LMFDB - Embedded newform 460.2.o.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label			79.1
Character	$\chi$	$=$	460.79
Dual form			460.2.o.a.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.926113 - 1.06879i) q^{2} +(-2.78960 - 1.79277i) q^{3} +(-0.284630 + 1.97964i) q^{4} +(-2.03400 - 0.928896i) q^{5} +(0.667391 + 4.64180i) q^{6} +(-0.518076 + 1.76441i) q^{7} +(2.37942 - 1.52916i) q^{8} +(3.32161 + 7.27330i) q^{9} +O(q^{10})$	\(q+(-0.926113 - 1.06879i) q^{2} +(-2.78960 - 1.79277i) q^{3} +(-0.284630 + 1.97964i) q^{4} +(-2.03400 - 0.928896i) q^{5} +(0.667391 + 4.64180i) q^{6} +(-0.518076 + 1.76441i) q^{7} +(2.37942 - 1.52916i) q^{8} +(3.32161 + 7.27330i) q^{9} +(0.890917 + 3.03418i) q^{10} +(4.34304 - 5.01214i) q^{12} +(2.36558 - 1.08032i) q^{14} +(4.00875 + 6.23773i) q^{15} +(-3.83797 - 1.12693i) q^{16} +(4.69746 - 10.2860i) q^{18} +(2.41782 - 3.76220i) q^{20} +(4.60839 - 3.99319i) q^{21} +(-4.04789 + 2.57188i) q^{23} -9.37907 q^{24} +(3.27430 + 3.77875i) q^{25} +(2.35764 - 16.3977i) q^{27} +(-3.34543 - 1.52781i) q^{28} +(-0.803155 - 5.58606i) q^{29} +(2.95428 - 10.0614i) q^{30} +(2.34994 + 5.14566i) q^{32} +(2.69272 - 3.10756i) q^{35} +(-15.3440 + 4.50540i) q^{36} +(-6.26018 + 0.900078i) q^{40} +(5.30645 - 11.6195i) q^{41} +(-8.53578 - 1.22726i) q^{42} +(-6.56788 + 10.2198i) q^{43} -17.8793i q^{45} +(6.49761 + 1.94450i) q^{46} +12.7419 q^{47} +(8.68608 + 10.0243i) q^{48} +(3.04405 + 1.95629i) q^{49} +(1.00632 - 6.99909i) q^{50} +(-19.7092 + 12.6663i) q^{54} +(1.46534 + 4.99049i) q^{56} +(-5.22652 + 6.03173i) q^{58} +(-13.4895 + 6.16045i) q^{60} +(3.24883 + 5.05528i) q^{61} +(-14.5539 + 2.09253i) q^{63} +(3.32332 - 7.27706i) q^{64} +(11.7860 - 10.2126i) q^{67} +(15.9028 + 0.0824057i) q^{69} -5.81509 q^{70} +(19.0256 + 12.2270i) q^{72} +(-2.35958 - 16.4113i) q^{75} +(6.75963 + 5.85725i) q^{80} +(-20.2656 + 23.3877i) q^{81} +(-17.3332 + 5.08949i) q^{82} +(14.9100 - 6.80916i) q^{83} +(6.59341 + 10.2595i) q^{84} +(17.0055 - 2.44502i) q^{86} +(-7.77403 + 17.0227i) q^{87} +(-3.88181 + 6.04021i) q^{89} +(-19.1093 + 16.5583i) q^{90} +(-3.93926 - 8.74541i) q^{92} +(-11.8005 - 13.6185i) q^{94} +(2.66956 - 18.5672i) q^{96} +(-0.728267 - 5.06521i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.926113	−	1.06879i	−0.654861	−	0.755750i
$2$	−0.926113	−	1.06879i	−0.654861	−	0.755750i
$3$	−2.78960	−	1.79277i	−1.61058	−	1.03505i	−0.961679	−	0.274178i	$-0.911594\pi$
$3$	−2.78960	−	1.79277i	−1.61058	−	1.03505i	−0.648897	−	0.760876i	$-0.724769\pi$
$4$	−0.284630	+	1.97964i	−0.142315	+	0.989821i
$5$	−2.03400	−	0.928896i	−0.909632	−	0.415415i
$5$	−2.03400	−	0.928896i	−0.909632	−	0.415415i
$6$	0.667391	+	4.64180i	0.272461	+	1.89501i
$7$	−0.518076	+	1.76441i	−0.195814	+	0.666882i	0.801784	+	0.597614i	$0.203885\pi$
$7$	−0.518076	+	1.76441i	−0.195814	+	0.666882i	−0.997598	+	0.0692681i	$0.977934\pi$
$8$	2.37942	−	1.52916i	0.841254	−	0.540641i
$9$	3.32161	+	7.27330i	1.10720	+	2.42443i
$10$	0.890917	+	3.03418i	0.281733	+	0.959493i
$11$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$11$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$12$	4.34304	−	5.01214i	1.25373	−	1.44688i
$13$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$13$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$14$	2.36558	−	1.08032i	0.632227	−	0.288729i
$15$	4.00875	+	6.23773i	1.03505	+	1.61058i
$16$	−3.83797	−	1.12693i	−0.959493	−	0.281733i
$17$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$17$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$18$	4.69746	−	10.2860i	1.10720	−	2.42443i
$19$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$19$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$20$	2.41782	−	3.76220i	0.540641	−	0.841254i
$21$	4.60839	−	3.99319i	1.00563	−	0.871386i
$22$		0			0
$23$	−4.04789	+	2.57188i	−0.844044	+	0.536274i
$23$	−4.04789	+	2.57188i	−0.844044	+	0.536274i
$24$	−9.37907			−1.91450
$25$	3.27430	+	3.77875i	0.654861	+	0.755750i
$26$		0			0
$27$	2.35764	−	16.3977i	0.453727	−	3.15574i
$28$	−3.34543	−	1.52781i	−0.632227	−	0.288729i
$29$	−0.803155	−	5.58606i	−0.149142	−	1.03731i	−0.917628	−	0.397440i	$-0.869899\pi$
$29$	−0.803155	−	5.58606i	−0.149142	−	1.03731i	0.768486	−	0.639866i	$-0.221010\pi$
$30$	2.95428	−	10.0614i	0.539376	−	1.83694i
$31$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$31$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$32$	2.34994	+	5.14566i	0.415415	+	0.909632i
$33$		0			0
$34$		0			0
$35$	2.69272	−	3.10756i	0.455152	−	0.525273i
$36$	−15.3440	+	4.50540i	−2.55733	+	0.750899i
$37$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$37$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$38$		0			0
$39$		0			0
$40$	−6.26018	+	0.900078i	−0.989821	+	0.142315i
$41$	5.30645	−	11.6195i	0.828729	−	1.81466i	0.349713	−	0.936857i	$-0.386279\pi$
$41$	5.30645	−	11.6195i	0.828729	−	1.81466i	0.479016	−	0.877806i	$-0.340994\pi$
$42$	−8.53578	−	1.22726i	−1.31710	−	0.189370i
$43$	−6.56788	+	10.2198i	−1.00159	+	1.55851i	−0.183826	+	0.982959i	$0.558848\pi$
$43$	−6.56788	+	10.2198i	−1.00159	+	1.55851i	−0.817766	+	0.575550i	$0.804788\pi$
$44$		0			0
$45$		−	17.8793i		−	2.66529i
$46$	6.49761	+	1.94450i	0.958020	+	0.286701i
$47$	12.7419			1.85860			0.929300	−	0.369325i	$-0.120411\pi$
$47$	12.7419			1.85860			0.929300	+	0.369325i	$0.120411\pi$
$48$	8.68608	+	10.0243i	1.25373	+	1.44688i
$49$	3.04405	+	1.95629i	0.434865	+	0.279471i
$50$	1.00632	−	6.99909i	0.142315	−	0.989821i
$51$		0			0
$52$		0			0
$53$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$53$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$54$	−19.7092	+	12.6663i	−2.68208	+	1.72367i
$55$		0			0
$56$	1.46534	+	4.99049i	0.195814	+	0.666882i
$57$		0			0
$58$	−5.22652	+	6.03173i	−0.686276	+	0.792005i
$59$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$59$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$60$	−13.4895	+	6.16045i	−1.74149	+	0.795310i
$61$	3.24883	+	5.05528i	0.415970	+	0.647262i	0.984497	−	0.175403i	$-0.0561228\pi$
$61$	3.24883	+	5.05528i	0.415970	+	0.647262i	−0.568527	+	0.822665i	$0.692486\pi$
$62$		0			0
$63$	−14.5539	+	2.09253i	−1.83362	+	0.263635i
$64$	3.32332	−	7.27706i	0.415415	−	0.909632i
$65$		0			0
$66$		0			0
$67$	11.7860	−	10.2126i	1.43989	−	1.24767i	0.520770	−	0.853697i	$-0.325645\pi$
$67$	11.7860	−	10.2126i	1.43989	−	1.24767i	0.919121	−	0.393975i	$-0.128900\pi$
$68$		0			0
$69$	15.9028	+	0.0824057i	1.91447	+	0.00992048i
$70$	−5.81509			−0.695036
$71$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$71$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$72$	19.0256	+	12.2270i	2.24219	+	1.44097i
$73$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$73$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$74$		0			0
$75$	−2.35958	−	16.4113i	−0.272461	−	1.89501i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$79$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$80$	6.75963	+	5.85725i	0.755750	+	0.654861i
$81$	−20.2656	+	23.3877i	−2.25173	+	2.59864i
$82$	−17.3332	+	5.08949i	−1.91413	+	0.562040i
$83$	14.9100	−	6.80916i	1.63658	−	0.747403i	0.636862	−	0.770978i	$-0.280232\pi$
$83$	14.9100	−	6.80916i	1.63658	−	0.747403i	0.999722	+	0.0235755i	$0.00750500\pi$
$84$	6.59341	+	10.2595i	0.719400	+	1.11941i
$85$		0			0
$86$	17.0055	−	2.44502i	1.83375	−	0.263653i
$87$	−7.77403	+	17.0227i	−0.833463	+	1.82503i
$88$		0			0
$89$	−3.88181	+	6.04021i	−0.411471	+	0.640261i	−0.983697	−	0.179835i	$-0.942444\pi$
$89$	−3.88181	+	6.04021i	−0.411471	+	0.640261i	0.572226	+	0.820096i	$0.306080\pi$
$90$	−19.1093	+	16.5583i	−2.01429	+	1.74539i
$91$		0			0
$92$	−3.93926	−	8.74541i	−0.410696	−	0.911772i
$93$		0			0
$94$	−11.8005	−	13.6185i	−1.21712	−	1.40464i
$95$		0			0
$96$	2.66956	−	18.5672i	0.272461	−	1.89501i
$97$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$97$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$98$	−0.728267	−	5.06521i	−0.0735660	−	0.511663i
$99$		0			0
$100$	−8.41254	+	5.40641i	−0.841254	+	0.540641i
$101$	8.29925	+	18.1728i	0.825806	+	1.80826i	0.512789	+	0.858515i	$0.328612\pi$
$101$	8.29925	+	18.1728i	0.825806	+	1.80826i	0.313017	+	0.949748i	$0.398660\pi$
$102$		0			0
$103$	−3.78588	−	3.28048i	−0.373034	−	0.323236i	0.448087	−	0.893990i	$-0.352105\pi$
$103$	−3.78588	−	3.28048i	−0.373034	−	0.323236i	−0.821121	+	0.570754i	$0.806651\pi$
$104$		0			0
$105$	−13.0827	+	3.84143i	−1.27674	+	0.374886i
$106$		0			0
$107$	11.1720	+	17.3840i	1.08004	+	1.68057i	0.580366	+	0.814356i	$0.302910\pi$
$107$	11.1720	+	17.3840i	1.08004	+	1.68057i	0.499672	+	0.866215i	$0.333454\pi$
$108$	31.7906	+	9.33455i	3.05905	+	0.898218i
$109$	−3.27246	+	0.470509i	−0.313445	+	0.0450666i	−0.297242	−	0.954802i	$-0.596067\pi$
$109$	−3.27246	+	0.470509i	−0.313445	+	0.0450666i	−0.0162029	+	0.999869i	$0.505158\pi$
$110$		0			0
$111$		0			0
$112$	3.97672	−	6.18790i	0.375765	−	0.584702i
$113$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$113$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$114$		0			0
$115$	10.6224	−	1.47113i	0.990546	−	0.137184i
$116$	11.2870			1.04797
$117$		0			0
$118$		0			0
$119$		0			0
$120$	19.0770	+	8.71218i	1.74149	+	0.795310i
$121$	1.56546	+	10.8880i	0.142315	+	0.989821i
$122$	2.39425	−	8.15408i	0.216765	−	0.738235i
$123$	−35.6340	+	22.9006i	−3.21301	+	2.06487i
$124$		0			0
$125$	−3.14987	−	10.7275i	−0.281733	−	0.959493i
$126$	15.7150	+	13.6172i	1.40001	+	1.21311i
$127$	5.49982	−	6.34713i	0.488030	−	0.563217i	−0.457308	−	0.889308i	$-0.651186\pi$
$127$	5.49982	−	6.34713i	0.488030	−	0.563217i	0.945338	+	0.326092i	$0.105732\pi$
$128$	−10.8554	+	3.18744i	−0.959493	+	0.281733i
$129$	36.6435	−	16.7345i	3.22628	−	1.47339i
$130$		0			0
$131$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$131$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$132$		0			0
$133$		0			0
$134$	−21.8304	−	3.13873i	−1.88586	−	0.271145i
$135$	−20.0272	+	31.1629i	−1.72367	+	2.68208i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	−14.6397	−	17.0731i	−1.24621	−	1.45336i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	5.38543	+	6.21512i	0.455152	+	0.525273i
$141$	−35.5449	−	22.8433i	−2.99342	−	1.92375i
$142$		0			0
$143$		0			0
$144$	−4.55173	−	31.6580i	−0.379311	−	2.63816i
$145$	−3.55526	+	12.1081i	−0.295248	+	1.00552i
$146$		0			0
$147$	−4.98451	−	10.9145i	−0.411115	−	0.900217i
$148$		0			0
$149$	−17.9029	−	15.5130i	−1.46666	−	1.27087i	−0.891647	−	0.452731i	$-0.850450\pi$
$149$	−17.9029	−	15.5130i	−1.46666	−	1.27087i	−0.575017	−	0.818141i	$-0.695005\pi$
$150$	−15.3550	+	17.7206i	−1.25373	+	1.44688i
$151$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$151$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$157$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$158$		0			0
$159$		0			0
$160$		−	12.6491i		−	1.00000i
$161$	−2.44073	−	8.47455i	−0.192356	−	0.667888i
$162$	43.7648			3.43849
$163$	13.1622	+	15.1900i	1.03094	+	1.18977i	0.981592	+	0.190992i	$0.0611704\pi$
$163$	13.1622	+	15.1900i	1.03094	+	1.18977i	0.0493527	+	0.998781i	$0.484284\pi$
$164$	21.4921	+	13.8121i	1.67825	+	1.07855i
$165$		0			0
$166$	−21.0859	−	9.62961i	−1.63658	−	0.747403i
$167$	−0.849447	−	5.90804i	−0.0657322	−	0.457178i	−0.995931	−	0.0901210i	$-0.971275\pi$
$167$	−0.849447	−	5.90804i	−0.0657322	−	0.457178i	0.930199	−	0.367057i	$-0.119634\pi$
$168$	4.85907	−	16.5485i	0.374886	−	1.27674i
$169$	10.9363	−	7.02833i	0.841254	−	0.540641i
$170$		0			0
$171$		0			0
$172$	−18.3622	−	15.9109i	−1.40010	−	1.21320i
$173$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$173$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$174$	25.3934	−	7.45617i	1.92507	−	0.565251i
$175$	−8.36358	+	3.81952i	−0.632227	+	0.288729i
$176$		0			0
$177$		0			0
$178$	10.0507	−	1.44507i	0.753333	−	0.108313i
$179$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$179$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$180$	35.3947	+	5.08899i	2.63816	+	0.379311i
$181$	11.6194	−	18.0802i	0.863664	−	1.34389i	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	11.6194	−	18.0802i	0.863664	−	1.34389i	0.937993	−	0.346653i	$-0.112682\pi$
$182$		0			0
$183$		−	19.9266i		−	1.47302i
$184$	−5.69882	+	12.3095i	−0.420123	+	0.907467i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−3.62673	+	25.2245i	−0.264506	+	1.83968i
$189$	27.7108	+	12.6551i	2.01566	+	0.920522i
$190$		0			0
$191$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$191$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$192$	−22.3168	+	14.3421i	−1.61058	+	1.03505i
$193$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$193$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$194$		0			0
$195$		0			0
$196$	−4.73919	+	5.46932i	−0.338514	+	0.390666i
$197$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$197$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$198$		0			0
$199$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$199$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$200$	13.5693	+	3.98430i	0.959493	+	0.281733i
$201$	−51.1871	+	7.35960i	−3.61046	+	0.519106i
$202$	11.7369	−	25.7002i	0.825806	−	1.80826i
$203$	10.2722	+	1.47692i	0.720965	+	0.103659i
$204$		0			0
$205$	−21.5866	+	18.7049i	−1.50768	+	1.30641i
$206$			7.08441i			0.493595i
$207$	−32.1516	−	20.8988i	−2.23469	−	1.45256i
$208$		0			0
$209$		0			0
$210$	16.2218	+	10.4251i	1.11941	+	0.719400i
$211$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$211$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$212$		0			0
$213$		0			0
$214$	8.23330	−	28.0400i	0.562817	−	1.91678i
$215$	22.8522	−	14.6862i	1.55851	−	1.00159i
$216$	−19.4650	−	42.6223i	−1.32442	−	2.90008i
$217$		0			0
$218$	3.53355	+	3.06184i	0.239322	+	0.207374i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.05203	+	0.308904i	0.0704492	+	0.0206858i	0.316767	−	0.948503i	$-0.397403\pi$
$223$	1.05203	+	0.308904i	0.0704492	+	0.0206858i	−0.246318	+	0.969189i	$0.579221\pi$
$224$	−10.2965	+	1.48041i	−0.687962	+	0.0989140i
$225$	−16.6080	+	36.3665i	−1.10720	+	2.42443i
$226$		0			0
$227$	−1.52354	+	2.37067i	−0.101121	+	0.157347i	−0.888127	−	0.459598i	$-0.847994\pi$
$227$	−1.52354	+	2.37067i	−0.101121	+	0.157347i	0.787006	+	0.616945i	$0.211630\pi$
$228$		0			0
$229$			28.1523i			1.86035i	0.367112	+	0.930177i	$0.380346\pi$
$229$			28.1523i			1.86035i	−0.367112	+	0.930177i	$0.619654\pi$
$230$	−11.4099	−	9.99071i	−0.752346	−	0.658768i
$231$		0			0
$232$	−10.4530	−	12.0635i	−0.686276	−	0.792005i
$233$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$233$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$234$		0			0
$235$	−25.9171	−	11.8359i	−1.69064	−	0.772091i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$239$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$240$	−8.35597	−	28.4578i	−0.539376	−	1.83694i
$241$	15.6905	+	13.5959i	1.01071	+	0.875787i	0.992277	−	0.124043i	$-0.0395862\pi$
$241$	15.6905	+	13.5959i	1.01071	+	0.875787i	0.0184349	+	0.999830i	$0.494132\pi$
$242$	10.1872	−	11.7567i	0.654861	−	0.755750i
$243$	50.7757	−	14.9091i	3.25726	−	0.956419i
$244$	−10.9324	+	4.99264i	−0.699872	+	0.319621i
$245$	−4.37441	−	6.80671i	−0.279471	−	0.434865i
$246$	57.4770	+	16.8768i	3.66460	+	1.07602i
$247$		0			0
$248$		0			0
$249$	−53.8001	−	7.73529i	−3.40944	−	0.490204i
$250$	−8.54828	+	13.3014i	−0.540641	+	0.841254i
$251$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$251$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$252$		−	29.4071i		−	1.85247i
$253$		0			0
$254$	−11.8772			−0.745243
$255$		0			0
$256$	13.4601	+	8.65025i	0.841254	+	0.540641i
$257$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$257$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$258$	−51.8218	−	23.6662i	−3.22628	−	1.47339i
$259$		0			0
$260$		0			0
$261$	37.9614	−	24.3963i	2.34975	−	1.51009i
$262$		0			0
$263$	5.47924	+	18.6606i	0.337864	+	1.15066i	0.936801	+	0.349863i	$0.113772\pi$
$263$	5.47924	+	18.6606i	0.337864	+	1.15066i	−0.598937	+	0.800796i	$0.704410\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	21.6574	−	9.89059i	1.32541	−	0.605294i
$268$	16.8627	+	26.2389i	1.03006	+	1.60280i
$269$	−7.77284	−	2.28231i	−0.473919	−	0.139155i	0.0360466	−	0.999350i	$-0.488524\pi$
$269$	−7.77284	−	2.28231i	−0.473919	−	0.139155i	−0.509965	+	0.860195i	$0.670342\pi$
$270$	51.8541	−	7.45550i	3.15574	−	0.453727i
$271$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$271$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−4.68954	+	31.4584i	−0.282277	+	1.89357i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	1.65515	−	11.5118i	0.0989140	−	0.687962i
$281$	14.8570	+	6.78498i	0.886296	+	0.404758i	0.805932	−	0.592008i	$-0.201664\pi$
$281$	14.8570	+	6.78498i	0.886296	+	0.404758i	0.0803640	+	0.996766i	$0.474392\pi$
$282$	8.50384	+	59.1455i	0.506396	+	3.52206i
$283$	3.40625	−	11.6006i	0.202480	−	0.689585i	−0.794162	−	0.607706i	$-0.792090\pi$
$283$	3.40625	−	11.6006i	0.202480	−	0.689585i	0.996642	−	0.0818787i	$-0.0260920\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	17.7524	+	15.3825i	1.04789	+	0.908002i
$288$	−29.6203	+	34.1837i	−1.74539	+	2.01429i
$289$	16.3114	−	4.78945i	0.959493	−	0.281733i
$290$	16.2336	−	7.41363i	0.953270	−	0.435344i
$291$		0			0
$292$		0			0
$293$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$293$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$294$	−7.04916	+	15.4355i	−0.411115	+	0.900217i
$295$		0			0
$296$		0			0
$297$		0			0
$298$			33.5012i			1.94068i
$299$		0			0
$300$	33.1600			1.91450
$301$	−14.6293	−	16.8831i	−0.843216	−	0.973123i
$302$		0			0
$303$	9.42804	−	65.5735i	0.541627	−	3.76710i
$304$		0			0
$305$	−1.91229	−	13.3002i	−0.109497	−	0.761570i
$306$		0			0
$307$	−4.81979	+	3.09749i	−0.275080	+	0.176783i	−0.670906	−	0.741542i	$-0.734095\pi$
$307$	−4.81979	+	3.09749i	−0.275080	+	0.176783i	0.395826	+	0.918325i	$0.370458\pi$
$308$		0			0
$309$	4.67995	+	15.9384i	0.266233	+	0.906706i
$310$		0			0
$311$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$311$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$312$		0			0
$313$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$313$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$314$		0			0
$315$	31.5464	+	9.26285i	1.77744	+	0.521902i
$316$		0			0
$317$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$317$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$318$		0			0
$319$		0			0
$320$	−13.5193	+	11.7145i	−0.755750	+	0.654861i
$321$		−	68.5231i		−	3.82458i
$322$	−6.79714	+	10.4570i	−0.378790	+	0.582747i
$323$		0			0
$324$	−40.5312	−	46.7755i	−2.25173	−	2.59864i
$325$		0			0
$326$	4.04525	−	28.1353i	0.224046	−	1.55827i
$327$	9.97237	+	4.55423i	0.551473	+	0.251850i
$328$	−5.14183	−	35.7622i	−0.283910	−	1.97464i
$329$	−6.60129	+	22.4819i	−0.363941	+	1.23947i
$330$		0			0
$331$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$331$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$332$	9.23589	+	31.4545i	0.506885	+	1.72629i
$333$		0			0
$334$	−5.52777	+	6.37939i	−0.302466	+	0.349065i
$335$	−33.4592	+	9.82451i	−1.82807	+	0.536771i
$336$	−22.1869	+	10.1324i	−1.21040	+	0.552769i
$337$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$337$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$338$	−17.6401	−	5.17959i	−0.959493	−	0.281733i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−14.7569	+	12.7870i	−0.796800	+	0.690431i
$344$			34.3607i			1.85260i
$345$	−32.2697	−	14.9396i	−1.73734	−	0.804323i
$346$		0			0
$347$	3.16835	+	3.65647i	0.170086	+	0.196289i	0.834393	−	0.551171i	$-0.185819\pi$
$347$	3.16835	+	3.65647i	0.170086	+	0.196289i	−0.664307	+	0.747460i	$0.731273\pi$
$348$	−31.4862	−	20.2350i	−1.68784	−	1.08471i
$349$	−4.62616	+	32.1756i	−0.247632	+	1.72232i	0.364188	+	0.931325i	$0.381346\pi$
$349$	−4.62616	+	32.1756i	−0.247632	+	1.72232i	−0.611821	+	0.790996i	$0.709563\pi$
$350$	11.8279	+	5.40162i	0.632227	+	0.288729i
$351$		0			0
$352$		0			0
$353$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$353$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$354$		0			0
$355$		0			0
$356$	−10.8526	−	9.40381i	−0.575185	−	0.498401i
$357$		0			0
$358$		0			0
$359$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$359$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$360$	−27.3404	−	42.5425i	−1.44097	−	2.24219i
$361$	18.2304	+	5.35292i	0.959493	+	0.281733i
$362$	−30.0848	+	4.32554i	−1.58122	+	0.227345i
$363$	15.1527	−	33.1798i	0.795310	−	1.74149i
$364$		0			0
$365$		0			0
$366$	−21.2974	+	18.4543i	−1.11323	+	0.964620i
$367$			17.9834i			0.938727i	0.883005	+	0.469364i	$0.155517\pi$
$367$			17.9834i			0.938727i	−0.883005	+	0.469364i	$0.844483\pi$
$368$	18.4340	−	5.30912i	0.960940	−	0.276757i
$369$	102.138			5.31710
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$373$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$374$		0			0
$375$	−10.4450	+	35.5723i	−0.539376	+	1.83694i
$376$	30.3184	−	19.4845i	1.56355	−	1.00484i
$377$		0			0
$378$	−12.1377	−	41.3371i	−0.624294	−	2.12615i
$379$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$379$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$380$		0			0
$381$	−26.7212	+	7.84606i	−1.36897	+	0.401966i
$382$		0			0
$383$	−18.8564	−	29.3411i	−0.963516	−	1.49926i	−0.863547	−	0.504269i	$-0.831762\pi$
$383$	−18.8564	−	29.3411i	−0.963516	−	1.49926i	−0.0999690	−	0.994991i	$-0.531874\pi$
$384$	35.9966	+	10.5696i	1.83694	+	0.539376i
$385$		0			0
$386$		0			0
$387$	−96.1478	−	13.8240i	−4.88747	−	0.702712i
$388$		0			0
$389$	−29.2009	+	25.3028i	−1.48055	+	1.28290i	−0.608424	+	0.793612i	$0.708198\pi$
$389$	−29.2009	+	25.3028i	−1.48055	+	1.28290i	−0.872122	+	0.489289i	$0.837257\pi$
$390$		0			0
$391$		0			0
$392$	10.2346			0.516925
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$397$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$398$		0			0
$399$		0			0
$400$	−8.30830	−	18.1926i	−0.415415	−	0.909632i
$401$	5.73778	+	19.5411i	0.286531	+	0.975836i	0.969439	+	0.245331i	$0.0788968\pi$
$401$	5.73778	+	19.5411i	0.286531	+	0.975836i	−0.682908	+	0.730504i	$0.739285\pi$
$402$	55.2709	+	47.8925i	2.75666	+	2.38866i
$403$		0			0
$404$	−38.3379	+	11.2570i	−1.90738	+	0.560058i
$405$	62.9449	−	28.7460i	3.12776	−	1.42840i
$406$	−7.93468	−	12.3466i	−0.393791	−	0.612751i
$407$		0			0
$408$		0			0
$409$	14.5189	−	31.7919i	0.717913	−	1.57201i	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	14.5189	−	31.7919i	0.717913	−	1.57201i	0.816806	−	0.576912i	$-0.195742\pi$
$410$	39.9833	+	5.74874i	1.97464	+	0.283910i
$411$		0			0
$412$	7.57176	−	6.56097i	0.373034	−	0.323236i
$413$		0			0
$414$	7.43957	+	53.7179i	0.365635	+	2.64009i
$415$	−36.6519			−1.79917
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$419$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$420$	−3.88094	−	26.9925i	−0.189370	−	1.31710i
$421$	−10.2452	+	34.8919i	−0.499321	+	1.70053i	0.194948	+	0.980814i	$0.437546\pi$
$421$	−10.2452	+	34.8919i	−0.499321	+	1.70053i	−0.694269	+	0.719716i	$0.744272\pi$
$422$		0			0
$423$	42.3237	+	92.6759i	2.05785	+	4.50606i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.6027	+	3.11323i	−0.513100	+	0.150660i
$428$	−37.5939	+	17.1686i	−1.81717	+	0.829874i
$429$		0			0
$430$	−36.8603	−	10.8231i	−1.77756	−	0.521939i
$431$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$431$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$432$	−27.5276	+	60.2771i	−1.32442	+	2.90008i
$433$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$433$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$434$		0			0
$435$	31.6247	−	27.4030i	1.51629	−	1.31387i
$436$		−	6.61223i		−	0.316668i
$437$		0			0
$438$		0			0
$439$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$439$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$440$		0			0
$441$	−4.11757	+	28.6384i	−0.196075	+	1.36373i
$442$		0			0
$443$	−2.16702	−	15.0719i	−0.102958	−	0.716089i	−0.974274	−	0.225367i	$-0.927642\pi$
$443$	−2.16702	−	15.0719i	−0.102958	−	0.716089i	0.871316	−	0.490722i	$-0.163267\pi$
$444$		0			0
$445$	13.5063	−	8.67998i	0.640261	−	0.411471i
$446$	−0.644145	−	1.41048i	−0.0305012	−	0.0667883i
$447$	22.1308	+	75.3707i	1.04675	+	3.56491i
$448$	11.1179	+	9.63375i	0.525273	+	0.455152i
$449$	4.37179	−	5.04532i	0.206318	−	0.238103i	−0.643155	−	0.765736i	$-0.722375\pi$
$449$	4.37179	−	5.04532i	0.206318	−	0.238103i	0.849473	+	0.527633i	$0.176920\pi$
$450$	54.2491	−	15.9290i	2.55733	−	0.750899i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	3.94472	−	0.567165i	0.185135	−	0.0266184i
$455$		0			0
$456$		0			0
$457$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$457$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$458$	30.0889	−	26.0722i	1.40596	−	1.21827i
$459$		0			0
$460$	−0.111137	+	21.4473i	−0.00518177	+	0.999987i
$461$	20.7445			0.966169			0.483084	−	0.875574i	$-0.339516\pi$
$461$	20.7445			0.966169			0.483084	+	0.875574i	$0.339516\pi$
$462$		0			0
$463$	20.0170	+	12.8642i	0.930269	+	0.597848i	0.915620	−	0.402045i	$-0.131700\pi$
$463$	20.0170	+	12.8642i	0.930269	+	0.597848i	0.0146494	+	0.999893i	$0.495337\pi$
$464$	−3.21262	+	22.3443i	−0.149142	+	1.03731i
$465$		0			0
$466$		0			0
$467$	−8.01825	+	27.3076i	−0.371040	+	1.26365i	0.536578	+	0.843851i	$0.319717\pi$
$467$	−8.01825	+	27.3076i	−0.371040	+	1.26365i	−0.907618	+	0.419797i	$0.862101\pi$
$468$		0			0
$469$	11.9132	+	26.0862i	0.550100	+	1.20455i
$470$	11.3520	+	38.6613i	0.523628	+	1.78331i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$479$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$480$	−22.6769	+	35.2859i	−1.03505	+	1.61058i
$481$		0			0
$482$		−	29.3611i		−	1.33736i
$483$	−8.38425	+	28.0162i	−0.381496	+	1.27478i
$484$	−22.0000			−1.00000
$485$		0			0
$486$	−62.9588	−	40.4611i	−2.85587	−	1.83535i
$487$	−4.32646	+	30.0912i	−0.196051	+	1.36356i	0.619554	+	0.784954i	$0.287313\pi$
$487$	−4.32646	+	30.0912i	−0.196051	+	1.36356i	−0.815605	+	0.578609i	$0.803596\pi$
$488$	15.4607	+	7.06066i	0.699872	+	0.319621i
$489$	−9.48517	−	65.9708i	−0.428934	−	2.98330i
$490$	−3.22376	+	10.9791i	−0.145634	+	0.495985i
$491$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$491$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$492$	−35.1924	−	77.0607i	−1.58660	−	3.47416i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	41.5576	+	64.6649i	1.86224	+	2.89770i
$499$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$499$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$500$	22.1331	−	3.18226i	0.989821	−	0.142315i
$501$	−8.22211	+	18.0039i	−0.367337	+	0.804356i
$502$		0			0
$503$	14.5540	−	22.6465i	0.648932	−	1.00976i	−0.348441	−	0.937331i	$-0.613289\pi$
$503$	14.5540	−	22.6465i	0.648932	−	1.00976i	0.997374	−	0.0724280i	$-0.0230747\pi$
$504$	−31.4301	+	27.2343i	−1.40001	+	1.21311i
$505$		−	44.6726i		−	1.98791i
$506$		0			0
$507$	−43.1080			−1.91450
$508$	10.9996	+	12.6943i	0.488030	+	0.563217i
$509$	−36.5207	−	23.4704i	−1.61875	−	1.04031i	−0.956793	−	0.290770i	$-0.906089\pi$
$509$	−36.5207	−	23.4704i	−1.61875	−	1.04031i	−0.661960	−	0.749539i	$-0.730275\pi$
$510$		0			0
$511$		0			0
$512$	−3.22022	−	22.3971i	−0.142315	−	0.989821i
$513$		0			0
$514$		0			0
$515$	4.65325	+	10.1892i	0.205047	+	0.448989i
$516$	22.6986	+	77.3042i	0.999249	+	3.40313i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−16.6373	−	25.8882i	−0.728895	−	1.13418i	−0.985829	−	0.167754i	$-0.946349\pi$
$521$	−16.6373	−	25.8882i	−0.728895	−	1.13418i	0.256934	−	0.966429i	$-0.417288\pi$
$522$	−61.2311	−	17.9791i	−2.68001	−	0.786922i
$523$	13.0724	−	1.87953i	0.571617	−	0.0821861i	0.149555	−	0.988753i	$-0.452216\pi$
$523$	13.0724	−	1.87953i	0.571617	−	0.0821861i	0.422061	+	0.906567i	$0.361307\pi$
$524$		0			0
$525$	30.1785	+	4.33902i	1.31710	+	0.189370i
$526$	14.8699	−	23.1379i	0.648357	−	1.00886i
$527$		0			0
$528$		0			0
$529$	9.77085	−	20.8214i	0.424820	−	0.905278i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−30.6281	−	13.9874i	−1.32541	−	0.605294i
$535$	−6.57593	−	45.7366i	−0.284302	−	1.97736i
$536$	12.4271	−	42.3229i	0.536771	−	1.82807i
$537$		0			0
$538$	4.75921	+	10.4212i	0.205184	+	0.449291i
$539$		0			0
$540$	−55.9912	−	48.5166i	−2.40948	−	2.08782i
$541$	11.4343	−	13.1959i	0.491601	−	0.567337i	−0.454692	−	0.890649i	$-0.650251\pi$
$541$	11.4343	−	13.1959i	0.491601	−	0.567337i	0.946293	+	0.323311i	$0.104796\pi$
$542$		0			0
$543$	−64.8270	+	29.6055i	−2.78199	+	1.27049i
$544$		0			0
$545$	7.09324	+	2.08276i	0.303841	+	0.0892158i
$546$		0			0
$547$	9.24861	−	20.2516i	0.395442	−	0.865897i	−0.602270	−	0.798292i	$-0.705737\pi$
$547$	9.24861	−	20.2516i	0.395442	−	0.865897i	0.997712	−	0.0676046i	$-0.0215356\pi$
$548$		0			0
$549$	−25.9772	+	40.4214i	−1.10868	+	1.72514i
$550$		0			0
$551$		0			0
$552$	37.9655	−	24.1219i	1.61592	−	1.02669i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$557$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$558$		0			0
$559$		0			0
$560$	−13.8366	+	8.89222i	−0.584702	+	0.375765i
$561$		0			0
$562$	−6.50756	−	22.1627i	−0.274505	−	0.934878i
$563$	−34.6974	−	30.0654i	−1.46232	−	1.26711i	−0.896848	−	0.442338i	$-0.854149\pi$
$563$	−34.6974	−	30.0654i	−1.46232	−	1.26711i	−0.565471	−	0.824768i	$-0.691306\pi$
$564$	55.3387	−	63.8643i	2.33018	−	2.68917i
$565$		0			0
$566$	−15.5532	+	7.10291i	−0.653750	+	0.298558i
$567$	−30.7663	−	47.8733i	−1.29206	−	2.01049i
$568$		0			0
$569$	45.3323	−	6.51780i	1.90043	−	0.273240i	0.910360	−	0.413818i	$-0.135805\pi$
$569$	45.3323	−	6.51780i	1.90043	−	0.273240i	0.990070	+	0.140578i	$0.0448960\pi$
$570$		0			0
$571$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$571$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$572$		0			0
$573$		0			0
$574$		−	33.2195i		−	1.38656i
$575$	−22.9725	−	6.87484i	−0.958020	−	0.286701i
$576$	63.9670			2.66529
$577$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$577$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$578$	−20.2251	−	12.9979i	−0.841254	−	0.540641i
$579$		0			0
$580$	−22.9578	−	10.4845i	−0.953270	−	0.435344i
$581$	4.28961	+	29.8349i	0.177963	+	1.23776i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	31.6692	−	36.5482i	1.30713	−	1.50851i	0.606023	−	0.795447i	$-0.292764\pi$
$587$	31.6692	−	36.5482i	1.30713	−	1.50851i	0.701104	−	0.713059i	$-0.252691\pi$
$588$	23.0256	−	6.76094i	0.949562	−	0.278817i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$593$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$594$		0			0
$595$		0			0
$596$	35.8058	−	31.0259i	1.46666	−	1.27087i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−30.7099	−	35.4412i	−1.25373	−	1.44688i
$601$	−10.1642	−	6.53215i	−0.414607	−	0.266452i	0.316665	−	0.948537i	$-0.397437\pi$
$601$	−10.1642	−	6.53215i	−0.414607	−	0.266452i	−0.731272	+	0.682085i	$0.761073\pi$
$602$	−4.49612	+	31.2712i	−0.183248	+	1.27452i
$603$	113.428	+	51.8009i	4.61915	+	2.10950i
$604$		0			0
$605$	6.92970	−	23.6004i	0.281733	−	0.959493i
$606$	−78.8158	+	50.6518i	−3.20167	+	2.05759i
$607$	−9.26049	−	20.2777i	−0.375872	−	0.823045i	−0.999157	−	0.0410500i	$-0.986930\pi$
$607$	−9.26049	−	20.2777i	−0.375872	−	0.823045i	0.623285	−	0.781995i	$-0.285798\pi$
$608$		0			0
$609$	−26.0075	−	22.5356i	−1.05388	−	0.913189i
$610$	−12.4442	+	14.3614i	−0.503851	+	0.581475i
$611$		0			0
$612$		0			0
$613$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$613$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$614$	7.77425	+	2.28272i	0.313743	+	0.0921233i
$615$	93.7517	−	13.4795i	3.78043	−	0.543544i
$616$		0			0
$617$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$617$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$618$	12.7007	−	19.7627i	0.510897	−	0.794971i
$619$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$619$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$620$		0			0
$621$	32.6295	+	72.4397i	1.30938	+	2.90691i
$622$		0			0
$623$	−8.64630	−	9.97836i	−0.346407	−	0.399775i
$624$		0			0
$625$	−3.55787	+	24.7455i	−0.142315	+	0.989821i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−19.3154	−	42.2949i	−0.769546	−	1.68507i
$631$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$631$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−17.0825	+	7.80130i	−0.677897	+	0.309585i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	25.0407	+	3.60031i	0.989821	+	0.142315i
$641$	5.14697	−	8.00885i	0.203293	−	0.316330i	−0.724605	−	0.689165i	$-0.757978\pi$
$641$	5.14697	−	8.00885i	0.203293	−	0.316330i	0.927898	+	0.372834i	$0.121614\pi$
$642$	−73.2368	+	63.4601i	−2.89043	+	2.50457i
$643$		−	35.2467i		−	1.38999i	−0.719012	−	0.694997i	$-0.755406\pi$
$643$		−	35.2467i		−	1.38999i	0.719012	−	0.694997i	$-0.244594\pi$
$644$	17.4713	−	2.41966i	0.688465	−	0.0953478i
$645$	−90.0775			−3.54680
$646$		0			0
$647$	−8.56277	−	5.50296i	−0.336637	−	0.216344i	0.361390	−	0.932415i	$-0.382302\pi$
$647$	−8.56277	−	5.50296i	−0.336637	−	0.216344i	−0.698027	+	0.716071i	$0.745939\pi$
$648$	−12.4568	+	86.6387i	−0.489348	+	3.40349i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−33.8171	+	21.7330i	−1.32438	+	0.851128i
$653$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$653$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$654$	−4.36802	−	14.8761i	−0.170803	−	0.581702i
$655$		0			0
$656$	−33.4604	+	38.6154i	−1.30641	+	1.50768i
$657$		0			0
$658$	30.1420	−	13.7654i	1.17506	−	0.536631i
$659$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$659$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$660$		0			0
$661$	45.3619	−	6.52206i	1.76437	−	0.253679i	0.817647	−	0.575720i	$-0.195278\pi$
$661$	45.3619	−	6.52206i	1.76437	−	0.253679i	0.946726	+	0.322041i	$0.104369\pi$
$662$		0			0
$663$		0			0
$664$	25.0649	−	39.0017i	0.972705	−	1.51356i
$665$		0			0
$666$		0			0
$667$	17.6178	+	20.5462i	0.682163	+	0.795550i
$668$	11.9376			0.461879
$669$	−2.38095	−	2.74777i	−0.0920529	−	0.106235i
$670$	41.4874	+	26.6623i	1.60280	+	1.03006i
$671$		0			0
$672$	31.3771	+	14.3294i	1.21040	+	0.552769i
$673$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$673$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$674$		0			0
$675$	69.6824	−	44.7822i	2.68208	−	1.72367i
$676$	10.8008	+	23.6504i	0.415415	+	0.909632i
$677$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$677$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	8.50012	−	3.88187i	0.325725	−	0.148754i
$682$		0			0
$683$	−48.0543	−	14.1100i	−1.83875	−	0.539905i	−0.838757	−	0.544505i	$-0.816717\pi$
$683$	−48.0543	−	14.1100i	−1.83875	−	0.539905i	−0.999989	+	0.00460060i	$0.998536\pi$
$684$		0			0
$685$		0			0
$686$	27.3332	+	3.92992i	1.04359	+	0.150045i
$687$	50.4704	−	78.5335i	1.92557	−	2.99624i
$688$	36.7244	−	31.8219i	1.40010	−	1.21320i
$689$		0			0
$690$	13.9180	+	48.3254i	0.529850	+	1.83971i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	0.973753	−	6.77260i	0.0369632	−	0.257084i
$695$		0			0
$696$	7.53285	+	52.3921i	0.285532	+	1.98592i
$697$		0			0
$698$	38.6734	−	24.8539i	1.46381	−	0.940733i
$699$		0			0
$700$	−5.18076	−	17.6441i	−0.195814	−	0.666882i
$701$	−38.3117	−	33.1973i	−1.44701	−	1.25384i	−0.912745	−	0.408531i	$-0.866041\pi$
$701$	−38.3117	−	33.1973i	−1.44701	−	1.25384i	−0.534270	−	0.845314i	$-0.679413\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	51.0792	+	79.4807i	1.92375	+	2.99342i
$706$		0			0
$707$	−36.3638	+	5.22833i	−1.36760	+	0.196632i
$708$		0			0
$709$	26.5597	+	3.81871i	0.997470	+	0.143415i	0.621664	−	0.783284i	$-0.286457\pi$
$709$	26.5597	+	3.81871i	0.997470	+	0.143415i	0.375806	+	0.926698i	$0.377366\pi$
$710$		0			0
$711$		0			0
$712$			20.3081i			0.761079i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$719$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$720$	−20.1487	+	68.6203i	−0.750899	+	2.55733i
$721$	7.74948	−	4.98029i	0.288606	−	0.185476i
$722$	−11.1622	−	24.4419i	−0.415415	−	0.909632i
$723$	−19.3959	−	66.0564i	−0.721341	−	2.45666i
$724$	32.4850	+	28.1484i	1.20730	+	1.04613i
$725$	18.4786	−	21.3254i	0.686276	−	0.792005i
$726$	−49.4953	+	14.5331i	−1.83694	+	0.539376i
$727$	16.8036	−	7.67394i	0.623210	−	0.284611i	−0.0786754	−	0.996900i	$-0.525069\pi$
$727$	16.8036	−	7.67394i	0.623210	−	0.284611i	0.701886	+	0.712290i	$0.252342\pi$
$728$		0			0
$729$	−79.2939	−	23.2828i	−2.93681	−	0.862326i
$730$		0			0
$731$		0			0
$732$	39.4475	+	5.67170i	1.45802	+	0.209632i
$733$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$733$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$734$	19.2205	−	16.6547i	0.709443	−	0.614736i
$735$			26.8303i			0.989650i
$736$	−22.7463	−	14.7853i	−0.838441	−	0.544993i
$737$		0			0
$738$	−94.5915	−	109.164i	−3.48196	−	4.01840i
$739$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$739$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.4376	+	42.3585i	−0.456290	+	1.55398i	0.334804	+	0.942288i	$0.391330\pi$
$743$	−12.4376	+	42.3585i	−0.456290	+	1.55398i	−0.791094	+	0.611694i	$0.790488\pi$
$744$		0			0
$745$	22.0046	+	48.1833i	0.806186	+	1.76530i
$746$		0			0
$747$	99.0502	+	85.8275i	3.62406	+	3.14026i
$748$		0			0
$749$	−36.4603	+	10.7057i	−1.33223	+	0.391178i
$750$	47.6926	−	21.7805i	1.74149	−	0.795310i
$751$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$751$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$752$	−48.9032	−	14.3593i	−1.78331	−	0.523628i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−32.9399	+	51.2554i	−1.19801	+	1.86414i
$757$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$757$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.7893	+	22.8381i	0.717362	+	0.827880i	0.990987	−	0.133956i	$-0.0427681\pi$
$761$	19.7893	+	22.8381i	0.717362	+	0.827880i	−0.273625	+	0.961837i	$0.588223\pi$
$762$	33.1327	+	21.2931i	1.20027	+	0.771367i
$763$	0.865216	−	6.01771i	0.0313229	−	0.217856i
$764$		0			0
$765$		0			0
$766$	−13.8964	+	47.3267i	−0.502096	+	1.70998i
$767$		0			0
$768$	−22.0403	−	48.2615i	−0.795310	−	1.74149i
$769$	6.05582	+	20.6242i	0.218378	+	0.743728i	0.993691	+	0.112151i	$0.0357740\pi$
$769$	6.05582	+	20.6242i	0.218378	+	0.743728i	−0.775313	+	0.631577i	$0.782408\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$773$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$774$	74.2688	+	115.565i	2.66954	+	4.15388i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	54.0867	+	7.77650i	1.93910	+	0.278801i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−93.4922			−3.34114
$784$	−9.47838	−	10.9386i	−0.338514	−	0.390666i
$785$		0			0
$786$		0			0
$787$	−1.76132	−	0.804366i	−0.0627842	−	0.0286726i	0.383775	−	0.923426i	$-0.374624\pi$
$787$	−1.76132	−	0.804366i	−0.0627842	−	0.0286726i	−0.446560	+	0.894754i	$0.647351\pi$
$788$		0			0
$789$	18.1692	−	61.8785i	0.646839	−	2.20293i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$797$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$798$		0			0
$799$		0			0
$800$	−11.7497	+	25.7283i	−0.415415	+	0.909632i
$801$	−56.8261	−	8.17036i	−2.00785	−	0.288685i
$802$	15.5715	−	24.2298i	0.549849	−	0.855582i
$803$		0			0
$804$		−	103.427i		−	3.64759i
$805$	−2.90755	+	19.5044i	−0.102478	+	0.687440i
$806$		0			0
$807$	17.5915	+	20.3016i	0.619249	+	0.714651i
$808$	47.5366	+	30.5499i	1.67233	+	1.07474i
$809$	6.95660	−	48.3842i	0.244581	−	1.70110i	−0.383983	−	0.923340i	$-0.625448\pi$
$809$	6.95660	−	48.3842i	0.244581	−	1.70110i	0.628564	−	0.777758i	$-0.283643\pi$
$810$	−89.0176	−	40.6530i	−3.12776	−	1.42840i
$811$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$811$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$812$	−5.84753	+	19.9149i	−0.205208	+	0.698875i
$813$		0			0
$814$		0			0
$815$	−12.6620	−	43.1228i	−0.443530	−	1.51053i
$816$		0			0
$817$		0			0
$818$	−47.4251	+	13.9253i	−1.65818	+	0.486885i
$819$		0			0
$820$	−30.8849	−	48.0578i	−1.07855	−	1.67825i
$821$	46.4547	+	13.6403i	1.62128	+	0.476051i	0.961362	−	0.275286i	$-0.0887726\pi$
$821$	46.4547	+	13.6403i	1.62128	+	0.476051i	0.659919	+	0.751337i	$0.270591\pi$
$822$		0			0
$823$	20.1333	−	44.0859i	0.701804	−	1.53674i	−0.135966	−	0.990714i	$-0.543414\pi$
$823$	20.1333	−	44.0859i	0.701804	−	1.53674i	0.837770	−	0.546023i	$-0.183859\pi$
$824$	−14.0246	−	2.01643i	−0.488570	−	0.0702458i
$825$		0			0
$826$		0			0
$827$			47.4342i			1.64945i	0.565536	+	0.824724i	$0.308669\pi$
$827$			47.4342i			1.64945i	−0.565536	+	0.824724i	$0.691331\pi$
$828$	50.5234	−	57.7002i	1.75581	−	2.00522i
$829$	−49.9518			−1.73490			−0.867448	−	0.497527i	$-0.834241\pi$
$829$	−49.9518			−1.73490			−0.867448	+	0.497527i	$0.834241\pi$
$830$	33.9438	+	39.1732i	1.17821	+	1.35972i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3.76018	+	12.8060i	−0.130126	+	0.443169i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$839$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$840$	−25.2552	+	29.1460i	−0.871386	+	1.00563i
$841$	−2.73375	+	0.802701i	−0.0942671	+	0.0276793i
$842$	46.7804	−	21.3639i	1.61216	−	0.736249i
$843$	−29.2813	−	45.5626i	−1.00850	−	1.56926i
$844$		0			0
$845$	−28.7730	+	4.13693i	−0.989821	+	0.142315i
$846$	59.8547	−	131.064i	2.05785	−	4.50606i
$847$	−20.0219	−	2.87872i	−0.687962	−	0.0989140i
$848$		0			0
$849$	−30.2993	+	26.2545i	−1.03987	+	0.901051i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$853$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$854$	13.1467	+	8.44886i	0.449870	+	0.289114i
$855$		0			0
$856$	53.1658	+	24.2800i	1.81717	+	0.829874i
$857$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$857$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$858$		0			0
$859$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$859$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$860$	22.5691	+	49.4194i	0.769599	+	1.68519i
$861$	−21.9448	−	74.7370i	−0.747875	−	2.54703i
$862$		0			0
$863$	−38.1828	+	44.0653i	−1.29976	+	1.50000i	−0.556840	+	0.830620i	$0.687986\pi$
$863$	−38.1828	+	44.0653i	−1.29976	+	1.50000i	−0.742919	+	0.669382i	$0.766559\pi$
$864$	89.9173	−	26.4021i	3.05905	−	0.898218i
$865$		0			0
$866$		0			0
$867$	−54.0886	−	15.8818i	−1.83694	−	0.539376i
$868$		0			0
$869$		0			0
$870$	−58.5761	−	8.42198i	−1.98592	−	0.285532i
$871$		0			0
$872$	−7.06709	+	6.12367i	−0.239322	+	0.207374i
$873$		0			0
$874$		0			0
$875$	20.5595			0.695036
$876$		0			0
$877$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$877$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−11.9514	+	40.7026i	−0.402651	+	1.37130i	0.469873	+	0.882734i	$0.344300\pi$
$881$	−11.9514	+	40.7026i	−0.402651	+	1.37130i	−0.872524	+	0.488570i	$0.837519\pi$
$882$	34.4218	−	22.1215i	1.15904	−	0.744870i
$883$	−8.05455	−	17.6370i	−0.271057	−	0.593533i	0.724332	−	0.689452i	$-0.242148\pi$
$883$	−8.05455	−	17.6370i	−0.271057	−	0.593533i	−0.995389	+	0.0959188i	$0.969421\pi$
$884$		0			0
$885$		0			0
$886$	−14.1018	+	16.2744i	−0.473761	+	0.546749i
$887$	−12.2404	+	3.59411i	−0.410993	+	0.120678i	−0.480692	−	0.876890i	$-0.659614\pi$
$887$	−12.2404	+	3.59411i	−0.410993	+	0.120678i	0.0696988	+	0.997568i	$0.477796\pi$
$888$		0			0
$889$	8.34959	+	12.9922i	0.280036	+	0.435745i
$890$	−21.7855	−	6.39679i	−0.730250	−	0.214421i
$891$		0			0
$892$	−0.910959	+	1.99472i	−0.0305012	+	0.0667883i
$893$		0			0
$894$	60.0599	−	93.4551i	2.00870	−	3.12560i
$895$		0			0
$896$		−	20.8047i		−	0.695036i
$897$		0			0
$898$	−9.44117			−0.315056
$899$		0			0
$900$	−67.2656	−	43.2290i	−2.24219	−	1.44097i
$901$		0			0
$902$		0			0
$903$	10.5424	+	73.3238i	0.350828	+	2.44006i
$904$		0			0
$905$	−40.4285	+	25.9818i	−1.34389	+	0.863664i
$906$		0			0
$907$	11.9884	+	40.8289i	0.398070	+	1.35570i	0.878112	+	0.478455i	$0.158803\pi$
$907$	11.9884	+	40.8289i	0.398070	+	1.35570i	−0.480042	+	0.877245i	$0.659379\pi$
$908$	−4.25944	−	3.69082i	−0.141354	−	0.122484i
$909$	−104.610	+	120.726i	−3.46968	+	4.00422i
$910$		0			0
$911$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$911$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−18.5097	+	40.5306i	−0.611913	+	1.33990i
$916$	−55.7314	−	8.01297i	−1.84142	−	0.264756i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	23.0256	−	19.7439i	0.759133	−	0.650936i
$921$	18.9984			0.626018
$922$	−19.2118	−	22.1716i	−0.632706	−	0.730182i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−4.78892	−	33.3077i	−0.157374	−	1.09456i
$927$	11.2848	−	38.4323i	0.370640	−	1.26228i
$928$	26.8566	−	17.2597i	0.881611	−	0.566577i
$929$	−24.8015	−	54.3077i	−0.813710	−	1.78178i	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−24.8015	−	54.3077i	−0.813710	−	1.78178i	−0.223150	−	0.974784i	$-0.571634\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	36.6120	−	16.7201i	1.19798	−	0.547099i
$935$		0			0
$936$		0			0
$937$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$937$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$938$	16.8478	−	36.8915i	0.550100	−	1.20455i
$939$		0			0
$940$	30.8077	−	47.9377i	1.00484	−	1.56355i
$941$	−26.6084	+	23.0563i	−0.867410	+	0.751615i	−0.969999	−	0.243109i	$-0.921833\pi$
$941$	−26.6084	+	23.0563i	−0.867410	+	0.751615i	0.102589	+	0.994724i	$0.467287\pi$
$942$		0			0
$943$	8.40406	+	60.6821i	0.273674	+	1.97608i
$944$		0			0
$945$	−44.6084	−	51.4809i	−1.45111	−	1.67467i
$946$		0			0
$947$	−4.64703	+	32.3208i	−0.151008	+	1.05029i	0.763526	+	0.645777i	$0.223466\pi$
$947$	−4.64703	+	32.3208i	−0.151008	+	1.05029i	−0.914534	+	0.404509i	$0.867443\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$953$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	58.7147	−	8.44190i	1.89501	−	0.272461i
$961$	12.8779	−	28.1986i	0.415415	−	0.909632i
$962$		0			0
$963$	−89.3299	+	139.000i	−2.87861	+	4.47921i
$964$	−31.3809	+	27.1917i	−1.01071	+	0.875787i
$965$		0			0
$966$	37.7083	−	16.9852i	1.21324	−	0.546490i
$967$	−0.506843			−0.0162990			−0.00814949	−	0.999967i	$-0.502594\pi$
$967$	−0.506843			−0.0162990			−0.00814949	+	0.999967i	$0.502594\pi$
$968$	20.3745	+	23.5134i	0.654861	+	0.755750i
$969$		0			0
$970$		0			0
$971$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$971$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$972$	15.0624	+	104.761i	0.483127	+	3.36022i
$973$		0			0
$974$	36.1680	−	23.2438i	1.15890	−	0.744778i
$975$		0			0
$976$	−6.77197	−	23.0632i	−0.216765	−	0.738235i
$977$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$977$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$978$	−61.7247	+	71.2341i	−1.97374	+	2.27781i
$979$		0			0
$980$	14.7199	−	6.72237i	0.470211	−	0.214738i
$981$	−14.2920	−	22.2388i	−0.456308	−	0.710029i
$982$		0			0
$983$	−61.4261	+	8.83173i	−1.95919	+	0.281689i	−0.999999	−	0.00108163i	$-0.999656\pi$
$983$	−61.4261	+	8.83173i	−1.95919	+	0.281689i	−0.959188	+	0.282770i	$0.908747\pi$
$984$	−49.7696	+	108.980i	−1.58660	+	3.47416i
$985$		0			0
$986$		0			0
$987$	58.7198	−	50.8810i	1.86907	−	1.61956i
$988$		0			0
$989$	0.301897	−	58.2606i	0.00959977	−	1.85258i
$990$		0			0
$991$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$991$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	30.6262	−	104.303i	0.970429	−	3.30498i
$997$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$997$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.a.79.1	✓	40
4.3	odd	2	inner	460.2.o.a.79.4	yes	40
5.4	even	2	inner	460.2.o.a.79.4	yes	40
20.19	odd	2	CM	460.2.o.a.79.1	✓	40
23.7	odd	22	inner	460.2.o.a.99.1	yes	40
92.7	even	22	inner	460.2.o.a.99.4	yes	40
115.99	odd	22	inner	460.2.o.a.99.4	yes	40
460.99	even	22	inner	460.2.o.a.99.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.a.79.1	✓	40	1.1	even	1	trivial
460.2.o.a.79.1	✓	40	20.19	odd	2	CM
460.2.o.a.79.4	yes	40	4.3	odd	2	inner
460.2.o.a.79.4	yes	40	5.4	even	2	inner
460.2.o.a.99.1	yes	40	23.7	odd	22	inner
460.2.o.a.99.1	yes	40	460.99	even	22	inner
460.2.o.a.99.4	yes	40	92.7	even	22	inner
460.2.o.a.99.4	yes	40	115.99	odd	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.926113 - 1.06879i) q^{2} +(-2.78960 - 1.79277i) q^{3} +(-0.284630 + 1.97964i) q^{4} +(-2.03400 - 0.928896i) q^{5} +(0.667391 + 4.64180i) q^{6} +(-0.518076 + 1.76441i) q^{7} +(2.37942 - 1.52916i) q^{8} +(3.32161 + 7.27330i) q^{9} +O(q^{10})\)	\(q+(-0.926113 - 1.06879i) q^{2} +(-2.78960 - 1.79277i) q^{3} +(-0.284630 + 1.97964i) q^{4} +(-2.03400 - 0.928896i) q^{5} +(0.667391 + 4.64180i) q^{6} +(-0.518076 + 1.76441i) q^{7} +(2.37942 - 1.52916i) q^{8} +(3.32161 + 7.27330i) q^{9} +(0.890917 + 3.03418i) q^{10} +(4.34304 - 5.01214i) q^{12} +(2.36558 - 1.08032i) q^{14} +(4.00875 + 6.23773i) q^{15} +(-3.83797 - 1.12693i) q^{16} +(4.69746 - 10.2860i) q^{18} +(2.41782 - 3.76220i) q^{20} +(4.60839 - 3.99319i) q^{21} +(-4.04789 + 2.57188i) q^{23} -9.37907 q^{24} +(3.27430 + 3.77875i) q^{25} +(2.35764 - 16.3977i) q^{27} +(-3.34543 - 1.52781i) q^{28} +(-0.803155 - 5.58606i) q^{29} +(2.95428 - 10.0614i) q^{30} +(2.34994 + 5.14566i) q^{32} +(2.69272 - 3.10756i) q^{35} +(-15.3440 + 4.50540i) q^{36} +(-6.26018 + 0.900078i) q^{40} +(5.30645 - 11.6195i) q^{41} +(-8.53578 - 1.22726i) q^{42} +(-6.56788 + 10.2198i) q^{43} -17.8793i q^{45} +(6.49761 + 1.94450i) q^{46} +12.7419 q^{47} +(8.68608 + 10.0243i) q^{48} +(3.04405 + 1.95629i) q^{49} +(1.00632 - 6.99909i) q^{50} +(-19.7092 + 12.6663i) q^{54} +(1.46534 + 4.99049i) q^{56} +(-5.22652 + 6.03173i) q^{58} +(-13.4895 + 6.16045i) q^{60} +(3.24883 + 5.05528i) q^{61} +(-14.5539 + 2.09253i) q^{63} +(3.32332 - 7.27706i) q^{64} +(11.7860 - 10.2126i) q^{67} +(15.9028 + 0.0824057i) q^{69} -5.81509 q^{70} +(19.0256 + 12.2270i) q^{72} +(-2.35958 - 16.4113i) q^{75} +(6.75963 + 5.85725i) q^{80} +(-20.2656 + 23.3877i) q^{81} +(-17.3332 + 5.08949i) q^{82} +(14.9100 - 6.80916i) q^{83} +(6.59341 + 10.2595i) q^{84} +(17.0055 - 2.44502i) q^{86} +(-7.77403 + 17.0227i) q^{87} +(-3.88181 + 6.04021i) q^{89} +(-19.1093 + 16.5583i) q^{90} +(-3.93926 - 8.74541i) q^{92} +(-11.8005 - 13.6185i) q^{94} +(2.66956 - 18.5672i) q^{96} +(-0.728267 - 5.06521i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Introduction

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