LMFDB - Embedded newform 153.4.l.c.100.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,4,Mod(19,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.19"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			100.2
Character	$\chi$	$=$	153.100
Dual form			153.4.l.c.127.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.10148 - 3.10148i) q^{2} +11.2384i q^{4} +(-14.1902 + 5.87778i) q^{5} +(-30.3663 - 12.5781i) q^{7} +(10.0437 - 10.0437i) q^{8} +(62.2405 + 25.7809i) q^{10} +(9.27937 - 22.4024i) q^{11} -35.4963i q^{13} +(55.1697 + 133.191i) q^{14} +27.6061 q^{16} +(27.6397 + 64.4131i) q^{17} +(85.2385 + 85.2385i) q^{19} +(-66.0566 - 159.475i) q^{20} +(-98.2604 + 40.7008i) q^{22} +(6.73036 - 16.2485i) q^{23} +(78.4256 - 78.4256i) q^{25} +(-110.091 + 110.091i) q^{26} +(141.358 - 341.268i) q^{28} +(148.649 - 61.5726i) q^{29} +(-3.83777 - 9.26519i) q^{31} +(-165.969 - 165.969i) q^{32} +(114.052 - 285.500i) q^{34} +504.836 q^{35} +(-58.4926 - 141.214i) q^{37} -528.731i q^{38} +(-83.4879 + 201.558i) q^{40} +(-118.200 - 48.9599i) q^{41} +(-388.481 + 388.481i) q^{43} +(251.766 + 104.285i) q^{44} +(-71.2686 + 29.5204i) q^{46} +313.972i q^{47} +(521.365 + 521.365i) q^{49} -486.471 q^{50} +398.921 q^{52} +(-47.5976 - 47.5976i) q^{53} +372.437i q^{55} +(-431.322 + 178.660i) q^{56} +(-651.999 - 270.067i) q^{58} +(190.559 - 190.559i) q^{59} +(-343.420 - 142.249i) q^{61} +(-16.8330 + 40.6386i) q^{62} +808.654i q^{64} +(208.640 + 503.700i) q^{65} +546.810 q^{67} +(-723.898 + 310.625i) q^{68} +(-1565.74 - 1565.74i) q^{70} +(262.350 + 633.368i) q^{71} +(529.771 - 219.438i) q^{73} +(-256.558 + 619.385i) q^{74} +(-957.941 + 957.941i) q^{76} +(-563.561 + 563.561i) q^{77} +(34.7038 - 83.7824i) q^{79} +(-391.736 + 162.262i) q^{80} +(214.746 + 518.442i) q^{82} +(-106.789 - 106.789i) q^{83} +(-770.819 - 751.576i) q^{85} +2409.73 q^{86} +(-131.804 - 318.203i) q^{88} -611.215i q^{89} +(-446.477 + 1077.89i) q^{91} +(182.607 + 75.6382i) q^{92} +(973.777 - 973.777i) q^{94} +(-1710.56 - 708.539i) q^{95} +(437.503 - 181.220i) q^{97} -3234.01i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 32 q^{5} + 128 q^{10} - 112 q^{11} - 256 q^{14} - 1024 q^{16} + 112 q^{17} - 32 q^{19} + 640 q^{20} + 728 q^{22} - 208 q^{23} + 296 q^{25} - 1472 q^{26} - 328 q^{28} + 1272 q^{29} - 192 q^{31} + 960 q^{32}+ \cdots + 1008 q^{97}+O(q^{100}) $ 40 * q - 32 * q^5 + 128 * q^10 - 112 * q^11 - 256 * q^14 - 1024 * q^16 + 112 * q^17 - 32 * q^19 + 640 * q^20 + 728 * q^22 - 208 * q^23 + 296 * q^25 - 1472 * q^26 - 328 * q^28 + 1272 * q^29 - 192 * q^31 + 960 * q^32 + 24 * q^34 + 992 * q^35 - 1120 * q^37 + 2984 * q^40 + 1320 * q^41 + 672 * q^43 - 3744 * q^44 - 384 * q^46 - 2096 * q^49 + 448 * q^50 + 960 * q^52 - 2120 * q^53 - 5680 * q^56 + 1000 * q^58 + 832 * q^59 - 208 * q^61 + 4432 * q^62 + 2376 * q^65 - 2272 * q^67 + 4560 * q^68 - 4792 * q^70 - 256 * q^71 - 1416 * q^73 + 2704 * q^74 - 264 * q^76 - 6048 * q^77 + 1920 * q^79 - 1312 * q^80 + 8328 * q^82 - 4960 * q^83 + 3192 * q^85 + 15616 * q^86 - 248 * q^88 + 1232 * q^91 - 944 * q^92 - 10000 * q^94 - 4528 * q^95 + 1008 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	−3.10148	−	3.10148i	−1.09654	−	1.09654i	−0.994812	−	0.101727i	$-0.967563\pi$
$2$	−3.10148	−	3.10148i	−1.09654	−	1.09654i	−0.101727	−	0.994812i	$-0.532437\pi$
$3$		0			0
$3$		0			0
$4$			11.2384i			1.40480i
$5$	−14.1902	+	5.87778i	−1.26921	+	0.525725i	−0.912724	−	0.408576i	$-0.866026\pi$
$5$	−14.1902	+	5.87778i	−1.26921	+	0.525725i	−0.356487	+	0.934300i	$0.616026\pi$
$6$		0			0
$7$	−30.3663	−	12.5781i	−1.63963	−	0.679155i	−0.643366	−	0.765559i	$-0.722463\pi$
$7$	−30.3663	−	12.5781i	−1.63963	−	0.679155i	−0.996260	+	0.0864033i	$0.972463\pi$
$8$	10.0437	−	10.0437i	0.443874	−	0.443874i
$9$		0			0
$10$	62.2405	+	25.7809i	1.96822	+	0.815262i
$11$	9.27937	−	22.4024i	0.254349	−	0.614052i	−0.744197	−	0.667960i	$-0.767168\pi$
$11$	9.27937	−	22.4024i	0.254349	−	0.614052i	0.998546	+	0.0539077i	$0.0171677\pi$
$12$		0			0
$13$		−	35.4963i		−	0.757301i	−0.925540	−	0.378650i	$-0.876388\pi$
$13$		−	35.4963i		−	0.757301i	0.925540	−	0.378650i	$-0.123612\pi$
$14$	55.1697	+	133.191i	1.05319	+	2.54263i
$15$		0			0
$16$	27.6061			0.431345
$17$	27.6397	+	64.4131i	0.394330	+	0.918969i
$17$	27.6397	+	64.4131i	0.394330	+	0.918969i
$18$		0			0
$19$	85.2385	+	85.2385i	1.02921	+	1.02921i	0.999560	+	0.0296525i	$0.00944006\pi$
$19$	85.2385	+	85.2385i	1.02921	+	1.02921i	0.0296525	+	0.999560i	$0.490560\pi$
$20$	−66.0566	−	159.475i	−0.738536	−	1.78298i
$21$		0			0
$22$	−98.2604	+	40.7008i	−0.952236	+	0.394429i
$23$	6.73036	−	16.2485i	0.0610164	−	0.147307i	−0.890431	−	0.455119i	$-0.849597\pi$
$23$	6.73036	−	16.2485i	0.0610164	−	0.147307i	0.951447	+	0.307812i	$0.0995968\pi$
$24$		0			0
$25$	78.4256	−	78.4256i	0.627405	−	0.627405i
$26$	−110.091	+	110.091i	−0.830410	+	0.830410i
$27$		0			0
$28$	141.358	−	341.268i	0.954075	−	2.30334i
$29$	148.649	−	61.5726i	0.951845	−	0.394267i	0.147921	−	0.988999i	$-0.452742\pi$
$29$	148.649	−	61.5726i	0.951845	−	0.394267i	0.803924	+	0.594732i	$0.202742\pi$
$30$		0			0
$31$	−3.83777	−	9.26519i	−0.0222349	−	0.0536799i	0.912372	−	0.409362i	$-0.134249\pi$
$31$	−3.83777	−	9.26519i	−0.0222349	−	0.0536799i	−0.934607	+	0.355682i	$0.884249\pi$
$32$	−165.969	−	165.969i	−0.916861	−	0.916861i
$33$		0			0
$34$	114.052	−	285.500i	0.575287	−	1.44008i
$35$	504.836			2.43808
$36$		0			0
$37$	−58.4926	−	141.214i	−0.259895	−	0.627443i	0.739036	−	0.673666i	$-0.235281\pi$
$37$	−58.4926	−	141.214i	−0.259895	−	0.627443i	−0.998931	+	0.0462235i	$0.985281\pi$
$38$		−	528.731i		−	2.25714i
$39$		0			0
$40$	−83.4879	+	201.558i	−0.330015	+	0.796726i
$41$	−118.200	−	48.9599i	−0.450236	−	0.186494i	0.146031	−	0.989280i	$-0.453350\pi$
$41$	−118.200	−	48.9599i	−0.450236	−	0.186494i	−0.596267	+	0.802786i	$0.703350\pi$
$42$		0			0
$43$	−388.481	+	388.481i	−1.37774	+	1.37774i	−0.529309	+	0.848429i	$0.677549\pi$
$43$	−388.481	+	388.481i	−1.37774	+	1.37774i	−0.848429	+	0.529309i	$0.822451\pi$
$44$	251.766	+	104.285i	0.862618	+	0.357308i
$45$		0			0
$46$	−71.2686	+	29.5204i	−0.228434	+	0.0946206i
$47$			313.972i			0.974415i	0.873286	+	0.487207i	$0.161984\pi$
$47$			313.972i			0.974415i	−0.873286	+	0.487207i	$0.838016\pi$
$48$		0			0
$49$	521.365	+	521.365i	1.52002	+	1.52002i
$50$	−486.471			−1.37595
$51$		0			0
$52$	398.921			1.06385
$53$	−47.5976	−	47.5976i	−0.123359	−	0.123359i	0.642732	−	0.766091i	$-0.277801\pi$
$53$	−47.5976	−	47.5976i	−0.123359	−	0.123359i	−0.766091	+	0.642732i	$0.777801\pi$
$54$		0			0
$55$			372.437i			0.913080i
$56$	−431.322	+	178.660i	−1.02925	+	0.426328i
$57$		0			0
$58$	−651.999	−	270.067i	−1.47606	−	0.611406i
$59$	190.559	−	190.559i	0.420487	−	0.420487i	−0.464885	−	0.885371i	$-0.653904\pi$
$59$	190.559	−	190.559i	0.420487	−	0.420487i	0.885371	+	0.464885i	$0.153904\pi$
$60$		0			0
$61$	−343.420	−	142.249i	−0.720827	−	0.298576i	−0.00805052	−	0.999968i	$-0.502563\pi$
$61$	−343.420	−	142.249i	−0.720827	−	0.298576i	−0.712776	+	0.701391i	$0.752563\pi$
$62$	−16.8330	+	40.6386i	−0.0344806	+	0.0832436i
$63$		0			0
$64$			808.654i			1.57940i
$65$	208.640	+	503.700i	0.398132	+	0.961175i
$66$		0			0
$67$	546.810			0.997067			0.498533	−	0.866870i	$-0.333872\pi$
$67$	546.810			0.997067			0.498533	+	0.866870i	$0.333872\pi$
$68$	−723.898	+	310.625i	−1.29096	+	0.553953i
$69$		0			0
$70$	−1565.74	−	1565.74i	−2.67345	−	2.67345i
$71$	262.350	+	633.368i	0.438524	+	1.05869i	0.976459	+	0.215704i	$0.0692045\pi$
$71$	262.350	+	633.368i	0.438524	+	1.05869i	−0.537935	+	0.842986i	$0.680795\pi$
$72$		0			0
$73$	529.771	−	219.438i	0.849384	−	0.351826i	0.0848374	−	0.996395i	$-0.472963\pi$
$73$	529.771	−	219.438i	0.849384	−	0.351826i	0.764547	+	0.644568i	$0.222963\pi$
$74$	−256.558	+	619.385i	−0.403030	+	0.973001i
$75$		0			0
$76$	−957.941	+	957.941i	−1.44583	+	1.44583i
$77$	−563.561	+	563.561i	−0.834074	+	0.834074i
$78$		0			0
$79$	34.7038	−	83.7824i	0.0494239	−	0.119320i	−0.897239	−	0.441545i	$-0.854431\pi$
$79$	34.7038	−	83.7824i	0.0494239	−	0.119320i	0.946663	+	0.322225i	$0.104431\pi$
$80$	−391.736	+	162.262i	−0.547468	+	0.226768i
$81$		0			0
$82$	214.746	+	518.442i	0.289203	+	0.698199i
$83$	−106.789	−	106.789i	−0.141224	−	0.141224i	0.632960	−	0.774184i	$-0.281840\pi$
$83$	−106.789	−	106.789i	−0.141224	−	0.141224i	−0.774184	+	0.632960i	$0.781840\pi$
$84$		0			0
$85$	−770.819	−	751.576i	−0.983612	−	0.959057i
$86$	2409.73			3.02149
$87$		0			0
$88$	−131.804	−	318.203i	−0.159663	−	0.385461i
$89$		−	611.215i		−	0.727962i	−0.931406	−	0.363981i	$-0.881417\pi$
$89$		−	611.215i		−	0.727962i	0.931406	−	0.363981i	$-0.118583\pi$
$90$		0			0
$91$	−446.477	+	1077.89i	−0.514325	+	1.24169i
$92$	182.607	+	75.6382i	0.206936	+	0.0857156i
$93$		0			0
$94$	973.777	−	973.777i	1.06848	−	1.06848i
$95$	−1710.56	−	708.539i	−1.84737	−	0.765206i
$96$		0			0
$97$	437.503	−	181.220i	0.457955	−	0.189691i	−0.141766	−	0.989900i	$-0.545278\pi$
$97$	437.503	−	181.220i	0.457955	−	0.189691i	0.599721	+	0.800209i	$0.295278\pi$
$98$		−	3234.01i		−	3.33351i
$99$		0			0
$100$	881.376	+	881.376i	0.881376	+	0.881376i
$101$	612.477			0.603404			0.301702	−	0.953402i	$-0.402445\pi$
$101$	612.477			0.603404			0.301702	+	0.953402i	$0.402445\pi$
$102$		0			0
$103$	1748.00			1.67219			0.836096	−	0.548583i	$-0.184832\pi$
$103$	1748.00			1.67219			0.836096	+	0.548583i	$0.184832\pi$
$104$	−356.515	−	356.515i	−0.336146	−	0.336146i
$105$		0			0
$106$			295.246i			0.270536i
$107$	−480.322	+	198.956i	−0.433967	+	0.179755i	−0.588963	−	0.808160i	$-0.700464\pi$
$107$	−480.322	+	198.956i	−0.433967	+	0.179755i	0.154996	+	0.987915i	$0.450464\pi$
$108$		0			0
$109$	822.066	+	340.511i	0.722382	+	0.299221i	0.713418	−	0.700739i	$-0.247146\pi$
$109$	822.066	+	340.511i	0.722382	+	0.299221i	0.00896493	+	0.999960i	$0.497146\pi$
$110$	1155.11	−	1155.11i	1.00123	−	1.00123i
$111$		0			0
$112$	−838.294	−	347.233i	−0.707244	−	0.292950i
$113$	−729.892	+	1762.11i	−0.607632	+	1.46695i	0.257936	+	0.966162i	$0.416958\pi$
$113$	−729.892	+	1762.11i	−0.607632	+	1.46695i	−0.865568	+	0.500791i	$0.833042\pi$
$114$		0			0
$115$			270.130i			0.219041i
$116$	691.975	+	1670.58i	0.553865	+	1.33715i
$117$		0			0
$118$	−1182.03			−0.922160
$119$	−29.1180	−	2303.64i	−0.0224306	−	1.77458i
$120$		0			0
$121$	525.399	+	525.399i	0.394740	+	0.394740i
$122$	623.928	+	1506.29i	0.463014	+	1.11782i
$123$		0			0
$124$	104.126	−	43.1302i	0.0754093	−	0.0312356i
$125$	82.8148	−	199.933i	0.0592574	−	0.143060i
$126$		0			0
$127$	−488.380	+	488.380i	−0.341234	+	0.341234i	−0.856831	−	0.515597i	$-0.827570\pi$
$127$	−488.380	+	488.380i	−0.341234	+	0.341234i	0.515597	+	0.856831i	$0.327570\pi$
$128$	1180.27	−	1180.27i	0.815016	−	0.815016i
$129$		0			0
$130$	915.126	−	2209.31i	0.617399	−	1.49053i
$131$	2697.13	−	1117.19i	1.79885	−	0.745109i	0.811964	−	0.583707i	$-0.198398\pi$
$131$	2697.13	−	1117.19i	1.79885	−	0.745109i	0.986889	−	0.161402i	$-0.0516017\pi$
$132$		0			0
$133$	−1516.24	−	3660.52i	−0.988529	−	2.38652i
$134$	−1695.92	−	1695.92i	−1.09332	−	1.09332i
$135$		0			0
$136$	924.553	+	369.342i	0.582940	+	0.232874i
$137$	−288.798			−0.180100			−0.0900498	−	0.995937i	$-0.528703\pi$
$137$	−288.798			−0.180100			−0.0900498	+	0.995937i	$0.528703\pi$
$138$		0			0
$139$	725.418	+	1751.31i	0.442656	+	1.06867i	0.975013	+	0.222146i	$0.0713061\pi$
$139$	725.418	+	1751.31i	0.442656	+	1.06867i	−0.532358	+	0.846519i	$0.678694\pi$
$140$			5673.53i			3.42501i
$141$		0			0
$142$	1150.71	−	2778.05i	0.680036	−	1.64175i
$143$	−795.202	−	329.384i	−0.465022	−	0.192618i
$144$		0			0
$145$	−1747.46	+	1747.46i	−1.00082	+	1.00082i
$146$	−2323.66	−	962.491i	−1.31717	−	0.545591i
$147$		0			0
$148$	1587.01	−	657.361i	0.881429	−	0.365100i
$149$			1741.86i			0.957708i	0.877895	+	0.478854i	$0.158948\pi$
$149$			1741.86i			0.957708i	−0.877895	+	0.478854i	$0.841052\pi$
$150$		0			0
$151$	−1445.53	−	1445.53i	−0.779042	−	0.779042i	0.200626	−	0.979668i	$-0.435702\pi$
$151$	−1445.53	−	1445.53i	−0.779042	−	0.779042i	−0.979668	+	0.200626i	$0.935702\pi$
$152$	1712.22			0.913682
$153$		0			0
$154$	3495.74			1.82919
$155$	108.918	+	108.918i	0.0564417	+	0.0564417i
$156$		0			0
$157$			2739.20i			1.39243i	0.717832	+	0.696216i	$0.245135\pi$
$157$			2739.20i			1.39243i	−0.717832	+	0.696216i	$0.754865\pi$
$158$	−367.483	+	152.216i	−0.185034	+	0.0766436i
$159$		0			0
$160$	3330.68	+	1379.61i	1.64571	+	0.681674i
$161$	−408.752	+	408.752i	−0.200088	+	0.200088i
$162$		0			0
$163$	−647.547	−	268.223i	−0.311165	−	0.128889i	0.221636	−	0.975130i	$-0.428860\pi$
$163$	−647.547	−	268.223i	−0.311165	−	0.128889i	−0.532800	+	0.846241i	$0.678860\pi$
$164$	550.229	−	1328.37i	0.261986	−	0.632489i
$165$		0			0
$166$			662.406i			0.309715i
$167$	−228.576	−	551.832i	−0.105915	−	0.255701i	0.862033	−	0.506852i	$-0.169191\pi$
$167$	−228.576	−	551.832i	−0.105915	−	0.255701i	−0.967948	+	0.251151i	$0.919191\pi$
$168$		0			0
$169$	937.011			0.426496
$170$	59.6819	+	4721.68i	0.0269258	+	2.13021i
$171$		0			0
$172$	−4365.89	−	4365.89i	−1.93544	−	1.93544i
$173$	−952.894	−	2300.49i	−0.418770	−	1.01100i	−0.982705	−	0.185181i	$-0.940713\pi$
$173$	−952.894	−	2300.49i	−0.418770	−	1.01100i	0.563935	−	0.825819i	$-0.309287\pi$
$174$		0			0
$175$	−3367.94	+	1395.05i	−1.45481	+	0.602604i
$176$	256.167	−	618.442i	0.109712	−	0.264868i
$177$		0			0
$178$	−1895.67	+	1895.67i	−0.798239	+	0.798239i
$179$	−1796.06	+	1796.06i	−0.749963	+	0.749963i	−0.974472	−	0.224509i	$-0.927922\pi$
$179$	−1796.06	+	1796.06i	−0.749963	+	0.749963i	0.224509	+	0.974472i	$0.427922\pi$
$180$		0			0
$181$	391.473	−	945.100i	0.160762	−	0.388115i	−0.822888	−	0.568204i	$-0.807639\pi$
$181$	391.473	−	945.100i	0.160762	−	0.388115i	0.983650	+	0.180089i	$0.0576386\pi$
$182$	4727.80	−	1958.32i	1.92554	−	0.797584i
$183$		0			0
$184$	−95.5979	−	230.794i	−0.0383020	−	0.0924692i
$185$	1660.05	+	1660.05i	0.659724	+	0.659724i
$186$		0			0
$187$	1699.49	−	21.4815i	0.664592	−	0.00840042i
$188$	−3528.53			−1.36885
$189$		0			0
$190$	3107.76	+	7502.81i	1.18664	+	2.86479i
$191$			4381.51i			1.65987i	0.557861	+	0.829935i	$0.311622\pi$
$191$			4381.51i			1.65987i	−0.557861	+	0.829935i	$0.688378\pi$
$192$		0			0
$193$	1087.86	−	2626.33i	0.405730	−	0.979519i	−0.580518	−	0.814247i	$-0.697150\pi$
$193$	1087.86	−	2626.33i	0.405730	−	0.979519i	0.986248	−	0.165272i	$-0.0528501\pi$
$194$	−1918.96	−	794.857i	−0.710170	−	0.294162i
$195$		0			0
$196$	−5859.29	+	5859.29i	−2.13531	+	2.13531i
$197$	1971.22	+	816.507i	0.712913	+	0.295298i	0.709509	−	0.704696i	$-0.248917\pi$
$197$	1971.22	+	816.507i	0.712913	+	0.295298i	0.00340354	+	0.999994i	$0.498917\pi$
$198$		0			0
$199$	−1966.44	+	814.528i	−0.700490	+	0.290152i	−0.704363	−	0.709840i	$-0.748767\pi$
$199$	−1966.44	+	814.528i	−0.700490	+	0.290152i	0.00387288	+	0.999993i	$0.498767\pi$
$200$		−	1575.37i		−	0.556978i
$201$		0			0
$202$	−1899.59	−	1899.59i	−0.661656	−	0.661656i
$203$	−5288.40			−1.82844
$204$		0			0
$205$	1965.05			0.669489
$206$	−5421.40	−	5421.40i	−1.83362	−	1.83362i
$207$		0			0
$208$		−	979.913i		−	0.326658i
$209$	2700.50	−	1118.59i	0.893770	−	0.370211i
$210$		0			0
$211$	−700.253	−	290.054i	−0.228471	−	0.0946358i	0.265511	−	0.964108i	$-0.414459\pi$
$211$	−700.253	−	290.054i	−0.228471	−	0.0946358i	−0.493982	+	0.869472i	$0.664459\pi$
$212$	534.919	−	534.919i	0.173294	−	0.173294i
$213$		0			0
$214$	2106.77	+	872.651i	0.672970	+	0.278753i
$215$	3229.22	−	7796.03i	1.02433	−	2.47295i
$216$		0			0
$217$			329.622i			0.103116i
$218$	−1493.53	−	3605.71i	−0.464013	−	1.12023i
$219$		0			0
$220$	−4185.58			−1.28269
$221$	2286.43	−	981.107i	0.695936	−	0.298626i
$222$		0			0
$223$	−2128.53	−	2128.53i	−0.639180	−	0.639180i	0.311173	−	0.950353i	$-0.399278\pi$
$223$	−2128.53	−	2128.53i	−0.639180	−	0.639180i	−0.950353	+	0.311173i	$0.899278\pi$
$224$	2952.29	+	7127.47i	0.880618	+	2.12600i
$225$		0			0
$226$	7728.91	−	3201.42i	2.27486	−	0.942280i
$227$	−1100.16	+	2656.01i	−0.321674	+	0.776589i	0.677484	+	0.735538i	$0.263071\pi$
$227$	−1100.16	+	2656.01i	−0.321674	+	0.776589i	−0.999157	+	0.0410507i	$0.986929\pi$
$228$		0			0
$229$	2808.48	−	2808.48i	0.810436	−	0.810436i	−0.174263	−	0.984699i	$-0.555754\pi$
$229$	2808.48	−	2808.48i	0.810436	−	0.810436i	0.984699	+	0.174263i	$0.0557543\pi$
$230$	837.802	−	837.802i	0.240187	−	0.240187i
$231$		0			0
$232$	874.576	−	2111.41i	0.247494	−	0.597504i
$233$	4912.30	−	2034.74i	1.38118	−	0.572105i	0.436385	−	0.899760i	$-0.356259\pi$
$233$	4912.30	−	2034.74i	1.38118	−	0.572105i	0.944797	+	0.327655i	$0.106259\pi$
$234$		0			0
$235$	−1845.46	−	4455.33i	−0.512274	−	1.23674i
$236$	2141.58	+	2141.58i	0.590698	+	0.590698i
$237$		0			0
$238$	−7054.40	+	7235.01i	−1.92130	+	1.97049i
$239$	−653.157			−0.176775			−0.0883874	−	0.996086i	$-0.528171\pi$
$239$	−653.157			−0.176775			−0.0883874	+	0.996086i	$0.528171\pi$
$240$		0			0
$241$	−197.944	−	477.879i	−0.0529074	−	0.127730i	0.895216	−	0.445633i	$-0.147021\pi$
$241$	−197.944	−	477.879i	−0.0529074	−	0.127730i	−0.948123	+	0.317903i	$0.897021\pi$
$242$		−	3259.03i		−	0.865695i
$243$		0			0
$244$	1598.65	−	3859.48i	0.419439	−	1.01261i
$245$	−10462.8	−	4333.82i	−2.72833	−	1.13011i
$246$		0			0
$247$	3025.65	−	3025.65i	0.779423	−	0.779423i
$248$	−131.603	−	54.5116i	−0.0336967	−	0.0139576i
$249$		0			0
$250$	−876.935	+	363.238i	−0.221849	+	0.0918929i
$251$			4658.77i			1.17155i	0.810474	+	0.585774i	$0.199210\pi$
$251$			4658.77i			1.17155i	−0.810474	+	0.585774i	$0.800790\pi$
$252$		0			0
$253$	−301.552	−	301.552i	−0.0749345	−	0.0749345i
$254$	3029.40			0.748352
$255$		0			0
$256$	−851.930			−0.207991
$257$	3720.91	+	3720.91i	0.903129	+	0.903129i	0.995706	−	0.0925769i	$-0.0295104\pi$
$257$	3720.91	+	3720.91i	0.903129	+	0.903129i	−0.0925769	+	0.995706i	$0.529510\pi$
$258$		0			0
$259$			5023.86i			1.20528i
$260$	−5660.77	+	2344.77i	−1.35025	+	0.559294i
$261$		0			0
$262$	−11830.1	−	4900.17i	−2.78955	−	1.15547i
$263$	1119.45	−	1119.45i	0.262466	−	0.262466i	−0.563589	−	0.826055i	$-0.690580\pi$
$263$	1119.45	−	1119.45i	0.262466	−	0.262466i	0.826055	+	0.563589i	$0.190580\pi$
$264$		0			0
$265$	955.188	+	395.652i	0.221422	+	0.0917159i
$266$	−6650.45	+	16055.6i	−1.53295	+	3.70087i
$267$		0			0
$268$			6145.25i			1.40068i
$269$	−120.806	−	291.651i	−0.0273816	−	0.0661050i	0.909597	−	0.415491i	$-0.136390\pi$
$269$	−120.806	−	291.651i	−0.0273816	−	0.0661050i	−0.936979	+	0.349386i	$0.886390\pi$
$270$		0			0
$271$	−413.058			−0.0925885			−0.0462943	−	0.998928i	$-0.514741\pi$
$271$	−413.058			−0.0925885			−0.0462943	+	0.998928i	$0.514741\pi$
$272$	763.022	+	1778.19i	0.170092	+	0.396392i
$273$		0			0
$274$	895.700	+	895.700i	0.197486	+	0.197486i
$275$	−1029.18	−	2484.66i	−0.225680	−	0.544839i
$276$		0			0
$277$	432.799	−	179.271i	0.0938785	−	0.0388858i	−0.335250	−	0.942129i	$-0.608821\pi$
$277$	432.799	−	179.271i	0.0938785	−	0.0388858i	0.429128	+	0.903243i	$0.358821\pi$
$278$	3181.80	−	7681.54i	0.686444	−	1.65722i
$279$		0			0
$280$	5070.44	−	5070.44i	1.08220	−	1.08220i
$281$	965.659	−	965.659i	0.205005	−	0.205005i	−0.597135	−	0.802140i	$-0.703695\pi$
$281$	965.659	−	965.659i	0.205005	−	0.205005i	0.802140	+	0.597135i	$0.203695\pi$
$282$		0			0
$283$	−2739.67	+	6614.15i	−0.575465	+	1.38929i	0.321381	+	0.946950i	$0.395853\pi$
$283$	−2739.67	+	6614.15i	−0.575465	+	1.38929i	−0.896845	+	0.442344i	$0.854147\pi$
$284$	−7118.02	+	2948.38i	−1.48724	+	0.616036i
$285$		0			0
$286$	1444.73	+	3487.88i	0.298701	+	0.721129i
$287$	2973.46	+	2973.46i	0.611560	+	0.611560i
$288$		0			0
$289$	−3385.10	+	3560.71i	−0.689008	+	0.724754i
$290$	10839.4			2.19487
$291$		0			0
$292$	2466.13	+	5953.76i	0.494244	+	1.19321i
$293$		−	769.318i		−	0.153393i	−0.997055	−	0.0766963i	$-0.975563\pi$
$293$		−	769.318i		−	0.153393i	0.997055	−	0.0766963i	$-0.0244372\pi$
$294$		0			0
$295$	−1584.01	+	3824.14i	−0.312626	+	0.754747i
$296$	−2005.80	−	830.828i	−0.393866	−	0.163145i
$297$		0			0
$298$	5402.33	−	5402.33i	1.05016	−	1.05016i
$299$	−576.763	−	238.903i	−0.111555	−	0.0462077i
$300$		0			0
$301$	16683.1	−	6910.36i	3.19467	−	1.32328i
$302$			8966.55i			1.70850i
$303$		0			0
$304$	2353.10	+	2353.10i	0.443945	+	0.443945i
$305$	5709.32			1.07185
$306$		0			0
$307$	−420.567			−0.0781857			−0.0390929	−	0.999236i	$-0.512447\pi$
$307$	−420.567			−0.0781857			−0.0390929	+	0.999236i	$0.512447\pi$
$308$	−6333.50	−	6333.50i	−1.17170	−	1.17170i
$309$		0			0
$310$		−	675.611i		−	0.123781i
$311$	−3282.14	+	1359.51i	−0.598434	+	0.247880i	−0.661275	−	0.750144i	$-0.729984\pi$
$311$	−3282.14	+	1359.51i	−0.598434	+	0.247880i	0.0628401	+	0.998024i	$0.479984\pi$
$312$		0			0
$313$	6018.22	+	2492.83i	1.08680	+	0.450169i	0.852891	−	0.522088i	$-0.174847\pi$
$313$	6018.22	+	2492.83i	1.08680	+	0.450169i	0.233913	+	0.972258i	$0.424847\pi$
$314$	8495.57	−	8495.57i	1.52686	−	1.52686i
$315$		0			0
$316$	941.578	+	390.014i	0.167620	+	0.0694304i
$317$	2260.27	−	5456.77i	0.400471	−	0.966823i	−0.587080	−	0.809529i	$-0.699723\pi$
$317$	2260.27	−	5456.77i	0.400471	−	0.966823i	0.987552	−	0.157295i	$-0.0502772\pi$
$318$		0			0
$319$		−	3901.46i		−	0.684764i
$320$	−4753.09	−	11475.0i	−0.830331	−	2.00460i
$321$		0			0
$322$	2535.47			0.438809
$323$	−3134.51	+	7846.44i	−0.539965	+	1.35166i
$324$		0			0
$325$	−2783.82	−	2783.82i	−0.475134	−	0.475134i
$326$	1176.47	+	2840.24i	0.199873	+	0.482536i
$327$		0			0
$328$	−1678.90	+	695.425i	−0.282628	+	0.117068i
$329$	3949.18	−	9534.16i	0.661779	−	1.59768i
$330$		0			0
$331$	−6263.20	+	6263.20i	−1.04005	+	1.04005i	−0.0408867	+	0.999164i	$0.513018\pi$
$331$	−6263.20	+	6263.20i	−1.04005	+	1.04005i	−0.999164	+	0.0408867i	$0.986982\pi$
$332$	1200.13	−	1200.13i	0.198391	−	0.198391i
$333$		0			0
$334$	−1002.57	+	2420.42i	−0.164246	+	0.396525i
$335$	−7759.35	+	3214.03i	−1.26549	+	0.524183i
$336$		0			0
$337$	−3140.02	−	7580.69i	−0.507561	−	1.22536i	−0.945283	−	0.326250i	$-0.894215\pi$
$337$	−3140.02	−	7580.69i	−0.507561	−	1.22536i	0.437722	−	0.899110i	$-0.355785\pi$
$338$	−2906.12	−	2906.12i	−0.467669	−	0.467669i
$339$		0			0
$340$	8446.49	−	8662.75i	1.34728	−	1.38177i
$341$	−243.175			−0.0386177
$342$		0			0
$343$	−4959.83	−	11974.1i	−0.780775	−	1.88496i
$344$			7803.59i			1.22309i
$345$		0			0
$346$	−4179.54	+	10090.3i	−0.649403	+	1.56780i
$347$	4736.58	+	1961.96i	0.732775	+	0.303525i	0.717692	−	0.696361i	$-0.245199\pi$
$347$	4736.58	+	1961.96i	0.732775	+	0.303525i	0.0150834	+	0.999886i	$0.495199\pi$
$348$		0			0
$349$	−372.255	+	372.255i	−0.0570956	+	0.0570956i	−0.735078	−	0.677982i	$-0.762855\pi$
$349$	−372.255	+	372.255i	−0.0570956	+	0.0570956i	0.677982	+	0.735078i	$0.262855\pi$
$350$	14772.3	+	6118.90i	2.25604	+	0.934482i
$351$		0			0
$352$	−5258.21	+	2178.02i	−0.796203	+	0.329798i
$353$			2498.19i			0.376672i	0.982105	+	0.188336i	$0.0603093\pi$
$353$			2498.19i			0.376672i	−0.982105	+	0.188336i	$0.939691\pi$
$354$		0			0
$355$	−7445.60	−	7445.60i	−1.11316	−	1.11316i
$356$	6869.05			1.02264
$357$		0			0
$358$	11140.9			1.64473
$359$	−3683.94	−	3683.94i	−0.541590	−	0.541590i	0.382405	−	0.923995i	$-0.375096\pi$
$359$	−3683.94	−	3683.94i	−0.541590	−	0.541590i	−0.923995	+	0.382405i	$0.875096\pi$
$360$		0			0
$361$			7672.19i			1.11856i
$362$	−4145.36	+	1717.06i	−0.601865	+	0.249301i
$363$		0			0
$364$	−12113.7	−	5017.68i	−1.74432	−	0.722521i
$365$	−6227.76	+	6227.76i	−0.893084	+	0.893084i
$366$		0			0
$367$	4953.51	+	2051.81i	0.704553	+	0.291835i	0.706048	−	0.708164i	$-0.250476\pi$
$367$	4953.51	+	2051.81i	0.704553	+	0.291835i	−0.00149555	+	0.999999i	$0.500476\pi$
$368$	185.799	−	448.558i	0.0263191	−	0.0635399i
$369$		0			0
$370$		−	10297.2i		−	1.44683i
$371$	846.674	+	2044.05i	0.118483	+	0.286043i
$372$		0			0
$373$	6085.54			0.844764			0.422382	−	0.906418i	$-0.361194\pi$
$373$	6085.54			0.844764			0.422382	+	0.906418i	$0.361194\pi$
$374$	−5337.55	−	5204.30i	−0.737963	−	0.719540i
$375$		0			0
$376$	3153.45	+	3153.45i	0.432518	+	0.432518i
$377$	−2185.60	−	5276.51i	−0.298579	−	0.720832i
$378$		0			0
$379$	−5629.32	+	2331.74i	−0.762952	+	0.316025i	−0.730014	−	0.683432i	$-0.760486\pi$
$379$	−5629.32	+	2331.74i	−0.762952	+	0.316025i	−0.0329382	+	0.999457i	$0.510486\pi$
$380$	7962.82	−	19224.0i	1.07496	−	2.59518i
$381$		0			0
$382$	13589.2	−	13589.2i	1.82011	−	1.82011i
$383$	4813.71	−	4813.71i	0.642217	−	0.642217i	−0.308883	−	0.951100i	$-0.599955\pi$
$383$	4813.71	−	4813.71i	0.642217	−	0.642217i	0.951100	+	0.308883i	$0.0999552\pi$
$384$		0			0
$385$	4684.56	−	11309.5i	0.620123	−	1.49711i
$386$	−11519.5	+	4771.53i	−1.51898	+	0.629182i
$387$		0			0
$388$	2036.61	+	4916.82i	0.266478	+	0.643334i
$389$	−3245.79	−	3245.79i	−0.423055	−	0.423055i	0.463199	−	0.886254i	$-0.346701\pi$
$389$	−3245.79	−	3245.79i	−0.423055	−	0.423055i	−0.886254	+	0.463199i	$0.846701\pi$
$390$		0			0
$391$	1232.64	−	15.5806i	0.159431	−	0.00201520i
$392$	10472.9			1.34939
$393$		0			0
$394$	−3581.33	−	8646.09i	−0.457931	−	1.10554i
$395$			1392.87i			0.177425i
$396$		0			0
$397$	−1756.69	+	4241.04i	−0.222081	+	0.536150i	−0.995172	−	0.0981444i	$-0.968709\pi$
$397$	−1756.69	+	4241.04i	−0.222081	+	0.536150i	0.773092	+	0.634294i	$0.218709\pi$
$398$	8625.13	+	3572.65i	1.08628	+	0.449951i
$399$		0			0
$400$	2165.02	−	2165.02i	0.270628	−	0.270628i
$401$	1659.84	+	687.528i	0.206704	+	0.0856197i	0.483634	−	0.875271i	$-0.339317\pi$
$401$	1659.84	+	687.528i	0.206704	+	0.0856197i	−0.276929	+	0.960890i	$0.589317\pi$
$402$		0			0
$403$	−328.880	+	136.227i	−0.0406518	+	0.0168385i
$404$			6883.24i			0.847659i
$405$		0			0
$406$	16401.9	+	16401.9i	2.00495	+	2.00495i
$407$	−3706.30			−0.451387
$408$		0			0
$409$	−11163.3			−1.34961			−0.674803	−	0.737998i	$-0.735772\pi$
$409$	−11163.3			−1.34961			−0.674803	+	0.737998i	$0.735772\pi$
$410$	−6094.57	−	6094.57i	−0.734121	−	0.734121i
$411$		0			0
$412$			19644.7i			2.34909i
$413$	−8183.46	+	3389.70i	−0.975017	+	0.403865i
$414$		0			0
$415$	2143.03	+	887.673i	0.253488	+	0.104998i
$416$	−5891.31	+	5891.31i	−0.694339	+	0.694339i
$417$		0			0
$418$	−11844.8	−	4906.29i	−1.38600	−	0.574102i
$419$	−1692.23	+	4085.40i	−0.197305	+	0.476337i	−0.991305	−	0.131581i	$-0.957995\pi$
$419$	−1692.23	+	4085.40i	−0.197305	+	0.476337i	0.794000	+	0.607917i	$0.207995\pi$
$420$		0			0
$421$			11888.9i			1.37632i	0.725559	+	0.688160i	$0.241581\pi$
$421$			11888.9i			1.37632i	−0.725559	+	0.688160i	$0.758419\pi$
$422$	1272.22	+	3071.42i	0.146756	+	0.354299i
$423$		0			0
$424$	−956.115			−0.109512
$425$	7219.29	+	2883.98i	0.823970	+	0.329161i
$426$		0			0
$427$	8639.17	+	8639.17i	0.979107	+	0.979107i
$428$	−2235.94	−	5398.03i	−0.252519	−	0.609635i
$429$		0			0
$430$	−34194.6	+	14163.9i	−3.83491	+	1.58847i
$431$	−952.700	+	2300.02i	−0.106473	+	0.257049i	−0.968133	−	0.250438i	$-0.919425\pi$
$431$	−952.700	+	2300.02i	−0.106473	+	0.257049i	0.861660	+	0.507487i	$0.169425\pi$
$432$		0			0
$433$	−1298.56	+	1298.56i	−0.144122	+	0.144122i	−0.775486	−	0.631364i	$-0.782495\pi$
$433$	−1298.56	+	1298.56i	−0.144122	+	0.144122i	0.631364	+	0.775486i	$0.282495\pi$
$434$	1022.31	−	1022.31i	0.113071	−	0.113071i
$435$		0			0
$436$	−3826.79	+	9238.68i	−0.420344	+	1.01480i
$437$	1958.68	−	811.314i	0.214409	−	0.0888110i
$438$		0			0
$439$	−1409.49	−	3402.81i	−0.153238	−	0.369948i	0.828554	−	0.559909i	$-0.189164\pi$
$439$	−1409.49	−	3402.81i	−0.153238	−	0.369948i	−0.981792	+	0.189961i	$0.939164\pi$
$440$	3740.66	+	3740.66i	0.405293	+	0.405293i
$441$		0			0
$442$	−10134.2	−	4048.43i	−1.09058	−	0.435666i
$443$	16524.1			1.77220			0.886099	−	0.463497i	$-0.153405\pi$
$443$	16524.1			1.77220			0.886099	+	0.463497i	$0.153405\pi$
$444$		0			0
$445$	3592.59	+	8673.27i	0.382708	+	0.923938i
$446$			13203.2i			1.40177i
$447$		0			0
$448$	10171.4	−	24555.8i	1.07266	−	2.58963i
$449$	−7226.66	−	2993.38i	−0.759570	−	0.314624i	−0.0309307	−	0.999522i	$-0.509847\pi$
$449$	−7226.66	−	2993.38i	−0.759570	−	0.314624i	−0.728640	+	0.684897i	$0.759847\pi$
$450$		0			0
$451$	−2193.64	+	2193.64i	−0.229034	+	0.229034i
$452$	−19803.3	−	8202.79i	−2.06077	−	0.853599i
$453$		0			0
$454$	11649.7	−	4825.45i	1.20429	−	0.498832i
$455$		−	17919.8i		−	1.84636i
$456$		0			0
$457$	−2384.11	−	2384.11i	−0.244035	−	0.244035i	0.574482	−	0.818517i	$-0.305204\pi$
$457$	−2384.11	−	2384.11i	−0.244035	−	0.244035i	−0.818517	+	0.574482i	$0.805204\pi$
$458$	−17420.9			−1.77735
$459$		0			0
$460$	−3035.82			−0.307708
$461$	−4367.31	−	4367.31i	−0.441228	−	0.441228i	0.451197	−	0.892425i	$-0.350997\pi$
$461$	−4367.31	−	4367.31i	−0.441228	−	0.441228i	−0.892425	+	0.451197i	$0.850997\pi$
$462$		0			0
$463$		−	13819.6i		−	1.38715i	−0.720383	−	0.693577i	$-0.756034\pi$
$463$		−	13819.6i		−	1.38715i	0.720383	−	0.693577i	$-0.243966\pi$
$464$	4103.62	−	1699.78i	0.410573	−	0.170065i
$465$		0			0
$466$	−21546.1	−	8924.69i	−2.14186	−	0.887186i
$467$	−4160.60	+	4160.60i	−0.412269	+	0.412269i	−0.882528	−	0.470259i	$-0.844160\pi$
$467$	−4160.60	+	4160.60i	−0.412269	+	0.412269i	0.470259	+	0.882528i	$0.344160\pi$
$468$		0			0
$469$	−16604.6	−	6877.85i	−1.63482	−	0.677163i
$470$	−8094.46	+	19541.8i	−0.794404	+	1.91786i
$471$		0			0
$472$		−	3827.85i		−	0.373287i
$473$	5098.04	+	12307.8i	0.495577	+	1.19643i
$474$		0			0
$475$	13369.8			1.29147
$476$	25889.2	−	327.238i	2.49292	−	0.0315104i
$477$		0			0
$478$	2025.75	+	2025.75i	0.193841	+	0.193841i
$479$	1773.81	+	4282.36i	0.169202	+	0.408489i	0.985621	−	0.168971i	$-0.0540443\pi$
$479$	1773.81	+	4282.36i	0.169202	+	0.408489i	−0.816420	+	0.577459i	$0.804044\pi$
$480$		0			0
$481$	−5012.56	+	2076.27i	−0.475163	+	0.196819i
$482$	−868.213	+	2096.05i	−0.0820457	+	0.198076i
$483$		0			0
$484$	−5904.62	+	5904.62i	−0.554529	+	0.554529i
$485$	−5143.09	+	5143.09i	−0.481517	+	0.481517i
$486$		0			0
$487$	−6637.65	+	16024.7i	−0.617619	+	1.49106i	0.236841	+	0.971548i	$0.423888\pi$
$487$	−6637.65	+	16024.7i	−0.617619	+	1.49106i	−0.854461	+	0.519516i	$0.826112\pi$
$488$	−4877.93	+	2020.51i	−0.452487	+	0.187426i
$489$		0			0
$490$	19008.8	+	45891.3i	1.75251	+	4.23093i
$491$	12195.7	+	12195.7i	1.12094	+	1.12094i	0.991600	+	0.129343i	$0.0412869\pi$
$491$	12195.7	+	12195.7i	1.12094	+	1.12094i	0.129343	+	0.991600i	$0.458713\pi$
$492$		0			0
$493$	8074.70	+	7873.12i	0.737660	+	0.719245i
$494$	−18768.0			−1.70934
$495$		0			0
$496$	−105.946	−	255.775i	−0.00959093	−	0.0231545i
$497$		−	22532.9i		−	2.03368i
$498$		0			0
$499$	−95.7457	+	231.151i	−0.00858951	+	0.0207369i	−0.928116	−	0.372291i	$-0.878572\pi$
$499$	−95.7457	+	231.151i	−0.00858951	+	0.0207369i	0.919527	+	0.393028i	$0.128572\pi$
$500$	2246.91	+	930.703i	0.200970	+	0.0832446i
$501$		0			0
$502$	14449.1	−	14449.1i	1.28465	−	1.28465i
$503$	−12113.1	−	5017.40i	−1.07375	−	0.444761i	−0.225436	−	0.974258i	$-0.572381\pi$
$503$	−12113.1	−	5017.40i	−1.07375	−	0.444761i	−0.848312	+	0.529497i	$0.822381\pi$
$504$		0			0
$505$	−8691.19	+	3600.01i	−0.765847	+	0.317224i
$506$			1870.52i			0.164337i
$507$		0			0
$508$	−5488.59	−	5488.59i	−0.479364	−	0.479364i
$509$	4410.32			0.384055			0.192028	−	0.981390i	$-0.438494\pi$
$509$	4410.32			0.384055			0.192028	+	0.981390i	$0.438494\pi$
$510$		0			0
$511$	−18847.3			−1.63162
$512$	−6799.91	−	6799.91i	−0.586946	−	0.586946i
$513$		0			0
$514$		−	23080.7i		−	1.98063i
$515$	−24804.5	+	10274.4i	−2.12237	+	0.879113i
$516$		0			0
$517$	7033.72	+	2913.46i	0.598342	+	0.247841i
$518$	15581.4	−	15581.4i	1.32164	−	1.32164i
$519$		0			0
$520$	7154.55	+	2963.51i	0.603361	+	0.249920i
$521$	4507.02	−	10880.9i	0.378995	−	0.914975i	−0.613160	−	0.789959i	$-0.710102\pi$
$521$	4507.02	−	10880.9i	0.378995	−	0.914975i	0.992155	−	0.125016i	$-0.0398981\pi$
$522$		0			0
$523$		−	16556.5i		−	1.38425i	−0.721777	−	0.692126i	$-0.756674\pi$
$523$		−	16556.5i		−	1.38425i	0.721777	−	0.692126i	$-0.243326\pi$
$524$	12555.4	+	30311.4i	1.04673	+	2.52702i
$525$		0			0
$526$	−6943.93			−0.575608
$527$	490.725	−	503.289i	0.0405623	−	0.0416008i
$528$		0			0
$529$	8384.65	+	8384.65i	0.689131	+	0.689131i
$530$	−1735.39	−	4189.61i	−0.142228	−	0.343368i
$531$		0			0
$532$	41138.2	−	17040.0i	3.35257	−	1.38868i
$533$	−1737.89	+	4195.65i	−0.141232	+	0.340964i
$534$		0			0
$535$	5646.45	−	5646.45i	0.456294	−	0.456294i
$536$	5492.01	−	5492.01i	0.442572	−	0.442572i
$537$		0			0
$538$	−529.872	+	1279.23i	−0.0424618	+	0.102512i
$539$	16517.8	−	6841.89i	1.31998	−	0.546755i
$540$		0			0
$541$	6020.15	+	14533.9i	0.478423	+	1.15501i	0.960348	+	0.278802i	$0.0899375\pi$
$541$	6020.15	+	14533.9i	0.478423	+	1.15501i	−0.481926	+	0.876212i	$0.660063\pi$
$542$	1281.09	+	1281.09i	0.101527	+	0.101527i
$543$		0			0
$544$	6103.27	−	15278.0i	0.481021	−	1.20411i
$545$	−13666.8			−1.07416
$546$		0			0
$547$	−4768.76	−	11512.8i	−0.372756	−	0.899913i	−0.993281	−	0.115726i	$-0.963081\pi$
$547$	−4768.76	−	11512.8i	−0.372756	−	0.899913i	0.620525	−	0.784187i	$-0.286919\pi$
$548$		−	3245.61i		−	0.253003i
$549$		0			0
$550$	−4514.15	+	10898.1i	−0.349971	+	0.844904i
$551$	17919.0	+	7422.29i	1.38544	+	0.573866i
$552$		0			0
$553$	−2107.65	+	2107.65i	−0.162073	+	0.162073i
$554$	−1898.32	−	786.311i	−0.145581	−	0.0603017i
$555$		0			0
$556$	−19681.9	+	8152.51i	−1.50126	+	0.621841i
$557$			8819.07i			0.670873i	0.942063	+	0.335436i	$0.108884\pi$
$557$			8819.07i			0.670873i	−0.942063	+	0.335436i	$0.891116\pi$
$558$		0			0
$559$	13789.6	+	13789.6i	1.04336	+	1.04336i
$560$	13936.5			1.05165
$561$		0			0
$562$	−5989.95			−0.449592
$563$	−8057.59	−	8057.59i	−0.603174	−	0.603174i	0.337980	−	0.941153i	$-0.390256\pi$
$563$	−8057.59	−	8057.59i	−0.603174	−	0.603174i	−0.941153	+	0.337980i	$0.890256\pi$
$564$		0			0
$565$		−	29294.9i		−	2.18132i
$566$	29010.7	−	12016.6i	2.15443	−	0.892396i
$567$		0			0
$568$	8996.35	+	3726.41i	0.664575	+	0.275276i
$569$	7327.39	−	7327.39i	0.539860	−	0.539860i	−0.383628	−	0.923488i	$-0.625325\pi$
$569$	7327.39	−	7327.39i	0.539860	−	0.539860i	0.923488	+	0.383628i	$0.125325\pi$
$570$		0			0
$571$	−7063.11	−	2925.63i	−0.517656	−	0.214420i	0.108531	−	0.994093i	$-0.465385\pi$
$571$	−7063.11	−	2925.63i	−0.517656	−	0.214420i	−0.626187	+	0.779673i	$0.715385\pi$
$572$	3701.73	−	8936.78i	0.270590	−	0.653261i
$573$		0			0
$574$		−	18444.3i		−	1.34120i
$575$	−746.468	−	1802.13i	−0.0541389	−	0.130703i
$576$		0			0
$577$	8346.67			0.602212			0.301106	−	0.953591i	$-0.402644\pi$
$577$	8346.67			0.602212			0.301106	+	0.953591i	$0.402644\pi$
$578$	21542.3	−	544.675i	1.55024	−	0.0391963i
$579$		0			0
$580$	−19638.6	−	19638.6i	−1.40594	−	1.40594i
$581$	1899.57	+	4585.98i	0.135641	+	0.327467i
$582$		0			0
$583$	−1507.98	+	624.624i	−0.107125	+	0.0443727i
$584$	3116.90	−	7524.86i	0.220853	−	0.533187i
$585$		0			0
$586$	−2386.02	+	2386.02i	−0.168201	+	0.168201i
$587$	−2900.82	+	2900.82i	−0.203968	+	0.203968i	−0.801698	−	0.597729i	$-0.796070\pi$
$587$	−2900.82	+	2900.82i	−0.203968	+	0.203968i	0.597729	+	0.801698i	$0.296070\pi$
$588$		0			0
$589$	462.625	−	1116.88i	0.0323636	−	0.0781325i
$590$	16773.3	−	6947.73i	1.17042	−	0.484802i
$591$		0			0
$592$	−1614.75	−	3898.35i	−0.112104	−	0.270644i
$593$	14179.7	+	14179.7i	0.981940	+	0.981940i	0.999840	−	0.0178999i	$-0.00569801\pi$
$593$	14179.7	+	14179.7i	0.981940	+	0.981940i	−0.0178999	+	0.999840i	$0.505698\pi$
$594$		0			0
$595$	13953.5	+	32518.1i	0.961408	+	2.24052i
$596$	−19575.6			−1.34538
$597$		0			0
$598$	1047.87	+	2529.77i	0.0716562	+	0.172993i
$599$		−	96.8780i		−	0.00660822i	−0.999995	−	0.00330411i	$-0.998948\pi$
$599$		−	96.8780i		−	0.00660822i	0.999995	−	0.00330411i	$-0.00105173\pi$
$600$		0			0
$601$	7082.35	−	17098.3i	0.480690	−	1.16049i	−0.478591	−	0.878038i	$-0.658852\pi$
$601$	7082.35	−	17098.3i	0.480690	−	1.16049i	0.959282	−	0.282452i	$-0.0911476\pi$
$602$	−73174.6	−	30309.9i	−4.95411	−	2.05206i
$603$		0			0
$604$	16245.4	−	16245.4i	1.09440	−	1.09440i
$605$	−10543.7	−	4367.34i	−0.708533	−	0.293484i
$606$		0			0
$607$	−1862.54	+	771.490i	−0.124544	+	0.0515878i	−0.444085	−	0.895985i	$-0.646471\pi$
$607$	−1862.54	+	771.490i	−0.124544	+	0.0515878i	0.319541	+	0.947572i	$0.396471\pi$
$608$		−	28294.0i		−	1.88729i
$609$		0			0
$610$	−17707.3	−	17707.3i	−1.17533	−	1.17533i
$611$	11144.8			0.737925
$612$		0			0
$613$	26672.3			1.75740			0.878698	−	0.477378i	$-0.158413\pi$
$613$	26672.3			1.75740			0.878698	+	0.477378i	$0.158413\pi$
$614$	1304.38	+	1304.38i	0.0857337	+	0.0857337i
$615$		0			0
$616$			11320.5i			0.740448i
$617$	−10628.3	+	4402.38i	−0.693482	+	0.287250i	−0.701450	−	0.712718i	$-0.747464\pi$
$617$	−10628.3	+	4402.38i	−0.693482	+	0.287250i	0.00796782	+	0.999968i	$0.497464\pi$
$618$		0			0
$619$	28126.9	+	11650.6i	1.82636	+	0.756503i	0.971252	+	0.238052i	$0.0765089\pi$
$619$	28126.9	+	11650.6i	1.82636	+	0.756503i	0.855107	+	0.518451i	$0.173491\pi$
$620$	−1224.05	+	1224.05i	−0.0792891	+	0.0792891i
$621$		0			0
$622$	14396.0	+	5963.01i	0.928016	+	0.384397i
$623$	−7687.94	+	18560.3i	−0.494399	+	1.19359i
$624$		0			0
$625$			17187.7i			1.10001i
$626$	−10933.9	−	26396.8i	−0.698095	−	1.68535i
$627$		0			0
$628$	−30784.1			−1.95608
$629$	7479.29	−	7670.79i	0.474116	−	0.486255i
$630$		0			0
$631$	−2083.53	−	2083.53i	−0.131449	−	0.131449i	0.638321	−	0.769770i	$-0.279629\pi$
$631$	−2083.53	−	2083.53i	−0.131449	−	0.131449i	−0.769770	+	0.638321i	$0.779629\pi$
$632$	−492.932	−	1190.04i	−0.0310250	−	0.0749010i
$633$		0			0
$634$	−23934.3	+	9913.90i	−1.49929	+	0.621027i
$635$	4059.62	−	9800.80i	0.253703	−	0.612493i
$636$		0			0
$637$	18506.5	−	18506.5i	1.15111	−	1.15111i
$638$	−12100.3	+	12100.3i	−0.750870	+	0.750870i
$639$		0			0
$640$	−9810.91	+	23685.6i	−0.605953	+	1.46290i
$641$	−22435.1	+	9292.91i	−1.38242	+	0.572618i	−0.945128	−	0.326701i	$-0.894063\pi$
$641$	−22435.1	+	9292.91i	−1.38242	+	0.572618i	−0.437293	+	0.899319i	$0.644063\pi$
$642$		0			0
$643$	392.931	+	948.619i	0.0240990	+	0.0581802i	0.935471	−	0.353404i	$-0.114976\pi$
$643$	392.931	+	948.619i	0.0240990	+	0.0581802i	−0.911372	+	0.411584i	$0.864976\pi$
$644$	−4593.71	−	4593.71i	−0.281083	−	0.281083i
$645$		0			0
$646$	34057.2	−	14613.9i	2.07425	−	0.890059i
$647$	10184.4			0.618839			0.309419	−	0.950926i	$-0.399865\pi$
$647$	10184.4			0.618839			0.309419	+	0.950926i	$0.399865\pi$
$648$		0			0
$649$	−2500.71	−	6037.26i	−0.151251	−	0.365151i
$650$			17267.9i			1.04201i
$651$		0			0
$652$	3014.39	−	7277.38i	0.181062	−	0.437123i
$653$	19392.6	+	8032.67i	1.16216	+	0.481383i	0.878594	−	0.477570i	$-0.158482\pi$
$653$	19392.6	+	8032.67i	1.16216	+	0.481383i	0.283567	+	0.958953i	$0.408482\pi$
$654$		0			0
$655$	−31706.3	+	31706.3i	−1.89140	+	1.89140i
$656$	−3263.02	−	1351.59i	−0.194207	−	0.0804431i
$657$		0			0
$658$	−41818.3	+	17321.7i	−2.47758	+	1.02625i
$659$		−	2158.18i		−	0.127573i	−0.997964	−	0.0637866i	$-0.979682\pi$
$659$		−	2158.18i		−	0.127573i	0.997964	−	0.0637866i	$-0.0203177\pi$
$660$		0			0
$661$	7849.97	+	7849.97i	0.461919	+	0.461919i	0.899284	−	0.437365i	$-0.144088\pi$
$661$	7849.97	+	7849.97i	0.461919	+	0.461919i	−0.437365	+	0.899284i	$0.644088\pi$
$662$	38850.4			2.28091
$663$		0			0
$664$	−2145.11			−0.125371
$665$	43031.4	+	43031.4i	2.50930	+	2.50930i
$666$		0			0
$667$		−	2829.74i		−	0.164270i
$668$	6201.69	−	2568.82i	0.359207	−	0.148789i
$669$		0			0
$670$	34033.7	+	14097.2i	1.96244	+	0.812871i
$671$	−6373.45	+	6373.45i	−0.366683	+	0.366683i
$672$		0			0
$673$	7115.94	+	2947.52i	0.407577	+	0.168824i	0.577046	−	0.816712i	$-0.304205\pi$
$673$	7115.94	+	2947.52i	0.407577	+	0.168824i	−0.169469	+	0.985536i	$0.554205\pi$
$674$	−13772.6	+	33250.1i	−0.787095	+	1.90022i
$675$		0			0
$676$			10530.5i			0.599140i
$677$	7334.40	+	17706.8i	0.416372	+	1.00521i	0.983390	+	0.181506i	$0.0580972\pi$
$677$	7334.40	+	17706.8i	0.416372	+	1.00521i	−0.567017	+	0.823706i	$0.691903\pi$
$678$		0			0
$679$	−15564.7			−0.879706
$680$	−15290.5	+	193.272i	−0.862301	+	0.0108995i
$681$		0			0
$682$	754.201	+	754.201i	0.0423458	+	0.0423458i
$683$	−4270.16	−	10309.1i	−0.239229	−	0.577549i	0.757975	−	0.652284i	$-0.226189\pi$
$683$	−4270.16	−	10309.1i	−0.239229	−	0.577549i	−0.997203	+	0.0747346i	$0.976189\pi$
$684$		0			0
$685$	4098.10	−	1697.49i	0.228584	−	0.0946828i
$686$	−21754.6	+	52520.3i	−1.21078	+	2.92308i
$687$		0			0
$688$	−10724.4	+	10724.4i	−0.594280	+	0.594280i
$689$	−1689.54	+	1689.54i	−0.0934199	+	0.0934199i
$690$		0			0
$691$	−8903.52	+	21495.0i	−0.490168	+	1.18337i	0.464467	+	0.885590i	$0.346246\pi$
$691$	−8903.52	+	21495.0i	−0.490168	+	1.18337i	−0.954635	+	0.297779i	$0.903754\pi$
$692$	25853.7	−	10709.0i	1.42025	−	0.588286i
$693$		0			0
$694$	−8605.45	−	20775.4i	−0.470689	−	1.13634i
$695$	−20587.7	−	20587.7i	−1.12365	−	1.12365i
$696$		0			0
$697$	−113.340	−	8966.84i	−0.00615936	−	0.487293i
$698$	2309.09			0.125215
$699$		0			0
$700$	−15678.1	−	37850.2i	−0.846535	−	2.04372i
$701$			12642.2i			0.681153i	0.940217	+	0.340576i	$0.110622\pi$
$701$			12642.2i			0.681153i	−0.940217	+	0.340576i	$0.889378\pi$
$702$		0			0
$703$	7051.01	−	17022.6i	0.378284	−	0.913259i
$704$	18115.8	+	7503.80i	0.969836	+	0.401719i
$705$		0			0
$706$	7748.08	−	7748.08i	0.413035	−	0.413035i
$707$	−18598.7	−	7703.82i	−0.989357	−	0.409805i
$708$		0			0
$709$	6237.95	−	2583.84i	0.330425	−	0.136866i	−0.211303	−	0.977421i	$-0.567771\pi$
$709$	6237.95	−	2583.84i	0.330425	−	0.136866i	0.541727	+	0.840554i	$0.317771\pi$
$710$			46184.8i			2.44124i
$711$		0			0
$712$	−6138.88	−	6138.88i	−0.323124	−	0.323124i
$713$	−176.375			−0.00926410
$714$		0			0
$715$	13220.1			0.691476
$716$	−20184.7	−	20184.7i	−1.05355	−	1.05355i
$717$		0			0
$718$			22851.3i			1.18775i
$719$	5925.14	−	2454.27i	0.307330	−	0.127300i	−0.223688	−	0.974661i	$-0.571810\pi$
$719$	5925.14	−	2454.27i	0.307330	−	0.127300i	0.531018	+	0.847360i	$0.321810\pi$
$720$		0			0
$721$	−53080.4	−	21986.6i	−2.74177	−	1.13568i
$722$	23795.1	−	23795.1i	1.22654	−	1.22654i
$723$		0			0
$724$	10621.4	+	4399.52i	0.545222	+	0.225838i
$725$	6829.05	−	16486.8i	0.349827	−	0.844557i
$726$		0			0
$727$		−	5828.20i		−	0.297326i	−0.988888	−	0.148663i	$-0.952503\pi$
$727$		−	5828.20i		−	0.297326i	0.988888	−	0.148663i	$-0.0474970\pi$
$728$	6341.76	+	15310.4i	0.322859	+	0.779450i
$729$		0			0
$730$	38630.5			1.95860
$731$	−35760.7	−	14285.8i	−1.80938	−	0.722816i
$732$		0			0
$733$	8245.31	+	8245.31i	0.415481	+	0.415481i	0.883643	−	0.468162i	$-0.155084\pi$
$733$	8245.31	+	8245.31i	0.415481	+	0.415481i	−0.468162	+	0.883643i	$0.655084\pi$
$734$	−8999.56	−	21726.9i	−0.452561	−	1.09258i
$735$		0			0
$736$	−3813.79	+	1579.72i	−0.191003	+	0.0791161i
$737$	5074.06	−	12249.9i	0.253603	−	0.612251i
$738$		0			0
$739$	−9261.33	+	9261.33i	−0.461006	+	0.461006i	−0.898985	−	0.437979i	$-0.855694\pi$
$739$	−9261.33	+	9261.33i	−0.461006	+	0.461006i	0.437979	+	0.898985i	$0.355694\pi$
$740$	−18656.2	+	18656.2i	−0.926778	+	0.926778i
$741$		0			0
$742$	3713.65	−	8965.53i	0.183736	−	0.443578i
$743$	−14071.2	+	5828.48i	−0.694781	+	0.287788i	−0.701991	−	0.712186i	$-0.747705\pi$
$743$	−14071.2	+	5828.48i	−0.694781	+	0.287788i	0.00720941	+	0.999974i	$0.497705\pi$
$744$		0			0
$745$	−10238.2	−	24717.3i	−0.503490	−	1.21553i
$746$	−18874.2	−	18874.2i	−0.926317	−	0.926317i
$747$		0			0
$748$	241.416	+	19099.5i	0.0118009	+	0.933617i
$749$	17088.1			0.833625
$750$		0			0
$751$	−861.528	−	2079.91i	−0.0418610	−	0.101061i	0.901566	−	0.432641i	$-0.142418\pi$
$751$	−861.528	−	2079.91i	−0.0418610	−	0.101061i	−0.943427	+	0.331580i	$0.892418\pi$
$752$			8667.52i			0.420308i
$753$		0			0
$754$	−9586.38	+	23143.6i	−0.463018	+	1.11782i
$755$	29008.8	+	12015.9i	1.39833	+	0.579208i
$756$		0			0
$757$	−18222.9	+	18222.9i	−0.874929	+	0.874929i	−0.993005	−	0.118075i	$-0.962328\pi$
$757$	−18222.9	+	18222.9i	−0.874929	+	0.874929i	0.118075	+	0.993005i	$0.462328\pi$
$758$	24691.1	+	10227.4i	1.18314	+	0.490073i
$759$		0			0
$760$	−24296.8	+	10064.1i	−1.15966	+	0.480345i
$761$		−	31638.6i		−	1.50709i	−0.657395	−	0.753547i	$-0.728341\pi$
$761$		−	31638.6i		−	1.50709i	0.657395	−	0.753547i	$-0.271659\pi$
$762$		0			0
$763$	−20680.1	−	20680.1i	−0.981220	−	0.981220i
$764$	−49241.0			−2.33178
$765$		0			0
$766$	−29859.3			−1.40843
$767$	−6764.16	−	6764.16i	−0.318435	−	0.318435i
$768$		0			0
$769$		−	31684.4i		−	1.48578i	−0.669412	−	0.742891i	$-0.733454\pi$
$769$		−	31684.4i		−	1.48578i	0.669412	−	0.742891i	$-0.266546\pi$
$770$	−49605.4	+	20547.2i	−2.32163	+	0.961650i
$771$		0			0
$772$	29515.6	+	12225.8i	1.37602	+	0.569968i
$773$	16853.6	−	16853.6i	0.784192	−	0.784192i	−0.196343	−	0.980535i	$-0.562907\pi$
$773$	16853.6	−	16853.6i	0.784192	−	0.784192i	0.980535	+	0.196343i	$0.0629067\pi$
$774$		0			0
$775$	−1027.61	−	425.649i	−0.0476293	−	0.0197287i
$776$	2574.04	−	6214.28i	0.119076	−	0.287474i
$777$		0			0
$778$			20133.5i			0.927792i
$779$	−5901.89	−	14248.4i	−0.271447	−	0.655330i
$780$		0			0
$781$	16623.4			0.761629
$782$	−3871.34	−	3774.70i	−0.177032	−	0.172612i
$783$		0			0
$784$	14392.8	+	14392.8i	0.655650	+	0.655650i
$785$	−16100.4	−	38869.8i	−0.732036	−	1.76729i
$786$		0			0
$787$	−8050.64	+	3334.69i	−0.364644	+	0.151040i	−0.557479	−	0.830191i	$-0.688231\pi$
$787$	−8050.64	+	3334.69i	−0.364644	+	0.151040i	0.192836	+	0.981231i	$0.438231\pi$
$788$	−9176.21	+	22153.3i	−0.414834	+	1.00150i
$789$		0			0
$790$	4319.97	−	4319.97i	0.194554	−	0.194554i
$791$	44328.2	−	44328.2i	1.99258	−	1.99258i
$792$		0			0
$793$	−5049.33	+	12190.2i	−0.226112	+	0.545883i
$794$	18601.8	−	7705.14i	0.831429	−	0.344389i
$795$		0			0
$796$	−9153.96	−	22099.6i	−0.407605	−	0.984045i
$797$	5085.49	+	5085.49i	0.226019	+	0.226019i	0.811027	−	0.585008i	$-0.198909\pi$
$797$	5085.49	+	5085.49i	0.226019	+	0.226019i	−0.585008	+	0.811027i	$0.698909\pi$
$798$		0			0
$799$	−20223.9	+	8678.08i	−0.895457	+	0.384241i
$800$	−26032.5			−1.15049
$801$		0			0
$802$	−3015.60	−	7280.31i	−0.132774	−	0.320545i
$803$		−	13904.4i		−	0.611053i
$804$		0			0
$805$	3397.73	−	8202.84i	0.148763	−	0.359145i
$806$	1442.52	+	597.511i	0.0630404	+	0.0261122i
$807$		0			0
$808$	6151.56	−	6151.56i	0.267835	−	0.267835i
$809$	17501.4	+	7249.30i	0.760587	+	0.315046i	0.729053	−	0.684457i	$-0.239961\pi$
$809$	17501.4	+	7249.30i	0.760587	+	0.315046i	0.0315342	+	0.999503i	$0.489961\pi$
$810$		0			0
$811$	15374.2	−	6368.21i	0.665675	−	0.275731i	−0.0241496	−	0.999708i	$-0.507688\pi$
$811$	15374.2	−	6368.21i	0.665675	−	0.275731i	0.689824	+	0.723977i	$0.257688\pi$
$812$		−	59433.0i		−	2.56858i
$813$		0			0
$814$	11495.0	+	11495.0i	0.494963	+	0.494963i
$815$	10765.4			0.462694
$816$		0			0
$817$	−66227.0			−2.83597
$818$	34622.7	+	34622.7i	1.47990	+	1.47990i
$819$		0			0
$820$			22084.0i			0.940495i
$821$	3307.09	−	1369.84i	0.140583	−	0.0582312i	−0.311283	−	0.950317i	$-0.600759\pi$
$821$	3307.09	−	1369.84i	0.140583	−	0.0582312i	0.451865	+	0.892086i	$0.350759\pi$
$822$		0			0
$823$	18390.8	+	7617.71i	0.778934	+	0.322645i	0.736485	−	0.676454i	$-0.236484\pi$
$823$	18390.8	+	7617.71i	0.778934	+	0.322645i	0.0424485	+	0.999099i	$0.486484\pi$
$824$	17556.5	−	17556.5i	0.742243	−	0.742243i
$825$		0			0
$826$	35894.0	+	14867.8i	1.51200	+	0.626290i
$827$	−10540.9	+	25447.9i	−0.443219	+	1.07002i	0.531594	+	0.846999i	$0.321593\pi$
$827$	−10540.9	+	25447.9i	−0.443219	+	1.07002i	−0.974813	+	0.223025i	$0.928407\pi$
$828$		0			0
$829$			3808.15i			0.159545i	0.996813	+	0.0797723i	$0.0254193\pi$
$829$			3808.15i			0.159545i	−0.996813	+	0.0797723i	$0.974581\pi$
$830$	−3893.47	−	9399.68i	−0.162825	−	0.393093i
$831$		0			0
$832$	28704.2			1.19608
$833$	−19172.4	+	47993.1i	−0.797460	+	1.99623i
$834$		0			0
$835$	6487.09	+	6487.09i	0.268856	+	0.268856i
$836$	12571.1	+	30349.3i	0.520071	+	1.25556i
$837$		0			0
$838$	17919.2	−	7422.38i	0.738674	−	0.305969i
$839$	−11502.8	+	27770.3i	−0.473327	+	1.14271i	0.489356	+	0.872084i	$0.337232\pi$
$839$	−11502.8	+	27770.3i	−0.473327	+	1.14271i	−0.962684	+	0.270629i	$0.912768\pi$
$840$		0			0
$841$	1059.82	−	1059.82i	0.0434550	−	0.0434550i
$842$	36873.3	−	36873.3i	1.50919	−	1.50919i
$843$		0			0
$844$	3259.74	−	7869.70i	0.132944	−	0.320955i
$845$	−13296.4	+	5507.55i	−0.541313	+	0.224219i
$846$		0			0
$847$	−9345.88	−	22563.0i	−0.379136	−	0.915316i
$848$	−1313.98	−	1313.98i	−0.0532103	−	0.0532103i
$849$		0			0
$850$	−13445.9	−	31335.1i	−0.542577	−	1.26445i
$851$	−2688.19			−0.108284
$852$		0			0
$853$	16507.4	+	39852.4i	0.662606	+	1.59967i	0.793705	+	0.608302i	$0.208149\pi$
$853$	16507.4	+	39852.4i	0.662606	+	1.59967i	−0.131100	+	0.991369i	$0.541851\pi$
$854$		−	53588.4i		−	2.14726i
$855$		0			0
$856$	−2825.96	+	6822.48i	−0.112838	+	0.272415i
$857$	−21055.7	−	8721.57i	−0.839265	−	0.347635i	−0.0787016	−	0.996898i	$-0.525077\pi$
$857$	−21055.7	−	8721.57i	−0.839265	−	0.347635i	−0.760564	+	0.649263i	$0.775077\pi$
$858$		0			0
$859$	34423.0	−	34423.0i	1.36729	−	1.36729i	0.502997	−	0.864288i	$-0.332231\pi$
$859$	34423.0	−	34423.0i	1.36729	−	1.36729i	0.864288	−	0.502997i	$-0.167769\pi$
$860$	87614.6	+	36291.2i	3.47399	+	1.43897i
$861$		0			0
$862$	10088.2	−	4178.69i	0.398616	−	0.165112i
$863$			29580.9i			1.16680i	0.812187	+	0.583398i	$0.198277\pi$
$863$			29580.9i			1.16680i	−0.812187	+	0.583398i	$0.801723\pi$
$864$		0			0
$865$	27043.5	+	27043.5i	1.06302	+	1.06302i
$866$	8054.93			0.316071
$867$		0			0
$868$	−3704.41			−0.144857
$869$	−1554.90	−	1554.90i	−0.0606977	−	0.0606977i
$870$		0			0
$871$		−	19409.7i		−	0.755079i
$872$	11676.6	−	4836.61i	0.453463	−	0.187831i
$873$		0			0
$874$	−8591.10	−	3558.55i	−0.332492	−	0.137723i
$875$	−5029.56	+	5029.56i	−0.194320	+	0.194320i
$876$		0			0
$877$	−37189.1	−	15404.2i	−1.43191	−	0.593117i	−0.474089	−	0.880477i	$-0.657222\pi$
$877$	−37189.1	−	15404.2i	−1.43191	−	0.593117i	−0.957823	+	0.287360i	$0.907222\pi$
$878$	−6182.24	+	14925.3i	−0.237632	+	0.573693i
$879$		0			0
$880$			10281.5i			0.393852i
$881$	−15006.5	−	36229.0i	−0.573874	−	1.38546i	−0.898232	−	0.439521i	$-0.855148\pi$
$881$	−15006.5	−	36229.0i	−0.573874	−	1.38546i	0.324358	−	0.945934i	$-0.394852\pi$
$882$		0			0
$883$	−2775.62			−0.105784			−0.0528918	−	0.998600i	$-0.516844\pi$
$883$	−2775.62			−0.105784			−0.0528918	+	0.998600i	$0.516844\pi$
$884$	11026.0	+	25695.7i	0.419509	+	0.977648i
$885$		0			0
$886$	−51249.2	−	51249.2i	−1.94328	−	1.94328i
$887$	8537.38	+	20611.1i	0.323176	+	0.780216i	0.999066	+	0.0432133i	$0.0137595\pi$
$887$	8537.38	+	20611.1i	0.323176	+	0.780216i	−0.675890	+	0.737003i	$0.736240\pi$
$888$		0			0
$889$	20973.2	−	8687.38i	0.791246	−	0.327745i
$890$	15757.6	−	38042.3i	0.593480	−	1.43279i
$891$		0			0
$892$	23921.2	−	23921.2i	0.897917	−	0.897917i
$893$	−26762.5	+	26762.5i	−1.00288	+	1.00288i
$894$		0			0
$895$	14929.6	−	36043.2i	0.557588	−	1.34614i
$896$	−50686.0	+	20994.8i	−1.88984	+	0.782799i
$897$		0			0
$898$	13129.4	+	31697.3i	0.487901	+	1.17790i
$899$	−1140.96	−	1140.96i	−0.0423284	−	0.0423284i
$900$		0			0
$901$	1750.33	−	4381.49i	0.0647190	−	0.162007i
$902$	13607.0			0.502289
$903$		0			0
$904$	10367.4	+	25029.0i	0.381431	+	0.920855i
$905$			15712.2i			0.577116i
$906$		0			0
$907$	−12777.8	+	30848.3i	−0.467783	+	1.12933i	0.497346	+	0.867552i	$0.334308\pi$
$907$	−12777.8	+	30848.3i	−0.467783	+	1.12933i	−0.965129	+	0.261775i	$0.915692\pi$
$908$	−29849.2	−	12364.0i	−1.09095	−	0.451886i
$909$		0			0
$910$	−55578.0	+	55578.0i	−2.02461	+	2.02461i
$911$	−23350.5	−	9672.11i	−0.849218	−	0.351758i	−0.0847368	−	0.996403i	$-0.527005\pi$
$911$	−23350.5	−	9672.11i	−0.849218	−	0.351758i	−0.764482	+	0.644646i	$0.777005\pi$
$912$		0			0
$913$	−3383.25	+	1401.39i	−0.122639	+	0.0507987i
$914$			14788.6i			0.535188i
$915$		0			0
$916$	31562.8	+	31562.8i	1.13850	+	1.13850i
$917$	−95954.2			−3.45549
$918$		0			0
$919$	33518.4			1.20312			0.601562	−	0.798826i	$-0.294545\pi$
$919$	33518.4			1.20312			0.601562	+	0.798826i	$0.294545\pi$
$920$	2713.11	+	2713.11i	0.0972267	+	0.0972267i
$921$		0			0
$922$			27090.3i			0.967648i
$923$	22482.2	−	9312.45i	0.801746	−	0.332094i
$924$		0			0
$925$	−15662.1	−	6487.45i	−0.556720	−	0.230601i
$926$	−42861.3	+	42861.3i	−1.52107	+	1.52107i
$927$		0			0
$928$	−34890.4	−	14452.1i	−1.23420	−	0.511221i
$929$	1130.85	−	2730.12i	0.0399377	−	0.0964181i	−0.902652	−	0.430371i	$-0.858383\pi$
$929$	1130.85	−	2730.12i	0.0399377	−	0.0964181i	0.942590	+	0.333953i	$0.108383\pi$
$930$		0			0
$931$			88880.7i			3.12884i
$932$	22867.2	+	55206.2i	0.803690	+	1.94028i
$933$		0			0
$934$	25808.0			0.904137
$935$	−23989.8	+	10294.0i	−0.839092	+	0.360054i
$936$		0			0
$937$	−10680.8	−	10680.8i	−0.372388	−	0.372388i	0.495958	−	0.868346i	$-0.334817\pi$
$937$	−10680.8	−	10680.8i	−0.372388	−	0.372388i	−0.868346	+	0.495958i	$0.834817\pi$
$938$	30167.3	+	72830.4i	1.05010	+	2.53518i
$939$		0			0
$940$	50070.6	−	20739.9i	1.73736	−	0.719640i
$941$	17931.1	−	43289.5i	0.621187	−	1.49968i	−0.229124	−	0.973397i	$-0.573586\pi$
$941$	17931.1	−	43289.5i	0.621187	−	1.49968i	0.850311	−	0.526280i	$-0.176414\pi$
$942$		0			0
$943$	−1591.05	+	1591.05i	−0.0549435	+	0.0549435i
$944$	5260.59	−	5260.59i	0.181375	−	0.181375i
$945$		0			0
$946$	22360.8	−	53983.7i	0.768512	−	1.85535i
$947$	30143.3	−	12485.7i	1.03434	−	0.428440i	0.200066	−	0.979782i	$-0.435884\pi$
$947$	30143.3	−	12485.7i	1.03434	−	0.428440i	0.834279	+	0.551343i	$0.185884\pi$
$948$		0			0
$949$	−7789.26	−	18804.9i	−0.266438	−	0.643239i
$950$	−41466.0	−	41466.0i	−1.41614	−	1.41614i
$951$		0			0
$952$	−23429.6	−	22844.7i	−0.797646	−	0.777733i
$953$	20967.3			0.712693			0.356347	−	0.934354i	$-0.384022\pi$
$953$	20967.3			0.712693			0.356347	+	0.934354i	$0.384022\pi$
$954$		0			0
$955$	−25753.6	−	62174.6i	−0.872634	−	2.10673i
$956$		−	7340.41i		−	0.248333i
$957$		0			0
$958$	7780.22	−	18783.1i	0.262388	−	0.633460i
$959$	8769.71	+	3632.53i	0.295296	+	0.122316i
$960$		0			0
$961$	20994.3	−	20994.3i	0.704720	−	0.704720i
$962$	21985.9	+	9106.85i	0.736854	+	0.305215i
$963$		0			0
$964$	5370.58	−	2224.57i	0.179434	−	0.0743241i
$965$			43662.4i			1.45652i
$966$		0			0
$967$	8726.06	+	8726.06i	0.290187	+	0.290187i	0.837154	−	0.546967i	$-0.184218\pi$
$967$	8726.06	+	8726.06i	0.290187	+	0.290187i	−0.546967	+	0.837154i	$0.684218\pi$
$968$	10553.9			0.350430
$969$		0			0
$970$	31902.4			1.05600
$971$	5672.65	+	5672.65i	0.187481	+	0.187481i	0.794606	−	0.607125i	$-0.207677\pi$
$971$	5672.65	+	5672.65i	0.187481	+	0.187481i	−0.607125	+	0.794606i	$0.707677\pi$
$972$		0			0
$973$		−	62305.3i		−	2.05284i
$974$	70286.8	−	29113.8i	2.31225	−	0.957767i
$975$		0			0
$976$	−9480.48	−	3926.94i	−0.310925	−	0.128789i
$977$	−17438.5	+	17438.5i	−0.571042	+	0.571042i	−0.932420	−	0.361377i	$-0.882307\pi$
$977$	−17438.5	+	17438.5i	−0.571042	+	0.571042i	0.361377	+	0.932420i	$0.382307\pi$
$978$		0			0
$979$	−13692.7	−	5671.69i	−0.447007	−	0.185156i
$980$	48705.0	−	117584.i	1.58758	−	3.83275i
$981$		0			0
$982$		−	75649.3i		−	2.45832i
$983$	−9747.59	−	23532.8i	−0.316276	−	0.763559i	−0.999445	−	0.0332985i	$-0.989399\pi$
$983$	−9747.59	−	23532.8i	−0.316276	−	0.763559i	0.683169	−	0.730260i	$-0.260601\pi$
$984$		0			0
$985$	−32771.3			−1.06008
$986$	−625.196	−	49461.9i	−0.0201930	−	1.59755i
$987$		0			0
$988$	34003.4	+	34003.4i	1.09493	+	1.09493i
$989$	3697.62	+	8926.85i	0.118885	+	0.287015i
$990$		0			0
$991$	24184.4	−	10017.5i	0.775218	−	0.321106i	0.0402342	−	0.999190i	$-0.487190\pi$
$991$	24184.4	−	10017.5i	0.775218	−	0.321106i	0.734984	+	0.678084i	$0.237190\pi$
$992$	−900.787	+	2174.69i	−0.0288307	+	0.0696033i
$993$		0			0
$994$	−69885.4	+	69885.4i	−2.23001	+	2.23001i
$995$	23116.7	−	23116.7i	0.736530	−	0.736530i
$996$		0			0
$997$	−5625.82	+	13581.9i	−0.178708	+	0.431438i	−0.987696	−	0.156386i	$-0.950016\pi$
$997$	−5625.82	+	13581.9i	−0.178708	+	0.431438i	0.808988	+	0.587825i	$0.200016\pi$
$998$	1013.86	−	419.955i	0.0321576	−	0.0133201i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.c.100.2		40
3.2	odd	2		51.4.h.a.49.9	yes	40
17.8	even	8	inner	153.4.l.c.127.2		40
51.5	even	16		867.4.a.v.1.3		20
51.8	odd	8		51.4.h.a.25.9	✓	40
51.29	even	16		867.4.a.w.1.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.h.a.25.9	✓	40	51.8	odd	8
51.4.h.a.49.9	yes	40	3.2	odd	2
153.4.l.c.100.2		40	1.1	even	1	trivial
153.4.l.c.127.2		40	17.8	even	8	inner
867.4.a.v.1.3		20	51.5	even	16
867.4.a.w.1.3		20	51.29	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.10148 - 3.10148i) q^{2} +11.2384i q^{4} +(-14.1902 + 5.87778i) q^{5} +(-30.3663 - 12.5781i) q^{7} +(10.0437 - 10.0437i) q^{8} +(62.2405 + 25.7809i) q^{10} +(9.27937 - 22.4024i) q^{11} -35.4963i q^{13} +(55.1697 + 133.191i) q^{14} +27.6061 q^{16} +(27.6397 + 64.4131i) q^{17} +(85.2385 + 85.2385i) q^{19} +(-66.0566 - 159.475i) q^{20} +(-98.2604 + 40.7008i) q^{22} +(6.73036 - 16.2485i) q^{23} +(78.4256 - 78.4256i) q^{25} +(-110.091 + 110.091i) q^{26} +(141.358 - 341.268i) q^{28} +(148.649 - 61.5726i) q^{29} +(-3.83777 - 9.26519i) q^{31} +(-165.969 - 165.969i) q^{32} +(114.052 - 285.500i) q^{34} +504.836 q^{35} +(-58.4926 - 141.214i) q^{37} -528.731i q^{38} +(-83.4879 + 201.558i) q^{40} +(-118.200 - 48.9599i) q^{41} +(-388.481 + 388.481i) q^{43} +(251.766 + 104.285i) q^{44} +(-71.2686 + 29.5204i) q^{46} +313.972i q^{47} +(521.365 + 521.365i) q^{49} -486.471 q^{50} +398.921 q^{52} +(-47.5976 - 47.5976i) q^{53} +372.437i q^{55} +(-431.322 + 178.660i) q^{56} +(-651.999 - 270.067i) q^{58} +(190.559 - 190.559i) q^{59} +(-343.420 - 142.249i) q^{61} +(-16.8330 + 40.6386i) q^{62} +808.654i q^{64} +(208.640 + 503.700i) q^{65} +546.810 q^{67} +(-723.898 + 310.625i) q^{68} +(-1565.74 - 1565.74i) q^{70} +(262.350 + 633.368i) q^{71} +(529.771 - 219.438i) q^{73} +(-256.558 + 619.385i) q^{74} +(-957.941 + 957.941i) q^{76} +(-563.561 + 563.561i) q^{77} +(34.7038 - 83.7824i) q^{79} +(-391.736 + 162.262i) q^{80} +(214.746 + 518.442i) q^{82} +(-106.789 - 106.789i) q^{83} +(-770.819 - 751.576i) q^{85} +2409.73 q^{86} +(-131.804 - 318.203i) q^{88} -611.215i q^{89} +(-446.477 + 1077.89i) q^{91} +(182.607 + 75.6382i) q^{92} +(973.777 - 973.777i) q^{94} +(-1710.56 - 708.539i) q^{95} +(437.503 - 181.220i) q^{97} -3234.01i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 32 q^{5} + 128 q^{10} - 112 q^{11} - 256 q^{14} - 1024 q^{16} + 112 q^{17} - 32 q^{19} + 640 q^{20} + 728 q^{22} - 208 q^{23} + 296 q^{25} - 1472 q^{26} - 328 q^{28} + 1272 q^{29} - 192 q^{31} + 960 q^{32}+ \cdots + 1008 q^{97}+O(q^{100}) \) 40 * q - 32 * q^5 + 128 * q^10 - 112 * q^11 - 256 * q^14 - 1024 * q^16 + 112 * q^17 - 32 * q^19 + 640 * q^20 + 728 * q^22 - 208 * q^23 + 296 * q^25 - 1472 * q^26 - 328 * q^28 + 1272 * q^29 - 192 * q^31 + 960 * q^32 + 24 * q^34 + 992 * q^35 - 1120 * q^37 + 2984 * q^40 + 1320 * q^41 + 672 * q^43 - 3744 * q^44 - 384 * q^46 - 2096 * q^49 + 448 * q^50 + 960 * q^52 - 2120 * q^53 - 5680 * q^56 + 1000 * q^58 + 832 * q^59 - 208 * q^61 + 4432 * q^62 + 2376 * q^65 - 2272 * q^67 + 4560 * q^68 - 4792 * q^70 - 256 * q^71 - 1416 * q^73 + 2704 * q^74 - 264 * q^76 - 6048 * q^77 + 1920 * q^79 - 1312 * q^80 + 8328 * q^82 - 4960 * q^83 + 3192 * q^85 + 15616 * q^86 - 248 * q^88 + 1232 * q^91 - 944 * q^92 - 10000 * q^94 - 4528 * q^95 + 1008 * q^97

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