LMFDB - Embedded newform 1890.2.r.b.1529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(89,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 5]))

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

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

chi := DirichletCharacter("1890.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1529.4
Character	$\chi$	$=$	1890.1529
Dual form			1890.2.r.b.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.07866 - 0.824119i) q^{5} +(0.837534 + 2.50969i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.07866 - 0.824119i) q^{5} +(0.837534 + 2.50969i) q^{7} -1.00000 q^{8} +(-1.75304 + 1.38811i) q^{10} +0.811199i q^{11} +(-0.0126841 + 0.0219696i) q^{13} +(2.59222 + 0.529518i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.78721 - 1.60920i) q^{17} +(1.22111 - 0.705008i) q^{19} +(0.325622 + 2.21223i) q^{20} +(0.702519 + 0.405599i) q^{22} +3.53966 q^{23} +(3.64166 + 3.42613i) q^{25} +(0.0126841 + 0.0219696i) q^{26} +(1.75469 - 1.98017i) q^{28} +(4.38175 - 2.52980i) q^{29} +(2.89606 - 1.67204i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.78721 + 1.60920i) q^{34} +(0.327333 - 5.90702i) q^{35} +(9.76868 - 5.63995i) q^{37} -1.41002i q^{38} +(2.07866 + 0.824119i) q^{40} +(-0.973106 + 1.68547i) q^{41} +(-2.76069 + 1.59389i) q^{43} +(0.702519 - 0.405599i) q^{44} +(1.76983 - 3.06543i) q^{46} +(6.50911 + 3.75804i) q^{47} +(-5.59707 + 4.20390i) q^{49} +(4.78794 - 1.44070i) q^{50} +0.0253683 q^{52} +(5.33975 - 9.24872i) q^{53} +(0.668524 - 1.68621i) q^{55} +(-0.837534 - 2.50969i) q^{56} -5.05961i q^{58} +(1.80107 + 3.11955i) q^{59} +(0.527050 + 0.304293i) q^{61} -3.34408i q^{62} +1.00000 q^{64} +(0.0444715 - 0.0352140i) q^{65} +(0.879693 - 0.507891i) q^{67} +3.21840i q^{68} +(-4.95196 - 3.23699i) q^{70} +10.9830i q^{71} +(6.25999 - 10.8426i) q^{73} -11.2799i q^{74} +(-1.22111 - 0.705008i) q^{76} +(-2.03586 + 0.679406i) q^{77} +(-0.845656 + 1.46472i) q^{79} +(1.75304 - 1.38811i) q^{80} +(0.973106 + 1.68547i) q^{82} +(14.5567 - 8.40429i) q^{83} +(4.46750 + 5.64197i) q^{85} +3.18777i q^{86} -0.811199i q^{88} +(-2.31249 - 4.00536i) q^{89} +(-0.0657602 - 0.0134330i) q^{91} +(-1.76983 - 3.06543i) q^{92} +(6.50911 - 3.75804i) q^{94} +(-3.11928 + 0.459133i) q^{95} +(-3.19146 - 5.52778i) q^{97} +(0.842147 + 6.94916i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8}+O(q^{10}) $ 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8	$ 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61} + 48 q^{64} + 33 q^{65} - 33 q^{67} - 6 q^{70} + 18 q^{73} - 6 q^{77} + 3 q^{82} + 9 q^{83} - 33 q^{85} - 33 q^{89} - 3 q^{92} - 33 q^{95} + 24 q^{97} - 3 q^{98}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 - 3 * q^14 - 24 * q^16 + 6 * q^22 + 6 * q^23 - 3 * q^28 + 3 * q^29 + 24 * q^32 - 18 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 + 42 * q^55 - 9 * q^61 + 48 * q^64 + 33 * q^65 - 33 * q^67 - 6 * q^70 + 18 * q^73 - 6 * q^77 + 3 * q^82 + 9 * q^83 - 33 * q^85 - 33 * q^89 - 3 * q^92 - 33 * q^95 + 24 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.07866	−	0.824119i	−0.929605	−	0.368557i
$5$	−2.07866	−	0.824119i	−0.929605	−	0.368557i
$6$		0			0
$7$	0.837534	+	2.50969i	0.316558	+	0.948573i
$7$	0.837534	+	2.50969i	0.316558	+	0.948573i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.75304	+	1.38811i	−0.554359	+	0.438960i
$11$			0.811199i			0.244586i	0.992494	+	0.122293i	$0.0390247\pi$
$11$			0.811199i			0.244586i	−0.992494	+	0.122293i	$0.960975\pi$
$12$		0			0
$13$	−0.0126841	+	0.0219696i	−0.00351795	+	0.00609326i	−0.867779	−	0.496950i	$-0.834453\pi$
$13$	−0.0126841	+	0.0219696i	−0.00351795	+	0.00609326i	0.864261	+	0.503044i	$0.167786\pi$
$14$	2.59222	+	0.529518i	0.692800	+	0.141520i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.78721	−	1.60920i	−0.675999	−	0.390288i	0.122347	−	0.992487i	$-0.460958\pi$
$17$	−2.78721	−	1.60920i	−0.675999	−	0.390288i	−0.798346	+	0.602199i	$0.794291\pi$
$18$		0			0
$19$	1.22111	−	0.705008i	0.280142	−	0.161740i	−0.353346	−	0.935493i	$-0.614956\pi$
$19$	1.22111	−	0.705008i	0.280142	−	0.161740i	0.633488	+	0.773753i	$0.281623\pi$
$20$	0.325622	+	2.21223i	0.0728113	+	0.494670i
$21$		0			0
$22$	0.702519	+	0.405599i	0.149777	+	0.0864741i
$23$	3.53966			0.738069			0.369035	−	0.929416i	$-0.379688\pi$
$23$	3.53966			0.738069			0.369035	+	0.929416i	$0.379688\pi$
$24$		0			0
$25$	3.64166	+	3.42613i	0.728331	+	0.685225i
$26$	0.0126841	+	0.0219696i	0.00248756	+	0.00430859i
$27$		0			0
$28$	1.75469	−	1.98017i	0.331605	−	0.374217i
$29$	4.38175	−	2.52980i	0.813670	−	0.469773i	−0.0345586	−	0.999403i	$-0.511003\pi$
$29$	4.38175	−	2.52980i	0.813670	−	0.469773i	0.848229	+	0.529630i	$0.177669\pi$
$30$		0			0
$31$	2.89606	−	1.67204i	0.520148	−	0.300307i	−0.216847	−	0.976206i	$-0.569577\pi$
$31$	2.89606	−	1.67204i	0.520148	−	0.300307i	0.736995	+	0.675898i	$0.236244\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−2.78721	+	1.60920i	−0.478003	+	0.275975i
$35$	0.327333	−	5.90702i	0.0553293	−	0.998468i
$36$		0			0
$37$	9.76868	−	5.63995i	1.60596	−	0.927202i	0.615700	−	0.787981i	$-0.288873\pi$
$37$	9.76868	−	5.63995i	1.60596	−	0.927202i	0.990261	−	0.139222i	$-0.0444600\pi$
$38$		−	1.41002i		−	0.228735i
$39$		0			0
$40$	2.07866	+	0.824119i	0.328665	+	0.130305i
$41$	−0.973106	+	1.68547i	−0.151974	+	0.263226i	−0.931953	−	0.362579i	$-0.881896\pi$
$41$	−0.973106	+	1.68547i	−0.151974	+	0.263226i	0.779979	+	0.625805i	$0.215230\pi$
$42$		0			0
$43$	−2.76069	+	1.59389i	−0.421002	+	0.243065i	−0.695506	−	0.718521i	$-0.744820\pi$
$43$	−2.76069	+	1.59389i	−0.421002	+	0.243065i	0.274504	+	0.961586i	$0.411486\pi$
$44$	0.702519	−	0.405599i	0.105909	−	0.0611464i
$45$		0			0
$46$	1.76983	−	3.06543i	0.260947	−	0.451973i
$47$	6.50911	+	3.75804i	0.949451	+	0.548166i	0.892910	−	0.450234i	$-0.148660\pi$
$47$	6.50911	+	3.75804i	0.949451	+	0.548166i	0.0565410	+	0.998400i	$0.481993\pi$
$48$		0			0
$49$	−5.59707	+	4.20390i	−0.799582	+	0.600557i
$50$	4.78794	−	1.44070i	0.677117	−	0.203746i
$51$		0			0
$52$	0.0253683			0.00351795
$53$	5.33975	−	9.24872i	0.733471	−	1.27041i	−0.221920	−	0.975065i	$-0.571232\pi$
$53$	5.33975	−	9.24872i	0.733471	−	1.27041i	0.955391	−	0.295344i	$-0.0954343\pi$
$54$		0			0
$55$	0.668524	−	1.68621i	0.0901438	−	0.227368i
$56$	−0.837534	−	2.50969i	−0.111920	−	0.335371i
$57$		0			0
$58$		−	5.05961i		−	0.664359i
$59$	1.80107	+	3.11955i	0.234480	+	0.406131i	0.959121	−	0.282995i	$-0.0913280\pi$
$59$	1.80107	+	3.11955i	0.234480	+	0.406131i	−0.724642	+	0.689126i	$0.757995\pi$
$60$		0			0
$61$	0.527050	+	0.304293i	0.0674819	+	0.0389607i	0.533361	−	0.845888i	$-0.320929\pi$
$61$	0.527050	+	0.304293i	0.0674819	+	0.0389607i	−0.465879	+	0.884848i	$0.654262\pi$
$62$		−	3.34408i		−	0.424699i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.0444715	−	0.0352140i	0.00551602	−	0.00436776i
$66$		0			0
$67$	0.879693	−	0.507891i	0.107472	−	0.0620487i	−0.445301	−	0.895381i	$-0.646903\pi$
$67$	0.879693	−	0.507891i	0.107472	−	0.0620487i	0.552772	+	0.833332i	$0.313570\pi$
$68$			3.21840i			0.390288i
$69$		0			0
$70$	−4.95196	−	3.23699i	−0.591873	−	0.386894i
$71$			10.9830i			1.30344i	0.758460	+	0.651720i	$0.225952\pi$
$71$			10.9830i			1.30344i	−0.758460	+	0.651720i	$0.774048\pi$
$72$		0			0
$73$	6.25999	−	10.8426i	0.732676	−	1.26903i	−0.223059	−	0.974805i	$-0.571604\pi$
$73$	6.25999	−	10.8426i	0.732676	−	1.26903i	0.955735	−	0.294228i	$-0.0950624\pi$
$74$		−	11.2799i		−	1.31126i
$75$		0			0
$76$	−1.22111	−	0.705008i	−0.140071	−	0.0808700i
$77$	−2.03586	+	0.679406i	−0.232007	+	0.0774256i
$78$		0			0
$79$	−0.845656	+	1.46472i	−0.0951438	+	0.164794i	−0.909669	−	0.415335i	$-0.863664\pi$
$79$	−0.845656	+	1.46472i	−0.0951438	+	0.164794i	0.814525	+	0.580129i	$0.196998\pi$
$80$	1.75304	−	1.38811i	0.195996	−	0.155196i
$81$		0			0
$82$	0.973106	+	1.68547i	0.107462	+	0.186129i
$83$	14.5567	−	8.40429i	1.59780	−	0.922491i	0.605891	−	0.795548i	$-0.292817\pi$
$83$	14.5567	−	8.40429i	1.59780	−	0.922491i	0.991910	−	0.126943i	$-0.0405165\pi$
$84$		0			0
$85$	4.46750	+	5.64197i	0.484568	+	0.611958i
$86$			3.18777i			0.343746i
$87$		0			0
$88$		−	0.811199i		−	0.0864741i
$89$	−2.31249	−	4.00536i	−0.245124	−	0.424567i	0.717043	−	0.697029i	$-0.245495\pi$
$89$	−2.31249	−	4.00536i	−0.245124	−	0.424567i	−0.962166	+	0.272462i	$0.912162\pi$
$90$		0			0
$91$	−0.0657602	−	0.0134330i	−0.00689354	−	0.00140816i
$92$	−1.76983	−	3.06543i	−0.184517	−	0.319593i
$93$		0			0
$94$	6.50911	−	3.75804i	0.671364	−	0.387612i
$95$	−3.11928	+	0.459133i	−0.320032	+	0.0471060i
$96$		0			0
$97$	−3.19146	−	5.52778i	−0.324044	−	0.561261i	0.657274	−	0.753651i	$-0.271709\pi$
$97$	−3.19146	−	5.52778i	−0.324044	−	0.561261i	−0.981318	+	0.192391i	$0.938376\pi$
$98$	0.842147	+	6.94916i	0.0850697	+	0.701971i
$99$		0			0
$100$	1.14628	−	4.86683i	0.114628	−	0.486683i
$101$	−18.9158			−1.88219			−0.941094	−	0.338144i	$-0.890201\pi$
$101$	−18.9158			−1.88219			−0.941094	+	0.338144i	$0.890201\pi$
$102$		0			0
$103$	8.19236			0.807217			0.403609	−	0.914932i	$-0.367756\pi$
$103$	8.19236			0.807217			0.403609	+	0.914932i	$0.367756\pi$
$104$	0.0126841	−	0.0219696i	0.00124378	−	0.00215429i
$105$		0			0
$106$	−5.33975	−	9.24872i	−0.518642	−	0.898315i
$107$	−0.859971	−	1.48951i	−0.0831365	−	0.143997i	0.821459	−	0.570267i	$-0.193160\pi$
$107$	−0.859971	−	1.48951i	−0.0831365	−	0.143997i	−0.904596	+	0.426271i	$0.859827\pi$
$108$		0			0
$109$	6.77465	−	11.7340i	0.648894	−	1.12392i	−0.334494	−	0.942398i	$-0.608565\pi$
$109$	6.77465	−	11.7340i	0.648894	−	1.12392i	0.983387	−	0.181519i	$-0.0581014\pi$
$110$	−1.12604	−	1.42206i	−0.107363	−	0.135588i
$111$		0			0
$112$	−2.59222	−	0.529518i	−0.244942	−	0.0500348i
$113$	3.60588	−	6.24558i	0.339213	−	0.587534i	−0.645072	−	0.764122i	$-0.723173\pi$
$113$	3.60588	−	6.24558i	0.339213	−	0.587534i	0.984285	+	0.176588i	$0.0565059\pi$
$114$		0			0
$115$	−7.35774	−	2.91710i	−0.686113	−	0.272021i
$116$	−4.38175	−	2.52980i	−0.406835	−	0.234886i
$117$		0			0
$118$	3.60215			0.331605
$119$	1.70420	−	8.34280i	0.156224	−	0.764783i
$120$		0			0
$121$	10.3420			0.940178
$122$	0.527050	−	0.304293i	0.0477169	−	0.0275494i
$123$		0			0
$124$	−2.89606	−	1.67204i	−0.260074	−	0.150154i
$125$	−4.74623	−	10.1229i	−0.424516	−	0.905421i
$126$		0			0
$127$			16.3712i			1.45271i	0.687318	+	0.726356i	$0.258788\pi$
$127$			16.3712i			1.45271i	−0.687318	+	0.726356i	$0.741212\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.00826047	−	0.0561205i	−0.000724491	−	0.00492209i
$131$	−19.1309			−1.67148			−0.835738	−	0.549128i	$-0.814960\pi$
$131$	−19.1309			−1.67148			−0.835738	+	0.549128i	$0.814960\pi$
$132$		0			0
$133$	2.79207	+	2.47414i	0.242103	+	0.214535i
$134$		−	1.01578i		−	0.0877502i
$135$		0			0
$136$	2.78721	+	1.60920i	0.239002	+	0.137988i
$137$	−15.9510			−1.36279			−0.681393	−	0.731918i	$-0.738625\pi$
$137$	−15.9510			−1.36279			−0.681393	+	0.731918i	$0.738625\pi$
$138$		0			0
$139$	5.11887	+	2.95538i	0.434177	+	0.250672i	0.701124	−	0.713039i	$-0.252682\pi$
$139$	5.11887	+	2.95538i	0.434177	+	0.250672i	−0.266948	+	0.963711i	$0.586015\pi$
$140$	−5.27929	+	2.67003i	−0.446182	+	0.225659i
$141$		0			0
$142$	9.51153	+	5.49149i	0.798190	+	0.460835i
$143$	−0.0178217	−	0.0102894i	−0.00149032	−	0.000860439i
$144$		0			0
$145$	−11.1930	+	1.64752i	−0.929530	+	0.136819i
$146$	−6.25999	−	10.8426i	−0.518080	−	0.897342i
$147$		0			0
$148$	−9.76868	−	5.63995i	−0.802981	−	0.463601i
$149$			11.3296i			0.928155i	0.885795	+	0.464078i	$0.153614\pi$
$149$			11.3296i			0.928155i	−0.885795	+	0.464078i	$0.846386\pi$
$150$		0			0
$151$	12.2610			0.997783			0.498892	−	0.866664i	$-0.333741\pi$
$151$	12.2610			0.997783			0.498892	+	0.866664i	$0.333741\pi$
$152$	−1.22111	+	0.705008i	−0.0990451	+	0.0571837i
$153$		0			0
$154$	−0.429545	+	2.10281i	−0.0346137	+	0.169449i
$155$	−7.39788	+	1.08891i	−0.594212	+	0.0874631i
$156$		0			0
$157$	−1.40567	−	2.43469i	−0.112185	−	0.194310i	0.804466	−	0.593998i	$-0.202451\pi$
$157$	−1.40567	−	2.43469i	−0.112185	−	0.194310i	−0.916651	+	0.399689i	$0.869118\pi$
$158$	0.845656	+	1.46472i	0.0672768	+	0.116527i
$159$		0			0
$160$	−0.325622	−	2.21223i	−0.0257427	−	0.174892i
$161$	2.96458	+	8.88343i	0.233642	+	0.700113i
$162$		0			0
$163$	15.9183	−	9.19043i	1.24682	−	0.719850i	0.276343	−	0.961059i	$-0.410877\pi$
$163$	15.9183	−	9.19043i	1.24682	−	0.719850i	0.970473	+	0.241209i	$0.0775440\pi$
$164$	1.94621			0.151974
$165$		0			0
$166$		−	16.8086i		−	1.30460i
$167$	7.45421	+	4.30369i	0.576824	+	0.333029i	0.759870	−	0.650075i	$-0.225262\pi$
$167$	7.45421	+	4.30369i	0.576824	+	0.333029i	−0.183046	+	0.983104i	$0.558596\pi$
$168$		0			0
$169$	6.49968	+	11.2578i	0.499975	+	0.865983i
$170$	7.11984	−	1.04798i	0.546067	−	0.0803765i
$171$		0			0
$172$	2.76069	+	1.59389i	0.210501	+	0.121533i
$173$	3.38227	+	1.95275i	0.257149	+	0.148465i	0.623033	−	0.782195i	$-0.285900\pi$
$173$	3.38227	+	1.95275i	0.257149	+	0.148465i	−0.365884	+	0.930660i	$0.619233\pi$
$174$		0			0
$175$	−5.54850	+	12.0089i	−0.419427	+	0.907789i
$176$	−0.702519	−	0.405599i	−0.0529543	−	0.0305732i
$177$		0			0
$178$	−4.62499			−0.346658
$179$	16.4704	+	9.50922i	1.23106	+	0.710752i	0.967251	−	0.253823i	$-0.0816880\pi$
$179$	16.4704	+	9.50922i	1.23106	+	0.710752i	0.263808	+	0.964575i	$0.415021\pi$
$180$		0			0
$181$			14.5366i			1.08049i	0.841506	+	0.540247i	$0.181669\pi$
$181$			14.5366i			1.08049i	−0.841506	+	0.540247i	$0.818331\pi$
$182$	−0.0445134	+	0.0502335i	−0.00329955	+	0.00372355i
$183$		0			0
$184$	−3.53966			−0.260947
$185$	−24.9538	+	3.67299i	−1.83464	+	0.270043i
$186$		0			0
$187$	1.30538	−	2.26098i	0.0954588	−	0.165339i
$188$		−	7.51607i		−	0.548166i
$189$		0			0
$190$	−1.16202	+	2.93094i	−0.0843019	+	0.212633i
$191$	−2.20020	−	1.27028i	−0.159201	−	0.0919146i	0.418283	−	0.908317i	$-0.362632\pi$
$191$	−2.20020	−	1.27028i	−0.159201	−	0.0919146i	−0.577484	+	0.816402i	$0.695965\pi$
$192$		0			0
$193$	6.77602	−	3.91214i	0.487749	−	0.281602i	−0.235891	−	0.971779i	$-0.575801\pi$
$193$	6.77602	−	3.91214i	0.487749	−	0.281602i	0.723640	+	0.690178i	$0.242468\pi$
$194$	−6.38293			−0.458268
$195$		0			0
$196$	6.43922	+	2.74526i	0.459944	+	0.196090i
$197$	−2.27493			−0.162082			−0.0810412	−	0.996711i	$-0.525825\pi$
$197$	−2.27493			−0.162082			−0.0810412	+	0.996711i	$0.525825\pi$
$198$		0			0
$199$	−17.5140	−	10.1117i	−1.24154	−	0.716801i	−0.272128	−	0.962261i	$-0.587728\pi$
$199$	−17.5140	−	10.1117i	−1.24154	−	0.716801i	−0.969407	+	0.245460i	$0.921061\pi$
$200$	−3.64166	−	3.42613i	−0.257504	−	0.242264i
$201$		0			0
$202$	−9.45788	+	16.3815i	−0.665454	+	1.15260i
$203$	10.0189	+	8.87803i	0.703188	+	0.623115i
$204$		0			0
$205$	3.41178	−	2.70156i	0.238289	−	0.188685i
$206$	4.09618	−	7.09479i	0.285394	−	0.494318i
$207$		0			0
$208$	−0.0126841	−	0.0219696i	−0.000879487	−	0.00152332i
$209$	0.571902	+	0.990563i	0.0395593	+	0.0685186i
$210$		0			0
$211$	2.65419	−	4.59719i	0.182722	−	0.316483i	−0.760085	−	0.649824i	$-0.774843\pi$
$211$	2.65419	−	4.59719i	0.182722	−	0.316483i	0.942806	+	0.333341i	$0.108176\pi$
$212$	−10.6795			−0.733471
$213$		0			0
$214$	−1.71994			−0.117573
$215$	7.05209	−	1.03801i	0.480949	−	0.0707917i
$216$		0			0
$217$	6.62185	+	5.86782i	0.449520	+	0.398333i
$218$	−6.77465	−	11.7340i	−0.458837	−	0.794729i
$219$		0			0
$220$	−1.79456	+	0.264144i	−0.120989	+	0.0178086i
$221$	0.0707068	−	0.0408226i	0.00475625	−	0.00274602i
$222$		0			0
$223$	−4.61986	−	8.00184i	−0.309369	−	0.535843i	0.668856	−	0.743392i	$-0.266784\pi$
$223$	−4.61986	−	8.00184i	−0.309369	−	0.535843i	−0.978224	+	0.207550i	$0.933451\pi$
$224$	−1.75469	+	1.98017i	−0.117240	+	0.132306i
$225$		0			0
$226$	−3.60588	−	6.24558i	−0.239860	−	0.415450i
$227$			5.90173i			0.391712i	0.980633	+	0.195856i	$0.0627485\pi$
$227$			5.90173i			0.391712i	−0.980633	+	0.195856i	$0.937252\pi$
$228$		0			0
$229$			20.7806i			1.37322i	0.727026	+	0.686609i	$0.240902\pi$
$229$			20.7806i			1.37322i	−0.727026	+	0.686609i	$0.759098\pi$
$230$	−6.20515	+	4.91344i	−0.409156	+	0.323983i
$231$		0			0
$232$	−4.38175	+	2.52980i	−0.287676	+	0.166090i
$233$	14.0861	+	24.3978i	0.922811	+	1.59836i	0.795044	+	0.606551i	$0.207448\pi$
$233$	14.0861	+	24.3978i	0.922811	+	1.59836i	0.127767	+	0.991804i	$0.459219\pi$
$234$		0			0
$235$	−10.4332	−	13.1760i	−0.680584	−	0.859505i
$236$	1.80107	−	3.11955i	0.117240	−	0.203066i
$237$		0			0
$238$	−6.37297	−	5.64728i	−0.413099	−	0.366059i
$239$	−7.81549	−	4.51228i	−0.505542	−	0.291875i	0.225457	−	0.974253i	$-0.427612\pi$
$239$	−7.81549	−	4.51228i	−0.505542	−	0.291875i	−0.730999	+	0.682378i	$0.760946\pi$
$240$		0			0
$241$		−	2.46036i		−	0.158486i	−0.996855	−	0.0792429i	$-0.974750\pi$
$241$		−	2.46036i		−	0.158486i	0.996855	−	0.0792429i	$-0.0252503\pi$
$242$	5.17098	−	8.95640i	0.332403	−	0.575739i
$243$		0			0
$244$		−	0.608585i		−	0.0389607i
$245$	15.0989	−	4.12583i	0.964635	−	0.263589i
$246$		0			0
$247$			0.0357697i			0.00227597i
$248$	−2.89606	+	1.67204i	−0.183900	+	0.106175i
$249$		0			0
$250$	−11.1398	−	0.951098i	−0.704544	−	0.0601527i
$251$	28.8906			1.82356			0.911780	−	0.410679i	$-0.134708\pi$
$251$	28.8906			1.82356			0.911780	+	0.410679i	$0.134708\pi$
$252$		0			0
$253$			2.87136i			0.180521i
$254$	14.1779	+	8.18562i	0.889601	+	0.513612i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	2.59947i		−	0.162151i	−0.996708	−	0.0810754i	$-0.974165\pi$
$257$		−	2.59947i		−	0.162151i	0.996708	−	0.0810754i	$-0.0258354\pi$
$258$		0			0
$259$	22.3361	+	19.7927i	1.38790	+	1.22986i
$260$	−0.0527320	−	0.0209065i	−0.00327030	−	0.00129656i
$261$		0			0
$262$	−9.56546	+	16.5679i	−0.590956	+	1.02357i
$263$	−16.2231			−1.00036			−0.500179	−	0.865922i	$-0.666733\pi$
$263$	−16.2231			−1.00036			−0.500179	+	0.865922i	$0.666733\pi$
$264$		0			0
$265$	−18.7216	+	14.8244i	−1.15006	+	0.910653i
$266$	3.53870	−	1.18094i	0.216972	−	0.0724079i
$267$		0			0
$268$	−0.879693	−	0.507891i	−0.0537358	−	0.0310244i
$269$	−3.04488	+	5.27389i	−0.185650	+	0.321555i	−0.943795	−	0.330531i	$-0.892772\pi$
$269$	−3.04488	+	5.27389i	−0.185650	+	0.321555i	0.758145	+	0.652085i	$0.226106\pi$
$270$		0			0
$271$	−16.3148	+	9.41937i	−0.991055	+	0.572186i	−0.905590	−	0.424155i	$-0.860571\pi$
$271$	−16.3148	+	9.41937i	−0.991055	+	0.572186i	−0.0854657	+	0.996341i	$0.527238\pi$
$272$	2.78721	−	1.60920i	0.169000	−	0.0975720i
$273$		0			0
$274$	−7.97550	+	13.8140i	−0.481818	+	0.834532i
$275$	−2.77927	+	2.95411i	−0.167596	+	0.178139i
$276$		0			0
$277$		−	17.2370i		−	1.03567i	−0.855480	−	0.517835i	$-0.826738\pi$
$277$		−	17.2370i		−	1.03567i	0.855480	−	0.517835i	$-0.173262\pi$
$278$	5.11887	−	2.95538i	0.307009	−	0.177252i
$279$		0			0
$280$	−0.327333	+	5.90702i	−0.0195619	+	0.353012i
$281$	−6.70985	+	3.87393i	−0.400276	+	0.231099i	−0.686603	−	0.727032i	$-0.740899\pi$
$281$	−6.70985	+	3.87393i	−0.400276	+	0.231099i	0.286327	+	0.958132i	$0.407566\pi$
$282$		0			0
$283$	0.386787	+	0.669934i	0.0229921	+	0.0398235i	0.877293	−	0.479956i	$-0.159347\pi$
$283$	0.386787	+	0.669934i	0.0229921	+	0.0398235i	−0.854300	+	0.519780i	$0.826014\pi$
$284$	9.51153	−	5.49149i	0.564406	−	0.325860i
$285$		0			0
$286$	−0.0178217	+	0.0102894i	−0.00105382	+	0.000608422i
$287$	−5.04501	−	1.03055i	−0.297797	−	0.0608317i
$288$		0			0
$289$	−3.32096	−	5.75207i	−0.195351	−	0.338357i
$290$	−4.16972	+	10.5172i	−0.244854	+	0.617591i
$291$		0			0
$292$	−12.5200			−0.732676
$293$	22.8864	+	13.2135i	1.33704	+	0.771939i	0.986367	−	0.164560i	$-0.0526203\pi$
$293$	22.8864	+	13.2135i	1.33704	+	0.771939i	0.350671	+	0.936499i	$0.385954\pi$
$294$		0			0
$295$	−1.17294	−	7.96879i	−0.0682912	−	0.463961i
$296$	−9.76868	+	5.63995i	−0.567793	+	0.327815i
$297$		0			0
$298$	9.81170	+	5.66479i	0.568377	+	0.328152i
$299$	−0.0448975	+	0.0777647i	−0.00259649	+	0.00449725i
$300$		0			0
$301$	−6.31233	−	5.59354i	−0.363837	−	0.322406i
$302$	6.13048	−	10.6183i	0.352770	−	0.611015i
$303$		0			0
$304$			1.41002i			0.0808700i
$305$	−0.844785	−	1.06687i	−0.0483723	−	0.0610890i
$306$		0			0
$307$	−16.0600			−0.916592			−0.458296	−	0.888800i	$-0.651540\pi$
$307$	−16.0600			−0.916592			−0.458296	+	0.888800i	$0.651540\pi$
$308$	1.60631	+	1.42340i	0.0915281	+	0.0811057i
$309$		0			0
$310$	−2.75592	+	6.95121i	−0.156526	+	0.394802i
$311$	−10.0336	−	17.3787i	−0.568954	−	0.985457i	−0.996670	−	0.0815438i	$-0.974015\pi$
$311$	−10.0336	−	17.3787i	−0.568954	−	0.985457i	0.427716	−	0.903913i	$-0.359318\pi$
$312$		0			0
$313$	−5.07727	+	8.79409i	−0.286984	+	0.497071i	−0.973088	−	0.230432i	$-0.925986\pi$
$313$	−5.07727	+	8.79409i	−0.286984	+	0.497071i	0.686104	+	0.727503i	$0.259319\pi$
$314$	−2.81134			−0.158653
$315$		0			0
$316$	1.69131			0.0951438
$317$	−13.4765	+	23.3419i	−0.756913	+	1.31101i	0.187504	+	0.982264i	$0.439960\pi$
$317$	−13.4765	+	23.3419i	−0.756913	+	1.31101i	−0.944417	+	0.328749i	$0.893373\pi$
$318$		0			0
$319$	2.05217	+	3.55447i	0.114900	+	0.199012i
$320$	−2.07866	−	0.824119i	−0.116201	−	0.0460696i
$321$		0			0
$322$	9.17557	+	1.87431i	0.511335	+	0.104451i
$323$	−4.53799			−0.252501
$324$		0			0
$325$	−0.121462	+	0.0365482i	−0.00673749	+	0.00202733i
$326$		−	18.3809i		−	1.01802i
$327$		0			0
$328$	0.973106	−	1.68547i	0.0537308	−	0.0930644i
$329$	−3.97990	+	19.4833i	−0.219419	+	1.07415i
$330$		0			0
$331$	−10.0902	+	17.4767i	−0.554606	+	0.960606i	0.443328	+	0.896360i	$0.353798\pi$
$331$	−10.0902	+	17.4767i	−0.554606	+	0.960606i	−0.997934	+	0.0642467i	$0.979536\pi$
$332$	−14.5567	−	8.40429i	−0.798900	−	0.461245i
$333$		0			0
$334$	7.45421	−	4.30369i	0.407876	−	0.235487i
$335$	−2.24714	+	0.330761i	−0.122775	+	0.0180714i
$336$		0			0
$337$	18.8483	+	10.8821i	1.02673	+	0.592786i	0.916048	−	0.401070i	$-0.131361\pi$
$337$	18.8483	+	10.8821i	1.02673	+	0.592786i	0.110687	+	0.993855i	$0.464695\pi$
$338$	12.9994			0.707072
$339$		0			0
$340$	2.65234	−	6.68995i	0.143843	−	0.362814i
$341$	1.35636	+	2.34928i	0.0734508	+	0.127221i
$342$		0			0
$343$	−15.2382	−	10.5260i	−0.822786	−	0.568351i
$344$	2.76069	−	1.59389i	0.148847	−	0.0859366i
$345$		0			0
$346$	3.38227	−	1.95275i	0.181832	−	0.104981i
$347$	4.94667	+	8.56789i	0.265551	+	0.459949i	0.967708	−	0.252074i	$-0.0811127\pi$
$347$	4.94667	+	8.56789i	0.265551	+	0.459949i	−0.702157	+	0.712023i	$0.747779\pi$
$348$		0			0
$349$	−29.2025	+	16.8601i	−1.56318	+	0.902500i	−0.566242	+	0.824239i	$0.691603\pi$
$349$	−29.2025	+	16.8601i	−1.56318	+	0.902500i	−0.996933	+	0.0782606i	$0.975063\pi$
$350$	7.62578	+	10.8096i	0.407615	+	0.577797i
$351$		0			0
$352$	−0.702519	+	0.405599i	−0.0374444	+	0.0216185i
$353$		−	17.4221i		−	0.927282i	−0.886023	−	0.463641i	$-0.846543\pi$
$353$		−	17.4221i		−	0.927282i	0.886023	−	0.463641i	$-0.153457\pi$
$354$		0			0
$355$	9.05128	−	22.8299i	0.480392	−	1.21168i
$356$	−2.31249	+	4.00536i	−0.122562	+	0.212284i
$357$		0			0
$358$	16.4704	−	9.50922i	0.870490	−	0.502578i
$359$	29.8414	−	17.2289i	1.57497	−	0.909309i	0.579423	−	0.815027i	$-0.303278\pi$
$359$	29.8414	−	17.2289i	1.57497	−	0.909309i	0.995546	−	0.0942818i	$-0.0300555\pi$
$360$		0			0
$361$	−8.50593	+	14.7327i	−0.447680	+	0.775405i
$362$	12.5890	+	7.26828i	0.661665	+	0.382013i
$363$		0			0
$364$	0.0212468	+	0.0636665i	0.00111363	+	0.00333703i
$365$	−21.9480	+	17.3791i	−1.14881	+	0.909666i
$366$		0			0
$367$	−24.5156			−1.27970			−0.639852	−	0.768498i	$-0.721004\pi$
$367$	−24.5156			−1.27970			−0.639852	+	0.768498i	$0.721004\pi$
$368$	−1.76983	+	3.06543i	−0.0922587	+	0.159797i
$369$		0			0
$370$	−9.29598	+	23.4471i	−0.483275	+	1.21896i
$371$	27.6836	+	5.65499i	1.43726	+	0.293592i
$372$		0			0
$373$		−	21.8237i		−	1.12999i	−0.825094	−	0.564995i	$-0.808878\pi$
$373$		−	21.8237i		−	1.12999i	0.825094	−	0.564995i	$-0.191122\pi$
$374$	−1.30538	−	2.26098i	−0.0674996	−	0.116913i
$375$		0			0
$376$	−6.50911	−	3.75804i	−0.335682	−	0.193806i
$377$			0.128353i			0.00661054i
$378$		0			0
$379$	30.0822			1.54522			0.772610	−	0.634881i	$-0.218951\pi$
$379$	30.0822			1.54522			0.772610	+	0.634881i	$0.218951\pi$
$380$	1.95726	+	2.47181i	0.100405	+	0.126801i
$381$		0			0
$382$	−2.20020	+	1.27028i	−0.112572	+	0.0649934i
$383$		−	30.5710i		−	1.56211i	−0.624464	−	0.781054i	$-0.714682\pi$
$383$		−	30.5710i		−	1.56211i	0.624464	−	0.781054i	$-0.285318\pi$
$384$		0			0
$385$	4.79176	+	0.265532i	0.244211	+	0.0135328i
$386$		−	7.82427i		−	0.398245i
$387$		0			0
$388$	−3.19146	+	5.52778i	−0.162022	+	0.280630i
$389$		−	20.9647i		−	1.06295i	−0.847073	−	0.531476i	$-0.821638\pi$
$389$		−	20.9647i		−	1.06295i	0.847073	−	0.531476i	$-0.178362\pi$
$390$		0			0
$391$	−9.86578	−	5.69601i	−0.498934	−	0.288060i
$392$	5.59707	−	4.20390i	0.282695	−	0.212329i
$393$		0			0
$394$	−1.13747	+	1.97015i	−0.0573047	+	0.0992547i
$395$	2.96493	−	2.34773i	0.149182	−	0.118127i
$396$		0			0
$397$	−15.9516	−	27.6289i	−0.800586	−	1.38666i	−0.919231	−	0.393719i	$-0.871188\pi$
$397$	−15.9516	−	27.6289i	−0.800586	−	1.38666i	0.118645	−	0.992937i	$-0.462145\pi$
$398$	−17.5140	+	10.1117i	−0.877898	+	0.506855i
$399$		0			0
$400$	−4.78794	+	1.44070i	−0.239397	+	0.0720352i
$401$			8.65181i			0.432051i	0.976388	+	0.216026i	$0.0693094\pi$
$401$			8.65181i			0.432051i	−0.976388	+	0.216026i	$0.930691\pi$
$402$		0			0
$403$			0.0848336i			0.00422586i
$404$	9.45788	+	16.3815i	0.470547	+	0.815012i
$405$		0			0
$406$	12.6980	−	4.23759i	0.630193	−	0.210308i
$407$	4.57512	+	7.92434i	0.226780	+	0.392795i
$408$		0			0
$409$	21.9719	−	12.6855i	1.08644	−	0.627255i	0.153812	−	0.988100i	$-0.450845\pi$
$409$	21.9719	−	12.6855i	1.08644	−	0.627255i	0.932626	+	0.360845i	$0.117512\pi$
$410$	−0.633730	−	4.30547i	−0.0312977	−	0.212632i
$411$		0			0
$412$	−4.09618	−	7.09479i	−0.201804	−	0.349535i
$413$	−6.32064	+	7.13287i	−0.311019	+	0.350985i
$414$		0			0
$415$	−37.1845	+	5.47325i	−1.82531	+	0.268671i
$416$	−0.0253683			−0.00124378
$417$		0			0
$418$	1.14380			0.0559452
$419$	−4.57468	+	7.92357i	−0.223488	+	0.387092i	−0.955865	−	0.293808i	$-0.905078\pi$
$419$	−4.57468	+	7.92357i	−0.223488	+	0.387092i	0.732377	+	0.680899i	$0.238411\pi$
$420$		0			0
$421$	−15.3068	−	26.5121i	−0.746007	−	1.29212i	−0.949723	−	0.313092i	$-0.898635\pi$
$421$	−15.3068	−	26.5121i	−0.746007	−	1.29212i	0.203716	−	0.979030i	$-0.434698\pi$
$422$	−2.65419	−	4.59719i	−0.129204	−	0.223787i
$423$		0			0
$424$	−5.33975	+	9.24872i	−0.259321	+	0.449157i
$425$	−4.63676	−	15.4095i	−0.224916	−	0.747470i
$426$		0			0
$427$	−0.322257	+	1.57759i	−0.0155951	+	0.0763448i
$428$	−0.859971	+	1.48951i	−0.0415683	+	0.0719983i
$429$		0			0
$430$	2.62710	−	6.62630i	0.126690	−	0.319548i
$431$	2.69929	+	1.55843i	0.130020	+	0.0750671i	0.563599	−	0.826048i	$-0.309416\pi$
$431$	2.69929	+	1.55843i	0.130020	+	0.0750671i	−0.433579	+	0.901115i	$0.642750\pi$
$432$		0			0
$433$	25.2574			1.21379			0.606896	−	0.794781i	$-0.292415\pi$
$433$	25.2574			1.21379			0.606896	+	0.794781i	$0.292415\pi$
$434$	8.39260	−	2.80078i	0.402858	−	0.134442i
$435$		0			0
$436$	−13.5493			−0.648894
$437$	4.32231	−	2.49549i	0.206764	−	0.119375i
$438$		0			0
$439$	−7.18968	−	4.15097i	−0.343145	−	0.198115i	0.318517	−	0.947917i	$-0.396815\pi$
$439$	−7.18968	−	4.15097i	−0.343145	−	0.198115i	−0.661662	+	0.749802i	$0.730149\pi$
$440$	−0.668524	+	1.68621i	−0.0318706	+	0.0803867i
$441$		0			0
$442$		−	0.0816452i		−	0.00388346i
$443$	4.32317	−	7.48796i	0.205400	−	0.355764i	−0.744860	−	0.667221i	$-0.767484\pi$
$443$	4.32317	−	7.48796i	0.205400	−	0.355764i	0.950260	+	0.311457i	$0.100817\pi$
$444$		0			0
$445$	1.50600	+	10.2315i	0.0713912	+	0.485022i
$446$	−9.23972			−0.437514
$447$		0			0
$448$	0.837534	+	2.50969i	0.0395698	+	0.118572i
$449$			9.83537i			0.464160i	0.972697	+	0.232080i	$0.0745531\pi$
$449$			9.83537i			0.464160i	−0.972697	+	0.232080i	$0.925447\pi$
$450$		0			0
$451$	−1.36725	−	0.789382i	−0.0643813	−	0.0371705i
$452$	−7.21177			−0.339213
$453$		0			0
$454$	5.11105	+	2.95087i	0.239874	+	0.138491i
$455$	0.125623	+	0.0821168i	0.00588928	+	0.00384969i
$456$		0			0
$457$	19.5871	+	11.3086i	0.916245	+	0.528994i	0.882435	−	0.470434i	$-0.155903\pi$
$457$	19.5871	+	11.3086i	0.916245	+	0.528994i	0.0338098	+	0.999428i	$0.489236\pi$
$458$	17.9965	+	10.3903i	0.840921	+	0.485506i
$459$		0			0
$460$	1.15259	+	7.83054i	0.0537398	+	0.365101i
$461$	16.1968	+	28.0536i	0.754358	+	1.30659i	0.945693	+	0.325061i	$0.105385\pi$
$461$	16.1968	+	28.0536i	0.754358	+	1.30659i	−0.191335	+	0.981525i	$0.561282\pi$
$462$		0			0
$463$	−8.77792	−	5.06793i	−0.407944	−	0.235527i	0.281962	−	0.959426i	$-0.409015\pi$
$463$	−8.77792	−	5.06793i	−0.407944	−	0.235527i	−0.689906	+	0.723899i	$0.742348\pi$
$464$			5.05961i			0.234886i
$465$		0			0
$466$	28.1722			1.30505
$467$	−7.39730	+	4.27083i	−0.342306	+	0.197631i	−0.661291	−	0.750129i	$-0.729991\pi$
$467$	−7.39730	+	4.27083i	−0.342306	+	0.197631i	0.318985	+	0.947760i	$0.396658\pi$
$468$		0			0
$469$	2.01142	+	1.78238i	0.0928788	+	0.0823026i
$470$	−16.6273	+	2.44740i	−0.766960	+	0.112890i
$471$		0			0
$472$	−1.80107	−	3.11955i	−0.0829012	−	0.143589i
$473$	−1.29296	−	2.23947i	−0.0594503	−	0.102971i
$474$		0			0
$475$	6.86231	+	1.61628i	0.314864	+	0.0741600i
$476$	−8.07717	+	2.69552i	−0.370217	+	0.123549i
$477$		0			0
$478$	−7.81549	+	4.51228i	−0.357472	+	0.206387i
$479$	−18.0818			−0.826180			−0.413090	−	0.910690i	$-0.635550\pi$
$479$	−18.0818			−0.826180			−0.413090	+	0.910690i	$0.635550\pi$
$480$		0			0
$481$			0.286152i			0.0130474i
$482$	−2.13074	−	1.23018i	−0.0970523	−	0.0560332i
$483$		0			0
$484$	−5.17098	−	8.95640i	−0.235044	−	0.407109i
$485$	2.07842	+	14.1205i	0.0943763	+	0.641180i
$486$		0			0
$487$	−30.5288	−	17.6258i	−1.38339	−	0.798701i	−0.390832	−	0.920462i	$-0.627813\pi$
$487$	−30.5288	−	17.6258i	−1.38339	−	0.798701i	−0.992559	+	0.121761i	$0.961146\pi$
$488$	−0.527050	−	0.304293i	−0.0238584	−	0.0137747i
$489$		0			0
$490$	3.97639	−	15.1390i	0.179635	−	0.683909i
$491$	5.16468	+	2.98183i	0.233079	+	0.134568i	0.611992	−	0.790864i	$-0.290369\pi$
$491$	5.16468	+	2.98183i	0.233079	+	0.134568i	−0.378913	+	0.925432i	$0.623702\pi$
$492$		0			0
$493$	−16.2838			−0.733386
$494$	0.0309774	+	0.0178848i	0.00139374	+	0.000804677i
$495$		0			0
$496$			3.34408i			0.150154i
$497$	−27.5638	+	9.19862i	−1.23641	+	0.412614i
$498$		0			0
$499$	30.4296			1.36222			0.681109	−	0.732182i	$-0.261498\pi$
$499$	30.4296			1.36222			0.681109	+	0.732182i	$0.261498\pi$
$500$	−6.39358	+	9.17181i	−0.285930	+	0.410176i
$501$		0			0
$502$	14.4453	−	25.0200i	0.644726	−	1.11670i
$503$			23.6075i			1.05261i	0.850297	+	0.526304i	$0.176423\pi$
$503$			23.6075i			1.05261i	−0.850297	+	0.526304i	$0.823577\pi$
$504$		0			0
$505$	39.3194	+	15.5888i	1.74969	+	0.693694i
$506$	2.48667	+	1.43568i	0.110546	+	0.0638238i
$507$		0			0
$508$	14.1779	−	8.18562i	0.629043	−	0.363178i
$509$	−2.21813			−0.0983168			−0.0491584	−	0.998791i	$-0.515654\pi$
$509$	−2.21813			−0.0983168			−0.0491584	+	0.998791i	$0.515654\pi$
$510$		0			0
$511$	32.4546	+	6.62956i	1.43570	+	0.293274i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−2.25121	−	1.29974i	−0.0992966	−	0.0573289i
$515$	−17.0291	−	6.75148i	−0.750393	−	0.297506i
$516$		0			0
$517$	−3.04851	+	5.28018i	−0.134073	+	0.232222i
$518$	28.3090	−	9.44730i	1.24383	−	0.415091i
$519$		0			0
$520$	−0.0444715	+	0.0352140i	−0.00195021	+	0.00154424i
$521$	−5.51885	+	9.55893i	−0.241785	+	0.418785i	−0.961223	−	0.275773i	$-0.911066\pi$
$521$	−5.51885	+	9.55893i	−0.241785	+	0.418785i	0.719438	+	0.694557i	$0.244400\pi$
$522$		0			0
$523$	−11.2452	−	19.4773i	−0.491718	−	0.851681i	0.508236	−	0.861218i	$-0.330298\pi$
$523$	−11.2452	−	19.4773i	−0.491718	−	0.851681i	−0.999955	+	0.00953656i	$0.996964\pi$
$524$	9.56546	+	16.5679i	0.417869	+	0.723771i
$525$		0			0
$526$	−8.11154	+	14.0496i	−0.353680	+	0.612592i
$527$	−10.7626			−0.468825
$528$		0			0
$529$	−10.4708			−0.455254
$530$	3.47748	+	23.6255i	0.151052	+	1.02623i
$531$		0			0
$532$	0.746630	−	3.65507i	0.0323705	−	0.158468i
$533$	−0.0246860	−	0.0427574i	−0.00106927	−	0.00185203i
$534$		0			0
$535$	0.560051	+	3.80491i	0.0242131	+	0.164501i
$536$	−0.879693	+	0.507891i	−0.0379969	+	0.0219375i
$537$		0			0
$538$	3.04488	+	5.27389i	0.131274	+	0.227374i
$539$	−3.41020	−	4.54034i	−0.146888	−	0.195566i
$540$		0			0
$541$	10.9885	+	19.0326i	0.472433	+	0.818277i	0.999502	−	0.0315447i	$-0.0100427\pi$
$541$	10.9885	+	19.0326i	0.472433	+	0.818277i	−0.527070	+	0.849822i	$0.676709\pi$
$542$			18.8387i			0.809193i
$543$		0			0
$544$		−	3.21840i		−	0.137988i
$545$	−23.7524	+	18.8080i	−1.01744	+	0.805645i
$546$		0			0
$547$	−13.4100	+	7.74227i	−0.573371	+	0.331036i	−0.758494	−	0.651679i	$-0.774065\pi$
$547$	−13.4100	+	7.74227i	−0.573371	+	0.331036i	0.185124	+	0.982715i	$0.440731\pi$
$548$	7.97550	+	13.8140i	0.340696	+	0.590104i
$549$		0			0
$550$	1.16870	+	3.88397i	0.0498334	+	0.165613i
$551$	3.56706	−	6.17834i	0.151962	−	0.263206i
$552$		0			0
$553$	−4.38426	−	0.895581i	−0.186438	−	0.0380840i
$554$	−14.9277	−	8.61850i	−0.634216	−	0.366165i
$555$		0			0
$556$		−	5.91076i		−	0.250672i
$557$	6.99648	−	12.1183i	0.296451	−	0.513467i	−0.678871	−	0.734258i	$-0.737530\pi$
$557$	6.99648	−	12.1183i	0.296451	−	0.513467i	0.975321	+	0.220790i	$0.0708637\pi$
$558$		0			0
$559$		−	0.0808683i		−	0.00342036i
$560$	4.95196	+	3.23699i	0.209259	+	0.136788i
$561$		0			0
$562$			7.74787i			0.326824i
$563$	5.50514	−	3.17839i	0.232014	−	0.133953i	−0.379487	−	0.925197i	$-0.623899\pi$
$563$	5.50514	−	3.17839i	0.232014	−	0.133953i	0.611501	+	0.791244i	$0.290566\pi$
$564$		0			0
$565$	−12.6425	+	10.0108i	−0.531874	+	0.421156i
$566$	0.773573			0.0325157
$567$		0			0
$568$		−	10.9830i		−	0.460835i
$569$	−23.8982	−	13.7977i	−1.00187	−	0.578428i	−0.0930663	−	0.995660i	$-0.529667\pi$
$569$	−23.8982	−	13.7977i	−1.00187	−	0.578428i	−0.908800	+	0.417232i	$0.863000\pi$
$570$		0			0
$571$	11.5877	+	20.0705i	0.484931	+	0.839924i	0.999850	−	0.0173141i	$-0.00551152\pi$
$571$	11.5877	+	20.0705i	0.484931	+	0.839924i	−0.514919	+	0.857239i	$0.672178\pi$
$572$			0.0205787i			0.000860439i
$573$		0			0
$574$	−3.41499	+	3.85383i	−0.142539	+	0.160856i
$575$	12.8902	+	12.1273i	0.537559	+	0.505744i
$576$		0			0
$577$	−14.2815	+	24.7363i	−0.594546	+	1.02978i	0.399064	+	0.916923i	$0.369335\pi$
$577$	−14.2815	+	24.7363i	−0.594546	+	1.02978i	−0.993611	+	0.112862i	$0.963998\pi$
$578$	−6.64192			−0.276268
$579$		0			0
$580$	7.02331	+	8.86968i	0.291627	+	0.368294i
$581$	33.2839	+	29.4938i	1.38085	+	1.22361i
$582$		0			0
$583$	7.50255	+	4.33160i	0.310724	+	0.179396i
$584$	−6.25999	+	10.8426i	−0.259040	+	0.448671i
$585$		0			0
$586$	22.8864	−	13.2135i	0.945429	−	0.545843i
$587$	−1.01410	+	0.585492i	−0.0418564	+	0.0241658i	−0.520782	−	0.853690i	$-0.674360\pi$
$587$	−1.01410	+	0.585492i	−0.0418564	+	0.0241658i	0.478926	+	0.877855i	$0.341026\pi$
$588$		0			0
$589$	2.35760	−	4.08349i	0.0971434	−	0.168257i
$590$	−7.48764	−	2.96860i	−0.308261	−	0.122215i
$591$		0			0
$592$			11.2799i			0.463601i
$593$	−11.0764	+	6.39495i	−0.454853	+	0.262609i	−0.709877	−	0.704325i	$-0.751250\pi$
$593$	−11.0764	+	6.39495i	−0.454853	+	0.262609i	0.255025	+	0.966935i	$0.417916\pi$
$594$		0			0
$595$	−10.4179	+	15.9374i	−0.427093	+	0.653369i
$596$	9.81170	−	5.66479i	0.401903	−	0.232039i
$597$		0			0
$598$	0.0448975	+	0.0777647i	0.00183599	+	0.00318004i
$599$	31.9286	−	18.4340i	1.30457	−	0.753193i	0.323384	−	0.946268i	$-0.395179\pi$
$599$	31.9286	−	18.4340i	1.30457	−	0.753193i	0.981184	+	0.193075i	$0.0618460\pi$
$600$		0			0
$601$	−11.3731	+	6.56624i	−0.463917	+	0.267843i	−0.713690	−	0.700462i	$-0.752977\pi$
$601$	−11.3731	+	6.56624i	−0.463917	+	0.267843i	0.249773	+	0.968304i	$0.419644\pi$
$602$	−8.00032	+	2.66987i	−0.326069	+	0.108816i
$603$		0			0
$604$	−6.13048	−	10.6183i	−0.249446	−	0.432053i
$605$	−21.4974	−	8.52300i	−0.873994	−	0.346509i
$606$		0			0
$607$	7.14019			0.289811			0.144906	−	0.989445i	$-0.453712\pi$
$607$	7.14019			0.289811			0.144906	+	0.989445i	$0.453712\pi$
$608$	1.22111	+	0.705008i	0.0495225	+	0.0285919i
$609$		0			0
$610$	−1.34633	+	0.198169i	−0.0545114	+	0.00802362i
$611$	−0.165125	+	0.0953349i	−0.00668024	+	0.00385684i
$612$		0			0
$613$	7.59789	+	4.38664i	0.306876	+	0.177175i	0.645528	−	0.763737i	$-0.276638\pi$
$613$	7.59789	+	4.38664i	0.306876	+	0.177175i	−0.338652	+	0.940912i	$0.609971\pi$
$614$	−8.02999	+	13.9084i	−0.324064	+	0.561295i
$615$		0			0
$616$	2.03586	−	0.679406i	0.0820270	−	0.0273741i
$617$	−4.01634	+	6.95651i	−0.161692	+	0.280059i	−0.935476	−	0.353391i	$-0.885028\pi$
$617$	−4.01634	+	6.95651i	−0.161692	+	0.280059i	0.773784	+	0.633450i	$0.218362\pi$
$618$		0			0
$619$		−	45.2512i		−	1.81880i	−0.415923	−	0.909400i	$-0.636542\pi$
$619$		−	45.2512i		−	1.81880i	0.415923	−	0.909400i	$-0.363458\pi$
$620$	4.64196	+	5.86230i	0.186426	+	0.235436i
$621$		0			0
$622$	−20.0672			−0.804622
$623$	8.11541	−	9.15827i	0.325137	−	0.366918i
$624$		0			0
$625$	1.52332	+	24.9535i	0.0609328	+	0.998142i
$626$	5.07727	+	8.79409i	0.202929	+	0.351483i
$627$		0			0
$628$	−1.40567	+	2.43469i	−0.0560923	+	0.0971548i
$629$	−36.3032			−1.44750
$630$		0			0
$631$	−43.0078			−1.71212			−0.856058	−	0.516881i	$-0.827093\pi$
$631$	−43.0078			−1.71212			−0.856058	+	0.516881i	$0.827093\pi$
$632$	0.845656	−	1.46472i	0.0336384	−	0.0582634i
$633$		0			0
$634$	13.4765	+	23.3419i	0.535219	+	0.927026i
$635$	13.4919	−	34.0303i	0.535408	−	1.35045i
$636$		0			0
$637$	−0.0213638	−	0.176288i	−0.000846466	−	0.00698479i
$638$	4.10435			0.162493
$639$		0			0
$640$	−1.75304	+	1.38811i	−0.0692949	+	0.0548700i
$641$		−	2.57264i		−	0.101613i	−0.998709	−	0.0508065i	$-0.983821\pi$
$641$		−	2.57264i		−	0.101613i	0.998709	−	0.0508065i	$-0.0161792\pi$
$642$		0			0
$643$	17.2212	−	29.8280i	0.679137	−	1.17630i	−0.296104	−	0.955156i	$-0.595687\pi$
$643$	17.2212	−	29.8280i	0.679137	−	1.17630i	0.975241	−	0.221145i	$-0.0709793\pi$
$644$	6.21099	−	7.00912i	0.244747	−	0.276198i
$645$		0			0
$646$	−2.26900	+	3.93002i	−0.0892725	+	0.154624i
$647$	5.07916	+	2.93246i	0.199683	+	0.115287i	0.596507	−	0.802608i	$-0.296555\pi$
$647$	5.07916	+	2.93246i	0.199683	+	0.115287i	−0.396825	+	0.917894i	$0.629888\pi$
$648$		0			0
$649$	−2.53058	+	1.46103i	−0.0993338	+	0.0573504i
$650$	−0.0290792	+	0.123463i	−0.00114058	+	0.00484262i
$651$		0			0
$652$	−15.9183	−	9.19043i	−0.623408	−	0.359925i
$653$	10.1448			0.396998			0.198499	−	0.980101i	$-0.436393\pi$
$653$	10.1448			0.396998			0.198499	+	0.980101i	$0.436393\pi$
$654$		0			0
$655$	39.7667	+	15.7662i	1.55381	+	0.616035i
$656$	−0.973106	−	1.68547i	−0.0379934	−	0.0658065i
$657$		0			0
$658$	14.8831	+	13.1884i	0.580204	+	0.514136i
$659$	8.24098	−	4.75793i	0.321023	−	0.185343i	−0.330825	−	0.943692i	$-0.607327\pi$
$659$	8.24098	−	4.75793i	0.321023	−	0.185343i	0.651849	+	0.758349i	$0.273994\pi$
$660$		0			0
$661$	−10.6865	+	6.16988i	−0.415658	+	0.239980i	−0.693218	−	0.720728i	$-0.743808\pi$
$661$	−10.6865	+	6.16988i	−0.415658	+	0.239980i	0.277560	+	0.960708i	$0.410474\pi$
$662$	10.0902	+	17.4767i	0.392166	+	0.679251i
$663$		0			0
$664$	−14.5567	+	8.40429i	−0.564908	+	0.326150i
$665$	−3.76479	−	7.44389i	−0.145992	−	0.288662i
$666$		0			0
$667$	15.5099	−	8.95463i	0.600545	−	0.346725i
$668$		−	8.60738i		−	0.333029i
$669$		0			0
$670$	−0.837125	+	2.11147i	−0.0323410	+	0.0815730i
$671$	−0.246842	+	0.427542i	−0.00952922	+	0.0165051i
$672$		0			0
$673$	−26.7585	+	15.4490i	−1.03146	+	0.595515i	−0.917403	−	0.397959i	$-0.869719\pi$
$673$	−26.7585	+	15.4490i	−1.03146	+	0.595515i	−0.114059	+	0.993474i	$0.536385\pi$
$674$	18.8483	−	10.8821i	0.726011	−	0.419163i
$675$		0			0
$676$	6.49968	−	11.2578i	0.249988	−	0.432991i
$677$	31.4385	+	18.1510i	1.20828	+	0.697601i	0.962383	−	0.271695i	$-0.0875842\pi$
$677$	31.4385	+	18.1510i	1.20828	+	0.697601i	0.245897	+	0.969296i	$0.420918\pi$
$678$		0			0
$679$	11.2000	−	12.6393i	0.429818	−	0.485051i
$680$	−4.46750	−	5.64197i	−0.171321	−	0.216360i
$681$		0			0
$682$	2.71271			0.103875
$683$	11.4960	−	19.9116i	0.439882	−	0.761897i	−0.557798	−	0.829977i	$-0.688354\pi$
$683$	11.4960	−	19.9116i	0.439882	−	0.761897i	0.997680	+	0.0680791i	$0.0216870\pi$
$684$		0			0
$685$	33.1567	+	13.1455i	1.26685	+	0.502264i
$686$	−16.7349	+	7.93368i	−0.638941	+	0.302909i
$687$		0			0
$688$		−	3.18777i		−	0.121533i
$689$	0.135460	+	0.234624i	0.00516062	+	0.00893846i
$690$		0			0
$691$	3.23707	+	1.86892i	0.123144	+	0.0710971i	0.560307	−	0.828285i	$-0.310683\pi$
$691$	3.23707	+	1.86892i	0.123144	+	0.0710971i	−0.437163	+	0.899382i	$0.644017\pi$
$692$		−	3.90551i		−	0.148465i
$693$		0			0
$694$	9.89335			0.375546
$695$	−8.20481	−	10.3618i	−0.311226	−	0.393045i
$696$		0			0
$697$	5.42451	−	3.13184i	0.205468	−	0.118627i
$698$			33.7202i			1.27633i
$699$		0			0
$700$	13.1743	−	1.19932i	0.497941	−	0.0453300i
$701$		−	46.5565i		−	1.75842i	−0.476438	−	0.879208i	$-0.658072\pi$
$701$		−	46.5565i		−	1.75842i	0.476438	−	0.879208i	$-0.341928\pi$
$702$		0			0
$703$	7.95242	−	13.7740i	0.299931	−	0.519496i
$704$			0.811199i			0.0305732i
$705$		0			0
$706$	−15.0879	−	8.71103i	−0.567842	−	0.327844i
$707$	−15.8426	−	47.4727i	−0.595822	−	1.78539i
$708$		0			0
$709$	−14.5206	+	25.1504i	−0.545332	+	0.944544i	0.453253	+	0.891382i	$0.350263\pi$
$709$	−14.5206	+	25.1504i	−0.545332	+	0.944544i	−0.998586	+	0.0531619i	$0.983070\pi$
$710$	−15.2456	−	19.2536i	−0.572158	−	0.722574i
$711$		0			0
$712$	2.31249	+	4.00536i	0.0866644	+	0.150107i
$713$	10.2511	−	5.91845i	0.383905	−	0.221648i
$714$		0			0
$715$	0.0285656	+	0.0360752i	0.00106829	+	0.00134914i
$716$		−	19.0184i		−	0.710752i
$717$		0			0
$718$		−	34.4579i		−	1.28596i
$719$	−4.05625	−	7.02563i	−0.151273	−	0.262012i	0.780423	−	0.625252i	$-0.215004\pi$
$719$	−4.05625	−	7.02563i	−0.151273	−	0.262012i	−0.931696	+	0.363240i	$0.881670\pi$
$720$		0			0
$721$	6.86138	+	20.5603i	0.255531	+	0.765705i
$722$	8.50593	+	14.7327i	0.316558	+	0.548294i
$723$		0			0
$724$	12.5890	−	7.26828i	0.467868	−	0.270124i
$725$	24.6242	+	5.79975i	0.914521	+	0.215397i
$726$		0			0
$727$	5.53873	+	9.59336i	0.205420	+	0.355798i	0.950267	−	0.311438i	$-0.100811\pi$
$727$	5.53873	+	9.59336i	0.205420	+	0.355798i	−0.744846	+	0.667236i	$0.767477\pi$
$728$	0.0657602	+	0.0134330i	0.00243723	+	0.000497859i
$729$		0			0
$730$	4.07678	+	27.6971i	0.150889	+	1.02512i
$731$	10.2595			0.379462
$732$		0			0
$733$	−43.1585			−1.59409			−0.797047	−	0.603917i	$-0.793606\pi$
$733$	−43.1585			−1.59409			−0.797047	+	0.603917i	$0.793606\pi$
$734$	−12.2578	+	21.2311i	−0.452444	+	0.783656i
$735$		0			0
$736$	1.76983	+	3.06543i	0.0652367	+	0.112993i
$737$	0.412000	+	0.713605i	0.0151762	+	0.0262860i
$738$		0			0
$739$	19.9836	−	34.6126i	0.735108	−	1.27324i	−0.219568	−	0.975597i	$-0.570465\pi$
$739$	19.9836	−	34.6126i	0.735108	−	1.27324i	0.954676	−	0.297647i	$-0.0962017\pi$
$740$	15.6578	+	19.7741i	0.575591	+	0.726910i
$741$		0			0
$742$	18.7392	−	21.1472i	0.687937	−	0.776339i
$743$	−21.8276	+	37.8065i	−0.800777	+	1.38699i	0.118328	+	0.992975i	$0.462246\pi$
$743$	−21.8276	+	37.8065i	−0.800777	+	1.38699i	−0.919105	+	0.394012i	$0.871087\pi$
$744$		0			0
$745$	9.33692	−	23.5503i	0.342078	−	0.862818i
$746$	−18.8999	−	10.9119i	−0.691975	−	0.399512i
$747$		0			0
$748$	−2.61076			−0.0954588
$749$	3.01796	−	3.40578i	0.110274	−	0.124444i
$750$		0			0
$751$	−37.0594			−1.35232			−0.676159	−	0.736756i	$-0.736357\pi$
$751$	−37.0594			−1.35232			−0.676159	+	0.736756i	$0.736357\pi$
$752$	−6.50911	+	3.75804i	−0.237363	+	0.137042i
$753$		0			0
$754$	0.111157	+	0.0641767i	0.00404811	+	0.00233718i
$755$	−25.4864	−	10.1045i	−0.927544	−	0.367740i
$756$		0			0
$757$		−	15.5973i		−	0.566892i	−0.958988	−	0.283446i	$-0.908522\pi$
$757$		−	15.5973i		−	0.566892i	0.958988	−	0.283446i	$-0.0914777\pi$
$758$	15.0411	−	26.0520i	0.546318	−	0.946250i
$759$		0			0
$760$	3.11928	−	0.459133i	0.113148	−	0.0166545i
$761$	−14.7189			−0.533561			−0.266781	−	0.963757i	$-0.585960\pi$
$761$	−14.7189			−0.533561			−0.266781	+	0.963757i	$0.585960\pi$
$762$		0			0
$763$	35.1228	+	7.17460i	1.27153	+	0.259738i
$764$			2.54057i			0.0919146i
$765$		0			0
$766$	−26.4753	−	15.2855i	−0.956592	−	0.552288i
$767$	−0.0913803			−0.00329955
$768$		0			0
$769$	−27.7329	−	16.0116i	−1.00007	−	0.577393i	−0.0918044	−	0.995777i	$-0.529263\pi$
$769$	−27.7329	−	16.0116i	−1.00007	−	0.577393i	−0.908270	+	0.418384i	$0.862597\pi$
$770$	2.62584	−	4.01702i	0.0946287	−	0.144763i
$771$		0			0
$772$	−6.77602	−	3.91214i	−0.243874	−	0.140801i
$773$	40.9220	+	23.6263i	1.47186	+	0.849780i	0.999500	−	0.0316250i	$-0.0100682\pi$
$773$	40.9220	+	23.6263i	1.47186	+	0.849780i	0.472362	+	0.881405i	$0.343402\pi$
$774$		0			0
$775$	16.2751	+	3.83327i	0.584618	+	0.137695i
$776$	3.19146	+	5.52778i	0.114567	+	0.198436i
$777$		0			0
$778$	−18.1559	−	10.4823i	−0.650922	−	0.375810i
$779$			2.74419i			0.0983208i
$780$		0			0
$781$	−8.90937			−0.318802
$782$	−9.86578	+	5.69601i	−0.352799	+	0.203689i
$783$		0			0
$784$	−0.842147	−	6.94916i	−0.0300767	−	0.248184i
$785$	0.915435	+	6.21934i	0.0326733	+	0.221978i
$786$		0			0
$787$	−1.67726	−	2.90511i	−0.0597880	−	0.103556i	0.834582	−	0.550883i	$-0.185709\pi$
$787$	−1.67726	−	2.90511i	−0.0597880	−	0.103556i	−0.894370	+	0.447328i	$0.852376\pi$
$788$	1.13747	+	1.97015i	0.0405206	+	0.0701837i
$789$		0			0
$790$	−0.550729	−	3.74158i	−0.0195941	−	0.133119i
$791$	18.6945	+	3.81876i	0.664700	+	0.135780i
$792$		0			0
$793$	−0.0133704	+	0.00771938i	−0.000474795	+	0.000274123i
$794$	−31.9031			−1.13220
$795$		0			0
$796$			20.2234i			0.716801i
$797$	20.4799	+	11.8241i	0.725434	+	0.418830i	0.816749	−	0.576992i	$-0.195774\pi$
$797$	20.4799	+	11.8241i	0.725434	+	0.418830i	−0.0913154	+	0.995822i	$0.529107\pi$
$798$		0			0
$799$	−12.0949	−	20.9489i	−0.427885	−	0.741119i
$800$	−1.14628	+	4.86683i	−0.0405273	+	0.172068i
$801$		0			0
$802$	7.49269	+	4.32591i	0.264576	+	0.152753i
$803$	8.79552	+	5.07809i	0.310387	+	0.179202i
$804$		0			0
$805$	1.15865	−	20.9088i	0.0408369	−	0.736939i
$806$	0.0734680	+	0.0424168i	0.00258780	+	0.00149407i
$807$		0			0
$808$	18.9158			0.665454
$809$	−43.8535	−	25.3188i	−1.54181	−	0.890162i	−0.998725	−	0.0504816i	$-0.983924\pi$
$809$	−43.8535	−	25.3188i	−1.54181	−	0.890162i	−0.543081	−	0.839680i	$-0.682742\pi$
$810$		0			0
$811$		−	15.9122i		−	0.558754i	−0.960181	−	0.279377i	$-0.909872\pi$
$811$		−	15.9122i		−	0.558754i	0.960181	−	0.279377i	$-0.0901280\pi$
$812$	2.67915	−	13.1156i	0.0940199	−	0.460268i
$813$		0			0
$814$	9.15024			0.320716
$815$	−40.6627	+	5.98522i	−1.42435	+	0.209653i
$816$		0			0
$817$	−2.24741	+	3.89262i	−0.0786268	+	0.136186i
$818$		−	25.3709i		−	0.887073i
$819$		0			0
$820$	−4.04551	−	1.60391i	−0.141275	−	0.0560109i
$821$	−0.761382	−	0.439584i	−0.0265724	−	0.0153416i	0.486655	−	0.873594i	$-0.338217\pi$
$821$	−0.761382	−	0.439584i	−0.0265724	−	0.0153416i	−0.513227	+	0.858253i	$0.671550\pi$
$822$		0			0
$823$	18.4993	−	10.6806i	0.644846	−	0.372302i	−0.141633	−	0.989919i	$-0.545235\pi$
$823$	18.4993	−	10.6806i	0.644846	−	0.372302i	0.786479	+	0.617617i	$0.211902\pi$
$824$	−8.19236			−0.285394
$825$		0			0
$826$	3.01692	+	9.04027i	0.104972	+	0.314551i
$827$	−3.54960			−0.123432			−0.0617159	−	0.998094i	$-0.519657\pi$
$827$	−3.54960			−0.123432			−0.0617159	+	0.998094i	$0.519657\pi$
$828$		0			0
$829$	−22.4132	−	12.9403i	−0.778443	−	0.449434i	0.0574354	−	0.998349i	$-0.481708\pi$
$829$	−22.4132	−	12.9403i	−0.778443	−	0.449434i	−0.835878	+	0.548915i	$0.815041\pi$
$830$	−13.8523	+	34.9393i	−0.480819	+	1.21276i
$831$		0			0
$832$	−0.0126841	+	0.0219696i	−0.000439743	+	0.000761658i
$833$	22.3651	−	2.71036i	0.774906	−	0.0939086i
$834$		0			0
$835$	−11.9480	−	15.0891i	−0.413478	−	0.522178i
$836$	0.571902	−	0.990563i	0.0197796	−	0.0342593i
$837$		0			0
$838$	4.57468	+	7.92357i	0.158030	+	0.273715i
$839$	1.80168	+	3.12060i	0.0622009	+	0.107735i	0.895449	−	0.445164i	$-0.146855\pi$
$839$	1.80168	+	3.12060i	0.0622009	+	0.107735i	−0.833248	+	0.552899i	$0.813521\pi$
$840$		0			0
$841$	−1.70019	+	2.94482i	−0.0586273	+	0.101545i
$842$	−30.6136			−1.05501
$843$		0			0
$844$	−5.30837			−0.182722
$845$	−4.23288	−	28.7576i	−0.145615	−	0.989291i
$846$		0			0
$847$	8.66174	+	25.9551i	0.297621	+	0.891827i
$848$	5.33975	+	9.24872i	0.183368	+	0.317602i
$849$		0			0
$850$	−15.6634	−	3.68920i	−0.537250	−	0.126538i
$851$	34.5778	−	19.9635i	1.18531	−	0.684340i
$852$		0			0
$853$	9.42803	+	16.3298i	0.322810	+	0.559122i	0.981067	−	0.193671i	$-0.0620393\pi$
$853$	9.42803	+	16.3298i	0.322810	+	0.559122i	−0.658257	+	0.752793i	$0.728706\pi$
$854$	1.20510	+	1.06788i	0.0412378	+	0.0365420i
$855$		0			0
$856$	0.859971	+	1.48951i	0.0293932	+	0.0509105i
$857$		−	38.6241i		−	1.31937i	−0.751541	−	0.659687i	$-0.770689\pi$
$857$		−	38.6241i		−	1.31937i	0.751541	−	0.659687i	$-0.229311\pi$
$858$		0			0
$859$		−	12.8843i		−	0.439606i	−0.975544	−	0.219803i	$-0.929458\pi$
$859$		−	12.8843i		−	0.439606i	0.975544	−	0.219803i	$-0.0705415\pi$
$860$	−4.42499	−	5.58829i	−0.150891	−	0.190559i
$861$		0			0
$862$	2.69929	−	1.55843i	0.0919380	−	0.0530805i
$863$	−26.0756	−	45.1643i	−0.887625	−	1.53741i	−0.842676	−	0.538422i	$-0.819021\pi$
$863$	−26.0756	−	45.1643i	−0.887625	−	1.53741i	−0.0449489	−	0.998989i	$-0.514312\pi$
$864$		0			0
$865$	−5.42128	−	6.84650i	−0.184329	−	0.232788i
$866$	12.6287	−	21.8735i	0.429140	−	0.743293i
$867$		0			0
$868$	1.77075	−	8.66860i	0.0601033	−	0.294231i
$869$	−1.18818	−	0.685995i	−0.0403062	−	0.0232708i
$870$		0			0
$871$			0.0257686i			0.000873137i
$872$	−6.77465	+	11.7340i	−0.229419	+	0.397365i
$873$		0			0
$874$		−	4.99097i		−	0.168822i
$875$	21.4302	−	20.3898i	0.724474	−	0.689303i
$876$		0			0
$877$			7.39151i			0.249594i	0.992182	+	0.124797i	$0.0398279\pi$
$877$			7.39151i			0.249594i	−0.992182	+	0.124797i	$0.960172\pi$
$878$	−7.18968	+	4.15097i	−0.242640	+	0.140088i
$879$		0			0
$880$	1.12604	+	1.42206i	0.0379586	+	0.0479377i
$881$	33.1517			1.11691			0.558454	−	0.829535i	$-0.311395\pi$
$881$	33.1517			1.11691			0.558454	+	0.829535i	$0.311395\pi$
$882$		0			0
$883$		−	23.0244i		−	0.774834i	−0.921905	−	0.387417i	$-0.873367\pi$
$883$		−	23.0244i		−	0.774834i	0.921905	−	0.387417i	$-0.126633\pi$
$884$	−0.0707068	−	0.0408226i	−0.00237813	−	0.00137301i
$885$		0			0
$886$	−4.32317	−	7.48796i	−0.145240	−	0.251563i
$887$		−	2.61054i		−	0.0876533i	−0.999039	−	0.0438266i	$-0.986045\pi$
$887$		−	2.61054i		−	0.0876533i	0.999039	−	0.0438266i	$-0.0139549\pi$
$888$		0			0
$889$	−41.0867	+	13.7115i	−1.37800	+	0.459868i
$890$	9.61378	+	3.81154i	0.322255	+	0.127763i
$891$		0			0
$892$	−4.61986	+	8.00184i	−0.154684	+	0.267921i
$893$	10.5978			0.354641
$894$		0			0
$895$	−26.3997	−	33.3400i	−0.882446	−	1.11443i
$896$	2.59222	+	0.529518i	0.0866000	+	0.0176900i
$897$		0			0
$898$	8.51768	+	4.91769i	0.284239	+	0.164105i
$899$	8.45987	−	14.6529i	0.282152	−	0.488702i
$900$		0			0
$901$	−29.7660	+	17.1854i	−0.991651	+	0.572530i
$902$	−1.36725	+	0.789382i	−0.0455244	+	0.0262835i
$903$		0			0
$904$	−3.60588	+	6.24558i	−0.119930	+	0.207725i
$905$	11.9799	−	30.2166i	0.398224	−	1.00443i
$906$		0			0
$907$			34.9260i			1.15970i	0.814724	+	0.579849i	$0.196889\pi$
$907$			34.9260i			1.15970i	−0.814724	+	0.579849i	$0.803111\pi$
$908$	5.11105	−	2.95087i	0.169616	−	0.0979280i
$909$		0			0
$910$	0.133927	−	0.0677341i	0.00443962	−	0.00224536i
$911$	8.52724	−	4.92320i	0.282520	−	0.163113i	−0.352044	−	0.935984i	$-0.614513\pi$
$911$	8.52724	−	4.92320i	0.282520	−	0.163113i	0.634564	+	0.772871i	$0.281180\pi$
$912$		0			0
$913$	6.81755	+	11.8083i	0.225628	+	0.390799i
$914$	19.5871	−	11.3086i	0.647883	−	0.374055i
$915$		0			0
$916$	17.9965	−	10.3903i	0.594621	−	0.343305i
$917$	−16.0228	−	48.0127i	−0.529120	−	1.58552i
$918$		0			0
$919$	−25.5841	−	44.3130i	−0.843943	−	1.46175i	−0.886536	−	0.462660i	$-0.846895\pi$
$919$	−25.5841	−	44.3130i	−0.843943	−	1.46175i	0.0425930	−	0.999093i	$-0.486438\pi$
$920$	7.35774	+	2.91710i	0.242578	+	0.0961739i
$921$		0			0
$922$	32.3935			1.06682
$923$	−0.241291	−	0.139310i	−0.00794220	−	0.00458543i
$924$		0			0
$925$	54.8974	+	12.9300i	1.80501	+	0.425135i
$926$	−8.77792	+	5.06793i	−0.288460	+	0.166543i
$927$		0			0
$928$	4.38175	+	2.52980i	0.143838	+	0.0830449i
$929$	−10.3822	+	17.9825i	−0.340628	+	0.589985i	−0.984550	−	0.175106i	$-0.943973\pi$
$929$	−10.3822	+	17.9825i	−0.340628	+	0.589985i	0.643921	+	0.765092i	$0.277306\pi$
$930$		0			0
$931$	−3.87086	+	9.07941i	−0.126862	+	0.297566i
$932$	14.0861	−	24.3978i	0.461405	−	0.799178i
$933$		0			0
$934$			8.54166i			0.279492i
$935$	−4.57676	+	3.62403i	−0.149676	+	0.118518i
$936$		0			0
$937$	44.4914			1.45347			0.726735	−	0.686918i	$-0.241037\pi$
$937$	44.4914			1.45347			0.726735	+	0.686918i	$0.241037\pi$
$938$	2.54930	−	0.850752i	0.0832375	−	0.0277780i
$939$		0			0
$940$	−6.19414	+	15.6234i	−0.202031	+	0.509578i
$941$	−13.7232	−	23.7693i	−0.447364	−	0.774858i	0.550849	−	0.834605i	$-0.314304\pi$
$941$	−13.7232	−	23.7693i	−0.447364	−	0.774858i	−0.998214	+	0.0597471i	$0.980971\pi$
$942$		0			0
$943$	−3.44446	+	5.96598i	−0.112167	+	0.194279i
$944$	−3.60215			−0.117240
$945$		0			0
$946$	−2.58592			−0.0840754
$947$	22.1365	−	38.3415i	0.719338	−	1.24593i	−0.241924	−	0.970295i	$-0.577779\pi$
$947$	22.1365	−	38.3415i	0.719338	−	1.24593i	0.961262	−	0.275635i	$-0.0888881\pi$
$948$		0			0
$949$	0.158805	+	0.275059i	0.00515503	+	0.00892878i
$950$	4.83089	−	5.13479i	0.156735	−	0.166595i
$951$		0			0
$952$	−1.70420	+	8.34280i	−0.0552335	+	0.270392i
$953$	−23.6733			−0.766855			−0.383427	−	0.923571i	$-0.625256\pi$
$953$	−23.6733			−0.766855			−0.383427	+	0.923571i	$0.625256\pi$
$954$		0			0
$955$	3.52660	+	4.45371i	0.114118	+	0.144119i
$956$			9.02455i			0.291875i
$957$		0			0
$958$	−9.04091	+	15.6593i	−0.292099	+	0.505930i
$959$	−13.3595	−	40.0320i	−0.431401	−	1.29270i
$960$		0			0
$961$	−9.90856	+	17.1621i	−0.319631	+	0.553617i
$962$	0.247815	+	0.143076i	0.00798986	+	0.00461295i
$963$		0			0
$964$	−2.13074	+	1.23018i	−0.0686264	+	0.0396214i
$965$	−17.3091	+	2.54776i	−0.557200	+	0.0820152i
$966$		0			0
$967$	27.8500	+	16.0792i	0.895596	+	0.517073i	0.875769	−	0.482731i	$-0.160355\pi$
$967$	27.8500	+	16.0792i	0.895596	+	0.517073i	0.0198274	+	0.999803i	$0.493688\pi$
$968$	−10.3420			−0.332403
$969$		0			0
$970$	13.2679	+	5.26029i	0.426008	+	0.168898i
$971$	6.17807	+	10.7007i	0.198264	+	0.343403i	0.947966	−	0.318373i	$-0.103136\pi$
$971$	6.17807	+	10.7007i	0.198264	+	0.343403i	−0.749702	+	0.661776i	$0.769803\pi$
$972$		0			0
$973$	−3.12986	+	15.3220i	−0.100339	+	0.491201i
$974$	−30.5288	+	17.6258i	−0.978205	+	0.564767i
$975$		0			0
$976$	−0.527050	+	0.304293i	−0.0168705	+	0.00974017i
$977$	−4.18162	−	7.24278i	−0.133782	−	0.231717i	0.791350	−	0.611364i	$-0.209379\pi$
$977$	−4.18162	−	7.24278i	−0.133782	−	0.231717i	−0.925132	+	0.379647i	$0.876046\pi$
$978$		0			0
$979$	3.24914	−	1.87589i	0.103843	−	0.0599538i
$980$	−11.1225	−	11.0131i	−0.355296	−	0.351802i
$981$		0			0
$982$	5.16468	−	2.98183i	0.164812	−	0.0951541i
$983$			33.8162i			1.07857i	0.842124	+	0.539285i	$0.181305\pi$
$983$			33.8162i			1.07857i	−0.842124	+	0.539285i	$0.818695\pi$
$984$		0			0
$985$	4.72881	+	1.87482i	0.150673	+	0.0597366i
$986$	−8.14191	+	14.1022i	−0.259291	+	0.449106i
$987$		0			0
$988$	0.0309774	−	0.0178848i	0.000985524	−	0.000568993i
$989$	−9.77190	+	5.64181i	−0.310728	+	0.179399i
$990$		0			0
$991$	6.51443	−	11.2833i	0.206938	−	0.358427i	−0.743811	−	0.668390i	$-0.766984\pi$
$991$	6.51443	−	11.2833i	0.206938	−	0.358427i	0.950748	+	0.309964i	$0.100317\pi$
$992$	2.89606	+	1.67204i	0.0919500	+	0.0530873i
$993$		0			0
$994$	−5.81569	+	28.4703i	−0.184462	+	0.903023i
$995$	28.0724	+	35.4524i	0.889955	+	1.12392i
$996$		0			0
$997$	−23.0517			−0.730055			−0.365027	−	0.930997i	$-0.618940\pi$
$997$	−23.0517			−0.730055			−0.365027	+	0.930997i	$0.618940\pi$
$998$	15.2148	−	26.3528i	0.481617	−	0.834185i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.r.b.1529.4		48
3.2	odd	2		630.2.r.a.59.15	✓	48
5.4	even	2		1890.2.r.a.1529.4		48
7.5	odd	6		1890.2.bi.a.719.11		48
9.2	odd	6		1890.2.bi.b.899.6		48
9.7	even	3		630.2.bi.a.479.2	yes	48
15.14	odd	2		630.2.r.b.59.10	yes	48
21.5	even	6		630.2.bi.b.509.23	yes	48
35.19	odd	6		1890.2.bi.b.719.6		48
45.29	odd	6		1890.2.bi.a.899.11		48
45.34	even	6		630.2.bi.b.479.23	yes	48
63.47	even	6		1890.2.r.a.89.4		48
63.61	odd	6		630.2.r.b.299.10	yes	48
105.89	even	6		630.2.bi.a.509.2	yes	48
315.124	odd	6		630.2.r.a.299.15	yes	48
315.299	even	6	inner	1890.2.r.b.89.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.15	✓	48	3.2	odd	2
630.2.r.a.299.15	yes	48	315.124	odd	6
630.2.r.b.59.10	yes	48	15.14	odd	2
630.2.r.b.299.10	yes	48	63.61	odd	6
630.2.bi.a.479.2	yes	48	9.7	even	3
630.2.bi.a.509.2	yes	48	105.89	even	6
630.2.bi.b.479.23	yes	48	45.34	even	6
630.2.bi.b.509.23	yes	48	21.5	even	6
1890.2.r.a.89.4		48	63.47	even	6
1890.2.r.a.1529.4		48	5.4	even	2
1890.2.r.b.89.4		48	315.299	even	6	inner
1890.2.r.b.1529.4		48	1.1	even	1	trivial
1890.2.bi.a.719.11		48	7.5	odd	6
1890.2.bi.a.899.11		48	45.29	odd	6
1890.2.bi.b.719.6		48	35.19	odd	6
1890.2.bi.b.899.6		48	9.2	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.07866 - 0.824119i) q^{5} +(0.837534 + 2.50969i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.07866 - 0.824119i) q^{5} +(0.837534 + 2.50969i) q^{7} -1.00000 q^{8} +(-1.75304 + 1.38811i) q^{10} +0.811199i q^{11} +(-0.0126841 + 0.0219696i) q^{13} +(2.59222 + 0.529518i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.78721 - 1.60920i) q^{17} +(1.22111 - 0.705008i) q^{19} +(0.325622 + 2.21223i) q^{20} +(0.702519 + 0.405599i) q^{22} +3.53966 q^{23} +(3.64166 + 3.42613i) q^{25} +(0.0126841 + 0.0219696i) q^{26} +(1.75469 - 1.98017i) q^{28} +(4.38175 - 2.52980i) q^{29} +(2.89606 - 1.67204i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.78721 + 1.60920i) q^{34} +(0.327333 - 5.90702i) q^{35} +(9.76868 - 5.63995i) q^{37} -1.41002i q^{38} +(2.07866 + 0.824119i) q^{40} +(-0.973106 + 1.68547i) q^{41} +(-2.76069 + 1.59389i) q^{43} +(0.702519 - 0.405599i) q^{44} +(1.76983 - 3.06543i) q^{46} +(6.50911 + 3.75804i) q^{47} +(-5.59707 + 4.20390i) q^{49} +(4.78794 - 1.44070i) q^{50} +0.0253683 q^{52} +(5.33975 - 9.24872i) q^{53} +(0.668524 - 1.68621i) q^{55} +(-0.837534 - 2.50969i) q^{56} -5.05961i q^{58} +(1.80107 + 3.11955i) q^{59} +(0.527050 + 0.304293i) q^{61} -3.34408i q^{62} +1.00000 q^{64} +(0.0444715 - 0.0352140i) q^{65} +(0.879693 - 0.507891i) q^{67} +3.21840i q^{68} +(-4.95196 - 3.23699i) q^{70} +10.9830i q^{71} +(6.25999 - 10.8426i) q^{73} -11.2799i q^{74} +(-1.22111 - 0.705008i) q^{76} +(-2.03586 + 0.679406i) q^{77} +(-0.845656 + 1.46472i) q^{79} +(1.75304 - 1.38811i) q^{80} +(0.973106 + 1.68547i) q^{82} +(14.5567 - 8.40429i) q^{83} +(4.46750 + 5.64197i) q^{85} +3.18777i q^{86} -0.811199i q^{88} +(-2.31249 - 4.00536i) q^{89} +(-0.0657602 - 0.0134330i) q^{91} +(-1.76983 - 3.06543i) q^{92} +(6.50911 - 3.75804i) q^{94} +(-3.11928 + 0.459133i) q^{95} +(-3.19146 - 5.52778i) q^{97} +(0.842147 + 6.94916i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61} + 48 q^{64} + 33 q^{65} - 33 q^{67} - 6 q^{70} + 18 q^{73} - 6 q^{77} + 3 q^{82} + 9 q^{83} - 33 q^{85} - 33 q^{89} - 3 q^{92} - 33 q^{95} + 24 q^{97} - 3 q^{98}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 - 3 * q^14 - 24 * q^16 + 6 * q^22 + 6 * q^23 - 3 * q^28 + 3 * q^29 + 24 * q^32 - 18 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 + 42 * q^55 - 9 * q^61 + 48 * q^64 + 33 * q^65 - 33 * q^67 - 6 * q^70 + 18 * q^73 - 6 * q^77 + 3 * q^82 + 9 * q^83 - 33 * q^85 - 33 * q^89 - 3 * q^92 - 33 * q^95 + 24 * q^97 - 3 * q^98

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