LMFDB - Embedded newform 525.4.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.78066700.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 18x^{3} + 7x^{2} + 30x - 10 $ x^5 - x^4 - 18x^3 + 7x^2 + 30*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 5 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.35311$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20666 q^{2} -3.00000 q^{3} -3.13065 q^{4} +6.61998 q^{6} +7.00000 q^{7} +24.5616 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.20666 q^{2} -3.00000 q^{3} -3.13065 q^{4} +6.61998 q^{6} +7.00000 q^{7} +24.5616 q^{8} +9.00000 q^{9} +56.2010 q^{11} +9.39196 q^{12} +38.9026 q^{13} -15.4466 q^{14} -29.1538 q^{16} -119.322 q^{17} -19.8599 q^{18} -13.0045 q^{19} -21.0000 q^{21} -124.016 q^{22} -130.565 q^{23} -73.6847 q^{24} -85.8448 q^{26} -27.0000 q^{27} -21.9146 q^{28} +77.9925 q^{29} +61.0660 q^{31} -132.160 q^{32} -168.603 q^{33} +263.303 q^{34} -28.1759 q^{36} +167.391 q^{37} +28.6964 q^{38} -116.708 q^{39} +436.142 q^{41} +46.3398 q^{42} -393.030 q^{43} -175.946 q^{44} +288.112 q^{46} +365.271 q^{47} +87.4613 q^{48} +49.0000 q^{49} +357.966 q^{51} -121.791 q^{52} -282.048 q^{53} +59.5798 q^{54} +171.931 q^{56} +39.0134 q^{57} -172.103 q^{58} +414.842 q^{59} -563.802 q^{61} -134.752 q^{62} +63.0000 q^{63} +524.862 q^{64} +372.049 q^{66} +395.230 q^{67} +373.556 q^{68} +391.694 q^{69} +103.990 q^{71} +221.054 q^{72} -128.026 q^{73} -369.376 q^{74} +40.7125 q^{76} +393.407 q^{77} +257.534 q^{78} -641.999 q^{79} +81.0000 q^{81} -962.417 q^{82} +512.010 q^{83} +65.7437 q^{84} +867.283 q^{86} -233.977 q^{87} +1380.38 q^{88} +1225.10 q^{89} +272.318 q^{91} +408.753 q^{92} -183.198 q^{93} -806.028 q^{94} +396.480 q^{96} +186.760 q^{97} -108.126 q^{98} +505.809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 15 q^{3} + 27 q^{4} - 3 q^{6} + 35 q^{7} + 33 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + q^2 - 15 * q^3 + 27 * q^4 - 3 * q^6 + 35 * q^7 + 33 * q^8 + 45 * q^9	$ 5 q + q^{2} - 15 q^{3} + 27 q^{4} - 3 q^{6} + 35 q^{7} + 33 q^{8} + 45 q^{9} + 66 q^{11} - 81 q^{12} - 2 q^{13} + 7 q^{14} + 155 q^{16} + 108 q^{17} + 9 q^{18} + 174 q^{19} - 105 q^{21} - 506 q^{22} - 116 q^{23} - 99 q^{24} + 446 q^{26} - 135 q^{27} + 189 q^{28} + 370 q^{29} + 342 q^{31} - 55 q^{32} - 198 q^{33} + 112 q^{34} + 243 q^{36} - 408 q^{37} - 34 q^{38} + 6 q^{39} + 802 q^{41} - 21 q^{42} - 584 q^{43} + 290 q^{44} + 640 q^{46} + 716 q^{47} - 465 q^{48} + 245 q^{49} - 324 q^{51} + 338 q^{52} + 98 q^{53} - 27 q^{54} + 231 q^{56} - 522 q^{57} + 482 q^{58} + 704 q^{59} + 650 q^{61} + 2070 q^{62} + 315 q^{63} + 75 q^{64} + 1518 q^{66} + 180 q^{67} + 4520 q^{68} + 348 q^{69} + 1470 q^{71} + 297 q^{72} - 534 q^{73} - 1312 q^{74} + 4370 q^{76} + 462 q^{77} - 1338 q^{78} - 820 q^{79} + 405 q^{81} - 1338 q^{82} + 1520 q^{83} - 567 q^{84} + 832 q^{86} - 1110 q^{87} - 3258 q^{88} + 286 q^{89} - 14 q^{91} + 1288 q^{92} - 1026 q^{93} + 2540 q^{94} + 165 q^{96} + 278 q^{97} + 49 q^{98} + 594 q^{99}+O(q^{100}) $ 5 * q + q^2 - 15 * q^3 + 27 * q^4 - 3 * q^6 + 35 * q^7 + 33 * q^8 + 45 * q^9 + 66 * q^11 - 81 * q^12 - 2 * q^13 + 7 * q^14 + 155 * q^16 + 108 * q^17 + 9 * q^18 + 174 * q^19 - 105 * q^21 - 506 * q^22 - 116 * q^23 - 99 * q^24 + 446 * q^26 - 135 * q^27 + 189 * q^28 + 370 * q^29 + 342 * q^31 - 55 * q^32 - 198 * q^33 + 112 * q^34 + 243 * q^36 - 408 * q^37 - 34 * q^38 + 6 * q^39 + 802 * q^41 - 21 * q^42 - 584 * q^43 + 290 * q^44 + 640 * q^46 + 716 * q^47 - 465 * q^48 + 245 * q^49 - 324 * q^51 + 338 * q^52 + 98 * q^53 - 27 * q^54 + 231 * q^56 - 522 * q^57 + 482 * q^58 + 704 * q^59 + 650 * q^61 + 2070 * q^62 + 315 * q^63 + 75 * q^64 + 1518 * q^66 + 180 * q^67 + 4520 * q^68 + 348 * q^69 + 1470 * q^71 + 297 * q^72 - 534 * q^73 - 1312 * q^74 + 4370 * q^76 + 462 * q^77 - 1338 * q^78 - 820 * q^79 + 405 * q^81 - 1338 * q^82 + 1520 * q^83 - 567 * q^84 + 832 * q^86 - 1110 * q^87 - 3258 * q^88 + 286 * q^89 - 14 * q^91 + 1288 * q^92 - 1026 * q^93 + 2540 * q^94 + 165 * q^96 + 278 * q^97 + 49 * q^98 + 594 * 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 $

$2$	−2.20666	−0.780172	−0.390086	−	0.920778i	$-0.627555\pi$
$2$	−2.20666	−0.780172	−0.390086	+	0.920778i	$0.627555\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−3.13065	−0.391332
$5$	0	0
$5$	0	0
$6$	6.61998	0.450432
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	24.5616	1.08548
$9$	9.00000	0.333333
$10$	0	0
$11$	56.2010	1.54048	0.770238	−	0.637757i	$-0.220138\pi$
$11$	56.2010	1.54048	0.770238	+	0.637757i	$0.220138\pi$
$12$	9.39196	0.225936
$13$	38.9026	0.829972	0.414986	−	0.909828i	$-0.363786\pi$
$13$	38.9026	0.829972	0.414986	+	0.909828i	$0.363786\pi$
$14$	−15.4466	−0.294877
$15$	0	0
$16$	−29.1538	−0.455528
$17$	−119.322	−1.70235	−0.851173	−	0.524886i	$-0.824108\pi$
$17$	−119.322	−1.70235	−0.851173	+	0.524886i	$0.824108\pi$
$18$	−19.8599	−0.260057
$19$	−13.0045	−0.157023	−0.0785113	−	0.996913i	$-0.525017\pi$
$19$	−13.0045	−0.157023	−0.0785113	+	0.996913i	$0.525017\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	−124.016	−1.20184
$23$	−130.565	−1.18368	−0.591840	−	0.806055i	$-0.701598\pi$
$23$	−130.565	−1.18368	−0.591840	+	0.806055i	$0.701598\pi$
$24$	−73.6847	−0.626701
$25$	0	0
$26$	−85.8448	−0.647521
$27$	−27.0000	−0.192450
$28$	−21.9146	−0.147910
$29$	77.9925	0.499408	0.249704	−	0.968322i	$-0.419667\pi$
$29$	77.9925	0.499408	0.249704	+	0.968322i	$0.419667\pi$
$30$	0	0
$31$	61.0660	0.353799	0.176900	−	0.984229i	$-0.443393\pi$
$31$	61.0660	0.353799	0.176900	+	0.984229i	$0.443393\pi$
$32$	−132.160	−0.730088
$33$	−168.603	−0.889394
$34$	263.303	1.32812
$35$	0	0
$36$	−28.1759	−0.130444
$37$	167.391	0.743757	0.371878	−	0.928282i	$-0.378714\pi$
$37$	167.391	0.743757	0.371878	+	0.928282i	$0.378714\pi$
$38$	28.6964	0.122505
$39$	−116.708	−0.479185
$40$	0	0
$41$	436.142	1.66132	0.830658	−	0.556783i	$-0.187964\pi$
$41$	436.142	1.66132	0.830658	+	0.556783i	$0.187964\pi$
$42$	46.3398	0.170247
$43$	−393.030	−1.39387	−0.696936	−	0.717134i	$-0.745454\pi$
$43$	−393.030	−1.39387	−0.696936	+	0.717134i	$0.745454\pi$
$44$	−175.946	−0.602837
$45$	0	0
$46$	288.112	0.923474
$47$	365.271	1.13362	0.566811	−	0.823848i	$-0.308177\pi$
$47$	365.271	1.13362	0.566811	+	0.823848i	$0.308177\pi$
$48$	87.4613	0.262999
$49$	49.0000	0.142857
$50$	0	0
$51$	357.966	0.982849
$52$	−121.791	−0.324794
$53$	−282.048	−0.730987	−0.365494	−	0.930814i	$-0.619100\pi$
$53$	−282.048	−0.730987	−0.365494	+	0.930814i	$0.619100\pi$
$54$	59.5798	0.150144
$55$	0	0
$56$	171.931	0.410272
$57$	39.0134	0.0906570
$58$	−172.103	−0.389624
$59$	414.842	0.915388	0.457694	−	0.889110i	$-0.348676\pi$
$59$	414.842	0.915388	0.457694	+	0.889110i	$0.348676\pi$
$60$	0	0
$61$	−563.802	−1.18340	−0.591701	−	0.806158i	$-0.701543\pi$
$61$	−563.802	−1.18340	−0.591701	+	0.806158i	$0.701543\pi$
$62$	−134.752	−0.276024
$63$	63.0000	0.125988
$64$	524.862	1.02512
$65$	0	0
$66$	372.049	0.693880
$67$	395.230	0.720673	0.360336	−	0.932822i	$-0.382662\pi$
$67$	395.230	0.720673	0.360336	+	0.932822i	$0.382662\pi$
$68$	373.556	0.666182
$69$	391.694	0.683398
$70$	0	0
$71$	103.990	0.173821	0.0869107	−	0.996216i	$-0.472301\pi$
$71$	103.990	0.173821	0.0869107	+	0.996216i	$0.472301\pi$
$72$	221.054	0.361826
$73$	−128.026	−0.205264	−0.102632	−	0.994719i	$-0.532726\pi$
$73$	−128.026	−0.205264	−0.102632	+	0.994719i	$0.532726\pi$
$74$	−369.376	−0.580258
$75$	0	0
$76$	40.7125	0.0614479
$77$	393.407	0.582245
$78$	257.534	0.373846
$79$	−641.999	−0.914310	−0.457155	−	0.889387i	$-0.651132\pi$
$79$	−641.999	−0.914310	−0.457155	+	0.889387i	$0.651132\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−962.417	−1.29611
$83$	512.010	0.677113	0.338557	−	0.940946i	$-0.390061\pi$
$83$	512.010	0.677113	0.338557	+	0.940946i	$0.390061\pi$
$84$	65.7437	0.0853956
$85$	0	0
$86$	867.283	1.08746
$87$	−233.977	−0.288333
$88$	1380.38	1.67215
$89$	1225.10	1.45911	0.729554	−	0.683923i	$-0.239728\pi$
$89$	1225.10	1.45911	0.729554	+	0.683923i	$0.239728\pi$
$90$	0	0
$91$	272.318	0.313700
$92$	408.753	0.463212
$93$	−183.198	−0.204266
$94$	−806.028	−0.884420
$95$	0	0
$96$	396.480	0.421517
$97$	186.760	0.195491	0.0977454	−	0.995211i	$-0.468837\pi$
$97$	186.760	0.195491	0.0977454	+	0.995211i	$0.468837\pi$
$98$	−108.126	−0.111453
$99$	505.809	0.513492
$100$	0	0
$101$	1650.68	1.62623	0.813114	−	0.582104i	$-0.197770\pi$
$101$	1650.68	1.62623	0.813114	+	0.582104i	$0.197770\pi$
$102$	−789.910	−0.766792
$103$	−72.1876	−0.0690568	−0.0345284	−	0.999404i	$-0.510993\pi$
$103$	−72.1876	−0.0690568	−0.0345284	+	0.999404i	$0.510993\pi$
$104$	955.508	0.900916
$105$	0	0
$106$	622.385	0.570296
$107$	−1202.55	−1.08649	−0.543246	−	0.839574i	$-0.682805\pi$
$107$	−1202.55	−1.08649	−0.543246	+	0.839574i	$0.682805\pi$
$108$	84.5277	0.0753118
$109$	−1551.36	−1.36324	−0.681622	−	0.731704i	$-0.738725\pi$
$109$	−1551.36	−1.36324	−0.681622	+	0.731704i	$0.738725\pi$
$110$	0	0
$111$	−502.174	−0.429408
$112$	−204.076	−0.172173
$113$	2080.90	1.73234	0.866170	−	0.499749i	$-0.166574\pi$
$113$	2080.90	1.73234	0.866170	+	0.499749i	$0.166574\pi$
$114$	−86.0893	−0.0707281
$115$	0	0
$116$	−244.167	−0.195434
$117$	350.123	0.276657
$118$	−915.416	−0.714160
$119$	−835.255	−0.643426
$120$	0	0
$121$	1827.55	1.37306
$122$	1244.12	0.923257
$123$	−1308.43	−0.959161
$124$	−191.177	−0.138453
$125$	0	0
$126$	−139.020	−0.0982924
$127$	1414.70	0.988461	0.494231	−	0.869331i	$-0.335450\pi$
$127$	1414.70	0.988461	0.494231	+	0.869331i	$0.335450\pi$
$128$	−100.912	−0.0696832
$129$	1179.09	0.804752
$130$	0	0
$131$	−2472.51	−1.64904	−0.824520	−	0.565833i	$-0.808555\pi$
$131$	−2472.51	−1.64904	−0.824520	+	0.565833i	$0.808555\pi$
$132$	527.837	0.348048
$133$	−91.0313	−0.0593490
$134$	−872.139	−0.562249
$135$	0	0
$136$	−2930.74	−1.84786
$137$	−214.391	−0.133698	−0.0668491	−	0.997763i	$-0.521295\pi$
$137$	−214.391	−0.133698	−0.0668491	+	0.997763i	$0.521295\pi$
$138$	−864.336	−0.533168
$139$	942.774	0.575288	0.287644	−	0.957737i	$-0.407128\pi$
$139$	942.774	0.575288	0.287644	+	0.957737i	$0.407128\pi$
$140$	0	0
$141$	−1095.81	−0.654497
$142$	−229.470	−0.135611
$143$	2186.36	1.27855
$144$	−262.384	−0.151843
$145$	0	0
$146$	282.509	0.160141
$147$	−147.000	−0.0824786
$148$	−524.045	−0.291056
$149$	1693.07	0.930882	0.465441	−	0.885079i	$-0.345896\pi$
$149$	1693.07	0.930882	0.465441	+	0.885079i	$0.345896\pi$
$150$	0	0
$151$	2519.69	1.35795	0.678973	−	0.734163i	$-0.262425\pi$
$151$	2519.69	1.35795	0.678973	+	0.734163i	$0.262425\pi$
$152$	−319.410	−0.170445
$153$	−1073.90	−0.567448
$154$	−868.115	−0.454251
$155$	0	0
$156$	365.372	0.187520
$157$	1621.48	0.824258	0.412129	−	0.911125i	$-0.364785\pi$
$157$	1621.48	0.824258	0.412129	+	0.911125i	$0.364785\pi$
$158$	1416.67	0.713319
$159$	846.145	0.422036
$160$	0	0
$161$	−913.954	−0.447389
$162$	−178.739	−0.0866858
$163$	925.194	0.444582	0.222291	−	0.974980i	$-0.428647\pi$
$163$	925.194	0.444582	0.222291	+	0.974980i	$0.428647\pi$
$164$	−1365.41	−0.650126
$165$	0	0
$166$	−1129.83	−0.528265
$167$	2681.55	1.24254	0.621271	−	0.783596i	$-0.286617\pi$
$167$	2681.55	1.24254	0.621271	+	0.783596i	$0.286617\pi$
$168$	−515.793	−0.236871
$169$	−683.589	−0.311147
$170$	0	0
$171$	−117.040	−0.0523409
$172$	1230.44	0.545466
$173$	287.591	0.126388	0.0631940	−	0.998001i	$-0.479871\pi$
$173$	287.591	0.126388	0.0631940	+	0.998001i	$0.479871\pi$
$174$	516.308	0.224950
$175$	0	0
$176$	−1638.47	−0.701729
$177$	−1244.53	−0.528499
$178$	−2703.38	−1.13835
$179$	3683.47	1.53808	0.769038	−	0.639203i	$-0.220735\pi$
$179$	3683.47	1.53808	0.769038	+	0.639203i	$0.220735\pi$
$180$	0	0
$181$	3132.65	1.28645	0.643227	−	0.765676i	$-0.277595\pi$
$181$	3132.65	1.28645	0.643227	+	0.765676i	$0.277595\pi$
$182$	−600.913	−0.244740
$183$	1691.41	0.683237
$184$	−3206.88	−1.28486
$185$	0	0
$186$	404.256	0.159363
$187$	−6706.02	−2.62242
$188$	−1143.54	−0.443622
$189$	−189.000	−0.0727393
$190$	0	0
$191$	1586.93	0.601184	0.300592	−	0.953753i	$-0.402816\pi$
$191$	1586.93	0.601184	0.300592	+	0.953753i	$0.402816\pi$
$192$	−1574.59	−0.591854
$193$	−5179.00	−1.93157	−0.965783	−	0.259352i	$-0.916491\pi$
$193$	−5179.00	−1.93157	−0.965783	+	0.259352i	$0.916491\pi$
$194$	−412.116	−0.152516
$195$	0	0
$196$	−153.402	−0.0559045
$197$	903.798	0.326868	0.163434	−	0.986554i	$-0.447743\pi$
$197$	903.798	0.326868	0.163434	+	0.986554i	$0.447743\pi$
$198$	−1116.15	−0.400612
$199$	−1171.51	−0.417317	−0.208659	−	0.977989i	$-0.566910\pi$
$199$	−1171.51	−0.417317	−0.208659	+	0.977989i	$0.566910\pi$
$200$	0	0
$201$	−1185.69	−0.416081
$202$	−3642.50	−1.26874
$203$	545.947	0.188759
$204$	−1120.67	−0.384620
$205$	0	0
$206$	159.293	0.0538762
$207$	−1175.08	−0.394560
$208$	−1134.16	−0.378075
$209$	−730.864	−0.241889
$210$	0	0
$211$	−1103.16	−0.359928	−0.179964	−	0.983673i	$-0.557598\pi$
$211$	−1103.16	−0.359928	−0.179964	+	0.983673i	$0.557598\pi$
$212$	882.996	0.286059
$213$	−311.969	−0.100356
$214$	2653.61	0.847651
$215$	0	0
$216$	−663.162	−0.208900
$217$	427.462	0.133724
$218$	3423.33	1.06357
$219$	384.077	0.118509
$220$	0	0
$221$	−4641.94	−1.41290
$222$	1108.13	0.335012
$223$	4079.95	1.22517	0.612586	−	0.790404i	$-0.290129\pi$
$223$	4079.95	1.22517	0.612586	+	0.790404i	$0.290129\pi$
$224$	−925.120	−0.275947
$225$	0	0
$226$	−4591.83	−1.35152
$227$	931.964	0.272496	0.136248	−	0.990675i	$-0.456496\pi$
$227$	931.964	0.272496	0.136248	+	0.990675i	$0.456496\pi$
$228$	−122.137	−0.0354770
$229$	−1471.55	−0.424641	−0.212321	−	0.977200i	$-0.568102\pi$
$229$	−1471.55	−0.424641	−0.212321	+	0.977200i	$0.568102\pi$
$230$	0	0
$231$	−1180.22	−0.336159
$232$	1915.62	0.542097
$233$	2479.06	0.697034	0.348517	−	0.937303i	$-0.386685\pi$
$233$	2479.06	0.697034	0.348517	+	0.937303i	$0.386685\pi$
$234$	−772.603	−0.215840
$235$	0	0
$236$	−1298.73	−0.358220
$237$	1926.00	0.527877
$238$	1843.12	0.501983
$239$	−954.068	−0.258216	−0.129108	−	0.991631i	$-0.541211\pi$
$239$	−954.068	−0.258216	−0.129108	+	0.991631i	$0.541211\pi$
$240$	0	0
$241$	−5297.02	−1.41581	−0.707906	−	0.706306i	$-0.750360\pi$
$241$	−5297.02	−1.41581	−0.707906	+	0.706306i	$0.750360\pi$
$242$	−4032.77	−1.07123
$243$	−243.000	−0.0641500
$244$	1765.07	0.463103
$245$	0	0
$246$	2887.25	0.748311
$247$	−505.907	−0.130324
$248$	1499.88	0.384041
$249$	−1536.03	−0.390931
$250$	0	0
$251$	1855.17	0.466524	0.233262	−	0.972414i	$-0.425060\pi$
$251$	1855.17	0.466524	0.233262	+	0.972414i	$0.425060\pi$
$252$	−197.231	−0.0493032
$253$	−7337.87	−1.82343
$254$	−3121.77	−0.771170
$255$	0	0
$256$	−3976.22	−0.970757
$257$	6233.09	1.51288	0.756438	−	0.654065i	$-0.226938\pi$
$257$	6233.09	1.51288	0.756438	+	0.654065i	$0.226938\pi$
$258$	−2601.85	−0.627845
$259$	1171.74	0.281114
$260$	0	0
$261$	701.932	0.166469
$262$	5455.99	1.28653
$263$	1184.50	0.277716	0.138858	−	0.990312i	$-0.455657\pi$
$263$	1184.50	0.277716	0.138858	+	0.990312i	$0.455657\pi$
$264$	−4141.15	−0.965417
$265$	0	0
$266$	200.875	0.0463024
$267$	−3675.31	−0.842416
$268$	−1237.33	−0.282022
$269$	−1916.03	−0.434283	−0.217141	−	0.976140i	$-0.569673\pi$
$269$	−1916.03	−0.434283	−0.217141	+	0.976140i	$0.569673\pi$
$270$	0	0
$271$	−1168.95	−0.262025	−0.131013	−	0.991381i	$-0.541823\pi$
$271$	−1168.95	−0.262025	−0.131013	+	0.991381i	$0.541823\pi$
$272$	3478.69	0.775465
$273$	−816.954	−0.181115
$274$	473.088	0.104308
$275$	0	0
$276$	−1226.26	−0.267435
$277$	−7269.54	−1.57684	−0.788419	−	0.615138i	$-0.789100\pi$
$277$	−7269.54	−1.57684	−0.788419	+	0.615138i	$0.789100\pi$
$278$	−2080.38	−0.448824
$279$	549.594	0.117933
$280$	0	0
$281$	298.126	0.0632908	0.0316454	−	0.999499i	$-0.489925\pi$
$281$	298.126	0.0632908	0.0316454	+	0.999499i	$0.489925\pi$
$282$	2418.09	0.510620
$283$	4496.30	0.944444	0.472222	−	0.881480i	$-0.343452\pi$
$283$	4496.30	0.944444	0.472222	+	0.881480i	$0.343452\pi$
$284$	−325.556	−0.0680218
$285$	0	0
$286$	−4824.56	−0.997490
$287$	3053.00	0.627919
$288$	−1189.44	−0.243363
$289$	9324.77	1.89798
$290$	0	0
$291$	−560.280	−0.112867
$292$	400.804	0.0803264
$293$	1644.33	0.327859	0.163929	−	0.986472i	$-0.447583\pi$
$293$	1644.33	0.327859	0.163929	+	0.986472i	$0.447583\pi$
$294$	324.379	0.0643475
$295$	0	0
$296$	4111.40	0.807331
$297$	−1517.43	−0.296465
$298$	−3736.02	−0.726248
$299$	−5079.31	−0.982421
$300$	0	0
$301$	−2751.21	−0.526834
$302$	−5560.11	−1.05943
$303$	−4952.05	−0.938904
$304$	379.129	0.0715281
$305$	0	0
$306$	2369.73	0.442707
$307$	4726.18	0.878623	0.439312	−	0.898335i	$-0.355222\pi$
$307$	4726.18	0.878623	0.439312	+	0.898335i	$0.355222\pi$
$308$	−1231.62	−0.227851
$309$	216.563	0.0398700
$310$	0	0
$311$	−4853.99	−0.885031	−0.442515	−	0.896761i	$-0.645914\pi$
$311$	−4853.99	−0.885031	−0.442515	+	0.896761i	$0.645914\pi$
$312$	−2866.52	−0.520144
$313$	−1690.87	−0.305348	−0.152674	−	0.988277i	$-0.548788\pi$
$313$	−1690.87	−0.305348	−0.152674	+	0.988277i	$0.548788\pi$
$314$	−3578.06	−0.643063
$315$	0	0
$316$	2009.88	0.357799
$317$	3878.38	0.687166	0.343583	−	0.939122i	$-0.388359\pi$
$317$	3878.38	0.687166	0.343583	+	0.939122i	$0.388359\pi$
$318$	−1867.15	−0.329260
$319$	4383.25	0.769326
$320$	0	0
$321$	3607.64	0.627286
$322$	2016.78	0.349040
$323$	1551.72	0.267307
$324$	−253.583	−0.0434813
$325$	0	0
$326$	−2041.59	−0.346850
$327$	4654.09	0.787070
$328$	10712.3	1.80332
$329$	2556.90	0.428469
$330$	0	0
$331$	9927.71	1.64857	0.824284	−	0.566176i	$-0.191578\pi$
$331$	9927.71	1.64857	0.824284	+	0.566176i	$0.191578\pi$
$332$	−1602.93	−0.264976
$333$	1506.52	0.247919
$334$	−5917.26	−0.969396
$335$	0	0
$336$	612.229	0.0994043
$337$	5283.88	0.854099	0.427050	−	0.904228i	$-0.359553\pi$
$337$	5283.88	0.854099	0.427050	+	0.904228i	$0.359553\pi$
$338$	1508.45	0.242748
$339$	−6242.70	−1.00017
$340$	0	0
$341$	3431.97	0.545019
$342$	258.268	0.0408349
$343$	343.000	0.0539949
$344$	−9653.42	−1.51302
$345$	0	0
$346$	−634.615	−0.0986044
$347$	−10548.3	−1.63188	−0.815940	−	0.578137i	$-0.803780\pi$
$347$	−10548.3	−1.63188	−0.815940	+	0.578137i	$0.803780\pi$
$348$	732.502	0.112834
$349$	628.411	0.0963841	0.0481921	−	0.998838i	$-0.484654\pi$
$349$	628.411	0.0963841	0.0481921	+	0.998838i	$0.484654\pi$
$350$	0	0
$351$	−1050.37	−0.159728
$352$	−7427.52	−1.12468
$353$	2548.17	0.384209	0.192104	−	0.981375i	$-0.438469\pi$
$353$	2548.17	0.384209	0.192104	+	0.981375i	$0.438469\pi$
$354$	2746.25	0.412320
$355$	0	0
$356$	−3835.37	−0.570995
$357$	2505.76	0.371482
$358$	−8128.17	−1.19996
$359$	13046.3	1.91799	0.958996	−	0.283420i	$-0.0914689\pi$
$359$	13046.3	1.91799	0.958996	+	0.283420i	$0.0914689\pi$
$360$	0	0
$361$	−6689.88	−0.975344
$362$	−6912.69	−1.00366
$363$	−5482.64	−0.792738
$364$	−852.534	−0.122761
$365$	0	0
$366$	−3732.36	−0.533043
$367$	8068.23	1.14757	0.573785	−	0.819006i	$-0.305475\pi$
$367$	8068.23	1.14757	0.573785	+	0.819006i	$0.305475\pi$
$368$	3806.46	0.539199
$369$	3925.28	0.553772
$370$	0	0
$371$	−1974.34	−0.276287
$372$	573.530	0.0799358
$373$	−3623.32	−0.502972	−0.251486	−	0.967861i	$-0.580919\pi$
$373$	−3623.32	−0.502972	−0.251486	+	0.967861i	$0.580919\pi$
$374$	14797.9	2.04594
$375$	0	0
$376$	8971.62	1.23052
$377$	3034.11	0.414495
$378$	417.059	0.0567492
$379$	7486.58	1.01467	0.507335	−	0.861749i	$-0.330631\pi$
$379$	7486.58	1.01467	0.507335	+	0.861749i	$0.330631\pi$
$380$	0	0
$381$	−4244.11	−0.570688
$382$	−3501.81	−0.469027
$383$	8926.58	1.19093	0.595466	−	0.803381i	$-0.296967\pi$
$383$	8926.58	1.19093	0.595466	+	0.803381i	$0.296967\pi$
$384$	302.736	0.0402316
$385$	0	0
$386$	11428.3	1.50695
$387$	−3537.27	−0.464624
$388$	−584.681	−0.0765018
$389$	−12600.1	−1.64228	−0.821141	−	0.570725i	$-0.806662\pi$
$389$	−12600.1	−1.64228	−0.821141	+	0.570725i	$0.806662\pi$
$390$	0	0
$391$	15579.3	2.01503
$392$	1203.52	0.155068
$393$	7417.53	0.952074
$394$	−1994.37	−0.255013
$395$	0	0
$396$	−1583.51	−0.200946
$397$	−12713.4	−1.60722	−0.803612	−	0.595154i	$-0.797091\pi$
$397$	−12713.4	−1.60722	−0.803612	+	0.595154i	$0.797091\pi$
$398$	2585.12	0.325579
$399$	273.094	0.0342651
$400$	0	0
$401$	−6133.51	−0.763822	−0.381911	−	0.924199i	$-0.624734\pi$
$401$	−6133.51	−0.763822	−0.381911	+	0.924199i	$0.624734\pi$
$402$	2616.42	0.324614
$403$	2375.62	0.293643
$404$	−5167.72	−0.636395
$405$	0	0
$406$	−1204.72	−0.147264
$407$	9407.56	1.14574
$408$	8792.21	1.06686
$409$	10600.3	1.28154	0.640769	−	0.767733i	$-0.278615\pi$
$409$	10600.3	1.28154	0.640769	+	0.767733i	$0.278615\pi$
$410$	0	0
$411$	643.173	0.0771907
$412$	225.994	0.0270241
$413$	2903.90	0.345984
$414$	2593.01	0.307825
$415$	0	0
$416$	−5141.37	−0.605953
$417$	−2828.32	−0.332143
$418$	1612.77	0.188715
$419$	4296.43	0.500941	0.250470	−	0.968124i	$-0.419415\pi$
$419$	4296.43	0.500941	0.250470	+	0.968124i	$0.419415\pi$
$420$	0	0
$421$	3916.78	0.453425	0.226713	−	0.973962i	$-0.427202\pi$
$421$	3916.78	0.453425	0.226713	+	0.973962i	$0.427202\pi$
$422$	2434.30	0.280806
$423$	3287.44	0.377874
$424$	−6927.55	−0.793471
$425$	0	0
$426$	688.410	0.0782948
$427$	−3946.62	−0.447284
$428$	3764.76	0.425179
$429$	−6559.09	−0.738172
$430$	0	0
$431$	13408.9	1.49857	0.749287	−	0.662246i	$-0.230396\pi$
$431$	13408.9	1.49857	0.749287	+	0.662246i	$0.230396\pi$
$432$	787.152	0.0876663
$433$	7792.31	0.864837	0.432419	−	0.901673i	$-0.357660\pi$
$433$	7792.31	0.864837	0.432419	+	0.901673i	$0.357660\pi$
$434$	−943.263	−0.104327
$435$	0	0
$436$	4856.78	0.533481
$437$	1697.93	0.185865
$438$	−847.528	−0.0924576
$439$	1039.29	0.112990	0.0564948	−	0.998403i	$-0.482008\pi$
$439$	1039.29	0.112990	0.0564948	+	0.998403i	$0.482008\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	10243.2	1.10230
$443$	−2846.33	−0.305267	−0.152633	−	0.988283i	$-0.548775\pi$
$443$	−2846.33	−0.305267	−0.152633	+	0.988283i	$0.548775\pi$
$444$	1572.13	0.168041
$445$	0	0
$446$	−9003.05	−0.955845
$447$	−5079.20	−0.537445
$448$	3674.04	0.387460
$449$	7472.64	0.785425	0.392713	−	0.919661i	$-0.371537\pi$
$449$	7472.64	0.785425	0.392713	+	0.919661i	$0.371537\pi$
$450$	0	0
$451$	24511.6	2.55922
$452$	−6514.57	−0.677920
$453$	−7559.08	−0.784010
$454$	−2056.53	−0.212594
$455$	0	0
$456$	958.230	0.0984062
$457$	−11014.3	−1.12742	−0.563708	−	0.825974i	$-0.690626\pi$
$457$	−11014.3	−1.12742	−0.563708	+	0.825974i	$0.690626\pi$
$458$	3247.21	0.331293
$459$	3221.70	0.327616
$460$	0	0
$461$	7944.67	0.802647	0.401323	−	0.915936i	$-0.368550\pi$
$461$	7944.67	0.802647	0.401323	+	0.915936i	$0.368550\pi$
$462$	2604.34	0.262262
$463$	−7627.25	−0.765591	−0.382795	−	0.923833i	$-0.625039\pi$
$463$	−7627.25	−0.765591	−0.382795	+	0.923833i	$0.625039\pi$
$464$	−2273.77	−0.227494
$465$	0	0
$466$	−5470.45	−0.543806
$467$	−3284.28	−0.325436	−0.162718	−	0.986673i	$-0.552026\pi$
$467$	−3284.28	−0.325436	−0.162718	+	0.986673i	$0.552026\pi$
$468$	−1096.11	−0.108265
$469$	2766.61	0.272389
$470$	0	0
$471$	−4864.45	−0.475886
$472$	10189.2	0.993633
$473$	−22088.6	−2.14722
$474$	−4250.02	−0.411835
$475$	0	0
$476$	2614.89	0.251793
$477$	−2538.44	−0.243662
$478$	2105.30	0.201453
$479$	−2909.45	−0.277528	−0.138764	−	0.990325i	$-0.544313\pi$
$479$	−2909.45	−0.277528	−0.138764	+	0.990325i	$0.544313\pi$
$480$	0	0
$481$	6511.96	0.617297
$482$	11688.7	1.10458
$483$	2741.86	0.258300
$484$	−5721.42	−0.537323
$485$	0	0
$486$	536.218	0.0500481
$487$	−2201.84	−0.204876	−0.102438	−	0.994739i	$-0.532664\pi$
$487$	−2201.84	−0.204876	−0.102438	+	0.994739i	$0.532664\pi$
$488$	−13847.9	−1.28456
$489$	−2775.58	−0.256679
$490$	0	0
$491$	−11827.6	−1.08711	−0.543556	−	0.839373i	$-0.682922\pi$
$491$	−11827.6	−1.08711	−0.543556	+	0.839373i	$0.682922\pi$
$492$	4096.23	0.375350
$493$	−9306.23	−0.850165
$494$	1116.37	0.101675
$495$	0	0
$496$	−1780.30	−0.161165
$497$	727.928	0.0656983
$498$	3389.49	0.304994
$499$	1408.66	0.126374	0.0631868	−	0.998002i	$-0.479874\pi$
$499$	1408.66	0.126374	0.0631868	+	0.998002i	$0.479874\pi$
$500$	0	0
$501$	−8044.65	−0.717382
$502$	−4093.74	−0.363969
$503$	−11018.9	−0.976758	−0.488379	−	0.872632i	$-0.662412\pi$
$503$	−11018.9	−0.976758	−0.488379	+	0.872632i	$0.662412\pi$
$504$	1547.38	0.136757
$505$	0	0
$506$	16192.2	1.42259
$507$	2050.77	0.179641
$508$	−4428.95	−0.386816
$509$	7032.93	0.612434	0.306217	−	0.951962i	$-0.400937\pi$
$509$	7032.93	0.612434	0.306217	+	0.951962i	$0.400937\pi$
$510$	0	0
$511$	−896.180	−0.0775825
$512$	9581.46	0.827041
$513$	351.121	0.0302190
$514$	−13754.3	−1.18030
$515$	0	0
$516$	−3691.32	−0.314925
$517$	20528.6	1.74632
$518$	−2585.63	−0.219317
$519$	−862.773	−0.0729702
$520$	0	0
$521$	3049.04	0.256394	0.128197	−	0.991749i	$-0.459081\pi$
$521$	3049.04	0.256394	0.128197	+	0.991749i	$0.459081\pi$
$522$	−1548.93	−0.129875
$523$	8714.06	0.728564	0.364282	−	0.931289i	$-0.381314\pi$
$523$	8714.06	0.728564	0.364282	+	0.931289i	$0.381314\pi$
$524$	7740.58	0.645322
$525$	0	0
$526$	−2613.79	−0.216666
$527$	−7286.52	−0.602288
$528$	4915.41	0.405143
$529$	4880.17	0.401099
$530$	0	0
$531$	3733.58	0.305129
$532$	284.987	0.0232251
$533$	16967.1	1.37885
$534$	8110.15	0.657230
$535$	0	0
$536$	9707.48	0.782275
$537$	−11050.4	−0.888009
$538$	4228.02	0.338815
$539$	2753.85	0.220068
$540$	0	0
$541$	−5999.45	−0.476778	−0.238389	−	0.971170i	$-0.576619\pi$
$541$	−5999.45	−0.476778	−0.238389	+	0.971170i	$0.576619\pi$
$542$	2579.48	0.204425
$543$	−9397.95	−0.742734
$544$	15769.6	1.24286
$545$	0	0
$546$	1802.74	0.141301
$547$	7759.95	0.606566	0.303283	−	0.952901i	$-0.401917\pi$
$547$	7759.95	0.606566	0.303283	+	0.952901i	$0.401917\pi$
$548$	671.184	0.0523203
$549$	−5074.22	−0.394467
$550$	0	0
$551$	−1014.25	−0.0784184
$552$	9620.63	0.741814
$553$	−4493.99	−0.345577
$554$	16041.4	1.23021
$555$	0	0
$556$	−2951.50	−0.225128
$557$	−6392.82	−0.486306	−0.243153	−	0.969988i	$-0.578182\pi$
$557$	−6392.82	−0.486306	−0.243153	+	0.969988i	$0.578182\pi$
$558$	−1212.77	−0.0920081
$559$	−15289.9	−1.15687
$560$	0	0
$561$	20118.1	1.51406
$562$	−657.863	−0.0493777
$563$	−7682.70	−0.575111	−0.287555	−	0.957764i	$-0.592843\pi$
$563$	−7682.70	−0.575111	−0.287555	+	0.957764i	$0.592843\pi$
$564$	3430.61	0.256125
$565$	0	0
$566$	−9921.81	−0.736828
$567$	567.000	0.0419961
$568$	2554.15	0.188679
$569$	143.175	0.0105487	0.00527434	−	0.999986i	$-0.498321\pi$
$569$	143.175	0.0105487	0.00527434	+	0.999986i	$0.498321\pi$
$570$	0	0
$571$	1077.72	0.0789863	0.0394932	−	0.999220i	$-0.487426\pi$
$571$	1077.72	0.0789863	0.0394932	+	0.999220i	$0.487426\pi$
$572$	−6844.74	−0.500338
$573$	−4760.78	−0.347094
$574$	−6736.92	−0.489884
$575$	0	0
$576$	4723.76	0.341707
$577$	−12651.7	−0.912818	−0.456409	−	0.889770i	$-0.650865\pi$
$577$	−12651.7	−0.912818	−0.456409	+	0.889770i	$0.650865\pi$
$578$	−20576.6	−1.48075
$579$	15537.0	1.11519
$580$	0	0
$581$	3584.07	0.255925
$582$	1236.35	0.0880554
$583$	−15851.4	−1.12607
$584$	−3144.51	−0.222810
$585$	0	0
$586$	−3628.47	−0.255786
$587$	−2920.89	−0.205380	−0.102690	−	0.994713i	$-0.532745\pi$
$587$	−2920.89	−0.205380	−0.102690	+	0.994713i	$0.532745\pi$
$588$	460.206	0.0322765
$589$	−794.131	−0.0555545
$590$	0	0
$591$	−2711.39	−0.188717
$592$	−4880.09	−0.338802
$593$	−9801.70	−0.678765	−0.339382	−	0.940648i	$-0.610218\pi$
$593$	−9801.70	−0.678765	−0.339382	+	0.940648i	$0.610218\pi$
$594$	3348.44	0.231293
$595$	0	0
$596$	−5300.41	−0.364284
$597$	3514.53	0.240938
$598$	11208.3	0.766458
$599$	−6992.54	−0.476974	−0.238487	−	0.971146i	$-0.576651\pi$
$599$	−6992.54	−0.476974	−0.238487	+	0.971146i	$0.576651\pi$
$600$	0	0
$601$	−26159.1	−1.77546	−0.887730	−	0.460364i	$-0.847719\pi$
$601$	−26159.1	−1.77546	−0.887730	+	0.460364i	$0.847719\pi$
$602$	6070.98	0.411021
$603$	3557.07	0.240224
$604$	−7888.29	−0.531407
$605$	0	0
$606$	10927.5	0.732506
$607$	264.526	0.0176883	0.00884415	−	0.999961i	$-0.497185\pi$
$607$	264.526	0.0176883	0.00884415	+	0.999961i	$0.497185\pi$
$608$	1718.67	0.114640
$609$	−1637.84	−0.108980
$610$	0	0
$611$	14210.0	0.940875
$612$	3362.01	0.222061
$613$	29371.1	1.93521	0.967607	−	0.252461i	$-0.0812400\pi$
$613$	29371.1	1.93521	0.967607	+	0.252461i	$0.0812400\pi$
$614$	−10429.1	−0.685477
$615$	0	0
$616$	9662.68	0.632014
$617$	−26226.1	−1.71122	−0.855609	−	0.517622i	$-0.826817\pi$
$617$	−26226.1	−1.71122	−0.855609	+	0.517622i	$0.826817\pi$
$618$	−477.880	−0.0311054
$619$	−8903.12	−0.578105	−0.289052	−	0.957313i	$-0.593340\pi$
$619$	−8903.12	−0.578105	−0.289052	+	0.957313i	$0.593340\pi$
$620$	0	0
$621$	3525.25	0.227799
$622$	10711.1	0.690476
$623$	8575.72	0.551491
$624$	3402.47	0.218282
$625$	0	0
$626$	3731.18	0.238224
$627$	2192.59	0.139655
$628$	−5076.31	−0.322558
$629$	−19973.5	−1.26613
$630$	0	0
$631$	−14136.0	−0.891832	−0.445916	−	0.895075i	$-0.647122\pi$
$631$	−14136.0	−0.891832	−0.445916	+	0.895075i	$0.647122\pi$
$632$	−15768.5	−0.992464
$633$	3309.49	0.207805
$634$	−8558.27	−0.536108
$635$	0	0
$636$	−2648.99	−0.165156
$637$	1906.23	0.118567
$638$	−9672.34	−0.600206
$639$	935.908	0.0579404
$640$	0	0
$641$	17665.7	1.08854	0.544270	−	0.838910i	$-0.316807\pi$
$641$	17665.7	1.08854	0.544270	+	0.838910i	$0.316807\pi$
$642$	−7960.84	−0.489391
$643$	10890.0	0.667901	0.333951	−	0.942591i	$-0.391618\pi$
$643$	10890.0	0.667901	0.333951	+	0.942591i	$0.391618\pi$
$644$	2861.27	0.175078
$645$	0	0
$646$	−3424.12	−0.208545
$647$	24281.0	1.47540	0.737701	−	0.675128i	$-0.235911\pi$
$647$	24281.0	1.47540	0.737701	+	0.675128i	$0.235911\pi$
$648$	1989.49	0.120609
$649$	23314.5	1.41013
$650$	0	0
$651$	−1282.39	−0.0772053
$652$	−2896.46	−0.173979
$653$	1865.16	0.111776	0.0558878	−	0.998437i	$-0.482201\pi$
$653$	1865.16	0.111776	0.0558878	+	0.998437i	$0.482201\pi$
$654$	−10270.0	−0.614050
$655$	0	0
$656$	−12715.2	−0.756775
$657$	−1152.23	−0.0684214
$658$	−5642.20	−0.334279
$659$	−8327.14	−0.492230	−0.246115	−	0.969241i	$-0.579154\pi$
$659$	−8327.14	−0.492230	−0.246115	+	0.969241i	$0.579154\pi$
$660$	0	0
$661$	−20665.7	−1.21604	−0.608021	−	0.793921i	$-0.708036\pi$
$661$	−20665.7	−1.21604	−0.608021	+	0.793921i	$0.708036\pi$
$662$	−21907.1	−1.28617
$663$	13925.8	0.815737
$664$	12575.8	0.734991
$665$	0	0
$666$	−3324.38	−0.193419
$667$	−10183.1	−0.591140
$668$	−8395.00	−0.486246
$669$	−12239.8	−0.707353
$670$	0	0
$671$	−31686.2	−1.82300
$672$	2775.36	0.159318
$673$	−1283.48	−0.0735136	−0.0367568	−	0.999324i	$-0.511703\pi$
$673$	−1283.48	−0.0735136	−0.0367568	+	0.999324i	$0.511703\pi$
$674$	−11659.7	−0.666344
$675$	0	0
$676$	2140.08	0.121762
$677$	−13783.2	−0.782467	−0.391234	−	0.920291i	$-0.627952\pi$
$677$	−13783.2	−0.782467	−0.391234	+	0.920291i	$0.627952\pi$
$678$	13775.5	0.780302
$679$	1307.32	0.0738886
$680$	0	0
$681$	−2795.89	−0.157326
$682$	−7573.18	−0.425208
$683$	10796.5	0.604856	0.302428	−	0.953172i	$-0.402203\pi$
$683$	10796.5	0.604856	0.302428	+	0.953172i	$0.402203\pi$
$684$	366.412	0.0204826
$685$	0	0
$686$	−756.884	−0.0421253
$687$	4414.66	0.245167
$688$	11458.3	0.634947
$689$	−10972.4	−0.606699
$690$	0	0
$691$	−12082.4	−0.665173	−0.332587	−	0.943073i	$-0.607921\pi$
$691$	−12082.4	−0.665173	−0.332587	+	0.943073i	$0.607921\pi$
$692$	−900.348	−0.0494597
$693$	3540.66	0.194082
$694$	23276.5	1.27315
$695$	0	0
$696$	−5746.85	−0.312980
$697$	−52041.4	−2.82813
$698$	−1386.69	−0.0751962
$699$	−7437.19	−0.402433
$700$	0	0
$701$	−28753.5	−1.54922	−0.774610	−	0.632439i	$-0.782054\pi$
$701$	−28753.5	−1.54922	−0.774610	+	0.632439i	$0.782054\pi$
$702$	2317.81	0.124615
$703$	−2176.84	−0.116787
$704$	29497.8	1.57917
$705$	0	0
$706$	−5622.95	−0.299749
$707$	11554.8	0.614657
$708$	3896.18	0.206819
$709$	4577.21	0.242455	0.121228	−	0.992625i	$-0.461317\pi$
$709$	4577.21	0.242455	0.121228	+	0.992625i	$0.461317\pi$
$710$	0	0
$711$	−5777.99	−0.304770
$712$	30090.4	1.58383
$713$	−7973.07	−0.418785
$714$	−5529.37	−0.289820
$715$	0	0
$716$	−11531.7	−0.601898
$717$	2862.20	0.149081
$718$	−28788.8	−1.49636
$719$	30875.9	1.60150	0.800749	−	0.599000i	$-0.204435\pi$
$719$	30875.9	1.60150	0.800749	+	0.599000i	$0.204435\pi$
$720$	0	0
$721$	−505.313	−0.0261010
$722$	14762.3	0.760936
$723$	15891.1	0.817420
$724$	−9807.25	−0.503430
$725$	0	0
$726$	12098.3	0.618472
$727$	−520.090	−0.0265324	−0.0132662	−	0.999912i	$-0.504223\pi$
$727$	−520.090	−0.0265324	−0.0132662	+	0.999912i	$0.504223\pi$
$728$	6688.56	0.340514
$729$	729.000	0.0370370
$730$	0	0
$731$	46897.1	2.37285
$732$	−5295.21	−0.267372
$733$	393.396	0.0198232	0.00991160	−	0.999951i	$-0.496845\pi$
$733$	393.396	0.0198232	0.00991160	+	0.999951i	$0.496845\pi$
$734$	−17803.8	−0.895301
$735$	0	0
$736$	17255.5	0.864191
$737$	22212.3	1.11018
$738$	−8661.76	−0.432037
$739$	−9348.92	−0.465366	−0.232683	−	0.972553i	$-0.574750\pi$
$739$	−9348.92	−0.465366	−0.232683	+	0.972553i	$0.574750\pi$
$740$	0	0
$741$	1517.72	0.0752428
$742$	4356.69	0.215552
$743$	−33710.8	−1.66451	−0.832254	−	0.554394i	$-0.812950\pi$
$743$	−33710.8	−1.66451	−0.832254	+	0.554394i	$0.812950\pi$
$744$	−4499.63	−0.221726
$745$	0	0
$746$	7995.44	0.392405
$747$	4608.09	0.225704
$748$	20994.2	1.02624
$749$	−8417.83	−0.410655
$750$	0	0
$751$	−21116.6	−1.02604	−0.513019	−	0.858377i	$-0.671473\pi$
$751$	−21116.6	−1.02604	−0.513019	+	0.858377i	$0.671473\pi$
$752$	−10649.0	−0.516396
$753$	−5565.52	−0.269348
$754$	−6695.24	−0.323377
$755$	0	0
$756$	591.694	0.0284652
$757$	7385.25	0.354586	0.177293	−	0.984158i	$-0.443266\pi$
$757$	7385.25	0.354586	0.177293	+	0.984158i	$0.443266\pi$
$758$	−16520.3	−0.791616
$759$	22013.6	1.05276
$760$	0	0
$761$	−27682.0	−1.31862	−0.659311	−	0.751871i	$-0.729152\pi$
$761$	−27682.0	−1.31862	−0.659311	+	0.751871i	$0.729152\pi$
$762$	9365.30	0.445235
$763$	−10859.5	−0.515258
$764$	−4968.12	−0.235262
$765$	0	0
$766$	−19697.9	−0.929132
$767$	16138.4	0.759746
$768$	11928.7	0.560467
$769$	−22248.6	−1.04331	−0.521654	−	0.853157i	$-0.674685\pi$
$769$	−22248.6	−1.04331	−0.521654	+	0.853157i	$0.674685\pi$
$770$	0	0
$771$	−18699.3	−0.873460
$772$	16213.6	0.755883
$773$	11372.3	0.529152	0.264576	−	0.964365i	$-0.414768\pi$
$773$	11372.3	0.529152	0.264576	+	0.964365i	$0.414768\pi$
$774$	7805.54	0.362486
$775$	0	0
$776$	4587.12	0.212201
$777$	−3515.22	−0.162301
$778$	27804.0	1.28126
$779$	−5671.80	−0.260864
$780$	0	0
$781$	5844.32	0.267767
$782$	−34378.1	−1.57207
$783$	−2105.80	−0.0961112
$784$	−1428.53	−0.0650754
$785$	0	0
$786$	−16368.0	−0.742781
$787$	36561.9	1.65602	0.828012	−	0.560710i	$-0.189472\pi$
$787$	36561.9	1.65602	0.828012	+	0.560710i	$0.189472\pi$
$788$	−2829.48	−0.127914
$789$	−3553.50	−0.160339
$790$	0	0
$791$	14566.3	0.654763
$792$	12423.4	0.557384
$793$	−21933.4	−0.982190
$794$	28054.2	1.25391
$795$	0	0
$796$	3667.59	0.163309
$797$	7436.80	0.330521	0.165260	−	0.986250i	$-0.447154\pi$
$797$	7436.80	0.330521	0.165260	+	0.986250i	$0.447154\pi$
$798$	−602.625	−0.0267327
$799$	−43584.9	−1.92982
$800$	0	0
$801$	11025.9	0.486369
$802$	13534.6	0.595913
$803$	−7195.17	−0.316204
$804$	3711.99	0.162826
$805$	0	0
$806$	−5242.20	−0.229092
$807$	5748.08	0.250733
$808$	40543.4	1.76524
$809$	−30585.4	−1.32920	−0.664601	−	0.747198i	$-0.731399\pi$
$809$	−30585.4	−1.32920	−0.664601	+	0.747198i	$0.731399\pi$
$810$	0	0
$811$	23756.0	1.02859	0.514294	−	0.857614i	$-0.328054\pi$
$811$	23756.0	1.02859	0.514294	+	0.857614i	$0.328054\pi$
$812$	−1709.17	−0.0738672
$813$	3506.86	0.151280
$814$	−20759.3	−0.893873
$815$	0	0
$816$	−10436.1	−0.447715
$817$	5111.14	0.218869
$818$	−23391.2	−0.999821
$819$	2450.86	0.104567
$820$	0	0
$821$	−33842.2	−1.43861	−0.719306	−	0.694694i	$-0.755540\pi$
$821$	−33842.2	−1.43861	−0.719306	+	0.694694i	$0.755540\pi$
$822$	−1419.26	−0.0602220
$823$	18730.9	0.793340	0.396670	−	0.917961i	$-0.370166\pi$
$823$	18730.9	0.793340	0.396670	+	0.917961i	$0.370166\pi$
$824$	−1773.04	−0.0749597
$825$	0	0
$826$	−6407.91	−0.269927
$827$	19107.1	0.803409	0.401705	−	0.915769i	$-0.368418\pi$
$827$	19107.1	0.803409	0.401705	+	0.915769i	$0.368418\pi$
$828$	3678.78	0.154404
$829$	9942.59	0.416551	0.208275	−	0.978070i	$-0.433215\pi$
$829$	9942.59	0.416551	0.208275	+	0.978070i	$0.433215\pi$
$830$	0	0
$831$	21808.6	0.910388
$832$	20418.5	0.850822
$833$	−5846.78	−0.243192
$834$	6241.14	0.259128
$835$	0	0
$836$	2288.08	0.0946590
$837$	−1648.78	−0.0680887
$838$	−9480.75	−0.390820
$839$	37144.9	1.52847	0.764233	−	0.644940i	$-0.223118\pi$
$839$	37144.9	1.52847	0.764233	+	0.644940i	$0.223118\pi$
$840$	0	0
$841$	−18306.2	−0.750591
$842$	−8642.99	−0.353750
$843$	−894.379	−0.0365410
$844$	3453.62	0.140851
$845$	0	0
$846$	−7254.26	−0.294807
$847$	12792.8	0.518969
$848$	8222.78	0.332985
$849$	−13488.9	−0.545275
$850$	0	0
$851$	−21855.4	−0.880370
$852$	976.668	0.0392724
$853$	31377.2	1.25948	0.629739	−	0.776807i	$-0.283162\pi$
$853$	31377.2	1.25948	0.629739	+	0.776807i	$0.283162\pi$
$854$	8708.84	0.348958
$855$	0	0
$856$	−29536.4	−1.17936
$857$	24561.3	0.978993	0.489496	−	0.872005i	$-0.337181\pi$
$857$	24561.3	0.978993	0.489496	+	0.872005i	$0.337181\pi$
$858$	14473.7	0.575901
$859$	−39819.1	−1.58162	−0.790809	−	0.612063i	$-0.790340\pi$
$859$	−39819.1	−1.58162	−0.790809	+	0.612063i	$0.790340\pi$
$860$	0	0
$861$	−9158.99	−0.362529
$862$	−29588.9	−1.16914
$863$	−14702.2	−0.579919	−0.289959	−	0.957039i	$-0.593642\pi$
$863$	−14702.2	−0.579919	−0.289959	+	0.957039i	$0.593642\pi$
$864$	3568.32	0.140506
$865$	0	0
$866$	−17195.0	−0.674722
$867$	−27974.3	−1.09580
$868$	−1338.24	−0.0523303
$869$	−36081.0	−1.40847
$870$	0	0
$871$	15375.5	0.598138
$872$	−38103.9	−1.47977
$873$	1680.84	0.0651636
$874$	−3746.74	−0.145006
$875$	0	0
$876$	−1202.41	−0.0463764
$877$	−7208.31	−0.277546	−0.138773	−	0.990324i	$-0.544316\pi$
$877$	−7208.31	−0.277546	−0.138773	+	0.990324i	$0.544316\pi$
$878$	−2293.35	−0.0881512
$879$	−4932.98	−0.189289
$880$	0	0
$881$	3789.00	0.144898	0.0724488	−	0.997372i	$-0.476919\pi$
$881$	3789.00	0.144898	0.0724488	+	0.997372i	$0.476919\pi$
$882$	−973.137	−0.0371510
$883$	26953.7	1.02725	0.513626	−	0.858014i	$-0.328302\pi$
$883$	26953.7	1.02725	0.513626	+	0.858014i	$0.328302\pi$
$884$	14532.3	0.552912
$885$	0	0
$886$	6280.88	0.238160
$887$	37869.8	1.43353	0.716766	−	0.697314i	$-0.245621\pi$
$887$	37869.8	1.43353	0.716766	+	0.697314i	$0.245621\pi$
$888$	−12334.2	−0.466113
$889$	9902.92	0.373603
$890$	0	0
$891$	4552.28	0.171164
$892$	−12772.9	−0.479449
$893$	−4750.15	−0.178004
$894$	11208.1	0.419300
$895$	0	0
$896$	−706.385	−0.0263378
$897$	15237.9	0.567201
$898$	−16489.6	−0.612767
$899$	4762.69	0.176690
$900$	0	0
$901$	33654.6	1.24439
$902$	−54088.8	−1.99663
$903$	8253.62	0.304168
$904$	51110.1	1.88042
$905$	0	0
$906$	16680.3	0.611663
$907$	−11717.5	−0.428968	−0.214484	−	0.976728i	$-0.568807\pi$
$907$	−11717.5	−0.428968	−0.214484	+	0.976728i	$0.568807\pi$
$908$	−2917.66	−0.106636
$909$	14856.1	0.542076
$910$	0	0
$911$	−15909.2	−0.578589	−0.289294	−	0.957240i	$-0.593421\pi$
$911$	−15909.2	−0.578589	−0.289294	+	0.957240i	$0.593421\pi$
$912$	−1137.39	−0.0412968
$913$	28775.4	1.04308
$914$	24304.9	0.879578
$915$	0	0
$916$	4606.92	0.166176
$917$	−17307.6	−0.623279
$918$	−7109.19	−0.255597
$919$	−32933.3	−1.18212	−0.591060	−	0.806628i	$-0.701290\pi$
$919$	−32933.3	−1.18212	−0.591060	+	0.806628i	$0.701290\pi$
$920$	0	0
$921$	−14178.5	−0.507273
$922$	−17531.2	−0.626203
$923$	4045.47	0.144267
$924$	3694.86	0.131550
$925$	0	0
$926$	16830.7	0.597292
$927$	−649.688	−0.0230189
$928$	−10307.5	−0.364612
$929$	−30912.6	−1.09172	−0.545861	−	0.837876i	$-0.683797\pi$
$929$	−30912.6	−1.09172	−0.545861	+	0.837876i	$0.683797\pi$
$930$	0	0
$931$	−637.219	−0.0224318
$932$	−7761.09	−0.272771
$933$	14562.0	0.510973
$934$	7247.29	0.253896
$935$	0	0
$936$	8599.57	0.300305
$937$	45737.6	1.59465	0.797323	−	0.603553i	$-0.206249\pi$
$937$	45737.6	1.59465	0.797323	+	0.603553i	$0.206249\pi$
$938$	−6104.97	−0.212510
$939$	5072.62	0.176293
$940$	0	0
$941$	−2137.79	−0.0740595	−0.0370297	−	0.999314i	$-0.511790\pi$
$941$	−2137.79	−0.0740595	−0.0370297	+	0.999314i	$0.511790\pi$
$942$	10734.2	0.371273
$943$	−56944.8	−1.96647
$944$	−12094.2	−0.416984
$945$	0	0
$946$	48742.1	1.67520
$947$	−42513.2	−1.45881	−0.729405	−	0.684082i	$-0.760203\pi$
$947$	−42513.2	−1.45881	−0.729405	+	0.684082i	$0.760203\pi$
$948$	−6029.63	−0.206575
$949$	−4980.53	−0.170363
$950$	0	0
$951$	−11635.2	−0.396736
$952$	−20515.2	−0.698425
$953$	9012.85	0.306353	0.153177	−	0.988199i	$-0.451050\pi$
$953$	9012.85	0.306353	0.153177	+	0.988199i	$0.451050\pi$
$954$	5601.46	0.190099
$955$	0	0
$956$	2986.86	0.101048
$957$	−13149.8	−0.444171
$958$	6420.15	0.216520
$959$	−1500.74	−0.0505332
$960$	0	0
$961$	−26061.9	−0.874826
$962$	−14369.7	−0.481598
$963$	−10822.9	−0.362164
$964$	16583.1	0.554053
$965$	0	0
$966$	−6050.35	−0.201519
$967$	−29024.2	−0.965207	−0.482604	−	0.875839i	$-0.660309\pi$
$967$	−29024.2	−0.965207	−0.482604	+	0.875839i	$0.660309\pi$
$968$	44887.4	1.49043
$969$	−4655.16	−0.154330
$970$	0	0
$971$	12874.4	0.425498	0.212749	−	0.977107i	$-0.431758\pi$
$971$	12874.4	0.425498	0.212749	+	0.977107i	$0.431758\pi$
$972$	760.749	0.0251039
$973$	6599.42	0.217438
$974$	4858.70	0.159839
$975$	0	0
$976$	16437.0	0.539072
$977$	15195.8	0.497600	0.248800	−	0.968555i	$-0.419964\pi$
$977$	15195.8	0.497600	0.248800	+	0.968555i	$0.419964\pi$
$978$	6124.77	0.200254
$979$	68851.9	2.24772
$980$	0	0
$981$	−13962.3	−0.454415
$982$	26099.5	0.848134
$983$	−12042.2	−0.390728	−0.195364	−	0.980731i	$-0.562589\pi$
$983$	−12042.2	−0.390728	−0.195364	+	0.980731i	$0.562589\pi$
$984$	−32137.0	−1.04115
$985$	0	0
$986$	20535.7	0.663275
$987$	−7670.69	−0.247377
$988$	1583.82	0.0510001
$989$	51315.8	1.64990
$990$	0	0
$991$	11490.7	0.368330	0.184165	−	0.982895i	$-0.441042\pi$
$991$	11490.7	0.368330	0.184165	+	0.982895i	$0.441042\pi$
$992$	−8070.49	−0.258305
$993$	−29783.1	−0.951801
$994$	−1606.29	−0.0512560
$995$	0	0
$996$	4808.78	0.152984
$997$	−4076.85	−0.129504	−0.0647518	−	0.997901i	$-0.520626\pi$
$997$	−4076.85	−0.129504	−0.0647518	+	0.997901i	$0.520626\pi$
$998$	−3108.44	−0.0985931
$999$	−4519.57	−0.143136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.x.1.2		5
3.2	odd	2		1575.4.a.bo.1.4		5
5.2	odd	4		105.4.d.b.64.4	✓	10
5.3	odd	4		105.4.d.b.64.7	yes	10
5.4	even	2		525.4.a.w.1.4		5
15.2	even	4		315.4.d.b.64.7		10
15.8	even	4		315.4.d.b.64.4		10
15.14	odd	2		1575.4.a.bp.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.4	✓	10	5.2	odd	4
105.4.d.b.64.7	yes	10	5.3	odd	4
315.4.d.b.64.4		10	15.8	even	4
315.4.d.b.64.7		10	15.2	even	4
525.4.a.w.1.4		5	5.4	even	2
525.4.a.x.1.2		5	1.1	even	1	trivial
1575.4.a.bo.1.4		5	3.2	odd	2
1575.4.a.bp.1.2		5	15.14	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20666 q^{2} -3.00000 q^{3} -3.13065 q^{4} +6.61998 q^{6} +7.00000 q^{7} +24.5616 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.20666 q^{2} -3.00000 q^{3} -3.13065 q^{4} +6.61998 q^{6} +7.00000 q^{7} +24.5616 q^{8} +9.00000 q^{9} +56.2010 q^{11} +9.39196 q^{12} +38.9026 q^{13} -15.4466 q^{14} -29.1538 q^{16} -119.322 q^{17} -19.8599 q^{18} -13.0045 q^{19} -21.0000 q^{21} -124.016 q^{22} -130.565 q^{23} -73.6847 q^{24} -85.8448 q^{26} -27.0000 q^{27} -21.9146 q^{28} +77.9925 q^{29} +61.0660 q^{31} -132.160 q^{32} -168.603 q^{33} +263.303 q^{34} -28.1759 q^{36} +167.391 q^{37} +28.6964 q^{38} -116.708 q^{39} +436.142 q^{41} +46.3398 q^{42} -393.030 q^{43} -175.946 q^{44} +288.112 q^{46} +365.271 q^{47} +87.4613 q^{48} +49.0000 q^{49} +357.966 q^{51} -121.791 q^{52} -282.048 q^{53} +59.5798 q^{54} +171.931 q^{56} +39.0134 q^{57} -172.103 q^{58} +414.842 q^{59} -563.802 q^{61} -134.752 q^{62} +63.0000 q^{63} +524.862 q^{64} +372.049 q^{66} +395.230 q^{67} +373.556 q^{68} +391.694 q^{69} +103.990 q^{71} +221.054 q^{72} -128.026 q^{73} -369.376 q^{74} +40.7125 q^{76} +393.407 q^{77} +257.534 q^{78} -641.999 q^{79} +81.0000 q^{81} -962.417 q^{82} +512.010 q^{83} +65.7437 q^{84} +867.283 q^{86} -233.977 q^{87} +1380.38 q^{88} +1225.10 q^{89} +272.318 q^{91} +408.753 q^{92} -183.198 q^{93} -806.028 q^{94} +396.480 q^{96} +186.760 q^{97} -108.126 q^{98} +505.809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 15 q^{3} + 27 q^{4} - 3 q^{6} + 35 q^{7} + 33 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + q^2 - 15 * q^3 + 27 * q^4 - 3 * q^6 + 35 * q^7 + 33 * q^8 + 45 * q^9	\( 5 q + q^{2} - 15 q^{3} + 27 q^{4} - 3 q^{6} + 35 q^{7} + 33 q^{8} + 45 q^{9} + 66 q^{11} - 81 q^{12} - 2 q^{13} + 7 q^{14} + 155 q^{16} + 108 q^{17} + 9 q^{18} + 174 q^{19} - 105 q^{21} - 506 q^{22} - 116 q^{23} - 99 q^{24} + 446 q^{26} - 135 q^{27} + 189 q^{28} + 370 q^{29} + 342 q^{31} - 55 q^{32} - 198 q^{33} + 112 q^{34} + 243 q^{36} - 408 q^{37} - 34 q^{38} + 6 q^{39} + 802 q^{41} - 21 q^{42} - 584 q^{43} + 290 q^{44} + 640 q^{46} + 716 q^{47} - 465 q^{48} + 245 q^{49} - 324 q^{51} + 338 q^{52} + 98 q^{53} - 27 q^{54} + 231 q^{56} - 522 q^{57} + 482 q^{58} + 704 q^{59} + 650 q^{61} + 2070 q^{62} + 315 q^{63} + 75 q^{64} + 1518 q^{66} + 180 q^{67} + 4520 q^{68} + 348 q^{69} + 1470 q^{71} + 297 q^{72} - 534 q^{73} - 1312 q^{74} + 4370 q^{76} + 462 q^{77} - 1338 q^{78} - 820 q^{79} + 405 q^{81} - 1338 q^{82} + 1520 q^{83} - 567 q^{84} + 832 q^{86} - 1110 q^{87} - 3258 q^{88} + 286 q^{89} - 14 q^{91} + 1288 q^{92} - 1026 q^{93} + 2540 q^{94} + 165 q^{96} + 278 q^{97} + 49 q^{98} + 594 q^{99}+O(q^{100}) \) 5 * q + q^2 - 15 * q^3 + 27 * q^4 - 3 * q^6 + 35 * q^7 + 33 * q^8 + 45 * q^9 + 66 * q^11 - 81 * q^12 - 2 * q^13 + 7 * q^14 + 155 * q^16 + 108 * q^17 + 9 * q^18 + 174 * q^19 - 105 * q^21 - 506 * q^22 - 116 * q^23 - 99 * q^24 + 446 * q^26 - 135 * q^27 + 189 * q^28 + 370 * q^29 + 342 * q^31 - 55 * q^32 - 198 * q^33 + 112 * q^34 + 243 * q^36 - 408 * q^37 - 34 * q^38 + 6 * q^39 + 802 * q^41 - 21 * q^42 - 584 * q^43 + 290 * q^44 + 640 * q^46 + 716 * q^47 - 465 * q^48 + 245 * q^49 - 324 * q^51 + 338 * q^52 + 98 * q^53 - 27 * q^54 + 231 * q^56 - 522 * q^57 + 482 * q^58 + 704 * q^59 + 650 * q^61 + 2070 * q^62 + 315 * q^63 + 75 * q^64 + 1518 * q^66 + 180 * q^67 + 4520 * q^68 + 348 * q^69 + 1470 * q^71 + 297 * q^72 - 534 * q^73 - 1312 * q^74 + 4370 * q^76 + 462 * q^77 - 1338 * q^78 - 820 * q^79 + 405 * q^81 - 1338 * q^82 + 1520 * q^83 - 567 * q^84 + 832 * q^86 - 1110 * q^87 - 3258 * q^88 + 286 * q^89 - 14 * q^91 + 1288 * q^92 - 1026 * q^93 + 2540 * q^94 + 165 * q^96 + 278 * q^97 + 49 * q^98 + 594 * q^99

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