LMFDB - Embedded newform 192.2.s.a.107.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.11
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.486023 + 1.32807i) q^{2} +(0.609434 - 1.62129i) q^{3} +(-1.52756 - 1.29095i) q^{4} +(1.96325 + 2.93821i) q^{5} +(1.85700 + 1.59736i) q^{6} +(1.41332 - 3.41205i) q^{7} +(2.45691 - 1.40129i) q^{8} +(-2.25718 - 1.97614i) q^{9} +(-4.85635 + 1.17930i) q^{10} +(-1.35426 - 0.269378i) q^{11} +(-3.02396 + 1.68988i) q^{12} +(3.69962 + 2.47201i) q^{13} +(3.84455 + 3.53533i) q^{14} +(5.96017 - 1.39236i) q^{15} +(0.666898 + 3.94401i) q^{16} +(1.07694 + 1.07694i) q^{17} +(3.72150 - 2.03725i) q^{18} +(2.55792 + 1.70915i) q^{19} +(0.794095 - 7.02276i) q^{20} +(-4.67061 - 4.37082i) q^{21} +(1.01595 - 1.66763i) q^{22} +(0.348914 + 0.842354i) q^{23} +(-0.774573 - 4.83736i) q^{24} +(-2.86532 + 6.91750i) q^{25} +(-5.08112 + 3.71192i) q^{26} +(-4.57950 + 2.45523i) q^{27} +(-6.56372 + 3.38760i) q^{28} +(-1.64436 - 8.26676i) q^{29} +(-1.04763 + 8.59227i) q^{30} -7.50303 q^{31} +(-5.56207 - 1.03119i) q^{32} +(-1.26207 + 2.03148i) q^{33} +(-1.95367 + 0.906837i) q^{34} +(12.8000 - 2.54608i) q^{35} +(0.896889 + 5.93259i) q^{36} +(-1.83441 - 2.74539i) q^{37} +(-3.51308 + 2.56642i) q^{38} +(6.26253 - 4.49165i) q^{39} +(8.94080 + 4.46784i) q^{40} +(-9.24158 + 3.82799i) q^{41} +(8.07480 - 4.07860i) q^{42} +(-2.87193 - 0.571263i) q^{43} +(1.72096 + 2.15977i) q^{44} +(1.37491 - 10.5117i) q^{45} +(-1.28829 + 0.0539808i) q^{46} +(-3.91043 + 3.91043i) q^{47} +(6.80083 + 1.32238i) q^{48} +(-4.69487 - 4.69487i) q^{49} +(-7.79434 - 7.16743i) q^{50} +(2.40235 - 1.08971i) q^{51} +(-2.46017 - 8.55218i) q^{52} +(0.750588 - 3.77346i) q^{53} +(-1.03498 - 7.27522i) q^{54} +(-1.86725 - 4.50795i) q^{55} +(-1.30887 - 10.3636i) q^{56} +(4.32991 - 3.10552i) q^{57} +(11.7781 + 1.83400i) q^{58} +(-1.97738 + 1.32124i) q^{59} +(-10.9020 - 5.56737i) q^{60} +(2.15485 + 10.8331i) q^{61} +(3.64665 - 9.96458i) q^{62} +(-9.93280 + 4.90870i) q^{63} +(4.07280 - 6.88566i) q^{64} +15.7235i q^{65} +(-2.08456 - 2.66347i) q^{66} +(1.15899 - 0.230537i) q^{67} +(-0.254818 - 3.03536i) q^{68} +(1.57834 - 0.0523337i) q^{69} +(-2.83972 + 18.2368i) q^{70} +(7.50045 + 3.10679i) q^{71} +(-8.31483 - 1.69224i) q^{72} +(-3.51016 + 1.45396i) q^{73} +(4.53765 - 1.10191i) q^{74} +(9.46907 + 8.86128i) q^{75} +(-1.70096 - 5.91297i) q^{76} +(-2.83313 + 4.24007i) q^{77} +(2.92151 + 10.5001i) q^{78} +(8.03113 - 8.03113i) q^{79} +(-10.2791 + 9.70258i) q^{80} +(1.18974 + 8.92102i) q^{81} +(-0.592231 - 14.1340i) q^{82} +(-2.45014 + 3.66690i) q^{83} +(1.49214 + 12.7062i) q^{84} +(-1.04997 + 5.27857i) q^{85} +(2.15450 - 3.53649i) q^{86} +(-14.4050 - 2.37205i) q^{87} +(-3.70476 + 1.23586i) q^{88} +(-0.100607 - 0.0416728i) q^{89} +(13.2921 + 6.93493i) q^{90} +(13.6634 - 9.12957i) q^{91} +(0.554448 - 1.73718i) q^{92} +(-4.57260 + 12.1646i) q^{93} +(-3.29278 - 7.09391i) q^{94} +10.8712i q^{95} +(-5.06158 + 8.38930i) q^{96} +12.5267i q^{97} +(8.51695 - 3.95332i) q^{98} +(2.52447 + 3.28424i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−0.486023	+	1.32807i	−0.343670	+	0.939090i
$2$	−0.486023	+	1.32807i	−0.343670	+	0.939090i
$3$	0.609434	−	1.62129i	0.351857	−	0.936054i
$3$	0.609434	−	1.62129i	0.351857	−	0.936054i
$4$	−1.52756	−	1.29095i	−0.763782	−	0.645475i
$5$	1.96325	+	2.93821i	0.877993	+	1.31401i	0.948591	+	0.316504i	$0.102509\pi$
$5$	1.96325	+	2.93821i	0.877993	+	1.31401i	−0.0705987	+	0.997505i	$0.522491\pi$
$6$	1.85700	+	1.59736i	0.758117	+	0.652119i
$7$	1.41332	−	3.41205i	0.534184	−	1.28963i	−0.394546	−	0.918876i	$-0.629098\pi$
$7$	1.41332	−	3.41205i	0.534184	−	1.28963i	0.928730	−	0.370757i	$-0.120902\pi$
$8$	2.45691	−	1.40129i	0.868648	−	0.495429i
$9$	−2.25718	−	1.97614i	−0.752394	−	0.658714i
$10$	−4.85635	+	1.17930i	−1.53571	+	0.372929i
$11$	−1.35426	−	0.269378i	−0.408324	−	0.0812206i	−0.0133450	−	0.999911i	$-0.504248\pi$
$11$	−1.35426	−	0.269378i	−0.408324	−	0.0812206i	−0.394979	+	0.918690i	$0.629248\pi$
$12$	−3.02396	+	1.68988i	−0.872941	+	0.487826i
$13$	3.69962	+	2.47201i	1.02609	+	0.685612i	0.950244	−	0.311507i	$-0.100834\pi$
$13$	3.69962	+	2.47201i	1.02609	+	0.685612i	0.0758473	+	0.997119i	$0.475834\pi$
$14$	3.84455	+	3.53533i	1.02750	+	0.944856i
$15$	5.96017	−	1.39236i	1.53891	−	0.359506i
$16$	0.666898	+	3.94401i	0.166724	+	0.986004i
$17$	1.07694	+	1.07694i	0.261196	+	0.261196i	0.825540	−	0.564344i	$-0.190871\pi$
$17$	1.07694	+	1.07694i	0.261196	+	0.261196i	−0.564344	+	0.825540i	$0.690871\pi$
$18$	3.72150	−	2.03725i	0.877167	−	0.480186i
$19$	2.55792	+	1.70915i	0.586827	+	0.392105i	0.813242	−	0.581926i	$-0.197701\pi$
$19$	2.55792	+	1.70915i	0.586827	+	0.392105i	−0.226415	+	0.974031i	$0.572701\pi$
$20$	0.794095	−	7.02276i	0.177565	−	1.57034i
$21$	−4.67061	−	4.37082i	−1.01921	−	0.953791i
$22$	1.01595	−	1.66763i	0.216602	−	0.355540i
$23$	0.348914	+	0.842354i	0.0727537	+	0.175643i	0.956073	−	0.293129i	$-0.0946966\pi$
$23$	0.348914	+	0.842354i	0.0727537	+	0.175643i	−0.883319	+	0.468772i	$0.844697\pi$
$24$	−0.774573	−	4.83736i	−0.158109	−	0.987422i
$25$	−2.86532	+	6.91750i	−0.573065	+	1.38350i
$26$	−5.08112	+	3.71192i	−0.996489	+	0.727968i
$27$	−4.57950	+	2.45523i	−0.881326	+	0.472508i
$28$	−6.56372	+	3.38760i	−1.24043	+	0.640196i
$29$	−1.64436	−	8.26676i	−0.305350	−	1.53510i	−0.763255	−	0.646097i	$-0.776400\pi$
$29$	−1.64436	−	8.26676i	−0.305350	−	1.53510i	0.457905	−	0.889001i	$-0.348600\pi$
$30$	−1.04763	+	8.59227i	−0.191269	+	1.56873i
$31$	−7.50303			−1.34758			−0.673792	−	0.738921i	$-0.735336\pi$
$31$	−7.50303			−1.34758			−0.673792	+	0.738921i	$0.735336\pi$
$32$	−5.56207	−	1.03119i	−0.983245	−	0.182291i
$33$	−1.26207	+	2.03148i	−0.219698	+	0.353635i
$34$	−1.95367	+	0.906837i	−0.335052	+	0.155521i
$35$	12.8000	−	2.54608i	2.16360	−	0.430367i
$36$	0.896889	+	5.93259i	0.149481	+	0.988765i
$37$	−1.83441	−	2.74539i	−0.301576	−	0.451340i	0.649471	−	0.760386i	$-0.274990\pi$
$37$	−1.83441	−	2.74539i	−0.301576	−	0.451340i	−0.951047	+	0.309046i	$0.899990\pi$
$38$	−3.51308	+	2.56642i	−0.569897	+	0.416329i
$39$	6.26253	−	4.49165i	1.00281	−	0.719239i
$40$	8.94080	+	4.46784i	1.41367	+	0.706428i
$41$	−9.24158	+	3.82799i	−1.44329	+	0.597831i	−0.960594	−	0.277956i	$-0.910343\pi$
$41$	−9.24158	+	3.82799i	−1.44329	+	0.597831i	−0.482698	+	0.875787i	$0.660343\pi$
$42$	8.07480	−	4.07860i	1.24597	−	0.629341i
$43$	−2.87193	−	0.571263i	−0.437966	−	0.0871168i	−0.0288173	−	0.999585i	$-0.509174\pi$
$43$	−2.87193	−	0.571263i	−0.437966	−	0.0871168i	−0.409148	+	0.912468i	$0.634174\pi$
$44$	1.72096	+	2.15977i	0.259444	+	0.325597i
$45$	1.37491	−	10.5117i	0.204959	−	1.56700i
$46$	−1.28829	+	0.0539808i	−0.189948	+	0.00795903i
$47$	−3.91043	+	3.91043i	−0.570395	+	0.570395i	−0.932239	−	0.361844i	$-0.882147\pi$
$47$	−3.91043	+	3.91043i	−0.570395	+	0.570395i	0.361844	+	0.932239i	$0.382147\pi$
$48$	6.80083	+	1.32238i	0.981616	+	0.190869i
$49$	−4.69487	−	4.69487i	−0.670696	−	0.670696i
$50$	−7.79434	−	7.16743i	−1.10229	−	1.01363i
$51$	2.40235	−	1.08971i	0.336397	−	0.152590i
$52$	−2.46017	−	8.55218i	−0.341164	−	1.18597i
$53$	0.750588	−	3.77346i	0.103101	−	0.518325i	−0.894375	−	0.447319i	$-0.852379\pi$
$53$	0.750588	−	3.77346i	0.103101	−	0.518325i	0.997476	−	0.0710061i	$-0.0226210\pi$
$54$	−1.03498	−	7.27522i	−0.140843	−	0.990032i
$55$	−1.86725	−	4.50795i	−0.251780	−	0.607852i
$56$	−1.30887	−	10.3636i	−0.174905	−	1.38489i
$57$	4.32991	−	3.10552i	0.573510	−	0.411337i
$58$	11.7781	+	1.83400i	1.54654	+	0.240816i
$59$	−1.97738	+	1.32124i	−0.257433	+	0.172011i	−0.677589	−	0.735440i	$-0.736975\pi$
$59$	−1.97738	+	1.32124i	−0.257433	+	0.172011i	0.420156	+	0.907452i	$0.361975\pi$
$60$	−10.9020	−	5.56737i	−1.40744	−	0.718744i
$61$	2.15485	+	10.8331i	0.275900	+	1.38704i	0.831469	+	0.555572i	$0.187501\pi$
$61$	2.15485	+	10.8331i	0.275900	+	1.38704i	−0.555569	+	0.831471i	$0.687499\pi$
$62$	3.64665	−	9.96458i	0.463124	−	1.26550i
$63$	−9.93280	+	4.90870i	−1.25142	+	0.618438i
$64$	4.07280	−	6.88566i	0.509100	−	0.860708i
$65$			15.7235i			1.95025i
$66$	−2.08456	−	2.66347i	−0.256591	−	0.327850i
$67$	1.15899	−	0.230537i	0.141593	−	0.0281646i	−0.123785	−	0.992309i	$-0.539503\pi$
$67$	1.15899	−	0.230537i	0.141593	−	0.0281646i	0.265378	+	0.964144i	$0.414503\pi$
$68$	−0.254818	−	3.03536i	−0.0309012	−	0.368092i
$69$	1.57834	−	0.0523337i	0.190010	−	0.00630024i
$70$	−2.83972	+	18.2368i	−0.339412	+	2.17972i
$71$	7.50045	+	3.10679i	0.890139	+	0.368708i	0.780421	−	0.625255i	$-0.215005\pi$
$71$	7.50045	+	3.10679i	0.890139	+	0.368708i	0.109719	+	0.993963i	$0.465005\pi$
$72$	−8.31483	−	1.69224i	−0.979912	−	0.199432i
$73$	−3.51016	+	1.45396i	−0.410833	+	0.170173i	−0.578521	−	0.815667i	$-0.696370\pi$
$73$	−3.51016	+	1.45396i	−0.410833	+	0.170173i	0.167688	+	0.985840i	$0.446370\pi$
$74$	4.53765	−	1.10191i	0.527491	−	0.128095i
$75$	9.46907	+	8.86128i	1.09339	+	1.02321i
$76$	−1.70096	−	5.91297i	−0.195113	−	0.678265i
$77$	−2.83313	+	4.24007i	−0.322865	+	0.483201i
$78$	2.92151	+	10.5001i	0.330796	+	1.18891i
$79$	8.03113	−	8.03113i	0.903573	−	0.903573i	−0.0921705	−	0.995743i	$-0.529380\pi$
$79$	8.03113	−	8.03113i	0.903573	−	0.903573i	0.995743	+	0.0921705i	$0.0293805\pi$
$80$	−10.2791	+	9.70258i	−1.14923	+	1.08478i
$81$	1.18974	+	8.92102i	0.132193	+	0.991224i
$82$	−0.592231	−	14.1340i	−0.0654009	−	1.56084i
$83$	−2.45014	+	3.66690i	−0.268938	+	0.402494i	−0.941216	−	0.337804i	$-0.890316\pi$
$83$	−2.45014	+	3.66690i	−0.268938	+	0.402494i	0.672278	+	0.740298i	$0.265316\pi$
$84$	1.49214	+	12.7062i	0.162806	+	1.38636i
$85$	−1.04997	+	5.27857i	−0.113886	+	0.572542i
$86$	2.15450	−	3.53649i	0.232326	−	0.381350i
$87$	−14.4050	−	2.37205i	−1.54437	−	0.254310i
$88$	−3.70476	+	1.23586i	−0.394929	+	0.131743i
$89$	−0.100607	−	0.0416728i	−0.0106643	−	0.00441731i	0.377345	−	0.926073i	$-0.376837\pi$
$89$	−0.100607	−	0.0416728i	−0.0106643	−	0.00441731i	−0.388009	+	0.921655i	$0.626837\pi$
$90$	13.2921	+	6.93493i	1.40111	+	0.731006i
$91$	13.6634	−	9.12957i	1.43231	−	0.957039i
$92$	0.554448	−	1.73718i	0.0578052	−	0.181114i
$93$	−4.57260	+	12.1646i	−0.474156	+	1.26141i
$94$	−3.29278	−	7.09391i	−0.339625	−	0.731681i
$95$			10.8712i			1.11536i
$96$	−5.06158	+	8.38930i	−0.516595	+	0.856230i
$97$			12.5267i			1.27189i	0.771735	+	0.635945i	$0.219389\pi$
$97$			12.5267i			1.27189i	−0.771735	+	0.635945i	$0.780611\pi$
$98$	8.51695	−	3.95332i	0.860342	−	0.399346i
$99$	2.52447	+	3.28424i	0.253719	+	0.330078i
$100$	13.3071	−	6.86793i	1.33071	−	0.686793i
$101$	7.14638	−	4.77506i	0.711091	−	0.475136i	−0.146669	−	0.989186i	$-0.546855\pi$
$101$	7.14638	−	4.77506i	0.711091	−	0.475136i	0.857760	+	0.514050i	$0.171855\pi$
$102$	0.279616	+	3.72013i	0.0276861	+	0.368348i
$103$	−15.7808	−	6.53662i	−1.55493	−	0.644072i	−0.570729	−	0.821139i	$-0.693339\pi$
$103$	−15.7808	−	6.53662i	−1.55493	−	0.644072i	−0.984199	+	0.177066i	$0.943339\pi$
$104$	12.5536	+	0.889270i	1.23098	+	0.0872001i
$105$	3.67282	−	22.3043i	0.358430	−	2.17667i
$106$	4.64663	+	2.83083i	0.451321	+	0.274954i
$107$	−0.485556	+	2.44105i	−0.0469404	+	0.235986i	−0.997132	−	0.0756806i	$-0.975887\pi$
$107$	−0.485556	+	2.44105i	−0.0469404	+	0.235986i	0.950192	+	0.311666i	$0.100887\pi$
$108$	10.1651	+	2.16140i	0.978133	+	0.207981i
$109$	1.80331	−	2.69885i	0.172726	−	0.258503i	−0.734999	−	0.678068i	$-0.762817\pi$
$109$	1.80331	−	2.69885i	0.172726	−	0.258503i	0.907725	+	0.419565i	$0.137817\pi$
$110$	6.89442	−	0.288884i	0.657357	−	0.0275440i
$111$	−5.56904	+	1.30099i	−0.528590	+	0.123484i
$112$	14.3997	+	3.29866i	1.36064	+	0.311694i
$113$	7.35380	−	7.35380i	0.691788	−	0.691788i	−0.270837	−	0.962625i	$-0.587301\pi$
$113$	7.35380	−	7.35380i	0.691788	−	0.691788i	0.962625	+	0.270837i	$0.0873006\pi$
$114$	2.01993	+	7.25980i	0.189184	+	0.679942i
$115$	−1.79001	+	2.67894i	−0.166919	+	0.249812i
$116$	−8.16010	+	14.7508i	−0.757647	+	1.36958i
$117$	−3.46568	−	12.8908i	−0.320403	−	1.19175i
$118$	−0.793657	−	3.26827i	−0.0730621	−	0.300868i
$119$	5.19662	−	2.15251i	0.476373	−	0.197320i
$120$	12.6925	−	11.7728i	1.15866	−	1.07471i
$121$	−8.40123	−	3.47990i	−0.763748	−	0.316355i
$122$	−15.4345	−	2.40336i	−1.39738	−	0.217590i
$123$	0.574160	+	17.3162i	0.0517703	+	1.56135i
$124$	11.4613	+	9.68603i	1.02926	+	0.869831i
$125$	−8.62114	+	1.71485i	−0.771099	+	0.153381i
$126$	−1.69155	−	15.5772i	−0.150695	−	1.38773i
$127$		−	3.48281i		−	0.309050i	−0.987989	−	0.154525i	$-0.950615\pi$
$127$		−	3.48281i		−	0.309050i	0.987989	−	0.154525i	$-0.0493846\pi$
$128$	7.16520	+	8.75557i	0.633320	+	0.773890i
$129$	−2.67644	+	4.30810i	−0.235647	+	0.379307i
$130$	−20.8819	−	7.64196i	−1.83147	−	0.670245i
$131$	−1.52866	−	7.68509i	−0.133560	−	0.671449i	−0.988316	−	0.152420i	$-0.951293\pi$
$131$	−1.52866	−	7.68509i	−0.133560	−	0.671449i	0.854756	−	0.519030i	$-0.173707\pi$
$132$	4.55043	−	1.47394i	0.396064	−	0.128290i
$133$	9.44684	−	6.31218i	0.819145	−	0.547335i
$134$	−0.257125	+	1.65127i	−0.0222122	+	0.142648i
$135$	−16.2047	−	8.63533i	−1.39468	−	0.743211i
$136$	4.15504	+	1.13684i	0.356291	+	0.0974832i
$137$	−1.50317	−	3.62897i	−0.128424	−	0.310044i	0.846569	−	0.532280i	$-0.178665\pi$
$137$	−1.50317	−	3.62897i	−0.128424	−	0.310044i	−0.974993	+	0.222236i	$0.928665\pi$
$138$	−0.697608	+	2.12159i	−0.0593843	+	0.180602i
$139$	−4.01465	+	20.1830i	−0.340518	+	1.71190i	0.308581	+	0.951198i	$0.400146\pi$
$139$	−4.01465	+	20.1830i	−0.340518	+	1.71190i	−0.649100	+	0.760703i	$0.724854\pi$
$140$	−22.8397	−	12.6349i	−1.93031	−	1.06784i
$141$	3.95681	+	8.72311i	0.333223	+	0.734618i
$142$	−7.77143	+	8.45118i	−0.652164	+	0.709207i
$143$	−4.34433	−	4.34433i	−0.363291	−	0.363291i
$144$	6.28862	−	10.2202i	0.524051	−	0.851687i
$145$	21.0612	−	21.0612i	1.74904	−	1.74904i
$146$	−0.224943	−	5.36841i	−0.0186164	−	0.444293i
$147$	−10.4730	+	4.75055i	−0.863796	+	0.391819i
$148$	−0.741983	+	6.56189i	−0.0609906	+	0.539384i
$149$	20.3831	+	4.05445i	1.66985	+	0.332153i	0.937289	−	0.348552i	$-0.113327\pi$
$149$	20.3831	+	4.05445i	1.66985	+	0.332153i	0.732557	+	0.680705i	$0.238327\pi$
$150$	−16.3706	+	8.26884i	−1.33666	+	0.675148i
$151$	−2.14039	+	0.886580i	−0.174183	+	0.0721488i	−0.468071	−	0.883691i	$-0.655051\pi$
$151$	−2.14039	+	0.886580i	−0.174183	+	0.0721488i	0.293888	+	0.955840i	$0.405051\pi$
$152$	8.67957	+	0.614841i	0.704006	+	0.0498702i
$153$	−0.302664	−	4.55902i	−0.0244689	−	0.368575i
$154$	−4.25417	−	5.82337i	−0.342811	−	0.469261i
$155$	−14.7303	−	22.0455i	−1.18317	−	1.77074i
$156$	−15.3649	−	1.22333i	−1.23018	−	0.0979449i
$157$	1.80242	−	0.358524i	0.143849	−	0.0286133i	−0.122641	−	0.992451i	$-0.539136\pi$
$157$	1.80242	−	0.358524i	0.143849	−	0.0286133i	0.266489	+	0.963838i	$0.414136\pi$
$158$	6.76262	+	14.5693i	0.538005	+	1.15907i
$159$	−5.66045	−	3.51660i	−0.448903	−	0.278884i
$160$	−7.88988	−	18.3670i	−0.623750	−	1.45204i
$161$	3.36728			0.265379
$162$	−12.4260	−	2.75576i	−0.976280	−	0.216513i
$163$	−2.11463	−	10.6309i	−0.165630	−	0.832679i	−0.970847	−	0.239699i	$-0.922951\pi$
$163$	−2.11463	−	10.6309i	−0.165630	−	0.832679i	0.805217	−	0.592980i	$-0.202049\pi$
$164$	19.0588	+	6.08292i	1.48824	+	0.474996i
$165$	−8.44667	+	0.280070i	−0.657573	+	0.0218034i
$166$	−3.67908	−	5.03617i	−0.285552	−	0.390882i
$167$	−5.11061	+	12.3381i	−0.395471	+	0.954751i	0.593255	+	0.805014i	$0.297842\pi$
$167$	−5.11061	+	12.3381i	−0.395471	+	0.954751i	−0.988726	+	0.149736i	$0.952158\pi$
$168$	−17.6000	−	4.19384i	−1.35787	−	0.323562i
$169$	2.60150	+	6.28058i	0.200115	+	0.483121i
$170$	−6.50002	−	3.95995i	−0.498529	−	0.303714i
$171$	−2.39617	−	8.91266i	−0.183240	−	0.681568i
$172$	3.64959	+	4.58016i	0.278278	+	0.349234i
$173$	2.34005	+	1.56357i	0.177911	+	0.118876i	0.641337	−	0.767259i	$-0.278380\pi$
$173$	2.34005	+	1.56357i	0.177911	+	0.118876i	−0.463426	+	0.886136i	$0.653380\pi$
$174$	10.1514	−	17.9780i	0.769576	−	1.36291i
$175$	19.5532	+	19.5532i	1.47809	+	1.47809i
$176$	0.159282	−	5.52085i	0.0120063	−	0.416150i
$177$	0.937041	+	4.01113i	0.0704323	+	0.301495i
$178$	0.104242	−	0.113360i	0.00781326	−	0.00849666i
$179$	5.84520	+	3.90564i	0.436891	+	0.291921i	0.754499	−	0.656301i	$-0.227880\pi$
$179$	5.84520	+	3.90564i	0.436891	+	0.291921i	−0.317609	+	0.948222i	$0.602880\pi$
$180$	−15.6704	+	14.2824i	−1.16800	+	1.06455i
$181$	25.4769	+	5.06767i	1.89368	+	0.376677i	0.997722	−	0.0674565i	$-0.0214884\pi$
$181$	25.4769	+	5.06767i	1.89368	+	0.376677i	0.895961	+	0.444133i	$0.146488\pi$
$182$	5.48403	+	22.5831i	0.406504	+	1.67397i
$183$	18.8769	+	3.10845i	1.39542	+	0.229783i
$184$	2.03763	+	1.58066i	0.150216	+	0.116528i
$185$	4.46513	−	10.7798i	0.328283	−	0.792546i
$186$	−13.9331	−	11.9850i	−1.02163	−	0.878785i
$187$	−1.16835	−	1.74855i	−0.0854379	−	0.127867i
$188$	11.0216	−	0.925260i	0.803833	−	0.0674815i
$189$	1.90506	+	19.0955i	0.138573	+	1.38899i
$190$	−14.4378	−	5.28365i	−1.04742	−	0.383316i
$191$	5.07582			0.367273			0.183637	−	0.982994i	$-0.441213\pi$
$191$	5.07582			0.367273			0.183637	+	0.982994i	$0.441213\pi$
$192$	−8.68158	−	10.7995i	−0.626539	−	0.779390i
$193$	−10.3233			−0.743087			−0.371544	−	0.928416i	$-0.621171\pi$
$193$	−10.3233			−0.743087			−0.371544	+	0.928416i	$0.621171\pi$
$194$	−16.6363	−	6.08825i	−1.19442	−	0.437111i
$195$	25.4923	+	9.58240i	1.82554	+	0.686210i
$196$	1.11087	+	13.2326i	0.0793478	+	0.945182i
$197$	−2.22569	−	3.33097i	−0.158574	−	0.237322i	0.743672	−	0.668545i	$-0.233082\pi$
$197$	−2.22569	−	3.33097i	−0.158574	−	0.237322i	−0.902246	+	0.431223i	$0.858082\pi$
$198$	−5.58866	+	1.75647i	−0.397169	+	0.124827i
$199$	4.93691	−	11.9188i	0.349968	−	0.844898i	−0.646655	−	0.762783i	$-0.723832\pi$
$199$	4.93691	−	11.9188i	0.349968	−	0.844898i	0.996623	−	0.0821152i	$-0.0261675\pi$
$200$	2.65356	+	21.0108i	0.187635	+	1.48569i
$201$	0.332558	−	2.01956i	0.0234568	−	0.142448i
$202$	2.86833	+	11.8117i	0.201815	+	0.831069i
$203$	−30.5306	−	6.07291i	−2.14283	−	0.426235i
$204$	−5.07651	−	1.43672i	−0.355427	−	0.100590i
$205$	−29.3910	−	19.6384i	−2.05275	−	1.37161i
$206$	16.3509	−	17.7811i	1.13922	−	1.23887i
$207$	0.877047	−	2.59085i	0.0609590	−	0.180077i
$208$	−7.28237	+	16.2399i	−0.504942	+	1.12604i
$209$	−3.00367	−	3.00367i	−0.207768	−	0.207768i
$210$	27.8366	+	15.7182i	1.92091	+	1.08466i
$211$	−11.8550	−	7.92128i	−0.816134	−	0.545323i	0.0759927	−	0.997108i	$-0.475787\pi$
$211$	−11.8550	−	7.92128i	−0.816134	−	0.545323i	−0.892127	+	0.451785i	$0.850787\pi$
$212$	−6.01792	+	4.79523i	−0.413312	+	0.329338i
$213$	9.60803	−	10.2670i	0.658332	−	0.703486i
$214$	−3.00591	−	1.83126i	−0.205480	−	0.125183i
$215$	−3.95983	−	9.55988i	−0.270058	−	0.651978i
$216$	−7.81095	+	12.4495i	−0.531468	+	0.847078i
$217$	−10.6042	+	25.6007i	−0.719857	+	1.73789i
$218$	2.70782	+	3.70664i	0.183397	+	0.251045i
$219$	0.218079	+	6.57709i	0.0147364	+	0.444439i
$220$	−2.96719	+	9.29671i	−0.200048	+	0.626784i
$221$	1.32206	+	6.64647i	0.0889317	+	0.447090i
$222$	0.978875	−	8.02841i	0.0656978	−	0.538831i
$223$	15.0068			1.00493			0.502464	−	0.864598i	$-0.332427\pi$
$223$	15.0068			1.00493			0.502464	+	0.864598i	$0.332427\pi$
$224$	−11.3795	+	17.5207i	−0.760322	+	1.17065i
$225$	20.1375	−	9.95177i	1.34250	−	0.663452i
$226$	6.19228	+	13.3405i	0.411904	+	0.887398i
$227$	−14.3174	+	2.84791i	−0.950278	+	0.189022i	−0.645808	−	0.763500i	$-0.723479\pi$
$227$	−14.3174	+	2.84791i	−0.950278	+	0.189022i	−0.304470	+	0.952522i	$0.598479\pi$
$228$	−10.6233	−	0.845811i	−0.703544	−	0.0560152i
$229$	−9.15707	−	13.7045i	−0.605116	−	0.905620i	0.394797	−	0.918768i	$-0.370815\pi$
$229$	−9.15707	−	13.7045i	−0.605116	−	0.905620i	−0.999914	+	0.0131478i	$0.995815\pi$
$230$	−2.68784	−	3.67929i	−0.177231	−	0.242605i
$231$	5.14780	+	7.17737i	0.338700	+	0.472236i
$232$	−15.6241	−	18.0064i	−1.02577	−	1.18218i
$233$	−14.9724	+	6.20176i	−0.980873	+	0.406291i	−0.814749	−	0.579814i	$-0.803125\pi$
$233$	−14.9724	+	6.20176i	−0.980873	+	0.406291i	−0.166124	+	0.986105i	$0.553125\pi$
$234$	18.8043	+	1.66252i	1.22927	+	0.108682i
$235$	−19.1668	−	3.81252i	−1.25031	−	0.248702i
$236$	4.72624	+	0.534417i	0.307652	+	0.0347876i
$237$	−8.12637	−	17.9153i	−0.527865	−	1.16372i
$238$	0.333016	+	7.94767i	0.0215863	+	0.515171i
$239$	13.3330	−	13.3330i	0.862438	−	0.862438i	−0.129182	−	0.991621i	$-0.541235\pi$
$239$	13.3330	−	13.3330i	0.862438	−	0.862438i	0.991621	+	0.129182i	$0.0412353\pi$
$240$	9.46631	+	22.5785i	0.611048	+	1.45743i
$241$	12.8148	+	12.8148i	0.825476	+	0.825476i	0.986887	−	0.161411i	$-0.0516046\pi$
$241$	12.8148	+	12.8148i	0.825476	+	0.825476i	−0.161411	+	0.986887i	$0.551605\pi$
$242$	8.70476	−	9.46614i	0.559563	−	0.608507i
$243$	15.1886	+	3.50785i	0.974352	+	0.225029i
$244$	10.6934	−	19.3301i	0.684574	−	1.23748i
$245$	4.57732	−	23.0117i	0.292434	−	1.47017i
$246$	−23.2763	−	7.65355i	−1.48404	−	0.487973i
$247$	5.23831	+	12.6464i	0.333306	+	0.804671i
$248$	−18.4343	+	10.5139i	−1.17058	+	0.667633i
$249$	4.45191	+	6.20713i	0.282129	+	0.393361i
$250$	1.91262	−	12.2830i	0.120965	−	0.776844i
$251$	15.4290	−	10.3094i	0.973872	−	0.650721i	0.0366041	−	0.999330i	$-0.488346\pi$
$251$	15.4290	−	10.3094i	0.973872	−	0.650721i	0.937268	+	0.348609i	$0.113346\pi$
$252$	21.5099	+	5.32440i	1.35499	+	0.335406i
$253$	−0.245608	−	1.23475i	−0.0154412	−	0.0776283i
$254$	4.62543	+	1.69273i	0.290225	+	0.106211i
$255$	7.91822	+	4.91925i	0.495858	+	0.308056i
$256$	−15.1105	+	5.26051i	−0.944406	+	0.328782i
$257$		−	7.36483i		−	0.459405i	−0.973261	−	0.229703i	$-0.926225\pi$
$257$		−	7.36483i		−	0.459405i	0.973261	−	0.229703i	$-0.0737754\pi$
$258$	−4.42066	−	5.64834i	−0.275218	−	0.351650i
$259$	−11.9600	+	2.37900i	−0.743160	+	0.147824i
$260$	20.2982	−	24.0186i	1.25884	−	1.48957i
$261$	−12.6247	+	21.9091i	−0.781447	+	1.35614i
$262$	10.9493	+	1.70496i	0.676452	+	0.105333i
$263$	−21.2218	−	8.79034i	−1.30859	−	0.542036i	−0.384118	−	0.923284i	$-0.625494\pi$
$263$	−21.2218	−	8.79034i	−1.30859	−	0.542036i	−0.924473	+	0.381248i	$0.875494\pi$
$264$	−0.254110	+	6.75968i	−0.0156394	+	0.416029i
$265$	12.5608	−	5.20286i	0.771605	−	0.319609i
$266$	3.79166	+	15.6140i	0.232482	+	0.957354i
$267$	−0.128877	+	0.137717i	−0.00788715	+	0.00842812i
$268$	−2.06804	−	1.14403i	−0.126326	−	0.0698831i
$269$	3.20130	−	4.79109i	0.195187	−	0.292118i	−0.720947	−	0.692990i	$-0.756293\pi$
$269$	3.20130	−	4.79109i	0.195187	−	0.292118i	0.916134	+	0.400872i	$0.131293\pi$
$270$	19.3442	−	17.3241i	1.17725	−	1.05431i
$271$	−11.1155	+	11.1155i	−0.675220	+	0.675220i	−0.958915	−	0.283695i	$-0.908440\pi$
$271$	−11.1155	+	11.1155i	−0.675220	+	0.675220i	0.283695	+	0.958915i	$0.408440\pi$
$272$	−3.52925	+	4.96567i	−0.213992	+	0.301088i
$273$	−6.47479	−	27.7162i	−0.391872	−	1.67746i
$274$	5.55012	−	0.232556i	0.335295	−	0.0140492i
$275$	5.74381	−	8.59621i	0.346364	−	0.518371i
$276$	−2.47858	−	1.95762i	−0.149193	−	0.117835i
$277$	−0.155896	+	0.783742i	−0.00936688	+	0.0470905i	−0.985186	−	0.171489i	$-0.945142\pi$
$277$	−0.155896	+	0.783742i	−0.00936688	+	0.0470905i	0.975819	+	0.218579i	$0.0701422\pi$
$278$	−24.8533	−	15.1412i	−1.49060	−	0.908107i
$279$	16.9357	+	14.8270i	1.01391	+	0.887672i
$280$	27.8807	−	24.1920i	1.66619	−	1.44575i
$281$	−2.65178	−	1.09840i	−0.158192	−	0.0655253i	0.302182	−	0.953250i	$-0.402285\pi$
$281$	−2.65178	−	1.09840i	−0.158192	−	0.0655253i	−0.460374	+	0.887725i	$0.652285\pi$
$282$	−13.5080	+	1.01530i	−0.804392	+	0.0604605i
$283$	25.0238	−	16.7204i	1.48751	−	0.993922i	0.495384	−	0.868674i	$-0.335027\pi$
$283$	25.0238	−	16.7204i	1.48751	−	0.993922i	0.992125	−	0.125248i	$-0.0399727\pi$
$284$	−7.44670	−	14.4285i	−0.441880	−	0.856175i
$285$	17.6254	+	6.62527i	1.04404	+	0.392447i
$286$	7.88104	−	3.65815i	0.466016	−	0.216311i
$287$			36.9429i			2.18067i
$288$	10.5168	+	13.3190i	0.619710	+	0.784831i
$289$		−	14.6804i		−	0.863554i
$290$	17.7346	+	38.2071i	1.04141	+	2.24360i
$291$	20.3094	+	7.63417i	1.19056	+	0.447523i
$292$	7.23898	+	2.31043i	0.423629	+	0.135208i
$293$	−8.66794	+	5.79173i	−0.506386	+	0.338356i	−0.782378	−	0.622803i	$-0.785994\pi$
$293$	−8.66794	+	5.79173i	−0.506386	+	0.338356i	0.275992	+	0.961160i	$0.410994\pi$
$294$	−1.21898	−	16.2178i	−0.0710921	−	0.945839i
$295$	−7.76419	−	3.21603i	−0.452049	−	0.187245i
$296$	−8.35406	−	4.17464i	−0.485570	−	0.242646i
$297$	6.86321	−	2.09139i	0.398244	−	0.121355i
$298$	−15.2913	+	25.0997i	−0.885798	+	1.45399i
$299$	−0.791455	+	3.97891i	−0.0457710	+	0.230106i
$300$	−3.02513	−	25.7603i	−0.174656	−	1.48727i
$301$	−6.00813	+	8.99180i	−0.346303	+	0.518279i
$302$	−0.137163	−	3.27350i	−0.00789286	−	0.188369i
$303$	−3.38652	−	14.4965i	−0.194551	−	0.832799i
$304$	−5.03503	+	11.2283i	−0.288779	+	0.643987i
$305$	−27.5996	+	27.5996i	−1.58035	+	1.58035i
$306$	6.20183	+	1.81383i	0.354535	+	0.103690i
$307$	−1.97934	+	2.96229i	−0.112967	+	0.169067i	−0.883645	−	0.468158i	$-0.844918\pi$
$307$	−1.97934	+	2.96229i	−0.112967	+	0.169067i	0.770678	+	0.637225i	$0.219918\pi$
$308$	9.80150	−	2.81955i	0.558492	−	0.160659i
$309$	−20.2151	+	21.6017i	−1.15000	+	1.22888i
$310$	36.4373	−	8.84835i	2.06950	−	0.502553i
$311$	14.8552	−	6.15323i	0.842362	−	0.348918i	0.0805778	−	0.996748i	$-0.474323\pi$
$311$	14.8552	−	6.15323i	0.842362	−	0.348918i	0.761785	+	0.647830i	$0.224323\pi$
$312$	9.09237	−	19.8112i	0.514754	−	1.12159i
$313$	19.4086	+	8.03931i	1.09704	+	0.454409i	0.856456	−	0.516220i	$-0.172661\pi$
$313$	19.4086	+	8.03931i	1.09704	+	0.454409i	0.240583	+	0.970629i	$0.422661\pi$
$314$	−0.399872	+	2.56800i	−0.0225661	+	0.144921i
$315$	−33.9234	−	19.5477i	−1.91137	−	1.10139i
$316$	−22.6358	+	1.90027i	−1.27337	+	0.106899i
$317$	26.5384	−	5.27881i	1.49054	−	0.296488i	0.618449	−	0.785825i	$-0.287761\pi$
$317$	26.5384	−	5.27881i	1.49054	−	0.296488i	0.872095	+	0.489337i	$0.162761\pi$
$318$	7.42141	−	5.80835i	0.416172	−	0.325716i
$319$			11.6383i			0.651618i
$320$	28.2275	−	1.55154i	1.57796	−	0.0867337i
$321$	3.66175	+	2.27489i	0.204379	+	0.126972i
$322$	−1.63658	+	4.47200i	−0.0912028	+	0.249215i
$323$	0.914075	+	4.59536i	0.0508605	+	0.255693i
$324$	9.69919	−	15.1633i	0.538844	−	0.842406i
$325$	−27.7007	+	18.5090i	−1.53656	+	1.02670i
$326$	15.1464	+	2.35850i	0.838883	+	0.130625i
$327$	−3.27662	−	4.56847i	−0.181198	−	0.252637i
$328$	−17.3416	+	22.3551i	−0.957530	+	1.23435i
$329$	7.81591	+	18.8693i	0.430905	+	1.04030i
$330$	3.73333	−	11.3539i	0.205513	−	0.625013i
$331$	0.802821	−	4.03605i	0.0441270	−	0.221841i	−0.952429	−	0.304759i	$-0.901424\pi$
$331$	0.802821	−	4.03605i	0.0441270	−	0.221841i	0.996556	+	0.0829179i	$0.0264239\pi$
$332$	8.47652	−	2.43840i	0.465210	−	0.133825i
$333$	−1.28468	+	9.82191i	−0.0704000	+	0.538237i
$334$	−13.9020	−	12.7839i	−0.760686	−	0.699502i
$335$	2.95275	+	2.95275i	0.161326	+	0.161326i
$336$	14.1238	−	21.3358i	0.770514	−	1.16397i
$337$	4.18438	−	4.18438i	0.227938	−	0.227938i	−0.583893	−	0.811831i	$-0.698471\pi$
$337$	4.18438	−	4.18438i	0.227938	−	0.227938i	0.811831	+	0.583893i	$0.198471\pi$
$338$	−9.60547	+	0.402480i	−0.522468	+	0.0218920i
$339$	−7.44102	−	16.4043i	−0.404140	−	0.890961i
$340$	8.41827	−	6.70789i	0.456545	−	0.363786i
$341$	10.1610	+	2.02115i	0.550250	+	0.109452i
$342$	13.0013	+	1.14946i	0.703028	+	0.0621559i
$343$	1.22987	−	0.509431i	0.0664070	−	0.0275067i
$344$	−7.85658	+	2.62086i	−0.423598	+	0.141307i
$345$	3.25245	+	4.53476i	0.175106	+	0.244143i
$346$	−3.21386	+	2.34783i	−0.172778	+	0.126220i
$347$	4.27956	+	6.40482i	0.229739	+	0.343829i	0.928373	−	0.371651i	$-0.121208\pi$
$347$	4.27956	+	6.40482i	0.229739	+	0.343829i	−0.698634	+	0.715480i	$0.746208\pi$
$348$	18.9423	+	22.2195i	1.01541	+	1.19109i
$349$	−29.3368	+	5.83546i	−1.57036	+	0.312365i	−0.902089	−	0.431550i	$-0.857967\pi$
$349$	−29.3368	+	5.83546i	−1.57036	+	0.312365i	−0.668275	+	0.743915i	$0.732967\pi$
$350$	−35.4715	+	16.4648i	−1.89603	+	0.880082i
$351$	−23.0118	−	2.23717i	−1.22828	−	0.119411i
$352$	7.25469	+	2.89480i	0.386676	+	0.154293i
$353$	−34.8629			−1.85556			−0.927782	−	0.373122i	$-0.878287\pi$
$353$	−34.8629			−1.85556			−0.927782	+	0.373122i	$0.878287\pi$
$354$	−5.78250	−	0.705040i	−0.307336	−	0.0374724i
$355$	5.59686	+	28.1373i	0.297050	+	1.49337i
$356$	0.0998860	+	0.193536i	0.00529395	+	0.0102574i
$357$	−0.322856	−	9.73706i	−0.0170873	−	0.515340i
$358$	−8.02788	+	5.86463i	−0.424287	+	0.309955i
$359$	6.91509	−	16.6945i	0.364965	−	0.881103i	−0.629594	−	0.776924i	$-0.716779\pi$
$359$	6.91509	−	16.6945i	0.364965	−	0.881103i	0.994559	−	0.104178i	$-0.0332213\pi$
$360$	−11.3519	−	27.7530i	−0.598299	−	1.46271i
$361$	−3.64922	−	8.81000i	−0.192064	−	0.463684i
$362$	−19.1126	+	31.3722i	−1.00454	+	1.64889i
$363$	−10.7619	+	11.5001i	−0.564855	+	0.603598i
$364$	−32.6575	−	3.69273i	−1.71172	−	0.193551i
$365$	−11.1634	−	7.45912i	−0.584317	−	0.390428i
$366$	−13.3029	+	23.5592i	−0.695352	+	1.23146i
$367$	13.6204	+	13.6204i	0.710979	+	0.710979i	0.966740	−	0.255761i	$-0.0823260\pi$
$367$	13.6204	+	13.6204i	0.710979	+	0.710979i	−0.255761	+	0.966740i	$0.582326\pi$
$368$	−3.08957	+	1.93789i	−0.161055	+	0.101019i
$369$	28.4246	+	9.62220i	1.47972	+	0.500912i
$370$	12.1462	+	11.1693i	0.631451	+	0.580662i
$371$	−11.8144	−	7.89414i	−0.613374	−	0.409843i
$372$	22.6888	−	12.6792i	1.17636	−	0.657387i
$373$	9.51416	+	1.89248i	0.492625	+	0.0979891i	0.435150	−	0.900358i	$-0.356695\pi$
$373$	9.51416	+	1.89248i	0.492625	+	0.0979891i	0.0574743	+	0.998347i	$0.481695\pi$
$374$	2.89005	−	0.701813i	0.149441	−	0.0362899i
$375$	−2.47374	+	15.0225i	−0.127743	+	0.775758i
$376$	−4.12794	+	15.0872i	−0.212882	+	0.778063i
$377$	14.3520	−	34.6488i	0.739165	−	1.78450i
$378$	−26.2862	−	6.75080i	−1.35201	−	0.347224i
$379$	−8.54045	−	12.7817i	−0.438693	−	0.656551i	0.544575	−	0.838712i	$-0.316691\pi$
$379$	−8.54045	−	12.7817i	−0.438693	−	0.656551i	−0.983269	+	0.182161i	$0.941691\pi$
$380$	14.0342	−	16.6064i	0.719937	−	0.851892i
$381$	−5.64666	−	2.12254i	−0.289287	−	0.108741i
$382$	−2.46696	+	6.74106i	−0.126221	+	0.344903i
$383$	−0.474263			−0.0242337			−0.0121169	−	0.999927i	$-0.503857\pi$
$383$	−0.474263			−0.0242337			−0.0121169	+	0.999927i	$0.503857\pi$
$384$	18.5620	−	6.28095i	0.947241	−	0.320523i
$385$	−18.0204			−0.918403
$386$	5.01736	−	13.7101i	0.255377	−	0.697826i
$387$	5.35358	+	6.96479i	0.272138	+	0.354040i
$388$	16.1713	−	19.1353i	0.820973	−	0.971446i
$389$	−3.08095	−	4.61097i	−0.156210	−	0.233785i	0.745107	−	0.666945i	$-0.232399\pi$
$389$	−3.08095	−	4.61097i	−0.156210	−	0.233785i	−0.901317	+	0.433160i	$0.857399\pi$
$390$	−25.1160	+	29.1984i	−1.27180	+	1.47852i
$391$	−0.531404	+	1.28292i	−0.0268742	+	0.0648802i
$392$	−18.1137	−	4.95601i	−0.914881	−	0.250316i
$393$	−13.3914	−	2.20515i	−0.675507	−	0.111235i
$394$	5.50552	−	1.33695i	0.277364	−	0.0673543i
$395$	39.3643	+	7.83004i	1.98063	+	0.393972i
$396$	0.383493	−	8.27584i	0.0192713	−	0.415877i
$397$	18.6371	+	12.4529i	0.935369	+	0.624994i	0.927036	−	0.374972i	$-0.122348\pi$
$397$	18.6371	+	12.4529i	0.935369	+	0.624994i	0.00833284	+	0.999965i	$0.497348\pi$
$398$	13.4295	+	12.3494i	0.673162	+	0.619018i
$399$	−4.47667	−	19.1630i	−0.224114	−	0.959348i
$400$	−29.1936	−	6.68761i	−1.45968	−	0.334380i
$401$	1.22748	+	1.22748i	0.0612974	+	0.0612974i	0.737091	−	0.675794i	$-0.236199\pi$
$401$	1.22748	+	1.22748i	0.0612974	+	0.0612974i	−0.675794	+	0.737091i	$0.736199\pi$
$402$	2.52049	+	1.42321i	0.125711	+	0.0709834i
$403$	−27.7584	−	18.5476i	−1.38274	−	0.923920i
$404$	−17.0809	−	1.93141i	−0.849807	−	0.0960915i
$405$	−23.8761	+	21.0099i	−1.18641	+	1.04399i
$406$	22.9039	−	37.5953i	1.13670	−	1.86582i
$407$	1.74472	+	4.21212i	0.0864823	+	0.208787i
$408$	4.37537	−	6.04370i	0.216613	−	0.299208i
$409$	8.06274	−	19.4652i	0.398677	−	0.962491i	−0.589303	−	0.807912i	$-0.700598\pi$
$409$	8.06274	−	19.4652i	0.398677	−	0.962491i	0.987980	−	0.154580i	$-0.0494023\pi$
$410$	40.3660	−	29.4887i	1.99353	−	1.45634i
$411$	−6.79971	+	0.225461i	−0.335405	+	0.0111212i
$412$	15.6677	+	30.3573i	0.771893	+	1.49560i
$413$	1.71348	+	8.61426i	0.0843150	+	0.423880i
$414$	3.01458	+	2.42400i	0.148158	+	0.119133i
$415$	−15.5844			−0.765006
$416$	−18.0285	−	17.5645i	−0.883918	−	0.861171i
$417$	30.2759	+	18.8091i	1.48262	+	0.921087i
$418$	5.44895	−	2.52924i	0.266517	−	0.123709i
$419$	−7.02653	+	1.39766i	−0.343269	+	0.0682804i	−0.363714	−	0.931511i	$-0.618492\pi$
$419$	−7.02653	+	1.39766i	−0.343269	+	0.0682804i	0.0204456	+	0.999791i	$0.493492\pi$
$420$	−34.4041	+	29.3297i	−1.67875	+	1.43114i
$421$	4.50708	+	6.74533i	0.219662	+	0.328747i	0.924891	−	0.380232i	$-0.124156\pi$
$421$	4.50708	+	6.74533i	0.219662	+	0.328747i	−0.705229	+	0.708979i	$0.749156\pi$
$422$	16.2819	−	11.8944i	0.792589	−	0.579012i
$423$	16.5541	−	1.09899i	0.804889	−	0.0534348i
$424$	−3.44357	−	10.3228i	−0.167235	−	0.501321i
$425$	−10.5355	+	4.36394i	−0.511046	+	0.211682i
$426$	8.96566	+	17.7502i	0.434388	+	0.860000i
$427$	40.0087	+	7.95823i	1.93616	+	0.385126i
$428$	3.89299	−	3.10203i	0.188175	−	0.149942i
$429$	−9.69102	+	4.39585i	−0.467887	+	0.212234i
$430$	14.6208	−	0.612628i	0.705078	−	0.0295436i
$431$	8.97176	−	8.97176i	0.432154	−	0.432154i	−0.457206	−	0.889361i	$-0.651150\pi$
$431$	8.97176	−	8.97176i	0.432154	−	0.432154i	0.889361	+	0.457206i	$0.151150\pi$
$432$	−12.7375	−	16.4242i	−0.612834	−	0.790212i
$433$	−15.2633	−	15.2633i	−0.733509	−	0.733509i	0.237804	−	0.971313i	$-0.423572\pi$
$433$	−15.2633	−	15.2633i	−0.733509	−	0.733509i	−0.971313	+	0.237804i	$0.923572\pi$
$434$	−28.8458	−	26.5257i	−1.38464	−	1.27327i
$435$	−21.3110	−	46.9818i	−1.02178	−	2.25260i
$436$	−6.23875	+	1.79467i	−0.298782	+	0.0859493i
$437$	−0.547212	+	2.75102i	−0.0261767	+	0.131599i
$438$	−8.84086	−	2.90699i	−0.422433	−	0.138902i
$439$	−2.80587	−	6.77397i	−0.133917	−	0.323304i	0.842669	−	0.538432i	$-0.180983\pi$
$439$	−2.80587	−	6.77397i	−0.133917	−	0.323304i	−0.976586	+	0.215128i	$0.930983\pi$
$440$	−10.9046	−	8.45906i	−0.519856	−	0.403270i
$441$	1.31945	+	19.8749i	0.0628310	+	0.946424i
$442$	−9.46956	−	1.47454i	−0.450421	−	0.0701366i
$443$	−2.06022	+	1.37659i	−0.0978839	+	0.0654040i	−0.603549	−	0.797326i	$-0.706247\pi$
$443$	−2.06022	+	1.37659i	−0.0978839	+	0.0654040i	0.505665	+	0.862730i	$0.331247\pi$
$444$	10.1866	+	5.20201i	0.483433	+	0.246876i
$445$	−0.0750733	−	0.377419i	−0.00355881	−	0.0178914i
$446$	−7.29364	+	19.9301i	−0.345364	+	0.943718i
$447$	18.9956	−	30.5760i	0.898460	−	1.44620i
$448$	−17.7381	−	23.6282i	−0.838045	−	1.11633i
$449$		−	12.7302i		−	0.600774i	−0.953817	−	0.300387i	$-0.902884\pi$
$449$		−	12.7302i		−	0.600774i	0.953817	−	0.300387i	$-0.0971158\pi$
$450$	3.42940	+	31.5809i	0.161664	+	1.48874i
$451$	13.5466	−	2.69459i	0.637886	−	0.126883i
$452$	−20.7268	+	1.74001i	−0.974906	+	0.0818431i
$453$	0.132978	+	4.01051i	0.00624786	+	0.188430i
$454$	3.17635	−	20.3987i	0.149074	−	0.957358i
$455$	53.6492	+	22.2222i	2.51511	+	1.04179i
$456$	6.28646	−	13.6974i	0.294391	−	0.641441i
$457$	−24.7432	+	10.2490i	−1.15744	+	0.479426i	−0.877021	−	0.480453i	$-0.840472\pi$
$457$	−24.7432	+	10.2490i	−1.15744	+	0.479426i	−0.280416	+	0.959879i	$0.590472\pi$
$458$	22.6512	−	5.50055i	1.05842	−	0.257024i
$459$	−7.57597	−	2.28772i	−0.353616	−	0.106781i
$460$	6.19272	−	1.78143i	0.288737	−	0.0830598i
$461$	−10.5730	+	15.8236i	−0.492432	+	0.736976i	−0.991574	−	0.129544i	$-0.958649\pi$
$461$	−10.5730	+	15.8236i	−0.492432	+	0.736976i	0.499142	+	0.866520i	$0.333649\pi$
$462$	−12.0340	+	3.34829i	−0.559874	+	0.155777i
$463$	0.428275	−	0.428275i	0.0199036	−	0.0199036i	−0.697085	−	0.716989i	$-0.745520\pi$
$463$	0.428275	−	0.428275i	0.0199036	−	0.0199036i	0.716989	+	0.697085i	$0.245520\pi$
$464$	31.5076	−	11.9985i	1.46270	−	0.557015i
$465$	−44.7194	+	10.4469i	−2.07381	+	0.484464i
$466$	−0.959479	−	22.8986i	−0.0444470	−	1.06076i
$467$	−19.1176	+	28.6115i	−0.884657	+	1.32398i	0.0607716	+	0.998152i	$0.480644\pi$
$467$	−19.1176	+	28.6115i	−0.884657	+	1.32398i	−0.945428	+	0.325831i	$0.894356\pi$
$468$	−11.3473	+	24.1655i	−0.524527	+	1.11705i
$469$	0.851414	−	4.28035i	0.0393146	−	0.197648i
$470$	14.3788	−	23.6020i	0.663247	−	1.08868i
$471$	0.517184	−	3.14075i	0.0238306	−	0.144718i
$472$	−3.00680	+	6.01705i	−0.138399	+	0.276957i
$473$	3.73545	+	1.54727i	0.171756	+	0.0711437i
$474$	27.7424	−	2.08520i	1.27425	−	0.0957765i
$475$	−19.1523	+	12.7971i	−0.878767	+	0.587173i
$476$	−10.7169	−	3.42048i	−0.491211	−	0.156777i
$477$	−9.15110	+	7.03412i	−0.419000	+	0.322070i
$478$	11.2270	+	24.1873i	0.513513	+	1.10630i
$479$		−	1.62319i		−	0.0741654i	−0.999312	−	0.0370827i	$-0.988194\pi$
$479$		−	1.62319i		−	0.0741654i	0.999312	−	0.0370827i	$-0.0118065\pi$
$480$	−34.5867	+	1.59832i	−1.57866	+	0.0729528i
$481$		−	14.6916i		−	0.669880i
$482$	−23.2474	+	10.7907i	−1.05889	+	0.491505i
$483$	2.05213	−	5.45935i	0.0933753	−	0.248409i
$484$	8.34103	+	16.1613i	0.379138	+	0.734606i
$485$	−36.8060	+	24.5930i	−1.67127	+	1.11671i
$486$	−12.0407	+	18.4668i	−0.546178	+	0.837669i
$487$	−17.8470	−	7.39248i	−0.808726	−	0.334985i	−0.0602804	−	0.998181i	$-0.519199\pi$
$487$	−17.8470	−	7.39248i	−0.808726	−	0.334985i	−0.748446	+	0.663196i	$0.769199\pi$
$488$	20.4746	+	23.5965i	0.926841	+	1.06816i
$489$	−18.5246	−	3.05042i	−0.837711	−	0.137945i
$490$	28.3366	+	17.2633i	1.28012	+	0.779874i
$491$	−4.82274	+	24.2456i	−0.217647	+	1.09419i	0.705196	+	0.709012i	$0.250859\pi$
$491$	−4.82274	+	24.2456i	−0.217647	+	1.09419i	−0.922844	+	0.385175i	$0.874141\pi$
$492$	21.4773	−	27.1928i	0.968271	−	1.22595i
$493$	7.13191	−	10.6737i	0.321205	−	0.480717i
$494$	−19.3413	+	0.810423i	−0.870206	+	0.0364626i
$495$	−4.69361	+	13.8652i	−0.210962	+	0.623195i
$496$	−5.00375	−	29.5921i	−0.224675	−	1.32872i
$497$	21.2010	−	21.2010i	0.950996	−	0.950996i
$498$	−10.4073	+	2.89567i	−0.466360	+	0.129758i
$499$	7.36807	−	11.0271i	0.329840	−	0.493640i	−0.629071	−	0.777348i	$-0.716565\pi$
$499$	7.36807	−	11.0271i	0.329840	−	0.493640i	0.958911	+	0.283708i	$0.0915645\pi$
$500$	15.3831	+	8.50992i	0.687954	+	0.380575i
$501$	16.8891	+	15.8050i	0.754549	+	0.706117i
$502$	6.19272	+	25.5015i	0.276395	+	1.13819i
$503$	−22.2212	+	9.20431i	−0.990793	+	0.410400i	−0.818413	−	0.574631i	$-0.805146\pi$
$503$	−22.2212	+	9.20431i	−0.990793	+	0.410400i	−0.172380	+	0.985031i	$0.555146\pi$
$504$	−17.5255	+	25.9789i	−0.780647	+	1.15719i
$505$	28.0603	+	11.6229i	1.24867	+	0.517214i
$506$	1.75921	+	0.273933i	0.0782066	+	0.0121778i
$507$	11.7681	−	0.390200i	0.522640	−	0.0173294i
$508$	−4.49613	+	5.32021i	−0.199484	+	0.236046i
$509$	11.6720	−	2.32171i	0.517354	−	0.102908i	0.0704946	−	0.997512i	$-0.477542\pi$
$509$	11.6720	−	2.32171i	0.517354	−	0.102908i	0.446860	+	0.894604i	$0.352542\pi$
$510$	−10.3816	+	8.12512i	−0.459704	+	0.359786i
$511$			14.0318i			0.620728i
$512$	0.357706	−	22.6246i	0.0158085	−	0.999875i
$513$	−15.9103	−	1.54678i	−0.702459	−	0.0682919i
$514$	9.78104	+	3.57948i	0.431423	+	0.157884i
$515$	−11.7757	−	59.2004i	−0.518899	−	2.60868i
$516$	9.64996	−	3.12574i	0.424816	−	0.137603i
$517$	6.34911	−	4.24234i	0.279234	−	0.186578i
$518$	2.65336	−	17.0400i	0.116582	−	0.748697i
$519$	3.96111	−	2.84101i	0.173874	−	0.124707i
$520$	22.0331	+	38.6311i	0.966214	+	1.69409i
$521$	−3.86481	−	9.33049i	−0.169321	−	0.408776i	0.816327	−	0.577589i	$-0.196007\pi$
$521$	−3.86481	−	9.33049i	−0.169321	−	0.408776i	−0.985648	+	0.168813i	$0.946007\pi$
$522$	−22.9610	−	27.4148i	−1.00498	−	1.19991i
$523$	4.79573	−	24.1098i	0.209703	−	1.05425i	−0.722240	−	0.691642i	$-0.756888\pi$
$523$	4.79573	−	24.1098i	0.209703	−	1.05425i	0.931943	−	0.362604i	$-0.118112\pi$
$524$	−7.58594	+	13.7129i	−0.331393	+	0.599050i
$525$	43.6179	−	19.7851i	1.90364	−	0.863494i
$526$	21.9885	−	23.9118i	0.958744	−	1.04260i
$527$	−8.08030	−	8.08030i	−0.351983	−	0.351983i
$528$	−8.85385	−	3.62284i	−0.385314	−	0.157664i
$529$	15.6756	−	15.6756i	0.681549	−	0.681549i
$530$	0.804939	+	19.2104i	0.0349643	+	0.834447i
$531$	7.07427	+	0.925296i	0.306997	+	0.0401544i
$532$	−22.5794	−	2.55315i	−0.978939	−	0.110693i
$533$	−43.6532	−	8.68316i	−1.89083	−	0.376109i
$534$	−0.120261	−	0.238092i	−0.00520419	−	0.0103032i
$535$	−8.12560	+	3.36573i	−0.351300	+	0.145513i
$536$	2.52448	−	2.19048i	0.109041	−	0.0946144i
$537$	9.89444	−	7.09655i	0.426977	−	0.306239i
$538$	4.80702	+	6.58015i	0.207245	+	0.283691i
$539$	5.09336	+	7.62275i	0.219387	+	0.328335i
$540$	13.6059	+	34.1105i	0.585505	+	1.46788i
$541$	−2.98380	+	0.593515i	−0.128284	+	0.0255172i	−0.258815	−	0.965927i	$-0.583332\pi$
$541$	−2.98380	+	0.593515i	−0.128284	+	0.0255172i	0.130531	+	0.991444i	$0.458332\pi$
$542$	−9.35984	−	20.1646i	−0.402039	−	0.866145i
$543$	23.7427	−	38.2171i	1.01889	−	1.64005i
$544$	−4.87948	−	7.10054i	−0.209206	−	0.304433i
$545$	11.4701			0.491327
$546$	39.9560	+	4.87170i	1.70996	+	0.208490i
$547$	5.92667	+	29.7954i	0.253406	+	1.27396i	0.872490	+	0.488633i	$0.162504\pi$
$547$	5.92667	+	29.7954i	0.253406	+	1.27396i	−0.619084	+	0.785325i	$0.712496\pi$
$548$	−2.38863	+	7.48400i	−0.102037	+	0.319701i
$549$	16.5439	−	28.7107i	0.706078	−	1.22534i
$550$	8.62479	+	11.8062i	0.367762	+	0.503416i
$551$	9.92296	−	23.9561i	0.422732	−	1.02057i
$552$	3.80451	−	2.34029i	0.161931	−	0.0996093i
$553$	−16.0521	−	38.7532i	−0.682604	−	1.64795i
$554$	−0.965098	−	0.587958i	−0.0410031	−	0.0249799i
$555$	−14.7560	−	13.8089i	−0.626357	−	0.586153i
$556$	32.1879	−	25.6481i	1.36507	−	1.08772i
$557$	27.1192	+	18.1205i	1.14908	+	0.767790i	0.976140	−	0.217143i	$-0.0696736\pi$
$557$	27.1192	+	18.1205i	1.14908	+	0.767790i	0.172939	+	0.984933i	$0.444674\pi$
$558$	−27.9226	+	15.2856i	−1.18206	+	0.647090i
$559$	−9.21290	−	9.21290i	−0.389664	−	0.389664i
$560$	18.5781	+	48.7855i	0.785068	+	2.06156i
$561$	−3.54695	+	0.828604i	−0.149752	+	0.0349837i
$562$	2.74759	−	2.98791i	0.115900	−	0.126038i
$563$	34.3209	+	22.9325i	1.44645	+	0.966489i	0.997331	+	0.0730192i	$0.0232634\pi$
$563$	34.3209	+	22.9325i	1.44645	+	0.966489i	0.449123	+	0.893470i	$0.351737\pi$
$564$	5.21682	−	18.4331i	0.219668	−	0.776175i
$565$	36.0444	+	7.16968i	1.51640	+	0.301631i
$566$	10.0437	+	41.3599i	0.422170	+	1.73849i
$567$	32.1204	+	8.54879i	1.34893	+	0.359015i
$568$	22.7814	−	2.87718i	0.955886	−	0.120724i
$569$	−7.91757	+	19.1147i	−0.331922	+	0.801330i	0.666518	+	0.745489i	$0.267784\pi$
$569$	−7.91757	+	19.1147i	−0.331922	+	0.801330i	−0.998440	+	0.0558410i	$0.982216\pi$
$570$	−17.3652	+	20.1878i	−0.727348	+	0.845574i
$571$	11.8416	+	17.7222i	0.495556	+	0.741651i	0.991975	−	0.126431i	$-0.0403523\pi$
$571$	11.8416	+	17.7222i	0.495556	+	0.741651i	−0.496420	+	0.868083i	$0.665352\pi$
$572$	1.02793	+	12.2446i	0.0429798	+	0.511971i
$573$	3.09337	−	8.22939i	0.129228	−	0.343788i
$574$	−49.0629	−	17.9551i	−2.04785	−	0.749431i
$575$	−6.82674			−0.284695
$576$	−22.8001	+	7.49377i	−0.950003	+	0.312240i
$577$	25.7108			1.07036			0.535178	−	0.844739i	$-0.320245\pi$
$577$	25.7108			1.07036			0.535178	+	0.844739i	$0.320245\pi$
$578$	19.4967	+	7.13502i	0.810955	+	0.296778i
$579$	−6.29136	+	16.7371i	−0.261460	+	0.695570i
$580$	−59.3613	+	4.98336i	−2.46484	+	0.206923i
$581$	9.04880	+	13.5425i	0.375408	+	0.561837i
$582$	−20.0096	+	23.2620i	−0.829423	+	0.964240i
$583$	−2.03298	+	4.90804i	−0.0841973	+	0.203270i
$584$	−6.58674	+	8.49098i	−0.272561	+	0.351359i
$585$	31.0718	−	35.4907i	1.28466	−	1.46736i
$586$	−3.47903	−	14.3266i	−0.143717	−	0.591825i
$587$	27.2847	+	5.42726i	1.12616	+	0.224007i	0.722815	−	0.691042i	$-0.242848\pi$
$587$	27.2847	+	5.42726i	1.12616	+	0.224007i	0.403344	+	0.915049i	$0.367848\pi$
$588$	22.1308	+	6.26332i	0.912661	+	0.258295i
$589$	−19.1921	−	12.8238i	−0.790798	−	0.528395i
$590$	8.04471	−	8.74836i	0.331196	−	0.360164i
$591$	−6.75689	+	1.57848i	−0.277941	+	0.0649300i
$592$	9.60450	−	9.06584i	0.394743	−	0.372604i
$593$	24.6273	+	24.6273i	1.01132	+	1.01132i	0.999935	+	0.0113851i	$0.00362407\pi$
$593$	24.6273	+	24.6273i	1.01132	+	1.01132i	0.0113851	+	0.999935i	$0.496376\pi$
$594$	−0.558162	+	10.1313i	−0.0229017	+	0.415693i
$595$	16.5268	+	11.0429i	0.677533	+	0.452713i
$596$	−25.9023	−	32.5069i	−1.06100	−	1.33154i
$597$	−16.3151	−	15.2679i	−0.667732	−	0.624872i
$598$	−4.89963	−	2.98495i	−0.200361	−	0.122064i
$599$	13.3132	+	32.1409i	0.543963	+	1.31324i	0.921906	+	0.387414i	$0.126632\pi$
$599$	13.3132	+	32.1409i	0.543963	+	1.31324i	−0.377943	+	0.925829i	$0.623368\pi$
$600$	35.6818	+	8.50249i	1.45670	+	0.347113i
$601$	7.28047	−	17.5766i	0.296977	−	0.716965i	−0.703007	−	0.711183i	$-0.748160\pi$
$601$	7.28047	−	17.5766i	0.296977	−	0.716965i	0.999983	−	0.00578169i	$-0.00184038\pi$
$602$	−9.02169	−	12.3495i	−0.367697	−	0.503327i
$603$	−3.07162	−	1.76996i	−0.125086	−	0.0720783i
$604$	4.41411	+	1.40883i	0.179608	+	0.0573246i
$605$	−6.26903	−	31.5165i	−0.254872	−	1.28133i
$606$	20.8983	+	2.54806i	0.848935	+	0.103508i
$607$	−10.4645			−0.424739			−0.212370	−	0.977189i	$-0.568118\pi$
$607$	−10.4645			−0.424739			−0.212370	+	0.977189i	$0.568118\pi$
$608$	−12.4649	−	12.1441i	−0.505517	−	0.492508i
$609$	−28.4523	+	45.7980i	−1.15295	+	1.85583i
$610$	−23.2403	−	50.0683i	−0.940971	−	2.02721i
$611$	−24.1338	+	4.80050i	−0.976347	+	0.194208i
$612$	−5.42313	+	7.35492i	−0.219217	+	0.297305i
$613$	4.61631	+	6.90880i	0.186451	+	0.279044i	0.912906	−	0.408171i	$-0.133833\pi$
$613$	4.61631	+	6.90880i	0.186451	+	0.279044i	−0.726455	+	0.687215i	$0.758833\pi$
$614$	−2.97213	−	4.06845i	−0.119946	−	0.164189i
$615$	−49.7515	+	35.6831i	−2.00617	+	1.43888i
$616$	−1.01918	+	14.3875i	−0.0410638	+	0.579688i
$617$	−1.58520	+	0.656613i	−0.0638179	+	0.0264343i	−0.414364	−	0.910111i	$-0.635996\pi$
$617$	−1.58520	+	0.656613i	−0.0638179	+	0.0264343i	0.350546	+	0.936545i	$0.385996\pi$
$618$	−18.8636	−	37.3461i	−0.758805	−	1.50228i
$619$	24.9444	+	4.96175i	1.00260	+	0.199430i	0.668982	−	0.743279i	$-0.266730\pi$
$619$	24.9444	+	4.96175i	1.00260	+	0.199430i	0.333618	+	0.942708i	$0.391730\pi$
$620$	−5.95812	+	52.6920i	−0.239284	+	2.11616i
$621$	−3.66602	−	3.00090i	−0.147113	−	0.120422i
$622$	0.951971	+	22.7195i	0.0381706	+	0.910967i
$623$	−0.284379	+	0.284379i	−0.0113934	+	0.0113934i
$624$	21.8916	+	21.7040i	0.876365	+	0.868856i
$625$	4.50806	+	4.50806i	0.180322	+	0.180322i
$626$	−20.1098	+	21.8688i	−0.803750	+	0.874052i
$627$	−6.70037	+	3.03929i	−0.267587	+	0.121378i
$628$	−3.21615	−	1.77917i	−0.128338	−	0.0709965i
$629$	0.981069	−	4.93217i	0.0391178	−	0.196658i
$630$	42.4483	−	35.5522i	1.69118	−	1.41643i
$631$	11.2810	+	27.2347i	0.449089	+	1.08420i	0.972664	+	0.232217i	$0.0745980\pi$
$631$	11.2810	+	27.2347i	0.449089	+	1.08420i	−0.523575	+	0.851980i	$0.675402\pi$
$632$	8.47784	−	30.9857i	0.337230	−	1.23254i
$633$	−20.0676	+	14.3930i	−0.797614	+	0.572070i
$634$	−5.88761	+	37.8106i	−0.233827	+	1.50165i
$635$	10.2332	−	6.83763i	0.406094	−	0.271343i
$636$	4.10695	+	12.6792i	0.162851	+	0.502762i
$637$	−5.76349	−	28.9750i	−0.228358	−	1.14803i
$638$	−15.4565	−	5.65646i	−0.611928	−	0.223942i
$639$	−10.7904	−	21.8345i	−0.426862	−	0.863760i
$640$	−11.6586	+	38.2422i	−0.460848	+	1.51166i
$641$		−	7.35273i		−	0.290415i	−0.989401	−	0.145208i	$-0.953615\pi$
$641$		−	7.35273i		−	0.290415i	0.989401	−	0.145208i	$-0.0463850\pi$
$642$	−4.80091	+	3.75743i	−0.189477	+	0.148294i
$643$	−4.59538	+	0.914079i	−0.181224	+	0.0360477i	−0.284868	−	0.958567i	$-0.591950\pi$
$643$	−4.59538	+	0.914079i	−0.181224	+	0.0360477i	0.103644	+	0.994614i	$0.466950\pi$
$644$	−5.14373	−	4.34699i	−0.202691	−	0.171295i
$645$	−17.9126	+	0.593936i	−0.705309	+	0.0233862i
$646$	−6.54725	−	1.01949i	−0.257598	−	0.0401115i
$647$	−34.8538	−	14.4369i	−1.37024	−	0.567574i	−0.428389	−	0.903594i	$-0.640919\pi$
$647$	−34.8538	−	14.4369i	−1.37024	−	0.567574i	−0.941855	+	0.336021i	$0.890919\pi$
$648$	15.4240	+	20.2510i	0.605911	+	0.795533i
$649$	3.03380	−	1.25664i	0.119087	−	0.0493274i
$650$	−11.1182	−	45.7845i	−0.436091	−	1.79581i
$651$	35.0437	+	32.7944i	1.37347	+	1.28531i
$652$	−10.4938	+	18.9693i	−0.410968	+	0.742895i
$653$	2.26295	−	3.38674i	0.0885561	−	0.132534i	−0.784547	−	0.620070i	$-0.787104\pi$
$653$	2.26295	−	3.38674i	0.0885561	−	0.132534i	0.873103	+	0.487536i	$0.162104\pi$
$654$	7.65978	−	2.13122i	0.299521	−	0.0833373i
$655$	19.5793	−	19.5793i	0.765026	−	0.765026i
$656$	−21.2608	−	33.8960i	−0.830096	−	1.32342i
$657$	10.7963	+	3.65473i	0.421204	+	0.142585i
$658$	−28.8585	+	1.20920i	−1.12502	+	0.0471397i
$659$	−11.4690	+	17.1646i	−0.446770	+	0.668639i	−0.984681	−	0.174363i	$-0.944213\pi$
$659$	−11.4690	+	17.1646i	−0.446770	+	0.668639i	0.537911	+	0.843001i	$0.319213\pi$
$660$	13.2644	+	10.4764i	0.516315	+	0.407794i
$661$	−0.162121	+	0.815036i	−0.00630577	+	0.0317012i	−0.983810	−	0.179214i	$-0.942644\pi$
$661$	−0.162121	+	0.815036i	−0.00630577	+	0.0317012i	0.977504	+	0.210915i	$0.0676445\pi$
$662$	4.96999	+	3.02782i	0.193164	+	0.117680i
$663$	11.5816	+	1.90713i	0.449791	+	0.0740666i
$664$	−0.881404	+	12.4426i	−0.0342051	+	0.482866i
$665$	37.0931	+	15.3644i	1.43841	+	0.595808i
$666$	−12.4198	−	6.47982i	−0.481259	−	0.251088i
$667$	6.38980	−	4.26952i	0.247414	−	0.165317i
$668$	23.7346	−	12.2497i	0.918321	−	0.473955i
$669$	9.14563	−	24.3304i	0.353590	−	0.940666i
$670$	−5.35658	+	2.48637i	−0.206943	+	0.0960567i
$671$		−	15.2513i		−	0.588771i
$672$	21.4711	+	29.1271i	0.828266	+	1.12360i
$673$		−	24.8299i		−	0.957121i	−0.878055	−	0.478560i	$-0.841159\pi$
$673$		−	24.8299i		−	0.957121i	0.878055	−	0.478560i	$-0.158841\pi$
$674$	3.52346	+	7.59087i	0.135719	+	0.292390i
$675$	−3.86227	−	38.7137i	−0.148659	−	1.49009i
$676$	4.13396	−	12.9524i	0.158998	−	0.498169i
$677$	−9.22007	+	6.16065i	−0.354356	+	0.236773i	−0.719988	−	0.693986i	$-0.755853\pi$
$677$	−9.22007	+	6.16065i	−0.354356	+	0.236773i	0.365632	+	0.930759i	$0.380853\pi$
$678$	25.4027	−	1.90934i	0.975584	−	0.0733278i
$679$	42.7416	+	17.7041i	1.64027	+	0.679423i
$680$	4.81710	+	14.4403i	0.184727	+	0.553759i
$681$	−4.10821	+	24.9483i	−0.157427	+	0.956020i
$682$	−7.62273	+	12.5123i	−0.291890	+	0.479119i
$683$	2.21498	−	11.1355i	0.0847538	−	0.426086i	−0.914990	−	0.403475i	$-0.867802\pi$
$683$	2.21498	−	11.1355i	0.0847538	−	0.426086i	0.999744	−	0.0226109i	$-0.00719790\pi$
$684$	−7.84549	+	16.7080i	−0.299980	+	0.638846i
$685$	7.71159	−	11.5412i	0.294645	−	0.440967i
$686$	0.0788144	+	1.88096i	0.00300915	+	0.0718154i
$687$	−27.7997	+	6.49430i	−1.06062	+	0.247773i
$688$	0.337784	−	11.7079i	0.0128779	−	0.446360i
$689$	12.1049	−	12.1049i	0.461161	−	0.461161i
$690$	−7.60327	+	2.11550i	−0.289451	+	0.0805356i
$691$	−21.0411	+	31.4903i	−0.800442	+	1.19795i	0.176471	+	0.984306i	$0.443532\pi$
$691$	−21.0411	+	31.4903i	−0.800442	+	1.19795i	−0.976912	+	0.213640i	$0.931468\pi$
$692$	−1.55608	−	5.40934i	−0.0591534	−	0.205632i
$693$	14.7739	−	3.97196i	0.561212	−	0.150882i
$694$	−10.5860	+	2.57069i	−0.401841	+	0.0975820i
$695$	−67.1838	+	27.8284i	−2.54843	+	1.05559i
$696$	−38.7156	+	14.3576i	−1.46751	+	0.544222i
$697$	−14.0751	−	5.83010i	−0.533133	−	0.220831i
$698$	6.50845	−	41.7976i	0.246349	−	1.58206i
$699$	0.930204	+	28.0542i	0.0351835	+	1.06111i
$700$	−4.62656	−	55.1111i	−0.174867	−	2.08300i
$701$	22.0599	−	4.38799i	0.833192	−	0.165732i	0.239979	−	0.970778i	$-0.422859\pi$
$701$	22.0599	−	4.38799i	0.833192	−	0.165732i	0.593213	+	0.805046i	$0.297859\pi$
$702$	14.1554	−	29.4741i	0.534261	−	1.11243i
$703$		−	10.1578i		−	0.383108i
$704$	−7.37046	+	8.22783i	−0.277785	+	0.310098i
$705$	−17.8621	+	28.7516i	−0.672727	+	1.08285i
$706$	16.9442	−	46.3005i	0.637702	−	1.74254i
$707$	−6.19263	−	31.1325i	−0.232898	−	1.17086i
$708$	3.74677	−	7.33692i	0.140812	−	0.275738i
$709$	34.9257	−	23.3366i	1.31166	−	0.876426i	0.314324	−	0.949316i	$-0.398222\pi$
$709$	34.9257	−	23.3366i	1.31166	−	0.876426i	0.997340	+	0.0728900i	$0.0232222\pi$
$710$	−40.0886	−	6.24234i	−1.50450	−	0.234271i
$711$	−33.9984	+	2.25708i	−1.27504	+	0.0846470i
$712$	−0.305578	+	0.0385929i	−0.0114520	+	0.00144633i
$713$	−2.61792	−	6.32021i	−0.0980417	−	0.236694i
$714$	13.0885	+	4.30366i	0.489823	+	0.161060i
$715$	4.23556	−	21.2936i	0.158401	−	0.796335i
$716$	−3.88693	−	13.5120i	−0.145261	−	0.504966i
$717$	−13.4911	−	29.7422i	−0.503834	−	1.11074i
$718$	18.8107	+	17.2977i	0.702008	+	0.645544i
$719$	−25.4632	−	25.4632i	−0.949618	−	0.949618i	0.0491720	−	0.998790i	$-0.484342\pi$
$719$	−25.4632	−	25.4632i	−0.949618	−	0.949618i	−0.998790	+	0.0491720i	$0.984342\pi$
$720$	42.3754	−	1.58760i	1.57924	−	0.0591663i
$721$	−44.6065	+	44.6065i	−1.66123	+	1.66123i
$722$	13.4739	−	0.564573i	0.501448	−	0.0210112i
$723$	28.5864	−	12.9668i	1.06314	−	0.482241i
$724$	−32.3755	−	40.6306i	−1.20322	−	1.51002i
$725$	61.8969	+	12.3121i	2.29879	+	0.457259i
$726$	−10.0424	−	19.8820i	−0.372709	−	0.737889i
$727$	−9.12297	+	3.77886i	−0.338352	+	0.140150i	−0.545389	−	0.838183i	$-0.683618\pi$
$727$	−9.12297	+	3.77886i	−0.338352	+	0.140150i	0.207037	+	0.978333i	$0.433618\pi$
$728$	20.7765	−	41.5768i	0.770028	−	1.54094i
$729$	14.9437	−	22.4874i	0.553471	−	0.832868i
$730$	15.3319	−	11.2005i	0.567460	−	0.414548i
$731$	−2.47768	−	3.70811i	−0.0916402	−	0.137149i
$732$	−24.8229	−	29.1175i	−0.917480	−	1.07621i
$733$	−12.7770	+	2.54150i	−0.471928	+	0.0938724i	−0.425324	−	0.905041i	$-0.639840\pi$
$733$	−12.7770	+	2.54150i	−0.471928	+	0.0938724i	−0.0466042	+	0.998913i	$0.514840\pi$
$734$	−24.7087	+	11.4691i	−0.912016	+	0.423331i
$735$	−34.5192	−	21.4453i	−1.27326	−	0.791022i
$736$	−1.07206	−	5.04503i	−0.0395166	−	0.185962i
$737$	−1.63167			−0.0601033
$738$	−26.5940	+	33.0733i	−0.978938	+	1.21745i
$739$	3.73646	+	18.7844i	0.137448	+	0.690997i	0.986640	+	0.162914i	$0.0520892\pi$
$739$	3.73646	+	18.7844i	0.137448	+	0.690997i	−0.849192	+	0.528083i	$0.822911\pi$
$740$	−20.7369	+	10.7025i	−0.762305	+	0.393433i
$741$	23.6959	−	0.785695i	0.870491	−	0.0288632i
$742$	16.2261	−	11.8537i	0.595678	−	0.435163i
$743$	−15.5455	+	37.5302i	−0.570310	+	1.37685i	0.330982	+	0.943637i	$0.392620\pi$
$743$	−15.5455	+	37.5302i	−0.570310	+	1.37685i	−0.901292	+	0.433213i	$0.857380\pi$
$744$	5.81164	+	36.2948i	0.213065	+	1.33063i
$745$	28.1043	+	67.8497i	1.02966	+	2.48582i
$746$	−7.13746	+	11.7157i	−0.261321	+	0.428943i
$747$	12.7767	−	3.43503i	0.467476	−	0.125681i
$748$	−0.472572	+	4.17930i	−0.0172790	+	0.152810i
$749$	7.64275	+	5.10672i	0.279260	+	0.186596i
$750$	−18.7487	−	10.5866i	−0.684605	−	0.386567i
$751$	−15.2299	−	15.2299i	−0.555747	−	0.555747i	0.372346	−	0.928094i	$-0.378553\pi$
$751$	−15.2299	−	15.2299i	−0.555747	−	0.555747i	−0.928094	+	0.372346i	$0.878553\pi$
$752$	−18.0307	−	12.8149i	−0.657511	−	0.467313i
$753$	−7.31151	−	31.2979i	−0.266446	−	1.14056i
$754$	39.0407	+	35.9006i	1.42178	+	1.30742i
$755$	−6.80709	−	4.54835i	−0.247735	−	0.165531i
$756$	21.7412	−	31.6289i	0.790722	−	1.15033i
$757$	−47.7615	−	9.50036i	−1.73592	−	0.345296i	−0.777116	−	0.629357i	$-0.783318\pi$
$757$	−47.7615	−	9.50036i	−1.73592	−	0.345296i	−0.958806	+	0.284061i	$0.908318\pi$
$758$	21.1259	−	5.13015i	0.767326	−	0.186336i
$759$	−2.15158	−	0.354298i	−0.0780973	−	0.0128602i
$760$	15.2336	+	26.7095i	0.552583	+	0.968856i
$761$	−18.9859	+	45.8359i	−0.688237	+	1.66155i	0.0600660	+	0.998194i	$0.480869\pi$
$761$	−18.9859	+	45.8359i	−0.688237	+	1.66155i	−0.748303	+	0.663357i	$0.769131\pi$
$762$	5.56330	−	6.46758i	0.201537	−	0.234296i
$763$	−6.65995	−	9.96732i	−0.241106	−	0.360841i
$764$	−7.75363	−	6.55262i	−0.280517	−	0.237066i
$765$	12.8012	−	9.83980i	0.462828	−	0.355759i
$766$	0.230503	−	0.629857i	0.00832841	−	0.0227577i
$767$	−10.5817			−0.382083
$768$	−0.680021	+	27.7045i	−0.0245381	+	0.999699i
$769$	−33.7659			−1.21763			−0.608816	−	0.793312i	$-0.708355\pi$
$769$	−33.7659			−1.21763			−0.608816	+	0.793312i	$0.708355\pi$
$770$	8.75832	−	23.9324i	0.315628	−	0.862464i
$771$	−11.9405	−	4.48837i	−0.430028	−	0.161645i
$772$	15.7695	+	13.3269i	0.567556	+	0.479644i
$773$	−6.58543	−	9.85580i	−0.236862	−	0.354488i	0.693928	−	0.720045i	$-0.255879\pi$
$773$	−6.58543	−	9.85580i	−0.236862	−	0.354488i	−0.930789	+	0.365556i	$0.880879\pi$
$774$	−11.8517	+	3.72490i	−0.426001	+	0.133889i
$775$	21.4986	−	51.9022i	0.772252	−	1.86438i
$776$	17.5534	+	30.7768i	0.630131	+	1.10482i
$777$	−3.43179	+	20.8405i	−0.123115	+	0.747650i
$778$	7.62113	−	1.85069i	0.273231	−	0.0663506i
$779$	−30.1818	−	6.00353i	−1.08138	−	0.215099i
$780$	−26.5707	−	47.5470i	−0.951385	−	1.70246i
$781$	−9.32062	−	6.22784i	−0.333518	−	0.222850i
$782$	−1.44554	−	1.32927i	−0.0516925	−	0.0475347i
$783$	27.8271	+	33.8204i	0.994460	+	1.20864i
$784$	15.3856	−	21.6476i	0.549487	−	0.773130i
$785$	4.59202	+	4.59202i	0.163896	+	0.163896i
$786$	9.43713	−	16.7130i	0.336611	−	0.596134i
$787$	18.4705	+	12.3416i	0.658403	+	0.439931i	0.839371	−	0.543558i	$-0.182923\pi$
$787$	18.4705	+	12.3416i	0.658403	+	0.439931i	−0.180969	+	0.983489i	$0.557923\pi$
$788$	−0.900245	+	7.96152i	−0.0320699	+	0.283617i
$789$	−27.1850	+	29.0496i	−0.967811	+	1.03419i
$790$	−29.5308	+	48.4731i	−1.05066	+	1.72460i
$791$	−14.6983	−	35.4848i	−0.522611	−	1.26169i
$792$	10.8046	+	4.53156i	0.383923	+	0.161022i
$793$	−18.8075	+	45.4054i	−0.667875	+	1.61239i
$794$	−25.5965	+	18.6990i	−0.908384	+	0.663604i
$795$	−0.780378	−	23.5356i	−0.0276772	−	0.834721i
$796$	−22.9280	+	11.8333i	−0.812660	+	0.419422i
$797$	−6.18293	−	31.0837i	−0.219011	−	1.10104i	−0.921211	−	0.389062i	$-0.872799\pi$
$797$	−6.18293	−	31.0837i	−0.219011	−	1.10104i	0.702201	−	0.711979i	$-0.252201\pi$
$798$	27.6256	+	3.36829i	0.977935	+	0.119236i
$799$	−8.42259			−0.297970
$800$	23.0704	−	35.5209i	0.815662	−	1.25585i
$801$	0.144737	+	0.292877i	0.00511403	+	0.0103483i
$802$	−2.22677	+	1.03360i	−0.0786299	+	0.0364977i
$803$	5.14532	−	1.02347i	0.181575	−	0.0361174i
$804$	−3.11515	+	2.65568i	−0.109863	+	0.0936587i
$805$	6.61082	+	9.89379i	0.233001	+	0.348710i
$806$	38.1238	−	27.8507i	1.34285	−	0.980998i
$807$	−5.81678	−	8.11011i	−0.204760	−	0.285489i
$808$	10.8668	−	21.7460i	0.382292	−	0.765022i
$809$	42.0193	−	17.4049i	1.47732	−	0.611925i	0.508804	−	0.860882i	$-0.330088\pi$
$809$	42.0193	−	17.4049i	1.47732	−	0.611925i	0.968515	+	0.248957i	$0.0800878\pi$
$810$	−16.2984	−	41.9205i	−0.572666	−	1.47294i
$811$	−45.9109	−	9.13225i	−1.61215	−	0.320677i	−0.694937	−	0.719071i	$-0.744568\pi$
$811$	−45.9109	−	9.13225i	−1.61215	−	0.320677i	−0.917214	+	0.398394i	$0.869568\pi$
$812$	38.7976	+	48.6902i	1.36153	+	1.70869i
$813$	11.2473	+	24.7957i	0.394461	+	0.869622i
$814$	−6.44197	+	0.269926i	−0.225791	+	0.00946091i
$815$	27.0844	−	27.0844i	0.948726	−	0.948726i
$816$	5.89995	+	8.74819i	0.206540	+	0.306248i
$817$	−6.36980	−	6.36980i	−0.222851	−	0.222851i
$818$	21.9325	+	20.1685i	0.766853	+	0.705173i
$819$	−48.8820	−	6.39364i	−1.70808	−	0.223412i
$820$	19.5444	+	67.9412i	0.682518	+	2.37261i
$821$	−6.81834	+	34.2781i	−0.237962	+	1.19631i	0.658288	+	0.752766i	$0.271281\pi$
$821$	−6.81834	+	34.2781i	−0.237962	+	1.19631i	−0.896250	+	0.443549i	$0.853719\pi$
$822$	3.00539	−	9.14010i	0.104825	−	0.318797i
$823$	−3.45114	−	8.33178i	−0.120299	−	0.290428i	0.852246	−	0.523141i	$-0.175240\pi$
$823$	−3.45114	−	8.33178i	−0.120299	−	0.290428i	−0.972545	+	0.232713i	$0.925240\pi$
$824$	−47.9316	+	6.05353i	−1.66978	+	0.210885i
$825$	−10.4365	−	14.5512i	−0.363353	−	0.506608i
$826$	−12.2732	−	1.91110i	−0.427038	−	0.0664956i
$827$	1.42295	−	0.950787i	0.0494809	−	0.0330621i	−0.530584	−	0.847633i	$-0.678027\pi$
$827$	1.42295	−	0.950787i	0.0494809	−	0.0330621i	0.580065	+	0.814570i	$0.303027\pi$
$828$	−4.68440	+	2.82546i	−0.162794	+	0.0981916i
$829$	0.820323	+	4.12404i	0.0284910	+	0.143234i	0.992413	−	0.122953i	$-0.0392363\pi$
$829$	0.820323	+	4.12404i	0.0284910	+	0.143234i	−0.963922	+	0.266187i	$0.914236\pi$
$830$	7.57436	−	20.6972i	0.262910	−	0.718410i
$831$	1.17567	+	0.730392i	0.0407834	+	0.0253370i
$832$	32.0892	−	15.4064i	1.11249	−	0.534120i
$833$		−	10.1122i		−	0.350366i
$834$	−39.6947	+	31.0670i	−1.37452	+	1.07576i
$835$	−46.2854	+	9.20673i	−1.60177	+	0.318612i
$836$	0.710708	+	8.46588i	0.0245804	+	0.292799i
$837$	34.3602	−	18.4216i	1.18766	−	0.636745i
$838$	1.55886	−	10.0111i	0.0538498	−	0.345826i
$839$	51.5648	+	21.3589i	1.78022	+	0.737390i	0.992630	+	0.121185i	$0.0386693\pi$
$839$	51.5648	+	21.3589i	1.78022	+	0.737390i	0.787586	+	0.616205i	$0.211331\pi$
$840$	−22.2309	−	59.9462i	−0.767038	−	2.06834i
$841$	−38.8429	+	16.0892i	−1.33941	+	0.554801i
$842$	−11.1488	+	2.70736i	−0.384214	+	0.0933017i
$843$	−3.39692	+	3.62991i	−0.116996	+	0.125021i
$844$	7.88334	+	27.4045i	0.271356	+	0.943302i
$845$	−13.3463	+	19.9741i	−0.459126	+	0.687131i
$846$	−6.58614	+	22.5192i	−0.226436	+	0.774227i
$847$	−23.7472	+	23.7472i	−0.815964	+	0.815964i
$848$	15.3831	+	0.443818i	0.528259	+	0.0152408i
$849$	−11.8583	−	50.7608i	−0.406975	−	1.74211i
$850$	−0.675149	−	16.1129i	−0.0231574	−	0.552668i
$851$	1.67254	−	2.50313i	0.0573339	−	0.0858063i
$852$	−27.9311	+	3.28006i	−0.956904	+	0.112373i
$853$	1.80310	−	9.06478i	0.0617368	−	0.310372i	−0.937562	−	0.347819i	$-0.886922\pi$
$853$	1.80310	−	9.06478i	0.0617368	−	0.310372i	0.999299	+	0.0374467i	$0.0119224\pi$
$854$	−30.0143	+	49.2667i	−1.02707	+	1.68587i
$855$	21.4830	−	24.5383i	0.734703	−	0.839191i
$856$	2.22765	+	6.67785i	0.0761394	+	0.228244i
$857$	1.10169	+	0.456333i	0.0376329	+	0.0155880i	0.401420	−	0.915894i	$-0.368517\pi$
$857$	1.10169	+	0.456333i	0.0376329	+	0.0155880i	−0.363788	+	0.931482i	$0.618517\pi$
$858$	−1.12796	−	15.0069i	−0.0385080	−	0.512326i
$859$	−35.2780	+	23.5720i	−1.20367	+	0.804266i	−0.985172	−	0.171571i	$-0.945116\pi$
$859$	−35.2780	+	23.5720i	−1.20367	+	0.804266i	−0.218498	+	0.975837i	$0.570116\pi$
$860$	−6.29243	+	19.7153i	−0.214570	+	0.672285i
$861$	59.8952	+	22.5142i	2.04122	+	0.767283i
$862$	7.55468	+	16.2756i	0.257313	+	0.554351i
$863$		−	0.341243i		−	0.0116161i	−0.999983	−	0.00580803i	$-0.998151\pi$
$863$		−	0.341243i		−	0.0116161i	0.999983	−	0.00580803i	$-0.00184876\pi$
$864$	28.0033	−	8.93379i	0.952693	−	0.303934i
$865$			9.94525i			0.338149i
$866$	27.6892	−	12.8525i	0.940917	−	0.436746i
$867$	−23.8012	−	8.94673i	−0.808333	−	0.303847i
$868$	49.2478	−	25.4173i	1.67158	−	0.862718i
$869$	−13.0396	+	8.71280i	−0.442339	+	0.295561i
$870$	72.7529	−	5.46833i	2.46656	−	0.185394i
$871$	4.85771	+	2.01213i	0.164597	+	0.0681784i
$872$	0.648716	−	9.15778i	0.0219683	−	0.310122i
$873$	24.7544	−	28.2749i	0.837811	−	0.956962i
$874$	−3.38760	−	2.06380i	−0.114587	−	0.0698090i
$875$	−6.33325	+	31.8394i	−0.214103	+	1.07637i
$876$	8.15756	−	10.3285i	0.275619	−	0.348966i
$877$	25.7297	−	38.5072i	0.868829	−	1.30029i	−0.0839003	−	0.996474i	$-0.526738\pi$
$877$	25.7297	−	38.5072i	0.868829	−	1.30029i	0.952729	−	0.303820i	$-0.0982623\pi$
$878$	10.3601	−	0.434098i	0.349635	−	0.0146501i
$879$	4.10756	+	17.5829i	0.138545	+	0.593058i
$880$	16.5342	−	10.3708i	0.557366	−	0.349600i
$881$	22.1495	−	22.1495i	0.746235	−	0.746235i	−0.227535	−	0.973770i	$-0.573067\pi$
$881$	22.1495	−	22.1495i	0.746235	−	0.746235i	0.973770	+	0.227535i	$0.0730666\pi$
$882$	−27.0366	−	7.90733i	−0.910371	−	0.266254i
$883$	−27.6724	+	41.4147i	−0.931251	+	1.39372i	−0.0120494	+	0.999927i	$0.503836\pi$
$883$	−27.6724	+	41.4147i	−0.931251	+	1.39372i	−0.919201	+	0.393788i	$0.871164\pi$
$884$	6.56072	−	11.8596i	0.220661	−	0.398882i
$885$	−9.94589	+	10.6281i	−0.334328	+	0.357259i
$886$	−0.826905	−	3.40518i	−0.0277804	−	0.114399i
$887$	0.0137020	−	0.00567556i	0.000460069	−	0.000190567i	−0.382453	−	0.923975i	$-0.624921\pi$
$887$	0.0137020	−	0.00567556i	0.000460069	−	0.000190567i	0.382913	+	0.923784i	$0.374921\pi$
$888$	−11.8596	+	11.0002i	−0.397981	+	0.369143i
$889$	−11.8835	−	4.92232i	−0.398561	−	0.165089i
$890$	0.537728	+	0.0837314i	0.0180247	+	0.00280668i
$891$	0.791920	−	12.4018i	0.0265303	−	0.415477i
$892$	−22.9238	−	19.3730i	−0.767545	−	0.648655i
$893$	−16.6861	+	3.31907i	−0.558378	+	0.111068i
$894$	31.3749	+	40.0882i	1.04934	+	1.34075i
$895$			24.8422i			0.830383i
$896$	40.0011	−	12.0736i	1.33634	−	0.403351i
$897$	5.96864	+	3.70806i	0.199287	+	0.123809i
$898$	16.9066	+	6.18716i	0.564181	+	0.206468i
$899$	12.3377	+	62.0257i	0.411485	+	2.06867i
$900$	−43.6086	−	10.7945i	−1.45362	−	0.359818i
$901$	4.87212	−	3.25545i	0.162314	−	0.108455i
$902$	−3.00536	+	19.3006i	−0.100068	+	0.642639i
$903$	10.9168	+	15.2208i	0.363288	+	0.506518i
$904$	7.76284	−	28.3724i	0.258188	−	0.943652i
$905$	35.1277	+	84.8057i	1.16768	+	2.81904i
$906$	−5.39089	−	1.77260i	−0.179100	−	0.0588906i
$907$	0.607801	−	3.05562i	0.0201817	−	0.101460i	−0.969382	−	0.245559i	$-0.921028\pi$
$907$	0.607801	−	3.05562i	0.0201817	−	0.101460i	0.989563	+	0.144099i	$0.0460284\pi$
$908$	25.5472	+	14.1327i	0.847814	+	0.469009i
$909$	−25.5669	−	3.34408i	−0.847999	−	0.110916i
$910$	−55.5875	+	60.4496i	−1.84271	+	2.00389i
$911$	22.9549	+	22.9549i	0.760529	+	0.760529i	0.976418	−	0.215889i	$-0.0692649\pi$
$911$	22.9549	+	22.9549i	0.760529	+	0.760529i	−0.215889	+	0.976418i	$0.569265\pi$
$912$	15.1358	+	15.0062i	0.501198	+	0.496903i
$913$	4.30590	−	4.30590i	0.142505	−	0.142505i
$914$	−1.58562	−	37.8420i	−0.0524478	−	1.25170i
$915$	27.9269	+	61.5671i	0.923235	+	2.03535i
$916$	−3.70385	+	32.7558i	−0.122379	+	1.08228i
$917$	−28.3824	−	5.64561i	−0.937269	−	0.186434i
$918$	6.72035	−	8.94957i	0.221805	−	0.295380i
$919$	23.5333	−	9.74781i	0.776292	−	0.321551i	0.0408739	−	0.999164i	$-0.486986\pi$
$919$	23.5333	−	9.74781i	0.776292	−	0.321551i	0.735418	+	0.677614i	$0.236986\pi$
$920$	−0.643930	+	9.09022i	−0.0212297	+	0.299696i
$921$	3.59646	+	5.01440i	0.118507	+	0.165230i
$922$	−15.8762	−	21.7323i	−0.522853	−	0.715715i
$923$	20.0688	+	30.0351i	0.660573	+	0.988618i
$924$	1.40204	−	17.6094i	0.0461237	−	0.579308i
$925$	24.2474	−	4.82312i	0.797251	−	0.158583i
$926$	0.360629	+	0.776932i	0.0118510	+	0.0255316i
$927$	22.7028	+	45.9394i	0.745659	+	1.50885i
$928$	0.621430	+	47.6760i	0.0203995	+	1.56504i
$929$	−29.0039			−0.951588			−0.475794	−	0.879557i	$-0.657839\pi$
$929$	−29.0039			−0.951588			−0.475794	+	0.879557i	$0.657839\pi$
$930$	7.86037	−	64.4681i	0.257752	−	2.11399i
$931$	−3.98487	−	20.0333i	−0.130599	−	0.656566i
$932$	30.8774	+	9.85501i	1.01142	+	0.322811i
$933$	−0.922925	−	27.8347i	−0.0302152	−	0.911266i
$934$	−28.7066	−	39.2954i	−0.939309	−	1.28579i
$935$	2.84387	−	6.86570i	0.0930043	−	0.224532i
$936$	−26.5785	−	26.8150i	−0.868745	−	0.876475i
$937$	−3.33957	−	8.06243i	−0.109099	−	0.263388i	0.859896	−	0.510470i	$-0.170528\pi$
$937$	−3.33957	−	8.06243i	−0.109099	−	0.263388i	−0.968995	+	0.247082i	$0.920528\pi$
$938$	5.27081	+	3.21109i	0.172098	+	0.104846i
$939$	24.8623	−	26.5676i	0.811351	−	0.867001i
$940$	24.3568	+	30.5673i	0.794431	+	0.996995i
$941$	−15.0978	−	10.0880i	−0.492174	−	0.328860i	0.284593	−	0.958649i	$-0.408142\pi$
$941$	−15.0978	−	10.0880i	−0.492174	−	0.328860i	−0.776767	+	0.629788i	$0.783142\pi$
$942$	3.91978	+	2.21333i	0.127713	+	0.0721143i
$943$	−6.44904	−	6.44904i	−0.210010	−	0.210010i
$944$	−6.52972	−	6.91769i	−0.212524	−	0.225152i
$945$	−52.3666	+	43.0868i	−1.70348	+	1.40161i
$946$	−3.87041	+	4.20894i	−0.125838	+	0.136844i
$947$	32.9455	+	22.0135i	1.07059	+	0.715343i	0.960416	−	0.278570i	$-0.0898603\pi$
$947$	32.9455	+	22.0135i	1.07059	+	0.715343i	0.110170	+	0.993913i	$0.464860\pi$
$948$	−10.7141	+	37.8574i	−0.347979	+	1.22955i
$949$	−16.5805	−	3.29806i	−0.538225	−	0.107060i
$950$	−7.68711	−	31.6554i	−0.249403	−	1.02704i
$951$	7.61488	−	46.2436i	0.246929	−	1.49955i
$952$	9.75134	−	12.5705i	0.316043	−	0.407411i
$953$	17.0882	−	41.2546i	0.553542	−	1.33637i	−0.361260	−	0.932465i	$-0.617653\pi$
$953$	17.0882	−	41.2546i	0.553542	−	1.33637i	0.914802	−	0.403903i	$-0.132347\pi$
$954$	−4.89418	−	15.5721i	−0.158455	−	0.504165i
$955$	9.96510	+	14.9138i	0.322463	+	0.482600i
$956$	−37.5792	+	3.15476i	−1.21540	+	0.102032i
$957$	18.8690	+	7.09275i	0.609949	+	0.229276i
$958$	2.15571	+	0.788907i	0.0696480	+	0.0254884i
$959$	−14.5067			−0.468445
$960$	14.6873	−	46.7105i	0.474029	−	1.50758i
$961$	25.2954			0.815982
$962$	19.5115	+	7.14046i	0.629077	+	0.230218i
$963$	5.91985	−	4.55037i	0.190765	−	0.146634i
$964$	−3.03216	−	36.1188i	−0.0976593	−	1.16331i
$965$	−20.2672	−	30.3320i	−0.652425	−	0.976423i
$966$	6.25304	+	5.37876i	0.201188	+	0.173059i
$967$	−10.5437	+	25.4548i	−0.339063	+	0.818570i	0.658743	+	0.752368i	$0.271088\pi$
$967$	−10.5437	+	25.4548i	−0.339063	+	0.818570i	−0.997806	+	0.0662026i	$0.978912\pi$
$968$	−25.5174	+	3.22272i	−0.820160	+	0.103582i
$969$	8.00750	+	1.31859i	0.257238	+	0.0423591i
$970$	−14.7727	−	60.8338i	−0.474324	−	1.95326i
$971$	−23.0007	−	4.57513i	−0.738129	−	0.146823i	−0.188313	−	0.982109i	$-0.560302\pi$
$971$	−23.0007	−	4.57513i	−0.738129	−	0.146823i	−0.549815	+	0.835286i	$0.685302\pi$
$972$	−18.6731	−	24.9662i	−0.598942	−	0.800793i
$973$	63.1915	+	42.2232i	2.02583	+	1.35361i
$974$	18.4918	−	20.1093i	0.592516	−	0.644342i
$975$	13.1268	+	56.1911i	0.420395	+	1.79955i
$976$	−41.2890	+	15.7233i	−1.32163	+	0.503292i
$977$	−24.3302	−	24.3302i	−0.778392	−	0.778392i	0.201166	−	0.979557i	$-0.435527\pi$
$977$	−24.3302	−	24.3302i	−0.778392	−	0.778392i	−0.979557	+	0.201166i	$0.935527\pi$
$978$	13.0546	−	23.1195i	0.417439	−	0.739279i
$979$	0.125022	+	0.0835369i	0.00399572	+	0.00266985i
$980$	−36.6991	+	29.2428i	−1.17231	+	0.934127i
$981$	−9.40371	+	2.52819i	−0.300237	+	0.0807189i
$982$	−29.8559	−	18.1889i	−0.952741	−	0.580430i
$983$	−3.51432	−	8.48432i	−0.112089	−	0.270608i	0.857873	−	0.513861i	$-0.171785\pi$
$983$	−3.51432	−	8.48432i	−0.112089	−	0.270608i	−0.969963	+	0.243253i	$0.921785\pi$
$984$	25.6756	+	41.7398i	0.818509	+	1.33062i
$985$	5.41753	−	13.0791i	0.172617	−	0.416734i
$986$	10.7091	+	14.6594i	0.341048	+	0.466849i
$987$	35.3559	−	1.17231i	1.12539	−	0.0373150i
$988$	8.32402	−	26.0806i	0.264822	−	0.829733i
$989$	−0.520853	−	2.61851i	−0.0165622	−	0.0832636i
$990$	−16.1328	−	12.9723i	−0.512735	−	0.412286i
$991$	38.7994			1.23250			0.616252	−	0.787549i	$-0.288650\pi$
$991$	38.7994			1.23250			0.616252	+	0.787549i	$0.288650\pi$
$992$	41.7324	+	7.73707i	1.32500	+	0.245652i
$993$	−6.05436	−	3.76131i	−0.192129	−	0.119362i
$994$	17.8523	+	38.4607i	0.566242	+	1.21990i
$995$	44.7122	−	8.89382i	1.41747	−	0.281953i
$996$	1.21251	−	15.2290i	0.0384198	−	0.482548i
$997$	20.7514	+	31.0566i	0.657203	+	0.983574i	0.999040	+	0.0438142i	$0.0139510\pi$
$997$	20.7514	+	31.0566i	0.657203	+	0.983574i	−0.341837	+	0.939759i	$0.611049\pi$
$998$	11.0637	+	15.1448i	0.350217	+	0.479399i
$999$	15.1413	+	8.06864i	0.479048	+	0.255280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.107.11	✓	240
3.2	odd	2	inner	192.2.s.a.107.20	yes	240
4.3	odd	2		768.2.s.a.335.11		240
12.11	even	2		768.2.s.a.335.8		240
64.3	odd	16	inner	192.2.s.a.131.20	yes	240
64.61	even	16		768.2.s.a.431.8		240
192.125	odd	16		768.2.s.a.431.11		240
192.131	even	16	inner	192.2.s.a.131.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.11	✓	240	1.1	even	1	trivial
192.2.s.a.107.20	yes	240	3.2	odd	2	inner
192.2.s.a.131.11	yes	240	192.131	even	16	inner
192.2.s.a.131.20	yes	240	64.3	odd	16	inner
768.2.s.a.335.8		240	12.11	even	2
768.2.s.a.335.11		240	4.3	odd	2
768.2.s.a.431.8		240	64.61	even	16
768.2.s.a.431.11		240	192.125	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.486023 + 1.32807i) q^{2} +(0.609434 - 1.62129i) q^{3} +(-1.52756 - 1.29095i) q^{4} +(1.96325 + 2.93821i) q^{5} +(1.85700 + 1.59736i) q^{6} +(1.41332 - 3.41205i) q^{7} +(2.45691 - 1.40129i) q^{8} +(-2.25718 - 1.97614i) q^{9} +(-4.85635 + 1.17930i) q^{10} +(-1.35426 - 0.269378i) q^{11} +(-3.02396 + 1.68988i) q^{12} +(3.69962 + 2.47201i) q^{13} +(3.84455 + 3.53533i) q^{14} +(5.96017 - 1.39236i) q^{15} +(0.666898 + 3.94401i) q^{16} +(1.07694 + 1.07694i) q^{17} +(3.72150 - 2.03725i) q^{18} +(2.55792 + 1.70915i) q^{19} +(0.794095 - 7.02276i) q^{20} +(-4.67061 - 4.37082i) q^{21} +(1.01595 - 1.66763i) q^{22} +(0.348914 + 0.842354i) q^{23} +(-0.774573 - 4.83736i) q^{24} +(-2.86532 + 6.91750i) q^{25} +(-5.08112 + 3.71192i) q^{26} +(-4.57950 + 2.45523i) q^{27} +(-6.56372 + 3.38760i) q^{28} +(-1.64436 - 8.26676i) q^{29} +(-1.04763 + 8.59227i) q^{30} -7.50303 q^{31} +(-5.56207 - 1.03119i) q^{32} +(-1.26207 + 2.03148i) q^{33} +(-1.95367 + 0.906837i) q^{34} +(12.8000 - 2.54608i) q^{35} +(0.896889 + 5.93259i) q^{36} +(-1.83441 - 2.74539i) q^{37} +(-3.51308 + 2.56642i) q^{38} +(6.26253 - 4.49165i) q^{39} +(8.94080 + 4.46784i) q^{40} +(-9.24158 + 3.82799i) q^{41} +(8.07480 - 4.07860i) q^{42} +(-2.87193 - 0.571263i) q^{43} +(1.72096 + 2.15977i) q^{44} +(1.37491 - 10.5117i) q^{45} +(-1.28829 + 0.0539808i) q^{46} +(-3.91043 + 3.91043i) q^{47} +(6.80083 + 1.32238i) q^{48} +(-4.69487 - 4.69487i) q^{49} +(-7.79434 - 7.16743i) q^{50} +(2.40235 - 1.08971i) q^{51} +(-2.46017 - 8.55218i) q^{52} +(0.750588 - 3.77346i) q^{53} +(-1.03498 - 7.27522i) q^{54} +(-1.86725 - 4.50795i) q^{55} +(-1.30887 - 10.3636i) q^{56} +(4.32991 - 3.10552i) q^{57} +(11.7781 + 1.83400i) q^{58} +(-1.97738 + 1.32124i) q^{59} +(-10.9020 - 5.56737i) q^{60} +(2.15485 + 10.8331i) q^{61} +(3.64665 - 9.96458i) q^{62} +(-9.93280 + 4.90870i) q^{63} +(4.07280 - 6.88566i) q^{64} +15.7235i q^{65} +(-2.08456 - 2.66347i) q^{66} +(1.15899 - 0.230537i) q^{67} +(-0.254818 - 3.03536i) q^{68} +(1.57834 - 0.0523337i) q^{69} +(-2.83972 + 18.2368i) q^{70} +(7.50045 + 3.10679i) q^{71} +(-8.31483 - 1.69224i) q^{72} +(-3.51016 + 1.45396i) q^{73} +(4.53765 - 1.10191i) q^{74} +(9.46907 + 8.86128i) q^{75} +(-1.70096 - 5.91297i) q^{76} +(-2.83313 + 4.24007i) q^{77} +(2.92151 + 10.5001i) q^{78} +(8.03113 - 8.03113i) q^{79} +(-10.2791 + 9.70258i) q^{80} +(1.18974 + 8.92102i) q^{81} +(-0.592231 - 14.1340i) q^{82} +(-2.45014 + 3.66690i) q^{83} +(1.49214 + 12.7062i) q^{84} +(-1.04997 + 5.27857i) q^{85} +(2.15450 - 3.53649i) q^{86} +(-14.4050 - 2.37205i) q^{87} +(-3.70476 + 1.23586i) q^{88} +(-0.100607 - 0.0416728i) q^{89} +(13.2921 + 6.93493i) q^{90} +(13.6634 - 9.12957i) q^{91} +(0.554448 - 1.73718i) q^{92} +(-4.57260 + 12.1646i) q^{93} +(-3.29278 - 7.09391i) q^{94} +10.8712i q^{95} +(-5.06158 + 8.38930i) q^{96} +12.5267i q^{97} +(8.51695 - 3.95332i) q^{98} +(2.52447 + 3.28424i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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