LMFDB - Embedded newform 124.4.e.b.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,4,Mod(5,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("124.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	124.e (of order $3$, degree $2$, 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:	$7.31623684071$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.250722553392.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 46x^{4} - 24x^{3} + 2116x^{2} - 552x + 144 $ x^6 + 46x^4 - 24x^3 + 2116x^2 - 552x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.3
Root			$3.32396 - 5.75727i$ of defining polynomial
Character	$\chi$	$=$	124.25
Dual form			124.4.e.b.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82396 + 3.15920i) q^{3} +(6.14793 - 10.6485i) q^{5} +(10.8240 + 18.7477i) q^{7} +(6.84632 - 11.8582i) q^{9} +O(q^{10})$	\(q+(1.82396 + 3.15920i) q^{3} +(6.14793 - 10.6485i) q^{5} +(10.8240 + 18.7477i) q^{7} +(6.84632 - 11.8582i) q^{9} +(-13.2173 + 22.8930i) q^{11} +(38.8933 - 67.3652i) q^{13} +44.8544 q^{15} +(47.4403 + 82.1690i) q^{17} +(41.1129 + 71.2096i) q^{19} +(-39.4850 + 68.3901i) q^{21} -38.5778 q^{23} +(-13.0940 - 22.6795i) q^{25} +148.444 q^{27} +161.468 q^{29} +(-171.978 - 14.6470i) q^{31} -96.4313 q^{33} +266.180 q^{35} +(-211.875 - 366.978i) q^{37} +283.760 q^{39} +(-64.8671 + 112.353i) q^{41} +(-151.921 - 263.135i) q^{43} +(-84.1813 - 145.806i) q^{45} -361.513 q^{47} +(-62.8164 + 108.801i) q^{49} +(-173.059 + 299.747i) q^{51} +(-270.882 + 469.181i) q^{53} +(162.518 + 281.489i) q^{55} +(-149.977 + 259.767i) q^{57} +(-249.443 - 432.048i) q^{59} -442.096 q^{61} +296.417 q^{63} +(-478.226 - 828.313i) q^{65} +(31.3127 - 54.2352i) q^{67} +(-70.3646 - 121.875i) q^{69} +(342.802 - 593.751i) q^{71} +(183.270 - 317.433i) q^{73} +(47.7659 - 82.7330i) q^{75} -572.253 q^{77} +(262.179 + 454.108i) q^{79} +(85.9054 + 148.792i) q^{81} +(-562.745 + 974.703i) q^{83} +1166.64 q^{85} +(294.511 + 510.108i) q^{87} -899.421 q^{89} +1683.92 q^{91} +(-267.409 - 570.028i) q^{93} +1011.04 q^{95} -1016.48 q^{97} +(180.979 + 313.465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9	$ 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9} + 61 q^{11} + 113 q^{13} + 386 q^{15} + 123 q^{17} + 63 q^{19} + 43 q^{21} + 96 q^{23} + 4 q^{25} + 918 q^{27} + 332 q^{29} - 668 q^{31} - 1214 q^{33} + 278 q^{35} + 129 q^{37} - 14 q^{39} - 709 q^{41} + 107 q^{43} - 1214 q^{45} - 568 q^{47} + 262 q^{49} + 293 q^{51} - 1267 q^{53} + 909 q^{55} + 681 q^{57} - 989 q^{59} - 2500 q^{61} + 36 q^{63} - 551 q^{65} + 741 q^{67} + 440 q^{69} - 1089 q^{71} - 197 q^{73} - 500 q^{75} + 982 q^{77} + 677 q^{79} - 2423 q^{81} + q^{83} + 58 q^{85} + 1194 q^{87} - 564 q^{89} + 4054 q^{91} + 1439 q^{93} - 2094 q^{95} - 2092 q^{97} + 2086 q^{99}+O(q^{100}) $ 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9 + 61 * q^11 + 113 * q^13 + 386 * q^15 + 123 * q^17 + 63 * q^19 + 43 * q^21 + 96 * q^23 + 4 * q^25 + 918 * q^27 + 332 * q^29 - 668 * q^31 - 1214 * q^33 + 278 * q^35 + 129 * q^37 - 14 * q^39 - 709 * q^41 + 107 * q^43 - 1214 * q^45 - 568 * q^47 + 262 * q^49 + 293 * q^51 - 1267 * q^53 + 909 * q^55 + 681 * q^57 - 989 * q^59 - 2500 * q^61 + 36 * q^63 - 551 * q^65 + 741 * q^67 + 440 * q^69 - 1089 * q^71 - 197 * q^73 - 500 * q^75 + 982 * q^77 + 677 * q^79 - 2423 * q^81 + q^83 + 58 * q^85 + 1194 * q^87 - 564 * q^89 + 4054 * q^91 + 1439 * q^93 - 2094 * q^95 - 2092 * q^97 + 2086 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.82396	+	3.15920i	0.351022	+	0.607988i	0.986429	−	0.164190i	$-0.0525009\pi$
$3$	1.82396	+	3.15920i	0.351022	+	0.607988i	−0.635407	+	0.772177i	$0.719168\pi$
$4$		0			0
$5$	6.14793	−	10.6485i	0.549887	−	0.952433i	−0.448394	−	0.893836i	$-0.648004\pi$
$5$	6.14793	−	10.6485i	0.549887	−	0.952433i	0.998282	−	0.0585969i	$-0.0186627\pi$
$6$		0			0
$7$	10.8240	+	18.7477i	0.584439	+	1.01228i	0.994945	+	0.100420i	$0.0320187\pi$
$7$	10.8240	+	18.7477i	0.584439	+	1.01228i	−0.410506	+	0.911858i	$0.634648\pi$
$8$		0			0
$9$	6.84632	−	11.8582i	0.253567	−	0.439191i
$10$		0			0
$11$	−13.2173	+	22.8930i	−0.362287	+	0.627500i	−0.988337	−	0.152283i	$-0.951337\pi$
$11$	−13.2173	+	22.8930i	−0.362287	+	0.627500i	0.626050	+	0.779783i	$0.284671\pi$
$12$		0			0
$13$	38.8933	−	67.3652i	0.829774	−	1.43721i	−0.0684410	−	0.997655i	$-0.521802\pi$
$13$	38.8933	−	67.3652i	0.829774	−	1.43721i	0.898215	−	0.439556i	$-0.144864\pi$
$14$		0			0
$15$	44.8544			0.772090
$16$		0			0
$17$	47.4403	+	82.1690i	0.676822	+	1.17229i	0.975933	+	0.218071i	$0.0699765\pi$
$17$	47.4403	+	82.1690i	0.676822	+	1.17229i	−0.299111	+	0.954218i	$0.596690\pi$
$18$		0			0
$19$	41.1129	+	71.2096i	0.496418	+	0.859821i	0.999991	−	0.00413113i	$-0.00131498\pi$
$19$	41.1129	+	71.2096i	0.496418	+	0.859821i	−0.503573	+	0.863952i	$0.667982\pi$
$20$		0			0
$21$	−39.4850	+	68.3901i	−0.410302	+	0.710664i
$22$		0			0
$23$	−38.5778			−0.349741			−0.174870	−	0.984591i	$-0.555951\pi$
$23$	−38.5778			−0.349741			−0.174870	+	0.984591i	$0.555951\pi$
$24$		0			0
$25$	−13.0940	−	22.6795i	−0.104752	−	0.181436i
$26$		0			0
$27$	148.444			1.05807
$28$		0			0
$29$	161.468			1.03392			0.516962	−	0.856008i	$-0.327063\pi$
$29$	161.468			1.03392			0.516962	+	0.856008i	$0.327063\pi$
$30$		0			0
$31$	−171.978	−	14.6470i	−0.996393	−	0.0848608i
$31$	−171.978	−	14.6470i	−0.996393	−	0.0848608i
$32$		0			0
$33$	−96.4313			−0.508683
$34$		0			0
$35$	266.180			1.28550
$36$		0			0
$37$	−211.875	−	366.978i	−0.941405	−	1.63056i	−0.762794	−	0.646641i	$-0.776173\pi$
$37$	−211.875	−	366.978i	−0.941405	−	1.63056i	−0.178610	−	0.983920i	$-0.557160\pi$
$38$		0			0
$39$	283.760			1.16508
$40$		0			0
$41$	−64.8671	+	112.353i	−0.247086	+	0.427966i	−0.962716	−	0.270514i	$-0.912806\pi$
$41$	−64.8671	+	112.353i	−0.247086	+	0.427966i	0.715630	+	0.698480i	$0.246140\pi$
$42$		0			0
$43$	−151.921	−	263.135i	−0.538785	−	0.933203i	−0.998970	−	0.0453801i	$-0.985550\pi$
$43$	−151.921	−	263.135i	−0.538785	−	0.933203i	0.460185	−	0.887823i	$-0.347783\pi$
$44$		0			0
$45$	−84.1813	−	145.806i	−0.278867	−	0.483012i
$46$		0			0
$47$	−361.513			−1.12196			−0.560980	−	0.827829i	$-0.689576\pi$
$47$	−361.513			−1.12196			−0.560980	+	0.827829i	$0.689576\pi$
$48$		0			0
$49$	−62.8164	+	108.801i	−0.183138	+	0.317204i
$50$		0			0
$51$	−173.059	+	299.747i	−0.475158	+	0.822998i
$52$		0			0
$53$	−270.882	+	469.181i	−0.702047	+	1.21598i	0.265700	+	0.964056i	$0.414397\pi$
$53$	−270.882	+	469.181i	−0.702047	+	1.21598i	−0.967747	+	0.251925i	$0.918936\pi$
$54$		0			0
$55$	162.518	+	281.489i	0.398434	+	0.690108i
$56$		0			0
$57$	−149.977	+	259.767i	−0.348507	+	0.603632i
$58$		0			0
$59$	−249.443	−	432.048i	−0.550419	−	0.953354i	−0.998244	−	0.0592325i	$-0.981135\pi$
$59$	−249.443	−	432.048i	−0.550419	−	0.953354i	0.447825	−	0.894121i	$-0.352199\pi$
$60$		0			0
$61$	−442.096			−0.927945			−0.463972	−	0.885850i	$-0.653576\pi$
$61$	−442.096			−0.927945			−0.463972	+	0.885850i	$0.653576\pi$
$62$		0			0
$63$	296.417			0.592778
$64$		0			0
$65$	−478.226	−	828.313i	−0.912565	−	1.58061i
$66$		0			0
$67$	31.3127	−	54.2352i	0.0570964	−	0.0988939i	−0.836064	−	0.548631i	$-0.815149\pi$
$67$	31.3127	−	54.2352i	0.0570964	−	0.0988939i	0.893161	+	0.449737i	$0.148482\pi$
$68$		0			0
$69$	−70.3646	−	121.875i	−0.122767	−	0.212638i
$70$		0			0
$71$	342.802	−	593.751i	0.573002	−	0.992469i	−0.423253	−	0.906011i	$-0.639112\pi$
$71$	342.802	−	593.751i	0.573002	−	0.992469i	0.996256	−	0.0864578i	$-0.0275548\pi$
$72$		0			0
$73$	183.270	−	317.433i	0.293838	−	0.508942i	−0.680876	−	0.732399i	$-0.738401\pi$
$73$	183.270	−	317.433i	0.293838	−	0.508942i	0.974714	+	0.223457i	$0.0717341\pi$
$74$		0			0
$75$	47.7659	−	82.7330i	0.0735405	−	0.127376i
$76$		0			0
$77$	−572.253			−0.846939
$78$		0			0
$79$	262.179	+	454.108i	0.373386	+	0.646723i	0.990084	−	0.140477i	$-0.0448635\pi$
$79$	262.179	+	454.108i	0.373386	+	0.646723i	−0.616698	+	0.787200i	$0.711530\pi$
$80$		0			0
$81$	85.9054	+	148.792i	0.117840	+	0.204105i
$82$		0			0
$83$	−562.745	+	974.703i	−0.744208	+	1.28901i	0.206355	+	0.978477i	$0.433840\pi$
$83$	−562.745	+	974.703i	−0.744208	+	1.28901i	−0.950564	+	0.310530i	$0.899494\pi$
$84$		0			0
$85$	1166.64			1.48870
$86$		0			0
$87$	294.511	+	510.108i	0.362930	+	0.628613i
$88$		0			0
$89$	−899.421			−1.07122			−0.535609	−	0.844466i	$-0.679918\pi$
$89$	−899.421			−1.07122			−0.535609	+	0.844466i	$0.679918\pi$
$90$		0			0
$91$	1683.92			1.93981
$92$		0			0
$93$	−267.409	−	570.028i	−0.298161	−	0.635583i
$94$		0			0
$95$	1011.04			1.09190
$96$		0			0
$97$	−1016.48			−1.06400			−0.532000	−	0.846744i	$-0.678559\pi$
$97$	−1016.48			−1.06400			−0.532000	+	0.846744i	$0.678559\pi$
$98$		0			0
$99$	180.979	+	313.465i	0.183728	+	0.318227i
$100$		0			0
$101$	41.2254			0.0406147			0.0203073	−	0.999794i	$-0.493536\pi$
$101$	41.2254			0.0406147			0.0203073	+	0.999794i	$0.493536\pi$
$102$		0			0
$103$	603.805	−	1045.82i	0.577618	−	1.00046i	−0.418134	−	0.908385i	$-0.637316\pi$
$103$	603.805	−	1045.82i	0.577618	−	1.00046i	0.995752	−	0.0920781i	$-0.0293509\pi$
$104$		0			0
$105$	485.502	+	840.914i	0.451239	+	0.781570i
$106$		0			0
$107$	339.656	+	588.302i	0.306877	+	0.531526i	0.977677	−	0.210112i	$-0.0673828\pi$
$107$	339.656	+	588.302i	0.306877	+	0.531526i	−0.670801	+	0.741638i	$0.734049\pi$
$108$		0			0
$109$	1703.76			1.49716			0.748582	−	0.663042i	$-0.230735\pi$
$109$	1703.76			1.49716			0.748582	+	0.663042i	$0.230735\pi$
$110$		0			0
$111$	772.903	−	1338.71i	0.660907	−	1.14473i
$112$		0			0
$113$	−644.341	+	1116.03i	−0.536412	+	0.929093i	0.462682	+	0.886524i	$0.346887\pi$
$113$	−644.341	+	1116.03i	−0.536412	+	0.929093i	−0.999094	+	0.0425681i	$0.986446\pi$
$114$		0			0
$115$	−237.174	+	410.797i	−0.192318	+	0.333105i
$116$		0			0
$117$	−532.552	−	922.407i	−0.420807	−	0.728859i
$118$		0			0
$119$	−1026.98	+	1778.79i	−0.791122	+	1.37026i
$120$		0			0
$121$	316.107	+	547.514i	0.237496	+	0.411355i
$122$		0			0
$123$	−473.260			−0.346931
$124$		0			0
$125$	1214.98			0.869367
$126$		0			0
$127$	−515.888	−	893.544i	−0.360454	−	0.624324i	0.627582	−	0.778551i	$-0.284045\pi$
$127$	−515.888	−	893.544i	−0.360454	−	0.624324i	−0.988036	+	0.154226i	$0.950712\pi$
$128$		0			0
$129$	554.197	−	959.898i	0.378251	−	0.655150i
$130$		0			0
$131$	42.1780	+	73.0545i	0.0281306	+	0.0487237i	0.879748	−	0.475440i	$-0.157711\pi$
$131$	42.1780	+	73.0545i	0.0281306	+	0.0487237i	−0.851617	+	0.524164i	$0.824378\pi$
$132$		0			0
$133$	−890.009	+	1541.54i	−0.580252	+	1.00503i
$134$		0			0
$135$	912.621	−	1580.71i	0.581822	−	1.00774i
$136$		0			0
$137$	−580.954	+	1006.24i	−0.362294	+	0.627511i	−0.988338	−	0.152276i	$-0.951340\pi$
$137$	−580.954	+	1006.24i	−0.362294	+	0.627511i	0.626044	+	0.779788i	$0.284673\pi$
$138$		0			0
$139$	−1809.19			−1.10398			−0.551991	−	0.833850i	$-0.686132\pi$
$139$	−1809.19			−1.10398			−0.551991	+	0.833850i	$0.686132\pi$
$140$		0			0
$141$	−659.387	−	1142.09i	−0.393833	−	0.682138i
$142$		0			0
$143$	1028.13	+	1780.77i	0.601233	+	1.04137i
$144$		0			0
$145$	992.692	−	1719.39i	0.568542	−	0.984743i
$146$		0			0
$147$	−458.299			−0.257142
$148$		0			0
$149$	143.221	+	248.067i	0.0787460	+	0.136392i	0.902709	−	0.430251i	$-0.141575\pi$
$149$	143.221	+	248.067i	0.0787460	+	0.136392i	−0.823963	+	0.566643i	$0.808242\pi$
$150$		0			0
$151$	258.834			0.139494			0.0697472	−	0.997565i	$-0.477781\pi$
$151$	258.834			0.139494			0.0697472	+	0.997565i	$0.477781\pi$
$152$		0			0
$153$	1299.17			0.686479
$154$		0			0
$155$	−1213.28	+	1741.26i	−0.628728	+	0.902333i
$156$		0			0
$157$	3721.99			1.89202			0.946009	−	0.324140i	$-0.105075\pi$
$157$	3721.99			1.89202			0.946009	+	0.324140i	$0.105075\pi$
$158$		0			0
$159$	−1976.31			−0.985735
$160$		0			0
$161$	−417.565	−	723.244i	−0.204402	−	0.354035i
$162$		0			0
$163$	−1133.55			−0.544702			−0.272351	−	0.962198i	$-0.587801\pi$
$163$	−1133.55			−0.544702			−0.272351	+	0.962198i	$0.587801\pi$
$164$		0			0
$165$	−592.853	+	1026.85i	−0.279718	+	0.484486i
$166$		0			0
$167$	−1449.41	−	2510.45i	−0.671610	−	1.16326i	−0.977448	−	0.211178i	$-0.932270\pi$
$167$	−1449.41	−	2510.45i	−0.671610	−	1.16326i	0.305838	−	0.952084i	$-0.401063\pi$
$168$		0			0
$169$	−1926.88	−	3337.45i	−0.877051	−	1.51910i
$170$		0			0
$171$	1125.89			0.503502
$172$		0			0
$173$	−851.800	+	1475.36i	−0.374342	+	0.648379i	−0.990228	−	0.139456i	$-0.955465\pi$
$173$	−851.800	+	1475.36i	−0.374342	+	0.648379i	0.615886	+	0.787835i	$0.288798\pi$
$174$		0			0
$175$	283.458	−	490.964i	0.122442	−	0.212076i
$176$		0			0
$177$	909.950	−	1576.08i	0.386418	−	0.669296i
$178$		0			0
$179$	−1258.49	−	2179.78i	−0.525499	−	0.910191i	−0.999559	−	0.0296981i	$-0.990545\pi$
$179$	−1258.49	−	2179.78i	−0.525499	−	0.910191i	0.474060	−	0.880492i	$-0.342788\pi$
$180$		0			0
$181$	−744.336	+	1289.23i	−0.305669	+	0.529434i	−0.977410	−	0.211352i	$-0.932213\pi$
$181$	−744.336	+	1289.23i	−0.305669	+	0.529434i	0.671741	+	0.740786i	$0.265547\pi$
$182$		0			0
$183$	−806.367	−	1396.67i	−0.325729	−	0.564179i
$184$		0			0
$185$	−5210.36			−2.07067
$186$		0			0
$187$	−2508.13			−0.980815
$188$		0			0
$189$	1606.75	+	2782.97i	0.618380	+	1.07107i
$190$		0			0
$191$	−1710.55	+	2962.76i	−0.648016	+	1.12240i	0.335580	+	0.942012i	$0.391068\pi$
$191$	−1710.55	+	2962.76i	−0.648016	+	1.12240i	−0.983596	+	0.180386i	$0.942265\pi$
$192$		0			0
$193$	−158.115	−	273.864i	−0.0589710	−	0.102141i	0.835033	−	0.550200i	$-0.185449\pi$
$193$	−158.115	−	273.864i	−0.0589710	−	0.102141i	−0.894004	+	0.448059i	$0.852115\pi$
$194$		0			0
$195$	1744.54	−	3021.62i	0.640660	−	1.10966i
$196$		0			0
$197$	−277.978	+	481.472i	−0.100534	+	0.174129i	−0.911905	−	0.410402i	$-0.865388\pi$
$197$	−277.978	+	481.472i	−0.100534	+	0.174129i	0.811371	+	0.584531i	$0.198722\pi$
$198$		0			0
$199$	204.913	−	354.919i	0.0729943	−	0.126430i	−0.827218	−	0.561881i	$-0.810078\pi$
$199$	204.913	−	354.919i	0.0729943	−	0.126430i	0.900212	+	0.435451i	$0.143411\pi$
$200$		0			0
$201$	228.453			0.0801683
$202$		0			0
$203$	1747.72	+	3027.14i	0.604266	+	1.04662i
$204$		0			0
$205$	797.596	+	1381.48i	0.271739	+	0.470666i
$206$		0			0
$207$	−264.116	+	457.463i	−0.0886828	+	0.153603i
$208$		0			0
$209$	−2173.60			−0.719384
$210$		0			0
$211$	−1062.67	−	1840.59i	−0.346715	−	0.600529i	0.638949	−	0.769249i	$-0.279370\pi$
$211$	−1062.67	−	1840.59i	−0.346715	−	0.600529i	−0.985664	+	0.168721i	$0.946036\pi$
$212$		0			0
$213$	2501.04			0.804546
$214$		0			0
$215$	−3736.00			−1.18508
$216$		0			0
$217$	−1586.89	−	3382.72i	−0.496428	−	1.05822i
$218$		0			0
$219$	1337.11			0.412574
$220$		0			0
$221$	7380.44			2.24644
$222$		0			0
$223$	1694.92	+	2935.68i	0.508969	+	0.881559i	0.999946	+	0.0103872i	$0.00330641\pi$
$223$	1694.92	+	2935.68i	0.508969	+	0.881559i	−0.490977	+	0.871172i	$0.663360\pi$
$224$		0			0
$225$	−358.583			−0.106247
$226$		0			0
$227$	−215.957	+	374.049i	−0.0631435	+	0.109368i	−0.895869	−	0.444318i	$-0.853446\pi$
$227$	−215.957	+	374.049i	−0.0631435	+	0.109368i	0.832725	+	0.553686i	$0.186779\pi$
$228$		0			0
$229$	1614.64	+	2796.63i	0.465931	+	0.807016i	0.999243	−	0.0389027i	$-0.0123862\pi$
$229$	1614.64	+	2796.63i	0.465931	+	0.807016i	−0.533312	+	0.845918i	$0.679053\pi$
$230$		0			0
$231$	−1043.77	−	1807.86i	−0.297294	−	0.514929i
$232$		0			0
$233$	2132.86			0.599692			0.299846	−	0.953988i	$-0.403065\pi$
$233$	2132.86			0.599692			0.299846	+	0.953988i	$0.403065\pi$
$234$		0			0
$235$	−2222.56	+	3849.58i	−0.616952	+	1.06859i
$236$		0			0
$237$	−956.411	+	1656.55i	−0.262133	+	0.454028i
$238$		0			0
$239$	328.984	−	569.817i	0.0890385	−	0.154219i	−0.818066	−	0.575124i	$-0.804954\pi$
$239$	328.984	−	569.817i	0.0890385	−	0.154219i	0.907105	+	0.420904i	$0.138287\pi$
$240$		0			0
$241$	−451.457	−	781.947i	−0.120668	−	0.209003i	0.799363	−	0.600848i	$-0.205170\pi$
$241$	−451.457	−	781.947i	−0.120668	−	0.209003i	−0.920031	+	0.391845i	$0.871837\pi$
$242$		0			0
$243$	1690.61	−	2928.23i	0.446308	−	0.773029i
$244$		0			0
$245$	772.381	+	1337.80i	0.201411	+	0.348853i
$246$		0			0
$247$	6396.07			1.64766
$248$		0			0
$249$	−4105.71			−1.04493
$250$		0			0
$251$	1.12627	+	1.95077i	0.000283226	+	0.000490563i	0.866167	−	0.499755i	$-0.166577\pi$
$251$	1.12627	+	1.95077i	0.000283226	+	0.000490563i	−0.865884	+	0.500245i	$0.833243\pi$
$252$		0			0
$253$	509.894	−	883.163i	0.126707	−	0.219462i
$254$		0			0
$255$	2127.91	+	3685.64i	0.522567	+	0.905113i
$256$		0			0
$257$	2067.49	−	3581.00i	0.501815	−	0.869170i	−0.498182	−	0.867072i	$-0.665999\pi$
$257$	2067.49	−	3581.00i	0.501815	−	0.869170i	0.999998	−	0.00209744i	$-0.000667637\pi$
$258$		0			0
$259$	4586.65	−	7944.31i	1.10039	−	1.90593i
$260$		0			0
$261$	1105.46	−	1914.71i	0.262169	−	0.454091i
$262$		0			0
$263$	−1926.20			−0.451614			−0.225807	−	0.974172i	$-0.572502\pi$
$263$	−1926.20			−0.451614			−0.225807	+	0.974172i	$0.572502\pi$
$264$		0			0
$265$	3330.72	+	5768.98i	0.772093	+	1.33730i
$266$		0			0
$267$	−1640.51	−	2841.45i	−0.376021	−	0.651287i
$268$		0			0
$269$	2559.75	−	4433.61i	0.580187	−	1.00491i	−0.415269	−	0.909699i	$-0.636313\pi$
$269$	2559.75	−	4433.61i	0.580187	−	1.00491i	0.995457	−	0.0952155i	$-0.0303540\pi$
$270$		0			0
$271$	−5788.68			−1.29755			−0.648777	−	0.760979i	$-0.724719\pi$
$271$	−5788.68			−1.29755			−0.648777	+	0.760979i	$0.724719\pi$
$272$		0			0
$273$	3071.41	+	5319.83i	0.680916	+	1.17938i
$274$		0			0
$275$	692.268			0.151801
$276$		0			0
$277$	596.399			0.129365			0.0646826	−	0.997906i	$-0.479397\pi$
$277$	596.399			0.129365			0.0646826	+	0.997906i	$0.479397\pi$
$278$		0			0
$279$	−1351.10	+	1939.07i	−0.289923	+	0.416089i
$280$		0			0
$281$	3570.44			0.757988			0.378994	−	0.925399i	$-0.376270\pi$
$281$	3570.44			0.757988			0.378994	+	0.925399i	$0.376270\pi$
$282$		0			0
$283$	7888.42			1.65695			0.828476	−	0.560024i	$-0.189208\pi$
$283$	7888.42			1.65695			0.828476	+	0.560024i	$0.189208\pi$
$284$		0			0
$285$	1844.09	+	3194.06i	0.383279	+	0.663859i
$286$		0			0
$287$	−2808.47			−0.577627
$288$		0			0
$289$	−2044.67	+	3541.47i	−0.416175	+	0.720836i
$290$		0			0
$291$	−1854.02	−	3211.26i	−0.373487	−	0.646899i
$292$		0			0
$293$	3810.24	+	6599.52i	0.759715	+	1.31586i	0.942996	+	0.332804i	$0.107995\pi$
$293$	3810.24	+	6599.52i	0.759715	+	1.31586i	−0.183281	+	0.983061i	$0.558672\pi$
$294$		0			0
$295$	−6134.23			−1.21067
$296$		0			0
$297$	−1962.02	+	3398.32i	−0.383327	+	0.663942i
$298$		0			0
$299$	−1500.42	+	2598.80i	−0.290206	+	0.502651i
$300$		0			0
$301$	3288.78	−	5696.33i	0.629774	−	1.09080i
$302$		0			0
$303$	75.1937	+	130.239i	0.0142566	+	0.0246932i
$304$		0			0
$305$	−2717.98	+	4707.67i	−0.510265	+	0.883805i
$306$		0			0
$307$	1539.39	+	2666.29i	0.286180	+	0.495679i	0.972895	−	0.231248i	$-0.0742810\pi$
$307$	1539.39	+	2666.29i	0.286180	+	0.495679i	−0.686714	+	0.726927i	$0.740948\pi$
$308$		0			0
$309$	4405.27			0.811026
$310$		0			0
$311$	−5843.87			−1.06552			−0.532758	−	0.846268i	$-0.678844\pi$
$311$	−5843.87			−1.06552			−0.532758	+	0.846268i	$0.678844\pi$
$312$		0			0
$313$	−2514.32	−	4354.94i	−0.454051	−	0.786440i	0.544582	−	0.838708i	$-0.316688\pi$
$313$	−2514.32	−	4354.94i	−0.454051	−	0.786440i	−0.998633	+	0.0522679i	$0.983355\pi$
$314$		0			0
$315$	1822.35	−	3156.40i	0.325961	−	0.564582i
$316$		0			0
$317$	−5091.73	−	8819.13i	−0.902145	−	1.56256i	−0.824704	−	0.565564i	$-0.808658\pi$
$317$	−5091.73	−	8819.13i	−0.902145	−	1.56256i	−0.0774407	−	0.996997i	$-0.524675\pi$
$318$		0			0
$319$	−2134.16	+	3696.48i	−0.374578	+	0.648787i
$320$		0			0
$321$	−1239.04	+	2146.08i	−0.215441	+	0.373154i
$322$		0			0
$323$	−3900.82	+	6756.41i	−0.671973	+	1.16389i
$324$		0			0
$325$	−2037.08			−0.347682
$326$		0			0
$327$	3107.60	+	5382.52i	0.525538	+	0.910258i
$328$		0			0
$329$	−3913.01	−	6777.53i	−0.655718	−	1.13574i
$330$		0			0
$331$	4029.80	−	6979.82i	0.669178	−	1.15905i	−0.308957	−	0.951076i	$-0.599980\pi$
$331$	4029.80	−	6979.82i	0.669178	−	1.15905i	0.978134	−	0.207974i	$-0.0666869\pi$
$332$		0			0
$333$	−5802.24			−0.954838
$334$		0			0
$335$	−385.017	−	666.868i	−0.0627932	−	0.108761i
$336$		0			0
$337$	−7092.18			−1.14640			−0.573198	−	0.819417i	$-0.694298\pi$
$337$	−7092.18			−1.14640			−0.573198	+	0.819417i	$0.694298\pi$
$338$		0			0
$339$	−4701.02			−0.753169
$340$		0			0
$341$	2608.40	−	3743.50i	0.414231	−	0.594492i
$342$		0			0
$343$	4705.55			0.740746
$344$		0			0
$345$	−1730.39			−0.270031
$346$		0			0
$347$	5145.76	+	8912.72i	0.796078	+	1.37885i	0.922152	+	0.386827i	$0.126429\pi$
$347$	5145.76	+	8912.72i	0.796078	+	1.37885i	−0.126075	+	0.992021i	$0.540238\pi$
$348$		0			0
$349$	5926.39			0.908975			0.454487	−	0.890753i	$-0.349822\pi$
$349$	5926.39			0.908975			0.454487	+	0.890753i	$0.349822\pi$
$350$		0			0
$351$	5773.47	−	9999.94i	0.877963	−	1.52068i
$352$		0			0
$353$	−606.020	−	1049.66i	−0.0913744	−	0.158265i	0.816715	−	0.577041i	$-0.195793\pi$
$353$	−606.020	−	1049.66i	−0.0913744	−	0.158265i	−0.908090	+	0.418776i	$0.862459\pi$
$354$		0			0
$355$	−4215.05	−	7300.68i	−0.630173	−	1.09149i
$356$		0			0
$357$	−7492.73			−1.11080
$358$		0			0
$359$	5414.64	−	9378.43i	0.796027	−	1.37876i	−0.126158	−	0.992010i	$-0.540265\pi$
$359$	5414.64	−	9378.43i	0.796027	−	1.37876i	0.922185	−	0.386749i	$-0.126402\pi$
$360$		0			0
$361$	48.9609	−	84.8027i	0.00713820	−	0.0123637i
$362$		0			0
$363$	−1153.14	+	1997.29i	−0.166733	+	0.288789i
$364$		0			0
$365$	−2253.46	−	3903.11i	−0.323155	−	0.559721i
$366$		0			0
$367$	1606.05	−	2781.75i	0.228433	−	0.395658i	−0.728911	−	0.684609i	$-0.759973\pi$
$367$	1606.05	−	2781.75i	0.228433	−	0.395658i	0.957344	+	0.288951i	$0.0933064\pi$
$368$		0			0
$369$	888.201	+	1538.41i	0.125306	+	0.217036i
$370$		0			0
$371$	−11728.1			−1.64121
$372$		0			0
$373$	−10849.0			−1.50600			−0.753001	−	0.658019i	$-0.771395\pi$
$373$	−10849.0			−1.50600			−0.753001	+	0.658019i	$0.771395\pi$
$374$		0			0
$375$	2216.07	+	3838.35i	0.305167	+	0.528565i
$376$		0			0
$377$	6280.02	−	10877.3i	0.857924	−	1.48597i
$378$		0			0
$379$	3455.59	+	5985.26i	0.468343	+	0.811193i	0.999345	−	0.0361767i	$-0.0115179\pi$
$379$	3455.59	+	5985.26i	0.468343	+	0.811193i	−0.531003	+	0.847370i	$0.678185\pi$
$380$		0			0
$381$	1881.92	−	3259.58i	0.253054	−	0.438303i
$382$		0			0
$383$	−5995.58	+	10384.7i	−0.799895	+	1.38546i	0.119788	+	0.992799i	$0.461778\pi$
$383$	−5995.58	+	10384.7i	−0.799895	+	1.38546i	−0.919684	+	0.392660i	$0.871555\pi$
$384$		0			0
$385$	−3518.17	+	6093.65i	−0.465721	+	0.806653i
$386$		0			0
$387$	−4160.40			−0.546473
$388$		0			0
$389$	4640.58	+	8037.72i	0.604850	+	1.04763i	0.992075	+	0.125646i	$0.0401002\pi$
$389$	4640.58	+	8037.72i	0.604850	+	1.04763i	−0.387225	+	0.921985i	$0.626566\pi$
$390$		0			0
$391$	−1830.15	−	3169.90i	−0.236712	−	0.409997i
$392$		0			0
$393$	−153.862	+	266.497i	−0.0197489	+	0.0342062i
$394$		0			0
$395$	6447.44			0.821280
$396$		0			0
$397$	3217.95	+	5573.65i	0.406812	+	0.704618i	0.994530	−	0.104447i	$-0.0333072\pi$
$397$	3217.95	+	5573.65i	0.406812	+	0.704618i	−0.587719	+	0.809065i	$0.699974\pi$
$398$		0			0
$399$	−6493.37			−0.814725
$400$		0			0
$401$	−13998.8			−1.74330			−0.871652	−	0.490125i	$-0.836951\pi$
$401$	−13998.8			−1.74330			−0.871652	+	0.490125i	$0.836951\pi$
$402$		0			0
$403$	−7675.50	+	11015.7i	−0.948744	+	1.36161i
$404$		0			0
$405$	2112.56			0.259195
$406$		0			0
$407$	11201.6			1.36424
$408$		0			0
$409$	−658.336	−	1140.27i	−0.0795908	−	0.137855i	0.823483	−	0.567341i	$-0.192028\pi$
$409$	−658.336	−	1140.27i	−0.0795908	−	0.137855i	−0.903073	+	0.429486i	$0.858695\pi$
$410$		0			0
$411$	−4238.56			−0.508692
$412$		0			0
$413$	5399.92	−	9352.94i	0.643373	−	1.11435i
$414$		0			0
$415$	6919.43	+	11984.8i	0.818462	+	1.41762i
$416$		0			0
$417$	−3299.90	−	5715.59i	−0.387522	−	0.671208i
$418$		0			0
$419$	16922.7			1.97310			0.986551	−	0.163455i	$-0.0522640\pi$
$419$	16922.7			1.97310			0.986551	+	0.163455i	$0.0522640\pi$
$420$		0			0
$421$	4246.27	−	7354.75i	0.491568	−	0.851421i	−0.508384	−	0.861130i	$-0.669757\pi$
$421$	4246.27	−	7354.75i	0.491568	−	0.851421i	0.999953	+	0.00970873i	$0.00309043\pi$
$422$		0			0
$423$	−2475.03	+	4286.89i	−0.284492	+	0.492755i
$424$		0			0
$425$	1242.37	−	2151.84i	0.141797	−	0.245599i
$426$		0			0
$427$	−4785.23	−	8288.27i	−0.542327	−	0.939338i
$428$		0			0
$429$	−3750.53	+	6496.12i	−0.422092	+	0.731085i
$430$		0			0
$431$	−6007.76	−	10405.7i	−0.671424	−	1.16294i	−0.977500	−	0.210933i	$-0.932350\pi$
$431$	−6007.76	−	10405.7i	−0.671424	−	1.16294i	0.306077	−	0.952007i	$-0.400984\pi$
$432$		0			0
$433$	−11184.0			−1.24127			−0.620635	−	0.784099i	$-0.713125\pi$
$433$	−11184.0			−1.24127			−0.620635	+	0.784099i	$0.713125\pi$
$434$		0			0
$435$	7242.53			0.798283
$436$		0			0
$437$	−1586.05	−	2747.11i	−0.173618	−	0.300715i
$438$		0			0
$439$	2778.81	−	4813.04i	0.302108	−	0.523266i	−0.674505	−	0.738270i	$-0.735643\pi$
$439$	2778.81	−	4813.04i	0.302108	−	0.523266i	0.976613	+	0.215004i	$0.0689765\pi$
$440$		0			0
$441$	860.121	+	1489.77i	0.0928756	+	0.160865i
$442$		0			0
$443$	−5301.51	+	9182.49i	−0.568584	+	0.984816i	0.428123	+	0.903721i	$0.359175\pi$
$443$	−5301.51	+	9182.49i	−0.568584	+	0.984816i	−0.996706	+	0.0810951i	$0.974158\pi$
$444$		0			0
$445$	−5529.57	+	9577.50i	−0.589049	+	1.02026i
$446$		0			0
$447$	−522.461	+	904.929i	−0.0552831	+	0.0957532i
$448$		0			0
$449$	12925.0			1.35850			0.679251	−	0.733906i	$-0.262305\pi$
$449$	12925.0			1.35850			0.679251	+	0.733906i	$0.262305\pi$
$450$		0			0
$451$	−1714.73	−	2970.00i	−0.179032	−	0.310093i
$452$		0			0
$453$	472.104	+	817.709i	0.0489656	+	0.0848109i
$454$		0			0
$455$	10352.6	−	17931.2i	1.06668	−	1.84754i
$456$		0			0
$457$	1766.99			0.180868			0.0904338	−	0.995902i	$-0.471175\pi$
$457$	1766.99			0.180868			0.0904338	+	0.995902i	$0.471175\pi$
$458$		0			0
$459$	7042.22	+	12197.5i	0.716128	+	1.24037i
$460$		0			0
$461$	10180.0			1.02848			0.514241	−	0.857646i	$-0.328074\pi$
$461$	10180.0			1.02848			0.514241	+	0.857646i	$0.328074\pi$
$462$		0			0
$463$	15702.9			1.57619			0.788096	−	0.615553i	$-0.211067\pi$
$463$	15702.9			1.57619			0.788096	+	0.615553i	$0.211067\pi$
$464$		0			0
$465$	−7713.97	−	656.983i	−0.769305	−	0.0655201i
$466$		0			0
$467$	11524.9			1.14198			0.570992	−	0.820956i	$-0.306559\pi$
$467$	11524.9			1.14198			0.570992	+	0.820956i	$0.306559\pi$
$468$		0			0
$469$	1355.71			0.133477
$470$		0			0
$471$	6788.77	+	11758.5i	0.664140	+	1.15032i
$472$		0			0
$473$	8031.94			0.780780
$474$		0			0
$475$	1076.66	−	1864.84i	0.104002	−	0.180136i
$476$		0			0
$477$	3709.09	+	6424.32i	0.356032	+	0.616666i
$478$		0			0
$479$	−7657.62	−	13263.4i	−0.730450	−	1.26518i	−0.956691	−	0.291105i	$-0.905977\pi$
$479$	−7657.62	−	13263.4i	−0.730450	−	1.26518i	0.226241	−	0.974071i	$-0.427356\pi$
$480$		0			0
$481$	−32962.0			−3.12461
$482$		0			0
$483$	1523.25	−	2638.34i	0.143499	−	0.248548i
$484$		0			0
$485$	−6249.25	+	10824.0i	−0.585080	+	1.01339i
$486$		0			0
$487$	−4350.64	+	7535.52i	−0.404818	+	0.701165i	−0.994300	−	0.106616i	$-0.965998\pi$
$487$	−4350.64	+	7535.52i	−0.404818	+	0.701165i	0.589483	+	0.807781i	$0.299332\pi$
$488$		0			0
$489$	−2067.55	−	3581.10i	−0.191202	−	0.331172i
$490$		0			0
$491$	−282.883	+	489.968i	−0.0260007	+	0.0450345i	−0.878733	−	0.477314i	$-0.841611\pi$
$491$	−282.883	+	489.968i	−0.0260007	+	0.0450345i	0.852732	+	0.522348i	$0.174944\pi$
$492$		0			0
$493$	7660.08	+	13267.6i	0.699782	+	1.21206i
$494$		0			0
$495$	4450.59			0.404120
$496$		0			0
$497$	14841.9			1.33954
$498$		0			0
$499$	662.158	+	1146.89i	0.0594033	+	0.102890i	0.894198	−	0.447672i	$-0.147747\pi$
$499$	662.158	+	1146.89i	0.0594033	+	0.102890i	−0.834794	+	0.550562i	$0.814414\pi$
$500$		0			0
$501$	5287.35	−	9157.95i	0.471499	−	0.816661i
$502$		0			0
$503$	10227.8	+	17715.1i	0.906631	+	1.57033i	0.818713	+	0.574203i	$0.194688\pi$
$503$	10227.8	+	17715.1i	0.906631	+	1.57033i	0.0879181	+	0.996128i	$0.471979\pi$
$504$		0			0
$505$	253.451	−	438.990i	0.0223335	−	0.0386828i
$506$		0			0
$507$	7029.12	−	12174.8i	0.615728	−	1.06647i
$508$		0			0
$509$	−3879.01	+	6718.65i	−0.337788	+	0.585066i	−0.984016	−	0.178078i	$-0.943012\pi$
$509$	−3879.01	+	6718.65i	−0.337788	+	0.585066i	0.646228	+	0.763144i	$0.276345\pi$
$510$		0			0
$511$	7934.84			0.686921
$512$		0			0
$513$	6102.95	+	10570.6i	0.525247	+	0.909755i
$514$		0			0
$515$	−7424.29	−	12859.3i	−0.635249	−	1.10028i
$516$		0			0
$517$	4778.22	−	8276.12i	0.406472	−	0.704030i
$518$		0			0
$519$	−6214.61			−0.525609
$520$		0			0
$521$	1234.98	+	2139.05i	0.103849	+	0.179872i	0.913268	−	0.407360i	$-0.133551\pi$
$521$	1234.98	+	2139.05i	0.103849	+	0.179872i	−0.809418	+	0.587233i	$0.800217\pi$
$522$		0			0
$523$	16227.2			1.35672			0.678360	−	0.734730i	$-0.262691\pi$
$523$	16227.2			1.35672			0.678360	+	0.734730i	$0.262691\pi$
$524$		0			0
$525$	2068.07			0.171920
$526$		0			0
$527$	−6955.16	−	14826.1i	−0.574899	−	1.22550i
$528$		0			0
$529$	−10678.7			−0.877681
$530$		0			0
$531$	−6831.06			−0.558273
$532$		0			0
$533$	5045.79	+	8739.56i	0.410051	+	0.710230i
$534$		0			0
$535$	8352.72			0.674990
$536$		0			0
$537$	4590.89	−	7951.66i	0.368923	−	0.638994i
$538$		0			0
$539$	−1660.52	−	2876.11i	−0.132697	−	0.229838i
$540$		0			0
$541$	−7876.41	−	13642.3i	−0.625940	−	1.08416i	−0.988358	−	0.152144i	$-0.951382\pi$
$541$	−7876.41	−	13642.3i	−0.625940	−	1.08416i	0.362418	−	0.932015i	$-0.381951\pi$
$542$		0			0
$543$	−5430.57			−0.429186
$544$		0			0
$545$	10474.6	−	18142.6i	0.823272	−	1.42595i
$546$		0			0
$547$	−6498.46	+	11255.7i	−0.507960	+	0.879812i	0.491998	+	0.870596i	$0.336267\pi$
$547$	−6498.46	+	11255.7i	−0.507960	+	0.879812i	−0.999958	+	0.00921567i	$0.997067\pi$
$548$		0			0
$549$	−3026.73	+	5242.45i	−0.235296	+	0.407545i
$550$		0			0
$551$	6638.41	+	11498.1i	0.513259	+	0.888990i
$552$		0			0
$553$	−5675.64	+	9830.49i	−0.436442	+	0.755940i
$554$		0			0
$555$	−9503.50	−	16460.6i	−0.726849	−	1.25894i
$556$		0			0
$557$	−20739.6			−1.57767			−0.788837	−	0.614603i	$-0.789316\pi$
$557$	−20739.6			−1.57767			−0.788837	+	0.614603i	$0.789316\pi$
$558$		0			0
$559$	−23634.9			−1.78828
$560$		0			0
$561$	−4574.73	−	7923.67i	−0.344288	−	0.596324i
$562$		0			0
$563$	−1179.46	+	2042.88i	−0.0882918	+	0.152926i	−0.906789	−	0.421584i	$-0.861474\pi$
$563$	−1179.46	+	2042.88i	−0.0882918	+	0.152926i	0.818497	+	0.574510i	$0.194807\pi$
$564$		0			0
$565$	7922.73	+	13722.6i	0.589932	+	1.02179i
$566$		0			0
$567$	−1859.67	+	3221.05i	−0.137741	+	0.238574i
$568$		0			0
$569$	4721.26	−	8177.47i	0.347848	−	0.602491i	−0.638019	−	0.770021i	$-0.720246\pi$
$569$	4721.26	−	8177.47i	0.347848	−	0.602491i	0.985867	+	0.167530i	$0.0535791\pi$
$570$		0			0
$571$	289.602	−	501.605i	0.0212250	−	0.0367627i	−0.855218	−	0.518269i	$-0.826577\pi$
$571$	289.602	−	501.605i	0.0212250	−	0.0367627i	0.876443	+	0.481506i	$0.159910\pi$
$572$		0			0
$573$	−12479.9			−0.909872
$574$		0			0
$575$	505.138	+	874.925i	0.0366360	+	0.0634555i
$576$		0			0
$577$	5082.98	+	8803.99i	0.366737	+	0.635208i	0.989053	−	0.147559i	$-0.0471415\pi$
$577$	5082.98	+	8803.99i	0.366737	+	0.635208i	−0.622316	+	0.782766i	$0.713808\pi$
$578$		0			0
$579$	576.794	−	999.036i	0.0414002	−	0.0717073i
$580$		0			0
$581$	−24364.5			−1.73978
$582$		0			0
$583$	−7160.64	−	12402.6i	−0.508685	−	0.881069i
$584$		0			0
$585$	−13096.4			−0.925586
$586$		0			0
$587$	3724.43			0.261880			0.130940	−	0.991390i	$-0.458200\pi$
$587$	3724.43			0.261880			0.130940	+	0.991390i	$0.458200\pi$
$588$		0			0
$589$	−6027.51	−	12848.7i	−0.421662	−	0.898846i
$590$		0			0
$591$	−2028.09			−0.141158
$592$		0			0
$593$	21434.0			1.48430			0.742148	−	0.670236i	$-0.233807\pi$
$593$	21434.0			1.48430			0.742148	+	0.670236i	$0.233807\pi$
$594$		0			0
$595$	12627.6	+	21871.7i	0.870056	+	1.50698i
$596$		0			0
$597$	1495.01			0.102490
$598$		0			0
$599$	−7198.37	+	12467.9i	−0.491014	+	0.850462i	−0.999946	−	0.0103449i	$-0.996707\pi$
$599$	−7198.37	+	12467.9i	−0.491014	+	0.850462i	0.508932	+	0.860807i	$0.330040\pi$
$600$		0			0
$601$	−1037.88	−	1797.66i	−0.0704426	−	0.122010i	0.828653	−	0.559763i	$-0.189108\pi$
$601$	−1037.88	−	1797.66i	−0.0704426	−	0.122010i	−0.899095	+	0.437753i	$0.855775\pi$
$602$		0			0
$603$	−428.754	−	742.623i	−0.0289556	−	0.0501525i
$604$		0			0
$605$	7773.61			0.522384
$606$		0			0
$607$	−2491.35	+	4315.14i	−0.166591	+	0.288544i	−0.937219	−	0.348741i	$-0.886609\pi$
$607$	−2491.35	+	4315.14i	−0.166591	+	0.288544i	0.770628	+	0.637285i	$0.219943\pi$
$608$		0			0
$609$	−6375.56	+	11042.8i	−0.424221	+	0.734772i
$610$		0			0
$611$	−14060.5	+	24353.4i	−0.930974	+	1.61249i
$612$		0			0
$613$	3965.22	+	6867.97i	0.261262	+	0.452520i	0.966578	−	0.256374i	$-0.0825279\pi$
$613$	3965.22	+	6867.97i	0.261262	+	0.452520i	−0.705315	+	0.708894i	$0.749195\pi$
$614$		0			0
$615$	−2909.57	+	5039.52i	−0.190773	+	0.330428i
$616$		0			0
$617$	−2591.35	−	4488.35i	−0.169082	−	0.292859i	0.769015	−	0.639230i	$-0.220747\pi$
$617$	−2591.35	−	4488.35i	−0.169082	−	0.292859i	−0.938097	+	0.346371i	$0.887414\pi$
$618$		0			0
$619$	−12908.9			−0.838213			−0.419107	−	0.907937i	$-0.637657\pi$
$619$	−12908.9			−0.838213			−0.419107	+	0.907937i	$0.637657\pi$
$620$		0			0
$621$	−5726.64			−0.370052
$622$		0			0
$623$	−9735.30	−	16862.0i	−0.626062	−	1.08437i
$624$		0			0
$625$	9106.34	−	15772.7i	0.582806	−	1.00945i
$626$		0			0
$627$	−3964.57	−	6866.84i	−0.252519	−	0.437376i
$628$		0			0
$629$	20102.8	−	34819.1i	1.27433	−	2.20720i
$630$		0			0
$631$	1250.56	−	2166.03i	0.0788969	−	0.136653i	−0.823877	−	0.566768i	$-0.808194\pi$
$631$	1250.56	−	2166.03i	0.0788969	−	0.136653i	0.902774	+	0.430115i	$0.141527\pi$
$632$		0			0
$633$	3876.53	−	6714.34i	0.243409	−	0.421597i
$634$		0			0
$635$	−12686.6			−0.792836
$636$		0			0
$637$	4886.27	+	8463.27i	0.303927	+	0.526416i
$638$		0			0
$639$	−4693.87	−	8130.02i	−0.290589	−	0.503315i
$640$		0			0
$641$	3846.31	−	6662.00i	0.237005	−	0.410504i	−0.722849	−	0.691006i	$-0.757168\pi$
$641$	3846.31	−	6662.00i	0.237005	−	0.410504i	0.959853	+	0.280502i	$0.0905010\pi$
$642$		0			0
$643$	−20745.4			−1.27234			−0.636172	−	0.771547i	$-0.719483\pi$
$643$	−20745.4			−1.27234			−0.636172	+	0.771547i	$0.719483\pi$
$644$		0			0
$645$	−6814.33	−	11802.8i	−0.415991	−	0.720517i
$646$		0			0
$647$	7854.07			0.477241			0.238621	−	0.971113i	$-0.423305\pi$
$647$	7854.07			0.477241			0.238621	+	0.971113i	$0.423305\pi$
$648$		0			0
$649$	13187.8			0.797639
$650$		0			0
$651$	7792.27	−	11183.3i	0.469129	−	0.673282i
$652$		0			0
$653$	17977.8			1.07737			0.538687	−	0.842506i	$-0.318921\pi$
$653$	17977.8			1.07737			0.538687	+	0.842506i	$0.318921\pi$
$654$		0			0
$655$	1037.23			0.0618747
$656$		0			0
$657$	−2509.45	−	4346.50i	−0.149015	−	0.258102i
$658$		0			0
$659$	−10293.2			−0.608447			−0.304224	−	0.952601i	$-0.598397\pi$
$659$	−10293.2			−0.608447			−0.304224	+	0.952601i	$0.598397\pi$
$660$		0			0
$661$	15587.9	−	26999.0i	0.917245	−	1.58871i	0.113664	−	0.993519i	$-0.463741\pi$
$661$	15587.9	−	26999.0i	0.917245	−	1.58871i	0.803581	−	0.595195i	$-0.202925\pi$
$662$		0			0
$663$	13461.7	+	23316.3i	0.788548	+	1.36581i
$664$		0			0
$665$	10943.4	+	18954.6i	0.638147	+	1.10530i
$666$		0			0
$667$	−6229.08			−0.361606
$668$		0			0
$669$	−6182.93	+	10709.1i	−0.357318	+	0.618893i
$670$		0			0
$671$	5843.31	−	10120.9i	0.336183	−	0.582285i
$672$		0			0
$673$	−8413.06	+	14571.9i	−0.481872	+	0.834627i	−0.999784	−	0.0208075i	$-0.993376\pi$
$673$	−8413.06	+	14571.9i	−0.481872	+	0.834627i	0.517912	+	0.855434i	$0.326710\pi$
$674$		0			0
$675$	−1943.72	−	3366.63i	−0.110835	−	0.191973i
$676$		0			0
$677$	−4807.44	+	8326.72i	−0.272917	+	0.472706i	−0.969607	−	0.244666i	$-0.921322\pi$
$677$	−4807.44	+	8326.72i	−0.272917	+	0.472706i	0.696690	+	0.717372i	$0.254655\pi$
$678$		0			0
$679$	−11002.3	−	19056.6i	−0.621843	−	1.07706i
$680$		0			0
$681$	−1575.59			−0.0886591
$682$		0			0
$683$	−23178.4			−1.29853			−0.649266	−	0.760561i	$-0.724924\pi$
$683$	−23178.4			−1.29853			−0.649266	+	0.760561i	$0.724924\pi$
$684$		0			0
$685$	7143.33	+	12372.6i	0.398442	+	0.690121i
$686$		0			0
$687$	−5890.07	+	10201.9i	−0.327104	+	0.566560i
$688$		0			0
$689$	21071.0	+	36496.0i	1.16508	+	2.01798i
$690$		0			0
$691$	7889.50	−	13665.0i	0.434343	−	0.752304i	−0.562899	−	0.826526i	$-0.690314\pi$
$691$	7889.50	−	13665.0i	0.434343	−	0.752304i	0.997242	+	0.0742220i	$0.0236473\pi$
$692$		0			0
$693$	−3917.83	+	6785.88i	−0.214756	+	0.371968i
$694$		0			0
$695$	−11122.8	+	19265.2i	−0.607066	+	1.05147i
$696$		0			0
$697$	−12309.3			−0.668933
$698$		0			0
$699$	3890.26	+	6738.12i	0.210505	+	0.364606i
$700$		0			0
$701$	−8331.63	−	14430.8i	−0.448904	−	0.777524i	0.549411	−	0.835552i	$-0.314852\pi$
$701$	−8331.63	−	14430.8i	−0.448904	−	0.777524i	−0.998315	+	0.0580281i	$0.981519\pi$
$702$		0			0
$703$	17421.6	−	30175.0i	0.934661	−	1.61888i
$704$		0			0
$705$	−16215.5			−0.866254
$706$		0			0
$707$	446.223	+	772.880i	0.0237368	+	0.0411134i
$708$		0			0
$709$	4783.69			0.253392			0.126696	−	0.991942i	$-0.459563\pi$
$709$	4783.69			0.253392			0.126696	+	0.991942i	$0.459563\pi$
$710$		0			0
$711$	7179.85			0.378714
$712$		0			0
$713$	6634.55	+	565.051i	0.348479	+	0.0296793i
$714$		0			0
$715$	25283.4			1.32244
$716$		0			0
$717$	2400.22			0.125018
$718$		0			0
$719$	−9947.95	−	17230.4i	−0.515989	−	0.893719i	−0.999828	−	0.0185616i	$-0.994091\pi$
$719$	−9947.95	−	17230.4i	−0.515989	−	0.893719i	0.483839	−	0.875157i	$-0.339242\pi$
$720$		0			0
$721$	26142.2			1.35033
$722$		0			0
$723$	1646.88	−	2852.48i	0.0847140	−	0.146729i
$724$		0			0
$725$	−2114.26	−	3662.00i	−0.108306	−	0.187591i
$726$		0			0
$727$	−5222.29	−	9045.27i	−0.266415	−	0.461445i	0.701518	−	0.712652i	$-0.252506\pi$
$727$	−5222.29	−	9045.27i	−0.266415	−	0.461445i	−0.967933	+	0.251207i	$0.919173\pi$
$728$		0			0
$729$	16973.4			0.862336
$730$		0			0
$731$	14414.4	−	24966.4i	0.729323	−	1.26322i
$732$		0			0
$733$	−13075.3	+	22647.0i	−0.658863	+	1.14118i	0.322048	+	0.946723i	$0.395629\pi$
$733$	−13075.3	+	22647.0i	−0.658863	+	1.14118i	−0.980910	+	0.194460i	$0.937705\pi$
$734$		0			0
$735$	−2817.59	+	4880.21i	−0.141399	+	0.244910i
$736$		0			0
$737$	827.738	+	1433.68i	0.0413706	+	0.0716560i
$738$		0			0
$739$	−7963.41	+	13793.0i	−0.396399	+	0.686583i	−0.993279	−	0.115748i	$-0.963074\pi$
$739$	−7963.41	+	13793.0i	−0.396399	+	0.686583i	0.596880	+	0.802331i	$0.296407\pi$
$740$		0			0
$741$	11666.2	+	20206.4i	0.578365	+	1.00176i
$742$		0			0
$743$	22506.4			1.11128			0.555639	−	0.831424i	$-0.312474\pi$
$743$	22506.4			1.11128			0.555639	+	0.831424i	$0.312474\pi$
$744$		0			0
$745$	3522.06			0.173206
$746$		0			0
$747$	7705.46	+	13346.3i	0.377414	+	0.653700i
$748$		0			0
$749$	−7352.85	+	12735.5i	−0.358701	+	0.621289i
$750$		0			0
$751$	11794.9	+	20429.3i	0.573105	+	0.992646i	0.996245	+	0.0865822i	$0.0275945\pi$
$751$	11794.9	+	20429.3i	0.573105	+	0.992646i	−0.423140	+	0.906064i	$0.639072\pi$
$752$		0			0
$753$	−4.10857	+	7.11625i	−0.000198837	+	0.000344396i
$754$		0			0
$755$	1591.30	−	2756.20i	0.0767062	−	0.132859i
$756$		0			0
$757$	−13742.0	+	23801.9i	−0.659791	+	1.14279i	0.320878	+	0.947121i	$0.396022\pi$
$757$	−13742.0	+	23801.9i	−0.659791	+	1.14279i	−0.980669	+	0.195672i	$0.937311\pi$
$758$		0			0
$759$	3720.11			0.177907
$760$		0			0
$761$	3362.27	+	5823.63i	0.160161	+	0.277407i	0.934926	−	0.354842i	$-0.115465\pi$
$761$	3362.27	+	5823.63i	0.160161	+	0.277407i	−0.774765	+	0.632249i	$0.782132\pi$
$762$		0			0
$763$	18441.5	+	31941.6i	0.875002	+	1.51555i
$764$		0			0
$765$	7987.17	−	13834.2i	0.377486	−	0.653825i
$766$		0			0
$767$	−38806.7			−1.82689
$768$		0			0
$769$	2181.38	+	3778.27i	0.102292	+	0.177175i	0.912629	−	0.408790i	$-0.134049\pi$
$769$	2181.38	+	3778.27i	0.102292	+	0.177175i	−0.810336	+	0.585965i	$0.800716\pi$
$770$		0			0
$771$	15084.1			0.704593
$772$		0			0
$773$	−8740.49			−0.406693			−0.203346	−	0.979107i	$-0.565182\pi$
$773$	−8740.49			−0.406693			−0.203346	+	0.979107i	$0.565182\pi$
$774$		0			0
$775$	1919.69	+	4092.16i	0.0889774	+	0.189671i
$776$		0			0
$777$	33463.5			1.54504
$778$		0			0
$779$	−10667.5			−0.490632
$780$		0			0
$781$	9061.83	+	15695.6i	0.415183	+	0.719118i
$782$		0			0
$783$	23968.9			1.09397
$784$		0			0
$785$	22882.5	−	39633.6i	1.04040	−	1.80202i
$786$		0			0
$787$	−19156.6	−	33180.2i	−0.867673	−	1.50285i	−0.864368	−	0.502860i	$-0.832281\pi$
$787$	−19156.6	−	33180.2i	−0.867673	−	1.50285i	−0.00330519	−	0.999995i	$-0.501052\pi$
$788$		0			0
$789$	−3513.31	−	6085.24i	−0.158526	−	0.274576i
$790$		0			0
$791$	−27897.3			−1.25400
$792$		0			0
$793$	−17194.6	+	29781.9i	−0.769985	+	1.33365i
$794$		0			0
$795$	−12150.2	+	21044.8i	−0.542043	+	0.938846i
$796$		0			0
$797$	22087.7	−	38257.0i	0.981663	−	1.70029i	0.325745	−	0.945458i	$-0.394385\pi$
$797$	22087.7	−	38257.0i	0.981663	−	1.70029i	0.655917	−	0.754833i	$-0.272282\pi$
$798$		0			0
$799$	−17150.3	−	29705.2i	−0.759367	−	1.31526i
$800$		0			0
$801$	−6157.72	+	10665.5i	−0.271626	+	0.470470i
$802$		0			0
$803$	4844.67	+	8391.21i	0.212907	+	0.368766i
$804$		0			0
$805$	−10268.6			−0.449593
$806$		0			0
$807$	18675.5			0.814634
$808$		0			0
$809$	9712.67	+	16822.8i	0.422101	+	0.731100i	0.996145	−	0.0877248i	$-0.0279596\pi$
$809$	9712.67	+	16822.8i	0.422101	+	0.731100i	−0.574044	+	0.818824i	$0.694626\pi$
$810$		0			0
$811$	20243.6	−	35063.0i	0.876510	−	1.51816i	0.0213645	−	0.999772i	$-0.493199\pi$
$811$	20243.6	−	35063.0i	0.876510	−	1.51816i	0.855145	−	0.518388i	$-0.173468\pi$
$812$		0			0
$813$	−10558.3	−	18287.6i	−0.455470	−	0.788897i
$814$		0			0
$815$	−6968.97	+	12070.6i	−0.299525	+	0.518792i
$816$		0			0
$817$	12491.8	−	21636.5i	0.534925	−	0.926518i
$818$		0			0
$819$	11528.6	−	19968.2i	0.491872	−	0.851948i
$820$		0			0
$821$	−8517.07			−0.362056			−0.181028	−	0.983478i	$-0.557942\pi$
$821$	−8517.07			−0.362056			−0.181028	+	0.983478i	$0.557942\pi$
$822$		0			0
$823$	−15672.7	−	27145.8i	−0.663809	−	1.14975i	−0.979607	−	0.200924i	$-0.935606\pi$
$823$	−15672.7	−	27145.8i	−0.663809	−	1.14975i	0.315798	−	0.948826i	$-0.397728\pi$
$824$		0			0
$825$	1262.67	+	2187.01i	0.0532856	+	0.0922933i
$826$		0			0
$827$	−10925.3	+	18923.1i	−0.459381	+	0.795671i	−0.998928	−	0.0462839i	$-0.985262\pi$
$827$	−10925.3	+	18923.1i	−0.459381	+	0.795671i	0.539547	+	0.841955i	$0.318595\pi$
$828$		0			0
$829$	38335.3			1.60608			0.803040	−	0.595925i	$-0.203215\pi$
$829$	38335.3			1.60608			0.803040	+	0.595925i	$0.203215\pi$
$830$		0			0
$831$	1087.81	+	1884.14i	0.0454100	+	0.0786524i
$832$		0			0
$833$	−11920.1			−0.495807
$834$		0			0
$835$	−35643.5			−1.47724
$836$		0			0
$837$	−25529.1	−	2174.26i	−1.05426	−	0.0897890i
$838$		0			0
$839$	43450.1			1.78792			0.893959	−	0.448148i	$-0.147916\pi$
$839$	43450.1			1.78792			0.893959	+	0.448148i	$0.147916\pi$
$840$		0			0
$841$	1682.83			0.0689997
$842$		0			0
$843$	6512.35	+	11279.7i	0.266070	+	0.460847i
$844$		0			0
$845$	−47385.3			−1.92912
$846$		0			0
$847$	−6843.06	+	11852.5i	−0.277604	+	0.480824i
$848$		0			0
$849$	14388.2	+	24921.1i	0.581627	+	1.00741i
$850$		0			0
$851$	8173.67	+	14157.2i	0.329248	+	0.570274i
$852$		0			0
$853$	4393.93			0.176372			0.0881860	−	0.996104i	$-0.471893\pi$
$853$	4393.93			0.176372			0.0881860	+	0.996104i	$0.471893\pi$
$854$		0			0
$855$	6921.87	−	11989.0i	0.276869	−	0.479551i
$856$		0			0
$857$	10421.2	−	18050.0i	0.415379	−	0.719458i	−0.580089	−	0.814553i	$-0.696982\pi$
$857$	10421.2	−	18050.0i	0.415379	−	0.719458i	0.995468	+	0.0950953i	$0.0303156\pi$
$858$		0			0
$859$	14929.9	−	25859.3i	0.593016	−	1.02713i	−0.400808	−	0.916162i	$-0.631271\pi$
$859$	14929.9	−	25859.3i	0.593016	−	1.02713i	0.993824	−	0.110971i	$-0.0353962\pi$
$860$		0			0
$861$	−5122.55	−	8872.52i	−0.202760	−	0.351190i
$862$		0			0
$863$	−639.546	+	1107.73i	−0.0252264	+	0.0436935i	−0.878363	−	0.477994i	$-0.841364\pi$
$863$	−639.546	+	1107.73i	−0.0252264	+	0.0436935i	0.853137	+	0.521688i	$0.174697\pi$
$864$		0			0
$865$	10473.6	+	18140.8i	0.411692	+	0.713071i
$866$		0			0
$867$	−14917.6			−0.584346
$868$		0			0
$869$	−13861.2			−0.541092
$870$		0			0
$871$	−2435.71	−	4218.78i	−0.0947542	−	0.164119i
$872$		0			0
$873$	−6959.15	+	12053.6i	−0.269795	+	0.467300i
$874$		0			0
$875$	13150.9	+	22778.0i	0.508092	+	0.880042i
$876$		0			0
$877$	8484.96	−	14696.4i	0.326701	−	0.565863i	−0.655154	−	0.755495i	$-0.727396\pi$
$877$	8484.96	−	14696.4i	0.326701	−	0.565863i	0.981855	+	0.189632i	$0.0607296\pi$
$878$		0			0
$879$	−13899.5	+	24074.6i	−0.533353	+	0.923794i
$880$		0			0
$881$	−5240.42	+	9076.67i	−0.200402	+	0.347106i	−0.948658	−	0.316304i	$-0.897558\pi$
$881$	−5240.42	+	9076.67i	−0.200402	+	0.347106i	0.748256	+	0.663410i	$0.230891\pi$
$882$		0			0
$883$	−7017.74			−0.267458			−0.133729	−	0.991018i	$-0.542695\pi$
$883$	−7017.74			−0.267458			−0.133729	+	0.991018i	$0.542695\pi$
$884$		0			0
$885$	−11188.6	−	19379.2i	−0.424973	−	0.736075i
$886$		0			0
$887$	16601.2	+	28754.2i	0.628427	+	1.08847i	0.987867	+	0.155300i	$0.0496343\pi$
$887$	16601.2	+	28754.2i	0.628427	+	1.08847i	−0.359440	+	0.933168i	$0.617032\pi$
$888$		0			0
$889$	11167.9	−	19343.4i	0.421327	−	0.729759i
$890$		0			0
$891$	−4541.74			−0.170768
$892$		0			0
$893$	−14862.9	−	25743.2i	−0.556961	−	0.964686i
$894$		0			0
$895$	−30948.5			−1.15586
$896$		0			0
$897$	−10946.8			−0.407474
$898$		0			0
$899$	−27768.9	−	2365.02i	−1.03019	−	0.0877396i
$900$		0			0
$901$	−51402.9			−1.90064
$902$		0			0
$903$	23994.4			0.884258
$904$		0			0
$905$	9152.25	+	15852.2i	0.336167	+	0.582258i
$906$		0			0
$907$	4406.58			0.161321			0.0806605	−	0.996742i	$-0.474297\pi$
$907$	4406.58			0.161321			0.0806605	+	0.996742i	$0.474297\pi$
$908$		0			0
$909$	282.242	−	488.858i	0.0102986	−	0.0178376i
$910$		0			0
$911$	20352.6	+	35251.8i	0.740190	+	1.28205i	0.952409	+	0.304824i	$0.0985977\pi$
$911$	20352.6	+	35251.8i	0.740190	+	1.28205i	−0.212219	+	0.977222i	$0.568069\pi$
$912$		0			0
$913$	−14875.9	−	25765.8i	−0.539234	−	0.933982i
$914$		0			0
$915$	−19830.0			−0.716457
$916$		0			0
$917$	−913.067	+	1581.48i	−0.0328813	+	0.0569520i
$918$		0			0
$919$	−12940.5	+	22413.6i	−0.464492	+	0.804524i	−0.999178	−	0.0405266i	$-0.987096\pi$
$919$	−12940.5	+	22413.6i	−0.464492	+	0.804524i	0.534686	+	0.845051i	$0.320430\pi$
$920$		0			0
$921$	−5615.56	+	9726.44i	−0.200911	+	0.347988i
$922$		0			0
$923$	−26665.5	−	46185.9i	−0.950925	−	1.64705i
$924$		0			0
$925$	−5548.57	+	9610.41i	−0.197228	+	0.341609i
$926$		0			0
$927$	−8267.68	−	14320.0i	−0.292930	−	0.507370i
$928$		0			0
$929$	−34296.0			−1.21121			−0.605605	−	0.795765i	$-0.707069\pi$
$929$	−34296.0			−1.21121			−0.605605	+	0.795765i	$0.707069\pi$
$930$		0			0
$931$	−10330.2			−0.363652
$932$		0			0
$933$	−10659.0	−	18461.9i	−0.374019	−	0.647820i
$934$		0			0
$935$	−15419.8	+	26707.8i	−0.539338	+	0.934160i
$936$		0			0
$937$	−16564.0	−	28689.6i	−0.577504	−	1.00027i	−0.995765	−	0.0919394i	$-0.970693\pi$
$937$	−16564.0	−	28689.6i	−0.577504	−	1.00027i	0.418260	−	0.908327i	$-0.362640\pi$
$938$		0			0
$939$	9172.07	−	15886.5i	0.318764	−	0.552115i
$940$		0			0
$941$	−14608.3	+	25302.3i	−0.506075	+	0.876548i	0.493900	+	0.869519i	$0.335571\pi$
$941$	−14608.3	+	25302.3i	−0.506075	+	0.876548i	−0.999975	+	0.00702958i	$0.997762\pi$
$942$		0			0
$943$	2502.43	−	4334.34i	0.0864161	−	0.149677i
$944$		0			0
$945$	39512.7			1.36016
$946$		0			0
$947$	24238.7	+	41982.6i	0.831734	+	1.44060i	0.896662	+	0.442715i	$0.145985\pi$
$947$	24238.7	+	41982.6i	0.831734	+	1.44060i	−0.0649288	+	0.997890i	$0.520682\pi$
$948$		0			0
$949$	−14256.0	−	24692.1i	−0.487638	−	0.844614i
$950$		0			0
$951$	18574.3	−	32171.5i	0.633345	−	1.09699i
$952$		0			0
$953$	−3513.77			−0.119436			−0.0597178	−	0.998215i	$-0.519020\pi$
$953$	−3513.77			−0.119436			−0.0597178	+	0.998215i	$0.519020\pi$
$954$		0			0
$955$	21032.7	+	36429.7i	0.712672	+	1.23438i
$956$		0			0
$957$	−15570.5			−0.525940
$958$		0			0
$959$	−25152.9			−0.846955
$960$		0			0
$961$	29361.9	+	5037.94i	0.985597	+	0.169109i
$962$		0			0
$963$	9301.57			0.311255
$964$		0			0
$965$	−3888.33			−0.129710
$966$		0			0
$967$	2163.20	+	3746.78i	0.0719379	+	0.124600i	0.899751	−	0.436405i	$-0.143748\pi$
$967$	2163.20	+	3746.78i	0.0719379	+	0.124600i	−0.827813	+	0.561005i	$0.810415\pi$
$968$		0			0
$969$	−28459.8			−0.943509
$970$		0			0
$971$	−12032.3	+	20840.6i	−0.397668	+	0.688782i	−0.993438	−	0.114374i	$-0.963514\pi$
$971$	−12032.3	+	20840.6i	−0.397668	+	0.688782i	0.595769	+	0.803156i	$0.296847\pi$
$972$		0			0
$973$	−19582.6	−	33918.1i	−0.645210	−	1.11754i
$974$		0			0
$975$	−3715.55	−	6435.52i	−0.122044	−	0.211386i
$976$		0			0
$977$	24712.0			0.809219			0.404609	−	0.914490i	$-0.367407\pi$
$977$	24712.0			0.809219			0.404609	+	0.914490i	$0.367407\pi$
$978$		0			0
$979$	11887.9	−	20590.4i	0.388089	−	0.672189i
$980$		0			0
$981$	11664.5	−	20203.5i	0.379632	−	0.657542i
$982$		0			0
$983$	4816.26	−	8342.01i	0.156272	−	0.270670i	−0.777250	−	0.629192i	$-0.783386\pi$
$983$	4816.26	−	8342.01i	0.156272	−	0.270670i	0.933521	+	0.358522i	$0.116719\pi$
$984$		0			0
$985$	3417.97	+	5920.11i	0.110564	+	0.191503i
$986$		0			0
$987$	14274.4	−	24723.9i	0.460342	−	0.797336i
$988$		0			0
$989$	5860.79	+	10151.2i	0.188435	+	0.326379i
$990$		0			0
$991$	11158.6			0.357685			0.178842	−	0.983878i	$-0.442765\pi$
$991$	11158.6			0.357685			0.178842	+	0.983878i	$0.442765\pi$
$992$		0			0
$993$	29400.8			0.939584
$994$		0			0
$995$	−2519.58	−	4364.03i	−0.0802773	−	0.139044i
$996$		0			0
$997$	6164.49	−	10677.2i	0.195819	−	0.339168i	−0.751350	−	0.659904i	$-0.770597\pi$
$997$	6164.49	−	10677.2i	0.195819	−	0.339168i	0.947169	+	0.320736i	$0.103930\pi$
$998$		0			0
$999$	−31451.5	−	54475.5i	−0.996076	−	1.72525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.4.e.b.25.3	yes	6
3.2	odd	2		1116.4.i.d.397.1		6
4.3	odd	2		496.4.i.b.273.1		6
31.5	even	3	inner	124.4.e.b.5.3	✓	6
93.5	odd	6		1116.4.i.d.253.1		6
124.67	odd	6		496.4.i.b.129.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.4.e.b.5.3	✓	6	31.5	even	3	inner
124.4.e.b.25.3	yes	6	1.1	even	1	trivial
496.4.i.b.129.1		6	124.67	odd	6
496.4.i.b.273.1		6	4.3	odd	2
1116.4.i.d.253.1		6	93.5	odd	6
1116.4.i.d.397.1		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82396 + 3.15920i) q^{3} +(6.14793 - 10.6485i) q^{5} +(10.8240 + 18.7477i) q^{7} +(6.84632 - 11.8582i) q^{9} +O(q^{10})\)	\(q+(1.82396 + 3.15920i) q^{3} +(6.14793 - 10.6485i) q^{5} +(10.8240 + 18.7477i) q^{7} +(6.84632 - 11.8582i) q^{9} +(-13.2173 + 22.8930i) q^{11} +(38.8933 - 67.3652i) q^{13} +44.8544 q^{15} +(47.4403 + 82.1690i) q^{17} +(41.1129 + 71.2096i) q^{19} +(-39.4850 + 68.3901i) q^{21} -38.5778 q^{23} +(-13.0940 - 22.6795i) q^{25} +148.444 q^{27} +161.468 q^{29} +(-171.978 - 14.6470i) q^{31} -96.4313 q^{33} +266.180 q^{35} +(-211.875 - 366.978i) q^{37} +283.760 q^{39} +(-64.8671 + 112.353i) q^{41} +(-151.921 - 263.135i) q^{43} +(-84.1813 - 145.806i) q^{45} -361.513 q^{47} +(-62.8164 + 108.801i) q^{49} +(-173.059 + 299.747i) q^{51} +(-270.882 + 469.181i) q^{53} +(162.518 + 281.489i) q^{55} +(-149.977 + 259.767i) q^{57} +(-249.443 - 432.048i) q^{59} -442.096 q^{61} +296.417 q^{63} +(-478.226 - 828.313i) q^{65} +(31.3127 - 54.2352i) q^{67} +(-70.3646 - 121.875i) q^{69} +(342.802 - 593.751i) q^{71} +(183.270 - 317.433i) q^{73} +(47.7659 - 82.7330i) q^{75} -572.253 q^{77} +(262.179 + 454.108i) q^{79} +(85.9054 + 148.792i) q^{81} +(-562.745 + 974.703i) q^{83} +1166.64 q^{85} +(294.511 + 510.108i) q^{87} -899.421 q^{89} +1683.92 q^{91} +(-267.409 - 570.028i) q^{93} +1011.04 q^{95} -1016.48 q^{97} +(180.979 + 313.465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9	\( 6 q - 9 q^{3} - 3 q^{5} + 45 q^{7} - 38 q^{9} + 61 q^{11} + 113 q^{13} + 386 q^{15} + 123 q^{17} + 63 q^{19} + 43 q^{21} + 96 q^{23} + 4 q^{25} + 918 q^{27} + 332 q^{29} - 668 q^{31} - 1214 q^{33} + 278 q^{35} + 129 q^{37} - 14 q^{39} - 709 q^{41} + 107 q^{43} - 1214 q^{45} - 568 q^{47} + 262 q^{49} + 293 q^{51} - 1267 q^{53} + 909 q^{55} + 681 q^{57} - 989 q^{59} - 2500 q^{61} + 36 q^{63} - 551 q^{65} + 741 q^{67} + 440 q^{69} - 1089 q^{71} - 197 q^{73} - 500 q^{75} + 982 q^{77} + 677 q^{79} - 2423 q^{81} + q^{83} + 58 q^{85} + 1194 q^{87} - 564 q^{89} + 4054 q^{91} + 1439 q^{93} - 2094 q^{95} - 2092 q^{97} + 2086 q^{99}+O(q^{100}) \) 6 * q - 9 * q^3 - 3 * q^5 + 45 * q^7 - 38 * q^9 + 61 * q^11 + 113 * q^13 + 386 * q^15 + 123 * q^17 + 63 * q^19 + 43 * q^21 + 96 * q^23 + 4 * q^25 + 918 * q^27 + 332 * q^29 - 668 * q^31 - 1214 * q^33 + 278 * q^35 + 129 * q^37 - 14 * q^39 - 709 * q^41 + 107 * q^43 - 1214 * q^45 - 568 * q^47 + 262 * q^49 + 293 * q^51 - 1267 * q^53 + 909 * q^55 + 681 * q^57 - 989 * q^59 - 2500 * q^61 + 36 * q^63 - 551 * q^65 + 741 * q^67 + 440 * q^69 - 1089 * q^71 - 197 * q^73 - 500 * q^75 + 982 * q^77 + 677 * q^79 - 2423 * q^81 + q^83 + 58 * q^85 + 1194 * q^87 - 564 * q^89 + 4054 * q^91 + 1439 * q^93 - 2094 * q^95 - 2092 * q^97 + 2086 * q^99

Introduction

L-functions

Modular forms

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