LMFDB - Embedded newform 592.2.be.e.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 885 x^{16} + 9292 x^{14} + 58264 x^{12} + 224256 x^{10} + 523884 x^{8} + 706272 x^{6} + \cdots + 144 $ x^20 + 46x^18 + 885x^16 + 9292x^14 + 58264x^12 + 224256x^10 + 523884x^8 + 706272x^6 + 490896x^4 + 133632*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			415.1
Root			$-3.38161i$ of defining polynomial
Character	$\chi$	$=$	592.415
Dual form			592.2.be.e.495.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69080 + 2.92856i) q^{3} +(-3.56248 + 0.954562i) q^{5} +(1.92706 + 1.11259i) q^{7} +(-4.21763 - 7.30516i) q^{9} +O(q^{10})$	\(q+(-1.69080 + 2.92856i) q^{3} +(-3.56248 + 0.954562i) q^{5} +(1.92706 + 1.11259i) q^{7} +(-4.21763 - 7.30516i) q^{9} -2.24535 q^{11} +(-1.64362 + 0.440407i) q^{13} +(3.22795 - 12.0469i) q^{15} +(-1.39972 + 5.22382i) q^{17} +(0.234165 + 0.873916i) q^{19} +(-6.51656 + 3.76234i) q^{21} +(2.13932 - 2.13932i) q^{23} +(7.44991 - 4.30121i) q^{25} +18.3799 q^{27} +(4.32421 - 4.32421i) q^{29} +(2.78330 + 2.78330i) q^{31} +(3.79644 - 6.57563i) q^{33} +(-7.92713 - 2.12407i) q^{35} +(-0.473300 - 6.06432i) q^{37} +(1.48928 - 5.55809i) q^{39} +(-10.1520 - 5.86126i) q^{41} +(0.347671 - 0.347671i) q^{43} +(21.9984 + 21.9984i) q^{45} +9.31282i q^{47} +(-1.02430 - 1.77413i) q^{49} +(-12.9316 - 12.9316i) q^{51} +(1.97620 + 3.42288i) q^{53} +(7.99899 - 2.14332i) q^{55} +(-2.95524 - 0.791855i) q^{57} +(-7.10427 - 1.90358i) q^{59} +(0.0255759 + 0.0954505i) q^{61} -18.7700i q^{63} +(5.43497 - 3.13788i) q^{65} +(1.46993 - 2.54599i) q^{67} +(2.64795 + 9.88230i) q^{69} +(-8.21142 - 4.74087i) q^{71} -6.21278i q^{73} +29.0900i q^{75} +(-4.32691 - 2.49815i) q^{77} +(4.01895 + 14.9989i) q^{79} +(-18.4240 + 31.9112i) q^{81} +(-7.19254 + 4.15262i) q^{83} -19.9459i q^{85} +(5.35231 + 19.9751i) q^{87} +(-8.39237 - 2.24873i) q^{89} +(-3.65735 - 0.979984i) q^{91} +(-12.8571 + 3.44504i) q^{93} +(-1.66842 - 2.88978i) q^{95} +(-6.02255 - 6.02255i) q^{97} +(9.47005 + 16.4026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.69080	+	2.92856i	−0.976186	+	1.69080i	−0.300221	+	0.953870i	$0.597060\pi$
$3$	−1.69080	+	2.92856i	−0.976186	+	1.69080i	−0.675965	+	0.736934i	$0.736273\pi$
$4$		0			0
$5$	−3.56248	+	0.954562i	−1.59319	+	0.426893i	−0.942976	−	0.332860i	$-0.891986\pi$
$5$	−3.56248	+	0.954562i	−1.59319	+	0.426893i	−0.650211	+	0.759754i	$0.725320\pi$
$6$		0			0
$7$	1.92706	+	1.11259i	0.728360	+	0.420519i	0.817822	−	0.575471i	$-0.195181\pi$
$7$	1.92706	+	1.11259i	0.728360	+	0.420519i	−0.0894620	+	0.995990i	$0.528515\pi$
$8$		0			0
$9$	−4.21763	−	7.30516i	−1.40588	−	2.43505i
$10$		0			0
$11$	−2.24535			−0.676997			−0.338499	−	0.940967i	$-0.609919\pi$
$11$	−2.24535			−0.676997			−0.338499	+	0.940967i	$0.609919\pi$
$12$		0			0
$13$	−1.64362	+	0.440407i	−0.455859	+	0.122147i	−0.479440	−	0.877575i	$-0.659160\pi$
$13$	−1.64362	+	0.440407i	−0.455859	+	0.122147i	0.0235806	+	0.999722i	$0.492493\pi$
$14$		0			0
$15$	3.22795	−	12.0469i	0.833454	−	3.11049i
$16$		0			0
$17$	−1.39972	+	5.22382i	−0.339482	+	1.26696i	0.559446	+	0.828867i	$0.311014\pi$
$17$	−1.39972	+	5.22382i	−0.339482	+	1.26696i	−0.898928	+	0.438097i	$0.855653\pi$
$18$		0			0
$19$	0.234165	+	0.873916i	0.0537212	+	0.200490i	0.987571	−	0.157176i	$-0.0502391\pi$
$19$	0.234165	+	0.873916i	0.0537212	+	0.200490i	−0.933849	+	0.357667i	$0.883572\pi$
$20$		0			0
$21$	−6.51656	+	3.76234i	−1.42203	+	0.821009i
$22$		0			0
$23$	2.13932	−	2.13932i	0.446079	−	0.446079i	−0.447970	−	0.894049i	$-0.647853\pi$
$23$	2.13932	−	2.13932i	0.446079	−	0.446079i	0.894049	+	0.447970i	$0.147853\pi$
$24$		0			0
$25$	7.44991	−	4.30121i	1.48998	−	0.860242i
$26$		0			0
$27$	18.3799			3.53722
$28$		0			0
$29$	4.32421	−	4.32421i	0.802986	−	0.802986i	−0.180575	−	0.983561i	$-0.557796\pi$
$29$	4.32421	−	4.32421i	0.802986	−	0.802986i	0.983561	+	0.180575i	$0.0577958\pi$
$30$		0			0
$31$	2.78330	+	2.78330i	0.499896	+	0.499896i	0.911405	−	0.411510i	$-0.134998\pi$
$31$	2.78330	+	2.78330i	0.499896	+	0.499896i	−0.411510	+	0.911405i	$0.634998\pi$
$32$		0			0
$33$	3.79644	−	6.57563i	0.660875	−	1.14467i
$34$		0			0
$35$	−7.92713	−	2.12407i	−1.33993	−	0.359033i
$36$		0			0
$37$	−0.473300	−	6.06432i	−0.0778101	−	0.996968i
$37$	−0.473300	−	6.06432i	−0.0778101	−	0.996968i
$38$		0			0
$39$	1.48928	−	5.55809i	0.238476	−	0.890006i
$40$		0			0
$41$	−10.1520	−	5.86126i	−1.58547	−	0.915374i	−0.994039	−	0.109022i	$-0.965228\pi$
$41$	−10.1520	−	5.86126i	−1.58547	−	0.915374i	−0.591436	−	0.806352i	$-0.701439\pi$
$42$		0			0
$43$	0.347671	−	0.347671i	0.0530193	−	0.0530193i	−0.680100	−	0.733119i	$-0.738064\pi$
$43$	0.347671	−	0.347671i	0.0530193	−	0.0530193i	0.733119	+	0.680100i	$0.238064\pi$
$44$		0			0
$45$	21.9984	+	21.9984i	3.27933	+	3.27933i
$46$		0			0
$47$			9.31282i			1.35841i	0.733947	+	0.679207i	$0.237676\pi$
$47$			9.31282i			1.35841i	−0.733947	+	0.679207i	$0.762324\pi$
$48$		0			0
$49$	−1.02430	−	1.77413i	−0.146328	−	0.253447i
$50$		0			0
$51$	−12.9316	−	12.9316i	−1.81079	−	1.81079i
$52$		0			0
$53$	1.97620	+	3.42288i	0.271452	+	0.470169i	0.969234	−	0.246142i	$-0.0791629\pi$
$53$	1.97620	+	3.42288i	0.271452	+	0.470169i	−0.697782	+	0.716310i	$0.745830\pi$
$54$		0			0
$55$	7.99899	−	2.14332i	1.07858	−	0.289006i
$56$		0			0
$57$	−2.95524	−	0.791855i	−0.391431	−	0.104884i
$58$		0			0
$59$	−7.10427	−	1.90358i	−0.924897	−	0.247825i	−0.235220	−	0.971942i	$-0.575581\pi$
$59$	−7.10427	−	1.90358i	−0.924897	−	0.247825i	−0.689677	+	0.724117i	$0.742248\pi$
$60$		0			0
$61$	0.0255759	+	0.0954505i	0.00327466	+	0.0122212i	0.967544	−	0.252703i	$-0.0813196\pi$
$61$	0.0255759	+	0.0954505i	0.00327466	+	0.0122212i	−0.964269	+	0.264924i	$0.914653\pi$
$62$		0			0
$63$		−	18.7700i		−	2.36479i
$64$		0			0
$65$	5.43497	−	3.13788i	0.674125	−	0.389206i
$66$		0			0
$67$	1.46993	−	2.54599i	0.179580	−	0.311043i	−0.762156	−	0.647393i	$-0.775859\pi$
$67$	1.46993	−	2.54599i	0.179580	−	0.311043i	0.941737	+	0.336350i	$0.109193\pi$
$68$		0			0
$69$	2.64795	+	9.88230i	0.318776	+	1.18969i
$70$		0			0
$71$	−8.21142	−	4.74087i	−0.974516	−	0.562637i	−0.0739062	−	0.997265i	$-0.523547\pi$
$71$	−8.21142	−	4.74087i	−0.974516	−	0.562637i	−0.900610	+	0.434628i	$0.856880\pi$
$72$		0			0
$73$		−	6.21278i		−	0.727151i	−0.931565	−	0.363576i	$-0.881556\pi$
$73$		−	6.21278i		−	0.727151i	0.931565	−	0.363576i	$-0.118444\pi$
$74$		0			0
$75$			29.0900i			3.35902i
$76$		0			0
$77$	−4.32691	−	2.49815i	−0.493098	−	0.284690i
$78$		0			0
$79$	4.01895	+	14.9989i	0.452167	+	1.68751i	0.696285	+	0.717765i	$0.254835\pi$
$79$	4.01895	+	14.9989i	0.452167	+	1.68751i	−0.244118	+	0.969746i	$0.578498\pi$
$80$		0			0
$81$	−18.4240	+	31.9112i	−2.04711	+	3.54569i
$82$		0			0
$83$	−7.19254	+	4.15262i	−0.789484	+	0.455809i	−0.839781	−	0.542925i	$-0.817317\pi$
$83$	−7.19254	+	4.15262i	−0.789484	+	0.455809i	0.0502966	+	0.998734i	$0.483983\pi$
$84$		0			0
$85$		−	19.9459i		−	2.16343i
$86$		0			0
$87$	5.35231	+	19.9751i	0.573828	+	2.14156i
$88$		0			0
$89$	−8.39237	−	2.24873i	−0.889590	−	0.238365i	−0.215050	−	0.976603i	$-0.568991\pi$
$89$	−8.39237	−	2.24873i	−0.889590	−	0.238365i	−0.674540	+	0.738238i	$0.735658\pi$
$90$		0			0
$91$	−3.65735	−	0.979984i	−0.383394	−	0.102730i
$92$		0			0
$93$	−12.8571	+	3.44504i	−1.33322	+	0.357234i
$94$		0			0
$95$	−1.66842	−	2.88978i	−0.171176	−	0.296485i
$96$		0			0
$97$	−6.02255	−	6.02255i	−0.611498	−	0.611498i	0.331839	−	0.943336i	$-0.392331\pi$
$97$	−6.02255	−	6.02255i	−0.611498	−	0.611498i	−0.943336	+	0.331839i	$0.892331\pi$
$98$		0			0
$99$	9.47005	+	16.4026i	0.951776	+	1.64852i
$100$		0			0
$101$		−	1.38331i		−	0.137644i	−0.997629	−	0.0688222i	$-0.978076\pi$
$101$		−	1.38331i		−	0.137644i	0.997629	−	0.0688222i	$-0.0219241\pi$
$102$		0			0
$103$	−9.07886	−	9.07886i	−0.894567	−	0.894567i	0.100382	−	0.994949i	$-0.467994\pi$
$103$	−9.07886	−	9.07886i	−0.894567	−	0.894567i	−0.994949	+	0.100382i	$0.967994\pi$
$104$		0			0
$105$	19.6237	−	19.6237i	1.91508	−	1.91508i
$106$		0			0
$107$	−14.8966	−	8.60055i	−1.44011	−	0.831447i	−0.442252	−	0.896891i	$-0.645820\pi$
$107$	−14.8966	−	8.60055i	−1.44011	−	0.831447i	−0.997856	+	0.0654441i	$0.979154\pi$
$108$		0			0
$109$	2.16868	−	8.09363i	0.207722	−	0.775230i	−0.780880	−	0.624681i	$-0.785229\pi$
$109$	2.16868	−	8.09363i	0.207722	−	0.775230i	0.988603	−	0.150549i	$-0.0481041\pi$
$110$		0			0
$111$	18.5600	+	8.86749i	1.76163	+	0.841665i
$112$		0			0
$113$	11.2888	+	3.02482i	1.06196	+	0.284551i	0.747185	−	0.664616i	$-0.231405\pi$
$113$	11.2888	+	3.02482i	1.06196	+	0.284551i	0.314773	+	0.949167i	$0.398072\pi$
$114$		0			0
$115$	−5.57916	+	9.66339i	−0.520260	+	0.901116i
$116$		0			0
$117$	10.1494	+	10.1494i	0.938316	+	0.938316i
$118$		0			0
$119$	−8.50931	+	8.50931i	−0.780047	+	0.780047i
$120$		0			0
$121$	−5.95842			−0.541675
$122$		0			0
$123$	34.3301	−	19.8205i	3.09544	−	1.78715i
$124$		0			0
$125$	−9.39479	+	9.39479i	−0.840296	+	0.840296i
$126$		0			0
$127$	4.25566	−	2.45701i	0.377629	−	0.218024i	−0.299157	−	0.954204i	$-0.596705\pi$
$127$	4.25566	−	2.45701i	0.377629	−	0.218024i	0.676786	+	0.736180i	$0.263372\pi$
$128$		0			0
$129$	0.430331	+	1.60602i	0.0378885	+	0.141402i
$130$		0			0
$131$	4.36054	−	16.2738i	0.380983	−	1.42185i	−0.463421	−	0.886138i	$-0.653378\pi$
$131$	4.36054	−	16.2738i	0.380983	−	1.42185i	0.844403	−	0.535708i	$-0.179955\pi$
$132$		0			0
$133$	−0.521059	+	1.94462i	−0.0451815	+	0.168620i
$134$		0			0
$135$	−65.4781	+	17.5448i	−5.63546	+	1.51002i
$136$		0			0
$137$	−2.93781			−0.250994			−0.125497	−	0.992094i	$-0.540053\pi$
$137$	−2.93781			−0.250994			−0.125497	+	0.992094i	$0.540053\pi$
$138$		0			0
$139$	−0.0343652	−	0.0595222i	−0.00291481	−	0.00504861i	0.864564	−	0.502522i	$-0.167594\pi$
$139$	−0.0343652	−	0.0595222i	−0.00291481	−	0.00504861i	−0.867479	+	0.497474i	$0.834261\pi$
$140$		0			0
$141$	−27.2731	−	15.7461i	−2.29681	−	1.32606i
$142$		0			0
$143$	3.69050	−	0.988867i	0.308615	−	0.0826932i
$144$		0			0
$145$	−11.2772	+	19.5326i	−0.936518	+	1.62210i
$146$		0			0
$147$	6.92753			0.571373
$148$		0			0
$149$	2.52935			0.207213			0.103606	−	0.994618i	$-0.466962\pi$
$149$	2.52935			0.207213			0.103606	+	0.994618i	$0.466962\pi$
$150$		0			0
$151$	−6.25533	+	10.8345i	−0.509052	+	0.881703i	0.490894	+	0.871220i	$0.336670\pi$
$151$	−6.25533	+	10.8345i	−0.509052	+	0.881703i	−0.999945	+	0.0104835i	$0.996663\pi$
$152$		0			0
$153$	44.0644	−	11.8070i	3.56239	−	0.954540i
$154$		0			0
$155$	−12.5723	−	7.25861i	−1.00983	−	0.583025i
$156$		0			0
$157$	4.55127	+	7.88304i	0.363231	+	0.629135i	0.988491	−	0.151282i	$-0.0483402\pi$
$157$	4.55127	+	7.88304i	0.363231	+	0.629135i	−0.625260	+	0.780417i	$0.715007\pi$
$158$		0			0
$159$	−13.3655			−1.05995
$160$		0			0
$161$	6.50278	−	1.74241i	0.512491	−	0.137322i
$162$		0			0
$163$	−1.15480	+	4.30979i	−0.0904513	+	0.337569i	−0.996291	−	0.0860527i	$-0.972575\pi$
$163$	−1.15480	+	4.30979i	−0.0904513	+	0.337569i	0.905839	+	0.423621i	$0.139241\pi$
$164$		0			0
$165$	−7.24788	+	27.0494i	−0.564246	+	2.10580i
$166$		0			0
$167$	0.675910	+	2.52253i	0.0523035	+	0.195199i	0.987134	−	0.159895i	$-0.0511155\pi$
$167$	0.675910	+	2.52253i	0.0523035	+	0.195199i	−0.934831	+	0.355094i	$0.884449\pi$
$168$		0			0
$169$	−8.75079	+	5.05227i	−0.673138	+	0.388636i
$170$		0			0
$171$	5.39647	−	5.39647i	0.412679	−	0.412679i
$172$		0			0
$173$	3.60043	−	2.07871i	0.273735	−	0.158041i	−0.356849	−	0.934162i	$-0.616149\pi$
$173$	3.60043	−	2.07871i	0.273735	−	0.158041i	0.630584	+	0.776121i	$0.282815\pi$
$174$		0			0
$175$	19.1419			1.44699
$176$		0			0
$177$	17.5867	−	17.5867i	1.32190	−	1.32190i
$178$		0			0
$179$	0.117240	+	0.117240i	0.00876290	+	0.00876290i	0.711475	−	0.702712i	$-0.248028\pi$
$179$	0.117240	+	0.117240i	0.00876290	+	0.00876290i	−0.702712	+	0.711475i	$0.748028\pi$
$180$		0			0
$181$	0.0715957	−	0.124007i	0.00532167	−	0.00921740i	−0.863352	−	0.504602i	$-0.831639\pi$
$181$	0.0715957	−	0.124007i	0.00532167	−	0.00921740i	0.868674	+	0.495384i	$0.164973\pi$
$182$		0			0
$183$	−0.322776	−	0.0864876i	−0.0238603	−	0.00639335i
$184$		0			0
$185$	7.47489	+	21.1522i	0.549565	+	1.55514i
$186$		0			0
$187$	3.14285	−	11.7293i	0.229828	−	0.857731i
$188$		0			0
$189$	35.4192	+	20.4493i	2.57637	+	1.48747i
$190$		0			0
$191$	0.349825	−	0.349825i	0.0253124	−	0.0253124i	−0.694337	−	0.719650i	$-0.744302\pi$
$191$	0.349825	−	0.349825i	0.0253124	−	0.0253124i	0.719650	+	0.694337i	$0.244302\pi$
$192$		0			0
$193$	−6.15263	−	6.15263i	−0.442876	−	0.442876i	0.450102	−	0.892977i	$-0.351388\pi$
$193$	−6.15263	−	6.15263i	−0.442876	−	0.442876i	−0.892977	+	0.450102i	$0.851388\pi$
$194$		0			0
$195$			21.2222i			1.51975i
$196$		0			0
$197$	6.35633	+	11.0095i	0.452870	+	0.784393i	0.998563	−	0.0535916i	$-0.0170669\pi$
$197$	6.35633	+	11.0095i	0.452870	+	0.784393i	−0.545693	+	0.837985i	$0.683734\pi$
$198$		0			0
$199$	1.81433	+	1.81433i	0.128615	+	0.128615i	0.768484	−	0.639869i	$-0.221011\pi$
$199$	1.81433	+	1.81433i	0.128615	+	0.128615i	−0.639869	+	0.768484i	$0.721011\pi$
$200$		0			0
$201$	4.97072	+	8.60955i	0.350608	+	0.607271i
$202$		0			0
$203$	13.1441	−	3.52195i	0.922534	−	0.247192i
$204$		0			0
$205$	41.7612	+	11.1899i	2.91673	+	0.781534i
$206$		0			0
$207$	−24.6509	−	6.60520i	−1.71336	−	0.459093i
$208$		0			0
$209$	−0.525782	−	1.96224i	−0.0363691	−	0.135731i
$210$		0			0
$211$			21.8633i			1.50513i	0.658517	+	0.752566i	$0.271184\pi$
$211$			21.8633i			1.50513i	−0.658517	+	0.752566i	$0.728816\pi$
$212$		0			0
$213$	27.7678	−	16.0317i	1.90262	−	1.09848i
$214$		0			0
$215$	−0.906695	+	1.57044i	−0.0618361	+	0.107103i
$216$		0			0
$217$	2.26692	+	8.46025i	0.153888	+	0.574319i
$218$		0			0
$219$	18.1945	+	10.5046i	1.22947	+	0.709835i
$220$		0			0
$221$		−	9.20244i		−	0.619023i
$222$		0			0
$223$		−	22.1978i		−	1.48648i	−0.669027	−	0.743238i	$-0.733289\pi$
$223$		−	22.1978i		−	1.48648i	0.669027	−	0.743238i	$-0.266711\pi$
$224$		0			0
$225$	−62.8420	−	36.2819i	−4.18947	−	2.41879i
$226$		0			0
$227$	2.09989	+	7.83689i	0.139375	+	0.520153i	0.999942	+	0.0108156i	$0.00344277\pi$
$227$	2.09989	+	7.83689i	0.139375	+	0.520153i	−0.860567	+	0.509337i	$0.829891\pi$
$228$		0			0
$229$	0.836915	−	1.44958i	0.0553049	−	0.0957909i	−0.837048	−	0.547130i	$-0.815720\pi$
$229$	0.836915	−	1.44958i	0.0553049	−	0.0957909i	0.892352	+	0.451339i	$0.149054\pi$
$230$		0			0
$231$	14.6319	−	8.44775i	0.962710	−	0.555821i
$232$		0			0
$233$		−	16.4683i		−	1.07887i	−0.842027	−	0.539436i	$-0.818638\pi$
$233$		−	16.4683i		−	1.07887i	0.842027	−	0.539436i	$-0.181362\pi$
$234$		0			0
$235$	−8.88967	−	33.1767i	−0.579898	−	2.16421i
$236$		0			0
$237$	−50.7205	−	13.5905i	−3.29465	−	0.882798i
$238$		0			0
$239$	1.75647	+	0.470646i	0.113617	+	0.0304436i	0.315180	−	0.949032i	$-0.397935\pi$
$239$	1.75647	+	0.470646i	0.113617	+	0.0304436i	−0.201563	+	0.979476i	$0.564602\pi$
$240$		0			0
$241$	−6.49546	+	1.74045i	−0.418409	+	0.112112i	−0.461880	−	0.886942i	$-0.652825\pi$
$241$	−6.49546	+	1.74045i	−0.418409	+	0.112112i	0.0434711	+	0.999055i	$0.486158\pi$
$242$		0			0
$243$	−34.7327	−	60.1588i	−2.22810	−	3.85919i
$244$		0			0
$245$	5.34255	+	5.34255i	0.341323	+	0.341323i
$246$		0			0
$247$	−0.769758	−	1.33326i	−0.0489786	−	0.0848333i
$248$		0			0
$249$		−	28.0850i		−	1.77982i
$250$		0			0
$251$	16.0145	+	16.0145i	1.01083	+	1.01083i	0.999941	+	0.0108884i	$0.00346596\pi$
$251$	16.0145	+	16.0145i	1.01083	+	1.01083i	0.0108884	+	0.999941i	$0.496534\pi$
$252$		0			0
$253$	−4.80352	+	4.80352i	−0.301994	+	0.301994i
$254$		0			0
$255$	58.4126	+	33.7245i	3.65794	+	2.11191i
$256$		0			0
$257$	−5.97650	+	22.3046i	−0.372804	+	1.39132i	0.483723	+	0.875221i	$0.339284\pi$
$257$	−5.97650	+	22.3046i	−0.372804	+	1.39132i	−0.856527	+	0.516102i	$0.827383\pi$
$258$		0			0
$259$	5.83501	−	12.2129i	0.362570	−	0.758872i
$260$		0			0
$261$	−49.8270	−	13.3511i	−3.08421	−	0.826413i
$262$		0			0
$263$	−5.16290	+	8.94241i	−0.318358	+	0.551412i	−0.980146	−	0.198279i	$-0.936465\pi$
$263$	−5.16290	+	8.94241i	−0.318358	+	0.551412i	0.661788	+	0.749691i	$0.269798\pi$
$264$		0			0
$265$	−10.3075	−	10.3075i	−0.633186	−	0.633186i
$266$		0			0
$267$	20.7754	−	20.7754i	1.27143	−	1.27143i
$268$		0			0
$269$	−14.7077			−0.896742			−0.448371	−	0.893848i	$-0.647996\pi$
$269$	−14.7077			−0.896742			−0.448371	+	0.893848i	$0.647996\pi$
$270$		0			0
$271$	−9.50719	+	5.48898i	−0.577521	+	0.333432i	−0.760147	−	0.649751i	$-0.774873\pi$
$271$	−9.50719	+	5.48898i	−0.577521	+	0.333432i	0.182627	+	0.983182i	$0.441540\pi$
$272$		0			0
$273$	9.05380	−	9.05380i	0.547961	−	0.547961i
$274$		0			0
$275$	−16.7276	+	9.65770i	−1.00871	+	0.582381i
$276$		0			0
$277$	5.86068	+	21.8724i	0.352134	+	1.31418i	0.884053	+	0.467387i	$0.154805\pi$
$277$	5.86068	+	21.8724i	0.352134	+	1.31418i	−0.531918	+	0.846796i	$0.678529\pi$
$278$		0			0
$279$	8.59350	−	32.0714i	0.514480	−	1.92006i
$280$		0			0
$281$	−1.17082	+	4.36956i	−0.0698453	+	0.260666i	−0.992015	−	0.126119i	$-0.959748\pi$
$281$	−1.17082	+	4.36956i	−0.0698453	+	0.260666i	0.922170	+	0.386785i	$0.126415\pi$
$282$		0			0
$283$	−29.6518	+	7.94517i	−1.76262	+	0.472292i	−0.987244	−	0.159213i	$-0.949104\pi$
$283$	−29.6518	+	7.94517i	−1.76262	+	0.472292i	−0.775372	+	0.631505i	$0.782438\pi$
$284$		0			0
$285$	11.2839			0.668398
$286$		0			0
$287$	−13.0423	−	22.5900i	−0.769864	−	1.33344i
$288$		0			0
$289$	−10.6067	−	6.12378i	−0.623923	−	0.360222i
$290$		0			0
$291$	27.8203	−	7.45444i	1.63086	−	0.436987i
$292$		0			0
$293$	8.72269	−	15.1081i	0.509585	−	0.882627i	−0.490353	−	0.871524i	$-0.663132\pi$
$293$	8.72269	−	15.1081i	0.509585	−	0.882627i	0.999938	−	0.0111035i	$-0.00353442\pi$
$294$		0			0
$295$	27.1259			1.57933
$296$		0			0
$297$	−41.2693			−2.39469
$298$		0			0
$299$	−2.57406	+	4.45841i	−0.148862	+	0.257836i
$300$		0			0
$301$	1.05680	−	0.283168i	0.0609127	−	0.0163215i
$302$		0			0
$303$	4.05110	+	2.33890i	0.232729	+	0.134366i
$304$		0			0
$305$	−0.182227	−	0.315626i	−0.0104343	−	0.0180727i
$306$		0			0
$307$	−0.854439			−0.0487654			−0.0243827	−	0.999703i	$-0.507762\pi$
$307$	−0.854439			−0.0487654			−0.0243827	+	0.999703i	$0.507762\pi$
$308$		0			0
$309$	41.9386	−	11.2374i	2.38580	−	0.639273i
$310$		0			0
$311$	0.934573	−	3.48787i	0.0529948	−	0.197779i	−0.934353	−	0.356349i	$-0.884022\pi$
$311$	0.934573	−	3.48787i	0.0529948	−	0.197779i	0.987348	+	0.158570i	$0.0506882\pi$
$312$		0			0
$313$	0.828062	−	3.09037i	0.0468048	−	0.174678i	−0.938567	−	0.345098i	$-0.887846\pi$
$313$	0.828062	−	3.09037i	0.0468048	−	0.174678i	0.985372	+	0.170420i	$0.0545124\pi$
$314$		0			0
$315$	17.9171	+	66.8675i	1.00951	+	3.76756i
$316$		0			0
$317$	−16.1101	+	9.30117i	−0.904834	+	0.522406i	−0.878765	−	0.477254i	$-0.841632\pi$
$317$	−16.1101	+	9.30117i	−0.904834	+	0.522406i	−0.0260684	+	0.999660i	$0.508299\pi$
$318$		0			0
$319$	−9.70936	+	9.70936i	−0.543620	+	0.543620i
$320$		0			0
$321$	50.3744	−	29.0837i	2.81163	−	1.62329i
$322$		0			0
$323$	−4.89295			−0.272251
$324$		0			0
$325$	−10.3506	+	10.3506i	−0.574146	+	0.574146i
$326$		0			0
$327$	20.0359	+	20.0359i	1.10799	+	1.10799i
$328$		0			0
$329$	−10.3613	+	17.9463i	−0.571239	+	0.989414i
$330$		0			0
$331$	16.5479	+	4.43401i	0.909557	+	0.243715i	0.683116	−	0.730310i	$-0.260624\pi$
$331$	16.5479	+	4.43401i	0.909557	+	0.243715i	0.226441	+	0.974025i	$0.427291\pi$
$332$		0			0
$333$	−42.3046	+	29.0346i	−2.31828	+	1.59109i
$334$		0			0
$335$	−2.80628	+	10.4732i	−0.153323	+	0.572211i
$336$		0			0
$337$	8.22053	+	4.74613i	0.447801	+	0.258538i	0.706901	−	0.707313i	$-0.250093\pi$
$337$	8.22053	+	4.74613i	0.447801	+	0.258538i	−0.259100	+	0.965850i	$0.583426\pi$
$338$		0			0
$339$	−27.9454	+	27.9454i	−1.51779	+	1.51779i
$340$		0			0
$341$	−6.24947	−	6.24947i	−0.338428	−	0.338428i
$342$		0			0
$343$		−	20.1347i		−	1.08717i
$344$		0			0
$345$	−18.8665	−	32.6778i	−1.01574	−	1.75931i
$346$		0			0
$347$	−18.5219	−	18.5219i	−0.994309	−	0.994309i	0.00567537	−	0.999984i	$-0.498193\pi$
$347$	−18.5219	−	18.5219i	−0.994309	−	0.994309i	−0.999984	+	0.00567537i	$0.998193\pi$
$348$		0			0
$349$	−18.3727	−	31.8225i	−0.983471	−	1.70342i	−0.648545	−	0.761177i	$-0.724622\pi$
$349$	−18.3727	−	31.8225i	−0.983471	−	1.70342i	−0.334926	−	0.942244i	$-0.608711\pi$
$350$		0			0
$351$	−30.2097	+	8.09466i	−1.61247	+	0.432061i
$352$		0			0
$353$	10.8719	+	2.91311i	0.578652	+	0.155049i	0.536262	−	0.844052i	$-0.319836\pi$
$353$	10.8719	+	2.91311i	0.578652	+	0.155049i	0.0423904	+	0.999101i	$0.486503\pi$
$354$		0			0
$355$	33.7784	+	9.05090i	1.79277	+	0.480372i
$356$		0			0
$357$	−10.5324	−	39.3076i	−0.557435	−	2.08038i
$358$		0			0
$359$		−	14.9855i		−	0.790906i	−0.918486	−	0.395453i	$-0.870588\pi$
$359$		−	14.9855i		−	0.790906i	0.918486	−	0.395453i	$-0.129412\pi$
$360$		0			0
$361$	15.7456	−	9.09072i	0.828715	−	0.478459i
$362$		0			0
$363$	10.0745	−	17.4496i	0.528775	−	0.915865i
$364$		0			0
$365$	5.93049	+	22.1329i	0.310416	+	1.15849i
$366$		0			0
$367$	−15.7244	−	9.07848i	−0.820807	−	0.473893i	0.0298878	−	0.999553i	$-0.490485\pi$
$367$	−15.7244	−	9.07848i	−0.820807	−	0.473893i	−0.850695	+	0.525660i	$0.823818\pi$
$368$		0			0
$369$			98.8825i			5.14762i
$370$		0			0
$371$			8.79479i			0.456603i
$372$		0			0
$373$	−14.0275	−	8.09878i	−0.726316	−	0.419339i	0.0907568	−	0.995873i	$-0.471071\pi$
$373$	−14.0275	−	8.09878i	−0.726316	−	0.419339i	−0.817073	+	0.576534i	$0.804405\pi$
$374$		0			0
$375$	−11.6284	−	43.3980i	−0.600490	−	2.24106i
$376$		0			0
$377$	−5.20296	+	9.01179i	−0.267966	+	0.464131i
$378$		0			0
$379$	−7.60415	+	4.39026i	−0.390599	+	0.225512i	−0.682420	−	0.730961i	$-0.739072\pi$
$379$	−7.60415	+	4.39026i	−0.390599	+	0.225512i	0.291821	+	0.956473i	$0.405739\pi$
$380$		0			0
$381$			16.6173i			0.851329i
$382$		0			0
$383$	1.29995	+	4.85146i	0.0664241	+	0.247898i	0.991152	−	0.132730i	$-0.0423744\pi$
$383$	1.29995	+	4.85146i	0.0664241	+	0.247898i	−0.924728	+	0.380628i	$0.875708\pi$
$384$		0			0
$385$	17.7992	+	4.76927i	0.907129	+	0.243065i
$386$		0			0
$387$	−4.00614	−	1.07344i	−0.203643	−	0.0545661i
$388$		0			0
$389$	18.6891	−	5.00772i	0.947574	−	0.253902i	0.248241	−	0.968698i	$-0.420147\pi$
$389$	18.6891	−	5.00772i	0.947574	−	0.253902i	0.699332	+	0.714797i	$0.253481\pi$
$390$		0			0
$391$	8.18099	+	14.1699i	0.413730	+	0.716602i
$392$		0			0
$393$	40.2859	+	40.2859i	2.03215	+	2.03215i
$394$		0			0
$395$	−28.6348	−	49.5970i	−1.44077	−	2.49549i
$396$		0			0
$397$			9.94560i			0.499155i	0.968355	+	0.249578i	$0.0802918\pi$
$397$			9.94560i			0.499155i	−0.968355	+	0.249578i	$0.919708\pi$
$398$		0			0
$399$	−4.81392	−	4.81392i	−0.240997	−	0.240997i
$400$		0			0
$401$	0.160109	−	0.160109i	0.00799546	−	0.00799546i	−0.703098	−	0.711093i	$-0.748200\pi$
$401$	0.160109	−	0.160109i	0.00799546	−	0.00799546i	0.711093	+	0.703098i	$0.248200\pi$
$402$		0			0
$403$	−5.80048	−	3.34891i	−0.288943	−	0.166821i
$404$		0			0
$405$	35.1736	−	131.270i	1.74779	−	6.52285i
$406$		0			0
$407$	1.06272	+	13.6165i	0.0526772	+	0.674945i
$408$		0			0
$409$	18.8225	+	5.04347i	0.930713	+	0.249384i	0.692159	−	0.721746i	$-0.256660\pi$
$409$	18.8225	+	5.04347i	0.930713	+	0.249384i	0.238554	+	0.971129i	$0.423327\pi$
$410$		0			0
$411$	4.96726	−	8.60354i	0.245017	−	0.424381i
$412$		0			0
$413$	−11.5724	−	11.5724i	−0.569442	−	0.569442i
$414$		0			0
$415$	21.6593	−	21.6593i	1.06321	−	1.06321i
$416$		0			0
$417$	0.232419			0.0113816
$418$		0			0
$419$	−2.77545	+	1.60241i	−0.135589	+	0.0782826i	−0.566260	−	0.824226i	$-0.691610\pi$
$419$	−2.77545	+	1.60241i	−0.135589	+	0.0782826i	0.430671	+	0.902509i	$0.358277\pi$
$420$		0			0
$421$	−9.86149	+	9.86149i	−0.480620	+	0.480620i	−0.905330	−	0.424710i	$-0.860376\pi$
$421$	−9.86149	+	9.86149i	−0.480620	+	0.480620i	0.424710	+	0.905330i	$0.360376\pi$
$422$		0			0
$423$	68.0316	−	39.2781i	3.30781	−	1.90976i
$424$		0			0
$425$	12.0410	+	44.9375i	0.584073	+	2.17979i
$426$		0			0
$427$	−0.0569108	+	0.212394i	−0.00275411	+	0.0102785i
$428$		0			0
$429$	−3.34396	+	12.4798i	−0.161448	+	0.602532i
$430$		0			0
$431$	29.2587	−	7.83985i	1.40934	−	0.377632i	0.527653	−	0.849460i	$-0.323072\pi$
$431$	29.2587	−	7.83985i	1.40934	−	0.377632i	0.881691	+	0.471828i	$0.156406\pi$
$432$		0			0
$433$	−1.78465			−0.0857648			−0.0428824	−	0.999080i	$-0.513654\pi$
$433$	−1.78465			−0.0857648			−0.0428824	+	0.999080i	$0.513654\pi$
$434$		0			0
$435$	−38.1350	−	66.0517i	−1.82843	−	3.16694i
$436$		0			0
$437$	2.37054	+	1.36863i	0.113398	+	0.0654706i
$438$		0			0
$439$	19.5365	−	5.23480i	0.932428	−	0.249843i	0.239539	−	0.970887i	$-0.423004\pi$
$439$	19.5365	−	5.23480i	0.932428	−	0.249843i	0.692890	+	0.721043i	$0.256337\pi$
$440$		0			0
$441$	−8.64021	+	14.9653i	−0.411438	+	0.712632i
$442$		0			0
$443$	−10.2811			−0.488471			−0.244235	−	0.969716i	$-0.578537\pi$
$443$	−10.2811			−0.488471			−0.244235	+	0.969716i	$0.578537\pi$
$444$		0			0
$445$	32.0442			1.51904
$446$		0			0
$447$	−4.27664	+	7.40736i	−0.202278	+	0.350356i
$448$		0			0
$449$	−38.8724	+	10.4158i	−1.83450	+	0.491554i	−0.998375	−	0.0569809i	$-0.981853\pi$
$449$	−38.8724	+	10.4158i	−1.83450	+	0.491554i	−0.836128	+	0.548535i	$0.815186\pi$
$450$		0			0
$451$	22.7947	+	13.1605i	1.07336	+	0.619706i
$452$		0			0
$453$	−21.1531	−	36.6382i	−0.993858	−	1.72141i
$454$		0			0
$455$	13.9647			0.654674
$456$		0			0
$457$	20.3280	−	5.44687i	0.950904	−	0.254794i	0.250158	−	0.968205i	$-0.419517\pi$
$457$	20.3280	−	5.44687i	0.950904	−	0.254794i	0.700746	+	0.713411i	$0.252851\pi$
$458$		0			0
$459$	−25.7268	+	96.0136i	−1.20082	+	4.48153i
$460$		0			0
$461$	−3.74034	+	13.9591i	−0.174205	+	0.650142i	0.822481	+	0.568793i	$0.192589\pi$
$461$	−3.74034	+	13.9591i	−0.174205	+	0.650142i	−0.996686	+	0.0813490i	$0.974077\pi$
$462$		0			0
$463$	8.40172	+	31.3556i	0.390461	+	1.45722i	0.829376	+	0.558691i	$0.188696\pi$
$463$	8.40172	+	31.3556i	0.390461	+	1.45722i	−0.438915	+	0.898529i	$0.644637\pi$
$464$		0			0
$465$	42.5145	−	24.5458i	1.97156	−	1.13828i
$466$		0			0
$467$	1.99183	−	1.99183i	0.0921710	−	0.0921710i	−0.659518	−	0.751689i	$-0.729240\pi$
$467$	1.99183	−	1.99183i	0.0921710	−	0.0921710i	0.751689	+	0.659518i	$0.229240\pi$
$468$		0			0
$469$	5.66528	−	3.27085i	0.261598	−	0.151034i
$470$		0			0
$471$	−30.7812			−1.41832
$472$		0			0
$473$	−0.780641	+	0.780641i	−0.0358939	+	0.0358939i
$474$		0			0
$475$	5.50341	+	5.50341i	0.252514	+	0.252514i
$476$		0			0
$477$	16.6698	−	28.8729i	0.763257	−	1.32200i
$478$		0			0
$479$	17.5275	+	4.69648i	0.800852	+	0.214588i	0.635958	−	0.771724i	$-0.280605\pi$
$479$	17.5275	+	4.69648i	0.800852	+	0.214588i	0.164894	+	0.986311i	$0.447272\pi$
$480$		0			0
$481$	3.44870	+	9.75901i	0.157247	+	0.444973i
$482$		0			0
$483$	−5.89216	+	21.9899i	−0.268103	+	1.00057i
$484$		0			0
$485$	27.2041	+	15.7063i	1.23527	+	0.713186i
$486$		0			0
$487$	−15.5392	+	15.5392i	−0.704150	+	0.704150i	−0.965299	−	0.261148i	$-0.915899\pi$
$487$	−15.5392	+	15.5392i	−0.704150	+	0.704150i	0.261148	+	0.965299i	$0.415899\pi$
$488$		0			0
$489$	−10.6689	−	10.6689i	−0.482465	−	0.482465i
$490$		0			0
$491$			21.7679i			0.982371i	0.871055	+	0.491185i	$0.163436\pi$
$491$			21.7679i			0.982371i	−0.871055	+	0.491185i	$0.836564\pi$
$492$		0			0
$493$	16.5362	+	28.6416i	0.744755	+	1.28995i
$494$		0			0
$495$	−49.3941	−	49.3941i	−2.22010	−	2.22010i
$496$		0			0
$497$	−10.5493	−	18.2719i	−0.473199	−	0.819605i
$498$		0			0
$499$	−35.2268	+	9.43898i	−1.57697	+	0.422547i	−0.937985	−	0.346675i	$-0.887311\pi$
$499$	−35.2268	+	9.43898i	−1.57697	+	0.422547i	−0.638981	+	0.769222i	$0.720644\pi$
$500$		0			0
$501$	−8.53020	−	2.28566i	−0.381101	−	0.102116i
$502$		0			0
$503$	−18.8034	−	5.03837i	−0.838404	−	0.224650i	−0.186027	−	0.982545i	$-0.559561\pi$
$503$	−18.8034	−	5.03837i	−0.838404	−	0.224650i	−0.652377	+	0.757895i	$0.726228\pi$
$504$		0			0
$505$	1.32045	+	4.92800i	0.0587594	+	0.219293i
$506$		0			0
$507$		−	34.1696i		−	1.51753i
$508$		0			0
$509$	−1.39929	+	0.807881i	−0.0620225	+	0.0358087i	−0.530691	−	0.847566i	$-0.678067\pi$
$509$	−1.39929	+	0.807881i	−0.0620225	+	0.0358087i	0.468668	+	0.883374i	$0.344734\pi$
$510$		0			0
$511$	6.91227	−	11.9724i	0.305781	−	0.529628i
$512$		0			0
$513$	4.30394	+	16.0625i	0.190024	+	0.709178i
$514$		0			0
$515$	41.0096	+	23.6769i	1.80710	+	1.04333i
$516$		0			0
$517$		−	20.9105i		−	0.919643i
$518$		0			0
$519$			14.0587i			0.617110i
$520$		0			0
$521$	−25.5439	−	14.7478i	−1.11910	−	0.646112i	−0.177928	−	0.984044i	$-0.556939\pi$
$521$	−25.5439	−	14.7478i	−1.11910	−	0.646112i	−0.941171	+	0.337932i	$0.890273\pi$
$522$		0			0
$523$	1.23334	+	4.60290i	0.0539303	+	0.201271i	0.987634	−	0.156775i	$-0.0501098\pi$
$523$	1.23334	+	4.60290i	0.0539303	+	0.201271i	−0.933704	+	0.358046i	$0.883443\pi$
$524$		0			0
$525$	−32.3652	+	56.0581i	−1.41253	+	2.44658i
$526$		0			0
$527$	−18.4353	+	10.6436i	−0.803055	+	0.463644i
$528$		0			0
$529$			13.8466i			0.602027i
$530$		0			0
$531$	16.0572	+	59.9264i	0.696824	+	2.60058i
$532$		0			0
$533$	19.2674	+	5.16268i	0.834563	+	0.223621i
$534$		0			0
$535$	61.2785	+	16.4195i	2.64930	+	0.709878i
$536$		0			0
$537$	−0.541572	+	0.145114i	−0.0233706	+	0.00626213i
$538$		0			0
$539$	2.29990	+	3.98354i	0.0990636	+	0.171583i
$540$		0			0
$541$	−15.2476	−	15.2476i	−0.655544	−	0.655544i	0.298779	−	0.954322i	$-0.403421\pi$
$541$	−15.2476	−	15.2476i	−0.655544	−	0.655544i	−0.954322	+	0.298779i	$0.903421\pi$
$542$		0			0
$543$	0.242109	+	0.419344i	0.0103899	+	0.0179958i
$544$		0			0
$545$			30.9035i			1.32376i
$546$		0			0
$547$	16.4120	+	16.4120i	0.701727	+	0.701727i	0.964781	−	0.263054i	$-0.0847299\pi$
$547$	16.4120	+	16.4120i	0.701727	+	0.701727i	−0.263054	+	0.964781i	$0.584730\pi$
$548$		0			0
$549$	0.589411	−	0.589411i	0.0251554	−	0.0251554i
$550$		0			0
$551$	4.79158	+	2.76642i	0.204128	+	0.117853i
$552$		0			0
$553$	−8.94287	+	33.3752i	−0.380290	+	1.41926i
$554$		0			0
$555$	−74.5840	−	13.8736i	−3.16591	−	0.588900i
$556$		0			0
$557$	16.2429	+	4.35228i	0.688235	+	0.184412i	0.585955	−	0.810344i	$-0.300720\pi$
$557$	16.2429	+	4.35228i	0.688235	+	0.184412i	0.102280	+	0.994756i	$0.467386\pi$
$558$		0			0
$559$	−0.418323	+	0.724556i	−0.0176932	+	0.0306455i
$560$		0			0
$561$	29.0360	+	29.0360i	1.22590	+	1.22590i
$562$		0			0
$563$	10.2622	−	10.2622i	0.432500	−	0.432500i	−0.456978	−	0.889478i	$-0.651068\pi$
$563$	10.2622	−	10.2622i	0.432500	−	0.432500i	0.889478	+	0.456978i	$0.151068\pi$
$564$		0			0
$565$	−43.1033			−1.81337
$566$		0			0
$567$	−71.0081	+	40.9966i	−2.98206	+	1.72169i
$568$		0			0
$569$	18.0196	−	18.0196i	0.755422	−	0.755422i	−0.220064	−	0.975486i	$-0.570626\pi$
$569$	18.0196	−	18.0196i	0.755422	−	0.755422i	0.975486	+	0.220064i	$0.0706265\pi$
$570$		0			0
$571$	−6.10606	+	3.52533i	−0.255531	+	0.147531i	−0.622294	−	0.782784i	$-0.713799\pi$
$571$	−6.10606	+	3.52533i	−0.255531	+	0.147531i	0.366763	+	0.930314i	$0.380466\pi$
$572$		0			0
$573$	0.432997	+	1.61597i	0.0180887	+	0.0675080i
$574$		0			0
$575$	6.73609	−	25.1394i	0.280914	−	1.04839i
$576$		0			0
$577$	7.00038	−	26.1258i	0.291429	−	1.08763i	−0.652582	−	0.757718i	$-0.726314\pi$
$577$	7.00038	−	26.1258i	0.291429	−	1.08763i	0.944012	−	0.329912i	$-0.107019\pi$
$578$		0			0
$579$	28.4212	−	7.61544i	1.18114	−	0.316487i
$580$		0			0
$581$	−18.4806			−0.766705
$582$		0			0
$583$	−4.43725	−	7.68555i	−0.183772	−	0.318303i
$584$		0			0
$585$	−45.8454	−	26.4689i	−1.89547	−	1.09435i
$586$		0			0
$587$	−18.6785	+	5.00490i	−0.770946	+	0.206574i	−0.622789	−	0.782390i	$-0.714001\pi$
$587$	−18.6785	+	5.00490i	−0.770946	+	0.206574i	−0.148156	+	0.988964i	$0.547334\pi$
$588$		0			0
$589$	−1.78062	+	3.08412i	−0.0733692	+	0.127079i
$590$		0			0
$591$	−42.9892			−1.76834
$592$		0			0
$593$	−29.7962			−1.22359			−0.611793	−	0.791018i	$-0.709551\pi$
$593$	−29.7962			−1.22359			−0.611793	+	0.791018i	$0.709551\pi$
$594$		0			0
$595$	22.1915	−	38.4369i	0.909764	−	1.57576i
$596$		0			0
$597$	−8.38106	+	2.24570i	−0.343014	+	0.0919103i
$598$		0			0
$599$	−29.5202	−	17.0435i	−1.20616	−	0.696378i	−0.244244	−	0.969714i	$-0.578540\pi$
$599$	−29.5202	−	17.0435i	−1.20616	−	0.696378i	−0.961919	+	0.273336i	$0.911873\pi$
$600$		0			0
$601$	−11.1728	−	19.3518i	−0.455747	−	0.789377i	0.542984	−	0.839743i	$-0.317294\pi$
$601$	−11.1728	−	19.3518i	−0.455747	−	0.789377i	−0.998731	+	0.0503664i	$0.983961\pi$
$602$		0			0
$603$	−24.7985			−1.00987
$604$		0			0
$605$	21.2267	−	5.68768i	0.862989	−	0.231237i
$606$		0			0
$607$	−1.89549	+	7.07406i	−0.0769355	+	0.287127i	−0.993665	−	0.112381i	$-0.964152\pi$
$607$	−1.89549	+	7.07406i	−0.0769355	+	0.287127i	0.916730	+	0.399508i	$0.130819\pi$
$608$		0			0
$609$	−11.9098	+	44.4481i	−0.482611	+	1.80113i
$610$		0			0
$611$	−4.10143	−	15.3068i	−0.165926	−	0.619245i
$612$		0			0
$613$	−32.0603	+	18.5101i	−1.29491	+	0.747614i	−0.979519	−	0.201350i	$-0.935467\pi$
$613$	−32.0603	+	18.5101i	−1.29491	+	0.747614i	−0.315386	+	0.948964i	$0.602134\pi$
$614$		0			0
$615$	−103.380	+	103.380i	−4.16869	+	4.16869i
$616$		0			0
$617$	−4.68719	+	2.70615i	−0.188699	+	0.108945i	−0.591373	−	0.806398i	$-0.701414\pi$
$617$	−4.68719	+	2.70615i	−0.188699	+	0.108945i	0.402674	+	0.915343i	$0.368081\pi$
$618$		0			0
$619$	−7.61311			−0.305997			−0.152998	−	0.988226i	$-0.548893\pi$
$619$	−7.61311			−0.305997			−0.152998	+	0.988226i	$0.548893\pi$
$620$		0			0
$621$	39.3206	−	39.3206i	1.57788	−	1.57788i
$622$		0			0
$623$	−13.6707	−	13.6707i	−0.547705	−	0.547705i
$624$		0			0
$625$	2.99476	−	5.18707i	0.119790	−	0.207483i
$626$		0			0
$627$	6.63554	+	1.77799i	0.264998	+	0.0710060i
$628$		0			0
$629$	32.3414	+	6.01591i	1.28954	+	0.239870i
$630$		0			0
$631$	5.02517	−	18.7542i	0.200049	−	0.746592i	−0.790853	−	0.612006i	$-0.790363\pi$
$631$	5.02517	−	18.7542i	0.200049	−	0.746592i	0.990902	−	0.134586i	$-0.0429705\pi$
$632$		0			0
$633$	−64.0279	−	36.9665i	−2.54488	−	1.46929i
$634$		0			0
$635$	−12.8153	+	12.8153i	−0.508561	+	0.508561i
$636$		0			0
$637$	2.46490	+	2.46490i	0.0976628	+	0.0976628i
$638$		0			0
$639$			79.9809i			3.16400i
$640$		0			0
$641$	15.6487	+	27.1043i	0.618085	+	1.07055i	0.989835	+	0.142222i	$0.0454246\pi$
$641$	15.6487	+	27.1043i	0.618085	+	1.07055i	−0.371750	+	0.928333i	$0.621242\pi$
$642$		0			0
$643$	13.5185	+	13.5185i	0.533118	+	0.533118i	0.921499	−	0.388381i	$-0.126965\pi$
$643$	13.5185	+	13.5185i	0.533118	+	0.533118i	−0.388381	+	0.921499i	$0.626965\pi$
$644$		0			0
$645$	−3.06609	−	5.31062i	−0.120727	−	0.209105i
$646$		0			0
$647$	39.7135	−	10.6412i	1.56130	−	0.418349i	0.628225	−	0.778032i	$-0.283782\pi$
$647$	39.7135	−	10.6412i	1.56130	−	0.418349i	0.933075	+	0.359683i	$0.117115\pi$
$648$		0			0
$649$	15.9515	+	4.27420i	0.626153	+	0.167777i
$650$		0			0
$651$	−28.6093	−	7.66583i	−1.12128	−	0.300447i
$652$		0			0
$653$	−12.8265	−	47.8691i	−0.501940	−	1.87326i	−0.487049	−	0.873375i	$-0.661927\pi$
$653$	−12.8265	−	47.8691i	−0.501940	−	1.87326i	−0.0148905	−	0.999889i	$-0.504740\pi$
$654$		0			0
$655$			62.1373i			2.42791i
$656$		0			0
$657$	−45.3854	+	26.2032i	−1.77065	+	1.02229i
$658$		0			0
$659$	−15.7945	+	27.3569i	−0.615266	+	1.06567i	0.375072	+	0.926996i	$0.377618\pi$
$659$	−15.7945	+	27.3569i	−0.615266	+	1.06567i	−0.990338	+	0.138676i	$0.955715\pi$
$660$		0			0
$661$	−0.298892	−	1.11548i	−0.0116256	−	0.0433872i	0.959869	−	0.280447i	$-0.0904828\pi$
$661$	−0.298892	−	1.11548i	−0.0116256	−	0.0433872i	−0.971495	+	0.237060i	$0.923816\pi$
$662$		0			0
$663$	26.9499	+	15.5595i	1.04665	+	0.604282i
$664$		0			0
$665$		−	7.42504i		−	0.287931i
$666$		0			0
$667$		−	18.5018i		−	0.716391i
$668$		0			0
$669$	65.0076	+	37.5322i	2.51334	+	1.45108i
$670$		0			0
$671$	−0.0574267	−	0.214319i	−0.00221693	−	0.00827371i
$672$		0			0
$673$	15.1092	−	26.1699i	0.582416	−	1.00877i	−0.412776	−	0.910833i	$-0.635441\pi$
$673$	15.1092	−	26.1699i	0.582416	−	1.00877i	0.995192	−	0.0979421i	$-0.0312260\pi$
$674$		0			0
$675$	136.929	−	79.0560i	5.27040	−	3.04287i
$676$		0			0
$677$		−	10.1223i		−	0.389030i	−0.980900	−	0.194515i	$-0.937687\pi$
$677$		−	10.1223i		−	0.389030i	0.980900	−	0.194515i	$-0.0623133\pi$
$678$		0			0
$679$	−4.90519	−	18.3064i	−0.188244	−	0.702536i
$680$		0			0
$681$	−26.5013	−	7.10100i	−1.01553	−	0.272111i
$682$		0			0
$683$	−11.8895	−	3.18577i	−0.454938	−	0.121900i	0.0240711	−	0.999710i	$-0.492337\pi$
$683$	−11.8895	−	3.18577i	−0.454938	−	0.121900i	−0.479009	+	0.877810i	$0.659004\pi$
$684$		0			0
$685$	10.4659	−	2.80432i	0.399880	−	0.107148i
$686$		0			0
$687$	2.83012	+	4.90191i	0.107976	+	0.187019i
$688$		0			0
$689$	−4.75559	−	4.75559i	−0.181173	−	0.181173i
$690$		0			0
$691$	−11.2247	−	19.4417i	−0.427007	−	0.739598i	0.569598	−	0.821923i	$-0.307099\pi$
$691$	−11.2247	−	19.4417i	−0.427007	−	0.739598i	−0.996606	+	0.0823252i	$0.973765\pi$
$692$		0			0
$693$			42.1450i			1.60096i
$694$		0			0
$695$	0.179243	+	0.179243i	0.00679906	+	0.00679906i
$696$		0			0
$697$	44.8281	−	44.8281i	1.69799	−	1.69799i
$698$		0			0
$699$	48.2282	+	27.8446i	1.82416	+	1.05318i
$700$		0			0
$701$	−8.27953	+	30.8996i	−0.312714	+	1.16706i	0.613386	+	0.789784i	$0.289807\pi$
$701$	−8.27953	+	30.8996i	−0.312714	+	1.16706i	−0.926099	+	0.377280i	$0.876859\pi$
$702$		0			0
$703$	5.18888	−	1.83368i	0.195702	−	0.0691585i
$704$		0			0
$705$	112.191	+	30.0614i	4.22534	+	1.13218i
$706$		0			0
$707$	1.53905	−	2.66572i	0.0578820	−	0.100255i
$708$		0			0
$709$	−3.58877	−	3.58877i	−0.134779	−	0.134779i	0.636499	−	0.771278i	$-0.280382\pi$
$709$	−3.58877	−	3.58877i	−0.134779	−	0.134779i	−0.771278	+	0.636499i	$0.780382\pi$
$710$		0			0
$711$	92.6190	−	92.6190i	3.47348	−	3.47348i
$712$		0			0
$713$	11.9087			0.445986
$714$		0			0
$715$	−12.2034	+	7.04563i	−0.456381	+	0.263492i
$716$		0			0
$717$	−4.34817	+	4.34817i	−0.162385	+	0.162385i
$718$		0			0
$719$	1.26551	−	0.730641i	0.0471955	−	0.0272483i	−0.476217	−	0.879328i	$-0.657992\pi$
$719$	1.26551	−	0.730641i	0.0471955	−	0.0272483i	0.523412	+	0.852080i	$0.324659\pi$
$720$		0			0
$721$	−7.39447	−	27.5965i	−0.275385	−	1.02775i
$722$		0			0
$723$	5.88553	−	21.9651i	0.218885	−	0.816890i
$724$		0			0
$725$	13.6157	−	50.8144i	0.505673	−	1.88720i
$726$		0			0
$727$	4.50649	−	1.20751i	0.167136	−	0.0447840i	−0.174280	−	0.984696i	$-0.555760\pi$
$727$	4.50649	−	1.20751i	0.167136	−	0.0447840i	0.341417	+	0.939912i	$0.389093\pi$
$728$		0			0
$729$	124.361			4.60596
$730$		0			0
$731$	1.32953	+	2.30281i	0.0491744	+	0.0851726i
$732$		0			0
$733$	−13.7165	−	7.91921i	−0.506629	−	0.292503i	0.224818	−	0.974401i	$-0.427821\pi$
$733$	−13.7165	−	7.91921i	−0.506629	−	0.292503i	−0.731447	+	0.681898i	$0.761155\pi$
$734$		0			0
$735$	−24.6792	+	6.61276i	−0.910305	+	0.243915i
$736$		0			0
$737$	−3.30050	+	5.71664i	−0.121576	+	0.210575i
$738$		0			0
$739$	−44.4386			−1.63470			−0.817349	−	0.576142i	$-0.804557\pi$
$739$	−44.4386			−1.63470			−0.817349	+	0.576142i	$0.804557\pi$
$740$		0			0
$741$	5.20604			0.191249
$742$		0			0
$743$	−14.3596	+	24.8715i	−0.526802	+	0.912447i	0.472710	+	0.881218i	$0.343276\pi$
$743$	−14.3596	+	24.8715i	−0.526802	+	0.912447i	−0.999512	+	0.0312297i	$0.990058\pi$
$744$		0			0
$745$	−9.01076	+	2.41442i	−0.330129	+	0.0884577i
$746$		0			0
$747$	60.6710	+	35.0284i	2.21984	+	1.28162i
$748$		0			0
$749$	−19.1377	−	33.1475i	−0.699278	−	1.21118i
$750$		0			0
$751$	−47.6853			−1.74006			−0.870031	−	0.492997i	$-0.835901\pi$
$751$	−47.6853			−1.74006			−0.870031	+	0.492997i	$0.835901\pi$
$752$		0			0
$753$	−73.9770	+	19.8221i	−2.69587	+	0.722356i
$754$		0			0
$755$	11.9422	−	44.5689i	0.434621	−	1.62203i
$756$		0			0
$757$	−9.49430	+	35.4332i	−0.345076	+	1.28784i	0.547447	+	0.836840i	$0.315600\pi$
$757$	−9.49430	+	35.4332i	−0.345076	+	1.28784i	−0.892523	+	0.451002i	$0.851067\pi$
$758$		0			0
$759$	−5.94557	−	22.1892i	−0.215811	−	0.805416i
$760$		0			0
$761$	−7.46653	+	4.31080i	−0.270661	+	0.156266i	−0.629188	−	0.777253i	$-0.716613\pi$
$761$	−7.46653	+	4.31080i	−0.270661	+	0.156266i	0.358527	+	0.933519i	$0.383279\pi$
$762$		0			0
$763$	13.1841	−	13.1841i	0.477295	−	0.477295i
$764$		0			0
$765$	−145.708	+	84.1243i	−5.26807	+	3.04152i
$766$		0			0
$767$	12.5151			0.451894
$768$		0			0
$769$	0.936066	−	0.936066i	0.0337554	−	0.0337554i	−0.690028	−	0.723783i	$-0.742402\pi$
$769$	0.936066	−	0.936066i	0.0337554	−	0.0337554i	0.723783	+	0.690028i	$0.242402\pi$
$770$		0			0
$771$	−55.2152	−	55.2152i	−1.98853	−	1.98853i
$772$		0			0
$773$	10.0403	−	17.3904i	0.361126	−	0.625488i	−0.627021	−	0.779003i	$-0.715726\pi$
$773$	10.0403	−	17.3904i	0.361126	−	0.625488i	0.988146	+	0.153515i	$0.0490592\pi$
$774$		0			0
$775$	32.7069	+	8.76379i	1.17487	+	0.314805i
$776$		0			0
$777$	25.9003	+	37.7378i	0.929168	+	1.35384i
$778$		0			0
$779$	2.74500	−	10.2445i	0.0983500	−	0.367047i
$780$		0			0
$781$	18.4375	+	10.6449i	0.659745	+	0.380904i
$782$		0			0
$783$	79.4788	−	79.4788i	2.84034	−	2.84034i
$784$		0			0
$785$	−23.7386	−	23.7386i	−0.847269	−	0.847269i
$786$		0			0
$787$		−	9.87028i		−	0.351837i	−0.984405	−	0.175919i	$-0.943710\pi$
$787$		−	9.87028i		−	0.351837i	0.984405	−	0.175919i	$-0.0562896\pi$
$788$		0			0
$789$	−17.4589	−	30.2397i	−0.621553	−	1.07656i
$790$		0			0
$791$	18.3887	+	18.3887i	0.653828	+	0.653828i
$792$		0			0
$793$	−0.0840742	−	0.145621i	−0.00298556	−	0.00517114i
$794$		0			0
$795$	47.6141	−	12.7582i	1.68870	−	0.452486i
$796$		0			0
$797$	16.7087	+	4.47708i	0.591852	+	0.158586i	0.542299	−	0.840185i	$-0.317554\pi$
$797$	16.7087	+	4.47708i	0.591852	+	0.158586i	0.0495525	+	0.998772i	$0.484220\pi$
$798$		0			0
$799$	−48.6485	−	13.0353i	−1.72106	−	0.461157i
$800$		0			0
$801$	18.9686	+	70.7919i	0.670224	+	2.50131i
$802$		0			0
$803$			13.9499i			0.492280i
$804$		0			0
$805$	−21.5028	+	12.4146i	−0.757872	+	0.437558i
$806$		0			0
$807$	24.8678	−	43.0722i	0.875387	−	1.51621i
$808$		0			0
$809$	−9.78741	−	36.5271i	−0.344107	−	1.28422i	−0.893652	−	0.448761i	$-0.851866\pi$
$809$	−9.78741	−	36.5271i	−0.344107	−	1.28422i	0.549545	−	0.835464i	$-0.314801\pi$
$810$		0			0
$811$	−44.3926	−	25.6301i	−1.55883	−	0.899993i	−0.997369	−	0.0724929i	$-0.976905\pi$
$811$	−44.3926	−	25.6301i	−1.55883	−	0.899993i	−0.561465	−	0.827500i	$-0.689762\pi$
$812$		0			0
$813$		−	37.1231i		−	1.30197i
$814$		0			0
$815$		−	16.4559i		−	0.576423i
$816$		0			0
$817$	0.385248	+	0.222423i	0.0134781	+	0.00778159i
$818$		0			0
$819$	8.26643	+	30.8507i	0.288852	+	1.07801i
$820$		0			0
$821$	10.5449	−	18.2643i	0.368019	−	0.637428i	−0.621237	−	0.783623i	$-0.713369\pi$
$821$	10.5449	−	18.2643i	0.368019	−	0.637428i	0.989256	+	0.146195i	$0.0467027\pi$
$822$		0			0
$823$	−12.4962	+	7.21466i	−0.435588	+	0.251487i	−0.701725	−	0.712448i	$-0.747586\pi$
$823$	−12.4962	+	7.21466i	−0.435588	+	0.251487i	0.266136	+	0.963935i	$0.414253\pi$
$824$		0			0
$825$		−	65.3171i		−	2.27405i
$826$		0			0
$827$	5.07756	+	18.9497i	0.176564	+	0.658946i	0.996280	+	0.0861758i	$0.0274647\pi$
$827$	5.07756	+	18.9497i	0.176564	+	0.658946i	−0.819716	+	0.572770i	$0.805869\pi$
$828$		0			0
$829$	−9.51351	−	2.54914i	−0.330418	−	0.0885352i	0.0897964	−	0.995960i	$-0.471378\pi$
$829$	−9.51351	−	2.54914i	−0.330418	−	0.0885352i	−0.420214	+	0.907425i	$0.638045\pi$
$830$		0			0
$831$	−73.9637	−	19.8185i	−2.56577	−	0.687497i
$832$		0			0
$833$	10.7015	−	2.86745i	0.370784	−	0.0993514i
$834$		0			0
$835$	−4.81582	−	8.34125i	−0.166658	−	0.288661i
$836$		0			0
$837$	51.1569	+	51.1569i	1.76824	+	1.76824i
$838$		0			0
$839$	23.5761	+	40.8350i	0.813937	+	1.40978i	0.910089	+	0.414413i	$0.136013\pi$
$839$	23.5761	+	40.8350i	0.813937	+	1.40978i	−0.0961522	+	0.995367i	$0.530654\pi$
$840$		0			0
$841$		−	8.39766i		−	0.289574i
$842$		0			0
$843$	−10.8169	−	10.8169i	−0.372553	−	0.372553i
$844$		0			0
$845$	26.3518	−	26.3518i	0.906529	−	0.906529i
$846$		0			0
$847$	−11.4822	−	6.62927i	−0.394534	−	0.227784i
$848$		0			0
$849$	26.8675	−	100.271i	0.922089	−	3.44128i
$850$		0			0
$851$	−13.9861	−	11.9610i	−0.479436	−	0.410017i
$852$		0			0
$853$	−13.9940	−	3.74969i	−0.479146	−	0.128387i	0.0111590	−	0.999938i	$-0.496448\pi$
$853$	−13.9940	−	3.74969i	−0.479146	−	0.128387i	−0.490305	+	0.871551i	$0.663115\pi$
$854$		0			0
$855$	−14.0735	+	24.3761i	−0.481305	+	0.833644i
$856$		0			0
$857$	19.5698	+	19.5698i	0.668493	+	0.668493i	0.957367	−	0.288874i	$-0.0932809\pi$
$857$	19.5698	+	19.5698i	0.668493	+	0.668493i	−0.288874	+	0.957367i	$0.593281\pi$
$858$		0			0
$859$	−12.6106	+	12.6106i	−0.430269	+	0.430269i	−0.888720	−	0.458451i	$-0.848405\pi$
$859$	−12.6106	+	12.6106i	−0.430269	+	0.430269i	0.458451	+	0.888720i	$0.348405\pi$
$860$		0			0
$861$	88.2081			3.00612
$862$		0			0
$863$	19.9287	−	11.5058i	0.678381	−	0.391663i	−0.120864	−	0.992669i	$-0.538566\pi$
$863$	19.9287	−	11.5058i	0.678381	−	0.391663i	0.799245	+	0.601006i	$0.205233\pi$
$864$		0			0
$865$	−10.8422	+	10.8422i	−0.368645	+	0.368645i
$866$		0			0
$867$	35.8677	−	20.7082i	1.21813	−	0.703288i
$868$		0			0
$869$	−9.02393	−	33.6778i	−0.306116	−	1.14244i
$870$		0			0
$871$	−1.29474	+	4.83202i	−0.0438704	+	0.163727i
$872$		0			0
$873$	−18.5948	+	69.3966i	−0.629337	+	2.34872i
$874$		0			0
$875$	−28.5569	+	7.65179i	−0.965398	+	0.258678i
$876$		0			0
$877$	4.07980			0.137765			0.0688825	−	0.997625i	$-0.478057\pi$
$877$	4.07980			0.137765			0.0688825	+	0.997625i	$0.478057\pi$
$878$		0			0
$879$	29.4967	+	51.0898i	0.994900	+	1.72322i
$880$		0			0
$881$	6.76894	+	3.90805i	0.228051	+	0.131666i	0.609673	−	0.792653i	$-0.291301\pi$
$881$	6.76894	+	3.90805i	0.228051	+	0.131666i	−0.381621	+	0.924319i	$0.624634\pi$
$882$		0			0
$883$	−8.76344	+	2.34816i	−0.294913	+	0.0790217i	−0.403242	−	0.915093i	$-0.632117\pi$
$883$	−8.76344	+	2.34816i	−0.294913	+	0.0790217i	0.108329	+	0.994115i	$0.465450\pi$
$884$		0			0
$885$	−45.8645	+	79.4397i	−1.54172	+	2.67033i
$886$		0			0
$887$	22.3380			0.750036			0.375018	−	0.927017i	$-0.377636\pi$
$887$	22.3380			0.750036			0.375018	+	0.927017i	$0.377636\pi$
$888$		0			0
$889$	10.9346			0.366733
$890$		0			0
$891$	41.3682	−	71.6518i	1.38589	−	2.40043i
$892$		0			0
$893$	−8.13862	+	2.18074i	−0.272349	+	0.0729756i
$894$		0			0
$895$	−0.529576	−	0.305751i	−0.0177018	−	0.0102201i
$896$		0			0
$897$	−8.70447	−	15.0766i	−0.290634	−	0.503393i
$898$		0			0
$899$	24.0712			0.802819
$900$		0			0
$901$	−20.6466	+	5.53225i	−0.687839	+	0.184306i
$902$		0			0
$903$	−0.957562	+	3.57367i	−0.0318657	+	0.118924i
$904$		0			0
$905$	−0.136685	+	0.510116i	−0.00454357	+	0.0169568i
$906$		0			0
$907$	−4.12745	−	15.4038i	−0.137050	−	0.511476i	−0.999981	−	0.00615505i	$-0.998041\pi$
$907$	−4.12745	−	15.4038i	−0.137050	−	0.511476i	0.862931	−	0.505321i	$-0.168626\pi$
$908$		0			0
$909$	−10.1053	+	5.83429i	−0.335171	+	0.193511i
$910$		0			0
$911$	−17.9812	+	17.9812i	−0.595745	+	0.595745i	−0.939177	−	0.343432i	$-0.888410\pi$
$911$	−17.9812	+	17.9812i	−0.595745	+	0.595745i	0.343432	+	0.939177i	$0.388410\pi$
$912$		0			0
$913$	16.1498	−	9.32406i	0.534479	−	0.308581i
$914$		0			0
$915$	1.23244			0.0407432
$916$		0			0
$917$	26.5090	−	26.5090i	0.875405	−	0.875405i
$918$		0			0
$919$	10.7539	+	10.7539i	0.354739	+	0.354739i	0.861869	−	0.507130i	$-0.169294\pi$
$919$	10.7539	+	10.7539i	0.354739	+	0.354739i	−0.507130	+	0.861869i	$0.669294\pi$
$920$		0			0
$921$	1.44469	−	2.50227i	0.0476041	−	0.0824527i
$922$		0			0
$923$	15.5844	+	4.17582i	0.512966	+	0.137449i
$924$		0			0
$925$	−29.6100	−	43.1429i	−0.973570	−	1.41853i
$926$		0			0
$927$	−28.0312	+	104.614i	−0.920665	+	3.43597i
$928$		0			0
$929$	−28.8227	−	16.6408i	−0.945643	−	0.545967i	−0.0539184	−	0.998545i	$-0.517171\pi$
$929$	−28.8227	−	16.6408i	−0.945643	−	0.545967i	−0.891725	+	0.452578i	$0.850504\pi$
$930$		0			0
$931$	1.31059	−	1.31059i	0.0429528	−	0.0429528i
$932$		0			0
$933$	8.63426	+	8.63426i	0.282673	+	0.282673i
$934$		0			0
$935$			44.7854i			1.46464i
$936$		0			0
$937$	25.7295	+	44.5649i	0.840547	+	1.45587i	0.889433	+	0.457066i	$0.151100\pi$
$937$	25.7295	+	44.5649i	0.840547	+	1.45587i	−0.0488855	+	0.998804i	$0.515567\pi$
$938$		0			0
$939$	7.65024	+	7.65024i	0.249656	+	0.249656i
$940$		0			0
$941$	−20.0757	−	34.7722i	−0.654450	−	1.13354i	−0.982031	−	0.188718i	$-0.939567\pi$
$941$	−20.0757	−	34.7722i	−0.654450	−	1.13354i	0.327581	−	0.944823i	$-0.393767\pi$
$942$		0			0
$943$	−34.2575	+	9.17926i	−1.11558	+	0.298918i
$944$		0			0
$945$	−145.700	−	39.0403i	−4.73963	−	1.26998i
$946$		0			0
$947$	48.1856	+	12.9113i	1.56582	+	0.419561i	0.934501	−	0.355961i	$-0.115846\pi$
$947$	48.1856	+	12.9113i	1.56582	+	0.419561i	0.631321	+	0.775521i	$0.282513\pi$
$948$		0			0
$949$	2.73616	+	10.2115i	0.0888194	+	0.331478i
$950$		0			0
$951$		−	62.9058i		−	2.03986i
$952$		0			0
$953$	−31.6333	+	18.2635i	−1.02470	+	0.591613i	−0.915463	−	0.402403i	$-0.868175\pi$
$953$	−31.6333	+	18.2635i	−1.02470	+	0.591613i	−0.109241	+	0.994015i	$0.534842\pi$
$954$		0			0
$955$	−0.912312	+	1.58017i	−0.0295217	+	0.0511331i
$956$		0			0
$957$	−12.0178	−	44.8510i	−0.388480	−	1.44983i
$958$		0			0
$959$	−5.66133	−	3.26857i	−0.182814	−	0.105548i
$960$		0			0
$961$		−	15.5065i		−	0.500209i
$962$		0			0
$963$			145.096i			4.67565i
$964$		0			0
$965$	27.7916	+	16.0455i	0.894645	+	0.516523i
$966$		0			0
$967$	13.2093	+	49.2978i	0.424782	+	1.58531i	0.764398	+	0.644745i	$0.223037\pi$
$967$	13.2093	+	49.2978i	0.424782	+	1.58531i	−0.339615	+	0.940564i	$0.610297\pi$
$968$		0			0
$969$	8.27302	−	14.3293i	0.265768	−	0.460323i
$970$		0			0
$971$	4.23717	−	2.44633i	0.135977	−	0.0785066i	−0.430468	−	0.902606i	$-0.641652\pi$
$971$	4.23717	−	2.44633i	0.135977	−	0.0785066i	0.566445	+	0.824099i	$0.308318\pi$
$972$		0			0
$973$		−	0.152937i		−	0.00490294i
$974$		0			0
$975$	−12.8115	−	47.8130i	−0.410295	−	1.53124i
$976$		0			0
$977$	35.6417	+	9.55016i	1.14028	+	0.305537i	0.779063	−	0.626946i	$-0.215695\pi$
$977$	35.6417	+	9.55016i	1.14028	+	0.305537i	0.361215	+	0.932482i	$0.382362\pi$
$978$		0			0
$979$	18.8438	+	5.04918i	0.602250	+	0.161372i
$980$		0			0
$981$	−68.2720	+	18.2934i	−2.17976	+	0.584064i
$982$		0			0
$983$	2.24674	+	3.89146i	0.0716598	+	0.124118i	0.899629	−	0.436655i	$-0.143837\pi$
$983$	2.24674	+	3.89146i	0.0716598	+	0.124118i	−0.827969	+	0.560774i	$0.810504\pi$
$984$		0			0
$985$	−33.1535	−	33.1535i	−1.05636	−	1.05636i
$986$		0			0
$987$	−35.0379	−	60.6875i	−1.11527	−	1.93170i
$988$		0			0
$989$		−	1.48756i		−	0.0473016i
$990$		0			0
$991$	−39.8523	−	39.8523i	−1.26595	−	1.26595i	−0.948162	−	0.317788i	$-0.897060\pi$
$991$	−39.8523	−	39.8523i	−1.26595	−	1.26595i	−0.317788	−	0.948162i	$-0.602940\pi$
$992$		0			0
$993$	−40.9646	+	40.9646i	−1.29997	+	1.29997i
$994$		0			0
$995$	−8.19541	−	4.73162i	−0.259812	−	0.150003i
$996$		0			0
$997$	−0.708536	+	2.64429i	−0.0224396	+	0.0837455i	−0.976238	−	0.216703i	$-0.930470\pi$
$997$	−0.708536	+	2.64429i	−0.0224396	+	0.0837455i	0.953798	+	0.300449i	$0.0971364\pi$
$998$		0			0
$999$	−8.69923	−	111.462i	−0.275232	−	3.52650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.e.415.1	✓	20
4.3	odd	2		592.2.be.f.415.5	yes	20
37.14	odd	12		592.2.be.f.495.5	yes	20
148.51	even	12	inner	592.2.be.e.495.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.e.415.1	✓	20	1.1	even	1	trivial
592.2.be.e.495.1	yes	20	148.51	even	12	inner
592.2.be.f.415.5	yes	20	4.3	odd	2
592.2.be.f.495.5	yes	20	37.14	odd	12

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69080 + 2.92856i) q^{3} +(-3.56248 + 0.954562i) q^{5} +(1.92706 + 1.11259i) q^{7} +(-4.21763 - 7.30516i) q^{9} +O(q^{10})\)	\(q+(-1.69080 + 2.92856i) q^{3} +(-3.56248 + 0.954562i) q^{5} +(1.92706 + 1.11259i) q^{7} +(-4.21763 - 7.30516i) q^{9} -2.24535 q^{11} +(-1.64362 + 0.440407i) q^{13} +(3.22795 - 12.0469i) q^{15} +(-1.39972 + 5.22382i) q^{17} +(0.234165 + 0.873916i) q^{19} +(-6.51656 + 3.76234i) q^{21} +(2.13932 - 2.13932i) q^{23} +(7.44991 - 4.30121i) q^{25} +18.3799 q^{27} +(4.32421 - 4.32421i) q^{29} +(2.78330 + 2.78330i) q^{31} +(3.79644 - 6.57563i) q^{33} +(-7.92713 - 2.12407i) q^{35} +(-0.473300 - 6.06432i) q^{37} +(1.48928 - 5.55809i) q^{39} +(-10.1520 - 5.86126i) q^{41} +(0.347671 - 0.347671i) q^{43} +(21.9984 + 21.9984i) q^{45} +9.31282i q^{47} +(-1.02430 - 1.77413i) q^{49} +(-12.9316 - 12.9316i) q^{51} +(1.97620 + 3.42288i) q^{53} +(7.99899 - 2.14332i) q^{55} +(-2.95524 - 0.791855i) q^{57} +(-7.10427 - 1.90358i) q^{59} +(0.0255759 + 0.0954505i) q^{61} -18.7700i q^{63} +(5.43497 - 3.13788i) q^{65} +(1.46993 - 2.54599i) q^{67} +(2.64795 + 9.88230i) q^{69} +(-8.21142 - 4.74087i) q^{71} -6.21278i q^{73} +29.0900i q^{75} +(-4.32691 - 2.49815i) q^{77} +(4.01895 + 14.9989i) q^{79} +(-18.4240 + 31.9112i) q^{81} +(-7.19254 + 4.15262i) q^{83} -19.9459i q^{85} +(5.35231 + 19.9751i) q^{87} +(-8.39237 - 2.24873i) q^{89} +(-3.65735 - 0.979984i) q^{91} +(-12.8571 + 3.44504i) q^{93} +(-1.66842 - 2.88978i) q^{95} +(-6.02255 - 6.02255i) q^{97} +(9.47005 + 16.4026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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