LMFDB - Embedded newform 575.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, 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("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 $ x^7 - x^6 - 12x^5 + 9x^4 + 43x^3 - 14x^2 - 49*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.69496$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69496 q^{2} +3.30905 q^{3} +0.872898 q^{4} -5.60872 q^{6} +0.852729 q^{7} +1.91040 q^{8} +7.94982 q^{9} +O(q^{10})$	\(q-1.69496 q^{2} +3.30905 q^{3} +0.872898 q^{4} -5.60872 q^{6} +0.852729 q^{7} +1.91040 q^{8} +7.94982 q^{9} +1.80793 q^{11} +2.88846 q^{12} -2.70717 q^{13} -1.44534 q^{14} -4.98384 q^{16} -4.05059 q^{17} -13.4746 q^{18} +7.19786 q^{19} +2.82172 q^{21} -3.06438 q^{22} -1.00000 q^{23} +6.32160 q^{24} +4.58855 q^{26} +16.3792 q^{27} +0.744345 q^{28} -3.76202 q^{29} +4.00336 q^{31} +4.62664 q^{32} +5.98254 q^{33} +6.86559 q^{34} +6.93938 q^{36} -11.4649 q^{37} -12.2001 q^{38} -8.95816 q^{39} +6.09373 q^{41} -4.78271 q^{42} +11.4095 q^{43} +1.57814 q^{44} +1.69496 q^{46} -7.31241 q^{47} -16.4918 q^{48} -6.27285 q^{49} -13.4036 q^{51} -2.36308 q^{52} -0.406455 q^{53} -27.7622 q^{54} +1.62905 q^{56} +23.8181 q^{57} +6.37647 q^{58} -4.83620 q^{59} +9.22818 q^{61} -6.78554 q^{62} +6.77904 q^{63} +2.12571 q^{64} -10.1402 q^{66} +9.64544 q^{67} -3.53575 q^{68} -3.30905 q^{69} -7.31241 q^{71} +15.1873 q^{72} -5.46747 q^{73} +19.4326 q^{74} +6.28299 q^{76} +1.54168 q^{77} +15.1837 q^{78} +8.60655 q^{79} +30.3502 q^{81} -10.3287 q^{82} -2.49686 q^{83} +2.46307 q^{84} -19.3387 q^{86} -12.4487 q^{87} +3.45387 q^{88} -5.41541 q^{89} -2.30848 q^{91} -0.872898 q^{92} +13.2473 q^{93} +12.3943 q^{94} +15.3098 q^{96} -8.41317 q^{97} +10.6323 q^{98} +14.3727 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * 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 $

$2$	−1.69496	−1.19852	−0.599260	−	0.800555i	$-0.704538\pi$
$2$	−1.69496	−1.19852	−0.599260	+	0.800555i	$0.704538\pi$
$3$	3.30905	1.91048	0.955241	−	0.295829i	$-0.0955959\pi$
$3$	3.30905	1.91048	0.955241	+	0.295829i	$0.0955959\pi$
$4$	0.872898	0.436449
$5$	0	0
$5$	0	0
$6$	−5.60872	−2.28975
$7$	0.852729	0.322301	0.161151	−	0.986930i	$-0.448480\pi$
$7$	0.852729	0.322301	0.161151	+	0.986930i	$0.448480\pi$
$8$	1.91040	0.675427
$9$	7.94982	2.64994
$10$	0	0
$11$	1.80793	0.545112	0.272556	−	0.962140i	$-0.412131\pi$
$11$	1.80793	0.545112	0.272556	+	0.962140i	$0.412131\pi$
$12$	2.88846	0.833827
$13$	−2.70717	−0.750833	−0.375417	−	0.926856i	$-0.622500\pi$
$13$	−2.70717	−0.750833	−0.375417	+	0.926856i	$0.622500\pi$
$14$	−1.44534	−0.386284
$15$	0	0
$16$	−4.98384	−1.24596
$17$	−4.05059	−0.982411	−0.491206	−	0.871044i	$-0.663444\pi$
$17$	−4.05059	−0.982411	−0.491206	+	0.871044i	$0.663444\pi$
$18$	−13.4746	−3.17601
$19$	7.19786	1.65130	0.825651	−	0.564182i	$-0.190808\pi$
$19$	7.19786	1.65130	0.825651	+	0.564182i	$0.190808\pi$
$20$	0	0
$21$	2.82172	0.615750
$22$	−3.06438	−0.653327
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	6.32160	1.29039
$25$	0	0
$26$	4.58855	0.899888
$27$	16.3792	3.15218
$28$	0.744345	0.140668
$29$	−3.76202	−0.698589	−0.349294	−	0.937013i	$-0.613579\pi$
$29$	−3.76202	−0.698589	−0.349294	+	0.937013i	$0.613579\pi$
$30$	0	0
$31$	4.00336	0.719025	0.359512	−	0.933140i	$-0.382943\pi$
$31$	4.00336	0.719025	0.359512	+	0.933140i	$0.382943\pi$
$32$	4.62664	0.817882
$33$	5.98254	1.04143
$34$	6.86559	1.17744
$35$	0	0
$36$	6.93938	1.15656
$37$	−11.4649	−1.88482	−0.942411	−	0.334458i	$-0.891447\pi$
$37$	−11.4649	−1.88482	−0.942411	+	0.334458i	$0.891447\pi$
$38$	−12.2001	−1.97912
$39$	−8.95816	−1.43445
$40$	0	0
$41$	6.09373	0.951681	0.475841	−	0.879531i	$-0.342144\pi$
$41$	6.09373	0.951681	0.475841	+	0.879531i	$0.342144\pi$
$42$	−4.78271	−0.737989
$43$	11.4095	1.73993	0.869967	−	0.493111i	$-0.164140\pi$
$43$	11.4095	1.73993	0.869967	+	0.493111i	$0.164140\pi$
$44$	1.57814	0.237913
$45$	0	0
$46$	1.69496	0.249909
$47$	−7.31241	−1.06662	−0.533312	−	0.845918i	$-0.679053\pi$
$47$	−7.31241	−1.06662	−0.533312	+	0.845918i	$0.679053\pi$
$48$	−16.4918	−2.38039
$49$	−6.27285	−0.896122
$50$	0	0
$51$	−13.4036	−1.87688
$52$	−2.36308	−0.327700
$53$	−0.406455	−0.0558309	−0.0279155	−	0.999610i	$-0.508887\pi$
$53$	−0.406455	−0.0558309	−0.0279155	+	0.999610i	$0.508887\pi$
$54$	−27.7622	−3.77795
$55$	0	0
$56$	1.62905	0.217691
$57$	23.8181	3.15478
$58$	6.37647	0.837272
$59$	−4.83620	−0.629619	−0.314810	−	0.949155i	$-0.601941\pi$
$59$	−4.83620	−0.629619	−0.314810	+	0.949155i	$0.601941\pi$
$60$	0	0
$61$	9.22818	1.18155	0.590774	−	0.806837i	$-0.298823\pi$
$61$	9.22818	1.18155	0.590774	+	0.806837i	$0.298823\pi$
$62$	−6.78554	−0.861765
$63$	6.77904	0.854079
$64$	2.12571	0.265714
$65$	0	0
$66$	−10.1402	−1.24817
$67$	9.64544	1.17838	0.589189	−	0.807995i	$-0.299447\pi$
$67$	9.64544	1.17838	0.589189	+	0.807995i	$0.299447\pi$
$68$	−3.53575	−0.428772
$69$	−3.30905	−0.398363
$70$	0	0
$71$	−7.31241	−0.867823	−0.433912	−	0.900955i	$-0.642867\pi$
$71$	−7.31241	−0.867823	−0.433912	+	0.900955i	$0.642867\pi$
$72$	15.1873	1.78984
$73$	−5.46747	−0.639919	−0.319960	−	0.947431i	$-0.603669\pi$
$73$	−5.46747	−0.639919	−0.319960	+	0.947431i	$0.603669\pi$
$74$	19.4326	2.25900
$75$	0	0
$76$	6.28299	0.720709
$77$	1.54168	0.175690
$78$	15.1837	1.71922
$79$	8.60655	0.968313	0.484156	−	0.874982i	$-0.339127\pi$
$79$	8.60655	0.968313	0.484156	+	0.874982i	$0.339127\pi$
$80$	0	0
$81$	30.3502	3.37224
$82$	−10.3287	−1.14061
$83$	−2.49686	−0.274066	−0.137033	−	0.990566i	$-0.543757\pi$
$83$	−2.49686	−0.274066	−0.137033	+	0.990566i	$0.543757\pi$
$84$	2.46307	0.268744
$85$	0	0
$86$	−19.3387	−2.08534
$87$	−12.4487	−1.33464
$88$	3.45387	0.368183
$89$	−5.41541	−0.574033	−0.287016	−	0.957926i	$-0.592663\pi$
$89$	−5.41541	−0.574033	−0.287016	+	0.957926i	$0.592663\pi$
$90$	0	0
$91$	−2.30848	−0.241994
$92$	−0.872898	−0.0910059
$93$	13.2473	1.37368
$94$	12.3943	1.27837
$95$	0	0
$96$	15.3098	1.56255
$97$	−8.41317	−0.854228	−0.427114	−	0.904198i	$-0.640470\pi$
$97$	−8.41317	−0.854228	−0.427114	+	0.904198i	$0.640470\pi$
$98$	10.6323	1.07402
$99$	14.3727	1.44451
$100$	0	0
$101$	−1.87714	−0.186783	−0.0933913	−	0.995629i	$-0.529771\pi$
$101$	−1.87714	−0.186783	−0.0933913	+	0.995629i	$0.529771\pi$
$102$	22.7186	2.24948
$103$	7.10693	0.700267	0.350133	−	0.936700i	$-0.386136\pi$
$103$	7.10693	0.700267	0.350133	+	0.936700i	$0.386136\pi$
$104$	−5.17176	−0.507133
$105$	0	0
$106$	0.688927	0.0669145
$107$	0.543106	0.0525040	0.0262520	−	0.999655i	$-0.491643\pi$
$107$	0.543106	0.0525040	0.0262520	+	0.999655i	$0.491643\pi$
$108$	14.2974	1.37577
$109$	4.33841	0.415544	0.207772	−	0.978177i	$-0.433379\pi$
$109$	4.33841	0.415544	0.207772	+	0.978177i	$0.433379\pi$
$110$	0	0
$111$	−37.9380	−3.60092
$112$	−4.24987	−0.401575
$113$	−19.1171	−1.79838	−0.899192	−	0.437555i	$-0.855845\pi$
$113$	−19.1171	−1.79838	−0.899192	+	0.437555i	$0.855845\pi$
$114$	−40.3707	−3.78107
$115$	0	0
$116$	−3.28385	−0.304898
$117$	−21.5215	−1.98966
$118$	8.19717	0.754611
$119$	−3.45405	−0.316632
$120$	0	0
$121$	−7.73138	−0.702853
$122$	−15.6414	−1.41611
$123$	20.1645	1.81817
$124$	3.49452	0.313817
$125$	0	0
$126$	−11.4902	−1.02363
$127$	4.12091	0.365672	0.182836	−	0.983143i	$-0.441472\pi$
$127$	4.12091	0.365672	0.182836	+	0.983143i	$0.441472\pi$
$128$	−12.8563	−1.13635
$129$	37.7546	3.32411
$130$	0	0
$131$	1.60359	0.140107	0.0700533	−	0.997543i	$-0.477683\pi$
$131$	1.60359	0.140107	0.0700533	+	0.997543i	$0.477683\pi$
$132$	5.22214	0.454529
$133$	6.13782	0.532216
$134$	−16.3487	−1.41231
$135$	0	0
$136$	−7.73822	−0.663547
$137$	−0.497378	−0.0424939	−0.0212470	−	0.999774i	$-0.506764\pi$
$137$	−0.497378	−0.0424939	−0.0212470	+	0.999774i	$0.506764\pi$
$138$	5.60872	0.477446
$139$	−9.53966	−0.809143	−0.404572	−	0.914506i	$-0.632579\pi$
$139$	−9.53966	−0.809143	−0.404572	+	0.914506i	$0.632579\pi$
$140$	0	0
$141$	−24.1971	−2.03777
$142$	12.3943	1.04010
$143$	−4.89438	−0.409288
$144$	−39.6207	−3.30172
$145$	0	0
$146$	9.26716	0.766956
$147$	−20.7572	−1.71202
$148$	−10.0077	−0.822628
$149$	−20.4990	−1.67934	−0.839671	−	0.543096i	$-0.817252\pi$
$149$	−20.4990	−1.67934	−0.839671	+	0.543096i	$0.817252\pi$
$150$	0	0
$151$	9.11088	0.741433	0.370717	−	0.928746i	$-0.379112\pi$
$151$	9.11088	0.741433	0.370717	+	0.928746i	$0.379112\pi$
$152$	13.7508	1.11533
$153$	−32.2014	−2.60333
$154$	−2.61308	−0.210568
$155$	0	0
$156$	−7.81956	−0.626066
$157$	−9.67657	−0.772274	−0.386137	−	0.922441i	$-0.626191\pi$
$157$	−9.67657	−0.772274	−0.386137	+	0.922441i	$0.626191\pi$
$158$	−14.5878	−1.16054
$159$	−1.34498	−0.106664
$160$	0	0
$161$	−0.852729	−0.0672044
$162$	−51.4425	−4.04170
$163$	−8.10453	−0.634796	−0.317398	−	0.948292i	$-0.602809\pi$
$163$	−8.10453	−0.634796	−0.317398	+	0.948292i	$0.602809\pi$
$164$	5.31921	0.415360
$165$	0	0
$166$	4.23208	0.328473
$167$	−12.7841	−0.989267	−0.494633	−	0.869102i	$-0.664698\pi$
$167$	−12.7841	−0.989267	−0.494633	+	0.869102i	$0.664698\pi$
$168$	5.39061	0.415894
$169$	−5.67124	−0.436249
$170$	0	0
$171$	57.2217	4.37585
$172$	9.95933	0.759392
$173$	−0.922225	−0.0701155	−0.0350577	−	0.999385i	$-0.511162\pi$
$173$	−0.922225	−0.0701155	−0.0350577	+	0.999385i	$0.511162\pi$
$174$	21.1001	1.59959
$175$	0	0
$176$	−9.01045	−0.679188
$177$	−16.0032	−1.20288
$178$	9.17892	0.687989
$179$	−2.90586	−0.217194	−0.108597	−	0.994086i	$-0.534636\pi$
$179$	−2.90586	−0.217194	−0.108597	+	0.994086i	$0.534636\pi$
$180$	0	0
$181$	−5.82751	−0.433155	−0.216578	−	0.976265i	$-0.569489\pi$
$181$	−5.82751	−0.433155	−0.216578	+	0.976265i	$0.569489\pi$
$182$	3.91279	0.290035
$183$	30.5365	2.25732
$184$	−1.91040	−0.140836
$185$	0	0
$186$	−22.4537	−1.64639
$187$	−7.32318	−0.535524
$188$	−6.38299	−0.465527
$189$	13.9670	1.01595
$190$	0	0
$191$	0.0996100	0.00720753	0.00360376	−	0.999994i	$-0.498853\pi$
$191$	0.0996100	0.00720753	0.00360376	+	0.999994i	$0.498853\pi$
$192$	7.03410	0.507642
$193$	−8.18136	−0.588907	−0.294454	−	0.955666i	$-0.595138\pi$
$193$	−8.18136	−0.588907	−0.294454	+	0.955666i	$0.595138\pi$
$194$	14.2600	1.02381
$195$	0	0
$196$	−5.47556	−0.391111
$197$	8.79695	0.626757	0.313378	−	0.949628i	$-0.398539\pi$
$197$	8.79695	0.626757	0.313378	+	0.949628i	$0.398539\pi$
$198$	−24.3612	−1.73128
$199$	19.6838	1.39535	0.697673	−	0.716416i	$-0.254219\pi$
$199$	19.6838	1.39535	0.697673	+	0.716416i	$0.254219\pi$
$200$	0	0
$201$	31.9173	2.25127
$202$	3.18168	0.223862
$203$	−3.20798	−0.225156
$204$	−11.7000	−0.819161
$205$	0	0
$206$	−12.0460	−0.839284
$207$	−7.94982	−0.552551
$208$	13.4921	0.935509
$209$	13.0132	0.900144
$210$	0	0
$211$	0.781526	0.0538025	0.0269012	−	0.999638i	$-0.491436\pi$
$211$	0.781526	0.0538025	0.0269012	+	0.999638i	$0.491436\pi$
$212$	−0.354794	−0.0243673
$213$	−24.1971	−1.65796
$214$	−0.920544	−0.0629271
$215$	0	0
$216$	31.2908	2.12907
$217$	3.41378	0.231742
$218$	−7.35344	−0.498038
$219$	−18.0921	−1.22255
$220$	0	0
$221$	10.9656	0.737627
$222$	64.3035	4.31577
$223$	−15.5265	−1.03973	−0.519864	−	0.854249i	$-0.674017\pi$
$223$	−15.5265	−1.03973	−0.519864	+	0.854249i	$0.674017\pi$
$224$	3.94527	0.263604
$225$	0	0
$226$	32.4027	2.15540
$227$	0.373394	0.0247830	0.0123915	−	0.999923i	$-0.496056\pi$
$227$	0.373394	0.0247830	0.0123915	+	0.999923i	$0.496056\pi$
$228$	20.7907	1.37690
$229$	−6.50408	−0.429802	−0.214901	−	0.976636i	$-0.568943\pi$
$229$	−6.50408	−0.429802	−0.214901	+	0.976636i	$0.568943\pi$
$230$	0	0
$231$	5.10148	0.335653
$232$	−7.18694	−0.471846
$233$	−21.6113	−1.41580	−0.707901	−	0.706311i	$-0.750358\pi$
$233$	−21.6113	−1.41580	−0.707901	+	0.706311i	$0.750358\pi$
$234$	36.4781	2.38465
$235$	0	0
$236$	−4.22151	−0.274797
$237$	28.4795	1.84994
$238$	5.85448	0.379490
$239$	−11.4088	−0.737973	−0.368987	−	0.929435i	$-0.620295\pi$
$239$	−11.4088	−0.737973	−0.368987	+	0.929435i	$0.620295\pi$
$240$	0	0
$241$	−10.7415	−0.691919	−0.345959	−	0.938250i	$-0.612446\pi$
$241$	−10.7415	−0.691919	−0.345959	+	0.938250i	$0.612446\pi$
$242$	13.1044	0.842383
$243$	51.2927	3.29043
$244$	8.05525	0.515685
$245$	0	0
$246$	−34.1780	−2.17911
$247$	−19.4858	−1.23985
$248$	7.64800	0.485649
$249$	−8.26223	−0.523598
$250$	0	0
$251$	2.37284	0.149772	0.0748860	−	0.997192i	$-0.476141\pi$
$251$	2.37284	0.149772	0.0748860	+	0.997192i	$0.476141\pi$
$252$	5.91741	0.372762
$253$	−1.80793	−0.113664
$254$	−6.98479	−0.438265
$255$	0	0
$256$	17.5395	1.09622
$257$	9.76254	0.608971	0.304485	−	0.952517i	$-0.401516\pi$
$257$	9.76254	0.608971	0.304485	+	0.952517i	$0.401516\pi$
$258$	−63.9927	−3.98401
$259$	−9.77647	−0.607480
$260$	0	0
$261$	−29.9074	−1.85122
$262$	−2.71803	−0.167921
$263$	22.8169	1.40695	0.703476	−	0.710719i	$-0.251630\pi$
$263$	22.8169	1.40695	0.703476	+	0.710719i	$0.251630\pi$
$264$	11.4290	0.703408
$265$	0	0
$266$	−10.4034	−0.637872
$267$	−17.9199	−1.09668
$268$	8.41948	0.514302
$269$	−32.2387	−1.96563	−0.982815	−	0.184593i	$-0.940903\pi$
$269$	−32.2387	−1.96563	−0.982815	+	0.184593i	$0.940903\pi$
$270$	0	0
$271$	−21.6883	−1.31747	−0.658734	−	0.752376i	$-0.728908\pi$
$271$	−21.6883	−1.31747	−0.658734	+	0.752376i	$0.728908\pi$
$272$	20.1875	1.22405
$273$	−7.63888	−0.462326
$274$	0.843038	0.0509298
$275$	0	0
$276$	−2.88846	−0.173865
$277$	7.52661	0.452230	0.226115	−	0.974101i	$-0.427397\pi$
$277$	7.52661	0.452230	0.226115	+	0.974101i	$0.427397\pi$
$278$	16.1694	0.969774
$279$	31.8260	1.90537
$280$	0	0
$281$	6.71112	0.400352	0.200176	−	0.979760i	$-0.435849\pi$
$281$	6.71112	0.400352	0.200176	+	0.979760i	$0.435849\pi$
$282$	41.0132	2.44230
$283$	5.64413	0.335509	0.167754	−	0.985829i	$-0.446348\pi$
$283$	5.64413	0.335509	0.167754	+	0.985829i	$0.446348\pi$
$284$	−6.38299	−0.378761
$285$	0	0
$286$	8.29578	0.490540
$287$	5.19630	0.306728
$288$	36.7809	2.16734
$289$	−0.592760	−0.0348683
$290$	0	0
$291$	−27.8396	−1.63199
$292$	−4.77254	−0.279292
$293$	19.3764	1.13198	0.565990	−	0.824412i	$-0.308494\pi$
$293$	19.3764	1.13198	0.565990	+	0.824412i	$0.308494\pi$
$294$	35.1827	2.05189
$295$	0	0
$296$	−21.9025	−1.27306
$297$	29.6125	1.71829
$298$	34.7450	2.01272
$299$	2.70717	0.156560
$300$	0	0
$301$	9.72921	0.560782
$302$	−15.4426	−0.888622
$303$	−6.21156	−0.356845
$304$	−35.8730	−2.05746
$305$	0	0
$306$	54.5802	3.12014
$307$	−26.9822	−1.53995	−0.769977	−	0.638071i	$-0.779733\pi$
$307$	−26.9822	−1.53995	−0.769977	+	0.638071i	$0.779733\pi$
$308$	1.34572	0.0766798
$309$	23.5172	1.33785
$310$	0	0
$311$	26.0972	1.47984	0.739918	−	0.672697i	$-0.234864\pi$
$311$	26.0972	1.47984	0.739918	+	0.672697i	$0.234864\pi$
$312$	−17.1136	−0.968869
$313$	21.8861	1.23708	0.618538	−	0.785755i	$-0.287725\pi$
$313$	21.8861	1.23708	0.618538	+	0.785755i	$0.287725\pi$
$314$	16.4014	0.925586
$315$	0	0
$316$	7.51264	0.422619
$317$	27.0750	1.52069	0.760343	−	0.649522i	$-0.225031\pi$
$317$	27.0750	1.52069	0.760343	+	0.649522i	$0.225031\pi$
$318$	2.27969	0.127839
$319$	−6.80147	−0.380809
$320$	0	0
$321$	1.79716	0.100308
$322$	1.44534	0.0805458
$323$	−29.1555	−1.62226
$324$	26.4926	1.47181
$325$	0	0
$326$	13.7369	0.760815
$327$	14.3560	0.793890
$328$	11.6414	0.642791
$329$	−6.23550	−0.343774
$330$	0	0
$331$	21.5646	1.18530	0.592650	−	0.805460i	$-0.298082\pi$
$331$	21.5646	1.18530	0.592650	+	0.805460i	$0.298082\pi$
$332$	−2.17950	−0.119616
$333$	−91.1441	−4.99467
$334$	21.6686	1.18566
$335$	0	0
$336$	−14.0630	−0.767201
$337$	12.9476	0.705302	0.352651	−	0.935755i	$-0.385280\pi$
$337$	12.9476	0.705302	0.352651	+	0.935755i	$0.385280\pi$
$338$	9.61254	0.522853
$339$	−63.2594	−3.43578
$340$	0	0
$341$	7.23780	0.391949
$342$	−96.9886	−5.24454
$343$	−11.3181	−0.611122
$344$	21.7967	1.17520
$345$	0	0
$346$	1.56314	0.0840347
$347$	28.4938	1.52963	0.764815	−	0.644250i	$-0.222830\pi$
$347$	28.4938	1.52963	0.764815	+	0.644250i	$0.222830\pi$
$348$	−10.8664	−0.582502
$349$	−0.394806	−0.0211335	−0.0105667	−	0.999944i	$-0.503364\pi$
$349$	−0.394806	−0.0211335	−0.0105667	+	0.999944i	$0.503364\pi$
$350$	0	0
$351$	−44.3413	−2.36676
$352$	8.36464	0.445837
$353$	8.83611	0.470299	0.235149	−	0.971959i	$-0.424442\pi$
$353$	8.83611	0.470299	0.235149	+	0.971959i	$0.424442\pi$
$354$	27.1249	1.44167
$355$	0	0
$356$	−4.72710	−0.250536
$357$	−11.4296	−0.604920
$358$	4.92533	0.260312
$359$	24.6984	1.30353	0.651766	−	0.758421i	$-0.274029\pi$
$359$	24.6984	1.30353	0.651766	+	0.758421i	$0.274029\pi$
$360$	0	0
$361$	32.8091	1.72680
$362$	9.87741	0.519145
$363$	−25.5835	−1.34279
$364$	−2.01507	−0.105618
$365$	0	0
$366$	−51.7582	−2.70545
$367$	27.8223	1.45231	0.726156	−	0.687530i	$-0.241305\pi$
$367$	27.8223	1.45231	0.726156	+	0.687530i	$0.241305\pi$
$368$	4.98384	0.259801
$369$	48.4441	2.52190
$370$	0	0
$371$	−0.346596	−0.0179944
$372$	11.5636	0.599542
$373$	10.2143	0.528876	0.264438	−	0.964403i	$-0.414814\pi$
$373$	10.2143	0.528876	0.264438	+	0.964403i	$0.414814\pi$
$374$	12.4125	0.641836
$375$	0	0
$376$	−13.9696	−0.720427
$377$	10.1844	0.524524
$378$	−23.6736	−1.21764
$379$	−2.10451	−0.108101	−0.0540507	−	0.998538i	$-0.517213\pi$
$379$	−2.10451	−0.108101	−0.0540507	+	0.998538i	$0.517213\pi$
$380$	0	0
$381$	13.6363	0.698610
$382$	−0.168835	−0.00863836
$383$	30.0460	1.53528	0.767639	−	0.640882i	$-0.221431\pi$
$383$	30.0460	1.53528	0.767639	+	0.640882i	$0.221431\pi$
$384$	−42.5421	−2.17097
$385$	0	0
$386$	13.8671	0.705817
$387$	90.7035	4.61072
$388$	−7.34384	−0.372827
$389$	−28.5252	−1.44629	−0.723143	−	0.690698i	$-0.757303\pi$
$389$	−28.5252	−1.44629	−0.723143	+	0.690698i	$0.757303\pi$
$390$	0	0
$391$	4.05059	0.204847
$392$	−11.9836	−0.605265
$393$	5.30638	0.267671
$394$	−14.9105	−0.751180
$395$	0	0
$396$	12.5459	0.630456
$397$	−3.05896	−0.153525	−0.0767624	−	0.997049i	$-0.524458\pi$
$397$	−3.05896	−0.153525	−0.0767624	+	0.997049i	$0.524458\pi$
$398$	−33.3633	−1.67235
$399$	20.3104	1.01679
$400$	0	0
$401$	−25.4768	−1.27225	−0.636125	−	0.771586i	$-0.719464\pi$
$401$	−25.4768	−1.27225	−0.636125	+	0.771586i	$0.719464\pi$
$402$	−54.0985	−2.69819
$403$	−10.8378	−0.539868
$404$	−1.63855	−0.0815210
$405$	0	0
$406$	5.43740	0.269854
$407$	−20.7278	−1.02744
$408$	−25.6062	−1.26769
$409$	36.3411	1.79695	0.898477	−	0.439021i	$-0.144675\pi$
$409$	36.3411	1.79695	0.898477	+	0.439021i	$0.144675\pi$
$410$	0	0
$411$	−1.64585	−0.0811838
$412$	6.20362	0.305631
$413$	−4.12396	−0.202927
$414$	13.4746	0.662243
$415$	0	0
$416$	−12.5251	−0.614093
$417$	−31.5672	−1.54585
$418$	−22.0569	−1.07884
$419$	−22.3222	−1.09051	−0.545254	−	0.838271i	$-0.683567\pi$
$419$	−22.3222	−1.09051	−0.545254	+	0.838271i	$0.683567\pi$
$420$	0	0
$421$	20.7755	1.01254	0.506268	−	0.862376i	$-0.331025\pi$
$421$	20.7755	1.01254	0.506268	+	0.862376i	$0.331025\pi$
$422$	−1.32466	−0.0644833
$423$	−58.1324	−2.82649
$424$	−0.776491	−0.0377097
$425$	0	0
$426$	41.0132	1.98710
$427$	7.86913	0.380814
$428$	0.474076	0.0229153
$429$	−16.1957	−0.781938
$430$	0	0
$431$	−20.4694	−0.985975	−0.492988	−	0.870036i	$-0.664095\pi$
$431$	−20.4694	−0.985975	−0.492988	+	0.870036i	$0.664095\pi$
$432$	−81.6315	−3.92750
$433$	−5.00423	−0.240488	−0.120244	−	0.992744i	$-0.538368\pi$
$433$	−5.00423	−0.240488	−0.120244	+	0.992744i	$0.538368\pi$
$434$	−5.78623	−0.277748
$435$	0	0
$436$	3.78699	0.181364
$437$	−7.19786	−0.344320
$438$	30.6655	1.46525
$439$	−5.59393	−0.266984	−0.133492	−	0.991050i	$-0.542619\pi$
$439$	−5.59393	−0.266984	−0.133492	+	0.991050i	$0.542619\pi$
$440$	0	0
$441$	−49.8681	−2.37467
$442$	−18.5863	−0.884061
$443$	14.7055	0.698680	0.349340	−	0.936996i	$-0.386406\pi$
$443$	14.7055	0.698680	0.349340	+	0.936996i	$0.386406\pi$
$444$	−33.1160	−1.57162
$445$	0	0
$446$	26.3168	1.24613
$447$	−67.8322	−3.20835
$448$	1.81266	0.0856400
$449$	8.27733	0.390632	0.195316	−	0.980740i	$-0.437427\pi$
$449$	8.27733	0.390632	0.195316	+	0.980740i	$0.437427\pi$
$450$	0	0
$451$	11.0171	0.518773
$452$	−16.6873	−0.784902
$453$	30.1484	1.41649
$454$	−0.632889	−0.0297030
$455$	0	0
$456$	45.5020	2.13082
$457$	11.4431	0.535287	0.267643	−	0.963518i	$-0.413755\pi$
$457$	11.4431	0.535287	0.267643	+	0.963518i	$0.413755\pi$
$458$	11.0242	0.515125
$459$	−66.3454	−3.09674
$460$	0	0
$461$	−7.32589	−0.341201	−0.170600	−	0.985340i	$-0.554571\pi$
$461$	−7.32589	−0.341201	−0.170600	+	0.985340i	$0.554571\pi$
$462$	−8.64682	−0.402286
$463$	−30.3031	−1.40830	−0.704152	−	0.710050i	$-0.748672\pi$
$463$	−30.3031	−1.40830	−0.704152	+	0.710050i	$0.748672\pi$
$464$	18.7493	0.870414
$465$	0	0
$466$	36.6303	1.69687
$467$	19.1376	0.885583	0.442791	−	0.896625i	$-0.353988\pi$
$467$	19.1376	0.885583	0.442791	+	0.896625i	$0.353988\pi$
$468$	−18.7861	−0.868386
$469$	8.22494	0.379793
$470$	0	0
$471$	−32.0203	−1.47542
$472$	−9.23905	−0.425262
$473$	20.6276	0.948458
$474$	−48.2717	−2.21719
$475$	0	0
$476$	−3.01503	−0.138194
$477$	−3.23125	−0.147949
$478$	19.3375	0.884475
$479$	−19.7035	−0.900275	−0.450138	−	0.892959i	$-0.648625\pi$
$479$	−19.7035	−0.900275	−0.450138	+	0.892959i	$0.648625\pi$
$480$	0	0
$481$	31.0375	1.41519
$482$	18.2064	0.829278
$483$	−2.82172	−0.128393
$484$	−6.74871	−0.306759
$485$	0	0
$486$	−86.9393	−3.94365
$487$	−31.3608	−1.42110	−0.710548	−	0.703649i	$-0.751553\pi$
$487$	−31.3608	−1.42110	−0.710548	+	0.703649i	$0.751553\pi$
$488$	17.6295	0.798049
$489$	−26.8183	−1.21277
$490$	0	0
$491$	6.15290	0.277677	0.138838	−	0.990315i	$-0.455663\pi$
$491$	6.15290	0.277677	0.138838	+	0.990315i	$0.455663\pi$
$492$	17.6015	0.793538
$493$	15.2384	0.686301
$494$	33.0277	1.48599
$495$	0	0
$496$	−19.9521	−0.895877
$497$	−6.23550	−0.279700
$498$	14.0042	0.627542
$499$	32.4872	1.45433	0.727164	−	0.686464i	$-0.240838\pi$
$499$	32.4872	1.45433	0.727164	+	0.686464i	$0.240838\pi$
$500$	0	0
$501$	−42.3034	−1.88998
$502$	−4.02187	−0.179505
$503$	25.0323	1.11614	0.558068	−	0.829795i	$-0.311543\pi$
$503$	25.0323	1.11614	0.558068	+	0.829795i	$0.311543\pi$
$504$	12.9507	0.576868
$505$	0	0
$506$	3.06438	0.136228
$507$	−18.7664	−0.833446
$508$	3.59714	0.159597
$509$	−7.57178	−0.335613	−0.167807	−	0.985820i	$-0.553668\pi$
$509$	−7.57178	−0.335613	−0.167807	+	0.985820i	$0.553668\pi$
$510$	0	0
$511$	−4.66227	−0.206247
$512$	−4.01621	−0.177493
$513$	117.895	5.20520
$514$	−16.5471	−0.729863
$515$	0	0
$516$	32.9559	1.45080
$517$	−13.2203	−0.581430
$518$	16.5707	0.728077
$519$	−3.05169	−0.133954
$520$	0	0
$521$	33.1231	1.45115	0.725575	−	0.688143i	$-0.241574\pi$
$521$	33.1231	1.45115	0.725575	+	0.688143i	$0.241574\pi$
$522$	50.6918	2.21872
$523$	−12.1651	−0.531943	−0.265972	−	0.963981i	$-0.585693\pi$
$523$	−12.1651	−0.531943	−0.265972	+	0.963981i	$0.585693\pi$
$524$	1.39977	0.0611494
$525$	0	0
$526$	−38.6738	−1.68626
$527$	−16.2159	−0.706378
$528$	−29.8160	−1.29758
$529$	1.00000	0.0434783
$530$	0	0
$531$	−38.4469	−1.66845
$532$	5.35769	0.232285
$533$	−16.4968	−0.714554
$534$	30.3735	1.31439
$535$	0	0
$536$	18.4266	0.795908
$537$	−9.61565	−0.414946
$538$	54.6434	2.35585
$539$	−11.3409	−0.488487
$540$	0	0
$541$	−9.74714	−0.419062	−0.209531	−	0.977802i	$-0.567194\pi$
$541$	−9.74714	−0.419062	−0.209531	+	0.977802i	$0.567194\pi$
$542$	36.7608	1.57901
$543$	−19.2835	−0.827536
$544$	−18.7406	−0.803496
$545$	0	0
$546$	12.9476	0.554107
$547$	24.0053	1.02639	0.513196	−	0.858271i	$-0.328461\pi$
$547$	24.0053	1.02639	0.513196	+	0.858271i	$0.328461\pi$
$548$	−0.434160	−0.0185464
$549$	73.3624	3.13103
$550$	0	0
$551$	−27.0784	−1.15358
$552$	−6.32160	−0.269065
$553$	7.33905	0.312088
$554$	−12.7573	−0.542007
$555$	0	0
$556$	−8.32714	−0.353150
$557$	39.6594	1.68042	0.840211	−	0.542259i	$-0.182431\pi$
$557$	39.6594	1.68042	0.840211	+	0.542259i	$0.182431\pi$
$558$	−53.9439	−2.28363
$559$	−30.8875	−1.30640
$560$	0	0
$561$	−24.2328	−1.02311
$562$	−11.3751	−0.479829
$563$	11.5311	0.485980	0.242990	−	0.970029i	$-0.421872\pi$
$563$	11.5311	0.485980	0.242990	+	0.970029i	$0.421872\pi$
$564$	−21.1216	−0.889381
$565$	0	0
$566$	−9.56659	−0.402114
$567$	25.8805	1.08688
$568$	−13.9696	−0.586151
$569$	19.6982	0.825792	0.412896	−	0.910778i	$-0.364517\pi$
$569$	19.6982	0.825792	0.412896	+	0.910778i	$0.364517\pi$
$570$	0	0
$571$	−11.0271	−0.461470	−0.230735	−	0.973017i	$-0.574113\pi$
$571$	−11.0271	−0.461470	−0.230735	+	0.973017i	$0.574113\pi$
$572$	−4.27229	−0.178633
$573$	0.329615	0.0137698
$574$	−8.80754	−0.367619
$575$	0	0
$576$	16.8990	0.704127
$577$	1.72708	0.0718992	0.0359496	−	0.999354i	$-0.488554\pi$
$577$	1.72708	0.0718992	0.0359496	+	0.999354i	$0.488554\pi$
$578$	1.00471	0.0417903
$579$	−27.0725	−1.12510
$580$	0	0
$581$	−2.12914	−0.0883317
$582$	47.1871	1.95597
$583$	−0.734844	−0.0304341
$584$	−10.4450	−0.432219
$585$	0	0
$586$	−32.8422	−1.35670
$587$	−24.9467	−1.02966	−0.514829	−	0.857293i	$-0.672145\pi$
$587$	−24.9467	−1.02966	−0.514829	+	0.857293i	$0.672145\pi$
$588$	−18.1189	−0.747211
$589$	28.8156	1.18733
$590$	0	0
$591$	29.1096	1.19741
$592$	57.1394	2.34841
$593$	−15.4113	−0.632865	−0.316433	−	0.948615i	$-0.602485\pi$
$593$	−15.4113	−0.632865	−0.316433	+	0.948615i	$0.602485\pi$
$594$	−50.1921	−2.05941
$595$	0	0
$596$	−17.8935	−0.732947
$597$	65.1347	2.66578
$598$	−4.58855	−0.187640
$599$	0.251631	0.0102814	0.00514069	−	0.999987i	$-0.498364\pi$
$599$	0.251631	0.0102814	0.00514069	+	0.999987i	$0.498364\pi$
$600$	0	0
$601$	32.0537	1.30750	0.653749	−	0.756711i	$-0.273195\pi$
$601$	32.0537	1.30750	0.653749	+	0.756711i	$0.273195\pi$
$602$	−16.4906	−0.672109
$603$	76.6795	3.12263
$604$	7.95287	0.323598
$605$	0	0
$606$	10.5284	0.427685
$607$	4.85762	0.197165	0.0985825	−	0.995129i	$-0.468569\pi$
$607$	4.85762	0.197165	0.0985825	+	0.995129i	$0.468569\pi$
$608$	33.3019	1.35057
$609$	−10.6154	−0.430156
$610$	0	0
$611$	19.7959	0.800858
$612$	−28.1085	−1.13622
$613$	−36.1790	−1.46126	−0.730628	−	0.682776i	$-0.760773\pi$
$613$	−36.1790	−1.46126	−0.730628	+	0.682776i	$0.760773\pi$
$614$	45.7338	1.84567
$615$	0	0
$616$	2.94521	0.118666
$617$	−20.9998	−0.845421	−0.422710	−	0.906265i	$-0.638921\pi$
$617$	−20.9998	−0.845421	−0.422710	+	0.906265i	$0.638921\pi$
$618$	−39.8608	−1.60344
$619$	23.9554	0.962849	0.481424	−	0.876488i	$-0.340120\pi$
$619$	23.9554	0.962849	0.481424	+	0.876488i	$0.340120\pi$
$620$	0	0
$621$	−16.3792	−0.657275
$622$	−44.2338	−1.77361
$623$	−4.61788	−0.185011
$624$	44.6461	1.78727
$625$	0	0
$626$	−37.0962	−1.48266
$627$	43.0615	1.71971
$628$	−8.44665	−0.337058
$629$	46.4396	1.85167
$630$	0	0
$631$	−22.1439	−0.881533	−0.440767	−	0.897622i	$-0.645293\pi$
$631$	−22.1439	−0.881533	−0.440767	+	0.897622i	$0.645293\pi$
$632$	16.4419	0.654025
$633$	2.58611	0.102789
$634$	−45.8912	−1.82257
$635$	0	0
$636$	−1.17403	−0.0465534
$637$	16.9817	0.672838
$638$	11.5282	0.456407
$639$	−58.1324	−2.29968
$640$	0	0
$641$	3.05308	0.120589	0.0602947	−	0.998181i	$-0.480796\pi$
$641$	3.05308	0.120589	0.0602947	+	0.998181i	$0.480796\pi$
$642$	−3.04613	−0.120221
$643$	−0.865731	−0.0341411	−0.0170705	−	0.999854i	$-0.505434\pi$
$643$	−0.865731	−0.0341411	−0.0170705	+	0.999854i	$0.505434\pi$
$644$	−0.744345	−0.0293313
$645$	0	0
$646$	49.4175	1.94431
$647$	−34.7042	−1.36436	−0.682181	−	0.731184i	$-0.738968\pi$
$647$	−34.7042	−1.36436	−0.682181	+	0.731184i	$0.738968\pi$
$648$	57.9809	2.27771
$649$	−8.74352	−0.343213
$650$	0	0
$651$	11.2964	0.442740
$652$	−7.07442	−0.277056
$653$	49.4368	1.93461	0.967305	−	0.253614i	$-0.0816193\pi$
$653$	49.4368	1.93461	0.967305	+	0.253614i	$0.0816193\pi$
$654$	−24.3329	−0.951492
$655$	0	0
$656$	−30.3702	−1.18576
$657$	−43.4654	−1.69575
$658$	10.5689	0.412020
$659$	3.55117	0.138334	0.0691670	−	0.997605i	$-0.477966\pi$
$659$	3.55117	0.138334	0.0691670	+	0.997605i	$0.477966\pi$
$660$	0	0
$661$	23.8273	0.926776	0.463388	−	0.886156i	$-0.346634\pi$
$661$	23.8273	0.926776	0.463388	+	0.886156i	$0.346634\pi$
$662$	−36.5512	−1.42060
$663$	36.2858	1.40922
$664$	−4.76999	−0.185111
$665$	0	0
$666$	154.486	5.98620
$667$	3.76202	0.145666
$668$	−11.1592	−0.431764
$669$	−51.3778	−1.98638
$670$	0	0
$671$	16.6839	0.644075
$672$	13.0551	0.503611
$673$	16.7319	0.644969	0.322484	−	0.946575i	$-0.395482\pi$
$673$	16.7319	0.644969	0.322484	+	0.946575i	$0.395482\pi$
$674$	−21.9457	−0.845319
$675$	0	0
$676$	−4.95041	−0.190400
$677$	44.3491	1.70447	0.852237	−	0.523155i	$-0.175245\pi$
$677$	44.3491	1.70447	0.852237	+	0.523155i	$0.175245\pi$
$678$	107.222	4.11785
$679$	−7.17415	−0.275319
$680$	0	0
$681$	1.23558	0.0473476
$682$	−12.2678	−0.469758
$683$	−14.6621	−0.561028	−0.280514	−	0.959850i	$-0.590505\pi$
$683$	−14.6621	−0.561028	−0.280514	+	0.959850i	$0.590505\pi$
$684$	49.9487	1.90983
$685$	0	0
$686$	19.1838	0.732442
$687$	−21.5223	−0.821128
$688$	−56.8632	−2.16789
$689$	1.10034	0.0419197
$690$	0	0
$691$	−5.76181	−0.219189	−0.109595	−	0.993976i	$-0.534955\pi$
$691$	−5.76181	−0.219189	−0.109595	+	0.993976i	$0.534955\pi$
$692$	−0.805008	−0.0306018
$693$	12.2560	0.465569
$694$	−48.2960	−1.83329
$695$	0	0
$696$	−23.7820	−0.901453
$697$	−24.6832	−0.934942
$698$	0.669182	0.0253289
$699$	−71.5129	−2.70487
$700$	0	0
$701$	−26.8653	−1.01469	−0.507344	−	0.861744i	$-0.669373\pi$
$701$	−26.8653	−1.01469	−0.507344	+	0.861744i	$0.669373\pi$
$702$	75.1568	2.83661
$703$	−82.5229	−3.11241
$704$	3.84315	0.144844
$705$	0	0
$706$	−14.9769	−0.563662
$707$	−1.60069	−0.0602002
$708$	−13.9692	−0.524994
$709$	−9.88754	−0.371334	−0.185667	−	0.982613i	$-0.559445\pi$
$709$	−9.88754	−0.371334	−0.185667	+	0.982613i	$0.559445\pi$
$710$	0	0
$711$	68.4206	2.56597
$712$	−10.3456	−0.387717
$713$	−4.00336	−0.149927
$714$	19.3728	0.725008
$715$	0	0
$716$	−2.53652	−0.0947943
$717$	−37.7523	−1.40988
$718$	−41.8628	−1.56231
$719$	34.3363	1.28053	0.640264	−	0.768155i	$-0.278825\pi$
$719$	34.3363	1.28053	0.640264	+	0.768155i	$0.278825\pi$
$720$	0	0
$721$	6.06029	0.225697
$722$	−55.6103	−2.06960
$723$	−35.5441	−1.32190
$724$	−5.08682	−0.189050
$725$	0	0
$726$	43.3631	1.60936
$727$	−5.69413	−0.211184	−0.105592	−	0.994410i	$-0.533674\pi$
$727$	−5.69413	−0.211184	−0.105592	+	0.994410i	$0.533674\pi$
$728$	−4.41011	−0.163450
$729$	78.6797	2.91406
$730$	0	0
$731$	−46.2152	−1.70933
$732$	26.6553	0.985206
$733$	−33.8318	−1.24961	−0.624803	−	0.780783i	$-0.714821\pi$
$733$	−33.8318	−1.24961	−0.624803	+	0.780783i	$0.714821\pi$
$734$	−47.1577	−1.74062
$735$	0	0
$736$	−4.62664	−0.170540
$737$	17.4383	0.642348
$738$	−82.1109	−3.02255
$739$	31.2203	1.14846	0.574228	−	0.818695i	$-0.305302\pi$
$739$	31.2203	1.14846	0.574228	+	0.818695i	$0.305302\pi$
$740$	0	0
$741$	−64.4796	−2.36872
$742$	0.587467	0.0215666
$743$	−37.2922	−1.36812	−0.684059	−	0.729426i	$-0.739787\pi$
$743$	−37.2922	−1.36812	−0.684059	+	0.729426i	$0.739787\pi$
$744$	25.3076	0.927823
$745$	0	0
$746$	−17.3128	−0.633868
$747$	−19.8496	−0.726258
$748$	−6.39239	−0.233729
$749$	0.463122	0.0169221
$750$	0	0
$751$	−26.8983	−0.981534	−0.490767	−	0.871291i	$-0.663283\pi$
$751$	−26.8983	−0.981534	−0.490767	+	0.871291i	$0.663283\pi$
$752$	36.4439	1.32897
$753$	7.85184	0.286137
$754$	−17.2622	−0.628652
$755$	0	0
$756$	12.1918	0.443411
$757$	−20.7947	−0.755795	−0.377897	−	0.925847i	$-0.623353\pi$
$757$	−20.7947	−0.755795	−0.377897	+	0.925847i	$0.623353\pi$
$758$	3.56707	0.129562
$759$	−5.98254	−0.217152
$760$	0	0
$761$	13.3499	0.483934	0.241967	−	0.970284i	$-0.422207\pi$
$761$	13.3499	0.483934	0.241967	+	0.970284i	$0.422207\pi$
$762$	−23.1130	−0.837297
$763$	3.69949	0.133930
$764$	0.0869493	0.00314572
$765$	0	0
$766$	−50.9268	−1.84006
$767$	13.0924	0.472739
$768$	58.0391	2.09430
$769$	14.4273	0.520262	0.260131	−	0.965573i	$-0.416234\pi$
$769$	14.4273	0.520262	0.260131	+	0.965573i	$0.416234\pi$
$770$	0	0
$771$	32.3048	1.16343
$772$	−7.14149	−0.257028
$773$	34.9789	1.25811	0.629053	−	0.777363i	$-0.283443\pi$
$773$	34.9789	1.25811	0.629053	+	0.777363i	$0.283443\pi$
$774$	−153.739	−5.52604
$775$	0	0
$776$	−16.0725	−0.576969
$777$	−32.3508	−1.16058
$778$	48.3492	1.73340
$779$	43.8618	1.57151
$780$	0	0
$781$	−13.2203	−0.473061
$782$	−6.86559	−0.245513
$783$	−61.6189	−2.20208
$784$	31.2629	1.11653
$785$	0	0
$786$	−8.99411	−0.320809
$787$	−4.21165	−0.150129	−0.0750646	−	0.997179i	$-0.523916\pi$
$787$	−4.21165	−0.150129	−0.0750646	+	0.997179i	$0.523916\pi$
$788$	7.67884	0.273547
$789$	75.5023	2.68795
$790$	0	0
$791$	−16.3017	−0.579621
$792$	27.4576	0.975664
$793$	−24.9822	−0.887145
$794$	5.18482	0.184003
$795$	0	0
$796$	17.1819	0.608997
$797$	29.6417	1.04996	0.524982	−	0.851114i	$-0.324072\pi$
$797$	29.6417	1.04996	0.524982	+	0.851114i	$0.324072\pi$
$798$	−34.4253	−1.21864
$799$	29.6195	1.04786
$800$	0	0
$801$	−43.0516	−1.52115
$802$	43.1822	1.52482
$803$	−9.88482	−0.348828
$804$	27.8605	0.982564
$805$	0	0
$806$	18.3696	0.647042
$807$	−106.680	−3.75530
$808$	−3.58608	−0.126158
$809$	−48.5282	−1.70616	−0.853080	−	0.521780i	$-0.825268\pi$
$809$	−48.5282	−1.70616	−0.853080	+	0.521780i	$0.825268\pi$
$810$	0	0
$811$	−9.13032	−0.320609	−0.160304	−	0.987068i	$-0.551248\pi$
$811$	−9.13032	−0.320609	−0.160304	+	0.987068i	$0.551248\pi$
$812$	−2.80024	−0.0982690
$813$	−71.7676	−2.51700
$814$	35.1328	1.23141
$815$	0	0
$816$	66.8014	2.33852
$817$	82.1240	2.87315
$818$	−61.5969	−2.15368
$819$	−18.3520	−0.641271
$820$	0	0
$821$	−4.78799	−0.167102	−0.0835511	−	0.996503i	$-0.526626\pi$
$821$	−4.78799	−0.167102	−0.0835511	+	0.996503i	$0.526626\pi$
$822$	2.78966	0.0973004
$823$	17.8317	0.621572	0.310786	−	0.950480i	$-0.399408\pi$
$823$	17.8317	0.621572	0.310786	+	0.950480i	$0.399408\pi$
$824$	13.5771	0.472979
$825$	0	0
$826$	6.98996	0.243212
$827$	3.79532	0.131976	0.0659881	−	0.997820i	$-0.478980\pi$
$827$	3.79532	0.131976	0.0659881	+	0.997820i	$0.478980\pi$
$828$	−6.93938	−0.241160
$829$	29.5865	1.02758	0.513790	−	0.857916i	$-0.328241\pi$
$829$	29.5865	1.02758	0.513790	+	0.857916i	$0.328241\pi$
$830$	0	0
$831$	24.9059	0.863977
$832$	−5.75467	−0.199507
$833$	25.4087	0.880360
$834$	53.5053	1.85274
$835$	0	0
$836$	11.3592	0.392867
$837$	65.5719	2.26650
$838$	37.8352	1.30700
$839$	−11.3505	−0.391863	−0.195931	−	0.980618i	$-0.562773\pi$
$839$	−11.3505	−0.391863	−0.195931	+	0.980618i	$0.562773\pi$
$840$	0	0
$841$	−14.8472	−0.511974
$842$	−35.2137	−1.21354
$843$	22.2074	0.764865
$844$	0.682192	0.0234820
$845$	0	0
$846$	98.5322	3.38761
$847$	−6.59277	−0.226530
$848$	2.02571	0.0695632
$849$	18.6767	0.640983
$850$	0	0
$851$	11.4649	0.393012
$852$	−21.1216	−0.723615
$853$	−13.7072	−0.469325	−0.234663	−	0.972077i	$-0.575398\pi$
$853$	−13.7072	−0.469325	−0.234663	+	0.972077i	$0.575398\pi$
$854$	−13.3379	−0.456413
$855$	0	0
$856$	1.03755	0.0354626
$857$	−4.99347	−0.170574	−0.0852869	−	0.996356i	$-0.527181\pi$
$857$	−4.99347	−0.170574	−0.0852869	+	0.996356i	$0.527181\pi$
$858$	27.4512	0.937168
$859$	−36.7762	−1.25479	−0.627395	−	0.778701i	$-0.715879\pi$
$859$	−36.7762	−1.25479	−0.627395	+	0.778701i	$0.715879\pi$
$860$	0	0
$861$	17.1948	0.585998
$862$	34.6948	1.18171
$863$	−1.37292	−0.0467349	−0.0233674	−	0.999727i	$-0.507439\pi$
$863$	−1.37292	−0.0467349	−0.0233674	+	0.999727i	$0.507439\pi$
$864$	75.7807	2.57811
$865$	0	0
$866$	8.48199	0.288230
$867$	−1.96147	−0.0666152
$868$	2.97988	0.101144
$869$	15.5601	0.527839
$870$	0	0
$871$	−26.1118	−0.884766
$872$	8.28808	0.280670
$873$	−66.8832	−2.26365
$874$	12.2001	0.412674
$875$	0	0
$876$	−15.7926	−0.533582
$877$	−21.0051	−0.709293	−0.354646	−	0.935000i	$-0.615399\pi$
$877$	−21.0051	−0.709293	−0.354646	+	0.935000i	$0.615399\pi$
$878$	9.48150	0.319985
$879$	64.1175	2.16263
$880$	0	0
$881$	−24.4448	−0.823567	−0.411783	−	0.911282i	$-0.635094\pi$
$881$	−24.4448	−0.823567	−0.411783	+	0.911282i	$0.635094\pi$
$882$	84.5245	2.84609
$883$	−23.7703	−0.799935	−0.399967	−	0.916529i	$-0.630979\pi$
$883$	−23.7703	−0.799935	−0.399967	+	0.916529i	$0.630979\pi$
$884$	9.57186	0.321936
$885$	0	0
$886$	−24.9253	−0.837381
$887$	−34.6784	−1.16439	−0.582193	−	0.813051i	$-0.697805\pi$
$887$	−34.6784	−1.16439	−0.582193	+	0.813051i	$0.697805\pi$
$888$	−72.4766	−2.43216
$889$	3.51402	0.117856
$890$	0	0
$891$	54.8711	1.83825
$892$	−13.5530	−0.453788
$893$	−52.6337	−1.76132
$894$	114.973	3.84527
$895$	0	0
$896$	−10.9629	−0.366245
$897$	8.95816	0.299104
$898$	−14.0298	−0.468179
$899$	−15.0607	−0.502302
$900$	0	0
$901$	1.64638	0.0548489
$902$	−18.6735	−0.621759
$903$	32.1945	1.07136
$904$	−36.5212	−1.21468
$905$	0	0
$906$	−51.1004	−1.69770
$907$	1.14030	0.0378632	0.0189316	−	0.999821i	$-0.493974\pi$
$907$	1.14030	0.0378632	0.0189316	+	0.999821i	$0.493974\pi$
$908$	0.325935	0.0108165
$909$	−14.9229	−0.494963
$910$	0	0
$911$	26.8882	0.890847	0.445424	−	0.895320i	$-0.353053\pi$
$911$	26.8882	0.890847	0.445424	+	0.895320i	$0.353053\pi$
$912$	−118.706	−3.93074
$913$	−4.51415	−0.149397
$914$	−19.3957	−0.641552
$915$	0	0
$916$	−5.67739	−0.187586
$917$	1.36743	0.0451565
$918$	112.453	3.71150
$919$	44.6052	1.47139	0.735695	−	0.677312i	$-0.236855\pi$
$919$	44.6052	1.47139	0.735695	+	0.677312i	$0.236855\pi$
$920$	0	0
$921$	−89.2855	−2.94206
$922$	12.4171	0.408936
$923$	19.7959	0.651591
$924$	4.45307	0.146495
$925$	0	0
$926$	51.3626	1.68788
$927$	56.4989	1.85567
$928$	−17.4055	−0.571363
$929$	11.7066	0.384081	0.192040	−	0.981387i	$-0.438490\pi$
$929$	11.7066	0.384081	0.192040	+	0.981387i	$0.438490\pi$
$930$	0	0
$931$	−45.1511	−1.47977
$932$	−18.8644	−0.617925
$933$	86.3569	2.82720
$934$	−32.4375	−1.06139
$935$	0	0
$936$	−41.1146	−1.34387
$937$	10.7665	0.351726	0.175863	−	0.984415i	$-0.443728\pi$
$937$	10.7665	0.351726	0.175863	+	0.984415i	$0.443728\pi$
$938$	−13.9410	−0.455189
$939$	72.4223	2.36341
$940$	0	0
$941$	−31.0936	−1.01362	−0.506812	−	0.862057i	$-0.669176\pi$
$941$	−31.0936	−1.01362	−0.506812	+	0.862057i	$0.669176\pi$
$942$	54.2732	1.76831
$943$	−6.09373	−0.198439
$944$	24.1029	0.784481
$945$	0	0
$946$	−34.9630	−1.13675
$947$	31.9699	1.03888	0.519442	−	0.854506i	$-0.326140\pi$
$947$	31.9699	1.03888	0.519442	+	0.854506i	$0.326140\pi$
$948$	24.8597	0.807406
$949$	14.8014	0.480473
$950$	0	0
$951$	89.5927	2.90524
$952$	−6.59860	−0.213862
$953$	44.4559	1.44007	0.720033	−	0.693940i	$-0.244127\pi$
$953$	44.4559	1.44007	0.720033	+	0.693940i	$0.244127\pi$
$954$	5.47684	0.177319
$955$	0	0
$956$	−9.95870	−0.322087
$957$	−22.5064	−0.727529
$958$	33.3967	1.07900
$959$	−0.424129	−0.0136958
$960$	0	0
$961$	−14.9731	−0.483004
$962$	−52.6074	−1.69613
$963$	4.31759	0.139132
$964$	−9.37620	−0.301987
$965$	0	0
$966$	4.78271	0.153881
$967$	37.7617	1.21434	0.607168	−	0.794574i	$-0.292306\pi$
$967$	37.7617	1.21434	0.607168	+	0.794574i	$0.292306\pi$
$968$	−14.7700	−0.474726
$969$	−96.4772	−3.09929
$970$	0	0
$971$	34.7081	1.11384	0.556918	−	0.830568i	$-0.311984\pi$
$971$	34.7081	1.11384	0.556918	+	0.830568i	$0.311984\pi$
$972$	44.7733	1.43610
$973$	−8.13474	−0.260788
$974$	53.1554	1.70321
$975$	0	0
$976$	−45.9918	−1.47216
$977$	−4.66906	−0.149376	−0.0746882	−	0.997207i	$-0.523796\pi$
$977$	−4.66906	−0.149376	−0.0746882	+	0.997207i	$0.523796\pi$
$978$	45.4560	1.45352
$979$	−9.79070	−0.312912
$980$	0	0
$981$	34.4896	1.10117
$982$	−10.4289	−0.332801
$983$	28.9130	0.922182	0.461091	−	0.887353i	$-0.347458\pi$
$983$	28.9130	0.922182	0.461091	+	0.887353i	$0.347458\pi$
$984$	38.5221	1.22804
$985$	0	0
$986$	−25.8285	−0.822545
$987$	−20.6336	−0.656775
$988$	−17.0091	−0.541132
$989$	−11.4095	−0.362801
$990$	0	0
$991$	−45.9545	−1.45979	−0.729896	−	0.683558i	$-0.760432\pi$
$991$	−45.9545	−1.45979	−0.729896	+	0.683558i	$0.760432\pi$
$992$	18.5221	0.588077
$993$	71.3585	2.26449
$994$	10.5689	0.335226
$995$	0	0
$996$	−7.21208	−0.228524
$997$	32.8384	1.04000	0.520002	−	0.854165i	$-0.325931\pi$
$997$	32.8384	1.04000	0.520002	+	0.854165i	$0.325931\pi$
$998$	−55.0646	−1.74304
$999$	−187.786	−5.94130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.k.1.3	✓	7
3.2	odd	2		5175.2.a.cg.1.5		7
4.3	odd	2		9200.2.a.da.1.1		7
5.2	odd	4		575.2.b.f.24.4		14
5.3	odd	4		575.2.b.f.24.11		14
5.4	even	2		575.2.a.l.1.5	yes	7
15.14	odd	2		5175.2.a.cb.1.3		7
20.19	odd	2		9200.2.a.db.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.k.1.3	✓	7	1.1	even	1	trivial
575.2.a.l.1.5	yes	7	5.4	even	2
575.2.b.f.24.4		14	5.2	odd	4
575.2.b.f.24.11		14	5.3	odd	4
5175.2.a.cb.1.3		7	15.14	odd	2
5175.2.a.cg.1.5		7	3.2	odd	2
9200.2.a.da.1.1		7	4.3	odd	2
9200.2.a.db.1.7		7	20.19	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69496 q^{2} +3.30905 q^{3} +0.872898 q^{4} -5.60872 q^{6} +0.852729 q^{7} +1.91040 q^{8} +7.94982 q^{9} +O(q^{10})\)	\(q-1.69496 q^{2} +3.30905 q^{3} +0.872898 q^{4} -5.60872 q^{6} +0.852729 q^{7} +1.91040 q^{8} +7.94982 q^{9} +1.80793 q^{11} +2.88846 q^{12} -2.70717 q^{13} -1.44534 q^{14} -4.98384 q^{16} -4.05059 q^{17} -13.4746 q^{18} +7.19786 q^{19} +2.82172 q^{21} -3.06438 q^{22} -1.00000 q^{23} +6.32160 q^{24} +4.58855 q^{26} +16.3792 q^{27} +0.744345 q^{28} -3.76202 q^{29} +4.00336 q^{31} +4.62664 q^{32} +5.98254 q^{33} +6.86559 q^{34} +6.93938 q^{36} -11.4649 q^{37} -12.2001 q^{38} -8.95816 q^{39} +6.09373 q^{41} -4.78271 q^{42} +11.4095 q^{43} +1.57814 q^{44} +1.69496 q^{46} -7.31241 q^{47} -16.4918 q^{48} -6.27285 q^{49} -13.4036 q^{51} -2.36308 q^{52} -0.406455 q^{53} -27.7622 q^{54} +1.62905 q^{56} +23.8181 q^{57} +6.37647 q^{58} -4.83620 q^{59} +9.22818 q^{61} -6.78554 q^{62} +6.77904 q^{63} +2.12571 q^{64} -10.1402 q^{66} +9.64544 q^{67} -3.53575 q^{68} -3.30905 q^{69} -7.31241 q^{71} +15.1873 q^{72} -5.46747 q^{73} +19.4326 q^{74} +6.28299 q^{76} +1.54168 q^{77} +15.1837 q^{78} +8.60655 q^{79} +30.3502 q^{81} -10.3287 q^{82} -2.49686 q^{83} +2.46307 q^{84} -19.3387 q^{86} -12.4487 q^{87} +3.45387 q^{88} -5.41541 q^{89} -2.30848 q^{91} -0.872898 q^{92} +13.2473 q^{93} +12.3943 q^{94} +15.3098 q^{96} -8.41317 q^{97} +10.6323 q^{98} +14.3727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

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