LMFDB - Embedded newform 630.2.r.a.59.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.15
Character	$\chi$	$=$	630.59
Dual form			630.2.r.a.299.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.558726 + 1.63946i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.07866 + 0.824119i) q^{5} +(-1.69918 - 0.335859i) q^{6} +(0.837534 + 2.50969i) q^{7} +1.00000 q^{8} +(-2.37565 + 1.83202i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.558726 + 1.63946i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.07866 + 0.824119i) q^{5} +(-1.69918 - 0.335859i) q^{6} +(0.837534 + 2.50969i) q^{7} +1.00000 q^{8} +(-2.37565 + 1.83202i) q^{9} +(-1.75304 + 1.38811i) q^{10} -0.811199i q^{11} +(1.14045 - 1.30360i) q^{12} +(-0.0126841 + 0.0219696i) q^{13} +(-2.59222 - 0.529518i) q^{14} +(-0.189708 + 3.86833i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.78721 + 1.60920i) q^{17} +(-0.398746 - 2.97338i) q^{18} +(1.22111 - 0.705008i) q^{19} +(-0.325622 - 2.21223i) q^{20} +(-3.64658 + 2.77533i) q^{21} +(0.702519 + 0.405599i) q^{22} -3.53966 q^{23} +(0.558726 + 1.63946i) q^{24} +(3.64166 + 3.42613i) q^{25} +(-0.0126841 - 0.0219696i) q^{26} +(-4.33085 - 2.87119i) q^{27} +(1.75469 - 1.98017i) q^{28} +(-4.38175 + 2.52980i) q^{29} +(-3.25522 - 2.09846i) q^{30} +(2.89606 - 1.67204i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.32993 - 0.453237i) q^{33} +(-2.78721 + 1.60920i) q^{34} +(-0.327333 + 5.90702i) q^{35} +(2.77440 + 1.14137i) q^{36} +(9.76868 - 5.63995i) q^{37} +1.41002i q^{38} +(-0.0431052 - 0.00852016i) q^{39} +(2.07866 + 0.824119i) q^{40} +(0.973106 - 1.68547i) q^{41} +(-0.580217 - 4.54570i) q^{42} +(-2.76069 + 1.59389i) q^{43} +(-0.702519 + 0.405599i) q^{44} +(-6.44797 + 1.85032i) q^{45} +(1.76983 - 3.06543i) q^{46} +(-6.50911 - 3.75804i) q^{47} +(-1.69918 - 0.335859i) q^{48} +(-5.59707 + 4.20390i) q^{49} +(-4.78794 + 1.44070i) q^{50} +(-1.08093 + 5.46862i) q^{51} +0.0253683 q^{52} +(-5.33975 + 9.24872i) q^{53} +(4.65195 - 2.31503i) q^{54} +(0.668524 - 1.68621i) q^{55} +(0.837534 + 2.50969i) q^{56} +(1.83810 + 1.60805i) q^{57} -5.05961i q^{58} +(-1.80107 - 3.11955i) q^{59} +(3.44493 - 1.76987i) q^{60} +(0.527050 + 0.304293i) q^{61} +3.34408i q^{62} +(-6.58748 - 4.42777i) q^{63} +1.00000 q^{64} +(-0.0444715 + 0.0352140i) q^{65} +(-0.272448 + 1.37837i) q^{66} +(0.879693 - 0.507891i) q^{67} -3.21840i q^{68} +(-1.97770 - 5.80312i) q^{69} +(-4.95196 - 3.23699i) q^{70} -10.9830i q^{71} +(-2.37565 + 1.83202i) q^{72} +(6.25999 - 10.8426i) q^{73} +11.2799i q^{74} +(-3.58231 + 7.88461i) q^{75} +(-1.22111 - 0.705008i) q^{76} +(2.03586 - 0.679406i) q^{77} +(0.0289313 - 0.0330701i) q^{78} +(-0.845656 + 1.46472i) q^{79} +(-1.75304 + 1.38811i) q^{80} +(2.28744 - 8.70446i) q^{81} +(0.973106 + 1.68547i) q^{82} +(-14.5567 + 8.40429i) q^{83} +(4.22680 + 1.77037i) q^{84} +(4.46750 + 5.64197i) q^{85} -3.18777i q^{86} +(-6.59570 - 5.77023i) q^{87} -0.811199i q^{88} +(2.31249 + 4.00536i) q^{89} +(1.62156 - 6.50927i) q^{90} +(-0.0657602 - 0.0134330i) q^{91} +(1.76983 + 3.06543i) q^{92} +(4.35934 + 3.81376i) q^{93} +(6.50911 - 3.75804i) q^{94} +(3.11928 - 0.459133i) q^{95} +(1.14045 - 1.30360i) q^{96} +(-3.19146 - 5.52778i) q^{97} +(-0.842147 - 6.94916i) q^{98} +(1.48613 + 1.92712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9}+O(q^{10}) $ 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9	$ 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32} + 24 q^{33} + 18 q^{35} + 3 q^{41} + 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} + 42 q^{55} - 22 q^{57} - q^{60} - 9 q^{61} - 10 q^{63} + 48 q^{64} - 33 q^{65} - 24 q^{66} - 33 q^{67} + 42 q^{69} - 6 q^{70} + 3 q^{72} + 18 q^{73} + 9 q^{75} + 6 q^{77} - 18 q^{78} - 37 q^{81} + 3 q^{82} - 9 q^{83} - 13 q^{84} - 33 q^{85} - 18 q^{87} + 33 q^{89} + 39 q^{90} + 3 q^{92} - 32 q^{93} + 33 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^14 - 4 * q^15 - 24 * q^16 - 3 * q^18 + 5 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 3 * q^28 - 3 * q^29 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * q^35 + 3 * q^41 + 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 + 42 * q^55 - 22 * q^57 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * q^75 + 6 * q^77 - 18 * q^78 - 37 * q^81 + 3 * q^82 - 9 * q^83 - 13 * q^84 - 33 * q^85 - 18 * q^87 + 33 * q^89 + 39 * q^90 + 3 * q^92 - 32 * q^93 + 33 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	0.558726	+	1.63946i	0.322580	+	0.946542i
$3$	0.558726	+	1.63946i	0.322580	+	0.946542i
$4$	−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
$6$	−1.69918	−	0.335859i	−0.693686	−	0.137114i
$7$	0.837534	+	2.50969i	0.316558	+	0.948573i
$7$	0.837534	+	2.50969i	0.316558	+	0.948573i
$8$	1.00000			0.353553
$9$	−2.37565	+	1.83202i	−0.791884	+	0.610672i
$10$	−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	$-0.0390247\pi$
$12$	1.14045	−	1.30360i	0.329220	−	0.376317i
$13$	−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
$15$	−0.189708	+	3.86833i	−0.0489825	+	0.998800i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.78721	+	1.60920i	0.675999	+	0.390288i	0.798346	−	0.602199i	$-0.205709\pi$
$17$	2.78721	+	1.60920i	0.675999	+	0.390288i	−0.122347	+	0.992487i	$0.539042\pi$
$18$	−0.398746	−	2.97338i	−0.0939854	−	0.700833i
$19$	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
$21$	−3.64658	+	2.77533i	−0.795749	+	0.605627i
$22$	0.702519	+	0.405599i	0.149777	+	0.0864741i
$23$	−3.53966			−0.738069			−0.369035	−	0.929416i	$-0.620312\pi$
$23$	−3.53966			−0.738069			−0.369035	+	0.929416i	$0.620312\pi$
$24$	0.558726	+	1.63946i	0.114049	+	0.334653i
$25$	3.64166	+	3.42613i	0.728331	+	0.685225i
$26$	−0.0126841	−	0.0219696i	−0.00248756	−	0.00430859i
$27$	−4.33085	−	2.87119i	−0.833473	−	0.552561i
$28$	1.75469	−	1.98017i	0.331605	−	0.374217i
$29$	−4.38175	+	2.52980i	−0.813670	+	0.469773i	−0.848229	−	0.529630i	$-0.822331\pi$
$29$	−4.38175	+	2.52980i	−0.813670	+	0.469773i	0.0345586	+	0.999403i	$0.488997\pi$
$30$	−3.25522	−	2.09846i	−0.594319	−	0.383125i
$31$	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
$33$	1.32993	−	0.453237i	0.231511	−	0.0788985i
$34$	−2.78721	+	1.60920i	−0.478003	+	0.275975i
$35$	−0.327333	+	5.90702i	−0.0553293	+	0.998468i
$36$	2.77440	+	1.14137i	0.462400	+	0.190228i
$37$	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
$39$	−0.0431052	−	0.00852016i	−0.00690235	−	0.00136432i
$40$	2.07866	+	0.824119i	0.328665	+	0.130305i
$41$	0.973106	−	1.68547i	0.151974	−	0.263226i	−0.779979	−	0.625805i	$-0.784770\pi$
$41$	0.973106	−	1.68547i	0.151974	−	0.263226i	0.931953	+	0.362579i	$0.118104\pi$
$42$	−0.580217	−	4.54570i	−0.0895294	−	0.701416i
$43$	−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
$45$	−6.44797	+	1.85032i	−0.961207	+	0.275829i
$46$	1.76983	−	3.06543i	0.260947	−	0.451973i
$47$	−6.50911	−	3.75804i	−0.949451	−	0.548166i	−0.0565410	−	0.998400i	$-0.518007\pi$
$47$	−6.50911	−	3.75804i	−0.949451	−	0.548166i	−0.892910	+	0.450234i	$0.851340\pi$
$48$	−1.69918	−	0.335859i	−0.245255	−	0.0484771i
$49$	−5.59707	+	4.20390i	−0.799582	+	0.600557i
$50$	−4.78794	+	1.44070i	−0.677117	+	0.203746i
$51$	−1.08093	+	5.46862i	−0.151360	+	0.765760i
$52$	0.0253683			0.00351795
$53$	−5.33975	+	9.24872i	−0.733471	+	1.27041i	0.221920	+	0.975065i	$0.428768\pi$
$53$	−5.33975	+	9.24872i	−0.733471	+	1.27041i	−0.955391	+	0.295344i	$0.904566\pi$
$54$	4.65195	−	2.31503i	0.633050	−	0.315036i
$55$	0.668524	−	1.68621i	0.0901438	−	0.227368i
$56$	0.837534	+	2.50969i	0.111920	+	0.335371i
$57$	1.83810	+	1.60805i	0.243462	+	0.212992i
$58$		−	5.05961i		−	0.664359i
$59$	−1.80107	−	3.11955i	−0.234480	−	0.406131i	0.724642	−	0.689126i	$-0.242005\pi$
$59$	−1.80107	−	3.11955i	−0.234480	−	0.406131i	−0.959121	+	0.282995i	$0.908672\pi$
$60$	3.44493	−	1.76987i	0.444739	−	0.228490i
$61$	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
$63$	−6.58748	−	4.42777i	−0.829944	−	0.557846i
$64$	1.00000			0.125000
$65$	−0.0444715	+	0.0352140i	−0.00551602	+	0.00436776i
$66$	−0.272448	+	1.37837i	−0.0335361	+	0.169665i
$67$	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
$69$	−1.97770	−	5.80312i	−0.238087	−	0.698614i
$70$	−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	$-0.225952\pi$
$72$	−2.37565	+	1.83202i	−0.279973	+	0.215905i
$73$	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
$75$	−3.58231	+	7.88461i	−0.413649	+	0.910436i
$76$	−1.22111	−	0.705008i	−0.140071	−	0.0808700i
$77$	2.03586	−	0.679406i	0.232007	−	0.0774256i
$78$	0.0289313	−	0.0330701i	0.00327582	−	0.00374445i
$79$	−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
$81$	2.28744	−	8.70446i	0.254160	−	0.967162i
$82$	0.973106	+	1.68547i	0.107462	+	0.186129i
$83$	−14.5567	+	8.40429i	−1.59780	+	0.922491i	−0.605891	+	0.795548i	$0.707183\pi$
$83$	−14.5567	+	8.40429i	−1.59780	+	0.922491i	−0.991910	+	0.126943i	$0.959483\pi$
$84$	4.22680	+	1.77037i	0.461181	+	0.193163i
$85$	4.46750	+	5.64197i	0.484568	+	0.611958i
$86$		−	3.18777i		−	0.343746i
$87$	−6.59570	−	5.77023i	−0.707134	−	0.618634i
$88$		−	0.811199i		−	0.0864741i
$89$	2.31249	+	4.00536i	0.245124	+	0.424567i	0.962166	−	0.272462i	$-0.0878380\pi$
$89$	2.31249	+	4.00536i	0.245124	+	0.424567i	−0.717043	+	0.697029i	$0.754505\pi$
$90$	1.62156	−	6.50927i	0.170928	−	0.686137i
$91$	−0.0657602	−	0.0134330i	−0.00689354	−	0.00140816i
$92$	1.76983	+	3.06543i	0.184517	+	0.319593i
$93$	4.35934	+	3.81376i	0.452043	+	0.395468i
$94$	6.50911	−	3.75804i	0.671364	−	0.387612i
$95$	3.11928	−	0.459133i	0.320032	−	0.0471060i
$96$	1.14045	−	1.30360i	0.116397	−	0.133048i
$97$	−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
$99$	1.48613	+	1.92712i	0.149362	+	0.193683i
$100$	1.14628	−	4.86683i	0.114628	−	0.486683i
$101$	18.9158			1.88219			0.941094	−	0.338144i	$-0.109799\pi$
$101$	18.9158			1.88219			0.941094	+	0.338144i	$0.109799\pi$
$102$	−4.19550	−	3.67042i	−0.415417	−	0.363426i
$103$	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
$105$	−9.86720	+	2.76375i	−0.962940	+	0.269715i
$106$	−5.33975	−	9.24872i	−0.518642	−	0.898315i
$107$	0.859971	+	1.48951i	0.0831365	+	0.143997i	0.904596	−	0.426271i	$-0.140173\pi$
$107$	0.859971	+	1.48951i	0.0831365	+	0.143997i	−0.821459	+	0.570267i	$0.806840\pi$
$108$	−0.321097	+	5.18622i	−0.0308975	+	0.499044i
$109$	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
$111$	14.7045	+	12.8642i	1.39569	+	1.22101i
$112$	−2.59222	−	0.529518i	−0.244942	−	0.0500348i
$113$	−3.60588	+	6.24558i	−0.339213	+	0.587534i	−0.984285	−	0.176588i	$-0.943494\pi$
$113$	−3.60588	+	6.24558i	−0.339213	+	0.587534i	0.645072	+	0.764122i	$0.276827\pi$
$114$	−2.31166	+	0.787812i	−0.216507	+	0.0737854i
$115$	−7.35774	−	2.91710i	−0.686113	−	0.272021i
$116$	4.38175	+	2.52980i	0.406835	+	0.234886i
$117$	−0.0101155	−	0.0754296i	−0.000935179	−	0.00697347i
$118$	3.60215			0.331605
$119$	−1.70420	+	8.34280i	−0.156224	+	0.764783i
$120$	−0.189708	+	3.86833i	−0.0173179	+	0.353129i
$121$	10.3420			0.940178
$122$	−0.527050	+	0.304293i	−0.0477169	+	0.0275494i
$123$	3.30695	+	0.653652i	0.298178	+	0.0589378i
$124$	−2.89606	−	1.67204i	−0.260074	−	0.150154i
$125$	4.74623	+	10.1229i	0.424516	+	0.905421i
$126$	7.12830	−	3.49104i	0.635039	−	0.311006i
$127$			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
$129$	−4.15558	−	3.63550i	−0.365878	−	0.320088i
$130$	−0.00826047	−	0.0561205i	−0.000724491	−	0.00492209i
$131$	19.1309			1.67148			0.835738	−	0.549128i	$-0.185040\pi$
$131$	19.1309			1.67148			0.835738	+	0.549128i	$0.185040\pi$
$132$	−1.05748	−	0.925132i	−0.0920417	−	0.0805224i
$133$	2.79207	+	2.47414i	0.242103	+	0.214535i
$134$			1.01578i			0.0877502i
$135$	−6.63617	−	9.53736i	−0.571150	−	0.820845i
$136$	2.78721	+	1.60920i	0.239002	+	0.137988i
$137$	15.9510			1.36279			0.681393	−	0.731918i	$-0.261375\pi$
$137$	15.9510			1.36279			0.681393	+	0.731918i	$0.261375\pi$
$138$	6.01450	+	1.18882i	0.511988	+	0.101200i
$139$	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
$141$	2.52434	−	12.7711i	0.212588	−	1.07552i
$142$	9.51153	+	5.49149i	0.798190	+	0.460835i
$143$	0.0178217	+	0.0102894i	0.00149032	+	0.000860439i
$144$	−0.398746	−	2.97338i	−0.0332289	−	0.247782i
$145$	−11.1930	+	1.64752i	−0.929530	+	0.136819i
$146$	6.25999	+	10.8426i	0.518080	+	0.897342i
$147$	−10.0193	−	6.82734i	−0.826382	−	0.563110i
$148$	−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	$-0.153614\pi$
$150$	−5.03712	−	7.04467i	−0.411279	−	0.575195i
$151$	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
$153$	−9.56952	+	1.28332i	−0.773650	+	0.103751i
$154$	−0.429545	+	2.10281i	−0.0346137	+	0.169449i
$155$	7.39788	−	1.08891i	0.594212	−	0.0874631i
$156$	0.0141739	+	0.0415902i	0.00113482	+	0.00332988i
$157$	−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
$159$	−18.1463	−	3.58680i	−1.43910	−	0.284452i
$160$	−0.325622	−	2.21223i	−0.0257427	−	0.174892i
$161$	−2.96458	−	8.88343i	−0.233642	−	0.700113i
$162$	6.39456	+	6.33321i	0.502404	+	0.497584i
$163$	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
$165$	3.13799	+	0.153891i	0.244292	+	0.0119804i
$166$		−	16.8086i		−	1.30460i
$167$	−7.45421	−	4.30369i	−0.576824	−	0.333029i	0.183046	−	0.983104i	$-0.441404\pi$
$167$	−7.45421	−	4.30369i	−0.576824	−	0.333029i	−0.759870	+	0.650075i	$0.774738\pi$
$168$	−3.64658	+	2.77533i	−0.281340	+	0.214121i
$169$	6.49968	+	11.2578i	0.499975	+	0.865983i
$170$	−7.11984	+	1.04798i	−0.546067	+	0.0803765i
$171$	−1.60935	+	3.91195i	−0.123070	+	0.299154i
$172$	2.76069	+	1.59389i	0.210501	+	0.121533i
$173$	−3.38227	−	1.95275i	−0.257149	−	0.148465i	0.365884	−	0.930660i	$-0.380767\pi$
$173$	−3.38227	−	1.95275i	−0.257149	−	0.148465i	−0.623033	+	0.782195i	$0.714100\pi$
$174$	8.29502	−	2.82693i	0.628844	−	0.214309i
$175$	−5.54850	+	12.0089i	−0.419427	+	0.907789i
$176$	0.702519	+	0.405599i	0.0529543	+	0.0305732i
$177$	4.10807	−	4.69576i	0.308782	−	0.352955i
$178$	−4.62499			−0.346658
$179$	−16.4704	−	9.50922i	−1.23106	−	0.710752i	−0.263808	−	0.964575i	$-0.584979\pi$
$179$	−16.4704	−	9.50922i	−1.23106	−	0.710752i	−0.967251	+	0.253823i	$0.918312\pi$
$180$	4.82641	+	4.65895i	0.359739	+	0.347257i
$181$			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
$183$	−0.204399	+	1.03409i	−0.0151096	+	0.0764424i
$184$	−3.53966			−0.260947
$185$	24.9538	−	3.67299i	1.83464	−	0.270043i
$186$	−5.48248	+	1.86842i	−0.401995	+	0.137000i
$187$	1.30538	−	2.26098i	0.0954588	−	0.165339i
$188$			7.51607i			0.548166i
$189$	3.57855	−	13.2738i	0.260301	−	0.965527i
$190$	−1.16202	+	2.93094i	−0.0843019	+	0.212633i
$191$	2.20020	+	1.27028i	0.159201	+	0.0919146i	0.577484	−	0.816402i	$-0.304035\pi$
$191$	2.20020	+	1.27028i	0.159201	+	0.0919146i	−0.418283	+	0.908317i	$0.637368\pi$
$192$	0.558726	+	1.63946i	0.0403225	+	0.118318i
$193$	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
$195$	−0.0825793	−	0.0532343i	−0.00591363	−	0.00381219i
$196$	6.43922	+	2.74526i	0.459944	+	0.196090i
$197$	2.27493			0.162082			0.0810412	−	0.996711i	$-0.474175\pi$
$197$	2.27493			0.162082			0.0810412	+	0.996711i	$0.474175\pi$
$198$	−2.41200	+	0.323462i	−0.171414	+	0.0229875i
$199$	−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
$201$	1.32417	+	1.15845i	0.0934000	+	0.0817107i
$202$	−9.45788	+	16.3815i	−0.665454	+	1.15260i
$203$	−10.0189	−	8.87803i	−0.703188	−	0.623115i
$204$	5.27643	−	1.79820i	0.369424	−	0.125899i
$205$	3.41178	−	2.70156i	0.238289	−	0.188685i
$206$	−4.09618	+	7.09479i	−0.285394	+	0.494318i
$207$	8.40899	−	6.48471i	0.584465	−	0.450718i
$208$	−0.0126841	−	0.0219696i	−0.000879487	−	0.00152332i
$209$	−0.571902	−	0.990563i	−0.0395593	−	0.0685186i
$210$	2.54012	−	9.92712i	0.175285	−	0.685037i
$211$	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
$213$	18.0061	−	6.13647i	1.23376	−	0.420464i
$214$	−1.71994			−0.117573
$215$	−7.05209	+	1.03801i	−0.480949	+	0.0707917i
$216$	−4.33085	−	2.87119i	−0.294677	−	0.195360i
$217$	6.62185	+	5.86782i	0.449520	+	0.398333i
$218$	6.77465	+	11.7340i	0.458837	+	0.794729i
$219$	21.2736	+	4.20495i	1.43754	+	0.284144i
$220$	−1.79456	+	0.264144i	−0.120989	+	0.0178086i
$221$	−0.0707068	+	0.0408226i	−0.00475625	+	0.00274602i
$222$	−18.4929	+	6.30237i	−1.24116	+	0.422987i
$223$	−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
$225$	−14.9280	−	1.46771i	−0.995201	−	0.0978473i
$226$	−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	$-0.0627485\pi$
$228$	0.473567	−	2.39587i	0.0313627	−	0.158670i
$229$			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
$231$	2.25134	+	2.95810i	0.148128	+	0.194629i
$232$	−4.38175	+	2.52980i	−0.287676	+	0.166090i
$233$	−14.0861	−	24.3978i	−0.922811	−	1.59836i	−0.795044	−	0.606551i	$-0.792552\pi$
$233$	−14.0861	−	24.3978i	−0.922811	−	1.59836i	−0.127767	−	0.991804i	$-0.540781\pi$
$234$	0.0703817	+	0.0289545i	0.00460099	+	0.00189281i
$235$	−10.4332	−	13.1760i	−0.680584	−	0.859505i
$236$	−1.80107	+	3.11955i	−0.117240	+	0.203066i
$237$	−2.87384	−	0.568042i	−0.186676	−	0.0368983i
$238$	−6.37297	−	5.64728i	−0.413099	−	0.366059i
$239$	7.81549	+	4.51228i	0.505542	+	0.291875i	0.730999	−	0.682378i	$-0.239054\pi$
$239$	7.81549	+	4.51228i	0.505542	+	0.291875i	−0.225457	+	0.974253i	$0.572388\pi$
$240$	−3.25522	−	2.09846i	−0.210124	−	0.135455i
$241$		−	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
$243$	15.5487	−	1.11324i	0.997447	−	0.0714146i
$244$		−	0.608585i		−	0.0389607i
$245$	−15.0989	+	4.12583i	−0.964635	+	0.263589i
$246$	−2.21956	+	2.53708i	−0.141514	+	0.161758i
$247$			0.0357697i			0.00227597i
$248$	2.89606	−	1.67204i	0.183900	−	0.106175i
$249$	−21.9117	−	19.1694i	−1.38860	−	1.21481i
$250$	−11.1398	−	0.951098i	−0.704544	−	0.0601527i
$251$	−28.8906			−1.82356			−0.911780	−	0.410679i	$-0.865292\pi$
$251$	−28.8906			−1.82356			−0.911780	+	0.410679i	$0.865292\pi$
$252$	−0.540822	+	7.91881i	−0.0340686	+	0.498838i
$253$			2.87136i			0.180521i
$254$	−14.1779	−	8.18562i	−0.889601	−	0.513612i
$255$	−6.75368	+	10.4766i	−0.422932	+	0.656070i
$256$	−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	$0.974165\pi$
$258$	5.22622	−	1.78109i	0.325370	−	0.110886i
$259$	22.3361	+	19.7927i	1.38790	+	1.22986i
$260$	0.0527320	+	0.0209065i	0.00327030	+	0.00129656i
$261$	5.77487	−	14.0374i	0.357455	−	0.868891i
$262$	−9.56546	+	16.5679i	−0.590956	+	1.02357i
$263$	16.2231			1.00036			0.500179	−	0.865922i	$-0.333267\pi$
$263$	16.2231			1.00036			0.500179	+	0.865922i	$0.333267\pi$
$264$	1.32993	−	0.453237i	0.0818513	−	0.0278948i
$265$	−18.7216	+	14.8244i	−1.15006	+	0.910653i
$266$	−3.53870	+	1.18094i	−0.216972	+	0.0724079i
$267$	−5.27457	+	6.02914i	−0.322798	+	0.368977i
$268$	−0.879693	−	0.507891i	−0.0537358	−	0.0310244i
$269$	3.04488	−	5.27389i	0.185650	−	0.321555i	−0.758145	−	0.652085i	$-0.773894\pi$
$269$	3.04488	−	5.27389i	0.185650	−	0.321555i	0.943795	+	0.330531i	$0.107228\pi$
$270$	11.5777	−	0.978409i	0.704595	−	0.0595441i
$271$	−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
$273$	−0.0147191	−	0.115316i	−0.000890840	−	0.00697927i
$274$	−7.97550	+	13.8140i	−0.481818	+	0.834532i
$275$	2.77927	−	2.95411i	0.167596	−	0.178139i
$276$	−4.03680	+	4.61430i	−0.242987	+	0.277748i
$277$		−	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
$279$	−3.81682	+	9.27781i	−0.228507	+	0.555448i
$280$	−0.327333	+	5.90702i	−0.0195619	+	0.353012i
$281$	6.70985	−	3.87393i	0.400276	−	0.231099i	−0.286327	−	0.958132i	$-0.592434\pi$
$281$	6.70985	−	3.87393i	0.400276	−	0.231099i	0.686603	+	0.727032i	$0.259101\pi$
$282$	9.79795	+	8.57171i	0.583460	+	0.510438i
$283$	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
$285$	2.49555	+	4.85741i	0.147824	+	0.287728i
$286$	−0.0178217	+	0.0102894i	−0.00105382	+	0.000608422i
$287$	5.04501	+	1.03055i	0.297797	+	0.0608317i
$288$	2.77440	+	1.14137i	0.163483	+	0.0672557i
$289$	−3.32096	−	5.75207i	−0.195351	−	0.338357i
$290$	4.16972	−	10.5172i	0.244854	−	0.617591i
$291$	7.27941	−	8.32079i	0.426727	−	0.487773i
$292$	−12.5200			−0.732676
$293$	−22.8864	−	13.2135i	−1.33704	−	0.771939i	−0.350671	−	0.936499i	$-0.614046\pi$
$293$	−22.8864	−	13.2135i	−1.33704	−	0.771939i	−0.986367	+	0.164560i	$0.947380\pi$
$294$	10.9223	−	5.26334i	0.637003	−	0.306964i
$295$	−1.17294	−	7.96879i	−0.0682912	−	0.463961i
$296$	9.76868	−	5.63995i	0.567793	−	0.327815i
$297$	−2.32910	+	3.51318i	−0.135148	+	0.203855i
$298$	9.81170	+	5.66479i	0.568377	+	0.328152i
$299$	0.0448975	−	0.0777647i	0.00259649	−	0.00449725i
$300$	8.61943	−	0.839937i	0.497643	−	0.0484938i
$301$	−6.31233	−	5.59354i	−0.363837	−	0.322406i
$302$	−6.13048	+	10.6183i	−0.352770	+	0.611015i
$303$	10.5687	+	31.0116i	0.607157	+	1.78157i
$304$			1.41002i			0.0808700i
$305$	0.844785	+	1.06687i	0.0483723	+	0.0610890i
$306$	3.67337	−	8.92911i	0.209993	−	0.510443i
$307$	−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
$309$	4.57728	+	13.4310i	0.260393	+	0.764065i
$310$	−2.75592	+	6.95121i	−0.156526	+	0.394802i
$311$	10.0336	+	17.3787i	0.568954	+	0.985457i	0.996670	+	0.0815438i	$0.0259850\pi$
$311$	10.0336	+	17.3787i	0.568954	+	0.985457i	−0.427716	+	0.903913i	$0.640682\pi$
$312$	−0.0431052	−	0.00852016i	−0.00244035	−	0.000482359i
$313$	−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
$315$	−10.0441	−	14.6327i	−0.565922	−	0.824459i
$316$	1.69131			0.0951438
$317$	13.4765	−	23.3419i	0.756913	−	1.31101i	−0.187504	−	0.982264i	$-0.560040\pi$
$317$	13.4765	−	23.3419i	0.756913	−	1.31101i	0.944417	−	0.328749i	$-0.106627\pi$
$318$	12.1794	−	13.9218i	0.682989	−	0.780695i
$319$	2.05217	+	3.55447i	0.114900	+	0.199012i
$320$	2.07866	+	0.824119i	0.116201	+	0.0460696i
$321$	−1.96151	+	2.24212i	−0.109481	+	0.125143i
$322$	9.17557	+	1.87431i	0.511335	+	0.104451i
$323$	4.53799			0.252501
$324$	−8.68200	+	2.37125i	−0.482333	+	0.131736i
$325$	−0.121462	+	0.0365482i	−0.00673749	+	0.00202733i
$326$			18.3809i			1.01802i
$327$	23.0226	+	4.55065i	1.27316	+	0.251652i
$328$	0.973106	−	1.68547i	0.0537308	−	0.0930644i
$329$	3.97990	−	19.4833i	0.219419	−	1.07415i
$330$	−1.70227	+	2.64063i	−0.0937067	+	0.145362i
$331$	−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
$333$	−12.8745	+	31.2949i	−0.705518	+	1.71495i
$334$	7.45421	−	4.30369i	0.407876	−	0.235487i
$335$	2.24714	−	0.330761i	0.122775	−	0.0180714i
$336$	−0.580217	−	4.54570i	−0.0316534	−	0.247988i
$337$	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
$339$	−12.2541	−	2.42214i	−0.665549	−	0.131552i
$340$	2.65234	−	6.68995i	0.143843	−	0.362814i
$341$	−1.35636	−	2.34928i	−0.0734508	−	0.127221i
$342$	−2.58317	−	3.34971i	−0.139682	−	0.181131i
$343$	−15.2382	−	10.5260i	−0.822786	−	0.568351i
$344$	−2.76069	+	1.59389i	−0.148847	+	0.0859366i
$345$	0.671502	−	13.6926i	0.0361525	−	0.737183i
$346$	3.38227	−	1.95275i	0.181832	−	0.104981i
$347$	−4.94667	−	8.56789i	−0.265551	−	0.459949i	0.702157	−	0.712023i	$-0.252221\pi$
$347$	−4.94667	−	8.56789i	−0.265551	−	0.459949i	−0.967708	+	0.252074i	$0.918887\pi$
$348$	−1.69931	+	8.59716i	−0.0910928	+	0.460856i
$349$	−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
$351$	0.118012	−	0.0587284i	0.00629901	−	0.00313469i
$352$	−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	$0.846543\pi$
$354$	2.01261	+	5.90557i	0.106969	+	0.313878i
$355$	9.05128	−	22.8299i	0.480392	−	1.21168i
$356$	2.31249	−	4.00536i	0.122562	−	0.212284i
$357$	−14.6299	+	1.86737i	−0.774294	+	0.0988316i
$358$	16.4704	−	9.50922i	0.870490	−	0.502578i
$359$	−29.8414	+	17.2289i	−1.57497	+	0.909309i	−0.579423	+	0.815027i	$0.696722\pi$
$359$	−29.8414	+	17.2289i	−1.57497	+	0.909309i	−0.995546	+	0.0942818i	$0.969945\pi$
$360$	−6.44797	+	1.85032i	−0.339838	+	0.0975204i
$361$	−8.50593	+	14.7327i	−0.447680	+	0.775405i
$362$	−12.5890	−	7.26828i	−0.661665	−	0.382013i
$363$	5.77832	+	16.9552i	0.303283	+	0.889918i
$364$	0.0212468	+	0.0636665i	0.00111363	+	0.00333703i
$365$	21.9480	−	17.3791i	1.14881	−	0.909666i
$366$	−0.793352	−	0.694061i	−0.0414692	−	0.0362792i
$367$	−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
$369$	0.776044	+	5.78683i	0.0403993	+	0.301250i
$370$	−9.29598	+	23.4471i	−0.483275	+	1.21896i
$371$	−27.6836	−	5.65499i	−1.43726	−	0.293592i
$372$	1.12314	−	5.68218i	0.0582321	−	0.294607i
$373$		−	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
$375$	−13.9443	+	13.4372i	−0.720078	+	0.693893i
$376$	−6.50911	−	3.75804i	−0.335682	−	0.193806i
$377$		−	0.128353i		−	0.00661054i
$378$	9.70618	+	9.73602i	0.499232	+	0.500767i
$379$	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
$381$	−26.8400	+	9.14703i	−1.37505	+	0.468617i
$382$	−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	$0.714682\pi$
$384$	−1.69918	−	0.335859i	−0.0867107	−	0.0171392i
$385$	4.79176	+	0.265532i	0.244211	+	0.0135328i
$386$			7.82427i			0.398245i
$387$	3.63842	−	8.84415i	0.184951	−	0.449573i
$388$	−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	$0.821638\pi$
$390$	0.0873919	−	0.0448987i	0.00442526	−	0.00227353i
$391$	−9.86578	−	5.69601i	−0.498934	−	0.288060i
$392$	−5.59707	+	4.20390i	−0.282695	+	0.212329i
$393$	10.6889	+	31.3644i	0.539186	+	1.58212i
$394$	−1.13747	+	1.97015i	−0.0573047	+	0.0992547i
$395$	−2.96493	+	2.34773i	−0.149182	+	0.118127i
$396$	0.925875	−	2.25059i	0.0465270	−	0.113096i
$397$	−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
$399$	−2.49624	+	5.95985i	−0.124969	+	0.298366i
$400$	−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	$-0.0693094\pi$
$402$	−1.66533	+	0.567543i	−0.0830592	+	0.0283065i
$403$			0.0848336i			0.00422586i
$404$	−9.45788	−	16.3815i	−0.470547	−	0.815012i
$405$	11.9283	−	16.2085i	0.592723	−	0.805407i
$406$	12.6980	−	4.23759i	0.630193	−	0.210308i
$407$	−4.57512	−	7.92434i	−0.226780	−	0.392795i
$408$	−1.08093	+	5.46862i	−0.0535139	+	0.270737i
$409$	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
$411$	8.91223	+	26.1510i	0.439608	+	1.28993i
$412$	−4.09618	−	7.09479i	−0.201804	−	0.349535i
$413$	6.32064	−	7.13287i	0.311019	−	0.350985i
$414$	1.41142	+	10.5248i	0.0693677	+	0.517263i
$415$	−37.1845	+	5.47325i	−1.82531	+	0.268671i
$416$	0.0253683			0.00124378
$417$	−1.98518	+	10.0434i	−0.0972148	+	0.491829i
$418$	1.14380			0.0559452
$419$	4.57468	−	7.92357i	0.223488	−	0.387092i	−0.732377	−	0.680899i	$-0.761589\pi$
$419$	4.57468	−	7.92357i	0.223488	−	0.387092i	0.955865	+	0.293808i	$0.0949225\pi$
$420$	7.32708	+	7.16337i	0.357525	+	0.349537i
$421$	−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
$423$	22.3482	−	2.99701i	1.08660	−	0.145719i
$424$	−5.33975	+	9.24872i	−0.259321	+	0.449157i
$425$	4.63676	+	15.4095i	0.224916	+	0.747470i
$426$	−3.68873	+	18.6620i	−0.178720	+	0.904177i
$427$	−0.322257	+	1.57759i	−0.0155951	+	0.0763448i
$428$	0.859971	−	1.48951i	0.0415683	−	0.0719983i
$429$	−0.00691154	+	0.0349668i	−0.000333692	+	0.00168821i
$430$	2.62710	−	6.62630i	0.126690	−	0.319548i
$431$	−2.69929	−	1.55843i	−0.130020	−	0.0750671i	0.433579	−	0.901115i	$-0.357250\pi$
$431$	−2.69929	−	1.55843i	−0.130020	−	0.0750671i	−0.563599	+	0.826048i	$0.690584\pi$
$432$	4.65195	−	2.31503i	0.223817	−	0.111382i
$433$	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
$435$	−8.95487	−	17.4300i	−0.429353	−	0.835704i
$436$	−13.5493			−0.648894
$437$	−4.32231	+	2.49549i	−0.206764	+	0.119375i
$438$	−14.2784	+	16.3210i	−0.682249	+	0.779850i
$439$	−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
$441$	5.59508	−	20.2409i	0.266433	−	0.963854i
$442$		−	0.0816452i		−	0.00388346i
$443$	−4.32317	+	7.48796i	−0.205400	+	0.355764i	−0.950260	−	0.311457i	$-0.899183\pi$
$443$	−4.32317	+	7.48796i	−0.205400	+	0.355764i	0.744860	+	0.667221i	$0.232516\pi$
$444$	3.78846	−	19.1665i	0.179792	−	0.909604i
$445$	1.50600	+	10.2315i	0.0713912	+	0.485022i
$446$	9.23972			0.437514
$447$	18.5744	−	6.33013i	0.878538	−	0.299405i
$448$	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	$-0.0745531\pi$
$450$	8.73509	−	12.1942i	0.411776	−	0.574840i
$451$	−1.36725	−	0.789382i	−0.0643813	−	0.0371705i
$452$	7.21177			0.339213
$453$	6.85051	+	20.1013i	0.321865	+	0.944444i
$454$	5.11105	+	2.95087i	0.239874	+	0.138491i
$455$	−0.125623	−	0.0821168i	−0.00588928	−	0.00384969i
$456$	1.83810	+	1.60805i	0.0860768	+	0.0753040i
$457$	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
$459$	−7.45070	−	14.9718i	−0.347769	−	0.698825i
$460$	1.15259	+	7.83054i	0.0537398	+	0.365101i
$461$	−16.1968	−	28.0536i	−0.754358	−	1.30659i	−0.945693	−	0.325061i	$-0.894615\pi$
$461$	−16.1968	−	28.0536i	−0.754358	−	1.30659i	0.191335	−	0.981525i	$-0.438718\pi$
$462$	−3.68746	+	0.470671i	−0.171556	+	0.0218976i
$463$	−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
$465$	5.91861	+	11.5201i	0.274469	+	0.534233i
$466$	28.1722			1.30505
$467$	7.39730	−	4.27083i	0.342306	−	0.197631i	−0.318985	−	0.947760i	$-0.603342\pi$
$467$	7.39730	−	4.27083i	0.342306	−	0.197631i	0.661291	+	0.750129i	$0.270009\pi$
$468$	−0.0602662	+	0.0464751i	−0.00278580	+	0.00214831i
$469$	2.01142	+	1.78238i	0.0928788	+	0.0823026i
$470$	16.6273	−	2.44740i	0.766960	−	0.112890i
$471$	3.20619	−	3.66486i	0.147734	−	0.168868i
$472$	−1.80107	−	3.11955i	−0.0829012	−	0.143589i
$473$	1.29296	+	2.23947i	0.0594503	+	0.102971i
$474$	1.92886	−	2.20480i	0.0885954	−	0.101270i
$475$	6.86231	+	1.61628i	0.314864	+	0.0741600i
$476$	8.07717	−	2.69552i	0.370217	−	0.123549i
$477$	−4.25841	−	31.7542i	−0.194979	−	1.45393i
$478$	−7.81549	+	4.51228i	−0.357472	+	0.206387i
$479$	18.0818			0.826180			0.413090	−	0.910690i	$-0.364450\pi$
$479$	18.0818			0.826180			0.413090	+	0.910690i	$0.364450\pi$
$480$	3.44493	−	1.76987i	0.157239	−	0.0807834i
$481$			0.286152i			0.0130474i
$482$	2.13074	+	1.23018i	0.0970523	+	0.0560332i
$483$	12.9076	−	9.82371i	0.587318	−	0.446995i
$484$	−5.17098	−	8.95640i	−0.235044	−	0.407109i
$485$	−2.07842	−	14.1205i	−0.0943763	−	0.641180i
$486$	−6.81023	+	14.0222i	−0.308918	+	0.636058i
$487$	−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
$489$	23.9613	+	20.9625i	1.08357	+	0.947955i
$490$	3.97639	−	15.1390i	0.179635	−	0.683909i
$491$	−5.16468	−	2.98183i	−0.233079	−	0.134568i	0.378913	−	0.925432i	$-0.376298\pi$
$491$	−5.16468	−	2.98183i	−0.233079	−	0.134568i	−0.611992	+	0.790864i	$0.709631\pi$
$492$	−1.08740	−	3.19073i	−0.0490237	−	0.143849i
$493$	−16.2838			−0.733386
$494$	−0.0309774	−	0.0178848i	−0.00139374	−	0.000804677i
$495$	1.50098	+	5.23058i	0.0674638	+	0.235097i
$496$			3.34408i			0.150154i
$497$	27.5638	−	9.19862i	1.23641	−	0.412614i
$498$	27.5570	−	9.39139i	1.23486	−	0.420838i
$499$	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
$501$	2.89086	−	14.6255i	0.129154	−	0.653417i
$502$	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	$-0.176423\pi$
$504$	−6.58748	−	4.42777i	−0.293430	−	0.197229i
$505$	39.3194	+	15.5888i	1.74969	+	0.693694i
$506$	−2.48667	−	1.43568i	−0.110546	−	0.0638238i
$507$	−14.8251	+	16.9460i	−0.658407	+	0.752597i
$508$	14.1779	−	8.18562i	0.629043	−	0.363178i
$509$	2.21813			0.0983168			0.0491584	−	0.998791i	$-0.484346\pi$
$509$	2.21813			0.0983168			0.0491584	+	0.998791i	$0.484346\pi$
$510$	−5.69616	−	11.0872i	−0.252230	−	0.490947i
$511$	32.4546	+	6.62956i	1.43570	+	0.293274i
$512$	1.00000			0.0441942
$513$	−7.31266	−	0.452752i	−0.322862	−	0.0199895i
$514$	−2.25121	−	1.29974i	−0.0992966	−	0.0573289i
$515$	17.0291	+	6.75148i	0.750393	+	0.297506i
$516$	−1.07064	+	5.41659i	−0.0471324	+	0.238452i
$517$	−3.04851	+	5.28018i	−0.134073	+	0.232222i
$518$	−28.3090	+	9.44730i	−1.24383	+	0.415091i
$519$	1.31170	−	6.63614i	0.0575772	−	0.291294i
$520$	−0.0444715	+	0.0352140i	−0.00195021	+	0.00154424i
$521$	5.51885	−	9.55893i	0.241785	−	0.418785i	−0.719438	−	0.694557i	$-0.755600\pi$
$521$	5.51885	−	9.55893i	0.241785	−	0.418785i	0.961223	+	0.275773i	$0.0889337\pi$
$522$	9.26928	+	12.0199i	0.405705	+	0.526095i
$523$	−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
$525$	−22.7882	−	2.38684i	−0.994559	−	0.104170i
$526$	−8.11154	+	14.0496i	−0.353680	+	0.612592i
$527$	10.7626			0.468825
$528$	−0.272448	+	1.37837i	−0.0118568	+	0.0599858i
$529$	−10.4708			−0.455254
$530$	−3.47748	−	23.6255i	−0.151052	−	1.02623i
$531$	9.99379	+	4.11137i	0.433694	+	0.178418i
$532$	0.746630	−	3.65507i	0.0323705	−	0.158468i
$533$	0.0246860	+	0.0427574i	0.00106927	+	0.00185203i
$534$	−2.58410	−	7.58248i	−0.111825	−	0.328126i
$535$	0.560051	+	3.80491i	0.0242131	+	0.164501i
$536$	0.879693	−	0.507891i	0.0379969	−	0.0219375i
$537$	6.38751	−	32.3157i	0.275641	−	1.39452i
$538$	3.04488	+	5.27389i	0.131274	+	0.227374i
$539$	3.41020	+	4.54034i	0.146888	+	0.195566i
$540$	−4.94151	+	10.5158i	−0.212649	+	0.452527i
$541$	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
$543$	−23.8321	+	8.12195i	−1.02273	+	0.348546i
$544$		−	3.21840i		−	0.137988i
$545$	23.7524	−	18.8080i	1.01744	−	0.805645i
$546$	0.107227	+	0.0449111i	0.00458887	+	0.00192202i
$547$	−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
$549$	−1.80956	+	0.242671i	−0.0772300	+	0.0103570i
$550$	1.16870	+	3.88397i	0.0498334	+	0.165613i
$551$	−3.56706	+	6.17834i	−0.151962	+	0.263206i
$552$	−1.97770	−	5.80312i	−0.0841764	−	0.246997i
$553$	−4.38426	−	0.895581i	−0.186438	−	0.0380840i
$554$	14.9277	+	8.61850i	0.634216	+	0.366165i
$555$	19.9640	+	38.8585i	0.847425	+	1.64945i
$556$		−	5.91076i		−	0.250672i
$557$	−6.99648	+	12.1183i	−0.296451	+	0.513467i	−0.975321	−	0.220790i	$-0.929136\pi$
$557$	−6.99648	+	12.1183i	−0.296451	+	0.513467i	0.678871	+	0.734258i	$0.262470\pi$
$558$	−6.12641	−	7.94437i	−0.259352	−	0.336312i
$559$		−	0.0808683i		−	0.00342036i
$560$	−4.95196	−	3.23699i	−0.209259	−	0.136788i
$561$	4.43614	+	0.876847i	0.187294	+	0.0370205i
$562$			7.74787i			0.326824i
$563$	−5.50514	+	3.17839i	−0.232014	+	0.133953i	−0.611501	−	0.791244i	$-0.709434\pi$
$563$	−5.50514	+	3.17839i	−0.232014	+	0.133953i	0.379487	+	0.925197i	$0.376101\pi$
$564$	−12.3223	+	4.19942i	−0.518862	+	0.176828i
$565$	−12.6425	+	10.0108i	−0.531874	+	0.421156i
$566$	−0.773573			−0.0325157
$567$	23.7613	−	1.54952i	0.997880	−	0.0650739i
$568$		−	10.9830i		−	0.460835i
$569$	23.8982	+	13.7977i	1.00187	+	0.578428i	0.908800	−	0.417232i	$-0.137000\pi$
$569$	23.8982	+	13.7977i	1.00187	+	0.578428i	0.0930663	+	0.995660i	$0.470333\pi$
$570$	−5.45441	−	0.267492i	−0.228460	−	0.0112040i
$571$	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
$573$	−0.853273	+	4.31687i	−0.0356460	+	0.180340i
$574$	−3.41499	+	3.85383i	−0.142539	+	0.160856i
$575$	−12.8902	−	12.1273i	−0.537559	−	0.505744i
$576$	−2.37565	+	1.83202i	−0.0989855	+	0.0763340i
$577$	−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
$579$	10.1997	+	8.92319i	0.423886	+	0.370835i
$580$	7.02331	+	8.86968i	0.291627	+	0.368294i
$581$	−33.2839	−	29.4938i	−1.38085	−	1.22361i
$582$	3.56631	+	10.4645i	0.147828	+	0.433770i
$583$	7.50255	+	4.33160i	0.310724	+	0.179396i
$584$	6.25999	−	10.8426i	0.259040	−	0.448671i
$585$	0.0411362	−	0.165129i	0.00170077	−	0.00682724i
$586$	22.8864	−	13.2135i	0.945429	−	0.545843i
$587$	1.01410	−	0.585492i	0.0418564	−	0.0241658i	−0.478926	−	0.877855i	$-0.658974\pi$
$587$	1.01410	−	0.585492i	0.0418564	−	0.0241658i	0.520782	+	0.853690i	$0.325640\pi$
$588$	−0.902980	+	12.0907i	−0.0372382	+	0.498611i
$589$	2.35760	−	4.08349i	0.0971434	−	0.168257i
$590$	7.48764	+	2.96860i	0.308261	+	0.122215i
$591$	1.27106	+	3.72966i	0.0522846	+	0.153418i
$592$			11.2799i			0.463601i
$593$	11.0764	−	6.39495i	0.454853	−	0.262609i	−0.255025	−	0.966935i	$-0.582084\pi$
$593$	11.0764	−	6.39495i	0.454853	−	0.262609i	0.709877	+	0.704325i	$0.248750\pi$
$594$	−1.87795	−	3.77365i	−0.0770533	−	0.154835i
$595$	−10.4179	+	15.9374i	−0.427093	+	0.653369i
$596$	−9.81170	+	5.66479i	−0.401903	+	0.232039i
$597$	6.79222	−	34.3632i	0.277987	−	1.40639i
$598$	0.0448975	+	0.0777647i	0.00183599	+	0.00318004i
$599$	−31.9286	+	18.4340i	−1.30457	+	0.753193i	−0.981184	−	0.193075i	$-0.938154\pi$
$599$	−31.9286	+	18.4340i	−1.30457	+	0.753193i	−0.323384	+	0.946268i	$0.604821\pi$
$600$	−3.58231	+	7.88461i	−0.146247	+	0.321888i
$601$	−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
$603$	−1.15938	+	2.81818i	−0.0472136	+	0.114765i
$604$	−6.13048	−	10.6183i	−0.249446	−	0.432053i
$605$	21.4974	+	8.52300i	0.873994	+	0.346509i
$606$	−32.1412	−	6.35303i	−1.30565	−	0.258074i
$607$	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
$609$	8.95735	−	21.3859i	0.362970	−	0.866601i
$610$	−1.34633	+	0.198169i	−0.0545114	+	0.00802362i
$611$	0.165125	−	0.0953349i	0.00668024	−	0.00385684i
$612$	5.89615	+	7.64579i	0.238338	+	0.309063i
$613$	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
$615$	6.33535	+	4.08404i	0.255466	+	0.164685i
$616$	2.03586	−	0.679406i	0.0820270	−	0.0273741i
$617$	4.01634	−	6.95651i	0.161692	−	0.280059i	−0.773784	−	0.633450i	$-0.781638\pi$
$617$	4.01634	−	6.95651i	0.161692	−	0.280059i	0.935476	+	0.353391i	$0.114972\pi$
$618$	−13.9203	−	2.75148i	−0.559955	−	0.110681i
$619$		−	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
$621$	15.3297	+	10.1630i	0.615161	+	0.407828i
$622$	−20.0672			−0.804622
$623$	−8.11541	+	9.15827i	−0.325137	+	0.366918i
$624$	0.0289313	−	0.0330701i	0.00115818	−	0.00132386i
$625$	1.52332	+	24.9535i	0.0609328	+	0.998142i
$626$	−5.07727	−	8.79409i	−0.202929	−	0.351483i
$627$	1.30445	−	1.49106i	0.0520947	−	0.0595473i
$628$	−1.40567	+	2.43469i	−0.0560923	+	0.0971548i
$629$	36.3032			1.44750
$630$	17.6943	−	1.38212i	0.704959	−	0.0550648i
$631$	−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
$633$	9.01986	+	1.78286i	0.358507	+	0.0708625i
$634$	13.4765	+	23.3419i	0.535219	+	0.927026i
$635$	−13.4919	+	34.0303i	−0.535408	+	1.35045i
$636$	5.96691	+	17.5086i	0.236603	+	0.694261i
$637$	−0.0213638	−	0.176288i	−0.000846466	−	0.00698479i
$638$	−4.10435			−0.162493
$639$	20.1210	+	26.0917i	0.795974	+	1.03217i
$640$	−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	$0.983821\pi$
$642$	−0.960976	−	2.81977i	−0.0379267	−	0.111288i
$643$	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
$645$	−5.64196	−	10.9817i	−0.222152	−	0.432402i
$646$	−2.26900	+	3.93002i	−0.0892725	+	0.154624i
$647$	−5.07916	−	2.93246i	−0.199683	−	0.115287i	0.396825	−	0.917894i	$-0.370112\pi$
$647$	−5.07916	−	2.93246i	−0.199683	−	0.115287i	−0.596507	+	0.802608i	$0.703445\pi$
$648$	2.28744	−	8.70446i	0.0898591	−	0.341943i
$649$	−2.53058	+	1.46103i	−0.0993338	+	0.0573504i
$650$	0.0290792	−	0.123463i	0.00114058	−	0.00484262i
$651$	−5.92025	+	14.1348i	−0.232033	+	0.553985i
$652$	−15.9183	−	9.19043i	−0.623408	−	0.359925i
$653$	−10.1448			−0.396998			−0.198499	−	0.980101i	$-0.563607\pi$
$653$	−10.1448			−0.396998			−0.198499	+	0.980101i	$0.563607\pi$
$654$	−15.4523	+	17.6629i	−0.604233	+	0.690673i
$655$	39.7667	+	15.7662i	1.55381	+	0.616035i
$656$	0.973106	+	1.68547i	0.0379934	+	0.0658065i
$657$	4.99230	+	37.2267i	0.194768	+	1.45235i
$658$	14.8831	+	13.1884i	0.580204	+	0.514136i
$659$	−8.24098	+	4.75793i	−0.321023	+	0.185343i	−0.651849	−	0.758349i	$-0.726006\pi$
$659$	−8.24098	+	4.75793i	−0.321023	+	0.185343i	0.330825	+	0.943692i	$0.392673\pi$
$660$	−1.43572	−	2.79452i	−0.0558853	−	0.108777i
$661$	−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
$663$	−0.106433	−	0.0931123i	−0.00413350	−	0.00361618i
$664$	−14.5567	+	8.40429i	−0.564908	+	0.326150i
$665$	3.76479	+	7.44389i	0.145992	+	0.288662i
$666$	−20.6650	−	26.7971i	−0.800751	−	1.03837i
$667$	15.5099	−	8.95463i	0.600545	−	0.346725i
$668$			8.60738i			0.333029i
$669$	10.5374	−	12.0449i	0.407401	−	0.465683i
$670$	−0.837125	+	2.11147i	−0.0323410	+	0.0815730i
$671$	0.246842	−	0.427542i	0.00952922	−	0.0165051i
$672$	4.22680	+	1.77037i	0.163052	+	0.0682933i
$673$	−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
$675$	−5.93442	−	25.2939i	−0.228416	−	0.973564i
$676$	6.49968	−	11.2578i	0.249988	−	0.432991i
$677$	−31.4385	−	18.1510i	−1.20828	−	0.697601i	−0.245897	−	0.969296i	$-0.579082\pi$
$677$	−31.4385	−	18.1510i	−1.20828	−	0.697601i	−0.962383	+	0.271695i	$0.912416\pi$
$678$	8.22466	−	9.40126i	0.315866	−	0.361053i
$679$	11.2000	−	12.6393i	0.429818	−	0.485051i
$680$	4.46750	+	5.64197i	0.171321	+	0.216360i
$681$	9.67565	−	3.29745i	0.370772	−	0.126359i
$682$	2.71271			0.103875
$683$	−11.4960	+	19.9116i	−0.439882	+	0.761897i	−0.997680	−	0.0680791i	$-0.978313\pi$
$683$	−11.4960	+	19.9116i	−0.439882	+	0.761897i	0.557798	+	0.829977i	$0.311646\pi$
$684$	4.19252	−	0.562239i	0.160305	−	0.0214977i
$685$	33.1567	+	13.1455i	1.26685	+	0.502264i
$686$	16.7349	−	7.93368i	0.638941	−	0.302909i
$687$	−34.0689	+	11.6106i	−1.29981	+	0.442973i
$688$		−	3.18777i		−	0.121533i
$689$	−0.135460	−	0.234624i	−0.00516062	−	0.00893846i
$690$	11.5224	+	7.42782i	0.438649	+	0.282772i
$691$	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
$693$	−3.59180	+	5.34375i	−0.136441	+	0.202992i
$694$	9.89335			0.375546
$695$	8.20481	+	10.3618i	0.311226	+	0.393045i
$696$	−6.59570	−	5.77023i	−0.250009	−	0.218720i
$697$	5.42451	−	3.13184i	0.205468	−	0.118627i
$698$		−	33.7202i		−	1.27633i
$699$	32.1290	−	36.7253i	1.21523	−	1.38908i
$700$	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	$0.658072\pi$
$702$	−0.00814567	+	0.131565i	−0.000307438	+	0.00496562i
$703$	7.95242	−	13.7740i	0.299931	−	0.519496i
$704$		−	0.811199i		−	0.0305732i
$705$	15.7722	−	24.4665i	0.594015	−	0.921461i
$706$	−15.0879	−	8.71103i	−0.567842	−	0.327844i
$707$	15.8426	+	47.4727i	0.595822	+	1.78539i
$708$	−6.12068	−	1.20981i	−0.230029	−	0.0454676i
$709$	−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
$711$	−0.674405	−	5.02892i	−0.0252921	−	0.188599i
$712$	2.31249	+	4.00536i	0.0866644	+	0.150107i
$713$	−10.2511	+	5.91845i	−0.383905	+	0.221648i
$714$	5.69774	−	13.6035i	0.213233	−	0.509098i
$715$	0.0285656	+	0.0360752i	0.00106829	+	0.00134914i
$716$			19.0184i			0.710752i
$717$	−3.03098	+	15.3343i	−0.113194	+	0.572670i
$718$		−	34.4579i		−	1.28596i
$719$	4.05625	+	7.02563i	0.151273	+	0.262012i	0.931696	−	0.363240i	$-0.118330\pi$
$719$	4.05625	+	7.02563i	0.151273	+	0.262012i	−0.780423	+	0.625252i	$0.784996\pi$
$720$	1.62156	−	6.50927i	0.0604321	−	0.242586i
$721$	6.86138	+	20.5603i	0.255531	+	0.765705i
$722$	−8.50593	−	14.7327i	−0.316558	−	0.548294i
$723$	4.03366	−	1.37467i	0.150013	−	0.0511244i
$724$	12.5890	−	7.26828i	0.467868	−	0.270124i
$725$	−24.6242	−	5.79975i	−0.914521	−	0.215397i
$726$	−17.5728	−	3.47344i	−0.652188	−	0.128911i
$727$	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
$729$	10.5125	+	24.8694i	0.389354	+	0.921088i
$730$	4.07678	+	27.6971i	0.150889	+	1.02512i
$731$	−10.2595			−0.379462
$732$	0.997751	−	0.340032i	0.0368779	−	0.0125680i
$733$	−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
$735$	−15.2003	−	22.4489i	−0.560671	−	0.828039i
$736$	1.76983	+	3.06543i	0.0652367	+	0.112993i
$737$	−0.412000	−	0.713605i	−0.0151762	−	0.0262860i
$738$	−5.39956	−	2.22134i	−0.198761	−	0.0817687i
$739$	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
$741$	−0.0586429	+	0.0199854i	−0.00215430	+	0.000734183i
$742$	18.7392	−	21.1472i	0.687937	−	0.776339i
$743$	21.8276	−	37.8065i	0.800777	−	1.38699i	−0.118328	−	0.992975i	$-0.537754\pi$
$743$	21.8276	−	37.8065i	0.800777	−	1.38699i	0.919105	−	0.394012i	$-0.128913\pi$
$744$	4.35934	+	3.81376i	0.159821	+	0.139819i
$745$	9.33692	−	23.5503i	0.342078	−	0.862818i
$746$	18.8999	+	10.9119i	0.691975	+	0.399512i
$747$	19.1848	−	46.6337i	0.701933	−	1.70624i
$748$	−2.61076			−0.0954588
$749$	−3.01796	+	3.40578i	−0.110274	+	0.124444i
$750$	−4.66481	−	18.7947i	−0.170335	−	0.686284i
$751$	−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
$753$	−16.1419	−	47.3650i	−0.588245	−	1.72608i
$754$	0.111157	+	0.0641767i	0.00404811	+	0.00233718i
$755$	25.4864	+	10.1045i	0.927544	+	0.367740i
$756$	−13.2847	+	3.53779i	−0.483161	+	0.128668i
$757$		−	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
$759$	−4.70748	+	1.60430i	−0.170871	+	0.0582326i
$760$	3.11928	−	0.459133i	0.113148	−	0.0166545i
$761$	14.7189			0.533561			0.266781	−	0.963757i	$-0.414040\pi$
$761$	14.7189			0.533561			0.266781	+	0.963757i	$0.414040\pi$
$762$	5.49843	−	27.8176i	0.199187	−	1.00773i
$763$	35.1228	+	7.17460i	1.27153	+	0.259738i
$764$		−	2.54057i		−	0.0919146i
$765$	−20.9494	−	5.21883i	−0.757427	−	0.188687i
$766$	−26.4753	−	15.2855i	−0.956592	−	0.552288i
$767$	0.0913803			0.00329955
$768$	1.14045	−	1.30360i	0.0411525	−	0.0470396i
$769$	−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
$771$	−4.26173	+	1.45239i	−0.153482	+	0.0523067i
$772$	−6.77602	−	3.91214i	−0.243874	−	0.140801i
$773$	−40.9220	−	23.6263i	−1.47186	−	0.849780i	−0.472362	−	0.881405i	$-0.656598\pi$
$773$	−40.9220	−	23.6263i	−1.47186	−	0.849780i	−0.999500	+	0.0316250i	$0.989932\pi$
$774$	5.84005	+	7.57304i	0.209916	+	0.272207i
$775$	16.2751	+	3.83327i	0.584618	+	0.137695i
$776$	−3.19146	−	5.52778i	−0.114567	−	0.198436i
$777$	−19.9695	+	47.6778i	−0.716404	+	1.71043i
$778$	−18.1559	−	10.4823i	−0.650922	−	0.375810i
$779$		−	2.74419i		−	0.0983208i
$780$	−0.00481257	+	0.0981330i	−0.000172318	+	0.00351372i
$781$	−8.90937			−0.318802
$782$	9.86578	−	5.69601i	0.352799	−	0.203689i
$783$	26.2402	+	1.62462i	0.937750	+	0.0580593i
$784$	−0.842147	−	6.94916i	−0.0300767	−	0.248184i
$785$	−0.915435	−	6.21934i	−0.0326733	−	0.221978i
$786$	−32.5068	−	6.42529i	−1.15948	−	0.229183i
$787$	−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
$789$	9.06425	+	26.5971i	0.322696	+	0.946881i
$790$	−0.550729	−	3.74158i	−0.0195941	−	0.133119i
$791$	−18.6945	−	3.81876i	−0.664700	−	0.135780i
$792$	1.48613	+	1.92712i	0.0528073	+	0.0684774i
$793$	−0.0133704	+	0.00771938i	−0.000474795	+	0.000274123i
$794$	31.9031			1.13220
$795$	−34.7641	−	22.4105i	−1.23296	−	0.794818i
$796$			20.2234i			0.716801i
$797$	−20.4799	−	11.8241i	−0.725434	−	0.418830i	0.0913154	−	0.995822i	$-0.470893\pi$
$797$	−20.4799	−	11.8241i	−0.725434	−	0.418830i	−0.816749	+	0.576992i	$0.804226\pi$
$798$	−3.91326	−	5.14174i	−0.138528	−	0.182016i
$799$	−12.0949	−	20.9489i	−0.427885	−	0.741119i
$800$	1.14628	−	4.86683i	0.0405273	−	0.172068i
$801$	−12.8316	−	5.27881i	−0.453381	−	0.186518i
$802$	7.49269	+	4.32591i	0.264576	+	0.152753i
$803$	−8.79552	−	5.07809i	−0.310387	−	0.179202i
$804$	0.341159	−	1.72599i	0.0120318	−	0.0608710i
$805$	1.15865	−	20.9088i	0.0408369	−	0.736939i
$806$	−0.0734680	−	0.0424168i	−0.00258780	−	0.00149407i
$807$	10.3476	+	2.04530i	0.364252	+	0.0719980i
$808$	18.9158			0.665454
$809$	43.8535	+	25.3188i	1.54181	+	0.890162i	0.998725	+	0.0504816i	$0.0160756\pi$
$809$	43.8535	+	25.3188i	1.54181	+	0.890162i	0.543081	+	0.839680i	$0.317258\pi$
$810$	8.07281	+	18.4345i	0.283650	+	0.647721i
$811$		−	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
$813$	−24.5582	−	21.4846i	−0.861293	−	0.753500i
$814$	9.15024			0.320716
$815$	40.6627	−	5.98522i	1.42435	−	0.209653i
$816$	−4.19550	−	3.67042i	−0.146872	−	0.128490i
$817$	−2.24741	+	3.89262i	−0.0786268	+	0.136186i
$818$			25.3709i			0.887073i
$819$	0.180833	−	0.0885616i	0.00631880	−	0.00309459i
$820$	−4.04551	−	1.60391i	−0.141275	−	0.0560109i
$821$	0.761382	+	0.439584i	0.0265724	+	0.0153416i	0.513227	−	0.858253i	$-0.328450\pi$
$821$	0.761382	+	0.439584i	0.0265724	+	0.0153416i	−0.486655	+	0.873594i	$0.661783\pi$
$822$	−27.1036	−	5.35728i	−0.945345	−	0.186857i
$823$	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
$825$	6.39598	+	2.90596i	0.222680	+	0.101173i
$826$	3.01692	+	9.04027i	0.104972	+	0.314551i
$827$	3.54960			0.123432			0.0617159	−	0.998094i	$-0.480343\pi$
$827$	3.54960			0.123432			0.0617159	+	0.998094i	$0.480343\pi$
$828$	−9.82041	−	4.04005i	−0.341283	−	0.140401i
$829$	−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
$831$	28.2593	−	9.63075i	0.980306	−	0.334087i
$832$	−0.0126841	+	0.0219696i	−0.000439743	+	0.000761658i
$833$	−22.3651	+	2.71036i	−0.774906	+	0.0939086i
$834$	−7.70527	−	6.74093i	−0.266812	−	0.233419i
$835$	−11.9480	−	15.0891i	−0.413478	−	0.522178i
$836$	−0.571902	+	0.990563i	−0.0197796	+	0.0342593i
$837$	−17.3431	−	1.07377i	−0.599467	−	0.0371150i
$838$	4.57468	+	7.92357i	0.158030	+	0.273715i
$839$	−1.80168	−	3.12060i	−0.0622009	−	0.107735i	0.833248	−	0.552899i	$-0.186479\pi$
$839$	−1.80168	−	3.12060i	−0.0622009	−	0.107735i	−0.895449	+	0.445164i	$0.853145\pi$
$840$	−9.86720	+	2.76375i	−0.340451	+	0.0953586i
$841$	−1.70019	+	2.94482i	−0.0586273	+	0.101545i
$842$	30.6136			1.05501
$843$	10.1001	+	8.83606i	0.347867	+	0.304330i
$844$	−5.30837			−0.182722
$845$	4.23288	+	28.7576i	0.145615	+	0.989291i
$846$	−8.57860	+	20.8526i	−0.294938	+	0.716926i
$847$	8.66174	+	25.9551i	0.297621	+	0.891827i
$848$	−5.33975	−	9.24872i	−0.183368	−	0.317602i
$849$	−0.882222	+	1.00843i	−0.0302778	+	0.0346092i
$850$	−15.6634	−	3.68920i	−0.537250	−	0.126538i
$851$	−34.5778	+	19.9635i	−1.18531	+	0.684340i
$852$	−14.3174	−	12.5255i	−0.490506	−	0.429118i
$853$	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
$855$	−6.56919	+	6.80531i	−0.224662	+	0.232737i
$856$	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	$0.770689\pi$
$858$	−0.0268264	−	0.0234690i	−0.000915838	−	0.000801218i
$859$		−	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
$861$	1.12922	+	8.84688i	0.0384839	+	0.301501i
$862$	2.69929	−	1.55843i	0.0919380	−	0.0530805i
$863$	26.0756	+	45.1643i	0.887625	+	1.53741i	0.842676	+	0.538422i	$0.180979\pi$
$863$	26.0756	+	45.1643i	0.887625	+	1.53741i	0.0449489	+	0.998989i	$0.485688\pi$
$864$	−0.321097	+	5.18622i	−0.0109239	+	0.176439i
$865$	−5.42128	−	6.84650i	−0.184329	−	0.232788i
$866$	−12.6287	+	21.8735i	−0.429140	+	0.743293i
$867$	7.57478	−	8.65841i	0.257253	−	0.294055i
$868$	1.77075	−	8.66860i	0.0601033	−	0.294231i
$869$	1.18818	+	0.685995i	0.0403062	+	0.0232708i
$870$	19.5723	+	0.959849i	0.663561	+	0.0325419i
$871$			0.0257686i			0.000873137i
$872$	6.77465	−	11.7340i	0.229419	−	0.397365i
$873$	17.7088	+	7.28526i	0.599351	+	0.246569i
$874$		−	4.99097i		−	0.168822i
$875$	−21.4302	+	20.3898i	−0.724474	+	0.689303i
$876$	−6.99523	−	20.5260i	−0.236347	−	0.693509i
$877$			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
$879$	8.87572	−	44.9040i	0.299371	−	1.51458i
$880$	1.12604	+	1.42206i	0.0379586	+	0.0479377i
$881$	−33.1517			−1.11691			−0.558454	−	0.829535i	$-0.688605\pi$
$881$	−33.1517			−1.11691			−0.558454	+	0.829535i	$0.688605\pi$
$882$	14.7316	+	14.9659i	0.496039	+	0.503930i
$883$		−	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
$885$	12.4091	−	6.37535i	0.417129	−	0.214305i
$886$	−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	$0.986045\pi$
$888$	14.7045	+	12.8642i	0.493450	+	0.431693i
$889$	−41.0867	+	13.7115i	−1.37800	+	0.459868i
$890$	−9.61378	−	3.81154i	−0.322255	−	0.127763i
$891$	−7.06105	−	1.85557i	−0.236554	−	0.0621638i
$892$	−4.61986	+	8.00184i	−0.154684	+	0.267921i
$893$	−10.5978			−0.354641
$894$	−3.80514	+	19.2509i	−0.127263	+	0.643848i
$895$	−26.3997	−	33.3400i	−0.882446	−	1.11443i
$896$	−2.59222	−	0.529518i	−0.0866000	−	0.0176900i
$897$	0.152577	+	0.0301584i	0.00509441	+	0.00100696i
$898$	8.51768	+	4.91769i	0.284239	+	0.164105i
$899$	−8.45987	+	14.6529i	−0.282152	+	0.488702i
$900$	6.19294	+	13.6619i	0.206431	+	0.455397i
$901$	−29.7660	+	17.1854i	−0.991651	+	0.572530i
$902$	1.36725	−	0.789382i	0.0455244	−	0.0262835i
$903$	5.64352	−	13.4741i	0.187805	−	0.448389i
$904$	−3.60588	+	6.24558i	−0.119930	+	0.207725i
$905$	−11.9799	+	30.2166i	−0.398224	+	1.00443i
$906$	−20.8335	−	4.11795i	−0.692148	−	0.136810i
$907$			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
$909$	−44.9373	+	34.6540i	−1.49047	+	1.14940i
$910$	0.133927	−	0.0677341i	0.00443962	−	0.00224536i
$911$	−8.52724	+	4.92320i	−0.282520	+	0.163113i	−0.634564	−	0.772871i	$-0.718820\pi$
$911$	−8.52724	+	4.92320i	−0.282520	+	0.163113i	0.352044	+	0.935984i	$0.385487\pi$
$912$	−2.31166	+	0.787812i	−0.0765468	+	0.0260871i
$913$	6.81755	+	11.8083i	0.225628	+	0.390799i
$914$	−19.5871	+	11.3086i	−0.647883	+	0.374055i
$915$	−1.27709	+	1.98108i	−0.0422193	+	0.0654925i
$916$	17.9965	−	10.3903i	0.594621	−	0.343305i
$917$	16.0228	+	48.0127i	0.529120	+	1.58552i
$918$	16.6913	+	1.03342i	0.550896	+	0.0341078i
$919$	−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
$921$	−8.97312	−	26.3297i	−0.295674	−	0.867593i
$922$	32.3935			1.06682
$923$	0.241291	+	0.139310i	0.00794220	+	0.00458543i
$924$	1.43612	−	3.42877i	0.0472448	−	0.112798i
$925$	54.8974	+	12.9300i	1.80501	+	0.425135i
$926$	8.77792	−	5.06793i	0.288460	−	0.166543i
$927$	−19.4622	+	15.0085i	−0.639222	+	0.492945i
$928$	4.38175	+	2.52980i	0.143838	+	0.0830449i
$929$	10.3822	−	17.9825i	0.340628	−	0.589985i	−0.643921	−	0.765092i	$-0.722694\pi$
$929$	10.3822	−	17.9825i	0.340628	−	0.589985i	0.984550	+	0.175106i	$0.0560269\pi$
$930$	−12.9360	−	0.634400i	−0.424189	−	0.0208028i
$931$	−3.87086	+	9.07941i	−0.126862	+	0.297566i
$932$	−14.0861	+	24.3978i	−0.461405	+	0.799178i
$933$	−22.8857	+	26.1596i	−0.749243	+	0.856428i
$934$			8.54166i			0.279492i
$935$	4.57676	−	3.62403i	0.149676	−	0.118518i
$936$	−0.0101155	−	0.0754296i	−0.000330636	−	0.00246549i
$937$	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
$939$	−17.2544	−	3.41049i	−0.563075	−	0.111297i
$940$	−6.19414	+	15.6234i	−0.202031	+	0.509578i
$941$	13.7232	+	23.7693i	0.447364	+	0.774858i	0.998214	−	0.0597471i	$-0.0190294\pi$
$941$	13.7232	+	23.7693i	0.447364	+	0.774858i	−0.550849	+	0.834605i	$0.685696\pi$
$942$	1.57077	+	4.60908i	0.0511784	+	0.150172i
$943$	−3.44446	+	5.96598i	−0.112167	+	0.194279i
$944$	3.60215			0.117240
$945$	18.3778	−	24.6426i	0.597830	−	0.801623i
$946$	−2.58592			−0.0840754
$947$	−22.1365	+	38.3415i	−0.719338	+	1.24593i	0.241924	+	0.970295i	$0.422221\pi$
$947$	−22.1365	+	38.3415i	−0.719338	+	1.24593i	−0.961262	+	0.275635i	$0.911112\pi$
$948$	0.944980	+	2.77284i	0.0306915	+	0.0900576i
$949$	0.158805	+	0.275059i	0.00515503	+	0.00892878i
$950$	−4.83089	+	5.13479i	−0.156735	+	0.166595i
$951$	45.7978	+	9.05238i	1.48509	+	0.293543i
$952$	−1.70420	+	8.34280i	−0.0552335	+	0.270392i
$953$	23.6733			0.766855			0.383427	−	0.923571i	$-0.374744\pi$
$953$	23.6733			0.766855			0.383427	+	0.923571i	$0.374744\pi$
$954$	29.6292	+	12.1892i	0.959280	+	0.394641i
$955$	3.52660	+	4.45371i	0.114118	+	0.144119i
$956$		−	9.02455i		−	0.291875i
$957$	−4.68080	+	5.35042i	−0.151309	+	0.172955i
$958$	−9.04091	+	15.6593i	−0.292099	+	0.505930i
$959$	13.3595	+	40.0320i	0.431401	+	1.29270i
$960$	−0.189708	+	3.86833i	−0.00612281	+	0.124850i
$961$	−9.90856	+	17.1621i	−0.319631	+	0.553617i
$962$	−0.247815	−	0.143076i	−0.00798986	−	0.00461295i
$963$	−4.77180	−	1.96308i	−0.153769	−	0.0632595i
$964$	−2.13074	+	1.23018i	−0.0686264	+	0.0396214i
$965$	17.3091	−	2.54776i	0.557200	−	0.0820152i
$966$	2.05377	+	16.0902i	0.0660789	+	0.517694i
$967$	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
$969$	2.53549	+	7.43985i	0.0814518	+	0.239002i
$970$	13.2679	+	5.26029i	0.426008	+	0.168898i
$971$	−6.17807	−	10.7007i	−0.198264	−	0.343403i	0.749702	−	0.661776i	$-0.230197\pi$
$971$	−6.17807	−	10.7007i	−0.198264	−	0.343403i	−0.947966	+	0.318373i	$0.896864\pi$
$972$	−8.73843	−	12.9089i	−0.280285	−	0.414053i
$973$	−3.12986	+	15.3220i	−0.100339	+	0.491201i
$974$	30.5288	−	17.6258i	0.978205	−	0.564767i
$975$	−0.127783	−	0.178711i	−0.00409233	−	0.00572334i
$976$	−0.527050	+	0.304293i	−0.0168705	+	0.00974017i
$977$	4.18162	+	7.24278i	0.133782	+	0.231717i	0.925132	−	0.379647i	$-0.123954\pi$
$977$	4.18162	+	7.24278i	0.133782	+	0.231717i	−0.791350	+	0.611364i	$0.790621\pi$
$978$	−30.1347	+	10.2699i	−0.963600	+	0.328394i
$979$	3.24914	−	1.87589i	0.103843	−	0.0599538i
$980$	11.1225	+	11.0131i	0.355296	+	0.351802i
$981$	5.40273	+	40.2873i	0.172496	+	1.28627i
$982$	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	$-0.181305\pi$
$984$	3.30695	+	0.653652i	0.105422	+	0.0208377i
$985$	4.72881	+	1.87482i	0.150673	+	0.0597366i
$986$	8.14191	−	14.1022i	0.259291	−	0.449106i
$987$	34.1658	−	4.36095i	1.08751	−	0.138811i
$988$	0.0309774	−	0.0178848i	0.000985524	−	0.000568993i
$989$	9.77190	−	5.64181i	0.310728	−	0.179399i
$990$	−5.28031	−	1.31541i	−0.167819	−	0.0418064i
$991$	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
$993$	−34.2900	−	6.77775i	−1.08816	−	0.215085i
$994$	−5.81569	+	28.4703i	−0.184462	+	0.903023i
$995$	−28.0724	−	35.4524i	−0.889955	−	1.12392i
$996$	−5.64531	+	28.5607i	−0.178879	+	0.904982i
$997$	−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
$999$	−58.5001	−	3.62194i	−1.85086	−	0.114593i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.558726 + 1.63946i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.07866 + 0.824119i) q^{5} +(-1.69918 - 0.335859i) q^{6} +(0.837534 + 2.50969i) q^{7} +1.00000 q^{8} +(-2.37565 + 1.83202i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.558726 + 1.63946i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.07866 + 0.824119i) q^{5} +(-1.69918 - 0.335859i) q^{6} +(0.837534 + 2.50969i) q^{7} +1.00000 q^{8} +(-2.37565 + 1.83202i) q^{9} +(-1.75304 + 1.38811i) q^{10} -0.811199i q^{11} +(1.14045 - 1.30360i) q^{12} +(-0.0126841 + 0.0219696i) q^{13} +(-2.59222 - 0.529518i) q^{14} +(-0.189708 + 3.86833i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.78721 + 1.60920i) q^{17} +(-0.398746 - 2.97338i) q^{18} +(1.22111 - 0.705008i) q^{19} +(-0.325622 - 2.21223i) q^{20} +(-3.64658 + 2.77533i) q^{21} +(0.702519 + 0.405599i) q^{22} -3.53966 q^{23} +(0.558726 + 1.63946i) q^{24} +(3.64166 + 3.42613i) q^{25} +(-0.0126841 - 0.0219696i) q^{26} +(-4.33085 - 2.87119i) q^{27} +(1.75469 - 1.98017i) q^{28} +(-4.38175 + 2.52980i) q^{29} +(-3.25522 - 2.09846i) q^{30} +(2.89606 - 1.67204i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.32993 - 0.453237i) q^{33} +(-2.78721 + 1.60920i) q^{34} +(-0.327333 + 5.90702i) q^{35} +(2.77440 + 1.14137i) q^{36} +(9.76868 - 5.63995i) q^{37} +1.41002i q^{38} +(-0.0431052 - 0.00852016i) q^{39} +(2.07866 + 0.824119i) q^{40} +(0.973106 - 1.68547i) q^{41} +(-0.580217 - 4.54570i) q^{42} +(-2.76069 + 1.59389i) q^{43} +(-0.702519 + 0.405599i) q^{44} +(-6.44797 + 1.85032i) q^{45} +(1.76983 - 3.06543i) q^{46} +(-6.50911 - 3.75804i) q^{47} +(-1.69918 - 0.335859i) q^{48} +(-5.59707 + 4.20390i) q^{49} +(-4.78794 + 1.44070i) q^{50} +(-1.08093 + 5.46862i) q^{51} +0.0253683 q^{52} +(-5.33975 + 9.24872i) q^{53} +(4.65195 - 2.31503i) q^{54} +(0.668524 - 1.68621i) q^{55} +(0.837534 + 2.50969i) q^{56} +(1.83810 + 1.60805i) q^{57} -5.05961i q^{58} +(-1.80107 - 3.11955i) q^{59} +(3.44493 - 1.76987i) q^{60} +(0.527050 + 0.304293i) q^{61} +3.34408i q^{62} +(-6.58748 - 4.42777i) q^{63} +1.00000 q^{64} +(-0.0444715 + 0.0352140i) q^{65} +(-0.272448 + 1.37837i) q^{66} +(0.879693 - 0.507891i) q^{67} -3.21840i q^{68} +(-1.97770 - 5.80312i) q^{69} +(-4.95196 - 3.23699i) q^{70} -10.9830i q^{71} +(-2.37565 + 1.83202i) q^{72} +(6.25999 - 10.8426i) q^{73} +11.2799i q^{74} +(-3.58231 + 7.88461i) q^{75} +(-1.22111 - 0.705008i) q^{76} +(2.03586 - 0.679406i) q^{77} +(0.0289313 - 0.0330701i) q^{78} +(-0.845656 + 1.46472i) q^{79} +(-1.75304 + 1.38811i) q^{80} +(2.28744 - 8.70446i) q^{81} +(0.973106 + 1.68547i) q^{82} +(-14.5567 + 8.40429i) q^{83} +(4.22680 + 1.77037i) q^{84} +(4.46750 + 5.64197i) q^{85} -3.18777i q^{86} +(-6.59570 - 5.77023i) q^{87} -0.811199i q^{88} +(2.31249 + 4.00536i) q^{89} +(1.62156 - 6.50927i) q^{90} +(-0.0657602 - 0.0134330i) q^{91} +(1.76983 + 3.06543i) q^{92} +(4.35934 + 3.81376i) q^{93} +(6.50911 - 3.75804i) q^{94} +(3.11928 - 0.459133i) q^{95} +(1.14045 - 1.30360i) q^{96} +(-3.19146 - 5.52778i) q^{97} +(-0.842147 - 6.94916i) q^{98} +(1.48613 + 1.92712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32} + 24 q^{33} + 18 q^{35} + 3 q^{41} + 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} + 42 q^{55} - 22 q^{57} - q^{60} - 9 q^{61} - 10 q^{63} + 48 q^{64} - 33 q^{65} - 24 q^{66} - 33 q^{67} + 42 q^{69} - 6 q^{70} + 3 q^{72} + 18 q^{73} + 9 q^{75} + 6 q^{77} - 18 q^{78} - 37 q^{81} + 3 q^{82} - 9 q^{83} - 13 q^{84} - 33 q^{85} - 18 q^{87} + 33 q^{89} + 39 q^{90} + 3 q^{92} - 32 q^{93} + 33 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^14 - 4 * q^15 - 24 * q^16 - 3 * q^18 + 5 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 3 * q^28 - 3 * q^29 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * q^35 + 3 * q^41 + 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 + 42 * q^55 - 22 * q^57 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * q^75 + 6 * q^77 - 18 * q^78 - 37 * q^81 + 3 * q^82 - 9 * q^83 - 13 * q^84 - 33 * q^85 - 18 * q^87 + 33 * q^89 + 39 * q^90 + 3 * q^92 - 32 * q^93 + 33 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 26 * q^99

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