LMFDB - Embedded newform 175.10.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("175.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$90.1312713287$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 3718 x^{8} + 13493 x^{7} + 4507090 x^{6} - 16532868 x^{5} - 1970350208 x^{4} + \cdots + 455292166912 $ x^10 - 2x^9 - 3718x^8 + 13493x^7 + 4507090x^6 - 16532868x^5 - 1970350208x^4 + 4478267248x^3 + 226976580512x^2 - 929885920960*x + 455292166912
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3^{4}\cdot 5^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-43.8803$ of defining polynomial
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-41.8803 q^{2} -90.6666 q^{3} +1241.96 q^{4} +3797.14 q^{6} +2401.00 q^{7} -30570.9 q^{8} -11462.6 q^{9} +O(q^{10})$	\(q-41.8803 q^{2} -90.6666 q^{3} +1241.96 q^{4} +3797.14 q^{6} +2401.00 q^{7} -30570.9 q^{8} -11462.6 q^{9} +17914.2 q^{11} -112604. q^{12} -144485. q^{13} -100555. q^{14} +644436. q^{16} -427521. q^{17} +480056. q^{18} -246421. q^{19} -217691. q^{21} -750252. q^{22} -662408. q^{23} +2.77176e6 q^{24} +6.05109e6 q^{26} +2.82386e6 q^{27} +2.98194e6 q^{28} +5.66519e6 q^{29} +520754. q^{31} -1.13369e7 q^{32} -1.62422e6 q^{33} +1.79047e7 q^{34} -1.42360e7 q^{36} -1.97713e7 q^{37} +1.03202e7 q^{38} +1.31000e7 q^{39} -1.33323e7 q^{41} +9.11694e6 q^{42} -1.06340e6 q^{43} +2.22487e7 q^{44} +2.77418e7 q^{46} -1.82656e7 q^{47} -5.84288e7 q^{48} +5.76480e6 q^{49} +3.87619e7 q^{51} -1.79445e8 q^{52} -2.33547e7 q^{53} -1.18264e8 q^{54} -7.34008e7 q^{56} +2.23421e7 q^{57} -2.37260e8 q^{58} -6.04509e7 q^{59} -1.71295e8 q^{61} -2.18093e7 q^{62} -2.75216e7 q^{63} +1.44840e8 q^{64} +6.80228e7 q^{66} +3.29829e8 q^{67} -5.30964e8 q^{68} +6.00583e7 q^{69} -1.77209e8 q^{71} +3.50421e8 q^{72} -2.66033e8 q^{73} +8.28028e8 q^{74} -3.06044e8 q^{76} +4.30120e7 q^{77} -5.48632e8 q^{78} -5.22302e8 q^{79} -3.04124e7 q^{81} +5.58362e8 q^{82} +4.33848e8 q^{83} -2.70363e8 q^{84} +4.45357e7 q^{86} -5.13643e8 q^{87} -5.47654e8 q^{88} +3.49621e8 q^{89} -3.46909e8 q^{91} -8.22684e8 q^{92} -4.72150e7 q^{93} +7.64969e8 q^{94} +1.02788e9 q^{96} -1.43381e9 q^{97} -2.41432e8 q^{98} -2.05343e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 22 q^{2} - 77 q^{3} + 2368 q^{4} - 3101 q^{6} + 24010 q^{7} + 4053 q^{8} + 78909 q^{9}+O(q^{10}) $ 10 * q + 22 * q^2 - 77 * q^3 + 2368 * q^4 - 3101 * q^6 + 24010 * q^7 + 4053 * q^8 + 78909 * q^9	\( 10 q + 22 q^{2} - 77 q^{3} + 2368 q^{4} - 3101 q^{6} + 24010 q^{7} + 4053 q^{8} + 78909 q^{9} + 82084 q^{11} - 104559 q^{12} + 148820 q^{13} + 52822 q^{14} + 723600 q^{16} - 523957 q^{17} + 2497331 q^{18} + 420735 q^{19} - 184877 q^{21} - 806686 q^{22} + 2621633 q^{23} + 844067 q^{24} + 3191832 q^{26} + 1299109 q^{27} + 5685568 q^{28} + 2834185 q^{29} + 2703246 q^{31} - 16692042 q^{32} - 11878125 q^{33} + 12094173 q^{34} - 237163 q^{36} - 25124007 q^{37} + 5768035 q^{38} + 61507618 q^{39} + 28695317 q^{41} - 7445501 q^{42} + 11014435 q^{43} + 69407514 q^{44} + 66331723 q^{46} + 27042344 q^{47} + 11305371 q^{48} + 57648010 q^{49} + 155136395 q^{51} - 124108418 q^{52} + 70830926 q^{53} - 308844291 q^{54} + 9731253 q^{56} + 318268205 q^{57} - 122054573 q^{58} - 52453226 q^{59} + 31675770 q^{61} + 264124770 q^{62} + 189460509 q^{63} - 479129269 q^{64} + 190524257 q^{66} + 815451568 q^{67} - 744608123 q^{68} - 288052380 q^{69} + 383130007 q^{71} + 433340780 q^{72} - 918213947 q^{73} + 134394423 q^{74} + 769208867 q^{76} + 197083684 q^{77} - 521964250 q^{78} + 826459641 q^{79} + 1545430378 q^{81} + 50461551 q^{82} - 182898149 q^{83} - 251046159 q^{84} + 1785091749 q^{86} + 896634578 q^{87} - 354288923 q^{88} + 3022888365 q^{89} + 357316820 q^{91} + 2085715863 q^{92} - 2120751084 q^{93} + 3353587916 q^{94} + 6991945247 q^{96} + 1076163732 q^{97} + 126825622 q^{98} + 2388483031 q^{99}+O(q^{100}) \) 10 * q + 22 * q^2 - 77 * q^3 + 2368 * q^4 - 3101 * q^6 + 24010 * q^7 + 4053 * q^8 + 78909 * q^9 + 82084 * q^11 - 104559 * q^12 + 148820 * q^13 + 52822 * q^14 + 723600 * q^16 - 523957 * q^17 + 2497331 * q^18 + 420735 * q^19 - 184877 * q^21 - 806686 * q^22 + 2621633 * q^23 + 844067 * q^24 + 3191832 * q^26 + 1299109 * q^27 + 5685568 * q^28 + 2834185 * q^29 + 2703246 * q^31 - 16692042 * q^32 - 11878125 * q^33 + 12094173 * q^34 - 237163 * q^36 - 25124007 * q^37 + 5768035 * q^38 + 61507618 * q^39 + 28695317 * q^41 - 7445501 * q^42 + 11014435 * q^43 + 69407514 * q^44 + 66331723 * q^46 + 27042344 * q^47 + 11305371 * q^48 + 57648010 * q^49 + 155136395 * q^51 - 124108418 * q^52 + 70830926 * q^53 - 308844291 * q^54 + 9731253 * q^56 + 318268205 * q^57 - 122054573 * q^58 - 52453226 * q^59 + 31675770 * q^61 + 264124770 * q^62 + 189460509 * q^63 - 479129269 * q^64 + 190524257 * q^66 + 815451568 * q^67 - 744608123 * q^68 - 288052380 * q^69 + 383130007 * q^71 + 433340780 * q^72 - 918213947 * q^73 + 134394423 * q^74 + 769208867 * q^76 + 197083684 * q^77 - 521964250 * q^78 + 826459641 * q^79 + 1545430378 * q^81 + 50461551 * q^82 - 182898149 * q^83 - 251046159 * q^84 + 1785091749 * q^86 + 896634578 * q^87 - 354288923 * q^88 + 3022888365 * q^89 + 357316820 * q^91 + 2085715863 * q^92 - 2120751084 * q^93 + 3353587916 * q^94 + 6991945247 * q^96 + 1076163732 * q^97 + 126825622 * q^98 + 2388483031 * 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 $

$2$	−41.8803	−1.85087	−0.925433	−	0.378912i	$-0.876298\pi$
$2$	−41.8803	−1.85087	−0.925433	+	0.378912i	$0.876298\pi$
$3$	−90.6666	−0.646252	−0.323126	−	0.946356i	$-0.604734\pi$
$3$	−90.6666	−0.646252	−0.323126	+	0.946356i	$0.604734\pi$
$4$	1241.96	2.42570
$5$	0	0
$5$	0	0
$6$	3797.14	1.19612
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−30570.9	−2.63878
$9$	−11462.6	−0.582359
$10$	0	0
$11$	17914.2	0.368919	0.184459	−	0.982840i	$-0.440947\pi$
$11$	17914.2	0.368919	0.184459	+	0.982840i	$0.440947\pi$
$12$	−112604.	−1.56761
$13$	−144485.	−1.40307	−0.701534	−	0.712636i	$-0.747501\pi$
$13$	−144485.	−1.40307	−0.701534	+	0.712636i	$0.747501\pi$
$14$	−100555.	−0.699561
$15$	0	0
$16$	644436.	2.45833
$17$	−427521.	−1.24147	−0.620737	−	0.784019i	$-0.713167\pi$
$17$	−427521.	−1.24147	−0.620737	+	0.784019i	$0.713167\pi$
$18$	480056.	1.07787
$19$	−246421.	−0.433796	−0.216898	−	0.976194i	$-0.569594\pi$
$19$	−246421.	−0.433796	−0.216898	+	0.976194i	$0.569594\pi$
$20$	0	0
$21$	−217691.	−0.244260
$22$	−750252.	−0.682819
$23$	−662408.	−0.493572	−0.246786	−	0.969070i	$-0.579374\pi$
$23$	−662408.	−0.493572	−0.246786	+	0.969070i	$0.579374\pi$
$24$	2.77176e6	1.70532
$25$	0	0
$26$	6.05109e6	2.59689
$27$	2.82386e6	1.02260
$28$	2.98194e6	0.916829
$29$	5.66519e6	1.48738	0.743692	−	0.668522i	$-0.233073\pi$
$29$	5.66519e6	1.48738	0.743692	+	0.668522i	$0.233073\pi$
$30$	0	0
$31$	520754.	0.101276	0.0506379	−	0.998717i	$-0.483875\pi$
$31$	520754.	0.101276	0.0506379	+	0.998717i	$0.483875\pi$
$32$	−1.13369e7	−1.91125
$33$	−1.62422e6	−0.238414
$34$	1.79047e7	2.29780
$35$	0	0
$36$	−1.42360e7	−1.41263
$37$	−1.97713e7	−1.73431	−0.867156	−	0.498037i	$-0.834055\pi$
$37$	−1.97713e7	−1.73431	−0.867156	+	0.498037i	$0.834055\pi$
$38$	1.03202e7	0.802898
$39$	1.31000e7	0.906735
$40$	0	0
$41$	−1.33323e7	−0.736850	−0.368425	−	0.929658i	$-0.620103\pi$
$41$	−1.33323e7	−0.736850	−0.368425	+	0.929658i	$0.620103\pi$
$42$	9.11694e6	0.452093
$43$	−1.06340e6	−0.0474340	−0.0237170	−	0.999719i	$-0.507550\pi$
$43$	−1.06340e6	−0.0474340	−0.0237170	+	0.999719i	$0.507550\pi$
$44$	2.22487e7	0.894887
$45$	0	0
$46$	2.77418e7	0.913535
$47$	−1.82656e7	−0.546001	−0.273000	−	0.962014i	$-0.588016\pi$
$47$	−1.82656e7	−0.546001	−0.273000	+	0.962014i	$0.588016\pi$
$48$	−5.84288e7	−1.58870
$49$	5.76480e6	0.142857
$50$	0	0
$51$	3.87619e7	0.802305
$52$	−1.79445e8	−3.40343
$53$	−2.33547e7	−0.406568	−0.203284	−	0.979120i	$-0.565161\pi$
$53$	−2.33547e7	−0.406568	−0.203284	+	0.979120i	$0.565161\pi$
$54$	−1.18264e8	−1.89270
$55$	0	0
$56$	−7.34008e7	−0.997366
$57$	2.23421e7	0.280342
$58$	−2.37260e8	−2.75295
$59$	−6.04509e7	−0.649485	−0.324742	−	0.945803i	$-0.605278\pi$
$59$	−6.04509e7	−0.649485	−0.324742	+	0.945803i	$0.605278\pi$
$60$	0	0
$61$	−1.71295e8	−1.58402	−0.792009	−	0.610509i	$-0.790965\pi$
$61$	−1.71295e8	−1.58402	−0.792009	+	0.610509i	$0.790965\pi$
$62$	−2.18093e7	−0.187448
$63$	−2.75216e7	−0.220111
$64$	1.44840e8	1.07914
$65$	0	0
$66$	6.80228e7	0.441273
$67$	3.29829e8	1.99964	0.999821	−	0.0189426i	$-0.00602998\pi$
$67$	3.29829e8	1.99964	0.999821	+	0.0189426i	$0.00602998\pi$
$68$	−5.30964e8	−3.01145
$69$	6.00583e7	0.318972
$70$	0	0
$71$	−1.77209e8	−0.827603	−0.413802	−	0.910367i	$-0.635799\pi$
$71$	−1.77209e8	−0.827603	−0.413802	+	0.910367i	$0.635799\pi$
$72$	3.50421e8	1.53672
$73$	−2.66033e8	−1.09643	−0.548217	−	0.836336i	$-0.684693\pi$
$73$	−2.66033e8	−1.09643	−0.548217	+	0.836336i	$0.684693\pi$
$74$	8.28028e8	3.20998
$75$	0	0
$76$	−3.06044e8	−1.05226
$77$	4.30120e7	0.139438
$78$	−5.48632e8	−1.67825
$79$	−5.22302e8	−1.50869	−0.754345	−	0.656478i	$-0.772045\pi$
$79$	−5.22302e8	−1.50869	−0.754345	+	0.656478i	$0.772045\pi$
$80$	0	0
$81$	−3.04124e7	−0.0784997
$82$	5.58362e8	1.36381
$83$	4.33848e8	1.00343	0.501714	−	0.865033i	$-0.332703\pi$
$83$	4.33848e8	1.00343	0.501714	+	0.865033i	$0.332703\pi$
$84$	−2.70363e8	−0.592503
$85$	0	0
$86$	4.45357e7	0.0877940
$87$	−5.13643e8	−0.961225
$88$	−5.47654e8	−0.973496
$89$	3.49621e8	0.590667	0.295334	−	0.955394i	$-0.404569\pi$
$89$	3.49621e8	0.590667	0.295334	+	0.955394i	$0.404569\pi$
$90$	0	0
$91$	−3.46909e8	−0.530310
$92$	−8.22684e8	−1.19726
$93$	−4.72150e7	−0.0654496
$94$	7.64969e8	1.01057
$95$	0	0
$96$	1.02788e9	1.23515
$97$	−1.43381e9	−1.64444	−0.822219	−	0.569171i	$-0.807264\pi$
$97$	−1.43381e9	−1.64444	−0.822219	+	0.569171i	$0.807264\pi$
$98$	−2.41432e8	−0.264409
$99$	−2.05343e8	−0.214843
$100$	0	0
$101$	−9.03920e7	−0.0864339	−0.0432169	−	0.999066i	$-0.513761\pi$
$101$	−9.03920e7	−0.0864339	−0.0432169	+	0.999066i	$0.513761\pi$
$102$	−1.62336e9	−1.48496
$103$	−8.33294e8	−0.729510	−0.364755	−	0.931104i	$-0.618847\pi$
$103$	−8.33294e8	−0.729510	−0.364755	+	0.931104i	$0.618847\pi$
$104$	4.41705e9	3.70239
$105$	0	0
$106$	9.78102e8	0.752502
$107$	2.52855e9	1.86485	0.932426	−	0.361361i	$-0.117688\pi$
$107$	2.52855e9	1.86485	0.932426	+	0.361361i	$0.117688\pi$
$108$	3.50712e9	2.48053
$109$	4.52358e8	0.306947	0.153473	−	0.988153i	$-0.450954\pi$
$109$	4.52358e8	0.306947	0.153473	+	0.988153i	$0.450954\pi$
$110$	0	0
$111$	1.79260e9	1.12080
$112$	1.54729e9	0.929161
$113$	−6.53777e8	−0.377204	−0.188602	−	0.982054i	$-0.560396\pi$
$113$	−6.53777e8	−0.377204	−0.188602	+	0.982054i	$0.560396\pi$
$114$	−9.35695e8	−0.518874
$115$	0	0
$116$	7.03593e9	3.60795
$117$	1.65617e9	0.817089
$118$	2.53170e9	1.20211
$119$	−1.02648e9	−0.469233
$120$	0	0
$121$	−2.03703e9	−0.863899
$122$	7.17388e9	2.93180
$123$	1.20880e9	0.476190
$124$	6.46756e8	0.245665
$125$	0	0
$126$	1.15261e9	0.407396
$127$	1.52312e7	0.00519538	0.00259769	−	0.999997i	$-0.499173\pi$
$127$	1.52312e7	0.00519538	0.00259769	+	0.999997i	$0.499173\pi$
$128$	−2.61471e8	−0.0860950
$129$	9.64152e7	0.0306543
$130$	0	0
$131$	−2.71356e9	−0.805043	−0.402522	−	0.915410i	$-0.631866\pi$
$131$	−2.71356e9	−0.805043	−0.402522	+	0.915410i	$0.631866\pi$
$132$	−2.01722e9	−0.578322
$133$	−5.91656e8	−0.163960
$134$	−1.38133e10	−3.70107
$135$	0	0
$136$	1.30697e10	3.27598
$137$	1.23056e9	0.298441	0.149221	−	0.988804i	$-0.452324\pi$
$137$	1.23056e9	0.298441	0.149221	+	0.988804i	$0.452324\pi$
$138$	−2.51526e9	−0.590373
$139$	6.96230e9	1.58193	0.790963	−	0.611864i	$-0.209580\pi$
$139$	6.96230e9	1.58193	0.790963	+	0.611864i	$0.209580\pi$
$140$	0	0
$141$	1.65608e9	0.352854
$142$	7.42155e9	1.53178
$143$	−2.58834e9	−0.517618
$144$	−7.38689e9	−1.43163
$145$	0	0
$146$	1.11415e10	2.02935
$147$	−5.22675e8	−0.0923217
$148$	−2.45551e10	−4.20692
$149$	−1.00626e10	−1.67252	−0.836260	−	0.548333i	$-0.815263\pi$
$149$	−1.00626e10	−1.67252	−0.836260	+	0.548333i	$0.815263\pi$
$150$	0	0
$151$	−5.13484e9	−0.803768	−0.401884	−	0.915691i	$-0.631645\pi$
$151$	−5.13484e9	−0.803768	−0.401884	+	0.915691i	$0.631645\pi$
$152$	7.53330e9	1.14469
$153$	4.90049e9	0.722983
$154$	−1.80136e9	−0.258081
$155$	0	0
$156$	1.62697e10	2.19947
$157$	−1.15530e10	−1.51756	−0.758778	−	0.651350i	$-0.774203\pi$
$157$	−1.15530e10	−1.51756	−0.758778	+	0.651350i	$0.774203\pi$
$158$	2.18742e10	2.79238
$159$	2.11749e9	0.262745
$160$	0	0
$161$	−1.59044e9	−0.186553
$162$	1.27368e9	0.145292
$163$	1.42289e10	1.57880	0.789401	−	0.613878i	$-0.210391\pi$
$163$	1.42289e10	1.57880	0.789401	+	0.613878i	$0.210391\pi$
$164$	−1.65582e10	−1.78738
$165$	0	0
$166$	−1.81697e10	−1.85721
$167$	1.20098e10	1.19485	0.597425	−	0.801925i	$-0.296191\pi$
$167$	1.20098e10	1.19485	0.597425	+	0.801925i	$0.296191\pi$
$168$	6.65500e9	0.644550
$169$	1.02715e10	0.968601
$170$	0	0
$171$	2.82461e9	0.252625
$172$	−1.32070e9	−0.115061
$173$	−2.11473e10	−1.79493	−0.897467	−	0.441082i	$-0.854595\pi$
$173$	−2.11473e10	−1.79493	−0.897467	+	0.441082i	$0.854595\pi$
$174$	2.15115e10	1.77910
$175$	0	0
$176$	1.15446e10	0.906923
$177$	5.48088e9	0.419731
$178$	−1.46422e10	−1.09325
$179$	1.42300e10	1.03602	0.518008	−	0.855376i	$-0.326674\pi$
$179$	1.42300e10	1.03602	0.518008	+	0.855376i	$0.326674\pi$
$180$	0	0
$181$	−1.11433e10	−0.771718	−0.385859	−	0.922558i	$-0.626095\pi$
$181$	−1.11433e10	−0.771718	−0.385859	+	0.922558i	$0.626095\pi$
$182$	1.45287e10	0.981532
$183$	1.55307e10	1.02367
$184$	2.02504e10	1.30243
$185$	0	0
$186$	1.97738e9	0.121138
$187$	−7.65871e9	−0.458003
$188$	−2.26851e10	−1.32444
$189$	6.78009e9	0.386507
$190$	0	0
$191$	1.34757e10	0.732658	0.366329	−	0.930485i	$-0.380614\pi$
$191$	1.34757e10	0.732658	0.366329	+	0.930485i	$0.380614\pi$
$192$	−1.31322e10	−0.697398
$193$	−3.71752e9	−0.192862	−0.0964308	−	0.995340i	$-0.530743\pi$
$193$	−3.71752e9	−0.192862	−0.0964308	+	0.995340i	$0.530743\pi$
$194$	6.00482e10	3.04363
$195$	0	0
$196$	7.15965e9	0.346529
$197$	−1.56399e10	−0.739835	−0.369917	−	0.929065i	$-0.620614\pi$
$197$	−1.56399e10	−0.739835	−0.369917	+	0.929065i	$0.620614\pi$
$198$	8.59982e9	0.397645
$199$	1.50795e10	0.681628	0.340814	−	0.940131i	$-0.389297\pi$
$199$	1.50795e10	0.681628	0.340814	+	0.940131i	$0.389297\pi$
$200$	0	0
$201$	−2.99045e10	−1.29227
$202$	3.78565e9	0.159977
$203$	1.36021e10	0.562178
$204$	4.81407e10	1.94615
$205$	0	0
$206$	3.48986e10	1.35022
$207$	7.59289e9	0.287436
$208$	−9.31116e10	−3.44920
$209$	−4.41443e9	−0.160035
$210$	0	0
$211$	−4.79942e10	−1.66693	−0.833465	−	0.552572i	$-0.813647\pi$
$211$	−4.79942e10	−1.66693	−0.833465	+	0.552572i	$0.813647\pi$
$212$	−2.90056e10	−0.986213
$213$	1.60669e10	0.534840
$214$	−1.05896e11	−3.45159
$215$	0	0
$216$	−8.63281e10	−2.69842
$217$	1.25033e9	0.0382786
$218$	−1.89449e10	−0.568117
$219$	2.41203e10	0.708572
$220$	0	0
$221$	6.17706e10	1.74187
$222$	−7.50744e10	−2.07445
$223$	−4.88667e10	−1.32325	−0.661624	−	0.749836i	$-0.730133\pi$
$223$	−4.88667e10	−1.32325	−0.661624	+	0.749836i	$0.730133\pi$
$224$	−2.72198e10	−0.722386
$225$	0	0
$226$	2.73804e10	0.698155
$227$	7.42210e10	1.85529	0.927643	−	0.373469i	$-0.121832\pi$
$227$	7.42210e10	1.85529	0.927643	+	0.373469i	$0.121832\pi$
$228$	2.77480e10	0.680025
$229$	5.03645e10	1.21022	0.605111	−	0.796141i	$-0.293129\pi$
$229$	5.03645e10	1.21022	0.605111	+	0.796141i	$0.293129\pi$
$230$	0	0
$231$	−3.89975e9	−0.0901121
$232$	−1.73190e11	−3.92488
$233$	1.61411e10	0.358782	0.179391	−	0.983778i	$-0.442587\pi$
$233$	1.61411e10	0.358782	0.179391	+	0.983778i	$0.442587\pi$
$234$	−6.93610e10	−1.51232
$235$	0	0
$236$	−7.50776e10	−1.57546
$237$	4.73554e10	0.974994
$238$	4.29892e10	0.868487
$239$	7.03738e10	1.39515	0.697574	−	0.716513i	$-0.254263\pi$
$239$	7.03738e10	1.39515	0.697574	+	0.716513i	$0.254263\pi$
$240$	0	0
$241$	−5.44766e10	−1.04024	−0.520120	−	0.854093i	$-0.674113\pi$
$241$	−5.44766e10	−1.04024	−0.520120	+	0.854093i	$0.674113\pi$
$242$	8.53114e10	1.59896
$243$	−5.28247e10	−0.971871
$244$	−2.12741e11	−3.84236
$245$	0	0
$246$	−5.06248e10	−0.881364
$247$	3.56042e10	0.608646
$248$	−1.59199e10	−0.267245
$249$	−3.93356e10	−0.648468
$250$	0	0
$251$	−7.06124e10	−1.12292	−0.561461	−	0.827503i	$-0.689760\pi$
$251$	−7.06124e10	−1.12292	−0.561461	+	0.827503i	$0.689760\pi$
$252$	−3.41807e10	−0.533923
$253$	−1.18665e10	−0.182088
$254$	−6.37887e8	−0.00961594
$255$	0	0
$256$	−6.32077e10	−0.919793
$257$	9.27941e10	1.32685	0.663424	−	0.748243i	$-0.269102\pi$
$257$	9.27941e10	1.32685	0.663424	+	0.748243i	$0.269102\pi$
$258$	−4.03790e9	−0.0567370
$259$	−4.74709e10	−0.655508
$260$	0	0
$261$	−6.49376e10	−0.866191
$262$	1.13645e11	1.49003
$263$	4.82463e10	0.621818	0.310909	−	0.950440i	$-0.399367\pi$
$263$	4.82463e10	0.621818	0.310909	+	0.950440i	$0.399367\pi$
$264$	4.96539e10	0.629123
$265$	0	0
$266$	2.47787e10	0.303467
$267$	−3.16990e10	−0.381720
$268$	4.09634e11	4.85053
$269$	8.86234e9	0.103196	0.0515980	−	0.998668i	$-0.483569\pi$
$269$	8.86234e9	0.103196	0.0515980	+	0.998668i	$0.483569\pi$
$270$	0	0
$271$	1.28869e10	0.145140	0.0725700	−	0.997363i	$-0.476880\pi$
$271$	1.28869e10	0.145140	0.0725700	+	0.997363i	$0.476880\pi$
$272$	−2.75510e11	−3.05195
$273$	3.14531e10	0.342714
$274$	−5.15361e10	−0.552375
$275$	0	0
$276$	7.45900e10	0.773730
$277$	8.70886e10	0.888797	0.444398	−	0.895829i	$-0.353417\pi$
$277$	8.70886e10	0.888797	0.444398	+	0.895829i	$0.353417\pi$
$278$	−2.91583e11	−2.92793
$279$	−5.96918e9	−0.0589788
$280$	0	0
$281$	−6.45171e8	−0.00617301	−0.00308650	−	0.999995i	$-0.500982\pi$
$281$	−6.45171e8	−0.00617301	−0.00308650	+	0.999995i	$0.500982\pi$
$282$	−6.93571e10	−0.653085
$283$	1.50606e11	1.39573	0.697866	−	0.716228i	$-0.254133\pi$
$283$	1.50606e11	1.39573	0.697866	+	0.716228i	$0.254133\pi$
$284$	−2.20086e11	−2.00752
$285$	0	0
$286$	1.08400e11	0.958041
$287$	−3.20109e10	−0.278503
$288$	1.29950e11	1.11303
$289$	6.41867e10	0.541258
$290$	0	0
$291$	1.29998e11	1.06272
$292$	−3.30402e11	−2.65962
$293$	−3.41291e10	−0.270533	−0.135267	−	0.990809i	$-0.543189\pi$
$293$	−3.41291e10	−0.270533	−0.135267	+	0.990809i	$0.543189\pi$
$294$	2.18898e10	0.170875
$295$	0	0
$296$	6.04427e11	4.57647
$297$	5.05873e10	0.377257
$298$	4.21424e11	3.09561
$299$	9.57083e10	0.692515
$300$	0	0
$301$	−2.55323e9	−0.0179284
$302$	2.15049e11	1.48767
$303$	8.19554e9	0.0558580
$304$	−1.58802e11	−1.06641
$305$	0	0
$306$	−2.05234e11	−1.33814
$307$	2.41237e9	0.0154996	0.00774980	−	0.999970i	$-0.497533\pi$
$307$	2.41237e9	0.0154996	0.00774980	+	0.999970i	$0.497533\pi$
$308$	5.34192e10	0.338235
$309$	7.55520e10	0.471447
$310$	0	0
$311$	1.85156e11	1.12232	0.561159	−	0.827708i	$-0.310356\pi$
$311$	1.85156e11	1.12232	0.561159	+	0.827708i	$0.310356\pi$
$312$	−4.00479e11	−2.39268
$313$	1.86707e11	1.09954	0.549770	−	0.835316i	$-0.314715\pi$
$313$	1.86707e11	1.09954	0.549770	+	0.835316i	$0.314715\pi$
$314$	4.83841e11	2.80879
$315$	0	0
$316$	−6.48678e11	−3.65963
$317$	1.57521e11	0.876136	0.438068	−	0.898942i	$-0.355663\pi$
$317$	1.57521e11	0.876136	0.438068	+	0.898942i	$0.355663\pi$
$318$	−8.86812e10	−0.486306
$319$	1.01487e11	0.548724
$320$	0	0
$321$	−2.29255e11	−1.20516
$322$	6.66082e10	0.345284
$323$	1.05350e11	0.538547
$324$	−3.77710e10	−0.190417
$325$	0	0
$326$	−5.95911e11	−2.92215
$327$	−4.10138e10	−0.198365
$328$	4.07582e11	1.94439
$329$	−4.38557e10	−0.206369
$330$	0	0
$331$	1.01639e11	0.465409	0.232704	−	0.972548i	$-0.425243\pi$
$331$	1.01639e11	0.465409	0.232704	+	0.972548i	$0.425243\pi$
$332$	5.38822e11	2.43402
$333$	2.26630e11	1.00999
$334$	−5.02976e11	−2.21151
$335$	0	0
$336$	−1.40288e11	−0.600472
$337$	2.79605e11	1.18089	0.590447	−	0.807076i	$-0.298951\pi$
$337$	2.79605e11	1.18089	0.590447	+	0.807076i	$0.298951\pi$
$338$	−4.30175e11	−1.79275
$339$	5.92758e10	0.243769
$340$	0	0
$341$	9.32890e9	0.0373625
$342$	−1.18296e11	−0.467575
$343$	1.38413e10	0.0539949
$344$	3.25092e10	0.125168
$345$	0	0
$346$	8.85657e11	3.32218
$347$	2.78847e11	1.03248	0.516242	−	0.856443i	$-0.327330\pi$
$347$	2.78847e11	1.03248	0.516242	+	0.856443i	$0.327330\pi$
$348$	−6.37924e11	−2.33164
$349$	2.04430e11	0.737615	0.368808	−	0.929506i	$-0.379766\pi$
$349$	2.04430e11	0.737615	0.368808	+	0.929506i	$0.379766\pi$
$350$	0	0
$351$	−4.08007e11	−1.43478
$352$	−2.03091e11	−0.705097
$353$	−2.36809e11	−0.811732	−0.405866	−	0.913932i	$-0.633030\pi$
$353$	−2.36809e11	−0.811732	−0.405866	+	0.913932i	$0.633030\pi$
$354$	−2.29541e11	−0.776865
$355$	0	0
$356$	4.34216e11	1.43278
$357$	9.30674e10	0.303243
$358$	−5.95956e11	−1.91752
$359$	−2.04831e11	−0.650835	−0.325418	−	0.945570i	$-0.605505\pi$
$359$	−2.04831e11	−0.650835	−0.325418	+	0.945570i	$0.605505\pi$
$360$	0	0
$361$	−2.61965e11	−0.811821
$362$	4.66683e11	1.42835
$363$	1.84691e11	0.558296
$364$	−4.30847e11	−1.28637
$365$	0	0
$366$	−6.50432e11	−1.89468
$367$	−3.46737e11	−0.997707	−0.498853	−	0.866686i	$-0.666245\pi$
$367$	−3.46737e11	−0.997707	−0.498853	+	0.866686i	$0.666245\pi$
$368$	−4.26880e11	−1.21336
$369$	1.52823e11	0.429111
$370$	0	0
$371$	−5.60747e10	−0.153668
$372$	−5.86392e10	−0.158761
$373$	−2.79744e11	−0.748293	−0.374146	−	0.927370i	$-0.622064\pi$
$373$	−2.79744e11	−0.748293	−0.374146	+	0.927370i	$0.622064\pi$
$374$	3.20749e11	0.847702
$375$	0	0
$376$	5.58396e11	1.44078
$377$	−8.18537e11	−2.08690
$378$	−2.83952e11	−0.715373
$379$	−2.28677e11	−0.569307	−0.284653	−	0.958630i	$-0.591879\pi$
$379$	−2.28677e11	−0.569307	−0.284653	+	0.958630i	$0.591879\pi$
$380$	0	0
$381$	−1.38096e9	−0.00335752
$382$	−5.64367e11	−1.35605
$383$	1.53728e11	0.365055	0.182527	−	0.983201i	$-0.441572\pi$
$383$	1.53728e11	0.365055	0.182527	+	0.983201i	$0.441572\pi$
$384$	2.37067e10	0.0556391
$385$	0	0
$386$	1.55691e11	0.356961
$387$	1.21893e10	0.0276236
$388$	−1.78073e12	−3.98892
$389$	5.16942e11	1.14464	0.572320	−	0.820030i	$-0.306044\pi$
$389$	5.16942e11	1.14464	0.572320	+	0.820030i	$0.306044\pi$
$390$	0	0
$391$	2.83194e11	0.612757
$392$	−1.76235e11	−0.376969
$393$	2.46030e11	0.520261
$394$	6.55002e11	1.36933
$395$	0	0
$396$	−2.55027e11	−0.521145
$397$	5.37986e11	1.08696	0.543480	−	0.839422i	$-0.317106\pi$
$397$	5.37986e11	1.08696	0.543480	+	0.839422i	$0.317106\pi$
$398$	−6.31533e11	−1.26160
$399$	5.36434e10	0.105959
$400$	0	0
$401$	6.52208e11	1.25961	0.629805	−	0.776753i	$-0.283135\pi$
$401$	6.52208e11	1.25961	0.629805	+	0.776753i	$0.283135\pi$
$402$	1.25241e12	2.39182
$403$	−7.52414e10	−0.142097
$404$	−1.12263e11	−0.209663
$405$	0	0
$406$	−5.69660e11	−1.04052
$407$	−3.54187e11	−0.639820
$408$	−1.18499e12	−2.11711
$409$	9.51190e11	1.68079	0.840393	−	0.541977i	$-0.182324\pi$
$409$	9.51190e11	1.68079	0.840393	+	0.541977i	$0.182324\pi$
$410$	0	0
$411$	−1.11570e11	−0.192868
$412$	−1.03492e12	−1.76957
$413$	−1.45143e11	−0.245482
$414$	−3.17993e11	−0.532005
$415$	0	0
$416$	1.63801e12	2.68162
$417$	−6.31248e11	−1.02232
$418$	1.84878e11	0.296204
$419$	7.56270e11	1.19871	0.599355	−	0.800484i	$-0.295424\pi$
$419$	7.56270e11	1.19871	0.599355	+	0.800484i	$0.295424\pi$
$420$	0	0
$421$	3.10064e11	0.481040	0.240520	−	0.970644i	$-0.422682\pi$
$421$	3.10064e11	0.481040	0.240520	+	0.970644i	$0.422682\pi$
$422$	2.01001e12	3.08526
$423$	2.09371e11	0.317968
$424$	7.13975e11	1.07284
$425$	0	0
$426$	−6.72887e11	−0.989917
$427$	−4.11279e11	−0.598703
$428$	3.14036e12	4.52358
$429$	2.34676e11	0.334511
$430$	0	0
$431$	3.90592e11	0.545225	0.272612	−	0.962124i	$-0.412112\pi$
$431$	3.90592e11	0.545225	0.272612	+	0.962124i	$0.412112\pi$
$432$	1.81980e12	2.51389
$433$	1.34685e12	1.84129	0.920645	−	0.390401i	$-0.127664\pi$
$433$	1.34685e12	1.84129	0.920645	+	0.390401i	$0.127664\pi$
$434$	−5.23642e10	−0.0708486
$435$	0	0
$436$	5.61811e11	0.744562
$437$	1.63231e11	0.214110
$438$	−1.01017e12	−1.31147
$439$	−5.51446e10	−0.0708618	−0.0354309	−	0.999372i	$-0.511280\pi$
$439$	−5.51446e10	−0.0708618	−0.0354309	+	0.999372i	$0.511280\pi$
$440$	0	0
$441$	−6.60794e10	−0.0831941
$442$	−2.58697e12	−3.22397
$443$	9.36547e11	1.15535	0.577674	−	0.816268i	$-0.303960\pi$
$443$	9.36547e11	1.15535	0.577674	+	0.816268i	$0.303960\pi$
$444$	2.22633e12	2.71873
$445$	0	0
$446$	2.04655e12	2.44915
$447$	9.12340e11	1.08087
$448$	3.47761e11	0.407878
$449$	−6.52553e11	−0.757717	−0.378859	−	0.925455i	$-0.623683\pi$
$449$	−6.52553e11	−0.757717	−0.378859	+	0.925455i	$0.623683\pi$
$450$	0	0
$451$	−2.38838e11	−0.271837
$452$	−8.11965e11	−0.914986
$453$	4.65559e11	0.519437
$454$	−3.10840e12	−3.43388
$455$	0	0
$456$	−6.83019e11	−0.739760
$457$	−1.25408e12	−1.34494	−0.672469	−	0.740125i	$-0.734766\pi$
$457$	−1.25408e12	−1.34494	−0.672469	+	0.740125i	$0.734766\pi$
$458$	−2.10928e12	−2.23996
$459$	−1.20726e12	−1.26953
$460$	0	0
$461$	−1.34141e12	−1.38327	−0.691637	−	0.722245i	$-0.743110\pi$
$461$	−1.34141e12	−1.38327	−0.691637	+	0.722245i	$0.743110\pi$
$462$	1.63323e11	0.166785
$463$	−3.27852e11	−0.331561	−0.165781	−	0.986163i	$-0.553014\pi$
$463$	−3.27852e11	−0.331561	−0.165781	+	0.986163i	$0.553014\pi$
$464$	3.65085e12	3.65648
$465$	0	0
$466$	−6.75993e11	−0.664058
$467$	4.30694e9	0.00419028	0.00209514	−	0.999998i	$-0.499333\pi$
$467$	4.30694e9	0.00419028	0.00209514	+	0.999998i	$0.499333\pi$
$468$	2.05690e12	1.98201
$469$	7.91919e11	0.755793
$470$	0	0
$471$	1.04747e12	0.980723
$472$	1.84804e12	1.71385
$473$	−1.90500e10	−0.0174993
$474$	−1.98326e12	−1.80458
$475$	0	0
$476$	−1.27485e12	−1.13822
$477$	2.67705e11	0.236768
$478$	−2.94727e12	−2.58223
$479$	−8.03435e11	−0.697334	−0.348667	−	0.937247i	$-0.613366\pi$
$479$	−8.03435e11	−0.697334	−0.348667	+	0.937247i	$0.613366\pi$
$480$	0	0
$481$	2.85666e12	2.43336
$482$	2.28150e12	1.92534
$483$	1.44200e11	0.120560
$484$	−2.52991e12	−2.09556
$485$	0	0
$486$	2.21231e12	1.79880
$487$	−1.45804e12	−1.17460	−0.587300	−	0.809369i	$-0.699809\pi$
$487$	−1.45804e12	−1.17460	−0.587300	+	0.809369i	$0.699809\pi$
$488$	5.23664e12	4.17988
$489$	−1.29009e12	−1.02030
$490$	0	0
$491$	4.31635e11	0.335158	0.167579	−	0.985859i	$-0.446405\pi$
$491$	4.31635e11	0.335158	0.167579	+	0.985859i	$0.446405\pi$
$492$	1.50128e12	1.15510
$493$	−2.42199e12	−1.84655
$494$	−1.49111e12	−1.12652
$495$	0	0
$496$	3.35593e11	0.248969
$497$	−4.25478e11	−0.312805
$498$	1.64739e12	1.20023
$499$	8.68232e11	0.626878	0.313439	−	0.949608i	$-0.398519\pi$
$499$	8.68232e11	0.626878	0.313439	+	0.949608i	$0.398519\pi$
$500$	0	0
$501$	−1.08889e12	−0.772174
$502$	2.95727e12	2.07838
$503$	−1.96789e12	−1.37071	−0.685356	−	0.728209i	$-0.740353\pi$
$503$	−1.96789e12	−1.37071	−0.685356	+	0.728209i	$0.740353\pi$
$504$	8.41361e11	0.580825
$505$	0	0
$506$	4.96973e11	0.337020
$507$	−9.31285e11	−0.625960
$508$	1.89165e10	0.0126024
$509$	−3.59041e11	−0.237090	−0.118545	−	0.992949i	$-0.537823\pi$
$509$	−3.59041e11	−0.237090	−0.118545	+	0.992949i	$0.537823\pi$
$510$	0	0
$511$	−6.38745e11	−0.414413
$512$	2.78103e12	1.78851
$513$	−6.95858e11	−0.443601
$514$	−3.88625e12	−2.45582
$515$	0	0
$516$	1.19744e11	0.0743583
$517$	−3.27214e11	−0.201430
$518$	1.98809e12	1.21326
$519$	1.91736e12	1.15998
$520$	0	0
$521$	1.83943e12	1.09374	0.546870	−	0.837217i	$-0.315819\pi$
$521$	1.83943e12	1.09374	0.546870	+	0.837217i	$0.315819\pi$
$522$	2.71960e12	1.60320
$523$	1.14004e12	0.666288	0.333144	−	0.942876i	$-0.391890\pi$
$523$	1.14004e12	0.666288	0.333144	+	0.942876i	$0.391890\pi$
$524$	−3.37014e12	−1.95279
$525$	0	0
$526$	−2.02057e12	−1.15090
$527$	−2.22634e11	−0.125731
$528$	−1.04671e12	−0.586101
$529$	−1.36237e12	−0.756387
$530$	0	0
$531$	6.92923e11	0.378233
$532$	−7.34812e11	−0.397717
$533$	1.92633e12	1.03385
$534$	1.32756e12	0.706512
$535$	0	0
$536$	−1.00832e13	−5.27662
$537$	−1.29019e12	−0.669527
$538$	−3.71157e11	−0.191002
$539$	1.03272e11	0.0527026
$540$	0	0
$541$	−1.34361e12	−0.674349	−0.337174	−	0.941442i	$-0.609471\pi$
$541$	−1.34361e12	−0.674349	−0.337174	+	0.941442i	$0.609471\pi$
$542$	−5.39708e11	−0.268635
$543$	1.01032e12	0.498724
$544$	4.84675e12	2.37277
$545$	0	0
$546$	−1.31727e12	−0.634317
$547$	−2.78229e12	−1.32880	−0.664399	−	0.747378i	$-0.731312\pi$
$547$	−2.78229e12	−1.32880	−0.664399	+	0.747378i	$0.731312\pi$
$548$	1.52830e12	0.723930
$549$	1.96348e12	0.922467
$550$	0	0
$551$	−1.39602e12	−0.645222
$552$	−1.83604e12	−0.841697
$553$	−1.25405e12	−0.570231
$554$	−3.64730e12	−1.64504
$555$	0	0
$556$	8.64689e12	3.83728
$557$	−2.26550e12	−0.997278	−0.498639	−	0.866810i	$-0.666167\pi$
$557$	−2.26550e12	−0.997278	−0.498639	+	0.866810i	$0.666167\pi$
$558$	2.49991e11	0.109162
$559$	1.53646e11	0.0665532
$560$	0	0
$561$	6.94389e11	0.295985
$562$	2.70200e10	0.0114254
$563$	−3.59933e12	−1.50985	−0.754924	−	0.655812i	$-0.772326\pi$
$563$	−3.59933e12	−1.50985	−0.754924	+	0.655812i	$0.772326\pi$
$564$	2.05678e12	0.855919
$565$	0	0
$566$	−6.30741e12	−2.58331
$567$	−7.30202e10	−0.0296701
$568$	5.41743e12	2.18387
$569$	4.84791e9	0.00193887	0.000969437	−	1.00000i	$-0.499691\pi$
$569$	4.84791e9	0.00193887	0.000969437		1.00000i	$0.499691\pi$
$570$	0	0
$571$	1.35688e12	0.534168	0.267084	−	0.963673i	$-0.413940\pi$
$571$	1.35688e12	0.534168	0.267084	+	0.963673i	$0.413940\pi$
$572$	−3.21461e12	−1.25559
$573$	−1.22180e12	−0.473482
$574$	1.34063e12	0.515471
$575$	0	0
$576$	−1.66024e12	−0.628448
$577$	7.99931e11	0.300442	0.150221	−	0.988652i	$-0.452001\pi$
$577$	7.99931e11	0.300442	0.150221	+	0.988652i	$0.452001\pi$
$578$	−2.68816e12	−1.00180
$579$	3.37055e11	0.124637
$580$	0	0
$581$	1.04167e12	0.379261
$582$	−5.44437e12	−1.96695
$583$	−4.18381e11	−0.149990
$584$	8.13287e12	2.89325
$585$	0	0
$586$	1.42934e12	0.500720
$587$	−4.84019e12	−1.68264	−0.841319	−	0.540539i	$-0.818220\pi$
$587$	−4.84019e12	−1.68264	−0.841319	+	0.540539i	$0.818220\pi$
$588$	−6.49141e11	−0.223945
$589$	−1.28325e11	−0.0439330
$590$	0	0
$591$	1.41801e12	0.478120
$592$	−1.27413e13	−4.26351
$593$	4.74648e12	1.57625	0.788126	−	0.615514i	$-0.211051\pi$
$593$	4.74648e12	1.57625	0.788126	+	0.615514i	$0.211051\pi$
$594$	−2.11861e12	−0.698252
$595$	0	0
$596$	−1.24973e13	−4.05704
$597$	−1.36720e12	−0.440503
$598$	−4.00829e12	−1.28175
$599$	4.81772e11	0.152905	0.0764524	−	0.997073i	$-0.475641\pi$
$599$	4.81772e11	0.152905	0.0764524	+	0.997073i	$0.475641\pi$
$600$	0	0
$601$	3.58630e12	1.12127	0.560637	−	0.828062i	$-0.310556\pi$
$601$	3.58630e12	1.12127	0.560637	+	0.828062i	$0.310556\pi$
$602$	1.06930e11	0.0331830
$603$	−3.78069e12	−1.16451
$604$	−6.37726e12	−1.94970
$605$	0	0
$606$	−3.43232e11	−0.103386
$607$	−1.79863e12	−0.537767	−0.268883	−	0.963173i	$-0.586655\pi$
$607$	−1.79863e12	−0.537767	−0.268883	+	0.963173i	$0.586655\pi$
$608$	2.79364e12	0.829094
$609$	−1.23326e12	−0.363309
$610$	0	0
$611$	2.63911e12	0.766077
$612$	6.08621e12	1.75374
$613$	5.39256e12	1.54249	0.771246	−	0.636538i	$-0.219634\pi$
$613$	5.39256e12	1.54249	0.771246	+	0.636538i	$0.219634\pi$
$614$	−1.01031e11	−0.0286877
$615$	0	0
$616$	−1.31492e12	−0.367947
$617$	−1.58863e12	−0.441307	−0.220653	−	0.975352i	$-0.570819\pi$
$617$	−1.58863e12	−0.441307	−0.220653	+	0.975352i	$0.570819\pi$
$618$	−3.16414e12	−0.872585
$619$	1.32688e12	0.363265	0.181632	−	0.983367i	$-0.441862\pi$
$619$	1.32688e12	0.363265	0.181632	+	0.983367i	$0.441862\pi$
$620$	0	0
$621$	−1.87055e12	−0.504727
$622$	−7.75439e12	−2.07726
$623$	8.39441e11	0.223251
$624$	8.44211e12	2.22905
$625$	0	0
$626$	−7.81934e12	−2.03510
$627$	4.00241e11	0.103423
$628$	−1.43483e13	−3.68114
$629$	8.45265e12	2.15310
$630$	0	0
$631$	1.10467e12	0.277396	0.138698	−	0.990335i	$-0.455708\pi$
$631$	1.10467e12	0.277396	0.138698	+	0.990335i	$0.455708\pi$
$632$	1.59673e13	3.98111
$633$	4.35147e12	1.07726
$634$	−6.59702e12	−1.62161
$635$	0	0
$636$	2.62984e12	0.637342
$637$	−8.32929e11	−0.200438
$638$	−4.25032e12	−1.01561
$639$	2.03127e12	0.481962
$640$	0	0
$641$	1.97452e12	0.461956	0.230978	−	0.972959i	$-0.425807\pi$
$641$	1.97452e12	0.461956	0.230978	+	0.972959i	$0.425807\pi$
$642$	9.60127e12	2.23060
$643$	−2.07259e12	−0.478150	−0.239075	−	0.971001i	$-0.576844\pi$
$643$	−2.07259e12	−0.478150	−0.239075	+	0.971001i	$0.576844\pi$
$644$	−1.97526e12	−0.452521
$645$	0	0
$646$	−4.41209e12	−0.996778
$647$	2.08290e12	0.467304	0.233652	−	0.972320i	$-0.424932\pi$
$647$	2.08290e12	0.467304	0.233652	+	0.972320i	$0.424932\pi$
$648$	9.29735e11	0.207144
$649$	−1.08293e12	−0.239607
$650$	0	0
$651$	−1.13363e11	−0.0247376
$652$	1.76717e13	3.82970
$653$	−1.47665e12	−0.317811	−0.158906	−	0.987294i	$-0.550797\pi$
$653$	−1.47665e12	−0.317811	−0.158906	+	0.987294i	$0.550797\pi$
$654$	1.71767e12	0.367147
$655$	0	0
$656$	−8.59184e12	−1.81142
$657$	3.04942e12	0.638518
$658$	1.83669e12	0.381961
$659$	1.55484e12	0.321146	0.160573	−	0.987024i	$-0.448666\pi$
$659$	1.55484e12	0.321146	0.160573	+	0.987024i	$0.448666\pi$
$660$	0	0
$661$	4.00374e12	0.815754	0.407877	−	0.913037i	$-0.366269\pi$
$661$	4.00374e12	0.815754	0.407877	+	0.913037i	$0.366269\pi$
$662$	−4.25667e12	−0.861409
$663$	−5.60053e12	−1.12569
$664$	−1.32631e13	−2.64783
$665$	0	0
$666$	−9.49132e12	−1.86936
$667$	−3.75266e12	−0.734131
$668$	1.49157e13	2.89835
$669$	4.43058e12	0.855152
$670$	0	0
$671$	−3.06861e12	−0.584374
$672$	2.46793e12	0.466843
$673$	−4.45584e12	−0.837263	−0.418631	−	0.908156i	$-0.637490\pi$
$673$	−4.45584e12	−0.837263	−0.418631	+	0.908156i	$0.637490\pi$
$674$	−1.17100e13	−2.18568
$675$	0	0
$676$	1.27568e13	2.34954
$677$	2.28694e12	0.418413	0.209207	−	0.977871i	$-0.432912\pi$
$677$	2.28694e12	0.418413	0.209207	+	0.977871i	$0.432912\pi$
$678$	−2.48249e12	−0.451184
$679$	−3.44257e12	−0.621539
$680$	0	0
$681$	−6.72937e12	−1.19898
$682$	−3.90697e11	−0.0691529
$683$	1.06566e13	1.87380	0.936902	−	0.349593i	$-0.113680\pi$
$683$	1.06566e13	1.87380	0.936902	+	0.349593i	$0.113680\pi$
$684$	3.50805e12	0.612793
$685$	0	0
$686$	−5.79677e11	−0.0999373
$687$	−4.56638e12	−0.782108
$688$	−6.85296e11	−0.116608
$689$	3.37441e12	0.570442
$690$	0	0
$691$	4.44231e12	0.741237	0.370619	−	0.928785i	$-0.379146\pi$
$691$	4.44231e12	0.741237	0.370619	+	0.928785i	$0.379146\pi$
$692$	−2.62642e13	−4.35397
$693$	−4.93028e11	−0.0812030
$694$	−1.16782e13	−1.91099
$695$	0	0
$696$	1.57025e13	2.53646
$697$	5.69986e12	0.914780
$698$	−8.56159e12	−1.36523
$699$	−1.46346e12	−0.231864
$700$	0	0
$701$	−4.81518e12	−0.753150	−0.376575	−	0.926386i	$-0.622898\pi$
$701$	−4.81518e12	−0.753150	−0.376575	+	0.926386i	$0.622898\pi$
$702$	1.70875e13	2.65559
$703$	4.87205e12	0.752338
$704$	2.59470e12	0.398116
$705$	0	0
$706$	9.91765e12	1.50241
$707$	−2.17031e11	−0.0326689
$708$	6.80703e12	1.01814
$709$	−3.95390e12	−0.587649	−0.293824	−	0.955859i	$-0.594928\pi$
$709$	−3.95390e12	−0.587649	−0.293824	+	0.955859i	$0.594928\pi$
$710$	0	0
$711$	5.98693e12	0.878599
$712$	−1.06882e13	−1.55864
$713$	−3.44952e11	−0.0499868
$714$	−3.89769e12	−0.561261
$715$	0	0
$716$	1.76731e13	2.51306
$717$	−6.38055e12	−0.901617
$718$	8.57839e12	1.20461
$719$	−4.05417e12	−0.565747	−0.282873	−	0.959157i	$-0.591288\pi$
$719$	−4.05417e12	−0.565747	−0.282873	+	0.959157i	$0.591288\pi$
$720$	0	0
$721$	−2.00074e12	−0.275729
$722$	1.09712e13	1.50257
$723$	4.93921e12	0.672257
$724$	−1.38395e13	−1.87196
$725$	0	0
$726$	−7.73489e12	−1.03333
$727$	−1.30967e12	−0.173883	−0.0869413	−	0.996213i	$-0.527709\pi$
$727$	−1.30967e12	−0.173883	−0.0869413	+	0.996213i	$0.527709\pi$
$728$	1.06053e13	1.39937
$729$	5.38804e12	0.706573
$730$	0	0
$731$	4.54628e11	0.0588881
$732$	1.92885e13	2.48313
$733$	−6.59612e12	−0.843957	−0.421979	−	0.906606i	$-0.638664\pi$
$733$	−6.59612e12	−0.843957	−0.421979	+	0.906606i	$0.638664\pi$
$734$	1.45215e13	1.84662
$735$	0	0
$736$	7.50963e12	0.943340
$737$	5.90862e12	0.737705
$738$	−6.40026e12	−0.794226
$739$	−5.27965e12	−0.651186	−0.325593	−	0.945510i	$-0.605564\pi$
$739$	−5.27965e12	−0.651186	−0.325593	+	0.945510i	$0.605564\pi$
$740$	0	0
$741$	−3.22811e12	−0.393338
$742$	2.34842e12	0.284419
$743$	6.83406e12	0.822677	0.411338	−	0.911483i	$-0.365061\pi$
$743$	6.83406e12	0.822677	0.411338	+	0.911483i	$0.365061\pi$
$744$	1.44341e12	0.172707
$745$	0	0
$746$	1.17158e13	1.38499
$747$	−4.97302e12	−0.584356
$748$	−9.51180e12	−1.11098
$749$	6.07105e12	0.704848
$750$	0	0
$751$	1.37891e13	1.58181	0.790907	−	0.611937i	$-0.209609\pi$
$751$	1.37891e13	1.58181	0.790907	+	0.611937i	$0.209609\pi$
$752$	−1.17710e13	−1.34225
$753$	6.40219e12	0.725690
$754$	3.42806e13	3.86257
$755$	0	0
$756$	8.42060e12	0.937551
$757$	1.05410e13	1.16668	0.583340	−	0.812228i	$-0.301746\pi$
$757$	1.05410e13	1.16668	0.583340	+	0.812228i	$0.301746\pi$
$758$	9.57707e12	1.05371
$759$	1.07590e12	0.117675
$760$	0	0
$761$	−1.08245e13	−1.16998	−0.584989	−	0.811041i	$-0.698901\pi$
$761$	−1.08245e13	−1.16998	−0.584989	+	0.811041i	$0.698901\pi$
$762$	5.78350e10	0.00621432
$763$	1.08611e12	0.116015
$764$	1.67363e13	1.77721
$765$	0	0
$766$	−6.43816e12	−0.675667
$767$	8.73427e12	0.911271
$768$	5.73082e12	0.594418
$769$	4.08970e12	0.421718	0.210859	−	0.977516i	$-0.432374\pi$
$769$	4.08970e12	0.421718	0.210859	+	0.977516i	$0.432374\pi$
$770$	0	0
$771$	−8.41333e12	−0.857478
$772$	−4.61701e12	−0.467825
$773$	−4.29393e12	−0.432561	−0.216281	−	0.976331i	$-0.569393\pi$
$773$	−4.29393e12	−0.432561	−0.216281	+	0.976331i	$0.569393\pi$
$774$	−5.10493e11	−0.0511276
$775$	0	0
$776$	4.38328e13	4.33932
$777$	4.30402e12	0.423623
$778$	−2.16497e13	−2.11857
$779$	3.28536e12	0.319643
$780$	0	0
$781$	−3.17455e12	−0.305318
$782$	−1.18602e13	−1.13413
$783$	1.59977e13	1.52100
$784$	3.71505e12	0.351190
$785$	0	0
$786$	−1.03038e13	−0.962932
$787$	−7.54020e12	−0.700643	−0.350322	−	0.936630i	$-0.613928\pi$
$787$	−7.54020e12	−0.700643	−0.350322	+	0.936630i	$0.613928\pi$
$788$	−1.94241e13	−1.79462
$789$	−4.37433e12	−0.401851
$790$	0	0
$791$	−1.56972e12	−0.142570
$792$	6.27752e12	0.566924
$793$	2.47496e13	2.22249
$794$	−2.25310e13	−2.01182
$795$	0	0
$796$	1.87281e13	1.65343
$797$	1.93572e13	1.69934	0.849668	−	0.527318i	$-0.176802\pi$
$797$	1.93572e13	1.69934	0.849668	+	0.527318i	$0.176802\pi$
$798$	−2.24660e12	−0.196116
$799$	7.80893e12	0.677846
$800$	0	0
$801$	−4.00756e12	−0.343980
$802$	−2.73147e13	−2.33137
$803$	−4.76577e12	−0.404495
$804$	−3.71401e13	−3.13467
$805$	0	0
$806$	3.15113e12	0.263002
$807$	−8.03518e11	−0.0666906
$808$	2.76337e12	0.228080
$809$	−5.79345e12	−0.475520	−0.237760	−	0.971324i	$-0.576413\pi$
$809$	−5.79345e12	−0.475520	−0.237760	+	0.971324i	$0.576413\pi$
$810$	0	0
$811$	−1.10692e13	−0.898508	−0.449254	−	0.893404i	$-0.648310\pi$
$811$	−1.10692e13	−0.898508	−0.449254	+	0.893404i	$0.648310\pi$
$812$	1.68933e13	1.36368
$813$	−1.16841e12	−0.0937970
$814$	1.48335e13	1.18422
$815$	0	0
$816$	2.49796e13	1.97233
$817$	2.62044e11	0.0205767
$818$	−3.98361e13	−3.11091
$819$	3.97647e12	0.308831
$820$	0	0
$821$	−1.34256e12	−0.103131	−0.0515655	−	0.998670i	$-0.516421\pi$
$821$	−1.34256e12	−0.103131	−0.0515655	+	0.998670i	$0.516421\pi$
$822$	4.67260e12	0.356973
$823$	−1.24511e13	−0.946038	−0.473019	−	0.881052i	$-0.656836\pi$
$823$	−1.24511e13	−0.946038	−0.473019	+	0.881052i	$0.656836\pi$
$824$	2.54746e13	1.92502
$825$	0	0
$826$	6.07862e12	0.454354
$827$	5.15987e12	0.383587	0.191794	−	0.981435i	$-0.438570\pi$
$827$	5.15987e12	0.383587	0.191794	+	0.981435i	$0.438570\pi$
$828$	9.43007e12	0.697234
$829$	1.00619e13	0.739917	0.369958	−	0.929048i	$-0.379372\pi$
$829$	1.00619e13	0.739917	0.369958	+	0.929048i	$0.379372\pi$
$830$	0	0
$831$	−7.89603e12	−0.574387
$832$	−2.09273e13	−1.51411
$833$	−2.46458e12	−0.177353
$834$	2.64369e13	1.89218
$835$	0	0
$836$	−5.48254e12	−0.388198
$837$	1.47054e12	0.103565
$838$	−3.16728e13	−2.21865
$839$	−1.30895e13	−0.911995	−0.455998	−	0.889981i	$-0.650717\pi$
$839$	−1.30895e13	−0.911995	−0.455998	+	0.889981i	$0.650717\pi$
$840$	0	0
$841$	1.75872e13	1.21231
$842$	−1.29856e13	−0.890340
$843$	5.84955e10	0.00398932
$844$	−5.96068e13	−4.04348
$845$	0	0
$846$	−8.76850e12	−0.588517
$847$	−4.89091e12	−0.326523
$848$	−1.50506e13	−0.999478
$849$	−1.36549e13	−0.901994
$850$	0	0
$851$	1.30967e13	0.856007
$852$	1.99544e13	1.29736
$853$	−2.50527e13	−1.62026	−0.810129	−	0.586252i	$-0.800603\pi$
$853$	−2.50527e13	−1.62026	−0.810129	+	0.586252i	$0.800603\pi$
$854$	1.72245e13	1.10812
$855$	0	0
$856$	−7.73001e13	−4.92094
$857$	2.84942e13	1.80444	0.902220	−	0.431276i	$-0.141937\pi$
$857$	2.84942e13	1.80444	0.902220	+	0.431276i	$0.141937\pi$
$858$	−9.82831e12	−0.619136
$859$	4.43697e12	0.278046	0.139023	−	0.990289i	$-0.455604\pi$
$859$	4.43697e12	0.278046	0.139023	+	0.990289i	$0.455604\pi$
$860$	0	0
$861$	2.90232e12	0.179983
$862$	−1.63581e13	−1.00914
$863$	−8.01969e12	−0.492163	−0.246082	−	0.969249i	$-0.579143\pi$
$863$	−8.01969e12	−0.492163	−0.246082	+	0.969249i	$0.579143\pi$
$864$	−3.20138e13	−1.95445
$865$	0	0
$866$	−5.64063e13	−3.40798
$867$	−5.81959e12	−0.349789
$868$	1.55286e12	0.0928525
$869$	−9.35663e12	−0.556584
$870$	0	0
$871$	−4.76555e13	−2.80563
$872$	−1.38290e13	−0.809966
$873$	1.64351e13	0.957653
$874$	−6.83616e12	−0.396288
$875$	0	0
$876$	2.99564e13	1.71878
$877$	1.17030e13	0.668035	0.334017	−	0.942567i	$-0.391596\pi$
$877$	1.17030e13	0.668035	0.334017	+	0.942567i	$0.391596\pi$
$878$	2.30947e12	0.131156
$879$	3.09437e12	0.174832
$880$	0	0
$881$	−1.55473e13	−0.869488	−0.434744	−	0.900554i	$-0.643161\pi$
$881$	−1.55473e13	−0.869488	−0.434744	+	0.900554i	$0.643161\pi$
$882$	2.76743e12	0.153981
$883$	−2.41465e13	−1.33669	−0.668347	−	0.743850i	$-0.732998\pi$
$883$	−2.41465e13	−1.33669	−0.668347	+	0.743850i	$0.732998\pi$
$884$	7.67166e13	4.22527
$885$	0	0
$886$	−3.92229e13	−2.13839
$887$	1.01081e13	0.548293	0.274146	−	0.961688i	$-0.411605\pi$
$887$	1.01081e13	0.548293	0.274146	+	0.961688i	$0.411605\pi$
$888$	−5.48013e13	−2.95755
$889$	3.65701e10	0.00196367
$890$	0	0
$891$	−5.44814e11	−0.0289600
$892$	−6.06905e13	−3.20981
$893$	4.50102e12	0.236853
$894$	−3.82091e13	−2.00054
$895$	0	0
$896$	−6.27791e11	−0.0325409
$897$	−8.67754e12	−0.447539
$898$	2.73291e13	1.40243
$899$	2.95017e12	0.150636
$900$	0	0
$901$	9.98464e12	0.504744
$902$	1.00026e13	0.503135
$903$	2.31493e11	0.0115862
$904$	1.99866e13	0.995361
$905$	0	0
$906$	−1.94977e13	−0.961407
$907$	2.71747e13	1.33331	0.666656	−	0.745366i	$-0.267725\pi$
$907$	2.71747e13	1.33331	0.666656	+	0.745366i	$0.267725\pi$
$908$	9.21795e13	4.50037
$909$	1.03612e12	0.0503355
$910$	0	0
$911$	2.68508e13	1.29159	0.645795	−	0.763511i	$-0.276526\pi$
$911$	2.68508e13	1.29159	0.645795	+	0.763511i	$0.276526\pi$
$912$	1.43981e13	0.689172
$913$	7.77205e12	0.370184
$914$	5.25212e13	2.48930
$915$	0	0
$916$	6.25507e13	2.93564
$917$	−6.51527e12	−0.304278
$918$	5.05605e13	2.34974
$919$	2.37810e13	1.09979	0.549896	−	0.835233i	$-0.314667\pi$
$919$	2.37810e13	1.09979	0.549896	+	0.835233i	$0.314667\pi$
$920$	0	0
$921$	−2.18721e11	−0.0100166
$922$	5.61788e13	2.56025
$923$	2.56041e13	1.16118
$924$	−4.84334e12	−0.218585
$925$	0	0
$926$	1.37305e13	0.613675
$927$	9.55169e12	0.424836
$928$	−6.42255e13	−2.84277
$929$	2.18836e13	0.963938	0.481969	−	0.876188i	$-0.339922\pi$
$929$	2.18836e13	0.963938	0.481969	+	0.876188i	$0.339922\pi$
$930$	0	0
$931$	−1.42057e12	−0.0619709
$932$	2.00466e13	0.870299
$933$	−1.67875e13	−0.725300
$934$	−1.80376e11	−0.00775564
$935$	0	0
$936$	−5.06307e13	−2.15612
$937$	−1.19858e13	−0.507972	−0.253986	−	0.967208i	$-0.581742\pi$
$937$	−1.19858e13	−0.507972	−0.253986	+	0.967208i	$0.581742\pi$
$938$	−3.31658e13	−1.39887
$939$	−1.69281e13	−0.710580
$940$	0	0
$941$	2.02974e13	0.843891	0.421945	−	0.906621i	$-0.361347\pi$
$941$	2.02974e13	0.843891	0.421945	+	0.906621i	$0.361347\pi$
$942$	−4.38682e13	−1.81519
$943$	8.83144e12	0.363688
$944$	−3.89568e13	−1.59665
$945$	0	0
$946$	7.97821e11	0.0323888
$947$	−1.92261e13	−0.776813	−0.388406	−	0.921488i	$-0.626974\pi$
$947$	−1.92261e13	−0.776813	−0.388406	+	0.921488i	$0.626974\pi$
$948$	5.88135e13	2.36504
$949$	3.84379e13	1.53837
$950$	0	0
$951$	−1.42819e13	−0.566204
$952$	3.13804e13	1.23820
$953$	−6.52911e12	−0.256411	−0.128205	−	0.991748i	$-0.540922\pi$
$953$	−6.52911e12	−0.256411	−0.128205	+	0.991748i	$0.540922\pi$
$954$	−1.12116e13	−0.438226
$955$	0	0
$956$	8.74014e13	3.38421
$957$	−9.20151e12	−0.354614
$958$	3.36481e13	1.29067
$959$	2.95457e12	0.112800
$960$	0	0
$961$	−2.61684e13	−0.989743
$962$	−1.19638e14	−4.50382
$963$	−2.89837e13	−1.08601
$964$	−6.76578e13	−2.52331
$965$	0	0
$966$	−6.03914e12	−0.223140
$967$	6.89762e12	0.253677	0.126838	−	0.991923i	$-0.459517\pi$
$967$	6.89762e12	0.253677	0.126838	+	0.991923i	$0.459517\pi$
$968$	6.22739e13	2.27964
$969$	−9.55173e12	−0.348037
$970$	0	0
$971$	2.93298e13	1.05882	0.529411	−	0.848365i	$-0.322413\pi$
$971$	2.93298e13	1.05882	0.529411	+	0.848365i	$0.322413\pi$
$972$	−6.56061e13	−2.35747
$973$	1.67165e13	0.597912
$974$	6.10633e13	2.17403
$975$	0	0
$976$	−1.10389e14	−3.89404
$977$	−1.24827e12	−0.0438311	−0.0219155	−	0.999760i	$-0.506976\pi$
$977$	−1.24827e12	−0.0438311	−0.0219155	+	0.999760i	$0.506976\pi$
$978$	5.40292e13	1.88844
$979$	6.26319e12	0.217908
$980$	0	0
$981$	−5.18519e12	−0.178753
$982$	−1.80770e13	−0.620333
$983$	−3.38369e12	−0.115584	−0.0577922	−	0.998329i	$-0.518406\pi$
$983$	−3.38369e12	−0.115584	−0.0577922	+	0.998329i	$0.518406\pi$
$984$	−3.69541e13	−1.25656
$985$	0	0
$986$	1.01434e14	3.41771
$987$	3.97625e12	0.133366
$988$	4.42189e13	1.47639
$989$	7.04407e11	0.0234121
$990$	0	0
$991$	−1.77711e13	−0.585307	−0.292653	−	0.956219i	$-0.594538\pi$
$991$	−1.77711e13	−0.585307	−0.292653	+	0.956219i	$0.594538\pi$
$992$	−5.90372e12	−0.193564
$993$	−9.21527e12	−0.300771
$994$	1.78191e13	0.578959
$995$	0	0
$996$	−4.88532e13	−1.57299
$997$	−4.14514e13	−1.32865	−0.664326	−	0.747443i	$-0.731281\pi$
$997$	−4.14514e13	−1.32865	−0.664326	+	0.747443i	$0.731281\pi$
$998$	−3.63618e13	−1.16027
$999$	−5.58314e13	−1.77351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.a.k.1.1	yes	10
5.2	odd	4		175.10.b.i.99.1		20
5.3	odd	4		175.10.b.i.99.20		20
5.4	even	2		175.10.a.j.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.10.a.j.1.10	✓	10	5.4	even	2
175.10.a.k.1.1	yes	10	1.1	even	1	trivial
175.10.b.i.99.1		20	5.2	odd	4
175.10.b.i.99.20		20	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q-41.8803 q^{2} -90.6666 q^{3} +1241.96 q^{4} +3797.14 q^{6} +2401.00 q^{7} -30570.9 q^{8} -11462.6 q^{9} +O(q^{10})\)	\(q-41.8803 q^{2} -90.6666 q^{3} +1241.96 q^{4} +3797.14 q^{6} +2401.00 q^{7} -30570.9 q^{8} -11462.6 q^{9} +17914.2 q^{11} -112604. q^{12} -144485. q^{13} -100555. q^{14} +644436. q^{16} -427521. q^{17} +480056. q^{18} -246421. q^{19} -217691. q^{21} -750252. q^{22} -662408. q^{23} +2.77176e6 q^{24} +6.05109e6 q^{26} +2.82386e6 q^{27} +2.98194e6 q^{28} +5.66519e6 q^{29} +520754. q^{31} -1.13369e7 q^{32} -1.62422e6 q^{33} +1.79047e7 q^{34} -1.42360e7 q^{36} -1.97713e7 q^{37} +1.03202e7 q^{38} +1.31000e7 q^{39} -1.33323e7 q^{41} +9.11694e6 q^{42} -1.06340e6 q^{43} +2.22487e7 q^{44} +2.77418e7 q^{46} -1.82656e7 q^{47} -5.84288e7 q^{48} +5.76480e6 q^{49} +3.87619e7 q^{51} -1.79445e8 q^{52} -2.33547e7 q^{53} -1.18264e8 q^{54} -7.34008e7 q^{56} +2.23421e7 q^{57} -2.37260e8 q^{58} -6.04509e7 q^{59} -1.71295e8 q^{61} -2.18093e7 q^{62} -2.75216e7 q^{63} +1.44840e8 q^{64} +6.80228e7 q^{66} +3.29829e8 q^{67} -5.30964e8 q^{68} +6.00583e7 q^{69} -1.77209e8 q^{71} +3.50421e8 q^{72} -2.66033e8 q^{73} +8.28028e8 q^{74} -3.06044e8 q^{76} +4.30120e7 q^{77} -5.48632e8 q^{78} -5.22302e8 q^{79} -3.04124e7 q^{81} +5.58362e8 q^{82} +4.33848e8 q^{83} -2.70363e8 q^{84} +4.45357e7 q^{86} -5.13643e8 q^{87} -5.47654e8 q^{88} +3.49621e8 q^{89} -3.46909e8 q^{91} -8.22684e8 q^{92} -4.72150e7 q^{93} +7.64969e8 q^{94} +1.02788e9 q^{96} -1.43381e9 q^{97} -2.41432e8 q^{98} -2.05343e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22 q^{2} - 77 q^{3} + 2368 q^{4} - 3101 q^{6} + 24010 q^{7} + 4053 q^{8} + 78909 q^{9}+O(q^{10}) \) 10 * q + 22 * q^2 - 77 * q^3 + 2368 * q^4 - 3101 * q^6 + 24010 * q^7 + 4053 * q^8 + 78909 * q^9	\( 10 q + 22 q^{2} - 77 q^{3} + 2368 q^{4} - 3101 q^{6} + 24010 q^{7} + 4053 q^{8} + 78909 q^{9} + 82084 q^{11} - 104559 q^{12} + 148820 q^{13} + 52822 q^{14} + 723600 q^{16} - 523957 q^{17} + 2497331 q^{18} + 420735 q^{19} - 184877 q^{21} - 806686 q^{22} + 2621633 q^{23} + 844067 q^{24} + 3191832 q^{26} + 1299109 q^{27} + 5685568 q^{28} + 2834185 q^{29} + 2703246 q^{31} - 16692042 q^{32} - 11878125 q^{33} + 12094173 q^{34} - 237163 q^{36} - 25124007 q^{37} + 5768035 q^{38} + 61507618 q^{39} + 28695317 q^{41} - 7445501 q^{42} + 11014435 q^{43} + 69407514 q^{44} + 66331723 q^{46} + 27042344 q^{47} + 11305371 q^{48} + 57648010 q^{49} + 155136395 q^{51} - 124108418 q^{52} + 70830926 q^{53} - 308844291 q^{54} + 9731253 q^{56} + 318268205 q^{57} - 122054573 q^{58} - 52453226 q^{59} + 31675770 q^{61} + 264124770 q^{62} + 189460509 q^{63} - 479129269 q^{64} + 190524257 q^{66} + 815451568 q^{67} - 744608123 q^{68} - 288052380 q^{69} + 383130007 q^{71} + 433340780 q^{72} - 918213947 q^{73} + 134394423 q^{74} + 769208867 q^{76} + 197083684 q^{77} - 521964250 q^{78} + 826459641 q^{79} + 1545430378 q^{81} + 50461551 q^{82} - 182898149 q^{83} - 251046159 q^{84} + 1785091749 q^{86} + 896634578 q^{87} - 354288923 q^{88} + 3022888365 q^{89} + 357316820 q^{91} + 2085715863 q^{92} - 2120751084 q^{93} + 3353587916 q^{94} + 6991945247 q^{96} + 1076163732 q^{97} + 126825622 q^{98} + 2388483031 q^{99}+O(q^{100}) \) 10 * q + 22 * q^2 - 77 * q^3 + 2368 * q^4 - 3101 * q^6 + 24010 * q^7 + 4053 * q^8 + 78909 * q^9 + 82084 * q^11 - 104559 * q^12 + 148820 * q^13 + 52822 * q^14 + 723600 * q^16 - 523957 * q^17 + 2497331 * q^18 + 420735 * q^19 - 184877 * q^21 - 806686 * q^22 + 2621633 * q^23 + 844067 * q^24 + 3191832 * q^26 + 1299109 * q^27 + 5685568 * q^28 + 2834185 * q^29 + 2703246 * q^31 - 16692042 * q^32 - 11878125 * q^33 + 12094173 * q^34 - 237163 * q^36 - 25124007 * q^37 + 5768035 * q^38 + 61507618 * q^39 + 28695317 * q^41 - 7445501 * q^42 + 11014435 * q^43 + 69407514 * q^44 + 66331723 * q^46 + 27042344 * q^47 + 11305371 * q^48 + 57648010 * q^49 + 155136395 * q^51 - 124108418 * q^52 + 70830926 * q^53 - 308844291 * q^54 + 9731253 * q^56 + 318268205 * q^57 - 122054573 * q^58 - 52453226 * q^59 + 31675770 * q^61 + 264124770 * q^62 + 189460509 * q^63 - 479129269 * q^64 + 190524257 * q^66 + 815451568 * q^67 - 744608123 * q^68 - 288052380 * q^69 + 383130007 * q^71 + 433340780 * q^72 - 918213947 * q^73 + 134394423 * q^74 + 769208867 * q^76 + 197083684 * q^77 - 521964250 * q^78 + 826459641 * q^79 + 1545430378 * q^81 + 50461551 * q^82 - 182898149 * q^83 - 251046159 * q^84 + 1785091749 * q^86 + 896634578 * q^87 - 354288923 * q^88 + 3022888365 * q^89 + 357316820 * q^91 + 2085715863 * q^92 - 2120751084 * q^93 + 3353587916 * q^94 + 6991945247 * q^96 + 1076163732 * q^97 + 126825622 * q^98 + 2388483031 * q^99

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