LMFDB - Embedded newform 525.4.a.m.1.1

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:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.56155$ 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)

$f(q)$	$=$	$q-0.561553 q^{2} -3.00000 q^{3} -7.68466 q^{4} +1.68466 q^{6} -7.00000 q^{7} +8.80776 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.561553 q^{2} -3.00000 q^{3} -7.68466 q^{4} +1.68466 q^{6} -7.00000 q^{7} +8.80776 q^{8} +9.00000 q^{9} -25.8078 q^{11} +23.0540 q^{12} -15.5464 q^{13} +3.93087 q^{14} +56.5312 q^{16} -95.1619 q^{17} -5.05398 q^{18} -143.447 q^{19} +21.0000 q^{21} +14.4924 q^{22} +77.5227 q^{23} -26.4233 q^{24} +8.73012 q^{26} -27.0000 q^{27} +53.7926 q^{28} -204.170 q^{29} -40.6998 q^{31} -102.207 q^{32} +77.4233 q^{33} +53.4384 q^{34} -69.1619 q^{36} +95.6695 q^{37} +80.5530 q^{38} +46.6392 q^{39} +24.7301 q^{41} -11.7926 q^{42} +282.430 q^{43} +198.324 q^{44} -43.5331 q^{46} +257.417 q^{47} -169.594 q^{48} +49.0000 q^{49} +285.486 q^{51} +119.469 q^{52} +257.978 q^{53} +15.1619 q^{54} -61.6543 q^{56} +430.341 q^{57} +114.652 q^{58} -651.365 q^{59} +451.304 q^{61} +22.8551 q^{62} -63.0000 q^{63} -394.855 q^{64} -43.4773 q^{66} +832.071 q^{67} +731.287 q^{68} -232.568 q^{69} -174.965 q^{71} +79.2699 q^{72} -47.4166 q^{73} -53.7235 q^{74} +1102.34 q^{76} +180.654 q^{77} -26.1904 q^{78} -1.16006 q^{79} +81.0000 q^{81} -13.8873 q^{82} +1494.03 q^{83} -161.378 q^{84} -158.599 q^{86} +612.511 q^{87} -227.309 q^{88} +1309.13 q^{89} +108.825 q^{91} -595.736 q^{92} +122.099 q^{93} -144.553 q^{94} +306.622 q^{96} -1365.33 q^{97} -27.5161 q^{98} -232.270 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 9 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 9 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	$ 2 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 9 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} - 31 q^{11} + 9 q^{12} + 39 q^{13} - 21 q^{14} - 23 q^{16} - 79 q^{17} + 27 q^{18} - 56 q^{19} + 42 q^{21} - 4 q^{22} + 254 q^{23} + 9 q^{24} + 203 q^{26} - 54 q^{27} + 21 q^{28} - 62 q^{29} - 135 q^{31} - 291 q^{32} + 93 q^{33} + 111 q^{34} - 27 q^{36} + 113 q^{37} + 392 q^{38} - 117 q^{39} + 235 q^{41} + 63 q^{42} + 804 q^{43} + 174 q^{44} + 585 q^{46} + 152 q^{47} + 69 q^{48} + 98 q^{49} + 237 q^{51} + 375 q^{52} + 149 q^{53} - 81 q^{54} + 21 q^{56} + 168 q^{57} + 621 q^{58} - 441 q^{59} - 223 q^{61} - 313 q^{62} - 126 q^{63} - 431 q^{64} + 12 q^{66} + 1157 q^{67} + 807 q^{68} - 762 q^{69} + 619 q^{71} - 27 q^{72} + 268 q^{73} + 8 q^{74} + 1512 q^{76} + 217 q^{77} - 609 q^{78} - 427 q^{79} + 162 q^{81} + 735 q^{82} + 1211 q^{83} - 63 q^{84} + 1699 q^{86} + 186 q^{87} - 166 q^{88} + 466 q^{89} - 273 q^{91} + 231 q^{92} + 405 q^{93} - 520 q^{94} + 873 q^{96} + 172 q^{97} + 147 q^{98} - 279 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 9 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 - 31 * q^11 + 9 * q^12 + 39 * q^13 - 21 * q^14 - 23 * q^16 - 79 * q^17 + 27 * q^18 - 56 * q^19 + 42 * q^21 - 4 * q^22 + 254 * q^23 + 9 * q^24 + 203 * q^26 - 54 * q^27 + 21 * q^28 - 62 * q^29 - 135 * q^31 - 291 * q^32 + 93 * q^33 + 111 * q^34 - 27 * q^36 + 113 * q^37 + 392 * q^38 - 117 * q^39 + 235 * q^41 + 63 * q^42 + 804 * q^43 + 174 * q^44 + 585 * q^46 + 152 * q^47 + 69 * q^48 + 98 * q^49 + 237 * q^51 + 375 * q^52 + 149 * q^53 - 81 * q^54 + 21 * q^56 + 168 * q^57 + 621 * q^58 - 441 * q^59 - 223 * q^61 - 313 * q^62 - 126 * q^63 - 431 * q^64 + 12 * q^66 + 1157 * q^67 + 807 * q^68 - 762 * q^69 + 619 * q^71 - 27 * q^72 + 268 * q^73 + 8 * q^74 + 1512 * q^76 + 217 * q^77 - 609 * q^78 - 427 * q^79 + 162 * q^81 + 735 * q^82 + 1211 * q^83 - 63 * q^84 + 1699 * q^86 + 186 * q^87 - 166 * q^88 + 466 * q^89 - 273 * q^91 + 231 * q^92 + 405 * q^93 - 520 * q^94 + 873 * q^96 + 172 * q^97 + 147 * q^98 - 279 * 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 $

$2$	−0.561553	−0.198539	−0.0992695	−	0.995061i	$-0.531651\pi$
$2$	−0.561553	−0.198539	−0.0992695	+	0.995061i	$0.531651\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.68466	−0.960582
$5$	0	0
$5$	0	0
$6$	1.68466	0.114626
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.80776	0.389252
$9$	9.00000	0.333333
$10$	0	0
$11$	−25.8078	−0.707394	−0.353697	−	0.935360i	$-0.615076\pi$
$11$	−25.8078	−0.707394	−0.353697	+	0.935360i	$0.615076\pi$
$12$	23.0540	0.554592
$13$	−15.5464	−0.331677	−0.165838	−	0.986153i	$-0.553033\pi$
$13$	−15.5464	−0.331677	−0.165838	+	0.986153i	$0.553033\pi$
$14$	3.93087	0.0750407
$15$	0	0
$16$	56.5312	0.883301
$17$	−95.1619	−1.35766	−0.678828	−	0.734297i	$-0.737512\pi$
$17$	−95.1619	−1.35766	−0.678828	+	0.734297i	$0.737512\pi$
$18$	−5.05398	−0.0661796
$19$	−143.447	−1.73205	−0.866026	−	0.499999i	$-0.833334\pi$
$19$	−143.447	−1.73205	−0.866026	+	0.499999i	$0.833334\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	14.4924	0.140445
$23$	77.5227	0.702809	0.351405	−	0.936224i	$-0.385704\pi$
$23$	77.5227	0.702809	0.351405	+	0.936224i	$0.385704\pi$
$24$	−26.4233	−0.224735
$25$	0	0
$26$	8.73012	0.0658507
$27$	−27.0000	−0.192450
$28$	53.7926	0.363066
$29$	−204.170	−1.30736	−0.653681	−	0.756770i	$-0.726776\pi$
$29$	−204.170	−1.30736	−0.653681	+	0.756770i	$0.726776\pi$
$30$	0	0
$31$	−40.6998	−0.235803	−0.117902	−	0.993025i	$-0.537617\pi$
$31$	−40.6998	−0.235803	−0.117902	+	0.993025i	$0.537617\pi$
$32$	−102.207	−0.564621
$33$	77.4233	0.408414
$34$	53.4384	0.269548
$35$	0	0
$36$	−69.1619	−0.320194
$37$	95.6695	0.425080	0.212540	−	0.977152i	$-0.431826\pi$
$37$	95.6695	0.425080	0.212540	+	0.977152i	$0.431826\pi$
$38$	80.5530	0.343880
$39$	46.6392	0.191494
$40$	0	0
$41$	24.7301	0.0941999	0.0471000	−	0.998890i	$-0.485002\pi$
$41$	24.7301	0.0941999	0.0471000	+	0.998890i	$0.485002\pi$
$42$	−11.7926	−0.0433247
$43$	282.430	1.00163	0.500816	−	0.865554i	$-0.333033\pi$
$43$	282.430	1.00163	0.500816	+	0.865554i	$0.333033\pi$
$44$	198.324	0.679510
$45$	0	0
$46$	−43.5331	−0.139535
$47$	257.417	0.798895	0.399448	−	0.916756i	$-0.369202\pi$
$47$	257.417	0.798895	0.399448	+	0.916756i	$0.369202\pi$
$48$	−169.594	−0.509974
$49$	49.0000	0.142857
$50$	0	0
$51$	285.486	0.783843
$52$	119.469	0.318603
$53$	257.978	0.668604	0.334302	−	0.942466i	$-0.391499\pi$
$53$	257.978	0.668604	0.334302	+	0.942466i	$0.391499\pi$
$54$	15.1619	0.0382088
$55$	0	0
$56$	−61.6543	−0.147123
$57$	430.341	1.00000
$58$	114.652	0.259562
$59$	−651.365	−1.43730	−0.718648	−	0.695374i	$-0.755239\pi$
$59$	−651.365	−1.43730	−0.718648	+	0.695374i	$0.755239\pi$
$60$	0	0
$61$	451.304	0.947271	0.473636	−	0.880721i	$-0.342941\pi$
$61$	451.304	0.947271	0.473636	+	0.880721i	$0.342941\pi$
$62$	22.8551	0.0468161
$63$	−63.0000	−0.125988
$64$	−394.855	−0.771201
$65$	0	0
$66$	−43.4773	−0.0810861
$67$	832.071	1.51722	0.758609	−	0.651546i	$-0.225879\pi$
$67$	832.071	1.51722	0.758609	+	0.651546i	$0.225879\pi$
$68$	731.287	1.30414
$69$	−232.568	−0.405767
$70$	0	0
$71$	−174.965	−0.292458	−0.146229	−	0.989251i	$-0.546714\pi$
$71$	−174.965	−0.292458	−0.146229	+	0.989251i	$0.546714\pi$
$72$	79.2699	0.129751
$73$	−47.4166	−0.0760233	−0.0380116	−	0.999277i	$-0.512102\pi$
$73$	−47.4166	−0.0760233	−0.0380116	+	0.999277i	$0.512102\pi$
$74$	−53.7235	−0.0843950
$75$	0	0
$76$	1102.34	1.66378
$77$	180.654	0.267370
$78$	−26.1904	−0.0380189
$79$	−1.16006	−0.00165211	−0.000826057	−	1.00000i	$-0.500263\pi$
$79$	−1.16006	−0.00165211	−0.000826057		1.00000i	$0.500263\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−13.8873	−0.0187023
$83$	1494.03	1.97580	0.987898	−	0.155107i	$-0.0495722\pi$
$83$	1494.03	1.97580	0.987898	+	0.155107i	$0.0495722\pi$
$84$	−161.378	−0.209616
$85$	0	0
$86$	−158.599	−0.198863
$87$	612.511	0.754806
$88$	−227.309	−0.275354
$89$	1309.13	1.55919	0.779593	−	0.626286i	$-0.215426\pi$
$89$	1309.13	1.55919	0.779593	+	0.626286i	$0.215426\pi$
$90$	0	0
$91$	108.825	0.125362
$92$	−595.736	−0.675106
$93$	122.099	0.136141
$94$	−144.553	−0.158612
$95$	0	0
$96$	306.622	0.325984
$97$	−1365.33	−1.42916	−0.714580	−	0.699553i	$-0.753382\pi$
$97$	−1365.33	−1.42916	−0.714580	+	0.699553i	$0.753382\pi$
$98$	−27.5161	−0.0283627
$99$	−232.270	−0.235798
$100$	0	0
$101$	1155.99	1.13887	0.569434	−	0.822037i	$-0.307162\pi$
$101$	1155.99	1.13887	0.569434	+	0.822037i	$0.307162\pi$
$102$	−160.315	−0.155623
$103$	−78.2074	−0.0748156	−0.0374078	−	0.999300i	$-0.511910\pi$
$103$	−78.2074	−0.0748156	−0.0374078	+	0.999300i	$0.511910\pi$
$104$	−136.929	−0.129106
$105$	0	0
$106$	−144.868	−0.132744
$107$	−94.0814	−0.0850018	−0.0425009	−	0.999096i	$-0.513533\pi$
$107$	−94.0814	−0.0850018	−0.0425009	+	0.999096i	$0.513533\pi$
$108$	207.486	0.184864
$109$	−2128.25	−1.87018	−0.935088	−	0.354417i	$-0.884679\pi$
$109$	−2128.25	−1.87018	−0.935088	+	0.354417i	$0.884679\pi$
$110$	0	0
$111$	−287.009	−0.245420
$112$	−395.719	−0.333856
$113$	−596.493	−0.496578	−0.248289	−	0.968686i	$-0.579868\pi$
$113$	−596.493	−0.496578	−0.248289	+	0.968686i	$0.579868\pi$
$114$	−241.659	−0.198539
$115$	0	0
$116$	1568.98	1.25583
$117$	−139.918	−0.110559
$118$	365.776	0.285359
$119$	666.133	0.513146
$120$	0	0
$121$	−664.959	−0.499594
$122$	−253.431	−0.188070
$123$	−74.1904	−0.0543863
$124$	312.764	0.226508
$125$	0	0
$126$	35.3778	0.0250136
$127$	2088.21	1.45904	0.729522	−	0.683957i	$-0.239743\pi$
$127$	2088.21	1.45904	0.729522	+	0.683957i	$0.239743\pi$
$128$	1039.39	0.717735
$129$	−847.290	−0.578292
$130$	0	0
$131$	416.142	0.277546	0.138773	−	0.990324i	$-0.455684\pi$
$131$	416.142	0.277546	0.138773	+	0.990324i	$0.455684\pi$
$132$	−594.972	−0.392315
$133$	1004.13	0.654654
$134$	−467.252	−0.301227
$135$	0	0
$136$	−838.164	−0.528470
$137$	619.252	0.386177	0.193089	−	0.981181i	$-0.438150\pi$
$137$	619.252	0.386177	0.193089	+	0.981181i	$0.438150\pi$
$138$	130.599	0.0805605
$139$	−266.994	−0.162922	−0.0814610	−	0.996677i	$-0.525959\pi$
$139$	−266.994	−0.162922	−0.0814610	+	0.996677i	$0.525959\pi$
$140$	0	0
$141$	−772.250	−0.461242
$142$	98.2520	0.0580643
$143$	401.218	0.234626
$144$	508.781	0.294434
$145$	0	0
$146$	26.6270	0.0150936
$147$	−147.000	−0.0824786
$148$	−735.187	−0.408325
$149$	2551.80	1.40303	0.701515	−	0.712655i	$-0.252507\pi$
$149$	2551.80	1.40303	0.701515	+	0.712655i	$0.252507\pi$
$150$	0	0
$151$	1117.38	0.602195	0.301097	−	0.953593i	$-0.402647\pi$
$151$	1117.38	0.602195	0.301097	+	0.953593i	$0.402647\pi$
$152$	−1263.45	−0.674204
$153$	−856.457	−0.452552
$154$	−101.447	−0.0530833
$155$	0	0
$156$	−358.406	−0.183945
$157$	−456.104	−0.231854	−0.115927	−	0.993258i	$-0.536984\pi$
$157$	−456.104	−0.231854	−0.115927	+	0.993258i	$0.536984\pi$
$158$	0.651435	0.000328009 0
$159$	−773.935	−0.386019
$160$	0	0
$161$	−542.659	−0.265637
$162$	−45.4858	−0.0220599
$163$	−105.490	−0.0506907	−0.0253453	−	0.999679i	$-0.508069\pi$
$163$	−105.490	−0.0506907	−0.0253453	+	0.999679i	$0.508069\pi$
$164$	−190.043	−0.0904868
$165$	0	0
$166$	−838.976	−0.392272
$167$	−2482.54	−1.15033	−0.575164	−	0.818038i	$-0.695062\pi$
$167$	−2482.54	−1.15033	−0.575164	+	0.818038i	$0.695062\pi$
$168$	184.963	0.0849417
$169$	−1955.31	−0.889991
$170$	0	0
$171$	−1291.02	−0.577351
$172$	−2170.38	−0.962150
$173$	516.708	0.227079	0.113539	−	0.993534i	$-0.463781\pi$
$173$	516.708	0.227079	0.113539	+	0.993534i	$0.463781\pi$
$174$	−343.957	−0.149858
$175$	0	0
$176$	−1458.94	−0.624842
$177$	1954.09	0.829823
$178$	−735.146	−0.309559
$179$	3847.77	1.60668	0.803341	−	0.595519i	$-0.203054\pi$
$179$	3847.77	1.60668	0.803341	+	0.595519i	$0.203054\pi$
$180$	0	0
$181$	−3026.41	−1.24282	−0.621411	−	0.783484i	$-0.713440\pi$
$181$	−3026.41	−1.24282	−0.621411	+	0.783484i	$0.713440\pi$
$182$	−61.1109	−0.0248892
$183$	−1353.91	−0.546907
$184$	682.802	0.273570
$185$	0	0
$186$	−68.5653	−0.0270293
$187$	2455.92	0.960398
$188$	−1978.16	−0.767405
$189$	189.000	0.0727393
$190$	0	0
$191$	1271.09	0.481532	0.240766	−	0.970583i	$-0.422601\pi$
$191$	1271.09	0.481532	0.240766	+	0.970583i	$0.422601\pi$
$192$	1184.57	0.445253
$193$	−1896.09	−0.707170	−0.353585	−	0.935402i	$-0.615037\pi$
$193$	−1896.09	−0.707170	−0.353585	+	0.935402i	$0.615037\pi$
$194$	766.707	0.283744
$195$	0	0
$196$	−376.548	−0.137226
$197$	4067.89	1.47119	0.735597	−	0.677419i	$-0.236902\pi$
$197$	4067.89	1.47119	0.735597	+	0.677419i	$0.236902\pi$
$198$	130.432	0.0468151
$199$	78.1366	0.0278340	0.0139170	−	0.999903i	$-0.495570\pi$
$199$	78.1366	0.0278340	0.0139170	+	0.999903i	$0.495570\pi$
$200$	0	0
$201$	−2496.21	−0.875967
$202$	−649.152	−0.226110
$203$	1429.19	0.494136
$204$	−2193.86	−0.752946
$205$	0	0
$206$	43.9176	0.0148538
$207$	697.705	0.234270
$208$	−878.857	−0.292970
$209$	3702.05	1.22524
$210$	0	0
$211$	−1293.02	−0.421872	−0.210936	−	0.977500i	$-0.567651\pi$
$211$	−1293.02	−0.421872	−0.210936	+	0.977500i	$0.567651\pi$
$212$	−1982.47	−0.642250
$213$	524.895	0.168851
$214$	52.8317	0.0168762
$215$	0	0
$216$	−237.810	−0.0749116
$217$	284.899	0.0891253
$218$	1195.12	0.371303
$219$	142.250	0.0438921
$220$	0	0
$221$	1479.43	0.450303
$222$	161.170	0.0487255
$223$	−1786.65	−0.536515	−0.268257	−	0.963347i	$-0.586448\pi$
$223$	−1786.65	−0.536515	−0.268257	+	0.963347i	$0.586448\pi$
$224$	715.452	0.213407
$225$	0	0
$226$	334.962	0.0985901
$227$	−4242.02	−1.24032	−0.620161	−	0.784475i	$-0.712933\pi$
$227$	−4242.02	−1.24032	−0.620161	+	0.784475i	$0.712933\pi$
$228$	−3307.02	−0.960583
$229$	3403.36	0.982096	0.491048	−	0.871132i	$-0.336614\pi$
$229$	3403.36	0.982096	0.491048	+	0.871132i	$0.336614\pi$
$230$	0	0
$231$	−541.963	−0.154366
$232$	−1798.29	−0.508893
$233$	−3904.09	−1.09771	−0.548853	−	0.835919i	$-0.684935\pi$
$233$	−3904.09	−1.09771	−0.548853	+	0.835919i	$0.684935\pi$
$234$	78.5711	0.0219502
$235$	0	0
$236$	5005.51	1.38064
$237$	3.48018	0.000953848 0
$238$	−374.069	−0.101879
$239$	6667.83	1.80463	0.902314	−	0.431079i	$-0.141867\pi$
$239$	6667.83	1.80463	0.902314	+	0.431079i	$0.141867\pi$
$240$	0	0
$241$	−6003.99	−1.60478	−0.802388	−	0.596803i	$-0.796437\pi$
$241$	−6003.99	−1.60478	−0.802388	+	0.596803i	$0.796437\pi$
$242$	373.410	0.0991888
$243$	−243.000	−0.0641500
$244$	−3468.12	−0.909932
$245$	0	0
$246$	41.6618	0.0107978
$247$	2230.08	0.574481
$248$	−358.474	−0.0917869
$249$	−4482.09	−1.14073
$250$	0	0
$251$	728.467	0.183189	0.0915945	−	0.995796i	$-0.470804\pi$
$251$	728.467	0.183189	0.0915945	+	0.995796i	$0.470804\pi$
$252$	484.133	0.121022
$253$	−2000.69	−0.497163
$254$	−1172.64	−0.289677
$255$	0	0
$256$	2575.17	0.628703
$257$	−1479.86	−0.359187	−0.179593	−	0.983741i	$-0.557478\pi$
$257$	−1479.86	−0.359187	−0.179593	+	0.983741i	$0.557478\pi$
$258$	475.798	0.114814
$259$	−669.687	−0.160665
$260$	0	0
$261$	−1837.53	−0.435787
$262$	−233.686	−0.0551036
$263$	−6367.31	−1.49287	−0.746435	−	0.665458i	$-0.768236\pi$
$263$	−6367.31	−1.49287	−0.746435	+	0.665458i	$0.768236\pi$
$264$	681.926	0.158976
$265$	0	0
$266$	−563.871	−0.129974
$267$	−3927.39	−0.900197
$268$	−6394.18	−1.45741
$269$	1787.18	0.405079	0.202539	−	0.979274i	$-0.435081\pi$
$269$	1787.18	0.405079	0.202539	+	0.979274i	$0.435081\pi$
$270$	0	0
$271$	3907.65	0.875915	0.437957	−	0.898996i	$-0.355702\pi$
$271$	3907.65	0.875915	0.437957	+	0.898996i	$0.355702\pi$
$272$	−5379.62	−1.19922
$273$	−326.474	−0.0723778
$274$	−347.743	−0.0766712
$275$	0	0
$276$	1787.21	0.389773
$277$	3978.33	0.862942	0.431471	−	0.902127i	$-0.357995\pi$
$277$	3978.33	0.862942	0.431471	+	0.902127i	$0.357995\pi$
$278$	149.931	0.0323464
$279$	−366.298	−0.0786011
$280$	0	0
$281$	−6488.04	−1.37738	−0.688690	−	0.725055i	$-0.741814\pi$
$281$	−6488.04	−1.37738	−0.688690	+	0.725055i	$0.741814\pi$
$282$	433.659	0.0915746
$283$	−164.336	−0.0345185	−0.0172592	−	0.999851i	$-0.505494\pi$
$283$	−164.336	−0.0345185	−0.0172592	+	0.999851i	$0.505494\pi$
$284$	1344.55	0.280930
$285$	0	0
$286$	−225.305	−0.0465824
$287$	−173.111	−0.0356042
$288$	−919.867	−0.188207
$289$	4142.79	0.843231
$290$	0	0
$291$	4096.00	0.825126
$292$	364.381	0.0730266
$293$	5004.57	0.997851	0.498925	−	0.866645i	$-0.333728\pi$
$293$	5004.57	0.997851	0.498925	+	0.866645i	$0.333728\pi$
$294$	82.5483	0.0163752
$295$	0	0
$296$	842.634	0.165463
$297$	696.810	0.136138
$298$	−1432.97	−0.278556
$299$	−1205.20	−0.233105
$300$	0	0
$301$	−1977.01	−0.378581
$302$	−627.470	−0.119559
$303$	−3467.98	−0.657526
$304$	−8109.23	−1.52992
$305$	0	0
$306$	480.946	0.0898492
$307$	−190.167	−0.0353531	−0.0176765	−	0.999844i	$-0.505627\pi$
$307$	−190.167	−0.0353531	−0.0176765	+	0.999844i	$0.505627\pi$
$308$	−1388.27	−0.256831
$309$	234.622	0.0431948
$310$	0	0
$311$	−1182.57	−0.215619	−0.107810	−	0.994172i	$-0.534384\pi$
$311$	−1182.57	−0.215619	−0.107810	+	0.994172i	$0.534384\pi$
$312$	410.787	0.0745392
$313$	−4659.05	−0.841358	−0.420679	−	0.907209i	$-0.638208\pi$
$313$	−4659.05	−0.841358	−0.420679	+	0.907209i	$0.638208\pi$
$314$	256.127	0.0460320
$315$	0	0
$316$	8.91467	0.00158699
$317$	−3694.55	−0.654595	−0.327297	−	0.944921i	$-0.606138\pi$
$317$	−3694.55	−0.654595	−0.327297	+	0.944921i	$0.606138\pi$
$318$	434.605	0.0766398
$319$	5269.18	0.924820
$320$	0	0
$321$	282.244	0.0490758
$322$	304.732	0.0527392
$323$	13650.7	2.35153
$324$	−622.457	−0.106731
$325$	0	0
$326$	59.2379	0.0100641
$327$	6384.74	1.07975
$328$	217.817	0.0366675
$329$	−1801.92	−0.301954
$330$	0	0
$331$	−8632.79	−1.43354	−0.716769	−	0.697310i	$-0.754380\pi$
$331$	−8632.79	−1.43354	−0.716769	+	0.697310i	$0.754380\pi$
$332$	−11481.1	−1.89791
$333$	861.026	0.141693
$334$	1394.08	0.228385
$335$	0	0
$336$	1187.16	0.192752
$337$	−8136.61	−1.31522	−0.657610	−	0.753358i	$-0.728433\pi$
$337$	−8136.61	−1.31522	−0.657610	+	0.753358i	$0.728433\pi$
$338$	1098.01	0.176698
$339$	1789.48	0.286700
$340$	0	0
$341$	1050.37	0.166806
$342$	724.977	0.114627
$343$	−343.000	−0.0539949
$344$	2487.58	0.389887
$345$	0	0
$346$	−290.159	−0.0450839
$347$	8646.33	1.33763	0.668817	−	0.743427i	$-0.266801\pi$
$347$	8646.33	1.33763	0.668817	+	0.743427i	$0.266801\pi$
$348$	−4706.94	−0.725053
$349$	−7455.43	−1.14350	−0.571748	−	0.820429i	$-0.693734\pi$
$349$	−7455.43	−1.14350	−0.571748	+	0.820429i	$0.693734\pi$
$350$	0	0
$351$	419.753	0.0638312
$352$	2637.74	0.399410
$353$	5450.21	0.821771	0.410886	−	0.911687i	$-0.365220\pi$
$353$	5450.21	0.821771	0.410886	+	0.911687i	$0.365220\pi$
$354$	−1097.33	−0.164752
$355$	0	0
$356$	−10060.2	−1.49773
$357$	−1998.40	−0.296265
$358$	−2160.73	−0.318989
$359$	4775.79	0.702107	0.351053	−	0.936355i	$-0.385824\pi$
$359$	4775.79	0.702107	0.351053	+	0.936355i	$0.385824\pi$
$360$	0	0
$361$	13718.0	2.00000
$362$	1699.49	0.246749
$363$	1994.88	0.288441
$364$	−836.281	−0.120420
$365$	0	0
$366$	760.293	0.108582
$367$	9636.30	1.37060	0.685301	−	0.728260i	$-0.259671\pi$
$367$	9636.30	1.37060	0.685301	+	0.728260i	$0.259671\pi$
$368$	4382.46	0.620792
$369$	222.571	0.0314000
$370$	0	0
$371$	−1805.85	−0.252709
$372$	−938.292	−0.130775
$373$	12180.4	1.69082	0.845412	−	0.534115i	$-0.179355\pi$
$373$	12180.4	1.69082	0.845412	+	0.534115i	$0.179355\pi$
$374$	−1379.13	−0.190676
$375$	0	0
$376$	2267.27	0.310971
$377$	3174.11	0.433621
$378$	−106.133	−0.0144416
$379$	1689.39	0.228966	0.114483	−	0.993425i	$-0.463479\pi$
$379$	1689.39	0.228966	0.114483	+	0.993425i	$0.463479\pi$
$380$	0	0
$381$	−6264.63	−0.842380
$382$	−713.783	−0.0956029
$383$	1513.13	0.201872	0.100936	−	0.994893i	$-0.467816\pi$
$383$	1513.13	0.201872	0.100936	+	0.994893i	$0.467816\pi$
$384$	−3118.17	−0.414384
$385$	0	0
$386$	1064.76	0.140401
$387$	2541.87	0.333877
$388$	10492.1	1.37283
$389$	12165.5	1.58564	0.792822	−	0.609453i	$-0.208611\pi$
$389$	12165.5	1.58564	0.792822	+	0.609453i	$0.208611\pi$
$390$	0	0
$391$	−7377.21	−0.954173
$392$	431.580	0.0556074
$393$	−1248.43	−0.160241
$394$	−2284.34	−0.292089
$395$	0	0
$396$	1784.91	0.226503
$397$	7353.40	0.929613	0.464807	−	0.885412i	$-0.346124\pi$
$397$	7353.40	0.929613	0.464807	+	0.885412i	$0.346124\pi$
$398$	−43.8778	−0.00552612
$399$	−3012.39	−0.377965
$400$	0	0
$401$	7481.62	0.931707	0.465853	−	0.884862i	$-0.345747\pi$
$401$	7481.62	0.931707	0.465853	+	0.884862i	$0.345747\pi$
$402$	1401.76	0.173913
$403$	632.735	0.0782104
$404$	−8883.42	−1.09398
$405$	0	0
$406$	−802.567	−0.0981053
$407$	−2469.02	−0.300699
$408$	2514.49	0.305112
$409$	9248.94	1.11817	0.559084	−	0.829111i	$-0.311153\pi$
$409$	9248.94	1.11817	0.559084	+	0.829111i	$0.311153\pi$
$410$	0	0
$411$	−1857.76	−0.222959
$412$	600.997	0.0718665
$413$	4559.55	0.543247
$414$	−391.798	−0.0465116
$415$	0	0
$416$	1588.96	0.187272
$417$	800.983	0.0940631
$418$	−2078.89	−0.243258
$419$	−3363.39	−0.392154	−0.196077	−	0.980589i	$-0.562820\pi$
$419$	−3363.39	−0.392154	−0.196077	+	0.980589i	$0.562820\pi$
$420$	0	0
$421$	−3638.86	−0.421252	−0.210626	−	0.977567i	$-0.567550\pi$
$421$	−3638.86	−0.421252	−0.210626	+	0.977567i	$0.567550\pi$
$422$	726.097	0.0837579
$423$	2316.75	0.266298
$424$	2272.21	0.260255
$425$	0	0
$426$	−294.756	−0.0335234
$427$	−3159.13	−0.358035
$428$	722.983	0.0816512
$429$	−1203.65	−0.135461
$430$	0	0
$431$	11243.2	1.25653	0.628264	−	0.778000i	$-0.283766\pi$
$431$	11243.2	1.25653	0.628264	+	0.778000i	$0.283766\pi$
$432$	−1526.34	−0.169991
$433$	187.332	0.0207912	0.0103956	−	0.999946i	$-0.496691\pi$
$433$	187.332	0.0207912	0.0103956	+	0.999946i	$0.496691\pi$
$434$	−159.986	−0.0176948
$435$	0	0
$436$	16354.9	1.79646
$437$	−11120.4	−1.21730
$438$	−79.8809	−0.00871428
$439$	−11479.4	−1.24802	−0.624011	−	0.781415i	$-0.714498\pi$
$439$	−11479.4	−1.24802	−0.624011	+	0.781415i	$0.714498\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	−830.775	−0.0894026
$443$	−9490.56	−1.01786	−0.508928	−	0.860809i	$-0.669958\pi$
$443$	−9490.56	−1.01786	−0.508928	+	0.860809i	$0.669958\pi$
$444$	2205.56	0.235746
$445$	0	0
$446$	1003.30	0.106519
$447$	−7655.39	−0.810039
$448$	2763.99	0.291487
$449$	−5546.58	−0.582982	−0.291491	−	0.956574i	$-0.594151\pi$
$449$	−5546.58	−0.582982	−0.291491	+	0.956574i	$0.594151\pi$
$450$	0	0
$451$	−638.229	−0.0666364
$452$	4583.85	0.477004
$453$	−3352.15	−0.347677
$454$	2382.12	0.246252
$455$	0	0
$456$	3790.34	0.389252
$457$	1776.94	0.181885	0.0909426	−	0.995856i	$-0.471012\pi$
$457$	1776.94	0.181885	0.0909426	+	0.995856i	$0.471012\pi$
$458$	−1911.16	−0.194984
$459$	2569.37	0.261281
$460$	0	0
$461$	−9059.81	−0.915309	−0.457655	−	0.889130i	$-0.651310\pi$
$461$	−9059.81	−0.915309	−0.457655	+	0.889130i	$0.651310\pi$
$462$	304.341	0.0306477
$463$	14878.5	1.49344	0.746719	−	0.665139i	$-0.231628\pi$
$463$	14878.5	1.49344	0.746719	+	0.665139i	$0.231628\pi$
$464$	−11542.0	−1.15479
$465$	0	0
$466$	2192.35	0.217937
$467$	14275.8	1.41458	0.707288	−	0.706926i	$-0.249918\pi$
$467$	14275.8	1.41458	0.707288	+	0.706926i	$0.249918\pi$
$468$	1075.22	0.106201
$469$	−5824.50	−0.573455
$470$	0	0
$471$	1368.31	0.133861
$472$	−5737.07	−0.559470
$473$	−7288.89	−0.708548
$474$	−1.95431	−0.000189376 0
$475$	0	0
$476$	−5119.01	−0.492919
$477$	2321.80	0.222868
$478$	−3744.34	−0.358289
$479$	−15377.8	−1.46687	−0.733433	−	0.679761i	$-0.762083\pi$
$479$	−15377.8	−1.46687	−0.733433	+	0.679761i	$0.762083\pi$
$480$	0	0
$481$	−1487.32	−0.140989
$482$	3371.56	0.318610
$483$	1627.98	0.153365
$484$	5109.99	0.479901
$485$	0	0
$486$	136.457	0.0127363
$487$	19683.3	1.83149	0.915747	−	0.401756i	$-0.131600\pi$
$487$	19683.3	1.83149	0.915747	+	0.401756i	$0.131600\pi$
$488$	3974.98	0.368727
$489$	316.469	0.0292663
$490$	0	0
$491$	19585.1	1.80013	0.900065	−	0.435755i	$-0.143519\pi$
$491$	19585.1	1.80013	0.900065	+	0.435755i	$0.143519\pi$
$492$	570.128	0.0522426
$493$	19429.3	1.77495
$494$	−1252.31	−0.114057
$495$	0	0
$496$	−2300.81	−0.208285
$497$	1224.75	0.110539
$498$	2516.93	0.226478
$499$	−6888.47	−0.617977	−0.308988	−	0.951066i	$-0.599990\pi$
$499$	−6888.47	−0.617977	−0.308988	+	0.951066i	$0.599990\pi$
$500$	0	0
$501$	7447.62	0.664142
$502$	−409.073	−0.0363701
$503$	14878.0	1.31885	0.659423	−	0.751772i	$-0.270801\pi$
$503$	14878.0	1.31885	0.659423	+	0.751772i	$0.270801\pi$
$504$	−554.889	−0.0490411
$505$	0	0
$506$	1123.49	0.0987062
$507$	5865.93	0.513836
$508$	−16047.2	−1.40153
$509$	1935.28	0.168526	0.0842629	−	0.996444i	$-0.473146\pi$
$509$	1935.28	0.168526	0.0842629	+	0.996444i	$0.473146\pi$
$510$	0	0
$511$	331.917	0.0287341
$512$	−9761.22	−0.842557
$513$	3873.07	0.333334
$514$	831.019	0.0713126
$515$	0	0
$516$	6511.13	0.555497
$517$	−6643.35	−0.565134
$518$	376.064	0.0318983
$519$	−1550.12	−0.131104
$520$	0	0
$521$	−6892.28	−0.579570	−0.289785	−	0.957092i	$-0.593584\pi$
$521$	−6892.28	−0.579570	−0.289785	+	0.957092i	$0.593584\pi$
$522$	1031.87	0.0865207
$523$	−1074.60	−0.0898447	−0.0449223	−	0.998990i	$-0.514304\pi$
$523$	−1074.60	−0.0898447	−0.0449223	+	0.998990i	$0.514304\pi$
$524$	−3197.91	−0.266606
$525$	0	0
$526$	3575.58	0.296393
$527$	3873.07	0.320140
$528$	4376.83	0.360752
$529$	−6157.23	−0.506060
$530$	0	0
$531$	−5862.28	−0.479099
$532$	−7716.39	−0.628849
$533$	−384.464	−0.0312439
$534$	2205.44	0.178724
$535$	0	0
$536$	7328.69	0.590580
$537$	−11543.3	−0.927619
$538$	−1003.60	−0.0804239
$539$	−1264.58	−0.101056
$540$	0	0
$541$	8660.23	0.688230	0.344115	−	0.938928i	$-0.388179\pi$
$541$	8660.23	0.688230	0.344115	+	0.938928i	$0.388179\pi$
$542$	−2194.35	−0.173903
$543$	9079.22	0.717544
$544$	9726.25	0.766562
$545$	0	0
$546$	183.333	0.0143698
$547$	−15346.1	−1.19954	−0.599771	−	0.800171i	$-0.704742\pi$
$547$	−15346.1	−1.19954	−0.599771	+	0.800171i	$0.704742\pi$
$548$	−4758.74	−0.370955
$549$	4061.74	0.315757
$550$	0	0
$551$	29287.6	2.26442
$552$	−2048.41	−0.157946
$553$	8.12042	0.000624440 0
$554$	−2234.04	−0.171328
$555$	0	0
$556$	2051.76	0.156500
$557$	15544.9	1.18251	0.591257	−	0.806483i	$-0.298632\pi$
$557$	15544.9	1.18251	0.591257	+	0.806483i	$0.298632\pi$
$558$	205.696	0.0156054
$559$	−4390.77	−0.332218
$560$	0	0
$561$	−7367.75	−0.554486
$562$	3643.38	0.273464
$563$	−18511.9	−1.38576	−0.692881	−	0.721052i	$-0.743659\pi$
$563$	−18511.9	−1.38576	−0.692881	+	0.721052i	$0.743659\pi$
$564$	5934.48	0.443061
$565$	0	0
$566$	92.2831	0.00685326
$567$	−567.000	−0.0419961
$568$	−1541.05	−0.113840
$569$	2157.36	0.158948	0.0794738	−	0.996837i	$-0.474676\pi$
$569$	2157.36	0.158948	0.0794738	+	0.996837i	$0.474676\pi$
$570$	0	0
$571$	16010.3	1.17340	0.586700	−	0.809805i	$-0.300427\pi$
$571$	16010.3	1.17340	0.586700	+	0.809805i	$0.300427\pi$
$572$	−3083.22	−0.225378
$573$	−3813.26	−0.278013
$574$	97.2109	0.00706882
$575$	0	0
$576$	−3553.70	−0.257067
$577$	−2164.01	−0.156134	−0.0780668	−	0.996948i	$-0.524875\pi$
$577$	−2164.01	−0.156134	−0.0780668	+	0.996948i	$0.524875\pi$
$578$	−2326.40	−0.167414
$579$	5688.28	0.408285
$580$	0	0
$581$	−10458.2	−0.746780
$582$	−2300.12	−0.163820
$583$	−6657.84	−0.472967
$584$	−417.635	−0.0295922
$585$	0	0
$586$	−2810.33	−0.198112
$587$	27616.6	1.94184	0.970918	−	0.239412i	$-0.0769546\pi$
$587$	27616.6	1.94184	0.970918	+	0.239412i	$0.0769546\pi$
$588$	1129.64	0.0792275
$589$	5838.26	0.408424
$590$	0	0
$591$	−12203.7	−0.849395
$592$	5408.32	0.375474
$593$	−10205.4	−0.706718	−0.353359	−	0.935488i	$-0.614961\pi$
$593$	−10205.4	−0.706718	−0.353359	+	0.935488i	$0.614961\pi$
$594$	−391.295	−0.0270287
$595$	0	0
$596$	−19609.7	−1.34773
$597$	−234.410	−0.0160699
$598$	676.783	0.0462805
$599$	11090.5	0.756501	0.378251	−	0.925703i	$-0.376526\pi$
$599$	11090.5	0.756501	0.378251	+	0.925703i	$0.376526\pi$
$600$	0	0
$601$	−26537.0	−1.80111	−0.900555	−	0.434742i	$-0.856839\pi$
$601$	−26537.0	−1.80111	−0.900555	+	0.434742i	$0.856839\pi$
$602$	1110.20	0.0751631
$603$	7488.64	0.505740
$604$	−8586.71	−0.578457
$605$	0	0
$606$	1947.46	0.130544
$607$	−11234.5	−0.751226	−0.375613	−	0.926777i	$-0.622568\pi$
$607$	−11234.5	−0.751226	−0.375613	+	0.926777i	$0.622568\pi$
$608$	14661.3	0.977954
$609$	−4287.58	−0.285290
$610$	0	0
$611$	−4001.90	−0.264975
$612$	6581.58	0.434714
$613$	−10622.5	−0.699900	−0.349950	−	0.936768i	$-0.613801\pi$
$613$	−10622.5	−0.699900	−0.349950	+	0.936768i	$0.613801\pi$
$614$	106.789	0.00701896
$615$	0	0
$616$	1591.16	0.104074
$617$	20433.3	1.33325	0.666623	−	0.745395i	$-0.267739\pi$
$617$	20433.3	1.33325	0.666623	+	0.745395i	$0.267739\pi$
$618$	−131.753	−0.00857585
$619$	−7963.57	−0.517097	−0.258549	−	0.965998i	$-0.583244\pi$
$619$	−7963.57	−0.517097	−0.258549	+	0.965998i	$0.583244\pi$
$620$	0	0
$621$	−2093.11	−0.135256
$622$	664.077	0.0428088
$623$	−9163.91	−0.589317
$624$	2636.57	0.169146
$625$	0	0
$626$	2616.30	0.167042
$627$	−11106.1	−0.707394
$628$	3505.01	0.222715
$629$	−9104.09	−0.577113
$630$	0	0
$631$	−14703.1	−0.927608	−0.463804	−	0.885938i	$-0.653516\pi$
$631$	−14703.1	−0.927608	−0.463804	+	0.885938i	$0.653516\pi$
$632$	−10.2175	−0.000643088 0
$633$	3879.05	0.243568
$634$	2074.68	0.129963
$635$	0	0
$636$	5947.42	0.370803
$637$	−761.773	−0.0473824
$638$	−2958.92	−0.183613
$639$	−1574.68	−0.0974860
$640$	0	0
$641$	3353.41	0.206633	0.103317	−	0.994649i	$-0.467055\pi$
$641$	3353.41	0.206633	0.103317	+	0.994649i	$0.467055\pi$
$642$	−158.495	−0.00974345
$643$	31862.0	1.95415	0.977073	−	0.212906i	$-0.0682929\pi$
$643$	31862.0	1.95415	0.977073	+	0.212906i	$0.0682929\pi$
$644$	4170.15	0.255166
$645$	0	0
$646$	−7665.58	−0.466870
$647$	−8518.46	−0.517612	−0.258806	−	0.965929i	$-0.583329\pi$
$647$	−8518.46	−0.517612	−0.258806	+	0.965929i	$0.583329\pi$
$648$	713.429	0.0432502
$649$	16810.3	1.01673
$650$	0	0
$651$	−854.696	−0.0514565
$652$	810.651	0.0486925
$653$	−28509.3	−1.70851	−0.854254	−	0.519856i	$-0.825986\pi$
$653$	−28509.3	−1.70851	−0.854254	+	0.519856i	$0.825986\pi$
$654$	−3585.37	−0.214372
$655$	0	0
$656$	1398.02	0.0832068
$657$	−426.750	−0.0253411
$658$	1011.87	0.0599496
$659$	−27632.4	−1.63339	−0.816697	−	0.577066i	$-0.804197\pi$
$659$	−27632.4	−1.63339	−0.816697	+	0.577066i	$0.804197\pi$
$660$	0	0
$661$	−27052.8	−1.59188	−0.795941	−	0.605374i	$-0.793023\pi$
$661$	−27052.8	−1.59188	−0.795941	+	0.605374i	$0.793023\pi$
$662$	4847.77	0.284613
$663$	−4438.28	−0.259982
$664$	13159.1	0.769082
$665$	0	0
$666$	−483.511	−0.0281317
$667$	−15827.9	−0.918826
$668$	19077.5	1.10498
$669$	5359.94	0.309757
$670$	0	0
$671$	−11647.1	−0.670094
$672$	−2146.36	−0.123210
$673$	−1569.99	−0.0899235	−0.0449618	−	0.998989i	$-0.514317\pi$
$673$	−1569.99	−0.0899235	−0.0449618	+	0.998989i	$0.514317\pi$
$674$	4569.13	0.261122
$675$	0	0
$676$	15025.9	0.854909
$677$	13853.9	0.786482	0.393241	−	0.919435i	$-0.371354\pi$
$677$	13853.9	0.786482	0.393241	+	0.919435i	$0.371354\pi$
$678$	−1004.89	−0.0569210
$679$	9557.33	0.540172
$680$	0	0
$681$	12726.1	0.716100
$682$	−589.839	−0.0331174
$683$	−28337.1	−1.58754	−0.793769	−	0.608219i	$-0.791884\pi$
$683$	−28337.1	−1.58754	−0.793769	+	0.608219i	$0.791884\pi$
$684$	9921.07	0.554593
$685$	0	0
$686$	192.613	0.0107201
$687$	−10210.1	−0.567014
$688$	15966.1	0.884742
$689$	−4010.63	−0.221760
$690$	0	0
$691$	16936.5	0.932410	0.466205	−	0.884677i	$-0.345621\pi$
$691$	16936.5	0.932410	0.466205	+	0.884677i	$0.345621\pi$
$692$	−3970.73	−0.218128
$693$	1625.89	0.0891233
$694$	−4855.37	−0.265572
$695$	0	0
$696$	5394.86	0.293810
$697$	−2353.37	−0.127891
$698$	4186.62	0.227028
$699$	11712.3	0.633760
$700$	0	0
$701$	−29744.0	−1.60259	−0.801294	−	0.598271i	$-0.795855\pi$
$701$	−29744.0	−1.60259	−0.801294	+	0.598271i	$0.795855\pi$
$702$	−235.713	−0.0126730
$703$	−13723.5	−0.736261
$704$	10190.3	0.545543
$705$	0	0
$706$	−3060.58	−0.163154
$707$	−8091.96	−0.430452
$708$	−15016.5	−0.797113
$709$	34264.7	1.81500	0.907502	−	0.420047i	$-0.137986\pi$
$709$	34264.7	1.81500	0.907502	+	0.420047i	$0.137986\pi$
$710$	0	0
$711$	−10.4405	−0.000550705 0
$712$	11530.5	0.606916
$713$	−3155.16	−0.165725
$714$	1122.21	0.0588201
$715$	0	0
$716$	−29568.8	−1.54335
$717$	−20003.5	−1.04190
$718$	−2681.86	−0.139396
$719$	−25469.2	−1.32106	−0.660529	−	0.750801i	$-0.729668\pi$
$719$	−25469.2	−1.32106	−0.660529	+	0.750801i	$0.729668\pi$
$720$	0	0
$721$	547.452	0.0282776
$722$	−7703.40	−0.397079
$723$	18012.0	0.926518
$724$	23256.9	1.19383
$725$	0	0
$726$	−1120.23	−0.0572667
$727$	−24294.6	−1.23939	−0.619695	−	0.784843i	$-0.712744\pi$
$727$	−24294.6	−1.23939	−0.619695	+	0.784843i	$0.712744\pi$
$728$	958.503	0.0487974
$729$	729.000	0.0370370
$730$	0	0
$731$	−26876.6	−1.35987
$732$	10404.3	0.525349
$733$	−34870.8	−1.75714	−0.878569	−	0.477615i	$-0.841501\pi$
$733$	−34870.8	−1.75714	−0.878569	+	0.477615i	$0.841501\pi$
$734$	−5411.29	−0.272118
$735$	0	0
$736$	−7923.40	−0.396821
$737$	−21473.9	−1.07327
$738$	−124.985	−0.00623412
$739$	7028.81	0.349877	0.174938	−	0.984579i	$-0.444027\pi$
$739$	7028.81	0.349877	0.174938	+	0.984579i	$0.444027\pi$
$740$	0	0
$741$	−6690.25	−0.331677
$742$	1014.08	0.0501725
$743$	−1368.74	−0.0675831	−0.0337915	−	0.999429i	$-0.510758\pi$
$743$	−1368.74	−0.0675831	−0.0337915	+	0.999429i	$0.510758\pi$
$744$	1075.42	0.0529932
$745$	0	0
$746$	−6839.94	−0.335694
$747$	13446.3	0.658598
$748$	−18872.9	−0.922541
$749$	658.570	0.0321276
$750$	0	0
$751$	37144.0	1.80480	0.902400	−	0.430900i	$-0.141804\pi$
$751$	37144.0	1.80480	0.902400	+	0.430900i	$0.141804\pi$
$752$	14552.1	0.705665
$753$	−2185.40	−0.105764
$754$	−1782.43	−0.0860907
$755$	0	0
$756$	−1452.40	−0.0698721
$757$	−12042.4	−0.578189	−0.289095	−	0.957301i	$-0.593354\pi$
$757$	−12042.4	−0.578189	−0.289095	+	0.957301i	$0.593354\pi$
$758$	−948.683	−0.0454588
$759$	6002.07	0.287037
$760$	0	0
$761$	6112.92	0.291187	0.145593	−	0.989345i	$-0.453491\pi$
$761$	6112.92	0.291187	0.145593	+	0.989345i	$0.453491\pi$
$762$	3517.92	0.167245
$763$	14897.7	0.706860
$764$	−9767.88	−0.462552
$765$	0	0
$766$	−849.700	−0.0400795
$767$	10126.4	0.476717
$768$	−7725.50	−0.362982
$769$	−957.146	−0.0448837	−0.0224418	−	0.999748i	$-0.507144\pi$
$769$	−957.146	−0.0448837	−0.0224418	+	0.999748i	$0.507144\pi$
$770$	0	0
$771$	4439.58	0.207377
$772$	14570.8	0.679295
$773$	−32867.9	−1.52934	−0.764668	−	0.644424i	$-0.777097\pi$
$773$	−32867.9	−1.52934	−0.764668	+	0.644424i	$0.777097\pi$
$774$	−1427.39	−0.0662876
$775$	0	0
$776$	−12025.5	−0.556303
$777$	2009.06	0.0927601
$778$	−6831.58	−0.314812
$779$	−3547.46	−0.163159
$780$	0	0
$781$	4515.45	0.206883
$782$	4142.69	0.189440
$783$	5512.60	0.251602
$784$	2770.03	0.126186
$785$	0	0
$786$	701.057	0.0318141
$787$	−15320.0	−0.693900	−0.346950	−	0.937884i	$-0.612783\pi$
$787$	−15320.0	−0.693900	−0.346950	+	0.937884i	$0.612783\pi$
$788$	−31260.4	−1.41320
$789$	19101.9	0.861909
$790$	0	0
$791$	4175.45	0.187689
$792$	−2045.78	−0.0917848
$793$	−7016.15	−0.314188
$794$	−4129.32	−0.184564
$795$	0	0
$796$	−600.453	−0.0267368
$797$	−43629.0	−1.93904	−0.969522	−	0.245004i	$-0.921211\pi$
$797$	−43629.0	−1.93904	−0.969522	+	0.245004i	$0.921211\pi$
$798$	1691.61	0.0750407
$799$	−24496.3	−1.08463
$800$	0	0
$801$	11782.2	0.519729
$802$	−4201.33	−0.184980
$803$	1223.72	0.0537784
$804$	19182.5	0.841438
$805$	0	0
$806$	−355.314	−0.0155278
$807$	−5361.54	−0.233872
$808$	10181.7	0.443307
$809$	127.735	0.00555119	0.00277560	−	0.999996i	$-0.499116\pi$
$809$	127.735	0.00555119	0.00277560	+	0.999996i	$0.499116\pi$
$810$	0	0
$811$	16227.5	0.702618	0.351309	−	0.936260i	$-0.385737\pi$
$811$	16227.5	0.702618	0.351309	+	0.936260i	$0.385737\pi$
$812$	−10982.9	−0.474659
$813$	−11723.0	−0.505710
$814$	1386.48	0.0597005
$815$	0	0
$816$	16138.9	0.692369
$817$	−40513.7	−1.73488
$818$	−5193.77	−0.222000
$819$	979.423	0.0417873
$820$	0	0
$821$	34249.2	1.45591	0.727957	−	0.685623i	$-0.240470\pi$
$821$	34249.2	1.45591	0.727957	+	0.685623i	$0.240470\pi$
$822$	1043.23	0.0442661
$823$	6624.51	0.280578	0.140289	−	0.990111i	$-0.455197\pi$
$823$	6624.51	0.280578	0.140289	+	0.990111i	$0.455197\pi$
$824$	−688.832	−0.0291221
$825$	0	0
$826$	−2560.43	−0.107856
$827$	33786.8	1.42065	0.710327	−	0.703872i	$-0.248547\pi$
$827$	33786.8	1.42065	0.710327	+	0.703872i	$0.248547\pi$
$828$	−5361.62	−0.225035
$829$	−30283.8	−1.26876	−0.634378	−	0.773023i	$-0.718744\pi$
$829$	−30283.8	−1.26876	−0.634378	+	0.773023i	$0.718744\pi$
$830$	0	0
$831$	−11935.0	−0.498220
$832$	6138.57	0.255789
$833$	−4662.93	−0.193951
$834$	−449.794	−0.0186752
$835$	0	0
$836$	−28449.0	−1.17695
$837$	1098.89	0.0453804
$838$	1888.72	0.0778578
$839$	16810.9	0.691750	0.345875	−	0.938281i	$-0.387582\pi$
$839$	16810.9	0.691750	0.345875	+	0.938281i	$0.387582\pi$
$840$	0	0
$841$	17296.6	0.709195
$842$	2043.41	0.0836350
$843$	19464.1	0.795231
$844$	9936.39	0.405242
$845$	0	0
$846$	−1300.98	−0.0528706
$847$	4654.72	0.188829
$848$	14583.8	0.590579
$849$	493.007	0.0199293
$850$	0	0
$851$	7416.56	0.298750
$852$	−4033.64	−0.162195
$853$	−14875.8	−0.597112	−0.298556	−	0.954392i	$-0.596505\pi$
$853$	−14875.8	−0.597112	−0.298556	+	0.954392i	$0.596505\pi$
$854$	1774.02	0.0710839
$855$	0	0
$856$	−828.647	−0.0330871
$857$	3987.55	0.158941	0.0794703	−	0.996837i	$-0.474677\pi$
$857$	3987.55	0.158941	0.0794703	+	0.996837i	$0.474677\pi$
$858$	675.915	0.0268944
$859$	39344.7	1.56278	0.781388	−	0.624046i	$-0.214512\pi$
$859$	39344.7	1.56278	0.781388	+	0.624046i	$0.214512\pi$
$860$	0	0
$861$	519.333	0.0205561
$862$	−6313.63	−0.249470
$863$	15627.0	0.616397	0.308198	−	0.951322i	$-0.400274\pi$
$863$	15627.0	0.616397	0.308198	+	0.951322i	$0.400274\pi$
$864$	2759.60	0.108661
$865$	0	0
$866$	−105.197	−0.00412787
$867$	−12428.4	−0.486839
$868$	−2189.35	−0.0856122
$869$	29.9386	0.00116870
$870$	0	0
$871$	−12935.7	−0.503226
$872$	−18745.1	−0.727969
$873$	−12288.0	−0.476387
$874$	6244.69	0.241682
$875$	0	0
$876$	−1093.14	−0.0421619
$877$	14519.0	0.559034	0.279517	−	0.960141i	$-0.409826\pi$
$877$	14519.0	0.559034	0.279517	+	0.960141i	$0.409826\pi$
$878$	6446.29	0.247781
$879$	−15013.7	−0.576109
$880$	0	0
$881$	24177.7	0.924592	0.462296	−	0.886726i	$-0.347026\pi$
$881$	24177.7	0.924592	0.462296	+	0.886726i	$0.347026\pi$
$882$	−247.645	−0.00945423
$883$	−10340.3	−0.394089	−0.197044	−	0.980395i	$-0.563134\pi$
$883$	−10340.3	−0.394089	−0.197044	+	0.980395i	$0.563134\pi$
$884$	−11368.9	−0.432553
$885$	0	0
$886$	5329.45	0.202084
$887$	3222.62	0.121990	0.0609949	−	0.998138i	$-0.480573\pi$
$887$	3222.62	0.121990	0.0609949	+	0.998138i	$0.480573\pi$
$888$	−2527.90	−0.0955303
$889$	−14617.5	−0.551467
$890$	0	0
$891$	−2090.43	−0.0785993
$892$	13729.8	0.515367
$893$	−36925.6	−1.38373
$894$	4298.91	0.160824
$895$	0	0
$896$	−7275.74	−0.271278
$897$	3615.60	0.134583
$898$	3114.70	0.115745
$899$	8309.70	0.308280
$900$	0	0
$901$	−24549.7	−0.907735
$902$	358.399	0.0132299
$903$	5931.03	0.218574
$904$	−5253.77	−0.193294
$905$	0	0
$906$	1882.41	0.0690274
$907$	31692.8	1.16025	0.580123	−	0.814529i	$-0.303005\pi$
$907$	31692.8	1.16025	0.580123	+	0.814529i	$0.303005\pi$
$908$	32598.5	1.19143
$909$	10403.9	0.379623
$910$	0	0
$911$	2403.15	0.0873985	0.0436993	−	0.999045i	$-0.486086\pi$
$911$	2403.15	0.0873985	0.0436993	+	0.999045i	$0.486086\pi$
$912$	24327.7	0.883301
$913$	−38557.6	−1.39767
$914$	−997.843	−0.0361113
$915$	0	0
$916$	−26153.6	−0.943385
$917$	−2912.99	−0.104902
$918$	−1442.84	−0.0518745
$919$	19622.5	0.704339	0.352170	−	0.935936i	$-0.385444\pi$
$919$	19622.5	0.704339	0.352170	+	0.935936i	$0.385444\pi$
$920$	0	0
$921$	570.501	0.0204111
$922$	5087.56	0.181724
$923$	2720.07	0.0970014
$924$	4164.80	0.148281
$925$	0	0
$926$	−8355.06	−0.296506
$927$	−703.867	−0.0249385
$928$	20867.7	0.738165
$929$	−12930.5	−0.456660	−0.228330	−	0.973584i	$-0.573327\pi$
$929$	−12930.5	−0.456660	−0.228330	+	0.973584i	$0.573327\pi$
$930$	0	0
$931$	−7028.90	−0.247436
$932$	30001.6	1.05444
$933$	3547.72	0.124488
$934$	−8016.64	−0.280848
$935$	0	0
$936$	−1232.36	−0.0430352
$937$	18717.1	0.652573	0.326287	−	0.945271i	$-0.394203\pi$
$937$	18717.1	0.652573	0.326287	+	0.945271i	$0.394203\pi$
$938$	3270.76	0.113853
$939$	13977.2	0.485758
$940$	0	0
$941$	−10152.9	−0.351727	−0.175863	−	0.984415i	$-0.556272\pi$
$941$	−10152.9	−0.351727	−0.175863	+	0.984415i	$0.556272\pi$
$942$	−768.380	−0.0265766
$943$	1917.15	0.0662045
$944$	−36822.4	−1.26956
$945$	0	0
$946$	4093.09	0.140674
$947$	15836.2	0.543408	0.271704	−	0.962381i	$-0.412413\pi$
$947$	15836.2	0.543408	0.271704	+	0.962381i	$0.412413\pi$
$948$	−26.7440	−0.000916250 0
$949$	737.158	0.0252151
$950$	0	0
$951$	11083.6	0.377930
$952$	5867.15	0.199743
$953$	4847.86	0.164782	0.0823911	−	0.996600i	$-0.473744\pi$
$953$	4847.86	0.164782	0.0823911	+	0.996600i	$0.473744\pi$
$954$	−1303.82	−0.0442480
$955$	0	0
$956$	−51240.0	−1.73349
$957$	−15807.5	−0.533945
$958$	8635.44	0.291230
$959$	−4334.76	−0.145961
$960$	0	0
$961$	−28134.5	−0.944397
$962$	835.207	0.0279918
$963$	−846.732	−0.0283339
$964$	46138.6	1.54152
$965$	0	0
$966$	−914.195	−0.0304490
$967$	17153.8	0.570454	0.285227	−	0.958460i	$-0.407931\pi$
$967$	17153.8	0.570454	0.285227	+	0.958460i	$0.407931\pi$
$968$	−5856.80	−0.194468
$969$	−40952.1	−1.35766
$970$	0	0
$971$	50352.2	1.66414	0.832070	−	0.554670i	$-0.187156\pi$
$971$	50352.2	1.66414	0.832070	+	0.554670i	$0.187156\pi$
$972$	1867.37	0.0616214
$973$	1868.96	0.0615788
$974$	−11053.2	−0.363623
$975$	0	0
$976$	25512.8	0.836725
$977$	1510.03	0.0494474	0.0247237	−	0.999694i	$-0.492129\pi$
$977$	1510.03	0.0494474	0.0247237	+	0.999694i	$0.492129\pi$
$978$	−177.714	−0.00581049
$979$	−33785.7	−1.10296
$980$	0	0
$981$	−19154.2	−0.623392
$982$	−10998.1	−0.357396
$983$	−5310.89	−0.172321	−0.0861603	−	0.996281i	$-0.527460\pi$
$983$	−5310.89	−0.172321	−0.0861603	+	0.996281i	$0.527460\pi$
$984$	−653.451	−0.0211700
$985$	0	0
$986$	−10910.6	−0.352396
$987$	5405.75	0.174333
$988$	−17137.4	−0.551836
$989$	21894.7	0.703956
$990$	0	0
$991$	35845.4	1.14901	0.574505	−	0.818501i	$-0.305195\pi$
$991$	35845.4	1.14901	0.574505	+	0.818501i	$0.305195\pi$
$992$	4159.82	0.133140
$993$	25898.4	0.827654
$994$	−687.764	−0.0219462
$995$	0	0
$996$	34443.3	1.09576
$997$	−17857.5	−0.567253	−0.283627	−	0.958935i	$-0.591538\pi$
$997$	−17857.5	−0.567253	−0.283627	+	0.958935i	$0.591538\pi$
$998$	3868.24	0.122692
$999$	−2583.08	−0.0818067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.m.1.1	yes	2
3.2	odd	2		1575.4.a.o.1.2		2
5.2	odd	4		525.4.d.m.274.2		4
5.3	odd	4		525.4.d.m.274.3		4
5.4	even	2		525.4.a.j.1.2	✓	2
15.14	odd	2		1575.4.a.x.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.j.1.2	✓	2	5.4	even	2
525.4.a.m.1.1	yes	2	1.1	even	1	trivial
525.4.d.m.274.2		4	5.2	odd	4
525.4.d.m.274.3		4	5.3	odd	4
1575.4.a.o.1.2		2	3.2	odd	2
1575.4.a.x.1.1		2	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)

\(f(q)\)	\(=\)	\(q-0.561553 q^{2} -3.00000 q^{3} -7.68466 q^{4} +1.68466 q^{6} -7.00000 q^{7} +8.80776 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.561553 q^{2} -3.00000 q^{3} -7.68466 q^{4} +1.68466 q^{6} -7.00000 q^{7} +8.80776 q^{8} +9.00000 q^{9} -25.8078 q^{11} +23.0540 q^{12} -15.5464 q^{13} +3.93087 q^{14} +56.5312 q^{16} -95.1619 q^{17} -5.05398 q^{18} -143.447 q^{19} +21.0000 q^{21} +14.4924 q^{22} +77.5227 q^{23} -26.4233 q^{24} +8.73012 q^{26} -27.0000 q^{27} +53.7926 q^{28} -204.170 q^{29} -40.6998 q^{31} -102.207 q^{32} +77.4233 q^{33} +53.4384 q^{34} -69.1619 q^{36} +95.6695 q^{37} +80.5530 q^{38} +46.6392 q^{39} +24.7301 q^{41} -11.7926 q^{42} +282.430 q^{43} +198.324 q^{44} -43.5331 q^{46} +257.417 q^{47} -169.594 q^{48} +49.0000 q^{49} +285.486 q^{51} +119.469 q^{52} +257.978 q^{53} +15.1619 q^{54} -61.6543 q^{56} +430.341 q^{57} +114.652 q^{58} -651.365 q^{59} +451.304 q^{61} +22.8551 q^{62} -63.0000 q^{63} -394.855 q^{64} -43.4773 q^{66} +832.071 q^{67} +731.287 q^{68} -232.568 q^{69} -174.965 q^{71} +79.2699 q^{72} -47.4166 q^{73} -53.7235 q^{74} +1102.34 q^{76} +180.654 q^{77} -26.1904 q^{78} -1.16006 q^{79} +81.0000 q^{81} -13.8873 q^{82} +1494.03 q^{83} -161.378 q^{84} -158.599 q^{86} +612.511 q^{87} -227.309 q^{88} +1309.13 q^{89} +108.825 q^{91} -595.736 q^{92} +122.099 q^{93} -144.553 q^{94} +306.622 q^{96} -1365.33 q^{97} -27.5161 q^{98} -232.270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 9 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 9 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	\( 2 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 9 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} - 31 q^{11} + 9 q^{12} + 39 q^{13} - 21 q^{14} - 23 q^{16} - 79 q^{17} + 27 q^{18} - 56 q^{19} + 42 q^{21} - 4 q^{22} + 254 q^{23} + 9 q^{24} + 203 q^{26} - 54 q^{27} + 21 q^{28} - 62 q^{29} - 135 q^{31} - 291 q^{32} + 93 q^{33} + 111 q^{34} - 27 q^{36} + 113 q^{37} + 392 q^{38} - 117 q^{39} + 235 q^{41} + 63 q^{42} + 804 q^{43} + 174 q^{44} + 585 q^{46} + 152 q^{47} + 69 q^{48} + 98 q^{49} + 237 q^{51} + 375 q^{52} + 149 q^{53} - 81 q^{54} + 21 q^{56} + 168 q^{57} + 621 q^{58} - 441 q^{59} - 223 q^{61} - 313 q^{62} - 126 q^{63} - 431 q^{64} + 12 q^{66} + 1157 q^{67} + 807 q^{68} - 762 q^{69} + 619 q^{71} - 27 q^{72} + 268 q^{73} + 8 q^{74} + 1512 q^{76} + 217 q^{77} - 609 q^{78} - 427 q^{79} + 162 q^{81} + 735 q^{82} + 1211 q^{83} - 63 q^{84} + 1699 q^{86} + 186 q^{87} - 166 q^{88} + 466 q^{89} - 273 q^{91} + 231 q^{92} + 405 q^{93} - 520 q^{94} + 873 q^{96} + 172 q^{97} + 147 q^{98} - 279 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 9 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 - 31 * q^11 + 9 * q^12 + 39 * q^13 - 21 * q^14 - 23 * q^16 - 79 * q^17 + 27 * q^18 - 56 * q^19 + 42 * q^21 - 4 * q^22 + 254 * q^23 + 9 * q^24 + 203 * q^26 - 54 * q^27 + 21 * q^28 - 62 * q^29 - 135 * q^31 - 291 * q^32 + 93 * q^33 + 111 * q^34 - 27 * q^36 + 113 * q^37 + 392 * q^38 - 117 * q^39 + 235 * q^41 + 63 * q^42 + 804 * q^43 + 174 * q^44 + 585 * q^46 + 152 * q^47 + 69 * q^48 + 98 * q^49 + 237 * q^51 + 375 * q^52 + 149 * q^53 - 81 * q^54 + 21 * q^56 + 168 * q^57 + 621 * q^58 - 441 * q^59 - 223 * q^61 - 313 * q^62 - 126 * q^63 - 431 * q^64 + 12 * q^66 + 1157 * q^67 + 807 * q^68 - 762 * q^69 + 619 * q^71 - 27 * q^72 + 268 * q^73 + 8 * q^74 + 1512 * q^76 + 217 * q^77 - 609 * q^78 - 427 * q^79 + 162 * q^81 + 735 * q^82 + 1211 * q^83 - 63 * q^84 + 1699 * q^86 + 186 * q^87 - 166 * q^88 + 466 * q^89 - 273 * q^91 + 231 * q^92 + 405 * q^93 - 520 * q^94 + 873 * q^96 + 172 * q^97 + 147 * q^98 - 279 * q^99

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