LMFDB - Embedded newform 108.4.h.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	108.71
Dual form			108.4.h.b.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.71307 - 0.799546i) q^{2} +(6.72145 + 4.33844i) q^{4} +(14.2911 + 8.25096i) q^{5} +(-19.2620 + 11.1209i) q^{7} +(-14.7670 - 17.1446i) q^{8} +O(q^{10})$	\(q+(-2.71307 - 0.799546i) q^{2} +(6.72145 + 4.33844i) q^{4} +(14.2911 + 8.25096i) q^{5} +(-19.2620 + 11.1209i) q^{7} +(-14.7670 - 17.1446i) q^{8} +(-32.1756 - 33.8118i) q^{10} +(-6.37655 - 11.0445i) q^{11} +(-11.1766 + 19.3584i) q^{13} +(61.1508 - 14.7709i) q^{14} +(26.3558 + 58.3213i) q^{16} +117.295i q^{17} +27.7307i q^{19} +(60.2605 + 117.459i) q^{20} +(8.46941 + 35.0629i) q^{22} +(-17.5836 + 30.4556i) q^{23} +(73.6567 + 127.577i) q^{25} +(45.8008 - 43.5845i) q^{26} +(-177.716 - 8.81837i) q^{28} +(-1.01189 + 0.584217i) q^{29} +(119.361 + 68.9130i) q^{31} +(-24.8745 - 179.302i) q^{32} +(93.7830 - 318.230i) q^{34} -367.033 q^{35} +233.596 q^{37} +(22.1720 - 75.2352i) q^{38} +(-69.5764 - 366.856i) q^{40} +(-13.2561 - 7.65340i) q^{41} +(-361.460 + 208.689i) q^{43} +(5.05631 - 101.900i) q^{44} +(72.0561 - 68.5693i) q^{46} +(116.494 + 201.773i) q^{47} +(75.8499 - 131.376i) q^{49} +(-97.8316 - 405.017i) q^{50} +(-159.109 + 81.6278i) q^{52} -180.951i q^{53} -210.451i q^{55} +(475.105 + 166.017i) q^{56} +(3.21244 - 0.775964i) q^{58} +(313.716 - 543.373i) q^{59} +(-382.110 - 661.834i) q^{61} +(-268.735 - 282.400i) q^{62} +(-75.8742 + 506.347i) q^{64} +(-319.452 + 184.435i) q^{65} +(113.463 + 65.5077i) q^{67} +(-508.879 + 788.395i) q^{68} +(995.785 + 293.460i) q^{70} -22.6910 q^{71} +387.864 q^{73} +(-633.762 - 186.771i) q^{74} +(-120.308 + 186.390i) q^{76} +(245.650 + 141.826i) q^{77} +(486.411 - 280.830i) q^{79} +(-104.553 + 1050.93i) q^{80} +(29.8454 + 31.3630i) q^{82} +(342.111 + 592.554i) q^{83} +(-967.799 + 1676.28i) q^{85} +(1147.52 - 277.183i) q^{86} +(-95.1915 + 272.417i) q^{88} -278.003i q^{89} -497.177i q^{91} +(-250.317 + 128.421i) q^{92} +(-154.728 - 640.565i) q^{94} +(-228.805 + 396.302i) q^{95} +(-264.443 - 458.028i) q^{97} +(-310.827 + 295.786i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) $ 24 * q - 12 * q^4 + 72 * q^5	$ 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.71307	−	0.799546i	−0.959214	−	0.282682i
$2$	−2.71307	−	0.799546i	−0.959214	−	0.282682i
$3$		0			0
$3$		0			0
$4$	6.72145	+	4.33844i	0.840181	+	0.542305i
$5$	14.2911	+	8.25096i	1.27823	+	0.737988i	0.976523	−	0.215411i	$-0.0691093\pi$
$5$	14.2911	+	8.25096i	1.27823	+	0.737988i	0.301710	+	0.953400i	$0.402443\pi$
$6$		0			0
$7$	−19.2620	+	11.1209i	−1.04005	+	0.600473i	−0.919848	−	0.392276i	$-0.871688\pi$
$7$	−19.2620	+	11.1209i	−1.04005	+	0.600473i	−0.120203	+	0.992749i	$0.538355\pi$
$8$	−14.7670	−	17.1446i	−0.652613	−	0.757691i
$9$		0			0
$10$	−32.1756	−	33.8118i	−1.01748	−	1.06922i
$11$	−6.37655	−	11.0445i	−0.174782	−	0.302732i	0.765304	−	0.643669i	$-0.222589\pi$
$11$	−6.37655	−	11.0445i	−0.174782	−	0.302732i	−0.940086	+	0.340938i	$0.889255\pi$
$12$		0			0
$13$	−11.1766	+	19.3584i	−0.238449	+	0.413005i	−0.960269	−	0.279075i	$-0.909972\pi$
$13$	−11.1766	+	19.3584i	−0.238449	+	0.413005i	0.721821	+	0.692080i	$0.243306\pi$
$14$	61.1508	−	14.7709i	1.16737	−	0.281978i
$15$		0			0
$16$	26.3558	+	58.3213i	0.411810	+	0.911270i
$17$			117.295i			1.67343i	0.547639	+	0.836715i	$0.315527\pi$
$17$			117.295i			1.67343i	−0.547639	+	0.836715i	$0.684473\pi$
$18$		0			0
$19$			27.7307i			0.334835i	0.985886	+	0.167417i	$0.0535427\pi$
$19$			27.7307i			0.334835i	−0.985886	+	0.167417i	$0.946457\pi$
$20$	60.2605	+	117.459i	0.673733	+	1.31324i
$21$		0			0
$22$	8.46941	+	35.0629i	0.0820766	+	0.339792i
$23$	−17.5836	+	30.4556i	−0.159410	+	0.276106i	−0.934656	−	0.355553i	$-0.884292\pi$
$23$	−17.5836	+	30.4556i	−0.159410	+	0.276106i	0.775246	+	0.631659i	$0.217626\pi$
$24$		0			0
$25$	73.6567	+	127.577i	0.589254	+	1.02062i
$26$	45.8008	−	43.5845i	0.345472	−	0.328755i
$27$		0			0
$28$	−177.716	−	8.81837i	−1.19947	−	0.0595184i
$29$	−1.01189	+	0.584217i	−0.00647945	+	0.00374091i	−0.503236	−	0.864149i	$-0.667857\pi$
$29$	−1.01189	+	0.584217i	−0.00647945	+	0.00374091i	0.496757	+	0.867890i	$0.334524\pi$
$30$		0			0
$31$	119.361	+	68.9130i	0.691543	+	0.399263i	0.804190	−	0.594373i	$-0.202600\pi$
$31$	119.361	+	68.9130i	0.691543	+	0.399263i	−0.112647	+	0.993635i	$0.535933\pi$
$32$	−24.8745	−	179.302i	−0.137414	−	0.990514i
$33$		0			0
$34$	93.7830	−	318.230i	0.473049	−	1.60518i
$35$	−367.033			−1.77257
$36$		0			0
$37$	233.596			1.03792			0.518959	−	0.854799i	$-0.326320\pi$
$37$	233.596			1.03792			0.518959	+	0.854799i	$0.326320\pi$
$38$	22.1720	−	75.2352i	0.0946518	−	0.321178i
$39$		0			0
$40$	−69.5764	−	366.856i	−0.275025	−	1.45013i
$41$	−13.2561	−	7.65340i	−0.0504940	−	0.0291527i	0.474541	−	0.880234i	$-0.342614\pi$
$41$	−13.2561	−	7.65340i	−0.0504940	−	0.0291527i	−0.525034	+	0.851081i	$0.675948\pi$
$42$		0			0
$43$	−361.460	+	208.689i	−1.28191	+	0.740112i	−0.977198	−	0.212332i	$-0.931894\pi$
$43$	−361.460	+	208.689i	−1.28191	+	0.740112i	−0.304714	+	0.952444i	$0.598561\pi$
$44$	5.05631	−	101.900i	0.0173243	−	0.349135i
$45$		0			0
$46$	72.0561	−	68.5693i	0.230958	−	0.219782i
$47$	116.494	+	201.773i	0.361539	+	0.626204i	0.988214	−	0.153076i	$-0.0489180\pi$
$47$	116.494	+	201.773i	0.361539	+	0.626204i	−0.626675	+	0.779281i	$0.715585\pi$
$48$		0			0
$49$	75.8499	−	131.376i	0.221137	−	0.383020i
$50$	−97.8316	−	405.017i	−0.276710	−	1.14556i
$51$		0			0
$52$	−159.109	+	81.6278i	−0.424315	+	0.217687i
$53$		−	180.951i		−	0.468972i	−0.972120	−	0.234486i	$-0.924659\pi$
$53$		−	180.951i		−	0.468972i	0.972120	−	0.234486i	$-0.0753407\pi$
$54$		0			0
$55$		−	210.451i		−	0.515949i
$56$	475.105	+	166.017i	1.13372	+	0.396160i
$57$		0			0
$58$	3.21244	−	0.775964i	0.00727266	−	0.00175671i
$59$	313.716	−	543.373i	0.692244	−	1.19900i	−0.278857	−	0.960333i	$-0.589955\pi$
$59$	313.716	−	543.373i	0.692244	−	1.19900i	0.971101	−	0.238669i	$-0.0767112\pi$
$60$		0			0
$61$	−382.110	−	661.834i	−0.802035	−	1.38917i	−0.918274	−	0.395945i	$-0.870417\pi$
$61$	−382.110	−	661.834i	−0.802035	−	1.38917i	0.116239	−	0.993221i	$-0.462916\pi$
$62$	−268.735	−	282.400i	−0.550473	−	0.578465i
$63$		0			0
$64$	−75.8742	+	506.347i	−0.148192	+	0.988959i
$65$	−319.452	+	184.435i	−0.609586	+	0.351945i
$66$		0			0
$67$	113.463	+	65.5077i	0.206891	+	0.119448i	0.599866	−	0.800101i	$-0.295221\pi$
$67$	113.463	+	65.5077i	0.206891	+	0.119448i	−0.392975	+	0.919549i	$0.628554\pi$
$68$	−508.879	+	788.395i	−0.907510	+	1.40598i
$69$		0			0
$70$	995.785	+	293.460i	1.70027	+	0.501074i
$71$	−22.6910			−0.0379285			−0.0189643	−	0.999820i	$-0.506037\pi$
$71$	−22.6910			−0.0379285			−0.0189643	+	0.999820i	$0.506037\pi$
$72$		0			0
$73$	387.864			0.621863			0.310932	−	0.950432i	$-0.399359\pi$
$73$	387.864			0.621863			0.310932	+	0.950432i	$0.399359\pi$
$74$	−633.762	−	186.771i	−0.995586	−	0.293401i
$75$		0			0
$76$	−120.308	+	186.390i	−0.181583	+	0.281322i
$77$	245.650	+	141.826i	0.363565	+	0.209904i
$78$		0			0
$79$	486.411	−	280.830i	0.692729	−	0.399947i	−0.111905	−	0.993719i	$-0.535695\pi$
$79$	486.411	−	280.830i	0.692729	−	0.399947i	0.804633	+	0.593772i	$0.202362\pi$
$80$	−104.553	+	1050.93i	−0.146118	+	1.46873i
$81$		0			0
$82$	29.8454	+	31.3630i	0.0401935	+	0.0422374i
$83$	342.111	+	592.554i	0.452429	+	0.783629i	0.998536	−	0.0540856i	$-0.0172244\pi$
$83$	342.111	+	592.554i	0.452429	+	0.783629i	−0.546108	+	0.837715i	$0.683891\pi$
$84$		0			0
$85$	−967.799	+	1676.28i	−1.23497	+	2.13903i
$86$	1147.52	−	277.183i	1.43884	−	0.347552i
$87$		0			0
$88$	−95.1915	+	272.417i	−0.115312	+	0.329998i
$89$		−	278.003i		−	0.331103i	−0.986201	−	0.165552i	$-0.947060\pi$
$89$		−	278.003i		−	0.331103i	0.986201	−	0.165552i	$-0.0529405\pi$
$90$		0			0
$91$		−	497.177i		−	0.572728i
$92$	−250.317	+	128.421i	−0.283667	+	0.145530i
$93$		0			0
$94$	−154.728	−	640.565i	−0.169776	−	0.702865i
$95$	−228.805	+	396.302i	−0.247104	+	0.427997i
$96$		0			0
$97$	−264.443	−	458.028i	−0.276805	−	0.479440i	0.693784	−	0.720183i	$-0.255942\pi$
$97$	−264.443	−	458.028i	−0.276805	−	0.479440i	−0.970589	+	0.240743i	$0.922609\pi$
$98$	−310.827	+	295.786i	−0.320390	+	0.304887i
$99$		0			0
$100$	−58.4063	+	1177.06i	−0.0584063	+	1.17706i
$101$	1241.84	−	716.977i	1.22344	−	0.706355i	0.257793	−	0.966200i	$-0.417005\pi$
$101$	1241.84	−	716.977i	1.22344	−	0.706355i	0.965650	+	0.259845i	$0.0836714\pi$
$102$		0			0
$103$	199.095	+	114.948i	0.190460	+	0.109962i	0.592198	−	0.805792i	$-0.298260\pi$
$103$	199.095	+	114.948i	0.190460	+	0.109962i	−0.401738	+	0.915755i	$0.631594\pi$
$104$	496.937	−	94.2469i	0.468545	−	0.0888622i
$105$		0			0
$106$	−144.679	+	490.932i	−0.132570	+	0.449844i
$107$	1676.13			1.51437			0.757184	−	0.653201i	$-0.226574\pi$
$107$	1676.13			1.51437			0.757184	+	0.653201i	$0.226574\pi$
$108$		0			0
$109$	−540.666			−0.475104			−0.237552	−	0.971375i	$-0.576345\pi$
$109$	−540.666			−0.475104			−0.237552	+	0.971375i	$0.576345\pi$
$110$	−168.265	+	570.967i	−0.145850	+	0.494905i
$111$		0			0
$112$	−1156.25	−	830.284i	−0.975496	−	0.700486i
$113$	−1110.83	−	641.340i	−0.924764	−	0.533913i	−0.0396123	−	0.999215i	$-0.512612\pi$
$113$	−1110.83	−	641.340i	−0.924764	−	0.533913i	−0.885152	+	0.465302i	$0.845946\pi$
$114$		0			0
$115$	−502.576	+	290.163i	−0.407526	+	0.235285i
$116$	−9.33599	−	0.463257i	−0.00747263	−	0.000370796i
$117$		0			0
$118$	−1285.59	+	1223.38i	−1.00295	+	0.954414i
$119$	−1304.43	−	2259.34i	−1.00485	−	1.74045i
$120$		0			0
$121$	584.179	−	1011.83i	0.438902	−	0.760201i
$122$	507.523	+	2101.11i	0.376631	+	1.55923i
$123$		0			0
$124$	503.303	+	981.035i	0.364499	+	0.710480i
$125$			368.214i			0.263472i
$126$		0			0
$127$		−	2674.79i		−	1.86889i	−0.356109	−	0.934444i	$-0.615897\pi$
$127$		−	2674.79i		−	1.86889i	0.356109	−	0.934444i	$-0.384103\pi$
$128$	610.699	−	1313.09i	0.421709	−	0.906731i
$129$		0			0
$130$	1014.16	−	244.969i	0.684212	−	0.165271i
$131$	−413.401	+	716.031i	−0.275717	+	0.477557i	−0.970316	−	0.241841i	$-0.922249\pi$
$131$	−413.401	+	716.031i	−0.275717	+	0.477557i	0.694598	+	0.719398i	$0.255582\pi$
$132$		0			0
$133$	−308.391	−	534.149i	−0.201059	−	0.348245i
$134$	−255.455	−	268.446i	−0.164686	−	0.173061i
$135$		0			0
$136$	2010.98	−	1732.09i	1.26794	−	1.09210i
$137$	−560.929	+	323.852i	−0.349806	+	0.201960i	−0.664600	−	0.747200i	$-0.731398\pi$
$137$	−560.929	+	323.852i	−0.349806	+	0.201960i	0.314794	+	0.949160i	$0.398065\pi$
$138$		0			0
$139$	2312.71	+	1335.24i	1.41124	+	0.814777i	0.995505	−	0.0947110i	$-0.0301927\pi$
$139$	2312.71	+	1335.24i	1.41124	+	0.814777i	0.415730	+	0.909488i	$0.363526\pi$
$140$	−2467.00	−	1592.35i	−1.48928	−	0.961274i
$141$		0			0
$142$	61.5622	+	18.1425i	0.0363816	+	0.0107217i
$143$	285.073			0.166706
$144$		0			0
$145$	−19.2814			−0.0110430
$146$	−1052.30	−	310.115i	−0.596500	−	0.175790i
$147$		0			0
$148$	1570.11	+	1013.44i	0.872040	+	0.562869i
$149$	90.2485	+	52.1050i	0.0496204	+	0.0286484i	0.524605	−	0.851346i	$-0.324213\pi$
$149$	90.2485	+	52.1050i	0.0496204	+	0.0286484i	−0.474985	+	0.879994i	$0.657546\pi$
$150$		0			0
$151$	−2382.77	+	1375.69i	−1.28415	+	0.741407i	−0.977605	−	0.210448i	$-0.932508\pi$
$151$	−2382.77	+	1375.69i	−1.28415	+	0.741407i	−0.306549	+	0.951855i	$0.599174\pi$
$152$	475.431	−	409.498i	0.253701	−	0.218517i
$153$		0			0
$154$	−553.069	−	581.193i	−0.289400	−	0.304116i
$155$	1137.20	+	1969.68i	0.589302	+	1.02070i
$156$		0			0
$157$	581.545	−	1007.27i	0.295620	−	0.512029i	−0.679509	−	0.733667i	$-0.737807\pi$
$157$	581.545	−	1007.27i	0.295620	−	0.512029i	0.975129	+	0.221638i	$0.0711404\pi$
$158$	−1544.20	+	373.001i	−0.777533	+	0.187812i
$159$		0			0
$160$	1123.93	−	2767.66i	0.555341	−	1.36752i
$161$		−	782.182i		−	0.382886i
$162$		0			0
$163$			2930.45i			1.40816i	0.710120	+	0.704081i	$0.248641\pi$
$163$			2930.45i			1.40816i	−0.710120	+	0.704081i	$0.751359\pi$
$164$	−55.8963	−	108.953i	−0.0266144	−	0.0518767i
$165$		0			0
$166$	−454.396	−	1881.17i	−0.212458	−	0.879562i
$167$	−435.960	+	755.105i	−0.202010	+	0.349891i	−0.949176	−	0.314746i	$-0.898081\pi$
$167$	−435.960	+	755.105i	−0.202010	+	0.349891i	0.747166	+	0.664637i	$0.231414\pi$
$168$		0			0
$169$	848.667	+	1469.93i	0.386284	+	0.669064i
$170$	3965.96	−	3774.05i	1.78927	−	1.70268i
$171$		0			0
$172$	−3334.92	−	165.481i	−1.47840	−	0.0733592i
$173$	−2020.19	+	1166.36i	−0.887816	+	0.512581i	−0.873227	−	0.487313i	$-0.837977\pi$
$173$	−2020.19	+	1166.36i	−0.887816	+	0.512581i	−0.0145882	+	0.999894i	$0.504644\pi$
$174$		0			0
$175$	−2837.55	−	1638.26i	−1.22571	−	0.707662i
$176$	476.071	−	662.976i	0.203893	−	0.283941i
$177$		0			0
$178$	−222.276	+	754.239i	−0.0935971	+	0.317599i
$179$	−638.773			−0.266727			−0.133364	−	0.991067i	$-0.542578\pi$
$179$	−638.773			−0.266727			−0.133364	+	0.991067i	$0.542578\pi$
$180$		0			0
$181$	4031.01			1.65537			0.827686	−	0.561192i	$-0.189657\pi$
$181$	4031.01			1.65537			0.827686	+	0.561192i	$0.189657\pi$
$182$	−397.516	+	1348.87i	−0.161900	+	0.549369i
$183$		0			0
$184$	781.805	−	148.274i	0.313236	−	0.0594070i
$185$	3338.34	+	1927.39i	1.32670	+	0.765972i
$186$		0			0
$187$	1295.47	−	747.940i	0.506600	−	0.292486i
$188$	−92.3740	+	1861.61i	−0.0358355	+	0.722190i
$189$		0			0
$190$	937.624	−	892.252i	0.358013	−	0.340688i
$191$	−1831.72	−	3172.63i	−0.693918	−	1.20190i	−0.970544	−	0.240924i	$-0.922550\pi$
$191$	−1831.72	−	3172.63i	−0.693918	−	1.20190i	0.276626	−	0.960978i	$-0.410784\pi$
$192$		0			0
$193$	−708.828	+	1227.73i	−0.264366	+	0.457895i	−0.967397	−	0.253264i	$-0.918496\pi$
$193$	−708.828	+	1227.73i	−0.264366	+	0.457895i	0.703032	+	0.711159i	$0.251829\pi$
$194$	351.236	+	1454.10i	0.129986	+	0.538134i
$195$		0			0
$196$	1079.79	−	553.966i	0.393509	−	0.201883i
$197$			876.917i			0.317146i	0.987347	+	0.158573i	$0.0506893\pi$
$197$			876.917i			0.317146i	−0.987347	+	0.158573i	$0.949311\pi$
$198$		0			0
$199$			1485.45i			0.529149i	0.964365	+	0.264574i	$0.0852315\pi$
$199$			1485.45i			0.529149i	−0.964365	+	0.264574i	$0.914769\pi$
$200$	1099.57	−	3146.74i	0.388758	−	1.11254i
$201$		0			0
$202$	−3942.45	+	952.297i	−1.37322	+	0.331700i
$203$	12.9941	−	22.5064i	0.00449263	−	0.00778147i
$204$		0			0
$205$	−126.296	−	218.751i	−0.0430287	−	0.0745279i
$206$	−448.252	−	471.046i	−0.151608	−	0.159317i
$207$		0			0
$208$	−1423.58	−	141.626i	−0.474555	−	0.0472116i
$209$	306.272	−	176.826i	0.101365	−	0.0585231i
$210$		0			0
$211$	266.434	+	153.826i	0.0869294	+	0.0501887i	0.542835	−	0.839840i	$-0.317351\pi$
$211$	266.434	+	153.826i	0.0869294	+	0.0501887i	−0.455905	+	0.890028i	$0.650684\pi$
$212$	785.045	−	1216.25i	0.254326	−	0.394021i
$213$		0			0
$214$	−4547.45	−	1340.14i	−1.45260	−	0.428085i
$215$	−6887.55			−2.18478
$216$		0			0
$217$	−3065.50			−0.958986
$218$	1466.86	+	432.287i	0.455727	+	0.134304i
$219$		0			0
$220$	913.029	−	1414.53i	0.279802	−	0.433491i
$221$	−2270.66	−	1310.96i	−0.691135	−	0.399027i
$222$		0			0
$223$	3380.52	−	1951.74i	1.01514	−	0.586091i	0.102447	−	0.994738i	$-0.467333\pi$
$223$	3380.52	−	1951.74i	1.01514	−	0.586091i	0.912692	+	0.408647i	$0.133999\pi$
$224$	2473.14	+	3177.09i	0.737694	+	0.947671i
$225$		0			0
$226$	2500.98	+	2628.16i	0.736119	+	0.773551i
$227$	964.382	+	1670.36i	0.281975	+	0.488394i	0.971871	−	0.235514i	$-0.0756773\pi$
$227$	964.382	+	1670.36i	0.281975	+	0.488394i	−0.689896	+	0.723908i	$0.742344\pi$
$228$		0			0
$229$	−1148.71	+	1989.62i	−0.331479	+	0.574139i	−0.982802	−	0.184662i	$-0.940881\pi$
$229$	−1148.71	+	1989.62i	−0.331479	+	0.574139i	0.651323	+	0.758801i	$0.274214\pi$
$230$	1595.52	−	385.397i	0.457416	−	0.110488i
$231$		0			0
$232$	24.9588	+	8.72140i	0.00706303	+	0.00246805i
$233$			3366.60i			0.946580i	0.880907	+	0.473290i	$0.156934\pi$
$233$			3366.60i			0.946580i	−0.880907	+	0.473290i	$0.843066\pi$
$234$		0			0
$235$			3844.74i			1.06725i
$236$	4466.02	−	2291.21i	1.23184	−	0.631972i
$237$		0			0
$238$	1732.56	+	7172.70i	0.471871	+	1.95352i
$239$	307.571	−	532.729i	0.0832432	−	0.144182i	−0.821398	−	0.570355i	$-0.806805\pi$
$239$	307.571	−	532.729i	0.0832432	−	0.144182i	0.904641	+	0.426174i	$0.140139\pi$
$240$		0			0
$241$	2195.78	+	3803.20i	0.586898	+	1.01654i	0.994636	+	0.103438i	$0.0329844\pi$
$241$	2195.78	+	3803.20i	0.586898	+	1.01654i	−0.407738	+	0.913099i	$0.633682\pi$
$242$	−2393.92	+	2278.08i	−0.635897	+	0.605125i
$243$		0			0
$244$	302.995	−	6106.25i	0.0794971	−	1.60210i
$245$	2167.95	−	1251.67i	0.565329	−	0.326393i
$246$		0			0
$247$	−536.823	−	309.935i	−0.138288	−	0.0798408i
$248$	−581.110	−	3064.03i	−0.148792	−	0.784540i
$249$		0			0
$250$	294.404	−	998.988i	0.0744790	−	0.252726i
$251$	7726.08			1.94289			0.971446	−	0.237259i	$-0.0762489\pi$
$251$	7726.08			1.94289			0.971446	+	0.237259i	$0.0762489\pi$
$252$		0			0
$253$	448.490			0.111448
$254$	−2138.62	+	7256.87i	−0.528302	+	1.79266i
$255$		0			0
$256$	−2706.74	+	3074.21i	−0.660826	+	0.750539i
$257$	2222.83	+	1283.35i	0.539518	+	0.311491i	0.744884	−	0.667194i	$-0.232505\pi$
$257$	2222.83	+	1283.35i	0.539518	+	0.311491i	−0.205365	+	0.978685i	$0.565838\pi$
$258$		0			0
$259$	−4499.53	+	2597.81i	−1.07949	+	0.623243i
$260$	−2947.34	−	146.249i	−0.703024	−	0.0348844i
$261$		0			0
$262$	1694.08	−	1612.11i	0.399469	−	0.380138i
$263$	2003.92	+	3470.89i	0.469837	+	0.813781i	0.999405	−	0.0344862i	$-0.0109795\pi$
$263$	2003.92	+	3470.89i	0.469837	+	0.813781i	−0.529569	+	0.848267i	$0.677646\pi$
$264$		0			0
$265$	1493.02	−	2585.98i	0.346096	−	0.599456i
$266$	409.608	+	1695.75i	0.0944161	+	0.390877i
$267$		0			0
$268$	478.433	+	932.559i	0.109048	+	0.212556i
$269$			2242.21i			0.508214i	0.967176	+	0.254107i	$0.0817816\pi$
$269$			2242.21i			0.508214i	−0.967176	+	0.254107i	$0.918218\pi$
$270$		0			0
$271$		−	6324.08i		−	1.41757i	−0.705426	−	0.708784i	$-0.749244\pi$
$271$		−	6324.08i		−	1.41757i	0.705426	−	0.708784i	$-0.250756\pi$
$272$	−6840.81	+	3091.41i	−1.52495	+	0.689134i
$273$		0			0
$274$	1780.77	−	430.144i	0.392629	−	0.0948393i
$275$	939.352	−	1627.01i	0.205982	−	0.356771i
$276$		0			0
$277$	−625.852	−	1084.01i	−0.135754	−	0.235132i	0.790131	−	0.612938i	$-0.210012\pi$
$277$	−625.852	−	1084.01i	−0.135754	−	0.235132i	−0.925885	+	0.377805i	$0.876679\pi$
$278$	−5206.95	−	5471.73i	−1.12335	−	1.18048i
$279$		0			0
$280$	5419.96	+	6292.64i	1.15680	+	1.34306i
$281$	1190.34	−	687.240i	0.252703	−	0.145898i	−0.368298	−	0.929708i	$-0.620060\pi$
$281$	1190.34	−	687.240i	0.252703	−	0.145898i	0.621001	+	0.783810i	$0.286726\pi$
$282$		0			0
$283$	−4006.16	−	2312.96i	−0.841490	−	0.485835i	0.0162801	−	0.999867i	$-0.494818\pi$
$283$	−4006.16	−	2312.96i	−0.841490	−	0.485835i	−0.857771	+	0.514033i	$0.828151\pi$
$284$	−152.516	−	98.4436i	−0.0318669	−	0.0205689i
$285$		0			0
$286$	−773.422	−	227.929i	−0.159907	−	0.0471249i
$287$	340.452			0.0700217
$288$		0			0
$289$	−8845.19			−1.80037
$290$	52.3117	+	15.4164i	0.0105926	+	0.00312166i
$291$		0			0
$292$	2607.01	+	1682.73i	0.522478	+	0.337240i
$293$	−5522.68	−	3188.52i	−1.10116	−	0.635752i	−0.164631	−	0.986355i	$-0.552643\pi$
$293$	−5522.68	−	3188.52i	−1.10116	−	0.635752i	−0.936524	+	0.350603i	$0.885977\pi$
$294$		0			0
$295$	8966.70	−	5176.92i	1.76970	−	1.02174i
$296$	−3449.51	−	4004.91i	−0.677360	−	0.786422i
$297$		0			0
$298$	−203.190	−	213.522i	−0.0394982	−	0.0415067i
$299$	−393.049	−	680.781i	−0.0760221	−	0.131674i
$300$		0			0
$301$	4641.63	−	8039.54i	0.888835	−	1.53951i
$302$	7564.55	−	1827.21i	1.44136	−	0.348160i
$303$		0			0
$304$	−1617.29	+	730.865i	−0.305125	+	0.137888i
$305$		−	12611.1i		−	2.36757i
$306$		0			0
$307$			6609.36i			1.22872i	0.789027	+	0.614359i	$0.210585\pi$
$307$			6609.36i			1.22872i	−0.789027	+	0.614359i	$0.789415\pi$
$308$	1035.82	+	2019.02i	0.191628	+	0.373521i
$309$		0			0
$310$	−1510.44	−	6253.12i	−0.276732	−	1.14566i
$311$	2568.35	−	4448.51i	0.468288	−	0.811098i	−0.531055	−	0.847337i	$-0.678204\pi$
$311$	2568.35	−	4448.51i	0.468288	−	0.811098i	0.999343	+	0.0362387i	$0.0115377\pi$
$312$		0			0
$313$	−3101.42	−	5371.82i	−0.560072	−	0.970074i	−0.997489	−	0.0708150i	$-0.977440\pi$
$313$	−3101.42	−	5371.82i	−0.560072	−	0.970074i	0.437417	−	0.899259i	$-0.355893\pi$
$314$	−2383.13	+	2267.81i	−0.428305	+	0.407579i
$315$		0			0
$316$	4487.75	+	222.685i	0.798911	+	0.0396424i
$317$	−1580.62	+	912.574i	−0.280053	+	0.161689i	−0.633447	−	0.773786i	$-0.718361\pi$
$317$	−1580.62	+	912.574i	−0.280053	+	0.161689i	0.353395	+	0.935474i	$0.385027\pi$
$318$		0			0
$319$	12.9048	+	7.45058i	0.00226498	+	0.00130769i
$320$	−5262.17	+	6610.21i	−0.919264	+	1.15476i
$321$		0			0
$322$	−625.391	+	2122.11i	−0.108235	+	0.367269i
$323$	−3252.68			−0.560322
$324$		0			0
$325$	−3292.93			−0.562027
$326$	2343.03	−	7950.49i	0.398062	−	1.35073i
$327$		0			0
$328$	64.5375	+	340.288i	0.0108643	+	0.0572843i
$329$	−4487.80	−	2591.03i	−0.752038	−	0.434189i
$330$		0			0
$331$	3444.37	−	1988.61i	0.571963	−	0.330223i	−0.185970	−	0.982555i	$-0.559543\pi$
$331$	3444.37	−	1988.61i	0.571963	−	0.330223i	0.757933	+	0.652332i	$0.226209\pi$
$332$	−271.278	+	5467.05i	−0.0448443	+	0.903745i
$333$		0			0
$334$	1786.53	−	1700.08i	0.292678	−	0.278516i
$335$	1081.00	+	1872.35i	0.176303	+	0.305366i
$336$		0			0
$337$	578.847	−	1002.59i	0.0935662	−	0.162061i	−0.815443	−	0.578837i	$-0.803507\pi$
$337$	578.847	−	1002.59i	0.0935662	−	0.162061i	0.909009	+	0.416776i	$0.136840\pi$
$338$	−1127.21	−	4666.58i	−0.181397	−	0.750971i
$339$		0			0
$340$	−13777.4	+	7068.27i	−2.19761	+	1.12744i
$341$		−	1757.71i		−	0.279136i
$342$		0			0
$343$		−	4254.87i		−	0.669800i
$344$	8915.56	+	3115.39i	1.39737	+	0.488286i
$345$		0			0
$346$	6413.46	−	1549.17i	0.996502	−	0.240704i
$347$	1241.63	−	2150.56i	0.192086	−	0.332703i	−0.753855	−	0.657041i	$-0.771808\pi$
$347$	1241.63	−	2150.56i	0.192086	−	0.332703i	0.945941	+	0.324337i	$0.105141\pi$
$348$		0			0
$349$	2986.90	+	5173.47i	0.458124	+	0.793494i	0.998862	−	0.0476973i	$-0.0151883\pi$
$349$	2986.90	+	5173.47i	0.458124	+	0.793494i	−0.540738	+	0.841191i	$0.681855\pi$
$350$	6388.60	+	6713.46i	0.975671	+	1.02528i
$351$		0			0
$352$	−1821.69	+	1418.06i	−0.275842	+	0.214724i
$353$	893.160	−	515.666i	0.134669	−	0.0777511i	−0.431152	−	0.902279i	$-0.641893\pi$
$353$	893.160	−	515.666i	0.134669	−	0.0777511i	0.565821	+	0.824528i	$0.308559\pi$
$354$		0			0
$355$	−324.279	−	187.223i	−0.0484815	−	0.0279908i
$356$	1206.10	−	1868.58i	0.179559	−	0.278187i
$357$		0			0
$358$	1733.03	+	510.729i	0.255848	+	0.0753991i
$359$	−4218.99			−0.620249			−0.310125	−	0.950696i	$-0.600371\pi$
$359$	−4218.99			−0.620249			−0.310125	+	0.950696i	$0.600371\pi$
$360$		0			0
$361$	6090.01			0.887886
$362$	−10936.4	−	3222.98i	−1.58785	−	0.467944i
$363$		0			0
$364$	2156.97	−	3341.75i	0.310594	−	0.481196i
$365$	5542.99	+	3200.25i	0.794887	+	0.458928i
$366$		0			0
$367$	−2632.91	+	1520.11i	−0.374487	+	0.216210i	−0.675417	−	0.737436i	$-0.736036\pi$
$367$	−2632.91	+	1520.11i	−0.374487	+	0.216210i	0.300930	+	0.953646i	$0.402703\pi$
$368$	−2239.64	−	222.813i	−0.317254	−	0.0315623i
$369$		0			0
$370$	−7516.11	−	7898.31i	−1.05606	−	1.10977i
$371$	2012.34	+	3485.48i	0.281605	+	0.487754i
$372$		0			0
$373$	−2558.92	+	4432.17i	−0.355216	+	0.615253i	−0.987155	−	0.159766i	$-0.948926\pi$
$373$	−2558.92	+	4432.17i	−0.355216	+	0.615253i	0.631939	+	0.775018i	$0.282259\pi$
$374$	−4112.71	+	993.422i	−0.568618	+	0.137349i
$375$		0			0
$376$	1739.06	−	4976.81i	0.238524	−	0.682604i
$377$		−	26.1183i		−	0.00356806i
$378$		0			0
$379$		−	2840.61i		−	0.384993i	−0.981298	−	0.192497i	$-0.938342\pi$
$379$		−	2840.61i		−	0.384993i	0.981298	−	0.192497i	$-0.0616585\pi$
$380$	−3257.23	+	1671.06i	−0.439717	+	0.225589i
$381$		0			0
$382$	2432.91	+	10072.1i	0.325860	+	1.34904i
$383$	−2814.33	+	4874.56i	−0.375472	+	0.650336i	−0.990397	−	0.138249i	$-0.955853\pi$
$383$	−2814.33	+	4874.56i	−0.375472	+	0.650336i	0.614926	+	0.788585i	$0.289186\pi$
$384$		0			0
$385$	2340.41	+	4053.70i	0.309814	+	0.536613i
$386$	2904.72	−	2764.16i	0.383022	−	0.364487i
$387$		0			0
$388$	209.691	−	4225.88i	0.0274367	−	0.552930i
$389$	3084.76	−	1780.99i	0.402065	−	0.232132i	−0.285309	−	0.958435i	$-0.592096\pi$
$389$	3084.76	−	1780.99i	0.402065	−	0.232132i	0.687375	+	0.726303i	$0.258763\pi$
$390$		0			0
$391$	−3572.30	−	2062.47i	−0.462044	−	0.266761i
$392$	−3372.46	+	639.606i	−0.434528	+	0.0824106i
$393$		0			0
$394$	701.135	−	2379.13i	0.0896515	−	0.304211i
$395$	9268.46			1.18062
$396$		0			0
$397$	−9427.52			−1.19182			−0.595911	−	0.803050i	$-0.703209\pi$
$397$	−9427.52			−1.19182			−0.595911	+	0.803050i	$0.703209\pi$
$398$	1187.68	−	4030.12i	0.149581	−	0.507567i
$399$		0			0
$400$	−5499.18	+	7658.15i	−0.687397	+	0.957269i
$401$	7475.17	+	4315.79i	0.930903	+	0.537457i	0.887097	−	0.461583i	$-0.152718\pi$
$401$	7475.17	+	4315.79i	0.930903	+	0.537457i	0.0438059	+	0.999040i	$0.486052\pi$
$402$		0			0
$403$	−2668.10	+	1540.43i	−0.329795	+	0.190407i
$404$	11457.5	+	568.529i	1.41097	+	0.0700133i
$405$		0			0
$406$	−53.2487	+	50.6719i	−0.00650908	+	0.00619410i
$407$	−1489.54	−	2579.96i	−0.181410	−	0.314211i
$408$		0			0
$409$	−2932.40	+	5079.07i	−0.354518	+	0.614044i	−0.987035	−	0.160503i	$-0.948688\pi$
$409$	−2932.40	+	5079.07i	−0.354518	+	0.614044i	0.632517	+	0.774546i	$0.282022\pi$
$410$	167.748	+	694.465i	0.0202060	+	0.0836516i
$411$		0			0
$412$	839.514	+	1636.38i	0.100388	+	0.195676i
$413$			13955.3i			1.66270i
$414$		0			0
$415$			11291.0i			1.33555i
$416$	3749.02	+	1522.46i	0.441853	+	0.179434i
$417$		0			0
$418$	−972.317	+	234.863i	−0.113774	+	0.0274821i
$419$	−3477.85	+	6023.82i	−0.405500	+	0.702346i	−0.994379	−	0.105875i	$-0.966236\pi$
$419$	−3477.85	+	6023.82i	−0.405500	+	0.702346i	0.588880	+	0.808221i	$0.299569\pi$
$420$		0			0
$421$	4697.89	+	8136.99i	0.543851	+	0.941978i	0.998678	+	0.0513981i	$0.0163677\pi$
$421$	4697.89	+	8136.99i	0.543851	+	0.941978i	−0.454827	+	0.890580i	$0.650299\pi$
$422$	−599.863	−	630.366i	−0.0691964	−	0.0727151i
$423$		0			0
$424$	−3102.33	+	2672.09i	−0.355336	+	0.306057i
$425$	−14964.2	+	8639.59i	−1.70793	+	0.986074i
$426$		0			0
$427$	14720.4	+	8498.83i	1.66831	+	0.963202i
$428$	11266.0	+	7271.79i	1.27234	+	0.821250i
$429$		0			0
$430$	18686.4	+	5506.91i	2.09567	+	0.617597i
$431$	−7346.03			−0.820988			−0.410494	−	0.911863i	$-0.634644\pi$
$431$	−7346.03			−0.820988			−0.410494	+	0.911863i	$0.634644\pi$
$432$		0			0
$433$	13673.0			1.51751			0.758755	−	0.651376i	$-0.225808\pi$
$433$	13673.0			1.51751			0.758755	+	0.651376i	$0.225808\pi$
$434$	8316.92	+	2451.01i	0.919873	+	0.271088i
$435$		0			0
$436$	−3634.06	−	2345.65i	−0.399174	−	0.257652i
$437$	−844.556	−	487.604i	−0.0924498	−	0.0533759i
$438$		0			0
$439$	−4995.87	+	2884.37i	−0.543144	+	0.313584i	−0.746352	−	0.665551i	$-0.768196\pi$
$439$	−4995.87	+	2884.37i	−0.543144	+	0.313584i	0.203208	+	0.979135i	$0.434863\pi$
$440$	−3608.09	+	3107.72i	−0.390930	+	0.336715i
$441$		0			0
$442$	5112.26	+	5372.22i	0.550148	+	0.578124i
$443$	−4826.45	−	8359.66i	−0.517634	−	0.896568i	−0.999790	−	0.0204826i	$-0.993480\pi$
$443$	−4826.45	−	8359.66i	−0.517634	−	0.896568i	0.482157	−	0.876085i	$-0.339854\pi$
$444$		0			0
$445$	2293.79	−	3972.96i	0.244351	−	0.423228i
$446$	−10732.1	+	2592.33i	−1.13941	+	0.275225i
$447$		0			0
$448$	−4169.56	−	10597.0i	−0.439716	−	1.11755i
$449$			11492.2i			1.20791i	0.797018	+	0.603955i	$0.206410\pi$
$449$			11492.2i			1.20791i	−0.797018	+	0.603955i	$0.793590\pi$
$450$		0			0
$451$			195.209i			0.0203815i
$452$	−4683.99	−	9130.02i	−0.487426	−	0.950088i
$453$		0			0
$454$	−1280.90	−	5302.86i	−0.132413	−	0.548184i
$455$	4102.19	−	7105.19i	0.422667	−	0.732080i
$456$		0			0
$457$	−8821.06	−	15278.5i	−0.902914	−	1.56389i	−0.823693	−	0.567036i	$-0.808090\pi$
$457$	−8821.06	−	15278.5i	−0.902914	−	1.56389i	−0.0792214	−	0.996857i	$-0.525243\pi$
$458$	4707.31	−	4479.53i	0.480258	−	0.457018i
$459$		0			0
$460$	−4636.90	−	230.085i	−0.469992	−	0.0233213i
$461$	11142.2	−	6432.95i	1.12569	−	0.649918i	0.182843	−	0.983142i	$-0.441470\pi$
$461$	11142.2	−	6432.95i	1.12569	−	0.649918i	0.942848	+	0.333224i	$0.108137\pi$
$462$		0			0
$463$	−11984.7	−	6919.34i	−1.20297	−	0.694534i	−0.241754	−	0.970338i	$-0.577723\pi$
$463$	−11984.7	−	6919.34i	−1.20297	−	0.694534i	−0.961214	+	0.275804i	$0.911056\pi$
$464$	−60.7416	−	43.6174i	−0.00607728	−	0.00436398i
$465$		0			0
$466$	2691.75	−	9133.80i	0.267581	−	0.907972i
$467$	81.1441			0.00804047			0.00402024	−	0.999992i	$-0.498720\pi$
$467$	81.1441			0.00804047			0.00402024	+	0.999992i	$0.498720\pi$
$468$		0			0
$469$	−2914.03			−0.286902
$470$	3074.05	−	10431.0i	0.301692	−	1.02372i
$471$		0			0
$472$	−13948.5	+	2645.42i	−1.36024	+	0.257977i
$473$	4609.74	+	2661.44i	0.448110	+	0.258717i
$474$		0			0
$475$	−3537.80	+	2042.55i	−0.341738	+	0.197302i
$476$	1034.35	−	20845.3i	0.0995998	−	2.00723i
$477$		0			0
$478$	−1260.40	+	1199.41i	−0.120606	+	0.114769i
$479$	−7472.06	−	12942.0i	−0.712750	−	1.23452i	−0.963821	−	0.266550i	$-0.914116\pi$
$479$	−7472.06	−	12942.0i	−0.712750	−	1.23452i	0.251071	−	0.967969i	$-0.419217\pi$
$480$		0			0
$481$	−2610.81	+	4522.06i	−0.247490	+	0.428666i
$482$	−2916.45	−	12073.9i	−0.275603	−	1.14098i
$483$		0			0
$484$	8316.29	−	4266.52i	0.781019	−	0.400688i
$485$		−	8727.63i		−	0.817116i
$486$		0			0
$487$		−	5934.04i		−	0.552150i	−0.961136	−	0.276075i	$-0.910966\pi$
$487$		−	5934.04i		−	0.552150i	0.961136	−	0.276075i	$-0.0890338\pi$
$488$	−5704.27	+	16324.4i	−0.529140	+	1.51428i
$489$		0			0
$490$	−6882.57	+	1662.48i	−0.634536	+	0.153272i
$491$	−10032.4	+	17376.6i	−0.922110	+	1.59714i	−0.125965	+	0.992035i	$0.540203\pi$
$491$	−10032.4	+	17376.6i	−0.922110	+	1.59714i	−0.796145	+	0.605106i	$0.793131\pi$
$492$		0			0
$493$	−68.5259	−	118.690i	−0.00626015	−	0.0108429i
$494$	1208.63	+	1270.09i	0.110079	+	0.115676i
$495$		0			0
$496$	−873.242	+	8777.53i	−0.0790519	+	0.794602i
$497$	437.074	−	252.345i	0.0394476	−	0.0227751i
$498$		0			0
$499$	−8148.09	−	4704.30i	−0.730979	−	0.422031i	0.0878012	−	0.996138i	$-0.472016\pi$
$499$	−8148.09	−	4704.30i	−0.730979	−	0.422031i	−0.818780	+	0.574107i	$0.805349\pi$
$500$	−1597.47	+	2474.93i	−0.142882	+	0.221365i
$501$		0			0
$502$	−20961.4	−	6177.36i	−1.86365	−	0.549221i
$503$	12736.4			1.12900			0.564501	−	0.825432i	$-0.309069\pi$
$503$	12736.4			1.12900			0.564501	+	0.825432i	$0.309069\pi$
$504$		0			0
$505$	23663.0			2.08513
$506$	−1216.78	−	358.589i	−0.106902	−	0.0315044i
$507$		0			0
$508$	11604.4	−	17978.4i	1.01351	−	1.57021i
$509$	−7921.59	−	4573.53i	−0.689820	−	0.398268i	0.113724	−	0.993512i	$-0.463722\pi$
$509$	−7921.59	−	4573.53i	−0.689820	−	0.398268i	−0.803545	+	0.595244i	$0.797055\pi$
$510$		0			0
$511$	−7471.04	+	4313.40i	−0.646769	+	0.373412i
$512$	9801.54	−	6176.37i	0.846037	−	0.533124i
$513$		0			0
$514$	−5004.58	−	5259.07i	−0.429460	−	0.451299i
$515$	1896.86	+	3285.45i	0.162302	+	0.281115i
$516$		0			0
$517$	1485.66	−	2573.23i	0.126381	−	0.218899i
$518$	14284.6	−	3450.43i	1.21164	−	0.292671i
$519$		0			0
$520$	7879.40	+	2753.32i	0.664489	+	0.232194i
$521$		−	7691.78i		−	0.646801i	−0.946262	−	0.323400i	$-0.895174\pi$
$521$		−	7691.78i		−	0.646801i	0.946262	−	0.323400i	$-0.104826\pi$
$522$		0			0
$523$			9967.82i			0.833389i	0.909047	+	0.416694i	$0.136811\pi$
$523$			9967.82i			0.833389i	−0.909047	+	0.416694i	$0.863189\pi$
$524$	−5885.11	+	3019.25i	−0.490634	+	0.251711i
$525$		0			0
$526$	−2661.63	−	11019.0i	−0.220632	−	0.913404i
$527$	−8083.17	+	14000.5i	−0.668138	+	1.15725i
$528$		0			0
$529$	5465.14	+	9465.89i	0.449177	+	0.777997i
$530$	−6118.27	+	5822.21i	−0.501435	+	0.477171i
$531$		0			0
$532$	244.539	−	4928.19i	0.0199288	−	0.401624i
$533$	296.316	−	171.078i	0.0240804	−	0.0139028i
$534$		0			0
$535$	23953.7	+	13829.7i	1.93572	+	1.11759i
$536$	−552.395	−	2912.62i	−0.0445146	−	0.234713i
$537$		0			0
$538$	1792.75	−	6083.25i	0.143663	−	0.487486i
$539$	−1934.64			−0.154603
$540$		0			0
$541$	6050.08			0.480801			0.240400	−	0.970674i	$-0.422721\pi$
$541$	6050.08			0.480801			0.240400	+	0.970674i	$0.422721\pi$
$542$	−5056.40	+	17157.7i	−0.400721	+	1.35975i
$543$		0			0
$544$	21031.3	−	2917.66i	1.65755	−	0.229952i
$545$	−7726.70	−	4461.01i	−0.607294	−	0.350622i
$546$		0			0
$547$	11232.1	−	6484.87i	0.877972	−	0.506898i	0.00798299	−	0.999968i	$-0.497459\pi$
$547$	11232.1	−	6484.87i	0.877972	−	0.506898i	0.869989	+	0.493071i	$0.164126\pi$
$548$	−5175.27	−	256.800i	−0.403425	−	0.0200181i
$549$		0			0
$550$	−3849.39	+	3663.12i	−0.298434	+	0.283992i
$551$	−16.2007	−	28.0605i	−0.00125259	−	0.00216954i
$552$		0			0
$553$	−6246.17	+	10818.7i	−0.480315	+	0.831930i
$554$	831.263	+	3441.38i	0.0637491	+	0.263917i
$555$		0			0
$556$	9751.90	+	19008.4i	0.743836	+	1.44988i
$557$			2223.88i			0.169172i	0.996416	+	0.0845859i	$0.0269567\pi$
$557$			2223.88i			0.169172i	−0.996416	+	0.0845859i	$0.973043\pi$
$558$		0			0
$559$		−	9329.75i		−	0.705915i
$560$	−9673.46	−	21405.8i	−0.729961	−	1.61529i
$561$		0			0
$562$	−3778.94	+	912.800i	−0.283639	+	0.0685127i
$563$	8913.79	−	15439.1i	0.667267	−	1.15574i	−0.311398	−	0.950280i	$-0.600797\pi$
$563$	8913.79	−	15439.1i	0.667267	−	1.15574i	0.978665	−	0.205461i	$-0.0658695\pi$
$564$		0			0
$565$	−10583.3	−	18330.9i	−0.788043	−	1.36493i
$566$	9019.67	+	9478.33i	0.669832	+	0.703894i
$567$		0			0
$568$	335.077	+	389.028i	0.0247527	+	0.0287381i
$569$	−9765.76	+	5638.26i	−0.719511	+	0.415410i	−0.814573	−	0.580061i	$-0.803029\pi$
$569$	−9765.76	+	5638.26i	−0.719511	+	0.415410i	0.0950615	+	0.995471i	$0.469695\pi$
$570$		0			0
$571$	6527.00	+	3768.37i	0.478365	+	0.276184i	0.719735	−	0.694249i	$-0.244263\pi$
$571$	6527.00	+	3768.37i	0.478365	+	0.276184i	−0.241370	+	0.970433i	$0.577597\pi$
$572$	1916.10	+	1236.77i	0.140064	+	0.0904057i
$573$		0			0
$574$	−923.668	−	272.207i	−0.0671657	−	0.0197939i
$575$	−5180.59			−0.375731
$576$		0			0
$577$	−16888.0			−1.21847			−0.609233	−	0.792991i	$-0.708523\pi$
$577$	−16888.0			−1.21847			−0.609233	+	0.792991i	$0.708523\pi$
$578$	23997.6	+	7072.14i	1.72693	+	0.508931i
$579$		0			0
$580$	−129.599	−	83.6513i	−0.00927812	−	0.00598867i
$581$	−13179.5	−	7609.18i	−0.941097	−	0.543343i
$582$		0			0
$583$	−1998.51	+	1153.84i	−0.141973	+	0.0819679i
$584$	−5727.57	−	6649.77i	−0.405836	−	0.471180i
$585$		0			0
$586$	12434.0	+	13066.3i	0.876527	+	0.921099i
$587$	8103.83	+	14036.3i	0.569814	+	0.986947i	0.996584	+	0.0825870i	$0.0263182\pi$
$587$	8103.83	+	14036.3i	0.569814	+	0.986947i	−0.426770	+	0.904360i	$0.640348\pi$
$588$		0			0
$589$	−1911.00	+	3309.96i	−0.133687	+	0.231552i
$590$	−28466.4	+	6876.05i	−1.98635	+	0.479801i
$591$		0			0
$592$	6156.62	+	13623.6i	0.427425	+	0.945824i
$593$		−	22320.8i		−	1.54571i	−0.634583	−	0.772855i	$-0.718828\pi$
$593$		−	22320.8i		−	1.54571i	0.634583	−	0.772855i	$-0.281172\pi$
$594$		0			0
$595$		−	43051.3i		−	2.96627i
$596$	380.546	+	741.759i	0.0261540	+	0.0509793i
$597$		0			0
$598$	522.052	+	2161.27i	0.0356995	+	0.147794i
$599$	4883.72	−	8458.84i	0.333127	−	0.576993i	−0.649996	−	0.759938i	$-0.725229\pi$
$599$	4883.72	−	8458.84i	0.333127	−	0.576993i	0.983123	+	0.182944i	$0.0585628\pi$
$600$		0			0
$601$	−9316.81	−	16137.2i	−0.632347	−	1.09526i	−0.987071	−	0.160286i	$-0.948758\pi$
$601$	−9316.81	−	16137.2i	−0.632347	−	1.09526i	0.354724	−	0.934971i	$-0.384575\pi$
$602$	−19021.0	+	18100.6i	−1.28777	+	1.22546i
$603$		0			0
$604$	−21984.1	−	1090.86i	−1.48099	−	0.0734876i
$605$	16697.1	−	9640.08i	1.12204	−	0.647810i
$606$		0			0
$607$	371.545	+	214.512i	0.0248444	+	0.0143439i	0.512371	−	0.858764i	$-0.328767\pi$
$607$	371.545	+	214.512i	0.0248444	+	0.0143439i	−0.487526	+	0.873108i	$0.662101\pi$
$608$	4972.17	−	689.787i	0.331658	−	0.0460108i
$609$		0			0
$610$	−10083.2	+	34214.7i	−0.669270	+	2.27101i
$611$	−5208.01			−0.344834
$612$		0			0
$613$	−4211.54			−0.277492			−0.138746	−	0.990328i	$-0.544307\pi$
$613$	−4211.54			−0.277492			−0.138746	+	0.990328i	$0.544307\pi$
$614$	5284.49	−	17931.6i	0.347337	−	1.17860i
$615$		0			0
$616$	−1195.95	−	6305.92i	−0.0782246	−	0.412456i
$617$	23419.6	+	13521.3i	1.52810	+	0.882248i	0.999442	+	0.0334113i	$0.0106371\pi$
$617$	23419.6	+	13521.3i	1.52810	+	0.882248i	0.528656	+	0.848836i	$0.322696\pi$
$618$		0			0
$619$	−8368.15	+	4831.35i	−0.543367	+	0.313713i	−0.746442	−	0.665450i	$-0.768240\pi$
$619$	−8368.15	+	4831.35i	−0.543367	+	0.313713i	0.203075	+	0.979163i	$0.434906\pi$
$620$	−901.744	+	18172.8i	−0.0584111	+	1.17716i
$621$		0			0
$622$	−10524.9	+	10015.6i	−0.678471	+	0.645640i
$623$	3091.65	+	5354.89i	0.198819	+	0.344364i
$624$		0			0
$625$	6168.97	−	10685.0i	0.394814	−	0.683838i
$626$	4119.34	+	17053.8i	0.263006	+	1.08883i
$627$		0			0
$628$	8278.80	−	4247.29i	0.526051	−	0.269881i
$629$			27399.8i			1.73688i
$630$		0			0
$631$			10846.5i			0.684297i	0.939646	+	0.342149i	$0.111155\pi$
$631$			10846.5i			0.684297i	−0.939646	+	0.342149i	$0.888845\pi$
$632$	−11997.5	−	4192.33i	−0.755120	−	0.263864i
$633$		0			0
$634$	5017.98	−	1212.09i	0.314337	−	0.0759279i
$635$	22069.6	−	38225.6i	1.37922	−	2.38888i
$636$		0			0
$637$	1695.49	+	2936.67i	0.105459	+	0.182661i
$638$	−29.0545	−	30.5319i	−0.00180294	−	0.00189462i
$639$		0			0
$640$	19561.8	−	13726.6i	1.20820	−	0.847798i
$641$	−12772.5	+	7374.18i	−0.787023	+	0.454388i	−0.838914	−	0.544265i	$-0.816809\pi$
$641$	−12772.5	+	7374.18i	−0.787023	+	0.454388i	0.0518903	+	0.998653i	$0.483475\pi$
$642$		0			0
$643$	−12787.4	−	7382.82i	−0.784271	−	0.452799i	0.0536706	−	0.998559i	$-0.482908\pi$
$643$	−12787.4	−	7382.82i	−0.784271	−	0.452799i	−0.837942	+	0.545759i	$0.816241\pi$
$644$	3393.45	−	5257.40i	0.207641	−	0.321693i
$645$		0			0
$646$	8824.73	+	2600.67i	0.537468	+	0.158393i
$647$	27157.4			1.65018			0.825090	−	0.565002i	$-0.191125\pi$
$647$	27157.4			1.65018			0.825090	+	0.565002i	$0.191125\pi$
$648$		0			0
$649$	−8001.72			−0.483968
$650$	8933.93	+	2632.85i	0.539104	+	0.158875i
$651$		0			0
$652$	−12713.6	+	19696.9i	−0.763653	+	1.18311i
$653$	2658.60	+	1534.94i	0.159325	+	0.0919861i	0.577542	−	0.816361i	$-0.304012\pi$
$653$	2658.60	+	1534.94i	0.159325	+	0.0919861i	−0.418218	+	0.908347i	$0.637345\pi$
$654$		0			0
$655$	−11815.9	+	6821.90i	−0.704862	+	0.406952i
$656$	96.9813	−	974.823i	0.00577208	−	0.0580190i
$657$		0			0
$658$	10104.1	+	10617.9i	0.598628	+	0.629068i
$659$	579.767	+	1004.19i	0.0342709	+	0.0593589i	0.882652	−	0.470027i	$-0.155756\pi$
$659$	579.767	+	1004.19i	0.0342709	+	0.0593589i	−0.848381	+	0.529386i	$0.822422\pi$
$660$		0			0
$661$	−8919.74	+	15449.4i	−0.524868	+	0.909097i	0.474713	+	0.880141i	$0.342552\pi$
$661$	−8919.74	+	15449.4i	−0.524868	+	0.909097i	−0.999581	+	0.0289568i	$0.990781\pi$
$662$	−10934.8	+	2641.29i	−0.641983	+	0.155071i
$663$		0			0
$664$	5107.16	−	14615.6i	0.298488	−	0.854208i
$665$		−	10178.1i		−	0.593517i
$666$		0			0
$667$		−	41.0905i		−	0.00238535i
$668$	−6206.27	+	3184.01i	−0.359472	+	0.184421i
$669$		0			0
$670$	−1435.80	−	5944.13i	−0.0827908	−	0.342749i
$671$	−4873.09	+	8440.44i	−0.280363	+	0.485603i
$672$		0			0
$673$	6058.30	+	10493.3i	0.346999	+	0.601020i	0.985715	−	0.168423i	$-0.0538673\pi$
$673$	6058.30	+	10493.3i	0.346999	+	0.601020i	−0.638716	+	0.769443i	$0.720534\pi$
$674$	−2372.07	+	2257.28i	−0.135562	+	0.129002i
$675$		0			0
$676$	−672.953	+	13562.0i	−0.0382882	+	0.771620i
$677$	18626.5	−	10754.0i	1.05742	−	0.610504i	0.132705	−	0.991156i	$-0.457634\pi$
$677$	18626.5	−	10754.0i	1.05742	−	0.610504i	0.924718	+	0.380652i	$0.124300\pi$
$678$		0			0
$679$	10187.4	+	5881.70i	0.575783	+	0.332428i
$680$	43030.5	−	8160.98i	2.42668	−	0.460234i
$681$		0			0
$682$	−1405.37	+	4768.78i	−0.0789068	+	0.267751i
$683$	−33849.4			−1.89636			−0.948179	−	0.317738i	$-0.897077\pi$
$683$	−33849.4			−1.89636			−0.948179	+	0.317738i	$0.897077\pi$
$684$		0			0
$685$	−10688.4			−0.596178
$686$	−3401.97	+	11543.7i	−0.189341	+	0.642481i
$687$		0			0
$688$	−21697.6	−	15580.7i	−1.20234	−	0.863382i
$689$	3502.93	+	2022.42i	0.193688	+	0.111826i
$690$		0			0
$691$	−1786.94	+	1031.69i	−0.0983771	+	0.0567980i	−0.548381	−	0.836228i	$-0.684756\pi$
$691$	−1786.94	+	1031.69i	−0.0983771	+	0.0567980i	0.450004	+	0.893026i	$0.351422\pi$
$692$	−18638.8	−	924.866i	−1.02390	−	0.0508065i
$693$		0			0
$694$	−5088.08	+	4841.87i	−0.278301	+	0.264834i
$695$	22034.1	+	38164.2i	1.20259	+	2.08295i
$696$		0			0
$697$	897.708	−	1554.88i	0.0487850	−	0.0844981i
$698$	−3967.24	−	16424.1i	−0.215132	−	0.890634i
$699$		0			0
$700$	−11965.0	−	23322.0i	−0.646047	−	1.25927i
$701$		−	19641.7i		−	1.05828i	−0.848534	−	0.529141i	$-0.822514\pi$
$701$		−	19641.7i		−	1.05828i	0.848534	−	0.529141i	$-0.177486\pi$
$702$		0			0
$703$			6477.79i			0.347531i
$704$	6076.17	−	2390.75i	0.325290	−	0.127990i
$705$		0			0
$706$	−2835.50	+	684.914i	−0.151155	+	0.0365114i
$707$	−15946.9	+	27620.8i	−0.848295	+	1.46929i
$708$		0			0
$709$	2685.98	+	4652.26i	0.142277	+	0.246431i	0.928354	−	0.371698i	$-0.121224\pi$
$709$	2685.98	+	4652.26i	0.142277	+	0.246431i	−0.786077	+	0.618129i	$0.787891\pi$
$710$	730.097	+	767.223i	0.0385916	+	0.0405540i
$711$		0			0
$712$	−4766.24	+	4105.25i	−0.250874	+	0.216083i
$713$	−4197.58	+	2423.47i	−0.220478	+	0.127293i
$714$		0			0
$715$	4074.00	+	2352.13i	0.213090	+	0.123027i
$716$	−4293.48	−	2771.28i	−0.224099	−	0.144648i
$717$		0			0
$718$	11446.4	+	3373.27i	0.594952	+	0.175334i
$719$	12836.0			0.665788			0.332894	−	0.942964i	$-0.391975\pi$
$719$	12836.0			0.665788			0.332894	+	0.942964i	$0.391975\pi$
$720$		0			0
$721$	−5113.29			−0.264118
$722$	−16522.6	−	4869.24i	−0.851672	−	0.250990i
$723$		0			0
$724$	27094.2	+	17488.3i	1.39081	+	0.897717i
$725$	−149.065	−	86.0630i	−0.00763607	−	0.00440869i
$726$		0			0
$727$	29745.3	−	17173.5i	1.51746	−	0.876106i	0.517670	−	0.855580i	$-0.326800\pi$
$727$	29745.3	−	17173.5i	1.51746	−	0.876106i	0.999789	−	0.0205251i	$-0.00653380\pi$
$728$	−8523.89	+	7341.78i	−0.433951	+	0.373770i
$729$		0			0
$730$	−12479.8	−	13114.4i	−0.632735	−	0.664910i
$731$	−24478.3	−	42397.6i	−1.23852	−	2.14519i
$732$		0			0
$733$	−4537.51	+	7859.19i	−0.228645	+	0.396024i	−0.957407	−	0.288743i	$-0.906763\pi$
$733$	−4537.51	+	7859.19i	−0.228645	+	0.396024i	0.728762	+	0.684767i	$0.240096\pi$
$734$	8358.66	−	2019.03i	0.420332	−	0.101531i
$735$		0			0
$736$	5898.14	+	2395.20i	0.295392	+	0.119957i
$737$		−	1670.85i		−	0.0835098i
$738$		0			0
$739$		−	16863.2i		−	0.839410i	−0.907661	−	0.419705i	$-0.862134\pi$
$739$		−	16863.2i		−	0.839410i	0.907661	−	0.419705i	$-0.137866\pi$
$740$	14076.6	+	27438.1i	0.699280	+	1.36303i
$741$		0			0
$742$	−2672.81	−	11065.3i	−0.132240	−	0.547466i
$743$	15021.9	−	26018.6i	0.741721	−	1.28470i	−0.209990	−	0.977704i	$-0.567343\pi$
$743$	15021.9	−	26018.6i	0.741721	−	1.28470i	0.951711	−	0.306995i	$-0.0993235\pi$
$744$		0			0
$745$	859.832	+	1489.27i	0.0422843	+	0.0732386i
$746$	10486.2	−	9978.81i	0.514649	−	0.489745i
$747$		0			0
$748$	11952.3	+	593.081i	0.584252	+	0.0289909i
$749$	−32285.6	+	18640.1i	−1.57502	+	0.909338i
$750$		0			0
$751$	7313.00	+	4222.17i	0.355333	+	0.205152i	0.667032	−	0.745029i	$-0.267565\pi$
$751$	7313.00	+	4222.17i	0.355333	+	0.205152i	−0.311698	+	0.950181i	$0.600898\pi$
$752$	−8697.37	+	12111.9i	−0.421756	+	0.587337i
$753$		0			0
$754$	−20.8828	+	70.8605i	−0.00100863	+	0.00342253i
$755$	−45403.2			−2.18860
$756$		0			0
$757$	35193.1			1.68971			0.844857	−	0.534992i	$-0.179685\pi$
$757$	35193.1			1.68971			0.844857	+	0.534992i	$0.179685\pi$
$758$	−2271.20	+	7706.77i	−0.108831	+	0.369291i
$759$		0			0
$760$	10173.2	−	1929.40i	0.485553	−	0.0920878i
$761$	−13659.8	−	7886.50i	−0.650681	−	0.375671i	0.138036	−	0.990427i	$-0.455921\pi$
$761$	−13659.8	−	7886.50i	−0.650681	−	0.375671i	−0.788717	+	0.614756i	$0.789254\pi$
$762$		0			0
$763$	10414.3	−	6012.70i	0.494133	−	0.285288i
$764$	1452.47	−	29271.5i	0.0687806	−	1.38613i
$765$		0			0
$766$	11532.9	−	10974.8i	0.543996	−	0.517672i
$767$	7012.57	+	12146.1i	0.330129	+	0.571801i
$768$		0			0
$769$	10370.9	−	17962.9i	0.486325	−	0.842340i	−0.513551	−	0.858059i	$-0.671670\pi$
$769$	10370.9	−	17962.9i	0.486325	−	0.842340i	0.999876	+	0.0157189i	$0.00500369\pi$
$770$	−3108.55	−	12869.2i	−0.145486	−	0.602305i
$771$		0			0
$772$	−10090.8	+	5176.89i	−0.470434	+	0.241348i
$773$			35223.1i			1.63892i	0.573133	+	0.819462i	$0.305728\pi$
$773$			35223.1i			1.63892i	−0.573133	+	0.819462i	$0.694272\pi$
$774$		0			0
$775$			20303.6i			0.941067i
$776$	−3947.70	+	11297.4i	−0.182621	+	0.522622i
$777$		0			0
$778$	−9793.13	+	2365.52i	−0.451286	+	0.109008i
$779$	212.234	−	367.600i	0.00976133	−	0.0169071i
$780$		0			0
$781$	144.690	+	250.611i	0.00662923	+	0.0114822i
$782$	8042.85	+	8451.84i	0.367790	+	0.386493i
$783$		0			0
$784$	9661.09	+	961.144i	0.440101	+	0.0437839i
$785$	16621.8	−	9596.62i	0.755743	−	0.436329i
$786$		0			0
$787$	−19651.8	−	11346.0i	−0.890102	−	0.513901i	−0.0161261	−	0.999870i	$-0.505133\pi$
$787$	−19651.8	−	11346.0i	−0.890102	−	0.513901i	−0.873976	+	0.485969i	$0.838467\pi$
$788$	−3804.45	+	5894.15i	−0.171990	+	0.266460i
$789$		0			0
$790$	−25145.9	−	7410.56i	−1.13247	−	0.333742i
$791$	28529.2			1.28240
$792$		0			0
$793$	17082.8			0.764977
$794$	25577.5	+	7537.74i	1.14321	+	0.336907i
$795$		0			0
$796$	−6444.53	+	9984.37i	−0.286960	+	0.444581i
$797$	−27480.8	−	15866.1i	−1.22136	−	0.705150i	−0.256149	−	0.966637i	$-0.582454\pi$
$797$	−27480.8	−	15866.1i	−1.22136	−	0.705150i	−0.965207	+	0.261488i	$0.915787\pi$
$798$		0			0
$799$	−23667.0	+	13664.2i	−1.04791	+	0.605010i
$800$	21042.7	−	16380.2i	0.929964	−	0.723910i
$801$		0			0
$802$	−16829.9	−	17685.8i	−0.741005	−	0.778686i
$803$	−2473.24	−	4283.77i	−0.108691	−	0.188258i
$804$		0			0
$805$	6453.75	−	11178.2i	0.282565	−	0.489417i
$806$	8470.37	−	2046.01i	0.370169	−	0.0894140i
$807$		0			0
$808$	−30630.5	−	10703.3i	−1.33363	−	0.466015i
$809$		−	18376.4i		−	0.798613i	−0.916817	−	0.399307i	$-0.869251\pi$
$809$		−	18376.4i		−	0.798613i	0.916817	−	0.399307i	$-0.130749\pi$
$810$		0			0
$811$			28834.7i			1.24849i	0.781229	+	0.624244i	$0.214593\pi$
$811$			28834.7i			1.24849i	−0.781229	+	0.624244i	$0.785407\pi$
$812$	184.982	−	94.9015i	0.00799456	−	0.00410147i
$813$		0			0
$814$	1978.42	+	8190.55i	0.0851888	+	0.352677i
$815$	−24179.0	+	41879.2i	−1.03921	+	1.79996i
$816$		0			0
$817$	−5787.09	−	10023.5i	−0.247815	−	0.429228i
$818$	12016.8	−	11435.3i	0.513638	−	0.488783i
$819$		0			0
$820$	100.147	−	2018.25i	0.00426497	−	0.0859517i
$821$	14471.4	−	8355.08i	0.615172	−	0.355170i	−0.159815	−	0.987147i	$-0.551090\pi$
$821$	14471.4	−	8355.08i	0.615172	−	0.355170i	0.774987	+	0.631977i	$0.217756\pi$
$822$		0			0
$823$	453.509	+	261.833i	0.0192082	+	0.0110898i	0.509573	−	0.860427i	$-0.329803\pi$
$823$	453.509	+	261.833i	0.0192082	+	0.0110898i	−0.490365	+	0.871517i	$0.663137\pi$
$824$	−969.298	−	5110.83i	−0.0409795	−	0.216073i
$825$		0			0
$826$	11157.9	−	37861.6i	0.470015	−	1.59488i
$827$	28676.4			1.20577			0.602887	−	0.797826i	$-0.294017\pi$
$827$	28676.4			1.20577			0.602887	+	0.797826i	$0.294017\pi$
$828$		0			0
$829$	14521.0			0.608365			0.304183	−	0.952614i	$-0.401617\pi$
$829$	14521.0			0.608365			0.304183	+	0.952614i	$0.401617\pi$
$830$	9027.66	−	30633.2i	0.377536	−	1.28108i
$831$		0			0
$832$	−8954.07	−	7128.05i	−0.373109	−	0.297020i
$833$	15409.8	+	8896.84i	0.640957	+	0.370057i
$834$		0			0
$835$	−12460.7	+	7194.18i	−0.516431	+	0.298161i
$836$	2825.74	+	140.215i	0.116902	+	0.00580076i
$837$		0			0
$838$	14252.0	−	13562.3i	0.587501	−	0.559072i
$839$	−15594.8	−	27010.9i	−0.641706	−	1.11147i	−0.985052	−	0.172258i	$-0.944894\pi$
$839$	−15594.8	−	27010.9i	−0.641706	−	1.11147i	0.343346	−	0.939209i	$-0.388440\pi$
$840$		0			0
$841$	−12193.8	+	21120.3i	−0.499972	+	0.865977i
$842$	−6239.79	−	25832.4i	−0.255389	−	1.05730i
$843$		0			0
$844$	1123.46	+	2189.84i	0.0458188	+	0.0893099i
$845$			28009.3i			1.14029i
$846$		0			0
$847$			25986.4i			1.05420i
$848$	10553.3	−	4769.11i	0.427360	−	0.193127i
$849$		0			0
$850$	47506.6	−	11475.2i	1.91702	−	0.463054i
$851$	−4107.46	+	7114.32i	−0.165455	+	0.286576i
$852$		0			0
$853$	−6544.93	−	11336.2i	−0.262713	−	0.455032i	0.704249	−	0.709953i	$-0.251284\pi$
$853$	−6544.93	−	11336.2i	−0.262713	−	0.455032i	−0.966962	+	0.254921i	$0.917951\pi$
$854$	−33142.2	−	34827.5i	−1.32799	−	1.39552i
$855$		0			0
$856$	−24751.3	−	28736.5i	−0.988297	−	1.14742i
$857$	15414.8	−	8899.73i	0.614421	−	0.354736i	−0.160273	−	0.987073i	$-0.551237\pi$
$857$	15414.8	−	8899.73i	0.614421	−	0.354736i	0.774694	+	0.632337i	$0.217904\pi$
$858$		0			0
$859$	−36673.2	−	21173.3i	−1.45666	−	0.841004i	−0.457816	−	0.889047i	$-0.651368\pi$
$859$	−36673.2	−	21173.3i	−1.45666	−	0.841004i	−0.998845	+	0.0480428i	$0.984702\pi$
$860$	−46294.3	−	29881.2i	−1.83561	−	1.18482i
$861$		0			0
$862$	19930.3	+	5873.50i	0.787503	+	0.232079i
$863$	−41963.9			−1.65524			−0.827618	−	0.561291i	$-0.810305\pi$
$863$	−41963.9			−1.65524			−0.827618	+	0.561291i	$0.810305\pi$
$864$		0			0
$865$	−38494.2			−1.51311
$866$	−37095.7	−	10932.2i	−1.45562	−	0.428973i
$867$		0			0
$868$	−20604.6	−	13299.5i	−0.805722	−	0.520063i
$869$	−6203.26	−	3581.45i	−0.242153	−	0.139807i
$870$		0			0
$871$	−2536.26	+	1464.31i	−0.0986656	+	0.0569646i
$872$	7983.99	+	9269.50i	0.310060	+	0.359982i
$873$		0			0
$874$	1901.47	+	1998.16i	0.0735907	+	0.0773328i
$875$	−4094.88	−	7092.54i	−0.158208	−	0.274025i
$876$		0			0
$877$	21665.7	−	37526.1i	0.834206	−	1.44489i	−0.0604689	−	0.998170i	$-0.519260\pi$
$877$	21665.7	−	37526.1i	0.834206	−	1.44489i	0.894675	−	0.446717i	$-0.147407\pi$
$878$	15860.3	−	3831.05i	0.609635	−	0.147257i
$879$		0			0
$880$	12273.8	−	5546.60i	0.470169	−	0.212473i
$881$			38532.4i			1.47354i	0.676142	+	0.736771i	$0.263651\pi$
$881$			38532.4i			1.47354i	−0.676142	+	0.736771i	$0.736349\pi$
$882$		0			0
$883$			7198.92i			0.274364i	0.990546	+	0.137182i	$0.0438045\pi$
$883$			7198.92i			0.274364i	−0.990546	+	0.137182i	$0.956196\pi$
$884$	−9574.56	−	18662.7i	−0.364284	−	0.710061i
$885$		0			0
$886$	6410.55	+	26539.3i	0.243077	+	1.00633i
$887$	7110.04	−	12315.0i	0.269145	−	0.466173i	−0.699496	−	0.714636i	$-0.746592\pi$
$887$	7110.04	−	12315.0i	0.269145	−	0.466173i	0.968641	+	0.248463i	$0.0799255\pi$
$888$		0			0
$889$	29746.1	+	51521.7i	1.12222	+	1.94374i
$890$	−9399.76	+	8944.90i	−0.354023	+	0.336892i
$891$		0			0
$892$	31189.5	+	1547.64i	1.17074	+	0.0580928i
$893$	−5595.30	+	3230.45i	−0.209675	+	0.121056i
$894$		0			0
$895$	−9128.76	−	5270.49i	−0.340940	−	0.196842i
$896$	2839.45	+	32084.2i	0.105870	+	1.19627i
$897$		0			0
$898$	9188.57	−	31179.2i	0.341455	−	1.15864i
$899$	−161.041			−0.00597442
$900$		0			0
$901$	21224.7			0.784791
$902$	156.079	−	529.616i	0.00576148	−	0.0195502i
$903$		0			0
$904$	5408.11	+	28515.4i	0.198972	+	1.04912i
$905$	57607.4	+	33259.7i	2.11595	+	1.22164i
$906$		0			0
$907$	43283.2	−	24989.6i	1.58456	−	0.914845i	0.590377	−	0.807127i	$-0.298979\pi$
$907$	43283.2	−	24989.6i	1.58456	−	0.914845i	0.994181	−	0.107718i	$-0.0343544\pi$
$908$	−764.709	+	15411.1i	−0.0279491	+	0.563256i
$909$		0			0
$910$	−16810.4	+	15997.0i	−0.612374	+	0.582741i
$911$	7306.31	+	12654.9i	0.265718	+	0.460237i	0.967751	−	0.251907i	$-0.0810577\pi$
$911$	7306.31	+	12654.9i	0.265718	+	0.460237i	−0.702034	+	0.712144i	$0.747724\pi$
$912$		0			0
$913$	4362.98	−	7556.90i	0.158153	−	0.273929i
$914$	11716.2	+	48504.5i	0.424003	+	1.75535i
$915$		0			0
$916$	−16352.8	+	8389.53i	−0.589861	+	0.302618i
$917$		−	18389.6i		−	0.662244i
$918$		0			0
$919$			45594.4i			1.63658i	0.574804	+	0.818291i	$0.305078\pi$
$919$			45594.4i			1.63658i	−0.574804	+	0.818291i	$0.694922\pi$
$920$	12396.2	+	4331.65i	0.444230	+	0.155229i
$921$		0			0
$922$	−35372.9	+	8544.31i	−1.26350	+	0.305197i
$923$	253.608	−	439.263i	0.00904401	−	0.0156647i
$924$		0			0
$925$	17205.9	+	29801.5i	0.611597	+	1.05932i
$926$	26982.8	+	28354.9i	0.957571	+	1.00626i
$927$		0			0
$928$	129.922	+	166.903i	0.00459579	+	0.00590393i
$929$	−44791.1	+	25860.1i	−1.58186	+	0.913287i	−0.587272	+	0.809390i	$0.699798\pi$
$929$	−44791.1	+	25860.1i	−1.58186	+	0.913287i	−0.994588	+	0.103897i	$0.966869\pi$
$930$		0			0
$931$	3643.14	+	2103.37i	0.128248	+	0.0740442i
$932$	−14605.8	+	22628.4i	−0.513335	+	0.795299i
$933$		0			0
$934$	−220.149	−	64.8785i	−0.00771253	−	0.00227290i
$935$	24684.9			0.863404
$936$		0			0
$937$	−42197.0			−1.47120			−0.735601	−	0.677415i	$-0.763100\pi$
$937$	−42197.0			−1.47120			−0.735601	+	0.677415i	$0.763100\pi$
$938$	7905.95	+	2329.90i	0.275201	+	0.0811022i
$939$		0			0
$940$	−16680.2	+	25842.2i	−0.578774	+	0.896681i
$941$	9360.06	+	5404.03i	0.324261	+	0.187212i	0.653290	−	0.757108i	$-0.273388\pi$
$941$	9360.06	+	5404.03i	0.324261	+	0.187212i	−0.329029	+	0.944320i	$0.606722\pi$
$942$		0			0
$943$	466.178	−	269.148i	0.0160985	−	0.00929446i
$944$	39958.5	+	3975.31i	1.37769	+	0.137061i
$945$		0			0
$946$	−10378.6	−	10906.4i	−0.356699	−	0.374837i
$947$	−372.832	−	645.764i	−0.0127935	−	0.0221589i	0.859558	−	0.511039i	$-0.170739\pi$
$947$	−372.832	−	645.764i	−0.0127935	−	0.0221589i	−0.872351	+	0.488880i	$0.837406\pi$
$948$		0			0
$949$	−4335.00	+	7508.44i	−0.148283	+	0.256833i
$950$	11231.4	−	2712.94i	0.383573	−	0.0926519i
$951$		0			0
$952$	−19473.0	+	55727.6i	−0.662946	+	1.89721i
$953$		−	49163.3i		−	1.67110i	−0.549417	−	0.835548i	$-0.685150\pi$
$953$		−	49163.3i		−	1.67110i	0.549417	−	0.835548i	$-0.314850\pi$
$954$		0			0
$955$		−	60453.7i		−	2.04841i
$956$	4378.54	−	2246.33i	0.148130	−	0.0759954i
$957$		0			0
$958$	9924.47	+	41086.7i	0.334703	+	1.38565i
$959$	7203.08	−	12476.1i	0.242544	−	0.420098i
$960$		0			0
$961$	−5397.50	−	9348.74i	−0.181179	−	0.313811i
$962$	10698.9	−	10181.2i	0.358572	−	0.341221i
$963$		0			0
$964$	−1741.15	+	35089.3i	−0.0581728	+	1.17235i
$965$	−20259.8	+	11697.0i	−0.675842	+	0.390197i
$966$		0			0
$967$	14625.7	+	8444.18i	0.486383	+	0.280813i	0.723073	−	0.690772i	$-0.242729\pi$
$967$	14625.7	+	8444.18i	0.486383	+	0.280813i	−0.236690	+	0.971585i	$0.576062\pi$
$968$	−25973.9	+	4926.10i	−0.862431	+	0.163565i
$969$		0			0
$970$	−6978.14	+	23678.6i	−0.230984	+	0.783789i
$971$	22501.6			0.743677			0.371838	−	0.928297i	$-0.378728\pi$
$971$	22501.6			0.743677			0.371838	+	0.928297i	$0.378728\pi$
$972$		0			0
$973$	−59396.6			−1.95701
$974$	−4744.54	+	16099.4i	−0.156083	+	0.529629i
$975$		0			0
$976$	28528.2	−	39728.3i	0.935619	−	1.30294i
$977$	−11920.1	−	6882.06i	−0.390335	−	0.225360i	0.291970	−	0.956427i	$-0.405689\pi$
$977$	−11920.1	−	6882.06i	−0.390335	−	0.225360i	−0.682305	+	0.731068i	$0.739022\pi$
$978$		0			0
$979$	−3070.40	+	1772.70i	−0.100235	+	0.0578710i
$980$	20002.1	+	992.515i	0.651983	+	0.0323518i
$981$		0			0
$982$	41112.0	−	39122.6i	1.33598	−	1.27134i
$983$	−3892.24	−	6741.57i	−0.126290	−	0.218741i	0.795946	−	0.605367i	$-0.206974\pi$
$983$	−3892.24	−	6741.57i	−0.126290	−	0.218741i	−0.922237	+	0.386626i	$0.873640\pi$
$984$		0			0
$985$	−7235.40	+	12532.1i	−0.234050	+	0.405386i
$986$	91.0169	+	376.805i	0.00293972	+	0.0121703i
$987$		0			0
$988$	−2263.59	−	4412.19i	−0.0728892	−	0.142075i
$989$		−	14678.0i		−	0.471925i
$990$		0			0
$991$		−	47880.3i		−	1.53478i	−0.641179	−	0.767391i	$-0.721555\pi$
$991$		−	47880.3i		−	1.53478i	0.641179	−	0.767391i	$-0.278445\pi$
$992$	9387.21	−	23115.8i	0.300448	−	0.739847i
$993$		0			0
$994$	−1387.57	+	335.167i	−0.0442768	+	0.0106950i
$995$	−12256.4	+	21228.7i	−0.390506	+	0.676376i
$996$		0			0
$997$	−1245.57	−	2157.40i	−0.0395664	−	0.0685310i	0.845564	−	0.533874i	$-0.179264\pi$
$997$	−1245.57	−	2157.40i	−0.0395664	−	0.0685310i	−0.885130	+	0.465343i	$0.845931\pi$
$998$	18345.0	+	19277.9i	0.581864	+	0.611453i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.h.b.71.1		24
3.2	odd	2		36.4.h.b.23.12	yes	24
4.3	odd	2	inner	108.4.h.b.71.6		24
9.2	odd	6	inner	108.4.h.b.35.6		24
9.4	even	3		324.4.b.c.323.17		24
9.5	odd	6		324.4.b.c.323.8		24
9.7	even	3		36.4.h.b.11.7	✓	24
12.11	even	2		36.4.h.b.23.7	yes	24
36.7	odd	6		36.4.h.b.11.12	yes	24
36.11	even	6	inner	108.4.h.b.35.1		24
36.23	even	6		324.4.b.c.323.18		24
36.31	odd	6		324.4.b.c.323.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.7	✓	24	9.7	even	3
36.4.h.b.11.12	yes	24	36.7	odd	6
36.4.h.b.23.7	yes	24	12.11	even	2
36.4.h.b.23.12	yes	24	3.2	odd	2
108.4.h.b.35.1		24	36.11	even	6	inner
108.4.h.b.35.6		24	9.2	odd	6	inner
108.4.h.b.71.1		24	1.1	even	1	trivial
108.4.h.b.71.6		24	4.3	odd	2	inner
324.4.b.c.323.7		24	36.31	odd	6
324.4.b.c.323.8		24	9.5	odd	6
324.4.b.c.323.17		24	9.4	even	3
324.4.b.c.323.18		24	36.23	even	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.71307 - 0.799546i) q^{2} +(6.72145 + 4.33844i) q^{4} +(14.2911 + 8.25096i) q^{5} +(-19.2620 + 11.1209i) q^{7} +(-14.7670 - 17.1446i) q^{8} +O(q^{10})\)	\(q+(-2.71307 - 0.799546i) q^{2} +(6.72145 + 4.33844i) q^{4} +(14.2911 + 8.25096i) q^{5} +(-19.2620 + 11.1209i) q^{7} +(-14.7670 - 17.1446i) q^{8} +(-32.1756 - 33.8118i) q^{10} +(-6.37655 - 11.0445i) q^{11} +(-11.1766 + 19.3584i) q^{13} +(61.1508 - 14.7709i) q^{14} +(26.3558 + 58.3213i) q^{16} +117.295i q^{17} +27.7307i q^{19} +(60.2605 + 117.459i) q^{20} +(8.46941 + 35.0629i) q^{22} +(-17.5836 + 30.4556i) q^{23} +(73.6567 + 127.577i) q^{25} +(45.8008 - 43.5845i) q^{26} +(-177.716 - 8.81837i) q^{28} +(-1.01189 + 0.584217i) q^{29} +(119.361 + 68.9130i) q^{31} +(-24.8745 - 179.302i) q^{32} +(93.7830 - 318.230i) q^{34} -367.033 q^{35} +233.596 q^{37} +(22.1720 - 75.2352i) q^{38} +(-69.5764 - 366.856i) q^{40} +(-13.2561 - 7.65340i) q^{41} +(-361.460 + 208.689i) q^{43} +(5.05631 - 101.900i) q^{44} +(72.0561 - 68.5693i) q^{46} +(116.494 + 201.773i) q^{47} +(75.8499 - 131.376i) q^{49} +(-97.8316 - 405.017i) q^{50} +(-159.109 + 81.6278i) q^{52} -180.951i q^{53} -210.451i q^{55} +(475.105 + 166.017i) q^{56} +(3.21244 - 0.775964i) q^{58} +(313.716 - 543.373i) q^{59} +(-382.110 - 661.834i) q^{61} +(-268.735 - 282.400i) q^{62} +(-75.8742 + 506.347i) q^{64} +(-319.452 + 184.435i) q^{65} +(113.463 + 65.5077i) q^{67} +(-508.879 + 788.395i) q^{68} +(995.785 + 293.460i) q^{70} -22.6910 q^{71} +387.864 q^{73} +(-633.762 - 186.771i) q^{74} +(-120.308 + 186.390i) q^{76} +(245.650 + 141.826i) q^{77} +(486.411 - 280.830i) q^{79} +(-104.553 + 1050.93i) q^{80} +(29.8454 + 31.3630i) q^{82} +(342.111 + 592.554i) q^{83} +(-967.799 + 1676.28i) q^{85} +(1147.52 - 277.183i) q^{86} +(-95.1915 + 272.417i) q^{88} -278.003i q^{89} -497.177i q^{91} +(-250.317 + 128.421i) q^{92} +(-154.728 - 640.565i) q^{94} +(-228.805 + 396.302i) q^{95} +(-264.443 - 458.028i) q^{97} +(-310.827 + 295.786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 24 * q - 12 * q^4 + 72 * q^5	\( 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

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