LMFDB - Embedded newform 225.4.s.a.8.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(8,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.8");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.s (of order $20$, degree $8$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.10
Character	$\chi$	$=$	225.8
Dual form			225.4.s.a.197.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.992231 + 1.94736i) q^{2} +(1.89458 + 2.60767i) q^{4} +(10.3396 + 4.25357i) q^{5} +(-5.16515 + 5.16515i) q^{7} +(-24.2273 + 3.83723i) q^{8} +O(q^{10})$	\(q+(-0.992231 + 1.94736i) q^{2} +(1.89458 + 2.60767i) q^{4} +(10.3396 + 4.25357i) q^{5} +(-5.16515 + 5.16515i) q^{7} +(-24.2273 + 3.83723i) q^{8} +(-18.5425 + 15.9144i) q^{10} +(-44.0941 + 14.3270i) q^{11} +(22.5890 - 11.5096i) q^{13} +(-4.93340 - 15.1835i) q^{14} +(8.59828 - 26.4628i) q^{16} +(18.8953 + 119.300i) q^{17} +(31.6575 - 43.5729i) q^{19} +(8.49730 + 35.0209i) q^{20} +(15.8516 - 100.083i) q^{22} +(-39.8415 - 20.3003i) q^{23} +(88.8143 + 87.9603i) q^{25} +55.4091i q^{26} +(-23.2548 - 3.68320i) q^{28} +(-152.198 + 110.579i) q^{29} +(-100.992 - 73.3750i) q^{31} +(-95.7574 - 95.7574i) q^{32} +(-251.069 - 81.5772i) q^{34} +(-75.3759 + 31.4353i) q^{35} +(26.1609 + 51.3437i) q^{37} +(53.4406 + 104.883i) q^{38} +(-266.822 - 63.3771i) q^{40} +(-287.945 - 93.5590i) q^{41} +(-114.288 - 114.288i) q^{43} +(-120.900 - 87.8389i) q^{44} +(79.0640 - 57.4433i) q^{46} +(379.394 + 60.0901i) q^{47} +289.642i q^{49} +(-259.415 + 85.6768i) q^{50} +(72.8099 + 37.0985i) q^{52} +(-91.6969 + 578.952i) q^{53} +(-516.855 - 39.4214i) q^{55} +(105.318 - 144.958i) q^{56} +(-64.3207 - 406.105i) q^{58} +(198.720 - 611.598i) q^{59} +(-160.215 - 493.091i) q^{61} +(243.095 - 123.863i) q^{62} +(493.190 - 160.247i) q^{64} +(282.518 - 22.9214i) q^{65} +(338.865 - 53.6710i) q^{67} +(-275.296 + 275.296i) q^{68} +(13.5745 - 177.975i) q^{70} +(106.245 + 146.233i) q^{71} +(-418.644 + 821.636i) q^{73} -125.943 q^{74} +173.601 q^{76} +(153.751 - 301.754i) q^{77} +(557.717 + 767.632i) q^{79} +(201.464 - 237.041i) q^{80} +(467.901 - 467.901i) q^{82} +(174.512 - 27.6401i) q^{83} +(-312.081 + 1313.88i) q^{85} +(335.961 - 109.160i) q^{86} +(1013.30 - 516.304i) q^{88} +(-196.218 - 603.897i) q^{89} +(-57.2263 + 176.125i) q^{91} +(-22.5466 - 142.354i) q^{92} +(-493.464 + 679.195i) q^{94} +(512.666 - 315.868i) q^{95} +(-23.4280 + 147.918i) q^{97} +(-564.039 - 287.392i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{7}+O(q^{10}) $ 240 * q - 24 * q^7	$ 240 q - 24 q^{7} - 192 q^{10} + 108 q^{13} + 960 q^{16} - 240 q^{19} + 384 q^{22} + 144 q^{25} + 2016 q^{28} - 1320 q^{34} - 828 q^{37} - 2568 q^{40} + 96 q^{43} + 312 q^{52} + 1512 q^{55} + 3864 q^{58} + 5760 q^{64} - 3072 q^{67} - 7104 q^{70} - 9732 q^{73} - 4320 q^{79} - 11592 q^{82} - 2028 q^{85} + 1392 q^{88} + 5520 q^{94} + 23268 q^{97}+O(q^{100}) $ 240 * q - 24 * q^7 - 192 * q^10 + 108 * q^13 + 960 * q^16 - 240 * q^19 + 384 * q^22 + 144 * q^25 + 2016 * q^28 - 1320 * q^34 - 828 * q^37 - 2568 * q^40 + 96 * q^43 + 312 * q^52 + 1512 * q^55 + 3864 * q^58 + 5760 * q^64 - 3072 * q^67 - 7104 * q^70 - 9732 * q^73 - 4320 * q^79 - 11592 * q^82 - 2028 * q^85 + 1392 * q^88 + 5520 * q^94 + 23268 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$	−0.992231	+	1.94736i	−0.350807	+	0.688497i	−0.997222	−	0.0744890i	$-0.976267\pi$
$2$	−0.992231	+	1.94736i	−0.350807	+	0.688497i	0.646415	+	0.762986i	$0.276267\pi$
$3$		0			0
$3$		0			0
$4$	1.89458	+	2.60767i	0.236823	+	0.325958i
$5$	10.3396	+	4.25357i	0.924801	+	0.380451i
$5$	10.3396	+	4.25357i	0.924801	+	0.380451i
$6$		0			0
$7$	−5.16515	+	5.16515i	−0.278892	+	0.278892i	−0.832667	−	0.553775i	$-0.813187\pi$
$7$	−5.16515	+	5.16515i	−0.278892	+	0.278892i	0.553775	+	0.832667i	$0.313187\pi$
$8$	−24.2273	+	3.83723i	−1.07070	+	0.169583i
$9$		0			0
$10$	−18.5425	+	15.9144i	−0.586366	+	0.503258i
$11$	−44.0941	+	14.3270i	−1.20862	+	0.392706i	−0.842927	−	0.538029i	$-0.819169\pi$
$11$	−44.0941	+	14.3270i	−1.20862	+	0.392706i	−0.365697	+	0.930734i	$0.619169\pi$
$12$		0			0
$13$	22.5890	−	11.5096i	0.481927	−	0.245554i	−0.196110	−	0.980582i	$-0.562831\pi$
$13$	22.5890	−	11.5096i	0.481927	−	0.245554i	0.678037	+	0.735028i	$0.262831\pi$
$14$	−4.93340	−	15.1835i	−0.0941791	−	0.289854i
$15$		0			0
$16$	8.59828	−	26.4628i	0.134348	−	0.413481i
$17$	18.8953	+	119.300i	0.269575	+	1.70203i	0.636089	+	0.771616i	$0.280551\pi$
$17$	18.8953	+	119.300i	0.269575	+	1.70203i	−0.366514	+	0.930413i	$0.619449\pi$
$18$		0			0
$19$	31.6575	−	43.5729i	0.382249	−	0.526121i	−0.573929	−	0.818905i	$-0.694582\pi$
$19$	31.6575	−	43.5729i	0.382249	−	0.526121i	0.956179	+	0.292784i	$0.0945816\pi$
$20$	8.49730	+	35.0209i	0.0950028	+	0.391546i
$21$		0			0
$22$	15.8516	−	100.083i	0.153617	−	0.969897i
$23$	−39.8415	−	20.3003i	−0.361197	−	0.184039i	0.263969	−	0.964531i	$-0.414968\pi$
$23$	−39.8415	−	20.3003i	−0.361197	−	0.184039i	−0.625165	+	0.780492i	$0.714968\pi$
$24$		0			0
$25$	88.8143	+	87.9603i	0.710515	+	0.703682i
$26$			55.4091i			0.417947i
$27$		0			0
$28$	−23.2548	−	3.68320i	−0.156955	−	0.0248593i
$29$	−152.198	+	110.579i	−0.974569	+	0.708066i	−0.956488	−	0.291770i	$-0.905756\pi$
$29$	−152.198	+	110.579i	−0.974569	+	0.708066i	−0.0180810	+	0.999837i	$0.505756\pi$
$30$		0			0
$31$	−100.992	−	73.3750i	−0.585120	−	0.425114i	0.255447	−	0.966823i	$-0.417778\pi$
$31$	−100.992	−	73.3750i	−0.585120	−	0.425114i	−0.840566	+	0.541709i	$0.817778\pi$
$32$	−95.7574	−	95.7574i	−0.528990	−	0.528990i
$33$		0			0
$34$	−251.069	−	81.5772i	−1.26641	−	0.411482i
$35$	−75.3759	+	31.4353i	−0.364024	+	0.151815i
$36$		0			0
$37$	26.1609	+	51.3437i	0.116239	+	0.228131i	0.941794	−	0.336189i	$-0.109138\pi$
$37$	26.1609	+	51.3437i	0.116239	+	0.228131i	−0.825556	+	0.564321i	$0.809138\pi$
$38$	53.4406	+	104.883i	0.228137	+	0.447744i
$39$		0			0
$40$	−266.822	−	63.3771i	−1.05471	−	0.250520i
$41$	−287.945	−	93.5590i	−1.09682	−	0.356377i	−0.295939	−	0.955207i	$-0.595633\pi$
$41$	−287.945	−	93.5590i	−1.09682	−	0.356377i	−0.800876	+	0.598830i	$0.795633\pi$
$42$		0			0
$43$	−114.288	−	114.288i	−0.405321	−	0.405321i	0.474782	−	0.880103i	$-0.342527\pi$
$43$	−114.288	−	114.288i	−0.405321	−	0.405321i	−0.880103	+	0.474782i	$0.842527\pi$
$44$	−120.900	−	87.8389i	−0.414235	−	0.300959i
$45$		0			0
$46$	79.0640	−	57.4433i	0.253421	−	0.184121i
$47$	379.394	+	60.0901i	1.17745	+	0.186490i	0.714333	−	0.699805i	$-0.246730\pi$
$47$	379.394	+	60.0901i	1.17745	+	0.186490i	0.463120	+	0.886296i	$0.346730\pi$
$48$		0			0
$49$			289.642i			0.844438i
$50$	−259.415	+	85.6768i	−0.733736	+	0.242331i
$51$		0			0
$52$	72.8099	+	37.0985i	0.194172	+	0.0989353i
$53$	−91.6969	+	578.952i	−0.237652	+	1.50047i	0.523570	+	0.851983i	$0.324600\pi$
$53$	−91.6969	+	578.952i	−0.237652	+	1.50047i	−0.761222	+	0.648492i	$0.775400\pi$
$54$		0			0
$55$	−516.855	−	39.4214i	−1.26714	−	0.0966470i
$56$	105.318	−	144.958i	0.251316	−	0.345907i
$57$		0			0
$58$	−64.3207	−	406.105i	−0.145616	−	0.919382i
$59$	198.720	−	611.598i	0.438495	−	1.34955i	−0.450968	−	0.892540i	$-0.648921\pi$
$59$	198.720	−	611.598i	0.438495	−	1.34955i	0.889463	−	0.457007i	$-0.151079\pi$
$60$		0			0
$61$	−160.215	−	493.091i	−0.336285	−	1.03498i	−0.966085	−	0.258223i	$-0.916863\pi$
$61$	−160.215	−	493.091i	−0.336285	−	1.03498i	0.629800	−	0.776757i	$-0.283137\pi$
$62$	243.095	−	123.863i	0.497954	−	0.253720i
$63$		0			0
$64$	493.190	−	160.247i	0.963262	−	0.312983i
$65$	282.518	−	22.9214i	0.539108	−	0.0437392i
$66$		0			0
$67$	338.865	−	53.6710i	0.617895	−	0.0978650i	0.160363	−	0.987058i	$-0.448734\pi$
$67$	338.865	−	53.6710i	0.617895	−	0.0978650i	0.457532	+	0.889193i	$0.348734\pi$
$68$	−275.296	+	275.296i	−0.490949	+	0.490949i
$69$		0			0
$70$	13.5745	−	177.975i	0.0231780	−	0.303887i
$71$	106.245	+	146.233i	0.177591	+	0.244433i	0.888528	−	0.458823i	$-0.151729\pi$
$71$	106.245	+	146.233i	0.177591	+	0.244433i	−0.710937	+	0.703256i	$0.751729\pi$
$72$		0			0
$73$	−418.644	+	821.636i	−0.671214	+	1.31733i	0.264436	+	0.964403i	$0.414814\pi$
$73$	−418.644	+	821.636i	−0.671214	+	1.31733i	−0.935650	+	0.352928i	$0.885186\pi$
$74$	−125.943			−0.197845
$75$		0			0
$76$	173.601			0.262019
$77$	153.751	−	301.754i	0.227553	−	0.446598i
$78$		0			0
$79$	557.717	+	767.632i	0.794280	+	1.09323i	0.993562	+	0.113290i	$0.0361390\pi$
$79$	557.717	+	767.632i	0.794280	+	1.09323i	−0.199282	+	0.979942i	$0.563861\pi$
$80$	201.464	−	237.041i	0.281554	−	0.331275i
$81$		0			0
$82$	467.901	−	467.901i	0.630135	−	0.630135i
$83$	174.512	−	27.6401i	0.230786	−	0.0365529i	−0.0399702	−	0.999201i	$-0.512726\pi$
$83$	174.512	−	27.6401i	0.230786	−	0.0365529i	0.270756	+	0.962648i	$0.412726\pi$
$84$		0			0
$85$	−312.081	+	1313.88i	−0.398235	+	1.67660i
$86$	335.961	−	109.160i	0.421252	−	0.136873i
$87$		0			0
$88$	1013.30	−	516.304i	1.22748	−	0.625434i
$89$	−196.218	−	603.897i	−0.233697	−	0.719247i	−0.997292	−	0.0735502i	$-0.976567\pi$
$89$	−196.218	−	603.897i	−0.233697	−	0.719247i	0.763594	−	0.645697i	$-0.223433\pi$
$90$		0			0
$91$	−57.2263	+	176.125i	−0.0659225	+	0.202889i
$92$	−22.5466	−	142.354i	−0.0255505	−	0.161320i
$93$		0			0
$94$	−493.464	+	679.195i	−0.541456	+	0.745251i
$95$	512.666	−	315.868i	0.553668	−	0.341130i
$96$		0			0
$97$	−23.4280	+	147.918i	−0.0245232	+	0.154833i	−0.996911	−	0.0785365i	$-0.974975\pi$
$97$	−23.4280	+	147.918i	−0.0245232	+	0.154833i	0.972388	+	0.233370i	$0.0749753\pi$
$98$	−564.039	−	287.392i	−0.581393	−	0.296235i
$99$		0			0
$100$	−61.1053	+	398.246i	−0.0611053	+	0.398246i
$101$		−	58.1064i		−	0.0572456i	−0.999590	−	0.0286228i	$-0.990888\pi$
$101$		−	58.1064i		−	0.0572456i	0.999590	−	0.0286228i	$-0.00911216\pi$
$102$		0			0
$103$	1031.48	+	163.370i	0.986741	+	0.156284i	0.628890	−	0.777494i	$-0.283510\pi$
$103$	1031.48	+	163.370i	0.986741	+	0.156284i	0.357851	+	0.933779i	$0.383510\pi$
$104$	−503.104	+	365.526i	−0.474360	+	0.344642i
$105$		0			0
$106$	−1036.44	−	753.021i	−0.949702	−	0.689999i
$107$	831.888	+	831.888i	0.751604	+	0.751604i	0.974779	−	0.223174i	$-0.0716419\pi$
$107$	831.888	+	831.888i	0.751604	+	0.751604i	−0.223174	+	0.974779i	$0.571642\pi$
$108$		0			0
$109$	1706.89	+	554.601i	1.49991	+	0.487350i	0.939991	−	0.341198i	$-0.110833\pi$
$109$	1706.89	+	554.601i	1.49991	+	0.487350i	0.559918	+	0.828548i	$0.310833\pi$
$110$	589.608	−	967.390i	0.511063	−	0.838519i
$111$		0			0
$112$	92.2729	+	181.096i	0.0778479	+	0.152785i
$113$	636.465	+	1249.13i	0.529855	+	1.03990i	0.988492	+	0.151275i	$0.0483378\pi$
$113$	636.465	+	1249.13i	0.529855	+	1.03990i	−0.458637	+	0.888624i	$0.651662\pi$
$114$		0			0
$115$	−325.596	−	379.365i	−0.264018	−	0.307617i
$116$	−576.704	−	187.382i	−0.461600	−	0.149983i
$117$		0			0
$118$	993.827	+	993.827i	0.775332	+	0.775332i
$119$	−713.799	−	518.606i	−0.549865	−	0.399500i
$120$		0			0
$121$	662.220	−	481.131i	0.497536	−	0.361481i
$122$	1119.20	+	177.263i	0.830552	+	0.131546i
$123$		0			0
$124$		−	402.369i		−	0.291401i
$125$	544.159	+	1287.25i	0.389368	+	0.921082i
$126$		0			0
$127$	846.509	+	431.318i	0.591461	+	0.301364i	0.723985	−	0.689815i	$-0.242308\pi$
$127$	846.509	+	431.318i	0.591461	+	0.301364i	−0.132524	+	0.991180i	$0.542308\pi$
$128$	−7.82252	+	49.3895i	−0.00540172	+	0.0341051i
$129$		0			0
$130$	−235.686	+	572.908i	−0.159008	+	0.386518i
$131$	1673.69	−	2303.64i	1.11627	−	1.53641i	0.304421	−	0.952538i	$-0.401537\pi$
$131$	1673.69	−	2303.64i	1.11627	−	1.53641i	0.811846	−	0.583872i	$-0.198463\pi$
$132$		0			0
$133$	61.5445	+	388.577i	0.0401247	+	0.253337i
$134$	−231.716	+	713.148i	−0.149382	+	0.459751i
$135$		0			0
$136$	−915.562	−	2817.81i	−0.577270	−	1.77666i
$137$	1918.74	−	977.645i	1.19656	−	0.609678i	0.261857	−	0.965107i	$-0.415665\pi$
$137$	1918.74	−	977.645i	1.19656	−	0.609678i	0.934703	+	0.355429i	$0.115665\pi$
$138$		0			0
$139$	−1948.20	+	633.008i	−1.18881	+	0.386266i	−0.835631	−	0.549291i	$-0.814898\pi$
$139$	−1948.20	+	633.008i	−1.18881	+	0.386266i	−0.353175	+	0.935557i	$0.614898\pi$
$140$	−224.778	−	136.999i	−0.135695	−	0.0827036i
$141$		0			0
$142$	−390.189	+	61.7998i	−0.230591	+	0.0365220i
$143$	−831.139	+	831.139i	−0.486038	+	0.486038i
$144$		0			0
$145$	−2044.02	+	495.951i	−1.17067	+	0.284045i
$146$	−1184.63	−	1630.51i	−0.671512	−	0.924257i
$147$		0			0
$148$	−84.3233	+	165.494i	−0.0468333	+	0.0919156i
$149$	2.83258			0.00155741			0.000778706	−	1.00000i	$-0.499752\pi$
$149$	2.83258			0.00155741			0.000778706		1.00000i	$0.499752\pi$
$150$		0			0
$151$	−578.563			−0.311807			−0.155903	−	0.987772i	$-0.549829\pi$
$151$	−578.563			−0.311807			−0.155903	+	0.987772i	$0.549829\pi$
$152$	−599.777	+	1177.13i	−0.320055	+	0.628144i
$153$		0			0
$154$	435.068	+	598.819i	0.227654	+	0.313339i
$155$	−732.111	−	1188.24i	−0.379384	−	0.615755i
$156$		0			0
$157$	2086.25	−	2086.25i	1.06051	−	1.06051i	0.0624655	−	0.998047i	$-0.480104\pi$
$157$	2086.25	−	2086.25i	1.06051	−	1.06051i	0.998047	−	0.0624655i	$-0.0198963\pi$
$158$	−2048.24	+	324.410i	−1.03133	+	0.163346i
$159$		0			0
$160$	−582.782	−	1397.40i	−0.287956	−	0.690465i
$161$	310.641	−	100.934i	0.152062	−	0.0494079i
$162$		0			0
$163$	−315.608	+	160.810i	−0.151658	+	0.0772738i	−0.528173	−	0.849137i	$-0.677123\pi$
$163$	−315.608	+	160.810i	−0.151658	+	0.0772738i	0.376514	+	0.926411i	$0.377123\pi$
$164$	−301.564	−	928.120i	−0.143587	−	0.441914i
$165$		0			0
$166$	−119.331	+	367.264i	−0.0557947	+	0.171718i
$167$	160.116	+	1010.93i	0.0741924	+	0.468433i	0.996612	+	0.0822439i	$0.0262087\pi$
$167$	160.116	+	1010.93i	0.0741924	+	0.468433i	−0.922420	+	0.386189i	$0.873791\pi$
$168$		0			0
$169$	−913.575	+	1257.43i	−0.415829	+	0.572339i
$170$	−2248.95	−	1911.41i	−1.01463	−	0.862345i
$171$		0			0
$172$	81.4974	−	514.555i	0.0361286	−	0.228107i
$173$	1608.74	+	819.696i	0.706997	+	0.360233i	0.770230	−	0.637766i	$-0.220141\pi$
$173$	1608.74	+	819.696i	0.706997	+	0.360233i	−0.0632331	+	0.997999i	$0.520141\pi$
$174$		0			0
$175$	−913.068	+	4.41113i	−0.394408	+	0.00190543i
$176$			1290.04i			0.552502i
$177$		0			0
$178$	1370.70	+	217.098i	0.577182	+	0.0914166i
$179$	−2602.38	+	1890.74i	−1.08665	+	0.789500i	−0.978831	−	0.204670i	$-0.934388\pi$
$179$	−2602.38	+	1890.74i	−1.08665	+	0.789500i	−0.107823	+	0.994170i	$0.534388\pi$
$180$		0			0
$181$	−2642.96	−	1920.22i	−1.08536	−	0.788558i	−0.106748	−	0.994286i	$-0.534044\pi$
$181$	−2642.96	−	1920.22i	−1.08536	−	0.788558i	−0.978609	+	0.205728i	$0.934044\pi$
$182$	−286.197	−	286.197i	−0.116562	−	0.116562i
$183$		0			0
$184$	1043.15	+	338.939i	0.417945	+	0.135799i
$185$	52.0994	+	642.151i	0.0207050	+	0.255199i
$186$		0			0
$187$	−2542.38	−	4989.71i	−0.994211	−	1.95125i
$188$	562.098	+	1103.18i	0.218059	+	0.427966i
$189$		0			0
$190$	106.427	+	1311.76i	0.0406369	+	0.500869i
$191$	4484.69	+	1457.16i	1.69896	+	0.552024i	0.988434	−	0.151651i	$-0.0484589\pi$
$191$	4484.69	+	1457.16i	1.69896	+	0.552024i	0.710522	+	0.703675i	$0.248459\pi$
$192$		0			0
$193$	1540.32	+	1540.32i	0.574481	+	0.574481i	0.933377	−	0.358897i	$-0.116847\pi$
$193$	1540.32	+	1540.32i	0.574481	+	0.574481i	−0.358897	+	0.933377i	$0.616847\pi$
$194$	−264.805	−	192.392i	−0.0979995	−	0.0712008i
$195$		0			0
$196$	−755.291	+	548.751i	−0.275252	+	0.199982i
$197$	−1723.18	−	272.924i	−0.623204	−	0.0987058i	−0.163157	−	0.986600i	$-0.552168\pi$
$197$	−1723.18	−	272.924i	−0.623204	−	0.0987058i	−0.460047	+	0.887894i	$0.652168\pi$
$198$		0			0
$199$			1876.86i			0.668579i	0.942470	+	0.334289i	$0.108496\pi$
$199$			1876.86i			0.668579i	−0.942470	+	0.334289i	$0.891504\pi$
$200$	−2489.25	−	1790.24i	−0.880084	−	0.632945i
$201$		0			0
$202$	113.154	+	57.6550i	0.0394134	+	0.0200821i
$203$	214.972	−	1357.28i	0.0743257	−	0.469274i
$204$		0			0
$205$	−2579.27	−	2192.16i	−0.878753	−	0.746862i
$206$	−1341.60	+	1846.56i	−0.453757	+	0.624543i
$207$		0			0
$208$	−110.351	−	696.730i	−0.0367859	−	0.232257i
$209$	−771.640	+	2374.86i	−0.255385	+	0.785994i
$210$		0			0
$211$	798.756	+	2458.32i	0.260610	+	0.802074i	0.992672	+	0.120837i	$0.0385577\pi$
$211$	798.756	+	2458.32i	0.260610	+	0.802074i	−0.732063	+	0.681237i	$0.761442\pi$
$212$	−1683.44	+	857.756i	−0.545373	+	0.277882i
$213$		0			0
$214$	−2445.41	+	794.563i	−0.781145	+	0.253809i
$215$	−695.562	−	1667.83i	−0.220637	−	0.529046i
$216$		0			0
$217$	900.633	−	142.646i	0.281746	−	0.0446242i
$218$	−2773.64	+	2773.64i	−0.861717	+	0.861717i
$219$		0			0
$220$	−876.426	−	1422.47i	−0.268585	−	0.435924i
$221$	1799.92	+	2477.38i	0.547855	+	0.754058i
$222$		0			0
$223$	1889.23	−	3707.83i	0.567320	−	1.11343i	−0.412014	−	0.911178i	$-0.635174\pi$
$223$	1889.23	−	3707.83i	0.567320	−	1.11343i	0.979334	−	0.202251i	$-0.0648256\pi$
$224$	989.204			0.295062
$225$		0			0
$226$	−3064.04			−0.901843
$227$	−1732.22	+	3399.67i	−0.506481	+	0.994025i	0.486267	+	0.873810i	$0.338358\pi$
$227$	−1732.22	+	3399.67i	−0.506481	+	0.994025i	−0.992748	+	0.120215i	$0.961642\pi$
$228$		0			0
$229$	1037.51	+	1428.01i	0.299392	+	0.412078i	0.932036	−	0.362364i	$-0.118030\pi$
$229$	1037.51	+	1428.01i	0.299392	+	0.412078i	−0.632644	+	0.774443i	$0.718030\pi$
$230$	1061.83	−	257.637i	0.304413	−	0.0738611i
$231$		0			0
$232$	3263.04	−	3263.04i	0.923400	−	0.923400i
$233$	−1051.92	+	166.607i	−0.295765	+	0.0468446i	−0.302554	−	0.953132i	$-0.597839\pi$
$233$	−1051.92	+	166.607i	−0.295765	+	0.0468446i	0.00678853	+	0.999977i	$0.497839\pi$
$234$		0			0
$235$	3667.18	+	2235.09i	1.01796	+	0.620429i
$236$	1971.34	−	640.526i	0.543742	−	0.176672i
$237$		0			0
$238$	1718.17	−	875.450i	0.467951	−	0.238433i
$239$	−649.721	−	1999.63i	−0.175845	−	0.541195i	0.823826	−	0.566843i	$-0.191835\pi$
$239$	−649.721	−	1999.63i	−0.175845	−	0.541195i	−0.999671	+	0.0256476i	$0.991835\pi$
$240$		0			0
$241$	1007.15	−	3099.69i	0.269196	−	0.828499i	−0.721501	−	0.692413i	$-0.756548\pi$
$241$	1007.15	−	3099.69i	0.269196	−	0.828499i	0.990697	−	0.136086i	$-0.0434524\pi$
$242$	279.862	+	1766.98i	0.0743396	+	0.469362i
$243$		0			0
$244$	982.276	−	1351.99i	0.257720	−	0.354722i
$245$	−1232.01	+	2994.78i	−0.321267	+	0.780938i
$246$		0			0
$247$	213.602	−	1348.63i	0.0550251	−	0.347415i
$248$	2728.32	+	1390.15i	0.698583	+	0.355946i
$249$		0			0
$250$	−3046.68	−	217.576i	−0.770755	−	0.0550429i
$251$		−	3930.20i		−	0.988334i	−0.869367	−	0.494167i	$-0.835473\pi$
$251$		−	3930.20i		−	0.988334i	0.869367	−	0.494167i	$-0.164527\pi$
$252$		0			0
$253$	2047.62	+	324.310i	0.508824	+	0.0805898i
$254$	−1679.87	+	1220.49i	−0.414977	+	0.301498i
$255$		0			0
$256$	3267.84	+	2374.23i	0.797813	+	0.579645i
$257$	458.653	+	458.653i	0.111323	+	0.111323i	0.760574	−	0.649251i	$-0.224918\pi$
$257$	458.653	+	458.653i	0.111323	+	0.111323i	−0.649251	+	0.760574i	$0.724918\pi$
$258$		0			0
$259$	−400.324	−	130.073i	−0.0960421	−	0.0312060i
$260$	595.024	+	693.285i	0.141930	+	0.165368i
$261$		0			0
$262$	2825.33	+	5545.02i	0.666219	+	1.30753i
$263$	−936.074	−	1837.15i	−0.219471	−	0.430736i	0.754851	−	0.655897i	$-0.227709\pi$
$263$	−936.074	−	1837.15i	−0.219471	−	0.430736i	−0.974322	+	0.225161i	$0.927709\pi$
$264$		0			0
$265$	−3410.72	+	5596.09i	−0.790637	+	1.29723i
$266$	−817.766	−	265.708i	−0.188498	−	0.0612467i
$267$		0			0
$268$	781.963	+	781.963i	0.178231	+	0.178231i
$269$	736.996	+	535.459i	0.167046	+	0.121366i	0.668168	−	0.744011i	$-0.267079\pi$
$269$	736.996	+	535.459i	0.167046	+	0.121366i	−0.501121	+	0.865377i	$0.667079\pi$
$270$		0			0
$271$	714.336	−	518.996i	0.160121	−	0.116335i	−0.504839	−	0.863213i	$-0.668448\pi$
$271$	714.336	−	518.996i	0.160121	−	0.116335i	0.664961	+	0.746878i	$0.268448\pi$
$272$	3319.47	+	525.753i	0.739973	+	0.117200i
$273$		0			0
$274$			4706.53i			1.03771i
$275$	−5176.39	−	2606.08i	−1.13508	−	0.571464i
$276$		0			0
$277$	−3470.85	−	1768.48i	−0.752862	−	0.383603i	0.0350535	−	0.999385i	$-0.488840\pi$
$277$	−3470.85	−	1768.48i	−0.752862	−	0.383603i	−0.787916	+	0.615783i	$0.788840\pi$
$278$	700.367	−	4421.94i	0.151098	−	0.953994i
$279$		0			0
$280$	1705.53	−	1050.83i	0.364018	−	0.224282i
$281$	1202.97	−	1655.74i	0.255384	−	0.351506i	−0.662003	−	0.749501i	$-0.730294\pi$
$281$	1202.97	−	1655.74i	0.255384	−	0.351506i	0.917388	+	0.397994i	$0.130294\pi$
$282$		0			0
$283$	1004.79	+	6344.01i	0.211055	+	1.33255i	0.834640	+	0.550796i	$0.185676\pi$
$283$	1004.79	+	6344.01i	0.211055	+	1.33255i	−0.623585	+	0.781756i	$0.714324\pi$
$284$	−180.039	+	554.102i	−0.0376173	+	0.115774i
$285$		0			0
$286$	−793.848	−	2443.21i	−0.164130	−	0.505141i
$287$	1970.53	−	1004.03i	0.405284	−	0.206503i
$288$		0			0
$289$	−9202.91	+	2990.21i	−1.87317	+	0.608631i
$290$	1062.34	−	4472.55i	0.215114	−	0.905646i
$291$		0			0
$292$	−2935.71	+	464.970i	−0.588354	+	0.0931861i
$293$	5012.38	−	5012.38i	0.999407	−	0.999407i	−0.000592332	−	1.00000i	$-0.500189\pi$
$293$	5012.38	−	5012.38i	0.999407	−	0.999407i	1.00000		0.000592332i	$0.000188545\pi$
$294$		0			0
$295$	4656.16	−	5478.41i	0.918956	−	1.08124i
$296$	−830.826	−	1143.53i	−0.163145	−	0.224549i
$297$		0			0
$298$	−2.81058	+	5.51607i	−0.000546350	+	0.00107227i
$299$	−1133.63			−0.219262
$300$		0			0
$301$	1180.63			0.226082
$302$	574.069	−	1126.67i	0.109384	−	0.214678i
$303$		0			0
$304$	−880.859	−	1212.40i	−0.166187	−	0.228736i
$305$	440.838	−	5779.84i	0.0827617	−	1.08509i
$306$		0			0
$307$	995.605	−	995.605i	0.185089	−	0.185089i	−0.608480	−	0.793569i	$-0.708221\pi$
$307$	995.605	−	995.605i	0.185089	−	0.185089i	0.793569	+	0.608480i	$0.208221\pi$
$308$	1078.17	−	170.765i	0.199462	−	0.0315917i
$309$		0			0
$310$	3040.37	−	246.673i	0.557036	−	0.0451938i
$311$	431.038	−	140.053i	0.0785915	−	0.0255359i	−0.269457	−	0.963012i	$-0.586844\pi$
$311$	431.038	−	140.053i	0.0785915	−	0.0255359i	0.348049	+	0.937476i	$0.386844\pi$
$312$		0			0
$313$	−4113.61	+	2095.99i	−0.742859	+	0.378506i	−0.784093	−	0.620644i	$-0.786871\pi$
$313$	−4113.61	+	2095.99i	−0.742859	+	0.378506i	0.0412332	+	0.999150i	$0.486871\pi$
$314$	1992.64	+	6132.71i	0.358125	+	1.10219i
$315$		0			0
$316$	−945.088	+	2908.68i	−0.168245	+	0.517804i
$317$	−228.945	−	1445.50i	−0.0405641	−	0.256112i	0.959070	−	0.283170i	$-0.0913860\pi$
$317$	−228.945	−	1445.50i	−0.0405641	−	0.256112i	−0.999634	+	0.0270582i	$0.991386\pi$
$318$		0			0
$319$	5126.78	−	7056.40i	0.899826	−	1.23850i
$320$	5781.01	+	440.927i	1.00990	+	0.0770268i
$321$		0			0
$322$	−111.674	+	705.081i	−0.0193272	+	0.122027i
$323$	5796.42	+	2953.42i	0.998518	+	0.508770i
$324$		0			0
$325$	3018.61	+	964.710i	0.515208	+	0.164654i
$326$		−	774.164i		−	0.131524i
$327$		0			0
$328$	7335.13	+	1161.77i	1.23480	+	0.195573i
$329$	−2270.00	+	1649.25i	−0.380393	+	0.276372i
$330$		0			0
$331$	4471.53	+	3248.76i	0.742530	+	0.539480i	0.893502	−	0.449058i	$-0.148240\pi$
$331$	4471.53	+	3248.76i	0.742530	+	0.539480i	−0.150972	+	0.988538i	$0.548240\pi$
$332$	402.704	+	402.704i	0.0665700	+	0.0665700i
$333$		0			0
$334$	−2127.52	−	691.274i	−0.348542	−	0.113248i
$335$	3732.02	+	886.450i	0.608663	+	0.144573i
$336$		0			0
$337$	−2676.34	−	5252.62i	−0.432610	−	0.849046i	−0.999678	−	0.0253746i	$-0.991922\pi$
$337$	−2676.34	−	5252.62i	−0.432610	−	0.849046i	0.567068	−	0.823671i	$-0.308078\pi$
$338$	−1542.19	−	3026.72i	−0.248178	−	0.487077i
$339$		0			0
$340$	−4017.44	+	1675.46i	−0.640812	+	0.267248i
$341$	5504.40	+	1788.49i	0.874134	+	0.284023i
$342$		0			0
$343$	−3267.70	−	3267.70i	−0.514399	−	0.514399i
$344$	3207.45	+	2330.35i	0.502715	+	0.365244i
$345$		0			0
$346$	−3192.49	+	2319.48i	−0.496039	+	0.360393i
$347$	−7313.05	−	1158.27i	−1.13137	−	0.179191i	−0.437449	−	0.899243i	$-0.644118\pi$
$347$	−7313.05	−	1158.27i	−1.13137	−	0.179191i	−0.693920	+	0.720052i	$0.744118\pi$
$348$		0			0
$349$		−	7306.23i		−	1.12061i	−0.828286	−	0.560306i	$-0.810684\pi$
$349$		−	7306.23i		−	1.12061i	0.828286	−	0.560306i	$-0.189316\pi$
$350$	897.385	−	1782.45i	0.137049	−	0.272217i
$351$		0			0
$352$	5594.25	+	2850.41i	0.847087	+	0.431612i
$353$	637.248	−	4023.42i	0.0960829	−	0.606644i	−0.891918	−	0.452197i	$-0.850640\pi$
$353$	637.248	−	4023.42i	0.0960829	−	0.606644i	0.988001	−	0.154447i	$-0.0493596\pi$
$354$		0			0
$355$	476.514	+	1963.91i	0.0712415	+	0.293616i
$356$	1203.01	−	1655.80i	0.179100	−	0.246510i
$357$		0			0
$358$	−1099.79	−	6943.83i	−0.162363	−	1.02512i
$359$	3919.08	−	12061.7i	0.576158	−	1.77323i	−0.0560420	−	0.998428i	$-0.517848\pi$
$359$	3919.08	−	12061.7i	0.576158	−	1.77323i	0.632200	−	0.774805i	$-0.282152\pi$
$360$		0			0
$361$	1223.15	+	3764.48i	0.178328	+	0.548838i
$362$	6361.80	−	3241.50i	0.923670	−	0.470633i
$363$		0			0
$364$	−567.694	+	184.455i	−0.0817452	+	0.0265606i
$365$	−7823.50	+	6714.65i	−1.12192	+	0.962906i
$366$		0			0
$367$	−131.378	+	20.8083i	−0.0186863	+	0.00295962i	−0.165771	−	0.986164i	$-0.553011\pi$
$367$	−131.378	+	20.8083i	−0.0186863	+	0.00295962i	0.147084	+	0.989124i	$0.453011\pi$
$368$	−879.770	+	879.770i	−0.124623	+	0.124623i
$369$		0			0
$370$	−1302.20	−	535.705i	−0.182967	−	0.0752703i
$371$	−2516.75	−	3464.00i	−0.352191	−	0.484750i
$372$		0			0
$373$	−5269.46	+	10341.9i	−0.731480	+	1.43561i	0.162131	+	0.986769i	$0.448163\pi$
$373$	−5269.46	+	10341.9i	−0.731480	+	1.43561i	−0.893611	+	0.448841i	$0.851837\pi$
$374$	12239.4			1.69220
$375$		0			0
$376$	−9422.27			−1.29233
$377$	−2165.28	+	4249.60i	−0.295803	+	0.580545i
$378$		0			0
$379$	7702.11	+	10601.0i	1.04388	+	1.43678i	0.893996	+	0.448076i	$0.147890\pi$
$379$	7702.11	+	10601.0i	1.04388	+	1.43678i	0.149885	+	0.988703i	$0.452110\pi$
$380$	1794.97	+	738.425i	0.242315	+	0.0996852i
$381$		0			0
$382$	−7287.47	+	7287.47i	−0.976072	+	0.976072i
$383$	−11640.4	+	1843.65i	−1.55299	+	0.245969i	−0.873171	−	0.487413i	$-0.837941\pi$
$383$	−11640.4	+	1843.65i	−1.55299	+	0.245969i	−0.679816	+	0.733382i	$0.737941\pi$
$384$		0			0
$385$	2873.26	−	2466.02i	0.380350	−	0.326442i
$386$	−4527.92	+	1471.21i	−0.597060	+	0.193996i
$387$		0			0
$388$	−430.108	+	219.151i	−0.0562769	+	0.0286745i
$389$	−965.349	−	2971.04i	−0.125823	−	0.387243i	0.868227	−	0.496167i	$-0.165260\pi$
$389$	−965.349	−	2971.04i	−0.125823	−	0.387243i	−0.994050	+	0.108924i	$0.965260\pi$
$390$		0			0
$391$	1669.00	−	5136.67i	0.215870	−	0.664380i
$392$	−1111.42	−	7017.25i	−0.143202	−	0.904144i
$393$		0			0
$394$	2241.27	−	3084.85i	0.286583	−	0.394447i
$395$	2501.40	+	10309.3i	0.318630	+	1.31321i
$396$		0			0
$397$	−795.740	+	5024.11i	−0.100597	+	0.635145i	0.884942	+	0.465700i	$0.154198\pi$
$397$	−795.740	+	5024.11i	−0.100597	+	0.635145i	−0.985540	+	0.169445i	$0.945802\pi$
$398$	−3654.93	−	1862.28i	−0.460315	−	0.234542i
$399$		0			0
$400$	3091.32	−	1593.97i	0.386416	−	0.199246i
$401$			6130.78i			0.763483i	0.924269	+	0.381742i	$0.124676\pi$
$401$			6130.78i			0.763483i	−0.924269	+	0.381742i	$0.875324\pi$
$402$		0			0
$403$	−3125.83	−	495.082i	−0.386373	−	0.0611955i
$404$	151.522	−	110.087i	0.0186597	−	0.0135570i
$405$		0			0
$406$	2429.82	+	1765.37i	0.297020	+	0.215797i
$407$	−1889.15	−	1889.15i	−0.230077	−	0.230077i
$408$		0			0
$409$	12045.9	+	3913.95i	1.45631	+	0.473185i	0.926942	−	0.375205i	$-0.122428\pi$
$409$	12045.9	+	3913.95i	1.45631	+	0.473185i	0.529371	+	0.848390i	$0.322428\pi$
$410$	6828.16	−	2847.66i	0.822485	−	0.343014i
$411$		0			0
$412$	1528.20	+	2999.26i	0.182740	+	0.358648i
$413$	2132.58	+	4185.42i	0.254085	+	0.498671i
$414$		0			0
$415$	1921.96	+	456.514i	0.227338	+	0.0539985i
$416$	−3265.19	−	1060.93i	−0.384830	−	0.125039i
$417$		0			0
$418$	−3859.08	−	3859.08i	−0.451564	−	0.451564i
$419$	−13111.7	−	9526.22i	−1.52876	−	1.11071i	−0.956925	−	0.290336i	$-0.906233\pi$
$419$	−13111.7	−	9526.22i	−1.52876	−	1.11071i	−0.571832	−	0.820371i	$-0.693767\pi$
$420$		0			0
$421$	1956.47	−	1421.46i	0.226490	−	0.164555i	−0.468753	−	0.883329i	$-0.655297\pi$
$421$	1956.47	−	1421.46i	0.226490	−	0.164555i	0.695243	+	0.718774i	$0.255297\pi$
$422$	−5579.79	−	883.752i	−0.643649	−	0.101944i
$423$		0			0
$424$		−	14378.3i		−	1.64687i
$425$	−8815.49	+	12257.6i	−1.00615	+	1.39901i
$426$		0			0
$427$	3374.42	+	1719.35i	0.382435	+	0.194860i
$428$	−593.208	+	3745.37i	−0.0669948	+	0.422989i
$429$		0			0
$430$	3938.03	+	300.360i	0.441648	+	0.0336852i
$431$	−6319.50	+	8698.05i	−0.706264	+	0.972088i	0.293606	+	0.955927i	$0.405145\pi$
$431$	−6319.50	+	8698.05i	−0.706264	+	0.972088i	−0.999869	+	0.0161618i	$0.994855\pi$
$432$		0			0
$433$	−2699.86	−	17046.2i	−0.299647	−	1.89189i	−0.433922	−	0.900951i	$-0.642870\pi$
$433$	−2699.86	−	17046.2i	−0.299647	−	1.89189i	0.134275	−	0.990944i	$-0.457130\pi$
$434$	−615.852	+	1895.40i	−0.0681148	+	0.209636i
$435$		0			0
$436$	1787.62	+	5501.73i	0.196357	+	0.604323i
$437$	−2145.82	+	1093.35i	−0.234894	+	0.119685i
$438$		0			0
$439$	−5409.43	+	1757.63i	−0.588105	+	0.191087i	−0.587928	−	0.808913i	$-0.700056\pi$
$439$	−5409.43	+	1757.63i	−0.588105	+	0.191087i	−0.000176869		1.00000i	$0.500056\pi$
$440$	12673.3	−	1028.22i	1.37312	−	0.111405i
$441$		0			0
$442$	−6610.31	+	1046.97i	−0.711358	+	0.112668i
$443$	−968.174	+	968.174i	−0.103836	+	0.103836i	−0.757116	−	0.653280i	$-0.773392\pi$
$443$	−968.174	+	968.174i	−0.103836	+	0.103836i	0.653280	+	0.757116i	$0.273392\pi$
$444$		0			0
$445$	539.902	−	7078.68i	0.0575142	−	0.754071i
$446$	5345.93	+	7358.05i	0.567572	+	0.781196i
$447$		0			0
$448$	−1719.70	+	3375.10i	−0.181358	+	0.355935i
$449$	14144.0			1.48663			0.743313	−	0.668944i	$-0.233253\pi$
$449$	14144.0			1.48663			0.743313	+	0.668944i	$0.233253\pi$
$450$		0			0
$451$	14037.1			1.46559
$452$	−2051.49	+	4026.27i	−0.213482	+	0.418982i
$453$		0			0
$454$	−4901.62	−	6746.51i	−0.506706	−	0.697421i
$455$	−1340.85	+	1577.64i	−0.138154	+	0.162551i
$456$		0			0
$457$	1111.66	−	1111.66i	0.113789	−	0.113789i	−0.647920	−	0.761708i	$-0.724361\pi$
$457$	1111.66	−	1111.66i	0.113789	−	0.113789i	0.761708	+	0.647920i	$0.224361\pi$
$458$	−3810.32	+	603.495i	−0.388743	+	0.0615709i
$459$		0			0
$460$	372.389	−	1567.78i	0.0377450	−	0.158909i
$461$	−7973.59	+	2590.78i	−0.805568	+	0.261745i	−0.682720	−	0.730680i	$-0.739203\pi$
$461$	−7973.59	+	2590.78i	−0.805568	+	0.261745i	−0.122849	+	0.992425i	$0.539203\pi$
$462$		0			0
$463$	−10089.1	+	5140.66i	−1.01270	+	0.515997i	−0.879907	−	0.475146i	$-0.842395\pi$
$463$	−10089.1	+	5140.66i	−1.01270	+	0.515997i	−0.132795	+	0.991144i	$0.542395\pi$
$464$	1617.57	+	4978.37i	0.161840	+	0.498093i
$465$		0			0
$466$	719.299	−	2213.77i	0.0715040	−	0.220067i
$467$	−2388.78	−	15082.2i	−0.236701	−	1.49447i	−0.764234	−	0.644939i	$-0.776883\pi$
$467$	−2388.78	−	15082.2i	−0.236701	−	1.49447i	0.527532	−	0.849535i	$-0.323117\pi$
$468$		0			0
$469$	−1473.07	+	2027.51i	−0.145032	+	0.199620i
$470$	−7991.22	+	4923.61i	−0.784271	+	0.483211i
$471$		0			0
$472$	−2467.61	+	15579.9i	−0.240638	+	1.51933i
$473$	6676.85	+	3402.02i	0.649053	+	0.330709i
$474$		0			0
$475$	6644.33	−	1085.29i	0.641816	−	0.104835i
$476$		−	2843.89i		−	0.273844i
$477$		0			0
$478$	4538.69	+	718.857i	0.434299	+	0.0687861i
$479$	−12110.9	+	8799.06i	−1.15524	+	0.839330i	−0.989169	−	0.146784i	$-0.953108\pi$
$479$	−12110.9	+	8799.06i	−1.15524	+	0.839330i	−0.166070	+	0.986114i	$0.553108\pi$
$480$		0			0
$481$	1181.90	+	858.698i	0.112037	+	0.0813997i
$482$	5036.89	+	5036.89i	0.475984	+	0.475984i
$483$		0			0
$484$	2509.26	+	815.308i	0.235655	+	0.0765691i
$485$	−871.417	+	1429.76i	−0.0815856	+	0.133860i
$486$		0			0
$487$	−4971.53	−	9757.18i	−0.462591	−	0.907885i	−0.997995	−	0.0632896i	$-0.979841\pi$
$487$	−4971.53	−	9757.18i	−0.462591	−	0.907885i	0.535404	−	0.844596i	$-0.320159\pi$
$488$	5773.67	+	11331.5i	0.535578	+	1.05113i
$489$		0			0
$490$	−4609.49	−	5370.70i	−0.424971	−	0.495150i
$491$	−17197.9	−	5587.94i	−1.58071	−	0.513605i	−0.618474	−	0.785805i	$-0.712249\pi$
$491$	−17197.9	−	5587.94i	−1.58071	−	0.513605i	−0.962241	+	0.272200i	$0.912249\pi$
$492$		0			0
$493$	−16067.8	−	16067.8i	−1.46787	−	1.46787i
$494$	2414.33	+	1754.12i	0.219891	+	0.159760i
$495$		0			0
$496$	−2810.06	+	2041.63i	−0.254386	+	0.184823i
$497$	−1304.09	−	206.547i	−0.117699	−	0.0186417i
$498$		0			0
$499$		−	18750.3i		−	1.68212i	−0.540938	−	0.841062i	$-0.681931\pi$
$499$		−	18750.3i		−	1.68212i	0.540938	−	0.841062i	$-0.318069\pi$
$500$	−2325.77	+	3857.79i	−0.208023	+	0.345051i
$501$		0			0
$502$	7653.52	+	3899.66i	0.680465	+	0.346714i
$503$	2962.53	−	18704.7i	0.262610	−	1.65805i	−0.405578	−	0.914060i	$-0.632930\pi$
$503$	2962.53	−	18704.7i	0.262610	−	1.65805i	0.668188	−	0.743993i	$-0.267070\pi$
$504$		0			0
$505$	247.160	−	600.797i	0.0217791	−	0.0529408i
$506$	−2663.26	+	3665.66i	−0.233985	+	0.322052i
$507$		0			0
$508$	479.046	+	3024.58i	0.0418391	+	0.264161i
$509$	−3044.27	+	9369.30i	−0.265098	+	0.815888i	0.726573	+	0.687090i	$0.241112\pi$
$509$	−3044.27	+	9369.30i	−0.265098	+	0.815888i	−0.991671	+	0.128798i	$0.958888\pi$
$510$		0			0
$511$	−2081.51	−	6406.24i	−0.180197	−	0.554590i
$512$	−8222.38	+	4189.51i	−0.709729	+	0.361625i
$513$		0			0
$514$	−1348.25	+	438.075i	−0.115698	+	0.0375927i
$515$	9970.14	+	6076.63i	0.853081	+	0.519938i
$516$		0			0
$517$	−17589.9	+	2785.97i	−1.49633	+	0.236996i
$518$	650.513	−	650.513i	0.0551774	−	0.0551774i
$519$		0			0
$520$	−6756.68	+	1639.41i	−0.569808	+	0.138255i
$521$	−6265.96	−	8624.36i	−0.526904	−	0.725221i	0.459751	−	0.888048i	$-0.347939\pi$
$521$	−6265.96	−	8624.36i	−0.526904	−	0.725221i	−0.986655	+	0.162827i	$0.947939\pi$
$522$		0			0
$523$	−7110.22	+	13954.6i	−0.594471	+	1.16671i	0.376253	+	0.926517i	$0.377212\pi$
$523$	−7110.22	+	13954.6i	−0.594471	+	1.16671i	−0.970724	+	0.240198i	$0.922788\pi$
$524$	9178.06			0.765163
$525$		0			0
$526$	4506.40			0.373552
$527$	6845.37	−	13434.8i	0.565823	−	1.11049i
$528$		0			0
$529$	−5976.34	−	8225.72i	−0.491192	−	0.676068i
$530$	−7513.39	−	12194.5i	−0.615775	−	0.999427i
$531$		0			0
$532$	−896.677	+	896.677i	−0.0730750	+	0.0730750i
$533$	−7581.21	+	1200.75i	−0.616095	+	0.0975798i
$534$		0			0
$535$	5062.89	+	12139.9i	0.409136	+	0.981033i
$536$	−8003.84	+	2600.60i	−0.644987	+	0.209569i
$537$		0			0
$538$	−1774.00	+	903.900i	−0.142161	+	0.0724348i
$539$	−4149.71	−	12771.5i	−0.331616	−	1.02061i
$540$		0			0
$541$	−4552.42	+	14010.9i	−0.361782	+	1.11345i	0.590190	+	0.807264i	$0.299053\pi$
$541$	−4552.42	+	14010.9i	−0.361782	+	1.11345i	−0.951972	+	0.306186i	$0.900947\pi$
$542$	301.886	+	1906.04i	0.0239246	+	0.151054i
$543$		0			0
$544$	9614.49	−	13233.2i	0.757754	−	1.04296i
$545$	15289.5	+	12994.7i	1.20170	+	1.02134i
$546$		0			0
$547$	−2697.89	+	17033.8i	−0.210884	+	1.33147i	0.624164	+	0.781293i	$0.285440\pi$
$547$	−2697.89	+	17033.8i	−0.210884	+	1.33147i	−0.835048	+	0.550176i	$0.814560\pi$
$548$	6184.58	+	3151.20i	0.482102	+	0.245643i
$549$		0			0
$550$	10211.2	−	7494.48i	0.791647	−	0.581029i
$551$			10132.4i			0.783399i
$552$		0			0
$553$	−6845.63	−	1084.24i	−0.526412	−	0.0833755i
$554$	6887.76	−	5004.25i	0.528218	−	0.383773i
$555$		0			0
$556$	−5341.69	−	3880.97i	−0.407443	−	0.296025i
$557$	8544.98	+	8544.98i	0.650022	+	0.650022i	0.952998	−	0.302976i	$-0.0979802\pi$
$557$	8544.98	+	8544.98i	0.650022	+	0.650022i	−0.302976	+	0.952998i	$0.597980\pi$
$558$		0			0
$559$	−3897.07	−	1266.24i	−0.294863	−	0.0958069i
$560$	183.761	+	2264.95i	0.0138666	+	0.170913i
$561$		0			0
$562$	2030.71	+	3985.49i	0.152421	+	0.299142i
$563$	−6151.48	−	12073.0i	−0.460486	−	0.903756i	−0.998162	−	0.0606037i	$-0.980697\pi$
$563$	−6151.48	−	12073.0i	−0.460486	−	0.903756i	0.537675	−	0.843152i	$-0.319303\pi$
$564$		0			0
$565$	1267.52	+	15622.8i	0.0943802	+	1.16328i
$566$	−13351.1	−	4338.03i	−0.991497	−	0.322157i
$567$		0			0
$568$	−3135.15	−	3135.15i	−0.231599	−	0.231599i
$569$	−4621.06	−	3357.39i	−0.340465	−	0.247363i	0.404393	−	0.914585i	$-0.367483\pi$
$569$	−4621.06	−	3357.39i	−0.340465	−	0.247363i	−0.744858	+	0.667223i	$0.767483\pi$
$570$		0			0
$571$	16510.3	−	11995.4i	1.21004	−	0.879148i	0.214808	−	0.976656i	$-0.431087\pi$
$571$	16510.3	−	11995.4i	1.21004	−	0.879148i	0.995235	+	0.0975083i	$0.0310873\pi$
$572$	−3742.00	−	592.674i	−0.273533	−	0.0433233i
$573$		0			0
$574$			4833.56i			0.351479i
$575$	−1752.88	−	5307.43i	−0.127131	−	0.384930i
$576$		0			0
$577$	−1908.71	−	972.535i	−0.137713	−	0.0701684i	0.383776	−	0.923426i	$-0.374623\pi$
$577$	−1908.71	−	972.535i	−0.137713	−	0.0701684i	−0.521489	+	0.853258i	$0.674623\pi$
$578$	3308.39	−	20888.4i	0.238081	−	1.50319i
$579$		0			0
$580$	−5165.84	−	4390.51i	−0.369827	−	0.314320i
$581$	−758.618	+	1044.15i	−0.0541700	+	0.0745587i
$582$		0			0
$583$	−4251.37	−	26842.1i	−0.302013	−	1.90684i
$584$	6989.82	−	21512.4i	0.495275	−	1.52430i
$585$		0			0
$586$	4787.49	+	14734.4i	0.337490	+	1.03869i
$587$	15973.8	−	8139.06i	1.12319	−	0.572292i	0.209133	−	0.977887i	$-0.432936\pi$
$587$	15973.8	−	8139.06i	1.12319	−	0.572292i	0.914053	+	0.405596i	$0.132936\pi$
$588$		0			0
$589$	−6394.32	+	2077.64i	−0.447323	+	0.145344i
$590$	6048.46	+	14503.1i	0.422053	+	1.01200i
$591$		0			0
$592$	1583.64	−	250.823i	0.109944	−	0.0174135i
$593$	−6309.14	+	6309.14i	−0.436906	+	0.436906i	−0.890969	−	0.454063i	$-0.849974\pi$
$593$	−6309.14	+	6309.14i	−0.436906	+	0.436906i	0.454063	+	0.890969i	$0.349974\pi$
$594$		0			0
$595$	−5174.47	−	8398.37i	−0.356525	−	0.578654i
$596$	5.36656	+	7.38643i	0.000368830	+	0.000507651i
$597$		0			0
$598$	1124.82	−	2207.58i	0.0769186	−	0.150961i
$599$	14233.7			0.970906			0.485453	−	0.874263i	$-0.338655\pi$
$599$	14233.7			0.970906			0.485453	+	0.874263i	$0.338655\pi$
$600$		0			0
$601$	17922.2			1.21641			0.608203	−	0.793782i	$-0.291891\pi$
$601$	17922.2			1.21641			0.608203	+	0.793782i	$0.291891\pi$
$602$	−1171.46	+	2299.12i	−0.0793110	+	0.155657i
$603$		0			0
$604$	−1096.14	−	1508.70i	−0.0738429	−	0.101636i
$605$	8893.61	−	2157.90i	0.597647	−	0.145010i
$606$		0			0
$607$	6516.87	−	6516.87i	0.435769	−	0.435769i	−0.454816	−	0.890585i	$-0.650295\pi$
$607$	6516.87	−	6516.87i	0.435769	−	0.435769i	0.890585	+	0.454816i	$0.150295\pi$
$608$	−7203.87	+	1140.98i	−0.480519	+	0.0761067i
$609$		0			0
$610$	10818.0	+	6593.41i	0.718048	+	0.437638i
$611$	9261.73	−	3009.32i	0.613240	−	0.199254i
$612$		0			0
$613$	−1775.75	+	904.791i	−0.117002	+	0.0596153i	−0.511512	−	0.859276i	$-0.670914\pi$
$613$	−1775.75	+	904.791i	−0.117002	+	0.0596153i	0.394510	+	0.918892i	$0.370914\pi$
$614$	950.934	+	2926.68i	0.0625026	+	0.192363i
$615$		0			0
$616$	−2567.08	+	7900.66i	−0.167907	+	0.516764i
$617$	1339.00	+	8454.11i	0.0873681	+	0.551620i	0.992081	+	0.125599i	$0.0400852\pi$
$617$	1339.00	+	8454.11i	0.0873681	+	0.551620i	−0.904713	+	0.426022i	$0.859915\pi$
$618$		0			0
$619$	8159.98	−	11231.2i	0.529850	−	0.729276i	−0.457257	−	0.889334i	$-0.651168\pi$
$619$	8159.98	−	11231.2i	0.529850	−	0.729276i	0.987108	+	0.160058i	$0.0511682\pi$
$620$	1711.50	−	4160.33i	0.110864	−	0.269488i
$621$		0			0
$622$	−154.956	+	978.353i	−0.00998902	+	0.0630682i
$623$	4132.72	+	2105.72i	0.265769	+	0.135416i
$624$		0			0
$625$	150.968	+	15624.3i	0.00966198	+	0.999953i
$626$		−	10090.4i		−	0.644239i
$627$		0			0
$628$	9392.79	+	1487.67i	0.596836	+	0.0945296i
$629$	−5630.99	+	4091.15i	−0.356951	+	0.259340i
$630$		0			0
$631$	−3644.43	−	2647.83i	−0.229924	−	0.167050i	0.466858	−	0.884332i	$-0.345386\pi$
$631$	−3644.43	−	2647.83i	−0.229924	−	0.167050i	−0.696783	+	0.717282i	$0.745386\pi$
$632$	−16457.6	−	16457.6i	−1.03583	−	1.03583i
$633$		0			0
$634$	3042.08	+	988.432i	0.190562	+	0.0619174i
$635$	6917.92	+	8060.33i	0.432329	+	0.503724i
$636$		0			0
$637$	3333.68	+	6542.72i	0.207355	+	0.406957i
$638$	8654.43	+	16985.3i	0.537041	+	1.05400i
$639$		0			0
$640$	−290.963	+	477.393i	−0.0179708	+	0.0294853i
$641$	21641.6	+	7031.79i	1.33353	+	0.433290i	0.887120	−	0.461539i	$-0.152703\pi$
$641$	21641.6	+	7031.79i	1.33353	+	0.433290i	0.446409	+	0.894829i	$0.352703\pi$
$642$		0			0
$643$	8600.40	+	8600.40i	0.527475	+	0.527475i	0.919819	−	0.392343i	$-0.128335\pi$
$643$	8600.40	+	8600.40i	0.527475	+	0.527475i	−0.392343	+	0.919819i	$0.628335\pi$
$644$	851.736	+	618.823i	0.0521166	+	0.0378650i
$645$		0			0
$646$	−11502.8	+	8357.25i	−0.700574	+	0.508997i
$647$	−3939.43	−	623.944i	−0.239374	−	0.0379131i	0.0355947	−	0.999366i	$-0.488667\pi$
$647$	−3939.43	−	623.944i	−0.239374	−	0.0379131i	−0.274969	+	0.961453i	$0.588667\pi$
$648$		0			0
$649$			29814.9i			1.80329i
$650$	−4873.80	+	4921.12i	−0.294102	+	0.296957i
$651$		0			0
$652$	−1017.28	−	518.332i	−0.0611041	−	0.0311341i
$653$	4681.05	−	29555.0i	0.280526	−	1.77117i	−0.297075	−	0.954854i	$-0.596011\pi$
$653$	4681.05	−	29555.0i	0.280526	−	1.77117i	0.577601	−	0.816319i	$-0.303989\pi$
$654$		0			0
$655$	27103.9	−	16699.5i	1.61685	−	0.996189i
$656$	−4951.66	+	6815.38i	−0.294710	+	0.405634i
$657$		0			0
$658$	−959.328	−	6056.96i	−0.0568367	−	0.358853i
$659$	8077.03	−	24858.5i	0.477445	−	1.46943i	−0.365186	−	0.930935i	$-0.618995\pi$
$659$	8077.03	−	24858.5i	0.477445	−	1.46943i	0.842631	−	0.538491i	$-0.181005\pi$
$660$		0			0
$661$	995.227	+	3062.99i	0.0585625	+	0.180237i	0.976059	−	0.217508i	$-0.0697928\pi$
$661$	995.227	+	3062.99i	0.0585625	+	0.180237i	−0.917496	+	0.397745i	$0.869793\pi$
$662$	−10763.3	+	5484.18i	−0.631915	+	0.321977i
$663$		0			0
$664$	−4121.90	+	1339.29i	−0.240905	+	0.0782747i
$665$	−1016.49	+	4279.51i	−0.0592750	+	0.249552i
$666$		0			0
$667$	8308.58	−	1315.95i	0.482323	−	0.0763925i
$668$	−2332.82	+	2332.82i	−0.135119	+	0.135119i
$669$		0			0
$670$	−5429.27	+	6388.04i	−0.313061	+	0.368345i
$671$	14129.0	+	19447.0i	0.812885	+	1.11884i
$672$		0			0
$673$	−10850.9	+	21296.1i	−0.621504	+	1.21977i	0.338811	+	0.940854i	$0.389975\pi$
$673$	−10850.9	+	21296.1i	−0.621504	+	1.21977i	−0.960315	+	0.278916i	$0.910025\pi$
$674$	12884.3			0.736328
$675$		0			0
$676$	−5009.80			−0.285036
$677$	4248.15	−	8337.47i	0.241166	−	0.473316i	−0.738419	−	0.674342i	$-0.764428\pi$
$677$	4248.15	−	8337.47i	0.241166	−	0.473316i	0.979586	+	0.201026i	$0.0644275\pi$
$678$		0			0
$679$	−643.013	−	885.031i	−0.0363425	−	0.0500212i
$680$	2519.21	−	33029.4i	0.142069	−	1.86268i
$681$		0			0
$682$	−8944.47	+	8944.47i	−0.502201	+	0.502201i
$683$	10781.9	−	1707.69i	0.604038	−	0.0956702i	0.153078	−	0.988214i	$-0.451082\pi$
$683$	10781.9	−	1707.69i	0.604038	−	0.0956702i	0.450960	+	0.892544i	$0.351082\pi$
$684$		0			0
$685$	23997.4	−	1946.98i	1.33853	−	0.108599i
$686$	9605.70	−	3121.08i	0.534617	−	0.173708i
$687$		0			0
$688$	−4007.07	+	2041.70i	−0.222047	+	0.113138i
$689$	4592.19	+	14133.3i	0.253917	+	0.781475i
$690$		0			0
$691$	−5962.29	+	18350.0i	−0.328243	+	1.01023i	0.641712	+	0.766946i	$0.278224\pi$
$691$	−5962.29	+	18350.0i	−0.328243	+	1.01023i	−0.969955	+	0.243283i	$0.921776\pi$
$692$	910.401	+	5748.05i	0.0500119	+	0.315763i
$693$		0			0
$694$	9511.82	−	13091.9i	0.520265	−	0.716083i
$695$	−22836.1	−	1741.75i	−1.24636	−	0.0950623i
$696$		0			0
$697$	5720.79	−	36119.6i	0.310890	−	1.96288i
$698$	14227.9	+	7249.47i	0.771538	+	0.393118i
$699$		0			0
$700$	−1741.38	−	2372.62i	−0.0940259	−	0.128109i
$701$			11812.1i			0.636431i	0.948018	+	0.318215i	$0.103084\pi$
$701$			11812.1i			0.636431i	−0.948018	+	0.318215i	$0.896916\pi$
$702$		0			0
$703$	3065.38	+	485.509i	0.164457	+	0.0260474i
$704$	−19450.9	+	14131.9i	−1.04131	+	0.756557i
$705$		0			0
$706$	7202.77	+	5233.12i	0.383966	+	0.278968i
$707$	300.129	+	300.129i	0.0159653	+	0.0159653i
$708$		0			0
$709$	17657.3	+	5737.21i	0.935310	+	0.303901i	0.736732	−	0.676184i	$-0.236368\pi$
$709$	17657.3	+	5737.21i	0.935310	+	0.303901i	0.198578	+	0.980085i	$0.436368\pi$
$710$	−4297.26	−	1020.71i	−0.227146	−	0.0539529i
$711$		0			0
$712$	7071.12	+	13877.9i	0.372193	+	0.730470i
$713$	2534.14	+	4973.54i	0.133106	+	0.261235i
$714$		0			0
$715$	−12129.0	+	5058.33i	−0.634401	+	0.264575i
$716$	−9860.84	−	3203.98i	−0.514688	−	0.167232i
$717$		0			0
$718$	19599.8	+	19599.8i	1.01875	+	1.01875i
$719$	19051.1	+	13841.4i	0.988158	+	0.717939i	0.959517	−	0.281651i	$-0.0908820\pi$
$719$	19051.1	+	13841.4i	0.988158	+	0.717939i	0.0286412	+	0.999590i	$0.490882\pi$
$720$		0			0
$721$	−6171.56	+	4483.90i	−0.318781	+	0.231608i
$722$	−8544.45	−	1353.31i	−0.440432	−	0.0697575i
$723$		0			0
$724$		−	10530.0i		−	0.540529i
$725$	−23243.9	−	3566.45i	−1.19070	−	0.182696i
$726$		0			0
$727$	10468.0	+	5333.69i	0.534023	+	0.272098i	0.700137	−	0.714008i	$-0.253122\pi$
$727$	10468.0	+	5333.69i	0.534023	+	0.272098i	−0.166114	+	0.986107i	$0.553122\pi$
$728$	710.609	−	4486.61i	0.0361771	−	0.228413i
$729$		0			0
$730$	−5313.14	−	21897.7i	−0.269381	−	1.11023i
$731$	11475.1	−	15794.1i	0.580604	−	0.799133i
$732$		0			0
$733$	251.293	+	1586.60i	0.0126626	+	0.0799488i	0.993210	−	0.116332i	$-0.0371136\pi$
$733$	251.293	+	1586.60i	0.0126626	+	0.0799488i	−0.980548	+	0.196281i	$0.937114\pi$
$734$	89.8363	−	276.488i	0.00451760	−	0.0139037i
$735$		0			0
$736$	1871.22	+	5759.02i	0.0937147	+	0.288424i
$737$	−14173.0	+	7221.50i	−0.708370	+	0.360933i
$738$		0			0
$739$	−32947.6	+	10705.3i	−1.64005	+	0.532885i	−0.976550	−	0.215290i	$-0.930930\pi$
$739$	−32947.6	+	10705.3i	−1.64005	+	0.532885i	−0.663502	+	0.748175i	$0.730930\pi$
$740$	−1575.81	+	1352.46i	−0.0782809	+	0.0671859i
$741$		0			0
$742$	9242.87	−	1463.93i	0.457300	−	0.0724291i
$743$	−3214.35	+	3214.35i	−0.158712	+	0.158712i	−0.781996	−	0.623284i	$-0.785798\pi$
$743$	−3214.35	+	3214.35i	−0.158712	+	0.158712i	0.623284	+	0.781996i	$0.285798\pi$
$744$		0			0
$745$	29.2878	+	12.0486i	0.00144030	+	0.000592518i
$746$	−14910.9	−	20523.1i	−0.731805	−	1.00724i
$747$		0			0
$748$	8194.74	−	16083.1i	0.400574	−	0.786171i
$749$	−8593.66			−0.419233
$750$		0			0
$751$	18647.6			0.906073			0.453036	−	0.891492i	$-0.350341\pi$
$751$	18647.6			0.906073			0.453036	+	0.891492i	$0.350341\pi$
$752$	4852.29	−	9523.15i	0.235299	−	0.461800i
$753$		0			0
$754$	−6127.06	−	8433.17i	−0.295934	−	0.407318i
$755$	−5982.11	−	2460.96i	−0.288359	−	0.118627i
$756$		0			0
$757$	−16702.6	+	16702.6i	−0.801936	+	0.801936i	−0.983398	−	0.181462i	$-0.941917\pi$
$757$	−16702.6	+	16702.6i	−0.801936	+	0.801936i	0.181462	+	0.983398i	$0.441917\pi$
$758$	−28286.4	+	4480.12i	−1.35542	+	0.214677i
$759$		0			0
$760$	−11208.5	+	9619.85i	−0.534965	+	0.459143i
$761$	20051.5	−	6515.13i	0.955146	−	0.310346i	0.210341	−	0.977628i	$-0.432543\pi$
$761$	20051.5	−	6515.13i	0.955146	−	0.310346i	0.744805	+	0.667282i	$0.232543\pi$
$762$		0			0
$763$	−11680.9	+	5951.73i	−0.554231	+	0.282395i
$764$	4696.81	+	14455.3i	0.222414	+	0.684521i
$765$		0			0
$766$	7959.66	−	24497.3i	0.375450	−	1.15551i
$767$	−2550.40	−	16102.6i	−0.120064	−	0.758057i
$768$		0			0
$769$	600.350	−	826.311i	0.0281524	−	0.0387484i	−0.794709	−	0.606991i	$-0.792376\pi$
$769$	600.350	−	826.311i	0.0281524	−	0.0387484i	0.822861	+	0.568242i	$0.192376\pi$
$770$	1951.30	+	8042.14i	0.0913248	+	0.376388i
$771$		0			0
$772$	−1098.38	+	6934.91i	−0.0512068	+	0.323307i
$773$	28529.0	+	14536.2i	1.32745	+	0.676368i	0.966608	−	0.256260i	$-0.0824904\pi$
$773$	28529.0	+	14536.2i	1.32745	+	0.676368i	0.360839	+	0.932628i	$0.382490\pi$
$774$		0			0
$775$	−2515.45	−	15400.0i	−0.116591	−	0.713788i
$776$		−	3673.56i		−	0.169940i
$777$		0			0
$778$	6743.54	+	1068.07i	0.310755	+	0.0492188i
$779$	−13192.3	+	9584.74i	−0.606755	+	0.440833i
$780$		0			0
$781$	−6779.85	−	4925.85i	−0.310630	−	0.225686i
$782$	8346.92	+	8346.92i	0.381695	+	0.381695i
$783$		0			0
$784$	7664.74	+	2490.43i	0.349159	+	0.113449i
$785$	30444.9	−	12696.9i	1.38424	−	0.577291i
$786$		0			0
$787$	−19655.0	−	38575.2i	−0.890249	−	1.74721i	−0.620354	−	0.784322i	$-0.713011\pi$
$787$	−19655.0	−	38575.2i	−0.890249	−	1.74721i	−0.269895	−	0.962890i	$-0.586989\pi$
$788$	−2553.00	−	5010.55i	−0.115415	−	0.226514i
$789$		0			0
$790$	−22557.9	−	5358.08i	−1.01592	−	0.241306i
$791$	−9739.40	−	3164.52i	−0.437792	−	0.142247i
$792$		0			0
$793$	−9294.39	−	9294.39i	−0.416208	−	0.416208i
$794$	−8994.20	−	6534.67i	−0.402006	−	0.292074i
$795$		0			0
$796$	−4894.23	+	3555.87i	−0.217929	+	0.158335i
$797$	37377.3	+	5919.98i	1.66119	+	0.263107i	0.915245	−	0.402898i	$-0.131997\pi$
$797$	37377.3	+	5919.98i	1.66119	+	0.263107i	0.745947	+	0.666005i	$0.231997\pi$
$798$		0			0
$799$			46397.1i			2.05433i
$800$	−81.7784	−	16927.5i	−0.00361413	−	0.748096i
$801$		0			0
$802$	−11938.9	−	6083.16i	−0.525656	−	0.267835i
$803$	6688.13	−	42227.2i	0.293921	−	1.85575i
$804$		0			0
$805$	3641.23	+	277.723i	0.159424	+	0.0121596i
$806$	4065.65	−	5595.88i	0.177675	−	0.244549i
$807$		0			0
$808$	222.967	+	1407.76i	0.00970788	+	0.0612931i
$809$	−3018.16	+	9288.96i	−0.131166	+	0.403686i	−0.994974	−	0.100134i	$-0.968073\pi$
$809$	−3018.16	+	9288.96i	−0.131166	+	0.403686i	0.863808	+	0.503821i	$0.168073\pi$
$810$		0			0
$811$	−8273.95	−	25464.6i	−0.358246	−	1.10257i	−0.954103	−	0.299478i	$-0.903188\pi$
$811$	−8273.95	−	25464.6i	−0.358246	−	1.10257i	0.595857	−	0.803090i	$-0.296812\pi$
$812$	3946.62	−	2010.91i	0.170566	−	0.0869076i
$813$		0			0
$814$	5553.32	−	1804.38i	0.239120	−	0.0776948i
$815$	−3947.27	+	320.253i	−0.169653	+	0.0137644i
$816$		0			0
$817$	−8597.96	+	1361.78i	−0.368182	+	0.0583143i
$818$	−19574.2	+	19574.2i	−0.836671	+	0.836671i
$819$		0			0
$820$	829.767	−	10879.1i	0.0353375	−	0.463311i
$821$	13471.9	+	18542.5i	0.572684	+	0.788232i	0.992870	−	0.119206i	$-0.0380350\pi$
$821$	13471.9	+	18542.5i	0.572684	+	0.788232i	−0.420185	+	0.907438i	$0.638035\pi$
$822$		0			0
$823$	1084.27	−	2128.00i	0.0459237	−	0.0901304i	−0.866904	−	0.498475i	$-0.833894\pi$
$823$	1084.27	−	2128.00i	0.0459237	−	0.0901304i	0.912828	+	0.408344i	$0.133894\pi$
$824$	−25616.8			−1.08301
$825$		0			0
$826$	−10266.5			−0.432468
$827$	−15875.5	+	31157.5i	−0.667528	+	1.31010i	0.270225	+	0.962797i	$0.412902\pi$
$827$	−15875.5	+	31157.5i	−0.667528	+	1.31010i	−0.937754	+	0.347301i	$0.887098\pi$
$828$		0			0
$829$	−7630.64	−	10502.7i	−0.319690	−	0.440016i	0.618682	−	0.785641i	$-0.287667\pi$
$829$	−7630.64	−	10502.7i	−0.319690	−	0.440016i	−0.938373	+	0.345625i	$0.887667\pi$
$830$	−2796.02	+	3289.78i	−0.116929	+	0.137578i
$831$		0			0
$832$	9296.26	−	9296.26i	0.387368	−	0.387368i
$833$	−34554.3	+	5472.87i	−1.43726	+	0.227639i
$834$		0			0
$835$	−2644.53	+	11133.7i	−0.109602	+	0.461434i
$836$	−7654.78	+	2487.19i	−0.316682	+	0.102896i
$837$		0			0
$838$	31560.9	−	16081.1i	1.30102	−	0.662901i
$839$	8568.20	+	26370.2i	0.352571	+	1.08510i	0.957405	+	0.288750i	$0.0932396\pi$
$839$	8568.20	+	26370.2i	0.352571	+	1.08510i	−0.604834	+	0.796352i	$0.706760\pi$
$840$		0			0
$841$	3400.09	−	10464.4i	0.139411	−	0.429063i
$842$	826.826	+	5220.37i	0.0338412	+	0.213665i
$843$		0			0
$844$	−4897.17	+	6740.37i	−0.199724	+	0.274897i
$845$	−14794.6	+	9115.34i	−0.602306	+	0.371097i
$846$		0			0
$847$	−935.353	+	5905.59i	−0.0379446	+	0.239573i
$848$	14532.2	+	7404.54i	0.588489	+	0.299850i
$849$		0			0
$850$	−15123.0	−	29329.3i	−0.610250	−	1.18351i
$851$		−	2576.69i		−	0.103793i
$852$		0			0
$853$	38457.7	+	6091.10i	1.54369	+	0.244496i	0.869451	−	0.494019i	$-0.164473\pi$
$853$	38457.7	+	6091.10i	1.54369	+	0.244496i	0.674237	+	0.738515i	$0.264473\pi$
$854$	−6696.42	+	4865.23i	−0.268322	+	0.194947i
$855$		0			0
$856$	−23346.5	−	16962.3i	−0.932206	−	0.677287i
$857$	8923.33	+	8923.33i	0.355677	+	0.355677i	0.862217	−	0.506540i	$-0.169076\pi$
$857$	8923.33	+	8923.33i	0.355677	+	0.355677i	−0.506540	+	0.862217i	$0.669076\pi$
$858$		0			0
$859$	−15590.8	−	5065.77i	−0.619270	−	0.201213i	−0.0174536	−	0.999848i	$-0.505556\pi$
$859$	−15590.8	−	5065.77i	−0.619270	−	0.201213i	−0.601816	+	0.798635i	$0.705556\pi$
$860$	3031.34	−	4973.63i	0.120195	−	0.197209i
$861$		0			0
$862$	−10667.8	−	20936.8i	−0.421518	−	0.827275i
$863$	1394.17	+	2736.22i	0.0549922	+	0.107928i	0.916867	−	0.399193i	$-0.130710\pi$
$863$	1394.17	+	2736.22i	0.0549922	+	0.107928i	−0.861875	+	0.507121i	$0.830710\pi$
$864$		0			0
$865$	13147.1	+	15318.2i	0.516781	+	0.602122i
$866$	35874.1	+	11656.2i	1.40768	+	0.457384i
$867$		0			0
$868$	2078.30	+	2078.30i	0.0812695	+	0.0812695i
$869$	−35589.9	−	25857.6i	−1.38930	−	1.00939i
$870$		0			0
$871$	7036.88	−	5112.59i	0.273749	−	0.198890i
$872$	−43481.4	−	6886.77i	−1.68861	−	0.267449i
$873$		0			0
$874$		−	5263.56i		−	0.203710i
$875$	−9459.52	−	3838.19i	−0.365474	−	0.148291i
$876$		0			0
$877$	−17373.9	−	8852.43i	−0.668955	−	0.340850i	0.0863105	−	0.996268i	$-0.472492\pi$
$877$	−17373.9	−	8852.43i	−0.668955	−	0.340850i	−0.755266	+	0.655419i	$0.772492\pi$
$878$	1944.66	−	12278.1i	0.0747485	−	0.471943i
$879$		0			0
$880$	−5487.27	+	13338.5i	−0.210200	+	0.510955i
$881$	−1605.61	+	2209.93i	−0.0614011	+	0.0845113i	−0.838613	−	0.544727i	$-0.816633\pi$
$881$	−1605.61	+	2209.93i	−0.0614011	+	0.0845113i	0.777212	+	0.629239i	$0.216633\pi$
$882$		0			0
$883$	2149.44	+	13571.0i	0.0819190	+	0.517216i	0.994191	+	0.107631i	$0.0343265\pi$
$883$	2149.44	+	13571.0i	0.0819190	+	0.517216i	−0.912272	+	0.409585i	$0.865673\pi$
$884$	−3050.09	+	9387.20i	−0.116047	+	0.357156i
$885$		0			0
$886$	−924.734	−	2846.04i	−0.0350644	−	0.107917i
$887$	−26758.6	+	13634.2i	−1.01293	+	0.516112i	−0.879980	−	0.475012i	$-0.842444\pi$
$887$	−26758.6	+	13634.2i	−1.01293	+	0.516112i	−0.132947	+	0.991123i	$0.542444\pi$
$888$		0			0
$889$	−6600.17	+	2144.53i	−0.249002	+	0.0809056i
$890$	13249.0	+	8075.07i	0.498999	+	0.304131i
$891$		0			0
$892$	13248.1	−	2098.29i	0.497286	−	0.0787623i
$893$	14629.0	−	14629.0i	0.548197	−	0.548197i
$894$		0			0
$895$	−34949.9	+	8480.08i	−1.30530	+	0.316713i
$896$	−214.700	−	295.509i	−0.00800515	−	0.0110181i
$897$		0			0
$898$	−14034.1	+	27543.4i	−0.521518	+	1.02354i
$899$	23484.5			0.871249
$900$		0			0
$901$	−70801.5			−2.61791
$902$	−13928.0	+	27335.3i	−0.514138	+	1.00905i
$903$		0			0
$904$	−20213.0	−	27820.8i	−0.743667	−	1.02357i
$905$	−19159.3	−	31096.3i	−0.703732	−	1.14218i
$906$		0			0
$907$	21369.2	−	21369.2i	0.782309	−	0.782309i	−0.197911	−	0.980220i	$-0.563416\pi$
$907$	21369.2	−	21369.2i	0.782309	−	0.782309i	0.980220	+	0.197911i	$0.0634158\pi$
$908$	−12147.0	+	1923.90i	−0.443957	+	0.0703159i
$909$		0			0
$910$	−1741.80	−	4176.51i	−0.0634507	−	0.152143i
$911$	−21963.5	+	7136.36i	−0.798773	+	0.259537i	−0.679835	−	0.733365i	$-0.737949\pi$
$911$	−21963.5	+	7136.36i	−0.798773	+	0.259537i	−0.118937	+	0.992902i	$0.537949\pi$
$912$		0			0
$913$	−7298.96	+	3719.01i	−0.264579	+	0.134810i
$914$	1061.78	+	3267.84i	0.0384253	+	0.118261i
$915$		0			0
$916$	−1758.13	+	5410.98i	−0.0634174	+	0.195179i
$917$	3253.77	+	20543.5i	0.117174	+	0.739810i
$918$		0			0
$919$	−22738.6	+	31297.0i	−0.816190	+	1.12339i	0.174149	+	0.984719i	$0.444282\pi$
$919$	−22738.6	+	31297.0i	−0.816190	+	1.12339i	−0.990339	+	0.138669i	$0.955718\pi$
$920$	9344.03	+	7941.60i	0.334852	+	0.284594i
$921$		0			0
$922$	2866.46	−	18098.1i	0.102388	−	0.646453i
$923$	4083.05	+	2080.42i	0.145607	+	0.0741905i
$924$		0			0
$925$	−2192.74	+	6861.18i	−0.0779427	+	0.243886i
$926$		−	24747.9i		−	0.878257i
$927$		0			0
$928$	25162.8	+	3985.40i	0.890097	+	0.140978i
$929$	−22592.8	+	16414.6i	−0.797896	+	0.579706i	−0.910296	−	0.413957i	$-0.864146\pi$
$929$	−22592.8	+	16414.6i	−0.797896	+	0.579706i	0.112400	+	0.993663i	$0.464146\pi$
$930$		0			0
$931$	12620.5	+	9169.37i	0.444277	+	0.322786i
$932$	−2427.39	−	2427.39i	−0.0853132	−	0.0853132i
$933$		0			0
$934$	31740.7	+	10313.2i	1.11198	+	0.361303i
$935$	−5063.14	−	62405.7i	−0.177094	−	2.18276i
$936$		0			0
$937$	3917.80	+	7689.11i	0.136594	+	0.268081i	0.949164	−	0.314783i	$-0.101932\pi$
$937$	3917.80	+	7689.11i	0.136594	+	0.268081i	−0.812569	+	0.582865i	$0.801932\pi$
$938$	−2486.67	−	4880.36i	−0.0865593	−	0.169882i
$939$		0			0
$940$	1119.41	+	13797.3i	0.0388418	+	0.478744i
$941$	11089.8	+	3603.28i	0.384182	+	0.124828i	0.494739	−	0.869041i	$-0.335263\pi$
$941$	11089.8	+	3603.28i	0.384182	+	0.124828i	−0.110557	+	0.993870i	$0.535263\pi$
$942$		0			0
$943$	9572.89	+	9572.89i	0.330579	+	0.330579i
$944$	−14475.9	−	10517.4i	−0.499101	−	0.362618i
$945$		0			0
$946$	−13250.0	+	9626.66i	−0.455384	+	0.330856i
$947$	29913.5	+	4737.84i	1.02646	+	0.162576i	0.646887	−	0.762586i	$-0.276070\pi$
$947$	29913.5	+	4737.84i	1.02646	+	0.162576i	0.379574	+	0.925161i	$0.376070\pi$
$948$		0			0
$949$			23378.3i			0.799677i
$950$	−4479.26	+	14015.8i	−0.152975	+	0.478665i
$951$		0			0
$952$	19283.4	+	9825.40i	0.656491	+	0.334499i
$953$	−6138.80	+	38758.8i	−0.208662	+	1.31744i	0.631614	+	0.775283i	$0.282393\pi$
$953$	−6138.80	+	38758.8i	−0.208662	+	1.31744i	−0.840276	+	0.542159i	$0.817607\pi$
$954$		0			0
$955$	40171.7	+	34142.4i	1.36118	+	1.15688i
$956$	3983.43	−	5482.72i	0.134763	−	0.185485i
$957$		0			0
$958$	−5118.18	−	32314.9i	−0.172611	−	1.08982i
$959$	−4860.88	+	14960.3i	−0.163677	+	0.503746i
$960$		0			0
$961$	−4390.42	−	13512.3i	−0.147374	−	0.453571i
$962$	−2844.91	+	1449.55i	−0.0953468	+	0.0485816i
$963$		0			0
$964$	9991.07	−	3246.30i	0.333808	−	0.108461i
$965$	9374.43	+	22478.2i	0.312719	+	0.749842i
$966$		0			0
$967$	−14078.3	+	2229.78i	−0.468178	+	0.0741520i	−0.386066	−	0.922471i	$-0.626166\pi$
$967$	−14078.3	+	2229.78i	−0.468178	+	0.0741520i	−0.0821115	+	0.996623i	$0.526166\pi$
$968$	−14197.6	+	14197.6i	−0.471413	+	0.471413i
$969$		0			0
$970$	−1919.62	−	3115.62i	−0.0635416	−	0.103131i
$971$	11997.6	+	16513.3i	0.396521	+	0.545765i	0.959867	−	0.280457i	$-0.0904859\pi$
$971$	11997.6	+	16513.3i	0.396521	+	0.545765i	−0.563345	+	0.826222i	$0.690486\pi$
$972$		0			0
$973$	6793.16	−	13332.3i	0.223822	−	0.439275i
$974$	23933.7			0.787356
$975$		0			0
$976$	−14426.1			−0.473124
$977$	24953.4	−	48973.9i	0.817125	−	1.60370i	0.0200654	−	0.999799i	$-0.493613\pi$
$977$	24953.4	−	48973.9i	0.817125	−	1.60370i	0.797060	−	0.603900i	$-0.206387\pi$
$978$		0			0
$979$	17304.1	+	23817.0i	0.564904	+	0.777524i
$980$	−10143.5	+	2461.18i	−0.330636	+	0.0802240i
$981$		0			0
$982$	27946.1	−	27946.1i	0.908141	−	0.908141i
$983$	−50894.0	+	8060.82i	−1.65134	+	0.261547i	−0.911519	−	0.411257i	$-0.865090\pi$
$983$	−50894.0	+	8060.82i	−1.65134	+	0.261547i	−0.739821	+	0.672804i	$0.765090\pi$
$984$		0			0
$985$	−16656.0	−	10151.6i	−0.538787	−	0.328382i
$986$	47232.9	−	15346.9i	1.52556	−	0.495685i
$987$		0			0
$988$	3921.47	−	1998.09i	0.126274	−	0.0643398i
$989$	2233.34	+	6873.50i	0.0718058	+	0.220996i
$990$		0			0
$991$	11644.6	−	35838.4i	0.373262	−	1.14878i	−0.571381	−	0.820685i	$-0.693592\pi$
$991$	11644.6	−	35838.4i	0.373262	−	1.14878i	0.944644	−	0.328098i	$-0.106408\pi$
$992$	2644.54	+	16696.9i	0.0846412	+	0.534404i
$993$		0			0
$994$	1696.18	−	2334.59i	0.0541243	−	0.0744957i
$995$	−7983.36	+	19406.0i	−0.254361	+	0.618303i
$996$		0			0
$997$	5141.95	−	32465.0i	0.163337	−	1.03127i	−0.760738	−	0.649059i	$-0.775163\pi$
$997$	5141.95	−	32465.0i	0.163337	−	1.03127i	0.924075	−	0.382211i	$-0.124837\pi$
$998$	36513.7	+	18604.7i	1.15814	+	0.590101i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.s.a.8.10	✓	240
3.2	odd	2	inner	225.4.s.a.8.21	yes	240
25.22	odd	20	inner	225.4.s.a.197.21	yes	240
75.47	even	20	inner	225.4.s.a.197.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.s.a.8.10	✓	240	1.1	even	1	trivial
225.4.s.a.8.21	yes	240	3.2	odd	2	inner
225.4.s.a.197.10	yes	240	75.47	even	20	inner
225.4.s.a.197.21	yes	240	25.22	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.992231 + 1.94736i) q^{2} +(1.89458 + 2.60767i) q^{4} +(10.3396 + 4.25357i) q^{5} +(-5.16515 + 5.16515i) q^{7} +(-24.2273 + 3.83723i) q^{8} +O(q^{10})\)	\(q+(-0.992231 + 1.94736i) q^{2} +(1.89458 + 2.60767i) q^{4} +(10.3396 + 4.25357i) q^{5} +(-5.16515 + 5.16515i) q^{7} +(-24.2273 + 3.83723i) q^{8} +(-18.5425 + 15.9144i) q^{10} +(-44.0941 + 14.3270i) q^{11} +(22.5890 - 11.5096i) q^{13} +(-4.93340 - 15.1835i) q^{14} +(8.59828 - 26.4628i) q^{16} +(18.8953 + 119.300i) q^{17} +(31.6575 - 43.5729i) q^{19} +(8.49730 + 35.0209i) q^{20} +(15.8516 - 100.083i) q^{22} +(-39.8415 - 20.3003i) q^{23} +(88.8143 + 87.9603i) q^{25} +55.4091i q^{26} +(-23.2548 - 3.68320i) q^{28} +(-152.198 + 110.579i) q^{29} +(-100.992 - 73.3750i) q^{31} +(-95.7574 - 95.7574i) q^{32} +(-251.069 - 81.5772i) q^{34} +(-75.3759 + 31.4353i) q^{35} +(26.1609 + 51.3437i) q^{37} +(53.4406 + 104.883i) q^{38} +(-266.822 - 63.3771i) q^{40} +(-287.945 - 93.5590i) q^{41} +(-114.288 - 114.288i) q^{43} +(-120.900 - 87.8389i) q^{44} +(79.0640 - 57.4433i) q^{46} +(379.394 + 60.0901i) q^{47} +289.642i q^{49} +(-259.415 + 85.6768i) q^{50} +(72.8099 + 37.0985i) q^{52} +(-91.6969 + 578.952i) q^{53} +(-516.855 - 39.4214i) q^{55} +(105.318 - 144.958i) q^{56} +(-64.3207 - 406.105i) q^{58} +(198.720 - 611.598i) q^{59} +(-160.215 - 493.091i) q^{61} +(243.095 - 123.863i) q^{62} +(493.190 - 160.247i) q^{64} +(282.518 - 22.9214i) q^{65} +(338.865 - 53.6710i) q^{67} +(-275.296 + 275.296i) q^{68} +(13.5745 - 177.975i) q^{70} +(106.245 + 146.233i) q^{71} +(-418.644 + 821.636i) q^{73} -125.943 q^{74} +173.601 q^{76} +(153.751 - 301.754i) q^{77} +(557.717 + 767.632i) q^{79} +(201.464 - 237.041i) q^{80} +(467.901 - 467.901i) q^{82} +(174.512 - 27.6401i) q^{83} +(-312.081 + 1313.88i) q^{85} +(335.961 - 109.160i) q^{86} +(1013.30 - 516.304i) q^{88} +(-196.218 - 603.897i) q^{89} +(-57.2263 + 176.125i) q^{91} +(-22.5466 - 142.354i) q^{92} +(-493.464 + 679.195i) q^{94} +(512.666 - 315.868i) q^{95} +(-23.4280 + 147.918i) q^{97} +(-564.039 - 287.392i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{7}+O(q^{10}) \) 240 * q - 24 * q^7	\( 240 q - 24 q^{7} - 192 q^{10} + 108 q^{13} + 960 q^{16} - 240 q^{19} + 384 q^{22} + 144 q^{25} + 2016 q^{28} - 1320 q^{34} - 828 q^{37} - 2568 q^{40} + 96 q^{43} + 312 q^{52} + 1512 q^{55} + 3864 q^{58} + 5760 q^{64} - 3072 q^{67} - 7104 q^{70} - 9732 q^{73} - 4320 q^{79} - 11592 q^{82} - 2028 q^{85} + 1392 q^{88} + 5520 q^{94} + 23268 q^{97}+O(q^{100}) \) 240 * q - 24 * q^7 - 192 * q^10 + 108 * q^13 + 960 * q^16 - 240 * q^19 + 384 * q^22 + 144 * q^25 + 2016 * q^28 - 1320 * q^34 - 828 * q^37 - 2568 * q^40 + 96 * q^43 + 312 * q^52 + 1512 * q^55 + 3864 * q^58 + 5760 * q^64 - 3072 * q^67 - 7104 * q^70 - 9732 * q^73 - 4320 * q^79 - 11592 * q^82 - 2028 * q^85 + 1392 * q^88 + 5520 * q^94 + 23268 * q^97

Introduction

L-functions

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