LMFDB - Embedded newform 225.4.h.d.46.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.13
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20400 - 3.70554i) q^{2} +(-5.80928 - 4.22069i) q^{4} +(-3.34114 + 10.6694i) q^{5} +6.27975 q^{7} +(2.58263 - 1.87639i) q^{8} +O(q^{10})$	\(q+(1.20400 - 3.70554i) q^{2} +(-5.80928 - 4.22069i) q^{4} +(-3.34114 + 10.6694i) q^{5} +6.27975 q^{7} +(2.58263 - 1.87639i) q^{8} +(35.5133 + 25.2268i) q^{10} +(13.6357 - 41.9663i) q^{11} +(-13.2560 - 40.7979i) q^{13} +(7.56084 - 23.2699i) q^{14} +(-21.5951 - 66.4630i) q^{16} +(81.6862 - 59.3485i) q^{17} +(-65.1304 + 47.3200i) q^{19} +(64.4420 - 47.8798i) q^{20} +(-139.090 - 101.055i) q^{22} +(48.5949 - 149.560i) q^{23} +(-102.674 - 71.2962i) q^{25} -167.138 q^{26} +(-36.4808 - 26.5049i) q^{28} +(199.754 + 145.129i) q^{29} +(69.6687 - 50.6173i) q^{31} -246.744 q^{32} +(-121.568 - 374.147i) q^{34} +(-20.9815 + 67.0014i) q^{35} +(61.0938 + 188.027i) q^{37} +(96.9290 + 298.317i) q^{38} +(11.3911 + 33.8245i) q^{40} +(-17.2714 - 53.1560i) q^{41} +211.713 q^{43} +(-256.340 + 186.242i) q^{44} +(-495.692 - 360.141i) q^{46} +(-85.9089 - 62.4165i) q^{47} -303.565 q^{49} +(-387.810 + 294.620i) q^{50} +(-95.1871 + 292.956i) q^{52} +(153.468 + 111.501i) q^{53} +(402.198 + 285.700i) q^{55} +(16.2183 - 11.7833i) q^{56} +(778.288 - 565.459i) q^{58} +(140.608 + 432.747i) q^{59} +(171.878 - 528.986i) q^{61} +(-103.683 - 319.104i) q^{62} +(-124.319 + 382.615i) q^{64} +(479.580 - 5.12286i) q^{65} +(-773.054 + 561.657i) q^{67} -725.030 q^{68} +(223.015 + 158.418i) q^{70} +(-454.325 - 330.086i) q^{71} +(-54.7181 + 168.405i) q^{73} +770.300 q^{74} +578.084 q^{76} +(85.6286 - 263.538i) q^{77} +(-769.301 - 558.930i) q^{79} +(781.275 - 8.34556i) q^{80} -217.767 q^{82} +(-11.3373 + 8.23700i) q^{83} +(360.290 + 1069.84i) q^{85} +(254.903 - 784.511i) q^{86} +(-43.5293 - 133.970i) q^{88} +(143.004 - 440.120i) q^{89} +(-83.2445 - 256.200i) q^{91} +(-913.547 + 663.731i) q^{92} +(-334.722 + 243.189i) q^{94} +(-287.268 - 853.007i) q^{95} +(1052.46 + 764.659i) q^{97} +(-365.493 + 1124.87i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) $ 64 * q - 72 * q^4 + 20 * q^7	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) $ 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	1.20400	−	3.70554i	0.425680	−	1.31011i	−0.476662	−	0.879086i	$-0.658154\pi$
$2$	1.20400	−	3.70554i	0.425680	−	1.31011i	0.902342	−	0.431021i	$-0.141846\pi$
$3$		0			0
$3$		0			0
$4$	−5.80928	−	4.22069i	−0.726160	−	0.527586i
$5$	−3.34114	+	10.6694i	−0.298841	+	0.954303i
$5$	−3.34114	+	10.6694i	−0.298841	+	0.954303i
$6$		0			0
$7$	6.27975			0.339075			0.169537	−	0.985524i	$-0.445773\pi$
$7$	6.27975			0.339075			0.169537	+	0.985524i	$0.445773\pi$
$8$	2.58263	−	1.87639i	0.114137	−	0.0829257i
$9$		0			0
$10$	35.5133	+	25.2268i	1.12303	+	0.797741i
$11$	13.6357	−	41.9663i	0.373756	−	1.15030i	−0.570559	−	0.821257i	$-0.693273\pi$
$11$	13.6357	−	41.9663i	0.373756	−	1.15030i	0.944314	−	0.329045i	$-0.106727\pi$
$12$		0			0
$13$	−13.2560	−	40.7979i	−0.282812	−	0.870407i	−0.987046	−	0.160438i	$-0.948709\pi$
$13$	−13.2560	−	40.7979i	−0.282812	−	0.870407i	0.704233	−	0.709968i	$-0.251291\pi$
$14$	7.56084	−	23.2699i	0.144337	−	0.444224i
$15$		0			0
$16$	−21.5951	−	66.4630i	−0.337424	−	1.03848i
$17$	81.6862	−	59.3485i	1.16540	−	0.846713i	0.174949	−	0.984577i	$-0.444024\pi$
$17$	81.6862	−	59.3485i	1.16540	−	0.846713i	0.990451	+	0.137864i	$0.0440238\pi$
$18$		0			0
$19$	−65.1304	+	47.3200i	−0.786417	+	0.571366i	−0.906898	−	0.421350i	$-0.861556\pi$
$19$	−65.1304	+	47.3200i	−0.786417	+	0.571366i	0.120481	+	0.992716i	$0.461556\pi$
$20$	64.4420	−	47.8798i	0.720484	−	0.535313i
$21$		0			0
$22$	−139.090	−	101.055i	−1.34792	−	0.979320i
$23$	48.5949	−	149.560i	0.440554	−	1.35589i	−0.446733	−	0.894667i	$-0.647413\pi$
$23$	48.5949	−	149.560i	0.440554	−	1.35589i	0.887287	−	0.461218i	$-0.152587\pi$
$24$		0			0
$25$	−102.674	−	71.2962i	−0.821388	−	0.570369i
$26$	−167.138			−1.26071
$27$		0			0
$28$	−36.4808	−	26.5049i	−0.246223	−	0.178891i
$29$	199.754	+	145.129i	1.27908	+	0.929306i	0.999525	−	0.0308238i	$-0.00981308\pi$
$29$	199.754	+	145.129i	1.27908	+	0.929306i	0.279555	+	0.960130i	$0.409813\pi$
$30$		0			0
$31$	69.6687	−	50.6173i	0.403641	−	0.293262i	−0.367381	−	0.930070i	$-0.619746\pi$
$31$	69.6687	−	50.6173i	0.403641	−	0.293262i	0.771022	+	0.636808i	$0.219746\pi$
$32$	−246.744			−1.36308
$33$		0			0
$34$	−121.568	−	374.147i	−0.613197	−	1.88723i
$35$	−20.9815	+	67.0014i	−0.101329	+	0.323580i
$36$		0			0
$37$	61.0938	+	188.027i	0.271453	+	0.835446i	0.990136	+	0.140108i	$0.0447451\pi$
$37$	61.0938	+	188.027i	0.271453	+	0.835446i	−0.718683	+	0.695338i	$0.755255\pi$
$38$	96.9290	+	298.317i	0.413788	+	1.27351i
$39$		0			0
$40$	11.3911	+	33.8245i	0.0450273	+	0.133703i
$41$	−17.2714	−	53.1560i	−0.0657889	−	0.202477i	0.912758	−	0.408500i	$-0.133948\pi$
$41$	−17.2714	−	53.1560i	−0.0657889	−	0.202477i	−0.978547	+	0.206023i	$0.933948\pi$
$42$		0			0
$43$	211.713			0.750835			0.375418	−	0.926856i	$-0.377499\pi$
$43$	211.713			0.750835			0.375418	+	0.926856i	$0.377499\pi$
$44$	−256.340	+	186.242i	−0.878290	+	0.638115i
$45$		0			0
$46$	−495.692	−	360.141i	−1.58882	−	1.15435i
$47$	−85.9089	−	62.4165i	−0.266619	−	0.193710i	0.446441	−	0.894813i	$-0.352691\pi$
$47$	−85.9089	−	62.4165i	−0.266619	−	0.193710i	−0.713060	+	0.701103i	$0.752691\pi$
$48$		0			0
$49$	−303.565			−0.885028
$50$	−387.810	+	294.620i	−1.09689	+	0.833312i
$51$		0			0
$52$	−95.1871	+	292.956i	−0.253848	+	0.781263i
$53$	153.468	+	111.501i	0.397743	+	0.288978i	0.768621	−	0.639704i	$-0.220943\pi$
$53$	153.468	+	111.501i	0.397743	+	0.288978i	−0.370878	+	0.928682i	$0.620943\pi$
$54$		0			0
$55$	402.198	+	285.700i	0.986043	+	0.700433i
$56$	16.2183	−	11.7833i	0.0387011	−	0.0281180i
$57$		0			0
$58$	778.288	−	565.459i	1.76197	−	1.28014i
$59$	140.608	+	432.747i	0.310265	+	0.954896i	0.977660	+	0.210193i	$0.0674091\pi$
$59$	140.608	+	432.747i	0.310265	+	0.954896i	−0.667395	+	0.744703i	$0.732591\pi$
$60$		0			0
$61$	171.878	−	528.986i	0.360766	−	1.11032i	−0.591824	−	0.806067i	$-0.701592\pi$
$61$	171.878	−	528.986i	0.360766	−	1.11032i	0.952590	−	0.304256i	$-0.0984079\pi$
$62$	−103.683	−	319.104i	−0.212383	−	0.653649i
$63$		0			0
$64$	−124.319	+	382.615i	−0.242811	+	0.747295i
$65$	479.580	−	5.12286i	0.915148	−	0.00977558i
$66$		0			0
$67$	−773.054	+	561.657i	−1.40961	+	1.02414i	−0.416227	+	0.909261i	$0.636648\pi$
$67$	−773.054	+	561.657i	−1.40961	+	1.02414i	−0.993380	+	0.114878i	$0.963352\pi$
$68$	−725.030			−1.29298
$69$		0			0
$70$	223.015	+	158.418i	0.380790	+	0.270494i
$71$	−454.325	−	330.086i	−0.759415	−	0.551747i	0.139316	−	0.990248i	$-0.455510\pi$
$71$	−454.325	−	330.086i	−0.759415	−	0.551747i	−0.898731	+	0.438501i	$0.855510\pi$
$72$		0			0
$73$	−54.7181	+	168.405i	−0.0877298	+	0.270004i	−0.985291	−	0.170886i	$-0.945337\pi$
$73$	−54.7181	+	168.405i	−0.0877298	+	0.270004i	0.897561	+	0.440890i	$0.145337\pi$
$74$	770.300			1.21008
$75$		0			0
$76$	578.084			0.872510
$77$	85.6286	−	263.538i	0.126731	−	0.390038i
$78$		0			0
$79$	−769.301	−	558.930i	−1.09561	−	0.796007i	−0.115272	−	0.993334i	$-0.536774\pi$
$79$	−769.301	−	558.930i	−1.09561	−	0.796007i	−0.980338	+	0.197327i	$0.936774\pi$
$80$	781.275	−	8.34556i	1.09187	−	0.0116633i
$81$		0			0
$82$	−217.767			−0.293272
$83$	−11.3373	+	8.23700i	−0.0149931	+	0.0108931i	−0.595257	−	0.803536i	$-0.702950\pi$
$83$	−11.3373	+	8.23700i	−0.0149931	+	0.0108931i	0.580263	+	0.814429i	$0.302950\pi$
$84$		0			0
$85$	360.290	+	1069.84i	0.459752	+	1.36518i
$86$	254.903	−	784.511i	0.319615	−	0.983675i
$87$		0			0
$88$	−43.5293	−	133.970i	−0.0527300	−	0.162286i
$89$	143.004	−	440.120i	0.170319	−	0.524187i	−0.829070	−	0.559145i	$-0.811130\pi$
$89$	143.004	−	440.120i	0.170319	−	0.524187i	0.999389	+	0.0349577i	$0.0111297\pi$
$90$		0			0
$91$	−83.2445	−	256.200i	−0.0958945	−	0.295133i
$92$	−913.547	+	663.731i	−1.03526	+	0.752160i
$93$		0			0
$94$	−334.722	+	243.189i	−0.367275	+	0.266841i
$95$	−287.268	−	853.007i	−0.310242	−	0.921228i
$96$		0			0
$97$	1052.46	+	764.659i	1.10166	+	0.800406i	0.981331	−	0.192328i	$-0.0616038\pi$
$97$	1052.46	+	764.659i	1.10166	+	0.800406i	0.120333	+	0.992734i	$0.461604\pi$
$98$	−365.493	+	1124.87i	−0.376739	+	1.15948i
$99$		0			0
$100$	295.541	+	847.533i	0.295541	+	0.847533i
$101$	1277.21			1.25829			0.629143	−	0.777289i	$-0.283406\pi$
$101$	1277.21			1.25829			0.629143	+	0.777289i	$0.283406\pi$
$102$		0			0
$103$	895.730	+	650.786i	0.856883	+	0.622562i	0.927035	−	0.374975i	$-0.122349\pi$
$103$	895.730	+	650.786i	0.856883	+	0.622562i	−0.0701525	+	0.997536i	$0.522349\pi$
$104$	−110.788	−	80.4924i	−0.104459	−	0.0758936i
$105$		0			0
$106$	597.946	−	434.433i	0.547903	−	0.398075i
$107$	−184.425			−0.166627			−0.0833134	−	0.996523i	$-0.526550\pi$
$107$	−184.425			−0.166627			−0.0833134	+	0.996523i	$0.526550\pi$
$108$		0			0
$109$	251.160	+	772.991i	0.220704	+	0.679258i	0.998699	+	0.0509874i	$0.0162368\pi$
$109$	251.160	+	772.991i	0.220704	+	0.679258i	−0.777995	+	0.628270i	$0.783763\pi$
$110$	1542.92	−	1146.38i	1.33738	−	0.993661i
$111$		0			0
$112$	−135.612	−	417.371i	−0.114412	−	0.352124i
$113$	260.636	+	802.155i	0.216978	+	0.667791i	0.999007	+	0.0445486i	$0.0141850\pi$
$113$	260.636	+	802.155i	0.216978	+	0.667791i	−0.782029	+	0.623242i	$0.785815\pi$
$114$		0			0
$115$	1433.36	+	1018.18i	1.16227	+	0.825616i
$116$	−547.878	−	1686.20i	−0.438528	−	1.34965i
$117$		0			0
$118$	1772.86			1.38309
$119$	512.969	−	372.694i	0.395158	−	0.287099i
$120$		0			0
$121$	−498.437	−	362.135i	−0.374483	−	0.272078i
$122$	−1753.24	−	1273.80i	−1.30107	−	0.945284i
$123$		0			0
$124$	−618.365			−0.447829
$125$	1103.74	−	857.258i	0.789769	−	0.613404i
$126$		0			0
$127$	−540.633	+	1663.90i	−0.377744	+	1.16258i	0.563865	+	0.825867i	$0.309314\pi$
$127$	−540.633	+	1663.90i	−0.377744	+	1.16258i	−0.941609	+	0.336709i	$0.890686\pi$
$128$	−328.843	−	238.919i	−0.227078	−	0.164982i
$129$		0			0
$130$	558.433	−	1783.27i	0.376753	−	1.20310i
$131$	405.420	−	294.555i	0.270395	−	0.196453i	−0.444322	−	0.895867i	$-0.646556\pi$
$131$	405.420	−	294.555i	0.270395	−	0.196453i	0.714717	+	0.699414i	$0.246556\pi$
$132$		0			0
$133$	−409.002	+	297.158i	−0.266654	+	0.193736i
$134$	1150.48	+	3540.82i	0.741691	+	2.28269i
$135$		0			0
$136$	99.6044	−	306.551i	0.0628015	−	0.193283i
$137$	430.440	+	1324.76i	0.268430	+	0.826143i	0.990883	+	0.134723i	$0.0430145\pi$
$137$	430.440	+	1324.76i	0.268430	+	0.826143i	−0.722453	+	0.691420i	$0.756985\pi$
$138$		0			0
$139$	287.901	−	886.067i	0.175679	−	0.540685i	−0.823985	−	0.566612i	$-0.808254\pi$
$139$	287.901	−	886.067i	0.175679	−	0.540685i	0.999664	+	0.0259271i	$0.00825378\pi$
$140$	404.680	−	300.673i	0.244298	−	0.181511i
$141$		0			0
$142$	−1770.16	+	1286.10i	−1.04612	+	0.760047i
$143$	−1892.89			−1.10693
$144$		0			0
$145$	−2215.85	+	1646.36i	−1.26908	+	0.942915i
$146$	558.151	+	405.521i	0.316390	+	0.229871i
$147$		0			0
$148$	438.694	−	1350.16i	0.243652	−	0.749883i
$149$	−2907.55			−1.59863			−0.799313	−	0.600914i	$-0.794803\pi$
$149$	−2907.55			−1.59863			−0.799313	+	0.600914i	$0.794803\pi$
$150$		0			0
$151$	−760.111			−0.409648			−0.204824	−	0.978799i	$-0.565662\pi$
$151$	−760.111			−0.409648			−0.204824	+	0.978799i	$0.565662\pi$
$152$	−79.4170	+	244.420i	−0.0423788	+	0.130428i
$153$		0			0
$154$	−873.453	−	634.601i	−0.457045	−	0.332062i
$155$	307.285	+	912.445i	0.159237	+	0.472834i
$156$		0			0
$157$	2824.97			1.43603			0.718016	−	0.696027i	$-0.245051\pi$
$157$	2824.97			1.43603			0.718016	+	0.696027i	$0.245051\pi$
$158$	−2997.38	+	2177.72i	−1.50923	+	1.09652i
$159$		0			0
$160$	824.405	−	2632.61i	0.407344	−	1.30079i
$161$	305.164	−	939.198i	0.149381	−	0.459746i
$162$		0			0
$163$	49.8613	+	153.457i	0.0239598	+	0.0737406i	0.962321	−	0.271914i	$-0.0876568\pi$
$163$	49.8613	+	153.457i	0.0239598	+	0.0737406i	−0.938362	+	0.345655i	$0.887657\pi$
$164$	−124.020	+	381.696i	−0.0590510	+	0.181740i
$165$		0			0
$166$	16.8725	+	51.9281i	0.00788890	+	0.0242795i
$167$	−2368.72	+	1720.98i	−1.09759	+	0.797444i	−0.980665	−	0.195696i	$-0.937303\pi$
$167$	−2368.72	+	1720.98i	−1.09759	+	0.797444i	−0.116924	+	0.993141i	$0.537303\pi$
$168$		0			0
$169$	288.667	−	209.729i	0.131392	−	0.0954616i
$170$	4398.12	−	46.9806i	1.98424	−	0.0211956i
$171$		0			0
$172$	−1229.90	−	893.575i	−0.545227	−	0.396131i
$173$	−753.042	+	2317.62i	−0.330940	+	1.01853i	0.637747	+	0.770246i	$0.279867\pi$
$173$	−753.042	+	2317.62i	−0.330940	+	1.01853i	−0.968687	+	0.248284i	$0.920133\pi$
$174$		0			0
$175$	−644.764	−	447.722i	−0.278512	−	0.193398i
$176$	−3083.67			−1.32068
$177$		0			0
$178$	−1458.71	−	1059.81i	−0.614240	−	0.446271i
$179$	2801.84	+	2035.66i	1.16994	+	0.850012i	0.991002	−	0.133849i	$-0.0427336\pi$
$179$	2801.84	+	2035.66i	1.16994	+	0.850012i	0.178939	+	0.983860i	$0.442734\pi$
$180$		0			0
$181$	−3051.24	+	2216.86i	−1.25302	+	0.910374i	−0.998393	−	0.0566644i	$-0.981953\pi$
$181$	−3051.24	+	2216.86i	−1.25302	+	0.910374i	−0.254629	+	0.967039i	$0.581953\pi$
$182$	−1049.59			−0.427476
$183$		0			0
$184$	−155.130	−	477.441i	−0.0621540	−	0.191290i
$185$	−2210.27	+	23.6100i	−0.878390	+	0.00938294i
$186$		0			0
$187$	−1376.79	−	4237.32i	−0.538400	−	1.65703i
$188$	235.629	+	725.190i	0.0914094	+	0.281329i
$189$		0			0
$190$	−3506.72	+	37.4587i	−1.33897	+	0.0143029i
$191$	−651.128	−	2003.97i	−0.246670	−	0.759173i	−0.995357	−	0.0962491i	$-0.969315\pi$
$191$	−651.128	−	2003.97i	−0.246670	−	0.759173i	0.748687	−	0.662923i	$-0.230685\pi$
$192$		0			0
$193$	−3761.96			−1.40307			−0.701533	−	0.712637i	$-0.747501\pi$
$193$	−3761.96			−1.40307			−0.701533	+	0.712637i	$0.747501\pi$
$194$	4100.64	−	2979.29i	1.51757	−	1.10258i
$195$		0			0
$196$	1763.49	+	1281.25i	0.642673	+	0.466929i
$197$	−3061.21	−	2224.10i	−1.10712	−	0.804368i	−0.124911	−	0.992168i	$-0.539864\pi$
$197$	−3061.21	−	2224.10i	−1.10712	−	0.804368i	−0.982207	+	0.187800i	$0.939864\pi$
$198$		0			0
$199$	4606.97			1.64110			0.820552	−	0.571572i	$-0.193666\pi$
$199$	4606.97			1.64110			0.820552	+	0.571572i	$0.193666\pi$
$200$	−398.948	+	8.52407i	−0.141049	+	0.00301372i
$201$		0			0
$202$	1537.76	−	4732.75i	0.535627	−	1.64849i
$203$	1254.40	+	911.377i	0.433703	+	0.315104i
$204$		0			0
$205$	624.851	−	6.67464i	0.212885	−	0.00227403i
$206$	3489.98	−	2535.62i	1.18038	−	0.857596i
$207$		0			0
$208$	−2425.28	+	1762.07i	−0.808476	+	0.587393i
$209$	1097.75	+	3378.52i	0.363315	+	1.11817i
$210$		0			0
$211$	1167.51	−	3593.21i	0.380921	−	1.17236i	−0.558475	−	0.829522i	$-0.688613\pi$
$211$	1167.51	−	3593.21i	0.380921	−	1.17236i	0.939396	−	0.342834i	$-0.111387\pi$
$212$	−420.927	−	1295.48i	−0.136365	−	0.419688i
$213$		0			0
$214$	−222.049	+	683.396i	−0.0709296	+	0.218299i
$215$	−707.363	+	2258.86i	−0.224380	+	0.716525i
$216$		0			0
$217$	437.502	−	317.864i	0.136864	−	0.0994378i
$218$	3166.75			0.983850
$219$		0			0
$220$	−1130.63	−	3357.27i	−0.346486	−	1.02885i
$221$	−3504.13	−	2545.90i	−1.06657	−	0.774912i
$222$		0			0
$223$	−1039.82	+	3200.23i	−0.312248	+	0.961001i	0.664624	+	0.747178i	$0.268592\pi$
$223$	−1039.82	+	3200.23i	−0.312248	+	0.961001i	−0.976872	+	0.213823i	$0.931408\pi$
$224$	−1549.49			−0.462185
$225$		0			0
$226$	3286.23			0.967241
$227$	1868.95	−	5752.02i	0.546459	−	1.68183i	−0.171035	−	0.985265i	$-0.554711\pi$
$227$	1868.95	−	5752.02i	0.546459	−	1.68183i	0.717494	−	0.696564i	$-0.245289\pi$
$228$		0			0
$229$	1649.37	+	1198.34i	0.475953	+	0.345800i	0.799757	−	0.600324i	$-0.204962\pi$
$229$	1649.37	+	1198.34i	0.475953	+	0.345800i	−0.323804	+	0.946124i	$0.604962\pi$
$230$	5498.68	−	4085.46i	1.57640	−	1.17125i
$231$		0			0
$232$	788.211			0.223054
$233$	10.4656	−	7.60373i	0.00294260	−	0.00213793i	−0.586313	−	0.810085i	$-0.699421\pi$
$233$	10.4656	−	7.60373i	0.00294260	−	0.00213793i	0.589256	+	0.807947i	$0.299421\pi$
$234$		0			0
$235$	952.982	−	708.057i	0.264535	−	0.196547i
$236$	1009.66	−	3107.41i	0.278488	−	0.857099i
$237$		0			0
$238$	−763.416	−	2349.55i	−0.207920	−	0.639911i
$239$	−3.89930	+	12.0008i	−0.00105533	+	0.00324798i	−0.951583	−	0.307393i	$-0.900544\pi$
$239$	−3.89930	+	12.0008i	−0.00105533	+	0.00324798i	0.950527	+	0.310641i	$0.100544\pi$
$240$		0			0
$241$	2084.79	+	6416.33i	0.557233	+	1.71499i	0.689972	+	0.723836i	$0.257623\pi$
$241$	2084.79	+	6416.33i	0.557233	+	1.71499i	−0.132738	+	0.991151i	$0.542377\pi$
$242$	−1942.03	+	1410.97i	−0.515861	+	0.374795i
$243$		0			0
$244$	−3231.17	+	2347.59i	−0.847765	+	0.615937i
$245$	1014.25	−	3238.86i	0.264483	−	0.844585i
$246$		0			0
$247$	2793.92	+	2029.90i	0.719729	+	0.522914i
$248$	84.9509	−	261.452i	0.0217516	−	0.0669444i
$249$		0			0
$250$	−1847.70	−	5122.08i	−0.467436	−	1.29580i
$251$	923.332			0.232192			0.116096	−	0.993238i	$-0.462962\pi$
$251$	923.332			0.232192			0.116096	+	0.993238i	$0.462962\pi$
$252$		0			0
$253$	−5613.84	−	4078.70i	−1.39502	−	1.01354i
$254$	5514.72	+	4006.68i	1.36230	+	0.989769i
$255$		0			0
$256$	−3885.03	+	2822.64i	−0.948493	+	0.689120i
$257$	4139.37			1.00470			0.502348	−	0.864666i	$-0.332470\pi$
$257$	4139.37			1.00470			0.502348	+	0.864666i	$0.332470\pi$
$258$		0			0
$259$	383.654	+	1180.76i	0.0920428	+	0.283279i
$260$	−2807.64	−	1994.40i	−0.669701	−	0.475721i
$261$		0			0
$262$	−603.358	−	1856.95i	−0.142273	−	0.437872i
$263$	−580.001	−	1785.06i	−0.135986	−	0.418522i	0.859756	−	0.510705i	$-0.170616\pi$
$263$	−580.001	−	1785.06i	−0.135986	−	0.418522i	−0.995742	+	0.0921827i	$0.970616\pi$
$264$		0			0
$265$	−1702.41	+	1264.87i	−0.394634	+	0.293209i
$266$	608.690	+	1873.35i	0.140305	+	0.431815i
$267$		0			0
$268$	6861.47			1.56392
$269$	−1596.43	+	1159.87i	−0.361843	+	0.262895i	−0.753821	−	0.657080i	$-0.771791\pi$
$269$	−1596.43	+	1159.87i	−0.361843	+	0.262895i	0.391977	+	0.919975i	$0.371791\pi$
$270$		0			0
$271$	−4209.83	−	3058.62i	−0.943650	−	0.685602i	0.00564662	−	0.999984i	$-0.498203\pi$
$271$	−4209.83	−	3058.62i	−0.943650	−	0.685602i	−0.949296	+	0.314382i	$0.898203\pi$
$272$	−5708.50	−	4147.47i	−1.27253	−	0.924549i
$273$		0			0
$274$	5427.19			1.19660
$275$	−4392.06	+	3336.66i	−0.963095	+	0.731665i
$276$		0			0
$277$	465.229	−	1431.83i	0.100913	−	0.310578i	−0.887837	−	0.460159i	$-0.847792\pi$
$277$	465.229	−	1431.83i	0.100913	−	0.310578i	0.988749	+	0.149581i	$0.0477924\pi$
$278$	−2936.73	−	2133.66i	−0.633572	−	0.460317i
$279$		0			0
$280$	71.5333	+	212.410i	0.0152676	+	0.0453354i
$281$	−4394.85	+	3193.05i	−0.933007	+	0.677869i	−0.946727	−	0.322037i	$-0.895632\pi$
$281$	−4394.85	+	3193.05i	−0.933007	+	0.677869i	0.0137206	+	0.999906i	$0.495632\pi$
$282$		0			0
$283$	−1837.68	+	1335.15i	−0.386003	+	0.280448i	−0.763816	−	0.645435i	$-0.776676\pi$
$283$	−1837.68	+	1335.15i	−0.386003	+	0.280448i	0.377813	+	0.925882i	$0.376676\pi$
$284$	1246.11	+	3835.13i	0.260363	+	0.801314i
$285$		0			0
$286$	−2279.05	+	7014.18i	−0.471199	+	1.45020i
$287$	−108.460	−	333.806i	−0.0223073	−	0.0686549i
$288$		0			0
$289$	1632.19	−	5023.36i	0.332218	−	1.02246i
$290$	3432.76	+	10193.2i	0.695098	+	2.06401i
$291$		0			0
$292$	1028.66	−	747.364i	0.206157	−	0.149781i
$293$	5377.08			1.07212			0.536062	−	0.844178i	$-0.319911\pi$
$293$	5377.08			1.07212			0.536062	+	0.844178i	$0.319911\pi$
$294$		0			0
$295$	−5086.96	+	54.3387i	−1.00398	+	0.0107245i
$296$	510.596	+	370.970i	0.100263	+	0.0728452i
$297$		0			0
$298$	−3500.69	+	10774.0i	−0.680503	+	2.09437i
$299$	−6745.89			−1.30477
$300$		0			0
$301$	1329.50			0.254589
$302$	−915.176	+	2816.62i	−0.174379	+	0.536683i
$303$		0			0
$304$	4551.53	+	3306.88i	0.858711	+	0.623890i
$305$	5069.71	+	3601.26i	0.951773	+	0.676090i
$306$		0			0
$307$	8104.37			1.50665			0.753324	−	0.657649i	$-0.228449\pi$
$307$	8104.37			1.50665			0.753324	+	0.657649i	$0.228449\pi$
$308$	−1609.75	+	1169.55i	−0.297806	+	0.216369i
$309$		0			0
$310$	3751.08	−	40.0689i	0.687248	−	0.00734116i
$311$	233.023	−	717.171i	0.0424872	−	0.130762i	−0.927563	−	0.373667i	$-0.878100\pi$
$311$	233.023	−	717.171i	0.0424872	−	0.130762i	0.970050	+	0.242905i	$0.0781003\pi$
$312$		0			0
$313$	1329.80	+	4092.70i	0.240143	+	0.739084i	0.996397	+	0.0848065i	$0.0270272\pi$
$313$	1329.80	+	4092.70i	0.240143	+	0.739084i	−0.756254	+	0.654278i	$0.772973\pi$
$314$	3401.27	−	10468.0i	0.611289	−	1.88136i
$315$		0			0
$316$	2110.02	+	6493.97i	0.375626	+	1.15606i
$317$	−2940.89	+	2136.68i	−0.521062	+	0.378574i	−0.817004	−	0.576632i	$-0.804367\pi$
$317$	−2940.89	+	2136.68i	−0.521062	+	0.378574i	0.295942	+	0.955206i	$0.404367\pi$
$318$		0			0
$319$	8814.32	−	6403.98i	1.54704	−	1.12399i
$320$	−3666.92	−	2604.78i	−0.640584	−	0.455037i
$321$		0			0
$322$	−3112.82	−	2261.59i	−0.538729	−	0.391409i
$323$	−2511.88	+	7730.78i	−0.432708	+	1.33174i
$324$		0			0
$325$	−1547.69	+	5133.96i	−0.264155	+	0.876250i
$326$	628.676			0.106807
$327$		0			0
$328$	−144.347	−	104.875i	−0.0242995	−	0.0176547i
$329$	−539.486	−	391.960i	−0.0904038	−	0.0656822i
$330$		0			0
$331$	2978.03	−	2163.66i	0.494524	−	0.359292i	−0.312398	−	0.949951i	$-0.601132\pi$
$331$	2978.03	−	2163.66i	0.494524	−	0.359292i	0.806921	+	0.590659i	$0.201132\pi$
$332$	100.627			0.0166344
$333$		0			0
$334$	3525.20	+	10849.5i	0.577517	+	1.77741i
$335$	−3409.68	−	10124.6i	−0.556091	−	1.65125i
$336$		0			0
$337$	−85.2315	−	262.316i	−0.0137770	−	0.0424013i	0.943932	−	0.330141i	$-0.107096\pi$
$337$	−85.2315	−	262.316i	−0.0137770	−	0.0424013i	−0.957709	+	0.287740i	$0.907096\pi$
$338$	−429.604	−	1322.18i	−0.0691342	−	0.212773i
$339$		0			0
$340$	2422.43	−	7735.65i	0.386396	−	1.23390i
$341$	−1174.24	−	3613.94i	−0.186477	−	0.573917i
$342$		0			0
$343$	−4060.26			−0.639165
$344$	546.777	−	397.257i	0.0856984	−	0.0622635i
$345$		0			0
$346$	7681.39	+	5580.85i	1.19351	+	0.867135i
$347$	9022.35	+	6555.12i	1.39581	+	1.01411i	0.995200	+	0.0978631i	$0.0312007\pi$
$347$	9022.35	+	6555.12i	1.39581	+	1.01411i	0.400607	+	0.916250i	$0.368799\pi$
$348$		0			0
$349$	−8219.29			−1.26065			−0.630327	−	0.776330i	$-0.717079\pi$
$349$	−8219.29			−1.26065			−0.630327	+	0.776330i	$0.717079\pi$
$350$	−2435.35	+	1850.14i	−0.371929	+	0.282555i
$351$		0			0
$352$	−3364.52	+	10354.9i	−0.509458	+	1.56795i
$353$	1577.47	+	1146.10i	0.237848	+	0.172806i	0.700324	−	0.713825i	$-0.253039\pi$
$353$	1577.47	+	1146.10i	0.237848	+	0.172806i	−0.462476	+	0.886632i	$0.653039\pi$
$354$		0			0
$355$	5039.80	−	3744.52i	0.753478	−	0.559827i
$356$	−2688.36	+	1953.21i	−0.400232	+	0.290786i
$357$		0			0
$358$	10916.6	−	7931.40i	1.61163	−	1.17091i
$359$	3470.55	+	10681.2i	0.510219	+	1.57029i	0.791816	+	0.610759i	$0.209136\pi$
$359$	3470.55	+	10681.2i	0.510219	+	1.57029i	−0.281598	+	0.959533i	$0.590864\pi$
$360$		0			0
$361$	−116.764	+	359.361i	−0.0170234	+	0.0523927i
$362$	4540.95	+	13975.6i	0.659302	+	2.02912i
$363$		0			0
$364$	−597.751	+	1839.69i	−0.0860733	+	0.264906i
$365$	−1613.97	−	1146.48i	−0.231449	−	0.164409i
$366$		0			0
$367$	5303.29	−	3853.06i	0.754304	−	0.548034i	−0.142854	−	0.989744i	$-0.545628\pi$
$367$	5303.29	−	3853.06i	0.754304	−	0.548034i	0.897158	+	0.441710i	$0.145628\pi$
$368$	−10989.6			−1.55672
$369$		0			0
$370$	−2573.68	+	8218.67i	−0.361620	+	1.15478i
$371$	963.738	+	700.197i	0.134865	+	0.0979849i
$372$		0			0
$373$	−1346.23	+	4143.27i	−0.186877	+	0.575148i	−0.999976	−	0.00697762i	$-0.997779\pi$
$373$	−1346.23	+	4143.27i	−0.186877	+	0.575148i	0.813099	+	0.582126i	$0.197779\pi$
$374$	−17359.2			−2.40007
$375$		0			0
$376$	−338.989			−0.0464948
$377$	3273.03	−	10073.4i	0.447135	−	1.37614i
$378$		0			0
$379$	−4284.53	−	3112.90i	−0.580691	−	0.421896i	0.258282	−	0.966069i	$-0.416844\pi$
$379$	−4284.53	−	3112.90i	−0.580691	−	0.421896i	−0.838973	+	0.544173i	$0.816844\pi$
$380$	−1931.46	+	6167.82i	−0.260742	+	0.832639i
$381$		0			0
$382$	−8209.74			−1.09960
$383$	6312.15	−	4586.04i	0.842129	−	0.611843i	−0.0808353	−	0.996727i	$-0.525759\pi$
$383$	6312.15	−	4586.04i	0.842129	−	0.611843i	0.922965	+	0.384885i	$0.125759\pi$
$384$		0			0
$385$	2525.70	+	1794.13i	0.334342	+	0.237499i
$386$	−4529.41	+	13940.1i	−0.597257	+	1.83817i
$387$		0			0
$388$	−2886.66	−	8884.24i	−0.377701	−	1.16245i
$389$	4009.27	−	12339.3i	0.522566	−	1.60829i	−0.246514	−	0.969139i	$-0.579285\pi$
$389$	4009.27	−	12339.3i	0.522566	−	1.60829i	0.769079	−	0.639153i	$-0.220715\pi$
$390$		0			0
$391$	−4906.61	−	15101.0i	−0.634624	−	1.95317i
$392$	−783.997	+	569.607i	−0.101015	+	0.0733916i
$393$		0			0
$394$	−11927.2	+	8665.62i	−1.52509	+	1.10804i
$395$	8533.81	−	6340.54i	1.08704	−	0.807664i
$396$		0			0
$397$	8223.68	+	5974.85i	1.03963	+	0.755338i	0.970214	−	0.242249i	$-0.0778852\pi$
$397$	8223.68	+	5974.85i	1.03963	+	0.755338i	0.0694198	+	0.997588i	$0.477885\pi$
$398$	5546.81	−	17071.3i	0.698585	−	2.15002i
$399$		0			0
$400$	−2521.31	+	8363.64i	−0.315164	+	1.04546i
$401$	8213.85			1.02289			0.511447	−	0.859315i	$-0.329110\pi$
$401$	8213.85			1.02289			0.511447	+	0.859315i	$0.329110\pi$
$402$		0			0
$403$	−2988.61	−	2171.35i	−0.369412	−	0.268394i
$404$	−7419.66	−	5390.70i	−0.913718	−	0.663855i
$405$		0			0
$406$	4887.45	−	3550.94i	0.597439	−	0.434065i
$407$	8723.87			1.06247
$408$		0			0
$409$	−1231.90	−	3791.40i	−0.148933	−	0.458369i	0.848563	−	0.529095i	$-0.177468\pi$
$409$	−1231.90	−	3791.40i	−0.148933	−	0.458369i	−0.997496	+	0.0707261i	$0.977468\pi$
$410$	727.589	−	2323.45i	0.0876416	−	0.279870i
$411$		0			0
$412$	−2456.78	−	7561.20i	−0.293779	−	0.904159i
$413$	882.983	+	2717.54i	0.105203	+	0.323781i
$414$		0			0
$415$	−50.0047	−	148.483i	−0.00591479	−	0.0175633i
$416$	3270.84	+	10066.6i	0.385496	+	1.18643i
$417$		0			0
$418$	13840.9			1.61958
$419$	7445.57	−	5409.52i	0.868115	−	0.630722i	−0.0619658	−	0.998078i	$-0.519737\pi$
$419$	7445.57	−	5409.52i	0.868115	−	0.630722i	0.930080	+	0.367356i	$0.119737\pi$
$420$		0			0
$421$	−11708.9	−	8506.99i	−1.35548	−	0.984810i	−0.998718	−	0.0506132i	$-0.983882\pi$
$421$	−11708.9	−	8506.99i	−1.35548	−	0.984810i	−0.356757	−	0.934197i	$-0.616118\pi$
$422$	−11909.1	−	8652.48i	−1.37376	−	0.998095i
$423$		0			0
$424$	605.570			0.0693611
$425$	−12618.3	+	269.608i	−1.44019	+	0.0307716i
$426$		0			0
$427$	1079.35	−	3321.90i	0.122327	−	0.376482i
$428$	1071.38	+	778.402i	0.120998	+	0.0879100i
$429$		0			0
$430$	7518.62	+	5340.84i	0.843210	+	0.598972i
$431$	13496.0	−	9805.38i	1.50830	−	1.09584i	0.541375	−	0.840781i	$-0.317904\pi$
$431$	13496.0	−	9805.38i	1.50830	−	1.09584i	0.966925	−	0.255063i	$-0.0820961\pi$
$432$		0			0
$433$	−6033.95	+	4383.92i	−0.669684	+	0.486554i	−0.869919	−	0.493194i	$-0.835829\pi$
$433$	−6033.95	+	4383.92i	−0.669684	+	0.486554i	0.200235	+	0.979748i	$0.435829\pi$
$434$	−651.104	−	2003.89i	−0.0720138	−	0.221636i
$435$		0			0
$436$	1803.50	−	5550.59i	0.198100	−	0.609691i
$437$	3912.16	+	12040.4i	0.428247	+	1.31801i
$438$		0			0
$439$	3121.46	−	9606.85i	0.339360	−	1.04444i	−0.625174	−	0.780485i	$-0.714972\pi$
$439$	3121.46	−	9606.85i	0.339360	−	1.04444i	0.964534	−	0.263957i	$-0.0850278\pi$
$440$	1574.82	−	16.8221i	0.170628	−	0.00182265i
$441$		0			0
$442$	−13652.9	+	9919.42i	−1.46924	+	1.06746i
$443$	−3125.48			−0.335205			−0.167603	−	0.985855i	$-0.553603\pi$
$443$	−3125.48			−0.335205			−0.167603	+	0.985855i	$0.553603\pi$
$444$		0			0
$445$	4218.04	+	2996.27i	0.449335	+	0.319184i
$446$	10606.6	+	7706.18i	1.12610	+	0.818157i
$447$		0			0
$448$	−780.693	+	2402.73i	−0.0823310	+	0.253389i
$449$	−14568.3			−1.53123			−0.765614	−	0.643300i	$-0.777565\pi$
$449$	−14568.3			−1.53123			−0.765614	+	0.643300i	$0.777565\pi$
$450$		0			0
$451$	−2466.27			−0.257499
$452$	1871.54	−	5760.01i	0.194756	−	0.599398i
$453$		0			0
$454$	−19064.1	−	13850.9i	−1.97076	−	1.43184i
$455$	3011.64	−	32.1703i	0.310303	−	0.00331465i
$456$		0			0
$457$	−14908.3			−1.52600			−0.763000	−	0.646399i	$-0.776274\pi$
$457$	−14908.3			−1.52600			−0.763000	+	0.646399i	$0.776274\pi$
$458$	6426.33	−	4669.00i	0.655639	−	0.476349i
$459$		0			0
$460$	−4029.34	−	11964.6i	−0.408411	−	1.21273i
$461$	1140.13	−	3508.95i	0.115187	−	0.354508i	−0.876799	−	0.480856i	$-0.840326\pi$
$461$	1140.13	−	3508.95i	0.115187	−	0.354508i	0.991986	+	0.126349i	$0.0403258\pi$
$462$		0			0
$463$	−4273.76	−	13153.3i	−0.428981	−	1.32027i	−0.899130	−	0.437681i	$-0.855800\pi$
$463$	−4273.76	−	13153.3i	−0.428981	−	1.32027i	0.470149	−	0.882587i	$-0.344200\pi$
$464$	5332.04	−	16410.3i	0.533477	−	1.64187i
$465$		0			0
$466$	−15.5753	−	47.9358i	−0.00154831	−	0.00476520i
$467$	221.710	−	161.082i	0.0219690	−	0.0159614i	−0.576747	−	0.816923i	$-0.695678\pi$
$467$	221.710	−	161.082i	0.0219690	−	0.0159614i	0.598716	+	0.800962i	$0.295678\pi$
$468$		0			0
$469$	−4854.59	+	3527.06i	−0.477962	+	0.347260i
$470$	−1476.34	−	4383.82i	−0.144891	−	0.430235i
$471$		0			0
$472$	1175.14	+	853.791i	0.114598	+	0.0832605i
$473$	2886.85	−	8884.81i	0.280629	−	0.863687i
$474$		0			0
$475$	10060.9	−	214.965i	0.971844	−	0.0207648i
$476$	−4553.00			−0.438417
$477$		0			0
$478$	39.7747	+	28.8980i	0.00380597	+	0.00276520i
$479$	−11987.5	−	8709.43i	−1.14347	−	0.830781i	−0.155872	−	0.987777i	$-0.549819\pi$
$479$	−11987.5	−	8709.43i	−1.14347	−	0.830781i	−0.987599	+	0.156997i	$0.949819\pi$
$480$		0			0
$481$	6861.25	−	4984.99i	0.650408	−	0.472549i
$482$	26286.1			2.48402
$483$		0			0
$484$	1367.10	+	4207.49i	0.128390	+	0.395144i
$485$	−11674.9	+	8674.34i	−1.09305	+	0.812127i
$486$		0			0
$487$	5341.55	+	16439.6i	0.497020	+	1.52967i	0.813785	+	0.581166i	$0.197403\pi$
$487$	5341.55	+	16439.6i	0.497020	+	1.52967i	−0.316765	+	0.948504i	$0.602597\pi$
$488$	−548.688	−	1688.69i	−0.0508974	−	0.156646i
$489$		0			0
$490$	−10780.6	−	7657.96i	−0.993912	−	0.706023i
$491$	3045.75	+	9373.84i	0.279944	+	0.861580i	0.987869	+	0.155292i	$0.0496317\pi$
$491$	3045.75	+	9373.84i	0.279944	+	0.861580i	−0.707924	+	0.706288i	$0.750368\pi$
$492$		0			0
$493$	24930.3			2.27750
$494$	10885.8	−	7908.99i	0.991447	−	0.720329i
$495$		0			0
$496$	−4868.68	−	3537.30i	−0.440747	−	0.320221i
$497$	−2853.05	−	2072.86i	−0.257498	−	0.187083i
$498$		0			0
$499$	10126.4			0.908458			0.454229	−	0.890885i	$-0.349915\pi$
$499$	10126.4			0.908458			0.454229	+	0.890885i	$0.349915\pi$
$500$	−10030.1	+	321.523i	−0.897123	+	0.0287579i
$501$		0			0
$502$	1111.69	−	3421.44i	0.0988394	−	0.304196i
$503$	4874.27	+	3541.36i	0.432073	+	0.313920i	0.782477	−	0.622679i	$-0.213956\pi$
$503$	4874.27	+	3541.36i	0.432073	+	0.313920i	−0.350404	+	0.936599i	$0.613956\pi$
$504$		0			0
$505$	−4267.33	+	13627.1i	−0.376027	+	1.20079i
$506$	−21872.9	+	15891.6i	−1.92168	+	1.39618i
$507$		0			0
$508$	10163.5	−	7384.21i	0.887662	−	0.644924i
$509$	5588.13	+	17198.5i	0.486620	+	1.49766i	0.829621	+	0.558327i	$0.188557\pi$
$509$	5588.13	+	17198.5i	0.486620	+	1.49766i	−0.343001	+	0.939335i	$0.611443\pi$
$510$		0			0
$511$	−343.616	+	1057.54i	−0.0297469	+	0.0915516i
$512$	4776.96	+	14702.0i	0.412331	+	1.26903i
$513$		0			0
$514$	4983.81	−	15338.6i	0.427678	−	1.31626i
$515$	−9936.28	+	7382.56i	−0.850184	+	0.631679i
$516$		0			0
$517$	−3790.81	+	2754.19i	−0.322476	+	0.234292i
$518$	4837.29			0.410306
$519$		0			0
$520$	1228.97	−	913.112i	0.103642	−	0.0770050i
$521$	−7060.19	−	5129.53i	−0.593690	−	0.431341i	0.249943	−	0.968260i	$-0.419588\pi$
$521$	−7060.19	−	5129.53i	−0.593690	−	0.431341i	−0.843634	+	0.536919i	$0.819588\pi$
$522$		0			0
$523$	2270.43	−	6987.67i	0.189826	−	0.584225i	−0.810172	−	0.586192i	$-0.800626\pi$
$523$	2270.43	−	6987.67i	0.189826	−	0.584225i	0.999998	+	0.00196745i	$0.000626259\pi$
$524$	−3598.42			−0.299996
$525$		0			0
$526$	−7312.93			−0.606196
$527$	2686.91	−	8269.46i	0.222094	−	0.683536i
$528$		0			0
$529$	−10163.3	−	7384.10i	−0.835321	−	0.606896i
$530$	2637.33	+	7831.25i	0.216148	+	0.641826i
$531$		0			0
$532$	3630.22			0.295846
$533$	−1939.70	+	1409.27i	−0.157632	+	0.114526i
$534$		0			0
$535$	616.191	−	1967.71i	0.0497949	−	0.159012i
$536$	−942.627	+	2901.11i	−0.0759614	+	0.233785i
$537$		0			0
$538$	2375.85	+	7312.12i	0.190391	+	0.585962i
$539$	−4139.31	+	12739.5i	−0.330784	+	1.01805i
$540$		0			0
$541$	−6077.53	−	18704.7i	−0.482982	−	1.48647i	−0.834882	−	0.550429i	$-0.814464\pi$
$541$	−6077.53	−	18704.7i	−0.482982	−	1.48647i	0.351900	−	0.936038i	$-0.385536\pi$
$542$	−16402.5	+	11917.1i	−1.29990	+	0.944436i
$543$		0			0
$544$	−20155.5	+	14643.9i	−1.58853	+	1.15414i
$545$	−9086.53	+	97.0621i	−0.714173	+	0.00762878i
$546$		0			0
$547$	−19688.4	−	14304.5i	−1.53897	−	1.11812i	−0.950979	−	0.309254i	$-0.899921\pi$
$547$	−19688.4	−	14304.5i	−1.53897	−	1.11812i	−0.587987	−	0.808870i	$-0.700079\pi$
$548$	3090.84	−	9512.64i	0.240939	−	0.741533i
$549$		0			0
$550$	7076.07	+	20292.3i	0.548590	+	1.57321i
$551$	−19877.6			−1.53686
$552$		0			0
$553$	−4831.02	−	3509.94i	−0.371493	−	0.269906i
$554$	−4745.56	−	3447.85i	−0.363934	−	0.264413i
$555$		0			0
$556$	−5412.31	+	3932.27i	−0.412829	+	0.299938i
$557$	15077.6			1.14696			0.573481	−	0.819219i	$-0.305592\pi$
$557$	15077.6			1.14696			0.573481	+	0.819219i	$0.305592\pi$
$558$		0			0
$559$	−2806.47	−	8637.44i	−0.212346	−	0.653532i
$560$	4906.21	−	52.4080i	0.370224	−	0.00395472i
$561$		0			0
$562$	6540.55	+	20129.7i	0.490919	+	1.51089i
$563$	4431.52	+	13638.8i	0.331734	+	1.02097i	0.968309	+	0.249757i	$0.0803507\pi$
$563$	4431.52	+	13638.8i	0.331734	+	1.02097i	−0.636575	+	0.771215i	$0.719649\pi$
$564$		0			0
$565$	−9429.36	+	100.724i	−0.702117	+	0.00749999i
$566$	2734.89	+	8417.14i	0.203103	+	0.625086i
$567$		0			0
$568$	−1792.73			−0.132432
$569$	−3259.66	+	2368.28i	−0.240162	+	0.174488i	−0.701355	−	0.712812i	$-0.747421\pi$
$569$	−3259.66	+	2368.28i	−0.240162	+	0.174488i	0.461194	+	0.887300i	$0.347421\pi$
$570$		0			0
$571$	9126.02	+	6630.45i	0.668848	+	0.485947i	0.869639	−	0.493687i	$-0.164351\pi$
$571$	9126.02	+	6630.45i	0.668848	+	0.485947i	−0.200791	+	0.979634i	$0.564351\pi$
$572$	10996.3	+	7989.30i	0.803811	+	0.584003i
$573$		0			0
$574$	−1367.52			−0.0994411
$575$	−15652.4	+	11891.2i	−1.13522	+	0.862430i
$576$		0			0
$577$	−3864.21	+	11892.8i	−0.278802	+	0.858066i	0.709386	+	0.704820i	$0.248972\pi$
$577$	−3864.21	+	11892.8i	−0.278802	+	0.858066i	−0.988188	+	0.153245i	$0.951028\pi$
$578$	−16649.1	−	12096.3i	−1.19812	−	0.870483i
$579$		0			0
$580$	19821.3	−	211.731i	1.41903	−	0.0151580i
$581$	−71.1952	+	51.7263i	−0.00508377	+	0.00369358i
$582$		0			0
$583$	6771.91	−	4920.08i	0.481070	−	0.349518i
$584$	174.677	+	537.602i	0.0123771	+	0.0380927i
$585$		0			0
$586$	6474.03	−	19925.0i	0.456382	−	1.40460i
$587$	−5390.49	−	16590.2i	−0.379028	−	1.16653i	−0.940721	−	0.339182i	$-0.889850\pi$
$587$	−5390.49	−	16590.2i	−0.379028	−	1.16653i	0.561693	−	0.827346i	$-0.310150\pi$
$588$		0			0
$589$	−2142.34	+	6593.44i	−0.149870	+	0.461253i
$590$	−5923.36	+	18915.4i	−0.413323	+	1.31989i
$591$		0			0
$592$	11177.5	−	8120.95i	0.776003	−	0.563799i
$593$	17798.5			1.23254			0.616269	−	0.787536i	$-0.288643\pi$
$593$	17798.5			1.23254			0.616269	+	0.787536i	$0.288643\pi$
$594$		0			0
$595$	2262.53	+	6718.31i	0.155890	+	0.462897i
$596$	16890.8	+	12271.8i	1.16086	+	0.843414i
$597$		0			0
$598$	−8122.08	+	24997.2i	−0.555412	+	1.70938i
$599$	−23241.2			−1.58532			−0.792661	−	0.609662i	$-0.791305\pi$
$599$	−23241.2			−1.58532			−0.792661	+	0.609662i	$0.791305\pi$
$600$		0			0
$601$	−2735.11			−0.185637			−0.0928183	−	0.995683i	$-0.529588\pi$
$601$	−2735.11			−0.185637			−0.0928183	+	0.995683i	$0.529588\pi$
$602$	1600.73	−	4926.53i	0.108373	−	0.333539i
$603$		0			0
$604$	4415.70	+	3208.19i	0.297470	+	0.216125i
$605$	5529.13	−	4108.09i	0.371555	−	0.276062i
$606$		0			0
$607$	1676.42			0.112098			0.0560492	−	0.998428i	$-0.482150\pi$
$607$	1676.42			0.112098			0.0560492	+	0.998428i	$0.482150\pi$
$608$	16070.5	−	11675.9i	1.07195	−	0.778817i
$609$		0			0
$610$	19448.6	−	14450.1i	1.29090	−	0.959127i
$611$	−1407.65	+	4332.29i	−0.0932035	+	0.286851i
$612$		0			0
$613$	−611.200	−	1881.08i	−0.0402710	−	0.123941i	0.928900	−	0.370331i	$-0.120756\pi$
$613$	−611.200	−	1881.08i	−0.0402710	−	0.123941i	−0.969171	+	0.246390i	$0.920756\pi$
$614$	9757.70	−	30031.1i	0.641349	−	1.97387i
$615$		0			0
$616$	−273.353	−	841.295i	−0.0178794	−	0.0550272i
$617$	6781.95	−	4927.38i	0.442514	−	0.321505i	−0.344119	−	0.938926i	$-0.611822\pi$
$617$	6781.95	−	4927.38i	0.442514	−	0.321505i	0.786633	+	0.617421i	$0.211822\pi$
$618$		0			0
$619$	−15968.8	+	11602.0i	−1.03690	+	0.753350i	−0.969678	−	0.244388i	$-0.921413\pi$
$619$	−15968.8	+	11602.0i	−1.03690	+	0.753350i	−0.0672201	+	0.997738i	$0.521413\pi$
$620$	2066.05	−	6597.60i	0.133830	−	0.427365i
$621$		0			0
$622$	−2376.95	−	1726.95i	−0.153227	−	0.111326i
$623$	898.027	−	2763.84i	0.0577507	−	0.177738i
$624$		0			0
$625$	5458.71	+	14640.5i	0.349358	+	0.936989i
$626$	16766.8			1.07050
$627$		0			0
$628$	−16411.0	−	11923.3i	−1.04279	−	0.757631i
$629$	16149.7	+	11733.4i	1.02373	+	0.743787i
$630$		0			0
$631$	4438.84	−	3225.00i	0.280043	−	0.203463i	−0.438893	−	0.898539i	$-0.644629\pi$
$631$	4438.84	−	3225.00i	0.280043	−	0.203463i	0.718936	+	0.695076i	$0.244629\pi$
$632$	−3035.60			−0.191059
$633$		0			0
$634$	4376.72	+	13470.2i	0.274167	+	0.843798i
$635$	−15946.5	−	11327.6i	−0.996564	−	0.707907i
$636$		0			0
$637$	4024.06	+	12384.8i	0.250297	+	0.770335i
$638$	−13117.7	−	40372.3i	−0.814007	−	2.50526i
$639$		0			0
$640$	3647.84	−	2710.31i	0.225302	−	0.167398i
$641$	−2181.43	−	6713.77i	−0.134417	−	0.413694i	0.861082	−	0.508467i	$-0.169788\pi$
$641$	−2181.43	−	6713.77i	−0.134417	−	0.413694i	−0.995499	+	0.0947728i	$0.969788\pi$
$642$		0			0
$643$	21740.4			1.33337			0.666687	−	0.745338i	$-0.267712\pi$
$643$	21740.4			1.33337			0.666687	+	0.745338i	$0.267712\pi$
$644$	−5736.85	+	4168.06i	−0.351030	+	0.255038i
$645$		0			0
$646$	25622.4	+	18615.8i	1.56053	+	1.13379i
$647$	−3360.78	−	2441.75i	−0.204213	−	0.148370i	0.480978	−	0.876732i	$-0.340282\pi$
$647$	−3360.78	−	2441.75i	−0.204213	−	0.148370i	−0.685192	+	0.728363i	$0.740282\pi$
$648$		0			0
$649$	20078.1			1.21438
$650$	17160.7	+	11916.3i	1.03554	+	0.719072i
$651$		0			0
$652$	358.038	−	1101.93i	0.0215059	−	0.0661883i
$653$	14674.8	+	10661.8i	0.879430	+	0.638943i	0.933101	−	0.359616i	$-0.117092\pi$
$653$	14674.8	+	10661.8i	0.879430	+	0.638943i	−0.0536708	+	0.998559i	$0.517092\pi$
$654$		0			0
$655$	1788.17	+	5309.75i	0.106671	+	0.316747i
$656$	−3159.93	+	2295.82i	−0.188071	+	0.136641i
$657$		0			0
$658$	−2101.97	+	1527.17i	−0.124534	+	0.0904791i
$659$	1609.32	+	4952.97i	0.0951292	+	0.292778i	0.987287	−	0.158946i	$-0.0508094\pi$
$659$	1609.32	+	4952.97i	0.0951292	+	0.292778i	−0.892158	+	0.451723i	$0.850809\pi$
$660$		0			0
$661$	−5473.66	+	16846.2i	−0.322089	+	0.991287i	0.650649	+	0.759379i	$0.274497\pi$
$661$	−5473.66	+	16846.2i	−0.322089	+	0.991287i	−0.972738	+	0.231908i	$0.925503\pi$
$662$	−4431.99	−	13640.3i	−0.260203	−	0.800822i
$663$		0			0
$664$	−13.8241	+	42.5463i	−0.000807953	+	0.00248662i
$665$	−1803.97	−	5356.67i	−0.105195	−	0.312365i
$666$		0			0
$667$	31412.5	−	22822.5i	1.82354	−	1.32488i
$668$	21024.3			1.21775
$669$		0			0
$670$	−41622.5	+	444.610i	−2.40003	+	0.0256370i
$671$	−19855.9	−	14426.2i	−1.14237	−	0.829979i
$672$		0			0
$673$	−9178.90	+	28249.8i	−0.525737	+	1.61805i	0.237118	+	0.971481i	$0.423797\pi$
$673$	−9178.90	+	28249.8i	−0.525737	+	1.61805i	−0.762855	+	0.646570i	$0.776203\pi$
$674$	−1074.64			−0.0614149
$675$		0			0
$676$	−2562.15			−0.145776
$677$	−2158.52	+	6643.23i	−0.122538	+	0.377134i	−0.993445	−	0.114315i	$-0.963533\pi$
$677$	−2158.52	+	6643.23i	−0.122538	+	0.377134i	0.870906	+	0.491449i	$0.163533\pi$
$678$		0			0
$679$	6609.20	+	4801.87i	0.373546	+	0.271397i
$680$	2937.93	+	2086.95i	0.165683	+	0.117693i
$681$		0			0
$682$	−14805.4			−0.831272
$683$	3632.47	−	2639.14i	0.203503	−	0.147854i	−0.481366	−	0.876520i	$-0.659859\pi$
$683$	3632.47	−	2639.14i	0.203503	−	0.147854i	0.684869	+	0.728666i	$0.259859\pi$
$684$		0			0
$685$	−15572.6	+	166.346i	−0.868609	+	0.00927846i
$686$	−4888.57	+	15045.5i	−0.272080	+	0.837375i
$687$		0			0
$688$	−4571.97	−	14071.1i	−0.253350	−	0.779731i
$689$	2514.62	−	7739.21i	0.139041	−	0.427925i
$690$		0			0
$691$	10095.7	+	31071.4i	0.555802	+	1.71058i	0.693817	+	0.720151i	$0.255928\pi$
$691$	10095.7	+	31071.4i	0.555802	+	1.71058i	−0.138016	+	0.990430i	$0.544072\pi$
$692$	14156.6	−	10285.4i	0.777678	−	0.565016i
$693$		0			0
$694$	35153.2	−	25540.3i	1.92276	−	1.39697i
$695$	8491.92	+	6032.21i	0.463477	+	0.329230i
$696$		0			0
$697$	−4565.56	−	3317.08i	−0.248111	−	0.180263i
$698$	−9896.05	+	30456.9i	−0.536635	+	1.65159i
$699$		0			0
$700$	1855.92	+	5322.29i	0.100210	+	0.287377i
$701$	1911.12			0.102970			0.0514852	−	0.998674i	$-0.483605\pi$
$701$	1911.12			0.102970			0.0514852	+	0.998674i	$0.483605\pi$
$702$		0			0
$703$	−12876.5	−	9355.33i	−0.690820	−	0.501910i
$704$	14361.8	+	10434.4i	0.768862	+	0.558611i
$705$		0			0
$706$	6146.19	−	4465.47i	0.327642	−	0.238046i
$707$	8020.54			0.426653
$708$		0			0
$709$	10449.5	+	32160.3i	0.553512	+	1.70353i	0.699841	+	0.714298i	$0.253254\pi$
$709$	10449.5	+	32160.3i	0.553512	+	1.70353i	−0.146329	+	0.989236i	$0.546746\pi$
$710$	−7807.56	−	23183.6i	−0.412694	−	1.22544i
$711$		0			0
$712$	−456.512	−	1405.00i	−0.0240288	−	0.0739531i
$713$	−4184.76	−	12879.4i	−0.219805	−	0.676489i
$714$		0			0
$715$	6324.41	−	20196.1i	0.330797	−	1.05635i
$716$	−7684.81	−	23651.4i	−0.401110	−	1.23449i
$717$		0			0
$718$	43758.4			2.27444
$719$	−7234.32	+	5256.04i	−0.375236	+	0.272625i	−0.759379	−	0.650649i	$-0.774497\pi$
$719$	−7234.32	+	5256.04i	−0.375236	+	0.272625i	0.384143	+	0.923274i	$0.374497\pi$
$720$		0			0
$721$	5624.96	+	4086.77i	0.290547	+	0.211095i
$722$	1191.04	+	865.345i	0.0613935	+	0.0446050i
$723$		0			0
$724$	27082.2			1.39020
$725$	−10162.2	−	29142.6i	−0.520574	−	1.49287i
$726$		0			0
$727$	2679.13	−	8245.53i	0.136676	−	0.420646i	−0.859171	−	0.511689i	$-0.829020\pi$
$727$	2679.13	−	8245.53i	0.136676	−	0.420646i	0.995847	+	0.0910429i	$0.0290201\pi$
$728$	−695.723	−	505.472i	−0.0354192	−	0.0257336i
$729$		0			0
$730$	−6191.54	+	4600.26i	−0.313917	+	0.233237i
$731$	17294.0	−	12564.8i	0.875024	−	0.635742i
$732$		0			0
$733$	−19365.9	+	14070.2i	−0.975848	+	0.708995i	−0.956777	−	0.290823i	$-0.906071\pi$
$733$	−19365.9	+	14070.2i	−0.975848	+	0.708995i	−0.0190713	+	0.999818i	$0.506071\pi$
$734$	−7892.52	−	24290.7i	−0.396891	−	1.22151i
$735$		0			0
$736$	−11990.5	+	36902.9i	−0.600510	+	1.84818i
$737$	13029.5	+	40100.8i	0.651220	+	2.00425i
$738$		0			0
$739$	1440.41	−	4433.14i	0.0717003	−	0.220671i	−0.908784	−	0.417266i	$-0.862988\pi$
$739$	1440.41	−	4433.14i	0.0717003	−	0.220671i	0.980485	+	0.196595i	$0.0629884\pi$
$740$	12939.7	+	9191.70i	0.642802	+	0.456613i
$741$		0			0
$742$	3754.95	−	2728.13i	0.185780	−	0.134977i
$743$	−26436.5			−1.30533			−0.652666	−	0.757646i	$-0.726350\pi$
$743$	−26436.5			−1.30533			−0.652666	+	0.757646i	$0.726350\pi$
$744$		0			0
$745$	9714.52	−	31021.9i	0.477735	−	1.52557i
$746$	13732.2	+	9977.02i	0.673956	+	0.489658i
$747$		0			0
$748$	−9886.27	+	30426.8i	−0.483259	+	1.48732i
$749$	−1158.14			−0.0564989
$750$		0			0
$751$	−11047.7			−0.536802			−0.268401	−	0.963307i	$-0.586495\pi$
$751$	−11047.7			−0.536802			−0.268401	+	0.963307i	$0.586495\pi$
$752$	−2293.17	+	7057.66i	−0.111201	+	0.342242i
$753$		0			0
$754$	−33386.5	−	24256.7i	−1.61255	−	1.17159i
$755$	2539.64	−	8109.95i	0.122420	−	0.390929i
$756$		0			0
$757$	−1908.68			−0.0916411			−0.0458205	−	0.998950i	$-0.514590\pi$
$757$	−1908.68			−0.0916411			−0.0458205	+	0.998950i	$0.514590\pi$
$758$	−16693.6	+	12128.6i	−0.799918	+	0.581174i
$759$		0			0
$760$	−2342.48	−	1663.98i	−0.111804	−	0.0794195i
$761$	849.513	−	2614.53i	0.0404662	−	0.124542i	−0.928783	−	0.370625i	$-0.879144\pi$
$761$	849.513	−	2614.53i	0.0404662	−	0.124542i	0.969249	+	0.246083i	$0.0791435\pi$
$762$		0			0
$763$	1577.22	+	4854.19i	0.0748352	+	0.230319i
$764$	−4675.54	+	14389.8i	−0.221407	+	0.681421i
$765$		0			0
$766$	−9393.93	−	28911.5i	−0.443102	−	1.36373i
$767$	15791.2	−	11473.0i	0.743401	−	0.540113i
$768$		0			0
$769$	4062.71	−	2951.73i	0.190514	−	0.138416i	−0.488440	−	0.872598i	$-0.662434\pi$
$769$	4062.71	−	2951.73i	0.190514	−	0.138416i	0.678954	+	0.734181i	$0.262434\pi$
$770$	9689.16	−	7198.96i	0.453472	−	0.336925i
$771$		0			0
$772$	21854.3	+	15878.1i	1.01885	+	0.740239i
$773$	−4932.83	+	15181.7i	−0.229523	+	0.706400i	0.768278	+	0.640117i	$0.221114\pi$
$773$	−4932.83	+	15181.7i	−0.229523	+	0.706400i	−0.997801	+	0.0662830i	$0.978886\pi$
$774$		0			0
$775$	−10762.0	+	229.944i	−0.498814	+	0.0106578i
$776$	4152.93			0.192115
$777$		0			0
$778$	−40896.5	−	29713.1i	−1.88459	−	1.36923i
$779$	3640.24	+	2644.79i	0.167426	+	0.121642i
$780$		0			0
$781$	−20047.5	+	14565.4i	−0.918511	+	0.667337i
$782$	−61865.0			−2.82901
$783$		0			0
$784$	6555.52	+	20175.8i	0.298630	+	0.919088i
$785$	−9438.62	+	30140.8i	−0.429145	+	1.37041i
$786$		0			0
$787$	−837.844	−	2578.62i	−0.0379491	−	0.116795i	0.930287	−	0.366832i	$-0.119557\pi$
$787$	−837.844	−	2578.62i	−0.0379491	−	0.116795i	−0.968236	+	0.250036i	$0.919557\pi$
$788$	8396.20	+	25840.9i	0.379571	+	1.16820i
$789$		0			0
$790$	−13220.4	−	39256.4i	−0.595394	−	1.76795i
$791$	1636.73	+	5037.33i	0.0735719	+	0.226431i
$792$		0			0
$793$	−23859.9			−1.06846
$794$	32041.4	−	23279.4i	1.43212	−	1.04050i
$795$		0			0
$796$	−26763.2	−	19444.6i	−1.19170	−	0.865824i
$797$	−8061.78	−	5857.23i	−0.358297	−	0.260318i	0.394044	−	0.919092i	$-0.371076\pi$
$797$	−8061.78	−	5857.23i	−0.358297	−	0.260318i	−0.752342	+	0.658773i	$0.771076\pi$
$798$		0			0
$799$	−10721.9			−0.474735
$800$	25334.0	+	17591.9i	1.11962	+	0.777458i
$801$		0			0
$802$	9889.51	−	30436.8i	0.435425	−	1.34010i
$803$	6321.22	+	4592.63i	0.277797	+	0.201831i
$804$		0			0
$805$	9001.11	+	6393.92i	0.394096	+	0.279945i
$806$	−11644.3	+	8460.10i	−0.508876	+	0.369720i
$807$		0			0
$808$	3298.56	−	2396.54i	0.143618	−	0.104344i
$809$	−6432.96	−	19798.6i	−0.279568	−	0.860423i	−0.987974	−	0.154618i	$-0.950585\pi$
$809$	−6432.96	−	19798.6i	−0.279568	−	0.860423i	0.708406	−	0.705805i	$-0.249415\pi$
$810$		0			0
$811$	2921.02	−	8989.98i	0.126475	−	0.389249i	−0.867692	−	0.497102i	$-0.834398\pi$
$811$	2921.02	−	8989.98i	0.126475	−	0.389249i	0.994167	+	0.107853i	$0.0343976\pi$
$812$	−3440.54	−	10588.9i	−0.148694	−	0.457632i
$813$		0			0
$814$	10503.6	−	32326.7i	0.452272	−	1.39195i
$815$	−1803.90	+	19.2692i	−0.0775310	+	0.000828184i
$816$		0			0
$817$	−13788.9	+	10018.3i	−0.590470	+	0.429002i
$818$	−15532.4			−0.663910
$819$		0			0
$820$	−3658.10	−	2598.53i	−0.155788	−	0.110664i
$821$	−5597.81	−	4067.05i	−0.237960	−	0.172888i	0.462414	−	0.886664i	$-0.346983\pi$
$821$	−5597.81	−	4067.05i	−0.237960	−	0.172888i	−0.700374	+	0.713776i	$0.746983\pi$
$822$		0			0
$823$	−7712.15	+	23735.6i	−0.326645	+	1.00531i	0.644048	+	0.764985i	$0.277254\pi$
$823$	−7712.15	+	23735.6i	−0.326645	+	1.00531i	−0.970693	+	0.240324i	$0.922746\pi$
$824$	3534.47			0.149429
$825$		0			0
$826$	11133.1			0.468970
$827$	219.443	−	675.376i	0.00922706	−	0.0283980i	−0.946337	−	0.323182i	$-0.895248\pi$
$827$	219.443	−	675.376i	0.00922706	−	0.0283980i	0.955564	+	0.294784i	$0.0952476\pi$
$828$		0			0
$829$	17334.3	+	12594.1i	0.726230	+	0.527637i	0.888369	−	0.459131i	$-0.151839\pi$
$829$	17334.3	+	12594.1i	0.726230	+	0.527637i	−0.162139	+	0.986768i	$0.551839\pi$
$830$	−610.416	+	6.52045i	−0.0255275	+	0.000272685i
$831$		0			0
$832$	17257.8			0.719120
$833$	−24797.0	+	18016.1i	−1.03141	+	0.749365i
$834$		0			0
$835$	−10447.6	−	31022.9i	−0.433000	−	1.28574i
$836$	7882.56	−	24260.0i	0.326105	−	1.00365i
$837$		0			0
$838$	−11080.7	−	34103.0i	−0.456775	−	1.40581i
$839$	−9810.52	+	30193.7i	−0.403691	+	1.24243i	0.518292	+	0.855203i	$0.326568\pi$
$839$	−9810.52	+	30193.7i	−0.403691	+	1.24243i	−0.921983	+	0.387229i	$0.873432\pi$
$840$		0			0
$841$	11302.3	+	34785.0i	0.463419	+	1.42626i
$842$	−45620.5	+	33145.2i	−1.86721	+	1.35660i
$843$		0			0
$844$	−21948.2	+	15946.3i	−0.895129	+	0.650349i
$845$	1273.21	+	3780.65i	0.0518341	+	0.153915i
$846$		0			0
$847$	−3130.06	−	2274.12i	−0.126978	−	0.0922546i
$848$	4096.52	−	12607.8i	0.165890	−	0.510558i
$849$		0			0
$850$	−14193.5	+	47082.4i	−0.572744	+	1.89990i
$851$	31090.2			1.25236
$852$		0			0
$853$	2035.11	+	1478.59i	0.0816890	+	0.0593505i	0.627880	−	0.778310i	$-0.283923\pi$
$853$	2035.11	+	1478.59i	0.0816890	+	0.0593505i	−0.546191	+	0.837661i	$0.683923\pi$
$854$	−11009.9	−	7999.16i	−0.441160	−	0.320522i
$855$		0			0
$856$	−476.303	+	346.055i	−0.0190184	+	0.0138176i
$857$	14351.2			0.572027			0.286013	−	0.958226i	$-0.407670\pi$
$857$	14351.2			0.572027			0.286013	+	0.958226i	$0.407670\pi$
$858$		0			0
$859$	−1558.31	−	4795.99i	−0.0618963	−	0.190497i	0.915327	−	0.402712i	$-0.131932\pi$
$859$	−1558.31	−	4795.99i	−0.0618963	−	0.190497i	−0.977223	+	0.212215i	$0.931932\pi$
$860$	13643.2	−	10136.8i	0.540965	−	0.401932i
$861$		0			0
$862$	−20085.1	−	61815.5i	−0.793620	−	2.44251i
$863$	3735.81	+	11497.6i	0.147356	+	0.453515i	0.997306	−	0.0733474i	$-0.0233682\pi$
$863$	3735.81	+	11497.6i	0.147356	+	0.453515i	−0.849950	+	0.526863i	$0.823368\pi$
$864$		0			0
$865$	−22211.7	−	15778.0i	−0.873088	−	0.620196i
$866$	8979.91	+	27637.3i	0.352367	+	1.08447i
$867$		0			0
$868$	−3883.18			−0.151848
$869$	−33946.2	+	24663.3i	−1.32514	+	0.962769i
$870$		0			0
$871$	33162.0	+	24093.6i	1.29007	+	0.937292i
$872$	2099.09	+	1525.08i	0.0815185	+	0.0592267i
$873$		0			0
$874$	49326.4			1.90903
$875$	6931.19	−	5383.36i	0.267791	−	0.207990i
$876$		0			0
$877$	8126.34	−	25010.3i	0.312893	−	0.962985i	−0.663720	−	0.747981i	$-0.731023\pi$
$877$	8126.34	−	25010.3i	0.312893	−	0.962985i	0.976613	−	0.215004i	$-0.0689766\pi$
$878$	−31840.4	−	23133.4i	−1.22387	−	0.889196i
$879$		0			0
$880$	10303.0	−	32901.0i	0.394674	−	1.26033i
$881$	13701.2	−	9954.53i	0.523957	−	0.380677i	−0.294135	−	0.955764i	$-0.595032\pi$
$881$	13701.2	−	9954.53i	0.523957	−	0.380677i	0.818093	+	0.575086i	$0.195032\pi$
$882$		0			0
$883$	34929.9	−	25378.0i	1.33124	−	0.967201i	0.331520	−	0.943448i	$-0.392439\pi$
$883$	34929.9	−	25378.0i	1.33124	−	0.967201i	0.999718	−	0.0237528i	$-0.00756146\pi$
$884$	9611.01	+	29579.7i	0.365671	+	1.12542i
$885$		0			0
$886$	−3763.08	+	11581.6i	−0.142690	+	0.439155i
$887$	−2911.05	−	8959.28i	−0.110195	−	0.339147i	0.880719	−	0.473639i	$-0.157060\pi$
$887$	−2911.05	−	8959.28i	−0.110195	−	0.339147i	−0.990915	+	0.134492i	$0.957060\pi$
$888$		0			0
$889$	−3395.04	+	10448.9i	−0.128083	+	0.394200i
$890$	16181.3	−	12022.6i	0.609438	−	0.452807i
$891$		0			0
$892$	19547.8	−	14202.3i	0.733753	−	0.533103i
$893$	8548.83			0.320353
$894$		0			0
$895$	−31080.6	+	23092.6i	−1.16079	+	0.862460i
$896$	−2065.05	−	1500.35i	−0.0769962	−	0.0559410i
$897$		0			0
$898$	−17540.3	+	53983.5i	−0.651813	+	2.00607i
$899$	21262.6			0.788819
$900$		0			0
$901$	19153.6			0.708211
$902$	−2969.40	+	9138.86i	−0.109612	+	0.337351i
$903$		0			0
$904$	2178.29	+	1582.62i	0.0801424	+	0.0582268i
$905$	−13458.0	−	39961.9i	−0.494319	−	1.46782i
$906$		0			0
$907$	−11306.3			−0.413912			−0.206956	−	0.978350i	$-0.566356\pi$
$907$	−11306.3			−0.413912			−0.206956	+	0.978350i	$0.566356\pi$
$908$	−35134.7	+	25526.9i	−1.28413	+	0.932973i
$909$		0			0
$910$	3506.82	−	11198.5i	0.127747	−	0.407942i
$911$	2958.31	−	9104.73i	0.107588	−	0.331123i	−0.882741	−	0.469860i	$-0.844304\pi$
$911$	2958.31	−	9104.73i	0.107588	−	0.331123i	0.990329	+	0.138737i	$0.0443043\pi$
$912$		0			0
$913$	191.085	+	588.100i	0.00692662	+	0.0213179i
$914$	−17949.7	+	55243.4i	−0.649587	+	1.99922i
$915$		0			0
$916$	−4523.84	−	13922.9i	−0.163179	−	0.502213i
$917$	2545.93	−	1849.73i	0.0916839	−	0.0666123i
$918$		0			0
$919$	−24082.4	+	17496.9i	−0.864423	+	0.628040i	−0.929085	−	0.369867i	$-0.879403\pi$
$919$	−24082.4	+	17496.9i	−0.864423	+	0.628040i	0.0646620	+	0.997907i	$0.479403\pi$
$920$	5612.34	−	59.9509i	0.201123	−	0.00214839i
$921$		0			0
$922$	−11629.8	−	8449.57i	−0.415410	−	0.301813i
$923$	−7444.28	+	22911.1i	−0.265473	+	0.817041i
$924$		0			0
$925$	7132.91	−	23661.2i	0.253545	−	0.841054i
$926$	−53885.6			−1.91230
$927$		0			0
$928$	−49287.9	−	35809.8i	−1.74349	−	1.26672i
$929$	4596.53	+	3339.57i	0.162333	+	0.117942i	0.665986	−	0.745964i	$-0.268011\pi$
$929$	4596.53	+	3339.57i	0.162333	+	0.117942i	−0.503653	+	0.863906i	$0.668011\pi$
$930$		0			0
$931$	19771.3	−	14364.7i	0.696002	−	0.505675i
$932$	−92.8909			−0.00326474
$933$		0			0
$934$	−329.955	−	1015.50i	−0.0115594	−	0.0355761i
$935$	49809.9	−	532.068i	1.74220	−	0.0186101i
$936$		0			0
$937$	7040.36	+	21668.0i	0.245463	+	0.755456i	0.995560	+	0.0941287i	$0.0300065\pi$
$937$	7040.36	+	21668.0i	0.245463	+	0.755456i	−0.750098	+	0.661327i	$0.769993\pi$
$938$	7224.75	+	22235.5i	0.251489	+	0.774002i
$939$		0			0
$940$	−8524.63	+	91.0599i	−0.295790	+	0.00315962i
$941$	−12872.8	−	39618.5i	−0.445954	−	1.37251i	−0.881434	−	0.472307i	$-0.843421\pi$
$941$	−12872.8	−	39618.5i	−0.445954	−	1.37251i	0.435480	−	0.900198i	$-0.356579\pi$
$942$		0			0
$943$	−8789.30			−0.303520
$944$	25725.2	−	18690.5i	0.886954	−	0.644410i
$945$		0			0
$946$	−29447.3	−	21394.7i	−1.01206	−	0.735308i
$947$	−17508.0	−	12720.3i	−0.600776	−	0.436489i	0.245379	−	0.969427i	$-0.421088\pi$
$947$	−17508.0	−	12720.3i	−0.600776	−	0.436489i	−0.846154	+	0.532938i	$0.821088\pi$
$948$		0			0
$949$	7595.91			0.259825
$950$	11316.8	−	37539.9i	0.386490	−	1.28206i
$951$		0			0
$952$	625.491	−	1925.06i	0.0212944	−	0.0655374i
$953$	33254.6	+	24160.9i	1.13035	+	0.821245i	0.985745	−	0.168244i	$-0.0538098\pi$
$953$	33254.6	+	24160.9i	1.13035	+	0.821245i	0.144602	+	0.989490i	$0.453810\pi$
$954$		0			0
$955$	23556.7	−	251.632i	0.798196	−	0.00852630i
$956$	73.3038	−	53.2583i	0.00247993	−	0.00180178i
$957$		0			0
$958$	−46706.1	+	33934.0i	−1.57516	+	1.14442i
$959$	2703.05	+	8319.14i	0.0910179	+	0.280124i
$960$		0			0
$961$	−6914.31	+	21280.0i	−0.232094	+	0.714311i
$962$	−10211.1	−	31426.6i	−0.342224	−	1.05326i
$963$		0			0
$964$	14970.2	−	46073.5i	0.500163	−	1.53934i
$965$	12569.2	−	40138.0i	0.419293	−	1.33895i
$966$		0			0
$967$	−16333.9	+	11867.3i	−0.543189	+	0.394650i	−0.825268	−	0.564741i	$-0.808976\pi$
$967$	−16333.9	+	11867.3i	−0.543189	+	0.394650i	0.282079	+	0.959391i	$0.408976\pi$
$968$	−1966.79			−0.0653047
$969$		0			0
$970$	18086.5	+	53705.8i	0.598684	+	1.77772i
$971$	−18649.6	−	13549.7i	−0.616369	−	0.447818i	0.235282	−	0.971927i	$-0.424399\pi$
$971$	−18649.6	−	13549.7i	−0.616369	−	0.447818i	−0.851651	+	0.524109i	$0.824399\pi$
$972$		0			0
$973$	1807.94	−	5564.28i	0.0595684	−	0.183333i
$974$	67348.9			2.21560
$975$		0			0
$976$	−38869.7			−1.27478
$977$	3654.77	−	11248.2i	0.119679	−	0.368335i	−0.873215	−	0.487335i	$-0.837969\pi$
$977$	3654.77	−	11248.2i	0.119679	−	0.368335i	0.992894	+	0.119000i	$0.0379690\pi$
$978$		0			0
$979$	−16520.3	−	12002.7i	−0.539315	−	0.391836i
$980$	−19562.3	+	14534.6i	−0.637648	+	0.473767i
$981$		0			0
$982$	38402.3			1.24793
$983$	47814.5	−	34739.2i	1.55142	−	1.12717i	0.608788	−	0.793333i	$-0.291656\pi$
$983$	47814.5	−	34739.2i	1.55142	−	1.12717i	0.942630	−	0.333839i	$-0.108344\pi$
$984$		0			0
$985$	33957.8	−	25230.4i	1.09846	−	0.816148i
$986$	30016.2	−	92380.4i	0.969483	−	2.98376i
$987$		0			0
$988$	−7663.09	−	23584.6i	−0.246757	−	0.759439i
$989$	10288.2	−	31663.7i	0.330783	−	1.01805i
$990$		0			0
$991$	970.100	+	2985.66i	0.0310961	+	0.0957040i	0.965400	−	0.260774i	$-0.0839776\pi$
$991$	970.100	+	2985.66i	0.0310961	+	0.0957040i	−0.934304	+	0.356478i	$0.883978\pi$
$992$	−17190.3	+	12489.5i	−0.550194	+	0.399740i
$993$		0			0
$994$	−11116.2	+	8076.36i	−0.354711	+	0.257713i
$995$	−15392.6	+	49153.8i	−0.490429	+	1.56611i
$996$		0			0
$997$	−36538.2	−	26546.6i	−1.16066	−	0.843269i	−0.170798	−	0.985306i	$-0.554635\pi$
$997$	−36538.2	−	26546.6i	−1.16066	−	0.843269i	−0.989861	+	0.142037i	$0.954635\pi$
$998$	12192.2	−	37523.9i	0.386712	−	1.19018i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.46.13	yes	64
3.2	odd	2	inner	225.4.h.d.46.4	✓	64
25.6	even	5	inner	225.4.h.d.181.13	yes	64
75.56	odd	10	inner	225.4.h.d.181.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.46.4	✓	64	3.2	odd	2	inner
225.4.h.d.46.13	yes	64	1.1	even	1	trivial
225.4.h.d.181.4	yes	64	75.56	odd	10	inner
225.4.h.d.181.13	yes	64	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.20400 - 3.70554i) q^{2} +(-5.80928 - 4.22069i) q^{4} +(-3.34114 + 10.6694i) q^{5} +6.27975 q^{7} +(2.58263 - 1.87639i) q^{8} +O(q^{10})\)	\(q+(1.20400 - 3.70554i) q^{2} +(-5.80928 - 4.22069i) q^{4} +(-3.34114 + 10.6694i) q^{5} +6.27975 q^{7} +(2.58263 - 1.87639i) q^{8} +(35.5133 + 25.2268i) q^{10} +(13.6357 - 41.9663i) q^{11} +(-13.2560 - 40.7979i) q^{13} +(7.56084 - 23.2699i) q^{14} +(-21.5951 - 66.4630i) q^{16} +(81.6862 - 59.3485i) q^{17} +(-65.1304 + 47.3200i) q^{19} +(64.4420 - 47.8798i) q^{20} +(-139.090 - 101.055i) q^{22} +(48.5949 - 149.560i) q^{23} +(-102.674 - 71.2962i) q^{25} -167.138 q^{26} +(-36.4808 - 26.5049i) q^{28} +(199.754 + 145.129i) q^{29} +(69.6687 - 50.6173i) q^{31} -246.744 q^{32} +(-121.568 - 374.147i) q^{34} +(-20.9815 + 67.0014i) q^{35} +(61.0938 + 188.027i) q^{37} +(96.9290 + 298.317i) q^{38} +(11.3911 + 33.8245i) q^{40} +(-17.2714 - 53.1560i) q^{41} +211.713 q^{43} +(-256.340 + 186.242i) q^{44} +(-495.692 - 360.141i) q^{46} +(-85.9089 - 62.4165i) q^{47} -303.565 q^{49} +(-387.810 + 294.620i) q^{50} +(-95.1871 + 292.956i) q^{52} +(153.468 + 111.501i) q^{53} +(402.198 + 285.700i) q^{55} +(16.2183 - 11.7833i) q^{56} +(778.288 - 565.459i) q^{58} +(140.608 + 432.747i) q^{59} +(171.878 - 528.986i) q^{61} +(-103.683 - 319.104i) q^{62} +(-124.319 + 382.615i) q^{64} +(479.580 - 5.12286i) q^{65} +(-773.054 + 561.657i) q^{67} -725.030 q^{68} +(223.015 + 158.418i) q^{70} +(-454.325 - 330.086i) q^{71} +(-54.7181 + 168.405i) q^{73} +770.300 q^{74} +578.084 q^{76} +(85.6286 - 263.538i) q^{77} +(-769.301 - 558.930i) q^{79} +(781.275 - 8.34556i) q^{80} -217.767 q^{82} +(-11.3373 + 8.23700i) q^{83} +(360.290 + 1069.84i) q^{85} +(254.903 - 784.511i) q^{86} +(-43.5293 - 133.970i) q^{88} +(143.004 - 440.120i) q^{89} +(-83.2445 - 256.200i) q^{91} +(-913.547 + 663.731i) q^{92} +(-334.722 + 243.189i) q^{94} +(-287.268 - 853.007i) q^{95} +(1052.46 + 764.659i) q^{97} +(-365.493 + 1124.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 64 * q - 72 * q^4 + 20 * q^7	\( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

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