LMFDB - Embedded newform 6025.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.31056073.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 $ x^7 - 3x^6 - 3x^5 + 11x^4 + x^3 - 9x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.60363$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.60363 q^{2} -0.980039 q^{3} +4.77887 q^{4} -2.55166 q^{6} +1.30586 q^{7} +7.23513 q^{8} -2.03952 q^{9} +O(q^{10})$	\(q+2.60363 q^{2} -0.980039 q^{3} +4.77887 q^{4} -2.55166 q^{6} +1.30586 q^{7} +7.23513 q^{8} -2.03952 q^{9} -3.27094 q^{11} -4.68348 q^{12} -4.30649 q^{13} +3.39998 q^{14} +9.27984 q^{16} +1.02456 q^{17} -5.31016 q^{18} -7.01250 q^{19} -1.27980 q^{21} -8.51631 q^{22} -0.835873 q^{23} -7.09071 q^{24} -11.2125 q^{26} +4.93893 q^{27} +6.24054 q^{28} -1.11761 q^{29} -3.97344 q^{31} +9.69098 q^{32} +3.20565 q^{33} +2.66758 q^{34} -9.74661 q^{36} +11.3098 q^{37} -18.2579 q^{38} +4.22053 q^{39} +1.22869 q^{41} -3.33211 q^{42} -10.8406 q^{43} -15.6314 q^{44} -2.17630 q^{46} +0.151820 q^{47} -9.09461 q^{48} -5.29473 q^{49} -1.00411 q^{51} -20.5801 q^{52} -3.02053 q^{53} +12.8591 q^{54} +9.44808 q^{56} +6.87252 q^{57} -2.90984 q^{58} -4.15373 q^{59} +5.62714 q^{61} -10.3454 q^{62} -2.66334 q^{63} +6.67199 q^{64} +8.34632 q^{66} -12.9934 q^{67} +4.89626 q^{68} +0.819188 q^{69} -11.2862 q^{71} -14.7562 q^{72} -11.7148 q^{73} +29.4464 q^{74} -33.5118 q^{76} -4.27140 q^{77} +10.9887 q^{78} -1.66517 q^{79} +1.27823 q^{81} +3.19906 q^{82} +2.34322 q^{83} -6.11597 q^{84} -28.2250 q^{86} +1.09530 q^{87} -23.6657 q^{88} +18.1099 q^{89} -5.62368 q^{91} -3.99453 q^{92} +3.89413 q^{93} +0.395283 q^{94} -9.49754 q^{96} +7.17873 q^{97} -13.7855 q^{98} +6.67116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.60363	1.84104	0.920521	−	0.390694i	$-0.127765\pi$
$2$	2.60363	1.84104	0.920521	+	0.390694i	$0.127765\pi$
$3$	−0.980039	−0.565826	−0.282913	−	0.959146i	$-0.591301\pi$
$3$	−0.980039	−0.565826	−0.282913	+	0.959146i	$0.591301\pi$
$4$	4.77887	2.38943
$5$	0	0
$5$	0	0
$6$	−2.55166	−1.04171
$7$	1.30586	0.493569	0.246785	−	0.969070i	$-0.420626\pi$
$7$	1.30586	0.493569	0.246785	+	0.969070i	$0.420626\pi$
$8$	7.23513	2.55801
$9$	−2.03952	−0.679841
$10$	0	0
$11$	−3.27094	−0.986226	−0.493113	−	0.869965i	$-0.664141\pi$
$11$	−3.27094	−0.986226	−0.493113	+	0.869965i	$0.664141\pi$
$12$	−4.68348	−1.35200
$13$	−4.30649	−1.19441	−0.597203	−	0.802090i	$-0.703721\pi$
$13$	−4.30649	−1.19441	−0.597203	+	0.802090i	$0.703721\pi$
$14$	3.39998	0.908682
$15$	0	0
$16$	9.27984	2.31996
$17$	1.02456	0.248493	0.124247	−	0.992251i	$-0.460349\pi$
$17$	1.02456	0.248493	0.124247	+	0.992251i	$0.460349\pi$
$18$	−5.31016	−1.25162
$19$	−7.01250	−1.60878	−0.804388	−	0.594104i	$-0.797507\pi$
$19$	−7.01250	−1.60878	−0.804388	+	0.594104i	$0.797507\pi$
$20$	0	0
$21$	−1.27980	−0.279274
$22$	−8.51631	−1.81568
$23$	−0.835873	−0.174292	−0.0871458	−	0.996196i	$-0.527775\pi$
$23$	−0.835873	−0.174292	−0.0871458	+	0.996196i	$0.527775\pi$
$24$	−7.09071	−1.44739
$25$	0	0
$26$	−11.2125	−2.19895
$27$	4.93893	0.950498
$28$	6.24054	1.17935
$29$	−1.11761	−0.207535	−0.103767	−	0.994602i	$-0.533090\pi$
$29$	−1.11761	−0.207535	−0.103767	+	0.994602i	$0.533090\pi$
$30$	0	0
$31$	−3.97344	−0.713652	−0.356826	−	0.934171i	$-0.616141\pi$
$31$	−3.97344	−0.713652	−0.356826	+	0.934171i	$0.616141\pi$
$32$	9.69098	1.71314
$33$	3.20565	0.558032
$34$	2.66758	0.457486
$35$	0	0
$36$	−9.74661	−1.62444
$37$	11.3098	1.85932	0.929658	−	0.368423i	$-0.120102\pi$
$37$	11.3098	1.85932	0.929658	+	0.368423i	$0.120102\pi$
$38$	−18.2579	−2.96182
$39$	4.22053	0.675825
$40$	0	0
$41$	1.22869	0.191890	0.0959448	−	0.995387i	$-0.469413\pi$
$41$	1.22869	0.191890	0.0959448	+	0.995387i	$0.469413\pi$
$42$	−3.33211	−0.514156
$43$	−10.8406	−1.65318	−0.826591	−	0.562804i	$-0.809723\pi$
$43$	−10.8406	−1.65318	−0.826591	+	0.562804i	$0.809723\pi$
$44$	−15.6314	−2.35652
$45$	0	0
$46$	−2.17630	−0.320878
$47$	0.151820	0.0221453	0.0110726	−	0.999939i	$-0.496475\pi$
$47$	0.151820	0.0221453	0.0110726	+	0.999939i	$0.496475\pi$
$48$	−9.09461	−1.31269
$49$	−5.29473	−0.756389
$50$	0	0
$51$	−1.00411	−0.140604
$52$	−20.5801	−2.85395
$53$	−3.02053	−0.414902	−0.207451	−	0.978245i	$-0.566517\pi$
$53$	−3.02053	−0.414902	−0.207451	+	0.978245i	$0.566517\pi$
$54$	12.8591	1.74991
$55$	0	0
$56$	9.44808	1.26255
$57$	6.87252	0.910287
$58$	−2.90984	−0.382080
$59$	−4.15373	−0.540769	−0.270385	−	0.962752i	$-0.587151\pi$
$59$	−4.15373	−0.540769	−0.270385	+	0.962752i	$0.587151\pi$
$60$	0	0
$61$	5.62714	0.720482	0.360241	−	0.932859i	$-0.382694\pi$
$61$	5.62714	0.720482	0.360241	+	0.932859i	$0.382694\pi$
$62$	−10.3454	−1.31386
$63$	−2.66334	−0.335549
$64$	6.67199	0.833999
$65$	0	0
$66$	8.34632	1.02736
$67$	−12.9934	−1.58740	−0.793700	−	0.608309i	$-0.791848\pi$
$67$	−12.9934	−1.58740	−0.793700	+	0.608309i	$0.791848\pi$
$68$	4.89626	0.593758
$69$	0.819188	0.0986187
$70$	0	0
$71$	−11.2862	−1.33942	−0.669711	−	0.742622i	$-0.733582\pi$
$71$	−11.2862	−1.33942	−0.669711	+	0.742622i	$0.733582\pi$
$72$	−14.7562	−1.73904
$73$	−11.7148	−1.37112	−0.685560	−	0.728017i	$-0.740442\pi$
$73$	−11.7148	−1.37112	−0.685560	+	0.728017i	$0.740442\pi$
$74$	29.4464	3.42308
$75$	0	0
$76$	−33.5118	−3.84407
$77$	−4.27140	−0.486771
$78$	10.9887	1.24422
$79$	−1.66517	−0.187346	−0.0936732	−	0.995603i	$-0.529861\pi$
$79$	−1.66517	−0.187346	−0.0936732	+	0.995603i	$0.529861\pi$
$80$	0	0
$81$	1.27823	0.142025
$82$	3.19906	0.353277
$83$	2.34322	0.257201	0.128601	−	0.991696i	$-0.458951\pi$
$83$	2.34322	0.257201	0.128601	+	0.991696i	$0.458951\pi$
$84$	−6.11597	−0.667308
$85$	0	0
$86$	−28.2250	−3.04358
$87$	1.09530	0.117429
$88$	−23.6657	−2.52277
$89$	18.1099	1.91965	0.959825	−	0.280598i	$-0.0905329\pi$
$89$	18.1099	1.91965	0.959825	+	0.280598i	$0.0905329\pi$
$90$	0	0
$91$	−5.62368	−0.589522
$92$	−3.99453	−0.416458
$93$	3.89413	0.403802
$94$	0.395283	0.0407703
$95$	0	0
$96$	−9.49754	−0.969338
$97$	7.17873	0.728890	0.364445	−	0.931225i	$-0.381259\pi$
$97$	7.17873	0.728890	0.364445	+	0.931225i	$0.381259\pi$
$98$	−13.7855	−1.39254
$99$	6.67116	0.670477
$100$	0	0
$101$	−5.48113	−0.545393	−0.272696	−	0.962100i	$-0.587915\pi$
$101$	−5.48113	−0.545393	−0.272696	+	0.962100i	$0.587915\pi$
$102$	−2.61433	−0.258858
$103$	15.7371	1.55062	0.775311	−	0.631580i	$-0.217593\pi$
$103$	15.7371	1.55062	0.775311	+	0.631580i	$0.217593\pi$
$104$	−31.1580	−3.05530
$105$	0	0
$106$	−7.86433	−0.763851
$107$	11.1816	1.08097	0.540483	−	0.841355i	$-0.318242\pi$
$107$	11.1816	1.08097	0.540483	+	0.841355i	$0.318242\pi$
$108$	23.6025	2.27115
$109$	−0.296424	−0.0283922	−0.0141961	−	0.999899i	$-0.504519\pi$
$109$	−0.296424	−0.0283922	−0.0141961	+	0.999899i	$0.504519\pi$
$110$	0	0
$111$	−11.0840	−1.05205
$112$	12.1182	1.14506
$113$	−10.5881	−0.996045	−0.498023	−	0.867164i	$-0.665940\pi$
$113$	−10.5881	−0.996045	−0.498023	+	0.867164i	$0.665940\pi$
$114$	17.8935	1.67588
$115$	0	0
$116$	−5.34091	−0.495891
$117$	8.78319	0.812006
$118$	−10.8147	−0.995578
$119$	1.33794	0.122649
$120$	0	0
$121$	−0.300940	−0.0273582
$122$	14.6510	1.32644
$123$	−1.20417	−0.108576
$124$	−18.9886	−1.70522
$125$	0	0
$126$	−6.93433	−0.617759
$127$	−14.6989	−1.30432	−0.652160	−	0.758081i	$-0.726137\pi$
$127$	−14.6989	−1.30432	−0.652160	+	0.758081i	$0.726137\pi$
$128$	−2.01059	−0.177713
$129$	10.6242	0.935413
$130$	0	0
$131$	9.63853	0.842122	0.421061	−	0.907032i	$-0.361658\pi$
$131$	9.63853	0.842122	0.421061	+	0.907032i	$0.361658\pi$
$132$	15.3194	1.33338
$133$	−9.15735	−0.794043
$134$	−33.8300	−2.92247
$135$	0	0
$136$	7.41286	0.635647
$137$	−23.2376	−1.98532	−0.992661	−	0.120933i	$-0.961411\pi$
$137$	−23.2376	−1.98532	−0.992661	+	0.120933i	$0.961411\pi$
$138$	2.13286	0.181561
$139$	−1.29376	−0.109736	−0.0548678	−	0.998494i	$-0.517474\pi$
$139$	−1.29376	−0.109736	−0.0548678	+	0.998494i	$0.517474\pi$
$140$	0	0
$141$	−0.148790	−0.0125304
$142$	−29.3850	−2.46593
$143$	14.0863	1.17795
$144$	−18.9265	−1.57720
$145$	0	0
$146$	−30.5011	−2.52429
$147$	5.18904	0.427985
$148$	54.0480	4.44271
$149$	17.5316	1.43625	0.718123	−	0.695916i	$-0.245002\pi$
$149$	17.5316	1.43625	0.718123	+	0.695916i	$0.245002\pi$
$150$	0	0
$151$	5.26990	0.428858	0.214429	−	0.976740i	$-0.431211\pi$
$151$	5.26990	0.428858	0.214429	+	0.976740i	$0.431211\pi$
$152$	−50.7363	−4.11526
$153$	−2.08962	−0.168936
$154$	−11.1211	−0.896166
$155$	0	0
$156$	20.1693	1.61484
$157$	14.2165	1.13460	0.567299	−	0.823512i	$-0.307988\pi$
$157$	14.2165	1.13460	0.567299	+	0.823512i	$0.307988\pi$
$158$	−4.33548	−0.344912
$159$	2.96024	0.234762
$160$	0	0
$161$	−1.09153	−0.0860250
$162$	3.32802	0.261474
$163$	15.9688	1.25077	0.625386	−	0.780315i	$-0.284941\pi$
$163$	15.9688	1.25077	0.625386	+	0.780315i	$0.284941\pi$
$164$	5.87176	0.458508
$165$	0	0
$166$	6.10086	0.473518
$167$	21.5275	1.66585	0.832925	−	0.553386i	$-0.186665\pi$
$167$	21.5275	1.66585	0.832925	+	0.553386i	$0.186665\pi$
$168$	−9.25949	−0.714385
$169$	5.54585	0.426604
$170$	0	0
$171$	14.3021	1.09371
$172$	−51.8060	−3.95017
$173$	5.82531	0.442890	0.221445	−	0.975173i	$-0.428923\pi$
$173$	5.82531	0.442890	0.221445	+	0.975173i	$0.428923\pi$
$174$	2.85175	0.216191
$175$	0	0
$176$	−30.3538	−2.28801
$177$	4.07081	0.305981
$178$	47.1515	3.53416
$179$	−6.03932	−0.451400	−0.225700	−	0.974197i	$-0.572467\pi$
$179$	−6.03932	−0.451400	−0.225700	+	0.974197i	$0.572467\pi$
$180$	0	0
$181$	−4.03706	−0.300073	−0.150036	−	0.988680i	$-0.547939\pi$
$181$	−4.03706	−0.300073	−0.150036	+	0.988680i	$0.547939\pi$
$182$	−14.6420	−1.08533
$183$	−5.51482	−0.407667
$184$	−6.04765	−0.445839
$185$	0	0
$186$	10.1389	0.743417
$187$	−3.35129	−0.245071
$188$	0.725529	0.0529146
$189$	6.44956	0.469136
$190$	0	0
$191$	−16.4803	−1.19247	−0.596235	−	0.802810i	$-0.703337\pi$
$191$	−16.4803	−1.19247	−0.596235	+	0.802810i	$0.703337\pi$
$192$	−6.53881	−0.471898
$193$	23.0631	1.66012	0.830060	−	0.557674i	$-0.188306\pi$
$193$	23.0631	1.66012	0.830060	+	0.557674i	$0.188306\pi$
$194$	18.6907	1.34192
$195$	0	0
$196$	−25.3028	−1.80734
$197$	13.5540	0.965680	0.482840	−	0.875709i	$-0.339605\pi$
$197$	13.5540	0.965680	0.482840	+	0.875709i	$0.339605\pi$
$198$	17.3692	1.23438
$199$	−25.6725	−1.81988	−0.909938	−	0.414745i	$-0.863871\pi$
$199$	−25.6725	−1.81988	−0.909938	+	0.414745i	$0.863871\pi$
$200$	0	0
$201$	12.7341	0.898192
$202$	−14.2708	−1.00409
$203$	−1.45944	−0.102433
$204$	−4.79852	−0.335964
$205$	0	0
$206$	40.9735	2.85476
$207$	1.70478	0.118491
$208$	−39.9635	−2.77097
$209$	22.9375	1.58662
$210$	0	0
$211$	5.18301	0.356813	0.178407	−	0.983957i	$-0.442906\pi$
$211$	5.18301	0.356813	0.178407	+	0.983957i	$0.442906\pi$
$212$	−14.4347	−0.991380
$213$	11.0609	0.757879
$214$	29.1127	1.99010
$215$	0	0
$216$	35.7338	2.43138
$217$	−5.18877	−0.352237
$218$	−0.771777	−0.0522713
$219$	11.4810	0.775815
$220$	0	0
$221$	−4.41227	−0.296802
$222$	−28.8587	−1.93687
$223$	6.50914	0.435884	0.217942	−	0.975962i	$-0.430066\pi$
$223$	6.50914	0.435884	0.217942	+	0.975962i	$0.430066\pi$
$224$	12.6551	0.845553
$225$	0	0
$226$	−27.5675	−1.83376
$227$	−11.0460	−0.733150	−0.366575	−	0.930389i	$-0.619470\pi$
$227$	−11.0460	−0.733150	−0.366575	+	0.930389i	$0.619470\pi$
$228$	32.8429	2.17507
$229$	8.95679	0.591881	0.295941	−	0.955206i	$-0.404367\pi$
$229$	8.95679	0.591881	0.295941	+	0.955206i	$0.404367\pi$
$230$	0	0
$231$	4.18614	0.275428
$232$	−8.08605	−0.530875
$233$	6.46647	0.423632	0.211816	−	0.977310i	$-0.432062\pi$
$233$	6.46647	0.423632	0.211816	+	0.977310i	$0.432062\pi$
$234$	22.8681	1.49494
$235$	0	0
$236$	−19.8501	−1.29213
$237$	1.63193	0.106005
$238$	3.48349	0.225801
$239$	−25.0588	−1.62092	−0.810460	−	0.585794i	$-0.800783\pi$
$239$	−25.0588	−1.62092	−0.810460	+	0.585794i	$0.800783\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−0.783536	−0.0503676
$243$	−16.0695	−1.03086
$244$	26.8914	1.72154
$245$	0	0
$246$	−3.13520	−0.199893
$247$	30.1992	1.92153
$248$	−28.7484	−1.82552
$249$	−2.29644	−0.145531
$250$	0	0
$251$	−12.5611	−0.792847	−0.396424	−	0.918068i	$-0.629749\pi$
$251$	−12.5611	−0.792847	−0.396424	+	0.918068i	$0.629749\pi$
$252$	−12.7277	−0.801772
$253$	2.73409	0.171891
$254$	−38.2706	−2.40131
$255$	0	0
$256$	−18.5788	−1.16117
$257$	−16.0367	−1.00034	−0.500171	−	0.865927i	$-0.666730\pi$
$257$	−16.0367	−1.00034	−0.500171	+	0.865927i	$0.666730\pi$
$258$	27.6616	1.72213
$259$	14.7690	0.917702
$260$	0	0
$261$	2.27939	0.141091
$262$	25.0951	1.55038
$263$	−3.33210	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$263$	−3.33210	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$264$	23.1933	1.42745
$265$	0	0
$266$	−23.8423	−1.46187
$267$	−17.7485	−1.08619
$268$	−62.0939	−3.79299
$269$	−7.44101	−0.453686	−0.226843	−	0.973931i	$-0.572840\pi$
$269$	−7.44101	−0.453686	−0.226843	+	0.973931i	$0.572840\pi$
$270$	0	0
$271$	−20.6031	−1.25155	−0.625774	−	0.780005i	$-0.715217\pi$
$271$	−20.6031	−1.25155	−0.625774	+	0.780005i	$0.715217\pi$
$272$	9.50779	0.576495
$273$	5.51143	0.333567
$274$	−60.5020	−3.65506
$275$	0	0
$276$	3.91479	0.235643
$277$	−5.17667	−0.311036	−0.155518	−	0.987833i	$-0.549705\pi$
$277$	−5.17667	−0.311036	−0.155518	+	0.987833i	$0.549705\pi$
$278$	−3.36848	−0.202028
$279$	8.10393	0.485170
$280$	0	0
$281$	−14.1821	−0.846031	−0.423015	−	0.906123i	$-0.639028\pi$
$281$	−14.1821	−0.846031	−0.423015	+	0.906123i	$0.639028\pi$
$282$	−0.387393	−0.0230689
$283$	7.05196	0.419196	0.209598	−	0.977788i	$-0.432785\pi$
$283$	7.05196	0.419196	0.209598	+	0.977788i	$0.432785\pi$
$284$	−53.9351	−3.20046
$285$	0	0
$286$	36.6754	2.16866
$287$	1.60450	0.0947109
$288$	−19.7650	−1.16466
$289$	−15.9503	−0.938251
$290$	0	0
$291$	−7.03544	−0.412425
$292$	−55.9837	−3.27620
$293$	2.78966	0.162974	0.0814869	−	0.996674i	$-0.474033\pi$
$293$	2.78966	0.162974	0.0814869	+	0.996674i	$0.474033\pi$
$294$	13.5103	0.787937
$295$	0	0
$296$	81.8278	4.75614
$297$	−16.1550	−0.937405
$298$	45.6458	2.64419
$299$	3.59968	0.208175
$300$	0	0
$301$	−14.1564	−0.815960
$302$	13.7208	0.789546
$303$	5.37172	0.308597
$304$	−65.0749	−3.73230
$305$	0	0
$306$	−5.44060	−0.311018
$307$	−19.8285	−1.13167	−0.565837	−	0.824517i	$-0.691447\pi$
$307$	−19.8285	−1.13167	−0.565837	+	0.824517i	$0.691447\pi$
$308$	−20.4124	−1.16311
$309$	−15.4230	−0.877382
$310$	0	0
$311$	33.5109	1.90023	0.950114	−	0.311902i	$-0.100966\pi$
$311$	33.5109	1.90023	0.950114	+	0.311902i	$0.100966\pi$
$312$	30.5361	1.72877
$313$	−19.4152	−1.09741	−0.548705	−	0.836016i	$-0.684879\pi$
$313$	−19.4152	−1.09741	−0.548705	+	0.836016i	$0.684879\pi$
$314$	37.0144	2.08884
$315$	0	0
$316$	−7.95763	−0.447652
$317$	11.7255	0.658569	0.329284	−	0.944231i	$-0.393193\pi$
$317$	11.7255	0.658569	0.329284	+	0.944231i	$0.393193\pi$
$318$	7.70735	0.432207
$319$	3.65564	0.204676
$320$	0	0
$321$	−10.9584	−0.611638
$322$	−2.84195	−0.158376
$323$	−7.18475	−0.399770
$324$	6.10847	0.339359
$325$	0	0
$326$	41.5768	2.30272
$327$	0.290507	0.0160651
$328$	8.88976	0.490855
$329$	0.198256	0.0109302
$330$	0	0
$331$	4.93072	0.271017	0.135509	−	0.990776i	$-0.456733\pi$
$331$	4.93072	0.271017	0.135509	+	0.990776i	$0.456733\pi$
$332$	11.1979	0.614566
$333$	−23.0666	−1.26404
$334$	56.0496	3.06690
$335$	0	0
$336$	−11.8763	−0.647905
$337$	−34.4425	−1.87620	−0.938100	−	0.346364i	$-0.887416\pi$
$337$	−34.4425	−1.87620	−0.938100	+	0.346364i	$0.887416\pi$
$338$	14.4393	0.785395
$339$	10.3768	0.563588
$340$	0	0
$341$	12.9969	0.703822
$342$	37.2374	2.01357
$343$	−16.0552	−0.866900
$344$	−78.4334	−4.22885
$345$	0	0
$346$	15.1669	0.815378
$347$	23.4553	1.25915	0.629574	−	0.776940i	$-0.283229\pi$
$347$	23.4553	1.25915	0.629574	+	0.776940i	$0.283229\pi$
$348$	5.23430	0.280588
$349$	15.8727	0.849648	0.424824	−	0.905276i	$-0.360336\pi$
$349$	15.8727	0.849648	0.424824	+	0.905276i	$0.360336\pi$
$350$	0	0
$351$	−21.2694	−1.13528
$352$	−31.6986	−1.68954
$353$	28.4598	1.51476	0.757382	−	0.652972i	$-0.226478\pi$
$353$	28.4598	1.51476	0.757382	+	0.652972i	$0.226478\pi$
$354$	10.5989	0.563324
$355$	0	0
$356$	86.5450	4.58688
$357$	−1.31123	−0.0693978
$358$	−15.7241	−0.831047
$359$	−0.772338	−0.0407625	−0.0203812	−	0.999792i	$-0.506488\pi$
$359$	−0.772338	−0.0407625	−0.0203812	+	0.999792i	$0.506488\pi$
$360$	0	0
$361$	30.1751	1.58816
$362$	−10.5110	−0.552446
$363$	0.294933	0.0154800
$364$	−26.8748	−1.40862
$365$	0	0
$366$	−14.3585	−0.750532
$367$	23.3631	1.21954	0.609772	−	0.792577i	$-0.291261\pi$
$367$	23.3631	1.21954	0.609772	+	0.792577i	$0.291261\pi$
$368$	−7.75677	−0.404350
$369$	−2.50595	−0.130454
$370$	0	0
$371$	−3.94439	−0.204783
$372$	18.6095	0.964859
$373$	−27.7831	−1.43855	−0.719277	−	0.694724i	$-0.755527\pi$
$373$	−27.7831	−1.43855	−0.719277	+	0.694724i	$0.755527\pi$
$374$	−8.72550	−0.451185
$375$	0	0
$376$	1.09844	0.0566477
$377$	4.81297	0.247881
$378$	16.7922	0.863700
$379$	7.33328	0.376685	0.188343	−	0.982103i	$-0.439688\pi$
$379$	7.33328	0.376685	0.188343	+	0.982103i	$0.439688\pi$
$380$	0	0
$381$	14.4055	0.738018
$382$	−42.9084	−2.19539
$383$	33.4931	1.71142	0.855708	−	0.517459i	$-0.173122\pi$
$383$	33.4931	1.71142	0.855708	+	0.517459i	$0.173122\pi$
$384$	1.97046	0.100554
$385$	0	0
$386$	60.0477	3.05635
$387$	22.1097	1.12390
$388$	34.3062	1.74163
$389$	15.6882	0.795425	0.397713	−	0.917510i	$-0.369804\pi$
$389$	15.6882	0.795425	0.397713	+	0.917510i	$0.369804\pi$
$390$	0	0
$391$	−0.856405	−0.0433103
$392$	−38.3080	−1.93485
$393$	−9.44613	−0.476494
$394$	35.2894	1.77786
$395$	0	0
$396$	31.8806	1.60206
$397$	−8.34483	−0.418815	−0.209408	−	0.977828i	$-0.567154\pi$
$397$	−8.34483	−0.418815	−0.209408	+	0.977828i	$0.567154\pi$
$398$	−66.8416	−3.35047
$399$	8.97456	0.449290
$400$	0	0
$401$	−38.5766	−1.92642	−0.963211	−	0.268747i	$-0.913391\pi$
$401$	−38.5766	−1.92642	−0.963211	+	0.268747i	$0.913391\pi$
$402$	33.1548	1.65361
$403$	17.1116	0.852389
$404$	−26.1936	−1.30318
$405$	0	0
$406$	−3.79985	−0.188583
$407$	−36.9936	−1.83371
$408$	−7.26489	−0.359666
$409$	−19.5415	−0.966266	−0.483133	−	0.875547i	$-0.660501\pi$
$409$	−19.5415	−0.966266	−0.483133	+	0.875547i	$0.660501\pi$
$410$	0	0
$411$	22.7737	1.12335
$412$	75.2055	3.70511
$413$	−5.42419	−0.266907
$414$	4.43862	0.218146
$415$	0	0
$416$	−41.7341	−2.04618
$417$	1.26794	0.0620912
$418$	59.7206	2.92103
$419$	−29.7748	−1.45459	−0.727297	−	0.686323i	$-0.759224\pi$
$419$	−29.7748	−1.45459	−0.727297	+	0.686323i	$0.759224\pi$
$420$	0	0
$421$	−4.78920	−0.233411	−0.116706	−	0.993167i	$-0.537233\pi$
$421$	−4.78920	−0.233411	−0.116706	+	0.993167i	$0.537233\pi$
$422$	13.4946	0.656908
$423$	−0.309641	−0.0150553
$424$	−21.8539	−1.06132
$425$	0	0
$426$	28.7984	1.39529
$427$	7.34827	0.355608
$428$	53.4354	2.58290
$429$	−13.8051	−0.666517
$430$	0	0
$431$	5.35939	0.258153	0.129076	−	0.991635i	$-0.458799\pi$
$431$	5.35939	0.258153	0.129076	+	0.991635i	$0.458799\pi$
$432$	45.8325	2.20512
$433$	−21.5028	−1.03336	−0.516680	−	0.856179i	$-0.672832\pi$
$433$	−21.5028	−1.03336	−0.516680	+	0.856179i	$0.672832\pi$
$434$	−13.5096	−0.648482
$435$	0	0
$436$	−1.41657	−0.0678414
$437$	5.86156	0.280396
$438$	29.8923	1.42831
$439$	4.22306	0.201556	0.100778	−	0.994909i	$-0.467867\pi$
$439$	4.22306	0.201556	0.100778	+	0.994909i	$0.467867\pi$
$440$	0	0
$441$	10.7987	0.514225
$442$	−11.4879	−0.546424
$443$	−8.34030	−0.396260	−0.198130	−	0.980176i	$-0.563487\pi$
$443$	−8.34030	−0.396260	−0.198130	+	0.980176i	$0.563487\pi$
$444$	−52.9691	−2.51380
$445$	0	0
$446$	16.9474	0.802481
$447$	−17.1817	−0.812665
$448$	8.71269	0.411636
$449$	15.7796	0.744684	0.372342	−	0.928096i	$-0.378555\pi$
$449$	15.7796	0.744684	0.372342	+	0.928096i	$0.378555\pi$
$450$	0	0
$451$	−4.01898	−0.189247
$452$	−50.5992	−2.37998
$453$	−5.16470	−0.242659
$454$	−28.7597	−1.34976
$455$	0	0
$456$	49.7236	2.32852
$457$	8.71419	0.407633	0.203816	−	0.979009i	$-0.434665\pi$
$457$	8.71419	0.407633	0.203816	+	0.979009i	$0.434665\pi$
$458$	23.3201	1.08968
$459$	5.06025	0.236192
$460$	0	0
$461$	24.9140	1.16036	0.580181	−	0.814487i	$-0.302982\pi$
$461$	24.9140	1.16036	0.580181	+	0.814487i	$0.302982\pi$
$462$	10.8991	0.507074
$463$	2.87272	0.133507	0.0667534	−	0.997770i	$-0.478736\pi$
$463$	2.87272	0.133507	0.0667534	+	0.997770i	$0.478736\pi$
$464$	−10.3712	−0.481473
$465$	0	0
$466$	16.8363	0.779925
$467$	−4.87474	−0.225576	−0.112788	−	0.993619i	$-0.535978\pi$
$467$	−4.87474	−0.225576	−0.112788	+	0.993619i	$0.535978\pi$
$468$	41.9737	1.94023
$469$	−16.9676	−0.783492
$470$	0	0
$471$	−13.9327	−0.641985
$472$	−30.0528	−1.38329
$473$	35.4591	1.63041
$474$	4.24894	0.195160
$475$	0	0
$476$	6.39383	0.293061
$477$	6.16044	0.282067
$478$	−65.2438	−2.98418
$479$	0.194055	0.00886661	0.00443331	−	0.999990i	$-0.498589\pi$
$479$	0.194055	0.00886661	0.00443331	+	0.999990i	$0.498589\pi$
$480$	0	0
$481$	−48.7055	−2.22078
$482$	−2.60363	−0.118592
$483$	1.06975	0.0486752
$484$	−1.43815	−0.0653707
$485$	0	0
$486$	−41.8390	−1.89785
$487$	30.7592	1.39383	0.696915	−	0.717154i	$-0.254555\pi$
$487$	30.7592	1.39383	0.696915	+	0.717154i	$0.254555\pi$
$488$	40.7131	1.84300
$489$	−15.6500	−0.707719
$490$	0	0
$491$	−21.5528	−0.972663	−0.486332	−	0.873774i	$-0.661665\pi$
$491$	−21.5528	−0.972663	−0.486332	+	0.873774i	$0.661665\pi$
$492$	−5.75456	−0.259436
$493$	−1.14506	−0.0515710
$494$	78.6275	3.53762
$495$	0	0
$496$	−36.8729	−1.65564
$497$	−14.7382	−0.661097
$498$	−5.97908	−0.267929
$499$	21.8992	0.980341	0.490170	−	0.871627i	$-0.336935\pi$
$499$	21.8992	0.980341	0.490170	+	0.871627i	$0.336935\pi$
$500$	0	0
$501$	−21.0978	−0.942581
$502$	−32.7043	−1.45966
$503$	−4.44114	−0.198021	−0.0990104	−	0.995086i	$-0.531568\pi$
$503$	−4.44114	−0.198021	−0.0990104	+	0.995086i	$0.531568\pi$
$504$	−19.2696	−0.858336
$505$	0	0
$506$	7.11855	0.316458
$507$	−5.43515	−0.241383
$508$	−70.2443	−3.11659
$509$	29.6966	1.31628	0.658140	−	0.752895i	$-0.271343\pi$
$509$	29.6966	1.31628	0.658140	+	0.752895i	$0.271343\pi$
$510$	0	0
$511$	−15.2980	−0.676742
$512$	−44.3511	−1.96006
$513$	−34.6342	−1.52914
$514$	−41.7536	−1.84167
$515$	0	0
$516$	50.7719	2.23511
$517$	−0.496595	−0.0218402
$518$	38.4530	1.68953
$519$	−5.70903	−0.250598
$520$	0	0
$521$	−32.5336	−1.42532	−0.712661	−	0.701509i	$-0.752510\pi$
$521$	−32.5336	−1.42532	−0.712661	+	0.701509i	$0.752510\pi$
$522$	5.93468	0.259754
$523$	21.6812	0.948053	0.474027	−	0.880510i	$-0.342800\pi$
$523$	21.6812	0.948053	0.474027	+	0.880510i	$0.342800\pi$
$524$	46.0612	2.01219
$525$	0	0
$526$	−8.67555	−0.378272
$527$	−4.07105	−0.177338
$528$	29.7479	1.29461
$529$	−22.3013	−0.969622
$530$	0	0
$531$	8.47162	0.367637
$532$	−43.7618	−1.89731
$533$	−5.29135	−0.229194
$534$	−46.2103	−1.99972
$535$	0	0
$536$	−94.0092	−4.06058
$537$	5.91877	0.255414
$538$	−19.3736	−0.835255
$539$	17.3187	0.745971
$540$	0	0
$541$	6.08311	0.261533	0.130767	−	0.991413i	$-0.458256\pi$
$541$	6.08311	0.261533	0.130767	+	0.991413i	$0.458256\pi$
$542$	−53.6427	−2.30415
$543$	3.95648	0.169789
$544$	9.92903	0.425703
$545$	0	0
$546$	14.3497	0.614110
$547$	12.1956	0.521447	0.260723	−	0.965414i	$-0.416039\pi$
$547$	12.1956	0.521447	0.260723	+	0.965414i	$0.416039\pi$
$548$	−111.049	−4.74379
$549$	−11.4767	−0.489813
$550$	0	0
$551$	7.83723	0.333877
$552$	5.92694	0.252267
$553$	−2.17448	−0.0924684
$554$	−13.4781	−0.572630
$555$	0	0
$556$	−6.18273	−0.262206
$557$	37.5982	1.59309	0.796544	−	0.604581i	$-0.206659\pi$
$557$	37.5982	1.59309	0.796544	+	0.604581i	$0.206659\pi$
$558$	21.0996	0.893217
$559$	46.6851	1.97457
$560$	0	0
$561$	3.28439	0.138667
$562$	−36.9248	−1.55758
$563$	−20.6037	−0.868342	−0.434171	−	0.900830i	$-0.642959\pi$
$563$	−20.6037	−0.868342	−0.434171	+	0.900830i	$0.642959\pi$
$564$	−0.711047	−0.0299405
$565$	0	0
$566$	18.3607	0.771756
$567$	1.66919	0.0700992
$568$	−81.6569	−3.42625
$569$	20.5762	0.862601	0.431301	−	0.902208i	$-0.358055\pi$
$569$	20.5762	0.862601	0.431301	+	0.902208i	$0.358055\pi$
$570$	0	0
$571$	37.1320	1.55392	0.776962	−	0.629547i	$-0.216760\pi$
$571$	37.1320	1.55392	0.776962	+	0.629547i	$0.216760\pi$
$572$	67.3165	2.81464
$573$	16.1513	0.674730
$574$	4.17753	0.174367
$575$	0	0
$576$	−13.6077	−0.566986
$577$	34.7064	1.44484	0.722422	−	0.691452i	$-0.243029\pi$
$577$	34.7064	1.44484	0.722422	+	0.691452i	$0.243029\pi$
$578$	−41.5285	−1.72736
$579$	−22.6028	−0.939339
$580$	0	0
$581$	3.05992	0.126947
$582$	−18.3176	−0.759291
$583$	9.87998	0.409187
$584$	−84.7585	−3.50733
$585$	0	0
$586$	7.26324	0.300042
$587$	1.14455	0.0472405	0.0236203	−	0.999721i	$-0.492481\pi$
$587$	1.14455	0.0472405	0.0236203	+	0.999721i	$0.492481\pi$
$588$	24.7977	1.02264
$589$	27.8638	1.14811
$590$	0	0
$591$	−13.2834	−0.546407
$592$	104.953	4.31354
$593$	−3.60735	−0.148136	−0.0740680	−	0.997253i	$-0.523598\pi$
$593$	−3.60735	−0.148136	−0.0740680	+	0.997253i	$0.523598\pi$
$594$	−42.0615	−1.72580
$595$	0	0
$596$	83.7813	3.43181
$597$	25.1601	1.02973
$598$	9.37222	0.383258
$599$	−31.6723	−1.29410	−0.647048	−	0.762449i	$-0.723997\pi$
$599$	−31.6723	−1.29410	−0.647048	+	0.762449i	$0.723997\pi$
$600$	0	0
$601$	6.55665	0.267451	0.133726	−	0.991018i	$-0.457306\pi$
$601$	6.55665	0.267451	0.133726	+	0.991018i	$0.457306\pi$
$602$	−36.8579	−1.50222
$603$	26.5004	1.07918
$604$	25.1841	1.02473
$605$	0	0
$606$	13.9859	0.568140
$607$	9.16648	0.372056	0.186028	−	0.982544i	$-0.440438\pi$
$607$	9.16648	0.372056	0.186028	+	0.982544i	$0.440438\pi$
$608$	−67.9579	−2.75606
$609$	1.43031	0.0579592
$610$	0	0
$611$	−0.653812	−0.0264504
$612$	−9.98603	−0.403661
$613$	−7.92345	−0.320025	−0.160012	−	0.987115i	$-0.551153\pi$
$613$	−7.92345	−0.320025	−0.160012	+	0.987115i	$0.551153\pi$
$614$	−51.6260	−2.08346
$615$	0	0
$616$	−30.9041	−1.24516
$617$	−16.5959	−0.668126	−0.334063	−	0.942551i	$-0.608420\pi$
$617$	−16.5959	−0.668126	−0.334063	+	0.942551i	$0.608420\pi$
$618$	−40.1556	−1.61530
$619$	4.49086	0.180503	0.0902514	−	0.995919i	$-0.471233\pi$
$619$	4.49086	0.180503	0.0902514	+	0.995919i	$0.471233\pi$
$620$	0	0
$621$	−4.12832	−0.165664
$622$	87.2498	3.49840
$623$	23.6491	0.947481
$624$	39.1658	1.56789
$625$	0	0
$626$	−50.5499	−2.02038
$627$	−22.4796	−0.897749
$628$	67.9387	2.71105
$629$	11.5876	0.462028
$630$	0	0
$631$	−5.96553	−0.237484	−0.118742	−	0.992925i	$-0.537886\pi$
$631$	−5.96553	−0.237484	−0.118742	+	0.992925i	$0.537886\pi$
$632$	−12.0477	−0.479233
$633$	−5.07955	−0.201894
$634$	30.5288	1.21245
$635$	0	0
$636$	14.1466	0.560949
$637$	22.8017	0.903435
$638$	9.51791	0.376818
$639$	23.0184	0.910594
$640$	0	0
$641$	−1.73375	−0.0684789	−0.0342395	−	0.999414i	$-0.510901\pi$
$641$	−1.73375	−0.0684789	−0.0342395	+	0.999414i	$0.510901\pi$
$642$	−28.5316	−1.12605
$643$	−38.3312	−1.51163	−0.755817	−	0.654783i	$-0.772760\pi$
$643$	−38.3312	−1.51163	−0.755817	+	0.654783i	$0.772760\pi$
$644$	−5.21630	−0.205551
$645$	0	0
$646$	−18.7064	−0.735994
$647$	−29.2098	−1.14836	−0.574178	−	0.818730i	$-0.694678\pi$
$647$	−29.2098	−1.14836	−0.574178	+	0.818730i	$0.694678\pi$
$648$	9.24813	0.363301
$649$	13.5866	0.533321
$650$	0	0
$651$	5.08520	0.199305
$652$	76.3127	2.98864
$653$	42.7952	1.67471	0.837353	−	0.546662i	$-0.184102\pi$
$653$	42.7952	1.67471	0.837353	+	0.546662i	$0.184102\pi$
$654$	0.756371	0.0295765
$655$	0	0
$656$	11.4021	0.445177
$657$	23.8927	0.932143
$658$	0.516185	0.0201230
$659$	−23.7004	−0.923238	−0.461619	−	0.887078i	$-0.652731\pi$
$659$	−23.7004	−0.923238	−0.461619	+	0.887078i	$0.652731\pi$
$660$	0	0
$661$	24.1228	0.938268	0.469134	−	0.883127i	$-0.344566\pi$
$661$	24.1228	0.938268	0.469134	+	0.883127i	$0.344566\pi$
$662$	12.8378	0.498954
$663$	4.32420	0.167938
$664$	16.9535	0.657923
$665$	0	0
$666$	−60.0567	−2.32715
$667$	0.934180	0.0361716
$668$	102.877	3.98044
$669$	−6.37921	−0.246634
$670$	0	0
$671$	−18.4061	−0.710558
$672$	−12.4025	−0.478436
$673$	3.67522	0.141669	0.0708346	−	0.997488i	$-0.477434\pi$
$673$	3.67522	0.141669	0.0708346	+	0.997488i	$0.477434\pi$
$674$	−89.6753	−3.45416
$675$	0	0
$676$	26.5029	1.01934
$677$	−45.7769	−1.75935	−0.879675	−	0.475575i	$-0.842240\pi$
$677$	−45.7769	−1.75935	−0.879675	+	0.475575i	$0.842240\pi$
$678$	27.0172	1.03759
$679$	9.37443	0.359758
$680$	0	0
$681$	10.8255	0.414835
$682$	33.8391	1.29577
$683$	1.52419	0.0583215	0.0291608	−	0.999575i	$-0.490717\pi$
$683$	1.52419	0.0583215	0.0291608	+	0.999575i	$0.490717\pi$
$684$	68.3481	2.61335
$685$	0	0
$686$	−41.8018	−1.59600
$687$	−8.77800	−0.334902
$688$	−100.599	−3.83532
$689$	13.0079	0.495561
$690$	0	0
$691$	20.3036	0.772386	0.386193	−	0.922418i	$-0.373790\pi$
$691$	20.3036	0.772386	0.386193	+	0.922418i	$0.373790\pi$
$692$	27.8384	1.05826
$693$	8.71162	0.330927
$694$	61.0689	2.31814
$695$	0	0
$696$	7.92465	0.300383
$697$	1.25888	0.0476833
$698$	41.3267	1.56424
$699$	−6.33739	−0.239702
$700$	0	0
$701$	−10.3863	−0.392285	−0.196143	−	0.980575i	$-0.562842\pi$
$701$	−10.3863	−0.392285	−0.196143	+	0.980575i	$0.562842\pi$
$702$	−55.3777	−2.09010
$703$	−79.3098	−2.99123
$704$	−21.8237	−0.822511
$705$	0	0
$706$	74.0988	2.78874
$707$	−7.15759	−0.269189
$708$	19.4539	0.731122
$709$	34.9053	1.31090	0.655448	−	0.755240i	$-0.272480\pi$
$709$	34.9053	1.31090	0.655448	+	0.755240i	$0.272480\pi$
$710$	0	0
$711$	3.39615	0.127366
$712$	131.028	4.91048
$713$	3.32129	0.124383
$714$	−3.41396	−0.127764
$715$	0	0
$716$	−28.8611	−1.07859
$717$	24.5586	0.917159
$718$	−2.01088	−0.0750454
$719$	5.17696	0.193068	0.0965341	−	0.995330i	$-0.469224\pi$
$719$	5.17696	0.193068	0.0965341	+	0.995330i	$0.469224\pi$
$720$	0	0
$721$	20.5505	0.765339
$722$	78.5646	2.92387
$723$	0.980039	0.0364480
$724$	−19.2926	−0.717003
$725$	0	0
$726$	0.767896	0.0284993
$727$	7.00384	0.259758	0.129879	−	0.991530i	$-0.458541\pi$
$727$	7.00384	0.259758	0.129879	+	0.991530i	$0.458541\pi$
$728$	−40.6881	−1.50800
$729$	11.9141	0.441262
$730$	0	0
$731$	−11.1069	−0.410804
$732$	−26.3546	−0.974094
$733$	1.22518	0.0452530	0.0226265	−	0.999744i	$-0.492797\pi$
$733$	1.22518	0.0452530	0.0226265	+	0.999744i	$0.492797\pi$
$734$	60.8288	2.24523
$735$	0	0
$736$	−8.10042	−0.298586
$737$	42.5008	1.56554
$738$	−6.52455	−0.240172
$739$	−31.4569	−1.15716	−0.578580	−	0.815625i	$-0.696393\pi$
$739$	−31.4569	−1.15716	−0.578580	+	0.815625i	$0.696393\pi$
$740$	0	0
$741$	−29.5964	−1.08725
$742$	−10.2697	−0.377014
$743$	−17.5176	−0.642659	−0.321330	−	0.946967i	$-0.604130\pi$
$743$	−17.5176	−0.642659	−0.321330	+	0.946967i	$0.604130\pi$
$744$	28.1745	1.03293
$745$	0	0
$746$	−72.3368	−2.64844
$747$	−4.77904	−0.174856
$748$	−16.0154	−0.585580
$749$	14.6016	0.533532
$750$	0	0
$751$	−35.2893	−1.28773	−0.643863	−	0.765141i	$-0.722669\pi$
$751$	−35.2893	−1.28773	−0.643863	+	0.765141i	$0.722669\pi$
$752$	1.40887	0.0513761
$753$	12.3103	0.448614
$754$	12.5312	0.456359
$755$	0	0
$756$	30.8216	1.12097
$757$	17.2974	0.628686	0.314343	−	0.949309i	$-0.398216\pi$
$757$	17.2974	0.628686	0.314343	+	0.949309i	$0.398216\pi$
$758$	19.0931	0.693493
$759$	−2.67952	−0.0972603
$760$	0	0
$761$	9.53250	0.345553	0.172776	−	0.984961i	$-0.444726\pi$
$761$	9.53250	0.345553	0.172776	+	0.984961i	$0.444726\pi$
$762$	37.5066	1.35872
$763$	−0.387088	−0.0140135
$764$	−78.7570	−2.84933
$765$	0	0
$766$	87.2034	3.15079
$767$	17.8880	0.645897
$768$	18.2079	0.657023
$769$	−37.0399	−1.33569	−0.667847	−	0.744299i	$-0.732784\pi$
$769$	−37.0399	−1.33569	−0.667847	+	0.744299i	$0.732784\pi$
$770$	0	0
$771$	15.7166	0.566019
$772$	110.216	3.96675
$773$	6.97450	0.250855	0.125428	−	0.992103i	$-0.459970\pi$
$773$	6.97450	0.250855	0.125428	+	0.992103i	$0.459970\pi$
$774$	57.5655	2.06915
$775$	0	0
$776$	51.9391	1.86450
$777$	−14.4742	−0.519259
$778$	40.8463	1.46441
$779$	−8.61621	−0.308708
$780$	0	0
$781$	36.9164	1.32097
$782$	−2.22976	−0.0797360
$783$	−5.51980	−0.197261
$784$	−49.1342	−1.75479
$785$	0	0
$786$	−24.5942	−0.877246
$787$	−29.9359	−1.06710	−0.533550	−	0.845768i	$-0.679143\pi$
$787$	−29.9359	−1.06710	−0.533550	+	0.845768i	$0.679143\pi$
$788$	64.7726	2.30743
$789$	3.26559	0.116258
$790$	0	0
$791$	−13.8266	−0.491617
$792$	48.2667	1.71508
$793$	−24.2332	−0.860547
$794$	−21.7268	−0.771056
$795$	0	0
$796$	−122.685	−4.34847
$797$	10.7103	0.379380	0.189690	−	0.981844i	$-0.439252\pi$
$797$	10.7103	0.379380	0.189690	+	0.981844i	$0.439252\pi$
$798$	23.3664	0.827162
$799$	0.155550	0.00550295
$800$	0	0
$801$	−36.9357	−1.30506
$802$	−100.439	−3.54662
$803$	38.3186	1.35223
$804$	60.8544	2.14617
$805$	0	0
$806$	44.5522	1.56928
$807$	7.29248	0.256707
$808$	−39.6567	−1.39512
$809$	−30.4625	−1.07100	−0.535502	−	0.844534i	$-0.679878\pi$
$809$	−30.4625	−1.07100	−0.535502	+	0.844534i	$0.679878\pi$
$810$	0	0
$811$	−6.38159	−0.224088	−0.112044	−	0.993703i	$-0.535740\pi$
$811$	−6.38159	−0.224088	−0.112044	+	0.993703i	$0.535740\pi$
$812$	−6.97449	−0.244757
$813$	20.1918	0.708158
$814$	−96.3176	−3.37593
$815$	0	0
$816$	−9.31801	−0.326196
$817$	76.0199	2.65960
$818$	−50.8788	−1.77894
$819$	11.4696	0.400781
$820$	0	0
$821$	−31.3814	−1.09522	−0.547609	−	0.836734i	$-0.684462\pi$
$821$	−31.3814	−1.09522	−0.547609	+	0.836734i	$0.684462\pi$
$822$	59.2943	2.06813
$823$	8.61720	0.300377	0.150188	−	0.988657i	$-0.452012\pi$
$823$	8.61720	0.300377	0.150188	+	0.988657i	$0.452012\pi$
$824$	113.860	3.96650
$825$	0	0
$826$	−14.1226	−0.491387
$827$	18.2047	0.633039	0.316520	−	0.948586i	$-0.397486\pi$
$827$	18.2047	0.633039	0.316520	+	0.948586i	$0.397486\pi$
$828$	8.14693	0.283125
$829$	38.0162	1.32036	0.660179	−	0.751108i	$-0.270480\pi$
$829$	38.0162	1.32036	0.660179	+	0.751108i	$0.270480\pi$
$830$	0	0
$831$	5.07334	0.175992
$832$	−28.7328	−0.996132
$833$	−5.42479	−0.187958
$834$	3.30124	0.114313
$835$	0	0
$836$	109.615	3.79112
$837$	−19.6246	−0.678324
$838$	−77.5224	−2.67797
$839$	45.6228	1.57507	0.787537	−	0.616267i	$-0.211356\pi$
$839$	45.6228	1.57507	0.787537	+	0.616267i	$0.211356\pi$
$840$	0	0
$841$	−27.7509	−0.956929
$842$	−12.4693	−0.429720
$843$	13.8990	0.478706
$844$	24.7689	0.852582
$845$	0	0
$846$	−0.806189	−0.0277174
$847$	−0.392987	−0.0135032
$848$	−28.0300	−0.962556
$849$	−6.91120	−0.237192
$850$	0	0
$851$	−9.45354	−0.324063
$852$	52.8585	1.81090
$853$	−17.2406	−0.590307	−0.295153	−	0.955450i	$-0.595371\pi$
$853$	−17.2406	−0.590307	−0.295153	+	0.955450i	$0.595371\pi$
$854$	19.1321	0.654689
$855$	0	0
$856$	80.9003	2.76512
$857$	−9.87638	−0.337371	−0.168685	−	0.985670i	$-0.553952\pi$
$857$	−9.87638	−0.337371	−0.168685	+	0.985670i	$0.553952\pi$
$858$	−35.9433	−1.22708
$859$	25.8904	0.883369	0.441685	−	0.897170i	$-0.354381\pi$
$859$	25.8904	0.883369	0.441685	+	0.897170i	$0.354381\pi$
$860$	0	0
$861$	−1.57248	−0.0535899
$862$	13.9538	0.475270
$863$	14.8445	0.505311	0.252656	−	0.967556i	$-0.418696\pi$
$863$	14.8445	0.505311	0.252656	+	0.967556i	$0.418696\pi$
$864$	47.8630	1.62833
$865$	0	0
$866$	−55.9853	−1.90246
$867$	15.6319	0.530887
$868$	−24.7964	−0.841646
$869$	5.44668	0.184766
$870$	0	0
$871$	55.9561	1.89600
$872$	−2.14467	−0.0726275
$873$	−14.6412	−0.495529
$874$	15.2613	0.516221
$875$	0	0
$876$	54.8662	1.85376
$877$	−42.0781	−1.42088	−0.710439	−	0.703759i	$-0.751503\pi$
$877$	−42.0781	−1.42088	−0.710439	+	0.703759i	$0.751503\pi$
$878$	10.9953	0.371072
$879$	−2.73398	−0.0922148
$880$	0	0
$881$	−19.0418	−0.641534	−0.320767	−	0.947158i	$-0.603941\pi$
$881$	−19.0418	−0.641534	−0.320767	+	0.947158i	$0.603941\pi$
$882$	28.1158	0.946709
$883$	−6.51087	−0.219108	−0.109554	−	0.993981i	$-0.534942\pi$
$883$	−6.51087	−0.219108	−0.109554	+	0.993981i	$0.534942\pi$
$884$	−21.0857	−0.709188
$885$	0	0
$886$	−21.7150	−0.729531
$887$	−5.59140	−0.187741	−0.0938704	−	0.995584i	$-0.529924\pi$
$887$	−5.59140	−0.187741	−0.0938704	+	0.995584i	$0.529924\pi$
$888$	−80.1944	−2.69115
$889$	−19.1948	−0.643773
$890$	0	0
$891$	−4.18100	−0.140069
$892$	31.1063	1.04152
$893$	−1.06464	−0.0356268
$894$	−44.7346	−1.49615
$895$	0	0
$896$	−2.62555	−0.0877135
$897$	−3.52783	−0.117791
$898$	41.0841	1.37099
$899$	4.44076	0.148108
$900$	0	0
$901$	−3.09473	−0.103100
$902$	−10.4639	−0.348411
$903$	13.8738	0.461691
$904$	−76.6063	−2.54789
$905$	0	0
$906$	−13.4470	−0.446745
$907$	−18.3915	−0.610681	−0.305340	−	0.952243i	$-0.598770\pi$
$907$	−18.3915	−0.610681	−0.305340	+	0.952243i	$0.598770\pi$
$908$	−52.7874	−1.75181
$909$	11.1789	0.370780
$910$	0	0
$911$	−38.2665	−1.26783	−0.633913	−	0.773404i	$-0.718552\pi$
$911$	−38.2665	−1.26783	−0.633913	+	0.773404i	$0.718552\pi$
$912$	63.7759	2.11183
$913$	−7.66452	−0.253659
$914$	22.6885	0.750469
$915$	0	0
$916$	42.8033	1.41426
$917$	12.5866	0.415646
$918$	13.1750	0.434840
$919$	−4.89962	−0.161624	−0.0808118	−	0.996729i	$-0.525751\pi$
$919$	−4.89962	−0.161624	−0.0808118	+	0.996729i	$0.525751\pi$
$920$	0	0
$921$	19.4327	0.640330
$922$	64.8669	2.13628
$923$	48.6038	1.59981
$924$	20.0050	0.658116
$925$	0	0
$926$	7.47949	0.245791
$927$	−32.0962	−1.05418
$928$	−10.8307	−0.355536
$929$	17.9381	0.588528	0.294264	−	0.955724i	$-0.404925\pi$
$929$	17.9381	0.588528	0.294264	+	0.955724i	$0.404925\pi$
$930$	0	0
$931$	37.1292	1.21686
$932$	30.9024	1.01224
$933$	−32.8420	−1.07520
$934$	−12.6920	−0.415295
$935$	0	0
$936$	63.5475	2.07712
$937$	−29.8369	−0.974730	−0.487365	−	0.873198i	$-0.662042\pi$
$937$	−29.8369	−0.974730	−0.487365	+	0.873198i	$0.662042\pi$
$938$	−44.1773	−1.44244
$939$	19.0276	0.620943
$940$	0	0
$941$	26.8047	0.873809	0.436904	−	0.899508i	$-0.356075\pi$
$941$	26.8047	0.873809	0.436904	+	0.899508i	$0.356075\pi$
$942$	−36.2755	−1.18192
$943$	−1.02703	−0.0334448
$944$	−38.5459	−1.25456
$945$	0	0
$946$	92.3222	3.00165
$947$	−2.94622	−0.0957393	−0.0478697	−	0.998854i	$-0.515243\pi$
$947$	−2.94622	−0.0957393	−0.0478697	+	0.998854i	$0.515243\pi$
$948$	7.79879	0.253293
$949$	50.4499	1.63767
$950$	0	0
$951$	−11.4914	−0.372635
$952$	9.68017	0.313736
$953$	4.62861	0.149935	0.0749676	−	0.997186i	$-0.476115\pi$
$953$	4.62861	0.149935	0.0749676	+	0.997186i	$0.476115\pi$
$954$	16.0395	0.519297
$955$	0	0
$956$	−119.753	−3.87308
$957$	−3.58267	−0.115811
$958$	0.505247	0.0163238
$959$	−30.3451	−0.979894
$960$	0	0
$961$	−15.2117	−0.490702
$962$	−126.811	−4.08854
$963$	−22.8051	−0.734885
$964$	−4.77887	−0.153917
$965$	0	0
$966$	2.78522	0.0896130
$967$	−20.1721	−0.648689	−0.324345	−	0.945939i	$-0.605144\pi$
$967$	−20.1721	−0.648689	−0.324345	+	0.945939i	$0.605144\pi$
$968$	−2.17734	−0.0699825
$969$	7.04134	0.226200
$970$	0	0
$971$	30.0251	0.963550	0.481775	−	0.876295i	$-0.339992\pi$
$971$	30.0251	0.963550	0.481775	+	0.876295i	$0.339992\pi$
$972$	−76.7940	−2.46317
$973$	−1.68948	−0.0541621
$974$	80.0853	2.56610
$975$	0	0
$976$	52.2190	1.67149
$977$	−57.7096	−1.84629	−0.923147	−	0.384448i	$-0.874392\pi$
$977$	−57.7096	−1.84629	−0.923147	+	0.384448i	$0.874392\pi$
$978$	−40.7469	−1.30294
$979$	−59.2366	−1.89321
$980$	0	0
$981$	0.604563	0.0193022
$982$	−56.1154	−1.79071
$983$	3.33817	0.106471	0.0532356	−	0.998582i	$-0.483047\pi$
$983$	3.33817	0.106471	0.0532356	+	0.998582i	$0.483047\pi$
$984$	−8.71231	−0.277738
$985$	0	0
$986$	−2.98132	−0.0949444
$987$	−0.194299	−0.00618460
$988$	144.318	4.59137
$989$	9.06139	0.288136
$990$	0	0
$991$	4.48757	0.142552	0.0712762	−	0.997457i	$-0.477293\pi$
$991$	4.48757	0.142552	0.0712762	+	0.997457i	$0.477293\pi$
$992$	−38.5065	−1.22258
$993$	−4.83230	−0.153349
$994$	−38.3727	−1.21711
$995$	0	0
$996$	−10.9744	−0.347737
$997$	47.4116	1.50154	0.750770	−	0.660564i	$-0.229683\pi$
$997$	47.4116	1.50154	0.750770	+	0.660564i	$0.229683\pi$
$998$	57.0172	1.80485
$999$	55.8582	1.76728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.f.1.7		7
5.4	even	2		241.2.a.a.1.1	✓	7
15.14	odd	2		2169.2.a.e.1.7		7
20.19	odd	2		3856.2.a.j.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.1	✓	7	5.4	even	2
2169.2.a.e.1.7		7	15.14	odd	2
3856.2.a.j.1.2		7	20.19	odd	2
6025.2.a.f.1.7		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.60363 q^{2} -0.980039 q^{3} +4.77887 q^{4} -2.55166 q^{6} +1.30586 q^{7} +7.23513 q^{8} -2.03952 q^{9} +O(q^{10})\)	\(q+2.60363 q^{2} -0.980039 q^{3} +4.77887 q^{4} -2.55166 q^{6} +1.30586 q^{7} +7.23513 q^{8} -2.03952 q^{9} -3.27094 q^{11} -4.68348 q^{12} -4.30649 q^{13} +3.39998 q^{14} +9.27984 q^{16} +1.02456 q^{17} -5.31016 q^{18} -7.01250 q^{19} -1.27980 q^{21} -8.51631 q^{22} -0.835873 q^{23} -7.09071 q^{24} -11.2125 q^{26} +4.93893 q^{27} +6.24054 q^{28} -1.11761 q^{29} -3.97344 q^{31} +9.69098 q^{32} +3.20565 q^{33} +2.66758 q^{34} -9.74661 q^{36} +11.3098 q^{37} -18.2579 q^{38} +4.22053 q^{39} +1.22869 q^{41} -3.33211 q^{42} -10.8406 q^{43} -15.6314 q^{44} -2.17630 q^{46} +0.151820 q^{47} -9.09461 q^{48} -5.29473 q^{49} -1.00411 q^{51} -20.5801 q^{52} -3.02053 q^{53} +12.8591 q^{54} +9.44808 q^{56} +6.87252 q^{57} -2.90984 q^{58} -4.15373 q^{59} +5.62714 q^{61} -10.3454 q^{62} -2.66334 q^{63} +6.67199 q^{64} +8.34632 q^{66} -12.9934 q^{67} +4.89626 q^{68} +0.819188 q^{69} -11.2862 q^{71} -14.7562 q^{72} -11.7148 q^{73} +29.4464 q^{74} -33.5118 q^{76} -4.27140 q^{77} +10.9887 q^{78} -1.66517 q^{79} +1.27823 q^{81} +3.19906 q^{82} +2.34322 q^{83} -6.11597 q^{84} -28.2250 q^{86} +1.09530 q^{87} -23.6657 q^{88} +18.1099 q^{89} -5.62368 q^{91} -3.99453 q^{92} +3.89413 q^{93} +0.395283 q^{94} -9.49754 q^{96} +7.17873 q^{97} -13.7855 q^{98} +6.67116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * q^99

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