LMFDB - Embedded newform 175.10.b.f.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(99,175)]

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([1, 0]))

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

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

chi := DirichletCharacter("175.99");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.b (of order $2$, degree $1$, not minimal)

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:	no
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} + 2 x^{8} - 2016 x^{7} + 425617 x^{6} - 2170178 x^{5} + 5521250 x^{4} + \cdots + 231472080000 $ x^10 - 2x^9 + 2x^8 - 2016x^7 + 425617x^6 - 2170178x^5 + 5521250x^4 - 35024640x^3 + 21285642816x^2 - 99267638400*x + 231472080000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-18.2310 - 18.2310i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.f.99.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-36.4619i q^{2} +68.7273i q^{3} -817.473 q^{4} +2505.93 q^{6} +2401.00i q^{7} +11138.1i q^{8} +14959.6 q^{9} -75602.9 q^{11} -56182.7i q^{12} +49331.2i q^{13} +87545.1 q^{14} -12428.3 q^{16} -522841. i q^{17} -545455. i q^{18} -442202. q^{19} -165014. q^{21} +2.75663e6i q^{22} -2.11792e6i q^{23} -765493. q^{24} +1.79871e6 q^{26} +2.38089e6i q^{27} -1.96275e6i q^{28} +5.29101e6 q^{29} -5.41211e6 q^{31} +6.15588e6i q^{32} -5.19598e6i q^{33} -1.90638e7 q^{34} -1.22290e7 q^{36} +1.68073e7i q^{37} +1.61236e7i q^{38} -3.39040e6 q^{39} +2.98305e6 q^{41} +6.01674e6i q^{42} +1.11225e7i q^{43} +6.18033e7 q^{44} -7.72234e7 q^{46} +1.58154e7i q^{47} -854160. i q^{48} -5.76480e6 q^{49} +3.59335e7 q^{51} -4.03269e7i q^{52} +2.78375e7i q^{53} +8.68118e7 q^{54} -2.67427e7 q^{56} -3.03914e7i q^{57} -1.92920e8i q^{58} -1.71244e7 q^{59} +1.93532e8 q^{61} +1.97336e8i q^{62} +3.59179e7i q^{63} +2.18092e8 q^{64} -1.89455e8 q^{66} +1.93697e8i q^{67} +4.27409e8i q^{68} +1.45559e8 q^{69} +1.41665e8 q^{71} +1.66622e8i q^{72} +2.36977e7i q^{73} +6.12828e8 q^{74} +3.61488e8 q^{76} -1.81522e8i q^{77} +1.23620e8i q^{78} -2.51611e8 q^{79} +1.30817e8 q^{81} -1.08768e8i q^{82} -2.06819e8i q^{83} +1.34895e8 q^{84} +4.05548e8 q^{86} +3.63637e8i q^{87} -8.42074e8i q^{88} +6.94584e8 q^{89} -1.18444e8 q^{91} +1.73134e9i q^{92} -3.71959e8i q^{93} +5.76662e8 q^{94} -4.23077e8 q^{96} +1.39893e9i q^{97} +2.10196e8i q^{98} -1.13099e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 1664 q^{4} - 288 q^{6} - 135594 q^{9} + 20624 q^{11} - 9604 q^{14} - 1053392 q^{16} - 3310752 q^{19} + 672280 q^{21} - 13009152 q^{24} + 20438120 q^{26} + 6707452 q^{29} + 5356240 q^{31} - 43097224 q^{34}+ \cdots - 1396625336 q^{99}+O(q^{100}) $ 10 * q - 1664 * q^4 - 288 * q^6 - 135594 * q^9 + 20624 * q^11 - 9604 * q^14 - 1053392 * q^16 - 3310752 * q^19 + 672280 * q^21 - 13009152 * q^24 + 20438120 * q^26 + 6707452 * q^29 + 5356240 * q^31 - 43097224 * q^34 + 30780920 * q^36 + 36248 * q^39 + 12660388 * q^41 + 142451784 * q^44 - 285690944 * q^46 - 57648010 * q^49 - 35940424 * q^51 + 226558656 * q^54 - 67881072 * q^56 + 304670336 * q^59 + 514031396 * q^61 + 387976864 * q^64 + 366483328 * q^66 + 383914672 * q^69 + 1045577920 * q^71 + 488357736 * q^74 - 690113232 * q^76 - 928349800 * q^79 + 1730301978 * q^81 - 304389176 * q^84 + 1389121232 * q^86 + 2213416652 * q^89 + 761779676 * q^91 + 7205003488 * q^94 - 5304257280 * q^96 - 1396625336 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 36.4619i	− 1.61141i	−0.592320	−	0.805703i	$-0.701788\pi$
$2$	− 36.4619i	− 1.61141i	0.592320	−	0.805703i	$-0.298212\pi$
$3$	68.7273i	0.489873i	0.969539	+	0.244936i	$0.0787671\pi$
$3$	68.7273i	0.489873i	−0.969539	+	0.244936i	$0.921233\pi$
$4$	−817.473	−1.59663
$5$	0	0
$5$	0	0
$6$	2505.93	0.789384
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	11138.1i	0.961407i
$9$	14959.6	0.760024
$10$	0	0
$11$	−75602.9	−1.55694	−0.778469	−	0.627684i	$-0.784003\pi$
$11$	−75602.9	−1.55694	−0.778469	+	0.627684i	$0.784003\pi$
$12$	− 56182.7i	− 0.782144i
$13$	49331.2i	0.479045i	0.970891	+	0.239523i	$0.0769909\pi$
$13$	49331.2i	0.479045i	−0.970891	+	0.239523i	$0.923009\pi$
$14$	87545.1	0.609054
$15$	0	0
$16$	−12428.3	−0.0474100
$17$	− 522841.i	− 1.51827i	−0.650931	−	0.759137i	$-0.725621\pi$
$17$	− 522841.i	− 1.51827i	0.650931	−	0.759137i	$-0.274379\pi$
$18$	− 545455.i	− 1.22471i
$19$	−442202.	−0.778448	−0.389224	−	0.921143i	$-0.627257\pi$
$19$	−442202.	−0.778448	−0.389224	+	0.921143i	$0.627257\pi$
$20$	0	0
$21$	−165014.	−0.185155
$22$	2.75663e6i	2.50886i
$23$	− 2.11792e6i	− 1.57810i	−0.614330	−	0.789049i	$-0.710574\pi$
$23$	− 2.11792e6i	− 1.57810i	0.614330	−	0.789049i	$-0.289426\pi$
$24$	−765493.	−0.470967
$25$	0	0
$26$	1.79871e6	0.771936
$27$	2.38089e6i	0.862188i
$28$	− 1.96275e6i	− 0.603468i
$29$	5.29101e6	1.38914	0.694572	−	0.719423i	$-0.255594\pi$
$29$	5.29101e6	1.38914	0.694572	+	0.719423i	$0.255594\pi$
$30$	0	0
$31$	−5.41211e6	−1.05254	−0.526270	−	0.850317i	$-0.676410\pi$
$31$	−5.41211e6	−1.05254	−0.526270	+	0.850317i	$0.676410\pi$
$32$	6.15588e6i	1.03780i
$33$	− 5.19598e6i	− 0.762701i
$34$	−1.90638e7	−2.44655
$35$	0	0
$36$	−1.22290e7	−1.21348
$37$	1.68073e7i	1.47432i	0.675719	+	0.737159i	$0.263833\pi$
$37$	1.68073e7i	1.47432i	−0.675719	+	0.737159i	$0.736167\pi$
$38$	1.61236e7i	1.25440i
$39$	−3.39040e6	−0.234671
$40$	0	0
$41$	2.98305e6	0.164867	0.0824333	−	0.996597i	$-0.473731\pi$
$41$	2.98305e6	0.164867	0.0824333	+	0.996597i	$0.473731\pi$
$42$	6.01674e6i	0.298359i
$43$	1.11225e7i	0.496129i	0.968744	+	0.248065i	$0.0797945\pi$
$43$	1.11225e7i	0.496129i	−0.968744	+	0.248065i	$0.920206\pi$
$44$	6.18033e7	2.48585
$45$	0	0
$46$	−7.72234e7	−2.54296
$47$	1.58154e7i	0.472760i	0.971661	+	0.236380i	$0.0759611\pi$
$47$	1.58154e7i	0.472760i	−0.971661	+	0.236380i	$0.924039\pi$
$48$	− 854160.i	− 0.0232249i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	3.59335e7	0.743761
$52$	− 4.03269e7i	− 0.764856i
$53$	2.78375e7i	0.484605i	0.970201	+	0.242303i	$0.0779027\pi$
$53$	2.78375e7i	0.484605i	−0.970201	+	0.242303i	$0.922097\pi$
$54$	8.68118e7	1.38933
$55$	0	0
$56$	−2.67427e7	−0.363378
$57$	− 3.03914e7i	− 0.381341i
$58$	− 1.92920e8i	− 2.23847i
$59$	−1.71244e7	−0.183985	−0.0919925	−	0.995760i	$-0.529324\pi$
$59$	−1.71244e7	−0.183985	−0.0919925	+	0.995760i	$0.529324\pi$
$60$	0	0
$61$	1.93532e8	1.78965	0.894826	−	0.446416i	$-0.147300\pi$
$61$	1.93532e8	1.78965	0.894826	+	0.446416i	$0.147300\pi$
$62$	1.97336e8i	1.69607i
$63$	3.59179e7i	0.287262i
$64$	2.18092e8	1.62491
$65$	0	0
$66$	−1.89455e8	−1.22902
$67$	1.93697e8i	1.17432i	0.809471	+	0.587160i	$0.199754\pi$
$67$	1.93697e8i	1.17432i	−0.809471	+	0.587160i	$0.800246\pi$
$68$	4.27409e8i	2.42412i
$69$	1.45559e8	0.773068
$70$	0	0
$71$	1.41665e8	0.661605	0.330802	−	0.943700i	$-0.392681\pi$
$71$	1.41665e8	0.661605	0.330802	+	0.943700i	$0.392681\pi$
$72$	1.66622e8i	0.730693i
$73$	2.36977e7i	0.0976683i	0.998807	+	0.0488342i	$0.0155506\pi$
$73$	2.36977e7i	0.0976683i	−0.998807	+	0.0488342i	$0.984449\pi$
$74$	6.12828e8	2.37572
$75$	0	0
$76$	3.61488e8	1.24289
$77$	− 1.81522e8i	− 0.588467i
$78$	1.23620e8i	0.378151i
$79$	−2.51611e8	−0.726788	−0.363394	−	0.931636i	$-0.618382\pi$
$79$	−2.51611e8	−0.726788	−0.363394	+	0.931636i	$0.618382\pi$
$80$	0	0
$81$	1.30817e8	0.337662
$82$	− 1.08768e8i	− 0.265667i
$83$	− 2.06819e8i	− 0.478343i	−0.970977	−	0.239171i	$-0.923124\pi$
$83$	− 2.06819e8i	− 0.478343i	0.970977	−	0.239171i	$-0.0768757\pi$
$84$	1.34895e8	0.295623
$85$	0	0
$86$	4.05548e8	0.799465
$87$	3.63637e8i	0.680504i
$88$	− 8.42074e8i	− 1.49685i
$89$	6.94584e8	1.17346	0.586732	−	0.809781i	$-0.300414\pi$
$89$	6.94584e8	1.17346	0.586732	+	0.809781i	$0.300414\pi$
$90$	0	0
$91$	−1.18444e8	−0.181062
$92$	1.73134e9i	2.51963i
$93$	− 3.71959e8i	− 0.515611i
$94$	5.76662e8	0.761808
$95$	0	0
$96$	−4.23077e8	−0.508392
$97$	1.39893e9i	1.60443i	0.597033	+	0.802217i	$0.296346\pi$
$97$	1.39893e9i	1.60443i	−0.597033	+	0.802217i	$0.703654\pi$
$98$	2.10196e8i	0.230201i
$99$	−1.13099e9	−1.18331
$100$	0	0
$101$	−9.82882e8	−0.939843	−0.469922	−	0.882708i	$-0.655718\pi$
$101$	−9.82882e8	−0.939843	−0.469922	+	0.882708i	$0.655718\pi$
$102$	− 1.31020e9i	− 1.19850i
$103$	1.53146e9i	1.34072i	0.742037	+	0.670359i	$0.233860\pi$
$103$	1.53146e9i	1.34072i	−0.742037	+	0.670359i	$0.766140\pi$
$104$	−5.49457e8	−0.460558
$105$	0	0
$106$	1.01501e9	0.780895
$107$	− 5.19394e8i	− 0.383063i	−0.981487	−	0.191531i	$-0.938655\pi$
$107$	− 5.19394e8i	− 0.383063i	0.981487	−	0.191531i	$-0.0613454\pi$
$108$	− 1.94631e9i	− 1.37659i
$109$	1.24526e9	0.844967	0.422483	−	0.906371i	$-0.361158\pi$
$109$	1.24526e9	0.844967	0.422483	+	0.906371i	$0.361158\pi$
$110$	0	0
$111$	−1.15512e9	−0.722229
$112$	− 2.98402e7i	− 0.0179193i
$113$	− 1.12841e9i	− 0.651048i	−0.945534	−	0.325524i	$-0.894459\pi$
$113$	− 1.12841e9i	− 0.651048i	0.945534	−	0.325524i	$-0.105541\pi$
$114$	−1.10813e9	−0.614495
$115$	0	0
$116$	−4.32526e9	−2.21795
$117$	7.37973e8i	0.364086i
$118$	6.24391e8i	0.296474i
$119$	1.25534e9	0.573853
$120$	0	0
$121$	3.35784e9	1.42405
$122$	− 7.05655e9i	− 2.88385i
$123$	2.05017e8i	0.0807637i
$124$	4.42425e9	1.68051
$125$	0	0
$126$	1.30964e9	0.462896
$127$	− 3.31282e9i	− 1.13001i	−0.825088	−	0.565004i	$-0.808875\pi$
$127$	− 3.31282e9i	− 1.13001i	0.825088	−	0.565004i	$-0.191125\pi$
$128$	− 4.80025e9i	− 1.58059i
$129$	−7.64420e8	−0.243040
$130$	0	0
$131$	4.83380e9	1.43406	0.717031	−	0.697042i	$-0.245501\pi$
$131$	4.83380e9	1.43406	0.717031	+	0.697042i	$0.245501\pi$
$132$	4.24757e9i	1.21775i
$133$	− 1.06173e9i	− 0.294226i
$134$	7.06257e9	1.89231
$135$	0	0
$136$	5.82348e9	1.45968
$137$	− 3.43281e9i	− 0.832543i	−0.909240	−	0.416272i	$-0.863337\pi$
$137$	− 3.43281e9i	− 0.832543i	0.909240	−	0.416272i	$-0.136663\pi$
$138$	− 5.30735e9i	− 1.24573i
$139$	−3.96923e9	−0.901860	−0.450930	−	0.892559i	$-0.648908\pi$
$139$	−3.96923e9	−0.901860	−0.450930	+	0.892559i	$0.648908\pi$
$140$	0	0
$141$	−1.08695e9	−0.231592
$142$	− 5.16537e9i	− 1.06611i
$143$	− 3.72958e9i	− 0.745843i
$144$	−1.85921e8	−0.0360328
$145$	0	0
$146$	8.64065e8	0.157383
$147$	− 3.96199e8i	− 0.0699819i
$148$	− 1.37395e10i	− 2.35394i
$149$	−2.72837e8	−0.0453487	−0.0226744	−	0.999743i	$-0.507218\pi$
$149$	−2.72837e8	−0.0453487	−0.0226744	+	0.999743i	$0.507218\pi$
$150$	0	0
$151$	3.77089e9	0.590265	0.295133	−	0.955456i	$-0.404636\pi$
$151$	3.77089e9	0.590265	0.295133	+	0.955456i	$0.404636\pi$
$152$	− 4.92531e9i	− 0.748406i
$153$	− 7.82148e9i	− 1.15392i
$154$	−6.61866e9	−0.948259
$155$	0	0
$156$	2.77156e9	0.374682
$157$	9.54797e9i	1.25419i	0.778944	+	0.627094i	$0.215756\pi$
$157$	9.54797e9i	1.25419i	−0.778944	+	0.627094i	$0.784244\pi$
$158$	9.17422e9i	1.17115i
$159$	−1.91319e9	−0.237395
$160$	0	0
$161$	5.08512e9	0.596465
$162$	− 4.76984e9i	− 0.544110i
$163$	6.35428e9i	0.705054i	0.935802	+	0.352527i	$0.114678\pi$
$163$	6.35428e9i	0.705054i	−0.935802	+	0.352527i	$0.885322\pi$
$164$	−2.43856e9	−0.263230
$165$	0	0
$166$	−7.54102e9	−0.770804
$167$	− 2.04016e9i	− 0.202974i	−0.994837	−	0.101487i	$-0.967640\pi$
$167$	− 2.04016e9i	− 0.202974i	0.994837	−	0.101487i	$-0.0323600\pi$
$168$	− 1.83795e9i	− 0.178009i
$169$	8.17093e9	0.770516
$170$	0	0
$171$	−6.61515e9	−0.591640
$172$	− 9.09235e9i	− 0.792133i
$173$	1.72853e10i	1.46713i	0.679620	+	0.733564i	$0.262145\pi$
$173$	1.72853e10i	1.46713i	−0.679620	+	0.733564i	$0.737855\pi$
$174$	1.32589e10	1.09657
$175$	0	0
$176$	9.39611e8	0.0738144
$177$	− 1.17692e9i	− 0.0901293i
$178$	− 2.53259e10i	− 1.89092i
$179$	−6.95395e8	−0.0506282	−0.0253141	−	0.999680i	$-0.508059\pi$
$179$	−6.95395e8	−0.0506282	−0.0253141	+	0.999680i	$0.508059\pi$
$180$	0	0
$181$	1.80182e10	1.24784	0.623919	−	0.781489i	$-0.285539\pi$
$181$	1.80182e10	1.24784	0.623919	+	0.781489i	$0.285539\pi$
$182$	4.31870e9i	0.291764i
$183$	1.33009e10i	0.876702i
$184$	2.35897e10	1.51720
$185$	0	0
$186$	−1.35624e10	−0.830859
$187$	3.95283e10i	2.36386i
$188$	− 1.29287e10i	− 0.754822i
$189$	−5.71651e9	−0.325877
$190$	0	0
$191$	−2.60774e10	−1.41780	−0.708899	−	0.705310i	$-0.750808\pi$
$191$	−2.60774e10	−1.41780	−0.708899	+	0.705310i	$0.750808\pi$
$192$	1.49889e10i	0.796001i
$193$	− 9.94176e9i	− 0.515769i	−0.966176	−	0.257884i	$-0.916975\pi$
$193$	− 9.94176e9i	− 0.515769i	0.966176	−	0.257884i	$-0.0830254\pi$
$194$	5.10075e10	2.58539
$195$	0	0
$196$	4.71257e9	0.228090
$197$	3.35442e10i	1.58679i	0.608707	+	0.793395i	$0.291688\pi$
$197$	3.35442e10i	1.58679i	−0.608707	+	0.793395i	$0.708312\pi$
$198$	4.12379e10i	1.90679i
$199$	−1.19117e10	−0.538435	−0.269218	−	0.963079i	$-0.586765\pi$
$199$	−1.19117e10	−0.538435	−0.269218	+	0.963079i	$0.586765\pi$
$200$	0	0
$201$	−1.33123e10	−0.575268
$202$	3.58378e10i	1.51447i
$203$	1.27037e10i	0.525047i
$204$	−2.93746e10	−1.18751
$205$	0	0
$206$	5.58399e10	2.16044
$207$	− 3.16831e10i	− 1.19939i
$208$	− 6.13101e8i	− 0.0227115i
$209$	3.34318e10	1.21200
$210$	0	0
$211$	−4.45526e10	−1.54740	−0.773699	−	0.633554i	$-0.781596\pi$
$211$	−4.45526e10	−1.54740	−0.773699	+	0.633554i	$0.781596\pi$
$212$	− 2.27564e10i	− 0.773734i
$213$	9.73622e9i	0.324102i
$214$	−1.89381e10	−0.617269
$215$	0	0
$216$	−2.65187e10	−0.828914
$217$	− 1.29945e10i	− 0.397823i
$218$	− 4.54045e10i	− 1.36158i
$219$	−1.62868e9	−0.0478451
$220$	0	0
$221$	2.57924e10	0.727322
$222$	4.21180e10i	1.16380i
$223$	7.31712e10i	1.98138i	0.136129	+	0.990691i	$0.456534\pi$
$223$	7.31712e10i	1.98138i	−0.136129	+	0.990691i	$0.543466\pi$
$224$	−1.47803e10	−0.392253
$225$	0	0
$226$	−4.11440e10	−1.04910
$227$	2.44357e10i	0.610813i	0.952222	+	0.305406i	$0.0987923\pi$
$227$	2.44357e10i	0.610813i	−0.952222	+	0.305406i	$0.901208\pi$
$228$	2.48441e10i	0.608859i
$229$	4.16163e10	1.00001	0.500004	−	0.866023i	$-0.333332\pi$
$229$	4.16163e10	1.00001	0.500004	+	0.866023i	$0.333332\pi$
$230$	0	0
$231$	1.24755e10	0.288274
$232$	5.89319e10i	1.33553i
$233$	− 3.77622e10i	− 0.839375i	−0.907669	−	0.419687i	$-0.862140\pi$
$233$	− 3.77622e10i	− 0.839375i	0.907669	−	0.419687i	$-0.137860\pi$
$234$	2.69079e10	0.586690
$235$	0	0
$236$	1.39988e10	0.293755
$237$	− 1.72925e10i	− 0.356034i
$238$	− 4.57722e10i	− 0.924710i
$239$	3.14171e10	0.622839	0.311420	−	0.950273i	$-0.399196\pi$
$239$	3.14171e10	0.622839	0.311420	+	0.950273i	$0.399196\pi$
$240$	0	0
$241$	3.12996e10	0.597671	0.298835	−	0.954305i	$-0.403402\pi$
$241$	3.12996e10	0.597671	0.298835	+	0.954305i	$0.403402\pi$
$242$	− 1.22433e11i	− 2.29473i
$243$	5.58537e10i	1.02760i
$244$	−1.58207e11	−2.85740
$245$	0	0
$246$	7.47531e9	0.130143
$247$	− 2.18144e10i	− 0.372912i
$248$	− 6.02808e10i	− 1.01192i
$249$	1.42141e10	0.234327
$250$	0	0
$251$	7.69585e10	1.22384	0.611920	−	0.790919i	$-0.290397\pi$
$251$	7.69585e10	1.22384	0.611920	+	0.790919i	$0.290397\pi$
$252$	− 2.93619e10i	− 0.458651i
$253$	1.60121e11i	2.45700i
$254$	−1.20792e11	−1.82090
$255$	0	0
$256$	−6.33632e10	−0.922056
$257$	7.48449e10i	1.07020i	0.844790	+	0.535098i	$0.179725\pi$
$257$	7.48449e10i	1.07020i	−0.844790	+	0.535098i	$0.820275\pi$
$258$	2.78722e10i	0.391636i
$259$	−4.03544e10	−0.557240
$260$	0	0
$261$	7.91512e10	1.05578
$262$	− 1.76250e11i	− 2.31085i
$263$	8.16203e9i	0.105196i	0.998616	+	0.0525978i	$0.0167501\pi$
$263$	8.16203e9i	0.105196i	−0.998616	+	0.0525978i	$0.983250\pi$
$264$	5.78735e10	0.733267
$265$	0	0
$266$	−3.87127e10	−0.474117
$267$	4.77368e10i	0.574848i
$268$	− 1.58342e11i	− 1.87495i
$269$	6.23895e9	0.0726484	0.0363242	−	0.999340i	$-0.488435\pi$
$269$	6.23895e9	0.0726484	0.0363242	+	0.999340i	$0.488435\pi$
$270$	0	0
$271$	8.25889e10	0.930165	0.465083	−	0.885267i	$-0.346025\pi$
$271$	8.25889e10	0.930165	0.465083	+	0.885267i	$0.346025\pi$
$272$	6.49801e9i	0.0719814i
$273$	− 8.14035e9i	− 0.0886974i
$274$	−1.25167e11	−1.34156
$275$	0	0
$276$	−1.18990e11	−1.23430
$277$	− 8.98709e10i	− 0.917192i	−0.888645	−	0.458596i	$-0.848353\pi$
$277$	− 8.98709e10i	− 0.917192i	0.888645	−	0.458596i	$-0.151647\pi$
$278$	1.44726e11i	1.45326i
$279$	−8.09628e10	−0.799957
$280$	0	0
$281$	−1.64133e10	−0.157042	−0.0785211	−	0.996912i	$-0.525020\pi$
$281$	−1.64133e10	−0.157042	−0.0785211	+	0.996912i	$0.525020\pi$
$282$	3.96324e10i	0.373189i
$283$	− 2.99673e10i	− 0.277721i	−0.990312	−	0.138860i	$-0.955656\pi$
$283$	− 2.99673e10i	− 0.277721i	0.990312	−	0.138860i	$-0.0443439\pi$
$284$	−1.15807e11	−1.05634
$285$	0	0
$286$	−1.35988e11	−1.20186
$287$	7.16230e9i	0.0623137i
$288$	9.20893e10i	0.788756i
$289$	−1.54775e11	−1.30515
$290$	0	0
$291$	−9.61444e10	−0.785969
$292$	− 1.93722e10i	− 0.155940i
$293$	− 1.61513e11i	− 1.28028i	−0.768260	−	0.640138i	$-0.778877\pi$
$293$	− 1.61513e11i	− 1.28028i	0.768260	−	0.640138i	$-0.221123\pi$
$294$	−1.44462e10	−0.112769
$295$	0	0
$296$	−1.87202e11	−1.41742
$297$	− 1.80002e11i	− 1.34237i
$298$	9.94817e9i	0.0730752i
$299$	1.04479e11	0.755980
$300$	0	0
$301$	−2.67051e10	−0.187519
$302$	− 1.37494e11i	− 0.951157i
$303$	− 6.75508e10i	− 0.460404i
$304$	5.49580e9	0.0369063
$305$	0	0
$306$	−2.85186e11	−1.85944
$307$	− 1.65779e10i	− 0.106514i	−0.998581	−	0.0532570i	$-0.983040\pi$
$307$	− 1.65779e10i	− 0.106514i	0.998581	−	0.0532570i	$-0.0169603\pi$
$308$	1.48390e11i	0.939562i
$309$	−1.05253e11	−0.656782
$310$	0	0
$311$	3.53749e10	0.214424	0.107212	−	0.994236i	$-0.465808\pi$
$311$	3.53749e10	0.214424	0.107212	+	0.994236i	$0.465808\pi$
$312$	− 3.77627e10i	− 0.225615i
$313$	− 8.44655e9i	− 0.0497428i	−0.999691	−	0.0248714i	$-0.992082\pi$
$313$	− 8.44655e9i	− 0.0497428i	0.999691	−	0.0248714i	$-0.00791762\pi$
$314$	3.48137e11	2.02100
$315$	0	0
$316$	2.05685e11	1.16041
$317$	2.19980e11i	1.22354i	0.791037	+	0.611768i	$0.209541\pi$
$317$	2.19980e11i	1.22354i	−0.791037	+	0.611768i	$0.790459\pi$
$318$	6.97587e10i	0.382540i
$319$	−4.00015e11	−2.16281
$320$	0	0
$321$	3.56965e10	0.187652
$322$	− 1.85413e11i	− 0.961147i
$323$	2.31202e11i	1.18190i
$324$	−1.06939e11	−0.539120
$325$	0	0
$326$	2.31690e11	1.13613
$327$	8.55831e10i	0.413926i
$328$	3.32256e10i	0.158504i
$329$	−3.79729e10	−0.178687
$330$	0	0
$331$	6.96186e10	0.318786	0.159393	−	0.987215i	$-0.449046\pi$
$331$	6.96186e10	0.318786	0.159393	+	0.987215i	$0.449046\pi$
$332$	1.69069e11i	0.763734i
$333$	2.51430e11i	1.12052i
$334$	−7.43882e10	−0.327073
$335$	0	0
$336$	2.05084e9	0.00877818
$337$	2.90202e11i	1.22565i	0.790219	+	0.612825i	$0.209967\pi$
$337$	2.90202e11i	1.22565i	−0.790219	+	0.612825i	$0.790033\pi$
$338$	− 2.97928e11i	− 1.24161i
$339$	7.75524e10	0.318931
$340$	0	0
$341$	4.09171e11	1.63874
$342$	2.41201e11i	0.953371i
$343$	− 1.38413e10i	− 0.0539949i
$344$	−1.23884e11	−0.476982
$345$	0	0
$346$	6.30254e11	2.36414
$347$	1.42619e11i	0.528075i	0.964512	+	0.264038i	$0.0850543\pi$
$347$	1.42619e11i	0.528075i	−0.964512	+	0.264038i	$0.914946\pi$
$348$	− 2.97263e11i	− 1.08651i
$349$	−4.06617e11	−1.46714	−0.733569	−	0.679615i	$-0.762147\pi$
$349$	−4.06617e11	−1.46714	−0.733569	+	0.679615i	$0.762147\pi$
$350$	0	0
$351$	−1.17452e11	−0.413027
$352$	− 4.65402e11i	− 1.61580i
$353$	− 1.80418e11i	− 0.618435i	−0.950991	−	0.309217i	$-0.899933\pi$
$353$	− 1.80418e11i	− 0.618435i	0.950991	−	0.309217i	$-0.100067\pi$
$354$	−4.29127e10	−0.145235
$355$	0	0
$356$	−5.67803e11	−1.87358
$357$	8.62763e10i	0.281115i
$358$	2.53554e10i	0.0815826i
$359$	5.04299e11	1.60237	0.801186	−	0.598416i	$-0.204203\pi$
$359$	5.04299e11	1.60237	0.801186	+	0.598416i	$0.204203\pi$
$360$	0	0
$361$	−1.27145e11	−0.394018
$362$	− 6.56979e11i	− 2.01077i
$363$	2.30775e11i	0.697605i
$364$	9.68249e10	0.289089
$365$	0	0
$366$	4.84977e11	1.41272
$367$	− 1.80774e11i	− 0.520162i	−0.965587	−	0.260081i	$-0.916251\pi$
$367$	− 1.80774e11i	− 0.520162i	0.965587	−	0.260081i	$-0.0837492\pi$
$368$	2.63220e10i	0.0748177i
$369$	4.46251e10	0.125303
$370$	0	0
$371$	−6.68377e10	−0.183164
$372$	3.04067e11i	0.823239i
$373$	3.96719e11i	1.06119i	0.847625	+	0.530596i	$0.178032\pi$
$373$	3.96719e11i	1.06119i	−0.847625	+	0.530596i	$0.821968\pi$
$374$	1.44128e12	3.80913
$375$	0	0
$376$	−1.76154e11	−0.454515
$377$	2.61012e11i	0.665463i
$378$	2.08435e11i	0.525119i
$379$	7.29691e11	1.81661	0.908306	−	0.418306i	$-0.137376\pi$
$379$	7.29691e11	1.81661	0.908306	+	0.418306i	$0.137376\pi$
$380$	0	0
$381$	2.27681e11	0.553560
$382$	9.50833e11i	2.28465i
$383$	− 6.45922e11i	− 1.53386i	−0.641731	−	0.766930i	$-0.721783\pi$
$383$	− 6.45922e11i	− 1.53386i	0.641731	−	0.766930i	$-0.278217\pi$
$384$	3.29908e11	0.774288
$385$	0	0
$386$	−3.62496e11	−0.831113
$387$	1.66388e11i	0.377070i
$388$	− 1.14358e12i	− 2.56168i
$389$	−4.16712e11	−0.922706	−0.461353	−	0.887217i	$-0.652636\pi$
$389$	−4.16712e11	−0.922706	−0.461353	+	0.887217i	$0.652636\pi$
$390$	0	0
$391$	−1.10734e12	−2.39598
$392$	− 6.42091e10i	− 0.137344i
$393$	3.32214e11i	0.702508i
$394$	1.22309e12	2.55696
$395$	0	0
$396$	9.24550e11	1.88930
$397$	9.61738e11i	1.94312i	0.236793	+	0.971560i	$0.423904\pi$
$397$	9.61738e11i	1.94312i	−0.236793	+	0.971560i	$0.576096\pi$
$398$	4.34322e11i	0.867637i
$399$	7.29697e10	0.144133
$400$	0	0
$401$	2.17932e10	0.0420892	0.0210446	−	0.999779i	$-0.493301\pi$
$401$	2.17932e10	0.0420892	0.0210446	+	0.999779i	$0.493301\pi$
$402$	4.85391e11i	0.926990i
$403$	− 2.66986e11i	− 0.504215i
$404$	8.03480e11	1.50058
$405$	0	0
$406$	4.63202e11	0.846064
$407$	− 1.27068e12i	− 2.29542i
$408$	4.00232e11i	0.715057i
$409$	8.91299e11	1.57496	0.787478	−	0.616342i	$-0.211386\pi$
$409$	8.91299e11	1.57496	0.787478	+	0.616342i	$0.211386\pi$
$410$	0	0
$411$	2.35927e11	0.407840
$412$	− 1.25192e12i	− 2.14063i
$413$	− 4.11158e10i	− 0.0695398i
$414$	−1.15523e12	−1.93271
$415$	0	0
$416$	−3.03677e11	−0.497155
$417$	− 2.72794e11i	− 0.441797i
$418$	− 1.21899e12i	− 1.95302i
$419$	−1.00476e12	−1.59258	−0.796290	−	0.604915i	$-0.793207\pi$
$419$	−1.00476e12	−1.59258	−0.796290	+	0.604915i	$0.793207\pi$
$420$	0	0
$421$	−9.93627e11	−1.54154	−0.770768	−	0.637115i	$-0.780127\pi$
$421$	−9.93627e11	−1.54154	−0.770768	+	0.637115i	$0.780127\pi$
$422$	1.62447e12i	2.49348i
$423$	2.36592e11i	0.359309i
$424$	−3.10057e11	−0.465903
$425$	0	0
$426$	3.55001e11	0.522260
$427$	4.64670e11i	0.676425i
$428$	4.24590e11i	0.611608i
$429$	2.56324e11	0.365369
$430$	0	0
$431$	−5.70989e11	−0.797040	−0.398520	−	0.917160i	$-0.630476\pi$
$431$	−5.70989e11	−0.797040	−0.398520	+	0.917160i	$0.630476\pi$
$432$	− 2.95903e10i	− 0.0408764i
$433$	− 1.38637e11i	− 0.189532i	−0.995500	−	0.0947659i	$-0.969790\pi$
$433$	− 1.38637e11i	− 0.189532i	0.995500	−	0.0947659i	$-0.0302103\pi$
$434$	−4.73804e11	−0.641054
$435$	0	0
$436$	−1.01796e12	−1.34910
$437$	9.36549e11i	1.22847i
$438$	5.93848e10i	0.0770978i
$439$	−1.11468e12	−1.43238	−0.716189	−	0.697906i	$-0.754115\pi$
$439$	−1.11468e12	−1.43238	−0.716189	+	0.697906i	$0.754115\pi$
$440$	0	0
$441$	−8.62389e10	−0.108575
$442$	− 9.40441e11i	− 1.17201i
$443$	− 8.81863e11i	− 1.08789i	−0.839121	−	0.543944i	$-0.816930\pi$
$443$	− 8.81863e11i	− 1.08789i	0.839121	−	0.543944i	$-0.183070\pi$
$444$	9.44282e11	1.15313
$445$	0	0
$446$	2.66796e12	3.19281
$447$	− 1.87513e10i	− 0.0222151i
$448$	5.23639e11i	0.614159i
$449$	−9.45977e11	−1.09843	−0.549214	−	0.835681i	$-0.685073\pi$
$449$	−9.45977e11	−1.09843	−0.549214	+	0.835681i	$0.685073\pi$
$450$	0	0
$451$	−2.25527e11	−0.256687
$452$	9.22443e11i	1.03948i
$453$	2.59163e11i	0.289155i
$454$	8.90972e11	0.984266
$455$	0	0
$456$	3.38503e11	0.366624
$457$	− 2.09756e11i	− 0.224953i	−0.993654	−	0.112476i	$-0.964122\pi$
$457$	− 2.09756e11i	− 0.224953i	0.993654	−	0.112476i	$-0.0358783\pi$
$458$	− 1.51741e12i	− 1.61142i
$459$	1.24483e12	1.30904
$460$	0	0
$461$	1.13248e12	1.16782	0.583912	−	0.811817i	$-0.301521\pi$
$461$	1.13248e12	1.16782	0.583912	+	0.811817i	$0.301521\pi$
$462$	− 4.54882e11i	− 0.464526i
$463$	6.47872e11i	0.655202i	0.944816	+	0.327601i	$0.106240\pi$
$463$	6.47872e11i	0.655202i	−0.944816	+	0.327601i	$0.893760\pi$
$464$	−6.57580e10	−0.0658594
$465$	0	0
$466$	−1.37688e12	−1.35257
$467$	− 1.63471e12i	− 1.59043i	−0.606327	−	0.795216i	$-0.707358\pi$
$467$	− 1.63471e12i	− 1.59043i	0.606327	−	0.795216i	$-0.292642\pi$
$468$	− 6.03273e11i	− 0.581310i
$469$	−4.65067e11	−0.443851
$470$	0	0
$471$	−6.56206e11	−0.614393
$472$	− 1.90734e11i	− 0.176885i
$473$	− 8.40893e11i	− 0.772442i
$474$	−6.30519e11	−0.573714
$475$	0	0
$476$	−1.02621e12	−0.916229
$477$	4.16436e11i	0.368312i
$478$	− 1.14553e12i	− 1.00365i
$479$	1.44714e12	1.25603	0.628016	−	0.778200i	$-0.283867\pi$
$479$	1.44714e12	1.25603	0.628016	+	0.778200i	$0.283867\pi$
$480$	0	0
$481$	−8.29126e11	−0.706265
$482$	− 1.14124e12i	− 0.963089i
$483$	3.49487e11i	0.292192i
$484$	−2.74495e12	−2.27368
$485$	0	0
$486$	2.03654e12	1.65588
$487$	− 7.93797e11i	− 0.639483i	−0.947505	−	0.319742i	$-0.896404\pi$
$487$	− 7.93797e11i	− 0.639483i	0.947505	−	0.319742i	$-0.103596\pi$
$488$	2.15558e12i	1.72058i
$489$	−4.36713e11	−0.345387
$490$	0	0
$491$	8.93419e11	0.693726	0.346863	−	0.937916i	$-0.387247\pi$
$491$	8.93419e11	0.693726	0.346863	+	0.937916i	$0.387247\pi$
$492$	− 1.67596e11i	− 0.128949i
$493$	− 2.76636e12i	− 2.10910i
$494$	−7.95394e11	−0.600912
$495$	0	0
$496$	6.72630e10	0.0499010
$497$	3.40137e11i	0.250063i
$498$	− 5.18274e11i	− 0.377596i
$499$	2.29839e12	1.65948	0.829740	−	0.558150i	$-0.188489\pi$
$499$	2.29839e12	1.65948	0.829740	+	0.558150i	$0.188489\pi$
$500$	0	0
$501$	1.40215e11	0.0994315
$502$	− 2.80606e12i	− 1.97210i
$503$	1.28863e12i	0.897580i	0.893637	+	0.448790i	$0.148145\pi$
$503$	1.28863e12i	0.897580i	−0.893637	+	0.448790i	$0.851855\pi$
$504$	−4.00058e11	−0.276176
$505$	0	0
$506$	5.83831e12	3.95922
$507$	5.61566e11i	0.377455i
$508$	2.70814e12i	1.80420i
$509$	−2.18603e12	−1.44353	−0.721765	−	0.692139i	$-0.756669\pi$
$509$	−2.18603e12	−1.44353	−0.721765	+	0.692139i	$0.756669\pi$
$510$	0	0
$511$	−5.68982e10	−0.0369151
$512$	− 1.47382e11i	− 0.0947826i
$513$	− 1.05283e12i	− 0.671169i
$514$	2.72899e12	1.72452
$515$	0	0
$516$	6.24892e11	0.388044
$517$	− 1.19569e12i	− 0.736058i
$518$	1.47140e12i	0.897939i
$519$	−1.18797e12	−0.718707
$520$	0	0
$521$	−1.84809e12	−1.09889	−0.549443	−	0.835531i	$-0.685160\pi$
$521$	−1.84809e12	−1.09889	−0.549443	+	0.835531i	$0.685160\pi$
$522$	− 2.88600e12i	− 1.70130i
$523$	− 9.46663e11i	− 0.553271i	−0.960975	−	0.276635i	$-0.910781\pi$
$523$	− 9.46663e11i	− 0.553271i	0.960975	−	0.276635i	$-0.0892195\pi$
$524$	−3.95150e12	−2.28966
$525$	0	0
$526$	2.97603e11	0.169513
$527$	2.82967e12i	1.59804i
$528$	6.45769e10i	0.0361597i
$529$	−2.68443e12	−1.49039
$530$	0	0
$531$	−2.56174e11	−0.139833
$532$	8.67934e11i	0.469769i
$533$	1.47157e11i	0.0789786i
$534$	1.74058e12	0.926313
$535$	0	0
$536$	−2.15742e12	−1.12900
$537$	− 4.77926e10i	− 0.0248014i
$538$	− 2.27484e11i	− 0.117066i
$539$	4.35835e11	0.222420
$540$	0	0
$541$	−3.43412e12	−1.72357	−0.861783	−	0.507277i	$-0.830652\pi$
$541$	−3.43412e12	−1.72357	−0.861783	+	0.507277i	$0.830652\pi$
$542$	− 3.01135e12i	− 1.49887i
$543$	1.23834e12i	0.611282i
$544$	3.21855e12	1.57567
$545$	0	0
$546$	−2.96813e11	−0.142927
$547$	− 1.17006e12i	− 0.558809i	−0.960173	−	0.279405i	$-0.909863\pi$
$547$	− 1.17006e12i	− 0.558809i	0.960173	−	0.279405i	$-0.0901370\pi$
$548$	2.80623e12i	1.32926i
$549$	2.89515e12	1.36018
$550$	0	0
$551$	−2.33970e12	−1.08138
$552$	1.62125e12i	0.743233i
$553$	− 6.04118e11i	− 0.274700i
$554$	−3.27687e12	−1.47797
$555$	0	0
$556$	3.24473e12	1.43993
$557$	1.14677e12i	0.504812i	0.967621	+	0.252406i	$0.0812218\pi$
$557$	1.14677e12i	0.504812i	−0.967621	+	0.252406i	$0.918778\pi$
$558$	2.95206e12i	1.28905i
$559$	−5.48687e11	−0.237668
$560$	0	0
$561$	−2.71667e12	−1.15799
$562$	5.98459e11i	0.253059i
$563$	− 1.28982e12i	− 0.541056i	−0.962712	−	0.270528i	$-0.912802\pi$
$563$	− 1.28982e12i	− 0.541056i	0.962712	−	0.270528i	$-0.0871983\pi$
$564$	8.88554e11	0.369767
$565$	0	0
$566$	−1.09266e12	−0.447520
$567$	3.14092e11i	0.127624i
$568$	1.57788e12i	0.636072i
$569$	−2.06212e12	−0.824724	−0.412362	−	0.911020i	$-0.635296\pi$
$569$	−2.06212e12	−0.824724	−0.412362	+	0.911020i	$0.635296\pi$
$570$	0	0
$571$	−4.00715e12	−1.57751	−0.788756	−	0.614706i	$-0.789275\pi$
$571$	−4.00715e12	−1.57751	−0.788756	+	0.614706i	$0.789275\pi$
$572$	3.04883e12i	1.19083i
$573$	− 1.79223e12i	− 0.694541i
$574$	2.61151e11	0.100413
$575$	0	0
$576$	3.26256e12	1.23497
$577$	1.71845e12i	0.645424i	0.946497	+	0.322712i	$0.104595\pi$
$577$	1.71845e12i	0.645424i	−0.946497	+	0.322712i	$0.895405\pi$
$578$	5.64341e12i	2.10313i
$579$	6.83270e11	0.252661
$580$	0	0
$581$	4.96572e11	0.180796
$582$	3.50561e12i	1.26651i
$583$	− 2.10459e12i	− 0.754500i
$584$	−2.63948e11	−0.0938990
$585$	0	0
$586$	−5.88908e12	−2.06304
$587$	2.80000e12i	0.973389i	0.873572	+	0.486695i	$0.161798\pi$
$587$	2.80000e12i	0.973389i	−0.873572	+	0.486695i	$0.838202\pi$
$588$	3.23882e11i	0.111735i
$589$	2.39325e12	0.819348
$590$	0	0
$591$	−2.30540e12	−0.777326
$592$	− 2.08886e11i	− 0.0698975i
$593$	− 1.10112e12i	− 0.365669i	−0.983144	−	0.182834i	$-0.941473\pi$
$593$	− 1.10112e12i	− 0.365669i	0.983144	−	0.182834i	$-0.0585272\pi$
$594$	−6.56322e12	−2.16311
$595$	0	0
$596$	2.23037e11	0.0724050
$597$	− 8.18656e11i	− 0.263765i
$598$	− 3.80952e12i	− 1.21819i
$599$	−2.24275e12	−0.711805	−0.355902	−	0.934523i	$-0.615826\pi$
$599$	−2.24275e12	−0.711805	−0.355902	+	0.934523i	$0.615826\pi$
$600$	0	0
$601$	−9.54770e11	−0.298513	−0.149257	−	0.988798i	$-0.547688\pi$
$601$	−9.54770e11	−0.298513	−0.149257	+	0.988798i	$0.547688\pi$
$602$	9.73721e11i	0.302169i
$603$	2.89763e12i	0.892512i
$604$	−3.08260e12	−0.942434
$605$	0	0
$606$	−2.46303e12	−0.741897
$607$	5.12222e11i	0.153147i	0.997064	+	0.0765736i	$0.0243980\pi$
$607$	5.12222e11i	0.153147i	−0.997064	+	0.0765736i	$0.975602\pi$
$608$	− 2.72215e12i	− 0.807877i
$609$	−8.73091e11	−0.257206
$610$	0	0
$611$	−7.80195e11	−0.226474
$612$	6.39385e12i	1.84239i
$613$	1.54411e12i	0.441680i	0.975310	+	0.220840i	$0.0708798\pi$
$613$	1.54411e12i	0.441680i	−0.975310	+	0.220840i	$0.929120\pi$
$614$	−6.04463e11	−0.171637
$615$	0	0
$616$	2.02182e12	0.565756
$617$	2.69330e12i	0.748171i	0.927394	+	0.374085i	$0.122043\pi$
$617$	2.69330e12i	0.748171i	−0.927394	+	0.374085i	$0.877957\pi$
$618$	3.83772e12i	1.05834i
$619$	−2.16325e12	−0.592242	−0.296121	−	0.955150i	$-0.595693\pi$
$619$	−2.16325e12	−0.592242	−0.296121	+	0.955150i	$0.595693\pi$
$620$	0	0
$621$	5.04253e12	1.36062
$622$	− 1.28984e12i	− 0.345524i
$623$	1.66770e12i	0.443527i
$624$	4.21367e10	0.0111258
$625$	0	0
$626$	−3.07978e11	−0.0801557
$627$	2.29767e12i	0.593724i
$628$	− 7.80520e12i	− 2.00247i
$629$	8.78758e12	2.23842
$630$	0	0
$631$	−6.47015e11	−0.162473	−0.0812367	−	0.996695i	$-0.525887\pi$
$631$	−6.47015e11	−0.162473	−0.0812367	+	0.996695i	$0.525887\pi$
$632$	− 2.80248e12i	− 0.698739i
$633$	− 3.06198e12i	− 0.758028i
$634$	8.02090e12	1.97161
$635$	0	0
$636$	1.56398e12	0.379031
$637$	− 2.84385e11i	− 0.0684350i
$638$	1.45853e13i	3.48516i
$639$	2.11924e12	0.502836
$640$	0	0
$641$	4.33378e12	1.01392	0.506962	−	0.861968i	$-0.330768\pi$
$641$	4.33378e12	1.01392	0.506962	+	0.861968i	$0.330768\pi$
$642$	− 1.30156e12i	− 0.302383i
$643$	− 3.66638e12i	− 0.845840i	−0.906167	−	0.422920i	$-0.861005\pi$
$643$	− 3.66638e12i	− 0.845840i	0.906167	−	0.422920i	$-0.138995\pi$
$644$	−4.15695e12	−0.952332
$645$	0	0
$646$	8.43006e12	1.90452
$647$	5.62143e12i	1.26118i	0.776116	+	0.630591i	$0.217187\pi$
$647$	5.62143e12i	1.26118i	−0.776116	+	0.630591i	$0.782813\pi$
$648$	1.45706e12i	0.324630i
$649$	1.29466e12	0.286453
$650$	0	0
$651$	8.93075e11	0.194883
$652$	− 5.19446e12i	− 1.12571i
$653$	7.11463e12i	1.53124i	0.643294	+	0.765620i	$0.277567\pi$
$653$	7.11463e12i	1.53124i	−0.643294	+	0.765620i	$0.722433\pi$
$654$	3.12053e12	0.667003
$655$	0	0
$656$	−3.70741e10	−0.00781633
$657$	3.54507e11i	0.0742303i
$658$	1.38456e12i	0.287936i
$659$	−7.21268e12	−1.48975	−0.744873	−	0.667206i	$-0.767490\pi$
$659$	−7.21268e12	−1.48975	−0.744873	+	0.667206i	$0.767490\pi$
$660$	0	0
$661$	6.13573e12	1.25014	0.625072	−	0.780567i	$-0.285070\pi$
$661$	6.13573e12	1.25014	0.625072	+	0.780567i	$0.285070\pi$
$662$	− 2.53843e12i	− 0.513693i
$663$	1.77264e12i	0.356295i
$664$	2.30358e12	0.459882
$665$	0	0
$666$	9.16764e12	1.80561
$667$	− 1.12059e13i	− 2.19221i
$668$	1.66778e12i	0.324074i
$669$	−5.02886e12	−0.970626
$670$	0	0
$671$	−1.46316e13	−2.78637
$672$	− 1.01581e12i	− 0.192154i
$673$	− 5.72507e12i	− 1.07575i	−0.843023	−	0.537877i	$-0.819226\pi$
$673$	− 5.72507e12i	− 1.07575i	0.843023	−	0.537877i	$-0.180774\pi$
$674$	1.05813e13	1.97502
$675$	0	0
$676$	−6.67952e12	−1.23023
$677$	5.22145e12i	0.955306i	0.878549	+	0.477653i	$0.158512\pi$
$677$	5.22145e12i	0.955306i	−0.878549	+	0.477653i	$0.841488\pi$
$678$	− 2.82771e12i	− 0.513927i
$679$	−3.35882e12	−0.606419
$680$	0	0
$681$	−1.67940e12	−0.299221
$682$	− 1.49192e13i	− 2.64067i
$683$	− 8.77130e12i	− 1.54231i	−0.636649	−	0.771154i	$-0.719680\pi$
$683$	− 8.77130e12i	− 1.54231i	0.636649	−	0.771154i	$-0.280320\pi$
$684$	5.40771e12	0.944628
$685$	0	0
$686$	−5.04680e11	−0.0870077
$687$	2.86018e12i	0.489877i
$688$	− 1.38233e11i	− 0.0235215i
$689$	−1.37326e12	−0.232148
$690$	0	0
$691$	3.10716e12	0.518457	0.259229	−	0.965816i	$-0.416532\pi$
$691$	3.10716e12	0.518457	0.259229	+	0.965816i	$0.416532\pi$
$692$	− 1.41302e13i	− 2.34246i
$693$	− 2.71550e12i	− 0.447249i
$694$	5.20018e12	0.850943
$695$	0	0
$696$	−4.05023e12	−0.654242
$697$	− 1.55966e12i	− 0.250313i
$698$	1.48260e13i	2.36415i
$699$	2.59530e12	0.411187
$700$	0	0
$701$	2.85667e12	0.446816	0.223408	−	0.974725i	$-0.428282\pi$
$701$	2.85667e12	0.446816	0.223408	+	0.974725i	$0.428282\pi$
$702$	4.28253e12i	0.665554i
$703$	− 7.43225e12i	− 1.14768i
$704$	−1.64884e13	−2.52989
$705$	0	0
$706$	−6.57839e12	−0.996549
$707$	− 2.35990e12i	− 0.355227i
$708$	9.62097e11i	0.143903i
$709$	−3.61602e12	−0.537431	−0.268716	−	0.963220i	$-0.586599\pi$
$709$	−3.61602e12	−0.537431	−0.268716	+	0.963220i	$0.586599\pi$
$710$	0	0
$711$	−3.76399e12	−0.552376
$712$	7.73636e12i	1.12818i
$713$	1.14624e13i	1.66101i
$714$	3.14580e12	0.452990
$715$	0	0
$716$	5.68466e11	0.0808344
$717$	2.15921e12i	0.305112i
$718$	− 1.83877e13i	− 2.58207i
$719$	1.61890e12	0.225913	0.112956	−	0.993600i	$-0.463968\pi$
$719$	1.61890e12	0.225913	0.112956	+	0.993600i	$0.463968\pi$
$720$	0	0
$721$	−3.67703e12	−0.506744
$722$	4.63595e12i	0.634923i
$723$	2.15114e12i	0.292783i
$724$	−1.47294e13	−1.99233
$725$	0	0
$726$	8.41452e12	1.12412
$727$	9.74494e12i	1.29382i	0.762566	+	0.646911i	$0.223939\pi$
$727$	9.74494e12i	1.29382i	−0.762566	+	0.646911i	$0.776061\pi$
$728$	− 1.31925e12i	− 0.174074i
$729$	−1.26380e12	−0.165732
$730$	0	0
$731$	5.81531e12	0.753259
$732$	− 1.08731e13i	− 1.39977i
$733$	− 1.72463e12i	− 0.220662i	−0.993895	−	0.110331i	$-0.964809\pi$
$733$	− 1.72463e12i	− 0.220662i	0.993895	−	0.110331i	$-0.0351910\pi$
$734$	−6.59137e12	−0.838191
$735$	0	0
$736$	1.30377e13	1.63776
$737$	− 1.46441e13i	− 1.82834i
$738$	− 1.62712e12i	− 0.201913i
$739$	−3.28397e12	−0.405041	−0.202520	−	0.979278i	$-0.564913\pi$
$739$	−3.28397e12	−0.405041	−0.202520	+	0.979278i	$0.564913\pi$
$740$	0	0
$741$	1.49924e12	0.182680
$742$	2.43703e12i	0.295151i
$743$	− 4.22418e12i	− 0.508502i	−0.967138	−	0.254251i	$-0.918171\pi$
$743$	− 4.22418e12i	− 0.508502i	0.967138	−	0.254251i	$-0.0818289\pi$
$744$	4.14293e12	0.495712
$745$	0	0
$746$	1.44652e13	1.71001
$747$	− 3.09392e12i	− 0.363552i
$748$	− 3.23133e13i	− 3.77420i
$749$	1.24706e12	0.144784
$750$	0	0
$751$	4.20239e12	0.482077	0.241038	−	0.970516i	$-0.422512\pi$
$751$	4.20239e12	0.482077	0.241038	+	0.970516i	$0.422512\pi$
$752$	− 1.96558e11i	− 0.0224136i
$753$	5.28915e12i	0.599526i
$754$	9.51699e12	1.07233
$755$	0	0
$756$	4.67309e12	0.520303
$757$	1.42679e13i	1.57917i	0.613639	+	0.789587i	$0.289705\pi$
$757$	1.42679e13i	1.57917i	−0.613639	+	0.789587i	$0.710295\pi$
$758$	− 2.66059e13i	− 2.92730i
$759$	−1.10047e13	−1.20362
$760$	0	0
$761$	−1.04976e13	−1.13464	−0.567321	−	0.823497i	$-0.692020\pi$
$761$	−1.04976e13	−1.13464	−0.567321	+	0.823497i	$0.692020\pi$
$762$	− 8.30170e12i	− 0.892010i
$763$	2.98986e12i	0.319367i
$764$	2.13176e13	2.26369
$765$	0	0
$766$	−2.35516e13	−2.47167
$767$	− 8.44770e11i	− 0.0881372i
$768$	− 4.35478e12i	− 0.451690i
$769$	4.68130e12	0.482723	0.241361	−	0.970435i	$-0.422406\pi$
$769$	4.68130e12	0.482723	0.241361	+	0.970435i	$0.422406\pi$
$770$	0	0
$771$	−5.14388e12	−0.524260
$772$	8.12712e12i	0.823490i
$773$	1.76519e13i	1.77821i	0.457701	+	0.889106i	$0.348673\pi$
$773$	1.76519e13i	1.77821i	−0.457701	+	0.889106i	$0.651327\pi$
$774$	6.06682e12	0.607613
$775$	0	0
$776$	−1.55814e13	−1.54251
$777$	− 2.77345e12i	− 0.272977i
$778$	1.51941e13i	1.48685i
$779$	−1.31911e12	−0.128340
$780$	0	0
$781$	−1.07102e13	−1.03008
$782$	4.03756e13i	3.86090i
$783$	1.25973e13i	1.19770i
$784$	7.16464e10	0.00677286
$785$	0	0
$786$	1.21132e13	1.13202
$787$	− 1.53402e12i	− 0.142542i	−0.997457	−	0.0712712i	$-0.977294\pi$
$787$	− 1.53402e12i	− 0.142542i	0.997457	−	0.0712712i	$-0.0227056\pi$
$788$	− 2.74215e13i	− 2.53351i
$789$	−5.60954e11	−0.0515325
$790$	0	0
$791$	2.70931e12	0.246073
$792$	− 1.25971e13i	− 1.13764i
$793$	9.54716e12i	0.857324i
$794$	3.50668e13	3.13115
$795$	0	0
$796$	9.73746e12	0.859680
$797$	− 6.94555e12i	− 0.609740i	−0.952394	−	0.304870i	$-0.901387\pi$
$797$	− 6.94555e12i	− 0.609740i	0.952394	−	0.304870i	$-0.0986130\pi$
$798$	− 2.66061e12i	− 0.232257i
$799$	8.26897e12	0.717779
$800$	0	0
$801$	1.03907e13	0.891861
$802$	− 7.94621e11i	− 0.0678228i
$803$	− 1.79162e12i	− 0.152063i
$804$	1.08824e13	0.918488
$805$	0	0
$806$	−9.73482e12	−0.812494
$807$	4.28786e11i	0.0355885i
$808$	− 1.09475e13i	− 0.903572i
$809$	−2.20581e12	−0.181050	−0.0905251	−	0.995894i	$-0.528855\pi$
$809$	−2.20581e12	−0.181050	−0.0905251	+	0.995894i	$0.528855\pi$
$810$	0	0
$811$	9.32362e12	0.756816	0.378408	−	0.925639i	$-0.376472\pi$
$811$	9.32362e12	0.756816	0.378408	+	0.925639i	$0.376472\pi$
$812$	− 1.03849e13i	− 0.838304i
$813$	5.67611e12i	0.455663i
$814$	−4.63316e13	−3.69885
$815$	0	0
$816$	−4.46590e11	−0.0352617
$817$	− 4.91840e12i	− 0.386211i
$818$	− 3.24985e13i	− 2.53789i
$819$	−1.77187e12	−0.137612
$820$	0	0
$821$	−2.27617e12	−0.174848	−0.0874238	−	0.996171i	$-0.527863\pi$
$821$	−2.27617e12	−0.174848	−0.0874238	+	0.996171i	$0.527863\pi$
$822$	− 8.60237e12i	− 0.657196i
$823$	− 1.21606e13i	− 0.923969i	−0.886888	−	0.461984i	$-0.847138\pi$
$823$	− 1.21606e13i	− 0.923969i	0.886888	−	0.461984i	$-0.152862\pi$
$824$	−1.70576e13	−1.28898
$825$	0	0
$826$	−1.49916e12	−0.112057
$827$	− 1.00142e13i	− 0.744458i	−0.928141	−	0.372229i	$-0.878594\pi$
$827$	− 1.00142e13i	− 0.744458i	0.928141	−	0.372229i	$-0.121406\pi$
$828$	2.59001e13i	1.91498i
$829$	5.39146e12	0.396470	0.198235	−	0.980154i	$-0.436479\pi$
$829$	5.39146e12	0.396470	0.198235	+	0.980154i	$0.436479\pi$
$830$	0	0
$831$	6.17658e12	0.449307
$832$	1.07587e13i	0.778407i
$833$	3.01408e12i	0.216896i
$834$	−9.94660e12	−0.711914
$835$	0	0
$836$	−2.73296e13	−1.93510
$837$	− 1.28856e13i	− 0.907488i
$838$	3.66357e13i	2.56629i
$839$	1.69446e13	1.18060	0.590300	−	0.807184i	$-0.299010\pi$
$839$	1.69446e13	1.18060	0.590300	+	0.807184i	$0.299010\pi$
$840$	0	0
$841$	1.34876e13	0.929722
$842$	3.62296e13i	2.48404i
$843$	− 1.12804e12i	− 0.0769307i
$844$	3.64205e13	2.47062
$845$	0	0
$846$	8.62660e12	0.578993
$847$	8.06218e12i	0.538242i
$848$	− 3.45971e11i	− 0.0229751i
$849$	2.05957e12	0.136048
$850$	0	0
$851$	3.55966e13	2.32662
$852$	− 7.95910e12i	− 0.517470i
$853$	− 1.32813e13i	− 0.858956i	−0.903077	−	0.429478i	$-0.858698\pi$
$853$	− 1.32813e13i	− 0.858956i	0.903077	−	0.429478i	$-0.141302\pi$
$854$	1.69428e13	1.08999
$855$	0	0
$856$	5.78508e12	0.368279
$857$	− 8.21516e10i	− 0.00520238i	−0.999997	−	0.00260119i	$-0.999172\pi$
$857$	− 8.21516e10i	− 0.00520238i	0.999997	−	0.00260119i	$-0.000827986\pi$
$858$	− 9.34606e12i	− 0.588757i
$859$	1.80741e13	1.13263	0.566315	−	0.824189i	$-0.308369\pi$
$859$	1.80741e13	1.13263	0.566315	+	0.824189i	$0.308369\pi$
$860$	0	0
$861$	−4.92245e11	−0.0305258
$862$	2.08194e13i	1.28436i
$863$	1.87322e13i	1.14958i	0.818300	+	0.574791i	$0.194917\pi$
$863$	1.87322e13i	1.14958i	−0.818300	+	0.574791i	$0.805083\pi$
$864$	−1.46565e13	−0.894783
$865$	0	0
$866$	−5.05496e12	−0.305413
$867$	− 1.06373e13i	− 0.639359i
$868$	1.06226e13i	0.635175i
$869$	1.90225e13	1.13156
$870$	0	0
$871$	−9.55531e12	−0.562553
$872$	1.38698e13i	0.812357i
$873$	2.09273e13i	1.21941i
$874$	3.41484e13	1.97956
$875$	0	0
$876$	1.33140e12	0.0763907
$877$	1.95650e13i	1.11682i	0.829566	+	0.558409i	$0.188588\pi$
$877$	1.95650e13i	1.11682i	−0.829566	+	0.558409i	$0.811412\pi$
$878$	4.06432e13i	2.30814i
$879$	1.11004e13	0.627173
$880$	0	0
$881$	2.30530e12	0.128925	0.0644623	−	0.997920i	$-0.479467\pi$
$881$	2.30530e12	0.128925	0.0644623	+	0.997920i	$0.479467\pi$
$882$	3.14444e12i	0.174958i
$883$	− 6.82366e12i	− 0.377741i	−0.982002	−	0.188871i	$-0.939517\pi$
$883$	− 6.82366e12i	− 0.377741i	0.982002	−	0.188871i	$-0.0604826\pi$
$884$	−2.10846e13	−1.16126
$885$	0	0
$886$	−3.21544e13	−1.75303
$887$	6.96936e12i	0.378039i	0.981973	+	0.189020i	$0.0605310\pi$
$887$	6.96936e12i	0.378039i	−0.981973	+	0.189020i	$0.939469\pi$
$888$	− 1.28659e13i	− 0.694356i
$889$	7.95409e12	0.427103
$890$	0	0
$891$	−9.89014e12	−0.525718
$892$	− 5.98155e13i	− 3.16353i
$893$	− 6.99362e12i	− 0.368019i
$894$	−6.83710e11	−0.0357976
$895$	0	0
$896$	1.15254e13	0.597406
$897$	7.18059e12i	0.370334i
$898$	3.44921e13i	1.77001i
$899$	−2.86355e13	−1.46213
$900$	0	0
$901$	1.45546e13	0.735763
$902$	8.22315e12i	0.413627i
$903$	− 1.83537e12i	− 0.0918606i
$904$	1.25684e13	0.625923
$905$	0	0
$906$	9.44958e12	0.465946
$907$	2.37471e13i	1.16514i	0.812780	+	0.582571i	$0.197953\pi$
$907$	2.37471e13i	1.16514i	−0.812780	+	0.582571i	$0.802047\pi$
$908$	− 1.99755e13i	− 0.975240i
$909$	−1.47035e13	−0.714304
$910$	0	0
$911$	1.81347e13	0.872326	0.436163	−	0.899868i	$-0.356337\pi$
$911$	1.81347e13	0.872326	0.436163	+	0.899868i	$0.356337\pi$
$912$	3.77711e11i	0.0180794i
$913$	1.56361e13i	0.744749i
$914$	−7.64811e12	−0.362490
$915$	0	0
$916$	−3.40202e13	−1.59664
$917$	1.16060e13i	0.542024i
$918$	− 4.53888e13i	− 2.10939i
$919$	−6.30502e12	−0.291586	−0.145793	−	0.989315i	$-0.546573\pi$
$919$	−6.30502e12	−0.291586	−0.145793	+	0.989315i	$0.546573\pi$
$920$	0	0
$921$	1.13935e12	0.0521784
$922$	− 4.12925e13i	− 1.88184i
$923$	6.98848e12i	0.316939i
$924$	−1.01984e13	−0.460266
$925$	0	0
$926$	2.36227e13	1.05580
$927$	2.29099e13i	1.01898i
$928$	3.25708e13i	1.44166i
$929$	−4.17837e13	−1.84050	−0.920252	−	0.391327i	$-0.872016\pi$
$929$	−4.17837e13	−1.84050	−0.920252	+	0.391327i	$0.872016\pi$
$930$	0	0
$931$	2.54921e12	0.111207
$932$	3.08696e13i	1.34017i
$933$	2.43122e12i	0.105041i
$934$	−5.96047e13	−2.56283
$935$	0	0
$936$	−8.21964e12	−0.350035
$937$	− 2.80323e13i	− 1.18804i	−0.804451	−	0.594019i	$-0.797540\pi$
$937$	− 2.80323e13i	− 1.18804i	0.804451	−	0.594019i	$-0.202460\pi$
$938$	1.69572e13i	0.715225i
$939$	5.80508e11	0.0243676
$940$	0	0
$941$	−1.31067e13	−0.544931	−0.272465	−	0.962166i	$-0.587839\pi$
$941$	−1.31067e13	−0.544931	−0.272465	+	0.962166i	$0.587839\pi$
$942$	2.39265e13i	0.990035i
$943$	− 6.31785e12i	− 0.260176i
$944$	2.12827e11	0.00872274
$945$	0	0
$946$	−3.06606e13	−1.24472
$947$	2.61465e13i	1.05643i	0.849112	+	0.528213i	$0.177138\pi$
$947$	2.61465e13i	1.05643i	−0.849112	+	0.528213i	$0.822862\pi$
$948$	1.41362e13i	0.568453i
$949$	−1.16904e12	−0.0467875
$950$	0	0
$951$	−1.51186e13	−0.599377
$952$	1.39822e13i	0.551707i
$953$	− 1.54925e13i	− 0.608420i	−0.952605	−	0.304210i	$-0.901608\pi$
$953$	− 1.54925e13i	− 0.608420i	0.952605	−	0.304210i	$-0.0983925\pi$
$954$	1.51841e13	0.593500
$955$	0	0
$956$	−2.56826e13	−0.994442
$957$	− 2.74920e13i	− 1.05950i
$958$	− 5.27655e13i	− 2.02398i
$959$	8.24217e12	0.314672
$960$	0	0
$961$	2.85129e12	0.107842
$962$	3.02316e13i	1.13808i
$963$	− 7.76990e12i	− 0.291137i
$964$	−2.55866e13	−0.954257
$965$	0	0
$966$	1.27430e13	0.470840
$967$	− 9.68529e12i	− 0.356200i	−0.984012	−	0.178100i	$-0.943005\pi$
$967$	− 9.68529e12i	− 0.356200i	0.984012	−	0.178100i	$-0.0569950\pi$
$968$	3.74001e13i	1.36910i
$969$	−1.58899e13	−0.578979
$970$	0	0
$971$	2.06318e12	0.0744820	0.0372410	−	0.999306i	$-0.488143\pi$
$971$	2.06318e12	0.0744820	0.0372410	+	0.999306i	$0.488143\pi$
$972$	− 4.56589e13i	− 1.64069i
$973$	− 9.53011e12i	− 0.340871i
$974$	−2.89434e13	−1.03047
$975$	0	0
$976$	−2.40526e12	−0.0848474
$977$	3.09066e13i	1.08524i	0.839979	+	0.542619i	$0.182567\pi$
$977$	3.09066e13i	1.08524i	−0.839979	+	0.542619i	$0.817433\pi$
$978$	1.59234e13i	0.556558i
$979$	−5.25125e13	−1.82701
$980$	0	0
$981$	1.86285e13	0.642196
$982$	− 3.25758e13i	− 1.11787i
$983$	− 3.07721e13i	− 1.05115i	−0.850746	−	0.525577i	$-0.823849\pi$
$983$	− 3.07721e13i	− 1.05115i	0.850746	−	0.525577i	$-0.176151\pi$
$984$	−2.28350e12	−0.0776468
$985$	0	0
$986$	−1.00867e14	−3.39862
$987$	− 2.60977e12i	− 0.0875337i
$988$	1.78327e13i	0.595401i
$989$	2.35566e13	0.782940
$990$	0	0
$991$	3.91433e13	1.28922	0.644608	−	0.764513i	$-0.277021\pi$
$991$	3.91433e13	1.28922	0.644608	+	0.764513i	$0.277021\pi$
$992$	− 3.33163e13i	− 1.09233i
$993$	4.78469e12i	0.156165i
$994$	1.24020e13	0.402953
$995$	0	0
$996$	−1.16196e13	−0.374133
$997$	3.07488e13i	0.985599i	0.870143	+	0.492800i	$0.164026\pi$
$997$	3.07488e13i	0.985599i	−0.870143	+	0.492800i	$0.835974\pi$
$998$	− 8.38039e13i	− 2.67409i
$999$	−4.00164e13	−1.27114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.f.99.1		10
5.2	odd	4		175.10.a.f.1.5		5
5.3	odd	4		35.10.a.d.1.1	✓	5
5.4	even	2	inner	175.10.b.f.99.10		10
15.8	even	4		315.10.a.j.1.5		5
35.13	even	4		245.10.a.f.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.d.1.1	✓	5	5.3	odd	4
175.10.a.f.1.5		5	5.2	odd	4
175.10.b.f.99.1		10	1.1	even	1	trivial
175.10.b.f.99.10		10	5.4	even	2	inner
245.10.a.f.1.1		5	35.13	even	4
315.10.a.j.1.5		5	15.8	even	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.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-36.4619i q^{2} +68.7273i q^{3} -817.473 q^{4} +2505.93 q^{6} +2401.00i q^{7} +11138.1i q^{8} +14959.6 q^{9} -75602.9 q^{11} -56182.7i q^{12} +49331.2i q^{13} +87545.1 q^{14} -12428.3 q^{16} -522841. i q^{17} -545455. i q^{18} -442202. q^{19} -165014. q^{21} +2.75663e6i q^{22} -2.11792e6i q^{23} -765493. q^{24} +1.79871e6 q^{26} +2.38089e6i q^{27} -1.96275e6i q^{28} +5.29101e6 q^{29} -5.41211e6 q^{31} +6.15588e6i q^{32} -5.19598e6i q^{33} -1.90638e7 q^{34} -1.22290e7 q^{36} +1.68073e7i q^{37} +1.61236e7i q^{38} -3.39040e6 q^{39} +2.98305e6 q^{41} +6.01674e6i q^{42} +1.11225e7i q^{43} +6.18033e7 q^{44} -7.72234e7 q^{46} +1.58154e7i q^{47} -854160. i q^{48} -5.76480e6 q^{49} +3.59335e7 q^{51} -4.03269e7i q^{52} +2.78375e7i q^{53} +8.68118e7 q^{54} -2.67427e7 q^{56} -3.03914e7i q^{57} -1.92920e8i q^{58} -1.71244e7 q^{59} +1.93532e8 q^{61} +1.97336e8i q^{62} +3.59179e7i q^{63} +2.18092e8 q^{64} -1.89455e8 q^{66} +1.93697e8i q^{67} +4.27409e8i q^{68} +1.45559e8 q^{69} +1.41665e8 q^{71} +1.66622e8i q^{72} +2.36977e7i q^{73} +6.12828e8 q^{74} +3.61488e8 q^{76} -1.81522e8i q^{77} +1.23620e8i q^{78} -2.51611e8 q^{79} +1.30817e8 q^{81} -1.08768e8i q^{82} -2.06819e8i q^{83} +1.34895e8 q^{84} +4.05548e8 q^{86} +3.63637e8i q^{87} -8.42074e8i q^{88} +6.94584e8 q^{89} -1.18444e8 q^{91} +1.73134e9i q^{92} -3.71959e8i q^{93} +5.76662e8 q^{94} -4.23077e8 q^{96} +1.39893e9i q^{97} +2.10196e8i q^{98} -1.13099e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 1664 q^{4} - 288 q^{6} - 135594 q^{9} + 20624 q^{11} - 9604 q^{14} - 1053392 q^{16} - 3310752 q^{19} + 672280 q^{21} - 13009152 q^{24} + 20438120 q^{26} + 6707452 q^{29} + 5356240 q^{31} - 43097224 q^{34}+ \cdots - 1396625336 q^{99}+O(q^{100}) \) 10 * q - 1664 * q^4 - 288 * q^6 - 135594 * q^9 + 20624 * q^11 - 9604 * q^14 - 1053392 * q^16 - 3310752 * q^19 + 672280 * q^21 - 13009152 * q^24 + 20438120 * q^26 + 6707452 * q^29 + 5356240 * q^31 - 43097224 * q^34 + 30780920 * q^36 + 36248 * q^39 + 12660388 * q^41 + 142451784 * q^44 - 285690944 * q^46 - 57648010 * q^49 - 35940424 * q^51 + 226558656 * q^54 - 67881072 * q^56 + 304670336 * q^59 + 514031396 * q^61 + 387976864 * q^64 + 366483328 * q^66 + 383914672 * q^69 + 1045577920 * q^71 + 488357736 * q^74 - 690113232 * q^76 - 928349800 * q^79 + 1730301978 * q^81 - 304389176 * q^84 + 1389121232 * q^86 + 2213416652 * q^89 + 761779676 * q^91 + 7205003488 * q^94 - 5304257280 * q^96 - 1396625336 * q^99

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