
$369$	3816.91	0.538483
$370$	0	0
$371$	−1863.54	−0.260781
$372$	9855.08	1.37355
$373$	11929.0	1.65592	0.827960	−	0.560787i	$-0.189501\pi$
$373$	11929.0	1.65592	0.827960	+	0.560787i	$0.189501\pi$
$374$	−3246.49	−0.448855
$375$	0	0
$376$	6113.78	0.838549
$377$	6512.59	0.889696
$378$	−736.047	−0.100154
$379$	6556.08	0.888557	0.444279	−	0.895889i	$-0.353460\pi$
$379$	6556.08	0.888557	0.444279	+	0.895889i	$0.353460\pi$
$380$	0	0
$381$	6782.32	0.911992
$382$	16611.8	2.22496
$383$	−10703.1	−1.42795	−0.713975	−	0.700172i	$-0.753107\pi$
$383$	−10703.1	−1.42795	−0.713975	+	0.700172i	$0.753107\pi$
$384$	−6767.74	−0.899388
$385$	0	0
$386$	−6432.60	−0.848214
$387$	1596.15	0.209657
$388$	−16040.3	−2.09878
$389$	−6450.30	−0.840728	−0.420364	−	0.907355i	$-0.638098\pi$
$389$	−6450.30	−0.840728	−0.420364	+	0.907355i	$0.638098\pi$
$390$	0	0
$391$	4064.20	0.525667
$392$	13554.4	1.74644
$393$	171.383	0.0219978
$394$	−11439.6	−1.46274
$395$	0	0
$396$	1654.60	0.209966
$397$	12526.0	1.58353	0.791764	−	0.610828i	$-0.209163\pi$
$397$	12526.0	1.58353	0.791764	+	0.610828i	$0.209163\pi$
$398$	15110.7	1.90310
$399$	96.9365	0.0121626
$400$	0	0
$401$	9119.52	1.13568	0.567839	−	0.823139i	$-0.307779\pi$
$401$	9119.52	1.13568	0.567839	+	0.823139i	$0.307779\pi$
$402$	−4678.62	−0.580468
$403$	4830.08	0.597030
$404$	−21033.8	−2.59028
$405$	0	0
$406$	−7224.76	−0.883150
$407$	−1832.33	−0.223158
$408$	7714.63	0.936106
$409$	−596.921	−0.0721658	−0.0360829	−	0.999349i	$-0.511488\pi$
$409$	−596.921	−0.0721658	−0.0360829	+	0.999349i	$0.511488\pi$
$410$	0	0
$411$	5757.82	0.691027
$412$	8242.49	0.985627
$413$	−2285.54	−0.272310
$414$	−3062.84	−0.363600
$415$	0	0
$416$	1455.95	0.171596
$417$	5071.38	0.595555
$418$	−322.214	−0.0377033
$419$	11560.5	1.34789	0.673944	−	0.738782i	$-0.264599\pi$
$419$	11560.5	1.34789	0.673944	+	0.738782i	$0.264599\pi$
$420$	0	0
$421$	15182.6	1.75761	0.878805	−	0.477182i	$-0.158342\pi$
$421$	15182.6	1.75761	0.878805	+	0.477182i	$0.158342\pi$
$422$	−13958.5	−1.61017
$423$	−1270.33	−0.146018
$424$	−14719.6	−1.68596
$425$	0	0
$426$	−2292.13	−0.260691
$427$	−3631.05	−0.411519
$428$	18368.5	2.07448
$429$	810.935	0.0912641
$430$	0	0
$431$	−14902.7	−1.66551	−0.832757	−	0.553639i	$-0.813239\pi$
$431$	−14902.7	−1.66551	−0.832757	+	0.553639i	$0.813239\pi$
$432$	−2203.82	−0.245443
$433$	2269.85	0.251922	0.125961	−	0.992035i	$-0.459799\pi$
$433$	2269.85	0.251922	0.125961	+	0.992035i	$0.459799\pi$
$434$	−5358.26	−0.592637
$435$	0	0
$436$	21309.9	2.34074
$437$	403.372	0.0441554
$438$	−2294.71	−0.250332
$439$	−13418.7	−1.45886	−0.729431	−	0.684054i	$-0.760215\pi$
$439$	−13418.7	−1.45886	−0.729431	+	0.684054i	$0.760215\pi$
$440$	0	0
$441$	−2816.36	−0.304109
$442$	7252.59	0.780476
$443$	−11507.5	−1.23417	−0.617086	−	0.786896i	$-0.711687\pi$
$443$	−11507.5	−1.23417	−0.617086	+	0.786896i	$0.711687\pi$
$444$	8351.98	0.892719
$445$	0	0
$446$	7173.94	0.761650
$447$	6233.65	0.659601
$448$	1965.64	0.207294
$449$	−16203.8	−1.70313	−0.851564	−	0.524250i	$-0.824346\pi$
$449$	−16203.8	−1.70313	−0.851564	+	0.524250i	$0.824346\pi$
$450$	0	0
$451$	4665.11	0.487077
$452$	15817.8	1.64604
$453$	−8133.48	−0.843585
$454$	18188.3	1.88022
$455$	0	0
$456$	765.677	0.0786318
$457$	−4912.79	−0.502868	−0.251434	−	0.967874i	$-0.580902\pi$
$457$	−4912.79	−0.502868	−0.251434	+	0.967874i	$0.580902\pi$
$458$	8428.70	0.859929
$459$	−1602.95	−0.163005
$460$	0	0
$461$	−14270.8	−1.44178	−0.720888	−	0.693051i	$-0.756266\pi$
$461$	−14270.8	−1.44178	−0.720888	+	0.693051i	$0.756266\pi$
$462$	−899.613	−0.0905926
$463$	−6656.46	−0.668146	−0.334073	−	0.942547i	$-0.608423\pi$
$463$	−6656.46	−0.668146	−0.334073	+	0.942547i	$0.608423\pi$
$464$	−21631.9	−2.16430
$465$	0	0
$466$	−28744.8	−2.85746
$467$	−19347.7	−1.91714	−0.958571	−	0.284853i	$-0.908055\pi$
$467$	−19347.7	−1.91714	−0.958571	+	0.284853i	$0.908055\pi$
$468$	−3696.34	−0.365093
$469$	1720.33	0.169376
$470$	0	0
$471$	7023.70	0.687123
$472$	−18052.9	−1.76050
$473$	1950.86	0.189642
$474$	6010.22	0.582402
$475$	0	0
$476$	−5441.18	−0.523941
$477$	3058.45	0.293579
$478$	29012.9	2.77619
$479$	9826.69	0.937355	0.468678	−	0.883369i	$-0.344731\pi$
$479$	9826.69	0.937355	0.468678	+	0.883369i	$0.344731\pi$
$480$	0	0
$481$	4093.39	0.388030
$482$	4883.28	0.461467
$483$	1126.21	0.106095
$484$	2022.29	0.189922
$485$	0	0
$486$	1208.01	0.112750
$487$	−10278.1	−0.956353	−0.478176	−	0.878264i	$-0.658702\pi$
$487$	−10278.1	−0.956353	−0.478176	+	0.878264i	$0.658702\pi$
$488$	−28680.7	−2.66048
$489$	10569.0	0.977400
$490$	0	0
$491$	11397.1	1.04755	0.523773	−	0.851858i	$-0.324524\pi$
$491$	11397.1	1.04755	0.523773	+	0.851858i	$0.324524\pi$
$492$	−21264.1	−1.94850
$493$	−15734.0	−1.43737
$494$	719.819	0.0655591
$495$	0	0
$496$	−16043.3	−1.45235
$497$	842.817	0.0760674
$498$	9728.39	0.875381
$499$	−9179.17	−0.823479	−0.411740	−	0.911302i	$-0.635079\pi$
$499$	−9179.17	−0.823479	−0.411740	+	0.911302i	$0.635079\pi$
$500$	0	0
$501$	12035.7	1.07329
$502$	−21476.9	−1.90948
$503$	−6782.80	−0.601253	−0.300626	−	0.953742i	$-0.597196\pi$
$503$	−6782.80	−0.601253	−0.300626	+	0.953742i	$0.597196\pi$
$504$	2137.75	0.188935
$505$	0	0
$506$	−3743.47	−0.328889
$507$	4779.39	0.418659
$508$	−37784.6	−3.30004
$509$	6814.24	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$509$	6814.24	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$510$	0	0
$511$	843.765	0.0730449
$512$	23447.9	2.02395
$513$	−159.093	−0.0136923
$514$	−30942.4	−2.65527
$515$	0	0
$516$	−8892.23	−0.758641
$517$	−1552.62	−0.132078
$518$	−4541.01	−0.385175
$519$	9975.89	0.843724
$520$	0	0
$521$	206.712	0.0173824	0.00869118	−	0.999962i	$-0.497233\pi$
$521$	206.712	0.0173824	0.00869118	+	0.999962i	$0.497233\pi$
$522$	11857.4	0.994219
$523$	11375.9	0.951118	0.475559	−	0.879684i	$-0.342246\pi$
$523$	11375.9	0.951118	0.475559	+	0.879684i	$0.342246\pi$
$524$	−954.781	−0.0795989
$525$	0	0
$526$	−12870.3	−1.06686
$527$	−11669.1	−0.964547
$528$	−2693.56	−0.222012
$529$	−7480.63	−0.614830
$530$	0	0
$531$	3751.06	0.306557
$532$	−540.036	−0.0440104
$533$	−10421.8	−0.846936
$534$	18295.6	1.48264
$535$	0	0
$536$	13588.4	1.09502
$537$	79.9049	0.00642114
$538$	29188.7	2.33906
$539$	−3442.21	−0.275077
$540$	0	0
$541$	−10228.1	−0.812831	−0.406415	−	0.913688i	$-0.633221\pi$
$541$	−10228.1	−0.812831	−0.406415	+	0.913688i	$0.633221\pi$
$542$	16439.5	1.30284
$543$	−5802.76	−0.458601
$544$	−3517.49	−0.277226
$545$	0	0
$546$	2009.72	0.157524
$547$	15538.9	1.21461	0.607307	−	0.794467i	$-0.292250\pi$
$547$	15538.9	1.21461	0.607307	+	0.794467i	$0.292250\pi$
$548$	−32077.0	−2.50048
$549$	5959.31	0.463274
$550$	0	0
$551$	−1561.60	−0.120737
$552$	8895.62	0.685911
$553$	−2209.96	−0.169940
$554$	−14224.5	−1.09087
$555$	0	0
$556$	−28252.8	−2.15501
$557$	5191.17	0.394896	0.197448	−	0.980313i	$-0.436735\pi$
$557$	5191.17	0.394896	0.197448	+	0.980313i	$0.436735\pi$
$558$	8794.03	0.667170
$559$	−4358.17	−0.329752
$560$	0	0
$561$	−1959.17	−0.147444
$562$	14854.3	1.11493
$563$	−13722.9	−1.02727	−0.513635	−	0.858009i	$-0.671701\pi$
$563$	−13722.9	−1.02727	−0.513635	+	0.858009i	$0.671701\pi$
$564$	7077.04	0.528364
$565$	0	0
$566$	7231.13	0.537009
$567$	−444.184	−0.0328995
$568$	6657.20	0.491778
$569$	23209.0	1.70997	0.854986	−	0.518652i	$-0.173566\pi$
$569$	23209.0	1.70997	0.854986	+	0.518652i	$0.173566\pi$
$570$	0	0
$571$	−13130.5	−0.962337	−0.481168	−	0.876628i	$-0.659787\pi$
$571$	−13130.5	−0.962337	−0.481168	+	0.876628i	$0.659787\pi$
$572$	−4517.75	−0.330239
$573$	10024.8	0.730874
$574$	11561.4	0.840705
$575$	0	0
$576$	−3226.03	−0.233365
$577$	12261.0	0.884633	0.442317	−	0.896859i	$-0.354157\pi$
$577$	12261.0	0.884633	0.442317	+	0.896859i	$0.354157\pi$
$578$	6901.86	0.496677
$579$	−3881.90	−0.278629
$580$	0	0
$581$	−3577.13	−0.255429
$582$	−14313.3	−1.01943
$583$	3738.11	0.265552
$584$	6664.69	0.472238
$585$	0	0
$586$	−42685.5	−3.00908
$587$	3553.42	0.249856	0.124928	−	0.992166i	$-0.460130\pi$
$587$	3553.42	0.249856	0.124928	+	0.992166i	$0.460130\pi$
$588$	15690.0	1.10042
$589$	−1158.16	−0.0810208
$590$	0	0
$591$	−6903.50	−0.480494
$592$	−13596.4	−0.943933
$593$	−1942.83	−0.134540	−0.0672701	−	0.997735i	$-0.521429\pi$
$593$	−1942.83	−0.134540	−0.0672701	+	0.997735i	$0.521429\pi$
$594$	1476.45	0.101986
$595$	0	0
$596$	−34727.9	−2.38676
$597$	9118.92	0.625147
$598$	8362.84	0.571876
$599$	18585.4	1.26774	0.633871	−	0.773439i	$-0.281465\pi$
$599$	18585.4	1.26774	0.633871	+	0.773439i	$0.281465\pi$
$600$	0	0
$601$	8010.10	0.543658	0.271829	−	0.962346i	$-0.412371\pi$
$601$	8010.10	0.543658	0.271829	+	0.962346i	$0.412371\pi$
$602$	4834.75	0.327325
$603$	−2823.42	−0.190677
$604$	45311.9	3.05251
$605$	0	0
$606$	−18769.2	−1.25816
$607$	1537.69	0.102822	0.0514111	−	0.998678i	$-0.483628\pi$
$607$	1537.69	0.102822	0.0514111	+	0.998678i	$0.483628\pi$
$608$	−349.110	−0.0232867
$609$	−4359.94	−0.290105
$610$	0	0
$611$	3468.53	0.229659
$612$	8930.11	0.589834
$613$	−2298.75	−0.151461	−0.0757304	−	0.997128i	$-0.524129\pi$
$613$	−2298.75	−0.151461	−0.0757304	+	0.997128i	$0.524129\pi$
$614$	2629.93	0.172859
$615$	0	0
$616$	2612.81	0.170898
$617$	−6089.51	−0.397333	−0.198666	−	0.980067i	$-0.563661\pi$
$617$	−6089.51	−0.397333	−0.198666	+	0.980067i	$0.563661\pi$
$618$	7355.06	0.478744
$619$	12255.4	0.795775	0.397887	−	0.917434i	$-0.369743\pi$
$619$	12255.4	0.795775	0.397887	+	0.917434i	$0.369743\pi$
$620$	0	0
$621$	−1848.34	−0.119439
$622$	24895.9	1.60488
$623$	−6727.29	−0.432622
$624$	6017.36	0.386037
$625$	0	0
$626$	39066.6	2.49427
$627$	−194.447	−0.0123851
$628$	−39129.3	−2.48635
$629$	−9889.36	−0.626891
$630$	0	0
$631$	−25746.5	−1.62433	−0.812165	−	0.583428i	$-0.801711\pi$
$631$	−25746.5	−1.62433	−0.812165	+	0.583428i	$0.801711\pi$
$632$	−17455.9	−1.09867
$633$	−8423.58	−0.528922
$634$	38512.3	2.41249
$635$	0	0
$636$	−17038.8	−1.06231
$637$	7689.84	0.478308
$638$	14492.3	0.899305
$639$	−1383.24	−0.0856340
$640$	0	0
$641$	−598.022	−0.0368494	−0.0184247	−	0.999830i	$-0.505865\pi$
$641$	−598.022	−0.0368494	−0.0184247	+	0.999830i	$0.505865\pi$
$642$	16390.9	1.00763
$643$	−14610.9	−0.896109	−0.448054	−	0.894006i	$-0.647883\pi$
$643$	−14610.9	−0.896109	−0.448054	+	0.894006i	$0.647883\pi$
$644$	−6274.13	−0.383906
$645$	0	0
$646$	−1739.04	−0.105916
$647$	17252.3	1.04831	0.524156	−	0.851622i	$-0.324381\pi$
$647$	17252.3	1.04831	0.524156	+	0.851622i	$0.324381\pi$
$648$	−3508.50	−0.212696
$649$	4584.63	0.277292
$650$	0	0
$651$	−3233.56	−0.194675
$652$	−58880.5	−3.53671
$653$	17768.6	1.06484	0.532418	−	0.846481i	$-0.321283\pi$
$653$	17768.6	1.06484	0.532418	+	0.846481i	$0.321283\pi$
$654$	19015.6	1.13696
$655$	0	0
$656$	34616.4	2.06028
$657$	−1384.80	−0.0822314
$658$	−3847.82	−0.227969
$659$	−17594.9	−1.04006	−0.520031	−	0.854147i	$-0.674080\pi$
$659$	−17594.9	−1.04006	−0.520031	+	0.854147i	$0.674080\pi$
$660$	0	0
$661$	23355.9	1.37434	0.687170	−	0.726497i	$-0.258853\pi$
$661$	23355.9	1.37434	0.687170	+	0.726497i	$0.258853\pi$
$662$	−6736.44	−0.395497
$663$	4376.74	0.256378
$664$	−28254.8	−1.65136
$665$	0	0
$666$	7452.76	0.433617
$667$	−18142.6	−1.05320
$668$	−67051.4	−3.88368
$669$	4329.28	0.250194
$670$	0	0
$671$	7283.61	0.419047
$672$	−974.708	−0.0559527
$673$	2340.47	0.134054	0.0670271	−	0.997751i	$-0.478649\pi$
$673$	2340.47	0.134054	0.0670271	+	0.997751i	$0.478649\pi$
$674$	12910.1	0.737803
$675$	0	0
$676$	−26626.1	−1.51491
$677$	16562.2	0.940234	0.470117	−	0.882604i	$-0.344212\pi$
$677$	16562.2	0.940234	0.470117	+	0.882604i	$0.344212\pi$
$678$	14114.8	0.799522
$679$	5263.01	0.297461
$680$	0	0
$681$	10976.1	0.617630
$682$	10748.3	0.603478
$683$	−22303.4	−1.24951	−0.624755	−	0.780821i	$-0.714801\pi$
$683$	−22303.4	−1.24951	−0.624755	+	0.780821i	$0.714801\pi$
$684$	886.313	0.0495454
$685$	0	0
$686$	−17881.3	−0.995204
$687$	5086.49	0.282477
$688$	14475.9	0.802163
$689$	−8350.87	−0.461745
$690$	0	0
$691$	6244.91	0.343802	0.171901	−	0.985114i	$-0.445009\pi$
$691$	6244.91	0.343802	0.171901	+	0.985114i	$0.445009\pi$
$692$	−55576.0	−3.05301
$693$	−542.892	−0.0297587
$694$	1326.42	0.0725508
$695$	0	0
$696$	−34438.1	−1.87554
$697$	25178.3	1.36829
$698$	52443.5	2.84386
$699$	−17346.7	−0.938645
$700$	0	0
$701$	−15277.7	−0.823154	−0.411577	−	0.911375i	$-0.635022\pi$
$701$	−15277.7	−0.823154	−0.411577	+	0.911375i	$0.635022\pi$
$702$	−3298.37	−0.177335
$703$	−981.519	−0.0526582
$704$	−3942.93	−0.211086
$705$	0	0
$706$	35557.3	1.89549
$707$	6901.43	0.367122
$708$	−20897.3	−1.10928
$709$	−11732.1	−0.621449	−0.310725	−	0.950500i	$-0.600572\pi$
$709$	−11732.1	−0.621449	−0.310725	+	0.950500i	$0.600572\pi$
$710$	0	0
$711$	3627.00	0.191313
$712$	−53137.2	−2.79691
$713$	−13455.5	−0.706750
$714$	−4855.35	−0.254491
$715$	0	0
$716$	−445.153	−0.0232349
$717$	17508.5	0.911947
$718$	−1785.57	−0.0928093
$719$	−19006.2	−0.985828	−0.492914	−	0.870078i	$-0.664068\pi$
$719$	−19006.2	−0.985828	−0.492914	+	0.870078i	$0.664068\pi$
$720$	0	0
$721$	−2704.45	−0.139694
$722$	33925.1	1.74870
$723$	2946.92	0.151587
$724$	32327.4	1.65945
$725$	0	0
$726$	1804.56	0.0922498
$727$	−2650.77	−0.135229	−0.0676146	−	0.997712i	$-0.521539\pi$
$727$	−2650.77	−0.135229	−0.0676146	+	0.997712i	$0.521539\pi$
$728$	−5836.96	−0.297160
$729$	729.000	0.0370370
$730$	0	0
$731$	10529.1	0.532738
$732$	−33199.5	−1.67635
$733$	8854.22	0.446164	0.223082	−	0.974800i	$-0.428388\pi$
$733$	8854.22	0.446164	0.223082	+	0.974800i	$0.428388\pi$
$734$	44952.2	2.26051
$735$	0	0
$736$	−4055.96	−0.203131
$737$	−3450.84	−0.172474
$738$	−18974.7	−0.946435
$739$	17174.8	0.854921	0.427460	−	0.904034i	$-0.359408\pi$
$739$	17174.8	0.854921	0.427460	+	0.904034i	$0.359408\pi$
$740$	0	0
$741$	434.391	0.0215354
$742$	9264.06	0.458348
$743$	9800.30	0.483901	0.241950	−	0.970289i	$-0.422213\pi$
$743$	9800.30	0.483901	0.241950	+	0.970289i	$0.422213\pi$
$744$	−25541.1	−1.25858
$745$	0	0
$746$	−59301.6	−2.91044
$747$	5870.82	0.287553
$748$	10914.6	0.533525
$749$	−6026.92	−0.294017
$750$	0	0
$751$	2781.25	0.135139	0.0675695	−	0.997715i	$-0.478476\pi$
$751$	2781.25	0.135139	0.0675695	+	0.997715i	$0.478476\pi$
$752$	−11520.9	−0.558675
$753$	−12960.7	−0.627243
$754$	−32375.6	−1.56372
$755$	0	0
$756$	2474.57	0.119046
$757$	−3010.87	−0.144560	−0.0722800	−	0.997384i	$-0.523028\pi$
$757$	−3010.87	−0.144560	−0.0722800	+	0.997384i	$0.523028\pi$
$758$	−32591.8	−1.56172
$759$	−2259.08	−0.108036
$760$	0	0
$761$	−2709.54	−0.129068	−0.0645340	−	0.997916i	$-0.520556\pi$
$761$	−2709.54	−0.129068	−0.0645340	+	0.997916i	$0.520556\pi$
$762$	−33716.5	−1.60291
$763$	−6992.03	−0.331754
$764$	−55848.4	−2.64466
$765$	0	0
$766$	53207.7	2.50976
$767$	−10242.0	−0.482159
$768$	25041.2	1.17656
$769$	−28121.1	−1.31869	−0.659345	−	0.751841i	$-0.729166\pi$
$769$	−28121.1	−1.31869	−0.659345	+	0.751841i	$0.729166\pi$
$770$	0	0
$771$	−18672.9	−0.872227
$772$	21626.2	1.00822
$773$	−4274.61	−0.198897	−0.0994483	−	0.995043i	$-0.531708\pi$
$773$	−4274.61	−0.198897	−0.0994483	+	0.995043i	$0.531708\pi$
$774$	−7934.85	−0.368491
$775$	0	0
$776$	41571.2	1.92309
$777$	−2740.38	−0.126526
$778$	32065.9	1.47766
$779$	2498.95	0.114935
$780$	0	0
$781$	−1690.63	−0.0774589
$782$	−20204.1	−0.923909
$783$	7155.59	0.326590
$784$	−25542.2	−1.16355
$785$	0	0
$786$	−851.985	−0.0386632
$787$	−19107.9	−0.865469	−0.432734	−	0.901522i	$-0.642451\pi$
$787$	−19107.9	−0.865469	−0.432734	+	0.901522i	$0.642451\pi$
$788$	38459.6	1.73866
$789$	−7766.85	−0.350453
$790$	0	0
$791$	−5190.01	−0.233294
$792$	−4288.17	−0.192391
$793$	−16271.4	−0.728645
$794$	−62269.4	−2.78320
$795$	0	0
$796$	−50801.9	−2.26209
$797$	−27518.4	−1.22303	−0.611513	−	0.791234i	$-0.709439\pi$
$797$	−27518.4	−1.22303	−0.611513	+	0.791234i	$0.709439\pi$
$798$	−481.893	−0.0213770
$799$	−8379.74	−0.371031
$800$	0	0
$801$	11040.9	0.487030
$802$	−45335.2	−1.99606
$803$	−1692.53	−0.0743811
$804$	15729.4	0.689965
$805$	0	0
$806$	−24011.4	−1.04934
$807$	17614.6	0.768356
$808$	54512.7	2.37345
$809$	21986.6	0.955511	0.477755	−	0.878493i	$-0.341450\pi$
$809$	21986.6	0.955511	0.477755	+	0.878493i	$0.341450\pi$
$810$	0	0
$811$	11835.1	0.512437	0.256218	−	0.966619i	$-0.417523\pi$
$811$	11835.1	0.512437	0.256218	+	0.966619i	$0.417523\pi$
$812$	24289.4	1.04974
$813$	9920.79	0.427967
$814$	9108.93	0.392221
$815$	0	0
$816$	−14537.6	−0.623672
$817$	1045.01	0.0447494
$818$	2967.43	0.126838
$819$	1212.81	0.0517448
$820$	0	0
$821$	−7890.58	−0.335424	−0.167712	−	0.985836i	$-0.553638\pi$
$821$	−7890.58	−0.335424	−0.167712	+	0.985836i	$0.553638\pi$
$822$	−28623.4	−1.21455
$823$	−1000.74	−0.0423861	−0.0211930	−	0.999775i	$-0.506746\pi$
$823$	−1000.74	−0.0423861	−0.0211930	+	0.999775i	$0.506746\pi$
$824$	−21361.8	−0.903123
$825$	0	0
$826$	11362.0	0.478611
$827$	−22764.2	−0.957181	−0.478590	−	0.878038i	$-0.658852\pi$
$827$	−22764.2	−0.957181	−0.478590	+	0.878038i	$0.658852\pi$
$828$	10297.2	0.432188
$829$	39835.8	1.66894	0.834471	−	0.551051i	$-0.185773\pi$
$829$	39835.8	1.66894	0.834471	+	0.551051i	$0.185773\pi$
$830$	0	0
$831$	−8584.10	−0.358338
$832$	8808.43	0.367040
$833$	−18578.1	−0.772742
$834$	−25211.0	−1.04674
$835$	0	0
$836$	1083.27	0.0448155
$837$	5306.96	0.219158
$838$	−57469.7	−2.36904
$839$	23330.9	0.960037	0.480019	−	0.877258i	$-0.340630\pi$
$839$	23330.9	0.960037	0.480019	+	0.877258i	$0.340630\pi$
$840$	0	0
$841$	45847.5	1.87984
$842$	−75476.0	−3.08916
$843$	8964.14	0.366241
$844$	46928.1	1.91390
$845$	0	0
$846$	6315.09	0.256640
$847$	−663.535	−0.0269177
$848$	27737.8	1.12326
$849$	4363.79	0.176402
$850$	0	0
$851$	−11403.3	−0.459341
$852$	7706.08	0.309866
$853$	−22937.3	−0.920701	−0.460351	−	0.887737i	$-0.652276\pi$
$853$	−22937.3	−0.920701	−0.460351	+	0.887737i	$0.652276\pi$
$854$	18050.8	0.723284
$855$	0	0
$856$	−47605.2	−1.90083
$857$	38472.3	1.53348	0.766738	−	0.641961i	$-0.221879\pi$
$857$	38472.3	1.53348	0.766738	+	0.641961i	$0.221879\pi$
$858$	−4031.34	−0.160405
$859$	−22970.3	−0.912384	−0.456192	−	0.889881i	$-0.650787\pi$
$859$	−22970.3	−0.912384	−0.456192	+	0.889881i	$0.650787\pi$
$860$	0	0
$861$	6977.00	0.276162
$862$	74084.5	2.92730
$863$	33587.6	1.32484	0.662420	−	0.749133i	$-0.269530\pi$
$863$	33587.6	1.32484	0.662420	+	0.749133i	$0.269530\pi$
$864$	1599.70	0.0629895
$865$	0	0
$866$	−11284.0	−0.442777
$867$	4165.08	0.163153
$868$	18014.3	0.704430
$869$	4433.00	0.173049
$870$	0	0
$871$	7709.12	0.299901
$872$	−55228.3	−2.14480
$873$	−8637.71	−0.334871
$874$	−2005.25	−0.0776073
$875$	0	0
$876$	7714.74	0.297554
$877$	704.130	0.0271115	0.0135558	−	0.999908i	$-0.495685\pi$
$877$	704.130	0.0271115	0.0135558	+	0.999908i	$0.495685\pi$
$878$	66707.5	2.56409
$879$	−25759.5	−0.988450
$880$	0	0
$881$	9746.33	0.372715	0.186358	−	0.982482i	$-0.440332\pi$
$881$	9746.33	0.372715	0.186358	+	0.982482i	$0.440332\pi$
$882$	14000.7	0.534501
$883$	8774.24	0.334402	0.167201	−	0.985923i	$-0.446527\pi$
$883$	8774.24	0.334402	0.167201	+	0.985923i	$0.446527\pi$
$884$	−24383.0	−0.927701
$885$	0	0
$886$	57206.4	2.16917
$887$	13505.1	0.511224	0.255612	−	0.966779i	$-0.417723\pi$
$887$	13505.1	0.511224	0.255612	+	0.966779i	$0.417723\pi$
$888$	−21645.6	−0.817993
$889$	12397.5	0.467717
$890$	0	0
$891$	891.000	0.0335013
$892$	−24118.6	−0.905324
$893$	−831.689	−0.0311662
$894$	−30988.9	−1.15931
$895$	0	0
$896$	−12370.9	−0.461252
$897$	5046.75	0.187855
$898$	80552.8	2.99341
$899$	52091.1	1.93252
$900$	0	0
$901$	20175.1	0.745984
$902$	−23191.3	−0.856083
$903$	2917.64	0.107523
$904$	−40994.6	−1.50825
$905$	0	0
$906$	40433.4	1.48268
$907$	2523.23	0.0923732	0.0461866	−	0.998933i	$-0.485293\pi$
$907$	2523.23	0.0923732	0.0461866	+	0.998933i	$0.485293\pi$
$908$	−61148.4	−2.23489
$909$	−11326.7	−0.413293
$910$	0	0
$911$	−32285.3	−1.17416	−0.587080	−	0.809529i	$-0.699723\pi$
$911$	−32285.3	−1.17416	−0.587080	+	0.809529i	$0.699723\pi$
$912$	−1442.85	−0.0523877
$913$	7175.45	0.260101
$914$	24422.6	0.883838
$915$	0	0
$916$	−28337.0	−1.02214
$917$	313.274	0.0112816
$918$	7968.65	0.286497
$919$	−40956.5	−1.47011	−0.735055	−	0.678008i	$-0.762844\pi$
$919$	−40956.5	−1.47011	−0.735055	+	0.678008i	$0.762844\pi$
$920$	0	0
$921$	1587.09	0.0567821
$922$	70943.6	2.53406
$923$	3776.83	0.134687
$924$	3024.47	0.107682
$925$	0	0
$926$	33090.8	1.17433
$927$	4438.58	0.157262
$928$	15702.1	0.555437
$929$	−6728.41	−0.237623	−0.118812	−	0.992917i	$-0.537908\pi$
$929$	−6728.41	−0.237623	−0.118812	+	0.992917i	$0.537908\pi$
$930$	0	0
$931$	−1843.88	−0.0649095
$932$	96639.1	3.39648
$933$	15024.0	0.527185
$934$	96181.9	3.36956
$935$	0	0
$936$	9579.69	0.334532
$937$	36377.8	1.26831	0.634157	−	0.773205i	$-0.281347\pi$
$937$	36377.8	1.26831	0.634157	+	0.773205i	$0.281347\pi$
$938$	−8552.13	−0.297694
$939$	23575.6	0.819340
$940$	0	0
$941$	25907.0	0.897496	0.448748	−	0.893658i	$-0.351870\pi$
$941$	25907.0	0.897496	0.448748	+	0.893658i	$0.351870\pi$
$942$	−34916.4	−1.20768
$943$	29032.7	1.00258
$944$	34019.2	1.17291
$945$	0	0
$946$	−9698.15	−0.333313
$947$	−37096.3	−1.27293	−0.636466	−	0.771304i	$-0.719605\pi$
$947$	−37096.3	−1.27293	−0.636466	+	0.771304i	$0.719605\pi$
$948$	−20206.2	−0.692263
$949$	3781.07	0.129335
$950$	0	0
$951$	23241.1	0.792476
$952$	14101.7	0.480084
$953$	15323.7	0.520865	0.260432	−	0.965492i	$-0.416135\pi$
$953$	15323.7	0.520865	0.260432	+	0.965492i	$0.416135\pi$
$954$	−15204.3	−0.515992
$955$	0	0
$956$	−97540.4	−3.29988
$957$	8745.72	0.295412
$958$	−48850.7	−1.64749
$959$	10524.8	0.354395
$960$	0	0
$961$	8842.46	0.296817
$962$	−20349.2	−0.682000
$963$	9891.45	0.330994
$964$	−16417.4	−0.548516
$965$	0	0
$966$	−5598.62	−0.186473
$967$	53388.0	1.77543	0.887716	−	0.460391i	$-0.152291\pi$
$967$	53388.0	1.77543	0.887716	+	0.460391i	$0.152291\pi$
$968$	−5241.10	−0.174024
$969$	−1049.46	−0.0347921
$970$	0	0
$971$	−36325.7	−1.20056	−0.600281	−	0.799789i	$-0.704945\pi$
$971$	−36325.7	−1.20056	−0.600281	+	0.799789i	$0.704945\pi$
$972$	−4061.28	−0.134018
$973$	9270.07	0.305432
$974$	51094.6	1.68088
$975$	0	0
$976$	54046.4	1.77252
$977$	−48608.7	−1.59174	−0.795870	−	0.605468i	$-0.792986\pi$
$977$	−48608.7	−1.59174	−0.795870	+	0.605468i	$0.792986\pi$
$978$	−52541.1	−1.71787
$979$	13494.4	0.440535
$980$	0	0
$981$	11475.4	0.373477
$982$	−56657.7	−1.84116
$983$	−31762.6	−1.03059	−0.515295	−	0.857013i	$-0.672318\pi$
$983$	−31762.6	−1.03059	−0.515295	+	0.857013i	$0.672318\pi$
$984$	55109.6	1.78540
$985$	0	0
$986$	78217.2	2.52631
$987$	−2322.06	−0.0748854
$988$	−2420.01	−0.0779258
$989$	12140.9	0.390352
$990$	0	0
$991$	−5073.82	−0.162639	−0.0813195	−	0.996688i	$-0.525913\pi$
$991$	−5073.82	−0.162639	−0.0813195	+	0.996688i	$0.525913\pi$
$992$	11645.5	0.372726
$993$	−4065.25	−0.129916
$994$	−4189.83	−0.133696
$995$	0	0
$996$	−32706.5	−1.04051
$997$	−24607.0	−0.781657	−0.390828	−	0.920464i	$-0.627811\pi$
$997$	−24607.0	−0.781657	−0.390828	+	0.920464i	$0.627811\pi$
$998$	45631.8	1.44734
$999$	4497.54	0.142438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.r.1.1		3
3.2	odd	2		2475.4.a.t.1.3		3
5.2	odd	4		825.4.c.k.199.2		6
5.3	odd	4		825.4.c.k.199.5		6
5.4	even	2		165.4.a.e.1.3	✓	3
15.14	odd	2		495.4.a.k.1.1		3
55.54	odd	2		1815.4.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.3	✓	3	5.4	even	2
495.4.a.k.1.1		3	15.14	odd	2
825.4.a.r.1.1		3	1.1	even	1	trivial
825.4.c.k.199.2		6	5.2	odd	4
825.4.c.k.199.5		6	5.3	odd	4
1815.4.a.r.1.1		3	55.54	odd	2
2475.4.a.t.1.3		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q-4.97123 q^{2} -3.00000 q^{3} +16.7131 q^{4} +14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.97123 q^{2} -3.00000 q^{3} +16.7131 q^{4} +14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +11.0000 q^{11} -50.1393 q^{12} -24.5738 q^{13} +27.2610 q^{14} +81.6231 q^{16} +59.3687 q^{17} -44.7411 q^{18} +5.89234 q^{19} +16.4513 q^{21} -54.6835 q^{22} +68.4570 q^{23} +129.945 q^{24} +122.162 q^{26} -27.0000 q^{27} -91.6506 q^{28} -265.022 q^{29} -196.554 q^{31} -59.2482 q^{32} -33.0000 q^{33} -295.135 q^{34} +150.418 q^{36} -166.575 q^{37} -29.2922 q^{38} +73.7214 q^{39} +424.101 q^{41} -81.7830 q^{42} +177.351 q^{43} +183.844 q^{44} -340.316 q^{46} -141.148 q^{47} -244.869 q^{48} -312.928 q^{49} -178.106 q^{51} -410.704 q^{52} +339.828 q^{53} +134.223 q^{54} +237.528 q^{56} -17.6770 q^{57} +1317.48 q^{58} +416.784 q^{59} +662.146 q^{61} +977.115 q^{62} -49.3538 q^{63} -358.448 q^{64} +164.051 q^{66} -313.713 q^{67} +992.235 q^{68} -205.371 q^{69} -153.693 q^{71} -389.834 q^{72} -153.866 q^{73} +828.084 q^{74} +98.4793 q^{76} -60.3213 q^{77} -366.486 q^{78} +403.000 q^{79} +81.0000 q^{81} -2108.30 q^{82} +652.313 q^{83} +274.952 q^{84} -881.650 q^{86} +795.065 q^{87} -476.463 q^{88} +1226.77 q^{89} +134.757 q^{91} +1144.13 q^{92} +589.662 q^{93} +701.677 q^{94} +177.745 q^{96} -959.746 q^{97} +1555.64 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} + 33 q^{11} - 90 q^{12} - 114 q^{13} - 68 q^{14} + 178 q^{16} + 104 q^{17} + 18 q^{18} - 58 q^{19} + 30 q^{21} + 22 q^{22} - 120 q^{23} + 54 q^{24} - 120 q^{26} - 81 q^{27} - 676 q^{28} - 220 q^{29} + 248 q^{31} + 258 q^{32} - 99 q^{33} - 80 q^{34} + 270 q^{36} - 838 q^{37} - 600 q^{38} + 342 q^{39} + 156 q^{41} + 204 q^{42} - 122 q^{43} + 330 q^{44} - 1256 q^{46} - 504 q^{47} - 534 q^{48} + 279 q^{49} - 312 q^{51} - 520 q^{52} - 282 q^{53} - 54 q^{54} - 1644 q^{56} + 174 q^{57} + 1644 q^{58} + 548 q^{59} + 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} - 66 q^{66} + 428 q^{67} + 1704 q^{68} + 360 q^{69} - 912 q^{71} - 162 q^{72} - 618 q^{73} - 1612 q^{74} - 2752 q^{76} - 110 q^{77} + 360 q^{78} - 542 q^{79} + 243 q^{81} - 3372 q^{82} + 2028 q^{84} - 1548 q^{86} + 660 q^{87} - 198 q^{88} + 790 q^{89} - 772 q^{91} - 1912 q^{92} - 744 q^{93} - 424 q^{94} - 774 q^{96} - 2074 q^{97} + 3978 q^{98} + 297 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 + 33 * q^11 - 90 * q^12 - 114 * q^13 - 68 * q^14 + 178 * q^16 + 104 * q^17 + 18 * q^18 - 58 * q^19 + 30 * q^21 + 22 * q^22 - 120 * q^23 + 54 * q^24 - 120 * q^26 - 81 * q^27 - 676 * q^28 - 220 * q^29 + 248 * q^31 + 258 * q^32 - 99 * q^33 - 80 * q^34 + 270 * q^36 - 838 * q^37 - 600 * q^38 + 342 * q^39 + 156 * q^41 + 204 * q^42 - 122 * q^43 + 330 * q^44 - 1256 * q^46 - 504 * q^47 - 534 * q^48 + 279 * q^49 - 312 * q^51 - 520 * q^52 - 282 * q^53 - 54 * q^54 - 1644 * q^56 + 174 * q^57 + 1644 * q^58 + 548 * q^59 + 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 - 66 * q^66 + 428 * q^67 + 1704 * q^68 + 360 * q^69 - 912 * q^71 - 162 * q^72 - 618 * q^73 - 1612 * q^74 - 2752 * q^76 - 110 * q^77 + 360 * q^78 - 542 * q^79 + 243 * q^81 - 3372 * q^82 + 2028 * q^84 - 1548 * q^86 + 660 * q^87 - 198 * q^88 + 790 * q^89 - 772 * q^91 - 1912 * q^92 - 744 * q^93 - 424 * q^94 - 774 * q^96 - 2074 * q^97 + 3978 * q^98 + 297 * q^99

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