LMFDB - Embedded newform 175.10.b.b.99.4

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:	$4$
Coefficient field:	$\Q(i, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 97x^{2} + 2304 $ x^4 + 97*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$7.44622i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.b.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.8924i q^{2} +109.817i q^{3} +226.645 q^{4} -1855.08 q^{6} +2401.00i q^{7} +12477.5i q^{8} +7623.25 q^{9} +O(q^{10})$	\(q+16.8924i q^{2} +109.817i q^{3} +226.645 q^{4} -1855.08 q^{6} +2401.00i q^{7} +12477.5i q^{8} +7623.25 q^{9} -28548.3 q^{11} +24889.5i q^{12} +138149. i q^{13} -40558.8 q^{14} -94733.5 q^{16} +101010. i q^{17} +128775. i q^{18} +488928. q^{19} -263670. q^{21} -482250. i q^{22} -140071. i q^{23} -1.37024e6 q^{24} -2.33367e6 q^{26} +2.99869e6i q^{27} +544175. i q^{28} +6.31716e6 q^{29} -1.00903e6 q^{31} +4.78821e6i q^{32} -3.13508e6i q^{33} -1.70630e6 q^{34} +1.72777e6 q^{36} -1.19206e7i q^{37} +8.25919e6i q^{38} -1.51711e7 q^{39} -2.15106e7 q^{41} -4.45404e6i q^{42} +1.65957e7i q^{43} -6.47033e6 q^{44} +2.36615e6 q^{46} +2.67441e7i q^{47} -1.04033e7i q^{48} -5.76480e6 q^{49} -1.10926e7 q^{51} +3.13108e7i q^{52} +3.74991e7i q^{53} -5.06552e7 q^{54} -2.99585e7 q^{56} +5.36926e7i q^{57} +1.06712e8i q^{58} -1.81907e7 q^{59} -2.50111e7 q^{61} -1.70449e7i q^{62} +1.83034e7i q^{63} -1.29388e8 q^{64} +5.29592e7 q^{66} +2.18572e8i q^{67} +2.28934e7i q^{68} +1.53822e7 q^{69} +3.12688e8 q^{71} +9.51193e7i q^{72} -2.89038e8i q^{73} +2.01369e8 q^{74} +1.10813e8 q^{76} -6.85444e7i q^{77} -2.56276e8i q^{78} -4.68685e8 q^{79} -1.79258e8 q^{81} -3.63366e8i q^{82} -7.75407e7i q^{83} -5.97597e7 q^{84} -2.80342e8 q^{86} +6.93730e8i q^{87} -3.56212e8i q^{88} -3.37680e8 q^{89} -3.31695e8 q^{91} -3.17465e7i q^{92} -1.10808e8i q^{93} -4.51773e8 q^{94} -5.25827e8 q^{96} +7.36733e8i q^{97} -9.73816e7i q^{98} -2.17631e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9}+O(q^{10}) $ 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9	$ 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9} + 70632 q^{11} - 28812 q^{14} - 1504 q^{16} + 1850852 q^{19} + 412972 q^{21} - 6602592 q^{24} - 8254848 q^{26} + 20007168 q^{29} + 4934520 q^{31} + 4493352 q^{34} - 11225432 q^{36} - 94835888 q^{39} - 38206896 q^{41} + 37301952 q^{44} + 24735168 q^{46} - 23059204 q^{49} + 119942712 q^{51} - 105668944 q^{54} - 12562032 q^{56} + 14138436 q^{59} + 88632772 q^{61} - 294834304 q^{64} - 166516928 q^{66} + 390362304 q^{69} + 412987632 q^{71} - 7143048 q^{74} + 565023536 q^{76} - 937070192 q^{79} - 1171491268 q^{81} + 250357072 q^{84} - 833661216 q^{86} - 1272534792 q^{89} + 127397060 q^{91} + 304446384 q^{94} - 3429962368 q^{96} - 2818835720 q^{99}+O(q^{100}) $ 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9 + 70632 * q^11 - 28812 * q^14 - 1504 * q^16 + 1850852 * q^19 + 412972 * q^21 - 6602592 * q^24 - 8254848 * q^26 + 20007168 * q^29 + 4934520 * q^31 + 4493352 * q^34 - 11225432 * q^36 - 94835888 * q^39 - 38206896 * q^41 + 37301952 * q^44 + 24735168 * q^46 - 23059204 * q^49 + 119942712 * q^51 - 105668944 * q^54 - 12562032 * q^56 + 14138436 * q^59 + 88632772 * q^61 - 294834304 * q^64 - 166516928 * q^66 + 390362304 * q^69 + 412987632 * q^71 - 7143048 * q^74 + 565023536 * q^76 - 937070192 * q^79 - 1171491268 * q^81 + 250357072 * q^84 - 833661216 * q^86 - 1272534792 * q^89 + 127397060 * q^91 + 304446384 * q^94 - 3429962368 * q^96 - 2818835720 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	16.8924i	0.746548i	0.927721	+	0.373274i	$0.121765\pi$
$2$	16.8924i	0.746548i	−0.927721	+	0.373274i	$0.878235\pi$
$3$	109.817i	0.782751i	0.920231	+	0.391375i	$0.128001\pi$
$3$	109.817i	0.782751i	−0.920231	+	0.391375i	$0.871999\pi$
$4$	226.645	0.442667
$5$	0	0
$5$	0	0
$6$	−1855.08	−0.584361
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	12477.5i	1.07702i
$9$	7623.25	0.387301
$10$	0	0
$11$	−28548.3	−0.587912	−0.293956	−	0.955819i	$-0.594972\pi$
$11$	−28548.3	−0.587912	−0.293956	+	0.955819i	$0.594972\pi$
$12$	24889.5i	0.346498i
$13$	138149.i	1.34153i	0.741668	+	0.670767i	$0.234035\pi$
$13$	138149.i	1.34153i	−0.741668	+	0.670767i	$0.765965\pi$
$14$	−40558.8	−0.282168
$15$	0	0
$16$	−94733.5	−0.361380
$17$	101010.i	0.293321i	0.989187	+	0.146661i	$0.0468525\pi$
$17$	101010.i	0.293321i	−0.989187	+	0.146661i	$0.953147\pi$
$18$	128775.i	0.289139i
$19$	488928.	0.860704	0.430352	−	0.902661i	$-0.358389\pi$
$19$	488928.	0.860704	0.430352	+	0.902661i	$0.358389\pi$
$20$	0	0
$21$	−263670.	−0.295852
$22$	− 482250.i	− 0.438905i
$23$	− 140071.i	− 0.104370i	−0.998637	−	0.0521848i	$-0.983382\pi$
$23$	− 140071.i	− 0.104370i	0.998637	−	0.0521848i	$-0.0166185\pi$
$24$	−1.37024e6	−0.843038
$25$	0	0
$26$	−2.33367e6	−1.00152
$27$	2.99869e6i	1.08591i
$28$	544175.i	0.167312i
$29$	6.31716e6	1.65856	0.829279	−	0.558835i	$-0.188751\pi$
$29$	6.31716e6	1.65856	0.829279	+	0.558835i	$0.188751\pi$
$30$	0	0
$31$	−1.00903e6	−0.196234	−0.0981172	−	0.995175i	$-0.531282\pi$
$31$	−1.00903e6	−0.196234	−0.0981172	+	0.995175i	$0.531282\pi$
$32$	4.78821e6i	0.807232i
$33$	− 3.13508e6i	− 0.460189i
$34$	−1.70630e6	−0.218978
$35$	0	0
$36$	1.72777e6	0.171445
$37$	− 1.19206e7i	− 1.04566i	−0.852436	−	0.522832i	$-0.824876\pi$
$37$	− 1.19206e7i	− 1.04566i	0.852436	−	0.522832i	$-0.175124\pi$
$38$	8.25919e6i	0.642556i
$39$	−1.51711e7	−1.05009
$40$	0	0
$41$	−2.15106e7	−1.18884	−0.594422	−	0.804153i	$-0.702619\pi$
$41$	−2.15106e7	−1.18884	−0.594422	+	0.804153i	$0.702619\pi$
$42$	− 4.45404e6i	− 0.220868i
$43$	1.65957e7i	0.740265i	0.928979	+	0.370133i	$0.120688\pi$
$43$	1.65957e7i	0.740265i	−0.928979	+	0.370133i	$0.879312\pi$
$44$	−6.47033e6	−0.260249
$45$	0	0
$46$	2.36615e6	0.0779169
$47$	2.67441e7i	0.799443i	0.916637	+	0.399721i	$0.130893\pi$
$47$	2.67441e7i	0.799443i	−0.916637	+	0.399721i	$0.869107\pi$
$48$	− 1.04033e7i	− 0.282870i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	−1.10926e7	−0.229597
$52$	3.13108e7i	0.593853i
$53$	3.74991e7i	0.652799i	0.945232	+	0.326399i	$0.105835\pi$
$53$	3.74991e7i	0.652799i	−0.945232	+	0.326399i	$0.894165\pi$
$54$	−5.06552e7	−0.810684
$55$	0	0
$56$	−2.99585e7	−0.407075
$57$	5.36926e7i	0.673717i
$58$	1.06712e8i	1.23819i
$59$	−1.81907e7	−0.195441	−0.0977207	−	0.995214i	$-0.531155\pi$
$59$	−1.81907e7	−0.195441	−0.0977207	+	0.995214i	$0.531155\pi$
$60$	0	0
$61$	−2.50111e7	−0.231285	−0.115643	−	0.993291i	$-0.536893\pi$
$61$	−2.50111e7	−0.231285	−0.115643	+	0.993291i	$0.536893\pi$
$62$	− 1.70449e7i	− 0.146498i
$63$	1.83034e7i	0.146386i
$64$	−1.29388e8	−0.964017
$65$	0	0
$66$	5.29592e7	0.343553
$67$	2.18572e8i	1.32513i	0.749005	+	0.662564i	$0.230532\pi$
$67$	2.18572e8i	1.32513i	−0.749005	+	0.662564i	$0.769468\pi$
$68$	2.28934e7i	0.129844i
$69$	1.53822e7	0.0816954
$70$	0	0
$71$	3.12688e8	1.46032	0.730161	−	0.683275i	$-0.239445\pi$
$71$	3.12688e8	1.46032	0.730161	+	0.683275i	$0.239445\pi$
$72$	9.51193e7i	0.417131i
$73$	− 2.89038e8i	− 1.19125i	−0.803264	−	0.595624i	$-0.796905\pi$
$73$	− 2.89038e8i	− 1.19125i	0.803264	−	0.595624i	$-0.203095\pi$
$74$	2.01369e8	0.780638
$75$	0	0
$76$	1.10813e8	0.381005
$77$	− 6.85444e7i	− 0.222210i
$78$	− 2.56276e8i	− 0.783940i
$79$	−4.68685e8	−1.35381	−0.676907	−	0.736069i	$-0.736680\pi$
$79$	−4.68685e8	−1.35381	−0.676907	+	0.736069i	$0.736680\pi$
$80$	0	0
$81$	−1.79258e8	−0.462696
$82$	− 3.63366e8i	− 0.887529i
$83$	− 7.75407e7i	− 0.179341i	−0.995972	−	0.0896703i	$-0.971419\pi$
$83$	− 7.75407e7i	− 0.179341i	0.995972	−	0.0896703i	$-0.0285813\pi$
$84$	−5.97597e7	−0.130964
$85$	0	0
$86$	−2.80342e8	−0.552643
$87$	6.93730e8i	1.29824i
$88$	− 3.56212e8i	− 0.633193i
$89$	−3.37680e8	−0.570493	−0.285246	−	0.958454i	$-0.592075\pi$
$89$	−3.37680e8	−0.570493	−0.285246	+	0.958454i	$0.592075\pi$
$90$	0	0
$91$	−3.31695e8	−0.507052
$92$	− 3.17465e7i	− 0.0462010i
$93$	− 1.10808e8i	− 0.153603i
$94$	−4.51773e8	−0.596822
$95$	0	0
$96$	−5.25827e8	−0.631862
$97$	7.36733e8i	0.844962i	0.906372	+	0.422481i	$0.138841\pi$
$97$	7.36733e8i	0.844962i	−0.906372	+	0.422481i	$0.861159\pi$
$98$	− 9.73816e7i	− 0.106650i
$99$	−2.17631e8	−0.227699
$100$	0	0
$101$	1.97428e8	0.188783	0.0943914	−	0.995535i	$-0.469909\pi$
$101$	1.97428e8	0.188783	0.0943914	+	0.995535i	$0.469909\pi$
$102$	− 1.87381e8i	− 0.171405i
$103$	− 1.27449e9i	− 1.11576i	−0.829922	−	0.557879i	$-0.811615\pi$
$103$	− 1.27449e9i	− 1.11576i	0.829922	−	0.557879i	$-0.188385\pi$
$104$	−1.72375e9	−1.44486
$105$	0	0
$106$	−6.33451e8	−0.487345
$107$	− 1.81937e9i	− 1.34182i	−0.741541	−	0.670908i	$-0.765905\pi$
$107$	− 1.81937e9i	− 1.34182i	0.741541	−	0.670908i	$-0.234095\pi$
$108$	6.79639e8i	0.480697i
$109$	2.31425e8	0.157033	0.0785167	−	0.996913i	$-0.474982\pi$
$109$	2.31425e8	0.157033	0.0785167	+	0.996913i	$0.474982\pi$
$110$	0	0
$111$	1.30909e9	0.818494
$112$	− 2.27455e8i	− 0.136589i
$113$	− 1.51983e9i	− 0.876885i	−0.898759	−	0.438443i	$-0.855530\pi$
$113$	− 1.51983e9i	− 0.876885i	0.898759	−	0.438443i	$-0.144470\pi$
$114$	−9.06998e8	−0.502961
$115$	0	0
$116$	1.43175e9	0.734188
$117$	1.05314e9i	0.519578i
$118$	− 3.07286e8i	− 0.145906i
$119$	−2.42525e8	−0.110865
$120$	0	0
$121$	−1.54294e9	−0.654359
$122$	− 4.22498e8i	− 0.172666i
$123$	− 2.36223e9i	− 0.930569i
$124$	−2.28691e8	−0.0868665
$125$	0	0
$126$	−3.09190e8	−0.109284
$127$	− 4.20951e9i	− 1.43587i	−0.696111	−	0.717934i	$-0.745088\pi$
$127$	− 4.20951e9i	− 1.43587i	0.696111	−	0.717934i	$-0.254912\pi$
$128$	2.65883e8i	0.0875478i
$129$	−1.82249e9	−0.579443
$130$	0	0
$131$	−4.12131e9	−1.22268	−0.611342	−	0.791367i	$-0.709370\pi$
$131$	−4.12131e9	−1.22268	−0.611342	+	0.791367i	$0.709370\pi$
$132$	− 7.10552e8i	− 0.203710i
$133$	1.17392e9i	0.325315i
$134$	−3.69221e9	−0.989271
$135$	0	0
$136$	−1.26035e9	−0.315913
$137$	1.27942e9i	0.310292i	0.987892	+	0.155146i	$0.0495848\pi$
$137$	1.27942e9i	0.310292i	−0.987892	+	0.155146i	$0.950415\pi$
$138$	2.59843e8i	0.0609895i
$139$	4.02340e9	0.914170	0.457085	−	0.889423i	$-0.348893\pi$
$139$	4.02340e9	0.914170	0.457085	+	0.889423i	$0.348893\pi$
$140$	0	0
$141$	−2.93695e9	−0.625764
$142$	5.28206e9i	1.09020i
$143$	− 3.94391e9i	− 0.788705i
$144$	−7.22177e8	−0.139963
$145$	0	0
$146$	4.88256e9	0.889323
$147$	− 6.33072e8i	− 0.111822i
$148$	− 2.70176e9i	− 0.462880i
$149$	7.67785e8	0.127615	0.0638075	−	0.997962i	$-0.479676\pi$
$149$	7.67785e8	0.127615	0.0638075	+	0.997962i	$0.479676\pi$
$150$	0	0
$151$	−9.84752e9	−1.54145	−0.770727	−	0.637165i	$-0.780107\pi$
$151$	−9.84752e9	−1.54145	−0.770727	+	0.637165i	$0.780107\pi$
$152$	6.10061e9i	0.926995i
$153$	7.70023e8i	0.113604i
$154$	1.15788e9	0.165890
$155$	0	0
$156$	−3.43845e9	−0.464839
$157$	− 8.04096e9i	− 1.05623i	−0.849172	−	0.528116i	$-0.822898\pi$
$157$	− 8.04096e9i	− 1.05623i	0.849172	−	0.528116i	$-0.177102\pi$
$158$	− 7.91723e9i	− 1.01069i
$159$	−4.11803e9	−0.510979
$160$	0	0
$161$	3.36311e8	0.0394480
$162$	− 3.02811e9i	− 0.345425i
$163$	− 9.07348e9i	− 1.00677i	−0.864063	−	0.503384i	$-0.832088\pi$
$163$	− 9.07348e9i	− 1.00677i	0.864063	−	0.503384i	$-0.167912\pi$
$164$	−4.87527e9	−0.526262
$165$	0	0
$166$	1.30985e9	0.133886
$167$	8.83471e9i	0.878958i	0.898253	+	0.439479i	$0.144837\pi$
$167$	8.83471e9i	0.878958i	−0.898253	+	0.439479i	$0.855163\pi$
$168$	− 3.28995e9i	− 0.318638i
$169$	−8.48058e9	−0.799715
$170$	0	0
$171$	3.72722e9	0.333352
$172$	3.76134e9i	0.327691i
$173$	7.89871e9i	0.670423i	0.942143	+	0.335211i	$0.108808\pi$
$173$	7.89871e9i	0.670423i	−0.942143	+	0.335211i	$0.891192\pi$
$174$	−1.17188e10	−0.969196
$175$	0	0
$176$	2.70448e9	0.212460
$177$	− 1.99765e9i	− 0.152982i
$178$	− 5.70424e9i	− 0.425900i
$179$	−4.59871e9	−0.334810	−0.167405	−	0.985888i	$-0.553539\pi$
$179$	−4.59871e9	−0.334810	−0.167405	+	0.985888i	$0.553539\pi$
$180$	0	0
$181$	−6.70993e8	−0.0464691	−0.0232346	−	0.999730i	$-0.507396\pi$
$181$	−6.70993e8	−0.0464691	−0.0232346	+	0.999730i	$0.507396\pi$
$182$	− 5.60314e9i	− 0.378539i
$183$	− 2.74664e9i	− 0.181039i
$184$	1.74774e9	0.112408
$185$	0	0
$186$	1.87182e9	0.114672
$187$	− 2.88366e9i	− 0.172447i
$188$	6.06142e9i	0.353887i
$189$	−7.19985e9	−0.410436
$190$	0	0
$191$	1.00686e10	0.547416	0.273708	−	0.961813i	$-0.411750\pi$
$191$	1.00686e10	0.547416	0.273708	+	0.961813i	$0.411750\pi$
$192$	− 1.42090e10i	− 0.754585i
$193$	− 1.97876e10i	− 1.02656i	−0.858221	−	0.513281i	$-0.828430\pi$
$193$	− 1.97876e10i	− 1.02656i	0.858221	−	0.513281i	$-0.171570\pi$
$194$	−1.24452e10	−0.630805
$195$	0	0
$196$	−1.30657e9	−0.0632381
$197$	1.07508e10i	0.508560i	0.967131	+	0.254280i	$0.0818385\pi$
$197$	1.07508e10i	0.508560i	−0.967131	+	0.254280i	$0.918161\pi$
$198$	− 3.67631e9i	− 0.169988i
$199$	1.58060e9	0.0714468	0.0357234	−	0.999362i	$-0.488626\pi$
$199$	1.58060e9	0.0714468	0.0357234	+	0.999362i	$0.488626\pi$
$200$	0	0
$201$	−2.40029e10	−1.03724
$202$	3.33504e9i	0.140935i
$203$	1.51675e10i	0.626876i
$204$	−2.51408e9	−0.101635
$205$	0	0
$206$	2.15293e10	0.832967
$207$	− 1.06780e9i	− 0.0404225i
$208$	− 1.30873e10i	− 0.484803i
$209$	−1.39580e10	−0.506019
$210$	0	0
$211$	4.44247e10	1.54295	0.771477	−	0.636257i	$-0.219518\pi$
$211$	4.44247e10	1.54295	0.771477	+	0.636257i	$0.219518\pi$
$212$	8.49899e9i	0.288972i
$213$	3.43384e10i	1.14307i
$214$	3.07335e10	1.00173
$215$	0	0
$216$	−3.74162e10	−1.16955
$217$	− 2.42267e9i	− 0.0741697i
$218$	3.90934e9i	0.117233i
$219$	3.17412e10	0.932450
$220$	0	0
$221$	−1.39544e10	−0.393501
$222$	2.21137e10i	0.611045i
$223$	2.40745e10i	0.651907i	0.945386	+	0.325954i	$0.105685\pi$
$223$	2.40745e10i	0.651907i	−0.945386	+	0.325954i	$0.894315\pi$
$224$	−1.14965e10	−0.305105
$225$	0	0
$226$	2.56737e10	0.654636
$227$	1.71588e8i	0.00428915i	0.999998	+	0.00214458i	$0.000682640\pi$
$227$	1.71588e8i	0.00428915i	−0.999998	+	0.00214458i	$0.999317\pi$
$228$	1.21692e10i	0.298232i
$229$	1.11777e10	0.268592	0.134296	−	0.990941i	$-0.457123\pi$
$229$	1.11777e10	0.268592	0.134296	+	0.990941i	$0.457123\pi$
$230$	0	0
$231$	7.52733e9	0.173935
$232$	7.88225e10i	1.78630i
$233$	6.54487e9i	0.145479i	0.997351	+	0.0727393i	$0.0231741\pi$
$233$	6.54487e9i	0.145479i	−0.997351	+	0.0727393i	$0.976826\pi$
$234$	−1.77902e10	−0.387890
$235$	0	0
$236$	−4.12285e9	−0.0865154
$237$	− 5.14695e10i	− 1.05970i
$238$	− 4.09683e9i	− 0.0827660i
$239$	9.08610e9	0.180130	0.0900651	−	0.995936i	$-0.471292\pi$
$239$	9.08610e9	0.180130	0.0900651	+	0.995936i	$0.471292\pi$
$240$	0	0
$241$	−5.36400e10	−1.02426	−0.512132	−	0.858906i	$-0.671144\pi$
$241$	−5.36400e10	−1.02426	−0.512132	+	0.858906i	$0.671144\pi$
$242$	− 2.60641e10i	− 0.488510i
$243$	3.93376e10i	0.723735i
$244$	−5.66865e9	−0.102382
$245$	0	0
$246$	3.99038e10	0.694714
$247$	6.75448e10i	1.15466i
$248$	− 1.25902e10i	− 0.211348i
$249$	8.51528e9	0.140379
$250$	0	0
$251$	3.92651e10	0.624418	0.312209	−	0.950013i	$-0.398931\pi$
$251$	3.92651e10	0.624418	0.312209	+	0.950013i	$0.398931\pi$
$252$	4.14839e9i	0.0648003i
$253$	3.99880e9i	0.0613602i
$254$	7.11089e10	1.07194
$255$	0	0
$256$	−7.07381e10	−1.02938
$257$	7.70786e9i	0.110213i	0.998480	+	0.0551067i	$0.0175499\pi$
$257$	7.70786e9i	0.110213i	−0.998480	+	0.0551067i	$0.982450\pi$
$258$	− 3.07863e10i	− 0.432582i
$259$	2.86215e10	0.395224
$260$	0	0
$261$	4.81573e10	0.642362
$262$	− 6.96189e10i	− 0.912791i
$263$	3.65878e10i	0.471559i	0.971807	+	0.235779i	$0.0757643\pi$
$263$	3.65878e10i	0.471559i	−0.971807	+	0.235779i	$0.924236\pi$
$264$	3.91181e10	0.495632
$265$	0	0
$266$	−1.98303e10	−0.242863
$267$	− 3.70830e10i	− 0.446554i
$268$	4.95383e10i	0.586590i
$269$	1.65478e11	1.92688	0.963442	−	0.267916i	$-0.0863349\pi$
$269$	1.65478e11	1.92688	0.963442	+	0.267916i	$0.0863349\pi$
$270$	0	0
$271$	5.47248e10	0.616343	0.308171	−	0.951331i	$-0.400283\pi$
$271$	5.47248e10	0.616343	0.308171	+	0.951331i	$0.400283\pi$
$272$	− 9.56901e9i	− 0.106000i
$273$	− 3.64257e10i	− 0.396896i
$274$	−2.16125e10	−0.231648
$275$	0	0
$276$	3.48631e9	0.0361638
$277$	2.55019e10i	0.260264i	0.991497	+	0.130132i	$0.0415401\pi$
$277$	2.55019e10i	0.260264i	−0.991497	+	0.130132i	$0.958460\pi$
$278$	6.79651e10i	0.682472i
$279$	−7.69207e9	−0.0760019
$280$	0	0
$281$	−2.44664e10	−0.234095	−0.117047	−	0.993126i	$-0.537343\pi$
$281$	−2.44664e10	−0.234095	−0.117047	+	0.993126i	$0.537343\pi$
$282$	− 4.96123e10i	− 0.467163i
$283$	1.83938e11i	1.70464i	0.523024	+	0.852318i	$0.324804\pi$
$283$	1.83938e11i	1.70464i	−0.523024	+	0.852318i	$0.675196\pi$
$284$	7.08693e10	0.646436
$285$	0	0
$286$	6.66222e10	0.588806
$287$	− 5.16469e10i	− 0.449341i
$288$	3.65018e10i	0.312642i
$289$	1.08385e11	0.913963
$290$	0	0
$291$	−8.09057e10	−0.661395
$292$	− 6.55091e10i	− 0.527325i
$293$	1.39840e11i	1.10848i	0.832356	+	0.554241i	$0.186991\pi$
$293$	1.39840e11i	1.10848i	−0.832356	+	0.554241i	$0.813009\pi$
$294$	1.06941e10	0.0834801
$295$	0	0
$296$	1.48740e11	1.12620
$297$	− 8.56073e10i	− 0.638421i
$298$	1.29698e10i	0.0952706i
$299$	1.93507e10	0.140015
$300$	0	0
$301$	−3.98463e10	−0.279794
$302$	− 1.66349e11i	− 1.15077i
$303$	2.16809e10i	0.147770i
$304$	−4.63179e10	−0.311041
$305$	0	0
$306$	−1.30076e10	−0.0848106
$307$	1.22633e11i	0.787922i	0.919127	+	0.393961i	$0.128895\pi$
$307$	1.22633e11i	0.787922i	−0.919127	+	0.393961i	$0.871105\pi$
$308$	− 1.55353e10i	− 0.0983650i
$309$	1.39961e11	0.873361
$310$	0	0
$311$	−1.44117e11	−0.873564	−0.436782	−	0.899567i	$-0.643882\pi$
$311$	−1.44117e11	−0.873564	−0.436782	+	0.899567i	$0.643882\pi$
$312$	− 1.89297e11i	− 1.13096i
$313$	− 2.74753e11i	− 1.61805i	−0.587771	−	0.809027i	$-0.699994\pi$
$313$	− 2.74753e11i	− 1.61805i	0.587771	−	0.809027i	$-0.300006\pi$
$314$	1.35832e11	0.788528
$315$	0	0
$316$	−1.06225e11	−0.599288
$317$	1.23139e11i	0.684904i	0.939535	+	0.342452i	$0.111257\pi$
$317$	1.23139e11i	0.684904i	−0.939535	+	0.342452i	$0.888743\pi$
$318$	− 6.95636e10i	− 0.381470i
$319$	−1.80344e11	−0.975087
$320$	0	0
$321$	1.99797e11	1.05031
$322$	5.68112e9i	0.0294498i
$323$	4.93865e10i	0.252463i
$324$	−4.06280e10	−0.204820
$325$	0	0
$326$	1.53273e11	0.751601
$327$	2.54144e10i	0.122918i
$328$	− 2.68399e11i	− 1.28041i
$329$	−6.42126e10	−0.302161
$330$	0	0
$331$	3.37245e11	1.54426	0.772129	−	0.635466i	$-0.219192\pi$
$331$	3.37245e11	1.54426	0.772129	+	0.635466i	$0.219192\pi$
$332$	− 1.75742e10i	− 0.0793881i
$333$	− 9.08741e10i	− 0.404987i
$334$	−1.49240e11	−0.656184
$335$	0	0
$336$	2.49784e10	0.106915
$337$	2.84144e11i	1.20006i	0.799976	+	0.600032i	$0.204846\pi$
$337$	2.84144e11i	1.20006i	−0.799976	+	0.600032i	$0.795154\pi$
$338$	− 1.43258e11i	− 0.597025i
$339$	1.66903e11	0.686382
$340$	0	0
$341$	2.88060e10	0.115369
$342$	6.29619e10i	0.248863i
$343$	− 1.38413e10i	− 0.0539949i
$344$	−2.07073e11	−0.797280
$345$	0	0
$346$	−1.33429e11	−0.500503
$347$	− 1.38776e11i	− 0.513846i	−0.966432	−	0.256923i	$-0.917291\pi$
$347$	− 1.38776e11i	− 0.513846i	0.966432	−	0.256923i	$-0.0827087\pi$
$348$	1.57231e11i	0.574686i
$349$	1.52561e11	0.550463	0.275231	−	0.961378i	$-0.411246\pi$
$349$	1.52561e11	0.550463	0.275231	+	0.961378i	$0.411246\pi$
$350$	0	0
$351$	−4.14265e11	−1.45679
$352$	− 1.36695e11i	− 0.474582i
$353$	1.24628e11i	0.427199i	0.976921	+	0.213599i	$0.0685188\pi$
$353$	1.24628e11i	0.427199i	−0.976921	+	0.213599i	$0.931481\pi$
$354$	3.37452e10	0.114208
$355$	0	0
$356$	−7.65336e10	−0.252538
$357$	− 2.66333e10i	− 0.0867797i
$358$	− 7.76835e10i	− 0.249951i
$359$	7.69379e10	0.244464	0.122232	−	0.992502i	$-0.460995\pi$
$359$	7.69379e10	0.244464	0.122232	+	0.992502i	$0.460995\pi$
$360$	0	0
$361$	−8.36371e10	−0.259189
$362$	− 1.13347e10i	− 0.0346914i
$363$	− 1.69441e11i	− 0.512200i
$364$	−7.51772e10	−0.224455
$365$	0	0
$366$	4.63975e10	0.135154
$367$	4.36607e11i	1.25630i	0.778092	+	0.628150i	$0.216187\pi$
$367$	4.36607e11i	1.25630i	−0.778092	+	0.628150i	$0.783813\pi$
$368$	1.32695e10i	0.0377171i
$369$	−1.63981e11	−0.460441
$370$	0	0
$371$	−9.00353e10	−0.246735
$372$	− 2.51142e10i	− 0.0679948i
$373$	1.66545e11i	0.445495i	0.974876	+	0.222747i	$0.0715025\pi$
$373$	1.66545e11i	0.445495i	−0.974876	+	0.222747i	$0.928497\pi$
$374$	4.87120e10	0.128740
$375$	0	0
$376$	−3.33700e11	−0.861015
$377$	8.72707e11i	2.22501i
$378$	− 1.21623e11i	− 0.306410i
$379$	−4.10213e11	−1.02125	−0.510627	−	0.859803i	$-0.670587\pi$
$379$	−4.10213e11	−1.02125	−0.510627	+	0.859803i	$0.670587\pi$
$380$	0	0
$381$	4.62275e11	1.12393
$382$	1.70083e11i	0.408672i
$383$	7.01166e11i	1.66505i	0.553990	+	0.832523i	$0.313105\pi$
$383$	7.01166e11i	1.66505i	−0.553990	+	0.832523i	$0.686895\pi$
$384$	−2.91984e10	−0.0685281
$385$	0	0
$386$	3.34261e11	0.766377
$387$	1.26513e11i	0.286706i
$388$	1.66977e11i	0.374037i
$389$	−8.46752e11	−1.87492	−0.937461	−	0.348090i	$-0.886830\pi$
$389$	−8.46752e11	−1.87492	−0.937461	+	0.348090i	$0.886830\pi$
$390$	0	0
$391$	1.41486e10	0.0306138
$392$	− 7.19304e10i	− 0.153860i
$393$	− 4.52589e11i	− 0.957056i
$394$	−1.81607e11	−0.379665
$395$	0	0
$396$	−4.93250e10	−0.100795
$397$	− 8.75287e11i	− 1.76845i	−0.467059	−	0.884226i	$-0.654687\pi$
$397$	− 8.75287e11i	− 1.76845i	0.467059	−	0.884226i	$-0.345313\pi$
$398$	2.67002e10i	0.0533385i
$399$	−1.28916e11	−0.254641
$400$	0	0
$401$	−2.47491e11	−0.477980	−0.238990	−	0.971022i	$-0.576816\pi$
$401$	−2.47491e11	−0.477980	−0.238990	+	0.971022i	$0.576816\pi$
$402$	− 4.05468e11i	− 0.774353i
$403$	− 1.39396e11i	− 0.263255i
$404$	4.47461e10	0.0835679
$405$	0	0
$406$	−2.56216e11	−0.467993
$407$	3.40314e11i	0.614759i
$408$	− 1.38408e11i	− 0.247281i
$409$	9.48426e10	0.167590	0.0837951	−	0.996483i	$-0.473296\pi$
$409$	9.48426e10	0.167590	0.0837951	+	0.996483i	$0.473296\pi$
$410$	0	0
$411$	−1.40502e11	−0.242881
$412$	− 2.88858e11i	− 0.493909i
$413$	− 4.36760e10i	− 0.0738699i
$414$	1.80377e10	0.0301773
$415$	0	0
$416$	−6.61486e11	−1.08293
$417$	4.41838e11i	0.715567i
$418$	− 2.35786e11i	− 0.377767i
$419$	−9.93237e11	−1.57431	−0.787154	−	0.616756i	$-0.788446\pi$
$419$	−9.93237e11	−1.57431	−0.787154	+	0.616756i	$0.788446\pi$
$420$	0	0
$421$	3.88328e11	0.602461	0.301230	−	0.953551i	$-0.402603\pi$
$421$	3.88328e11	0.602461	0.301230	+	0.953551i	$0.402603\pi$
$422$	7.50441e11i	1.15189i
$423$	2.03877e11i	0.309625i
$424$	−4.67896e11	−0.703077
$425$	0	0
$426$	−5.80060e11	−0.853355
$427$	− 6.00516e10i	− 0.0874177i
$428$	− 4.12351e11i	− 0.593977i
$429$	4.33108e11	0.617359
$430$	0	0
$431$	2.08495e11	0.291036	0.145518	−	0.989356i	$-0.453515\pi$
$431$	2.08495e11	0.291036	0.145518	+	0.989356i	$0.453515\pi$
$432$	− 2.84076e11i	− 0.392426i
$433$	− 3.43270e11i	− 0.469289i	−0.972081	−	0.234645i	$-0.924607\pi$
$433$	− 3.43270e11i	− 0.469289i	0.972081	−	0.234645i	$-0.0753926\pi$
$434$	4.09249e10	0.0553712
$435$	0	0
$436$	5.24515e10	0.0695134
$437$	− 6.84848e10i	− 0.0898314i
$438$	5.36187e11i	0.696118i
$439$	−5.98857e11	−0.769543	−0.384771	−	0.923012i	$-0.625720\pi$
$439$	−5.98857e11	−0.769543	−0.384771	+	0.923012i	$0.625720\pi$
$440$	0	0
$441$	−4.39465e10	−0.0553288
$442$	− 2.35724e11i	− 0.293767i
$443$	− 3.05169e11i	− 0.376464i	−0.982125	−	0.188232i	$-0.939724\pi$
$443$	− 3.05169e11i	− 0.376464i	0.982125	−	0.188232i	$-0.0602757\pi$
$444$	2.96699e11	0.362320
$445$	0	0
$446$	−4.06678e11	−0.486680
$447$	8.43158e10i	0.0998907i
$448$	− 3.10661e11i	− 0.364364i
$449$	−2.40802e11	−0.279610	−0.139805	−	0.990179i	$-0.544648\pi$
$449$	−2.40802e11	−0.279610	−0.139805	+	0.990179i	$0.544648\pi$
$450$	0	0
$451$	6.14090e11	0.698936
$452$	− 3.44463e11i	− 0.388168i
$453$	− 1.08142e12i	− 1.20657i
$454$	−2.89855e9	−0.00320206
$455$	0	0
$456$	−6.69950e11	−0.725606
$457$	− 2.36226e11i	− 0.253341i	−0.991945	−	0.126671i	$-0.959571\pi$
$457$	− 2.36226e11i	− 0.253341i	0.991945	−	0.126671i	$-0.0404291\pi$
$458$	1.88819e11i	0.200517i
$459$	−3.02897e11	−0.318521
$460$	0	0
$461$	−1.17120e12	−1.20775	−0.603873	−	0.797081i	$-0.706376\pi$
$461$	−1.17120e12	−1.20775	−0.603873	+	0.797081i	$0.706376\pi$
$462$	1.27155e11i	0.129851i
$463$	− 1.78934e12i	− 1.80958i	−0.425856	−	0.904791i	$-0.640027\pi$
$463$	− 1.78934e12i	− 1.80958i	0.425856	−	0.904791i	$-0.359973\pi$
$464$	−5.98446e11	−0.599369
$465$	0	0
$466$	−1.10559e11	−0.108607
$467$	3.81202e11i	0.370877i	0.982656	+	0.185438i	$0.0593705\pi$
$467$	3.81202e11i	0.370877i	−0.982656	+	0.185438i	$0.940630\pi$
$468$	2.38690e11i	0.230000i
$469$	−5.24791e11	−0.500851
$470$	0	0
$471$	8.83034e11	0.826767
$472$	− 2.26975e11i	− 0.210494i
$473$	− 4.73778e11i	− 0.435211i
$474$	8.69446e11	0.791115
$475$	0	0
$476$	−5.49671e10	−0.0490762
$477$	2.85865e11i	0.252830i
$478$	1.53486e11i	0.134476i
$479$	1.71146e12	1.48545	0.742725	−	0.669597i	$-0.233533\pi$
$479$	1.71146e12	1.48545	0.742725	+	0.669597i	$0.233533\pi$
$480$	0	0
$481$	1.64682e12	1.40279
$482$	− 9.06111e11i	− 0.764663i
$483$	3.69327e10i	0.0308780i
$484$	−3.49701e11	−0.289663
$485$	0	0
$486$	−6.64508e11	−0.540303
$487$	− 7.38713e11i	− 0.595108i	−0.954705	−	0.297554i	$-0.903829\pi$
$487$	− 7.38713e11i	− 0.595108i	0.954705	−	0.297554i	$-0.0961708\pi$
$488$	− 3.12076e11i	− 0.249099i
$489$	9.96422e11	0.788049
$490$	0	0
$491$	1.52117e12	1.18116	0.590582	−	0.806978i	$-0.298898\pi$
$491$	1.52117e12	1.18116	0.590582	+	0.806978i	$0.298898\pi$
$492$	− 5.35387e11i	− 0.411932i
$493$	6.38095e11i	0.486490i
$494$	−1.14100e12	−0.862012
$495$	0	0
$496$	9.55887e10	0.0709151
$497$	7.50764e11i	0.551950i
$498$	1.43844e11i	0.104800i
$499$	1.67720e12	1.21097	0.605484	−	0.795857i	$-0.292979\pi$
$499$	1.67720e12	1.21097	0.605484	+	0.795857i	$0.292979\pi$
$500$	0	0
$501$	−9.70200e11	−0.688005
$502$	6.63284e11i	0.466158i
$503$	2.93328e11i	0.204314i	0.994768	+	0.102157i	$0.0325744\pi$
$503$	2.93328e11i	0.204314i	−0.994768	+	0.102157i	$0.967426\pi$
$504$	−2.28381e11	−0.157661
$505$	0	0
$506$	−6.75494e10	−0.0458083
$507$	− 9.31311e11i	− 0.625977i
$508$	− 9.54065e11i	− 0.635611i
$509$	2.87498e12	1.89848	0.949238	−	0.314559i	$-0.101857\pi$
$509$	2.87498e12	1.89848	0.949238	+	0.314559i	$0.101857\pi$
$510$	0	0
$511$	6.93980e11	0.450249
$512$	− 1.05881e12i	− 0.680930i
$513$	1.46614e12i	0.934648i
$514$	−1.30205e11	−0.0822796
$515$	0	0
$516$	−4.13058e11	−0.256500
$517$	− 7.63497e11i	− 0.470002i
$518$	4.83487e11i	0.295053i
$519$	−8.67412e11	−0.524774
$520$	0	0
$521$	1.69333e12	1.00687	0.503434	−	0.864034i	$-0.332070\pi$
$521$	1.69333e12	1.00687	0.503434	+	0.864034i	$0.332070\pi$
$522$	8.13494e11i	0.479554i
$523$	9.48465e11i	0.554324i	0.960823	+	0.277162i	$0.0893939\pi$
$523$	9.48465e11i	0.554324i	−0.960823	+	0.277162i	$0.910606\pi$
$524$	−9.34075e11	−0.541241
$525$	0	0
$526$	−6.18058e11	−0.352041
$527$	− 1.01922e11i	− 0.0575597i
$528$	2.96997e11i	0.166303i
$529$	1.78153e12	0.989107
$530$	0	0
$531$	−1.38673e11	−0.0756947
$532$	2.66063e11i	0.144006i
$533$	− 2.97166e12i	− 1.59488i
$534$	6.26422e11	0.333374
$535$	0	0
$536$	−2.72724e12	−1.42719
$537$	− 5.05017e11i	− 0.262072i
$538$	2.79533e12i	1.43851i
$539$	1.64575e11	0.0839875
$540$	0	0
$541$	2.60488e12	1.30738	0.653688	−	0.756764i	$-0.273221\pi$
$541$	2.60488e12	1.30738	0.653688	+	0.756764i	$0.273221\pi$
$542$	9.24436e11i	0.460129i
$543$	− 7.36864e10i	− 0.0363738i
$544$	−4.83657e11	−0.236778
$545$	0	0
$546$	6.15320e11	0.296301
$547$	− 2.01576e12i	− 0.962711i	−0.876525	−	0.481356i	$-0.840145\pi$
$547$	− 2.01576e12i	− 0.962711i	0.876525	−	0.481356i	$-0.159855\pi$
$548$	2.89974e11i	0.137356i
$549$	−1.90666e11	−0.0895772
$550$	0	0
$551$	3.08863e12	1.42753
$552$	1.91932e11i	0.0879875i
$553$	− 1.12531e12i	− 0.511693i
$554$	−4.30790e11	−0.194300
$555$	0	0
$556$	9.11886e11	0.404673
$557$	3.04194e12i	1.33907i	0.742782	+	0.669534i	$0.233506\pi$
$557$	3.04194e12i	1.33907i	−0.742782	+	0.669534i	$0.766494\pi$
$558$	− 1.29938e11i	− 0.0567390i
$559$	−2.29267e12	−0.993091
$560$	0	0
$561$	3.16674e11	0.134983
$562$	− 4.13297e11i	− 0.174763i
$563$	4.23912e12i	1.77823i	0.457684	+	0.889115i	$0.348679\pi$
$563$	4.23912e12i	1.77823i	−0.457684	+	0.889115i	$0.651321\pi$
$564$	−6.65647e11	−0.277005
$565$	0	0
$566$	−3.10716e12	−1.27259
$567$	− 4.30399e11i	− 0.174883i
$568$	3.90157e12i	1.57280i
$569$	−1.34119e11	−0.0536397	−0.0268199	−	0.999640i	$-0.508538\pi$
$569$	−1.34119e11	−0.0536397	−0.0268199	+	0.999640i	$0.508538\pi$
$570$	0	0
$571$	−1.51210e11	−0.0595277	−0.0297638	−	0.999557i	$-0.509476\pi$
$571$	−1.51210e11	−0.0595277	−0.0297638	+	0.999557i	$0.509476\pi$
$572$	− 8.93868e11i	− 0.349133i
$573$	1.10570e12i	0.428491i
$574$	8.72443e11	0.335454
$575$	0	0
$576$	−9.86359e11	−0.373365
$577$	1.84681e12i	0.693633i	0.937933	+	0.346817i	$0.112737\pi$
$577$	1.84681e12i	0.693633i	−0.937933	+	0.346817i	$0.887263\pi$
$578$	1.83089e12i	0.682317i
$579$	2.17301e12	0.803541
$580$	0	0
$581$	1.86175e11	0.0677843
$582$	− 1.36670e12i	− 0.493763i
$583$	− 1.07053e12i	− 0.383788i
$584$	3.60648e12	1.28300
$585$	0	0
$586$	−2.36225e12	−0.827535
$587$	2.97730e12i	1.03503i	0.855675	+	0.517513i	$0.173142\pi$
$587$	2.97730e12i	1.03503i	−0.855675	+	0.517513i	$0.826858\pi$
$588$	− 1.43483e11i	− 0.0494997i
$589$	−4.93342e11	−0.168900
$590$	0	0
$591$	−1.18062e12	−0.398076
$592$	1.12928e12i	0.377881i
$593$	1.06093e12i	0.352322i	0.984361	+	0.176161i	$0.0563679\pi$
$593$	1.06093e12i	0.352322i	−0.984361	+	0.176161i	$0.943632\pi$
$594$	1.44612e12	0.476611
$595$	0	0
$596$	1.74015e11	0.0564909
$597$	1.73576e11i	0.0559250i
$598$	3.26880e11i	0.104528i
$599$	4.53108e12	1.43807	0.719037	−	0.694972i	$-0.244583\pi$
$599$	4.53108e12	1.43807	0.719037	+	0.694972i	$0.244583\pi$
$600$	0	0
$601$	−1.05588e12	−0.330127	−0.165063	−	0.986283i	$-0.552783\pi$
$601$	−1.05588e12	−0.330127	−0.165063	+	0.986283i	$0.552783\pi$
$602$	− 6.73101e11i	− 0.208880i
$603$	1.66623e12i	0.513224i
$604$	−2.23190e12	−0.682351
$605$	0	0
$606$	−3.66244e11	−0.110317
$607$	3.25042e12i	0.971831i	0.874006	+	0.485916i	$0.161514\pi$
$607$	3.25042e12i	0.971831i	−0.874006	+	0.485916i	$0.838486\pi$
$608$	2.34109e12i	0.694788i
$609$	−1.66565e12	−0.490688
$610$	0	0
$611$	−3.69466e12	−1.07248
$612$	1.74522e11i	0.0502886i
$613$	− 2.48670e12i	− 0.711299i	−0.934619	−	0.355649i	$-0.884260\pi$
$613$	− 2.48670e12i	− 0.711299i	0.934619	−	0.355649i	$-0.115740\pi$
$614$	−2.07156e12	−0.588221
$615$	0	0
$616$	8.55264e11	0.239325
$617$	4.06622e12i	1.12956i	0.825243	+	0.564778i	$0.191038\pi$
$617$	4.06622e12i	1.12956i	−0.825243	+	0.564778i	$0.808962\pi$
$618$	2.36428e12i	0.652006i
$619$	4.24730e12	1.16280	0.581400	−	0.813618i	$-0.302505\pi$
$619$	4.24730e12	1.16280	0.581400	+	0.813618i	$0.302505\pi$
$620$	0	0
$621$	4.20030e11	0.113336
$622$	− 2.43450e12i	− 0.652157i
$623$	− 8.10769e11i	− 0.215626i
$624$	1.43721e12	0.379480
$625$	0	0
$626$	4.64125e12	1.20796
$627$	− 1.53283e12i	− 0.396086i
$628$	− 1.82245e12i	− 0.467559i
$629$	1.20410e12	0.306715
$630$	0	0
$631$	1.44130e12	0.361929	0.180965	−	0.983490i	$-0.442078\pi$
$631$	1.44130e12	0.361929	0.180965	+	0.983490i	$0.442078\pi$
$632$	− 5.84803e12i	− 1.45808i
$633$	4.87858e12i	1.20775i
$634$	−2.08012e12	−0.511314
$635$	0	0
$636$	−9.33333e11	−0.226193
$637$	− 7.96400e11i	− 0.191648i
$638$	− 3.04645e12i	− 0.727949i
$639$	2.38370e12	0.565585
$640$	0	0
$641$	6.00980e12	1.40604	0.703022	−	0.711168i	$-0.251833\pi$
$641$	6.00980e12	1.40604	0.703022	+	0.711168i	$0.251833\pi$
$642$	3.37506e12i	0.784105i
$643$	2.09069e12i	0.482327i	0.970485	+	0.241163i	$0.0775290\pi$
$643$	2.09069e12i	0.482327i	−0.970485	+	0.241163i	$0.922471\pi$
$644$	7.62234e10	0.0174623
$645$	0	0
$646$	−8.34259e11	−0.188475
$647$	1.34894e12i	0.302638i	0.988485	+	0.151319i	$0.0483520\pi$
$647$	1.34894e12i	0.302638i	−0.988485	+	0.151319i	$0.951648\pi$
$648$	− 2.23670e12i	− 0.498333i
$649$	5.19314e11	0.114902
$650$	0	0
$651$	2.66051e11	0.0580563
$652$	− 2.05646e12i	− 0.445663i
$653$	− 7.38295e12i	− 1.58899i	−0.607272	−	0.794494i	$-0.707736\pi$
$653$	− 7.38295e12i	− 1.58899i	0.607272	−	0.794494i	$-0.292264\pi$
$654$	−4.29312e11	−0.0917641
$655$	0	0
$656$	2.03777e12	0.429624
$657$	− 2.20341e12i	− 0.461372i
$658$	− 1.08471e12i	− 0.225578i
$659$	−3.34345e12	−0.690574	−0.345287	−	0.938497i	$-0.612218\pi$
$659$	−3.34345e12	−0.690574	−0.345287	+	0.938497i	$0.612218\pi$
$660$	0	0
$661$	8.14808e12	1.66016	0.830078	−	0.557648i	$-0.188296\pi$
$661$	8.14808e12	1.66016	0.830078	+	0.557648i	$0.188296\pi$
$662$	5.69690e12i	1.15286i
$663$	− 1.53243e12i	− 0.308013i
$664$	9.67516e11	0.193153
$665$	0	0
$666$	1.53509e12	0.302342
$667$	− 8.84853e11i	− 0.173103i
$668$	2.00235e12i	0.389085i
$669$	−2.64379e12	−0.510281
$670$	0	0
$671$	7.14023e11	0.135976
$672$	− 1.26251e12i	− 0.238821i
$673$	− 6.60403e12i	− 1.24091i	−0.784241	−	0.620457i	$-0.786947\pi$
$673$	− 6.60403e12i	− 1.24091i	0.784241	−	0.620457i	$-0.213053\pi$
$674$	−4.79989e12	−0.895905
$675$	0	0
$676$	−1.92208e12	−0.354007
$677$	− 3.16321e12i	− 0.578735i	−0.957218	−	0.289367i	$-0.906555\pi$
$677$	− 3.16321e12i	− 0.578735i	0.957218	−	0.289367i	$-0.0934449\pi$
$678$	2.81940e12i	0.512417i
$679$	−1.76890e12	−0.319366
$680$	0	0
$681$	−1.88433e10	−0.00335734
$682$	4.86603e11i	0.0861282i
$683$	7.85876e12i	1.38185i	0.722927	+	0.690925i	$0.242796\pi$
$683$	7.85876e12i	1.38185i	−0.722927	+	0.690925i	$0.757204\pi$
$684$	8.44757e11	0.147564
$685$	0	0
$686$	2.33813e11	0.0403098
$687$	1.22750e12i	0.210241i
$688$	− 1.57217e12i	− 0.267517i
$689$	−5.18045e12	−0.875752
$690$	0	0
$691$	3.21525e12	0.536492	0.268246	−	0.963350i	$-0.413556\pi$
$691$	3.21525e12	0.536492	0.268246	+	0.963350i	$0.413556\pi$
$692$	1.79021e12i	0.296774i
$693$	− 5.22531e11i	− 0.0860622i
$694$	2.34427e12	0.383611
$695$	0	0
$696$	−8.65604e12	−1.39823
$697$	− 2.17278e12i	− 0.348713i
$698$	2.57712e12i	0.410947i
$699$	−7.18737e11	−0.113874
$700$	0	0
$701$	−6.07789e12	−0.950652	−0.475326	−	0.879810i	$-0.657670\pi$
$701$	−6.07789e12	−0.950652	−0.475326	+	0.879810i	$0.657670\pi$
$702$	− 6.99795e12i	− 1.08756i
$703$	− 5.82834e12i	− 0.900007i
$704$	3.69381e12	0.566758
$705$	0	0
$706$	−2.10528e12	−0.318924
$707$	4.74025e11i	0.0713532i
$708$	− 4.52758e11i	− 0.0677200i
$709$	6.79921e12	1.01053	0.505266	−	0.862963i	$-0.331394\pi$
$709$	6.79921e12	1.01053	0.505266	+	0.862963i	$0.331394\pi$
$710$	0	0
$711$	−3.57290e12	−0.524334
$712$	− 4.21341e12i	− 0.614432i
$713$	1.41336e11i	0.0204809i
$714$	4.49901e11	0.0647851
$715$	0	0
$716$	−1.04228e12	−0.148209
$717$	9.97807e11i	0.140997i
$718$	1.29967e12i	0.182504i
$719$	−8.63238e11	−0.120462	−0.0602311	−	0.998184i	$-0.519184\pi$
$719$	−8.63238e11	−0.120462	−0.0602311	+	0.998184i	$0.519184\pi$
$720$	0	0
$721$	3.06006e12	0.421717
$722$	− 1.41283e12i	− 0.193497i
$723$	− 5.89058e12i	− 0.801744i
$724$	−1.52078e11	−0.0205703
$725$	0	0
$726$	2.86228e12	0.382382
$727$	9.34730e12i	1.24103i	0.784195	+	0.620514i	$0.213076\pi$
$727$	9.34730e12i	1.24103i	−0.784195	+	0.620514i	$0.786924\pi$
$728$	− 4.13873e12i	− 0.546105i
$729$	−7.84827e12	−1.02920
$730$	0	0
$731$	−1.67633e12	−0.217135
$732$	− 6.22513e11i	− 0.0801399i
$733$	− 1.12045e13i	− 1.43359i	−0.697286	−	0.716793i	$-0.745609\pi$
$733$	− 1.12045e13i	− 1.43359i	0.697286	−	0.716793i	$-0.254391\pi$
$734$	−7.37536e12	−0.937887
$735$	0	0
$736$	6.70692e11	0.0842506
$737$	− 6.23985e12i	− 0.779059i
$738$	− 2.77003e12i	− 0.343741i
$739$	4.55769e12	0.562140	0.281070	−	0.959687i	$-0.409311\pi$
$739$	4.55769e12	0.562140	0.281070	+	0.959687i	$0.409311\pi$
$740$	0	0
$741$	−7.41756e12	−0.903814
$742$	− 1.52092e12i	− 0.184199i
$743$	3.57016e12i	0.429772i	0.976639	+	0.214886i	$0.0689381\pi$
$743$	3.57016e12i	0.429772i	−0.976639	+	0.214886i	$0.931062\pi$
$744$	1.38261e12	0.165433
$745$	0	0
$746$	−2.81336e12	−0.332583
$747$	− 5.91112e11i	− 0.0694588i
$748$	− 6.53567e11i	− 0.0763366i
$749$	4.36830e12	0.507159
$750$	0	0
$751$	−2.38313e12	−0.273380	−0.136690	−	0.990614i	$-0.543646\pi$
$751$	−2.38313e12	−0.273380	−0.136690	+	0.990614i	$0.543646\pi$
$752$	− 2.53356e12i	− 0.288902i
$753$	4.31198e12i	0.488764i
$754$	−1.47422e13	−1.66108
$755$	0	0
$756$	−1.63181e12	−0.181686
$757$	− 4.96674e12i	− 0.549718i	−0.961484	−	0.274859i	$-0.911369\pi$
$757$	− 4.96674e12i	− 0.549718i	0.961484	−	0.274859i	$-0.0886312\pi$
$758$	− 6.92951e12i	− 0.762414i
$759$	−4.39135e11	−0.0480298
$760$	0	0
$761$	1.01660e13	1.09880	0.549401	−	0.835559i	$-0.314856\pi$
$761$	1.01660e13	1.09880	0.549401	+	0.835559i	$0.314856\pi$
$762$	7.80896e12i	0.839065i
$763$	5.55652e11i	0.0593530i
$764$	2.28200e12	0.242323
$765$	0	0
$766$	−1.18444e13	−1.24304
$767$	− 2.51303e12i	− 0.262191i
$768$	− 7.76824e12i	− 0.805744i
$769$	4.53519e12	0.467656	0.233828	−	0.972278i	$-0.424875\pi$
$769$	4.53519e12	0.467656	0.233828	+	0.972278i	$0.424875\pi$
$770$	0	0
$771$	−8.46453e11	−0.0862697
$772$	− 4.48476e12i	− 0.454424i
$773$	− 3.64760e12i	− 0.367451i	−0.982978	−	0.183725i	$-0.941184\pi$
$773$	− 3.64760e12i	− 0.367451i	0.982978	−	0.183725i	$-0.0588157\pi$
$774$	−2.13712e12	−0.214039
$775$	0	0
$776$	−9.19261e12	−0.910041
$777$	3.14312e12i	0.309362i
$778$	− 1.43037e13i	− 1.39972i
$779$	−1.05171e13	−1.02324
$780$	0	0
$781$	−8.92670e12	−0.858542
$782$	2.39004e11i	0.0228547i
$783$	1.89432e13i	1.80105i
$784$	5.46120e11	0.0516256
$785$	0	0
$786$	7.64533e12	0.714488
$787$	2.68084e12i	0.249106i	0.992213	+	0.124553i	$0.0397498\pi$
$787$	2.68084e12i	0.249106i	−0.992213	+	0.124553i	$0.960250\pi$
$788$	2.43662e12i	0.225123i
$789$	−4.01796e12	−0.369113
$790$	0	0
$791$	3.64912e12	0.331431
$792$	− 2.71549e12i	− 0.245237i
$793$	− 3.45525e12i	− 0.310277i
$794$	1.47857e13	1.32023
$795$	0	0
$796$	3.58235e11	0.0316271
$797$	9.88359e12i	0.867665i	0.900994	+	0.433833i	$0.142839\pi$
$797$	9.88359e12i	0.867665i	−0.900994	+	0.433833i	$0.857161\pi$
$798$	− 2.17770e12i	− 0.190102i
$799$	−2.70142e12	−0.234494
$800$	0	0
$801$	−2.57422e12	−0.220953
$802$	− 4.18073e12i	− 0.356835i
$803$	8.25153e12i	0.700349i
$804$	−5.44014e12	−0.459154
$805$	0	0
$806$	2.35474e12	0.196533
$807$	1.81723e13i	1.50827i
$808$	2.46341e12i	0.203323i
$809$	−1.62405e13	−1.33300	−0.666502	−	0.745503i	$-0.732209\pi$
$809$	−1.62405e13	−1.33300	−0.666502	+	0.745503i	$0.732209\pi$
$810$	0	0
$811$	−2.28548e13	−1.85517	−0.927584	−	0.373614i	$-0.878118\pi$
$811$	−2.28548e13	−1.85517	−0.927584	+	0.373614i	$0.878118\pi$
$812$	3.43764e12i	0.277497i
$813$	6.00971e12i	0.482443i
$814$	−5.74873e12	−0.458947
$815$	0	0
$816$	1.05084e12	0.0829718
$817$	8.11410e12i	0.637149i
$818$	1.60212e12i	0.125114i
$819$	−2.52860e12	−0.196382
$820$	0	0
$821$	1.65900e13	1.27439	0.637193	−	0.770704i	$-0.280095\pi$
$821$	1.65900e13	1.27439	0.637193	+	0.770704i	$0.280095\pi$
$822$	− 2.37342e12i	− 0.181322i
$823$	9.87616e12i	0.750393i	0.926945	+	0.375197i	$0.122425\pi$
$823$	9.87616e12i	0.750393i	−0.926945	+	0.375197i	$0.877575\pi$
$824$	1.59025e13	1.20169
$825$	0	0
$826$	7.37794e11	0.0551474
$827$	3.15367e12i	0.234445i	0.993106	+	0.117223i	$0.0373991\pi$
$827$	3.15367e12i	0.234445i	−0.993106	+	0.117223i	$0.962601\pi$
$828$	− 2.42012e11i	− 0.0178937i
$829$	−2.02328e13	−1.48785	−0.743927	−	0.668261i	$-0.767039\pi$
$829$	−2.02328e13	−1.48785	−0.743927	+	0.668261i	$0.767039\pi$
$830$	0	0
$831$	−2.80054e12	−0.203722
$832$	− 1.78748e13i	− 1.29326i
$833$	− 5.82302e11i	− 0.0419030i
$834$	−7.46372e12	−0.534205
$835$	0	0
$836$	−3.16353e12	−0.223998
$837$	− 3.02576e12i	− 0.213093i
$838$	− 1.67782e13i	− 1.17530i
$839$	2.38915e13	1.66462	0.832310	−	0.554311i	$-0.187018\pi$
$839$	2.38915e13	1.66462	0.832310	+	0.554311i	$0.187018\pi$
$840$	0	0
$841$	2.53993e13	1.75081
$842$	6.55980e12i	0.449766i
$843$	− 2.68682e12i	− 0.183238i
$844$	1.00686e13	0.683015
$845$	0	0
$846$	−3.44398e12	−0.231150
$847$	− 3.70461e12i	− 0.247324i
$848$	− 3.55242e12i	− 0.235908i
$849$	−2.01995e13	−1.33431
$850$	0	0
$851$	−1.66974e12	−0.109136
$852$	7.78264e12i	0.505998i
$853$	1.68078e13i	1.08703i	0.839400	+	0.543514i	$0.182906\pi$
$853$	1.68078e13i	1.08703i	−0.839400	+	0.543514i	$0.817094\pi$
$854$	1.01442e12	0.0652615
$855$	0	0
$856$	2.27012e13	1.44516
$857$	6.68278e12i	0.423198i	0.977357	+	0.211599i	$0.0678671\pi$
$857$	6.68278e12i	0.423198i	−0.977357	+	0.211599i	$0.932133\pi$
$858$	7.31625e12i	0.460888i
$859$	−2.04541e13	−1.28177	−0.640887	−	0.767635i	$-0.721433\pi$
$859$	−2.04541e13	−1.28177	−0.640887	+	0.767635i	$0.721433\pi$
$860$	0	0
$861$	5.67170e12	0.351722
$862$	3.52198e12i	0.217272i
$863$	− 1.87505e13i	− 1.15071i	−0.817905	−	0.575353i	$-0.804865\pi$
$863$	− 1.87505e13i	− 1.15071i	0.817905	−	0.575353i	$-0.195135\pi$
$864$	−1.43584e13	−0.876583
$865$	0	0
$866$	5.79867e12	0.350347
$867$	1.19025e13i	0.715405i
$868$	− 5.49088e11i	− 0.0328324i
$869$	1.33801e13	0.795924
$870$	0	0
$871$	−3.01954e13	−1.77771
$872$	2.88762e12i	0.169128i
$873$	5.61630e12i	0.327255i
$874$	1.15688e12	0.0670634
$875$	0	0
$876$	7.19400e12	0.412764
$877$	− 2.02759e13i	− 1.15740i	−0.815542	−	0.578699i	$-0.803561\pi$
$877$	− 2.02759e13i	− 1.15740i	0.815542	−	0.578699i	$-0.196439\pi$
$878$	− 1.01162e13i	− 0.574500i
$879$	−1.53568e13	−0.867665
$880$	0	0
$881$	−2.17613e13	−1.21701	−0.608505	−	0.793550i	$-0.708230\pi$
$881$	−2.17613e13	−1.21701	−0.608505	+	0.793550i	$0.708230\pi$
$882$	− 7.42364e11i	− 0.0413056i
$883$	− 3.44540e13i	− 1.90729i	−0.300933	−	0.953645i	$-0.597298\pi$
$883$	− 3.44540e13i	− 1.90729i	0.300933	−	0.953645i	$-0.402702\pi$
$884$	−3.16270e12	−0.174190
$885$	0	0
$886$	5.15505e12	0.281048
$887$	− 5.98069e12i	− 0.324410i	−0.986757	−	0.162205i	$-0.948139\pi$
$887$	− 5.98069e12i	− 0.324410i	0.986757	−	0.162205i	$-0.0518607\pi$
$888$	1.63342e13i	0.881534i
$889$	1.01070e13	0.542707
$890$	0	0
$891$	5.11751e12	0.272025
$892$	5.45638e12i	0.288578i
$893$	1.30759e13i	0.688084i
$894$	−1.42430e12	−0.0745732
$895$	0	0
$896$	−6.38384e11	−0.0330900
$897$	2.12503e12i	0.109597i
$898$	− 4.06774e12i	− 0.208742i
$899$	−6.37418e12	−0.325466
$900$	0	0
$901$	−3.78778e12	−0.191480
$902$	1.03735e13i	0.521789i
$903$	− 4.37579e12i	− 0.219009i
$904$	1.89637e13	0.944422
$905$	0	0
$906$	1.82679e13	0.900766
$907$	2.51683e12i	0.123487i	0.998092	+	0.0617434i	$0.0196661\pi$
$907$	2.51683e12i	0.123487i	−0.998092	+	0.0617434i	$0.980334\pi$
$908$	3.88897e10i	0.00189867i
$909$	1.50504e12	0.0731158
$910$	0	0
$911$	3.96021e13	1.90496	0.952478	−	0.304607i	$-0.0985252\pi$
$911$	3.96021e13	1.90496	0.952478	+	0.304607i	$0.0985252\pi$
$912$	− 5.08648e12i	− 0.243467i
$913$	2.21365e12i	0.105437i
$914$	3.99044e12	0.189131
$915$	0	0
$916$	2.53338e12	0.118897
$917$	− 9.89525e12i	− 0.462131i
$918$	− 5.11667e12i	− 0.237791i
$919$	4.00850e13	1.85380	0.926899	−	0.375310i	$-0.122464\pi$
$919$	4.00850e13	1.85380	0.926899	+	0.375310i	$0.122464\pi$
$920$	0	0
$921$	−1.34671e13	−0.616746
$922$	− 1.97844e13i	− 0.901640i
$923$	4.31975e13i	1.95907i
$924$	1.70603e12	0.0769953
$925$	0	0
$926$	3.02263e13	1.35094
$927$	− 9.71579e12i	− 0.432135i
$928$	3.02479e13i	1.33884i
$929$	8.38470e12	0.369332	0.184666	−	0.982801i	$-0.440880\pi$
$929$	8.38470e12	0.369332	0.184666	+	0.982801i	$0.440880\pi$
$930$	0	0
$931$	−2.81857e12	−0.122958
$932$	1.48336e12i	0.0643986i
$933$	− 1.58265e13i	− 0.683783i
$934$	−6.43944e12	−0.276877
$935$	0	0
$936$	−1.31406e13	−0.559596
$937$	− 2.33983e12i	− 0.0991645i	−0.998770	−	0.0495822i	$-0.984211\pi$
$937$	− 2.33983e12i	− 0.0991645i	0.998770	−	0.0495822i	$-0.0157890\pi$
$938$	− 8.86501e12i	− 0.373909i
$939$	3.01725e13	1.26653
$940$	0	0
$941$	−6.45893e12	−0.268539	−0.134270	−	0.990945i	$-0.542869\pi$
$941$	−6.45893e12	−0.268539	−0.134270	+	0.990945i	$0.542869\pi$
$942$	1.49166e13i	0.617221i
$943$	3.01302e12i	0.124079i
$944$	1.72327e12	0.0706285
$945$	0	0
$946$	8.00327e12	0.324906
$947$	2.43323e13i	0.983123i	0.870843	+	0.491561i	$0.163574\pi$
$947$	2.43323e13i	0.983123i	−0.870843	+	0.491561i	$0.836426\pi$
$948$	− 1.16653e13i	− 0.469093i
$949$	3.99302e13	1.59810
$950$	0	0
$951$	−1.35228e13	−0.536109
$952$	− 3.02611e12i	− 0.119404i
$953$	2.50351e12i	0.0983177i	0.998791	+	0.0491589i	$0.0156541\pi$
$953$	2.50351e12i	0.0983177i	−0.998791	+	0.0491589i	$0.984346\pi$
$954$	−4.82896e12	−0.188749
$955$	0	0
$956$	2.05932e12	0.0797377
$957$	− 1.98048e13i	− 0.763250i
$958$	2.89108e13i	1.10896i
$959$	−3.07189e12	−0.117279
$960$	0	0
$961$	−2.54215e13	−0.961492
$962$	2.78188e13i	1.04725i
$963$	− 1.38695e13i	− 0.519687i
$964$	−1.21573e13	−0.453408
$965$	0	0
$966$	−6.23883e11	−0.0230519
$967$	− 2.19887e13i	− 0.808686i	−0.914607	−	0.404343i	$-0.867500\pi$
$967$	− 2.19887e13i	− 0.808686i	0.914607	−	0.404343i	$-0.132500\pi$
$968$	− 1.92521e13i	− 0.704757i
$969$	−5.42348e12	−0.197615
$970$	0	0
$971$	−9.07743e12	−0.327700	−0.163850	−	0.986485i	$-0.552391\pi$
$971$	−9.07743e12	−0.327700	−0.163850	+	0.986485i	$0.552391\pi$
$972$	8.91568e12i	0.320373i
$973$	9.66019e12i	0.345524i
$974$	1.24787e13	0.444276
$975$	0	0
$976$	2.36939e12	0.0835818
$977$	− 2.73152e13i	− 0.959134i	−0.877505	−	0.479567i	$-0.840794\pi$
$977$	− 2.73152e13i	− 0.959134i	0.877505	−	0.479567i	$-0.159206\pi$
$978$	1.68320e13i	0.588316i
$979$	9.64018e12	0.335400
$980$	0	0
$981$	1.76421e12	0.0608192
$982$	2.56962e13i	0.881795i
$983$	1.07541e13i	0.367351i	0.982987	+	0.183676i	$0.0587996\pi$
$983$	1.07541e13i	0.367351i	−0.982987	+	0.183676i	$0.941200\pi$
$984$	2.94747e13	1.00224
$985$	0	0
$986$	−1.07790e13	−0.363188
$987$	− 7.05162e12i	− 0.236517i
$988$	1.53087e13i	0.511131i
$989$	2.32458e12	0.0772612
$990$	0	0
$991$	−2.06047e13	−0.678633	−0.339317	−	0.940672i	$-0.610196\pi$
$991$	−2.06047e13	−0.678633	−0.339317	+	0.940672i	$0.610196\pi$
$992$	− 4.83144e12i	− 0.158407i
$993$	3.70352e13i	1.20877i
$994$	−1.26822e13	−0.412057
$995$	0	0
$996$	1.92995e12	0.0621411
$997$	− 2.30380e13i	− 0.738444i	−0.929341	−	0.369222i	$-0.879624\pi$
$997$	− 2.30380e13i	− 0.738444i	0.929341	−	0.369222i	$-0.120376\pi$
$998$	2.83320e13i	0.904046i
$999$	3.57463e13	1.13550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.b.99.4		4
5.2	odd	4		7.10.a.a.1.1	✓	2
5.3	odd	4		175.10.a.b.1.2		2
5.4	even	2	inner	175.10.b.b.99.1		4
15.2	even	4		63.10.a.d.1.2		2
20.7	even	4		112.10.a.e.1.1		2
35.2	odd	12		49.10.c.c.18.2		4
35.12	even	12		49.10.c.b.18.2		4
35.17	even	12		49.10.c.b.30.2		4
35.27	even	4		49.10.a.b.1.1		2
35.32	odd	12		49.10.c.c.30.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.a.1.1	✓	2	5.2	odd	4
49.10.a.b.1.1		2	35.27	even	4
49.10.c.b.18.2		4	35.12	even	12
49.10.c.b.30.2		4	35.17	even	12
49.10.c.c.18.2		4	35.2	odd	12
49.10.c.c.30.2		4	35.32	odd	12
63.10.a.d.1.2		2	15.2	even	4
112.10.a.e.1.1		2	20.7	even	4
175.10.a.b.1.2		2	5.3	odd	4
175.10.b.b.99.1		4	5.4	even	2	inner
175.10.b.b.99.4		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+16.8924i q^{2} +109.817i q^{3} +226.645 q^{4} -1855.08 q^{6} +2401.00i q^{7} +12477.5i q^{8} +7623.25 q^{9} +O(q^{10})\)	\(q+16.8924i q^{2} +109.817i q^{3} +226.645 q^{4} -1855.08 q^{6} +2401.00i q^{7} +12477.5i q^{8} +7623.25 q^{9} -28548.3 q^{11} +24889.5i q^{12} +138149. i q^{13} -40558.8 q^{14} -94733.5 q^{16} +101010. i q^{17} +128775. i q^{18} +488928. q^{19} -263670. q^{21} -482250. i q^{22} -140071. i q^{23} -1.37024e6 q^{24} -2.33367e6 q^{26} +2.99869e6i q^{27} +544175. i q^{28} +6.31716e6 q^{29} -1.00903e6 q^{31} +4.78821e6i q^{32} -3.13508e6i q^{33} -1.70630e6 q^{34} +1.72777e6 q^{36} -1.19206e7i q^{37} +8.25919e6i q^{38} -1.51711e7 q^{39} -2.15106e7 q^{41} -4.45404e6i q^{42} +1.65957e7i q^{43} -6.47033e6 q^{44} +2.36615e6 q^{46} +2.67441e7i q^{47} -1.04033e7i q^{48} -5.76480e6 q^{49} -1.10926e7 q^{51} +3.13108e7i q^{52} +3.74991e7i q^{53} -5.06552e7 q^{54} -2.99585e7 q^{56} +5.36926e7i q^{57} +1.06712e8i q^{58} -1.81907e7 q^{59} -2.50111e7 q^{61} -1.70449e7i q^{62} +1.83034e7i q^{63} -1.29388e8 q^{64} +5.29592e7 q^{66} +2.18572e8i q^{67} +2.28934e7i q^{68} +1.53822e7 q^{69} +3.12688e8 q^{71} +9.51193e7i q^{72} -2.89038e8i q^{73} +2.01369e8 q^{74} +1.10813e8 q^{76} -6.85444e7i q^{77} -2.56276e8i q^{78} -4.68685e8 q^{79} -1.79258e8 q^{81} -3.63366e8i q^{82} -7.75407e7i q^{83} -5.97597e7 q^{84} -2.80342e8 q^{86} +6.93730e8i q^{87} -3.56212e8i q^{88} -3.37680e8 q^{89} -3.31695e8 q^{91} -3.17465e7i q^{92} -1.10808e8i q^{93} -4.51773e8 q^{94} -5.25827e8 q^{96} +7.36733e8i q^{97} -9.73816e7i q^{98} -2.17631e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9}+O(q^{10}) \) 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9	\( 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9} + 70632 q^{11} - 28812 q^{14} - 1504 q^{16} + 1850852 q^{19} + 412972 q^{21} - 6602592 q^{24} - 8254848 q^{26} + 20007168 q^{29} + 4934520 q^{31} + 4493352 q^{34} - 11225432 q^{36} - 94835888 q^{39} - 38206896 q^{41} + 37301952 q^{44} + 24735168 q^{46} - 23059204 q^{49} + 119942712 q^{51} - 105668944 q^{54} - 12562032 q^{56} + 14138436 q^{59} + 88632772 q^{61} - 294834304 q^{64} - 166516928 q^{66} + 390362304 q^{69} + 412987632 q^{71} - 7143048 q^{74} + 565023536 q^{76} - 937070192 q^{79} - 1171491268 q^{81} + 250357072 q^{84} - 833661216 q^{86} - 1272534792 q^{89} + 127397060 q^{91} + 304446384 q^{94} - 3429962368 q^{96} - 2818835720 q^{99}+O(q^{100}) \) 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9 + 70632 * q^11 - 28812 * q^14 - 1504 * q^16 + 1850852 * q^19 + 412972 * q^21 - 6602592 * q^24 - 8254848 * q^26 + 20007168 * q^29 + 4934520 * q^31 + 4493352 * q^34 - 11225432 * q^36 - 94835888 * q^39 - 38206896 * q^41 + 37301952 * q^44 + 24735168 * q^46 - 23059204 * q^49 + 119942712 * q^51 - 105668944 * q^54 - 12562032 * q^56 + 14138436 * q^59 + 88632772 * q^61 - 294834304 * q^64 - 166516928 * q^66 + 390362304 * q^69 + 412987632 * q^71 - 7143048 * q^74 + 565023536 * q^76 - 937070192 * q^79 - 1171491268 * q^81 + 250357072 * q^84 - 833661216 * q^86 - 1272534792 * q^89 + 127397060 * q^91 + 304446384 * q^94 - 3429962368 * q^96 - 2818835720 * q^99

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