LMFDB - Embedded newform 153.4.l.c.100.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(19,153)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			100.7
Character	$\chi$	$=$	153.100
Dual form			153.4.l.c.127.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.15816 + 2.15816i) q^{2} +1.31528i q^{4} +(-13.0882 + 5.42131i) q^{5} +(-26.4168 - 10.9422i) q^{7} +(14.4267 - 14.4267i) q^{8} +(-39.9464 - 16.5464i) q^{10} +(9.48236 - 22.8924i) q^{11} -31.8846i q^{13} +(-33.3966 - 80.6266i) q^{14} +72.7923 q^{16} +(-59.1905 + 37.5432i) q^{17} +(-66.3298 - 66.3298i) q^{19} +(-7.13054 - 17.2146i) q^{20} +(69.8699 - 28.9410i) q^{22} +(-23.6243 + 57.0340i) q^{23} +(53.5222 - 53.5222i) q^{25} +(68.8119 - 68.8119i) q^{26} +(14.3920 - 34.7454i) q^{28} +(-238.832 + 98.9273i) q^{29} +(73.8065 + 178.185i) q^{31} +(41.6837 + 41.6837i) q^{32} +(-208.766 - 46.7182i) q^{34} +405.070 q^{35} +(-130.945 - 316.128i) q^{37} -286.300i q^{38} +(-110.608 + 267.031i) q^{40} +(250.006 + 103.556i) q^{41} +(242.000 - 242.000i) q^{43} +(30.1099 + 12.4719i) q^{44} +(-174.073 + 72.1034i) q^{46} +47.9808i q^{47} +(335.578 + 335.578i) q^{49} +231.019 q^{50} +41.9371 q^{52} +(-157.349 - 157.349i) q^{53} +351.028i q^{55} +(-538.966 + 223.247i) q^{56} +(-728.937 - 301.935i) q^{58} +(-135.454 + 135.454i) q^{59} +(441.840 + 183.016i) q^{61} +(-225.265 + 543.837i) q^{62} -402.418i q^{64} +(172.856 + 417.312i) q^{65} +254.007 q^{67} +(-49.3797 - 77.8519i) q^{68} +(874.204 + 874.204i) q^{70} +(-364.361 - 879.646i) q^{71} +(-1058.45 + 438.426i) q^{73} +(399.656 - 964.854i) q^{74} +(87.2421 - 87.2421i) q^{76} +(-500.987 + 500.987i) q^{77} +(-76.8385 + 185.504i) q^{79} +(-952.720 + 394.630i) q^{80} +(316.063 + 763.043i) q^{82} +(169.307 + 169.307i) q^{83} +(571.164 - 812.263i) q^{85} +1044.55 q^{86} +(-193.463 - 467.061i) q^{88} -627.144i q^{89} +(-348.887 + 842.289i) q^{91} +(-75.0156 - 31.0725i) q^{92} +(-103.550 + 103.550i) q^{94} +(1227.73 + 508.544i) q^{95} +(1165.39 - 482.720i) q^{97} +1448.46i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.15816	+	2.15816i	0.763024	+	0.763024i	0.976868	−	0.213844i	$-0.0685985\pi$
$2$	2.15816	+	2.15816i	0.763024	+	0.763024i	−0.213844	+	0.976868i	$0.568599\pi$
$3$		0			0
$3$		0			0
$4$			1.31528i			0.164410i
$5$	−13.0882	+	5.42131i	−1.17064	+	0.484897i	−0.881406	−	0.472360i	$-0.843402\pi$
$5$	−13.0882	+	5.42131i	−1.17064	+	0.484897i	−0.289239	+	0.957257i	$0.593402\pi$
$6$		0			0
$7$	−26.4168	−	10.9422i	−1.42637	−	0.590823i	−0.469920	−	0.882709i	$-0.655717\pi$
$7$	−26.4168	−	10.9422i	−1.42637	−	0.590823i	−0.956453	+	0.291886i	$0.905717\pi$
$8$	14.4267	−	14.4267i	0.637575	−	0.637575i
$9$		0			0
$10$	−39.9464	−	16.5464i	−1.26322	−	0.523242i
$11$	9.48236	−	22.8924i	0.259913	−	0.627484i	−0.739020	−	0.673684i	$-0.764711\pi$
$11$	9.48236	−	22.8924i	0.259913	−	0.627484i	0.998932	+	0.0461995i	$0.0147110\pi$
$12$		0			0
$13$		−	31.8846i		−	0.680245i	−0.940381	−	0.340123i	$-0.889531\pi$
$13$		−	31.8846i		−	0.680245i	0.940381	−	0.340123i	$-0.110469\pi$
$14$	−33.3966	−	80.6266i	−0.637544	−	1.53917i
$15$		0			0
$16$	72.7923			1.13738
$17$	−59.1905	+	37.5432i	−0.844459	+	0.535621i
$17$	−59.1905	+	37.5432i	−0.844459	+	0.535621i
$18$		0			0
$19$	−66.3298	−	66.3298i	−0.800900	−	0.800900i	0.182336	−	0.983236i	$-0.441634\pi$
$19$	−66.3298	−	66.3298i	−0.800900	−	0.800900i	−0.983236	+	0.182336i	$0.941634\pi$
$20$	−7.13054	−	17.2146i	−0.0797218	−	0.192465i
$21$		0			0
$22$	69.8699	−	28.9410i	0.677105	−	0.280466i
$23$	−23.6243	+	57.0340i	−0.214174	+	0.517061i	−0.994057	−	0.108864i	$-0.965279\pi$
$23$	−23.6243	+	57.0340i	−0.214174	+	0.517061i	0.779883	+	0.625926i	$0.215279\pi$
$24$		0			0
$25$	53.5222	−	53.5222i	0.428178	−	0.428178i
$26$	68.8119	−	68.8119i	0.519043	−	0.519043i
$27$		0			0
$28$	14.3920	−	34.7454i	0.0971371	−	0.234510i
$29$	−238.832	+	98.9273i	−1.52931	+	0.633460i	−0.979430	−	0.201785i	$-0.935326\pi$
$29$	−238.832	+	98.9273i	−1.52931	+	0.633460i	−0.549878	+	0.835245i	$0.685326\pi$
$30$		0			0
$31$	73.8065	+	178.185i	0.427614	+	1.03235i	0.980042	+	0.198791i	$0.0637017\pi$
$31$	73.8065	+	178.185i	0.427614	+	1.03235i	−0.552427	+	0.833561i	$0.686298\pi$
$32$	41.6837	+	41.6837i	0.230272	+	0.230272i
$33$		0			0
$34$	−208.766	−	46.7182i	−1.05303	−	0.235650i
$35$	405.070			1.95627
$36$		0			0
$37$	−130.945	−	316.128i	−0.581816	−	1.40463i	−0.891165	−	0.453679i	$-0.850111\pi$
$37$	−130.945	−	316.128i	−0.581816	−	1.40463i	0.309350	−	0.950948i	$-0.399889\pi$
$38$		−	286.300i		−	1.22221i
$39$		0			0
$40$	−110.608	+	267.031i	−0.437216	+	1.05553i
$41$	250.006	+	103.556i	0.952304	+	0.394457i	0.804096	−	0.594499i	$-0.202650\pi$
$41$	250.006	+	103.556i	0.952304	+	0.394457i	0.148208	+	0.988956i	$0.452650\pi$
$42$		0			0
$43$	242.000	−	242.000i	0.858249	−	0.858249i	−0.132882	−	0.991132i	$-0.542423\pi$
$43$	242.000	−	242.000i	0.858249	−	0.858249i	0.991132	+	0.132882i	$0.0424233\pi$
$44$	30.1099	+	12.4719i	0.103165	+	0.0427322i
$45$		0			0
$46$	−174.073	+	72.1034i	−0.557950	+	0.231110i
$47$			47.9808i			0.148909i	0.997224	+	0.0744544i	$0.0237215\pi$
$47$			47.9808i			0.148909i	−0.997224	+	0.0744544i	$0.976278\pi$
$48$		0			0
$49$	335.578	+	335.578i	0.978362	+	0.978362i
$50$	231.019			0.653419
$51$		0			0
$52$	41.9371			0.111839
$53$	−157.349	−	157.349i	−0.407803	−	0.407803i	0.473169	−	0.880972i	$-0.343110\pi$
$53$	−157.349	−	157.349i	−0.407803	−	0.407803i	−0.880972	+	0.473169i	$0.843110\pi$
$54$		0			0
$55$			351.028i			0.860592i
$56$	−538.966	+	223.247i	−1.28611	+	0.532726i
$57$		0			0
$58$	−728.937	−	301.935i	−1.65024	−	0.683553i
$59$	−135.454	+	135.454i	−0.298892	+	0.298892i	−0.840580	−	0.541688i	$-0.817786\pi$
$59$	−135.454	+	135.454i	−0.298892	+	0.298892i	0.541688	+	0.840580i	$0.317786\pi$
$60$		0			0
$61$	441.840	+	183.016i	0.927406	+	0.384144i	0.794694	−	0.607011i	$-0.207631\pi$
$61$	441.840	+	183.016i	0.927406	+	0.384144i	0.132712	+	0.991155i	$0.457631\pi$
$62$	−225.265	+	543.837i	−0.461429	+	1.11399i
$63$		0			0
$64$		−	402.418i		−	0.785973i
$65$	172.856	+	417.312i	0.329849	+	0.796326i
$66$		0			0
$67$	254.007			0.463163			0.231581	−	0.972816i	$-0.425610\pi$
$67$	254.007			0.463163			0.231581	+	0.972816i	$0.425610\pi$
$68$	−49.3797	−	77.8519i	−0.0880613	−	0.138837i
$69$		0			0
$70$	874.204	+	874.204i	1.49268	+	1.49268i
$71$	−364.361	−	879.646i	−0.609038	−	1.47035i	−0.864048	−	0.503410i	$-0.832079\pi$
$71$	−364.361	−	879.646i	−0.609038	−	1.47035i	0.255010	−	0.966939i	$-0.417921\pi$
$72$		0			0
$73$	−1058.45	+	438.426i	−1.69702	+	0.702930i	−0.999902	−	0.0140222i	$-0.995536\pi$
$73$	−1058.45	+	438.426i	−1.69702	+	0.702930i	−0.697122	+	0.716952i	$0.745536\pi$
$74$	399.656	−	964.854i	0.627825	−	1.51570i
$75$		0			0
$76$	87.2421	−	87.2421i	0.131676	−	0.131676i
$77$	−500.987	+	500.987i	−0.741465	+	0.741465i
$78$		0			0
$79$	−76.8385	+	185.504i	−0.109430	+	0.264188i	−0.969103	−	0.246658i	$-0.920668\pi$
$79$	−76.8385	+	185.504i	−0.109430	+	0.264188i	0.859672	+	0.510846i	$0.170668\pi$
$80$	−952.720	+	394.630i	−1.33147	+	0.551512i
$81$		0			0
$82$	316.063	+	763.043i	0.425650	+	1.02761i
$83$	169.307	+	169.307i	0.223902	+	0.223902i	0.810139	−	0.586238i	$-0.199391\pi$
$83$	169.307	+	169.307i	0.223902	+	0.223902i	−0.586238	+	0.810139i	$0.699391\pi$
$84$		0			0
$85$	571.164	−	812.263i	0.728840	−	1.03650i
$86$	1044.55			1.30973
$87$		0			0
$88$	−193.463	−	467.061i	−0.234355	−	0.565782i
$89$		−	627.144i		−	0.746934i	−0.927643	−	0.373467i	$-0.878169\pi$
$89$		−	627.144i		−	0.746934i	0.927643	−	0.373467i	$-0.121831\pi$
$90$		0			0
$91$	−348.887	+	842.289i	−0.401905	+	0.970284i
$92$	−75.0156	−	31.0725i	−0.0850099	−	0.0352123i
$93$		0			0
$94$	−103.550	+	103.550i	−0.113621	+	0.113621i
$95$	1227.73	+	508.544i	1.32592	+	0.549216i
$96$		0			0
$97$	1165.39	−	482.720i	1.21987	−	0.505287i	0.322502	−	0.946569i	$-0.395476\pi$
$97$	1165.39	−	482.720i	1.21987	−	0.505287i	0.897369	+	0.441282i	$0.145476\pi$
$98$			1448.46i			1.49303i
$99$		0			0
$100$	70.3966	+	70.3966i	0.0703966	+	0.0703966i
$101$	−84.2445			−0.0829965			−0.0414982	−	0.999139i	$-0.513213\pi$
$101$	−84.2445			−0.0829965			−0.0414982	+	0.999139i	$0.513213\pi$
$102$		0			0
$103$	−223.403			−0.213714			−0.106857	−	0.994274i	$-0.534079\pi$
$103$	−223.403			−0.213714			−0.106857	+	0.994274i	$0.534079\pi$
$104$	−459.988	−	459.988i	−0.433707	−	0.433707i
$105$		0			0
$106$		−	679.168i		−	0.622327i
$107$	669.306	−	277.236i	0.604713	−	0.250480i	−0.0592534	−	0.998243i	$-0.518872\pi$
$107$	669.306	−	277.236i	0.604713	−	0.250480i	0.663966	+	0.747763i	$0.268872\pi$
$108$		0			0
$109$	−587.022	−	243.152i	−0.515839	−	0.213668i	0.109549	−	0.993981i	$-0.465059\pi$
$109$	−587.022	−	243.152i	−0.515839	−	0.213668i	−0.625388	+	0.780314i	$0.715059\pi$
$110$	−757.573	+	757.573i	−0.656652	+	0.656652i
$111$		0			0
$112$	−1922.94	−	796.508i	−1.62233	−	0.671990i
$113$	389.316	−	939.892i	0.324104	−	0.782457i	−0.674903	−	0.737907i	$-0.735815\pi$
$113$	389.316	−	939.892i	0.324104	−	0.782457i	0.999007	−	0.0445502i	$-0.0141855\pi$
$114$		0			0
$115$		−	874.547i		−	0.709147i
$116$	−130.117	−	314.130i	−0.104147	−	0.251433i
$117$		0			0
$118$	−584.663			−0.456124
$119$	1974.43	−	344.097i	1.52097	−	0.265070i
$120$		0			0
$121$	507.011	+	507.011i	0.380925	+	0.380925i
$122$	558.582	+	1348.54i	0.414522	+	1.00074i
$123$		0			0
$124$	−234.363	+	97.0761i	−0.169729	+	0.0703040i
$125$	267.315	−	645.355i	0.191275	−	0.461779i
$126$		0			0
$127$	1014.08	−	1014.08i	0.708547	−	0.708547i	−0.257683	−	0.966230i	$-0.582959\pi$
$127$	1014.08	−	1014.08i	0.708547	−	0.708547i	0.966230	+	0.257683i	$0.0829589\pi$
$128$	1201.95	−	1201.95i	0.829988	−	0.829988i
$129$		0			0
$130$	−527.574	+	1273.68i	−0.355933	+	0.859298i
$131$	−223.796	+	92.6993i	−0.149261	+	0.0618258i	−0.456063	−	0.889947i	$-0.650741\pi$
$131$	−223.796	+	92.6993i	−0.149261	+	0.0618258i	0.306803	+	0.951773i	$0.400741\pi$
$132$		0			0
$133$	1026.43	+	2478.02i	0.669192	+	1.61557i
$134$	548.187	+	548.187i	0.353404	+	0.353404i
$135$		0			0
$136$	−312.298	+	1395.54i	−0.196907	+	0.879904i
$137$	−3062.95			−1.91012			−0.955058	−	0.296420i	$-0.904207\pi$
$137$	−3062.95			−1.91012			−0.955058	+	0.296420i	$0.904207\pi$
$138$		0			0
$139$	−472.386	−	1140.44i	−0.288254	−	0.695906i	0.711725	−	0.702458i	$-0.247914\pi$
$139$	−472.386	−	1140.44i	−0.288254	−	0.695906i	−0.999979	+	0.00655249i	$0.997914\pi$
$140$			532.779i			0.321629i
$141$		0			0
$142$	1112.06	−	2684.76i	0.657200	−	1.58662i
$143$	−729.915	−	302.341i	−0.426843	−	0.176804i
$144$		0			0
$145$	2589.56	−	2589.56i	1.48311	−	1.48311i
$146$	−3230.50	−	1338.12i	−1.83122	−	0.758517i
$147$		0			0
$148$	415.797	−	172.229i	0.230934	−	0.0956562i
$149$		−	401.154i		−	0.220563i	−0.993900	−	0.110281i	$-0.964825\pi$
$149$		−	401.154i		−	0.220563i	0.993900	−	0.110281i	$-0.0351752\pi$
$150$		0			0
$151$	−1717.83	−	1717.83i	−0.925792	−	0.925792i	0.0716384	−	0.997431i	$-0.477177\pi$
$151$	−1717.83	−	1717.83i	−0.925792	−	0.925792i	−0.997431	+	0.0716384i	$0.977177\pi$
$152$	−1913.84			−1.02127
$153$		0			0
$154$	−2162.42			−1.13151
$155$	−1931.99	−	1931.99i	−1.00117	−	1.00117i
$156$		0			0
$157$		−	1806.56i		−	0.918340i	−0.888348	−	0.459170i	$-0.848147\pi$
$157$		−	1806.56i		−	0.918340i	0.888348	−	0.459170i	$-0.151853\pi$
$158$	−566.177	+	234.518i	−0.285080	+	0.118084i
$159$		0			0
$160$	−771.545	−	319.585i	−0.381225	−	0.157909i
$161$	1248.15	−	1248.15i	0.610984	−	0.610984i
$162$		0			0
$163$	−191.843	−	79.4641i	−0.0921860	−	0.0381847i	0.336114	−	0.941821i	$-0.390887\pi$
$163$	−191.843	−	79.4641i	−0.0921860	−	0.0381847i	−0.428300	+	0.903637i	$0.640887\pi$
$164$	−136.205	+	328.828i	−0.0648526	+	0.156568i
$165$		0			0
$166$			730.781i			0.341685i
$167$	402.027	+	970.580i	0.186286	+	0.449735i	0.989239	−	0.146308i	$-0.0467389\pi$
$167$	402.027	+	970.580i	0.186286	+	0.449735i	−0.802953	+	0.596043i	$0.796739\pi$
$168$		0			0
$169$	1180.37			0.537266
$170$	2985.65	−	520.329i	1.34699	−	0.234750i
$171$		0			0
$172$	318.298	+	318.298i	0.141105	+	0.141105i
$173$	−620.586	−	1498.23i	−0.272730	−	0.658428i	0.726868	−	0.686777i	$-0.240975\pi$
$173$	−620.586	−	1498.23i	−0.272730	−	0.658428i	−0.999598	+	0.0283487i	$0.990975\pi$
$174$		0			0
$175$	−1999.54	+	828.235i	−0.863719	+	0.357764i
$176$	690.242	−	1666.39i	0.295619	−	0.713688i
$177$		0			0
$178$	1353.47	−	1353.47i	0.569928	−	0.569928i
$179$	−803.119	+	803.119i	−0.335352	+	0.335352i	−0.854615	−	0.519263i	$-0.826207\pi$
$179$	−803.119	+	803.119i	−0.335352	+	0.335352i	0.519263	+	0.854615i	$0.326207\pi$
$180$		0			0
$181$	−1324.73	+	3198.17i	−0.544012	+	1.31336i	0.377859	+	0.925863i	$0.376660\pi$
$181$	−1324.73	+	3198.17i	−0.544012	+	1.31336i	−0.921871	+	0.387497i	$0.873340\pi$
$182$	−2570.74	+	1064.84i	−1.04701	+	0.433687i
$183$		0			0
$184$	481.991	+	1163.63i	0.193114	+	0.466217i
$185$	3427.66	+	3427.66i	1.36220	+	1.36220i
$186$		0			0
$187$	298.189	+	1711.01i	0.116608	+	0.669099i
$188$	−63.1081			−0.0244821
$189$		0			0
$190$	1552.12	+	3747.16i	0.592647	+	1.43078i
$191$			3577.24i			1.35518i	0.735438	+	0.677592i	$0.236976\pi$
$191$			3577.24i			1.35518i	−0.735438	+	0.677592i	$0.763024\pi$
$192$		0			0
$193$	330.669	−	798.305i	0.123327	−	0.297737i	−0.850143	−	0.526551i	$-0.823485\pi$
$193$	330.669	−	798.305i	0.123327	−	0.297737i	0.973470	+	0.228814i	$0.0734848\pi$
$194$	3556.88	+	1473.31i	1.31634	+	0.545244i
$195$		0			0
$196$	−441.379	+	441.379i	−0.160852	+	0.160852i
$197$	−1416.44	−	586.710i	−0.512271	−	0.212190i	0.111547	−	0.993759i	$-0.464419\pi$
$197$	−1416.44	−	586.710i	−0.512271	−	0.212190i	−0.623818	+	0.781570i	$0.714419\pi$
$198$		0			0
$199$	−4195.39	+	1737.79i	−1.49449	+	0.619038i	−0.972288	−	0.233785i	$-0.924889\pi$
$199$	−4195.39	+	1737.79i	−1.49449	+	0.619038i	−0.522200	+	0.852823i	$0.674889\pi$
$200$		−	1544.30i		−	0.545991i
$201$		0			0
$202$	−181.813	−	181.813i	−0.0633283	−	0.0633283i
$203$	7391.65			2.55563
$204$		0			0
$205$	−3833.55			−1.30608
$206$	−482.138	−	482.138i	−0.163069	−	0.163069i
$207$		0			0
$208$		−	2320.95i		−	0.773697i
$209$	−2147.41	+	889.488i	−0.710716	+	0.294388i
$210$		0			0
$211$	5246.53	+	2173.18i	1.71178	+	0.709043i	0.999978	+	0.00666523i	$0.00212162\pi$
$211$	5246.53	+	2173.18i	1.71178	+	0.709043i	0.711804	+	0.702378i	$0.247878\pi$
$212$	206.958	−	206.958i	0.0670468	−	0.0670468i
$213$		0			0
$214$	2042.78	+	846.149i	0.652532	+	0.270288i
$215$	−1855.39	+	4479.31i	−0.588543	+	1.42087i
$216$		0			0
$217$		−	5514.68i		−	1.72516i
$218$	−742.124	−	1791.65i	−0.230564	−	0.556631i
$219$		0			0
$220$	−461.699			−0.141490
$221$	1197.05	+	1887.26i	0.364354	+	0.574439i
$222$		0			0
$223$	3095.56	+	3095.56i	0.929571	+	0.929571i	0.997678	−	0.0681070i	$-0.0216959\pi$
$223$	3095.56	+	3095.56i	0.929571	+	0.929571i	−0.0681070	+	0.997678i	$0.521696\pi$
$224$	−645.039	−	1557.26i	−0.192404	−	0.464504i
$225$		0			0
$226$	2868.64	−	1188.23i	0.844332	−	0.349734i
$227$	333.945	−	806.214i	0.0976418	−	0.235728i	−0.867510	−	0.497421i	$-0.834281\pi$
$227$	333.945	−	806.214i	0.0976418	−	0.235728i	0.965151	+	0.261692i	$0.0842806\pi$
$228$		0			0
$229$	614.382	−	614.382i	0.177290	−	0.177290i	−0.612883	−	0.790174i	$-0.709990\pi$
$229$	614.382	−	614.382i	0.177290	−	0.177290i	0.790174	+	0.612883i	$0.209990\pi$
$230$	1887.41	−	1887.41i	0.541096	−	0.541096i
$231$		0			0
$232$	−2018.35	+	4872.74i	−0.571170	+	1.37893i
$233$	4206.17	−	1742.25i	1.18264	−	0.489866i	0.297289	−	0.954788i	$-0.403917\pi$
$233$	4206.17	−	1742.25i	1.18264	−	0.489866i	0.885352	+	0.464922i	$0.153917\pi$
$234$		0			0
$235$	−260.119	−	627.982i	−0.0722054	−	0.174319i
$236$	−178.160	−	178.160i	−0.0491408	−	0.0491408i
$237$		0			0
$238$	5003.74	+	3518.51i	1.36279	+	0.958282i
$239$	−6181.53			−1.67301			−0.836507	−	0.547957i	$-0.815406\pi$
$239$	−6181.53			−1.67301			−0.836507	+	0.547957i	$0.815406\pi$
$240$		0			0
$241$	−2305.23	−	5565.33i	−0.616154	−	1.48753i	−0.856136	−	0.516751i	$-0.827141\pi$
$241$	−2305.23	−	5565.33i	−0.616154	−	1.48753i	0.239981	−	0.970777i	$-0.422859\pi$
$242$			2188.42i			0.581309i
$243$		0			0
$244$	−240.717	+	581.142i	−0.0631570	+	0.152475i
$245$	−6211.39	−	2572.84i	−1.61972	−	0.670910i
$246$		0			0
$247$	−2114.90	+	2114.90i	−0.544809	+	0.544809i
$248$	3635.40	+	1505.83i	0.930838	+	0.385566i
$249$		0			0
$250$	1969.69	−	815.870i	0.498295	−	0.206401i
$251$			5937.89i			1.49321i	0.665267	+	0.746606i	$0.268318\pi$
$251$			5937.89i			1.49321i	−0.665267	+	0.746606i	$0.731682\pi$
$252$		0			0
$253$	1081.63	+	1081.63i	0.268781	+	0.268781i
$254$	4377.11			1.08128
$255$		0			0
$256$	1968.65			0.480628
$257$	−1537.77	−	1537.77i	−0.373242	−	0.373242i	0.495414	−	0.868657i	$-0.335016\pi$
$257$	−1537.77	−	1537.77i	−0.373242	−	0.373242i	−0.868657	+	0.495414i	$0.835016\pi$
$258$		0			0
$259$			9783.93i			2.34727i
$260$	−548.881	+	227.354i	−0.130924	+	0.0542304i
$261$		0			0
$262$	−683.046	−	282.927i	−0.161064	−	0.0667149i
$263$	2078.34	−	2078.34i	0.487284	−	0.487284i	−0.420164	−	0.907448i	$-0.638027\pi$
$263$	2078.34	−	2078.34i	0.487284	−	0.487284i	0.907448	+	0.420164i	$0.138027\pi$
$264$		0			0
$265$	2912.46	+	1206.38i	0.675135	+	0.279650i
$266$	−3132.75	+	7563.14i	−0.722111	+	1.74333i
$267$		0			0
$268$			334.090i			0.0761485i
$269$	−1135.69	−	2741.80i	−0.257413	−	0.621451i	0.741353	−	0.671116i	$-0.234185\pi$
$269$	−1135.69	−	2741.80i	−0.257413	−	0.621451i	−0.998766	+	0.0496648i	$0.984185\pi$
$270$		0			0
$271$	108.879			0.0244056			0.0122028	−	0.999926i	$-0.496116\pi$
$271$	108.879			0.0244056			0.0122028	+	0.999926i	$0.496116\pi$
$272$	−4308.61	+	2732.85i	−0.960470	+	0.609204i
$273$		0			0
$274$	−6610.33	−	6610.33i	−1.45746	−	1.45746i
$275$	−717.737	−	1732.77i	−0.157386	−	0.379964i
$276$		0			0
$277$	−7705.62	+	3191.77i	−1.67143	+	0.692329i	−0.998861	−	0.0477059i	$-0.984809\pi$
$277$	−7705.62	+	3191.77i	−1.67143	+	0.692329i	−0.672569	+	0.740035i	$0.734809\pi$
$278$	1441.77	−	3480.73i	0.311048	−	0.750937i
$279$		0			0
$280$	5843.81	−	5843.81i	1.24727	−	1.24727i
$281$	48.7818	−	48.7818i	0.0103561	−	0.0103561i	−0.701910	−	0.712266i	$-0.747669\pi$
$281$	48.7818	−	48.7818i	0.0103561	−	0.0103561i	0.712266	+	0.701910i	$0.247669\pi$
$282$		0			0
$283$	23.7003	−	57.2176i	0.00497822	−	0.0120185i	−0.921371	−	0.388685i	$-0.872930\pi$
$283$	23.7003	−	57.2176i	0.00497822	−	0.0120185i	0.926349	+	0.376666i	$0.122930\pi$
$284$	1156.98	−	479.236i	0.241740	−	0.100132i
$285$		0			0
$286$	−922.773	−	2227.77i	−0.190786	−	0.460597i
$287$	−5471.24	−	5471.24i	−1.12529	−	1.12529i
$288$		0			0
$289$	2094.02	−	4444.39i	0.426220	−	0.904619i
$290$	11177.4			2.26330
$291$		0			0
$292$	−576.652	−	1392.16i	−0.115569	−	0.279007i
$293$			1524.73i			0.304013i	0.988379	+	0.152007i	$0.0485735\pi$
$293$			1524.73i			0.304013i	−0.988379	+	0.152007i	$0.951427\pi$
$294$		0			0
$295$	1038.51	−	2507.19i	0.204965	−	0.494829i
$296$	−6449.78	−	2671.59i	−1.26651	−	0.524604i
$297$		0			0
$298$	865.753	−	865.753i	0.168294	−	0.168294i
$299$	1818.50	+	753.249i	0.351729	+	0.145691i
$300$		0			0
$301$	−9040.90	+	3744.86i	−1.73126	+	0.717110i
$302$		−	7414.67i		−	1.41280i
$303$		0			0
$304$	−4828.30	−	4828.30i	−0.910927	−	0.910927i
$305$	−6775.08			−1.27193
$306$		0			0
$307$	3344.78			0.621814			0.310907	−	0.950440i	$-0.399367\pi$
$307$	3344.78			0.621814			0.310907	+	0.950440i	$0.399367\pi$
$308$	−658.937	−	658.937i	−0.121904	−	0.121904i
$309$		0			0
$310$		−	8339.08i		−	1.52783i
$311$	−6452.97	+	2672.91i	−1.17657	+	0.487353i	−0.883361	−	0.468694i	$-0.844725\pi$
$311$	−6452.97	+	2672.91i	−1.17657	+	0.487353i	−0.293213	+	0.956047i	$0.594725\pi$
$312$		0			0
$313$	−9500.05	−	3935.05i	−1.71557	−	0.710614i	−0.999926	−	0.0121525i	$-0.996132\pi$
$313$	−9500.05	−	3935.05i	−1.71557	−	0.710614i	−0.715648	−	0.698461i	$-0.753868\pi$
$314$	3898.84	−	3898.84i	0.700715	−	0.700715i
$315$		0			0
$316$	−243.990	−	101.064i	−0.0434351	−	0.0179914i
$317$	2018.33	−	4872.67i	0.357604	−	0.863332i	−0.638032	−	0.770010i	$-0.720251\pi$
$317$	2018.33	−	4872.67i	0.357604	−	0.863332i	0.995636	−	0.0933224i	$-0.0297487\pi$
$318$		0			0
$319$			6405.50i			1.12426i
$320$	2181.64	+	5266.93i	0.381116	+	0.920096i
$321$		0			0
$322$	5387.43			0.932390
$323$	6416.32	+	1435.86i	1.10531	+	0.247348i
$324$		0			0
$325$	−1706.53	−	1706.53i	−0.291266	−	0.291266i
$326$	−242.532	−	585.524i	−0.0412043	−	0.0994759i
$327$		0			0
$328$	5100.73	−	2112.79i	0.858661	−	0.355669i
$329$	525.015	−	1267.50i	0.0879788	−	0.212400i
$330$		0			0
$331$	−1495.50	+	1495.50i	−0.248338	+	0.248338i	−0.820288	−	0.571950i	$-0.806187\pi$
$331$	−1495.50	+	1495.50i	−0.248338	+	0.248338i	0.571950	+	0.820288i	$0.306187\pi$
$332$	−222.686	+	222.686i	−0.0368116	+	0.0368116i
$333$		0			0
$334$	−1227.03	+	2962.30i	−0.201017	+	0.485299i
$335$	−3324.50	+	1377.05i	−0.542199	+	0.224586i
$336$		0			0
$337$	−2396.19	−	5784.92i	−0.387326	−	0.935089i	−0.990504	−	0.137482i	$-0.956099\pi$
$337$	−2396.19	−	5784.92i	−0.387326	−	0.935089i	0.603178	−	0.797607i	$-0.293901\pi$
$338$	2547.43	+	2547.43i	0.409947	+	0.409947i
$339$		0			0
$340$	1068.35	+	751.239i	0.170410	+	0.119828i
$341$	4778.94			0.758927
$342$		0			0
$343$	−1439.77	−	3475.91i	−0.226648	−	0.547176i
$344$		−	6982.52i		−	1.09440i
$345$		0			0
$346$	1894.09	−	4572.73i	0.294297	−	0.710496i
$347$	−248.118	−	102.774i	−0.0383851	−	0.0158996i	0.363408	−	0.931630i	$-0.381613\pi$
$347$	−248.118	−	102.774i	−0.0383851	−	0.0158996i	−0.401793	+	0.915730i	$0.631613\pi$
$348$		0			0
$349$	−1232.94	+	1232.94i	−0.189106	+	0.189106i	−0.795310	−	0.606203i	$-0.792692\pi$
$349$	−1232.94	+	1232.94i	−0.189106	+	0.189106i	0.606203	+	0.795310i	$0.292692\pi$
$350$	−6102.78	−	2527.85i	−0.932020	−	0.386055i
$351$		0			0
$352$	1349.50	−	558.982i	0.204343	−	0.0846415i
$353$			6175.36i			0.931108i	0.885020	+	0.465554i	$0.154145\pi$
$353$			6175.36i			0.931108i	−0.885020	+	0.465554i	$0.845855\pi$
$354$		0			0
$355$	9537.67	+	9537.67i	1.42594	+	1.42594i
$356$	824.869			0.122803
$357$		0			0
$358$	−3466.51			−0.511763
$359$	2296.76	+	2296.76i	0.337655	+	0.337655i	0.855484	−	0.517829i	$-0.173260\pi$
$359$	2296.76	+	2296.76i	0.337655	+	0.337655i	−0.517829	+	0.855484i	$0.673260\pi$
$360$		0			0
$361$			1940.29i			0.282882i
$362$	−9761.12	+	4043.19i	−1.41722	+	0.587031i
$363$		0			0
$364$	−1107.84	−	458.884i	−0.159524	−	0.0660771i
$365$	11476.4	−	11476.4i	1.64576	−	1.64576i
$366$		0			0
$367$	−2451.85	−	1015.59i	−0.348735	−	0.144451i	0.201439	−	0.979501i	$-0.435438\pi$
$367$	−2451.85	−	1015.59i	−0.348735	−	0.144451i	−0.550173	+	0.835050i	$0.685438\pi$
$368$	−1719.66	+	4151.63i	−0.243597	+	0.588095i
$369$		0			0
$370$			14794.9i			2.07878i
$371$	2434.92	+	5878.41i	0.340740	+	0.822619i
$372$		0			0
$373$	6982.38			0.969260			0.484630	−	0.874719i	$-0.338954\pi$
$373$	6982.38			0.969260			0.484630	+	0.874719i	$0.338954\pi$
$374$	−3049.09	+	4336.17i	−0.421563	+	0.599513i
$375$		0			0
$376$	692.203	+	692.203i	0.0949405	+	0.0949405i
$377$	3154.25	+	7615.04i	0.430908	+	1.04030i
$378$		0			0
$379$	7696.61	−	3188.04i	1.04314	−	0.432081i	0.205699	−	0.978615i	$-0.434053\pi$
$379$	7696.61	−	3188.04i	1.04314	−	0.432081i	0.837437	+	0.546534i	$0.184053\pi$
$380$	−668.876	+	1614.81i	−0.0902964	+	0.217995i
$381$		0			0
$382$	−7720.24	+	7720.24i	−1.03404	+	1.03404i
$383$	336.493	−	336.493i	0.0448929	−	0.0448929i	−0.684304	−	0.729197i	$-0.739894\pi$
$383$	336.493	−	336.493i	0.0448929	−	0.0448929i	0.729197	+	0.684304i	$0.239894\pi$
$384$		0			0
$385$	3841.02	−	9273.03i	0.508458	−	1.22753i
$386$	2436.50	−	1009.23i	0.321281	−	0.133079i
$387$		0			0
$388$	634.912	+	1532.81i	0.0830741	+	0.200559i
$389$	−2888.32	−	2888.32i	−0.376461	−	0.376461i	0.493363	−	0.869824i	$-0.335768\pi$
$389$	−2888.32	−	2888.32i	−0.376461	−	0.376461i	−0.869824	+	0.493363i	$0.835768\pi$
$390$		0			0
$391$	−742.906	−	4262.80i	−0.0960880	−	0.551353i
$392$	9682.56			1.24756
$393$		0			0
$394$	−1790.69	−	4323.12i	−0.228969	−	0.552780i
$395$		−	2844.49i		−	0.362333i
$396$		0			0
$397$	1582.16	−	3819.66i	0.200015	−	0.482880i	−0.791766	−	0.610825i	$-0.790838\pi$
$397$	1582.16	−	3819.66i	0.200015	−	0.482880i	0.991781	+	0.127945i	$0.0408380\pi$
$398$	−12804.7	−	5303.89i	−1.61267	−	0.667990i
$399$		0			0
$400$	3896.00	−	3896.00i	0.487000	−	0.487000i
$401$	2599.23	+	1076.64i	0.323690	+	0.134077i	0.538611	−	0.842555i	$-0.318949\pi$
$401$	2599.23	+	1076.64i	0.323690	+	0.134077i	−0.214921	+	0.976631i	$0.568949\pi$
$402$		0			0
$403$	5681.34	−	2353.29i	0.702253	−	0.290883i
$404$		−	110.805i		−	0.0136454i
$405$		0			0
$406$	15952.3	+	15952.3i	1.95000	+	1.95000i
$407$	−8478.61			−1.03260
$408$		0			0
$409$	1513.09			0.182928			0.0914638	−	0.995808i	$-0.470845\pi$
$409$	1513.09			0.182928			0.0914638	+	0.995808i	$0.470845\pi$
$410$	−8273.39	−	8273.39i	−0.996570	−	0.996570i
$411$		0			0
$412$		−	293.837i		−	0.0351366i
$413$	5060.44	−	2096.10i	0.602925	−	0.249740i
$414$		0			0
$415$	−3133.79	−	1298.06i	−0.370679	−	0.153540i
$416$	1329.07	−	1329.07i	0.156641	−	0.156641i
$417$		0			0
$418$	−6554.11	−	2714.80i	−0.766918	−	0.317668i
$419$	−5278.30	+	12742.9i	−0.615422	+	1.48576i	0.241545	+	0.970390i	$0.422346\pi$
$419$	−5278.30	+	12742.9i	−0.615422	+	1.48576i	−0.856967	+	0.515371i	$0.827654\pi$
$420$		0			0
$421$			960.953i			0.111245i	0.998452	+	0.0556223i	$0.0177143\pi$
$421$			960.953i			0.111245i	−0.998452	+	0.0556223i	$0.982286\pi$
$422$	6632.76	+	16012.9i	0.765113	+	1.84715i
$423$		0			0
$424$	−4540.05			−0.520010
$425$	−1158.61	+	5177.40i	−0.132237	+	0.590919i
$426$		0			0
$427$	−9669.39	−	9669.39i	−1.09587	−	1.09587i
$428$	364.642	+	880.323i	0.0411814	+	0.0994206i
$429$		0			0
$430$	−13671.3	+	5662.83i	−1.53323	+	0.635084i
$431$	4143.40	−	10003.0i	0.463064	−	1.11793i	−0.504069	−	0.863663i	$-0.668164\pi$
$431$	4143.40	−	10003.0i	0.463064	−	1.11793i	0.967133	−	0.254271i	$-0.0818356\pi$
$432$		0			0
$433$	−2177.03	+	2177.03i	−0.241620	+	0.241620i	−0.817520	−	0.575900i	$-0.804652\pi$
$433$	−2177.03	+	2177.03i	−0.241620	+	0.241620i	0.575900	+	0.817520i	$0.304652\pi$
$434$	11901.5	−	11901.5i	1.31634	−	1.31634i
$435$		0			0
$436$	319.813	−	772.097i	0.0351290	−	0.0848090i
$437$	5350.05	−	2216.06i	0.585646	−	0.242583i
$438$		0			0
$439$	5415.21	+	13073.5i	0.588733	+	1.42133i	0.884715	+	0.466133i	$0.154353\pi$
$439$	5415.21	+	13073.5i	0.588733	+	1.42133i	−0.295982	+	0.955194i	$0.595647\pi$
$440$	5064.16	+	5064.16i	0.548692	+	0.548692i
$441$		0			0
$442$	−1489.59	+	6656.42i	−0.160300	+	0.716321i
$443$	682.598			0.0732081			0.0366041	−	0.999330i	$-0.488346\pi$
$443$	682.598			0.0732081			0.0366041	+	0.999330i	$0.488346\pi$
$444$		0			0
$445$	3399.94	+	8208.19i	0.362186	+	0.874394i
$446$			13361.4i			1.41857i
$447$		0			0
$448$	−4403.34	+	10630.6i	−0.464371	+	1.12109i
$449$	−6827.10	−	2827.88i	−0.717574	−	0.297229i	−0.00613945	−	0.999981i	$-0.501954\pi$
$449$	−6827.10	−	2827.88i	−0.717574	−	0.297229i	−0.711435	+	0.702752i	$0.751954\pi$
$450$		0			0
$451$	4741.30	−	4741.30i	0.495031	−	0.495031i
$452$	1236.22	+	512.059i	0.128644	+	0.0532859i
$453$		0			0
$454$	2460.64	−	1019.23i	0.254369	−	0.105363i
$455$		−	12915.5i		−	1.33074i
$456$		0			0
$457$	−5514.99	−	5514.99i	−0.564508	−	0.564508i	0.366077	−	0.930585i	$-0.380701\pi$
$457$	−5514.99	−	5514.99i	−0.564508	−	0.564508i	−0.930585	+	0.366077i	$0.880701\pi$
$458$	2651.86			0.270553
$459$		0			0
$460$	1150.27			0.116591
$461$	3026.09	+	3026.09i	0.305725	+	0.305725i	0.843249	−	0.537524i	$-0.180640\pi$
$461$	3026.09	+	3026.09i	0.305725	+	0.305725i	−0.537524	+	0.843249i	$0.680640\pi$
$462$		0			0
$463$			17748.4i			1.78151i	0.454488	+	0.890753i	$0.349822\pi$
$463$			17748.4i			1.78151i	−0.454488	+	0.890753i	$0.650178\pi$
$464$	−17385.1	+	7201.14i	−1.73940	+	0.720484i
$465$		0			0
$466$	12837.6	+	5317.52i	1.27616	+	0.528604i
$467$	5468.93	−	5468.93i	0.541910	−	0.541910i	−0.382178	−	0.924089i	$-0.624826\pi$
$467$	5468.93	−	5468.93i	0.541910	−	0.541910i	0.924089	+	0.382178i	$0.124826\pi$
$468$		0			0
$469$	−6710.06	−	2779.40i	−0.660643	−	0.273647i
$470$	793.907	−	1916.66i	0.0779153	−	0.188104i
$471$		0			0
$472$			3908.31i			0.381133i
$473$	−3245.24	−	7834.71i	−0.315468	−	0.761608i
$474$		0			0
$475$	−7100.24			−0.685855
$476$	452.583	+	2596.92i	0.0435801	+	0.250062i
$477$		0			0
$478$	−13340.7	−	13340.7i	−1.27655	−	1.27655i
$479$	2316.69	+	5592.98i	0.220986	+	0.533506i	0.995024	−	0.0996317i	$-0.0317665\pi$
$479$	2316.69	+	5592.98i	0.220986	+	0.533506i	−0.774039	+	0.633138i	$0.781766\pi$
$480$		0			0
$481$	−10079.6	+	4175.12i	−0.955491	+	0.395777i
$482$	7035.79	−	16985.9i	0.664879	−	1.60516i
$483$		0			0
$484$	−666.860	+	666.860i	−0.0626277	+	0.0626277i
$485$	−12635.9	+	12635.9i	−1.18302	+	1.18302i
$486$		0			0
$487$	1675.08	−	4044.00i	0.155863	−	0.376286i	−0.826588	−	0.562807i	$-0.809721\pi$
$487$	1675.08	−	4044.00i	0.155863	−	0.376286i	0.982451	+	0.186521i	$0.0597213\pi$
$488$	9014.59	−	3733.96i	0.836211	−	0.346370i
$489$		0			0
$490$	−7852.56	−	18957.8i	−0.723964	−	1.74780i
$491$	−4596.83	−	4596.83i	−0.422510	−	0.422510i	0.463557	−	0.886067i	$-0.346573\pi$
$491$	−4596.83	−	4596.83i	−0.422510	−	0.422510i	−0.886067	+	0.463557i	$0.846573\pi$
$492$		0			0
$493$	10422.5	−	14822.1i	0.952143	−	1.35406i
$494$	−9128.56			−0.831403
$495$		0			0
$496$	5372.55	+	12970.5i	0.486360	+	1.17418i
$497$			27224.3i			2.45710i
$498$		0			0
$499$	3843.03	−	9277.90i	0.344765	−	0.832336i	−0.652455	−	0.757827i	$-0.726261\pi$
$499$	3843.03	−	9277.90i	0.344765	−	0.832336i	0.997220	−	0.0745090i	$-0.0237390\pi$
$500$	848.822	+	351.593i	0.0759209	+	0.0314475i
$501$		0			0
$502$	−12814.9	+	12814.9i	−1.13936	+	1.13936i
$503$	−6828.90	−	2828.62i	−0.605339	−	0.250740i	0.0588953	−	0.998264i	$-0.481242\pi$
$503$	−6828.90	−	2828.62i	−0.605339	−	0.250740i	−0.664234	+	0.747525i	$0.731242\pi$
$504$		0			0
$505$	1102.61	−	456.716i	0.0971594	−	0.0402447i
$506$			4668.67i			0.410173i
$507$		0			0
$508$	1333.80	+	1333.80i	0.116492	+	0.116492i
$509$	−3442.25			−0.299755			−0.149877	−	0.988705i	$-0.547888\pi$
$509$	−3442.25			−0.299755			−0.149877	+	0.988705i	$0.547888\pi$
$510$		0			0
$511$	32758.3			2.83590
$512$	−5366.95	−	5366.95i	−0.463258	−	0.463258i
$513$		0			0
$514$		−	6637.48i		−	0.569585i
$515$	2923.94	−	1211.14i	0.250183	−	0.103629i
$516$		0			0
$517$	1098.40	+	454.971i	0.0934380	+	0.0387033i
$518$	−21115.2	+	21115.2i	−1.79102	+	1.79102i
$519$		0			0
$520$	8514.16	+	3526.68i	0.718021	+	0.297414i
$521$	5880.96	−	14197.9i	0.494529	−	1.19390i	−0.457863	−	0.889023i	$-0.651385\pi$
$521$	5880.96	−	14197.9i	0.494529	−	1.19390i	0.952392	−	0.304876i	$-0.0986151\pi$
$522$		0			0
$523$		−	11007.6i		−	0.920321i	−0.887836	−	0.460161i	$-0.847792\pi$
$523$		−	11007.6i		−	0.920321i	0.887836	−	0.460161i	$-0.152208\pi$
$524$	−121.925	−	294.354i	−0.0101648	−	0.0245399i
$525$		0			0
$526$	8970.75			0.743618
$527$	−11058.3	−	7775.91i	−0.914052	−	0.642740i
$528$		0			0
$529$	5908.60	+	5908.60i	0.485625	+	0.485625i
$530$	3681.98	+	8889.09i	0.301764	+	0.728523i
$531$		0			0
$532$	−3259.28	+	1350.04i	−0.265616	+	0.110022i
$533$	3301.84	−	7971.35i	0.268328	−	0.647800i
$534$		0			0
$535$	−7257.03	+	7257.03i	−0.586447	+	0.586447i
$536$	3664.48	−	3664.48i	0.295301	−	0.295301i
$537$		0			0
$538$	3466.23	−	8368.22i	0.277769	−	0.670594i
$539$	10864.3	−	4500.13i	0.868196	−	0.359618i
$540$		0			0
$541$	5199.82	+	12553.5i	0.413231	+	0.997628i	0.984265	+	0.176701i	$0.0565426\pi$
$541$	5199.82	+	12553.5i	0.413231	+	0.997628i	−0.571034	+	0.820927i	$0.693457\pi$
$542$	234.978	+	234.978i	0.0186221	+	0.0186221i
$543$		0			0
$544$	−4032.22	−	902.339i	−0.317794	−	0.0711167i
$545$	9001.27			0.707471
$546$		0			0
$547$	2595.23	+	6265.45i	0.202860	+	0.489746i	0.992267	−	0.124124i	$-0.0396119\pi$
$547$	2595.23	+	6265.45i	0.202860	+	0.489746i	−0.789407	+	0.613870i	$0.789612\pi$
$548$		−	4028.64i		−	0.314042i
$549$		0			0
$550$	2190.60	−	5288.58i	0.169832	−	0.410010i
$551$	22403.5	+	9279.83i	1.73216	+	0.717485i
$552$		0			0
$553$	4059.65	−	4059.65i	0.312177	−	0.312177i
$554$	−23518.3	−	9741.59i	−1.80360	−	0.747077i
$555$		0			0
$556$	1500.00	−	621.319i	0.114414	−	0.0473917i
$557$		−	7966.39i		−	0.606009i	−0.952989	−	0.303004i	$-0.902010\pi$
$557$		−	7966.39i		−	0.606009i	0.952989	−	0.303004i	$-0.0979896\pi$
$558$		0			0
$559$	−7716.08	−	7716.08i	−0.583820	−	0.583820i
$560$	29485.9			2.22502
$561$		0			0
$562$	210.557			0.0158040
$563$	−10295.8	−	10295.8i	−0.770718	−	0.770718i	0.207514	−	0.978232i	$-0.433463\pi$
$563$	−10295.8	−	10295.8i	−0.770718	−	0.770718i	−0.978232	+	0.207514i	$0.933463\pi$
$564$		0			0
$565$			14412.1i			1.07314i
$566$	174.634	−	72.3356i	0.0129689	−	0.00537189i
$567$		0			0
$568$	−17946.9	−	7433.84i	−1.32576	−	0.549150i
$569$	1095.22	−	1095.22i	0.0806928	−	0.0806928i	−0.665608	−	0.746301i	$-0.731828\pi$
$569$	1095.22	−	1095.22i	0.0806928	−	0.0806928i	0.746301	+	0.665608i	$0.231828\pi$
$570$		0			0
$571$	7405.14	+	3067.31i	0.542724	+	0.224804i	0.637166	−	0.770727i	$-0.280107\pi$
$571$	7405.14	+	3067.31i	0.542724	+	0.224804i	−0.0944417	+	0.995530i	$0.530107\pi$
$572$	397.662	−	960.042i	0.0290683	−	0.0701772i
$573$		0			0
$574$		−	23615.6i		−	1.71724i
$575$	1788.16	+	4317.01i	0.129690	+	0.313099i
$576$		0			0
$577$	−13182.6			−0.951127			−0.475564	−	0.879681i	$-0.657756\pi$
$577$	−13182.6			−0.951127			−0.475564	+	0.879681i	$0.657756\pi$
$578$	14110.9	−	5072.47i	1.01546	−	0.365030i
$579$		0			0
$580$	3406.00	+	3406.00i	0.243838	+	0.243838i
$581$	−2619.96	−	6325.14i	−0.187081	−	0.451654i
$582$		0			0
$583$	−5094.14	+	2110.06i	−0.361883	+	0.149897i
$584$	−8944.95	+	21595.0i	−0.633809	+	1.53015i
$585$		0			0
$586$	−3290.61	+	3290.61i	−0.231969	+	0.231969i
$587$	12823.3	−	12823.3i	0.901659	−	0.901659i	−0.0939204	−	0.995580i	$-0.529940\pi$
$587$	12823.3	−	12823.3i	0.901659	−	0.901659i	0.995580	+	0.0939204i	$0.0299399\pi$
$588$		0			0
$589$	6923.39	−	16714.5i	0.484335	−	1.16929i
$590$	7652.19	−	3169.64i	0.533959	−	0.221173i
$591$		0			0
$592$	−9531.76	−	23011.7i	−0.661745	−	1.59759i
$593$	5570.08	+	5570.08i	0.385726	+	0.385726i	0.873160	−	0.487434i	$-0.162067\pi$
$593$	5570.08	+	5570.08i	0.385726	+	0.385726i	−0.487434	+	0.873160i	$0.662067\pi$
$594$		0			0
$595$	−23976.3	+	15207.6i	−1.65199	+	1.04782i
$596$	527.629			0.0362626
$597$		0			0
$598$	2298.99	+	5550.25i	0.157212	+	0.379543i
$599$			20932.7i			1.42786i	0.700218	+	0.713929i	$0.253086\pi$
$599$			20932.7i			1.42786i	−0.700218	+	0.713929i	$0.746914\pi$
$600$		0			0
$601$	10107.5	−	24401.6i	0.686012	−	1.65618i	−0.0666541	−	0.997776i	$-0.521232\pi$
$601$	10107.5	−	24401.6i	0.686012	−	1.65618i	0.752666	−	0.658403i	$-0.228768\pi$
$602$	−27593.7	−	11429.7i	−1.86816	−	0.773818i
$603$		0			0
$604$	2259.42	−	2259.42i	0.152209	−	0.152209i
$605$	−9384.53	−	3887.20i	−0.630637	−	0.261218i
$606$		0			0
$607$	3002.43	−	1243.65i	0.200766	−	0.0831599i	−0.280035	−	0.959990i	$-0.590346\pi$
$607$	3002.43	−	1243.65i	0.200766	−	0.0831599i	0.480801	+	0.876830i	$0.340346\pi$
$608$		−	5529.74i		−	0.368850i
$609$		0			0
$610$	−14621.7	−	14621.7i	−0.970515	−	0.970515i
$611$	1529.85			0.101295
$612$		0			0
$613$	2187.56			0.144135			0.0720676	−	0.997400i	$-0.477040\pi$
$613$	2187.56			0.144135			0.0720676	+	0.997400i	$0.477040\pi$
$614$	7218.57	+	7218.57i	0.474459	+	0.474459i
$615$		0			0
$616$			14455.2i			0.945479i
$617$	9976.71	−	4132.49i	0.650968	−	0.269640i	−0.0326642	−	0.999466i	$-0.510399\pi$
$617$	9976.71	−	4132.49i	0.650968	−	0.269640i	0.683632	+	0.729827i	$0.260399\pi$
$618$		0			0
$619$	4670.26	+	1934.48i	0.303253	+	0.125611i	0.529121	−	0.848546i	$-0.322522\pi$
$619$	4670.26	+	1934.48i	0.303253	+	0.125611i	−0.225868	+	0.974158i	$0.572522\pi$
$620$	2541.11	−	2541.11i	0.164602	−	0.164602i
$621$		0			0
$622$	−19695.1	−	8157.97i	−1.26962	−	0.525892i
$623$	−6862.33	+	16567.1i	−0.441306	+	1.06541i
$624$		0			0
$625$			19357.2i			1.23886i
$626$	−12010.1	−	28995.0i	−0.766808	−	1.85124i
$627$		0			0
$628$	2376.13			0.150984
$629$	19619.1	+	13795.7i	1.24367	+	0.874517i
$630$		0			0
$631$	−15620.9	−	15620.9i	−0.985514	−	0.985514i	0.0143826	−	0.999897i	$-0.495422\pi$
$631$	−15620.9	−	15620.9i	−0.985514	−	0.985514i	−0.999897	+	0.0143826i	$0.995422\pi$
$632$	1567.69	+	3784.74i	0.0986698	+	0.238210i
$633$		0			0
$634$	14871.8	−	6160.12i	0.931603	−	0.385883i
$635$	−7774.88	+	18770.2i	−0.485885	+	1.17303i
$636$		0			0
$637$	10699.8	−	10699.8i	0.665526	−	0.665526i
$638$	−13824.1	+	13824.1i	−0.857837	+	0.857837i
$639$		0			0
$640$	−9215.23	+	22247.5i	−0.569163	+	1.37408i
$641$	−19700.4	+	8160.17i	−1.21391	+	0.502820i	−0.895470	−	0.445122i	$-0.853160\pi$
$641$	−19700.4	+	8160.17i	−1.21391	+	0.502820i	−0.318444	+	0.947942i	$0.603160\pi$
$642$		0			0
$643$	5956.95	+	14381.3i	0.365348	+	0.882029i	0.994499	+	0.104746i	$0.0334029\pi$
$643$	5956.95	+	14381.3i	0.365348	+	0.882029i	−0.629151	+	0.777283i	$0.716597\pi$
$644$	1641.67	+	1641.67i	0.100452	+	0.100452i
$645$		0			0
$646$	10748.6	+	16946.2i	0.654642	+	1.03211i
$647$	15308.2			0.930179			0.465090	−	0.885264i	$-0.346022\pi$
$647$	15308.2			0.930179			0.465090	+	0.885264i	$0.346022\pi$
$648$		0			0
$649$	1816.45	+	4385.30i	0.109864	+	0.265236i
$650$		−	7365.93i		−	0.444485i
$651$		0			0
$652$	104.517	−	252.327i	0.00627794	−	0.0151563i
$653$	−4429.33	−	1834.69i	−0.265441	−	0.109949i	0.245994	−	0.969271i	$-0.420886\pi$
$653$	−4429.33	−	1834.69i	−0.265441	−	0.109949i	−0.511435	+	0.859322i	$0.670886\pi$
$654$		0			0
$655$	2426.54	−	2426.54i	0.144752	−	0.144752i
$656$	18198.5	+	7538.08i	1.08313	+	0.448647i
$657$		0			0
$658$	3868.53	−	1602.40i	0.229196	−	0.0949360i
$659$			6281.68i			0.371319i	0.982614	+	0.185660i	$0.0594422\pi$
$659$			6281.68i			0.371319i	−0.982614	+	0.185660i	$0.940558\pi$
$660$		0			0
$661$	−5609.86	−	5609.86i	−0.330103	−	0.330103i	0.522522	−	0.852626i	$-0.324991\pi$
$661$	−5609.86	−	5609.86i	−0.330103	−	0.330103i	−0.852626	+	0.522522i	$0.824991\pi$
$662$	−6455.03			−0.378976
$663$		0			0
$664$	4885.07			0.285508
$665$	−26868.2	−	26868.2i	−1.56677	−	1.56677i
$666$		0			0
$667$		−	15958.6i		−	0.926416i
$668$	−1276.58	+	528.778i	−0.0739408	+	0.0306273i
$669$		0			0
$670$	−10146.7	−	4202.89i	−0.585075	−	0.242346i
$671$	8379.36	−	8379.36i	0.482089	−	0.482089i
$672$		0			0
$673$	6275.87	+	2599.55i	0.359461	+	0.148893i	0.555102	−	0.831782i	$-0.312679\pi$
$673$	6275.87	+	2599.55i	0.359461	+	0.148893i	−0.195642	+	0.980675i	$0.562679\pi$
$674$	7313.41	−	17656.1i	0.417955	−	1.00903i
$675$		0			0
$676$			1552.52i			0.0883318i
$677$	−7822.14	−	18884.3i	−0.444061	−	1.07206i	−0.974511	−	0.224342i	$-0.927977\pi$
$677$	−7822.14	−	18884.3i	−0.444061	−	1.07206i	0.530450	−	0.847716i	$-0.322023\pi$
$678$		0			0
$679$	−36067.9			−2.03853
$680$	−3478.26	−	19958.2i	−0.196155	−	1.12554i
$681$		0			0
$682$	10313.7	+	10313.7i	0.579079	+	0.579079i
$683$	−5929.52	−	14315.1i	−0.332191	−	0.801981i	−0.998418	−	0.0562312i	$-0.982092\pi$
$683$	−5929.52	−	14315.1i	−0.332191	−	0.801981i	0.666227	−	0.745749i	$-0.267908\pi$
$684$		0			0
$685$	40088.6	−	16605.2i	2.23607	−	0.926209i
$686$	4394.31	−	10608.8i	0.244571	−	0.590446i
$687$		0			0
$688$	17615.8	−	17615.8i	0.976155	−	0.976155i
$689$	−5017.01	+	5017.01i	−0.277406	+	0.277406i
$690$		0			0
$691$	−3714.04	+	8966.47i	−0.204470	+	0.493634i	−0.992535	−	0.121958i	$-0.961083\pi$
$691$	−3714.04	+	8966.47i	−0.204470	+	0.493634i	0.788066	+	0.615591i	$0.211083\pi$
$692$	1970.59	−	816.243i	0.108252	−	0.0448395i
$693$		0			0
$694$	−313.675	−	757.278i	−0.0171570	−	0.0414206i
$695$	12365.4	+	12365.4i	0.674885	+	0.674885i
$696$		0			0
$697$	−18685.8	+	3256.50i	−1.01546	+	0.176971i
$698$	−5321.78			−0.288585
$699$		0			0
$700$	−1089.36	−	2629.95i	−0.0588199	−	0.142004i
$701$		−	30452.5i		−	1.64076i	−0.571817	−	0.820381i	$-0.693761\pi$
$701$		−	30452.5i		−	1.64076i	0.571817	−	0.820381i	$-0.306239\pi$
$702$		0			0
$703$	−12283.2	+	29654.3i	−0.658990	+	1.59094i
$704$	−9212.33	−	3815.87i	−0.493186	−	0.204284i
$705$		0			0
$706$	−13327.4	+	13327.4i	−0.710457	+	0.710457i
$707$	2225.47	+	921.821i	0.118384	+	0.0490363i
$708$		0			0
$709$	5263.37	−	2180.16i	0.278801	−	0.115483i	−0.238902	−	0.971044i	$-0.576787\pi$
$709$	5263.37	−	2180.16i	0.278801	−	0.115483i	0.517703	+	0.855561i	$0.326787\pi$
$710$			41167.6i			2.17604i
$711$		0			0
$712$	−9047.60	−	9047.60i	−0.476226	−	0.476226i
$713$	−11906.2			−0.625373
$714$		0			0
$715$	11192.4			0.585414
$716$	−1056.33	−	1056.33i	−0.0551351	−	0.0551351i
$717$		0			0
$718$			9913.52i			0.515278i
$719$	−11159.0	+	4622.22i	−0.578806	+	0.239749i	−0.652827	−	0.757507i	$-0.726417\pi$
$719$	−11159.0	+	4622.22i	−0.578806	+	0.239749i	0.0740206	+	0.997257i	$0.476417\pi$
$720$		0			0
$721$	5901.59	+	2444.52i	0.304836	+	0.126267i
$722$	−4187.44	+	4187.44i	−0.215846	+	0.215846i
$723$		0			0
$724$	−4206.49	−	1742.38i	−0.215929	−	0.0894408i
$725$	−7487.99	+	18077.6i	−0.383582	+	0.926049i
$726$		0			0
$727$		−	8425.17i		−	0.429810i	−0.976635	−	0.214905i	$-0.931056\pi$
$727$		−	8425.17i		−	0.429810i	0.976635	−	0.214905i	$-0.0689443\pi$
$728$	7118.14	+	17184.7i	0.362384	+	0.874873i
$729$		0			0
$730$	49535.9			2.51151
$731$	−5238.65	+	23409.6i	−0.265060	+	1.18445i
$732$		0			0
$733$	565.689	+	565.689i	0.0285050	+	0.0285050i	0.721216	−	0.692711i	$-0.243584\pi$
$733$	565.689	+	565.689i	0.0285050	+	0.0285050i	−0.692711	+	0.721216i	$0.743584\pi$
$734$	−3099.68	−	7483.29i	−0.155874	−	0.376312i
$735$		0			0
$736$	−3362.13	+	1392.64i	−0.168383	+	0.0697465i
$737$	2408.59	−	5814.84i	0.120382	−	0.290627i
$738$		0			0
$739$	−543.927	+	543.927i	−0.0270753	+	0.0270753i	−0.720515	−	0.693440i	$-0.756094\pi$
$739$	−543.927	+	543.927i	−0.0270753	+	0.0270753i	0.693440	+	0.720515i	$0.256094\pi$
$740$	−4508.33	+	4508.33i	−0.223959	+	0.223959i
$741$		0			0
$742$	−7431.59	+	17941.4i	−0.367685	+	0.887670i
$743$	−15615.9	+	6468.30i	−0.771050	+	0.319379i	−0.733298	−	0.679908i	$-0.762020\pi$
$743$	−15615.9	+	6468.30i	−0.771050	+	0.319379i	−0.0377524	+	0.999287i	$0.512020\pi$
$744$		0			0
$745$	2174.78	+	5250.39i	0.106950	+	0.258200i
$746$	15069.1	+	15069.1i	0.739568	+	0.739568i
$747$		0			0
$748$	−2250.46	+	392.202i	−0.110006	+	0.0191716i
$749$	−20714.5			−1.01054
$750$		0			0
$751$	7431.35	+	17940.9i	0.361084	+	0.871733i	0.995142	+	0.0984478i	$0.0313878\pi$
$751$	7431.35	+	17940.9i	0.361084	+	0.871733i	−0.634059	+	0.773285i	$0.718612\pi$
$752$			3492.63i			0.169366i
$753$		0			0
$754$	−9627.08	+	23241.8i	−0.464984	+	1.12257i
$755$	31796.1	+	13170.4i	1.53269	+	0.634860i
$756$		0			0
$757$	−25663.7	+	25663.7i	−1.23218	+	1.23218i	−0.269058	+	0.963124i	$0.586712\pi$
$757$	−25663.7	+	25663.7i	−1.23218	+	1.23218i	−0.963124	+	0.269058i	$0.913288\pi$
$758$	23490.8	+	9730.20i	1.12563	+	0.466249i
$759$		0			0
$760$	25048.7	−	10375.5i	1.19554	−	0.495210i
$761$			31667.1i			1.50845i	0.656615	+	0.754226i	$0.271988\pi$
$761$			31667.1i			1.50845i	−0.656615	+	0.754226i	$0.728012\pi$
$762$		0			0
$763$	12846.6	+	12846.6i	0.609540	+	0.609540i
$764$	−4705.07			−0.222805
$765$		0			0
$766$	1452.41			0.0685087
$767$	4318.90	+	4318.90i	0.203320	+	0.203320i
$768$		0			0
$769$		−	13702.7i		−	0.642562i	−0.946984	−	0.321281i	$-0.895887\pi$
$769$		−	13702.7i		−	0.642562i	0.946984	−	0.321281i	$-0.104113\pi$
$770$	28302.2	−	11723.1i	1.32460	−	0.548666i
$771$		0			0
$772$	1049.99	+	434.921i	0.0489509	+	0.0202761i
$773$	11122.5	−	11122.5i	0.517529	−	0.517529i	−0.399294	−	0.916823i	$-0.630745\pi$
$773$	11122.5	−	11122.5i	0.517529	−	0.517529i	0.916823	+	0.399294i	$0.130745\pi$
$774$		0			0
$775$	13487.1	+	5586.55i	0.625125	+	0.258935i
$776$	9848.65	−	23776.8i	0.455601	−	1.09992i
$777$		0			0
$778$		−	12466.9i		−	0.574497i
$779$	−9714.03	−	23451.7i	−0.446779	−	1.07862i
$780$		0			0
$781$	−23592.2			−1.08092
$782$	7596.48	−	10803.1i	0.347378	−	0.494013i
$783$		0			0
$784$	24427.5	+	24427.5i	1.11277	+	1.11277i
$785$	9793.94	+	23644.7i	0.445300	+	1.07505i
$786$		0			0
$787$	7222.24	−	2991.55i	0.327122	−	0.135498i	−0.213078	−	0.977035i	$-0.568349\pi$
$787$	7222.24	−	2991.55i	0.327122	−	0.135498i	0.540200	+	0.841537i	$0.318349\pi$
$788$	771.687	−	1863.02i	0.0348860	−	0.0842223i
$789$		0			0
$790$	6138.85	−	6138.85i	0.276469	−	0.276469i
$791$	−20569.0	+	20569.0i	−0.924587	+	0.924587i
$792$		0			0
$793$	5835.38	−	14087.9i	0.261312	−	0.630863i
$794$	11658.0	−	4828.89i	0.521065	−	0.215832i
$795$		0			0
$796$	−2285.67	−	5518.10i	−0.101776	−	0.245709i
$797$	−5541.68	−	5541.68i	−0.246294	−	0.246294i	0.573154	−	0.819448i	$-0.305720\pi$
$797$	−5541.68	−	5541.68i	−0.246294	−	0.246294i	−0.819448	+	0.573154i	$0.805720\pi$
$798$		0			0
$799$	−1801.35	−	2840.00i	−0.0797587	−	0.125747i
$800$	4462.01			0.197195
$801$		0			0
$802$	3286.00	+	7933.10i	0.144679	+	0.349286i
$803$			28387.9i			1.24756i
$804$		0			0
$805$	−9569.47	+	23102.7i	−0.418981	+	1.01151i
$806$	17340.0	+	7182.46i	0.757786	+	0.313885i
$807$		0			0
$808$	−1215.37	+	1215.37i	−0.0529165	+	0.0529165i
$809$	28656.9	+	11870.1i	1.24539	+	0.515859i	0.905397	−	0.424567i	$-0.139574\pi$
$809$	28656.9	+	11870.1i	1.24539	+	0.515859i	0.339998	+	0.940426i	$0.389574\pi$
$810$		0			0
$811$	1192.77	−	494.063i	0.0516448	−	0.0213920i	−0.356712	−	0.934215i	$-0.616102\pi$
$811$	1192.77	−	494.063i	0.0516448	−	0.0213920i	0.408356	+	0.912823i	$0.366102\pi$
$812$			9722.08i			0.420170i
$813$		0			0
$814$	−18298.2	−	18298.2i	−0.787900	−	0.787900i
$815$	2941.68			0.126433
$816$		0			0
$817$	−32103.7			−1.37474
$818$	3265.48	+	3265.48i	0.139578	+	0.139578i
$819$		0			0
$820$		−	5042.18i		−	0.214732i
$821$	30591.6	−	12671.4i	1.30043	−	0.538656i	0.378353	−	0.925661i	$-0.376491\pi$
$821$	30591.6	−	12671.4i	1.30043	−	0.538656i	0.922077	+	0.387006i	$0.126491\pi$
$822$		0			0
$823$	−24159.3	−	10007.1i	−1.02326	−	0.423847i	−0.192984	−	0.981202i	$-0.561816\pi$
$823$	−24159.3	−	10007.1i	−1.02326	−	0.423847i	−0.830275	+	0.557354i	$0.811816\pi$
$824$	−3222.96	+	3222.96i	−0.136259	+	0.136259i
$825$		0			0
$826$	15444.9	+	6397.50i	0.650603	+	0.269488i
$827$	13700.4	−	33075.7i	0.576069	−	1.39075i	−0.320245	−	0.947335i	$-0.603765\pi$
$827$	13700.4	−	33075.7i	0.576069	−	1.39075i	0.896314	−	0.443419i	$-0.146235\pi$
$828$		0			0
$829$			11205.6i			0.469465i	0.972060	+	0.234733i	$0.0754215\pi$
$829$			11205.6i			0.469465i	−0.972060	+	0.234733i	$0.924579\pi$
$830$	−3961.79	−	9564.62i	−0.165682	−	0.399991i
$831$		0			0
$832$	−12830.9			−0.534655
$833$	−32461.7	−	7264.36i	−1.35022	−	0.302155i
$834$		0			0
$835$	−10523.6	−	10523.6i	−0.436150	−	0.436150i
$836$	−1169.92	−	2824.45i	−0.0484003	−	0.116849i
$837$		0			0
$838$	−38892.7	+	16109.9i	−1.60325	+	0.664089i
$839$	10303.4	−	24874.7i	0.423974	−	1.02356i	−0.557189	−	0.830386i	$-0.688120\pi$
$839$	10303.4	−	24874.7i	0.423974	−	1.02356i	0.981164	−	0.193179i	$-0.0618798\pi$
$840$		0			0
$841$	30008.3	−	30008.3i	1.23040	−	1.23040i
$842$	−2073.89	+	2073.89i	−0.0848823	+	0.0848823i
$843$		0			0
$844$	−2858.34	+	6900.65i	−0.116574	+	0.281434i
$845$	−15449.0	+	6399.18i	−0.628948	+	0.260519i
$846$		0			0
$847$	−7845.79	−	18941.4i	−0.318282	−	0.768400i
$848$	−11453.8	−	11453.8i	−0.463827	−	0.463827i
$849$		0			0
$850$	−13674.1	+	8673.17i	−0.551786	+	0.349985i
$851$	21123.5			0.850888
$852$		0			0
$853$	−4129.59	−	9969.72i	−0.165762	−	0.400184i	0.819071	−	0.573692i	$-0.194490\pi$
$853$	−4129.59	−	9969.72i	−0.165762	−	0.400184i	−0.984832	+	0.173509i	$0.944490\pi$
$854$		−	41736.1i		−	1.67234i
$855$		0			0
$856$	5656.27	−	13655.4i	0.225850	−	0.545249i
$857$	−11053.3	−	4578.42i	−0.440575	−	0.182492i	0.151359	−	0.988479i	$-0.451635\pi$
$857$	−11053.3	−	4578.42i	−0.440575	−	0.182492i	−0.591933	+	0.805987i	$0.701635\pi$
$858$		0			0
$859$	21946.1	−	21946.1i	0.871699	−	0.871699i	−0.120958	−	0.992658i	$-0.538597\pi$
$859$	21946.1	−	21946.1i	0.871699	−	0.871699i	0.992658	+	0.120958i	$0.0385968\pi$
$860$	−5891.54	−	2440.36i	−0.233605	−	0.0967622i
$861$		0			0
$862$	30530.2	−	12646.0i	1.20634	−	0.499682i
$863$		−	25781.2i		−	1.01692i	−0.861086	−	0.508460i	$-0.830215\pi$
$863$		−	25781.2i		−	1.01692i	0.861086	−	0.508460i	$-0.169785\pi$
$864$		0			0
$865$	16244.7	+	16244.7i	0.638540	+	0.638540i
$866$	−9396.74			−0.368723
$867$		0			0
$868$	7253.34			0.283634
$869$	3518.04	+	3518.04i	0.137332	+	0.137332i
$870$		0			0
$871$		−	8098.91i		−	0.315064i
$872$	−11976.7	+	4960.89i	−0.465115	+	0.192657i
$873$		0			0
$874$	16328.8	+	6763.63i	0.631958	+	0.261766i
$875$	−14123.2	+	14123.2i	−0.545659	+	0.545659i
$876$		0			0
$877$	1002.54	+	415.266i	0.0386014	+	0.0159892i	0.401901	−	0.915683i	$-0.368350\pi$
$877$	1002.54	+	415.266i	0.0386014	+	0.0159892i	−0.363299	+	0.931673i	$0.618350\pi$
$878$	−16527.7	+	39901.4i	−0.635289	+	1.53372i
$879$		0			0
$880$			25552.1i			0.978820i
$881$	19397.5	+	46829.6i	0.741790	+	1.79084i	0.598438	+	0.801169i	$0.295788\pi$
$881$	19397.5	+	46829.6i	0.741790	+	1.79084i	0.143352	+	0.989672i	$0.454212\pi$
$882$		0			0
$883$	8717.22			0.332229			0.166114	−	0.986106i	$-0.446878\pi$
$883$	8717.22			0.332229			0.166114	+	0.986106i	$0.446878\pi$
$884$	−2482.27	+	1574.45i	−0.0944434	+	0.0599033i
$885$		0			0
$886$	1473.15	+	1473.15i	0.0558595	+	0.0558595i
$887$	−8163.91	−	19709.4i	−0.309039	−	0.746085i	−0.999737	−	0.0229422i	$-0.992697\pi$
$887$	−8163.91	−	19709.4i	−0.309039	−	0.746085i	0.690698	−	0.723143i	$-0.257303\pi$
$888$		0			0
$889$	−37885.2	+	15692.6i	−1.42928	+	0.592027i
$890$	−10376.9	+	25052.2i	−0.390827	+	0.943540i
$891$		0			0
$892$	−4071.53	+	4071.53i	−0.152831	+	0.152831i
$893$	3182.56	−	3182.56i	0.119261	−	0.119261i
$894$		0			0
$895$	6157.43	−	14865.4i	0.229967	−	0.555189i
$896$	−44903.7	+	18599.7i	−1.67425	+	0.693497i
$897$		0			0
$898$	−8630.95	−	20837.0i	−0.320733	−	0.774319i
$899$	−35254.7	−	35254.7i	−1.30791	−	1.30791i
$900$		0			0
$901$	15220.9	+	3406.18i	0.562801	+	0.125945i
$902$	20464.9			0.755441
$903$		0			0
$904$	−7942.98	−	19176.1i	−0.292234	−	0.705516i
$905$		−	49040.1i		−	1.80127i
$906$		0			0
$907$	−573.574	+	1384.73i	−0.0209980	+	0.0506937i	−0.934031	−	0.357193i	$-0.883734\pi$
$907$	−573.574	+	1384.73i	−0.0209980	+	0.0506937i	0.913033	+	0.407886i	$0.133734\pi$
$908$	1060.39	+	439.230i	0.0387560	+	0.0160533i
$909$		0			0
$910$	27873.6	−	27873.6i	1.01539	−	1.01539i
$911$	19906.2	+	8245.42i	0.723953	+	0.299871i	0.714065	−	0.700080i	$-0.246852\pi$
$911$	19906.2	+	8245.42i	0.723953	+	0.299871i	0.00988880	+	0.999951i	$0.496852\pi$
$912$		0			0
$913$	5481.27	−	2270.42i	0.198690	−	0.0823000i
$914$		−	23804.4i		−	0.861466i
$915$		0			0
$916$	808.083	+	808.083i	0.0291483	+	0.0291483i
$917$	6926.31			0.249430
$918$		0			0
$919$	−28763.1			−1.03244			−0.516218	−	0.856457i	$-0.672660\pi$
$919$	−28763.1			−1.03244			−0.516218	+	0.856457i	$0.672660\pi$
$920$	−12616.8	−	12616.8i	−0.452135	−	0.452135i
$921$		0			0
$922$			13061.6i			0.466551i
$923$	−28047.1	+	11617.5i	−1.00020	+	0.414295i
$924$		0			0
$925$	−23928.3	−	9911.45i	−0.850551	−	0.352310i
$926$	−38303.8	+	38303.8i	−1.35933	+	1.35933i
$927$		0			0
$928$	−14079.0	−	5831.73i	−0.498025	−	0.206289i
$929$	2451.91	−	5919.45i	0.0865928	−	0.209054i	−0.874651	−	0.484753i	$-0.838909\pi$
$929$	2451.91	−	5919.45i	0.0865928	−	0.209054i	0.961244	+	0.275700i	$0.0889095\pi$
$930$		0			0
$931$		−	44517.7i		−	1.56714i
$932$	2291.55	+	5532.28i	0.0805387	+	0.194438i
$933$		0			0
$934$	23605.6			0.826980
$935$	−13178.7	−	20777.5i	−0.460951	−	0.726734i
$936$		0			0
$937$	22219.0	+	22219.0i	0.774668	+	0.774668i	0.978919	−	0.204251i	$-0.0654759\pi$
$937$	22219.0	+	22219.0i	0.774668	+	0.774668i	−0.204251	+	0.978919i	$0.565476\pi$
$938$	−8482.98	−	20479.7i	−0.295287	−	0.712886i
$939$		0			0
$940$	825.971	−	342.129i	0.0286598	−	0.0118713i
$941$	238.278	−	575.254i	0.00825466	−	0.0199285i	−0.919698	−	0.392625i	$-0.871567\pi$
$941$	238.278	−	575.254i	0.00825466	−	0.0199285i	0.927953	+	0.372697i	$0.121567\pi$
$942$		0			0
$943$	−11812.4	+	11812.4i	−0.407917	+	0.407917i
$944$	−9860.02	+	9860.02i	−0.339954	+	0.339954i
$945$		0			0
$946$	9904.79	−	23912.3i	0.340415	−	0.821834i
$947$	−13515.5	+	5598.31i	−0.463775	+	0.192102i	−0.602321	−	0.798254i	$-0.705757\pi$
$947$	−13515.5	+	5598.31i	−0.463775	+	0.192102i	0.138546	+	0.990356i	$0.455757\pi$
$948$		0			0
$949$	13979.0	+	33748.4i	0.478165	+	1.15439i
$950$	−15323.4	−	15323.4i	−0.523324	−	0.523324i
$951$		0			0
$952$	23520.3	−	33448.6i	0.800731	−	1.13873i
$953$	−26989.7			−0.917400			−0.458700	−	0.888591i	$-0.651685\pi$
$953$	−26989.7			−0.917400			−0.458700	+	0.888591i	$0.651685\pi$
$954$		0			0
$955$	−19393.3	−	46819.7i	−0.657124	−	1.58644i
$956$		−	8130.44i		−	0.275060i
$957$		0			0
$958$	−7070.75	+	17070.3i	−0.238461	+	0.575695i
$959$	80913.4	+	33515.4i	2.72454	+	1.12854i
$960$		0			0
$961$	−5236.98	+	5236.98i	−0.175791	+	0.175791i
$962$	−30764.0	−	12742.8i	−1.03105	−	0.427075i
$963$		0			0
$964$	7319.96	−	3032.02i	0.244564	−	0.101302i
$965$			12241.0i			0.408345i
$966$		0			0
$967$	−19597.4	−	19597.4i	−0.651716	−	0.651716i	0.301690	−	0.953406i	$-0.402449\pi$
$967$	−19597.4	−	19597.4i	−0.651716	−	0.651716i	−0.953406	+	0.301690i	$0.902449\pi$
$968$	14629.0			0.485736
$969$		0			0
$970$	−54540.5			−1.80535
$971$	−2578.82	−	2578.82i	−0.0852298	−	0.0852298i	0.663207	−	0.748436i	$-0.269195\pi$
$971$	−2578.82	−	2578.82i	−0.0852298	−	0.0852298i	−0.748436	+	0.663207i	$0.769195\pi$
$972$		0			0
$973$			35295.7i			1.16293i
$974$	12342.7	−	5112.51i	0.406042	−	0.168188i
$975$		0			0
$976$	32162.5	+	13322.1i	1.05481	+	0.436917i
$977$	2187.08	−	2187.08i	0.0716181	−	0.0716181i	−0.670390	−	0.742009i	$-0.733873\pi$
$977$	2187.08	−	2187.08i	0.0716181	−	0.0716181i	0.742009	+	0.670390i	$0.233873\pi$
$978$		0			0
$979$	−14356.8	−	5946.80i	−0.468689	−	0.194137i
$980$	3384.01	−	8169.71i	0.110304	−	0.266298i
$981$		0			0
$982$		−	19841.4i		−	0.644770i
$983$	−22875.0	−	55225.3i	−0.742218	−	1.79187i	−0.596609	−	0.802532i	$-0.703486\pi$
$983$	−22875.0	−	55225.3i	−0.742218	−	1.79187i	−0.145609	−	0.989342i	$-0.546514\pi$
$984$		0			0
$985$	21719.4			0.702577
$986$	54481.7	−	9494.89i	1.75969	−	0.306672i
$987$		0			0
$988$	−2781.68	−	2781.68i	−0.0895718	−	0.0895718i
$989$	8085.17	+	19519.3i	0.259953	+	0.627582i
$990$		0			0
$991$	23466.0	−	9719.93i	0.752192	−	0.311568i	0.0265561	−	0.999647i	$-0.491546\pi$
$991$	23466.0	−	9719.93i	0.752192	−	0.311568i	0.725635	+	0.688079i	$0.241546\pi$
$992$	−4350.87	+	10503.9i	−0.139254	+	0.336190i
$993$		0			0
$994$	−58754.4	+	58754.4i	−1.87483	+	1.87483i
$995$	45489.0	−	45489.0i	1.44935	−	1.44935i
$996$		0			0
$997$	2523.61	−	6092.54i	0.0801642	−	0.193533i	−0.878716	−	0.477345i	$-0.841599\pi$
$997$	2523.61	−	6092.54i	0.0801642	−	0.193533i	0.958880	+	0.283812i	$0.0915991\pi$
$998$	28317.0	−	11729.3i	0.898156	−	0.372028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.c.100.7		40
3.2	odd	2		51.4.h.a.49.4	yes	40
17.8	even	8	inner	153.4.l.c.127.7		40
51.5	even	16		867.4.a.w.1.15		20
51.8	odd	8		51.4.h.a.25.4	✓	40
51.29	even	16		867.4.a.v.1.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.h.a.25.4	✓	40	51.8	odd	8
51.4.h.a.49.4	yes	40	3.2	odd	2
153.4.l.c.100.7		40	1.1	even	1	trivial
153.4.l.c.127.7		40	17.8	even	8	inner
867.4.a.v.1.15		20	51.29	even	16
867.4.a.w.1.15		20	51.5	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.15816 + 2.15816i) q^{2} +1.31528i q^{4} +(-13.0882 + 5.42131i) q^{5} +(-26.4168 - 10.9422i) q^{7} +(14.4267 - 14.4267i) q^{8} +(-39.9464 - 16.5464i) q^{10} +(9.48236 - 22.8924i) q^{11} -31.8846i q^{13} +(-33.3966 - 80.6266i) q^{14} +72.7923 q^{16} +(-59.1905 + 37.5432i) q^{17} +(-66.3298 - 66.3298i) q^{19} +(-7.13054 - 17.2146i) q^{20} +(69.8699 - 28.9410i) q^{22} +(-23.6243 + 57.0340i) q^{23} +(53.5222 - 53.5222i) q^{25} +(68.8119 - 68.8119i) q^{26} +(14.3920 - 34.7454i) q^{28} +(-238.832 + 98.9273i) q^{29} +(73.8065 + 178.185i) q^{31} +(41.6837 + 41.6837i) q^{32} +(-208.766 - 46.7182i) q^{34} +405.070 q^{35} +(-130.945 - 316.128i) q^{37} -286.300i q^{38} +(-110.608 + 267.031i) q^{40} +(250.006 + 103.556i) q^{41} +(242.000 - 242.000i) q^{43} +(30.1099 + 12.4719i) q^{44} +(-174.073 + 72.1034i) q^{46} +47.9808i q^{47} +(335.578 + 335.578i) q^{49} +231.019 q^{50} +41.9371 q^{52} +(-157.349 - 157.349i) q^{53} +351.028i q^{55} +(-538.966 + 223.247i) q^{56} +(-728.937 - 301.935i) q^{58} +(-135.454 + 135.454i) q^{59} +(441.840 + 183.016i) q^{61} +(-225.265 + 543.837i) q^{62} -402.418i q^{64} +(172.856 + 417.312i) q^{65} +254.007 q^{67} +(-49.3797 - 77.8519i) q^{68} +(874.204 + 874.204i) q^{70} +(-364.361 - 879.646i) q^{71} +(-1058.45 + 438.426i) q^{73} +(399.656 - 964.854i) q^{74} +(87.2421 - 87.2421i) q^{76} +(-500.987 + 500.987i) q^{77} +(-76.8385 + 185.504i) q^{79} +(-952.720 + 394.630i) q^{80} +(316.063 + 763.043i) q^{82} +(169.307 + 169.307i) q^{83} +(571.164 - 812.263i) q^{85} +1044.55 q^{86} +(-193.463 - 467.061i) q^{88} -627.144i q^{89} +(-348.887 + 842.289i) q^{91} +(-75.0156 - 31.0725i) q^{92} +(-103.550 + 103.550i) q^{94} +(1227.73 + 508.544i) q^{95} +(1165.39 - 482.720i) q^{97} +1448.46i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 32 q^{5} + 128 q^{10} - 112 q^{11} - 256 q^{14} - 1024 q^{16} + 112 q^{17} - 32 q^{19} + 640 q^{20} + 728 q^{22} - 208 q^{23} + 296 q^{25} - 1472 q^{26} - 328 q^{28} + 1272 q^{29} - 192 q^{31} + 960 q^{32}+ \cdots + 1008 q^{97}+O(q^{100}) \) 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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