LMFDB - Embedded newform 76.4.i.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	76.9
Dual form			76.4.i.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.487209 + 0.408817i) q^{3} +(-11.6536 - 4.24157i) q^{5} +(-11.7723 + 20.3903i) q^{7} +(-4.61826 + 26.1915i) q^{9} +O(q^{10})$	\(q+(-0.487209 + 0.408817i) q^{3} +(-11.6536 - 4.24157i) q^{5} +(-11.7723 + 20.3903i) q^{7} +(-4.61826 + 26.1915i) q^{9} +(-4.55487 - 7.88927i) q^{11} +(-56.3691 - 47.2993i) q^{13} +(7.41177 - 2.69766i) q^{15} +(16.4400 + 93.2359i) q^{17} +(-81.2372 + 16.1095i) q^{19} +(-2.60031 - 14.7471i) q^{21} +(139.956 - 50.9397i) q^{23} +(22.0601 + 18.5106i) q^{25} +(-17.0435 - 29.5203i) q^{27} +(-16.1046 + 91.3335i) q^{29} +(151.575 - 262.535i) q^{31} +(5.44444 + 1.98161i) q^{33} +(223.677 - 187.687i) q^{35} +121.088 q^{37} +46.8003 q^{39} +(-349.185 + 293.001i) q^{41} +(157.410 + 57.2924i) q^{43} +(164.912 - 285.636i) q^{45} +(-55.5902 + 315.267i) q^{47} +(-105.676 - 183.037i) q^{49} +(-46.1261 - 38.7044i) q^{51} +(-167.795 + 61.0725i) q^{53} +(19.6178 + 111.258i) q^{55} +(32.9937 - 41.0598i) q^{57} +(-32.3928 - 183.708i) q^{59} +(-357.222 + 130.018i) q^{61} +(-479.684 - 402.503i) q^{63} +(456.280 + 790.301i) q^{65} +(-17.3972 + 98.6644i) q^{67} +(-47.3627 + 82.0346i) q^{69} +(-277.355 - 100.949i) q^{71} +(-772.692 + 648.366i) q^{73} -18.3153 q^{75} +214.486 q^{77} +(-179.441 + 150.569i) q^{79} +(-654.401 - 238.182i) q^{81} +(-240.739 + 416.973i) q^{83} +(203.881 - 1156.27i) q^{85} +(-29.4924 - 51.0824i) q^{87} +(235.676 + 197.756i) q^{89} +(1628.04 - 592.560i) q^{91} +(33.4803 + 189.876i) q^{93} +(1015.04 + 156.840i) q^{95} +(-130.277 - 738.840i) q^{97} +(227.667 - 82.8640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.487209	+	0.408817i	−0.0937635	+	0.0786769i	−0.688464	−	0.725270i	$-0.741715\pi$
$3$	−0.487209	+	0.408817i	−0.0937635	+	0.0786769i	0.594701	+	0.803947i	$0.297270\pi$
$4$		0			0
$5$	−11.6536	−	4.24157i	−1.04233	−	0.379377i	−0.236567	−	0.971615i	$-0.576022\pi$
$5$	−11.6536	−	4.24157i	−1.04233	−	0.379377i	−0.805763	+	0.592238i	$0.798245\pi$
$6$		0			0
$7$	−11.7723	+	20.3903i	−0.635647	+	1.10097i	0.350731	+	0.936476i	$0.385933\pi$
$7$	−11.7723	+	20.3903i	−0.635647	+	1.10097i	−0.986378	+	0.164497i	$0.947400\pi$
$8$		0			0
$9$	−4.61826	+	26.1915i	−0.171047	+	0.970054i
$10$		0			0
$11$	−4.55487	−	7.88927i	−0.124850	−	0.216246i	0.796825	−	0.604211i	$-0.206511\pi$
$11$	−4.55487	−	7.88927i	−0.124850	−	0.216246i	−0.921674	+	0.387965i	$0.873178\pi$
$12$		0			0
$13$	−56.3691	−	47.2993i	−1.20261	−	1.00911i	−0.999551	−	0.0299473i	$-0.990466\pi$
$13$	−56.3691	−	47.2993i	−1.20261	−	1.00911i	−0.203063	−	0.979166i	$-0.565090\pi$
$14$		0			0
$15$	7.41177	−	2.69766i	0.127581	−	0.0464356i
$16$		0			0
$17$	16.4400	+	93.2359i	0.234546	+	1.33018i	0.843567	+	0.537024i	$0.180451\pi$
$17$	16.4400	+	93.2359i	0.234546	+	1.33018i	−0.609021	+	0.793154i	$0.708437\pi$
$18$		0			0
$19$	−81.2372	+	16.1095i	−0.980900	+	0.194514i
$19$	−81.2372	+	16.1095i	−0.980900	+	0.194514i
$20$		0			0
$21$	−2.60031	−	14.7471i	−0.0270207	−	0.153242i
$22$		0			0
$23$	139.956	−	50.9397i	1.26882	−	0.461812i	0.382098	−	0.924122i	$-0.375202\pi$
$23$	139.956	−	50.9397i	1.26882	−	0.461812i	0.886718	+	0.462310i	$0.152979\pi$
$24$		0			0
$25$	22.0601	+	18.5106i	0.176481	+	0.148085i
$26$		0			0
$27$	−17.0435	−	29.5203i	−0.121483	−	0.210414i
$28$		0			0
$29$	−16.1046	+	91.3335i	−0.103122	+	0.584835i	0.888832	+	0.458234i	$0.151518\pi$
$29$	−16.1046	+	91.3335i	−0.103122	+	0.584835i	−0.991954	+	0.126601i	$0.959593\pi$
$30$		0			0
$31$	151.575	−	262.535i	0.878183	−	1.52106i	0.0248492	−	0.999691i	$-0.492089\pi$
$31$	151.575	−	262.535i	0.878183	−	1.52106i	0.853333	−	0.521366i	$-0.174577\pi$
$32$		0			0
$33$	5.44444	+	1.98161i	0.0287199	+	0.0104532i
$34$		0			0
$35$	223.677	−	187.687i	1.08024	−	0.906427i
$36$		0			0
$37$	121.088			0.538022			0.269011	−	0.963137i	$-0.413303\pi$
$37$	121.088			0.538022			0.269011	+	0.963137i	$0.413303\pi$
$38$		0			0
$39$	46.8003			0.192155
$40$		0			0
$41$	−349.185	+	293.001i	−1.33008	+	1.11607i	−0.346027	+	0.938225i	$0.612469\pi$
$41$	−349.185	+	293.001i	−1.33008	+	1.11607i	−0.984058	+	0.177849i	$0.943086\pi$
$42$		0			0
$43$	157.410	+	57.2924i	0.558250	+	0.203186i	0.605708	−	0.795687i	$-0.292890\pi$
$43$	157.410	+	57.2924i	0.558250	+	0.203186i	−0.0474582	+	0.998873i	$0.515112\pi$
$44$		0			0
$45$	164.912	−	285.636i	0.546303	−	0.946225i
$46$		0			0
$47$	−55.5902	+	315.267i	−0.172525	+	0.978436i	0.768438	+	0.639925i	$0.221034\pi$
$47$	−55.5902	+	315.267i	−0.172525	+	0.978436i	−0.940962	+	0.338511i	$0.890077\pi$
$48$		0			0
$49$	−105.676	−	183.037i	−0.308095	−	0.533635i
$50$		0			0
$51$	−46.1261	−	38.7044i	−0.126646	−	0.106269i
$52$		0			0
$53$	−167.795	+	61.0725i	−0.434876	+	0.158282i	−0.550176	−	0.835049i	$-0.685439\pi$
$53$	−167.795	+	61.0725i	−0.434876	+	0.158282i	0.115300	+	0.993331i	$0.463217\pi$
$54$		0			0
$55$	19.6178	+	111.258i	0.0480957	+	0.272764i
$56$		0			0
$57$	32.9937	−	41.0598i	0.0766688	−	0.0954124i
$58$		0			0
$59$	−32.3928	−	183.708i	−0.0714776	−	0.405370i	−0.999463	−	0.0327541i	$-0.989572\pi$
$59$	−32.3928	−	183.708i	−0.0714776	−	0.405370i	0.927986	−	0.372615i	$-0.121539\pi$
$60$		0			0
$61$	−357.222	+	130.018i	−0.749796	+	0.272903i	−0.688520	−	0.725218i	$-0.741739\pi$
$61$	−357.222	+	130.018i	−0.749796	+	0.272903i	−0.0612759	+	0.998121i	$0.519517\pi$
$62$		0			0
$63$	−479.684	−	402.503i	−0.959278	−	0.804930i
$64$		0			0
$65$	456.280	+	790.301i	0.870686	+	1.50807i
$66$		0			0
$67$	−17.3972	+	98.6644i	−0.0317225	+	0.179907i	−0.996552	−	0.0829687i	$-0.973560\pi$
$67$	−17.3972	+	98.6644i	−0.0317225	+	0.179907i	0.964830	+	0.262876i	$0.0846709\pi$
$68$		0			0
$69$	−47.3627	+	82.0346i	−0.0826347	+	0.143128i
$70$		0			0
$71$	−277.355	−	100.949i	−0.463605	−	0.168739i	0.0996481	−	0.995023i	$-0.468228\pi$
$71$	−277.355	−	100.949i	−0.463605	−	0.168739i	−0.563253	+	0.826284i	$0.690451\pi$
$72$		0			0
$73$	−772.692	+	648.366i	−1.23886	+	1.03953i	−0.241248	+	0.970464i	$0.577557\pi$
$73$	−772.692	+	648.366i	−1.23886	+	1.03953i	−0.997612	+	0.0690636i	$0.977999\pi$
$74$		0			0
$75$	−18.3153			−0.0281983
$76$		0			0
$77$	214.486			0.317441
$78$		0			0
$79$	−179.441	+	150.569i	−0.255553	+	0.214434i	−0.761559	−	0.648096i	$-0.775566\pi$
$79$	−179.441	+	150.569i	−0.255553	+	0.214434i	0.506006	+	0.862530i	$0.331121\pi$
$80$		0			0
$81$	−654.401	−	238.182i	−0.897669	−	0.326725i
$82$		0			0
$83$	−240.739	+	416.973i	−0.318369	+	0.551430i	−0.980148	−	0.198268i	$-0.936468\pi$
$83$	−240.739	+	416.973i	−0.318369	+	0.551430i	0.661779	+	0.749699i	$0.269802\pi$
$84$		0			0
$85$	203.881	−	1156.27i	0.260164	−	1.47547i
$86$		0			0
$87$	−29.4924	−	51.0824i	−0.0363439	−	0.0629495i
$88$		0			0
$89$	235.676	+	197.756i	0.280693	+	0.235529i	0.772254	−	0.635314i	$-0.219129\pi$
$89$	235.676	+	197.756i	0.280693	+	0.235529i	−0.491561	+	0.870843i	$0.663574\pi$
$90$		0			0
$91$	1628.04	−	592.560i	1.87544	−	0.682606i
$92$		0			0
$93$	33.4803	+	189.876i	0.0373306	+	0.211712i
$94$		0			0
$95$	1015.04	+	156.840i	1.09622	+	0.169383i
$96$		0			0
$97$	−130.277	−	738.840i	−0.136368	−	0.773380i	−0.973898	−	0.226988i	$-0.927112\pi$
$97$	−130.277	−	738.840i	−0.136368	−	0.773380i	0.837530	−	0.546392i	$-0.183999\pi$
$98$		0			0
$99$	227.667	−	82.8640i	0.231125	−	0.0841226i
$100$		0			0
$101$	608.044	+	510.209i	0.599036	+	0.502651i	0.891136	−	0.453737i	$-0.149910\pi$
$101$	608.044	+	510.209i	0.599036	+	0.502651i	−0.292100	+	0.956388i	$0.594354\pi$
$102$		0			0
$103$	73.0667	+	126.555i	0.0698978	+	0.121067i	0.898856	−	0.438244i	$-0.144399\pi$
$103$	73.0667	+	126.555i	0.0698978	+	0.121067i	−0.828958	+	0.559310i	$0.811066\pi$
$104$		0			0
$105$	−32.2477	+	182.886i	−0.0299720	+	0.169980i
$106$		0			0
$107$	−22.8619	+	39.5979i	−0.0206555	+	0.0357764i	−0.876168	−	0.482005i	$-0.839909\pi$
$107$	−22.8619	+	39.5979i	−0.0206555	+	0.0357764i	0.855513	+	0.517782i	$0.173242\pi$
$108$		0			0
$109$	−852.808	−	310.397i	−0.749396	−	0.272758i	−0.0610443	−	0.998135i	$-0.519443\pi$
$109$	−852.808	−	310.397i	−0.749396	−	0.272758i	−0.688352	+	0.725377i	$0.741665\pi$
$110$		0			0
$111$	−58.9954	+	49.5030i	−0.0504468	+	0.0423299i
$112$		0			0
$113$	1960.08			1.63176			0.815880	−	0.578222i	$-0.196253\pi$
$113$	1960.08			1.63176			0.815880	+	0.578222i	$0.196253\pi$
$114$		0			0
$115$	−1847.05			−1.49773
$116$		0			0
$117$	1499.16	−	1257.95i	1.18460	−	0.993995i
$118$		0			0
$119$	−2094.65	−	762.389i	−1.61358	−	0.587295i
$120$		0			0
$121$	624.006	−	1080.81i	0.468825	−	0.812029i
$122$		0			0
$123$	50.3423	−	285.505i	0.0369042	−	0.209294i
$124$		0			0
$125$	596.529	+	1033.22i	0.426841	+	0.739311i
$126$		0			0
$127$	1773.09	+	1487.80i	1.23887	+	1.03953i	0.997612	+	0.0690727i	$0.0220041\pi$
$127$	1773.09	+	1487.80i	1.23887	+	1.03953i	0.241257	+	0.970461i	$0.422440\pi$
$128$		0			0
$129$	−100.114	+	36.4384i	−0.0683295	+	0.0248699i
$130$		0			0
$131$	438.208	+	2485.20i	0.292263	+	1.65750i	0.678125	+	0.734947i	$0.262793\pi$
$131$	438.208	+	2485.20i	0.292263	+	1.65750i	−0.385862	+	0.922557i	$0.626096\pi$
$132$		0			0
$133$	627.876	−	1846.10i	0.409352	−	1.20359i
$134$		0			0
$135$	73.4065	+	416.309i	0.0467987	+	0.265409i
$136$		0			0
$137$	−468.586	+	170.551i	−0.292219	+	0.106359i	−0.483970	−	0.875085i	$-0.660806\pi$
$137$	−468.586	+	170.551i	−0.292219	+	0.106359i	0.191751	+	0.981444i	$0.438583\pi$
$138$		0			0
$139$	−1944.18	−	1631.36i	−1.18636	−	0.995472i	−0.999915	−	0.0130056i	$-0.995860\pi$
$139$	−1944.18	−	1631.36i	−1.18636	−	0.995472i	−0.186442	−	0.982466i	$-0.559695\pi$
$140$		0			0
$141$	−101.803	−	176.327i	−0.0608038	−	0.105315i
$142$		0			0
$143$	−116.403	+	660.153i	−0.0680706	+	0.386047i
$144$		0			0
$145$	575.073	−	996.056i	0.329360	−	0.570469i
$146$		0			0
$147$	126.315	+	45.9750i	0.0708728	+	0.0257956i
$148$		0			0
$149$	106.087	−	89.0175i	0.0583287	−	0.0489436i	−0.613157	−	0.789961i	$-0.710101\pi$
$149$	106.087	−	89.0175i	0.0583287	−	0.0489436i	0.671486	+	0.741017i	$0.265656\pi$
$150$		0			0
$151$	−2233.00			−1.20344			−0.601719	−	0.798708i	$-0.705517\pi$
$151$	−2233.00			−1.20344			−0.601719	+	0.798708i	$0.705517\pi$
$152$		0			0
$153$	−2517.91			−1.33046
$154$		0			0
$155$	−2879.96	+	2416.57i	−1.49241	+	1.25228i
$156$		0			0
$157$	−811.730	−	295.446i	−0.412631	−	0.150186i	0.127359	−	0.991857i	$-0.459350\pi$
$157$	−811.730	−	295.446i	−0.412631	−	0.150186i	−0.539990	+	0.841671i	$0.681572\pi$
$158$		0			0
$159$	56.7839	−	98.3526i	0.0283224	−	0.0490558i
$160$		0			0
$161$	−608.931	+	3453.42i	−0.298078	+	1.69048i
$162$		0			0
$163$	1150.21	+	1992.22i	0.552708	+	0.957319i	0.998078	+	0.0619721i	$0.0197390\pi$
$163$	1150.21	+	1992.22i	0.552708	+	0.957319i	−0.445370	+	0.895347i	$0.646928\pi$
$164$		0			0
$165$	−55.0422	−	46.1859i	−0.0259699	−	0.0217913i
$166$		0			0
$167$	2764.36	−	1006.14i	1.28091	−	0.466215i	0.390180	−	0.920739i	$-0.372413\pi$
$167$	2764.36	−	1006.14i	1.28091	−	0.466215i	0.890734	+	0.454524i	$0.150191\pi$
$168$		0			0
$169$	558.748	+	3168.82i	0.254323	+	1.44234i
$170$		0			0
$171$	−46.7554	−	2202.12i	−0.0209092	−	0.984796i
$172$		0			0
$173$	−754.902	−	4281.26i	−0.331758	−	1.88149i	−0.457156	−	0.889386i	$-0.651132\pi$
$173$	−754.902	−	4281.26i	−0.331758	−	1.88149i	0.125399	−	0.992106i	$-0.459979\pi$
$174$		0			0
$175$	−637.135	+	231.898i	−0.275217	+	0.100171i
$176$		0			0
$177$	90.8852	+	76.2617i	0.0385952	+	0.0323852i
$178$		0			0
$179$	14.0424	+	24.3222i	0.00586358	+	0.0101560i	0.868942	−	0.494913i	$-0.164800\pi$
$179$	14.0424	+	24.3222i	0.00586358	+	0.0101560i	−0.863079	+	0.505069i	$0.831467\pi$
$180$		0			0
$181$	−133.580	+	757.572i	−0.0548561	+	0.311104i	−0.999873	−	0.0159161i	$-0.994934\pi$
$181$	−133.580	+	757.572i	−0.0548561	+	0.311104i	0.945017	+	0.327021i	$0.106045\pi$
$182$		0			0
$183$	120.888	−	209.384i	0.0488323	−	0.0845800i
$184$		0			0
$185$	−1411.12	−	513.604i	−0.560796	−	0.204113i
$186$		0			0
$187$	660.680	−	554.377i	0.258362	−	0.216792i
$188$		0			0
$189$	802.570			0.308880
$190$		0			0
$191$	661.098			0.250447			0.125223	−	0.992129i	$-0.460035\pi$
$191$	661.098			0.250447			0.125223	+	0.992129i	$0.460035\pi$
$192$		0			0
$193$	−2367.74	+	1986.77i	−0.883076	+	0.740989i	−0.966809	−	0.255499i	$-0.917760\pi$
$193$	−2367.74	+	1986.77i	−0.883076	+	0.740989i	0.0837331	+	0.996488i	$0.473316\pi$
$194$		0			0
$195$	−545.392	−	198.507i	−0.200289	−	0.0728993i
$196$		0			0
$197$	921.515	−	1596.11i	0.333275	−	0.577249i	−0.649877	−	0.760040i	$-0.725180\pi$
$197$	921.515	−	1596.11i	0.333275	−	0.577249i	0.983152	+	0.182790i	$0.0585129\pi$
$198$		0			0
$199$	475.983	−	2699.43i	0.169555	−	0.961596i	−0.774687	−	0.632345i	$-0.782093\pi$
$199$	475.983	−	2699.43i	0.169555	−	0.961596i	0.944242	−	0.329251i	$-0.106796\pi$
$200$		0			0
$201$	−31.8596	−	55.1825i	−0.0111801	−	0.0193645i
$202$		0			0
$203$	−1672.73	−	1403.59i	−0.578338	−	0.485283i
$204$		0			0
$205$	5312.04	−	1933.42i	1.80980	−	0.658713i
$206$		0			0
$207$	687.833	+	3900.90i	0.230955	+	1.30981i
$208$		0			0
$209$	497.117	+	567.525i	0.164528	+	0.187830i
$210$		0			0
$211$	266.871	+	1513.50i	0.0870718	+	0.493809i	0.996890	+	0.0788022i	$0.0251096\pi$
$211$	266.871	+	1513.50i	0.0870718	+	0.493809i	−0.909818	+	0.415006i	$0.863779\pi$
$212$		0			0
$213$	176.400	−	64.2042i	0.0567451	−	0.0206535i
$214$		0			0
$215$	−1591.38	−	1335.33i	−0.504796	−	0.423575i
$216$		0			0
$217$	3568.79	+	6181.32i	1.11643	+	1.93371i
$218$		0			0
$219$	111.400	−	631.780i	0.0343731	−	0.194939i
$220$		0			0
$221$	3483.28	−	6033.23i	1.06023	−	1.83637i
$222$		0			0
$223$	251.077	+	91.3844i	0.0753961	+	0.0274419i	0.379443	−	0.925215i	$-0.376116\pi$
$223$	251.077	+	91.3844i	0.0753961	+	0.0274419i	−0.304047	+	0.952657i	$0.598338\pi$
$224$		0			0
$225$	−586.698	+	492.298i	−0.173837	+	0.145866i
$226$		0			0
$227$	6003.50			1.75536			0.877679	−	0.479249i	$-0.159091\pi$
$227$	6003.50			1.75536			0.877679	+	0.479249i	$0.159091\pi$
$228$		0			0
$229$	−3538.88			−1.02121			−0.510603	−	0.859817i	$-0.670578\pi$
$229$	−3538.88			−1.02121			−0.510603	+	0.859817i	$0.670578\pi$
$230$		0			0
$231$	−104.500	+	87.6856i	−0.0297644	+	0.0249753i
$232$		0			0
$233$	−903.470	−	328.836i	−0.254027	−	0.0924582i	0.211868	−	0.977298i	$-0.432045\pi$
$233$	−903.470	−	328.836i	−0.254027	−	0.0924582i	−0.465895	+	0.884840i	$0.654268\pi$
$234$		0			0
$235$	1985.05	−	3438.21i	0.551024	−	0.954401i
$236$		0			0
$237$	25.8701	−	146.717i	0.00709049	−	0.0402122i
$238$		0			0
$239$	−3104.19	−	5376.61i	−0.840139	−	1.45516i	−0.889777	−	0.456396i	$-0.849140\pi$
$239$	−3104.19	−	5376.61i	−0.840139	−	1.45516i	0.0496380	−	0.998767i	$-0.484193\pi$
$240$		0			0
$241$	−3802.92	−	3191.03i	−1.01646	−	0.852914i	−0.0272848	−	0.999628i	$-0.508686\pi$
$241$	−3802.92	−	3191.03i	−1.01646	−	0.852914i	−0.989179	+	0.146713i	$0.953131\pi$
$242$		0			0
$243$	1281.05	−	466.264i	0.338187	−	0.123090i
$244$		0			0
$245$	455.148	+	2581.27i	0.118687	+	0.673108i
$246$		0			0
$247$	5341.24	+	2934.39i	1.37593	+	0.755914i
$248$		0			0
$249$	−53.1752	−	301.571i	−0.0135335	−	0.0767523i
$250$		0			0
$251$	3425.45	−	1246.76i	0.861404	−	0.313525i	0.126723	−	0.991938i	$-0.459554\pi$
$251$	3425.45	−	1246.76i	0.861404	−	0.313525i	0.734681	+	0.678413i	$0.237332\pi$
$252$		0			0
$253$	−1039.36	−	872.124i	−0.258276	−	0.216719i
$254$		0			0
$255$	373.368	+	646.693i	0.0916911	+	0.158814i
$256$		0			0
$257$	−877.986	+	4979.31i	−0.213102	+	1.20856i	0.671067	+	0.741396i	$0.265836\pi$
$257$	−877.986	+	4979.31i	−0.213102	+	1.20856i	−0.884170	+	0.467166i	$0.845275\pi$
$258$		0			0
$259$	−1425.49	+	2469.03i	−0.341992	+	0.592348i
$260$		0			0
$261$	−2317.78	−	843.604i	−0.549683	−	0.200068i
$262$		0			0
$263$	−2777.74	+	2330.80i	−0.651265	+	0.546476i	−0.907455	−	0.420150i	$-0.861977\pi$
$263$	−2777.74	+	2330.80i	−0.651265	+	0.546476i	0.256189	+	0.966627i	$0.417533\pi$
$264$		0			0
$265$	2214.46			0.513333
$266$		0			0
$267$	−195.670			−0.0448494
$268$		0			0
$269$	−6373.18	+	5347.73i	−1.44453	+	1.21211i	−0.508082	+	0.861309i	$0.669645\pi$
$269$	−6373.18	+	5347.73i	−1.44453	+	1.21211i	−0.936451	+	0.350799i	$0.885910\pi$
$270$		0			0
$271$	−4938.65	−	1797.52i	−1.10702	−	0.402921i	−0.277118	−	0.960836i	$-0.589379\pi$
$271$	−4938.65	−	1797.52i	−1.10702	−	0.402921i	−0.829898	+	0.557915i	$0.811602\pi$
$272$		0			0
$273$	−550.950	+	954.273i	−0.122143	+	0.211558i
$274$		0			0
$275$	45.5543	−	258.351i	0.00998918	−	0.0566515i
$276$		0			0
$277$	−1602.28	−	2775.24i	−0.347552	−	0.601978i	0.638262	−	0.769819i	$-0.279654\pi$
$277$	−1602.28	−	2775.24i	−0.347552	−	0.601978i	−0.985814	+	0.167842i	$0.946320\pi$
$278$		0			0
$279$	6176.17	+	5182.42i	1.32530	+	1.11206i
$280$		0			0
$281$	−2014.91	+	733.366i	−0.427756	+	0.155690i	−0.546921	−	0.837184i	$-0.684200\pi$
$281$	−2014.91	+	733.366i	−0.427756	+	0.155690i	0.119166	+	0.992874i	$0.461978\pi$
$282$		0			0
$283$	32.5861	+	184.805i	0.00684467	+	0.0388181i	0.988039	−	0.154205i	$-0.0492818\pi$
$283$	32.5861	+	184.805i	0.00684467	+	0.0388181i	−0.981194	+	0.193023i	$0.938171\pi$
$284$		0			0
$285$	−558.653	+	338.550i	−0.116111	+	0.0703648i
$286$		0			0
$287$	−1863.65	−	10569.3i	−0.383303	−	2.17382i
$288$		0			0
$289$	−3805.94	+	1385.25i	−0.774668	+	0.281956i
$290$		0			0
$291$	365.523	+	306.710i	0.0736334	+	0.0617858i
$292$		0			0
$293$	2416.33	+	4185.21i	0.481787	+	0.834480i	0.999781	−	0.0209038i	$-0.00665438\pi$
$293$	2416.33	+	4185.21i	0.481787	+	0.834480i	−0.517994	+	0.855384i	$0.673321\pi$
$294$		0			0
$295$	−401.719	+	2278.26i	−0.0792847	+	0.449646i
$296$		0			0
$297$	−155.262	+	268.922i	−0.0303341	+	0.0525402i
$298$		0			0
$299$	−10298.6	−	3748.38i	−1.99192	−	0.724998i
$300$		0			0
$301$	−3021.29	+	2535.16i	−0.578553	+	0.485463i
$302$		0			0
$303$	−504.827			−0.0957146
$304$		0			0
$305$	4714.40			0.885068
$306$		0			0
$307$	1935.93	−	1624.43i	0.359899	−	0.301991i	−0.444851	−	0.895604i	$-0.646743\pi$
$307$	1935.93	−	1624.43i	0.359899	−	0.301991i	0.804751	+	0.593613i	$0.202299\pi$
$308$		0			0
$309$	−87.3367	−	31.7879i	−0.0160790	−	0.00585228i
$310$		0			0
$311$	1049.61	−	1817.98i	0.191376	−	0.331472i	−0.754331	−	0.656495i	$-0.772038\pi$
$311$	1049.61	−	1817.98i	0.191376	−	0.331472i	0.945706	+	0.325022i	$0.105372\pi$
$312$		0			0
$313$	−518.398	+	2939.98i	−0.0936153	+	0.530919i	0.901548	+	0.432680i	$0.142432\pi$
$313$	−518.398	+	2939.98i	−0.0936153	+	0.530919i	−0.995163	+	0.0982388i	$0.968679\pi$
$314$		0			0
$315$	3882.81	+	6725.22i	0.694512	+	1.20293i
$316$		0			0
$317$	3399.89	+	2852.85i	0.602387	+	0.505463i	0.892212	−	0.451617i	$-0.149153\pi$
$317$	3399.89	+	2852.85i	0.602387	+	0.505463i	−0.289825	+	0.957080i	$0.593597\pi$
$318$		0			0
$319$	793.909	−	288.959i	0.139343	−	0.0507166i
$320$		0			0
$321$	−5.04979	−	28.6388i	−0.000878044	−	0.00497963i
$322$		0			0
$323$	−2837.52	−	7309.38i	−0.488804	−	1.25915i
$324$		0			0
$325$	−367.968	−	2086.85i	−0.0628037	−	0.356178i
$326$		0			0
$327$	542.391	−	197.414i	0.0917257	−	0.0333854i
$328$		0			0
$329$	−5773.97	−	4844.94i	−0.967567	−	0.811885i
$330$		0			0
$331$	1681.74	+	2912.86i	0.279265	+	0.483701i	0.971202	−	0.238257i	$-0.0765759\pi$
$331$	1681.74	+	2912.86i	0.279265	+	0.483701i	−0.691937	+	0.721958i	$0.743243\pi$
$332$		0			0
$333$	−559.218	+	3171.48i	−0.0920268	+	0.521910i
$334$		0			0
$335$	621.231	−	1076.00i	0.101318	−	0.175488i
$336$		0			0
$337$	7503.91	+	2731.20i	1.21295	+	0.441477i	0.867726	−	0.497043i	$-0.165581\pi$
$337$	7503.91	+	2731.20i	1.21295	+	0.441477i	0.345223	+	0.938521i	$0.387803\pi$
$338$		0			0
$339$	−954.969	+	801.314i	−0.152999	+	0.128382i
$340$		0			0
$341$	−2761.62			−0.438563
$342$		0			0
$343$	−3099.59			−0.487937
$344$		0			0
$345$	899.901	−	755.107i	0.140432	−	0.117836i
$346$		0			0
$347$	899.706	+	327.466i	0.139189	+	0.0506608i	0.410676	−	0.911782i	$-0.365293\pi$
$347$	899.706	+	327.466i	0.139189	+	0.0506608i	−0.271486	+	0.962442i	$0.587515\pi$
$348$		0			0
$349$	533.406	−	923.886i	0.0818125	−	0.141703i	−0.822216	−	0.569176i	$-0.807262\pi$
$349$	533.406	−	923.886i	0.0818125	−	0.141703i	0.904029	+	0.427472i	$0.140596\pi$
$350$		0			0
$351$	−435.559	+	2470.18i	−0.0662349	+	0.375637i
$352$		0			0
$353$	−3212.37	−	5564.00i	−0.484355	−	0.838928i	0.515483	−	0.856900i	$-0.327613\pi$
$353$	−3212.37	−	5564.00i	−0.484355	−	0.838928i	−0.999838	+	0.0179716i	$0.994279\pi$
$354$		0			0
$355$	2804.00	+	2352.84i	0.419214	+	0.351762i
$356$		0			0
$357$	1332.21	−	484.884i	0.197501	−	0.0718846i
$358$		0			0
$359$	802.261	+	4549.85i	0.117943	+	0.668891i	0.985251	+	0.171117i	$0.0547377\pi$
$359$	802.261	+	4549.85i	0.117943	+	0.668891i	−0.867307	+	0.497773i	$0.834151\pi$
$360$		0			0
$361$	6339.97	−	2617.37i	0.924329	−	0.381597i
$362$		0			0
$363$	137.832	+	781.685i	0.0199292	+	0.113024i
$364$		0			0
$365$	11754.7	−	4278.37i	1.68567	−	0.613535i
$366$		0			0
$367$	945.525	+	793.390i	0.134485	+	0.112846i	0.707549	−	0.706664i	$-0.249801\pi$
$367$	945.525	+	793.390i	0.134485	+	0.112846i	−0.573064	+	0.819511i	$0.694245\pi$
$368$		0			0
$369$	−6061.49	−	10498.8i	−0.855145	−	1.48115i
$370$		0			0
$371$	730.057	−	4140.36i	0.102164	−	0.579399i
$372$		0			0
$373$	693.753	−	1201.62i	0.0963034	−	0.166802i	−0.813848	−	0.581077i	$-0.802631\pi$
$373$	693.753	−	1201.62i	0.0963034	−	0.166802i	0.910152	+	0.414275i	$0.135965\pi$
$374$		0			0
$375$	−713.032	−	259.522i	−0.0981888	−	0.0357378i
$376$		0			0
$377$	5227.81	−	4386.66i	0.714181	−	0.599269i
$378$		0			0
$379$	6225.46			0.843747			0.421874	−	0.906655i	$-0.361373\pi$
$379$	6225.46			0.843747			0.421874	+	0.906655i	$0.361373\pi$
$380$		0			0
$381$	−1472.10			−0.197948
$382$		0			0
$383$	10045.3	−	8429.02i	1.34019	−	1.12455i	0.358610	−	0.933487i	$-0.383251\pi$
$383$	10045.3	−	8429.02i	1.34019	−	1.12455i	0.981578	−	0.191064i	$-0.0611936\pi$
$384$		0			0
$385$	−2499.54	−	909.757i	−0.330878	−	0.120430i
$386$		0			0
$387$	−2227.53	+	3858.20i	−0.292588	+	0.506778i
$388$		0			0
$389$	674.219	−	3823.69i	0.0878773	−	0.498377i	−0.908821	−	0.417186i	$-0.863016\pi$
$389$	674.219	−	3823.69i	0.0878773	−	0.498377i	0.996699	−	0.0811913i	$-0.0258725\pi$
$390$		0			0
$391$	7050.28	+	12211.4i	0.911888	+	1.57944i
$392$		0			0
$393$	−1229.49	−	1031.67i	−0.157811	−	0.132419i
$394$		0			0
$395$	2729.78	−	993.558i	0.347722	−	0.126560i
$396$		0			0
$397$	131.271	+	744.473i	0.0165952	+	0.0941159i	0.991980	−	0.126392i	$-0.0403397\pi$
$397$	131.271	+	744.473i	0.0165952	+	0.0941159i	−0.975385	+	0.220508i	$0.929229\pi$
$398$		0			0
$399$	448.809	+	1156.12i	0.0563122	+	0.145059i
$400$		0			0
$401$	1716.21	+	9733.14i	0.213725	+	1.21209i	0.883106	+	0.469174i	$0.155448\pi$
$401$	1716.21	+	9733.14i	0.213725	+	1.21209i	−0.669381	+	0.742920i	$0.733440\pi$
$402$		0			0
$403$	−20961.9	+	7629.51i	−2.59103	+	0.943059i
$404$		0			0
$405$	6615.86	+	5551.37i	0.811716	+	0.681110i
$406$		0			0
$407$	−551.542	−	955.298i	−0.0671718	−	0.116345i
$408$		0			0
$409$	2025.12	−	11485.0i	0.244831	−	1.38850i	−0.576055	−	0.817411i	$-0.695409\pi$
$409$	2025.12	−	11485.0i	0.244831	−	1.38850i	0.820886	−	0.571093i	$-0.193480\pi$
$410$		0			0
$411$	158.575	−	274.660i	0.0190315	−	0.0329635i
$412$		0			0
$413$	4127.21	+	1502.18i	0.491735	+	0.178977i
$414$		0			0
$415$	4574.10	−	3838.13i	0.541045	−	0.453991i
$416$		0			0
$417$	1614.15			0.189558
$418$		0			0
$419$	−12085.1			−1.40906			−0.704529	−	0.709675i	$-0.748842\pi$
$419$	−12085.1			−1.40906			−0.704529	+	0.709675i	$0.748842\pi$
$420$		0			0
$421$	−9066.64	+	7607.81i	−1.04960	+	0.880717i	−0.993051	−	0.117683i	$-0.962453\pi$
$421$	−9066.64	+	7607.81i	−1.04960	+	0.880717i	−0.0565468	+	0.998400i	$0.518009\pi$
$422$		0			0
$423$	−8000.58	−	2911.97i	−0.919626	−	0.334716i
$424$		0			0
$425$	−1363.18	+	2361.10i	−0.155586	+	0.269483i
$426$		0			0
$427$	1554.23	−	8814.48i	0.176146	−	0.998975i
$428$		0			0
$429$	−213.169	−	369.220i	−0.0239905	−	0.0415527i
$430$		0			0
$431$	−9718.14	−	8154.49i	−1.08609	−	0.911341i	−0.0896811	−	0.995971i	$-0.528585\pi$
$431$	−9718.14	−	8154.49i	−1.08609	−	0.911341i	−0.996412	+	0.0846298i	$0.973029\pi$
$432$		0			0
$433$	4690.74	−	1707.29i	0.520606	−	0.189485i	−0.0683329	−	0.997663i	$-0.521768\pi$
$433$	4690.74	−	1707.29i	0.520606	−	0.189485i	0.588939	+	0.808177i	$0.299546\pi$
$434$		0			0
$435$	127.024	+	720.388i	0.0140007	+	0.0794022i
$436$		0			0
$437$	−10549.0	+	6392.81i	−1.15475	+	0.699793i
$438$		0			0
$439$	2862.76	+	16235.5i	0.311235	+	1.76510i	0.592595	+	0.805500i	$0.298103\pi$
$439$	2862.76	+	16235.5i	0.311235	+	1.76510i	−0.281360	+	0.959602i	$0.590786\pi$
$440$		0			0
$441$	5282.04	−	1922.51i	0.570353	−	0.207592i
$442$		0			0
$443$	4879.09	+	4094.04i	0.523279	+	0.439083i	0.865773	−	0.500437i	$-0.166827\pi$
$443$	4879.09	+	4094.04i	0.523279	+	0.439083i	−0.342494	+	0.939520i	$0.611272\pi$
$444$		0			0
$445$	−1907.69	−	3304.21i	−0.203220	−	0.351988i
$446$		0			0
$447$	−15.2947	+	86.7403i	−0.00161837	+	0.00917825i
$448$		0			0
$449$	−413.640	+	716.446i	−0.0434764	+	0.0753033i	−0.886945	−	0.461876i	$-0.847177\pi$
$449$	−413.640	+	716.446i	−0.0434764	+	0.0753033i	0.843468	+	0.537179i	$0.180510\pi$
$450$		0			0
$451$	3902.05	+	1420.23i	0.407407	+	0.148284i
$452$		0			0
$453$	1087.94	−	912.889i	0.112838	−	0.0946827i
$454$		0			0
$455$	−21486.0			−2.21380
$456$		0			0
$457$	1602.17			0.163996			0.0819980	−	0.996632i	$-0.473870\pi$
$457$	1602.17			0.163996			0.0819980	+	0.996632i	$0.473870\pi$
$458$		0			0
$459$	2472.15	−	2074.38i	0.251395	−	0.210945i
$460$		0			0
$461$	6484.31	+	2360.10i	0.655107	+	0.238439i	0.648122	−	0.761536i	$-0.275554\pi$
$461$	6484.31	+	2360.10i	0.655107	+	0.238439i	0.00698461	+	0.999976i	$0.497777\pi$
$462$		0			0
$463$	−879.929	+	1524.08i	−0.0883235	+	0.152981i	−0.906803	−	0.421556i	$-0.861484\pi$
$463$	−879.929	+	1524.08i	−0.0883235	+	0.152981i	0.818479	+	0.574536i	$0.194818\pi$
$464$		0			0
$465$	415.206	−	2354.75i	0.0414080	−	0.234836i
$466$		0			0
$467$	4579.92	+	7932.65i	0.453819	+	0.786037i	0.998619	−	0.0525283i	$-0.0167280\pi$
$467$	4579.92	+	7932.65i	0.453819	+	0.786037i	−0.544801	+	0.838566i	$0.683395\pi$
$468$		0			0
$469$	−1806.99	−	1516.25i	−0.177909	−	0.149283i
$470$		0			0
$471$	516.266	−	187.905i	0.0505059	−	0.0183826i
$472$		0			0
$473$	−264.985	−	1502.81i	−0.0257591	−	0.146087i
$474$		0			0
$475$	−2090.29	−	1148.37i	−0.201914	−	0.110928i
$476$		0			0
$477$	−824.654	−	4676.85i	−0.0791579	−	0.448927i
$478$		0			0
$479$	−5277.18	+	1920.74i	−0.503383	+	0.183216i	−0.581215	−	0.813750i	$-0.697422\pi$
$479$	−5277.18	+	1920.74i	−0.503383	+	0.183216i	0.0778320	+	0.996966i	$0.475200\pi$
$480$		0			0
$481$	−6825.65	−	5727.40i	−0.647033	−	0.542925i
$482$		0			0
$483$	−1115.14	−	1931.48i	−0.105053	−	0.181957i
$484$		0			0
$485$	−1615.64	+	9162.73i	−0.151262	+	0.857852i
$486$		0			0
$487$	−4819.77	+	8348.09i	−0.448470	+	0.776773i	−0.998287	−	0.0585126i	$-0.981364\pi$
$487$	−4819.77	+	8348.09i	−0.448470	+	0.776773i	0.549817	+	0.835285i	$0.314698\pi$
$488$		0			0
$489$	−1374.85	−	500.404i	−0.127143	−	0.0462762i
$490$		0			0
$491$	−8222.46	+	6899.46i	−0.755752	+	0.634151i	−0.937017	−	0.349283i	$-0.886425\pi$
$491$	−8222.46	+	6899.46i	−0.755752	+	0.634151i	0.181265	+	0.983434i	$0.441981\pi$
$492$		0			0
$493$	−8780.32			−0.802121
$494$		0			0
$495$	−3004.61			−0.272823
$496$		0			0
$497$	5323.50	−	4466.95i	0.480466	−	0.403159i
$498$		0			0
$499$	17191.6	+	6257.21i	1.54228	+	0.561345i	0.966592	−	0.256321i	$-0.0825105\pi$
$499$	17191.6	+	6257.21i	1.54228	+	0.561345i	0.575692	+	0.817667i	$0.304733\pi$
$500$		0			0
$501$	−935.493	+	1620.32i	−0.0834226	+	0.144492i
$502$		0			0
$503$	−1968.92	+	11166.3i	−0.174532	+	0.989822i	0.764150	+	0.645039i	$0.223159\pi$
$503$	−1968.92	+	11166.3i	−0.174532	+	0.989822i	−0.938682	+	0.344783i	$0.887952\pi$
$504$		0			0
$505$	−4921.81	−	8524.83i	−0.433699	−	0.751188i
$506$		0			0
$507$	−1567.69	−	1315.45i	−0.137325	−	0.115229i
$508$		0			0
$509$	−11741.0	+	4273.38i	−1.02242	+	0.372130i	−0.798190	−	0.602406i	$-0.794209\pi$
$509$	−11741.0	+	4273.38i	−1.02242	+	0.372130i	−0.224230	+	0.974536i	$0.571987\pi$
$510$		0			0
$511$	−4123.97	−	23388.2i	−0.357013	−	2.02472i
$512$		0			0
$513$	1860.13	+	2123.58i	0.160091	+	0.182765i
$514$		0			0
$515$	−314.698	−	1784.74i	−0.0269267	−	0.152709i
$516$		0			0
$517$	2740.43	−	997.437i	0.233122	−	0.0848495i
$518$		0			0
$519$	2118.05	+	1777.25i	0.179137	+	0.150314i
$520$		0			0
$521$	5044.86	+	8737.96i	0.424222	+	0.734773i	0.996347	−	0.0853925i	$-0.0272144\pi$
$521$	5044.86	+	8737.96i	0.424222	+	0.734773i	−0.572126	+	0.820166i	$0.693881\pi$
$522$		0			0
$523$	3093.35	−	17543.3i	0.258628	−	1.46675i	−0.527956	−	0.849272i	$-0.677041\pi$
$523$	3093.35	−	17543.3i	0.258628	−	1.46675i	0.786584	−	0.617483i	$-0.211848\pi$
$524$		0			0
$525$	215.614	−	373.455i	0.0179241	−	0.0310455i
$526$		0			0
$527$	26969.6	+	9816.14i	2.22925	+	0.811381i
$528$		0			0
$529$	7672.28	−	6437.81i	0.630581	−	0.529121i
$530$		0			0
$531$	4961.19			0.405456
$532$		0			0
$533$	33542.0			2.72582
$534$		0			0
$535$	434.381	−	364.489i	0.0351026	−	0.0294546i
$536$		0			0
$537$	−16.7850	−	6.10922i	−0.00134883	−	0.000490936i
$538$		0			0
$539$	−962.685	+	1667.42i	−0.0769309	+	0.133248i
$540$		0			0
$541$	−303.813	+	1723.01i	−0.0241440	+	0.136928i	−0.994497	−	0.104764i	$-0.966591\pi$
$541$	−303.813	+	1723.01i	−0.0241440	+	0.136928i	0.970353	+	0.241692i	$0.0777023\pi$
$542$		0			0
$543$	−244.627	−	423.706i	−0.0193332	−	0.0334861i
$544$		0			0
$545$	8621.71	+	7234.48i	0.677640	+	0.568607i
$546$		0			0
$547$	−16099.8	+	5859.84i	−1.25846	+	0.458042i	−0.883252	−	0.468899i	$-0.844651\pi$
$547$	−16099.8	+	5859.84i	−1.25846	+	0.458042i	−0.375208	+	0.926941i	$0.622429\pi$
$548$		0			0
$549$	−1755.62	−	9956.61i	−0.136481	−	0.774021i
$550$		0			0
$551$	−163.043	−	7679.12i	−0.0126059	−	0.593723i
$552$		0			0
$553$	−957.702	−	5431.40i	−0.0736449	−	0.417661i
$554$		0			0
$555$	897.479	−	326.656i	0.0686412	−	0.0249834i
$556$		0			0
$557$	−4886.39	−	4100.17i	−0.371711	−	0.311902i	0.437727	−	0.899108i	$-0.355784\pi$
$557$	−4886.39	−	4100.17i	−0.371711	−	0.311902i	−0.809438	+	0.587205i	$0.800228\pi$
$558$		0			0
$559$	−6163.15	−	10674.9i	−0.466321	−	0.807692i
$560$		0			0
$561$	−95.2509	+	540.195i	−0.00716844	+	0.0406543i
$562$		0			0
$563$	−3076.06	+	5327.89i	−0.230267	+	0.398835i	−0.957887	−	0.287146i	$-0.907293\pi$
$563$	−3076.06	+	5327.89i	−0.230267	+	0.398835i	0.727619	+	0.685981i	$0.240627\pi$
$564$		0			0
$565$	−22842.0	−	8313.81i	−1.70083	−	0.619052i
$566$		0			0
$567$	12560.4	−	10539.5i	0.930316	−	0.780628i
$568$		0			0
$569$	19506.0			1.43714			0.718571	−	0.695453i	$-0.244796\pi$
$569$	19506.0			1.43714			0.718571	+	0.695453i	$0.244796\pi$
$570$		0			0
$571$	16435.2			1.20454			0.602268	−	0.798294i	$-0.294264\pi$
$571$	16435.2			1.20454			0.602268	+	0.798294i	$0.294264\pi$
$572$		0			0
$573$	−322.093	+	270.268i	−0.0234828	+	0.0197044i
$574$		0			0
$575$	4030.36	+	1466.93i	0.292309	+	0.106392i
$576$		0			0
$577$	4213.78	−	7298.47i	0.304024	−	0.526585i	−0.673020	−	0.739625i	$-0.735003\pi$
$577$	4213.78	−	7298.47i	0.304024	−	0.526585i	0.977044	+	0.213040i	$0.0683364\pi$
$578$		0			0
$579$	341.359	−	1935.95i	0.0245016	−	0.138955i
$580$		0			0
$581$	−5668.14	−	9817.50i	−0.404740	−	0.701030i
$582$		0			0
$583$	1246.10	+	1045.60i	0.0885219	+	0.0742787i
$584$		0			0
$585$	−22806.3	+	8300.83i	−1.61184	+	0.586662i
$586$		0			0
$587$	−1828.38	−	10369.3i	−0.128561	−	0.729106i	−0.979129	−	0.203241i	$-0.934853\pi$
$587$	−1828.38	−	10369.3i	−0.128561	−	0.729106i	0.850568	−	0.525865i	$-0.176258\pi$
$588$		0			0
$589$	−8084.22	+	23769.4i	−0.565543	+	1.66282i
$590$		0			0
$591$	203.547	+	1154.37i	0.0141672	+	0.0803459i
$592$		0			0
$593$	11969.6	−	4356.59i	0.828894	−	0.301693i	0.107489	−	0.994206i	$-0.465719\pi$
$593$	11969.6	−	4356.59i	0.828894	−	0.301693i	0.721405	+	0.692513i	$0.243497\pi$
$594$		0			0
$595$	21176.4	+	17769.2i	1.45908	+	1.22431i
$596$		0			0
$597$	871.670	+	1509.78i	0.0597573	+	0.103503i
$598$		0			0
$599$	−1877.26	+	10646.5i	−0.128051	+	0.726214i	0.851398	+	0.524521i	$0.175755\pi$
$599$	−1877.26	+	10646.5i	−0.128051	+	0.726214i	−0.979449	+	0.201693i	$0.935356\pi$
$600$		0			0
$601$	−1724.46	+	2986.85i	−0.117042	+	0.202722i	−0.918594	−	0.395202i	$-0.870675\pi$
$601$	−1724.46	+	2986.85i	−0.117042	+	0.202722i	0.801552	+	0.597925i	$0.204008\pi$
$602$		0			0
$603$	−2503.82	−	911.315i	−0.169093	−	0.0615450i
$604$		0			0
$605$	−11856.3	+	9948.58i	−0.796736	+	0.668541i
$606$		0			0
$607$	−8510.57			−0.569083			−0.284541	−	0.958664i	$-0.591841\pi$
$607$	−8510.57			−0.569083			−0.284541	+	0.958664i	$0.591841\pi$
$608$		0			0
$609$	1388.78			0.0924076
$610$		0			0
$611$	18045.5	−	15142.0i	1.19483	−	1.00258i
$612$		0			0
$613$	24494.5	+	8915.28i	1.61391	+	0.587414i	0.982207	−	0.187799i	$-0.0601354\pi$
$613$	24494.5	+	8915.28i	1.61391	+	0.587414i	0.631700	+	0.775213i	$0.282358\pi$
$614$		0			0
$615$	−1797.66	+	3113.64i	−0.117868	+	0.204153i
$616$		0			0
$617$	−3151.80	+	17874.7i	−0.205651	+	1.16630i	0.690761	+	0.723083i	$0.257276\pi$
$617$	−3151.80	+	17874.7i	−0.205651	+	1.16630i	−0.896412	+	0.443222i	$0.853835\pi$
$618$		0			0
$619$	−11181.3	−	19366.5i	−0.726030	−	1.25752i	−0.958549	−	0.284929i	$-0.908030\pi$
$619$	−11181.3	−	19366.5i	−0.726030	−	1.25752i	0.232519	−	0.972592i	$-0.425303\pi$
$620$		0			0
$621$	−3889.10	−	3263.34i	−0.251311	−	0.210875i
$622$		0			0
$623$	−6806.77	+	2477.46i	−0.437733	+	0.159322i
$624$		0			0
$625$	−3194.32	−	18115.9i	−0.204437	−	1.15942i
$626$		0			0
$627$	−474.214	−	73.2739i	−0.0302046	−	0.00466711i
$628$		0			0
$629$	1990.69	+	11289.8i	0.126191	+	0.715665i
$630$		0			0
$631$	19631.4	−	7145.24i	1.23853	−	0.450789i	0.362020	−	0.932170i	$-0.382087\pi$
$631$	19631.4	−	7145.24i	1.23853	−	0.450789i	0.876511	+	0.481382i	$0.159865\pi$
$632$		0			0
$633$	−748.766	−	628.290i	−0.0470155	−	0.0394507i
$634$		0			0
$635$	−14352.3	−	24858.9i	−0.896934	−	1.55354i
$636$		0			0
$637$	−2700.63	+	15316.1i	−0.167980	+	0.952660i
$638$		0			0
$639$	3924.90	−	6798.12i	0.242984	−	0.420860i
$640$		0			0
$641$	−11016.0	−	4009.48i	−0.678789	−	0.247059i	−0.0204616	−	0.999791i	$-0.506514\pi$
$641$	−11016.0	−	4009.48i	−0.678789	−	0.247059i	−0.658328	+	0.752732i	$0.728736\pi$
$642$		0			0
$643$	−16146.4	+	13548.4i	−0.990281	+	0.830945i	−0.985608	−	0.169044i	$-0.945932\pi$
$643$	−16146.4	+	13548.4i	−0.990281	+	0.830945i	−0.00467298	+	0.999989i	$0.501487\pi$
$644$		0			0
$645$	1321.24			0.0806570
$646$		0			0
$647$	−6266.71			−0.380788			−0.190394	−	0.981708i	$-0.560977\pi$
$647$	−6266.71			−0.380788			−0.190394	+	0.981708i	$0.560977\pi$
$648$		0			0
$649$	−1301.78	+	1092.32i	−0.0787355	+	0.0660669i
$650$		0			0
$651$	−4265.77	−	1552.61i	−0.256819	−	0.0934743i
$652$		0			0
$653$	−13548.7	+	23467.1i	−0.811950	+	1.40634i	0.0995479	+	0.995033i	$0.468260\pi$
$653$	−13548.7	+	23467.1i	−0.811950	+	1.40634i	−0.911498	+	0.411305i	$0.865073\pi$
$654$		0			0
$655$	5434.44	−	30820.2i	0.324185	−	1.83854i
$656$		0			0
$657$	−13413.1	−	23232.3i	−0.796494	−	1.37957i
$658$		0			0
$659$	6270.54	+	5261.60i	0.370661	+	0.311021i	0.809023	−	0.587777i	$-0.199997\pi$
$659$	6270.54	+	5261.60i	0.370661	+	0.311021i	−0.438362	+	0.898798i	$0.644441\pi$
$660$		0			0
$661$	−15790.3	+	5747.21i	−0.929156	+	0.338185i	−0.761875	−	0.647724i	$-0.775721\pi$
$661$	−15790.3	+	5747.21i	−0.929156	+	0.338185i	−0.167281	+	0.985909i	$0.553499\pi$
$662$		0			0
$663$	769.397	+	4363.47i	0.0450693	+	0.255600i
$664$		0			0
$665$	−15147.4	+	18850.5i	−0.883293	+	1.09924i
$666$		0			0
$667$	2398.58	+	13603.0i	0.139240	+	0.789671i
$668$		0			0
$669$	−159.686	+	58.1211i	−0.00922844	+	0.00335888i
$670$		0			0
$671$	2652.84	+	2226.00i	0.152626	+	0.128068i
$672$		0			0
$673$	4235.98	+	7336.94i	0.242623	+	0.420235i	0.961461	−	0.274943i	$-0.0886589\pi$
$673$	4235.98	+	7336.94i	0.242623	+	0.420235i	−0.718838	+	0.695178i	$0.755326\pi$
$674$		0			0
$675$	170.456	−	966.705i	0.00971980	−	0.0551237i
$676$		0			0
$677$	−12543.1	+	21725.3i	−0.712071	+	1.23334i	0.252008	+	0.967725i	$0.418909\pi$
$677$	−12543.1	+	21725.3i	−0.712071	+	1.23334i	−0.964079	+	0.265617i	$0.914424\pi$
$678$		0			0
$679$	16598.8	+	6041.48i	0.938152	+	0.341459i
$680$		0			0
$681$	−2924.96	+	2454.33i	−0.164588	+	0.138106i
$682$		0			0
$683$	−13096.2			−0.733691			−0.366846	−	0.930282i	$-0.619562\pi$
$683$	−13096.2			−0.733691			−0.366846	+	0.930282i	$0.619562\pi$
$684$		0			0
$685$	6184.12			0.344939
$686$		0			0
$687$	1724.18	−	1446.76i	0.0957517	−	0.0803452i
$688$		0			0
$689$	12347.2	+	4494.00i	0.682713	+	0.248487i
$690$		0			0
$691$	−10285.2	+	17814.5i	−0.566234	+	0.980746i	0.430700	+	0.902495i	$0.358267\pi$
$691$	−10285.2	+	17814.5i	−0.566234	+	0.980746i	−0.996934	+	0.0782504i	$0.975067\pi$
$692$		0			0
$693$	−990.552	+	5617.70i	−0.0542972	+	0.307935i
$694$		0			0
$695$	15737.2	+	27257.7i	0.858916	+	1.48769i
$696$		0			0
$697$	−33058.8	−	27739.6i	−1.79654	−	1.50748i
$698$		0			0
$699$	574.613	−	209.142i	0.0310928	−	0.0113168i
$700$		0			0
$701$	−2431.65	−	13790.6i	−0.131016	−	0.743027i	−0.977552	−	0.210696i	$-0.932427\pi$
$701$	−2431.65	−	13790.6i	−0.131016	−	0.743027i	0.846536	−	0.532331i	$-0.178684\pi$
$702$		0			0
$703$	−9836.88	+	1950.67i	−0.527746	+	0.104653i
$704$		0			0
$705$	438.464	+	2486.65i	0.0234234	+	0.132841i
$706$		0			0
$707$	−17561.4	+	6391.84i	−0.934180	+	0.340014i
$708$		0			0
$709$	17267.3	+	14489.0i	0.914653	+	0.767485i	0.972998	−	0.230812i	$-0.0741381\pi$
$709$	17267.3	+	14489.0i	0.914653	+	0.767485i	−0.0583455	+	0.998296i	$0.518583\pi$
$710$		0			0
$711$	−3114.91	−	5395.18i	−0.164301	−	0.284578i
$712$		0			0
$713$	7840.30	−	44464.5i	0.411811	−	2.33550i
$714$		0			0
$715$	4156.60	−	7199.43i	0.217410	−	0.376564i
$716$		0			0
$717$	3710.44	+	1350.49i	0.193262	+	0.0703416i
$718$		0			0
$719$	17868.2	−	14993.2i	0.926805	−	0.777682i	−0.0484360	−	0.998826i	$-0.515424\pi$
$719$	17868.2	−	14993.2i	0.926805	−	0.777682i	0.975241	+	0.221145i	$0.0709793\pi$
$720$		0			0
$721$	−3440.67			−0.177721
$722$		0			0
$723$	3157.37			0.162412
$724$		0			0
$725$	−2045.91	+	1716.72i	−0.104804	+	0.0879411i
$726$		0			0
$727$	−14596.5	−	5312.71i	−0.744644	−	0.271028i	−0.0582936	−	0.998299i	$-0.518566\pi$
$727$	−14596.5	−	5312.71i	−0.744644	−	0.271028i	−0.686350	+	0.727271i	$0.740788\pi$
$728$		0			0
$729$	8967.86	−	15532.8i	0.455615	−	0.789148i
$730$		0			0
$731$	−2753.90	+	15618.1i	−0.139339	+	0.790228i
$732$		0			0
$733$	5231.51	+	9061.25i	0.263616	+	0.456596i	0.967200	−	0.254016i	$-0.0817516\pi$
$733$	5231.51	+	9061.25i	0.263616	+	0.456596i	−0.703584	+	0.710612i	$0.748418\pi$
$734$		0			0
$735$	−1277.02	−	1071.55i	−0.0640866	−	0.0537750i
$736$		0			0
$737$	857.631	−	312.152i	0.0428647	−	0.0156015i
$738$		0			0
$739$	−1398.55	−	7931.56i	−0.0696163	−	0.394814i	−0.999628	−	0.0272831i	$-0.991314\pi$
$739$	−1398.55	−	7931.56i	−0.0696163	−	0.394814i	0.930011	−	0.367531i	$-0.119797\pi$
$740$		0			0
$741$	−3801.93	+	753.928i	−0.188485	+	0.0373768i
$742$		0			0
$743$	241.941	+	1372.12i	0.0119461	+	0.0677498i	0.990198	−	0.139671i	$-0.0446043\pi$
$743$	241.941	+	1372.12i	0.0119461	+	0.0677498i	−0.978252	+	0.207420i	$0.933493\pi$
$744$		0			0
$745$	−1613.87	+	587.400i	−0.0793659	+	0.0288868i
$746$		0			0
$747$	−9809.33	−	8231.01i	−0.480461	−	0.403155i
$748$		0			0
$749$	−538.276	−	932.322i	−0.0262593	−	0.0454824i
$750$		0			0
$751$	−66.9282	+	379.569i	−0.00325199	+	0.0184430i	−0.986391	−	0.164419i	$-0.947425\pi$
$751$	−66.9282	+	379.569i	−0.00325199	+	0.0184430i	0.983139	+	0.182862i	$0.0585362\pi$
$752$		0			0
$753$	−1159.21	+	2007.81i	−0.0561010	+	0.0971698i
$754$		0			0
$755$	26022.5	+	9471.42i	1.25438	+	0.456557i
$756$		0			0
$757$	21534.8	−	18069.8i	1.03394	−	0.867582i	0.0426294	−	0.999091i	$-0.486427\pi$
$757$	21534.8	−	18069.8i	1.03394	−	0.867582i	0.991315	+	0.131509i	$0.0419821\pi$
$758$		0			0
$759$	862.923			0.0412676
$760$		0			0
$761$	34065.9			1.62272			0.811359	−	0.584549i	$-0.198728\pi$
$761$	34065.9			1.62272			0.811359	+	0.584549i	$0.198728\pi$
$762$		0			0
$763$	16368.6	−	13734.9i	0.776650	−	0.651687i
$764$		0			0
$765$	29342.7	+	10679.9i	1.38678	+	0.504747i
$766$		0			0
$767$	−6863.33	+	11887.6i	−0.323104	+	0.559632i
$768$		0			0
$769$	−2215.11	+	12562.5i	−0.103874	+	0.589098i	0.887790	+	0.460248i	$0.152240\pi$
$769$	−2215.11	+	12562.5i	−0.103874	+	0.589098i	−0.991664	+	0.128850i	$0.958871\pi$
$770$		0			0
$771$	−1607.86	−	2784.90i	−0.0751047	−	0.130085i
$772$		0			0
$773$	−16855.2	−	14143.2i	−0.784271	−	0.658081i	0.160050	−	0.987109i	$-0.448835\pi$
$773$	−16855.2	−	14143.2i	−0.784271	−	0.658081i	−0.944320	+	0.329028i	$0.893279\pi$
$774$		0			0
$775$	8203.44	−	2985.81i	0.380227	−	0.138391i
$776$		0			0
$777$	−314.867	−	1785.70i	−0.0145377	−	0.0824474i
$778$		0			0
$779$	23646.7	−	29427.7i	1.08759	−	1.35348i
$780$		0			0
$781$	466.903	+	2647.94i	0.0213919	+	0.121320i
$782$		0			0
$783$	2970.67	−	1081.24i	0.135585	−	0.0493489i
$784$		0			0
$785$	8206.43	+	6886.01i	0.373121	+	0.313086i
$786$		0			0
$787$	−10362.7	−	17948.8i	−0.469367	−	0.812968i	0.530020	−	0.847985i	$-0.322185\pi$
$787$	−10362.7	−	17948.8i	−0.469367	−	0.812968i	−0.999387	+	0.0350177i	$0.988851\pi$
$788$		0			0
$789$	400.469	−	2271.17i	0.0180698	−	0.102479i
$790$		0			0
$791$	−23074.7	+	39966.6i	−1.03722	+	1.79652i
$792$		0			0
$793$	26286.0	+	9567.33i	1.17711	+	0.428431i
$794$		0			0
$795$	−1078.91	+	905.310i	−0.0481319	+	0.0403874i
$796$		0			0
$797$	−35388.8			−1.57282			−0.786409	−	0.617706i	$-0.788062\pi$
$797$	−35388.8			−1.57282			−0.786409	+	0.617706i	$0.788062\pi$
$798$		0			0
$799$	−30308.1			−1.34196
$800$		0			0
$801$	−6267.93	+	5259.42i	−0.276488	+	0.232001i
$802$		0			0
$803$	8634.64	+	3142.75i	0.379464	+	0.138114i
$804$		0			0
$805$	21744.1	−	37662.0i	0.952026	−	1.64896i
$806$		0			0
$807$	918.827	−	5210.93i	0.0400796	−	0.227303i
$808$		0			0
$809$	10512.7	+	18208.6i	0.456871	+	0.791323i	0.998794	−	0.0491048i	$-0.0156368\pi$
$809$	10512.7	+	18208.6i	0.456871	+	0.791323i	−0.541923	+	0.840428i	$0.682304\pi$
$810$		0			0
$811$	34953.2	+	29329.2i	1.51341	+	1.26990i	0.856781	+	0.515680i	$0.172461\pi$
$811$	34953.2	+	29329.2i	1.51341	+	1.26990i	0.656624	+	0.754218i	$0.271984\pi$
$812$		0			0
$813$	3141.01	−	1143.23i	0.135498	−	0.0493173i
$814$		0			0
$815$	−4953.96	−	28095.3i	−0.212920	−	1.20753i
$816$		0			0
$817$	−13710.5	−	2118.49i	−0.587110	−	0.0907182i
$818$		0			0
$819$	8001.27	+	45377.4i	0.341376	+	1.93604i
$820$		0			0
$821$	−20725.4	+	7543.43i	−0.881025	+	0.320667i	−0.742623	−	0.669709i	$-0.766419\pi$
$821$	−20725.4	+	7543.43i	−0.881025	+	0.320667i	−0.138401	+	0.990376i	$0.544196\pi$
$822$		0			0
$823$	−20648.1	−	17325.8i	−0.874541	−	0.733827i	0.0905079	−	0.995896i	$-0.471151\pi$
$823$	−20648.1	−	17325.8i	−0.874541	−	0.733827i	−0.965049	+	0.262068i	$0.915595\pi$
$824$		0			0
$825$	83.4238	+	144.494i	0.00352054	+	0.00609775i
$826$		0			0
$827$	6215.01	−	35247.1i	0.261327	−	1.48206i	−0.517968	−	0.855400i	$-0.673311\pi$
$827$	6215.01	−	35247.1i	0.261327	−	1.48206i	0.779295	−	0.626657i	$-0.215577\pi$
$828$		0			0
$829$	20246.0	−	35067.1i	0.848217	−	1.46915i	−0.0345809	−	0.999402i	$-0.511010\pi$
$829$	20246.0	−	35067.1i	0.848217	−	1.46915i	0.882798	−	0.469753i	$-0.155657\pi$
$830$		0			0
$831$	1915.21	+	697.080i	0.0799494	+	0.0290992i
$832$		0			0
$833$	15328.3	−	12862.0i	0.637567	−	0.534983i
$834$		0			0
$835$	−36482.4			−1.51201
$836$		0			0
$837$	−10333.5			−0.426736
$838$		0			0
$839$	10951.5	−	9189.37i	0.450639	−	0.378131i	−0.389034	−	0.921224i	$-0.627191\pi$
$839$	10951.5	−	9189.37i	0.450639	−	0.378131i	0.839673	+	0.543092i	$0.182747\pi$
$840$		0			0
$841$	14835.7	+	5399.76i	0.608295	+	0.221401i
$842$		0			0
$843$	681.869	−	1181.03i	0.0278586	−	0.0482525i
$844$		0			0
$845$	6929.32	−	39298.1i	0.282102	−	1.59988i
$846$		0			0
$847$	14692.0	+	25447.4i	0.596015	+	1.03233i
$848$		0			0
$849$	−91.4277	−	76.7169i	−0.00369586	−	0.00310120i
$850$		0			0
$851$	16947.0	−	6168.21i	0.682651	−	0.248465i
$852$		0			0
$853$	2536.26	+	14383.8i	0.101805	+	0.577366i	0.992448	+	0.122663i	$0.0391434\pi$
$853$	2536.26	+	14383.8i	0.101805	+	0.577366i	−0.890643	+	0.454703i	$0.849745\pi$
$854$		0			0
$855$	−8795.56	+	25860.9i	−0.351815	+	1.03442i
$856$		0			0
$857$	−2686.51	−	15235.9i	−0.107082	−	0.607293i	−0.990368	−	0.138458i	$-0.955785\pi$
$857$	−2686.51	−	15235.9i	−0.107082	−	0.607293i	0.883286	−	0.468834i	$-0.155326\pi$
$858$		0			0
$859$	−18339.2	+	6674.93i	−0.728435	+	0.265129i	−0.679502	−	0.733673i	$-0.737804\pi$
$859$	−18339.2	+	6674.93i	−0.728435	+	0.265129i	−0.0489329	+	0.998802i	$0.515582\pi$
$860$		0			0
$861$	5228.89	+	4387.56i	0.206969	+	0.173668i
$862$		0			0
$863$	−6228.93	−	10788.8i	−0.245696	−	0.425557i	0.716631	−	0.697452i	$-0.245683\pi$
$863$	−6228.93	−	10788.8i	−0.245696	−	0.425557i	−0.962327	+	0.271895i	$0.912350\pi$
$864$		0			0
$865$	−9361.92	+	53094.1i	−0.367994	+	2.08700i
$866$		0			0
$867$	1287.98	−	2230.84i	0.0504521	−	0.0873857i
$868$		0			0
$869$	2005.21	+	729.835i	0.0782761	+	0.0284902i
$870$		0			0
$871$	5647.42	−	4738.75i	0.219696	−	0.184347i
$872$		0			0
$873$	19952.9			0.773545
$874$		0			0
$875$	−28090.2			−1.08528
$876$		0			0
$877$	−4234.83	+	3553.44i	−0.163056	+	0.136820i	−0.720665	−	0.693284i	$-0.756163\pi$
$877$	−4234.83	+	3553.44i	−0.163056	+	0.136820i	0.557609	+	0.830104i	$0.311719\pi$
$878$		0			0
$879$	−2888.25	−	1051.24i	−0.110828	−	0.0403382i
$880$		0			0
$881$	−13812.6	+	23924.1i	−0.528215	+	0.914896i	0.471244	+	0.882003i	$0.343805\pi$
$881$	−13812.6	+	23924.1i	−0.528215	+	0.914896i	−0.999459	+	0.0328926i	$0.989528\pi$
$882$		0			0
$883$	−2196.33	+	12456.0i	−0.0837061	+	0.474721i	0.913922	+	0.405889i	$0.133038\pi$
$883$	−2196.33	+	12456.0i	−0.0837061	+	0.474721i	−0.997628	+	0.0688314i	$0.978073\pi$
$884$		0			0
$885$	−735.671	−	1274.22i	−0.0279427	−	0.0483982i
$886$		0			0
$887$	6132.26	+	5145.57i	0.232132	+	0.194782i	0.751433	−	0.659810i	$-0.229363\pi$
$887$	6132.26	+	5145.57i	0.232132	+	0.194782i	−0.519301	+	0.854592i	$0.673808\pi$
$888$		0			0
$889$	−51210.1	+	18639.0i	−1.93198	+	0.703184i
$890$		0			0
$891$	1101.63	+	6247.63i	0.0414207	+	0.234909i
$892$		0			0
$893$	−562.796	−	26507.0i	−0.0210899	−	0.993306i
$894$		0			0
$895$	−60.4808	−	343.004i	−0.00225883	−	0.0128104i
$896$		0			0
$897$	6549.97	−	2384.00i	0.243810	−	0.0887394i
$898$		0			0
$899$	21537.2	+	18071.9i	0.799007	+	0.670446i
$900$		0			0
$901$	−8452.70	−	14640.5i	−0.312542	−	0.541338i
$902$		0			0
$903$	435.583	−	2470.31i	0.0160524	−	0.0910374i
$904$		0			0
$905$	4769.98	−	8261.86i	0.175204	−	0.303462i
$906$		0			0
$907$	−36211.6	−	13180.0i	−1.32567	−	0.482506i	−0.420403	−	0.907338i	$-0.638111\pi$
$907$	−36211.6	−	13180.0i	−1.32567	−	0.482506i	−0.905272	+	0.424831i	$0.860333\pi$
$908$		0			0
$909$	−16171.2	+	13569.3i	−0.590061	+	0.495120i
$910$		0			0
$911$	−11245.9			−0.408994			−0.204497	−	0.978867i	$-0.565556\pi$
$911$	−11245.9			−0.408994			−0.204497	+	0.978867i	$0.565556\pi$
$912$		0			0
$913$	4386.15			0.158993
$914$		0			0
$915$	−2296.90	+	1927.33i	−0.0829870	+	0.0696344i
$916$		0			0
$917$	−55832.7	−	20321.5i	−2.01064	−	0.731814i
$918$		0			0
$919$	−5725.98	+	9917.68i	−0.205531	+	0.355989i	−0.950302	−	0.311331i	$-0.899225\pi$
$919$	−5725.98	+	9917.68i	−0.205531	+	0.355989i	0.744771	+	0.667320i	$0.232559\pi$
$920$		0			0
$921$	−279.104	+	1582.88i	−0.00998567	+	0.0566315i
$922$		0			0
$923$	10859.4	+	18809.1i	0.387262	+	0.670757i
$924$		0			0
$925$	2671.22	+	2241.42i	0.0949504	+	0.0796728i
$926$		0			0
$927$	−3652.10	+	1329.26i	−0.129397	+	0.0470966i
$928$		0			0
$929$	2123.93	+	12045.4i	0.0750097	+	0.425401i	0.999069	+	0.0431510i	$0.0137397\pi$
$929$	2123.93	+	12045.4i	0.0750097	+	0.425401i	−0.924059	+	0.382250i	$0.875149\pi$
$930$		0			0
$931$	11533.5	+	13167.0i	0.406009	+	0.463514i
$932$		0			0
$933$	231.840	+	1314.83i	0.00813517	+	0.0461368i
$934$		0			0
$935$	−10050.7	+	3658.17i	−0.351545	+	0.127952i
$936$		0			0
$937$	4357.59	+	3656.45i	0.151928	+	0.127482i	0.715583	−	0.698527i	$-0.246161\pi$
$937$	4357.59	+	3656.45i	0.151928	+	0.127482i	−0.563656	+	0.826010i	$0.690605\pi$
$938$		0			0
$939$	−949.346	−	1644.32i	−0.0329933	−	0.0571461i
$940$		0			0
$941$	4735.31	−	26855.3i	0.164046	−	0.930348i	−0.785998	−	0.618230i	$-0.787850\pi$
$941$	4735.31	−	26855.3i	0.164046	−	0.930348i	0.950043	−	0.312119i	$-0.101039\pi$
$942$		0			0
$943$	−33945.0	+	58794.5i	−1.17222	+	2.03034i
$944$		0			0
$945$	−9352.83	−	3404.15i	−0.321955	−	0.117182i
$946$		0			0
$947$	−29576.2	+	24817.4i	−1.01489	+	0.851590i	−0.988976	−	0.148074i	$-0.952693\pi$
$947$	−29576.2	+	24817.4i	−1.01489	+	0.851590i	−0.0259095	+	0.999664i	$0.508248\pi$
$948$		0			0
$949$	74223.2			2.53887
$950$		0			0
$951$	−2822.75			−0.0962502
$952$		0			0
$953$	−2823.61	+	2369.29i	−0.0959766	+	0.0805339i	−0.689513	−	0.724273i	$-0.742176\pi$
$953$	−2823.61	+	2369.29i	−0.0959766	+	0.0805339i	0.593537	+	0.804807i	$0.297731\pi$
$954$		0			0
$955$	−7704.18	−	2804.09i	−0.261048	−	0.0950139i
$956$		0			0
$957$	−268.668	+	465.347i	−0.00907503	+	0.0157184i
$958$		0			0
$959$	2038.76	−	11562.4i	0.0686498	−	0.389332i
$960$		0			0
$961$	−31054.4	−	53787.8i	−1.04241	−	1.80551i
$962$		0			0
$963$	−931.545	−	781.659i	−0.0311720	−	0.0261564i
$964$		0			0
$965$	36019.7	−	13110.1i	1.20157	−	0.437336i
$966$		0			0
$967$	915.089	+	5189.73i	0.0304315	+	0.172586i	0.996236	−	0.0866874i	$-0.0276281\pi$
$967$	915.089	+	5189.73i	0.0304315	+	0.172586i	−0.965804	+	0.259273i	$0.916517\pi$
$968$		0			0
$969$	4370.67	+	2401.17i	0.144898	+	0.0796045i
$970$		0			0
$971$	−5887.22	−	33388.1i	−0.194573	−	1.10348i	−0.913026	−	0.407901i	$-0.866261\pi$
$971$	−5887.22	−	33388.1i	−0.194573	−	1.10348i	0.718454	−	0.695575i	$-0.244850\pi$
$972$		0			0
$973$	56151.7	−	20437.5i	1.85009	−	0.673378i
$974$		0			0
$975$	1032.42	+	866.302i	0.0339116	+	0.0284552i
$976$		0			0
$977$	10015.5	+	17347.3i	0.327967	+	0.568055i	0.982108	−	0.188317i	$-0.0603032\pi$
$977$	10015.5	+	17347.3i	0.327967	+	0.568055i	−0.654141	+	0.756372i	$0.726970\pi$
$978$		0			0
$979$	486.674	−	2760.07i	0.0158878	−	0.0901043i
$980$		0			0
$981$	12068.2	−	20902.8i	0.392771	−	0.680300i
$982$		0			0
$983$	−32009.3	−	11650.4i	−1.03859	−	0.378017i	−0.234247	−	0.972177i	$-0.575263\pi$
$983$	−32009.3	−	11650.4i	−1.03859	−	0.378017i	−0.804347	+	0.594160i	$0.797485\pi$
$984$		0			0
$985$	−17509.0	+	14691.8i	−0.566378	+	0.475247i
$986$		0			0
$987$	4793.83			0.154599
$988$		0			0
$989$	24948.8			0.802151
$990$		0			0
$991$	37860.1	−	31768.4i	1.21359	−	1.01832i	0.214454	−	0.976734i	$-0.431203\pi$
$991$	37860.1	−	31768.4i	1.21359	−	1.01832i	0.999135	−	0.0415878i	$-0.0132416\pi$
$992$		0			0
$993$	−2010.18	−	731.647i	−0.0642409	−	0.0233818i
$994$		0			0
$995$	−16996.7	+	29439.2i	−0.541540	+	0.937975i
$996$		0			0
$997$	−8730.95	+	49515.7i	−0.277344	+	1.57290i	0.454073	+	0.890964i	$0.349971\pi$
$997$	−8730.95	+	49515.7i	−0.277344	+	1.57290i	−0.731417	+	0.681931i	$0.761141\pi$
$998$		0			0
$999$	−2063.77	−	3574.56i	−0.0653603	−	0.113207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.i.a.9.3	✓	30
19.6	even	9		1444.4.a.j.1.8		15
19.13	odd	18		1444.4.a.k.1.8		15
19.17	even	9	inner	76.4.i.a.17.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.i.a.9.3	✓	30	1.1	even	1	trivial
76.4.i.a.17.3	yes	30	19.17	even	9	inner
1444.4.a.j.1.8		15	19.6	even	9
1444.4.a.k.1.8		15	19.13	odd	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.487209 + 0.408817i) q^{3} +(-11.6536 - 4.24157i) q^{5} +(-11.7723 + 20.3903i) q^{7} +(-4.61826 + 26.1915i) q^{9} +O(q^{10})\)	\(q+(-0.487209 + 0.408817i) q^{3} +(-11.6536 - 4.24157i) q^{5} +(-11.7723 + 20.3903i) q^{7} +(-4.61826 + 26.1915i) q^{9} +(-4.55487 - 7.88927i) q^{11} +(-56.3691 - 47.2993i) q^{13} +(7.41177 - 2.69766i) q^{15} +(16.4400 + 93.2359i) q^{17} +(-81.2372 + 16.1095i) q^{19} +(-2.60031 - 14.7471i) q^{21} +(139.956 - 50.9397i) q^{23} +(22.0601 + 18.5106i) q^{25} +(-17.0435 - 29.5203i) q^{27} +(-16.1046 + 91.3335i) q^{29} +(151.575 - 262.535i) q^{31} +(5.44444 + 1.98161i) q^{33} +(223.677 - 187.687i) q^{35} +121.088 q^{37} +46.8003 q^{39} +(-349.185 + 293.001i) q^{41} +(157.410 + 57.2924i) q^{43} +(164.912 - 285.636i) q^{45} +(-55.5902 + 315.267i) q^{47} +(-105.676 - 183.037i) q^{49} +(-46.1261 - 38.7044i) q^{51} +(-167.795 + 61.0725i) q^{53} +(19.6178 + 111.258i) q^{55} +(32.9937 - 41.0598i) q^{57} +(-32.3928 - 183.708i) q^{59} +(-357.222 + 130.018i) q^{61} +(-479.684 - 402.503i) q^{63} +(456.280 + 790.301i) q^{65} +(-17.3972 + 98.6644i) q^{67} +(-47.3627 + 82.0346i) q^{69} +(-277.355 - 100.949i) q^{71} +(-772.692 + 648.366i) q^{73} -18.3153 q^{75} +214.486 q^{77} +(-179.441 + 150.569i) q^{79} +(-654.401 - 238.182i) q^{81} +(-240.739 + 416.973i) q^{83} +(203.881 - 1156.27i) q^{85} +(-29.4924 - 51.0824i) q^{87} +(235.676 + 197.756i) q^{89} +(1628.04 - 592.560i) q^{91} +(33.4803 + 189.876i) q^{93} +(1015.04 + 156.840i) q^{95} +(-130.277 - 738.840i) q^{97} +(227.667 - 82.8640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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