LMFDB - Embedded newform 425.4.a.g.1.3

Newspace parameters

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	425.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$25.0758117524$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.2636.1
Defining polynomial:	$ x^{3} - 14x - 4 $ x^3 - 14*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.58966$ of defining polynomial
Character	$\chi$	$=$	425.1

$q$-expansion

$f(q)$	$=$	$q+5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -42.6523 q^{6} -3.81828 q^{7} +46.9339 q^{8} +44.8316 q^{9} +O(q^{10})$	\(q+5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -42.6523 q^{6} -3.81828 q^{7} +46.9339 q^{8} +44.8316 q^{9} -52.3720 q^{11} -146.845 q^{12} +8.06025 q^{13} -19.2156 q^{14} +97.5862 q^{16} +17.0000 q^{17} +225.616 q^{18} -66.5154 q^{19} +32.3613 q^{21} -263.563 q^{22} -180.226 q^{23} -397.782 q^{24} +40.5633 q^{26} -151.129 q^{27} -66.1562 q^{28} -41.2800 q^{29} -34.9114 q^{31} +115.632 q^{32} +443.871 q^{33} +85.5527 q^{34} +776.759 q^{36} -130.368 q^{37} -334.739 q^{38} -68.3134 q^{39} -17.9081 q^{41} +162.859 q^{42} -277.620 q^{43} -907.405 q^{44} -906.987 q^{46} -463.789 q^{47} -827.078 q^{48} -328.421 q^{49} -144.081 q^{51} +139.653 q^{52} +329.944 q^{53} -760.560 q^{54} -179.207 q^{56} +563.741 q^{57} -207.742 q^{58} +678.656 q^{59} +340.280 q^{61} -175.692 q^{62} -171.180 q^{63} -198.770 q^{64} +2233.79 q^{66} -15.3925 q^{67} +294.545 q^{68} +1527.48 q^{69} -670.203 q^{71} +2104.12 q^{72} -193.480 q^{73} -656.080 q^{74} -1152.46 q^{76} +199.971 q^{77} -343.788 q^{78} +1080.15 q^{79} +70.4207 q^{81} -90.1229 q^{82} +865.668 q^{83} +560.697 q^{84} -1397.13 q^{86} +349.863 q^{87} -2458.02 q^{88} +1129.46 q^{89} -30.7763 q^{91} -3122.61 q^{92} +295.886 q^{93} -2334.02 q^{94} -980.023 q^{96} +379.412 q^{97} -1652.78 q^{98} -2347.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) $ 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} - 28 q^{11} - 22 q^{12} - 30 q^{13} + 92 q^{14} + 137 q^{16} + 51 q^{17} + 103 q^{18} + 80 q^{19} - 192 q^{21} - 286 q^{22} - 142 q^{23} - 666 q^{24} + 26 q^{26} + 20 q^{27} - 476 q^{28} - 456 q^{29} + 230 q^{31} + 71 q^{32} + 332 q^{33} - 17 q^{34} + 1313 q^{36} - 356 q^{37} - 724 q^{38} + 268 q^{39} - 294 q^{41} + 1128 q^{42} - 556 q^{43} - 1122 q^{44} - 704 q^{46} - 640 q^{47} - 774 q^{48} - 269 q^{49} - 68 q^{51} + 774 q^{52} - 302 q^{53} - 1100 q^{54} + 684 q^{56} + 720 q^{57} + 1304 q^{58} + 636 q^{59} - 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} + 2468 q^{66} - 1008 q^{67} + 425 q^{68} + 576 q^{69} - 402 q^{71} + 927 q^{72} - 838 q^{73} + 836 q^{74} - 908 q^{76} + 504 q^{77} - 1308 q^{78} - 594 q^{79} - 505 q^{81} - 358 q^{82} + 2396 q^{83} - 2040 q^{84} - 1264 q^{86} - 1428 q^{87} - 1838 q^{88} - 170 q^{89} - 1016 q^{91} - 4896 q^{92} - 632 q^{93} - 2016 q^{94} + 678 q^{96} + 270 q^{97} - 2857 q^{98} - 2920 q^{99}+O(q^{100}) \) 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 - 28 * q^11 - 22 * q^12 - 30 * q^13 + 92 * q^14 + 137 * q^16 + 51 * q^17 + 103 * q^18 + 80 * q^19 - 192 * q^21 - 286 * q^22 - 142 * q^23 - 666 * q^24 + 26 * q^26 + 20 * q^27 - 476 * q^28 - 456 * q^29 + 230 * q^31 + 71 * q^32 + 332 * q^33 - 17 * q^34 + 1313 * q^36 - 356 * q^37 - 724 * q^38 + 268 * q^39 - 294 * q^41 + 1128 * q^42 - 556 * q^43 - 1122 * q^44 - 704 * q^46 - 640 * q^47 - 774 * q^48 - 269 * q^49 - 68 * q^51 + 774 * q^52 - 302 * q^53 - 1100 * q^54 + 684 * q^56 + 720 * q^57 + 1304 * q^58 + 636 * q^59 - 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 + 2468 * q^66 - 1008 * q^67 + 425 * q^68 + 576 * q^69 - 402 * q^71 + 927 * q^72 - 838 * q^73 + 836 * q^74 - 908 * q^76 + 504 * q^77 - 1308 * q^78 - 594 * q^79 - 505 * q^81 - 358 * q^82 + 2396 * q^83 - 2040 * q^84 - 1264 * q^86 - 1428 * q^87 - 1838 * q^88 - 170 * q^89 - 1016 * q^91 - 4896 * q^92 - 632 * q^93 - 2016 * q^94 + 678 * q^96 + 270 * q^97 - 2857 * q^98 - 2920 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5.03251	1.77926	0.889630	−	0.456681i	$-0.150962\pi$
$2$	5.03251	1.77926	0.889630	+	0.456681i	$0.150962\pi$
$3$	−8.47535	−1.63108	−0.815541	−	0.578699i	$-0.803561\pi$
$3$	−8.47535	−1.63108	−0.815541	+	0.578699i	$0.803561\pi$
$4$	17.3261	2.16577
$5$	0	0
$5$	0	0
$6$	−42.6523	−2.90212
$7$	−3.81828	−0.206168	−0.103084	−	0.994673i	$-0.532871\pi$
$7$	−3.81828	−0.206168	−0.103084	+	0.994673i	$0.532871\pi$
$8$	46.9339	2.07421
$9$	44.8316	1.66043
$10$	0	0
$11$	−52.3720	−1.43552	−0.717761	−	0.696289i	$-0.754833\pi$
$11$	−52.3720	−1.43552	−0.717761	+	0.696289i	$0.754833\pi$
$12$	−146.845	−3.53255
$13$	8.06025	0.171962	0.0859811	−	0.996297i	$-0.472598\pi$
$13$	8.06025	0.171962	0.0859811	+	0.996297i	$0.472598\pi$
$14$	−19.2156	−0.366827
$15$	0	0
$16$	97.5862	1.52478
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	225.616	2.95434
$19$	−66.5154	−0.803141	−0.401570	−	0.915828i	$-0.631535\pi$
$19$	−66.5154	−0.803141	−0.401570	+	0.915828i	$0.631535\pi$
$20$	0	0
$21$	32.3613	0.336277
$22$	−263.563	−2.55417
$23$	−180.226	−1.63390	−0.816948	−	0.576711i	$-0.804336\pi$
$23$	−180.226	−1.63390	−0.816948	+	0.576711i	$0.804336\pi$
$24$	−397.782	−3.38320
$25$	0	0
$26$	40.5633	0.305966
$27$	−151.129	−1.07722
$28$	−66.1562	−0.446512
$29$	−41.2800	−0.264328	−0.132164	−	0.991228i	$-0.542193\pi$
$29$	−41.2800	−0.264328	−0.132164	+	0.991228i	$0.542193\pi$
$30$	0	0
$31$	−34.9114	−0.202267	−0.101133	−	0.994873i	$-0.532247\pi$
$31$	−34.9114	−0.202267	−0.101133	+	0.994873i	$0.532247\pi$
$32$	115.632	0.638783
$33$	443.871	2.34146
$34$	85.5527	0.431534
$35$	0	0
$36$	776.759	3.59611
$37$	−130.368	−0.579255	−0.289627	−	0.957139i	$-0.593531\pi$
$37$	−130.368	−0.579255	−0.289627	+	0.957139i	$0.593531\pi$
$38$	−334.739	−1.42900
$39$	−68.3134	−0.280485
$40$	0	0
$41$	−17.9081	−0.0682142	−0.0341071	−	0.999418i	$-0.510859\pi$
$41$	−17.9081	−0.0682142	−0.0341071	+	0.999418i	$0.510859\pi$
$42$	162.859	0.598325
$43$	−277.620	−0.984573	−0.492287	−	0.870433i	$-0.663839\pi$
$43$	−277.620	−0.984573	−0.492287	+	0.870433i	$0.663839\pi$
$44$	−907.405	−3.10901
$45$	0	0
$46$	−906.987	−2.90713
$47$	−463.789	−1.43937	−0.719687	−	0.694299i	$-0.755715\pi$
$47$	−463.789	−1.43937	−0.719687	+	0.694299i	$0.755715\pi$
$48$	−827.078	−2.48705
$49$	−328.421	−0.957495
$50$	0	0
$51$	−144.081	−0.395596
$52$	139.653	0.372431
$53$	329.944	0.855118	0.427559	−	0.903987i	$-0.359374\pi$
$53$	329.944	0.855118	0.427559	+	0.903987i	$0.359374\pi$
$54$	−760.560	−1.91665
$55$	0	0
$56$	−179.207	−0.427635
$57$	563.741	1.30999
$58$	−207.742	−0.470308
$59$	678.656	1.49752	0.748759	−	0.662843i	$-0.230650\pi$
$59$	678.656	1.49752	0.748759	+	0.662843i	$0.230650\pi$
$60$	0	0
$61$	340.280	0.714237	0.357118	−	0.934059i	$-0.383759\pi$
$61$	340.280	0.714237	0.357118	+	0.934059i	$0.383759\pi$
$62$	−175.692	−0.359885
$63$	−171.180	−0.342328
$64$	−198.770	−0.388223
$65$	0	0
$66$	2233.79	4.16606
$67$	−15.3925	−0.0280671	−0.0140336	−	0.999902i	$-0.504467\pi$
$67$	−15.3925	−0.0280671	−0.0140336	+	0.999902i	$0.504467\pi$
$68$	294.545	0.525276
$69$	1527.48	2.66502
$70$	0	0
$71$	−670.203	−1.12026	−0.560130	−	0.828405i	$-0.689249\pi$
$71$	−670.203	−1.12026	−0.560130	+	0.828405i	$0.689249\pi$
$72$	2104.12	3.44408
$73$	−193.480	−0.310207	−0.155103	−	0.987898i	$-0.549571\pi$
$73$	−193.480	−0.310207	−0.155103	+	0.987898i	$0.549571\pi$
$74$	−656.080	−1.03065
$75$	0	0
$76$	−1152.46	−1.73942
$77$	199.971	0.295959
$78$	−343.788	−0.499055
$79$	1080.15	1.53831	0.769156	−	0.639061i	$-0.220677\pi$
$79$	1080.15	1.53831	0.769156	+	0.639061i	$0.220677\pi$
$80$	0	0
$81$	70.4207	0.0965990
$82$	−90.1229	−0.121371
$83$	865.668	1.14481	0.572406	−	0.819970i	$-0.306010\pi$
$83$	865.668	1.14481	0.572406	+	0.819970i	$0.306010\pi$
$84$	560.697	0.728298
$85$	0	0
$86$	−1397.13	−1.75181
$87$	349.863	0.431141
$88$	−2458.02	−2.97757
$89$	1129.46	1.34520	0.672599	−	0.740008i	$-0.265178\pi$
$89$	1129.46	1.34520	0.672599	+	0.740008i	$0.265178\pi$
$90$	0	0
$91$	−30.7763	−0.0354531
$92$	−3122.61	−3.53864
$93$	295.886	0.329914
$94$	−2334.02	−2.56102
$95$	0	0
$96$	−980.023	−1.04191
$97$	379.412	0.397149	0.198574	−	0.980086i	$-0.436369\pi$
$97$	379.412	0.397149	0.198574	+	0.980086i	$0.436369\pi$
$98$	−1652.78	−1.70363
$99$	−2347.92	−2.38359
$100$	0	0
$101$	131.732	0.129780	0.0648902	−	0.997892i	$-0.479330\pi$
$101$	131.732	0.129780	0.0648902	+	0.997892i	$0.479330\pi$
$102$	−725.089	−0.703868
$103$	−195.988	−0.187488	−0.0937442	−	0.995596i	$-0.529884\pi$
$103$	−195.988	−0.187488	−0.0937442	+	0.995596i	$0.529884\pi$
$104$	378.299	0.356685
$105$	0	0
$106$	1660.45	1.52148
$107$	485.147	0.438326	0.219163	−	0.975688i	$-0.429667\pi$
$107$	485.147	0.438326	0.219163	+	0.975688i	$0.429667\pi$
$108$	−2618.49	−2.33300
$109$	−1255.12	−1.10292	−0.551460	−	0.834201i	$-0.685929\pi$
$109$	−1255.12	−1.10292	−0.551460	+	0.834201i	$0.685929\pi$
$110$	0	0
$111$	1104.92	0.944812
$112$	−372.612	−0.314362
$113$	1013.35	0.843612	0.421806	−	0.906686i	$-0.361396\pi$
$113$	1013.35	0.843612	0.421806	+	0.906686i	$0.361396\pi$
$114$	2837.03	2.33081
$115$	0	0
$116$	−715.224	−0.572473
$117$	361.354	0.285531
$118$	3415.34	2.66447
$119$	−64.9108	−0.0500031
$120$	0	0
$121$	1411.83	1.06073
$122$	1712.46	1.27081
$123$	151.778	0.111263
$124$	−604.880	−0.438063
$125$	0	0
$126$	−861.464	−0.609090
$127$	−1927.72	−1.34691	−0.673456	−	0.739227i	$-0.735191\pi$
$127$	−1927.72	−1.34691	−0.673456	+	0.739227i	$0.735191\pi$
$128$	−1925.37	−1.32953
$129$	2352.93	1.60592
$130$	0	0
$131$	−406.738	−0.271274	−0.135637	−	0.990759i	$-0.543308\pi$
$131$	−406.738	−0.271274	−0.135637	+	0.990759i	$0.543308\pi$
$132$	7690.58	5.07105
$133$	253.975	0.165582
$134$	−77.4631	−0.0499387
$135$	0	0
$136$	797.877	0.503069
$137$	130.552	0.0814149	0.0407074	−	0.999171i	$-0.487039\pi$
$137$	130.552	0.0814149	0.0407074	+	0.999171i	$0.487039\pi$
$138$	7687.03	4.74177
$139$	2073.54	1.26529	0.632644	−	0.774443i	$-0.281970\pi$
$139$	2073.54	1.26529	0.632644	+	0.774443i	$0.281970\pi$
$140$	0	0
$141$	3930.78	2.34774
$142$	−3372.80	−1.99323
$143$	−422.131	−0.246856
$144$	4374.95	2.53180
$145$	0	0
$146$	−973.689	−0.551939
$147$	2783.48	1.56175
$148$	−2258.78	−1.25453
$149$	−1852.73	−1.01867	−0.509334	−	0.860569i	$-0.670108\pi$
$149$	−1852.73	−1.01867	−0.509334	+	0.860569i	$0.670108\pi$
$150$	0	0
$151$	2050.86	1.10527	0.552637	−	0.833422i	$-0.313622\pi$
$151$	2050.86	1.10527	0.552637	+	0.833422i	$0.313622\pi$
$152$	−3121.83	−1.66588
$153$	762.138	0.402714
$154$	1006.36	0.526588
$155$	0	0
$156$	−1183.61	−0.607465
$157$	262.991	0.133688	0.0668438	−	0.997763i	$-0.478707\pi$
$157$	262.991	0.133688	0.0668438	+	0.997763i	$0.478707\pi$
$158$	5435.88	2.73706
$159$	−2796.39	−1.39477
$160$	0	0
$161$	688.152	0.336857
$162$	354.393	0.171875
$163$	1444.98	0.694354	0.347177	−	0.937800i	$-0.387140\pi$
$163$	1444.98	0.694354	0.347177	+	0.937800i	$0.387140\pi$
$164$	−310.279	−0.147736
$165$	0	0
$166$	4356.48	2.03692
$167$	501.565	0.232409	0.116204	−	0.993225i	$-0.462927\pi$
$167$	501.565	0.232409	0.116204	+	0.993225i	$0.462927\pi$
$168$	1518.84	0.697508
$169$	−2132.03	−0.970429
$170$	0	0
$171$	−2981.99	−1.33356
$172$	−4810.08	−2.13236
$173$	2590.14	1.13829	0.569146	−	0.822237i	$-0.307274\pi$
$173$	2590.14	1.13829	0.569146	+	0.822237i	$0.307274\pi$
$174$	1760.69	0.767112
$175$	0	0
$176$	−5110.79	−2.18886
$177$	−5751.85	−2.44257
$178$	5684.02	2.39346
$179$	2165.65	0.904294	0.452147	−	0.891943i	$-0.350658\pi$
$179$	2165.65	0.904294	0.452147	+	0.891943i	$0.350658\pi$
$180$	0	0
$181$	−1925.56	−0.790750	−0.395375	−	0.918520i	$-0.629385\pi$
$181$	−1925.56	−0.790750	−0.395375	+	0.918520i	$0.629385\pi$
$182$	−154.882	−0.0630803
$183$	−2884.00	−1.16498
$184$	−8458.69	−3.38904
$185$	0	0
$186$	1489.05	0.587003
$187$	−890.324	−0.348165
$188$	−8035.68	−3.11735
$189$	577.055	0.222088
$190$	0	0
$191$	−2783.52	−1.05449	−0.527247	−	0.849712i	$-0.676776\pi$
$191$	−2783.52	−1.05449	−0.527247	+	0.849712i	$0.676776\pi$
$192$	1684.65	0.633223
$193$	−2258.27	−0.842246	−0.421123	−	0.907004i	$-0.638364\pi$
$193$	−2258.27	−0.842246	−0.421123	+	0.907004i	$0.638364\pi$
$194$	1909.39	0.706631
$195$	0	0
$196$	−5690.27	−2.07371
$197$	1270.70	0.459560	0.229780	−	0.973243i	$-0.426199\pi$
$197$	1270.70	0.459560	0.229780	+	0.973243i	$0.426199\pi$
$198$	−11815.9	−4.24102
$199$	−4794.36	−1.70786	−0.853928	−	0.520392i	$-0.825786\pi$
$199$	−4794.36	−1.70786	−0.853928	+	0.520392i	$0.825786\pi$
$200$	0	0
$201$	130.457	0.0457798
$202$	662.942	0.230913
$203$	157.619	0.0544960
$204$	−2496.37	−0.856769
$205$	0	0
$206$	−986.313	−0.333591
$207$	−8079.80	−2.71297
$208$	786.569	0.262205
$209$	3483.54	1.15293
$210$	0	0
$211$	−2807.00	−0.915837	−0.457918	−	0.888994i	$-0.651405\pi$
$211$	−2807.00	−0.915837	−0.457918	+	0.888994i	$0.651405\pi$
$212$	5716.66	1.85199
$213$	5680.21	1.82724
$214$	2441.50	0.779896
$215$	0	0
$216$	−7093.09	−2.23437
$217$	133.302	0.0417009
$218$	−6316.38	−1.96238
$219$	1639.81	0.505973
$220$	0	0
$221$	137.024	0.0417070
$222$	5560.51	1.68107
$223$	−4684.30	−1.40665	−0.703327	−	0.710866i	$-0.748303\pi$
$223$	−4684.30	−1.40665	−0.703327	+	0.710866i	$0.748303\pi$
$224$	−441.516	−0.131697
$225$	0	0
$226$	5099.70	1.50101
$227$	1395.72	0.408095	0.204047	−	0.978961i	$-0.434590\pi$
$227$	1395.72	0.408095	0.204047	+	0.978961i	$0.434590\pi$
$228$	9767.47	2.83713
$229$	894.638	0.258163	0.129082	−	0.991634i	$-0.458797\pi$
$229$	894.638	0.258163	0.129082	+	0.991634i	$0.458797\pi$
$230$	0	0
$231$	−1694.83	−0.482733
$232$	−1937.43	−0.548270
$233$	−1196.13	−0.336313	−0.168156	−	0.985760i	$-0.553781\pi$
$233$	−1196.13	−0.336313	−0.168156	+	0.985760i	$0.553781\pi$
$234$	1818.52	0.508035
$235$	0	0
$236$	11758.5	3.24328
$237$	−9154.67	−2.50911
$238$	−326.664	−0.0889685
$239$	4948.82	1.33938	0.669691	−	0.742639i	$-0.266426\pi$
$239$	4948.82	1.33938	0.669691	+	0.742639i	$0.266426\pi$
$240$	0	0
$241$	−6702.73	−1.79154	−0.895770	−	0.444518i	$-0.853375\pi$
$241$	−6702.73	−1.79154	−0.895770	+	0.444518i	$0.853375\pi$
$242$	7105.03	1.88731
$243$	3483.65	0.919656
$244$	5895.75	1.54687
$245$	0	0
$246$	763.824	0.197966
$247$	−536.130	−0.138110
$248$	−1638.53	−0.419543
$249$	−7336.85	−1.86728
$250$	0	0
$251$	−4756.08	−1.19602	−0.598010	−	0.801489i	$-0.704042\pi$
$251$	−4756.08	−1.19602	−0.598010	+	0.801489i	$0.704042\pi$
$252$	−2965.89	−0.741402
$253$	9438.77	2.34550
$254$	−9701.29	−2.39651
$255$	0	0
$256$	−8099.28	−1.97736
$257$	−2892.84	−0.702143	−0.351071	−	0.936349i	$-0.614183\pi$
$257$	−2892.84	−0.702143	−0.351071	+	0.936349i	$0.614183\pi$
$258$	11841.1	2.85735
$259$	497.784	0.119424
$260$	0	0
$261$	−1850.65	−0.438898
$262$	−2046.92	−0.482667
$263$	−5415.48	−1.26971	−0.634853	−	0.772633i	$-0.718939\pi$
$263$	−5415.48	−1.26971	−0.634853	+	0.772633i	$0.718939\pi$
$264$	20832.6	4.85666
$265$	0	0
$266$	1278.13	0.294613
$267$	−9572.58	−2.19413
$268$	−266.693	−0.0607869
$269$	5787.00	1.31167	0.655835	−	0.754904i	$-0.272317\pi$
$269$	5787.00	1.31167	0.655835	+	0.754904i	$0.272317\pi$
$270$	0	0
$271$	5465.13	1.22503	0.612515	−	0.790459i	$-0.290158\pi$
$271$	5465.13	1.22503	0.612515	+	0.790459i	$0.290158\pi$
$272$	1658.97	0.369815
$273$	260.840	0.0578270
$274$	657.006	0.144858
$275$	0	0
$276$	26465.3	5.77182
$277$	1207.65	0.261952	0.130976	−	0.991386i	$-0.458189\pi$
$277$	1207.65	0.261952	0.130976	+	0.991386i	$0.458189\pi$
$278$	10435.1	2.25128
$279$	−1565.13	−0.335850
$280$	0	0
$281$	−1197.18	−0.254155	−0.127077	−	0.991893i	$-0.540560\pi$
$281$	−1197.18	−0.254155	−0.127077	+	0.991893i	$0.540560\pi$
$282$	19781.7	4.17724
$283$	−3164.73	−0.664748	−0.332374	−	0.943148i	$-0.607850\pi$
$283$	−3164.73	−0.664748	−0.332374	+	0.943148i	$0.607850\pi$
$284$	−11612.0	−2.42622
$285$	0	0
$286$	−2124.38	−0.439221
$287$	68.3784	0.0140636
$288$	5183.98	1.06066
$289$	289.000	0.0588235
$290$	0	0
$291$	−3215.65	−0.647782
$292$	−3352.26	−0.671836
$293$	−7456.21	−1.48668	−0.743339	−	0.668915i	$-0.766759\pi$
$293$	−7456.21	−1.48668	−0.743339	+	0.668915i	$0.766759\pi$
$294$	14007.9	2.77877
$295$	0	0
$296$	−6118.70	−1.20149
$297$	7914.94	1.54637
$298$	−9323.89	−1.81248
$299$	−1452.66	−0.280969
$300$	0	0
$301$	1060.03	0.202988
$302$	10321.0	1.96657
$303$	−1116.47	−0.211683
$304$	−6490.98	−1.22462
$305$	0	0
$306$	3835.46	0.716532
$307$	6535.48	1.21498	0.607491	−	0.794327i	$-0.292176\pi$
$307$	6535.48	1.21498	0.607491	+	0.794327i	$0.292176\pi$
$308$	3464.73	0.640978
$309$	1661.07	0.305809
$310$	0	0
$311$	−8935.89	−1.62928	−0.814642	−	0.579963i	$-0.803067\pi$
$311$	−8935.89	−1.62928	−0.814642	+	0.579963i	$0.803067\pi$
$312$	−3206.22	−0.581783
$313$	2628.71	0.474707	0.237353	−	0.971423i	$-0.423720\pi$
$313$	2628.71	0.474707	0.237353	+	0.971423i	$0.423720\pi$
$314$	1323.50	0.237865
$315$	0	0
$316$	18714.9	3.33163
$317$	−4268.54	−0.756293	−0.378147	−	0.925746i	$-0.623438\pi$
$317$	−4268.54	−0.756293	−0.378147	+	0.925746i	$0.623438\pi$
$318$	−14072.9	−2.48166
$319$	2161.92	0.379449
$320$	0	0
$321$	−4111.79	−0.714946
$322$	3463.13	0.599357
$323$	−1130.76	−0.194790
$324$	1220.12	0.209211
$325$	0	0
$326$	7271.89	1.23544
$327$	10637.5	1.79895
$328$	−840.500	−0.141490
$329$	1770.88	0.296753
$330$	0	0
$331$	992.298	0.164778	0.0823892	−	0.996600i	$-0.473745\pi$
$331$	992.298	0.164778	0.0823892	+	0.996600i	$0.473745\pi$
$332$	14998.7	2.47940
$333$	−5844.63	−0.961812
$334$	2524.13	0.413516
$335$	0	0
$336$	3158.02	0.512750
$337$	−8042.26	−1.29997	−0.649985	−	0.759947i	$-0.725225\pi$
$337$	−8042.26	−1.29997	−0.649985	+	0.759947i	$0.725225\pi$
$338$	−10729.5	−1.72665
$339$	−8588.52	−1.37600
$340$	0	0
$341$	1828.38	0.290359
$342$	−15006.9	−2.37275
$343$	2563.68	0.403573
$344$	−13029.8	−2.04221
$345$	0	0
$346$	13034.9	2.02532
$347$	7414.16	1.14701	0.573506	−	0.819202i	$-0.305583\pi$
$347$	7414.16	1.14701	0.573506	+	0.819202i	$0.305583\pi$
$348$	6061.78	0.933751
$349$	−859.194	−0.131781	−0.0658905	−	0.997827i	$-0.520989\pi$
$349$	−859.194	−0.131781	−0.0658905	+	0.997827i	$0.520989\pi$
$350$	0	0
$351$	−1218.14	−0.185241
$352$	−6055.89	−0.916988
$353$	−569.084	−0.0858053	−0.0429027	−	0.999079i	$-0.513661\pi$
$353$	−569.084	−0.0858053	−0.0429027	+	0.999079i	$0.513661\pi$
$354$	−28946.3	−4.34598
$355$	0	0
$356$	19569.2	2.91339
$357$	550.142	0.0815592
$358$	10898.7	1.60897
$359$	−5005.21	−0.735835	−0.367918	−	0.929858i	$-0.619929\pi$
$359$	−5005.21	−0.735835	−0.367918	+	0.929858i	$0.619929\pi$
$360$	0	0
$361$	−2434.71	−0.354965
$362$	−9690.40	−1.40695
$363$	−11965.7	−1.73013
$364$	−533.235	−0.0767833
$365$	0	0
$366$	−14513.7	−2.07280
$367$	10975.3	1.56105	0.780523	−	0.625127i	$-0.214953\pi$
$367$	10975.3	1.56105	0.780523	+	0.625127i	$0.214953\pi$
$368$	−17587.5	−2.49134
$369$	−802.851	−0.113265
$370$	0	0
$371$	−1259.82	−0.176298
$372$	5126.57	0.714517
$373$	3211.72	0.445835	0.222918	−	0.974837i	$-0.428442\pi$
$373$	3211.72	0.445835	0.222918	+	0.974837i	$0.428442\pi$
$374$	−4480.56	−0.619477
$375$	0	0
$376$	−21767.4	−2.98556
$377$	−332.727	−0.0454544
$378$	2904.03	0.395152
$379$	8051.48	1.09123	0.545616	−	0.838035i	$-0.316296\pi$
$379$	8051.48	1.09123	0.545616	+	0.838035i	$0.316296\pi$
$380$	0	0
$381$	16338.1	2.19692
$382$	−14008.1	−1.87622
$383$	2584.16	0.344763	0.172382	−	0.985030i	$-0.444854\pi$
$383$	2584.16	0.344763	0.172382	+	0.985030i	$0.444854\pi$
$384$	16318.2	2.16858
$385$	0	0
$386$	−11364.7	−1.49858
$387$	−12446.2	−1.63482
$388$	6573.74	0.860132
$389$	−5174.31	−0.674417	−0.337208	−	0.941430i	$-0.609483\pi$
$389$	−5174.31	−0.674417	−0.337208	+	0.941430i	$0.609483\pi$
$390$	0	0
$391$	−3063.83	−0.396278
$392$	−15414.1	−1.98604
$393$	3447.25	0.442470
$394$	6394.79	0.817677
$395$	0	0
$396$	−40680.4	−5.16230
$397$	5149.36	0.650980	0.325490	−	0.945545i	$-0.394471\pi$
$397$	5149.36	0.650980	0.325490	+	0.945545i	$0.394471\pi$
$398$	−24127.7	−3.03872
$399$	−2152.53	−0.270078
$400$	0	0
$401$	8700.49	1.08350	0.541748	−	0.840541i	$-0.317763\pi$
$401$	8700.49	1.08350	0.541748	+	0.840541i	$0.317763\pi$
$402$	656.527	0.0814542
$403$	−281.394	−0.0347823
$404$	2282.41	0.281074
$405$	0	0
$406$	793.219	0.0969625
$407$	6827.65	0.831533
$408$	−6762.29	−0.820547
$409$	12346.0	1.49260	0.746299	−	0.665611i	$-0.231829\pi$
$409$	12346.0	1.49260	0.746299	+	0.665611i	$0.231829\pi$
$410$	0	0
$411$	−1106.48	−0.132794
$412$	−3395.72	−0.406056
$413$	−2591.30	−0.308740
$414$	−40661.7	−4.82708
$415$	0	0
$416$	932.023	0.109847
$417$	−17574.0	−2.06379
$418$	17531.0	2.05136
$419$	−5763.33	−0.671974	−0.335987	−	0.941867i	$-0.609070\pi$
$419$	−5763.33	−0.671974	−0.335987	+	0.941867i	$0.609070\pi$
$420$	0	0
$421$	−1876.12	−0.217188	−0.108594	−	0.994086i	$-0.534635\pi$
$421$	−1876.12	−0.217188	−0.108594	+	0.994086i	$0.534635\pi$
$422$	−14126.2	−1.62951
$423$	−20792.4	−2.38998
$424$	15485.6	1.77369
$425$	0	0
$426$	28585.7	3.25113
$427$	−1299.29	−0.147253
$428$	8405.72	0.949313
$429$	3577.71	0.402642
$430$	0	0
$431$	83.9299	0.00937996	0.00468998	−	0.999989i	$-0.498507\pi$
$431$	83.9299	0.00937996	0.00468998	+	0.999989i	$0.498507\pi$
$432$	−14748.1	−1.64252
$433$	15345.0	1.70308	0.851539	−	0.524291i	$-0.175669\pi$
$433$	15345.0	1.70308	0.851539	+	0.524291i	$0.175669\pi$
$434$	670.842	0.0741968
$435$	0	0
$436$	−21746.3	−2.38867
$437$	11987.8	1.31225
$438$	8252.36	0.900258
$439$	3064.74	0.333194	0.166597	−	0.986025i	$-0.446722\pi$
$439$	3064.74	0.333194	0.166597	+	0.986025i	$0.446722\pi$
$440$	0	0
$441$	−14723.6	−1.58985
$442$	689.575	0.0742076
$443$	1792.97	0.192295	0.0961474	−	0.995367i	$-0.469348\pi$
$443$	1792.97	0.192295	0.0961474	+	0.995367i	$0.469348\pi$
$444$	19144.0	2.04624
$445$	0	0
$446$	−23573.8	−2.50281
$447$	15702.6	1.66153
$448$	758.960	0.0800391
$449$	2499.19	0.262681	0.131341	−	0.991337i	$-0.458072\pi$
$449$	2499.19	0.262681	0.131341	+	0.991337i	$0.458072\pi$
$450$	0	0
$451$	937.885	0.0979231
$452$	17557.5	1.82707
$453$	−17381.7	−1.80279
$454$	7024.00	0.726107
$455$	0	0
$456$	26458.6	2.71719
$457$	−14784.4	−1.51331	−0.756656	−	0.653813i	$-0.773168\pi$
$457$	−14784.4	−1.51331	−0.756656	+	0.653813i	$0.773168\pi$
$458$	4502.28	0.459340
$459$	−2569.20	−0.261263
$460$	0	0
$461$	−17746.9	−1.79297	−0.896483	−	0.443078i	$-0.853887\pi$
$461$	−17746.9	−1.79297	−0.896483	+	0.443078i	$0.853887\pi$
$462$	−8529.23	−0.858909
$463$	−18486.4	−1.85559	−0.927793	−	0.373096i	$-0.878296\pi$
$463$	−18486.4	−1.85559	−0.927793	+	0.373096i	$0.878296\pi$
$464$	−4028.36	−0.403043
$465$	0	0
$466$	−6019.52	−0.598388
$467$	−7406.57	−0.733908	−0.366954	−	0.930239i	$-0.619599\pi$
$467$	−7406.57	−0.733908	−0.366954	+	0.930239i	$0.619599\pi$
$468$	6260.87	0.618395
$469$	58.7731	0.00578655
$470$	0	0
$471$	−2228.94	−0.218055
$472$	31852.0	3.10616
$473$	14539.5	1.41338
$474$	−46071.0	−4.46437
$475$	0	0
$476$	−1124.65	−0.108295
$477$	14791.9	1.41986
$478$	24905.0	2.38311
$479$	−18550.9	−1.76955	−0.884775	−	0.466019i	$-0.845688\pi$
$479$	−18550.9	−1.76955	−0.884775	+	0.466019i	$0.845688\pi$
$480$	0	0
$481$	−1050.80	−0.0996100
$482$	−33731.6	−3.18762
$483$	−5832.34	−0.549442
$484$	24461.5	2.29729
$485$	0	0
$486$	17531.5	1.63631
$487$	−10203.4	−0.949406	−0.474703	−	0.880146i	$-0.657444\pi$
$487$	−10203.4	−0.949406	−0.474703	+	0.880146i	$0.657444\pi$
$488$	15970.7	1.48147
$489$	−12246.7	−1.13255
$490$	0	0
$491$	−1247.46	−0.114658	−0.0573290	−	0.998355i	$-0.518258\pi$
$491$	−1247.46	−0.114658	−0.0573290	+	0.998355i	$0.518258\pi$
$492$	2629.73	0.240970
$493$	−701.760	−0.0641089
$494$	−2698.08	−0.245734
$495$	0	0
$496$	−3406.87	−0.308413
$497$	2559.03	0.230962
$498$	−36922.7	−3.32238
$499$	70.0303	0.00628254	0.00314127	−	0.999995i	$-0.499000\pi$
$499$	70.0303	0.00628254	0.00314127	+	0.999995i	$0.499000\pi$
$500$	0	0
$501$	−4250.94	−0.379078
$502$	−23935.0	−2.12803
$503$	−1444.29	−0.128028	−0.0640138	−	0.997949i	$-0.520390\pi$
$503$	−1444.29	−0.128028	−0.0640138	+	0.997949i	$0.520390\pi$
$504$	−8034.15	−0.710058
$505$	0	0
$506$	47500.7	4.17325
$507$	18069.7	1.58285
$508$	−33400.0	−2.91710
$509$	14272.8	1.24289	0.621445	−	0.783458i	$-0.286546\pi$
$509$	14272.8	1.24289	0.621445	+	0.783458i	$0.286546\pi$
$510$	0	0
$511$	738.761	0.0639547
$512$	−25356.7	−2.18871
$513$	10052.4	0.865157
$514$	−14558.3	−1.24929
$515$	0	0
$516$	40767.2	3.47805
$517$	24289.6	2.06625
$518$	2505.10	0.212486
$519$	−21952.3	−1.85665
$520$	0	0
$521$	14874.0	1.25075	0.625376	−	0.780324i	$-0.284946\pi$
$521$	14874.0	1.25075	0.625376	+	0.780324i	$0.284946\pi$
$522$	−9313.42	−0.780914
$523$	8142.90	0.680811	0.340406	−	0.940279i	$-0.389436\pi$
$523$	8142.90	0.680811	0.340406	+	0.940279i	$0.389436\pi$
$524$	−7047.21	−0.587517
$525$	0	0
$526$	−27253.4	−2.25914
$527$	−593.494	−0.0490569
$528$	43315.7	3.57022
$529$	20314.2	1.66962
$530$	0	0
$531$	30425.3	2.48652
$532$	4400.40	0.358612
$533$	−144.344	−0.0117303
$534$	−48174.1	−3.90393
$535$	0	0
$536$	−722.432	−0.0582170
$537$	−18354.7	−1.47498
$538$	29123.1	2.33380
$539$	17200.0	1.37451
$540$	0	0
$541$	3179.67	0.252689	0.126344	−	0.991986i	$-0.459676\pi$
$541$	3179.67	0.252689	0.126344	+	0.991986i	$0.459676\pi$
$542$	27503.3	2.17965
$543$	16319.8	1.28978
$544$	1965.75	0.154928
$545$	0	0
$546$	1312.68	0.102889
$547$	−2107.07	−0.164702	−0.0823509	−	0.996603i	$-0.526243\pi$
$547$	−2107.07	−0.164702	−0.0823509	+	0.996603i	$0.526243\pi$
$548$	2261.97	0.176326
$549$	15255.3	1.18594
$550$	0	0
$551$	2745.76	0.212292
$552$	71690.4	5.52780
$553$	−4124.33	−0.317151
$554$	6077.51	0.466081
$555$	0	0
$556$	35926.4	2.74032
$557$	−467.382	−0.0355540	−0.0177770	−	0.999842i	$-0.505659\pi$
$557$	−467.382	−0.0355540	−0.0177770	+	0.999842i	$0.505659\pi$
$558$	−7876.55	−0.597565
$559$	−2237.69	−0.169309
$560$	0	0
$561$	7545.81	0.567887
$562$	−6024.80	−0.452208
$563$	−14612.6	−1.09387	−0.546935	−	0.837175i	$-0.684206\pi$
$563$	−14612.6	−1.09387	−0.546935	+	0.837175i	$0.684206\pi$
$564$	68105.2	5.08466
$565$	0	0
$566$	−15926.5	−1.18276
$567$	−268.886	−0.0199156
$568$	−31455.3	−2.32365
$569$	11602.3	0.854821	0.427410	−	0.904058i	$-0.359426\pi$
$569$	11602.3	0.854821	0.427410	+	0.904058i	$0.359426\pi$
$570$	0	0
$571$	−10534.9	−0.772104	−0.386052	−	0.922477i	$-0.626161\pi$
$571$	−10534.9	−0.772104	−0.386052	+	0.922477i	$0.626161\pi$
$572$	−7313.91	−0.534633
$573$	23591.3	1.71997
$574$	344.115	0.0250228
$575$	0	0
$576$	−8911.18	−0.644617
$577$	−14404.7	−1.03930	−0.519650	−	0.854379i	$-0.673938\pi$
$577$	−14404.7	−1.03930	−0.519650	+	0.854379i	$0.673938\pi$
$578$	1454.40	0.104662
$579$	19139.6	1.37377
$580$	0	0
$581$	−3305.37	−0.236024
$582$	−16182.8	−1.15257
$583$	−17279.8	−1.22754
$584$	−9080.77	−0.643433
$585$	0	0
$586$	−37523.5	−2.64519
$587$	11004.9	0.773799	0.386900	−	0.922122i	$-0.373546\pi$
$587$	11004.9	0.773799	0.386900	+	0.922122i	$0.373546\pi$
$588$	48227.0	3.38240
$589$	2322.14	0.162449
$590$	0	0
$591$	−10769.6	−0.749581
$592$	−12722.2	−0.883239
$593$	−1853.59	−0.128361	−0.0641804	−	0.997938i	$-0.520443\pi$
$593$	−1853.59	−0.128361	−0.0641804	+	0.997938i	$0.520443\pi$
$594$	39832.0	2.75139
$595$	0	0
$596$	−32100.7	−2.20620
$597$	40633.9	2.78565
$598$	−7310.53	−0.499916
$599$	19074.7	1.30112	0.650559	−	0.759456i	$-0.274535\pi$
$599$	19074.7	1.30112	0.650559	+	0.759456i	$0.274535\pi$
$600$	0	0
$601$	−27776.0	−1.88520	−0.942600	−	0.333923i	$-0.891627\pi$
$601$	−27776.0	−1.88520	−0.942600	+	0.333923i	$0.891627\pi$
$602$	5334.62	0.361168
$603$	−690.073	−0.0466035
$604$	35533.4	2.39377
$605$	0	0
$606$	−5618.67	−0.376638
$607$	−18728.3	−1.25232	−0.626159	−	0.779695i	$-0.715374\pi$
$607$	−18728.3	−1.25232	−0.626159	+	0.779695i	$0.715374\pi$
$608$	−7691.32	−0.513033
$609$	−1335.88	−0.0888874
$610$	0	0
$611$	−3738.25	−0.247518
$612$	13204.9	0.872184
$613$	24405.3	1.60802	0.804012	−	0.594613i	$-0.202695\pi$
$613$	24405.3	1.60802	0.804012	+	0.594613i	$0.202695\pi$
$614$	32889.8	2.16177
$615$	0	0
$616$	9385.43	0.613880
$617$	22516.4	1.46917	0.734584	−	0.678518i	$-0.237377\pi$
$617$	22516.4	1.46917	0.734584	+	0.678518i	$0.237377\pi$
$618$	8359.35	0.544114
$619$	−5146.53	−0.334179	−0.167089	−	0.985942i	$-0.553437\pi$
$619$	−5146.53	−0.334179	−0.167089	+	0.985942i	$0.553437\pi$
$620$	0	0
$621$	27237.4	1.76006
$622$	−44969.9	−2.89892
$623$	−4312.60	−0.277337
$624$	−6666.45	−0.427679
$625$	0	0
$626$	13229.0	0.844627
$627$	−29524.3	−1.88052
$628$	4556.62	0.289536
$629$	−2216.26	−0.140490
$630$	0	0
$631$	−3858.77	−0.243447	−0.121724	−	0.992564i	$-0.538842\pi$
$631$	−3858.77	−0.243447	−0.121724	+	0.992564i	$0.538842\pi$
$632$	50695.8	3.19078
$633$	23790.3	1.49381
$634$	−21481.5	−1.34564
$635$	0	0
$636$	−48450.7	−3.02075
$637$	−2647.15	−0.164653
$638$	10879.9	0.675138
$639$	−30046.3	−1.86011
$640$	0	0
$641$	18689.3	1.15161	0.575805	−	0.817587i	$-0.304689\pi$
$641$	18689.3	1.15161	0.575805	+	0.817587i	$0.304689\pi$
$642$	−20692.6	−1.27208
$643$	−26473.5	−1.62366	−0.811831	−	0.583893i	$-0.801529\pi$
$643$	−26473.5	−1.62366	−0.811831	+	0.583893i	$0.801529\pi$
$644$	11923.0	0.729555
$645$	0	0
$646$	−5690.57	−0.346583
$647$	−14397.7	−0.874855	−0.437427	−	0.899254i	$-0.644110\pi$
$647$	−14397.7	−0.874855	−0.437427	+	0.899254i	$0.644110\pi$
$648$	3305.12	0.200366
$649$	−35542.6	−2.14972
$650$	0	0
$651$	−1129.78	−0.0680177
$652$	25036.0	1.50381
$653$	−20939.5	−1.25486	−0.627431	−	0.778672i	$-0.715893\pi$
$653$	−20939.5	−1.25486	−0.627431	+	0.778672i	$0.715893\pi$
$654$	53533.6	3.20081
$655$	0	0
$656$	−1747.59	−0.104012
$657$	−8674.02	−0.515077
$658$	8911.96	0.528001
$659$	4031.76	0.238323	0.119162	−	0.992875i	$-0.461979\pi$
$659$	4031.76	0.238323	0.119162	+	0.992875i	$0.461979\pi$
$660$	0	0
$661$	6691.52	0.393752	0.196876	−	0.980428i	$-0.436920\pi$
$661$	6691.52	0.393752	0.196876	+	0.980428i	$0.436920\pi$
$662$	4993.75	0.293184
$663$	−1161.33	−0.0680275
$664$	40629.2	2.37458
$665$	0	0
$666$	−29413.1	−1.71131
$667$	7439.71	0.431884
$668$	8690.19	0.503344
$669$	39701.1	2.29437
$670$	0	0
$671$	−17821.2	−1.02530
$672$	3742.01	0.214808
$673$	−10319.2	−0.591048	−0.295524	−	0.955335i	$-0.595494\pi$
$673$	−10319.2	−0.591048	−0.295524	+	0.955335i	$0.595494\pi$
$674$	−40472.7	−2.31298
$675$	0	0
$676$	−36939.9	−2.10172
$677$	19813.3	1.12480	0.562398	−	0.826866i	$-0.309879\pi$
$677$	19813.3	1.12480	0.562398	+	0.826866i	$0.309879\pi$
$678$	−43221.8	−2.44826
$679$	−1448.70	−0.0818793
$680$	0	0
$681$	−11829.3	−0.665636
$682$	9201.33	0.516624
$683$	−5924.61	−0.331916	−0.165958	−	0.986133i	$-0.553072\pi$
$683$	−5924.61	−0.331916	−0.165958	+	0.986133i	$0.553072\pi$
$684$	−51666.4	−2.88818
$685$	0	0
$686$	12901.7	0.718061
$687$	−7582.38	−0.421085
$688$	−27091.9	−1.50126
$689$	2659.43	0.147048
$690$	0	0
$691$	1973.16	0.108629	0.0543143	−	0.998524i	$-0.482703\pi$
$691$	1973.16	0.108629	0.0543143	+	0.998524i	$0.482703\pi$
$692$	44877.1	2.46528
$693$	8965.03	0.491419
$694$	37311.8	2.04083
$695$	0	0
$696$	16420.4	0.894274
$697$	−304.439	−0.0165444
$698$	−4323.90	−0.234473
$699$	10137.6	0.548554
$700$	0	0
$701$	−12840.1	−0.691815	−0.345907	−	0.938269i	$-0.612429\pi$
$701$	−12840.1	−0.691815	−0.345907	+	0.938269i	$0.612429\pi$
$702$	−6130.30	−0.329591
$703$	8671.50	0.465223
$704$	10410.0	0.557302
$705$	0	0
$706$	−2863.92	−0.152670
$707$	−502.990	−0.0267566
$708$	−99657.5	−5.29005
$709$	−27749.7	−1.46990	−0.734952	−	0.678119i	$-0.762796\pi$
$709$	−27749.7	−1.46990	−0.734952	+	0.678119i	$0.762796\pi$
$710$	0	0
$711$	48425.0	2.55426
$712$	53010.0	2.79022
$713$	6291.92	0.330483
$714$	2768.60	0.145115
$715$	0	0
$716$	37522.4	1.95849
$717$	−41943.0	−2.18464
$718$	−25188.8	−1.30924
$719$	16888.3	0.875979	0.437989	−	0.898980i	$-0.355691\pi$
$719$	16888.3	0.875979	0.437989	+	0.898980i	$0.355691\pi$
$720$	0	0
$721$	748.339	0.0386541
$722$	−12252.7	−0.631575
$723$	56808.0	2.92215
$724$	−33362.6	−1.71258
$725$	0	0
$726$	−60217.6	−3.07835
$727$	−2135.25	−0.108930	−0.0544649	−	0.998516i	$-0.517345\pi$
$727$	−2135.25	−0.108930	−0.0544649	+	0.998516i	$0.517345\pi$
$728$	−1444.45	−0.0735371
$729$	−31426.5	−1.59663
$730$	0	0
$731$	−4719.54	−0.238794
$732$	−49968.6	−2.52308
$733$	−4795.27	−0.241633	−0.120817	−	0.992675i	$-0.538551\pi$
$733$	−4795.27	−0.241633	−0.120817	+	0.992675i	$0.538551\pi$
$734$	55233.1	2.77751
$735$	0	0
$736$	−20839.9	−1.04371
$737$	806.138	0.0402910
$738$	−4040.36	−0.201528
$739$	−32747.6	−1.63010	−0.815048	−	0.579393i	$-0.803290\pi$
$739$	−32747.6	−1.63010	−0.815048	+	0.579393i	$0.803290\pi$
$740$	0	0
$741$	4543.89	0.225269
$742$	−6340.05	−0.313680
$743$	−12299.4	−0.607298	−0.303649	−	0.952784i	$-0.598205\pi$
$743$	−12299.4	−0.607298	−0.303649	+	0.952784i	$0.598205\pi$
$744$	13887.1	0.684309
$745$	0	0
$746$	16163.0	0.793257
$747$	38809.3	1.90088
$748$	−15425.9	−0.754046
$749$	−1852.43	−0.0903688
$750$	0	0
$751$	30102.6	1.46266	0.731332	−	0.682021i	$-0.238899\pi$
$751$	30102.6	1.46266	0.731332	+	0.682021i	$0.238899\pi$
$752$	−45259.4	−2.19474
$753$	40309.4	1.95081
$754$	−1674.45	−0.0808753
$755$	0	0
$756$	9998.14	0.480990
$757$	−38826.3	−1.86416	−0.932078	−	0.362257i	$-0.882006\pi$
$757$	−38826.3	−1.86416	−0.932078	+	0.362257i	$0.882006\pi$
$758$	40519.2	1.94159
$759$	−79996.9	−3.82570
$760$	0	0
$761$	19981.6	0.951815	0.475907	−	0.879495i	$-0.342120\pi$
$761$	19981.6	0.951815	0.475907	+	0.879495i	$0.342120\pi$
$762$	82221.8	3.90890
$763$	4792.39	0.227387
$764$	−48227.7	−2.28379
$765$	0	0
$766$	13004.8	0.613424
$767$	5470.14	0.257517
$768$	68644.2	3.22524
$769$	−22407.7	−1.05077	−0.525384	−	0.850865i	$-0.676078\pi$
$769$	−22407.7	−1.05077	−0.525384	+	0.850865i	$0.676078\pi$
$770$	0	0
$771$	24517.9	1.14525
$772$	−39127.0	−1.82411
$773$	6902.77	0.321184	0.160592	−	0.987021i	$-0.448660\pi$
$773$	6902.77	0.321184	0.160592	+	0.987021i	$0.448660\pi$
$774$	−62635.4	−2.90876
$775$	0	0
$776$	17807.3	0.823768
$777$	−4218.89	−0.194790
$778$	−26039.8	−1.19996
$779$	1191.17	0.0547856
$780$	0	0
$781$	35099.9	1.60816
$782$	−15418.8	−0.705082
$783$	6238.62	0.284738
$784$	−32049.3	−1.45997
$785$	0	0
$786$	17348.3	0.787270
$787$	22185.9	1.00488	0.502442	−	0.864611i	$-0.332435\pi$
$787$	22185.9	1.00488	0.502442	+	0.864611i	$0.332435\pi$
$788$	22016.3	0.995301
$789$	45898.1	2.07099
$790$	0	0
$791$	−3869.27	−0.173926
$792$	−110197.	−4.94405
$793$	2742.74	0.122822
$794$	25914.2	1.15826
$795$	0	0
$796$	−83067.8	−3.69882
$797$	16291.1	0.724040	0.362020	−	0.932170i	$-0.382087\pi$
$797$	16291.1	0.724040	0.362020	+	0.932170i	$0.382087\pi$
$798$	−10832.6	−0.480539
$799$	−7884.41	−0.349100
$800$	0	0
$801$	50635.5	2.23361
$802$	43785.3	1.92782
$803$	10132.9	0.445309
$804$	2260.32	0.0991485
$805$	0	0
$806$	−1416.12	−0.0618867
$807$	−49046.8	−2.13944
$808$	6182.70	0.269191
$809$	17696.8	0.769082	0.384541	−	0.923108i	$-0.374360\pi$
$809$	17696.8	0.769082	0.384541	+	0.923108i	$0.374360\pi$
$810$	0	0
$811$	−3095.34	−0.134022	−0.0670111	−	0.997752i	$-0.521346\pi$
$811$	−3095.34	−0.134022	−0.0670111	+	0.997752i	$0.521346\pi$
$812$	2730.93	0.118026
$813$	−46318.9	−1.99812
$814$	34360.2	1.47951
$815$	0	0
$816$	−14060.3	−0.603198
$817$	18466.0	0.790751
$818$	62131.5	2.65572
$819$	−1379.75	−0.0588674
$820$	0	0
$821$	12323.5	0.523864	0.261932	−	0.965086i	$-0.415640\pi$
$821$	12323.5	0.523864	0.261932	+	0.965086i	$0.415640\pi$
$822$	−5568.36	−0.236276
$823$	34436.5	1.45854	0.729271	−	0.684225i	$-0.239860\pi$
$823$	34436.5	1.45854	0.729271	+	0.684225i	$0.239860\pi$
$824$	−9198.50	−0.388889
$825$	0	0
$826$	−13040.8	−0.549329
$827$	−18761.6	−0.788880	−0.394440	−	0.918922i	$-0.629061\pi$
$827$	−18761.6	−0.788880	−0.394440	+	0.918922i	$0.629061\pi$
$828$	−139992.	−5.87567
$829$	22423.8	0.939457	0.469728	−	0.882811i	$-0.344352\pi$
$829$	22423.8	0.939457	0.469728	+	0.882811i	$0.344352\pi$
$830$	0	0
$831$	−10235.3	−0.427265
$832$	−1602.13	−0.0667596
$833$	−5583.15	−0.232227
$834$	−88441.1	−3.67202
$835$	0	0
$836$	60356.4	2.49697
$837$	5276.13	0.217885
$838$	−29004.0	−1.19562
$839$	9128.63	0.375632	0.187816	−	0.982204i	$-0.439859\pi$
$839$	9128.63	0.375632	0.187816	+	0.982204i	$0.439859\pi$
$840$	0	0
$841$	−22685.0	−0.930131
$842$	−9441.58	−0.386435
$843$	10146.5	0.414547
$844$	−48634.4	−1.98349
$845$	0	0
$846$	−104638.	−4.25240
$847$	−5390.75	−0.218688
$848$	32198.0	1.30387
$849$	26822.2	1.08426
$850$	0	0
$851$	23495.7	0.946442
$852$	98416.1	3.95737
$853$	−27204.8	−1.09200	−0.545999	−	0.837786i	$-0.683850\pi$
$853$	−27204.8	−1.09200	−0.545999	+	0.837786i	$0.683850\pi$
$854$	−6538.68	−0.262001
$855$	0	0
$856$	22769.8	0.909179
$857$	38060.0	1.51704	0.758520	−	0.651649i	$-0.225923\pi$
$857$	38060.0	1.51704	0.758520	+	0.651649i	$0.225923\pi$
$858$	18004.9	0.716405
$859$	−33326.2	−1.32372	−0.661860	−	0.749627i	$-0.730233\pi$
$859$	−33326.2	−1.32372	−0.661860	+	0.749627i	$0.730233\pi$
$860$	0	0
$861$	−579.531	−0.0229389
$862$	422.378	0.0166894
$863$	41724.2	1.64578	0.822890	−	0.568201i	$-0.192360\pi$
$863$	41724.2	1.64578	0.822890	+	0.568201i	$0.192360\pi$
$864$	−17475.4	−0.688108
$865$	0	0
$866$	77223.8	3.03022
$867$	−2449.38	−0.0959460
$868$	2309.60	0.0903146
$869$	−56569.7	−2.20828
$870$	0	0
$871$	−124.068	−0.00482649
$872$	−58907.5	−2.28768
$873$	17009.6	0.659438
$874$	60328.6	2.33483
$875$	0	0
$876$	28411.6	1.09582
$877$	49337.3	1.89966	0.949830	−	0.312767i	$-0.101256\pi$
$877$	49337.3	1.89966	0.949830	+	0.312767i	$0.101256\pi$
$878$	15423.3	0.592838
$879$	63194.0	2.42489
$880$	0	0
$881$	8845.46	0.338265	0.169132	−	0.985593i	$-0.445903\pi$
$881$	8845.46	0.338265	0.169132	+	0.985593i	$0.445903\pi$
$882$	−74096.8	−2.82876
$883$	−14724.2	−0.561165	−0.280582	−	0.959830i	$-0.590528\pi$
$883$	−14724.2	−0.561165	−0.280582	+	0.959830i	$0.590528\pi$
$884$	2374.10	0.0903277
$885$	0	0
$886$	9023.14	0.342143
$887$	−3864.38	−0.146283	−0.0731415	−	0.997322i	$-0.523302\pi$
$887$	−3864.38	−0.146283	−0.0731415	+	0.997322i	$0.523302\pi$
$888$	51858.1	1.95974
$889$	7360.60	0.277690
$890$	0	0
$891$	−3688.07	−0.138670
$892$	−81160.9	−3.04649
$893$	30849.1	1.15602
$894$	79023.2	2.95630
$895$	0	0
$896$	7351.61	0.274107
$897$	12311.8	0.458283
$898$	12577.2	0.467379
$899$	1441.14	0.0534648
$900$	0	0
$901$	5609.04	0.207397
$902$	4719.92	0.174231
$903$	−8984.15	−0.331089
$904$	47560.6	1.74982
$905$	0	0
$906$	−87473.7	−3.20764
$907$	743.409	0.0272155	0.0136078	−	0.999907i	$-0.495668\pi$
$907$	743.409	0.0272155	0.0136078	+	0.999907i	$0.495668\pi$
$908$	24182.5	0.883839
$909$	5905.76	0.215491
$910$	0	0
$911$	16291.0	0.592475	0.296238	−	0.955114i	$-0.404268\pi$
$911$	16291.0	0.592475	0.296238	+	0.955114i	$0.404268\pi$
$912$	55013.4	1.99745
$913$	−45336.8	−1.64340
$914$	−74402.5	−2.69258
$915$	0	0
$916$	15500.6	0.559122
$917$	1553.04	0.0559280
$918$	−12929.5	−0.464856
$919$	−6188.99	−0.222150	−0.111075	−	0.993812i	$-0.535429\pi$
$919$	−6188.99	−0.222150	−0.111075	+	0.993812i	$0.535429\pi$
$920$	0	0
$921$	−55390.5	−1.98174
$922$	−89311.6	−3.19015
$923$	−5402.00	−0.192643
$924$	−29364.8	−1.04549
$925$	0	0
$926$	−93033.0	−3.30157
$927$	−8786.47	−0.311311
$928$	−4773.30	−0.168848
$929$	−31661.7	−1.11818	−0.559089	−	0.829108i	$-0.688849\pi$
$929$	−31661.7	−1.11818	−0.559089	+	0.829108i	$0.688849\pi$
$930$	0	0
$931$	21845.0	0.769003
$932$	−20724.3	−0.728376
$933$	75734.8	2.65750
$934$	−37273.6	−1.30581
$935$	0	0
$936$	16959.8	0.592251
$937$	−35010.5	−1.22064	−0.610322	−	0.792153i	$-0.708960\pi$
$937$	−35010.5	−1.22064	−0.610322	+	0.792153i	$0.708960\pi$
$938$	295.776	0.0102958
$939$	−22279.2	−0.774286
$940$	0	0
$941$	−45625.8	−1.58061	−0.790307	−	0.612711i	$-0.790079\pi$
$941$	−45625.8	−1.58061	−0.790307	+	0.612711i	$0.790079\pi$
$942$	−11217.2	−0.387977
$943$	3227.51	0.111455
$944$	66227.5	2.28339
$945$	0	0
$946$	73170.2	2.51477
$947$	21508.4	0.738044	0.369022	−	0.929421i	$-0.379693\pi$
$947$	21508.4	0.738044	0.369022	+	0.929421i	$0.379693\pi$
$948$	−158615.	−5.43416
$949$	−1559.50	−0.0533439
$950$	0	0
$951$	36177.4	1.23358
$952$	−3046.52	−0.103717
$953$	−35686.7	−1.21302	−0.606509	−	0.795076i	$-0.707431\pi$
$953$	−35686.7	−1.21302	−0.606509	+	0.795076i	$0.707431\pi$
$954$	74440.5	2.52631
$955$	0	0
$956$	85744.0	2.90079
$957$	−18323.0	−0.618912
$958$	−93357.8	−3.14849
$959$	−498.486	−0.0167851
$960$	0	0
$961$	−28572.2	−0.959088
$962$	−5288.17	−0.177232
$963$	21749.9	0.727810
$964$	−116133.	−3.88006
$965$	0	0
$966$	−29351.3	−0.977600
$967$	3731.33	0.124086	0.0620432	−	0.998073i	$-0.480238\pi$
$967$	3731.33	0.124086	0.0620432	+	0.998073i	$0.480238\pi$
$968$	66262.5	2.20016
$969$	9583.60	0.317719
$970$	0	0
$971$	17645.1	0.583171	0.291585	−	0.956545i	$-0.405817\pi$
$971$	17645.1	0.583171	0.291585	+	0.956545i	$0.405817\pi$
$972$	60358.3	1.99176
$973$	−7917.35	−0.260862
$974$	−51348.7	−1.68924
$975$	0	0
$976$	33206.7	1.08906
$977$	−24941.2	−0.816723	−0.408362	−	0.912820i	$-0.633900\pi$
$977$	−24941.2	−0.816723	−0.408362	+	0.912820i	$0.633900\pi$
$978$	−61631.8	−2.01510
$979$	−59152.1	−1.93106
$980$	0	0
$981$	−56268.9	−1.83132
$982$	−6277.85	−0.204006
$983$	22506.2	0.730252	0.365126	−	0.930958i	$-0.381026\pi$
$983$	22506.2	0.730252	0.365126	+	0.930958i	$0.381026\pi$
$984$	7123.53	0.230782
$985$	0	0
$986$	−3531.62	−0.114066
$987$	−15008.8	−0.484029
$988$	−9289.07	−0.299114
$989$	50034.2	1.60869
$990$	0	0
$991$	32694.1	1.04799	0.523997	−	0.851720i	$-0.324440\pi$
$991$	32694.1	1.04799	0.523997	+	0.851720i	$0.324440\pi$
$992$	−4036.88	−0.129205
$993$	−8410.08	−0.268767
$994$	12878.3	0.410941
$995$	0	0
$996$	−127119.	−4.04410
$997$	−18248.8	−0.579686	−0.289843	−	0.957074i	$-0.593603\pi$
$997$	−18248.8	−0.579686	−0.289843	+	0.957074i	$0.593603\pi$
$998$	352.428	0.0111783
$999$	19702.5	0.623983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.a.g.1.3		3
5.2	odd	4		425.4.b.f.324.6		6
5.3	odd	4		425.4.b.f.324.1		6
5.4	even	2		17.4.a.b.1.1	✓	3
15.14	odd	2		153.4.a.g.1.3		3
20.19	odd	2		272.4.a.h.1.1		3
35.34	odd	2		833.4.a.d.1.1		3
40.19	odd	2		1088.4.a.x.1.3		3
40.29	even	2		1088.4.a.v.1.1		3
55.54	odd	2		2057.4.a.e.1.3		3
60.59	even	2		2448.4.a.bi.1.2		3
85.4	even	4		289.4.b.b.288.5		6
85.64	even	4		289.4.b.b.288.6		6
85.84	even	2		289.4.a.b.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.1	✓	3	5.4	even	2
153.4.a.g.1.3		3	15.14	odd	2
272.4.a.h.1.1		3	20.19	odd	2
289.4.a.b.1.1		3	85.84	even	2
289.4.b.b.288.5		6	85.4	even	4
289.4.b.b.288.6		6	85.64	even	4
425.4.a.g.1.3		3	1.1	even	1	trivial
425.4.b.f.324.1		6	5.3	odd	4
425.4.b.f.324.6		6	5.2	odd	4
833.4.a.d.1.1		3	35.34	odd	2
1088.4.a.v.1.1		3	40.29	even	2
1088.4.a.x.1.3		3	40.19	odd	2
2057.4.a.e.1.3		3	55.54	odd	2
2448.4.a.bi.1.2		3	60.59	even	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.a (trivial)

\(f(q)\)	\(=\)	\(q+5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -42.6523 q^{6} -3.81828 q^{7} +46.9339 q^{8} +44.8316 q^{9} +O(q^{10})\)	\(q+5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -42.6523 q^{6} -3.81828 q^{7} +46.9339 q^{8} +44.8316 q^{9} -52.3720 q^{11} -146.845 q^{12} +8.06025 q^{13} -19.2156 q^{14} +97.5862 q^{16} +17.0000 q^{17} +225.616 q^{18} -66.5154 q^{19} +32.3613 q^{21} -263.563 q^{22} -180.226 q^{23} -397.782 q^{24} +40.5633 q^{26} -151.129 q^{27} -66.1562 q^{28} -41.2800 q^{29} -34.9114 q^{31} +115.632 q^{32} +443.871 q^{33} +85.5527 q^{34} +776.759 q^{36} -130.368 q^{37} -334.739 q^{38} -68.3134 q^{39} -17.9081 q^{41} +162.859 q^{42} -277.620 q^{43} -907.405 q^{44} -906.987 q^{46} -463.789 q^{47} -827.078 q^{48} -328.421 q^{49} -144.081 q^{51} +139.653 q^{52} +329.944 q^{53} -760.560 q^{54} -179.207 q^{56} +563.741 q^{57} -207.742 q^{58} +678.656 q^{59} +340.280 q^{61} -175.692 q^{62} -171.180 q^{63} -198.770 q^{64} +2233.79 q^{66} -15.3925 q^{67} +294.545 q^{68} +1527.48 q^{69} -670.203 q^{71} +2104.12 q^{72} -193.480 q^{73} -656.080 q^{74} -1152.46 q^{76} +199.971 q^{77} -343.788 q^{78} +1080.15 q^{79} +70.4207 q^{81} -90.1229 q^{82} +865.668 q^{83} +560.697 q^{84} -1397.13 q^{86} +349.863 q^{87} -2458.02 q^{88} +1129.46 q^{89} -30.7763 q^{91} -3122.61 q^{92} +295.886 q^{93} -2334.02 q^{94} -980.023 q^{96} +379.412 q^{97} -1652.78 q^{98} -2347.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) \) 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} - 28 q^{11} - 22 q^{12} - 30 q^{13} + 92 q^{14} + 137 q^{16} + 51 q^{17} + 103 q^{18} + 80 q^{19} - 192 q^{21} - 286 q^{22} - 142 q^{23} - 666 q^{24} + 26 q^{26} + 20 q^{27} - 476 q^{28} - 456 q^{29} + 230 q^{31} + 71 q^{32} + 332 q^{33} - 17 q^{34} + 1313 q^{36} - 356 q^{37} - 724 q^{38} + 268 q^{39} - 294 q^{41} + 1128 q^{42} - 556 q^{43} - 1122 q^{44} - 704 q^{46} - 640 q^{47} - 774 q^{48} - 269 q^{49} - 68 q^{51} + 774 q^{52} - 302 q^{53} - 1100 q^{54} + 684 q^{56} + 720 q^{57} + 1304 q^{58} + 636 q^{59} - 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} + 2468 q^{66} - 1008 q^{67} + 425 q^{68} + 576 q^{69} - 402 q^{71} + 927 q^{72} - 838 q^{73} + 836 q^{74} - 908 q^{76} + 504 q^{77} - 1308 q^{78} - 594 q^{79} - 505 q^{81} - 358 q^{82} + 2396 q^{83} - 2040 q^{84} - 1264 q^{86} - 1428 q^{87} - 1838 q^{88} - 170 q^{89} - 1016 q^{91} - 4896 q^{92} - 632 q^{93} - 2016 q^{94} + 678 q^{96} + 270 q^{97} - 2857 q^{98} - 2920 q^{99}+O(q^{100}) \) 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 - 28 * q^11 - 22 * q^12 - 30 * q^13 + 92 * q^14 + 137 * q^16 + 51 * q^17 + 103 * q^18 + 80 * q^19 - 192 * q^21 - 286 * q^22 - 142 * q^23 - 666 * q^24 + 26 * q^26 + 20 * q^27 - 476 * q^28 - 456 * q^29 + 230 * q^31 + 71 * q^32 + 332 * q^33 - 17 * q^34 + 1313 * q^36 - 356 * q^37 - 724 * q^38 + 268 * q^39 - 294 * q^41 + 1128 * q^42 - 556 * q^43 - 1122 * q^44 - 704 * q^46 - 640 * q^47 - 774 * q^48 - 269 * q^49 - 68 * q^51 + 774 * q^52 - 302 * q^53 - 1100 * q^54 + 684 * q^56 + 720 * q^57 + 1304 * q^58 + 636 * q^59 - 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 + 2468 * q^66 - 1008 * q^67 + 425 * q^68 + 576 * q^69 - 402 * q^71 + 927 * q^72 - 838 * q^73 + 836 * q^74 - 908 * q^76 + 504 * q^77 - 1308 * q^78 - 594 * q^79 - 505 * q^81 - 358 * q^82 + 2396 * q^83 - 2040 * q^84 - 1264 * q^86 - 1428 * q^87 - 1838 * q^88 - 170 * q^89 - 1016 * q^91 - 4896 * q^92 - 632 * q^93 - 2016 * q^94 + 678 * q^96 + 270 * q^97 - 2857 * q^98 - 2920 * q^99

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