LMFDB - Embedded newform 108.4.h.b.35.6

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			35.6
Character	$\chi$	$=$	108.35
Dual form			108.4.h.b.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.664105 - 2.74936i) q^{2} +(-7.11793 + 3.65173i) q^{4} +(14.2911 - 8.25096i) q^{5} +(19.2620 + 11.1209i) q^{7} +(14.7670 + 17.1446i) q^{8} +O(q^{10})$	\(q+(-0.664105 - 2.74936i) q^{2} +(-7.11793 + 3.65173i) q^{4} +(14.2911 - 8.25096i) q^{5} +(19.2620 + 11.1209i) q^{7} +(14.7670 + 17.1446i) q^{8} +(-32.1756 - 33.8118i) q^{10} +(6.37655 - 11.0445i) q^{11} +(-11.1766 - 19.3584i) q^{13} +(17.7834 - 60.3436i) q^{14} +(37.3298 - 51.9854i) q^{16} -117.295i q^{17} +27.7307i q^{19} +(-71.5926 + 110.917i) q^{20} +(-34.6000 - 10.1967i) q^{22} +(17.5836 + 30.4556i) q^{23} +(73.6567 - 127.577i) q^{25} +(-45.8008 + 43.5845i) q^{26} +(-177.716 - 8.81837i) q^{28} +(-1.01189 - 0.584217i) q^{29} +(-119.361 + 68.9130i) q^{31} +(-167.717 - 68.1091i) q^{32} +(-322.487 + 77.8965i) q^{34} +367.033 q^{35} +233.596 q^{37} +(76.2416 - 18.4161i) q^{38} +(352.495 + 123.173i) q^{40} +(-13.2561 + 7.65340i) q^{41} +(361.460 + 208.689i) q^{43} +(-5.05631 + 101.900i) q^{44} +(72.0561 - 68.5693i) q^{46} +(-116.494 + 201.773i) q^{47} +(75.8499 + 131.376i) q^{49} +(-399.671 - 117.784i) q^{50} +(150.246 + 96.9781i) q^{52} +180.951i q^{53} -210.451i q^{55} +(93.7774 + 494.461i) q^{56} +(-0.934217 + 3.17004i) q^{58} +(-313.716 - 543.373i) q^{59} +(-382.110 + 661.834i) q^{61} +(268.735 + 282.400i) q^{62} +(-75.8742 + 506.347i) q^{64} +(-319.452 - 184.435i) q^{65} +(-113.463 + 65.5077i) q^{67} +(428.330 + 834.900i) q^{68} +(-243.749 - 1009.11i) q^{70} +22.6910 q^{71} +387.864 q^{73} +(-155.133 - 642.240i) q^{74} +(-101.265 - 197.385i) q^{76} +(245.650 - 141.826i) q^{77} +(-486.411 - 280.830i) q^{79} +(104.553 - 1050.93i) q^{80} +(29.8454 + 31.3630i) q^{82} +(-342.111 + 592.554i) q^{83} +(-967.799 - 1676.28i) q^{85} +(333.713 - 1132.38i) q^{86} +(283.516 - 53.7704i) q^{88} +278.003i q^{89} -497.177i q^{91} +(-236.374 - 152.571i) q^{92} +(632.110 + 186.284i) q^{94} +(228.805 + 396.302i) q^{95} +(-264.443 + 458.028i) q^{97} +(310.827 - 295.786i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.664105	−	2.74936i	−0.234797	−	0.972044i
$2$	−0.664105	−	2.74936i	−0.234797	−	0.972044i
$3$		0			0
$3$		0			0
$4$	−7.11793	+	3.65173i	−0.889741	+	0.456466i
$5$	14.2911	−	8.25096i	1.27823	−	0.737988i	0.301710	−	0.953400i	$-0.402443\pi$
$5$	14.2911	−	8.25096i	1.27823	−	0.737988i	0.976523	+	0.215411i	$0.0691093\pi$
$6$		0			0
$7$	19.2620	+	11.1209i	1.04005	+	0.600473i	0.919848	−	0.392276i	$-0.128312\pi$
$7$	19.2620	+	11.1209i	1.04005	+	0.600473i	0.120203	+	0.992749i	$0.461645\pi$
$8$	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	$-0.777411\pi$
$11$	6.37655	−	11.0445i	0.174782	−	0.302732i	0.940086	+	0.340938i	$0.110745\pi$
$12$		0			0
$13$	−11.1766	−	19.3584i	−0.238449	−	0.413005i	0.721821	−	0.692080i	$-0.243306\pi$
$13$	−11.1766	−	19.3584i	−0.238449	−	0.413005i	−0.960269	+	0.279075i	$0.909972\pi$
$14$	17.7834	−	60.3436i	0.339486	−	1.15196i
$15$		0			0
$16$	37.3298	−	51.9854i	0.583278	−	0.812273i
$17$		−	117.295i		−	1.67343i	−0.547639	−	0.836715i	$-0.684473\pi$
$17$		−	117.295i		−	1.67343i	0.547639	−	0.836715i	$-0.315527\pi$
$18$		0			0
$19$			27.7307i			0.334835i	0.985886	+	0.167417i	$0.0535427\pi$
$19$			27.7307i			0.334835i	−0.985886	+	0.167417i	$0.946457\pi$
$20$	−71.5926	+	110.917i	−0.800430	+	1.24009i
$21$		0			0
$22$	−34.6000	−	10.1967i	−0.335307	−	0.0988156i
$23$	17.5836	+	30.4556i	0.159410	+	0.276106i	0.934656	−	0.355553i	$-0.115708\pi$
$23$	17.5836	+	30.4556i	0.159410	+	0.276106i	−0.775246	+	0.631659i	$0.782374\pi$
$24$		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	0.496757	−	0.867890i	$-0.334524\pi$
$29$	−1.01189	−	0.584217i	−0.00647945	−	0.00374091i	−0.503236	+	0.864149i	$0.667857\pi$
$30$		0			0
$31$	−119.361	+	68.9130i	−0.691543	+	0.399263i	−0.804190	−	0.594373i	$-0.797400\pi$
$31$	−119.361	+	68.9130i	−0.691543	+	0.399263i	0.112647	+	0.993635i	$0.464067\pi$
$32$	−167.717	−	68.1091i	−0.926517	−	0.376253i
$33$		0			0
$34$	−322.487	+	77.8965i	−1.62665	+	0.392916i
$35$	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	$0.326320\pi$
$38$	76.2416	−	18.4161i	0.325474	−	0.0786180i
$39$		0			0
$40$	352.495	+	123.173i	1.39336	+	0.486885i
$41$	−13.2561	+	7.65340i	−0.0504940	+	0.0291527i	−0.525034	−	0.851081i	$-0.675948\pi$
$41$	−13.2561	+	7.65340i	−0.0504940	+	0.0291527i	0.474541	+	0.880234i	$0.342614\pi$
$42$		0			0
$43$	361.460	+	208.689i	1.28191	+	0.740112i	0.977198	−	0.212332i	$-0.0681059\pi$
$43$	361.460	+	208.689i	1.28191	+	0.740112i	0.304714	+	0.952444i	$0.401439\pi$
$44$	−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	$-0.951082\pi$
$47$	−116.494	+	201.773i	−0.361539	+	0.626204i	0.626675	+	0.779281i	$0.284415\pi$
$48$		0			0
$49$	75.8499	+	131.376i	0.221137	+	0.383020i
$50$	−399.671	−	117.784i	−1.13044	−	0.333143i
$51$		0			0
$52$	150.246	+	96.9781i	0.400680	+	0.258624i
$53$			180.951i			0.468972i	0.972120	+	0.234486i	$0.0753407\pi$
$53$			180.951i			0.468972i	−0.972120	+	0.234486i	$0.924659\pi$
$54$		0			0
$55$		−	210.451i		−	0.515949i
$56$	93.7774	+	494.461i	0.223777	+	1.17991i
$57$		0			0
$58$	−0.934217	+	3.17004i	−0.00211498	+	0.00717666i
$59$	−313.716	−	543.373i	−0.692244	−	1.19900i	−0.971101	−	0.238669i	$-0.923289\pi$
$59$	−313.716	−	543.373i	−0.692244	−	1.19900i	0.278857	−	0.960333i	$-0.410045\pi$
$60$		0			0
$61$	−382.110	+	661.834i	−0.802035	+	1.38917i	0.116239	+	0.993221i	$0.462916\pi$
$61$	−382.110	+	661.834i	−0.802035	+	1.38917i	−0.918274	+	0.395945i	$0.870417\pi$
$62$	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	$-0.704779\pi$
$67$	−113.463	+	65.5077i	−0.206891	+	0.119448i	0.392975	+	0.919549i	$0.371446\pi$
$68$	428.330	+	834.900i	0.763863	+	1.48892i
$69$		0			0
$70$	−243.749	−	1009.11i	−0.416194	−	1.72302i
$71$	22.6910			0.0379285			0.0189643	−	0.999820i	$-0.493963\pi$
$71$	22.6910			0.0379285			0.0189643	+	0.999820i	$0.493963\pi$
$72$		0			0
$73$	387.864			0.621863			0.310932	−	0.950432i	$-0.399359\pi$
$73$	387.864			0.621863			0.310932	+	0.950432i	$0.399359\pi$
$74$	−155.133	−	642.240i	−0.243700	−	1.00890i
$75$		0			0
$76$	−101.265	−	197.385i	−0.152840	−	0.297916i
$77$	245.650	−	141.826i	0.363565	−	0.209904i
$78$		0			0
$79$	−486.411	−	280.830i	−0.692729	−	0.399947i	0.111905	−	0.993719i	$-0.464305\pi$
$79$	−486.411	−	280.830i	−0.692729	−	0.399947i	−0.804633	+	0.593772i	$0.797638\pi$
$80$	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	$-0.982776\pi$
$83$	−342.111	+	592.554i	−0.452429	+	0.783629i	0.546108	+	0.837715i	$0.316109\pi$
$84$		0			0
$85$	−967.799	−	1676.28i	−1.23497	−	2.13903i
$86$	333.713	−	1132.38i	0.418433	−	1.41985i
$87$		0			0
$88$	283.516	−	53.7704i	0.343442	−	0.0651357i
$89$			278.003i			0.331103i	0.986201	+	0.165552i	$0.0529405\pi$
$89$			278.003i			0.331103i	−0.986201	+	0.165552i	$0.947060\pi$
$90$		0			0
$91$		−	497.177i		−	0.572728i
$92$	−236.374	−	152.571i	−0.267866	−	0.172898i
$93$		0			0
$94$	632.110	+	186.284i	0.693587	+	0.204402i
$95$	228.805	+	396.302i	0.247104	+	0.427997i
$96$		0			0
$97$	−264.443	+	458.028i	−0.276805	+	0.479440i	−0.970589	−	0.240743i	$-0.922609\pi$
$97$	−264.443	+	458.028i	−0.276805	+	0.479440i	0.693784	+	0.720183i	$0.255942\pi$
$98$	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	0.965650	−	0.259845i	$-0.0836714\pi$
$101$	1241.84	+	716.977i	1.22344	+	0.706355i	0.257793	+	0.966200i	$0.417005\pi$
$102$		0			0
$103$	−199.095	+	114.948i	−0.190460	+	0.109962i	−0.592198	−	0.805792i	$-0.701740\pi$
$103$	−199.095	+	114.948i	−0.190460	+	0.109962i	0.401738	+	0.915755i	$0.368406\pi$
$104$	166.848	−	477.484i	0.157316	−	0.450203i
$105$		0			0
$106$	497.498	−	120.170i	0.455862	−	0.110113i
$107$	−1676.13			−1.51437			−0.757184	−	0.653201i	$-0.773426\pi$
$107$	−1676.13			−1.51437			−0.757184	+	0.653201i	$0.773426\pi$
$108$		0			0
$109$	−540.666			−0.475104			−0.237552	−	0.971375i	$-0.576345\pi$
$109$	−540.666			−0.475104			−0.237552	+	0.971375i	$0.576345\pi$
$110$	−578.604	+	139.762i	−0.501525	+	0.121143i
$111$		0			0
$112$	1297.17	−	586.202i	1.09439	−	0.494562i
$113$	−1110.83	+	641.340i	−0.924764	+	0.533913i	−0.885152	−	0.465302i	$-0.845946\pi$
$113$	−1110.83	+	641.340i	−0.924764	+	0.533913i	−0.0396123	+	0.999215i	$0.512612\pi$
$114$		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
$122$	2073.38	+	611.029i	1.53865	+	0.453442i
$123$		0			0
$124$	597.950	−	926.391i	0.433044	−	0.670906i
$125$		−	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	$-0.384103\pi$
$128$	1442.52	−	127.662i	0.996107	−	0.0881552i
$129$		0			0
$130$	−294.929	+	1000.77i	−0.198977	+	0.675180i
$131$	413.401	+	716.031i	0.275717	+	0.477557i	0.970316	−	0.241841i	$-0.0777513\pi$
$131$	413.401	+	716.031i	0.275717	+	0.477557i	−0.694598	+	0.719398i	$0.744418\pi$
$132$		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	0.314794	−	0.949160i	$-0.398065\pi$
$137$	−560.929	−	323.852i	−0.349806	−	0.201960i	−0.664600	+	0.747200i	$0.731398\pi$
$138$		0			0
$139$	−2312.71	+	1335.24i	−1.41124	+	0.814777i	−0.995505	−	0.0947110i	$-0.969807\pi$
$139$	−2312.71	+	1335.24i	−1.41124	+	0.814777i	−0.415730	+	0.909488i	$0.636474\pi$
$140$	−2612.52	+	1340.30i	−1.57713	+	0.809117i
$141$		0			0
$142$	−15.0692	−	62.3857i	−0.00890550	−	0.0368682i
$143$	−285.073			−0.166706
$144$		0			0
$145$	−19.2814			−0.0110430
$146$	−257.583	−	1066.38i	−0.146012	−	0.604479i
$147$		0			0
$148$	−1662.72	+	853.030i	−0.923479	+	0.473774i
$149$	90.2485	−	52.1050i	0.0496204	−	0.0286484i	−0.474985	−	0.879994i	$-0.657546\pi$
$149$	90.2485	−	52.1050i	0.0496204	−	0.0286484i	0.524605	+	0.851346i	$0.324213\pi$
$150$		0			0
$151$	2382.77	+	1375.69i	1.28415	+	0.741407i	0.977605	−	0.210448i	$-0.0674924\pi$
$151$	2382.77	+	1375.69i	1.28415	+	0.741407i	0.306549	+	0.951855i	$0.400826\pi$
$152$	−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	0.975129	−	0.221638i	$-0.0711404\pi$
$157$	581.545	+	1007.27i	0.295620	+	0.512029i	−0.679509	+	0.733667i	$0.737807\pi$
$158$	−449.073	+	1523.82i	−0.226116	+	0.767269i
$159$		0			0
$160$	−2958.83	+	410.477i	−1.46198	+	0.202819i
$161$			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	$0.751359\pi$
$164$	66.4077	−	102.884i	0.0316193	−	0.0489871i
$165$		0			0
$166$	1856.34	+	547.067i	0.867951	+	0.255787i
$167$	435.960	+	755.105i	0.202010	+	0.349891i	0.949176	−	0.314746i	$-0.101919\pi$
$167$	435.960	+	755.105i	0.202010	+	0.349891i	−0.747166	+	0.664637i	$0.768586\pi$
$168$		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	−0.0145882	−	0.999894i	$-0.504644\pi$
$173$	−2020.19	−	1166.36i	−0.887816	−	0.512581i	−0.873227	+	0.487313i	$0.837977\pi$
$174$		0			0
$175$	2837.55	−	1638.26i	1.22571	−	0.707662i
$176$	−336.119	−	743.778i	−0.143954	−	0.318547i
$177$		0			0
$178$	764.328	−	184.623i	0.321847	−	0.0777420i
$179$	638.773			0.266727			0.133364	−	0.991067i	$-0.457422\pi$
$179$	638.773			0.266727			0.133364	+	0.991067i	$0.457422\pi$
$180$		0			0
$181$	4031.01			1.65537			0.827686	−	0.561192i	$-0.189657\pi$
$181$	4031.01			1.65537			0.827686	+	0.561192i	$0.189657\pi$
$182$	−1366.92	+	330.178i	−0.556717	+	0.134475i
$183$		0			0
$184$	−262.494	+	751.200i	−0.105170	+	0.300974i
$185$	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	−0.276626	−	0.960978i	$-0.589216\pi$
$191$	1831.72	−	3172.63i	0.693918	−	1.20190i	0.970544	−	0.240924i	$-0.0774505\pi$
$192$		0			0
$193$	−708.828	−	1227.73i	−0.264366	−	0.457895i	0.703032	−	0.711159i	$-0.251829\pi$
$193$	−708.828	−	1227.73i	−0.264366	−	0.457895i	−0.967397	+	0.253264i	$0.918496\pi$
$194$	1434.90	+	422.868i	0.531030	+	0.156496i
$195$		0			0
$196$	−1019.64	−	658.141i	−0.371590	−	0.239847i
$197$		−	876.917i		−	0.317146i	−0.987347	−	0.158573i	$-0.949311\pi$
$197$		−	876.917i		−	0.317146i	0.987347	−	0.158573i	$-0.0506893\pi$
$198$		0			0
$199$			1485.45i			0.529149i	0.964365	+	0.264574i	$0.0852315\pi$
$199$			1485.45i			0.529149i	−0.964365	+	0.264574i	$0.914769\pi$
$200$	3274.94	−	621.111i	1.15787	−	0.219596i
$201$		0			0
$202$	1146.51	−	3890.41i	0.399348	−	1.35509i
$203$	−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	$-0.682649\pi$
$211$	−266.434	+	153.826i	−0.0869294	+	0.0501887i	0.455905	+	0.890028i	$0.349316\pi$
$212$	−660.783	−	1288.00i	−0.214070	−	0.417264i
$213$		0			0
$214$	1113.13	+	4608.28i	0.355569	+	1.47203i
$215$	6887.55			2.18478
$216$		0			0
$217$	−3065.50			−0.958986
$218$	359.059	+	1486.48i	0.111553	+	0.461823i
$219$		0			0
$220$	768.509	+	1497.97i	0.235513	+	0.459061i
$221$	−2270.66	+	1310.96i	−0.691135	+	0.399027i
$222$		0			0
$223$	−3380.52	−	1951.74i	−1.01514	−	0.586091i	−0.102447	−	0.994738i	$-0.532667\pi$
$223$	−3380.52	−	1951.74i	−1.01514	−	0.586091i	−0.912692	+	0.408647i	$0.866001\pi$
$224$	−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	$-0.924323\pi$
$227$	−964.382	+	1670.36i	−0.281975	+	0.488394i	0.689896	+	0.723908i	$0.257656\pi$
$228$		0			0
$229$	−1148.71	−	1989.62i	−0.331479	−	0.574139i	0.651323	−	0.758801i	$-0.274214\pi$
$229$	−1148.71	−	1989.62i	−0.331479	−	0.574139i	−0.982802	+	0.184662i	$0.940881\pi$
$230$	463.997	−	1574.46i	0.133022	−	0.451378i
$231$		0			0
$232$	−4.92642	−	25.9756i	−0.00139412	−	0.00735079i
$233$		−	3366.60i		−	0.946580i	−0.880907	−	0.473290i	$-0.843066\pi$
$233$		−	3366.60i		−	0.946580i	0.880907	−	0.473290i	$-0.156934\pi$
$234$		0			0
$235$			3844.74i			1.06725i
$236$	4217.26	+	2722.08i	1.16322	+	0.750816i
$237$		0			0
$238$	−7078.02	−	2085.91i	−1.92773	−	0.568106i
$239$	−307.571	−	532.729i	−0.0832432	−	0.144182i	0.821398	−	0.570355i	$-0.193195\pi$
$239$	−307.571	−	532.729i	−0.0832432	−	0.144182i	−0.904641	+	0.426174i	$0.859861\pi$
$240$		0			0
$241$	2195.78	−	3803.20i	0.586898	−	1.01654i	−0.407738	−	0.913099i	$-0.633682\pi$
$241$	2195.78	−	3803.20i	0.586898	−	1.01654i	0.994636	−	0.103438i	$-0.0329844\pi$
$242$	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
$248$	−2944.08	−	1028.76i	−0.753828	−	0.263412i
$249$		0			0
$250$	−1012.35	+	244.533i	−0.256107	+	0.0618624i
$251$	−7726.08			−1.94289			−0.971446	−	0.237259i	$-0.923751\pi$
$251$	−7726.08			−1.94289			−0.971446	+	0.237259i	$0.923751\pi$
$252$		0			0
$253$	448.490			0.111448
$254$	−7353.94	+	1776.34i	−1.81664	+	0.438809i
$255$		0			0
$256$	−1308.97	−	3881.21i	−0.319573	−	0.947562i
$257$	2222.83	−	1283.35i	0.539518	−	0.311491i	−0.205365	−	0.978685i	$-0.565838\pi$
$257$	2222.83	−	1283.35i	0.539518	−	0.311491i	0.744884	+	0.667194i	$0.232505\pi$
$258$		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	$-0.989021\pi$
$263$	−2003.92	+	3470.89i	−0.469837	+	0.813781i	0.529569	+	0.848267i	$0.322354\pi$
$264$		0			0
$265$	1493.02	+	2585.98i	0.346096	+	0.599456i
$266$	1673.37	+	493.146i	0.385717	+	0.113672i
$267$		0			0
$268$	568.403	−	880.614i	0.129555	−	0.200717i
$269$		−	2242.21i		−	0.508214i	−0.967176	−	0.254107i	$-0.918218\pi$
$269$		−	2242.21i		−	0.508214i	0.967176	−	0.254107i	$-0.0817816\pi$
$270$		0			0
$271$		−	6324.08i		−	1.41757i	−0.705426	−	0.708784i	$-0.749244\pi$
$271$		−	6324.08i		−	1.41757i	0.705426	−	0.708784i	$-0.250756\pi$
$272$	−6097.65	−	4378.61i	−1.35928	−	0.976075i
$273$		0			0
$274$	−517.870	+	1757.27i	−0.114181	+	0.387446i
$275$	−939.352	−	1627.01i	−0.205982	−	0.356771i
$276$		0			0
$277$	−625.852	+	1084.01i	−0.135754	+	0.235132i	−0.925885	−	0.377805i	$-0.876679\pi$
$277$	−625.852	+	1084.01i	−0.135754	+	0.235132i	0.790131	+	0.612938i	$0.210012\pi$
$278$	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	0.621001	−	0.783810i	$-0.286726\pi$
$281$	1190.34	+	687.240i	0.252703	+	0.145898i	−0.368298	+	0.929708i	$0.620060\pi$
$282$		0			0
$283$	4006.16	−	2312.96i	0.841490	−	0.485835i	−0.0162801	−	0.999867i	$-0.505182\pi$
$283$	4006.16	−	2312.96i	0.841490	−	0.485835i	0.857771	+	0.514033i	$0.171849\pi$
$284$	−161.513	+	82.8613i	−0.0337466	+	0.0173131i
$285$		0			0
$286$	189.318	+	783.767i	0.0391421	+	0.162046i
$287$	−340.452			−0.0700217
$288$		0			0
$289$	−8845.19			−1.80037
$290$	12.8049	+	53.0115i	0.00259286	+	0.0107343i
$291$		0			0
$292$	−2760.79	+	1416.37i	−0.553297	+	0.283859i
$293$	−5522.68	+	3188.52i	−1.10116	+	0.635752i	−0.936524	−	0.350603i	$-0.885977\pi$
$293$	−5522.68	+	3188.52i	−1.10116	+	0.635752i	−0.164631	+	0.986355i	$0.552643\pi$
$294$		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
$302$	2199.86	−	7464.70i	0.419165	−	1.42233i
$303$		0			0
$304$	1441.59	+	1035.18i	0.271977	+	0.195302i
$305$			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	$0.789415\pi$
$308$	−1230.61	+	1906.56i	−0.227664	+	0.352715i
$309$		0			0
$310$	6170.58	+	1818.48i	1.13053	+	0.333171i
$311$	−2568.35	−	4448.51i	−0.468288	−	0.811098i	0.531055	−	0.847337i	$-0.321796\pi$
$311$	−2568.35	−	4448.51i	−0.468288	−	0.811098i	−0.999343	+	0.0362387i	$0.988462\pi$
$312$		0			0
$313$	−3101.42	+	5371.82i	−0.560072	+	0.970074i	0.437417	+	0.899259i	$0.355893\pi$
$313$	−3101.42	+	5371.82i	−0.560072	+	0.970074i	−0.997489	+	0.0708150i	$0.977440\pi$
$314$	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	0.353395	−	0.935474i	$-0.385027\pi$
$317$	−1580.62	−	912.574i	−0.280053	−	0.161689i	−0.633447	+	0.773786i	$0.718361\pi$
$318$		0			0
$319$	−12.9048	+	7.45058i	−0.00226498	+	0.00130769i
$320$	3093.52	+	7862.28i	0.540416	+	1.37348i
$321$		0			0
$322$	2150.50	−	519.451i	0.372182	−	0.0899003i
$323$	3252.68			0.560322
$324$		0			0
$325$	−3292.93			−0.562027
$326$	8056.84	−	1946.13i	1.36880	−	0.330632i
$327$		0			0
$328$	−326.966	−	114.253i	−0.0550418	−	0.0192334i
$329$	−4487.80	+	2591.03i	−0.752038	+	0.434189i
$330$		0			0
$331$	−3444.37	−	1988.61i	−0.571963	−	0.330223i	0.185970	−	0.982555i	$-0.440457\pi$
$331$	−3444.37	−	1988.61i	−0.571963	−	0.330223i	−0.757933	+	0.652332i	$0.773791\pi$
$332$	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	0.909009	−	0.416776i	$-0.136840\pi$
$337$	578.847	+	1002.59i	0.0935662	+	0.162061i	−0.815443	+	0.578837i	$0.803507\pi$
$338$	−4604.98	−	1357.10i	−0.741059	−	0.218392i
$339$		0			0
$340$	13010.0	+	8397.48i	2.07520	+	1.33946i
$341$			1757.71i			0.279136i
$342$		0			0
$343$		−	4254.87i		−	0.669800i
$344$	1759.78	+	9278.79i	0.275816	+	1.45430i
$345$		0			0
$346$	−1865.11	+	6328.80i	−0.289795	+	0.983348i
$347$	−1241.63	−	2150.56i	−0.192086	−	0.332703i	0.753855	−	0.657041i	$-0.228192\pi$
$347$	−1241.63	−	2150.56i	−0.192086	−	0.332703i	−0.945941	+	0.324337i	$0.894859\pi$
$348$		0			0
$349$	2986.90	−	5173.47i	0.458124	−	0.793494i	−0.540738	−	0.841191i	$-0.681855\pi$
$349$	2986.90	−	5173.47i	0.458124	−	0.793494i	0.998862	+	0.0476973i	$0.0151883\pi$
$350$	−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	0.565821	−	0.824528i	$-0.308559\pi$
$353$	893.160	+	515.666i	0.134669	+	0.0777511i	−0.431152	+	0.902279i	$0.641893\pi$
$354$		0			0
$355$	324.279	−	187.223i	0.0484815	−	0.0279908i
$356$	−1015.19	−	1978.80i	−0.151137	−	0.294596i
$357$		0			0
$358$	−424.213	−	1756.22i	−0.0626267	−	0.259271i
$359$	4218.99			0.620249			0.310125	−	0.950696i	$-0.399629\pi$
$359$	4218.99			0.620249			0.310125	+	0.950696i	$0.399629\pi$
$360$		0			0
$361$	6090.01			0.887886
$362$	−2677.01	−	11082.7i	−0.388676	−	1.60909i
$363$		0			0
$364$	1815.55	+	3538.87i	0.261431	+	0.509580i
$365$	5542.99	−	3200.25i	0.794887	−	0.458928i
$366$		0			0
$367$	2632.91	+	1520.11i	0.374487	+	0.216210i	0.675417	−	0.737436i	$-0.263964\pi$
$367$	2632.91	+	1520.11i	0.374487	+	0.216210i	−0.300930	+	0.953646i	$0.597297\pi$
$368$	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	0.631939	−	0.775018i	$-0.282259\pi$
$373$	−2558.92	−	4432.17i	−0.355216	−	0.615253i	−0.987155	+	0.159766i	$0.948926\pi$
$374$	−1196.03	+	4058.42i	−0.165361	+	0.561112i
$375$		0			0
$376$	−5179.57	+	982.335i	−0.710415	+	0.134734i
$377$			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	$-0.0616585\pi$
$380$	−3075.80	−	1985.31i	−0.415224	−	0.268012i
$381$		0			0
$382$	−9939.14	−	2929.09i	−1.33123	−	0.392317i
$383$	2814.33	+	4874.56i	0.375472	+	0.650336i	0.990397	−	0.138249i	$-0.0441474\pi$
$383$	2814.33	+	4874.56i	0.375472	+	0.650336i	−0.614926	+	0.788585i	$0.710814\pi$
$384$		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	0.687375	−	0.726303i	$-0.258763\pi$
$389$	3084.76	+	1780.99i	0.402065	+	0.232132i	−0.285309	+	0.958435i	$0.592096\pi$
$390$		0			0
$391$	3572.30	−	2062.47i	0.462044	−	0.266761i
$392$	−1132.31	+	3240.44i	−0.145894	+	0.417517i
$393$		0			0
$394$	−2410.96	+	582.365i	−0.308280	+	0.0744648i
$395$	−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	$0.703209\pi$
$398$	4084.03	−	986.494i	0.514356	−	0.124242i
$399$		0			0
$400$	−3882.56	−	8591.50i	−0.485321	−	1.07394i
$401$	7475.17	−	4315.79i	0.930903	−	0.537457i	0.0438059	−	0.999040i	$-0.486052\pi$
$401$	7475.17	−	4315.79i	0.930903	−	0.537457i	0.887097	+	0.461583i	$0.152718\pi$
$402$		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	0.632517	−	0.774546i	$-0.282022\pi$
$409$	−2932.40	−	5079.07i	−0.354518	−	0.614044i	−0.987035	+	0.160503i	$0.948688\pi$
$410$	685.298	+	201.959i	0.0825474	+	0.0243269i
$411$		0			0
$412$	997.387	−	1545.23i	0.119266	−	0.184777i
$413$		−	13955.3i		−	1.66270i
$414$		0			0
$415$			11291.0i			1.33555i
$416$	556.025	+	4007.98i	0.0655321	+	0.472373i
$417$		0			0
$418$	282.762	−	959.482i	0.0330869	−	0.112272i
$419$	3477.85	+	6023.82i	0.405500	+	0.702346i	0.994379	−	0.105875i	$-0.0337642\pi$
$419$	3477.85	+	6023.82i	0.405500	+	0.702346i	−0.588880	+	0.808221i	$0.700431\pi$
$420$		0			0
$421$	4697.89	−	8136.99i	0.543851	−	0.941978i	−0.454827	−	0.890580i	$-0.650299\pi$
$421$	4697.89	−	8136.99i	0.543851	−	0.941978i	0.998678	−	0.0513981i	$-0.0163677\pi$
$422$	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
$428$	11930.6	−	6120.76i	1.34740	−	0.691258i
$429$		0			0
$430$	−4574.06	−	18936.3i	−0.512978	−	2.12370i
$431$	7346.03			0.820988			0.410494	−	0.911863i	$-0.365356\pi$
$431$	7346.03			0.820988			0.410494	+	0.911863i	$0.365356\pi$
$432$		0			0
$433$	13673.0			1.51751			0.758755	−	0.651376i	$-0.225808\pi$
$433$	13673.0			1.51751			0.758755	+	0.651376i	$0.225808\pi$
$434$	2035.82	+	8428.17i	0.225167	+	0.932177i
$435$		0			0
$436$	3848.42	−	1974.36i	0.422720	−	0.216869i
$437$	−844.556	+	487.604i	−0.0924498	+	0.0533759i
$438$		0			0
$439$	4995.87	+	2884.37i	0.543144	+	0.313584i	0.746352	−	0.665551i	$-0.231804\pi$
$439$	4995.87	+	2884.37i	0.543144	+	0.313584i	−0.203208	+	0.979135i	$0.565137\pi$
$440$	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	−0.482157	−	0.876085i	$-0.660146\pi$
$443$	4826.45	−	8359.66i	0.517634	−	0.896568i	0.999790	−	0.0204826i	$-0.00652029\pi$
$444$		0			0
$445$	2293.79	+	3972.96i	0.244351	+	0.423228i
$446$	−3121.02	+	10590.4i	−0.331355	+	1.12437i
$447$		0			0
$448$	−7092.53	+	8909.46i	−0.747970	+	0.939582i
$449$		−	11492.2i		−	1.20791i	−0.797018	−	0.603955i	$-0.793590\pi$
$449$		−	11492.2i		−	1.20791i	0.797018	−	0.603955i	$-0.206410\pi$
$450$		0			0
$451$			195.209i			0.0203815i
$452$	5564.83	−	8621.46i	0.579088	−	0.897167i
$453$		0			0
$454$	5232.86	+	1542.14i	0.540948	+	0.159419i
$455$	−4102.19	−	7105.19i	−0.422667	−	0.732080i
$456$		0			0
$457$	−8821.06	+	15278.5i	−0.902914	+	1.56389i	−0.0792214	+	0.996857i	$0.525243\pi$
$457$	−8821.06	+	15278.5i	−0.902914	+	1.56389i	−0.823693	+	0.567036i	$0.808090\pi$
$458$	−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	0.942848	−	0.333224i	$-0.108137\pi$
$461$	11142.2	+	6432.95i	1.12569	+	0.649918i	0.182843	+	0.983142i	$0.441470\pi$
$462$		0			0
$463$	11984.7	−	6919.34i	1.20297	−	0.694534i	0.241754	−	0.970338i	$-0.422277\pi$
$463$	11984.7	−	6919.34i	1.20297	−	0.694534i	0.961214	+	0.275804i	$0.0889440\pi$
$464$	−68.1446	+	30.7950i	−0.00681796	+	0.00308109i
$465$		0			0
$466$	−9255.98	+	2235.78i	−0.920118	+	0.222254i
$467$	−81.1441			−0.00804047			−0.00402024	−	0.999992i	$-0.501280\pi$
$467$	−81.1441			−0.00804047			−0.00402024	+	0.999992i	$0.501280\pi$
$468$		0			0
$469$	−2914.03			−0.286902
$470$	10570.6	−	2553.31i	1.03741	−	0.250586i
$471$		0			0
$472$	4683.27	−	13402.5i	0.456706	−	1.30699i
$473$	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	−0.251071	−	0.967969i	$-0.580783\pi$
$479$	7472.06	−	12942.0i	0.712750	−	1.23452i	0.963821	−	0.266550i	$-0.0858838\pi$
$480$		0			0
$481$	−2610.81	−	4522.06i	−0.247490	−	0.428666i
$482$	−11914.6	−	3511.25i	−1.12592	−	0.331811i
$483$		0			0
$484$	−7853.06	−	5068.86i	−0.737515	−	0.476038i
$485$			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	$-0.0890338\pi$
$488$	−16989.5	+	3222.15i	−1.57598	+	0.298893i
$489$		0			0
$490$	2001.53	−	6791.72i	0.184531	−	0.626160i
$491$	10032.4	+	17376.6i	0.922110	+	1.59714i	0.796145	+	0.605106i	$0.206869\pi$
$491$	10032.4	+	17376.6i	0.922110	+	1.59714i	0.125965	+	0.992035i	$0.459797\pi$
$492$		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	$-0.527984\pi$
$499$	8148.09	−	4704.30i	0.730979	−	0.422031i	0.818780	+	0.574107i	$0.194651\pi$
$500$	1344.62	+	2620.92i	0.120266	+	0.234422i
$501$		0			0
$502$	5130.93	+	21241.8i	0.456185	+	1.88858i
$503$	−12736.4			−1.12900			−0.564501	−	0.825432i	$-0.690931\pi$
$503$	−12736.4			−1.12900			−0.564501	+	0.825432i	$0.690931\pi$
$504$		0			0
$505$	23663.0			2.08513
$506$	−297.845	−	1233.06i	−0.0261676	−	0.108332i
$507$		0			0
$508$	9767.58	+	19038.9i	0.853084	+	1.66283i
$509$	−7921.59	+	4573.53i	−0.689820	+	0.398268i	−0.803545	−	0.595244i	$-0.797055\pi$
$509$	−7921.59	+	4573.53i	−0.689820	+	0.398268i	0.113724	+	0.993512i	$0.463722\pi$
$510$		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
$518$	4154.13	−	14096.0i	0.352359	−	1.19565i
$519$		0			0
$520$	−1555.26	−	8200.42i	−0.131159	−	0.691562i
$521$			7691.78i			0.646801i	0.946262	+	0.323400i	$0.104826\pi$
$521$			7691.78i			0.646801i	−0.946262	+	0.323400i	$0.895174\pi$
$522$		0			0
$523$			9967.82i			0.833389i	0.909047	+	0.416694i	$0.136811\pi$
$523$			9967.82i			0.833389i	−0.909047	+	0.416694i	$0.863189\pi$
$524$	−5557.30	−	3587.03i	−0.463305	−	0.299046i
$525$		0			0
$526$	10873.5	+	3204.45i	0.901347	+	0.265629i
$527$	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
$536$	−2798.60	−	977.923i	−0.225525	−	0.0788057i
$537$		0			0
$538$	−6164.62	+	1489.06i	−0.494007	+	0.119327i
$539$	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	$0.422721\pi$
$542$	−17387.2	+	4199.86i	−1.37794	+	0.332840i
$543$		0			0
$544$	−7988.88	+	19672.5i	−0.629633	+	1.55046i
$545$	−7726.70	+	4461.01i	−0.607294	+	0.350622i
$546$		0			0
$547$	−11232.1	−	6484.87i	−0.877972	−	0.506898i	−0.00798299	−	0.999968i	$-0.502541\pi$
$547$	−11232.1	−	6484.87i	−0.877972	−	0.506898i	−0.869989	+	0.493071i	$0.835874\pi$
$548$	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
$554$	3395.95	+	1000.80i	0.260434	+	0.0767504i
$555$		0			0
$556$	11585.8	−	17949.6i	0.883716	−	1.36912i
$557$		−	2223.88i		−	0.169172i	−0.996416	−	0.0845859i	$-0.973043\pi$
$557$		−	2223.88i		−	0.169172i	0.996416	−	0.0845859i	$-0.0269567\pi$
$558$		0			0
$559$		−	9329.75i		−	0.705915i
$560$	13701.3	−	19080.4i	1.03390	−	1.43981i
$561$		0			0
$562$	1098.96	−	3729.06i	0.0824855	−	0.279895i
$563$	−8913.79	−	15439.1i	−0.667267	−	1.15574i	−0.978665	−	0.205461i	$-0.934131\pi$
$563$	−8913.79	−	15439.1i	−0.667267	−	1.15574i	0.311398	−	0.950280i	$-0.399203\pi$
$564$		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	0.0950615	−	0.995471i	$-0.469695\pi$
$569$	−9765.76	−	5638.26i	−0.719511	−	0.415410i	−0.814573	+	0.580061i	$0.803029\pi$
$570$		0			0
$571$	−6527.00	+	3768.37i	−0.478365	+	0.276184i	−0.719735	−	0.694249i	$-0.755737\pi$
$571$	−6527.00	+	3768.37i	−0.478365	+	0.276184i	0.241370	+	0.970433i	$0.422403\pi$
$572$	2029.13	−	1041.01i	0.148325	−	0.0760957i
$573$		0			0
$574$	226.096	+	936.023i	0.0164409	+	0.0680642i
$575$	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	$0.708523\pi$
$578$	5874.14	+	24318.6i	0.422720	+	1.75004i
$579$		0			0
$580$	137.244	−	70.4104i	0.00982540	−	0.00504075i
$581$	−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	0.426770	+	0.904360i	$0.359652\pi$
$587$	−8103.83	+	14036.3i	−0.569814	+	0.986947i	−0.996584	+	0.0825870i	$0.973682\pi$
$588$		0			0
$589$	−1911.00	−	3309.96i	−0.133687	−	0.231552i
$590$	−8278.38	+	28090.7i	−0.577654	+	1.96013i
$591$		0			0
$592$	8720.10	−	12143.6i	0.605395	−	0.843073i
$593$			22320.8i			1.54571i	0.634583	+	0.772855i	$0.281172\pi$
$593$			22320.8i			1.54571i	−0.634583	+	0.772855i	$0.718828\pi$
$594$		0			0
$595$		−	43051.3i		−	2.96627i
$596$	−452.109	+	700.442i	−0.0310723	+	0.0481397i
$597$		0			0
$598$	−2132.74	−	628.522i	−0.145843	−	0.0429802i
$599$	−4883.72	−	8458.84i	−0.333127	−	0.576993i	0.649996	−	0.759938i	$-0.274771\pi$
$599$	−4883.72	−	8458.84i	−0.333127	−	0.576993i	−0.983123	+	0.182944i	$0.941437\pi$
$600$		0			0
$601$	−9316.81	+	16137.2i	−0.632347	+	1.09526i	0.354724	+	0.934971i	$0.384575\pi$
$601$	−9316.81	+	16137.2i	−0.632347	+	1.09526i	−0.987071	+	0.160286i	$0.948758\pi$
$602$	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	$-0.671233\pi$
$607$	−371.545	+	214.512i	−0.0248444	+	0.0143439i	0.487526	+	0.873108i	$0.337899\pi$
$608$	1888.71	−	4650.92i	0.125983	−	0.310230i
$609$		0			0
$610$	34672.4	−	8375.10i	2.30138	−	0.555898i
$611$	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	$0.544307\pi$
$614$	18171.5	−	4389.31i	1.19437	−	0.288499i
$615$		0			0
$616$	6059.06	+	2117.23i	0.396309	+	0.138483i
$617$	23419.6	−	13521.3i	1.52810	−	0.882248i	0.528656	−	0.848836i	$-0.322696\pi$
$617$	23419.6	−	13521.3i	1.52810	−	0.882248i	0.999442	−	0.0334113i	$-0.0106371\pi$
$618$		0			0
$619$	8368.15	+	4831.35i	0.543367	+	0.313713i	0.746442	−	0.665450i	$-0.231760\pi$
$619$	8368.15	+	4831.35i	0.543367	+	0.313713i	−0.203075	+	0.979163i	$0.565094\pi$
$620$	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
$626$	16828.7	+	4959.46i	1.07446	+	0.316645i
$627$		0			0
$628$	−7817.66	−	5046.00i	−0.496749	−	0.320633i
$629$		−	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	$0.888845\pi$
$632$	−2368.10	−	12486.3i	−0.149048	−	0.785885i
$633$		0			0
$634$	−1459.29	+	4951.75i	−0.0914130	+	0.310188i
$635$	−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	0.0518903	−	0.998653i	$-0.483475\pi$
$641$	−12772.5	−	7374.18i	−0.787023	−	0.454388i	−0.838914	+	0.544265i	$0.816809\pi$
$642$		0			0
$643$	12787.4	−	7382.82i	0.784271	−	0.452799i	−0.0536706	−	0.998559i	$-0.517092\pi$
$643$	12787.4	−	7382.82i	0.784271	−	0.452799i	0.837942	+	0.545759i	$0.183759\pi$
$644$	−2856.31	−	5567.52i	−0.174774	−	0.340669i
$645$		0			0
$646$	−2160.12	−	8942.78i	−0.131562	−	0.544658i
$647$	−27157.4			−1.65018			−0.825090	−	0.565002i	$-0.808875\pi$
$647$	−27157.4			−1.65018			−0.825090	+	0.565002i	$0.808875\pi$
$648$		0			0
$649$	−8001.72			−0.483968
$650$	2186.85	+	9053.43i	0.131962	+	0.546315i
$651$		0			0
$652$	−10701.2	−	20858.7i	−0.642777	−	1.25290i
$653$	2658.60	−	1534.94i	0.159325	−	0.0919861i	−0.418218	−	0.908347i	$-0.637345\pi$
$653$	2658.60	−	1534.94i	0.159325	−	0.0919861i	0.577542	+	0.816361i	$0.304012\pi$
$654$		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	$-0.844244\pi$
$659$	−579.767	+	1004.19i	−0.0342709	+	0.0593589i	0.848381	+	0.529386i	$0.177578\pi$
$660$		0			0
$661$	−8919.74	−	15449.4i	−0.524868	−	0.909097i	−0.999581	−	0.0289568i	$-0.990781\pi$
$661$	−8919.74	−	15449.4i	−0.524868	−	0.909097i	0.474713	−	0.880141i	$-0.342552\pi$
$662$	−3179.97	+	10790.5i	−0.186697	+	0.633509i
$663$		0			0
$664$	−15211.0	+	2884.86i	−0.889010	+	0.168606i
$665$			10178.1i			0.593517i
$666$		0			0
$667$		−	41.0905i		−	0.00238535i
$668$	−5860.57	−	3782.78i	−0.339449	−	0.219102i
$669$		0			0
$670$	5865.67	+	1728.62i	0.338225	+	0.0996755i
$671$	4873.09	+	8440.44i	0.280363	+	0.485603i
$672$		0			0
$673$	6058.30	−	10493.3i	0.346999	−	0.601020i	−0.638716	−	0.769443i	$-0.720534\pi$
$673$	6058.30	−	10493.3i	0.346999	−	0.601020i	0.985715	+	0.168423i	$0.0538673\pi$
$674$	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	0.924718	−	0.380652i	$-0.124300\pi$
$677$	18626.5	+	10754.0i	1.05742	+	0.610504i	0.132705	+	0.991156i	$0.457634\pi$
$678$		0			0
$679$	−10187.4	+	5881.70i	−0.575783	+	0.332428i
$680$	14447.6	−	41346.0i	0.814768	−	2.33169i
$681$		0			0
$682$	4832.57	−	1167.30i	0.271332	−	0.0655402i
$683$	33849.4			1.89636			0.948179	−	0.317738i	$-0.102923\pi$
$683$	33849.4			1.89636			0.948179	+	0.317738i	$0.102923\pi$
$684$		0			0
$685$	−10688.4			−0.596178
$686$	−11698.2	+	2825.68i	−0.651075	+	0.157267i
$687$		0			0
$688$	24342.0	−	11000.3i	1.34888	−	0.609570i
$689$	3502.93	−	2022.42i	0.193688	−	0.111826i
$690$		0			0
$691$	1786.94	+	1031.69i	0.0983771	+	0.0567980i	0.548381	−	0.836228i	$-0.315244\pi$
$691$	1786.94	+	1031.69i	0.0983771	+	0.0567980i	−0.450004	+	0.893026i	$0.648578\pi$
$692$	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
$698$	−16207.3	−	4776.33i	−0.878877	−	0.259007i
$699$		0			0
$700$	−14215.0	+	22023.0i	−0.767538	+	1.18913i
$701$			19641.7i			1.05828i	0.848534	+	0.529141i	$0.177486\pi$
$701$			19641.7i			1.05828i	−0.848534	+	0.529141i	$0.822514\pi$
$702$		0			0
$703$			6477.79i			0.347531i
$704$	5108.54	+	4066.74i	0.273488	+	0.217715i
$705$		0			0
$706$	824.598	−	2798.07i	0.0439577	−	0.149160i
$707$	15946.9	+	27620.8i	0.848295	+	1.46929i
$708$		0			0
$709$	2685.98	−	4652.26i	0.142277	−	0.246431i	−0.786077	−	0.618129i	$-0.787891\pi$
$709$	2685.98	−	4652.26i	0.142277	−	0.246431i	0.928354	+	0.371698i	$0.121224\pi$
$710$	−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
$716$	−4546.74	+	2332.63i	−0.237318	+	0.121752i
$717$		0			0
$718$	−2801.85	−	11599.5i	−0.145633	−	0.602910i
$719$	−12836.0			−0.665788			−0.332894	−	0.942964i	$-0.608025\pi$
$719$	−12836.0			−0.665788			−0.332894	+	0.942964i	$0.608025\pi$
$720$		0			0
$721$	−5113.29			−0.264118
$722$	−4044.41	−	16743.6i	−0.208473	−	0.863065i
$723$		0			0
$724$	−28692.4	+	14720.1i	−1.47285	+	0.755620i
$725$	−149.065	+	86.0630i	−0.00763607	+	0.00440869i
$726$		0			0
$727$	−29745.3	−	17173.5i	−1.51746	−	0.876106i	−0.999789	−	0.0205251i	$-0.993466\pi$
$727$	−29745.3	−	17173.5i	−1.51746	−	0.876106i	−0.517670	−	0.855580i	$-0.673200\pi$
$728$	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	0.728762	−	0.684767i	$-0.240096\pi$
$733$	−4537.51	−	7859.19i	−0.228645	−	0.396024i	−0.957407	+	0.288743i	$0.906763\pi$
$734$	2430.80	−	8248.33i	0.122238	−	0.414784i
$735$		0			0
$736$	−874.765	−	6305.54i	−0.0438101	−	0.315795i
$737$			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	$-0.137866\pi$
$740$	−16723.8	+	25909.8i	−0.830781	+	1.28711i
$741$		0			0
$742$	10919.2	+	3217.92i	0.540239	+	0.159210i
$743$	−15021.9	−	26018.6i	−0.741721	−	1.28470i	−0.951711	−	0.306995i	$-0.900677\pi$
$743$	−15021.9	−	26018.6i	−0.741721	−	1.28470i	0.209990	−	0.977704i	$-0.432657\pi$
$744$		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	$-0.732435\pi$
$751$	−7313.00	+	4222.17i	−0.355333	+	0.205152i	0.311698	+	0.950181i	$0.399102\pi$
$752$	6140.57	+	13588.1i	0.297771	+	0.658920i
$753$		0			0
$754$	71.8084	−	17.3453i	0.00346831	−	0.000837769i
$755$	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	$0.179685\pi$
$758$	−7809.86	+	1886.47i	−0.374231	+	0.0903952i
$759$		0			0
$760$	−3415.68	+	9774.93i	−0.163026	+	0.466545i
$761$	−13659.8	+	7886.50i	−0.650681	+	0.375671i	−0.788717	−	0.614756i	$-0.789254\pi$
$761$	−13659.8	+	7886.50i	−0.650681	+	0.375671i	0.138036	+	0.990427i	$0.455921\pi$
$762$		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	0.999876	−	0.0157189i	$-0.00500369\pi$
$769$	10370.9	+	17962.9i	0.486325	+	0.842340i	−0.513551	+	0.858059i	$0.671670\pi$
$770$	−12699.4	−	3742.53i	−0.594355	−	0.175158i
$771$		0			0
$772$	9528.70	+	6150.42i	0.444230	+	0.286734i
$773$		−	35223.1i		−	1.63892i	−0.573133	−	0.819462i	$-0.694272\pi$
$773$		−	35223.1i		−	1.63892i	0.573133	−	0.819462i	$-0.305728\pi$
$774$		0			0
$775$			20303.6i			0.941067i
$776$	−11757.7	+	2229.92i	−0.543915	+	0.103156i
$777$		0			0
$778$	2847.96	−	9663.86i	0.131239	−	0.445329i
$779$	−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	$-0.494867\pi$
$787$	19651.8	−	11346.0i	0.890102	−	0.513901i	0.873976	+	0.485969i	$0.161533\pi$
$788$	3202.26	+	6241.83i	0.144766	+	0.282178i
$789$		0			0
$790$	6155.23	+	25482.3i	0.277207	+	1.14762i
$791$	−28529.2			−1.28240
$792$		0			0
$793$	17082.8			0.764977
$794$	6260.87	+	25919.6i	0.279836	+	1.15850i
$795$		0			0
$796$	−5424.45	−	10573.3i	−0.241538	−	0.470805i
$797$	−27480.8	+	15866.1i	−1.22136	+	0.705150i	−0.965207	−	0.261488i	$-0.915787\pi$
$797$	−27480.8	+	15866.1i	−1.22136	+	0.705150i	−0.256149	+	0.966637i	$0.582454\pi$
$798$		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
$806$	2463.28	−	8358.56i	0.107650	−	0.365282i
$807$		0			0
$808$	6045.92	+	31878.4i	0.263236	+	1.38797i
$809$			18376.4i			0.798613i	0.916817	+	0.399307i	$0.130749\pi$
$809$			18376.4i			0.798613i	−0.916817	+	0.399307i	$0.869251\pi$
$810$		0			0
$811$			28834.7i			1.24849i	0.781229	+	0.624244i	$0.214593\pi$
$811$			28834.7i			1.24849i	−0.781229	+	0.624244i	$0.785407\pi$
$812$	174.678	+	112.748i	0.00754926	+	0.00487276i
$813$		0			0
$814$	−8082.44	−	2381.91i	−0.348021	−	0.102563i
$815$	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	0.774987	−	0.631977i	$-0.217756\pi$
$821$	14471.4	+	8355.08i	0.615172	+	0.355170i	−0.159815	+	0.987147i	$0.551090\pi$
$822$		0			0
$823$	−453.509	+	261.833i	−0.0192082	+	0.0110898i	−0.509573	−	0.860427i	$-0.670197\pi$
$823$	−453.509	+	261.833i	−0.0192082	+	0.0110898i	0.490365	+	0.871517i	$0.336863\pi$
$824$	−4910.76	−	1715.98i	−0.207615	−	0.0725473i
$825$		0			0
$826$	−38368.0	+	9267.77i	−1.61622	+	0.390396i
$827$	−28676.4			−1.20577			−0.602887	−	0.797826i	$-0.705983\pi$
$827$	−28676.4			−1.20577			−0.602887	+	0.797826i	$0.705983\pi$
$828$		0			0
$829$	14521.0			0.608365			0.304183	−	0.952614i	$-0.401617\pi$
$829$	14521.0			0.608365			0.304183	+	0.952614i	$0.401617\pi$
$830$	31042.9	−	7498.40i	1.29821	−	0.313582i
$831$		0			0
$832$	10650.1	−	4190.43i	0.443781	−	0.174612i
$833$	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	−0.343346	−	0.939209i	$-0.611560\pi$
$839$	15594.8	−	27010.9i	0.641706	−	1.11147i	0.985052	−	0.172258i	$-0.0551064\pi$
$840$		0			0
$841$	−12193.8	−	21120.3i	−0.499972	−	0.865977i
$842$	−25491.4	−	7512.37i	−1.04334	−	0.307474i
$843$		0			0
$844$	1334.73	−	2067.87i	0.0544352	−	0.0843352i
$845$		−	28009.3i		−	1.14029i
$846$		0			0
$847$			25986.4i			1.05420i
$848$	9406.81	+	6754.86i	0.380933	+	0.273541i
$849$		0			0
$850$	−13815.5	+	46879.5i	−0.557491	+	1.89171i
$851$	4107.46	+	7114.32i	0.165455	+	0.286576i
$852$		0			0
$853$	−6544.93	+	11336.2i	−0.262713	+	0.455032i	−0.966962	−	0.254921i	$-0.917951\pi$
$853$	−6544.93	+	11336.2i	−0.262713	+	0.455032i	0.704249	+	0.709953i	$0.251284\pi$
$854$	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	0.774694	−	0.632337i	$-0.217904\pi$
$857$	15414.8	+	8899.73i	0.614421	+	0.354736i	−0.160273	+	0.987073i	$0.551237\pi$
$858$		0			0
$859$	36673.2	−	21173.3i	1.45666	−	0.841004i	0.457816	−	0.889047i	$-0.348632\pi$
$859$	36673.2	−	21173.3i	1.45666	−	0.841004i	0.998845	+	0.0480428i	$0.0152984\pi$
$860$	−49025.1	+	25151.4i	−1.94388	+	0.997275i
$861$		0			0
$862$	−4878.54	−	20196.9i	−0.192765	−	0.798037i
$863$	41963.9			1.65524			0.827618	−	0.561291i	$-0.189695\pi$
$863$	41963.9			1.65524			0.827618	+	0.561291i	$0.189695\pi$
$864$		0			0
$865$	−38494.2			−1.51311
$866$	−9080.31	−	37591.9i	−0.356306	−	1.47509i
$867$		0			0
$868$	21820.0	−	11194.4i	0.853249	−	0.437744i
$869$	−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	0.894675	+	0.446717i	$0.147407\pi$
$877$	21665.7	+	37526.1i	0.834206	+	1.44489i	−0.0604689	+	0.998170i	$0.519260\pi$
$878$	4612.37	−	15651.0i	0.177289	−	0.601588i
$879$		0			0
$880$	−10940.4	−	7856.09i	−0.419091	−	0.300942i
$881$		−	38532.4i		−	1.47354i	−0.676142	−	0.736771i	$-0.736349\pi$
$881$		−	38532.4i		−	1.47354i	0.676142	−	0.736771i	$-0.263651\pi$
$882$		0			0
$883$			7198.92i			0.274364i	0.990546	+	0.137182i	$0.0438045\pi$
$883$			7198.92i			0.274364i	−0.990546	+	0.137182i	$0.956196\pi$
$884$	11375.1	−	17623.2i	0.432789	−	0.670510i
$885$		0			0
$886$	−26189.0	−	7717.94i	−0.993042	−	0.292652i
$887$	−7110.04	−	12315.0i	−0.269145	−	0.466173i	0.699496	−	0.714636i	$-0.253408\pi$
$887$	−7110.04	−	12315.0i	−0.269145	−	0.466173i	−0.968641	+	0.248463i	$0.920075\pi$
$888$		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
$896$	29205.5	+	13583.1i	1.08894	+	0.506450i
$897$		0			0
$898$	−31596.3	+	7632.05i	−1.17414	+	0.283614i
$899$	161.041			0.00597442
$900$		0			0
$901$	21224.7			0.784791
$902$	536.700	−	129.640i	0.0198117	−	0.00478551i
$903$		0			0
$904$	−27399.1	−	9574.14i	−1.00805	−	0.352247i
$905$	57607.4	−	33259.7i	2.11595	−	1.22164i
$906$		0			0
$907$	−43283.2	−	24989.6i	−1.58456	−	0.914845i	−0.994181	−	0.107718i	$-0.965646\pi$
$907$	−43283.2	−	24989.6i	−1.58456	−	0.914845i	−0.590377	−	0.807127i	$-0.701021\pi$
$908$	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	$-0.918942\pi$
$911$	−7306.31	+	12654.9i	−0.265718	+	0.460237i	0.702034	+	0.712144i	$0.252276\pi$
$912$		0			0
$913$	4362.98	+	7556.90i	0.158153	+	0.273929i
$914$	47864.2	+	14105.7i	1.73218	+	0.510476i
$915$		0			0
$916$	15442.0	+	9967.21i	0.557005	+	0.359526i
$917$			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	$0.694922\pi$
$920$	2446.80	+	12901.3i	0.0876833	+	0.462329i
$921$		0			0
$922$	10286.9	−	34906.0i	0.367441	−	1.24682i
$923$	−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	−0.994588	−	0.103897i	$-0.966869\pi$
$929$	−44791.1	−	25860.1i	−1.58186	−	0.913287i	−0.587272	−	0.809390i	$-0.699798\pi$
$930$		0			0
$931$	−3643.14	+	2103.37i	−0.128248	+	0.0740442i
$932$	12293.9	+	23963.2i	0.432081	+	0.842211i
$933$		0			0
$934$	53.8882	+	223.094i	0.00188788	+	0.00781570i
$935$	−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	$0.763100\pi$
$938$	1935.22	+	8011.70i	0.0673638	+	0.278882i
$939$		0			0
$940$	−14039.9	−	27366.6i	−0.487162	−	0.949574i
$941$	9360.06	−	5404.03i	0.324261	−	0.187212i	−0.329029	−	0.944320i	$-0.606722\pi$
$941$	9360.06	−	5404.03i	0.324261	−	0.187212i	0.653290	+	0.757108i	$0.273388\pi$
$942$		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	$-0.829261\pi$
$947$	372.832	−	645.764i	0.0127935	−	0.0221589i	0.872351	+	0.488880i	$0.162594\pi$
$948$		0			0
$949$	−4335.00	−	7508.44i	−0.148283	−	0.256833i
$950$	3266.23	−	11083.1i	0.111548	−	0.378510i
$951$		0			0
$952$	57998.0	−	10999.7i	1.97450	−	0.374476i
$953$			49163.3i			1.67110i	0.549417	+	0.835548i	$0.314850\pi$
$953$			49163.3i			1.67110i	−0.549417	+	0.835548i	$0.685150\pi$
$954$		0			0
$955$		−	60453.7i		−	2.04841i
$956$	4134.65	+	2668.76i	0.139879	+	0.0902865i
$957$		0			0
$958$	−40544.4	−	11948.5i	−1.36736	−	0.402963i
$959$	−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	$-0.757271\pi$
$967$	−14625.7	+	8444.18i	−0.486383	+	0.280813i	0.236690	+	0.971585i	$0.423938\pi$
$968$	−8720.83	+	24957.1i	−0.289564	+	0.828670i
$969$		0			0
$970$	23995.4	−	5796.06i	0.794273	−	0.191856i
$971$	−22501.6			−0.743677			−0.371838	−	0.928297i	$-0.621272\pi$
$971$	−22501.6			−0.743677			−0.371838	+	0.928297i	$0.621272\pi$
$972$		0			0
$973$	−59396.6			−1.95701
$974$	−16314.8	+	3940.83i	−0.536714	+	0.129643i
$975$		0			0
$976$	20141.6	+	44570.3i	0.660572	+	1.46174i
$977$	−11920.1	+	6882.06i	−0.390335	+	0.225360i	−0.682305	−	0.731068i	$-0.739022\pi$
$977$	−11920.1	+	6882.06i	−0.390335	+	0.225360i	0.291970	+	0.956427i	$0.405689\pi$
$978$		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	$-0.793026\pi$
$983$	3892.24	−	6741.57i	0.126290	−	0.218741i	0.922237	+	0.386626i	$0.126360\pi$
$984$		0			0
$985$	−7235.40	−	12532.1i	−0.234050	−	0.405386i
$986$	371.831	+	109.579i	0.0120096	+	0.00353927i
$987$		0			0
$988$	−2689.27	+	4166.43i	−0.0865962	+	0.134162i
$989$			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	$-0.278445\pi$
$992$	24712.5	−	3428.35i	0.790950	−	0.109728i
$993$		0			0
$994$	403.523	−	1369.26i	0.0128762	−	0.0436923i
$995$	12256.4	+	21228.7i	0.390506	+	0.676376i
$996$		0			0
$997$	−1245.57	+	2157.40i	−0.0395664	+	0.0685310i	−0.885130	−	0.465343i	$-0.845931\pi$
$997$	−1245.57	+	2157.40i	−0.0395664	+	0.0685310i	0.845564	+	0.533874i	$0.179264\pi$
$998$	−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.35.6		24
3.2	odd	2		36.4.h.b.11.7	✓	24
4.3	odd	2	inner	108.4.h.b.35.1		24
9.2	odd	6		324.4.b.c.323.17		24
9.4	even	3		36.4.h.b.23.12	yes	24
9.5	odd	6	inner	108.4.h.b.71.1		24
9.7	even	3		324.4.b.c.323.8		24
12.11	even	2		36.4.h.b.11.12	yes	24
36.7	odd	6		324.4.b.c.323.18		24
36.11	even	6		324.4.b.c.323.7		24
36.23	even	6	inner	108.4.h.b.71.6		24
36.31	odd	6		36.4.h.b.23.7	yes	24

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

\(f(q)\)	\(=\)	\(q+(-0.664105 - 2.74936i) q^{2} +(-7.11793 + 3.65173i) q^{4} +(14.2911 - 8.25096i) q^{5} +(19.2620 + 11.1209i) q^{7} +(14.7670 + 17.1446i) q^{8} +O(q^{10})\)	\(q+(-0.664105 - 2.74936i) q^{2} +(-7.11793 + 3.65173i) q^{4} +(14.2911 - 8.25096i) q^{5} +(19.2620 + 11.1209i) q^{7} +(14.7670 + 17.1446i) q^{8} +(-32.1756 - 33.8118i) q^{10} +(6.37655 - 11.0445i) q^{11} +(-11.1766 - 19.3584i) q^{13} +(17.7834 - 60.3436i) q^{14} +(37.3298 - 51.9854i) q^{16} -117.295i q^{17} +27.7307i q^{19} +(-71.5926 + 110.917i) q^{20} +(-34.6000 - 10.1967i) q^{22} +(17.5836 + 30.4556i) q^{23} +(73.6567 - 127.577i) q^{25} +(-45.8008 + 43.5845i) q^{26} +(-177.716 - 8.81837i) q^{28} +(-1.01189 - 0.584217i) q^{29} +(-119.361 + 68.9130i) q^{31} +(-167.717 - 68.1091i) q^{32} +(-322.487 + 77.8965i) q^{34} +367.033 q^{35} +233.596 q^{37} +(76.2416 - 18.4161i) q^{38} +(352.495 + 123.173i) q^{40} +(-13.2561 + 7.65340i) q^{41} +(361.460 + 208.689i) q^{43} +(-5.05631 + 101.900i) q^{44} +(72.0561 - 68.5693i) q^{46} +(-116.494 + 201.773i) q^{47} +(75.8499 + 131.376i) q^{49} +(-399.671 - 117.784i) q^{50} +(150.246 + 96.9781i) q^{52} +180.951i q^{53} -210.451i q^{55} +(93.7774 + 494.461i) q^{56} +(-0.934217 + 3.17004i) q^{58} +(-313.716 - 543.373i) q^{59} +(-382.110 + 661.834i) q^{61} +(268.735 + 282.400i) q^{62} +(-75.8742 + 506.347i) q^{64} +(-319.452 - 184.435i) q^{65} +(-113.463 + 65.5077i) q^{67} +(428.330 + 834.900i) q^{68} +(-243.749 - 1009.11i) q^{70} +22.6910 q^{71} +387.864 q^{73} +(-155.133 - 642.240i) q^{74} +(-101.265 - 197.385i) q^{76} +(245.650 - 141.826i) q^{77} +(-486.411 - 280.830i) q^{79} +(104.553 - 1050.93i) q^{80} +(29.8454 + 31.3630i) q^{82} +(-342.111 + 592.554i) q^{83} +(-967.799 - 1676.28i) q^{85} +(333.713 - 1132.38i) q^{86} +(283.516 - 53.7704i) q^{88} +278.003i q^{89} -497.177i q^{91} +(-236.374 - 152.571i) q^{92} +(632.110 + 186.284i) q^{94} +(228.805 + 396.302i) q^{95} +(-264.443 + 458.028i) q^{97} +(310.827 - 295.786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 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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