LMFDB - Embedded newform 644.4.i.b.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,4,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	644.i (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:	$37.9972300437$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.1
Character	$\chi$	$=$	644.93
Dual form			644.4.i.b.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.78776 - 8.29265i) q^{3} +(1.66948 - 2.89162i) q^{5} +(-18.1145 + 3.85540i) q^{7} +(-32.3454 + 56.0238i) q^{9} +O(q^{10})$	\(q+(-4.78776 - 8.29265i) q^{3} +(1.66948 - 2.89162i) q^{5} +(-18.1145 + 3.85540i) q^{7} +(-32.3454 + 56.0238i) q^{9} +(-11.8745 - 20.5673i) q^{11} -40.9661 q^{13} -31.9723 q^{15} +(-12.8961 - 22.3367i) q^{17} +(3.14471 - 5.44680i) q^{19} +(118.700 + 131.759i) q^{21} +(11.5000 - 19.9186i) q^{23} +(56.9257 + 98.5982i) q^{25} +360.909 q^{27} -194.354 q^{29} +(118.928 + 205.989i) q^{31} +(-113.705 + 196.943i) q^{33} +(-19.0934 + 58.8169i) q^{35} +(-25.8033 + 44.6926i) q^{37} +(196.136 + 339.718i) q^{39} -346.338 q^{41} +68.3209 q^{43} +(108.000 + 187.061i) q^{45} +(214.217 - 371.034i) q^{47} +(313.272 - 139.678i) q^{49} +(-123.487 + 213.886i) q^{51} +(-29.3669 - 50.8650i) q^{53} -79.2971 q^{55} -60.2246 q^{57} +(300.708 + 520.842i) q^{59} +(387.367 - 670.939i) q^{61} +(369.926 - 1139.55i) q^{63} +(-68.3921 + 118.459i) q^{65} +(-509.983 - 883.316i) q^{67} -220.237 q^{69} -534.313 q^{71} +(227.149 + 393.434i) q^{73} +(545.094 - 944.130i) q^{75} +(294.397 + 326.786i) q^{77} +(3.80610 - 6.59235i) q^{79} +(-854.622 - 1480.25i) q^{81} +1165.57 q^{83} -86.1191 q^{85} +(930.523 + 1611.71i) q^{87} +(-533.005 + 923.191i) q^{89} +(742.081 - 157.941i) q^{91} +(1138.80 - 1972.45i) q^{93} +(-10.5001 - 18.1866i) q^{95} -511.622 q^{97} +1536.35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−4.78776	−	8.29265i	−0.921406	−	1.59592i	−0.797242	−	0.603660i	$-0.793709\pi$
$3$	−4.78776	−	8.29265i	−0.921406	−	1.59592i	−0.124164	−	0.992262i	$-0.539625\pi$
$4$		0			0
$5$	1.66948	−	2.89162i	0.149323	−	0.258635i	−0.781655	−	0.623712i	$-0.785624\pi$
$5$	1.66948	−	2.89162i	0.149323	−	0.258635i	0.930977	+	0.365077i	$0.118957\pi$
$6$		0			0
$7$	−18.1145	+	3.85540i	−0.978092	+	0.208172i
$7$	−18.1145	+	3.85540i	−0.978092	+	0.208172i
$8$		0			0
$9$	−32.3454	+	56.0238i	−1.19798	+	2.07496i
$10$		0			0
$11$	−11.8745	−	20.5673i	−0.325482	−	0.563752i	0.656127	−	0.754650i	$-0.272193\pi$
$11$	−11.8745	−	20.5673i	−0.325482	−	0.563752i	−0.981610	+	0.190898i	$0.938860\pi$
$12$		0			0
$13$	−40.9661			−0.873997			−0.436998	−	0.899462i	$-0.643958\pi$
$13$	−40.9661			−0.873997			−0.436998	+	0.899462i	$0.643958\pi$
$14$		0			0
$15$	−31.9723			−0.550347
$16$		0			0
$17$	−12.8961	−	22.3367i	−0.183986	−	0.318673i	0.759248	−	0.650801i	$-0.225567\pi$
$17$	−12.8961	−	22.3367i	−0.183986	−	0.318673i	−0.943234	+	0.332128i	$0.892233\pi$
$18$		0			0
$19$	3.14471	−	5.44680i	0.0379709	−	0.0657675i	−0.846415	−	0.532523i	$-0.821244\pi$
$19$	3.14471	−	5.44680i	0.0379709	−	0.0657675i	0.884386	+	0.466756i	$0.154577\pi$
$20$		0			0
$21$	118.700	+	131.759i	1.23345	+	1.36915i
$22$		0			0
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$		0			0
$25$	56.9257	+	98.5982i	0.455405	+	0.788785i
$26$		0			0
$27$	360.909			2.57248
$28$		0			0
$29$	−194.354			−1.24451			−0.622254	−	0.782816i	$-0.713783\pi$
$29$	−194.354			−1.24451			−0.622254	+	0.782816i	$0.713783\pi$
$30$		0			0
$31$	118.928	+	205.989i	0.689034	+	1.19344i	0.972151	+	0.234356i	$0.0752982\pi$
$31$	118.928	+	205.989i	0.689034	+	1.19344i	−0.283117	+	0.959085i	$0.591368\pi$
$32$		0			0
$33$	−113.705	+	196.943i	−0.599803	+	1.03889i
$34$		0			0
$35$	−19.0934	+	58.8169i	−0.0922109	+	0.284053i
$36$		0			0
$37$	−25.8033	+	44.6926i	−0.114650	+	0.198579i	−0.917640	−	0.397414i	$-0.869908\pi$
$37$	−25.8033	+	44.6926i	−0.114650	+	0.198579i	0.802990	+	0.595992i	$0.203241\pi$
$38$		0			0
$39$	196.136	+	339.718i	0.805305	+	1.39483i
$40$		0			0
$41$	−346.338			−1.31924			−0.659621	−	0.751599i	$-0.729283\pi$
$41$	−346.338			−1.31924			−0.659621	+	0.751599i	$0.729283\pi$
$42$		0			0
$43$	68.3209			0.242299			0.121149	−	0.992634i	$-0.461342\pi$
$43$	68.3209			0.242299			0.121149	+	0.992634i	$0.461342\pi$
$44$		0			0
$45$	108.000	+	187.061i	0.357770	+	0.619677i
$46$		0			0
$47$	214.217	−	371.034i	0.664824	−	1.15151i	−0.314509	−	0.949255i	$-0.601840\pi$
$47$	214.217	−	371.034i	0.664824	−	1.15151i	0.979333	−	0.202255i	$-0.0648269\pi$
$48$		0			0
$49$	313.272	−	139.678i	0.913329	−	0.407223i
$50$		0			0
$51$	−123.487	+	213.886i	−0.339052	+	0.587255i
$52$		0			0
$53$	−29.3669	−	50.8650i	−0.0761104	−	0.131827i	0.825458	−	0.564463i	$-0.190917\pi$
$53$	−29.3669	−	50.8650i	−0.0761104	−	0.131827i	−0.901569	+	0.432636i	$0.857583\pi$
$54$		0			0
$55$	−79.2971			−0.194408
$56$		0			0
$57$	−60.2246			−0.139946
$58$		0			0
$59$	300.708	+	520.842i	0.663541	+	1.14929i	0.979679	+	0.200573i	$0.0642803\pi$
$59$	300.708	+	520.842i	0.663541	+	1.14929i	−0.316138	+	0.948713i	$0.602386\pi$
$60$		0			0
$61$	387.367	−	670.939i	0.813069	−	1.40828i	−0.0976370	−	0.995222i	$-0.531128\pi$
$61$	387.367	−	670.939i	0.813069	−	1.40828i	0.910706	−	0.413055i	$-0.135538\pi$
$62$		0			0
$63$	369.926	−	1139.55i	0.739783	−	2.27889i
$64$		0			0
$65$	−68.3921	+	118.459i	−0.130508	+	0.226046i
$66$		0			0
$67$	−509.983	−	883.316i	−0.929915	−	1.61066i	−0.783459	−	0.621444i	$-0.786547\pi$
$67$	−509.983	−	883.316i	−0.929915	−	1.61066i	−0.146456	−	0.989217i	$-0.546787\pi$
$68$		0			0
$69$	−220.237			−0.384253
$70$		0			0
$71$	−534.313			−0.893117			−0.446559	−	0.894754i	$-0.647351\pi$
$71$	−534.313			−0.893117			−0.446559	+	0.894754i	$0.647351\pi$
$72$		0			0
$73$	227.149	+	393.434i	0.364189	+	0.630794i	0.988646	−	0.150266i	$-0.0480129\pi$
$73$	227.149	+	393.434i	0.364189	+	0.630794i	−0.624457	+	0.781060i	$0.714680\pi$
$74$		0			0
$75$	545.094	−	944.130i	0.839226	−	1.45358i
$76$		0			0
$77$	294.397	+	326.786i	0.435709	+	0.483645i
$78$		0			0
$79$	3.80610	−	6.59235i	0.00542050	−	0.00938858i	−0.863302	−	0.504687i	$-0.831608\pi$
$79$	3.80610	−	6.59235i	0.00542050	−	0.00938858i	0.868723	+	0.495298i	$0.164941\pi$
$80$		0			0
$81$	−854.622	−	1480.25i	−1.17232	−	2.03052i
$82$		0			0
$83$	1165.57			1.54142			0.770709	−	0.637187i	$-0.219902\pi$
$83$	1165.57			1.54142			0.770709	+	0.637187i	$0.219902\pi$
$84$		0			0
$85$	−86.1191			−0.109893
$86$		0			0
$87$	930.523	+	1611.71i	1.14670	+	1.98614i
$88$		0			0
$89$	−533.005	+	923.191i	−0.634813	+	1.09953i	0.351741	+	0.936097i	$0.385590\pi$
$89$	−533.005	+	923.191i	−0.634813	+	1.09953i	−0.986555	+	0.163432i	$0.947744\pi$
$90$		0			0
$91$	742.081	−	157.941i	0.854849	−	0.181942i
$92$		0			0
$93$	1138.80	−	1972.45i	1.26976	−	2.19929i
$94$		0			0
$95$	−10.5001	−	18.1866i	−0.0113398	−	0.0196412i
$96$		0			0
$97$	−511.622			−0.535540			−0.267770	−	0.963483i	$-0.586287\pi$
$97$	−511.622			−0.535540			−0.267770	+	0.963483i	$0.586287\pi$
$98$		0			0
$99$	1536.35			1.55968
$100$		0			0
$101$	−38.6757	−	66.9883i	−0.0381028	−	0.0659959i	0.846345	−	0.532635i	$-0.178798\pi$
$101$	−38.6757	−	66.9883i	−0.0381028	−	0.0659959i	−0.884448	+	0.466639i	$0.845465\pi$
$102$		0			0
$103$	397.282	−	688.113i	0.380052	−	0.658269i	−0.611017	−	0.791617i	$-0.709239\pi$
$103$	397.282	−	688.113i	0.380052	−	0.658269i	0.991069	+	0.133348i	$0.0425727\pi$
$104$		0			0
$105$	579.163	−	123.266i	0.538290	−	0.114567i
$106$		0			0
$107$	171.471	−	296.997i	0.154923	−	0.268334i	−0.778108	−	0.628130i	$-0.783820\pi$
$107$	171.471	−	296.997i	0.154923	−	0.268334i	0.933031	+	0.359796i	$0.117154\pi$
$108$		0			0
$109$	324.394	+	561.868i	0.285058	+	0.493735i	0.972623	−	0.232387i	$-0.0746537\pi$
$109$	324.394	+	561.868i	0.285058	+	0.493735i	−0.687565	+	0.726123i	$0.741320\pi$
$110$		0			0
$111$	494.160			0.422555
$112$		0			0
$113$	−1147.09			−0.954947			−0.477474	−	0.878646i	$-0.658447\pi$
$113$	−1147.09			−0.954947			−0.477474	+	0.878646i	$0.658447\pi$
$114$		0			0
$115$	−38.3980	−	66.5073i	−0.0311359	−	0.0539290i
$116$		0			0
$117$	1325.06	−	2295.08i	1.04703	−	1.81351i
$118$		0			0
$119$	319.724	+	354.899i	0.246294	+	0.273391i
$120$		0			0
$121$	383.491	−	664.226i	0.288122	−	0.499043i
$122$		0			0
$123$	1658.18	+	2872.06i	1.21556	+	2.10541i
$124$		0			0
$125$	797.515			0.570655
$126$		0			0
$127$	436.455			0.304954			0.152477	−	0.988307i	$-0.451275\pi$
$127$	436.455			0.304954			0.152477	+	0.988307i	$0.451275\pi$
$128$		0			0
$129$	−327.104	−	566.562i	−0.223255	−	0.386690i
$130$		0			0
$131$	253.652	−	439.338i	0.169173	−	0.293016i	−0.768956	−	0.639301i	$-0.779224\pi$
$131$	253.652	−	439.338i	0.169173	−	0.293016i	0.938129	+	0.346285i	$0.112557\pi$
$132$		0			0
$133$	−35.9653	+	110.790i	−0.0234480	+	0.0722311i
$134$		0			0
$135$	602.530	−	1043.61i	0.384130	−	0.665332i
$136$		0			0
$137$	−556.826	−	964.452i	−0.347247	−	0.601450i	0.638512	−	0.769612i	$-0.279550\pi$
$137$	−556.826	−	964.452i	−0.347247	−	0.601450i	−0.985759	+	0.168162i	$0.946217\pi$
$138$		0			0
$139$	3035.93			1.85255			0.926274	−	0.376851i	$-0.122993\pi$
$139$	3035.93			1.85255			0.926274	+	0.376851i	$0.122993\pi$
$140$		0			0
$141$	−4102.48			−2.45029
$142$		0			0
$143$	486.454	+	842.562i	0.284471	+	0.492717i
$144$		0			0
$145$	−324.471	+	562.000i	−0.185833	+	0.321873i
$146$		0			0
$147$	−2658.17	−	1929.11i	−1.49144	−	1.08238i
$148$		0			0
$149$	275.172	−	476.612i	0.151295	−	0.262051i	−0.780409	−	0.625270i	$-0.784989\pi$
$149$	275.172	−	476.612i	0.151295	−	0.262051i	0.931704	+	0.363219i	$0.118322\pi$
$150$		0			0
$151$	339.682	+	588.346i	0.183066	+	0.317079i	0.942923	−	0.333011i	$-0.108065\pi$
$151$	339.682	+	588.346i	0.183066	+	0.317079i	−0.759857	+	0.650090i	$0.774731\pi$
$152$		0			0
$153$	1668.52			0.881644
$154$		0			0
$155$	794.189			0.411554
$156$		0			0
$157$	689.336	+	1193.96i	0.350414	+	0.606934i	0.986322	−	0.164830i	$-0.0527076\pi$
$157$	689.336	+	1193.96i	0.350414	+	0.606934i	−0.635908	+	0.771765i	$0.719374\pi$
$158$		0			0
$159$	−281.204	+	487.059i	−0.140257	+	0.242933i
$160$		0			0
$161$	−131.523	+	405.153i	−0.0643817	+	0.198326i
$162$		0			0
$163$	−1067.89	+	1849.65i	−0.513153	+	0.888807i	0.486731	+	0.873552i	$0.338189\pi$
$163$	−1067.89	+	1849.65i	−0.513153	+	0.888807i	−0.999884	+	0.0152550i	$0.995144\pi$
$164$		0			0
$165$	379.656	+	657.584i	0.179128	+	0.310259i
$166$		0			0
$167$	−1500.30			−0.695189			−0.347594	−	0.937645i	$-0.613001\pi$
$167$	−1500.30			−0.695189			−0.347594	+	0.937645i	$0.613001\pi$
$168$		0			0
$169$	−518.778			−0.236130
$170$		0			0
$171$	203.434	+	352.358i	0.0909765	+	0.157576i
$172$		0			0
$173$	−1494.45	+	2588.47i	−0.656770	+	1.13756i	0.324677	+	0.945825i	$0.394745\pi$
$173$	−1494.45	+	2588.47i	−0.656770	+	1.13756i	−0.981447	+	0.191734i	$0.938589\pi$
$174$		0			0
$175$	−1411.32	−	1566.59i	−0.609632	−	0.676702i
$176$		0			0
$177$	2879.44	−	4987.34i	1.22278	−	2.11792i
$178$		0			0
$179$	53.7831	+	93.1551i	0.0224578	+	0.0388980i	0.877036	−	0.480425i	$-0.159518\pi$
$179$	53.7831	+	93.1551i	0.0224578	+	0.0388980i	−0.854578	+	0.519323i	$0.826184\pi$
$180$		0			0
$181$	−683.380			−0.280637			−0.140318	−	0.990106i	$-0.544813\pi$
$181$	−683.380			−0.280637			−0.140318	+	0.990106i	$0.544813\pi$
$182$		0			0
$183$	−7418.48			−2.99667
$184$		0			0
$185$	86.1560	+	149.227i	0.0342396	+	0.0593047i
$186$		0			0
$187$	−306.270	+	530.476i	−0.119768	+	0.207445i
$188$		0			0
$189$	−6537.69	+	1391.45i	−2.51612	+	0.535519i
$190$		0			0
$191$	−483.649	+	837.705i	−0.183223	+	0.317352i	−0.942976	−	0.332860i	$-0.891986\pi$
$191$	−483.649	+	837.705i	−0.183223	+	0.317352i	0.759753	+	0.650212i	$0.225320\pi$
$192$		0			0
$193$	1211.70	+	2098.73i	0.451917	+	0.782744i	0.998505	−	0.0546579i	$-0.0174068\pi$
$193$	1211.70	+	2098.73i	0.451917	+	0.782744i	−0.546588	+	0.837402i	$0.684073\pi$
$194$		0			0
$195$	1309.78			0.481002
$196$		0			0
$197$	5126.40			1.85402			0.927008	−	0.375043i	$-0.122372\pi$
$197$	5126.40			1.85402			0.927008	+	0.375043i	$0.122372\pi$
$198$		0			0
$199$	2073.50	+	3591.40i	0.738624	+	1.27933i	0.953115	+	0.302609i	$0.0978575\pi$
$199$	2073.50	+	3591.40i	0.738624	+	1.27933i	−0.214491	+	0.976726i	$0.568809\pi$
$200$		0			0
$201$	−4883.36	+	8458.22i	−1.71366	+	2.96814i
$202$		0			0
$203$	3520.64	−	749.315i	1.21724	−	0.259072i
$204$		0			0
$205$	−578.204	+	1001.48i	−0.196993	+	0.341201i
$206$		0			0
$207$	743.944	+	1288.55i	0.249796	+	0.432658i
$208$		0			0
$209$	−149.368			−0.0494354
$210$		0			0
$211$	3723.31			1.21480			0.607402	−	0.794395i	$-0.292212\pi$
$211$	3723.31			1.21480			0.607402	+	0.794395i	$0.292212\pi$
$212$		0			0
$213$	2558.17	+	4430.87i	0.822923	+	1.42535i
$214$		0			0
$215$	114.060	−	197.558i	0.0361807	−	0.0626668i
$216$		0			0
$217$	−2948.49	−	3272.87i	−0.922380	−	1.02386i
$218$		0			0
$219$	2175.07	−	3767.34i	0.671132	−	1.16243i
$220$		0			0
$221$	528.303	+	915.048i	0.160803	+	0.278519i
$222$		0			0
$223$	2598.15			0.780202			0.390101	−	0.920772i	$-0.372440\pi$
$223$	2598.15			0.780202			0.390101	+	0.920772i	$0.372440\pi$
$224$		0			0
$225$	−7365.13			−2.18226
$226$		0			0
$227$	980.894	+	1698.96i	0.286803	+	0.496757i	0.973045	−	0.230616i	$-0.0740742\pi$
$227$	980.894	+	1698.96i	0.286803	+	0.496757i	−0.686242	+	0.727373i	$0.740741\pi$
$228$		0			0
$229$	−3347.00	+	5797.18i	−0.965835	+	1.67288i	−0.258481	+	0.966016i	$0.583222\pi$
$229$	−3347.00	+	5797.18i	−0.965835	+	1.67288i	−0.707355	+	0.706859i	$0.750112\pi$
$230$		0			0
$231$	1300.42	−	4005.90i	0.370395	−	1.14099i
$232$		0			0
$233$	−2427.98	+	4205.38i	−0.682671	+	1.18242i	0.291492	+	0.956573i	$0.405848\pi$
$233$	−2427.98	+	4205.38i	−0.682671	+	1.18242i	−0.974163	+	0.225847i	$0.927485\pi$
$234$		0			0
$235$	−715.261	−	1238.87i	−0.198547	−	0.343893i
$236$		0			0
$237$	−72.8908			−0.0199779
$238$		0			0
$239$	−2169.99			−0.587302			−0.293651	−	0.955913i	$-0.594870\pi$
$239$	−2169.99			−0.587302			−0.293651	+	0.955913i	$0.594870\pi$
$240$		0			0
$241$	1497.68	+	2594.07i	0.400309	+	0.693355i	0.993763	−	0.111513i	$-0.0355696\pi$
$241$	1497.68	+	2594.07i	0.400309	+	0.693355i	−0.593454	+	0.804868i	$0.702236\pi$
$242$		0			0
$243$	−3311.19	+	5735.15i	−0.874127	+	1.51403i
$244$		0			0
$245$	119.106	−	1139.05i	0.0310587	−	0.297026i
$246$		0			0
$247$	−128.827	+	223.134i	−0.0331864	+	0.0574805i
$248$		0			0
$249$	−5580.47	−	9665.65i	−1.42027	−	2.45998i
$250$		0			0
$251$	−2462.64			−0.619286			−0.309643	−	0.950853i	$-0.600209\pi$
$251$	−2462.64			−0.619286			−0.309643	+	0.950853i	$0.600209\pi$
$252$		0			0
$253$	−546.229			−0.135736
$254$		0			0
$255$	412.318	+	714.155i	0.101256	+	0.175381i
$256$		0			0
$257$	515.500	−	892.872i	0.125121	−	0.216715i	−0.796659	−	0.604428i	$-0.793402\pi$
$257$	515.500	−	892.872i	0.125121	−	0.216715i	0.921780	+	0.387713i	$0.126735\pi$
$258$		0			0
$259$	295.106	−	909.067i	0.0707992	−	0.218095i
$260$		0			0
$261$	6286.47	−	10888.5i	1.49089	−	2.58230i
$262$		0			0
$263$	−1013.53	−	1755.48i	−0.237631	−	0.411588i	0.722403	−	0.691472i	$-0.243037\pi$
$263$	−1013.53	−	1755.48i	−0.237631	−	0.411588i	−0.960034	+	0.279884i	$0.909704\pi$
$264$		0			0
$265$	−196.110			−0.0454601
$266$		0			0
$267$	10207.6			2.33968
$268$		0			0
$269$	109.241	+	189.211i	0.0247604	+	0.0428862i	0.878140	−	0.478404i	$-0.158784\pi$
$269$	109.241	+	189.211i	0.0247604	+	0.0428862i	−0.853380	+	0.521290i	$0.825451\pi$
$270$		0			0
$271$	53.4531	−	92.5835i	0.0119817	−	0.0207529i	−0.859972	−	0.510341i	$-0.829519\pi$
$271$	53.4531	−	92.5835i	0.0119817	−	0.0207529i	0.871954	+	0.489588i	$0.162853\pi$
$272$		0			0
$273$	−4862.66	−	5397.64i	−1.07803	−	1.19663i
$274$		0			0
$275$	1351.93	−	2341.61i	0.296453	−	0.513472i
$276$		0			0
$277$	1879.96	+	3256.18i	0.407782	+	0.706299i	0.994641	−	0.103390i	$-0.0329690\pi$
$277$	1879.96	+	3256.18i	0.407782	+	0.706299i	−0.586859	+	0.809689i	$0.699636\pi$
$278$		0			0
$279$	−15387.0			−3.30179
$280$		0			0
$281$	−8707.88			−1.84864			−0.924321	−	0.381616i	$-0.875368\pi$
$281$	−8707.88			−1.84864			−0.924321	+	0.381616i	$0.875368\pi$
$282$		0			0
$283$	−2317.76	−	4014.47i	−0.486842	−	0.843236i	0.513043	−	0.858363i	$-0.328518\pi$
$283$	−2317.76	−	4014.47i	−0.486842	−	0.843236i	−0.999886	+	0.0151271i	$0.995185\pi$
$284$		0			0
$285$	−100.544	+	174.147i	−0.0208972	+	0.0361950i
$286$		0			0
$287$	6273.75	−	1335.27i	1.29034	−	0.274630i
$288$		0			0
$289$	2123.88	−	3678.67i	0.432298	−	0.748763i
$290$		0			0
$291$	2449.53	+	4242.71i	0.493450	+	0.854680i
$292$		0			0
$293$	8971.01			1.78871			0.894355	−	0.447359i	$-0.147635\pi$
$293$	8971.01			1.78871			0.894355	+	0.447359i	$0.147635\pi$
$294$		0			0
$295$	2008.11			0.396327
$296$		0			0
$297$	−4285.63	−	7422.92i	−0.837297	−	1.45024i
$298$		0			0
$299$	−471.110	+	815.987i	−0.0911204	+	0.157825i
$300$		0			0
$301$	−1237.60	+	263.405i	−0.236990	+	0.0504399i
$302$		0			0
$303$	−370.341	+	641.449i	−0.0702162	+	0.121618i
$304$		0			0
$305$	−1293.40	−	2240.24i	−0.242819	−	0.420576i
$306$		0			0
$307$	−3408.37			−0.633636			−0.316818	−	0.948486i	$-0.602614\pi$
$307$	−3408.37			−0.633636			−0.316818	+	0.948486i	$0.602614\pi$
$308$		0			0
$309$	−7608.37			−1.40073
$310$		0			0
$311$	648.231	+	1122.77i	0.118192	+	0.204715i	0.919051	−	0.394138i	$-0.128957\pi$
$311$	648.231	+	1122.77i	0.118192	+	0.204715i	−0.800859	+	0.598853i	$0.795623\pi$
$312$		0			0
$313$	−235.760	+	408.349i	−0.0425749	+	0.0737420i	−0.886528	−	0.462676i	$-0.846889\pi$
$313$	−235.760	+	408.349i	−0.0425749	+	0.0737420i	0.843953	+	0.536418i	$0.180223\pi$
$314$		0			0
$315$	−2677.56	−	2972.14i	−0.478932	−	0.531623i
$316$		0			0
$317$	3669.35	−	6355.51i	0.650131	−	1.12606i	−0.332960	−	0.942941i	$-0.608047\pi$
$317$	3669.35	−	6355.51i	0.650131	−	1.12606i	0.983091	−	0.183119i	$-0.0586192\pi$
$318$		0			0
$319$	2307.87	+	3997.34i	0.405065	+	0.701594i
$320$		0			0
$321$	−3283.85			−0.570987
$322$		0			0
$323$	−162.218			−0.0279444
$324$		0			0
$325$	−2332.02	−	4039.18i	−0.398023	−	0.689396i
$326$		0			0
$327$	3106.25	−	5380.18i	0.525309	−	0.909861i
$328$		0			0
$329$	−2449.95	+	7547.00i	−0.410547	+	1.26468i
$330$		0			0
$331$	−4751.17	+	8229.28i	−0.788967	+	1.36653i	0.137633	+	0.990483i	$0.456051\pi$
$331$	−4751.17	+	8229.28i	−0.788967	+	1.36653i	−0.926600	+	0.376048i	$0.877283\pi$
$332$		0			0
$333$	−1669.23	−	2891.20i	−0.274695	−	0.475786i
$334$		0			0
$335$	−3405.62			−0.555430
$336$		0			0
$337$	4955.14			0.800960			0.400480	−	0.916306i	$-0.368843\pi$
$337$	4955.14			0.800960			0.400480	+	0.916306i	$0.368843\pi$
$338$		0			0
$339$	5491.99	+	9512.41i	0.879894	+	1.52402i
$340$		0			0
$341$	2824.42	−	4892.04i	0.448537	−	0.776889i
$342$		0			0
$343$	−5136.25	+	3737.98i	−0.808547	+	0.588432i
$344$		0			0
$345$	−367.681	+	636.843i	−0.0573777	+	0.0993810i
$346$		0			0
$347$	1221.28	+	2115.31i	0.188938	+	0.327251i	0.944897	−	0.327369i	$-0.106162\pi$
$347$	1221.28	+	2115.31i	0.188938	+	0.327251i	−0.755958	+	0.654620i	$0.772829\pi$
$348$		0			0
$349$	4073.53			0.624788			0.312394	−	0.949953i	$-0.398869\pi$
$349$	4073.53			0.624788			0.312394	+	0.949953i	$0.398869\pi$
$350$		0			0
$351$	−14785.0			−2.24834
$352$		0			0
$353$	5126.53	+	8879.41i	0.772968	+	1.33882i	0.935930	+	0.352187i	$0.114562\pi$
$353$	5126.53	+	8879.41i	0.772968	+	1.33882i	−0.162962	+	0.986632i	$0.552105\pi$
$354$		0			0
$355$	−892.025	+	1545.03i	−0.133363	+	0.230991i
$356$		0			0
$357$	1412.29	−	4350.53i	0.209374	−	0.644970i
$358$		0			0
$359$	2693.48	−	4665.24i	0.395978	−	0.685855i	−0.597247	−	0.802057i	$-0.703739\pi$
$359$	2693.48	−	4665.24i	0.395978	−	0.685855i	0.993226	+	0.116203i	$0.0370722\pi$
$360$		0			0
$361$	3409.72	+	5905.81i	0.497116	+	0.861031i
$362$		0			0
$363$	−7344.26			−1.06191
$364$		0			0
$365$	1516.88			0.217527
$366$		0			0
$367$	4119.89	+	7135.86i	0.585985	+	1.01496i	0.994752	+	0.102317i	$0.0326258\pi$
$367$	4119.89	+	7135.86i	0.585985	+	1.01496i	−0.408766	+	0.912639i	$0.634041\pi$
$368$		0			0
$369$	11202.4	−	19403.2i	1.58042	−	2.73737i
$370$		0			0
$371$	728.072	+	808.173i	0.101886	+	0.113095i
$372$		0			0
$373$	−4720.99	+	8176.99i	−0.655344	+	1.13509i	0.326463	+	0.945210i	$0.394143\pi$
$373$	−4720.99	+	8176.99i	−0.655344	+	1.13509i	−0.981807	+	0.189879i	$0.939190\pi$
$374$		0			0
$375$	−3818.31	−	6613.51i	−0.525805	−	0.910721i
$376$		0			0
$377$	7961.94			1.08769
$378$		0			0
$379$	−4728.50			−0.640862			−0.320431	−	0.947272i	$-0.603828\pi$
$379$	−4728.50			−0.640862			−0.320431	+	0.947272i	$0.603828\pi$
$380$		0			0
$381$	−2089.65	−	3619.37i	−0.280986	−	0.486683i
$382$		0			0
$383$	−3870.80	+	6704.43i	−0.516420	+	0.894465i	0.483398	+	0.875400i	$0.339402\pi$
$383$	−3870.80	+	6704.43i	−0.516420	+	0.894465i	−0.999818	+	0.0190649i	$0.993931\pi$
$384$		0			0
$385$	1436.43	−	305.723i	0.190149	−	0.0404703i
$386$		0			0
$387$	−2209.87	+	3827.60i	−0.290268	+	0.502759i
$388$		0			0
$389$	4441.06	+	7692.15i	0.578845	+	1.00259i	0.995612	+	0.0935761i	$0.0298299\pi$
$389$	4441.06	+	7692.15i	0.578845	+	1.00259i	−0.416767	+	0.909013i	$0.636837\pi$
$390$		0			0
$391$	−593.221			−0.0767275
$392$		0			0
$393$	−4857.70			−0.623508
$394$		0			0
$395$	−12.7084	−	22.0116i	−0.00161881	−	0.00280386i
$396$		0			0
$397$	−1363.43	+	2361.52i	−0.172364	+	0.298543i	−0.939246	−	0.343245i	$-0.888474\pi$
$397$	−1363.43	+	2361.52i	−0.172364	+	0.298543i	0.766882	+	0.641788i	$0.221807\pi$
$398$		0			0
$399$	1090.94	−	232.190i	0.136880	−	0.0291329i
$400$		0			0
$401$	6137.68	−	10630.8i	0.764342	−	1.32388i	−0.176252	−	0.984345i	$-0.556397\pi$
$401$	6137.68	−	10630.8i	0.764342	−	1.32388i	0.940594	−	0.339534i	$-0.110269\pi$
$402$		0			0
$403$	−4872.01	−	8438.56i	−0.602213	−	1.04306i
$404$		0			0
$405$	−5707.10			−0.700217
$406$		0			0
$407$	1225.61			0.149266
$408$		0			0
$409$	2530.09	+	4382.24i	0.305880	+	0.529799i	0.977457	−	0.211136i	$-0.0677162\pi$
$409$	2530.09	+	4382.24i	0.305880	+	0.529799i	−0.671577	+	0.740935i	$0.734383\pi$
$410$		0			0
$411$	−5331.91	+	9235.13i	−0.639911	+	1.10836i
$412$		0			0
$413$	−7455.25	−	8275.45i	−0.888253	−	0.985977i
$414$		0			0
$415$	1945.89	−	3370.38i	0.230169	−	0.398664i
$416$		0			0
$417$	−14535.3	−	25175.9i	−1.70695	−	2.95652i
$418$		0			0
$419$	−8680.23			−1.01207			−0.506035	−	0.862513i	$-0.668889\pi$
$419$	−8680.23			−1.01207			−0.506035	+	0.862513i	$0.668889\pi$
$420$		0			0
$421$	9145.49			1.05873			0.529363	−	0.848395i	$-0.322431\pi$
$421$	9145.49			1.05873			0.529363	+	0.848395i	$0.322431\pi$
$422$		0			0
$423$	13857.8	+	24002.5i	1.59289	+	2.75896i
$424$		0			0
$425$	1468.24	−	2543.06i	0.167577	−	0.290251i
$426$		0			0
$427$	−4430.22	+	13647.2i	−0.502092	+	1.54668i
$428$		0			0
$429$	4658.05	−	8067.98i	0.524226	−	0.907985i
$430$		0			0
$431$	4303.46	+	7453.82i	0.480952	+	0.833034i	0.999761	−	0.0218562i	$-0.00695761\pi$
$431$	4303.46	+	7453.82i	0.480952	+	0.833034i	−0.518809	+	0.854890i	$0.673624\pi$
$432$		0			0
$433$	−9395.60			−1.04278			−0.521390	−	0.853319i	$-0.674586\pi$
$433$	−9395.60			−1.04278			−0.521390	+	0.853319i	$0.674586\pi$
$434$		0			0
$435$	6213.96			0.684911
$436$		0			0
$437$	−72.3284	−	125.276i	−0.00791747	−	0.0137135i
$438$		0			0
$439$	−2674.83	+	4632.93i	−0.290803	+	0.503685i	−0.974000	−	0.226549i	$-0.927256\pi$
$439$	−2674.83	+	4632.93i	−0.290803	+	0.503685i	0.683197	+	0.730234i	$0.260589\pi$
$440$		0			0
$441$	−2307.62	+	22068.6i	−0.249176	+	2.38296i
$442$		0			0
$443$	−2675.03	+	4633.29i	−0.286895	+	0.496917i	−0.973067	−	0.230523i	$-0.925956\pi$
$443$	−2675.03	+	4633.29i	−0.286895	+	0.496917i	0.686172	+	0.727439i	$0.259290\pi$
$444$		0			0
$445$	1779.68	+	3082.50i	0.189584	+	0.328369i
$446$		0			0
$447$	−5269.84			−0.557617
$448$		0			0
$449$	−16873.0			−1.77346			−0.886730	−	0.462287i	$-0.847029\pi$
$449$	−16873.0			−1.77346			−0.886730	+	0.462287i	$0.847029\pi$
$450$		0			0
$451$	4112.60	+	7123.24i	0.429390	+	0.743725i
$452$		0			0
$453$	3252.63	−	5633.73i	0.337356	−	0.584317i
$454$		0			0
$455$	782.184	−	2409.50i	0.0805920	−	0.248262i
$456$		0			0
$457$	−1139.00	+	1972.81i	−0.116587	+	0.201935i	−0.918413	−	0.395623i	$-0.870529\pi$
$457$	−1139.00	+	1972.81i	−0.116587	+	0.201935i	0.801826	+	0.597558i	$0.203862\pi$
$458$		0			0
$459$	−4654.32	−	8061.52i	−0.473301	−	0.819781i
$460$		0			0
$461$	−11446.5			−1.15644			−0.578219	−	0.815881i	$-0.696252\pi$
$461$	−11446.5			−1.15644			−0.578219	+	0.815881i	$0.696252\pi$
$462$		0			0
$463$	15976.1			1.60361			0.801806	−	0.597585i	$-0.203873\pi$
$463$	15976.1			1.60361			0.801806	+	0.597585i	$0.203873\pi$
$464$		0			0
$465$	−3802.39	−	6585.93i	−0.379208	−	0.656807i
$466$		0			0
$467$	8031.64	−	13911.2i	0.795846	−	1.37845i	−0.126455	−	0.991972i	$-0.540360\pi$
$467$	8031.64	−	13911.2i	0.795846	−	1.37845i	0.922301	−	0.386473i	$-0.126307\pi$
$468$		0			0
$469$	12643.6	+	14034.7i	1.24484	+	1.38179i
$470$		0			0
$471$	6600.75	−	11432.8i	0.645747	−	1.11847i
$472$		0			0
$473$	−811.279	−	1405.18i	−0.0788640	−	0.136596i
$474$		0			0
$475$	716.060			0.0691686
$476$		0			0
$477$	3799.53			0.364714
$478$		0			0
$479$	8333.36	+	14433.8i	0.794908	+	1.37682i	0.922898	+	0.385045i	$0.125814\pi$
$479$	8333.36	+	14433.8i	0.794908	+	1.37682i	−0.127990	+	0.991775i	$0.540853\pi$
$480$		0			0
$481$	1057.06	−	1830.88i	0.100203	−	0.173557i
$482$		0			0
$483$	3989.49	−	849.103i	0.375835	−	0.0799908i
$484$		0			0
$485$	−854.143	+	1479.42i	−0.0799683	+	0.138509i
$486$		0			0
$487$	4433.81	+	7679.59i	0.412557	+	0.714570i	0.995169	−	0.0981810i	$-0.0313024\pi$
$487$	4433.81	+	7679.59i	0.412557	+	0.714570i	−0.582612	+	0.812751i	$0.697969\pi$
$488$		0			0
$489$	20451.3			1.89129
$490$		0			0
$491$	−3172.58			−0.291602			−0.145801	−	0.989314i	$-0.546576\pi$
$491$	−3172.58			−0.291602			−0.145801	+	0.989314i	$0.546576\pi$
$492$		0			0
$493$	2506.41	+	4341.24i	0.228972	+	0.396591i
$494$		0			0
$495$	2564.90	−	4442.53i	0.232896	−	0.403388i
$496$		0			0
$497$	9678.83	−	2059.99i	0.873551	−	0.185922i
$498$		0			0
$499$	−7893.23	+	13671.5i	−0.708115	+	1.22649i	0.257441	+	0.966294i	$0.417121\pi$
$499$	−7893.23	+	13671.5i	−0.708115	+	1.22649i	−0.965556	+	0.260197i	$0.916212\pi$
$500$		0			0
$501$	7183.07	+	12441.4i	0.640551	+	1.10947i
$502$		0			0
$503$	14652.1			1.29882			0.649410	−	0.760439i	$-0.275016\pi$
$503$	14652.1			1.29882			0.649410	+	0.760439i	$0.275016\pi$
$504$		0			0
$505$	−258.273			−0.0227584
$506$		0			0
$507$	2483.79	+	4302.04i	0.217572	+	0.376845i
$508$		0			0
$509$	5137.78	−	8898.89i	0.447403	−	0.774924i	−0.550813	−	0.834628i	$-0.685682\pi$
$509$	5137.78	−	8898.89i	0.447403	−	0.774924i	0.998216	+	0.0597041i	$0.0190157\pi$
$510$		0			0
$511$	−5631.55	−	6251.12i	−0.487524	−	0.541161i
$512$		0			0
$513$	1134.96	−	1965.80i	0.0976793	−	0.169186i
$514$		0			0
$515$	−1326.51	−	2297.58i	−0.113501	−	0.196589i
$516$		0			0
$517$	−10174.9			−0.865554
$518$		0			0
$519$	28620.4			2.42061
$520$		0			0
$521$	−7039.82	−	12193.3i	−0.591977	−	1.02534i	−0.993966	−	0.109690i	$-0.965014\pi$
$521$	−7039.82	−	12193.3i	−0.591977	−	1.02534i	0.401988	−	0.915645i	$-0.368319\pi$
$522$		0			0
$523$	1959.26	−	3393.53i	0.163810	−	0.283726i	−0.772422	−	0.635109i	$-0.780955\pi$
$523$	1959.26	−	3393.53i	0.163810	−	0.283726i	0.936232	+	0.351383i	$0.114288\pi$
$524$		0			0
$525$	−6234.11	+	19204.0i	−0.518245	+	1.59644i
$526$		0			0
$527$	3067.41	−	5312.90i	0.253545	−	0.439153i
$528$		0			0
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	−38906.1			−3.17963
$532$		0			0
$533$	14188.1			1.15301
$534$		0			0
$535$	−572.535	−	991.659i	−0.0462670	−	0.0801368i
$536$		0			0
$537$	515.002	−	892.009i	0.0413854	−	0.0716816i
$538$		0			0
$539$	−6592.75	−	4784.55i	−0.526845	−	0.382347i
$540$		0			0
$541$	2267.13	−	3926.79i	0.180169	−	0.312062i	−0.761769	−	0.647849i	$-0.775669\pi$
$541$	2267.13	−	3926.79i	0.180169	−	0.312062i	0.941938	+	0.335787i	$0.109002\pi$
$542$		0			0
$543$	3271.86	+	5667.04i	0.258580	+	0.447874i
$544$		0			0
$545$	2166.28			0.170263
$546$		0			0
$547$	−14111.3			−1.10302			−0.551512	−	0.834167i	$-0.685949\pi$
$547$	−14111.3			−1.10302			−0.551512	+	0.834167i	$0.685949\pi$
$548$		0			0
$549$	25059.0	+	43403.5i	1.94808	+	3.37417i
$550$		0			0
$551$	−611.189	+	1058.61i	−0.0472550	+	0.0818481i
$552$		0			0
$553$	−43.5294	+	134.091i	−0.00334731	+	0.0103113i
$554$		0			0
$555$	824.990	−	1428.92i	0.0630971	−	0.109287i
$556$		0			0
$557$	1313.10	+	2274.35i	0.0998880	+	0.173011i	0.911638	−	0.410994i	$-0.134818\pi$
$557$	1313.10	+	2274.35i	0.0998880	+	0.173011i	−0.811750	+	0.584005i	$0.801485\pi$
$558$		0			0
$559$	−2798.84			−0.211768
$560$		0			0
$561$	5865.40			0.441421
$562$		0			0
$563$	−701.694	−	1215.37i	−0.0525273	−	0.0909800i	0.838566	−	0.544800i	$-0.183394\pi$
$563$	−701.694	−	1215.37i	−0.0525273	−	0.0909800i	−0.891094	+	0.453820i	$0.850061\pi$
$564$		0			0
$565$	−1915.04	+	3316.95i	−0.142595	+	0.246982i
$566$		0			0
$567$	21188.0	+	23519.1i	1.56934	+	1.74199i
$568$		0			0
$569$	893.747	−	1548.02i	0.0658486	−	0.114053i	−0.831222	−	0.555941i	$-0.812358\pi$
$569$	893.747	−	1548.02i	0.0658486	−	0.114053i	0.897070	+	0.441888i	$0.145691\pi$
$570$		0			0
$571$	−7209.40	−	12487.0i	−0.528378	−	0.915178i	−0.999453	−	0.0330846i	$-0.989467\pi$
$571$	−7209.40	−	12487.0i	−0.528378	−	0.915178i	0.471074	−	0.882094i	$-0.343866\pi$
$572$		0			0
$573$	9262.40			0.675292
$574$		0			0
$575$	2618.58			0.189917
$576$		0			0
$577$	−10870.8	−	18828.8i	−0.784331	−	1.35850i	−0.929398	−	0.369079i	$-0.879673\pi$
$577$	−10870.8	−	18828.8i	−0.784331	−	1.35850i	0.145067	−	0.989422i	$-0.453660\pi$
$578$		0			0
$579$	11602.7	−	20096.4i	0.832799	−	1.44245i
$580$		0			0
$581$	−21113.7	+	4493.74i	−1.50765	+	0.320881i
$582$		0			0
$583$	−697.436	+	1208.00i	−0.0495452	+	0.0858149i
$584$		0			0
$585$	−4424.33	−	7663.17i	−0.312690	−	0.541595i
$586$		0			0
$587$	15867.4			1.11570			0.557850	−	0.829942i	$-0.311626\pi$
$587$	15867.4			1.11570			0.557850	+	0.829942i	$0.311626\pi$
$588$		0			0
$589$	1495.97			0.104653
$590$		0			0
$591$	−24544.0	−	42511.5i	−1.70830	−	2.95886i
$592$		0			0
$593$	6448.79	−	11169.6i	0.446577	−	0.773494i	−0.551584	−	0.834120i	$-0.685976\pi$
$593$	6448.79	−	11169.6i	0.446577	−	0.773494i	0.998161	+	0.0606257i	$0.0193096\pi$
$594$		0			0
$595$	1560.01	−	332.024i	0.107486	−	0.0228767i
$596$		0			0
$597$	19854.8	−	34389.6i	1.36115	−	2.35757i
$598$		0			0
$599$	−12707.8	−	22010.5i	−0.866820	−	1.50138i	−0.865228	−	0.501378i	$-0.832827\pi$
$599$	−12707.8	−	22010.5i	−0.866820	−	1.50138i	−0.00159162	−	0.999999i	$-0.500507\pi$
$600$		0			0
$601$	−1466.24			−0.0995161			−0.0497581	−	0.998761i	$-0.515845\pi$
$601$	−1466.24			−0.0995161			−0.0497581	+	0.998761i	$0.515845\pi$
$602$		0			0
$603$	65982.4			4.45607
$604$		0			0
$605$	−1280.46	−	2217.82i	−0.0860464	−	0.149037i
$606$		0			0
$607$	5452.01	−	9443.16i	0.364564	−	0.631443i	−0.624142	−	0.781311i	$-0.714551\pi$
$607$	5452.01	−	9443.16i	0.364564	−	0.631443i	0.988706	+	0.149868i	$0.0478848\pi$
$608$		0			0
$609$	−23069.8	−	25607.9i	−1.53503	−	1.70391i
$610$		0			0
$611$	−8775.63	+	15199.8i	−0.581054	+	1.00641i
$612$		0			0
$613$	8061.98	+	13963.8i	0.531191	+	0.920050i	0.999337	+	0.0363991i	$0.0115888\pi$
$613$	8061.98	+	13963.8i	0.531191	+	0.920050i	−0.468146	+	0.883651i	$0.655078\pi$
$614$		0			0
$615$	11073.2			0.726041
$616$		0			0
$617$	13116.8			0.855855			0.427927	−	0.903813i	$-0.359244\pi$
$617$	13116.8			0.855855			0.427927	+	0.903813i	$0.359244\pi$
$618$		0			0
$619$	−14586.2	−	25264.0i	−0.947121	−	1.64046i	−0.751448	−	0.659792i	$-0.770644\pi$
$619$	−14586.2	−	25264.0i	−0.947121	−	1.64046i	−0.195673	−	0.980669i	$-0.562689\pi$
$620$		0			0
$621$	4150.45	−	7188.80i	0.268200	−	0.464535i
$622$		0			0
$623$	6095.85	−	18778.1i	0.392014	−	1.20759i
$624$		0			0
$625$	−5784.28	+	10018.7i	−0.370194	+	0.641194i
$626$		0			0
$627$	715.139	+	1238.66i	0.0455501	+	0.0788950i
$628$		0			0
$629$	1331.05			0.0843757
$630$		0			0
$631$	−15951.8			−1.00639			−0.503195	−	0.864173i	$-0.667842\pi$
$631$	−15951.8			−1.00639			−0.503195	+	0.864173i	$0.667842\pi$
$632$		0			0
$633$	−17826.3	−	30876.1i	−1.11933	−	1.93873i
$634$		0			0
$635$	728.653	−	1262.06i	0.0455366	−	0.0788716i
$636$		0			0
$637$	−12833.5	+	5722.05i	−0.798246	+	0.355912i
$638$		0			0
$639$	17282.6	−	29934.3i	1.06993	−	1.85318i
$640$		0			0
$641$	6518.87	+	11291.0i	0.401684	+	0.695738i	0.993929	−	0.110020i	$-0.0350916\pi$
$641$	6518.87	+	11291.0i	0.401684	+	0.695738i	−0.592245	+	0.805758i	$0.701758\pi$
$642$		0			0
$643$	19299.4			1.18366			0.591832	−	0.806062i	$-0.298405\pi$
$643$	19299.4			1.18366			0.591832	+	0.806062i	$0.298405\pi$
$644$		0			0
$645$	−2184.38			−0.133348
$646$		0			0
$647$	−9815.11	−	17000.3i	−0.596402	−	1.03300i	−0.993347	−	0.115156i	$-0.963263\pi$
$647$	−9815.11	−	17000.3i	−0.596402	−	1.03300i	0.396946	−	0.917842i	$-0.370070\pi$
$648$		0			0
$649$	7141.54	−	12369.5i	0.431942	−	0.748145i
$650$		0			0
$651$	−13024.1	+	40120.5i	−0.784111	+	2.41543i
$652$		0			0
$653$	−10576.6	+	18319.2i	−0.633836	+	1.09784i	0.352925	+	0.935652i	$0.385187\pi$
$653$	−10576.6	+	18319.2i	−0.633836	+	1.09784i	−0.986761	+	0.162184i	$0.948146\pi$
$654$		0			0
$655$	−846.933	−	1466.93i	−0.0505227	−	0.0875080i
$656$		0			0
$657$	−29388.9			−1.74516
$658$		0			0
$659$	13370.0			0.790321			0.395160	−	0.918612i	$-0.370689\pi$
$659$	13370.0			0.790321			0.395160	+	0.918612i	$0.370689\pi$
$660$		0			0
$661$	11766.8	+	20380.7i	0.692398	+	1.19927i	0.971050	+	0.238876i	$0.0767789\pi$
$661$	11766.8	+	20380.7i	0.692398	+	1.19927i	−0.278652	+	0.960392i	$0.589888\pi$
$662$		0			0
$663$	5058.78	−	8762.07i	0.296330	−	0.513259i
$664$		0			0
$665$	260.320	+	288.960i	0.0151801	+	0.0168502i
$666$		0			0
$667$	−2235.08	+	3871.26i	−0.129749	+	0.224732i
$668$		0			0
$669$	−12439.3	−	21545.5i	−0.718882	−	1.24514i
$670$		0			0
$671$	−18399.2			−1.05856
$672$		0			0
$673$	−6350.64			−0.363743			−0.181872	−	0.983322i	$-0.558216\pi$
$673$	−6350.64			−0.363743			−0.181872	+	0.983322i	$0.558216\pi$
$674$		0			0
$675$	20545.0	+	35585.0i	1.17152	+	2.02914i
$676$		0			0
$677$	−181.956	+	315.157i	−0.0103296	+	0.0178914i	−0.871144	−	0.491028i	$-0.836621\pi$
$677$	−181.956	+	315.157i	−0.0103296	+	0.0178914i	0.860814	+	0.508919i	$0.169955\pi$
$678$		0			0
$679$	9267.79	−	1972.51i	0.523807	−	0.111485i
$680$		0			0
$681$	9392.58	−	16268.4i	0.528524	−	0.915430i
$682$		0			0
$683$	−13290.4	−	23019.7i	−0.744573	−	1.28964i	−0.950394	−	0.311049i	$-0.899320\pi$
$683$	−13290.4	−	23019.7i	−0.744573	−	1.28964i	0.205821	−	0.978590i	$-0.434014\pi$
$684$		0			0
$685$	−3718.44			−0.207408
$686$		0			0
$687$	64098.7			3.55970
$688$		0			0
$689$	1203.05	+	2083.74i	0.0665203	+	0.115216i
$690$		0			0
$691$	−13926.5	+	24121.5i	−0.766701	+	1.32797i	0.172641	+	0.984985i	$0.444770\pi$
$691$	−13926.5	+	24121.5i	−0.766701	+	1.32797i	−0.939342	+	0.342981i	$0.888563\pi$
$692$		0			0
$693$	−27830.2	+	5923.23i	−1.52551	+	0.324683i
$694$		0			0
$695$	5068.42	−	8778.76i	0.276628	−	0.479133i
$696$		0			0
$697$	4466.41	+	7736.05i	0.242722	+	0.420407i
$698$		0			0
$699$	46498.4			2.51607
$700$		0			0
$701$	−2221.76			−0.119707			−0.0598535	−	0.998207i	$-0.519063\pi$
$701$	−2221.76			−0.119707			−0.0598535	+	0.998207i	$0.519063\pi$
$702$		0			0
$703$	162.288	+	281.091i	0.00870668	+	0.0150804i
$704$		0			0
$705$	−6849.00	+	11862.8i	−0.365884	+	0.633730i
$706$		0			0
$707$	958.859	+	1064.35i	0.0510065	+	0.0566181i
$708$		0			0
$709$	6892.33	−	11937.9i	0.365087	−	0.632349i	−0.623703	−	0.781661i	$-0.714373\pi$
$709$	6892.33	−	11937.9i	0.365087	−	0.632349i	0.988790	+	0.149312i	$0.0477059\pi$
$710$		0			0
$711$	246.219	+	426.464i	0.0129873	+	0.0224946i
$712$		0			0
$713$	5470.67			0.287347
$714$		0			0
$715$	3248.50			0.169912
$716$		0			0
$717$	10389.4	+	17995.0i	0.541143	+	0.937288i
$718$		0			0
$719$	−3874.46	+	6710.76i	−0.200964	+	0.348080i	−0.948839	−	0.315760i	$-0.897741\pi$
$719$	−3874.46	+	6710.76i	−0.200964	+	0.348080i	0.747875	+	0.663839i	$0.231074\pi$
$720$		0			0
$721$	−4543.62	+	13996.5i	−0.234692	+	0.722965i
$722$		0			0
$723$	14341.1	−	24839.6i	0.737693	−	1.27772i
$724$		0			0
$725$	−11063.8	−	19163.0i	−0.566755	−	0.981649i
$726$		0			0
$727$	12274.4			0.626181			0.313090	−	0.949723i	$-0.398636\pi$
$727$	12274.4			0.626181			0.313090	+	0.949723i	$0.398636\pi$
$728$		0			0
$729$	17263.2			0.877060
$730$		0			0
$731$	−881.073	−	1526.06i	−0.0445796	−	0.0772141i
$732$		0			0
$733$	3048.33	−	5279.86i	0.153605	−	0.266052i	−0.778945	−	0.627092i	$-0.784245\pi$
$733$	3048.33	−	5279.86i	0.153605	−	0.266052i	0.932550	+	0.361040i	$0.117578\pi$
$734$		0			0
$735$	−10016.0	+	4465.81i	−0.502648	+	0.224114i
$736$		0			0
$737$	−12111.6	+	20977.9i	−0.605342	+	1.04848i
$738$		0			0
$739$	5182.05	+	8975.58i	0.257950	+	0.446782i	0.965693	−	0.259688i	$-0.0836198\pi$
$739$	5182.05	+	8975.58i	0.257950	+	0.446782i	−0.707743	+	0.706470i	$0.750286\pi$
$740$		0			0
$741$	2467.17			0.122313
$742$		0			0
$743$	33394.7			1.64890			0.824450	−	0.565934i	$-0.191484\pi$
$743$	33394.7			1.64890			0.824450	+	0.565934i	$0.191484\pi$
$744$		0			0
$745$	−918.789	−	1591.39i	−0.0451836	−	0.0782604i
$746$		0			0
$747$	−37700.8	+	65299.6i	−1.84658	+	3.19838i
$748$		0			0
$749$	−1961.07	+	6041.04i	−0.0956690	+	0.294706i
$750$		0			0
$751$	−7753.44	+	13429.3i	−0.376734	+	0.652522i	−0.990585	−	0.136900i	$-0.956286\pi$
$751$	−7753.44	+	13429.3i	−0.376734	+	0.652522i	0.613851	+	0.789422i	$0.289619\pi$
$752$		0			0
$753$	11790.6	+	20421.8i	0.570613	+	0.988331i
$754$		0			0
$755$	2268.37			0.109343
$756$		0			0
$757$	33998.3			1.63235			0.816175	−	0.577804i	$-0.196090\pi$
$757$	33998.3			1.63235			0.816175	+	0.577804i	$0.196090\pi$
$758$		0			0
$759$	2615.21	+	4529.68i	0.125068	+	0.216623i
$760$		0			0
$761$	3366.90	−	5831.65i	0.160381	−	0.277789i	−0.774624	−	0.632422i	$-0.782061\pi$
$761$	3366.90	−	5831.65i	0.160381	−	0.277789i	0.935005	+	0.354633i	$0.115394\pi$
$762$		0			0
$763$	−8042.48	−	8927.29i	−0.381595	−	0.423578i
$764$		0			0
$765$	2785.55	−	4824.72i	0.131650	−	0.228024i
$766$		0			0
$767$	−12318.9	−	21336.9i	−0.579932	−	1.00447i
$768$		0			0
$769$	−23787.0			−1.11545			−0.557725	−	0.830026i	$-0.688326\pi$
$769$	−23787.0			−1.11545			−0.557725	+	0.830026i	$0.688326\pi$
$770$		0			0
$771$	−9872.37			−0.461147
$772$		0			0
$773$	9449.29	+	16366.6i	0.439673	+	0.761536i	0.997664	−	0.0683108i	$-0.0217610\pi$
$773$	9449.29	+	16366.6i	0.439673	+	0.761536i	−0.557991	+	0.829847i	$0.688428\pi$
$774$		0			0
$775$	−13540.1	+	23452.1i	−0.627579	+	1.08700i
$776$		0			0
$777$	−8951.47	+	1905.19i	−0.413298	+	0.0879642i
$778$		0			0
$779$	−1089.13	+	1886.43i	−0.0500927	+	0.0867632i
$780$		0			0
$781$	6344.72	+	10989.4i	0.290694	+	0.503497i
$782$		0			0
$783$	−70144.3			−3.20147
$784$		0			0
$785$	4603.32			0.209299
$786$		0			0
$787$	4114.20	+	7126.00i	0.186347	+	0.322763i	0.944030	−	0.329860i	$-0.107002\pi$
$787$	4114.20	+	7126.00i	0.186347	+	0.322763i	−0.757682	+	0.652624i	$0.773668\pi$
$788$		0			0
$789$	−9705.08	+	16809.7i	−0.437909	+	0.758480i
$790$		0			0
$791$	20779.0	−	4422.49i	0.934027	−	0.198794i
$792$		0			0
$793$	−15868.9	+	27485.7i	−0.710620	+	1.23083i
$794$		0			0
$795$	938.927	+	1626.27i	0.0418872	+	0.0725507i
$796$		0			0
$797$	−39076.1			−1.73669			−0.868347	−	0.495957i	$-0.834817\pi$
$797$	−39076.1			−1.73669			−0.868347	+	0.495957i	$0.834817\pi$
$798$		0			0
$799$	−11050.2			−0.489274
$800$		0			0
$801$	−34480.5	−	59721.9i	−1.52098	−	2.63442i
$802$		0			0
$803$	5394.58	−	9343.69i	0.237074	−	0.410625i
$804$		0			0
$805$	951.974	+	1056.71i	0.0416804	+	0.0462659i
$806$		0			0
$807$	1046.04	−	1811.79i	0.0456287	−	0.0790312i
$808$		0			0
$809$	−2851.19	−	4938.40i	−0.123909	−	0.214617i	0.797397	−	0.603455i	$-0.206210\pi$
$809$	−2851.19	−	4938.40i	−0.123909	−	0.214617i	−0.921306	+	0.388838i	$0.872876\pi$
$810$		0			0
$811$	−45022.1			−1.94937			−0.974686	−	0.223577i	$-0.928226\pi$
$811$	−45022.1			−1.94937			−0.974686	+	0.223577i	$0.928226\pi$
$812$		0			0
$813$	−1023.68			−0.0441601
$814$		0			0
$815$	3565.65	+	6175.89i	0.153251	+	0.265438i
$816$		0			0
$817$	214.850	−	372.130i	0.00920029	−	0.0159354i
$818$		0			0
$819$	−15154.4	+	46682.9i	−0.646568	+	1.99174i
$820$		0			0
$821$	−3993.57	+	6917.06i	−0.169764	+	0.294040i	−0.938337	−	0.345722i	$-0.887634\pi$
$821$	−3993.57	+	6917.06i	−0.169764	+	0.294040i	0.768573	+	0.639762i	$0.220967\pi$
$822$		0			0
$823$	−16236.6	−	28122.6i	−0.687693	−	1.19112i	−0.972582	−	0.232559i	$-0.925290\pi$
$823$	−16236.6	−	28122.6i	−0.687693	−	1.19112i	0.284889	−	0.958561i	$-0.408043\pi$
$824$		0			0
$825$	−25890.9			−1.09261
$826$		0			0
$827$	−1070.09			−0.0449950			−0.0224975	−	0.999747i	$-0.507162\pi$
$827$	−1070.09			−0.0449950			−0.0224975	+	0.999747i	$0.507162\pi$
$828$		0			0
$829$	−13348.9	−	23120.9i	−0.559258	−	0.968663i	−0.997559	−	0.0698349i	$-0.977753\pi$
$829$	−13348.9	−	23120.9i	−0.559258	−	0.968663i	0.438300	−	0.898829i	$-0.355581\pi$
$830$		0			0
$831$	18001.6	−	31179.6i	0.751465	−	1.30158i
$832$		0			0
$833$	−7159.92	−	5196.16i	−0.297811	−	0.216130i
$834$		0			0
$835$	−2504.72	+	4338.29i	−0.103808	+	0.179800i
$836$		0			0
$837$	42922.1	+	74343.2i	1.77253	+	3.07011i
$838$		0			0
$839$	7821.68			0.321853			0.160926	−	0.986966i	$-0.448552\pi$
$839$	7821.68			0.321853			0.160926	+	0.986966i	$0.448552\pi$
$840$		0			0
$841$	13384.6			0.548798
$842$		0			0
$843$	41691.3	+	72211.4i	1.70335	+	2.95029i
$844$		0			0
$845$	−866.089	+	1500.11i	−0.0352596	+	0.0610714i
$846$		0			0
$847$	−4385.89	+	13510.6i	−0.177923	+	0.548089i
$848$		0			0
$849$	−22193.8	+	38440.7i	−0.897159	+	1.55392i
$850$		0			0
$851$	593.475	+	1027.93i	0.0239061	+	0.0414065i
$852$		0			0
$853$	−4016.02			−0.161203			−0.0806013	−	0.996746i	$-0.525684\pi$
$853$	−4016.02			−0.161203			−0.0806013	+	0.996746i	$0.525684\pi$
$854$		0			0
$855$	1358.51			0.0543394
$856$		0			0
$857$	4898.50	+	8484.45i	0.195250	+	0.338184i	0.946983	−	0.321285i	$-0.104115\pi$
$857$	4898.50	+	8484.45i	0.195250	+	0.338184i	−0.751732	+	0.659469i	$0.770781\pi$
$858$		0			0
$859$	6099.68	−	10564.9i	0.242280	−	0.419641i	−0.719084	−	0.694924i	$-0.755438\pi$
$859$	6099.68	−	10564.9i	0.242280	−	0.419641i	0.961363	+	0.275283i	$0.0887715\pi$
$860$		0			0
$861$	−41110.2	−	45633.0i	−1.62721	−	1.80624i
$862$		0			0
$863$	2448.07	−	4240.19i	0.0965624	−	0.167251i	−0.813697	−	0.581289i	$-0.802549\pi$
$863$	2448.07	−	4240.19i	0.0965624	−	0.167251i	0.910260	+	0.414038i	$0.135882\pi$
$864$		0			0
$865$	4989.92	+	8642.79i	0.196141	+	0.339727i
$866$		0			0
$867$	−40674.6			−1.59329
$868$		0			0
$869$	−180.783			−0.00705711
$870$		0			0
$871$	20892.0	+	36186.0i	0.812743	+	1.40771i
$872$		0			0
$873$	16548.6	−	28663.1i	0.641565	−	1.11122i
$874$		0			0
$875$	−14446.6	+	3074.74i	−0.558153	+	0.118795i
$876$		0			0
$877$	−4781.82	+	8282.36i	−0.184117	+	0.318900i	−0.943279	−	0.332002i	$-0.892276\pi$
$877$	−4781.82	+	8282.36i	−0.184117	+	0.318900i	0.759162	+	0.650902i	$0.225609\pi$
$878$		0			0
$879$	−42951.1	−	74393.4i	−1.64813	−	2.85464i
$880$		0			0
$881$	−34827.1			−1.33184			−0.665922	−	0.746021i	$-0.731962\pi$
$881$	−34827.1			−1.33184			−0.665922	+	0.746021i	$0.731962\pi$
$882$		0			0
$883$	18496.8			0.704944			0.352472	−	0.935822i	$-0.385341\pi$
$883$	18496.8			0.704944			0.352472	+	0.935822i	$0.385341\pi$
$884$		0			0
$885$	−9614.34	−	16652.5i	−0.365178	−	0.632506i
$886$		0			0
$887$	4366.40	−	7562.82i	0.165287	−	0.286285i	−0.771470	−	0.636265i	$-0.780478\pi$
$887$	4366.40	−	7562.82i	0.165287	−	0.286285i	0.936757	+	0.349980i	$0.113812\pi$
$888$		0			0
$889$	−7906.18	+	1682.71i	−0.298273	+	0.0634830i
$890$		0			0
$891$	−20296.5	+	35154.5i	−0.763140	+	1.32180i
$892$		0			0
$893$	−1347.30	−	2333.59i	−0.0504879	−	0.0874476i
$894$		0			0
$895$	359.159			0.0134138
$896$		0			0
$897$	9022.26			0.335836
$898$		0			0
$899$	−23114.1	−	40034.8i	−0.857507	−	1.48525i
$900$		0			0
$901$	−757.437	+	1311.92i	−0.0280065	+	0.0485087i
$902$		0			0
$903$	8109.66	+	9001.87i	0.298862	+	0.331743i
$904$		0			0
$905$	−1140.89	+	1976.08i	−0.0419055	+	0.0725824i
$906$		0			0
$907$	−21269.8	−	36840.4i	−0.778669	−	1.34869i	−0.932709	−	0.360630i	$-0.882562\pi$
$907$	−21269.8	−	36840.4i	−0.778669	−	1.34869i	0.154040	−	0.988065i	$-0.450771\pi$
$908$		0			0
$909$	5003.92			0.182585
$910$		0			0
$911$	−17917.1			−0.651612			−0.325806	−	0.945437i	$-0.605636\pi$
$911$	−17917.1			−0.651612			−0.325806	+	0.945437i	$0.605636\pi$
$912$		0			0
$913$	−13840.6	−	23972.6i	−0.501705	−	0.868978i
$914$		0			0
$915$	−12385.0	+	21451.4i	−0.447470	+	0.775042i
$916$		0			0
$917$	−2900.96	+	8936.32i	−0.104469	+	0.321814i
$918$		0			0
$919$	15299.9	−	26500.2i	0.549180	−	0.951207i	−0.449151	−	0.893456i	$-0.648274\pi$
$919$	15299.9	−	26500.2i	0.549180	−	0.951207i	0.998331	−	0.0577515i	$-0.0183931\pi$
$920$		0			0
$921$	16318.5	+	28264.5i	0.583836	+	1.01123i
$922$		0			0
$923$	21888.7			0.780581
$924$		0			0
$925$	−5875.48			−0.208848
$926$		0			0
$927$	25700.5	+	44514.5i	0.910587	+	1.57718i
$928$		0			0
$929$	−7906.80	+	13695.0i	−0.279240	+	0.483657i	−0.971196	−	0.238282i	$-0.923416\pi$
$929$	−7906.80	+	13695.0i	−0.279240	+	0.483657i	0.691956	+	0.721939i	$0.256749\pi$
$930$		0			0
$931$	224.353	−	2145.57i	0.00789783	−	0.0755299i
$932$		0			0
$933$	6207.16	−	10751.1i	0.217806	−	0.377252i
$934$		0			0
$935$	1022.62	+	1771.24i	0.0357683	+	0.0619525i
$936$		0			0
$937$	42281.2			1.47414			0.737069	−	0.675818i	$-0.236209\pi$
$937$	42281.2			1.47414			0.737069	+	0.675818i	$0.236209\pi$
$938$		0			0
$939$	4515.06			0.156915
$940$		0			0
$941$	11546.0	+	19998.3i	0.399989	+	0.692801i	0.993724	−	0.111860i	$-0.0356807\pi$
$941$	11546.0	+	19998.3i	0.399989	+	0.692801i	−0.593735	+	0.804660i	$0.702347\pi$
$942$		0			0
$943$	−3982.89	+	6898.56i	−0.137540	+	0.238227i
$944$		0			0
$945$	−6890.99	+	21227.5i	−0.237211	+	0.730722i
$946$		0			0
$947$	14274.6	−	24724.4i	0.489824	−	0.848399i	−0.510108	−	0.860110i	$-0.670394\pi$
$947$	14274.6	−	24724.4i	0.489824	−	0.848399i	0.999931	+	0.0117110i	$0.00372782\pi$
$948$		0			0
$949$	−9305.42	−	16117.5i	−0.318300	−	0.551312i
$950$		0			0
$951$	−70272.0			−2.39614
$952$		0			0
$953$	−17352.0			−0.589807			−0.294904	−	0.955527i	$-0.595288\pi$
$953$	−17352.0			−0.589807			−0.294904	+	0.955527i	$0.595288\pi$
$954$		0			0
$955$	1614.89	+	2797.06i	0.0547188	+	0.0947758i
$956$		0			0
$957$	22099.1	−	38276.7i	0.746459	−	1.29290i
$958$		0			0
$959$	13805.0	+	15323.8i	0.464845	+	0.515986i
$960$		0			0
$961$	−13392.1	+	23195.8i	−0.449535	+	0.778618i
$962$		0			0
$963$	11092.6	+	19212.9i	0.371188	+	0.642916i
$964$		0			0
$965$	8091.63			0.269926
$966$		0			0
$967$	−11100.6			−0.369152			−0.184576	−	0.982818i	$-0.559091\pi$
$967$	−11100.6			−0.369152			−0.184576	+	0.982818i	$0.559091\pi$
$968$		0			0
$969$	776.662	+	1345.22i	0.0257482	+	0.0445971i
$970$		0			0
$971$	15407.0	−	26685.8i	0.509202	−	0.881964i	−0.490741	−	0.871305i	$-0.663274\pi$
$971$	15407.0	−	26685.8i	0.509202	−	0.881964i	0.999943	−	0.0106584i	$-0.00339275\pi$
$972$		0			0
$973$	−54994.4	+	11704.7i	−1.81196	+	0.385649i
$974$		0			0
$975$	−22330.4	+	38677.3i	−0.733481	+	1.27043i
$976$		0			0
$977$	3730.82	+	6461.98i	0.122170	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$977$	3730.82	+	6461.98i	0.122170	+	0.211604i	−0.798453	+	0.602057i	$0.794348\pi$
$978$		0			0
$979$	25316.7			0.826482
$980$		0			0
$981$	−41970.7			−1.36597
$982$		0			0
$983$	−6933.67	−	12009.5i	−0.224974	−	0.389667i	0.731337	−	0.682016i	$-0.238896\pi$
$983$	−6933.67	−	12009.5i	−0.224974	−	0.389667i	−0.956312	+	0.292349i	$0.905563\pi$
$984$		0			0
$985$	8558.42	−	14823.6i	0.276847	−	0.479512i
$986$		0			0
$987$	74314.4	−	15816.7i	2.39661	−	0.510083i
$988$		0			0
$989$	785.690	−	1360.86i	0.0252614	−	0.0437540i
$990$		0			0
$991$	1727.99	+	2992.96i	0.0553898	+	0.0959379i	0.892391	−	0.451263i	$-0.149027\pi$
$991$	1727.99	+	2992.96i	0.0553898	+	0.0959379i	−0.837001	+	0.547201i	$0.815693\pi$
$992$		0			0
$993$	90990.0			2.90784
$994$		0			0
$995$	13846.6			0.441174
$996$		0			0
$997$	30513.8	+	52851.5i	0.969290	+	1.67886i	0.697617	+	0.716471i	$0.254244\pi$
$997$	30513.8	+	52851.5i	0.969290	+	1.67886i	0.271674	+	0.962389i	$0.412423\pi$
$998$		0			0
$999$	−9312.63	+	16130.0i	−0.294934	+	0.510840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.4.i.b.93.1	✓	44
7.4	even	3	inner	644.4.i.b.277.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.4.i.b.93.1	✓	44	1.1	even	1	trivial
644.4.i.b.277.1	yes	44	7.4	even	3	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.78776 - 8.29265i) q^{3} +(1.66948 - 2.89162i) q^{5} +(-18.1145 + 3.85540i) q^{7} +(-32.3454 + 56.0238i) q^{9} +O(q^{10})\)	\(q+(-4.78776 - 8.29265i) q^{3} +(1.66948 - 2.89162i) q^{5} +(-18.1145 + 3.85540i) q^{7} +(-32.3454 + 56.0238i) q^{9} +(-11.8745 - 20.5673i) q^{11} -40.9661 q^{13} -31.9723 q^{15} +(-12.8961 - 22.3367i) q^{17} +(3.14471 - 5.44680i) q^{19} +(118.700 + 131.759i) q^{21} +(11.5000 - 19.9186i) q^{23} +(56.9257 + 98.5982i) q^{25} +360.909 q^{27} -194.354 q^{29} +(118.928 + 205.989i) q^{31} +(-113.705 + 196.943i) q^{33} +(-19.0934 + 58.8169i) q^{35} +(-25.8033 + 44.6926i) q^{37} +(196.136 + 339.718i) q^{39} -346.338 q^{41} +68.3209 q^{43} +(108.000 + 187.061i) q^{45} +(214.217 - 371.034i) q^{47} +(313.272 - 139.678i) q^{49} +(-123.487 + 213.886i) q^{51} +(-29.3669 - 50.8650i) q^{53} -79.2971 q^{55} -60.2246 q^{57} +(300.708 + 520.842i) q^{59} +(387.367 - 670.939i) q^{61} +(369.926 - 1139.55i) q^{63} +(-68.3921 + 118.459i) q^{65} +(-509.983 - 883.316i) q^{67} -220.237 q^{69} -534.313 q^{71} +(227.149 + 393.434i) q^{73} +(545.094 - 944.130i) q^{75} +(294.397 + 326.786i) q^{77} +(3.80610 - 6.59235i) q^{79} +(-854.622 - 1480.25i) q^{81} +1165.57 q^{83} -86.1191 q^{85} +(930.523 + 1611.71i) q^{87} +(-533.005 + 923.191i) q^{89} +(742.081 - 157.941i) q^{91} +(1138.80 - 1972.45i) q^{93} +(-10.5001 - 18.1866i) q^{95} -511.622 q^{97} +1536.35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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