LMFDB - Embedded newform 825.4.a.o.1.3

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:	3.3.3368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 15x + 11 $ x^3 - x^2 - 15*x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.76300$ 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)

$f(q)$	$=$	$q+3.76300 q^{2} +3.00000 q^{3} +6.16019 q^{4} +11.2890 q^{6} -23.6321 q^{7} -6.92320 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.76300 q^{2} +3.00000 q^{3} +6.16019 q^{4} +11.2890 q^{6} -23.6321 q^{7} -6.92320 q^{8} +9.00000 q^{9} +11.0000 q^{11} +18.4806 q^{12} +7.39511 q^{13} -88.9277 q^{14} -75.3336 q^{16} +8.68828 q^{17} +33.8670 q^{18} -69.7002 q^{19} -70.8963 q^{21} +41.3930 q^{22} -10.1643 q^{23} -20.7696 q^{24} +27.8278 q^{26} +27.0000 q^{27} -145.578 q^{28} -73.2803 q^{29} -290.970 q^{31} -228.095 q^{32} +33.0000 q^{33} +32.6940 q^{34} +55.4417 q^{36} -105.618 q^{37} -262.282 q^{38} +22.1853 q^{39} +40.5108 q^{41} -266.783 q^{42} -77.3133 q^{43} +67.7621 q^{44} -38.2485 q^{46} -472.981 q^{47} -226.001 q^{48} +215.477 q^{49} +26.0648 q^{51} +45.5553 q^{52} +205.479 q^{53} +101.601 q^{54} +163.610 q^{56} -209.101 q^{57} -275.754 q^{58} +330.261 q^{59} -931.991 q^{61} -1094.92 q^{62} -212.689 q^{63} -255.653 q^{64} +124.179 q^{66} -418.252 q^{67} +53.5215 q^{68} -30.4930 q^{69} -506.329 q^{71} -62.3088 q^{72} +612.497 q^{73} -397.441 q^{74} -429.367 q^{76} -259.953 q^{77} +83.4835 q^{78} +54.6657 q^{79} +81.0000 q^{81} +152.442 q^{82} +538.964 q^{83} -436.735 q^{84} -290.930 q^{86} -219.841 q^{87} -76.1552 q^{88} +781.086 q^{89} -174.762 q^{91} -62.6144 q^{92} -872.909 q^{93} -1779.83 q^{94} -684.285 q^{96} -531.762 q^{97} +810.839 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9	$ 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9} + 33 q^{11} + 21 q^{12} - 45 q^{13} - 116 q^{14} - 85 q^{16} + 58 q^{17} - 9 q^{18} - 169 q^{19} - 48 q^{21} - 11 q^{22} - 155 q^{23} + 9 q^{24} + 167 q^{26} + 81 q^{27} - 100 q^{28} - 277 q^{29} - 173 q^{31} - 97 q^{32} + 99 q^{33} - 146 q^{34} + 63 q^{36} - 60 q^{37} - 169 q^{38} - 135 q^{39} + 44 q^{41} - 348 q^{42} + 109 q^{43} + 77 q^{44} + 425 q^{46} - 270 q^{47} - 255 q^{48} - 427 q^{49} + 174 q^{51} - 45 q^{52} + 148 q^{53} - 27 q^{54} + 168 q^{56} - 507 q^{57} + 783 q^{58} - 684 q^{59} - 1038 q^{61} - 953 q^{62} - 144 q^{63} - 1129 q^{64} - 33 q^{66} - 314 q^{67} + 366 q^{68} - 465 q^{69} - 1459 q^{71} + 27 q^{72} + 1170 q^{73} - 1764 q^{74} + 211 q^{76} - 176 q^{77} + 501 q^{78} - 506 q^{79} + 243 q^{81} + 1040 q^{82} + 347 q^{83} - 300 q^{84} - 527 q^{86} - 831 q^{87} + 33 q^{88} - 607 q^{89} - 398 q^{91} - 687 q^{92} - 519 q^{93} - 1822 q^{94} - 291 q^{96} - 1263 q^{97} + 2273 q^{98} + 297 q^{99}+O(q^{100}) $ 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9 + 33 * q^11 + 21 * q^12 - 45 * q^13 - 116 * q^14 - 85 * q^16 + 58 * q^17 - 9 * q^18 - 169 * q^19 - 48 * q^21 - 11 * q^22 - 155 * q^23 + 9 * q^24 + 167 * q^26 + 81 * q^27 - 100 * q^28 - 277 * q^29 - 173 * q^31 - 97 * q^32 + 99 * q^33 - 146 * q^34 + 63 * q^36 - 60 * q^37 - 169 * q^38 - 135 * q^39 + 44 * q^41 - 348 * q^42 + 109 * q^43 + 77 * q^44 + 425 * q^46 - 270 * q^47 - 255 * q^48 - 427 * q^49 + 174 * q^51 - 45 * q^52 + 148 * q^53 - 27 * q^54 + 168 * q^56 - 507 * q^57 + 783 * q^58 - 684 * q^59 - 1038 * q^61 - 953 * q^62 - 144 * q^63 - 1129 * q^64 - 33 * q^66 - 314 * q^67 + 366 * q^68 - 465 * q^69 - 1459 * q^71 + 27 * q^72 + 1170 * q^73 - 1764 * q^74 + 211 * q^76 - 176 * q^77 + 501 * q^78 - 506 * q^79 + 243 * q^81 + 1040 * q^82 + 347 * q^83 - 300 * q^84 - 527 * q^86 - 831 * q^87 + 33 * q^88 - 607 * q^89 - 398 * q^91 - 687 * q^92 - 519 * q^93 - 1822 * q^94 - 291 * q^96 - 1263 * q^97 + 2273 * 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 $

$2$	3.76300	1.33042	0.665211	−	0.746655i	$-0.268341\pi$
$2$	3.76300	1.33042	0.665211	+	0.746655i	$0.268341\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	6.16019	0.770024
$5$	0	0
$5$	0	0
$6$	11.2890	0.768120
$7$	−23.6321	−1.27601	−0.638007	−	0.770031i	$-0.720241\pi$
$7$	−23.6321	−1.27601	−0.638007	+	0.770031i	$0.720241\pi$
$8$	−6.92320	−0.305965
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	18.4806	0.444574
$13$	7.39511	0.157772	0.0788860	−	0.996884i	$-0.474864\pi$
$13$	7.39511	0.157772	0.0788860	+	0.996884i	$0.474864\pi$
$14$	−88.9277	−1.69764
$15$	0	0
$16$	−75.3336	−1.17709
$17$	8.68828	0.123954	0.0619770	−	0.998078i	$-0.480259\pi$
$17$	8.68828	0.123954	0.0619770	+	0.998078i	$0.480259\pi$
$18$	33.8670	0.443474
$19$	−69.7002	−0.841597	−0.420798	−	0.907154i	$-0.638250\pi$
$19$	−69.7002	−0.841597	−0.420798	+	0.907154i	$0.638250\pi$
$20$	0	0
$21$	−70.8963	−0.736707
$22$	41.3930	0.401137
$23$	−10.1643	−0.0921484	−0.0460742	−	0.998938i	$-0.514671\pi$
$23$	−10.1643	−0.0921484	−0.0460742	+	0.998938i	$0.514671\pi$
$24$	−20.7696	−0.176649
$25$	0	0
$26$	27.8278	0.209903
$27$	27.0000	0.192450
$28$	−145.578	−0.982562
$29$	−73.2803	−0.469235	−0.234617	−	0.972088i	$-0.575384\pi$
$29$	−73.2803	−0.469235	−0.234617	+	0.972088i	$0.575384\pi$
$30$	0	0
$31$	−290.970	−1.68580	−0.842898	−	0.538073i	$-0.819153\pi$
$31$	−290.970	−1.68580	−0.842898	+	0.538073i	$0.819153\pi$
$32$	−228.095	−1.26006
$33$	33.0000	0.174078
$34$	32.6940	0.164911
$35$	0	0
$36$	55.4417	0.256675
$37$	−105.618	−0.469284	−0.234642	−	0.972082i	$-0.575392\pi$
$37$	−105.618	−0.469284	−0.234642	+	0.972082i	$0.575392\pi$
$38$	−262.282	−1.11968
$39$	22.1853	0.0910897
$40$	0	0
$41$	40.5108	0.154310	0.0771551	−	0.997019i	$-0.475416\pi$
$41$	40.5108	0.154310	0.0771551	+	0.997019i	$0.475416\pi$
$42$	−266.783	−0.980132
$43$	−77.3133	−0.274190	−0.137095	−	0.990558i	$-0.543777\pi$
$43$	−77.3133	−0.274190	−0.137095	+	0.990558i	$0.543777\pi$
$44$	67.7621	0.232171
$45$	0	0
$46$	−38.2485	−0.122596
$47$	−472.981	−1.46790	−0.733951	−	0.679202i	$-0.762326\pi$
$47$	−472.981	−1.46790	−0.733951	+	0.679202i	$0.762326\pi$
$48$	−226.001	−0.679591
$49$	215.477	0.628212
$50$	0	0
$51$	26.0648	0.0715648
$52$	45.5553	0.121488
$53$	205.479	0.532541	0.266271	−	0.963898i	$-0.414208\pi$
$53$	205.479	0.532541	0.266271	+	0.963898i	$0.414208\pi$
$54$	101.601	0.256040
$55$	0	0
$56$	163.610	0.390416
$57$	−209.101	−0.485896
$58$	−275.754	−0.624281
$59$	330.261	0.728751	0.364376	−	0.931252i	$-0.381282\pi$
$59$	330.261	0.728751	0.364376	+	0.931252i	$0.381282\pi$
$60$	0	0
$61$	−931.991	−1.95622	−0.978109	−	0.208094i	$-0.933274\pi$
$61$	−931.991	−1.95622	−0.978109	+	0.208094i	$0.933274\pi$
$62$	−1094.92	−2.24282
$63$	−212.689	−0.425338
$64$	−255.653	−0.499323
$65$	0	0
$66$	124.179	0.231597
$67$	−418.252	−0.762652	−0.381326	−	0.924441i	$-0.624532\pi$
$67$	−418.252	−0.762652	−0.381326	+	0.924441i	$0.624532\pi$
$68$	53.5215	0.0954475
$69$	−30.4930	−0.0532019
$70$	0	0
$71$	−506.329	−0.846340	−0.423170	−	0.906050i	$-0.639083\pi$
$71$	−506.329	−0.846340	−0.423170	+	0.906050i	$0.639083\pi$
$72$	−62.3088	−0.101988
$73$	612.497	0.982018	0.491009	−	0.871154i	$-0.336628\pi$
$73$	612.497	0.982018	0.491009	+	0.871154i	$0.336628\pi$
$74$	−397.441	−0.624346
$75$	0	0
$76$	−429.367	−0.648050
$77$	−259.953	−0.384733
$78$	83.4835	0.121188
$79$	54.6657	0.0778528	0.0389264	−	0.999242i	$-0.487606\pi$
$79$	54.6657	0.0778528	0.0389264	+	0.999242i	$0.487606\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	152.442	0.205298
$83$	538.964	0.712759	0.356379	−	0.934341i	$-0.384011\pi$
$83$	538.964	0.712759	0.356379	+	0.934341i	$0.384011\pi$
$84$	−436.735	−0.567282
$85$	0	0
$86$	−290.930	−0.364788
$87$	−219.841	−0.270913
$88$	−76.1552	−0.0922519
$89$	781.086	0.930280	0.465140	−	0.885237i	$-0.346004\pi$
$89$	781.086	0.930280	0.465140	+	0.885237i	$0.346004\pi$
$90$	0	0
$91$	−174.762	−0.201319
$92$	−62.6144	−0.0709565
$93$	−872.909	−0.973295
$94$	−1779.83	−1.95293
$95$	0	0
$96$	−684.285	−0.727495
$97$	−531.762	−0.556621	−0.278311	−	0.960491i	$-0.589774\pi$
$97$	−531.762	−0.556621	−0.278311	+	0.960491i	$0.589774\pi$
$98$	810.839	0.835787
$99$	99.0000	0.100504
$100$	0	0
$101$	1898.16	1.87004	0.935022	−	0.354591i	$-0.115380\pi$
$101$	1898.16	1.87004	0.935022	+	0.354591i	$0.115380\pi$
$102$	98.0820	0.0952115
$103$	1308.66	1.25190	0.625952	−	0.779861i	$-0.284710\pi$
$103$	1308.66	1.25190	0.625952	+	0.779861i	$0.284710\pi$
$104$	−51.1978	−0.0482727
$105$	0	0
$106$	773.218	0.708505
$107$	206.655	0.186711	0.0933554	−	0.995633i	$-0.470241\pi$
$107$	206.655	0.186711	0.0933554	+	0.995633i	$0.470241\pi$
$108$	166.325	0.148191
$109$	595.701	0.523466	0.261733	−	0.965140i	$-0.415706\pi$
$109$	595.701	0.523466	0.261733	+	0.965140i	$0.415706\pi$
$110$	0	0
$111$	−316.854	−0.270941
$112$	1780.29	1.50198
$113$	1513.00	1.25957	0.629785	−	0.776769i	$-0.283143\pi$
$113$	1513.00	1.25957	0.629785	+	0.776769i	$0.283143\pi$
$114$	−786.847	−0.646447
$115$	0	0
$116$	−451.421	−0.361322
$117$	66.5560	0.0525907
$118$	1242.77	0.969547
$119$	−205.322	−0.158167
$120$	0	0
$121$	121.000	0.0909091
$122$	−3507.09	−2.60260
$123$	121.532	0.0890911
$124$	−1792.43	−1.29810
$125$	0	0
$126$	−800.349	−0.565879
$127$	77.9297	0.0544499	0.0272250	−	0.999629i	$-0.491333\pi$
$127$	77.9297	0.0544499	0.0272250	+	0.999629i	$0.491333\pi$
$128$	862.735	0.595748
$129$	−231.940	−0.158304
$130$	0	0
$131$	−8.60213	−0.00573719	−0.00286859	−	0.999996i	$-0.500913\pi$
$131$	−8.60213	−0.00573719	−0.00286859	+	0.999996i	$0.500913\pi$
$132$	203.286	0.134044
$133$	1647.16	1.07389
$134$	−1573.89	−1.01465
$135$	0	0
$136$	−60.1507	−0.0379256
$137$	−665.161	−0.414807	−0.207403	−	0.978255i	$-0.566501\pi$
$137$	−665.161	−0.414807	−0.207403	+	0.978255i	$0.566501\pi$
$138$	−114.745	−0.0707810
$139$	745.658	0.455006	0.227503	−	0.973777i	$-0.426944\pi$
$139$	745.658	0.455006	0.227503	+	0.973777i	$0.426944\pi$
$140$	0	0
$141$	−1418.94	−0.847494
$142$	−1905.32	−1.12599
$143$	81.3462	0.0475700
$144$	−678.002	−0.392362
$145$	0	0
$146$	2304.83	1.30650
$147$	646.430	0.362698
$148$	−650.628	−0.361360
$149$	−2398.49	−1.31874	−0.659370	−	0.751819i	$-0.729177\pi$
$149$	−2398.49	−1.31874	−0.659370	+	0.751819i	$0.729177\pi$
$150$	0	0
$151$	−3254.28	−1.75384	−0.876920	−	0.480637i	$-0.840405\pi$
$151$	−3254.28	−1.75384	−0.876920	+	0.480637i	$0.840405\pi$
$152$	482.549	0.257499
$153$	78.1945	0.0413180
$154$	−978.205	−0.511857
$155$	0	0
$156$	136.666	0.0701413
$157$	2492.15	1.26685	0.633424	−	0.773805i	$-0.281649\pi$
$157$	2492.15	1.26685	0.633424	+	0.773805i	$0.281649\pi$
$158$	205.707	0.103577
$159$	616.437	0.307463
$160$	0	0
$161$	240.205	0.117583
$162$	304.803	0.147825
$163$	−807.550	−0.388050	−0.194025	−	0.980997i	$-0.562154\pi$
$163$	−807.550	−0.388050	−0.194025	+	0.980997i	$0.562154\pi$
$164$	249.554	0.118823
$165$	0	0
$166$	2028.12	0.948270
$167$	1833.28	0.849484	0.424742	−	0.905314i	$-0.360365\pi$
$167$	1833.28	0.849484	0.424742	+	0.905314i	$0.360365\pi$
$168$	490.829	0.225407
$169$	−2142.31	−0.975108
$170$	0	0
$171$	−627.302	−0.280532
$172$	−476.265	−0.211133
$173$	−1046.74	−0.460011	−0.230005	−	0.973189i	$-0.573874\pi$
$173$	−1046.74	−0.460011	−0.230005	+	0.973189i	$0.573874\pi$
$174$	−827.262	−0.360429
$175$	0	0
$176$	−828.669	−0.354905
$177$	990.783	0.420745
$178$	2939.23	1.23767
$179$	1880.80	0.785348	0.392674	−	0.919678i	$-0.371550\pi$
$179$	1880.80	0.785348	0.392674	+	0.919678i	$0.371550\pi$
$180$	0	0
$181$	−1921.82	−0.789216	−0.394608	−	0.918850i	$-0.629120\pi$
$181$	−1921.82	−0.789216	−0.394608	+	0.918850i	$0.629120\pi$
$182$	−657.630	−0.267840
$183$	−2795.97	−1.12942
$184$	70.3698	0.0281942
$185$	0	0
$186$	−3284.76	−1.29489
$187$	95.5711	0.0373735
$188$	−2913.66	−1.13032
$189$	−638.067	−0.245569
$190$	0	0
$191$	203.716	0.0771747	0.0385874	−	0.999255i	$-0.487714\pi$
$191$	203.716	0.0771747	0.0385874	+	0.999255i	$0.487714\pi$
$192$	−766.960	−0.288284
$193$	2858.36	1.06606	0.533030	−	0.846096i	$-0.321053\pi$
$193$	2858.36	1.06606	0.533030	+	0.846096i	$0.321053\pi$
$194$	−2001.02	−0.740542
$195$	0	0
$196$	1327.38	0.483738
$197$	−1140.57	−0.412499	−0.206250	−	0.978499i	$-0.566126\pi$
$197$	−1140.57	−0.412499	−0.206250	+	0.978499i	$0.566126\pi$
$198$	372.537	0.133712
$199$	−3223.56	−1.14830	−0.574151	−	0.818749i	$-0.694668\pi$
$199$	−3223.56	−1.14830	−0.574151	+	0.818749i	$0.694668\pi$
$200$	0	0
$201$	−1254.76	−0.440317
$202$	7142.80	2.48795
$203$	1731.77	0.598750
$204$	160.564	0.0551067
$205$	0	0
$206$	4924.50	1.66556
$207$	−91.4791	−0.0307161
$208$	−557.100	−0.185711
$209$	−766.703	−0.253751
$210$	0	0
$211$	1679.38	0.547930	0.273965	−	0.961740i	$-0.411665\pi$
$211$	1679.38	0.547930	0.273965	+	0.961740i	$0.411665\pi$
$212$	1265.79	0.410070
$213$	−1518.99	−0.488635
$214$	777.642	0.248404
$215$	0	0
$216$	−186.926	−0.0588830
$217$	6876.23	2.15110
$218$	2241.62	0.696431
$219$	1837.49	0.566969
$220$	0	0
$221$	64.2508	0.0195565
$222$	−1192.32	−0.360466
$223$	−6121.75	−1.83831	−0.919154	−	0.393898i	$-0.871126\pi$
$223$	−6121.75	−1.83831	−0.919154	+	0.393898i	$0.871126\pi$
$224$	5390.36	1.60785
$225$	0	0
$226$	5693.44	1.67576
$227$	−1760.23	−0.514671	−0.257335	−	0.966322i	$-0.582845\pi$
$227$	−1760.23	−0.514671	−0.257335	+	0.966322i	$0.582845\pi$
$228$	−1288.10	−0.374152
$229$	−5780.58	−1.66808	−0.834042	−	0.551700i	$-0.813979\pi$
$229$	−5780.58	−1.66808	−0.834042	+	0.551700i	$0.813979\pi$
$230$	0	0
$231$	−779.860	−0.222126
$232$	507.334	0.143569
$233$	5433.94	1.52785	0.763925	−	0.645305i	$-0.223270\pi$
$233$	5433.94	1.52785	0.763925	+	0.645305i	$0.223270\pi$
$234$	250.451	0.0699678
$235$	0	0
$236$	2034.47	0.561156
$237$	163.997	0.0449484
$238$	−772.629	−0.210429
$239$	583.827	0.158011	0.0790055	−	0.996874i	$-0.474826\pi$
$239$	583.827	0.158011	0.0790055	+	0.996874i	$0.474826\pi$
$240$	0	0
$241$	4217.86	1.12737	0.563686	−	0.825989i	$-0.309383\pi$
$241$	4217.86	1.12737	0.563686	+	0.825989i	$0.309383\pi$
$242$	455.323	0.120948
$243$	243.000	0.0641500
$244$	−5741.25	−1.50633
$245$	0	0
$246$	457.327	0.118529
$247$	−515.441	−0.132780
$248$	2014.44	0.515795
$249$	1616.89	0.411511
$250$	0	0
$251$	−4836.75	−1.21631	−0.608153	−	0.793820i	$-0.708089\pi$
$251$	−4836.75	−1.21631	−0.608153	+	0.793820i	$0.708089\pi$
$252$	−1310.21	−0.327521
$253$	−111.808	−0.0277838
$254$	293.250	0.0724414
$255$	0	0
$256$	5291.70	1.29192
$257$	−4654.14	−1.12964	−0.564819	−	0.825215i	$-0.691054\pi$
$257$	−4654.14	−1.12964	−0.564819	+	0.825215i	$0.691054\pi$
$258$	−872.790	−0.210611
$259$	2495.98	0.598813
$260$	0	0
$261$	−659.523	−0.156412
$262$	−32.3698	−0.00763288
$263$	5102.11	1.19624	0.598118	−	0.801408i	$-0.295916\pi$
$263$	5102.11	1.19624	0.598118	+	0.801408i	$0.295916\pi$
$264$	−228.466	−0.0532617
$265$	0	0
$266$	6198.28	1.42873
$267$	2343.26	0.537097
$268$	−2576.52	−0.587260
$269$	4475.15	1.01433	0.507165	−	0.861849i	$-0.330694\pi$
$269$	4475.15	1.01433	0.507165	+	0.861849i	$0.330694\pi$
$270$	0	0
$271$	−7829.40	−1.75499	−0.877495	−	0.479586i	$-0.840787\pi$
$271$	−7829.40	−1.75499	−0.877495	+	0.479586i	$0.840787\pi$
$272$	−654.519	−0.145905
$273$	−524.286	−0.116232
$274$	−2503.00	−0.551868
$275$	0	0
$276$	−187.843	−0.0409668
$277$	3692.51	0.800943	0.400472	−	0.916309i	$-0.368846\pi$
$277$	3692.51	0.800943	0.400472	+	0.916309i	$0.368846\pi$
$278$	2805.91	0.605351
$279$	−2618.73	−0.561932
$280$	0	0
$281$	−1296.21	−0.275179	−0.137589	−	0.990489i	$-0.543935\pi$
$281$	−1296.21	−0.275179	−0.137589	+	0.990489i	$0.543935\pi$
$282$	−5339.49	−1.12752
$283$	1168.50	0.245442	0.122721	−	0.992441i	$-0.460838\pi$
$283$	1168.50	0.245442	0.122721	+	0.992441i	$0.460838\pi$
$284$	−3119.08	−0.651703
$285$	0	0
$286$	306.106	0.0632882
$287$	−957.355	−0.196902
$288$	−2052.85	−0.420019
$289$	−4837.51	−0.984635
$290$	0	0
$291$	−1595.29	−0.321365
$292$	3773.10	0.756178
$293$	−8879.43	−1.77045	−0.885224	−	0.465164i	$-0.845995\pi$
$293$	−8879.43	−1.77045	−0.885224	+	0.465164i	$0.845995\pi$
$294$	2432.52	0.482542
$295$	0	0
$296$	731.215	0.143584
$297$	297.000	0.0580259
$298$	−9025.54	−1.75448
$299$	−75.1665	−0.0145384
$300$	0	0
$301$	1827.08	0.349870
$302$	−12245.9	−2.33335
$303$	5694.49	1.07967
$304$	5250.77	0.990632
$305$	0	0
$306$	294.246	0.0549704
$307$	−4724.14	−0.878244	−0.439122	−	0.898427i	$-0.644710\pi$
$307$	−4724.14	−0.878244	−0.439122	+	0.898427i	$0.644710\pi$
$308$	−1601.36	−0.296253
$309$	3925.98	0.722788
$310$	0	0
$311$	53.7156	0.00979399	0.00489700	−	0.999988i	$-0.498441\pi$
$311$	53.7156	0.00979399	0.00489700	+	0.999988i	$0.498441\pi$
$312$	−153.593	−0.0278703
$313$	−4663.77	−0.842210	−0.421105	−	0.907012i	$-0.638358\pi$
$313$	−4663.77	−0.842210	−0.421105	+	0.907012i	$0.638358\pi$
$314$	9377.96	1.68544
$315$	0	0
$316$	336.751	0.0599486
$317$	8664.97	1.53525	0.767624	−	0.640901i	$-0.221439\pi$
$317$	8664.97	1.53525	0.767624	+	0.640901i	$0.221439\pi$
$318$	2319.65	0.409056
$319$	−806.084	−0.141480
$320$	0	0
$321$	619.964	0.107798
$322$	903.892	0.156435
$323$	−605.575	−0.104319
$324$	498.976	0.0855582
$325$	0	0
$326$	−3038.81	−0.516271
$327$	1787.10	0.302223
$328$	−280.464	−0.0472135
$329$	11177.5	1.87306
$330$	0	0
$331$	−3422.54	−0.568337	−0.284169	−	0.958774i	$-0.591718\pi$
$331$	−3422.54	−0.568337	−0.284169	+	0.958774i	$0.591718\pi$
$332$	3320.12	0.548841
$333$	−950.563	−0.156428
$334$	6898.66	1.13017
$335$	0	0
$336$	5340.87	0.867168
$337$	118.863	0.0192134	0.00960668	−	0.999954i	$-0.496942\pi$
$337$	118.863	0.0192134	0.00960668	+	0.999954i	$0.496942\pi$
$338$	−8061.53	−1.29731
$339$	4539.01	0.727213
$340$	0	0
$341$	−3200.67	−0.508287
$342$	−2360.54	−0.373226
$343$	3013.65	0.474407
$344$	535.255	0.0838925
$345$	0	0
$346$	−3938.87	−0.612009
$347$	−10434.7	−1.61431	−0.807154	−	0.590341i	$-0.798993\pi$
$347$	−10434.7	−1.61431	−0.807154	+	0.590341i	$0.798993\pi$
$348$	−1354.26	−0.208610
$349$	7528.91	1.15477	0.577383	−	0.816473i	$-0.304074\pi$
$349$	7528.91	1.15477	0.577383	+	0.816473i	$0.304074\pi$
$350$	0	0
$351$	199.668	0.0303632
$352$	−2509.04	−0.379922
$353$	−215.454	−0.0324857	−0.0162428	−	0.999868i	$-0.505170\pi$
$353$	−215.454	−0.0324857	−0.0162428	+	0.999868i	$0.505170\pi$
$354$	3728.32	0.559768
$355$	0	0
$356$	4811.64	0.716338
$357$	−615.967	−0.0913177
$358$	7077.45	1.04485
$359$	9105.02	1.33856	0.669282	−	0.743008i	$-0.266602\pi$
$359$	9105.02	1.33856	0.669282	+	0.743008i	$0.266602\pi$
$360$	0	0
$361$	−2000.88	−0.291715
$362$	−7231.83	−1.04999
$363$	363.000	0.0524864
$364$	−1076.57	−0.155021
$365$	0	0
$366$	−10521.3	−1.50261
$367$	3763.06	0.535232	0.267616	−	0.963526i	$-0.413764\pi$
$367$	3763.06	0.535232	0.267616	+	0.963526i	$0.413764\pi$
$368$	765.717	0.108467
$369$	364.597	0.0514368
$370$	0	0
$371$	−4855.90	−0.679530
$372$	−5377.29	−0.749461
$373$	375.989	0.0521929	0.0260965	−	0.999659i	$-0.491692\pi$
$373$	375.989	0.0521929	0.0260965	+	0.999659i	$0.491692\pi$
$374$	359.634	0.0497226
$375$	0	0
$376$	3274.54	0.449127
$377$	−541.916	−0.0740321
$378$	−2401.05	−0.326711
$379$	2967.48	0.402187	0.201094	−	0.979572i	$-0.435550\pi$
$379$	2967.48	0.402187	0.201094	+	0.979572i	$0.435550\pi$
$380$	0	0
$381$	233.789	0.0314367
$382$	766.584	0.102675
$383$	−1550.93	−0.206916	−0.103458	−	0.994634i	$-0.532991\pi$
$383$	−1550.93	−0.206916	−0.103458	+	0.994634i	$0.532991\pi$
$384$	2588.20	0.343955
$385$	0	0
$386$	10756.0	1.41831
$387$	−695.820	−0.0913966
$388$	−3275.76	−0.428612
$389$	−7511.63	−0.979061	−0.489530	−	0.871986i	$-0.662832\pi$
$389$	−7511.63	−0.979061	−0.489530	+	0.871986i	$0.662832\pi$
$390$	0	0
$391$	−88.3107	−0.0114222
$392$	−1491.79	−0.192211
$393$	−25.8064	−0.00331237
$394$	−4291.97	−0.548798
$395$	0	0
$396$	609.859	0.0773903
$397$	11125.1	1.40643	0.703217	−	0.710975i	$-0.251746\pi$
$397$	11125.1	1.40643	0.703217	+	0.710975i	$0.251746\pi$
$398$	−12130.3	−1.52773
$399$	4941.49	0.620010
$400$	0	0
$401$	−13478.0	−1.67845	−0.839225	−	0.543784i	$-0.816991\pi$
$401$	−13478.0	−1.67845	−0.839225	+	0.543784i	$0.816991\pi$
$402$	−4721.66	−0.585808
$403$	−2151.75	−0.265971
$404$	11693.1	1.43998
$405$	0	0
$406$	6516.65	0.796591
$407$	−1161.80	−0.141494
$408$	−180.452	−0.0218963
$409$	12911.4	1.56095	0.780474	−	0.625188i	$-0.214978\pi$
$409$	12911.4	1.56095	0.780474	+	0.625188i	$0.214978\pi$
$410$	0	0
$411$	−1995.48	−0.239489
$412$	8061.61	0.963997
$413$	−7804.76	−0.929897
$414$	−344.236	−0.0408654
$415$	0	0
$416$	−1686.79	−0.198802
$417$	2236.97	0.262698
$418$	−2885.10	−0.337596
$419$	−8906.41	−1.03844	−0.519220	−	0.854640i	$-0.673778\pi$
$419$	−8906.41	−1.03844	−0.519220	+	0.854640i	$0.673778\pi$
$420$	0	0
$421$	1852.36	0.214439	0.107219	−	0.994235i	$-0.465805\pi$
$421$	1852.36	0.214439	0.107219	+	0.994235i	$0.465805\pi$
$422$	6319.51	0.728978
$423$	−4256.83	−0.489301
$424$	−1422.57	−0.162939
$425$	0	0
$426$	−5715.95	−0.650091
$427$	22024.9	2.49616
$428$	1273.03	0.143772
$429$	244.039	0.0274646
$430$	0	0
$431$	−4090.74	−0.457178	−0.228589	−	0.973523i	$-0.573411\pi$
$431$	−4090.74	−0.457178	−0.228589	+	0.973523i	$0.573411\pi$
$432$	−2034.01	−0.226530
$433$	8253.94	0.916071	0.458036	−	0.888934i	$-0.348553\pi$
$433$	8253.94	0.916071	0.458036	+	0.888934i	$0.348553\pi$
$434$	25875.3	2.86187
$435$	0	0
$436$	3669.63	0.403082
$437$	708.458	0.0775518
$438$	6914.48	0.754308
$439$	979.240	0.106461	0.0532307	−	0.998582i	$-0.483048\pi$
$439$	979.240	0.106461	0.0532307	+	0.998582i	$0.483048\pi$
$440$	0	0
$441$	1939.29	0.209404
$442$	241.776	0.0260183
$443$	89.5194	0.00960089	0.00480045	−	0.999988i	$-0.498472\pi$
$443$	89.5194	0.00960089	0.00480045	+	0.999988i	$0.498472\pi$
$444$	−1951.88	−0.208631
$445$	0	0
$446$	−23036.2	−2.44573
$447$	−7195.48	−0.761375
$448$	6041.63	0.637143
$449$	−17119.1	−1.79933	−0.899666	−	0.436579i	$-0.856190\pi$
$449$	−17119.1	−1.79933	−0.899666	+	0.436579i	$0.856190\pi$
$450$	0	0
$451$	445.619	0.0465263
$452$	9320.40	0.969899
$453$	−9762.85	−1.01258
$454$	−6623.74	−0.684730
$455$	0	0
$456$	1447.65	0.148667
$457$	−1780.97	−0.182298	−0.0911492	−	0.995837i	$-0.529054\pi$
$457$	−1780.97	−0.182298	−0.0911492	+	0.995837i	$0.529054\pi$
$458$	−21752.3	−2.21926
$459$	234.583	0.0238549
$460$	0	0
$461$	−7216.14	−0.729043	−0.364522	−	0.931195i	$-0.618767\pi$
$461$	−7216.14	−0.729043	−0.364522	+	0.931195i	$0.618767\pi$
$462$	−2934.61	−0.295521
$463$	9451.28	0.948679	0.474339	−	0.880342i	$-0.342687\pi$
$463$	9451.28	0.948679	0.474339	+	0.880342i	$0.342687\pi$
$464$	5520.47	0.552330
$465$	0	0
$466$	20447.9	2.03269
$467$	7188.38	0.712289	0.356144	−	0.934431i	$-0.384091\pi$
$467$	7188.38	0.712289	0.356144	+	0.934431i	$0.384091\pi$
$468$	409.998	0.0404961
$469$	9884.19	0.973154
$470$	0	0
$471$	7476.44	0.731415
$472$	−2286.46	−0.222972
$473$	−850.446	−0.0826714
$474$	617.122	0.0598003
$475$	0	0
$476$	−1264.83	−0.121792
$477$	1849.31	0.177514
$478$	2196.94	0.210221
$479$	−8224.85	−0.784558	−0.392279	−	0.919846i	$-0.628313\pi$
$479$	−8224.85	−0.784558	−0.392279	+	0.919846i	$0.628313\pi$
$480$	0	0
$481$	−781.058	−0.0740399
$482$	15871.8	1.49988
$483$	720.615	0.0678864
$484$	745.383	0.0700022
$485$	0	0
$486$	914.410	0.0853466
$487$	−4817.49	−0.448257	−0.224129	−	0.974560i	$-0.571954\pi$
$487$	−4817.49	−0.448257	−0.224129	+	0.974560i	$0.571954\pi$
$488$	6452.36	0.598534
$489$	−2422.65	−0.224041
$490$	0	0
$491$	−4944.04	−0.454422	−0.227211	−	0.973846i	$-0.572961\pi$
$491$	−4944.04	−0.454422	−0.227211	+	0.973846i	$0.572961\pi$
$492$	748.663	0.0686023
$493$	−636.680	−0.0581635
$494$	−1939.61	−0.176654
$495$	0	0
$496$	21919.8	1.98433
$497$	11965.6	1.07994
$498$	6084.37	0.547484
$499$	−3616.97	−0.324485	−0.162242	−	0.986751i	$-0.551873\pi$
$499$	−3616.97	−0.324485	−0.162242	+	0.986751i	$0.551873\pi$
$500$	0	0
$501$	5499.85	0.490450
$502$	−18200.7	−1.61820
$503$	−1176.71	−0.104308	−0.0521540	−	0.998639i	$-0.516609\pi$
$503$	−1176.71	−0.104308	−0.0521540	+	0.998639i	$0.516609\pi$
$504$	1472.49	0.130139
$505$	0	0
$506$	−420.733	−0.0369642
$507$	−6426.94	−0.562979
$508$	480.062	0.0419278
$509$	−14606.6	−1.27196	−0.635981	−	0.771705i	$-0.719404\pi$
$509$	−14606.6	−1.27196	−0.635981	+	0.771705i	$0.719404\pi$
$510$	0	0
$511$	−14474.6	−1.25307
$512$	13010.8	1.12305
$513$	−1881.91	−0.161965
$514$	−17513.5	−1.50290
$515$	0	0
$516$	−1428.79	−0.121898
$517$	−5202.79	−0.442589
$518$	9392.38	0.796674
$519$	−3140.21	−0.265587
$520$	0	0
$521$	4175.52	0.351119	0.175559	−	0.984469i	$-0.443827\pi$
$521$	4175.52	0.351119	0.175559	+	0.984469i	$0.443827\pi$
$522$	−2481.79	−0.208094
$523$	7136.72	0.596686	0.298343	−	0.954459i	$-0.403566\pi$
$523$	7136.72	0.596686	0.298343	+	0.954459i	$0.403566\pi$
$524$	−52.9908	−0.00441777
$525$	0	0
$526$	19199.3	1.59150
$527$	−2528.03	−0.208961
$528$	−2486.01	−0.204905
$529$	−12063.7	−0.991509
$530$	0	0
$531$	2972.35	0.242917
$532$	10146.8	0.826920
$533$	299.582	0.0243458
$534$	8817.68	0.714566
$535$	0	0
$536$	2895.64	0.233345
$537$	5642.39	0.453421
$538$	16840.0	1.34949
$539$	2370.24	0.189413
$540$	0	0
$541$	18984.0	1.50866	0.754329	−	0.656496i	$-0.227962\pi$
$541$	18984.0	1.50866	0.754329	+	0.656496i	$0.227962\pi$
$542$	−29462.1	−2.33488
$543$	−5765.47	−0.455654
$544$	−1981.75	−0.156189
$545$	0	0
$546$	−1972.89	−0.154637
$547$	13084.1	1.02273	0.511366	−	0.859363i	$-0.329140\pi$
$547$	13084.1	1.02273	0.511366	+	0.859363i	$0.329140\pi$
$548$	−4097.52	−0.319411
$549$	−8387.92	−0.652073
$550$	0	0
$551$	5107.66	0.394907
$552$	211.109	0.0162779
$553$	−1291.87	−0.0993413
$554$	13894.9	1.06559
$555$	0	0
$556$	4593.40	0.350366
$557$	−11677.1	−0.888284	−0.444142	−	0.895956i	$-0.646491\pi$
$557$	−11677.1	−0.888284	−0.444142	+	0.895956i	$0.646491\pi$
$558$	−9854.28	−0.747607
$559$	−571.740	−0.0432595
$560$	0	0
$561$	286.713	0.0215776
$562$	−4877.63	−0.366104
$563$	13214.1	0.989180	0.494590	−	0.869127i	$-0.335318\pi$
$563$	13214.1	0.989180	0.494590	+	0.869127i	$0.335318\pi$
$564$	−8740.97	−0.652591
$565$	0	0
$566$	4397.06	0.326541
$567$	−1914.20	−0.141779
$568$	3505.41	0.258951
$569$	−22207.0	−1.63614	−0.818070	−	0.575118i	$-0.804956\pi$
$569$	−22207.0	−1.63614	−0.818070	+	0.575118i	$0.804956\pi$
$570$	0	0
$571$	−7251.49	−0.531463	−0.265731	−	0.964047i	$-0.585613\pi$
$571$	−7251.49	−0.531463	−0.265731	+	0.964047i	$0.585613\pi$
$572$	501.109	0.0366301
$573$	611.148	0.0445569
$574$	−3602.53	−0.261963
$575$	0	0
$576$	−2300.88	−0.166441
$577$	−8190.57	−0.590949	−0.295475	−	0.955351i	$-0.595478\pi$
$577$	−8190.57	−0.590949	−0.295475	+	0.955351i	$0.595478\pi$
$578$	−18203.6	−1.30998
$579$	8575.09	0.615490
$580$	0	0
$581$	−12736.9	−0.909490
$582$	−6003.07	−0.427552
$583$	2260.27	0.160567
$584$	−4240.44	−0.300463
$585$	0	0
$586$	−33413.3	−2.35545
$587$	9678.56	0.680540	0.340270	−	0.940328i	$-0.389482\pi$
$587$	9678.56	0.680540	0.340270	+	0.940328i	$0.389482\pi$
$588$	3982.13	0.279286
$589$	20280.7	1.41876
$590$	0	0
$591$	−3421.71	−0.238156
$592$	7956.59	0.552388
$593$	−12938.6	−0.895994	−0.447997	−	0.894035i	$-0.647863\pi$
$593$	−12938.6	−0.895994	−0.447997	+	0.894035i	$0.647863\pi$
$594$	1117.61	0.0771989
$595$	0	0
$596$	−14775.2	−1.01546
$597$	−9670.69	−0.662973
$598$	−282.852	−0.0193423
$599$	−11678.3	−0.796601	−0.398300	−	0.917255i	$-0.630400\pi$
$599$	−11678.3	−0.796601	−0.398300	+	0.917255i	$0.630400\pi$
$600$	0	0
$601$	17335.0	1.17655	0.588277	−	0.808660i	$-0.299807\pi$
$601$	17335.0	1.17655	0.588277	+	0.808660i	$0.299807\pi$
$602$	6875.29	0.465475
$603$	−3764.27	−0.254217
$604$	−20047.0	−1.35050
$605$	0	0
$606$	21428.4	1.43642
$607$	10259.9	0.686057	0.343028	−	0.939325i	$-0.388547\pi$
$607$	10259.9	0.686057	0.343028	+	0.939325i	$0.388547\pi$
$608$	15898.3	1.06046
$609$	5195.31	0.345689
$610$	0	0
$611$	−3497.75	−0.231594
$612$	481.693	0.0318158
$613$	8691.75	0.572686	0.286343	−	0.958127i	$-0.407560\pi$
$613$	8691.75	0.572686	0.286343	+	0.958127i	$0.407560\pi$
$614$	−17777.0	−1.16844
$615$	0	0
$616$	1799.71	0.117715
$617$	7438.86	0.485377	0.242688	−	0.970104i	$-0.421971\pi$
$617$	7438.86	0.485377	0.242688	+	0.970104i	$0.421971\pi$
$618$	14773.5	0.961613
$619$	−8091.72	−0.525418	−0.262709	−	0.964875i	$-0.584616\pi$
$619$	−8091.72	−0.525418	−0.262709	+	0.964875i	$0.584616\pi$
$620$	0	0
$621$	−274.437	−0.0177340
$622$	202.132	0.0130301
$623$	−18458.7	−1.18705
$624$	−1671.30	−0.107220
$625$	0	0
$626$	−17549.8	−1.12050
$627$	−2300.11	−0.146503
$628$	15352.1	0.975503
$629$	−917.639	−0.0581696
$630$	0	0
$631$	10374.5	0.654518	0.327259	−	0.944935i	$-0.393875\pi$
$631$	10374.5	0.654518	0.327259	+	0.944935i	$0.393875\pi$
$632$	−378.462	−0.0238202
$633$	5038.14	0.316347
$634$	32606.3	2.04253
$635$	0	0
$636$	3797.37	0.236754
$637$	1593.47	0.0991142
$638$	−3033.29	−0.188228
$639$	−4556.96	−0.282113
$640$	0	0
$641$	25560.8	1.57502	0.787511	−	0.616300i	$-0.211369\pi$
$641$	25560.8	1.57502	0.787511	+	0.616300i	$0.211369\pi$
$642$	2332.93	0.143416
$643$	−22746.6	−1.39508	−0.697541	−	0.716544i	$-0.745723\pi$
$643$	−22746.6	−1.39508	−0.697541	+	0.716544i	$0.745723\pi$
$644$	1479.71	0.0905415
$645$	0	0
$646$	−2278.78	−0.138789
$647$	24638.3	1.49711	0.748555	−	0.663073i	$-0.230748\pi$
$647$	24638.3	1.49711	0.748555	+	0.663073i	$0.230748\pi$
$648$	−560.779	−0.0339961
$649$	3632.87	0.219727
$650$	0	0
$651$	20628.7	1.24194
$652$	−4974.66	−0.298808
$653$	−17926.1	−1.07428	−0.537139	−	0.843493i	$-0.680495\pi$
$653$	−17926.1	−1.07428	−0.537139	+	0.843493i	$0.680495\pi$
$654$	6724.87	0.402085
$655$	0	0
$656$	−3051.82	−0.181637
$657$	5512.47	0.327339
$658$	42061.1	2.49197
$659$	−28662.2	−1.69426	−0.847132	−	0.531382i	$-0.821673\pi$
$659$	−28662.2	−1.69426	−0.847132	+	0.531382i	$0.821673\pi$
$660$	0	0
$661$	13447.8	0.791312	0.395656	−	0.918399i	$-0.370517\pi$
$661$	13447.8	0.791312	0.395656	+	0.918399i	$0.370517\pi$
$662$	−12879.0	−0.756129
$663$	192.752	0.0112909
$664$	−3731.35	−0.218079
$665$	0	0
$666$	−3576.97	−0.208115
$667$	744.847	0.0432392
$668$	11293.4	0.654123
$669$	−18365.3	−1.06135
$670$	0	0
$671$	−10251.9	−0.589822
$672$	16171.1	0.928294
$673$	−9621.01	−0.551059	−0.275529	−	0.961293i	$-0.588853\pi$
$673$	−9621.01	−0.551059	−0.275529	+	0.961293i	$0.588853\pi$
$674$	447.283	0.0255619
$675$	0	0
$676$	−13197.1	−0.750857
$677$	15901.5	0.902723	0.451361	−	0.892341i	$-0.350939\pi$
$677$	15901.5	0.902723	0.451361	+	0.892341i	$0.350939\pi$
$678$	17080.3	0.967501
$679$	12566.7	0.710257
$680$	0	0
$681$	−5280.68	−0.297145
$682$	−12044.1	−0.676236
$683$	611.084	0.0342350	0.0171175	−	0.999853i	$-0.494551\pi$
$683$	611.084	0.0342350	0.0171175	+	0.999853i	$0.494551\pi$
$684$	−3864.30	−0.216017
$685$	0	0
$686$	11340.4	0.631162
$687$	−17341.7	−0.963069
$688$	5824.29	0.322745
$689$	1519.54	0.0840201
$690$	0	0
$691$	24067.1	1.32497	0.662487	−	0.749074i	$-0.269501\pi$
$691$	24067.1	1.32497	0.662487	+	0.749074i	$0.269501\pi$
$692$	−6448.09	−0.354219
$693$	−2339.58	−0.128244
$694$	−39265.9	−2.14771
$695$	0	0
$696$	1522.00	0.0828899
$697$	351.969	0.0191274
$698$	28331.3	1.53633
$699$	16301.8	0.882105
$700$	0	0
$701$	10093.5	0.543834	0.271917	−	0.962321i	$-0.412342\pi$
$701$	10093.5	0.543834	0.271917	+	0.962321i	$0.412342\pi$
$702$	751.352	0.0403959
$703$	7361.61	0.394948
$704$	−2812.19	−0.150551
$705$	0	0
$706$	−810.753	−0.0432197
$707$	−44857.6	−2.38620
$708$	6103.41	0.323984
$709$	−4970.98	−0.263313	−0.131657	−	0.991295i	$-0.542030\pi$
$709$	−4970.98	−0.263313	−0.131657	+	0.991295i	$0.542030\pi$
$710$	0	0
$711$	491.991	0.0259509
$712$	−5407.61	−0.284633
$713$	2957.52	0.155343
$714$	−2317.89	−0.121491
$715$	0	0
$716$	11586.1	0.604737
$717$	1751.48	0.0912277
$718$	34262.2	1.78086
$719$	−35411.6	−1.83676	−0.918381	−	0.395698i	$-0.870503\pi$
$719$	−35411.6	−1.83676	−0.918381	+	0.395698i	$0.870503\pi$
$720$	0	0
$721$	−30926.4	−1.59745
$722$	−7529.30	−0.388105
$723$	12653.6	0.650888
$724$	−11838.8	−0.607715
$725$	0	0
$726$	1365.97	0.0698291
$727$	34598.6	1.76505	0.882525	−	0.470266i	$-0.155842\pi$
$727$	34598.6	1.76505	0.882525	+	0.470266i	$0.155842\pi$
$728$	1209.91	0.0615966
$729$	729.000	0.0370370
$730$	0	0
$731$	−671.719	−0.0339869
$732$	−17223.7	−0.869683
$733$	−32108.2	−1.61793	−0.808966	−	0.587856i	$-0.799972\pi$
$733$	−32108.2	−1.61793	−0.808966	+	0.587856i	$0.799972\pi$
$734$	14160.4	0.712085
$735$	0	0
$736$	2318.44	0.116112
$737$	−4600.78	−0.229948
$738$	1371.98	0.0684326
$739$	−27536.9	−1.37072	−0.685359	−	0.728206i	$-0.740355\pi$
$739$	−27536.9	−1.37072	−0.685359	+	0.728206i	$0.740355\pi$
$740$	0	0
$741$	−1546.32	−0.0766608
$742$	−18272.8	−0.904062
$743$	2437.44	0.120351	0.0601757	−	0.998188i	$-0.480834\pi$
$743$	2437.44	0.120351	0.0601757	+	0.998188i	$0.480834\pi$
$744$	6043.32	0.297794
$745$	0	0
$746$	1414.85	0.0694386
$747$	4850.67	0.237586
$748$	588.736	0.0287785
$749$	−4883.69	−0.238246
$750$	0	0
$751$	−29534.7	−1.43507	−0.717534	−	0.696523i	$-0.754729\pi$
$751$	−29534.7	−1.43507	−0.717534	+	0.696523i	$0.754729\pi$
$752$	35631.4	1.72785
$753$	−14510.3	−0.702235
$754$	−2039.23	−0.0984940
$755$	0	0
$756$	−3930.62	−0.189094
$757$	747.476	0.0358883	0.0179442	−	0.999839i	$-0.494288\pi$
$757$	747.476	0.0358883	0.0179442	+	0.999839i	$0.494288\pi$
$758$	11166.6	0.535079
$759$	−335.423	−0.0160410
$760$	0	0
$761$	−21031.2	−1.00181	−0.500906	−	0.865502i	$-0.667000\pi$
$761$	−21031.2	−1.00181	−0.500906	+	0.865502i	$0.667000\pi$
$762$	879.749	0.0418241
$763$	−14077.7	−0.667950
$764$	1254.93	0.0594264
$765$	0	0
$766$	−5836.15	−0.275286
$767$	2442.32	0.114976
$768$	15875.1	0.745890
$769$	23107.4	1.08358	0.541790	−	0.840514i	$-0.317747\pi$
$769$	23107.4	1.08358	0.541790	+	0.840514i	$0.317747\pi$
$770$	0	0
$771$	−13962.4	−0.652197
$772$	17608.1	0.820892
$773$	−24367.7	−1.13382	−0.566912	−	0.823778i	$-0.691862\pi$
$773$	−24367.7	−1.13382	−0.566912	+	0.823778i	$0.691862\pi$
$774$	−2618.37	−0.121596
$775$	0	0
$776$	3681.49	0.170307
$777$	7487.94	0.345725
$778$	−28266.3	−1.30256
$779$	−2823.61	−0.129867
$780$	0	0
$781$	−5569.62	−0.255181
$782$	−332.313	−0.0151963
$783$	−1978.57	−0.0903043
$784$	−16232.6	−0.739460
$785$	0	0
$786$	−97.1095	−0.00440685
$787$	−11308.1	−0.512188	−0.256094	−	0.966652i	$-0.582436\pi$
$787$	−11308.1	−0.512188	−0.256094	+	0.966652i	$0.582436\pi$
$788$	−7026.14	−0.317634
$789$	15306.3	0.690647
$790$	0	0
$791$	−35755.5	−1.60723
$792$	−685.397	−0.0307506
$793$	−6892.18	−0.308636
$794$	41863.9	1.87115
$795$	0	0
$796$	−19857.8	−0.884221
$797$	−43620.5	−1.93867	−0.969333	−	0.245752i	$-0.920965\pi$
$797$	−43620.5	−1.93867	−0.969333	+	0.245752i	$0.920965\pi$
$798$	18594.8	0.824875
$799$	−4109.39	−0.181952
$800$	0	0
$801$	7029.77	0.310093
$802$	−50717.7	−2.23305
$803$	6737.47	0.296090
$804$	−7729.55	−0.339055
$805$	0	0
$806$	−8097.06	−0.353854
$807$	13425.4	0.585623
$808$	−13141.4	−0.572168
$809$	−7491.05	−0.325551	−0.162776	−	0.986663i	$-0.552045\pi$
$809$	−7491.05	−0.325551	−0.162776	+	0.986663i	$0.552045\pi$
$810$	0	0
$811$	−7335.75	−0.317624	−0.158812	−	0.987309i	$-0.550766\pi$
$811$	−7335.75	−0.317624	−0.158812	+	0.987309i	$0.550766\pi$
$812$	10668.0	0.461052
$813$	−23488.2	−1.01324
$814$	−4371.85	−0.188247
$815$	0	0
$816$	−1963.56	−0.0842380
$817$	5388.76	0.230757
$818$	48585.7	2.07672
$819$	−1572.86	−0.0671064
$820$	0	0
$821$	−37482.9	−1.59338	−0.796689	−	0.604390i	$-0.793417\pi$
$821$	−37482.9	−1.59338	−0.796689	+	0.604390i	$0.793417\pi$
$822$	−7509.01	−0.318621
$823$	−1213.87	−0.0514128	−0.0257064	−	0.999670i	$-0.508184\pi$
$823$	−1213.87	−0.0514128	−0.0257064	+	0.999670i	$0.508184\pi$
$824$	−9060.12	−0.383039
$825$	0	0
$826$	−29369.4	−1.23716
$827$	7999.10	0.336343	0.168172	−	0.985758i	$-0.446214\pi$
$827$	7999.10	0.336343	0.168172	+	0.985758i	$0.446214\pi$
$828$	−563.529	−0.0236522
$829$	−14809.5	−0.620451	−0.310225	−	0.950663i	$-0.600405\pi$
$829$	−14809.5	−0.620451	−0.310225	+	0.950663i	$0.600405\pi$
$830$	0	0
$831$	11077.5	0.462425
$832$	−1890.58	−0.0787791
$833$	1872.12	0.0778693
$834$	8417.74	0.349499
$835$	0	0
$836$	−4723.04	−0.195394
$837$	−7856.18	−0.324432
$838$	−33514.8	−1.38156
$839$	−44598.1	−1.83516	−0.917578	−	0.397555i	$-0.869859\pi$
$839$	−44598.1	−1.83516	−0.917578	+	0.397555i	$0.869859\pi$
$840$	0	0
$841$	−19019.0	−0.779819
$842$	6970.45	0.285294
$843$	−3888.62	−0.158875
$844$	10345.3	0.421919
$845$	0	0
$846$	−16018.5	−0.650977
$847$	−2859.49	−0.116001
$848$	−15479.5	−0.626848
$849$	3505.50	0.141706
$850$	0	0
$851$	1073.54	0.0432438
$852$	−9357.25	−0.376261
$853$	−28250.2	−1.13396	−0.566980	−	0.823732i	$-0.691888\pi$
$853$	−28250.2	−1.13396	−0.566980	+	0.823732i	$0.691888\pi$
$854$	82879.9	3.32095
$855$	0	0
$856$	−1430.71	−0.0571270
$857$	−28018.4	−1.11679	−0.558395	−	0.829575i	$-0.688583\pi$
$857$	−28018.4	−1.11679	−0.558395	+	0.829575i	$0.688583\pi$
$858$	918.319	0.0365395
$859$	17367.5	0.689837	0.344919	−	0.938633i	$-0.387906\pi$
$859$	17367.5	0.689837	0.344919	+	0.938633i	$0.387906\pi$
$860$	0	0
$861$	−2872.07	−0.113681
$862$	−15393.4	−0.608240
$863$	49064.8	1.93532	0.967662	−	0.252252i	$-0.0811712\pi$
$863$	49064.8	1.93532	0.967662	+	0.252252i	$0.0811712\pi$
$864$	−6158.56	−0.242498
$865$	0	0
$866$	31059.6	1.21876
$867$	−14512.5	−0.568480
$868$	42358.9	1.65640
$869$	601.323	0.0234735
$870$	0	0
$871$	−3093.02	−0.120325
$872$	−4124.15	−0.160162
$873$	−4785.86	−0.185540
$874$	2665.93	0.103177
$875$	0	0
$876$	11319.3	0.436579
$877$	−42355.0	−1.63082	−0.815409	−	0.578885i	$-0.803488\pi$
$877$	−42355.0	−1.63082	−0.815409	+	0.578885i	$0.803488\pi$
$878$	3684.89	0.141639
$879$	−26638.3	−1.02217
$880$	0	0
$881$	−36424.8	−1.39294	−0.696472	−	0.717584i	$-0.745248\pi$
$881$	−36424.8	−1.39294	−0.696472	+	0.717584i	$0.745248\pi$
$882$	7297.55	0.278596
$883$	27158.6	1.03506	0.517532	−	0.855664i	$-0.326851\pi$
$883$	27158.6	1.03506	0.517532	+	0.855664i	$0.326851\pi$
$884$	395.797	0.0150589
$885$	0	0
$886$	336.862	0.0127732
$887$	−45832.2	−1.73494	−0.867472	−	0.497486i	$-0.834257\pi$
$887$	−45832.2	−1.73494	−0.867472	+	0.497486i	$0.834257\pi$
$888$	2193.64	0.0828985
$889$	−1841.64	−0.0694789
$890$	0	0
$891$	891.000	0.0335013
$892$	−37711.2	−1.41554
$893$	32966.9	1.23538
$894$	−27076.6	−1.01295
$895$	0	0
$896$	−20388.2	−0.760183
$897$	−225.500	−0.00839377
$898$	−64419.2	−2.39387
$899$	21322.4	0.791035
$900$	0	0
$901$	1785.26	0.0660106
$902$	1676.86	0.0618996
$903$	5481.23	0.201998
$904$	−10474.8	−0.385384
$905$	0	0
$906$	−36737.6	−1.34716
$907$	−42596.1	−1.55940	−0.779702	−	0.626151i	$-0.784629\pi$
$907$	−42596.1	−1.55940	−0.779702	+	0.626151i	$0.784629\pi$
$908$	−10843.3	−0.396309
$909$	17083.5	0.623348
$910$	0	0
$911$	45531.0	1.65588	0.827941	−	0.560816i	$-0.189512\pi$
$911$	45531.0	1.65588	0.827941	+	0.560816i	$0.189512\pi$
$912$	15752.3	0.571942
$913$	5928.60	0.214905
$914$	−6701.80	−0.242534
$915$	0	0
$916$	−35609.5	−1.28447
$917$	203.286	0.00732073
$918$	882.738	0.0317372
$919$	14353.6	0.515215	0.257607	−	0.966250i	$-0.417066\pi$
$919$	14353.6	0.515215	0.257607	+	0.966250i	$0.417066\pi$
$920$	0	0
$921$	−14172.4	−0.507055
$922$	−27154.3	−0.969936
$923$	−3744.36	−0.133529
$924$	−4804.09	−0.171042
$925$	0	0
$926$	35565.2	1.26214
$927$	11777.9	0.417302
$928$	16714.9	0.591263
$929$	38477.7	1.35890	0.679448	−	0.733724i	$-0.262219\pi$
$929$	38477.7	1.35890	0.679448	+	0.733724i	$0.262219\pi$
$930$	0	0
$931$	−15018.8	−0.528701
$932$	33474.1	1.17648
$933$	161.147	0.00565456
$934$	27049.9	0.947645
$935$	0	0
$936$	−460.780	−0.0160909
$937$	6917.67	0.241185	0.120592	−	0.992702i	$-0.461521\pi$
$937$	6917.67	0.241185	0.120592	+	0.992702i	$0.461521\pi$
$938$	37194.2	1.29471
$939$	−13991.3	−0.486250
$940$	0	0
$941$	41270.2	1.42972	0.714862	−	0.699265i	$-0.246489\pi$
$941$	41270.2	1.42972	0.714862	+	0.699265i	$0.246489\pi$
$942$	28133.9	0.973091
$943$	−411.766	−0.0142194
$944$	−24879.7	−0.857803
$945$	0	0
$946$	−3200.23	−0.109988
$947$	7099.57	0.243617	0.121808	−	0.992554i	$-0.461131\pi$
$947$	7099.57	0.243617	0.121808	+	0.992554i	$0.461131\pi$
$948$	1010.25	0.0346113
$949$	4529.48	0.154935
$950$	0	0
$951$	25994.9	0.886375
$952$	1421.49	0.0483935
$953$	−27983.8	−0.951191	−0.475595	−	0.879664i	$-0.657767\pi$
$953$	−27983.8	−0.951191	−0.475595	+	0.879664i	$0.657767\pi$
$954$	6958.96	0.236168
$955$	0	0
$956$	3596.49	0.121672
$957$	−2418.25	−0.0816833
$958$	−30950.2	−1.04379
$959$	15719.2	0.529299
$960$	0	0
$961$	54872.3	1.84191
$962$	−2939.12	−0.0985043
$963$	1859.89	0.0622370
$964$	25982.9	0.868103
$965$	0	0
$966$	2711.68	0.0903176
$967$	−22702.4	−0.754972	−0.377486	−	0.926015i	$-0.623211\pi$
$967$	−22702.4	−0.754972	−0.377486	+	0.926015i	$0.623211\pi$
$968$	−837.707	−0.0278150
$969$	−1816.73	−0.0602287
$970$	0	0
$971$	11642.7	0.384791	0.192396	−	0.981317i	$-0.438374\pi$
$971$	11642.7	0.384791	0.192396	+	0.981317i	$0.438374\pi$
$972$	1496.93	0.0493971
$973$	−17621.5	−0.580595
$974$	−18128.2	−0.596372
$975$	0	0
$976$	70210.2	2.30264
$977$	6166.32	0.201922	0.100961	−	0.994890i	$-0.467808\pi$
$977$	6166.32	0.201922	0.100961	+	0.994890i	$0.467808\pi$
$978$	−9116.44	−0.298069
$979$	8591.94	0.280490
$980$	0	0
$981$	5361.31	0.174489
$982$	−18604.4	−0.604573
$983$	−18059.0	−0.585953	−0.292976	−	0.956120i	$-0.594646\pi$
$983$	−18059.0	−0.585953	−0.292976	+	0.956120i	$0.594646\pi$
$984$	−841.392	−0.0272587
$985$	0	0
$986$	−2395.83	−0.0773821
$987$	33532.6	1.08141
$988$	−3175.22	−0.102244
$989$	785.839	0.0252662
$990$	0	0
$991$	−62330.7	−1.99798	−0.998991	−	0.0449065i	$-0.985701\pi$
$991$	−62330.7	−1.99798	−0.998991	+	0.0449065i	$0.985701\pi$
$992$	66368.7	2.12420
$993$	−10267.6	−0.328130
$994$	45026.7	1.43678
$995$	0	0
$996$	9960.36	0.316874
$997$	−13560.3	−0.430752	−0.215376	−	0.976531i	$-0.569098\pi$
$997$	−13560.3	−0.430752	−0.215376	+	0.976531i	$0.569098\pi$
$998$	−13610.7	−0.431702
$999$	−2851.69	−0.0903138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.o.1.3	✓	3
3.2	odd	2		2475.4.a.y.1.1		3
5.2	odd	4		825.4.c.n.199.5		6
5.3	odd	4		825.4.c.n.199.2		6
5.4	even	2		825.4.a.q.1.1	yes	3
15.14	odd	2		2475.4.a.v.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.o.1.3	✓	3	1.1	even	1	trivial
825.4.a.q.1.1	yes	3	5.4	even	2
825.4.c.n.199.2		6	5.3	odd	4
825.4.c.n.199.5		6	5.2	odd	4
2475.4.a.v.1.3		3	15.14	odd	2
2475.4.a.y.1.1		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)

\(f(q)\)	\(=\)	\(q+3.76300 q^{2} +3.00000 q^{3} +6.16019 q^{4} +11.2890 q^{6} -23.6321 q^{7} -6.92320 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.76300 q^{2} +3.00000 q^{3} +6.16019 q^{4} +11.2890 q^{6} -23.6321 q^{7} -6.92320 q^{8} +9.00000 q^{9} +11.0000 q^{11} +18.4806 q^{12} +7.39511 q^{13} -88.9277 q^{14} -75.3336 q^{16} +8.68828 q^{17} +33.8670 q^{18} -69.7002 q^{19} -70.8963 q^{21} +41.3930 q^{22} -10.1643 q^{23} -20.7696 q^{24} +27.8278 q^{26} +27.0000 q^{27} -145.578 q^{28} -73.2803 q^{29} -290.970 q^{31} -228.095 q^{32} +33.0000 q^{33} +32.6940 q^{34} +55.4417 q^{36} -105.618 q^{37} -262.282 q^{38} +22.1853 q^{39} +40.5108 q^{41} -266.783 q^{42} -77.3133 q^{43} +67.7621 q^{44} -38.2485 q^{46} -472.981 q^{47} -226.001 q^{48} +215.477 q^{49} +26.0648 q^{51} +45.5553 q^{52} +205.479 q^{53} +101.601 q^{54} +163.610 q^{56} -209.101 q^{57} -275.754 q^{58} +330.261 q^{59} -931.991 q^{61} -1094.92 q^{62} -212.689 q^{63} -255.653 q^{64} +124.179 q^{66} -418.252 q^{67} +53.5215 q^{68} -30.4930 q^{69} -506.329 q^{71} -62.3088 q^{72} +612.497 q^{73} -397.441 q^{74} -429.367 q^{76} -259.953 q^{77} +83.4835 q^{78} +54.6657 q^{79} +81.0000 q^{81} +152.442 q^{82} +538.964 q^{83} -436.735 q^{84} -290.930 q^{86} -219.841 q^{87} -76.1552 q^{88} +781.086 q^{89} -174.762 q^{91} -62.6144 q^{92} -872.909 q^{93} -1779.83 q^{94} -684.285 q^{96} -531.762 q^{97} +810.839 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9	\( 3 q - q^{2} + 9 q^{3} + 7 q^{4} - 3 q^{6} - 16 q^{7} + 3 q^{8} + 27 q^{9} + 33 q^{11} + 21 q^{12} - 45 q^{13} - 116 q^{14} - 85 q^{16} + 58 q^{17} - 9 q^{18} - 169 q^{19} - 48 q^{21} - 11 q^{22} - 155 q^{23} + 9 q^{24} + 167 q^{26} + 81 q^{27} - 100 q^{28} - 277 q^{29} - 173 q^{31} - 97 q^{32} + 99 q^{33} - 146 q^{34} + 63 q^{36} - 60 q^{37} - 169 q^{38} - 135 q^{39} + 44 q^{41} - 348 q^{42} + 109 q^{43} + 77 q^{44} + 425 q^{46} - 270 q^{47} - 255 q^{48} - 427 q^{49} + 174 q^{51} - 45 q^{52} + 148 q^{53} - 27 q^{54} + 168 q^{56} - 507 q^{57} + 783 q^{58} - 684 q^{59} - 1038 q^{61} - 953 q^{62} - 144 q^{63} - 1129 q^{64} - 33 q^{66} - 314 q^{67} + 366 q^{68} - 465 q^{69} - 1459 q^{71} + 27 q^{72} + 1170 q^{73} - 1764 q^{74} + 211 q^{76} - 176 q^{77} + 501 q^{78} - 506 q^{79} + 243 q^{81} + 1040 q^{82} + 347 q^{83} - 300 q^{84} - 527 q^{86} - 831 q^{87} + 33 q^{88} - 607 q^{89} - 398 q^{91} - 687 q^{92} - 519 q^{93} - 1822 q^{94} - 291 q^{96} - 1263 q^{97} + 2273 q^{98} + 297 q^{99}+O(q^{100}) \) 3 * q - q^2 + 9 * q^3 + 7 * q^4 - 3 * q^6 - 16 * q^7 + 3 * q^8 + 27 * q^9 + 33 * q^11 + 21 * q^12 - 45 * q^13 - 116 * q^14 - 85 * q^16 + 58 * q^17 - 9 * q^18 - 169 * q^19 - 48 * q^21 - 11 * q^22 - 155 * q^23 + 9 * q^24 + 167 * q^26 + 81 * q^27 - 100 * q^28 - 277 * q^29 - 173 * q^31 - 97 * q^32 + 99 * q^33 - 146 * q^34 + 63 * q^36 - 60 * q^37 - 169 * q^38 - 135 * q^39 + 44 * q^41 - 348 * q^42 + 109 * q^43 + 77 * q^44 + 425 * q^46 - 270 * q^47 - 255 * q^48 - 427 * q^49 + 174 * q^51 - 45 * q^52 + 148 * q^53 - 27 * q^54 + 168 * q^56 - 507 * q^57 + 783 * q^58 - 684 * q^59 - 1038 * q^61 - 953 * q^62 - 144 * q^63 - 1129 * q^64 - 33 * q^66 - 314 * q^67 + 366 * q^68 - 465 * q^69 - 1459 * q^71 + 27 * q^72 + 1170 * q^73 - 1764 * q^74 + 211 * q^76 - 176 * q^77 + 501 * q^78 - 506 * q^79 + 243 * q^81 + 1040 * q^82 + 347 * q^83 - 300 * q^84 - 527 * q^86 - 831 * q^87 + 33 * q^88 - 607 * q^89 - 398 * q^91 - 687 * q^92 - 519 * q^93 - 1822 * q^94 - 291 * q^96 - 1263 * q^97 + 2273 * q^98 + 297 * q^99

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