LMFDB - Embedded newform 304.3.r.a.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,3,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	304.r (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:	$8.28340003655$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	304.65
Dual form			304.3.r.a.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.275255 - 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +2.89898 q^{7} +(-4.44949 - 7.70674i) q^{9} +O(q^{10})$	\(q+(-0.275255 - 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +2.89898 q^{7} +(-4.44949 - 7.70674i) q^{9} +5.10102 q^{11} +(-0.151531 + 0.0874863i) q^{13} +(-0.275255 + 0.158919i) q^{15} +(5.94949 - 10.3048i) q^{17} +(3.34847 - 18.7026i) q^{19} +(-0.797959 - 0.460702i) q^{21} +(-8.52270 - 14.7618i) q^{23} +(12.0000 + 20.7846i) q^{25} +5.68896i q^{27} +(38.5454 - 22.2542i) q^{29} -31.1769i q^{31} +(-1.40408 - 0.810647i) q^{33} +(1.44949 - 2.51059i) q^{35} -21.9917i q^{37} +0.0556128 q^{39} +(-46.9393 - 27.1004i) q^{41} +(18.6691 - 32.3359i) q^{43} -8.89898 q^{45} +(40.7702 + 70.6160i) q^{47} -40.5959 q^{49} +(-3.27526 + 1.89097i) q^{51} +(48.2878 - 27.8789i) q^{53} +(2.55051 - 4.41761i) q^{55} +(-3.89388 + 4.61586i) q^{57} +(29.9166 + 17.2723i) q^{59} +(38.0959 + 65.9841i) q^{61} +(-12.8990 - 22.3417i) q^{63} +0.174973i q^{65} +(-102.659 + 59.2702i) q^{67} +5.41767i q^{69} +(-65.4773 - 37.8033i) q^{71} +(-14.6918 + 25.4470i) q^{73} -7.62809i q^{75} +14.7878 q^{77} +(57.2196 + 33.0358i) q^{79} +(-39.1413 + 67.7948i) q^{81} +30.6969 q^{83} +(-5.94949 - 10.3048i) q^{85} -14.1464 q^{87} +(-8.84847 + 5.10867i) q^{89} +(-0.439285 + 0.253621i) q^{91} +(-4.95459 + 8.58161i) q^{93} +(-14.5227 - 12.2512i) q^{95} +(-128.848 - 74.3907i) q^{97} +(-22.6969 - 39.3123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 2 * q^5 - 8 * q^7 - 8 * q^9	$ 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9} + 40 q^{11} - 30 q^{13} - 6 q^{15} + 14 q^{17} - 16 q^{19} + 36 q^{21} + 10 q^{23} + 48 q^{25} + 66 q^{29} - 84 q^{33} - 4 q^{35} + 108 q^{39} + 18 q^{41} - 38 q^{43} - 16 q^{45} + 70 q^{47} - 84 q^{49} - 18 q^{51} - 42 q^{53} + 20 q^{55} + 102 q^{57} - 42 q^{59} + 74 q^{61} - 32 q^{63} - 102 q^{67} - 306 q^{71} + 98 q^{73} - 176 q^{77} + 126 q^{79} + 10 q^{81} + 64 q^{83} - 14 q^{85} + 12 q^{87} - 6 q^{89} + 204 q^{91} - 108 q^{93} - 14 q^{95} - 486 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 + 2 * q^5 - 8 * q^7 - 8 * q^9 + 40 * q^11 - 30 * q^13 - 6 * q^15 + 14 * q^17 - 16 * q^19 + 36 * q^21 + 10 * q^23 + 48 * q^25 + 66 * q^29 - 84 * q^33 - 4 * q^35 + 108 * q^39 + 18 * q^41 - 38 * q^43 - 16 * q^45 + 70 * q^47 - 84 * q^49 - 18 * q^51 - 42 * q^53 + 20 * q^55 + 102 * q^57 - 42 * q^59 + 74 * q^61 - 32 * q^63 - 102 * q^67 - 306 * q^71 + 98 * q^73 - 176 * q^77 + 126 * q^79 + 10 * q^81 + 64 * q^83 - 14 * q^85 + 12 * q^87 - 6 * q^89 + 204 * q^91 - 108 * q^93 - 14 * q^95 - 486 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.275255	−	0.158919i	−0.0917517	−	0.0529729i	0.453422	−	0.891296i	$-0.350203\pi$
$3$	−0.275255	−	0.158919i	−0.0917517	−	0.0529729i	−0.545174	+	0.838323i	$0.683536\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.100000	−	0.173205i	−0.811684	−	0.584096i	$-0.801449\pi$
$5$	0.500000	−	0.866025i	0.100000	−	0.173205i	0.911684	+	0.410891i	$0.134782\pi$
$6$		0			0
$7$	2.89898			0.414140			0.207070	−	0.978326i	$-0.433607\pi$
$7$	2.89898			0.414140			0.207070	+	0.978326i	$0.433607\pi$
$8$		0			0
$9$	−4.44949	−	7.70674i	−0.494388	−	0.856305i
$10$		0			0
$11$	5.10102			0.463729			0.231865	−	0.972748i	$-0.425517\pi$
$11$	5.10102			0.463729			0.231865	+	0.972748i	$0.425517\pi$
$12$		0			0
$13$	−0.151531	+	0.0874863i	−0.0116562	+	0.00672972i	−0.505817	−	0.862641i	$-0.668809\pi$
$13$	−0.151531	+	0.0874863i	−0.0116562	+	0.00672972i	0.494161	+	0.869371i	$0.335475\pi$
$14$		0			0
$15$	−0.275255	+	0.158919i	−0.0183503	+	0.0105946i
$16$		0			0
$17$	5.94949	−	10.3048i	0.349970	−	0.606166i	−0.636274	−	0.771463i	$-0.719525\pi$
$17$	5.94949	−	10.3048i	0.349970	−	0.606166i	0.986244	+	0.165298i	$0.0528584\pi$
$18$		0			0
$19$	3.34847	−	18.7026i	0.176235	−	0.984348i
$19$	3.34847	−	18.7026i	0.176235	−	0.984348i
$20$		0			0
$21$	−0.797959	−	0.460702i	−0.0379980	−	0.0219382i
$22$		0			0
$23$	−8.52270	−	14.7618i	−0.370552	−	0.641815i	0.619098	−	0.785314i	$-0.287498\pi$
$23$	−8.52270	−	14.7618i	−0.370552	−	0.641815i	−0.989651	+	0.143498i	$0.954165\pi$
$24$		0			0
$25$	12.0000	+	20.7846i	0.480000	+	0.831384i
$26$		0			0
$27$			5.68896i			0.210702i
$28$		0			0
$29$	38.5454	−	22.2542i	1.32915	−	0.767386i	0.343983	−	0.938976i	$-0.388224\pi$
$29$	38.5454	−	22.2542i	1.32915	−	0.767386i	0.985169	+	0.171589i	$0.0548903\pi$
$30$		0			0
$31$		−	31.1769i		−	1.00571i	−0.864372	−	0.502853i	$-0.832284\pi$
$31$		−	31.1769i		−	1.00571i	0.864372	−	0.502853i	$-0.167716\pi$
$32$		0			0
$33$	−1.40408	−	0.810647i	−0.0425479	−	0.0245651i
$34$		0			0
$35$	1.44949	−	2.51059i	0.0414140	−	0.0717311i
$36$		0			0
$37$		−	21.9917i		−	0.594371i	−0.954820	−	0.297186i	$-0.903952\pi$
$37$		−	21.9917i		−	0.594371i	0.954820	−	0.297186i	$-0.0960480\pi$
$38$		0			0
$39$	0.0556128			0.00142597
$40$		0			0
$41$	−46.9393	−	27.1004i	−1.14486	−	0.660986i	−0.197231	−	0.980357i	$-0.563195\pi$
$41$	−46.9393	−	27.1004i	−1.14486	−	0.660986i	−0.947630	+	0.319371i	$0.896528\pi$
$42$		0			0
$43$	18.6691	−	32.3359i	0.434166	−	0.751997i	−0.563061	−	0.826415i	$-0.690377\pi$
$43$	18.6691	−	32.3359i	0.434166	−	0.751997i	0.997227	+	0.0744178i	$0.0237098\pi$
$44$		0			0
$45$	−8.89898			−0.197755
$46$		0			0
$47$	40.7702	+	70.6160i	0.867450	+	1.50247i	0.864594	+	0.502472i	$0.167576\pi$
$47$	40.7702	+	70.6160i	0.867450	+	1.50247i	0.00285637	+	0.999996i	$0.499091\pi$
$48$		0			0
$49$	−40.5959			−0.828488
$50$		0			0
$51$	−3.27526	+	1.89097i	−0.0642207	+	0.0370778i
$52$		0			0
$53$	48.2878	−	27.8789i	0.911090	−	0.526018i	0.0303081	−	0.999541i	$-0.490351\pi$
$53$	48.2878	−	27.8789i	0.911090	−	0.526018i	0.880782	+	0.473523i	$0.157018\pi$
$54$		0			0
$55$	2.55051	−	4.41761i	0.0463729	−	0.0803202i
$56$		0			0
$57$	−3.89388	+	4.61586i	−0.0683136	+	0.0809799i
$58$		0			0
$59$	29.9166	+	17.2723i	0.507061	+	0.292752i	0.731625	−	0.681708i	$-0.238762\pi$
$59$	29.9166	+	17.2723i	0.507061	+	0.292752i	−0.224564	+	0.974459i	$0.572096\pi$
$60$		0			0
$61$	38.0959	+	65.9841i	0.624523	+	1.08171i	0.988633	+	0.150350i	$0.0480400\pi$
$61$	38.0959	+	65.9841i	0.624523	+	1.08171i	−0.364110	+	0.931356i	$0.618627\pi$
$62$		0			0
$63$	−12.8990	−	22.3417i	−0.204746	−	0.354630i
$64$		0			0
$65$			0.174973i			0.00269189i
$66$		0			0
$67$	−102.659	+	59.2702i	−1.53222	+	0.884629i	−0.532964	+	0.846138i	$0.678922\pi$
$67$	−102.659	+	59.2702i	−1.53222	+	0.884629i	−0.999259	+	0.0384912i	$0.987745\pi$
$68$		0			0
$69$			5.41767i			0.0785169i
$70$		0			0
$71$	−65.4773	−	37.8033i	−0.922215	−	0.532441i	−0.0378743	−	0.999283i	$-0.512059\pi$
$71$	−65.4773	−	37.8033i	−0.922215	−	0.532441i	−0.884341	+	0.466841i	$0.845392\pi$
$72$		0			0
$73$	−14.6918	+	25.4470i	−0.201258	+	0.348589i	−0.948934	−	0.315475i	$-0.897836\pi$
$73$	−14.6918	+	25.4470i	−0.201258	+	0.348589i	0.747676	+	0.664064i	$0.231170\pi$
$74$		0			0
$75$		−	7.62809i		−	0.101708i
$76$		0			0
$77$	14.7878			0.192049
$78$		0			0
$79$	57.2196	+	33.0358i	0.724299	+	0.418174i	0.816333	−	0.577582i	$-0.196003\pi$
$79$	57.2196	+	33.0358i	0.724299	+	0.418174i	−0.0920338	+	0.995756i	$0.529337\pi$
$80$		0			0
$81$	−39.1413	+	67.7948i	−0.483226	+	0.836972i
$82$		0			0
$83$	30.6969			0.369843			0.184921	−	0.982753i	$-0.440797\pi$
$83$	30.6969			0.369843			0.184921	+	0.982753i	$0.440797\pi$
$84$		0			0
$85$	−5.94949	−	10.3048i	−0.0699940	−	0.121233i
$86$		0			0
$87$	−14.1464			−0.162603
$88$		0			0
$89$	−8.84847	+	5.10867i	−0.0994210	+	0.0574007i	−0.548886	−	0.835897i	$-0.684948\pi$
$89$	−8.84847	+	5.10867i	−0.0994210	+	0.0574007i	0.449465	+	0.893298i	$0.351615\pi$
$90$		0			0
$91$	−0.439285	+	0.253621i	−0.00482730	+	0.00278704i
$92$		0			0
$93$	−4.95459	+	8.58161i	−0.0532752	+	0.0922753i
$94$		0			0
$95$	−14.5227	−	12.2512i	−0.152871	−	0.128960i
$96$		0			0
$97$	−128.848	−	74.3907i	−1.32833	−	0.766914i	−0.343293	−	0.939228i	$-0.611542\pi$
$97$	−128.848	−	74.3907i	−1.32833	−	0.766914i	−0.985042	+	0.172314i	$0.944876\pi$
$98$		0			0
$99$	−22.6969	−	39.3123i	−0.229262	−	0.397093i
$100$		0			0
$101$	70.2423	+	121.663i	0.695469	+	1.20459i	0.970022	+	0.243015i	$0.0781366\pi$
$101$	70.2423	+	121.663i	0.695469	+	1.20459i	−0.274554	+	0.961572i	$0.588530\pi$
$102$		0			0
$103$			113.965i			1.10646i	0.833028	+	0.553230i	$0.186605\pi$
$103$			113.965i			1.10646i	−0.833028	+	0.553230i	$0.813395\pi$
$104$		0			0
$105$	−0.797959	+	0.460702i	−0.00759961	+	0.00438764i
$106$		0			0
$107$			113.965i			1.06510i	0.846399	+	0.532549i	$0.178766\pi$
$107$			113.965i			1.06510i	−0.846399	+	0.532549i	$0.821234\pi$
$108$		0			0
$109$	59.2423	+	34.2036i	0.543508	+	0.313794i	0.746499	−	0.665386i	$-0.231733\pi$
$109$	59.2423	+	34.2036i	0.543508	+	0.313794i	−0.202992	+	0.979180i	$0.565066\pi$
$110$		0			0
$111$	−3.49490	+	6.05334i	−0.0314856	+	0.0545346i
$112$		0			0
$113$			81.9313i			0.725056i	0.931973	+	0.362528i	$0.118086\pi$
$113$			81.9313i			0.725056i	−0.931973	+	0.362528i	$0.881914\pi$
$114$		0			0
$115$	−17.0454			−0.148221
$116$		0			0
$117$	1.34847	+	0.778539i	0.0115254	+	0.00665418i
$118$		0			0
$119$	17.2474	−	29.8735i	0.144937	−	0.251037i
$120$		0			0
$121$	−94.9796			−0.784955
$122$		0			0
$123$	8.61352	+	14.9191i	0.0700286	+	0.121293i
$124$		0			0
$125$	49.0000			0.392000
$126$		0			0
$127$	−116.174	+	67.0732i	−0.914758	+	0.528136i	−0.881959	−	0.471326i	$-0.843775\pi$
$127$	−116.174	+	67.0732i	−0.914758	+	0.528136i	−0.0327989	+	0.999462i	$0.510442\pi$
$128$		0			0
$129$	−10.2775	+	5.93375i	−0.0796709	+	0.0459980i
$130$		0			0
$131$	41.3763	−	71.6658i	0.315849	−	0.547067i	−0.663768	−	0.747938i	$-0.731044\pi$
$131$	41.3763	−	71.6658i	0.315849	−	0.547067i	0.979618	+	0.200871i	$0.0643772\pi$
$132$		0			0
$133$	9.70714	−	54.2185i	0.0729860	−	0.407658i
$134$		0			0
$135$	4.92679	+	2.84448i	0.0364947	+	0.0210702i
$136$		0			0
$137$	5.94949	+	10.3048i	0.0434269	+	0.0752177i	0.886922	−	0.461919i	$-0.152839\pi$
$137$	5.94949	+	10.3048i	0.0434269	+	0.0752177i	−0.843495	+	0.537137i	$0.819506\pi$
$138$		0			0
$139$	20.8712	+	36.1499i	0.150152	+	0.260071i	0.931283	−	0.364296i	$-0.118690\pi$
$139$	20.8712	+	36.1499i	0.150152	+	0.260071i	−0.781131	+	0.624367i	$0.785357\pi$
$140$		0			0
$141$		−	25.9165i		−	0.183805i
$142$		0			0
$143$	−0.772962	+	0.446270i	−0.00540533	+	0.00312077i
$144$		0			0
$145$		−	44.5084i		−	0.306955i
$146$		0			0
$147$	11.1742	+	6.45145i	0.0760152	+	0.0438874i
$148$		0			0
$149$	17.8383	−	30.8968i	0.119720	−	0.207361i	−0.799937	−	0.600084i	$-0.795134\pi$
$149$	17.8383	−	30.8968i	0.119720	−	0.207361i	0.919657	+	0.392723i	$0.128467\pi$
$150$		0			0
$151$		−	85.5527i		−	0.566574i	−0.959035	−	0.283287i	$-0.908575\pi$
$151$		−	85.5527i		−	0.566574i	0.959035	−	0.283287i	$-0.0914249\pi$
$152$		0			0
$153$	−105.889			−0.692083
$154$		0			0
$155$	−27.0000	−	15.5885i	−0.174194	−	0.100571i
$156$		0			0
$157$	100.076	−	173.336i	0.637424	−	1.10405i	−0.348573	−	0.937282i	$-0.613333\pi$
$157$	100.076	−	173.336i	0.637424	−	1.10405i	0.985996	−	0.166768i	$-0.0533332\pi$
$158$		0			0
$159$	−17.7219			−0.111459
$160$		0			0
$161$	−24.7071	−	42.7940i	−0.153461	−	0.265801i
$162$		0			0
$163$	127.303			0.781000			0.390500	−	0.920603i	$-0.372302\pi$
$163$	127.303			0.781000			0.390500	+	0.920603i	$0.372302\pi$
$164$		0			0
$165$	−1.40408	+	0.810647i	−0.00850959	+	0.00491301i
$166$		0			0
$167$	158.917	−	91.7505i	0.951596	−	0.549404i	0.0580198	−	0.998315i	$-0.481521\pi$
$167$	158.917	−	91.7505i	0.951596	−	0.549404i	0.893576	+	0.448911i	$0.148188\pi$
$168$		0			0
$169$	−84.4847	+	146.332i	−0.499909	+	0.865869i
$170$		0			0
$171$	−159.035	+	57.4113i	−0.930030	+	0.335739i
$172$		0			0
$173$	−57.6214	−	33.2677i	−0.333072	−	0.192299i	0.324132	−	0.946012i	$-0.394928\pi$
$173$	−57.6214	−	33.2677i	−0.333072	−	0.192299i	−0.657204	+	0.753713i	$0.728261\pi$
$174$		0			0
$175$	34.7878	+	60.2542i	0.198787	+	0.344309i
$176$		0			0
$177$	−5.48979	−	9.50860i	−0.0310158	−	0.0537209i
$178$		0			0
$179$		−	24.2134i		−	0.135270i	−0.997710	−	0.0676351i	$-0.978455\pi$
$179$		−	24.2134i		−	0.135270i	0.997710	−	0.0676351i	$-0.0215454\pi$
$180$		0			0
$181$	30.8939	−	17.8366i	0.170684	−	0.0985447i	−0.412224	−	0.911082i	$-0.635248\pi$
$181$	30.8939	−	17.8366i	0.170684	−	0.0985447i	0.582909	+	0.812538i	$0.301915\pi$
$182$		0			0
$183$		−	24.2166i		−	0.132331i
$184$		0			0
$185$	−19.0454	−	10.9959i	−0.102948	−	0.0594371i
$186$		0			0
$187$	30.3485	−	52.5651i	0.162291	−	0.281097i
$188$		0			0
$189$			16.4922i			0.0872602i
$190$		0			0
$191$	180.252			0.943728			0.471864	−	0.881671i	$-0.343581\pi$
$191$	180.252			0.943728			0.471864	+	0.881671i	$0.343581\pi$
$192$		0			0
$193$	188.985	+	109.110i	0.979195	+	0.565339i	0.902027	−	0.431679i	$-0.142079\pi$
$193$	188.985	+	109.110i	0.979195	+	0.565339i	0.0771682	+	0.997018i	$0.475412\pi$
$194$		0			0
$195$	0.0278064	−	0.0481621i	0.000142597	−	0.000246985i
$196$		0			0
$197$	340.091			1.72635			0.863175	−	0.504905i	$-0.168473\pi$
$197$	340.091			1.72635			0.863175	+	0.504905i	$0.168473\pi$
$198$		0			0
$199$	−166.694	−	288.723i	−0.837659	−	1.45087i	−0.891847	−	0.452337i	$-0.850590\pi$
$199$	−166.694	−	288.723i	−0.837659	−	1.45087i	0.0541881	−	0.998531i	$-0.482743\pi$
$200$		0			0
$201$	37.6765			0.187445
$202$		0			0
$203$	111.742	−	64.5145i	0.550455	−	0.317805i
$204$		0			0
$205$	−46.9393	+	27.1004i	−0.228972	+	0.132197i
$206$		0			0
$207$	−75.8434	+	131.365i	−0.366393	+	0.634611i
$208$		0			0
$209$	17.0806	−	95.4024i	0.0817254	−	0.456471i
$210$		0			0
$211$	−302.750	−	174.793i	−1.43483	−	0.828401i	−0.437349	−	0.899292i	$-0.644082\pi$
$211$	−302.750	−	174.793i	−1.43483	−	0.828401i	−0.997484	+	0.0708908i	$0.977416\pi$
$212$		0			0
$213$	12.0153	+	20.8111i	0.0564099	+	0.0977048i
$214$		0			0
$215$	−18.6691	−	32.3359i	−0.0868332	−	0.150399i
$216$		0			0
$217$		−	90.3812i		−	0.416503i
$218$		0			0
$219$	8.08801	−	4.66961i	0.0369315	−	0.0213224i
$220$		0			0
$221$			2.08200i			0.00942080i
$222$		0			0
$223$	27.5227	+	15.8902i	0.123420	+	0.0712567i	0.560439	−	0.828196i	$-0.310632\pi$
$223$	27.5227	+	15.8902i	0.123420	+	0.0712567i	−0.437019	+	0.899452i	$0.643966\pi$
$224$		0			0
$225$	106.788	−	184.962i	0.474612	−	0.822053i
$226$		0			0
$227$		−	249.730i		−	1.10013i	−0.835121	−	0.550066i	$-0.814603\pi$
$227$		−	249.730i		−	1.10013i	0.835121	−	0.550066i	$-0.185397\pi$
$228$		0			0
$229$	−259.687			−1.13400			−0.567002	−	0.823717i	$-0.691897\pi$
$229$	−259.687			−1.13400			−0.567002	+	0.823717i	$0.691897\pi$
$230$		0			0
$231$	−4.07041	−	2.35005i	−0.0176208	−	0.0101734i
$232$		0			0
$233$	195.141	−	337.995i	0.837516	−	1.45062i	−0.0544486	−	0.998517i	$-0.517340\pi$
$233$	195.141	−	337.995i	0.837516	−	1.45062i	0.891965	−	0.452104i	$-0.149327\pi$
$234$		0			0
$235$	81.5403			0.346980
$236$		0			0
$237$	−10.5000	−	18.1865i	−0.0443038	−	0.0767364i
$238$		0			0
$239$	296.677			1.24132			0.620662	−	0.784078i	$-0.286864\pi$
$239$	296.677			1.24132			0.620662	+	0.784078i	$0.286864\pi$
$240$		0			0
$241$	−99.7270	+	57.5774i	−0.413805	+	0.238911i	−0.692423	−	0.721491i	$-0.743457\pi$
$241$	−99.7270	+	57.5774i	−0.413805	+	0.238911i	0.278618	+	0.960402i	$0.410124\pi$
$242$		0			0
$243$	65.8888	−	38.0409i	0.271147	−	0.156547i
$244$		0			0
$245$	−20.2980	+	35.1571i	−0.0828488	+	0.143498i
$246$		0			0
$247$	1.12883	+	3.12697i	0.00457015	+	0.0126598i
$248$		0			0
$249$	−8.44949	−	4.87832i	−0.0339337	−	0.0195916i
$250$		0			0
$251$	244.962	+	424.287i	0.975944	+	1.69038i	0.676783	+	0.736182i	$0.263373\pi$
$251$	244.962	+	424.287i	0.975944	+	1.69038i	0.299161	+	0.954203i	$0.403293\pi$
$252$		0			0
$253$	−43.4745	−	75.3000i	−0.171836	−	0.297629i
$254$		0			0
$255$			3.78194i			0.0148311i
$256$		0			0
$257$	−197.379	+	113.957i	−0.768010	+	0.443411i	−0.832164	−	0.554529i	$-0.812898\pi$
$257$	−197.379	+	113.957i	−0.768010	+	0.443411i	0.0641543	+	0.997940i	$0.479565\pi$
$258$		0			0
$259$		−	63.7536i		−	0.246153i
$260$		0			0
$261$	−343.015	−	198.040i	−1.31423	−	0.758773i
$262$		0			0
$263$	67.9620	−	117.714i	0.258411	−	0.447580i	−0.707406	−	0.706808i	$-0.750135\pi$
$263$	67.9620	−	117.714i	0.258411	−	0.447580i	0.965816	+	0.259227i	$0.0834679\pi$
$264$		0			0
$265$		−	55.7579i		−	0.210407i
$266$		0			0
$267$	3.24745			0.0121627
$268$		0			0
$269$	225.090	+	129.956i	0.836767	+	0.483108i	0.856164	−	0.516704i	$-0.172841\pi$
$269$	225.090	+	129.956i	0.836767	+	0.483108i	−0.0193970	+	0.999812i	$0.506175\pi$
$270$		0			0
$271$	−116.492	+	201.770i	−0.429860	+	0.744540i	−0.996860	−	0.0791780i	$-0.974770\pi$
$271$	−116.492	+	201.770i	−0.429860	+	0.744540i	0.567000	+	0.823718i	$0.308104\pi$
$272$		0			0
$273$	0.161220			0.000590551
$274$		0			0
$275$	61.2122	+	106.023i	0.222590	+	0.385537i
$276$		0			0
$277$	−9.44387			−0.0340934			−0.0170467	−	0.999855i	$-0.505426\pi$
$277$	−9.44387			−0.0340934			−0.0170467	+	0.999855i	$0.505426\pi$
$278$		0			0
$279$	−240.272	+	138.721i	−0.861192	+	0.497209i
$280$		0			0
$281$	135.591	−	78.2834i	0.482530	−	0.278589i	−0.238940	−	0.971034i	$-0.576800\pi$
$281$	135.591	−	78.2834i	0.482530	−	0.278589i	0.721470	+	0.692446i	$0.243467\pi$
$282$		0			0
$283$	1.46709	−	2.54108i	0.00518407	−	0.00897907i	−0.863422	−	0.504483i	$-0.831683\pi$
$283$	1.46709	−	2.54108i	0.00518407	−	0.00897907i	0.868606	+	0.495504i	$0.165017\pi$
$284$		0			0
$285$	2.05051	+	5.68012i	0.00719477	+	0.0199303i
$286$		0			0
$287$	−136.076	−	78.5635i	−0.474132	−	0.273741i
$288$		0			0
$289$	73.7071	+	127.665i	0.255042	+	0.441746i
$290$		0			0
$291$	23.6441	+	40.9528i	0.0812513	+	0.140731i
$292$		0			0
$293$			332.361i			1.13434i	0.823601	+	0.567169i	$0.191961\pi$
$293$			332.361i			1.13434i	−0.823601	+	0.567169i	$0.808039\pi$
$294$		0			0
$295$	29.9166	−	17.2723i	0.101412	−	0.0585503i
$296$		0			0
$297$			29.0195i			0.0977088i
$298$		0			0
$299$	2.58290	+	1.49124i	0.00863847	+	0.00498743i
$300$		0			0
$301$	54.1214	−	93.7411i	0.179805	−	0.311432i
$302$		0			0
$303$		−	44.6513i		−	0.147364i
$304$		0			0
$305$	76.1918			0.249809
$306$		0			0
$307$	−222.962	−	128.727i	−0.726261	−	0.419307i	0.0907920	−	0.995870i	$-0.471060\pi$
$307$	−222.962	−	128.727i	−0.726261	−	0.419307i	−0.817053	+	0.576563i	$0.804393\pi$
$308$		0			0
$309$	18.1112	−	31.3696i	0.0586124	−	0.101520i
$310$		0			0
$311$	−217.666			−0.699892			−0.349946	−	0.936770i	$-0.613800\pi$
$311$	−217.666			−0.699892			−0.349946	+	0.936770i	$0.613800\pi$
$312$		0			0
$313$	155.121	+	268.677i	0.495594	+	0.858394i	0.999987	−	0.00508018i	$-0.00161708\pi$
$313$	155.121	+	268.677i	0.495594	+	0.858394i	−0.504393	+	0.863474i	$0.668284\pi$
$314$		0			0
$315$	−25.7980			−0.0818983
$316$		0			0
$317$	−298.939	+	172.593i	−0.943026	+	0.544456i	−0.890908	−	0.454185i	$-0.849931\pi$
$317$	−298.939	+	172.593i	−0.943026	+	0.544456i	−0.0521185	+	0.998641i	$0.516597\pi$
$318$		0			0
$319$	196.621	−	113.519i	0.616367	−	0.355859i
$320$		0			0
$321$	18.1112	−	31.3696i	0.0564213	−	0.0977245i
$322$		0			0
$323$	−172.805	−	145.776i	−0.535001	−	0.451320i
$324$		0			0
$325$	−3.63674	−	2.09967i	−0.0111900	−	0.00646053i
$326$		0			0
$327$	−10.8712	−	18.8294i	−0.0332452	−	0.0575823i
$328$		0			0
$329$	118.192	+	204.714i	0.359246	+	0.622232i
$330$		0			0
$331$			487.318i			1.47226i	0.676841	+	0.736130i	$0.263349\pi$
$331$			487.318i			1.47226i	−0.676841	+	0.736130i	$0.736651\pi$
$332$		0			0
$333$	−169.485	+	97.8520i	−0.508963	+	0.293850i
$334$		0			0
$335$			118.540i			0.353852i
$336$		0			0
$337$	144.393	+	83.3655i	0.428467	+	0.247376i	0.698693	−	0.715421i	$-0.253765\pi$
$337$	144.393	+	83.3655i	0.428467	+	0.247376i	−0.270226	+	0.962797i	$0.587099\pi$
$338$		0			0
$339$	13.0204	−	22.5520i	0.0384083	−	0.0665251i
$340$		0			0
$341$		−	159.034i		−	0.466376i
$342$		0			0
$343$	−259.737			−0.757250
$344$		0			0
$345$	4.69184	+	2.70883i	0.0135995	+	0.00785169i
$346$		0			0
$347$	188.871	−	327.134i	0.544297	−	0.942751i	−0.454353	−	0.890822i	$-0.650130\pi$
$347$	188.871	−	327.134i	0.544297	−	0.942751i	0.998651	−	0.0519291i	$-0.0165370\pi$
$348$		0			0
$349$	−586.434			−1.68033			−0.840163	−	0.542334i	$-0.817541\pi$
$349$	−586.434			−1.68033			−0.840163	+	0.542334i	$0.817541\pi$
$350$		0			0
$351$	−0.497706	−	0.862053i	−0.00141797	−	0.00245599i
$352$		0			0
$353$	476.817			1.35076			0.675379	−	0.737471i	$-0.263980\pi$
$353$	476.817			1.35076			0.675379	+	0.737471i	$0.263980\pi$
$354$		0			0
$355$	−65.4773	+	37.8033i	−0.184443	+	0.106488i
$356$		0			0
$357$	−9.49490	+	5.48188i	−0.0265964	+	0.0153554i
$358$		0			0
$359$	−123.704	+	214.262i	−0.344580	+	0.596831i	−0.985277	−	0.170963i	$-0.945312\pi$
$359$	−123.704	+	214.262i	−0.344580	+	0.596831i	0.640697	+	0.767794i	$0.278645\pi$
$360$		0			0
$361$	−338.576	−	125.250i	−0.937882	−	0.346954i
$362$		0			0
$363$	26.1436	+	15.0940i	0.0720210	+	0.0415813i
$364$		0			0
$365$	14.6918	+	25.4470i	0.0402516	+	0.0697178i
$366$		0			0
$367$	241.962	+	419.090i	0.659297	+	1.14194i	0.980798	+	0.195027i	$0.0624793\pi$
$367$	241.962	+	419.090i	0.659297	+	1.14194i	−0.321501	+	0.946909i	$0.604187\pi$
$368$		0			0
$369$			482.332i			1.30713i
$370$		0			0
$371$	139.985	−	80.8205i	0.377319	−	0.217845i
$372$		0			0
$373$			140.908i			0.377768i	0.981999	+	0.188884i	$0.0604871\pi$
$373$			140.908i			0.377768i	−0.981999	+	0.188884i	$0.939513\pi$
$374$		0			0
$375$	−13.4875	−	7.78701i	−0.0359667	−	0.0207654i
$376$		0			0
$377$	−3.89388	+	6.74439i	−0.0103286	+	0.0178896i
$378$		0			0
$379$			468.633i			1.23650i	0.785982	+	0.618249i	$0.212158\pi$
$379$			468.633i			1.23650i	−0.785982	+	0.618249i	$0.787842\pi$
$380$		0			0
$381$	42.6367			0.111907
$382$		0			0
$383$	482.552	+	278.602i	1.25993	+	0.727420i	0.973060	−	0.230551i	$-0.0740528\pi$
$383$	482.552	+	278.602i	1.25993	+	0.727420i	0.286867	+	0.957970i	$0.407386\pi$
$384$		0			0
$385$	7.39388	−	12.8066i	0.0192049	−	0.0332638i
$386$		0			0
$387$	−332.272			−0.858585
$388$		0			0
$389$	−46.5602	−	80.6446i	−0.119692	−	0.207313i	0.799954	−	0.600062i	$-0.204857\pi$
$389$	−46.5602	−	80.6446i	−0.119692	−	0.207313i	−0.919646	+	0.392749i	$0.871524\pi$
$390$		0			0
$391$	−202.823			−0.518729
$392$		0			0
$393$	−22.7781	+	13.1509i	−0.0579595	+	0.0334629i
$394$		0			0
$395$	57.2196	−	33.0358i	0.144860	−	0.0836349i
$396$		0			0
$397$	−129.682	+	224.615i	−0.326654	+	0.565781i	−0.981846	−	0.189681i	$-0.939255\pi$
$397$	−129.682	+	224.615i	−0.326654	+	0.565781i	0.655192	+	0.755463i	$0.272588\pi$
$398$		0			0
$399$	−11.2883	+	13.3813i	−0.0282914	+	0.0335370i
$400$		0			0
$401$	−389.484	−	224.869i	−0.971282	−	0.560770i	−0.0716553	−	0.997429i	$-0.522828\pi$
$401$	−389.484	−	224.869i	−0.971282	−	0.560770i	−0.899627	+	0.436659i	$0.856161\pi$
$402$		0			0
$403$	2.72755	+	4.72426i	0.00676812	+	0.0117227i
$404$		0			0
$405$	39.1413	+	67.7948i	0.0966452	+	0.167394i
$406$		0			0
$407$		−	112.180i		−	0.275627i
$408$		0			0
$409$	90.8326	−	52.4423i	0.222085	−	0.128221i	−0.384830	−	0.922987i	$-0.625740\pi$
$409$	90.8326	−	52.4423i	0.222085	−	0.128221i	0.606915	+	0.794767i	$0.292407\pi$
$410$		0			0
$411$		−	3.78194i		−	0.00920180i
$412$		0			0
$413$	86.7276	+	50.0722i	0.209994	+	0.121240i
$414$		0			0
$415$	15.3485	−	26.5843i	0.0369843	−	0.0640586i
$416$		0			0
$417$		−	13.2673i		−	0.0318160i
$418$		0			0
$419$	−463.121			−1.10530			−0.552651	−	0.833413i	$-0.686384\pi$
$419$	−463.121			−1.10530			−0.552651	+	0.833413i	$0.686384\pi$
$420$		0			0
$421$	−418.711	−	241.743i	−0.994563	−	0.574211i	−0.0879282	−	0.996127i	$-0.528025\pi$
$421$	−418.711	−	241.743i	−0.994563	−	0.574211i	−0.906635	+	0.421915i	$0.861358\pi$
$422$		0			0
$423$	362.813	−	628.410i	0.857713	−	1.48560i
$424$		0			0
$425$	285.576			0.671942
$426$		0			0
$427$	110.439	+	191.286i	0.258640	+	0.447978i
$428$		0			0
$429$	0.283682			0.000661264
$430$		0			0
$431$	−392.447	+	226.579i	−0.910549	+	0.525706i	−0.880608	−	0.473846i	$-0.842865\pi$
$431$	−392.447	+	226.579i	−0.910549	+	0.525706i	−0.0299413	+	0.999552i	$0.509532\pi$
$432$		0			0
$433$	650.651	−	375.654i	1.50266	−	0.867560i	0.502663	−	0.864482i	$-0.332354\pi$
$433$	650.651	−	375.654i	1.50266	−	0.867560i	0.999995	−	0.00307767i	$-0.000979653\pi$
$434$		0			0
$435$	−7.07321	+	12.2512i	−0.0162603	+	0.0281636i
$436$		0			0
$437$	−304.621	+	109.968i	−0.697074	+	0.251642i
$438$		0			0
$439$	−543.325	−	313.689i	−1.23764	−	0.714553i	−0.269031	−	0.963132i	$-0.586703\pi$
$439$	−543.325	−	313.689i	−1.23764	−	0.714553i	−0.968612	+	0.248578i	$0.920037\pi$
$440$		0			0
$441$	180.631	+	312.862i	0.409594	+	0.709438i
$442$		0			0
$443$	220.628	+	382.139i	0.498032	+	0.862617i	0.999997	−	0.00227061i	$-0.000722758\pi$
$443$	220.628	+	382.139i	0.498032	+	0.862617i	−0.501965	+	0.864888i	$0.667389\pi$
$444$		0			0
$445$			10.2173i			0.0229603i
$446$		0			0
$447$	−9.82015	+	5.66966i	−0.0219690	+	0.0126838i
$448$		0			0
$449$		−	347.932i		−	0.774904i	−0.921890	−	0.387452i	$-0.873355\pi$
$449$		−	347.932i		−	0.774904i	0.921890	−	0.387452i	$-0.126645\pi$
$450$		0			0
$451$	−239.438	−	138.240i	−0.530905	−	0.306518i
$452$		0			0
$453$	−13.5959	+	23.5488i	−0.0300131	+	0.0519842i
$454$		0			0
$455$			0.507242i			0.00111482i
$456$		0			0
$457$	443.576			0.970625			0.485312	−	0.874341i	$-0.338706\pi$
$457$	443.576			0.970625			0.485312	+	0.874341i	$0.338706\pi$
$458$		0			0
$459$	58.6237	+	33.8464i	0.127721	+	0.0737395i
$460$		0			0
$461$	−97.8076	+	169.408i	−0.212164	+	0.367479i	−0.952392	−	0.304878i	$-0.901384\pi$
$461$	−97.8076	+	169.408i	−0.212164	+	0.367479i	0.740227	+	0.672357i	$0.234718\pi$
$462$		0			0
$463$	720.958			1.55715			0.778573	−	0.627555i	$-0.215944\pi$
$463$	720.958			1.55715			0.778573	+	0.627555i	$0.215944\pi$
$464$		0			0
$465$	4.95459	+	8.58161i	0.0106550	+	0.0184551i
$466$		0			0
$467$	−271.889			−0.582203			−0.291101	−	0.956692i	$-0.594022\pi$
$467$	−271.889			−0.582203			−0.291101	+	0.956692i	$0.594022\pi$
$468$		0			0
$469$	−297.606	+	171.823i	−0.634555	+	0.366360i
$470$		0			0
$471$	−55.0926	+	31.8077i	−0.116969	+	0.0675323i
$472$		0			0
$473$	95.2316	−	164.946i	0.201335	−	0.348723i
$474$		0			0
$475$	428.908	−	154.835i	0.902965	−	0.325968i
$476$		0			0
$477$	−429.712	−	248.094i	−0.900863	−	0.520114i
$478$		0			0
$479$	173.599	+	300.682i	0.362419	+	0.627728i	0.988358	−	0.152144i	$-0.0486176\pi$
$479$	173.599	+	300.682i	0.362419	+	0.627728i	−0.625939	+	0.779872i	$0.715284\pi$
$480$		0			0
$481$	1.92398	+	3.33243i	0.00399995	+	0.00692812i
$482$		0			0
$483$			15.7057i			0.0325170i
$484$		0			0
$485$	−128.848	+	74.3907i	−0.265667	+	0.153383i
$486$		0			0
$487$		−	495.960i		−	1.01840i	−0.860648	−	0.509200i	$-0.829942\pi$
$487$		−	495.960i		−	1.01840i	0.860648	−	0.509200i	$-0.170058\pi$
$488$		0			0
$489$	−35.0408	−	20.2308i	−0.0716581	−	0.0413718i
$490$		0			0
$491$	267.174	−	462.759i	0.544143	−	0.942483i	−0.454517	−	0.890738i	$-0.650188\pi$
$491$	267.174	−	462.759i	0.544143	−	0.942483i	0.998660	−	0.0517455i	$-0.0164785\pi$
$492$		0			0
$493$		−	529.605i		−	1.07425i
$494$		0			0
$495$	−45.3939			−0.0917048
$496$		0			0
$497$	−189.817	−	109.591i	−0.381926	−	0.220505i
$498$		0			0
$499$	395.457	−	684.951i	0.792499	−	1.37265i	−0.131917	−	0.991261i	$-0.542113\pi$
$499$	395.457	−	684.951i	0.792499	−	1.37265i	0.924415	−	0.381387i	$-0.124554\pi$
$500$		0			0
$501$	−58.3235			−0.116414
$502$		0			0
$503$	209.841	+	363.455i	0.417178	+	0.722574i	0.995654	−	0.0931256i	$-0.0296858\pi$
$503$	209.841	+	363.455i	0.417178	+	0.722574i	−0.578476	+	0.815699i	$0.696352\pi$
$504$		0			0
$505$	140.485			0.278188
$506$		0			0
$507$	46.5097	−	26.8524i	0.0917351	−	0.0529633i
$508$		0			0
$509$	695.515	−	401.556i	1.36643	−	0.788911i	0.375963	−	0.926635i	$-0.377312\pi$
$509$	695.515	−	401.556i	1.36643	−	0.788911i	0.990471	+	0.137724i	$0.0439786\pi$
$510$		0			0
$511$	−42.5913	+	73.7703i	−0.0833490	+	0.144365i
$512$		0			0
$513$	106.398	+	19.0493i	0.207404	+	0.0371332i
$514$		0			0
$515$	98.6969	+	56.9827i	0.191645	+	0.110646i
$516$		0			0
$517$	207.969	+	360.214i	0.402262	+	0.696738i
$518$		0			0
$519$	10.5737	+	18.3142i	0.0203733	+	0.0352875i
$520$		0			0
$521$			413.663i			0.793979i	0.917823	+	0.396990i	$0.129945\pi$
$521$			413.663i			0.793979i	−0.917823	+	0.396990i	$0.870055\pi$
$522$		0			0
$523$	−434.144	+	250.653i	−0.830103	+	0.479260i	−0.853888	−	0.520457i	$-0.825762\pi$
$523$	−434.144	+	250.653i	−0.830103	+	0.479260i	0.0237853	+	0.999717i	$0.492428\pi$
$524$		0			0
$525$		−	22.1137i		−	0.0421213i
$526$		0			0
$527$	−321.272	−	185.487i	−0.609625	−	0.351967i
$528$		0			0
$529$	119.227	−	206.507i	0.225382	−	0.390373i
$530$		0			0
$531$		−	307.413i		−	0.578931i
$532$		0			0
$533$	9.48366			0.0177930
$534$		0			0
$535$	98.6969	+	56.9827i	0.184480	+	0.106510i
$536$		0			0
$537$	−3.84795	+	6.66485i	−0.00716565	+	0.0124113i
$538$		0			0
$539$	−207.081			−0.384194
$540$		0			0
$541$	196.576	+	340.480i	0.363357	+	0.629352i	0.988511	−	0.151149i	$-0.0482973\pi$
$541$	196.576	+	340.480i	0.363357	+	0.629352i	−0.625154	+	0.780501i	$0.714964\pi$
$542$		0			0
$543$	−11.3383			−0.0208808
$544$		0			0
$545$	59.2423	−	34.2036i	0.108702	−	0.0627589i
$546$		0			0
$547$	418.159	−	241.424i	0.764460	−	0.441361i	−0.0664350	−	0.997791i	$-0.521162\pi$
$547$	418.159	−	241.424i	0.764460	−	0.441361i	0.830895	+	0.556430i	$0.187829\pi$
$548$		0			0
$549$	339.015	−	587.191i	0.617513	−	1.06956i
$550$		0			0
$551$	−287.144	−	795.417i	−0.521132	−	1.44359i
$552$		0			0
$553$	165.879	+	95.7700i	0.299961	+	0.173183i
$554$		0			0
$555$	3.49490	+	6.05334i	0.00629711	+	0.0109069i
$556$		0			0
$557$	75.8531	+	131.381i	0.136181	+	0.235873i	0.926048	−	0.377405i	$-0.123184\pi$
$557$	75.8531	+	131.381i	0.136181	+	0.235873i	−0.789867	+	0.613279i	$0.789850\pi$
$558$		0			0
$559$			6.53318i			0.0116873i
$560$		0			0
$561$	−16.7071	+	9.64587i	−0.0297810	+	0.0171941i
$562$		0			0
$563$		−	176.634i		−	0.313737i	−0.987620	−	0.156868i	$-0.949860\pi$
$563$		−	176.634i		−	0.313737i	0.987620	−	0.156868i	$-0.0501399\pi$
$564$		0			0
$565$	70.9546	+	40.9657i	0.125583	+	0.0725056i
$566$		0			0
$567$	−113.470	+	196.536i	−0.200123	+	0.346624i
$568$		0			0
$569$		−	957.928i		−	1.68353i	−0.539844	−	0.841765i	$-0.681517\pi$
$569$		−	957.928i		−	1.68353i	0.539844	−	0.841765i	$-0.318483\pi$
$570$		0			0
$571$	−833.242			−1.45927			−0.729634	−	0.683838i	$-0.760309\pi$
$571$	−833.242			−1.45927			−0.729634	+	0.683838i	$0.760309\pi$
$572$		0			0
$573$	−49.6153	−	28.6454i	−0.0865887	−	0.0499920i
$574$		0			0
$575$	204.545	−	354.282i	0.355730	−	0.616143i
$576$		0			0
$577$	−484.595			−0.839852			−0.419926	−	0.907558i	$-0.637944\pi$
$577$	−484.595			−0.839852			−0.419926	+	0.907558i	$0.637944\pi$
$578$		0			0
$579$	−34.6793	−	60.0664i	−0.0598952	−	0.103742i
$580$		0			0
$581$	88.9898			0.153167
$582$		0			0
$583$	246.317	−	142.211i	0.422499	−	0.243930i
$584$		0			0
$585$	1.34847	−	0.778539i	0.00230508	−	0.00133084i
$586$		0			0
$587$	−309.432	+	535.952i	−0.527141	+	0.913035i	0.472358	+	0.881407i	$0.343403\pi$
$587$	−309.432	+	535.952i	−0.527141	+	0.913035i	−0.999500	+	0.0316288i	$0.989931\pi$
$588$		0			0
$589$	−583.090	−	104.395i	−0.989966	−	0.177241i
$590$		0			0
$591$	−93.6117	−	54.0468i	−0.158396	−	0.0914497i
$592$		0			0
$593$	93.9699	+	162.761i	0.158465	+	0.274470i	0.934315	−	0.356447i	$-0.116012\pi$
$593$	93.9699	+	162.761i	0.158465	+	0.274470i	−0.775850	+	0.630917i	$0.782679\pi$
$594$		0			0
$595$	−17.2474	−	29.8735i	−0.0289873	−	0.0502075i
$596$		0			0
$597$			105.963i			0.177493i
$598$		0			0
$599$	69.5533	−	40.1566i	0.116116	−	0.0670394i	−0.440817	−	0.897597i	$-0.645311\pi$
$599$	69.5533	−	40.1566i	0.116116	−	0.0670394i	0.556933	+	0.830557i	$0.311978\pi$
$600$		0			0
$601$			665.929i			1.10804i	0.832505	+	0.554018i	$0.186906\pi$
$601$			665.929i			1.10804i	−0.832505	+	0.554018i	$0.813094\pi$
$602$		0			0
$603$	913.560	+	527.444i	1.51502	+	0.874700i
$604$		0			0
$605$	−47.4898	+	82.2547i	−0.0784955	+	0.135958i
$606$		0			0
$607$			105.952i			0.174550i	0.996184	+	0.0872751i	$0.0278159\pi$
$607$			105.952i			0.174550i	−0.996184	+	0.0872751i	$0.972184\pi$
$608$		0			0
$609$	−41.0102			−0.0673402
$610$		0			0
$611$	−12.3559	−	7.13366i	−0.0202224	−	0.0116754i
$612$		0			0
$613$	569.171	−	985.833i	0.928501	−	1.60821i	0.142668	−	0.989771i	$-0.454432\pi$
$613$	569.171	−	985.833i	0.928501	−	1.60821i	0.785832	−	0.618440i	$-0.212235\pi$
$614$		0			0
$615$	17.2270			0.0280114
$616$		0			0
$617$	−459.131	−	795.238i	−0.744135	−	1.28888i	−0.950598	−	0.310425i	$-0.899529\pi$
$617$	−459.131	−	795.238i	−0.744135	−	1.28888i	0.206463	−	0.978454i	$-0.433805\pi$
$618$		0			0
$619$	1123.85			1.81559			0.907793	−	0.419418i	$-0.137766\pi$
$619$	1123.85			1.81559			0.907793	+	0.419418i	$0.137766\pi$
$620$		0			0
$621$	83.9791	−	48.4853i	0.135232	−	0.0780762i
$622$		0			0
$623$	−25.6515	+	14.8099i	−0.0411742	+	0.0237719i
$624$		0			0
$625$	−275.500	+	477.180i	−0.440800	+	0.763488i
$626$		0			0
$627$	−19.8627	+	23.5456i	−0.0316790	+	0.0375528i
$628$		0			0
$629$	−226.621	−	130.840i	−0.360288	−	0.208012i
$630$		0			0
$631$	40.2753	+	69.7588i	0.0638277	+	0.110553i	0.896173	−	0.443704i	$-0.146336\pi$
$631$	40.2753	+	69.7588i	0.0638277	+	0.110553i	−0.832346	+	0.554257i	$0.813003\pi$
$632$		0			0
$633$	55.5556	+	96.2251i	0.0877656	+	0.152014i
$634$		0			0
$635$			134.146i			0.211254i
$636$		0			0
$637$	6.15153	−	3.55159i	0.00965703	−	0.00557549i
$638$		0			0
$639$			672.822i			1.05293i
$640$		0			0
$641$	−428.893	−	247.621i	−0.669100	−	0.386305i	0.126636	−	0.991949i	$-0.459582\pi$
$641$	−428.893	−	247.621i	−0.669100	−	0.386305i	−0.795735	+	0.605644i	$0.792915\pi$
$642$		0			0
$643$	245.123	−	424.566i	0.381218	−	0.660289i	−0.610019	−	0.792387i	$-0.708838\pi$
$643$	245.123	−	424.566i	0.381218	−	0.660289i	0.991237	+	0.132098i	$0.0421714\pi$
$644$		0			0
$645$			11.8675i			0.0183992i
$646$		0			0
$647$	494.132			0.763727			0.381864	−	0.924219i	$-0.375282\pi$
$647$	494.132			0.763727			0.381864	+	0.924219i	$0.375282\pi$
$648$		0			0
$649$	152.605	+	88.1066i	0.235139	+	0.135757i
$650$		0			0
$651$	−14.3633	+	24.8779i	−0.0220634	+	0.0382149i
$652$		0			0
$653$	475.383			0.727998			0.363999	−	0.931399i	$-0.381411\pi$
$653$	475.383			0.727998			0.363999	+	0.931399i	$0.381411\pi$
$654$		0			0
$655$	−41.3763	−	71.6658i	−0.0631699	−	0.109413i
$656$		0			0
$657$	261.485			0.397998
$658$		0			0
$659$	−494.082	+	285.259i	−0.749746	+	0.432866i	−0.825602	−	0.564253i	$-0.809164\pi$
$659$	−494.082	+	285.259i	−0.749746	+	0.432866i	0.0758563	+	0.997119i	$0.475831\pi$
$660$		0			0
$661$	−18.6964	+	10.7944i	−0.0282851	+	0.0163304i	−0.514076	−	0.857745i	$-0.671865\pi$
$661$	−18.6964	+	10.7944i	−0.0282851	+	0.0163304i	0.485791	+	0.874075i	$0.338532\pi$
$662$		0			0
$663$	0.330868	−	0.573080i	0.000499047	−	0.000864374i
$664$		0			0
$665$	−42.1010	−	35.5159i	−0.0633098	−	0.0534073i
$666$		0			0
$667$	−657.022	−	379.332i	−0.985041	−	0.568714i
$668$		0			0
$669$	−5.05051	−	8.74774i	−0.00754934	−	0.0130758i
$670$		0			0
$671$	194.328	+	336.586i	0.289610	+	0.501619i
$672$		0			0
$673$		−	256.395i		−	0.380973i	−0.981690	−	0.190486i	$-0.938993\pi$
$673$		−	256.395i		−	0.380973i	0.981690	−	0.190486i	$-0.0610065\pi$
$674$		0			0
$675$	−118.243	+	68.2675i	−0.175175	+	0.101137i
$676$		0			0
$677$			662.815i			0.979048i	0.871990	+	0.489524i	$0.162829\pi$
$677$			662.815i			0.979048i	−0.871990	+	0.489524i	$0.837171\pi$
$678$		0			0
$679$	−373.529	−	215.657i	−0.550116	−	0.317610i
$680$		0			0
$681$	−39.6867	+	68.7394i	−0.0582771	+	0.100939i
$682$		0			0
$683$		−	310.334i		−	0.454369i	−0.973852	−	0.227184i	$-0.927048\pi$
$683$		−	310.334i		−	0.454369i	0.973852	−	0.227184i	$-0.0729520\pi$
$684$		0			0
$685$	11.8990			0.0173708
$686$		0			0
$687$	71.4801	+	41.2691i	0.104047	+	0.0600714i
$688$		0			0
$689$	−4.87805	+	8.44904i	−0.00707990	+	0.0122628i
$690$		0			0
$691$	−187.789			−0.271764			−0.135882	−	0.990725i	$-0.543387\pi$
$691$	−187.789			−0.271764			−0.135882	+	0.990725i	$0.543387\pi$
$692$		0			0
$693$	−65.7980	−	113.965i	−0.0949465	−	0.164452i
$694$		0			0
$695$	41.7423			0.0600609
$696$		0			0
$697$	−558.530	+	322.467i	−0.801334	+	0.462650i
$698$		0			0
$699$	−107.427	+	62.0232i	−0.153687	+	0.0887313i
$700$		0			0
$701$	−270.818	+	469.070i	−0.386331	+	0.669144i	−0.991953	−	0.126608i	$-0.959591\pi$
$701$	−270.818	+	469.070i	−0.386331	+	0.669144i	0.605622	+	0.795752i	$0.292924\pi$
$702$		0			0
$703$	−411.303	−	73.6387i	−0.585068	−	0.104749i
$704$		0			0
$705$	−22.4444	−	12.9583i	−0.0318360	−	0.0183805i
$706$		0			0
$707$	203.631	+	352.699i	0.288021	+	0.498868i
$708$		0			0
$709$	245.621	+	425.429i	0.346434	+	0.600041i	0.985613	−	0.169017i	$-0.0540593\pi$
$709$	245.621	+	425.429i	0.346434	+	0.600041i	−0.639180	+	0.769058i	$0.720726\pi$
$710$		0			0
$711$		−	587.969i		−	0.826961i
$712$		0			0
$713$	−460.226	+	265.712i	−0.645478	+	0.372667i
$714$		0			0
$715$			0.892539i			0.00124831i
$716$		0			0
$717$	−81.6617	−	47.1474i	−0.113894	−	0.0657565i
$718$		0			0
$719$	−287.734	+	498.370i	−0.400186	+	0.693143i	−0.993748	−	0.111645i	$-0.964388\pi$
$719$	−287.734	+	498.370i	−0.400186	+	0.693143i	0.593562	+	0.804788i	$0.297721\pi$
$720$		0			0
$721$			330.383i			0.458229i
$722$		0			0
$723$	36.6005			0.0506231
$724$		0			0
$725$	925.090	+	534.101i	1.27599	+	0.736691i
$726$		0			0
$727$	−409.552	+	709.365i	−0.563346	+	0.975743i	0.433856	+	0.900982i	$0.357153\pi$
$727$	−409.552	+	709.365i	−0.563346	+	0.975743i	−0.997201	+	0.0747610i	$0.976181\pi$
$728$		0			0
$729$	680.362			0.933282
$730$		0			0
$731$	−222.144	−	384.764i	−0.303890	−	0.526353i
$732$		0			0
$733$	804.332			1.09731			0.548657	−	0.836047i	$-0.315139\pi$
$733$	804.332			1.09731			0.548657	+	0.836047i	$0.315139\pi$
$734$		0			0
$735$	11.1742	−	6.45145i	0.0152030	−	0.00877748i
$736$		0			0
$737$	−523.665	+	302.338i	−0.710536	+	0.410228i
$738$		0			0
$739$	37.9314	−	65.6991i	0.0513280	−	0.0889027i	−0.839220	−	0.543792i	$-0.816988\pi$
$739$	37.9314	−	65.6991i	0.0513280	−	0.0889027i	0.890548	+	0.454890i	$0.150321\pi$
$740$		0			0
$741$	0.186218	−	1.04011i	0.000251306	−	0.00140365i
$742$		0			0
$743$	−505.810	−	292.030i	−0.680767	−	0.393041i	0.119377	−	0.992849i	$-0.461910\pi$
$743$	−505.810	−	292.030i	−0.680767	−	0.393041i	−0.800144	+	0.599808i	$0.795244\pi$
$744$		0			0
$745$	−17.8383	−	30.8968i	−0.0239440	−	0.0414722i
$746$		0			0
$747$	−136.586	−	236.573i	−0.182846	−	0.316698i
$748$		0			0
$749$			330.383i			0.441099i
$750$		0			0
$751$	−513.931	+	296.718i	−0.684329	+	0.395098i	−0.801484	−	0.598016i	$-0.795956\pi$
$751$	−513.931	+	296.718i	−0.684329	+	0.395098i	0.117155	+	0.993114i	$0.462623\pi$
$752$		0			0
$753$		−	155.716i		−	0.206794i
$754$		0			0
$755$	−74.0908	−	42.7764i	−0.0981335	−	0.0566574i
$756$		0			0
$757$	278.257	−	481.956i	0.367579	−	0.636665i	−0.621608	−	0.783329i	$-0.713520\pi$
$757$	278.257	−	481.956i	0.367579	−	0.636665i	0.989186	+	0.146664i	$0.0468535\pi$
$758$		0			0
$759$			27.6356i			0.0364106i
$760$		0			0
$761$	−1211.85			−1.59244			−0.796219	−	0.605008i	$-0.793170\pi$
$761$	−1211.85			−1.59244			−0.796219	+	0.605008i	$0.793170\pi$
$762$		0			0
$763$	171.742	+	99.1555i	0.225088	+	0.129955i
$764$		0			0
$765$	−52.9444	+	91.7024i	−0.0692083	+	0.119872i
$766$		0			0
$767$	−6.04438			−0.00788054
$768$		0			0
$769$	479.115	+	829.852i	0.623037	+	1.07913i	0.988917	+	0.148469i	$0.0474347\pi$
$769$	479.115	+	829.852i	0.623037	+	1.07913i	−0.365880	+	0.930662i	$0.619232\pi$
$770$		0			0
$771$	72.4393			0.0939550
$772$		0			0
$773$	−404.409	+	233.486i	−0.523168	+	0.302051i	−0.738230	−	0.674549i	$-0.764338\pi$
$773$	−404.409	+	233.486i	−0.523168	+	0.302051i	0.215062	+	0.976600i	$0.431005\pi$
$774$		0			0
$775$	648.000	−	374.123i	0.836129	−	0.482739i
$776$		0			0
$777$	−10.1316	+	17.5485i	−0.0130394	+	0.0225850i
$778$		0			0
$779$	−664.023	+	787.142i	−0.852405	+	1.01045i
$780$		0			0
$781$	−334.001	−	192.836i	−0.427658	−	0.246909i
$782$		0			0
$783$	126.603	+	219.283i	0.161690	+	0.280055i
$784$		0			0
$785$	−100.076	−	173.336i	−0.127485	−	0.220810i
$786$		0			0
$787$			1410.48i			1.79223i	0.443824	+	0.896114i	$0.353621\pi$
$787$			1410.48i			1.79223i	−0.443824	+	0.896114i	$0.646379\pi$
$788$		0			0
$789$	−37.4138	+	21.6009i	−0.0474192	+	0.0273775i
$790$		0			0
$791$			237.517i			0.300275i
$792$		0			0
$793$	−11.5454	−	6.66574i	−0.0145592	−	0.00840573i
$794$		0			0
$795$	−8.86097	+	15.3476i	−0.0111459	+	0.0193052i
$796$		0			0
$797$			774.540i			0.971819i	0.874009	+	0.485909i	$0.161511\pi$
$797$			774.540i			0.971819i	−0.874009	+	0.485909i	$0.838489\pi$
$798$		0			0
$799$	970.246			1.21433
$800$		0			0
$801$	78.7423	+	45.4619i	0.0983051	+	0.0567564i
$802$		0			0
$803$	−74.9434	+	129.806i	−0.0933292	+	0.161651i
$804$		0			0
$805$	−49.4143			−0.0613842
$806$		0			0
$807$	−41.3048	−	71.5421i	−0.0511832	−	0.0886519i
$808$		0			0
$809$	−1114.09			−1.37712			−0.688559	−	0.725180i	$-0.741756\pi$
$809$	−1114.09			−1.37712			−0.688559	+	0.725180i	$0.741756\pi$
$810$		0			0
$811$	13.7656	−	7.94755i	0.0169736	−	0.00979970i	−0.491489	−	0.870884i	$-0.663547\pi$
$811$	13.7656	−	7.94755i	0.0169736	−	0.00979970i	0.508463	+	0.861084i	$0.330214\pi$
$812$		0			0
$813$	64.1301	−	37.0255i	0.0788808	−	0.0455419i
$814$		0			0
$815$	63.6515	−	110.248i	0.0781000	−	0.135273i
$816$		0			0
$817$	−542.253	−	457.437i	−0.663712	−	0.559899i
$818$		0			0
$819$	3.90918	+	2.25697i	0.00477312	+	0.00275576i
$820$		0			0
$821$	102.444	+	177.439i	0.124780	+	0.216125i	0.921647	−	0.388030i	$-0.126844\pi$
$821$	102.444	+	177.439i	0.124780	+	0.216125i	−0.796867	+	0.604155i	$0.793511\pi$
$822$		0			0
$823$	621.052	+	1075.69i	0.754619	+	1.30704i	0.945563	+	0.325438i	$0.105512\pi$
$823$	621.052	+	1075.69i	0.754619	+	1.30704i	−0.190944	+	0.981601i	$0.561155\pi$
$824$		0			0
$825$		−	38.9111i		−	0.0471649i
$826$		0			0
$827$	990.128	−	571.651i	1.19725	−	0.691234i	0.237311	−	0.971434i	$-0.423734\pi$
$827$	990.128	−	571.651i	1.19725	−	0.691234i	0.959942	+	0.280200i	$0.0904007\pi$
$828$		0			0
$829$		−	1080.66i		−	1.30357i	−0.758404	−	0.651784i	$-0.774021\pi$
$829$		−	1080.66i		−	1.30357i	0.758404	−	0.651784i	$-0.225979\pi$
$830$		0			0
$831$	2.59947	+	1.50081i	0.00312813	+	0.00180603i
$832$		0			0
$833$	−241.525	+	418.334i	−0.289946	+	0.502201i
$834$		0			0
$835$		−	183.501i		−	0.219762i
$836$		0			0
$837$	177.364			0.211905
$838$		0			0
$839$	−582.598	−	336.363i	−0.694395	−	0.400909i	0.110861	−	0.993836i	$-0.464639\pi$
$839$	−582.598	−	336.363i	−0.694395	−	0.400909i	−0.805257	+	0.592927i	$0.797972\pi$
$840$		0			0
$841$	569.999	−	987.267i	0.677763	−	1.17392i
$842$		0			0
$843$	−49.7628			−0.0590306
$844$		0			0
$845$	84.4847	+	146.332i	0.0999819	+	0.173174i
$846$		0			0
$847$	−275.344			−0.325081
$848$		0			0
$849$	−0.807649	+	0.466296i	−0.000951294	+	0.000549230i
$850$		0			0
$851$	−324.637	+	187.429i	−0.381477	+	0.220246i
$852$		0			0
$853$	−123.620	+	214.117i	−0.144924	+	0.251016i	−0.929345	−	0.369213i	$-0.879627\pi$
$853$	−123.620	+	214.117i	−0.144924	+	0.251016i	0.784420	+	0.620229i	$0.212961\pi$
$854$		0			0
$855$	−29.7980	+	166.434i	−0.0348514	+	0.194660i
$856$		0			0
$857$	−615.227	−	355.201i	−0.717884	−	0.414470i	0.0960894	−	0.995373i	$-0.469367\pi$
$857$	−615.227	−	355.201i	−0.717884	−	0.414470i	−0.813973	+	0.580902i	$0.802700\pi$
$858$		0			0
$859$	505.183	+	875.003i	0.588106	+	1.01863i	0.994480	+	0.104923i	$0.0334597\pi$
$859$	505.183	+	875.003i	0.588106	+	1.01863i	−0.406374	+	0.913707i	$0.633207\pi$
$860$		0			0
$861$	24.9704	+	43.2500i	0.0290016	+	0.0502323i
$862$		0			0
$863$		−	455.826i		−	0.528188i	−0.964497	−	0.264094i	$-0.914927\pi$
$863$		−	455.826i		−	0.528188i	0.964497	−	0.264094i	$-0.0850729\pi$
$864$		0			0
$865$	−57.6214	+	33.2677i	−0.0666144	+	0.0384598i
$866$		0			0
$867$		−	46.8538i		−	0.0540412i
$868$		0			0
$869$	291.879	+	168.516i	0.335879	+	0.193920i
$870$		0			0
$871$	10.3707	−	17.9625i	0.0119066	−	0.0206229i
$872$		0			0
$873$			1324.00i			1.51661i
$874$		0			0
$875$	142.050			0.162343
$876$		0			0
$877$	564.060	+	325.660i	0.643170	+	0.371334i	0.785834	−	0.618437i	$-0.212234\pi$
$877$	564.060	+	325.660i	0.643170	+	0.371334i	−0.142665	+	0.989771i	$0.545567\pi$
$878$		0			0
$879$	52.8184	−	91.4841i	0.0600892	−	0.104077i
$880$		0			0
$881$	−518.293			−0.588301			−0.294150	−	0.955759i	$-0.595037\pi$
$881$	−518.293			−0.588301			−0.294150	+	0.955759i	$0.595037\pi$
$882$		0			0
$883$	−336.532	−	582.890i	−0.381123	−	0.660125i	0.610100	−	0.792325i	$-0.291129\pi$
$883$	−336.532	−	582.890i	−0.381123	−	0.660125i	−0.991223	+	0.132200i	$0.957796\pi$
$884$		0			0
$885$	−10.9796			−0.0124063
$886$		0			0
$887$	−1296.33	+	748.434i	−1.46147	+	0.843781i	−0.999080	−	0.0428947i	$-0.986342\pi$
$887$	−1296.33	+	748.434i	−1.46147	+	0.843781i	−0.462392	+	0.886676i	$0.653009\pi$
$888$		0			0
$889$	−336.787	+	194.444i	−0.378838	+	0.218722i
$890$		0			0
$891$	−199.661	+	345.822i	−0.224086	+	0.388128i
$892$		0			0
$893$	1457.22	−	526.053i	1.63183	−	0.589085i
$894$		0			0
$895$	−20.9694	−	12.1067i	−0.0234295	−	0.0135270i
$896$		0			0
$897$	−0.473972	−	0.820943i	−0.000528397	−	0.000915210i
$898$		0			0
$899$	−693.817	−	1201.73i	−0.771766	−	1.33674i
$900$		0			0
$901$		−	663.462i		−	0.736362i
$902$		0			0
$903$	−29.7944	+	17.2018i	−0.0329949	+	0.0190496i
$904$		0			0
$905$		−	35.6732i		−	0.0394179i
$906$		0			0
$907$	−243.114	−	140.362i	−0.268042	−	0.154754i	0.359956	−	0.932969i	$-0.382792\pi$
$907$	−243.114	−	140.362i	−0.268042	−	0.154754i	−0.627997	+	0.778215i	$0.716125\pi$
$908$		0			0
$909$	625.085	−	1082.68i	0.687662	−	1.19107i
$910$		0			0
$911$		−	783.689i		−	0.860252i	−0.902769	−	0.430126i	$-0.858469\pi$
$911$		−	783.689i		−	0.860252i	0.902769	−	0.430126i	$-0.141531\pi$
$912$		0			0
$913$	156.586			0.171507
$914$		0			0
$915$	−20.9722	−	12.1083i	−0.0229204	−	0.0132331i
$916$		0			0
$917$	119.949	−	207.758i	0.130806	−	0.226562i
$918$		0			0
$919$	220.334			0.239754			0.119877	−	0.992789i	$-0.461750\pi$
$919$	220.334			0.239754			0.119877	+	0.992789i	$0.461750\pi$
$920$		0			0
$921$	40.9143	+	70.8656i	0.0444238	+	0.0769442i
$922$		0			0
$923$	13.2291			0.0143327
$924$		0			0
$925$	457.090	−	263.901i	0.494151	−	0.285298i
$926$		0			0
$927$	878.302	−	507.088i	0.947467	−	0.547020i
$928$		0			0
$929$	−614.742	+	1064.76i	−0.661724	+	1.14614i	0.318438	+	0.947944i	$0.396842\pi$
$929$	−614.742	+	1064.76i	−0.661724	+	1.14614i	−0.980162	+	0.198196i	$0.936492\pi$
$930$		0			0
$931$	−135.934	+	759.250i	−0.146009	+	0.815521i
$932$		0			0
$933$	59.9138	+	34.5912i	0.0642163	+	0.0370753i
$934$		0			0
$935$	−30.3485	−	52.5651i	−0.0324583	−	0.0562193i
$936$		0			0
$937$	67.1061	+	116.231i	0.0716181	+	0.124046i	0.899611	−	0.436693i	$-0.143850\pi$
$937$	67.1061	+	116.231i	0.0716181	+	0.124046i	−0.827993	+	0.560739i	$0.810517\pi$
$938$		0			0
$939$		−	98.6064i		−	0.105012i
$940$		0			0
$941$	−518.348	+	299.268i	−0.550848	+	0.318032i	−0.749464	−	0.662045i	$-0.769689\pi$
$941$	−518.348	+	299.268i	−0.550848	+	0.318032i	0.198616	+	0.980077i	$0.436355\pi$
$942$		0			0
$943$			923.875i			0.979719i
$944$		0			0
$945$	14.2827	+	8.24609i	0.0151139	+	0.00872602i
$946$		0			0
$947$	410.265	−	710.600i	0.433226	−	0.750369i	−0.563923	−	0.825827i	$-0.690709\pi$
$947$	410.265	−	710.600i	0.433226	−	0.750369i	0.997149	+	0.0754579i	$0.0240419\pi$
$948$		0			0
$949$		−	5.14134i		−	0.00541764i
$950$		0			0
$951$	109.713			0.115366
$952$		0			0
$953$	−68.1367	−	39.3388i	−0.0714971	−	0.0412789i	0.463825	−	0.885927i	$-0.346477\pi$
$953$	−68.1367	−	39.3388i	−0.0714971	−	0.0412789i	−0.535322	+	0.844648i	$0.679810\pi$
$954$		0			0
$955$	90.1260	−	156.103i	0.0943728	−	0.163458i
$956$		0			0
$957$	−72.1612			−0.0754036
$958$		0			0
$959$	17.2474	+	29.8735i	0.0179848	+	0.0311506i
$960$		0			0
$961$	−11.0000			−0.0114464
$962$		0			0
$963$	878.302	−	507.088i	0.912048	−	0.526571i
$964$		0			0
$965$	188.985	−	109.110i	0.195839	−	0.113068i
$966$		0			0
$967$	664.628	−	1151.17i	0.687310	−	1.19046i	−0.285395	−	0.958410i	$-0.592125\pi$
$967$	664.628	−	1151.17i	0.687310	−	1.19046i	0.972705	−	0.232045i	$-0.0745417\pi$
$968$		0			0
$969$	24.3990	+	67.5877i	0.0251795	+	0.0697499i
$970$		0			0
$971$	492.584	+	284.393i	0.507296	+	0.292887i	0.731721	−	0.681604i	$-0.238717\pi$
$971$	492.584	+	284.393i	0.507296	+	0.292887i	−0.224426	+	0.974491i	$0.572051\pi$
$972$		0			0
$973$	60.5051	+	104.798i	0.0621841	+	0.107706i
$974$		0			0
$975$	0.667354	+	1.15589i	0.000684466	+	0.00118553i
$976$		0			0
$977$		−	884.903i		−	0.905735i	−0.891578	−	0.452867i	$-0.850401\pi$
$977$		−	884.903i		−	0.905735i	0.891578	−	0.452867i	$-0.149599\pi$
$978$		0			0
$979$	−45.1362	+	26.0594i	−0.0461044	+	0.0266184i
$980$		0			0
$981$		−	608.754i		−	0.620544i
$982$		0			0
$983$	−290.842	−	167.917i	−0.295871	−	0.170821i	0.344715	−	0.938707i	$-0.387975\pi$
$983$	−290.842	−	167.917i	−0.295871	−	0.170821i	−0.640587	+	0.767886i	$0.721309\pi$
$984$		0			0
$985$	170.045	−	294.527i	0.172635	−	0.299012i
$986$		0			0
$987$		−	75.1315i		−	0.0761211i
$988$		0			0
$989$	−636.446			−0.643525
$990$		0			0
$991$	491.433	+	283.729i	0.495896	+	0.286306i	0.727017	−	0.686619i	$-0.240906\pi$
$991$	491.433	+	283.729i	0.495896	+	0.286306i	−0.231121	+	0.972925i	$0.574239\pi$
$992$		0			0
$993$	77.4439	−	134.137i	0.0779898	−	0.135082i
$994$		0			0
$995$	−333.388			−0.335064
$996$		0			0
$997$	217.379	+	376.511i	0.218033	+	0.377644i	0.954206	−	0.299149i	$-0.0967027\pi$
$997$	217.379	+	376.511i	0.218033	+	0.377644i	−0.736174	+	0.676793i	$0.763369\pi$
$998$		0			0
$999$	125.110			0.125235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.3.r.a.65.2		4
4.3	odd	2		38.3.d.a.27.2	✓	4
12.11	even	2		342.3.m.a.217.1		4
19.12	odd	6	inner	304.3.r.a.145.2		4
76.11	odd	6		722.3.b.b.721.1		4
76.27	even	6		722.3.b.b.721.4		4
76.31	even	6		38.3.d.a.31.2	yes	4
228.107	odd	6		342.3.m.a.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.d.a.27.2	✓	4	4.3	odd	2
38.3.d.a.31.2	yes	4	76.31	even	6
304.3.r.a.65.2		4	1.1	even	1	trivial
304.3.r.a.145.2		4	19.12	odd	6	inner
342.3.m.a.145.1		4	228.107	odd	6
342.3.m.a.217.1		4	12.11	even	2
722.3.b.b.721.1		4	76.11	odd	6
722.3.b.b.721.4		4	76.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.275255 - 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +2.89898 q^{7} +(-4.44949 - 7.70674i) q^{9} +O(q^{10})\)	\(q+(-0.275255 - 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +2.89898 q^{7} +(-4.44949 - 7.70674i) q^{9} +5.10102 q^{11} +(-0.151531 + 0.0874863i) q^{13} +(-0.275255 + 0.158919i) q^{15} +(5.94949 - 10.3048i) q^{17} +(3.34847 - 18.7026i) q^{19} +(-0.797959 - 0.460702i) q^{21} +(-8.52270 - 14.7618i) q^{23} +(12.0000 + 20.7846i) q^{25} +5.68896i q^{27} +(38.5454 - 22.2542i) q^{29} -31.1769i q^{31} +(-1.40408 - 0.810647i) q^{33} +(1.44949 - 2.51059i) q^{35} -21.9917i q^{37} +0.0556128 q^{39} +(-46.9393 - 27.1004i) q^{41} +(18.6691 - 32.3359i) q^{43} -8.89898 q^{45} +(40.7702 + 70.6160i) q^{47} -40.5959 q^{49} +(-3.27526 + 1.89097i) q^{51} +(48.2878 - 27.8789i) q^{53} +(2.55051 - 4.41761i) q^{55} +(-3.89388 + 4.61586i) q^{57} +(29.9166 + 17.2723i) q^{59} +(38.0959 + 65.9841i) q^{61} +(-12.8990 - 22.3417i) q^{63} +0.174973i q^{65} +(-102.659 + 59.2702i) q^{67} +5.41767i q^{69} +(-65.4773 - 37.8033i) q^{71} +(-14.6918 + 25.4470i) q^{73} -7.62809i q^{75} +14.7878 q^{77} +(57.2196 + 33.0358i) q^{79} +(-39.1413 + 67.7948i) q^{81} +30.6969 q^{83} +(-5.94949 - 10.3048i) q^{85} -14.1464 q^{87} +(-8.84847 + 5.10867i) q^{89} +(-0.439285 + 0.253621i) q^{91} +(-4.95459 + 8.58161i) q^{93} +(-14.5227 - 12.2512i) q^{95} +(-128.848 - 74.3907i) q^{97} +(-22.6969 - 39.3123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 2 * q^5 - 8 * q^7 - 8 * q^9	\( 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9} + 40 q^{11} - 30 q^{13} - 6 q^{15} + 14 q^{17} - 16 q^{19} + 36 q^{21} + 10 q^{23} + 48 q^{25} + 66 q^{29} - 84 q^{33} - 4 q^{35} + 108 q^{39} + 18 q^{41} - 38 q^{43} - 16 q^{45} + 70 q^{47} - 84 q^{49} - 18 q^{51} - 42 q^{53} + 20 q^{55} + 102 q^{57} - 42 q^{59} + 74 q^{61} - 32 q^{63} - 102 q^{67} - 306 q^{71} + 98 q^{73} - 176 q^{77} + 126 q^{79} + 10 q^{81} + 64 q^{83} - 14 q^{85} + 12 q^{87} - 6 q^{89} + 204 q^{91} - 108 q^{93} - 14 q^{95} - 486 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 + 2 * q^5 - 8 * q^7 - 8 * q^9 + 40 * q^11 - 30 * q^13 - 6 * q^15 + 14 * q^17 - 16 * q^19 + 36 * q^21 + 10 * q^23 + 48 * q^25 + 66 * q^29 - 84 * q^33 - 4 * q^35 + 108 * q^39 + 18 * q^41 - 38 * q^43 - 16 * q^45 + 70 * q^47 - 84 * q^49 - 18 * q^51 - 42 * q^53 + 20 * q^55 + 102 * q^57 - 42 * q^59 + 74 * q^61 - 32 * q^63 - 102 * q^67 - 306 * q^71 + 98 * q^73 - 176 * q^77 + 126 * q^79 + 10 * q^81 + 64 * q^83 - 14 * q^85 + 12 * q^87 - 6 * q^89 + 204 * q^91 - 108 * q^93 - 14 * q^95 - 486 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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