LMFDB - Embedded newform 124.6.f.a.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,6,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, degree $4$, 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:	$19.8875936568$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	124.97
Dual form			124.6.f.a.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.47947 + 13.7864i) q^{3} +7.66625 q^{5} +(-38.1042 + 27.6843i) q^{7} +(26.5924 + 19.3205i) q^{9} +O(q^{10})$	\(q+(-4.47947 + 13.7864i) q^{3} +7.66625 q^{5} +(-38.1042 + 27.6843i) q^{7} +(26.5924 + 19.3205i) q^{9} +(-56.1604 + 40.8029i) q^{11} +(-242.942 + 747.699i) q^{13} +(-34.3407 + 105.690i) q^{15} +(-631.151 - 458.558i) q^{17} +(-216.975 - 667.780i) q^{19} +(-210.980 - 649.330i) q^{21} +(1104.86 + 802.725i) q^{23} -3066.23 q^{25} +(-3235.24 + 2350.54i) q^{27} +(-2503.84 - 7706.02i) q^{29} +(1177.30 - 5219.49i) q^{31} +(-310.956 - 957.025i) q^{33} +(-292.116 + 212.235i) q^{35} -10296.4 q^{37} +(-9219.81 - 6698.59i) q^{39} +(-2147.55 - 6609.47i) q^{41} +(919.063 + 2828.59i) q^{43} +(203.864 + 148.116i) q^{45} +(-5914.86 + 18204.1i) q^{47} +(-4508.14 + 13874.6i) q^{49} +(9149.08 - 6647.19i) q^{51} +(-17684.0 - 12848.1i) q^{53} +(-430.540 + 312.806i) q^{55} +10178.2 q^{57} +(-3342.09 + 10285.9i) q^{59} -11865.1 q^{61} -1548.15 q^{63} +(-1862.46 + 5732.05i) q^{65} +15114.8 q^{67} +(-16015.8 + 11636.2i) q^{69} +(10929.7 + 7940.91i) q^{71} +(23055.5 - 16750.8i) q^{73} +(13735.1 - 42272.2i) q^{75} +(1010.35 - 3109.53i) q^{77} +(51195.3 + 37195.6i) q^{79} +(-15445.0 - 47534.9i) q^{81} +(8502.79 + 26168.9i) q^{83} +(-4838.56 - 3515.42i) q^{85} +117454. q^{87} +(7626.82 - 5541.21i) q^{89} +(-11442.4 - 35216.1i) q^{91} +(66684.3 + 39611.2i) q^{93} +(-1663.38 - 5119.37i) q^{95} +(-71240.6 + 51759.3i) q^{97} -2281.77 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−4.47947	+	13.7864i	−0.287358	+	0.884397i	0.698324	+	0.715782i	$0.253930\pi$
$3$	−4.47947	+	13.7864i	−0.287358	+	0.884397i	−0.985682	+	0.168615i	$0.946070\pi$
$4$		0			0
$5$	7.66625			0.137138			0.0685690	−	0.997646i	$-0.478157\pi$
$5$	7.66625			0.137138			0.0685690	+	0.997646i	$0.478157\pi$
$6$		0			0
$7$	−38.1042	+	27.6843i	−0.293919	+	0.213545i	−0.724966	−	0.688785i	$-0.758144\pi$
$7$	−38.1042	+	27.6843i	−0.293919	+	0.213545i	0.431047	+	0.902330i	$0.358144\pi$
$8$		0			0
$9$	26.5924	+	19.3205i	0.109434	+	0.0795081i
$10$		0			0
$11$	−56.1604	+	40.8029i	−0.139942	+	0.101674i	−0.655554	−	0.755148i	$-0.727565\pi$
$11$	−56.1604	+	40.8029i	−0.139942	+	0.101674i	0.515612	+	0.856822i	$0.327565\pi$
$12$		0			0
$13$	−242.942	+	747.699i	−0.398698	+	1.22707i	0.527345	+	0.849651i	$0.323187\pi$
$13$	−242.942	+	747.699i	−0.398698	+	1.22707i	−0.926044	+	0.377416i	$0.876813\pi$
$14$		0			0
$15$	−34.3407	+	105.690i	−0.0394077	+	0.121284i
$16$		0			0
$17$	−631.151	−	458.558i	−0.529677	−	0.384833i	0.290560	−	0.956857i	$-0.406158\pi$
$17$	−631.151	−	458.558i	−0.529677	−	0.384833i	−0.820237	+	0.572024i	$0.806158\pi$
$18$		0			0
$19$	−216.975	−	667.780i	−0.137888	−	0.424375i	0.858140	−	0.513415i	$-0.171620\pi$
$19$	−216.975	−	667.780i	−0.137888	−	0.424375i	−0.996028	+	0.0890406i	$0.971620\pi$
$20$		0			0
$21$	−210.980	−	649.330i	−0.104398	−	0.321305i
$22$		0			0
$23$	1104.86	+	802.725i	0.435498	+	0.316408i	0.783844	−	0.620958i	$-0.213256\pi$
$23$	1104.86	+	802.725i	0.435498	+	0.316408i	−0.348345	+	0.937366i	$0.613256\pi$
$24$		0			0
$25$	−3066.23			−0.981193
$26$		0			0
$27$	−3235.24	+	2350.54i	−0.854076	+	0.620523i
$28$		0			0
$29$	−2503.84	−	7706.02i	−0.552855	−	1.70151i	−0.701542	−	0.712628i	$-0.747505\pi$
$29$	−2503.84	−	7706.02i	−0.552855	−	1.70151i	0.148687	−	0.988884i	$-0.452495\pi$
$30$		0			0
$31$	1177.30	−	5219.49i	0.220030	−	0.975493i
$31$	1177.30	−	5219.49i	0.220030	−	0.975493i
$32$		0			0
$33$	−310.956	−	957.025i	−0.0497066	−	0.152981i
$34$		0			0
$35$	−292.116	+	212.235i	−0.0403075	+	0.0292851i
$36$		0			0
$37$	−10296.4			−1.23647			−0.618233	−	0.785995i	$-0.712151\pi$
$37$	−10296.4			−1.23647			−0.618233	+	0.785995i	$0.712151\pi$
$38$		0			0
$39$	−9219.81	−	6698.59i	−0.970646	−	0.705215i
$40$		0			0
$41$	−2147.55	−	6609.47i	−0.199519	−	0.614055i	−0.999894	−	0.0145559i	$-0.995367\pi$
$41$	−2147.55	−	6609.47i	−0.199519	−	0.614055i	0.800376	−	0.599499i	$-0.204633\pi$
$42$		0			0
$43$	919.063	+	2828.59i	0.0758009	+	0.233291i	0.981777	−	0.190038i	$-0.0608612\pi$
$43$	919.063	+	2828.59i	0.0758009	+	0.233291i	−0.905976	+	0.423330i	$0.860861\pi$
$44$		0			0
$45$	203.864	+	148.116i	0.0150075	+	0.0109036i
$46$		0			0
$47$	−5914.86	+	18204.1i	−0.390571	+	1.20205i	0.541787	+	0.840516i	$0.317748\pi$
$47$	−5914.86	+	18204.1i	−0.390571	+	1.20205i	−0.932358	+	0.361537i	$0.882252\pi$
$48$		0			0
$49$	−4508.14	+	13874.6i	−0.268230	+	0.825527i
$50$		0			0
$51$	9149.08	−	6647.19i	0.492552	−	0.357860i
$52$		0			0
$53$	−17684.0	−	12848.1i	−0.864748	−	0.628276i	0.0644243	−	0.997923i	$-0.479479\pi$
$53$	−17684.0	−	12848.1i	−0.864748	−	0.628276i	−0.929173	+	0.369646i	$0.879479\pi$
$54$		0			0
$55$	−430.540	+	312.806i	−0.0191914	+	0.0139434i
$56$		0			0
$57$	10178.2			0.414939
$58$		0			0
$59$	−3342.09	+	10285.9i	−0.124994	+	0.384692i	−0.993900	−	0.110285i	$-0.964824\pi$
$59$	−3342.09	+	10285.9i	−0.124994	+	0.384692i	0.868906	+	0.494977i	$0.164824\pi$
$60$		0			0
$61$	−11865.1			−0.408271			−0.204135	−	0.978943i	$-0.565438\pi$
$61$	−11865.1			−0.408271			−0.204135	+	0.978943i	$0.565438\pi$
$62$		0			0
$63$	−1548.15			−0.0491431
$64$		0			0
$65$	−1862.46	+	5732.05i	−0.0546767	+	0.168278i
$66$		0			0
$67$	15114.8			0.411354			0.205677	−	0.978620i	$-0.434060\pi$
$67$	15114.8			0.411354			0.205677	+	0.978620i	$0.434060\pi$
$68$		0			0
$69$	−16015.8	+	11636.2i	−0.404974	+	0.294231i
$70$		0			0
$71$	10929.7	+	7940.91i	0.257314	+	0.186949i	0.708962	−	0.705247i	$-0.249164\pi$
$71$	10929.7	+	7940.91i	0.257314	+	0.186949i	−0.451648	+	0.892196i	$0.649164\pi$
$72$		0			0
$73$	23055.5	−	16750.8i	0.506370	−	0.367899i	−0.305075	−	0.952328i	$-0.598682\pi$
$73$	23055.5	−	16750.8i	0.506370	−	0.367899i	0.811445	+	0.584429i	$0.198682\pi$
$74$		0			0
$75$	13735.1	−	42272.2i	0.281954	−	0.867764i
$76$		0			0
$77$	1010.35	−	3109.53i	0.0194197	−	0.0597678i
$78$		0			0
$79$	51195.3	+	37195.6i	0.922916	+	0.670538i	0.944248	−	0.329235i	$-0.106791\pi$
$79$	51195.3	+	37195.6i	0.922916	+	0.670538i	−0.0213319	+	0.999772i	$0.506791\pi$
$80$		0			0
$81$	−15445.0	−	47534.9i	−0.261563	−	0.805008i
$82$		0			0
$83$	8502.79	+	26168.9i	0.135477	+	0.416956i	0.995664	−	0.0930233i	$-0.0296531\pi$
$83$	8502.79	+	26168.9i	0.135477	+	0.416956i	−0.860187	+	0.509979i	$0.829653\pi$
$84$		0			0
$85$	−4838.56	−	3515.42i	−0.0726388	−	0.0527752i
$86$		0			0
$87$	117454.			1.66368
$88$		0			0
$89$	7626.82	−	5541.21i	0.102063	−	0.0741531i	−0.535583	−	0.844482i	$-0.679908\pi$
$89$	7626.82	−	5541.21i	0.102063	−	0.0741531i	0.637646	+	0.770329i	$0.279908\pi$
$90$		0			0
$91$	−11442.4	−	35216.1i	−0.144849	−	0.445798i
$92$		0			0
$93$	66684.3	+	39611.2i	0.799496	+	0.474910i
$94$		0			0
$95$	−1663.38	−	5119.37i	−0.0189096	−	0.0581979i
$96$		0			0
$97$	−71240.6	+	51759.3i	−0.768773	+	0.558546i	−0.901589	−	0.432594i	$-0.857598\pi$
$97$	−71240.6	+	51759.3i	−0.768773	+	0.558546i	0.132816	+	0.991141i	$0.457598\pi$
$98$		0			0
$99$	−2281.77			−0.0233983
$100$		0			0
$101$	133697.	+	97136.8i	1.30412	+	0.947502i	0.999987	−	0.00512605i	$-0.00163168\pi$
$101$	133697.	+	97136.8i	1.30412	+	0.947502i	0.304138	+	0.952628i	$0.401632\pi$
$102$		0			0
$103$	−115.787	−	356.357i	−0.00107539	−	0.00330972i	0.950517	−	0.310671i	$-0.100554\pi$
$103$	−115.787	−	356.357i	−0.00107539	−	0.00330972i	−0.951593	+	0.307362i	$0.900554\pi$
$104$		0			0
$105$	−1617.43	−	4977.92i	−0.0143170	−	0.0440631i
$106$		0			0
$107$	65847.4	+	47840.9i	0.556006	+	0.403962i	0.829995	−	0.557771i	$-0.188343\pi$
$107$	65847.4	+	47840.9i	0.556006	+	0.403962i	−0.273989	+	0.961733i	$0.588343\pi$
$108$		0			0
$109$	−13495.5	+	41534.9i	−0.108798	+	0.334847i	−0.990603	−	0.136767i	$-0.956329\pi$
$109$	−13495.5	+	41534.9i	−0.108798	+	0.334847i	0.881805	+	0.471615i	$0.156329\pi$
$110$		0			0
$111$	46122.5	−	141951.i	0.355309	−	1.09353i
$112$		0			0
$113$	−74938.0	+	54445.7i	−0.552085	+	0.401114i	−0.828554	−	0.559909i	$-0.810836\pi$
$113$	−74938.0	+	54445.7i	−0.552085	+	0.401114i	0.276468	+	0.961023i	$0.410836\pi$
$114$		0			0
$115$	8470.11	+	6153.89i	0.0597234	+	0.0433916i
$116$		0			0
$117$	−20906.3	+	15189.3i	−0.141193	+	0.102583i
$118$		0			0
$119$	36744.3			0.237861
$120$		0			0
$121$	−48278.4	+	148586.i	−0.299771	+	0.922600i
$122$		0			0
$123$	100741.			0.600402
$124$		0			0
$125$	−47463.5			−0.271697
$126$		0			0
$127$	−26708.3	+	82199.8i	−0.146939	+	0.452232i	−0.997255	−	0.0740400i	$-0.976411\pi$
$127$	−26708.3	+	82199.8i	−0.146939	+	0.452232i	0.850316	+	0.526272i	$0.176411\pi$
$128$		0			0
$129$	−43112.9			−0.228104
$130$		0			0
$131$	−17007.0	+	12356.3i	−0.0865866	+	0.0629088i	−0.630236	−	0.776403i	$-0.717042\pi$
$131$	−17007.0	+	12356.3i	−0.0865866	+	0.0629088i	0.543650	+	0.839312i	$0.317042\pi$
$132$		0			0
$133$	26754.7	+	19438.4i	0.131151	+	0.0952865i
$134$		0			0
$135$	−24802.1	+	18019.8i	−0.117126	+	0.0850973i
$136$		0			0
$137$	−7985.45	+	24576.7i	−0.0363494	+	0.111872i	−0.967585	−	0.252546i	$-0.918732\pi$
$137$	−7985.45	+	24576.7i	−0.0363494	+	0.111872i	0.931235	+	0.364418i	$0.118732\pi$
$138$		0			0
$139$	83168.7	−	255967.i	0.365109	−	1.12369i	−0.584803	−	0.811175i	$-0.698828\pi$
$139$	83168.7	−	255967.i	0.365109	−	1.12369i	0.949913	−	0.312516i	$-0.101172\pi$
$140$		0			0
$141$	−224473.	−	163089.i	−0.950858	−	0.690839i
$142$		0			0
$143$	−16864.6	−	51903.9i	−0.0689661	−	0.212256i
$144$		0			0
$145$	−19195.0	−	59076.3i	−0.0758174	−	0.233342i
$146$		0			0
$147$	−171087.	−	124302.i	−0.653016	−	0.474444i
$148$		0			0
$149$	−287167.			−1.05966			−0.529832	−	0.848102i	$-0.677745\pi$
$149$	−287167.			−1.05966			−0.529832	+	0.848102i	$0.677745\pi$
$150$		0			0
$151$	−2045.93	+	1486.45i	−0.00730211	+	0.00530529i	−0.591430	−	0.806356i	$-0.701437\pi$
$151$	−2045.93	+	1486.45i	−0.00730211	+	0.00530529i	0.584128	+	0.811661i	$0.301437\pi$
$152$		0			0
$153$	−7924.23	−	24388.3i	−0.0273671	−	0.0842272i
$154$		0			0
$155$	9025.46	−	40013.9i	0.0301745	−	0.133777i
$156$		0			0
$157$	−70930.6	−	218302.i	−0.229660	−	0.706820i	−0.997785	−	0.0665203i	$-0.978810\pi$
$157$	−70930.6	−	218302.i	−0.229660	−	0.706820i	0.768125	−	0.640299i	$-0.221190\pi$
$158$		0			0
$159$	256344.	−	186245.i	0.804138	−	0.584241i
$160$		0			0
$161$	−64322.5			−0.195568
$162$		0			0
$163$	−340592.	−	247455.i	−1.00407	−	0.729502i	−0.0411159	−	0.999154i	$-0.513091\pi$
$163$	−340592.	−	247455.i	−1.00407	−	0.729502i	−0.962958	+	0.269652i	$0.913091\pi$
$164$		0			0
$165$	−2383.87	−	7336.79i	−0.00681667	−	0.0209796i
$166$		0			0
$167$	61390.9	+	188942.i	0.170338	+	0.524248i	0.999390	−	0.0349244i	$-0.0111190\pi$
$167$	61390.9	+	188942.i	0.170338	+	0.524248i	−0.829051	+	0.559172i	$0.811119\pi$
$168$		0			0
$169$	−199651.	−	145055.i	−0.537717	−	0.390674i
$170$		0			0
$171$	7131.96	−	21949.9i	0.0186517	−	0.0574040i
$172$		0			0
$173$	−196958.	+	606176.i	−0.500333	+	1.53987i	0.308144	+	0.951340i	$0.400292\pi$
$173$	−196958.	+	606176.i	−0.500333	+	1.53987i	−0.808477	+	0.588528i	$0.799708\pi$
$174$		0			0
$175$	116836.	−	84886.4i	0.288391	−	0.209528i
$176$		0			0
$177$	−126835.	−	92150.8i	−0.304302	−	0.221088i
$178$		0			0
$179$	−211081.	+	153359.i	−0.492399	+	0.357749i	−0.806106	−	0.591771i	$-0.798429\pi$
$179$	−211081.	+	153359.i	−0.492399	+	0.357749i	0.313707	+	0.949520i	$0.398429\pi$
$180$		0			0
$181$	−491700.			−1.11559			−0.557794	−	0.829980i	$-0.688352\pi$
$181$	−491700.			−1.11559			−0.557794	+	0.829980i	$0.688352\pi$
$182$		0			0
$183$	53149.5	−	163577.i	0.117320	−	0.361073i
$184$		0			0
$185$	−78935.0			−0.169567
$186$		0			0
$187$	54156.2			0.113252
$188$		0			0
$189$	58203.1	−	179131.i	0.118520	−	0.364767i
$190$		0			0
$191$	710664.			1.40955			0.704776	−	0.709430i	$-0.251048\pi$
$191$	710664.			1.40955			0.704776	+	0.709430i	$0.251048\pi$
$192$		0			0
$193$	−83335.6	+	60546.8i	−0.161041	+	0.117003i	−0.665387	−	0.746498i	$-0.731734\pi$
$193$	−83335.6	+	60546.8i	−0.161041	+	0.117003i	0.504346	+	0.863502i	$0.331734\pi$
$194$		0			0
$195$	−70681.4	−	51353.0i	−0.133112	−	0.0967118i
$196$		0			0
$197$	−7080.28	+	5144.12i	−0.0129982	+	0.00944378i	−0.594265	−	0.804269i	$-0.702557\pi$
$197$	−7080.28	+	5144.12i	−0.0129982	+	0.00944378i	0.581267	+	0.813713i	$0.302557\pi$
$198$		0			0
$199$	−198162.	+	609880.i	−0.354722	+	1.09172i	0.601449	+	0.798912i	$0.294590\pi$
$199$	−198162.	+	609880.i	−0.354722	+	1.09172i	−0.956171	+	0.292810i	$0.905410\pi$
$200$		0			0
$201$	−67706.3	+	208379.i	−0.118206	+	0.363800i
$202$		0			0
$203$	308742.	+	224315.i	0.525843	+	0.382047i
$204$		0			0
$205$	−16463.6	−	50669.9i	−0.0273616	−	0.0842103i
$206$		0			0
$207$	13871.7	+	42692.7i	0.0225011	+	0.0692513i
$208$		0			0
$209$	39432.8	+	28649.6i	0.0624442	+	0.0453683i
$210$		0			0
$211$	−280390.			−0.433567			−0.216783	−	0.976220i	$-0.569557\pi$
$211$	−280390.			−0.433567			−0.216783	+	0.976220i	$0.569557\pi$
$212$		0			0
$213$	−158436.	+	115110.i	−0.239279	+	0.173846i
$214$		0			0
$215$	7045.77	+	21684.6i	0.0103952	+	0.0319931i
$216$		0			0
$217$	99638.1	+	231477.i	0.143640	+	0.333702i
$218$		0			0
$219$	127657.	+	392887.i	0.179859	+	0.553550i
$220$		0			0
$221$	496197.	−	360508.i	0.683397	−	0.496517i
$222$		0			0
$223$	1.42675e6			1.92126			0.960629	−	0.277833i	$-0.0896161\pi$
$223$	1.42675e6			1.92126			0.960629	+	0.277833i	$0.0896161\pi$
$224$		0			0
$225$	−81538.2	−	59241.0i	−0.107375	−	0.0780128i
$226$		0			0
$227$	−40839.5	−	125691.i	−0.0526037	−	0.161898i	0.921303	−	0.388844i	$-0.127126\pi$
$227$	−40839.5	−	125691.i	−0.0526037	−	0.161898i	−0.973907	+	0.226947i	$0.927126\pi$
$228$		0			0
$229$	−194910.	−	599872.i	−0.245610	−	0.755909i	−0.995536	−	0.0943874i	$-0.969911\pi$
$229$	−194910.	−	599872.i	−0.245610	−	0.755909i	0.749926	−	0.661522i	$-0.230089\pi$
$230$		0			0
$231$	38343.3	+	27858.0i	0.0472780	+	0.0343495i
$232$		0			0
$233$	261170.	−	803799.i	0.315162	−	0.969969i	−0.660526	−	0.750803i	$-0.729667\pi$
$233$	261170.	−	803799.i	0.315162	−	0.969969i	0.975688	−	0.219166i	$-0.0703335\pi$
$234$		0			0
$235$	−45344.8	+	139557.i	−0.0535621	+	0.164847i
$236$		0			0
$237$	−742120.	+	539182.i	−0.858229	+	0.623540i
$238$		0			0
$239$	1.01500e6	+	737437.i	1.14939	+	0.835084i	0.988400	−	0.151871i	$-0.0485298\pi$
$239$	1.01500e6	+	737437.i	1.14939	+	0.835084i	0.160995	+	0.986955i	$0.448530\pi$
$240$		0			0
$241$	987657.	−	717575.i	1.09538	−	0.795838i	0.115078	−	0.993356i	$-0.463288\pi$
$241$	987657.	−	717575.i	1.09538	−	0.795838i	0.980299	+	0.197518i	$0.0632882\pi$
$242$		0			0
$243$	−247230.			−0.268588
$244$		0			0
$245$	−34560.5	+	106366.i	−0.0367845	+	0.113211i
$246$		0			0
$247$	552011.			0.575712
$248$		0			0
$249$	−398862.			−0.407685
$250$		0			0
$251$	129908.	−	399815.i	0.130152	−	0.400566i	−0.864653	−	0.502370i	$-0.832461\pi$
$251$	129908.	−	399815.i	0.130152	−	0.400566i	0.994804	+	0.101804i	$0.0324614\pi$
$252$		0			0
$253$	−94802.8			−0.0931150
$254$		0			0
$255$	70139.1	−	50959.0i	0.0675476	−	0.0490762i
$256$		0			0
$257$	1.25461e6	+	911527.i	1.18488	+	0.860868i	0.992714	−	0.120494i	$-0.0384478\pi$
$257$	1.25461e6	+	911527.i	1.18488	+	0.860868i	0.192169	+	0.981362i	$0.438448\pi$
$258$		0			0
$259$	392337.	−	285050.i	0.363421	−	0.264041i
$260$		0			0
$261$	82301.0	−	253297.i	0.0747832	−	0.230159i
$262$		0			0
$263$	−17114.9	+	52674.3i	−0.0152576	+	0.0469580i	−0.958395	−	0.285444i	$-0.907859\pi$
$263$	−17114.9	+	52674.3i	−0.0152576	+	0.0469580i	0.943138	+	0.332402i	$0.107859\pi$
$264$		0			0
$265$	−135570.	−	98497.1i	−0.118590	−	0.0861606i
$266$		0			0
$267$	42229.1	+	129968.i	0.0362522	+	0.111573i
$268$		0			0
$269$	601092.	+	1.84997e6i	0.506478	+	1.55878i	0.798272	+	0.602298i	$0.205748\pi$
$269$	601092.	+	1.84997e6i	0.506478	+	1.55878i	−0.291794	+	0.956481i	$0.594252\pi$
$270$		0			0
$271$	−1.67443e6	−	1.21654e6i	−1.38498	−	1.00625i	−0.996395	−	0.0848311i	$-0.972965\pi$
$271$	−1.67443e6	−	1.21654e6i	−1.38498	−	1.00625i	−0.388582	−	0.921414i	$-0.627035\pi$
$272$		0			0
$273$	536759.			0.435886
$274$		0			0
$275$	172201.	−	125111.i	0.137310	−	0.0997618i
$276$		0			0
$277$	109493.	+	336985.i	0.0857409	+	0.263883i	0.984730	−	0.174087i	$-0.0556975\pi$
$277$	109493.	+	336985.i	0.0857409	+	0.263883i	−0.898989	+	0.437970i	$0.855697\pi$
$278$		0			0
$279$	132150.	−	116053.i	0.101638	−	0.0892575i
$280$		0			0
$281$	−71687.1	−	220630.i	−0.0541596	−	0.166686i	0.920318	−	0.391171i	$-0.127930\pi$
$281$	−71687.1	−	220630.i	−0.0541596	−	0.166686i	−0.974478	+	0.224485i	$0.927930\pi$
$282$		0			0
$283$	−235046.	+	170771.i	−0.174456	+	0.126750i	−0.671587	−	0.740926i	$-0.734387\pi$
$283$	−235046.	+	170771.i	−0.174456	+	0.126750i	0.497131	+	0.867676i	$0.334387\pi$
$284$		0			0
$285$	78028.7			0.0569039
$286$		0			0
$287$	264809.	+	192395.i	0.189770	+	0.137876i
$288$		0			0
$289$	−250684.	−	771526.i	−0.176556	−	0.543383i
$290$		0			0
$291$	−394454.	−	1.21400e6i	−0.273064	−	0.840403i
$292$		0			0
$293$	2.13135e6	+	1.54851e6i	1.45039	+	1.05377i	0.985740	+	0.168276i	$0.0538201\pi$
$293$	2.13135e6	+	1.54851e6i	1.45039	+	1.05377i	0.464651	+	0.885494i	$0.346180\pi$
$294$		0			0
$295$	−25621.3	+	78854.3i	−0.0171414	+	0.0527558i
$296$		0			0
$297$	85783.5	−	264014.i	0.0564303	−	0.173675i
$298$		0			0
$299$	−868613.	+	631084.i	−0.561886	+	0.408234i
$300$		0			0
$301$	−113328.	−	82337.3i	−0.0720974	−	0.0523818i
$302$		0			0
$303$	−1.93806e6	+	1.40808e6i	−1.21272	+	0.881092i
$304$		0			0
$305$	−90961.1			−0.0559895
$306$		0			0
$307$	−757162.	+	2.33031e6i	−0.458504	+	1.41113i	0.408468	+	0.912773i	$0.366063\pi$
$307$	−757162.	+	2.33031e6i	−0.458504	+	1.41113i	−0.866972	+	0.498357i	$0.833937\pi$
$308$		0			0
$309$	5431.54			0.00323613
$310$		0			0
$311$	312629.			0.183285			0.0916427	−	0.995792i	$-0.470788\pi$
$311$	312629.			0.183285			0.0916427	+	0.995792i	$0.470788\pi$
$312$		0			0
$313$	419104.	−	1.28987e6i	0.241803	−	0.744192i	−0.754343	−	0.656480i	$-0.772045\pi$
$313$	419104.	−	1.28987e6i	0.241803	−	0.744192i	0.996146	−	0.0877117i	$-0.0279554\pi$
$314$		0			0
$315$	−11868.5			−0.00673939
$316$		0			0
$317$	−1.88682e6	+	1.37086e6i	−1.05459	+	0.766204i	−0.973080	−	0.230469i	$-0.925974\pi$
$317$	−1.88682e6	+	1.37086e6i	−1.05459	+	0.766204i	−0.0815090	+	0.996673i	$0.525974\pi$
$318$		0			0
$319$	455045.	+	330609.i	0.250367	+	0.181902i
$320$		0			0
$321$	−954515.	+	693496.i	−0.517035	+	0.375648i
$322$		0			0
$323$	−169272.	+	520966.i	−0.0902773	+	0.277845i
$324$		0			0
$325$	744916.	−	2.29262e6i	0.391200	−	1.20399i
$326$		0			0
$327$	−512163.	−	372108.i	−0.264874	−	0.192442i
$328$		0			0
$329$	−278586.	−	857399.i	−0.141896	−	0.436710i
$330$		0			0
$331$	−964733.	−	2.96914e6i	−0.483991	−	1.48957i	−0.833437	−	0.552614i	$-0.813630\pi$
$331$	−964733.	−	2.96914e6i	−0.483991	−	1.48957i	0.349447	−	0.936956i	$-0.386370\pi$
$332$		0			0
$333$	−273806.	−	198932.i	−0.135311	−	0.0983092i
$334$		0			0
$335$	115874.			0.0564123
$336$		0			0
$337$	−256319.	+	186227.i	−0.122944	+	0.0893239i	−0.647558	−	0.762016i	$-0.724210\pi$
$337$	−256319.	+	186227.i	−0.122944	+	0.0893239i	0.524614	+	0.851340i	$0.324210\pi$
$338$		0			0
$339$	−414926.	−	1.27701e6i	−0.196097	−	0.603526i
$340$		0			0
$341$	146853.	+	341166.i	0.0683907	+	0.158884i
$342$		0			0
$343$	−456948.	−	1.40634e6i	−0.209716	−	0.645439i
$344$		0			0
$345$	−122781.	+	89206.0i	−0.0555373	+	0.0403502i
$346$		0			0
$347$	−1.85951e6			−0.829037			−0.414518	−	0.910041i	$-0.636050\pi$
$347$	−1.85951e6			−0.829037			−0.414518	+	0.910041i	$0.636050\pi$
$348$		0			0
$349$	−371885.	−	270190.i	−0.163435	−	0.118742i	0.503062	−	0.864251i	$-0.332207\pi$
$349$	−371885.	−	270190.i	−0.163435	−	0.118742i	−0.666497	+	0.745508i	$0.732207\pi$
$350$		0			0
$351$	−971519.	−	2.99003e6i	−0.420904	−	1.29541i
$352$		0			0
$353$	−248118.	−	763630.i	−0.105980	−	0.326172i	0.883980	−	0.467526i	$-0.154854\pi$
$353$	−248118.	−	763630.i	−0.105980	−	0.326172i	−0.989959	+	0.141354i	$0.954854\pi$
$354$		0			0
$355$	83790.0	+	60877.0i	0.0352875	+	0.0256379i
$356$		0			0
$357$	−164595.	+	506572.i	−0.0683512	+	0.210364i
$358$		0			0
$359$	−928091.	+	2.85637e6i	−0.380062	+	1.16971i	0.559937	+	0.828535i	$0.310825\pi$
$359$	−928091.	+	2.85637e6i	−0.380062	+	1.16971i	−0.940000	+	0.341176i	$0.889175\pi$
$360$		0			0
$361$	1.60435e6	−	1.16563e6i	0.647936	−	0.470753i
$362$		0			0
$363$	−1.83220e6	−	1.33117e6i	−0.729803	−	0.530233i
$364$		0			0
$365$	176749.	−	128416.i	0.0694425	−	0.0504530i
$366$		0			0
$367$	−4.42890e6			−1.71645			−0.858225	−	0.513274i	$-0.828433\pi$
$367$	−4.42890e6			−1.71645			−0.858225	+	0.513274i	$0.828433\pi$
$368$		0			0
$369$	70589.8	−	217253.i	0.0269883	−	0.0830616i
$370$		0			0
$371$	1.02952e6			0.388331
$372$		0			0
$373$	−1.23004e6			−0.457769			−0.228885	−	0.973454i	$-0.573508\pi$
$373$	−1.23004e6			−0.457769			−0.228885	+	0.973454i	$0.573508\pi$
$374$		0			0
$375$	212611.	−	654350.i	0.0780743	−	0.240288i
$376$		0			0
$377$	6.37007e6			2.30829
$378$		0			0
$379$	−846007.	+	614660.i	−0.302535	+	0.219805i	−0.728687	−	0.684847i	$-0.759869\pi$
$379$	−846007.	+	614660.i	−0.302535	+	0.219805i	0.426152	+	0.904652i	$0.359869\pi$
$380$		0			0
$381$	−1.01360e6	−	736423.i	−0.357729	−	0.259905i
$382$		0			0
$383$	−1.50698e6	+	1.09489e6i	−0.524942	+	0.381393i	−0.818463	−	0.574560i	$-0.805173\pi$
$383$	−1.50698e6	+	1.09489e6i	−0.524942	+	0.381393i	0.293520	+	0.955953i	$0.405173\pi$
$384$		0			0
$385$	7745.56	−	23838.4i	0.00266318	−	0.00819644i
$386$		0			0
$387$	−30209.6	+	92975.5i	−0.0102534	+	0.0315567i
$388$		0			0
$389$	2.83165e6	+	2.05731e6i	0.948779	+	0.689329i	0.950518	−	0.310670i	$-0.100553\pi$
$389$	2.83165e6	+	2.05731e6i	0.948779	+	0.689329i	−0.00173850	+	0.999998i	$0.500553\pi$
$390$		0			0
$391$	−329235.	−	1.01328e6i	−0.108909	−	0.335188i
$392$		0			0
$393$	−94166.8	−	289815.i	−0.0307550	−	0.0946543i
$394$		0			0
$395$	392476.	+	285150.i	0.126567	+	0.0919563i
$396$		0			0
$397$	−2.43661e6			−0.775908			−0.387954	−	0.921679i	$-0.626818\pi$
$397$	−2.43661e6			−0.775908			−0.387954	+	0.921679i	$0.626818\pi$
$398$		0			0
$399$	−387832.	+	281776.i	−0.121958	+	0.0886079i
$400$		0			0
$401$	−999598.	−	3.07645e6i	−0.310431	−	0.955407i	−0.977595	−	0.210496i	$-0.932492\pi$
$401$	−999598.	−	3.07645e6i	−0.310431	−	0.955407i	0.667164	−	0.744911i	$-0.267508\pi$
$402$		0			0
$403$	3.61660e6	+	2.14830e6i	1.10927	+	0.658919i
$404$		0			0
$405$	−118405.	−	364415.i	−0.0358702	−	0.110397i
$406$		0			0
$407$	578252.	−	420125.i	0.173034	−	0.125716i
$408$		0			0
$409$	−1.02879e6			−0.304103			−0.152051	−	0.988373i	$-0.548588\pi$
$409$	−1.02879e6			−0.304103			−0.152051	+	0.988373i	$0.548588\pi$
$410$		0			0
$411$	−303053.	−	220181.i	−0.0884940	−	0.0642947i
$412$		0			0
$413$	−157410.	−	484460.i	−0.0454107	−	0.139760i
$414$		0			0
$415$	65184.5	+	200617.i	0.0185791	+	0.0571805i
$416$		0			0
$417$	3.15631e6	+	2.29319e6i	0.888872	+	0.645803i
$418$		0			0
$419$	−926805.	+	2.85241e6i	−0.257901	+	0.793739i	0.735343	+	0.677695i	$0.237021\pi$
$419$	−926805.	+	2.85241e6i	−0.257901	+	0.793739i	−0.993244	+	0.116043i	$0.962979\pi$
$420$		0			0
$421$	−1.43178e6	+	4.40658e6i	−0.393706	+	1.21170i	0.536259	+	0.844054i	$0.319837\pi$
$421$	−1.43178e6	+	4.40658e6i	−0.393706	+	1.21170i	−0.929965	+	0.367649i	$0.880163\pi$
$422$		0			0
$423$	−509001.	+	369811.i	−0.138315	+	0.100491i
$424$		0			0
$425$	1.93525e6	+	1.40604e6i	0.519715	+	0.377595i
$426$		0			0
$427$	452111.	−	328478.i	0.119998	−	0.0871840i
$428$		0			0
$429$	791111.			0.207536
$430$		0			0
$431$	−1.64481e6	+	5.06219e6i	−0.426502	+	1.31264i	0.475046	+	0.879961i	$0.342431\pi$
$431$	−1.64481e6	+	5.06219e6i	−0.426502	+	1.31264i	−0.901548	+	0.432678i	$0.857569\pi$
$432$		0			0
$433$	7.67566e6			1.96742			0.983708	−	0.179776i	$-0.0575373\pi$
$433$	7.67566e6			1.96742			0.983708	+	0.179776i	$0.0575373\pi$
$434$		0			0
$435$	900432.			0.228154
$436$		0			0
$437$	296318.	−	911972.i	0.0742257	−	0.228443i
$438$		0			0
$439$	−3.07198e6			−0.760777			−0.380388	−	0.924827i	$-0.624210\pi$
$439$	−3.07198e6			−0.760777			−0.380388	+	0.924827i	$0.624210\pi$
$440$		0			0
$441$	−387947.	+	281860.i	−0.0949895	+	0.0690139i
$442$		0			0
$443$	3.61483e6	+	2.62633e6i	0.875143	+	0.635828i	0.931962	−	0.362556i	$-0.118096\pi$
$443$	3.61483e6	+	2.62633e6i	0.875143	+	0.635828i	−0.0568192	+	0.998384i	$0.518096\pi$
$444$		0			0
$445$	58469.1	−	42480.3i	0.0139967	−	0.0101692i
$446$		0			0
$447$	1.28635e6	−	3.95899e6i	0.304503	−	0.937164i
$448$		0			0
$449$	919164.	−	2.82890e6i	0.215168	−	0.662219i	−0.783974	−	0.620794i	$-0.786810\pi$
$449$	919164.	−	2.82890e6i	0.215168	−	0.662219i	0.999142	−	0.0414246i	$-0.0131896\pi$
$450$		0			0
$451$	390293.	+	283565.i	0.0903545	+	0.0656464i
$452$		0			0
$453$	−11328.2	−	34864.5i	−0.00259367	−	0.00798248i
$454$		0			0
$455$	−87720.4	−	269976.i	−0.0198643	−	0.0611359i
$456$		0			0
$457$	−4.11469e6	−	2.98949e6i	−0.921608	−	0.669587i	0.0223158	−	0.999751i	$-0.492896\pi$
$457$	−4.11469e6	−	2.98949e6i	−0.921608	−	0.669587i	−0.943924	+	0.330164i	$0.892896\pi$
$458$		0			0
$459$	3.11978e6			0.691182
$460$		0			0
$461$	577716.	−	419736.i	0.126608	−	0.0919864i	−0.522679	−	0.852530i	$-0.675067\pi$
$461$	577716.	−	419736.i	0.126608	−	0.0919864i	0.649287	+	0.760543i	$0.275067\pi$
$462$		0			0
$463$	20506.2	+	63111.7i	0.00444563	+	0.0136822i	0.953255	−	0.302168i	$-0.0977103\pi$
$463$	20506.2	+	63111.7i	0.00444563	+	0.0136822i	−0.948809	+	0.315850i	$0.897710\pi$
$464$		0			0
$465$	511218.	+	303670.i	0.109641	+	0.0651282i
$466$		0			0
$467$	1.61316e6	+	4.96480e6i	0.342283	+	1.05344i	0.963022	+	0.269422i	$0.0868326\pi$
$467$	1.61316e6	+	4.96480e6i	0.342283	+	1.05344i	−0.620739	+	0.784017i	$0.713167\pi$
$468$		0			0
$469$	−575937.	+	418443.i	−0.120905	+	0.0878424i
$470$		0			0
$471$	3.32733e6			0.691104
$472$		0			0
$473$	−167030.	−	121354.i	−0.0343274	−	0.0249403i
$474$		0			0
$475$	665295.	+	2.04757e6i	0.135294	+	0.416393i
$476$		0			0
$477$	−222026.	−	683325.i	−0.0446794	−	0.137509i
$478$		0			0
$479$	4.17904e6	+	3.03625e6i	0.832220	+	0.604643i	0.920186	−	0.391480i	$-0.128037\pi$
$479$	4.17904e6	+	3.03625e6i	0.832220	+	0.604643i	−0.0879668	+	0.996123i	$0.528037\pi$
$480$		0			0
$481$	2.50144e6	−	7.69863e6i	0.492977	−	1.51723i
$482$		0			0
$483$	288131.	−	886775.i	0.0561981	−	0.172960i
$484$		0			0
$485$	−546148.	+	396800.i	−0.105428	+	0.0765980i
$486$		0			0
$487$	2.33807e6	+	1.69871e6i	0.446719	+	0.324561i	0.788299	−	0.615292i	$-0.210962\pi$
$487$	2.33807e6	+	1.69871e6i	0.446719	+	0.324561i	−0.341580	+	0.939853i	$0.610962\pi$
$488$		0			0
$489$	4.93718e6	−	3.58707e6i	0.933698	−	0.678371i
$490$		0			0
$491$	−3.05116e6			−0.571164			−0.285582	−	0.958354i	$-0.592187\pi$
$491$	−3.05116e6			−0.571164			−0.285582	+	0.958354i	$0.592187\pi$
$492$		0			0
$493$	−1.95336e6	+	6.01182e6i	−0.361963	+	1.11401i
$494$		0			0
$495$	−17492.6			−0.00320879
$496$		0			0
$497$	−636306.			−0.115551
$498$		0			0
$499$	2.21767e6	−	6.82528e6i	0.398699	−	1.22707i	−0.527344	−	0.849652i	$-0.676812\pi$
$499$	2.21767e6	−	6.82528e6i	0.398699	−	1.22707i	0.926043	−	0.377417i	$-0.123188\pi$
$500$		0			0
$501$	−2.87982e6			−0.512591
$502$		0			0
$503$	3.13263e6	−	2.27599e6i	0.552064	−	0.401098i	−0.276482	−	0.961019i	$-0.589169\pi$
$503$	3.13263e6	−	2.27599e6i	0.552064	−	0.401098i	0.828546	+	0.559921i	$0.189169\pi$
$504$		0			0
$505$	1.02496e6	+	744675.i	0.178845	+	0.129939i
$506$		0			0
$507$	2.89411e6	−	2.10269e6i	0.500028	−	0.363292i
$508$		0			0
$509$	−1.68724e6	+	5.19281e6i	−0.288658	+	0.888398i	0.696620	+	0.717440i	$0.254686\pi$
$509$	−1.68724e6	+	5.19281e6i	−0.288658	+	0.888398i	−0.985278	+	0.170958i	$0.945314\pi$
$510$		0			0
$511$	−414777.	+	1.27655e6i	−0.0702687	+	0.216265i
$512$		0			0
$513$	2.27161e6	+	1.65042e6i	0.381101	+	0.276886i
$514$		0			0
$515$	−887.654	−	2731.92i	−0.000147478	−	0.000453889i
$516$		0			0
$517$	−410598.	−	1.26369e6i	−0.0675602	−	0.207929i
$518$		0			0
$519$	−7.47470e6	−	5.43069e6i	−1.21808	−	0.884987i
$520$		0			0
$521$	−3.20581e6			−0.517420			−0.258710	−	0.965955i	$-0.583297\pi$
$521$	−3.20581e6			−0.517420			−0.258710	+	0.965955i	$0.583297\pi$
$522$		0			0
$523$	−1.92228e6	+	1.39662e6i	−0.307300	+	0.223267i	−0.730737	−	0.682659i	$-0.760824\pi$
$523$	−1.92228e6	+	1.39662e6i	−0.307300	+	0.223267i	0.423437	+	0.905926i	$0.360824\pi$
$524$		0			0
$525$	646913.	+	1.99099e6i	0.102435	+	0.315262i
$526$		0			0
$527$	−3.13649e6	+	2.75443e6i	−0.491946	+	0.432021i
$528$		0			0
$529$	−1.41260e6	−	4.34753e6i	−0.219472	−	0.675466i
$530$		0			0
$531$	−287603.	+	208956.i	−0.0442646	+	0.0321601i
$532$		0			0
$533$	5.46363e6			0.833034
$534$		0			0
$535$	504803.	+	366761.i	0.0762495	+	0.0553985i
$536$		0			0
$537$	−1.16874e6	−	3.59701e6i	−0.174897	−	0.538278i
$538$		0			0
$539$	−312947.	−	963151.i	−0.0463979	−	0.142798i
$540$		0			0
$541$	478240.	+	347461.i	0.0702510	+	0.0510403i	0.622356	−	0.782734i	$-0.286175\pi$
$541$	478240.	+	347461.i	0.0702510	+	0.0510403i	−0.552105	+	0.833774i	$0.686175\pi$
$542$		0			0
$543$	2.20255e6	−	6.77876e6i	0.320573	−	0.986622i
$544$		0			0
$545$	−103460.	+	318417.i	−0.0149204	+	0.0459203i
$546$		0			0
$547$	−5.61284e6	+	4.07797e6i	−0.802074	+	0.582741i	−0.911522	−	0.411252i	$-0.865092\pi$
$547$	−5.61284e6	+	4.07797e6i	−0.802074	+	0.582741i	0.109448	+	0.993993i	$0.465092\pi$
$548$		0			0
$549$	−315522.	−	229240.i	−0.0446785	−	0.0324609i
$550$		0			0
$551$	−4.60266e6	+	3.34403e6i	−0.645847	+	0.469235i
$552$		0			0
$553$	−2.98049e6			−0.414452
$554$		0			0
$555$	353587.	−	1.08823e6i	0.0487263	−	0.149964i
$556$		0			0
$557$	−7.58172e6			−1.03545			−0.517726	−	0.855547i	$-0.673221\pi$
$557$	−7.58172e6			−1.03545			−0.517726	+	0.855547i	$0.673221\pi$
$558$		0			0
$559$	−2.33821e6			−0.316486
$560$		0			0
$561$	−242591.	+	746619.i	−0.0325438	+	0.100159i
$562$		0			0
$563$	1.32821e7			1.76602			0.883011	−	0.469353i	$-0.155513\pi$
$563$	1.32821e7			1.76602			0.883011	+	0.469353i	$0.155513\pi$
$564$		0			0
$565$	−574494.	+	417394.i	−0.0757119	+	0.0550079i
$566$		0			0
$567$	1.90449e6	+	1.38369e6i	0.248783	+	0.180752i
$568$		0			0
$569$	−1.05049e7	+	7.63228e6i	−1.36023	+	0.988265i	−0.361800	+	0.932256i	$0.617838\pi$
$569$	−1.05049e7	+	7.63228e6i	−1.36023	+	0.988265i	−0.998430	+	0.0560091i	$0.982162\pi$
$570$		0			0
$571$	−2.01870e6	+	6.21292e6i	−0.259108	+	0.797453i	0.733884	+	0.679275i	$0.237706\pi$
$571$	−2.01870e6	+	6.21292e6i	−0.259108	+	0.797453i	−0.992992	+	0.118179i	$0.962294\pi$
$572$		0			0
$573$	−3.18340e6	+	9.79749e6i	−0.405046	+	1.24660i
$574$		0			0
$575$	−3.38774e6	−	2.46134e6i	−0.427308	−	0.310457i
$576$		0			0
$577$	492015.	+	1.51427e6i	0.0615232	+	0.189349i	0.977094	−	0.212808i	$-0.0682608\pi$
$577$	492015.	+	1.51427e6i	0.0615232	+	0.189349i	−0.915571	+	0.402156i	$0.868261\pi$
$578$		0			0
$579$	−461423.	−	1.42011e6i	−0.0572009	−	0.176046i
$580$		0			0
$581$	−1.04846e6	−	761750.i	−0.128858	−	0.0936208i
$582$		0			0
$583$	1.51738e6			0.184894
$584$		0			0
$585$	−160273.	+	116445.i	−0.0193629	+	0.0140680i
$586$		0			0
$587$	−492479.	−	1.51569e6i	−0.0589919	−	0.181558i	0.917218	−	0.398385i	$-0.130429\pi$
$587$	−492479.	−	1.51569e6i	−0.0589919	−	0.181558i	−0.976210	+	0.216827i	$0.930429\pi$
$588$		0			0
$589$	−3.74092e6	+	346323.i	−0.444314	+	0.0411333i
$590$		0			0
$591$	−39203.0	−	120654.i	−0.00461690	−	0.0142094i
$592$		0			0
$593$	5.00583e6	−	3.63695e6i	0.584574	−	0.424718i	−0.255796	−	0.966731i	$-0.582338\pi$
$593$	5.00583e6	−	3.63695e6i	0.584574	−	0.424718i	0.840370	+	0.542013i	$0.182338\pi$
$594$		0			0
$595$	281691.			0.0326198
$596$		0			0
$597$	−7.52039e6	−	5.46388e6i	−0.863583	−	0.627430i
$598$		0			0
$599$	−3.66316e6	−	1.12740e7i	−0.417146	−	1.28384i	−0.910317	−	0.413912i	$-0.864162\pi$
$599$	−3.66316e6	−	1.12740e7i	−0.417146	−	1.28384i	0.493170	−	0.869933i	$-0.335838\pi$
$600$		0			0
$601$	−958682.	−	2.95052e6i	−0.108265	−	0.333206i	0.882218	−	0.470841i	$-0.156050\pi$
$601$	−958682.	−	2.95052e6i	−0.108265	−	0.333206i	−0.990483	+	0.137636i	$0.956050\pi$
$602$		0			0
$603$	401938.	+	292025.i	0.0450159	+	0.0327060i
$604$		0			0
$605$	−370114.	+	1.13909e6i	−0.0411100	+	0.126524i
$606$		0			0
$607$	2.20754e6	−	6.79412e6i	0.243185	−	0.748448i	−0.752744	−	0.658313i	$-0.771270\pi$
$607$	2.20754e6	−	6.79412e6i	0.243185	−	0.748448i	0.995930	−	0.0901347i	$-0.0287298\pi$
$608$		0			0
$609$	−4.47549e6	+	3.25163e6i	−0.488987	+	0.355270i
$610$		0			0
$611$	−1.21742e7	−	8.84507e6i	−1.31928	−	0.958513i
$612$		0			0
$613$	−5.27411e6	+	3.83186e6i	−0.566889	+	0.411869i	−0.833974	−	0.551804i	$-0.813940\pi$
$613$	−5.27411e6	+	3.83186e6i	−0.566889	+	0.411869i	0.267085	+	0.963673i	$0.413940\pi$
$614$		0			0
$615$	772303.			0.0823379
$616$		0			0
$617$	105426.	−	324469.i	0.0111490	−	0.0343131i	−0.945327	−	0.326123i	$-0.894258\pi$
$617$	105426.	−	324469.i	0.0111490	−	0.0343131i	0.956476	+	0.291810i	$0.0942576\pi$
$618$		0			0
$619$	9.76427e6			1.02427			0.512134	−	0.858906i	$-0.328855\pi$
$619$	9.76427e6			1.02427			0.512134	+	0.858906i	$0.328855\pi$
$620$		0			0
$621$	−5.46131e6			−0.568287
$622$		0			0
$623$	−137209.	+	422286.i	−0.0141633	+	0.0435900i
$624$		0			0
$625$	9.21810e6			0.943933
$626$		0			0
$627$	−571612.	+	415301.i	−0.0580674	+	0.0421885i
$628$		0			0
$629$	6.49860e6	+	4.72151e6i	0.654928	+	0.475833i
$630$		0			0
$631$	−3.57854e6	+	2.59996e6i	−0.357793	+	0.259952i	−0.752131	−	0.659014i	$-0.770974\pi$
$631$	−3.57854e6	+	2.59996e6i	−0.357793	+	0.259952i	0.394338	+	0.918965i	$0.370974\pi$
$632$		0			0
$633$	1.25600e6	−	3.86556e6i	0.124589	−	0.383445i
$634$		0			0
$635$	−204753.	+	630164.i	−0.0201510	+	0.0620182i
$636$		0			0
$637$	−9.27883e6	−	6.74146e6i	−0.906034	−	0.658272i
$638$		0			0
$639$	137225.	+	422335.i	0.0132948	+	0.0409171i
$640$		0			0
$641$	−4.12903e6	−	1.27079e7i	−0.396920	−	1.22159i	−0.927456	−	0.373932i	$-0.878009\pi$
$641$	−4.12903e6	−	1.27079e7i	−0.396920	−	1.22159i	0.530536	−	0.847662i	$-0.321991\pi$
$642$		0			0
$643$	2.40472e6	+	1.74713e6i	0.229371	+	0.166647i	0.696535	−	0.717523i	$-0.254724\pi$
$643$	2.40472e6	+	1.74713e6i	0.229371	+	0.166647i	−0.467164	+	0.884171i	$0.654724\pi$
$644$		0			0
$645$	−330514.			−0.0312817
$646$		0			0
$647$	4.80093e6	−	3.48808e6i	0.450884	−	0.327586i	−0.339061	−	0.940764i	$-0.610109\pi$
$647$	4.80093e6	−	3.48808e6i	0.450884	−	0.327586i	0.789945	+	0.613178i	$0.210109\pi$
$648$		0			0
$649$	−232002.	−	714028.i	−0.0216212	−	0.0665432i
$650$		0			0
$651$	−3.63756e6	+	336754.i	−0.336401	+	0.0311430i
$652$		0			0
$653$	358915.	+	1.10463e6i	0.0329389	+	0.101375i	0.966174	−	0.257890i	$-0.0830272\pi$
$653$	358915.	+	1.10463e6i	0.0329389	+	0.101375i	−0.933235	+	0.359266i	$0.883027\pi$
$654$		0			0
$655$	−130380.	+	94726.8i	−0.0118743	+	0.00862719i
$656$		0			0
$657$	936734.			0.0846648
$658$		0			0
$659$	−1.24317e7	−	9.03215e6i	−1.11511	−	0.810173i	−0.131647	−	0.991297i	$-0.542027\pi$
$659$	−1.24317e7	−	9.03215e6i	−1.11511	−	0.810173i	−0.983460	+	0.181124i	$0.942027\pi$
$660$		0			0
$661$	2.03873e6	+	6.27457e6i	0.181491	+	0.558573i	0.999870	−	0.0161058i	$-0.00512686\pi$
$661$	2.03873e6	+	6.27457e6i	0.181491	+	0.558573i	−0.818379	+	0.574679i	$0.805127\pi$
$662$		0			0
$663$	2.74740e6	+	8.45564e6i	0.242739	+	0.747072i
$664$		0			0
$665$	205108.	+	149020.i	0.0179857	+	0.0130674i
$666$		0			0
$667$	3.41943e6	−	1.05239e7i	0.297605	−	0.915933i
$668$		0			0
$669$	−6.39108e6	+	1.96697e7i	−0.552089	+	1.69916i
$670$		0			0
$671$	666351.	−	484133.i	0.0571343	−	0.0415105i
$672$		0			0
$673$	−300246.	−	218142.i	−0.0255529	−	0.0185653i	0.574936	−	0.818199i	$-0.305027\pi$
$673$	−300246.	−	218142.i	−0.0255529	−	0.0185653i	−0.600488	+	0.799633i	$0.705027\pi$
$674$		0			0
$675$	9.91998e6	−	7.20729e6i	0.838014	−	0.608853i
$676$		0			0
$677$	3.24779e6			0.272343			0.136172	−	0.990685i	$-0.456520\pi$
$677$	3.24779e6			0.272343			0.136172	+	0.990685i	$0.456520\pi$
$678$		0			0
$679$	1.28164e6	−	3.94449e6i	0.106682	−	0.328335i
$680$		0			0
$681$	1.91577e6			0.158298
$682$		0			0
$683$	8.80299e6			0.722068			0.361034	−	0.932553i	$-0.382424\pi$
$683$	8.80299e6			0.722068			0.361034	+	0.932553i	$0.382424\pi$
$684$		0			0
$685$	−61218.4	+	188411.i	−0.00498489	+	0.0153419i
$686$		0			0
$687$	9.14316e6			0.739102
$688$		0			0
$689$	1.39027e7	−	1.01009e7i	1.11571	−	0.810612i
$690$		0			0
$691$	3.45209e6	+	2.50809e6i	0.275034	+	0.199824i	0.716749	−	0.697332i	$-0.245630\pi$
$691$	3.45209e6	+	2.50809e6i	0.275034	+	0.199824i	−0.441714	+	0.897156i	$0.645630\pi$
$692$		0			0
$693$	86945.0	−	63169.2i	0.00687720	−	0.00499658i
$694$		0			0
$695$	637592.	−	1.96231e6i	0.0500704	−	0.154101i
$696$		0			0
$697$	−1.67540e6	+	5.15635e6i	−0.130628	+	0.402032i
$698$		0			0
$699$	9.91158e6	+	7.20119e6i	0.767273	+	0.557457i
$700$		0			0
$701$	503090.	+	1.54835e6i	0.0386679	+	0.119008i	0.968527	−	0.248908i	$-0.0800716\pi$
$701$	503090.	+	1.54835e6i	0.0386679	+	0.119008i	−0.929859	+	0.367915i	$0.880072\pi$
$702$		0			0
$703$	2.23407e6	+	6.87575e6i	0.170494	+	0.524725i
$704$		0			0
$705$	−1.72086e6	−	1.25028e6i	−0.130399	−	0.0947403i
$706$		0			0
$707$	−7.78359e6			−0.585641
$708$		0			0
$709$	−1.20919e7	+	8.78527e6i	−0.903397	+	0.656356i	−0.939336	−	0.342998i	$-0.888558\pi$
$709$	−1.20919e7	+	8.78527e6i	−0.903397	+	0.656356i	0.0359396	+	0.999354i	$0.488558\pi$
$710$		0			0
$711$	642768.	+	1.97824e6i	0.0476848	+	0.146759i
$712$		0			0
$713$	5.49056e6	−	4.82175e6i	0.404476	−	0.355206i
$714$		0			0
$715$	−129288.	−	397908.i	−0.00945787	−	0.0291083i
$716$		0			0
$717$	−1.47132e7	+	1.06898e7i	−1.06883	+	0.776553i
$718$		0			0
$719$	−5.59210e6			−0.403416			−0.201708	−	0.979446i	$-0.564649\pi$
$719$	−5.59210e6			−0.403416			−0.201708	+	0.979446i	$0.564649\pi$
$720$		0			0
$721$	14277.5	+	10373.2i	0.00102285	+	0.000743146i
$722$		0			0
$723$	5.46859e6	+	1.68306e7i	0.389071	+	1.19744i
$724$		0			0
$725$	7.67734e6	+	2.36284e7i	0.542457	+	1.66951i
$726$		0			0
$727$	1.75180e7	+	1.27276e7i	1.22928	+	0.893121i	0.996836	−	0.0794892i	$-0.0253289\pi$
$727$	1.75180e7	+	1.27276e7i	1.22928	+	0.893121i	0.232440	+	0.972611i	$0.425329\pi$
$728$		0			0
$729$	4.86060e6	−	1.49594e7i	0.338744	−	1.04255i
$730$		0			0
$731$	717003.	−	2.20671e6i	0.0496281	−	0.152740i
$732$		0			0
$733$	−6.03086e6	+	4.38168e6i	−0.414590	+	0.301218i	−0.775458	−	0.631400i	$-0.782481\pi$
$733$	−6.03086e6	+	4.38168e6i	−0.414590	+	0.301218i	0.360867	+	0.932617i	$0.382481\pi$
$734$		0			0
$735$	−1.31160e6	−	952930.i	−0.0895533	−	0.0650643i
$736$		0			0
$737$	−848854.	+	616728.i	−0.0575658	+	0.0418240i
$738$		0			0
$739$	2.82949e7			1.90589			0.952944	−	0.303145i	$-0.0980366\pi$
$739$	2.82949e7			1.90589			0.952944	+	0.303145i	$0.0980366\pi$
$740$		0			0
$741$	−2.47271e6	+	7.61023e6i	−0.165435	+	0.509158i
$742$		0			0
$743$	1.38181e7			0.918284			0.459142	−	0.888363i	$-0.348157\pi$
$743$	1.38181e7			0.918284			0.459142	+	0.888363i	$0.348157\pi$
$744$		0			0
$745$	−2.20149e6			−0.145320
$746$		0			0
$747$	−279486.	+	860170.i	−0.0183256	+	0.0564005i
$748$		0			0
$749$	−3.83351e6			−0.249684
$750$		0			0
$751$	7.47317e6	−	5.42958e6i	0.483510	−	0.351290i	−0.319173	−	0.947696i	$-0.603405\pi$
$751$	7.47317e6	−	5.42958e6i	0.483510	−	0.351290i	0.802683	+	0.596406i	$0.203405\pi$
$752$		0			0
$753$	4.93008e6	+	3.58191e6i	0.316859	+	0.230212i
$754$		0			0
$755$	−15684.6	+	11395.5i	−0.00100140	+	0.000727557i
$756$		0			0
$757$	6.05547e6	−	1.86368e7i	0.384068	−	1.18204i	−0.553086	−	0.833124i	$-0.686550\pi$
$757$	6.05547e6	−	1.86368e7i	0.384068	−	1.18204i	0.937154	−	0.348915i	$-0.113450\pi$
$758$		0			0
$759$	424666.	−	1.30699e6i	0.0267573	−	0.0823506i
$760$		0			0
$761$	−6.65064e6	−	4.83197e6i	−0.416296	−	0.302456i	0.359850	−	0.933010i	$-0.382828\pi$
$761$	−6.65064e6	−	4.83197e6i	−0.416296	−	0.302456i	−0.776146	+	0.630554i	$0.782828\pi$
$762$		0			0
$763$	−635629.	−	1.95627e6i	−0.0395269	−	0.121651i
$764$		0			0
$765$	−60749.1	−	186967.i	−0.00375307	−	0.0115508i
$766$		0			0
$767$	−6.87883e6	−	4.99776e6i	−0.422208	−	0.306752i
$768$		0			0
$769$	2.82187e7			1.72076			0.860381	−	0.509651i	$-0.170225\pi$
$769$	2.82187e7			1.72076			0.860381	+	0.509651i	$0.170225\pi$
$770$		0			0
$771$	−1.81866e7	+	1.32134e7i	−1.10183	+	0.800530i
$772$		0			0
$773$	−6.92986e6	−	2.13279e7i	−0.417134	−	1.28381i	−0.910328	−	0.413887i	$-0.864171\pi$
$773$	−6.92986e6	−	2.13279e7i	−0.417134	−	1.28381i	0.493194	−	0.869919i	$-0.335829\pi$
$774$		0			0
$775$	−3.60986e6	+	1.60042e7i	−0.215892	+	0.957147i
$776$		0			0
$777$	2.17234e6	+	6.68578e6i	0.129085	+	0.397283i
$778$		0			0
$779$	−3.94771e6	+	2.86818e6i	−0.233078	+	0.169341i
$780$		0			0
$781$	−937830.			−0.0550170
$782$		0			0
$783$	2.62138e7	+	1.90454e7i	1.52801	+	1.11016i
$784$		0			0
$785$	−543772.	−	1.67356e6i	−0.0314951	−	0.0969319i
$786$		0			0
$787$	3.39011e6	+	1.04337e7i	0.195109	+	0.600482i	0.999975	+	0.00702686i	$0.00223674\pi$
$787$	3.39011e6	+	1.04337e7i	0.195109	+	0.600482i	−0.804867	+	0.593456i	$0.797763\pi$
$788$		0			0
$789$	−649522.	−	471906.i	−0.0371451	−	0.0269875i
$790$		0			0
$791$	1.34816e6	−	4.14922e6i	0.0766127	−	0.235790i
$792$		0			0
$793$	2.88254e6	−	8.87155e6i	0.162777	−	0.500976i
$794$		0			0
$795$	1.96520e6	−	1.42780e6i	0.110278	−	0.0801216i
$796$		0			0
$797$	−2.15644e7	−	1.56674e7i	−1.20252	−	0.873679i	−0.207987	−	0.978132i	$-0.566691\pi$
$797$	−2.15644e7	−	1.56674e7i	−1.20252	−	0.873679i	−0.994530	+	0.104452i	$0.966691\pi$
$798$		0			0
$799$	1.20808e7	−	8.77720e6i	0.669465	−	0.486395i
$800$		0			0
$801$	309874.			0.0170649
$802$		0			0
$803$	−611325.	+	1.88147e6i	−0.0334567	+	0.102969i
$804$		0			0
$805$	−493113.			−0.0268199
$806$		0			0
$807$	−2.81970e7			−1.52412
$808$		0			0
$809$	−2.01584e6	+	6.20410e6i	−0.108289	+	0.333279i	−0.990488	−	0.137597i	$-0.956062\pi$
$809$	−2.01584e6	+	6.20410e6i	−0.108289	+	0.333279i	0.882199	+	0.470876i	$0.156062\pi$
$810$		0			0
$811$	−6.58521e6			−0.351574			−0.175787	−	0.984428i	$-0.556247\pi$
$811$	−6.58521e6			−0.351574			−0.175787	+	0.984428i	$0.556247\pi$
$812$		0			0
$813$	2.42723e7	−	1.76348e7i	1.28790	−	0.935717i
$814$		0			0
$815$	−2.61106e6	−	1.89705e6i	−0.137697	−	0.100043i
$816$		0			0
$817$	1.68946e6	−	1.22746e6i	0.0885508	−	0.0643359i
$818$		0			0
$819$	376112.	−	1.15755e6i	0.0195933	−	0.0603019i
$820$		0			0
$821$	−3.85615e6	+	1.18680e7i	−0.199662	+	0.614497i	0.800228	+	0.599696i	$0.204712\pi$
$821$	−3.85615e6	+	1.18680e7i	−0.199662	+	0.614497i	−0.999890	+	0.0148016i	$0.995288\pi$
$822$		0			0
$823$	1.74947e7	+	1.27107e7i	0.900342	+	0.654136i	0.938554	−	0.345133i	$-0.112166\pi$
$823$	1.74947e7	+	1.27107e7i	0.900342	+	0.654136i	−0.0382121	+	0.999270i	$0.512166\pi$
$824$		0			0
$825$	953463.	+	2.93446e6i	0.0487718	+	0.150104i
$826$		0			0
$827$	−1.18719e7	−	3.65378e7i	−0.603608	−	1.85772i	−0.506089	−	0.862481i	$-0.668909\pi$
$827$	−1.18719e7	−	3.65378e7i	−0.603608	−	1.85772i	−0.0975195	−	0.995234i	$-0.531091\pi$
$828$		0			0
$829$	−1.06158e7	−	7.71282e6i	−0.536496	−	0.389787i	0.286286	−	0.958144i	$-0.407579\pi$
$829$	−1.06158e7	−	7.71282e6i	−0.536496	−	0.389787i	−0.822782	+	0.568357i	$0.807579\pi$
$830$		0			0
$831$	−5.13628e6			−0.258016
$832$		0			0
$833$	9.20764e6	−	6.68974e6i	0.459765	−	0.334039i
$834$		0			0
$835$	470638.	+	1.44847e6i	0.0233599	+	0.0718943i
$836$		0			0
$837$	8.45978e6	+	1.96536e7i	0.417393	+	0.969679i
$838$		0			0
$839$	−1.00716e7	−	3.09972e7i	−0.493961	−	1.52026i	−0.818569	−	0.574408i	$-0.805232\pi$
$839$	−1.00716e7	−	3.09972e7i	−0.493961	−	1.52026i	0.324608	−	0.945849i	$-0.394768\pi$
$840$		0			0
$841$	−3.65197e7	+	2.65331e7i	−1.78048	+	1.29359i
$842$		0			0
$843$	3.36281e6			0.162980
$844$		0			0
$845$	−1.53057e6	−	1.11202e6i	−0.0737415	−	0.0535763i
$846$		0			0
$847$	−2.27388e6	−	6.99828e6i	−0.108908	−	0.335184i
$848$		0			0
$849$	−1.30143e6	−	4.00539e6i	−0.0619658	−	0.190711i
$850$		0			0
$851$	−1.13761e7	−	8.26521e6i	−0.538479	−	0.391228i
$852$		0			0
$853$	4.52584e6	−	1.39291e7i	0.212974	−	0.655467i	−0.786317	−	0.617823i	$-0.788015\pi$
$853$	4.52584e6	−	1.39291e7i	0.212974	−	0.655467i	0.999291	−	0.0376437i	$-0.0119852\pi$
$854$		0			0
$855$	54675.4	−	168273.i	0.00255786	−	0.00787228i
$856$		0			0
$857$	2.20447e7	−	1.60164e7i	1.02530	−	0.744927i	0.0579410	−	0.998320i	$-0.481546\pi$
$857$	2.20447e7	−	1.60164e7i	1.02530	−	0.744927i	0.967364	+	0.253393i	$0.0815465\pi$
$858$		0			0
$859$	−3.00112e7	−	2.18044e7i	−1.38772	−	1.00824i	−0.996111	−	0.0881017i	$-0.971920\pi$
$859$	−3.00112e7	−	2.18044e7i	−1.38772	−	1.00824i	−0.391605	−	0.920133i	$-0.628080\pi$
$860$		0			0
$861$	−3.83864e6	+	2.78893e6i	−0.176469	+	0.128212i
$862$		0			0
$863$	1.04948e7			0.479673			0.239836	−	0.970813i	$-0.422906\pi$
$863$	1.04948e7			0.479673			0.239836	+	0.970813i	$0.422906\pi$
$864$		0			0
$865$	−1.50993e6	+	4.64710e6i	−0.0686147	+	0.211174i
$866$		0			0
$867$	1.17595e7			0.531301
$868$		0			0
$869$	−4.39284e6			−0.197331
$870$		0			0
$871$	−3.67202e6	+	1.13013e7i	−0.164006	+	0.504759i
$872$		0			0
$873$	−2.89447e6			−0.128539
$874$		0			0
$875$	1.80856e6	−	1.31399e6i	0.0798569	−	0.0580194i
$876$		0			0
$877$	−2.29729e6	−	1.66908e6i	−0.100859	−	0.0732787i	0.536212	−	0.844083i	$-0.319855\pi$
$877$	−2.29729e6	−	1.66908e6i	−0.100859	−	0.0732787i	−0.637072	+	0.770804i	$0.719855\pi$
$878$		0			0
$879$	−3.08957e7	+	2.24470e7i	−1.34873	+	0.979912i
$880$		0			0
$881$	2.11869e6	−	6.52064e6i	0.0919659	−	0.283042i	−0.894485	−	0.447098i	$-0.852458\pi$
$881$	2.11869e6	−	6.52064e6i	0.0919659	−	0.283042i	0.986451	+	0.164056i	$0.0524577\pi$
$882$		0			0
$883$	−1.11114e7	+	3.41975e7i	−0.479589	+	1.47602i	0.360079	+	0.932922i	$0.382750\pi$
$883$	−1.11114e7	+	3.41975e7i	−0.479589	+	1.47602i	−0.839668	+	0.543101i	$0.817250\pi$
$884$		0			0
$885$	−972346.	−	706451.i	−0.0417314	−	0.0303196i
$886$		0			0
$887$	−3.88459e6	−	1.19555e7i	−0.165782	−	0.510223i	0.833311	−	0.552804i	$-0.186442\pi$
$887$	−3.88459e6	−	1.19555e7i	−0.165782	−	0.510223i	−0.999093	+	0.0425804i	$0.986442\pi$
$888$		0			0
$889$	−1.25795e6	−	3.87156e6i	−0.0533835	−	0.164298i
$890$		0			0
$891$	2.80696e6	+	2.03938e6i	0.118452	+	0.0860604i
$892$		0			0
$893$	1.34397e7			0.563976
$894$		0			0
$895$	−1.61820e6	+	1.17569e6i	−0.0675266	+	0.0490609i
$896$		0			0
$897$	−4.80945e6	−	1.48020e7i	−0.199579	−	0.614240i
$898$		0			0
$899$	−4.31693e7	+	3.99648e6i	−1.78146	+	0.164922i
$900$		0			0
$901$	5.26962e6	+	1.62182e7i	0.216256	+	0.665567i
$902$		0			0
$903$	1.64278e6	−	1.19355e6i	0.0670441	−	0.0487104i
$904$		0			0
$905$	−3.76949e6			−0.152989
$906$		0			0
$907$	−2.05594e7	−	1.49373e7i	−0.829837	−	0.602912i	0.0896760	−	0.995971i	$-0.471417\pi$
$907$	−2.05594e7	−	1.49373e7i	−0.829837	−	0.602912i	−0.919513	+	0.393059i	$0.871417\pi$
$908$		0			0
$909$	1.67860e6	+	5.16619e6i	0.0673809	+	0.207377i
$910$		0			0
$911$	1.30369e7	+	4.01235e7i	0.520449	+	1.60178i	0.773143	+	0.634232i	$0.218684\pi$
$911$	1.30369e7	+	4.01235e7i	0.520449	+	1.60178i	−0.252694	+	0.967546i	$0.581316\pi$
$912$		0			0
$913$	−1.54529e6	−	1.12272e6i	−0.0613525	−	0.0445752i
$914$		0			0
$915$	407457.	−	1.25403e6i	0.0160890	−	0.0495169i
$916$		0			0
$917$	305963.	−	941656.i	0.0120156	−	0.0369802i
$918$		0			0
$919$	−1.44894e7	+	1.05272e7i	−0.565930	+	0.411172i	−0.833624	−	0.552332i	$-0.813738\pi$
$919$	−1.44894e7	+	1.05272e7i	−0.565930	+	0.411172i	0.267695	+	0.963504i	$0.413738\pi$
$920$		0			0
$921$	−2.87348e7	−	2.08771e7i	−1.11624	−	0.810999i
$922$		0			0
$923$	−8.59270e6	+	6.24296e6i	−0.331990	+	0.241205i
$924$		0			0
$925$	3.15712e7			1.21321
$926$		0			0
$927$	3805.92	−	11713.4i	0.000145466	−	0.000447698i
$928$		0			0
$929$	2.40552e7			0.914469			0.457235	−	0.889346i	$-0.348840\pi$
$929$	2.40552e7			0.914469			0.457235	+	0.889346i	$0.348840\pi$
$930$		0			0
$931$	1.02434e7			0.387318
$932$		0			0
$933$	−1.40041e6	+	4.31002e6i	−0.0526685	+	0.162097i
$934$		0			0
$935$	415175.			0.0155311
$936$		0			0
$937$	1.03607e7	−	7.52750e6i	0.385514	−	0.280093i	−0.378101	−	0.925765i	$-0.623423\pi$
$937$	1.03607e7	−	7.52750e6i	0.385514	−	0.280093i	0.763615	+	0.645672i	$0.223423\pi$
$938$		0			0
$939$	1.59053e7	+	1.15559e7i	0.588677	+	0.427699i
$940$		0			0
$941$	−3.22425e7	+	2.34256e7i	−1.18701	+	0.862415i	−0.992945	−	0.118573i	$-0.962168\pi$
$941$	−3.22425e7	+	2.34256e7i	−1.18701	+	0.862415i	−0.194067	+	0.980988i	$0.562168\pi$
$942$		0			0
$943$	2.93286e6	−	9.02641e6i	0.107402	−	0.330549i
$944$		0			0
$945$	446199.	−	1.37326e6i	0.0162536	−	0.0500234i
$946$		0			0
$947$	−4.41761e7	−	3.20958e7i	−1.60071	−	1.16298i	−0.886140	−	0.463417i	$-0.846623\pi$
$947$	−4.41761e7	−	3.20958e7i	−1.60071	−	1.16298i	−0.714569	−	0.699565i	$-0.753377\pi$
$948$		0			0
$949$	6.92341e6	+	2.13081e7i	0.249548	+	0.768030i
$950$		0			0
$951$	−1.04472e7	−	3.21532e7i	−0.374584	−	1.15285i
$952$		0			0
$953$	3.14267e6	+	2.28329e6i	0.112090	+	0.0814382i	0.642418	−	0.766354i	$-0.277931\pi$
$953$	3.14267e6	+	2.28329e6i	0.112090	+	0.0814382i	−0.530328	+	0.847792i	$0.677931\pi$
$954$		0			0
$955$	5.44813e6			0.193303
$956$		0			0
$957$	−6.59627e6	+	4.79247e6i	−0.232819	+	0.169153i
$958$		0			0
$959$	−376109.	−	1.15755e6i	−0.0132059	−	0.0406435i
$960$		0			0
$961$	−2.58571e7	−	1.22898e7i	−0.903173	−	0.429276i
$962$		0			0
$963$	826728.	+	2.54441e6i	0.0287274	+	0.0884140i
$964$		0			0
$965$	−638871.	+	464167.i	−0.0220849	+	0.0160456i
$966$		0			0
$967$	−8.83375e6			−0.303794			−0.151897	−	0.988396i	$-0.548538\pi$
$967$	−8.83375e6			−0.303794			−0.151897	+	0.988396i	$0.548538\pi$
$968$		0			0
$969$	−6.42398e6	−	4.66730e6i	−0.219783	−	0.159682i
$970$		0			0
$971$	−1.29088e6	−	3.97291e6i	−0.0439376	−	0.135226i	0.926681	−	0.375848i	$-0.122649\pi$
$971$	−1.29088e6	−	3.97291e6i	−0.0439376	−	0.135226i	−0.970619	+	0.240622i	$0.922649\pi$
$972$		0			0
$973$	3.91719e6	+	1.20559e7i	0.132646	+	0.408241i
$974$		0			0
$975$	2.82701e7	+	2.05394e7i	0.952391	+	0.691952i
$976$		0			0
$977$	8.10720e6	−	2.49514e7i	0.271728	−	0.836293i	−0.718339	−	0.695694i	$-0.755097\pi$
$977$	8.10720e6	−	2.49514e7i	0.271728	−	0.836293i	0.990067	−	0.140599i	$-0.0449029\pi$
$978$		0			0
$979$	−202228.	+	622393.i	−0.00674348	+	0.0207543i
$980$		0			0
$981$	−1.16135e6	+	843771.i	−0.0385293	+	0.0279932i
$982$		0			0
$983$	−3.05288e7	−	2.21805e7i	−1.00769	−	0.732128i	−0.0439647	−	0.999033i	$-0.513999\pi$
$983$	−3.05288e7	−	2.21805e7i	−1.00769	−	0.732128i	−0.963723	+	0.266905i	$0.913999\pi$
$984$		0			0
$985$	−54279.2	+	39436.1i	−0.00178255	+	0.00129510i
$986$		0			0
$987$	1.30684e7			0.427000
$988$		0			0
$989$	−1.25514e6	+	3.86294e6i	−0.0408040	+	0.125582i
$990$		0			0
$991$	−1.63985e7			−0.530419			−0.265209	−	0.964191i	$-0.585441\pi$
$991$	−1.63985e7			−0.530419			−0.265209	+	0.964191i	$0.585441\pi$
$992$		0			0
$993$	4.52552e7			1.45645
$994$		0			0
$995$	−1.51916e6	+	4.67550e6i	−0.0486459	+	0.149717i
$996$		0			0
$997$	5.56156e7			1.77198			0.885990	−	0.463705i	$-0.153480\pi$
$997$	5.56156e7			1.77198			0.885990	+	0.463705i	$0.153480\pi$
$998$		0			0
$999$	3.33114e7	−	2.42022e7i	1.05604	−	0.767256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.97.5	✓	56
31.8	even	5	inner	124.6.f.a.101.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.97.5	✓	56	1.1	even	1	trivial
124.6.f.a.101.5	yes	56	31.8	even	5	inner

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.47947 + 13.7864i) q^{3} +7.66625 q^{5} +(-38.1042 + 27.6843i) q^{7} +(26.5924 + 19.3205i) q^{9} +O(q^{10})\)	\(q+(-4.47947 + 13.7864i) q^{3} +7.66625 q^{5} +(-38.1042 + 27.6843i) q^{7} +(26.5924 + 19.3205i) q^{9} +(-56.1604 + 40.8029i) q^{11} +(-242.942 + 747.699i) q^{13} +(-34.3407 + 105.690i) q^{15} +(-631.151 - 458.558i) q^{17} +(-216.975 - 667.780i) q^{19} +(-210.980 - 649.330i) q^{21} +(1104.86 + 802.725i) q^{23} -3066.23 q^{25} +(-3235.24 + 2350.54i) q^{27} +(-2503.84 - 7706.02i) q^{29} +(1177.30 - 5219.49i) q^{31} +(-310.956 - 957.025i) q^{33} +(-292.116 + 212.235i) q^{35} -10296.4 q^{37} +(-9219.81 - 6698.59i) q^{39} +(-2147.55 - 6609.47i) q^{41} +(919.063 + 2828.59i) q^{43} +(203.864 + 148.116i) q^{45} +(-5914.86 + 18204.1i) q^{47} +(-4508.14 + 13874.6i) q^{49} +(9149.08 - 6647.19i) q^{51} +(-17684.0 - 12848.1i) q^{53} +(-430.540 + 312.806i) q^{55} +10178.2 q^{57} +(-3342.09 + 10285.9i) q^{59} -11865.1 q^{61} -1548.15 q^{63} +(-1862.46 + 5732.05i) q^{65} +15114.8 q^{67} +(-16015.8 + 11636.2i) q^{69} +(10929.7 + 7940.91i) q^{71} +(23055.5 - 16750.8i) q^{73} +(13735.1 - 42272.2i) q^{75} +(1010.35 - 3109.53i) q^{77} +(51195.3 + 37195.6i) q^{79} +(-15445.0 - 47534.9i) q^{81} +(8502.79 + 26168.9i) q^{83} +(-4838.56 - 3515.42i) q^{85} +117454. q^{87} +(7626.82 - 5541.21i) q^{89} +(-11442.4 - 35216.1i) q^{91} +(66684.3 + 39611.2i) q^{93} +(-1663.38 - 5119.37i) q^{95} +(-71240.6 + 51759.3i) q^{97} -2281.77 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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