LMFDB - Embedded newform 633.2.d.a.632.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(632,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("633.632");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.d (of order $2$, degree $1$, 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:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			632.17
Character	$\chi$	$=$	633.632
Dual form			633.2.d.a.632.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55050 q^{2} +(-1.58549 - 0.697289i) q^{3} +0.404037 q^{4} +3.05483i q^{5} +(2.45830 + 1.08114i) q^{6} -1.87042i q^{7} +2.47453 q^{8} +(2.02757 + 2.21109i) q^{9} +O(q^{10})$	\(q-1.55050 q^{2} +(-1.58549 - 0.697289i) q^{3} +0.404037 q^{4} +3.05483i q^{5} +(2.45830 + 1.08114i) q^{6} -1.87042i q^{7} +2.47453 q^{8} +(2.02757 + 2.21109i) q^{9} -4.73649i q^{10} -3.63571i q^{11} +(-0.640597 - 0.281730i) q^{12} -3.56435 q^{13} +2.90008i q^{14} +(2.13010 - 4.84340i) q^{15} -4.64483 q^{16} -2.71142 q^{17} +(-3.14375 - 3.42829i) q^{18} +5.44492 q^{19} +1.23426i q^{20} +(-1.30423 + 2.96554i) q^{21} +5.63716i q^{22} -1.21310 q^{23} +(-3.92336 - 1.72547i) q^{24} -4.33196 q^{25} +5.52650 q^{26} +(-1.67293 - 4.91948i) q^{27} -0.755719i q^{28} -1.12027 q^{29} +(-3.30271 + 7.50968i) q^{30} +7.12653i q^{31} +2.25272 q^{32} +(-2.53514 + 5.76440i) q^{33} +4.20404 q^{34} +5.71381 q^{35} +(0.819214 + 0.893363i) q^{36} +4.14318 q^{37} -8.44232 q^{38} +(5.65124 + 2.48538i) q^{39} +7.55927i q^{40} +3.56967 q^{41} +(2.02220 - 4.59806i) q^{42} +8.68990 q^{43} -1.46896i q^{44} +(-6.75451 + 6.19389i) q^{45} +1.88091 q^{46} +2.43183i q^{47} +(7.36434 + 3.23879i) q^{48} +3.50152 q^{49} +6.71668 q^{50} +(4.29893 + 1.89064i) q^{51} -1.44013 q^{52} +5.03222i q^{53} +(2.59387 + 7.62763i) q^{54} +11.1065 q^{55} -4.62842i q^{56} +(-8.63288 - 3.79668i) q^{57} +1.73698 q^{58} -2.00137i q^{59} +(0.860637 - 1.95691i) q^{60} +7.72503i q^{61} -11.0496i q^{62} +(4.13568 - 3.79242i) q^{63} +5.79683 q^{64} -10.8885i q^{65} +(3.93073 - 8.93767i) q^{66} +10.4292i q^{67} -1.09551 q^{68} +(1.92337 + 0.845885i) q^{69} -8.85924 q^{70} +6.67751i q^{71} +(5.01730 + 5.47143i) q^{72} -8.63060 q^{73} -6.42399 q^{74} +(6.86829 + 3.02063i) q^{75} +2.19995 q^{76} -6.80032 q^{77} +(-8.76223 - 3.85357i) q^{78} +1.49382 q^{79} -14.1891i q^{80} +(-0.777881 + 8.96632i) q^{81} -5.53476 q^{82} +3.53342i q^{83} +(-0.526955 + 1.19819i) q^{84} -8.28291i q^{85} -13.4737 q^{86} +(1.77618 + 0.781155i) q^{87} -8.99669i q^{88} +17.9793 q^{89} +(10.4728 - 9.60359i) q^{90} +6.66683i q^{91} -0.490139 q^{92} +(4.96925 - 11.2991i) q^{93} -3.77054i q^{94} +16.6333i q^{95} +(-3.57167 - 1.57080i) q^{96} +18.3345i q^{97} -5.42909 q^{98} +(8.03890 - 7.37168i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.55050			−1.09637			−0.548183	−	0.836358i	$-0.684680\pi$
$2$	−1.55050			−1.09637			−0.548183	+	0.836358i	$0.684680\pi$
$3$	−1.58549	−	0.697289i	−0.915385	−	0.402580i
$3$	−1.58549	−	0.697289i	−0.915385	−	0.402580i
$4$	0.404037			0.202018
$5$			3.05483i			1.36616i	0.730344	+	0.683080i	$0.239360\pi$
$5$			3.05483i			1.36616i	−0.730344	+	0.683080i	$0.760640\pi$
$6$	2.45830	+	1.08114i	1.00360	+	0.441375i
$7$		−	1.87042i		−	0.706953i	−0.935443	−	0.353477i	$-0.884999\pi$
$7$		−	1.87042i		−	0.706953i	0.935443	−	0.353477i	$-0.115001\pi$
$8$	2.47453			0.874880
$9$	2.02757	+	2.21109i	0.675858	+	0.737032i
$10$		−	4.73649i		−	1.49781i
$11$		−	3.63571i		−	1.09621i	−0.836410	−	0.548104i	$-0.815350\pi$
$11$		−	3.63571i		−	1.09621i	0.836410	−	0.548104i	$-0.184650\pi$
$12$	−0.640597	−	0.281730i	−0.184924	−	0.0813286i
$13$	−3.56435			−0.988572			−0.494286	−	0.869299i	$-0.664570\pi$
$13$	−3.56435			−0.988572			−0.494286	+	0.869299i	$0.664570\pi$
$14$			2.90008i			0.775079i
$15$	2.13010	−	4.84340i	0.549989	−	1.25056i
$16$	−4.64483			−1.16121
$17$	−2.71142			−0.657615			−0.328808	−	0.944397i	$-0.606647\pi$
$17$	−2.71142			−0.657615			−0.328808	+	0.944397i	$0.606647\pi$
$18$	−3.14375	−	3.42829i	−0.740988	−	0.808056i
$19$	5.44492			1.24915			0.624575	−	0.780965i	$-0.285272\pi$
$19$	5.44492			1.24915			0.624575	+	0.780965i	$0.285272\pi$
$20$			1.23426i			0.275989i
$21$	−1.30423	+	2.96554i	−0.284605	+	0.647134i
$22$			5.63716i			1.20185i
$23$	−1.21310			−0.252950			−0.126475	−	0.991970i	$-0.540366\pi$
$23$	−1.21310			−0.252950			−0.126475	+	0.991970i	$0.540366\pi$
$24$	−3.92336	−	1.72547i	−0.800852	−	0.352209i
$25$	−4.33196			−0.866392
$26$	5.52650			1.08384
$27$	−1.67293	−	4.91948i	−0.321956	−	0.946755i
$28$		−	0.755719i		−	0.142817i
$29$	−1.12027			−0.208029			−0.104015	−	0.994576i	$-0.533169\pi$
$29$	−1.12027			−0.208029			−0.104015	+	0.994576i	$0.533169\pi$
$30$	−3.30271	+	7.50968i	−0.602989	+	1.37107i
$31$			7.12653i			1.27996i	0.768391	+	0.639981i	$0.221058\pi$
$31$			7.12653i			1.27996i	−0.768391	+	0.639981i	$0.778942\pi$
$32$	2.25272			0.398228
$33$	−2.53514	+	5.76440i	−0.441312	+	1.00345i
$34$	4.20404			0.720987
$35$	5.71381			0.965810
$36$	0.819214	+	0.893363i	0.136536	+	0.148894i
$37$	4.14318			0.681135			0.340567	−	0.940220i	$-0.389381\pi$
$37$	4.14318			0.681135			0.340567	+	0.940220i	$0.389381\pi$
$38$	−8.44232			−1.36953
$39$	5.65124	+	2.48538i	0.904923	+	0.397979i
$40$			7.55927i			1.19523i
$41$	3.56967			0.557489			0.278745	−	0.960365i	$-0.410082\pi$
$41$	3.56967			0.557489			0.278745	+	0.960365i	$0.410082\pi$
$42$	2.02220	−	4.59806i	0.312032	−	0.709496i
$43$	8.68990			1.32520			0.662599	−	0.748975i	$-0.269453\pi$
$43$	8.68990			1.32520			0.662599	+	0.748975i	$0.269453\pi$
$44$		−	1.46896i		−	0.221454i
$45$	−6.75451	+	6.19389i	−1.00690	+	0.923330i
$46$	1.88091			0.277326
$47$			2.43183i			0.354719i	0.984146	+	0.177359i	$0.0567555\pi$
$47$			2.43183i			0.354719i	−0.984146	+	0.177359i	$0.943245\pi$
$48$	7.36434	+	3.23879i	1.06295	+	0.467479i
$49$	3.50152			0.500217
$50$	6.71668			0.949882
$51$	4.29893	+	1.89064i	0.601971	+	0.264743i
$52$	−1.44013			−0.199710
$53$			5.03222i			0.691228i	0.938377	+	0.345614i	$0.112329\pi$
$53$			5.03222i			0.691228i	−0.938377	+	0.345614i	$0.887671\pi$
$54$	2.59387	+	7.62763i	0.352982	+	1.03799i
$55$	11.1065			1.49760
$56$		−	4.62842i		−	0.618499i
$57$	−8.63288	−	3.79668i	−1.14345	−	0.502883i
$58$	1.73698			0.228076
$59$		−	2.00137i		−	0.260556i	−0.991477	−	0.130278i	$-0.958413\pi$
$59$		−	2.00137i		−	0.260556i	0.991477	−	0.130278i	$-0.0415870\pi$
$60$	0.860637	−	1.95691i	0.111108	−	0.252636i
$61$			7.72503i			0.989089i	0.869152	+	0.494545i	$0.164665\pi$
$61$			7.72503i			0.989089i	−0.869152	+	0.494545i	$0.835335\pi$
$62$		−	11.0496i		−	1.40331i
$63$	4.13568	−	3.79242i	0.521047	−	0.477800i
$64$	5.79683			0.724604
$65$		−	10.8885i		−	1.35055i
$66$	3.93073	−	8.93767i	0.483839	−	1.10015i
$67$			10.4292i			1.27413i	0.770810	+	0.637065i	$0.219852\pi$
$67$			10.4292i			1.27413i	−0.770810	+	0.637065i	$0.780148\pi$
$68$	−1.09551			−0.132850
$69$	1.92337	+	0.845885i	0.231546	+	0.101833i
$70$	−8.85924			−1.05888
$71$			6.67751i			0.792475i	0.918148	+	0.396237i	$0.129684\pi$
$71$			6.67751i			0.792475i	−0.918148	+	0.396237i	$0.870316\pi$
$72$	5.01730	+	5.47143i	0.591295	+	0.644814i
$73$	−8.63060			−1.01014			−0.505068	−	0.863080i	$-0.668533\pi$
$73$	−8.63060			−1.01014			−0.505068	+	0.863080i	$0.668533\pi$
$74$	−6.42399			−0.746773
$75$	6.86829	+	3.02063i	0.793082	+	0.348792i
$76$	2.19995			0.252351
$77$	−6.80032			−0.774968
$78$	−8.76223	−	3.85357i	−0.992127	−	0.436331i
$79$	1.49382			0.168068			0.0840342	−	0.996463i	$-0.473220\pi$
$79$	1.49382			0.168068			0.0840342	+	0.996463i	$0.473220\pi$
$80$		−	14.1891i		−	1.58639i
$81$	−0.777881	+	8.96632i	−0.0864312	+	0.996258i
$82$	−5.53476			−0.611212
$83$			3.53342i			0.387844i	0.981017	+	0.193922i	$0.0621208\pi$
$83$			3.53342i			0.387844i	−0.981017	+	0.193922i	$0.937879\pi$
$84$	−0.526955	+	1.19819i	−0.0574955	+	0.130733i
$85$		−	8.28291i		−	0.898407i
$86$	−13.4737			−1.45290
$87$	1.77618	+	0.781155i	0.190427	+	0.0837486i
$88$		−	8.99669i		−	0.959051i
$89$	17.9793			1.90580			0.952901	−	0.303281i	$-0.0980822\pi$
$89$	17.9793			1.90580			0.952901	+	0.303281i	$0.0980822\pi$
$90$	10.4728	−	9.60359i	1.10393	−	1.01231i
$91$			6.66683i			0.698874i
$92$	−0.490139			−0.0511005
$93$	4.96925	−	11.2991i	0.515287	−	1.17166i
$94$		−	3.77054i		−	0.388901i
$95$			16.6333i			1.70654i
$96$	−3.57167	−	1.57080i	−0.364532	−	0.160319i
$97$			18.3345i			1.86159i	0.365541	+	0.930795i	$0.380884\pi$
$97$			18.3345i			1.86159i	−0.365541	+	0.930795i	$0.619116\pi$
$98$	−5.42909			−0.548421
$99$	8.03890	−	7.37168i	0.807940	−	0.740882i
$100$	−1.75027			−0.175027
$101$			13.7310i			1.36628i	0.730286	+	0.683141i	$0.239387\pi$
$101$			13.7310i			1.36628i	−0.730286	+	0.683141i	$0.760613\pi$
$102$	−6.66548	−	2.93143i	−0.659980	−	0.290255i
$103$	−7.79457			−0.768022			−0.384011	−	0.923328i	$-0.625458\pi$
$103$	−7.79457			−0.768022			−0.384011	+	0.923328i	$0.625458\pi$
$104$	−8.82010			−0.864882
$105$	−9.05921	−	3.98418i	−0.884088	−	0.388816i
$106$		−	7.80243i		−	0.757839i
$107$		−	6.84821i		−	0.662042i	−0.943623	−	0.331021i	$-0.892607\pi$
$107$		−	6.84821i		−	0.662042i	0.943623	−	0.331021i	$-0.107393\pi$
$108$	−0.675926	−	1.98765i	−0.0650410	−	0.191262i
$109$	−16.0371			−1.53608			−0.768039	−	0.640403i	$-0.778768\pi$
$109$	−16.0371			−1.53608			−0.768039	+	0.640403i	$0.778768\pi$
$110$	−17.2205			−1.64191
$111$	−6.56899	−	2.88900i	−0.623500	−	0.274211i
$112$			8.68779i			0.820919i
$113$		−	0.798026i		−	0.0750720i	−0.999295	−	0.0375360i	$-0.988049\pi$
$113$		−	0.798026i		−	0.0750720i	0.999295	−	0.0375360i	$-0.0119509\pi$
$114$	13.3852	+	5.88674i	1.25364	+	0.551344i
$115$		−	3.70582i		−	0.345570i
$116$	−0.452631			−0.0420258
$117$	−7.22698	−	7.88111i	−0.668134	−	0.728609i
$118$			3.10312i			0.285665i
$119$			5.07149i			0.464903i
$120$	5.27100	−	11.9852i	0.481174	−	1.09409i
$121$	−2.21840			−0.201673
$122$		−	11.9776i		−	1.08440i
$123$	−5.65969	−	2.48910i	−0.510317	−	0.224434i
$124$			2.87938i			0.258576i
$125$			2.04075i			0.182531i
$126$	−6.41235	+	5.88013i	−0.571258	+	0.523844i
$127$			6.66979i			0.591848i	0.955211	+	0.295924i	$0.0956275\pi$
$127$			6.66979i			0.591848i	−0.955211	+	0.295924i	$0.904372\pi$
$128$	−13.4934			−1.19266
$129$	−13.7778	−	6.05938i	−1.21307	−	0.533498i
$130$			16.8825i			1.48069i
$131$	17.8176			1.55673			0.778367	−	0.627809i	$-0.216048\pi$
$131$	17.8176			1.55673			0.778367	+	0.627809i	$0.216048\pi$
$132$	−1.02429	+	2.32903i	−0.0891531	+	0.202716i
$133$		−	10.1843i		−	0.883090i
$134$		−	16.1704i		−	1.39691i
$135$	15.0282	−	5.11052i	1.29342	−	0.439843i
$136$	−6.70949			−0.575334
$137$		−	13.6875i		−	1.16940i	−0.811250	−	0.584700i	$-0.801212\pi$
$137$		−	13.6875i		−	1.16940i	0.811250	−	0.584700i	$-0.198788\pi$
$138$	−2.98218	−	1.31154i	−0.253860	−	0.111646i
$139$	−7.77214			−0.659225			−0.329612	−	0.944116i	$-0.606918\pi$
$139$	−7.77214			−0.659225			−0.329612	+	0.944116i	$0.606918\pi$
$140$	2.30859			0.195111
$141$	1.69569	−	3.85565i	0.142803	−	0.324704i
$142$		−	10.3535i		−	0.868843i
$143$			12.9589i			1.08368i
$144$	−9.41774	−	10.2702i	−0.784811	−	0.855846i
$145$		−	3.42224i		−	0.284201i
$146$	13.3817			1.10748
$147$	−5.55164	−	2.44157i	−0.457891	−	0.201378i
$148$	1.67400			0.137602
$149$	4.07410			0.333764			0.166882	−	0.985977i	$-0.446630\pi$
$149$	4.07410			0.333764			0.166882	+	0.985977i	$0.446630\pi$
$150$	−10.6492	−	4.68347i	−0.869508	−	0.382404i
$151$	19.8336			1.61404			0.807019	−	0.590526i	$-0.201080\pi$
$151$	19.8336			1.61404			0.807019	+	0.590526i	$0.201080\pi$
$152$	13.4736			1.09286
$153$	−5.49760	−	5.99520i	−0.444455	−	0.484683i
$154$	10.5439			0.849648
$155$	−21.7703			−1.74863
$156$	2.28331	+	1.00418i	0.182811	+	0.0803991i
$157$		−	10.6574i		−	0.850552i	−0.905064	−	0.425276i	$-0.860177\pi$
$157$		−	10.6574i		−	0.850552i	0.905064	−	0.425276i	$-0.139823\pi$
$158$	−2.31617			−0.184264
$159$	3.50891	−	7.97854i	0.278275	−	0.632739i
$160$			6.88165i			0.544043i
$161$			2.26902i			0.178824i
$162$	1.20610	−	13.9022i	0.0947602	−	1.09226i
$163$	−5.45685			−0.427413			−0.213707	−	0.976898i	$-0.568554\pi$
$163$	−5.45685			−0.427413			−0.213707	+	0.976898i	$0.568554\pi$
$164$	1.44228			0.112623
$165$	−17.6092	−	7.74442i	−1.37088	−	0.602902i
$166$		−	5.47856i		−	0.425219i
$167$	2.37270			0.183605			0.0918026	−	0.995777i	$-0.470737\pi$
$167$	2.37270			0.183605			0.0918026	+	0.995777i	$0.470737\pi$
$168$	−3.22735	+	7.33833i	−0.248995	+	0.566165i
$169$	−0.295438			−0.0227260
$170$			12.8426i			0.984983i
$171$	11.0400	+	12.0392i	0.844248	+	0.920663i
$172$	3.51104			0.267714
$173$		−	17.7539i		−	1.34980i	−0.737908	−	0.674902i	$-0.764186\pi$
$173$		−	17.7539i		−	1.34980i	0.737908	−	0.674902i	$-0.235814\pi$
$174$	−2.75397	−	1.21118i	−0.208778	−	0.0918191i
$175$			8.10259i			0.612498i
$176$			16.8873i			1.27292i
$177$	−1.39553	+	3.17316i	−0.104895	+	0.238509i
$178$	−27.8768			−2.08946
$179$			4.96203i			0.370879i	0.982656	+	0.185440i	$0.0593709\pi$
$179$			4.96203i			0.370879i	−0.982656	+	0.185440i	$0.940629\pi$
$180$	−2.72907	+	2.50256i	−0.203413	+	0.186530i
$181$		−	4.99539i		−	0.371304i	−0.982616	−	0.185652i	$-0.940560\pi$
$181$		−	4.99539i		−	0.371304i	0.982616	−	0.185652i	$-0.0594398\pi$
$182$		−	10.3369i		−	0.766221i
$183$	5.38658	−	12.2480i	0.398188	−	0.905397i
$184$	−3.00187			−0.221301
$185$			12.6567i			0.930539i
$186$	−7.70480	+	17.5191i	−0.564944	+	1.28457i
$187$			9.85793i			0.720883i
$188$			0.982548i			0.0716597i
$189$	−9.20151	+	3.12909i	−0.669311	+	0.227608i
$190$		−	25.7898i		−	1.87099i
$191$	11.9396			0.863919			0.431959	−	0.901893i	$-0.357822\pi$
$191$	11.9396			0.863919			0.431959	+	0.901893i	$0.357822\pi$
$192$	−9.19083	−	4.04207i	−0.663291	−	0.291711i
$193$	26.7328			1.92427			0.962133	−	0.272581i	$-0.0878772\pi$
$193$	26.7328			1.92427			0.962133	+	0.272581i	$0.0878772\pi$
$194$		−	28.4276i		−	2.04098i
$195$	−7.59240	+	17.2636i	−0.543703	+	1.23627i
$196$	1.41474			0.101053
$197$	17.9186			1.27665			0.638323	−	0.769768i	$-0.279628\pi$
$197$	17.9186			1.27665			0.638323	+	0.769768i	$0.279628\pi$
$198$	−12.4643	+	11.4298i	−0.885798	+	0.812277i
$199$	−8.22574			−0.583107			−0.291554	−	0.956554i	$-0.594172\pi$
$199$	−8.22574			−0.583107			−0.291554	+	0.956554i	$0.594172\pi$
$200$	−10.7196			−0.757989
$201$	7.27217	−	16.5354i	0.512939	−	1.16632i
$202$		−	21.2898i		−	1.49795i
$203$			2.09538i			0.147067i
$204$	1.73693	+	0.763889i	0.121609	+	0.0534829i
$205$			10.9047i			0.761619i
$206$	12.0855			0.842033
$207$	−2.45966	−	2.68229i	−0.170958	−	0.186432i
$208$	16.5558			1.14794
$209$		−	19.7962i		−	1.36933i
$210$	14.0463	+	6.17745i	0.969284	+	0.426285i
$211$	3.39101	−	14.1245i	0.233447	−	0.972370i
$211$	3.39101	−	14.1245i	0.233447	−	0.972370i
$212$			2.03320i			0.139641i
$213$	4.65616	−	10.5871i	0.319035	−	0.725419i
$214$			10.6181i			0.725840i
$215$			26.5461i			1.81043i
$216$	−4.13973	−	12.1734i	−0.281673	−	0.828297i
$217$	13.3296			0.904873
$218$	24.8655			1.68410
$219$	13.6838	+	6.01803i	0.924663	+	0.406661i
$220$	4.48742			0.302542
$221$	9.66443			0.650100
$222$	10.1852	+	4.47938i	0.683585	+	0.300636i
$223$			2.78407i			0.186435i	0.995646	+	0.0932174i	$0.0297152\pi$
$223$			2.78407i			0.186435i	−0.995646	+	0.0932174i	$0.970285\pi$
$224$		−	4.21353i		−	0.281528i
$225$	−8.78337	−	9.57837i	−0.585558	−	0.638558i
$226$			1.23734i			0.0823064i
$227$		−	13.6328i		−	0.904839i	−0.891805	−	0.452420i	$-0.850561\pi$
$227$		−	13.6328i		−	0.904839i	0.891805	−	0.452420i	$-0.149439\pi$
$228$	−3.48800	−	1.53400i	−0.230998	−	0.101592i
$229$			18.7149i			1.23671i	0.785898	+	0.618356i	$0.212201\pi$
$229$			18.7149i			1.23671i	−0.785898	+	0.618356i	$0.787799\pi$
$230$			5.74586i			0.378871i
$231$	10.7819	+	4.74179i	0.709394	+	0.311987i
$232$	−2.77215			−0.182001
$233$	−23.4961			−1.53928			−0.769639	−	0.638479i	$-0.779564\pi$
$233$	−23.4961			−1.53928			−0.769639	+	0.638479i	$0.779564\pi$
$234$	11.2054	+	12.2196i	0.732520	+	0.798822i
$235$	−7.42881			−0.484602
$236$		−	0.808627i		−	0.0526371i
$237$	−2.36845	−	1.04163i	−0.153847	−	0.0676610i
$238$		−	7.86333i		−	0.509704i
$239$	−4.77015			−0.308556			−0.154278	−	0.988028i	$-0.549305\pi$
$239$	−4.77015			−0.308556			−0.154278	+	0.988028i	$0.549305\pi$
$240$	−9.89394	+	22.4968i	−0.638651	+	1.45216i
$241$	17.0609			1.09899			0.549493	−	0.835498i	$-0.314821\pi$
$241$	17.0609			1.09899			0.549493	+	0.835498i	$0.314821\pi$
$242$	3.43963			0.221108
$243$	7.48545	−	13.6736i	0.480192	−	0.877164i
$244$			3.12120i			0.199814i
$245$			10.6965i			0.683377i
$246$	8.77533	+	3.85933i	0.559495	+	0.246062i
$247$	−19.4076			−1.23487
$248$			17.6348i			1.11981i
$249$	2.46382	−	5.60222i	0.156138	−	0.355026i
$250$		−	3.16418i		−	0.200120i
$251$	−8.23964			−0.520081			−0.260041	−	0.965598i	$-0.583736\pi$
$251$	−8.23964			−0.520081			−0.260041	+	0.965598i	$0.583736\pi$
$252$	1.67097	−	1.53228i	0.105261	−	0.0965244i
$253$			4.41050i			0.277286i
$254$		−	10.3415i		−	0.648882i
$255$	−5.77558	+	13.1325i	−0.361681	+	0.822388i
$256$	9.32778			0.582987
$257$			29.2209i			1.82275i	0.411575	+	0.911376i	$0.364979\pi$
$257$			29.2209i			1.82275i	−0.411575	+	0.911376i	$0.635021\pi$
$258$	21.3624	+	9.39504i	1.32996	+	0.584909i
$259$		−	7.74950i		−	0.481530i
$260$		−	4.39933i		−	0.272835i
$261$	−2.27144	−	2.47703i	−0.140598	−	0.153324i
$262$	−27.6262			−1.70675
$263$		−	16.0038i		−	0.986838i	−0.869792	−	0.493419i	$-0.835747\pi$
$263$		−	16.0038i		−	0.986838i	0.869792	−	0.493419i	$-0.164253\pi$
$264$	−6.27330	+	14.2642i	−0.386095	+	0.877900i
$265$	−15.3725			−0.944328
$266$			15.7907i			0.968190i
$267$	−28.5061	−	12.5368i	−1.74454	−	0.767238i
$268$			4.21378i			0.257397i
$269$		−	7.47467i		−	0.455739i	−0.973692	−	0.227869i	$-0.926824\pi$
$269$		−	7.47467i		−	0.455739i	0.973692	−	0.227869i	$-0.0731759\pi$
$270$	−23.3011	+	7.92383i	−1.41806	+	0.482229i
$271$			24.4241i			1.48366i	0.670590	+	0.741828i	$0.266041\pi$
$271$			24.4241i			1.48366i	−0.670590	+	0.741828i	$0.733959\pi$
$272$	12.5941			0.763627
$273$	4.64871	−	10.5702i	0.281353	−	0.639738i
$274$			21.2224i			1.28209i
$275$			15.7498i			0.949746i
$276$	0.777111	+	0.341769i	0.0467766	+	0.0205721i
$277$	−12.4094			−0.745612			−0.372806	−	0.927909i	$-0.621604\pi$
$277$	−12.4094			−0.745612			−0.372806	+	0.927909i	$0.621604\pi$
$278$	12.0507			0.722751
$279$	−15.7574	+	14.4496i	−0.943372	+	0.865073i
$280$	14.1390			0.844968
$281$			23.1825i			1.38295i	0.722398	+	0.691477i	$0.243040\pi$
$281$			23.1825i			1.38295i	−0.722398	+	0.691477i	$0.756960\pi$
$282$	−2.62916	+	5.97816i	−0.156564	+	0.355994i
$283$		−	4.84548i		−	0.288034i	−0.989575	−	0.144017i	$-0.953998\pi$
$283$		−	4.84548i		−	0.288034i	0.989575	−	0.144017i	$-0.0460020\pi$
$284$			2.69796i			0.160094i
$285$	11.5982	−	26.3719i	0.687018	−	1.56214i
$286$		−	20.0928i		−	1.18811i
$287$		−	6.67680i		−	0.394119i
$288$	4.56755	+	4.98097i	0.269146	+	0.293506i
$289$	−9.64822			−0.567542
$290$			5.30617i			0.311589i
$291$	12.7845	−	29.0693i	0.749440	−	1.70407i
$292$	−3.48708			−0.204066
$293$		−	6.90218i		−	0.403229i	−0.979465	−	0.201615i	$-0.935381\pi$
$293$		−	6.90218i		−	0.403229i	0.979465	−	0.201615i	$-0.0646189\pi$
$294$	8.60779	+	3.78565i	0.502017	+	0.220784i
$295$	6.11383			0.355961
$296$	10.2524			0.595911
$297$	−17.8858	+	6.08230i	−1.03784	+	0.352931i
$298$	−6.31688			−0.365927
$299$	4.32393			0.250059
$300$	2.77504	+	1.22044i	0.160217	+	0.0704624i
$301$		−	16.2538i		−	0.936852i
$302$	−30.7519			−1.76958
$303$	9.57446	−	21.7703i	0.550038	−	1.25067i
$304$	−25.2907			−1.45052
$305$	−23.5986			−1.35125
$306$	8.52401	+	9.29553i	0.487285	+	0.531390i
$307$	6.05351			0.345492			0.172746	−	0.984966i	$-0.444736\pi$
$307$	6.05351			0.345492			0.172746	+	0.984966i	$0.444736\pi$
$308$	−2.74758			−0.156558
$309$	12.3582	+	5.43507i	0.703036	+	0.309191i
$310$	33.7547			1.91714
$311$			34.1449i			1.93618i	0.250600	+	0.968091i	$0.419372\pi$
$311$			34.1449i			1.93618i	−0.250600	+	0.968091i	$0.580628\pi$
$312$	13.9842	+	6.15016i	0.791699	+	0.348184i
$313$			25.9225i			1.46522i	0.680646	+	0.732612i	$0.261699\pi$
$313$			25.9225i			1.46522i	−0.680646	+	0.732612i	$0.738301\pi$
$314$			16.5242i			0.932517i
$315$	11.5852	+	12.6338i	0.652751	+	0.711833i
$316$	0.603560			0.0339529
$317$	−35.2057			−1.97735			−0.988675	−	0.150073i	$-0.952049\pi$
$317$	−35.2057			−1.97735			−0.988675	+	0.150073i	$0.952049\pi$
$318$	−5.44055	+	12.3707i	−0.305091	+	0.693714i
$319$			4.07299i			0.228044i
$320$			17.7083i			0.989924i
$321$	−4.77519	+	10.8578i	−0.266525	+	0.606023i
$322$		−	3.51810i		−	0.196056i
$323$	−14.7634			−0.821460
$324$	−0.314292	+	3.62272i	−0.0174607	+	0.201262i
$325$	15.4406			0.856490
$326$	8.46082			0.468601
$327$	25.4268	+	11.1825i	1.40610	+	0.618395i
$328$	8.83328			0.487736
$329$	4.54855			0.250769
$330$	27.3030	+	12.0077i	1.50298	+	0.661002i
$331$	13.9531			0.766931			0.383466	−	0.923555i	$-0.374730\pi$
$331$	13.9531			0.766931			0.383466	+	0.923555i	$0.374730\pi$
$332$			1.42763i			0.0783515i
$333$	8.40061	+	9.16097i	0.460351	+	0.502018i
$334$	−3.67886			−0.201298
$335$	−31.8594			−1.74066
$336$	6.05790	−	13.7744i	0.330486	−	0.751456i
$337$	33.8938			1.84631			0.923157	−	0.384423i	$-0.125600\pi$
$337$	33.8938			1.84631			0.923157	+	0.384423i	$0.125600\pi$
$338$	0.458075			0.0249160
$339$	−0.556455	+	1.26527i	−0.0302225	+	0.0687198i
$340$		−	3.34660i		−	0.181495i
$341$	25.9100			1.40311
$342$	−17.1174	−	18.6668i	−0.925605	−	1.00938i
$343$		−	19.6423i		−	1.06058i
$344$	21.5035			1.15939
$345$	−2.58403	+	5.87556i	−0.139120	+	0.316329i
$346$			27.5273i			1.47988i
$347$		−	16.7480i		−	0.899079i	−0.893261	−	0.449539i	$-0.851588\pi$
$347$		−	16.7480i		−	0.899079i	0.893261	−	0.449539i	$-0.148412\pi$
$348$	0.717644	+	0.315615i	0.0384697	+	0.0169187i
$349$		−	18.9762i		−	1.01577i	−0.861424	−	0.507887i	$-0.830427\pi$
$349$		−	18.9762i		−	1.01577i	0.861424	−	0.507887i	$-0.169573\pi$
$350$		−	12.5630i		−	0.671522i
$351$	5.96291	+	17.5347i	0.318277	+	0.935935i
$352$		−	8.19023i		−	0.436541i
$353$	29.1078			1.54925			0.774625	−	0.632421i	$-0.217939\pi$
$353$	29.1078			1.54925			0.774625	+	0.632421i	$0.217939\pi$
$354$	2.16377	−	4.91997i	0.115003	−	0.261493i
$355$	−20.3986			−1.08265
$356$	7.26430			0.385007
$357$	3.53630	−	8.04082i	0.187161	−	0.425565i
$358$		−	7.69360i		−	0.406619i
$359$			18.7876i			0.991574i	0.868444	+	0.495787i	$0.165120\pi$
$359$			18.7876i			0.991574i	−0.868444	+	0.495787i	$0.834880\pi$
$360$	−16.7143	+	15.3270i	−0.880919	+	0.807803i
$361$	10.6471			0.560376
$362$			7.74533i			0.407085i
$363$	3.51726	+	1.54687i	0.184609	+	0.0811896i
$364$			2.69364i			0.141185i
$365$		−	26.3650i		−	1.38001i
$366$	−8.35188	+	18.9904i	−0.436560	+	0.992647i
$367$		−	27.3892i		−	1.42971i	−0.699275	−	0.714853i	$-0.746494\pi$
$367$		−	27.3892i		−	1.42971i	0.699275	−	0.714853i	$-0.253506\pi$
$368$	5.63466			0.293727
$369$	7.23778	+	7.89289i	0.376784	+	0.410887i
$370$		−	19.6242i		−	1.02021i
$371$	9.41237			0.488666
$372$	2.00776	−	4.56523i	0.104097	−	0.236696i
$373$		−	29.2330i		−	1.51363i	−0.653631	−	0.756814i	$-0.726755\pi$
$373$		−	29.2330i		−	1.51363i	0.653631	−	0.756814i	$-0.273245\pi$
$374$		−	15.2847i		−	0.790352i
$375$	1.42300	−	3.23560i	0.0734832	−	0.167086i
$376$			6.01764i			0.310336i
$377$	3.99304			0.205652
$378$	14.2669	−	4.85164i	0.733810	−	0.249541i
$379$		−	35.8169i		−	1.83979i	−0.392167	−	0.919894i	$-0.628274\pi$
$379$		−	35.8169i		−	1.83979i	0.392167	−	0.919894i	$-0.371726\pi$
$380$			6.72045i			0.344752i
$381$	4.65077	−	10.5749i	0.238266	−	0.541769i
$382$	−18.5123			−0.947171
$383$			22.2931i			1.13913i	0.821948	+	0.569563i	$0.192887\pi$
$383$			22.2931i			1.13913i	−0.821948	+	0.569563i	$0.807113\pi$
$384$	21.3937	+	9.40880i	1.09174	+	0.480141i
$385$		−	20.7738i		−	1.05873i
$386$	−41.4490			−2.10970
$387$	17.6194	+	19.2142i	0.895646	+	0.976713i
$388$			7.40783i			0.376075i
$389$		−	32.7322i		−	1.65959i	−0.558071	−	0.829793i	$-0.688458\pi$
$389$		−	32.7322i		−	1.65959i	0.558071	−	0.829793i	$-0.311542\pi$
$390$	11.7720	−	26.7671i	0.596098	−	1.35540i
$391$	3.28923			0.166344
$392$	8.66464			0.437630
$393$	−28.2497	−	12.4241i	−1.42501	−	0.626710i
$394$	−27.7827			−1.39967
$395$			4.56337i			0.229608i
$396$	3.24801	−	2.97843i	0.163219	−	0.149672i
$397$			18.5956i			0.933289i	0.884445	+	0.466644i	$0.154537\pi$
$397$			18.5956i			0.933289i	−0.884445	+	0.466644i	$0.845463\pi$
$398$	12.7540			0.639299
$399$	−7.10140	+	16.1471i	−0.355515	+	0.808367i
$400$	20.1212			1.00606
$401$	14.2904			0.713626			0.356813	−	0.934176i	$-0.383863\pi$
$401$	14.2904			0.713626			0.356813	+	0.934176i	$0.383863\pi$
$402$	−11.2755	+	25.6381i	−0.562369	+	1.27871i
$403$		−	25.4014i		−	1.26533i
$404$			5.54781i			0.276014i
$405$	−27.3905	−	2.37629i	−1.36105	−	0.118079i
$406$		−	3.24888i		−	0.161239i
$407$		−	15.0634i		−	0.746666i
$408$	10.6379	+	4.67846i	0.526652	+	0.231618i
$409$			21.8195i			1.07890i	0.842017	+	0.539451i	$0.181368\pi$
$409$			21.8195i			1.07890i	−0.842017	+	0.539451i	$0.818632\pi$
$410$		−	16.9077i		−	0.835014i
$411$	−9.54413	+	21.7014i	−0.470777	+	1.07045i
$412$	−3.14929			−0.155155
$413$	−3.74341			−0.184201
$414$	3.81369	+	4.15888i	0.187433	+	0.204398i
$415$	−10.7940			−0.529856
$416$	−8.02946			−0.393677
$417$	12.3227	+	5.41943i	0.603444	+	0.265391i
$418$			30.6939i			1.50129i
$419$		−	6.52580i		−	0.318806i	−0.987214	−	0.159403i	$-0.949043\pi$
$419$		−	6.52580i		−	0.318806i	0.987214	−	0.159403i	$-0.0509570\pi$
$420$	−3.66025	−	1.60975i	−0.178602	−	0.0785480i
$421$			7.31068i			0.356301i	0.984003	+	0.178150i	$0.0570114\pi$
$421$			7.31068i			0.356301i	−0.984003	+	0.178150i	$0.942989\pi$
$422$	−5.25774	+	21.9000i	−0.255943	+	1.06607i
$423$	−5.37700	+	4.93071i	−0.261439	+	0.239740i
$424$			12.4524i			0.604741i
$425$	11.7457			0.569752
$426$	−7.21935	+	16.4153i	−0.349779	+	0.795325i
$427$	14.4491			0.699240
$428$		−	2.76693i		−	0.133745i
$429$	9.03613	−	20.5463i	0.436268	−	0.991985i
$430$		−	41.1597i		−	1.98490i
$431$			12.4358i			0.599012i	0.954094	+	0.299506i	$0.0968219\pi$
$431$			12.4358i			0.599012i	−0.954094	+	0.299506i	$0.903178\pi$
$432$	7.77048	+	22.8501i	0.373857	+	1.09938i
$433$	−8.93972			−0.429616			−0.214808	−	0.976656i	$-0.568913\pi$
$433$	−8.93972			−0.429616			−0.214808	+	0.976656i	$0.568913\pi$
$434$	−20.6675			−0.992072
$435$	−2.38629	+	5.42593i	−0.114414	+	0.260154i
$436$	−6.47959			−0.310316
$437$	−6.60526			−0.315972
$438$	−21.2166	−	9.33093i	−1.01377	−	0.445849i
$439$		−	11.7990i		−	0.563134i	−0.959542	−	0.281567i	$-0.909146\pi$
$439$		−	11.7990i		−	0.563134i	0.959542	−	0.281567i	$-0.0908541\pi$
$440$	27.4833			1.31022
$441$	7.09960	+	7.74220i	0.338076	+	0.368676i
$442$	−14.9847			−0.712747
$443$		−	1.07957i		−	0.0512921i	−0.999671	−	0.0256460i	$-0.991836\pi$
$443$		−	1.07957i		−	0.0512921i	0.999671	−	0.0256460i	$-0.00816428\pi$
$444$	−2.65411	−	1.16726i	−0.125959	−	0.0553957i
$445$			54.9236i			2.60363i
$446$		−	4.31668i		−	0.204401i
$447$	−6.45946	−	2.84083i	−0.305522	−	0.134367i
$448$		−	10.8425i		−	0.512261i
$449$	−15.6316			−0.737703			−0.368851	−	0.929488i	$-0.620249\pi$
$449$	−15.6316			−0.737703			−0.368851	+	0.929488i	$0.620249\pi$
$450$	13.6186	+	14.8512i	0.641986	+	0.700093i
$451$		−	12.9783i		−	0.611125i
$452$		−	0.322432i		−	0.0151659i
$453$	−31.4461	−	13.8298i	−1.47747	−	0.649780i
$454$			21.1376i			0.992035i
$455$	−20.3660			−0.954773
$456$	−21.3624	−	9.39502i	−1.00038	−	0.439962i
$457$		−	6.46181i		−	0.302270i	−0.988513	−	0.151135i	$-0.951707\pi$
$457$		−	6.46181i		−	0.302270i	0.988513	−	0.151135i	$-0.0482929\pi$
$458$		−	29.0173i		−	1.35589i
$459$	4.53602	+	13.3388i	0.211723	+	0.622600i
$460$		−	1.49729i		−	0.0698114i
$461$	−8.15970			−0.380035			−0.190018	−	0.981781i	$-0.560855\pi$
$461$	−8.15970			−0.380035			−0.190018	+	0.981781i	$0.560855\pi$
$462$	−16.7172	−	7.35212i	−0.777755	−	0.342052i
$463$		−	29.1960i		−	1.35685i	−0.734668	−	0.678427i	$-0.762662\pi$
$463$		−	29.1960i		−	1.35685i	0.734668	−	0.678427i	$-0.237338\pi$
$464$	5.20348			0.241565
$465$	34.5166	+	15.1802i	1.60067	+	0.703965i
$466$	36.4305			1.68761
$467$			8.03728i			0.371921i	0.982557	+	0.185961i	$0.0595397\pi$
$467$			8.03728i			0.371921i	−0.982557	+	0.185961i	$0.940460\pi$
$468$	−2.91996	−	3.18426i	−0.134975	−	0.147192i
$469$	19.5070			0.900750
$470$	11.5183			0.531301
$471$	−7.43129	+	16.8972i	−0.342416	+	0.778583i
$472$		−	4.95246i		−	0.227955i
$473$		−	31.5940i		−	1.45269i
$474$	3.67227	+	1.61504i	0.168673	+	0.0741812i
$475$	−23.5872			−1.08225
$476$			2.04907i			0.0939189i
$477$	−11.1267	+	10.2032i	−0.509457	+	0.467172i
$478$	7.39610			0.338290
$479$	0.169055			0.00772432			0.00386216	−	0.999993i	$-0.498771\pi$
$479$	0.169055			0.00772432			0.00386216	+	0.999993i	$0.498771\pi$
$480$	4.79851	−	10.9108i	0.219021	−	0.498008i
$481$	−14.7677			−0.673351
$482$	−26.4528			−1.20489
$483$	1.58216	−	3.59751i	0.0719909	−	0.163692i
$484$	−0.896317			−0.0407417
$485$	−56.0088			−2.54323
$486$	−11.6061	+	21.2009i	−0.526466	+	0.961692i
$487$	−27.6163			−1.25141			−0.625707	−	0.780058i	$-0.715190\pi$
$487$	−27.6163			−1.25141			−0.625707	+	0.780058i	$0.715190\pi$
$488$			19.1159i			0.865334i
$489$	8.65179	+	3.80500i	0.391248	+	0.172068i
$490$		−	16.5849i		−	0.749231i
$491$		−	15.6813i		−	0.707687i	−0.935305	−	0.353843i	$-0.884875\pi$
$491$		−	15.6813i		−	0.707687i	0.935305	−	0.353843i	$-0.115125\pi$
$492$	−2.28672	−	1.00569i	−0.103093	−	0.0453398i
$493$	3.03753			0.136803
$494$	30.0914			1.35387
$495$	22.5192	+	24.5574i	1.01216	+	1.10378i
$496$		−	33.1015i		−	1.48630i
$497$	12.4898			0.560243
$498$	−3.82014	+	8.68622i	−0.171185	+	0.389239i
$499$			29.3157i			1.31235i	0.754607	+	0.656177i	$0.227827\pi$
$499$			29.3157i			1.31235i	−0.754607	+	0.656177i	$0.772173\pi$
$500$			0.824539i			0.0368745i
$501$	−3.76190	−	1.65446i	−0.168069	−	0.0739158i
$502$	12.7755			0.570199
$503$			35.8753i			1.59960i	0.600266	+	0.799800i	$0.295061\pi$
$503$			35.8753i			1.59960i	−0.600266	+	0.799800i	$0.704939\pi$
$504$	10.2339	−	9.38447i	0.455853	−	0.418018i
$505$	−41.9457			−1.86656
$506$		−	6.83846i		−	0.304007i
$507$	0.468414	+	0.206005i	0.0208030	+	0.00914902i
$508$			2.69484i			0.119564i
$509$		−	10.9387i		−	0.484848i	−0.970170	−	0.242424i	$-0.922057\pi$
$509$		−	10.9387i		−	0.484848i	0.970170	−	0.242424i	$-0.0779425\pi$
$510$	8.95502	−	20.3619i	0.396535	−	0.901638i
$511$			16.1429i			0.714118i
$512$	12.5241			0.553492
$513$	−9.10898	−	26.7862i	−0.402171	−	1.18264i
$514$		−	45.3069i		−	1.99840i
$515$		−	23.8111i		−	1.04924i
$516$	−5.56673	−	2.44821i	−0.245061	−	0.107776i
$517$	8.84143			0.388846
$518$			12.0156i			0.527934i
$519$	−12.3796	+	28.1487i	−0.543404	+	1.23559i
$520$		−	26.9439i		−	1.18157i
$521$		−	29.5186i		−	1.29323i	−0.762815	−	0.646616i	$-0.776183\pi$
$521$		−	29.5186i		−	1.29323i	0.762815	−	0.646616i	$-0.223817\pi$
$522$	3.52185	+	3.84062i	0.154147	+	0.168100i
$523$	11.9605			0.522996			0.261498	−	0.965204i	$-0.415783\pi$
$523$	11.9605			0.522996			0.261498	+	0.965204i	$0.415783\pi$
$524$	7.19898			0.314489
$525$	5.64985	−	12.8466i	0.246580	−	0.560671i
$526$			24.8138i			1.08194i
$527$		−	19.3230i		−	0.841722i
$528$	11.7753	−	26.7746i	0.512454	−	1.16522i
$529$	−21.5284			−0.936016
$530$	23.8351			1.03533
$531$	4.42522	−	4.05793i	0.192038	−	0.176099i
$532$		−	4.11483i		−	0.178400i
$533$	−12.7236			−0.551118
$534$	44.1985	+	19.4382i	1.91266	+	0.841174i
$535$	20.9201			0.904455
$536$			25.8074i			1.11471i
$537$	3.45997	−	7.86726i	0.149309	−	0.339497i
$538$			11.5894i			0.499656i
$539$		−	12.7305i		−	0.548343i
$540$	6.07193	−	2.06484i	0.261294	−	0.0888564i
$541$	−40.5643			−1.74400			−0.871998	−	0.489510i	$-0.837176\pi$
$541$	−40.5643			−1.74400			−0.871998	+	0.489510i	$0.837176\pi$
$542$		−	37.8694i		−	1.62663i
$543$	−3.48323	+	7.92015i	−0.149480	+	0.339886i
$544$	−6.10805			−0.261881
$545$		−	48.9906i		−	2.09853i
$546$	−7.20781	+	16.3891i	−0.308466	+	0.701387i
$547$	24.0870			1.02989			0.514943	−	0.857224i	$-0.327813\pi$
$547$	24.0870			1.02989			0.514943	+	0.857224i	$0.327813\pi$
$548$		−	5.53024i		−	0.236240i
$549$	−17.0808	+	15.6631i	−0.728990	+	0.668484i
$550$		−	24.4199i		−	1.04127i
$551$	−6.09980			−0.259860
$552$	4.75944	+	2.09317i	0.202575	+	0.0890913i
$553$		−	2.79408i		−	0.118816i
$554$	19.2408			0.817463
$555$	8.82538	−	20.0671i	0.374617	−	0.851801i
$556$	−3.14023			−0.133175
$557$	−6.55396			−0.277700			−0.138850	−	0.990313i	$-0.544341\pi$
$557$	−6.55396			−0.277700			−0.138850	+	0.990313i	$0.544341\pi$
$558$	24.4318	−	22.4040i	1.03428	−	0.948436i
$559$	−30.9738			−1.31005
$560$	−26.5397			−1.12151
$561$	6.87383	−	15.6297i	0.290213	−	0.659886i
$562$		−	35.9444i		−	1.51622i
$563$	−12.9989			−0.547840			−0.273920	−	0.961752i	$-0.588320\pi$
$563$	−12.9989			−0.547840			−0.273920	+	0.961752i	$0.588320\pi$
$564$	0.685120	−	1.55782i	0.0288488	−	0.0655962i
$565$	2.43783			0.102560
$566$			7.51290i			0.315791i
$567$	16.7708	+	1.45497i	0.704307	+	0.0611028i
$568$			16.5237i			0.693320i
$569$	23.9233			1.00292			0.501459	−	0.865181i	$-0.332797\pi$
$569$	23.9233			1.00292			0.501459	+	0.865181i	$0.332797\pi$
$570$	−17.9830	+	40.8896i	−0.753224	+	1.71268i
$571$			9.58427i			0.401089i	0.979685	+	0.200545i	$0.0642712\pi$
$571$			9.58427i			0.401089i	−0.979685	+	0.200545i	$0.935729\pi$
$572$			5.23588i			0.218923i
$573$	−18.9301	−	8.32536i	−0.790818	−	0.347797i
$574$			10.3523i			0.432098i
$575$	5.25512			0.219154
$576$	11.7535	+	12.8173i	0.489729	+	0.534056i
$577$			16.4136i			0.683306i	0.939826	+	0.341653i	$0.110987\pi$
$577$			16.4136i			0.683306i	−0.939826	+	0.341653i	$0.889013\pi$
$578$	14.9595			0.622234
$579$	−42.3846	−	18.6405i	−1.76144	−	0.774671i
$580$		−	1.38271i		−	0.0574139i
$581$	6.60899			0.274187
$582$	−19.8223	+	45.0718i	−0.821660	+	1.86829i
$583$	18.2957			0.757730
$584$	−21.3567			−0.883747
$585$	24.0754	−	22.0772i	0.995395	−	0.912778i
$586$			10.7018i			0.442087i
$587$	5.51405			0.227589			0.113795	−	0.993504i	$-0.463699\pi$
$587$	5.51405			0.227589			0.113795	+	0.993504i	$0.463699\pi$
$588$	−2.24306	−	0.986485i	−0.0925024	−	0.0406820i
$589$			38.8034i			1.59886i
$590$	−9.47947			−0.390264
$591$	−28.4098	−	12.4944i	−1.16862	−	0.513953i
$592$	−19.2444			−0.790939
$593$		−	9.51762i		−	0.390842i	−0.980719	−	0.195421i	$-0.937393\pi$
$593$		−	9.51762i		−	0.390842i	0.980719	−	0.195421i	$-0.0626073\pi$
$594$	27.7319	−	9.43058i	1.13785	−	0.386941i
$595$	−15.4925			−0.635132
$596$	1.64609			0.0674263
$597$	13.0419	+	5.73572i	0.533768	+	0.234747i
$598$	−6.70423			−0.274156
$599$	36.9163			1.50836			0.754179	−	0.656669i	$-0.228035\pi$
$599$	36.9163			1.50836			0.754179	+	0.656669i	$0.228035\pi$
$600$	16.9958	+	7.47465i	0.693851	+	0.305151i
$601$	−16.4120			−0.669461			−0.334730	−	0.942314i	$-0.608645\pi$
$601$	−16.4120			−0.669461			−0.334730	+	0.942314i	$0.608645\pi$
$602$			25.2014i			1.02713i
$603$	−23.0599	+	21.1460i	−0.939074	+	0.861131i
$604$	8.01351			0.326065
$605$		−	6.77684i		−	0.275518i
$606$	−14.8452	+	33.7548i	−0.603043	+	1.37120i
$607$	−5.93411			−0.240858			−0.120429	−	0.992722i	$-0.538427\pi$
$607$	−5.93411			−0.240858			−0.120429	+	0.992722i	$0.538427\pi$
$608$	12.2659			0.497446
$609$	1.46109	−	3.32221i	0.0592063	−	0.134623i
$610$	36.5896			1.48147
$611$		−	8.66788i		−	0.350665i
$612$	−2.22123	−	2.42228i	−0.0897880	−	0.0979149i
$613$			19.4445i			0.785356i	0.919676	+	0.392678i	$0.128451\pi$
$613$			19.4445i			0.785356i	−0.919676	+	0.392678i	$0.871549\pi$
$614$	−9.38594			−0.378786
$615$	7.60375	−	17.2894i	0.306613	−	0.697175i
$616$	−16.8276			−0.678004
$617$	−18.0169			−0.725333			−0.362666	−	0.931919i	$-0.618134\pi$
$617$	−18.0169			−0.725333			−0.362666	+	0.931919i	$0.618134\pi$
$618$	−19.1614	−	8.42706i	−0.770785	−	0.338986i
$619$		−	16.9518i		−	0.681349i	−0.940181	−	0.340675i	$-0.889345\pi$
$619$		−	16.9518i		−	0.681349i	0.940181	−	0.340675i	$-0.110655\pi$
$620$	−8.79599			−0.353256
$621$	2.02944	+	5.96785i	0.0814387	+	0.239481i
$622$		−	52.9416i		−	2.12276i
$623$		−	33.6289i		−	1.34731i
$624$	−26.2491	−	11.5442i	−1.05080	−	0.462136i
$625$	−27.8939			−1.11576
$626$		−	40.1927i		−	1.60642i
$627$	−13.8037	+	31.3867i	−0.551265	+	1.25346i
$628$		−	4.30598i		−	0.171827i
$629$	−11.2339			−0.447925
$630$	−17.9628	−	19.5886i	−0.715654	−	0.780429i
$631$	20.6236			0.821013			0.410506	−	0.911858i	$-0.365352\pi$
$631$	20.6236			0.821013			0.410506	+	0.911858i	$0.365352\pi$
$632$	3.69652			0.147040
$633$	−15.2253	+	20.0298i	−0.605150	+	0.796111i
$634$	54.5863			2.16790
$635$	−20.3750			−0.808559
$636$	1.41773	−	3.22362i	0.0562166	−	0.127825i
$637$	−12.4806			−0.494501
$638$		−	6.31515i		−	0.250019i
$639$	−14.7646	+	13.5392i	−0.584079	+	0.535601i
$640$		−	41.2199i		−	1.62936i
$641$	32.4330			1.28103			0.640514	−	0.767947i	$-0.278721\pi$
$641$	32.4330			1.28103			0.640514	+	0.767947i	$0.278721\pi$
$642$	7.40391	−	16.8350i	0.292209	−	0.664423i
$643$			20.0173i			0.789404i	0.918809	+	0.394702i	$0.129152\pi$
$643$			20.0173i			0.789404i	−0.918809	+	0.394702i	$0.870848\pi$
$644$			0.916766i			0.0361257i
$645$	18.5103	−	42.0887i	0.728844	−	1.65724i
$646$	22.8907			0.900621
$647$		−	13.9957i		−	0.550226i	−0.961412	−	0.275113i	$-0.911285\pi$
$647$		−	13.9957i		−	0.550226i	0.961412	−	0.275113i	$-0.0887153\pi$
$648$	−1.92489	+	22.1875i	−0.0756169	+	0.871606i
$649$	−7.27640			−0.285624
$650$	−23.9406			−0.939027
$651$	−21.1340	−	9.29460i	−0.828307	−	0.364284i
$652$	−2.20477			−0.0863453
$653$			34.8310i			1.36304i	0.731798	+	0.681521i	$0.238681\pi$
$653$			34.8310i			1.36304i	−0.731798	+	0.681521i	$0.761319\pi$
$654$	−39.4241	−	17.3385i	−1.54160	−	0.677987i
$655$			54.4298i			2.12675i
$656$	−16.5805			−0.647361
$657$	−17.4992	−	19.0831i	−0.682709	−	0.744502i
$658$	−7.05250			−0.274935
$659$	−4.55326			−0.177370			−0.0886849	−	0.996060i	$-0.528266\pi$
$659$	−4.55326			−0.177370			−0.0886849	+	0.996060i	$0.528266\pi$
$660$	−7.11477	−	3.12903i	−0.276942	−	0.121797i
$661$			0.955706i			0.0371727i	0.999827	+	0.0185863i	$0.00591655\pi$
$661$			0.955706i			0.0371727i	−0.999827	+	0.0185863i	$0.994083\pi$
$662$	−21.6342			−0.840837
$663$	−15.3229	−	6.73890i	−0.595091	−	0.261717i
$664$			8.74358i			0.339317i
$665$	31.1112			1.20644
$666$	−13.0251	−	14.2040i	−0.504713	−	0.550395i
$667$	1.35901			0.0526210
$668$	0.958658			0.0370916
$669$	1.94130	−	4.41412i	0.0750550	−	0.170660i
$670$	49.3978			1.90840
$671$	28.0860			1.08425
$672$	−2.93805	+	6.68052i	−0.113338	+	0.257707i
$673$			13.2675i			0.511425i	0.966753	+	0.255713i	$0.0823101\pi$
$673$			13.2675i			0.511425i	−0.966753	+	0.255713i	$0.917690\pi$
$674$	−52.5522			−2.02424
$675$	7.24707	+	21.3110i	0.278940	+	0.820260i
$676$	−0.119368			−0.00459106
$677$		−	49.4135i		−	1.89911i	−0.313595	−	0.949557i	$-0.601533\pi$
$677$		−	49.4135i		−	1.89911i	0.313595	−	0.949557i	$-0.398467\pi$
$678$	0.862782	−	1.96179i	0.0331349	−	0.0753420i
$679$	34.2933			1.31606
$680$		−	20.4963i		−	0.785998i
$681$	−9.50599	+	21.6147i	−0.364270	+	0.828276i
$682$	−40.1733			−1.53832
$683$	35.8399			1.37138			0.685688	−	0.727895i	$-0.259501\pi$
$683$	35.8399			1.37138			0.685688	+	0.727895i	$0.259501\pi$
$684$	4.46056	+	4.86429i	0.170554	+	0.185991i
$685$	41.8128			1.59759
$686$			30.4553i			1.16279i
$687$	13.0497	−	29.6723i	0.497876	−	1.13207i
$688$	−40.3631			−1.53883
$689$		−	17.9366i		−	0.683328i
$690$	4.00653	−	9.11002i	0.152526	−	0.346813i
$691$	−15.0405			−0.572166			−0.286083	−	0.958205i	$-0.592353\pi$
$691$	−15.0405			−0.572166			−0.286083	+	0.958205i	$0.592353\pi$
$692$		−	7.17322i		−	0.272685i
$693$	−13.7881	−	15.0361i	−0.523768	−	0.571176i
$694$			25.9677i			0.985719i
$695$		−	23.7425i		−	0.900606i
$696$	4.39523	+	1.93299i	0.166601	+	0.0732699i
$697$	−9.67888			−0.366614
$698$			29.4226i			1.11366i
$699$	37.2528	+	16.3836i	1.40903	+	0.619683i
$700$			3.27374i			0.123736i
$701$	−44.0303			−1.66300			−0.831501	−	0.555524i	$-0.812518\pi$
$701$	−44.0303			−1.66300			−0.831501	+	0.555524i	$0.812518\pi$
$702$	−9.24546	−	27.1875i	−0.348948	−	1.02613i
$703$	22.5593			0.850840
$704$		−	21.0756i		−	0.794317i
$705$	11.7783	+	5.18003i	0.443597	+	0.195091i
$706$	−45.1315			−1.69855
$707$	25.6827			0.965897
$708$	−0.563847	+	1.28207i	−0.0211907	+	0.0481832i
$709$	27.8726			1.04678			0.523389	−	0.852094i	$-0.324667\pi$
$709$	27.8726			1.04678			0.523389	+	0.852094i	$0.324667\pi$
$710$	31.6280			1.18698
$711$	3.02884	+	3.30299i	0.113590	+	0.123872i
$712$	44.4904			1.66735
$713$		−	8.64522i		−	0.323766i
$714$	−5.48302	+	12.4673i	−0.205197	+	0.466575i
$715$	−39.5873			−1.48048
$716$			2.00484i			0.0749244i
$717$	7.56304	+	3.32618i	0.282447	+	0.124218i
$718$		−	29.1302i		−	1.08713i
$719$	27.5911			1.02897			0.514487	−	0.857498i	$-0.327982\pi$
$719$	27.5911			1.02897			0.514487	+	0.857498i	$0.327982\pi$
$720$	31.3735	−	28.7695i	1.16922	−	1.07218i
$721$			14.5791i			0.542956i
$722$	−16.5083			−0.614377
$723$	−27.0499	−	11.8964i	−1.00600	−	0.442430i
$724$		−	2.01832i		−	0.0750103i
$725$	4.85298			0.180235
$726$	−5.45350	−	2.39842i	−0.202398	−	0.0890135i
$727$			10.6719i			0.395797i	0.980222	+	0.197899i	$0.0634117\pi$
$727$			10.6719i			0.395797i	−0.980222	+	0.197899i	$0.936588\pi$
$728$			16.4973i			0.611431i
$729$	−21.4026	+	16.4599i	−0.792689	+	0.609627i
$730$			40.8788i			1.51299i
$731$	−23.5619			−0.871470
$732$	2.17638	−	4.94863i	0.0804412	−	0.182907i
$733$	−13.4107			−0.495336			−0.247668	−	0.968845i	$-0.579664\pi$
$733$	−13.4107			−0.495336			−0.247668	+	0.968845i	$0.579664\pi$
$734$			42.4668i			1.56748i
$735$	7.45858	−	16.9593i	0.275114	−	0.625553i
$736$	−2.73278			−0.100732
$737$	37.9176			1.39671
$738$	−11.2221	−	12.2379i	−0.413093	−	0.450483i
$739$		−	41.4486i		−	1.52471i	−0.647157	−	0.762356i	$-0.724042\pi$
$739$		−	41.4486i		−	1.52471i	0.647157	−	0.762356i	$-0.275958\pi$
$740$			5.11377i			0.187986i
$741$	30.7706	+	13.5327i	1.13039	+	0.497136i
$742$	−14.5938			−0.535756
$743$	8.39628			0.308030			0.154015	−	0.988069i	$-0.450780\pi$
$743$	8.39628			0.308030			0.154015	+	0.988069i	$0.450780\pi$
$744$	12.2966	−	27.9599i	0.450815	−	1.02506i
$745$			12.4457i			0.455974i
$746$			45.3256i			1.65949i
$747$	−7.81274	+	7.16428i	−0.285853	+	0.262127i
$748$			3.98297i			0.145632i
$749$	−12.8090			−0.468032
$750$	−2.20635	+	5.01678i	−0.0805645	+	0.183187i
$751$			20.1895i			0.736724i	0.929682	+	0.368362i	$0.120081\pi$
$751$			20.1895i			0.736724i	−0.929682	+	0.368362i	$0.879919\pi$
$752$		−	11.2954i		−	0.411902i
$753$	13.0639	+	5.74541i	0.476074	+	0.209374i
$754$	−6.19119			−0.225470
$755$			60.5883i			2.20503i
$756$	−3.71775	+	1.26427i	−0.135213	+	0.0459809i
$757$			40.0764i			1.45660i	0.685257	+	0.728301i	$0.259690\pi$
$757$			40.0764i			1.45660i	−0.685257	+	0.728301i	$0.740310\pi$
$758$			55.5339i			2.01708i
$759$	3.07540	−	6.99282i	0.111630	−	0.253823i
$760$			41.1596i			1.49302i
$761$	29.9839			1.08692			0.543458	−	0.839436i	$-0.317115\pi$
$761$	29.9839			1.08692			0.543458	+	0.839436i	$0.317115\pi$
$762$	−7.21100	+	16.3963i	−0.261227	+	0.593977i
$763$			29.9962i			1.08594i
$764$	4.82403			0.174527
$765$	18.3143	−	16.7942i	0.662155	−	0.607196i
$766$		−	34.5654i		−	1.24890i
$767$			7.13357i			0.257578i
$768$	−14.7891	−	6.50417i	−0.533657	−	0.234699i
$769$	12.9719			0.467780			0.233890	−	0.972263i	$-0.424855\pi$
$769$	12.9719			0.467780			0.233890	+	0.972263i	$0.424855\pi$
$770$			32.2096i			1.16076i
$771$	20.3754	−	46.3296i	0.733804	−	1.66852i
$772$	10.8010			0.388737
$773$	−43.7442			−1.57337			−0.786685	−	0.617354i	$-0.788205\pi$
$773$	−43.7442			−1.57337			−0.786685	+	0.617354i	$0.788205\pi$
$774$	−27.3188	−	29.7915i	−0.981955	−	1.07083i
$775$		−	30.8718i		−	1.10895i
$776$			45.3694i			1.62867i
$777$	−5.40364	+	12.2868i	−0.193855	+	0.440786i
$778$			50.7511i			1.81951i
$779$	19.4366			0.696388
$780$	−3.06761	+	6.97511i	−0.109838	+	0.249749i
$781$	24.2775			0.868718
$782$	−5.09994			−0.182374
$783$	1.87414	+	5.51116i	0.0669763	+	0.196953i
$784$	−16.2640			−0.580856
$785$	32.5565			1.16199
$786$	43.8011	+	19.2634i	1.56233	+	0.687104i
$787$	50.2493			1.79119			0.895597	−	0.444865i	$-0.146748\pi$
$787$	50.2493			1.79119			0.895597	+	0.444865i	$0.146748\pi$
$788$	7.23977			0.257906
$789$	−11.1593	+	25.3739i	−0.397281	+	0.903336i
$790$		−	7.07549i		−	0.251735i
$791$	−1.49265			−0.0530724
$792$	19.8925	−	18.2415i	0.706851	−	0.648182i
$793$		−	27.5347i		−	0.977786i
$794$		−	28.8325i		−	1.02323i
$795$	24.3730	+	10.7191i	0.864423	+	0.380168i
$796$	−3.32350			−0.117798
$797$	25.4058			0.899921			0.449961	−	0.893048i	$-0.351438\pi$
$797$	25.4058			0.899921			0.449961	+	0.893048i	$0.351438\pi$
$798$	11.0107	−	25.0360i	0.389774	−	0.886266i
$799$		−	6.59370i		−	0.233268i
$800$	−9.75867			−0.345021
$801$	36.4544	+	39.7539i	1.28805	+	1.40464i
$802$	−22.1571			−0.782395
$803$			31.3784i			1.10732i
$804$	2.93822	−	6.68091i	0.103623	−	0.235618i
$805$	−6.93145			−0.244302
$806$			39.3848i			1.38727i
$807$	−5.21201	+	11.8510i	−0.183471	+	0.417176i
$808$			33.9777i			1.19533i
$809$		−	11.3691i		−	0.399717i	−0.979825	−	0.199858i	$-0.935952\pi$
$809$		−	11.3691i		−	0.399717i	0.979825	−	0.199858i	$-0.0640482\pi$
$810$	42.4689	+	3.68443i	1.49221	+	0.129458i
$811$	−7.53165			−0.264472			−0.132236	−	0.991218i	$-0.542216\pi$
$811$	−7.53165			−0.264472			−0.132236	+	0.991218i	$0.542216\pi$
$812$			0.846611i			0.0297102i
$813$	17.0306	−	38.7242i	0.597291	−	1.35812i
$814$			23.3558i			0.818619i
$815$		−	16.6697i		−	0.583915i
$816$	−19.9678	−	8.78171i	−0.699013	−	0.307421i
$817$	47.3158			1.65537
$818$		−	33.8310i		−	1.18287i
$819$	−14.7410	+	13.5175i	−0.515092	+	0.472340i
$820$			4.40591i			0.153861i
$821$		−	8.41877i		−	0.293817i	−0.989150	−	0.146909i	$-0.953068\pi$
$821$		−	8.41877i		−	0.293817i	0.989150	−	0.146909i	$-0.0469323\pi$
$822$	14.7981	−	33.6479i	0.516144	−	1.17361i
$823$		−	4.83163i		−	0.168420i	−0.996448	−	0.0842099i	$-0.973163\pi$
$823$		−	4.83163i		−	0.168420i	0.996448	−	0.0842099i	$-0.0268366\pi$
$824$	−19.2879			−0.671927
$825$	10.9821	−	24.9711i	0.382349	−	0.869383i
$826$	5.80413			0.201952
$827$			25.2608i			0.878403i	0.898389	+	0.439202i	$0.144739\pi$
$827$			25.2608i			0.878403i	−0.898389	+	0.439202i	$0.855261\pi$
$828$	−0.993793	−	1.08374i	−0.0345367	−	0.0376627i
$829$	−43.9036			−1.52484			−0.762418	−	0.647085i	$-0.775988\pi$
$829$	−43.9036			−1.52484			−0.762418	+	0.647085i	$0.775988\pi$
$830$	16.7360			0.580916
$831$	19.6751	+	8.65298i	0.682521	+	0.300168i
$832$	−20.6619			−0.716323
$833$	−9.49409			−0.328951
$834$	−19.1063	−	8.40281i	−0.661596	−	0.290965i
$835$			7.24819i			0.250834i
$836$		−	7.99837i		−	0.276629i
$837$	35.0588	−	11.9222i	1.21181	−	0.412091i
$838$			10.1182i			0.349528i
$839$	−45.6067			−1.57452			−0.787259	−	0.616622i	$-0.788501\pi$
$839$	−45.6067			−1.57452			−0.787259	+	0.616622i	$0.788501\pi$
$840$	−22.4173	−	9.85899i	−0.773471	−	0.340168i
$841$	−27.7450			−0.956724
$842$		−	11.3352i		−	0.390636i
$843$	16.1649	−	36.7557i	0.556750	−	1.26593i
$844$	1.37009	−	5.70681i	0.0471605	−	0.196436i
$845$		−	0.902510i		−	0.0310473i
$846$	8.33702	−	7.64505i	0.286633	−	0.262842i
$847$			4.14935i			0.142573i
$848$		−	23.3738i		−	0.802659i
$849$	−3.37871	+	7.68248i	−0.115957	+	0.263662i
$850$	−18.2117			−0.624657
$851$	−5.02611			−0.172293
$852$	1.88126	−	4.27760i	0.0644509	−	0.146548i
$853$	13.1930			0.451719			0.225860	−	0.974160i	$-0.427481\pi$
$853$	13.1930			0.451719			0.225860	+	0.974160i	$0.427481\pi$
$854$	−22.4032			−0.766623
$855$	−36.7777	+	33.7252i	−1.25777	+	1.15338i
$856$		−	16.9461i		−	0.579207i
$857$			11.4571i			0.391367i	0.980667	+	0.195684i	$0.0626926\pi$
$857$			11.4571i			0.391367i	−0.980667	+	0.195684i	$0.937307\pi$
$858$	−14.0105	+	31.8569i	−0.478310	+	1.08758i
$859$		−	32.2425i		−	1.10010i	−0.835132	−	0.550050i	$-0.814609\pi$
$859$		−	32.2425i		−	1.10010i	0.835132	−	0.550050i	$-0.185391\pi$
$860$			10.7256i			0.365740i
$861$	−4.65566	+	10.5860i	−0.158664	+	0.360770i
$862$		−	19.2817i		−	0.656737i
$863$		−	14.4055i		−	0.490368i	−0.969477	−	0.245184i	$-0.921152\pi$
$863$		−	14.4055i		−	0.490368i	0.969477	−	0.245184i	$-0.0788484\pi$
$864$	−3.76864	−	11.0822i	−0.128212	−	0.377024i
$865$	54.2350			1.84405
$866$	13.8610			0.471016
$867$	15.2972	+	6.72760i	0.519519	+	0.228481i
$868$	5.38565			0.182801
$869$		−	5.43112i		−	0.184238i
$870$	3.69993	−	8.41289i	0.125439	−	0.285224i
$871$		−	37.1733i		−	1.25957i
$872$	−39.6844			−1.34388
$873$	−40.5394	+	37.1747i	−1.37205	+	1.25817i
$874$	10.2414			0.346421
$875$	3.81707			0.129040
$876$	5.52874	+	2.43150i	0.186799	+	0.0821529i
$877$			48.7287i			1.64545i	0.568440	+	0.822725i	$0.307547\pi$
$877$			48.7287i			1.64545i	−0.568440	+	0.822725i	$0.692453\pi$
$878$			18.2942i			0.617401i
$879$	−4.81281	+	10.9434i	−0.162332	+	0.369110i
$880$	−51.5876			−1.73902
$881$			21.7027i			0.731183i	0.930775	+	0.365591i	$0.119133\pi$
$881$			21.7027i			0.731183i	−0.930775	+	0.365591i	$0.880867\pi$
$882$	−11.0079	−	12.0042i	−0.370655	−	0.404204i
$883$		−	27.5896i		−	0.928464i	−0.885714	−	0.464232i	$-0.846330\pi$
$883$		−	27.5896i		−	0.928464i	0.885714	−	0.464232i	$-0.153670\pi$
$884$	3.90478			0.131332
$885$	−9.69344	−	4.26311i	−0.325841	−	0.143303i
$886$			1.67387i			0.0562349i
$887$			48.5574i			1.63040i	0.579181	+	0.815199i	$0.303372\pi$
$887$			48.5574i			1.63040i	−0.579181	+	0.815199i	$0.696628\pi$
$888$	−16.2552	−	7.14892i	−0.545488	−	0.239902i
$889$	12.4753			0.418409
$890$		−	85.1588i		−	2.85453i
$891$	32.5990	+	2.82815i	1.09211	+	0.0947466i
$892$			1.12486i			0.0376633i
$893$			13.2411i			0.443097i
$894$	10.0154	+	4.40469i	0.334964	+	0.147315i
$895$	−15.1581			−0.506680
$896$			25.2383i			0.843153i
$897$	−6.85555	−	3.01503i	−0.228900	−	0.100669i
$898$	24.2368			0.808792
$899$		−	7.98365i		−	0.266270i
$900$	−3.54880	−	3.87001i	−0.118293	−	0.129000i
$901$		−	13.6444i		−	0.454562i
$902$			20.1228i			0.670016i
$903$	−11.3336	+	25.7703i	−0.377158	+	0.857580i
$904$		−	1.97474i		−	0.0656790i
$905$	15.2600			0.507261
$906$	48.7570	+	21.4430i	1.61984	+	0.712396i
$907$			49.2433i			1.63510i	0.575861	+	0.817548i	$0.304667\pi$
$907$			49.2433i			1.63510i	−0.575861	+	0.817548i	$0.695333\pi$
$908$		−	5.50814i		−	0.182794i
$909$	−30.3605	+	27.8406i	−1.00699	+	0.923413i
$910$	31.5774			1.04678
$911$	−32.4014			−1.07351			−0.536753	−	0.843740i	$-0.680349\pi$
$911$	−32.4014			−1.07351			−0.536753	+	0.843740i	$0.680349\pi$
$912$	40.0982	+	17.6349i	1.32779	+	0.583951i
$913$	12.8465			0.425158
$914$			10.0190i			0.331399i
$915$	37.4155	+	16.4551i	1.23692	+	0.543988i
$916$			7.56149i			0.249839i
$917$		−	33.3265i		−	1.10054i
$918$	−7.03307	−	20.6817i	−0.232126	−	0.682598i
$919$		−	33.5604i		−	1.10706i	−0.832830	−	0.553528i	$-0.813281\pi$
$919$		−	33.5604i		−	1.10706i	0.832830	−	0.553528i	$-0.186719\pi$
$920$		−	9.17019i		−	0.302332i
$921$	−9.59780	−	4.22105i	−0.316258	−	0.139088i
$922$	12.6516			0.416658
$923$		−	23.8010i		−	0.783418i
$924$	4.35626	+	1.91586i	0.143311	+	0.0630270i
$925$	−17.9481			−0.590130
$926$			45.2683i			1.48761i
$927$	−15.8041	−	17.2345i	−0.519074	−	0.566057i
$928$	−2.52366			−0.0828431
$929$	−49.0177			−1.60822			−0.804110	−	0.594481i	$-0.797358\pi$
$929$	−49.0177			−1.60822			−0.804110	+	0.594481i	$0.797358\pi$
$930$	−53.5179	−	23.5368i	−1.75492	−	0.771803i
$931$	19.0655			0.624847
$932$	−9.49327			−0.310962
$933$	23.8089	−	54.1365i	0.779468	−	1.77235i
$934$		−	12.4618i		−	0.407762i
$935$	−30.1143			−0.984842
$936$	−17.8834	−	19.5021i	−0.584537	−	0.637445i
$937$	−33.4688			−1.09338			−0.546688	−	0.837336i	$-0.684112\pi$
$937$	−33.4688			−1.09338			−0.546688	+	0.837336i	$0.684112\pi$
$938$	−30.2455			−0.987551
$939$	18.0755	−	41.0999i	0.589870	−	1.34124i
$940$	−3.00151			−0.0978985
$941$	−8.32128			−0.271266			−0.135633	−	0.990759i	$-0.543307\pi$
$941$	−8.32128			−0.271266			−0.135633	+	0.990759i	$0.543307\pi$
$942$	11.5222	−	26.1991i	0.375413	−	0.853611i
$943$	−4.33039			−0.141017
$944$			9.29602i			0.302560i
$945$	−9.55882	−	28.1090i	−0.310948	−	0.914386i
$946$			48.9863i			1.59268i
$947$		−	47.5865i		−	1.54635i	−0.634191	−	0.773176i	$-0.718667\pi$
$947$		−	47.5865i		−	1.54635i	0.634191	−	0.773176i	$-0.281333\pi$
$948$	−0.956940	−	0.420856i	−0.0310800	−	0.0136688i
$949$	30.7625			0.998592
$950$	36.5718			1.18655
$951$	55.8184	+	24.5486i	1.81004	+	0.796042i
$952$			12.5496i			0.406734i
$953$			59.8782i			1.93964i	0.243813	+	0.969822i	$0.421602\pi$
$953$			59.8782i			1.93964i	−0.243813	+	0.969822i	$0.578398\pi$
$954$	17.2519	−	15.8200i	0.558551	−	0.512192i
$955$			36.4734i			1.18025i
$956$	−1.92732			−0.0623339
$957$	2.84005	−	6.45770i	0.0918059	−	0.208748i
$958$	−0.262119			−0.00846869
$959$	−25.6013			−0.826711
$960$	12.3478	−	28.0764i	0.398524	−	0.906161i
$961$	−19.7874			−0.638302
$962$	22.8973			0.738239
$963$	15.1421	−	13.8853i	0.487946	−	0.447446i
$964$	6.89321			0.222015
$965$			81.6639i			2.62885i
$966$	−2.45314	+	5.57793i	−0.0789283	+	0.179467i
$967$	−23.7599			−0.764066			−0.382033	−	0.924149i	$-0.624776\pi$
$967$	−23.7599			−0.764066			−0.382033	+	0.924149i	$0.624776\pi$
$968$	−5.48952			−0.176440
$969$	23.4073	+	10.2944i	0.751952	+	0.330704i
$970$	86.8414			2.78831
$971$	42.1698			1.35329			0.676647	−	0.736308i	$-0.263432\pi$
$971$	42.1698			1.35329			0.676647	+	0.736308i	$0.263432\pi$
$972$	3.02439	−	5.52465i	0.0970075	−	0.177203i
$973$			14.5372i			0.466041i
$974$	42.8190			1.37201
$975$	−24.4810	−	10.7666i	−0.784018	−	0.344806i
$976$		−	35.8815i		−	1.14854i
$977$	8.30026			0.265549			0.132774	−	0.991146i	$-0.457611\pi$
$977$	8.30026			0.265549			0.132774	+	0.991146i	$0.457611\pi$
$978$	−13.4146	−	5.89964i	−0.428951	−	0.188650i
$979$		−	65.3676i		−	2.08916i
$980$			4.32179i			0.138055i
$981$	−32.5165	−	35.4596i	−1.03817	−	1.13214i
$982$			24.3138i			0.775884i
$983$			41.1764i			1.31332i	0.754186	+	0.656661i	$0.228032\pi$
$983$			41.1764i			1.31332i	−0.754186	+	0.656661i	$0.771968\pi$
$984$	−14.0051	−	6.15935i	−0.446466	−	0.196353i
$985$			54.7382i			1.74410i
$986$	−4.70967			−0.149987
$987$	−7.21169	−	3.17165i	−0.229550	−	0.100955i
$988$	−7.84137			−0.249467
$989$	−10.5418			−0.335209
$990$	−34.9159	−	38.0762i	−1.10970	−	1.21014i
$991$		−	44.5293i		−	1.41452i	−0.706954	−	0.707260i	$-0.749931\pi$
$991$		−	44.5293i		−	1.41452i	0.706954	−	0.707260i	$-0.250069\pi$
$992$			16.0540i			0.509716i
$993$	−22.1225	−	9.72934i	−0.702037	−	0.308751i
$994$	−19.3653			−0.614231
$995$		−	25.1282i		−	0.796618i
$996$	0.995473	−	2.26350i	0.0315428	−	0.0717218i
$997$		−	24.6717i		−	0.781360i	−0.920527	−	0.390680i	$-0.872240\pi$
$997$		−	24.6717i		−	0.781360i	0.920527	−	0.390680i	$-0.127760\pi$
$998$		−	45.4539i		−	1.43882i
$999$	−6.93126	−	20.3823i	−0.219295	−	0.644868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.d.a.632.17	✓	68
3.2	odd	2	inner	633.2.d.a.632.51	yes	68
211.210	odd	2	inner	633.2.d.a.632.52	yes	68
633.632	even	2	inner	633.2.d.a.632.18	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.d.a.632.17	✓	68	1.1	even	1	trivial
633.2.d.a.632.18	yes	68	633.632	even	2	inner
633.2.d.a.632.51	yes	68	3.2	odd	2	inner
633.2.d.a.632.52	yes	68	211.210	odd	2	inner

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:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.55050 q^{2} +(-1.58549 - 0.697289i) q^{3} +0.404037 q^{4} +3.05483i q^{5} +(2.45830 + 1.08114i) q^{6} -1.87042i q^{7} +2.47453 q^{8} +(2.02757 + 2.21109i) q^{9} +O(q^{10})\)	\(q-1.55050 q^{2} +(-1.58549 - 0.697289i) q^{3} +0.404037 q^{4} +3.05483i q^{5} +(2.45830 + 1.08114i) q^{6} -1.87042i q^{7} +2.47453 q^{8} +(2.02757 + 2.21109i) q^{9} -4.73649i q^{10} -3.63571i q^{11} +(-0.640597 - 0.281730i) q^{12} -3.56435 q^{13} +2.90008i q^{14} +(2.13010 - 4.84340i) q^{15} -4.64483 q^{16} -2.71142 q^{17} +(-3.14375 - 3.42829i) q^{18} +5.44492 q^{19} +1.23426i q^{20} +(-1.30423 + 2.96554i) q^{21} +5.63716i q^{22} -1.21310 q^{23} +(-3.92336 - 1.72547i) q^{24} -4.33196 q^{25} +5.52650 q^{26} +(-1.67293 - 4.91948i) q^{27} -0.755719i q^{28} -1.12027 q^{29} +(-3.30271 + 7.50968i) q^{30} +7.12653i q^{31} +2.25272 q^{32} +(-2.53514 + 5.76440i) q^{33} +4.20404 q^{34} +5.71381 q^{35} +(0.819214 + 0.893363i) q^{36} +4.14318 q^{37} -8.44232 q^{38} +(5.65124 + 2.48538i) q^{39} +7.55927i q^{40} +3.56967 q^{41} +(2.02220 - 4.59806i) q^{42} +8.68990 q^{43} -1.46896i q^{44} +(-6.75451 + 6.19389i) q^{45} +1.88091 q^{46} +2.43183i q^{47} +(7.36434 + 3.23879i) q^{48} +3.50152 q^{49} +6.71668 q^{50} +(4.29893 + 1.89064i) q^{51} -1.44013 q^{52} +5.03222i q^{53} +(2.59387 + 7.62763i) q^{54} +11.1065 q^{55} -4.62842i q^{56} +(-8.63288 - 3.79668i) q^{57} +1.73698 q^{58} -2.00137i q^{59} +(0.860637 - 1.95691i) q^{60} +7.72503i q^{61} -11.0496i q^{62} +(4.13568 - 3.79242i) q^{63} +5.79683 q^{64} -10.8885i q^{65} +(3.93073 - 8.93767i) q^{66} +10.4292i q^{67} -1.09551 q^{68} +(1.92337 + 0.845885i) q^{69} -8.85924 q^{70} +6.67751i q^{71} +(5.01730 + 5.47143i) q^{72} -8.63060 q^{73} -6.42399 q^{74} +(6.86829 + 3.02063i) q^{75} +2.19995 q^{76} -6.80032 q^{77} +(-8.76223 - 3.85357i) q^{78} +1.49382 q^{79} -14.1891i q^{80} +(-0.777881 + 8.96632i) q^{81} -5.53476 q^{82} +3.53342i q^{83} +(-0.526955 + 1.19819i) q^{84} -8.28291i q^{85} -13.4737 q^{86} +(1.77618 + 0.781155i) q^{87} -8.99669i q^{88} +17.9793 q^{89} +(10.4728 - 9.60359i) q^{90} +6.66683i q^{91} -0.490139 q^{92} +(4.96925 - 11.2991i) q^{93} -3.77054i q^{94} +16.6333i q^{95} +(-3.57167 - 1.57080i) q^{96} +18.3345i q^{97} -5.42909 q^{98} +(8.03890 - 7.37168i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

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