LMFDB - Embedded newform 121.7.b.c.120.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,7,Mod(120,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("121.120");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	121.b (of order $2$, degree $1$, 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:	$27.8365441180$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 825 x^{18} + 275175 x^{16} + 47589550 x^{14} + 4569013705 x^{12} + 245564683275 x^{10} + \cdots + 17\!\cdots\!25 $ x^20 + 825x^18 + 275175x^16 + 47589550x^14 + 4569013705x^12 + 245564683275x^10 + 7342625961605x^8 + 117784752305650x^6 + 929387807009775x^4 + 2945657032798125*x^2 + 1742746483878125
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{14}\cdot 5\cdot 11^{16} $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			120.20
Root			$-13.3023i$ of defining polynomial
Character	$\chi$	$=$	121.120
Dual form			121.7.b.c.120.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.4779i q^{2} +25.0244 q^{3} -145.610 q^{4} -162.774 q^{5} +362.301i q^{6} +372.119i q^{7} -1181.54i q^{8} -102.779 q^{9} +O(q^{10})$	\(q+14.4779i q^{2} +25.0244 q^{3} -145.610 q^{4} -162.774 q^{5} +362.301i q^{6} +372.119i q^{7} -1181.54i q^{8} -102.779 q^{9} -2356.62i q^{10} -3643.79 q^{12} -710.808i q^{13} -5387.51 q^{14} -4073.31 q^{15} +7787.16 q^{16} +2839.03i q^{17} -1488.03i q^{18} -6116.85i q^{19} +23701.4 q^{20} +9312.06i q^{21} +16105.1 q^{23} -29567.3i q^{24} +10870.3 q^{25} +10291.0 q^{26} -20814.8 q^{27} -54184.2i q^{28} -22645.4i q^{29} -58973.1i q^{30} +20823.4 q^{31} +37123.4i q^{32} -41103.2 q^{34} -60571.3i q^{35} +14965.7 q^{36} -18505.0 q^{37} +88559.2 q^{38} -17787.6i q^{39} +192323. i q^{40} +13965.4i q^{41} -134819. q^{42} -42621.5i q^{43} +16729.8 q^{45} +233167. i q^{46} -23279.6 q^{47} +194869. q^{48} -20823.8 q^{49} +157379. i q^{50} +71044.9i q^{51} +103501. i q^{52} -235062. q^{53} -301354. i q^{54} +439673. q^{56} -153071. i q^{57} +327858. q^{58} +7559.59 q^{59} +593114. q^{60} -187883. i q^{61} +301479. i q^{62} -38246.2i q^{63} -39090.3 q^{64} +115701. i q^{65} -148760. q^{67} -413390. i q^{68} +403019. q^{69} +876945. q^{70} -612219. q^{71} +121438. i q^{72} +198720. i q^{73} -267914. i q^{74} +272022. q^{75} +890673. i q^{76} +257526. q^{78} +473282. i q^{79} -1.26754e6 q^{80} -445951. q^{81} -202189. q^{82} -38684.2i q^{83} -1.35593e6i q^{84} -462119. i q^{85} +617070. q^{86} -566688. i q^{87} -974721. q^{89} +242212. i q^{90} +264506. q^{91} -2.34505e6 q^{92} +521093. q^{93} -337040. i q^{94} +995663. i q^{95} +928990. i q^{96} -564565. q^{97} -301485. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 46 q^{3} - 420 q^{4} - 174 q^{5} + 66 q^{9}+O(q^{10}) $ 20 * q + 46 * q^3 - 420 * q^4 - 174 * q^5 + 66 * q^9	$ 20 q + 46 q^{3} - 420 q^{4} - 174 q^{5} + 66 q^{9} - 3006 q^{12} + 7180 q^{14} - 6260 q^{15} + 30740 q^{16} + 5384 q^{20} + 7816 q^{23} + 98014 q^{25} + 44540 q^{26} + 95428 q^{27} - 2806 q^{31} - 228190 q^{34} + 646034 q^{36} + 74594 q^{37} + 571430 q^{38} - 467120 q^{42} - 805524 q^{45} + 706194 q^{47} + 379386 q^{48} + 646590 q^{49} - 900854 q^{53} - 862620 q^{56} + 1621260 q^{58} + 741246 q^{59} + 1763880 q^{60} + 232380 q^{64} - 960956 q^{67} + 1742196 q^{69} + 1180480 q^{70} - 622350 q^{71} + 480120 q^{75} + 1703080 q^{78} - 2615744 q^{80} + 299384 q^{81} + 287430 q^{82} + 670190 q^{86} + 1111620 q^{89} - 1964640 q^{91} - 9325476 q^{92} - 3775388 q^{93} - 308266 q^{97}+O(q^{100}) $ 20 * q + 46 * q^3 - 420 * q^4 - 174 * q^5 + 66 * q^9 - 3006 * q^12 + 7180 * q^14 - 6260 * q^15 + 30740 * q^16 + 5384 * q^20 + 7816 * q^23 + 98014 * q^25 + 44540 * q^26 + 95428 * q^27 - 2806 * q^31 - 228190 * q^34 + 646034 * q^36 + 74594 * q^37 + 571430 * q^38 - 467120 * q^42 - 805524 * q^45 + 706194 * q^47 + 379386 * q^48 + 646590 * q^49 - 900854 * q^53 - 862620 * q^56 + 1621260 * q^58 + 741246 * q^59 + 1763880 * q^60 + 232380 * q^64 - 960956 * q^67 + 1742196 * q^69 + 1180480 * q^70 - 622350 * q^71 + 480120 * q^75 + 1703080 * q^78 - 2615744 * q^80 + 299384 * q^81 + 287430 * q^82 + 670190 * q^86 + 1111620 * q^89 - 1964640 * q^91 - 9325476 * q^92 - 3775388 * q^93 - 308266 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	14.4779i	1.80974i	0.425690	+	0.904869i	$0.360031\pi$
$2$	14.4779i	1.80974i	−0.425690	+	0.904869i	$0.639969\pi$
$3$	25.0244	0.926830	0.463415	−	0.886141i	$-0.346624\pi$
$3$	25.0244	0.926830	0.463415	+	0.886141i	$0.346624\pi$
$4$	−145.610	−2.27515
$5$	−162.774	−1.30219	−0.651095	−	0.758996i	$-0.725690\pi$
$5$	−162.774	−1.30219	−0.651095	+	0.758996i	$0.725690\pi$
$6$	362.301i	1.67732i
$7$	372.119i	1.08490i	0.840089	+	0.542448i	$0.182502\pi$
$7$	372.119i	1.08490i	−0.840089	+	0.542448i	$0.817498\pi$
$8$	− 1181.54i	− 2.30769i
$9$	−102.779	−0.140987
$10$	− 2356.62i	− 2.35662i
$11$	0	0
$11$	0	0
$12$	−3643.79	−2.10868
$13$	− 710.808i	− 0.323536i	−0.986829	−	0.161768i	$-0.948280\pi$
$13$	− 710.808i	− 0.323536i	0.986829	−	0.161768i	$-0.0517196\pi$
$14$	−5387.51	−1.96338
$15$	−4073.31	−1.20691
$16$	7787.16	1.90116
$17$	2839.03i	0.577860i	0.957350	+	0.288930i	$0.0932995\pi$
$17$	2839.03i	0.577860i	−0.957350	+	0.288930i	$0.906700\pi$
$18$	− 1488.03i	− 0.255149i
$19$	− 6116.85i	− 0.891800i	−0.895083	−	0.445900i	$-0.852884\pi$
$19$	− 6116.85i	− 0.891800i	0.895083	−	0.445900i	$-0.147116\pi$
$20$	23701.4	2.96268
$21$	9312.06i	1.00551i
$22$	0	0
$23$	16105.1	1.32367	0.661833	−	0.749651i	$-0.269779\pi$
$23$	16105.1	1.32367	0.661833	+	0.749651i	$0.269779\pi$
$24$	− 29567.3i	− 2.13883i
$25$	10870.3	0.695698
$26$	10291.0	0.585515
$27$	−20814.8	−1.05750
$28$	− 54184.2i	− 2.46830i
$29$	− 22645.4i	− 0.928509i	−0.885702	−	0.464254i	$-0.846322\pi$
$29$	− 22645.4i	− 0.928509i	0.885702	−	0.464254i	$-0.153678\pi$
$30$	− 58973.1i	− 2.18419i
$31$	20823.4	0.698983	0.349491	−	0.936940i	$-0.386354\pi$
$31$	20823.4	0.698983	0.349491	+	0.936940i	$0.386354\pi$
$32$	37123.4i	1.13292i
$33$	0	0
$34$	−41103.2	−1.04578
$35$	− 60571.3i	− 1.41274i
$36$	14965.7	0.320766
$37$	−18505.0	−0.365329	−0.182664	−	0.983175i	$-0.558472\pi$
$37$	−18505.0	−0.365329	−0.182664	+	0.983175i	$0.558472\pi$
$38$	88559.2	1.61392
$39$	− 17787.6i	− 0.299863i
$40$	192323.i	3.00505i
$41$	13965.4i	0.202629i	0.994854	+	0.101314i	$0.0323048\pi$
$41$	13965.4i	0.202629i	−0.994854	+	0.101314i	$0.967695\pi$
$42$	−134819.	−1.81972
$43$	− 42621.5i	− 0.536073i	−0.963409	−	0.268036i	$-0.913625\pi$
$43$	− 42621.5i	− 0.536073i	0.963409	−	0.268036i	$-0.0863747\pi$
$44$	0	0
$45$	16729.8	0.183592
$46$	233167.i	2.39549i
$47$	−23279.6	−0.224224	−0.112112	−	0.993696i	$-0.535762\pi$
$47$	−23279.6	−0.224224	−0.112112	+	0.993696i	$0.535762\pi$
$48$	194869.	1.76205
$49$	−20823.8	−0.176999
$50$	157379.i	1.25903i
$51$	71044.9i	0.535578i
$52$	103501.i	0.736093i
$53$	−235062.	−1.57890	−0.789449	−	0.613816i	$-0.789633\pi$
$53$	−235062.	−1.57890	−0.789449	+	0.613816i	$0.789633\pi$
$54$	− 301354.i	− 1.91380i
$55$	0	0
$56$	439673.	2.50360
$57$	− 153071.i	− 0.826546i
$58$	327858.	1.68036
$59$	7559.59	0.0368080	0.0184040	−	0.999831i	$-0.494141\pi$
$59$	7559.59	0.0368080	0.0184040	+	0.999831i	$0.494141\pi$
$60$	593114.	2.74590
$61$	− 187883.i	− 0.827750i	−0.910334	−	0.413875i	$-0.864175\pi$
$61$	− 187883.i	− 0.827750i	0.910334	−	0.413875i	$-0.135825\pi$
$62$	301479.i	1.26498i
$63$	− 38246.2i	− 0.152956i
$64$	−39090.3	−0.149117
$65$	115701.i	0.421305i
$66$	0	0
$67$	−148760.	−0.494610	−0.247305	−	0.968938i	$-0.579545\pi$
$67$	−148760.	−0.494610	−0.247305	+	0.968938i	$0.579545\pi$
$68$	− 413390.i	− 1.31472i
$69$	403019.	1.22681
$70$	876945.	2.55669
$71$	−612219.	−1.71053	−0.855267	−	0.518187i	$-0.826607\pi$
$71$	−612219.	−1.71053	−0.855267	+	0.518187i	$0.826607\pi$
$72$	121438.i	0.325354i
$73$	198720.i	0.510826i	0.966832	+	0.255413i	$0.0822114\pi$
$73$	198720.i	0.510826i	−0.966832	+	0.255413i	$0.917789\pi$
$74$	− 267914.i	− 0.661150i
$75$	272022.	0.644794
$76$	890673.i	2.02898i
$77$	0	0
$78$	257526.	0.542673
$79$	473282.i	0.959928i	0.877288	+	0.479964i	$0.159350\pi$
$79$	473282.i	0.959928i	−0.877288	+	0.479964i	$0.840650\pi$
$80$	−1.26754e6	−2.47567
$81$	−445951.	−0.839136
$82$	−202189.	−0.366705
$83$	− 38684.2i	− 0.0676549i	−0.999428	−	0.0338275i	$-0.989230\pi$
$83$	− 38684.2i	− 0.0676549i	0.999428	−	0.0338275i	$-0.0107697\pi$
$84$	− 1.35593e6i	− 2.28770i
$85$	− 462119.i	− 0.752484i
$86$	617070.	0.970151
$87$	− 566688.i	− 0.860570i
$88$	0	0
$89$	−974721.	−1.38264	−0.691322	−	0.722547i	$-0.742971\pi$
$89$	−974721.	−1.38264	−0.691322	+	0.722547i	$0.742971\pi$
$90$	242212.i	0.332253i
$91$	264506.	0.351003
$92$	−2.34505e6	−3.01154
$93$	521093.	0.647838
$94$	− 337040.i	− 0.405787i
$95$	995663.i	1.16129i
$96$	928990.i	1.05002i
$97$	−564565.	−0.618584	−0.309292	−	0.950967i	$-0.600092\pi$
$97$	−564565.	−0.618584	−0.309292	+	0.950967i	$0.600092\pi$
$98$	− 301485.i	− 0.320323i
$99$	0	0
$100$	−1.58282e6	−1.58282
$101$	− 1.93351e6i	− 1.87664i	−0.345763	−	0.938322i	$-0.612380\pi$
$101$	− 1.93351e6i	− 1.87664i	0.345763	−	0.938322i	$-0.387620\pi$
$102$	−1.02858e6	−0.969256
$103$	−1.71686e6	−1.57117	−0.785585	−	0.618754i	$-0.787638\pi$
$103$	−1.71686e6	−1.57117	−0.785585	+	0.618754i	$0.787638\pi$
$104$	−839846.	−0.746620
$105$	− 1.51576e6i	− 1.30937i
$106$	− 3.40320e6i	− 2.85739i
$107$	− 7420.82i	− 0.00605760i	−0.999995	−	0.00302880i	$-0.999036\pi$
$107$	− 7420.82i	− 0.00605760i	0.999995	−	0.00302880i	$-0.000964099\pi$
$108$	3.03083e6	2.40597
$109$	− 1.90513e6i	− 1.47111i	−0.677465	−	0.735555i	$-0.736922\pi$
$109$	− 1.90513e6i	− 1.47111i	0.677465	−	0.735555i	$-0.263078\pi$
$110$	0	0
$111$	−463077.	−0.338598
$112$	2.89775e6i	2.06256i
$113$	1.53738e6	1.06548	0.532740	−	0.846279i	$-0.321162\pi$
$113$	1.53738e6	1.06548	0.532740	+	0.846279i	$0.321162\pi$
$114$	2.21614e6	1.49583
$115$	−2.62148e6	−1.72367
$116$	3.29739e6i	2.11250i
$117$	73056.5i	0.0456143i
$118$	109447.i	0.0666128i
$119$	−1.05646e6	−0.626918
$120$	4.81277e6i	2.78517i
$121$	0	0
$122$	2.72016e6	1.49801
$123$	349475.i	0.187802i
$124$	−3.03209e6	−1.59029
$125$	773943.	0.396259
$126$	553725.	0.276810
$127$	− 247727.i	− 0.120938i	−0.998170	−	0.0604689i	$-0.980740\pi$
$127$	− 247727.i	− 0.120938i	0.998170	−	0.0604689i	$-0.0192596\pi$
$128$	1.80995e6i	0.863051i
$129$	− 1.06658e6i	− 0.496848i
$130$	−1.67511e6	−0.762452
$131$	2.12748e6i	0.946348i	0.880969	+	0.473174i	$0.156892\pi$
$131$	2.12748e6i	0.946348i	−0.880969	+	0.473174i	$0.843108\pi$
$132$	0	0
$133$	2.27620e6	0.967510
$134$	− 2.15374e6i	− 0.895114i
$135$	3.38810e6	1.37707
$136$	3.35441e6	1.33352
$137$	1.34789e6	0.524193	0.262097	−	0.965042i	$-0.415586\pi$
$137$	1.34789e6	0.524193	0.262097	+	0.965042i	$0.415586\pi$
$138$	5.83487e6i	2.22021i
$139$	− 4.50669e6i	− 1.67808i	−0.544067	−	0.839042i	$-0.683116\pi$
$139$	− 4.50669e6i	− 1.67808i	0.544067	−	0.839042i	$-0.316884\pi$
$140$	8.81976e6i	3.21420i
$141$	−582558.	−0.207817
$142$	− 8.86365e6i	− 3.09562i
$143$	0	0
$144$	−800360.	−0.268039
$145$	3.68608e6i	1.20909i
$146$	−2.87705e6	−0.924460
$147$	−521103.	−0.164048
$148$	2.69451e6	0.831179
$149$	− 3.68939e6i	− 1.11531i	−0.830073	−	0.557655i	$-0.811701\pi$
$149$	− 3.68939e6i	− 1.11531i	0.830073	−	0.557655i	$-0.188299\pi$
$150$	3.93831e6i	1.16691i
$151$	− 2.18265e6i	− 0.633948i	−0.948434	−	0.316974i	$-0.897333\pi$
$151$	− 2.18265e6i	− 0.633948i	0.948434	−	0.316974i	$-0.102667\pi$
$152$	−7.22729e6	−2.05800
$153$	− 291793.i	− 0.0814707i
$154$	0	0
$155$	−3.38950e6	−0.910208
$156$	2.59004e6i	0.682233i
$157$	2.14250e6	0.553633	0.276817	−	0.960923i	$-0.410721\pi$
$157$	2.14250e6	0.553633	0.276817	+	0.960923i	$0.410721\pi$
$158$	−6.85213e6	−1.73722
$159$	−5.88227e6	−1.46337
$160$	− 6.04271e6i	− 1.47527i
$161$	5.99300e6i	1.43604i
$162$	− 6.45644e6i	− 1.51862i
$163$	−812522.	−0.187617	−0.0938085	−	0.995590i	$-0.529904\pi$
$163$	−812522.	−0.187617	−0.0938085	+	0.995590i	$0.529904\pi$
$164$	− 2.03349e6i	− 0.461011i
$165$	0	0
$166$	560066.	0.122438
$167$	4.90943e6i	1.05410i	0.849834	+	0.527050i	$0.176702\pi$
$167$	4.90943e6i	1.05410i	−0.849834	+	0.527050i	$0.823298\pi$
$168$	1.10025e7	2.32041
$169$	4.32156e6	0.895325
$170$	6.69051e6	1.36180
$171$	628687.i	0.125732i
$172$	6.20611e6i	1.21965i
$173$	8.15962e6i	1.57591i	0.615732	+	0.787955i	$0.288860\pi$
$173$	8.15962e6i	1.57591i	−0.615732	+	0.787955i	$0.711140\pi$
$174$	8.20445e6	1.55741
$175$	4.04504e6i	0.754760i
$176$	0	0
$177$	189174.	0.0341147
$178$	− 1.41119e7i	− 2.50222i
$179$	−6.74676e6	−1.17635	−0.588174	−	0.808734i	$-0.700153\pi$
$179$	−6.74676e6	−1.17635	−0.588174	+	0.808734i	$0.700153\pi$
$180$	−2.43602e6	−0.417699
$181$	1.57247e6	0.265184	0.132592	−	0.991171i	$-0.457670\pi$
$181$	1.57247e6	0.265184	0.132592	+	0.991171i	$0.457670\pi$
$182$	3.82949e6i	0.635223i
$183$	− 4.70167e6i	− 0.767183i
$184$	− 1.90287e7i	− 3.05461i
$185$	3.01213e6	0.475728
$186$	7.54433e6i	1.17242i
$187$	0	0
$188$	3.38974e6	0.510144
$189$	− 7.74558e6i	− 1.14728i
$190$	−1.44151e7	−2.10163
$191$	−253801.	−0.0364245	−0.0182122	−	0.999834i	$-0.505797\pi$
$191$	−253801.	−0.0364245	−0.0182122	+	0.999834i	$0.505797\pi$
$192$	−978210.	−0.138206
$193$	− 1.26326e7i	− 1.75720i	−0.477559	−	0.878600i	$-0.658478\pi$
$193$	− 1.26326e7i	− 1.75720i	0.477559	−	0.878600i	$-0.341522\pi$
$194$	− 8.17371e6i	− 1.11947i
$195$	2.89535e6i	0.390478i
$196$	3.03215e6	0.402701
$197$	9.97446e6i	1.30464i	0.757943	+	0.652320i	$0.226204\pi$
$197$	9.97446e6i	1.30464i	−0.757943	+	0.652320i	$0.773796\pi$
$198$	0	0
$199$	−9.29580e6	−1.17958	−0.589790	−	0.807557i	$-0.700789\pi$
$199$	−9.29580e6	−1.17958	−0.589790	+	0.807557i	$0.700789\pi$
$200$	− 1.28436e7i	− 1.60546i
$201$	−3.72264e6	−0.458419
$202$	2.79931e7	3.39623
$203$	8.42679e6	1.00734
$204$	− 1.03448e7i	− 1.21852i
$205$	− 2.27319e6i	− 0.263861i
$206$	− 2.48565e7i	− 2.84340i
$207$	−1.65527e6	−0.186620
$208$	− 5.53518e6i	− 0.615094i
$209$	0	0
$210$	2.19450e7	2.36962
$211$	8.15249e6i	0.867846i	0.900950	+	0.433923i	$0.142871\pi$
$211$	8.15249e6i	0.867846i	−0.900950	+	0.433923i	$0.857129\pi$
$212$	3.42272e7	3.59223
$213$	−1.53204e7	−1.58537
$214$	107438.	0.0109627
$215$	6.93767e6i	0.698068i
$216$	2.45934e7i	2.44038i
$217$	7.74879e6i	0.758324i
$218$	2.75823e7	2.66232
$219$	4.97284e6i	0.473448i
$220$	0	0
$221$	2.01800e6	0.186958
$222$	− 6.70438e6i	− 0.612773i
$223$	−1.04386e7	−0.941299	−0.470650	−	0.882320i	$-0.655980\pi$
$223$	−1.04386e7	−0.941299	−0.470650	+	0.882320i	$0.655980\pi$
$224$	−1.38143e7	−1.22910
$225$	−1.11724e6	−0.0980843
$226$	2.22580e7i	1.92824i
$227$	4.92940e6i	0.421422i	0.977548	+	0.210711i	$0.0675778\pi$
$227$	4.92940e6i	0.421422i	−0.977548	+	0.210711i	$0.932422\pi$
$228$	2.22886e7i	1.88052i
$229$	−1.76076e7	−1.46621	−0.733103	−	0.680118i	$-0.761929\pi$
$229$	−1.76076e7	−1.46621	−0.733103	+	0.680118i	$0.761929\pi$
$230$	− 3.79535e7i	− 3.11938i
$231$	0	0
$232$	−2.67564e7	−2.14271
$233$	1.97573e7i	1.56192i	0.624578	+	0.780962i	$0.285271\pi$
$233$	1.97573e7i	1.56192i	−0.624578	+	0.780962i	$0.714729\pi$
$234$	−1.05770e6	−0.0825499
$235$	3.78931e6	0.291982
$236$	−1.10075e6	−0.0837438
$237$	1.18436e7i	0.889690i
$238$	− 1.52953e7i	− 1.13456i
$239$	1.14100e7i	0.835777i	0.908498	+	0.417888i	$0.137230\pi$
$239$	1.14100e7i	0.835777i	−0.908498	+	0.417888i	$0.862770\pi$
$240$	−3.17195e7	−2.29453
$241$	− 5.25355e6i	− 0.375320i	−0.982234	−	0.187660i	$-0.939910\pi$
$241$	− 5.25355e6i	− 0.375320i	0.982234	−	0.187660i	$-0.0600904\pi$
$242$	0	0
$243$	4.01431e6	0.279764
$244$	2.73576e7i	1.88326i
$245$	3.38957e6	0.230487
$246$	−5.05966e6	−0.339873
$247$	−4.34791e6	−0.288529
$248$	− 2.46036e7i	− 1.61304i
$249$	− 968049.i	− 0.0627046i
$250$	1.12051e7i	0.717124i
$251$	−1.62325e7	−1.02651	−0.513255	−	0.858236i	$-0.671561\pi$
$251$	−1.62325e7	−1.02651	−0.513255	+	0.858236i	$0.671561\pi$
$252$	5.56902e6i	0.347998i
$253$	0	0
$254$	3.58656e6	0.218866
$255$	− 1.15642e7i	− 0.697424i
$256$	−2.87061e7	−1.71101
$257$	6.11374e6	0.360170	0.180085	−	0.983651i	$-0.442363\pi$
$257$	6.11374e6	0.360170	0.180085	+	0.983651i	$0.442363\pi$
$258$	1.54418e7	0.899165
$259$	− 6.88607e6i	− 0.396344i
$260$	− 1.68472e7i	− 0.958533i
$261$	2.32748e6i	0.130908i
$262$	−3.08014e7	−1.71264
$263$	1.50722e7i	0.828535i	0.910155	+	0.414267i	$0.135962\pi$
$263$	1.50722e7i	0.828535i	−0.910155	+	0.414267i	$0.864038\pi$
$264$	0	0
$265$	3.82618e7	2.05602
$266$	3.29546e7i	1.75094i
$267$	−2.43918e7	−1.28147
$268$	2.16610e7	1.12531
$269$	−1.58221e7	−0.812844	−0.406422	−	0.913685i	$-0.633224\pi$
$269$	−1.58221e7	−0.812844	−0.406422	+	0.913685i	$0.633224\pi$
$270$	4.90526e7i	2.49213i
$271$	9.82125e6i	0.493468i	0.969083	+	0.246734i	$0.0793573\pi$
$271$	9.82125e6i	0.493468i	−0.969083	+	0.246734i	$0.920643\pi$
$272$	2.21080e7i	1.09861i
$273$	6.61909e6	0.325320
$274$	1.95146e7i	0.948653i
$275$	0	0
$276$	−5.86835e7	−2.79119
$277$	− 1.42316e7i	− 0.669599i	−0.942289	−	0.334799i	$-0.891331\pi$
$277$	− 1.42316e7i	− 0.669599i	0.942289	−	0.334799i	$-0.108669\pi$
$278$	6.52475e7	3.03689
$279$	−2.14022e6	−0.0985474
$280$	−7.15672e7	−3.26017
$281$	394430.i	0.0177767i	0.999960	+	0.00888835i	$0.00282929\pi$
$281$	394430.i	0.0177767i	−0.999960	+	0.00888835i	$0.997171\pi$
$282$	− 8.43422e6i	− 0.376095i
$283$	− 1.35826e7i	− 0.599273i	−0.954053	−	0.299637i	$-0.903135\pi$
$283$	− 1.35826e7i	− 0.599273i	0.954053	−	0.299637i	$-0.0968654\pi$
$284$	8.91450e7	3.89172
$285$	2.49159e7i	1.07632i
$286$	0	0
$287$	−5.19678e6	−0.219831
$288$	− 3.81552e6i	− 0.159726i
$289$	1.60775e7	0.666078
$290$	−5.33667e7	−2.18814
$291$	−1.41279e7	−0.573322
$292$	− 2.89355e7i	− 1.16221i
$293$	− 2.61168e7i	− 1.03828i	−0.854688	−	0.519142i	$-0.826251\pi$
$293$	− 2.61168e7i	− 1.03828i	0.854688	−	0.519142i	$-0.173749\pi$
$294$	− 7.54448e6i	− 0.296885i
$295$	−1.23050e6	−0.0479310
$296$	2.18643e7i	0.843066i
$297$	0	0
$298$	5.34146e7	2.01842
$299$	− 1.14476e7i	− 0.428254i
$300$	−3.96091e7	−1.46700
$301$	1.58603e7	0.581583
$302$	3.16002e7	1.14728
$303$	− 4.83849e7i	− 1.73933i
$304$	− 4.76329e7i	− 1.69546i
$305$	3.05825e7i	1.07789i
$306$	4.22456e6	0.147441
$307$	− 3.16482e7i	− 1.09379i	−0.837201	−	0.546895i	$-0.815810\pi$
$307$	− 3.16482e7i	− 1.09379i	0.837201	−	0.546895i	$-0.184190\pi$
$308$	0	0
$309$	−4.29634e7	−1.45621
$310$	− 4.90729e7i	− 1.64724i
$311$	7.22348e6	0.240141	0.120070	−	0.992765i	$-0.461688\pi$
$311$	7.22348e6	0.240141	0.120070	+	0.992765i	$0.461688\pi$
$312$	−2.10166e7	−0.691990
$313$	2.64765e7	0.863432	0.431716	−	0.902010i	$-0.357908\pi$
$313$	2.64765e7	0.863432	0.431716	+	0.902010i	$0.357908\pi$
$314$	3.10189e7i	1.00193i
$315$	6.22548e6i	0.199178i
$316$	− 6.89144e7i	− 2.18398i
$317$	1.65878e7	0.520729	0.260364	−	0.965510i	$-0.416157\pi$
$317$	1.65878e7	0.520729	0.260364	+	0.965510i	$0.416157\pi$
$318$	− 8.51630e7i	− 2.64831i
$319$	0	0
$320$	6.36287e6	0.194179
$321$	− 185702.i	− 0.00561437i
$322$	−8.67661e7	−2.59886
$323$	1.73659e7	0.515335
$324$	6.49348e7	1.90916
$325$	− 7.72669e6i	− 0.225083i
$326$	− 1.17636e7i	− 0.339538i
$327$	− 4.76747e7i	− 1.36347i
$328$	1.65006e7	0.467604
$329$	− 8.66279e6i	− 0.243260i
$330$	0	0
$331$	−4.76366e7	−1.31358	−0.656791	−	0.754073i	$-0.728086\pi$
$331$	−4.76366e7	−1.31358	−0.656791	+	0.754073i	$0.728086\pi$
$332$	5.63279e6i	0.153925i
$333$	1.90193e6	0.0515066
$334$	−7.10783e7	−1.90765
$335$	2.42143e7	0.644076
$336$	7.25145e7i	1.91164i
$337$	579196.i	0.0151334i	0.999971	+	0.00756669i	$0.00240857\pi$
$337$	579196.i	0.0151334i	−0.999971	+	0.00756669i	$0.997591\pi$
$338$	6.25671e7i	1.62030i
$339$	3.84720e7	0.987519
$340$	6.72890e7i	1.71201i
$341$	0	0
$342$	−9.10206e6	−0.227542
$343$	3.60305e7i	0.892870i
$344$	−5.03589e7	−1.23709
$345$	−6.56010e7	−1.59754
$346$	−1.18134e8	−2.85199
$347$	4.56460e7i	1.09248i	0.837628	+	0.546241i	$0.183942\pi$
$347$	4.56460e7i	1.09248i	−0.837628	+	0.546241i	$0.816058\pi$
$348$	8.25152e7i	1.95793i
$349$	− 2.02863e6i	− 0.0477230i	−0.999715	−	0.0238615i	$-0.992404\pi$
$349$	− 2.02863e6i	− 0.0477230i	0.999715	−	0.0238615i	$-0.00759607\pi$
$350$	−5.85638e7	−1.36592
$351$	1.47953e7i	0.342139i
$352$	0	0
$353$	4.45069e7	1.01182	0.505910	−	0.862586i	$-0.331157\pi$
$353$	4.45069e7	1.01182	0.505910	+	0.862586i	$0.331157\pi$
$354$	2.73885e6i	0.0617387i
$355$	9.96532e7	2.22744
$356$	1.41929e8	3.14572
$357$	−2.64372e7	−0.581046
$358$	− 9.76789e7i	− 2.12888i
$359$	4.70618e7i	1.01715i	0.861018	+	0.508575i	$0.169828\pi$
$359$	4.70618e7i	1.01715i	−0.861018	+	0.508575i	$0.830172\pi$
$360$	− 1.97669e7i	− 0.423672i
$361$	9.62998e6	0.204693
$362$	2.27661e7i	0.479914i
$363$	0	0
$364$	−3.85146e7	−0.798584
$365$	− 3.23464e7i	− 0.665192i
$366$	6.80703e7	1.38840
$367$	3.76939e7	0.762558	0.381279	−	0.924460i	$-0.375484\pi$
$367$	3.76939e7	0.762558	0.381279	+	0.924460i	$0.375484\pi$
$368$	1.25413e8	2.51650
$369$	− 1.43535e6i	− 0.0285680i
$370$	4.36093e7i	0.860942i
$371$	− 8.74709e7i	− 1.71294i
$372$	−7.58762e7	−1.47393
$373$	− 3.76414e7i	− 0.725336i	−0.931918	−	0.362668i	$-0.881866\pi$
$373$	− 3.76414e7i	− 0.725336i	0.931918	−	0.362668i	$-0.118134\pi$
$374$	0	0
$375$	1.93674e7	0.367264
$376$	2.75057e7i	0.517439i
$377$	−1.60965e7	−0.300406
$378$	1.12140e8	2.07627
$379$	2.75233e7	0.505572	0.252786	−	0.967522i	$-0.418653\pi$
$379$	2.75233e7	0.505572	0.252786	+	0.967522i	$0.418653\pi$
$380$	− 1.44978e8i	− 2.64212i
$381$	− 6.19921e6i	− 0.112089i
$382$	− 3.67451e6i	− 0.0659188i
$383$	−5.62447e7	−1.00112	−0.500559	−	0.865702i	$-0.666872\pi$
$383$	−5.62447e7	−1.00112	−0.500559	+	0.865702i	$0.666872\pi$
$384$	4.52929e7i	0.799902i
$385$	0	0
$386$	1.82894e8	3.18007
$387$	4.38062e6i	0.0755792i
$388$	8.22061e7	1.40737
$389$	−5.81715e7	−0.988237	−0.494119	−	0.869395i	$-0.664509\pi$
$389$	−5.81715e7	−0.988237	−0.494119	+	0.869395i	$0.664509\pi$
$390$	−4.19185e7	−0.706663
$391$	4.57227e7i	0.764894i
$392$	2.46041e7i	0.408460i
$393$	5.32388e7i	0.877103i
$394$	−1.44409e8	−2.36106
$395$	− 7.70379e7i	− 1.25001i
$396$	0	0
$397$	−7.35626e7	−1.17567	−0.587835	−	0.808981i	$-0.700020\pi$
$397$	−7.35626e7	−1.17567	−0.587835	+	0.808981i	$0.700020\pi$
$398$	− 1.34584e8i	− 2.13473i
$399$	5.69605e7	0.896717
$400$	8.46486e7	1.32263
$401$	−1.18864e8	−1.84339	−0.921695	−	0.387916i	$-0.873195\pi$
$401$	−1.18864e8	−1.84339	−0.921695	+	0.387916i	$0.873195\pi$
$402$	− 5.38960e7i	− 0.829619i
$403$	− 1.48014e7i	− 0.226146i
$404$	2.81537e8i	4.26965i
$405$	7.25891e7	1.09271
$406$	1.22002e8i	1.82301i
$407$	0	0
$408$	8.39422e7	1.23595
$409$	− 1.77594e6i	− 0.0259572i	−0.999916	−	0.0129786i	$-0.995869\pi$
$409$	− 1.77594e6i	− 0.0259572i	0.999916	−	0.0129786i	$-0.00413133\pi$
$410$	3.29111e7	0.477519
$411$	3.37300e7	0.485838
$412$	2.49991e8	3.57465
$413$	2.81307e6i	0.0399329i
$414$	− 2.39648e7i	− 0.337733i
$415$	6.29677e6i	0.0880995i
$416$	2.63876e7	0.366539
$417$	− 1.12777e8i	− 1.55530i
$418$	0	0
$419$	8.72576e7	1.18621	0.593104	−	0.805126i	$-0.297902\pi$
$419$	8.72576e7	1.18621	0.593104	+	0.805126i	$0.297902\pi$
$420$	2.20709e8i	2.97901i
$421$	−2.14183e7	−0.287038	−0.143519	−	0.989648i	$-0.545842\pi$
$421$	−2.14183e7	−0.287038	−0.143519	+	0.989648i	$0.545842\pi$
$422$	−1.18031e8	−1.57057
$423$	2.39266e6	0.0316126
$424$	2.77734e8i	3.64361i
$425$	3.08610e7i	0.402016i
$426$	− 2.21807e8i	− 2.86911i
$427$	6.99151e7	0.898022
$428$	1.08054e6i	0.0137820i
$429$	0	0
$430$	−1.00443e8	−1.26332
$431$	1.51624e7i	0.189380i	0.995507	+	0.0946902i	$0.0301861\pi$
$431$	1.51624e7i	0.189380i	−0.995507	+	0.0946902i	$0.969814\pi$
$432$	−1.62088e8	−2.01048
$433$	3.18992e7	0.392931	0.196465	−	0.980511i	$-0.437054\pi$
$433$	3.18992e7	0.392931	0.196465	+	0.980511i	$0.437054\pi$
$434$	−1.12186e8	−1.37237
$435$	9.22419e7i	1.12062i
$436$	2.77405e8i	3.34700i
$437$	− 9.85123e7i	− 1.18045i
$438$	−7.19964e7	−0.856817
$439$	− 7.17575e7i	− 0.848152i	−0.905626	−	0.424076i	$-0.860599\pi$
$439$	− 7.17575e7i	− 0.848152i	0.905626	−	0.424076i	$-0.139401\pi$
$440$	0	0
$441$	2.14026e6	0.0249546
$442$	2.92165e7i	0.338346i
$443$	−4.46302e7	−0.513355	−0.256678	−	0.966497i	$-0.582628\pi$
$443$	−4.46302e7	−0.513355	−0.256678	+	0.966497i	$0.582628\pi$
$444$	6.74284e7	0.770361
$445$	1.58659e8	1.80046
$446$	− 1.51129e8i	− 1.70350i
$447$	− 9.23248e7i	− 1.03370i
$448$	− 1.45462e7i	− 0.161777i
$449$	−1.65949e8	−1.83331	−0.916653	−	0.399685i	$-0.869120\pi$
$449$	−1.65949e8	−1.83331	−0.916653	+	0.399685i	$0.869120\pi$
$450$	− 1.61753e7i	− 0.177507i
$451$	0	0
$452$	−2.23857e8	−2.42413
$453$	− 5.46195e7i	− 0.587562i
$454$	−7.13674e7	−0.762663
$455$	−4.30545e7	−0.457072
$456$	−1.80859e8	−1.90741
$457$	− 3.95226e7i	− 0.414092i	−0.978331	−	0.207046i	$-0.933615\pi$
$457$	− 3.95226e7i	− 0.414092i	0.978331	−	0.207046i	$-0.0663849\pi$
$458$	− 2.54922e8i	− 2.65345i
$459$	− 5.90937e7i	− 0.611087i
$460$	3.81713e8	3.92160
$461$	− 2.68720e7i	− 0.274282i	−0.990552	−	0.137141i	$-0.956209\pi$
$461$	− 2.68720e7i	− 0.274282i	0.990552	−	0.137141i	$-0.0437914\pi$
$462$	0	0
$463$	−6.14457e7	−0.619082	−0.309541	−	0.950886i	$-0.600175\pi$
$463$	−6.14457e7	−0.619082	−0.309541	+	0.950886i	$0.600175\pi$
$464$	− 1.76343e8i	− 1.76525i
$465$	−8.48203e7	−0.843608
$466$	−2.86044e8	−2.82667
$467$	8.98862e7	0.882556	0.441278	−	0.897370i	$-0.354525\pi$
$467$	8.98862e7	0.882556	0.441278	+	0.897370i	$0.354525\pi$
$468$	− 1.06377e7i	− 0.103779i
$469$	− 5.53566e7i	− 0.536600i
$470$	5.48613e7i	0.528411i
$471$	5.36148e7	0.513124
$472$	− 8.93194e6i	− 0.0849414i
$473$	0	0
$474$	−1.71470e8	−1.61011
$475$	− 6.64920e7i	− 0.620424i
$476$	1.53830e8	1.42633
$477$	2.41595e7	0.222604
$478$	−1.65192e8	−1.51254
$479$	− 1.07853e8i	− 0.981356i	−0.871341	−	0.490678i	$-0.836749\pi$
$479$	− 1.07853e8i	− 0.981356i	0.871341	−	0.490678i	$-0.163251\pi$
$480$	− 1.51215e8i	− 1.36732i
$481$	1.31535e7i	0.118197i
$482$	7.60605e7	0.679231
$483$	1.49971e8i	1.33097i
$484$	0	0
$485$	9.18963e7	0.805514
$486$	5.81188e7i	0.506300i
$487$	1.55025e6	0.0134219	0.00671097	−	0.999977i	$-0.497864\pi$
$487$	1.55025e6	0.0134219	0.00671097	+	0.999977i	$0.497864\pi$
$488$	−2.21991e8	−1.91019
$489$	−2.03329e7	−0.173889
$490$	4.90739e7i	0.417121i
$491$	3.83404e7i	0.323901i	0.986799	+	0.161950i	$0.0517785\pi$
$491$	3.83404e7i	0.323901i	−0.986799	+	0.161950i	$0.948222\pi$
$492$	− 5.08869e7i	− 0.427278i
$493$	6.42909e7	0.536548
$494$	− 6.29486e7i	− 0.522162i
$495$	0	0
$496$	1.62155e8	1.32888
$497$	− 2.27819e8i	− 1.85575i
$498$	1.40153e7	0.113479
$499$	5.76300e7	0.463818	0.231909	−	0.972738i	$-0.425503\pi$
$499$	5.76300e7	0.463818	0.231909	+	0.972738i	$0.425503\pi$
$500$	−1.12694e8	−0.901548
$501$	1.22856e8i	0.976971i
$502$	− 2.35012e8i	− 1.85772i
$503$	6.25239e7i	0.491295i	0.969359	+	0.245648i	$0.0790006\pi$
$503$	6.25239e7i	0.491295i	−0.969359	+	0.245648i	$0.920999\pi$
$504$	−4.51893e7	−0.352975
$505$	3.14724e8i	2.44375i
$506$	0	0
$507$	1.08144e8	0.829813
$508$	3.60714e7i	0.275152i
$509$	−1.27992e8	−0.970575	−0.485288	−	0.874355i	$-0.661285\pi$
$509$	−1.27992e8	−0.970575	−0.485288	+	0.874355i	$0.661285\pi$
$510$	1.67426e8	1.26215
$511$	−7.39475e7	−0.554193
$512$	− 2.99767e8i	− 2.23344i
$513$	1.27321e8i	0.943079i
$514$	8.85142e7i	0.651814i
$515$	2.79460e8	2.04596
$516$	1.55304e8i	1.13040i
$517$	0	0
$518$	9.96959e7	0.717279
$519$	2.04190e8i	1.46060i
$520$	1.36705e8	0.972241
$521$	2.06752e8	1.46196	0.730982	−	0.682397i	$-0.239062\pi$
$521$	2.06752e8	1.46196	0.730982	+	0.682397i	$0.239062\pi$
$522$	−3.36970e7	−0.236908
$523$	1.18436e8i	0.827903i	0.910299	+	0.413952i	$0.135852\pi$
$523$	1.18436e8i	0.827903i	−0.910299	+	0.413952i	$0.864148\pi$
$524$	− 3.09781e8i	− 2.15308i
$525$	1.01225e8i	0.699534i
$526$	−2.18215e8	−1.49943
$527$	5.91182e7i	0.403914i
$528$	0	0
$529$	1.11337e8	0.752094
$530$	5.53951e8i	3.72086i
$531$	−776970.	−0.00518944
$532$	−3.31437e8	−2.20123
$533$	9.92670e6	0.0655576
$534$	− 3.53142e8i	− 2.31913i
$535$	1.20792e6i	0.00788815i
$536$	1.75766e8i	1.14141i
$537$	−1.68834e8	−1.09027
$538$	− 2.29071e8i	− 1.47104i
$539$	0	0
$540$	−4.93340e8	−3.13303
$541$	− 2.88330e7i	− 0.182095i	−0.995847	−	0.0910476i	$-0.970978\pi$
$541$	− 2.88330e7i	− 0.182095i	0.995847	−	0.0910476i	$-0.0290215\pi$
$542$	−1.42191e8	−0.893047
$543$	3.93502e7	0.245781
$544$	−1.05394e8	−0.654666
$545$	3.10105e8i	1.91566i
$546$	9.58306e7i	0.588744i
$547$	1.98408e8i	1.21227i	0.795363	+	0.606133i	$0.207280\pi$
$547$	1.98408e8i	1.21227i	−0.795363	+	0.606133i	$0.792720\pi$
$548$	−1.96265e8	−1.19262
$549$	1.93106e7i	0.116702i
$550$	0	0
$551$	−1.38519e8	−0.828044
$552$	− 4.76182e8i	− 2.83110i
$553$	−1.76117e8	−1.04142
$554$	2.06044e8	1.21180
$555$	7.53767e7	0.440918
$556$	6.56218e8i	3.81789i
$557$	2.06738e8i	1.19634i	0.801370	+	0.598169i	$0.204105\pi$
$557$	2.06738e8i	1.19634i	−0.801370	+	0.598169i	$0.795895\pi$
$558$	− 3.09859e7i	− 0.178345i
$559$	−3.02957e7	−0.173439
$560$	− 4.71678e8i	− 2.68585i
$561$	0	0
$562$	−5.71052e6	−0.0321712
$563$	2.88417e8i	1.61620i	0.589044	+	0.808101i	$0.299504\pi$
$563$	2.88417e8i	1.61620i	−0.589044	+	0.808101i	$0.700496\pi$
$564$	8.48261e7	0.472816
$565$	−2.50245e8	−1.38746
$566$	1.96648e8	1.08453
$567$	− 1.65947e8i	− 0.910375i
$568$	7.23360e8i	3.94738i
$569$	− 9.92786e7i	− 0.538913i	−0.963013	−	0.269457i	$-0.913156\pi$
$569$	− 9.92786e7i	− 0.538913i	0.963013	−	0.269457i	$-0.0868441\pi$
$570$	−3.60730e8	−1.94786
$571$	− 3.34829e8i	− 1.79852i	−0.437416	−	0.899259i	$-0.644106\pi$
$571$	− 3.34829e8i	− 1.79852i	0.437416	−	0.899259i	$-0.355894\pi$
$572$	0	0
$573$	−6.35122e6	−0.0337593
$574$	− 7.52385e7i	− 0.397836i
$575$	1.75067e8	0.920873
$576$	4.01767e6	0.0210236
$577$	2.59579e8	1.35127	0.675634	−	0.737237i	$-0.263870\pi$
$577$	2.59579e8	1.35127	0.675634	+	0.737237i	$0.263870\pi$
$578$	2.32768e8i	1.20543i
$579$	− 3.16123e8i	− 1.62862i
$580$	− 5.36728e8i	− 2.75087i
$581$	1.43951e7	0.0733986
$582$	− 2.04542e8i	− 1.03756i
$583$	0	0
$584$	2.34795e8	1.17883
$585$	− 1.18917e7i	− 0.0593985i
$586$	3.78116e8	1.87902
$587$	1.03541e8	0.511914	0.255957	−	0.966688i	$-0.417609\pi$
$587$	1.03541e8	0.511914	0.255957	+	0.966688i	$0.417609\pi$
$588$	7.58777e7	0.373235
$589$	− 1.27374e8i	− 0.623353i
$590$	− 1.78151e7i	− 0.0867426i
$591$	2.49605e8i	1.20918i
$592$	−1.44101e8	−0.694549
$593$	2.40665e8i	1.15412i	0.816703	+	0.577058i	$0.195799\pi$
$593$	2.40665e8i	1.15412i	−0.816703	+	0.577058i	$0.804201\pi$
$594$	0	0
$595$	1.71963e8	0.816366
$596$	5.37211e8i	2.53750i
$597$	−2.32622e8	−1.09327
$598$	1.65737e8	0.775027
$599$	3.24032e7	0.150767	0.0753836	−	0.997155i	$-0.475982\pi$
$599$	3.24032e7	0.150767	0.0753836	+	0.997155i	$0.475982\pi$
$600$	− 3.21405e8i	− 1.48798i
$601$	7.72514e7i	0.355863i	0.984043	+	0.177932i	$0.0569406\pi$
$601$	7.72514e7i	0.355863i	−0.984043	+	0.177932i	$0.943059\pi$
$602$	2.29624e8i	1.05251i
$603$	1.52895e7	0.0697335
$604$	3.17815e8i	1.44233i
$605$	0	0
$606$	7.00511e8	3.14773
$607$	− 1.27114e8i	− 0.568367i	−0.958770	−	0.284183i	$-0.908278\pi$
$607$	− 1.27114e8i	− 0.568367i	0.958770	−	0.284183i	$-0.0917225\pi$
$608$	2.27078e8	1.01033
$609$	2.10875e8	0.933629
$610$	−4.42770e8	−1.95069
$611$	1.65473e7i	0.0725445i
$612$	4.24880e7i	0.185358i
$613$	− 2.08591e8i	− 0.905554i	−0.891624	−	0.452777i	$-0.850433\pi$
$613$	− 2.08591e8i	− 0.905554i	0.891624	−	0.452777i	$-0.149567\pi$
$614$	4.58199e8	1.97947
$615$	− 5.68853e7i	− 0.244554i
$616$	0	0
$617$	−1.61919e8	−0.689353	−0.344677	−	0.938721i	$-0.612011\pi$
$617$	−1.61919e8	−0.689353	−0.344677	+	0.938721i	$0.612011\pi$
$618$	− 6.22019e8i	− 2.63535i
$619$	−3.24662e8	−1.36886	−0.684430	−	0.729078i	$-0.739949\pi$
$619$	−3.24662e8	−1.36886	−0.684430	+	0.729078i	$0.739949\pi$
$620$	4.93544e8	2.07086
$621$	−3.35223e8	−1.39978
$622$	1.04581e8i	0.434591i
$623$	− 3.62712e8i	− 1.50002i
$624$	− 1.38514e8i	− 0.570087i
$625$	−2.95826e8	−1.21170
$626$	3.83325e8i	1.56259i
$627$	0	0
$628$	−3.11969e8	−1.25960
$629$	− 5.25362e7i	− 0.211109i
$630$	−9.01319e7	−0.360460
$631$	−1.68751e8	−0.671674	−0.335837	−	0.941920i	$-0.609019\pi$
$631$	−1.68751e8	−0.671674	−0.335837	+	0.941920i	$0.609019\pi$
$632$	5.59200e8	2.21522
$633$	2.04011e8i	0.804345i
$634$	2.40157e8i	0.942383i
$635$	4.03234e7i	0.157484i
$636$	8.56516e8	3.32939
$637$	1.48017e7i	0.0572657i
$638$	0	0
$639$	6.29235e7	0.241163
$640$	− 2.94612e8i	− 1.12386i
$641$	3.47450e8	1.31922	0.659611	−	0.751607i	$-0.270721\pi$
$641$	3.47450e8	1.31922	0.659611	+	0.751607i	$0.270721\pi$
$642$	2.68857e6	0.0101605
$643$	5.13312e8	1.93085	0.965424	−	0.260683i	$-0.0839479\pi$
$643$	5.13312e8	1.93085	0.965424	+	0.260683i	$0.0839479\pi$
$644$	− 8.72639e8i	− 3.26721i
$645$	1.73611e8i	0.646991i
$646$	2.51422e8i	0.932622i
$647$	2.84049e7	0.104877	0.0524385	−	0.998624i	$-0.483301\pi$
$647$	2.84049e7	0.104877	0.0524385	+	0.998624i	$0.483301\pi$
$648$	5.26908e8i	1.93646i
$649$	0	0
$650$	1.11866e8	0.407342
$651$	1.93909e8i	0.702837i
$652$	1.18311e8	0.426857
$653$	−1.32170e8	−0.474670	−0.237335	−	0.971428i	$-0.576274\pi$
$653$	−1.32170e8	−0.474670	−0.237335	+	0.971428i	$0.576274\pi$
$654$	6.90230e8	2.46752
$655$	− 3.46297e8i	− 1.23232i
$656$	1.08751e8i	0.385230i
$657$	− 2.04243e7i	− 0.0720197i
$658$	1.25419e8	0.440236
$659$	− 2.85200e8i	− 0.996536i	−0.867023	−	0.498268i	$-0.833970\pi$
$659$	− 2.85200e8i	− 0.996536i	0.867023	−	0.498268i	$-0.166030\pi$
$660$	0	0
$661$	9.10777e7	0.315361	0.157680	−	0.987490i	$-0.449598\pi$
$661$	9.10777e7	0.315361	0.157680	+	0.987490i	$0.449598\pi$
$662$	− 6.89678e8i	− 2.37724i
$663$	5.04993e7	0.173279
$664$	−4.57068e7	−0.156127
$665$	−3.70506e8	−1.25988
$666$	2.75360e7i	0.0932134i
$667$	− 3.64705e8i	− 1.22904i
$668$	− 7.14861e8i	− 2.39824i
$669$	−2.61220e8	−0.872424
$670$	3.50572e8i	1.16561i
$671$	0	0
$672$	−3.45695e8	−1.13916
$673$	− 2.32922e8i	− 0.764126i	−0.924136	−	0.382063i	$-0.875214\pi$
$673$	− 2.32922e8i	− 0.764126i	0.924136	−	0.382063i	$-0.124786\pi$
$674$	−8.38554e6	−0.0273874
$675$	−2.26263e8	−0.735701
$676$	−6.29261e8	−2.03700
$677$	− 3.18322e8i	− 1.02589i	−0.858421	−	0.512945i	$-0.828554\pi$
$677$	− 3.18322e8i	− 1.02589i	0.858421	−	0.512945i	$-0.171446\pi$
$678$	5.56994e8i	1.78715i
$679$	− 2.10085e8i	− 0.671099i
$680$	−5.46011e8	−1.73650
$681$	1.23355e8i	0.390586i
$682$	0	0
$683$	−4.29254e8	−1.34726	−0.673631	−	0.739067i	$-0.735266\pi$
$683$	−4.29254e8	−1.34726	−0.673631	+	0.739067i	$0.735266\pi$
$684$	− 9.15429e7i	− 0.286059i
$685$	−2.19400e8	−0.682599
$686$	−5.21646e8	−1.61586
$687$	−4.40621e8	−1.35892
$688$	− 3.31901e8i	− 1.01916i
$689$	1.67084e8i	0.510830i
$690$	− 9.49764e8i	− 2.89114i
$691$	2.95852e8	0.896685	0.448342	−	0.893862i	$-0.352015\pi$
$691$	2.95852e8	0.896685	0.448342	+	0.893862i	$0.352015\pi$
$692$	− 1.18812e9i	− 3.58544i
$693$	0	0
$694$	−6.60858e8	−1.97710
$695$	7.33571e8i	2.18518i
$696$	−6.69562e8	−1.98593
$697$	−3.96480e7	−0.117091
$698$	2.93704e7	0.0863660
$699$	4.94415e8i	1.44764i
$700$	− 5.88998e8i	− 1.71719i
$701$	− 2.12037e8i	− 0.615543i	−0.951460	−	0.307772i	$-0.900417\pi$
$701$	− 2.12037e8i	− 0.615543i	0.951460	−	0.307772i	$-0.0995833\pi$
$702$	−2.14205e8	−0.619182
$703$	1.13192e8i	0.325800i
$704$	0	0
$705$	9.48252e7	0.270618
$706$	6.44367e8i	1.83113i
$707$	7.19496e8	2.03596
$708$	−2.75456e7	−0.0776162
$709$	−2.35552e8	−0.660920	−0.330460	−	0.943820i	$-0.607204\pi$
$709$	−2.35552e8	−0.660920	−0.330460	+	0.943820i	$0.607204\pi$
$710$	1.44277e9i	4.03108i
$711$	− 4.86437e7i	− 0.135337i
$712$	1.15167e9i	3.19071i
$713$	3.35362e8	0.925221
$714$	− 3.82755e8i	− 1.05154i
$715$	0	0
$716$	9.82393e8	2.67637
$717$	2.85527e8i	0.774623i
$718$	−6.81356e8	−1.84078
$719$	−3.12847e6	−0.00841678	−0.00420839	−	0.999991i	$-0.501340\pi$
$719$	−3.12847e6	−0.00841678	−0.00420839	+	0.999991i	$0.501340\pi$
$720$	1.30278e8	0.349037
$721$	− 6.38876e8i	− 1.70456i
$722$	1.39422e8i	0.370441i
$723$	− 1.31467e8i	− 0.347858i
$724$	−2.28967e8	−0.603334
$725$	− 2.46162e8i	− 0.645962i
$726$	0	0
$727$	−5.03036e8	−1.30917	−0.654584	−	0.755989i	$-0.727156\pi$
$727$	−5.03036e8	−1.30917	−0.654584	+	0.755989i	$0.727156\pi$
$728$	− 3.12523e8i	− 0.810005i
$729$	4.25554e8	1.09843
$730$	4.68308e8	1.20382
$731$	1.21004e8	0.309775
$732$	6.84609e8i	1.74546i
$733$	6.68108e8i	1.69643i	0.529655	+	0.848213i	$0.322321\pi$
$733$	6.68108e8i	1.69643i	−0.529655	+	0.848213i	$0.677679\pi$
$734$	5.45728e8i	1.38003i
$735$	8.48219e7	0.213622
$736$	5.97874e8i	1.49960i
$737$	0	0
$738$	2.07809e7	0.0517005
$739$	− 5.87420e8i	− 1.45551i	−0.685836	−	0.727756i	$-0.740563\pi$
$739$	− 5.87420e8i	− 1.45551i	0.685836	−	0.727756i	$-0.259437\pi$
$740$	−4.38595e8	−1.08235
$741$	−1.08804e8	−0.267417
$742$	1.26640e9	3.09997
$743$	− 3.35744e8i	− 0.818543i	−0.912413	−	0.409272i	$-0.865783\pi$
$743$	− 3.35744e8i	− 0.818543i	0.912413	−	0.409272i	$-0.134217\pi$
$744$	− 6.15691e8i	− 1.49501i
$745$	6.00536e8i	1.45235i
$746$	5.44968e8	1.31267
$747$	3.97594e6i	0.00953845i
$748$	0	0
$749$	2.76143e6	0.00657187
$750$	2.80400e8i	0.664652i
$751$	7.83351e8	1.84943	0.924713	−	0.380666i	$-0.124305\pi$
$751$	7.83351e8	1.84943	0.924713	+	0.380666i	$0.124305\pi$
$752$	−1.81282e8	−0.426286
$753$	−4.06208e8	−0.951401
$754$	− 2.33044e8i	− 0.543656i
$755$	3.55278e8i	0.825521i
$756$	1.12783e9i	2.61023i
$757$	−7.19179e8	−1.65787	−0.828933	−	0.559348i	$-0.811052\pi$
$757$	−7.19179e8	−1.65787	−0.828933	+	0.559348i	$0.811052\pi$
$758$	3.98480e8i	0.914952i
$759$	0	0
$760$	1.17641e9	2.67990
$761$	− 5.02329e8i	− 1.13982i	−0.821709	−	0.569908i	$-0.806979\pi$
$761$	− 5.02329e8i	− 1.13982i	0.821709	−	0.569908i	$-0.193021\pi$
$762$	8.97516e7	0.202851
$763$	7.08936e8	1.59600
$764$	3.69559e7	0.0828712
$765$	4.74963e7i	0.106090i
$766$	− 8.14305e8i	− 1.81176i
$767$	− 5.37342e6i	− 0.0119087i
$768$	−7.18352e8	−1.58582
$769$	2.81032e8i	0.617984i	0.951065	+	0.308992i	$0.0999916\pi$
$769$	2.81032e8i	0.617984i	−0.951065	+	0.308992i	$0.900008\pi$
$770$	0	0
$771$	1.52993e8	0.333817
$772$	1.83943e9i	3.99789i
$773$	−8.13108e8	−1.76039	−0.880197	−	0.474609i	$-0.842590\pi$
$773$	−8.13108e8	−1.76039	−0.880197	+	0.474609i	$0.842590\pi$
$774$	−6.34221e7	−0.136779
$775$	2.26356e8	0.486281
$776$	6.67054e8i	1.42750i
$777$	− 1.72320e8i	− 0.367343i
$778$	− 8.42201e8i	− 1.78845i
$779$	8.54241e7	0.180704
$780$	− 4.21590e8i	− 0.888397i
$781$	0	0
$782$	−6.61969e8	−1.38426
$783$	4.71359e8i	0.981899i
$784$	−1.62158e8	−0.336505
$785$	−3.48743e8	−0.720936
$786$	−7.70786e8	−1.58733
$787$	− 7.44194e8i	− 1.52673i	−0.645967	−	0.763365i	$-0.723546\pi$
$787$	− 7.44194e8i	− 1.52673i	0.645967	−	0.763365i	$-0.276454\pi$
$788$	− 1.45238e9i	− 2.96825i
$789$	3.77174e8i	0.767911i
$790$	1.11535e9	2.26219
$791$	5.72089e8i	1.15594i
$792$	0	0
$793$	−1.33549e8	−0.267807
$794$	− 1.06503e9i	− 2.12766i
$795$	9.57480e8	1.90558
$796$	1.35356e9	2.68372
$797$	−1.99634e8	−0.394329	−0.197165	−	0.980370i	$-0.563173\pi$
$797$	−1.99634e8	−0.394329	−0.197165	+	0.980370i	$0.563173\pi$
$798$	8.24669e8i	1.62282i
$799$	− 6.60914e7i	− 0.129570i
$800$	4.03542e8i	0.788167i
$801$	1.00181e8	0.194934
$802$	− 1.72090e9i	− 3.33605i
$803$	0	0
$804$	5.42052e8	1.04297
$805$	− 9.75503e8i	− 1.87000i
$806$	2.14294e8	0.409265
$807$	−3.95939e8	−0.753368
$808$	−2.28451e9	−4.33071
$809$	1.20683e7i	0.0227929i	0.999935	+	0.0113964i	$0.00362768\pi$
$809$	1.20683e7i	0.0227929i	−0.999935	+	0.0113964i	$0.996372\pi$
$810$	1.05094e9i	1.97753i
$811$	− 7.23042e8i	− 1.35551i	−0.735290	−	0.677753i	$-0.762954\pi$
$811$	− 7.23042e8i	− 1.35551i	0.735290	−	0.677753i	$-0.237046\pi$
$812$	−1.22702e9	−2.29184
$813$	2.45771e8i	0.457360i
$814$	0	0
$815$	1.32257e8	0.244313
$816$	5.53238e8i	1.01822i
$817$	−2.60710e8	−0.478070
$818$	2.57118e7	0.0469757
$819$	−2.71857e7	−0.0494868
$820$	3.30999e8i	0.600323i
$821$	2.99189e8i	0.540649i	0.962769	+	0.270325i	$0.0871310\pi$
$821$	2.99189e8i	0.540649i	−0.962769	+	0.270325i	$0.912869\pi$
$822$	4.88340e8i	0.879239i
$823$	−7.79496e8	−1.39835	−0.699173	−	0.714953i	$-0.746448\pi$
$823$	−7.79496e8	−1.39835	−0.699173	+	0.714953i	$0.746448\pi$
$824$	2.02853e9i	3.62577i
$825$	0	0
$826$	−4.07274e7	−0.0722680
$827$	4.43736e8i	0.784527i	0.919853	+	0.392263i	$0.128308\pi$
$827$	4.43736e8i	0.784527i	−0.919853	+	0.392263i	$0.871692\pi$
$828$	2.41023e8	0.424588
$829$	−7.64000e8	−1.34100	−0.670501	−	0.741909i	$-0.733921\pi$
$829$	−7.64000e8	−1.34100	−0.670501	+	0.741909i	$0.733921\pi$
$830$	−9.11641e7	−0.159437
$831$	− 3.56137e8i	− 0.620604i
$832$	2.77857e7i	0.0482449i
$833$	− 5.91194e7i	− 0.102281i
$834$	1.63278e9	2.81468
$835$	− 7.99127e8i	− 1.37264i
$836$	0	0
$837$	−4.33434e8	−0.739175
$838$	1.26331e9i	2.14673i
$839$	−6.27880e7	−0.106314	−0.0531570	−	0.998586i	$-0.516928\pi$
$839$	−6.27880e7	−0.106314	−0.0531570	+	0.998586i	$0.516928\pi$
$840$	−1.79093e9	−3.02162
$841$	8.20090e7	0.137871
$842$	− 3.10092e8i	− 0.519463i
$843$	9.87037e6i	0.0164760i
$844$	− 1.18708e9i	− 1.97448i
$845$	−7.03437e8	−1.16588
$846$	3.46408e7i	0.0572106i
$847$	0	0
$848$	−1.83046e9	−3.00174
$849$	− 3.39897e8i	− 0.555424i
$850$	−4.46803e8	−0.727544
$851$	−2.98024e8	−0.483574
$852$	2.23080e9	3.60697
$853$	2.36263e8i	0.380670i	0.981719	+	0.190335i	$0.0609573\pi$
$853$	2.36263e8i	0.380670i	−0.981719	+	0.190335i	$0.939043\pi$
$854$	1.01222e9i	1.62519i
$855$	− 1.02334e8i	− 0.163727i
$856$	−8.76798e6	−0.0139791
$857$	4.83150e7i	0.0767609i	0.999263	+	0.0383804i	$0.0122199\pi$
$857$	4.83150e7i	0.0767609i	−0.999263	+	0.0383804i	$0.987780\pi$
$858$	0	0
$859$	−4.09758e8	−0.646469	−0.323235	−	0.946319i	$-0.604770\pi$
$859$	−4.09758e8	−0.646469	−0.323235	+	0.946319i	$0.604770\pi$
$860$	− 1.01019e9i	− 1.58821i
$861$	−1.30046e8	−0.203746
$862$	−2.19519e8	−0.342729
$863$	−4.79911e8	−0.746670	−0.373335	−	0.927697i	$-0.621786\pi$
$863$	−4.79911e8	−0.746670	−0.373335	+	0.927697i	$0.621786\pi$
$864$	− 7.72715e8i	− 1.19806i
$865$	− 1.32817e9i	− 2.05213i
$866$	4.61834e8i	0.711102i
$867$	4.02330e8	0.617341
$868$	− 1.12830e9i	− 1.72530i
$869$	0	0
$870$	−1.33547e9	−2.02804
$871$	1.05740e8i	0.160024i
$872$	−2.25098e9	−3.39486
$873$	5.80256e7	0.0872122
$874$	1.42625e9	2.13630
$875$	2.87999e8i	0.429899i
$876$	− 7.24094e8i	− 1.07717i
$877$	6.02378e8i	0.893038i	0.894774	+	0.446519i	$0.147336\pi$
$877$	6.02378e8i	0.893038i	−0.894774	+	0.446519i	$0.852664\pi$
$878$	1.03890e9	1.53493
$879$	− 6.53556e8i	− 0.962313i
$880$	0	0
$881$	6.92476e8	1.01269	0.506346	−	0.862331i	$-0.330996\pi$
$881$	6.92476e8	1.01269	0.506346	+	0.862331i	$0.330996\pi$
$882$	3.09865e7i	0.0451613i
$883$	−9.18743e8	−1.33448	−0.667240	−	0.744843i	$-0.732524\pi$
$883$	−9.18743e8	−1.33448	−0.667240	+	0.744843i	$0.732524\pi$
$884$	−2.93841e8	−0.425359
$885$	−3.07926e7	−0.0444239
$886$	− 6.46152e8i	− 0.929039i
$887$	8.58633e8i	1.23037i	0.788382	+	0.615187i	$0.210919\pi$
$887$	8.58633e8i	1.23037i	−0.788382	+	0.615187i	$0.789081\pi$
$888$	5.47142e8i	0.781378i
$889$	9.21839e7	0.131205
$890$	2.29705e9i	3.25837i
$891$	0	0
$892$	1.51996e9	2.14160
$893$	1.42398e8i	0.199963i
$894$	1.33667e9	1.87073
$895$	1.09820e9	1.53183
$896$	−6.73517e8	−0.936321
$897$	− 2.86469e8i	− 0.396918i
$898$	− 2.40259e9i	− 3.31780i
$899$	− 4.71554e8i	− 0.649012i
$900$	1.62681e8	0.223157
$901$	− 6.67346e8i	− 0.912382i
$902$	0	0
$903$	3.96894e8	0.539029
$904$	− 1.81647e9i	− 2.45880i
$905$	−2.55958e8	−0.345320
$906$	7.90777e8	1.06333
$907$	−6.58009e8	−0.881880	−0.440940	−	0.897536i	$-0.645355\pi$
$907$	−6.58009e8	−0.881880	−0.440940	+	0.897536i	$0.645355\pi$
$908$	− 7.17769e8i	− 0.958798i
$909$	1.98725e8i	0.264582i
$910$	− 6.23340e8i	− 0.827181i
$911$	5.36332e8	0.709380	0.354690	−	0.934984i	$-0.384586\pi$
$911$	5.36332e8	0.709380	0.354690	+	0.934984i	$0.384586\pi$
$912$	− 1.19199e9i	− 1.57140i
$913$	0	0
$914$	5.72204e8	0.749397
$915$	7.65308e8i	0.999018i
$916$	2.56384e9	3.33584
$917$	−7.91675e8	−1.02669
$918$	8.55553e8	1.10591
$919$	5.71950e8i	0.736904i	0.929647	+	0.368452i	$0.120112\pi$
$919$	5.71950e8i	0.736904i	−0.929647	+	0.368452i	$0.879888\pi$
$920$	3.09738e9i	3.97768i
$921$	− 7.91977e8i	− 1.01376i
$922$	3.89051e8	0.496379
$923$	4.35170e8i	0.553419i
$924$	0	0
$925$	−2.01155e8	−0.254159
$926$	− 8.89604e8i	− 1.12038i
$927$	1.76458e8	0.221514
$928$	8.40673e8	1.05192
$929$	−3.67676e8	−0.458583	−0.229292	−	0.973358i	$-0.573641\pi$
$929$	−3.67676e8	−0.458583	−0.229292	+	0.973358i	$0.573641\pi$
$930$	− 1.22802e9i	− 1.52671i
$931$	1.27376e8i	0.157848i
$932$	− 2.87686e9i	− 3.55362i
$933$	1.80763e8	0.222569
$934$	1.30136e9i	1.59720i
$935$	0	0
$936$	8.63189e7	0.105264
$937$	− 6.22648e8i	− 0.756875i	−0.925627	−	0.378437i	$-0.876462\pi$
$937$	− 6.22648e8i	− 0.756875i	0.925627	−	0.378437i	$-0.123538\pi$
$938$	8.01448e8	0.971106
$939$	6.62559e8	0.800254
$940$	−5.51760e8	−0.664304
$941$	1.31363e9i	1.57653i	0.615335	+	0.788266i	$0.289021\pi$
$941$	1.31363e9i	1.57653i	−0.615335	+	0.788266i	$0.710979\pi$
$942$	7.76230e8i	0.928620i
$943$	2.24913e8i	0.268213i
$944$	5.88677e7	0.0699780
$945$	1.26078e9i	1.49397i
$946$	0	0
$947$	1.01794e9	1.19859	0.599297	−	0.800527i	$-0.295447\pi$
$947$	1.01794e9	1.19859	0.599297	+	0.800527i	$0.295447\pi$
$948$	− 1.72454e9i	− 2.02418i
$949$	1.41252e8	0.165270
$950$	9.62664e8	1.12280
$951$	4.15100e8	0.482627
$952$	1.24824e9i	1.44673i
$953$	− 4.87341e8i	− 0.563059i	−0.959553	−	0.281530i	$-0.909158\pi$
$953$	− 4.87341e8i	− 0.563059i	0.959553	−	0.281530i	$-0.0908418\pi$
$954$	3.49779e8i	0.402855i
$955$	4.13122e7	0.0474316
$956$	− 1.66140e9i	− 1.90152i
$957$	0	0
$958$	1.56149e9	1.77600
$959$	5.01575e8i	0.568695i
$960$	1.59227e8	0.179971
$961$	−4.53890e8	−0.511423
$962$	−1.90435e8	−0.213906
$963$	762708.i	0 0.000854042i
$964$	7.64968e8i	0.853911i
$965$	2.05626e9i	2.28821i
$966$	−2.17127e9	−2.40870
$967$	8.21587e8i	0.908602i	0.890848	+	0.454301i	$0.150111\pi$
$967$	8.21587e8i	0.908602i	−0.890848	+	0.454301i	$0.849889\pi$
$968$	0	0
$969$	4.34572e8	0.477628
$970$	1.33047e9i	1.45777i
$971$	−3.70971e8	−0.405212	−0.202606	−	0.979260i	$-0.564941\pi$
$971$	−3.70971e8	−0.405212	−0.202606	+	0.979260i	$0.564941\pi$
$972$	−5.84523e8	−0.636506
$973$	1.67703e9	1.82055
$974$	2.24444e7i	0.0242902i
$975$	− 1.93356e8i	− 0.208614i
$976$	− 1.46308e9i	− 1.57369i
$977$	−6.99539e8	−0.750116	−0.375058	−	0.927001i	$-0.622377\pi$
$977$	−6.99539e8	−0.750116	−0.375058	+	0.927001i	$0.622377\pi$
$978$	− 2.94377e8i	− 0.314693i
$979$	0	0
$980$	−4.93554e8	−0.524393
$981$	1.95808e8i	0.207407i
$982$	−5.55089e8	−0.586176
$983$	5.54544e8	0.583816	0.291908	−	0.956446i	$-0.405710\pi$
$983$	5.54544e8	0.583816	0.291908	+	0.956446i	$0.405710\pi$
$984$	4.12917e8	0.433389
$985$	− 1.62358e9i	− 1.69889i
$986$	9.30797e8i	0.971012i
$987$	− 2.16781e8i	− 0.225460i
$988$	6.33098e8	0.656447
$989$	− 6.86422e8i	− 0.709582i
$990$	0	0
$991$	−1.59329e9	−1.63710	−0.818549	−	0.574437i	$-0.805221\pi$
$991$	−1.59329e9	−1.63710	−0.818549	+	0.574437i	$0.805221\pi$
$992$	7.73035e8i	0.791888i
$993$	−1.19208e9	−1.21747
$994$	3.29834e9	3.35843
$995$	1.51311e9	1.53604
$996$	1.40957e8i	0.142662i
$997$	− 1.60547e8i	− 0.162000i	−0.996714	−	0.0810001i	$-0.974189\pi$
$997$	− 1.60547e8i	− 0.162000i	0.996714	−	0.0810001i	$-0.0258114\pi$
$998$	8.34362e8i	0.839388i
$999$	3.85178e8	0.386336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.7.b.c.120.20		20
11.3	even	5		11.7.d.a.2.5	✓	20
11.7	odd	10		11.7.d.a.6.5	yes	20
11.10	odd	2	inner	121.7.b.c.120.1		20
33.14	odd	10		99.7.k.a.46.1		20
33.29	even	10		99.7.k.a.28.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.2.5	✓	20	11.3	even	5
11.7.d.a.6.5	yes	20	11.7	odd	10
99.7.k.a.28.1		20	33.29	even	10
99.7.k.a.46.1		20	33.14	odd	10
121.7.b.c.120.1		20	11.10	odd	2	inner
121.7.b.c.120.20		20	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	121.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+14.4779i q^{2} +25.0244 q^{3} -145.610 q^{4} -162.774 q^{5} +362.301i q^{6} +372.119i q^{7} -1181.54i q^{8} -102.779 q^{9} +O(q^{10})\)	\(q+14.4779i q^{2} +25.0244 q^{3} -145.610 q^{4} -162.774 q^{5} +362.301i q^{6} +372.119i q^{7} -1181.54i q^{8} -102.779 q^{9} -2356.62i q^{10} -3643.79 q^{12} -710.808i q^{13} -5387.51 q^{14} -4073.31 q^{15} +7787.16 q^{16} +2839.03i q^{17} -1488.03i q^{18} -6116.85i q^{19} +23701.4 q^{20} +9312.06i q^{21} +16105.1 q^{23} -29567.3i q^{24} +10870.3 q^{25} +10291.0 q^{26} -20814.8 q^{27} -54184.2i q^{28} -22645.4i q^{29} -58973.1i q^{30} +20823.4 q^{31} +37123.4i q^{32} -41103.2 q^{34} -60571.3i q^{35} +14965.7 q^{36} -18505.0 q^{37} +88559.2 q^{38} -17787.6i q^{39} +192323. i q^{40} +13965.4i q^{41} -134819. q^{42} -42621.5i q^{43} +16729.8 q^{45} +233167. i q^{46} -23279.6 q^{47} +194869. q^{48} -20823.8 q^{49} +157379. i q^{50} +71044.9i q^{51} +103501. i q^{52} -235062. q^{53} -301354. i q^{54} +439673. q^{56} -153071. i q^{57} +327858. q^{58} +7559.59 q^{59} +593114. q^{60} -187883. i q^{61} +301479. i q^{62} -38246.2i q^{63} -39090.3 q^{64} +115701. i q^{65} -148760. q^{67} -413390. i q^{68} +403019. q^{69} +876945. q^{70} -612219. q^{71} +121438. i q^{72} +198720. i q^{73} -267914. i q^{74} +272022. q^{75} +890673. i q^{76} +257526. q^{78} +473282. i q^{79} -1.26754e6 q^{80} -445951. q^{81} -202189. q^{82} -38684.2i q^{83} -1.35593e6i q^{84} -462119. i q^{85} +617070. q^{86} -566688. i q^{87} -974721. q^{89} +242212. i q^{90} +264506. q^{91} -2.34505e6 q^{92} +521093. q^{93} -337040. i q^{94} +995663. i q^{95} +928990. i q^{96} -564565. q^{97} -301485. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 46 q^{3} - 420 q^{4} - 174 q^{5} + 66 q^{9}+O(q^{10}) \) 20 * q + 46 * q^3 - 420 * q^4 - 174 * q^5 + 66 * q^9	\( 20 q + 46 q^{3} - 420 q^{4} - 174 q^{5} + 66 q^{9} - 3006 q^{12} + 7180 q^{14} - 6260 q^{15} + 30740 q^{16} + 5384 q^{20} + 7816 q^{23} + 98014 q^{25} + 44540 q^{26} + 95428 q^{27} - 2806 q^{31} - 228190 q^{34} + 646034 q^{36} + 74594 q^{37} + 571430 q^{38} - 467120 q^{42} - 805524 q^{45} + 706194 q^{47} + 379386 q^{48} + 646590 q^{49} - 900854 q^{53} - 862620 q^{56} + 1621260 q^{58} + 741246 q^{59} + 1763880 q^{60} + 232380 q^{64} - 960956 q^{67} + 1742196 q^{69} + 1180480 q^{70} - 622350 q^{71} + 480120 q^{75} + 1703080 q^{78} - 2615744 q^{80} + 299384 q^{81} + 287430 q^{82} + 670190 q^{86} + 1111620 q^{89} - 1964640 q^{91} - 9325476 q^{92} - 3775388 q^{93} - 308266 q^{97}+O(q^{100}) \) 20 * q + 46 * q^3 - 420 * q^4 - 174 * q^5 + 66 * q^9 - 3006 * q^12 + 7180 * q^14 - 6260 * q^15 + 30740 * q^16 + 5384 * q^20 + 7816 * q^23 + 98014 * q^25 + 44540 * q^26 + 95428 * q^27 - 2806 * q^31 - 228190 * q^34 + 646034 * q^36 + 74594 * q^37 + 571430 * q^38 - 467120 * q^42 - 805524 * q^45 + 706194 * q^47 + 379386 * q^48 + 646590 * q^49 - 900854 * q^53 - 862620 * q^56 + 1621260 * q^58 + 741246 * q^59 + 1763880 * q^60 + 232380 * q^64 - 960956 * q^67 + 1742196 * q^69 + 1180480 * q^70 - 622350 * q^71 + 480120 * q^75 + 1703080 * q^78 - 2615744 * q^80 + 299384 * q^81 + 287430 * q^82 + 670190 * q^86 + 1111620 * q^89 - 1964640 * q^91 - 9325476 * q^92 - 3775388 * q^93 - 308266 * q^97

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