LMFDB - Embedded newform 304.3.r.a.145.2

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			145.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.3.r.a.65.2

$q$-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 $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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	−0.545174	−	0.838323i	$-0.683536\pi$
$3$	−0.275255	+	0.158919i	−0.0917517	+	0.0529729i	0.453422	+	0.891296i	$0.350203\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.100000	+	0.173205i	0.911684	−	0.410891i	$-0.134782\pi$
$5$	0.500000	+	0.866025i	0.100000	+	0.173205i	−0.811684	+	0.584096i	$0.801449\pi$
$6$		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	0.494161	−	0.869371i	$-0.335475\pi$
$13$	−0.151531	−	0.0874863i	−0.0116562	−	0.00672972i	−0.505817	+	0.862641i	$0.668809\pi$
$14$		0			0
$15$	−0.275255	−	0.158919i	−0.0183503	−	0.0105946i
$16$		0			0
$17$	5.94949	+	10.3048i	0.349970	+	0.606166i	0.986244	−	0.165298i	$-0.0528584\pi$
$17$	5.94949	+	10.3048i	0.349970	+	0.606166i	−0.636274	+	0.771463i	$0.719525\pi$
$18$		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	−0.989651	−	0.143498i	$-0.954165\pi$
$23$	−8.52270	+	14.7618i	−0.370552	+	0.641815i	0.619098	+	0.785314i	$0.287498\pi$
$24$		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	0.985169	−	0.171589i	$-0.0548903\pi$
$29$	38.5454	+	22.2542i	1.32915	+	0.767386i	0.343983	+	0.938976i	$0.388224\pi$
$30$		0			0
$31$			31.1769i			1.00571i	0.864372	+	0.502853i	$0.167716\pi$
$31$			31.1769i			1.00571i	−0.864372	+	0.502853i	$0.832284\pi$
$32$		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	$0.0960480\pi$
$37$			21.9917i			0.594371i	−0.954820	+	0.297186i	$0.903952\pi$
$38$		0			0
$39$	0.0556128			0.00142597
$40$		0			0
$41$	−46.9393	+	27.1004i	−1.14486	+	0.660986i	−0.947630	−	0.319371i	$-0.896528\pi$
$41$	−46.9393	+	27.1004i	−1.14486	+	0.660986i	−0.197231	+	0.980357i	$0.563195\pi$
$42$		0			0
$43$	18.6691	+	32.3359i	0.434166	+	0.751997i	0.997227	−	0.0744178i	$-0.0237098\pi$
$43$	18.6691	+	32.3359i	0.434166	+	0.751997i	−0.563061	+	0.826415i	$0.690377\pi$
$44$		0			0
$45$	−8.89898			−0.197755
$46$		0			0
$47$	40.7702	−	70.6160i	0.867450	−	1.50247i	0.00285637	−	0.999996i	$-0.499091\pi$
$47$	40.7702	−	70.6160i	0.867450	−	1.50247i	0.864594	−	0.502472i	$-0.167576\pi$
$48$		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	0.880782	−	0.473523i	$-0.157018\pi$
$53$	48.2878	+	27.8789i	0.911090	+	0.526018i	0.0303081	+	0.999541i	$0.490351\pi$
$54$		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	−0.224564	−	0.974459i	$-0.572096\pi$
$59$	29.9166	−	17.2723i	0.507061	−	0.292752i	0.731625	+	0.681708i	$0.238762\pi$
$60$		0			0
$61$	38.0959	−	65.9841i	0.624523	−	1.08171i	−0.364110	−	0.931356i	$-0.618627\pi$
$61$	38.0959	−	65.9841i	0.624523	−	1.08171i	0.988633	−	0.150350i	$-0.0480400\pi$
$62$		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	−0.999259	−	0.0384912i	$-0.987745\pi$
$67$	−102.659	−	59.2702i	−1.53222	−	0.884629i	−0.532964	−	0.846138i	$-0.678922\pi$
$68$		0			0
$69$		−	5.41767i		−	0.0785169i
$70$		0			0
$71$	−65.4773	+	37.8033i	−0.922215	+	0.532441i	−0.884341	−	0.466841i	$-0.845392\pi$
$71$	−65.4773	+	37.8033i	−0.922215	+	0.532441i	−0.0378743	+	0.999283i	$0.512059\pi$
$72$		0			0
$73$	−14.6918	−	25.4470i	−0.201258	−	0.348589i	0.747676	−	0.664064i	$-0.231170\pi$
$73$	−14.6918	−	25.4470i	−0.201258	−	0.348589i	−0.948934	+	0.315475i	$0.897836\pi$
$74$		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	−0.0920338	−	0.995756i	$-0.529337\pi$
$79$	57.2196	−	33.0358i	0.724299	−	0.418174i	0.816333	+	0.577582i	$0.196003\pi$
$80$		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	0.449465	−	0.893298i	$-0.351615\pi$
$89$	−8.84847	−	5.10867i	−0.0994210	−	0.0574007i	−0.548886	+	0.835897i	$0.684948\pi$
$90$		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	−0.985042	−	0.172314i	$-0.944876\pi$
$97$	−128.848	+	74.3907i	−1.32833	+	0.766914i	−0.343293	+	0.939228i	$0.611542\pi$
$98$		0			0
$99$	−22.6969	+	39.3123i	−0.229262	+	0.397093i
$100$		0			0
$101$	70.2423	−	121.663i	0.695469	−	1.20459i	−0.274554	−	0.961572i	$-0.588530\pi$
$101$	70.2423	−	121.663i	0.695469	−	1.20459i	0.970022	−	0.243015i	$-0.0781366\pi$
$102$		0			0
$103$		−	113.965i		−	1.10646i	−0.833028	−	0.553230i	$-0.813395\pi$
$103$		−	113.965i		−	1.10646i	0.833028	−	0.553230i	$-0.186605\pi$
$104$		0			0
$105$	−0.797959	−	0.460702i	−0.00759961	−	0.00438764i
$106$		0			0
$107$		−	113.965i		−	1.06510i	−0.846399	−	0.532549i	$-0.821234\pi$
$107$		−	113.965i		−	1.06510i	0.846399	−	0.532549i	$-0.178766\pi$
$108$		0			0
$109$	59.2423	−	34.2036i	0.543508	−	0.313794i	−0.202992	−	0.979180i	$-0.565066\pi$
$109$	59.2423	−	34.2036i	0.543508	−	0.313794i	0.746499	+	0.665386i	$0.231733\pi$
$110$		0			0
$111$	−3.49490	−	6.05334i	−0.0314856	−	0.0545346i
$112$		0			0
$113$		−	81.9313i		−	0.725056i	−0.931973	−	0.362528i	$-0.881914\pi$
$113$		−	81.9313i		−	0.725056i	0.931973	−	0.362528i	$-0.118086\pi$
$114$		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	−0.0327989	−	0.999462i	$-0.510442\pi$
$127$	−116.174	−	67.0732i	−0.914758	−	0.528136i	−0.881959	+	0.471326i	$0.843775\pi$
$128$		0			0
$129$	−10.2775	−	5.93375i	−0.0796709	−	0.0459980i
$130$		0			0
$131$	41.3763	+	71.6658i	0.315849	+	0.547067i	0.979618	−	0.200871i	$-0.0643772\pi$
$131$	41.3763	+	71.6658i	0.315849	+	0.547067i	−0.663768	+	0.747938i	$0.731044\pi$
$132$		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	−0.843495	−	0.537137i	$-0.819506\pi$
$137$	5.94949	−	10.3048i	0.0434269	−	0.0752177i	0.886922	+	0.461919i	$0.152839\pi$
$138$		0			0
$139$	20.8712	−	36.1499i	0.150152	−	0.260071i	−0.781131	−	0.624367i	$-0.785357\pi$
$139$	20.8712	−	36.1499i	0.150152	−	0.260071i	0.931283	+	0.364296i	$0.118690\pi$
$140$		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	0.919657	−	0.392723i	$-0.128467\pi$
$149$	17.8383	+	30.8968i	0.119720	+	0.207361i	−0.799937	+	0.600084i	$0.795134\pi$
$150$		0			0
$151$			85.5527i			0.566574i	0.959035	+	0.283287i	$0.0914249\pi$
$151$			85.5527i			0.566574i	−0.959035	+	0.283287i	$0.908575\pi$
$152$		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	0.985996	+	0.166768i	$0.0533332\pi$
$157$	100.076	+	173.336i	0.637424	+	1.10405i	−0.348573	+	0.937282i	$0.613333\pi$
$158$		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	0.893576	−	0.448911i	$-0.148188\pi$
$167$	158.917	+	91.7505i	0.951596	+	0.549404i	0.0580198	+	0.998315i	$0.481521\pi$
$168$		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	−0.657204	−	0.753713i	$-0.728261\pi$
$173$	−57.6214	+	33.2677i	−0.333072	+	0.192299i	0.324132	+	0.946012i	$0.394928\pi$
$174$		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	$0.0215454\pi$
$179$			24.2134i			0.135270i	−0.997710	+	0.0676351i	$0.978455\pi$
$180$		0			0
$181$	30.8939	+	17.8366i	0.170684	+	0.0985447i	0.582909	−	0.812538i	$-0.301915\pi$
$181$	30.8939	+	17.8366i	0.170684	+	0.0985447i	−0.412224	+	0.911082i	$0.635248\pi$
$182$		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	0.0771682	−	0.997018i	$-0.475412\pi$
$193$	188.985	−	109.110i	0.979195	−	0.565339i	0.902027	+	0.431679i	$0.142079\pi$
$194$		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	0.0541881	+	0.998531i	$0.482743\pi$
$199$	−166.694	+	288.723i	−0.837659	+	1.45087i	−0.891847	+	0.452337i	$0.850590\pi$
$200$		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	−0.997484	−	0.0708908i	$-0.977416\pi$
$211$	−302.750	+	174.793i	−1.43483	+	0.828401i	−0.437349	+	0.899292i	$0.644082\pi$
$212$		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	−0.437019	−	0.899452i	$-0.643966\pi$
$223$	27.5227	−	15.8902i	0.123420	−	0.0712567i	0.560439	+	0.828196i	$0.310632\pi$
$224$		0			0
$225$	106.788	+	184.962i	0.474612	+	0.822053i
$226$		0			0
$227$			249.730i			1.10013i	0.835121	+	0.550066i	$0.185397\pi$
$227$			249.730i			1.10013i	−0.835121	+	0.550066i	$0.814603\pi$
$228$		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	0.891965	+	0.452104i	$0.149327\pi$
$233$	195.141	+	337.995i	0.837516	+	1.45062i	−0.0544486	+	0.998517i	$0.517340\pi$
$234$		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	0.278618	−	0.960402i	$-0.410124\pi$
$241$	−99.7270	−	57.5774i	−0.413805	−	0.238911i	−0.692423	+	0.721491i	$0.743457\pi$
$242$		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	0.299161	−	0.954203i	$-0.403293\pi$
$251$	244.962	−	424.287i	0.975944	−	1.69038i	0.676783	−	0.736182i	$-0.263373\pi$
$252$		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	0.0641543	−	0.997940i	$-0.479565\pi$
$257$	−197.379	−	113.957i	−0.768010	−	0.443411i	−0.832164	+	0.554529i	$0.812898\pi$
$258$		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	0.965816	−	0.259227i	$-0.0834679\pi$
$263$	67.9620	+	117.714i	0.258411	+	0.447580i	−0.707406	+	0.706808i	$0.750135\pi$
$264$		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	−0.0193970	−	0.999812i	$-0.506175\pi$
$269$	225.090	−	129.956i	0.836767	−	0.483108i	0.856164	+	0.516704i	$0.172841\pi$
$270$		0			0
$271$	−116.492	−	201.770i	−0.429860	−	0.744540i	0.567000	−	0.823718i	$-0.308104\pi$
$271$	−116.492	−	201.770i	−0.429860	−	0.744540i	−0.996860	+	0.0791780i	$0.974770\pi$
$272$		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	0.721470	−	0.692446i	$-0.243467\pi$
$281$	135.591	+	78.2834i	0.482530	+	0.278589i	−0.238940	+	0.971034i	$0.576800\pi$
$282$		0			0
$283$	1.46709	+	2.54108i	0.00518407	+	0.00897907i	0.868606	−	0.495504i	$-0.165017\pi$
$283$	1.46709	+	2.54108i	0.00518407	+	0.00897907i	−0.863422	+	0.504483i	$0.831683\pi$
$284$		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	$-0.808039\pi$
$293$		−	332.361i		−	1.13434i	0.823601	−	0.567169i	$-0.191961\pi$
$294$		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	−0.817053	−	0.576563i	$-0.804393\pi$
$307$	−222.962	+	128.727i	−0.726261	+	0.419307i	0.0907920	+	0.995870i	$0.471060\pi$
$308$		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	−0.504393	−	0.863474i	$-0.668284\pi$
$313$	155.121	−	268.677i	0.495594	−	0.858394i	0.999987	+	0.00508018i	$0.00161708\pi$
$314$		0			0
$315$	−25.7980			−0.0818983
$316$		0			0
$317$	−298.939	−	172.593i	−0.943026	−	0.544456i	−0.0521185	−	0.998641i	$-0.516597\pi$
$317$	−298.939	−	172.593i	−0.943026	−	0.544456i	−0.890908	+	0.454185i	$0.849931\pi$
$318$		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	$-0.736651\pi$
$331$		−	487.318i		−	1.47226i	0.676841	−	0.736130i	$-0.263349\pi$
$332$		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	−0.270226	−	0.962797i	$-0.587099\pi$
$337$	144.393	−	83.3655i	0.428467	−	0.247376i	0.698693	+	0.715421i	$0.253765\pi$
$338$		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	0.998651	+	0.0519291i	$0.0165370\pi$
$347$	188.871	+	327.134i	0.544297	+	0.942751i	−0.454353	+	0.890822i	$0.650130\pi$
$348$		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	0.640697	−	0.767794i	$-0.278645\pi$
$359$	−123.704	−	214.262i	−0.344580	−	0.596831i	−0.985277	+	0.170963i	$0.945312\pi$
$360$		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	−0.321501	−	0.946909i	$-0.604187\pi$
$367$	241.962	−	419.090i	0.659297	−	1.14194i	0.980798	−	0.195027i	$-0.0624793\pi$
$368$		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	$-0.939513\pi$
$373$		−	140.908i		−	0.377768i	0.981999	−	0.188884i	$-0.0604871\pi$
$374$		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	$-0.787842\pi$
$379$		−	468.633i		−	1.23650i	0.785982	−	0.618249i	$-0.212158\pi$
$380$		0			0
$381$	42.6367			0.111907
$382$		0			0
$383$	482.552	−	278.602i	1.25993	−	0.727420i	0.286867	−	0.957970i	$-0.407386\pi$
$383$	482.552	−	278.602i	1.25993	−	0.727420i	0.973060	+	0.230551i	$0.0740528\pi$
$384$		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	−0.919646	−	0.392749i	$-0.871524\pi$
$389$	−46.5602	+	80.6446i	−0.119692	+	0.207313i	0.799954	+	0.600062i	$0.204857\pi$
$390$		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	0.655192	−	0.755463i	$-0.272588\pi$
$397$	−129.682	−	224.615i	−0.326654	−	0.565781i	−0.981846	+	0.189681i	$0.939255\pi$
$398$		0			0
$399$	−11.2883	−	13.3813i	−0.0282914	−	0.0335370i
$400$		0			0
$401$	−389.484	+	224.869i	−0.971282	+	0.560770i	−0.899627	−	0.436659i	$-0.856161\pi$
$401$	−389.484	+	224.869i	−0.971282	+	0.560770i	−0.0716553	+	0.997429i	$0.522828\pi$
$402$		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	0.606915	−	0.794767i	$-0.292407\pi$
$409$	90.8326	+	52.4423i	0.222085	+	0.128221i	−0.384830	+	0.922987i	$0.625740\pi$
$410$		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	−0.906635	−	0.421915i	$-0.861358\pi$
$421$	−418.711	+	241.743i	−0.994563	+	0.574211i	−0.0879282	+	0.996127i	$0.528025\pi$
$422$		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	−0.0299413	−	0.999552i	$-0.509532\pi$
$431$	−392.447	−	226.579i	−0.910549	−	0.525706i	−0.880608	+	0.473846i	$0.842865\pi$
$432$		0			0
$433$	650.651	+	375.654i	1.50266	+	0.867560i	0.999995	+	0.00307767i	$0.000979653\pi$
$433$	650.651	+	375.654i	1.50266	+	0.867560i	0.502663	+	0.864482i	$0.332354\pi$
$434$		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	−0.968612	−	0.248578i	$-0.920037\pi$
$439$	−543.325	+	313.689i	−1.23764	+	0.714553i	−0.269031	+	0.963132i	$0.586703\pi$
$440$		0			0
$441$	180.631	−	312.862i	0.409594	−	0.709438i
$442$		0			0
$443$	220.628	−	382.139i	0.498032	−	0.862617i	−0.501965	−	0.864888i	$-0.667389\pi$
$443$	220.628	−	382.139i	0.498032	−	0.862617i	0.999997	+	0.00227061i	$0.000722758\pi$
$444$		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	$0.126645\pi$
$449$			347.932i			0.774904i	−0.921890	+	0.387452i	$0.873355\pi$
$450$		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	0.740227	−	0.672357i	$-0.234718\pi$
$461$	−97.8076	−	169.408i	−0.212164	−	0.367479i	−0.952392	+	0.304878i	$0.901384\pi$
$462$		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	−0.625939	−	0.779872i	$-0.715284\pi$
$479$	173.599	−	300.682i	0.362419	−	0.627728i	0.988358	+	0.152144i	$0.0486176\pi$
$480$		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	$0.170058\pi$
$487$			495.960i			1.01840i	−0.860648	+	0.509200i	$0.829942\pi$
$488$		0			0
$489$	−35.0408	+	20.2308i	−0.0716581	+	0.0413718i
$490$		0			0
$491$	267.174	+	462.759i	0.544143	+	0.942483i	0.998660	+	0.0517455i	$0.0164785\pi$
$491$	267.174	+	462.759i	0.544143	+	0.942483i	−0.454517	+	0.890738i	$0.650188\pi$
$492$		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	0.924415	+	0.381387i	$0.124554\pi$
$499$	395.457	+	684.951i	0.792499	+	1.37265i	−0.131917	+	0.991261i	$0.542113\pi$
$500$		0			0
$501$	−58.3235			−0.116414
$502$		0			0
$503$	209.841	−	363.455i	0.417178	−	0.722574i	−0.578476	−	0.815699i	$-0.696352\pi$
$503$	209.841	−	363.455i	0.417178	−	0.722574i	0.995654	+	0.0931256i	$0.0296858\pi$
$504$		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	0.990471	−	0.137724i	$-0.0439786\pi$
$509$	695.515	+	401.556i	1.36643	+	0.788911i	0.375963	+	0.926635i	$0.377312\pi$
$510$		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	$-0.870055\pi$
$521$		−	413.663i		−	0.793979i	0.917823	−	0.396990i	$-0.129945\pi$
$522$		0			0
$523$	−434.144	−	250.653i	−0.830103	−	0.479260i	0.0237853	−	0.999717i	$-0.492428\pi$
$523$	−434.144	−	250.653i	−0.830103	−	0.479260i	−0.853888	+	0.520457i	$0.825762\pi$
$524$		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	−0.625154	−	0.780501i	$-0.714964\pi$
$541$	196.576	−	340.480i	0.363357	−	0.629352i	0.988511	+	0.151149i	$0.0482973\pi$
$542$		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	0.830895	−	0.556430i	$-0.187829\pi$
$547$	418.159	+	241.424i	0.764460	+	0.441361i	−0.0664350	+	0.997791i	$0.521162\pi$
$548$		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	−0.789867	−	0.613279i	$-0.789850\pi$
$557$	75.8531	−	131.381i	0.136181	−	0.235873i	0.926048	+	0.377405i	$0.123184\pi$
$558$		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	$0.0501399\pi$
$563$			176.634i			0.313737i	−0.987620	+	0.156868i	$0.949860\pi$
$564$		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	$0.318483\pi$
$569$			957.928i			1.68353i	−0.539844	+	0.841765i	$0.681517\pi$
$570$		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	−0.999500	−	0.0316288i	$-0.989931\pi$
$587$	−309.432	−	535.952i	−0.527141	−	0.913035i	0.472358	−	0.881407i	$-0.343403\pi$
$588$		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	−0.775850	−	0.630917i	$-0.782679\pi$
$593$	93.9699	−	162.761i	0.158465	−	0.274470i	0.934315	+	0.356447i	$0.116012\pi$
$594$		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	0.556933	−	0.830557i	$-0.311978\pi$
$599$	69.5533	+	40.1566i	0.116116	+	0.0670394i	−0.440817	+	0.897597i	$0.645311\pi$
$600$		0			0
$601$		−	665.929i		−	1.10804i	−0.832505	−	0.554018i	$-0.813094\pi$
$601$		−	665.929i		−	1.10804i	0.832505	−	0.554018i	$-0.186906\pi$
$602$		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	$-0.972184\pi$
$607$		−	105.952i		−	0.174550i	0.996184	−	0.0872751i	$-0.0278159\pi$
$608$		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	0.785832	+	0.618440i	$0.212235\pi$
$613$	569.171	+	985.833i	0.928501	+	1.60821i	0.142668	+	0.989771i	$0.454432\pi$
$614$		0			0
$615$	17.2270			0.0280114
$616$		0			0
$617$	−459.131	+	795.238i	−0.744135	+	1.28888i	0.206463	+	0.978454i	$0.433805\pi$
$617$	−459.131	+	795.238i	−0.744135	+	1.28888i	−0.950598	+	0.310425i	$0.899529\pi$
$618$		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	−0.832346	−	0.554257i	$-0.813003\pi$
$631$	40.2753	−	69.7588i	0.0638277	−	0.110553i	0.896173	+	0.443704i	$0.146336\pi$
$632$		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	−0.795735	−	0.605644i	$-0.792915\pi$
$641$	−428.893	+	247.621i	−0.669100	+	0.386305i	0.126636	+	0.991949i	$0.459582\pi$
$642$		0			0
$643$	245.123	+	424.566i	0.381218	+	0.660289i	0.991237	−	0.132098i	$-0.0421714\pi$
$643$	245.123	+	424.566i	0.381218	+	0.660289i	−0.610019	+	0.792387i	$0.708838\pi$
$644$		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	0.0758563	−	0.997119i	$-0.475831\pi$
$659$	−494.082	−	285.259i	−0.749746	−	0.432866i	−0.825602	+	0.564253i	$0.809164\pi$
$660$		0			0
$661$	−18.6964	−	10.7944i	−0.0282851	−	0.0163304i	0.485791	−	0.874075i	$-0.338532\pi$
$661$	−18.6964	−	10.7944i	−0.0282851	−	0.0163304i	−0.514076	+	0.857745i	$0.671865\pi$
$662$		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	$0.0610065\pi$
$673$			256.395i			0.380973i	−0.981690	+	0.190486i	$0.938993\pi$
$674$		0			0
$675$	−118.243	−	68.2675i	−0.175175	−	0.101137i
$676$		0			0
$677$		−	662.815i		−	0.979048i	−0.871990	−	0.489524i	$-0.837171\pi$
$677$		−	662.815i		−	0.979048i	0.871990	−	0.489524i	$-0.162829\pi$
$678$		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	$0.0729520\pi$
$683$			310.334i			0.454369i	−0.973852	+	0.227184i	$0.927048\pi$
$684$		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	0.605622	−	0.795752i	$-0.292924\pi$
$701$	−270.818	−	469.070i	−0.386331	−	0.669144i	−0.991953	+	0.126608i	$0.959591\pi$
$702$		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	−0.639180	−	0.769058i	$-0.720726\pi$
$709$	245.621	−	425.429i	0.346434	−	0.600041i	0.985613	+	0.169017i	$0.0540593\pi$
$710$		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	0.593562	−	0.804788i	$-0.297721\pi$
$719$	−287.734	−	498.370i	−0.400186	−	0.693143i	−0.993748	+	0.111645i	$0.964388\pi$
$720$		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	−0.997201	−	0.0747610i	$-0.976181\pi$
$727$	−409.552	−	709.365i	−0.563346	−	0.975743i	0.433856	−	0.900982i	$-0.357153\pi$
$728$		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	0.890548	−	0.454890i	$-0.150321\pi$
$739$	37.9314	+	65.6991i	0.0513280	+	0.0889027i	−0.839220	+	0.543792i	$0.816988\pi$
$740$		0			0
$741$	0.186218	+	1.04011i	0.000251306	+	0.00140365i
$742$		0			0
$743$	−505.810	+	292.030i	−0.680767	+	0.393041i	−0.800144	−	0.599808i	$-0.795244\pi$
$743$	−505.810	+	292.030i	−0.680767	+	0.393041i	0.119377	+	0.992849i	$0.461910\pi$
$744$		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	0.117155	−	0.993114i	$-0.462623\pi$
$751$	−513.931	−	296.718i	−0.684329	−	0.395098i	−0.801484	+	0.598016i	$0.795956\pi$
$752$		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	0.989186	−	0.146664i	$-0.0468535\pi$
$757$	278.257	+	481.956i	0.367579	+	0.636665i	−0.621608	+	0.783329i	$0.713520\pi$
$758$		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	−0.365880	−	0.930662i	$-0.619232\pi$
$769$	479.115	−	829.852i	0.623037	−	1.07913i	0.988917	−	0.148469i	$-0.0474347\pi$
$770$		0			0
$771$	72.4393			0.0939550
$772$		0			0
$773$	−404.409	−	233.486i	−0.523168	−	0.302051i	0.215062	−	0.976600i	$-0.431005\pi$
$773$	−404.409	−	233.486i	−0.523168	−	0.302051i	−0.738230	+	0.674549i	$0.764338\pi$
$774$		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	$-0.646379\pi$
$787$		−	1410.48i		−	1.79223i	0.443824	−	0.896114i	$-0.353621\pi$
$788$		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	$-0.838489\pi$
$797$		−	774.540i		−	0.971819i	0.874009	−	0.485909i	$-0.161511\pi$
$798$		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	0.508463	−	0.861084i	$-0.330214\pi$
$811$	13.7656	+	7.94755i	0.0169736	+	0.00979970i	−0.491489	+	0.870884i	$0.663547\pi$
$812$		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	−0.796867	−	0.604155i	$-0.793511\pi$
$821$	102.444	−	177.439i	0.124780	−	0.216125i	0.921647	+	0.388030i	$0.126844\pi$
$822$		0			0
$823$	621.052	−	1075.69i	0.754619	−	1.30704i	−0.190944	−	0.981601i	$-0.561155\pi$
$823$	621.052	−	1075.69i	0.754619	−	1.30704i	0.945563	−	0.325438i	$-0.105512\pi$
$824$		0			0
$825$			38.9111i			0.0471649i
$826$		0			0
$827$	990.128	+	571.651i	1.19725	+	0.691234i	0.959942	−	0.280200i	$-0.0904007\pi$
$827$	990.128	+	571.651i	1.19725	+	0.691234i	0.237311	+	0.971434i	$0.423734\pi$
$828$		0			0
$829$			1080.66i			1.30357i	0.758404	+	0.651784i	$0.225979\pi$
$829$			1080.66i			1.30357i	−0.758404	+	0.651784i	$0.774021\pi$
$830$		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	−0.805257	−	0.592927i	$-0.797972\pi$
$839$	−582.598	+	336.363i	−0.694395	+	0.400909i	0.110861	+	0.993836i	$0.464639\pi$
$840$		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	0.784420	−	0.620229i	$-0.212961\pi$
$853$	−123.620	−	214.117i	−0.144924	−	0.251016i	−0.929345	+	0.369213i	$0.879627\pi$
$854$		0			0
$855$	−29.7980	−	166.434i	−0.0348514	−	0.194660i
$856$		0			0
$857$	−615.227	+	355.201i	−0.717884	+	0.414470i	−0.813973	−	0.580902i	$-0.802700\pi$
$857$	−615.227	+	355.201i	−0.717884	+	0.414470i	0.0960894	+	0.995373i	$0.469367\pi$
$858$		0			0
$859$	505.183	−	875.003i	0.588106	−	1.01863i	−0.406374	−	0.913707i	$-0.633207\pi$
$859$	505.183	−	875.003i	0.588106	−	1.01863i	0.994480	−	0.104923i	$-0.0334597\pi$
$860$		0			0
$861$	24.9704	−	43.2500i	0.0290016	−	0.0502323i
$862$		0			0
$863$			455.826i			0.528188i	0.964497	+	0.264094i	$0.0850729\pi$
$863$			455.826i			0.528188i	−0.964497	+	0.264094i	$0.914927\pi$
$864$		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	−0.142665	−	0.989771i	$-0.545567\pi$
$877$	564.060	−	325.660i	0.643170	−	0.371334i	0.785834	+	0.618437i	$0.212234\pi$
$878$		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	−0.991223	−	0.132200i	$-0.957796\pi$
$883$	−336.532	+	582.890i	−0.381123	+	0.660125i	0.610100	+	0.792325i	$0.291129\pi$
$884$		0			0
$885$	−10.9796			−0.0124063
$886$		0			0
$887$	−1296.33	−	748.434i	−1.46147	−	0.843781i	−0.462392	−	0.886676i	$-0.653009\pi$
$887$	−1296.33	−	748.434i	−1.46147	−	0.843781i	−0.999080	+	0.0428947i	$0.986342\pi$
$888$		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	−0.627997	−	0.778215i	$-0.716125\pi$
$907$	−243.114	+	140.362i	−0.268042	+	0.154754i	0.359956	+	0.932969i	$0.382792\pi$
$908$		0			0
$909$	625.085	+	1082.68i	0.687662	+	1.19107i
$910$		0			0
$911$			783.689i			0.860252i	0.902769	+	0.430126i	$0.141531\pi$
$911$			783.689i			0.860252i	−0.902769	+	0.430126i	$0.858469\pi$
$912$		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	−0.980162	−	0.198196i	$-0.936492\pi$
$929$	−614.742	−	1064.76i	−0.661724	−	1.14614i	0.318438	−	0.947944i	$-0.396842\pi$
$930$		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	−0.827993	−	0.560739i	$-0.810517\pi$
$937$	67.1061	−	116.231i	0.0716181	−	0.124046i	0.899611	+	0.436693i	$0.143850\pi$
$938$		0			0
$939$			98.6064i			0.105012i
$940$		0			0
$941$	−518.348	−	299.268i	−0.550848	−	0.318032i	0.198616	−	0.980077i	$-0.436355\pi$
$941$	−518.348	−	299.268i	−0.550848	−	0.318032i	−0.749464	+	0.662045i	$0.769689\pi$
$942$		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	0.997149	−	0.0754579i	$-0.0240419\pi$
$947$	410.265	+	710.600i	0.433226	+	0.750369i	−0.563923	+	0.825827i	$0.690709\pi$
$948$		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	−0.535322	−	0.844648i	$-0.679810\pi$
$953$	−68.1367	+	39.3388i	−0.0714971	+	0.0412789i	0.463825	+	0.885927i	$0.346477\pi$
$954$		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	0.972705	+	0.232045i	$0.0745417\pi$
$967$	664.628	+	1151.17i	0.687310	+	1.19046i	−0.285395	+	0.958410i	$0.592125\pi$
$968$		0			0
$969$	24.3990	−	67.5877i	0.0251795	−	0.0697499i
$970$		0			0
$971$	492.584	−	284.393i	0.507296	−	0.292887i	−0.224426	−	0.974491i	$-0.572051\pi$
$971$	492.584	−	284.393i	0.507296	−	0.292887i	0.731721	+	0.681604i	$0.238717\pi$
$972$		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	$0.149599\pi$
$977$			884.903i			0.905735i	−0.891578	+	0.452867i	$0.850401\pi$
$978$		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	−0.640587	−	0.767886i	$-0.721309\pi$
$983$	−290.842	+	167.917i	−0.295871	+	0.170821i	0.344715	+	0.938707i	$0.387975\pi$
$984$		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	−0.231121	−	0.972925i	$-0.574239\pi$
$991$	491.433	−	283.729i	0.495896	−	0.286306i	0.727017	+	0.686619i	$0.240906\pi$
$992$		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	−0.736174	−	0.676793i	$-0.763369\pi$
$997$	217.379	−	376.511i	0.218033	−	0.377644i	0.954206	+	0.299149i	$0.0967027\pi$
$998$		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.145.2		4
4.3	odd	2		38.3.d.a.31.2	yes	4
12.11	even	2		342.3.m.a.145.1		4
19.8	odd	6	inner	304.3.r.a.65.2		4
76.7	odd	6		722.3.b.b.721.4		4
76.27	even	6		38.3.d.a.27.2	✓	4
76.31	even	6		722.3.b.b.721.1		4
228.179	odd	6		342.3.m.a.217.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.d.a.27.2	✓	4	76.27	even	6
38.3.d.a.31.2	yes	4	4.3	odd	2
304.3.r.a.65.2		4	19.8	odd	6	inner
304.3.r.a.145.2		4	1.1	even	1	trivial
342.3.m.a.145.1		4	12.11	even	2
342.3.m.a.217.1		4	228.179	odd	6
722.3.b.b.721.1		4	76.31	even	6
722.3.b.b.721.4		4	76.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
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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