LMFDB - Embedded newform 315.2.bl.j.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.j.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.29184 + 1.32320i) q^{2} +(-1.70895 + 0.281919i) q^{3} +(2.50170 - 4.33307i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(3.54362 - 2.90740i) q^{6} +(-1.33893 - 2.28195i) q^{7} +7.94816i q^{8} +(2.84104 - 0.963574i) q^{9} +O(q^{10})$	\(q+(-2.29184 + 1.32320i) q^{2} +(-1.70895 + 0.281919i) q^{3} +(2.50170 - 4.33307i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(3.54362 - 2.90740i) q^{6} +(-1.33893 - 2.28195i) q^{7} +7.94816i q^{8} +(2.84104 - 0.963574i) q^{9} -2.64639i q^{10} +(0.416342 - 0.240375i) q^{11} +(-3.05371 + 8.11029i) q^{12} +(2.11934 + 1.22360i) q^{13} +(6.08807 + 3.45820i) q^{14} +(0.610327 - 1.62096i) q^{15} +(-5.51359 - 9.54981i) q^{16} +1.67521 q^{17} +(-5.23623 + 5.96762i) q^{18} +7.56459i q^{19} +(2.50170 + 4.33307i) q^{20} +(2.93149 + 3.52227i) q^{21} +(-0.636127 + 1.10180i) q^{22} +(-2.87783 - 1.66152i) q^{23} +(-2.24074 - 13.5830i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.47625 q^{26} +(-4.58356 + 2.44765i) q^{27} +(-13.2374 + 0.0929230i) q^{28} +(-2.15024 + 1.24144i) q^{29} +(0.746070 + 4.52256i) q^{30} +(-8.09553 - 4.67396i) q^{31} +(11.5059 + 6.64295i) q^{32} +(-0.643743 + 0.528165i) q^{33} +(-3.83933 + 2.21664i) q^{34} +(2.64569 - 0.0185720i) q^{35} +(2.93220 - 14.7210i) q^{36} +4.34966 q^{37} +(-10.0094 - 17.3369i) q^{38} +(-3.96680 - 1.49359i) q^{39} +(-6.88331 - 3.97408i) q^{40} +(-4.37827 + 7.58339i) q^{41} +(-11.3792 - 4.19355i) q^{42} +(5.73592 + 9.93491i) q^{43} -2.40538i q^{44} +(-0.586041 + 2.94220i) q^{45} +8.79406 q^{46} +(0.433925 + 0.751580i) q^{47} +(12.1147 + 14.7658i) q^{48} +(-3.41455 + 6.11072i) q^{49} +(2.29184 + 1.32320i) q^{50} +(-2.86286 + 0.472275i) q^{51} +(10.6039 - 6.12215i) q^{52} +7.15905i q^{53} +(7.26608 - 11.6746i) q^{54} +0.480750i q^{55} +(18.1373 - 10.6420i) q^{56} +(-2.13260 - 12.9275i) q^{57} +(3.28534 - 5.69038i) q^{58} +(-4.89709 + 8.48201i) q^{59} +(-5.49686 - 6.69973i) q^{60} +(7.60094 - 4.38841i) q^{61} +24.7383 q^{62} +(-6.00277 - 5.19295i) q^{63} -13.1054 q^{64} +(-2.11934 + 1.22360i) q^{65} +(0.776491 - 2.06227i) q^{66} +(-0.821072 + 1.42214i) q^{67} +(4.19088 - 7.25882i) q^{68} +(5.38650 + 2.02814i) q^{69} +(-6.03892 + 3.54333i) q^{70} +4.44038i q^{71} +(7.65865 + 22.5811i) q^{72} +9.10515i q^{73} +(-9.96874 + 5.75546i) q^{74} +(1.09863 + 1.33904i) q^{75} +(32.7779 + 18.9243i) q^{76} +(-1.10597 - 0.628225i) q^{77} +(11.0676 - 1.82578i) q^{78} +(5.20988 + 9.02378i) q^{79} +11.0272 q^{80} +(7.14305 - 5.47511i) q^{81} -23.1732i q^{82} +(-3.09425 - 5.35940i) q^{83} +(22.5959 - 3.89069i) q^{84} +(-0.837607 + 1.45078i) q^{85} +(-26.2917 - 15.1795i) q^{86} +(3.32467 - 2.72776i) q^{87} +(1.91054 + 3.30915i) q^{88} +11.7120 q^{89} +(-2.55000 - 7.51852i) q^{90} +(-0.0454493 - 6.47452i) q^{91} +(-14.3989 + 8.31323i) q^{92} +(15.1526 + 5.70529i) q^{93} +(-1.98898 - 1.14834i) q^{94} +(-6.55113 - 3.78229i) q^{95} +(-21.5359 - 8.10875i) q^{96} +(-12.3950 + 7.15625i) q^{97} +(-0.260064 - 18.5229i) q^{98} +(0.951226 - 1.08409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.29184	+	1.32320i	−1.62058	+	0.935641i	−0.633813	+	0.773487i	$0.718511\pi$
$2$	−2.29184	+	1.32320i	−1.62058	+	0.935641i	−0.986765	+	0.162155i	$0.948156\pi$
$3$	−1.70895	+	0.281919i	−0.986665	+	0.162766i
$3$	−1.70895	+	0.281919i	−0.986665	+	0.162766i
$4$	2.50170	−	4.33307i	1.25085	−	2.16653i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	3.54362	−	2.90740i	1.44668	−	1.18694i
$7$	−1.33893	−	2.28195i	−0.506067	−	0.862494i
$7$	−1.33893	−	2.28195i	−0.506067	−	0.862494i
$8$			7.94816i			2.81010i
$9$	2.84104	−	0.963574i	0.947014	−	0.321191i
$10$		−	2.64639i		−	0.836863i
$11$	0.416342	−	0.240375i	0.125532	−	0.0724758i	−0.435919	−	0.899986i	$-0.643577\pi$
$11$	0.416342	−	0.240375i	0.125532	−	0.0724758i	0.561451	+	0.827510i	$0.310243\pi$
$12$	−3.05371	+	8.11029i	−0.881530	+	2.34124i
$13$	2.11934	+	1.22360i	0.587798	+	0.339365i	0.764226	−	0.644948i	$-0.223121\pi$
$13$	2.11934	+	1.22360i	0.587798	+	0.339365i	−0.176428	+	0.984314i	$0.556454\pi$
$14$	6.08807	+	3.45820i	1.62711	+	0.924242i
$15$	0.610327	−	1.62096i	0.157586	−	0.418529i
$16$	−5.51359	−	9.54981i	−1.37840	−	2.38745i
$17$	1.67521			0.406299			0.203150	−	0.979148i	$-0.434882\pi$
$17$	1.67521			0.406299			0.203150	+	0.979148i	$0.434882\pi$
$18$	−5.23623	+	5.96762i	−1.23419	+	1.40658i
$19$			7.56459i			1.73544i	0.497057	+	0.867718i	$0.334414\pi$
$19$			7.56459i			1.73544i	−0.497057	+	0.867718i	$0.665586\pi$
$20$	2.50170	+	4.33307i	0.559397	+	0.968903i
$21$	2.93149	+	3.52227i	0.639703	+	0.768622i
$22$	−0.636127	+	1.10180i	−0.135623	+	0.234906i
$23$	−2.87783	−	1.66152i	−0.600070	−	0.346450i	0.168999	−	0.985616i	$-0.445946\pi$
$23$	−2.87783	−	1.66152i	−0.600070	−	0.346450i	−0.769069	+	0.639166i	$0.779280\pi$
$24$	−2.24074	−	13.5830i	−0.457390	−	2.77263i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−6.47625			−1.27010
$27$	−4.58356	+	2.44765i	−0.882106	+	0.471050i
$28$	−13.2374	+	0.0929230i	−2.50164	+	0.0175608i
$29$	−2.15024	+	1.24144i	−0.399290	+	0.230530i	−0.686177	−	0.727434i	$-0.740713\pi$
$29$	−2.15024	+	1.24144i	−0.399290	+	0.230530i	0.286888	+	0.957964i	$0.407379\pi$
$30$	0.746070	+	4.52256i	0.136213	+	0.825703i
$31$	−8.09553	−	4.67396i	−1.45400	−	0.839468i	−0.455296	−	0.890340i	$-0.650466\pi$
$31$	−8.09553	−	4.67396i	−1.45400	−	0.839468i	−0.998705	+	0.0508724i	$0.983800\pi$
$32$	11.5059	+	6.64295i	2.03398	+	1.17432i
$33$	−0.643743	+	0.528165i	−0.112061	+	0.0919417i
$34$	−3.83933	+	2.21664i	−0.658439	+	0.380150i
$35$	2.64569	−	0.0185720i	0.447203	−	0.00313924i
$36$	2.93220	−	14.7210i	0.488700	−	2.45350i
$37$	4.34966			0.715080			0.357540	−	0.933898i	$-0.383616\pi$
$37$	4.34966			0.715080			0.357540	+	0.933898i	$0.383616\pi$
$38$	−10.0094	−	17.3369i	−1.62374	−	2.81241i
$39$	−3.96680	−	1.49359i	−0.635197	−	0.239166i
$40$	−6.88331	−	3.97408i	−1.08835	−	0.628358i
$41$	−4.37827	+	7.58339i	−0.683771	+	1.18433i	0.290051	+	0.957011i	$0.406328\pi$
$41$	−4.37827	+	7.58339i	−0.683771	+	1.18433i	−0.973821	+	0.227315i	$0.927005\pi$
$42$	−11.3792	−	4.19355i	−1.75584	−	0.647079i
$43$	5.73592	+	9.93491i	0.874720	+	1.51506i	0.857061	+	0.515215i	$0.172288\pi$
$43$	5.73592	+	9.93491i	0.874720	+	1.51506i	0.0176587	+	0.999844i	$0.494379\pi$
$44$		−	2.40538i		−	0.362625i
$45$	−0.586041	+	2.94220i	−0.0873619	+	0.438598i
$46$	8.79406			1.29661
$47$	0.433925	+	0.751580i	0.0632944	+	0.109629i	0.895936	−	0.444183i	$-0.146506\pi$
$47$	0.433925	+	0.751580i	0.0632944	+	0.109629i	−0.832642	+	0.553812i	$0.813173\pi$
$48$	12.1147	+	14.7658i	1.74861	+	2.13126i
$49$	−3.41455	+	6.11072i	−0.487793	+	0.872959i
$50$	2.29184	+	1.32320i	0.324116	+	0.187128i
$51$	−2.86286	+	0.472275i	−0.400881	+	0.0661318i
$52$	10.6039	−	6.12215i	1.47049	−	0.848990i
$53$			7.15905i			0.983371i	0.870773	+	0.491686i	$0.163619\pi$
$53$			7.15905i			0.983371i	−0.870773	+	0.491686i	$0.836381\pi$
$54$	7.26608	−	11.6746i	0.988788	−	1.58871i
$55$			0.480750i			0.0648244i
$56$	18.1373	−	10.6420i	2.42370	−	1.42210i
$57$	−2.13260	−	12.9275i	−0.282470	−	1.71229i
$58$	3.28534	−	5.69038i	0.431387	−	0.747184i
$59$	−4.89709	+	8.48201i	−0.637547	+	1.10426i	0.348423	+	0.937338i	$0.386717\pi$
$59$	−4.89709	+	8.48201i	−0.637547	+	1.10426i	−0.985969	+	0.166926i	$0.946616\pi$
$60$	−5.49686	−	6.69973i	−0.709642	−	0.864932i
$61$	7.60094	−	4.38841i	0.973201	−	0.561878i	0.0729905	−	0.997333i	$-0.476746\pi$
$61$	7.60094	−	4.38841i	0.973201	−	0.561878i	0.900211	+	0.435455i	$0.143412\pi$
$62$	24.7383			3.14176
$63$	−6.00277	−	5.19295i	−0.756278	−	0.654250i
$64$	−13.1054			−1.63817
$65$	−2.11934	+	1.22360i	−0.262871	+	0.151769i
$66$	0.776491	−	2.06227i	0.0955795	−	0.253848i
$67$	−0.821072	+	1.42214i	−0.100310	+	0.173742i	−0.911812	−	0.410607i	$-0.865317\pi$
$67$	−0.821072	+	1.42214i	−0.100310	+	0.173742i	0.811502	+	0.584349i	$0.198650\pi$
$68$	4.19088	−	7.25882i	0.508219	−	0.880261i
$69$	5.38650	+	2.02814i	0.648458	+	0.244159i
$70$	−6.03892	+	3.54333i	−0.721789	+	0.423509i
$71$			4.44038i			0.526976i	0.964663	+	0.263488i	$0.0848729\pi$
$71$			4.44038i			0.526976i	−0.964663	+	0.263488i	$0.915127\pi$
$72$	7.65865	+	22.5811i	0.902580	+	2.66121i
$73$			9.10515i			1.06568i	0.846217	+	0.532839i	$0.178875\pi$
$73$			9.10515i			1.06568i	−0.846217	+	0.532839i	$0.821125\pi$
$74$	−9.96874	+	5.75546i	−1.15884	+	0.669058i
$75$	1.09863	+	1.33904i	0.126858	+	0.154619i
$76$	32.7779	+	18.9243i	3.75988	+	2.17077i
$77$	−1.10597	−	0.628225i	−0.126037	−	0.0715929i
$78$	11.0676	−	1.82578i	1.25316	−	0.206729i
$79$	5.20988	+	9.02378i	0.586157	+	1.01525i	0.994730	+	0.102529i	$0.0326933\pi$
$79$	5.20988	+	9.02378i	0.586157	+	1.01525i	−0.408573	+	0.912726i	$0.633973\pi$
$80$	11.0272			1.23288
$81$	7.14305	−	5.47511i	0.793672	−	0.608346i
$82$		−	23.1732i		−	2.55906i
$83$	−3.09425	−	5.35940i	−0.339638	−	0.588271i	0.644726	−	0.764413i	$-0.276971\pi$
$83$	−3.09425	−	5.35940i	−0.339638	−	0.588271i	−0.984365	+	0.176143i	$0.943638\pi$
$84$	22.5959	−	3.89069i	2.46542	−	0.424509i
$85$	−0.837607	+	1.45078i	−0.0908512	+	0.157359i
$86$	−26.2917	−	15.1795i	−2.83510	−	1.63685i
$87$	3.32467	−	2.72776i	0.356442	−	0.292447i
$88$	1.91054	+	3.30915i	0.203664	+	0.352757i
$89$	11.7120			1.24147			0.620733	−	0.784022i	$-0.286835\pi$
$89$	11.7120			1.24147			0.620733	+	0.784022i	$0.286835\pi$
$90$	−2.55000	−	7.51852i	−0.268793	−	0.792521i
$91$	−0.0454493	−	6.47452i	−0.00476438	−	0.678714i
$92$	−14.3989	+	8.31323i	−1.50119	+	0.866714i
$93$	15.1526	+	5.70529i	1.57125	+	0.591611i
$94$	−1.98898	−	1.14834i	−0.205147	−	0.118442i
$95$	−6.55113	−	3.78229i	−0.672131	−	0.388055i
$96$	−21.5359	−	8.10875i	−2.19800	−	0.827596i
$97$	−12.3950	+	7.15625i	−1.25852	+	0.726607i	−0.972787	−	0.231702i	$-0.925570\pi$
$97$	−12.3950	+	7.15625i	−1.25852	+	0.726607i	−0.285733	+	0.958309i	$0.592237\pi$
$98$	−0.260064	−	18.5229i	−0.0262705	−	1.87110i
$99$	0.951226	−	1.08409i	0.0956018	−	0.108955i
$100$	−5.00340			−0.500340
$101$	−4.47001	−	7.74228i	−0.444782	−	0.770385i	0.553255	−	0.833012i	$-0.313386\pi$
$101$	−4.47001	−	7.74228i	−0.444782	−	0.770385i	−0.998037	+	0.0626267i	$0.980052\pi$
$102$	5.93632	−	4.87051i	0.587783	−	0.482252i
$103$	3.19538	+	1.84485i	0.314850	+	0.181779i	0.649095	−	0.760708i	$-0.275148\pi$
$103$	3.19538	+	1.84485i	0.314850	+	0.181779i	−0.334245	+	0.942486i	$0.608481\pi$
$104$	−9.72537	+	16.8448i	−0.953651	+	1.65177i
$105$	−4.51612	+	0.777609i	−0.440728	+	0.0758869i
$106$	−9.47283	−	16.4074i	−0.920083	−	1.59363i
$107$		−	15.8496i		−	1.53224i	−0.642696	−	0.766121i	$-0.722184\pi$
$107$		−	15.8496i		−	1.53224i	0.642696	−	0.766121i	$-0.277816\pi$
$108$	−0.860851	+	25.9841i	−0.0828354	+	2.50033i
$109$	0.387096			0.0370771			0.0185386	−	0.999828i	$-0.494099\pi$
$109$	0.387096			0.0370771			0.0185386	+	0.999828i	$0.494099\pi$
$110$	−0.636127	−	1.10180i	−0.0606523	−	0.105053i
$111$	−7.43337	+	1.22625i	−0.705544	+	0.116391i
$112$	−14.4099	+	25.3682i	−1.36160	+	2.39707i
$113$	11.7616	+	6.79054i	1.10643	+	0.638800i	0.937904	−	0.346896i	$-0.112764\pi$
$113$	11.7616	+	6.79054i	1.10643	+	0.638800i	0.168531	+	0.985696i	$0.446098\pi$
$114$	21.9933	+	26.8060i	2.05986	+	2.51061i
$115$	2.87783	−	1.66152i	0.268359	−	0.154937i
$116$			12.4228i			1.15343i
$117$	7.20016	+	1.43416i	0.665655	+	0.132588i
$118$		−	25.9192i		−	2.38606i
$119$	−2.24299	−	3.82275i	−0.205614	−	0.350431i
$120$	12.8836	+	4.85098i	1.17611	+	0.442832i
$121$	−5.38444	+	9.32612i	−0.489495	+	0.847829i
$122$	−11.6134	+	20.1151i	−1.05143	+	1.82113i
$123$	5.34435	−	14.1940i	0.481884	−	1.27983i
$124$	−40.5052	+	23.3857i	−3.63747	+	2.10009i
$125$	1.00000			0.0894427
$126$	20.6287	+	3.95858i	1.83775	+	0.352658i
$127$	−11.5404			−1.02405			−0.512023	−	0.858972i	$-0.671104\pi$
$127$	−11.5404			−1.02405			−0.512023	+	0.858972i	$0.671104\pi$
$128$	7.02362	−	4.05509i	0.620806	−	0.358422i
$129$	−12.6033	−	15.3612i	−1.10966	−	1.35248i
$130$	3.23813	−	5.60860i	0.284002	−	0.491907i
$131$	3.11736	−	5.39943i	0.272365	−	0.471751i	−0.697102	−	0.716972i	$-0.745527\pi$
$131$	3.11736	−	5.39943i	0.272365	−	0.471751i	0.969467	+	0.245222i	$0.0788607\pi$
$132$	0.678125	+	4.11069i	0.0590232	+	0.357790i
$133$	17.2620	−	10.1284i	1.49680	−	0.878246i
$134$		−	4.34576i		−	0.375416i
$135$	0.172053	−	5.19330i	0.0148080	−	0.446968i
$136$			13.3149i			1.14174i
$137$	−8.06205	+	4.65462i	−0.688787	+	0.397671i	−0.803157	−	0.595767i	$-0.796848\pi$
$137$	−8.06205	+	4.65462i	−0.688787	+	0.397671i	0.114370	+	0.993438i	$0.463515\pi$
$138$	−15.0286	+	2.47922i	−1.27932	+	0.211045i
$139$	−5.73961	−	3.31377i	−0.486828	−	0.281070i	0.236430	−	0.971649i	$-0.424023\pi$
$139$	−5.73961	−	3.31377i	−0.486828	−	0.281070i	−0.723257	+	0.690579i	$0.757356\pi$
$140$	6.53823	−	11.5104i	0.552582	−	0.972806i
$141$	−0.953442	−	1.16208i	−0.0802943	−	0.0978650i
$142$	−5.87549	−	10.1766i	−0.493060	−	0.854005i
$143$	1.17649			0.0983832
$144$	−24.8663	−	21.8187i	−2.07219	−	1.81822i
$145$		−	2.48288i		−	0.206192i
$146$	−12.0479	−	20.8676i	−0.997092	−	1.72701i
$147$	4.11258	−	11.4056i	0.339200	−	0.940714i
$148$	10.8815	−	18.8474i	0.894457	−	1.54924i
$149$	−1.90195	−	1.09809i	−0.155814	−	0.0899593i	0.420066	−	0.907494i	$-0.362007\pi$
$149$	−1.90195	−	1.09809i	−0.155814	−	0.0899593i	−0.575880	+	0.817534i	$0.695340\pi$
$150$	−4.28969	−	1.61517i	−0.350252	−	0.131878i
$151$	7.34693	+	12.7253i	0.597885	+	1.03557i	0.993133	+	0.116992i	$0.0373253\pi$
$151$	7.34693	+	12.7253i	0.597885	+	1.03557i	−0.395248	+	0.918574i	$0.629341\pi$
$152$	−60.1246			−4.87675
$153$	4.75936	−	1.61419i	0.384771	−	0.130500i
$154$	3.36599	−	0.0236283i	0.271239	−	0.00190402i
$155$	8.09553	−	4.67396i	0.650249	−	0.375421i
$156$	−16.3956	+	13.4519i	−1.31270	+	1.07702i
$157$	0.189863	+	0.109618i	0.0151527	+	0.00874843i	0.507557	−	0.861618i	$-0.330549\pi$
$157$	0.189863	+	0.109618i	0.0151527	+	0.00874843i	−0.492405	+	0.870366i	$0.663882\pi$
$158$	−23.8805	−	13.7874i	−1.89983	−	1.09687i
$159$	−2.01828	−	12.2345i	−0.160060	−	0.970258i
$160$	−11.5059	+	6.64295i	−0.909624	+	0.525172i
$161$	0.0617153	+	8.79171i	0.00486385	+	0.692884i
$162$	−9.12610	+	21.9998i	−0.717014	+	1.72846i
$163$	0.189405			0.0148353			0.00741767	−	0.999972i	$-0.497639\pi$
$163$	0.189405			0.0148353			0.00741767	+	0.999972i	$0.497639\pi$
$164$	21.9062	+	37.9427i	1.71059	+	2.96283i
$165$	−0.135533	−	0.821580i	−0.0105512	−	0.0639599i
$166$	14.1831	+	8.18861i	1.10082	+	0.635559i
$167$	7.34495	−	12.7218i	0.568369	−	0.984444i	−0.428358	−	0.903609i	$-0.640908\pi$
$167$	7.34495	−	12.7218i	0.568369	−	0.984444i	0.996727	−	0.0808354i	$-0.0257588\pi$
$168$	−27.9956	+	23.2999i	−2.15990	+	1.79763i
$169$	−3.50561	−	6.07189i	−0.269662	−	0.467069i
$170$		−	4.43327i		−	0.340017i
$171$	7.28904	+	21.4913i	0.557407	+	1.64348i
$172$	57.3982			4.37657
$173$	6.72946	+	11.6558i	0.511632	+	0.886172i	0.999909	+	0.0134836i	$0.00429208\pi$
$173$	6.72946	+	11.6558i	0.511632	+	0.886172i	−0.488277	+	0.872688i	$0.662375\pi$
$174$	−4.01027	+	10.6508i	−0.304018	+	0.807435i
$175$	−1.30676	+	2.30052i	−0.0987817	+	0.173903i
$176$	−4.59108	−	2.65066i	−0.346065	−	0.199801i
$177$	5.97765	−	15.8759i	0.449308	−	1.19331i
$178$	−26.8420	+	15.4972i	−2.01189	+	1.16157i
$179$			9.89757i			0.739779i	0.929076	+	0.369890i	$0.120604\pi$
$179$			9.89757i			0.739779i	−0.929076	+	0.369890i	$0.879396\pi$
$180$	11.2827	+	9.89986i	0.840960	+	0.737892i
$181$		−	2.15683i		−	0.160316i	−0.996782	−	0.0801579i	$-0.974458\pi$
$181$		−	2.15683i		−	0.160316i	0.996782	−	0.0801579i	$-0.0255424\pi$
$182$	8.67123	+	14.7785i	0.642754	+	1.09545i
$183$	−11.7525	+	9.64244i	−0.868768	+	0.712789i
$184$	13.2060	−	22.8735i	0.973560	−	1.68626i
$185$	−2.17483	+	3.76692i	−0.159897	+	0.276949i
$186$	−42.2765	+	6.97420i	−3.09987	+	0.511373i
$187$	0.697462	−	0.402680i	0.0510035	−	0.0294469i
$188$	4.34219			0.316687
$189$	11.7225	+	7.18221i	0.852683	+	0.522429i
$190$	20.0189			1.45232
$191$	6.81409	−	3.93412i	0.493051	−	0.284663i	−0.232789	−	0.972527i	$-0.574785\pi$
$191$	6.81409	−	3.93412i	0.493051	−	0.284663i	0.725839	+	0.687864i	$0.241452\pi$
$192$	22.3965	−	3.69466i	1.61633	−	0.266639i
$193$	−0.497334	+	0.861407i	−0.0357989	+	0.0620054i	−0.883370	−	0.468677i	$-0.844731\pi$
$193$	−0.497334	+	0.861407i	−0.0357989	+	0.0620054i	0.847571	+	0.530682i	$0.178064\pi$
$194$	18.9382	−	32.8020i	1.35969	−	2.35505i
$195$	3.27689	−	2.68856i	0.234663	−	0.192532i
$196$	17.9360	+	30.0826i	1.28114	+	2.14876i
$197$			4.69706i			0.334652i	0.985902	+	0.167326i	$0.0535132\pi$
$197$			4.69706i			0.334652i	−0.985902	+	0.167326i	$0.946487\pi$
$198$	−0.745594	+	3.74323i	−0.0529870	+	0.266020i
$199$		−	9.68483i		−	0.686539i	−0.939237	−	0.343270i	$-0.888466\pi$
$199$		−	9.68483i		−	0.686539i	0.939237	−	0.343270i	$-0.111534\pi$
$200$	6.88331	−	3.97408i	0.486724	−	0.281010i
$201$	1.00224	−	2.66184i	0.0706929	−	0.187752i
$202$	20.4891	+	11.8294i	1.44161	+	0.832313i
$203$	5.71192	+	3.24453i	0.400898	+	0.227721i
$204$	−5.11562	+	13.5865i	−0.358165	+	0.951243i
$205$	−4.37827	−	7.58339i	−0.305792	−	0.529647i
$206$	−9.76441			−0.680318
$207$	−9.77704	−	1.94744i	−0.679551	−	0.135356i
$208$		−	26.9857i		−	1.87112i
$209$	1.81834	+	3.14946i	0.125777	+	0.217852i
$210$	9.32131	−	7.75787i	0.643231	−	0.535344i
$211$	1.26986	−	2.19946i	0.0874206	−	0.151417i	−0.819000	−	0.573794i	$-0.805471\pi$
$211$	1.26986	−	2.19946i	0.0874206	−	0.151417i	0.906420	+	0.422377i	$0.138804\pi$
$212$	31.0206	+	17.9098i	2.13051	+	1.23005i
$213$	−1.25183	−	7.58839i	−0.0857739	−	0.519948i
$214$	20.9722	+	36.3249i	1.43363	+	2.48312i
$215$	−11.4718			−0.782373
$216$	−19.4543	−	36.4309i	−1.32370	−	2.47881i
$217$	0.173609	+	24.7317i	0.0117854	+	1.67889i
$218$	−0.887165	+	0.512205i	−0.0600864	+	0.0346909i
$219$	−2.56692	−	15.5603i	−0.173456	−	1.05147i
$220$	2.08312	+	1.20269i	0.140444	+	0.0810855i
$221$	3.55034	+	2.04979i	0.238822	+	0.137884i
$222$	15.4135	−	12.6462i	1.03449	−	0.848757i
$223$	−8.28018	+	4.78057i	−0.554482	+	0.320130i	−0.750928	−	0.660384i	$-0.770393\pi$
$223$	−8.28018	+	4.78057i	−0.554482	+	0.320130i	0.196446	+	0.980515i	$0.437060\pi$
$224$	−0.246746	−	35.1503i	−0.0164864	−	2.34858i
$225$	−2.25500	−	1.97863i	−0.150333	−	0.131909i
$226$	−35.9409			−2.39075
$227$	−11.4471	−	19.8269i	−0.759769	−	1.31596i	−0.942968	−	0.332883i	$-0.891979\pi$
$227$	−11.4471	−	19.8269i	−0.759769	−	1.31596i	0.183199	−	0.983076i	$-0.441355\pi$
$228$	−61.3510	−	23.1000i	−4.06307	−	1.52984i
$229$	1.40123	+	0.808999i	0.0925957	+	0.0534602i	0.545583	−	0.838057i	$-0.316308\pi$
$229$	1.40123	+	0.808999i	0.0925957	+	0.0534602i	−0.452987	+	0.891517i	$0.649642\pi$
$230$	−4.39703	+	7.61588i	−0.289931	+	0.502176i
$231$	2.06717	+	0.761811i	0.136010	+	0.0501235i
$232$	−9.86718	−	17.0905i	−0.647812	−	1.12204i
$233$		−	6.57892i		−	0.430999i	−0.976504	−	0.215500i	$-0.930862\pi$
$233$		−	6.57892i		−	0.430999i	0.976504	−	0.215500i	$-0.0691380\pi$
$234$	−18.3993	+	6.24035i	−1.20280	+	0.407944i
$235$	−0.867849			−0.0566123
$236$	24.5021	+	42.4388i	1.59495	+	2.76253i
$237$	−11.4474	−	13.9524i	−0.743590	−	0.906309i
$238$	10.1988	+	5.79322i	0.661092	+	0.375519i
$239$	8.73965	+	5.04584i	0.565321	+	0.326388i	0.755278	−	0.655404i	$-0.227502\pi$
$239$	8.73965	+	5.04584i	0.565321	+	0.326388i	−0.189958	+	0.981792i	$0.560835\pi$
$240$	−18.8449	+	3.10878i	−1.21643	+	0.200671i
$241$	11.9883	−	6.92143i	0.772232	−	0.445848i	−0.0614383	−	0.998111i	$-0.519569\pi$
$241$	11.9883	−	6.92143i	0.772232	−	0.445848i	0.833670	+	0.552263i	$0.186235\pi$
$242$		−	28.4987i		−	1.83196i
$243$	−10.6636	+	11.3705i	−0.684070	+	0.729416i
$244$		−	43.9139i		−	2.81130i
$245$	−3.58476	−	6.01244i	−0.229022	−	0.384121i
$246$	6.53299	+	39.6020i	0.416528	+	2.52493i
$247$	−9.25603	+	16.0319i	−0.588947	+	1.02009i
$248$	37.1494	−	64.3446i	2.35899	−	4.08589i
$249$	6.79885	+	8.28664i	0.430860	+	0.525144i
$250$	−2.29184	+	1.32320i	−0.144949	+	0.0836863i
$251$	−12.2445			−0.772864			−0.386432	−	0.922318i	$-0.626293\pi$
$251$	−12.2445			−0.772864			−0.386432	+	0.922318i	$0.626293\pi$
$252$	−37.5185	+	13.0192i	−2.36344	+	0.820134i
$253$	−1.59755			−0.100437
$254$	26.4488	−	15.2702i	1.65955	−	0.958139i
$255$	1.02243	−	2.71545i	0.0640270	−	0.170048i
$256$	2.37403	−	4.11194i	0.148377	−	0.256996i
$257$	0.661944	−	1.14652i	0.0412910	−	0.0715180i	−0.844641	−	0.535333i	$-0.820186\pi$
$257$	0.661944	−	1.14652i	0.0412910	−	0.0715180i	0.885932	+	0.463815i	$0.153520\pi$
$258$	49.2106	+	18.5289i	3.06372	+	1.15356i
$259$	−5.82388	−	9.92569i	−0.361878	−	0.616752i
$260$			12.2443i			0.759360i
$261$	−4.91270	+	5.59891i	−0.304089	+	0.346564i
$262$			16.4995i			1.01934i
$263$	14.2887	−	8.24957i	0.881078	−	0.508690i	0.0100641	−	0.999949i	$-0.496796\pi$
$263$	14.2887	−	8.24957i	0.881078	−	0.508690i	0.871014	+	0.491259i	$0.163463\pi$
$264$	−4.19794	−	5.11657i	−0.258365	−	0.314903i
$265$	−6.19992	−	3.57953i	−0.380858	−	0.219888i
$266$	−26.1598	+	46.0538i	−1.60396	+	2.82374i
$267$	−20.0152	+	3.30183i	−1.22491	+	0.202069i
$268$	4.10815	+	7.11552i	0.250945	+	0.434649i
$269$	19.0205			1.15970			0.579850	−	0.814723i	$-0.303111\pi$
$269$	19.0205			1.15970			0.579850	+	0.814723i	$0.303111\pi$
$270$	6.47744	+	12.1299i	0.394204	+	0.738202i
$271$		−	24.0830i		−	1.46294i	−0.681874	−	0.731469i	$-0.738835\pi$
$271$		−	24.0830i		−	1.46294i	0.681874	−	0.731469i	$-0.261165\pi$
$272$	−9.23644	−	15.9980i	−0.560041	−	0.970020i
$273$	1.90296	+	11.0518i	0.115173	+	0.668888i
$274$	12.3180	−	21.3353i	0.744155	−	1.28891i
$275$	−0.416342	−	0.240375i	−0.0251064	−	0.0144952i
$276$	22.2634	−	18.2663i	1.34010	−	1.09950i
$277$	−7.15729	−	12.3968i	−0.430040	−	0.744851i	0.566836	−	0.823830i	$-0.308167\pi$
$277$	−7.15729	−	12.3968i	−0.430040	−	0.744851i	−0.996876	+	0.0789793i	$0.974834\pi$
$278$	17.5391			1.05192
$279$	−27.5035	−	5.47827i	−1.64659	−	0.327975i
$280$	0.147613	+	21.0283i	0.00882157	+	1.25668i
$281$	−2.01049	+	1.16076i	−0.119936	+	0.0692449i	−0.558768	−	0.829324i	$-0.688726\pi$
$281$	−2.01049	+	1.16076i	−0.119936	+	0.0692449i	0.438832	+	0.898569i	$0.355392\pi$
$282$	3.72280	+	1.40172i	0.221690	+	0.0834712i
$283$	−12.8584	−	7.42377i	−0.764350	−	0.441297i	0.0665056	−	0.997786i	$-0.478815\pi$
$283$	−12.8584	−	7.42377i	−0.764350	−	0.441297i	−0.830855	+	0.556489i	$0.812148\pi$
$284$	19.2404	+	11.1085i	1.14171	+	0.659167i
$285$	12.2619	+	4.61687i	0.726330	+	0.273480i
$286$	−2.69634	+	1.55673i	−0.159438	+	0.0920514i
$287$	23.1671	−	0.162626i	1.36751	−	0.00959953i
$288$	39.0898	+	7.78609i	2.30339	+	0.458800i
$289$	−14.1937			−0.834921
$290$	3.28534	+	5.69038i	0.192922	+	0.334151i
$291$	19.1650	−	15.7241i	1.12347	−	0.921762i
$292$	39.4532	+	22.7783i	2.30883	+	1.33300i
$293$	−7.64032	+	13.2334i	−0.446352	+	0.773105i	−0.998145	−	0.0608761i	$-0.980611\pi$
$293$	−7.64032	+	13.2334i	−0.446352	+	0.773105i	0.551793	+	0.833981i	$0.313944\pi$
$294$	5.66641	+	31.5815i	0.330472	+	1.84187i
$295$	−4.89709	−	8.48201i	−0.285120	−	0.493842i
$296$			34.5718i			2.00945i
$297$	−1.31997	+	2.12083i	−0.0765927	+	0.123063i
$298$	5.81197			0.336679
$299$	−4.06606	−	7.04263i	−0.235147	−	0.407286i
$300$	8.55057	−	1.41055i	0.493667	−	0.0814384i
$301$	14.9909	−	26.3912i	0.864063	−	1.52116i
$302$	−33.6760	−	19.4429i	−1.93784	−	1.11881i
$303$	9.82173	+	11.9710i	0.564244	+	0.687716i
$304$	72.2404	−	41.7080i	4.14327	−	2.39212i
$305$			8.77681i			0.502559i
$306$	−8.77180	+	9.99704i	−0.501451	+	0.571493i
$307$			28.1095i			1.60429i	0.597126	+	0.802147i	$0.296309\pi$
$307$			28.1095i			1.60429i	−0.597126	+	0.802147i	$0.703691\pi$
$308$	−5.48895	+	3.22063i	−0.312762	+	0.183513i
$309$	−5.98085	−	2.25193i	−0.340239	−	0.128108i
$310$	−12.3691	+	21.4240i	−0.702520	+	1.21680i
$311$	−11.8328	+	20.4951i	−0.670979	+	1.16217i	0.306648	+	0.951823i	$0.400792\pi$
$311$	−11.8328	+	20.4951i	−0.670979	+	1.16217i	−0.977627	+	0.210346i	$0.932541\pi$
$312$	11.8713	−	31.5288i	0.672081	−	1.78497i
$313$	0.558139	−	0.322242i	0.0315479	−	0.0182142i	−0.484143	−	0.874989i	$-0.660869\pi$
$313$	0.558139	−	0.322242i	0.0315479	−	0.0182142i	0.515691	+	0.856775i	$0.327535\pi$
$314$	−0.580182			−0.0327416
$315$	7.49861	−	2.60208i	0.422499	−	0.146611i
$316$	52.1342			2.93278
$317$	−0.0222580	+	0.0128507i	−0.00125013	+	0.000721765i	−0.500625	−	0.865664i	$-0.666896\pi$
$317$	−0.0222580	+	0.0128507i	−0.00125013	+	0.000721765i	0.499375	+	0.866386i	$0.333563\pi$
$318$	20.8142	+	25.3689i	1.16720	+	1.42262i
$319$	−0.596824	+	1.03373i	−0.0334157	+	0.0578777i
$320$	6.55269	−	11.3496i	0.366307	−	0.634462i
$321$	4.46832	+	27.0863i	0.249397	+	1.51181i
$322$	−11.7746	−	20.0676i	−0.656173	−	1.11832i
$323$			12.6723i			0.705106i
$324$	−5.85428	−	44.6484i	−0.325238	−	2.48047i
$325$		−	2.44720i		−	0.135746i
$326$	−0.434086	+	0.250620i	−0.0240418	+	0.0138805i
$327$	−0.661530	+	0.109130i	−0.0365827	+	0.00603490i
$328$	−60.2740	−	34.7992i	−3.32807	−	1.92146i
$329$	1.13407	−	1.99650i	0.0625233	−	0.110071i
$330$	1.39773	+	1.70360i	0.0769426	+	0.0937799i
$331$	7.89959	+	13.6825i	0.434201	+	0.752058i	0.997230	−	0.0743793i	$-0.0236976\pi$
$331$	7.89959	+	13.6825i	0.434201	+	0.752058i	−0.563029	+	0.826437i	$0.690364\pi$
$332$	−30.9635			−1.69934
$333$	12.3576	−	4.19122i	0.677191	−	0.229678i
$334$			38.8752i			2.12716i
$335$	−0.821072	−	1.42214i	−0.0448599	−	0.0776997i
$336$	17.4740	−	47.4155i	0.953284	−	2.58673i
$337$	15.8902	−	27.5227i	0.865595	−	1.49926i	−0.000859299	−	1.00000i	$-0.500274\pi$
$337$	15.8902	−	27.5227i	0.865595	−	1.49926i	0.866455	−	0.499256i	$-0.166393\pi$
$338$	16.0686	+	9.27722i	0.874017	+	0.504614i
$339$	−22.0143	−	8.28891i	−1.19566	−	0.450192i
$340$	4.19088	+	7.25882i	0.227282	+	0.393665i
$341$	−4.49401			−0.243365
$342$	−45.1426	−	39.6099i	−2.44103	−	2.14186i
$343$	18.5162	−	0.389986i	0.999778	−	0.0210573i
$344$	−78.9643	+	45.5900i	−4.25747	+	2.45805i
$345$	−4.44967	+	3.65077i	−0.239562	+	0.196551i
$346$	−30.8458	−	17.8088i	−1.65828	−	0.957407i
$347$	27.7552	+	16.0245i	1.48998	+	0.860238i	0.999934	−	0.0114614i	$-0.00364835\pi$
$347$	27.7552	+	16.0245i	1.48998	+	0.860238i	0.490041	+	0.871699i	$0.336982\pi$
$348$	−3.50224	−	21.2301i	−0.187740	−	1.13805i
$349$	8.08075	−	4.66543i	0.432553	−	0.249735i	−0.267881	−	0.963452i	$-0.586323\pi$
$349$	8.08075	−	4.66543i	0.432553	−	0.249735i	0.700434	+	0.713718i	$0.252990\pi$
$350$	−0.0491488	−	7.00152i	−0.00262711	−	0.374247i
$351$	−12.7090	−	0.421049i	−0.678359	−	0.0224739i
$352$	6.38720			0.340439
$353$	−3.71199	−	6.42935i	−0.197569	−	0.342200i	0.750171	−	0.661244i	$-0.229971\pi$
$353$	−3.71199	−	6.42935i	−0.197569	−	0.342200i	−0.947740	+	0.319045i	$0.896638\pi$
$354$	7.30714	+	44.2948i	0.388370	+	2.35424i
$355$	−3.84548	−	2.22019i	−0.204097	−	0.117835i
$356$	29.2998	−	50.7487i	1.55289	−	2.68968i
$357$	4.91087	+	5.90055i	0.259911	+	0.312290i
$358$	−13.0964	−	22.6837i	−0.692168	−	1.19887i
$359$		−	10.1776i		−	0.537155i	−0.963258	−	0.268578i	$-0.913446\pi$
$359$		−	10.1776i		−	0.537155i	0.963258	−	0.268578i	$-0.0865536\pi$
$360$	−23.3851	−	4.65795i	−1.23250	−	0.245496i
$361$	−38.2230			−2.01174
$362$	2.85391	+	4.94311i	0.149998	+	0.259804i
$363$	6.57254	−	17.4559i	0.344969	−	0.916196i
$364$	−28.1682	−	16.0004i	−1.47642	−	0.838647i
$365$	−7.88529	−	4.55258i	−0.412735	−	0.238293i
$366$	14.1760	−	37.6498i	0.740992	−	1.96799i
$367$	−14.2963	+	8.25396i	−0.746260	+	0.430853i	−0.824341	−	0.566094i	$-0.808454\pi$
$367$	−14.2963	+	8.25396i	−0.746260	+	0.430853i	0.0780812	+	0.996947i	$0.475121\pi$
$368$			36.6437i			1.91018i
$369$	−5.13170	+	25.7635i	−0.267145	+	1.34119i
$370$		−	11.5109i		−	0.598424i
$371$	16.3366	−	9.58544i	0.848152	−	0.497651i
$372$	62.6286	−	51.3842i	3.24714	−	2.66415i
$373$	−9.94969	+	17.2334i	−0.515176	+	0.892310i	0.484669	+	0.874698i	$0.338940\pi$
$373$	−9.94969	+	17.2334i	−0.515176	+	0.892310i	−0.999845	+	0.0176129i	$0.994393\pi$
$374$	−1.06565	+	1.84576i	−0.0551034	+	0.0954419i
$375$	−1.70895	+	0.281919i	−0.0882500	+	0.0145583i
$376$	−5.97368	+	3.44890i	−0.308069	+	0.177864i
$377$	−6.07611			−0.312936
$378$	−36.3695	−	0.949392i	−1.87065	−	0.0488314i
$379$	−8.97114			−0.460817			−0.230408	−	0.973094i	$-0.574006\pi$
$379$	−8.97114			−0.460817			−0.230408	+	0.973094i	$0.574006\pi$
$380$	−32.7779	+	18.9243i	−1.68147	+	0.970797i
$381$	19.7220	−	3.25347i	1.01039	−	0.166680i
$382$	−10.4112	+	18.0328i	−0.532685	+	0.922637i
$383$	−13.3051	+	23.0451i	−0.679860	+	1.17755i	0.295163	+	0.955447i	$0.404626\pi$
$383$	−13.3051	+	23.0451i	−0.679860	+	1.17755i	−0.975023	+	0.222105i	$0.928707\pi$
$384$	−10.8598	+	8.91005i	−0.554188	+	0.454689i
$385$	1.09705	−	0.643690i	0.0559106	−	0.0328055i
$386$		−	2.63228i		−	0.133980i
$387$	25.8690	+	22.6985i	1.31500	+	1.15383i
$388$			71.6111i			3.63550i
$389$	−5.36341	+	3.09657i	−0.271936	+	0.157002i	−0.629767	−	0.776784i	$-0.716850\pi$
$389$	−5.36341	+	3.09657i	−0.271936	+	0.157002i	0.357831	+	0.933786i	$0.383516\pi$
$390$	−3.95263	+	10.4977i	−0.200149	+	0.531573i
$391$	−4.82099	−	2.78340i	−0.243808	−	0.140762i
$392$	−48.5690	−	27.1394i	−2.45310	−	1.37075i
$393$	−3.80522	+	10.1062i	−0.191948	+	0.509792i
$394$	−6.21514	−	10.7649i	−0.313114	−	0.542330i
$395$	−10.4198			−0.524275
$396$	−2.31777	−	6.83380i	−0.116472	−	0.343411i
$397$			18.2059i			0.913728i	0.889537	+	0.456864i	$0.151027\pi$
$397$			18.2059i			0.913728i	−0.889537	+	0.456864i	$0.848973\pi$
$398$	12.8149	+	22.1961i	0.642354	+	1.11259i
$399$	−26.6445	+	22.1755i	−1.33389	+	1.11016i
$400$	−5.51359	+	9.54981i	−0.275679	+	0.477491i
$401$	−10.5752	−	6.10560i	−0.528101	−	0.304899i	0.212142	−	0.977239i	$-0.431956\pi$
$401$	−10.5752	−	6.10560i	−0.528101	−	0.304899i	−0.740243	+	0.672340i	$0.765289\pi$
$402$	1.22515	+	7.42669i	0.0611051	+	0.370410i
$403$	−11.4381	−	19.8114i	−0.569773	−	0.986875i
$404$	−44.7304			−2.22542
$405$	1.17006	+	8.92362i	0.0581409	+	0.443418i
$406$	−17.3840	+	0.122031i	−0.862752	+	0.00605628i
$407$	1.81095	−	1.04555i	0.0897653	−	0.0518260i
$408$	−3.75372	−	22.7545i	−0.185837	−	1.12652i
$409$	8.51078	+	4.91370i	0.420831	+	0.242967i	0.695433	−	0.718591i	$-0.255213\pi$
$409$	8.51078	+	4.91370i	0.420831	+	0.242967i	−0.274602	+	0.961558i	$0.588546\pi$
$410$	20.0686	+	11.5866i	0.991118	+	0.572222i
$411$	12.4654	−	10.2274i	0.614874	−	0.504480i
$412$	15.9877	−	9.23052i	0.787659	−	0.454755i
$413$	25.9123	−	0.181897i	1.27506	−	0.00895058i
$414$	24.9843	−	8.47373i	1.22791	−	0.416461i
$415$	6.18850			0.303782
$416$	16.2566	+	28.1573i	0.797047	+	1.38053i
$417$	10.7429	+	4.04496i	0.526084	+	0.198083i
$418$	−8.33470	−	4.81204i	−0.407663	−	0.235365i
$419$	−6.80583	+	11.7880i	−0.332486	+	0.575883i	−0.982999	−	0.183612i	$-0.941221\pi$
$419$	−6.80583	+	11.7880i	−0.332486	+	0.575883i	0.650512	+	0.759496i	$0.274554\pi$
$420$	−7.92853	+	21.5140i	−0.386873	+	1.04978i
$421$	−5.81042	−	10.0639i	−0.283183	−	0.490487i	0.688984	−	0.724776i	$-0.258057\pi$
$421$	−5.81042	−	10.0639i	−0.283183	−	0.490487i	−0.972167	+	0.234290i	$0.924724\pi$
$422$			6.72108i			0.327177i
$423$	1.95700	+	1.71715i	0.0951527	+	0.0834908i
$424$	−56.9013			−2.76337
$425$	−0.837607	−	1.45078i	−0.0406299	−	0.0703731i
$426$	12.9099	+	15.7350i	0.625488	+	0.762363i
$427$	−20.1912	−	11.4692i	−0.977121	−	0.555033i
$428$	−68.6775	−	39.6510i	−3.31965	−	1.91660i
$429$	−2.01057	+	0.331676i	−0.0970712	+	0.0160135i
$430$	26.2917	−	15.1795i	1.26790	−	0.732020i
$431$		−	18.4817i		−	0.890234i	−0.895472	−	0.445117i	$-0.853162\pi$
$431$		−	18.4817i		−	0.890234i	0.895472	−	0.445117i	$-0.146838\pi$
$432$	48.6464	+	30.2768i	2.34050	+	1.45669i
$433$		−	24.7189i		−	1.18791i	−0.804496	−	0.593957i	$-0.797565\pi$
$433$		−	24.7189i		−	1.18791i	0.804496	−	0.593957i	$-0.202435\pi$
$434$	−33.1227	−	56.4514i	−1.58994	−	2.70975i
$435$	0.699973	+	4.24313i	0.0335611	+	0.203443i
$436$	0.968398	−	1.67732i	0.0463779	−	0.0803288i
$437$	12.5687	−	21.7696i	0.601242	−	1.04138i
$438$	26.4723	+	32.2652i	1.26489	+	1.54169i
$439$	7.73659	−	4.46672i	0.369247	−	0.213185i	−0.303882	−	0.952710i	$-0.598283\pi$
$439$	7.73659	−	4.46672i	0.369247	−	0.213185i	0.673130	+	0.739525i	$0.264950\pi$
$440$	−3.82108			−0.182163
$441$	−3.81275	+	20.6510i	−0.181560	+	0.983380i
$442$	−10.8491			−0.516039
$443$	10.4862	−	6.05424i	0.498217	−	0.287646i	−0.229760	−	0.973247i	$-0.573794\pi$
$443$	10.4862	−	6.05424i	0.498217	−	0.287646i	0.727977	+	0.685602i	$0.240461\pi$
$444$	−13.2826	+	35.2770i	−0.630364	+	1.67417i
$445$	−5.85598	+	10.1429i	−0.277600	+	0.480818i
$446$	12.6513	−	21.9126i	0.599054	−	1.03759i
$447$	3.55992	+	1.34039i	0.168379	+	0.0633984i
$448$	17.5471	+	29.9058i	0.829025	+	1.41291i
$449$		−	23.6639i		−	1.11677i	−0.829582	−	0.558385i	$-0.811421\pi$
$449$		−	23.6639i		−	1.11677i	0.829582	−	0.558385i	$-0.188579\pi$
$450$	7.78622	+	1.55090i	0.367046	+	0.0731099i
$451$			4.20971i			0.198227i
$452$	58.8478	−	33.9758i	2.76797	−	1.59809i
$453$	−16.1431	−	19.6756i	−0.758467	−	0.924442i
$454$	52.4698	+	30.2935i	2.46253	+	1.42174i
$455$	5.62982	+	3.19790i	0.263930	+	0.149920i
$456$	102.750	−	16.9503i	4.81171	−	0.793770i
$457$	9.11862	+	15.7939i	0.426551	+	0.738808i	0.996564	−	0.0828278i	$-0.0263951\pi$
$457$	9.11862	+	15.7939i	0.426551	+	0.738808i	−0.570013	+	0.821636i	$0.693062\pi$
$458$	−4.28186			−0.200078
$459$	−7.67844	+	4.10034i	−0.358399	+	0.191387i
$460$		−	16.6265i		−	0.775213i
$461$	−3.53911	−	6.12993i	−0.164833	−	0.285499i	0.771763	−	0.635910i	$-0.219375\pi$
$461$	−3.53911	−	6.12993i	−0.164833	−	0.285499i	−0.936596	+	0.350411i	$0.886042\pi$
$462$	−5.74565	+	0.989316i	−0.267312	+	0.0460272i
$463$	−14.2242	+	24.6370i	−0.661055	+	1.14498i	0.319284	+	0.947659i	$0.396558\pi$
$463$	−14.2242	+	24.6370i	−0.661055	+	1.14498i	−0.980339	+	0.197322i	$0.936776\pi$
$464$	23.7111	+	13.6896i	1.10076	+	0.635523i
$465$	−12.5172	+	10.2699i	−0.580472	+	0.476254i
$466$	8.70520	+	15.0778i	0.403261	+	0.698468i
$467$	31.3508			1.45074			0.725371	−	0.688358i	$-0.241668\pi$
$467$	31.3508			1.45074			0.725371	+	0.688358i	$0.241668\pi$
$468$	24.2269	−	27.6109i	1.11989	−	1.27632i
$469$	4.34460	−	0.0304978i	0.200615	−	0.00140826i
$470$	1.98898	−	1.14834i	0.0917446	−	0.0529688i
$471$	−0.355370	−	0.133805i	−0.0163746	−	0.00616541i
$472$	−67.4164	−	38.9229i	−3.10309	−	1.79157i
$473$	4.77621	+	2.75755i	0.219610	+	0.126792i
$474$	44.6975	+	16.8296i	2.05303	+	0.773011i
$475$	6.55113	−	3.78229i	0.300586	−	0.173544i
$476$	−22.1755	+	0.155666i	−1.01641	+	0.00713493i
$477$	6.89828	+	20.3392i	0.315850	+	0.931267i
$478$	−26.7065			−1.22153
$479$	17.6341	+	30.5432i	0.805725	+	1.39556i	0.915801	+	0.401633i	$0.131557\pi$
$479$	17.6341	+	30.5432i	0.805725	+	1.39556i	−0.110076	+	0.993923i	$0.535110\pi$
$480$	17.7903	−	14.5962i	0.812013	−	0.666224i
$481$	9.21840	+	5.32224i	0.420323	+	0.242673i
$482$	−18.3168	+	31.7257i	−0.834308	+	1.44506i
$483$	−2.58402	−	15.0072i	−0.117577	−	0.682852i
$484$	26.9405	+	46.6623i	1.22457	+	2.12101i
$485$		−	14.3125i		−	0.649897i
$486$	9.39392	−	40.1694i	0.426117	−	1.82212i
$487$	−8.56395			−0.388070			−0.194035	−	0.980995i	$-0.562157\pi$
$487$	−8.56395			−0.388070			−0.194035	+	0.980995i	$0.562157\pi$
$488$	34.8798	+	60.4135i	1.57893	+	2.73479i
$489$	−0.323684	+	0.0533969i	−0.0146375	+	0.00241469i
$490$	16.1714	+	9.03624i	0.730547	+	0.408216i
$491$	24.0809	+	13.9031i	1.08676	+	0.627439i	0.932711	−	0.360625i	$-0.117437\pi$
$491$	24.0809	+	13.9031i	1.08676	+	0.627439i	0.154045	+	0.988064i	$0.450770\pi$
$492$	−48.1335	−	58.6665i	−2.17002	−	2.64489i
$493$	−3.60211	+	2.07968i	−0.162231	+	0.0936641i
$494$		−	48.9902i		−	2.20417i
$495$	0.463239	+	1.36583i	0.0208210	+	0.0613896i
$496$			103.081i			4.62848i
$497$	10.1327	−	5.94534i	0.454513	−	0.266685i
$498$	−26.5467	−	9.99546i	−1.18959	−	0.447907i
$499$	−10.7626	+	18.6414i	−0.481801	+	0.834503i	−0.999782	−	0.0208887i	$-0.993350\pi$
$499$	−10.7626	+	18.6414i	−0.481801	+	0.834503i	0.517981	+	0.855392i	$0.326684\pi$
$500$	2.50170	−	4.33307i	0.111879	−	0.193781i
$501$	−8.96564	+	23.8117i	−0.400555	+	1.06383i
$502$	28.0624	−	16.2018i	1.25249	−	0.723123i
$503$	−4.51669			−0.201389			−0.100695	−	0.994917i	$-0.532106\pi$
$503$	−4.51669			−0.201389			−0.100695	+	0.994917i	$0.532106\pi$
$504$	41.2744	−	47.7110i	1.83851	−	2.12522i
$505$	8.94001			0.397825
$506$	3.66134	−	2.11387i	0.162766	−	0.0939731i
$507$	7.70270	+	9.38828i	0.342089	+	0.416948i
$508$	−28.8706	+	50.0054i	−1.28093	+	2.21863i
$509$	7.09838	−	12.2947i	0.314630	−	0.544955i	−0.664729	−	0.747085i	$-0.731453\pi$
$509$	7.09838	−	12.2947i	0.314630	−	0.544955i	0.979359	+	0.202130i	$0.0647862\pi$
$510$	1.24983	+	7.57626i	0.0553432	+	0.335482i
$511$	20.7775	−	12.1911i	0.919141	−	0.539304i
$512$			28.7856i			1.27215i
$513$	−18.5155	−	34.6727i	−0.817477	−	1.53084i
$514$			3.50353i			0.154534i
$515$	−3.19538	+	1.84485i	−0.140805	+	0.0812939i
$516$	−98.0908	+	16.1817i	−4.31821	+	0.712358i
$517$	0.361322	+	0.208609i	0.0158909	+	0.00917463i
$518$	26.4811	+	15.0420i	1.16351	+	0.660907i
$519$	−14.7863	−	18.0220i	−0.649048	−	0.791078i
$520$	−9.72537	−	16.8448i	−0.426486	−	0.738695i
$521$	−19.8625			−0.870194			−0.435097	−	0.900384i	$-0.643286\pi$
$521$	−19.8625			−0.870194			−0.435097	+	0.900384i	$0.643286\pi$
$522$	3.85069	−	19.3323i	0.168540	−	0.846151i
$523$			4.53244i			0.198190i	0.995078	+	0.0990949i	$0.0315947\pi$
$523$			4.53244i			0.198190i	−0.995078	+	0.0990949i	$0.968405\pi$
$524$	−15.5974	−	27.0155i	−0.681376	−	1.18018i
$525$	1.58463	−	4.29988i	0.0691589	−	0.187662i
$526$	−21.8316	+	37.8135i	−0.951904	+	1.64875i
$527$	−13.5618	−	7.82988i	−0.590759	−	0.341075i
$528$	8.59321	+	3.23554i	0.373971	+	0.140809i
$529$	−5.97872	−	10.3554i	−0.259944	−	0.450237i
$530$	18.9457			0.822947
$531$	−5.73980	+	28.8165i	−0.249086	+	1.25053i
$532$	−0.702924	−	100.136i	−0.0304756	−	4.34143i
$533$	−18.5581	+	10.7145i	−0.803839	+	0.464096i
$534$	41.5027	−	34.0513i	1.79600	−	1.47354i
$535$	13.7262	+	7.92482i	0.593435	+	0.342620i
$536$	−11.3034	−	6.52601i	−0.488232	−	0.281881i
$537$	−2.79032	−	16.9145i	−0.120411	−	0.729914i
$538$	−43.5920	+	25.1679i	−1.87938	+	1.08506i
$539$	0.0472439	+	3.36492i	0.00203494	+	0.144937i
$540$	−22.0725	−	13.7376i	−0.949849	−	0.591172i
$541$	−5.98535			−0.257330			−0.128665	−	0.991688i	$-0.541069\pi$
$541$	−5.98535			−0.257330			−0.128665	+	0.991688i	$0.541069\pi$
$542$	31.8666	+	55.1945i	1.36879	+	2.37081i
$543$	0.608052	+	3.68592i	0.0260940	+	0.158178i
$544$	19.2749	+	11.1284i	0.826405	+	0.477125i
$545$	−0.193548	+	0.335235i	−0.00829070	+	0.0143599i
$546$	−18.9851	−	22.8111i	−0.812485	−	0.976225i
$547$	10.4545	+	18.1076i	0.447000	+	0.774227i	0.998189	−	0.0601535i	$-0.0191590\pi$
$547$	10.4545	+	18.1076i	0.447000	+	0.774227i	−0.551189	+	0.834380i	$0.685826\pi$
$548$			46.5778i			1.98971i
$549$	17.3661	−	19.7917i	0.741165	−	0.844690i
$550$	1.27225			0.0542491
$551$	−9.39100	−	16.2657i	−0.400070	−	0.692941i
$552$	−16.1200	+	42.8128i	−0.686112	+	1.82223i
$553$	13.6161	−	23.9708i	0.579016	−	1.01934i
$554$	32.8068	+	18.9410i	1.39383	+	0.804726i
$555$	2.65472	−	7.05061i	0.112686	−	0.299282i
$556$	−28.7175	+	16.5801i	−1.21790	+	0.703152i
$557$		−	6.61023i		−	0.280085i	−0.990146	−	0.140042i	$-0.955276\pi$
$557$		−	6.61023i		−	0.280085i	0.990146	−	0.140042i	$-0.0447238\pi$
$558$	70.2825	−	23.8372i	2.97529	−	1.00911i
$559$			28.0739i			1.18740i
$560$	−14.7646	−	25.1634i	−0.623917	−	1.06335i
$561$	−1.07841	+	0.884789i	−0.0455304	+	0.0373558i
$562$	3.07182	−	5.32054i	0.129577	−	0.224433i
$563$	17.8046	−	30.8386i	0.750376	−	1.29969i	−0.197264	−	0.980350i	$-0.563206\pi$
$563$	17.8046	−	30.8386i	0.750376	−	1.29969i	0.947640	−	0.319340i	$-0.103461\pi$
$564$	−7.42061	+	1.22415i	−0.312464	+	0.0515460i
$565$	−11.7616	+	6.79054i	−0.494813	+	0.285680i
$566$	39.2924			1.65158
$567$	−22.0579	−	8.96927i	−0.926346	−	0.376674i
$568$	−35.2928			−1.48085
$569$	6.17541	−	3.56537i	0.258887	−	0.149468i	−0.364940	−	0.931031i	$-0.618911\pi$
$569$	6.17541	−	3.56537i	0.258887	−	0.149468i	0.623827	+	0.781563i	$0.285577\pi$
$570$	−34.2113	+	5.64371i	−1.43295	+	0.236389i
$571$	6.63406	−	11.4905i	0.277627	−	0.480864i	−0.693168	−	0.720776i	$-0.743785\pi$
$571$	6.63406	−	11.4905i	0.277627	−	0.480864i	0.970794	+	0.239913i	$0.0771188\pi$
$572$	2.94323	−	5.09782i	0.123062	−	0.213150i
$573$	−10.5359	+	8.64425i	−0.440142	+	0.361119i
$574$	−52.8801	+	31.0273i	−2.20717	+	1.29505i
$575$			3.32304i			0.138580i
$576$	−37.2329	+	12.6280i	−1.55137	+	0.526167i
$577$		−	15.5278i		−	0.646431i	−0.946325	−	0.323216i	$-0.895236\pi$
$577$		−	15.5278i		−	0.646431i	0.946325	−	0.323216i	$-0.104764\pi$
$578$	32.5296	−	18.7810i	1.35305	−	0.781186i
$579$	0.607072	−	1.61231i	0.0252291	−	0.0670054i
$580$	−10.7585	−	6.21142i	−0.446722	−	0.257915i
$581$	−8.08688	+	14.2368i	−0.335500	+	0.590640i
$582$	−23.1170	+	61.3961i	−0.958232	+	2.54495i
$583$	1.72086	+	2.98061i	0.0712706	+	0.123444i
$584$	−72.3692			−2.99466
$585$	−4.84210	+	5.51844i	−0.200196	+	0.228159i
$586$		−	40.4386i		−	1.67050i
$587$	0.392239	+	0.679379i	0.0161895	+	0.0280410i	0.874007	−	0.485914i	$-0.161513\pi$
$587$	0.392239	+	0.679379i	0.0161895	+	0.0280410i	−0.857817	+	0.513955i	$0.828180\pi$
$588$	−39.1326	−	46.3533i	−1.61380	−	1.91158i
$589$	35.3566	−	61.2394i	1.45684	−	2.52332i
$590$	22.4467	+	12.9596i	0.924117	+	0.533539i
$591$	−1.32419	−	8.02706i	−0.0544700	−	0.330189i
$592$	−23.9822	−	41.5385i	−0.985664	−	1.70722i
$593$	−19.0652			−0.782915			−0.391458	−	0.920196i	$-0.628029\pi$
$593$	−19.0652			−0.782915			−0.391458	+	0.920196i	$0.628029\pi$
$594$	0.218896	−	6.60720i	0.00898140	−	0.271097i
$595$	4.43209	−	0.0311120i	0.181698	−	0.00127547i
$596$	−9.51623	+	5.49420i	−0.389800	+	0.225051i
$597$	2.73034	+	16.5509i	0.111745	+	0.677384i
$598$	18.6376	+	10.7604i	0.762147	+	0.440026i
$599$	−23.2495	−	13.4231i	−0.949949	−	0.548453i	−0.0568837	−	0.998381i	$-0.518116\pi$
$599$	−23.2495	−	13.4231i	−0.949949	−	0.548453i	−0.893065	+	0.449928i	$0.851450\pi$
$600$	−10.6429	+	8.73206i	−0.434494	+	0.356485i
$601$	−4.55755	+	2.63130i	−0.185906	+	0.107333i	−0.590065	−	0.807356i	$-0.700898\pi$
$601$	−4.55755	+	2.63130i	−0.185906	+	0.107333i	0.404158	+	0.914689i	$0.367564\pi$
$602$	0.563827	+	80.3204i	0.0229799	+	3.27361i
$603$	−0.962364	+	4.83152i	−0.0391905	+	0.196755i
$604$	73.5192			2.99145
$605$	−5.38444	−	9.32612i	−0.218909	−	0.379161i
$606$	−38.3499	−	14.4396i	−1.55786	−	0.586569i
$607$	−20.6187	−	11.9042i	−0.836889	−	0.483178i	0.0193166	−	0.999813i	$-0.493851\pi$
$607$	−20.6187	−	11.9042i	−0.836889	−	0.483178i	−0.856205	+	0.516635i	$0.827184\pi$
$608$	−50.2512	+	87.0376i	−2.03796	+	3.52984i
$609$	−10.6761	−	3.93445i	−0.432617	−	0.159432i
$610$	−11.6134	−	20.1151i	−0.470215	−	0.814436i
$611$			2.12380i			0.0859198i
$612$	4.91206	−	24.6608i	0.198558	−	0.996855i
$613$	33.2558			1.34319			0.671595	−	0.740919i	$-0.265610\pi$
$613$	33.2558			1.34319			0.671595	+	0.740919i	$0.265610\pi$
$614$	−37.1944	−	64.4226i	−1.50104	−	2.59989i
$615$	9.62016	+	11.7253i	0.387922	+	0.472811i
$616$	4.99323	−	8.79047i	0.201183	−	0.354178i
$617$	19.9690	+	11.5291i	0.803922	+	0.464145i	0.844841	−	0.535018i	$-0.179695\pi$
$617$	19.9690	+	11.5291i	0.803922	+	0.464145i	−0.0409186	+	0.999162i	$0.513028\pi$
$618$	16.6869	−	2.75278i	0.671246	−	0.110733i
$619$	20.1409	−	11.6284i	0.809532	−	0.467383i	−0.0372616	−	0.999306i	$-0.511863\pi$
$619$	20.1409	−	11.6284i	0.809532	−	0.467383i	0.846793	+	0.531922i	$0.178530\pi$
$620$		−	46.7713i		−	1.87838i
$621$	17.2575	+	0.571739i	0.692521	+	0.0229431i
$622$		−	62.6287i		−	2.51118i
$623$	−15.6815	−	26.7261i	−0.628265	−	1.07076i
$624$	7.60779	+	46.1173i	0.304555	+	1.84617i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−0.852778	+	1.47706i	−0.0340839	+	0.0590350i
$627$	−3.99535	−	4.86965i	−0.159559	−	0.194475i
$628$	0.949960	−	0.548460i	0.0379075	−	0.0218859i
$629$	7.28661			0.290536
$630$	−13.7426	+	15.8857i	−0.547518	+	0.632901i
$631$	26.4943			1.05472			0.527360	−	0.849642i	$-0.323182\pi$
$631$	26.4943			1.05472			0.527360	+	0.849642i	$0.323182\pi$
$632$	−71.7225	+	41.4090i	−2.85297	+	1.64716i
$633$	−1.55006	+	4.11677i	−0.0616092	+	0.163627i
$634$	0.0340079	−	0.0589034i	0.00135063	−	0.00233935i
$635$	5.77020	−	9.99429i	0.228984	−	0.396611i
$636$	−58.0620	−	21.8617i	−2.30231	−	0.866871i
$637$	−14.7137	+	8.77262i	−0.582976	+	0.347584i
$638$		−	3.15886i		−	0.125060i
$639$	4.27863	+	12.6153i	0.169260	+	0.499053i
$640$			8.11017i			0.320583i
$641$	−17.5767	+	10.1479i	−0.694237	+	0.400818i	−0.805197	−	0.593007i	$-0.797941\pi$
$641$	−17.5767	+	10.1479i	−0.694237	+	0.400818i	0.110961	+	0.993825i	$0.464607\pi$
$642$	−46.0812	−	56.1651i	−1.81868	−	2.21666i
$643$	1.49144	+	0.861082i	0.0588166	+	0.0339578i	0.529120	−	0.848547i	$-0.322522\pi$
$643$	1.49144	+	0.861082i	0.0588166	+	0.0339578i	−0.470303	+	0.882505i	$0.655855\pi$
$644$	38.2495	+	21.7268i	1.50724	+	0.856155i
$645$	19.6048	−	3.23414i	0.771940	−	0.127344i
$646$	−16.7679	−	29.0429i	−0.659726	−	1.14268i
$647$	24.6714			0.969932			0.484966	−	0.874533i	$-0.338832\pi$
$647$	24.6714			0.969932			0.484966	+	0.874533i	$0.338832\pi$
$648$	43.5171	+	56.7741i	1.70951	+	2.23030i
$649$			4.70855i			0.184827i
$650$	3.23813	+	5.60860i	0.127010	+	0.219987i
$651$	−7.26903	−	42.2163i	−0.284896	−	1.65459i
$652$	0.473834	−	0.820704i	0.0185568	−	0.0321412i
$653$	−39.0506	−	22.5459i	−1.52817	−	0.882288i	−0.999439	−	0.0334968i	$-0.989336\pi$
$653$	−39.0506	−	22.5459i	−1.52817	−	0.882288i	−0.528728	−	0.848791i	$-0.677331\pi$
$654$	1.37172	−	1.12544i	0.0536386	−	0.0440083i
$655$	3.11736	+	5.39943i	0.121805	+	0.210973i
$656$	96.5599			3.77003
$657$	8.77349	+	25.8681i	0.342286	+	1.00921i
$658$	0.0426537	+	6.07627i	0.00166282	+	0.236878i
$659$	28.9505	−	16.7146i	1.12775	−	0.651107i	0.184382	−	0.982855i	$-0.440972\pi$
$659$	28.9505	−	16.7146i	1.12775	−	0.651107i	0.943368	+	0.331748i	$0.107638\pi$
$660$	−3.89902	−	1.46807i	−0.151769	−	0.0571446i
$661$	−5.96517	−	3.44399i	−0.232018	−	0.133956i	0.379485	−	0.925198i	$-0.376101\pi$
$661$	−5.96517	−	3.44399i	−0.232018	−	0.133956i	−0.611503	+	0.791242i	$0.709435\pi$
$662$	−36.2092	−	20.9054i	−1.40731	−	0.812512i
$663$	−6.64525	−	2.50209i	−0.258080	−	0.0971730i
$664$	42.5974	−	24.5936i	1.65310	−	0.954418i
$665$	0.140489	+	20.0135i	0.00544794	+	0.776091i
$666$	−22.7758	+	25.9571i	−0.882545	+	1.00582i
$667$	8.25071			0.319469
$668$	−36.7497	−	63.6523i	−1.42189	−	2.46278i
$669$	12.8027	−	10.5041i	0.494981	−	0.406112i
$670$	3.76353	+	2.17288i	0.145398	+	0.0839456i
$671$	2.10973	−	3.65416i	0.0814451	−	0.141067i
$672$	10.3312	+	60.0007i	0.398536	+	2.31458i
$673$	−23.8334	−	41.2806i	−0.918708	−	1.59125i	−0.801379	−	0.598157i	$-0.795900\pi$
$673$	−23.8334	−	41.2806i	−0.918708	−	1.59125i	−0.117329	−	0.993093i	$-0.537433\pi$
$674$			84.1035i			3.23955i
$675$	4.41151	+	2.74565i	0.169799	+	0.105680i
$676$	−35.0799			−1.34923
$677$	12.1034	+	20.9636i	0.465170	+	0.805698i	0.999209	−	0.0397617i	$-0.0126599\pi$
$677$	12.1034	+	20.9636i	0.465170	+	0.805698i	−0.534039	+	0.845460i	$0.679327\pi$
$678$	61.4213	−	10.1324i	2.35887	−	0.389134i
$679$	32.9261	+	18.7030i	1.26359	+	0.717755i
$680$	−11.5310	−	6.65744i	−0.442194	−	0.255301i
$681$	25.1521	+	30.6561i	0.963831	+	1.17474i
$682$	10.2996	−	5.94646i	0.394391	−	0.227702i
$683$		−	9.94301i		−	0.380459i	−0.981740	−	0.190229i	$-0.939077\pi$
$683$		−	9.94301i		−	0.380459i	0.981740	−	0.190229i	$-0.0609231\pi$
$684$	111.358	+	22.1809i	4.25789	+	0.848106i
$685$		−	9.30925i		−	0.355688i
$686$	−41.9201	+	25.3943i	−1.60052	+	0.969559i
$687$	−2.62270	−	0.987508i	−0.100062	−	0.0376758i
$688$	63.2510	−	109.554i	2.41142	−	4.17670i
$689$	−8.75981	+	15.1724i	−0.333722	+	0.578024i
$690$	5.36725	−	14.2548i	0.204328	−	0.542670i
$691$	16.2295	−	9.37009i	0.617399	−	0.356455i	−0.158457	−	0.987366i	$-0.550652\pi$
$691$	16.2295	−	9.37009i	0.617399	−	0.356455i	0.775855	+	0.630911i	$0.217319\pi$
$692$	67.3403			2.55990
$693$	−3.74746	−	0.719125i	−0.142354	−	0.0273173i
$694$	−84.8140			−3.21950
$695$	5.73961	−	3.31377i	0.217716	−	0.125698i
$696$	21.6807	+	26.4251i	0.821804	+	1.00164i
$697$	−7.33454	+	12.7038i	−0.277815	+	0.481191i
$698$	−12.3465	+	21.3849i	−0.467324	+	0.809429i
$699$	1.85472	+	11.2431i	0.0701521	+	0.425252i
$700$	6.69918	+	11.4175i	0.253205	+	0.431540i
$701$			14.3261i			0.541088i	0.962708	+	0.270544i	$0.0872035\pi$
$701$			14.3261i			0.541088i	−0.962708	+	0.270544i	$0.912796\pi$
$702$	29.6843	−	15.8516i	1.12036	−	0.598280i
$703$			32.9034i			1.24098i
$704$	−5.45632	+	3.15021i	−0.205643	+	0.118728i
$705$	1.48311	−	0.244664i	0.0558573	−	0.00921457i
$706$	17.0146	+	9.82337i	0.640352	+	0.369708i
$707$	−11.6824	+	20.5667i	−0.439363	+	0.773489i
$708$	−53.8372	−	65.6184i	−2.02333	−	2.46609i
$709$	−4.08736	−	7.07951i	−0.153504	−	0.265876i	0.779009	−	0.627012i	$-0.215722\pi$
$709$	−4.08736	−	7.07951i	−0.153504	−	0.265876i	−0.932513	+	0.361136i	$0.882389\pi$
$710$	11.7510			0.441006
$711$	23.4966	+	20.6168i	0.881191	+	0.773192i
$712$			93.0886i			3.48864i
$713$	15.5317	+	26.9017i	0.581668	+	1.00748i
$714$	−19.0625	−	7.02510i	−0.713398	−	0.262908i
$715$	−0.588246	+	1.01887i	−0.0219991	+	0.0381036i
$716$	42.8868	+	24.7607i	1.60276	+	0.925352i
$717$	−16.3582	−	6.15922i	−0.610907	−	0.230020i
$718$	13.4670	+	23.3256i	0.502585	+	0.870502i
$719$	−36.8392			−1.37387			−0.686934	−	0.726720i	$-0.741044\pi$
$719$	−36.8392			−1.37387			−0.686934	+	0.726720i	$0.741044\pi$
$720$	31.3287	−	10.6255i	1.16755	−	0.395989i
$721$	−0.0685251	−	9.76180i	−0.00255201	−	0.363548i
$722$	87.6011	−	50.5765i	3.26018	−	1.88226i
$723$	−18.5361	+	15.2081i	−0.689365	+	0.565596i
$724$	−9.34568	−	5.39573i	−0.347329	−	0.200531i
$725$	2.15024	+	1.24144i	0.0798579	+	0.0461060i
$726$	8.03433	+	48.7029i	0.298182	+	1.80753i
$727$	12.6568	−	7.30741i	0.469415	−	0.271017i	−0.246580	−	0.969122i	$-0.579307\pi$
$727$	12.6568	−	7.30741i	0.469415	−	0.271017i	0.715995	+	0.698106i	$0.245973\pi$
$728$	51.4606	−	0.361239i	1.90726	−	0.0133884i
$729$	15.0180	−	22.4379i	0.556223	−	0.831033i
$730$	24.0958			0.891826
$731$	9.60890	+	16.6431i	0.355398	+	0.615567i
$732$	12.3802	+	75.0468i	0.457584	+	2.77381i
$733$	2.31316	+	1.33551i	0.0854386	+	0.0493280i	0.542111	−	0.840307i	$-0.317625\pi$
$733$	2.31316	+	1.33551i	0.0854386	+	0.0493280i	−0.456672	+	0.889635i	$0.650959\pi$
$734$	21.8432	−	37.8336i	0.806248	−	1.39646i
$735$	7.82121	+	9.26437i	0.288490	+	0.341722i
$736$	−22.0748	−	38.2346i	−0.813687	−	1.40935i
$737$			0.789461i			0.0290802i
$738$	−22.3291	−	65.8362i	−0.821947	−	2.42346i
$739$	−49.4092			−1.81755			−0.908773	−	0.417290i	$-0.862980\pi$
$739$	−49.4092			−1.81755			−0.908773	+	0.417290i	$0.862980\pi$
$740$	10.8815	+	18.8474i	0.400013	+	0.692843i
$741$	11.2984	−	30.0072i	0.415057	−	1.10234i
$742$	−24.7574	+	43.5848i	−0.908873	+	1.60005i
$743$	14.6586	+	8.46315i	0.537772	+	0.310483i	0.744175	−	0.667984i	$-0.232843\pi$
$743$	14.6586	+	8.46315i	0.537772	+	0.310483i	−0.206404	+	0.978467i	$0.566176\pi$
$744$	−45.3466	+	120.435i	−1.66249	+	4.41537i
$745$	1.90195	−	1.09809i	0.0696822	−	0.0402310i
$746$		−	52.6616i		−	1.92808i
$747$	−13.9551	−	12.2447i	−0.510590	−	0.448012i
$748$		−	4.02953i		−	0.147334i
$749$	−36.1680	+	21.2215i	−1.32155	+	0.775417i
$750$	3.54362	−	2.90740i	0.129395	−	0.106163i
$751$	11.0234	−	19.0931i	0.402249	−	0.696716i	−0.591748	−	0.806123i	$-0.701562\pi$
$751$	11.0234	−	19.0931i	0.402249	−	0.696716i	0.993997	+	0.109407i	$0.0348953\pi$
$752$	4.78496	−	8.28780i	0.174490	−	0.302225i
$753$	20.9252	−	3.45195i	0.762557	−	0.125796i
$754$	13.9255	−	8.03989i	0.507137	−	0.292795i
$755$	−14.6939			−0.534764
$756$	60.4470	−	32.8265i	2.19844	−	1.19389i
$757$	3.26715			0.118747			0.0593734	−	0.998236i	$-0.481090\pi$
$757$	3.26715			0.118747			0.0593734	+	0.998236i	$0.481090\pi$
$758$	20.5604	−	11.8706i	0.746789	−	0.431159i
$759$	2.73014	−	0.450381i	0.0990978	−	0.0163478i
$760$	30.0623	−	52.0694i	1.09047	−	1.88876i
$761$	−18.9793	+	32.8731i	−0.687999	+	1.19165i	0.284485	+	0.958681i	$0.408177\pi$
$761$	−18.9793	+	32.8731i	−0.687999	+	1.19165i	−0.972484	+	0.232969i	$0.925156\pi$
$762$	−40.8948	+	33.5525i	−1.48146	+	1.21548i
$763$	−0.518294	−	0.883333i	−0.0187635	−	0.0319788i
$764$		−	39.3679i		−	1.42428i
$765$	−0.981745	+	4.92882i	−0.0354951	+	0.178202i
$766$		−	70.4212i		−	2.54442i
$767$	−20.7572	+	11.9842i	−0.749498	+	0.432723i
$768$	−2.89787	+	7.69639i	−0.104568	+	0.277720i
$769$	−28.3234	−	16.3525i	−1.02137	−	0.589688i	−0.106869	−	0.994273i	$-0.534082\pi$
$769$	−28.3234	−	16.3525i	−1.02137	−	0.589688i	−0.914500	+	0.404585i	$0.867416\pi$
$770$	−1.66253	+	2.92684i	−0.0599134	+	0.105476i
$771$	−0.808005	+	2.14597i	−0.0290996	+	0.0772851i
$772$	2.48836	+	4.30996i	0.0895579	+	0.155119i
$773$	26.0766			0.937910			0.468955	−	0.883222i	$-0.344631\pi$
$773$	26.0766			0.937910			0.468955	+	0.883222i	$0.344631\pi$
$774$	−89.3223	−	17.7916i	−3.21062	−	0.639507i
$775$			9.34792i			0.335787i
$776$	−56.8790	−	98.5174i	−2.04184	−	3.53657i
$777$	12.7510	+	15.3207i	0.457439	+	0.549626i
$778$	8.19474	−	14.1937i	0.293796	−	0.508869i
$779$	−57.3652	−	33.1198i	−2.05532	−	1.18664i
$780$	−3.45191	−	20.9249i	−0.123598	−	0.749233i
$781$	1.06736	+	1.84871i	0.0381930	+	0.0661522i
$782$	14.7319			0.526813
$783$	6.81714	−	10.9533i	0.243625	−	0.391437i
$784$	77.1826	−	1.08365i	2.75652	−	0.0387019i
$785$	−0.189863	+	0.109618i	−0.00677650	+	0.00391242i
$786$	−4.65154	−	28.1969i	−0.165915	−	1.00575i
$787$	37.1248	+	21.4340i	1.32336	+	0.764041i	0.984263	−	0.176711i	$-0.0565458\pi$
$787$	37.1248	+	21.4340i	1.32336	+	0.764041i	0.339095	+	0.940752i	$0.389879\pi$
$788$	20.3527	+	11.7506i	0.725035	+	0.418599i
$789$	−22.0930	+	18.1264i	−0.786531	+	0.645317i
$790$	23.8805	−	13.7874i	0.849629	−	0.490533i
$791$	−0.252228	−	35.9313i	−0.00896818	−	1.27757i
$792$	8.61655	+	7.56050i	0.306176	+	0.268651i
$793$	21.4786			0.762728
$794$	−24.0900	−	41.7251i	−0.854921	−	1.48077i
$795$	11.6045	+	4.36936i	0.411570	+	0.154965i
$796$	−41.9650	−	24.2285i	−1.48741	−	0.858757i
$797$	14.9190	−	25.8404i	0.528456	−	0.915313i	−0.470993	−	0.882137i	$-0.656104\pi$
$797$	14.9190	−	25.8404i	0.528456	−	0.915313i	0.999450	−	0.0331765i	$-0.0105624\pi$
$798$	31.7225	−	86.0787i	1.12296	−	3.04715i
$799$	0.726917	+	1.25906i	0.0257165	+	0.0445422i
$800$		−	13.2859i		−	0.469728i
$801$	33.2742	−	11.2853i	1.17569	−	0.398748i
$802$	32.3156			1.14110
$803$	2.18865	+	3.79086i	0.0772358	+	0.133776i
$804$	−9.02663	−	11.0019i	−0.318345	−	0.388008i
$805$	−7.64470	−	4.34241i	−0.269440	−	0.153050i
$806$	52.4287	+	30.2697i	1.84672	+	1.06621i
$807$	−32.5051	+	5.36225i	−1.14424	+	0.188760i
$808$	61.5369	−	35.5283i	2.16486	−	1.24988i
$809$			41.4017i			1.45561i	0.685787	+	0.727803i	$0.259458\pi$
$809$			41.4017i			1.45561i	−0.685787	+	0.727803i	$0.740542\pi$
$810$	−14.4893	−	18.9033i	−0.509102	−	0.664195i
$811$			4.39372i			0.154284i	0.997020	+	0.0771421i	$0.0245795\pi$
$811$			4.39372i			0.154284i	−0.997020	+	0.0771421i	$0.975420\pi$
$812$	28.3483	−	16.6333i	0.994829	−	0.583714i
$813$	6.78947	+	41.1567i	0.238117	+	1.44343i
$814$	−2.76694	+	4.79248i	−0.0969811	+	0.167976i
$815$	−0.0947024	+	0.164029i	−0.00331728	+	0.00574570i
$816$	20.2948	+	24.7359i	0.710460	+	0.865929i
$817$	−75.1535	+	43.3899i	−2.62929	+	1.51802i
$818$	−26.0072			−0.909319
$819$	−6.36781	−	18.3506i	−0.222509	−	0.641222i
$820$	−43.8124			−1.53000
$821$	−42.0658	+	24.2867i	−1.46811	+	0.847612i	−0.999362	−	0.0357212i	$-0.988627\pi$
$821$	−42.0658	+	24.2867i	−1.46811	+	0.847612i	−0.468745	+	0.883333i	$0.655294\pi$
$822$	−15.0360	+	39.9338i	−0.524440	+	1.39285i
$823$	−2.91070	+	5.04148i	−0.101461	+	0.175735i	−0.912287	−	0.409552i	$-0.865685\pi$
$823$	−2.91070	+	5.04148i	−0.101461	+	0.175735i	0.810826	+	0.585287i	$0.199018\pi$
$824$	−14.6632	+	25.3974i	−0.510816	+	0.884760i
$825$	0.779275	+	0.293415i	0.0271309	+	0.0102154i
$826$	−59.1463	+	34.7040i	−2.05796	+	1.20751i
$827$			25.5824i			0.889587i	0.895633	+	0.444794i	$0.146723\pi$
$827$			25.5824i			0.889587i	−0.895633	+	0.444794i	$0.853277\pi$
$828$	−32.8976	+	37.4927i	−1.14327	+	1.30296i
$829$		−	22.1655i		−	0.769840i	−0.922950	−	0.384920i	$-0.874229\pi$
$829$		−	22.1655i		−	0.769840i	0.922950	−	0.384920i	$-0.125771\pi$
$830$	−14.1831	+	8.18861i	−0.492302	+	0.284231i
$831$	15.7264	+	19.1678i	0.545542	+	0.664922i
$832$	−27.7747	−	16.0357i	−0.962915	−	0.555939i
$833$	−5.72010	+	10.2368i	−0.198190	+	0.354683i
$834$	−29.9734	+	4.94460i	−1.03789	+	0.171218i
$835$	7.34495	+	12.7218i	0.254182	+	0.440257i
$836$	18.1957			0.629313
$837$	48.5466	+	1.60834i	1.67802	+	0.0555924i
$838$		−	36.0218i		−	1.24435i
$839$	13.1411	+	22.7611i	0.453682	+	0.785800i	0.998611	−	0.0526820i	$-0.0167770\pi$
$839$	13.1411	+	22.7611i	0.453682	+	0.785800i	−0.544930	+	0.838482i	$0.683444\pi$
$840$	−6.18056	−	35.8948i	−0.213250	−	1.23849i
$841$	−11.4176	+	19.7759i	−0.393712	+	0.681929i
$842$	26.6331	+	15.3767i	0.917839	+	0.529914i
$843$	3.10859	−	2.55047i	0.107066	−	0.0878430i
$844$	−6.35360	−	11.0048i	−0.218700	−	0.378799i
$845$	7.01122			0.241193
$846$	−6.75727	−	1.34594i	−0.232320	−	0.0462745i
$847$	28.4911	−	0.199999i	0.978965	−	0.00687206i
$848$	68.3676	−	39.4720i	2.34775	−	1.35548i
$849$	24.0672	+	9.06186i	0.825985	+	0.311002i
$850$	3.83933	+	2.21664i	0.131688	+	0.0760300i
$851$	−12.5176	−	7.22704i	−0.429098	−	0.247740i
$852$	−36.0127	−	13.5596i	−1.23378	−	0.464545i
$853$	13.4318	−	7.75487i	0.459897	−	0.265522i	−0.252104	−	0.967700i	$-0.581122\pi$
$853$	13.4318	−	7.75487i	0.459897	−	0.265522i	0.712001	+	0.702178i	$0.247789\pi$
$854$	61.4511	−	0.431369i	2.10281	−	0.0147612i
$855$	−22.2565	−	4.43316i	−0.761158	−	0.151611i
$856$	125.975			4.30575
$857$	−24.0488	−	41.6538i	−0.821492	−	1.42287i	−0.904571	−	0.426322i	$-0.859809\pi$
$857$	−24.0488	−	41.6538i	−0.821492	−	1.42287i	0.0830798	−	0.996543i	$-0.473524\pi$
$858$	4.16904	−	3.42053i	0.142329	−	0.116775i
$859$	−13.1701	−	7.60376i	−0.449358	−	0.259437i	0.258201	−	0.966091i	$-0.416870\pi$
$859$	−13.1701	−	7.60376i	−0.449358	−	0.259437i	−0.707559	+	0.706654i	$0.750204\pi$
$860$	−28.6991	+	49.7083i	−0.978630	+	1.69504i
$861$	−39.5456	+	6.80916i	−1.34771	+	0.232056i
$862$	24.4550	+	42.3573i	0.832940	+	1.44269i
$863$		−	42.4695i		−	1.44568i	−0.691016	−	0.722840i	$-0.742836\pi$
$863$		−	42.4695i		−	1.44568i	0.691016	−	0.722840i	$-0.257164\pi$
$864$	−68.9977	−	2.28589i	−2.34735	−	0.0777674i
$865$	−13.4589			−0.457617
$866$	32.7080	+	56.6519i	1.11146	+	1.92511i
$867$	24.2563	−	4.00147i	0.823787	−	0.135897i
$868$	107.598	+	61.1189i	3.65212	+	2.07451i
$869$	4.33818	+	2.50465i	0.147163	+	0.0849645i
$870$	−7.21873	−	8.79839i	−0.244738	−	0.298293i
$871$	−3.48025	+	2.00933i	−0.117924	+	0.0680834i
$872$			3.07671i			0.104190i
$873$	−28.3191	+	32.2747i	−0.958456	+	1.09233i
$874$			66.5234i			2.25019i
$875$	−1.33893	−	2.28195i	−0.0452640	−	0.0771438i
$876$	−73.8454	−	27.8045i	−2.49500	−	0.939426i
$877$	4.84601	−	8.39354i	0.163638	−	0.283430i	−0.772533	−	0.634975i	$-0.781010\pi$
$877$	4.84601	−	8.39354i	0.163638	−	0.283430i	0.936171	+	0.351545i	$0.114344\pi$
$878$	−11.8207	+	20.4741i	−0.398929	+	0.690966i
$879$	9.32619	−	24.7693i	0.314565	−	0.835447i
$880$	4.59108	−	2.65066i	0.154765	−	0.0893537i
$881$	−39.3000			−1.32405			−0.662026	−	0.749481i	$-0.730303\pi$
$881$	−39.3000			−1.32405			−0.662026	+	0.749481i	$0.730303\pi$
$882$	−18.5871	−	52.3738i	−0.625859	−	1.76352i
$883$	2.71246			0.0912816			0.0456408	−	0.998958i	$-0.485467\pi$
$883$	2.71246			0.0912816			0.0456408	+	0.998958i	$0.485467\pi$
$884$	17.7638	−	10.2559i	0.597460	−	0.344944i
$885$	10.7601	+	13.1148i	0.361698	+	0.440848i
$886$	−16.0219	+	27.7507i	−0.538266	+	0.932304i
$887$	19.7052	−	34.1304i	0.661636	−	1.14599i	−0.318549	−	0.947906i	$-0.603196\pi$
$887$	19.7052	−	34.1304i	0.661636	−	1.14599i	0.980186	−	0.198081i	$-0.0634710\pi$
$888$	−9.74647	−	59.0816i	−0.327070	−	1.98265i
$889$	15.4518	+	26.3346i	0.518235	+	0.883233i
$890$		−	30.9945i		−	1.03894i
$891$	1.65787	−	3.99653i	0.0555407	−	0.133889i
$892$			47.8381i			1.60174i
$893$	−5.68539	+	3.28246i	−0.190254	+	0.109843i
$894$	−9.93239	+	1.63851i	−0.332189	+	0.0547999i
$895$	−8.57155	−	4.94878i	−0.286515	−	0.165420i
$896$	−18.6576	−	10.5980i	−0.623307	−	0.354056i
$897$	8.93417	+	10.8892i	0.298303	+	0.363581i
$898$	31.3120	+	54.2340i	1.04490	+	1.80981i
$899$	23.2098			0.774090
$900$	−14.2149	+	4.82114i	−0.473829	+	0.160705i
$901$			11.9929i			0.399543i
$902$	−5.57027	−	9.64799i	−0.185470	−	0.321243i
$903$	−18.1786	+	49.3275i	−0.604947	+	1.64152i
$904$	−53.9723	+	93.4828i	−1.79509	+	3.10919i
$905$	1.86787	+	1.07841i	0.0620900	+	0.0358477i
$906$	63.0321	+	23.7330i	2.09410	+	0.788477i
$907$	5.16288	+	8.94237i	0.171431	+	0.296926i	0.938920	−	0.344135i	$-0.111828\pi$
$907$	5.16288	+	8.94237i	0.171431	+	0.296926i	−0.767490	+	0.641061i	$0.778494\pi$
$908$	−114.548			−3.80142
$909$	−20.1597	−	17.6890i	−0.668656	−	0.586706i
$910$	−17.1341	+	0.120277i	−0.567991	+	0.00398714i
$911$	3.63331	−	2.09769i	0.120377	−	0.0694997i	−0.438602	−	0.898681i	$-0.644526\pi$
$911$	3.63331	−	2.09769i	0.120377	−	0.0694997i	0.558979	+	0.829181i	$0.311193\pi$
$912$	−111.697	+	91.6430i	−3.69866	+	3.03460i
$913$	−2.57653	−	1.48756i	−0.0852708	−	0.0492311i
$914$	−41.7969	−	24.1314i	−1.38252	−	0.798197i
$915$	−2.47435	−	14.9992i	−0.0817996	−	0.495857i
$916$	7.01089	−	4.04774i	0.231646	−	0.133741i
$917$	−16.4951	+	0.115791i	−0.544717	+	0.00382376i
$918$	12.1722	−	19.5574i	0.401744	−	0.645491i
$919$	47.6361			1.57137			0.785686	−	0.618626i	$-0.212310\pi$
$919$	47.6361			1.57137			0.785686	+	0.618626i	$0.212310\pi$
$920$	13.2060	+	22.8735i	0.435389	+	0.754117i
$921$	−7.92462	−	48.0379i	−0.261125	−	1.58290i
$922$	16.2222	+	9.36589i	0.534249	+	0.308449i
$923$	−5.43324	+	9.41065i	−0.178837	+	0.309755i
$924$	8.47241	−	7.05135i	0.278722	−	0.231973i
$925$	−2.17483	−	3.76692i	−0.0715080	−	0.123855i
$926$		−	75.2857i		−	2.47404i
$927$	10.8559	+	2.16232i	0.356553	+	0.0710199i
$928$	−32.9874			−1.08286
$929$	12.3716	+	21.4282i	0.405898	+	0.703036i	0.994426	−	0.105441i	$-0.0336256\pi$
$929$	12.3716	+	21.4282i	0.405898	+	0.703036i	−0.588528	+	0.808477i	$0.700292\pi$
$930$	15.0984	−	40.0997i	0.495097	−	1.31492i
$931$	−46.2250	−	25.8297i	−1.51496	−	0.846533i
$932$	−28.5069	−	16.4585i	−0.933774	−	0.539115i
$933$	14.4438	−	38.3610i	0.472869	−	1.25588i
$934$	−71.8511	+	41.4833i	−2.35104	+	1.35737i
$935$			0.805360i			0.0263381i
$936$	−11.3989	+	57.2280i	−0.372586	+	1.87056i
$937$			22.1037i			0.722096i	0.932547	+	0.361048i	$0.117581\pi$
$937$			22.1037i			0.722096i	−0.932547	+	0.361048i	$0.882419\pi$
$938$	−9.91678	+	5.81865i	−0.323794	+	0.189986i
$939$	−0.862987	+	0.708046i	−0.0281625	+	0.0231062i
$940$	−2.17110	+	3.76045i	−0.0708134	+	0.122652i
$941$	1.88553	−	3.26583i	0.0614664	−	0.106463i	−0.833655	−	0.552286i	$-0.813756\pi$
$941$	1.88553	−	3.26583i	0.0614664	−	0.106463i	0.895121	+	0.445823i	$0.147089\pi$
$942$	0.991504	−	0.163565i	0.0323049	−	0.00532922i
$943$	25.1999	−	14.5491i	0.820620	−	0.473785i
$944$	108.002			3.51517
$945$	−12.0812	+	6.56084i	−0.393002	+	0.213424i
$946$	−14.5951			−0.474528
$947$	−50.6640	+	29.2509i	−1.64636	+	0.950525i	−0.667856	+	0.744291i	$0.732788\pi$
$947$	−50.6640	+	29.2509i	−1.64636	+	0.950525i	−0.978503	+	0.206235i	$0.933879\pi$
$948$	−89.0949	+	14.6976i	−2.89367	+	0.477357i
$949$	−11.1411	+	19.2969i	−0.361654	+	0.626403i
$950$	−10.0094	+	17.3369i	−0.324749	+	0.562482i
$951$	0.0344150	−	0.0282361i	0.00111598	−	0.000915619i
$952$	30.3838	−	17.8276i	0.984745	−	0.577797i
$953$			27.6547i			0.895824i	0.894078	+	0.447912i	$0.147832\pi$
$953$			27.6547i			0.895824i	−0.894078	+	0.447912i	$0.852168\pi$
$954$	−42.7225	−	37.4864i	−1.38319	−	1.21367i
$955$			7.86824i			0.254610i
$956$	43.7279	−	25.2463i	1.41426	−	0.816524i
$957$	0.728515	−	1.93485i	0.0235496	−	0.0625448i
$958$	−80.8294	−	46.6669i	−2.61148	−	1.50774i
$959$	21.4161	+	12.1649i	0.691562	+	0.392827i
$960$	−7.99857	+	21.2433i	−0.258153	+	0.685623i
$961$	28.1918	+	48.8296i	0.909413	+	1.57515i
$962$	−28.1695			−0.908221
$963$	−15.2723	−	45.0295i	−0.492143	−	1.45105i
$964$		−	69.2613i		−	2.23076i
$965$	−0.497334	−	0.861407i	−0.0160097	−	0.0277297i
$966$	25.7797	+	30.9750i	0.829447	+	0.996605i
$967$	−6.96009	+	12.0552i	−0.223821	+	0.387670i	−0.955965	−	0.293480i	$-0.905187\pi$
$967$	−6.96009	+	12.0552i	−0.223821	+	0.387670i	0.732144	+	0.681150i	$0.238520\pi$
$968$	−74.1256	−	42.7964i	−2.38249	−	1.37553i
$969$	−3.57257	−	21.6564i	−0.114767	−	0.695703i
$970$	18.9382	+	32.8020i	0.608070	+	1.05321i
$971$	−23.1240			−0.742083			−0.371042	−	0.928616i	$-0.620999\pi$
$971$	−23.1240			−0.742083			−0.371042	+	0.928616i	$0.620999\pi$
$972$	22.5919	+	74.6516i	0.724637	+	2.39445i
$973$	0.123086	+	17.5344i	0.00394597	+	0.562126i
$974$	19.6272	−	11.3318i	0.628897	−	0.363094i
$975$	0.689913	+	4.18215i	0.0220949	+	0.133936i
$976$	−83.8169	−	48.3917i	−2.68291	−	1.54898i
$977$	−31.0824	−	17.9454i	−0.994413	−	0.574125i	−0.0878228	−	0.996136i	$-0.527991\pi$
$977$	−31.0824	−	17.9454i	−0.994413	−	0.574125i	−0.906591	+	0.422011i	$0.861324\pi$
$978$	0.671179	−	0.550675i	0.0214619	−	0.0176086i
$979$	4.87618	−	2.81527i	0.155843	−	0.0899763i
$980$	−35.0203	+	0.491690i	−1.11868	+	0.0157065i
$981$	1.09976	−	0.372996i	0.0351126	−	0.0119089i
$982$	−73.5862			−2.34823
$983$	22.4178	+	38.8288i	0.715018	+	1.23845i	0.962953	+	0.269670i	$0.0869147\pi$
$983$	22.4178	+	38.8288i	0.715018	+	1.23845i	−0.247935	+	0.968777i	$0.579752\pi$
$984$	112.816	+	42.4778i	3.59644	+	1.35414i
$985$	−4.06778	−	2.34853i	−0.129610	−	0.0748304i
$986$	5.50365	−	9.53261i	0.175272	−	0.303580i
$987$	−1.37522	+	3.73165i	−0.0437737	+	0.118780i
$988$	46.3116	+	80.2140i	1.47337	+	2.55195i
$989$		−	38.1213i		−	1.21219i
$990$	−2.86893	−	2.51732i	−0.0911807	−	0.0800056i
$991$	1.13276			0.0359833			0.0179916	−	0.999838i	$-0.494273\pi$
$991$	1.13276			0.0359833			0.0179916	+	0.999838i	$0.494273\pi$
$992$	−62.0978	−	107.557i	−1.97161	−	3.41492i
$993$	−17.3574	−	21.1557i	−0.550820	−	0.671355i
$994$	−15.3557	+	27.0333i	−0.487053	+	0.857445i
$995$	8.38731	+	4.84241i	0.265895	+	0.153515i
$996$	52.9152	−	8.72922i	1.67668	−	0.276596i
$997$	35.0610	−	20.2425i	1.11039	−	0.641086i	0.171462	−	0.985191i	$-0.445151\pi$
$997$	35.0610	−	20.2425i	1.11039	−	0.641086i	0.938931	+	0.344105i	$0.111817\pi$
$998$		−	56.9642i		−	1.80317i
$999$	−19.9369	+	10.6464i	−0.630777	+	0.336839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.j.41.1	yes	24
3.2	odd	2		945.2.bl.j.881.12		24
7.6	odd	2		315.2.bl.i.41.1	✓	24
9.2	odd	6		315.2.bl.i.146.1	yes	24
9.7	even	3		945.2.bl.i.251.12		24
21.20	even	2		945.2.bl.i.881.12		24
63.20	even	6	inner	315.2.bl.j.146.1	yes	24
63.34	odd	6		945.2.bl.j.251.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.1	✓	24	7.6	odd	2
315.2.bl.i.146.1	yes	24	9.2	odd	6
315.2.bl.j.41.1	yes	24	1.1	even	1	trivial
315.2.bl.j.146.1	yes	24	63.20	even	6	inner
945.2.bl.i.251.12		24	9.7	even	3
945.2.bl.i.881.12		24	21.20	even	2
945.2.bl.j.251.12		24	63.34	odd	6
945.2.bl.j.881.12		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.29184 + 1.32320i) q^{2} +(-1.70895 + 0.281919i) q^{3} +(2.50170 - 4.33307i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(3.54362 - 2.90740i) q^{6} +(-1.33893 - 2.28195i) q^{7} +7.94816i q^{8} +(2.84104 - 0.963574i) q^{9} +O(q^{10})\)	\(q+(-2.29184 + 1.32320i) q^{2} +(-1.70895 + 0.281919i) q^{3} +(2.50170 - 4.33307i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(3.54362 - 2.90740i) q^{6} +(-1.33893 - 2.28195i) q^{7} +7.94816i q^{8} +(2.84104 - 0.963574i) q^{9} -2.64639i q^{10} +(0.416342 - 0.240375i) q^{11} +(-3.05371 + 8.11029i) q^{12} +(2.11934 + 1.22360i) q^{13} +(6.08807 + 3.45820i) q^{14} +(0.610327 - 1.62096i) q^{15} +(-5.51359 - 9.54981i) q^{16} +1.67521 q^{17} +(-5.23623 + 5.96762i) q^{18} +7.56459i q^{19} +(2.50170 + 4.33307i) q^{20} +(2.93149 + 3.52227i) q^{21} +(-0.636127 + 1.10180i) q^{22} +(-2.87783 - 1.66152i) q^{23} +(-2.24074 - 13.5830i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.47625 q^{26} +(-4.58356 + 2.44765i) q^{27} +(-13.2374 + 0.0929230i) q^{28} +(-2.15024 + 1.24144i) q^{29} +(0.746070 + 4.52256i) q^{30} +(-8.09553 - 4.67396i) q^{31} +(11.5059 + 6.64295i) q^{32} +(-0.643743 + 0.528165i) q^{33} +(-3.83933 + 2.21664i) q^{34} +(2.64569 - 0.0185720i) q^{35} +(2.93220 - 14.7210i) q^{36} +4.34966 q^{37} +(-10.0094 - 17.3369i) q^{38} +(-3.96680 - 1.49359i) q^{39} +(-6.88331 - 3.97408i) q^{40} +(-4.37827 + 7.58339i) q^{41} +(-11.3792 - 4.19355i) q^{42} +(5.73592 + 9.93491i) q^{43} -2.40538i q^{44} +(-0.586041 + 2.94220i) q^{45} +8.79406 q^{46} +(0.433925 + 0.751580i) q^{47} +(12.1147 + 14.7658i) q^{48} +(-3.41455 + 6.11072i) q^{49} +(2.29184 + 1.32320i) q^{50} +(-2.86286 + 0.472275i) q^{51} +(10.6039 - 6.12215i) q^{52} +7.15905i q^{53} +(7.26608 - 11.6746i) q^{54} +0.480750i q^{55} +(18.1373 - 10.6420i) q^{56} +(-2.13260 - 12.9275i) q^{57} +(3.28534 - 5.69038i) q^{58} +(-4.89709 + 8.48201i) q^{59} +(-5.49686 - 6.69973i) q^{60} +(7.60094 - 4.38841i) q^{61} +24.7383 q^{62} +(-6.00277 - 5.19295i) q^{63} -13.1054 q^{64} +(-2.11934 + 1.22360i) q^{65} +(0.776491 - 2.06227i) q^{66} +(-0.821072 + 1.42214i) q^{67} +(4.19088 - 7.25882i) q^{68} +(5.38650 + 2.02814i) q^{69} +(-6.03892 + 3.54333i) q^{70} +4.44038i q^{71} +(7.65865 + 22.5811i) q^{72} +9.10515i q^{73} +(-9.96874 + 5.75546i) q^{74} +(1.09863 + 1.33904i) q^{75} +(32.7779 + 18.9243i) q^{76} +(-1.10597 - 0.628225i) q^{77} +(11.0676 - 1.82578i) q^{78} +(5.20988 + 9.02378i) q^{79} +11.0272 q^{80} +(7.14305 - 5.47511i) q^{81} -23.1732i q^{82} +(-3.09425 - 5.35940i) q^{83} +(22.5959 - 3.89069i) q^{84} +(-0.837607 + 1.45078i) q^{85} +(-26.2917 - 15.1795i) q^{86} +(3.32467 - 2.72776i) q^{87} +(1.91054 + 3.30915i) q^{88} +11.7120 q^{89} +(-2.55000 - 7.51852i) q^{90} +(-0.0454493 - 6.47452i) q^{91} +(-14.3989 + 8.31323i) q^{92} +(15.1526 + 5.70529i) q^{93} +(-1.98898 - 1.14834i) q^{94} +(-6.55113 - 3.78229i) q^{95} +(-21.5359 - 8.10875i) q^{96} +(-12.3950 + 7.15625i) q^{97} +(-0.260064 - 18.5229i) q^{98} +(0.951226 - 1.08409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

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