LMFDB - Embedded newform 175.10.a.k.1.9

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			1.9
Root			$32.5212$ 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)

$f(q)$	$=$	$q+34.5212 q^{2} -75.4776 q^{3} +679.716 q^{4} -2605.58 q^{6} +2401.00 q^{7} +5789.77 q^{8} -13986.1 q^{9} +O(q^{10})$	\(q+34.5212 q^{2} -75.4776 q^{3} +679.716 q^{4} -2605.58 q^{6} +2401.00 q^{7} +5789.77 q^{8} -13986.1 q^{9} -73499.6 q^{11} -51303.4 q^{12} +143632. q^{13} +82885.5 q^{14} -148145. q^{16} +475448. q^{17} -482818. q^{18} -333356. q^{19} -181222. q^{21} -2.53730e6 q^{22} +2.57885e6 q^{23} -436998. q^{24} +4.95836e6 q^{26} +2.54127e6 q^{27} +1.63200e6 q^{28} +3.19624e6 q^{29} -2.09212e6 q^{31} -8.07850e6 q^{32} +5.54757e6 q^{33} +1.64131e7 q^{34} -9.50660e6 q^{36} -1.01249e7 q^{37} -1.15079e7 q^{38} -1.08410e7 q^{39} +2.80868e7 q^{41} -6.25600e6 q^{42} +3.72938e7 q^{43} -4.99588e7 q^{44} +8.90252e7 q^{46} -2.31645e6 q^{47} +1.11816e7 q^{48} +5.76480e6 q^{49} -3.58857e7 q^{51} +9.76291e7 q^{52} -2.16352e7 q^{53} +8.77276e7 q^{54} +1.39012e7 q^{56} +2.51609e7 q^{57} +1.10338e8 q^{58} -1.65589e8 q^{59} +6.98946e7 q^{61} -7.22224e7 q^{62} -3.35807e7 q^{63} -2.03030e8 q^{64} +1.91509e8 q^{66} +2.63551e8 q^{67} +3.23170e8 q^{68} -1.94646e8 q^{69} -3.16956e7 q^{71} -8.09764e7 q^{72} +1.89554e8 q^{73} -3.49524e8 q^{74} -2.26587e8 q^{76} -1.76472e8 q^{77} -3.74245e8 q^{78} +1.08296e8 q^{79} +8.34803e7 q^{81} +9.69591e8 q^{82} +6.18530e8 q^{83} -1.23179e8 q^{84} +1.28743e9 q^{86} -2.41244e8 q^{87} -4.25545e8 q^{88} +8.42628e8 q^{89} +3.44861e8 q^{91} +1.75289e9 q^{92} +1.57908e8 q^{93} -7.99667e7 q^{94} +6.09746e8 q^{96} +3.19881e8 q^{97} +1.99008e8 q^{98} +1.02797e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	34.5212	1.52564	0.762819	−	0.646612i	$-0.223815\pi$
$2$	34.5212	1.52564	0.762819	+	0.646612i	$0.223815\pi$
$3$	−75.4776	−0.537988	−0.268994	−	0.963142i	$-0.586691\pi$
$3$	−75.4776	−0.537988	−0.268994	+	0.963142i	$0.586691\pi$
$4$	679.716	1.32757
$5$	0	0
$5$	0	0
$6$	−2605.58	−0.820775
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	5789.77	0.499754
$9$	−13986.1	−0.710569
$10$	0	0
$11$	−73499.6	−1.51362	−0.756811	−	0.653633i	$-0.773244\pi$
$11$	−73499.6	−1.51362	−0.756811	+	0.653633i	$0.773244\pi$
$12$	−51303.4	−0.714217
$13$	143632.	1.39478	0.697391	−	0.716691i	$-0.254344\pi$
$13$	143632.	1.39478	0.697391	+	0.716691i	$0.254344\pi$
$14$	82885.5	0.576637
$15$	0	0
$16$	−148145.	−0.565127
$17$	475448.	1.38065	0.690324	−	0.723501i	$-0.257468\pi$
$17$	475448.	1.38065	0.690324	+	0.723501i	$0.257468\pi$
$18$	−482818.	−1.08407
$19$	−333356.	−0.586836	−0.293418	−	0.955984i	$-0.594793\pi$
$19$	−333356.	−0.586836	−0.293418	+	0.955984i	$0.594793\pi$
$20$	0	0
$21$	−181222.	−0.203340
$22$	−2.53730e6	−2.30924
$23$	2.57885e6	1.92155	0.960775	−	0.277330i	$-0.0894496\pi$
$23$	2.57885e6	1.92155	0.960775	+	0.277330i	$0.0894496\pi$
$24$	−436998.	−0.268862
$25$	0	0
$26$	4.95836e6	2.12793
$27$	2.54127e6	0.920266
$28$	1.63200e6	0.501774
$29$	3.19624e6	0.839166	0.419583	−	0.907717i	$-0.362176\pi$
$29$	3.19624e6	0.839166	0.419583	+	0.907717i	$0.362176\pi$
$30$	0	0
$31$	−2.09212e6	−0.406872	−0.203436	−	0.979088i	$-0.565211\pi$
$31$	−2.09212e6	−0.406872	−0.203436	+	0.979088i	$0.565211\pi$
$32$	−8.07850e6	−1.36193
$33$	5.54757e6	0.814311
$34$	1.64131e7	2.10637
$35$	0	0
$36$	−9.50660e6	−0.943330
$37$	−1.01249e7	−0.888142	−0.444071	−	0.895992i	$-0.646466\pi$
$37$	−1.01249e7	−0.888142	−0.444071	+	0.895992i	$0.646466\pi$
$38$	−1.15079e7	−0.895300
$39$	−1.08410e7	−0.750376
$40$	0	0
$41$	2.80868e7	1.55230	0.776148	−	0.630551i	$-0.217171\pi$
$41$	2.80868e7	1.55230	0.776148	+	0.630551i	$0.217171\pi$
$42$	−6.25600e6	−0.310224
$43$	3.72938e7	1.66352	0.831762	−	0.555132i	$-0.187332\pi$
$43$	3.72938e7	1.66352	0.831762	+	0.555132i	$0.187332\pi$
$44$	−4.99588e7	−2.00944
$45$	0	0
$46$	8.90252e7	2.93159
$47$	−2.31645e6	−0.0692441	−0.0346220	−	0.999400i	$-0.511023\pi$
$47$	−2.31645e6	−0.0692441	−0.0346220	+	0.999400i	$0.511023\pi$
$48$	1.11816e7	0.304032
$49$	5.76480e6	0.142857
$50$	0	0
$51$	−3.58857e7	−0.742772
$52$	9.76291e7	1.85167
$53$	−2.16352e7	−0.376635	−0.188317	−	0.982108i	$-0.560303\pi$
$53$	−2.16352e7	−0.376635	−0.188317	+	0.982108i	$0.560303\pi$
$54$	8.77276e7	1.40399
$55$	0	0
$56$	1.39012e7	0.188889
$57$	2.51609e7	0.315711
$58$	1.10338e8	1.28026
$59$	−1.65589e8	−1.77908	−0.889542	−	0.456854i	$-0.848976\pi$
$59$	−1.65589e8	−1.77908	−0.889542	+	0.456854i	$0.848976\pi$
$60$	0	0
$61$	6.98946e7	0.646338	0.323169	−	0.946341i	$-0.395252\pi$
$61$	6.98946e7	0.646338	0.323169	+	0.946341i	$0.395252\pi$
$62$	−7.22224e7	−0.620740
$63$	−3.35807e7	−0.268570
$64$	−2.03030e8	−1.51269
$65$	0	0
$66$	1.91509e8	1.24234
$67$	2.63551e8	1.59782	0.798910	−	0.601450i	$-0.205410\pi$
$67$	2.63551e8	1.59782	0.798910	+	0.601450i	$0.205410\pi$
$68$	3.23170e8	1.83291
$69$	−1.94646e8	−1.03377
$70$	0	0
$71$	−3.16956e7	−0.148026	−0.0740128	−	0.997257i	$-0.523581\pi$
$71$	−3.16956e7	−0.148026	−0.0740128	+	0.997257i	$0.523581\pi$
$72$	−8.09764e7	−0.355109
$73$	1.89554e8	0.781234	0.390617	−	0.920553i	$-0.372262\pi$
$73$	1.89554e8	0.781234	0.390617	+	0.920553i	$0.372262\pi$
$74$	−3.49524e8	−1.35498
$75$	0	0
$76$	−2.26587e8	−0.779066
$77$	−1.76472e8	−0.572096
$78$	−3.74245e8	−1.14480
$79$	1.08296e8	0.312816	0.156408	−	0.987693i	$-0.450009\pi$
$79$	1.08296e8	0.312816	0.156408	+	0.987693i	$0.450009\pi$
$80$	0	0
$81$	8.34803e7	0.215477
$82$	9.69591e8	2.36824
$83$	6.18530e8	1.43057	0.715285	−	0.698832i	$-0.246297\pi$
$83$	6.18530e8	1.43057	0.715285	+	0.698832i	$0.246297\pi$
$84$	−1.23179e8	−0.269949
$85$	0	0
$86$	1.28743e9	2.53794
$87$	−2.41244e8	−0.451461
$88$	−4.25545e8	−0.756439
$89$	8.42628e8	1.42358	0.711788	−	0.702394i	$-0.247886\pi$
$89$	8.42628e8	1.42358	0.711788	+	0.702394i	$0.247886\pi$
$90$	0	0
$91$	3.44861e8	0.527178
$92$	1.75289e9	2.55099
$93$	1.57908e8	0.218892
$94$	−7.99667e7	−0.105641
$95$	0	0
$96$	6.09746e8	0.732704
$97$	3.19881e8	0.366873	0.183436	−	0.983032i	$-0.441278\pi$
$97$	3.19881e8	0.366873	0.183436	+	0.983032i	$0.441278\pi$
$98$	1.99008e8	0.217948
$99$	1.02797e9	1.07553
$100$	0	0
$101$	1.56866e8	0.149997	0.0749984	−	0.997184i	$-0.476105\pi$
$101$	1.56866e8	0.149997	0.0749984	+	0.997184i	$0.476105\pi$
$102$	−1.23882e9	−1.13320
$103$	−9.32141e8	−0.816045	−0.408022	−	0.912972i	$-0.633782\pi$
$103$	−9.32141e8	−0.816045	−0.408022	+	0.912972i	$0.633782\pi$
$104$	8.31596e8	0.697048
$105$	0	0
$106$	−7.46875e8	−0.574608
$107$	−1.48998e8	−0.109889	−0.0549444	−	0.998489i	$-0.517498\pi$
$107$	−1.48998e8	−0.109889	−0.0549444	+	0.998489i	$0.517498\pi$
$108$	1.72734e9	1.22172
$109$	1.20228e9	0.815804	0.407902	−	0.913026i	$-0.366260\pi$
$109$	1.20228e9	0.815804	0.407902	+	0.913026i	$0.366260\pi$
$110$	0	0
$111$	7.64203e8	0.477810
$112$	−3.55695e8	−0.213598
$113$	6.52154e8	0.376268	0.188134	−	0.982143i	$-0.439756\pi$
$113$	6.52154e8	0.376268	0.188134	+	0.982143i	$0.439756\pi$
$114$	8.68586e8	0.481660
$115$	0	0
$116$	2.17253e9	1.11405
$117$	−2.00886e9	−0.991089
$118$	−5.71632e9	−2.71424
$119$	1.14155e9	0.521836
$120$	0	0
$121$	3.04424e9	1.29105
$122$	2.41285e9	0.986077
$123$	−2.11992e9	−0.835117
$124$	−1.42204e9	−0.540152
$125$	0	0
$126$	−1.15925e9	−0.409740
$127$	−2.21740e9	−0.756359	−0.378180	−	0.925732i	$-0.623450\pi$
$127$	−2.21740e9	−0.756359	−0.378180	+	0.925732i	$0.623450\pi$
$128$	−2.87265e9	−0.945883
$129$	−2.81485e9	−0.894956
$130$	0	0
$131$	−4.76302e9	−1.41306	−0.706531	−	0.707682i	$-0.749741\pi$
$131$	−4.76302e9	−1.41306	−0.706531	+	0.707682i	$0.749741\pi$
$132$	3.77077e9	1.08105
$133$	−8.00388e8	−0.221803
$134$	9.09810e9	2.43769
$135$	0	0
$136$	2.75273e9	0.689984
$137$	4.02607e9	0.976426	0.488213	−	0.872725i	$-0.337649\pi$
$137$	4.02607e9	0.976426	0.488213	+	0.872725i	$0.337649\pi$
$138$	−6.71941e9	−1.57716
$139$	−9.50451e8	−0.215955	−0.107977	−	0.994153i	$-0.534437\pi$
$139$	−9.50451e8	−0.215955	−0.107977	+	0.994153i	$0.534437\pi$
$140$	0	0
$141$	1.74840e8	0.0372525
$142$	−1.09417e9	−0.225833
$143$	−1.05569e10	−2.11117
$144$	2.07197e9	0.401562
$145$	0	0
$146$	6.54365e9	1.19188
$147$	−4.35113e8	−0.0768554
$148$	−6.88205e9	−1.17907
$149$	−5.39464e9	−0.896653	−0.448326	−	0.893870i	$-0.647980\pi$
$149$	−5.39464e9	−0.896653	−0.448326	+	0.893870i	$0.647980\pi$
$150$	0	0
$151$	−3.53405e9	−0.553193	−0.276597	−	0.960986i	$-0.589207\pi$
$151$	−3.53405e9	−0.553193	−0.276597	+	0.960986i	$0.589207\pi$
$152$	−1.93005e9	−0.293274
$153$	−6.64967e9	−0.981045
$154$	−6.09205e9	−0.872811
$155$	0	0
$156$	−7.36881e9	−0.996177
$157$	5.27741e9	0.693222	0.346611	−	0.938009i	$-0.387332\pi$
$157$	5.27741e9	0.693222	0.346611	+	0.938009i	$0.387332\pi$
$158$	3.73850e9	0.477244
$159$	1.63298e9	0.202625
$160$	0	0
$161$	6.19183e9	0.726277
$162$	2.88184e9	0.328740
$163$	7.17624e9	0.796256	0.398128	−	0.917330i	$-0.369660\pi$
$163$	7.17624e9	0.796256	0.398128	+	0.917330i	$0.369660\pi$
$164$	1.90910e10	2.06078
$165$	0	0
$166$	2.13524e10	2.18253
$167$	−1.65713e10	−1.64866	−0.824332	−	0.566107i	$-0.808449\pi$
$167$	−1.65713e10	−1.64866	−0.824332	+	0.566107i	$0.808449\pi$
$168$	−1.04923e9	−0.101620
$169$	1.00257e10	0.945419
$170$	0	0
$171$	4.66236e9	0.416988
$172$	2.53492e10	2.20845
$173$	−1.98279e10	−1.68294	−0.841470	−	0.540303i	$-0.818310\pi$
$173$	−1.98279e10	−1.68294	−0.841470	+	0.540303i	$0.818310\pi$
$174$	−8.32806e9	−0.688767
$175$	0	0
$176$	1.08886e10	0.855389
$177$	1.24982e10	0.957126
$178$	2.90886e10	2.17186
$179$	−1.32723e10	−0.966288	−0.483144	−	0.875541i	$-0.660505\pi$
$179$	−1.32723e10	−0.966288	−0.483144	+	0.875541i	$0.660505\pi$
$180$	0	0
$181$	−6.10348e9	−0.422692	−0.211346	−	0.977411i	$-0.567785\pi$
$181$	−6.10348e9	−0.422692	−0.211346	+	0.977411i	$0.567785\pi$
$182$	1.19050e10	0.804283
$183$	−5.27548e9	−0.347722
$184$	1.49310e10	0.960301
$185$	0	0
$186$	5.45118e9	0.333950
$187$	−3.49452e10	−2.08978
$188$	−1.57453e9	−0.0919264
$189$	6.10158e9	0.347828
$190$	0	0
$191$	2.38399e10	1.29615	0.648075	−	0.761577i	$-0.275575\pi$
$191$	2.38399e10	1.29615	0.648075	+	0.761577i	$0.275575\pi$
$192$	1.53242e10	0.813809
$193$	2.81131e10	1.45848	0.729242	−	0.684256i	$-0.239873\pi$
$193$	2.81131e10	1.45848	0.729242	+	0.684256i	$0.239873\pi$
$194$	1.10427e10	0.559715
$195$	0	0
$196$	3.91843e9	0.189653
$197$	2.19893e10	1.04019	0.520096	−	0.854108i	$-0.325896\pi$
$197$	2.19893e10	1.04019	0.520096	+	0.854108i	$0.325896\pi$
$198$	3.54869e10	1.64087
$199$	−2.23288e10	−1.00931	−0.504657	−	0.863320i	$-0.668381\pi$
$199$	−2.23288e10	−1.00931	−0.504657	+	0.863320i	$0.668381\pi$
$200$	0	0
$201$	−1.98922e10	−0.859608
$202$	5.41520e9	0.228841
$203$	7.67417e9	0.317175
$204$	−2.43921e10	−0.986082
$205$	0	0
$206$	−3.21787e10	−1.24499
$207$	−3.60682e10	−1.36539
$208$	−2.12783e10	−0.788230
$209$	2.45015e10	0.888249
$210$	0	0
$211$	−1.66190e10	−0.577211	−0.288606	−	0.957448i	$-0.593192\pi$
$211$	−1.66190e10	−0.577211	−0.288606	+	0.957448i	$0.593192\pi$
$212$	−1.47058e10	−0.500009
$213$	2.39231e9	0.0796359
$214$	−5.14360e9	−0.167651
$215$	0	0
$216$	1.47133e10	0.459906
$217$	−5.02317e9	−0.153783
$218$	4.15042e10	1.24462
$219$	−1.43071e10	−0.420294
$220$	0	0
$221$	6.82896e10	1.92570
$222$	2.63812e10	0.728965
$223$	6.97318e10	1.88825	0.944124	−	0.329591i	$-0.106911\pi$
$223$	6.97318e10	1.88825	0.944124	+	0.329591i	$0.106911\pi$
$224$	−1.93965e10	−0.514762
$225$	0	0
$226$	2.25132e10	0.574048
$227$	1.20946e10	0.302326	0.151163	−	0.988509i	$-0.451698\pi$
$227$	1.20946e10	0.302326	0.151163	+	0.988509i	$0.451698\pi$
$228$	1.71023e10	0.419128
$229$	−9.47582e9	−0.227697	−0.113848	−	0.993498i	$-0.536318\pi$
$229$	−9.47582e9	−0.227697	−0.113848	+	0.993498i	$0.536318\pi$
$230$	0	0
$231$	1.33197e10	0.307781
$232$	1.85055e10	0.419377
$233$	−9.90393e9	−0.220144	−0.110072	−	0.993924i	$-0.535108\pi$
$233$	−9.90393e9	−0.220144	−0.110072	+	0.993924i	$0.535108\pi$
$234$	−6.93483e10	−1.51204
$235$	0	0
$236$	−1.12553e11	−2.36186
$237$	−8.17390e9	−0.168291
$238$	3.94077e10	0.796132
$239$	−1.14928e10	−0.227843	−0.113922	−	0.993490i	$-0.536341\pi$
$239$	−1.14928e10	−0.227843	−0.113922	+	0.993490i	$0.536341\pi$
$240$	0	0
$241$	−2.01418e10	−0.384612	−0.192306	−	0.981335i	$-0.561597\pi$
$241$	−2.01418e10	−0.384612	−0.192306	+	0.981335i	$0.561597\pi$
$242$	1.05091e11	1.96968
$243$	−5.63206e10	−1.03619
$244$	4.75085e10	0.858059
$245$	0	0
$246$	−7.31824e10	−1.27409
$247$	−4.78806e10	−0.818509
$248$	−1.21129e10	−0.203336
$249$	−4.66852e10	−0.769630
$250$	0	0
$251$	1.02411e11	1.62860	0.814300	−	0.580444i	$-0.197121\pi$
$251$	1.02411e11	1.62860	0.814300	+	0.580444i	$0.197121\pi$
$252$	−2.28253e10	−0.356545
$253$	−1.89545e11	−2.90850
$254$	−7.65475e10	−1.15393
$255$	0	0
$256$	4.78391e9	0.0696150
$257$	−5.09073e10	−0.727916	−0.363958	−	0.931415i	$-0.618575\pi$
$257$	−5.09073e10	−0.727916	−0.363958	+	0.931415i	$0.618575\pi$
$258$	−9.71721e10	−1.36538
$259$	−2.43099e10	−0.335686
$260$	0	0
$261$	−4.47030e10	−0.596286
$262$	−1.64425e11	−2.15582
$263$	5.74976e10	0.741053	0.370526	−	0.928822i	$-0.379177\pi$
$263$	5.74976e10	0.741053	0.370526	+	0.928822i	$0.379177\pi$
$264$	3.21191e10	0.406955
$265$	0	0
$266$	−2.76304e10	−0.338391
$267$	−6.35996e10	−0.765867
$268$	1.79140e11	2.12122
$269$	−1.22952e11	−1.43169	−0.715847	−	0.698257i	$-0.753959\pi$
$269$	−1.22952e11	−1.43169	−0.715847	+	0.698257i	$0.753959\pi$
$270$	0	0
$271$	−1.23159e11	−1.38709	−0.693543	−	0.720415i	$-0.743951\pi$
$271$	−1.23159e11	−1.38709	−0.693543	+	0.720415i	$0.743951\pi$
$272$	−7.04351e10	−0.780241
$273$	−2.60293e10	−0.283616
$274$	1.38985e11	1.48967
$275$	0	0
$276$	−1.32304e11	−1.37240
$277$	−9.36533e10	−0.955794	−0.477897	−	0.878416i	$-0.658601\pi$
$277$	−9.36533e10	−0.955794	−0.477897	+	0.878416i	$0.658601\pi$
$278$	−3.28107e10	−0.329469
$279$	2.92606e10	0.289111
$280$	0	0
$281$	5.80890e10	0.555796	0.277898	−	0.960611i	$-0.410362\pi$
$281$	5.80890e10	0.555796	0.277898	+	0.960611i	$0.410362\pi$
$282$	6.03570e9	0.0568338
$283$	1.79267e11	1.66135	0.830675	−	0.556758i	$-0.187955\pi$
$283$	1.79267e11	1.66135	0.830675	+	0.556758i	$0.187955\pi$
$284$	−2.15440e10	−0.196514
$285$	0	0
$286$	−3.64437e11	−3.22089
$287$	6.74364e10	0.586713
$288$	1.12987e11	0.967747
$289$	1.07463e11	0.906187
$290$	0	0
$291$	−2.41438e10	−0.197373
$292$	1.28843e11	1.03714
$293$	−7.38582e10	−0.585456	−0.292728	−	0.956196i	$-0.594563\pi$
$293$	−7.38582e10	−0.585456	−0.292728	+	0.956196i	$0.594563\pi$
$294$	−1.50207e10	−0.117254
$295$	0	0
$296$	−5.86207e10	−0.443852
$297$	−1.86782e11	−1.39293
$298$	−1.86230e11	−1.36797
$299$	3.70406e11	2.68014
$300$	0	0
$301$	8.95425e10	0.628753
$302$	−1.22000e11	−0.843972
$303$	−1.18399e10	−0.0806965
$304$	4.93849e10	0.331637
$305$	0	0
$306$	−2.29555e11	−1.49672
$307$	1.00563e10	0.0646125	0.0323062	−	0.999478i	$-0.489715\pi$
$307$	1.00563e10	0.0646125	0.0323062	+	0.999478i	$0.489715\pi$
$308$	−1.19951e11	−0.759497
$309$	7.03558e10	0.439022
$310$	0	0
$311$	1.00521e11	0.609303	0.304652	−	0.952464i	$-0.401460\pi$
$311$	1.00521e11	0.609303	0.304652	+	0.952464i	$0.401460\pi$
$312$	−6.27669e10	−0.375003
$313$	−9.41335e10	−0.554364	−0.277182	−	0.960817i	$-0.589400\pi$
$313$	−9.41335e10	−0.554364	−0.277182	+	0.960817i	$0.589400\pi$
$314$	1.82183e11	1.05761
$315$	0	0
$316$	7.36103e10	0.415285
$317$	−3.20813e11	−1.78437	−0.892187	−	0.451666i	$-0.850830\pi$
$317$	−3.20813e11	−1.78437	−0.892187	+	0.451666i	$0.850830\pi$
$318$	5.63724e10	0.309132
$319$	−2.34922e11	−1.27018
$320$	0	0
$321$	1.12460e10	0.0591189
$322$	2.13750e11	1.10804
$323$	−1.58493e11	−0.810214
$324$	5.67429e10	0.286061
$325$	0	0
$326$	2.47733e11	1.21480
$327$	−9.07452e10	−0.438893
$328$	1.62616e11	0.775766
$329$	−5.56180e9	−0.0261718
$330$	0	0
$331$	−1.08204e11	−0.495469	−0.247735	−	0.968828i	$-0.579686\pi$
$331$	−1.08204e11	−0.495469	−0.247735	+	0.968828i	$0.579686\pi$
$332$	4.20425e11	1.89918
$333$	1.41608e11	0.631086
$334$	−5.72061e11	−2.51526
$335$	0	0
$336$	2.68470e10	0.114913
$337$	−1.11484e11	−0.470845	−0.235422	−	0.971893i	$-0.575647\pi$
$337$	−1.11484e11	−0.470845	−0.235422	+	0.971893i	$0.575647\pi$
$338$	3.46099e11	1.44237
$339$	−4.92230e10	−0.202428
$340$	0	0
$341$	1.53770e11	0.615851
$342$	1.60950e11	0.636172
$343$	1.38413e10	0.0539949
$344$	2.15923e11	0.831352
$345$	0	0
$346$	−6.84483e11	−2.56756
$347$	1.49912e11	0.555079	0.277539	−	0.960714i	$-0.410481\pi$
$347$	1.49912e11	0.555079	0.277539	+	0.960714i	$0.410481\pi$
$348$	−1.63978e11	−0.599347
$349$	−3.21380e11	−1.15959	−0.579795	−	0.814763i	$-0.696867\pi$
$349$	−3.21380e11	−1.15959	−0.579795	+	0.814763i	$0.696867\pi$
$350$	0	0
$351$	3.65007e11	1.28357
$352$	5.93766e11	2.06145
$353$	2.53637e11	0.869412	0.434706	−	0.900572i	$-0.356852\pi$
$353$	2.53637e11	0.869412	0.434706	+	0.900572i	$0.356852\pi$
$354$	4.31455e11	1.46023
$355$	0	0
$356$	5.72748e11	1.88990
$357$	−8.61615e10	−0.280741
$358$	−4.58175e11	−1.47421
$359$	−1.69408e11	−0.538281	−0.269141	−	0.963101i	$-0.586740\pi$
$359$	−1.69408e11	−0.538281	−0.269141	+	0.963101i	$0.586740\pi$
$360$	0	0
$361$	−2.11562e11	−0.655623
$362$	−2.10700e11	−0.644875
$363$	−2.29772e11	−0.694571
$364$	2.34407e11	0.699866
$365$	0	0
$366$	−1.82116e11	−0.530498
$367$	−2.60523e11	−0.749634	−0.374817	−	0.927099i	$-0.622294\pi$
$367$	−2.60523e11	−0.749634	−0.374817	+	0.927099i	$0.622294\pi$
$368$	−3.82044e11	−1.08592
$369$	−3.92825e11	−1.10301
$370$	0	0
$371$	−5.19462e10	−0.142355
$372$	1.07333e11	0.290595
$373$	6.04820e11	1.61784	0.808922	−	0.587917i	$-0.200052\pi$
$373$	6.04820e11	1.61784	0.808922	+	0.587917i	$0.200052\pi$
$374$	−1.20635e12	−3.18825
$375$	0	0
$376$	−1.34117e10	−0.0346050
$377$	4.59082e11	1.17045
$378$	2.10634e11	0.530659
$379$	2.04406e10	0.0508882	0.0254441	−	0.999676i	$-0.491900\pi$
$379$	2.04406e10	0.0508882	0.0254441	+	0.999676i	$0.491900\pi$
$380$	0	0
$381$	1.67364e11	0.406912
$382$	8.22984e11	1.97745
$383$	5.08691e11	1.20798	0.603990	−	0.796992i	$-0.293577\pi$
$383$	5.08691e11	1.20798	0.603990	+	0.796992i	$0.293577\pi$
$384$	2.16821e11	0.508874
$385$	0	0
$386$	9.70500e11	2.22512
$387$	−5.21596e11	−1.18205
$388$	2.17428e11	0.487049
$389$	8.31376e10	0.184087	0.0920437	−	0.995755i	$-0.470660\pi$
$389$	8.31376e10	0.184087	0.0920437	+	0.995755i	$0.470660\pi$
$390$	0	0
$391$	1.22611e12	2.65298
$392$	3.33768e10	0.0713934
$393$	3.59501e11	0.760210
$394$	7.59098e11	1.58696
$395$	0	0
$396$	6.98731e11	1.42785
$397$	4.51154e11	0.911523	0.455761	−	0.890102i	$-0.349367\pi$
$397$	4.51154e11	0.911523	0.455761	+	0.890102i	$0.349367\pi$
$398$	−7.70818e11	−1.53985
$399$	6.04114e10	0.119327
$400$	0	0
$401$	−3.41391e11	−0.659330	−0.329665	−	0.944098i	$-0.606936\pi$
$401$	−3.41391e11	−0.659330	−0.329665	+	0.944098i	$0.606936\pi$
$402$	−6.86703e11	−1.31145
$403$	−3.00495e11	−0.567498
$404$	1.06624e11	0.199131
$405$	0	0
$406$	2.64922e11	0.483894
$407$	7.44175e11	1.34431
$408$	−2.07770e11	−0.371203
$409$	2.55445e11	0.451380	0.225690	−	0.974199i	$-0.427536\pi$
$409$	2.55445e11	0.451380	0.225690	+	0.974199i	$0.427536\pi$
$410$	0	0
$411$	−3.03878e11	−0.525305
$412$	−6.33591e11	−1.08336
$413$	−3.97578e11	−0.672430
$414$	−1.24512e12	−2.08310
$415$	0	0
$416$	−1.16033e12	−1.89960
$417$	7.17378e10	0.116181
$418$	8.45823e11	1.35515
$419$	1.92629e11	0.305323	0.152661	−	0.988279i	$-0.451216\pi$
$419$	1.92629e11	0.305323	0.152661	+	0.988279i	$0.451216\pi$
$420$	0	0
$421$	4.59988e11	0.713637	0.356819	−	0.934174i	$-0.383861\pi$
$421$	4.59988e11	0.713637	0.356819	+	0.934174i	$0.383861\pi$
$422$	−5.73710e11	−0.880615
$423$	3.23982e10	0.0492027
$424$	−1.25263e11	−0.188225
$425$	0	0
$426$	8.25855e10	0.121496
$427$	1.67817e11	0.244293
$428$	−1.01276e11	−0.145885
$429$	7.96810e11	1.13579
$430$	0	0
$431$	1.28918e12	1.79956	0.899778	−	0.436348i	$-0.143728\pi$
$431$	1.28918e12	1.79956	0.899778	+	0.436348i	$0.143728\pi$
$432$	−3.76475e11	−0.520067
$433$	1.17775e12	1.61012	0.805060	−	0.593194i	$-0.202133\pi$
$433$	1.17775e12	1.61012	0.805060	+	0.593194i	$0.202133\pi$
$434$	−1.73406e11	−0.234618
$435$	0	0
$436$	8.17208e11	1.08304
$437$	−8.59676e11	−1.12763
$438$	−4.93899e11	−0.641217
$439$	−4.63546e10	−0.0595666	−0.0297833	−	0.999556i	$-0.509482\pi$
$439$	−4.63546e10	−0.0595666	−0.0297833	+	0.999556i	$0.509482\pi$
$440$	0	0
$441$	−8.06272e10	−0.101510
$442$	2.35744e12	2.93792
$443$	−9.68521e11	−1.19479	−0.597396	−	0.801946i	$-0.703798\pi$
$443$	−9.68521e11	−1.19479	−0.597396	+	0.801946i	$0.703798\pi$
$444$	5.19441e11	0.634326
$445$	0	0
$446$	2.40723e12	2.88078
$447$	4.07175e11	0.482388
$448$	−4.87474e11	−0.571743
$449$	1.55933e12	1.81062	0.905312	−	0.424746i	$-0.139637\pi$
$449$	1.55933e12	1.81062	0.905312	+	0.424746i	$0.139637\pi$
$450$	0	0
$451$	−2.06437e12	−2.34959
$452$	4.43280e11	0.499522
$453$	2.66742e11	0.297611
$454$	4.17521e11	0.461240
$455$	0	0
$456$	1.45676e11	0.157778
$457$	−4.03171e9	−0.00432381	−0.00216190	−	0.999998i	$-0.500688\pi$
$457$	−4.03171e9	−0.00432381	−0.00216190	+	0.999998i	$0.500688\pi$
$458$	−3.27117e11	−0.347383
$459$	1.20824e12	1.27056
$460$	0	0
$461$	2.65942e10	0.0274241	0.0137120	−	0.999906i	$-0.495635\pi$
$461$	2.65942e10	0.0274241	0.0137120	+	0.999906i	$0.495635\pi$
$462$	4.59813e11	0.469562
$463$	−1.32574e11	−0.134074	−0.0670369	−	0.997750i	$-0.521355\pi$
$463$	−1.32574e11	−0.134074	−0.0670369	+	0.997750i	$0.521355\pi$
$464$	−4.73506e11	−0.474236
$465$	0	0
$466$	−3.41896e11	−0.335859
$467$	−4.42476e11	−0.430490	−0.215245	−	0.976560i	$-0.569055\pi$
$467$	−4.42476e11	−0.430490	−0.215245	+	0.976560i	$0.569055\pi$
$468$	−1.36545e12	−1.31574
$469$	6.32786e11	0.603919
$470$	0	0
$471$	−3.98326e11	−0.372945
$472$	−9.58719e11	−0.889104
$473$	−2.74108e12	−2.51795
$474$	−2.82173e11	−0.256752
$475$	0	0
$476$	7.75930e11	0.692774
$477$	3.02593e11	0.267625
$478$	−3.96747e11	−0.347607
$479$	4.01081e11	0.348115	0.174058	−	0.984735i	$-0.444312\pi$
$479$	4.01081e11	0.348115	0.174058	+	0.984735i	$0.444312\pi$
$480$	0	0
$481$	−1.45426e12	−1.23877
$482$	−6.95321e11	−0.586778
$483$	−4.67345e11	−0.390728
$484$	2.06922e12	1.71396
$485$	0	0
$486$	−1.94426e12	−1.58085
$487$	−5.86647e11	−0.472603	−0.236302	−	0.971680i	$-0.575935\pi$
$487$	−5.86647e11	−0.472603	−0.236302	+	0.971680i	$0.575935\pi$
$488$	4.04673e11	0.323010
$489$	−5.41646e11	−0.428376
$490$	0	0
$491$	−3.03493e10	−0.0235658	−0.0117829	−	0.999931i	$-0.503751\pi$
$491$	−3.03493e10	−0.0235658	−0.0117829	+	0.999931i	$0.503751\pi$
$492$	−1.44095e12	−1.10868
$493$	1.51964e12	1.15859
$494$	−1.65290e12	−1.24875
$495$	0	0
$496$	3.09936e11	0.229935
$497$	−7.61012e10	−0.0559484
$498$	−1.61163e12	−1.17418
$499$	−1.57589e12	−1.13782	−0.568909	−	0.822401i	$-0.692634\pi$
$499$	−1.57589e12	−1.13782	−0.568909	+	0.822401i	$0.692634\pi$
$500$	0	0
$501$	1.25076e12	0.886961
$502$	3.53535e12	2.48465
$503$	1.78713e12	1.24480	0.622401	−	0.782698i	$-0.286157\pi$
$503$	1.78713e12	1.24480	0.622401	+	0.782698i	$0.286157\pi$
$504$	−1.94424e11	−0.134219
$505$	0	0
$506$	−6.54332e12	−4.43732
$507$	−7.56715e11	−0.508624
$508$	−1.50721e12	−1.00412
$509$	6.00957e11	0.396838	0.198419	−	0.980117i	$-0.436419\pi$
$509$	6.00957e11	0.396838	0.198419	+	0.980117i	$0.436419\pi$
$510$	0	0
$511$	4.55120e11	0.295279
$512$	1.63594e12	1.05209
$513$	−8.47146e11	−0.540045
$514$	−1.75738e12	−1.11054
$515$	0	0
$516$	−1.91330e12	−1.18812
$517$	1.70258e11	0.104809
$518$	−8.39206e11	−0.512135
$519$	1.49656e12	0.905402
$520$	0	0
$521$	−2.25638e12	−1.34166	−0.670829	−	0.741612i	$-0.734062\pi$
$521$	−2.25638e12	−1.34166	−0.670829	+	0.741612i	$0.734062\pi$
$522$	−1.54320e12	−0.909716
$523$	1.73920e12	1.01647	0.508233	−	0.861219i	$-0.330299\pi$
$523$	1.73920e12	1.01647	0.508233	+	0.861219i	$0.330299\pi$
$524$	−3.23750e12	−1.87594
$525$	0	0
$526$	1.98489e12	1.13058
$527$	−9.94692e11	−0.561747
$528$	−8.21843e11	−0.460189
$529$	4.84934e12	2.69235
$530$	0	0
$531$	2.31594e12	1.26416
$532$	−5.44036e11	−0.294459
$533$	4.03416e12	2.16512
$534$	−2.19554e12	−1.16844
$535$	0	0
$536$	1.52590e12	0.798517
$537$	1.00176e12	0.519851
$538$	−4.24446e12	−2.18425
$539$	−4.23710e11	−0.216232
$540$	0	0
$541$	−2.16584e12	−1.08702	−0.543511	−	0.839402i	$-0.682905\pi$
$541$	−2.16584e12	−1.08702	−0.543511	+	0.839402i	$0.682905\pi$
$542$	−4.25159e12	−2.11619
$543$	4.60676e11	0.227403
$544$	−3.84091e12	−1.88035
$545$	0	0
$546$	−8.98563e11	−0.432695
$547$	1.14846e12	0.548494	0.274247	−	0.961659i	$-0.411571\pi$
$547$	1.14846e12	0.548494	0.274247	+	0.961659i	$0.411571\pi$
$548$	2.73659e12	1.29627
$549$	−9.77555e11	−0.459267
$550$	0	0
$551$	−1.06548e12	−0.492453
$552$	−1.12695e12	−0.516631
$553$	2.60018e11	0.118233
$554$	−3.23303e12	−1.45820
$555$	0	0
$556$	−6.46037e11	−0.286695
$557$	2.12857e11	0.0937002	0.0468501	−	0.998902i	$-0.485082\pi$
$557$	2.12857e11	0.0937002	0.0468501	+	0.998902i	$0.485082\pi$
$558$	1.01011e12	0.441078
$559$	5.35659e12	2.32025
$560$	0	0
$561$	2.63758e12	1.12428
$562$	2.00531e12	0.847944
$563$	2.37188e12	0.994960	0.497480	−	0.867475i	$-0.334259\pi$
$563$	2.37188e12	0.994960	0.497480	+	0.867475i	$0.334259\pi$
$564$	1.18842e11	0.0494553
$565$	0	0
$566$	6.18851e12	2.53462
$567$	2.00436e11	0.0814427
$568$	−1.83510e11	−0.0739763
$569$	3.00721e12	1.20270	0.601352	−	0.798984i	$-0.294629\pi$
$569$	3.00721e12	1.20270	0.601352	+	0.798984i	$0.294629\pi$
$570$	0	0
$571$	−1.15800e12	−0.455876	−0.227938	−	0.973676i	$-0.573198\pi$
$571$	−1.15800e12	−0.455876	−0.227938	+	0.973676i	$0.573198\pi$
$572$	−7.17569e12	−2.80273
$573$	−1.79938e12	−0.697313
$574$	2.32799e12	0.895111
$575$	0	0
$576$	2.83960e12	1.07487
$577$	1.40046e12	0.525993	0.262997	−	0.964797i	$-0.415289\pi$
$577$	1.40046e12	0.525993	0.262997	+	0.964797i	$0.415289\pi$
$578$	3.70975e12	1.38251
$579$	−2.12191e12	−0.784646
$580$	0	0
$581$	1.48509e12	0.540705
$582$	−8.33475e11	−0.301120
$583$	1.59018e12	0.570083
$584$	1.09748e12	0.390425
$585$	0	0
$586$	−2.54968e12	−0.893194
$587$	−2.32190e12	−0.807183	−0.403592	−	0.914939i	$-0.632238\pi$
$587$	−2.32190e12	−0.807183	−0.403592	+	0.914939i	$0.632238\pi$
$588$	−2.95754e11	−0.102031
$589$	6.97419e11	0.238767
$590$	0	0
$591$	−1.65970e12	−0.559611
$592$	1.49995e12	0.501913
$593$	3.71697e12	1.23436	0.617181	−	0.786821i	$-0.288274\pi$
$593$	3.71697e12	1.23436	0.617181	+	0.786821i	$0.288274\pi$
$594$	−6.44794e12	−2.12511
$595$	0	0
$596$	−3.66682e12	−1.19037
$597$	1.68533e12	0.542999
$598$	1.27869e13	4.08893
$599$	1.12352e12	0.356584	0.178292	−	0.983978i	$-0.442943\pi$
$599$	1.12352e12	0.356584	0.178292	+	0.983978i	$0.442943\pi$
$600$	0	0
$601$	−4.34901e12	−1.35974	−0.679870	−	0.733333i	$-0.737964\pi$
$601$	−4.34901e12	−1.35974	−0.679870	+	0.733333i	$0.737964\pi$
$602$	3.09112e12	0.959249
$603$	−3.68606e12	−1.13536
$604$	−2.40215e12	−0.734403
$605$	0	0
$606$	−4.08727e11	−0.123114
$607$	−1.40532e12	−0.420170	−0.210085	−	0.977683i	$-0.567374\pi$
$607$	−1.40532e12	−0.420170	−0.210085	+	0.977683i	$0.567374\pi$
$608$	2.69302e12	0.799232
$609$	−5.79228e11	−0.170636
$610$	0	0
$611$	−3.32717e11	−0.0965804
$612$	−4.51989e12	−1.30241
$613$	−3.27928e12	−0.938006	−0.469003	−	0.883196i	$-0.655387\pi$
$613$	−3.27928e12	−0.938006	−0.469003	+	0.883196i	$0.655387\pi$
$614$	3.47157e11	0.0985752
$615$	0	0
$616$	−1.02173e12	−0.285907
$617$	1.13802e12	0.316130	0.158065	−	0.987429i	$-0.449474\pi$
$617$	1.13802e12	0.316130	0.158065	+	0.987429i	$0.449474\pi$
$618$	2.42877e12	0.669789
$619$	−3.44712e12	−0.943732	−0.471866	−	0.881670i	$-0.656419\pi$
$619$	−3.44712e12	−0.943732	−0.471866	+	0.881670i	$0.656419\pi$
$620$	0	0
$621$	6.55355e12	1.76834
$622$	3.47010e12	0.929576
$623$	2.02315e12	0.538061
$624$	1.60604e12	0.424058
$625$	0	0
$626$	−3.24960e12	−0.845758
$627$	−1.84932e12	−0.477867
$628$	3.58714e12	0.920301
$629$	−4.81386e12	−1.22621
$630$	0	0
$631$	−7.29203e11	−0.183112	−0.0915560	−	0.995800i	$-0.529184\pi$
$631$	−7.29203e11	−0.183112	−0.0915560	+	0.995800i	$0.529184\pi$
$632$	6.27007e11	0.156331
$633$	1.25436e12	0.310533
$634$	−1.10749e13	−2.72231
$635$	0	0
$636$	1.10996e12	0.268999
$637$	8.28011e11	0.199255
$638$	−8.10980e12	−1.93784
$639$	4.43299e11	0.105182
$640$	0	0
$641$	2.95909e12	0.692304	0.346152	−	0.938178i	$-0.387488\pi$
$641$	2.95909e12	0.692304	0.346152	+	0.938178i	$0.387488\pi$
$642$	3.88227e11	0.0901940
$643$	−1.02370e12	−0.236170	−0.118085	−	0.993004i	$-0.537675\pi$
$643$	−1.02370e12	−0.236170	−0.118085	+	0.993004i	$0.537675\pi$
$644$	4.20869e12	0.964184
$645$	0	0
$646$	−5.47139e12	−1.23609
$647$	−6.36352e12	−1.42767	−0.713835	−	0.700314i	$-0.753043\pi$
$647$	−6.36352e12	−1.42767	−0.713835	+	0.700314i	$0.753043\pi$
$648$	4.83331e11	0.107686
$649$	1.21707e13	2.69286
$650$	0	0
$651$	3.79137e11	0.0827335
$652$	4.87781e12	1.05709
$653$	6.00751e12	1.29296	0.646480	−	0.762931i	$-0.276240\pi$
$653$	6.00751e12	1.29296	0.646480	+	0.762931i	$0.276240\pi$
$654$	−3.13264e12	−0.669592
$655$	0	0
$656$	−4.16091e12	−0.877245
$657$	−2.65113e12	−0.555121
$658$	−1.92000e11	−0.0399287
$659$	−3.82594e12	−0.790230	−0.395115	−	0.918632i	$-0.629295\pi$
$659$	−3.82594e12	−0.790230	−0.395115	+	0.918632i	$0.629295\pi$
$660$	0	0
$661$	−1.32332e12	−0.269625	−0.134812	−	0.990871i	$-0.543043\pi$
$661$	−1.32332e12	−0.269625	−0.134812	+	0.990871i	$0.543043\pi$
$662$	−3.73533e12	−0.755906
$663$	−5.15434e12	−1.03601
$664$	3.58114e12	0.714933
$665$	0	0
$666$	4.88848e12	0.962809
$667$	8.24263e12	1.61250
$668$	−1.12638e13	−2.18872
$669$	−5.26319e12	−1.01585
$670$	0	0
$671$	−5.13722e12	−0.978311
$672$	1.46400e12	0.276936
$673$	−7.34027e10	−0.0137925	−0.00689627	−	0.999976i	$-0.502195\pi$
$673$	−7.34027e10	−0.0137925	−0.00689627	+	0.999976i	$0.502195\pi$
$674$	−3.84856e12	−0.718338
$675$	0	0
$676$	6.81462e12	1.25511
$677$	2.07291e12	0.379256	0.189628	−	0.981856i	$-0.439272\pi$
$677$	2.07291e12	0.379256	0.189628	+	0.981856i	$0.439272\pi$
$678$	−1.69924e12	−0.308831
$679$	7.68034e11	0.138665
$680$	0	0
$681$	−9.12873e11	−0.162648
$682$	5.30832e12	0.939566
$683$	3.77858e12	0.664409	0.332204	−	0.943207i	$-0.392208\pi$
$683$	3.77858e12	0.664409	0.332204	+	0.943207i	$0.392208\pi$
$684$	3.16908e12	0.553580
$685$	0	0
$686$	4.77818e11	0.0823767
$687$	7.15213e11	0.122498
$688$	−5.52489e12	−0.940103
$689$	−3.10752e12	−0.525323
$690$	0	0
$691$	−5.37636e12	−0.897093	−0.448546	−	0.893760i	$-0.648058\pi$
$691$	−5.37636e12	−0.897093	−0.448546	+	0.893760i	$0.648058\pi$
$692$	−1.34773e13	−2.23422
$693$	2.46817e12	0.406513
$694$	5.17516e12	0.846849
$695$	0	0
$696$	−1.39675e12	−0.225620
$697$	1.33538e13	2.14317
$698$	−1.10944e13	−1.76911
$699$	7.47525e11	0.118435
$700$	0	0
$701$	3.69140e12	0.577377	0.288689	−	0.957423i	$-0.406781\pi$
$701$	3.69140e12	0.577377	0.288689	+	0.957423i	$0.406781\pi$
$702$	1.26005e13	1.95826
$703$	3.37519e12	0.521194
$704$	1.49226e13	2.28964
$705$	0	0
$706$	8.75585e12	1.32641
$707$	3.76635e11	0.0566935
$708$	8.49525e12	1.27065
$709$	6.26266e12	0.930788	0.465394	−	0.885104i	$-0.345913\pi$
$709$	6.26266e12	0.930788	0.465394	+	0.885104i	$0.345913\pi$
$710$	0	0
$711$	−1.51464e12	−0.222277
$712$	4.87862e12	0.711438
$713$	−5.39526e12	−0.781825
$714$	−2.97440e12	−0.428310
$715$	0	0
$716$	−9.02138e12	−1.28282
$717$	8.67452e11	0.122577
$718$	−5.84818e12	−0.821222
$719$	8.85785e12	1.23609	0.618043	−	0.786144i	$-0.287926\pi$
$719$	8.85785e12	1.23609	0.618043	+	0.786144i	$0.287926\pi$
$720$	0	0
$721$	−2.23807e12	−0.308436
$722$	−7.30337e12	−1.00024
$723$	1.52026e12	0.206916
$724$	−4.14863e12	−0.561153
$725$	0	0
$726$	−7.93201e12	−1.05966
$727$	−2.26322e12	−0.300485	−0.150243	−	0.988649i	$-0.548005\pi$
$727$	−2.26322e12	−0.300485	−0.150243	+	0.988649i	$0.548005\pi$
$728$	1.99666e12	0.263459
$729$	2.60781e12	0.341980
$730$	0	0
$731$	1.77313e13	2.29674
$732$	−3.58583e12	−0.461625
$733$	−4.70099e12	−0.601480	−0.300740	−	0.953706i	$-0.597234\pi$
$733$	−4.70099e12	−0.601480	−0.300740	+	0.953706i	$0.597234\pi$
$734$	−8.99359e12	−1.14367
$735$	0	0
$736$	−2.08333e13	−2.61702
$737$	−1.93709e13	−2.41850
$738$	−1.35608e13	−1.68280
$739$	5.07549e12	0.626006	0.313003	−	0.949752i	$-0.398665\pi$
$739$	5.07549e12	0.626006	0.313003	+	0.949752i	$0.398665\pi$
$740$	0	0
$741$	3.61392e12	0.440348
$742$	−1.79325e12	−0.217181
$743$	−7.44569e12	−0.896304	−0.448152	−	0.893957i	$-0.647918\pi$
$743$	−7.44569e12	−0.896304	−0.448152	+	0.893957i	$0.647918\pi$
$744$	9.14250e11	0.109392
$745$	0	0
$746$	2.08791e13	2.46824
$747$	−8.65084e12	−1.01652
$748$	−2.37528e13	−2.77433
$749$	−3.57744e11	−0.0415341
$750$	0	0
$751$	3.72543e12	0.427363	0.213681	−	0.976903i	$-0.431455\pi$
$751$	3.72543e12	0.427363	0.213681	+	0.976903i	$0.431455\pi$
$752$	3.43170e11	0.0391317
$753$	−7.72973e12	−0.876167
$754$	1.58481e13	1.78569
$755$	0	0
$756$	4.14734e12	0.461766
$757$	−3.49366e12	−0.386678	−0.193339	−	0.981132i	$-0.561932\pi$
$757$	−3.49366e12	−0.386678	−0.193339	+	0.981132i	$0.561932\pi$
$758$	7.05635e11	0.0776370
$759$	1.43064e13	1.56474
$760$	0	0
$761$	−3.26552e12	−0.352957	−0.176478	−	0.984305i	$-0.556471\pi$
$761$	−3.26552e12	−0.352957	−0.176478	+	0.984305i	$0.556471\pi$
$762$	5.77763e12	0.620801
$763$	2.88667e12	0.308345
$764$	1.62044e13	1.72073
$765$	0	0
$766$	1.75606e13	1.84294
$767$	−2.37838e13	−2.48143
$768$	−3.61078e11	−0.0374520
$769$	−4.86084e9	−0.000501237 0	−0.000250618	−	1.00000i	$-0.500080\pi$
$769$	−4.86084e9	−0.000501237 0	−0.000250618		1.00000i	$0.500080\pi$
$770$	0	0
$771$	3.84236e12	0.391610
$772$	1.91089e13	1.93624
$773$	3.89554e12	0.392428	0.196214	−	0.980561i	$-0.437135\pi$
$773$	3.89554e12	0.392428	0.196214	+	0.980561i	$0.437135\pi$
$774$	−1.80062e13	−1.80338
$775$	0	0
$776$	1.85204e12	0.183346
$777$	1.83485e12	0.180595
$778$	2.87001e12	0.280851
$779$	−9.36290e12	−0.910944
$780$	0	0
$781$	2.32961e12	0.224055
$782$	4.23269e13	4.04749
$783$	8.12249e12	0.772256
$784$	−8.54025e11	−0.0807325
$785$	0	0
$786$	1.24104e13	1.15981
$787$	−8.01458e12	−0.744723	−0.372361	−	0.928088i	$-0.621452\pi$
$787$	−8.01458e12	−0.744723	−0.372361	+	0.928088i	$0.621452\pi$
$788$	1.49465e13	1.38093
$789$	−4.33979e12	−0.398678
$790$	0	0
$791$	1.56582e12	0.142216
$792$	5.95173e12	0.537502
$793$	1.00391e13	0.901500
$794$	1.55744e13	1.39065
$795$	0	0
$796$	−1.51772e13	−1.33994
$797$	−6.75610e12	−0.593107	−0.296554	−	0.955016i	$-0.595837\pi$
$797$	−6.75610e12	−0.593107	−0.296554	+	0.955016i	$0.595837\pi$
$798$	2.08547e12	0.182051
$799$	−1.10135e12	−0.0956016
$800$	0	0
$801$	−1.17851e13	−1.01155
$802$	−1.17853e13	−1.00590
$803$	−1.39322e13	−1.18249
$804$	−1.35210e13	−1.14119
$805$	0	0
$806$	−1.03735e13	−0.865797
$807$	9.28013e12	0.770235
$808$	9.08217e11	0.0749615
$809$	−2.29849e13	−1.88657	−0.943287	−	0.331980i	$-0.892283\pi$
$809$	−2.29849e13	−1.88657	−0.943287	+	0.331980i	$0.892283\pi$
$810$	0	0
$811$	1.93159e13	1.56791	0.783953	−	0.620820i	$-0.213200\pi$
$811$	1.93159e13	1.56791	0.783953	+	0.620820i	$0.213200\pi$
$812$	5.21625e12	0.421072
$813$	9.29573e12	0.746236
$814$	2.56898e13	2.05093
$815$	0	0
$816$	5.31627e12	0.419761
$817$	−1.24321e13	−0.976216
$818$	8.81828e12	0.688643
$819$	−4.82327e12	−0.374597
$820$	0	0
$821$	1.92989e13	1.48248	0.741239	−	0.671242i	$-0.234239\pi$
$821$	1.92989e13	1.48248	0.741239	+	0.671242i	$0.234239\pi$
$822$	−1.04903e13	−0.801426
$823$	2.71361e12	0.206181	0.103091	−	0.994672i	$-0.467127\pi$
$823$	2.71361e12	0.206181	0.103091	+	0.994672i	$0.467127\pi$
$824$	−5.39688e12	−0.407822
$825$	0	0
$826$	−1.37249e13	−1.02589
$827$	2.18887e13	1.62722	0.813608	−	0.581413i	$-0.197500\pi$
$827$	2.18887e13	1.62722	0.813608	+	0.581413i	$0.197500\pi$
$828$	−2.45161e13	−1.81266
$829$	5.10841e11	0.0375656	0.0187828	−	0.999824i	$-0.494021\pi$
$829$	5.10841e11	0.0375656	0.0187828	+	0.999824i	$0.494021\pi$
$830$	0	0
$831$	7.06873e12	0.514206
$832$	−2.91616e13	−2.10987
$833$	2.74086e12	0.197235
$834$	2.47648e12	0.177250
$835$	0	0
$836$	1.66541e13	1.17921
$837$	−5.31662e12	−0.374431
$838$	6.64980e12	0.465812
$839$	2.05337e11	0.0143067	0.00715333	−	0.999974i	$-0.497723\pi$
$839$	2.05337e11	0.0143067	0.00715333	+	0.999974i	$0.497723\pi$
$840$	0	0
$841$	−4.29121e12	−0.295800
$842$	1.58794e13	1.08875
$843$	−4.38442e12	−0.299012
$844$	−1.12962e13	−0.766288
$845$	0	0
$846$	1.11842e12	0.0750655
$847$	7.30921e12	0.487972
$848$	3.20515e12	0.212847
$849$	−1.35306e13	−0.893786
$850$	0	0
$851$	−2.61106e13	−1.70661
$852$	1.62609e12	0.105722
$853$	−2.79154e12	−0.180540	−0.0902699	−	0.995917i	$-0.528773\pi$
$853$	−2.79154e12	−0.180540	−0.0902699	+	0.995917i	$0.528773\pi$
$854$	5.79325e12	0.372702
$855$	0	0
$856$	−8.62664e11	−0.0549174
$857$	2.96194e13	1.87570	0.937849	−	0.347043i	$-0.112814\pi$
$857$	2.96194e13	1.87570	0.937849	+	0.347043i	$0.112814\pi$
$858$	2.75069e13	1.73280
$859$	−2.24640e13	−1.40772	−0.703861	−	0.710337i	$-0.748542\pi$
$859$	−2.24640e13	−1.40772	−0.703861	+	0.710337i	$0.748542\pi$
$860$	0	0
$861$	−5.08994e12	−0.315644
$862$	4.45040e13	2.74547
$863$	−7.77409e12	−0.477091	−0.238545	−	0.971131i	$-0.576671\pi$
$863$	−7.77409e12	−0.477091	−0.238545	+	0.971131i	$0.576671\pi$
$864$	−2.05296e13	−1.25334
$865$	0	0
$866$	4.06574e13	2.45646
$867$	−8.11104e12	−0.487518
$868$	−3.41433e12	−0.204158
$869$	−7.95968e12	−0.473486
$870$	0	0
$871$	3.78544e13	2.22861
$872$	6.96091e12	0.407701
$873$	−4.47389e12	−0.260688
$874$	−2.96771e13	−1.72036
$875$	0	0
$876$	−9.72478e12	−0.557970
$877$	3.28029e13	1.87246	0.936232	−	0.351382i	$-0.114288\pi$
$877$	3.28029e13	1.87246	0.936232	+	0.351382i	$0.114288\pi$
$878$	−1.60022e12	−0.0908770
$879$	5.57464e12	0.314968
$880$	0	0
$881$	−5.06411e11	−0.0283212	−0.0141606	−	0.999900i	$-0.504508\pi$
$881$	−5.06411e11	−0.0283212	−0.0141606	+	0.999900i	$0.504508\pi$
$882$	−2.78335e12	−0.154867
$883$	6.22478e12	0.344588	0.172294	−	0.985046i	$-0.444882\pi$
$883$	6.22478e12	0.344588	0.172294	+	0.985046i	$0.444882\pi$
$884$	4.64175e13	2.55651
$885$	0	0
$886$	−3.34346e13	−1.82282
$887$	−1.38537e13	−0.751467	−0.375734	−	0.926728i	$-0.622609\pi$
$887$	−1.38537e13	−0.751467	−0.375734	+	0.926728i	$0.622609\pi$
$888$	4.42455e12	0.238787
$889$	−5.32399e12	−0.285877
$890$	0	0
$891$	−6.13576e12	−0.326151
$892$	4.73978e13	2.50678
$893$	7.72202e11	0.0406349
$894$	1.40562e13	0.735950
$895$	0	0
$896$	−6.89722e12	−0.357510
$897$	−2.79574e13	−1.44189
$898$	5.38299e13	2.76236
$899$	−6.68690e12	−0.341434
$900$	0	0
$901$	−1.02864e13	−0.520000
$902$	−7.12645e13	−3.58462
$903$	−6.75846e12	−0.338262
$904$	3.77582e12	0.188041
$905$	0	0
$906$	9.20826e12	0.454047
$907$	−5.14770e12	−0.252569	−0.126285	−	0.991994i	$-0.540305\pi$
$907$	−5.14770e12	−0.252569	−0.126285	+	0.991994i	$0.540305\pi$
$908$	8.22091e12	0.401359
$909$	−2.19395e12	−0.106583
$910$	0	0
$911$	−8.84191e12	−0.425318	−0.212659	−	0.977126i	$-0.568212\pi$
$911$	−8.84191e12	−0.425318	−0.212659	+	0.977126i	$0.568212\pi$
$912$	−3.72746e12	−0.178417
$913$	−4.54617e13	−2.16534
$914$	−1.39180e11	−0.00659656
$915$	0	0
$916$	−6.44087e12	−0.302284
$917$	−1.14360e13	−0.534087
$918$	4.17099e13	1.93842
$919$	−2.96054e13	−1.36915	−0.684575	−	0.728942i	$-0.740012\pi$
$919$	−2.96054e13	−1.36915	−0.684575	+	0.728942i	$0.740012\pi$
$920$	0	0
$921$	−7.59027e11	−0.0347607
$922$	9.18063e11	0.0418392
$923$	−4.55251e12	−0.206463
$924$	9.05363e12	0.408600
$925$	0	0
$926$	−4.57662e12	−0.204548
$927$	1.30370e13	0.579856
$928$	−2.58208e13	−1.14289
$929$	8.00822e12	0.352749	0.176374	−	0.984323i	$-0.443563\pi$
$929$	8.00822e12	0.352749	0.176374	+	0.984323i	$0.443563\pi$
$930$	0	0
$931$	−1.92173e12	−0.0838338
$932$	−6.73186e12	−0.292256
$933$	−7.58706e12	−0.327798
$934$	−1.52748e13	−0.656772
$935$	0	0
$936$	−1.16308e13	−0.495301
$937$	−3.02864e13	−1.28357	−0.641786	−	0.766884i	$-0.721806\pi$
$937$	−3.02864e13	−1.28357	−0.641786	+	0.766884i	$0.721806\pi$
$938$	2.18445e13	0.921362
$939$	7.10497e12	0.298241
$940$	0	0
$941$	1.99053e13	0.827589	0.413795	−	0.910370i	$-0.364203\pi$
$941$	1.99053e13	0.827589	0.413795	+	0.910370i	$0.364203\pi$
$942$	−1.37507e13	−0.568979
$943$	7.24317e13	2.98281
$944$	2.45311e13	1.00541
$945$	0	0
$946$	−9.46255e13	−3.84148
$947$	−4.15065e12	−0.167703	−0.0838516	−	0.996478i	$-0.526722\pi$
$947$	−4.15065e12	−0.167703	−0.0838516	+	0.996478i	$0.526722\pi$
$948$	−5.55593e12	−0.223419
$949$	2.72261e13	1.08965
$950$	0	0
$951$	2.42142e13	0.959972
$952$	6.60931e12	0.260789
$953$	4.14207e13	1.62667	0.813336	−	0.581795i	$-0.197649\pi$
$953$	4.14207e13	1.62667	0.813336	+	0.581795i	$0.197649\pi$
$954$	1.04459e13	0.408299
$955$	0	0
$956$	−7.81186e12	−0.302478
$957$	1.77314e13	0.683342
$958$	1.38458e13	0.531097
$959$	9.66660e12	0.369054
$960$	0	0
$961$	−2.20627e13	−0.834455
$962$	−5.02028e13	−1.88991
$963$	2.08391e12	0.0780836
$964$	−1.36907e13	−0.510599
$965$	0	0
$966$	−1.61333e13	−0.596110
$967$	−5.18381e13	−1.90647	−0.953235	−	0.302230i	$-0.902269\pi$
$967$	−5.18381e13	−1.90647	−0.953235	+	0.302230i	$0.902269\pi$
$968$	1.76254e13	0.645209
$969$	1.19627e13	0.435885
$970$	0	0
$971$	8.98175e12	0.324246	0.162123	−	0.986771i	$-0.448166\pi$
$971$	8.98175e12	0.324246	0.162123	+	0.986771i	$0.448166\pi$
$972$	−3.82820e13	−1.37561
$973$	−2.28203e12	−0.0816233
$974$	−2.02518e13	−0.721021
$975$	0	0
$976$	−1.03545e13	−0.365263
$977$	2.62767e12	0.0922667	0.0461333	−	0.998935i	$-0.485310\pi$
$977$	2.62767e12	0.0922667	0.0461333	+	0.998935i	$0.485310\pi$
$978$	−1.86983e13	−0.653547
$979$	−6.19328e13	−2.15476
$980$	0	0
$981$	−1.68152e13	−0.579685
$982$	−1.04770e12	−0.0359529
$983$	−5.62882e13	−1.92277	−0.961384	−	0.275212i	$-0.911252\pi$
$983$	−5.62882e13	−1.92277	−0.961384	+	0.275212i	$0.911252\pi$
$984$	−1.22739e13	−0.417353
$985$	0	0
$986$	5.24600e13	1.76759
$987$	4.19791e11	0.0140801
$988$	−3.25452e13	−1.08663
$989$	9.61754e13	3.19654
$990$	0	0
$991$	−2.25521e13	−0.742770	−0.371385	−	0.928479i	$-0.621117\pi$
$991$	−2.25521e13	−0.742770	−0.371385	+	0.928479i	$0.621117\pi$
$992$	1.69012e13	0.554133
$993$	8.16697e12	0.266556
$994$	−2.62711e12	−0.0853570
$995$	0	0
$996$	−3.17327e13	−1.02174
$997$	5.75508e13	1.84469	0.922344	−	0.386370i	$-0.126271\pi$
$997$	5.75508e13	1.84469	0.922344	+	0.386370i	$0.126271\pi$
$998$	−5.44015e13	−1.73590
$999$	−2.57300e13	−0.817327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.a.k.1.9	yes	10
5.2	odd	4		175.10.b.i.99.18		20
5.3	odd	4		175.10.b.i.99.3		20
5.4	even	2		175.10.a.j.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.10.a.j.1.2	✓	10	5.4	even	2
175.10.a.k.1.9	yes	10	1.1	even	1	trivial
175.10.b.i.99.3		20	5.3	odd	4
175.10.b.i.99.18		20	5.2	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)

\(f(q)\)	\(=\)	\(q+34.5212 q^{2} -75.4776 q^{3} +679.716 q^{4} -2605.58 q^{6} +2401.00 q^{7} +5789.77 q^{8} -13986.1 q^{9} +O(q^{10})\)	\(q+34.5212 q^{2} -75.4776 q^{3} +679.716 q^{4} -2605.58 q^{6} +2401.00 q^{7} +5789.77 q^{8} -13986.1 q^{9} -73499.6 q^{11} -51303.4 q^{12} +143632. q^{13} +82885.5 q^{14} -148145. q^{16} +475448. q^{17} -482818. q^{18} -333356. q^{19} -181222. q^{21} -2.53730e6 q^{22} +2.57885e6 q^{23} -436998. q^{24} +4.95836e6 q^{26} +2.54127e6 q^{27} +1.63200e6 q^{28} +3.19624e6 q^{29} -2.09212e6 q^{31} -8.07850e6 q^{32} +5.54757e6 q^{33} +1.64131e7 q^{34} -9.50660e6 q^{36} -1.01249e7 q^{37} -1.15079e7 q^{38} -1.08410e7 q^{39} +2.80868e7 q^{41} -6.25600e6 q^{42} +3.72938e7 q^{43} -4.99588e7 q^{44} +8.90252e7 q^{46} -2.31645e6 q^{47} +1.11816e7 q^{48} +5.76480e6 q^{49} -3.58857e7 q^{51} +9.76291e7 q^{52} -2.16352e7 q^{53} +8.77276e7 q^{54} +1.39012e7 q^{56} +2.51609e7 q^{57} +1.10338e8 q^{58} -1.65589e8 q^{59} +6.98946e7 q^{61} -7.22224e7 q^{62} -3.35807e7 q^{63} -2.03030e8 q^{64} +1.91509e8 q^{66} +2.63551e8 q^{67} +3.23170e8 q^{68} -1.94646e8 q^{69} -3.16956e7 q^{71} -8.09764e7 q^{72} +1.89554e8 q^{73} -3.49524e8 q^{74} -2.26587e8 q^{76} -1.76472e8 q^{77} -3.74245e8 q^{78} +1.08296e8 q^{79} +8.34803e7 q^{81} +9.69591e8 q^{82} +6.18530e8 q^{83} -1.23179e8 q^{84} +1.28743e9 q^{86} -2.41244e8 q^{87} -4.25545e8 q^{88} +8.42628e8 q^{89} +3.44861e8 q^{91} +1.75289e9 q^{92} +1.57908e8 q^{93} -7.99667e7 q^{94} +6.09746e8 q^{96} +3.19881e8 q^{97} +1.99008e8 q^{98} +1.02797e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22 q^{2} - 77 q^{3} + 2368 q^{4} - 3101 q^{6} + 24010 q^{7} + 4053 q^{8} + 78909 q^{9}+O(q^{10}) \) 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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