LMFDB - Embedded newform 252.4.bm.a.173.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (of order $6$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.9
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46664 - 4.98488i) q^{3} -2.27383 q^{5} +(17.2174 + 6.82357i) q^{7} +(-22.6980 + 14.6220i) q^{9} +O(q^{10})$	\(q+(-1.46664 - 4.98488i) q^{3} -2.27383 q^{5} +(17.2174 + 6.82357i) q^{7} +(-22.6980 + 14.6220i) q^{9} -35.8853i q^{11} +(70.2337 - 40.5494i) q^{13} +(3.33487 + 11.3347i) q^{15} +(-25.8458 - 44.7662i) q^{17} +(-9.61456 - 5.55097i) q^{19} +(8.76302 - 95.8343i) q^{21} +30.5607i q^{23} -119.830 q^{25} +(106.178 + 91.7014i) q^{27} +(-167.883 - 96.9271i) q^{29} +(-162.817 - 94.0025i) q^{31} +(-178.884 + 52.6306i) q^{33} +(-39.1494 - 15.5156i) q^{35} +(25.3619 - 43.9281i) q^{37} +(-305.141 - 290.635i) q^{39} +(-151.024 - 261.582i) q^{41} +(28.1579 - 48.7709i) q^{43} +(51.6112 - 33.2479i) q^{45} +(-54.1374 - 93.7687i) q^{47} +(249.878 + 234.968i) q^{49} +(-185.248 + 194.494i) q^{51} +(548.106 - 316.449i) q^{53} +81.5969i q^{55} +(-13.5698 + 56.0686i) q^{57} +(-343.355 + 594.708i) q^{59} +(340.820 - 196.773i) q^{61} +(-490.574 + 96.8714i) q^{63} +(-159.699 + 92.2024i) q^{65} +(-9.43901 + 16.3488i) q^{67} +(152.341 - 44.8214i) q^{69} -1116.45i q^{71} +(458.520 - 264.726i) q^{73} +(175.746 + 597.336i) q^{75} +(244.866 - 617.851i) q^{77} +(-231.785 - 401.464i) q^{79} +(301.395 - 663.779i) q^{81} +(-212.584 + 368.205i) q^{83} +(58.7688 + 101.791i) q^{85} +(-236.947 + 979.031i) q^{87} +(-74.5855 + 129.186i) q^{89} +(1485.93 - 218.911i) q^{91} +(-229.797 + 949.490i) q^{93} +(21.8618 + 12.6219i) q^{95} +(1059.18 + 611.519i) q^{97} +(524.714 + 814.523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.46664	−	4.98488i	−0.282254	−	0.959340i
$3$	−1.46664	−	4.98488i	−0.282254	−	0.959340i
$4$		0			0
$5$	−2.27383			−0.203377			−0.101689	−	0.994816i	$-0.532425\pi$
$5$	−2.27383			−0.203377			−0.101689	+	0.994816i	$0.532425\pi$
$6$		0			0
$7$	17.2174	+	6.82357i	0.929652	+	0.368438i
$7$	17.2174	+	6.82357i	0.929652	+	0.368438i
$8$		0			0
$9$	−22.6980	+	14.6220i	−0.840665	+	0.541555i
$10$		0			0
$11$		−	35.8853i		−	0.983620i	−0.870702	−	0.491810i	$-0.836335\pi$
$11$		−	35.8853i		−	0.983620i	0.870702	−	0.491810i	$-0.163665\pi$
$12$		0			0
$13$	70.2337	−	40.5494i	1.49841	−	0.865107i	0.498411	−	0.866941i	$-0.333917\pi$
$13$	70.2337	−	40.5494i	1.49841	−	0.865107i	0.999998	+	0.00183406i	$0.000583799\pi$
$14$		0			0
$15$	3.33487	+	11.3347i	0.0574040	+	0.195108i
$16$		0			0
$17$	−25.8458	−	44.7662i	−0.368737	−	0.638670i	0.620632	−	0.784102i	$-0.286876\pi$
$17$	−25.8458	−	44.7662i	−0.368737	−	0.638670i	−0.989368	+	0.145432i	$0.953543\pi$
$18$		0			0
$19$	−9.61456	−	5.55097i	−0.116091	−	0.0670252i	0.440830	−	0.897591i	$-0.354684\pi$
$19$	−9.61456	−	5.55097i	−0.116091	−	0.0670252i	−0.556921	+	0.830565i	$0.688017\pi$
$20$		0			0
$21$	8.76302	−	95.8343i	0.0910594	−	0.995845i
$22$		0			0
$23$			30.5607i			0.277059i	0.990358	+	0.138529i	$0.0442375\pi$
$23$			30.5607i			0.277059i	−0.990358	+	0.138529i	$0.955762\pi$
$24$		0			0
$25$	−119.830			−0.958638
$26$		0			0
$27$	106.178	+	91.7014i	0.756816	+	0.653627i
$28$		0			0
$29$	−167.883	−	96.9271i	−1.07500	−	0.620652i	−0.145457	−	0.989365i	$-0.546465\pi$
$29$	−167.883	−	96.9271i	−1.07500	−	0.620652i	−0.929543	+	0.368713i	$0.879799\pi$
$30$		0			0
$31$	−162.817	−	94.0025i	−0.943317	−	0.544624i	−0.0523183	−	0.998630i	$-0.516661\pi$
$31$	−162.817	−	94.0025i	−0.943317	−	0.544624i	−0.890998	+	0.454006i	$0.849994\pi$
$32$		0			0
$33$	−178.884	+	52.6306i	−0.943626	+	0.277631i
$34$		0			0
$35$	−39.1494	−	15.5156i	−0.189070	−	0.0749319i
$36$		0			0
$37$	25.3619	−	43.9281i	0.112688	−	0.195182i	−0.804165	−	0.594406i	$-0.797387\pi$
$37$	25.3619	−	43.9281i	0.112688	−	0.195182i	0.916853	+	0.399224i	$0.130720\pi$
$38$		0			0
$39$	−305.141	−	290.635i	−1.25286	−	1.19330i
$40$		0			0
$41$	−151.024	−	261.582i	−0.575269	−	0.996396i	−0.996012	−	0.0892157i	$-0.971564\pi$
$41$	−151.024	−	261.582i	−0.575269	−	0.996396i	0.420743	−	0.907180i	$-0.361769\pi$
$42$		0			0
$43$	28.1579	−	48.7709i	0.0998613	−	0.172965i	−0.811766	−	0.583983i	$-0.801493\pi$
$43$	28.1579	−	48.7709i	0.0998613	−	0.172965i	0.911627	+	0.411018i	$0.134827\pi$
$44$		0			0
$45$	51.6112	−	33.2479i	0.170972	−	0.110140i
$46$		0			0
$47$	−54.1374	−	93.7687i	−0.168016	−	0.291012i	0.769706	−	0.638398i	$-0.220403\pi$
$47$	−54.1374	−	93.7687i	−0.168016	−	0.291012i	−0.937722	+	0.347386i	$0.887069\pi$
$48$		0			0
$49$	249.878	+	234.968i	0.728506	+	0.685039i
$50$		0			0
$51$	−185.248	+	194.494i	−0.508625	+	0.534011i
$52$		0			0
$53$	548.106	−	316.449i	1.42053	−	0.820145i	0.424188	−	0.905574i	$-0.360560\pi$
$53$	548.106	−	316.449i	1.42053	−	0.820145i	0.996344	+	0.0854295i	$0.0272262\pi$
$54$		0			0
$55$			81.5969i			0.200046i
$56$		0			0
$57$	−13.5698	+	56.0686i	−0.0315328	+	0.130289i
$58$		0			0
$59$	−343.355	+	594.708i	−0.757644	+	1.31228i	0.186405	+	0.982473i	$0.440316\pi$
$59$	−343.355	+	594.708i	−0.757644	+	1.31228i	−0.944049	+	0.329805i	$0.893017\pi$
$60$		0			0
$61$	340.820	−	196.773i	0.715370	−	0.413019i	−0.0976763	−	0.995218i	$-0.531141\pi$
$61$	340.820	−	196.773i	0.715370	−	0.413019i	0.813046	+	0.582199i	$0.197808\pi$
$62$		0			0
$63$	−490.574	+	96.8714i	−0.981056	+	0.193725i
$64$		0			0
$65$	−159.699	+	92.2024i	−0.304742	+	0.175943i
$66$		0			0
$67$	−9.43901	+	16.3488i	−0.0172113	+	0.0298109i	−0.874503	−	0.485020i	$-0.838812\pi$
$67$	−9.43901	+	16.3488i	−0.0172113	+	0.0298109i	0.857291	+	0.514831i	$0.172145\pi$
$68$		0			0
$69$	152.341	−	44.8214i	0.265793	−	0.0782010i
$70$		0			0
$71$		−	1116.45i		−	1.86618i	−0.359649	−	0.933088i	$-0.617103\pi$
$71$		−	1116.45i		−	1.86618i	0.359649	−	0.933088i	$-0.382897\pi$
$72$		0			0
$73$	458.520	−	264.726i	0.735146	−	0.424437i	−0.0851557	−	0.996368i	$-0.527139\pi$
$73$	458.520	−	264.726i	0.735146	−	0.424437i	0.820302	+	0.571931i	$0.193805\pi$
$74$		0			0
$75$	175.746	+	597.336i	0.270579	+	0.919659i
$76$		0			0
$77$	244.866	−	617.851i	0.362403	−	0.914425i
$78$		0			0
$79$	−231.785	−	401.464i	−0.330100	−	0.571749i	0.652432	−	0.757848i	$-0.273749\pi$
$79$	−231.785	−	401.464i	−0.330100	−	0.571749i	−0.982531	+	0.186098i	$0.940416\pi$
$80$		0			0
$81$	301.395	−	663.779i	0.413436	−	0.910533i
$82$		0			0
$83$	−212.584	+	368.205i	−0.281133	+	0.486937i	−0.971664	−	0.236366i	$-0.924044\pi$
$83$	−212.584	+	368.205i	−0.281133	+	0.486937i	0.690531	+	0.723303i	$0.257377\pi$
$84$		0			0
$85$	58.7688	+	101.791i	0.0749926	+	0.129891i
$86$		0			0
$87$	−236.947	+	979.031i	−0.291993	+	1.20647i
$88$		0			0
$89$	−74.5855	+	129.186i	−0.0888320	+	0.153862i	−0.907018	−	0.421093i	$-0.861647\pi$
$89$	−74.5855	+	129.186i	−0.0888320	+	0.153862i	0.818186	+	0.574954i	$0.194980\pi$
$90$		0			0
$91$	1485.93	−	218.911i	1.71174	−	0.252177i
$92$		0			0
$93$	−229.797	+	949.490i	−0.256225	+	1.05868i
$94$		0			0
$95$	21.8618	+	12.6219i	0.0236103	+	0.0136314i
$96$		0			0
$97$	1059.18	+	611.519i	1.10870	+	0.640106i	0.938491	−	0.345302i	$-0.112224\pi$
$97$	1059.18	+	611.519i	1.10870	+	0.640106i	0.170205	+	0.985409i	$0.445557\pi$
$98$		0			0
$99$	524.714	+	814.523i	0.532684	+	0.826895i
$100$		0			0
$101$	123.959			0.122123			0.0610614	−	0.998134i	$-0.480551\pi$
$101$	123.959			0.122123			0.0610614	+	0.998134i	$0.480551\pi$
$102$		0			0
$103$			1762.40i			1.68597i	0.537941	+	0.842983i	$0.319202\pi$
$103$			1762.40i			1.68597i	−0.537941	+	0.842983i	$0.680798\pi$
$104$		0			0
$105$	−19.9256	+	217.910i	−0.0185194	+	0.202532i
$106$		0			0
$107$	−1378.50	−	795.876i	−1.24546	−	0.719068i	−0.275261	−	0.961369i	$-0.588764\pi$
$107$	−1378.50	−	795.876i	−1.24546	−	0.719068i	−0.970201	+	0.242301i	$0.922098\pi$
$108$		0			0
$109$	304.355	+	527.159i	0.267449	+	0.463236i	0.968202	−	0.250168i	$-0.0804859\pi$
$109$	304.355	+	527.159i	0.267449	+	0.463236i	−0.700753	+	0.713404i	$0.747153\pi$
$110$		0			0
$111$	−256.173	−	61.9994i	−0.219053	−	0.0530155i
$112$		0			0
$113$	207.921	−	120.043i	0.173093	−	0.0999354i	−0.410950	−	0.911658i	$-0.634803\pi$
$113$	207.921	−	120.043i	0.173093	−	0.0999354i	0.584044	+	0.811722i	$0.301470\pi$
$114$		0			0
$115$		−	69.4898i		−	0.0563474i
$116$		0			0
$117$	−1001.25	+	1947.35i	−0.791158	+	1.53874i
$118$		0			0
$119$	−139.532	−	947.118i	−0.107486	−	0.729598i
$120$		0			0
$121$	43.2460			0.0324914
$122$		0			0
$123$	−1082.46	+	1136.48i	−0.793510	+	0.833115i
$124$		0			0
$125$	556.700			0.398342
$126$		0			0
$127$	2223.59			1.55364			0.776819	−	0.629724i	$-0.216832\pi$
$127$	2223.59			1.55364			0.776819	+	0.629724i	$0.216832\pi$
$128$		0			0
$129$	−284.414	−	68.8344i	−0.194118	−	0.0469809i
$130$		0			0
$131$	567.320			0.378374			0.189187	−	0.981941i	$-0.439415\pi$
$131$	567.320			0.378374			0.189187	+	0.981941i	$0.439415\pi$
$132$		0			0
$133$	−127.660	−	161.179i	−0.0832297	−	0.105083i
$134$		0			0
$135$	−241.431	−	208.513i	−0.153919	−	0.132933i
$136$		0			0
$137$		−	307.624i		−	0.191840i	−0.995389	−	0.0959201i	$-0.969421\pi$
$137$		−	307.624i		−	0.191840i	0.995389	−	0.0959201i	$-0.0305793\pi$
$138$		0			0
$139$	−505.917	+	292.091i	−0.308715	+	0.178237i	−0.646351	−	0.763040i	$-0.723706\pi$
$139$	−505.917	+	292.091i	−0.308715	+	0.178237i	0.337636	+	0.941277i	$0.390373\pi$
$140$		0			0
$141$	−388.025	+	407.393i	−0.231756	+	0.243324i
$142$		0			0
$143$	−1455.13	−	2520.36i	−0.850937	−	1.47387i
$144$		0			0
$145$	381.736	+	220.395i	0.218631	+	0.126226i
$146$		0			0
$147$	804.809	−	1590.22i	0.451561	−	0.892240i
$148$		0			0
$149$			2838.08i			1.56043i	0.625511	+	0.780215i	$0.284891\pi$
$149$			2838.08i			1.56043i	−0.625511	+	0.780215i	$0.715109\pi$
$150$		0			0
$151$	−1644.45			−0.886251			−0.443125	−	0.896460i	$-0.646130\pi$
$151$	−1644.45			−0.886251			−0.443125	+	0.896460i	$0.646130\pi$
$152$		0			0
$153$	1241.22	+	638.185i	0.655859	+	0.337217i
$154$		0			0
$155$	370.218	+	213.745i	0.191849	+	0.110764i
$156$		0			0
$157$	2908.44	+	1679.19i	1.47847	+	0.853592i	0.999703	−	0.0243522i	$-0.00775231\pi$
$157$	2908.44	+	1679.19i	1.47847	+	0.853592i	0.478762	+	0.877945i	$0.341086\pi$
$158$		0			0
$159$	−2381.33	−	2268.13i	−1.18775	−	1.13128i
$160$		0			0
$161$	−208.533	+	526.176i	−0.102079	+	0.257568i
$162$		0			0
$163$	−361.999	+	627.001i	−0.173951	+	0.301292i	−0.939798	−	0.341731i	$-0.888987\pi$
$163$	−361.999	+	627.001i	−0.173951	+	0.301292i	0.765847	+	0.643023i	$0.222320\pi$
$164$		0			0
$165$	406.750	−	119.673i	0.191912	−	0.0564638i
$166$		0			0
$167$	1939.60	+	3359.48i	0.898745	+	1.55667i	0.829100	+	0.559101i	$0.188854\pi$
$167$	1939.60	+	3359.48i	0.898745	+	1.55667i	0.0696458	+	0.997572i	$0.477813\pi$
$168$		0			0
$169$	2190.01	−	3793.21i	0.996820	−	1.72654i
$170$		0			0
$171$	299.397	−	14.5883i	0.133892	−	0.00652394i
$172$		0			0
$173$	−1447.37	−	2506.92i	−0.636079	−	1.10172i	−0.986285	−	0.165049i	$-0.947222\pi$
$173$	−1447.37	−	2506.92i	−0.636079	−	1.10172i	0.350206	−	0.936673i	$-0.386112\pi$
$174$		0			0
$175$	−2063.16	−	817.667i	−0.891200	−	0.353199i
$176$		0			0
$177$	3468.12	+	839.362i	1.47277	+	0.356442i
$178$		0			0
$179$	−565.314	+	326.384i	−0.236053	+	0.136285i	−0.613361	−	0.789802i	$-0.710183\pi$
$179$	−565.314	+	326.384i	−0.236053	+	0.136285i	0.377308	+	0.926088i	$0.376850\pi$
$180$		0			0
$181$			287.007i			0.117862i	0.998262	+	0.0589310i	$0.0187692\pi$
$181$			287.007i			0.117862i	−0.998262	+	0.0589310i	$0.981231\pi$
$182$		0			0
$183$	−1480.75	−	1410.35i	−0.598141	−	0.569706i
$184$		0			0
$185$	−57.6686	+	99.8849i	−0.0229183	+	0.0396956i
$186$		0			0
$187$	−1606.45	+	927.483i	−0.628209	+	0.362697i
$188$		0			0
$189$	1202.38	+	2303.38i	0.462755	+	0.886486i
$190$		0			0
$191$	3161.26	−	1825.15i	1.19759	−	0.691431i	0.237576	−	0.971369i	$-0.423647\pi$
$191$	3161.26	−	1825.15i	1.19759	−	0.691431i	0.960018	+	0.279938i	$0.0903138\pi$
$192$		0			0
$193$	1447.64	−	2507.39i	0.539915	−	0.935161i	−0.458993	−	0.888440i	$-0.651790\pi$
$193$	1447.64	−	2507.39i	0.539915	−	0.935161i	0.998908	−	0.0467208i	$-0.0148771\pi$
$194$		0			0
$195$	693.838	+	660.853i	0.254804	+	0.242691i
$196$		0			0
$197$		−	3842.00i		−	1.38950i	−0.719253	−	0.694748i	$-0.755516\pi$
$197$		−	3842.00i		−	1.38950i	0.719253	−	0.694748i	$-0.244484\pi$
$198$		0			0
$199$	−2033.43	+	1174.00i	−0.724353	+	0.418205i	−0.816353	−	0.577554i	$-0.804007\pi$
$199$	−2033.43	+	1174.00i	−0.724353	+	0.418205i	0.0920000	+	0.995759i	$0.470674\pi$
$200$		0			0
$201$	95.3405	+	23.0745i	0.0334567	+	0.00809726i
$202$		0			0
$203$	−2229.11	−	2814.39i	−0.770705	−	0.973062i
$204$		0			0
$205$	343.403	+	594.792i	0.116997	+	0.202644i
$206$		0			0
$207$	−446.859	−	693.666i	−0.150043	−	0.232914i
$208$		0			0
$209$	−199.198	+	345.021i	−0.0659274	+	0.114190i
$210$		0			0
$211$	829.419	+	1436.60i	0.270614	+	0.468717i	0.969019	−	0.246985i	$-0.0794400\pi$
$211$	829.419	+	1436.60i	0.270614	+	0.468717i	−0.698405	+	0.715702i	$0.746107\pi$
$212$		0			0
$213$	−5565.37	+	1637.43i	−1.79030	+	0.526736i
$214$		0			0
$215$	−64.0261	+	110.896i	−0.0203095	+	0.0351771i
$216$		0			0
$217$	−2161.85	−	2729.47i	−0.676296	−	0.853865i
$218$		0			0
$219$	−1992.11	−	1897.41i	−0.614677	−	0.585456i
$220$		0			0
$221$	−3630.49	−	2096.06i	−1.10504	−	0.637993i
$222$		0			0
$223$	125.129	+	72.2431i	0.0375750	+	0.0216940i	0.518670	−	0.854975i	$-0.326427\pi$
$223$	125.129	+	72.2431i	0.0375750	+	0.0216940i	−0.481095	+	0.876669i	$0.659761\pi$
$224$		0			0
$225$	2719.89	−	1752.15i	0.805893	−	0.519155i
$226$		0			0
$227$	2839.68			0.830291			0.415146	−	0.909755i	$-0.363731\pi$
$227$	2839.68			0.830291			0.415146	+	0.909755i	$0.363731\pi$
$228$		0			0
$229$		−	4927.76i		−	1.42199i	−0.703197	−	0.710995i	$-0.748245\pi$
$229$		−	4927.76i		−	1.42199i	0.703197	−	0.710995i	$-0.251755\pi$
$230$		0			0
$231$	−3439.04	−	314.463i	−0.979534	−	0.0895678i
$232$		0			0
$233$	−3636.65	−	2099.62i	−1.02251	−	0.590347i	−0.107680	−	0.994186i	$-0.534342\pi$
$233$	−3636.65	−	2099.62i	−1.02251	−	0.590347i	−0.914830	+	0.403839i	$0.867676\pi$
$234$		0			0
$235$	123.099	+	213.214i	0.0341706	+	0.0591852i
$236$		0			0
$237$	−1661.30	+	1744.22i	−0.455330	+	0.478056i
$238$		0			0
$239$	−2362.56	+	1364.02i	−0.639420	+	0.369169i	−0.784391	−	0.620267i	$-0.787024\pi$
$239$	−2362.56	+	1364.02i	−0.639420	+	0.369169i	0.144971	+	0.989436i	$0.453691\pi$
$240$		0			0
$241$			4003.83i			1.07016i	0.844801	+	0.535081i	$0.179719\pi$
$241$			4003.83i			1.07016i	−0.844801	+	0.535081i	$0.820281\pi$
$242$		0			0
$243$	−3750.89	−	528.896i	−0.990205	−	0.139624i
$244$		0			0
$245$	−568.178	−	534.277i	−0.148162	−	0.139321i
$246$		0			0
$247$	−900.354			−0.231936
$248$		0			0
$249$	2147.24	+	519.679i	0.546489	+	0.132262i
$250$		0			0
$251$	4710.33			1.18452			0.592258	−	0.805748i	$-0.298237\pi$
$251$	4710.33			1.18452			0.592258	+	0.805748i	$0.298237\pi$
$252$		0			0
$253$	1096.68			0.272521
$254$		0			0
$255$	421.221	−	442.245i	0.103443	−	0.108606i
$256$		0			0
$257$	−5785.36			−1.40420			−0.702102	−	0.712076i	$-0.747755\pi$
$257$	−5785.36			−1.40420			−0.702102	+	0.712076i	$0.747755\pi$
$258$		0			0
$259$	736.413	−	583.269i	0.176674	−	0.139933i
$260$		0			0
$261$	5227.86	−	254.730i	1.23983	−	0.0604115i
$262$		0			0
$263$			8000.76i			1.87585i	0.346841	+	0.937924i	$0.387254\pi$
$263$			8000.76i			1.87585i	−0.346841	+	0.937924i	$0.612746\pi$
$264$		0			0
$265$	−1246.30	+	719.551i	−0.288904	+	0.166799i
$266$		0			0
$267$	753.365	+	182.331i	0.172679	+	0.0417920i
$268$		0			0
$269$	2493.11	+	4318.20i	0.565084	+	0.978755i	0.997042	+	0.0768609i	$0.0244897\pi$
$269$	2493.11	+	4318.20i	0.565084	+	0.978755i	−0.431957	+	0.901894i	$0.642177\pi$
$270$		0			0
$271$	−6058.94	−	3498.13i	−1.35813	−	0.784119i	−0.368762	−	0.929524i	$-0.620218\pi$
$271$	−6058.94	−	3498.13i	−1.35813	−	0.784119i	−0.989372	+	0.145404i	$0.953552\pi$
$272$		0			0
$273$	−3270.57	−	7086.13i	−0.725069	−	1.57096i
$274$		0			0
$275$			4300.12i			0.942935i
$276$		0			0
$277$	−4323.37			−0.937784			−0.468892	−	0.883256i	$-0.655347\pi$
$277$	−4323.37			−0.937784			−0.468892	+	0.883256i	$0.655347\pi$
$278$		0			0
$279$	5070.12	−	247.044i	1.08796	−	0.0530113i
$280$		0			0
$281$	7203.44	+	4158.91i	1.52926	+	0.882917i	0.999393	+	0.0348341i	$0.0110903\pi$
$281$	7203.44	+	4158.91i	1.52926	+	0.882917i	0.529864	+	0.848083i	$0.322243\pi$
$282$		0			0
$283$	−1814.49	−	1047.60i	−0.381132	−	0.220047i	0.297178	−	0.954822i	$-0.403954\pi$
$283$	−1814.49	−	1047.60i	−0.381132	−	0.220047i	−0.678311	+	0.734775i	$0.737288\pi$
$284$		0			0
$285$	30.8554	−	127.490i	0.00641305	−	0.0264978i
$286$		0			0
$287$	−815.324	−	5534.28i	−0.167690	−	1.13825i
$288$		0			0
$289$	1120.49	−	1940.75i	0.228067	−	0.395023i
$290$		0			0
$291$	1494.91	−	6176.76i	0.301145	−	1.24429i
$292$		0			0
$293$	1520.43	+	2633.47i	0.303156	+	0.525081i	0.976849	−	0.213930i	$-0.0686265\pi$
$293$	1520.43	+	2633.47i	0.303156	+	0.525081i	−0.673693	+	0.739011i	$0.735293\pi$
$294$		0			0
$295$	780.729	−	1352.26i	0.154088	−	0.266887i
$296$		0			0
$297$	3290.73	−	3810.24i	0.642921	−	0.744420i
$298$		0			0
$299$	1239.22	+	2146.39i	0.239685	+	0.415147i
$300$		0			0
$301$	817.597	−	647.570i	0.156563	−	0.124004i
$302$		0			0
$303$	−181.803	−	617.921i	−0.0344696	−	0.117157i
$304$		0			0
$305$	−774.966	+	447.427i	−0.145490	+	0.0839986i
$306$		0			0
$307$			1893.14i			0.351945i	0.984395	+	0.175972i	$0.0563069\pi$
$307$			1893.14i			0.351945i	−0.984395	+	0.175972i	$0.943693\pi$
$308$		0			0
$309$	8785.34	−	2584.80i	1.61741	−	0.475871i
$310$		0			0
$311$	−1608.97	+	2786.81i	−0.293364	+	0.508121i	−0.974603	−	0.223940i	$-0.928108\pi$
$311$	−1608.97	+	2786.81i	−0.293364	+	0.508121i	0.681239	+	0.732061i	$0.261441\pi$
$312$		0			0
$313$	−809.473	+	467.350i	−0.146179	+	0.0843967i	−0.571306	−	0.820737i	$-0.693563\pi$
$313$	−809.473	+	467.350i	−0.146179	+	0.0843967i	0.425126	+	0.905134i	$0.360230\pi$
$314$		0			0
$315$	1115.48	−	220.269i	0.199524	−	0.0393992i
$316$		0			0
$317$	4377.12	−	2527.13i	0.775531	−	0.447753i	−0.0593129	−	0.998239i	$-0.518891\pi$
$317$	4377.12	−	2527.13i	0.775531	−	0.447753i	0.834844	+	0.550486i	$0.185558\pi$
$318$		0			0
$319$	−3478.26	+	6024.52i	−0.610486	+	1.05739i
$320$		0			0
$321$	−1945.59	+	8038.90i	−0.338294	+	1.39778i
$322$		0			0
$323$			573.876i			0.0988586i
$324$		0			0
$325$	−8416.08	+	4859.03i	−1.43643	+	0.829324i
$326$		0			0
$327$	2181.44	−	2290.32i	0.368912	−	0.387325i
$328$		0			0
$329$	−292.267	−	1983.86i	−0.0489764	−	0.332444i
$330$		0			0
$331$	1117.20	+	1935.05i	0.185519	+	0.321329i	0.943751	−	0.330656i	$-0.107270\pi$
$331$	1117.20	+	1935.05i	0.185519	+	0.321329i	−0.758232	+	0.651985i	$0.773937\pi$
$332$		0			0
$333$	66.6526	+	1367.92i	0.0109686	+	0.225110i
$334$		0			0
$335$	21.4627	−	37.1744i	0.00350039	−	0.00606285i
$336$		0			0
$337$	−4391.12	−	7605.65i	−0.709791	−	1.22939i	−0.964934	−	0.262492i	$-0.915456\pi$
$337$	−4391.12	−	7605.65i	−0.709791	−	1.22939i	0.255143	−	0.966903i	$-0.417878\pi$
$338$		0			0
$339$	−903.343	−	860.399i	−0.144728	−	0.137848i
$340$		0			0
$341$	−3373.31	+	5842.74i	−0.535703	+	0.927865i
$342$		0			0
$343$	2698.92	+	5750.60i	0.424863	+	0.905258i
$344$		0			0
$345$	−346.398	+	101.916i	−0.0540563	+	0.0159043i
$346$		0			0
$347$	10192.7	+	5884.78i	1.57687	+	0.910408i	0.995292	+	0.0969201i	$0.0308991\pi$
$347$	10192.7	+	5884.78i	1.57687	+	0.910408i	0.581581	+	0.813488i	$0.302434\pi$
$348$		0			0
$349$	7683.47	+	4436.06i	1.17847	+	0.680391i	0.955661	−	0.294470i	$-0.0951431\pi$
$349$	7683.47	+	4436.06i	1.17847	+	0.680391i	0.222812	+	0.974861i	$0.428476\pi$
$350$		0			0
$351$	11175.7	+	2135.05i	1.69948	+	0.324674i
$352$		0			0
$353$	11038.0			1.66429			0.832145	−	0.554558i	$-0.187113\pi$
$353$	11038.0			1.66429			0.832145	+	0.554558i	$0.187113\pi$
$354$		0			0
$355$			2538.62i			0.379538i
$356$		0			0
$357$	−4516.62	+	2084.62i	−0.669594	+	0.309048i
$358$		0			0
$359$	3344.50	+	1930.95i	0.491689	+	0.283877i	0.725275	−	0.688460i	$-0.241713\pi$
$359$	3344.50	+	1930.95i	0.491689	+	0.283877i	−0.233586	+	0.972336i	$0.575046\pi$
$360$		0			0
$361$	−3367.87	−	5833.33i	−0.491015	−	0.850463i
$362$		0			0
$363$	−63.4261	−	215.576i	−0.00917082	−	0.0311702i
$364$		0			0
$365$	−1042.59	+	601.942i	−0.149512	+	0.0863208i
$366$		0			0
$367$			1829.41i			0.260202i	0.991501	+	0.130101i	$0.0415302\pi$
$367$			1829.41i			0.260202i	−0.991501	+	0.130101i	$0.958470\pi$
$368$		0			0
$369$	7252.79	+	3729.10i	1.02321	+	0.526095i
$370$		0			0
$371$	11596.3	−	1708.39i	1.62277	−	0.239071i
$372$		0			0
$373$	−161.571			−0.0224285			−0.0112142	−	0.999937i	$-0.503570\pi$
$373$	−161.571			−0.0224285			−0.0112142	+	0.999937i	$0.503570\pi$
$374$		0			0
$375$	−816.476	−	2775.08i	−0.112434	−	0.382146i
$376$		0			0
$377$	−15721.4			−2.14772
$378$		0			0
$379$	3831.91			0.519345			0.259673	−	0.965697i	$-0.416385\pi$
$379$	3831.91			0.519345			0.259673	+	0.965697i	$0.416385\pi$
$380$		0			0
$381$	−3261.20	−	11084.3i	−0.438520	−	1.49047i
$382$		0			0
$383$	−7002.25			−0.934199			−0.467100	−	0.884205i	$-0.654701\pi$
$383$	−7002.25			−0.934199			−0.467100	+	0.884205i	$0.654701\pi$
$384$		0			0
$385$	−556.782	+	1404.89i	−0.0737046	+	0.185973i
$386$		0			0
$387$	74.0006	+	1518.72i	0.00972005	+	0.199486i
$388$		0			0
$389$			4083.32i			0.532217i	0.963943	+	0.266109i	$0.0857380\pi$
$389$			4083.32i			0.532217i	−0.963943	+	0.266109i	$0.914262\pi$
$390$		0			0
$391$	1368.09	−	789.866i	0.176949	−	0.102162i
$392$		0			0
$393$	−832.051	−	2828.02i	−0.106798	−	0.362989i
$394$		0			0
$395$	527.039	+	912.858i	0.0671347	+	0.116281i
$396$		0			0
$397$	−922.738	−	532.743i	−0.116652	−	0.0673492i	0.440539	−	0.897734i	$-0.354787\pi$
$397$	−922.738	−	532.743i	−0.116652	−	0.0673492i	−0.557191	+	0.830384i	$0.688121\pi$
$398$		0			0
$399$	−616.226	+	872.761i	−0.0773180	+	0.109506i
$400$		0			0
$401$			5038.89i			0.627507i	0.949504	+	0.313754i	$0.101587\pi$
$401$			5038.89i			0.627507i	−0.949504	+	0.313754i	$0.898413\pi$
$402$		0			0
$403$	−15247.0			−1.88463
$404$		0			0
$405$	−685.320	+	1509.32i	−0.0840835	+	0.185182i
$406$		0			0
$407$	−1576.37	−	910.119i	−0.191985	−	0.110843i
$408$		0			0
$409$	2265.25	+	1307.84i	0.273861	+	0.158114i	0.630641	−	0.776075i	$-0.282792\pi$
$409$	2265.25	+	1307.84i	0.273861	+	0.158114i	−0.356780	+	0.934189i	$0.616125\pi$
$410$		0			0
$411$	−1533.47	+	451.173i	−0.184040	+	0.0541477i
$412$		0			0
$413$	−9969.71	+	7896.42i	−1.18784	+	0.940817i
$414$		0			0
$415$	483.378	−	837.235i	0.0571761	−	0.0990320i
$416$		0			0
$417$	2198.04	+	2093.54i	0.258125	+	0.245854i
$418$		0			0
$419$	2301.75	+	3986.75i	0.268372	+	0.464834i	0.968442	−	0.249241i	$-0.0801811\pi$
$419$	2301.75	+	3986.75i	0.268372	+	0.464834i	−0.700070	+	0.714075i	$0.746848\pi$
$420$		0			0
$421$	2846.57	−	4930.40i	0.329532	−	0.570767i	−0.652887	−	0.757456i	$-0.726442\pi$
$421$	2846.57	−	4930.40i	0.329532	−	0.570767i	0.982419	+	0.186689i	$0.0597756\pi$
$422$		0			0
$423$	2599.89	+	1336.76i	0.298844	+	0.153654i
$424$		0			0
$425$	3097.09	+	5364.32i	0.353485	+	0.612254i
$426$		0			0
$427$	7210.73	−	1062.30i	0.817217	−	0.120394i
$428$		0			0
$429$	−10429.5	+	10950.1i	−1.17376	+	1.23234i
$430$		0			0
$431$	1672.76	−	965.770i	0.186947	−	0.107934i	−0.403606	−	0.914933i	$-0.632243\pi$
$431$	1672.76	−	965.770i	0.186947	−	0.107934i	0.590552	+	0.806999i	$0.298910\pi$
$432$		0			0
$433$		−	1114.83i		−	0.123731i	−0.998084	−	0.0618655i	$-0.980295\pi$
$433$		−	1114.83i		−	0.123731i	0.998084	−	0.0618655i	$-0.0197050\pi$
$434$		0			0
$435$	538.776	−	2226.15i	0.0593847	−	0.245369i
$436$		0			0
$437$	169.642	−	293.828i	0.0185699	−	0.0321641i
$438$		0			0
$439$	482.187	−	278.391i	0.0524226	−	0.0302662i	−0.473560	−	0.880762i	$-0.657031\pi$
$439$	482.187	−	278.391i	0.0524226	−	0.0302662i	0.525982	+	0.850496i	$0.323698\pi$
$440$		0			0
$441$	−9107.42	−	1679.59i	−0.983416	−	0.181362i
$442$		0			0
$443$	−4712.38	+	2720.69i	−0.505399	+	0.291792i	−0.730940	−	0.682441i	$-0.760918\pi$
$443$	−4712.38	+	2720.69i	−0.505399	+	0.291792i	0.225541	+	0.974234i	$0.427585\pi$
$444$		0			0
$445$	169.595	−	293.746i	0.0180664	−	0.0312919i
$446$		0			0
$447$	14147.5	−	4162.42i	1.49698	−	0.440438i
$448$		0			0
$449$		−	4960.39i		−	0.521370i	−0.965424	−	0.260685i	$-0.916052\pi$
$449$		−	4960.39i		−	0.521370i	0.965424	−	0.260685i	$-0.0839485\pi$
$450$		0			0
$451$	−9386.94	+	5419.55i	−0.980075	+	0.565846i
$452$		0			0
$453$	2411.82	+	8197.40i	0.250148	+	0.850215i
$454$		0			0
$455$	−3378.75	+	497.766i	−0.348128	+	0.0512871i
$456$		0			0
$457$	−3881.71	−	6723.33i	−0.397328	−	0.688192i	0.596067	−	0.802935i	$-0.296729\pi$
$457$	−3881.71	−	6723.33i	−0.397328	−	0.688192i	−0.993395	+	0.114742i	$0.963396\pi$
$458$		0			0
$459$	1360.86	−	7123.30i	0.138387	−	0.724373i
$460$		0			0
$461$	−623.184	+	1079.39i	−0.0629601	+	0.109050i	−0.895787	−	0.444483i	$-0.853387\pi$
$461$	−623.184	+	1079.39i	−0.0629601	+	0.109050i	0.832827	+	0.553533i	$0.186721\pi$
$462$		0			0
$463$	−3542.90	−	6136.49i	−0.355621	−	0.615954i	0.631603	−	0.775292i	$-0.282397\pi$
$463$	−3542.90	−	6136.49i	−0.355621	−	0.615954i	−0.987224	+	0.159338i	$0.949064\pi$
$464$		0			0
$465$	522.520	−	2158.98i	0.0521102	−	0.215312i
$466$		0			0
$467$	6642.20	−	11504.6i	0.658168	−	1.13998i	−0.322921	−	0.946426i	$-0.604665\pi$
$467$	6642.20	−	11504.6i	0.658168	−	1.13998i	0.981089	−	0.193555i	$-0.0620017\pi$
$468$		0			0
$469$	−274.073	+	217.077i	−0.0269840	+	0.0213724i
$470$		0			0
$471$	4104.93	−	16961.0i	0.401582	−	1.65928i
$472$		0			0
$473$	−1750.16	−	1010.45i	−0.170132	−	0.0982256i
$474$		0			0
$475$	1152.11	+	665.171i	0.111289	+	0.0642529i
$476$		0			0
$477$	−7813.78	+	15197.2i	−0.750039	+	1.45876i
$478$		0			0
$479$	12928.9			1.23327			0.616633	−	0.787251i	$-0.288496\pi$
$479$	12928.9			1.23327			0.616633	+	0.787251i	$0.288496\pi$
$480$		0			0
$481$		−	4113.64i		−	0.389950i
$482$		0			0
$483$	2928.77	+	267.804i	0.275908	+	0.0252288i
$484$		0			0
$485$	−2408.39	−	1390.49i	−0.225484	−	0.130183i
$486$		0			0
$487$	−3884.93	−	6728.90i	−0.361485	−	0.626110i	0.626721	−	0.779244i	$-0.284397\pi$
$487$	−3884.93	−	6728.90i	−0.361485	−	0.626110i	−0.988205	+	0.153134i	$0.951063\pi$
$488$		0			0
$489$	3656.44	+	884.940i	0.338139	+	0.0818371i
$490$		0			0
$491$	−1821.57	+	1051.68i	−0.167426	+	0.0966636i	−0.581372	−	0.813638i	$-0.697484\pi$
$491$	−1821.57	+	1051.68i	−0.167426	+	0.0966636i	0.413945	+	0.910302i	$0.364150\pi$
$492$		0			0
$493$			10020.6i			0.915428i
$494$		0			0
$495$	−1193.11	−	1852.08i	−0.108336	−	0.168172i
$496$		0			0
$497$	7618.19	−	19222.4i	0.687571	−	1.73489i
$498$		0			0
$499$	−5097.19			−0.457278			−0.228639	−	0.973511i	$-0.573428\pi$
$499$	−5097.19			−0.457278			−0.228639	+	0.973511i	$0.573428\pi$
$500$		0			0
$501$	13901.9	−	14595.8i	1.23970	−	1.30158i
$502$		0			0
$503$	13933.6			1.23512			0.617562	−	0.786523i	$-0.288121\pi$
$503$	13933.6			1.23512			0.617562	+	0.786523i	$0.288121\pi$
$504$		0			0
$505$	−281.862			−0.0248370
$506$		0			0
$507$	−22120.7	−	5353.68i	−1.93770	−	0.468965i
$508$		0			0
$509$	−10622.1			−0.924985			−0.462492	−	0.886623i	$-0.653045\pi$
$509$	−10622.1			−0.924985			−0.462492	+	0.886623i	$0.653045\pi$
$510$		0			0
$511$	9700.90	−	1429.16i	0.839809	−	0.123723i
$512$		0			0
$513$	−511.827	−	1471.06i	−0.0440501	−	0.126606i
$514$		0			0
$515$		−	4007.39i		−	0.342887i
$516$		0			0
$517$	−3364.92	+	1942.74i	−0.286245	+	0.165264i
$518$		0			0
$519$	−10373.9	+	10891.7i	−0.877390	+	0.921182i
$520$		0			0
$521$	−5442.58	−	9426.83i	−0.457666	−	0.792700i	0.541171	−	0.840912i	$-0.317981\pi$
$521$	−5442.58	−	9426.83i	−0.457666	−	0.792700i	−0.998837	+	0.0482119i	$0.984648\pi$
$522$		0			0
$523$	9617.88	+	5552.89i	0.804131	+	0.464265i	0.844914	−	0.534903i	$-0.179652\pi$
$523$	9617.88	+	5552.89i	0.804131	+	0.464265i	−0.0407825	+	0.999168i	$0.512985\pi$
$524$		0			0
$525$	−1050.07	+	11483.8i	−0.0872930	+	0.954655i
$526$		0			0
$527$			9718.27i			0.803291i
$528$		0			0
$529$	11233.0			0.923238
$530$		0			0
$531$	−902.357	−	18519.2i	−0.0737457	−	1.51349i
$532$		0			0
$533$	−21214.0	−	12247.9i	−1.72398	−	0.995339i
$534$		0			0
$535$	3134.47	+	1809.68i	0.253299	+	0.146242i
$536$		0			0
$537$	2456.09	+	2339.33i	0.197371	+	0.187988i
$538$		0			0
$539$	8431.91	−	8966.93i	0.673818	−	0.716574i
$540$		0			0
$541$	−3329.27	+	5766.47i	−0.264578	+	0.458262i	−0.967453	−	0.253051i	$-0.918566\pi$
$541$	−3329.27	+	5766.47i	−0.264578	+	0.458262i	0.702875	+	0.711313i	$0.251899\pi$
$542$		0			0
$543$	1430.69	−	420.934i	0.113070	−	0.0332670i
$544$		0			0
$545$	−692.051	−	1198.67i	−0.0543931	−	0.0942115i
$546$		0			0
$547$	−2063.26	+	3573.67i	−0.161277	+	0.279340i	−0.935327	−	0.353784i	$-0.884895\pi$
$547$	−2063.26	+	3573.67i	−0.161277	+	0.279340i	0.774050	+	0.633125i	$0.218228\pi$
$548$		0			0
$549$	−4858.72	+	9449.81i	−0.377714	+	0.734623i
$550$		0			0
$551$	1076.08	+	1863.82i	0.0831987	+	0.144104i
$552$		0			0
$553$	−1251.32	−	8493.76i	−0.0962235	−	0.653149i
$554$		0			0
$555$	582.492	+	140.976i	0.0445503	+	0.0107822i
$556$		0			0
$557$	−11144.8	+	6434.47i	−0.847795	+	0.489475i	−0.859906	−	0.510452i	$-0.829478\pi$
$557$	−11144.8	+	6434.47i	−0.847795	+	0.489475i	0.0121114	+	0.999927i	$0.496145\pi$
$558$		0			0
$559$		−	4567.14i		−	0.345563i
$560$		0			0
$561$	6979.46	+	6647.66i	0.525264	+	0.500293i
$562$		0			0
$563$	7709.20	−	13352.7i	0.577094	−	0.999557i	−0.418716	−	0.908117i	$-0.637520\pi$
$563$	7709.20	−	13352.7i	0.577094	−	0.999557i	0.995811	−	0.0914398i	$-0.0291469\pi$
$564$		0			0
$565$	−472.775	+	272.957i	−0.0352032	+	0.0203246i
$566$		0			0
$567$	9718.58	−	9371.95i	0.719827	−	0.694153i
$568$		0			0
$569$	−18070.5	+	10433.0i	−1.33138	+	0.768674i	−0.985512	−	0.169608i	$-0.945750\pi$
$569$	−18070.5	+	10433.0i	−1.33138	+	0.768674i	−0.345871	+	0.938282i	$0.612417\pi$
$570$		0			0
$571$	−725.032	+	1255.79i	−0.0531377	+	0.0920373i	−0.891371	−	0.453275i	$-0.850256\pi$
$571$	−725.032	+	1255.79i	−0.0531377	+	0.0920373i	0.838233	+	0.545312i	$0.183589\pi$
$572$		0			0
$573$	−13734.6	−	13081.6i	−1.00134	−	0.953740i
$574$		0			0
$575$		−	3662.08i		−	0.265599i
$576$		0			0
$577$	18532.1	−	10699.5i	1.33709	−	0.771969i	0.350715	−	0.936482i	$-0.385939\pi$
$577$	18532.1	−	10699.5i	1.33709	−	0.771969i	0.986375	+	0.164513i	$0.0526052\pi$
$578$		0			0
$579$	−14622.2	−	3538.89i	−1.04953	−	0.254009i
$580$		0			0
$581$	−6172.61	+	4888.96i	−0.440763	+	0.349102i
$582$		0			0
$583$	−11355.9	−	19669.0i	−0.806711	−	1.39726i
$584$		0			0
$585$	2276.66	−	4427.92i	0.160903	−	0.312944i
$586$		0			0
$587$	859.708	−	1489.06i	0.0604496	−	0.104702i	−0.834217	−	0.551437i	$-0.814080\pi$
$587$	859.708	−	1489.06i	0.0604496	−	0.104702i	0.894666	+	0.446735i	$0.147413\pi$
$588$		0			0
$589$	1043.61	+	1807.59i	0.0730071	+	0.126452i
$590$		0			0
$591$	−19151.9	+	5634.81i	−1.33300	+	0.392191i
$592$		0			0
$593$	7790.59	−	13493.7i	0.539496	−	0.934435i	−0.459435	−	0.888211i	$-0.651948\pi$
$593$	7790.59	−	13493.7i	0.539496	−	0.934435i	0.998931	−	0.0462235i	$-0.0147186\pi$
$594$		0			0
$595$	317.271	+	2153.58i	0.0218602	+	0.148384i
$596$		0			0
$597$	8834.56	+	8414.57i	0.605652	+	0.576860i
$598$		0			0
$599$	18704.4	+	10799.0i	1.27586	+	0.736619i	0.976085	−	0.217391i	$-0.0697546\pi$
$599$	18704.4	+	10799.0i	1.27586	+	0.736619i	0.299777	+	0.954009i	$0.403088\pi$
$600$		0			0
$601$	−23499.2	−	13567.3i	−1.59493	−	0.920832i	−0.992444	−	0.122702i	$-0.960844\pi$
$601$	−23499.2	−	13567.3i	−1.59493	−	0.920832i	−0.602485	−	0.798131i	$-0.705822\pi$
$602$		0			0
$603$	−24.8063	−	509.103i	−0.00167527	−	0.0343819i
$604$		0			0
$605$	−98.3339			−0.00660800
$606$		0			0
$607$			17722.6i			1.18507i	0.805544	+	0.592536i	$0.201873\pi$
$607$			17722.6i			1.18507i	−0.805544	+	0.592536i	$0.798127\pi$
$608$		0			0
$609$	−10760.1	+	15239.5i	−0.715962	+	1.01402i
$610$		0			0
$611$	−7604.53	−	4390.48i	−0.503513	−	0.290703i
$612$		0			0
$613$	−11100.2	−	19226.2i	−0.731377	−	1.26678i	−0.956295	−	0.292404i	$-0.905545\pi$
$613$	−11100.2	−	19226.2i	−0.731377	−	1.26678i	0.224918	−	0.974378i	$-0.427789\pi$
$614$		0			0
$615$	2461.31	−	2584.16i	0.161382	−	0.169437i
$616$		0			0
$617$	−18959.9	+	10946.5i	−1.23711	+	0.714247i	−0.968503	−	0.249003i	$-0.919897\pi$
$617$	−18959.9	+	10946.5i	−1.23711	+	0.714247i	−0.268609	+	0.963249i	$0.586564\pi$
$618$		0			0
$619$			30676.8i			1.99193i	0.0897290	+	0.995966i	$0.471400\pi$
$619$			30676.8i			1.99193i	−0.0897290	+	0.995966i	$0.528600\pi$
$620$		0			0
$621$	−2802.46	+	3244.89i	−0.181093	+	0.209683i
$622$		0			0
$623$	−2165.68	+	1715.31i	−0.139271	+	0.110309i
$624$		0			0
$625$	13712.9			0.877624
$626$		0			0
$627$	2012.04	+	486.957i	0.128155	+	0.0310163i
$628$		0			0
$629$	−2621.99			−0.166209
$630$		0			0
$631$	16086.9			1.01491			0.507454	−	0.861679i	$-0.330587\pi$
$631$	16086.9			1.01491			0.507454	+	0.861679i	$0.330587\pi$
$632$		0			0
$633$	5944.79	−	6241.51i	0.373277	−	0.391908i
$634$		0			0
$635$	−5056.06			−0.315974
$636$		0			0
$637$	27077.7	+	6370.29i	1.68423	+	0.396233i
$638$		0			0
$639$	16324.7	+	25341.2i	1.01064	+	1.56883i
$640$		0			0
$641$		−	3092.92i		−	0.190582i	−0.995449	−	0.0952909i	$-0.969622\pi$
$641$		−	3092.92i		−	0.190582i	0.995449	−	0.0952909i	$-0.0303781\pi$
$642$		0			0
$643$	−6233.64	+	3598.99i	−0.382318	+	0.220732i	−0.678826	−	0.734299i	$-0.737511\pi$
$643$	−6233.64	+	3598.99i	−0.382318	+	0.220732i	0.296508	+	0.955030i	$0.404178\pi$
$644$		0			0
$645$	646.708	+	156.518i	0.0394792	+	0.00955484i
$646$		0			0
$647$	−5869.52	−	10166.3i	−0.356653	−	0.617742i	0.630746	−	0.775989i	$-0.282749\pi$
$647$	−5869.52	−	10166.3i	−0.356653	−	0.617742i	−0.987399	+	0.158248i	$0.949416\pi$
$648$		0			0
$649$	21341.3	+	12321.4i	1.29078	+	0.745234i
$650$		0			0
$651$	−10435.4	+	14779.7i	−0.628259	+	0.889805i
$652$		0			0
$653$		−	9750.43i		−	0.584324i	−0.956369	−	0.292162i	$-0.905625\pi$
$653$		−	9750.43i		−	0.584324i	0.956369	−	0.292162i	$-0.0943747\pi$
$654$		0			0
$655$	−1289.99			−0.0769526
$656$		0			0
$657$	−6536.64	+	12713.2i	−0.388156	+	0.754931i
$658$		0			0
$659$	−18192.1	−	10503.2i	−1.07536	−	0.620862i	−0.145722	−	0.989326i	$-0.546551\pi$
$659$	−18192.1	−	10503.2i	−1.07536	−	0.620862i	−0.929642	+	0.368464i	$0.879884\pi$
$660$		0			0
$661$	11450.1	+	6610.70i	0.673761	+	0.388996i	0.797500	−	0.603319i	$-0.206155\pi$
$661$	11450.1	+	6610.70i	0.673761	+	0.388996i	−0.123739	+	0.992315i	$0.539489\pi$
$662$		0			0
$663$	−5124.01	+	21171.7i	−0.300151	+	1.24018i
$664$		0			0
$665$	290.277	+	366.493i	0.0169270	+	0.0213714i
$666$		0			0
$667$	2962.16	−	5130.62i	0.171957	−	0.297838i
$668$		0			0
$669$	176.605	−	729.705i	0.0102062	−	0.0421704i
$670$		0			0
$671$	−7061.24	−	12230.4i	−0.406254	−	0.703652i
$672$		0			0
$673$	13521.6	−	23420.1i	0.774471	−	1.34142i	−0.160620	−	0.987016i	$-0.551349\pi$
$673$	13521.6	−	23420.1i	0.774471	−	1.34142i	0.935091	−	0.354407i	$-0.115317\pi$
$674$		0			0
$675$	−12723.3	−	10988.6i	−0.725513	−	0.626592i
$676$		0			0
$677$	5441.73	+	9425.35i	0.308926	+	0.535075i	0.978128	−	0.208006i	$-0.0666972\pi$
$677$	5441.73	+	9425.35i	0.308926	+	0.535075i	−0.669202	+	0.743081i	$0.733364\pi$
$678$		0			0
$679$	14063.6	+	17756.2i	0.794862	+	1.00356i
$680$		0			0
$681$	−4164.77	−	14155.4i	−0.234353	−	0.796531i
$682$		0			0
$683$	−2604.50	+	1503.71i	−0.145913	+	0.0842429i	−0.571179	−	0.820825i	$-0.693514\pi$
$683$	−2604.50	+	1503.71i	−0.145913	+	0.0842429i	0.425266	+	0.905068i	$0.360181\pi$
$684$		0			0
$685$			699.484i			0.0390159i
$686$		0			0
$687$	−24564.3	+	7227.23i	−1.36417	+	0.401363i
$688$		0			0
$689$	25663.7	−	44450.8i	1.41903	−	2.45782i
$690$		0			0
$691$	29630.4	−	17107.1i	1.63125	−	0.941803i	0.647543	−	0.762029i	$-0.275797\pi$
$691$	29630.4	−	17107.1i	1.63125	−	0.941803i	0.983708	−	0.179774i	$-0.0575367\pi$
$692$		0			0
$693$	3476.26	+	17604.4i	0.190551	+	0.964986i
$694$		0			0
$695$	1150.37	−	664.165i	0.0627855	−	0.0362492i
$696$		0			0
$697$	−7806.68	+	13521.6i	−0.424246	+	0.734815i
$698$		0			0
$699$	−5132.71	+	21207.6i	−0.277735	+	1.14756i
$700$		0			0
$701$			12333.8i			0.664537i	0.943185	+	0.332268i	$0.107814\pi$
$701$			12333.8i			0.664537i	−0.943185	+	0.332268i	$0.892186\pi$
$702$		0			0
$703$	−487.687	+	281.566i	−0.0261642	+	0.0151059i
$704$		0			0
$705$	882.302	−	926.340i	0.0471339	−	0.0494865i
$706$		0			0
$707$	2134.25	+	845.844i	0.113532	+	0.0449947i
$708$		0			0
$709$	4263.60	+	7384.77i	0.225843	+	0.391172i	0.956572	−	0.291496i	$-0.0941530\pi$
$709$	4263.60	+	7384.77i	0.225843	+	0.391172i	−0.730729	+	0.682668i	$0.760820\pi$
$710$		0			0
$711$	11131.2	+	5723.25i	0.587137	+	0.301883i
$712$		0			0
$713$	2872.79	−	4975.81i	0.150893	−	0.261354i
$714$		0			0
$715$	3308.71	+	5730.85i	0.173061	+	0.299751i
$716$		0			0
$717$	10264.5	+	9776.54i	0.534637	+	0.509221i
$718$		0			0
$719$	13463.9	−	23320.1i	0.698355	−	1.20959i	−0.270681	−	0.962669i	$-0.587249\pi$
$719$	13463.9	−	23320.1i	0.698355	−	1.20959i	0.969036	−	0.246918i	$-0.0794178\pi$
$720$		0			0
$721$	−12025.9	+	30343.9i	−0.621174	+	1.56736i
$722$		0			0
$723$	19958.6	−	5872.15i	1.02665	−	0.302058i
$724$		0			0
$725$	20117.3	+	11614.7i	1.03054	+	0.594980i
$726$		0			0
$727$	−21031.5	−	12142.6i	−1.07293	−	0.619454i	−0.143946	−	0.989586i	$-0.545979\pi$
$727$	−21031.5	−	12142.6i	−1.07293	−	0.619454i	−0.928979	+	0.370132i	$0.879313\pi$
$728$		0			0
$729$	2864.71	+	19473.4i	0.145542	+	0.989352i
$730$		0			0
$731$	−2911.05			−0.147290
$732$		0			0
$733$		−	15292.3i		−	0.770578i	−0.922796	−	0.385289i	$-0.874102\pi$
$733$		−	15292.3i		−	0.770578i	0.922796	−	0.385289i	$-0.125898\pi$
$734$		0			0
$735$	−1829.99	+	3615.89i	−0.0918372	+	0.181461i
$736$		0			0
$737$	586.683	+	338.722i	0.0293226	+	0.0169294i
$738$		0			0
$739$	12820.2	+	22205.3i	0.638158	+	1.10532i	0.985837	+	0.167709i	$0.0536368\pi$
$739$	12820.2	+	22205.3i	0.638158	+	1.10532i	−0.347678	+	0.937614i	$0.613030\pi$
$740$		0			0
$741$	1320.49	+	4488.15i	0.0654649	+	0.222505i
$742$		0			0
$743$	−10166.3	+	5869.52i	−0.501973	+	0.289814i	−0.729528	−	0.683951i	$-0.760260\pi$
$743$	−10166.3	+	5869.52i	−0.501973	+	0.289814i	0.227555	+	0.973765i	$0.426927\pi$
$744$		0			0
$745$		−	6453.29i		−	0.317356i
$746$		0			0
$747$	−558.682	−	11465.9i	−0.0273643	−	0.561601i
$748$		0			0
$749$	−18303.4	−	23109.2i	−0.892915	−	1.12736i
$750$		0			0
$751$	−11654.7			−0.566293			−0.283147	−	0.959077i	$-0.591378\pi$
$751$	−11654.7			−0.566293			−0.283147	+	0.959077i	$0.591378\pi$
$752$		0			0
$753$	−6908.34	−	23480.4i	−0.334334	−	1.13635i
$754$		0			0
$755$	3739.20			0.180243
$756$		0			0
$757$	28915.3			1.38830			0.694151	−	0.719829i	$-0.255780\pi$
$757$	28915.3			1.38830			0.694151	+	0.719829i	$0.255780\pi$
$758$		0			0
$759$	−1608.43	−	5466.82i	−0.0769200	−	0.261440i
$760$		0			0
$761$	12569.3			0.598732			0.299366	−	0.954138i	$-0.403225\pi$
$761$	12569.3			0.598732			0.299366	+	0.954138i	$0.403225\pi$
$762$		0			0
$763$	1643.10	+	11153.1i	0.0779610	+	0.529186i
$764$		0			0
$765$	−2822.31	−	1451.12i	−0.133387	−	0.0685822i
$766$		0			0
$767$			55691.4i			2.62177i
$768$		0			0
$769$	18621.1	−	10750.9i	0.873206	−	0.504146i	0.00479362	−	0.999989i	$-0.498474\pi$
$769$	18621.1	−	10750.9i	0.873206	−	0.504146i	0.868412	+	0.495843i	$0.165141\pi$
$770$		0			0
$771$	8485.01	+	28839.3i	0.396343	+	1.34711i
$772$		0			0
$773$	15174.1	+	26282.4i	0.706049	+	1.22291i	0.966311	+	0.257376i	$0.0828577\pi$
$773$	15174.1	+	26282.4i	0.706049	+	1.22291i	−0.260262	+	0.965538i	$0.583809\pi$
$774$		0			0
$775$	19510.3	+	11264.3i	0.904299	+	0.522097i
$776$		0			0
$777$	−3987.57	−	2815.48i	−0.184110	−	0.129993i
$778$		0			0
$779$			3353.32i			0.154230i
$780$		0			0
$781$	−40064.2			−1.83561
$782$		0			0
$783$	−8937.16	−	25686.6i	−0.407903	−	1.17237i
$784$		0			0
$785$	−6613.30	−	3818.19i	−0.300686	−	0.173601i
$786$		0			0
$787$	−6038.65	−	3486.41i	−0.273513	−	0.157913i	0.356970	−	0.934116i	$-0.383810\pi$
$787$	−6038.65	−	3486.41i	−0.273513	−	0.157913i	−0.630483	+	0.776203i	$0.717143\pi$
$788$		0			0
$789$	39882.8	−	11734.2i	1.79958	−	0.529466i
$790$		0			0
$791$	4398.98	−	648.067i	0.197736	−	0.0291310i
$792$		0			0
$793$	15958.0	−	27640.1i	0.714611	−	1.23774i
$794$		0			0
$795$	5414.74	+	5157.32i	0.241561	+	0.230077i
$796$		0			0
$797$	8953.19	+	15507.4i	0.397915	+	0.689209i	0.993469	−	0.114107i	$-0.0364005\pi$
$797$	8953.19	+	15507.4i	0.397915	+	0.689209i	−0.595553	+	0.803316i	$0.703067\pi$
$798$		0			0
$799$	−2798.44	+	4847.05i	−0.123907	+	0.214614i
$800$		0			0
$801$	−196.015	−	4022.85i	−0.00864651	−	0.177454i
$802$		0			0
$803$	−9499.79	−	16454.1i	−0.417485	−	0.723105i
$804$		0			0
$805$	474.169	−	1196.43i	0.0207606	−	0.0523835i
$806$		0			0
$807$	17869.2	−	18761.1i	0.779461	−	0.818365i
$808$		0			0
$809$	18644.0	−	10764.1i	0.810245	−	0.467795i	−0.0367961	−	0.999323i	$-0.511715\pi$
$809$	18644.0	−	10764.1i	0.810245	−	0.467795i	0.847041	+	0.531528i	$0.178382\pi$
$810$		0			0
$811$		−	23203.9i		−	1.00469i	−0.864669	−	0.502343i	$-0.832472\pi$
$811$		−	23203.9i		−	1.00469i	0.864669	−	0.502343i	$-0.167528\pi$
$812$		0			0
$813$	−8551.49	+	35333.6i	−0.368898	+	1.52423i
$814$		0			0
$815$	823.124	−	1425.69i	0.0353776	−	0.0612758i
$816$		0			0
$817$	−541.451	+	312.607i	−0.0231860	+	0.0133865i
$818$		0			0
$819$	−30526.7	+	26696.1i	−1.30243	+	1.13900i
$820$		0			0
$821$	−1805.76	+	1042.56i	−0.0767620	+	0.0443186i	−0.537890	−	0.843015i	$-0.680778\pi$
$821$	−1805.76	+	1042.56i	−0.0767620	+	0.0443186i	0.461128	+	0.887334i	$0.347445\pi$
$822$		0			0
$823$	−19506.4	+	33786.1i	−0.826185	+	1.43100i	0.0748245	+	0.997197i	$0.476160\pi$
$823$	−19506.4	+	33786.1i	−0.826185	+	1.43100i	−0.901010	+	0.433798i	$0.857173\pi$
$824$		0			0
$825$	21435.6	−	6306.71i	0.904595	−	0.266147i
$826$		0			0
$827$			8515.43i			0.358054i	0.983844	+	0.179027i	$0.0572949\pi$
$827$			8515.43i			0.358054i	−0.983844	+	0.179027i	$0.942705\pi$
$828$		0			0
$829$	−19851.6	+	11461.3i	−0.831696	+	0.480180i	−0.854433	−	0.519562i	$-0.826095\pi$
$829$	−19851.6	+	11461.3i	−0.831696	+	0.480180i	0.0227370	+	0.999741i	$0.492762\pi$
$830$		0			0
$831$	6340.80	+	21551.5i	0.264693	+	0.899653i
$832$		0			0
$833$	4060.36	−	17259.0i	0.168887	−	0.717874i
$834$		0			0
$835$	−4410.30	−	7638.87i	−0.182784	−	0.316592i
$836$		0			0
$837$	−8667.50	−	24911.6i	−0.357936	−	1.02876i
$838$		0			0
$839$	−14263.6	+	24705.3i	−0.586929	+	1.01659i	0.407703	+	0.913115i	$0.366330\pi$
$839$	−14263.6	+	24705.3i	−0.586929	+	1.01659i	−0.994632	+	0.103477i	$0.967003\pi$
$840$		0			0
$841$	6595.22	+	11423.2i	0.270418	+	0.468377i
$842$		0			0
$843$	10166.8	−	42007.8i	0.415378	−	1.71628i
$844$		0			0
$845$	−4979.71	+	8625.11i	−0.202730	+	0.351139i
$846$		0			0
$847$	744.584	+	295.092i	0.0302057	+	0.0119711i
$848$		0			0
$849$	−2560.95	+	10581.5i	−0.103524	+	0.427745i
$850$		0			0
$851$	1342.48	+	775.078i	0.0540769	+	0.0312213i
$852$		0			0
$853$	3816.92	+	2203.70i	0.153211	+	0.0884563i	0.574645	−	0.818402i	$-0.305140\pi$
$853$	3816.92	+	2203.70i	0.153211	+	0.0884563i	−0.421435	+	0.906859i	$0.638473\pi$
$854$		0			0
$855$	−680.777	+	33.1712i	−0.0272305	+	0.00132682i
$856$		0			0
$857$	7140.75			0.284625			0.142312	−	0.989822i	$-0.454546\pi$
$857$	7140.75			0.284625			0.142312	+	0.989822i	$0.454546\pi$
$858$		0			0
$859$		−	35576.0i		−	1.41308i	−0.707671	−	0.706542i	$-0.750254\pi$
$859$		−	35576.0i		−	1.41308i	0.707671	−	0.706542i	$-0.249746\pi$
$860$		0			0
$861$	−26391.9	+	12181.1i	−1.04464	+	0.482148i
$862$		0			0
$863$	−10089.3	−	5825.03i	−0.397963	−	0.229764i	0.287642	−	0.957738i	$-0.407129\pi$
$863$	−10089.3	−	5825.03i	−0.397963	−	0.229764i	−0.685605	+	0.727974i	$0.740462\pi$
$864$		0			0
$865$	3291.07	+	5700.31i	0.129364	+	0.224065i
$866$		0			0
$867$	−11317.7	−	2739.14i	−0.443334	−	0.107297i
$868$		0			0
$869$	−14406.6	+	8317.68i	−0.562384	+	0.324693i
$870$		0			0
$871$			1530.99i			0.0595585i
$872$		0			0
$873$	−32982.9	+	1607.11i	−1.27870	+	0.0623051i
$874$		0			0
$875$	9584.93	+	3798.68i	0.370320	+	0.146765i
$876$		0			0
$877$	−12477.0			−0.480410			−0.240205	−	0.970722i	$-0.577215\pi$
$877$	−12477.0			−0.480410			−0.240205	+	0.970722i	$0.577215\pi$
$878$		0			0
$879$	10897.6	−	11441.5i	0.418164	−	0.439035i
$880$		0			0
$881$	−25422.6			−0.972203			−0.486101	−	0.873902i	$-0.661581\pi$
$881$	−25422.6			−0.972203			−0.486101	+	0.873902i	$0.661581\pi$
$882$		0			0
$883$	−32619.3			−1.24318			−0.621589	−	0.783344i	$-0.713512\pi$
$883$	−32619.3			−1.24318			−0.621589	+	0.783344i	$0.713512\pi$
$884$		0			0
$885$	−7885.91	−	1908.56i	−0.299528	−	0.0724922i
$886$		0			0
$887$	−10413.3			−0.394187			−0.197094	−	0.980385i	$-0.563150\pi$
$887$	−10413.3			−0.394187			−0.197094	+	0.980385i	$0.563150\pi$
$888$		0			0
$889$	38284.5	+	15172.8i	1.44434	+	0.572420i
$890$		0			0
$891$	−23819.9	−	10815.6i	−0.895619	−	0.406664i
$892$		0			0
$893$			1202.06i			0.0450452i
$894$		0			0
$895$	1285.43	−	742.141i	0.0480078	−	0.0277173i
$896$		0			0
$897$	8882.01	−	9325.33i	0.330615	−	0.347117i
$898$		0			0
$899$	18222.8	+	31562.8i	0.676044	+	1.17094i
$900$		0			0
$901$	−28332.5	−	16357.8i	−1.04760	−	0.604835i
$902$		0			0
$903$	−4427.17	−	3125.87i	−0.163153	−	0.115196i
$904$		0			0
$905$		−	652.603i		−	0.0239705i
$906$		0			0
$907$	−20279.5			−0.742413			−0.371206	−	0.928550i	$-0.621056\pi$
$907$	−20279.5			−0.742413			−0.371206	+	0.928550i	$0.621056\pi$
$908$		0			0
$909$	−2813.62	+	1812.53i	−0.102664	+	0.0661362i
$910$		0			0
$911$	−37900.7	−	21882.0i	−1.37838	−	0.795810i	−0.386419	−	0.922323i	$-0.626288\pi$
$911$	−37900.7	−	21882.0i	−1.37838	−	0.795810i	−0.991965	+	0.126513i	$0.959621\pi$
$912$		0			0
$913$	13213.2	+	7628.62i	0.478961	+	0.276529i
$914$		0			0
$915$	3366.96	+	3206.90i	0.121648	+	0.115865i
$916$		0			0
$917$	9767.77	+	3871.15i	0.351756	+	0.139407i
$918$		0			0
$919$	−669.644	+	1159.86i	−0.0240365	+	0.0416324i	−0.877793	−	0.479039i	$-0.840985\pi$
$919$	−669.644	+	1159.86i	−0.0240365	+	0.0416324i	0.853757	+	0.520672i	$0.174318\pi$
$920$		0			0
$921$	9437.05	−	2776.54i	0.337635	−	0.0993378i
$922$		0			0
$923$	−45271.5	−	78412.5i	−1.61444	−	2.79629i
$924$		0			0
$925$	−3039.11	+	5263.89i	−0.108027	+	0.187109i
$926$		0			0
$927$	−25769.8	−	40002.9i	−0.913043	−	1.41733i
$928$		0			0
$929$	−13738.7	−	23796.1i	−0.485202	−	0.840394i	0.514654	−	0.857398i	$-0.327920\pi$
$929$	−13738.7	−	23796.1i	−0.485202	−	0.840394i	−0.999855	+	0.0170042i	$0.994587\pi$
$930$		0			0
$931$	−1098.16	−	3646.18i	−0.0386582	−	0.128355i
$932$		0			0
$933$	16251.7	+	3933.26i	0.570263	+	0.138016i
$934$		0			0
$935$	3652.78	−	2108.94i	0.127763	−	0.0737642i
$936$		0			0
$937$			7077.24i			0.246749i	0.992360	+	0.123374i	$0.0393716\pi$
$937$			7077.24i			0.246749i	−0.992360	+	0.123374i	$0.960628\pi$
$938$		0			0
$939$	3516.88	+	3349.69i	0.122225	+	0.116414i
$940$		0			0
$941$	14910.6	−	25825.9i	0.516548	−	0.894687i	−0.483268	−	0.875473i	$-0.660550\pi$
$941$	14910.6	−	25825.9i	0.516548	−	0.894687i	0.999815	−	0.0192144i	$-0.00611652\pi$
$942$		0			0
$943$	7994.13	−	4615.41i	0.276060	−	0.159383i
$944$		0			0
$945$	−2734.01	−	5237.48i	−0.0941137	−	0.180291i
$946$		0			0
$947$	32500.6	−	18764.2i	1.11523	−	0.643881i	0.175054	−	0.984559i	$-0.443990\pi$
$947$	32500.6	−	18764.2i	1.11523	−	0.643881i	0.940180	+	0.340678i	$0.110657\pi$
$948$		0			0
$949$	21469.0	−	37185.4i	0.734366	−	1.27196i
$950$		0			0
$951$	−19017.1	−	18113.0i	−0.648444	−	0.617618i
$952$		0			0
$953$			32602.0i			1.10817i	0.832462	+	0.554083i	$0.186931\pi$
$953$			32602.0i			1.10817i	−0.832462	+	0.554083i	$0.813069\pi$
$954$		0			0
$955$	−7188.15	+	4150.08i	−0.243563	+	0.140621i
$956$		0			0
$957$	35132.8	+	8502.91i	1.18671	+	0.287210i
$958$		0			0
$959$	2099.10	−	5296.49i	0.0706813	−	0.178345i
$960$		0			0
$961$	2777.44	+	4810.68i	0.0932310	+	0.161481i
$962$		0			0
$963$	42926.4	−	2091.61i	1.43643	−	0.0699909i
$964$		0			0
$965$	−3291.69	+	5701.37i	−0.109806	+	0.190190i
$966$		0			0
$967$	−25441.4	−	44065.9i	−0.846061	−	1.46542i	−0.884696	−	0.466168i	$-0.845634\pi$
$967$	−25441.4	−	44065.9i	−0.846061	−	1.46542i	0.0386347	−	0.999253i	$-0.487699\pi$
$968$		0			0
$969$	2860.70	−	841.667i	0.0948390	−	0.0279032i
$970$		0			0
$971$	−5033.66	+	8718.55i	−0.166362	+	0.288148i	−0.937138	−	0.348958i	$-0.886535\pi$
$971$	−5033.66	+	8718.55i	−0.166362	+	0.288148i	0.770776	+	0.637106i	$0.219869\pi$
$972$		0			0
$973$	−10703.7	+	1576.89i	−0.352666	+	0.0519557i
$974$		0			0
$975$	36565.0	+	34826.7i	1.20104	+	1.14395i
$976$		0			0
$977$	38948.3	+	22486.8i	1.27540	+	0.736354i	0.975999	−	0.217773i	$-0.0698793\pi$
$977$	38948.3	+	22486.8i	1.27540	+	0.736354i	0.299403	+	0.954127i	$0.403213\pi$
$978$		0			0
$979$	4635.87	+	2676.52i	0.151341	+	0.0873770i
$980$		0			0
$981$	−14616.4	−	7515.16i	−0.475703	−	0.244588i
$982$		0			0
$983$	−2838.80			−0.0921096			−0.0460548	−	0.998939i	$-0.514665\pi$
$983$	−2838.80			−0.0921096			−0.0460548	+	0.998939i	$0.514665\pi$
$984$		0			0
$985$			8736.03i			0.282592i
$986$		0			0
$987$	−9460.66	+	4366.52i	−0.305102	+	0.140819i
$988$		0			0
$989$	1490.47	+	860.525i	0.0479214	+	0.0276675i
$990$		0			0
$991$	−17603.9	−	30490.9i	−0.564285	−	0.977371i	−0.997116	−	0.0758954i	$-0.975818\pi$
$991$	−17603.9	−	30490.9i	−0.564285	−	0.977371i	0.432831	−	0.901475i	$-0.357515\pi$
$992$		0			0
$993$	8007.44	−	8407.11i	0.255900	−	0.268672i
$994$		0			0
$995$	4623.67	−	2669.48i	0.147317	−	0.0850534i
$996$		0			0
$997$			42405.2i			1.34703i	0.739175	+	0.673513i	$0.235216\pi$
$997$			42405.2i			1.34703i	−0.739175	+	0.673513i	$0.764784\pi$
$998$		0			0
$999$	6721.16	−	2338.49i	0.212861	−	0.0740608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.9	yes	48
3.2	odd	2		756.4.bm.a.89.13		48
7.3	odd	6		252.4.w.a.101.18	yes	48
9.4	even	3		756.4.w.a.341.13		48
9.5	odd	6		252.4.w.a.5.18	✓	48
21.17	even	6		756.4.w.a.521.13		48
63.31	odd	6		756.4.bm.a.17.13		48
63.59	even	6	inner	252.4.bm.a.185.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.18	✓	48	9.5	odd	6
252.4.w.a.101.18	yes	48	7.3	odd	6
252.4.bm.a.173.9	yes	48	1.1	even	1	trivial
252.4.bm.a.185.9	yes	48	63.59	even	6	inner
756.4.w.a.341.13		48	9.4	even	3
756.4.w.a.521.13		48	21.17	even	6
756.4.bm.a.17.13		48	63.31	odd	6
756.4.bm.a.89.13		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46664 - 4.98488i) q^{3} -2.27383 q^{5} +(17.2174 + 6.82357i) q^{7} +(-22.6980 + 14.6220i) q^{9} +O(q^{10})\)	\(q+(-1.46664 - 4.98488i) q^{3} -2.27383 q^{5} +(17.2174 + 6.82357i) q^{7} +(-22.6980 + 14.6220i) q^{9} -35.8853i q^{11} +(70.2337 - 40.5494i) q^{13} +(3.33487 + 11.3347i) q^{15} +(-25.8458 - 44.7662i) q^{17} +(-9.61456 - 5.55097i) q^{19} +(8.76302 - 95.8343i) q^{21} +30.5607i q^{23} -119.830 q^{25} +(106.178 + 91.7014i) q^{27} +(-167.883 - 96.9271i) q^{29} +(-162.817 - 94.0025i) q^{31} +(-178.884 + 52.6306i) q^{33} +(-39.1494 - 15.5156i) q^{35} +(25.3619 - 43.9281i) q^{37} +(-305.141 - 290.635i) q^{39} +(-151.024 - 261.582i) q^{41} +(28.1579 - 48.7709i) q^{43} +(51.6112 - 33.2479i) q^{45} +(-54.1374 - 93.7687i) q^{47} +(249.878 + 234.968i) q^{49} +(-185.248 + 194.494i) q^{51} +(548.106 - 316.449i) q^{53} +81.5969i q^{55} +(-13.5698 + 56.0686i) q^{57} +(-343.355 + 594.708i) q^{59} +(340.820 - 196.773i) q^{61} +(-490.574 + 96.8714i) q^{63} +(-159.699 + 92.2024i) q^{65} +(-9.43901 + 16.3488i) q^{67} +(152.341 - 44.8214i) q^{69} -1116.45i q^{71} +(458.520 - 264.726i) q^{73} +(175.746 + 597.336i) q^{75} +(244.866 - 617.851i) q^{77} +(-231.785 - 401.464i) q^{79} +(301.395 - 663.779i) q^{81} +(-212.584 + 368.205i) q^{83} +(58.7688 + 101.791i) q^{85} +(-236.947 + 979.031i) q^{87} +(-74.5855 + 129.186i) q^{89} +(1485.93 - 218.911i) q^{91} +(-229.797 + 949.490i) q^{93} +(21.8618 + 12.6219i) q^{95} +(1059.18 + 611.519i) q^{97} +(524.714 + 814.523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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