LMFDB - Embedded newform 71.2.c.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(5,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("71.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.c (of order $5$, degree $4$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + \cdots + 961 $ x^20 - 6x^19 + 28x^18 - 91x^17 + 268x^16 - 604x^15 + 1278x^14 - 1990x^13 + 3162x^12 - 4046x^11 + 6406x^10 - 8426x^9 + 12709x^8 - 13621x^7 + 17787x^6 - 13514x^5 + 9316x^4 - 1639x^3 - 228x^2 + 620*x + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.1
Root			$0.699129 - 2.15170i$ of defining polynomial
Character	$\chi$	$=$	71.5
Dual form			71.2.c.a.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.699129 - 2.15170i) q^{2} +(-0.874263 - 2.69071i) q^{3} +(-2.52299 + 1.83306i) q^{4} +(3.04432 + 2.21183i) q^{5} +(-5.17837 + 3.76230i) q^{6} +(-0.0944386 - 0.290652i) q^{7} +(2.04740 + 1.48752i) q^{8} +(-4.04851 + 2.94142i) q^{9} +O(q^{10})$	\(q+(-0.699129 - 2.15170i) q^{2} +(-0.874263 - 2.69071i) q^{3} +(-2.52299 + 1.83306i) q^{4} +(3.04432 + 2.21183i) q^{5} +(-5.17837 + 3.76230i) q^{6} +(-0.0944386 - 0.290652i) q^{7} +(2.04740 + 1.48752i) q^{8} +(-4.04851 + 2.94142i) q^{9} +(2.63081 - 8.09681i) q^{10} +(0.449733 + 1.38413i) q^{11} +(7.13798 + 5.18605i) q^{12} +(1.46929 - 4.52202i) q^{13} +(-0.559371 + 0.406407i) q^{14} +(3.28984 - 10.1251i) q^{15} +(-0.158089 + 0.486547i) q^{16} +(-1.53712 + 4.73076i) q^{17} +(9.15947 + 6.65475i) q^{18} +(-0.873269 - 2.68765i) q^{19} -11.7352 q^{20} +(-0.699495 + 0.508213i) q^{21} +(2.66382 - 1.93538i) q^{22} +2.29768 q^{23} +(2.21252 - 6.80944i) q^{24} +(2.83061 + 8.71172i) q^{25} -10.7573 q^{26} +(4.58740 + 3.33294i) q^{27} +(0.771050 + 0.560201i) q^{28} +(2.50006 + 1.81640i) q^{29} -24.0861 q^{30} +(0.352558 + 1.08506i) q^{31} +6.21888 q^{32} +(3.33111 - 2.42020i) q^{33} +11.2538 q^{34} +(0.355371 - 1.09372i) q^{35} +(4.82257 - 14.8423i) q^{36} -1.09670 q^{37} +(-5.17247 + 3.75802i) q^{38} -13.4520 q^{39} +(2.94279 + 9.05699i) q^{40} -6.01914 q^{41} +(1.58256 + 1.14980i) q^{42} +(-2.12616 - 1.54474i) q^{43} +(-3.67187 - 2.66777i) q^{44} -18.8309 q^{45} +(-1.60637 - 4.94390i) q^{46} +(-1.43593 + 4.41933i) q^{47} +1.44736 q^{48} +(5.58756 - 4.05960i) q^{49} +(16.7660 - 12.1812i) q^{50} +14.0729 q^{51} +(4.58212 + 14.1023i) q^{52} +(-1.35241 - 0.982584i) q^{53} +(3.96430 - 12.2009i) q^{54} +(-1.69234 + 5.20848i) q^{55} +(0.238998 - 0.735561i) q^{56} +(-6.46820 + 4.69942i) q^{57} +(2.16048 - 6.64926i) q^{58} +(10.6813 + 7.76045i) q^{59} +(10.2597 + 31.5760i) q^{60} +(-1.17884 + 3.62810i) q^{61} +(2.08824 - 1.51720i) q^{62} +(1.23726 + 0.898925i) q^{63} +(-4.03162 - 12.4081i) q^{64} +(14.4749 - 10.5166i) q^{65} +(-7.53641 - 5.47552i) q^{66} +(-12.2439 + 8.89568i) q^{67} +(-4.79364 - 14.7533i) q^{68} +(-2.00877 - 6.18237i) q^{69} -2.60180 q^{70} +(-8.04988 + 2.48988i) q^{71} -12.6644 q^{72} +(-3.17629 - 9.77562i) q^{73} +(0.766733 + 2.35976i) q^{74} +(20.9660 - 15.2327i) q^{75} +(7.12986 + 5.18015i) q^{76} +(0.359829 - 0.261431i) q^{77} +(9.40467 + 28.9446i) q^{78} +(-7.69667 - 5.59196i) q^{79} +(-1.55743 + 1.13154i) q^{80} +(0.318187 - 0.979278i) q^{81} +(4.20816 + 12.9514i) q^{82} +(2.58105 + 1.87524i) q^{83} +(0.833235 - 2.56443i) q^{84} +(-15.1431 + 11.0021i) q^{85} +(-1.83737 + 5.65483i) q^{86} +(2.70168 - 8.31493i) q^{87} +(-1.13815 + 3.50287i) q^{88} +(-4.87553 - 3.54228i) q^{89} +(13.1652 + 40.5183i) q^{90} -1.45309 q^{91} +(-5.79701 + 4.21178i) q^{92} +(2.61135 - 1.89726i) q^{93} +10.5130 q^{94} +(3.28610 - 10.1136i) q^{95} +(-5.43694 - 16.7332i) q^{96} +9.88821 q^{97} +(-12.6415 - 9.18456i) q^{98} +(-5.89206 - 4.28083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.699129	−	2.15170i	−0.494359	−	1.52148i	−0.817953	−	0.575285i	$-0.804891\pi$
$2$	−0.699129	−	2.15170i	−0.494359	−	1.52148i	0.323594	−	0.946196i	$-0.395109\pi$
$3$	−0.874263	−	2.69071i	−0.504756	−	1.55348i	−0.801180	−	0.598423i	$-0.795794\pi$
$3$	−0.874263	−	2.69071i	−0.504756	−	1.55348i	0.296424	−	0.955057i	$-0.404206\pi$
$4$	−2.52299	+	1.83306i	−1.26150	+	0.916530i
$5$	3.04432	+	2.21183i	1.36146	+	0.989159i	0.998351	+	0.0574124i	$0.0182850\pi$
$5$	3.04432	+	2.21183i	1.36146	+	0.989159i	0.363110	+	0.931746i	$0.381715\pi$
$6$	−5.17837	+	3.76230i	−2.11406	+	1.53595i
$7$	−0.0944386	−	0.290652i	−0.0356944	−	0.109856i	0.931622	−	0.363429i	$-0.118394\pi$
$7$	−0.0944386	−	0.290652i	−0.0356944	−	0.109856i	−0.967316	+	0.253573i	$0.918394\pi$
$8$	2.04740	+	1.48752i	0.723865	+	0.525919i
$9$	−4.04851	+	2.94142i	−1.34950	+	0.980472i
$10$	2.63081	−	8.09681i	0.831936	−	2.56043i
$11$	0.449733	+	1.38413i	0.135599	+	0.417332i	0.995683	−	0.0928213i	$-0.0295885\pi$
$11$	0.449733	+	1.38413i	0.135599	+	0.417332i	−0.860083	+	0.510154i	$0.829589\pi$
$12$	7.13798	+	5.18605i	2.06056	+	1.49708i
$13$	1.46929	−	4.52202i	0.407509	−	1.25418i	−0.511274	−	0.859418i	$-0.670826\pi$
$13$	1.46929	−	4.52202i	0.407509	−	1.25418i	0.918782	−	0.394765i	$-0.129174\pi$
$14$	−0.559371	+	0.406407i	−0.149498	+	0.108617i
$15$	3.28984	−	10.1251i	0.849433	−	2.61429i
$16$	−0.158089	+	0.486547i	−0.0395221	+	0.121637i
$17$	−1.53712	+	4.73076i	−0.372806	+	1.14738i	0.572141	+	0.820155i	$0.306113\pi$
$17$	−1.53712	+	4.73076i	−0.372806	+	1.14738i	−0.944947	+	0.327223i	$0.893887\pi$
$18$	9.15947	+	6.65475i	2.15891	+	1.56854i
$19$	−0.873269	−	2.68765i	−0.200342	−	0.616588i	−0.999873	−	0.0159632i	$-0.994919\pi$
$19$	−0.873269	−	2.68765i	−0.200342	−	0.616588i	0.799531	−	0.600625i	$-0.205081\pi$
$20$	−11.7352			−2.62407
$21$	−0.699495	+	0.508213i	−0.152642	+	0.110901i
$22$	2.66382	−	1.93538i	0.567928	−	0.412624i
$23$	2.29768			0.479098			0.239549	−	0.970884i	$-0.423000\pi$
$23$	2.29768			0.479098			0.239549	+	0.970884i	$0.423000\pi$
$24$	2.21252	−	6.80944i	0.451629	−	1.38997i
$25$	2.83061	+	8.71172i	0.566122	+	1.74234i
$26$	−10.7573			−2.10967
$27$	4.58740	+	3.33294i	0.882845	+	0.641425i
$28$	0.771050	+	0.560201i	0.145715	+	0.105868i
$29$	2.50006	+	1.81640i	0.464249	+	0.337297i	0.795196	−	0.606353i	$-0.207368\pi$
$29$	2.50006	+	1.81640i	0.464249	+	0.337297i	−0.330947	+	0.943649i	$0.607368\pi$
$30$	−24.0861			−4.39751
$31$	0.352558	+	1.08506i	0.0633212	+	0.194883i	0.977712	−	0.209949i	$-0.0673299\pi$
$31$	0.352558	+	1.08506i	0.0633212	+	0.194883i	−0.914391	+	0.404832i	$0.867330\pi$
$32$	6.21888			1.09935
$33$	3.33111	−	2.42020i	0.579873	−	0.421302i
$34$	11.2538			1.93001
$35$	0.355371	−	1.09372i	0.0600686	−	0.184872i
$36$	4.82257	−	14.8423i	0.803761	−	2.47372i
$37$	−1.09670			−0.180296			−0.0901480	−	0.995928i	$-0.528734\pi$
$37$	−1.09670			−0.180296			−0.0901480	+	0.995928i	$0.528734\pi$
$38$	−5.17247	+	3.75802i	−0.839086	+	0.609632i
$39$	−13.4520			−2.15404
$40$	2.94279	+	9.05699i	0.465297	+	1.43204i
$41$	−6.01914			−0.940032			−0.470016	−	0.882658i	$-0.655752\pi$
$41$	−6.01914			−0.940032			−0.470016	+	0.882658i	$0.655752\pi$
$42$	1.58256	+	1.14980i	0.244194	+	0.177417i
$43$	−2.12616	−	1.54474i	−0.324236	−	0.235571i	0.413745	−	0.910393i	$-0.364221\pi$
$43$	−2.12616	−	1.54474i	−0.324236	−	0.235571i	−0.737981	+	0.674822i	$0.764221\pi$
$44$	−3.67187	−	2.66777i	−0.553556	−	0.402182i
$45$	−18.8309			−2.80714
$46$	−1.60637	−	4.94390i	−0.236847	−	0.728939i
$47$	−1.43593	+	4.41933i	−0.209452	+	0.644626i	0.790049	+	0.613043i	$0.210055\pi$
$47$	−1.43593	+	4.41933i	−0.209452	+	0.644626i	−0.999501	+	0.0315828i	$0.989945\pi$
$48$	1.44736			0.208909
$49$	5.58756	−	4.05960i	0.798223	−	0.579943i
$50$	16.7660	−	12.1812i	2.37108	−	1.72269i
$51$	14.0729			1.97060
$52$	4.58212	+	14.1023i	0.635426	+	1.95564i
$53$	−1.35241	−	0.982584i	−0.185768	−	0.134968i	0.491015	−	0.871151i	$-0.336626\pi$
$53$	−1.35241	−	0.982584i	−0.185768	−	0.134968i	−0.676782	+	0.736183i	$0.736626\pi$
$54$	3.96430	−	12.2009i	0.539473	−	1.66033i
$55$	−1.69234	+	5.20848i	−0.228195	+	0.702311i
$56$	0.238998	−	0.735561i	0.0319375	−	0.0982934i
$57$	−6.46820	+	4.69942i	−0.856734	+	0.622453i
$58$	2.16048	−	6.64926i	0.283684	−	0.873091i
$59$	10.6813	+	7.76045i	1.39059	+	1.01032i	0.995800	+	0.0915546i	$0.0291836\pi$
$59$	10.6813	+	7.76045i	1.39059	+	1.01032i	0.394793	+	0.918770i	$0.370816\pi$
$60$	10.2597	+	31.5760i	1.32452	+	4.07644i
$61$	−1.17884	+	3.62810i	−0.150935	+	0.464531i	−0.997726	−	0.0673945i	$-0.978531\pi$
$61$	−1.17884	+	3.62810i	−0.150935	+	0.464531i	0.846791	+	0.531926i	$0.178531\pi$
$62$	2.08824	−	1.51720i	0.265207	−	0.192684i
$63$	1.23726	+	0.898925i	0.155881	+	0.113254i
$64$	−4.03162	−	12.4081i	−0.503953	−	1.55101i
$65$	14.4749	−	10.5166i	1.79539	−	1.30443i
$66$	−7.53641	−	5.47552i	−0.927668	−	0.673990i
$67$	−12.2439	+	8.89568i	−1.49582	+	1.08678i	−0.523817	+	0.851831i	$0.675492\pi$
$67$	−12.2439	+	8.89568i	−1.49582	+	1.08678i	−0.972008	+	0.234949i	$0.924508\pi$
$68$	−4.79364	−	14.7533i	−0.581314	−	1.78910i
$69$	−2.00877	−	6.18237i	−0.241828	−	0.744270i
$70$	−2.60180			−0.310975
$71$	−8.04988	+	2.48988i	−0.955344	+	0.295495i
$71$	−8.04988	+	2.48988i	−0.955344	+	0.295495i
$72$	−12.6644			−1.49251
$73$	−3.17629	−	9.77562i	−0.371757	−	1.14415i	−0.945641	−	0.325213i	$-0.894564\pi$
$73$	−3.17629	−	9.77562i	−0.371757	−	1.14415i	0.573884	−	0.818937i	$-0.305436\pi$
$74$	0.766733	+	2.35976i	0.0891309	+	0.274317i
$75$	20.9660	−	15.2327i	2.42094	−	1.75892i
$76$	7.12986	+	5.18015i	0.817852	+	0.594204i
$77$	0.359829	−	0.261431i	0.0410064	−	0.0297929i
$78$	9.40467	+	28.9446i	1.06487	+	3.27733i
$79$	−7.69667	−	5.59196i	−0.865943	−	0.629144i	0.0635522	−	0.997979i	$-0.479757\pi$
$79$	−7.69667	−	5.59196i	−0.865943	−	0.629144i	−0.929495	+	0.368834i	$0.879757\pi$
$80$	−1.55743	+	1.13154i	−0.174126	+	0.126510i
$81$	0.318187	−	0.979278i	0.0353541	−	0.108809i
$82$	4.20816	+	12.9514i	0.464713	+	1.43024i
$83$	2.58105	+	1.87524i	0.283307	+	0.205834i	0.720358	−	0.693602i	$-0.243977\pi$
$83$	2.58105	+	1.87524i	0.283307	+	0.205834i	−0.437052	+	0.899436i	$0.643977\pi$
$84$	0.833235	−	2.56443i	0.0909133	−	0.279802i
$85$	−15.1431	+	11.0021i	−1.64250	+	1.19335i
$86$	−1.83737	+	5.65483i	−0.198128	+	0.609776i
$87$	2.70168	−	8.31493i	0.289651	−	0.891454i
$88$	−1.13815	+	3.50287i	−0.121327	+	0.373407i
$89$	−4.87553	−	3.54228i	−0.516805	−	0.375481i	0.298594	−	0.954380i	$-0.403482\pi$
$89$	−4.87553	−	3.54228i	−0.516805	−	0.375481i	−0.815399	+	0.578899i	$0.803482\pi$
$90$	13.1652	+	40.5183i	1.38773	+	4.27101i
$91$	−1.45309			−0.152325
$92$	−5.79701	+	4.21178i	−0.604380	+	0.439108i
$93$	2.61135	−	1.89726i	0.270785	−	0.196737i
$94$	10.5130			1.08433
$95$	3.28610	−	10.1136i	0.337146	−	1.03763i
$96$	−5.43694	−	16.7332i	−0.554905	−	1.70782i
$97$	9.88821			1.00400			0.501998	−	0.864869i	$-0.332599\pi$
$97$	9.88821			1.00400			0.501998	+	0.864869i	$0.332599\pi$
$98$	−12.6415	−	9.18456i	−1.27698	−	0.927780i
$99$	−5.89206	−	4.28083i	−0.592175	−	0.430240i
$100$	−23.1107	−	16.7909i	−2.31107	−	1.67909i
$101$	9.13241			0.908709			0.454354	−	0.890821i	$-0.349870\pi$
$101$	9.13241			0.908709			0.454354	+	0.890821i	$0.349870\pi$
$102$	−9.83880	−	30.2807i	−0.974186	−	2.99824i
$103$	−7.31852			−0.721115			−0.360558	−	0.932737i	$-0.617414\pi$
$103$	−7.31852			−0.721115			−0.360558	+	0.932737i	$0.617414\pi$
$104$	9.73484	−	7.07278i	0.954580	−	0.693543i
$105$	−3.25356			−0.317515
$106$	−1.16871	+	3.59693i	−0.113516	+	0.349365i
$107$	0.569166	−	1.75171i	0.0550233	−	0.169344i	−0.919768	−	0.392462i	$-0.871623\pi$
$107$	0.569166	−	1.75171i	0.0550233	−	0.169344i	0.974792	+	0.223118i	$0.0716234\pi$
$108$	−17.6834			−1.70159
$109$	−6.59507	+	4.79160i	−0.631694	+	0.458952i	−0.856987	−	0.515339i	$-0.827666\pi$
$109$	−6.59507	+	4.79160i	−0.631694	+	0.458952i	0.225293	+	0.974291i	$0.427666\pi$
$110$	12.3902			1.18136
$111$	0.958803	+	2.95089i	0.0910055	+	0.280086i
$112$	0.156345			0.0147732
$113$	−13.7579	−	9.99568i	−1.29423	−	0.940315i	−0.294351	−	0.955697i	$-0.595103\pi$
$113$	−13.7579	−	9.99568i	−1.29423	−	0.940315i	−0.999882	+	0.0153827i	$0.995103\pi$
$114$	14.6338	+	10.6321i	1.37058	+	0.995788i
$115$	6.99485	+	5.08206i	0.652273	+	0.473904i
$116$	−9.63718			−0.894790
$117$	7.35269	+	22.6293i	0.679757	+	2.09208i
$118$	9.23051	−	28.4086i	0.849737	−	2.61522i
$119$	1.52017			0.139354
$120$	21.7969	−	15.8364i	1.98978	−	1.44566i
$121$	7.18562	−	5.22066i	0.653238	−	0.474605i
$122$	8.63075			0.781391
$123$	5.26232	+	16.1957i	0.474487	+	1.46032i
$124$	−2.87848	−	2.09134i	−0.258495	−	0.187808i
$125$	−4.83741	+	14.8880i	−0.432671	+	1.33162i
$126$	1.06921	−	3.29068i	0.0952526	−	0.293157i
$127$	4.88548	−	15.0360i	0.433516	−	1.33423i	−0.461083	−	0.887357i	$-0.652539\pi$
$127$	4.88548	−	15.0360i	0.433516	−	1.33423i	0.894599	−	0.446869i	$-0.147461\pi$
$128$	−13.8174	+	10.0389i	−1.22130	+	0.887325i
$129$	−2.29763	+	7.07138i	−0.202295	+	0.622600i
$130$	−32.7485	−	23.7932i	−2.87223	−	2.08680i
$131$	−3.18326	−	9.79708i	−0.278123	−	0.855975i	−0.988376	−	0.152028i	$-0.951419\pi$
$131$	−3.18326	−	9.79708i	−0.278123	−	0.855975i	0.710253	−	0.703946i	$-0.248581\pi$
$132$	−3.96801	+	12.2123i	−0.345371	+	1.06294i
$133$	−0.698699	+	0.507635i	−0.0605849	+	0.0440175i
$134$	27.7009	+	20.1258i	2.39299	+	1.73861i
$135$	6.59362	+	20.2931i	0.567488	+	1.74655i
$136$	−10.1842	+	7.39926i	−0.873289	+	0.634482i
$137$	−2.13373	−	1.55024i	−0.182297	−	0.132446i	0.492894	−	0.870089i	$-0.335939\pi$
$137$	−2.13373	−	1.55024i	−0.182297	−	0.132446i	−0.675191	+	0.737643i	$0.735939\pi$
$138$	−11.8982	+	8.64455i	−1.01284	+	0.735873i
$139$	5.73840	+	17.6610i	0.486725	+	1.49798i	0.829467	+	0.558555i	$0.188644\pi$
$139$	5.73840	+	17.6610i	0.486725	+	1.49798i	−0.342743	+	0.939429i	$0.611356\pi$
$140$	1.10825	+	3.41086i	0.0936646	+	0.288270i
$141$	13.1465			1.10714
$142$	10.9854	+	15.5802i	0.921872	+	1.30746i
$143$	6.91987			0.578669
$144$	−0.791112	−	2.43479i	−0.0659260	−	0.202899i
$145$	3.59341	+	11.0594i	0.298417	+	0.918432i
$146$	−18.8135	+	13.6688i	−1.55702	+	1.13124i
$147$	−15.8082	−	11.4853i	−1.30384	−	0.947293i
$148$	2.76696	−	2.01031i	0.227443	−	0.165247i
$149$	1.75596	+	5.40428i	0.143854	+	0.442736i	0.996862	−	0.0791618i	$-0.0252244\pi$
$149$	1.75596	+	5.40428i	0.143854	+	0.442736i	−0.853008	+	0.521897i	$0.825224\pi$
$150$	−47.4341	−	34.4629i	−3.87297	−	2.81388i
$151$	2.68036	−	1.94740i	0.218125	−	0.158477i	−0.473357	−	0.880870i	$-0.656958\pi$
$151$	2.68036	−	1.94740i	0.218125	−	0.158477i	0.691482	+	0.722394i	$0.256958\pi$
$152$	2.21000	−	6.80169i	0.179255	−	0.551690i
$153$	−7.69210	−	23.6738i	−0.621869	−	1.91392i
$154$	−0.814089	−	0.591470i	−0.0656011	−	0.0476620i
$155$	−1.32667	+	4.08307i	−0.106561	+	0.327960i
$156$	33.9392	−	24.6583i	2.71731	−	1.97424i
$157$	−4.09150	+	12.5924i	−0.326537	+	1.00498i	0.644204	+	0.764853i	$0.277189\pi$
$157$	−4.09150	+	12.5924i	−0.326537	+	1.00498i	−0.970742	+	0.240126i	$0.922811\pi$
$158$	−6.65124	+	20.4704i	−0.529144	+	1.62854i
$159$	−1.46148	+	4.49798i	−0.115903	+	0.356713i
$160$	18.9322	+	13.7551i	1.49673	+	1.08743i
$161$	−0.216989	−	0.667824i	−0.0171011	−	0.0526319i
$162$	−2.32956			−0.183028
$163$	8.82889	−	6.41457i	0.691532	−	0.502428i	−0.185631	−	0.982619i	$-0.559433\pi$
$163$	8.82889	−	6.41457i	0.691532	−	0.502428i	0.877163	+	0.480192i	$0.159433\pi$
$164$	15.1862	−	11.0334i	1.18585	−	0.861567i
$165$	15.4940			1.20621
$166$	2.23047	−	6.86467i	0.173118	−	0.532802i
$167$	−2.62354	−	8.07444i	−0.203016	−	0.624819i	−0.999789	−	0.0205402i	$-0.993461\pi$
$167$	−2.62354	−	8.07444i	−0.203016	−	0.624819i	0.796773	−	0.604279i	$-0.206539\pi$
$168$	−2.18812			−0.168818
$169$	−7.77262	−	5.64714i	−0.597894	−	0.434395i
$170$	34.2602	+	24.8915i	2.62764	+	1.90909i
$171$	11.4409	+	8.31232i	0.874909	+	0.635659i
$172$	8.19589			0.624931
$173$	2.09031	+	6.43331i	0.158923	+	0.489115i	0.998537	−	0.0540681i	$-0.0172188\pi$
$173$	2.09031	+	6.43331i	0.158923	+	0.489115i	−0.839614	+	0.543183i	$0.817219\pi$
$174$	−19.7800			−1.49952
$175$	2.26476	−	1.64544i	0.171200	−	0.124384i
$176$	−0.744543			−0.0561221
$177$	11.5428	−	35.5250i	0.867609	−	2.67023i
$178$	−4.21330	+	12.9672i	−0.315800	+	0.971932i
$179$	−15.6928			−1.17294			−0.586468	−	0.809973i	$-0.699482\pi$
$179$	−15.6928			−1.17294			−0.586468	+	0.809973i	$0.699482\pi$
$180$	47.5101	−	34.5181i	3.54119	−	2.57283i
$181$	13.0230			0.967988			0.483994	−	0.875071i	$-0.339186\pi$
$181$	13.0230			0.967988			0.483994	+	0.875071i	$0.339186\pi$
$182$	1.01590	+	3.12662i	0.0753035	+	0.231760i
$183$	10.7928			0.797825
$184$	4.70426	+	3.41785i	0.346803	+	0.251967i
$185$	−3.33870	−	2.42570i	−0.245466	−	0.178341i
$186$	−5.90800	−	4.29241i	−0.433196	−	0.314735i
$187$	−7.23930			−0.529390
$188$	−4.47807	−	13.7821i	−0.326597	−	1.00516i
$189$	0.535498	−	1.64809i	0.0389518	−	0.119881i
$190$	−24.0587			−1.74541
$191$	−7.42472	+	5.39437i	−0.537234	+	0.390323i	−0.823057	−	0.567959i	$-0.807733\pi$
$191$	−7.42472	+	5.39437i	−0.537234	+	0.390323i	0.285823	+	0.958282i	$0.407733\pi$
$192$	−29.8617	+	21.6958i	−2.15509	+	1.56576i
$193$	7.94284			0.571738			0.285869	−	0.958269i	$-0.407718\pi$
$193$	7.94284			0.571738			0.285869	+	0.958269i	$0.407718\pi$
$194$	−6.91313	−	21.2764i	−0.496334	−	1.52756i
$195$	−40.9521	−	29.7534i	−2.93264	−	2.13069i
$196$	−6.65587	+	20.4847i	−0.475419	+	1.46319i
$197$	8.28956	−	25.5127i	0.590607	−	1.81770i	0.0151266	−	0.999886i	$-0.495185\pi$
$197$	8.28956	−	25.5127i	0.590607	−	1.81770i	0.575480	−	0.817816i	$-0.304815\pi$
$198$	−5.09175	+	15.6708i	−0.361855	+	1.11368i
$199$	−8.77645	+	6.37647i	−0.622146	+	0.452016i	−0.853671	−	0.520813i	$-0.825629\pi$
$199$	−8.77645	+	6.37647i	−0.622146	+	0.452016i	0.231524	+	0.972829i	$0.425629\pi$
$200$	−7.16350	+	22.0470i	−0.506536	+	1.55896i
$201$	34.6400	+	25.1674i	2.44332	+	1.77517i
$202$	−6.38473	−	19.6502i	−0.449228	−	1.38258i
$203$	0.291838	−	0.898184i	0.0204830	−	0.0630402i
$204$	−35.5059	+	25.7965i	−2.48591	+	1.80612i
$205$	−18.3242	−	13.3133i	−1.27982	−	0.929841i
$206$	5.11659	+	15.7472i	0.356490	+	1.09716i
$207$	−9.30217	+	6.75842i	−0.646545	+	0.469743i
$208$	1.96789	+	1.42976i	0.136449	+	0.0991360i
$209$	3.32733	−	2.41744i	0.230156	−	0.167218i
$210$	2.27466	+	7.00069i	0.156967	+	0.483093i
$211$	−1.60411	−	4.93695i	−0.110432	−	0.339873i	0.880535	−	0.473981i	$-0.157183\pi$
$211$	−1.60411	−	4.93695i	−0.110432	−	0.339873i	−0.990967	+	0.134107i	$0.957183\pi$
$212$	5.21325			0.358048
$213$	13.7373	+	19.4830i	0.941261	+	1.33496i
$214$	−4.16708			−0.284855
$215$	−3.05600	−	9.40539i	−0.208417	−	0.641442i
$216$	4.43442	+	13.6477i	0.301724	+	0.928610i
$217$	0.282080	−	0.204943i	0.0191488	−	0.0139125i
$218$	14.9209	+	10.8407i	1.01057	+	0.734222i
$219$	−23.5264	+	17.0929i	−1.58977	+	1.15503i
$220$	−5.27770	−	16.2431i	−0.355822	−	1.09511i
$221$	19.1341	+	13.9018i	1.28710	+	0.935133i
$222$	5.67910	−	4.12611i	0.381156	−	0.276926i
$223$	3.02613	−	9.31346i	0.202645	−	0.623676i	−0.797157	−	0.603772i	$-0.793664\pi$
$223$	3.02613	−	9.31346i	0.202645	−	0.623676i	0.999802	−	0.0199041i	$-0.00633609\pi$
$224$	−0.587302	−	1.80753i	−0.0392408	−	0.120771i
$225$	−37.0846	−	26.9435i	−2.47230	−	1.79623i
$226$	−11.8892	+	36.5911i	−0.790855	+	2.43400i
$227$	−1.77278	+	1.28800i	−0.117664	+	0.0854876i	−0.645061	−	0.764131i	$-0.723168\pi$
$227$	−1.77278	+	1.28800i	−0.117664	+	0.0854876i	0.527397	+	0.849619i	$0.323168\pi$
$228$	7.70488	−	23.7132i	0.510268	−	1.57044i
$229$	7.40942	−	22.8039i	0.489629	−	1.50692i	−0.335535	−	0.942028i	$-0.608917\pi$
$229$	7.40942	−	22.8039i	0.489629	−	1.50692i	0.825163	−	0.564894i	$-0.191083\pi$
$230$	6.04475	−	18.6038i	0.398579	−	1.22670i
$231$	−1.01802	−	0.739635i	−0.0669808	−	0.0486644i
$232$	2.41668	+	7.43779i	0.158663	+	0.488315i
$233$	−15.3190			−1.00358			−0.501792	−	0.864988i	$-0.667326\pi$
$233$	−15.3190			−1.00358			−0.501792	+	0.864988i	$0.667326\pi$
$234$	43.5509	−	31.6416i	2.84701	−	2.06847i
$235$	−14.1462	+	10.2778i	−0.922797	+	0.670452i
$236$	−41.1743			−2.68022
$237$	−8.31740	+	25.5983i	−0.540273	+	1.66279i
$238$	−1.06279	−	3.27094i	−0.0688907	−	0.212024i
$239$	3.29853			0.213364			0.106682	−	0.994293i	$-0.465977\pi$
$239$	3.29853			0.213364			0.106682	+	0.994293i	$0.465977\pi$
$240$	4.40624	+	3.20132i	0.284421	+	0.206644i
$241$	−2.69283	−	1.95645i	−0.173460	−	0.126026i	0.497668	−	0.867368i	$-0.334190\pi$
$241$	−2.69283	−	1.95645i	−0.173460	−	0.126026i	−0.671128	+	0.741341i	$0.734190\pi$
$242$	−16.2570	−	11.8114i	−1.04504	−	0.759264i
$243$	14.0979			0.904380
$244$	−3.67632	−	11.3146i	−0.235353	−	0.724341i
$245$	25.9894			1.66040
$246$	31.1693	−	22.6458i	1.98728	−	1.44385i
$247$	−13.4367			−0.854955
$248$	−0.892227	+	2.74599i	−0.0566565	+	0.174371i
$249$	2.78921	−	8.58429i	0.176759	−	0.544007i
$250$	35.4165			2.23994
$251$	21.7995	−	15.8383i	1.37597	−	0.999703i	0.378729	−	0.925508i	$-0.376361\pi$
$251$	21.7995	−	15.8383i	1.37597	−	0.999703i	0.997244	−	0.0741952i	$-0.0236388\pi$
$252$	−4.76939			−0.300443
$253$	1.03334	+	3.18029i	0.0649655	+	0.199943i
$254$	−35.7684			−2.24431
$255$	42.8425	+	31.1269i	2.68290	+	1.94924i
$256$	10.1511	+	7.37520i	0.634443	+	0.460950i
$257$	10.9490	+	7.95492i	0.682980	+	0.496214i	0.874345	−	0.485305i	$-0.161291\pi$
$257$	10.9490	+	7.95492i	0.682980	+	0.496214i	−0.191365	+	0.981519i	$0.561291\pi$
$258$	16.8218			1.04728
$259$	0.103571	+	0.318757i	0.00643556	+	0.0198066i
$260$	−17.2424	+	53.0668i	−1.06933	+	3.29106i
$261$	−15.4643			−0.957216
$262$	−18.8548	+	13.6988i	−1.16486	+	0.846318i
$263$	−4.68963	+	3.40722i	−0.289175	+	0.210098i	−0.722909	−	0.690943i	$-0.757196\pi$
$263$	−4.68963	+	3.40722i	−0.289175	+	0.210098i	0.433734	+	0.901041i	$0.357196\pi$
$264$	10.4202			0.641321
$265$	−1.94386	−	5.98259i	−0.119411	−	0.367508i
$266$	1.58076	+	1.14849i	0.0969225	+	0.0704183i
$267$	−5.26874	+	16.2155i	−0.322442	+	0.992373i
$268$	14.5848	−	44.8874i	0.890909	−	2.74194i
$269$	−0.724238	+	2.22898i	−0.0441576	+	0.135903i	−0.970705	−	0.240276i	$-0.922762\pi$
$269$	−0.724238	+	2.22898i	−0.0441576	+	0.135903i	0.926547	+	0.376179i	$0.122762\pi$
$270$	39.0548	−	28.3749i	2.37680	−	1.72684i
$271$	−5.63923	+	17.3558i	−0.342559	+	1.05429i	0.620319	+	0.784350i	$0.287003\pi$
$271$	−5.63923	+	17.3558i	−0.342559	+	1.05429i	−0.962878	+	0.269938i	$0.912997\pi$
$272$	−2.05873	−	1.49576i	−0.124829	−	0.0906937i
$273$	1.27039	+	3.90984i	0.0768872	+	0.236635i
$274$	−1.84391	+	5.67496i	−0.111394	+	0.342837i
$275$	−10.7852	+	7.83589i	−0.650371	+	0.472522i
$276$	16.4008	+	11.9159i	0.987210	+	0.717250i
$277$	−5.80952	−	17.8799i	−0.349060	−	1.07430i	−0.959374	−	0.282138i	$-0.908957\pi$
$277$	−5.80952	−	17.8799i	−0.349060	−	1.07430i	0.610314	−	0.792160i	$-0.291043\pi$
$278$	33.9892	−	24.6946i	2.03854	−	1.48108i
$279$	−4.61895	−	3.35586i	−0.276529	−	0.200910i
$280$	2.35452	−	1.71066i	0.140709	−	0.102231i
$281$	−8.19406	−	25.2187i	−0.488817	−	1.50442i	−0.826376	−	0.563119i	$-0.809601\pi$
$281$	−8.19406	−	25.2187i	−0.488817	−	1.50442i	0.337559	−	0.941304i	$-0.390399\pi$
$282$	−9.19111	−	28.2873i	−0.547322	−	1.68449i
$283$	6.58352			0.391350			0.195675	−	0.980669i	$-0.437310\pi$
$283$	6.58352			0.391350			0.195675	+	0.980669i	$0.437310\pi$
$284$	15.7457	−	21.0379i	0.934333	−	1.24837i
$285$	−30.0855			−1.78211
$286$	−4.83789	−	14.8895i	−0.286070	−	0.880433i
$287$	0.568439	+	1.74948i	0.0335539	+	0.103268i
$288$	−25.1772	+	18.2923i	−1.48358	+	1.07788i
$289$	−6.26408	−	4.55112i	−0.368475	−	0.267713i
$290$	21.2842	−	15.4639i	1.24985	−	0.908070i
$291$	−8.64490	−	26.6063i	−0.506773	−	1.55969i
$292$	25.9331	+	18.8415i	1.51762	+	1.10261i
$293$	−16.4556	+	11.9557i	−0.961344	+	0.698457i	−0.953462	−	0.301512i	$-0.902509\pi$
$293$	−16.4556	+	11.9557i	−0.961344	+	0.698457i	−0.00788116	+	0.999969i	$0.502509\pi$
$294$	−13.6610	+	42.0442i	−0.796725	+	2.45207i
$295$	15.3526	+	47.2506i	0.893865	+	2.75103i
$296$	−2.24538	−	1.63136i	−0.130510	−	0.0948211i
$297$	−2.55014	+	7.84851i	−0.147974	+	0.455417i
$298$	10.4007	−	7.55658i	0.602498	−	0.437741i
$299$	3.37596	−	10.3901i	0.195237	−	0.600877i
$300$	−24.9746	+	76.8638i	−1.44191	+	4.43773i
$301$	−0.248192	+	0.763856i	−0.0143055	+	0.0440279i
$302$	−6.06413	−	4.40585i	−0.348952	−	0.253528i
$303$	−7.98413	−	24.5726i	−0.458676	−	1.41166i
$304$	1.44572			0.0829176
$305$	−11.6135	+	8.43771i	−0.664987	+	0.483142i
$306$	−45.5612	+	33.1022i	−2.60456	+	1.89232i
$307$	27.0530			1.54399			0.771997	−	0.635626i	$-0.219258\pi$
$307$	27.0530			1.54399			0.771997	+	0.635626i	$0.219258\pi$
$308$	−0.428627	+	1.31918i	−0.0244233	+	0.0751671i
$309$	6.39831	+	19.6920i	0.363987	+	1.12024i
$310$	9.71304			0.551664
$311$	−14.3053	−	10.3934i	−0.811181	−	0.589358i	0.102991	−	0.994682i	$-0.467159\pi$
$311$	−14.3053	−	10.3934i	−0.811181	−	0.589358i	−0.914173	+	0.405324i	$0.867159\pi$
$312$	−27.5416	−	20.0101i	−1.55924	−	1.13285i
$313$	−5.42977	−	3.94496i	−0.306909	−	0.222982i	0.423660	−	0.905821i	$-0.360745\pi$
$313$	−5.42977	−	3.94496i	−0.306909	−	0.222982i	−0.730569	+	0.682839i	$0.760745\pi$
$314$	29.9554			1.69048
$315$	1.77836	+	5.47323i	0.100199	+	0.308381i
$316$	29.6690			1.66901
$317$	−25.7254	+	18.6906i	−1.44488	+	1.04977i	−0.457890	+	0.889009i	$0.651395\pi$
$317$	−25.7254	+	18.6906i	−1.44488	+	1.04977i	−0.986994	+	0.160760i	$0.948605\pi$
$318$	10.7001			0.600029
$319$	−1.38978	+	4.27731i	−0.0778128	+	0.239483i
$320$	15.1709	−	46.6913i	0.848081	−	2.61012i
$321$	−5.21094			−0.290846
$322$	−1.28525	+	0.933790i	−0.0716243	+	0.0520381i
$323$	14.0569			0.782148
$324$	0.992293	+	3.05396i	0.0551274	+	0.169665i
$325$	43.5536			2.41592
$326$	−19.9748	−	14.5125i	−1.10630	−	0.803773i
$327$	18.6586	+	13.5563i	1.03182	+	0.749664i
$328$	−12.3236	−	8.95362i	−0.680457	−	0.494381i
$329$	1.42009			0.0782924
$330$	−10.8323	−	33.3385i	−0.596300	−	1.83522i
$331$	−5.87825	+	18.0914i	−0.323098	+	0.994393i	0.649194	+	0.760623i	$0.275106\pi$
$331$	−5.87825	+	18.0914i	−0.323098	+	0.994393i	−0.972292	+	0.233770i	$0.924894\pi$
$332$	−9.94938			−0.546043
$333$	4.43999	−	3.22584i	0.243310	−	0.176775i
$334$	−15.5396	+	11.2902i	−0.850287	+	0.617770i
$335$	−56.9499			−3.11150
$336$	−0.136687	−	0.420679i	−0.00745689	−	0.0229499i
$337$	20.9253	+	15.2031i	1.13987	+	0.828166i	0.987102	−	0.160096i	$-0.0511803\pi$
$337$	20.9253	+	15.2031i	1.13987	+	0.828166i	0.152771	+	0.988262i	$0.451180\pi$
$338$	−6.71688	+	20.6724i	−0.365350	+	1.12443i
$339$	−14.8674	+	45.7573i	−0.807488	+	2.48519i
$340$	18.0384	−	55.5164i	0.978268	−	3.01080i
$341$	−1.34331	+	0.975975i	−0.0727445	+	0.0528520i
$342$	9.88692	−	30.4288i	0.534623	−	1.64540i
$343$	−3.43831	−	2.49808i	−0.185652	−	0.134884i
$344$	−2.05525	−	6.32542i	−0.110812	−	0.341044i
$345$	7.55898	−	23.2642i	0.406962	−	1.25250i
$346$	12.3811	−	8.99543i	0.665614	−	0.483597i
$347$	−9.57578	−	6.95721i	−0.514055	−	0.373483i	0.300305	−	0.953843i	$-0.402912\pi$
$347$	−9.57578	−	6.95721i	−0.514055	−	0.373483i	−0.814360	+	0.580361i	$0.802912\pi$
$348$	8.42544	+	25.9308i	0.451651	+	1.39004i
$349$	11.0322	−	8.01536i	0.590540	−	0.429052i	−0.251969	−	0.967735i	$-0.581078\pi$
$349$	11.0322	−	8.01536i	0.590540	−	0.429052i	0.842508	+	0.538683i	$0.181078\pi$
$350$	−5.12386	−	3.72270i	−0.273882	−	0.198987i
$351$	21.8119	−	15.8472i	1.16423	−	0.845863i
$352$	2.79683	+	8.60776i	0.149072	+	0.458795i
$353$	10.3472	+	31.8456i	0.550728	+	1.69497i	0.706965	+	0.707248i	$0.250064\pi$
$353$	10.3472	+	31.8456i	0.550728	+	1.69497i	−0.156237	+	0.987720i	$0.549936\pi$
$354$	−84.5091			−4.49161
$355$	−30.0136	−	10.2249i	−1.59295	−	0.542683i
$356$	18.7941			0.996087
$357$	−1.32903	−	4.09033i	−0.0703396	−	0.216483i
$358$	10.9713	+	33.7662i	0.579851	+	1.78460i
$359$	27.7687	−	20.1751i	1.46558	−	1.06480i	0.483709	−	0.875229i	$-0.339289\pi$
$359$	27.7687	−	20.1751i	1.46558	−	1.06480i	0.981866	−	0.189574i	$-0.0607108\pi$
$360$	−38.5543	−	28.0113i	−2.03199	−	1.47633i
$361$	8.91048	−	6.47385i	0.468973	−	0.340729i
$362$	−9.10473	−	28.0215i	−0.478534	−	1.47278i
$363$	−20.3294	−	14.7702i	−1.06702	−	0.775232i
$364$	3.66614	−	2.66360i	0.192158	−	0.139611i
$365$	11.9523	−	36.7855i	0.625614	−	1.92544i
$366$	−7.54555	−	23.2228i	−0.394412	−	1.21388i
$367$	−2.28765	−	1.66208i	−0.119414	−	0.0867597i	0.526475	−	0.850191i	$-0.323513\pi$
$367$	−2.28765	−	1.66208i	−0.119414	−	0.0867597i	−0.645890	+	0.763431i	$0.723513\pi$
$368$	−0.363236	+	1.11793i	−0.0189350	+	0.0582759i
$369$	24.3686	−	17.7048i	1.26858	−	0.921675i
$370$	−2.88520	+	8.87975i	−0.149995	+	0.461636i
$371$	−0.157870	+	0.485875i	−0.00819621	+	0.0252254i
$372$	−3.11063	+	9.57353i	−0.161279	+	0.496364i
$373$	−7.51713	−	5.46152i	−0.389222	−	0.282787i	0.375914	−	0.926654i	$-0.377329\pi$
$373$	−7.51713	−	5.46152i	−0.389222	−	0.282787i	−0.765137	+	0.643868i	$0.777329\pi$
$374$	5.06121	+	15.5768i	0.261709	+	0.805457i
$375$	44.2884			2.28704
$376$	−9.51378	+	6.91217i	−0.490636	+	0.356468i
$377$	11.8871	−	8.63648i	0.612217	−	0.444802i
$378$	−3.92059			−0.201653
$379$	3.76299	−	11.5813i	0.193292	−	0.594891i	−0.806700	−	0.590961i	$-0.798749\pi$
$379$	3.76299	−	11.5813i	0.193292	−	0.594891i	0.999992	−	0.00393059i	$-0.00125115\pi$
$380$	10.2480	+	31.5400i	0.525710	+	1.61797i
$381$	−44.7286			−2.29151
$382$	16.7979	+	12.2044i	0.859455	+	0.624431i
$383$	1.14664	+	0.833080i	0.0585904	+	0.0425684i	0.616695	−	0.787202i	$-0.288471\pi$
$383$	1.14664	+	0.833080i	0.0585904	+	0.0425684i	−0.558105	+	0.829771i	$0.688471\pi$
$384$	39.0919	+	28.4019i	1.99490	+	1.44938i
$385$	1.67368			0.0852984
$386$	−5.55307	−	17.0906i	−0.282644	−	0.869889i
$387$	13.1515			0.668529
$388$	−24.9479	+	18.1257i	−1.26654	+	0.920192i
$389$	1.31977			0.0669148			0.0334574	−	0.999440i	$-0.489348\pi$
$389$	1.31977			0.0669148			0.0334574	+	0.999440i	$0.489348\pi$
$390$	−35.3896	+	108.918i	−1.79202	+	5.51528i
$391$	−3.53180	+	10.8698i	−0.178611	+	0.549707i
$392$	17.4787			0.882809
$393$	−23.5781	+	17.1305i	−1.18936	+	0.864117i
$394$	−60.6910			−3.05757
$395$	−11.0627	−	34.0474i	−0.556623	−	1.71311i
$396$	22.7126			1.14135
$397$	13.4715	+	9.78763i	0.676116	+	0.491227i	0.872067	−	0.489386i	$-0.162779\pi$
$397$	13.4715	+	9.78763i	0.676116	+	0.491227i	−0.195951	+	0.980614i	$0.562779\pi$
$398$	19.8561	+	14.4263i	0.995297	+	0.723126i
$399$	1.97674	+	1.43619i	0.0989609	+	0.0718993i
$400$	−4.68614			−0.234307
$401$	6.41993	+	19.7585i	0.320596	+	0.986693i	0.973389	+	0.229157i	$0.0735969\pi$
$401$	6.41993	+	19.7585i	0.320596	+	0.986693i	−0.652793	+	0.757536i	$0.726403\pi$
$402$	29.9349	−	92.1301i	1.49302	−	4.59503i
$403$	5.42468			0.270223
$404$	−23.0410	+	16.7403i	−1.14633	+	0.832859i
$405$	3.13465	−	2.27746i	0.155762	−	0.113168i
$406$	−2.13665			−0.106040
$407$	−0.493221	−	1.51798i	−0.0244480	−	0.0752433i
$408$	28.8129	+	20.9338i	1.42645	+	1.03638i
$409$	7.07958	−	21.7887i	0.350063	−	1.07738i	−0.608755	−	0.793359i	$-0.708331\pi$
$409$	7.07958	−	21.7887i	0.350063	−	1.07738i	0.958817	−	0.284024i	$-0.0916694\pi$
$410$	−15.8352	+	48.7358i	−0.782046	+	2.40689i
$411$	−2.30581	+	7.09656i	−0.113737	+	0.350047i
$412$	18.4646	−	13.4153i	0.909683	−	0.660924i
$413$	1.24686	−	3.83744i	0.0613540	−	0.188828i
$414$	21.0455	+	15.2905i	1.03433	+	0.751485i
$415$	3.70982	+	11.4177i	0.182108	+	0.560471i
$416$	9.13736	−	28.1219i	0.447996	−	1.37879i
$417$	42.5036	−	30.8807i	2.08141	−	1.51223i
$418$	−7.52784	−	5.46930i	−0.368199	−	0.267512i
$419$	3.61761	+	11.1339i	0.176732	+	0.543925i	0.999708	−	0.0241505i	$-0.00768810\pi$
$419$	3.61761	+	11.1339i	0.176732	+	0.543925i	−0.822976	+	0.568076i	$0.807688\pi$
$420$	8.20871	−	5.96398i	0.400544	−	0.291012i
$421$	−27.4395	−	19.9360i	−1.33732	−	0.971620i	−0.999538	−	0.0303957i	$-0.990323\pi$
$421$	−27.4395	−	19.9360i	−1.33732	−	0.971620i	−0.337782	−	0.941224i	$-0.609677\pi$
$422$	−9.50134	+	6.90313i	−0.462518	+	0.336039i
$423$	−7.18572	−	22.1154i	−0.349382	−	1.07529i
$424$	−1.30731	−	4.02349i	−0.0634886	−	0.195398i
$425$	−45.5640			−2.21018
$426$	32.3175	−	43.1796i	1.56579	−	2.09206i
$427$	1.16584			0.0564191
$428$	1.77499	+	5.46287i	0.0857975	+	0.264058i
$429$	−6.04979	−	18.6193i	−0.292087	−	0.898951i
$430$	−18.1010	+	13.1512i	−0.872909	+	0.634205i
$431$	21.4347	+	15.5732i	1.03247	+	0.750135i	0.968802	−	0.247836i	$-0.0797194\pi$
$431$	21.4347	+	15.5732i	1.03247	+	0.750135i	0.0636702	+	0.997971i	$0.479719\pi$
$432$	−2.34685	+	1.70508i	−0.112913	+	0.0820359i
$433$	2.40411	+	7.39910i	0.115534	+	0.355578i	0.992058	−	0.125780i	$-0.0401435\pi$
$433$	2.40411	+	7.39910i	0.115534	+	0.355578i	−0.876524	+	0.481359i	$0.840143\pi$
$434$	−0.638186	−	0.463670i	−0.0306339	−	0.0222569i
$435$	26.6160	−	19.3376i	1.27614	−	0.927168i
$436$	7.85602	−	24.1783i	0.376235	−	1.15793i
$437$	−2.00649	−	6.17534i	−0.0959834	−	0.295406i
$438$	53.2268	+	38.6716i	2.54328	+	1.84780i
$439$	−6.04310	+	18.5987i	−0.288421	+	0.887670i	0.696931	+	0.717138i	$0.254548\pi$
$439$	−6.04310	+	18.5987i	−0.288421	+	0.887670i	−0.985352	+	0.170531i	$0.945452\pi$
$440$	−11.2126	+	8.14645i	−0.534541	+	0.388367i
$441$	−10.6803	+	32.8707i	−0.508587	+	1.56527i
$442$	16.5352	−	50.8900i	0.786497	−	2.42059i
$443$	−5.68075	+	17.4836i	−0.269901	+	0.830669i	0.720623	+	0.693327i	$0.243856\pi$
$443$	−5.68075	+	17.4836i	−0.269901	+	0.830669i	−0.990524	+	0.137342i	$0.956144\pi$
$444$	−7.82821	−	5.68753i	−0.371510	−	0.269918i
$445$	−7.00776	−	21.5677i	−0.332200	−	1.02241i
$446$	−22.1554			−1.04909
$447$	13.0062	−	9.44952i	0.615170	−	0.446947i
$448$	−3.22569	+	2.34360i	−0.152399	+	0.110725i
$449$	−0.695155			−0.0328064			−0.0164032	−	0.999865i	$-0.505222\pi$
$449$	−0.695155			−0.0328064			−0.0164032	+	0.999865i	$0.505222\pi$
$450$	−32.0474	+	98.6318i	−1.51073	+	4.64955i
$451$	−2.70700	−	8.33130i	−0.127468	−	0.392306i
$452$	53.0337			2.49449
$453$	−7.58322	−	5.50953i	−0.356291	−	0.258860i
$454$	4.01079	+	2.91401i	0.188236	+	0.136761i
$455$	−4.42367	−	3.21399i	−0.207385	−	0.150674i
$456$	−20.2335			−0.947520
$457$	1.28890	+	3.96682i	0.0602920	+	0.185560i	0.976666	−	0.214763i	$-0.0688980\pi$
$457$	1.28890	+	3.96682i	0.0602920	+	0.185560i	−0.916374	+	0.400323i	$0.868898\pi$
$458$	−54.2472			−2.53480
$459$	−22.8187	+	16.5788i	−1.06509	+	0.773831i
$460$	−26.9637			−1.25719
$461$	−10.8501	+	33.3932i	−0.505339	+	1.55527i	0.294860	+	0.955540i	$0.404727\pi$
$461$	−10.8501	+	33.3932i	−0.505339	+	1.55527i	−0.800200	+	0.599734i	$0.795273\pi$
$462$	−0.879744	+	2.70757i	−0.0409294	+	0.125968i
$463$	5.01996			0.233297			0.116649	−	0.993173i	$-0.462785\pi$
$463$	5.01996			0.233297			0.116649	+	0.993173i	$0.462785\pi$
$464$	−1.27899	+	0.929242i	−0.0593757	+	0.0431390i
$465$	12.1462			0.563266
$466$	10.7100	+	32.9620i	0.496131	+	1.52693i
$467$	0.218936			0.0101312			0.00506558	−	0.999987i	$-0.498388\pi$
$467$	0.218936			0.0101312			0.00506558	+	0.999987i	$0.498388\pi$
$468$	−60.0316	−	43.6155i	−2.77496	−	2.01613i
$469$	3.74184	+	2.71860i	0.172782	+	0.125533i
$470$	32.0048	+	23.2529i	1.47627	+	1.07257i
$471$	37.4594			1.72604
$472$	10.3251	+	31.7775i	0.475253	+	1.46268i
$473$	1.18193	−	3.63761i	0.0543453	−	0.167258i
$474$	60.8948			2.79699
$475$	20.9421	−	15.2153i	0.960891	−	0.698128i
$476$	−3.83537	+	2.78656i	−0.175794	+	0.127722i
$477$	8.36544			0.383027
$478$	−2.30610	−	7.09744i	−0.105478	−	0.324629i
$479$	23.4760	+	17.0563i	1.07265	+	0.779323i	0.976386	−	0.216034i	$-0.0693121\pi$
$479$	23.4760	+	17.0563i	1.07265	+	0.779323i	0.0962596	+	0.995356i	$0.469312\pi$
$480$	20.4591	−	62.9667i	0.933826	−	2.87402i
$481$	−1.61137	+	4.95929i	−0.0734722	+	0.226124i
$482$	−2.32707	+	7.16197i	−0.105995	+	0.326219i
$483$	−1.60721	+	1.16771i	−0.0731307	+	0.0531326i
$484$	−8.55947	+	26.3433i	−0.389067	+	1.19742i
$485$	30.1028	+	21.8710i	1.36690	+	0.993111i
$486$	−9.85624	−	30.3344i	−0.447088	−	1.37600i
$487$	1.67228	−	5.14673i	0.0757780	−	0.233221i	−0.905992	−	0.423296i	$-0.860873\pi$
$487$	1.67228	−	5.14673i	0.0757780	−	0.233221i	0.981770	+	0.190075i	$0.0608731\pi$
$488$	−7.81045	+	5.67463i	−0.353563	+	0.256878i
$489$	−24.9785	−	18.1479i	−1.12957	−	0.820678i
$490$	−18.1700	−	55.9214i	−0.820836	−	2.52627i
$491$	13.9634	−	10.1450i	0.630161	−	0.457839i	−0.226295	−	0.974059i	$-0.572661\pi$
$491$	13.9634	−	10.1450i	0.630161	−	0.457839i	0.856456	+	0.516220i	$0.172661\pi$
$492$	−42.9645	−	31.2156i	−1.93699	−	1.40731i
$493$	−12.4358	+	9.03515i	−0.560081	+	0.406923i
$494$	9.39397	+	28.9117i	0.422655	+	1.30080i
$495$	−8.46885	−	26.0644i	−0.380647	−	1.17151i
$496$	−0.583668			−0.0262075
$497$	1.48391	+	2.10457i	0.0665624	+	0.0944029i
$498$	−20.4208			−0.915079
$499$	8.26965	+	25.4514i	0.370200	+	1.13936i	0.946660	+	0.322234i	$0.104434\pi$
$499$	8.26965	+	25.4514i	0.370200	+	1.13936i	−0.576460	+	0.817125i	$0.695566\pi$
$500$	−15.0859	−	46.4296i	−0.674661	−	2.07639i
$501$	−19.4323	+	14.1184i	−0.868170	+	0.630762i
$502$	−49.3199	−	35.8330i	−2.20125	−	1.59930i
$503$	−6.03587	+	4.38532i	−0.269126	+	0.195532i	−0.714161	−	0.699982i	$-0.753191\pi$
$503$	−6.03587	+	4.38532i	−0.269126	+	0.195532i	0.445034	+	0.895513i	$0.353191\pi$
$504$	1.19600	+	3.68092i	0.0532742	+	0.163961i
$505$	27.8020	+	20.1993i	1.23717	+	0.898857i
$506$	6.12059	−	4.44687i	0.272093	−	0.197687i
$507$	−8.39948	+	25.8509i	−0.373034	+	1.14808i
$508$	15.2358	+	46.8910i	0.675979	+	2.08045i
$509$	31.9204	+	23.1916i	1.41485	+	1.02795i	0.992595	+	0.121470i	$0.0387609\pi$
$509$	31.9204	+	23.1916i	1.41485	+	1.02795i	0.422254	+	0.906478i	$0.361239\pi$
$510$	37.0232	−	113.946i	1.63942	−	5.04561i
$511$	−2.54134	+	1.84639i	−0.112422	+	0.0816795i
$512$	−1.78329	+	5.48841i	−0.0788111	+	0.242556i
$513$	4.95173	−	15.2399i	0.218624	−	0.672856i
$514$	9.46182	−	29.1205i	0.417343	−	1.28445i
$515$	−22.2799	−	16.1873i	−0.981770	−	0.713297i
$516$	−7.16537	−	22.0527i	−0.315438	−	0.970817i
$517$	−6.76273			−0.297425
$518$	0.613460	−	0.445705i	0.0269539	−	0.0195832i
$519$	15.4827	−	11.2488i	0.679613	−	0.493768i
$520$	45.2797			1.98565
$521$	0.996791	−	3.06781i	0.0436702	−	0.134403i	−0.926844	−	0.375446i	$-0.877490\pi$
$521$	0.996791	−	3.06781i	0.0436702	−	0.134403i	0.970514	+	0.241043i	$0.0774895\pi$
$522$	10.8115	+	33.2745i	0.473208	+	1.45638i
$523$	−2.33576			−0.102136			−0.0510678	−	0.998695i	$-0.516262\pi$
$523$	−2.33576			−0.102136			−0.0510678	+	0.998695i	$0.516262\pi$
$524$	25.9900	+	18.8828i	1.13538	+	0.824900i
$525$	−6.40740	−	4.65525i	−0.279642	−	0.203172i
$526$	10.6100	+	7.70859i	0.462616	+	0.336110i
$527$	−5.67509			−0.247211
$528$	0.650927	+	2.00335i	0.0283280	+	0.0871845i
$529$	−17.7207			−0.770465
$530$	−11.5137	+	8.36521i	−0.500124	+	0.363362i
$531$	−66.0703			−2.86721
$532$	0.832287	−	2.56151i	0.0360842	−	0.111056i
$533$	−8.84388	+	27.2187i	−0.383071	+	1.17897i
$534$	38.5744			1.66928
$535$	5.60720	−	4.07387i	0.242421	−	0.176129i
$536$	−38.3006			−1.65433
$537$	13.7196	+	42.2247i	0.592046	+	1.82213i
$538$	5.30242			0.228603
$539$	8.13194	+	5.90820i	0.350267	+	0.254484i
$540$	−53.8340	−	39.1127i	−2.31665	−	1.68314i
$541$	−26.6953	−	19.3953i	−1.14772	−	0.833869i	−0.159546	−	0.987190i	$-0.551003\pi$
$541$	−26.6953	−	19.3953i	−1.14772	−	0.833869i	−0.988176	+	0.153321i	$0.951003\pi$
$542$	41.2869			1.77342
$543$	−11.3855	−	35.0409i	−0.488598	−	1.50375i
$544$	−9.55915	+	29.4200i	−0.409845	+	1.26137i
$545$	−30.6757			−1.31400
$546$	7.52464	−	5.46697i	0.322025	−	0.233965i
$547$	16.7710	−	12.1849i	0.717078	−	0.520988i	−0.168371	−	0.985724i	$-0.553851\pi$
$547$	16.7710	−	12.1849i	0.717078	−	0.520988i	0.885449	+	0.464736i	$0.153851\pi$
$548$	8.22507			0.351358
$549$	−5.89921	−	18.1559i	−0.251772	−	0.774874i
$550$	24.4007	+	17.7281i	1.04045	+	0.755931i
$551$	2.69861	−	8.30547i	0.114965	−	0.353825i
$552$	5.08366	−	15.6459i	0.216375	−	0.665933i
$553$	−0.898451	+	2.76515i	−0.0382060	+	0.117586i
$554$	−34.4105	+	25.0007i	−1.46196	+	1.06218i
$555$	−3.60796	+	11.1042i	−0.153149	+	0.471345i
$556$	−46.8516	−	34.0396i	−1.98695	−	1.44360i
$557$	6.64657	+	20.4560i	0.281624	+	0.866751i	0.987390	+	0.158305i	$0.0506030\pi$
$557$	6.64657	+	20.4560i	0.281624	+	0.866751i	−0.705766	+	0.708445i	$0.749397\pi$
$558$	−3.99156	+	12.2848i	−0.168976	+	0.520056i
$559$	−10.1093	+	7.34485i	−0.427579	+	0.310654i
$560$	0.475965	+	0.345809i	0.0201132	+	0.0146131i
$561$	6.32906	+	19.4788i	0.267213	+	0.822397i
$562$	−48.5344	+	35.2623i	−2.04730	+	1.48745i
$563$	−10.5002	−	7.62886i	−0.442532	−	0.321518i	0.344108	−	0.938930i	$-0.388181\pi$
$563$	−10.5002	−	7.62886i	−0.442532	−	0.321518i	−0.786640	+	0.617412i	$0.788181\pi$
$564$	−33.1685	+	24.0983i	−1.39665	+	1.01472i
$565$	−19.7746	−	60.8601i	−0.831925	−	2.56040i
$566$	−4.60273	−	14.1658i	−0.193467	−	0.595431i
$567$	−0.314678			−0.0132152
$568$	−20.1851	−	6.87659i	−0.846947	−	0.288535i
$569$	33.0614			1.38600			0.693002	−	0.720936i	$-0.256288\pi$
$569$	33.0614			1.38600			0.693002	+	0.720936i	$0.256288\pi$
$570$	21.0337	+	64.7350i	0.881004	+	2.71145i
$571$	−0.543795	−	1.67363i	−0.0227571	−	0.0700392i	0.939033	−	0.343827i	$-0.111723\pi$
$571$	−0.543795	−	1.67363i	−0.0227571	−	0.0700392i	−0.961790	+	0.273788i	$0.911723\pi$
$572$	−17.4588	+	12.6845i	−0.729988	+	0.530367i
$573$	21.0058	+	15.2616i	0.877531	+	0.637564i
$574$	3.36693	−	2.44622i	0.140533	−	0.102103i
$575$	6.50382	+	20.0167i	0.271228	+	0.834754i
$576$	52.8193	+	38.3755i	2.20081	+	1.59898i
$577$	20.1406	−	14.6330i	0.838463	−	0.609179i	−0.0834779	−	0.996510i	$-0.526603\pi$
$577$	20.1406	−	14.6330i	0.838463	−	0.609179i	0.921941	+	0.387331i	$0.126603\pi$
$578$	−5.41324	+	16.6602i	−0.225161	+	0.692974i
$579$	−6.94414	−	21.3719i	−0.288588	−	0.888184i
$580$	−29.3386	−	21.3158i	−1.21822	−	0.885089i
$581$	0.301292	−	0.927281i	0.0124997	−	0.0384701i
$582$	−51.2048	+	37.2024i	−2.12251	+	1.54209i
$583$	0.751805	−	2.31382i	0.0311366	−	0.0958285i
$584$	8.03833	−	24.7394i	0.332628	−	1.02372i
$585$	−27.6681	+	85.1535i	−1.14393	+	3.52067i
$586$	37.2295	+	27.0488i	1.53794	+	1.11738i
$587$	−1.05733	−	3.25414i	−0.0436409	−	0.134313i	0.926862	−	0.375402i	$-0.122495\pi$
$587$	−1.05733	−	3.25414i	−0.0436409	−	0.134313i	−0.970503	+	0.241089i	$0.922495\pi$
$588$	60.9372			2.51301
$589$	2.60838	−	1.89510i	0.107477	−	0.0780863i
$590$	90.9355	−	66.0685i	3.74375	−	2.72000i
$591$	−75.8943			−3.12187
$592$	0.173375	−	0.533594i	0.00712568	−	0.0219306i
$593$	−8.19330	−	25.2164i	−0.336459	−	1.03551i	−0.965999	−	0.258545i	$-0.916757\pi$
$593$	−8.19330	−	25.2164i	−0.336459	−	1.03551i	0.629541	−	0.776968i	$-0.283243\pi$
$594$	18.6705			0.766060
$595$	4.62787	+	3.36235i	0.189724	+	0.137843i
$596$	−14.3366	−	10.4162i	−0.587251	−	0.426663i
$597$	24.8301	+	18.0401i	1.01623	+	0.738334i
$598$	−24.7167			−1.01074
$599$	−8.08505	−	24.8832i	−0.330346	−	1.01670i	−0.968969	−	0.247182i	$-0.920496\pi$
$599$	−8.08505	−	24.8832i	−0.330346	−	1.01670i	0.638623	−	0.769520i	$-0.279504\pi$
$600$	65.5847			2.67749
$601$	−3.67630	+	2.67099i	−0.149960	+	0.108952i	−0.660235	−	0.751059i	$-0.729543\pi$
$601$	−3.67630	+	2.67099i	−0.149960	+	0.108952i	0.510276	+	0.860011i	$0.329543\pi$
$602$	1.81711			0.0740597
$603$	23.4035	−	72.0285i	0.953064	−	2.93323i
$604$	−3.19283	+	9.82653i	−0.129915	+	0.399836i
$605$	33.4225			1.35882
$606$	−47.2909	+	34.3589i	−1.92106	+	1.39573i
$607$	−43.2054			−1.75365			−0.876826	−	0.480807i	$-0.840344\pi$
$607$	−43.2054			−1.75365			−0.876826	+	0.480807i	$0.840344\pi$
$608$	−5.43075	−	16.7141i	−0.220246	−	0.677848i
$609$	−2.67189			−0.108271
$610$	26.2747	+	19.0897i	1.06383	+	0.772920i
$611$	17.8745	+	12.9866i	0.723125	+	0.525381i
$612$	62.8027	+	45.6288i	2.53865	+	1.84444i
$613$	−4.95216			−0.200016			−0.100008	−	0.994987i	$-0.531887\pi$
$613$	−4.95216			−0.200016			−0.100008	+	0.994987i	$0.531887\pi$
$614$	−18.9135	−	58.2098i	−0.763287	−	2.34916i
$615$	−19.8020	+	60.9443i	−0.798494	+	2.45751i
$616$	1.12560			0.0453517
$617$	−18.3205	+	13.3106i	−0.737555	+	0.535865i	−0.891944	−	0.452145i	$-0.850659\pi$
$617$	−18.3205	+	13.3106i	−0.737555	+	0.535865i	0.154390	+	0.988010i	$0.450659\pi$
$618$	37.8980	−	27.5345i	1.52448	−	1.10760i
$619$	47.3685			1.90390			0.951951	−	0.306252i	$-0.0990750\pi$
$619$	47.3685			1.90390			0.951951	+	0.306252i	$0.0990750\pi$
$620$	−4.13733	−	12.7334i	−0.166159	−	0.511386i
$621$	10.5404	+	7.65802i	0.422970	+	0.307306i
$622$	−12.3623	+	38.0471i	−0.495682	+	1.52555i
$623$	−0.569133	+	1.75161i	−0.0228018	+	0.0701768i
$624$	2.12660	−	6.54501i	0.0851323	−	0.262010i
$625$	−10.6031	+	7.70363i	−0.424126	+	0.308145i
$626$	−4.69225	+	14.4413i	−0.187540	+	0.577189i
$627$	−9.41359	−	6.83937i	−0.375942	−	0.273138i
$628$	−12.7597	−	39.2704i	−0.509168	−	1.56706i
$629$	1.68575	−	5.18821i	0.0672154	−	0.206868i
$630$	10.5334	−	7.65299i	0.419662	−	0.304902i
$631$	24.4631	+	17.7735i	0.973860	+	0.707551i	0.956328	−	0.292295i	$-0.0944190\pi$
$631$	24.4631	+	17.7735i	0.973860	+	0.707551i	0.0175323	+	0.999846i	$0.494419\pi$
$632$	−7.44000	−	22.8980i	−0.295947	−	0.910832i
$633$	−11.8815	+	8.63238i	−0.472246	+	0.343106i
$634$	58.2019	+	42.2862i	2.31149	+	1.67940i
$635$	48.1299	−	34.9684i	1.90998	−	1.38768i
$636$	−4.55776	−	14.0273i	−0.180727	−	0.556220i
$637$	−10.1478	−	31.2318i	−0.402072	−	1.23745i
$638$	10.1751			0.402837
$639$	25.2662	−	33.7584i	0.999517	−	1.33546i
$640$	−64.2690			−2.54046
$641$	−3.81294	−	11.7350i	−0.150602	−	0.463506i	0.847087	−	0.531455i	$-0.178355\pi$
$641$	−3.81294	−	11.7350i	−0.150602	−	0.463506i	−0.997689	+	0.0679489i	$0.978355\pi$
$642$	3.64312	+	11.2124i	0.143783	+	0.442517i
$643$	19.3304	−	14.0444i	0.762318	−	0.553856i	−0.137303	−	0.990529i	$-0.543843\pi$
$643$	19.3304	−	14.0444i	0.762318	−	0.553856i	0.899620	+	0.436673i	$0.143843\pi$
$644$	1.77162	+	1.28716i	0.0698117	+	0.0507212i
$645$	−22.6354	+	16.4456i	−0.891268	+	0.647544i
$646$	−9.82761	−	30.2463i	−0.386662	−	1.19002i
$647$	−34.0383	−	24.7303i	−1.33818	−	0.972247i	−0.999509	−	0.0313439i	$-0.990021\pi$
$647$	−34.0383	−	24.7303i	−1.33818	−	0.972247i	−0.338675	−	0.940903i	$-0.609979\pi$
$648$	2.10815	−	1.53166i	0.0828161	−	0.0601694i
$649$	−5.93776	+	18.2745i	−0.233077	+	0.717339i
$650$	−30.4496	−	93.7142i	−1.19433	−	3.67577i
$651$	−0.798054	−	0.579820i	−0.0312782	−	0.0227250i
$652$	−10.5169	+	32.3678i	−0.411875	+	1.26762i
$653$	20.5133	−	14.9038i	0.802746	−	0.583229i	−0.108973	−	0.994045i	$-0.534756\pi$
$653$	20.5133	−	14.9038i	0.802746	−	0.583229i	0.911718	+	0.410816i	$0.134756\pi$
$654$	16.1242	−	49.6253i	0.630508	−	1.94050i
$655$	11.9786	−	36.8662i	0.468041	−	1.44048i
$656$	0.951557	−	2.92859i	0.0371521	−	0.114342i
$657$	41.6134	+	30.2339i	1.62349	+	1.17954i
$658$	−0.992830	−	3.05562i	−0.0387045	−	0.119120i
$659$	25.6968			1.00100			0.500502	−	0.865735i	$-0.333149\pi$
$659$	25.6968			1.00100			0.500502	+	0.865735i	$0.333149\pi$
$660$	−39.0913	+	28.4015i	−1.52163	+	1.10553i
$661$	−22.8602	+	16.6089i	−0.889160	+	0.646013i	−0.935659	−	0.352906i	$-0.885194\pi$
$661$	−22.8602	+	16.6089i	−0.889160	+	0.646013i	0.0464986	+	0.998918i	$0.485194\pi$
$662$	43.0369			1.67268
$663$	20.6773	−	63.6381i	0.803039	−	2.47150i
$664$	2.49497	+	7.67874i	0.0968237	+	0.297993i
$665$	−3.24986			−0.126024
$666$	−10.0452	−	7.29825i	−0.389243	−	0.282801i
$667$	5.74432	+	4.17349i	0.222421	+	0.161598i
$668$	21.4201	+	15.5626i	0.828769	+	0.602136i
$669$	−27.7054			−1.07115
$670$	39.8153	+	122.539i	1.53820	+	4.73409i
$671$	−5.55195			−0.214331
$672$	−4.35007	+	3.16051i	−0.167808	+	0.121919i
$673$	−20.9110			−0.806059			−0.403029	−	0.915187i	$-0.632043\pi$
$673$	−20.9110			−0.806059			−0.403029	+	0.915187i	$0.632043\pi$
$674$	18.0830	−	55.6538i	0.696532	−	2.14371i
$675$	−16.0505	+	49.3984i	−0.617785	+	1.90135i
$676$	29.9618			1.15238
$677$	−35.4169	+	25.7319i	−1.36118	+	0.988955i	−0.362811	+	0.931863i	$0.618183\pi$
$677$	−35.4169	+	25.7319i	−1.36118	+	0.988955i	−0.998369	+	0.0570928i	$0.981817\pi$
$678$	108.850			4.18036
$679$	−0.933828	−	2.87403i	−0.0358370	−	0.110295i
$680$	−47.3699			−1.81655
$681$	5.01551	+	3.64398i	0.192195	+	0.139638i
$682$	3.03915	+	2.20807i	0.116375	+	0.0845515i
$683$	−7.18527	−	5.22040i	−0.274937	−	0.199753i	0.441769	−	0.897129i	$-0.354351\pi$
$683$	−7.18527	−	5.22040i	−0.274937	−	0.199753i	−0.716706	+	0.697375i	$0.754351\pi$
$684$	−44.1023			−1.68629
$685$	−3.06688	−	9.43887i	−0.117179	−	0.360641i
$686$	−2.97129	+	9.14470i	−0.113444	+	0.349146i
$687$	−67.8363			−2.58812
$688$	1.08771	−	0.790269i	0.0414686	−	0.0301287i
$689$	−6.43035	+	4.67192i	−0.244977	+	0.177986i
$690$	−55.3422			−2.10684
$691$	7.92916	+	24.4035i	0.301640	+	0.928351i	0.980910	+	0.194463i	$0.0622964\pi$
$691$	7.92916	+	24.4035i	0.301640	+	0.928351i	−0.679270	+	0.733888i	$0.737704\pi$
$692$	−17.0665	−	12.3995i	−0.648770	−	0.471359i
$693$	−0.687795	+	2.11682i	−0.0261272	+	0.0804112i
$694$	−8.27511	+	25.4682i	−0.314119	+	0.966759i
$695$	−21.5935	+	66.4580i	−0.819088	+	2.52089i
$696$	17.9001	−	13.0052i	0.678501	−	0.492960i
$697$	9.25213	−	28.4751i	0.350449	−	1.07857i
$698$	−24.9596	−	18.1342i	−0.944733	−	0.686389i
$699$	13.3929	+	41.2190i	0.506565	+	1.55905i
$700$	−2.69777	+	8.30288i	−0.101966	+	0.313819i
$701$	−2.27243	+	1.65102i	−0.0858286	+	0.0623582i	−0.629872	−	0.776699i	$-0.716893\pi$
$701$	−2.27243	+	1.65102i	−0.0858286	+	0.0623582i	0.544043	+	0.839057i	$0.316893\pi$
$702$	−49.3478	−	35.8533i	−1.86251	−	1.35319i
$703$	0.957712	+	2.94753i	0.0361208	+	0.111168i
$704$	15.3613	−	11.1606i	0.578950	−	0.420632i
$705$	40.0221	+	29.0778i	1.50732	+	1.09513i
$706$	61.2880	−	44.5283i	2.30660	−	1.67585i
$707$	−0.862451	−	2.65435i	−0.0324358	−	0.0998272i
$708$	35.9972	+	110.788i	1.35286	+	4.16367i
$709$	10.6279			0.399139			0.199570	−	0.979884i	$-0.436046\pi$
$709$	10.6279			0.399139			0.199570	+	0.979884i	$0.436046\pi$
$710$	−1.01762	+	71.7287i	−0.0381905	+	2.69193i
$711$	47.6083			1.78545
$712$	−4.71294	−	14.5049i	−0.176625	−	0.543596i
$713$	0.810063	+	2.49312i	0.0303371	+	0.0933680i
$714$	−7.87199	+	5.71933i	−0.294602	+	0.214041i
$715$	21.0663	+	15.3056i	0.787835	+	0.572395i
$716$	39.5928	−	28.7658i	1.47965	−	1.07503i
$717$	−2.88378	−	8.87537i	−0.107697	−	0.331457i
$718$	−62.8247	−	45.6448i	−2.34460	−	1.70345i
$719$	−22.0639	+	16.0304i	−0.822846	+	0.597833i	−0.917526	−	0.397675i	$-0.869817\pi$
$719$	−22.0639	+	16.0304i	−0.822846	+	0.597833i	0.0946802	+	0.995508i	$0.469817\pi$
$720$	2.97694	−	9.16209i	0.110944	−	0.341451i
$721$	0.691150	+	2.12714i	0.0257398	+	0.0792189i
$722$	−20.1593	−	14.6466i	−0.750253	−	0.545091i
$723$	−2.91000	+	8.95607i	−0.108224	+	0.333080i
$724$	−32.8568	+	23.8718i	−1.22111	+	0.887190i
$725$	−8.74726	+	26.9213i	−0.324865	+	0.999832i
$726$	−17.5681	+	54.0689i	−0.652012	+	2.00669i
$727$	3.94438	−	12.1395i	0.146289	−	0.450231i	−0.850886	−	0.525351i	$-0.823934\pi$
$727$	3.94438	−	12.1395i	0.146289	−	0.450231i	0.997174	+	0.0751202i	$0.0239340\pi$
$728$	−2.97506	−	2.16151i	−0.110263	−	0.0801108i
$729$	−13.2798	−	40.8711i	−0.491845	−	1.51374i
$730$	−87.5075			−3.23880
$731$	10.5760	−	7.68389i	0.391166	−	0.284199i
$732$	−27.2301	+	19.7838i	−1.00645	+	0.731231i
$733$	−28.1304			−1.03902			−0.519509	−	0.854465i	$-0.673885\pi$
$733$	−28.1304			−1.03902			−0.519509	+	0.854465i	$0.673885\pi$
$734$	−1.97692	+	6.08434i	−0.0729696	+	0.224577i
$735$	−22.7216	−	69.9299i	−0.838099	−	2.57940i
$736$	14.2890			0.526698
$737$	−17.8193	−	12.9465i	−0.656381	−	0.476889i
$738$	−55.1322	−	40.0559i	−2.02944	−	1.47448i
$739$	2.13190	+	1.54892i	0.0784232	+	0.0569778i	0.626306	−	0.779577i	$-0.284566\pi$
$739$	2.13190	+	1.54892i	0.0784232	+	0.0569778i	−0.547883	+	0.836555i	$0.684566\pi$
$740$	12.8700			0.473109
$741$	11.7472	+	36.1541i	0.431544	+	1.32816i
$742$	1.15583			0.0424318
$743$	−12.3030	+	8.93866i	−0.451354	+	0.327928i	−0.790130	−	0.612939i	$-0.789987\pi$
$743$	−12.3030	+	8.93866i	−0.451354	+	0.327928i	0.338776	+	0.940867i	$0.389987\pi$
$744$	8.16870			0.299479
$745$	−6.60763	+	20.3362i	−0.242085	+	0.745061i
$746$	−6.49609	+	19.9929i	−0.237839	+	0.731992i
$747$	−15.9653			−0.584138
$748$	18.2647	−	13.2701i	0.667823	−	0.485202i
$749$	−0.562890			−0.0205675
$750$	−30.9633	−	95.2954i	−1.13062	−	3.47969i
$751$	−25.7267			−0.938781			−0.469390	−	0.882991i	$-0.655526\pi$
$751$	−25.7267			−0.938781			−0.469390	+	0.882991i	$0.655526\pi$
$752$	−1.92321	−	1.39729i	−0.0701321	−	0.0509540i
$753$	−61.6746	−	44.8093i	−2.24755	−	1.63294i
$754$	−26.8937	−	19.5394i	−0.979412	−	0.711584i
$755$	12.4672			0.453727
$756$	1.67000	+	5.13973i	0.0607373	+	0.186930i
$757$	11.0644	−	34.0528i	0.402143	−	1.23767i	−0.521114	−	0.853487i	$-0.674483\pi$
$757$	11.0644	−	34.0528i	0.402143	−	1.23767i	0.923257	−	0.384182i	$-0.125517\pi$
$758$	−27.5503			−1.00067
$759$	7.65382	−	5.56083i	0.277816	−	0.201845i
$760$	21.7721	−	15.8184i	0.789758	−	0.573793i
$761$	23.0273			0.834737			0.417369	−	0.908737i	$-0.362952\pi$
$761$	23.0273			0.834737			0.417369	+	0.908737i	$0.362952\pi$
$762$	31.2710	+	96.2424i	1.13283	+	3.48649i
$763$	2.01552	+	1.46436i	0.0729666	+	0.0530134i
$764$	8.84428	−	27.2199i	0.319975	−	0.984781i
$765$	28.9452	−	89.0843i	1.04652	−	3.22085i
$766$	0.990890	−	3.04965i	0.0358023	−	0.110188i
$767$	50.7870	−	36.8989i	1.83381	−	1.33234i
$768$	10.9698	−	33.7615i	0.395837	−	1.21826i
$769$	−8.88149	−	6.45278i	−0.320275	−	0.232693i	0.416018	−	0.909356i	$-0.363425\pi$
$769$	−8.88149	−	6.45278i	−0.320275	−	0.232693i	−0.736293	+	0.676663i	$0.763425\pi$
$770$	−1.17012	−	3.60124i	−0.0421680	−	0.129780i
$771$	11.8320	−	36.4153i	0.426120	−	1.31146i
$772$	−20.0397	+	14.5597i	−0.721245	+	0.524015i
$773$	8.77603	+	6.37616i	0.315652	+	0.229335i	0.734318	−	0.678806i	$-0.237502\pi$
$773$	8.77603	+	6.37616i	0.315652	+	0.229335i	−0.418666	+	0.908140i	$0.637502\pi$
$774$	−9.19461	−	28.2981i	−0.330493	−	1.01715i
$775$	−8.45480	+	6.14277i	−0.303705	+	0.220655i
$776$	20.2451	+	14.7089i	0.726758	+	0.528020i
$777$	0.767134	−	0.557356i	0.0275208	−	0.0199950i
$778$	−0.922687	−	2.83974i	−0.0330799	−	0.101810i
$779$	5.25633	+	16.1773i	0.188328	+	0.579613i
$780$	157.862			5.65235
$781$	−7.06662	−	10.0223i	−0.252864	−	0.358627i
$782$	25.8576			0.924666
$783$	5.41481	+	16.6651i	0.193510	+	0.595561i
$784$	1.09185	+	3.36038i	0.0389948	+	0.120014i
$785$	−40.3079	+	29.2854i	−1.43865	+	1.04524i
$786$	53.3437	+	38.7565i	1.90271	+	1.38240i
$787$	30.2166	−	21.9537i	1.07711	−	0.782564i	0.0999307	−	0.994994i	$-0.468138\pi$
$787$	30.2166	−	21.9537i	1.07711	−	0.782564i	0.977176	+	0.212430i	$0.0681379\pi$
$788$	25.8517	+	79.5634i	0.920930	+	2.83433i
$789$	13.2678	+	9.63962i	0.472346	+	0.343179i
$790$	−65.5255	+	47.6071i	−2.33129	+	1.69378i
$791$	−1.60599	+	4.94273i	−0.0571025	+	0.175743i
$792$	−5.69557	−	17.5292i	−0.202383	−	0.622872i
$793$	14.6743	+	10.6615i	0.521099	+	0.378601i
$794$	11.6417	−	35.8295i	0.413149	−	1.27154i
$795$	−14.3980	+	10.4607i	−0.510643	+	0.371004i
$796$	10.4545	−	32.1755i	0.370549	−	1.14043i
$797$	1.24782	−	3.84041i	0.0442002	−	0.136034i	−0.926521	−	0.376243i	$-0.877216\pi$
$797$	1.24782	−	3.84041i	0.0442002	−	0.136034i	0.970721	+	0.240209i	$0.0772158\pi$
$798$	1.70824	−	5.25744i	0.0604712	−	0.186111i
$799$	−18.6996	−	13.5861i	−0.661545	−	0.480640i
$800$	17.6032	+	54.1771i	0.622368	+	1.91545i
$801$	30.1580			1.06558
$802$	38.0260	−	27.6275i	1.34274	−	0.975561i
$803$	12.1023	−	8.79283i	0.427081	−	0.310292i
$804$	−133.530			−4.70923
$805$	0.816527	−	2.51301i	0.0287788	−	0.0885720i
$806$	−3.79255	−	11.6723i	−0.133587	−	0.411138i
$807$	6.63069			0.233411
$808$	18.6977	+	13.5847i	0.657783	+	0.477907i
$809$	−6.11746	−	4.44459i	−0.215078	−	0.156264i	0.475030	−	0.879970i	$-0.342437\pi$
$809$	−6.11746	−	4.44459i	−0.215078	−	0.156264i	−0.690108	+	0.723706i	$0.742437\pi$
$810$	−7.09193	−	5.15259i	−0.249185	−	0.181044i
$811$	24.6747			0.866447			0.433223	−	0.901287i	$-0.357376\pi$
$811$	24.6747			0.866447			0.433223	+	0.901287i	$0.357376\pi$
$812$	0.910122	+	2.80107i	0.0319390	+	0.0982982i
$813$	51.6294			1.81072
$814$	−2.92140	+	2.12252i	−0.102395	+	0.0743944i
$815$	41.0659			1.43847
$816$	−2.22477	+	6.84714i	−0.0778825	+	0.239698i
$817$	−2.29502	+	7.06334i	−0.0802925	+	0.247115i
$818$	−51.8323			−1.81227
$819$	5.88286	−	4.27415i	0.205564	−	0.149351i
$820$	70.6358			2.46671
$821$	−10.7701	−	33.1469i	−0.375878	−	1.15683i	−0.942884	−	0.333120i	$-0.891899\pi$
$821$	−10.7701	−	33.1469i	−0.375878	−	1.15683i	0.567007	−	0.823713i	$-0.308101\pi$
$822$	16.8817			0.588817
$823$	29.9436	+	21.7553i	1.04377	+	0.758343i	0.971018	−	0.239007i	$-0.0768219\pi$
$823$	29.9436	+	21.7553i	1.04377	+	0.758343i	0.0727519	+	0.997350i	$0.476822\pi$
$824$	−14.9839	−	10.8865i	−0.521990	−	0.379248i
$825$	30.5132	+	22.1691i	1.06233	+	0.771829i
$826$	−9.12873			−0.317629
$827$	13.8921	+	42.7556i	0.483076	+	1.48676i	0.834748	+	0.550633i	$0.185613\pi$
$827$	13.8921	+	42.7556i	0.483076	+	1.48676i	−0.351671	+	0.936124i	$0.614387\pi$
$828$	11.0807	−	34.1029i	0.385081	−	1.18516i
$829$	49.8182			1.73026			0.865129	−	0.501549i	$-0.167236\pi$
$829$	49.8182			1.73026			0.865129	+	0.501549i	$0.167236\pi$
$830$	21.9737	−	15.9648i	0.762718	−	0.554147i
$831$	−43.0304	+	31.2634i	−1.49271	+	1.08452i
$832$	−62.0331			−2.15061
$833$	10.6163	+	32.6735i	0.367832	+	1.13207i
$834$	−96.1615	−	69.8654i	−3.32980	−	2.41924i
$835$	9.87235	−	30.3840i	0.341647	−	1.05148i
$836$	−3.96349	+	12.1984i	−0.137080	+	0.421890i
$837$	−1.99912	+	6.15266i	−0.0690997	+	0.212667i
$838$	21.4275	−	15.5680i	0.740202	−	0.537789i
$839$	−4.39829	+	13.5366i	−0.151846	+	0.467334i	−0.997828	−	0.0658781i	$-0.979015\pi$
$839$	−4.39829	+	13.5366i	−0.151846	+	0.467334i	0.845982	+	0.533212i	$0.179015\pi$
$840$	−6.66135	−	4.83975i	−0.229838	−	0.166987i
$841$	−6.01051	−	18.4984i	−0.207259	−	0.637878i
$842$	−23.7124	+	72.9794i	−0.817185	+	2.51504i
$843$	−60.6924	+	44.0956i	−2.09036	+	1.51873i
$844$	13.0969	+	9.51544i	0.450813	+	0.327535i
$845$	−11.1718	−	34.3834i	−0.384323	−	1.18282i
$846$	−42.5619	+	30.9230i	−1.46331	+	1.06316i
$847$	−2.19599	−	1.59548i	−0.0754552	−	0.0548214i
$848$	0.691873	−	0.502675i	0.0237590	−	0.0172619i
$849$	−5.75573	−	17.7143i	−0.197536	−	0.607954i
$850$	31.8552	+	98.0401i	1.09262	+	3.36275i
$851$	−2.51986			−0.0863795
$852$	−70.3725	−	23.9743i	−2.41092	−	0.821346i
$853$	−20.9629			−0.717757			−0.358878	−	0.933384i	$-0.616841\pi$
$853$	−20.9629			−0.717757			−0.358878	+	0.933384i	$0.616841\pi$
$854$	−0.815075	−	2.50854i	−0.0278913	−	0.0858406i
$855$	16.4444	+	50.6107i	0.562387	+	1.73085i
$856$	3.77102	−	2.73981i	0.128891	−	0.0936447i
$857$	−30.5329	−	22.1834i	−1.04298	−	0.757772i	−0.0721181	−	0.997396i	$-0.522976\pi$
$857$	−30.5329	−	22.1834i	−1.04298	−	0.757772i	−0.970866	+	0.239624i	$0.922976\pi$
$858$	−35.8336	+	26.0347i	−1.22334	+	0.888809i
$859$	−12.8597	−	39.5780i	−0.438767	−	1.35039i	−0.889177	−	0.457563i	$-0.848722\pi$
$859$	−12.8597	−	39.5780i	−0.438767	−	1.35039i	0.450410	−	0.892822i	$-0.351278\pi$
$860$	24.9509	+	18.1279i	0.850818	+	0.618156i
$861$	4.21036	−	3.05900i	0.143489	−	0.104251i
$862$	18.5232	−	57.0087i	0.630904	−	1.94172i
$863$	−7.20722	−	22.1815i	−0.245337	−	0.755069i	−0.995581	−	0.0939078i	$-0.970064\pi$
$863$	−7.20722	−	22.1815i	−0.245337	−	0.755069i	0.750244	−	0.661161i	$-0.229936\pi$
$864$	28.5285	+	20.7272i	0.970559	+	0.705152i
$865$	−7.86580	+	24.2084i	−0.267445	+	0.823111i
$866$	14.2399	−	10.3459i	0.483890	−	0.351567i
$867$	−6.76927	+	20.8337i	−0.229897	+	0.707549i
$868$	−0.336012	+	1.03414i	−0.0114050	+	0.0351010i
$869$	4.27858	−	13.1681i	0.145141	−	0.446698i
$870$	−60.2167	−	43.7500i	−2.04154	−	1.48326i
$871$	22.2366	+	68.4373i	0.753459	+	2.31891i
$872$	−20.6304			−0.698633
$873$	−40.0325	+	29.0853i	−1.35490	+	0.984389i
$874$	−11.8847	+	8.63472i	−0.402005	+	0.292074i
$875$	4.78407			0.161731
$876$	28.0245	−	86.2506i	0.946861	−	2.91414i
$877$	1.16596	+	3.58847i	0.0393718	+	0.121174i	0.968811	−	0.247802i	$-0.0797084\pi$
$877$	1.16596	+	3.58847i	0.0393718	+	0.121174i	−0.929439	+	0.368976i	$0.879708\pi$
$878$	44.2438			1.49316
$879$	46.5556	+	33.8247i	1.57028	+	1.14088i
$880$	−2.26663	−	1.64680i	−0.0764080	−	0.0555136i
$881$	−33.1171	−	24.0610i	−1.11574	−	0.810634i	−0.132184	−	0.991225i	$-0.542199\pi$
$881$	−33.1171	−	24.0610i	−1.11574	−	0.810634i	−0.983558	+	0.180591i	$0.942199\pi$
$882$	78.1947			2.63295
$883$	7.81579	+	24.0545i	0.263022	+	0.809500i	0.992142	+	0.125114i	$0.0399296\pi$
$883$	7.81579	+	24.0545i	0.263022	+	0.809500i	−0.729120	+	0.684386i	$0.760070\pi$
$884$	−73.7580			−2.48075
$885$	113.715	−	82.6189i	3.82249	−	2.77720i
$886$	41.5909			1.39727
$887$	−5.31282	+	16.3512i	−0.178387	+	0.549019i	−0.999772	−	0.0213555i	$-0.993202\pi$
$887$	−5.31282	+	16.3512i	−0.178387	+	0.549019i	0.821385	+	0.570374i	$0.193202\pi$
$888$	−2.42647	+	7.46790i	−0.0814269	+	0.250606i
$889$	−4.83161			−0.162047
$890$	−41.5078	+	30.1572i	−1.39134	+	1.01087i
$891$	1.49855			0.0502033
$892$	9.43725	+	29.0449i	0.315982	+	0.972494i
$893$	13.1315			0.439431
$894$	−29.4255	−	21.3789i	−0.984136	−	0.715017i
$895$	−47.7739	−	34.7098i	−1.59690	−	1.16022i
$896$	4.22274	+	3.06800i	0.141072	+	0.102495i
$897$	−30.9083			−1.03200
$898$	0.486003	+	1.49576i	0.0162181	+	0.0499143i
$899$	−1.08949	+	3.35310i	−0.0363365	+	0.111832i
$900$	142.953			4.76510
$901$	6.72718	−	4.88758i	0.224115	−	0.162829i
$902$	−16.0339	+	11.6493i	−0.533871	+	0.387880i
$903$	2.27230			0.0756173
$904$	−13.2991	−	40.9303i	−0.442321	−	1.36132i
$905$	39.6460	+	28.8045i	1.31788	+	0.957494i
$906$	−6.55320	+	20.1687i	−0.217715	+	0.670059i
$907$	−7.11508	+	21.8980i	−0.236252	+	0.727110i	0.760700	+	0.649103i	$0.224856\pi$
$907$	−7.11508	+	21.8980i	−0.236252	+	0.727110i	−0.996953	+	0.0780070i	$0.975144\pi$
$908$	2.11173	−	6.49923i	0.0700801	−	0.215684i
$909$	−36.9727	+	26.8622i	−1.22631	+	0.890963i
$910$	−3.82281	+	11.7654i	−0.126725	+	0.390019i
$911$	−9.17411	−	6.66538i	−0.303952	−	0.220834i	0.425345	−	0.905031i	$-0.360153\pi$
$911$	−9.17411	−	6.66538i	−0.303952	−	0.220834i	−0.729297	+	0.684197i	$0.760153\pi$
$912$	−1.26394	−	3.89000i	−0.0418532	−	0.128811i
$913$	−1.43480	+	4.41587i	−0.0474851	+	0.146144i
$914$	7.63429	−	5.54663i	0.252520	−	0.183466i
$915$	32.8567	+	23.8718i	1.08621	+	0.789176i
$916$	23.1069	+	71.1159i	0.763475	+	2.34973i
$917$	−2.54692	+	1.85044i	−0.0841066	+	0.0611070i
$918$	51.6257	+	37.5083i	1.70390	+	1.23796i
$919$	−17.3014	+	12.5702i	−0.570720	+	0.414652i	−0.835367	−	0.549693i	$-0.814745\pi$
$919$	−17.3014	+	12.5702i	−0.570720	+	0.414652i	0.264647	+	0.964345i	$0.414745\pi$
$920$	6.76159	+	20.8100i	0.222923	+	0.686086i
$921$	−23.6514	−	72.7916i	−0.779340	−	2.39856i
$922$	79.4376			2.61614
$923$	−0.568333	+	40.0601i	−0.0187069	+	1.31859i
$924$	3.92425			0.129098
$925$	−3.10432	−	9.55412i	−0.102070	−	0.314138i
$926$	−3.50960	−	10.8014i	−0.115333	−	0.354957i
$927$	29.6291	−	21.5268i	0.973148	−	0.707033i
$928$	15.5475	+	11.2960i	0.510373	+	0.370808i
$929$	23.6562	−	17.1872i	0.776134	−	0.563894i	−0.127683	−	0.991815i	$-0.540754\pi$
$929$	23.6562	−	17.1872i	0.776134	−	0.563894i	0.903816	+	0.427921i	$0.140754\pi$
$930$	−8.49176	−	26.1349i	−0.278456	−	0.856999i
$931$	−15.7902	−	11.4723i	−0.517503	−	0.375988i
$932$	38.6498	−	28.0807i	1.26602	−	0.919815i
$933$	−15.4591	+	47.5781i	−0.506107	+	1.55764i
$934$	−0.153065	−	0.471085i	−0.00500843	−	0.0154144i
$935$	−22.0387	−	16.0121i	−0.720744	−	0.523651i
$936$	−18.6077	+	57.2685i	−0.608210	+	1.87188i
$937$	−5.05235	+	3.67075i	−0.165053	+	0.119918i	−0.667246	−	0.744838i	$-0.732527\pi$
$937$	−5.05235	+	3.67075i	−0.165053	+	0.119918i	0.502193	+	0.864756i	$0.332527\pi$
$938$	3.23359	−	9.95196i	0.105580	−	0.324943i
$939$	−5.86768	+	18.0588i	−0.191484	+	0.589328i
$940$	16.8509	−	51.8617i	0.549616	−	1.69154i
$941$	−39.3822	−	28.6129i	−1.28382	−	0.932753i	−0.284163	−	0.958776i	$-0.591716\pi$
$941$	−39.3822	−	28.6129i	−1.28382	−	0.932753i	−0.999661	+	0.0260234i	$0.991716\pi$
$942$	−26.1889	−	80.6013i	−0.853282	−	2.62613i
$943$	−13.8300			−0.450368
$944$	−5.46442	+	3.97013i	−0.177852	+	0.129217i
$945$	5.27553	−	3.83289i	0.171613	−	0.124684i
$946$	−8.65337			−0.281345
$947$	−7.88331	+	24.2623i	−0.256173	+	0.788420i	0.737423	+	0.675431i	$0.236042\pi$
$947$	−7.88331	+	24.2623i	−0.256173	+	0.788420i	−0.993596	+	0.112989i	$0.963958\pi$
$948$	−25.9385	−	79.8306i	−0.842445	−	2.59278i
$949$	−48.8725			−1.58647
$950$	−47.3801	−	34.4237i	−1.53721	−	1.11685i
$951$	72.7817	+	52.8790i	2.36011	+	1.71472i
$952$	3.11239	+	2.26129i	0.100873	+	0.0732887i
$953$	−41.0505			−1.32976			−0.664878	−	0.746952i	$-0.731517\pi$
$953$	−41.0505			−1.32976			−0.664878	+	0.746952i	$0.731517\pi$
$954$	−5.84852	−	17.9999i	−0.189353	−	0.582768i
$955$	−34.5346			−1.11751
$956$	−8.32216	+	6.04640i	−0.269158	+	0.195555i
$957$	12.7240			0.411309
$958$	20.2873	−	62.4378i	0.655452	−	2.01727i
$959$	−0.249075	+	0.766575i	−0.00804306	+	0.0247540i
$960$	−138.896			−4.48285
$961$	24.0265	−	17.4562i	0.775047	−	0.563105i
$962$	11.7974			0.380365
$963$	2.84824	+	8.76598i	0.0917833	+	0.282480i
$964$	10.3803			0.334326
$965$	24.1805	+	17.5682i	0.778399	+	0.565540i
$966$	3.63620	+	2.64186i	0.116993	+	0.0850004i
$967$	−14.8192	−	10.7668i	−0.476555	−	0.346237i	0.323436	−	0.946250i	$-0.395162\pi$
$967$	−14.8192	−	10.7668i	−0.476555	−	0.346237i	−0.799990	+	0.600013i	$0.795162\pi$
$968$	22.4777			0.722460
$969$	−12.2895	−	37.8231i	−0.394794	−	1.21505i
$970$	26.0140	−	80.0629i	0.835260	−	2.57066i
$971$	6.47250			0.207712			0.103856	−	0.994592i	$-0.466882\pi$
$971$	6.47250			0.207712			0.103856	+	0.994592i	$0.466882\pi$
$972$	−35.5688	+	25.8423i	−1.14087	+	0.828891i
$973$	4.59127	−	3.33575i	0.147189	−	0.106939i
$974$	−12.2434			−0.392302
$975$	−38.0773	−	117.190i	−1.21945	−	3.75308i
$976$	−1.57888	−	1.14712i	−0.0505387	−	0.0367185i
$977$	−5.83151	+	17.9475i	−0.186566	+	0.574192i	−0.999972	−	0.00750475i	$-0.997611\pi$
$977$	−5.83151	+	17.9475i	−0.186566	+	0.574192i	0.813405	+	0.581697i	$0.197611\pi$
$978$	−21.5857	+	66.4339i	−0.690234	+	2.12432i
$979$	2.71031	−	8.34147i	0.0866219	−	0.266595i
$980$	−65.5711	+	47.6402i	−2.09459	+	1.52181i
$981$	12.6061	−	38.7977i	0.402483	−	1.23872i
$982$	−31.5913	−	22.9524i	−1.00812	−	0.732441i
$983$	14.1109	+	43.4288i	0.450067	+	1.38516i	0.876831	+	0.480799i	$0.159653\pi$
$983$	14.1109	+	43.4288i	0.450067	+	1.38516i	−0.426764	+	0.904363i	$0.640347\pi$
$984$	−13.3175	+	40.9870i	−0.424546	+	1.30662i
$985$	81.6656	−	59.3335i	2.60208	−	1.89052i
$986$	28.1352	+	20.4414i	0.896006	+	0.650987i
$987$	−1.24154	−	3.82106i	−0.0395186	−	0.121626i
$988$	33.9006	−	24.6302i	1.07852	−	0.783592i
$989$	−4.88522	−	3.54932i	−0.155341	−	0.112862i
$990$	−50.1620	+	36.4448i	−1.59425	+	1.15829i
$991$	−2.68825	−	8.27360i	−0.0853952	−	0.262819i	0.899237	−	0.437463i	$-0.144123\pi$
$991$	−2.68825	−	8.27360i	−0.0853952	−	0.262819i	−0.984632	+	0.174643i	$0.944123\pi$
$992$	2.19251	+	6.74786i	0.0696124	+	0.214245i
$993$	53.8178			1.70785
$994$	3.49096	−	4.66429i	0.110727	−	0.147942i
$995$	−40.8220			−1.29414
$996$	8.69838	+	26.7709i	0.275619	+	0.848268i
$997$	6.35875	+	19.5702i	0.201384	+	0.619795i	0.999843	+	0.0177460i	$0.00564902\pi$
$997$	6.35875	+	19.5702i	0.201384	+	0.619795i	−0.798459	+	0.602049i	$0.794351\pi$
$998$	48.9821	−	35.5876i	1.55050	−	1.12650i
$999$	−5.03099	−	3.65523i	−0.159173	−	0.115646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.c.a.5.1	✓	20
3.2	odd	2		639.2.f.c.289.5		20
71.25	even	5		5041.2.a.i.1.1		10
71.46	odd	10		5041.2.a.j.1.1		10
71.57	even	5	inner	71.2.c.a.57.1	yes	20
213.128	odd	10		639.2.f.c.199.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.c.a.5.1	✓	20	1.1	even	1	trivial
71.2.c.a.57.1	yes	20	71.57	even	5	inner
639.2.f.c.199.5		20	213.128	odd	10
639.2.f.c.289.5		20	3.2	odd	2
5041.2.a.i.1.1		10	71.25	even	5
5041.2.a.j.1.1		10	71.46	odd	10

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.699129 - 2.15170i) q^{2} +(-0.874263 - 2.69071i) q^{3} +(-2.52299 + 1.83306i) q^{4} +(3.04432 + 2.21183i) q^{5} +(-5.17837 + 3.76230i) q^{6} +(-0.0944386 - 0.290652i) q^{7} +(2.04740 + 1.48752i) q^{8} +(-4.04851 + 2.94142i) q^{9} +O(q^{10})\)	\(q+(-0.699129 - 2.15170i) q^{2} +(-0.874263 - 2.69071i) q^{3} +(-2.52299 + 1.83306i) q^{4} +(3.04432 + 2.21183i) q^{5} +(-5.17837 + 3.76230i) q^{6} +(-0.0944386 - 0.290652i) q^{7} +(2.04740 + 1.48752i) q^{8} +(-4.04851 + 2.94142i) q^{9} +(2.63081 - 8.09681i) q^{10} +(0.449733 + 1.38413i) q^{11} +(7.13798 + 5.18605i) q^{12} +(1.46929 - 4.52202i) q^{13} +(-0.559371 + 0.406407i) q^{14} +(3.28984 - 10.1251i) q^{15} +(-0.158089 + 0.486547i) q^{16} +(-1.53712 + 4.73076i) q^{17} +(9.15947 + 6.65475i) q^{18} +(-0.873269 - 2.68765i) q^{19} -11.7352 q^{20} +(-0.699495 + 0.508213i) q^{21} +(2.66382 - 1.93538i) q^{22} +2.29768 q^{23} +(2.21252 - 6.80944i) q^{24} +(2.83061 + 8.71172i) q^{25} -10.7573 q^{26} +(4.58740 + 3.33294i) q^{27} +(0.771050 + 0.560201i) q^{28} +(2.50006 + 1.81640i) q^{29} -24.0861 q^{30} +(0.352558 + 1.08506i) q^{31} +6.21888 q^{32} +(3.33111 - 2.42020i) q^{33} +11.2538 q^{34} +(0.355371 - 1.09372i) q^{35} +(4.82257 - 14.8423i) q^{36} -1.09670 q^{37} +(-5.17247 + 3.75802i) q^{38} -13.4520 q^{39} +(2.94279 + 9.05699i) q^{40} -6.01914 q^{41} +(1.58256 + 1.14980i) q^{42} +(-2.12616 - 1.54474i) q^{43} +(-3.67187 - 2.66777i) q^{44} -18.8309 q^{45} +(-1.60637 - 4.94390i) q^{46} +(-1.43593 + 4.41933i) q^{47} +1.44736 q^{48} +(5.58756 - 4.05960i) q^{49} +(16.7660 - 12.1812i) q^{50} +14.0729 q^{51} +(4.58212 + 14.1023i) q^{52} +(-1.35241 - 0.982584i) q^{53} +(3.96430 - 12.2009i) q^{54} +(-1.69234 + 5.20848i) q^{55} +(0.238998 - 0.735561i) q^{56} +(-6.46820 + 4.69942i) q^{57} +(2.16048 - 6.64926i) q^{58} +(10.6813 + 7.76045i) q^{59} +(10.2597 + 31.5760i) q^{60} +(-1.17884 + 3.62810i) q^{61} +(2.08824 - 1.51720i) q^{62} +(1.23726 + 0.898925i) q^{63} +(-4.03162 - 12.4081i) q^{64} +(14.4749 - 10.5166i) q^{65} +(-7.53641 - 5.47552i) q^{66} +(-12.2439 + 8.89568i) q^{67} +(-4.79364 - 14.7533i) q^{68} +(-2.00877 - 6.18237i) q^{69} -2.60180 q^{70} +(-8.04988 + 2.48988i) q^{71} -12.6644 q^{72} +(-3.17629 - 9.77562i) q^{73} +(0.766733 + 2.35976i) q^{74} +(20.9660 - 15.2327i) q^{75} +(7.12986 + 5.18015i) q^{76} +(0.359829 - 0.261431i) q^{77} +(9.40467 + 28.9446i) q^{78} +(-7.69667 - 5.59196i) q^{79} +(-1.55743 + 1.13154i) q^{80} +(0.318187 - 0.979278i) q^{81} +(4.20816 + 12.9514i) q^{82} +(2.58105 + 1.87524i) q^{83} +(0.833235 - 2.56443i) q^{84} +(-15.1431 + 11.0021i) q^{85} +(-1.83737 + 5.65483i) q^{86} +(2.70168 - 8.31493i) q^{87} +(-1.13815 + 3.50287i) q^{88} +(-4.87553 - 3.54228i) q^{89} +(13.1652 + 40.5183i) q^{90} -1.45309 q^{91} +(-5.79701 + 4.21178i) q^{92} +(2.61135 - 1.89726i) q^{93} +10.5130 q^{94} +(3.28610 - 10.1136i) q^{95} +(-5.43694 - 16.7332i) q^{96} +9.88821 q^{97} +(-12.6415 - 9.18456i) q^{98} +(-5.89206 - 4.28083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

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