LMFDB - Embedded newform 1890.2.r.b.89.4

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			89.4
Character	$\chi$	$=$	1890.89
Dual form			1890.2.r.b.1529.4

$q$-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 $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

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

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	$-0.960975\pi$
$11$		−	0.811199i		−	0.244586i	0.992494	−	0.122293i	$-0.0390247\pi$
$12$		0			0
$13$	−0.0126841	−	0.0219696i	−0.00351795	−	0.00609326i	0.864261	−	0.503044i	$-0.167786\pi$
$13$	−0.0126841	−	0.0219696i	−0.00351795	−	0.00609326i	−0.867779	+	0.496950i	$0.834453\pi$
$14$	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	−0.798346	−	0.602199i	$-0.794291\pi$
$17$	−2.78721	+	1.60920i	−0.675999	+	0.390288i	0.122347	+	0.992487i	$0.460958\pi$
$18$		0			0
$19$	1.22111	+	0.705008i	0.280142	+	0.161740i	0.633488	−	0.773753i	$-0.281623\pi$
$19$	1.22111	+	0.705008i	0.280142	+	0.161740i	−0.353346	+	0.935493i	$0.614956\pi$
$20$	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	0.848229	−	0.529630i	$-0.177669\pi$
$29$	4.38175	+	2.52980i	0.813670	+	0.469773i	−0.0345586	+	0.999403i	$0.511003\pi$
$30$		0			0
$31$	2.89606	+	1.67204i	0.520148	+	0.300307i	0.736995	−	0.675898i	$-0.236244\pi$
$31$	2.89606	+	1.67204i	0.520148	+	0.300307i	−0.216847	+	0.976206i	$0.569577\pi$
$32$	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	0.990261	+	0.139222i	$0.0444600\pi$
$37$	9.76868	+	5.63995i	1.60596	+	0.927202i	0.615700	+	0.787981i	$0.288873\pi$
$38$			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	0.779979	−	0.625805i	$-0.215230\pi$
$41$	−0.973106	−	1.68547i	−0.151974	−	0.263226i	−0.931953	+	0.362579i	$0.881896\pi$
$42$		0			0
$43$	−2.76069	−	1.59389i	−0.421002	−	0.243065i	0.274504	−	0.961586i	$-0.411486\pi$
$43$	−2.76069	−	1.59389i	−0.421002	−	0.243065i	−0.695506	+	0.718521i	$0.744820\pi$
$44$	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	0.0565410	−	0.998400i	$-0.481993\pi$
$47$	6.50911	−	3.75804i	0.949451	−	0.548166i	0.892910	+	0.450234i	$0.148660\pi$
$48$		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	0.955391	+	0.295344i	$0.0954343\pi$
$53$	5.33975	+	9.24872i	0.733471	+	1.27041i	−0.221920	+	0.975065i	$0.571232\pi$
$54$		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	−0.724642	−	0.689126i	$-0.757995\pi$
$59$	1.80107	−	3.11955i	0.234480	−	0.406131i	0.959121	+	0.282995i	$0.0913280\pi$
$60$		0			0
$61$	0.527050	−	0.304293i	0.0674819	−	0.0389607i	−0.465879	−	0.884848i	$-0.654262\pi$
$61$	0.527050	−	0.304293i	0.0674819	−	0.0389607i	0.533361	+	0.845888i	$0.320929\pi$
$62$			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	0.552772	−	0.833332i	$-0.313570\pi$
$67$	0.879693	+	0.507891i	0.107472	+	0.0620487i	−0.445301	+	0.895381i	$0.646903\pi$
$68$		−	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	$-0.774048\pi$
$71$		−	10.9830i		−	1.30344i	0.758460	−	0.651720i	$-0.225952\pi$
$72$		0			0
$73$	6.25999	+	10.8426i	0.732676	+	1.26903i	0.955735	+	0.294228i	$0.0950624\pi$
$73$	6.25999	+	10.8426i	0.732676	+	1.26903i	−0.223059	+	0.974805i	$0.571604\pi$
$74$			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	0.814525	−	0.580129i	$-0.196998\pi$
$79$	−0.845656	−	1.46472i	−0.0951438	−	0.164794i	−0.909669	+	0.415335i	$0.863664\pi$
$80$	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	0.991910	+	0.126943i	$0.0405165\pi$
$83$	14.5567	+	8.40429i	1.59780	+	0.922491i	0.605891	+	0.795548i	$0.292817\pi$
$84$		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	−0.962166	−	0.272462i	$-0.912162\pi$
$89$	−2.31249	+	4.00536i	−0.245124	+	0.424567i	0.717043	+	0.697029i	$0.245495\pi$
$90$		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	−0.981318	−	0.192391i	$-0.938376\pi$
$97$	−3.19146	+	5.52778i	−0.324044	+	0.561261i	0.657274	+	0.753651i	$0.271709\pi$
$98$	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	−0.904596	−	0.426271i	$-0.859827\pi$
$107$	−0.859971	+	1.48951i	−0.0831365	+	0.143997i	0.821459	+	0.570267i	$0.193160\pi$
$108$		0			0
$109$	6.77465	+	11.7340i	0.648894	+	1.12392i	0.983387	+	0.181519i	$0.0581014\pi$
$109$	6.77465	+	11.7340i	0.648894	+	1.12392i	−0.334494	+	0.942398i	$0.608565\pi$
$110$	−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	0.984285	−	0.176588i	$-0.0565059\pi$
$113$	3.60588	+	6.24558i	0.339213	+	0.587534i	−0.645072	+	0.764122i	$0.723173\pi$
$114$		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	$-0.741212\pi$
$127$		−	16.3712i		−	1.45271i	0.687318	−	0.726356i	$-0.258788\pi$
$128$	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	−0.266948	−	0.963711i	$-0.586015\pi$
$139$	5.11887	−	2.95538i	0.434177	−	0.250672i	0.701124	+	0.713039i	$0.252682\pi$
$140$	−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	$-0.846386\pi$
$149$		−	11.3296i		−	0.928155i	0.885795	−	0.464078i	$-0.153614\pi$
$150$		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	−0.916651	−	0.399689i	$-0.869118\pi$
$157$	−1.40567	+	2.43469i	−0.112185	+	0.194310i	0.804466	+	0.593998i	$0.202451\pi$
$158$	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	0.970473	−	0.241209i	$-0.0775440\pi$
$163$	15.9183	+	9.19043i	1.24682	+	0.719850i	0.276343	+	0.961059i	$0.410877\pi$
$164$	1.94621			0.151974
$165$		0			0
$166$			16.8086i			1.30460i
$167$	7.45421	−	4.30369i	0.576824	−	0.333029i	−0.183046	−	0.983104i	$-0.558596\pi$
$167$	7.45421	−	4.30369i	0.576824	−	0.333029i	0.759870	+	0.650075i	$0.225262\pi$
$168$		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	−0.365884	−	0.930660i	$-0.619233\pi$
$173$	3.38227	−	1.95275i	0.257149	−	0.148465i	0.623033	+	0.782195i	$0.285900\pi$
$174$		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	0.263808	−	0.964575i	$-0.415021\pi$
$179$	16.4704	−	9.50922i	1.23106	−	0.710752i	0.967251	+	0.253823i	$0.0816880\pi$
$180$		0			0
$181$		−	14.5366i		−	1.08049i	−0.841506	−	0.540247i	$-0.818331\pi$
$181$		−	14.5366i		−	1.08049i	0.841506	−	0.540247i	$-0.181669\pi$
$182$	−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	−0.577484	−	0.816402i	$-0.695965\pi$
$191$	−2.20020	+	1.27028i	−0.159201	+	0.0919146i	0.418283	+	0.908317i	$0.362632\pi$
$192$		0			0
$193$	6.77602	+	3.91214i	0.487749	+	0.281602i	0.723640	−	0.690178i	$-0.242468\pi$
$193$	6.77602	+	3.91214i	0.487749	+	0.281602i	−0.235891	+	0.971779i	$0.575801\pi$
$194$	−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	−0.969407	−	0.245460i	$-0.921061\pi$
$199$	−17.5140	+	10.1117i	−1.24154	+	0.716801i	−0.272128	+	0.962261i	$0.587728\pi$
$200$	−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	0.942806	−	0.333341i	$-0.108176\pi$
$211$	2.65419	+	4.59719i	0.182722	+	0.316483i	−0.760085	+	0.649824i	$0.774843\pi$
$212$	−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	−0.978224	−	0.207550i	$-0.933451\pi$
$223$	−4.61986	+	8.00184i	−0.309369	+	0.535843i	0.668856	+	0.743392i	$0.266784\pi$
$224$	−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	$-0.937252\pi$
$227$		−	5.90173i		−	0.391712i	0.980633	−	0.195856i	$-0.0627485\pi$
$228$		0			0
$229$		−	20.7806i		−	1.37322i	−0.727026	−	0.686609i	$-0.759098\pi$
$229$		−	20.7806i		−	1.37322i	0.727026	−	0.686609i	$-0.240902\pi$
$230$	−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	0.127767	−	0.991804i	$-0.459219\pi$
$233$	14.0861	−	24.3978i	0.922811	−	1.59836i	0.795044	−	0.606551i	$-0.207448\pi$
$234$		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	−0.730999	−	0.682378i	$-0.760946\pi$
$239$	−7.81549	+	4.51228i	−0.505542	+	0.291875i	0.225457	+	0.974253i	$0.427612\pi$
$240$		0			0
$241$			2.46036i			0.158486i	0.996855	+	0.0792429i	$0.0252503\pi$
$241$			2.46036i			0.158486i	−0.996855	+	0.0792429i	$0.974750\pi$
$242$	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	$0.0258354\pi$
$257$			2.59947i			0.162151i	−0.996708	+	0.0810754i	$0.974165\pi$
$258$		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	0.758145	−	0.652085i	$-0.226106\pi$
$269$	−3.04488	−	5.27389i	−0.185650	−	0.321555i	−0.943795	+	0.330531i	$0.892772\pi$
$270$		0			0
$271$	−16.3148	−	9.41937i	−0.991055	−	0.572186i	−0.0854657	−	0.996341i	$-0.527238\pi$
$271$	−16.3148	−	9.41937i	−0.991055	−	0.572186i	−0.905590	+	0.424155i	$0.860571\pi$
$272$	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	$0.173262\pi$
$277$			17.2370i			1.03567i	−0.855480	+	0.517835i	$0.826738\pi$
$278$	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	0.286327	−	0.958132i	$-0.407566\pi$
$281$	−6.70985	−	3.87393i	−0.400276	−	0.231099i	−0.686603	+	0.727032i	$0.740899\pi$
$282$		0			0
$283$	0.386787	−	0.669934i	0.0229921	−	0.0398235i	−0.854300	−	0.519780i	$-0.826014\pi$
$283$	0.386787	−	0.669934i	0.0229921	−	0.0398235i	0.877293	+	0.479956i	$0.159347\pi$
$284$	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	0.350671	−	0.936499i	$-0.385954\pi$
$293$	22.8864	−	13.2135i	1.33704	−	0.771939i	0.986367	+	0.164560i	$0.0526203\pi$
$294$		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	0.427716	+	0.903913i	$0.359318\pi$
$311$	−10.0336	+	17.3787i	−0.568954	+	0.985457i	−0.996670	+	0.0815438i	$0.974015\pi$
$312$		0			0
$313$	−5.07727	−	8.79409i	−0.286984	−	0.497071i	0.686104	−	0.727503i	$-0.259319\pi$
$313$	−5.07727	−	8.79409i	−0.286984	−	0.497071i	−0.973088	+	0.230432i	$0.925986\pi$
$314$	−2.81134			−0.158653
$315$		0			0
$316$	1.69131			0.0951438
$317$	−13.4765	−	23.3419i	−0.756913	−	1.31101i	−0.944417	−	0.328749i	$-0.893373\pi$
$317$	−13.4765	−	23.3419i	−0.756913	−	1.31101i	0.187504	−	0.982264i	$-0.439960\pi$
$318$		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	−0.997934	−	0.0642467i	$-0.979536\pi$
$331$	−10.0902	−	17.4767i	−0.554606	−	0.960606i	0.443328	−	0.896360i	$-0.353798\pi$
$332$	−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	0.110687	−	0.993855i	$-0.464695\pi$
$337$	18.8483	−	10.8821i	1.02673	−	0.592786i	0.916048	+	0.401070i	$0.131361\pi$
$338$	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	−0.702157	−	0.712023i	$-0.747779\pi$
$347$	4.94667	−	8.56789i	0.265551	−	0.459949i	0.967708	+	0.252074i	$0.0811127\pi$
$348$		0			0
$349$	−29.2025	−	16.8601i	−1.56318	−	0.902500i	−0.996933	−	0.0782606i	$-0.975063\pi$
$349$	−29.2025	−	16.8601i	−1.56318	−	0.902500i	−0.566242	−	0.824239i	$-0.691603\pi$
$350$	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	$0.153457\pi$
$353$			17.4221i			0.927282i	−0.886023	+	0.463641i	$0.846543\pi$
$354$		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	0.995546	+	0.0942818i	$0.0300555\pi$
$359$	29.8414	+	17.2289i	1.57497	+	0.909309i	0.579423	+	0.815027i	$0.303278\pi$
$360$		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	$0.191122\pi$
$373$			21.8237i			1.12999i	−0.825094	+	0.564995i	$0.808878\pi$
$374$	−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	$0.285318\pi$
$383$			30.5710i			1.56211i	−0.624464	+	0.781054i	$0.714682\pi$
$384$		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	$0.178362\pi$
$389$			20.9647i			1.06295i	−0.847073	+	0.531476i	$0.821638\pi$
$390$		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	0.118645	+	0.992937i	$0.462145\pi$
$397$	−15.9516	+	27.6289i	−0.800586	+	1.38666i	−0.919231	+	0.393719i	$0.871188\pi$
$398$	−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	$-0.930691\pi$
$401$		−	8.65181i		−	0.432051i	0.976388	−	0.216026i	$-0.0693094\pi$
$402$		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	0.932626	−	0.360845i	$-0.117512\pi$
$409$	21.9719	+	12.6855i	1.08644	+	0.627255i	0.153812	+	0.988100i	$0.450845\pi$
$410$	−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	0.732377	−	0.680899i	$-0.238411\pi$
$419$	−4.57468	−	7.92357i	−0.223488	−	0.387092i	−0.955865	+	0.293808i	$0.905078\pi$
$420$		0			0
$421$	−15.3068	+	26.5121i	−0.746007	+	1.29212i	0.203716	+	0.979030i	$0.434698\pi$
$421$	−15.3068	+	26.5121i	−0.746007	+	1.29212i	−0.949723	+	0.313092i	$0.898635\pi$
$422$	−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	−0.433579	−	0.901115i	$-0.642750\pi$
$431$	2.69929	−	1.55843i	0.130020	−	0.0750671i	0.563599	+	0.826048i	$0.309416\pi$
$432$		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	−0.661662	−	0.749802i	$-0.730149\pi$
$439$	−7.18968	+	4.15097i	−0.343145	+	0.198115i	0.318517	+	0.947917i	$0.396815\pi$
$440$	−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	0.950260	−	0.311457i	$-0.100817\pi$
$443$	4.32317	+	7.48796i	0.205400	+	0.355764i	−0.744860	+	0.667221i	$0.767484\pi$
$444$		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	$-0.925447\pi$
$449$		−	9.83537i		−	0.464160i	0.972697	−	0.232080i	$-0.0745531\pi$
$450$		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	0.0338098	−	0.999428i	$-0.489236\pi$
$457$	19.5871	−	11.3086i	0.916245	−	0.528994i	0.882435	+	0.470434i	$0.155903\pi$
$458$	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	−0.191335	−	0.981525i	$-0.561282\pi$
$461$	16.1968	−	28.0536i	0.754358	−	1.30659i	0.945693	−	0.325061i	$-0.105385\pi$
$462$		0			0
$463$	−8.77792	+	5.06793i	−0.407944	+	0.235527i	−0.689906	−	0.723899i	$-0.742348\pi$
$463$	−8.77792	+	5.06793i	−0.407944	+	0.235527i	0.281962	+	0.959426i	$0.409015\pi$
$464$		−	5.05961i		−	0.234886i
$465$		0			0
$466$	28.1722			1.30505
$467$	−7.39730	−	4.27083i	−0.342306	−	0.197631i	0.318985	−	0.947760i	$-0.396658\pi$
$467$	−7.39730	−	4.27083i	−0.342306	−	0.197631i	−0.661291	+	0.750129i	$0.729991\pi$
$468$		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	−0.992559	−	0.121761i	$-0.961146\pi$
$487$	−30.5288	+	17.6258i	−1.38339	+	0.798701i	−0.390832	+	0.920462i	$0.627813\pi$
$488$	−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	−0.378913	−	0.925432i	$-0.623702\pi$
$491$	5.16468	−	2.98183i	0.233079	−	0.134568i	0.611992	+	0.790864i	$0.290369\pi$
$492$		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	$-0.823577\pi$
$503$		−	23.6075i		−	1.05261i	0.850297	−	0.526304i	$-0.176423\pi$
$504$		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	0.719438	−	0.694557i	$-0.244400\pi$
$521$	−5.51885	−	9.55893i	−0.241785	−	0.418785i	−0.961223	+	0.275773i	$0.911066\pi$
$522$		0			0
$523$	−11.2452	+	19.4773i	−0.491718	+	0.851681i	−0.999955	−	0.00953656i	$-0.996964\pi$
$523$	−11.2452	+	19.4773i	−0.491718	+	0.851681i	0.508236	+	0.861218i	$0.330298\pi$
$524$	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	−0.527070	−	0.849822i	$-0.676709\pi$
$541$	10.9885	−	19.0326i	0.472433	−	0.818277i	0.999502	+	0.0315447i	$0.0100427\pi$
$542$		−	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	0.185124	−	0.982715i	$-0.440731\pi$
$547$	−13.4100	−	7.74227i	−0.573371	−	0.331036i	−0.758494	+	0.651679i	$0.774065\pi$
$548$	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	0.975321	−	0.220790i	$-0.0708637\pi$
$557$	6.99648	+	12.1183i	0.296451	+	0.513467i	−0.678871	+	0.734258i	$0.737530\pi$
$558$		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	0.611501	−	0.791244i	$-0.290566\pi$
$563$	5.50514	+	3.17839i	0.232014	+	0.133953i	−0.379487	+	0.925197i	$0.623899\pi$
$564$		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	−0.908800	−	0.417232i	$-0.863000\pi$
$569$	−23.8982	+	13.7977i	−1.00187	+	0.578428i	−0.0930663	+	0.995660i	$0.529667\pi$
$570$		0			0
$571$	11.5877	−	20.0705i	0.484931	−	0.839924i	−0.514919	−	0.857239i	$-0.672178\pi$
$571$	11.5877	−	20.0705i	0.484931	−	0.839924i	0.999850	+	0.0173141i	$0.00551152\pi$
$572$		−	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	−0.993611	−	0.112862i	$-0.963998\pi$
$577$	−14.2815	−	24.7363i	−0.594546	−	1.02978i	0.399064	−	0.916923i	$-0.369335\pi$
$578$	−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	0.478926	−	0.877855i	$-0.341026\pi$
$587$	−1.01410	−	0.585492i	−0.0418564	−	0.0241658i	−0.520782	+	0.853690i	$0.674360\pi$
$588$		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	0.255025	−	0.966935i	$-0.417916\pi$
$593$	−11.0764	−	6.39495i	−0.454853	−	0.262609i	−0.709877	+	0.704325i	$0.751250\pi$
$594$		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	0.981184	−	0.193075i	$-0.0618460\pi$
$599$	31.9286	+	18.4340i	1.30457	+	0.753193i	0.323384	+	0.946268i	$0.395179\pi$
$600$		0			0
$601$	−11.3731	−	6.56624i	−0.463917	−	0.267843i	0.249773	−	0.968304i	$-0.419644\pi$
$601$	−11.3731	−	6.56624i	−0.463917	−	0.267843i	−0.713690	+	0.700462i	$0.752977\pi$
$602$	−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	−0.338652	−	0.940912i	$-0.609971\pi$
$613$	7.59789	−	4.38664i	0.306876	−	0.177175i	0.645528	+	0.763737i	$0.276638\pi$
$614$	−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	0.773784	−	0.633450i	$-0.218362\pi$
$617$	−4.01634	−	6.95651i	−0.161692	−	0.280059i	−0.935476	+	0.353391i	$0.885028\pi$
$618$		0			0
$619$			45.2512i			1.81880i	0.415923	+	0.909400i	$0.363458\pi$
$619$			45.2512i			1.81880i	−0.415923	+	0.909400i	$0.636542\pi$
$620$	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	$0.0161792\pi$
$641$			2.57264i			0.101613i	−0.998709	+	0.0508065i	$0.983821\pi$
$642$		0			0
$643$	17.2212	+	29.8280i	0.679137	+	1.17630i	0.975241	+	0.221145i	$0.0709793\pi$
$643$	17.2212	+	29.8280i	0.679137	+	1.17630i	−0.296104	+	0.955156i	$0.595687\pi$
$644$	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	−0.396825	−	0.917894i	$-0.629888\pi$
$647$	5.07916	−	2.93246i	0.199683	−	0.115287i	0.596507	+	0.802608i	$0.296555\pi$
$648$		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	0.651849	−	0.758349i	$-0.273994\pi$
$659$	8.24098	+	4.75793i	0.321023	+	0.185343i	−0.330825	+	0.943692i	$0.607327\pi$
$660$		0			0
$661$	−10.6865	−	6.16988i	−0.415658	−	0.239980i	0.277560	−	0.960708i	$-0.410474\pi$
$661$	−10.6865	−	6.16988i	−0.415658	−	0.239980i	−0.693218	+	0.720728i	$0.743808\pi$
$662$	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	−0.114059	−	0.993474i	$-0.536385\pi$
$673$	−26.7585	−	15.4490i	−1.03146	−	0.595515i	−0.917403	+	0.397959i	$0.869719\pi$
$674$	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	0.245897	−	0.969296i	$-0.420918\pi$
$677$	31.4385	−	18.1510i	1.20828	−	0.697601i	0.962383	+	0.271695i	$0.0875842\pi$
$678$		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	0.997680	−	0.0680791i	$-0.0216870\pi$
$683$	11.4960	+	19.9116i	0.439882	+	0.761897i	−0.557798	+	0.829977i	$0.688354\pi$
$684$		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	−0.437163	−	0.899382i	$-0.644017\pi$
$691$	3.23707	−	1.86892i	0.123144	−	0.0710971i	0.560307	+	0.828285i	$0.310683\pi$
$692$			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	$0.341928\pi$
$701$			46.5565i			1.75842i	−0.476438	+	0.879208i	$0.658072\pi$
$702$		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	−0.998586	−	0.0531619i	$-0.983070\pi$
$709$	−14.5206	−	25.1504i	−0.545332	−	0.944544i	0.453253	−	0.891382i	$-0.350263\pi$
$710$	−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	−0.931696	−	0.363240i	$-0.881670\pi$
$719$	−4.05625	+	7.02563i	−0.151273	+	0.262012i	0.780423	+	0.625252i	$0.215004\pi$
$720$		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	−0.744846	−	0.667236i	$-0.767477\pi$
$727$	5.53873	−	9.59336i	0.205420	−	0.355798i	0.950267	+	0.311438i	$0.100811\pi$
$728$	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	0.954676	+	0.297647i	$0.0962017\pi$
$739$	19.9836	+	34.6126i	0.735108	+	1.27324i	−0.219568	+	0.975597i	$0.570465\pi$
$740$	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	−0.919105	−	0.394012i	$-0.871087\pi$
$743$	−21.8276	−	37.8065i	−0.800777	−	1.38699i	0.118328	−	0.992975i	$-0.462246\pi$
$744$		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	$0.0914777\pi$
$757$			15.5973i			0.566892i	−0.958988	+	0.283446i	$0.908522\pi$
$758$	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	−0.908270	−	0.418384i	$-0.862597\pi$
$769$	−27.7329	+	16.0116i	−1.00007	+	0.577393i	−0.0918044	+	0.995777i	$0.529263\pi$
$770$	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	0.472362	−	0.881405i	$-0.343402\pi$
$773$	40.9220	−	23.6263i	1.47186	−	0.849780i	0.999500	+	0.0316250i	$0.0100682\pi$
$774$		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	−0.894370	−	0.447328i	$-0.852376\pi$
$787$	−1.67726	+	2.90511i	−0.0597880	+	0.103556i	0.834582	+	0.550883i	$0.185709\pi$
$788$	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	−0.0913154	−	0.995822i	$-0.529107\pi$
$797$	20.4799	−	11.8241i	0.725434	−	0.418830i	0.816749	+	0.576992i	$0.195774\pi$
$798$		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	−0.543081	+	0.839680i	$0.682742\pi$
$809$	−43.8535	+	25.3188i	−1.54181	+	0.890162i	−0.998725	+	0.0504816i	$0.983924\pi$
$810$		0			0
$811$			15.9122i			0.558754i	0.960181	+	0.279377i	$0.0901280\pi$
$811$			15.9122i			0.558754i	−0.960181	+	0.279377i	$0.909872\pi$
$812$	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	−0.513227	−	0.858253i	$-0.671550\pi$
$821$	−0.761382	+	0.439584i	−0.0265724	+	0.0153416i	0.486655	+	0.873594i	$0.338217\pi$
$822$		0			0
$823$	18.4993	+	10.6806i	0.644846	+	0.372302i	0.786479	−	0.617617i	$-0.211902\pi$
$823$	18.4993	+	10.6806i	0.644846	+	0.372302i	−0.141633	+	0.989919i	$0.545235\pi$
$824$	−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	−0.835878	−	0.548915i	$-0.815041\pi$
$829$	−22.4132	+	12.9403i	−0.778443	+	0.449434i	0.0574354	+	0.998349i	$0.481708\pi$
$830$	−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	−0.833248	−	0.552899i	$-0.813521\pi$
$839$	1.80168	−	3.12060i	0.0622009	−	0.107735i	0.895449	+	0.445164i	$0.146855\pi$
$840$		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	−0.658257	−	0.752793i	$-0.728706\pi$
$853$	9.42803	−	16.3298i	0.322810	−	0.559122i	0.981067	+	0.193671i	$0.0620393\pi$
$854$	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	$0.229311\pi$
$857$			38.6241i			1.31937i	−0.751541	+	0.659687i	$0.770689\pi$
$858$		0			0
$859$			12.8843i			0.439606i	0.975544	+	0.219803i	$0.0705415\pi$
$859$			12.8843i			0.439606i	−0.975544	+	0.219803i	$0.929458\pi$
$860$	−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	−0.0449489	+	0.998989i	$0.514312\pi$
$863$	−26.0756	+	45.1643i	−0.887625	+	1.53741i	−0.842676	+	0.538422i	$0.819021\pi$
$864$		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	$-0.960172\pi$
$877$		−	7.39151i		−	0.249594i	0.992182	−	0.124797i	$-0.0398279\pi$
$878$	−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	$0.126633\pi$
$883$			23.0244i			0.774834i	−0.921905	+	0.387417i	$0.873367\pi$
$884$	−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	$0.0139549\pi$
$887$			2.61054i			0.0876533i	−0.999039	+	0.0438266i	$0.986045\pi$
$888$		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	$-0.803111\pi$
$907$		−	34.9260i		−	1.15970i	0.814724	−	0.579849i	$-0.196889\pi$
$908$	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	0.634564	−	0.772871i	$-0.281180\pi$
$911$	8.52724	+	4.92320i	0.282520	+	0.163113i	−0.352044	+	0.935984i	$0.614513\pi$
$912$		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	0.0425930	+	0.999093i	$0.486438\pi$
$919$	−25.5841	+	44.3130i	−0.843943	+	1.46175i	−0.886536	+	0.462660i	$0.846895\pi$
$920$	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	0.643921	−	0.765092i	$-0.277306\pi$
$929$	−10.3822	−	17.9825i	−0.340628	−	0.589985i	−0.984550	+	0.175106i	$0.943973\pi$
$930$		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	−0.998214	−	0.0597471i	$-0.980971\pi$
$941$	−13.7232	+	23.7693i	−0.447364	+	0.774858i	0.550849	+	0.834605i	$0.314304\pi$
$942$		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	0.961262	+	0.275635i	$0.0888881\pi$
$947$	22.1365	+	38.3415i	0.719338	+	1.24593i	−0.241924	+	0.970295i	$0.577779\pi$
$948$		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	0.0198274	−	0.999803i	$-0.493688\pi$
$967$	27.8500	−	16.0792i	0.895596	−	0.517073i	0.875769	+	0.482731i	$0.160355\pi$
$968$	−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	−0.749702	−	0.661776i	$-0.769803\pi$
$971$	6.17807	−	10.7007i	0.198264	−	0.343403i	0.947966	+	0.318373i	$0.103136\pi$
$972$		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	−0.925132	−	0.379647i	$-0.876046\pi$
$977$	−4.18162	+	7.24278i	−0.133782	+	0.231717i	0.791350	+	0.611364i	$0.209379\pi$
$978$		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	$-0.818695\pi$
$983$		−	33.8162i		−	1.07857i	0.842124	−	0.539285i	$-0.181305\pi$
$984$		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	0.950748	−	0.309964i	$-0.100317\pi$
$991$	6.51443	+	11.2833i	0.206938	+	0.358427i	−0.743811	+	0.668390i	$0.766984\pi$
$992$	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.89.4		48
3.2	odd	2		630.2.r.a.299.15	yes	48
5.4	even	2		1890.2.r.a.89.4		48
7.3	odd	6		1890.2.bi.a.899.11		48
9.4	even	3		630.2.bi.a.509.2	yes	48
9.5	odd	6		1890.2.bi.b.719.6		48
15.14	odd	2		630.2.r.b.299.10	yes	48
21.17	even	6		630.2.bi.b.479.23	yes	48
35.24	odd	6		1890.2.bi.b.899.6		48
45.4	even	6		630.2.bi.b.509.23	yes	48
45.14	odd	6		1890.2.bi.a.719.11		48
63.31	odd	6		630.2.r.b.59.10	yes	48
63.59	even	6		1890.2.r.a.1529.4		48
105.59	even	6		630.2.bi.a.479.2	yes	48
315.59	even	6	inner	1890.2.r.b.1529.4		48
315.94	odd	6		630.2.r.a.59.15	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.15	✓	48	315.94	odd	6
630.2.r.a.299.15	yes	48	3.2	odd	2
630.2.r.b.59.10	yes	48	63.31	odd	6
630.2.r.b.299.10	yes	48	15.14	odd	2
630.2.bi.a.479.2	yes	48	105.59	even	6
630.2.bi.a.509.2	yes	48	9.4	even	3
630.2.bi.b.479.23	yes	48	21.17	even	6
630.2.bi.b.509.23	yes	48	45.4	even	6
1890.2.r.a.89.4		48	5.4	even	2
1890.2.r.a.1529.4		48	63.59	even	6
1890.2.r.b.89.4		48	1.1	even	1	trivial
1890.2.r.b.1529.4		48	315.59	even	6	inner
1890.2.bi.a.719.11		48	45.14	odd	6
1890.2.bi.a.899.11		48	7.3	odd	6
1890.2.bi.b.719.6		48	9.5	odd	6
1890.2.bi.b.899.6		48	35.24	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more