LMFDB - Embedded newform 76.3.h.a.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(65,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("76.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.h (of order $6$, degree $2$, 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:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 56x^{6} - 154x^{5} + 917x^{4} - 1582x^{3} + 4294x^{2} - 3528x + 4971 $ x^8 - 4x^7 + 56x^6 - 154x^5 + 917x^4 - 1582x^3 + 4294x^2 - 3528*x + 4971
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$0.500000 - 4.68383i$ of defining polynomial
Character	$\chi$	$=$	76.65
Dual form			76.3.h.a.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.30632 - 1.90890i) q^{3} +(-1.55796 + 2.69846i) q^{5} -11.1883 q^{7} +(2.78782 + 4.82865i) q^{9} +O(q^{10})$	\(q+(-3.30632 - 1.90890i) q^{3} +(-1.55796 + 2.69846i) q^{5} -11.1883 q^{7} +(2.78782 + 4.82865i) q^{9} -5.69156 q^{11} +(-6.74507 + 3.89427i) q^{13} +(10.3022 - 5.94799i) q^{15} +(9.15210 - 15.8519i) q^{17} +(17.9748 - 6.15688i) q^{19} +(36.9920 + 21.3573i) q^{21} +(-17.0743 - 29.5736i) q^{23} +(7.64552 + 13.2424i) q^{25} +13.0735i q^{27} +(-33.1640 + 19.1473i) q^{29} +10.4564i q^{31} +(18.8181 + 10.8646i) q^{33} +(17.4309 - 30.1912i) q^{35} -30.1044i q^{37} +29.7351 q^{39} +(-33.0491 - 19.0809i) q^{41} +(-29.7055 + 51.4514i) q^{43} -17.3732 q^{45} +(-30.9846 - 53.6669i) q^{47} +76.1775 q^{49} +(-60.5195 + 34.9409i) q^{51} +(-45.3846 + 26.2028i) q^{53} +(8.86722 - 15.3585i) q^{55} +(-71.1832 - 13.9555i) q^{57} +(73.7726 + 42.5926i) q^{59} +(1.82516 + 3.16127i) q^{61} +(-31.1909 - 54.0242i) q^{63} -24.2685i q^{65} +(-96.7411 + 55.8535i) q^{67} +130.373i q^{69} +(-55.4406 - 32.0086i) q^{71} +(37.7842 - 65.4442i) q^{73} -58.3783i q^{75} +63.6787 q^{77} +(85.4278 + 49.3218i) q^{79} +(50.0465 - 86.6831i) q^{81} +60.0975 q^{83} +(28.5172 + 49.3932i) q^{85} +146.201 q^{87} +(17.4003 - 10.0461i) q^{89} +(75.4657 - 43.5701i) q^{91} +(19.9602 - 34.5721i) q^{93} +(-11.3899 + 58.0965i) q^{95} +(-50.1828 - 28.9730i) q^{97} +(-15.8670 - 27.4825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9	$ 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} - 10 q^{11} + 9 q^{13} + 33 q^{15} + 23 q^{17} - 33 q^{19} - 31 q^{23} - 73 q^{25} - 105 q^{29} - 111 q^{33} - 68 q^{35} + 234 q^{39} + 18 q^{41} - 41 q^{43} + 200 q^{45} + 107 q^{47} + 312 q^{49} - 9 q^{51} + 39 q^{53} + 70 q^{55} - 381 q^{57} + 348 q^{59} - 45 q^{61} - 358 q^{63} - 432 q^{67} - 243 q^{71} + 16 q^{73} + 544 q^{77} + 75 q^{79} - 68 q^{81} - 82 q^{83} + 109 q^{85} + 414 q^{87} - 213 q^{89} + 222 q^{91} + 288 q^{93} - 385 q^{95} + 144 q^{97} - 388 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9 - 10 * q^11 + 9 * q^13 + 33 * q^15 + 23 * q^17 - 33 * q^19 - 31 * q^23 - 73 * q^25 - 105 * q^29 - 111 * q^33 - 68 * q^35 + 234 * q^39 + 18 * q^41 - 41 * q^43 + 200 * q^45 + 107 * q^47 + 312 * q^49 - 9 * q^51 + 39 * q^53 + 70 * q^55 - 381 * q^57 + 348 * q^59 - 45 * q^61 - 358 * q^63 - 432 * q^67 - 243 * q^71 + 16 * q^73 + 544 * q^77 + 75 * q^79 - 68 * q^81 - 82 * q^83 + 109 * q^85 + 414 * q^87 - 213 * q^89 + 222 * q^91 + 288 * q^93 - 385 * q^95 + 144 * q^97 - 388 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−3.30632	−	1.90890i	−1.10211	−	0.636301i	−0.165332	−	0.986238i	$-0.552870\pi$
$3$	−3.30632	−	1.90890i	−1.10211	−	0.636301i	−0.936773	+	0.349937i	$0.886203\pi$
$4$		0			0
$5$	−1.55796	+	2.69846i	−0.311592	+	0.539693i	−0.978707	−	0.205262i	$-0.934196\pi$
$5$	−1.55796	+	2.69846i	−0.311592	+	0.539693i	0.667115	+	0.744955i	$0.267529\pi$
$6$		0			0
$7$	−11.1883			−1.59832			−0.799162	−	0.601115i	$-0.794723\pi$
$7$	−11.1883			−1.59832			−0.799162	+	0.601115i	$0.794723\pi$
$8$		0			0
$9$	2.78782	+	4.82865i	0.309758	+	0.536516i
$10$		0			0
$11$	−5.69156			−0.517414			−0.258707	−	0.965956i	$-0.583296\pi$
$11$	−5.69156			−0.517414			−0.258707	+	0.965956i	$0.583296\pi$
$12$		0			0
$13$	−6.74507	+	3.89427i	−0.518852	+	0.299559i	−0.736465	−	0.676476i	$-0.763506\pi$
$13$	−6.74507	+	3.89427i	−0.518852	+	0.299559i	0.217613	+	0.976035i	$0.430173\pi$
$14$		0			0
$15$	10.3022	−	5.94799i	0.686814	−	0.396532i
$16$		0			0
$17$	9.15210	−	15.8519i	0.538359	−	0.932464i	−0.460634	−	0.887590i	$-0.652378\pi$
$17$	9.15210	−	15.8519i	0.538359	−	0.932464i	0.998993	−	0.0448743i	$-0.0142887\pi$
$18$		0			0
$19$	17.9748	−	6.15688i	0.946041	−	0.324046i
$19$	17.9748	−	6.15688i	0.946041	−	0.324046i
$20$		0			0
$21$	36.9920	+	21.3573i	1.76152	+	1.01702i
$22$		0			0
$23$	−17.0743	−	29.5736i	−0.742362	−	1.28581i	−0.951417	−	0.307905i	$-0.900372\pi$
$23$	−17.0743	−	29.5736i	−0.742362	−	1.28581i	0.209055	−	0.977904i	$-0.432961\pi$
$24$		0			0
$25$	7.64552	+	13.2424i	0.305821	+	0.529697i
$26$		0			0
$27$			13.0735i			0.484205i
$28$		0			0
$29$	−33.1640	+	19.1473i	−1.14359	+	0.660250i	−0.947316	−	0.320300i	$-0.896216\pi$
$29$	−33.1640	+	19.1473i	−1.14359	+	0.660250i	−0.196271	+	0.980550i	$0.562883\pi$
$30$		0			0
$31$			10.4564i			0.337303i	0.985676	+	0.168651i	$0.0539412\pi$
$31$			10.4564i			0.337303i	−0.985676	+	0.168651i	$0.946059\pi$
$32$		0			0
$33$	18.8181	+	10.8646i	0.570245	+	0.329231i
$34$		0			0
$35$	17.4309	−	30.1912i	0.498025	−	0.862605i
$36$		0			0
$37$		−	30.1044i		−	0.813633i	−0.913510	−	0.406816i	$-0.866639\pi$
$37$		−	30.1044i		−	0.813633i	0.913510	−	0.406816i	$-0.133361\pi$
$38$		0			0
$39$	29.7351			0.762439
$40$		0			0
$41$	−33.0491	−	19.0809i	−0.806076	−	0.465388i	0.0395153	−	0.999219i	$-0.487419\pi$
$41$	−33.0491	−	19.0809i	−0.806076	−	0.465388i	−0.845591	+	0.533831i	$0.820752\pi$
$42$		0			0
$43$	−29.7055	+	51.4514i	−0.690825	+	1.19654i	0.280743	+	0.959783i	$0.409419\pi$
$43$	−29.7055	+	51.4514i	−0.690825	+	1.19654i	−0.971568	+	0.236761i	$0.923914\pi$
$44$		0			0
$45$	−17.3732			−0.386072
$46$		0			0
$47$	−30.9846	−	53.6669i	−0.659246	−	1.14185i	−0.980811	−	0.194961i	$-0.937542\pi$
$47$	−30.9846	−	53.6669i	−0.659246	−	1.14185i	0.321565	−	0.946888i	$-0.395791\pi$
$48$		0			0
$49$	76.1775			1.55464
$50$		0			0
$51$	−60.5195	+	34.9409i	−1.18666	+	0.685116i
$52$		0			0
$53$	−45.3846	+	26.2028i	−0.856313	+	0.494392i	−0.862776	−	0.505587i	$-0.831276\pi$
$53$	−45.3846	+	26.2028i	−0.856313	+	0.494392i	0.00646316	+	0.999979i	$0.497943\pi$
$54$		0			0
$55$	8.86722	−	15.3585i	0.161222	−	0.279245i
$56$		0			0
$57$	−71.1832	−	13.9555i	−1.24883	−	0.244834i
$58$		0			0
$59$	73.7726	+	42.5926i	1.25038	+	0.721909i	0.971185	−	0.238325i	$-0.0765985\pi$
$59$	73.7726	+	42.5926i	1.25038	+	0.721909i	0.279197	+	0.960234i	$0.409932\pi$
$60$		0			0
$61$	1.82516	+	3.16127i	0.0299206	+	0.0518240i	0.880598	−	0.473864i	$-0.157141\pi$
$61$	1.82516	+	3.16127i	0.0299206	+	0.0518240i	−0.850677	+	0.525688i	$0.823808\pi$
$62$		0			0
$63$	−31.1909	−	54.0242i	−0.495093	−	0.857527i
$64$		0			0
$65$		−	24.2685i		−	0.373361i
$66$		0			0
$67$	−96.7411	+	55.8535i	−1.44390	+	0.833635i	−0.998107	−	0.0615024i	$-0.980411\pi$
$67$	−96.7411	+	55.8535i	−1.44390	+	0.833635i	−0.445791	+	0.895137i	$0.647077\pi$
$68$		0			0
$69$			130.373i			1.88946i
$70$		0			0
$71$	−55.4406	−	32.0086i	−0.780853	−	0.450826i	0.0558793	−	0.998438i	$-0.482204\pi$
$71$	−55.4406	−	32.0086i	−0.780853	−	0.450826i	−0.836733	+	0.547612i	$0.815537\pi$
$72$		0			0
$73$	37.7842	−	65.4442i	0.517592	−	0.896496i	−0.482199	−	0.876062i	$-0.660162\pi$
$73$	37.7842	−	65.4442i	0.517592	−	0.896496i	0.999791	−	0.0204344i	$-0.00650493\pi$
$74$		0			0
$75$		−	58.3783i		−	0.778377i
$76$		0			0
$77$	63.6787			0.826996
$78$		0			0
$79$	85.4278	+	49.3218i	1.08137	+	0.624326i	0.931264	−	0.364344i	$-0.118707\pi$
$79$	85.4278	+	49.3218i	1.08137	+	0.624326i	0.150101	+	0.988671i	$0.452040\pi$
$80$		0			0
$81$	50.0465	−	86.6831i	0.617858	−	1.07016i
$82$		0			0
$83$	60.0975			0.724067			0.362033	−	0.932165i	$-0.382083\pi$
$83$	60.0975			0.724067			0.362033	+	0.932165i	$0.382083\pi$
$84$		0			0
$85$	28.5172	+	49.3932i	0.335496	+	0.581097i
$86$		0			0
$87$	146.201			1.68047
$88$		0			0
$89$	17.4003	−	10.0461i	0.195509	−	0.112877i	−0.399050	−	0.916929i	$-0.630660\pi$
$89$	17.4003	−	10.0461i	0.195509	−	0.112877i	0.594559	+	0.804052i	$0.297327\pi$
$90$		0			0
$91$	75.4657	−	43.5701i	0.829293	−	0.478793i
$92$		0			0
$93$	19.9602	−	34.5721i	0.214626	−	0.371743i
$94$		0			0
$95$	−11.3899	+	58.0965i	−0.119893	+	0.611542i
$96$		0			0
$97$	−50.1828	−	28.9730i	−0.517348	−	0.298691i	0.218501	−	0.975837i	$-0.429883\pi$
$97$	−50.1828	−	28.9730i	−0.517348	−	0.298691i	−0.735849	+	0.677146i	$0.763217\pi$
$98$		0			0
$99$	−15.8670	−	27.4825i	−0.160273	−	0.277601i
$100$		0			0
$101$	−64.2010	−	111.199i	−0.635654	−	1.10098i	−0.986376	−	0.164505i	$-0.947397\pi$
$101$	−64.2010	−	111.199i	−0.635654	−	1.10098i	0.350723	−	0.936479i	$-0.385936\pi$
$102$		0			0
$103$			192.337i			1.86735i	0.358123	+	0.933674i	$0.383417\pi$
$103$			192.337i			1.86735i	−0.358123	+	0.933674i	$0.616583\pi$
$104$		0			0
$105$	−115.264	+	66.5477i	−1.09775	+	0.633788i
$106$		0			0
$107$		−	81.0841i		−	0.757795i	−0.925439	−	0.378898i	$-0.876303\pi$
$107$		−	81.0841i		−	0.757795i	0.925439	−	0.378898i	$-0.123697\pi$
$108$		0			0
$109$	3.27848	+	1.89283i	0.0300778	+	0.0173655i	0.514964	−	0.857212i	$-0.327805\pi$
$109$	3.27848	+	1.89283i	0.0300778	+	0.0173655i	−0.484886	+	0.874578i	$0.661139\pi$
$110$		0			0
$111$	−57.4664	+	99.5347i	−0.517715	+	0.896709i
$112$		0			0
$113$		−	149.144i		−	1.31986i	−0.751328	−	0.659929i	$-0.770586\pi$
$113$		−	149.144i		−	1.31986i	0.751328	−	0.659929i	$-0.229414\pi$
$114$		0			0
$115$	106.404			0.925256
$116$		0			0
$117$	−37.6081	−	21.7130i	−0.321437	−	0.185582i
$118$		0			0
$119$	−102.396	+	177.355i	−0.860472	+	1.49038i
$120$		0			0
$121$	−88.6062			−0.732282
$122$		0			0
$123$	72.8472	+	126.175i	0.592254	+	1.02581i
$124$		0			0
$125$	−125.544			−1.00435
$126$		0			0
$127$	19.5249	−	11.2727i	0.153739	−	0.0887614i	−0.421157	−	0.906988i	$-0.638376\pi$
$127$	19.5249	−	11.2727i	0.153739	−	0.0887614i	0.574896	+	0.818226i	$0.305042\pi$
$128$		0			0
$129$	196.431	−	113.410i	1.52272	−	0.879145i
$130$		0			0
$131$	75.0267	−	129.950i	0.572723	−	0.991985i	−0.423562	−	0.905867i	$-0.639221\pi$
$131$	75.0267	−	129.950i	0.572723	−	0.991985i	0.996285	−	0.0861177i	$-0.0274461\pi$
$132$		0			0
$133$	−201.107	+	68.8848i	−1.51208	+	0.517931i
$134$		0			0
$135$	−35.2785	−	20.3680i	−0.261322	−	0.150874i
$136$		0			0
$137$	−36.0632	−	62.4633i	−0.263235	−	0.455936i	0.703865	−	0.710334i	$-0.251456\pi$
$137$	−36.0632	−	62.4633i	−0.263235	−	0.455936i	−0.967100	+	0.254398i	$0.918123\pi$
$138$		0			0
$139$	−63.7916	−	110.490i	−0.458932	−	0.794894i	0.539973	−	0.841683i	$-0.318435\pi$
$139$	−63.7916	−	110.490i	−0.458932	−	0.794894i	−0.998905	+	0.0467887i	$0.985101\pi$
$140$		0			0
$141$			236.586i			1.67792i
$142$		0			0
$143$	38.3900	−	22.1645i	0.268461	−	0.154996i
$144$		0			0
$145$		−	119.323i		−	0.822914i
$146$		0			0
$147$	−251.867	−	145.415i	−1.71338	−	0.989220i
$148$		0			0
$149$	−107.009	+	185.345i	−0.718180	+	1.24392i	0.243541	+	0.969891i	$0.421691\pi$
$149$	−107.009	+	185.345i	−0.718180	+	1.24392i	−0.961720	+	0.274033i	$0.911642\pi$
$150$		0			0
$151$		−	67.1874i		−	0.444950i	−0.974938	−	0.222475i	$-0.928586\pi$
$151$		−	67.1874i		−	0.444950i	0.974938	−	0.222475i	$-0.0714135\pi$
$152$		0			0
$153$	102.058			0.667043
$154$		0			0
$155$	−28.2162	−	16.2906i	−0.182040	−	0.105101i
$156$		0			0
$157$	110.750	−	191.824i	0.705411	−	1.22181i	−0.261131	−	0.965303i	$-0.584096\pi$
$157$	110.750	−	191.824i	0.705411	−	1.22181i	0.966543	−	0.256505i	$-0.0825711\pi$
$158$		0			0
$159$	200.074			1.25833
$160$		0			0
$161$	191.032	+	330.878i	1.18654	+	2.05514i
$162$		0			0
$163$	−126.587			−0.776606			−0.388303	−	0.921532i	$-0.626939\pi$
$163$	−126.587			−0.776606			−0.388303	+	0.921532i	$0.626939\pi$
$164$		0			0
$165$	−58.6357	+	33.8533i	−0.355368	+	0.205172i
$166$		0			0
$167$	−161.012	+	92.9605i	−0.964146	+	0.556650i	−0.897447	−	0.441123i	$-0.854580\pi$
$167$	−161.012	+	92.9605i	−0.964146	+	0.556650i	−0.0666994	+	0.997773i	$0.521247\pi$
$168$		0			0
$169$	−54.1693	+	93.8240i	−0.320529	+	0.555172i
$170$		0			0
$171$	79.8398	+	69.6296i	0.466900	+	0.407191i
$172$		0			0
$173$	235.750	+	136.110i	1.36272	+	0.786765i	0.989985	−	0.141174i	$-0.0450876\pi$
$173$	235.750	+	136.110i	1.36272	+	0.786765i	0.372732	+	0.927939i	$0.378421\pi$
$174$		0			0
$175$	−85.5402	−	148.160i	−0.488801	−	0.846629i
$176$		0			0
$177$	−162.610	−	281.649i	−0.918702	−	1.59124i
$178$		0			0
$179$			23.6065i			0.131880i	0.997824	+	0.0659400i	$0.0210046\pi$
$179$			23.6065i			0.131880i	−0.997824	+	0.0659400i	$0.978995\pi$
$180$		0			0
$181$	49.3722	−	28.5050i	0.272774	−	0.157486i	−0.357373	−	0.933962i	$-0.616328\pi$
$181$	49.3722	−	28.5050i	0.272774	−	0.157486i	0.630148	+	0.776475i	$0.282994\pi$
$182$		0			0
$183$		−	13.9362i		−	0.0761541i
$184$		0			0
$185$	81.2357	+	46.9015i	0.439112	+	0.253521i
$186$		0			0
$187$	−52.0897	+	90.2220i	−0.278554	+	0.482471i
$188$		0			0
$189$		−	146.270i		−	0.773917i
$190$		0			0
$191$	158.384			0.829238			0.414619	−	0.909995i	$-0.363915\pi$
$191$	158.384			0.829238			0.414619	+	0.909995i	$0.363915\pi$
$192$		0			0
$193$	160.689	+	92.7739i	0.832586	+	0.480694i	0.854737	−	0.519061i	$-0.173718\pi$
$193$	160.689	+	92.7739i	0.832586	+	0.480694i	−0.0221514	+	0.999755i	$0.507052\pi$
$194$		0			0
$195$	−46.3261	+	80.2392i	−0.237570	+	0.411483i
$196$		0			0
$197$	19.8590			0.100807			0.0504035	−	0.998729i	$-0.483949\pi$
$197$	19.8590			0.100807			0.0504035	+	0.998729i	$0.483949\pi$
$198$		0			0
$199$	−67.6494	−	117.172i	−0.339947	−	0.588805i	0.644475	−	0.764625i	$-0.277076\pi$
$199$	−67.6494	−	117.172i	−0.339947	−	0.588805i	−0.984422	+	0.175820i	$0.943742\pi$
$200$		0			0
$201$	426.476			2.12177
$202$		0			0
$203$	371.048	−	214.225i	1.82782	−	1.05529i
$204$		0			0
$205$	102.978	−	59.4546i	0.502333	−	0.290022i
$206$		0			0
$207$	95.2003	−	164.892i	0.459905	−	0.796579i
$208$		0			0
$209$	−102.305	+	35.0422i	−0.489495	+	0.167666i
$210$		0			0
$211$	−94.9925	−	54.8439i	−0.450201	−	0.259924i	0.257714	−	0.966221i	$-0.417031\pi$
$211$	−94.9925	−	54.8439i	−0.450201	−	0.259924i	−0.707915	+	0.706297i	$0.750364\pi$
$212$		0			0
$213$	122.203	+	211.661i	0.573722	+	0.993715i
$214$		0			0
$215$	−92.5598	−	160.318i	−0.430511	−	0.745666i
$216$		0			0
$217$		−	116.989i		−	0.539119i
$218$		0			0
$219$	−249.853	+	144.253i	−1.14088	+	0.658689i
$220$		0			0
$221$			142.563i			0.645081i
$222$		0			0
$223$	44.5718	+	25.7335i	0.199874	+	0.115397i	0.596597	−	0.802541i	$-0.296519\pi$
$223$	44.5718	+	25.7335i	0.199874	+	0.115397i	−0.396723	+	0.917938i	$0.629853\pi$
$224$		0			0
$225$	−42.6287	+	73.8351i	−0.189461	+	0.328156i
$226$		0			0
$227$			153.761i			0.677361i	0.940901	+	0.338681i	$0.109981\pi$
$227$			153.761i			0.677361i	−0.940901	+	0.338681i	$0.890019\pi$
$228$		0			0
$229$	−58.5939			−0.255869			−0.127934	−	0.991783i	$-0.540835\pi$
$229$	−58.5939			−0.255869			−0.127934	+	0.991783i	$0.540835\pi$
$230$		0			0
$231$	−210.542	−	121.556i	−0.911437	−	0.526218i
$232$		0			0
$233$	−140.348	+	243.089i	−0.602351	+	1.04330i	0.390113	+	0.920767i	$0.372436\pi$
$233$	−140.348	+	243.089i	−0.602351	+	1.04330i	−0.992464	+	0.122535i	$0.960898\pi$
$234$		0			0
$235$	193.091			0.821663
$236$		0			0
$237$	−188.301	−	326.147i	−0.794519	−	1.37615i
$238$		0			0
$239$	−46.5330			−0.194699			−0.0973494	−	0.995250i	$-0.531036\pi$
$239$	−46.5330			−0.194699			−0.0973494	+	0.995250i	$0.531036\pi$
$240$		0			0
$241$	−217.033	+	125.304i	−0.900553	+	0.519934i	−0.877380	−	0.479797i	$-0.840710\pi$
$241$	−217.033	+	125.304i	−0.900553	+	0.519934i	−0.0231734	+	0.999731i	$0.507377\pi$
$242$		0			0
$243$	−229.041	+	132.237i	−0.942555	+	0.544185i
$244$		0			0
$245$	−118.681	+	205.562i	−0.484414	+	0.839029i
$246$		0			0
$247$	−97.2647	+	111.527i	−0.393784	+	0.451527i
$248$		0			0
$249$	−198.702	−	114.720i	−0.797998	−	0.460724i
$250$		0			0
$251$	−54.5360	−	94.4592i	−0.217275	−	0.376331i	0.736699	−	0.676221i	$-0.236383\pi$
$251$	−54.5360	−	94.4592i	−0.217275	−	0.376331i	−0.953974	+	0.299890i	$0.903050\pi$
$252$		0			0
$253$	97.1796	+	168.320i	0.384109	+	0.665296i
$254$		0			0
$255$		−	217.746i		−	0.853907i
$256$		0			0
$257$	103.211	−	59.5890i	0.401600	−	0.231864i	−0.285574	−	0.958357i	$-0.592184\pi$
$257$	103.211	−	59.5890i	0.401600	−	0.231864i	0.687174	+	0.726493i	$0.258851\pi$
$258$		0			0
$259$			336.816i			1.30045i
$260$		0			0
$261$	−184.911	−	106.758i	−0.708470	−	0.409035i
$262$		0			0
$263$	229.768	−	397.969i	0.873641	−	1.51319i	0.0154385	−	0.999881i	$-0.495086\pi$
$263$	229.768	−	397.969i	0.873641	−	1.51319i	0.858203	−	0.513311i	$-0.171581\pi$
$264$		0			0
$265$		−	163.292i		−	0.616195i
$266$		0			0
$267$	−76.7077			−0.287295
$268$		0			0
$269$	296.027	+	170.911i	1.10047	+	0.635358i	0.936345	−	0.351082i	$-0.114186\pi$
$269$	296.027	+	170.911i	1.10047	+	0.635358i	0.164127	+	0.986439i	$0.447519\pi$
$270$		0			0
$271$	−58.9909	+	102.175i	−0.217679	+	0.377031i	−0.954098	−	0.299495i	$-0.903182\pi$
$271$	−58.9909	+	102.175i	−0.217679	+	0.377031i	0.736419	+	0.676526i	$0.236515\pi$
$272$		0			0
$273$	−332.685			−1.21863
$274$		0			0
$275$	−43.5150	−	75.3701i	−0.158236	−	0.274073i
$276$		0			0
$277$	−181.314			−0.654563			−0.327281	−	0.944927i	$-0.606133\pi$
$277$	−181.314			−0.654563			−0.327281	+	0.944927i	$0.606133\pi$
$278$		0			0
$279$	−50.4902	+	29.1505i	−0.180968	+	0.104482i
$280$		0			0
$281$	−196.670	+	113.547i	−0.699892	+	0.404083i	−0.807307	−	0.590131i	$-0.799076\pi$
$281$	−196.670	+	113.547i	−0.699892	+	0.404083i	0.107415	+	0.994214i	$0.465743\pi$
$282$		0			0
$283$	162.854	−	282.071i	0.575455	−	0.996718i	−0.420537	−	0.907276i	$-0.638158\pi$
$283$	162.854	−	282.071i	0.575455	−	0.996718i	0.995992	−	0.0894423i	$-0.0285085\pi$
$284$		0			0
$285$	148.559	−	170.343i	0.521260	−	0.597696i
$286$		0			0
$287$	369.763	+	213.482i	1.28837	+	0.743841i
$288$		0			0
$289$	−23.0217	−	39.8748i	−0.0796599	−	0.137975i
$290$		0			0
$291$	110.613	+	191.588i	0.380115	+	0.658378i
$292$		0			0
$293$			51.8203i			0.176861i	0.996082	+	0.0884305i	$0.0281851\pi$
$293$			51.8203i			0.176861i	−0.996082	+	0.0884305i	$0.971815\pi$
$294$		0			0
$295$	−229.869	+	132.715i	−0.779218	+	0.449882i
$296$		0			0
$297$		−	74.4088i		−	0.250535i
$298$		0			0
$299$	230.335	+	132.984i	0.770352	+	0.444763i
$300$		0			0
$301$	332.353	−	575.652i	1.10416	−	1.91246i
$302$		0			0
$303$			490.214i			1.61787i
$304$		0			0
$305$	−11.3741			−0.0372921
$306$		0			0
$307$	−9.83046	−	5.67562i	−0.0320211	−	0.0184874i	0.483904	−	0.875121i	$-0.339218\pi$
$307$	−9.83046	−	5.67562i	−0.0320211	−	0.0184874i	−0.515925	+	0.856634i	$0.672552\pi$
$308$		0			0
$309$	367.152	−	635.927i	1.18820	−	2.05802i
$310$		0			0
$311$	−120.753			−0.388274			−0.194137	−	0.980974i	$-0.562191\pi$
$311$	−120.753			−0.388274			−0.194137	+	0.980974i	$0.562191\pi$
$312$		0			0
$313$	64.8317	+	112.292i	0.207130	+	0.358760i	0.950809	−	0.309777i	$-0.100254\pi$
$313$	64.8317	+	112.292i	0.207130	+	0.358760i	−0.743679	+	0.668537i	$0.766921\pi$
$314$		0			0
$315$	194.377			0.617068
$316$		0			0
$317$	−438.037	+	252.901i	−1.38182	+	0.797794i	−0.992375	−	0.123255i	$-0.960667\pi$
$317$	−438.037	+	252.901i	−1.38182	+	0.797794i	−0.389445	+	0.921050i	$0.627333\pi$
$318$		0			0
$319$	188.755	−	108.978i	0.591708	−	0.341623i
$320$		0			0
$321$	−154.782	+	268.090i	−0.482186	+	0.835171i
$322$		0			0
$323$	66.9088	−	341.283i	0.207148	−	1.05660i
$324$		0			0
$325$	−103.139	−	59.5475i	−0.317351	−	0.183223i
$326$		0			0
$327$	−7.22647	−	12.5166i	−0.0220993	−	0.0382771i
$328$		0			0
$329$	346.664	+	600.440i	1.05369	+	1.82504i
$330$		0			0
$331$		−	80.9684i		−	0.244618i	−0.992492	−	0.122309i	$-0.960970\pi$
$331$		−	80.9684i		−	0.244618i	0.992492	−	0.122309i	$-0.0390298\pi$
$332$		0			0
$333$	145.364	−	83.9257i	0.436527	−	0.252029i
$334$		0			0
$335$		−	348.070i		−	1.03902i
$336$		0			0
$337$	392.289	+	226.488i	1.16406	+	0.672071i	0.952274	−	0.305245i	$-0.0987384\pi$
$337$	392.289	+	226.488i	1.16406	+	0.672071i	0.211787	+	0.977316i	$0.432072\pi$
$338$		0			0
$339$	−284.702	+	493.117i	−0.839827	+	1.45462i
$340$		0			0
$341$		−	59.5131i		−	0.174525i
$342$		0			0
$343$	−304.069			−0.886498
$344$		0			0
$345$	−351.807	−	203.116i	−1.01973	−	0.588741i
$346$		0			0
$347$	−132.251	+	229.065i	−0.381126	+	0.660130i	−0.991224	−	0.132197i	$-0.957797\pi$
$347$	−132.251	+	229.065i	−0.381126	+	0.660130i	0.610097	+	0.792326i	$0.291130\pi$
$348$		0			0
$349$	−252.830			−0.724440			−0.362220	−	0.932093i	$-0.617981\pi$
$349$	−252.830			−0.724440			−0.362220	+	0.932093i	$0.617981\pi$
$350$		0			0
$351$	−50.9119	−	88.1820i	−0.145048	−	0.251231i
$352$		0			0
$353$	49.2202			0.139434			0.0697170	−	0.997567i	$-0.477790\pi$
$353$	49.2202			0.139434			0.0697170	+	0.997567i	$0.477790\pi$
$354$		0			0
$355$	172.748	−	99.7363i	0.486615	−	0.280947i
$356$		0			0
$357$	677.108	−	390.929i	1.89666	−	1.09504i
$358$		0			0
$359$	2.28868	−	3.96411i	0.00637515	−	0.0110421i	−0.862820	−	0.505511i	$-0.831304\pi$
$359$	2.28868	−	3.96411i	0.00637515	−	0.0110421i	0.869195	+	0.494469i	$0.164637\pi$
$360$		0			0
$361$	285.186	−	221.337i	0.789988	−	0.613122i
$362$		0			0
$363$	292.960	+	169.141i	0.807052	+	0.465952i
$364$		0			0
$365$	117.733	+	203.919i	0.322555	+	0.558682i
$366$		0			0
$367$	248.170	+	429.843i	0.676212	+	1.17123i	0.976113	+	0.217264i	$0.0697132\pi$
$367$	248.170	+	429.843i	0.676212	+	1.17123i	−0.299901	+	0.953970i	$0.596954\pi$
$368$		0			0
$369$		−	212.777i		−	0.576630i
$370$		0			0
$371$	507.775	−	293.164i	1.36867	−	0.790199i
$372$		0			0
$373$		−	4.20799i		−	0.0112815i	−0.999984	−	0.00564073i	$-0.998204\pi$
$373$		−	4.20799i		−	0.0112815i	0.999984	−	0.00564073i	$-0.00179551\pi$
$374$		0			0
$375$	415.087	+	239.651i	1.10690	+	0.639068i
$376$		0			0
$377$	149.129	−	258.299i	0.395568	−	0.685144i
$378$		0			0
$379$		−	248.684i		−	0.656157i	−0.944650	−	0.328079i	$-0.893599\pi$
$379$		−	248.684i		−	0.656157i	0.944650	−	0.328079i	$-0.106401\pi$
$380$		0			0
$381$	−86.0739			−0.225916
$382$		0			0
$383$	−527.607	−	304.614i	−1.37756	−	0.795337i	−0.385699	−	0.922625i	$-0.626040\pi$
$383$	−527.607	−	304.614i	−1.37756	−	0.795337i	−0.991866	+	0.127288i	$0.959373\pi$
$384$		0			0
$385$	−99.2088	+	171.835i	−0.257685	+	0.446324i
$386$		0			0
$387$	−331.254			−0.855953
$388$		0			0
$389$	−229.333	−	397.216i	−0.589544	−	1.02112i	−0.994292	−	0.106692i	$-0.965974\pi$
$389$	−229.333	−	397.216i	−0.589544	−	1.02112i	0.404748	−	0.914428i	$-0.367359\pi$
$390$		0			0
$391$	−625.064			−1.59863
$392$		0			0
$393$	−496.124	+	286.437i	−1.26240	+	0.728848i
$394$		0			0
$395$	−266.186	+	153.683i	−0.673889	+	0.389070i
$396$		0			0
$397$	−51.9676	+	90.0104i	−0.130901	+	0.226727i	−0.924024	−	0.382334i	$-0.875120\pi$
$397$	−51.9676	+	90.0104i	−0.130901	+	0.226727i	0.793123	+	0.609061i	$0.208454\pi$
$398$		0			0
$399$	796.417	+	156.138i	1.99603	+	0.391324i
$400$		0			0
$401$	−640.104	−	369.564i	−1.59627	−	0.921606i	−0.992198	−	0.124676i	$-0.960211\pi$
$401$	−640.104	−	369.564i	−1.59627	−	0.921606i	−0.604071	−	0.796930i	$-0.706456\pi$
$402$		0			0
$403$	−40.7200	−	70.5290i	−0.101042	−	0.175010i
$404$		0			0
$405$	155.941	+	270.097i	0.385039	+	0.666907i
$406$		0			0
$407$			171.341i			0.420985i
$408$		0			0
$409$	−244.207	+	140.993i	−0.597084	+	0.344726i	−0.767893	−	0.640578i	$-0.778695\pi$
$409$	−244.207	+	140.993i	−0.597084	+	0.344726i	0.170810	+	0.985304i	$0.445362\pi$
$410$		0			0
$411$			275.364i			0.669987i
$412$		0			0
$413$	−825.387	−	476.538i	−1.99852	−	1.15384i
$414$		0			0
$415$	−93.6295	+	162.171i	−0.225613	+	0.390774i
$416$		0			0
$417$			487.088i			1.16808i
$418$		0			0
$419$	−491.659			−1.17341			−0.586705	−	0.809801i	$-0.699575\pi$
$419$	−491.659			−1.17341			−0.586705	+	0.809801i	$0.699575\pi$
$420$		0			0
$421$	185.865	+	107.309i	0.441484	+	0.254891i	0.704227	−	0.709975i	$-0.251294\pi$
$421$	185.865	+	107.309i	0.441484	+	0.254891i	−0.262743	+	0.964866i	$0.584627\pi$
$422$		0			0
$423$	172.759	−	299.227i	0.408413	−	0.707393i
$424$		0			0
$425$	279.890			0.658565
$426$		0			0
$427$	−20.4204	−	35.3691i	−0.0478229	−	0.0828316i
$428$		0			0
$429$	−169.239			−0.394497
$430$		0			0
$431$	81.8737	−	47.2698i	0.189962	−	0.109675i	−0.402003	−	0.915638i	$-0.631686\pi$
$431$	81.8737	−	47.2698i	0.189962	−	0.109675i	0.591965	+	0.805964i	$0.298352\pi$
$432$		0			0
$433$	−329.028	+	189.964i	−0.759880	+	0.438717i	−0.829253	−	0.558874i	$-0.811233\pi$
$433$	−329.028	+	189.964i	−0.759880	+	0.438717i	0.0693729	+	0.997591i	$0.477900\pi$
$434$		0			0
$435$	−227.775	+	394.518i	−0.523621	+	0.906939i
$436$		0			0
$437$	−488.988	−	426.455i	−1.11897	−	0.975869i
$438$		0			0
$439$	239.645	+	138.359i	0.545887	+	0.315168i	0.747462	−	0.664305i	$-0.231272\pi$
$439$	239.645	+	138.359i	0.545887	+	0.315168i	−0.201574	+	0.979473i	$0.564606\pi$
$440$		0			0
$441$	212.369	+	367.834i	0.481562	+	0.834091i
$442$		0			0
$443$	7.38439	+	12.7901i	0.0166691	+	0.0288717i	0.874240	−	0.485495i	$-0.161360\pi$
$443$	7.38439	+	12.7901i	0.0166691	+	0.0288717i	−0.857571	+	0.514366i	$0.828027\pi$
$444$		0			0
$445$			62.6054i			0.140686i
$446$		0			0
$447$	707.610	−	408.539i	1.58302	−	0.913957i
$448$		0			0
$449$		−	402.117i		−	0.895584i	−0.894138	−	0.447792i	$-0.852211\pi$
$449$		−	402.117i		−	0.895584i	0.894138	−	0.447792i	$-0.147789\pi$
$450$		0			0
$451$	188.101	+	108.600i	0.417075	+	0.240799i
$452$		0			0
$453$	−128.254	+	222.143i	−0.283122	+	0.490382i
$454$		0			0
$455$			271.522i			0.596752i
$456$		0			0
$457$	−645.600			−1.41269			−0.706345	−	0.707867i	$-0.749657\pi$
$457$	−645.600			−1.41269			−0.706345	+	0.707867i	$0.749657\pi$
$458$		0			0
$459$	207.240	+	119.650i	0.451504	+	0.260676i
$460$		0			0
$461$	114.286	−	197.948i	0.247908	−	0.429389i	−0.715037	−	0.699086i	$-0.753590\pi$
$461$	114.286	−	197.948i	0.247908	−	0.429389i	0.962945	+	0.269697i	$0.0869236\pi$
$462$		0			0
$463$	56.6097			0.122267			0.0611336	−	0.998130i	$-0.480528\pi$
$463$	56.6097			0.122267			0.0611336	+	0.998130i	$0.480528\pi$
$464$		0			0
$465$	62.1944	+	107.724i	0.133751	+	0.231664i
$466$		0			0
$467$	−440.857			−0.944020			−0.472010	−	0.881593i	$-0.656471\pi$
$467$	−440.857			−0.944020			−0.472010	+	0.881593i	$0.656471\pi$
$468$		0			0
$469$	1082.37	−	624.905i	2.30782	−	1.33242i
$470$		0			0
$471$	−732.347	+	422.820i	−1.55488	+	0.897708i
$472$		0			0
$473$	169.070	−	292.838i	0.357443	−	0.619109i
$474$		0			0
$475$	218.959	+	190.957i	0.460966	+	0.402016i
$476$		0			0
$477$	−253.048	−	146.097i	−0.530499	−	0.306284i
$478$		0			0
$479$	61.8700	+	107.162i	0.129165	+	0.223720i	0.923353	−	0.383951i	$-0.125437\pi$
$479$	61.8700	+	107.162i	0.129165	+	0.223720i	−0.794188	+	0.607672i	$0.792104\pi$
$480$		0			0
$481$	117.235	+	203.056i	0.243731	+	0.422155i
$482$		0			0
$483$		−	1458.65i		−	3.01998i
$484$		0			0
$485$	156.365	−	90.2776i	0.322403	−	0.186139i
$486$		0			0
$487$		−	614.532i		−	1.26187i	−0.775834	−	0.630937i	$-0.782671\pi$
$487$		−	614.532i		−	1.26187i	0.775834	−	0.630937i	$-0.217329\pi$
$488$		0			0
$489$	418.536	+	241.642i	0.855902	+	0.494155i
$490$		0			0
$491$	412.325	−	714.168i	0.839766	−	1.45452i	−0.0503251	−	0.998733i	$-0.516026\pi$
$491$	412.325	−	714.168i	0.839766	−	1.45452i	0.890091	−	0.455784i	$-0.150641\pi$
$492$		0			0
$493$			700.950i			1.42181i
$494$		0			0
$495$	98.8808			0.199759
$496$		0			0
$497$	620.284	+	358.121i	1.24806	+	0.720566i
$498$		0			0
$499$	−223.004	+	386.253i	−0.446901	+	0.774055i	−0.998182	−	0.0602642i	$-0.980806\pi$
$499$	−223.004	+	386.253i	−0.446901	+	0.774055i	0.551282	+	0.834319i	$0.314139\pi$
$500$		0			0
$501$	709.811			1.41679
$502$		0			0
$503$	206.009	+	356.818i	0.409560	+	0.709380i	0.994840	−	0.101452i	$-0.0323487\pi$
$503$	206.009	+	356.818i	0.409560	+	0.709380i	−0.585280	+	0.810831i	$0.699015\pi$
$504$		0			0
$505$	400.090			0.792258
$506$		0			0
$507$	358.202	−	206.808i	0.706513	−	0.407905i
$508$		0			0
$509$	115.980	−	66.9613i	0.227859	−	0.131555i	−0.381725	−	0.924276i	$-0.624670\pi$
$509$	115.980	−	66.9613i	0.227859	−	0.131555i	0.609584	+	0.792721i	$0.291336\pi$
$510$		0			0
$511$	−422.740	+	732.208i	−0.827281	+	1.43289i
$512$		0			0
$513$	80.4922	+	234.994i	0.156905	+	0.458078i
$514$		0			0
$515$	−519.014	−	299.653i	−1.00780	−	0.581851i
$516$		0			0
$517$	176.351	+	305.448i	0.341104	+	0.590809i
$518$		0			0
$519$	−519.643	−	900.048i	−1.00124	−	1.73420i
$520$		0			0
$521$		−	82.8330i		−	0.158989i	−0.996835	−	0.0794943i	$-0.974669\pi$
$521$		−	82.8330i		−	0.158989i	0.996835	−	0.0794943i	$-0.0253305\pi$
$522$		0			0
$523$	716.232	−	413.517i	1.36947	−	0.790663i	0.378608	−	0.925557i	$-0.376403\pi$
$523$	716.232	−	413.517i	1.36947	−	0.790663i	0.990860	+	0.134894i	$0.0430694\pi$
$524$		0			0
$525$			653.152i			1.24410i
$526$		0			0
$527$	165.753	+	95.6978i	0.314523	+	0.181590i
$528$		0			0
$529$	−318.566	+	551.772i	−0.602203	+	1.04305i
$530$		0			0
$531$			474.962i			0.894467i
$532$		0			0
$533$	297.225			0.557645
$534$		0			0
$535$	218.803	+	126.326i	0.408977	+	0.236123i
$536$		0			0
$537$	45.0625	−	78.0506i	0.0839153	−	0.145346i
$538$		0			0
$539$	−433.568			−0.804394
$540$		0			0
$541$	−369.791	−	640.497i	−0.683533	−	1.18391i	−0.973895	−	0.226997i	$-0.927109\pi$
$541$	−369.791	−	640.497i	−0.683533	−	1.18391i	0.290363	−	0.956917i	$-0.406224\pi$
$542$		0			0
$543$	−217.653			−0.400835
$544$		0			0
$545$	−10.2155	+	5.89792i	−0.0187440	+	0.0108219i
$546$		0			0
$547$	−187.501	+	108.254i	−0.342781	+	0.197905i	−0.661501	−	0.749944i	$-0.730080\pi$
$547$	−187.501	+	108.254i	−0.342781	+	0.197905i	0.318720	+	0.947849i	$0.396747\pi$
$548$		0			0
$549$	−10.1764	+	17.6261i	−0.0185363	+	0.0321058i
$550$		0			0
$551$	−478.229	+	548.355i	−0.867929	+	0.995199i
$552$		0			0
$553$	−955.790	−	551.826i	−1.72837	−	0.997876i
$554$		0			0
$555$	−179.061	−	310.142i	−0.322632	−	0.558815i
$556$		0			0
$557$	339.435	+	587.919i	0.609399	+	1.05551i	0.991340	+	0.131323i	$0.0419224\pi$
$557$	339.435	+	587.919i	0.609399	+	1.05551i	−0.381941	+	0.924187i	$0.624744\pi$
$558$		0			0
$559$		−	462.724i		−	0.827771i
$560$		0			0
$561$	344.450	−	198.868i	0.613993	−	0.354489i
$562$		0			0
$563$		−	186.539i		−	0.331331i	−0.986182	−	0.165665i	$-0.947023\pi$
$563$		−	186.539i		−	0.331331i	0.986182	−	0.165665i	$-0.0529771\pi$
$564$		0			0
$565$	402.460	+	232.360i	0.712319	+	0.411257i
$566$		0			0
$567$	−559.934	+	969.834i	−0.987538	+	1.71047i
$568$		0			0
$569$		−	298.679i		−	0.524919i	−0.964943	−	0.262460i	$-0.915466\pi$
$569$		−	298.679i		−	0.524919i	0.964943	−	0.262460i	$-0.0845337\pi$
$570$		0			0
$571$	767.923			1.34487			0.672437	−	0.740155i	$-0.265248\pi$
$571$	767.923			1.34487			0.672437	+	0.740155i	$0.265248\pi$
$572$		0			0
$573$	−523.669	−	302.341i	−0.913908	−	0.527645i
$574$		0			0
$575$	261.084	−	452.212i	0.454060	−	0.786455i
$576$		0			0
$577$	978.315			1.69552			0.847760	−	0.530381i	$-0.177951\pi$
$577$	978.315			1.69552			0.847760	+	0.530381i	$0.177951\pi$
$578$		0			0
$579$	−354.193	−	613.480i	−0.611732	−	1.05955i
$580$		0			0
$581$	−672.388			−1.15729
$582$		0			0
$583$	258.309	−	149.135i	0.443068	−	0.255806i
$584$		0			0
$585$	117.184	−	67.6561i	0.200314	−	0.115651i
$586$		0			0
$587$	−53.0636	+	91.9088i	−0.0903979	+	0.156574i	−0.907679	−	0.419666i	$-0.862147\pi$
$587$	−53.0636	+	91.9088i	−0.0903979	+	0.156574i	0.817281	+	0.576240i	$0.195481\pi$
$588$		0			0
$589$	64.3786	+	187.951i	0.109302	+	0.319102i
$590$		0			0
$591$	−65.6601	−	37.9089i	−0.111100	−	0.0641436i
$592$		0			0
$593$	505.114	+	874.883i	0.851794	+	1.47535i	0.879587	+	0.475737i	$0.157819\pi$
$593$	505.114	+	874.883i	0.851794	+	1.47535i	−0.0277931	+	0.999614i	$0.508848\pi$
$594$		0			0
$595$	−319.058	−	552.625i	−0.536232	−	0.928781i
$596$		0			0
$597$			516.545i			0.865234i
$598$		0			0
$599$	434.029	−	250.587i	0.724589	−	0.418342i	−0.0918505	−	0.995773i	$-0.529278\pi$
$599$	434.029	−	250.587i	0.724589	−	0.418342i	0.816439	+	0.577431i	$0.195945\pi$
$600$		0			0
$601$		−	119.762i		−	0.199271i	−0.995024	−	0.0996354i	$-0.968232\pi$
$601$		−	119.762i		−	0.199271i	0.995024	−	0.0996354i	$-0.0317676\pi$
$602$		0			0
$603$	−539.394	−	311.419i	−0.894517	−	0.516450i
$604$		0			0
$605$	138.045	−	239.101i	0.228173	−	0.395208i
$606$		0			0
$607$			209.144i			0.344554i	0.985049	+	0.172277i	$0.0551123\pi$
$607$			209.144i			0.344554i	−0.985049	+	0.172277i	$0.944888\pi$
$608$		0			0
$609$	−1635.74			−2.68594
$610$		0			0
$611$	417.986	+	241.325i	0.684102	+	0.394967i
$612$		0			0
$613$	219.716	−	380.559i	0.358427	−	0.620814i	−0.629271	−	0.777186i	$-0.716647\pi$
$613$	219.716	−	380.559i	0.358427	−	0.620814i	0.987698	+	0.156372i	$0.0499799\pi$
$614$		0			0
$615$	−453.972			−0.738166
$616$		0			0
$617$	563.808	+	976.543i	0.913788	+	1.58273i	0.808665	+	0.588269i	$0.200190\pi$
$617$	563.808	+	976.543i	0.913788	+	1.58273i	0.105123	+	0.994459i	$0.466476\pi$
$618$		0			0
$619$	−620.601			−1.00259			−0.501293	−	0.865278i	$-0.667142\pi$
$619$	−620.601			−1.00259			−0.501293	+	0.865278i	$0.667142\pi$
$620$		0			0
$621$	386.632	−	223.222i	0.622596	−	0.359456i
$622$		0			0
$623$	−194.679	+	112.398i	−0.312486	+	0.180414i
$624$		0			0
$625$	4.45378	−	7.71418i	0.00712605	−	0.0123427i
$626$		0			0
$627$	405.143	+	79.4288i	0.646162	+	0.126681i
$628$		0			0
$629$	−477.212	−	275.519i	−0.758684	−	0.438026i
$630$		0			0
$631$	−463.672	−	803.103i	−0.734820	−	1.27275i	−0.954802	−	0.297242i	$-0.903933\pi$
$631$	−463.672	−	803.103i	−0.734820	−	1.27275i	0.219982	−	0.975504i	$-0.429400\pi$
$632$		0			0
$633$	209.383	+	362.663i	0.330780	+	0.572927i
$634$		0			0
$635$			70.2496i			0.110629i
$636$		0			0
$637$	−513.822	+	296.655i	−0.806629	+	0.465707i
$638$		0			0
$639$		−	356.937i		−	0.558587i
$640$		0			0
$641$	−1104.18	−	637.501i	−1.72259	−	0.994541i	−0.913473	−	0.406900i	$-0.866610\pi$
$641$	−1104.18	−	637.501i	−1.72259	−	0.994541i	−0.809122	−	0.587641i	$-0.800057\pi$
$642$		0			0
$643$	−472.236	+	817.936i	−0.734426	+	1.27206i	0.220549	+	0.975376i	$0.429215\pi$
$643$	−472.236	+	817.936i	−0.734426	+	1.27206i	−0.954975	+	0.296687i	$0.904118\pi$
$644$		0			0
$645$			706.751i			1.09574i
$646$		0			0
$647$	−360.339			−0.556938			−0.278469	−	0.960445i	$-0.589827\pi$
$647$	−360.339			−0.556938			−0.278469	+	0.960445i	$0.589827\pi$
$648$		0			0
$649$	−419.881	−	242.418i	−0.646966	−	0.373526i
$650$		0			0
$651$	−223.320	+	386.802i	−0.343042	+	0.594166i
$652$		0			0
$653$	−39.7164			−0.0608214			−0.0304107	−	0.999537i	$-0.509682\pi$
$653$	−39.7164			−0.0608214			−0.0304107	+	0.999537i	$0.509682\pi$
$654$		0			0
$655$	233.777	+	404.914i	0.356911	+	0.618189i
$656$		0			0
$657$	421.343			0.641313
$658$		0			0
$659$	−628.656	+	362.954i	−0.953954	+	0.550765i	−0.894307	−	0.447454i	$-0.852331\pi$
$659$	−628.656	+	362.954i	−0.953954	+	0.550765i	−0.0596469	+	0.998220i	$0.518997\pi$
$660$		0			0
$661$	103.278	−	59.6276i	0.156245	−	0.0902082i	−0.419839	−	0.907599i	$-0.637913\pi$
$661$	103.278	−	59.6276i	0.156245	−	0.0902082i	0.576084	+	0.817390i	$0.304580\pi$
$662$		0			0
$663$	272.139	−	471.358i	0.410466	−	0.710947i
$664$		0			0
$665$	127.433	−	649.999i	0.191629	−	0.977443i
$666$		0			0
$667$	1132.51	+	653.853i	1.69791	+	0.980290i
$668$		0			0
$669$	−98.2457	−	170.166i	−0.146855	−	0.254359i
$670$		0			0
$671$	−10.3880	−	17.9925i	−0.0154814	−	0.0268145i
$672$		0			0
$673$			667.240i			0.991442i	0.868482	+	0.495721i	$0.165096\pi$
$673$			667.240i			0.991442i	−0.868482	+	0.495721i	$0.834904\pi$
$674$		0			0
$675$	−173.126	+	99.9541i	−0.256482	+	0.148080i
$676$		0			0
$677$		−	1141.27i		−	1.68577i	−0.538091	−	0.842887i	$-0.680854\pi$
$677$		−	1141.27i		−	1.68577i	0.538091	−	0.842887i	$-0.319146\pi$
$678$		0			0
$679$	561.458	+	324.158i	0.826890	+	0.477405i
$680$		0			0
$681$	293.515	−	508.383i	0.431006	−	0.746524i
$682$		0			0
$683$			2.99894i			0.00439083i	0.999998	+	0.00219542i	$0.000698823\pi$
$683$			2.99894i			0.00439083i	−0.999998	+	0.00219542i	$0.999301\pi$
$684$		0			0
$685$	224.740			0.328087
$686$		0			0
$687$	193.730	+	111.850i	0.281994	+	0.162810i
$688$		0			0
$689$	204.081	−	353.479i	0.296199	−	0.513033i
$690$		0			0
$691$	−85.0487			−0.123081			−0.0615403	−	0.998105i	$-0.519601\pi$
$691$	−85.0487			−0.123081			−0.0615403	+	0.998105i	$0.519601\pi$
$692$		0			0
$693$	177.525	+	307.482i	0.256169	+	0.443697i
$694$		0			0
$695$	397.539			0.571998
$696$		0			0
$697$	−604.937	+	349.261i	−0.867916	+	0.501091i
$698$		0			0
$699$	928.068	−	535.820i	1.32771	−	0.766553i
$700$		0			0
$701$	−317.774	+	550.401i	−0.453316	+	0.785166i	−0.998590	−	0.0530922i	$-0.983092\pi$
$701$	−317.774	+	550.401i	−0.453316	+	0.785166i	0.545274	+	0.838258i	$0.316426\pi$
$702$		0			0
$703$	−185.349	−	541.120i	−0.263655	−	0.769730i
$704$		0			0
$705$	−638.420	−	368.592i	−0.905560	−	0.522825i
$706$		0			0
$707$	718.298	+	1244.13i	1.01598	+	1.75973i
$708$		0			0
$709$	86.7540	+	150.262i	0.122361	+	0.211936i	0.920698	−	0.390275i	$-0.127620\pi$
$709$	86.7540	+	150.262i	0.122361	+	0.211936i	−0.798337	+	0.602211i	$0.794287\pi$
$710$		0			0
$711$			550.001i			0.773560i
$712$		0			0
$713$	309.233	−	178.536i	0.433707	−	0.250401i
$714$		0			0
$715$			138.125i			0.193182i
$716$		0			0
$717$	153.853	+	88.8270i	0.214579	+	0.123887i
$718$		0			0
$719$	453.267	−	785.082i	0.630413	−	1.09191i	−0.357054	−	0.934084i	$-0.616219\pi$
$719$	453.267	−	785.082i	0.630413	−	1.09191i	0.987467	−	0.157824i	$-0.0504480\pi$
$720$		0			0
$721$		−	2151.92i		−	2.98463i
$722$		0			0
$723$	956.774			1.32334
$724$		0			0
$725$	−507.113	−	292.782i	−0.699466	−	0.403837i
$726$		0			0
$727$	−129.255	+	223.876i	−0.177792	+	0.307944i	−0.941124	−	0.338062i	$-0.890229\pi$
$727$	−129.255	+	223.876i	−0.177792	+	0.307944i	0.763332	+	0.646006i	$0.223562\pi$
$728$		0			0
$729$	108.872			0.149345
$730$		0			0
$731$	543.734	+	941.776i	0.743823	+	1.28834i
$732$		0			0
$733$	−11.6270			−0.0158621			−0.00793107	−	0.999969i	$-0.502525\pi$
$733$	−11.6270			−0.0158621			−0.00793107	+	0.999969i	$0.502525\pi$
$734$		0			0
$735$	784.796	−	453.102i	1.06775	−	0.616466i
$736$		0			0
$737$	550.608	−	317.894i	0.747093	−	0.431335i
$738$		0			0
$739$	−192.783	+	333.910i	−0.260870	+	0.451840i	−0.966473	−	0.256767i	$-0.917343\pi$
$739$	−192.783	+	333.910i	−0.260870	+	0.451840i	0.705603	+	0.708607i	$0.250676\pi$
$740$		0			0
$741$	534.482	−	183.075i	0.721299	−	0.247065i
$742$		0			0
$743$	781.647	+	451.284i	1.05202	+	0.607381i	0.923213	−	0.384289i	$-0.125553\pi$
$743$	781.647	+	451.284i	1.05202	+	0.607381i	0.128802	+	0.991670i	$0.458887\pi$
$744$		0			0
$745$	−333.431	−	577.519i	−0.447558	−	0.775193i
$746$		0			0
$747$	167.541	+	290.190i	0.224285	+	0.388474i
$748$		0			0
$749$			907.191i			1.21120i
$750$		0			0
$751$	446.578	−	257.832i	0.594645	−	0.343318i	−0.172287	−	0.985047i	$-0.555116\pi$
$751$	446.578	−	257.832i	0.594645	−	0.343318i	0.766932	+	0.641728i	$0.221782\pi$
$752$		0			0
$753$			416.416i			0.553009i
$754$		0			0
$755$	181.303	+	104.675i	0.240136	+	0.138643i
$756$		0			0
$757$	−70.3485	+	121.847i	−0.0929306	+	0.160961i	−0.908743	−	0.417356i	$-0.862957\pi$
$757$	−70.3485	+	121.847i	−0.0929306	+	0.160961i	0.815812	+	0.578317i	$0.196290\pi$
$758$		0			0
$759$		−	742.025i		−	0.977635i
$760$		0			0
$761$	918.492			1.20695			0.603477	−	0.797381i	$-0.293782\pi$
$761$	918.492			1.20695			0.603477	+	0.797381i	$0.293782\pi$
$762$		0			0
$763$	−36.6806	−	21.1775i	−0.0480742	−	0.0277556i
$764$		0			0
$765$	−159.002	+	275.399i	−0.207845	+	0.359998i
$766$		0			0
$767$	−663.468			−0.865017
$768$		0			0
$769$	−501.724	−	869.012i	−0.652437	−	1.13005i	−0.982530	−	0.186106i	$-0.940413\pi$
$769$	−501.724	−	869.012i	−0.652437	−	1.13005i	0.330092	−	0.943949i	$-0.392920\pi$
$770$		0			0
$771$	−454.999			−0.590141
$772$		0			0
$773$	−365.934	+	211.272i	−0.473395	+	0.273314i	−0.717660	−	0.696394i	$-0.754787\pi$
$773$	−365.934	+	211.272i	−0.473395	+	0.273314i	0.244265	+	0.969708i	$0.421453\pi$
$774$		0			0
$775$	−138.468	+	79.9445i	−0.178668	+	0.103154i
$776$		0			0
$777$	642.950	−	1113.62i	0.827477	−	1.43323i
$778$		0			0
$779$	−711.530	−	139.496i	−0.913388	−	0.179071i
$780$		0			0
$781$	315.543	+	182.179i	0.404025	+	0.233264i
$782$		0			0
$783$	−250.322	−	433.571i	−0.319697	−	0.553731i
$784$		0			0
$785$	345.087	+	597.708i	0.439601	+	0.761411i
$786$		0			0
$787$		−	1279.25i		−	1.62547i	−0.582633	−	0.812735i	$-0.697978\pi$
$787$		−	1279.25i		−	1.62547i	0.582633	−	0.812735i	$-0.302022\pi$
$788$		0			0
$789$	−1519.37	+	877.208i	−1.92569	+	1.11180i
$790$		0			0
$791$			1668.66i			2.10956i
$792$		0			0
$793$	−24.6216	−	14.2153i	−0.0310487	−	0.0179260i
$794$		0			0
$795$	−311.708	+	539.894i	−0.392085	+	0.679111i
$796$		0			0
$797$			726.878i			0.912018i	0.889975	+	0.456009i	$0.150721\pi$
$797$			726.878i			0.912018i	−0.889975	+	0.456009i	$0.849279\pi$
$798$		0			0
$799$	−1134.30			−1.41964
$800$		0			0
$801$	97.0176	+	56.0132i	0.121121	+	0.0699290i
$802$		0			0
$803$	−215.051	+	372.480i	−0.267810	+	0.463860i
$804$		0			0
$805$	−1190.48			−1.47886
$806$		0			0
$807$	−652.506	−	1130.17i	−0.808557	−	1.40046i
$808$		0			0
$809$	908.429			1.12290			0.561452	−	0.827509i	$-0.310243\pi$
$809$	908.429			1.12290			0.561452	+	0.827509i	$0.310243\pi$
$810$		0			0
$811$	−1028.49	+	593.797i	−1.26817	+	0.732179i	−0.974642	−	0.223771i	$-0.928163\pi$
$811$	−1028.49	+	593.797i	−1.26817	+	0.732179i	−0.293530	+	0.955950i	$0.594830\pi$
$812$		0			0
$813$	390.085	−	225.216i	0.479810	−	0.277018i
$814$		0			0
$815$	197.217	−	341.590i	0.241984	−	0.419129i
$816$		0			0
$817$	−217.170	+	1107.72i	−0.265813	+	1.35584i
$818$		0			0
$819$	420.770	+	242.931i	0.513760	+	0.296620i
$820$		0			0
$821$	−19.4768	−	33.7348i	−0.0237233	−	0.0410899i	0.853920	−	0.520404i	$-0.174219\pi$
$821$	−19.4768	−	33.7348i	−0.0237233	−	0.0410899i	−0.877643	+	0.479314i	$0.840885\pi$
$822$		0			0
$823$	−30.7697	−	53.2947i	−0.0373873	−	0.0647566i	0.846726	−	0.532029i	$-0.178570\pi$
$823$	−30.7697	−	53.2947i	−0.0373873	−	0.0647566i	−0.884114	+	0.467272i	$0.845237\pi$
$824$		0			0
$825$			332.263i			0.402743i
$826$		0			0
$827$	−811.008	+	468.236i	−0.980662	+	0.566186i	−0.902470	−	0.430753i	$-0.858248\pi$
$827$	−811.008	+	468.236i	−0.980662	+	0.566186i	−0.0781923	+	0.996938i	$0.524915\pi$
$828$		0			0
$829$			188.937i			0.227909i	0.993486	+	0.113955i	$0.0363518\pi$
$829$			188.937i			0.227909i	−0.993486	+	0.113955i	$0.963648\pi$
$830$		0			0
$831$	599.481	+	346.111i	0.721397	+	0.416499i
$832$		0			0
$833$	697.183	−	1207.56i	0.836955	−	1.44965i
$834$		0			0
$835$		−	579.315i		−	0.693790i
$836$		0			0
$837$	−136.702			−0.163324
$838$		0			0
$839$	−543.333	−	313.694i	−0.647596	−	0.373890i	0.139939	−	0.990160i	$-0.455310\pi$
$839$	−543.333	−	313.694i	−0.647596	−	0.373890i	−0.787535	+	0.616270i	$0.788643\pi$
$840$		0			0
$841$	312.735	−	541.673i	0.371861	−	0.644082i
$842$		0			0
$843$	867.003			1.02847
$844$		0			0
$845$	−168.787	−	292.348i	−0.199748	−	0.345974i
$846$		0			0
$847$	991.350			1.17042
$848$		0			0
$849$	−1076.89	+	621.744i	−1.26842	+	0.732325i
$850$		0			0
$851$	−890.296	+	514.013i	−1.04618	+	0.604010i
$852$		0			0
$853$	−20.1765	+	34.9468i	−0.0236536	+	0.0409693i	−0.877610	−	0.479375i	$-0.840863\pi$
$853$	−20.1765	+	34.9468i	−0.0236536	+	0.0409693i	0.853956	+	0.520345i	$0.174197\pi$
$854$		0			0
$855$	−312.280	+	106.965i	−0.365240	+	0.125105i
$856$		0			0
$857$	1068.27	+	616.764i	1.24652	+	0.719678i	0.970413	−	0.241449i	$-0.0776227\pi$
$857$	1068.27	+	616.764i	1.24652	+	0.719678i	0.276106	+	0.961127i	$0.410956\pi$
$858$		0			0
$859$	−465.744	−	806.693i	−0.542194	−	0.939107i	−0.998778	−	0.0494265i	$-0.984261\pi$
$859$	−465.744	−	806.693i	−0.542194	−	0.939107i	0.456584	−	0.889680i	$-0.349073\pi$
$860$		0			0
$861$	−815.035	−	1411.68i	−0.946614	−	1.63958i
$862$		0			0
$863$		−	426.295i		−	0.493968i	−0.969020	−	0.246984i	$-0.920560\pi$
$863$		−	426.295i		−	0.493968i	0.969020	−	0.246984i	$-0.0794396\pi$
$864$		0			0
$865$	−734.578	+	424.109i	−0.849223	+	0.490299i
$866$		0			0
$867$			175.785i			0.202751i
$868$		0			0
$869$	−486.218	−	280.718i	−0.559514	−	0.323035i
$870$		0			0
$871$	435.017	−	753.472i	0.499446	−	0.865066i
$872$		0			0
$873$		−	323.086i		−	0.370087i
$874$		0			0
$875$	1404.62			1.60528
$876$		0			0
$877$	1027.85	+	593.427i	1.17200	+	0.676656i	0.954151	−	0.299326i	$-0.0967619\pi$
$877$	1027.85	+	593.427i	1.17200	+	0.676656i	0.217851	+	0.975982i	$0.430095\pi$
$878$		0			0
$879$	98.9199	−	171.334i	0.112537	−	0.194920i
$880$		0			0
$881$	−310.782			−0.352761			−0.176380	−	0.984322i	$-0.556439\pi$
$881$	−310.782			−0.352761			−0.176380	+	0.984322i	$0.556439\pi$
$882$		0			0
$883$	−124.778	−	216.122i	−0.141312	−	0.244759i	0.786679	−	0.617362i	$-0.211799\pi$
$883$	−124.778	−	216.122i	−0.141312	−	0.244759i	−0.927991	+	0.372603i	$0.878465\pi$
$884$		0			0
$885$	1013.36			1.14504
$886$		0			0
$887$	−16.0576	+	9.27083i	−0.0181032	+	0.0104519i	−0.509024	−	0.860752i	$-0.669994\pi$
$887$	−16.0576	+	9.27083i	−0.0181032	+	0.0104519i	0.490921	+	0.871204i	$0.336660\pi$
$888$		0			0
$889$	−218.450	+	126.122i	−0.245725	+	0.141870i
$890$		0			0
$891$	−284.843	+	493.362i	−0.319689	+	0.553717i
$892$		0			0
$893$	−887.362	−	773.882i	−0.993686	−	0.866610i
$894$		0			0
$895$	−63.7013	−	36.7780i	−0.0711747	−	0.0410927i
$896$		0			0
$897$	−507.707	−	879.375i	−0.566006	−	0.980351i
$898$		0			0
$899$	−200.211	−	346.776i	−0.222704	−	0.385735i
$900$		0			0
$901$			959.242i			1.06464i
$902$		0			0
$903$	−2197.73	+	1268.86i	−2.43381	+	1.40516i
$904$		0			0
$905$			177.639i			0.196286i
$906$		0			0
$907$	−639.562	−	369.251i	−0.705140	−	0.407113i	0.104119	−	0.994565i	$-0.466798\pi$
$907$	−639.562	−	369.251i	−0.705140	−	0.407113i	−0.809259	+	0.587452i	$0.800131\pi$
$908$		0			0
$909$	357.962	−	620.008i	0.393797	−	0.682077i
$910$		0			0
$911$			1646.37i			1.80722i	0.428359	+	0.903609i	$0.359092\pi$
$911$			1646.37i			1.80722i	−0.428359	+	0.903609i	$0.640908\pi$
$912$		0			0
$913$	−342.049			−0.374643
$914$		0			0
$915$	37.6063	+	21.7120i	0.0410998	+	0.0237290i
$916$		0			0
$917$	−839.419	+	1453.92i	−0.915397	+	1.58551i
$918$		0			0
$919$	1110.40			1.20827			0.604136	−	0.796882i	$-0.293519\pi$
$919$	1110.40			1.20827			0.604136	+	0.796882i	$0.293519\pi$
$920$		0			0
$921$	21.6684	+	37.5308i	0.0235271	+	0.0407501i
$922$		0			0
$923$	498.601			0.540196
$924$		0			0
$925$	398.656	−	230.164i	0.430979	−	0.248826i
$926$		0			0
$927$	−928.727	+	536.201i	−1.00186	+	0.578426i
$928$		0			0
$929$	757.979	−	1312.86i	0.815908	−	1.41319i	−0.0927656	−	0.995688i	$-0.529571\pi$
$929$	757.979	−	1312.86i	0.815908	−	1.41319i	0.908674	−	0.417507i	$-0.137096\pi$
$930$		0			0
$931$	1369.27	−	469.015i	1.47076	−	0.503776i
$932$		0			0
$933$	399.248	+	230.506i	0.427919	+	0.247059i
$934$		0			0
$935$	−162.307	−	281.124i	−0.173591	−	0.300668i
$936$		0			0
$937$	−496.916	−	860.684i	−0.530327	−	0.918552i	−0.999374	−	0.0353795i	$-0.988736\pi$
$937$	−496.916	−	860.684i	−0.530327	−	0.918552i	0.469047	−	0.883173i	$-0.344597\pi$
$938$		0			0
$939$		−	495.030i		−	0.527188i
$940$		0			0
$941$	379.535	−	219.125i	0.403332	−	0.232864i	−0.284589	−	0.958650i	$-0.591857\pi$
$941$	379.535	−	219.125i	0.403332	−	0.232864i	0.687921	+	0.725786i	$0.258524\pi$
$942$		0			0
$943$			1303.18i			1.38195i
$944$		0			0
$945$	394.705	+	227.883i	0.417678	+	0.241146i
$946$		0			0
$947$	91.6405	−	158.726i	0.0967693	−	0.167609i	−0.813576	−	0.581458i	$-0.802482\pi$
$947$	91.6405	−	158.726i	0.0967693	−	0.167609i	0.910346	+	0.413849i	$0.135816\pi$
$948$		0			0
$949$			588.568i			0.620198i
$950$		0			0
$951$	1931.05			2.03055
$952$		0			0
$953$	158.904	+	91.7433i	0.166741	+	0.0962679i	0.581048	−	0.813869i	$-0.302643\pi$
$953$	158.904	+	91.7433i	0.166741	+	0.0962679i	−0.414307	+	0.910137i	$0.635976\pi$
$954$		0			0
$955$	−246.757	+	427.395i	−0.258384	+	0.447534i
$956$		0			0
$957$	−832.112			−0.869500
$958$		0			0
$959$	403.485	+	698.856i	0.420735	+	0.728734i
$960$		0			0
$961$	851.664			0.886227
$962$		0			0
$963$	391.526	−	226.048i	0.406570	−	0.234733i
$964$		0			0
$965$	−500.694	+	289.076i	−0.518854	+	0.299560i
$966$		0			0
$967$	712.541	−	1234.16i	0.736857	−	1.27627i	−0.217047	−	0.976161i	$-0.569642\pi$
$967$	712.541	−	1234.16i	0.736857	−	1.27627i	0.953904	−	0.300113i	$-0.0970243\pi$
$968$		0			0
$969$	−872.697	+	1000.67i	−0.900616	+	1.03268i
$970$		0			0
$971$	−143.906	−	83.0843i	−0.148204	−	0.0855657i	0.424064	−	0.905632i	$-0.360603\pi$
$971$	−143.906	−	83.0843i	−0.148204	−	0.0855657i	−0.572268	+	0.820066i	$0.693936\pi$
$972$		0			0
$973$	713.718	+	1236.20i	0.733523	+	1.27050i
$974$		0			0
$975$	227.341	+	393.766i	0.233170	+	0.403862i
$976$		0			0
$977$		−	959.257i		−	0.981839i	−0.871205	−	0.490920i	$-0.836661\pi$
$977$		−	959.257i		−	0.981839i	0.871205	−	0.490920i	$-0.163339\pi$
$978$		0			0
$979$	−99.0347	+	57.1777i	−0.101159	+	0.0584042i
$980$		0			0
$981$			21.1075i			0.0215163i
$982$		0			0
$983$	−94.1725	−	54.3705i	−0.0958011	−	0.0553108i	0.451334	−	0.892355i	$-0.350948\pi$
$983$	−94.1725	−	54.3705i	−0.0958011	−	0.0553108i	−0.547135	+	0.837044i	$0.684282\pi$
$984$		0			0
$985$	−30.9395	+	53.5888i	−0.0314107	+	0.0544049i
$986$		0			0
$987$		−	2646.99i		−	2.68186i
$988$		0			0
$989$	2028.80			2.05137
$990$		0			0
$991$	−1596.80	−	921.912i	−1.61130	−	0.930284i	−0.989070	−	0.147450i	$-0.952894\pi$
$991$	−1596.80	−	921.912i	−1.61130	−	0.930284i	−0.622230	−	0.782834i	$-0.713773\pi$
$992$		0			0
$993$	−154.561	+	267.707i	−0.155650	+	0.269594i
$994$		0			0
$995$	421.580			0.423699
$996$		0			0
$997$	−537.881	−	931.637i	−0.539499	−	0.934440i	−0.998931	−	0.0462269i	$-0.985280\pi$
$997$	−537.881	−	931.637i	−0.539499	−	0.934440i	0.459432	−	0.888213i	$-0.348053\pi$
$998$		0			0
$999$	393.571			0.393965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.h.a.65.1	✓	8
3.2	odd	2		684.3.y.h.217.3		8
4.3	odd	2		304.3.r.c.65.4		8
19.8	odd	6		1444.3.c.b.721.2		8
19.11	even	3		1444.3.c.b.721.7		8
19.12	odd	6	inner	76.3.h.a.69.1	yes	8
57.50	even	6		684.3.y.h.145.3		8
76.31	even	6		304.3.r.c.145.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.h.a.65.1	✓	8	1.1	even	1	trivial
76.3.h.a.69.1	yes	8	19.12	odd	6	inner
304.3.r.c.65.4		8	4.3	odd	2
304.3.r.c.145.4		8	76.31	even	6
684.3.y.h.145.3		8	57.50	even	6
684.3.y.h.217.3		8	3.2	odd	2
1444.3.c.b.721.2		8	19.8	odd	6
1444.3.c.b.721.7		8	19.11	even	3

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.30632 - 1.90890i) q^{3} +(-1.55796 + 2.69846i) q^{5} -11.1883 q^{7} +(2.78782 + 4.82865i) q^{9} +O(q^{10})\)	\(q+(-3.30632 - 1.90890i) q^{3} +(-1.55796 + 2.69846i) q^{5} -11.1883 q^{7} +(2.78782 + 4.82865i) q^{9} -5.69156 q^{11} +(-6.74507 + 3.89427i) q^{13} +(10.3022 - 5.94799i) q^{15} +(9.15210 - 15.8519i) q^{17} +(17.9748 - 6.15688i) q^{19} +(36.9920 + 21.3573i) q^{21} +(-17.0743 - 29.5736i) q^{23} +(7.64552 + 13.2424i) q^{25} +13.0735i q^{27} +(-33.1640 + 19.1473i) q^{29} +10.4564i q^{31} +(18.8181 + 10.8646i) q^{33} +(17.4309 - 30.1912i) q^{35} -30.1044i q^{37} +29.7351 q^{39} +(-33.0491 - 19.0809i) q^{41} +(-29.7055 + 51.4514i) q^{43} -17.3732 q^{45} +(-30.9846 - 53.6669i) q^{47} +76.1775 q^{49} +(-60.5195 + 34.9409i) q^{51} +(-45.3846 + 26.2028i) q^{53} +(8.86722 - 15.3585i) q^{55} +(-71.1832 - 13.9555i) q^{57} +(73.7726 + 42.5926i) q^{59} +(1.82516 + 3.16127i) q^{61} +(-31.1909 - 54.0242i) q^{63} -24.2685i q^{65} +(-96.7411 + 55.8535i) q^{67} +130.373i q^{69} +(-55.4406 - 32.0086i) q^{71} +(37.7842 - 65.4442i) q^{73} -58.3783i q^{75} +63.6787 q^{77} +(85.4278 + 49.3218i) q^{79} +(50.0465 - 86.6831i) q^{81} +60.0975 q^{83} +(28.5172 + 49.3932i) q^{85} +146.201 q^{87} +(17.4003 - 10.0461i) q^{89} +(75.4657 - 43.5701i) q^{91} +(19.9602 - 34.5721i) q^{93} +(-11.3899 + 58.0965i) q^{95} +(-50.1828 - 28.9730i) q^{97} +(-15.8670 - 27.4825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9	\( 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} - 10 q^{11} + 9 q^{13} + 33 q^{15} + 23 q^{17} - 33 q^{19} - 31 q^{23} - 73 q^{25} - 105 q^{29} - 111 q^{33} - 68 q^{35} + 234 q^{39} + 18 q^{41} - 41 q^{43} + 200 q^{45} + 107 q^{47} + 312 q^{49} - 9 q^{51} + 39 q^{53} + 70 q^{55} - 381 q^{57} + 348 q^{59} - 45 q^{61} - 358 q^{63} - 432 q^{67} - 243 q^{71} + 16 q^{73} + 544 q^{77} + 75 q^{79} - 68 q^{81} - 82 q^{83} + 109 q^{85} + 414 q^{87} - 213 q^{89} + 222 q^{91} + 288 q^{93} - 385 q^{95} + 144 q^{97} - 388 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9 - 10 * q^11 + 9 * q^13 + 33 * q^15 + 23 * q^17 - 33 * q^19 - 31 * q^23 - 73 * q^25 - 105 * q^29 - 111 * q^33 - 68 * q^35 + 234 * q^39 + 18 * q^41 - 41 * q^43 + 200 * q^45 + 107 * q^47 + 312 * q^49 - 9 * q^51 + 39 * q^53 + 70 * q^55 - 381 * q^57 + 348 * q^59 - 45 * q^61 - 358 * q^63 - 432 * q^67 - 243 * q^71 + 16 * q^73 + 544 * q^77 + 75 * q^79 - 68 * q^81 - 82 * q^83 + 109 * q^85 + 414 * q^87 - 213 * q^89 + 222 * q^91 + 288 * q^93 - 385 * q^95 + 144 * q^97 - 388 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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