LMFDB - Embedded newform 175.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.14360.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 17x - 14 $ x^3 - 17*x - 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.48565$ of defining polynomial
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} +2.96363 q^{6} -7.00000 q^{7} +13.4206 q^{8} -26.2771 q^{9} +O(q^{10})$	\(q-3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} +2.96363 q^{6} -7.00000 q^{7} +13.4206 q^{8} -26.2771 q^{9} -6.90764 q^{11} -3.52829 q^{12} +22.1364 q^{13} +24.3996 q^{14} -79.9776 q^{16} -88.3030 q^{17} +91.5928 q^{18} +36.9560 q^{19} +5.95167 q^{21} +24.0776 q^{22} +95.5283 q^{23} -11.4107 q^{24} -77.1598 q^{26} +45.2982 q^{27} -29.0483 q^{28} +269.029 q^{29} +197.114 q^{31} +171.409 q^{32} +5.87314 q^{33} +307.793 q^{34} -109.044 q^{36} -2.14546 q^{37} -128.816 q^{38} -18.8212 q^{39} +174.127 q^{41} -20.7454 q^{42} +17.0345 q^{43} -28.6650 q^{44} -332.978 q^{46} +528.029 q^{47} +68.0000 q^{48} +49.0000 q^{49} +75.0786 q^{51} +91.8608 q^{52} +641.114 q^{53} -157.894 q^{54} -93.9441 q^{56} -31.4214 q^{57} -937.742 q^{58} -642.975 q^{59} +142.967 q^{61} -687.070 q^{62} +183.940 q^{63} +42.3480 q^{64} -20.4717 q^{66} -478.797 q^{67} -366.436 q^{68} -81.2218 q^{69} +105.550 q^{71} -352.654 q^{72} -986.512 q^{73} +7.47834 q^{74} +153.358 q^{76} +48.3534 q^{77} +65.6042 q^{78} -1099.86 q^{79} +670.967 q^{81} -606.947 q^{82} +1236.62 q^{83} +24.6980 q^{84} -59.3763 q^{86} -228.739 q^{87} -92.7045 q^{88} -711.698 q^{89} -154.955 q^{91} +396.420 q^{92} -167.594 q^{93} -1840.52 q^{94} -145.739 q^{96} +636.553 q^{97} -170.797 q^{98} +181.513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9	\( 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9} - 74 q^{11} + 152 q^{12} - 44 q^{13} - 21 q^{14} - 79 q^{16} + 52 q^{17} + 411 q^{18} + 168 q^{19} + 14 q^{21} - 184 q^{22} + 124 q^{23} + 420 q^{24} - 446 q^{26} - 170 q^{27} - 91 q^{28} + 332 q^{29} + 320 q^{31} + 183 q^{32} + 106 q^{33} + 582 q^{34} + 181 q^{36} + 54 q^{37} + 460 q^{38} - 982 q^{39} + 362 q^{41} - 168 q^{42} + 16 q^{43} - 264 q^{44} - 336 q^{46} + 730 q^{47} + 204 q^{48} + 147 q^{49} - 1178 q^{51} - 1202 q^{52} - 110 q^{53} - 180 q^{54} - 105 q^{56} + 956 q^{57} - 450 q^{58} - 180 q^{59} + 1222 q^{61} - 464 q^{62} - 567 q^{63} - 391 q^{64} - 532 q^{66} - 204 q^{67} - 918 q^{68} - 716 q^{69} - 136 q^{71} - 765 q^{72} - 310 q^{73} + 502 q^{74} + 1796 q^{76} + 518 q^{77} - 3788 q^{78} - 1034 q^{79} + 2283 q^{81} + 6 q^{82} + 1660 q^{83} - 1064 q^{84} + 764 q^{86} + 1574 q^{87} + 20 q^{88} + 242 q^{89} + 308 q^{91} - 96 q^{92} - 1376 q^{93} - 1108 q^{94} - 3156 q^{96} - 100 q^{97} + 147 q^{98} - 3488 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9 - 74 * q^11 + 152 * q^12 - 44 * q^13 - 21 * q^14 - 79 * q^16 + 52 * q^17 + 411 * q^18 + 168 * q^19 + 14 * q^21 - 184 * q^22 + 124 * q^23 + 420 * q^24 - 446 * q^26 - 170 * q^27 - 91 * q^28 + 332 * q^29 + 320 * q^31 + 183 * q^32 + 106 * q^33 + 582 * q^34 + 181 * q^36 + 54 * q^37 + 460 * q^38 - 982 * q^39 + 362 * q^41 - 168 * q^42 + 16 * q^43 - 264 * q^44 - 336 * q^46 + 730 * q^47 + 204 * q^48 + 147 * q^49 - 1178 * q^51 - 1202 * q^52 - 110 * q^53 - 180 * q^54 - 105 * q^56 + 956 * q^57 - 450 * q^58 - 180 * q^59 + 1222 * q^61 - 464 * q^62 - 567 * q^63 - 391 * q^64 - 532 * q^66 - 204 * q^67 - 918 * q^68 - 716 * q^69 - 136 * q^71 - 765 * q^72 - 310 * q^73 + 502 * q^74 + 1796 * q^76 + 518 * q^77 - 3788 * q^78 - 1034 * q^79 + 2283 * q^81 + 6 * q^82 + 1660 * q^83 - 1064 * q^84 + 764 * q^86 + 1574 * q^87 + 20 * q^88 + 242 * q^89 + 308 * q^91 - 96 * q^92 - 1376 * q^93 - 1108 * q^94 - 3156 * q^96 - 100 * q^97 + 147 * q^98 - 3488 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.48565	−1.23236	−0.616182	−	0.787604i	$-0.711321\pi$
$2$	−3.48565	−1.23236	−0.616182	+	0.787604i	$0.711321\pi$
$3$	−0.850238	−0.163628	−0.0818142	−	0.996648i	$-0.526071\pi$
$3$	−0.850238	−0.163628	−0.0818142	+	0.996648i	$0.526071\pi$
$4$	4.14976	0.518720
$5$	0	0
$5$	0	0
$6$	2.96363	0.201650
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	13.4206	0.593112
$9$	−26.2771	−0.973226
$10$	0	0
$11$	−6.90764	−0.189339	−0.0946696	−	0.995509i	$-0.530179\pi$
$11$	−6.90764	−0.189339	−0.0946696	+	0.995509i	$0.530179\pi$
$12$	−3.52829	−0.0848774
$13$	22.1364	0.472272	0.236136	−	0.971720i	$-0.424119\pi$
$13$	22.1364	0.472272	0.236136	+	0.971720i	$0.424119\pi$
$14$	24.3996	0.465790
$15$	0	0
$16$	−79.9776	−1.24965
$17$	−88.3030	−1.25980	−0.629901	−	0.776676i	$-0.716904\pi$
$17$	−88.3030	−1.25980	−0.629901	+	0.776676i	$0.716904\pi$
$18$	91.5928	1.19937
$19$	36.9560	0.446225	0.223113	−	0.974793i	$-0.428378\pi$
$19$	36.9560	0.446225	0.223113	+	0.974793i	$0.428378\pi$
$20$	0	0
$21$	5.95167	0.0618457
$22$	24.0776	0.233335
$23$	95.5283	0.866045	0.433022	−	0.901383i	$-0.357447\pi$
$23$	95.5283	0.866045	0.433022	+	0.901383i	$0.357447\pi$
$24$	−11.4107	−0.0970500
$25$	0	0
$26$	−77.1598	−0.582010
$27$	45.2982	0.322876
$28$	−29.0483	−0.196058
$29$	269.029	1.72267	0.861336	−	0.508035i	$-0.169628\pi$
$29$	269.029	1.72267	0.861336	+	0.508035i	$0.169628\pi$
$30$	0	0
$31$	197.114	1.14202	0.571012	−	0.820942i	$-0.306551\pi$
$31$	197.114	1.14202	0.571012	+	0.820942i	$0.306551\pi$
$32$	171.409	0.946911
$33$	5.87314	0.0309813
$34$	307.793	1.55253
$35$	0	0
$36$	−109.044	−0.504832
$37$	−2.14546	−0.00953276	−0.00476638	−	0.999989i	$-0.501517\pi$
$37$	−2.14546	−0.00953276	−0.00476638	+	0.999989i	$0.501517\pi$
$38$	−128.816	−0.549912
$39$	−18.8212	−0.0772771
$40$	0	0
$41$	174.127	0.663271	0.331636	−	0.943408i	$-0.392400\pi$
$41$	174.127	0.663271	0.331636	+	0.943408i	$0.392400\pi$
$42$	−20.7454	−0.0762164
$43$	17.0345	0.0604125	0.0302062	−	0.999544i	$-0.490384\pi$
$43$	17.0345	0.0604125	0.0302062	+	0.999544i	$0.490384\pi$
$44$	−28.6650	−0.0982140
$45$	0	0
$46$	−332.978	−1.06728
$47$	528.029	1.63874	0.819371	−	0.573264i	$-0.194323\pi$
$47$	528.029	1.63874	0.819371	+	0.573264i	$0.194323\pi$
$48$	68.0000	0.204478
$49$	49.0000	0.142857
$50$	0	0
$51$	75.0786	0.206139
$52$	91.8608	0.244977
$53$	641.114	1.66158	0.830790	−	0.556586i	$-0.187889\pi$
$53$	641.114	1.66158	0.830790	+	0.556586i	$0.187889\pi$
$54$	−157.894	−0.397900
$55$	0	0
$56$	−93.9441	−0.224175
$57$	−31.4214	−0.0730151
$58$	−937.742	−2.12296
$59$	−642.975	−1.41878	−0.709391	−	0.704815i	$-0.751030\pi$
$59$	−642.975	−1.41878	−0.709391	+	0.704815i	$0.751030\pi$
$60$	0	0
$61$	142.967	0.300083	0.150042	−	0.988680i	$-0.452059\pi$
$61$	142.967	0.300083	0.150042	+	0.988680i	$0.452059\pi$
$62$	−687.070	−1.40739
$63$	183.940	0.367845
$64$	42.3480	0.0827109
$65$	0	0
$66$	−20.4717	−0.0381802
$67$	−478.797	−0.873050	−0.436525	−	0.899692i	$-0.643791\pi$
$67$	−478.797	−0.873050	−0.436525	+	0.899692i	$0.643791\pi$
$68$	−366.436	−0.653484
$69$	−81.2218	−0.141710
$70$	0	0
$71$	105.550	0.176430	0.0882150	−	0.996101i	$-0.471884\pi$
$71$	105.550	0.176430	0.0882150	+	0.996101i	$0.471884\pi$
$72$	−352.654	−0.577232
$73$	−986.512	−1.58168	−0.790839	−	0.612024i	$-0.790356\pi$
$73$	−986.512	−1.58168	−0.790839	+	0.612024i	$0.790356\pi$
$74$	7.47834	0.0117478
$75$	0	0
$76$	153.358	0.231466
$77$	48.3534	0.0715635
$78$	65.6042	0.0952335
$79$	−1099.86	−1.56638	−0.783190	−	0.621783i	$-0.786409\pi$
$79$	−1099.86	−1.56638	−0.783190	+	0.621783i	$0.786409\pi$
$80$	0	0
$81$	670.967	0.920394
$82$	−606.947	−0.817391
$83$	1236.62	1.63538	0.817691	−	0.575657i	$-0.195254\pi$
$83$	1236.62	1.63538	0.817691	+	0.575657i	$0.195254\pi$
$84$	24.6980	0.0320806
$85$	0	0
$86$	−59.3763	−0.0744501
$87$	−228.739	−0.281878
$88$	−92.7045	−0.112299
$89$	−711.698	−0.847638	−0.423819	−	0.905747i	$-0.639311\pi$
$89$	−711.698	−0.847638	−0.423819	+	0.905747i	$0.639311\pi$
$90$	0	0
$91$	−154.955	−0.178502
$92$	396.420	0.449235
$93$	−167.594	−0.186867
$94$	−1840.52	−2.01953
$95$	0	0
$96$	−145.739	−0.154942
$97$	636.553	0.666311	0.333156	−	0.942872i	$-0.391887\pi$
$97$	636.553	0.666311	0.333156	+	0.942872i	$0.391887\pi$
$98$	−170.797	−0.176052
$99$	181.513	0.184270
$100$	0	0
$101$	1742.05	1.71624	0.858121	−	0.513448i	$-0.171632\pi$
$101$	1742.05	1.71624	0.858121	+	0.513448i	$0.171632\pi$
$102$	−261.698	−0.254039
$103$	−1454.62	−1.39154	−0.695769	−	0.718266i	$-0.744936\pi$
$103$	−1454.62	−1.39154	−0.695769	+	0.718266i	$0.744936\pi$
$104$	297.083	0.280110
$105$	0	0
$106$	−2234.70	−2.04767
$107$	1181.67	1.06763	0.533813	−	0.845603i	$-0.320759\pi$
$107$	1181.67	1.06763	0.533813	+	0.845603i	$0.320759\pi$
$108$	187.977	0.167482
$109$	2204.43	1.93712	0.968559	−	0.248784i	$-0.0800310\pi$
$109$	2204.43	1.93712	0.968559	+	0.248784i	$0.0800310\pi$
$110$	0	0
$111$	1.82416	0.00155983
$112$	559.843	0.472323
$113$	−236.886	−0.197207	−0.0986034	−	0.995127i	$-0.531438\pi$
$113$	−236.886	−0.197207	−0.0986034	+	0.995127i	$0.531438\pi$
$114$	109.524	0.0899812
$115$	0	0
$116$	1116.41	0.893585
$117$	−581.680	−0.459627
$118$	2241.19	1.74846
$119$	618.121	0.476160
$120$	0	0
$121$	−1283.28	−0.964151
$122$	−498.334	−0.369811
$123$	−148.050	−0.108530
$124$	817.976	0.592390
$125$	0	0
$126$	−641.149	−0.453319
$127$	1667.21	1.16489	0.582446	−	0.812869i	$-0.302096\pi$
$127$	1667.21	1.16489	0.582446	+	0.812869i	$0.302096\pi$
$128$	−1518.88	−1.04884
$129$	−14.4834	−0.00988520
$130$	0	0
$131$	891.722	0.594733	0.297367	−	0.954763i	$-0.403892\pi$
$131$	891.722	0.594733	0.297367	+	0.954763i	$0.403892\pi$
$132$	24.3721	0.0160706
$133$	−258.692	−0.168657
$134$	1668.92	1.07591
$135$	0	0
$136$	−1185.08	−0.747203
$137$	400.425	0.249713	0.124856	−	0.992175i	$-0.460153\pi$
$137$	400.425	0.249713	0.124856	+	0.992175i	$0.460153\pi$
$138$	283.111	0.174638
$139$	515.050	0.314287	0.157144	−	0.987576i	$-0.449771\pi$
$139$	515.050	0.314287	0.157144	+	0.987576i	$0.449771\pi$
$140$	0	0
$141$	−448.950	−0.268145
$142$	−367.912	−0.217426
$143$	−152.910	−0.0894195
$144$	2101.58	1.21619
$145$	0	0
$146$	3438.64	1.94920
$147$	−41.6617	−0.0233755
$148$	−8.90316	−0.00494483
$149$	218.374	0.120066	0.0600332	−	0.998196i	$-0.480879\pi$
$149$	218.374	0.120066	0.0600332	+	0.998196i	$0.480879\pi$
$150$	0	0
$151$	−175.011	−0.0943190	−0.0471595	−	0.998887i	$-0.515017\pi$
$151$	−175.011	−0.0943190	−0.0471595	+	0.998887i	$0.515017\pi$
$152$	495.971	0.264661
$153$	2320.35	1.22607
$154$	−168.543	−0.0881922
$155$	0	0
$156$	−78.1036	−0.0400852
$157$	919.642	0.467487	0.233743	−	0.972298i	$-0.424902\pi$
$157$	919.642	0.467487	0.233743	+	0.972298i	$0.424902\pi$
$158$	3833.73	1.93035
$159$	−545.099	−0.271882
$160$	0	0
$161$	−668.698	−0.327334
$162$	−2338.76	−1.13426
$163$	−2368.51	−1.13813	−0.569067	−	0.822291i	$-0.692695\pi$
$163$	−2368.51	−1.13813	−0.569067	+	0.822291i	$0.692695\pi$
$164$	722.587	0.344052
$165$	0	0
$166$	−4310.43	−2.01539
$167$	−1079.37	−0.500144	−0.250072	−	0.968227i	$-0.580454\pi$
$167$	−1079.37	−0.500144	−0.250072	+	0.968227i	$0.580454\pi$
$168$	79.8749	0.0366814
$169$	−1706.98	−0.776959
$170$	0	0
$171$	−971.095	−0.434278
$172$	70.6891	0.0313372
$173$	881.271	0.387294	0.193647	−	0.981071i	$-0.437968\pi$
$173$	881.271	0.387294	0.193647	+	0.981071i	$0.437968\pi$
$174$	797.305	0.347376
$175$	0	0
$176$	552.456	0.236608
$177$	546.682	0.232153
$178$	2480.73	1.04460
$179$	−3377.72	−1.41041	−0.705203	−	0.709006i	$-0.749144\pi$
$179$	−3377.72	−1.41041	−0.705203	+	0.709006i	$0.749144\pi$
$180$	0	0
$181$	1435.58	0.589533	0.294767	−	0.955569i	$-0.404758\pi$
$181$	1435.58	0.589533	0.294767	+	0.955569i	$0.404758\pi$
$182$	540.118	0.219979
$183$	−121.556	−0.0491021
$184$	1282.05	0.513661
$185$	0	0
$186$	584.174	0.230289
$187$	609.965	0.238530
$188$	2191.19	0.850049
$189$	−317.088	−0.122036
$190$	0	0
$191$	−1588.14	−0.601642	−0.300821	−	0.953681i	$-0.597261\pi$
$191$	−1588.14	−0.601642	−0.300821	+	0.953681i	$0.597261\pi$
$192$	−36.0059	−0.0135339
$193$	977.704	0.364646	0.182323	−	0.983239i	$-0.441638\pi$
$193$	977.704	0.364646	0.182323	+	0.983239i	$0.441638\pi$
$194$	−2218.80	−0.821138
$195$	0	0
$196$	203.338	0.0741029
$197$	−359.682	−0.130083	−0.0650413	−	0.997883i	$-0.520718\pi$
$197$	−359.682	−0.130083	−0.0650413	+	0.997883i	$0.520718\pi$
$198$	−632.689	−0.227087
$199$	2818.38	1.00397	0.501983	−	0.864877i	$-0.332604\pi$
$199$	2818.38	1.00397	0.501983	+	0.864877i	$0.332604\pi$
$200$	0	0
$201$	407.091	0.142856
$202$	−6072.18	−2.11503
$203$	−1883.21	−0.651109
$204$	311.558	0.106929
$205$	0	0
$206$	5070.31	1.71488
$207$	−2510.21	−0.842857
$208$	−1770.42	−0.590174
$209$	−255.278	−0.0844879
$210$	0	0
$211$	−1009.64	−0.329415	−0.164708	−	0.986342i	$-0.552668\pi$
$211$	−1009.64	−0.329415	−0.164708	+	0.986342i	$0.552668\pi$
$212$	2660.47	0.861895
$213$	−89.7430	−0.0288690
$214$	−4118.88	−1.31570
$215$	0	0
$216$	607.929	0.191501
$217$	−1379.80	−0.431644
$218$	−7683.86	−2.38723
$219$	838.770	0.258808
$220$	0	0
$221$	−1954.71	−0.594969
$222$	−6.35837	−0.00192228
$223$	−1277.28	−0.383555	−0.191778	−	0.981438i	$-0.561425\pi$
$223$	−1277.28	−0.383555	−0.191778	+	0.981438i	$0.561425\pi$
$224$	−1199.86	−0.357899
$225$	0	0
$226$	825.702	0.243030
$227$	−1399.87	−0.409307	−0.204654	−	0.978834i	$-0.565607\pi$
$227$	−1399.87	−0.409307	−0.204654	+	0.978834i	$0.565607\pi$
$228$	−130.391	−0.0378744
$229$	3182.00	0.918222	0.459111	−	0.888379i	$-0.348168\pi$
$229$	3182.00	0.918222	0.459111	+	0.888379i	$0.348168\pi$
$230$	0	0
$231$	−41.1120	−0.0117098
$232$	3610.53	1.02174
$233$	3027.84	0.851332	0.425666	−	0.904880i	$-0.360040\pi$
$233$	3027.84	0.851332	0.425666	+	0.904880i	$0.360040\pi$
$234$	2027.53	0.566428
$235$	0	0
$236$	−2668.19	−0.735951
$237$	935.144	0.256304
$238$	−2154.55	−0.586802
$239$	−4995.69	−1.35207	−0.676034	−	0.736870i	$-0.736303\pi$
$239$	−4995.69	−1.35207	−0.676034	+	0.736870i	$0.736303\pi$
$240$	0	0
$241$	−3756.52	−1.00406	−0.502030	−	0.864850i	$-0.667413\pi$
$241$	−3756.52	−1.00406	−0.502030	+	0.864850i	$0.667413\pi$
$242$	4473.08	1.18818
$243$	−1793.53	−0.473479
$244$	593.280	0.155659
$245$	0	0
$246$	516.050	0.133748
$247$	818.072	0.210740
$248$	2645.39	0.677347
$249$	−1051.42	−0.267595
$250$	0	0
$251$	6565.46	1.65103	0.825514	−	0.564381i	$-0.190885\pi$
$251$	6565.46	1.65103	0.825514	+	0.564381i	$0.190885\pi$
$252$	763.306	0.190809
$253$	−659.875	−0.163976
$254$	−5811.33	−1.43557
$255$	0	0
$256$	4955.51	1.20984
$257$	6879.44	1.66976	0.834879	−	0.550433i	$-0.185537\pi$
$257$	6879.44	1.66976	0.834879	+	0.550433i	$0.185537\pi$
$258$	50.4840	0.0121822
$259$	15.0182	0.00360304
$260$	0	0
$261$	−7069.31	−1.67655
$262$	−3108.23	−0.732928
$263$	−3080.15	−0.722169	−0.361084	−	0.932533i	$-0.617593\pi$
$263$	−3080.15	−0.722169	−0.361084	+	0.932533i	$0.617593\pi$
$264$	78.8209	0.0183754
$265$	0	0
$266$	901.709	0.207847
$267$	605.113	0.138698
$268$	−1986.89	−0.452869
$269$	6710.33	1.52095	0.760476	−	0.649366i	$-0.224966\pi$
$269$	6710.33	1.52095	0.760476	+	0.649366i	$0.224966\pi$
$270$	0	0
$271$	7842.95	1.75803	0.879014	−	0.476796i	$-0.158202\pi$
$271$	7842.95	1.75803	0.879014	+	0.476796i	$0.158202\pi$
$272$	7062.26	1.57431
$273$	131.749	0.0292080
$274$	−1395.74	−0.307737
$275$	0	0
$276$	−337.051	−0.0735076
$277$	−5446.87	−1.18148	−0.590742	−	0.806861i	$-0.701165\pi$
$277$	−5446.87	−1.18148	−0.590742	+	0.806861i	$0.701165\pi$
$278$	−1795.28	−0.387316
$279$	−5179.58	−1.11145
$280$	0	0
$281$	2126.76	0.451501	0.225751	−	0.974185i	$-0.427517\pi$
$281$	2126.76	0.451501	0.225751	+	0.974185i	$0.427517\pi$
$282$	1564.88	0.330452
$283$	3426.38	0.719707	0.359853	−	0.933009i	$-0.382827\pi$
$283$	3426.38	0.719707	0.359853	+	0.933009i	$0.382827\pi$
$284$	438.009	0.0915178
$285$	0	0
$286$	532.991	0.110197
$287$	−1218.89	−0.250693
$288$	−4504.14	−0.921558
$289$	2884.42	0.587099
$290$	0	0
$291$	−541.222	−0.109028
$292$	−4093.79	−0.820448
$293$	1749.82	0.348894	0.174447	−	0.984667i	$-0.444186\pi$
$293$	1749.82	0.348894	0.174447	+	0.984667i	$0.444186\pi$
$294$	145.218	0.0288071
$295$	0	0
$296$	−28.7934	−0.00565399
$297$	−312.904	−0.0611330
$298$	−761.176	−0.147966
$299$	2114.65	0.409008
$300$	0	0
$301$	−119.241	−0.0228338
$302$	610.026	0.116235
$303$	−1481.16	−0.280826
$304$	−2955.65	−0.557625
$305$	0	0
$306$	−8087.92	−1.51097
$307$	−7970.33	−1.48173	−0.740864	−	0.671655i	$-0.765584\pi$
$307$	−7970.33	−1.48173	−0.740864	+	0.671655i	$0.765584\pi$
$308$	200.655	0.0371214
$309$	1236.78	0.227695
$310$	0	0
$311$	−2560.72	−0.466898	−0.233449	−	0.972369i	$-0.575001\pi$
$311$	−2560.72	−0.466898	−0.233449	+	0.972369i	$0.575001\pi$
$312$	−252.592	−0.0458339
$313$	4861.11	0.877848	0.438924	−	0.898524i	$-0.355360\pi$
$313$	4861.11	0.877848	0.438924	+	0.898524i	$0.355360\pi$
$314$	−3205.55	−0.576114
$315$	0	0
$316$	−4564.16	−0.812513
$317$	−8166.16	−1.44687	−0.723434	−	0.690394i	$-0.757437\pi$
$317$	−8166.16	−1.44687	−0.723434	+	0.690394i	$0.757437\pi$
$318$	1900.03	0.335057
$319$	−1858.36	−0.326169
$320$	0	0
$321$	−1004.70	−0.174694
$322$	2330.85	0.403395
$323$	−3263.32	−0.562155
$324$	2784.35	0.477427
$325$	0	0
$326$	8255.79	1.40259
$327$	−1874.29	−0.316968
$328$	2336.89	0.393394
$329$	−3696.20	−0.619386
$330$	0	0
$331$	2974.89	0.494002	0.247001	−	0.969015i	$-0.420555\pi$
$331$	2974.89	0.494002	0.247001	+	0.969015i	$0.420555\pi$
$332$	5131.68	0.848306
$333$	56.3766	0.00927753
$334$	3762.30	0.616359
$335$	0	0
$336$	−476.000	−0.0772855
$337$	−3496.34	−0.565157	−0.282578	−	0.959244i	$-0.591190\pi$
$337$	−3496.34	−0.565157	−0.282578	+	0.959244i	$0.591190\pi$
$338$	5949.94	0.957497
$339$	201.410	0.0322686
$340$	0	0
$341$	−1361.59	−0.216230
$342$	3384.90	0.535188
$343$	−343.000	−0.0539949
$344$	228.613	0.0358314
$345$	0	0
$346$	−3071.80	−0.477287
$347$	−3959.08	−0.612491	−0.306246	−	0.951953i	$-0.599073\pi$
$347$	−3959.08	−0.612491	−0.306246	+	0.951953i	$0.599073\pi$
$348$	−949.213	−0.146216
$349$	5581.65	0.856099	0.428050	−	0.903755i	$-0.359201\pi$
$349$	5581.65	0.856099	0.428050	+	0.903755i	$0.359201\pi$
$350$	0	0
$351$	1002.74	0.152485
$352$	−1184.03	−0.179287
$353$	9896.43	1.49216	0.746082	−	0.665854i	$-0.231933\pi$
$353$	9896.43	1.49216	0.746082	+	0.665854i	$0.231933\pi$
$354$	−1905.54	−0.286097
$355$	0	0
$356$	−2953.38	−0.439687
$357$	−525.550	−0.0779133
$358$	11773.5	1.73813
$359$	11917.6	1.75205	0.876025	−	0.482265i	$-0.160186\pi$
$359$	11917.6	1.75205	0.876025	+	0.482265i	$0.160186\pi$
$360$	0	0
$361$	−5493.26	−0.800883
$362$	−5003.92	−0.726519
$363$	1091.10	0.157762
$364$	−643.025	−0.0925926
$365$	0	0
$366$	423.702	0.0605117
$367$	7101.58	1.01008	0.505040	−	0.863096i	$-0.331478\pi$
$367$	7101.58	1.01008	0.505040	+	0.863096i	$0.331478\pi$
$368$	−7640.12	−1.08225
$369$	−4575.56	−0.645513
$370$	0	0
$371$	−4487.80	−0.628018
$372$	−695.475	−0.0969319
$373$	−294.316	−0.0408555	−0.0204277	−	0.999791i	$-0.506503\pi$
$373$	−294.316	−0.0408555	−0.0204277	+	0.999791i	$0.506503\pi$
$374$	−2126.12	−0.293955
$375$	0	0
$376$	7086.45	0.971957
$377$	5955.34	0.813569
$378$	1105.26	0.150392
$379$	−9436.57	−1.27896	−0.639478	−	0.768810i	$-0.720849\pi$
$379$	−9436.57	−1.27896	−0.639478	+	0.768810i	$0.720849\pi$
$380$	0	0
$381$	−1417.53	−0.190610
$382$	5535.70	0.741442
$383$	3160.82	0.421699	0.210849	−	0.977519i	$-0.432377\pi$
$383$	3160.82	0.421699	0.210849	+	0.977519i	$0.432377\pi$
$384$	1291.41	0.171620
$385$	0	0
$386$	−3407.93	−0.449376
$387$	−447.617	−0.0587950
$388$	2641.55	0.345629
$389$	7822.76	1.01961	0.509807	−	0.860289i	$-0.329717\pi$
$389$	7822.76	1.01961	0.509807	+	0.860289i	$0.329717\pi$
$390$	0	0
$391$	−8435.43	−1.09104
$392$	657.609	0.0847302
$393$	−758.176	−0.0973153
$394$	1253.73	0.160309
$395$	0	0
$396$	753.234	0.0955844
$397$	7935.18	1.00316	0.501581	−	0.865111i	$-0.332752\pi$
$397$	7935.18	1.00316	0.501581	+	0.865111i	$0.332752\pi$
$398$	−9823.87	−1.23725
$399$	219.950	0.0275971
$400$	0	0
$401$	−488.380	−0.0608193	−0.0304097	−	0.999538i	$-0.509681\pi$
$401$	−488.380	−0.0608193	−0.0304097	+	0.999538i	$0.509681\pi$
$402$	−1418.98	−0.176050
$403$	4363.39	0.539345
$404$	7229.09	0.890249
$405$	0	0
$406$	6564.20	0.802403
$407$	14.8201	0.00180492
$408$	1007.60	0.122264
$409$	11230.6	1.35775	0.678874	−	0.734254i	$-0.262468\pi$
$409$	11230.6	1.35775	0.678874	+	0.734254i	$0.262468\pi$
$410$	0	0
$411$	−340.457	−0.0408601
$412$	−6036.34	−0.721818
$413$	4500.82	0.536249
$414$	8749.70	1.03871
$415$	0	0
$416$	3794.38	0.447199
$417$	−437.915	−0.0514263
$418$	889.811	0.104120
$419$	−7369.62	−0.859259	−0.429629	−	0.903005i	$-0.641356\pi$
$419$	−7369.62	−0.859259	−0.429629	+	0.903005i	$0.641356\pi$
$420$	0	0
$421$	11972.5	1.38599	0.692997	−	0.720941i	$-0.256290\pi$
$421$	11972.5	1.38599	0.692997	+	0.720941i	$0.256290\pi$
$422$	3519.26	0.405959
$423$	−13875.1	−1.59487
$424$	8604.12	0.985503
$425$	0	0
$426$	312.813	0.0355770
$427$	−1000.77	−0.113421
$428$	4903.63	0.553799
$429$	130.010	0.0146316
$430$	0	0
$431$	−3568.60	−0.398825	−0.199412	−	0.979916i	$-0.563903\pi$
$431$	−3568.60	−0.398825	−0.199412	+	0.979916i	$0.563903\pi$
$432$	−3622.84	−0.403482
$433$	−2291.60	−0.254335	−0.127168	−	0.991881i	$-0.540589\pi$
$433$	−2291.60	−0.254335	−0.127168	+	0.991881i	$0.540589\pi$
$434$	4809.49	0.531943
$435$	0	0
$436$	9147.85	1.00482
$437$	3530.34	0.386451
$438$	−2923.66	−0.318945
$439$	−7329.66	−0.796870	−0.398435	−	0.917197i	$-0.630446\pi$
$439$	−7329.66	−0.796870	−0.398435	+	0.917197i	$0.630446\pi$
$440$	0	0
$441$	−1287.58	−0.139032
$442$	6813.44	0.733218
$443$	−8297.38	−0.889889	−0.444944	−	0.895558i	$-0.646777\pi$
$443$	−8297.38	−0.889889	−0.444944	+	0.895558i	$0.646777\pi$
$444$	7.56981	0.000809116 0
$445$	0	0
$446$	4452.14	0.472679
$447$	−185.670	−0.0196463
$448$	−296.436	−0.0312618
$449$	9758.62	1.02570	0.512848	−	0.858479i	$-0.328590\pi$
$449$	9758.62	1.02570	0.512848	+	0.858479i	$0.328590\pi$
$450$	0	0
$451$	−1202.81	−0.125583
$452$	−983.021	−0.102295
$453$	148.801	0.0154333
$454$	4879.47	0.504416
$455$	0	0
$456$	−421.693	−0.0433061
$457$	11745.0	1.20220	0.601102	−	0.799172i	$-0.294728\pi$
$457$	11745.0	1.20220	0.601102	+	0.799172i	$0.294728\pi$
$458$	−11091.4	−1.13158
$459$	−3999.97	−0.406759
$460$	0	0
$461$	−10748.6	−1.08593	−0.542963	−	0.839756i	$-0.682698\pi$
$461$	−10748.6	−1.08593	−0.542963	+	0.839756i	$0.682698\pi$
$462$	143.302	0.0144308
$463$	9862.51	0.989957	0.494978	−	0.868905i	$-0.335176\pi$
$463$	9862.51	0.989957	0.494978	+	0.868905i	$0.335176\pi$
$464$	−21516.3	−2.15274
$465$	0	0
$466$	−10554.0	−1.04915
$467$	4660.78	0.461831	0.230916	−	0.972974i	$-0.425828\pi$
$467$	4660.78	0.461831	0.230916	+	0.972974i	$0.425828\pi$
$468$	−2413.83	−0.238418
$469$	3351.58	0.329982
$470$	0	0
$471$	−781.915	−0.0764941
$472$	−8629.10	−0.841497
$473$	−117.668	−0.0114384
$474$	−3259.58	−0.315860
$475$	0	0
$476$	2565.05	0.246994
$477$	−16846.6	−1.61709
$478$	17413.2	1.66624
$479$	−16293.2	−1.55419	−0.777094	−	0.629385i	$-0.783307\pi$
$479$	−16293.2	−1.55419	−0.777094	+	0.629385i	$0.783307\pi$
$480$	0	0
$481$	−47.4928	−0.00450205
$482$	13093.9	1.23737
$483$	568.553	0.0535612
$484$	−5325.33	−0.500124
$485$	0	0
$486$	6251.63	0.583498
$487$	3515.00	0.327063	0.163531	−	0.986538i	$-0.447711\pi$
$487$	3515.00	0.327063	0.163531	+	0.986538i	$0.447711\pi$
$488$	1918.70	0.177983
$489$	2013.80	0.186231
$490$	0	0
$491$	−2516.79	−0.231326	−0.115663	−	0.993288i	$-0.536899\pi$
$491$	−2516.79	−0.231326	−0.115663	+	0.993288i	$0.536899\pi$
$492$	−614.371	−0.0562967
$493$	−23756.1	−2.17023
$494$	−2851.51	−0.259708
$495$	0	0
$496$	−15764.7	−1.42713
$497$	−738.853	−0.0666842
$498$	3664.89	0.329775
$499$	−8747.48	−0.784751	−0.392376	−	0.919805i	$-0.628347\pi$
$499$	−8747.48	−0.784751	−0.392376	+	0.919805i	$0.628347\pi$
$500$	0	0
$501$	917.720	0.0818377
$502$	−22884.9	−2.03467
$503$	−11426.1	−1.01285	−0.506426	−	0.862284i	$-0.669034\pi$
$503$	−11426.1	−1.01285	−0.506426	+	0.862284i	$0.669034\pi$
$504$	2468.58	0.218173
$505$	0	0
$506$	2300.09	0.202078
$507$	1451.34	0.127133
$508$	6918.54	0.604254
$509$	−8078.44	−0.703478	−0.351739	−	0.936098i	$-0.614410\pi$
$509$	−8078.44	−0.703478	−0.351739	+	0.936098i	$0.614410\pi$
$510$	0	0
$511$	6905.58	0.597818
$512$	−5122.12	−0.442125
$513$	1674.04	0.144075
$514$	−23979.3	−2.05775
$515$	0	0
$516$	−60.1026	−0.00512765
$517$	−3647.43	−0.310278
$518$	−52.3484	−0.00444026
$519$	−749.290	−0.0633723
$520$	0	0
$521$	7226.14	0.607645	0.303822	−	0.952729i	$-0.401737\pi$
$521$	7226.14	0.607645	0.303822	+	0.952729i	$0.401737\pi$
$522$	24641.1	2.06612
$523$	−9333.06	−0.780318	−0.390159	−	0.920748i	$-0.627580\pi$
$523$	−9333.06	−0.780318	−0.390159	+	0.920748i	$0.627580\pi$
$524$	3700.43	0.308500
$525$	0	0
$526$	10736.3	0.889974
$527$	−17405.8	−1.43872
$528$	−469.719	−0.0387157
$529$	−3041.35	−0.249967
$530$	0	0
$531$	16895.5	1.38080
$532$	−1073.51	−0.0874859
$533$	3854.55	0.313244
$534$	−2109.21	−0.170926
$535$	0	0
$536$	−6425.73	−0.517816
$537$	2871.87	0.230782
$538$	−23389.9	−1.87437
$539$	−338.474	−0.0270484
$540$	0	0
$541$	15263.1	1.21296	0.606482	−	0.795097i	$-0.292580\pi$
$541$	15263.1	1.21296	0.606482	+	0.795097i	$0.292580\pi$
$542$	−27337.8	−2.16653
$543$	−1220.58	−0.0964644
$544$	−15135.9	−1.19292
$545$	0	0
$546$	−459.229	−0.0359949
$547$	13226.0	1.03382	0.516912	−	0.856039i	$-0.327082\pi$
$547$	13226.0	1.03382	0.516912	+	0.856039i	$0.327082\pi$
$548$	1661.67	0.129531
$549$	−3756.76	−0.292049
$550$	0	0
$551$	9942.24	0.768700
$552$	−1090.04	−0.0840496
$553$	7699.03	0.592036
$554$	18985.9	1.45602
$555$	0	0
$556$	2137.33	0.163027
$557$	−6993.63	−0.532010	−0.266005	−	0.963972i	$-0.585704\pi$
$557$	−6993.63	−0.532010	−0.266005	+	0.963972i	$0.585704\pi$
$558$	18054.2	1.36971
$559$	377.082	0.0285311
$560$	0	0
$561$	−518.616	−0.0390302
$562$	−7413.14	−0.556413
$563$	−392.197	−0.0293590	−0.0146795	−	0.999892i	$-0.504673\pi$
$563$	−392.197	−0.0293590	−0.0146795	+	0.999892i	$0.504673\pi$
$564$	−1863.04	−0.139092
$565$	0	0
$566$	−11943.2	−0.886940
$567$	−4696.77	−0.347876
$568$	1416.55	0.104643
$569$	8811.72	0.649221	0.324610	−	0.945848i	$-0.394767\pi$
$569$	8811.72	0.649221	0.324610	+	0.945848i	$0.394767\pi$
$570$	0	0
$571$	−24775.6	−1.81581	−0.907905	−	0.419175i	$-0.862319\pi$
$571$	−24775.6	−1.81581	−0.907905	+	0.419175i	$0.862319\pi$
$572$	−634.541	−0.0463837
$573$	1350.30	0.0984458
$574$	4248.63	0.308945
$575$	0	0
$576$	−1112.78	−0.0804964
$577$	8850.62	0.638572	0.319286	−	0.947658i	$-0.396557\pi$
$577$	8850.62	0.638572	0.319286	+	0.947658i	$0.396557\pi$
$578$	−10054.1	−0.723520
$579$	−831.281	−0.0596664
$580$	0	0
$581$	−8656.35	−0.618117
$582$	1886.51	0.134362
$583$	−4428.58	−0.314602
$584$	−13239.6	−0.938112
$585$	0	0
$586$	−6099.28	−0.429964
$587$	46.0232	0.00323608	0.00161804	−	0.999999i	$-0.499485\pi$
$587$	46.0232	0.00323608	0.00161804	+	0.999999i	$0.499485\pi$
$588$	−172.886	−0.0121253
$589$	7284.54	0.509600
$590$	0	0
$591$	305.815	0.0212852
$592$	171.589	0.0119126
$593$	2729.93	0.189047	0.0945235	−	0.995523i	$-0.469867\pi$
$593$	2729.93	0.189047	0.0945235	+	0.995523i	$0.469867\pi$
$594$	1090.67	0.0753381
$595$	0	0
$596$	906.200	0.0622809
$597$	−2396.29	−0.164277
$598$	−7370.94	−0.504047
$599$	−5505.07	−0.375511	−0.187756	−	0.982216i	$-0.560121\pi$
$599$	−5505.07	−0.375511	−0.187756	+	0.982216i	$0.560121\pi$
$600$	0	0
$601$	−7446.97	−0.505438	−0.252719	−	0.967540i	$-0.581325\pi$
$601$	−7446.97	−0.505438	−0.252719	+	0.967540i	$0.581325\pi$
$602$	415.634	0.0281395
$603$	12581.4	0.849674
$604$	−726.253	−0.0489252
$605$	0	0
$606$	5162.80	0.346080
$607$	24071.4	1.60960	0.804799	−	0.593547i	$-0.202273\pi$
$607$	24071.4	1.60960	0.804799	+	0.593547i	$0.202273\pi$
$608$	6334.59	0.422536
$609$	1601.17	0.106540
$610$	0	0
$611$	11688.7	0.773932
$612$	9628.88	0.635988
$613$	4108.61	0.270710	0.135355	−	0.990797i	$-0.456782\pi$
$613$	4108.61	0.270710	0.135355	+	0.990797i	$0.456782\pi$
$614$	27781.8	1.82603
$615$	0	0
$616$	648.932	0.0424451
$617$	−3542.46	−0.231141	−0.115571	−	0.993299i	$-0.536870\pi$
$617$	−3542.46	−0.231141	−0.115571	+	0.993299i	$0.536870\pi$
$618$	−4310.97	−0.280603
$619$	6484.81	0.421077	0.210538	−	0.977586i	$-0.432478\pi$
$619$	6484.81	0.421077	0.210538	+	0.977586i	$0.432478\pi$
$620$	0	0
$621$	4327.26	0.279625
$622$	8925.79	0.575388
$623$	4981.88	0.320377
$624$	1505.28	0.0965693
$625$	0	0
$626$	−16944.1	−1.08183
$627$	217.047	0.0138246
$628$	3816.29	0.242495
$629$	189.451	0.0120094
$630$	0	0
$631$	3250.84	0.205094	0.102547	−	0.994728i	$-0.467301\pi$
$631$	3250.84	0.205094	0.102547	+	0.994728i	$0.467301\pi$
$632$	−14760.8	−0.929038
$633$	858.436	0.0539017
$634$	28464.4	1.78307
$635$	0	0
$636$	−2262.03	−0.141031
$637$	1084.68	0.0674674
$638$	6477.58	0.401959
$639$	−2773.56	−0.171706
$640$	0	0
$641$	2800.61	0.172570	0.0862852	−	0.996270i	$-0.472500\pi$
$641$	2800.61	0.172570	0.0862852	+	0.996270i	$0.472500\pi$
$642$	3502.03	0.215287
$643$	−18910.6	−1.15982	−0.579908	−	0.814682i	$-0.696911\pi$
$643$	−18910.6	−1.15982	−0.579908	+	0.814682i	$0.696911\pi$
$644$	−2774.94	−0.169795
$645$	0	0
$646$	11374.8	0.692780
$647$	24522.7	1.49009	0.745043	−	0.667016i	$-0.232429\pi$
$647$	24522.7	1.49009	0.745043	+	0.667016i	$0.232429\pi$
$648$	9004.77	0.545897
$649$	4441.43	0.268631
$650$	0	0
$651$	1173.16	0.0706293
$652$	−9828.74	−0.590373
$653$	15299.6	0.916875	0.458438	−	0.888727i	$-0.348409\pi$
$653$	15299.6	0.916875	0.458438	+	0.888727i	$0.348409\pi$
$654$	6533.12	0.390619
$655$	0	0
$656$	−13926.3	−0.828857
$657$	25922.7	1.53933
$658$	12883.7	0.763309
$659$	−2203.13	−0.130230	−0.0651151	−	0.997878i	$-0.520741\pi$
$659$	−2203.13	−0.130230	−0.0651151	+	0.997878i	$0.520741\pi$
$660$	0	0
$661$	−3162.36	−0.186084	−0.0930421	−	0.995662i	$-0.529659\pi$
$661$	−3162.36	−0.186084	−0.0930421	+	0.995662i	$0.529659\pi$
$662$	−10369.4	−0.608790
$663$	1661.97	0.0973538
$664$	16596.2	0.969965
$665$	0	0
$666$	−196.509	−0.0114333
$667$	25699.9	1.49191
$668$	−4479.12	−0.259435
$669$	1085.99	0.0627605
$670$	0	0
$671$	−987.565	−0.0568175
$672$	1020.17	0.0585624
$673$	4443.07	0.254484	0.127242	−	0.991872i	$-0.459387\pi$
$673$	4443.07	0.254484	0.127242	+	0.991872i	$0.459387\pi$
$674$	12187.0	0.696479
$675$	0	0
$676$	−7083.56	−0.403025
$677$	−4456.32	−0.252984	−0.126492	−	0.991968i	$-0.540372\pi$
$677$	−4456.32	−0.252984	−0.126492	+	0.991968i	$0.540372\pi$
$678$	−702.044	−0.0397667
$679$	−4455.87	−0.251842
$680$	0	0
$681$	1190.23	0.0669743
$682$	4746.03	0.266474
$683$	10046.8	0.562858	0.281429	−	0.959582i	$-0.409192\pi$
$683$	10046.8	0.562858	0.281429	+	0.959582i	$0.409192\pi$
$684$	−4029.81	−0.225269
$685$	0	0
$686$	1195.58	0.0665414
$687$	−2705.46	−0.150247
$688$	−1362.38	−0.0754944
$689$	14191.9	0.784717
$690$	0	0
$691$	31811.2	1.75131	0.875655	−	0.482938i	$-0.160430\pi$
$691$	31811.2	1.75131	0.875655	+	0.482938i	$0.160430\pi$
$692$	3657.06	0.200897
$693$	−1270.59	−0.0696474
$694$	13800.0	0.754812
$695$	0	0
$696$	−3069.81	−0.167185
$697$	−15376.0	−0.835590
$698$	−19455.7	−1.05503
$699$	−2574.39	−0.139302
$700$	0	0
$701$	−13907.2	−0.749312	−0.374656	−	0.927164i	$-0.622239\pi$
$701$	−13907.2	−0.749312	−0.374656	+	0.927164i	$0.622239\pi$
$702$	−3495.20	−0.187917
$703$	−79.2877	−0.00425376
$704$	−292.524	−0.0156604
$705$	0	0
$706$	−34495.5	−1.83889
$707$	−12194.3	−0.648678
$708$	2268.60	0.120423
$709$	−228.952	−0.0121276	−0.00606381	−	0.999982i	$-0.501930\pi$
$709$	−228.952	−0.0121276	−0.00606381	+	0.999982i	$0.501930\pi$
$710$	0	0
$711$	28901.1	1.52444
$712$	−9551.40	−0.502744
$713$	18830.0	0.989043
$714$	1831.88	0.0960176
$715$	0	0
$716$	−14016.7	−0.731606
$717$	4247.53	0.221237
$718$	−41540.5	−2.15916
$719$	36162.2	1.87569	0.937846	−	0.347052i	$-0.112817\pi$
$719$	36162.2	1.87569	0.937846	+	0.347052i	$0.112817\pi$
$720$	0	0
$721$	10182.4	0.525952
$722$	19147.6	0.986979
$723$	3193.93	0.164293
$724$	5957.30	0.305803
$725$	0	0
$726$	−3803.19	−0.194421
$727$	−22268.3	−1.13602	−0.568010	−	0.823021i	$-0.692287\pi$
$727$	−22268.3	−1.13602	−0.568010	+	0.823021i	$0.692287\pi$
$728$	−2079.58	−0.105872
$729$	−16591.2	−0.842919
$730$	0	0
$731$	−1504.20	−0.0761077
$732$	−504.429	−0.0254703
$733$	2333.20	0.117570	0.0587848	−	0.998271i	$-0.481277\pi$
$733$	2333.20	0.117570	0.0587848	+	0.998271i	$0.481277\pi$
$734$	−24753.6	−1.24479
$735$	0	0
$736$	16374.4	0.820067
$737$	3307.35	0.165302
$738$	15948.8	0.795506
$739$	−4829.15	−0.240383	−0.120192	−	0.992751i	$-0.538351\pi$
$739$	−4829.15	−0.240383	−0.120192	+	0.992751i	$0.538351\pi$
$740$	0	0
$741$	−695.556	−0.0344830
$742$	15642.9	0.773947
$743$	25459.0	1.25707	0.628533	−	0.777783i	$-0.283656\pi$
$743$	25459.0	1.25707	0.628533	+	0.777783i	$0.283656\pi$
$744$	−2249.21	−0.110833
$745$	0	0
$746$	1025.88	0.0503488
$747$	−32494.8	−1.59160
$748$	2531.21	0.123730
$749$	−8271.66	−0.403525
$750$	0	0
$751$	−5707.08	−0.277303	−0.138651	−	0.990341i	$-0.544277\pi$
$751$	−5707.08	−0.277303	−0.138651	+	0.990341i	$0.544277\pi$
$752$	−42230.4	−2.04785
$753$	−5582.21	−0.270155
$754$	−20758.2	−1.00261
$755$	0	0
$756$	−1315.84	−0.0633023
$757$	1900.91	0.0912677	0.0456339	−	0.998958i	$-0.485469\pi$
$757$	1900.91	0.0912677	0.0456339	+	0.998958i	$0.485469\pi$
$758$	32892.6	1.57614
$759$	561.051	0.0268312
$760$	0	0
$761$	−11583.8	−0.551791	−0.275896	−	0.961188i	$-0.588974\pi$
$761$	−11583.8	−0.551791	−0.275896	+	0.961188i	$0.588974\pi$
$762$	4941.01	0.234900
$763$	−15431.0	−0.732162
$764$	−6590.40	−0.312084
$765$	0	0
$766$	−11017.5	−0.519686
$767$	−14233.1	−0.670051
$768$	−4213.37	−0.197965
$769$	−26059.7	−1.22202	−0.611012	−	0.791622i	$-0.709237\pi$
$769$	−26059.7	−1.22202	−0.611012	+	0.791622i	$0.709237\pi$
$770$	0	0
$771$	−5849.17	−0.273220
$772$	4057.24	0.189149
$773$	16213.6	0.754413	0.377206	−	0.926129i	$-0.376885\pi$
$773$	16213.6	0.754413	0.377206	+	0.926129i	$0.376885\pi$
$774$	1560.24	0.0724568
$775$	0	0
$776$	8542.92	0.395197
$777$	−12.7691	−0.000589561 0
$778$	−27267.4	−1.25653
$779$	6435.04	0.295968
$780$	0	0
$781$	−729.103	−0.0334051
$782$	29403.0	1.34456
$783$	12186.6	0.556209
$784$	−3918.90	−0.178521
$785$	0	0
$786$	2642.74	0.119928
$787$	1371.34	0.0621131	0.0310565	−	0.999518i	$-0.490113\pi$
$787$	1371.34	0.0621131	0.0310565	+	0.999518i	$0.490113\pi$
$788$	−1492.59	−0.0674765
$789$	2618.86	0.118167
$790$	0	0
$791$	1658.20	0.0745371
$792$	2436.01	0.109293
$793$	3164.78	0.141721
$794$	−27659.3	−1.23626
$795$	0	0
$796$	11695.6	0.520778
$797$	−7991.49	−0.355173	−0.177587	−	0.984105i	$-0.556829\pi$
$797$	−7991.49	−0.355173	−0.177587	+	0.984105i	$0.556829\pi$
$798$	−766.668	−0.0340097
$799$	−46626.5	−2.06449
$800$	0	0
$801$	18701.3	0.824943
$802$	1702.32	0.0749515
$803$	6814.47	0.299474
$804$	1689.33	0.0741022
$805$	0	0
$806$	−15209.3	−0.664669
$807$	−5705.38	−0.248871
$808$	23379.3	1.01792
$809$	−17661.4	−0.767542	−0.383771	−	0.923428i	$-0.625375\pi$
$809$	−17661.4	−0.767542	−0.383771	+	0.923428i	$0.625375\pi$
$810$	0	0
$811$	−24180.6	−1.04697	−0.523486	−	0.852034i	$-0.675369\pi$
$811$	−24180.6	−1.04697	−0.523486	+	0.852034i	$0.675369\pi$
$812$	−7814.85	−0.337743
$813$	−6668.38	−0.287663
$814$	−51.6576	−0.00222432
$815$	0	0
$816$	−6004.60	−0.257602
$817$	629.526	0.0269576
$818$	−39146.1	−1.67324
$819$	4071.76	0.173723
$820$	0	0
$821$	−23340.9	−0.992208	−0.496104	−	0.868263i	$-0.665237\pi$
$821$	−23340.9	−0.992208	−0.496104	+	0.868263i	$0.665237\pi$
$822$	1186.71	0.0503545
$823$	−20630.4	−0.873792	−0.436896	−	0.899512i	$-0.643922\pi$
$823$	−20630.4	−0.873792	−0.436896	+	0.899512i	$0.643922\pi$
$824$	−19521.9	−0.825337
$825$	0	0
$826$	−15688.3	−0.660854
$827$	−24113.7	−1.01393	−0.506963	−	0.861968i	$-0.669232\pi$
$827$	−24113.7	−1.01393	−0.506963	+	0.861968i	$0.669232\pi$
$828$	−10416.8	−0.437207
$829$	41738.9	1.74868	0.874338	−	0.485317i	$-0.161296\pi$
$829$	41738.9	1.74868	0.874338	+	0.485317i	$0.161296\pi$
$830$	0	0
$831$	4631.14	0.193324
$832$	937.432	0.0390620
$833$	−4326.85	−0.179972
$834$	1526.42	0.0633760
$835$	0	0
$836$	−1059.34	−0.0438256
$837$	8928.91	0.368732
$838$	25687.9	1.05892
$839$	30403.0	1.25105	0.625523	−	0.780205i	$-0.284886\pi$
$839$	30403.0	1.25105	0.625523	+	0.780205i	$0.284886\pi$
$840$	0	0
$841$	47987.8	1.96760
$842$	−41731.9	−1.70805
$843$	−1808.25	−0.0738784
$844$	−4189.77	−0.170874
$845$	0	0
$846$	48363.6	1.96545
$847$	8982.99	0.364415
$848$	−51274.7	−2.07639
$849$	−2913.24	−0.117764
$850$	0	0
$851$	−204.952	−0.00825579
$852$	−372.412	−0.0149749
$853$	−5900.43	−0.236843	−0.118421	−	0.992963i	$-0.537783\pi$
$853$	−5900.43	−0.236843	−0.118421	+	0.992963i	$0.537783\pi$
$854$	3488.33	0.139776
$855$	0	0
$856$	15858.7	0.633221
$857$	18226.2	0.726480	0.363240	−	0.931696i	$-0.381670\pi$
$857$	18226.2	0.726480	0.363240	+	0.931696i	$0.381670\pi$
$858$	−453.170	−0.0180314
$859$	−19944.2	−0.792186	−0.396093	−	0.918210i	$-0.629634\pi$
$859$	−19944.2	−0.792186	−0.396093	+	0.918210i	$0.629634\pi$
$860$	0	0
$861$	1036.35	0.0410205
$862$	12438.9	0.491497
$863$	−30830.3	−1.21608	−0.608038	−	0.793908i	$-0.708043\pi$
$863$	−30830.3	−1.21608	−0.608038	+	0.793908i	$0.708043\pi$
$864$	7764.53	0.305735
$865$	0	0
$866$	7987.70	0.313433
$867$	−2452.44	−0.0960662
$868$	−5725.83	−0.223903
$869$	7597.44	0.296577
$870$	0	0
$871$	−10598.8	−0.412317
$872$	29584.7	1.14893
$873$	−16726.8	−0.648471
$874$	−12305.5	−0.476248
$875$	0	0
$876$	3480.70	0.134249
$877$	45885.6	1.76676	0.883379	−	0.468659i	$-0.155263\pi$
$877$	45885.6	1.76676	0.883379	+	0.468659i	$0.155263\pi$
$878$	25548.6	0.982033
$879$	−1487.77	−0.0570889
$880$	0	0
$881$	41132.6	1.57298	0.786489	−	0.617605i	$-0.211897\pi$
$881$	41132.6	1.57298	0.786489	+	0.617605i	$0.211897\pi$
$882$	4488.05	0.171338
$883$	−19850.0	−0.756520	−0.378260	−	0.925699i	$-0.623477\pi$
$883$	−19850.0	−0.756520	−0.378260	+	0.925699i	$0.623477\pi$
$884$	−8111.58	−0.308622
$885$	0	0
$886$	28921.8	1.09667
$887$	−29029.3	−1.09888	−0.549441	−	0.835532i	$-0.685159\pi$
$887$	−29029.3	−1.09888	−0.549441	+	0.835532i	$0.685159\pi$
$888$	24.4812	0.000925154 0
$889$	−11670.5	−0.440288
$890$	0	0
$891$	−4634.80	−0.174267
$892$	−5300.40	−0.198958
$893$	19513.8	0.731248
$894$	647.181	0.0242114
$895$	0	0
$896$	10632.2	0.396425
$897$	−1797.96	−0.0669254
$898$	−34015.2	−1.26403
$899$	53029.4	1.96733
$900$	0	0
$901$	−56612.3	−2.09326
$902$	4192.57	0.154764
$903$	101.384	0.00373625
$904$	−3179.15	−0.116966
$905$	0	0
$906$	−518.668	−0.0190194
$907$	21029.1	0.769856	0.384928	−	0.922947i	$-0.374226\pi$
$907$	21029.1	0.769856	0.384928	+	0.922947i	$0.374226\pi$
$908$	−5809.14	−0.212316
$909$	−45776.0	−1.67029
$910$	0	0
$911$	−19225.5	−0.699198	−0.349599	−	0.936899i	$-0.613682\pi$
$911$	−19225.5	−0.699198	−0.349599	+	0.936899i	$0.613682\pi$
$912$	2513.01	0.0912433
$913$	−8542.13	−0.309642
$914$	−40938.9	−1.48155
$915$	0	0
$916$	13204.6	0.476300
$917$	−6242.05	−0.224788
$918$	13942.5	0.501276
$919$	21316.8	0.765154	0.382577	−	0.923924i	$-0.375037\pi$
$919$	21316.8	0.765154	0.382577	+	0.923924i	$0.375037\pi$
$920$	0	0
$921$	6776.68	0.242453
$922$	37465.9	1.33826
$923$	2336.50	0.0833229
$924$	−170.605	−0.00607412
$925$	0	0
$926$	−34377.3	−1.21999
$927$	38223.3	1.35428
$928$	46114.1	1.63122
$929$	19989.6	0.705959	0.352979	−	0.935631i	$-0.385169\pi$
$929$	19989.6	0.705959	0.352979	+	0.935631i	$0.385169\pi$
$930$	0	0
$931$	1810.84	0.0637465
$932$	12564.8	0.441603
$933$	2177.23	0.0763978
$934$	−16245.9	−0.569144
$935$	0	0
$936$	−7806.49	−0.272610
$937$	−55676.4	−1.94116	−0.970580	−	0.240779i	$-0.922597\pi$
$937$	−55676.4	−1.94116	−0.970580	+	0.240779i	$0.922597\pi$
$938$	−11682.4	−0.406658
$939$	−4133.10	−0.143641
$940$	0	0
$941$	−108.842	−0.00377062	−0.00188531	−	0.999998i	$-0.500600\pi$
$941$	−108.842	−0.00377062	−0.00188531	+	0.999998i	$0.500600\pi$
$942$	2725.48	0.0942686
$943$	16634.1	0.574422
$944$	51423.6	1.77298
$945$	0	0
$946$	410.150	0.0140963
$947$	7785.95	0.267169	0.133585	−	0.991037i	$-0.457351\pi$
$947$	7785.95	0.267169	0.133585	+	0.991037i	$0.457351\pi$
$948$	3880.62	0.132950
$949$	−21837.8	−0.746982
$950$	0	0
$951$	6943.18	0.236749
$952$	8295.55	0.282416
$953$	−41445.5	−1.40876	−0.704381	−	0.709822i	$-0.748776\pi$
$953$	−41445.5	−1.40876	−0.704381	+	0.709822i	$0.748776\pi$
$954$	58721.4	1.99285
$955$	0	0
$956$	−20730.9	−0.701345
$957$	1580.05	0.0533706
$958$	56792.5	1.91532
$959$	−2802.98	−0.0943825
$960$	0	0
$961$	9062.92	0.304217
$962$	165.543	0.00554817
$963$	−31050.8	−1.03904
$964$	−15588.7	−0.520826
$965$	0	0
$966$	−1981.78	−0.0660068
$967$	−39155.0	−1.30211	−0.651055	−	0.759030i	$-0.725673\pi$
$967$	−39155.0	−1.30211	−0.651055	+	0.759030i	$0.725673\pi$
$968$	−17222.4	−0.571849
$969$	2774.60	0.0919846
$970$	0	0
$971$	−43440.8	−1.43572	−0.717859	−	0.696189i	$-0.754878\pi$
$971$	−43440.8	−1.43572	−0.717859	+	0.696189i	$0.754878\pi$
$972$	−7442.74	−0.245603
$973$	−3605.35	−0.118789
$974$	−12252.0	−0.403061
$975$	0	0
$976$	−11434.2	−0.374999
$977$	−11297.8	−0.369957	−0.184978	−	0.982743i	$-0.559222\pi$
$977$	−11297.8	−0.369957	−0.184978	+	0.982743i	$0.559222\pi$
$978$	−7019.39	−0.229504
$979$	4916.15	0.160491
$980$	0	0
$981$	−57925.9	−1.88525
$982$	8772.66	0.285078
$983$	−10865.9	−0.352563	−0.176282	−	0.984340i	$-0.556407\pi$
$983$	−10865.9	−0.352563	−0.176282	+	0.984340i	$0.556407\pi$
$984$	−1986.91	−0.0643704
$985$	0	0
$986$	82805.5	2.67451
$987$	3142.65	0.101349
$988$	3394.80	0.109315
$989$	1627.28	0.0523199
$990$	0	0
$991$	13884.1	0.445048	0.222524	−	0.974927i	$-0.428570\pi$
$991$	13884.1	0.445048	0.222524	+	0.974927i	$0.428570\pi$
$992$	33787.1	1.08139
$993$	−2529.36	−0.0808328
$994$	2575.38	0.0821792
$995$	0	0
$996$	−4363.15	−0.138807
$997$	−31665.7	−1.00588	−0.502940	−	0.864321i	$-0.667748\pi$
$997$	−31665.7	−1.00588	−0.502940	+	0.864321i	$0.667748\pi$
$998$	30490.7	0.967099
$999$	−97.1857	−0.00307790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.a.f.1.1		3
3.2	odd	2		1575.4.a.ba.1.3		3
5.2	odd	4		175.4.b.e.99.2		6
5.3	odd	4		175.4.b.e.99.5		6
5.4	even	2		35.4.a.c.1.3	✓	3
7.6	odd	2		1225.4.a.y.1.1		3
15.14	odd	2		315.4.a.p.1.1		3
20.19	odd	2		560.4.a.u.1.2		3
35.4	even	6		245.4.e.m.226.1		6
35.9	even	6		245.4.e.m.116.1		6
35.19	odd	6		245.4.e.n.116.1		6
35.24	odd	6		245.4.e.n.226.1		6
35.34	odd	2		245.4.a.l.1.3		3
40.19	odd	2		2240.4.a.bv.1.2		3
40.29	even	2		2240.4.a.bt.1.2		3
105.104	even	2		2205.4.a.bm.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.3	✓	3	5.4	even	2
175.4.a.f.1.1		3	1.1	even	1	trivial
175.4.b.e.99.2		6	5.2	odd	4
175.4.b.e.99.5		6	5.3	odd	4
245.4.a.l.1.3		3	35.34	odd	2
245.4.e.m.116.1		6	35.9	even	6
245.4.e.m.226.1		6	35.4	even	6
245.4.e.n.116.1		6	35.19	odd	6
245.4.e.n.226.1		6	35.24	odd	6
315.4.a.p.1.1		3	15.14	odd	2
560.4.a.u.1.2		3	20.19	odd	2
1225.4.a.y.1.1		3	7.6	odd	2
1575.4.a.ba.1.3		3	3.2	odd	2
2205.4.a.bm.1.1		3	105.104	even	2
2240.4.a.bt.1.2		3	40.29	even	2
2240.4.a.bv.1.2		3	40.19	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q-3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} +2.96363 q^{6} -7.00000 q^{7} +13.4206 q^{8} -26.2771 q^{9} +O(q^{10})\)	\(q-3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} +2.96363 q^{6} -7.00000 q^{7} +13.4206 q^{8} -26.2771 q^{9} -6.90764 q^{11} -3.52829 q^{12} +22.1364 q^{13} +24.3996 q^{14} -79.9776 q^{16} -88.3030 q^{17} +91.5928 q^{18} +36.9560 q^{19} +5.95167 q^{21} +24.0776 q^{22} +95.5283 q^{23} -11.4107 q^{24} -77.1598 q^{26} +45.2982 q^{27} -29.0483 q^{28} +269.029 q^{29} +197.114 q^{31} +171.409 q^{32} +5.87314 q^{33} +307.793 q^{34} -109.044 q^{36} -2.14546 q^{37} -128.816 q^{38} -18.8212 q^{39} +174.127 q^{41} -20.7454 q^{42} +17.0345 q^{43} -28.6650 q^{44} -332.978 q^{46} +528.029 q^{47} +68.0000 q^{48} +49.0000 q^{49} +75.0786 q^{51} +91.8608 q^{52} +641.114 q^{53} -157.894 q^{54} -93.9441 q^{56} -31.4214 q^{57} -937.742 q^{58} -642.975 q^{59} +142.967 q^{61} -687.070 q^{62} +183.940 q^{63} +42.3480 q^{64} -20.4717 q^{66} -478.797 q^{67} -366.436 q^{68} -81.2218 q^{69} +105.550 q^{71} -352.654 q^{72} -986.512 q^{73} +7.47834 q^{74} +153.358 q^{76} +48.3534 q^{77} +65.6042 q^{78} -1099.86 q^{79} +670.967 q^{81} -606.947 q^{82} +1236.62 q^{83} +24.6980 q^{84} -59.3763 q^{86} -228.739 q^{87} -92.7045 q^{88} -711.698 q^{89} -154.955 q^{91} +396.420 q^{92} -167.594 q^{93} -1840.52 q^{94} -145.739 q^{96} +636.553 q^{97} -170.797 q^{98} +181.513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9	\( 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9} - 74 q^{11} + 152 q^{12} - 44 q^{13} - 21 q^{14} - 79 q^{16} + 52 q^{17} + 411 q^{18} + 168 q^{19} + 14 q^{21} - 184 q^{22} + 124 q^{23} + 420 q^{24} - 446 q^{26} - 170 q^{27} - 91 q^{28} + 332 q^{29} + 320 q^{31} + 183 q^{32} + 106 q^{33} + 582 q^{34} + 181 q^{36} + 54 q^{37} + 460 q^{38} - 982 q^{39} + 362 q^{41} - 168 q^{42} + 16 q^{43} - 264 q^{44} - 336 q^{46} + 730 q^{47} + 204 q^{48} + 147 q^{49} - 1178 q^{51} - 1202 q^{52} - 110 q^{53} - 180 q^{54} - 105 q^{56} + 956 q^{57} - 450 q^{58} - 180 q^{59} + 1222 q^{61} - 464 q^{62} - 567 q^{63} - 391 q^{64} - 532 q^{66} - 204 q^{67} - 918 q^{68} - 716 q^{69} - 136 q^{71} - 765 q^{72} - 310 q^{73} + 502 q^{74} + 1796 q^{76} + 518 q^{77} - 3788 q^{78} - 1034 q^{79} + 2283 q^{81} + 6 q^{82} + 1660 q^{83} - 1064 q^{84} + 764 q^{86} + 1574 q^{87} + 20 q^{88} + 242 q^{89} + 308 q^{91} - 96 q^{92} - 1376 q^{93} - 1108 q^{94} - 3156 q^{96} - 100 q^{97} + 147 q^{98} - 3488 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9 - 74 * q^11 + 152 * q^12 - 44 * q^13 - 21 * q^14 - 79 * q^16 + 52 * q^17 + 411 * q^18 + 168 * q^19 + 14 * q^21 - 184 * q^22 + 124 * q^23 + 420 * q^24 - 446 * q^26 - 170 * q^27 - 91 * q^28 + 332 * q^29 + 320 * q^31 + 183 * q^32 + 106 * q^33 + 582 * q^34 + 181 * q^36 + 54 * q^37 + 460 * q^38 - 982 * q^39 + 362 * q^41 - 168 * q^42 + 16 * q^43 - 264 * q^44 - 336 * q^46 + 730 * q^47 + 204 * q^48 + 147 * q^49 - 1178 * q^51 - 1202 * q^52 - 110 * q^53 - 180 * q^54 - 105 * q^56 + 956 * q^57 - 450 * q^58 - 180 * q^59 + 1222 * q^61 - 464 * q^62 - 567 * q^63 - 391 * q^64 - 532 * q^66 - 204 * q^67 - 918 * q^68 - 716 * q^69 - 136 * q^71 - 765 * q^72 - 310 * q^73 + 502 * q^74 + 1796 * q^76 + 518 * q^77 - 3788 * q^78 - 1034 * q^79 + 2283 * q^81 + 6 * q^82 + 1660 * q^83 - 1064 * q^84 + 764 * q^86 + 1574 * q^87 + 20 * q^88 + 242 * q^89 + 308 * q^91 - 96 * q^92 - 1376 * q^93 - 1108 * q^94 - 3156 * q^96 - 100 * q^97 + 147 * q^98 - 3488 * q^99

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