LMFDB - Embedded newform 144.4.i.d.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(49,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("144.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.i (of order $3$, degree $2$, 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:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6831243.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 49x^{2} + 48 $ x^6 + 13x^4 + 49x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.1
Root			$2.63162i$ of defining polynomial
Character	$\chi$	$=$	144.97
Dual form			144.4.i.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.16718 - 0.547914i) q^{3} +(2.44901 + 4.24182i) q^{5} +(-5.32725 + 9.22708i) q^{7} +(26.3996 + 5.66234i) q^{9} +O(q^{10})$	\(q+(-5.16718 - 0.547914i) q^{3} +(2.44901 + 4.24182i) q^{5} +(-5.32725 + 9.22708i) q^{7} +(26.3996 + 5.66234i) q^{9} +(17.7268 - 30.7038i) q^{11} +(-36.3501 - 62.9603i) q^{13} +(-10.3304 - 23.2601i) q^{15} -127.417 q^{17} +46.3913 q^{19} +(32.5825 - 44.7591i) q^{21} +(-65.5739 - 113.577i) q^{23} +(50.5047 - 87.4766i) q^{25} +(-133.309 - 43.7231i) q^{27} +(68.7549 - 119.087i) q^{29} +(-53.0640 - 91.9096i) q^{31} +(-108.421 + 148.939i) q^{33} -52.1861 q^{35} +137.401 q^{37} +(153.331 + 345.244i) q^{39} +(35.8986 + 62.1782i) q^{41} +(188.459 - 326.421i) q^{43} +(40.6343 + 125.849i) q^{45} +(-306.813 + 531.416i) q^{47} +(114.741 + 198.737i) q^{49} +(658.388 + 69.8136i) q^{51} -431.757 q^{53} +173.653 q^{55} +(-239.712 - 25.4184i) q^{57} +(-142.878 - 247.471i) q^{59} +(21.9682 - 38.0500i) q^{61} +(-192.884 + 213.426i) q^{63} +(178.044 - 308.381i) q^{65} +(-22.6052 - 39.1533i) q^{67} +(276.602 + 622.804i) q^{69} -357.328 q^{71} +530.718 q^{73} +(-308.897 + 424.336i) q^{75} +(188.871 + 327.134i) q^{77} +(-97.5540 + 168.969i) q^{79} +(664.876 + 298.967i) q^{81} +(380.352 - 658.789i) q^{83} +(-312.047 - 540.480i) q^{85} +(-420.519 + 577.673i) q^{87} -1214.67 q^{89} +774.586 q^{91} +(223.833 + 503.988i) q^{93} +(113.613 + 196.783i) q^{95} +(552.402 - 956.788i) q^{97} +(641.836 - 710.191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 6 q^{5} + 6 q^{7} + 39 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 6 * q^5 + 6 * q^7 + 39 * q^9	$ 6 q + 3 q^{3} + 6 q^{5} + 6 q^{7} + 39 q^{9} - 51 q^{11} + 12 q^{13} + 180 q^{15} - 222 q^{17} - 30 q^{19} - 120 q^{21} - 210 q^{23} - 3 q^{25} - 648 q^{27} + 456 q^{29} - 48 q^{31} - 603 q^{33} + 1104 q^{35} - 96 q^{37} + 36 q^{39} + 897 q^{41} - 129 q^{43} + 1494 q^{45} - 522 q^{47} - 225 q^{49} + 1647 q^{51} - 2208 q^{53} + 216 q^{55} - 645 q^{57} - 453 q^{59} - 402 q^{61} - 1896 q^{63} + 1110 q^{65} + 213 q^{67} - 198 q^{69} - 120 q^{71} + 750 q^{73} - 921 q^{75} + 1128 q^{77} - 552 q^{79} - 549 q^{81} + 612 q^{83} + 1188 q^{85} + 1386 q^{87} - 924 q^{89} + 264 q^{91} - 1998 q^{93} + 2184 q^{95} + 93 q^{97} + 1854 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 6 * q^5 + 6 * q^7 + 39 * q^9 - 51 * q^11 + 12 * q^13 + 180 * q^15 - 222 * q^17 - 30 * q^19 - 120 * q^21 - 210 * q^23 - 3 * q^25 - 648 * q^27 + 456 * q^29 - 48 * q^31 - 603 * q^33 + 1104 * q^35 - 96 * q^37 + 36 * q^39 + 897 * q^41 - 129 * q^43 + 1494 * q^45 - 522 * q^47 - 225 * q^49 + 1647 * q^51 - 2208 * q^53 + 216 * q^55 - 645 * q^57 - 453 * q^59 - 402 * q^61 - 1896 * q^63 + 1110 * q^65 + 213 * q^67 - 198 * q^69 - 120 * q^71 + 750 * q^73 - 921 * q^75 + 1128 * q^77 - 552 * q^79 - 549 * q^81 + 612 * q^83 + 1188 * q^85 + 1386 * q^87 - 924 * q^89 + 264 * q^91 - 1998 * q^93 + 2184 * q^95 + 93 * q^97 + 1854 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−5.16718	−	0.547914i	−0.994425	−	0.105446i
$3$	−5.16718	−	0.547914i	−0.994425	−	0.105446i
$4$		0			0
$5$	2.44901	+	4.24182i	0.219047	+	0.379400i	0.954517	−	0.298157i	$-0.0963720\pi$
$5$	2.44901	+	4.24182i	0.219047	+	0.379400i	−0.735470	+	0.677557i	$0.763039\pi$
$6$		0			0
$7$	−5.32725	+	9.22708i	−0.287645	+	0.498215i	−0.973247	−	0.229761i	$-0.926206\pi$
$7$	−5.32725	+	9.22708i	−0.287645	+	0.498215i	0.685602	+	0.727976i	$0.259539\pi$
$8$		0			0
$9$	26.3996	+	5.66234i	0.977762	+	0.209716i
$10$		0			0
$11$	17.7268	−	30.7038i	0.485895	−	0.841594i	−0.513974	−	0.857806i	$-0.671827\pi$
$11$	17.7268	−	30.7038i	0.485895	−	0.841594i	0.999869	+	0.0162115i	$0.00516051\pi$
$12$		0			0
$13$	−36.3501	−	62.9603i	−0.775517	−	1.34323i	−0.934504	−	0.355954i	$-0.884156\pi$
$13$	−36.3501	−	62.9603i	−0.775517	−	1.34323i	0.158987	−	0.987281i	$-0.449177\pi$
$14$		0			0
$15$	−10.3304	−	23.2601i	−0.177819	−	0.400382i
$16$		0			0
$17$	−127.417			−1.81784			−0.908918	−	0.416975i	$-0.863090\pi$
$17$	−127.417			−1.81784			−0.908918	+	0.416975i	$0.863090\pi$
$18$		0			0
$19$	46.3913			0.560152			0.280076	−	0.959978i	$-0.409640\pi$
$19$	46.3913			0.560152			0.280076	+	0.959978i	$0.409640\pi$
$20$		0			0
$21$	32.5825	−	44.7591i	0.338576	−	0.465107i
$22$		0			0
$23$	−65.5739	−	113.577i	−0.594483	−	1.02967i	−0.993620	−	0.112783i	$-0.964024\pi$
$23$	−65.5739	−	113.577i	−0.594483	−	1.02967i	0.399137	−	0.916891i	$-0.369310\pi$
$24$		0			0
$25$	50.5047	−	87.4766i	0.404037	−	0.699813i
$26$		0			0
$27$	−133.309	−	43.7231i	−0.950197	−	0.311648i
$28$		0			0
$29$	68.7549	−	119.087i	0.440258	−	0.762548i	−0.557451	−	0.830210i	$-0.688220\pi$
$29$	68.7549	−	119.087i	0.440258	−	0.762548i	0.997708	+	0.0676615i	$0.0215538\pi$
$30$		0			0
$31$	−53.0640	−	91.9096i	−0.307438	−	0.532498i	0.670363	−	0.742033i	$-0.266138\pi$
$31$	−53.0640	−	91.9096i	−0.307438	−	0.532498i	−0.977801	+	0.209535i	$0.932805\pi$
$32$		0			0
$33$	−108.421	+	148.939i	−0.571929	+	0.785667i
$34$		0			0
$35$	−52.1861			−0.252030
$36$		0			0
$37$	137.401			0.610500			0.305250	−	0.952272i	$-0.401260\pi$
$37$	137.401			0.610500			0.305250	+	0.952272i	$0.401260\pi$
$38$		0			0
$39$	153.331	+	345.244i	0.629554	+	1.41752i
$40$		0			0
$41$	35.8986	+	62.1782i	0.136742	+	0.236844i	0.926261	−	0.376881i	$-0.123004\pi$
$41$	35.8986	+	62.1782i	0.136742	+	0.236844i	−0.789520	+	0.613725i	$0.789670\pi$
$42$		0			0
$43$	188.459	−	326.421i	0.668367	−	1.15765i	−0.309994	−	0.950739i	$-0.600327\pi$
$43$	188.459	−	326.421i	0.668367	−	1.15765i	0.978361	−	0.206907i	$-0.0663396\pi$
$44$		0			0
$45$	40.6343	+	125.849i	0.134609	+	0.416900i
$46$		0			0
$47$	−306.813	+	531.416i	−0.952198	+	1.64926i	−0.211544	+	0.977368i	$0.567849\pi$
$47$	−306.813	+	531.416i	−0.952198	+	1.64926i	−0.740654	+	0.671887i	$0.765484\pi$
$48$		0			0
$49$	114.741	+	198.737i	0.334521	+	0.579407i
$50$		0			0
$51$	658.388	+	69.8136i	1.80770	+	0.191684i
$52$		0			0
$53$	−431.757			−1.11899			−0.559494	−	0.828835i	$-0.689004\pi$
$53$	−431.757			−1.11899			−0.559494	+	0.828835i	$0.689004\pi$
$54$		0			0
$55$	173.653			0.425734
$56$		0			0
$57$	−239.712	−	25.4184i	−0.557029	−	0.0590658i
$58$		0			0
$59$	−142.878	−	247.471i	−0.315272	−	0.546068i	0.664223	−	0.747535i	$-0.268763\pi$
$59$	−142.878	−	247.471i	−0.315272	−	0.546068i	−0.979495	+	0.201467i	$0.935429\pi$
$60$		0			0
$61$	21.9682	−	38.0500i	0.0461104	−	0.0798656i	−0.842049	−	0.539401i	$-0.818651\pi$
$61$	21.9682	−	38.0500i	0.0461104	−	0.0798656i	0.888159	+	0.459535i	$0.151984\pi$
$62$		0			0
$63$	−192.884	+	213.426i	−0.385732	+	0.426812i
$64$		0			0
$65$	178.044	−	308.381i	0.339748	−	0.588462i
$66$		0			0
$67$	−22.6052	−	39.1533i	−0.0412188	−	0.0713930i	0.844680	−	0.535272i	$-0.179791\pi$
$67$	−22.6052	−	39.1533i	−0.0412188	−	0.0713930i	−0.885899	+	0.463879i	$0.846457\pi$
$68$		0			0
$69$	276.602	+	622.804i	0.482593	+	1.08662i
$70$		0			0
$71$	−357.328			−0.597282			−0.298641	−	0.954366i	$-0.596533\pi$
$71$	−357.328			−0.597282			−0.298641	+	0.954366i	$0.596533\pi$
$72$		0			0
$73$	530.718			0.850901			0.425451	−	0.904982i	$-0.360116\pi$
$73$	530.718			0.850901			0.425451	+	0.904982i	$0.360116\pi$
$74$		0			0
$75$	−308.897	+	424.336i	−0.475577	+	0.653307i
$76$		0			0
$77$	188.871	+	327.134i	0.279530	+	0.484160i
$78$		0			0
$79$	−97.5540	+	168.969i	−0.138933	+	0.240639i	−0.927093	−	0.374832i	$-0.877701\pi$
$79$	−97.5540	+	168.969i	−0.138933	+	0.240639i	0.788160	+	0.615470i	$0.211034\pi$
$80$		0			0
$81$	664.876	+	298.967i	0.912038	+	0.410106i
$82$		0			0
$83$	380.352	−	658.789i	0.503001	−	0.871223i	−0.496993	−	0.867754i	$-0.665563\pi$
$83$	380.352	−	658.789i	0.503001	−	0.871223i	0.999994	−	0.00346848i	$-0.00110405\pi$
$84$		0			0
$85$	−312.047	−	540.480i	−0.398191	−	0.689686i
$86$		0			0
$87$	−420.519	+	577.673i	−0.518211	+	0.711874i
$88$		0			0
$89$	−1214.67			−1.44668			−0.723339	−	0.690493i	$-0.757393\pi$
$89$	−1214.67			−1.44668			−0.723339	+	0.690493i	$0.757393\pi$
$90$		0			0
$91$	774.586			0.892293
$92$		0			0
$93$	223.833	+	503.988i	0.249574	+	0.561948i
$94$		0			0
$95$	113.613	+	196.783i	0.122699	+	0.212522i
$96$		0			0
$97$	552.402	−	956.788i	0.578226	−	1.00152i	−0.417457	−	0.908697i	$-0.637078\pi$
$97$	552.402	−	956.788i	0.578226	−	1.00152i	0.995683	−	0.0928202i	$-0.0295882\pi$
$98$		0			0
$99$	641.836	−	710.191i	0.651586	−	0.720979i
$100$		0			0
$101$	−508.962	+	881.547i	−0.501421	+	0.868487i	0.498577	+	0.866845i	$0.333856\pi$
$101$	−508.962	+	881.547i	−0.501421	+	0.868487i	−0.999999	+	0.00164208i	$0.999477\pi$
$102$		0			0
$103$	416.128	+	720.756i	0.398081	+	0.689497i	0.993489	−	0.113927i	$-0.0363429\pi$
$103$	416.128	+	720.756i	0.398081	+	0.689497i	−0.595408	+	0.803423i	$0.703010\pi$
$104$		0			0
$105$	269.655	+	28.5935i	0.250625	+	0.0265756i
$106$		0			0
$107$	−481.992			−0.435476			−0.217738	−	0.976007i	$-0.569868\pi$
$107$	−481.992			−0.435476			−0.217738	+	0.976007i	$0.569868\pi$
$108$		0			0
$109$	−904.531			−0.794847			−0.397424	−	0.917635i	$-0.630096\pi$
$109$	−904.531			−0.794847			−0.397424	+	0.917635i	$0.630096\pi$
$110$		0			0
$111$	−709.974	−	75.2837i	−0.607097	−	0.0643749i
$112$		0			0
$113$	−400.494	−	693.675i	−0.333410	−	0.577482i	0.649768	−	0.760132i	$-0.274866\pi$
$113$	−400.494	−	693.675i	−0.333410	−	0.577482i	−0.983178	+	0.182650i	$0.941533\pi$
$114$		0			0
$115$	321.183	−	556.305i	0.260439	−	0.451093i
$116$		0			0
$117$	−603.126	−	1867.95i	−0.476573	−	1.47600i
$118$		0			0
$119$	678.784	−	1175.69i	0.522891	−	0.905673i
$120$		0			0
$121$	37.0186	+	64.1181i	0.0278126	+	0.0481729i
$122$		0			0
$123$	−151.426	−	340.955i	−0.111005	−	0.249942i
$124$		0			0
$125$	1107.00			0.792105
$126$		0			0
$127$	−1755.04			−1.22626			−0.613129	−	0.789982i	$-0.710090\pi$
$127$	−1755.04			−1.22626			−0.613129	+	0.789982i	$0.710090\pi$
$128$		0			0
$129$	−1152.65	+	1583.42i	−0.786710	+	1.08071i
$130$		0			0
$131$	551.870	+	955.868i	0.368070	+	0.637516i	0.989264	−	0.146141i	$-0.0466854\pi$
$131$	551.870	+	955.868i	0.368070	+	0.637516i	−0.621194	+	0.783657i	$0.713352\pi$
$132$		0			0
$133$	−247.138	+	428.056i	−0.161125	+	0.279076i
$134$		0			0
$135$	−141.010	−	672.551i	−0.0898981	−	0.428770i
$136$		0			0
$137$	1063.25	−	1841.61i	0.663064	−	1.14846i	−0.316742	−	0.948512i	$-0.602589\pi$
$137$	1063.25	−	1841.61i	0.663064	−	1.14846i	0.979806	−	0.199949i	$-0.0640777\pi$
$138$		0			0
$139$	−1127.73	−	1953.29i	−0.688151	−	1.19191i	−0.972435	−	0.233173i	$-0.925089\pi$
$139$	−1127.73	−	1953.29i	−0.688151	−	1.19191i	0.284284	−	0.958740i	$-0.408244\pi$
$140$		0			0
$141$	1876.53	−	2577.82i	1.12080	−	1.53966i
$142$		0			0
$143$	−2577.49			−1.50728
$144$		0			0
$145$	673.527			0.385748
$146$		0			0
$147$	−483.996	−	1089.78i	−0.271560	−	0.611451i
$148$		0			0
$149$	342.725	+	593.617i	0.188437	+	0.326383i	0.944729	−	0.327851i	$-0.106324\pi$
$149$	342.725	+	593.617i	0.188437	+	0.326383i	−0.756292	+	0.654234i	$0.772991\pi$
$150$		0			0
$151$	270.165	−	467.939i	0.145601	−	0.252188i	−0.783996	−	0.620766i	$-0.786822\pi$
$151$	270.165	−	467.939i	0.145601	−	0.252188i	0.929597	+	0.368578i	$0.120155\pi$
$152$		0			0
$153$	−3363.76	−	721.480i	−1.77741	−	0.381230i
$154$		0			0
$155$	259.909	−	450.176i	0.134686	−	0.233284i
$156$		0			0
$157$	236.664	+	409.913i	0.120304	+	0.208373i	0.919888	−	0.392182i	$-0.128280\pi$
$157$	236.664	+	409.913i	0.120304	+	0.208373i	−0.799583	+	0.600555i	$0.794946\pi$
$158$		0			0
$159$	2230.97	+	236.565i	1.11275	+	0.117993i
$160$		0			0
$161$	1397.31			0.683999
$162$		0			0
$163$	198.981			0.0956160			0.0478080	−	0.998857i	$-0.484776\pi$
$163$	198.981			0.0956160			0.0478080	+	0.998857i	$0.484776\pi$
$164$		0			0
$165$	−897.298	−	95.1469i	−0.423361	−	0.0448920i
$166$		0			0
$167$	2137.82	+	3702.82i	0.990598	+	1.71577i	0.613778	+	0.789479i	$0.289649\pi$
$167$	2137.82	+	3702.82i	0.990598	+	1.71577i	0.376819	+	0.926287i	$0.377018\pi$
$168$		0			0
$169$	−1544.17	+	2674.57i	−0.702852	+	1.21738i
$170$		0			0
$171$	1224.71	+	262.683i	0.547696	+	0.117473i
$172$		0			0
$173$	−7.55237	+	13.0811i	−0.00331905	+	0.00574877i	−0.867680	−	0.497123i	$-0.834390\pi$
$173$	−7.55237	+	13.0811i	−0.00331905	+	0.00574877i	0.864361	+	0.502872i	$0.167723\pi$
$174$		0			0
$175$	538.102	+	932.021i	0.232438	+	0.402595i
$176$		0			0
$177$	602.682	+	1357.01i	0.255934	+	0.576268i
$178$		0			0
$179$	309.915			0.129408			0.0647042	−	0.997904i	$-0.479390\pi$
$179$	309.915			0.129408			0.0647042	+	0.997904i	$0.479390\pi$
$180$		0			0
$181$	−2253.32			−0.925348			−0.462674	−	0.886529i	$-0.653110\pi$
$181$	−2253.32			−0.925348			−0.462674	+	0.886529i	$0.653110\pi$
$182$		0			0
$183$	−134.362	+	184.575i	−0.0542749	+	0.0745582i
$184$		0			0
$185$	336.496	+	582.828i	0.133728	+	0.231624i
$186$		0			0
$187$	−2258.70	+	3912.19i	−0.883277	+	1.52988i
$188$		0			0
$189$	1113.61	−	997.128i	0.428587	−	0.383759i
$190$		0			0
$191$	1849.28	−	3203.04i	0.700571	−	1.21342i	−0.267695	−	0.963504i	$-0.586262\pi$
$191$	1849.28	−	3203.04i	0.700571	−	1.21342i	0.968266	−	0.249921i	$-0.0804046\pi$
$192$		0			0
$193$	1781.64	+	3085.89i	0.664482	+	1.15092i	0.979425	+	0.201807i	$0.0646813\pi$
$193$	1781.64	+	3085.89i	0.664482	+	1.15092i	−0.314943	+	0.949111i	$0.601985\pi$
$194$		0			0
$195$	−1088.95	+	1495.91i	−0.399905	+	0.549356i
$196$		0			0
$197$	89.0014			0.0321883			0.0160941	−	0.999870i	$-0.494877\pi$
$197$	89.0014			0.0321883			0.0160941	+	0.999870i	$0.494877\pi$
$198$		0			0
$199$	−287.103			−0.102272			−0.0511362	−	0.998692i	$-0.516284\pi$
$199$	−287.103			−0.102272			−0.0511362	+	0.998692i	$0.516284\pi$
$200$		0			0
$201$	95.3524	+	214.698i	0.0334609	+	0.0753414i
$202$		0			0
$203$	732.550	+	1268.81i	0.253276	+	0.438686i
$204$		0			0
$205$	−175.832	+	304.550i	−0.0599056	+	0.103760i
$206$		0			0
$207$	−1088.01	−	3369.69i	−0.365323	−	1.13145i
$208$		0			0
$209$	822.371	−	1424.39i	0.272175	−	0.471421i
$210$		0			0
$211$	2529.93	+	4381.97i	0.825438	+	1.42970i	0.901584	+	0.432605i	$0.142405\pi$
$211$	2529.93	+	4381.97i	0.825438	+	1.42970i	−0.0761454	+	0.997097i	$0.524261\pi$
$212$		0			0
$213$	1846.38	+	195.785i	0.593952	+	0.0629810i
$214$		0			0
$215$	1846.16			0.585614
$216$		0			0
$217$	1130.74			0.353732
$218$		0			0
$219$	−2742.32	−	290.787i	−0.846157	−	0.0897242i
$220$		0			0
$221$	4631.63	+	8022.23i	1.40976	+	2.44178i
$222$		0			0
$223$	−199.857	+	346.162i	−0.0600153	+	0.103949i	−0.894472	−	0.447124i	$-0.852448\pi$
$223$	−199.857	+	346.162i	−0.0600153	+	0.103949i	0.834457	+	0.551073i	$0.185782\pi$
$224$		0			0
$225$	1828.62	−	2023.37i	0.541815	−	0.599518i
$226$		0			0
$227$	−187.709	+	325.121i	−0.0548840	+	0.0950619i	−0.892162	−	0.451715i	$-0.850812\pi$
$227$	−187.709	+	325.121i	−0.0548840	+	0.0950619i	0.837278	+	0.546777i	$0.184146\pi$
$228$		0			0
$229$	−2413.28	−	4179.93i	−0.696394	−	1.20619i	−0.969709	−	0.244265i	$-0.921453\pi$
$229$	−2413.28	−	4179.93i	−0.696394	−	1.20619i	0.273315	−	0.961925i	$-0.411880\pi$
$230$		0			0
$231$	−796.689	−	1793.84i	−0.226919	−	0.510936i
$232$		0			0
$233$	−3858.19			−1.08480			−0.542401	−	0.840120i	$-0.682484\pi$
$233$	−3858.19			−1.08480			−0.542401	+	0.840120i	$0.682484\pi$
$234$		0			0
$235$	−3005.56			−0.834303
$236$		0			0
$237$	596.660	−	819.640i	0.163533	−	0.224647i
$238$		0			0
$239$	652.603	+	1130.34i	0.176625	+	0.305924i	0.940722	−	0.339177i	$-0.110149\pi$
$239$	652.603	+	1130.34i	0.176625	+	0.305924i	−0.764097	+	0.645101i	$0.776815\pi$
$240$		0			0
$241$	1108.07	−	1919.23i	0.296170	−	0.512982i	−0.679086	−	0.734058i	$-0.737624\pi$
$241$	1108.07	−	1919.23i	0.296170	−	0.512982i	0.975256	+	0.221077i	$0.0709572\pi$
$242$		0			0
$243$	−3271.73	−	1909.11i	−0.863709	−	0.503990i
$244$		0			0
$245$	−562.003	+	973.418i	−0.146551	+	0.253834i
$246$		0			0
$247$	−1686.33	−	2920.81i	−0.434407	−	0.752415i
$248$		0			0
$249$	−2326.31	+	3195.68i	−0.592064	+	0.813326i
$250$		0			0
$251$	2993.80			0.752856			0.376428	−	0.926446i	$-0.377152\pi$
$251$	2993.80			0.752856			0.376428	+	0.926446i	$0.377152\pi$
$252$		0			0
$253$	−4649.67			−1.15542
$254$		0			0
$255$	1316.27	+	2963.74i	0.323246	+	0.727829i
$256$		0			0
$257$	−1467.52	−	2541.81i	−0.356191	−	0.616941i	0.631130	−	0.775677i	$-0.282591\pi$
$257$	−1467.52	−	2541.81i	−0.356191	−	0.616941i	−0.987321	+	0.158736i	$0.949258\pi$
$258$		0			0
$259$	−731.968	+	1267.81i	−0.175607	+	0.304161i
$260$		0			0
$261$	2489.41	−	2754.53i	0.590386	−	0.653262i
$262$		0			0
$263$	776.883	−	1345.60i	0.182147	−	0.315488i	−0.760464	−	0.649380i	$-0.775029\pi$
$263$	776.883	−	1345.60i	0.182147	−	0.315488i	0.942611	+	0.333892i	$0.108362\pi$
$264$		0			0
$265$	−1057.38	−	1831.43i	−0.245110	−	0.424543i
$266$		0			0
$267$	6276.40	+	665.532i	1.43861	+	0.152546i
$268$		0			0
$269$	−1762.62			−0.399513			−0.199756	−	0.979846i	$-0.564015\pi$
$269$	−1762.62			−0.399513			−0.199756	+	0.979846i	$0.564015\pi$
$270$		0			0
$271$	6924.63			1.55218			0.776091	−	0.630621i	$-0.217200\pi$
$271$	6924.63			1.55218			0.776091	+	0.630621i	$0.217200\pi$
$272$		0			0
$273$	−4002.43	−	424.406i	−0.887319	−	0.0940888i
$274$		0			0
$275$	−1790.58	−	3101.37i	−0.392639	−	0.680071i
$276$		0			0
$277$	−3012.48	+	5217.76i	−0.653437	+	1.13179i	0.328846	+	0.944384i	$0.393340\pi$
$277$	−3012.48	+	5217.76i	−0.653437	+	1.13179i	−0.982283	+	0.187403i	$0.939993\pi$
$278$		0			0
$279$	−880.444	−	2726.84i	−0.188928	−	0.585132i
$280$		0			0
$281$	3168.74	−	5488.42i	0.672709	−	1.16517i	−0.304424	−	0.952537i	$-0.598464\pi$
$281$	3168.74	−	5488.42i	0.672709	−	1.16517i	0.977133	−	0.212629i	$-0.0682026\pi$
$282$		0			0
$283$	−984.338	−	1704.92i	−0.206759	−	0.358117i	0.743933	−	0.668254i	$-0.232958\pi$
$283$	−984.338	−	1704.92i	−0.206759	−	0.358117i	−0.950692	+	0.310137i	$0.899625\pi$
$284$		0			0
$285$	−479.239	−	1079.07i	−0.0996058	−	0.224275i
$286$		0			0
$287$	−764.963			−0.157332
$288$		0			0
$289$	11322.1			2.30453
$290$		0			0
$291$	−3378.60	+	4641.23i	−0.680609	+	0.934962i
$292$		0			0
$293$	587.208	+	1017.07i	0.117082	+	0.202792i	0.918610	−	0.395165i	$-0.129313\pi$
$293$	587.208	+	1017.07i	0.117082	+	0.202792i	−0.801528	+	0.597957i	$0.795979\pi$
$294$		0			0
$295$	699.818	−	1212.12i	0.138119	−	0.239228i
$296$		0			0
$297$	−3705.61	+	3318.02i	−0.723977	+	0.648253i
$298$		0			0
$299$	−4767.24	+	8257.10i	−0.922062	+	1.59706i
$300$		0			0
$301$	2007.94	+	3477.86i	0.384504	+	0.665981i
$302$		0			0
$303$	3112.91	−	4276.25i	0.590205	−	0.810773i
$304$		0			0
$305$	215.202			0.0404013
$306$		0			0
$307$	−3258.92			−0.605851			−0.302926	−	0.953014i	$-0.597963\pi$
$307$	−3258.92			−0.605851			−0.302926	+	0.953014i	$0.597963\pi$
$308$		0			0
$309$	−1755.30	−	3952.28i	−0.323157	−	0.727629i
$310$		0			0
$311$	−3979.01	−	6891.84i	−0.725495	−	1.25659i	−0.958770	−	0.284183i	$-0.908278\pi$
$311$	−3979.01	−	6891.84i	−0.725495	−	1.25659i	0.233275	−	0.972411i	$-0.425056\pi$
$312$		0			0
$313$	2098.13	−	3634.06i	0.378892	−	0.656260i	−0.612009	−	0.790850i	$-0.709639\pi$
$313$	2098.13	−	3634.06i	0.378892	−	0.656260i	0.990901	+	0.134590i	$0.0429719\pi$
$314$		0			0
$315$	−1377.69	−	295.496i	−0.246426	−	0.0528549i
$316$		0			0
$317$	2416.78	−	4185.99i	0.428202	−	0.741667i	−0.568512	−	0.822675i	$-0.692481\pi$
$317$	2416.78	−	4185.99i	0.428202	−	0.741667i	0.996713	+	0.0810079i	$0.0258139\pi$
$318$		0			0
$319$	−2437.61	−	4222.07i	−0.427838	−	0.741037i
$320$		0			0
$321$	2490.54	+	264.090i	0.433048	+	0.0459192i
$322$		0			0
$323$	−5911.05			−1.01826
$324$		0			0
$325$	−7343.41			−1.25335
$326$		0			0
$327$	4673.88	+	495.605i	0.790416	+	0.0838135i
$328$		0			0
$329$	−3268.94	−	5661.98i	−0.547789	−	0.948799i
$330$		0			0
$331$	5270.34	−	9128.50i	0.875179	−	1.51585i	0.0186067	−	0.999827i	$-0.494077\pi$
$331$	5270.34	−	9128.50i	0.875179	−	1.51585i	0.856572	−	0.516027i	$-0.172590\pi$
$332$		0			0
$333$	3627.32	+	778.009i	0.596924	+	0.128032i
$334$		0			0
$335$	110.721	−	191.774i	0.0180577	−	0.0312768i
$336$		0			0
$337$	2437.45	+	4221.79i	0.393995	+	0.682420i	0.992972	−	0.118346i	$-0.0377593\pi$
$337$	2437.45	+	4221.79i	0.393995	+	0.682420i	−0.598977	+	0.800766i	$0.704426\pi$
$338$		0			0
$339$	1689.35	+	3803.78i	0.270658	+	0.609420i
$340$		0			0
$341$	−3762.63			−0.597530
$342$		0			0
$343$	−6099.51			−0.960182
$344$		0			0
$345$	−1964.42	+	2698.55i	−0.306553	+	0.421116i
$346$		0			0
$347$	−135.378	−	234.482i	−0.0209437	−	0.0362756i	0.855364	−	0.518028i	$-0.173334\pi$
$347$	−135.378	−	234.482i	−0.0209437	−	0.0362756i	−0.876307	+	0.481753i	$0.840000\pi$
$348$		0			0
$349$	5219.99	−	9041.30i	0.800630	−	1.38673i	−0.118572	−	0.992945i	$-0.537832\pi$
$349$	5219.99	−	9041.30i	0.800630	−	1.38673i	0.919202	−	0.393786i	$-0.128835\pi$
$350$		0			0
$351$	2092.99	+	9982.52i	0.318277	+	1.51803i
$352$		0			0
$353$	−32.9627	+	57.0931i	−0.00497005	+	0.00860838i	−0.868500	−	0.495690i	$-0.834915\pi$
$353$	−32.9627	+	57.0931i	−0.00497005	+	0.00860838i	0.863530	+	0.504298i	$0.168249\pi$
$354$		0			0
$355$	−875.101	−	1515.72i	−0.130833	−	0.226609i
$356$		0			0
$357$	−4151.58	+	5703.08i	−0.615475	+	0.845488i
$358$		0			0
$359$	−1973.98			−0.290203			−0.145101	−	0.989417i	$-0.546351\pi$
$359$	−1973.98			−0.290203			−0.145101	+	0.989417i	$0.546351\pi$
$360$		0			0
$361$	−4706.85			−0.686230
$362$		0			0
$363$	−156.151	−	351.593i	−0.0225779	−	0.0508371i
$364$		0			0
$365$	1299.73	+	2251.21i	0.186387	+	0.322832i
$366$		0			0
$367$	2187.97	−	3789.68i	0.311202	−	0.539018i	−0.667421	−	0.744681i	$-0.732602\pi$
$367$	2187.97	−	3789.68i	0.311202	−	0.539018i	0.978623	+	0.205663i	$0.0659351\pi$
$368$		0			0
$369$	595.633	+	1844.75i	0.0840310	+	0.260254i
$370$		0			0
$371$	2300.08	−	3983.85i	0.321871	−	0.557497i
$372$		0			0
$373$	−5417.10	−	9382.69i	−0.751975	−	1.30246i	−0.946864	−	0.321633i	$-0.895768\pi$
$373$	−5417.10	−	9382.69i	−0.751975	−	1.30246i	0.194890	−	0.980825i	$-0.437565\pi$
$374$		0			0
$375$	−5720.07	−	606.541i	−0.787689	−	0.0835243i
$376$		0			0
$377$	−9997.01			−1.36571
$378$		0			0
$379$	9390.04			1.27265			0.636325	−	0.771421i	$-0.280454\pi$
$379$	9390.04			1.27265			0.636325	+	0.771421i	$0.280454\pi$
$380$		0			0
$381$	9068.63	+	961.612i	1.21942	+	0.129304i
$382$		0			0
$383$	3566.61	+	6177.55i	0.475836	+	0.824173i	0.999617	−	0.0276806i	$-0.00881215\pi$
$383$	3566.61	+	6177.55i	0.475836	+	0.824173i	−0.523781	+	0.851853i	$0.675479\pi$
$384$		0			0
$385$	−925.094	+	1602.31i	−0.122460	+	0.212107i
$386$		0			0
$387$	6823.55	−	7550.26i	0.896281	−	0.991734i
$388$		0			0
$389$	−4243.29	+	7349.59i	−0.553068	+	0.957941i	0.444983	+	0.895539i	$0.353210\pi$
$389$	−4243.29	+	7349.59i	−0.553068	+	0.957941i	−0.998051	+	0.0624026i	$0.980124\pi$
$390$		0			0
$391$	8355.24	+	14471.7i	1.08067	+	1.87178i
$392$		0			0
$393$	−2327.88	−	5241.52i	−0.298794	−	0.672773i
$394$		0			0
$395$	−955.645			−0.121731
$396$		0			0
$397$	13046.4			1.64932			0.824660	−	0.565628i	$-0.191366\pi$
$397$	13046.4			1.64932			0.824660	+	0.565628i	$0.191366\pi$
$398$		0			0
$399$	1511.55	−	2076.43i	0.189654	−	0.260530i
$400$		0			0
$401$	1302.03	+	2255.19i	0.162146	+	0.280844i	0.935638	−	0.352961i	$-0.114825\pi$
$401$	1302.03	+	2255.19i	0.162146	+	0.280844i	−0.773492	+	0.633806i	$0.781492\pi$
$402$		0			0
$403$	−3857.77	+	6681.85i	−0.476847	+	0.825923i
$404$		0			0
$405$	360.127	+	3552.46i	0.0441848	+	0.435859i
$406$		0			0
$407$	2435.68	−	4218.72i	0.296639	−	0.513794i
$408$		0			0
$409$	3996.52	+	6922.18i	0.483167	+	0.836870i	0.999813	−	0.0193290i	$-0.00615301\pi$
$409$	3996.52	+	6922.18i	0.483167	+	0.836870i	−0.516646	+	0.856199i	$0.672820\pi$
$410$		0			0
$411$	−6503.06	+	8933.35i	−0.780468	+	1.07214i
$412$		0			0
$413$	3044.58			0.362746
$414$		0			0
$415$	3725.95			0.440722
$416$		0			0
$417$	4756.97	+	10710.9i	0.558632	+	1.25783i
$418$		0			0
$419$	−139.200	−	241.102i	−0.0162300	−	0.0281112i	0.857796	−	0.513990i	$-0.171833\pi$
$419$	−139.200	−	241.102i	−0.0162300	−	0.0281112i	−0.874026	+	0.485879i	$0.838500\pi$
$420$		0			0
$421$	429.620	−	744.124i	0.0497350	−	0.0861435i	−0.840086	−	0.542453i	$-0.817496\pi$
$421$	429.620	−	744.124i	0.0497350	−	0.0861435i	0.889821	+	0.456309i	$0.150829\pi$
$422$		0			0
$423$	−11108.8	+	12291.9i	−1.27690	+	1.41289i
$424$		0			0
$425$	−6435.16	+	11146.0i	−0.734473	+	1.27215i
$426$		0			0
$427$	234.060	+	405.404i	0.0265269	+	0.0459459i
$428$		0			0
$429$	13318.4	+	1412.24i	1.49887	+	0.158937i
$430$		0			0
$431$	−9455.34			−1.05672			−0.528362	−	0.849019i	$-0.677193\pi$
$431$	−9455.34			−1.05672			−0.528362	+	0.849019i	$0.677193\pi$
$432$		0			0
$433$	1527.61			0.169544			0.0847718	−	0.996400i	$-0.472984\pi$
$433$	1527.61			0.169544			0.0847718	+	0.996400i	$0.472984\pi$
$434$		0			0
$435$	−3480.24	−	369.035i	−0.383597	−	0.0406756i
$436$		0			0
$437$	−3042.06	−	5269.00i	−0.333001	−	0.576774i
$438$		0			0
$439$	−1303.03	+	2256.91i	−0.141663	+	0.245368i	−0.928123	−	0.372274i	$-0.878578\pi$
$439$	−1303.03	+	2256.91i	−0.141663	+	0.245368i	0.786460	+	0.617641i	$0.211912\pi$
$440$		0			0
$441$	1903.79	+	5896.27i	0.205571	+	0.636677i
$442$		0			0
$443$	726.222	−	1257.85i	0.0778868	−	0.134904i	−0.824451	−	0.565933i	$-0.808516\pi$
$443$	726.222	−	1257.85i	0.0778868	−	0.134904i	0.902338	+	0.431029i	$0.141849\pi$
$444$		0			0
$445$	−2974.73	−	5152.39i	−0.316890	−	0.548869i
$446$		0			0
$447$	−1445.67	−	3255.11i	−0.152971	−	0.344433i
$448$		0			0
$449$	12241.5			1.28666			0.643331	−	0.765589i	$-0.277552\pi$
$449$	12241.5			1.28666			0.643331	+	0.765589i	$0.277552\pi$
$450$		0			0
$451$	2545.47			0.265769
$452$		0			0
$453$	−1652.38	+	2269.90i	−0.171381	+	0.235429i
$454$		0			0
$455$	1896.97	+	3285.65i	0.195454	+	0.338536i
$456$		0			0
$457$	4878.13	−	8449.16i	0.499320	−	0.864847i	−0.500680	−	0.865632i	$-0.666917\pi$
$457$	4878.13	−	8449.16i	0.499320	−	0.864847i	1.00000		0.000785332i	$0.000249979\pi$
$458$		0			0
$459$	16985.9	+	5571.07i	1.72730	+	0.566526i
$460$		0			0
$461$	−5122.00	+	8871.56i	−0.517474	+	0.896290i	0.482321	+	0.875995i	$0.339794\pi$
$461$	−5122.00	+	8871.56i	−0.517474	+	0.896290i	−0.999794	+	0.0202956i	$0.993539\pi$
$462$		0			0
$463$	−6943.67	−	12026.8i	−0.696976	−	1.20720i	−0.969510	−	0.245051i	$-0.921195\pi$
$463$	−6943.67	−	12026.8i	−0.696976	−	1.20720i	0.272534	−	0.962146i	$-0.412138\pi$
$464$		0			0
$465$	−1589.66	+	2183.73i	−0.158534	+	0.217781i
$466$		0			0
$467$	14367.2			1.42363			0.711815	−	0.702367i	$-0.247874\pi$
$467$	14367.2			1.42363			0.711815	+	0.702367i	$0.247874\pi$
$468$		0			0
$469$	481.694			0.0474255
$470$		0			0
$471$	−998.287	−	2247.77i	−0.0976616	−	0.219897i
$472$		0			0
$473$	−6681.57	−	11572.8i	−0.649512	−	1.12499i
$474$		0			0
$475$	2342.98	−	4058.15i	0.226322	−	0.392002i
$476$		0			0
$477$	−11398.2	−	2444.75i	−1.09410	−	0.234670i
$478$		0			0
$479$	−5185.59	+	8981.71i	−0.494647	+	0.856753i	−0.999981	−	0.00617045i	$-0.998036\pi$
$479$	−5185.59	+	8981.71i	−0.494647	+	0.856753i	0.505334	+	0.862924i	$0.331369\pi$
$480$		0			0
$481$	−4994.53	−	8650.78i	−0.473453	−	0.820045i
$482$		0			0
$483$	−7220.18	−	765.608i	−0.680186	−	0.0721250i
$484$		0			0
$485$	5411.36			0.506634
$486$		0			0
$487$	4805.47			0.447139			0.223569	−	0.974688i	$-0.428229\pi$
$487$	4805.47			0.447139			0.223569	+	0.974688i	$0.428229\pi$
$488$		0			0
$489$	−1028.17	−	109.025i	−0.0950830	−	0.0100823i
$490$		0			0
$491$	−8774.67	−	15198.2i	−0.806508	−	1.39691i	−0.915268	−	0.402845i	$-0.868021\pi$
$491$	−8774.67	−	15198.2i	−0.806508	−	1.39691i	0.108760	−	0.994068i	$-0.465312\pi$
$492$		0			0
$493$	−8760.56	+	15173.7i	−0.800316	+	1.38619i
$494$		0			0
$495$	4584.37	+	983.283i	0.416267	+	0.0892834i
$496$		0			0
$497$	1903.58	−	3297.09i	0.171805	−	0.297575i
$498$		0			0
$499$	−397.080	−	687.763i	−0.0356227	−	0.0617004i	0.847664	−	0.530533i	$-0.178008\pi$
$499$	−397.080	−	687.763i	−0.0356227	−	0.0617004i	−0.883287	+	0.468832i	$0.844675\pi$
$500$		0			0
$501$	−9017.70	−	20304.5i	−0.804154	−	1.81065i
$502$		0			0
$503$	−6389.32			−0.566374			−0.283187	−	0.959065i	$-0.591392\pi$
$503$	−6389.32			−0.566374			−0.283187	+	0.959065i	$0.591392\pi$
$504$		0			0
$505$	−4985.82			−0.439338
$506$		0			0
$507$	9444.43	−	12973.9i	0.827301	−	1.13648i
$508$		0			0
$509$	−6935.53	−	12012.7i	−0.603953	−	1.04608i	−0.992216	−	0.124529i	$-0.960258\pi$
$509$	−6935.53	−	12012.7i	−0.603953	−	1.04608i	0.388263	−	0.921549i	$-0.373075\pi$
$510$		0			0
$511$	−2827.27	+	4896.97i	−0.244757	+	0.423932i
$512$		0			0
$513$	−6184.38	−	2028.37i	−0.532255	−	0.174570i
$514$		0			0
$515$	−2038.21	+	3530.28i	−0.174397	+	0.302064i
$516$		0			0
$517$	10877.7	+	18840.7i	0.925336	+	1.60273i
$518$		0			0
$519$	46.1918	−	63.4543i	0.00390673	−	0.00536674i
$520$		0			0
$521$	13682.5			1.15056			0.575280	−	0.817956i	$-0.304893\pi$
$521$	13682.5			1.15056			0.575280	+	0.817956i	$0.304893\pi$
$522$		0			0
$523$	−8390.18			−0.701485			−0.350743	−	0.936472i	$-0.614071\pi$
$523$	−8390.18			−0.701485			−0.350743	+	0.936472i	$0.614071\pi$
$524$		0			0
$525$	−2269.81	−	5110.76i	−0.188690	−	0.424860i
$526$		0			0
$527$	6761.27	+	11710.9i	0.558872	+	0.967995i
$528$		0			0
$529$	−2516.37	+	4358.48i	−0.206819	+	0.358221i
$530$		0			0
$531$	−2370.64	−	7342.16i	−0.193742	−	0.600042i
$532$		0			0
$533$	2609.84	−	4520.37i	0.212091	−	0.367353i
$534$		0			0
$535$	−1180.40	−	2044.52i	−0.0953894	−	0.165219i
$536$		0			0
$537$	−1601.39	−	169.807i	−0.128687	−	0.0136456i
$538$		0			0
$539$	8135.96			0.650168
$540$		0			0
$541$	−3447.33			−0.273960			−0.136980	−	0.990574i	$-0.543740\pi$
$541$	−3447.33			−0.273960			−0.136980	+	0.990574i	$0.543740\pi$
$542$		0			0
$543$	11643.3	+	1234.62i	0.920189	+	0.0975743i
$544$		0			0
$545$	−2215.21	−	3836.85i	−0.174108	−	0.301565i
$546$		0			0
$547$	7269.23	−	12590.7i	0.568208	−	0.984166i	−0.428535	−	0.903525i	$-0.640970\pi$
$547$	7269.23	−	12590.7i	0.568208	−	0.984166i	0.996743	−	0.0806404i	$-0.0256965\pi$
$548$		0			0
$549$	795.403	−	880.113i	0.0618342	−	0.0684195i
$550$		0			0
$551$	3189.63	−	5524.60i	0.246611	−	0.427143i
$552$		0			0
$553$	−1039.39	−	1800.28i	−0.0799265	−	0.138437i
$554$		0			0
$555$	−1419.40	−	3195.95i	−0.108559	−	0.244433i
$556$		0			0
$557$	14894.7			1.13305			0.566525	−	0.824044i	$-0.308287\pi$
$557$	14894.7			1.13305			0.566525	+	0.824044i	$0.308287\pi$
$558$		0			0
$559$	−27402.1			−2.07332
$560$		0			0
$561$	13814.7	−	18977.4i	1.03967	−	1.42821i
$562$		0			0
$563$	−6068.66	−	10511.2i	−0.454287	−	0.786848i	0.544360	−	0.838852i	$-0.316773\pi$
$563$	−6068.66	−	10511.2i	−0.454287	−	0.786848i	−0.998647	+	0.0520035i	$0.983439\pi$
$564$		0			0
$565$	1961.63	−	3397.64i	0.146064	−	0.252991i
$566$		0			0
$567$	−6300.55	+	4542.19i	−0.466664	+	0.336427i
$568$		0			0
$569$	260.242	−	450.752i	0.0191738	−	0.0332100i	−0.856279	−	0.516513i	$-0.827230\pi$
$569$	260.242	−	450.752i	0.0191738	−	0.0332100i	0.875453	+	0.483303i	$0.160563\pi$
$570$		0			0
$571$	−2295.73	−	3976.33i	−0.168255	−	0.291426i	0.769552	−	0.638585i	$-0.220480\pi$
$571$	−2295.73	−	3976.33i	−0.168255	−	0.291426i	−0.937806	+	0.347159i	$0.887146\pi$
$572$		0			0
$573$	−11310.5	+	15537.5i	−0.824616	+	1.13279i
$574$		0			0
$575$	−13247.1			−0.960772
$576$		0			0
$577$	−5429.84			−0.391763			−0.195881	−	0.980628i	$-0.562757\pi$
$577$	−5429.84			−0.391763			−0.195881	+	0.980628i	$0.562757\pi$
$578$		0			0
$579$	−7515.25	−	16921.5i	−0.539418	−	1.21457i
$580$		0			0
$581$	4052.46	+	7019.07i	0.289371	+	0.501205i
$582$		0			0
$583$	−7653.68	+	13256.6i	−0.543710	+	0.941734i
$584$		0			0
$585$	6446.45	−	7132.99i	0.455603	−	0.504125i
$586$		0			0
$587$	−9893.33	+	17135.7i	−0.695641	+	1.20489i	0.274323	+	0.961638i	$0.411546\pi$
$587$	−9893.33	+	17135.7i	−0.695641	+	1.20489i	−0.969964	+	0.243248i	$0.921787\pi$
$588$		0			0
$589$	−2461.71	−	4263.80i	−0.172212	−	0.298280i
$590$		0			0
$591$	−459.887	−	48.7651i	−0.0320088	−	0.00339413i
$592$		0			0
$593$	2181.13			0.151042			0.0755212	−	0.997144i	$-0.475938\pi$
$593$	2181.13			0.151042			0.0755212	+	0.997144i	$0.475938\pi$
$594$		0			0
$595$	6649.41			0.458150
$596$		0			0
$597$	1483.51	+	157.308i	0.101702	+	0.0107842i
$598$		0			0
$599$	2043.62	+	3539.65i	0.139399	+	0.241446i	0.927269	−	0.374395i	$-0.122150\pi$
$599$	2043.62	+	3539.65i	0.139399	+	0.241446i	−0.787870	+	0.615841i	$0.788816\pi$
$600$		0			0
$601$	−5842.45	+	10119.4i	−0.396537	+	0.686822i	−0.993296	−	0.115598i	$-0.963121\pi$
$601$	−5842.45	+	10119.4i	−0.396537	+	0.686822i	0.596759	+	0.802420i	$0.296455\pi$
$602$		0			0
$603$	−375.067	−	1161.63i	−0.0253299	−	0.0784497i
$604$		0			0
$605$	−181.318	+	314.052i	−0.0121845	+	0.0211042i
$606$		0			0
$607$	1865.37	+	3230.92i	0.124733	+	0.216045i	0.921629	−	0.388073i	$-0.126859\pi$
$607$	1865.37	+	3230.92i	0.124733	+	0.216045i	−0.796895	+	0.604117i	$0.793526\pi$
$608$		0			0
$609$	−3090.02	−	6957.57i	−0.205606	−	0.462947i
$610$		0			0
$611$	44610.8			2.95378
$612$		0			0
$613$	−2259.79			−0.148894			−0.0744470	−	0.997225i	$-0.523719\pi$
$613$	−2259.79			−0.148894			−0.0744470	+	0.997225i	$0.523719\pi$
$614$		0			0
$615$	1075.42	−	1477.33i	0.0705127	−	0.0968643i
$616$		0			0
$617$	11613.8	+	20115.7i	0.757787	+	1.31253i	0.943977	+	0.330012i	$0.107053\pi$
$617$	11613.8	+	20115.7i	0.757787	+	1.31253i	−0.186190	+	0.982514i	$0.559614\pi$
$618$		0			0
$619$	−4199.81	+	7274.28i	−0.272705	+	0.472339i	−0.969554	−	0.244879i	$-0.921252\pi$
$619$	−4199.81	+	7274.28i	−0.272705	+	0.472339i	0.696848	+	0.717218i	$0.254585\pi$
$620$		0			0
$621$	3775.64	+	18008.0i	0.243980	+	1.16366i
$622$		0			0
$623$	6470.83	−	11207.8i	0.416129	−	0.720757i
$624$		0			0
$625$	−3602.02	−	6238.89i	−0.230529	−	0.399289i
$626$		0			0
$627$	−5029.78	+	6909.48i	−0.320367	+	0.440093i
$628$		0			0
$629$	−17507.2			−1.10979
$630$		0			0
$631$	22475.2			1.41795			0.708973	−	0.705236i	$-0.249159\pi$
$631$	22475.2			1.41795			0.708973	+	0.705236i	$0.249159\pi$
$632$		0			0
$633$	−10671.7	−	24028.6i	−0.670080	−	1.50877i
$634$		0			0
$635$	−4298.13	−	7444.57i	−0.268608	−	0.465242i
$636$		0			0
$637$	8341.68	−	14448.2i	0.518853	−	0.898680i
$638$		0			0
$639$	−9433.31	−	2023.31i	−0.584000	−	0.125260i
$640$		0			0
$641$	−4437.04	+	7685.17i	−0.273405	+	0.473551i	−0.969731	−	0.244174i	$-0.921483\pi$
$641$	−4437.04	+	7685.17i	−0.273405	+	0.473551i	0.696327	+	0.717725i	$0.254816\pi$
$642$		0			0
$643$	10676.6	+	18492.4i	0.654810	+	1.13416i	0.981941	+	0.189185i	$0.0605846\pi$
$643$	10676.6	+	18492.4i	0.654810	+	1.13416i	−0.327132	+	0.944979i	$0.606082\pi$
$644$		0			0
$645$	−9539.44	−	1011.54i	−0.582349	−	0.0617506i
$646$		0			0
$647$	24145.6			1.46718			0.733588	−	0.679595i	$-0.237844\pi$
$647$	24145.6			1.46718			0.733588	+	0.679595i	$0.237844\pi$
$648$		0			0
$649$	−10131.1			−0.612757
$650$		0			0
$651$	−5842.75	−	619.549i	−0.351760	−	0.0372996i
$652$		0			0
$653$	−5847.64	−	10128.4i	−0.350438	−	0.606976i	0.635889	−	0.771781i	$-0.280634\pi$
$653$	−5847.64	−	10128.4i	−0.350438	−	0.606976i	−0.986326	+	0.164805i	$0.947300\pi$
$654$		0			0
$655$	−2703.08	+	4681.87i	−0.161249	+	0.279291i
$656$		0			0
$657$	14010.7	+	3005.10i	0.831979	+	0.178448i
$658$		0			0
$659$	−2914.45	+	5047.97i	−0.172277	+	0.298393i	−0.939216	−	0.343328i	$-0.888446\pi$
$659$	−2914.45	+	5047.97i	−0.172277	+	0.298393i	0.766938	+	0.641721i	$0.221779\pi$
$660$		0			0
$661$	810.655	+	1404.10i	0.0477017	+	0.0826218i	0.888890	−	0.458120i	$-0.151477\pi$
$661$	810.655	+	1404.10i	0.0477017	+	0.0826218i	−0.841189	+	0.540742i	$0.818144\pi$
$662$		0			0
$663$	−19537.0	−	43990.0i	−1.14443	−	2.57682i
$664$		0			0
$665$	−2420.98			−0.141175
$666$		0			0
$667$	−18034.1			−1.04690
$668$		0			0
$669$	1222.36	−	1679.18i	0.0706417	−	0.0970416i
$670$		0			0
$671$	−778.853	−	1349.01i	−0.0448096	−	0.0776126i
$672$		0			0
$673$	−10188.2	+	17646.5i	−0.583545	+	1.01073i	0.411510	+	0.911405i	$0.365002\pi$
$673$	−10188.2	+	17646.5i	−0.583545	+	1.01073i	−0.995055	+	0.0993246i	$0.968332\pi$
$674$		0			0
$675$	−10557.5	+	9453.21i	−0.602011	+	0.539043i
$676$		0			0
$677$	5675.10	−	9829.57i	0.322174	−	0.558022i	−0.658762	−	0.752351i	$-0.728920\pi$
$677$	5675.10	−	9829.57i	0.322174	−	0.558022i	0.980936	+	0.194329i	$0.0622530\pi$
$678$		0			0
$679$	5885.57	+	10194.1i	0.332647	+	0.576162i
$680$		0			0
$681$	1148.06	−	1577.11i	0.0646019	−	0.0887446i
$682$		0			0
$683$	3508.08			0.196534			0.0982670	−	0.995160i	$-0.468670\pi$
$683$	3508.08			0.196534			0.0982670	+	0.995160i	$0.468670\pi$
$684$		0			0
$685$	10415.7			0.580968
$686$		0			0
$687$	10179.6	+	22920.7i	0.565323	+	1.27290i
$688$		0			0
$689$	15694.4	+	27183.5i	0.867793	+	1.50306i
$690$		0			0
$691$	−8769.38	+	15189.0i	−0.482783	+	0.836204i	−0.999805	−	0.0197680i	$-0.993707\pi$
$691$	−8769.38	+	15189.0i	−0.482783	+	0.836204i	0.517022	+	0.855972i	$0.327041\pi$
$692$		0			0
$693$	3133.76	+	9705.64i	0.171778	+	0.532016i
$694$		0			0
$695$	5523.67	−	9567.27i	0.301474	−	0.522169i
$696$		0			0
$697$	−4574.10	−	7922.57i	−0.248574	−	0.430543i
$698$		0			0
$699$	19936.0	+	2113.96i	1.07875	+	0.114388i
$700$		0			0
$701$	15208.5			0.819428			0.409714	−	0.912214i	$-0.365629\pi$
$701$	15208.5			0.819428			0.409714	+	0.912214i	$0.365629\pi$
$702$		0			0
$703$	6374.19			0.341973
$704$		0			0
$705$	15530.3	+	1646.79i	0.829651	+	0.0879739i
$706$		0			0
$707$	−5422.73	−	9392.45i	−0.288462	−	0.499632i
$708$		0			0
$709$	−97.2400	+	168.425i	−0.00515081	+	0.00892146i	−0.868589	−	0.495533i	$-0.834973\pi$
$709$	−97.2400	+	168.425i	−0.00515081	+	0.00892146i	0.863439	+	0.504454i	$0.168306\pi$
$710$		0			0
$711$	−3532.14	+	3908.31i	−0.186309	+	0.206151i
$712$		0			0
$713$	−6959.23	+	12053.7i	−0.365533	+	0.633122i
$714$		0			0
$715$	−6312.32	−	10933.3i	−0.330164	−	0.571861i
$716$		0			0
$717$	−2752.79	−	6198.26i	−0.143382	−	0.322843i
$718$		0			0
$719$	−1001.11			−0.0519266			−0.0259633	−	0.999663i	$-0.508265\pi$
$719$	−1001.11			−0.0519266			−0.0259633	+	0.999663i	$0.508265\pi$
$720$		0			0
$721$	−8867.29			−0.458024
$722$		0			0
$723$	−6777.17	+	9309.89i	−0.348611	+	0.478892i
$724$		0			0
$725$	−6944.89	−	12028.9i	−0.355761	−	0.616196i
$726$		0			0
$727$	−7492.50	+	12977.4i	−0.382231	+	0.662043i	−0.991381	−	0.131012i	$-0.958177\pi$
$727$	−7492.50	+	12977.4i	−0.382231	+	0.662043i	0.609150	+	0.793055i	$0.291511\pi$
$728$		0			0
$729$	15859.6	+	11657.4i	0.805751	+	0.592255i
$730$		0			0
$731$	−24013.0	+	41591.6i	−1.21498	+	2.10441i
$732$		0			0
$733$	15849.0	+	27451.3i	0.798632	+	1.38327i	0.920507	+	0.390725i	$0.127776\pi$
$733$	15849.0	+	27451.3i	0.798632	+	1.38327i	−0.121876	+	0.992545i	$0.538891\pi$
$734$		0			0
$735$	3437.32	−	4721.90i	0.172500	−	0.236966i
$736$		0			0
$737$	−1602.87			−0.0801120
$738$		0			0
$739$	1333.07			0.0663570			0.0331785	−	0.999449i	$-0.489437\pi$
$739$	1333.07			0.0663570			0.0331785	+	0.999449i	$0.489437\pi$
$740$		0			0
$741$	7113.22	+	16016.3i	0.352646	+	0.794027i
$742$		0			0
$743$	1103.33	+	1911.02i	0.0544780	+	0.0943586i	0.891978	−	0.452078i	$-0.149317\pi$
$743$	1103.33	+	1911.02i	0.0544780	+	0.0943586i	−0.837500	+	0.546437i	$0.815984\pi$
$744$		0			0
$745$	−1678.68	+	2907.55i	−0.0825530	+	0.142986i
$746$		0			0
$747$	13771.4	−	15238.1i	0.674525	−	0.746361i
$748$		0			0
$749$	2567.69	−	4447.37i	0.125262	−	0.216961i
$750$		0			0
$751$	−8344.02	−	14452.3i	−0.405430	−	0.702225i	0.588942	−	0.808175i	$-0.299545\pi$
$751$	−8344.02	−	14452.3i	−0.405430	−	0.702225i	−0.994371	+	0.105951i	$0.966211\pi$
$752$		0			0
$753$	−15469.5	−	1640.34i	−0.748659	−	0.0793857i
$754$		0			0
$755$	2646.55			0.127573
$756$		0			0
$757$	17183.8			0.825039			0.412519	−	0.910949i	$-0.364649\pi$
$757$	17183.8			0.825039			0.412519	+	0.910949i	$0.364649\pi$
$758$		0			0
$759$	24025.7	+	2547.62i	1.14898	+	0.121835i
$760$		0			0
$761$	9476.94	+	16414.5i	0.451431	+	0.781901i	0.998475	−	0.0552024i	$-0.0175804\pi$
$761$	9476.94	+	16414.5i	0.451431	+	0.781901i	−0.547044	+	0.837104i	$0.684247\pi$
$762$		0			0
$763$	4818.67	−	8346.17i	0.228634	−	0.396005i
$764$		0			0
$765$	−5177.51	−	16035.4i	−0.244697	−	0.757856i
$766$		0			0
$767$	−10387.2	+	17991.2i	−0.488998	+	0.846969i
$768$		0			0
$769$	−3124.38	−	5411.58i	−0.146512	−	0.253767i	0.783424	−	0.621488i	$-0.213471\pi$
$769$	−3124.38	−	5411.58i	−0.146512	−	0.253767i	−0.929936	+	0.367721i	$0.880138\pi$
$770$		0			0
$771$	6190.23	+	13938.1i	0.289151	+	0.651060i
$772$		0			0
$773$	4856.58			0.225975			0.112988	−	0.993596i	$-0.463958\pi$
$773$	4856.58			0.225975			0.112988	+	0.993596i	$0.463958\pi$
$774$		0			0
$775$	−10719.9			−0.496866
$776$		0			0
$777$	4476.86	−	6149.93i	0.206701	−	0.283948i
$778$		0			0
$779$	1665.38	+	2884.52i	0.0765962	+	0.132669i
$780$		0			0
$781$	−6334.29	+	10971.3i	−0.290216	+	0.502669i
$782$		0			0
$783$	−14372.5	+	12869.2i	−0.655979	+	0.587366i
$784$		0			0
$785$	−1159.18	+	2007.77i	−0.0527046	+	0.0912870i
$786$		0			0
$787$	8239.01	+	14270.4i	0.373175	+	0.646359i	0.990052	−	0.140701i	$-0.0449356\pi$
$787$	8239.01	+	14270.4i	0.373175	+	0.646359i	−0.616877	+	0.787060i	$0.711602\pi$
$788$		0			0
$789$	−4751.57	+	6527.30i	−0.214399	+	0.294522i
$790$		0			0
$791$	8534.13			0.383614
$792$		0			0
$793$	−3194.19			−0.143038
$794$		0			0
$795$	4460.20	+	10042.7i	0.198977	+	0.448023i
$796$		0			0
$797$	−16373.1	−	28359.1i	−0.727687	−	1.26039i	−0.957859	−	0.287240i	$-0.907262\pi$
$797$	−16373.1	−	28359.1i	−0.727687	−	1.26039i	0.230172	−	0.973150i	$-0.426071\pi$
$798$		0			0
$799$	39093.3	−	67711.5i	1.73094	−	2.99808i
$800$		0			0
$801$	−32066.7	−	6877.85i	−1.41451	−	0.303392i
$802$		0			0
$803$	9407.94	−	16295.0i	0.413448	−	0.716114i
$804$		0			0
$805$	3422.04	+	5927.15i	0.149828	+	0.259509i
$806$		0			0
$807$	9107.78	+	965.764i	0.397285	+	0.0421270i
$808$		0			0
$809$	3011.82			0.130890			0.0654451	−	0.997856i	$-0.479153\pi$
$809$	3011.82			0.130890			0.0654451	+	0.997856i	$0.479153\pi$
$810$		0			0
$811$	−3560.24			−0.154151			−0.0770757	−	0.997025i	$-0.524558\pi$
$811$	−3560.24			−0.154151			−0.0770757	+	0.997025i	$0.524558\pi$
$812$		0			0
$813$	−35780.8	−	3794.10i	−1.54353	−	0.163671i
$814$		0			0
$815$	487.308	+	844.042i	0.0209444	+	0.0362767i
$816$		0			0
$817$	8742.87	−	15143.1i	0.374387	−	0.648457i
$818$		0			0
$819$	20448.7	+	4385.97i	0.872450	+	0.187128i
$820$		0			0
$821$	19040.8	−	32979.7i	0.809415	−	1.40195i	−0.103855	−	0.994592i	$-0.533118\pi$
$821$	19040.8	−	32979.7i	0.809415	−	1.40195i	0.913270	−	0.407355i	$-0.133549\pi$
$822$		0			0
$823$	2560.88	+	4435.58i	0.108465	+	0.187867i	0.915149	−	0.403117i	$-0.132073\pi$
$823$	2560.88	+	4435.58i	0.108465	+	0.187867i	−0.806684	+	0.590984i	$0.798740\pi$
$824$		0			0
$825$	7552.95	+	17006.4i	0.318739	+	0.717682i
$826$		0			0
$827$	−43712.2			−1.83800			−0.918998	−	0.394261i	$-0.871000\pi$
$827$	−43712.2			−1.83800			−0.918998	+	0.394261i	$0.871000\pi$
$828$		0			0
$829$	−14707.1			−0.616161			−0.308080	−	0.951360i	$-0.599687\pi$
$829$	−14707.1			−0.616161			−0.308080	+	0.951360i	$0.599687\pi$
$830$		0			0
$831$	18424.9	−	25310.6i	0.769137	−	1.05657i
$832$		0			0
$833$	−14619.9	−	25322.5i	−0.608104	−	1.05327i
$834$		0			0
$835$	−10471.1	+	18136.5i	−0.433974	+	0.751665i
$836$		0			0
$837$	3055.34	+	14572.5i	0.126175	+	0.601791i
$838$		0			0
$839$	17324.8	−	30007.4i	0.712893	−	1.23477i	−0.250873	−	0.968020i	$-0.580718\pi$
$839$	17324.8	−	30007.4i	0.712893	−	1.23477i	0.963767	−	0.266747i	$-0.0859489\pi$
$840$		0			0
$841$	2740.02	+	4745.85i	0.112347	+	0.194590i
$842$		0			0
$843$	−19380.6	+	26623.5i	−0.791820	+	1.08774i
$844$		0			0
$845$	−15126.7			−0.615829
$846$		0			0
$847$	−788.830			−0.0320006
$848$		0			0
$849$	4152.10	+	9348.98i	0.167844	+	0.377922i
$850$		0			0
$851$	−9009.89	−	15605.6i	−0.362932	−	0.628616i
$852$		0			0
$853$	14870.1	−	25755.7i	0.596883	−	1.03383i	−0.396395	−	0.918080i	$-0.629739\pi$
$853$	14870.1	−	25755.7i	0.596883	−	1.03383i	0.993278	−	0.115752i	$-0.0369276\pi$
$854$		0			0
$855$	1885.08	+	5838.31i	0.0754016	+	0.233528i
$856$		0			0
$857$	927.130	−	1605.84i	0.0369547	−	0.0640073i	−0.846957	−	0.531662i	$-0.821568\pi$
$857$	927.130	−	1605.84i	0.0369547	−	0.0640073i	0.883911	+	0.467655i	$0.154901\pi$
$858$		0			0
$859$	−23001.2	−	39839.3i	−0.913611	−	1.58242i	−0.808922	−	0.587916i	$-0.799948\pi$
$859$	−23001.2	−	39839.3i	−0.913611	−	1.58242i	−0.104690	−	0.994505i	$-0.533385\pi$
$860$		0			0
$861$	3952.71	+	419.134i	0.156455	+	0.0165901i
$862$		0			0
$863$	−38032.8			−1.50018			−0.750088	−	0.661338i	$-0.769989\pi$
$863$	−38032.8			−1.50018			−0.750088	+	0.661338i	$0.769989\pi$
$864$		0			0
$865$	−73.9835			−0.00290811
$866$		0			0
$867$	−58503.6	−	6203.56i	−2.29168	−	0.243003i
$868$		0			0
$869$	3458.65	+	5990.55i	0.135013	+	0.233850i
$870$		0			0
$871$	−1643.40	+	2846.45i	−0.0639317	+	0.110733i
$872$		0			0
$873$	20000.8	−	22130.9i	0.775402	−	0.857982i
$874$		0			0
$875$	−5897.27	+	10214.4i	−0.227845	+	0.394639i
$876$		0			0
$877$	−5753.61	−	9965.55i	−0.221534	−	0.383709i	0.733740	−	0.679431i	$-0.237773\pi$
$877$	−5753.61	−	9965.55i	−0.221534	−	0.383709i	−0.955274	+	0.295722i	$0.904440\pi$
$878$		0			0
$879$	−2476.94	−	5577.15i	−0.0950458	−	0.214007i
$880$		0			0
$881$	−30567.4			−1.16895			−0.584473	−	0.811413i	$-0.698699\pi$
$881$	−30567.4			−1.16895			−0.584473	+	0.811413i	$0.698699\pi$
$882$		0			0
$883$	17998.2			0.685944			0.342972	−	0.939346i	$-0.388566\pi$
$883$	17998.2			0.685944			0.342972	+	0.939346i	$0.388566\pi$
$884$		0			0
$885$	−4280.23	+	5879.81i	−0.162574	+	0.223331i
$886$		0			0
$887$	−5896.25	−	10212.6i	−0.223198	−	0.386590i	0.732579	−	0.680682i	$-0.238316\pi$
$887$	−5896.25	−	10212.6i	−0.223198	−	0.386590i	−0.955777	+	0.294092i	$0.904983\pi$
$888$		0			0
$889$	9349.56	−	16193.9i	0.352727	−	0.610941i
$890$		0			0
$891$	20965.6	−	15114.5i	0.788297	−	0.568298i
$892$		0			0
$893$	−14233.5	+	24653.1i	−0.533376	+	0.923834i
$894$		0			0
$895$	758.985	+	1314.60i	0.0283465	+	0.0490975i
$896$		0			0
$897$	29157.4	−	40053.9i	1.08533	−	1.49093i
$898$		0			0
$899$	−14593.7			−0.541408
$900$		0			0
$901$	55013.2			2.03414
$902$		0			0
$903$	−8469.83	−	19070.9i	−0.312136	−	0.702813i
$904$		0			0
$905$	−5518.41	−	9558.17i	−0.202694	−	0.351077i
$906$		0			0
$907$	9309.99	−	16125.4i	0.340830	−	0.590335i	−0.643757	−	0.765230i	$-0.722625\pi$
$907$	9309.99	−	16125.4i	0.340830	−	0.590335i	0.984587	+	0.174895i	$0.0559585\pi$
$908$		0			0
$909$	−18428.0	+	20390.6i	−0.672407	+	0.744018i
$910$		0			0
$911$	6798.87	−	11776.0i	0.247263	−	0.428272i	−0.715502	−	0.698610i	$-0.753802\pi$
$911$	6798.87	−	11776.0i	0.247263	−	0.428272i	0.962765	+	0.270338i	$0.0871355\pi$
$912$		0			0
$913$	−13484.9	−	23356.5i	−0.488811	−	0.846645i
$914$		0			0
$915$	−1111.99	−	117.912i	−0.0401761	−	0.00426016i
$916$		0			0
$917$	−11759.8			−0.423493
$918$		0			0
$919$	18959.3			0.680532			0.340266	−	0.940329i	$-0.389483\pi$
$919$	18959.3			0.680532			0.340266	+	0.940329i	$0.389483\pi$
$920$		0			0
$921$	16839.4	+	1785.61i	0.602474	+	0.0638846i
$922$		0			0
$923$	12988.9	+	22497.5i	0.463202	+	0.802290i
$924$		0			0
$925$	6939.37	−	12019.3i	0.246665	−	0.427236i
$926$		0			0
$927$	6904.45	+	21383.9i	0.244630	+	0.757648i
$928$		0			0
$929$	−25581.7	+	44308.7i	−0.903452	+	1.56483i	−0.0804709	+	0.996757i	$0.525642\pi$
$929$	−25581.7	+	44308.7i	−0.903452	+	1.56483i	−0.822981	+	0.568068i	$0.807691\pi$
$930$		0			0
$931$	5322.97	+	9219.65i	0.187383	+	0.324556i
$932$		0			0
$933$	16784.1	+	37791.6i	0.588947	+	1.32609i
$934$		0			0
$935$	−22126.4			−0.773915
$936$		0			0
$937$	−33124.9			−1.15490			−0.577452	−	0.816425i	$-0.695953\pi$
$937$	−33124.9			−1.15490			−0.577452	+	0.816425i	$0.695953\pi$
$938$		0			0
$939$	−12832.6	+	17628.3i	−0.445980	+	0.612649i
$940$		0			0
$941$	−8372.95	−	14502.4i	−0.290064	−	0.502406i	0.683761	−	0.729706i	$-0.260343\pi$
$941$	−8372.95	−	14502.4i	−0.290064	−	0.502406i	−0.973825	+	0.227301i	$0.927010\pi$
$942$		0			0
$943$	4708.02	−	8154.53i	0.162581	−	0.281599i
$944$		0			0
$945$	6956.88	+	2281.74i	0.239479	+	0.0785448i
$946$		0			0
$947$	15822.5	−	27405.3i	0.542937	−	0.940395i	−0.455796	−	0.890084i	$-0.650645\pi$
$947$	15822.5	−	27405.3i	0.542937	−	0.940395i	0.998734	−	0.0503108i	$-0.0160212\pi$
$948$		0			0
$949$	−19291.7	−	33414.1i	−0.659888	−	1.14296i
$950$		0			0
$951$	−14781.5	+	20305.6i	−0.504020	+	0.692380i
$952$		0			0
$953$	44345.0			1.50732			0.753660	−	0.657264i	$-0.228286\pi$
$953$	44345.0			1.50732			0.753660	+	0.657264i	$0.228286\pi$
$954$		0			0
$955$	18115.6			0.613830
$956$		0			0
$957$	10282.3	+	23151.8i	0.347313	+	0.782019i
$958$		0			0
$959$	11328.4	+	19621.4i	0.381454	+	0.660697i
$960$		0			0
$961$	9263.92	−	16045.6i	0.310964	−	0.538605i
$962$		0			0
$963$	−12724.4	−	2729.20i	−0.425792	−	0.0913264i
$964$		0			0
$965$	−8726.52	+	15114.8i	−0.291105	+	0.504209i
$966$		0			0
$967$	5676.13	+	9831.34i	0.188761	+	0.326944i	0.944837	−	0.327540i	$-0.106219\pi$
$967$	5676.13	+	9831.34i	0.188761	+	0.326944i	−0.756076	+	0.654483i	$0.772886\pi$
$968$		0			0
$969$	30543.5	+	3238.74i	1.01259	+	0.107372i
$970$		0			0
$971$	38458.3			1.27105			0.635523	−	0.772082i	$-0.280785\pi$
$971$	38458.3			1.27105			0.635523	+	0.772082i	$0.280785\pi$
$972$		0			0
$973$	24030.9			0.791772
$974$		0			0
$975$	37944.7	+	4023.55i	1.24636	+	0.132161i
$976$		0			0
$977$	3682.62	+	6378.48i	0.120591	+	0.208870i	0.920001	−	0.391916i	$-0.128188\pi$
$977$	3682.62	+	6378.48i	0.120591	+	0.208870i	−0.799410	+	0.600786i	$0.794854\pi$
$978$		0			0
$979$	−21532.2	+	37294.8i	−0.702933	+	1.21752i
$980$		0			0
$981$	−23879.2	−	5121.76i	−0.777172	−	0.166692i
$982$		0			0
$983$	25870.7	−	44809.4i	0.839418	−	1.45391i	−0.0509649	−	0.998700i	$-0.516230\pi$
$983$	25870.7	−	44809.4i	0.839418	−	1.45391i	0.890382	−	0.455213i	$-0.150437\pi$
$984$		0			0
$985$	217.966	+	377.528i	0.00705073	+	0.0122122i
$986$		0			0
$987$	13789.0	+	31047.6i	0.444688	+	1.00127i
$988$		0			0
$989$	−49432.0			−1.58933
$990$		0			0
$991$	−7427.40			−0.238082			−0.119041	−	0.992889i	$-0.537982\pi$
$991$	−7427.40			−0.238082			−0.119041	+	0.992889i	$0.537982\pi$
$992$		0			0
$993$	−32234.5	+	44280.9i	−1.03014	+	1.41512i
$994$		0			0
$995$	−703.120	−	1217.84i	−0.0224024	−	0.0388021i
$996$		0			0
$997$	−21293.1	+	36880.8i	−0.676389	+	1.17154i	0.299672	+	0.954042i	$0.403123\pi$
$997$	−21293.1	+	36880.8i	−0.676389	+	1.17154i	−0.976061	+	0.217498i	$0.930211\pi$
$998$		0			0
$999$	−18316.7	−	6007.57i	−0.580096	−	0.190261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.i.d.97.1		6
3.2	odd	2		432.4.i.d.289.2		6
4.3	odd	2		36.4.e.a.25.3	yes	6
9.2	odd	6		1296.4.a.w.1.2		3
9.4	even	3	inner	144.4.i.d.49.1		6
9.5	odd	6		432.4.i.d.145.2		6
9.7	even	3		1296.4.a.v.1.2		3
12.11	even	2		108.4.e.a.73.2		6
36.7	odd	6		324.4.a.c.1.2		3
36.11	even	6		324.4.a.d.1.2		3
36.23	even	6		108.4.e.a.37.2		6
36.31	odd	6		36.4.e.a.13.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.e.a.13.3	✓	6	36.31	odd	6
36.4.e.a.25.3	yes	6	4.3	odd	2
108.4.e.a.37.2		6	36.23	even	6
108.4.e.a.73.2		6	12.11	even	2
144.4.i.d.49.1		6	9.4	even	3	inner
144.4.i.d.97.1		6	1.1	even	1	trivial
324.4.a.c.1.2		3	36.7	odd	6
324.4.a.d.1.2		3	36.11	even	6
432.4.i.d.145.2		6	9.5	odd	6
432.4.i.d.289.2		6	3.2	odd	2
1296.4.a.v.1.2		3	9.7	even	3
1296.4.a.w.1.2		3	9.2	odd	6

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.16718 - 0.547914i) q^{3} +(2.44901 + 4.24182i) q^{5} +(-5.32725 + 9.22708i) q^{7} +(26.3996 + 5.66234i) q^{9} +O(q^{10})\)	\(q+(-5.16718 - 0.547914i) q^{3} +(2.44901 + 4.24182i) q^{5} +(-5.32725 + 9.22708i) q^{7} +(26.3996 + 5.66234i) q^{9} +(17.7268 - 30.7038i) q^{11} +(-36.3501 - 62.9603i) q^{13} +(-10.3304 - 23.2601i) q^{15} -127.417 q^{17} +46.3913 q^{19} +(32.5825 - 44.7591i) q^{21} +(-65.5739 - 113.577i) q^{23} +(50.5047 - 87.4766i) q^{25} +(-133.309 - 43.7231i) q^{27} +(68.7549 - 119.087i) q^{29} +(-53.0640 - 91.9096i) q^{31} +(-108.421 + 148.939i) q^{33} -52.1861 q^{35} +137.401 q^{37} +(153.331 + 345.244i) q^{39} +(35.8986 + 62.1782i) q^{41} +(188.459 - 326.421i) q^{43} +(40.6343 + 125.849i) q^{45} +(-306.813 + 531.416i) q^{47} +(114.741 + 198.737i) q^{49} +(658.388 + 69.8136i) q^{51} -431.757 q^{53} +173.653 q^{55} +(-239.712 - 25.4184i) q^{57} +(-142.878 - 247.471i) q^{59} +(21.9682 - 38.0500i) q^{61} +(-192.884 + 213.426i) q^{63} +(178.044 - 308.381i) q^{65} +(-22.6052 - 39.1533i) q^{67} +(276.602 + 622.804i) q^{69} -357.328 q^{71} +530.718 q^{73} +(-308.897 + 424.336i) q^{75} +(188.871 + 327.134i) q^{77} +(-97.5540 + 168.969i) q^{79} +(664.876 + 298.967i) q^{81} +(380.352 - 658.789i) q^{83} +(-312.047 - 540.480i) q^{85} +(-420.519 + 577.673i) q^{87} -1214.67 q^{89} +774.586 q^{91} +(223.833 + 503.988i) q^{93} +(113.613 + 196.783i) q^{95} +(552.402 - 956.788i) q^{97} +(641.836 - 710.191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 6 q^{5} + 6 q^{7} + 39 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 6 * q^5 + 6 * q^7 + 39 * q^9	\( 6 q + 3 q^{3} + 6 q^{5} + 6 q^{7} + 39 q^{9} - 51 q^{11} + 12 q^{13} + 180 q^{15} - 222 q^{17} - 30 q^{19} - 120 q^{21} - 210 q^{23} - 3 q^{25} - 648 q^{27} + 456 q^{29} - 48 q^{31} - 603 q^{33} + 1104 q^{35} - 96 q^{37} + 36 q^{39} + 897 q^{41} - 129 q^{43} + 1494 q^{45} - 522 q^{47} - 225 q^{49} + 1647 q^{51} - 2208 q^{53} + 216 q^{55} - 645 q^{57} - 453 q^{59} - 402 q^{61} - 1896 q^{63} + 1110 q^{65} + 213 q^{67} - 198 q^{69} - 120 q^{71} + 750 q^{73} - 921 q^{75} + 1128 q^{77} - 552 q^{79} - 549 q^{81} + 612 q^{83} + 1188 q^{85} + 1386 q^{87} - 924 q^{89} + 264 q^{91} - 1998 q^{93} + 2184 q^{95} + 93 q^{97} + 1854 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 6 * q^5 + 6 * q^7 + 39 * q^9 - 51 * q^11 + 12 * q^13 + 180 * q^15 - 222 * q^17 - 30 * q^19 - 120 * q^21 - 210 * q^23 - 3 * q^25 - 648 * q^27 + 456 * q^29 - 48 * q^31 - 603 * q^33 + 1104 * q^35 - 96 * q^37 + 36 * q^39 + 897 * q^41 - 129 * q^43 + 1494 * q^45 - 522 * q^47 - 225 * q^49 + 1647 * q^51 - 2208 * q^53 + 216 * q^55 - 645 * q^57 - 453 * q^59 - 402 * q^61 - 1896 * q^63 + 1110 * q^65 + 213 * q^67 - 198 * q^69 - 120 * q^71 + 750 * q^73 - 921 * q^75 + 1128 * q^77 - 552 * q^79 - 549 * q^81 + 612 * q^83 + 1188 * q^85 + 1386 * q^87 - 924 * q^89 + 264 * q^91 - 1998 * q^93 + 2184 * q^95 + 93 * q^97 + 1854 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more