LMFDB - Embedded newform 1890.2.bq.a.289.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(289,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("1890.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bq (of order $6$, degree $2$, 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.33
Character	$\chi$	$=$	1890.289
Dual form			1890.2.bq.a.739.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.409739 - 2.19821i) q^{5} +(-1.55043 - 2.14387i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.409739 - 2.19821i) q^{5} +(-1.55043 - 2.14387i) q^{7} -1.00000i q^{8} +(-0.744259 - 2.10857i) q^{10} -3.47091 q^{11} +(1.09687 - 0.633281i) q^{13} +(-2.41464 - 1.08143i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.66021 + 2.69057i) q^{17} +(-2.23829 + 3.87684i) q^{19} +(-1.69883 - 1.45395i) q^{20} +(-3.00590 + 1.73546i) q^{22} -4.79776i q^{23} +(-4.66423 - 1.80138i) q^{25} +(0.633281 - 1.09687i) q^{26} +(-2.63186 + 0.270774i) q^{28} +(-1.04810 + 1.81537i) q^{29} +(-0.401878 + 0.696072i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.69057 + 4.66021i) q^{34} +(-5.34794 + 2.52973i) q^{35} +(5.27556 + 3.04584i) q^{37} +4.47658i q^{38} +(-2.19821 - 0.409739i) q^{40} +(-2.28878 - 3.96429i) q^{41} +(0.972049 + 0.561213i) q^{43} +(-1.73546 + 3.00590i) q^{44} +(-2.39888 - 4.15498i) q^{46} +(8.44192 - 4.87394i) q^{47} +(-2.19235 + 6.64783i) q^{49} +(-4.94003 + 0.772070i) q^{50} -1.26656i q^{52} +(-6.88082 + 3.97264i) q^{53} +(-1.42217 + 7.62978i) q^{55} +(-2.14387 + 1.55043i) q^{56} +2.09621i q^{58} +(6.06736 - 10.5090i) q^{59} +(5.34164 + 9.25199i) q^{61} +0.803755i q^{62} -1.00000 q^{64} +(-0.942649 - 2.67064i) q^{65} +(-1.42681 - 0.823771i) q^{67} +5.38114i q^{68} +(-3.36659 + 4.86478i) q^{70} -10.0748 q^{71} +(-3.28654 + 1.89748i) q^{73} +6.09169 q^{74} +(2.23829 + 3.87684i) q^{76} +(5.38139 + 7.44118i) q^{77} +(0.797244 + 1.38087i) q^{79} +(-2.10857 + 0.744259i) q^{80} +(-3.96429 - 2.28878i) q^{82} +(-9.12037 - 5.26565i) q^{83} +(4.00496 + 11.3465i) q^{85} +1.12243 q^{86} +3.47091i q^{88} +(4.84020 - 8.38348i) q^{89} +(-3.05829 - 1.36970i) q^{91} +(-4.15498 - 2.39888i) q^{92} +(4.87394 - 8.44192i) q^{94} +(7.60497 + 6.50872i) q^{95} +(7.48401 + 4.32089i) q^{97} +(1.42528 + 6.85336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4}+O(q^{10}) $ 96 * q + 48 * q^4	$ 96 q + 48 q^{4} + 8 q^{11} + 2 q^{14} - 48 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} + 12 q^{49} + 12 q^{50} + 12 q^{55} + 4 q^{56} + 24 q^{59} - 6 q^{61} - 96 q^{64} - 18 q^{65} + 6 q^{70} + 32 q^{71} + 8 q^{86} + 66 q^{89} - 12 q^{94} - 30 q^{95}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^11 + 2 * q^14 - 48 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 + 12 * q^49 + 12 * q^50 + 12 * q^55 + 4 * q^56 + 24 * q^59 - 6 * q^61 - 96 * q^64 - 18 * q^65 + 6 * q^70 + 32 * q^71 + 8 * q^86 + 66 * q^89 - 12 * q^94 - 30 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.409739	−	2.19821i	0.183241	−	0.983068i
$5$	0.409739	−	2.19821i	0.183241	−	0.983068i
$6$		0			0
$7$	−1.55043	−	2.14387i	−0.586006	−	0.810307i
$7$	−1.55043	−	2.14387i	−0.586006	−	0.810307i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.744259	−	2.10857i	−0.235355	−	0.666789i
$11$	−3.47091			−1.04652			−0.523260	−	0.852173i	$-0.675284\pi$
$11$	−3.47091			−1.04652			−0.523260	+	0.852173i	$0.675284\pi$
$12$		0			0
$13$	1.09687	−	0.633281i	0.304218	−	0.175640i	−0.340118	−	0.940383i	$-0.610467\pi$
$13$	1.09687	−	0.633281i	0.304218	−	0.175640i	0.644336	+	0.764742i	$0.277134\pi$
$14$	−2.41464	−	1.08143i	−0.645341	−	0.289025i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.66021	+	2.69057i	−1.13027	+	0.652560i	−0.944002	−	0.329940i	$-0.892971\pi$
$17$	−4.66021	+	2.69057i	−1.13027	+	0.652560i	−0.186264	+	0.982500i	$0.559638\pi$
$18$		0			0
$19$	−2.23829	+	3.87684i	−0.513499	+	0.889407i	0.486378	+	0.873749i	$0.338318\pi$
$19$	−2.23829	+	3.87684i	−0.513499	+	0.889407i	−0.999877	+	0.0156586i	$0.995016\pi$
$20$	−1.69883	−	1.45395i	−0.379871	−	0.325113i
$21$		0			0
$22$	−3.00590	+	1.73546i	−0.640859	+	0.370000i
$23$		−	4.79776i		−	1.00040i	−0.865909	−	0.500201i	$-0.833259\pi$
$23$		−	4.79776i		−	1.00040i	0.865909	−	0.500201i	$-0.166741\pi$
$24$		0			0
$25$	−4.66423	−	1.80138i	−0.932846	−	0.360277i
$26$	0.633281	−	1.09687i	0.124197	−	0.215115i
$27$		0			0
$28$	−2.63186	+	0.270774i	−0.497375	+	0.0511715i
$29$	−1.04810	+	1.81537i	−0.194628	+	0.337105i	−0.946778	−	0.321886i	$-0.895683\pi$
$29$	−1.04810	+	1.81537i	−0.194628	+	0.337105i	0.752151	+	0.658991i	$0.229017\pi$
$30$		0			0
$31$	−0.401878	+	0.696072i	−0.0721793	+	0.125018i	−0.899856	−	0.436187i	$-0.856329\pi$
$31$	−0.401878	+	0.696072i	−0.0721793	+	0.125018i	0.827677	+	0.561205i	$0.189662\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−2.69057	+	4.66021i	−0.461429	+	0.799219i
$35$	−5.34794	+	2.52973i	−0.903967	+	0.427603i
$36$		0			0
$37$	5.27556	+	3.04584i	0.867296	+	0.500734i	0.866449	−	0.499266i	$-0.166397\pi$
$37$	5.27556	+	3.04584i	0.867296	+	0.500734i	0.000847502		1.00000i	$0.499730\pi$
$38$			4.47658i			0.726198i
$39$		0			0
$40$	−2.19821	−	0.409739i	−0.347567	−	0.0647855i
$41$	−2.28878	−	3.96429i	−0.357448	−	0.619118i	0.630086	−	0.776526i	$-0.283020\pi$
$41$	−2.28878	−	3.96429i	−0.357448	−	0.619118i	−0.987534	+	0.157407i	$0.949686\pi$
$42$		0			0
$43$	0.972049	+	0.561213i	0.148236	+	0.0855841i	0.572283	−	0.820056i	$-0.306058\pi$
$43$	0.972049	+	0.561213i	0.148236	+	0.0855841i	−0.424047	+	0.905640i	$0.639391\pi$
$44$	−1.73546	+	3.00590i	−0.261630	+	0.453156i
$45$		0			0
$46$	−2.39888	−	4.15498i	−0.353696	−	0.612619i
$47$	8.44192	−	4.87394i	1.23138	−	0.710938i	0.264063	−	0.964506i	$-0.414937\pi$
$47$	8.44192	−	4.87394i	1.23138	−	0.710938i	0.967318	+	0.253568i	$0.0816041\pi$
$48$		0			0
$49$	−2.19235	+	6.64783i	−0.313193	+	0.949689i
$50$	−4.94003	+	0.772070i	−0.698626	+	0.109187i
$51$		0			0
$52$		−	1.26656i		−	0.175640i
$53$	−6.88082	+	3.97264i	−0.945153	+	0.545684i	−0.891572	−	0.452879i	$-0.850397\pi$
$53$	−6.88082	+	3.97264i	−0.945153	+	0.545684i	−0.0535811	+	0.998564i	$0.517064\pi$
$54$		0			0
$55$	−1.42217	+	7.62978i	−0.191765	+	1.02880i
$56$	−2.14387	+	1.55043i	−0.286487	+	0.207184i
$57$		0			0
$58$			2.09621i			0.275245i
$59$	6.06736	−	10.5090i	0.789904	−	1.36815i	−0.136122	−	0.990692i	$-0.543464\pi$
$59$	6.06736	−	10.5090i	0.789904	−	1.36815i	0.926025	−	0.377461i	$-0.123203\pi$
$60$		0			0
$61$	5.34164	+	9.25199i	0.683927	+	1.18460i	0.973773	+	0.227522i	$0.0730625\pi$
$61$	5.34164	+	9.25199i	0.683927	+	1.18460i	−0.289846	+	0.957073i	$0.593604\pi$
$62$			0.803755i			0.102077i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.942649	−	2.67064i	−0.116921	−	0.331252i
$66$		0			0
$67$	−1.42681	−	0.823771i	−0.174313	−	0.100640i	0.410305	−	0.911948i	$-0.365422\pi$
$67$	−1.42681	−	0.823771i	−0.174313	−	0.100640i	−0.584618	+	0.811309i	$0.698756\pi$
$68$			5.38114i			0.652560i
$69$		0			0
$70$	−3.36659	+	4.86478i	−0.402384	+	0.581453i
$71$	−10.0748			−1.19566			−0.597829	−	0.801624i	$-0.703970\pi$
$71$	−10.0748			−1.19566			−0.597829	+	0.801624i	$0.703970\pi$
$72$		0			0
$73$	−3.28654	+	1.89748i	−0.384660	+	0.222084i	−0.679844	−	0.733357i	$-0.737952\pi$
$73$	−3.28654	+	1.89748i	−0.384660	+	0.222084i	0.295184	+	0.955440i	$0.404619\pi$
$74$	6.09169			0.708145
$75$		0			0
$76$	2.23829	+	3.87684i	0.256750	+	0.444704i
$77$	5.38139	+	7.44118i	0.613267	+	0.848001i
$78$		0			0
$79$	0.797244	+	1.38087i	0.0896970	+	0.155360i	0.907383	−	0.420305i	$-0.138077\pi$
$79$	0.797244	+	1.38087i	0.0896970	+	0.155360i	−0.817686	+	0.575664i	$0.804743\pi$
$80$	−2.10857	+	0.744259i	−0.235746	+	0.0832107i
$81$		0			0
$82$	−3.96429	−	2.28878i	−0.437783	−	0.252754i
$83$	−9.12037	−	5.26565i	−1.00109	−	0.577980i	−0.0925198	−	0.995711i	$-0.529492\pi$
$83$	−9.12037	−	5.26565i	−1.00109	−	0.577980i	−0.908571	+	0.417731i	$0.862825\pi$
$84$		0			0
$85$	4.00496	+	11.3465i	0.434399	+	1.23070i
$86$	1.12243			0.121034
$87$		0			0
$88$			3.47091i			0.370000i
$89$	4.84020	−	8.38348i	0.513061	−	0.888647i	−0.486825	−	0.873500i	$-0.661845\pi$
$89$	4.84020	−	8.38348i	0.513061	−	0.888647i	0.999885	−	0.0151474i	$-0.00482174\pi$
$90$		0			0
$91$	−3.05829	−	1.36970i	−0.320596	−	0.143584i
$92$	−4.15498	−	2.39888i	−0.433187	−	0.250101i
$93$		0			0
$94$	4.87394	−	8.44192i	0.502709	−	0.870717i
$95$	7.60497	+	6.50872i	0.780254	+	0.667781i
$96$		0			0
$97$	7.48401	+	4.32089i	0.759886	+	0.438720i	0.829255	−	0.558871i	$-0.188765\pi$
$97$	7.48401	+	4.32089i	0.759886	+	0.438720i	−0.0693689	+	0.997591i	$0.522099\pi$
$98$	1.42528	+	6.85336i	0.143975	+	0.692294i
$99$		0			0
$100$	−3.89216	+	3.13865i	−0.389216	+	0.313865i
$101$	−16.7232			−1.66402			−0.832011	−	0.554759i	$-0.812811\pi$
$101$	−16.7232			−1.66402			−0.832011	+	0.554759i	$0.812811\pi$
$102$		0			0
$103$		−	18.9924i		−	1.87138i	−0.352827	−	0.935688i	$-0.614780\pi$
$103$		−	18.9924i		−	1.87138i	0.352827	−	0.935688i	$-0.385220\pi$
$104$	−0.633281	−	1.09687i	−0.0620983	−	0.107557i
$105$		0			0
$106$	−3.97264	+	6.88082i	−0.385857	+	0.668324i
$107$	−6.00586	−	3.46749i	−0.580608	−	0.335214i	0.180767	−	0.983526i	$-0.442142\pi$
$107$	−6.00586	−	3.46749i	−0.580608	−	0.335214i	−0.761375	+	0.648312i	$0.775475\pi$
$108$		0			0
$109$	−7.96687	−	13.7990i	−0.763088	−	1.32171i	−0.941252	−	0.337706i	$-0.890349\pi$
$109$	−7.96687	−	13.7990i	−0.763088	−	1.32171i	0.178164	−	0.984001i	$-0.442984\pi$
$110$	2.58326	+	7.31867i	0.246304	+	0.697808i
$111$		0			0
$112$	−1.08143	+	2.41464i	−0.102186	+	0.228162i
$113$	6.92378	−	3.99745i	0.651335	−	0.376048i	−0.137633	−	0.990483i	$-0.543949\pi$
$113$	6.92378	−	3.99745i	0.651335	−	0.376048i	0.788967	+	0.614435i	$0.210616\pi$
$114$		0			0
$115$	−10.5465	−	1.96583i	−0.983464	−	0.183315i
$116$	1.04810	+	1.81537i	0.0973139	+	0.168553i
$117$		0			0
$118$		−	12.1347i		−	1.11709i
$119$	12.9935	+	5.81934i	1.19112	+	0.533458i
$120$		0			0
$121$	1.04722			0.0952021
$122$	9.25199	+	5.34164i	0.837635	+	0.483609i
$123$		0			0
$124$	0.401878	+	0.696072i	0.0360897	+	0.0625091i
$125$	−5.87093	+	9.51484i	−0.525112	+	0.851033i
$126$		0			0
$127$		−	10.7133i		−	0.950654i	−0.879809	−	0.475327i	$-0.842330\pi$
$127$		−	10.7133i		−	0.950654i	0.879809	−	0.475327i	$-0.157670\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.15168	−	1.84151i	−0.188715	−	0.161511i
$131$	−0.981159			−0.0857243			−0.0428621	−	0.999081i	$-0.513648\pi$
$131$	−0.981159			−0.0857243			−0.0428621	+	0.999081i	$0.513648\pi$
$132$		0			0
$133$	11.7817	−	1.21214i	1.02161	−	0.105106i
$134$	−1.64754			−0.142326
$135$		0			0
$136$	2.69057	+	4.66021i	0.230715	+	0.399609i
$137$		−	13.6426i		−	1.16557i	−0.812627	−	0.582784i	$-0.801963\pi$
$137$		−	13.6426i		−	1.16557i	0.812627	−	0.582784i	$-0.198037\pi$
$138$		0			0
$139$	−9.40894	−	16.2968i	−0.798056	−	1.38227i	−0.920881	−	0.389845i	$-0.872529\pi$
$139$	−9.40894	−	16.2968i	−0.798056	−	1.38227i	0.122825	−	0.992428i	$-0.460805\pi$
$140$	−0.483158	+	5.89632i	−0.0408343	+	0.498330i
$141$		0			0
$142$	−8.72503	+	5.03740i	−0.732188	+	0.422729i
$143$	−3.80715	+	2.19806i	−0.318370	+	0.183811i
$144$		0			0
$145$	3.56111	+	3.04778i	0.295734	+	0.253104i
$146$	−1.89748	+	3.28654i	−0.157037	+	0.271996i
$147$		0			0
$148$	5.27556	−	3.04584i	0.433648	−	0.250367i
$149$	−16.3368			−1.33837			−0.669183	−	0.743098i	$-0.733356\pi$
$149$	−16.3368			−1.33837			−0.669183	+	0.743098i	$0.733356\pi$
$150$		0			0
$151$	7.62140			0.620221			0.310111	−	0.950701i	$-0.399634\pi$
$151$	7.62140			0.620221			0.310111	+	0.950701i	$0.399634\pi$
$152$	3.87684	+	2.23829i	0.314453	+	0.181549i
$153$		0			0
$154$	8.38101	+	3.75356i	0.675361	+	0.302470i
$155$	1.36545	+	1.16862i	0.109675	+	0.0938657i
$156$		0			0
$157$	19.8612	+	11.4669i	1.58510	+	0.915156i	0.994098	+	0.108483i	$0.0345993\pi$
$157$	19.8612	+	11.4669i	1.58510	+	0.915156i	0.590998	+	0.806673i	$0.298734\pi$
$158$	1.38087	+	0.797244i	0.109856	+	0.0634253i
$159$		0			0
$160$	−1.45395	+	1.69883i	−0.114945	+	0.134305i
$161$	−10.2858	+	7.43858i	−0.810633	+	0.586242i
$162$		0			0
$163$	−1.35549	−	0.782594i	−0.106170	−	0.0612975i	0.445975	−	0.895046i	$-0.352857\pi$
$163$	−1.35549	−	0.782594i	−0.106170	−	0.0612975i	−0.552145	+	0.833748i	$0.686190\pi$
$164$	−4.57757			−0.357448
$165$		0			0
$166$	−10.5313			−0.817387
$167$	−5.24110	+	3.02595i	−0.405568	+	0.234155i	−0.688884	−	0.724872i	$-0.741899\pi$
$167$	−5.24110	+	3.02595i	−0.405568	+	0.234155i	0.283315	+	0.959027i	$0.408566\pi$
$168$		0			0
$169$	−5.69791	+	9.86907i	−0.438301	+	0.759159i
$170$	9.14167	+	7.82390i	0.701134	+	0.600066i
$171$		0			0
$172$	0.972049	−	0.561213i	0.0741180	−	0.0427921i
$173$	13.2888	−	7.67227i	1.01033	−	0.583312i	0.0990384	−	0.995084i	$-0.468423\pi$
$173$	13.2888	−	7.67227i	1.01033	−	0.583312i	0.911287	+	0.411772i	$0.135090\pi$
$174$		0			0
$175$	3.36961	+	12.7924i	0.254719	+	0.967015i
$176$	1.73546	+	3.00590i	0.130815	+	0.226578i
$177$		0			0
$178$		−	9.68041i		−	0.725577i
$179$	−4.10439	−	7.10902i	−0.306777	−	0.531353i	0.670879	−	0.741567i	$-0.265917\pi$
$179$	−4.10439	−	7.10902i	−0.306777	−	0.531353i	−0.977655	+	0.210214i	$0.932584\pi$
$180$		0			0
$181$	8.42895			0.626519			0.313260	−	0.949668i	$-0.398579\pi$
$181$	8.42895			0.626519			0.313260	+	0.949668i	$0.398579\pi$
$182$	−3.33341	+	0.342952i	−0.247089	+	0.0254213i
$183$		0			0
$184$	−4.79776			−0.353696
$185$	8.85700	−	10.3488i	0.651180	−	0.760856i
$186$		0			0
$187$	16.1752	−	9.33874i	1.18285	−	0.682916i
$188$		−	9.74789i		−	0.710938i
$189$		0			0
$190$	9.84046	+	1.83423i	0.713902	+	0.133069i
$191$	1.26841	+	2.19694i	0.0917786	+	0.158965i	0.908260	−	0.418407i	$-0.137411\pi$
$191$	1.26841	+	2.19694i	0.0917786	+	0.158965i	−0.816481	+	0.577372i	$0.804078\pi$
$192$		0			0
$193$	−21.8742	−	12.6290i	−1.57454	−	0.909059i	−0.995602	−	0.0936844i	$-0.970136\pi$
$193$	−21.8742	−	12.6290i	−1.57454	−	0.909059i	−0.578934	−	0.815374i	$-0.696531\pi$
$194$	8.64179			0.620444
$195$		0			0
$196$	4.66101	+	5.22255i	0.332929	+	0.373039i
$197$			5.46911i			0.389658i	0.980837	+	0.194829i	$0.0624152\pi$
$197$			5.46911i			0.389658i	−0.980837	+	0.194829i	$0.937585\pi$
$198$		0			0
$199$	0.308443	+	0.534239i	0.0218649	+	0.0378712i	0.876751	−	0.480945i	$-0.159706\pi$
$199$	0.308443	+	0.534239i	0.0218649	+	0.0378712i	−0.854886	+	0.518816i	$0.826373\pi$
$200$	−1.80138	+	4.66423i	−0.127377	+	0.329811i
$201$		0			0
$202$	−14.4827	+	8.36161i	−1.01900	+	0.588321i
$203$	5.51692	−	0.567598i	0.387212	−	0.0398376i
$204$		0			0
$205$	−9.65213	+	3.40690i	−0.674134	+	0.237948i
$206$	−9.49620	−	16.4479i	−0.661632	−	1.14598i
$207$		0			0
$208$	−1.09687	−	0.633281i	−0.0760545	−	0.0439101i
$209$	7.76891	−	13.4562i	0.537387	−	0.930781i
$210$		0			0
$211$	−1.33497	−	2.31223i	−0.0919029	−	0.159180i	0.816409	−	0.577474i	$-0.195962\pi$
$211$	−1.33497	−	2.31223i	−0.0919029	−	0.159180i	−0.908312	+	0.418294i	$0.862628\pi$
$212$			7.94528i			0.545684i
$213$		0			0
$214$	−6.93497			−0.474065
$215$	1.63195	−	1.90681i	0.111298	−	0.130044i
$216$		0			0
$217$	2.11537	−	0.217636i	0.143601	−	0.0147741i
$218$	−13.7990	−	7.96687i	−0.934588	−	0.539584i
$219$		0			0
$220$	5.89650	+	5.04652i	0.397542	+	0.340237i
$221$	−3.40777	+	5.90244i	−0.229232	+	0.397041i
$222$		0			0
$223$	0.443085	+	0.255815i	0.0296712	+	0.0171307i	0.514762	−	0.857333i	$-0.327880\pi$
$223$	0.443085	+	0.255815i	0.0296712	+	0.0171307i	−0.485091	+	0.874464i	$0.661214\pi$
$224$	0.270774	+	2.63186i	0.0180919	+	0.175848i
$225$		0			0
$226$	3.99745	−	6.92378i	0.265906	−	0.460563i
$227$		−	13.9482i		−	0.925773i	−0.886417	−	0.462887i	$-0.846814\pi$
$227$		−	13.9482i		−	0.925773i	0.886417	−	0.462887i	$-0.153186\pi$
$228$		0			0
$229$	−11.8977			−0.786223			−0.393111	−	0.919491i	$-0.628601\pi$
$229$	−11.8977			−0.786223			−0.393111	+	0.919491i	$0.628601\pi$
$230$	−10.1164	+	3.57078i	−0.667057	+	0.235450i
$231$		0			0
$232$	1.81537	+	1.04810i	0.119185	+	0.0688113i
$233$	−22.7879	−	13.1566i	−1.49288	−	0.861916i	−0.492915	−	0.870077i	$-0.664069\pi$
$233$	−22.7879	−	13.1566i	−1.49288	−	0.861916i	−0.999967	+	0.00816149i	$0.997402\pi$
$234$		0			0
$235$	−7.25495	−	20.5541i	−0.473261	−	1.34080i
$236$	−6.06736	−	10.5090i	−0.394952	−	0.684077i
$237$		0			0
$238$	14.1624	−	1.45707i	0.918013	−	0.0944481i
$239$	5.80430	+	10.0533i	0.375449	+	0.650297i	0.990394	−	0.138273i	$-0.0441552\pi$
$239$	5.80430	+	10.0533i	0.375449	+	0.650297i	−0.614945	+	0.788570i	$0.710822\pi$
$240$		0			0
$241$	17.8233			1.14810			0.574049	−	0.818821i	$-0.305372\pi$
$241$	17.8233			1.14810			0.574049	+	0.818821i	$0.305372\pi$
$242$	0.906921	−	0.523611i	0.0582991	−	0.0336590i
$243$		0			0
$244$	10.6833			0.683927
$245$	13.7150	+	7.54312i	0.876219	+	0.481912i
$246$		0			0
$247$			5.66987i			0.360765i
$248$	0.696072	+	0.401878i	0.0442006	+	0.0255193i
$249$		0			0
$250$	−0.326955	+	11.1756i	−0.0206784	+	0.706804i
$251$	27.6972			1.74823			0.874117	−	0.485716i	$-0.161441\pi$
$251$	27.6972			1.74823			0.874117	+	0.485716i	$0.161441\pi$
$252$		0			0
$253$			16.6526i			1.04694i
$254$	−5.35666	−	9.27801i	−0.336107	−	0.582154i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$			12.1096i			0.755378i	0.925933	+	0.377689i	$0.123281\pi$
$257$			12.1096i			0.755378i	−0.925933	+	0.377689i	$0.876719\pi$
$258$		0			0
$259$	−1.64947	−	16.0325i	−0.102493	−	0.996209i
$260$	−2.78416	−	0.518960i	−0.172667	−	0.0321845i
$261$		0			0
$262$	−0.849709	+	0.490580i	−0.0524952	+	0.0303081i
$263$		−	18.9579i		−	1.16900i	−0.811395	−	0.584499i	$-0.801291\pi$
$263$		−	18.9579i		−	1.16900i	0.811395	−	0.584499i	$-0.198709\pi$
$264$		0			0
$265$	5.91335	+	16.7532i	0.363254	+	1.02914i
$266$	9.59721	−	6.94062i	0.588443	−	0.425556i
$267$		0			0
$268$	−1.42681	+	0.823771i	−0.0871565	+	0.0503199i
$269$	14.0626	+	24.3571i	0.857412	+	1.48508i	0.874389	+	0.485225i	$0.161262\pi$
$269$	14.0626	+	24.3571i	0.857412	+	1.48508i	−0.0169778	+	0.999856i	$0.505404\pi$
$270$		0			0
$271$	−5.11495	+	8.85936i	−0.310711	+	0.538168i	−0.978517	−	0.206168i	$-0.933901\pi$
$271$	−5.11495	+	8.85936i	−0.310711	+	0.538168i	0.667805	+	0.744336i	$0.267234\pi$
$272$	4.66021	+	2.69057i	0.282567	+	0.163140i
$273$		0			0
$274$	−6.82131	−	11.8149i	−0.412091	−	0.713762i
$275$	16.1891	+	6.25244i	0.976241	+	0.377036i
$276$		0			0
$277$			9.49033i			0.570218i	0.958495	+	0.285109i	$0.0920299\pi$
$277$			9.49033i			0.570218i	−0.958495	+	0.285109i	$0.907970\pi$
$278$	−16.2968	−	9.40894i	−0.977415	−	0.564311i
$279$		0			0
$280$	2.52973	+	5.34794i	0.151180	+	0.319601i
$281$	2.73218	−	4.73228i	0.162988	−	0.282304i	−0.772951	−	0.634466i	$-0.781220\pi$
$281$	2.73218	−	4.73228i	0.162988	−	0.282304i	0.935939	+	0.352162i	$0.114553\pi$
$282$		0			0
$283$	22.2341	+	12.8368i	1.32168	+	0.763071i	0.983996	−	0.178190i	$-0.0570241\pi$
$283$	22.2341	+	12.8368i	1.32168	+	0.763071i	0.337681	+	0.941261i	$0.390357\pi$
$284$	−5.03740	+	8.72503i	−0.298914	+	0.517735i
$285$		0			0
$286$	−2.19806	+	3.80715i	−0.129974	+	0.225122i
$287$	−4.95033	+	11.0532i	−0.292209	+	0.652449i
$288$		0			0
$289$	5.97835	−	10.3548i	0.351668	−	0.609107i
$290$	4.60790	+	0.858898i	0.270585	+	0.0504362i
$291$		0			0
$292$			3.79496i			0.222084i
$293$	18.1103	−	10.4560i	1.05801	−	0.610844i	0.133131	−	0.991098i	$-0.457497\pi$
$293$	18.1103	−	10.4560i	1.05801	−	0.610844i	0.924882	+	0.380254i	$0.124164\pi$
$294$		0			0
$295$	−20.6149	−	17.6433i	−1.20024	−	1.02723i
$296$	3.04584	−	5.27556i	0.177036	−	0.306636i
$297$		0			0
$298$	−14.1481	+	8.16842i	−0.819578	+	0.473184i
$299$	−3.03833	−	5.26254i	−0.175711	−	0.304341i
$300$		0			0
$301$	−0.303924	−	2.95406i	−0.0175179	−	0.170269i
$302$	6.60033	−	3.81070i	0.379806	−	0.219281i
$303$		0			0
$304$	4.47658			0.256750
$305$	22.5265	−	7.95112i	1.28986	−	0.455280i
$306$		0			0
$307$			1.32689i			0.0757295i	0.999283	+	0.0378647i	$0.0120556\pi$
$307$			1.32689i			0.0757295i	−0.999283	+	0.0378647i	$0.987944\pi$
$308$	9.13495	−	0.939833i	0.520512	−	0.0535519i
$309$		0			0
$310$	1.76682	+	0.329330i	0.100349	+	0.0187047i
$311$	−11.1100	+	19.2432i	−0.629992	+	1.09118i	0.357560	+	0.933890i	$0.383609\pi$
$311$	−11.1100	+	19.2432i	−0.629992	+	1.09118i	−0.987553	+	0.157289i	$0.949725\pi$
$312$		0			0
$313$	13.9308	−	8.04294i	0.787415	−	0.454614i	−0.0516370	−	0.998666i	$-0.516444\pi$
$313$	13.9308	−	8.04294i	0.787415	−	0.454614i	0.839052	+	0.544052i	$0.183111\pi$
$314$	22.9337			1.29423
$315$		0			0
$316$	1.59449			0.0896970
$317$	9.15516	−	5.28574i	0.514205	−	0.296876i	−0.220355	−	0.975420i	$-0.570722\pi$
$317$	9.15516	−	5.28574i	0.514205	−	0.296876i	0.734561	+	0.678543i	$0.237388\pi$
$318$		0			0
$319$	3.63787	−	6.30098i	0.203682	−	0.352787i
$320$	−0.409739	+	2.19821i	−0.0229051	+	0.122884i
$321$		0			0
$322$	−5.18845	+	11.5849i	−0.289141	+	0.645600i
$323$		−	24.0891i		−	1.34036i
$324$		0			0
$325$	−6.25685	+	0.977874i	−0.347068	+	0.0542427i
$326$	−1.56519			−0.0866877
$327$		0			0
$328$	−3.96429	+	2.28878i	−0.218891	+	0.126377i
$329$	−23.5377	−	10.5417i	−1.29767	−	0.581182i
$330$		0			0
$331$	0.382136	+	0.661879i	0.0210041	+	0.0363802i	0.876336	−	0.481700i	$-0.159980\pi$
$331$	0.382136	+	0.661879i	0.0210041	+	0.0363802i	−0.855332	+	0.518080i	$0.826647\pi$
$332$	−9.12037	+	5.26565i	−0.500545	+	0.288990i
$333$		0			0
$334$	−3.02595	+	5.24110i	−0.165573	+	0.286780i
$335$	−2.39544	+	2.79890i	−0.130877	+	0.152920i
$336$		0			0
$337$	−19.0299	+	10.9869i	−1.03662	+	0.598494i	−0.918875	−	0.394549i	$-0.870901\pi$
$337$	−19.0299	+	10.9869i	−1.03662	+	0.598494i	−0.117748	+	0.993044i	$0.537567\pi$
$338$			11.3958i			0.619851i
$339$		0			0
$340$	11.8289	+	2.20487i	0.641510	+	0.119576i
$341$	1.39488	−	2.41601i	0.0755371	−	0.130834i
$342$		0			0
$343$	17.6512	−	5.60684i	0.953073	−	0.302741i
$344$	0.561213	−	0.972049i	0.0302586	−	0.0524094i
$345$		0			0
$346$	7.67227	−	13.2888i	0.412464	−	0.714408i
$347$	−0.148996	−	0.0860231i	−0.00799855	−	0.00461796i	0.495995	−	0.868325i	$-0.334803\pi$
$347$	−0.148996	−	0.0860231i	−0.00799855	−	0.00461796i	−0.503994	+	0.863707i	$0.668137\pi$
$348$		0			0
$349$	8.18168	−	14.1711i	0.437955	−	0.758561i	−0.559576	−	0.828779i	$-0.689036\pi$
$349$	8.18168	−	14.1711i	0.437955	−	0.758561i	0.997532	+	0.0702180i	$0.0223695\pi$
$350$	9.31437	+	9.39374i	0.497874	+	0.502117i
$351$		0			0
$352$	3.00590	+	1.73546i	0.160215	+	0.0925001i
$353$			31.6825i			1.68629i	0.537686	+	0.843145i	$0.319298\pi$
$353$			31.6825i			1.68629i	−0.537686	+	0.843145i	$0.680702\pi$
$354$		0			0
$355$	−4.12804	+	22.1465i	−0.219094	+	1.17541i
$356$	−4.84020	−	8.38348i	−0.256530	−	0.444324i
$357$		0			0
$358$	−7.10902	−	4.10439i	−0.375723	−	0.216924i
$359$	2.57635	−	4.46237i	0.135974	−	0.235515i	−0.789995	−	0.613113i	$-0.789917\pi$
$359$	2.57635	−	4.46237i	0.135974	−	0.235515i	0.925969	+	0.377599i	$0.123250\pi$
$360$		0			0
$361$	−0.519903	−	0.900498i	−0.0273633	−	0.0473946i
$362$	7.29969	−	4.21448i	0.383663	−	0.221508i
$363$		0			0
$364$	−2.71534	+	1.96371i	−0.142323	+	0.102926i
$365$	2.82444	+	8.00196i	0.147838	+	0.418842i
$366$		0			0
$367$			12.1302i			0.633189i	0.948561	+	0.316595i	$0.102540\pi$
$367$			12.1302i			0.633189i	−0.948561	+	0.316595i	$0.897460\pi$
$368$	−4.15498	+	2.39888i	−0.216593	+	0.125050i
$369$		0			0
$370$	2.49600	−	13.3908i	0.129761	−	0.696154i
$371$	19.1850	+	8.59229i	0.996037	+	0.446089i
$372$		0			0
$373$		−	23.2810i		−	1.20545i	−0.797951	−	0.602723i	$-0.794082\pi$
$373$		−	23.2810i		−	1.20545i	0.797951	−	0.602723i	$-0.205918\pi$
$374$	9.33874	−	16.1752i	0.482895	−	0.836398i
$375$		0			0
$376$	−4.87394	−	8.44192i	−0.251354	−	0.435359i
$377$			2.65497i			0.136738i
$378$		0			0
$379$	21.3552			1.09694			0.548472	−	0.836169i	$-0.315210\pi$
$379$	21.3552			1.09694			0.548472	+	0.836169i	$0.315210\pi$
$380$	9.43920	−	3.33174i	0.484221	−	0.170915i
$381$		0			0
$382$	2.19694	+	1.26841i	0.112405	+	0.0648973i
$383$		−	37.9472i		−	1.93901i	−0.245066	−	0.969506i	$-0.578810\pi$
$383$		−	37.9472i		−	1.93901i	0.245066	−	0.969506i	$-0.421190\pi$
$384$		0			0
$385$	18.5622	−	8.78047i	0.946018	−	0.447494i
$386$	−25.2581			−1.28560
$387$		0			0
$388$	7.48401	−	4.32089i	0.379943	−	0.219360i
$389$	−10.9095			−0.553133			−0.276566	−	0.960995i	$-0.589197\pi$
$389$	−10.9095			−0.553133			−0.276566	+	0.960995i	$0.589197\pi$
$390$		0			0
$391$	12.9087	+	22.3586i	0.652822	+	1.13072i
$392$	6.64783	+	2.19235i	0.335766	+	0.110731i
$393$		0			0
$394$	2.73456	+	4.73639i	0.137765	+	0.238616i
$395$	3.36209	−	1.18671i	0.169165	−	0.0597100i
$396$		0			0
$397$	−13.6408	−	7.87551i	−0.684611	−	0.395260i	0.116979	−	0.993134i	$-0.462679\pi$
$397$	−13.6408	−	7.87551i	−0.684611	−	0.395260i	−0.801590	+	0.597874i	$0.796012\pi$
$398$	0.534239	+	0.308443i	0.0267790	+	0.0154609i
$399$		0			0
$400$	0.772070	+	4.94003i	0.0386035	+	0.247002i
$401$	20.0433			1.00091			0.500456	−	0.865762i	$-0.333166\pi$
$401$	20.0433			1.00091			0.500456	+	0.865762i	$0.333166\pi$
$402$		0			0
$403$			1.01801i			0.0507104i
$404$	−8.36161	+	14.4827i	−0.416006	+	0.720543i
$405$		0			0
$406$	4.49399	−	3.25001i	0.223033	−	0.161296i
$407$	−18.3110	−	10.5719i	−0.907642	−	0.524027i
$408$		0			0
$409$	2.94275	−	5.09700i	0.145510	−	0.252030i	−0.784053	−	0.620694i	$-0.786851\pi$
$409$	2.94275	−	5.09700i	0.145510	−	0.252030i	0.929563	+	0.368663i	$0.120184\pi$
$410$	−6.65555	+	7.77653i	−0.328694	+	0.384055i
$411$		0			0
$412$	−16.4479	−	9.49620i	−0.810330	−	0.467844i
$413$	−31.9369	+	3.28577i	−1.57151	+	0.161682i
$414$		0			0
$415$	−15.3120	+	17.8909i	−0.751634	+	0.878231i
$416$	−1.26656			−0.0620983
$417$		0			0
$418$		−	15.5378i		−	0.759980i
$419$	7.67105	+	13.2867i	0.374755	+	0.649096i	0.990290	−	0.139014i	$-0.0443933\pi$
$419$	7.67105	+	13.2867i	0.374755	+	0.649096i	−0.615535	+	0.788110i	$0.711060\pi$
$420$		0			0
$421$	12.8961	−	22.3367i	0.628518	−	1.08862i	−0.359332	−	0.933210i	$-0.616995\pi$
$421$	12.8961	−	22.3367i	0.628518	−	1.08862i	0.987849	−	0.155415i	$-0.0496713\pi$
$422$	−2.31223	−	1.33497i	−0.112558	−	0.0649851i
$423$		0			0
$424$	3.97264	+	6.88082i	0.192929	+	0.334162i
$425$	26.5830	−	4.15462i	1.28947	−	0.201529i
$426$		0			0
$427$	11.5532	−	25.7963i	0.559100	−	1.24837i
$428$	−6.00586	+	3.46749i	−0.290304	+	0.167607i
$429$		0			0
$430$	0.459902	−	2.46732i	0.0221784	−	0.118985i
$431$	11.7207	+	20.3008i	0.564565	+	0.977855i	0.997090	+	0.0762332i	$0.0242893\pi$
$431$	11.7207	+	20.3008i	0.564565	+	0.977855i	−0.432525	+	0.901622i	$0.642377\pi$
$432$		0			0
$433$		−	15.3466i		−	0.737511i	−0.929526	−	0.368755i	$-0.879784\pi$
$433$		−	15.3466i		−	0.737511i	0.929526	−	0.368755i	$-0.120216\pi$
$434$	1.72315	−	1.24616i	0.0827137	−	0.0598178i
$435$		0			0
$436$	−15.9337			−0.763088
$437$	18.6001	+	10.7388i	0.889765	+	0.513706i
$438$		0			0
$439$	−4.21185	−	7.29513i	−0.201020	−	0.348178i	0.747837	−	0.663882i	$-0.231092\pi$
$439$	−4.21185	−	7.29513i	−0.201020	−	0.348178i	−0.948857	+	0.315705i	$0.897759\pi$
$440$	7.62978	+	1.42217i	0.363736	+	0.0677992i
$441$		0			0
$442$			6.81555i			0.324183i
$443$	−30.2687	+	17.4756i	−1.43811	+	0.830291i	−0.997718	−	0.0675157i	$-0.978493\pi$
$443$	−30.2687	+	17.4756i	−1.43811	+	0.830291i	−0.440389	+	0.897807i	$0.645159\pi$
$444$		0			0
$445$	−16.4454	−	14.0748i	−0.779587	−	0.667210i
$446$	0.511630			0.0242264
$447$		0			0
$448$	1.55043	+	2.14387i	0.0732508	+	0.101288i
$449$	6.45132			0.304457			0.152228	−	0.988345i	$-0.451355\pi$
$449$	6.45132			0.304457			0.152228	+	0.988345i	$0.451355\pi$
$450$		0			0
$451$	7.94417	+	13.7597i	0.374076	+	0.647919i
$452$		−	7.99489i		−	0.376048i
$453$		0			0
$454$	−6.97409	−	12.0795i	−0.327310	−	0.566918i
$455$	−4.26399	+	6.16154i	−0.199899	+	0.288858i
$456$		0			0
$457$	−7.31453	+	4.22305i	−0.342159	+	0.197546i	−0.661226	−	0.750186i	$-0.729964\pi$
$457$	−7.31453	+	4.22305i	−0.342159	+	0.197546i	0.319067	+	0.947732i	$0.396630\pi$
$458$	−10.3037	+	5.94886i	−0.481461	+	0.277972i
$459$		0			0
$460$	−6.97570	+	8.15060i	−0.325243	+	0.380024i
$461$	2.44623	−	4.23699i	0.113932	−	0.197336i	−0.803420	−	0.595412i	$-0.796989\pi$
$461$	2.44623	−	4.23699i	0.113932	−	0.197336i	0.917352	+	0.398076i	$0.130322\pi$
$462$		0			0
$463$	1.94441	−	1.12261i	0.0903645	−	0.0521720i	−0.454137	−	0.890932i	$-0.650052\pi$
$463$	1.94441	−	1.12261i	0.0903645	−	0.0521720i	0.544501	+	0.838760i	$0.316719\pi$
$464$	2.09621			0.0973139
$465$		0			0
$466$	−26.3131			−1.21893
$467$	17.4863	+	10.0957i	0.809169	+	0.467174i	0.846667	−	0.532123i	$-0.178606\pi$
$467$	17.4863	+	10.0957i	0.809169	+	0.467174i	−0.0374982	+	0.999297i	$0.511939\pi$
$468$		0			0
$469$	0.446112	+	4.33610i	0.0205995	+	0.200223i
$470$	−16.5600	−	14.1729i	−0.763858	−	0.653748i
$471$		0			0
$472$	−10.5090	−	6.06736i	−0.483715	−	0.279273i
$473$	−3.37389	−	1.94792i	−0.155132	−	0.0895654i
$474$		0			0
$475$	17.4236	−	14.0504i	0.799448	−	0.644678i
$476$	11.5365	−	8.34307i	0.528773	−	0.382404i
$477$		0			0
$478$	10.0533	+	5.80430i	0.459829	+	0.265483i
$479$	6.12157			0.279702			0.139851	−	0.990173i	$-0.455338\pi$
$479$	6.12157			0.279702			0.139851	+	0.990173i	$0.455338\pi$
$480$		0			0
$481$	7.71550			0.351796
$482$	15.4354	−	8.91164i	0.703064	−	0.405914i
$483$		0			0
$484$	0.523611	−	0.906921i	0.0238005	−	0.0412237i
$485$	12.5647	−	14.6810i	0.570534	−	0.666628i
$486$		0			0
$487$	6.81398	−	3.93405i	0.308771	−	0.178269i	−0.337605	−	0.941288i	$-0.609617\pi$
$487$	6.81398	−	3.93405i	0.308771	−	0.178269i	0.646376	+	0.763019i	$0.276284\pi$
$488$	9.25199	−	5.34164i	0.418818	−	0.241805i
$489$		0			0
$490$	15.6491	−	0.324965i	0.706954	−	0.0146804i
$491$	2.26524	+	3.92352i	0.102229	+	0.177066i	0.912603	−	0.408848i	$-0.134069\pi$
$491$	2.26524	+	3.92352i	0.102229	+	0.177066i	−0.810374	+	0.585913i	$0.800736\pi$
$492$		0			0
$493$		−	11.2800i		−	0.508025i
$494$	2.83493	+	4.91025i	0.127550	+	0.220923i
$495$		0			0
$496$	0.803755			0.0360897
$497$	15.6202	+	21.5990i	0.700663	+	0.968850i
$498$		0			0
$499$	30.8462			1.38086			0.690432	−	0.723397i	$-0.257420\pi$
$499$	30.8462			1.38086			0.690432	+	0.723397i	$0.257420\pi$
$500$	5.30463	+	9.84179i	0.237230	+	0.440138i
$501$		0			0
$502$	23.9865	−	13.8486i	1.07057	−	0.618094i
$503$		−	13.8010i		−	0.615357i	−0.951490	−	0.307678i	$-0.900448\pi$
$503$		−	13.8010i		−	0.615357i	0.951490	−	0.307678i	$-0.0995521\pi$
$504$		0			0
$505$	−6.85216	+	36.7611i	−0.304917	+	1.63585i
$506$	8.32630	+	14.4216i	0.370149	+	0.641117i
$507$		0			0
$508$	−9.27801	−	5.35666i	−0.411645	−	0.237663i
$509$	26.4825			1.17381			0.586907	−	0.809654i	$-0.300345\pi$
$509$	26.4825			1.17381			0.586907	+	0.809654i	$0.300345\pi$
$510$		0			0
$511$	9.16349	+	4.10400i	0.405369	+	0.181550i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	6.05481	+	10.4872i	0.267066	+	0.462573i
$515$	−41.7492	−	7.78193i	−1.83969	−	0.342913i
$516$		0			0
$517$	−29.3011	+	16.9170i	−1.28866	+	0.744010i
$518$	−9.44472	−	13.0598i	−0.414977	−	0.573814i
$519$		0			0
$520$	−2.67064	+	0.942649i	−0.117115	+	0.0413379i
$521$	19.1388	+	33.1494i	0.838486	+	1.45230i	0.891160	+	0.453689i	$0.149892\pi$
$521$	19.1388	+	33.1494i	0.838486	+	1.45230i	−0.0526739	+	0.998612i	$0.516774\pi$
$522$		0			0
$523$	−27.4538	−	15.8505i	−1.20047	−	0.693093i	−0.239812	−	0.970819i	$-0.577086\pi$
$523$	−27.4538	−	15.8505i	−1.20047	−	0.693093i	−0.960660	+	0.277727i	$0.910419\pi$
$524$	−0.490580	+	0.849709i	−0.0214311	+	0.0371197i
$525$		0			0
$526$	−9.47897	−	16.4181i	−0.413303	−	0.715862i
$527$		−	4.32512i		−	0.188405i
$528$		0			0
$529$	−0.0185089			−0.000804734
$530$	13.4977	+	11.5520i	0.586303	+	0.501788i
$531$		0			0
$532$	4.84112	−	10.8094i	0.209889	−	0.468645i
$533$	−5.02102	−	2.89888i	−0.217484	−	0.125565i
$534$		0			0
$535$	−10.0831	+	11.7814i	−0.435930	+	0.509353i
$536$	−0.823771	+	1.42681i	−0.0355815	+	0.0616290i
$537$		0			0
$538$	24.3571	+	14.0626i	1.05011	+	0.606282i
$539$	7.60947	−	23.0740i	0.327763	−	0.993868i
$540$		0			0
$541$	11.9014	−	20.6137i	0.511679	−	0.886254i	−0.488229	−	0.872715i	$-0.662357\pi$
$541$	11.9014	−	20.6137i	0.511679	−	0.886254i	0.999908	−	0.0135387i	$-0.00430964\pi$
$542$			10.2299i			0.439412i
$543$		0			0
$544$	5.38114			0.230715
$545$	−33.5974	+	11.8588i	−1.43916	+	0.507976i
$546$		0			0
$547$	−35.3481	−	20.4082i	−1.51137	−	0.872593i	−0.999912	−	0.0132874i	$-0.995770\pi$
$547$	−35.3481	−	20.4082i	−1.51137	−	0.872593i	−0.511463	−	0.859305i	$-0.670896\pi$
$548$	−11.8149	−	6.82131i	−0.504706	−	0.291392i
$549$		0			0
$550$	17.1464	−	2.67979i	0.731125	−	0.114266i
$551$	−4.69192	−	8.12665i	−0.199883	−	0.346207i
$552$		0			0
$553$	1.72433	−	3.85012i	0.0733260	−	0.163724i
$554$	4.74516	+	8.21886i	0.201603	+	0.349186i
$555$		0			0
$556$	−18.8179			−0.798056
$557$	−33.1268	+	19.1258i	−1.40363	+	0.810384i	−0.994763	−	0.102211i	$-0.967408\pi$
$557$	−33.1268	+	19.1258i	−1.40363	+	0.810384i	−0.408864	+	0.912595i	$0.634075\pi$
$558$		0			0
$559$	1.42162			0.0601281
$560$	4.86478	+	3.36659i	0.205575	+	0.142264i
$561$		0			0
$562$		−	5.46437i		−	0.230500i
$563$	−15.5128	−	8.95634i	−0.653788	−	0.377465i	0.136118	−	0.990693i	$-0.456537\pi$
$563$	−15.5128	−	8.95634i	−0.653788	−	0.377465i	−0.789906	+	0.613228i	$0.789871\pi$
$564$		0			0
$565$	−5.95027	−	16.8578i	−0.250330	−	0.709214i
$566$	25.6737			1.07914
$567$		0			0
$568$			10.0748i			0.422729i
$569$	−12.6209	−	21.8600i	−0.529094	−	0.916417i	−0.999424	−	0.0339268i	$-0.989199\pi$
$569$	−12.6209	−	21.8600i	−0.529094	−	0.916417i	0.470331	−	0.882490i	$-0.344135\pi$
$570$		0			0
$571$	−5.07238	+	8.78561i	−0.212272	+	0.367666i	−0.952425	−	0.304772i	$-0.901420\pi$
$571$	−5.07238	+	8.78561i	−0.212272	+	0.367666i	0.740153	+	0.672439i	$0.234753\pi$
$572$			4.39612i			0.183811i
$573$		0			0
$574$	1.23949	+	12.0475i	0.0517352	+	0.502853i
$575$	−8.64261	+	22.3778i	−0.360422	+	0.933221i
$576$		0			0
$577$	−12.4685	+	7.19867i	−0.519069	+	0.299685i	−0.736554	−	0.676379i	$-0.763548\pi$
$577$	−12.4685	+	7.19867i	−0.519069	+	0.299685i	0.217485	+	0.976064i	$0.430215\pi$
$578$		−	11.9567i		−	0.497333i
$579$		0			0
$580$	4.42000	−	1.56012i	0.183531	−	0.0647805i
$581$	2.85160	+	27.7169i	0.118304	+	1.14989i
$582$		0			0
$583$	23.8827	−	13.7887i	0.989121	−	0.571069i
$584$	1.89748	+	3.28654i	0.0785184	+	0.135998i
$585$		0			0
$586$	10.4560	−	18.1103i	0.431932	−	0.748128i
$587$	−13.2170	−	7.63087i	−0.545526	−	0.314960i	0.201790	−	0.979429i	$-0.435324\pi$
$587$	−13.2170	−	7.63087i	−0.545526	−	0.314960i	−0.747316	+	0.664469i	$0.768658\pi$
$588$		0			0
$589$	−1.79904	−	3.11603i	−0.0741281	−	0.128394i
$590$	−26.6746	−	4.97207i	−1.09818	−	0.204697i
$591$		0			0
$592$		−	6.09169i		−	0.250367i
$593$	24.0106	+	13.8625i	0.985996	+	0.569265i	0.904075	−	0.427374i	$-0.140561\pi$
$593$	24.0106	+	13.8625i	0.985996	+	0.569265i	0.0819210	+	0.996639i	$0.473894\pi$
$594$		0			0
$595$	18.1161	−	26.1781i	0.742687	−	1.07320i
$596$	−8.16842	+	14.1481i	−0.334591	+	0.579529i
$597$		0			0
$598$	−5.26254	−	3.03833i	−0.215201	−	0.124247i
$599$	7.87216	−	13.6350i	0.321648	−	0.557110i	−0.659181	−	0.751985i	$-0.729097\pi$
$599$	7.87216	−	13.6350i	0.321648	−	0.557110i	0.980828	+	0.194875i	$0.0624300\pi$
$600$		0			0
$601$	9.82777	−	17.0222i	0.400883	−	0.694350i	−0.592950	−	0.805239i	$-0.702037\pi$
$601$	9.82777	−	17.0222i	0.400883	−	0.694350i	0.993833	+	0.110890i	$0.0353701\pi$
$602$	−1.74024	−	2.40633i	−0.0709268	−	0.0980748i
$603$		0			0
$604$	3.81070	−	6.60033i	0.155055	−	0.268564i
$605$	0.429088	−	2.30201i	0.0174449	−	0.0935901i
$606$		0			0
$607$		−	30.4855i		−	1.23737i	−0.785640	−	0.618684i	$-0.787666\pi$
$607$		−	30.4855i		−	1.23737i	0.785640	−	0.618684i	$-0.212334\pi$
$608$	3.87684	−	2.23829i	0.157226	−	0.0907747i
$609$		0			0
$610$	15.5329	−	18.1491i	0.628910	−	0.734836i
$611$	6.17315	−	10.6922i	0.249739	−	0.432560i
$612$		0			0
$613$	16.0145	−	9.24599i	0.646821	−	0.373442i	−0.140416	−	0.990093i	$-0.544844\pi$
$613$	16.0145	−	9.24599i	0.646821	−	0.373442i	0.787237	+	0.616650i	$0.211511\pi$
$614$	0.663444	+	1.14912i	0.0267744	+	0.0463746i
$615$		0			0
$616$	7.44118	−	5.38139i	0.299814	−	0.216822i
$617$	−23.0855	+	13.3284i	−0.929386	+	0.536582i	−0.886617	−	0.462503i	$-0.846951\pi$
$617$	−23.0855	+	13.3284i	−0.929386	+	0.536582i	−0.0427690	+	0.999085i	$0.513618\pi$
$618$		0			0
$619$	−17.7946			−0.715223			−0.357612	−	0.933870i	$-0.616409\pi$
$619$	−17.7946			−0.715223			−0.357612	+	0.933870i	$0.616409\pi$
$620$	1.69478	−	0.598202i	0.0680638	−	0.0240244i
$621$		0			0
$622$			22.2201i			0.890944i
$623$	−25.4775	+	2.62120i	−1.02073	+	0.105016i
$624$		0			0
$625$	18.5100	+	16.8041i	0.740401	+	0.672165i
$626$	8.04294	−	13.9308i	0.321461	−	0.556786i
$627$		0			0
$628$	19.8612	−	11.4669i	0.792548	−	0.457578i
$629$	−32.7803			−1.30703
$630$		0			0
$631$	−47.9581			−1.90918			−0.954592	−	0.297917i	$-0.903708\pi$
$631$	−47.9581			−1.90918			−0.954592	+	0.297917i	$0.903708\pi$
$632$	1.38087	−	0.797244i	0.0549279	−	0.0317127i
$633$		0			0
$634$	5.28574	−	9.15516i	0.209923	−	0.363598i
$635$	−23.5501	−	4.38967i	−0.934557	−	0.174199i
$636$		0			0
$637$	1.80520	+	8.68020i	0.0715247	+	0.343922i
$638$		−	7.27575i		−	0.288050i
$639$		0			0
$640$	0.744259	+	2.10857i	0.0294194	+	0.0833487i
$641$	45.6152			1.80169			0.900847	−	0.434138i	$-0.142947\pi$
$641$	45.6152			1.80169			0.900847	+	0.434138i	$0.142947\pi$
$642$		0			0
$643$	26.8259	−	15.4880i	1.05791	−	0.610786i	0.133058	−	0.991108i	$-0.457520\pi$
$643$	26.8259	−	15.4880i	1.05791	−	0.610786i	0.924854	+	0.380323i	$0.124187\pi$
$644$	1.29911	+	12.6270i	0.0511921	+	0.497575i
$645$		0			0
$646$	−12.0446	−	20.8618i	−0.473887	−	0.820797i
$647$	−20.4304	+	11.7955i	−0.803203	+	0.463729i	−0.844590	−	0.535414i	$-0.820156\pi$
$647$	−20.4304	+	11.7955i	−0.803203	+	0.463729i	0.0413872	+	0.999143i	$0.486822\pi$
$648$		0			0
$649$	−21.0593	+	36.4757i	−0.826649	+	1.43180i
$650$	−4.92966	+	3.97529i	−0.193357	+	0.155924i
$651$		0			0
$652$	−1.35549	+	0.782594i	−0.0530852	+	0.0306487i
$653$			41.1381i			1.60986i	0.593371	+	0.804929i	$0.297797\pi$
$653$			41.1381i			1.60986i	−0.593371	+	0.804929i	$0.702203\pi$
$654$		0			0
$655$	−0.402020	+	2.15679i	−0.0157082	+	0.0842728i
$656$	−2.28878	+	3.96429i	−0.0893620	+	0.154780i
$657$		0			0
$658$	−25.6551	+	2.63947i	−1.00014	+	0.102897i
$659$	−3.78262	+	6.55169i	−0.147350	+	0.255218i	−0.930247	−	0.366933i	$-0.880408\pi$
$659$	−3.78262	+	6.55169i	−0.147350	+	0.255218i	0.782897	+	0.622151i	$0.213741\pi$
$660$		0			0
$661$	−15.8444	+	27.4433i	−0.616275	+	1.06742i	0.373884	+	0.927475i	$0.378026\pi$
$661$	−15.8444	+	27.4433i	−0.616275	+	1.06742i	−0.990159	+	0.139945i	$0.955308\pi$
$662$	0.661879	+	0.382136i	0.0257247	+	0.0148521i
$663$		0			0
$664$	−5.26565	+	9.12037i	−0.204347	+	0.353939i
$665$	2.16290	−	26.3954i	0.0838736	−	1.02357i
$666$		0			0
$667$	8.70970	+	5.02855i	0.337241	+	0.194706i
$668$			6.05190i			0.234155i
$669$		0			0
$670$	−0.675063	+	3.62164i	−0.0260800	+	0.139916i
$671$	−18.5403	−	32.1128i	−0.715742	−	1.23970i
$672$		0			0
$673$	−25.5771	−	14.7669i	−0.985924	−	0.569223i	−0.0818702	−	0.996643i	$-0.526089\pi$
$673$	−25.5771	−	14.7669i	−0.985924	−	0.569223i	−0.904053	+	0.427420i	$0.859423\pi$
$674$	−10.9869	+	19.0299i	−0.423199	+	0.733003i
$675$		0			0
$676$	5.69791	+	9.86907i	0.219150	+	0.379580i
$677$	8.62081	−	4.97723i	0.331325	−	0.191290i	−0.325104	−	0.945678i	$-0.605399\pi$
$677$	8.62081	−	4.97723i	0.331325	−	0.191290i	0.656429	+	0.754388i	$0.272066\pi$
$678$		0			0
$679$	−2.33997	−	22.7440i	−0.0897999	−	0.872833i
$680$	11.3465	−	4.00496i	0.435120	−	0.153583i
$681$		0			0
$682$		−	2.78976i		−	0.106826i
$683$	19.6627	−	11.3523i	0.752372	−	0.434382i	−0.0741781	−	0.997245i	$-0.523633\pi$
$683$	19.6627	−	11.3523i	0.752372	−	0.434382i	0.826550	+	0.562863i	$0.190300\pi$
$684$		0			0
$685$	−29.9893	−	5.58992i	−1.14583	−	0.213580i
$686$	12.4829	−	13.6812i	0.476600	−	0.522352i
$687$		0			0
$688$		−	1.12243i		−	0.0427921i
$689$	−5.03159	+	8.71498i	−0.191688	+	0.332014i
$690$		0			0
$691$	−20.0532	−	34.7332i	−0.762861	−	1.32131i	−0.941370	−	0.337376i	$-0.890461\pi$
$691$	−20.0532	−	34.7332i	−0.762861	−	1.32131i	0.178509	−	0.983938i	$-0.442873\pi$
$692$		−	15.3445i		−	0.583312i
$693$		0			0
$694$	−0.172046			−0.00653079
$695$	−39.6789	+	14.0054i	−1.50511	+	0.531254i
$696$		0			0
$697$	21.3324	+	12.3163i	0.808023	+	0.466512i
$698$		−	16.3634i		−	0.619362i
$699$		0			0
$700$	12.7634	+	3.47803i	0.482410	+	0.131457i
$701$	−11.4107			−0.430976			−0.215488	−	0.976507i	$-0.569134\pi$
$701$	−11.4107			−0.430976			−0.215488	+	0.976507i	$0.569134\pi$
$702$		0			0
$703$	−23.6165	+	13.6350i	−0.890712	+	0.514253i
$704$	3.47091			0.130815
$705$		0			0
$706$	15.8413	+	27.4379i	0.596194	+	1.03264i
$707$	25.9281	+	35.8524i	0.975128	+	1.34837i
$708$		0			0
$709$	4.86044	+	8.41853i	0.182538	+	0.316164i	0.942744	−	0.333517i	$-0.108236\pi$
$709$	4.86044	+	8.41853i	0.182538	+	0.316164i	−0.760206	+	0.649682i	$0.774902\pi$
$710$	7.49825	+	21.2434i	0.281404	+	0.797252i
$711$		0			0
$712$	−8.38348	−	4.84020i	−0.314184	−	0.181394i
$713$	3.33959	+	1.92811i	0.125069	+	0.0722084i
$714$		0			0
$715$	3.27185	+	9.26954i	0.122360	+	0.346661i
$716$	−8.20879			−0.306777
$717$		0			0
$718$		−	5.15270i		−	0.192297i
$719$	−5.60867	+	9.71450i	−0.209168	+	0.362290i	−0.951453	−	0.307795i	$-0.900409\pi$
$719$	−5.60867	+	9.71450i	−0.209168	+	0.362290i	0.742285	+	0.670085i	$0.233742\pi$
$720$		0			0
$721$	−40.7172	+	29.4463i	−1.51639	+	1.09664i
$722$	−0.900498	−	0.519903i	−0.0335131	−	0.0193488i
$723$		0			0
$724$	4.21448	−	7.29969i	0.156630	−	0.271291i
$725$	8.15877	−	6.57925i	0.303009	−	0.244347i
$726$		0			0
$727$	−33.4268	−	19.2990i	−1.23973	−	0.715760i	−0.270693	−	0.962666i	$-0.587253\pi$
$727$	−33.4268	−	19.2990i	−1.23973	−	0.715760i	−0.969039	+	0.246906i	$0.920586\pi$
$728$	−1.36970	+	3.05829i	−0.0507645	+	0.113348i
$729$		0			0
$730$	6.44701	+	5.51768i	0.238615	+	0.204219i
$731$	−6.03993			−0.223395
$732$		0			0
$733$		−	30.8858i		−	1.14079i	−0.821369	−	0.570397i	$-0.806789\pi$
$733$		−	30.8858i		−	1.14079i	0.821369	−	0.570397i	$-0.193211\pi$
$734$	6.06508	+	10.5050i	0.223866	+	0.387748i
$735$		0			0
$736$	−2.39888	+	4.15498i	−0.0884239	+	0.153155i
$737$	4.95234	+	2.85924i	0.182422	+	0.105321i
$738$		0			0
$739$	23.3669	+	40.4726i	0.859564	+	1.48881i	0.872346	+	0.488889i	$0.162598\pi$
$739$	23.3669	+	40.4726i	0.859564	+	1.48881i	−0.0127823	+	0.999918i	$0.504069\pi$
$740$	−4.53379	−	12.8448i	−0.166666	−	0.472183i
$741$		0			0
$742$	20.9109	−	2.15138i	0.767662	−	0.0789795i
$743$	3.00097	−	1.73261i	0.110095	−	0.0635633i	−0.443941	−	0.896056i	$-0.646420\pi$
$743$	3.00097	−	1.73261i	0.110095	−	0.0635633i	0.554036	+	0.832492i	$0.313087\pi$
$744$		0			0
$745$	−6.69384	+	35.9117i	−0.245243	+	1.31570i
$746$	−11.6405	−	20.1620i	−0.426189	−	0.738182i
$747$		0			0
$748$		−	18.6775i		−	0.682916i
$749$	1.87781	+	18.2519i	0.0686137	+	0.666909i
$750$		0			0
$751$	19.8306			0.723630			0.361815	−	0.932250i	$-0.382157\pi$
$751$	19.8306			0.723630			0.361815	+	0.932250i	$0.382157\pi$
$752$	−8.44192	−	4.87394i	−0.307845	−	0.177734i
$753$		0			0
$754$	1.32749	+	2.29927i	0.0483442	+	0.0837346i
$755$	3.12279	−	16.7534i	0.113650	−	0.609719i
$756$		0			0
$757$			38.7051i			1.40676i	0.710813	+	0.703381i	$0.248327\pi$
$757$			38.7051i			1.40676i	−0.710813	+	0.703381i	$0.751673\pi$
$758$	18.4942	−	10.6776i	0.671738	−	0.387828i
$759$		0			0
$760$	6.50872	−	7.60497i	0.236096	−	0.275861i
$761$	−6.54573			−0.237283			−0.118641	−	0.992937i	$-0.537854\pi$
$761$	−6.54573			−0.237283			−0.118641	+	0.992937i	$0.537854\pi$
$762$		0			0
$763$	−17.2313	+	38.4743i	−0.623813	+	1.39286i
$764$	2.53681			0.0917786
$765$		0			0
$766$	−18.9736	−	32.8633i	−0.685545	−	1.18740i
$767$		−	15.3694i		−	0.554956i
$768$		0			0
$769$	7.72709	+	13.3837i	0.278646	+	0.482629i	0.971049	−	0.238882i	$-0.0767810\pi$
$769$	7.72709	+	13.3837i	0.278646	+	0.482629i	−0.692402	+	0.721511i	$0.743448\pi$
$770$	11.6851	−	16.8852i	0.421103	−	0.608501i
$771$		0			0
$772$	−21.8742	+	12.6290i	−0.787268	+	0.454529i
$773$	27.8499	−	16.0792i	1.00169	−	0.578327i	0.0929440	−	0.995671i	$-0.470372\pi$
$773$	27.8499	−	16.0792i	1.00169	−	0.578327i	0.908749	+	0.417344i	$0.137039\pi$
$774$		0			0
$775$	3.12834	−	2.52270i	0.112373	−	0.0906182i
$776$	4.32089	−	7.48401i	0.155111	−	0.268660i
$777$		0			0
$778$	−9.44789	+	5.45474i	−0.338723	+	0.195562i
$779$	20.4919			0.734197
$780$		0			0
$781$	34.9687			1.25128
$782$	22.3586	+	12.9087i	0.799540	+	0.461615i
$783$		0			0
$784$	6.85336	−	1.42528i	0.244763	−	0.0509028i
$785$	33.3445	−	38.9606i	1.19012	−	1.39056i
$786$		0			0
$787$	29.1039	+	16.8031i	1.03744	+	0.598967i	0.919107	−	0.394007i	$-0.128912\pi$
$787$	29.1039	+	16.8031i	1.03744	+	0.598967i	0.118333	+	0.992974i	$0.462245\pi$
$788$	4.73639	+	2.73456i	0.168727	+	0.0974145i
$789$		0			0
$790$	2.31830	−	2.70877i	0.0824815	−	0.0963737i
$791$	−19.3048	−	8.64594i	−0.686400	−	0.307414i
$792$		0			0
$793$	11.7182	+	6.76551i	0.416126	+	0.240250i
$794$	−15.7510			−0.558983
$795$		0			0
$796$	0.616886			0.0218649
$797$	28.6922	−	16.5655i	1.01633	−	0.586779i	0.103292	−	0.994651i	$-0.467062\pi$
$797$	28.6922	−	16.5655i	1.01633	−	0.586779i	0.913039	+	0.407872i	$0.133729\pi$
$798$		0			0
$799$	−26.2274	+	45.4272i	−0.927858	+	1.60710i
$800$	3.13865	+	3.89216i	0.110968	+	0.137609i
$801$		0			0
$802$	17.3580	−	10.0216i	0.612931	−	0.353876i
$803$	11.4073	−	6.58599i	0.402554	−	0.232415i
$804$		0			0
$805$	12.1370	+	25.6581i	0.427775	+	0.904330i
$806$	0.509003	+	0.881618i	0.0179288	+	0.0310537i
$807$		0			0
$808$			16.7232i			0.588321i
$809$	−23.6277	−	40.9244i	−0.830707	−	1.43883i	−0.897478	−	0.441058i	$-0.854603\pi$
$809$	−23.6277	−	40.9244i	−0.830707	−	1.43883i	0.0667716	−	0.997768i	$-0.478730\pi$
$810$		0			0
$811$	−15.8024			−0.554898			−0.277449	−	0.960740i	$-0.589489\pi$
$811$	−15.8024			−0.554898			−0.277449	+	0.960740i	$0.589489\pi$
$812$	2.26691	−	5.06159i	0.0795528	−	0.177627i
$813$		0			0
$814$	−21.1437			−0.741087
$815$	−2.27570	+	2.65899i	−0.0797143	+	0.0931405i
$816$		0			0
$817$	−4.35146	+	2.51232i	−0.152238	+	0.0878948i
$818$		−	5.88551i		−	0.205782i
$819$		0			0
$820$	−1.87561	+	10.0624i	−0.0654991	+	0.351396i
$821$	13.4257	+	23.2541i	0.468562	+	0.811573i	0.999354	−	0.0359289i	$-0.0114390\pi$
$821$	13.4257	+	23.2541i	0.468562	+	0.811573i	−0.530793	+	0.847502i	$0.678106\pi$
$822$		0			0
$823$	−35.1842	−	20.3136i	−1.22644	−	0.708088i	−0.260160	−	0.965566i	$-0.583775\pi$
$823$	−35.1842	−	20.3136i	−1.22644	−	0.708088i	−0.966284	+	0.257478i	$0.917109\pi$
$824$	−18.9924			−0.661632
$825$		0			0
$826$	−26.0153	+	18.8140i	−0.905187	+	0.654623i
$827$		−	17.9942i		−	0.625721i	−0.949799	−	0.312860i	$-0.898713\pi$
$827$		−	17.9942i		−	0.625721i	0.949799	−	0.312860i	$-0.101287\pi$
$828$		0			0
$829$	1.45002	+	2.51150i	0.0503611	+	0.0872280i	0.890107	−	0.455752i	$-0.150629\pi$
$829$	1.45002	+	2.51150i	0.0503611	+	0.0872280i	−0.839746	+	0.542980i	$0.817296\pi$
$830$	−4.31508	+	23.1500i	−0.149779	+	0.803547i
$831$		0			0
$832$	−1.09687	+	0.633281i	−0.0380273	+	0.0219551i
$833$	−7.66963	−	36.8789i	−0.265737	−	1.27778i
$834$		0			0
$835$	4.50418	+	12.7609i	0.155874	+	0.441608i
$836$	−7.76891	−	13.4562i	−0.268693	−	0.465391i
$837$		0			0
$838$	13.2867	+	7.67105i	0.458980	+	0.264992i
$839$	−13.7374	+	23.7938i	−0.474267	+	0.821454i	−0.999566	−	0.0294638i	$-0.990620\pi$
$839$	−13.7374	+	23.7938i	−0.474267	+	0.821454i	0.525299	+	0.850918i	$0.323953\pi$
$840$		0			0
$841$	12.3030	+	21.3094i	0.424240	+	0.734805i
$842$		−	25.7922i		−	0.888858i
$843$		0			0
$844$	−2.66993			−0.0919029
$845$	19.3596	+	16.5689i	0.665991	+	0.569989i
$846$		0			0
$847$	−1.62364	−	2.24511i	−0.0557890	−	0.0771429i
$848$	6.88082	+	3.97264i	0.236288	+	0.136421i
$849$		0			0
$850$	20.9443	−	16.8895i	0.718382	−	0.579306i
$851$	14.6132	−	25.3109i	0.500935	−	0.867645i
$852$		0			0
$853$	8.41825	+	4.86028i	0.288235	+	0.166413i	0.637146	−	0.770743i	$-0.280115\pi$
$853$	8.41825	+	4.86028i	0.288235	+	0.166413i	−0.348910	+	0.937156i	$0.613448\pi$
$854$	−2.89275	−	28.1169i	−0.0989880	−	0.962139i
$855$		0			0
$856$	−3.46749	+	6.00586i	−0.118516	+	0.205276i
$857$			9.15622i			0.312771i	0.987696	+	0.156385i	$0.0499842\pi$
$857$			9.15622i			0.312771i	−0.987696	+	0.156385i	$0.950016\pi$
$858$		0			0
$859$	4.16787			0.142206			0.0711029	−	0.997469i	$-0.477348\pi$
$859$	4.16787			0.142206			0.0711029	+	0.997469i	$0.477348\pi$
$860$	−0.835375	−	2.36672i	−0.0284860	−	0.0807043i
$861$		0			0
$862$	20.3008	+	11.7207i	0.691448	+	0.399208i
$863$	17.7700	+	10.2595i	0.604897	+	0.349237i	0.770966	−	0.636877i	$-0.219774\pi$
$863$	17.7700	+	10.2595i	0.604897	+	0.349237i	−0.166069	+	0.986114i	$0.553107\pi$
$864$		0			0
$865$	−11.4203	−	32.3551i	−0.388302	−	1.10011i
$866$	−7.67330	−	13.2906i	−0.260749	−	0.451631i
$867$		0			0
$868$	0.869207	−	1.94078i	0.0295028	−	0.0658744i
$869$	−2.76716	−	4.79287i	−0.0938696	−	0.162587i
$870$		0			0
$871$	−2.08671			−0.0707056
$872$	−13.7990	+	7.96687i	−0.467294	+	0.269792i
$873$		0			0
$874$	21.4776			0.726490
$875$	29.5010	−	2.16555i	0.997317	−	0.0732090i
$876$		0			0
$877$			29.9389i			1.01096i	0.862837	+	0.505482i	$0.168685\pi$
$877$			29.9389i			1.01096i	−0.862837	+	0.505482i	$0.831315\pi$
$878$	−7.29513	−	4.21185i	−0.246199	−	0.142143i
$879$		0			0
$880$	7.31867	−	2.58326i	0.246712	−	0.0870816i
$881$	−20.5399			−0.692006			−0.346003	−	0.938233i	$-0.612461\pi$
$881$	−20.5399			−0.692006			−0.346003	+	0.938233i	$0.612461\pi$
$882$		0			0
$883$		−	45.7939i		−	1.54109i	−0.637387	−	0.770543i	$-0.719985\pi$
$883$		−	45.7939i		−	1.54109i	0.637387	−	0.770543i	$-0.280015\pi$
$884$	3.40777	+	5.90244i	0.114616	+	0.198520i
$885$		0			0
$886$	−17.4756	+	30.2687i	−0.587105	+	1.01690i
$887$			41.4730i			1.39253i	0.717786	+	0.696264i	$0.245156\pi$
$887$			41.4730i			1.39253i	−0.717786	+	0.696264i	$0.754844\pi$
$888$		0			0
$889$	−22.9680	+	16.6102i	−0.770321	+	0.557089i
$890$	−21.2795	−	3.96644i	−0.713292	−	0.132955i
$891$		0			0
$892$	0.443085	−	0.255815i	0.0148356	−	0.00856533i
$893$			43.6372i			1.46026i
$894$		0			0
$895$	−17.3088	+	6.10946i	−0.578570	+	0.204217i
$896$	2.41464	+	1.08143i	0.0806676	+	0.0361281i
$897$		0			0
$898$	5.58701	−	3.22566i	0.186441	−	0.107642i
$899$	−0.842418	−	1.45911i	−0.0280962	−	0.0486641i
$900$		0			0
$901$	21.3774	−	37.0267i	0.712183	−	1.23354i
$902$	13.7597	+	7.94417i	0.458148	+	0.264512i
$903$		0			0
$904$	−3.99745	−	6.92378i	−0.132953	−	0.230282i
$905$	3.45367	−	18.5286i	0.114804	−	0.615911i
$906$		0			0
$907$			42.1046i			1.39806i	0.715093	+	0.699029i	$0.246384\pi$
$907$			42.1046i			1.39806i	−0.715093	+	0.699029i	$0.753616\pi$
$908$	−12.0795	−	6.97409i	−0.400872	−	0.231443i
$909$		0			0
$910$	−0.611950	+	7.46805i	−0.0202859	+	0.247563i
$911$	−3.01653	+	5.22479i	−0.0999422	+	0.173105i	−0.911661	−	0.410944i	$-0.865199\pi$
$911$	−3.01653	+	5.22479i	−0.0999422	+	0.173105i	0.811718	+	0.584049i	$0.198532\pi$
$912$		0			0
$913$	31.6560	+	18.2766i	1.04766	+	0.604867i
$914$	−4.22305	+	7.31453i	−0.139686	+	0.241943i
$915$		0			0
$916$	−5.94886	+	10.3037i	−0.196556	+	0.340445i
$917$	1.52122	+	2.10348i	0.0502350	+	0.0694630i
$918$		0			0
$919$	9.15312	−	15.8537i	0.301933	−	0.522964i	−0.674640	−	0.738147i	$-0.735701\pi$
$919$	9.15312	−	15.8537i	0.301933	−	0.522964i	0.976574	+	0.215182i	$0.0690346\pi$
$920$	−1.96583	+	10.5465i	−0.0648115	+	0.347707i
$921$		0			0
$922$		−	4.89245i		−	0.161124i
$923$	−11.0508	+	6.38017i	−0.363741	+	0.210006i
$924$		0			0
$925$	−19.1197	−	23.7098i	−0.628651	−	0.779574i
$926$	1.12261	−	1.94441i	0.0368912	−	0.0638974i
$927$		0			0
$928$	1.81537	−	1.04810i	0.0595924	−	0.0344057i
$929$	12.1430	+	21.0323i	0.398399	+	0.690048i	0.993529	−	0.113582i	$-0.0362325\pi$
$929$	12.1430	+	21.0323i	0.398399	+	0.690048i	−0.595129	+	0.803630i	$0.702899\pi$
$930$		0			0
$931$	−20.8654	−	23.3792i	−0.683836	−	0.766221i
$932$	−22.7879	+	13.1566i	−0.746441	+	0.430958i
$933$		0			0
$934$	20.1914			0.660684
$935$	−13.9009	−	39.3828i	−0.454607	−	1.28796i
$936$		0			0
$937$			30.0447i			0.981519i	0.871295	+	0.490759i	$0.163281\pi$
$937$			30.0447i			0.981519i	−0.871295	+	0.490759i	$0.836719\pi$
$938$	2.55439	+	3.53212i	0.0834039	+	0.115328i
$939$		0			0
$940$	−21.4279	−	3.99409i	−0.698900	−	0.130273i
$941$	8.68388	−	15.0409i	0.283087	−	0.490320i	−0.689057	−	0.724707i	$-0.741975\pi$
$941$	8.68388	−	15.0409i	0.283087	−	0.490320i	0.972143	+	0.234387i	$0.0753083\pi$
$942$		0			0
$943$	−19.0197	+	10.9810i	−0.619367	+	0.357592i
$944$	−12.1347			−0.394952
$945$		0			0
$946$	−3.89584			−0.126665
$947$	10.6480	−	6.14764i	0.346014	−	0.199771i	−0.316914	−	0.948454i	$-0.602647\pi$
$947$	10.6480	−	6.14764i	0.346014	−	0.199771i	0.662928	+	0.748683i	$0.269313\pi$
$948$		0			0
$949$	−2.40328	+	4.16260i	−0.0780137	+	0.135124i
$950$	8.06404	−	20.8798i	0.261632	−	0.677430i
$951$		0			0
$952$	5.81934	−	12.9935i	0.188606	−	0.421123i
$953$		−	13.8549i		−	0.448804i	−0.974497	−	0.224402i	$-0.927957\pi$
$953$		−	13.8549i		−	0.448804i	0.974497	−	0.224402i	$-0.0720428\pi$
$954$		0			0
$955$	5.34905	−	1.88804i	0.173091	−	0.0610957i
$956$	11.6086			0.375449
$957$		0			0
$958$	5.30143	−	3.06078i	0.171282	−	0.0988894i
$959$	−29.2480	+	21.1519i	−0.944468	+	0.683030i
$960$		0			0
$961$	15.1770	+	26.2873i	0.489580	+	0.847978i
$962$	6.68182	−	3.85775i	0.215430	−	0.124379i
$963$		0			0
$964$	8.91164	−	15.4354i	0.287025	−	0.497141i
$965$	−36.7240	+	42.9093i	−1.18219	+	1.38130i
$966$		0			0
$967$	17.6627	−	10.1976i	0.567994	−	0.327932i	−0.188354	−	0.982101i	$-0.560315\pi$
$967$	17.6627	−	10.1976i	0.567994	−	0.327932i	0.756348	+	0.654170i	$0.226982\pi$
$968$		−	1.04722i		−	0.0336590i
$969$		0			0
$970$	3.54088	−	18.9964i	0.113691	−	0.609939i
$971$	−18.1140	+	31.3744i	−0.581306	+	1.00685i	0.414019	+	0.910268i	$0.364125\pi$
$971$	−18.1140	+	31.3744i	−0.581306	+	1.00685i	−0.995325	+	0.0965834i	$0.969209\pi$
$972$		0			0
$973$	−20.3503	+	45.4385i	−0.652399	+	1.45669i
$974$	3.93405	−	6.81398i	0.126055	−	0.218334i
$975$		0			0
$976$	5.34164	−	9.25199i	0.170982	−	0.296149i
$977$	−19.0899	−	11.0216i	−0.610740	−	0.352611i	0.162515	−	0.986706i	$-0.448039\pi$
$977$	−19.0899	−	11.0216i	−0.610740	−	0.352611i	−0.773255	+	0.634095i	$0.781373\pi$
$978$		0			0
$979$	−16.7999	+	29.0983i	−0.536928	+	0.929986i
$980$	13.3900	−	8.10598i	0.427729	−	0.258936i
$981$		0			0
$982$	3.92352	+	2.26524i	0.125204	+	0.0722868i
$983$			10.6202i			0.338732i	0.985553	+	0.169366i	$0.0541719\pi$
$983$			10.6202i			0.338732i	−0.985553	+	0.169366i	$0.945828\pi$
$984$		0			0
$985$	12.0222	+	2.24091i	0.383060	+	0.0714013i
$986$	−5.63999	−	9.76876i	−0.179614	−	0.311101i
$987$		0			0
$988$	4.91025	+	2.83493i	0.156216	+	0.0901913i
$989$	2.69256	−	4.66366i	0.0856185	−	0.148296i
$990$		0			0
$991$	16.2764	+	28.1916i	0.517038	+	0.895535i	0.999804	+	0.0197864i	$0.00629862\pi$
$991$	16.2764	+	28.1916i	0.517038	+	0.895535i	−0.482767	+	0.875749i	$0.660368\pi$
$992$	0.696072	−	0.401878i	0.0221003	−	0.0127596i
$993$		0			0
$994$	24.3270	+	10.8952i	0.771607	+	0.345575i
$995$	1.30075	−	0.459123i	0.0412365	−	0.0145552i
$996$		0			0
$997$		−	3.02320i		−	0.0957458i	−0.998853	−	0.0478729i	$-0.984756\pi$
$997$		−	3.02320i		−	0.0957458i	0.998853	−	0.0478729i	$-0.0152442\pi$
$998$	26.7136	−	15.4231i	0.845603	−	0.488209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bq.a.289.33		96
3.2	odd	2		630.2.bq.a.79.3	yes	96
5.4	even	2	inner	1890.2.bq.a.289.7		96
7.4	even	3		1890.2.ba.a.1369.32		96
9.4	even	3		1890.2.ba.a.1549.23		96
9.5	odd	6		630.2.ba.a.499.7	✓	96
15.14	odd	2		630.2.bq.a.79.46	yes	96
21.11	odd	6		630.2.ba.a.529.18	yes	96
35.4	even	6		1890.2.ba.a.1369.23		96
45.4	even	6		1890.2.ba.a.1549.32		96
45.14	odd	6		630.2.ba.a.499.42	yes	96
63.4	even	3	inner	1890.2.bq.a.739.7		96
63.32	odd	6		630.2.bq.a.319.46	yes	96
105.74	odd	6		630.2.ba.a.529.31	yes	96
315.4	even	6	inner	1890.2.bq.a.739.33		96
315.284	odd	6		630.2.bq.a.319.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ba.a.499.7	✓	96	9.5	odd	6
630.2.ba.a.499.42	yes	96	45.14	odd	6
630.2.ba.a.529.18	yes	96	21.11	odd	6
630.2.ba.a.529.31	yes	96	105.74	odd	6
630.2.bq.a.79.3	yes	96	3.2	odd	2
630.2.bq.a.79.46	yes	96	15.14	odd	2
630.2.bq.a.319.3	yes	96	315.284	odd	6
630.2.bq.a.319.46	yes	96	63.32	odd	6
1890.2.ba.a.1369.23		96	35.4	even	6
1890.2.ba.a.1369.32		96	7.4	even	3
1890.2.ba.a.1549.23		96	9.4	even	3
1890.2.ba.a.1549.32		96	45.4	even	6
1890.2.bq.a.289.7		96	5.4	even	2	inner
1890.2.bq.a.289.33		96	1.1	even	1	trivial
1890.2.bq.a.739.7		96	63.4	even	3	inner
1890.2.bq.a.739.33		96	315.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.409739 - 2.19821i) q^{5} +(-1.55043 - 2.14387i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.409739 - 2.19821i) q^{5} +(-1.55043 - 2.14387i) q^{7} -1.00000i q^{8} +(-0.744259 - 2.10857i) q^{10} -3.47091 q^{11} +(1.09687 - 0.633281i) q^{13} +(-2.41464 - 1.08143i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.66021 + 2.69057i) q^{17} +(-2.23829 + 3.87684i) q^{19} +(-1.69883 - 1.45395i) q^{20} +(-3.00590 + 1.73546i) q^{22} -4.79776i q^{23} +(-4.66423 - 1.80138i) q^{25} +(0.633281 - 1.09687i) q^{26} +(-2.63186 + 0.270774i) q^{28} +(-1.04810 + 1.81537i) q^{29} +(-0.401878 + 0.696072i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.69057 + 4.66021i) q^{34} +(-5.34794 + 2.52973i) q^{35} +(5.27556 + 3.04584i) q^{37} +4.47658i q^{38} +(-2.19821 - 0.409739i) q^{40} +(-2.28878 - 3.96429i) q^{41} +(0.972049 + 0.561213i) q^{43} +(-1.73546 + 3.00590i) q^{44} +(-2.39888 - 4.15498i) q^{46} +(8.44192 - 4.87394i) q^{47} +(-2.19235 + 6.64783i) q^{49} +(-4.94003 + 0.772070i) q^{50} -1.26656i q^{52} +(-6.88082 + 3.97264i) q^{53} +(-1.42217 + 7.62978i) q^{55} +(-2.14387 + 1.55043i) q^{56} +2.09621i q^{58} +(6.06736 - 10.5090i) q^{59} +(5.34164 + 9.25199i) q^{61} +0.803755i q^{62} -1.00000 q^{64} +(-0.942649 - 2.67064i) q^{65} +(-1.42681 - 0.823771i) q^{67} +5.38114i q^{68} +(-3.36659 + 4.86478i) q^{70} -10.0748 q^{71} +(-3.28654 + 1.89748i) q^{73} +6.09169 q^{74} +(2.23829 + 3.87684i) q^{76} +(5.38139 + 7.44118i) q^{77} +(0.797244 + 1.38087i) q^{79} +(-2.10857 + 0.744259i) q^{80} +(-3.96429 - 2.28878i) q^{82} +(-9.12037 - 5.26565i) q^{83} +(4.00496 + 11.3465i) q^{85} +1.12243 q^{86} +3.47091i q^{88} +(4.84020 - 8.38348i) q^{89} +(-3.05829 - 1.36970i) q^{91} +(-4.15498 - 2.39888i) q^{92} +(4.87394 - 8.44192i) q^{94} +(7.60497 + 6.50872i) q^{95} +(7.48401 + 4.32089i) q^{97} +(1.42528 + 6.85336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4}+O(q^{10}) \) 96 * q + 48 * q^4	\( 96 q + 48 q^{4} + 8 q^{11} + 2 q^{14} - 48 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} + 12 q^{49} + 12 q^{50} + 12 q^{55} + 4 q^{56} + 24 q^{59} - 6 q^{61} - 96 q^{64} - 18 q^{65} + 6 q^{70} + 32 q^{71} + 8 q^{86} + 66 q^{89} - 12 q^{94} - 30 q^{95}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^11 + 2 * q^14 - 48 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 + 12 * q^49 + 12 * q^50 + 12 * q^55 + 4 * q^56 + 24 * q^59 - 6 * q^61 - 96 * q^64 - 18 * q^65 + 6 * q^70 + 32 * q^71 + 8 * q^86 + 66 * q^89 - 12 * q^94 - 30 * q^95

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