LMFDB - Embedded newform 189.4.i.a.143.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(143,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.i (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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.5
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.72062i q^{2} -5.84303 q^{4} +(-6.83336 + 11.8357i) q^{5} +(18.4941 + 0.984293i) q^{7} -8.02526i q^{8} +O(q^{10})$	\(q-3.72062i q^{2} -5.84303 q^{4} +(-6.83336 + 11.8357i) q^{5} +(18.4941 + 0.984293i) q^{7} -8.02526i q^{8} +(44.0363 + 25.4243i) q^{10} +(21.3043 - 12.3000i) q^{11} +(2.03747 - 1.17634i) q^{13} +(3.66218 - 68.8095i) q^{14} -76.6032 q^{16} +(63.8439 - 110.581i) q^{17} +(87.2223 - 50.3578i) q^{19} +(39.9275 - 69.1565i) q^{20} +(-45.7638 - 79.2652i) q^{22} +(-42.0276 - 24.2647i) q^{23} +(-30.8895 - 53.5022i) q^{25} +(-4.37670 - 7.58067i) q^{26} +(-108.062 - 5.75126i) q^{28} +(171.644 + 99.0987i) q^{29} -42.9953i q^{31} +220.810i q^{32} +(-411.430 - 237.539i) q^{34} +(-138.026 + 212.165i) q^{35} +(-42.0011 - 72.7481i) q^{37} +(-187.363 - 324.521i) q^{38} +(94.9848 + 54.8395i) q^{40} +(-92.8172 - 160.764i) q^{41} +(-185.452 + 321.213i) q^{43} +(-124.482 + 71.8695i) q^{44} +(-90.2797 + 156.369i) q^{46} +504.729 q^{47} +(341.062 + 36.4072i) q^{49} +(-199.062 + 114.928i) q^{50} +(-11.9050 + 6.87337i) q^{52} +(-372.688 - 215.171i) q^{53} +336.202i q^{55} +(7.89921 - 148.420i) q^{56} +(368.709 - 638.622i) q^{58} +312.164 q^{59} -548.565i q^{61} -159.969 q^{62} +208.723 q^{64} +32.1533i q^{65} -651.533 q^{67} +(-373.042 + 646.128i) q^{68} +(789.385 + 513.545i) q^{70} +18.9019i q^{71} +(525.319 + 303.293i) q^{73} +(-270.668 + 156.270i) q^{74} +(-509.643 + 294.243i) q^{76} +(406.110 - 206.508i) q^{77} +435.435 q^{79} +(523.457 - 906.654i) q^{80} +(-598.142 + 345.338i) q^{82} +(-424.248 + 734.819i) q^{83} +(872.537 + 1511.28i) q^{85} +(1195.11 + 689.998i) q^{86} +(-98.7110 - 170.972i) q^{88} +(147.005 + 254.620i) q^{89} +(38.8391 - 19.7498i) q^{91} +(245.569 + 141.779i) q^{92} -1877.91i q^{94} +1376.45i q^{95} +(900.965 + 520.172i) q^{97} +(135.457 - 1268.96i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	3.72062i		−	1.31544i	−0.753263	−	0.657719i	$-0.771521\pi$
$2$		−	3.72062i		−	1.31544i	0.753263	−	0.657719i	$-0.228479\pi$
$3$		0			0
$3$		0			0
$4$	−5.84303			−0.730379
$5$	−6.83336	+	11.8357i	−0.611194	+	1.05862i	0.379845	+	0.925050i	$0.375977\pi$
$5$	−6.83336	+	11.8357i	−0.611194	+	1.05862i	−0.991039	+	0.133569i	$0.957356\pi$
$6$		0			0
$7$	18.4941	+	0.984293i	0.998587	+	0.0531468i
$7$	18.4941	+	0.984293i	0.998587	+	0.0531468i
$8$		−	8.02526i		−	0.354670i
$9$		0			0
$10$	44.0363	+	25.4243i	1.39255	+	0.803988i
$11$	21.3043	−	12.3000i	0.583953	−	0.337145i	−0.178750	−	0.983895i	$-0.557205\pi$
$11$	21.3043	−	12.3000i	0.583953	−	0.337145i	0.762703	+	0.646749i	$0.223872\pi$
$12$		0			0
$13$	2.03747	−	1.17634i	0.0434688	−	0.0250967i	−0.478108	−	0.878301i	$-0.658677\pi$
$13$	2.03747	−	1.17634i	0.0434688	−	0.0250967i	0.521577	+	0.853204i	$0.325344\pi$
$14$	3.66218	−	68.8095i	0.0699114	−	1.31358i
$15$		0			0
$16$	−76.6032			−1.19693
$17$	63.8439	−	110.581i	0.910848	−	1.57764i	0.0979801	−	0.995188i	$-0.468762\pi$
$17$	63.8439	−	110.581i	0.910848	−	1.57764i	0.812868	−	0.582447i	$-0.197905\pi$
$18$		0			0
$19$	87.2223	−	50.3578i	1.05317	−	0.608046i	0.129633	−	0.991562i	$-0.458620\pi$
$19$	87.2223	−	50.3578i	1.05317	−	0.608046i	0.923534	+	0.383516i	$0.125287\pi$
$20$	39.9275	−	69.1565i	0.446403	−	0.773193i
$21$		0			0
$22$	−45.7638	−	79.2652i	−0.443494	−	0.768154i
$23$	−42.0276	−	24.2647i	−0.381016	−	0.219980i	0.297244	−	0.954801i	$-0.403932\pi$
$23$	−42.0276	−	24.2647i	−0.381016	−	0.219980i	−0.678260	+	0.734822i	$0.737266\pi$
$24$		0			0
$25$	−30.8895	−	53.5022i	−0.247116	−	0.428018i
$26$	−4.37670	−	7.58067i	−0.0330132	−	0.0571805i
$27$		0			0
$28$	−108.062	−	5.75126i	−0.729347	−	0.0388173i
$29$	171.644	+	99.0987i	1.09909	+	0.634557i	0.935981	−	0.352051i	$-0.114516\pi$
$29$	171.644	+	99.0987i	1.09909	+	0.634557i	0.163105	+	0.986609i	$0.447849\pi$
$30$		0			0
$31$		−	42.9953i		−	0.249103i	−0.992213	−	0.124551i	$-0.960251\pi$
$31$		−	42.9953i		−	0.249103i	0.992213	−	0.124551i	$-0.0397492\pi$
$32$			220.810i			1.21981i
$33$		0			0
$34$	−411.430	−	237.539i	−2.07528	−	1.19817i
$35$	−138.026	+	212.165i	−0.666592	+	1.02464i
$36$		0			0
$37$	−42.0011	−	72.7481i	−0.186620	−	0.323235i	0.757501	−	0.652834i	$-0.226420\pi$
$37$	−42.0011	−	72.7481i	−0.186620	−	0.323235i	−0.944121	+	0.329598i	$0.893087\pi$
$38$	−187.363	−	324.521i	−0.799848	−	1.38538i
$39$		0			0
$40$	94.9848	+	54.8395i	0.375460	+	0.216772i
$41$	−92.8172	−	160.764i	−0.353551	−	0.612369i	0.633318	−	0.773892i	$-0.281693\pi$
$41$	−92.8172	−	160.764i	−0.353551	−	0.612369i	−0.986869	+	0.161523i	$0.948359\pi$
$42$		0			0
$43$	−185.452	+	321.213i	−0.657702	+	1.13917i	0.323507	+	0.946226i	$0.395138\pi$
$43$	−185.452	+	321.213i	−0.657702	+	1.13917i	−0.981209	+	0.192948i	$0.938195\pi$
$44$	−124.482	+	71.8695i	−0.426507	+	0.246244i
$45$		0			0
$46$	−90.2797	+	156.369i	−0.289370	+	0.501203i
$47$	504.729			1.56643			0.783215	−	0.621750i	$-0.213578\pi$
$47$	504.729			1.56643			0.783215	+	0.621750i	$0.213578\pi$
$48$		0			0
$49$	341.062	+	36.4072i	0.994351	+	0.106143i
$50$	−199.062	+	114.928i	−0.563031	+	0.325066i
$51$		0			0
$52$	−11.9050	+	6.87337i	−0.0317487	+	0.0183301i
$53$	−372.688	−	215.171i	−0.965898	−	0.557661i	−0.0679145	−	0.997691i	$-0.521635\pi$
$53$	−372.688	−	215.171i	−0.965898	−	0.557661i	−0.897983	+	0.440030i	$0.854968\pi$
$54$		0			0
$55$			336.202i			0.824245i
$56$	7.89921	−	148.420i	0.0188496	−	0.354169i
$57$		0			0
$58$	368.709	−	638.622i	0.834721	−	1.44578i
$59$	312.164			0.688819			0.344410	−	0.938819i	$-0.388079\pi$
$59$	312.164			0.688819			0.344410	+	0.938819i	$0.388079\pi$
$60$		0			0
$61$		−	548.565i		−	1.15142i	−0.817655	−	0.575709i	$-0.804726\pi$
$61$		−	548.565i		−	1.15142i	0.817655	−	0.575709i	$-0.195274\pi$
$62$	−159.969			−0.327679
$63$		0			0
$64$	208.723			0.407663
$65$			32.1533i			0.0613558i
$66$		0			0
$67$	−651.533			−1.18802			−0.594010	−	0.804457i	$-0.702456\pi$
$67$	−651.533			−1.18802			−0.594010	+	0.804457i	$0.702456\pi$
$68$	−373.042	+	646.128i	−0.665265	+	1.15227i
$69$		0			0
$70$	789.385	+	513.545i	1.34785	+	0.876862i
$71$			18.9019i			0.0315950i	0.999875	+	0.0157975i	$0.00502871\pi$
$71$			18.9019i			0.0315950i	−0.999875	+	0.0157975i	$0.994971\pi$
$72$		0			0
$73$	525.319	+	303.293i	0.842245	+	0.486271i	0.858027	−	0.513605i	$-0.171690\pi$
$73$	525.319	+	303.293i	0.842245	+	0.486271i	−0.0157815	+	0.999875i	$0.505024\pi$
$74$	−270.668	+	156.270i	−0.425196	+	0.245487i
$75$		0			0
$76$	−509.643	+	294.243i	−0.769211	+	0.444104i
$77$	406.110	−	206.508i	0.601046	−	0.305634i
$78$		0			0
$79$	435.435			0.620130			0.310065	−	0.950715i	$-0.399649\pi$
$79$	435.435			0.620130			0.310065	+	0.950715i	$0.399649\pi$
$80$	523.457	−	906.654i	0.731554	−	1.26709i
$81$		0			0
$82$	−598.142	+	345.338i	−0.805534	+	0.465075i
$83$	−424.248	+	734.819i	−0.561051	+	0.971769i	0.436354	+	0.899775i	$0.356270\pi$
$83$	−424.248	+	734.819i	−0.561051	+	0.971769i	−0.997405	+	0.0719942i	$0.977064\pi$
$84$		0			0
$85$	872.537	+	1511.28i	1.11341	+	1.92848i
$86$	1195.11	+	689.998i	1.49851	+	0.865167i
$87$		0			0
$88$	−98.7110	−	170.972i	−0.119575	−	0.207110i
$89$	147.005	+	254.620i	0.175084	+	0.303254i	0.940190	−	0.340650i	$-0.110647\pi$
$89$	147.005	+	254.620i	0.175084	+	0.303254i	−0.765106	+	0.643904i	$0.777314\pi$
$90$		0			0
$91$	38.8391	−	19.7498i	0.0447411	−	0.0227510i
$92$	245.569	+	141.779i	0.278286	+	0.160669i
$93$		0			0
$94$		−	1877.91i		−	2.06054i
$95$			1376.45i			1.48654i
$96$		0			0
$97$	900.965	+	520.172i	0.943084	+	0.544490i	0.890926	−	0.454149i	$-0.150057\pi$
$97$	900.965	+	520.172i	0.943084	+	0.544490i	0.0521583	+	0.998639i	$0.483390\pi$
$98$	135.457	−	1268.96i	0.139625	−	1.30801i
$99$		0			0
$100$	180.489	+	312.615i	0.180489	+	0.312615i
$101$	−124.628	−	215.862i	−0.122782	−	0.212664i	0.798082	−	0.602549i	$-0.205848\pi$
$101$	−124.628	−	215.862i	−0.122782	−	0.212664i	−0.920864	+	0.389885i	$0.872515\pi$
$102$		0			0
$103$	650.861	+	375.775i	0.622634	+	0.359478i	0.777894	−	0.628396i	$-0.216288\pi$
$103$	650.861	+	375.775i	0.622634	+	0.359478i	−0.155260	+	0.987874i	$0.549622\pi$
$104$	−9.44041	−	16.3513i	−0.00890104	−	0.0154171i
$105$		0			0
$106$	−800.571	+	1386.63i	−0.733569	+	1.27058i
$107$	−1406.36	+	811.965i	−1.27064	+	0.733604i	−0.975108	−	0.221729i	$-0.928830\pi$
$107$	−1406.36	+	811.965i	−1.27064	+	0.733604i	−0.295531	+	0.955333i	$0.595497\pi$
$108$		0			0
$109$	724.736	−	1255.28i	0.636854	−	1.10306i	−0.349265	−	0.937024i	$-0.613569\pi$
$109$	724.736	−	1255.28i	0.636854	−	1.10306i	0.986119	−	0.166040i	$-0.0530981\pi$
$110$	1250.88			1.08424
$111$		0			0
$112$	−1416.71	−	75.4000i	−1.19523	−	0.0636128i
$113$	−227.719	+	131.473i	−0.189575	+	0.109451i	−0.591784	−	0.806097i	$-0.701576\pi$
$113$	−227.719	+	131.473i	−0.189575	+	0.109451i	0.402209	+	0.915548i	$0.368243\pi$
$114$		0			0
$115$	574.380	−	331.618i	0.465750	−	0.268901i
$116$	−1002.92	−	579.037i	−0.802749	−	0.463467i
$117$		0			0
$118$		−	1161.45i		−	0.906100i
$119$	1289.58	−	1982.25i	0.993408	−	1.52700i
$120$		0			0
$121$	−362.918	+	628.593i	−0.272666	+	0.472271i
$122$	−2041.00			−1.51462
$123$		0			0
$124$			251.223i			0.181939i
$125$	−864.022			−0.618244
$126$		0			0
$127$	−368.812			−0.257691			−0.128846	−	0.991665i	$-0.541127\pi$
$127$	−368.812			−0.257691			−0.128846	+	0.991665i	$0.541127\pi$
$128$			989.896i			0.683557i
$129$		0			0
$130$	119.630			0.0807098
$131$	−551.575	+	955.356i	−0.367873	+	0.637174i	−0.989233	−	0.146351i	$-0.953247\pi$
$131$	−551.575	+	955.356i	−0.367873	+	0.637174i	0.621360	+	0.783525i	$0.286580\pi$
$132$		0			0
$133$	1662.66	−	845.470i	1.08399	−	0.551215i
$134$			2424.11i			1.56277i
$135$		0			0
$136$	−887.441	−	512.364i	−0.559540	−	0.323050i
$137$	−1078.05	+	622.413i	−0.672293	+	0.388148i	−0.796945	−	0.604052i	$-0.793552\pi$
$137$	−1078.05	+	622.413i	−0.672293	+	0.388148i	0.124652	+	0.992201i	$0.460219\pi$
$138$		0			0
$139$	−1997.85	+	1153.46i	−1.21910	+	0.703848i	−0.964726	−	0.263257i	$-0.915203\pi$
$139$	−1997.85	+	1153.46i	−1.21910	+	0.703848i	−0.254376	+	0.967106i	$0.581870\pi$
$140$	806.493	−	1239.69i	0.486865	−	0.748376i
$141$		0			0
$142$	70.3270			0.0415613
$143$	28.9380	−	50.1220i	0.0169225	−	0.0293106i
$144$		0			0
$145$	−2345.81	+	1354.35i	−1.34351	+	0.775675i
$146$	1128.44	−	1954.51i	0.639659	−	1.10792i
$147$		0			0
$148$	245.414	+	425.069i	0.136303	+	0.236084i
$149$	−286.796	−	165.582i	−0.157686	−	0.0910402i	0.419080	−	0.907949i	$-0.362353\pi$
$149$	−286.796	−	165.582i	−0.157686	−	0.0910402i	−0.576767	+	0.816909i	$0.695686\pi$
$150$		0			0
$151$	−914.722	−	1584.35i	−0.492974	−	0.853856i	0.506993	−	0.861950i	$-0.330757\pi$
$151$	−914.722	−	1584.35i	−0.492974	−	0.853856i	−0.999967	+	0.00809418i	$0.997424\pi$
$152$	−404.135	−	699.982i	−0.215656	−	0.373527i
$153$		0			0
$154$	−768.339	−	1510.98i	−0.402042	−	0.790639i
$155$	508.880	+	293.802i	0.263705	+	0.152250i
$156$		0			0
$157$			43.4645i			0.0220946i	0.999939	+	0.0110473i	$0.00351653\pi$
$157$			43.4645i			0.0220946i	−0.999939	+	0.0110473i	$0.996483\pi$
$158$		−	1620.09i		−	0.815743i
$159$		0			0
$160$	−2613.44	−	1508.87i	−1.29132	−	0.745542i
$161$	−753.379	−	490.120i	−0.368786	−	0.239919i
$162$		0			0
$163$	−1337.78	−	2317.11i	−0.642841	−	1.11343i	−0.984796	−	0.173717i	$-0.944422\pi$
$163$	−1337.78	−	2317.11i	−0.642841	−	1.11343i	0.341954	−	0.939717i	$-0.388911\pi$
$164$	542.334	+	939.350i	0.258227	+	0.447261i
$165$		0			0
$166$	2733.98	+	1578.47i	1.27830	+	0.738029i
$167$	−1300.57	−	2252.66i	−0.602644	−	1.04381i	−0.992419	−	0.122900i	$-0.960781\pi$
$167$	−1300.57	−	2252.66i	−0.602644	−	1.04381i	0.389775	−	0.920910i	$-0.372553\pi$
$168$		0			0
$169$	−1095.73	+	1897.86i	−0.498740	+	0.863844i
$170$	5622.89	−	3246.38i	2.53680	−	1.46462i
$171$		0			0
$172$	1083.60	−	1876.86i	0.480372	−	0.832028i
$173$	−1751.09			−0.769552			−0.384776	−	0.923010i	$-0.625721\pi$
$173$	−1751.09			−0.769552			−0.384776	+	0.923010i	$0.625721\pi$
$174$		0			0
$175$	−518.612	−	1019.88i	−0.224019	−	0.440546i
$176$	−1631.98	+	942.222i	−0.698948	+	0.403538i
$177$		0			0
$178$	947.344	−	546.949i	0.398913	−	0.230312i
$179$	3563.92	+	2057.63i	1.48816	+	0.859187i	0.999909	−	0.0135177i	$-0.00430295\pi$
$179$	3563.92	+	2057.63i	1.48816	+	0.859187i	0.488248	+	0.872705i	$0.337636\pi$
$180$		0			0
$181$			2733.54i			1.12256i	0.827628	+	0.561278i	$0.189690\pi$
$181$			2733.54i			1.12256i	−0.827628	+	0.561278i	$0.810310\pi$
$182$	−73.4815	−	144.506i	−0.0299276	−	0.0588542i
$183$		0			0
$184$	−194.730	+	337.283i	−0.0780202	+	0.135135i
$185$	1148.03			0.456244
$186$		0			0
$187$		−	3141.13i		−	1.22835i
$188$	−2949.15			−1.14409
$189$		0			0
$190$	5121.26			1.95545
$191$		−	210.385i		−	0.0797012i	−0.999206	−	0.0398506i	$-0.987312\pi$
$191$		−	210.385i		−	0.0797012i	0.999206	−	0.0398506i	$-0.0126882\pi$
$192$		0			0
$193$	827.826			0.308747			0.154374	−	0.988013i	$-0.450664\pi$
$193$	827.826			0.308747			0.154374	+	0.988013i	$0.450664\pi$
$194$	1935.37	−	3352.15i	0.716243	−	1.24057i
$195$		0			0
$196$	−1992.84	−	212.728i	−0.726253	−	0.0775249i
$197$			4969.34i			1.79721i	0.438756	+	0.898606i	$0.355419\pi$
$197$			4969.34i			1.79721i	−0.438756	+	0.898606i	$0.644581\pi$
$198$		0			0
$199$	1994.86	+	1151.74i	0.710614	+	0.410273i	0.811288	−	0.584646i	$-0.198767\pi$
$199$	1994.86	+	1151.74i	0.710614	+	0.410273i	−0.100674	+	0.994919i	$0.532100\pi$
$200$	−429.369	+	247.897i	−0.151805	+	0.0876447i
$201$		0			0
$202$	−803.142	+	463.694i	−0.279747	+	0.161512i
$203$	3076.86	+	2001.69i	1.06381	+	0.692074i
$204$		0			0
$205$	2537.01			0.864354
$206$	1398.12	−	2421.61i	0.472871	−	0.819036i
$207$		0			0
$208$	−156.077	+	90.1112i	−0.0520289	+	0.0300389i
$209$	1238.81	−	2145.68i	0.410000	−	0.710141i
$210$		0			0
$211$	−1406.66	−	2436.40i	−0.458949	−	0.794923i	0.539957	−	0.841693i	$-0.318441\pi$
$211$	−1406.66	−	2436.40i	−0.458949	−	0.794923i	−0.998906	+	0.0467701i	$0.985107\pi$
$212$	2177.63	+	1257.25i	0.705471	+	0.407304i
$213$		0			0
$214$	3021.02	+	5232.55i	0.965011	+	1.67145i
$215$	−2534.52	−	4389.92i	−0.803967	−	1.39251i
$216$		0			0
$217$	42.3200	−	795.159i	0.0132390	−	0.248751i
$218$	−4670.42	−	2696.47i	−1.45101	−	0.837743i
$219$		0			0
$220$		−	1964.44i		−	0.602011i
$221$		−	300.408i		−	0.0914372i
$222$		0			0
$223$	−3655.84	−	2110.70i	−1.09782	−	0.633825i	−0.162170	−	0.986763i	$-0.551849\pi$
$223$	−3655.84	−	2110.70i	−1.09782	−	0.633825i	−0.935647	+	0.352938i	$0.885183\pi$
$224$	−217.341	+	4083.67i	−0.0648292	+	1.21809i
$225$		0			0
$226$	489.163	+	847.256i	0.143976	+	0.249374i
$227$	622.021	+	1077.37i	0.181872	+	0.315012i	0.942518	−	0.334155i	$-0.108451\pi$
$227$	622.021	+	1077.37i	0.181872	+	0.315012i	−0.760646	+	0.649167i	$0.775118\pi$
$228$		0			0
$229$	4050.44	+	2338.52i	1.16882	+	0.674820i	0.953402	−	0.301702i	$-0.0975546\pi$
$229$	4050.44	+	2338.52i	1.16882	+	0.674820i	0.215420	+	0.976522i	$0.430888\pi$
$230$	−1233.83	−	2137.05i	−0.353722	−	0.612665i
$231$		0			0
$232$	795.293	−	1377.49i	0.225058	−	0.389812i
$233$	651.597	−	376.200i	0.183208	−	0.105775i	−0.405591	−	0.914055i	$-0.632934\pi$
$233$	651.597	−	376.200i	0.183208	−	0.105775i	0.588799	+	0.808279i	$0.299601\pi$
$234$		0			0
$235$	−3448.99	+	5973.83i	−0.957393	+	1.65825i
$236$	−1823.99			−0.503099
$237$		0			0
$238$	−7375.21	−	4798.04i	−2.00867	−	1.30677i
$239$	1800.76	−	1039.67i	0.487370	−	0.281383i	−0.236113	−	0.971726i	$-0.575874\pi$
$239$	1800.76	−	1039.67i	0.487370	−	0.281383i	0.723483	+	0.690343i	$0.242540\pi$
$240$		0			0
$241$	−3383.00	+	1953.17i	−0.904224	+	0.522054i	−0.878568	−	0.477617i	$-0.841501\pi$
$241$	−3383.00	+	1953.17i	−0.904224	+	0.522054i	−0.0256558	+	0.999671i	$0.508167\pi$
$242$	2338.76	+	1350.28i	0.621244	+	0.358675i
$243$		0			0
$244$			3205.28i			0.840972i
$245$	−2761.51	+	3787.94i	−0.720107	+	0.987765i
$246$		0			0
$247$	118.476	−	205.206i	0.0305199	−	0.0528620i
$248$	−345.048			−0.0883492
$249$		0			0
$250$			3214.70i			0.813262i
$251$	−1877.00			−0.472012			−0.236006	−	0.971752i	$-0.575838\pi$
$251$	−1877.00			−0.472012			−0.236006	+	0.971752i	$0.575838\pi$
$252$		0			0
$253$	−1193.83			−0.296661
$254$			1372.21i			0.338977i
$255$		0			0
$256$	5352.82			1.30684
$257$	−2650.88	+	4591.46i	−0.643414	+	1.11443i	0.341251	+	0.939972i	$0.389149\pi$
$257$	−2650.88	+	4591.46i	−0.643414	+	1.11443i	−0.984665	+	0.174454i	$0.944184\pi$
$258$		0			0
$259$	−705.167	−	1386.75i	−0.169177	−	0.332697i
$260$		−	187.873i		−	0.0448130i
$261$		0			0
$262$	3554.52	+	2052.20i	0.838164	+	0.483914i
$263$	1436.08	−	829.124i	0.336703	−	0.194395i	−0.322110	−	0.946702i	$-0.604392\pi$
$263$	1436.08	−	829.124i	0.336703	−	0.194395i	0.658813	+	0.752307i	$0.271059\pi$
$264$		0			0
$265$	5093.41	−	2940.68i	1.18070	−	0.681678i
$266$	−3145.67	−	6186.15i	−0.725089	−	1.42593i
$267$		0			0
$268$	3806.93			0.867706
$269$	−1903.76	+	3297.40i	−0.431502	+	0.747383i	−0.997003	−	0.0773642i	$-0.975350\pi$
$269$	−1903.76	+	3297.40i	−0.431502	+	0.747383i	0.565501	+	0.824748i	$0.308683\pi$
$270$		0			0
$271$	2510.98	−	1449.71i	0.562845	−	0.324959i	−0.191442	−	0.981504i	$-0.561316\pi$
$271$	2510.98	−	1449.71i	0.562845	−	0.324959i	0.754287	+	0.656545i	$0.227983\pi$
$272$	−4890.65	+	8470.85i	−1.09022	+	1.88831i
$273$		0			0
$274$	2315.76	+	4011.02i	0.510585	+	0.884360i
$275$	−1316.16	−	759.885i	−0.288609	−	0.166628i
$276$		0			0
$277$	2187.01	+	3788.01i	0.474385	+	0.821659i	0.999570	−	0.0293295i	$-0.00933721\pi$
$277$	2187.01	+	3788.01i	0.474385	+	0.821659i	−0.525185	+	0.850988i	$0.676004\pi$
$278$	4291.58	+	7433.23i	0.925870	+	1.60365i
$279$		0			0
$280$	1702.68	+	1107.70i	0.363409	+	0.236420i
$281$	−1910.31	−	1102.92i	−0.405550	−	0.234144i	0.283326	−	0.959024i	$-0.408562\pi$
$281$	−1910.31	−	1102.92i	−0.405550	−	0.234144i	−0.688876	+	0.724879i	$0.741896\pi$
$282$		0			0
$283$		−	5547.66i		−	1.16528i	−0.812730	−	0.582640i	$-0.802020\pi$
$283$		−	5547.66i		−	1.16528i	0.812730	−	0.582640i	$-0.197980\pi$
$284$		−	110.445i		−	0.0230763i
$285$		0			0
$286$	−186.485	−	107.667i	−0.0385563	−	0.0222605i
$287$	−1558.33	−	3064.54i	−0.320506	−	0.630294i
$288$		0			0
$289$	−5695.59	−	9865.05i	−1.15929	−	2.00795i
$290$	5039.04	+	8727.87i	1.02035	+	1.76730i
$291$		0			0
$292$	−3069.45	−	1772.15i	−0.615158	−	0.355162i
$293$	−332.172	−	575.338i	−0.0662310	−	0.114715i	0.831008	−	0.556260i	$-0.187764\pi$
$293$	−332.172	−	575.338i	−0.0662310	−	0.114715i	−0.897239	+	0.441544i	$0.854431\pi$
$294$		0			0
$295$	−2133.13	+	3694.69i	−0.421002	+	0.729197i
$296$	−583.822	+	337.070i	−0.114642	+	0.0661885i
$297$		0			0
$298$	−616.068	+	1067.06i	−0.119758	+	0.207427i
$299$	−114.174			−0.0220831
$300$		0			0
$301$	−3745.94	+	5757.99i	−0.717316	+	1.10261i
$302$	−5894.75	+	3403.34i	−1.12319	+	0.648477i
$303$		0			0
$304$	−6681.51	+	3857.57i	−1.26056	+	0.727786i
$305$	6492.66	+	3748.54i	1.21891	+	0.703740i
$306$		0			0
$307$			3371.17i			0.626720i	0.949634	+	0.313360i	$0.101455\pi$
$307$			3371.17i			0.626720i	−0.949634	+	0.313360i	$0.898545\pi$
$308$	−2372.91	+	1206.63i	−0.438991	+	0.223228i
$309$		0			0
$310$	1093.13	−	1893.35i	0.200276	−	0.346888i
$311$	4957.37			0.903881			0.451940	−	0.892048i	$-0.350732\pi$
$311$	4957.37			0.903881			0.451940	+	0.892048i	$0.350732\pi$
$312$		0			0
$313$		−	7901.00i		−	1.42681i	−0.700753	−	0.713404i	$-0.747153\pi$
$313$		−	7901.00i		−	1.42681i	0.700753	−	0.713404i	$-0.252847\pi$
$314$	161.715			0.0290641
$315$		0			0
$316$	−2544.26			−0.452930
$317$		−	6001.53i		−	1.06334i	−0.846951	−	0.531671i	$-0.821564\pi$
$317$		−	6001.53i		−	1.06334i	0.846951	−	0.531671i	$-0.178436\pi$
$318$		0			0
$319$	4875.67			0.855753
$320$	−1426.28	+	2470.39i	−0.249161	+	0.431560i
$321$		0			0
$322$	−1823.55	+	2803.04i	−0.315598	+	0.485116i
$323$		−	12860.2i		−	2.21535i
$324$		0			0
$325$	−125.873	−	72.6730i	−0.0214837	−	0.0124036i
$326$	−8621.08	+	4977.38i	−1.46465	+	0.845618i
$327$		0			0
$328$	−1290.17	+	744.882i	−0.217189	+	0.125394i
$329$	9334.50	+	496.801i	1.56422	+	0.0832508i
$330$		0			0
$331$	6753.39			1.12145			0.560725	−	0.828002i	$-0.310522\pi$
$331$	6753.39			1.12145			0.560725	+	0.828002i	$0.310522\pi$
$332$	2478.89	−	4293.57i	0.409780	−	0.709760i
$333$		0			0
$334$	−8381.30	+	4838.95i	−1.37307	+	0.792741i
$335$	4452.16	−	7711.36i	0.726111	−	1.25766i
$336$		0			0
$337$	−622.587	−	1078.35i	−0.100636	−	0.174307i	0.811311	−	0.584615i	$-0.198755\pi$
$337$	−622.587	−	1078.35i	−0.100636	−	0.174307i	−0.911947	+	0.410308i	$0.865421\pi$
$338$	7061.24	+	4076.81i	1.13633	+	0.656062i
$339$		0			0
$340$	−5098.26	−	8830.44i	−0.813212	−	1.40852i
$341$	−528.844	−	915.984i	−0.0839838	−	0.145464i
$342$		0			0
$343$	6271.80	+	1009.02i	0.987304	+	0.158840i
$344$	2577.81	+	1488.30i	0.404030	+	0.233267i
$345$		0			0
$346$			6515.13i			1.01230i
$347$		−	9502.44i		−	1.47008i	−0.678024	−	0.735040i	$-0.737163\pi$
$347$		−	9502.44i		−	1.47008i	0.678024	−	0.735040i	$-0.262837\pi$
$348$		0			0
$349$	3593.91	+	2074.94i	0.551225	+	0.318250i	0.749616	−	0.661873i	$-0.230238\pi$
$349$	3593.91	+	2074.94i	0.551225	+	0.318250i	−0.198391	+	0.980123i	$0.563572\pi$
$350$	−3794.59	+	1929.56i	−0.579512	+	0.294684i
$351$		0			0
$352$	2715.97	+	4704.19i	0.411254	+	0.712313i
$353$	−433.888	−	751.517i	−0.0654208	−	0.113312i	0.831460	−	0.555585i	$-0.187506\pi$
$353$	−433.888	−	751.517i	−0.0654208	−	0.113312i	−0.896881	+	0.442273i	$0.854172\pi$
$354$		0			0
$355$	−223.718	−	129.164i	−0.0334471	−	0.0193107i
$356$	−858.954	−	1487.75i	−0.127878	−	0.221491i
$357$		0			0
$358$	7655.67	−	13260.0i	1.13021	−	1.95758i
$359$	−1830.91	+	1057.08i	−0.269170	+	0.155405i	−0.628510	−	0.777801i	$-0.716335\pi$
$359$	−1830.91	+	1057.08i	−0.269170	+	0.155405i	0.359341	+	0.933206i	$0.383002\pi$
$360$		0			0
$361$	1642.32	−	2844.59i	0.239441	−	0.414724i
$362$	10170.5			1.47665
$363$		0			0
$364$	−226.938	+	115.399i	−0.0326780	+	0.0166169i
$365$	−7179.38	+	4145.02i	−1.02955	+	0.594411i
$366$		0			0
$367$	−271.211	+	156.584i	−0.0385753	+	0.0222714i	−0.519164	−	0.854675i	$-0.673756\pi$
$367$	−271.211	+	156.584i	−0.0385753	+	0.0222714i	0.480588	+	0.876946i	$0.340423\pi$
$368$	3219.45	+	1858.75i	0.456048	+	0.263299i
$369$		0			0
$370$		−	4271.40i		−	0.600161i
$371$	−6680.72	−	4346.23i	−0.934895	−	0.608208i
$372$		0			0
$373$	−2703.78	+	4683.09i	−0.375326	+	0.650083i	−0.990376	−	0.138405i	$-0.955802\pi$
$373$	−2703.78	+	4683.09i	−0.375326	+	0.650083i	0.615050	+	0.788488i	$0.289136\pi$
$374$	−11687.0			−1.61582
$375$		0			0
$376$		−	4050.58i		−	0.555566i
$377$	466.294			0.0637012
$378$		0			0
$379$	793.227			0.107508			0.0537538	−	0.998554i	$-0.482881\pi$
$379$	793.227			0.107508			0.0537538	+	0.998554i	$0.482881\pi$
$380$		−	8042.66i		−	1.08574i
$381$		0			0
$382$	−782.763			−0.104842
$383$	5099.84	−	8833.18i	0.680391	−	1.17847i	−0.294471	−	0.955660i	$-0.595143\pi$
$383$	5099.84	−	8833.18i	0.680391	−	1.17847i	0.974862	−	0.222811i	$-0.0715233\pi$
$384$		0			0
$385$	−330.921	+	6217.75i	−0.0438060	+	0.823080i
$386$		−	3080.03i		−	0.406138i
$387$		0			0
$388$	−5264.37	−	3039.38i	−0.688809	−	0.397684i
$389$	8551.58	−	4937.26i	1.11461	−	0.643519i	0.174589	−	0.984641i	$-0.444140\pi$
$389$	8551.58	−	4937.26i	1.11461	−	0.643519i	0.940019	+	0.341122i	$0.110807\pi$
$390$		0			0
$391$	−5366.42	+	3098.30i	−0.694096	+	0.400736i
$392$	292.177	−	2737.11i	0.0376459	−	0.352666i
$393$		0			0
$394$	18489.0			2.36412
$395$	−2975.48	+	5153.69i	−0.379020	+	0.656481i
$396$		0			0
$397$	9104.46	−	5256.46i	1.15098	−	0.664520i	0.201856	−	0.979415i	$-0.435303\pi$
$397$	9104.46	−	5256.46i	1.15098	−	0.664520i	0.949126	+	0.314896i	$0.101970\pi$
$398$	4285.17	−	7422.14i	0.539689	−	0.934769i
$399$		0			0
$400$	2366.24	+	4098.44i	0.295780	+	0.512306i
$401$	383.072	+	221.167i	0.0477050	+	0.0275425i	0.523663	−	0.851926i	$-0.324565\pi$
$401$	383.072	+	221.167i	0.0477050	+	0.0275425i	−0.475958	+	0.879468i	$0.657899\pi$
$402$		0			0
$403$	−50.5769	−	87.6018i	−0.00625166	−	0.0108282i
$404$	728.206	+	1261.29i	0.0896773	+	0.155326i
$405$		0			0
$406$	7447.52	−	11447.8i	0.910380	−	1.39937i
$407$	−1789.61	−	1033.23i	−0.217955	−	0.125836i
$408$		0			0
$409$			8194.64i			0.990706i	0.868692	+	0.495353i	$0.164961\pi$
$409$			8194.64i			0.990706i	−0.868692	+	0.495353i	$0.835039\pi$
$410$		−	9439.26i		−	1.13700i
$411$		0			0
$412$	−3803.00	−	2195.66i	−0.454759	−	0.262555i
$413$	5773.20	+	307.261i	0.687846	+	0.0366086i
$414$		0			0
$415$	−5798.07	−	10042.6i	−0.685822	−	1.18788i
$416$	259.746	+	449.894i	0.0306133	+	0.0530237i
$417$		0			0
$418$	−7983.25	−	4609.13i	−0.934147	−	0.539330i
$419$	7956.71	+	13781.4i	0.927711	+	1.60684i	0.787142	+	0.616772i	$0.211560\pi$
$419$	7956.71	+	13781.4i	0.927711	+	1.60684i	0.140569	+	0.990071i	$0.455107\pi$
$420$		0			0
$421$	−6044.72	+	10469.8i	−0.699766	+	1.21203i	0.268781	+	0.963201i	$0.413379\pi$
$421$	−6044.72	+	10469.8i	−0.699766	+	1.21203i	−0.968547	+	0.248829i	$0.919954\pi$
$422$	−9064.92	+	5233.64i	−1.04567	+	0.603719i
$423$		0			0
$424$	−1726.81	+	2990.92i	−0.197786	+	0.342575i
$425$	−7888.43			−0.900342
$426$		0			0
$427$	539.948	−	10145.2i	0.0611942	−	1.14979i
$428$	8217.44	−	4744.34i	0.928049	−	0.535809i
$429$		0			0
$430$	−16333.2	+	9430.00i	−1.83176	+	1.05757i
$431$	−7013.76	−	4049.40i	−0.783854	−	0.452558i	0.0539405	−	0.998544i	$-0.482822\pi$
$431$	−7013.76	−	4049.40i	−0.783854	−	0.452558i	−0.837794	+	0.545986i	$0.816155\pi$
$432$		0			0
$433$		−	760.926i		−	0.0844522i	−0.999108	−	0.0422261i	$-0.986555\pi$
$433$		−	760.926i		−	0.0844522i	0.999108	−	0.0422261i	$-0.0134450\pi$
$434$	−2958.49	−	157.457i	−0.327216	−	0.0174151i
$435$		0			0
$436$	−4234.66	+	7334.64i	−0.465145	+	0.805655i
$437$	−4887.67			−0.535032
$438$		0			0
$439$			2640.98i			0.287123i	0.989641	+	0.143561i	$0.0458555\pi$
$439$			2640.98i			0.287123i	−0.989641	+	0.143561i	$0.954145\pi$
$440$	2698.11			0.292335
$441$		0			0
$442$	−1117.70			−0.120280
$443$			6531.03i			0.700449i	0.936666	+	0.350224i	$0.113895\pi$
$443$			6531.03i			0.700449i	−0.936666	+	0.350224i	$0.886105\pi$
$444$		0			0
$445$	−4018.15			−0.428041
$446$	−7853.12	+	13602.0i	−0.833758	+	1.44411i
$447$		0			0
$448$	3860.15	+	205.445i	0.407087	+	0.0216660i
$449$			6932.75i			0.728678i	0.931266	+	0.364339i	$0.118705\pi$
$449$			6932.75i			0.728678i	−0.931266	+	0.364339i	$0.881295\pi$
$450$		0			0
$451$	−3954.81	−	2283.31i	−0.412915	−	0.238396i
$452$	1330.57	−	768.204i	0.138462	−	0.0799409i
$453$		0			0
$454$	4008.49	−	2314.31i	0.414379	−	0.239242i
$455$	−31.6483	+	594.646i	−0.00326087	+	0.0612691i
$456$		0			0
$457$	−14591.5			−1.49357			−0.746784	−	0.665066i	$-0.768403\pi$
$457$	−14591.5			−1.49357			−0.746784	+	0.665066i	$0.768403\pi$
$458$	8700.75	−	15070.1i	0.887684	−	1.53751i
$459$		0			0
$460$	−3356.12	+	1937.66i	−0.340174	+	0.196399i
$461$	5053.02	−	8752.08i	0.510504	−	0.884219i	−0.489422	−	0.872047i	$-0.662792\pi$
$461$	5053.02	−	8752.08i	0.510504	−	0.884219i	0.999926	−	0.0121719i	$-0.00387455\pi$
$462$		0			0
$463$	−8356.28	−	14473.5i	−0.838768	−	1.45279i	−0.890925	−	0.454150i	$-0.849943\pi$
$463$	−8356.28	−	14473.5i	−0.838768	−	1.45279i	0.0521577	−	0.998639i	$-0.483390\pi$
$464$	−13148.5	−	7591.28i	−1.31552	−	0.759518i
$465$		0			0
$466$	−1399.70	−	2424.35i	−0.139141	−	0.240999i
$467$	−1460.16	−	2529.07i	−0.144685	−	0.250602i	0.784570	−	0.620040i	$-0.212884\pi$
$467$	−1460.16	−	2529.07i	−0.144685	−	0.250602i	−0.929256	+	0.369438i	$0.879550\pi$
$468$		0			0
$469$	−12049.5	−	641.299i	−1.18634	−	0.0631395i
$470$	22226.4	+	12832.4i	2.18133	+	1.25939i
$471$		0			0
$472$		−	2505.20i		−	0.244303i
$473$			9124.27i			0.886965i
$474$		0			0
$475$	−5388.51	−	3111.06i	−0.520509	−	0.300516i
$476$	−7535.05	+	11582.4i	−0.725564	+	1.11529i
$477$		0			0
$478$	−3868.21	−	6699.94i	−0.370142	−	0.641105i
$479$	3147.51	+	5451.65i	0.300237	+	0.520026i	0.976189	−	0.216920i	$-0.0696009\pi$
$479$	3147.51	+	5451.65i	0.300237	+	0.520026i	−0.675953	+	0.736945i	$0.736268\pi$
$480$		0			0
$481$	−171.152	−	98.8149i	−0.0162243	−	0.00936709i
$482$	7267.02	+	12586.9i	0.686730	+	1.18945i
$483$		0			0
$484$	2120.54	−	3672.89i	0.199149	−	0.344937i
$485$	−12313.2	+	7109.05i	−1.15281	+	0.665578i
$486$		0			0
$487$	2731.42	−	4730.96i	0.254153	−	0.440206i	−0.710512	−	0.703685i	$-0.751537\pi$
$487$	2731.42	−	4730.96i	0.254153	−	0.440206i	0.964665	+	0.263479i	$0.0848700\pi$
$488$	−4402.37			−0.408373
$489$		0			0
$490$	14093.5	+	10274.5i	1.29934	+	0.947256i
$491$	−3732.70	+	2155.07i	−0.343084	+	0.198080i	−0.661635	−	0.749826i	$-0.730137\pi$
$491$	−3732.70	+	2155.07i	−0.343084	+	0.198080i	0.318551	+	0.947906i	$0.396804\pi$
$492$		0			0
$493$	21916.8	−	12653.7i	2.00220	−	1.15597i
$494$	−763.493	−	440.803i	−0.0695368	−	0.0401471i
$495$		0			0
$496$			3293.58i			0.298157i
$497$	−18.6050	+	349.574i	−0.00167918	+	0.0315504i
$498$		0			0
$499$	−9015.59	+	15615.5i	−0.808804	+	1.40089i	0.104889	+	0.994484i	$0.466551\pi$
$499$	−9015.59	+	15615.5i	−0.808804	+	1.40089i	−0.913693	+	0.406405i	$0.866782\pi$
$500$	5048.51			0.451553
$501$		0			0
$502$			6983.59i			0.620902i
$503$	−8764.80			−0.776945			−0.388472	−	0.921460i	$-0.626997\pi$
$503$	−8764.80			−0.776945			−0.388472	+	0.921460i	$0.626997\pi$
$504$		0			0
$505$	3406.51			0.300174
$506$			4441.77i			0.390239i
$507$		0			0
$508$	2154.98			0.188212
$509$	758.058	−	1313.00i	0.0660125	−	0.114337i	−0.831130	−	0.556078i	$-0.812306\pi$
$509$	758.058	−	1313.00i	0.0660125	−	0.114337i	0.897143	+	0.441741i	$0.145639\pi$
$510$		0			0
$511$	9416.76	+	6126.19i	0.815211	+	0.530346i
$512$		−	11996.6i		−	1.03551i
$513$		0			0
$514$	17083.1	+	9862.93i	1.46596	+	0.846372i
$515$	−8895.13	+	5135.61i	−0.761100	+	0.439421i
$516$		0			0
$517$	10752.9	−	6208.18i	0.914722	−	0.528115i
$518$	−5159.57	+	2623.66i	−0.437642	+	0.222542i
$519$		0			0
$520$	258.039			0.0217611
$521$	2984.80	−	5169.82i	0.250991	−	0.434729i	−0.712808	−	0.701359i	$-0.752577\pi$
$521$	2984.80	−	5169.82i	0.250991	−	0.434729i	0.963799	+	0.266630i	$0.0859102\pi$
$522$		0			0
$523$	−10006.2	+	5777.11i	−0.836601	+	0.483012i	−0.856107	−	0.516798i	$-0.827124\pi$
$523$	−10006.2	+	5777.11i	−0.836601	+	0.483012i	0.0195064	+	0.999810i	$0.493791\pi$
$524$	3222.87	−	5582.18i	0.268687	−	0.465379i
$525$		0			0
$526$	−3084.86	−	5343.13i	−0.255715	−	0.442912i
$527$	−4754.46	−	2744.99i	−0.392993	−	0.226895i
$528$		0			0
$529$	−4905.95	−	8497.36i	−0.403218	−	0.698394i
$530$	−10941.2	−	18950.7i	−0.896706	−	1.55314i
$531$		0			0
$532$	−9715.00	+	4940.11i	−0.791727	+	0.402596i
$533$	−378.225	−	218.368i	−0.0307369	−	0.0177459i
$534$		0			0
$535$		−	22193.8i		−	1.79350i
$536$			5228.72i			0.421355i
$537$		0			0
$538$	12268.4	+	7083.16i	0.983137	+	0.567615i
$539$	7713.90	−	3419.45i	0.616440	−	0.273258i
$540$		0			0
$541$	11902.5	+	20615.7i	0.945891	+	1.63833i	0.753957	+	0.656924i	$0.228143\pi$
$541$	11902.5	+	20615.7i	0.945891	+	1.63833i	0.191935	+	0.981408i	$0.438524\pi$
$542$	−5393.84	−	9342.40i	−0.427463	−	0.740388i
$543$		0			0
$544$	24417.3	+	14097.4i	1.92442	+	1.11106i
$545$	9904.76	+	17155.5i	0.778483	+	1.34837i
$546$		0			0
$547$	−6766.49	+	11719.9i	−0.528911	+	0.916100i	0.470521	+	0.882389i	$0.344066\pi$
$547$	−6766.49	+	11719.9i	−0.528911	+	0.916100i	−0.999432	+	0.0337115i	$0.989267\pi$
$548$	6299.09	−	3636.78i	0.491029	−	0.283495i
$549$		0			0
$550$	−2827.24	+	4896.93i	−0.219189	+	0.379647i
$551$	19961.6			1.54336
$552$		0			0
$553$	8052.97	+	428.596i	0.619254	+	0.0329579i
$554$	14093.8	−	8137.03i	1.08084	−	0.624024i
$555$		0			0
$556$	11673.5	−	6739.69i	0.890406	−	0.514076i
$557$	11739.1	+	6777.54i	0.892997	+	0.515572i	0.874922	−	0.484264i	$-0.160913\pi$
$557$	11739.1	+	6777.54i	0.892997	+	0.515572i	0.0180757	+	0.999837i	$0.494246\pi$
$558$		0			0
$559$			872.617i			0.0660246i
$560$	10573.3	−	16252.5i	0.797862	−	1.22642i
$561$		0			0
$562$	−4103.54	+	7107.54i	−0.308003	+	0.533476i
$563$	−9865.16			−0.738484			−0.369242	−	0.929333i	$-0.620383\pi$
$563$	−9865.16			−0.738484			−0.369242	+	0.929333i	$0.620383\pi$
$564$		0			0
$565$		−	3593.62i		−	0.267584i
$566$	−20640.7			−1.53285
$567$		0			0
$568$	151.693			0.0112058
$569$			6262.01i			0.461366i	0.973029	+	0.230683i	$0.0740960\pi$
$569$			6262.01i			0.461366i	−0.973029	+	0.230683i	$0.925904\pi$
$570$		0			0
$571$	−10100.3			−0.740255			−0.370128	−	0.928981i	$-0.620686\pi$
$571$	−10100.3			−0.740255			−0.370128	+	0.928981i	$0.620686\pi$
$572$	−169.085	+	292.865i	−0.0123598	+	0.0214078i
$573$		0			0
$574$	−11402.0	+	5797.96i	−0.829113	+	0.421606i
$575$			2998.10i			0.217442i
$576$		0			0
$577$	15135.0	+	8738.22i	1.09199	+	0.630462i	0.934106	−	0.356995i	$-0.116199\pi$
$577$	15135.0	+	8738.22i	1.09199	+	0.630462i	0.157886	+	0.987457i	$0.449532\pi$
$578$	−36704.1	+	21191.1i	−2.64133	+	1.52497i
$579$		0			0
$580$	13706.6	−	7913.53i	0.981271	−	0.566537i
$581$	−8569.35	+	13172.2i	−0.611905	+	0.940578i
$582$		0			0
$583$	−10586.5			−0.752052
$584$	2434.00	−	4215.82i	0.172465	−	0.298719i
$585$		0			0
$586$	−2140.62	+	1235.89i	−0.150901	+	0.0871228i
$587$	−3676.64	+	6368.12i	−0.258520	+	0.447769i	−0.965846	−	0.259118i	$-0.916568\pi$
$587$	−3676.64	+	6368.12i	−0.258520	+	0.447769i	0.707326	+	0.706888i	$0.249901\pi$
$588$		0			0
$589$	−2165.15	−	3750.15i	−0.151466	−	0.262347i
$590$	13746.6	+	7936.58i	0.959215	+	0.553803i
$591$		0			0
$592$	3217.42	+	5572.74i	0.223370	+	0.386889i
$593$	−4475.21	−	7751.29i	−0.309907	−	0.536775i	0.668435	−	0.743771i	$-0.266965\pi$
$593$	−4475.21	−	7751.29i	−0.309907	−	0.536775i	−0.978342	+	0.206996i	$0.933631\pi$
$594$		0			0
$595$	14649.2	+	28808.5i	1.00934	+	1.98493i
$596$	1675.76	+	967.500i	0.115171	+	0.0664939i
$597$		0			0
$598$			424.797i			0.0290489i
$599$		−	12548.8i		−	0.855978i	−0.903784	−	0.427989i	$-0.859222\pi$
$599$		−	12548.8i		−	0.855978i	0.903784	−	0.427989i	$-0.140778\pi$
$600$		0			0
$601$	8672.73	+	5007.20i	0.588632	+	0.339847i	0.764556	−	0.644557i	$-0.222958\pi$
$601$	8672.73	+	5007.20i	0.588632	+	0.339847i	−0.175924	+	0.984404i	$0.556291\pi$
$602$	21423.3	+	13937.2i	1.45041	+	0.943585i
$603$		0			0
$604$	5344.75	+	9257.38i	0.360058	+	0.623638i
$605$	−4959.90	−	8590.80i	−0.333304	−	0.577299i
$606$		0			0
$607$	−769.474	−	444.256i	−0.0514530	−	0.0297064i	0.474053	−	0.880496i	$-0.342791\pi$
$607$	−769.474	−	444.256i	−0.0514530	−	0.0297064i	−0.525506	+	0.850790i	$0.676124\pi$
$608$	11119.5	+	19259.5i	0.741702	+	1.28467i
$609$		0			0
$610$	13946.9	−	24156.7i	0.925727	−	1.60341i
$611$	1028.37	−	593.731i	0.0680908	−	0.0393122i
$612$		0			0
$613$	−6545.70	+	11337.5i	−0.431286	+	0.747009i	−0.996984	−	0.0776029i	$-0.975273\pi$
$613$	−6545.70	+	11337.5i	−0.431286	+	0.747009i	0.565698	+	0.824612i	$0.308607\pi$
$614$	12542.9			0.824411
$615$		0			0
$616$	−1657.28	−	3259.14i	−0.108399	−	0.213173i
$617$	7968.85	−	4600.82i	0.519957	−	0.300198i	−0.216960	−	0.976181i	$-0.569614\pi$
$617$	7968.85	−	4600.82i	0.519957	−	0.300198i	0.736917	+	0.675983i	$0.236281\pi$
$618$		0			0
$619$	1455.41	−	840.280i	0.0945037	−	0.0545617i	−0.452003	−	0.892016i	$-0.649291\pi$
$619$	1455.41	−	840.280i	0.0945037	−	0.0545617i	0.546507	+	0.837455i	$0.315957\pi$
$620$	−2973.40	−	1716.70i	−0.192605	−	0.111200i
$621$		0			0
$622$		−	18444.5i		−	1.18900i
$623$	2468.10	+	4853.66i	0.158720	+	0.312131i
$624$		0			0
$625$	9765.37	−	16914.1i	0.624983	−	1.08250i
$626$	−29396.6			−1.87688
$627$		0			0
$628$		−	253.965i		−	0.0161374i
$629$	−10726.1			−0.679930
$630$		0			0
$631$	−341.784			−0.0215629			−0.0107815	−	0.999942i	$-0.503432\pi$
$631$	−341.784			−0.0215629			−0.0107815	+	0.999942i	$0.503432\pi$
$632$		−	3494.48i		−	0.219941i
$633$		0			0
$634$	−22329.4			−1.39876
$635$	2520.23	−	4365.16i	0.157499	−	0.272797i
$636$		0			0
$637$	737.733	−	327.025i	0.0458870	−	0.0203410i
$638$		−	18140.5i		−	1.12569i
$639$		0			0
$640$	−11716.1	−	6764.31i	−0.723626	−	0.417786i
$641$	3851.53	−	2223.68i	0.237326	−	0.137020i	−0.376621	−	0.926367i	$-0.622914\pi$
$641$	3851.53	−	2223.68i	0.237326	−	0.137020i	0.613947	+	0.789347i	$0.289581\pi$
$642$		0			0
$643$	3417.70	−	1973.21i	0.209612	−	0.121020i	−0.391519	−	0.920170i	$-0.628050\pi$
$643$	3417.70	−	1973.21i	0.209612	−	0.121020i	0.601131	+	0.799150i	$0.294717\pi$
$644$	4402.02	+	2863.79i	0.269354	+	0.175232i
$645$		0			0
$646$	−47847.8			−2.91416
$647$	815.600	−	1412.66i	0.0495588	−	0.0858384i	−0.840182	−	0.542305i	$-0.817552\pi$
$647$	815.600	−	1412.66i	0.0495588	−	0.0858384i	0.889741	+	0.456466i	$0.150885\pi$
$648$		0			0
$649$	6650.44	−	3839.63i	0.402238	−	0.232232i
$650$	−270.389	+	468.327i	−0.0163162	+	0.0282605i
$651$		0			0
$652$	7816.70	+	13538.9i	0.469518	+	0.813229i
$653$	9217.89	+	5321.95i	0.552410	+	0.318934i	0.750094	−	0.661332i	$-0.230008\pi$
$653$	9217.89	+	5321.95i	0.552410	+	0.318934i	−0.197683	+	0.980266i	$0.563342\pi$
$654$		0			0
$655$	−7538.22	−	13056.6i	−0.449683	−	0.778874i
$656$	7110.10	+	12315.0i	0.423175	+	0.732960i
$657$		0			0
$658$	1848.41	−	34730.1i	0.109511	−	2.05763i
$659$	−23.4141	−	13.5182i	−0.00138404	−	0.000799079i	0.499308	−	0.866425i	$-0.333588\pi$
$659$	−23.4141	−	13.5182i	−0.00138404	−	0.000799079i	−0.500692	+	0.865626i	$0.666921\pi$
$660$		0			0
$661$			7757.38i			0.456471i	0.973606	+	0.228235i	$0.0732955\pi$
$661$			7757.38i			0.456471i	−0.973606	+	0.228235i	$0.926704\pi$
$662$		−	25126.8i		−	1.47520i
$663$		0			0
$664$	5897.11	+	3404.70i	0.344657	+	0.198988i
$665$	−1354.83	+	25456.2i	−0.0790047	+	1.48444i
$666$		0			0
$667$	−4809.19	−	8329.77i	−0.279180	−	0.483553i
$668$	7599.30	+	13162.4i	0.440158	+	0.762377i
$669$		0			0
$670$	−28691.1	−	16564.8i	−1.65438	−	0.955155i
$671$	−6747.36	−	11686.8i	−0.388195	−	0.672374i
$672$		0			0
$673$	−16598.3	+	28749.0i	−0.950693	+	1.64665i	−0.206762	+	0.978391i	$0.566293\pi$
$673$	−16598.3	+	28749.0i	−0.950693	+	1.64665i	−0.743931	+	0.668257i	$0.767041\pi$
$674$	−4012.14	+	2316.41i	−0.229291	+	0.132381i
$675$		0			0
$676$	6402.40	−	11089.3i	0.364270	−	0.630933i
$677$	−10932.0			−0.620605			−0.310303	−	0.950638i	$-0.600430\pi$
$677$	−10932.0			−0.620605			−0.310303	+	0.950638i	$0.600430\pi$
$678$		0			0
$679$	16150.5	+	10506.9i	0.912813	+	0.593842i
$680$	12128.4	−	7002.33i	0.683975	−	0.394893i
$681$		0			0
$682$	−3408.03	+	1967.63i	−0.191349	+	0.110476i
$683$	−12991.1	−	7500.40i	−0.727804	−	0.420198i	0.0898144	−	0.995959i	$-0.471373\pi$
$683$	−12991.1	−	7500.40i	−0.727804	−	0.420198i	−0.817618	+	0.575761i	$0.804706\pi$
$684$		0			0
$685$		−	17012.7i		−	0.948936i
$686$	3754.19	−	23335.0i	0.208944	−	1.29874i
$687$		0			0
$688$	14206.2	−	24605.9i	0.787220	−	1.36351i
$689$	−1012.46			−0.0559818
$690$		0			0
$691$		−	1059.56i		−	0.0583325i	−0.999575	−	0.0291662i	$-0.990715\pi$
$691$		−	1059.56i		−	0.0583325i	0.999575	−	0.0291662i	$-0.00928522\pi$
$692$	10231.6			0.562065
$693$		0			0
$694$	−35355.0			−1.93380
$695$		−	31527.9i		−	1.72075i
$696$		0			0
$697$	−23703.2			−1.28813
$698$	7720.08	−	13371.6i	0.418638	−	0.725102i
$699$		0			0
$700$	3030.27	+	5959.19i	0.163619	+	0.321766i
$701$			21617.3i			1.16473i	0.812928	+	0.582365i	$0.197872\pi$
$701$			21617.3i			1.16473i	−0.812928	+	0.582365i	$0.802128\pi$
$702$		0			0
$703$	−7326.87	−	4230.17i	−0.393084	−	0.226947i
$704$	4446.70	−	2567.31i	0.238056	−	0.137442i
$705$		0			0
$706$	−2796.11	+	1614.34i	−0.149055	+	0.0860571i
$707$	−2092.41	−	4114.85i	−0.111306	−	0.218889i
$708$		0			0
$709$	−25066.6			−1.32778			−0.663889	−	0.747831i	$-0.731095\pi$
$709$	−25066.6			−1.32778			−0.663889	+	0.747831i	$0.731095\pi$
$710$	−480.569	+	832.370i	−0.0254020	+	0.0439976i
$711$		0			0
$712$	2043.39	−	1179.75i	0.107555	−	0.0620970i
$713$	−1043.27	+	1806.99i	−0.0547975	+	0.0949121i
$714$		0			0
$715$	395.487	+	685.003i	0.0206858	+	0.0358289i
$716$	−20824.1	−	12022.8i	−1.08692	−	0.627533i
$717$		0			0
$718$	3932.99	+	6812.14i	0.204426	+	0.354076i
$719$	1208.60	+	2093.36i	0.0626888	+	0.108580i	0.895666	−	0.444726i	$-0.146699\pi$
$719$	1208.60	+	2093.36i	0.0626888	+	0.108580i	−0.832978	+	0.553307i	$0.813366\pi$
$720$		0			0
$721$	11667.2	+	7590.25i	0.602648	+	0.392061i
$722$	−10583.6	−	6110.47i	−0.545544	−	0.314970i
$723$		0			0
$724$		−	15972.2i		−	0.819891i
$725$		−	12244.4i		−	0.627238i
$726$		0			0
$727$	−3918.13	−	2262.13i	−0.199884	−	0.115403i	0.396718	−	0.917941i	$-0.370149\pi$
$727$	−3918.13	−	2262.13i	−0.199884	−	0.115403i	−0.596601	+	0.802538i	$0.703483\pi$
$728$	−158.497	−	311.694i	−0.00806909	−	0.0158683i
$729$		0			0
$730$	15422.0	+	26711.8i	0.781912	+	1.35431i
$731$	23680.0	+	41014.9i	1.19813	+	2.07523i
$732$		0			0
$733$	25576.2	+	14766.4i	1.28878	+	0.744080i	0.978437	−	0.206544i	$-0.0662216\pi$
$733$	25576.2	+	14766.4i	1.28878	+	0.744080i	0.310346	+	0.950624i	$0.399555\pi$
$734$	582.590	+	1009.08i	0.0292967	+	0.0507434i
$735$		0			0
$736$	5357.87	−	9280.11i	0.268334	−	0.464768i
$737$	−13880.4	+	8013.87i	−0.693748	+	0.400536i
$738$		0			0
$739$	11492.3	−	19905.2i	0.572057	−	0.990832i	−0.424298	−	0.905523i	$-0.639479\pi$
$739$	11492.3	−	19905.2i	0.572057	−	0.990832i	0.996355	−	0.0853088i	$-0.0271877\pi$
$740$	−6708.00			−0.333231
$741$		0			0
$742$	−16170.7	+	24856.5i	−0.800060	+	1.22980i
$743$	−12127.5	+	7001.83i	−0.598810	+	0.345723i	−0.768573	−	0.639762i	$-0.779033\pi$
$743$	−12127.5	+	7001.83i	−0.598810	+	0.345723i	0.169763	+	0.985485i	$0.445700\pi$
$744$		0			0
$745$	3919.56	−	2262.96i	0.192754	−	0.111286i
$746$	17424.0	+	10059.8i	0.855145	+	0.493718i
$747$		0			0
$748$			18353.7i			0.897164i
$749$	−26808.6	+	13632.3i	−1.30783	+	0.665037i
$750$		0			0
$751$	−13995.6	+	24241.1i	−0.680036	+	1.17786i	0.294933	+	0.955518i	$0.404703\pi$
$751$	−13995.6	+	24241.1i	−0.680036	+	1.17786i	−0.974969	+	0.222339i	$0.928631\pi$
$752$	−38663.9			−1.87490
$753$		0			0
$754$		−	1734.90i		−	0.0837950i
$755$	25002.5			1.20521
$756$		0			0
$757$	32553.0			1.56296			0.781479	−	0.623932i	$-0.214466\pi$
$757$	32553.0			1.56296			0.781479	+	0.623932i	$0.214466\pi$
$758$		−	2951.30i		−	0.141420i
$759$		0			0
$760$	11046.4			0.527230
$761$	−7445.71	+	12896.3i	−0.354674	+	0.614313i	−0.987062	−	0.160339i	$-0.948741\pi$
$761$	−7445.71	+	12896.3i	−0.354674	+	0.614313i	0.632388	+	0.774651i	$0.282075\pi$
$762$		0			0
$763$	14638.9	−	22501.9i	0.694579	−	1.06766i
$764$			1229.29i			0.0582121i
$765$		0			0
$766$	−32864.9	−	18974.6i	−1.55021	−	0.895012i
$767$	636.027	−	367.210i	0.0299421	−	0.0172871i
$768$		0			0
$769$	−6873.39	+	3968.36i	−0.322316	+	0.186089i	−0.652424	−	0.757854i	$-0.726248\pi$
$769$	−6873.39	+	3968.36i	−0.322316	+	0.186089i	0.330108	+	0.943943i	$0.392915\pi$
$770$	23133.9	+	1231.23i	1.08271	+	0.0576241i
$771$		0			0
$772$	−4837.02			−0.225503
$773$	8421.63	−	14586.7i	0.391856	−	0.678715i	−0.600838	−	0.799371i	$-0.705166\pi$
$773$	8421.63	−	14586.7i	0.391856	−	0.678715i	0.992694	+	0.120656i	$0.0384997\pi$
$774$		0			0
$775$	−2300.34	+	1328.10i	−0.106620	+	0.0615573i
$776$	4174.52	−	7230.48i	0.193114	−	0.334483i
$777$		0			0
$778$	−18369.7	−	31817.2i	−0.846510	−	1.46620i
$779$	−16191.5	−	9348.14i	−0.744697	−	0.429951i
$780$		0			0
$781$	232.494	+	402.692i	0.0106521	+	0.0184500i
$782$	11527.6	+	19966.4i	0.527144	+	0.913041i
$783$		0			0
$784$	−26126.5	−	2788.91i	−1.19016	−	0.127046i
$785$	−514.434	−	297.009i	−0.0233897	−	0.0135041i
$786$		0			0
$787$			33935.6i			1.53707i	0.639807	+	0.768536i	$0.279014\pi$
$787$			33935.6i			1.53707i	−0.639807	+	0.768536i	$0.720986\pi$
$788$		−	29036.0i		−	1.31265i
$789$		0			0
$790$	19174.9	+	11070.6i	0.863561	+	0.498577i
$791$	−4340.86	+	2207.34i	−0.195124	+	0.0992212i
$792$		0			0
$793$	−645.297	−	1117.69i	−0.0288968	−	0.0500507i
$794$	−19557.3	−	33874.3i	−0.874135	−	1.51405i
$795$		0			0
$796$	−11656.1	−	6729.63i	−0.519018	−	0.299655i
$797$	−12449.1	−	21562.5i	−0.553288	−	0.958324i	−0.998034	−	0.0626670i	$-0.980039\pi$
$797$	−12449.1	−	21562.5i	−0.553288	−	0.958324i	0.444746	−	0.895657i	$-0.353294\pi$
$798$		0			0
$799$	32223.9	−	55813.4i	1.42678	−	2.47126i
$800$	11813.8	−	6820.71i	0.522102	−	0.301435i
$801$		0			0
$802$	822.878	−	1425.27i	0.0362305	−	0.0627530i
$803$	14922.1			0.655776
$804$		0			0
$805$	10949.0	−	5567.62i	0.479382	−	0.243767i
$806$	−325.933	+	188.178i	−0.0142438	+	0.00822367i
$807$		0			0
$808$	−1732.35	+	1000.17i	−0.0754256	+	0.0435470i
$809$	5709.11	+	3296.16i	0.248111	+	0.143247i	0.618899	−	0.785471i	$-0.287579\pi$
$809$	5709.11	+	3296.16i	0.248111	+	0.143247i	−0.370788	+	0.928718i	$0.620912\pi$
$810$		0			0
$811$		−	184.817i		−	0.00800222i	−0.999992	−	0.00400111i	$-0.998726\pi$
$811$		−	184.817i		−	0.00800222i	0.999992	−	0.00400111i	$-0.00127360\pi$
$812$	−17978.2	−	11695.9i	−0.776983	−	0.505476i
$813$		0			0
$814$	−3844.26	+	6658.45i	−0.165530	+	0.286706i
$815$	36566.2			1.57160
$816$		0			0
$817$			37355.9i			1.59965i
$818$	30489.2			1.30321
$819$		0			0
$820$	−14823.8			−0.631306
$821$			6921.45i			0.294227i	0.989120	+	0.147113i	$0.0469982\pi$
$821$			6921.45i			0.294227i	−0.989120	+	0.147113i	$0.953002\pi$
$822$		0			0
$823$	8628.73			0.365466			0.182733	−	0.983163i	$-0.441506\pi$
$823$	8628.73			0.365466			0.182733	+	0.983163i	$0.441506\pi$
$824$	3015.69	−	5223.33i	0.127496	−	0.220829i
$825$		0			0
$826$	1143.20	−	21479.9i	0.0481563	−	0.904819i
$827$		−	36959.2i		−	1.55405i	−0.629472	−	0.777023i	$-0.716729\pi$
$827$		−	36959.2i		−	1.55405i	0.629472	−	0.777023i	$-0.283271\pi$
$828$		0			0
$829$	−12723.8	−	7346.11i	−0.533073	−	0.307770i	0.209194	−	0.977874i	$-0.432916\pi$
$829$	−12723.8	−	7346.11i	−0.533073	−	0.307770i	−0.742267	+	0.670104i	$0.766249\pi$
$830$	−37364.6	+	21572.4i	−1.56258	+	0.902157i
$831$		0			0
$832$	425.269	−	245.529i	0.0177206	−	0.0102310i
$833$	25800.7	−	35390.6i	1.07316	−	1.47204i
$834$		0			0
$835$	35549.2			1.47333
$836$	−7238.39	+	12537.3i	−0.299456	+	0.518672i
$837$		0			0
$838$	51275.5	−	29603.9i	2.11370	−	1.22035i
$839$	−3876.68	+	6714.61i	−0.159521	+	0.276298i	−0.934696	−	0.355448i	$-0.884328\pi$
$839$	−3876.68	+	6714.61i	−0.159521	+	0.276298i	0.775175	+	0.631746i	$0.217662\pi$
$840$		0			0
$841$	7446.60	+	12897.9i	0.305326	+	0.528841i
$842$	38954.0	+	22490.1i	1.59435	+	0.920499i
$843$		0			0
$844$	8219.14	+	14236.0i	0.335207	+	0.580595i
$845$	−14975.1	−	25937.6i	−0.609654	−	1.05595i
$846$		0			0
$847$	−7330.56	+	11268.0i	−0.297380	+	0.457112i
$848$	28549.1	+	16482.8i	1.15611	+	0.667479i
$849$		0			0
$850$			29349.9i			1.18434i
$851$			4076.57i			0.164210i
$852$		0			0
$853$	8892.58	+	5134.13i	0.356947	+	0.206084i	0.667741	−	0.744394i	$-0.267261\pi$
$853$	8892.58	+	5134.13i	0.356947	+	0.206084i	−0.310794	+	0.950477i	$0.600595\pi$
$854$	−37746.5	−	2008.94i	−1.51248	−	0.0804972i
$855$		0			0
$856$	6516.23	+	11286.4i	0.260187	+	0.450657i
$857$	13906.9	+	24087.5i	0.554320	+	0.960110i	0.997956	+	0.0639028i	$0.0203548\pi$
$857$	13906.9	+	24087.5i	0.554320	+	0.960110i	−0.443637	+	0.896207i	$0.646312\pi$
$858$		0			0
$859$	497.469	+	287.214i	0.0197595	+	0.0114082i	0.509847	−	0.860265i	$-0.329702\pi$
$859$	497.469	+	287.214i	0.0197595	+	0.0114082i	−0.490088	+	0.871673i	$0.663035\pi$
$860$	14809.3	+	25650.4i	0.587201	+	1.01706i
$861$		0			0
$862$	−15066.3	+	26095.6i	−0.595313	+	1.03111i
$863$	26652.7	−	15388.0i	1.05130	−	0.606967i	0.128285	−	0.991737i	$-0.459053\pi$
$863$	26652.7	−	15388.0i	1.05130	−	0.606967i	0.923012	+	0.384771i	$0.125720\pi$
$864$		0			0
$865$	11965.8	−	20725.4i	0.470346	−	0.814663i
$866$	−2831.12			−0.111092
$867$		0			0
$868$	−247.277	+	4646.14i	−0.00966950	+	0.181682i
$869$	9276.63	−	5355.87i	0.362127	−	0.209074i
$870$		0			0
$871$	−1327.48	+	766.422i	−0.0516418	+	0.0298154i
$872$	−10073.9	−	5816.20i	−0.391223	−	0.225873i
$873$		0			0
$874$			18185.2i			0.703801i
$875$	−15979.3	−	850.451i	−0.617370	−	0.0328577i
$876$		0			0
$877$	18861.3	−	32668.7i	0.726227	−	1.25786i	−0.232240	−	0.972659i	$-0.574605\pi$
$877$	18861.3	−	32668.7i	0.726227	−	1.25786i	0.958467	−	0.285204i	$-0.0920612\pi$
$878$	9826.08			0.377693
$879$		0			0
$880$		−	25754.2i		−	0.986560i
$881$	30628.9			1.17130			0.585650	−	0.810564i	$-0.300839\pi$
$881$	30628.9			1.17130			0.585650	+	0.810564i	$0.300839\pi$
$882$		0			0
$883$	−26121.2			−0.995524			−0.497762	−	0.867314i	$-0.665845\pi$
$883$	−26121.2			−0.995524			−0.497762	+	0.867314i	$0.665845\pi$
$884$			1755.29i			0.0667838i
$885$		0			0
$886$	24299.5			0.921397
$887$	−14137.3	+	24486.6i	−0.535158	+	0.926921i	0.463997	+	0.885837i	$0.346415\pi$
$887$	−14137.3	+	24486.6i	−0.535158	+	0.926921i	−0.999156	+	0.0410848i	$0.986919\pi$
$888$		0			0
$889$	−6820.84	−	363.019i	−0.257327	−	0.0136955i
$890$			14950.0i			0.563062i
$891$		0			0
$892$	21361.2	+	12332.9i	0.801823	+	0.462933i
$893$	44023.6	−	25417.0i	1.64971	−	0.952463i
$894$		0			0
$895$	−48707.1	+	28121.1i	−1.81910	+	1.05026i
$896$	−974.348	+	18307.2i	−0.0363289	+	0.682591i
$897$		0			0
$898$	25794.1			0.958532
$899$	4260.78	−	7379.88i	0.158070	−	0.273785i
$900$		0			0
$901$	−47587.7	+	27474.8i	−1.75957	+	1.01589i
$902$	−8495.33	+	14714.3i	−0.313596	+	0.543164i
$903$		0			0
$904$	1055.11	+	1827.50i	0.0388190	+	0.0672365i
$905$	−32353.4	−	18679.3i	−1.18836	−	0.686099i
$906$		0			0
$907$	13072.0	+	22641.3i	0.478553	+	0.828878i	0.999698	−	0.0245901i	$-0.00782805\pi$
$907$	13072.0	+	22641.3i	0.478553	+	0.828878i	−0.521144	+	0.853469i	$0.674495\pi$
$908$	−3634.49	−	6295.12i	−0.132836	−	0.230078i
$909$		0			0
$910$	2212.45	+	117.751i	0.0805957	+	0.00428947i
$911$	−29605.2	−	17092.5i	−1.07669	−	0.621626i	−0.146687	−	0.989183i	$-0.546861\pi$
$911$	−29605.2	−	17092.5i	−1.07669	−	0.621626i	−0.930001	+	0.367557i	$0.880194\pi$
$912$		0			0
$913$			20873.1i			0.756624i
$914$			54289.4i			1.96470i
$915$		0			0
$916$	−23666.8	−	13664.0i	−0.853683	−	0.492874i
$917$	−11141.2	+	17125.5i	−0.401217	+	0.616723i
$918$		0			0
$919$	−6975.24	−	12081.5i	−0.250372	−	0.433657i	0.713256	−	0.700903i	$-0.247220\pi$
$919$	−6975.24	−	12081.5i	−0.250372	−	0.433657i	−0.963628	+	0.267246i	$0.913886\pi$
$920$	−2661.32	−	4609.55i	−0.0953709	−	0.165187i
$921$		0			0
$922$	−32563.2	−	18800.4i	−1.16314	−	0.671537i
$923$	22.2350	+	38.5122i	0.000792931	+	0.00137340i
$924$		0			0
$925$	−2594.79	+	4494.31i	−0.0922337	+	0.159753i
$926$	−53850.5	+	31090.6i	−1.91105	+	1.10335i
$927$		0			0
$928$	−21881.9	+	37900.6i	−0.774041	+	1.34068i
$929$	−31483.5			−1.11188			−0.555942	−	0.831221i	$-0.687643\pi$
$929$	−31483.5			−1.11188			−0.555942	+	0.831221i	$0.687643\pi$
$930$		0			0
$931$	31581.6	−	13999.6i	1.11176	−	0.492825i
$932$	−3807.30	+	2198.15i	−0.133811	+	0.0772561i
$933$		0			0
$934$	−9409.71	+	5432.70i	−0.329652	+	0.190325i
$935$	37177.5	+	21464.5i	1.30036	+	0.750762i
$936$		0			0
$937$		−	40165.8i		−	1.40038i	−0.713955	−	0.700192i	$-0.753098\pi$
$937$		−	40165.8i		−	1.40038i	0.713955	−	0.700192i	$-0.246902\pi$
$938$	−2386.03	+	44831.6i	−0.0830562	+	1.56056i
$939$		0			0
$940$	20152.6	−	34905.3i	0.699260	−	1.21115i
$941$	−1053.93			−0.0365114			−0.0182557	−	0.999833i	$-0.505811\pi$
$941$	−1053.93			−0.0365114			−0.0182557	+	0.999833i	$0.505811\pi$
$942$		0			0
$943$			9008.71i			0.311097i
$944$	−23912.8			−0.824466
$945$		0			0
$946$	33948.0			1.16675
$947$			42313.5i			1.45196i	0.687716	+	0.725980i	$0.258613\pi$
$947$			42313.5i			1.45196i	−0.687716	+	0.725980i	$0.741387\pi$
$948$		0			0
$949$	1427.10			0.0488151
$950$	−11575.1	+	20048.6i	−0.395311	+	0.684698i
$951$		0			0
$952$	−15908.1	−	10349.2i	−0.541580	−	0.352332i
$953$			20155.3i			0.685095i	0.939501	+	0.342547i	$0.111290\pi$
$953$			20155.3i			0.685095i	−0.939501	+	0.342547i	$0.888710\pi$
$954$		0			0
$955$	2490.06	+	1437.64i	0.0843732	+	0.0487129i
$956$	−10521.9	+	6074.81i	−0.355965	+	0.205516i
$957$		0			0
$958$	20283.5	−	11710.7i	0.684062	−	0.394943i
$959$	−20550.2	+	10449.8i	−0.691971	+	0.351870i
$960$		0			0
$961$	27942.4			0.937948
$962$	−367.653	+	636.794i	−0.0123218	+	0.0213420i
$963$		0			0
$964$	19767.0	−	11412.5i	0.660426	−	0.381297i
$965$	−5656.83	+	9797.92i	−0.188705	+	0.326846i
$966$		0			0
$967$	−2887.13	−	5000.66i	−0.0960123	−	0.166298i	0.814018	−	0.580839i	$-0.197275\pi$
$967$	−2887.13	−	5000.66i	−0.0960123	−	0.166298i	−0.910031	+	0.414541i	$0.863942\pi$
$968$	5044.62	+	2912.51i	0.167500	+	0.0967064i
$969$		0			0
$970$	26450.1	+	45812.9i	0.875527	+	1.51646i
$971$	5434.98	+	9413.66i	0.179626	+	0.311121i	0.941752	−	0.336307i	$-0.109178\pi$
$971$	5434.98	+	9413.66i	0.179626	+	0.311121i	−0.762126	+	0.647428i	$0.775845\pi$
$972$		0			0
$973$	−38083.7	+	19365.7i	−1.25479	+	0.638062i
$974$	−17602.1	−	10162.6i	−0.579064	−	0.334323i
$975$		0			0
$976$			42021.8i			1.37816i
$977$		−	32409.0i		−	1.06127i	−0.847602	−	0.530633i	$-0.821954\pi$
$977$		−	32409.0i		−	1.06127i	0.847602	−	0.530633i	$-0.178046\pi$
$978$		0			0
$979$	6263.66	+	3616.33i	0.204482	+	0.118058i
$980$	16135.6	−	22133.0i	0.525951	−	0.721443i
$981$		0			0
$982$	8018.22	+	13888.0i	0.260562	+	0.451306i
$983$	14236.2	+	24657.9i	0.461918	+	0.800065i	0.999057	−	0.0434287i	$-0.0138281\pi$
$983$	14236.2	+	24657.9i	0.461918	+	0.800065i	−0.537139	+	0.843494i	$0.680495\pi$
$984$		0			0
$985$	−58815.7	−	33957.3i	−1.90256	−	1.09845i
$986$	−47079.6	−	81544.3i	−1.52061	−	2.63377i
$987$		0			0
$988$	−692.257	+	1199.02i	−0.0222911	+	0.0386093i
$989$	15588.2	−	8999.87i	0.501190	−	0.289362i
$990$		0			0
$991$	9926.08	−	17192.5i	0.318176	−	0.551097i	−0.661932	−	0.749564i	$-0.730263\pi$
$991$	9926.08	−	17192.5i	0.318176	−	0.551097i	0.980107	+	0.198468i	$0.0635964\pi$
$992$	9493.78			0.303859
$993$		0			0
$994$	1300.63	+	69.2223i	0.0415026	+	0.00220885i
$995$	−27263.2	+	15740.4i	−0.868646	+	0.501513i
$996$		0			0
$997$	8045.34	−	4644.98i	0.255565	−	0.147551i	−0.366745	−	0.930322i	$-0.619528\pi$
$997$	8045.34	−	4644.98i	0.255565	−	0.147551i	0.622310	+	0.782771i	$0.286194\pi$
$998$	58099.2	+	33543.6i	1.84278	+	1.06393i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.i.a.143.5		44
3.2	odd	2		63.4.i.a.38.18	yes	44
7.5	odd	6		189.4.s.a.89.5		44
9.4	even	3		63.4.s.a.59.18	yes	44
9.5	odd	6		189.4.s.a.17.5		44
21.5	even	6		63.4.s.a.47.18	yes	44
63.5	even	6	inner	189.4.i.a.152.18		44
63.40	odd	6		63.4.i.a.5.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.5	✓	44	63.40	odd	6
63.4.i.a.38.18	yes	44	3.2	odd	2
63.4.s.a.47.18	yes	44	21.5	even	6
63.4.s.a.59.18	yes	44	9.4	even	3
189.4.i.a.143.5		44	1.1	even	1	trivial
189.4.i.a.152.18		44	63.5	even	6	inner
189.4.s.a.17.5		44	9.5	odd	6
189.4.s.a.89.5		44	7.5	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.72062i q^{2} -5.84303 q^{4} +(-6.83336 + 11.8357i) q^{5} +(18.4941 + 0.984293i) q^{7} -8.02526i q^{8} +O(q^{10})\)	\(q-3.72062i q^{2} -5.84303 q^{4} +(-6.83336 + 11.8357i) q^{5} +(18.4941 + 0.984293i) q^{7} -8.02526i q^{8} +(44.0363 + 25.4243i) q^{10} +(21.3043 - 12.3000i) q^{11} +(2.03747 - 1.17634i) q^{13} +(3.66218 - 68.8095i) q^{14} -76.6032 q^{16} +(63.8439 - 110.581i) q^{17} +(87.2223 - 50.3578i) q^{19} +(39.9275 - 69.1565i) q^{20} +(-45.7638 - 79.2652i) q^{22} +(-42.0276 - 24.2647i) q^{23} +(-30.8895 - 53.5022i) q^{25} +(-4.37670 - 7.58067i) q^{26} +(-108.062 - 5.75126i) q^{28} +(171.644 + 99.0987i) q^{29} -42.9953i q^{31} +220.810i q^{32} +(-411.430 - 237.539i) q^{34} +(-138.026 + 212.165i) q^{35} +(-42.0011 - 72.7481i) q^{37} +(-187.363 - 324.521i) q^{38} +(94.9848 + 54.8395i) q^{40} +(-92.8172 - 160.764i) q^{41} +(-185.452 + 321.213i) q^{43} +(-124.482 + 71.8695i) q^{44} +(-90.2797 + 156.369i) q^{46} +504.729 q^{47} +(341.062 + 36.4072i) q^{49} +(-199.062 + 114.928i) q^{50} +(-11.9050 + 6.87337i) q^{52} +(-372.688 - 215.171i) q^{53} +336.202i q^{55} +(7.89921 - 148.420i) q^{56} +(368.709 - 638.622i) q^{58} +312.164 q^{59} -548.565i q^{61} -159.969 q^{62} +208.723 q^{64} +32.1533i q^{65} -651.533 q^{67} +(-373.042 + 646.128i) q^{68} +(789.385 + 513.545i) q^{70} +18.9019i q^{71} +(525.319 + 303.293i) q^{73} +(-270.668 + 156.270i) q^{74} +(-509.643 + 294.243i) q^{76} +(406.110 - 206.508i) q^{77} +435.435 q^{79} +(523.457 - 906.654i) q^{80} +(-598.142 + 345.338i) q^{82} +(-424.248 + 734.819i) q^{83} +(872.537 + 1511.28i) q^{85} +(1195.11 + 689.998i) q^{86} +(-98.7110 - 170.972i) q^{88} +(147.005 + 254.620i) q^{89} +(38.8391 - 19.7498i) q^{91} +(245.569 + 141.779i) q^{92} -1877.91i q^{94} +1376.45i q^{95} +(900.965 + 520.172i) q^{97} +(135.457 - 1268.96i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

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