LMFDB - Embedded newform 675.2.q.a.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(143,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("675.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.q (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Root			$2.24352 - 0.601150i$ of defining polynomial
Character	$\chi$	$=$	675.557
Dual form			675.2.q.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24352 - 0.601150i) q^{2} +(2.93996 + 1.69739i) q^{4} +(0.201351 - 0.751454i) q^{7} +(-2.29074 - 2.29074i) q^{8} +O(q^{10})$	\(q+(-2.24352 - 0.601150i) q^{2} +(2.93996 + 1.69739i) q^{4} +(0.201351 - 0.751454i) q^{7} +(-2.29074 - 2.29074i) q^{8} +(0.220188 - 0.127126i) q^{11} +(0.992714 + 3.70486i) q^{13} +(-0.903473 + 1.56486i) q^{14} +(0.367473 + 0.636483i) q^{16} +(3.93311 - 3.93311i) q^{17} +0.440377i q^{19} +(-0.570419 + 0.152843i) q^{22} +(-3.42258 + 0.917076i) q^{23} -8.90871i q^{26} +(1.86747 - 1.86747i) q^{28} +(2.76265 + 4.78505i) q^{29} +(-0.0971829 + 0.168326i) q^{31} +(1.23512 + 4.60955i) q^{32} +(-11.1884 + 6.45964i) q^{34} +(0.123005 + 0.123005i) q^{37} +(0.264732 - 0.987995i) q^{38} +(3.88223 + 2.24141i) q^{41} +(-1.33488 - 0.357680i) q^{43} +0.863127 q^{44} +8.22993 q^{46} +(4.17348 + 1.11828i) q^{47} +(5.53804 + 3.19739i) q^{49} +(-3.37004 + 12.5772i) q^{52} +(0.938022 + 0.938022i) q^{53} +(-2.18263 + 1.26014i) q^{56} +(-3.32153 - 12.3961i) q^{58} +(4.02279 - 6.96768i) q^{59} +(-1.44186 - 2.49737i) q^{61} +(0.319221 - 0.319221i) q^{62} -12.5540i q^{64} +(12.9666 - 3.47438i) q^{67} +(18.2392 - 4.88718i) q^{68} +2.15986i q^{71} +(9.18432 - 9.18432i) q^{73} +(-0.202021 - 0.349910i) q^{74} +(-0.747490 + 1.29469i) q^{76} +(-0.0511939 - 0.191058i) q^{77} +(11.9729 - 6.91256i) q^{79} +(-7.36245 - 7.36245i) q^{82} +(-1.39384 + 5.20187i) q^{83} +(2.77981 + 1.60493i) q^{86} +(-0.795606 - 0.213182i) q^{88} -0.285526 q^{89} +2.98392 q^{91} +(-11.6189 - 3.11327i) q^{92} +(-8.69105 - 5.01778i) q^{94} +(2.34065 - 8.73543i) q^{97} +(-10.5026 - 10.5026i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) $ 16 * q - 6 * q^2 + 2 * q^7	$ 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.24352	−	0.601150i	−1.58641	−	0.425077i	−0.645507	−	0.763754i	$-0.723354\pi$
$2$	−2.24352	−	0.601150i	−1.58641	−	0.425077i	−0.940903	+	0.338677i	$0.890021\pi$
$3$		0			0
$3$		0			0
$4$	2.93996	+	1.69739i	1.46998	+	0.848694i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.201351	−	0.751454i	0.0761037	−	0.284023i	−0.917378	−	0.398018i	$-0.869698\pi$
$7$	0.201351	−	0.751454i	0.0761037	−	0.284023i	0.993481	+	0.113995i	$0.0363648\pi$
$8$	−2.29074	−	2.29074i	−0.809899	−	0.809899i
$9$		0			0
$10$		0			0
$11$	0.220188	−	0.127126i	0.0663893	−	0.0383299i	−0.466438	−	0.884554i	$-0.654463\pi$
$11$	0.220188	−	0.127126i	0.0663893	−	0.0383299i	0.532827	+	0.846224i	$0.321130\pi$
$12$		0			0
$13$	0.992714	+	3.70486i	0.275329	+	1.02754i	0.955620	+	0.294601i	$0.0951868\pi$
$13$	0.992714	+	3.70486i	0.275329	+	1.02754i	−0.680291	+	0.732942i	$0.738147\pi$
$14$	−0.903473	+	1.56486i	−0.241463	+	0.418227i
$15$		0			0
$16$	0.367473	+	0.636483i	0.0918684	+	0.159121i
$17$	3.93311	−	3.93311i	0.953920	−	0.953920i	−0.0450642	−	0.998984i	$-0.514349\pi$
$17$	3.93311	−	3.93311i	0.953920	−	0.953920i	0.998984	+	0.0450642i	$0.0143492\pi$
$18$		0			0
$19$			0.440377i			0.101029i	0.998723	+	0.0505147i	$0.0160862\pi$
$19$			0.440377i			0.101029i	−0.998723	+	0.0505147i	$0.983914\pi$
$20$		0			0
$21$		0			0
$22$	−0.570419	+	0.152843i	−0.121614	+	0.0325863i
$23$	−3.42258	+	0.917076i	−0.713656	+	0.191224i	−0.597339	−	0.801989i	$-0.703775\pi$
$23$	−3.42258	+	0.917076i	−0.713656	+	0.191224i	−0.116317	+	0.993212i	$0.537109\pi$
$24$		0			0
$25$		0			0
$26$		−	8.90871i		−	1.74714i
$27$		0			0
$28$	1.86747	−	1.86747i	0.352919	−	0.352919i
$29$	2.76265	+	4.78505i	0.513011	+	0.888561i	0.999886	+	0.0150897i	$0.00480338\pi$
$29$	2.76265	+	4.78505i	0.513011	+	0.888561i	−0.486875	+	0.873472i	$0.661863\pi$
$30$		0			0
$31$	−0.0971829	+	0.168326i	−0.0174546	+	0.0302322i	−0.874621	−	0.484808i	$-0.838890\pi$
$31$	−0.0971829	+	0.168326i	−0.0174546	+	0.0302322i	0.857166	+	0.515040i	$0.172223\pi$
$32$	1.23512	+	4.60955i	0.218341	+	0.814861i
$33$		0			0
$34$	−11.1884	+	6.45964i	−1.91880	+	1.10782i
$35$		0			0
$36$		0			0
$37$	0.123005	+	0.123005i	0.0202220	+	0.0202220i	0.717145	−	0.696924i	$-0.245448\pi$
$37$	0.123005	+	0.123005i	0.0202220	+	0.0202220i	−0.696924	+	0.717145i	$0.745448\pi$
$38$	0.264732	−	0.987995i	0.0429453	−	0.160274i
$39$		0			0
$40$		0			0
$41$	3.88223	+	2.24141i	0.606303	+	0.350049i	0.771517	−	0.636209i	$-0.219498\pi$
$41$	3.88223	+	2.24141i	0.606303	+	0.350049i	−0.165214	+	0.986258i	$0.552832\pi$
$42$		0			0
$43$	−1.33488	−	0.357680i	−0.203567	−	0.0545456i	0.155595	−	0.987821i	$-0.450271\pi$
$43$	−1.33488	−	0.357680i	−0.203567	−	0.0545456i	−0.359162	+	0.933275i	$0.616937\pi$
$44$	0.863127			0.130121
$45$		0			0
$46$	8.22993			1.21344
$47$	4.17348	+	1.11828i	0.608765	+	0.163118i	0.550015	−	0.835155i	$-0.314622\pi$
$47$	4.17348	+	1.11828i	0.608765	+	0.163118i	0.0587499	+	0.998273i	$0.481289\pi$
$48$		0			0
$49$	5.53804	+	3.19739i	0.791148	+	0.456770i
$50$		0			0
$51$		0			0
$52$	−3.37004	+	12.5772i	−0.467341	+	1.74414i
$53$	0.938022	+	0.938022i	0.128847	+	0.128847i	0.768589	−	0.639742i	$-0.220959\pi$
$53$	0.938022	+	0.938022i	0.128847	+	0.128847i	−0.639742	+	0.768589i	$0.720959\pi$
$54$		0			0
$55$		0			0
$56$	−2.18263	+	1.26014i	−0.291666	+	0.168393i
$57$		0			0
$58$	−3.32153	−	12.3961i	−0.436139	−	1.62769i
$59$	4.02279	−	6.96768i	0.523723	−	0.907114i	−0.475896	−	0.879502i	$-0.657876\pi$
$59$	4.02279	−	6.96768i	0.523723	−	0.907114i	0.999619	−	0.0276128i	$-0.00879055\pi$
$60$		0			0
$61$	−1.44186	−	2.49737i	−0.184611	−	0.319755i	0.758835	−	0.651283i	$-0.225769\pi$
$61$	−1.44186	−	2.49737i	−0.184611	−	0.319755i	−0.943445	+	0.331528i	$0.892436\pi$
$62$	0.319221	−	0.319221i	0.0405411	−	0.0405411i
$63$		0			0
$64$		−	12.5540i		−	1.56925i
$65$		0			0
$66$		0			0
$67$	12.9666	−	3.47438i	1.58412	−	0.424463i	0.643919	−	0.765093i	$-0.277307\pi$
$67$	12.9666	−	3.47438i	1.58412	−	0.424463i	0.940197	+	0.340631i	$0.110641\pi$
$68$	18.2392	−	4.88718i	2.21183	−	0.592658i
$69$		0			0
$70$		0			0
$71$			2.15986i			0.256328i	0.991753	+	0.128164i	$0.0409085\pi$
$71$			2.15986i			0.256328i	−0.991753	+	0.128164i	$0.959092\pi$
$72$		0			0
$73$	9.18432	−	9.18432i	1.07494	−	1.07494i	0.0779897	−	0.996954i	$-0.475150\pi$
$73$	9.18432	−	9.18432i	1.07494	−	1.07494i	0.996954	−	0.0779897i	$-0.0248501\pi$
$74$	−0.202021	−	0.349910i	−0.0234844	−	0.0406762i
$75$		0			0
$76$	−0.747490	+	1.29469i	−0.0857430	+	0.148511i
$77$	−0.0511939	−	0.191058i	−0.00583409	−	0.0217731i
$78$		0			0
$79$	11.9729	−	6.91256i	1.34706	−	0.777723i	0.359225	−	0.933251i	$-0.383041\pi$
$79$	11.9729	−	6.91256i	1.34706	−	0.777723i	0.987832	+	0.155528i	$0.0497079\pi$
$80$		0			0
$81$		0			0
$82$	−7.36245	−	7.36245i	−0.813047	−	0.813047i
$83$	−1.39384	+	5.20187i	−0.152993	+	0.570979i	0.846275	+	0.532746i	$0.178840\pi$
$83$	−1.39384	+	5.20187i	−0.152993	+	0.570979i	−0.999269	+	0.0382335i	$0.987827\pi$
$84$		0			0
$85$		0			0
$86$	2.77981	+	1.60493i	0.299755	+	0.173064i
$87$		0			0
$88$	−0.795606	−	0.213182i	−0.0848119	−	0.0227253i
$89$	−0.285526			−0.0302657			−0.0151328	−	0.999885i	$-0.504817\pi$
$89$	−0.285526			−0.0302657			−0.0151328	+	0.999885i	$0.504817\pi$
$90$		0			0
$91$	2.98392			0.312799
$92$	−11.6189	−	3.11327i	−1.21135	−	0.324581i
$93$		0			0
$94$	−8.69105	−	5.01778i	−0.896413	−	0.517545i
$95$		0			0
$96$		0			0
$97$	2.34065	−	8.73543i	0.237657	−	0.886948i	−0.739276	−	0.673402i	$-0.764832\pi$
$97$	2.34065	−	8.73543i	0.237657	−	0.886948i	0.976933	−	0.213546i	$-0.0685012\pi$
$98$	−10.5026	−	10.5026i	−1.06092	−	1.06092i
$99$		0			0
$100$		0			0
$101$	11.3943	−	6.57848i	1.13377	−	0.654583i	0.188890	−	0.981998i	$-0.439511\pi$
$101$	11.3943	−	6.57848i	1.13377	−	0.654583i	0.944881	+	0.327415i	$0.106178\pi$
$102$		0			0
$103$	4.23579	+	15.8082i	0.417364	+	1.55763i	0.780052	+	0.625714i	$0.215192\pi$
$103$	4.23579	+	15.8082i	0.417364	+	1.55763i	−0.362688	+	0.931911i	$0.618141\pi$
$104$	6.21282	−	10.7609i	0.609217	−	1.05520i
$105$		0			0
$106$	−1.54058	−	2.66836i	−0.149634	−	0.259175i
$107$	−5.81401	+	5.81401i	−0.562062	+	0.562062i	−0.929893	−	0.367831i	$-0.880101\pi$
$107$	−5.81401	+	5.81401i	−0.562062	+	0.562062i	0.367831	+	0.929893i	$0.380101\pi$
$108$		0			0
$109$			8.81907i			0.844713i	0.906430	+	0.422357i	$0.138797\pi$
$109$			8.81907i			0.844713i	−0.906430	+	0.422357i	$0.861203\pi$
$110$		0			0
$111$		0			0
$112$	0.552279	−	0.147983i	0.0521854	−	0.0139830i
$113$	13.0092	−	3.48580i	1.22380	−	0.327916i	0.411638	−	0.911347i	$-0.364957\pi$
$113$	13.0092	−	3.48580i	1.22380	−	0.327916i	0.812163	+	0.583431i	$0.198290\pi$
$114$		0			0
$115$		0			0
$116$			18.7571i			1.74156i
$117$		0			0
$118$	−13.2138	+	13.2138i	−1.21643	+	1.21643i
$119$	−2.16361	−	3.74749i	−0.198338	−	0.343532i
$120$		0			0
$121$	−5.46768	+	9.47030i	−0.497062	+	0.860936i
$122$	1.73354	+	6.46967i	0.156948	+	0.585736i
$123$		0			0
$124$	−0.571428	+	0.329914i	−0.0513157	+	0.0296272i
$125$		0			0
$126$		0			0
$127$	6.72167	+	6.72167i	0.596452	+	0.596452i	0.939366	−	0.342915i	$-0.111414\pi$
$127$	6.72167	+	6.72167i	0.596452	+	0.596452i	−0.342915	+	0.939366i	$0.611414\pi$
$128$	−5.07660	+	18.9461i	−0.448712	+	1.67462i
$129$		0			0
$130$		0			0
$131$	−11.6482	−	6.72508i	−1.01771	−	0.587573i	−0.104267	−	0.994549i	$-0.533250\pi$
$131$	−11.6482	−	6.72508i	−1.01771	−	0.587573i	−0.913439	+	0.406977i	$0.866583\pi$
$132$		0			0
$133$	0.330923	+	0.0886705i	0.0286946	+	0.00768870i
$134$	−31.1794			−2.69349
$135$		0			0
$136$	−18.0195			−1.54516
$137$	9.45618	+	2.53378i	0.807896	+	0.216475i	0.639048	−	0.769167i	$-0.279329\pi$
$137$	9.45618	+	2.53378i	0.807896	+	0.216475i	0.168848	+	0.985642i	$0.445995\pi$
$138$		0			0
$139$	−6.84922	−	3.95440i	−0.580943	−	0.335408i	0.180565	−	0.983563i	$-0.442207\pi$
$139$	−6.84922	−	3.95440i	−0.580943	−	0.335408i	−0.761508	+	0.648155i	$0.775541\pi$
$140$		0			0
$141$		0			0
$142$	1.29840	−	4.84570i	0.108959	−	0.406642i
$143$	0.689567	+	0.689567i	0.0576645	+	0.0576645i
$144$		0			0
$145$		0			0
$146$	−26.1264	+	15.0841i	−2.16224	+	1.24837i
$147$		0			0
$148$	0.152843	+	0.570419i	0.0125636	+	0.0468882i
$149$	−4.56755	+	7.91123i	−0.374188	+	0.648113i	−0.990205	−	0.139620i	$-0.955412\pi$
$149$	−4.56755	+	7.91123i	−0.374188	+	0.648113i	0.616017	+	0.787733i	$0.288745\pi$
$150$		0			0
$151$	−7.34991	−	12.7304i	−0.598127	−	1.03599i	−0.993097	−	0.117293i	$-0.962578\pi$
$151$	−7.34991	−	12.7304i	−0.598127	−	1.03599i	0.394970	−	0.918694i	$-0.370755\pi$
$152$	1.00879	−	1.00879i	0.0818235	−	0.0818235i
$153$		0			0
$154$			0.459419i			0.0370210i
$155$		0			0
$156$		0			0
$157$	−16.3566	+	4.38274i	−1.30540	+	0.349781i	−0.843490	−	0.537146i	$-0.819503\pi$
$157$	−16.3566	+	4.38274i	−1.30540	+	0.349781i	−0.461911	+	0.886926i	$0.652836\pi$
$158$	−31.0169	+	8.31097i	−2.46758	+	0.661185i
$159$		0			0
$160$		0			0
$161$			2.75656i			0.217248i
$162$		0			0
$163$	−9.74771	+	9.74771i	−0.763499	+	0.763499i	−0.976953	−	0.213454i	$-0.931529\pi$
$163$	−9.74771	+	9.74771i	−0.763499	+	0.763499i	0.213454	+	0.976953i	$0.431529\pi$
$164$	7.60907	+	13.1793i	0.594169	+	1.02913i
$165$		0			0
$166$	6.25421	−	10.8326i	0.485421	−	0.840773i
$167$	−5.10613	−	19.0563i	−0.395124	−	1.47462i	−0.821568	−	0.570110i	$-0.806900\pi$
$167$	−5.10613	−	19.0563i	−0.395124	−	1.47462i	0.426444	−	0.904514i	$-0.359766\pi$
$168$		0			0
$169$	−1.48218	+	0.855737i	−0.114014	+	0.0658259i
$170$		0			0
$171$		0			0
$172$	−3.31737	−	3.31737i	−0.252947	−	0.252947i
$173$	−2.68653	+	10.0263i	−0.204253	+	0.762284i	0.785422	+	0.618960i	$0.212446\pi$
$173$	−2.68653	+	10.0263i	−0.204253	+	0.762284i	−0.989676	+	0.143324i	$0.954221\pi$
$174$		0			0
$175$		0			0
$176$	0.161827	+	0.0934307i	0.0121981	+	0.00704260i
$177$		0			0
$178$	0.640584	+	0.171644i	0.0480138	+	0.0128653i
$179$	15.1015			1.12874			0.564370	−	0.825522i	$-0.309119\pi$
$179$	15.1015			1.12874			0.564370	+	0.825522i	$0.309119\pi$
$180$		0			0
$181$	−7.82954			−0.581965			−0.290983	−	0.956728i	$-0.593982\pi$
$181$	−7.82954			−0.581965			−0.290983	+	0.956728i	$0.593982\pi$
$182$	−6.69448	−	1.79378i	−0.496228	−	0.132964i
$183$		0			0
$184$	9.94101	+	5.73945i	0.732861	+	0.423118i
$185$		0			0
$186$		0			0
$187$	0.366025	−	1.36603i	0.0267664	−	0.0998937i
$188$	10.3717	+	10.3717i	0.756436	+	0.756436i
$189$		0			0
$190$		0			0
$191$	−9.93557	+	5.73631i	−0.718913	+	0.415065i	−0.814352	−	0.580371i	$-0.802908\pi$
$191$	−9.93557	+	5.73631i	−0.718913	+	0.415065i	0.0954396	+	0.995435i	$0.469574\pi$
$192$		0			0
$193$	−1.42826	−	5.33034i	−0.102808	−	0.383686i	0.895279	−	0.445506i	$-0.146976\pi$
$193$	−1.42826	−	5.33034i	−0.102808	−	0.383686i	−0.998087	+	0.0618198i	$0.980310\pi$
$194$	−10.5026	+	18.1910i	−0.754043	+	1.30604i
$195$		0			0
$196$	10.8544	+	18.8004i	0.775315	+	1.34289i
$197$	−2.32295	+	2.32295i	−0.165504	+	0.165504i	−0.785000	−	0.619496i	$-0.787337\pi$
$197$	−2.32295	+	2.32295i	−0.165504	+	0.165504i	0.619496	+	0.785000i	$0.287337\pi$
$198$		0			0
$199$			17.1978i			1.21912i	0.792741	+	0.609558i	$0.208653\pi$
$199$			17.1978i			1.21912i	−0.792741	+	0.609558i	$0.791347\pi$
$200$		0			0
$201$		0			0
$202$	−29.5179	+	7.90930i	−2.07687	+	0.556497i
$203$	4.15201	−	1.11253i	0.291414	−	0.0780841i
$204$		0			0
$205$		0			0
$206$		−	38.0123i		−	2.64844i
$207$		0			0
$208$	−1.99328	+	1.99328i	−0.138209	+	0.138209i
$209$	0.0559832	+	0.0969658i	0.00387244	+	0.00670726i
$210$		0			0
$211$	−2.27479	+	3.94005i	−0.156603	+	0.271245i	−0.933642	−	0.358209i	$-0.883388\pi$
$211$	−2.27479	+	3.94005i	−0.156603	+	0.271245i	0.777039	+	0.629453i	$0.216721\pi$
$212$	1.16556	+	4.34993i	0.0800511	+	0.298755i
$213$		0			0
$214$	16.5390	−	9.54878i	1.13058	−	0.652741i
$215$		0			0
$216$		0			0
$217$	0.106921	+	0.106921i	0.00725827	+	0.00725827i
$218$	5.30158	−	19.7858i	0.359068	−	1.34006i
$219$		0			0
$220$		0			0
$221$	18.4761	+	10.6672i	1.24284	+	0.717552i
$222$		0			0
$223$	−17.6922	−	4.74061i	−1.18476	−	0.317455i	−0.387946	−	0.921682i	$-0.626815\pi$
$223$	−17.6922	−	4.74061i	−1.18476	−	0.317455i	−0.796812	+	0.604227i	$0.793482\pi$
$224$	3.71256			0.248056
$225$		0			0
$226$	−31.2819			−2.08084
$227$	−10.8961	−	2.91961i	−0.723202	−	0.193781i	−0.121602	−	0.992579i	$-0.538803\pi$
$227$	−10.8961	−	2.91961i	−0.723202	−	0.193781i	−0.601600	+	0.798798i	$0.705470\pi$
$228$		0			0
$229$	−4.22418	−	2.43883i	−0.279142	−	0.161163i	0.353893	−	0.935286i	$-0.384858\pi$
$229$	−4.22418	−	2.43883i	−0.279142	−	0.161163i	−0.633035	+	0.774123i	$0.718191\pi$
$230$		0			0
$231$		0			0
$232$	4.63279	−	17.2898i	0.304158	−	1.13513i
$233$	−7.90742	−	7.90742i	−0.518033	−	0.518033i	0.398943	−	0.916976i	$-0.369377\pi$
$233$	−7.90742	−	7.90742i	−0.518033	−	0.518033i	−0.916976	+	0.398943i	$0.869377\pi$
$234$		0			0
$235$		0			0
$236$	23.6537	−	13.6565i	1.53972	−	0.888960i
$237$		0			0
$238$	2.60131	+	9.70823i	0.168618	+	0.629291i
$239$	11.1362	−	19.2884i	0.720340	−	1.24767i	−0.240523	−	0.970643i	$-0.577319\pi$
$239$	11.1362	−	19.2884i	0.720340	−	1.24767i	0.960864	−	0.277022i	$-0.0893476\pi$
$240$		0			0
$241$	14.4746	+	25.0708i	0.932392	+	1.61495i	0.779220	+	0.626750i	$0.215615\pi$
$241$	14.4746	+	25.0708i	0.932392	+	1.61495i	0.153171	+	0.988200i	$0.451051\pi$
$242$	17.9599	−	17.9599i	1.15451	−	1.15451i
$243$		0			0
$244$		−	9.78955i		−	0.626712i
$245$		0			0
$246$		0			0
$247$	−1.63153	+	0.437168i	−0.103812	+	0.0278163i
$248$	0.608211	−	0.162970i	0.0386214	−	0.0103486i
$249$		0			0
$250$		0			0
$251$			20.4218i			1.28901i	0.764599	+	0.644507i	$0.222937\pi$
$251$			20.4218i			1.28901i	−0.764599	+	0.644507i	$0.777063\pi$
$252$		0			0
$253$	−0.637027	+	0.637027i	−0.0400496	+	0.0400496i
$254$	−11.0395	−	19.1209i	−0.692679	−	1.19975i
$255$		0			0
$256$	10.2249	−	17.7101i	0.639057	−	1.10688i
$257$	1.90043	+	7.09249i	0.118545	+	0.442417i	0.999528	−	0.0307319i	$-0.00978380\pi$
$257$	1.90043	+	7.09249i	0.118545	+	0.442417i	−0.880982	+	0.473149i	$0.843117\pi$
$258$		0			0
$259$	0.117200	−	0.0676656i	0.00728247	−	0.00420453i
$260$		0			0
$261$		0			0
$262$	22.0902	+	22.0902i	1.36473	+	1.36473i
$263$	3.78069	−	14.1097i	0.233127	−	0.870044i	−0.745857	−	0.666107i	$-0.767960\pi$
$263$	3.78069	−	14.1097i	0.233127	−	0.870044i	0.978984	−	0.203937i	$-0.0653738\pi$
$264$		0			0
$265$		0			0
$266$	−0.689128	−	0.397868i	−0.0422532	−	0.0243949i
$267$		0			0
$268$	44.0185	+	11.7947i	2.68886	+	0.720478i
$269$	3.76010			0.229257			0.114629	−	0.993408i	$-0.463432\pi$
$269$	3.76010			0.229257			0.114629	+	0.993408i	$0.463432\pi$
$270$		0			0
$271$	14.0785			0.855209			0.427604	−	0.903966i	$-0.359358\pi$
$271$	14.0785			0.855209			0.427604	+	0.903966i	$0.359358\pi$
$272$	3.94867	+	1.05804i	0.239423	+	0.0641533i
$273$		0			0
$274$	−19.6920	−	11.3692i	−1.18964	−	0.686837i
$275$		0			0
$276$		0			0
$277$	−0.541447	+	2.02071i	−0.0325324	+	0.121413i	−0.980283	−	0.197601i	$-0.936685\pi$
$277$	−0.541447	+	2.02071i	−0.0325324	+	0.121413i	0.947750	+	0.319014i	$0.103352\pi$
$278$	12.9892	+	12.9892i	0.779040	+	0.779040i
$279$		0			0
$280$		0			0
$281$	−8.02672	+	4.63423i	−0.478834	+	0.276455i	−0.719930	−	0.694046i	$-0.755826\pi$
$281$	−8.02672	+	4.63423i	−0.478834	+	0.276455i	0.241097	+	0.970501i	$0.422493\pi$
$282$		0			0
$283$	−8.33602	−	31.1104i	−0.495525	−	1.84932i	−0.527071	−	0.849821i	$-0.676710\pi$
$283$	−8.33602	−	31.1104i	−0.495525	−	1.84932i	0.0315464	−	0.999502i	$-0.489957\pi$
$284$	−3.66612	+	6.34991i	−0.217544	+	0.376798i
$285$		0			0
$286$	−1.13253	−	1.96159i	−0.0669677	−	0.115991i
$287$	2.46601	−	2.46601i	0.145564	−	0.145564i
$288$		0			0
$289$		−	13.9387i		−	0.819926i
$290$		0			0
$291$		0			0
$292$	42.5909	−	11.4122i	2.49244	−	0.667849i
$293$	6.37987	−	1.70948i	0.372716	−	0.0998690i	−0.0675984	−	0.997713i	$-0.521534\pi$
$293$	6.37987	−	1.70948i	0.372716	−	0.0998690i	0.440314	+	0.897844i	$0.354867\pi$
$294$		0			0
$295$		0			0
$296$		−	0.563547i		−	0.0327555i
$297$		0			0
$298$	15.0032	−	15.0032i	0.869114	−	0.869114i
$299$	−6.79528	−	11.7698i	−0.392981	−	0.680663i
$300$		0			0
$301$	−0.537559	+	0.931080i	−0.0309844	+	0.0536666i
$302$	8.83680	+	32.9794i	0.508501	+	1.89775i
$303$		0			0
$304$	−0.280292	+	0.161827i	−0.0160759	+	0.00928140i
$305$		0			0
$306$		0			0
$307$	−5.82120	−	5.82120i	−0.332233	−	0.332233i	0.521201	−	0.853434i	$-0.325484\pi$
$307$	−5.82120	−	5.82120i	−0.332233	−	0.332233i	−0.853434	+	0.521201i	$0.825484\pi$
$308$	0.173792	−	0.648600i	0.00990271	−	0.0369574i
$309$		0			0
$310$		0			0
$311$	−9.98678	−	5.76587i	−0.566299	−	0.326953i	0.189371	−	0.981906i	$-0.439355\pi$
$311$	−9.98678	−	5.76587i	−0.566299	−	0.326953i	−0.755670	+	0.654953i	$0.772688\pi$
$312$		0			0
$313$	6.43287	+	1.72368i	0.363607	+	0.0974283i	0.435997	−	0.899948i	$-0.356396\pi$
$313$	6.43287	+	1.72368i	0.363607	+	0.0974283i	−0.0723896	+	0.997376i	$0.523063\pi$
$314$	39.3311			2.21958
$315$		0			0
$316$	46.9331			2.64020
$317$	1.93788	+	0.519254i	0.108842	+	0.0291642i	0.312829	−	0.949809i	$-0.398723\pi$
$317$	1.93788	+	0.519254i	0.108842	+	0.0291642i	−0.203987	+	0.978974i	$0.565390\pi$
$318$		0			0
$319$	1.21661	+	0.702408i	0.0681169	+	0.0393273i
$320$		0			0
$321$		0			0
$322$	1.65711	−	6.18441i	0.0923470	−	0.344644i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$		0			0
$325$		0			0
$326$	27.7290	−	16.0094i	1.53577	−	0.886677i
$327$		0			0
$328$	−3.75870	−	14.0277i	−0.207540	−	0.774548i
$329$	1.68067	−	2.91101i	0.0926585	−	0.160489i
$330$		0			0
$331$	−11.7700	−	20.3862i	−0.646937	−	1.12053i	−0.983850	−	0.178992i	$-0.942716\pi$
$331$	−11.7700	−	20.3862i	−0.646937	−	1.12053i	0.336913	−	0.941536i	$-0.390617\pi$
$332$	−12.9274	+	12.9274i	−0.709484	+	0.709484i
$333$		0			0
$334$			45.8229i			2.50732i
$335$		0			0
$336$		0			0
$337$	−11.0048	+	2.94873i	−0.599470	+	0.160627i	−0.545778	−	0.837930i	$-0.683766\pi$
$337$	−11.0048	+	2.94873i	−0.599470	+	0.160627i	−0.0536923	+	0.998558i	$0.517099\pi$
$338$	3.83973	−	1.02885i	0.208854	−	0.0559622i
$339$		0			0
$340$		0			0
$341$			0.0494178i			0.00267612i
$342$		0			0
$343$	7.36850	−	7.36850i	0.397861	−	0.397861i
$344$	2.23851	+	3.87721i	0.120692	+	0.209045i
$345$		0			0
$346$	12.0546	−	20.8792i	0.648059	−	1.12247i
$347$	−3.69845	−	13.8028i	−0.198543	−	0.740974i	−0.991321	−	0.131463i	$-0.958033\pi$
$347$	−3.69845	−	13.8028i	−0.198543	−	0.740974i	0.792778	−	0.609511i	$-0.208634\pi$
$348$		0			0
$349$	−15.2113	+	8.78224i	−0.814242	+	0.470103i	−0.848427	−	0.529313i	$-0.822450\pi$
$349$	−15.2113	+	8.78224i	−0.814242	+	0.470103i	0.0341849	+	0.999416i	$0.489116\pi$
$350$		0			0
$351$		0			0
$352$	0.857952	+	0.857952i	0.0457290	+	0.0457290i
$353$	4.51136	−	16.8366i	0.240116	−	0.896124i	−0.735660	−	0.677351i	$-0.763128\pi$
$353$	4.51136	−	16.8366i	0.240116	−	0.896124i	0.975776	−	0.218773i	$-0.0702054\pi$
$354$		0			0
$355$		0			0
$356$	−0.839435	−	0.484648i	−0.0444900	−	0.0256863i
$357$		0			0
$358$	−33.8806	−	9.07828i	−1.79064	−	0.479802i
$359$	−34.0577			−1.79750			−0.898748	−	0.438465i	$-0.855522\pi$
$359$	−34.0577			−1.79750			−0.898748	+	0.438465i	$0.855522\pi$
$360$		0			0
$361$	18.8061			0.989793
$362$	17.5658	+	4.70673i	0.923236	+	0.247380i
$363$		0			0
$364$	8.77260	+	5.06486i	0.459809	+	0.265471i
$365$		0			0
$366$		0			0
$367$	−3.65315	+	13.6337i	−0.190693	+	0.711675i	0.802647	+	0.596454i	$0.203424\pi$
$367$	−3.65315	+	13.6337i	−0.190693	+	0.711675i	−0.993340	+	0.115221i	$0.963242\pi$
$368$	−1.84141	−	1.84141i	−0.0959901	−	0.0959901i
$369$		0			0
$370$		0			0
$371$	0.893752	−	0.516008i	0.0464013	−	0.0267898i
$372$		0			0
$373$	5.57233	+	20.7962i	0.288524	+	1.07679i	0.946225	+	0.323508i	$0.104862\pi$
$373$	5.57233	+	20.7962i	0.288524	+	1.07679i	−0.657701	+	0.753279i	$0.728471\pi$
$374$	−1.64237	+	2.84467i	−0.0849251	+	0.147095i
$375$		0			0
$376$	−6.99867	−	12.1221i	−0.360929	−	0.625147i
$377$	−14.9854	+	14.9854i	−0.771788	+	0.771788i
$378$		0			0
$379$		−	9.52893i		−	0.489468i	−0.969590	−	0.244734i	$-0.921299\pi$
$379$		−	9.52893i		−	0.489468i	0.969590	−	0.244734i	$-0.0787007\pi$
$380$		0			0
$381$		0			0
$382$	25.7391	−	6.89676i	1.31693	−	0.352869i
$383$	−9.61802	+	2.57714i	−0.491458	+	0.131686i	−0.496033	−	0.868304i	$-0.665210\pi$
$383$	−9.61802	+	2.57714i	−0.491458	+	0.131686i	0.00457478	+	0.999990i	$0.498544\pi$
$384$		0			0
$385$		0			0
$386$			12.8173i			0.652385i
$387$		0			0
$388$	21.7088	−	21.7088i	1.10210	−	1.10210i
$389$	14.5672	+	25.2312i	0.738587	+	1.27927i	0.953131	+	0.302557i	$0.0978401\pi$
$389$	14.5672	+	25.2312i	0.738587	+	1.27927i	−0.214544	+	0.976714i	$0.568827\pi$
$390$		0			0
$391$	−9.85441	+	17.0683i	−0.498359	+	0.863183i
$392$	−5.36182	−	20.0106i	−0.270813	−	1.01069i
$393$		0			0
$394$	6.60804	−	3.81516i	0.332908	−	0.192205i
$395$		0			0
$396$		0			0
$397$	18.9354	+	18.9354i	0.950338	+	0.950338i	0.998824	−	0.0484856i	$-0.0154395\pi$
$397$	18.9354	+	18.9354i	0.950338	+	0.950338i	−0.0484856	+	0.998824i	$0.515439\pi$
$398$	10.3384	−	38.5836i	0.518219	−	1.93402i
$399$		0			0
$400$		0			0
$401$	−21.2096	−	12.2453i	−1.05916	−	0.611503i	−0.133957	−	0.990987i	$-0.542768\pi$
$401$	−21.2096	−	12.2453i	−1.05916	−	0.611503i	−0.925198	+	0.379484i	$0.876102\pi$
$402$		0			0
$403$	−0.720098	−	0.192950i	−0.0358706	−	0.00961151i
$404$	44.6649			2.22216
$405$		0			0
$406$	−9.98392			−0.495493
$407$	0.0427215	+	0.0114472i	0.00211763	+	0.000567417i
$408$		0			0
$409$	−12.2649	−	7.08116i	−0.606462	−	0.350141i	0.165118	−	0.986274i	$-0.447200\pi$
$409$	−12.2649	−	7.08116i	−0.606462	−	0.350141i	−0.771579	+	0.636133i	$0.780533\pi$
$410$		0			0
$411$		0			0
$412$	−14.3795	+	53.6652i	−0.708429	+	2.64389i
$413$	−4.42589	−	4.42589i	−0.217784	−	0.217784i
$414$		0			0
$415$		0			0
$416$	−15.8516	+	9.15193i	−0.777189	+	0.448710i
$417$		0			0
$418$	−0.0673086	−	0.251199i	−0.00329217	−	0.0122866i
$419$	−13.8808	+	24.0422i	−0.678120	+	1.17454i	0.297426	+	0.954745i	$0.403872\pi$
$419$	−13.8808	+	24.0422i	−0.678120	+	1.17454i	−0.975546	+	0.219794i	$0.929461\pi$
$420$		0			0
$421$	−0.429901	−	0.744611i	−0.0209521	−	0.0362901i	0.855359	−	0.518035i	$-0.173336\pi$
$421$	−0.429901	−	0.744611i	−0.0209521	−	0.0362901i	−0.876311	+	0.481745i	$0.840003\pi$
$422$	7.47211	−	7.47211i	0.363737	−	0.363737i
$423$		0			0
$424$		−	4.29753i		−	0.208706i
$425$		0			0
$426$		0			0
$427$	−2.16698	+	0.580639i	−0.104867	+	0.0280991i
$428$	−26.9616	+	7.22434i	−1.30324	+	0.349202i
$429$		0			0
$430$		0			0
$431$		−	25.5770i		−	1.23200i	−0.787746	−	0.616000i	$-0.788752\pi$
$431$		−	25.5770i		−	1.23200i	0.787746	−	0.616000i	$-0.211248\pi$
$432$		0			0
$433$	−6.30733	+	6.30733i	−0.303111	+	0.303111i	−0.842230	−	0.539119i	$-0.818757\pi$
$433$	−6.30733	+	6.30733i	−0.303111	+	0.303111i	0.539119	+	0.842230i	$0.318757\pi$
$434$	−0.175604	−	0.304155i	−0.00842927	−	0.0145999i
$435$		0			0
$436$	−14.9694	+	25.9277i	−0.716903	+	1.24171i
$437$	−0.403859	−	1.50722i	−0.0193192	−	0.0721002i
$438$		0			0
$439$	12.4666	−	7.19760i	0.594999	−	0.343523i	−0.172073	−	0.985084i	$-0.555046\pi$
$439$	12.4666	−	7.19760i	0.594999	−	0.343523i	0.767072	+	0.641561i	$0.221713\pi$
$440$		0			0
$441$		0			0
$442$	−35.0390	−	35.0390i	−1.66663	−	1.66663i
$443$	−5.67359	+	21.1741i	−0.269560	+	1.00601i	0.689839	+	0.723962i	$0.257681\pi$
$443$	−5.67359	+	21.1741i	−0.269560	+	1.00601i	−0.959400	+	0.282050i	$0.908986\pi$
$444$		0			0
$445$		0			0
$446$	36.8430	+	21.2713i	1.74457	+	1.00723i
$447$		0			0
$448$	−9.43376	−	2.52777i	−0.445703	−	0.119426i
$449$	−23.6447			−1.11586			−0.557931	−	0.829888i	$-0.688404\pi$
$449$	−23.6447			−1.11586			−0.557931	+	0.829888i	$0.688404\pi$
$450$		0			0
$451$	1.13976			0.0536693
$452$	44.1632	+	11.8335i	2.07726	+	0.556601i
$453$		0			0
$454$	22.6906	+	13.1004i	1.06492	+	0.614833i
$455$		0			0
$456$		0			0
$457$	1.47628	−	5.50956i	0.0690575	−	0.257726i	−0.922763	−	0.385369i	$-0.874074\pi$
$457$	1.47628	−	5.50956i	0.0690575	−	0.257726i	0.991820	+	0.127642i	$0.0407410\pi$
$458$	8.01095	+	8.01095i	0.374327	+	0.374327i
$459$		0			0
$460$		0			0
$461$	27.8943	−	16.1048i	1.29916	−	0.750073i	0.318905	−	0.947787i	$-0.396685\pi$
$461$	27.8943	−	16.1048i	1.29916	−	0.750073i	0.980260	+	0.197713i	$0.0633515\pi$
$462$		0			0
$463$	1.65471	+	6.17544i	0.0769007	+	0.286997i	0.993658	−	0.112448i	$-0.0358693\pi$
$463$	1.65471	+	6.17544i	0.0769007	+	0.286997i	−0.916757	+	0.399446i	$0.869203\pi$
$464$	−2.03040	+	3.51676i	−0.0942590	+	0.163261i
$465$		0			0
$466$	12.9869	+	22.4940i	0.601608	+	1.04202i
$467$	−12.7982	+	12.7982i	−0.592230	+	0.592230i	−0.938233	−	0.346003i	$-0.887539\pi$
$467$	−12.7982	+	12.7982i	−0.592230	+	0.592230i	0.346003	+	0.938233i	$0.387539\pi$
$468$		0			0
$469$		−	10.4433i		−	0.482228i
$470$		0			0
$471$		0			0
$472$	−25.1763	+	6.74597i	−1.15883	+	0.310508i
$473$	−0.339395	+	0.0909406i	−0.0156054	+	0.00418145i
$474$		0			0
$475$		0			0
$476$		−	14.6900i		−	0.673314i
$477$		0			0
$478$	−36.5795	+	36.5795i	−1.67311	+	1.67311i
$479$	1.76166	+	3.05128i	0.0804921	+	0.139416i	0.903461	−	0.428669i	$-0.141017\pi$
$479$	1.76166	+	3.05128i	0.0804921	+	0.139416i	−0.822969	+	0.568086i	$0.807684\pi$
$480$		0			0
$481$	−0.333609	+	0.577827i	−0.0152112	+	0.0263467i
$482$	−17.4028	−	64.9482i	−0.792677	−	2.95831i
$483$		0			0
$484$	−32.1495	+	18.5615i	−1.46134	+	0.843706i
$485$		0			0
$486$		0			0
$487$	−29.3442	−	29.3442i	−1.32971	−	1.32971i	−0.905616	−	0.424098i	$-0.860591\pi$
$487$	−29.3442	−	29.3442i	−1.32971	−	1.32971i	−0.424098	−	0.905616i	$-0.639409\pi$
$488$	−2.41790	+	9.02373i	−0.109453	+	0.408485i
$489$		0			0
$490$		0			0
$491$	−17.9001	−	10.3346i	−0.807819	−	0.466395i	0.0383788	−	0.999263i	$-0.487781\pi$
$491$	−17.9001	−	10.3346i	−0.807819	−	0.466395i	−0.846198	+	0.532869i	$0.821114\pi$
$492$		0			0
$493$	29.6859	+	7.95433i	1.33699	+	0.358245i
$494$	3.92319			0.176513
$495$		0			0
$496$	−0.142849			−0.00641409
$497$	1.62304	+	0.434891i	0.0728031	+	0.0195075i
$498$		0			0
$499$	22.6691	+	13.0880i	1.01481	+	0.585901i	0.912596	−	0.408862i	$-0.134074\pi$
$499$	22.6691	+	13.0880i	1.01481	+	0.585901i	0.102214	+	0.994762i	$0.467407\pi$
$500$		0			0
$501$		0			0
$502$	12.2766	−	45.8168i	0.547930	−	2.04490i
$503$	−6.72022	−	6.72022i	−0.299640	−	0.299640i	0.541233	−	0.840873i	$-0.317958\pi$
$503$	−6.72022	−	6.72022i	−0.299640	−	0.299640i	−0.840873	+	0.541233i	$0.817958\pi$
$504$		0			0
$505$		0			0
$506$	1.81213	−	1.04624i	0.0805592	−	0.0465109i
$507$		0			0
$508$	8.35217	+	31.1707i	0.370568	+	1.38298i
$509$	11.9676	−	20.7285i	0.530454	−	0.918773i	−0.468915	−	0.883243i	$-0.655355\pi$
$509$	11.9676	−	20.7285i	0.530454	−	0.918773i	0.999369	−	0.0355293i	$-0.0113117\pi$
$510$		0			0
$511$	−5.05232	−	8.75087i	−0.223501	−	0.387116i
$512$	−5.84717	+	5.84717i	−0.258411	+	0.258411i
$513$		0			0
$514$		−	17.0546i		−	0.752246i
$515$		0			0
$516$		0			0
$517$	1.06111	−	0.284325i	0.0466678	−	0.0125046i
$518$	−0.303618	+	0.0813543i	−0.0133402	+	0.00357450i
$519$		0			0
$520$		0			0
$521$			3.23141i			0.141571i	0.997492	+	0.0707853i	$0.0225505\pi$
$521$			3.23141i			0.141571i	−0.997492	+	0.0707853i	$0.977449\pi$
$522$		0			0
$523$	8.67002	−	8.67002i	0.379114	−	0.379114i	−0.491669	−	0.870782i	$-0.663613\pi$
$523$	8.67002	−	8.67002i	0.379114	−	0.379114i	0.870782	+	0.491669i	$0.163613\pi$
$524$	−22.8301	−	39.5429i	−0.997339	−	1.72744i
$525$		0			0
$526$	−16.9641	+	29.3827i	−0.739672	+	1.28115i
$527$	0.279813	+	1.04427i	0.0121888	+	0.0454893i
$528$		0			0
$529$	−9.04559	+	5.22247i	−0.393286	+	0.227064i
$530$		0			0
$531$		0			0
$532$	0.822392	+	0.822392i	0.0356552	+	0.0356552i
$533$	−4.45016	+	16.6082i	−0.192758	+	0.719381i
$534$		0			0
$535$		0			0
$536$	−37.6619	−	21.7441i	−1.62675	−	0.939202i
$537$		0			0
$538$	−8.43586	−	2.26038i	−0.363696	−	0.0974520i
$539$	1.62588			0.0700317
$540$		0			0
$541$	−11.1502			−0.479386			−0.239693	−	0.970849i	$-0.577047\pi$
$541$	−11.1502			−0.479386			−0.239693	+	0.970849i	$0.577047\pi$
$542$	−31.5855	−	8.46330i	−1.35671	−	0.363530i
$543$		0			0
$544$	22.9878	+	13.2720i	0.985592	+	0.569032i
$545$		0			0
$546$		0			0
$547$	−3.54511	+	13.2305i	−0.151578	+	0.565697i	0.847796	+	0.530323i	$0.177929\pi$
$547$	−3.54511	+	13.2305i	−0.151578	+	0.565697i	−0.999374	+	0.0353748i	$0.988737\pi$
$548$	23.5000	+	23.5000i	1.00387	+	1.00387i
$549$		0			0
$550$		0			0
$551$	−2.10722	+	1.21661i	−0.0897708	+	0.0518292i
$552$		0			0
$553$	−2.78371	−	10.3889i	−0.118375	−	0.441782i
$554$	2.42950	−	4.20802i	0.103220	−	0.178781i
$555$		0			0
$556$	−13.4243	−	23.2516i	−0.569317	−	0.986086i
$557$	11.8934	−	11.8934i	0.503938	−	0.503938i	−0.408721	−	0.912659i	$-0.634025\pi$
$557$	11.8934	−	11.8934i	0.503938	−	0.503938i	0.912659	+	0.408721i	$0.134025\pi$
$558$		0			0
$559$		−	5.30061i		−	0.224192i
$560$		0			0
$561$		0			0
$562$	20.7940	−	5.57173i	0.877141	−	0.235029i
$563$	−23.7986	+	6.37683i	−1.00299	+	0.268751i	−0.722699	−	0.691163i	$-0.757099\pi$
$563$	−23.7986	+	6.37683i	−1.00299	+	0.268751i	−0.280294	+	0.959914i	$0.590432\pi$
$564$		0			0
$565$		0			0
$566$			74.8082i			3.14442i
$567$		0			0
$568$	4.94768	−	4.94768i	0.207600	−	0.207600i
$569$	−6.24856	−	10.8228i	−0.261953	−	0.453716i	0.704808	−	0.709399i	$-0.251033\pi$
$569$	−6.24856	−	10.8228i	−0.261953	−	0.453716i	−0.966761	+	0.255682i	$0.917700\pi$
$570$		0			0
$571$	13.7065	−	23.7404i	0.573601	−	0.993506i	−0.422591	−	0.906320i	$-0.638879\pi$
$571$	13.7065	−	23.7404i	0.573601	−	0.993506i	0.996192	−	0.0871853i	$-0.0277872\pi$
$572$	0.856838	+	3.19776i	0.0358262	+	0.133705i
$573$		0			0
$574$	−7.01498	+	4.05010i	−0.292800	+	0.169048i
$575$		0			0
$576$		0			0
$577$	11.1638	+	11.1638i	0.464755	+	0.464755i	0.900210	−	0.435455i	$-0.143413\pi$
$577$	11.1638	+	11.1638i	0.464755	+	0.464755i	−0.435455	+	0.900210i	$0.643413\pi$
$578$	−8.37928	+	31.2719i	−0.348532	+	1.30074i
$579$		0			0
$580$		0			0
$581$	3.62831	+	2.09481i	0.150528	+	0.0869072i
$582$		0			0
$583$	0.325788	+	0.0872947i	0.0134928	+	0.00361538i
$584$	−42.0778			−1.74119
$585$		0			0
$586$	−15.3410			−0.633733
$587$	17.7860	+	4.76574i	0.734106	+	0.196703i	0.606457	−	0.795116i	$-0.292590\pi$
$587$	17.7860	+	4.76574i	0.734106	+	0.196703i	0.127649	+	0.991819i	$0.459257\pi$
$588$		0			0
$589$	−0.0741267	−	0.0427971i	−0.00305434	−	0.00176342i
$590$		0			0
$591$		0			0
$592$	−0.0330896	+	0.123492i	−0.00135997	+	0.00507549i
$593$	−14.5424	−	14.5424i	−0.597186	−	0.597186i	0.342377	−	0.939563i	$-0.388768\pi$
$593$	−14.5424	−	14.5424i	−0.597186	−	0.597186i	−0.939563	+	0.342377i	$0.888768\pi$
$594$		0			0
$595$		0			0
$596$	−26.8568	+	15.5058i	−1.10010	+	0.635143i
$597$		0			0
$598$	8.16997	+	30.4907i	0.334095	+	1.24686i
$599$	−17.6972	+	30.6525i	−0.723089	+	1.25243i	0.236666	+	0.971591i	$0.423945\pi$
$599$	−17.6972	+	30.6525i	−0.723089	+	1.25243i	−0.959756	+	0.280836i	$0.909388\pi$
$600$		0			0
$601$	7.31737	+	12.6741i	0.298482	+	0.516986i	0.975789	−	0.218715i	$-0.0701864\pi$
$601$	7.31737	+	12.6741i	0.298482	+	0.516986i	−0.677307	+	0.735700i	$0.736853\pi$
$602$	1.76575	−	1.76575i	0.0719664	−	0.0719664i
$603$		0			0
$604$		−	49.9026i		−	2.03051i
$605$		0			0
$606$		0			0
$607$	7.54883	−	2.02270i	0.306397	−	0.0820989i	−0.102344	−	0.994749i	$-0.532634\pi$
$607$	7.54883	−	2.02270i	0.306397	−	0.0820989i	0.408742	+	0.912650i	$0.365968\pi$
$608$	−2.02994	+	0.543920i	−0.0823248	+	0.0220589i
$609$		0			0
$610$		0			0
$611$			16.5723i			0.670444i
$612$		0			0
$613$	−3.49830	+	3.49830i	−0.141295	+	0.141295i	−0.774216	−	0.632921i	$-0.781856\pi$
$613$	−3.49830	+	3.49830i	−0.141295	+	0.141295i	0.632921	+	0.774216i	$0.281856\pi$
$614$	9.56058	+	16.5594i	0.385833	+	0.668283i
$615$		0			0
$616$	−0.320393	+	0.554937i	−0.0129090	+	0.0223590i
$617$	6.40561	+	23.9061i	0.257880	+	0.962421i	0.966466	+	0.256796i	$0.0826670\pi$
$617$	6.40561	+	23.9061i	0.257880	+	0.962421i	−0.708585	+	0.705625i	$0.750666\pi$
$618$		0			0
$619$	−15.4357	+	8.91182i	−0.620414	+	0.358196i	−0.777030	−	0.629463i	$-0.783275\pi$
$619$	−15.4357	+	8.91182i	−0.620414	+	0.358196i	0.156616	+	0.987660i	$0.449941\pi$
$620$		0			0
$621$		0			0
$622$	18.9394	+	18.9394i	0.759402	+	0.759402i
$623$	−0.0574910	+	0.214559i	−0.00230333	+	0.00859614i
$624$		0			0
$625$		0			0
$626$	−13.3961	−	7.73424i	−0.535416	−	0.309122i
$627$		0			0
$628$	−55.5270	−	14.8784i	−2.21577	−	0.593714i
$629$	0.967588			0.0385803
$630$		0			0
$631$	−29.9153			−1.19091			−0.595454	−	0.803389i	$-0.703028\pi$
$631$	−29.9153			−1.19091			−0.595454	+	0.803389i	$0.703028\pi$
$632$	−43.2617	−	11.5919i	−1.72086	−	0.461102i
$633$		0			0
$634$	−4.03553	−	2.32991i	−0.160271	−	0.0925327i
$635$		0			0
$636$		0			0
$637$	−6.34819	+	23.6917i	−0.251524	+	0.938701i
$638$	−2.30723	−	2.30723i	−0.0913441	−	0.0913441i
$639$		0			0
$640$		0			0
$641$	13.7403	−	7.93299i	0.542711	−	0.313334i	−0.203466	−	0.979082i	$-0.565221\pi$
$641$	13.7403	−	7.93299i	0.542711	−	0.313334i	0.746177	+	0.665748i	$0.231887\pi$
$642$		0			0
$643$	−6.01727	−	22.4568i	−0.237298	−	0.885608i	−0.977099	−	0.212783i	$-0.931747\pi$
$643$	−6.01727	−	22.4568i	−0.237298	−	0.885608i	0.739801	−	0.672825i	$-0.234919\pi$
$644$	−4.67895	+	8.10419i	−0.184377	+	0.319350i
$645$		0			0
$646$	−2.84467	−	4.92712i	−0.111922	−	0.193855i
$647$	−8.90965	+	8.90965i	−0.350274	+	0.350274i	−0.860212	−	0.509937i	$-0.829669\pi$
$647$	−8.90965	+	8.90965i	−0.350274	+	0.350274i	0.509937	+	0.860212i	$0.329669\pi$
$648$		0			0
$649$		−	2.04560i		−	0.0802969i
$650$		0			0
$651$		0			0
$652$	−45.2035	+	12.1122i	−1.77031	+	0.474352i
$653$	14.0422	−	3.76260i	0.549515	−	0.147242i	0.0266300	−	0.999645i	$-0.491522\pi$
$653$	14.0422	−	3.76260i	0.549515	−	0.147242i	0.522885	+	0.852403i	$0.324856\pi$
$654$		0			0
$655$		0			0
$656$			3.29463i			0.128634i
$657$		0			0
$658$	−5.52058	+	5.52058i	−0.215215	+	0.215215i
$659$	4.50735	+	7.80696i	0.175582	+	0.304116i	0.940362	−	0.340174i	$-0.110486\pi$
$659$	4.50735	+	7.80696i	0.175582	+	0.304116i	−0.764781	+	0.644291i	$0.777153\pi$
$660$		0			0
$661$	15.0034	−	25.9866i	0.583564	−	1.01076i	−0.411488	−	0.911415i	$-0.634991\pi$
$661$	15.0034	−	25.9866i	0.583564	−	1.01076i	0.995053	−	0.0993481i	$-0.0316757\pi$
$662$	14.1511	+	52.8125i	0.549996	+	2.05261i
$663$		0			0
$664$	15.1090	−	8.72321i	0.586345	−	0.338526i
$665$		0			0
$666$		0			0
$667$	−13.8436	−	13.8436i	−0.536028	−	0.536028i
$668$	17.3342	−	64.6920i	0.670679	−	2.50301i
$669$		0			0
$670$		0			0
$671$	−0.634959	−	0.366594i	−0.0245123	−	0.0141522i
$672$		0			0
$673$	−26.2818	−	7.04218i	−1.01309	−	0.271456i	−0.286169	−	0.958179i	$-0.592382\pi$
$673$	−26.2818	−	7.04218i	−1.01309	−	0.271456i	−0.726919	+	0.686723i	$0.759049\pi$
$674$	26.4622			1.01928
$675$		0			0
$676$	−5.81007			−0.223464
$677$	16.7622	+	4.49141i	0.644223	+	0.172619i	0.566116	−	0.824326i	$-0.308446\pi$
$677$	16.7622	+	4.49141i	0.644223	+	0.172619i	0.0781075	+	0.996945i	$0.475112\pi$
$678$		0			0
$679$	−6.09297	−	3.51778i	−0.233827	−	0.135000i
$680$		0			0
$681$		0			0
$682$	0.0297075	−	0.110870i	0.00113756	−	0.00424543i
$683$	27.4945	+	27.4945i	1.05205	+	1.05205i	0.998569	+	0.0534806i	$0.0170315\pi$
$683$	27.4945	+	27.4945i	1.05205	+	1.05205i	0.0534806	+	0.998569i	$0.482968\pi$
$684$		0			0
$685$		0			0
$686$	−20.9610	+	12.1018i	−0.800293	+	0.462049i
$687$		0			0
$688$	−0.262876	−	0.981065i	−0.0100220	−	0.0374028i
$689$	−2.54405	+	4.40643i	−0.0969207	+	0.167872i
$690$		0			0
$691$	−9.07512	−	15.7186i	−0.345234	−	0.597962i	0.640162	−	0.768240i	$-0.278867\pi$
$691$	−9.07512	−	15.7186i	−0.345234	−	0.597962i	−0.985396	+	0.170277i	$0.945534\pi$
$692$	−24.9168	+	24.9168i	−0.947195	+	0.947195i
$693$		0			0
$694$			33.1902i			1.25988i
$695$		0			0
$696$		0			0
$697$	24.0850	−	6.45355i	0.912283	−	0.244446i
$698$	39.4063	−	10.5589i	1.49155	−	0.399660i
$699$		0			0
$700$		0			0
$701$		−	5.23510i		−	0.197727i	−0.995101	−	0.0988635i	$-0.968479\pi$
$701$		−	5.23510i		−	0.197727i	0.995101	−	0.0988635i	$-0.0315207\pi$
$702$		0			0
$703$	−0.0541687	+	0.0541687i	−0.00204301	+	0.00204301i
$704$	−1.59594	−	2.76425i	−0.0601492	−	0.104181i
$705$		0			0
$706$	−20.2427	+	35.0614i	−0.761844	+	1.31955i
$707$	−2.64917	−	9.88684i	−0.0996323	−	0.371833i
$708$		0			0
$709$	−14.7176	+	8.49720i	−0.552730	+	0.319119i	−0.750222	−	0.661186i	$-0.770054\pi$
$709$	−14.7176	+	8.49720i	−0.552730	+	0.319119i	0.197492	+	0.980304i	$0.436720\pi$
$710$		0			0
$711$		0			0
$712$	0.654066	+	0.654066i	0.0245121	+	0.0245121i
$713$	0.178248	−	0.665231i	0.00667545	−	0.0249131i
$714$		0			0
$715$		0			0
$716$	44.3979	+	25.6331i	1.65923	+	0.957955i
$717$		0			0
$718$	76.4092	+	20.4738i	2.85157	+	0.764075i
$719$	49.3502			1.84045			0.920225	−	0.391389i	$-0.128005\pi$
$719$	49.3502			1.84045			0.920225	+	0.391389i	$0.128005\pi$
$720$		0			0
$721$	12.7320			0.474164
$722$	−42.1918	−	11.3053i	−1.57022	−	0.420739i
$723$		0			0
$724$	−23.0186	−	13.2898i	−0.855478	−	0.493910i
$725$		0			0
$726$		0			0
$727$	10.1550	−	37.8991i	0.376630	−	1.40560i	−0.474319	−	0.880353i	$-0.657306\pi$
$727$	10.1550	−	37.8991i	0.376630	−	1.40560i	0.850949	−	0.525249i	$-0.176028\pi$
$728$	−6.83537	−	6.83537i	−0.253336	−	0.253336i
$729$		0			0
$730$		0			0
$731$	−6.65702	+	3.84343i	−0.246219	+	0.142155i
$732$		0			0
$733$	1.96236	+	7.32362i	0.0724813	+	0.270504i	0.992650	−	0.121017i	$-0.0386156\pi$
$733$	1.96236	+	7.32362i	0.0724813	+	0.270504i	−0.920169	+	0.391521i	$0.871949\pi$
$734$	16.3918	−	28.3915i	0.605034	−	1.04795i
$735$		0			0
$736$	−8.45462	−	14.6438i	−0.311641	−	0.539778i
$737$	2.41340	−	2.41340i	0.0888987	−	0.0888987i
$738$		0			0
$739$		−	43.8329i		−	1.61242i	−0.591629	−	0.806210i	$-0.701515\pi$
$739$		−	43.8329i		−	1.61242i	0.591629	−	0.806210i	$-0.298485\pi$
$740$		0			0
$741$		0			0
$742$	−2.31535	+	0.620396i	−0.0849992	+	0.0227755i
$743$	−9.01884	+	2.41659i	−0.330869	+	0.0886561i	−0.420429	−	0.907325i	$-0.638121\pi$
$743$	−9.01884	+	2.41659i	−0.330869	+	0.0886561i	0.0895603	+	0.995981i	$0.471454\pi$
$744$		0			0
$745$		0			0
$746$		−	50.0066i		−	1.83087i
$747$		0			0
$748$	3.39477	−	3.39477i	0.124125	−	0.124125i
$749$	3.19830	+	5.53962i	0.116863	+	0.202413i
$750$		0			0
$751$	23.6963	−	41.0432i	0.864689	−	1.49769i	−0.00266566	−	0.999996i	$-0.500849\pi$
$751$	23.6963	−	41.0432i	0.864689	−	1.49769i	0.867355	−	0.497690i	$-0.165818\pi$
$752$	0.821878	+	3.06729i	0.0299708	+	0.111853i
$753$		0			0
$754$	42.6286	−	24.6116i	1.55244	−	0.896303i
$755$		0			0
$756$		0			0
$757$	−1.37906	−	1.37906i	−0.0501227	−	0.0501227i	0.681601	−	0.731724i	$-0.261284\pi$
$757$	−1.37906	−	1.37906i	−0.0501227	−	0.0501227i	−0.731724	+	0.681601i	$0.761284\pi$
$758$	−5.72832	+	21.3784i	−0.208062	+	0.776497i
$759$		0			0
$760$		0			0
$761$	41.8540	+	24.1644i	1.51720	+	0.875958i	0.999796	+	0.0202203i	$0.00643676\pi$
$761$	41.8540	+	24.1644i	1.51720	+	0.875958i	0.517409	+	0.855738i	$0.326897\pi$
$762$		0			0
$763$	6.62712	+	1.77573i	0.239918	+	0.0642858i
$764$	−38.9469			−1.40905
$765$		0			0
$766$	23.1275			0.835631
$767$	29.8078	+	7.98696i	1.07630	+	0.288393i
$768$		0			0
$769$	−25.7542	−	14.8692i	−0.928719	−	0.536196i	−0.0423126	−	0.999104i	$-0.513473\pi$
$769$	−25.7542	−	14.8692i	−0.928719	−	0.536196i	−0.886406	+	0.462908i	$0.846806\pi$
$770$		0			0
$771$		0			0
$772$	4.84862	−	18.0953i	0.174506	−	0.651264i
$773$	14.1444	+	14.1444i	0.508738	+	0.508738i	0.914139	−	0.405401i	$-0.132868\pi$
$773$	14.1444	+	14.1444i	0.508738	+	0.508738i	−0.405401	+	0.914139i	$0.632868\pi$
$774$		0			0
$775$		0			0
$776$	−25.3724	+	14.6488i	−0.910816	+	0.525860i
$777$		0			0
$778$	−17.5142	−	65.3638i	−0.627913	−	2.34340i
$779$	−0.987064	+	1.70964i	−0.0353652	+	0.0612544i
$780$		0			0
$781$	0.274574	+	0.475576i	0.00982503	+	0.0170175i
$782$	32.3692	−	32.3692i	1.15752	−	1.15752i
$783$		0			0
$784$			4.69982i			0.167851i
$785$		0			0
$786$		0			0
$787$	1.74131	−	0.466583i	0.0620710	−	0.0166319i	−0.227650	−	0.973743i	$-0.573104\pi$
$787$	1.74131	−	0.466583i	0.0620710	−	0.0166319i	0.289721	+	0.957111i	$0.406438\pi$
$788$	−10.7723	+	2.88644i	−0.383749	+	0.102825i
$789$		0			0
$790$		0			0
$791$		−	10.4777i		−	0.372543i
$792$		0			0
$793$	7.82105	−	7.82105i	0.277733	−	0.277733i
$794$	−31.0989	−	53.8649i	−1.10366	−	1.91159i
$795$		0			0
$796$	−29.1913	+	50.5607i	−1.03466	+	1.79208i
$797$	1.83545	+	6.85000i	0.0650150	+	0.242639i	0.990784	−	0.135450i	$-0.0432479\pi$
$797$	1.83545	+	6.85000i	0.0650150	+	0.242639i	−0.925769	+	0.378089i	$0.876581\pi$
$798$		0			0
$799$	20.8131	−	12.0165i	0.736315	−	0.425112i
$800$		0			0
$801$		0			0
$802$	40.2228	+	40.2228i	1.42032	+	1.42032i
$803$	0.854717	−	3.18985i	0.0301623	−	0.112567i
$804$		0			0
$805$		0			0
$806$	1.49956	+	0.865774i	0.0528199	+	0.0304956i
$807$		0			0
$808$	−41.1709	−	11.0317i	−1.44839	−	0.388094i
$809$	−24.7868			−0.871457			−0.435728	−	0.900078i	$-0.643509\pi$
$809$	−24.7868			−0.871457			−0.435728	+	0.900078i	$0.643509\pi$
$810$		0			0
$811$	−5.24853			−0.184301			−0.0921505	−	0.995745i	$-0.529374\pi$
$811$	−5.24853			−0.184301			−0.0921505	+	0.995745i	$0.529374\pi$
$812$	14.0951	+	3.77678i	0.494642	+	0.132539i
$813$		0			0
$814$	−0.0889652	−	0.0513641i	−0.00311823	−	0.00180031i
$815$		0			0
$816$		0			0
$817$	0.157514	−	0.587849i	0.00551071	−	0.0205662i
$818$	23.2598	+	23.2598i	0.813260	+	0.813260i
$819$		0			0
$820$		0			0
$821$	−23.5611	+	13.6030i	−0.822288	+	0.474748i	−0.851205	−	0.524834i	$-0.824128\pi$
$821$	−23.5611	+	13.6030i	−0.822288	+	0.474748i	0.0289167	+	0.999582i	$0.490794\pi$
$822$		0			0
$823$	8.71001	+	32.5062i	0.303612	+	1.13309i	0.934134	+	0.356923i	$0.116174\pi$
$823$	8.71001	+	32.5062i	0.303612	+	1.13309i	−0.630522	+	0.776171i	$0.717159\pi$
$824$	26.5093	−	45.9155i	0.923496	−	1.59954i
$825$		0			0
$826$	7.26896	+	12.5902i	0.252920	+	0.438070i
$827$	9.12836	−	9.12836i	0.317424	−	0.317424i	−0.530353	−	0.847777i	$-0.677941\pi$
$827$	9.12836	−	9.12836i	0.317424	−	0.317424i	0.847777	+	0.530353i	$0.177941\pi$
$828$		0			0
$829$			44.3456i			1.54019i	0.637931	+	0.770093i	$0.279790\pi$
$829$			44.3456i			1.54019i	−0.637931	+	0.770093i	$0.720210\pi$
$830$		0			0
$831$		0			0
$832$	46.5109	−	12.4626i	1.61247	−	0.432061i
$833$	34.3574	−	9.20604i	1.19041	−	0.318970i
$834$		0			0
$835$		0			0
$836$			0.380101i			0.0131461i
$837$		0			0
$838$	45.5948	−	45.5948i	1.57505	−	1.57505i
$839$	−23.9660	−	41.5104i	−0.827399	−	1.43310i	−0.900072	−	0.435742i	$-0.856486\pi$
$839$	−23.9660	−	41.5104i	−0.827399	−	1.43310i	0.0726721	−	0.997356i	$-0.476847\pi$
$840$		0			0
$841$	−0.764464	+	1.32409i	−0.0263608	+	0.0456583i
$842$	0.516871	+	1.92899i	0.0178125	+	0.0664773i
$843$		0			0
$844$	−13.3756	+	7.72240i	−0.460407	+	0.265816i
$845$		0			0
$846$		0			0
$847$	6.01556	+	6.01556i	0.206697	+	0.206697i
$848$	−0.252337	+	0.941733i	−0.00866527	+	0.0323392i
$849$		0			0
$850$		0			0
$851$	−0.533801	−	0.308190i	−0.0182985	−	0.0105646i
$852$		0			0
$853$	5.60190	+	1.50103i	0.191806	+	0.0513941i	0.353443	−	0.935456i	$-0.385011\pi$
$853$	5.60190	+	1.50103i	0.191806	+	0.0513941i	−0.161637	+	0.986850i	$0.551678\pi$
$854$	5.21071			0.178307
$855$		0			0
$856$	26.6368			0.910427
$857$	−30.7371	−	8.23598i	−1.04996	−	0.281336i	−0.307724	−	0.951476i	$-0.599567\pi$
$857$	−30.7371	−	8.23598i	−1.04996	−	0.281336i	−0.742235	+	0.670140i	$0.766234\pi$
$858$		0			0
$859$	−10.3188	−	5.95757i	−0.352074	−	0.203270i	0.313525	−	0.949580i	$-0.398490\pi$
$859$	−10.3188	−	5.95757i	−0.352074	−	0.203270i	−0.665598	+	0.746310i	$0.731824\pi$
$860$		0			0
$861$		0			0
$862$	−15.3756	+	57.3825i	−0.523695	+	1.95446i
$863$	−13.3552	−	13.3552i	−0.454617	−	0.454617i	0.442267	−	0.896884i	$-0.354174\pi$
$863$	−13.3552	−	13.3552i	−0.454617	−	0.454617i	−0.896884	+	0.442267i	$0.854174\pi$
$864$		0			0
$865$		0			0
$866$	17.9423	−	10.3590i	0.609704	−	0.352013i
$867$		0			0
$868$	0.132857	+	0.495830i	0.00450947	+	0.0168296i
$869$	1.75753	−	3.04413i	0.0596201	−	0.103265i
$870$		0			0
$871$	25.7442	+	44.5902i	0.872308	+	1.51088i
$872$	20.2022	−	20.2022i	0.684132	−	0.684132i
$873$		0			0
$874$			3.62427i			0.122593i
$875$		0			0
$876$		0			0
$877$	6.46168	−	1.73140i	0.218195	−	0.0584653i	−0.148065	−	0.988978i	$-0.547305\pi$
$877$	6.46168	−	1.73140i	0.218195	−	0.0584653i	0.366261	+	0.930512i	$0.380638\pi$
$878$	−32.2960	+	8.65368i	−1.08994	+	0.292048i
$879$		0			0
$880$		0			0
$881$		−	13.4495i		−	0.453126i	−0.973996	−	0.226563i	$-0.927251\pi$
$881$		−	13.4495i		−	0.453126i	0.973996	−	0.226563i	$-0.0727490\pi$
$882$		0			0
$883$	−32.5618	+	32.5618i	−1.09579	+	1.09579i	−0.100896	+	0.994897i	$0.532171\pi$
$883$	−32.5618	+	32.5618i	−1.09579	+	1.09579i	−0.994897	+	0.100896i	$0.967829\pi$
$884$	36.2127	+	62.7222i	1.21796	+	2.10957i
$885$		0			0
$886$	25.4576	−	44.0939i	0.855266	−	1.48136i
$887$	6.81864	+	25.4475i	0.228948	+	0.854444i	0.980784	+	0.195095i	$0.0625015\pi$
$887$	6.81864	+	25.4475i	0.228948	+	0.854444i	−0.751837	+	0.659349i	$0.770832\pi$
$888$		0			0
$889$	6.40444	−	3.69760i	0.214798	−	0.124014i
$890$		0			0
$891$		0			0
$892$	−43.9677	−	43.9677i	−1.47215	−	1.47215i
$893$	−0.492465	+	1.83790i	−0.0164797	+	0.0615031i
$894$		0			0
$895$		0			0
$896$	13.2150	+	7.62966i	0.441481	+	0.254889i
$897$		0			0
$898$	53.0474	+	14.2140i	1.77021	+	0.474327i
$899$	−1.07393			−0.0358175
$900$		0			0
$901$	7.37869			0.245820
$902$	−2.55708	−	0.685169i	−0.0851416	−	0.0228136i
$903$		0			0
$904$	−37.7857	−	21.8156i	−1.25673	−	0.725576i
$905$		0			0
$906$		0			0
$907$	12.1728	−	45.4294i	0.404190	−	1.50846i	−0.401354	−	0.915923i	$-0.631460\pi$
$907$	12.1728	−	45.4294i	0.404190	−	1.50846i	0.805544	−	0.592536i	$-0.201873\pi$
$908$	−27.0785	−	27.0785i	−0.898632	−	0.898632i
$909$		0			0
$910$		0			0
$911$	19.0663	−	11.0079i	0.631694	−	0.364709i	−0.149714	−	0.988729i	$-0.547835\pi$
$911$	19.0663	−	11.0079i	0.631694	−	0.364709i	0.781408	+	0.624021i	$0.214502\pi$
$912$		0			0
$913$	0.354385	+	1.32258i	0.0117284	+	0.0437711i
$914$	−6.62414	+	11.4733i	−0.219107	+	0.379505i
$915$		0			0
$916$	−8.27929	−	14.3402i	−0.273556	−	0.473812i
$917$	−7.39896	+	7.39896i	−0.244335	+	0.244335i
$918$		0			0
$919$			28.3896i			0.936486i	0.883600	+	0.468243i	$0.155113\pi$
$919$			28.3896i			0.936486i	−0.883600	+	0.468243i	$0.844887\pi$
$920$		0			0
$921$		0			0
$922$	−72.2628	+	19.3627i	−2.37985	+	0.637678i
$923$	−8.00199	+	2.14413i	−0.263389	+	0.0705748i
$924$		0			0
$925$		0			0
$926$		−	14.8495i		−	0.487984i
$927$		0			0
$928$	−18.6447	+	18.6447i	−0.612042	+	0.612042i
$929$	18.9202	+	32.7708i	0.620753	+	1.07518i	0.989346	+	0.145585i	$0.0465063\pi$
$929$	18.9202	+	32.7708i	0.620753	+	1.07518i	−0.368593	+	0.929591i	$0.620160\pi$
$930$		0			0
$931$	−1.40805	+	2.43882i	−0.0461471	+	0.0799292i
$932$	−9.82556	−	36.6695i	−0.321847	−	1.20115i
$933$		0			0
$934$	36.4067	−	21.0194i	1.19126	−	0.687776i
$935$		0			0
$936$		0			0
$937$	−36.4371	−	36.4371i	−1.19035	−	1.19035i	−0.976969	−	0.213379i	$-0.931553\pi$
$937$	−36.4371	−	36.4371i	−1.19035	−	1.19035i	−0.213379	−	0.976969i	$-0.568447\pi$
$938$	−6.27801	+	23.4299i	−0.204984	+	0.765012i
$939$		0			0
$940$		0			0
$941$	−27.0690	−	15.6283i	−0.882423	−	0.509467i	−0.0109667	−	0.999940i	$-0.503491\pi$
$941$	−27.0690	−	15.6283i	−0.882423	−	0.509467i	−0.871457	+	0.490473i	$0.836824\pi$
$942$		0			0
$943$	−15.3428	−	4.11108i	−0.499630	−	0.133875i
$944$	5.91308			0.192454
$945$		0			0
$946$	0.816109			0.0265340
$947$	14.5266	+	3.89239i	0.472050	+	0.126486i	0.486999	−	0.873403i	$-0.338092\pi$
$947$	14.5266	+	3.89239i	0.472050	+	0.126486i	−0.0149482	+	0.999888i	$0.504758\pi$
$948$		0			0
$949$	43.1441	+	24.9092i	1.40052	+	0.808588i
$950$		0			0
$951$		0			0
$952$	−3.62825	+	13.5408i	−0.117592	+	0.438860i
$953$	−37.2073	−	37.2073i	−1.20526	−	1.20526i	−0.972544	−	0.232720i	$-0.925237\pi$
$953$	−37.2073	−	37.2073i	−1.20526	−	1.20526i	−0.232720	−	0.972544i	$-0.574763\pi$
$954$		0			0
$955$		0			0
$956$	65.4799	−	37.8048i	2.11777	−	1.22270i
$957$		0			0
$958$	−2.11804	−	7.90463i	−0.0684308	−	0.255387i
$959$	3.80803	−	6.59570i	0.122968	−	0.212986i
$960$		0			0
$961$	15.4811	+	26.8141i	0.499391	+	0.864970i
$962$	1.09582	−	1.09582i	0.0353306	−	0.0353306i
$963$		0			0
$964$			98.2761i			3.16526i
$965$		0			0
$966$		0			0
$967$	−19.0216	+	5.09683i	−0.611694	+	0.163903i	−0.551349	−	0.834275i	$-0.685887\pi$
$967$	−19.0216	+	5.09683i	−0.611694	+	0.163903i	−0.0603451	+	0.998178i	$0.519220\pi$
$968$	34.2190	−	9.16896i	1.09984	−	0.294701i
$969$		0			0
$970$		0			0
$971$		−	6.75294i		−	0.216712i	−0.994112	−	0.108356i	$-0.965441\pi$
$971$		−	6.75294i		−	0.216712i	0.994112	−	0.108356i	$-0.0345586\pi$
$972$		0			0
$973$	−4.35065	+	4.35065i	−0.139475	+	0.139475i
$974$	48.1942	+	83.4747i	1.54424	+	2.67470i
$975$		0			0
$976$	1.05969	−	1.83543i	0.0339198	−	0.0587508i
$977$	−7.67249	−	28.6341i	−0.245465	−	0.916086i	−0.973149	−	0.230175i	$-0.926070\pi$
$977$	−7.67249	−	28.6341i	−0.245465	−	0.916086i	0.727685	−	0.685912i	$-0.240596\pi$
$978$		0			0
$979$	−0.0628695	+	0.0362977i	−0.00200932	+	0.00116008i
$980$		0			0
$981$		0			0
$982$	33.9466	+	33.9466i	1.08328	+	1.08328i
$983$	−4.57606	+	17.0781i	−0.145954	+	0.544706i	0.853758	+	0.520671i	$0.174318\pi$
$983$	−4.57606	+	17.0781i	−0.145954	+	0.544706i	−0.999711	+	0.0240353i	$0.992349\pi$
$984$		0			0
$985$		0			0
$986$	−61.8194	−	35.6914i	−1.96873	−	1.13665i
$987$		0			0
$988$	−5.53869	−	1.48409i	−0.176209	−	0.0472151i
$989$	4.89674			0.155707
$990$		0			0
$991$	−61.9280			−1.96721			−0.983603	−	0.180345i	$-0.942279\pi$
$991$	−61.9280			−1.96721			−0.983603	+	0.180345i	$0.942279\pi$
$992$	−0.895938	−	0.240066i	−0.0284461	−	0.00762210i
$993$		0			0
$994$	−3.37988	−	1.95138i	−0.107203	−	0.0618939i
$995$		0			0
$996$		0			0
$997$	−6.50403	+	24.2734i	−0.205985	+	0.768745i	0.783163	+	0.621817i	$0.213605\pi$
$997$	−6.50403	+	24.2734i	−0.205985	+	0.768745i	−0.989147	+	0.146928i	$0.953061\pi$
$998$	−42.9908	−	42.9908i	−1.36085	−	1.36085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.q.a.557.1		16
3.2	odd	2		225.2.p.b.32.4		16
5.2	odd	4		135.2.m.a.98.4		16
5.3	odd	4	inner	675.2.q.a.368.1		16
5.4	even	2		135.2.m.a.17.4		16
9.2	odd	6	inner	675.2.q.a.332.1		16
9.7	even	3		225.2.p.b.182.4		16
15.2	even	4		45.2.l.a.23.1	yes	16
15.8	even	4		225.2.p.b.68.4		16
15.14	odd	2		45.2.l.a.32.1	yes	16
45.2	even	12		135.2.m.a.8.4		16
45.4	even	6		405.2.f.a.242.1		16
45.7	odd	12		45.2.l.a.38.1	yes	16
45.14	odd	6		405.2.f.a.242.8		16
45.22	odd	12		405.2.f.a.323.8		16
45.29	odd	6		135.2.m.a.62.4		16
45.32	even	12		405.2.f.a.323.1		16
45.34	even	6		45.2.l.a.2.1	✓	16
45.38	even	12	inner	675.2.q.a.143.1		16
45.43	odd	12		225.2.p.b.218.4		16
60.47	odd	4		720.2.cu.c.113.4		16
60.59	even	2		720.2.cu.c.257.2		16
180.7	even	12		720.2.cu.c.353.2		16
180.79	odd	6		720.2.cu.c.497.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.1	✓	16	45.34	even	6
45.2.l.a.23.1	yes	16	15.2	even	4
45.2.l.a.32.1	yes	16	15.14	odd	2
45.2.l.a.38.1	yes	16	45.7	odd	12
135.2.m.a.8.4		16	45.2	even	12
135.2.m.a.17.4		16	5.4	even	2
135.2.m.a.62.4		16	45.29	odd	6
135.2.m.a.98.4		16	5.2	odd	4
225.2.p.b.32.4		16	3.2	odd	2
225.2.p.b.68.4		16	15.8	even	4
225.2.p.b.182.4		16	9.7	even	3
225.2.p.b.218.4		16	45.43	odd	12
405.2.f.a.242.1		16	45.4	even	6
405.2.f.a.242.8		16	45.14	odd	6
405.2.f.a.323.1		16	45.32	even	12
405.2.f.a.323.8		16	45.22	odd	12
675.2.q.a.143.1		16	45.38	even	12	inner
675.2.q.a.332.1		16	9.2	odd	6	inner
675.2.q.a.368.1		16	5.3	odd	4	inner
675.2.q.a.557.1		16	1.1	even	1	trivial
720.2.cu.c.113.4		16	60.47	odd	4
720.2.cu.c.257.2		16	60.59	even	2
720.2.cu.c.353.2		16	180.7	even	12
720.2.cu.c.497.4		16	180.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.24352 - 0.601150i) q^{2} +(2.93996 + 1.69739i) q^{4} +(0.201351 - 0.751454i) q^{7} +(-2.29074 - 2.29074i) q^{8} +O(q^{10})\)	\(q+(-2.24352 - 0.601150i) q^{2} +(2.93996 + 1.69739i) q^{4} +(0.201351 - 0.751454i) q^{7} +(-2.29074 - 2.29074i) q^{8} +(0.220188 - 0.127126i) q^{11} +(0.992714 + 3.70486i) q^{13} +(-0.903473 + 1.56486i) q^{14} +(0.367473 + 0.636483i) q^{16} +(3.93311 - 3.93311i) q^{17} +0.440377i q^{19} +(-0.570419 + 0.152843i) q^{22} +(-3.42258 + 0.917076i) q^{23} -8.90871i q^{26} +(1.86747 - 1.86747i) q^{28} +(2.76265 + 4.78505i) q^{29} +(-0.0971829 + 0.168326i) q^{31} +(1.23512 + 4.60955i) q^{32} +(-11.1884 + 6.45964i) q^{34} +(0.123005 + 0.123005i) q^{37} +(0.264732 - 0.987995i) q^{38} +(3.88223 + 2.24141i) q^{41} +(-1.33488 - 0.357680i) q^{43} +0.863127 q^{44} +8.22993 q^{46} +(4.17348 + 1.11828i) q^{47} +(5.53804 + 3.19739i) q^{49} +(-3.37004 + 12.5772i) q^{52} +(0.938022 + 0.938022i) q^{53} +(-2.18263 + 1.26014i) q^{56} +(-3.32153 - 12.3961i) q^{58} +(4.02279 - 6.96768i) q^{59} +(-1.44186 - 2.49737i) q^{61} +(0.319221 - 0.319221i) q^{62} -12.5540i q^{64} +(12.9666 - 3.47438i) q^{67} +(18.2392 - 4.88718i) q^{68} +2.15986i q^{71} +(9.18432 - 9.18432i) q^{73} +(-0.202021 - 0.349910i) q^{74} +(-0.747490 + 1.29469i) q^{76} +(-0.0511939 - 0.191058i) q^{77} +(11.9729 - 6.91256i) q^{79} +(-7.36245 - 7.36245i) q^{82} +(-1.39384 + 5.20187i) q^{83} +(2.77981 + 1.60493i) q^{86} +(-0.795606 - 0.213182i) q^{88} -0.285526 q^{89} +2.98392 q^{91} +(-11.6189 - 3.11327i) q^{92} +(-8.69105 - 5.01778i) q^{94} +(2.34065 - 8.73543i) q^{97} +(-10.5026 - 10.5026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) \) 16 * q - 6 * q^2 + 2 * q^7	\( 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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