LMFDB - Embedded newform 1148.2.i.e.821.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			821.4
Character	$\chi$	$=$	1148.821
Dual form			1148.2.i.e.165.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23867 - 2.14545i) q^{3} +(1.74922 - 3.02973i) q^{5} +(1.19623 + 2.35988i) q^{7} +(-1.56862 + 2.71694i) q^{9} +O(q^{10})$	\(q+(-1.23867 - 2.14545i) q^{3} +(1.74922 - 3.02973i) q^{5} +(1.19623 + 2.35988i) q^{7} +(-1.56862 + 2.71694i) q^{9} +(0.443416 + 0.768019i) q^{11} -6.85228 q^{13} -8.66684 q^{15} +(-1.51449 - 2.62318i) q^{17} +(-3.03700 + 5.26024i) q^{19} +(3.58125 - 5.48957i) q^{21} +(2.26135 - 3.91677i) q^{23} +(-3.61953 - 6.26920i) q^{25} +0.340013 q^{27} -7.22633 q^{29} +(-4.86035 - 8.41836i) q^{31} +(1.09850 - 1.90265i) q^{33} +(9.24228 + 0.503671i) q^{35} +(-3.52836 + 6.11129i) q^{37} +(8.48773 + 14.7012i) q^{39} -1.00000 q^{41} +4.25996 q^{43} +(5.48773 + 9.50503i) q^{45} +(5.88048 - 10.1853i) q^{47} +(-4.13805 + 5.64593i) q^{49} +(-3.75192 + 6.49852i) q^{51} +(-3.11863 - 5.40162i) q^{53} +3.10252 q^{55} +15.0474 q^{57} +(-0.226725 - 0.392700i) q^{59} +(0.902499 - 1.56317i) q^{61} +(-8.28808 - 0.451671i) q^{63} +(-11.9861 + 20.7606i) q^{65} +(-0.193195 - 0.334623i) q^{67} -11.2043 q^{69} +0.406313 q^{71} +(-1.23633 - 2.14139i) q^{73} +(-8.96682 + 15.5310i) q^{75} +(-1.28200 + 1.96514i) q^{77} +(-7.07942 + 12.2619i) q^{79} +(4.28471 + 7.42133i) q^{81} +7.79158 q^{83} -10.5967 q^{85} +(8.95106 + 15.5037i) q^{87} +(2.57323 - 4.45696i) q^{89} +(-8.19692 - 16.1705i) q^{91} +(-12.0408 + 20.8552i) q^{93} +(10.6247 + 18.4026i) q^{95} -11.4082 q^{97} -2.78221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−1.23867	−	2.14545i	−0.715149	−	1.23867i	−0.962902	−	0.269851i	$-0.913026\pi$
$3$	−1.23867	−	2.14545i	−0.715149	−	1.23867i	0.247754	−	0.968823i	$-0.420308\pi$
$4$		0			0
$5$	1.74922	−	3.02973i	0.782274	−	1.35494i	−0.148340	−	0.988936i	$-0.547393\pi$
$5$	1.74922	−	3.02973i	0.782274	−	1.35494i	0.930614	−	0.366002i	$-0.119274\pi$
$6$		0			0
$7$	1.19623	+	2.35988i	0.452134	+	0.891950i
$7$	1.19623	+	2.35988i	0.452134	+	0.891950i
$8$		0			0
$9$	−1.56862	+	2.71694i	−0.522875	+	0.905646i
$10$		0			0
$11$	0.443416	+	0.768019i	0.133695	+	0.231566i	0.925098	−	0.379728i	$-0.123982\pi$
$11$	0.443416	+	0.768019i	0.133695	+	0.231566i	−0.791403	+	0.611294i	$0.790649\pi$
$12$		0			0
$13$	−6.85228			−1.90048			−0.950240	−	0.311519i	$-0.899162\pi$
$13$	−6.85228			−1.90048			−0.950240	+	0.311519i	$0.899162\pi$
$14$		0			0
$15$	−8.66684			−2.23777
$16$		0			0
$17$	−1.51449	−	2.62318i	−0.367318	−	0.636214i	0.621827	−	0.783155i	$-0.286391\pi$
$17$	−1.51449	−	2.62318i	−0.367318	−	0.636214i	−0.989145	+	0.146941i	$0.953057\pi$
$18$		0			0
$19$	−3.03700	+	5.26024i	−0.696735	+	1.20678i	0.272857	+	0.962055i	$0.412031\pi$
$19$	−3.03700	+	5.26024i	−0.696735	+	1.20678i	−0.969592	+	0.244726i	$0.921302\pi$
$20$		0			0
$21$	3.58125	−	5.48957i	0.781492	−	1.19792i
$22$		0			0
$23$	2.26135	−	3.91677i	0.471524	−	0.816704i	−0.527945	−	0.849279i	$-0.677037\pi$
$23$	2.26135	−	3.91677i	0.471524	−	0.816704i	0.999469	+	0.0325746i	$0.0103706\pi$
$24$		0			0
$25$	−3.61953	−	6.26920i	−0.723905	−	1.25384i
$26$		0			0
$27$	0.340013			0.0654355
$28$		0			0
$29$	−7.22633			−1.34189			−0.670947	−	0.741505i	$-0.734112\pi$
$29$	−7.22633			−1.34189			−0.670947	+	0.741505i	$0.734112\pi$
$30$		0			0
$31$	−4.86035	−	8.41836i	−0.872944	−	1.51198i	−0.858937	−	0.512081i	$-0.828875\pi$
$31$	−4.86035	−	8.41836i	−0.872944	−	1.51198i	−0.0140066	−	0.999902i	$-0.504459\pi$
$32$		0			0
$33$	1.09850	−	1.90265i	0.191223	−	0.331209i
$34$		0			0
$35$	9.24228	+	0.503671i	1.56223	+	0.0851360i
$36$		0			0
$37$	−3.52836	+	6.11129i	−0.580058	+	1.00469i	0.415414	+	0.909633i	$0.363637\pi$
$37$	−3.52836	+	6.11129i	−0.580058	+	1.00469i	−0.995472	+	0.0950575i	$0.969697\pi$
$38$		0			0
$39$	8.48773	+	14.7012i	1.35913	+	2.35407i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	4.25996			0.649638			0.324819	−	0.945776i	$-0.394697\pi$
$43$	4.25996			0.649638			0.324819	+	0.945776i	$0.394697\pi$
$44$		0			0
$45$	5.48773	+	9.50503i	0.818063	+	1.41693i
$46$		0			0
$47$	5.88048	−	10.1853i	0.857756	−	1.48568i	−0.0163078	−	0.999867i	$-0.505191\pi$
$47$	5.88048	−	10.1853i	0.857756	−	1.48568i	0.874064	−	0.485811i	$-0.161476\pi$
$48$		0			0
$49$	−4.13805	+	5.64593i	−0.591150	+	0.806562i
$50$		0			0
$51$	−3.75192	+	6.49852i	−0.525374	+	0.909975i
$52$		0			0
$53$	−3.11863	−	5.40162i	−0.428376	−	0.741969i	0.568353	−	0.822785i	$-0.307581\pi$
$53$	−3.11863	−	5.40162i	−0.428376	−	0.741969i	−0.996729	+	0.0808157i	$0.974247\pi$
$54$		0			0
$55$	3.10252			0.418344
$56$		0			0
$57$	15.0474			1.99308
$58$		0			0
$59$	−0.226725	−	0.392700i	−0.0295171	−	0.0511252i	0.850889	−	0.525345i	$-0.176064\pi$
$59$	−0.226725	−	0.392700i	−0.0295171	−	0.0511252i	−0.880407	+	0.474220i	$0.842730\pi$
$60$		0			0
$61$	0.902499	−	1.56317i	0.115553	−	0.200144i	−0.802448	−	0.596723i	$-0.796469\pi$
$61$	0.902499	−	1.56317i	0.115553	−	0.200144i	0.918001	+	0.396579i	$0.129803\pi$
$62$		0			0
$63$	−8.28808	−	0.451671i	−1.04420	−	0.0569052i
$64$		0			0
$65$	−11.9861	+	20.7606i	−1.48670	+	2.57503i
$66$		0			0
$67$	−0.193195	−	0.334623i	−0.0236025	−	0.0408807i	0.853983	−	0.520301i	$-0.174180\pi$
$67$	−0.193195	−	0.334623i	−0.0236025	−	0.0408807i	−0.877585	+	0.479420i	$0.840847\pi$
$68$		0			0
$69$	−11.2043			−1.34884
$70$		0			0
$71$	0.406313			0.0482205			0.0241103	−	0.999709i	$-0.492325\pi$
$71$	0.406313			0.0482205			0.0241103	+	0.999709i	$0.492325\pi$
$72$		0			0
$73$	−1.23633	−	2.14139i	−0.144701	−	0.250630i	0.784560	−	0.620053i	$-0.212889\pi$
$73$	−1.23633	−	2.14139i	−0.144701	−	0.250630i	−0.929262	+	0.369423i	$0.879556\pi$
$74$		0			0
$75$	−8.96682	+	15.5310i	−1.03540	+	1.79336i
$76$		0			0
$77$	−1.28200	+	1.96514i	−0.146098	+	0.223948i
$78$		0			0
$79$	−7.07942	+	12.2619i	−0.796497	+	1.37957i	0.125388	+	0.992108i	$0.459982\pi$
$79$	−7.07942	+	12.2619i	−0.796497	+	1.37957i	−0.921884	+	0.387465i	$0.873351\pi$
$80$		0			0
$81$	4.28471	+	7.42133i	0.476079	+	0.824593i
$82$		0			0
$83$	7.79158			0.855237			0.427618	−	0.903959i	$-0.359353\pi$
$83$	7.79158			0.855237			0.427618	+	0.903959i	$0.359353\pi$
$84$		0			0
$85$	−10.5967			−1.14937
$86$		0			0
$87$	8.95106	+	15.5037i	0.959654	+	1.66217i
$88$		0			0
$89$	2.57323	−	4.45696i	0.272761	−	0.472437i	−0.696806	−	0.717259i	$-0.745396\pi$
$89$	2.57323	−	4.45696i	0.272761	−	0.472437i	0.969568	+	0.244823i	$0.0787297\pi$
$90$		0			0
$91$	−8.19692	−	16.1705i	−0.859271	−	1.69513i
$92$		0			0
$93$	−12.0408	+	20.8552i	−1.24857	+	2.16258i
$94$		0			0
$95$	10.6247	+	18.4026i	1.09008	+	1.88807i
$96$		0			0
$97$	−11.4082			−1.15833			−0.579165	−	0.815211i	$-0.696621\pi$
$97$	−11.4082			−1.15833			−0.579165	+	0.815211i	$0.696621\pi$
$98$		0			0
$99$	−2.78221			−0.279623
$100$		0			0
$101$	−3.61734	−	6.26542i	−0.359939	−	0.623433i	0.628011	−	0.778204i	$-0.283869\pi$
$101$	−3.61734	−	6.26542i	−0.359939	−	0.623433i	−0.987950	+	0.154772i	$0.950536\pi$
$102$		0			0
$103$	4.90807	−	8.50102i	0.483606	−	0.837631i	−0.516216	−	0.856458i	$-0.672660\pi$
$103$	4.90807	−	8.50102i	0.483606	−	0.837631i	0.999823	+	0.0188274i	$0.00599330\pi$
$104$		0			0
$105$	−10.3676	−	20.4527i	−1.01177	−	1.99598i
$106$		0			0
$107$	−4.95757	+	8.58676i	−0.479266	+	0.830114i	−0.999717	−	0.0237779i	$-0.992431\pi$
$107$	−4.95757	+	8.58676i	−0.479266	+	0.830114i	0.520451	+	0.853892i	$0.325764\pi$
$108$		0			0
$109$	−2.22138	−	3.84755i	−0.212770	−	0.368528i	0.739810	−	0.672815i	$-0.234915\pi$
$109$	−2.22138	−	3.84755i	−0.212770	−	0.368528i	−0.952580	+	0.304287i	$0.901582\pi$
$110$		0			0
$111$	17.4819			1.65931
$112$		0			0
$113$	13.0359			1.22631			0.613157	−	0.789961i	$-0.289899\pi$
$113$	13.0359			1.22631			0.613157	+	0.789961i	$0.289899\pi$
$114$		0			0
$115$	−7.91119	−	13.7026i	−0.737722	−	1.27777i
$116$		0			0
$117$	10.7486	−	18.6172i	0.993713	−	1.72116i
$118$		0			0
$119$	4.37869	−	6.71195i	0.401394	−	0.615284i
$120$		0			0
$121$	5.10676	−	8.84518i	0.464251	−	0.804107i
$122$		0			0
$123$	1.23867	+	2.14545i	0.111687	+	0.193448i
$124$		0			0
$125$	−7.83317			−0.700620
$126$		0			0
$127$	21.6259			1.91899			0.959496	−	0.281722i	$-0.0909057\pi$
$127$	21.6259			1.91899			0.959496	+	0.281722i	$0.0909057\pi$
$128$		0			0
$129$	−5.27670	−	9.13952i	−0.464588	−	0.804690i
$130$		0			0
$131$	−1.06570	+	1.84584i	−0.0931104	+	0.161272i	−0.908818	−	0.417192i	$-0.863014\pi$
$131$	−1.06570	+	1.84584i	−0.0931104	+	0.161272i	0.815708	+	0.578464i	$0.196348\pi$
$132$		0			0
$133$	−16.0465	−	0.874476i	−1.39141	−	0.0758267i
$134$		0			0
$135$	0.594756	−	1.03015i	0.0511885	−	0.0886610i
$136$		0			0
$137$	−1.17833	−	2.04094i	−0.100672	−	0.174369i	0.811290	−	0.584644i	$-0.198766\pi$
$137$	−1.17833	−	2.04094i	−0.100672	−	0.174369i	−0.911962	+	0.410275i	$0.865433\pi$
$138$		0			0
$139$	12.9520			1.09858			0.549288	−	0.835633i	$-0.314899\pi$
$139$	12.9520			1.09858			0.549288	+	0.835633i	$0.314899\pi$
$140$		0			0
$141$	−29.1360			−2.45369
$142$		0			0
$143$	−3.03841	−	5.26268i	−0.254085	−	0.440087i
$144$		0			0
$145$	−12.6404	+	21.8938i	−1.04973	+	1.81818i
$146$		0			0
$147$	17.2387	+	1.88450i	1.42183	+	0.155431i
$148$		0			0
$149$	7.25237	−	12.5615i	0.594137	−	1.02908i	−0.399531	−	0.916720i	$-0.630827\pi$
$149$	7.25237	−	12.5615i	0.594137	−	1.02908i	0.993668	−	0.112356i	$-0.0358397\pi$
$150$		0			0
$151$	−5.81582	−	10.0733i	−0.473285	−	0.819753i	0.526248	−	0.850331i	$-0.323598\pi$
$151$	−5.81582	−	10.0733i	−0.473285	−	0.819753i	−0.999532	+	0.0305782i	$0.990265\pi$
$152$		0			0
$153$	9.50268			0.768246
$154$		0			0
$155$	−34.0072			−2.73152
$156$		0			0
$157$	−2.80145	−	4.85225i	−0.223580	−	0.387252i	0.732313	−	0.680969i	$-0.238441\pi$
$157$	−2.80145	−	4.85225i	−0.223580	−	0.387252i	−0.955892	+	0.293717i	$0.905108\pi$
$158$		0			0
$159$	−7.72592	+	13.3817i	−0.612705	+	1.06124i
$160$		0			0
$161$	11.9482	+	0.651135i	0.941651	+	0.0513166i
$162$		0			0
$163$	−3.71166	+	6.42878i	−0.290719	+	0.503541i	−0.973980	−	0.226634i	$-0.927228\pi$
$163$	−3.71166	+	6.42878i	−0.290719	+	0.503541i	0.683261	+	0.730175i	$0.260561\pi$
$164$		0			0
$165$	−3.84301	−	6.65630i	−0.299178	−	0.518192i
$166$		0			0
$167$	17.5163			1.35545			0.677726	−	0.735314i	$-0.262965\pi$
$167$	17.5163			1.35545			0.677726	+	0.735314i	$0.262965\pi$
$168$		0			0
$169$	33.9537			2.61182
$170$		0			0
$171$	−9.52782	−	16.5027i	−0.728611	−	1.26199i
$172$		0			0
$173$	−4.79532	+	8.30573i	−0.364581	+	0.631473i	−0.988709	−	0.149849i	$-0.952121\pi$
$173$	−4.79532	+	8.30573i	−0.364581	+	0.631473i	0.624128	+	0.781322i	$0.285454\pi$
$174$		0			0
$175$	10.4648	−	16.0411i	0.791061	−	1.21259i
$176$		0			0
$177$	−0.561678	+	0.972854i	−0.0422183	+	0.0731242i
$178$		0			0
$179$	−12.3204	−	21.3396i	−0.920870	−	1.59499i	−0.798073	−	0.602561i	$-0.794147\pi$
$179$	−12.3204	−	21.3396i	−0.920870	−	1.59499i	−0.122797	−	0.992432i	$-0.539186\pi$
$180$		0			0
$181$	−3.27455			−0.243395			−0.121698	−	0.992567i	$-0.538834\pi$
$181$	−3.27455			−0.243395			−0.121698	+	0.992567i	$0.538834\pi$
$182$		0			0
$183$	−4.47160			−0.330551
$184$		0			0
$185$	12.3437	+	21.3800i	0.907529	+	1.57189i
$186$		0			0
$187$	1.34310	−	2.32632i	0.0982172	−	0.170117i
$188$		0			0
$189$	0.406735	+	0.802389i	0.0295856	+	0.0583652i
$190$		0			0
$191$	−0.503649	+	0.872346i	−0.0364428	+	0.0631207i	−0.883672	−	0.468108i	$-0.844936\pi$
$191$	−0.503649	+	0.872346i	−0.0364428	+	0.0631207i	0.847229	+	0.531228i	$0.178269\pi$
$192$		0			0
$193$	−9.95890	−	17.2493i	−0.716857	−	1.24163i	−0.962239	−	0.272207i	$-0.912246\pi$
$193$	−9.95890	−	17.2493i	−0.716857	−	1.24163i	0.245381	−	0.969427i	$-0.421087\pi$
$194$		0			0
$195$	59.3876			4.25283
$196$		0			0
$197$	7.96044			0.567158			0.283579	−	0.958949i	$-0.408478\pi$
$197$	7.96044			0.567158			0.283579	+	0.958949i	$0.408478\pi$
$198$		0			0
$199$	8.09817	+	14.0264i	0.574064	+	0.994308i	0.996143	+	0.0877487i	$0.0279672\pi$
$199$	8.09817	+	14.0264i	0.574064	+	0.994308i	−0.422079	+	0.906559i	$0.638699\pi$
$200$		0			0
$201$	−0.478611	+	0.828978i	−0.0337586	+	0.0584716i
$202$		0			0
$203$	−8.64437	−	17.0532i	−0.606716	−	1.19690i
$204$		0			0
$205$	−1.74922	+	3.02973i	−0.122171	+	0.211606i
$206$		0			0
$207$	7.09442	+	12.2879i	0.493096	+	0.854068i
$208$		0			0
$209$	−5.38661			−0.372600
$210$		0			0
$211$	10.1084			0.695894			0.347947	−	0.937514i	$-0.386879\pi$
$211$	10.1084			0.695894			0.347947	+	0.937514i	$0.386879\pi$
$212$		0			0
$213$	−0.503289	−	0.871723i	−0.0344848	−	0.0597295i
$214$		0			0
$215$	7.45160	−	12.9066i	0.508195	−	0.880220i
$216$		0			0
$217$	14.0522	−	21.5402i	0.953926	−	1.46224i
$218$		0			0
$219$	−3.06282	+	5.30496i	−0.206966	+	0.358476i
$220$		0			0
$221$	10.3777	+	17.9747i	0.698081	+	1.20911i
$222$		0			0
$223$	5.60799			0.375539			0.187770	−	0.982213i	$-0.439874\pi$
$223$	5.60799			0.375539			0.187770	+	0.982213i	$0.439874\pi$
$224$		0			0
$225$	22.7107			1.51405
$226$		0			0
$227$	2.58294	+	4.47379i	0.171436	+	0.296936i	0.938922	−	0.344130i	$-0.111826\pi$
$227$	2.58294	+	4.47379i	0.171436	+	0.296936i	−0.767486	+	0.641066i	$0.778493\pi$
$228$		0			0
$229$	−3.19748	+	5.53820i	−0.211296	+	0.365975i	−0.952120	−	0.305724i	$-0.901102\pi$
$229$	−3.19748	+	5.53820i	−0.211296	+	0.365975i	0.740825	+	0.671698i	$0.234435\pi$
$230$		0			0
$231$	5.80408	+	0.316302i	0.381880	+	0.0208111i
$232$		0			0
$233$	−7.09617	+	12.2909i	−0.464885	+	0.805205i	−0.999196	−	0.0400830i	$-0.987238\pi$
$233$	−7.09617	+	12.2909i	−0.464885	+	0.805205i	0.534311	+	0.845288i	$0.320571\pi$
$234$		0			0
$235$	−20.5725	−	35.6326i	−1.34200	−	2.32441i
$236$		0			0
$237$	35.0763			2.27845
$238$		0			0
$239$	−15.2318			−0.985266			−0.492633	−	0.870237i	$-0.663966\pi$
$239$	−15.2318			−0.985266			−0.492633	+	0.870237i	$0.663966\pi$
$240$		0			0
$241$	3.45261	+	5.98009i	0.222402	+	0.385211i	0.955537	−	0.294872i	$-0.0952770\pi$
$241$	3.45261	+	5.98009i	0.222402	+	0.385211i	−0.733135	+	0.680083i	$0.761944\pi$
$242$		0			0
$243$	11.1247	−	19.2686i	0.713652	−	1.23608i
$244$		0			0
$245$	9.86732	+	22.4132i	0.630400	+	1.43192i
$246$		0			0
$247$	20.8104	−	36.0446i	1.32413	−	2.29346i
$248$		0			0
$249$	−9.65122	−	16.7164i	−0.611621	−	1.05936i
$250$		0			0
$251$	−21.2459			−1.34103			−0.670515	−	0.741896i	$-0.733927\pi$
$251$	−21.2459			−1.34103			−0.670515	+	0.741896i	$0.733927\pi$
$252$		0			0
$253$	4.01088			0.252162
$254$		0			0
$255$	13.1259	+	22.7347i	0.821973	+	1.42370i
$256$		0			0
$257$	3.03100	−	5.24984i	0.189068	−	0.327476i	−0.755871	−	0.654720i	$-0.772787\pi$
$257$	3.03100	−	5.24984i	0.189068	−	0.327476i	0.944940	+	0.327244i	$0.106120\pi$
$258$		0			0
$259$	−18.6426	−	1.01596i	−1.15840	−	0.0631285i
$260$		0			0
$261$	11.3354	−	19.6335i	0.701643	−	1.21528i
$262$		0			0
$263$	7.59918	+	13.1622i	0.468586	+	0.811614i	0.999355	−	0.0359021i	$-0.0114304\pi$
$263$	7.59918	+	13.1622i	0.468586	+	0.811614i	−0.530770	+	0.847516i	$0.678097\pi$
$264$		0			0
$265$	−21.8206			−1.34043
$266$		0			0
$267$	−12.7495			−0.780260
$268$		0			0
$269$	−9.44666	−	16.3621i	−0.575973	−	0.997615i	−0.995935	−	0.0900731i	$-0.971290\pi$
$269$	−9.44666	−	16.3621i	−0.575973	−	0.997615i	0.419962	−	0.907542i	$-0.362043\pi$
$270$		0			0
$271$	−7.47889	+	12.9538i	−0.454310	+	0.786889i	−0.998648	−	0.0519774i	$-0.983448\pi$
$271$	−7.47889	+	12.9538i	−0.454310	+	0.786889i	0.544338	+	0.838866i	$0.316781\pi$
$272$		0			0
$273$	−24.5397	+	37.6161i	−1.48521	+	2.27663i
$274$		0			0
$275$	3.20991	−	5.55973i	0.193565	−	0.335264i
$276$		0			0
$277$	6.54857	+	11.3425i	0.393465	+	0.681502i	0.992904	−	0.118919i	$-0.0379428\pi$
$277$	6.54857	+	11.3425i	0.393465	+	0.681502i	−0.599439	+	0.800421i	$0.704609\pi$
$278$		0			0
$279$	30.4962			1.82576
$280$		0			0
$281$	−21.2844			−1.26972			−0.634860	−	0.772627i	$-0.718942\pi$
$281$	−21.2844			−1.26972			−0.634860	+	0.772627i	$0.718942\pi$
$282$		0			0
$283$	−11.3842	−	19.7179i	−0.676717	−	1.17211i	−0.975964	−	0.217933i	$-0.930069\pi$
$283$	−11.3842	−	19.7179i	−0.676717	−	1.17211i	0.299246	−	0.954176i	$-0.403265\pi$
$284$		0			0
$285$	26.3212	−	45.5896i	1.55913	−	2.70050i
$286$		0			0
$287$	−1.19623	−	2.35988i	−0.0706114	−	0.139299i
$288$		0			0
$289$	3.91262	−	6.77686i	0.230154	−	0.398639i
$290$		0			0
$291$	14.1311	+	24.4757i	0.828377	+	1.43479i
$292$		0			0
$293$	4.51752			0.263916			0.131958	−	0.991255i	$-0.457874\pi$
$293$	4.51752			0.263916			0.131958	+	0.991255i	$0.457874\pi$
$294$		0			0
$295$	−1.58637			−0.0923620
$296$		0			0
$297$	0.150767	+	0.261136i	0.00874839	+	0.0151527i
$298$		0			0
$299$	−15.4954	+	26.8388i	−0.896122	+	1.55213i
$300$		0			0
$301$	5.09591	+	10.0530i	0.293723	+	0.579445i
$302$		0			0
$303$	−8.96141	+	15.5216i	−0.514820	+	0.891694i
$304$		0			0
$305$	−3.15733	−	5.46866i	−0.180788	−	0.313135i
$306$		0			0
$307$	4.60882			0.263039			0.131520	−	0.991314i	$-0.458014\pi$
$307$	4.60882			0.263039			0.131520	+	0.991314i	$0.458014\pi$
$308$		0			0
$309$	−24.3180			−1.38340
$310$		0			0
$311$	7.98942	+	13.8381i	0.453039	+	0.784686i	0.998573	−	0.0534024i	$-0.0170066\pi$
$311$	7.98942	+	13.8381i	0.453039	+	0.784686i	−0.545534	+	0.838088i	$0.683673\pi$
$312$		0			0
$313$	16.2064	−	28.0704i	0.916042	−	1.58663i	0.110674	−	0.993857i	$-0.464699\pi$
$313$	16.2064	−	28.0704i	0.916042	−	1.58663i	0.805368	−	0.592775i	$-0.201968\pi$
$314$		0			0
$315$	−15.8661	+	24.3206i	−0.893954	+	1.37031i
$316$		0			0
$317$	6.55810	−	11.3590i	0.368340	−	0.637983i	−0.620966	−	0.783837i	$-0.713260\pi$
$317$	6.55810	−	11.3590i	0.368340	−	0.637983i	0.989306	+	0.145854i	$0.0465930\pi$
$318$		0			0
$319$	−3.20427	−	5.54995i	−0.179405	−	0.310738i
$320$		0			0
$321$	24.5632			1.37099
$322$		0			0
$323$	18.3981			1.02370
$324$		0			0
$325$	24.8020	+	42.9583i	1.37577	+	2.38290i
$326$		0			0
$327$	−5.50314	+	9.53172i	−0.304324	+	0.527105i
$328$		0			0
$329$	31.0705	+	1.69323i	1.71297	+	0.0933508i
$330$		0			0
$331$	−13.3179	+	23.0673i	−0.732017	+	1.26789i	0.224002	+	0.974589i	$0.428088\pi$
$331$	−13.3179	+	23.0673i	−0.732017	+	1.26789i	−0.956020	+	0.293303i	$0.905246\pi$
$332$		0			0
$333$	−11.0693	−	19.1726i	−0.606595	−	1.05065i
$334$		0			0
$335$	−1.35176			−0.0738545
$336$		0			0
$337$	−22.0648			−1.20194			−0.600972	−	0.799270i	$-0.705220\pi$
$337$	−22.0648			−1.20194			−0.600972	+	0.799270i	$0.705220\pi$
$338$		0			0
$339$	−16.1472	−	27.9678i	−0.876997	−	1.51900i
$340$		0			0
$341$	4.31031	−	7.46567i	0.233416	−	0.404289i
$342$		0			0
$343$	−18.2738	−	3.01144i	−0.986692	−	0.162603i
$344$		0			0
$345$	−19.5988	+	33.9461i	−1.05516	+	1.82759i
$346$		0			0
$347$	−14.7429	−	25.5355i	−0.791440	−	1.37082i	−0.925075	−	0.379784i	$-0.875998\pi$
$347$	−14.7429	−	25.5355i	−0.791440	−	1.37082i	0.133635	−	0.991031i	$-0.457335\pi$
$348$		0			0
$349$	−14.9842			−0.802084			−0.401042	−	0.916060i	$-0.631352\pi$
$349$	−14.9842			−0.802084			−0.401042	+	0.916060i	$0.631352\pi$
$350$		0			0
$351$	−2.32986			−0.124359
$352$		0			0
$353$	−9.13251	−	15.8180i	−0.486075	−	0.841906i	0.513797	−	0.857912i	$-0.328238\pi$
$353$	−9.13251	−	15.8180i	−0.486075	−	0.841906i	−0.999872	+	0.0160057i	$0.994905\pi$
$354$		0			0
$355$	0.710730	−	1.23102i	0.0377216	−	0.0653358i
$356$		0			0
$357$	−19.8239	−	1.08033i	−1.04919	−	0.0571772i
$358$		0			0
$359$	−10.0887	+	17.4742i	−0.532462	+	0.922252i	0.466819	+	0.884353i	$0.345400\pi$
$359$	−10.0887	+	17.4742i	−0.532462	+	0.922252i	−0.999282	+	0.0378990i	$0.987933\pi$
$360$		0			0
$361$	−8.94673	−	15.4962i	−0.470880	−	0.815589i
$362$		0			0
$363$	−25.3025			−1.32803
$364$		0			0
$365$	−8.65044			−0.452785
$366$		0			0
$367$	−8.61678	−	14.9247i	−0.449792	−	0.779063i	0.548580	−	0.836098i	$-0.315169\pi$
$367$	−8.61678	−	14.9247i	−0.449792	−	0.779063i	−0.998372	+	0.0570350i	$0.981835\pi$
$368$		0			0
$369$	1.56862	−	2.71694i	0.0816593	−	0.141438i
$370$		0			0
$371$	9.01655	−	13.8212i	0.468116	−	0.717559i
$372$		0			0
$373$	5.35096	−	9.26814i	0.277062	−	0.479886i	−0.693591	−	0.720369i	$-0.743972\pi$
$373$	5.35096	−	9.26814i	0.277062	−	0.479886i	0.970653	+	0.240483i	$0.0773058\pi$
$374$		0			0
$375$	9.70274	+	16.8056i	0.501047	+	0.867840i
$376$		0			0
$377$	49.5168			2.55024
$378$		0			0
$379$	24.9770			1.28298			0.641492	−	0.767130i	$-0.278316\pi$
$379$	24.9770			1.28298			0.641492	+	0.767130i	$0.278316\pi$
$380$		0			0
$381$	−26.7875	−	46.3973i	−1.37236	−	2.37700i
$382$		0			0
$383$	2.11376	−	3.66113i	0.108008	−	0.187075i	−0.806955	−	0.590613i	$-0.798886\pi$
$383$	2.11376	−	3.66113i	0.108008	−	0.187075i	0.914963	+	0.403537i	$0.132219\pi$
$384$		0			0
$385$	3.71134	+	7.32158i	0.189148	+	0.373142i
$386$		0			0
$387$	−6.68228	+	11.5740i	−0.339679	+	0.588342i
$388$		0			0
$389$	−12.7521	−	22.0872i	−0.646555	−	1.11987i	−0.983940	−	0.178499i	$-0.942876\pi$
$389$	−12.7521	−	22.0872i	−0.646555	−	1.11987i	0.337385	−	0.941367i	$-0.390458\pi$
$390$		0			0
$391$	−13.6992			−0.692798
$392$		0			0
$393$	5.28020			0.266351
$394$		0			0
$395$	24.7669	+	42.8975i	1.24616	+	2.15841i
$396$		0			0
$397$	15.1213	−	26.1909i	0.758917	−	1.31448i	−0.184486	−	0.982835i	$-0.559062\pi$
$397$	15.1213	−	26.1909i	0.758917	−	1.31448i	0.943403	−	0.331648i	$-0.107605\pi$
$398$		0			0
$399$	18.0002	+	35.5100i	0.901138	+	1.77773i
$400$		0			0
$401$	−2.90854	+	5.03775i	−0.145246	+	0.251573i	−0.929465	−	0.368911i	$-0.879731\pi$
$401$	−2.90854	+	5.03775i	−0.145246	+	0.251573i	0.784219	+	0.620484i	$0.213064\pi$
$402$		0			0
$403$	33.3044	+	57.6850i	1.65901	+	2.87349i
$404$		0			0
$405$	29.9796			1.48970
$406$		0			0
$407$	−6.25812			−0.310203
$408$		0			0
$409$	0.218381	+	0.378248i	0.0107983	+	0.0187031i	0.871374	−	0.490619i	$-0.163229\pi$
$409$	0.218381	+	0.378248i	0.0107983	+	0.0187031i	−0.860576	+	0.509322i	$0.829896\pi$
$410$		0			0
$411$	−2.91914	+	5.05611i	−0.143991	+	0.249399i
$412$		0			0
$413$	0.655508	−	1.00481i	0.0322554	−	0.0494432i
$414$		0			0
$415$	13.6292	−	23.6064i	0.669029	−	1.15879i
$416$		0			0
$417$	−16.0433	−	27.7879i	−0.785645	−	1.36078i
$418$		0			0
$419$	−7.44035			−0.363485			−0.181743	−	0.983346i	$-0.558174\pi$
$419$	−7.44035			−0.363485			−0.181743	+	0.983346i	$0.558174\pi$
$420$		0			0
$421$	22.7010			1.10638			0.553189	−	0.833056i	$-0.313411\pi$
$421$	22.7010			1.10638			0.553189	+	0.833056i	$0.313411\pi$
$422$		0			0
$423$	18.4485	+	31.9538i	0.896998	+	1.55365i
$424$		0			0
$425$	−10.9635	+	18.9893i	−0.531807	+	0.921117i
$426$		0			0
$427$	4.76850	+	0.259866i	0.230764	+	0.0125758i
$428$		0			0
$429$	−7.52719	+	13.0375i	−0.363416	+	0.629456i
$430$		0			0
$431$	−16.6559	−	28.8488i	−0.802285	−	1.38960i	−0.918109	−	0.396328i	$-0.870284\pi$
$431$	−16.6559	−	28.8488i	−0.802285	−	1.38960i	0.115824	−	0.993270i	$-0.463049\pi$
$432$		0			0
$433$	−13.8756			−0.666816			−0.333408	−	0.942783i	$-0.608199\pi$
$433$	−13.8756			−0.666816			−0.333408	+	0.942783i	$0.608199\pi$
$434$		0			0
$435$	62.6294			3.00285
$436$		0			0
$437$	13.7354	+	23.7905i	0.657055	+	1.13805i
$438$		0			0
$439$	−12.5297	+	21.7021i	−0.598010	+	1.03578i	0.395104	+	0.918636i	$0.370709\pi$
$439$	−12.5297	+	21.7021i	−0.598010	+	1.03578i	−0.993114	+	0.117148i	$0.962625\pi$
$440$		0			0
$441$	−8.84859	−	20.0992i	−0.421362	−	0.957103i
$442$		0			0
$443$	−6.33694	+	10.9759i	−0.301077	+	0.521481i	−0.976380	−	0.216059i	$-0.930680\pi$
$443$	−6.33694	+	10.9759i	−0.301077	+	0.521481i	0.675303	+	0.737540i	$0.264013\pi$
$444$		0			0
$445$	−9.00227	−	15.5924i	−0.426748	−	0.739150i
$446$		0			0
$447$	−35.9333			−1.69959
$448$		0			0
$449$	−35.8184			−1.69037			−0.845187	−	0.534470i	$-0.820511\pi$
$449$	−35.8184			−1.69037			−0.845187	+	0.534470i	$0.820511\pi$
$450$		0			0
$451$	−0.443416	−	0.768019i	−0.0208796	−	0.0361646i
$452$		0			0
$453$	−14.4078	+	24.9551i	−0.676938	+	1.17249i
$454$		0			0
$455$	−63.3306	−	3.45129i	−2.96899	−	0.161799i
$456$		0			0
$457$	10.5519	−	18.2764i	0.493595	−	0.854932i	−0.506378	−	0.862312i	$-0.669016\pi$
$457$	10.5519	−	18.2764i	0.493595	−	0.854932i	0.999973	+	0.00738004i	$0.00234916\pi$
$458$		0			0
$459$	−0.514947	−	0.891914i	−0.0240357	−	0.0416310i
$460$		0			0
$461$	−33.8364			−1.57592			−0.787958	−	0.615729i	$-0.788862\pi$
$461$	−33.8364			−1.57592			−0.787958	+	0.615729i	$0.788862\pi$
$462$		0			0
$463$	31.5226			1.46498			0.732490	−	0.680778i	$-0.238358\pi$
$463$	31.5226			1.46498			0.732490	+	0.680778i	$0.238358\pi$
$464$		0			0
$465$	42.1238	+	72.9606i	1.95345	+	3.38347i
$466$		0			0
$467$	−16.5774	+	28.7129i	−0.767112	+	1.32868i	0.172011	+	0.985095i	$0.444974\pi$
$467$	−16.5774	+	28.7129i	−0.767112	+	1.32868i	−0.939123	+	0.343582i	$0.888360\pi$
$468$		0			0
$469$	0.558564	−	0.856204i	0.0257921	−	0.0395358i
$470$		0			0
$471$	−6.94016	+	12.0207i	−0.319785	+	0.553885i
$472$		0			0
$473$	1.88893	+	3.27173i	0.0868533	+	0.150434i
$474$		0			0
$475$	43.9700			2.01748
$476$		0			0
$477$	19.5678			0.895948
$478$		0			0
$479$	3.90158	+	6.75774i	0.178268	+	0.308769i	0.941287	−	0.337607i	$-0.109617\pi$
$479$	3.90158	+	6.75774i	0.178268	+	0.308769i	−0.763020	+	0.646375i	$0.776284\pi$
$480$		0			0
$481$	24.1773	−	41.8763i	1.10239	−	1.90939i
$482$		0			0
$483$	−13.4030	−	26.4408i	−0.609856	−	1.20310i
$484$		0			0
$485$	−19.9555	+	34.5639i	−0.906131	+	1.56946i
$486$		0			0
$487$	−5.98268	−	10.3623i	−0.271101	−	0.469561i	0.698043	−	0.716056i	$-0.254054\pi$
$487$	−5.98268	−	10.3623i	−0.271101	−	0.469561i	−0.969144	+	0.246495i	$0.920721\pi$
$488$		0			0
$489$	18.3901			0.831630
$490$		0			0
$491$	4.00762			0.180861			0.0904307	−	0.995903i	$-0.471176\pi$
$491$	4.00762			0.180861			0.0904307	+	0.995903i	$0.471176\pi$
$492$		0			0
$493$	10.9442	+	18.9559i	0.492903	+	0.853733i
$494$		0			0
$495$	−4.86669	+	8.42936i	−0.218742	+	0.378872i
$496$		0			0
$497$	0.486045	+	0.958850i	0.0218021	+	0.0430103i
$498$		0			0
$499$	5.87026	−	10.1676i	0.262789	−	0.455164i	−0.704193	−	0.710008i	$-0.748691\pi$
$499$	5.87026	−	10.1676i	0.262789	−	0.455164i	0.966982	+	0.254845i	$0.0820244\pi$
$500$		0			0
$501$	−21.6970	−	37.5803i	−0.969350	−	1.67896i
$502$		0			0
$503$	−5.10200			−0.227487			−0.113743	−	0.993510i	$-0.536284\pi$
$503$	−5.10200			−0.227487			−0.113743	+	0.993510i	$0.536284\pi$
$504$		0			0
$505$	−25.3101			−1.12628
$506$		0			0
$507$	−42.0576	−	72.8458i	−1.86784	−	3.23520i
$508$		0			0
$509$	11.0976	−	19.2216i	0.491892	−	0.851982i	−0.508064	−	0.861319i	$-0.669639\pi$
$509$	11.0976	−	19.2216i	0.491892	−	0.851982i	0.999956	+	0.00933710i	$0.00297214\pi$
$510$		0			0
$511$	3.57447	−	5.47919i	0.158125	−	0.242385i
$512$		0			0
$513$	−1.03262	+	1.78855i	−0.0455912	+	0.0789663i
$514$		0			0
$515$	−17.1706	−	29.7403i	−0.756625	−	1.31051i
$516$		0			0
$517$	10.4300			0.458711
$518$		0			0
$519$	23.7593			1.04292
$520$		0			0
$521$	13.4526	+	23.3006i	0.589370	+	1.02082i	0.994315	+	0.106478i	$0.0339575\pi$
$521$	13.4526	+	23.3006i	0.589370	+	1.02082i	−0.404945	+	0.914341i	$0.632709\pi$
$522$		0			0
$523$	−14.2559	+	24.6920i	−0.623369	+	1.07971i	0.365485	+	0.930817i	$0.380903\pi$
$523$	−14.2559	+	24.6920i	−0.623369	+	1.07971i	−0.988854	+	0.148889i	$0.952430\pi$
$524$		0			0
$525$	−47.3777	−	2.58191i	−2.06773	−	0.112684i
$526$		0			0
$527$	−14.7219	+	25.4991i	−0.641297	+	1.11076i
$528$		0			0
$529$	1.27258	+	2.20418i	0.0553298	+	0.0958340i
$530$		0			0
$531$	1.42259			0.0617351
$532$		0			0
$533$	6.85228			0.296805
$534$		0			0
$535$	17.3437	+	30.0402i	0.749835	+	1.29875i
$536$		0			0
$537$	−30.5219	+	52.8655i	−1.31712	+	2.28131i
$538$		0			0
$539$	−6.17106	−	0.674605i	−0.265806	−	0.0290573i
$540$		0			0
$541$	6.58149	−	11.3995i	0.282960	−	0.490101i	−0.689152	−	0.724617i	$-0.742017\pi$
$541$	6.58149	−	11.3995i	0.282960	−	0.490101i	0.972112	+	0.234515i	$0.0753502\pi$
$542$		0			0
$543$	4.05610	+	7.02537i	0.174064	+	0.301487i
$544$		0			0
$545$	−15.5427			−0.665778
$546$		0			0
$547$	−13.8254			−0.591133			−0.295567	−	0.955322i	$-0.595508\pi$
$547$	−13.8254			−0.591133			−0.295567	+	0.955322i	$0.595508\pi$
$548$		0			0
$549$	2.83136	+	4.90406i	0.120840	+	0.209300i
$550$		0			0
$551$	21.9463	−	38.0122i	0.934946	−	1.61937i
$552$		0			0
$553$	−37.4052	−	2.03845i	−1.59063	−	0.0866838i
$554$		0			0
$555$	30.5797	−	52.9656i	1.29804	−	2.24826i
$556$		0			0
$557$	17.1545	+	29.7125i	0.726861	+	1.25896i	0.958204	+	0.286087i	$0.0923547\pi$
$557$	17.1545	+	29.7125i	0.726861	+	1.25896i	−0.231343	+	0.972872i	$0.574312\pi$
$558$		0			0
$559$	−29.1904			−1.23462
$560$		0			0
$561$	−6.65465			−0.280960
$562$		0			0
$563$	6.74820	+	11.6882i	0.284403	+	0.492600i	0.972464	−	0.233052i	$-0.0748713\pi$
$563$	6.74820	+	11.6882i	0.284403	+	0.492600i	−0.688061	+	0.725653i	$0.741538\pi$
$564$		0			0
$565$	22.8026	−	39.4953i	0.959314	−	1.66158i
$566$		0			0
$567$	−12.3879	+	18.9890i	−0.520244	+	0.797465i
$568$		0			0
$569$	3.60709	−	6.24766i	0.151217	−	0.261916i	−0.780458	−	0.625208i	$-0.785014\pi$
$569$	3.60709	−	6.24766i	0.151217	−	0.261916i	0.931675	+	0.363292i	$0.118347\pi$
$570$		0			0
$571$	4.54829	+	7.87787i	0.190340	+	0.329679i	0.945363	−	0.326020i	$-0.105708\pi$
$571$	4.54829	+	7.87787i	0.190340	+	0.329679i	−0.755023	+	0.655698i	$0.772374\pi$
$572$		0			0
$573$	2.49543			0.104248
$574$		0			0
$575$	−32.7401			−1.36536
$576$		0			0
$577$	12.7965	+	22.1643i	0.532727	+	0.922710i	0.999270	+	0.0382113i	$0.0121660\pi$
$577$	12.7965	+	22.1643i	0.532727	+	0.922710i	−0.466543	+	0.884499i	$0.654501\pi$
$578$		0			0
$579$	−24.6717	+	42.7326i	−1.02532	+	1.77590i
$580$		0			0
$581$	9.32055	+	18.3872i	0.386681	+	0.762828i
$582$		0			0
$583$	2.76570	−	4.79033i	0.114543	−	0.198395i
$584$		0			0
$585$	−37.6035	−	65.1311i	−1.55471	−	2.69284i
$586$		0			0
$587$	14.8861			0.614416			0.307208	−	0.951642i	$-0.400605\pi$
$587$	14.8861			0.614416			0.307208	+	0.951642i	$0.400605\pi$
$588$		0			0
$589$	59.0435			2.43284
$590$		0			0
$591$	−9.86038	−	17.0787i	−0.405602	−	0.702523i
$592$		0			0
$593$	−4.92927	+	8.53774i	−0.202421	+	0.350603i	−0.949308	−	0.314348i	$-0.898214\pi$
$593$	−4.92927	+	8.53774i	−0.202421	+	0.350603i	0.746887	+	0.664951i	$0.231548\pi$
$594$		0			0
$595$	−12.6761	−	25.0069i	−0.519671	−	1.02518i
$596$		0			0
$597$	20.0620	−	34.7484i	0.821082	−	1.42216i
$598$		0			0
$599$	−5.64079	−	9.77014i	−0.230476	−	0.399197i	0.727472	−	0.686137i	$-0.240695\pi$
$599$	−5.64079	−	9.77014i	−0.230476	−	0.399197i	−0.957948	+	0.286940i	$0.907362\pi$
$600$		0			0
$601$	4.84169			0.197497			0.0987483	−	0.995112i	$-0.468516\pi$
$601$	4.84169			0.197497			0.0987483	+	0.995112i	$0.468516\pi$
$602$		0			0
$603$	1.21220			0.0493646
$604$		0			0
$605$	−17.8657	−	30.9443i	−0.726343	−	1.25806i
$606$		0			0
$607$	14.4863	−	25.0911i	0.587982	−	1.01841i	−0.406514	−	0.913644i	$-0.633256\pi$
$607$	14.4863	−	25.0911i	0.587982	−	1.01841i	0.994496	−	0.104770i	$-0.0334108\pi$
$608$		0			0
$609$	−25.8793	+	39.6694i	−1.04868	+	1.60749i
$610$		0			0
$611$	−40.2947	+	69.7925i	−1.63015	+	2.82350i
$612$		0			0
$613$	−2.02993	−	3.51594i	−0.0819881	−	0.142008i	0.822116	−	0.569320i	$-0.192794\pi$
$613$	−2.02993	−	3.51594i	−0.0819881	−	0.142008i	−0.904104	+	0.427313i	$0.859460\pi$
$614$		0			0
$615$	8.66684			0.349481
$616$		0			0
$617$	31.0323			1.24931			0.624657	−	0.780900i	$-0.285239\pi$
$617$	31.0323			1.24931			0.624657	+	0.780900i	$0.285239\pi$
$618$		0			0
$619$	6.42969	+	11.1366i	0.258431	+	0.447616i	0.965822	−	0.259207i	$-0.0834612\pi$
$619$	6.42969	+	11.1366i	0.258431	+	0.447616i	−0.707391	+	0.706823i	$0.750128\pi$
$620$		0			0
$621$	0.768888	−	1.33175i	0.0308544	−	0.0534414i
$622$		0			0
$623$	13.5961	+	0.740937i	0.544715	+	0.0296850i
$624$		0			0
$625$	4.39570	−	7.61358i	0.175828	−	0.304543i
$626$		0			0
$627$	6.67226	+	11.5567i	0.266464	+	0.461530i
$628$		0			0
$629$	21.3747			0.852264
$630$		0			0
$631$	−28.0819			−1.11792			−0.558961	−	0.829194i	$-0.688800\pi$
$631$	−28.0819			−1.11792			−0.558961	+	0.829194i	$0.688800\pi$
$632$		0			0
$633$	−12.5211	−	21.6871i	−0.497668	−	0.861986i
$634$		0			0
$635$	37.8285	−	65.5208i	1.50118	−	2.60012i
$636$		0			0
$637$	28.3551	−	38.6875i	1.12347	−	1.53285i
$638$		0			0
$639$	−0.637353	+	1.10393i	−0.0252133	+	0.0436707i
$640$		0			0
$641$	14.5642	+	25.2260i	0.575253	+	0.996367i	0.996014	+	0.0891955i	$0.0284296\pi$
$641$	14.5642	+	25.2260i	0.575253	+	0.996367i	−0.420762	+	0.907171i	$0.638237\pi$
$642$		0			0
$643$	−34.0791			−1.34395			−0.671974	−	0.740575i	$-0.734553\pi$
$643$	−34.0791			−1.34395			−0.671974	+	0.740575i	$0.734553\pi$
$644$		0			0
$645$	−36.9204			−1.45374
$646$		0			0
$647$	−3.52306	−	6.10212i	−0.138506	−	0.239899i	0.788425	−	0.615130i	$-0.210897\pi$
$647$	−3.52306	−	6.10212i	−0.138506	−	0.239899i	−0.926931	+	0.375231i	$0.877563\pi$
$648$		0			0
$649$	0.201067	−	0.348259i	0.00789258	−	0.0136704i
$650$		0			0
$651$	−63.6193	−	3.46703i	−2.49344	−	0.135883i
$652$		0			0
$653$	−6.78950	+	11.7598i	−0.265694	+	0.460195i	−0.967745	−	0.251931i	$-0.918934\pi$
$653$	−6.78950	+	11.7598i	−0.265694	+	0.460195i	0.702051	+	0.712126i	$0.252268\pi$
$654$		0			0
$655$	3.72827	+	6.45756i	0.145676	+	0.252318i
$656$		0			0
$657$	7.75735			0.302643
$658$		0			0
$659$	38.7358			1.50893			0.754466	−	0.656339i	$-0.227896\pi$
$659$	38.7358			1.50893			0.754466	+	0.656339i	$0.227896\pi$
$660$		0			0
$661$	−13.3349	−	23.0968i	−0.518668	−	0.898360i	−0.999765	−	0.0216921i	$-0.993095\pi$
$661$	−13.3349	−	23.0968i	−0.518668	−	0.898360i	0.481096	−	0.876668i	$-0.340239\pi$
$662$		0			0
$663$	25.7092	−	44.5297i	0.998464	−	1.72939i
$664$		0			0
$665$	−30.7182	+	47.0869i	−1.19120	+	1.82595i
$666$		0			0
$667$	−16.3413	+	28.3039i	−0.632736	+	1.09593i
$668$		0			0
$669$	−6.94647	−	12.0316i	−0.268566	−	0.465170i
$670$		0			0
$671$	1.60073			0.0617955
$672$		0			0
$673$	−43.4682			−1.67558			−0.837789	−	0.545995i	$-0.816152\pi$
$673$	−43.4682			−1.67558			−0.837789	+	0.545995i	$0.816152\pi$
$674$		0			0
$675$	−1.23068	−	2.13161i	−0.0473691	−	0.0820456i
$676$		0			0
$677$	18.6375	−	32.2810i	0.716296	−	1.24066i	−0.246162	−	0.969229i	$-0.579169\pi$
$677$	18.6375	−	32.2810i	0.716296	−	1.24066i	0.962458	−	0.271432i	$-0.0874972\pi$
$678$		0			0
$679$	−13.6469	−	26.9220i	−0.523720	−	1.03317i
$680$		0			0
$681$	6.39885	−	11.0831i	0.245204	−	0.424706i
$682$		0			0
$683$	13.8993	+	24.0743i	0.531842	+	0.921177i	0.999309	+	0.0371663i	$0.0118331\pi$
$683$	13.8993	+	24.0743i	0.531842	+	0.921177i	−0.467468	+	0.884010i	$0.654834\pi$
$684$		0			0
$685$	−8.24466			−0.315012
$686$		0			0
$687$	15.8425			0.604431
$688$		0			0
$689$	21.3697	+	37.0134i	0.814120	+	1.41010i
$690$		0			0
$691$	−15.5640	+	26.9577i	−0.592084	+	1.02552i	0.401867	+	0.915698i	$0.368361\pi$
$691$	−15.5640	+	26.9577i	−0.592084	+	1.02552i	−0.993951	+	0.109822i	$0.964972\pi$
$692$		0			0
$693$	−3.32818	−	6.56568i	−0.126427	−	0.249410i
$694$		0			0
$695$	22.6559	−	39.2412i	0.859387	−	1.48850i
$696$		0			0
$697$	1.51449	+	2.62318i	0.0573655	+	0.0993600i
$698$		0			0
$699$	35.1593			1.32985
$700$		0			0
$701$	−12.0547			−0.455301			−0.227651	−	0.973743i	$-0.573104\pi$
$701$	−12.0547			−0.455301			−0.227651	+	0.973743i	$0.573104\pi$
$702$		0			0
$703$	−21.4312	−	37.1200i	−0.808294	−	1.40001i
$704$		0			0
$705$	−50.9652	+	88.2743i	−1.91946	+	3.32460i
$706$		0			0
$707$	10.4584	−	16.0314i	0.393330	−	0.602923i
$708$		0			0
$709$	−23.2451	+	40.2618i	−0.872989	+	1.51206i	−0.0141000	+	0.999901i	$0.504488\pi$
$709$	−23.2451	+	40.2618i	−0.872989	+	1.51206i	−0.858889	+	0.512161i	$0.828845\pi$
$710$		0			0
$711$	−22.2099	−	38.4687i	−0.832936	−	1.44269i
$712$		0			0
$713$	−43.9638			−1.64646
$714$		0			0
$715$	−21.2594			−0.795055
$716$		0			0
$717$	18.8673	+	32.6791i	0.704612	+	1.22042i
$718$		0			0
$719$	−6.29419	+	10.9019i	−0.234734	+	0.406571i	−0.959195	−	0.282744i	$-0.908755\pi$
$719$	−6.29419	+	10.9019i	−0.234734	+	0.406571i	0.724462	+	0.689315i	$0.242088\pi$
$720$		0			0
$721$	25.9326	+	1.41323i	0.965780	+	0.0526316i
$722$		0			0
$723$	8.55330	−	14.8148i	0.318101	−	0.550967i
$724$		0			0
$725$	26.1559	+	45.3033i	0.971404	+	1.68252i
$726$		0			0
$727$	−6.55299			−0.243037			−0.121519	−	0.992589i	$-0.538776\pi$
$727$	−6.55299			−0.243037			−0.121519	+	0.992589i	$0.538776\pi$
$728$		0			0
$729$	−29.4114			−1.08931
$730$		0			0
$731$	−6.45168	−	11.1746i	−0.238624	−	0.413309i
$732$		0			0
$733$	−3.05388	+	5.28948i	−0.112798	+	0.195371i	−0.916897	−	0.399123i	$-0.869315\pi$
$733$	−3.05388	+	5.28948i	−0.112798	+	0.195371i	0.804100	+	0.594495i	$0.202648\pi$
$734$		0			0
$735$	35.8638	−	48.9324i	1.32286	−	1.80490i
$736$		0			0
$737$	0.171331	−	0.296755i	0.00631107	−	0.0109311i
$738$		0			0
$739$	−11.0019	−	19.0558i	−0.404711	−	0.700979i	0.589577	−	0.807712i	$-0.299294\pi$
$739$	−11.0019	−	19.0558i	−0.404711	−	0.700979i	−0.994288	+	0.106733i	$0.965961\pi$
$740$		0			0
$741$	−103.109			−3.78780
$742$		0			0
$743$	34.6353			1.27065			0.635323	−	0.772247i	$-0.280867\pi$
$743$	34.6353			1.27065			0.635323	+	0.772247i	$0.280867\pi$
$744$		0			0
$745$	−25.3719	−	43.9455i	−0.929556	−	1.61004i
$746$		0			0
$747$	−12.2221	+	21.1692i	−0.447182	+	0.774541i
$748$		0			0
$749$	−26.1941	−	1.42749i	−0.957113	−	0.0521592i
$750$		0			0
$751$	10.1770	−	17.6270i	0.371363	−	0.643219i	−0.618413	−	0.785853i	$-0.712224\pi$
$751$	10.1770	−	17.6270i	0.371363	−	0.643219i	0.989775	+	0.142635i	$0.0455574\pi$
$752$		0			0
$753$	26.3168	+	45.5820i	0.959036	+	1.66110i
$754$		0			0
$755$	−40.6925			−1.48095
$756$		0			0
$757$	29.9426			1.08828			0.544141	−	0.838994i	$-0.316856\pi$
$757$	29.9426			1.08828			0.544141	+	0.838994i	$0.316856\pi$
$758$		0			0
$759$	−4.96817	−	8.60512i	−0.180333	−	0.312346i
$760$		0			0
$761$	−26.6719	+	46.1971i	−0.966855	+	1.67464i	−0.262308	+	0.964984i	$0.584484\pi$
$761$	−26.6719	+	46.1971i	−0.966855	+	1.67464i	−0.704547	+	0.709658i	$0.748850\pi$
$762$		0			0
$763$	6.42246	−	9.84476i	0.232508	−	0.356404i
$764$		0			0
$765$	16.6223	−	28.7906i	0.600979	−	1.04093i
$766$		0			0
$767$	1.55359	+	2.69089i	0.0560967	+	0.0971624i
$768$		0			0
$769$	0.577705			0.0208326			0.0104163	−	0.999946i	$-0.496684\pi$
$769$	0.577705			0.0208326			0.0104163	+	0.999946i	$0.496684\pi$
$770$		0			0
$771$	−15.0177			−0.540848
$772$		0			0
$773$	3.95513	+	6.85049i	0.142256	+	0.246395i	0.928346	−	0.371717i	$-0.121231\pi$
$773$	3.95513	+	6.85049i	0.142256	+	0.246395i	−0.786090	+	0.618112i	$0.787898\pi$
$774$		0			0
$775$	−35.1843	+	60.9410i	−1.26386	+	2.18906i
$776$		0			0
$777$	20.9125	+	41.2552i	0.750230	+	1.48002i
$778$		0			0
$779$	3.03700	−	5.26024i	0.108812	−	0.188468i
$780$		0			0
$781$	0.180166	+	0.312056i	0.00644684	+	0.0111662i
$782$		0			0
$783$	−2.45704			−0.0878075
$784$		0			0
$785$	−19.6014			−0.699603
$786$		0			0
$787$	12.3446	+	21.3814i	0.440036	+	0.762165i	0.997692	−	0.0679078i	$-0.0216324\pi$
$787$	12.3446	+	21.3814i	0.440036	+	0.762165i	−0.557656	+	0.830072i	$0.688299\pi$
$788$		0			0
$789$	18.8258	−	32.6073i	0.670217	−	1.16085i
$790$		0			0
$791$	15.5940	+	30.7631i	0.554458	+	1.09381i
$792$		0			0
$793$	−6.18417	+	10.7113i	−0.219606	+	0.380369i
$794$		0			0
$795$	27.0286	+	46.8149i	0.958606	+	1.66036i
$796$		0			0
$797$	−11.1868			−0.396258			−0.198129	−	0.980176i	$-0.563486\pi$
$797$	−11.1868			−0.396258			−0.198129	+	0.980176i	$0.563486\pi$
$798$		0			0
$799$	−35.6238			−1.26028
$800$		0			0
$801$	8.07285	+	13.9826i	0.285240	+	0.494050i
$802$		0			0
$803$	1.09642	−	1.89905i	0.0386917	−	0.0670160i
$804$		0			0
$805$	22.8728	−	35.0609i	0.806160	−	1.23574i
$806$		0			0
$807$	−23.4027	+	40.5346i	−0.823813	+	1.42689i
$808$		0			0
$809$	−2.14982	−	3.72359i	−0.0755836	−	0.130915i	0.825756	−	0.564027i	$-0.190749\pi$
$809$	−2.14982	−	3.72359i	−0.0755836	−	0.130915i	−0.901340	+	0.433112i	$0.857415\pi$
$810$		0			0
$811$	19.4277			0.682199			0.341100	−	0.940027i	$-0.389201\pi$
$811$	19.4277			0.682199			0.341100	+	0.940027i	$0.389201\pi$
$812$		0			0
$813$	37.0556			1.29960
$814$		0			0
$815$	12.9850	+	22.4907i	0.454844	+	0.787814i
$816$		0			0
$817$	−12.9375	+	22.4084i	−0.452626	+	0.783971i
$818$		0			0
$819$	56.7922	+	3.09497i	1.98448	+	0.108147i
$820$		0			0
$821$	−23.5670	+	40.8193i	−0.822495	+	1.42460i	0.0813230	+	0.996688i	$0.474085\pi$
$821$	−23.5670	+	40.8193i	−0.822495	+	1.42460i	−0.903818	+	0.427916i	$0.859248\pi$
$822$		0			0
$823$	−2.97483	−	5.15256i	−0.103696	−	0.179607i	0.809509	−	0.587108i	$-0.199734\pi$
$823$	−2.97483	−	5.15256i	−0.103696	−	0.179607i	−0.913205	+	0.407501i	$0.866400\pi$
$824$		0			0
$825$	−15.9041			−0.553710
$826$		0			0
$827$	4.01224			0.139519			0.0697596	−	0.997564i	$-0.477777\pi$
$827$	4.01224			0.139519			0.0697596	+	0.997564i	$0.477777\pi$
$828$		0			0
$829$	−1.54549	−	2.67686i	−0.0536769	−	0.0929712i	0.837938	−	0.545765i	$-0.183761\pi$
$829$	−1.54549	−	2.67686i	−0.0536769	−	0.0929712i	−0.891615	+	0.452794i	$0.850427\pi$
$830$		0			0
$831$	16.2231	−	28.0992i	0.562773	−	0.974751i
$832$		0			0
$833$	21.0773	+	2.30412i	0.730286	+	0.0798331i
$834$		0			0
$835$	30.6398	−	53.0697i	1.06034	−	1.83655i
$836$		0			0
$837$	−1.65258	−	2.86235i	−0.0571215	−	0.0989373i
$838$		0			0
$839$	35.1218			1.21254			0.606270	−	0.795259i	$-0.292665\pi$
$839$	35.1218			1.21254			0.606270	+	0.795259i	$0.292665\pi$
$840$		0			0
$841$	23.2198			0.800682
$842$		0			0
$843$	26.3644	+	45.6645i	0.908038	+	1.57277i
$844$		0			0
$845$	59.3924	−	102.871i	2.04316	−	3.53886i
$846$		0			0
$847$	26.9824	+	1.47045i	0.927127	+	0.0505251i
$848$		0			0
$849$	−28.2025	+	48.8481i	−0.967907	+	1.67646i
$850$		0			0
$851$	15.9577	+	27.6395i	0.547023	+	0.947471i
$852$		0			0
$853$	−21.6536			−0.741405			−0.370702	−	0.928752i	$-0.620883\pi$
$853$	−21.6536			−0.741405			−0.370702	+	0.928752i	$0.620883\pi$
$854$		0			0
$855$	−66.6649			−2.27989
$856$		0			0
$857$	27.3808	+	47.4249i	0.935310	+	1.62001i	0.774079	+	0.633089i	$0.218213\pi$
$857$	27.3808	+	47.4249i	0.935310	+	1.62001i	0.161231	+	0.986917i	$0.448454\pi$
$858$		0			0
$859$	−0.131578	+	0.227899i	−0.00448937	+	0.00777582i	−0.868261	−	0.496107i	$-0.834762\pi$
$859$	−0.131578	+	0.227899i	−0.00448937	+	0.00777582i	0.863772	+	0.503883i	$0.168096\pi$
$860$		0			0
$861$	−3.58125	+	5.48957i	−0.122049	+	0.187084i
$862$		0			0
$863$	27.0062	−	46.7761i	0.919302	−	1.59228i	0.118825	−	0.992915i	$-0.462087\pi$
$863$	27.0062	−	46.7761i	0.919302	−	1.59228i	0.800477	−	0.599363i	$-0.204579\pi$
$864$		0			0
$865$	16.7761	+	29.0571i	0.570405	+	0.987970i
$866$		0			0
$867$	−19.3859			−0.658378
$868$		0			0
$869$	−12.5565			−0.425950
$870$		0			0
$871$	1.32382	+	2.29293i	0.0448561	+	0.0776930i
$872$		0			0
$873$	17.8952	−	30.9954i	0.605661	−	1.04904i
$874$		0			0
$875$	−9.37030	−	18.4853i	−0.316774	−	0.624918i
$876$		0			0
$877$	−0.770125	+	1.33389i	−0.0260053	+	0.0450424i	−0.878735	−	0.477310i	$-0.841612\pi$
$877$	−0.770125	+	1.33389i	−0.0260053	+	0.0450424i	0.852730	+	0.522352i	$0.174945\pi$
$878$		0			0
$879$	−5.59573	−	9.69209i	−0.188739	−	0.326906i
$880$		0			0
$881$	6.28992			0.211913			0.105956	−	0.994371i	$-0.466210\pi$
$881$	6.28992			0.211913			0.105956	+	0.994371i	$0.466210\pi$
$882$		0			0
$883$	−6.57266			−0.221188			−0.110594	−	0.993866i	$-0.535275\pi$
$883$	−6.57266			−0.221188			−0.110594	+	0.993866i	$0.535275\pi$
$884$		0			0
$885$	1.96499	+	3.40347i	0.0660525	+	0.114406i
$886$		0			0
$887$	12.3072	−	21.3166i	0.413234	−	0.715742i	−0.582007	−	0.813184i	$-0.697733\pi$
$887$	12.3072	−	21.3166i	0.413234	−	0.715742i	0.995241	+	0.0974414i	$0.0310658\pi$
$888$		0			0
$889$	25.8697	+	51.0346i	0.867641	+	1.71165i
$890$		0			0
$891$	−3.79982	+	6.58147i	−0.127299	+	0.220488i
$892$		0			0
$893$	35.7180	+	61.8654i	1.19526	+	2.07025i
$894$		0			0
$895$	−86.2042			−2.88149
$896$		0			0
$897$	76.7750			2.56344
$898$		0			0
$899$	35.1224	+	60.8338i	1.17140	+	2.02892i
$900$		0			0
$901$	−9.44627	+	16.3614i	−0.314701	+	0.545078i
$902$		0			0
$903$	15.2560	−	23.3854i	0.507687	−	0.778216i
$904$		0			0
$905$	−5.72790	+	9.92102i	−0.190402	+	0.329786i
$906$		0			0
$907$	10.7143	+	18.5576i	0.355761	+	0.616196i	0.987248	−	0.159190i	$-0.0508884\pi$
$907$	10.7143	+	18.5576i	0.355761	+	0.616196i	−0.631487	+	0.775387i	$0.717555\pi$
$908$		0			0
$909$	22.6970			0.752812
$910$		0			0
$911$	20.6989			0.685786			0.342893	−	0.939374i	$-0.388593\pi$
$911$	20.6989			0.685786			0.342893	+	0.939374i	$0.388593\pi$
$912$		0			0
$913$	3.45491	+	5.98408i	0.114341	+	0.198044i
$914$		0			0
$915$	−7.82181	+	13.5478i	−0.258581	+	0.447876i
$916$		0			0
$917$	−5.63078	−	0.306858i	−0.185945	−	0.0101333i
$918$		0			0
$919$	6.79498	−	11.7693i	0.224146	−	0.388232i	−0.731917	−	0.681394i	$-0.761374\pi$
$919$	6.79498	−	11.7693i	0.224146	−	0.388232i	0.956063	+	0.293162i	$0.0947075\pi$
$920$		0			0
$921$	−5.70882	−	9.88796i	−0.188112	−	0.325819i
$922$		0			0
$923$	−2.78417			−0.0916421
$924$		0			0
$925$	51.0839			1.67963
$926$		0			0
$927$	15.3978	+	26.6698i	0.505731	+	0.875952i
$928$		0			0
$929$	21.4207	−	37.1017i	0.702790	−	1.21727i	−0.264694	−	0.964333i	$-0.585271\pi$
$929$	21.4207	−	37.1017i	0.702790	−	1.21727i	0.967483	−	0.252935i	$-0.0813959\pi$
$930$		0			0
$931$	−17.1317	−	38.9138i	−0.561468	−	1.27535i
$932$		0			0
$933$	19.7926	−	34.2818i	0.647980	−	1.12233i
$934$		0			0
$935$	−4.69875	−	8.13847i	−0.153666	−	0.266157i
$936$		0			0
$937$	−17.0062			−0.555568			−0.277784	−	0.960644i	$-0.589600\pi$
$937$	−17.0062			−0.555568			−0.277784	+	0.960644i	$0.589600\pi$
$938$		0			0
$939$	−80.2979			−2.62042
$940$		0			0
$941$	−21.9090	−	37.9475i	−0.714213	−	1.23705i	−0.963262	−	0.268563i	$-0.913451\pi$
$941$	−21.9090	−	37.9475i	−0.714213	−	1.23705i	0.249049	−	0.968491i	$-0.419882\pi$
$942$		0			0
$943$	−2.26135	+	3.91677i	−0.0736397	+	0.127548i
$944$		0			0
$945$	3.14249	+	0.171255i	0.102225	+	0.00557091i
$946$		0			0
$947$	7.60114	−	13.1656i	0.247004	−	0.427823i	−0.715689	−	0.698419i	$-0.753887\pi$
$947$	7.60114	−	13.1656i	0.247004	−	0.427823i	0.962693	+	0.270596i	$0.0872206\pi$
$948$		0			0
$949$	8.47168	+	14.6734i	0.275002	+	0.476318i
$950$		0			0
$951$	−32.4934			−1.05367
$952$		0			0
$953$	19.0486			0.617044			0.308522	−	0.951217i	$-0.400166\pi$
$953$	19.0486			0.617044			0.308522	+	0.951217i	$0.400166\pi$
$954$		0			0
$955$	1.76198	+	3.05184i	0.0570164	+	0.0987554i
$956$		0			0
$957$	−7.93808	+	13.7492i	−0.256602	+	0.444447i
$958$		0			0
$959$	3.40680	−	5.22216i	0.110011	−	0.168632i
$960$		0			0
$961$	−31.7459	+	54.9855i	−1.02406	+	1.77373i
$962$		0			0
$963$	−15.5531	−	26.9388i	−0.501193	−	0.868091i
$964$		0			0
$965$	−69.6812			−2.24312
$966$		0			0
$967$	−12.3278			−0.396435			−0.198218	−	0.980158i	$-0.563515\pi$
$967$	−12.3278			−0.396435			−0.198218	+	0.980158i	$0.563515\pi$
$968$		0			0
$969$	−22.7892	−	39.4720i	−0.732094	−	1.26802i
$970$		0			0
$971$	0.479522	−	0.830556i	0.0153886	−	0.0266538i	−0.858229	−	0.513268i	$-0.828435\pi$
$971$	0.479522	−	0.830556i	0.0153886	−	0.0266538i	0.873617	+	0.486614i	$0.161768\pi$
$972$		0			0
$973$	15.4936	+	30.5652i	0.496703	+	0.979875i
$974$		0			0
$975$	61.4431	−	106.423i	1.96776	−	3.40825i
$976$		0			0
$977$	18.8592	+	32.6650i	0.603358	+	1.04505i	0.992309	+	0.123788i	$0.0395042\pi$
$977$	18.8592	+	32.6650i	0.603358	+	1.04505i	−0.388951	+	0.921258i	$0.627162\pi$
$978$		0			0
$979$	4.56404			0.145867
$980$		0			0
$981$	13.9381			0.445008
$982$		0			0
$983$	16.1081	+	27.9000i	0.513768	+	0.889872i	0.999872	+	0.0159714i	$0.00508408\pi$
$983$	16.1081	+	27.9000i	0.513768	+	0.889872i	−0.486105	+	0.873901i	$0.661583\pi$
$984$		0			0
$985$	13.9245	−	24.1180i	0.443673	−	0.768464i
$986$		0			0
$987$	−34.8534	−	68.7574i	−1.10940	−	2.18857i
$988$		0			0
$989$	9.63327	−	16.6853i	0.306320	−	0.530562i
$990$		0			0
$991$	−5.68292	−	9.84311i	−0.180524	−	0.312677i	0.761535	−	0.648124i	$-0.224446\pi$
$991$	−5.68292	−	9.84311i	−0.180524	−	0.312677i	−0.942059	+	0.335447i	$0.891113\pi$
$992$		0			0
$993$	65.9861			2.09400
$994$		0			0
$995$	56.6618			1.79630
$996$		0			0
$997$	5.17518	+	8.96368i	0.163900	+	0.283883i	0.936264	−	0.351297i	$-0.114259\pi$
$997$	5.17518	+	8.96368i	0.163900	+	0.283883i	−0.772364	+	0.635180i	$0.780926\pi$
$998$		0			0
$999$	−1.19969	+	2.07792i	−0.0379564	+	0.0657424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.e.821.4	yes	30
7.2	even	3		8036.2.a.q.1.12		15
7.4	even	3	inner	1148.2.i.e.165.4	✓	30
7.5	odd	6		8036.2.a.r.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.e.165.4	✓	30	7.4	even	3	inner
1148.2.i.e.821.4	yes	30	1.1	even	1	trivial
8036.2.a.q.1.12		15	7.2	even	3
8036.2.a.r.1.4		15	7.5	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23867 - 2.14545i) q^{3} +(1.74922 - 3.02973i) q^{5} +(1.19623 + 2.35988i) q^{7} +(-1.56862 + 2.71694i) q^{9} +O(q^{10})\)	\(q+(-1.23867 - 2.14545i) q^{3} +(1.74922 - 3.02973i) q^{5} +(1.19623 + 2.35988i) q^{7} +(-1.56862 + 2.71694i) q^{9} +(0.443416 + 0.768019i) q^{11} -6.85228 q^{13} -8.66684 q^{15} +(-1.51449 - 2.62318i) q^{17} +(-3.03700 + 5.26024i) q^{19} +(3.58125 - 5.48957i) q^{21} +(2.26135 - 3.91677i) q^{23} +(-3.61953 - 6.26920i) q^{25} +0.340013 q^{27} -7.22633 q^{29} +(-4.86035 - 8.41836i) q^{31} +(1.09850 - 1.90265i) q^{33} +(9.24228 + 0.503671i) q^{35} +(-3.52836 + 6.11129i) q^{37} +(8.48773 + 14.7012i) q^{39} -1.00000 q^{41} +4.25996 q^{43} +(5.48773 + 9.50503i) q^{45} +(5.88048 - 10.1853i) q^{47} +(-4.13805 + 5.64593i) q^{49} +(-3.75192 + 6.49852i) q^{51} +(-3.11863 - 5.40162i) q^{53} +3.10252 q^{55} +15.0474 q^{57} +(-0.226725 - 0.392700i) q^{59} +(0.902499 - 1.56317i) q^{61} +(-8.28808 - 0.451671i) q^{63} +(-11.9861 + 20.7606i) q^{65} +(-0.193195 - 0.334623i) q^{67} -11.2043 q^{69} +0.406313 q^{71} +(-1.23633 - 2.14139i) q^{73} +(-8.96682 + 15.5310i) q^{75} +(-1.28200 + 1.96514i) q^{77} +(-7.07942 + 12.2619i) q^{79} +(4.28471 + 7.42133i) q^{81} +7.79158 q^{83} -10.5967 q^{85} +(8.95106 + 15.5037i) q^{87} +(2.57323 - 4.45696i) q^{89} +(-8.19692 - 16.1705i) q^{91} +(-12.0408 + 20.8552i) q^{93} +(10.6247 + 18.4026i) q^{95} -11.4082 q^{97} -2.78221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more