LMFDB - Embedded newform 975.2.v.c.196.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(196,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("975.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.v (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.5
Character	$\chi$	$=$	975.196
Dual form			975.2.v.c.781.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.557974 + 1.71727i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.01964 - 0.740813i) q^{4} +(0.882029 + 2.05476i) q^{5} +(-1.46080 + 1.06133i) q^{6} +4.37508 q^{7} +(-1.08048 + 0.785017i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.557974 + 1.71727i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.01964 - 0.740813i) q^{4} +(0.882029 + 2.05476i) q^{5} +(-1.46080 + 1.06133i) q^{6} +4.37508 q^{7} +(-1.08048 + 0.785017i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-4.02072 + 0.368180i) q^{10} +(-1.62156 + 4.99066i) q^{11} +(-0.389468 - 1.19866i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.44118 + 7.51318i) q^{14} +(-0.494179 + 2.18078i) q^{15} +(-1.52414 - 4.69082i) q^{16} +(0.848825 - 0.616708i) q^{17} -1.80564 q^{18} +(6.44536 - 4.68283i) q^{19} +(0.622836 - 2.74853i) q^{20} +(3.53951 + 2.57161i) q^{21} +(-7.66550 - 5.56931i) q^{22} +(2.26249 - 6.96322i) q^{23} -1.33555 q^{24} +(-3.44405 + 3.62471i) q^{25} -1.80564 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.46101 - 3.24111i) q^{28} +(-2.59612 - 1.88619i) q^{29} +(-3.46924 - 2.06545i) q^{30} +(0.362929 - 0.263683i) q^{31} +6.23473 q^{32} +(-4.24530 + 3.08439i) q^{33} +(0.585430 + 1.80177i) q^{34} +(3.85895 + 8.98972i) q^{35} +(0.389468 - 1.19866i) q^{36} +(0.879475 + 2.70675i) q^{37} +(4.44533 + 13.6813i) q^{38} +(-0.309017 + 0.951057i) q^{39} +(-2.56604 - 1.52772i) q^{40} +(2.68162 + 8.25317i) q^{41} +(-6.39110 + 4.64340i) q^{42} +0.278799 q^{43} +(5.35055 - 3.88740i) q^{44} +(-1.68163 + 1.47381i) q^{45} +(10.6953 + 7.77059i) q^{46} +(-7.33588 - 5.32983i) q^{47} +(1.52414 - 4.69082i) q^{48} +12.1413 q^{49} +(-4.30291 - 7.93685i) q^{50} +1.04921 q^{51} +(0.389468 - 1.19866i) q^{52} +(-7.77644 - 5.64992i) q^{53} +(-1.46080 - 1.06133i) q^{54} +(-11.6848 + 1.06999i) q^{55} +(-4.72720 + 3.43451i) q^{56} +7.96690 q^{57} +(4.68766 - 3.40578i) q^{58} +(-3.18943 - 9.81604i) q^{59} +(2.11943 - 1.85752i) q^{60} +(2.33115 - 7.17454i) q^{61} +(0.250310 + 0.770375i) q^{62} +(1.35197 + 4.16095i) q^{63} +(-0.430537 + 1.32506i) q^{64} +(-1.68163 + 1.47381i) q^{65} +(-2.92796 - 9.01134i) q^{66} +(-2.93026 + 2.12896i) q^{67} -1.32236 q^{68} +(5.92327 - 4.30350i) q^{69} +(-17.5910 + 1.61082i) q^{70} +(2.74674 + 1.99563i) q^{71} +(-1.08048 - 0.785017i) q^{72} +(-1.97199 + 6.06915i) q^{73} -5.13893 q^{74} +(-4.91685 + 0.908092i) q^{75} -10.0411 q^{76} +(-7.09446 + 21.8345i) q^{77} +(-1.46080 - 1.06133i) q^{78} +(-10.3685 - 7.53316i) q^{79} +(8.29416 - 7.26918i) q^{80} +(-0.809017 + 0.587785i) q^{81} -15.6692 q^{82} +(7.70443 - 5.59760i) q^{83} +(-1.70395 - 5.24423i) q^{84} +(2.01587 + 1.20017i) q^{85} +(-0.155562 + 0.478772i) q^{86} +(-0.991628 - 3.05192i) q^{87} +(-2.16568 - 6.66528i) q^{88} +(5.03948 - 15.5099i) q^{89} +(-1.59263 - 3.71016i) q^{90} +(1.35197 + 4.16095i) q^{91} +(-7.46536 + 5.42390i) q^{92} +0.448605 q^{93} +(13.2460 - 9.62377i) q^{94} +(15.3071 + 9.11325i) q^{95} +(5.04400 + 3.66468i) q^{96} +(-12.5597 - 9.12514i) q^{97} +(-6.77454 + 20.8499i) q^{98} -5.24749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) $ 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9	\( 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 17 q^{13} - 26 q^{14} - q^{15} - 19 q^{16} - 7 q^{17} + 4 q^{18} - 8 q^{19} + 55 q^{20} - q^{21} - 26 q^{22} - 15 q^{23} - 18 q^{24} + 3 q^{25} + 4 q^{26} + 17 q^{27} + 9 q^{28} - 25 q^{29} - 28 q^{30} - 26 q^{31} + 180 q^{32} + 8 q^{33} + 26 q^{34} - 46 q^{35} - 19 q^{36} - 8 q^{37} + 8 q^{38} + 17 q^{39} + 82 q^{40} - 9 q^{41} - 4 q^{42} - 100 q^{43} - 5 q^{44} + 6 q^{45} + 32 q^{46} + 2 q^{47} + 19 q^{48} + 204 q^{49} - 29 q^{50} + 2 q^{51} - 19 q^{52} - 31 q^{53} + q^{54} - 37 q^{55} - 17 q^{56} + 8 q^{57} + 11 q^{58} - 13 q^{59} - 25 q^{60} + 14 q^{61} - 46 q^{62} + q^{63} - 56 q^{64} + 6 q^{65} - 39 q^{66} - 12 q^{67} + 26 q^{68} - 10 q^{69} + 117 q^{70} + 7 q^{71} - 12 q^{72} - 10 q^{73} + 76 q^{74} + 2 q^{75} + 6 q^{76} - 5 q^{77} + q^{78} - 46 q^{79} + 128 q^{80} - 17 q^{81} + 102 q^{82} + 28 q^{83} - 4 q^{84} - 40 q^{85} - 60 q^{86} + 64 q^{88} - 38 q^{89} - 17 q^{90} + q^{91} - 42 q^{92} - 64 q^{93} + 39 q^{94} - 49 q^{95} + 60 q^{96} - 34 q^{97} + 53 q^{98} + 12 q^{99}+O(q^{100}) \) 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 17 * q^13 - 26 * q^14 - q^15 - 19 * q^16 - 7 * q^17 + 4 * q^18 - 8 * q^19 + 55 * q^20 - q^21 - 26 * q^22 - 15 * q^23 - 18 * q^24 + 3 * q^25 + 4 * q^26 + 17 * q^27 + 9 * q^28 - 25 * q^29 - 28 * q^30 - 26 * q^31 + 180 * q^32 + 8 * q^33 + 26 * q^34 - 46 * q^35 - 19 * q^36 - 8 * q^37 + 8 * q^38 + 17 * q^39 + 82 * q^40 - 9 * q^41 - 4 * q^42 - 100 * q^43 - 5 * q^44 + 6 * q^45 + 32 * q^46 + 2 * q^47 + 19 * q^48 + 204 * q^49 - 29 * q^50 + 2 * q^51 - 19 * q^52 - 31 * q^53 + q^54 - 37 * q^55 - 17 * q^56 + 8 * q^57 + 11 * q^58 - 13 * q^59 - 25 * q^60 + 14 * q^61 - 46 * q^62 + q^63 - 56 * q^64 + 6 * q^65 - 39 * q^66 - 12 * q^67 + 26 * q^68 - 10 * q^69 + 117 * q^70 + 7 * q^71 - 12 * q^72 - 10 * q^73 + 76 * q^74 + 2 * q^75 + 6 * q^76 - 5 * q^77 + q^78 - 46 * q^79 + 128 * q^80 - 17 * q^81 + 102 * q^82 + 28 * q^83 - 4 * q^84 - 40 * q^85 - 60 * q^86 + 64 * q^88 - 38 * q^89 - 17 * q^90 + q^91 - 42 * q^92 - 64 * q^93 + 39 * q^94 - 49 * q^95 + 60 * q^96 - 34 * q^97 + 53 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.557974	+	1.71727i	−0.394547	+	1.21429i	0.534766	+	0.845000i	$0.320400\pi$
$2$	−0.557974	+	1.71727i	−0.394547	+	1.21429i	−0.929313	+	0.369292i	$0.879600\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−1.01964	−	0.740813i	−0.509821	−	0.370406i
$5$	0.882029	+	2.05476i	0.394456	+	0.918915i
$5$	0.882029	+	2.05476i	0.394456	+	0.918915i
$6$	−1.46080	+	1.06133i	−0.596367	+	0.433286i
$7$	4.37508			1.65362			0.826812	−	0.562478i	$-0.190152\pi$
$7$	4.37508			1.65362			0.826812	+	0.562478i	$0.190152\pi$
$8$	−1.08048	+	0.785017i	−0.382009	+	0.277546i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−4.02072	+	0.368180i	−1.27146	+	0.116429i
$11$	−1.62156	+	4.99066i	−0.488919	+	1.50474i	0.337304	+	0.941396i	$0.390485\pi$
$11$	−1.62156	+	4.99066i	−0.488919	+	1.50474i	−0.826223	+	0.563343i	$0.809515\pi$
$12$	−0.389468	−	1.19866i	−0.112430	−	0.346023i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	−2.44118	+	7.51318i	−0.652433	+	2.00798i
$15$	−0.494179	+	2.18078i	−0.127596	+	0.563074i
$16$	−1.52414	−	4.69082i	−0.381035	−	1.17271i
$17$	0.848825	−	0.616708i	0.205870	−	0.149574i	−0.480073	−	0.877229i	$-0.659390\pi$
$17$	0.848825	−	0.616708i	0.205870	−	0.149574i	0.685943	+	0.727655i	$0.259390\pi$
$18$	−1.80564			−0.425594
$19$	6.44536	−	4.68283i	1.47867	−	1.07431i	0.500684	−	0.865630i	$-0.333082\pi$
$19$	6.44536	−	4.68283i	1.47867	−	1.07431i	0.977983	−	0.208685i	$-0.0669182\pi$
$20$	0.622836	−	2.74853i	0.139270	−	0.614591i
$21$	3.53951	+	2.57161i	0.772385	+	0.561171i
$22$	−7.66550	−	5.56931i	−1.63429	−	1.18738i
$23$	2.26249	−	6.96322i	0.471761	−	1.45193i	−0.378516	−	0.925595i	$-0.623565\pi$
$23$	2.26249	−	6.96322i	0.471761	−	1.45193i	0.850277	−	0.526336i	$-0.176435\pi$
$24$	−1.33555			−0.272618
$25$	−3.44405	+	3.62471i	−0.688810	+	0.724942i
$26$	−1.80564			−0.354116
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−4.46101	−	3.24111i	−0.843052	−	0.612513i
$29$	−2.59612	−	1.88619i	−0.482087	−	0.350256i	0.320046	−	0.947402i	$-0.396302\pi$
$29$	−2.59612	−	1.88619i	−0.482087	−	0.350256i	−0.802133	+	0.597145i	$0.796302\pi$
$30$	−3.46924	−	2.06545i	−0.633394	−	0.377099i
$31$	0.362929	−	0.263683i	0.0651840	−	0.0473590i	−0.554716	−	0.832040i	$-0.687173\pi$
$31$	0.362929	−	0.263683i	0.0651840	−	0.0473590i	0.619900	+	0.784681i	$0.287173\pi$
$32$	6.23473			1.10215
$33$	−4.24530	+	3.08439i	−0.739013	+	0.536924i
$34$	0.585430	+	1.80177i	0.100400	+	0.309001i
$35$	3.85895	+	8.98972i	0.652281	+	1.51954i
$36$	0.389468	−	1.19866i	0.0649114	−	0.199777i
$37$	0.879475	+	2.70675i	0.144585	+	0.444986i	0.996957	−	0.0779487i	$-0.0248370\pi$
$37$	0.879475	+	2.70675i	0.144585	+	0.444986i	−0.852373	+	0.522935i	$0.824837\pi$
$38$	4.44533	+	13.6813i	0.721127	+	2.21940i
$39$	−0.309017	+	0.951057i	−0.0494823	+	0.152291i
$40$	−2.56604	−	1.52772i	−0.405726	−	0.241554i
$41$	2.68162	+	8.25317i	0.418798	+	1.28893i	0.908809	+	0.417213i	$0.136993\pi$
$41$	2.68162	+	8.25317i	0.418798	+	1.28893i	−0.490010	+	0.871717i	$0.663007\pi$
$42$	−6.39110	+	4.64340i	−0.986167	+	0.716493i
$43$	0.278799			0.0425164			0.0212582	−	0.999774i	$-0.493233\pi$
$43$	0.278799			0.0425164			0.0212582	+	0.999774i	$0.493233\pi$
$44$	5.35055	−	3.88740i	0.806626	−	0.586048i
$45$	−1.68163	+	1.47381i	−0.250682	+	0.219703i
$46$	10.6953	+	7.77059i	1.57694	+	1.14571i
$47$	−7.33588	−	5.32983i	−1.07005	−	0.777436i	−0.0941275	−	0.995560i	$-0.530006\pi$
$47$	−7.33588	−	5.32983i	−1.07005	−	0.777436i	−0.975921	+	0.218124i	$0.930006\pi$
$48$	1.52414	−	4.69082i	0.219991	−	0.677062i
$49$	12.1413			1.73447
$50$	−4.30291	−	7.93685i	−0.608524	−	1.12244i
$51$	1.04921			0.146918
$52$	0.389468	−	1.19866i	0.0540095	−	0.166224i
$53$	−7.77644	−	5.64992i	−1.06818	−	0.776076i	−0.0925929	−	0.995704i	$-0.529516\pi$
$53$	−7.77644	−	5.64992i	−1.06818	−	0.776076i	−0.975584	+	0.219628i	$0.929516\pi$
$54$	−1.46080	−	1.06133i	−0.198789	−	0.144429i
$55$	−11.6848	+	1.06999i	−1.57558	+	0.144277i
$56$	−4.72720	+	3.43451i	−0.631699	+	0.458956i
$57$	7.96690			1.05524
$58$	4.68766	−	3.40578i	0.615520	−	0.447201i
$59$	−3.18943	−	9.81604i	−0.415228	−	1.27794i	−0.912047	−	0.410086i	$-0.865499\pi$
$59$	−3.18943	−	9.81604i	−0.415228	−	1.27794i	0.496819	−	0.867854i	$-0.334501\pi$
$60$	2.11943	−	1.85752i	0.273618	−	0.239804i
$61$	2.33115	−	7.17454i	0.298473	−	0.918605i	−0.683560	−	0.729895i	$-0.739569\pi$
$61$	2.33115	−	7.17454i	0.298473	−	0.918605i	0.982033	−	0.188711i	$-0.0604308\pi$
$62$	0.250310	+	0.770375i	0.0317894	+	0.0978378i
$63$	1.35197	+	4.16095i	0.170333	+	0.524230i
$64$	−0.430537	+	1.32506i	−0.0538171	+	0.165632i
$65$	−1.68163	+	1.47381i	−0.208580	+	0.182804i
$66$	−2.92796	−	9.01134i	−0.360407	−	1.10922i
$67$	−2.93026	+	2.12896i	−0.357989	+	0.260094i	−0.752213	−	0.658920i	$-0.771013\pi$
$67$	−2.93026	+	2.12896i	−0.357989	+	0.260094i	0.394224	+	0.919014i	$0.371013\pi$
$68$	−1.32236			−0.160360
$69$	5.92327	−	4.30350i	0.713077	−	0.518081i
$70$	−17.5910	+	1.61082i	−2.10252	+	0.192529i
$71$	2.74674	+	1.99563i	0.325978	+	0.236837i	0.738722	−	0.674010i	$-0.235430\pi$
$71$	2.74674	+	1.99563i	0.325978	+	0.236837i	−0.412744	+	0.910847i	$0.635430\pi$
$72$	−1.08048	−	0.785017i	−0.127336	−	0.0925152i
$73$	−1.97199	+	6.06915i	−0.230804	+	0.710341i	0.766847	+	0.641830i	$0.221825\pi$
$73$	−1.97199	+	6.06915i	−0.230804	+	0.710341i	−0.997650	+	0.0685105i	$0.978175\pi$
$74$	−5.13893			−0.597389
$75$	−4.91685	+	0.908092i	−0.567748	+	0.104857i
$76$	−10.0411			−1.15179
$77$	−7.09446	+	21.8345i	−0.808489	+	2.48827i
$78$	−1.46080	−	1.06133i	−0.165403	−	0.120172i
$79$	−10.3685	−	7.53316i	−1.16655	−	0.847546i	−0.175956	−	0.984398i	$-0.556302\pi$
$79$	−10.3685	−	7.53316i	−1.16655	−	0.847546i	−0.990592	+	0.136852i	$0.956302\pi$
$80$	8.29416	−	7.26918i	0.927315	−	0.812719i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−15.6692			−1.73037
$83$	7.70443	−	5.59760i	0.845671	−	0.614416i	−0.0782779	−	0.996932i	$-0.524942\pi$
$83$	7.70443	−	5.59760i	0.845671	−	0.614416i	0.923949	+	0.382516i	$0.124942\pi$
$84$	−1.70395	−	5.24423i	−0.185917	−	0.572193i
$85$	2.01587	+	1.20017i	0.218652	+	0.130177i
$86$	−0.155562	+	0.478772i	−0.0167747	+	0.0516273i
$87$	−0.991628	−	3.05192i	−0.106314	−	0.327200i
$88$	−2.16568	−	6.66528i	−0.230862	−	0.710521i
$89$	5.03948	−	15.5099i	0.534184	−	1.64405i	−0.211223	−	0.977438i	$-0.567745\pi$
$89$	5.03948	−	15.5099i	0.534184	−	1.64405i	0.745407	−	0.666610i	$-0.232255\pi$
$90$	−1.59263	−	3.71016i	−0.167878	−	0.391085i
$91$	1.35197	+	4.16095i	0.141725	+	0.436186i
$92$	−7.46536	+	5.42390i	−0.778318	+	0.565481i
$93$	0.448605			0.0465182
$94$	13.2460	−	9.62377i	1.36622	−	0.992616i
$95$	15.3071	+	9.11325i	1.57047	+	0.935000i
$96$	5.04400	+	3.66468i	0.514801	+	0.374025i
$97$	−12.5597	−	9.12514i	−1.27524	−	0.926517i	−0.275843	−	0.961203i	$-0.588957\pi$
$97$	−12.5597	−	9.12514i	−1.27524	−	0.926517i	−0.999398	+	0.0346852i	$0.988957\pi$
$98$	−6.77454	+	20.8499i	−0.684332	+	2.10616i
$99$	−5.24749			−0.527392
$100$	6.19693	−	1.14451i	0.619693	−	0.114451i
$101$	2.85304			0.283888			0.141944	−	0.989875i	$-0.454665\pi$
$101$	2.85304			0.283888			0.141944	+	0.989875i	$0.454665\pi$
$102$	−0.585430	+	1.80177i	−0.0579662	+	0.178402i
$103$	4.63127	+	3.36482i	0.456333	+	0.331545i	0.792091	−	0.610403i	$-0.208992\pi$
$103$	4.63127	+	3.36482i	0.456333	+	0.331545i	−0.335758	+	0.941948i	$0.608992\pi$
$104$	−1.08048	−	0.785017i	−0.105950	−	0.0769773i
$105$	−2.16207	+	9.54107i	−0.210997	+	0.931113i
$106$	14.0415	−	10.2017i	1.36383	−	0.990880i
$107$	−6.60802			−0.638821			−0.319411	−	0.947616i	$-0.603485\pi$
$107$	−6.60802			−0.638821			−0.319411	+	0.947616i	$0.603485\pi$
$108$	1.01964	−	0.740813i	0.0981150	−	0.0712847i
$109$	2.20665	+	6.79136i	0.211359	+	0.650495i	0.999392	+	0.0348624i	$0.0110993\pi$
$109$	2.20665	+	6.79136i	0.211359	+	0.650495i	−0.788034	+	0.615632i	$0.788901\pi$
$110$	4.68239	−	20.6630i	0.446448	−	1.97014i
$111$	−0.879475	+	2.70675i	−0.0834761	+	0.256913i
$112$	−6.66823	−	20.5227i	−0.630089	−	1.93921i
$113$	2.18401	+	6.72170i	0.205455	+	0.632324i	0.999694	+	0.0247197i	$0.00786933\pi$
$113$	2.18401	+	6.72170i	0.205455	+	0.632324i	−0.794240	+	0.607604i	$0.792131\pi$
$114$	−4.44533	+	13.6813i	−0.416343	+	1.28137i
$115$	16.3033	−	1.49290i	1.52029	−	0.139214i
$116$	1.24979	+	3.84647i	0.116041	+	0.357136i
$117$	−0.809017	+	0.587785i	−0.0747936	+	0.0543408i
$118$	18.6364			1.71562
$119$	3.71368	−	2.69814i	0.340432	−	0.247338i
$120$	−1.17800	−	2.74423i	−0.107536	−	0.250513i
$121$	−13.3780	−	9.71968i	−1.21618	−	0.883607i
$122$	11.0199	+	8.00641i	0.997693	+	0.724867i
$123$	−2.68162	+	8.25317i	−0.241793	+	0.744164i
$124$	−0.565398			−0.0507742
$125$	−10.4857	−	3.87958i	−0.937865	−	0.347000i
$126$	−7.89983			−0.703773
$127$	−5.61747	+	17.2888i	−0.498469	+	1.53413i	0.313010	+	0.949750i	$0.398663\pi$
$127$	−5.61747	+	17.2888i	−0.498469	+	1.53413i	−0.811479	+	0.584381i	$0.801337\pi$
$128$	8.05275	+	5.85066i	0.711769	+	0.517131i
$129$	0.225553	+	0.163874i	0.0198588	+	0.0144283i
$130$	−1.59263	−	3.71016i	−0.139683	−	0.325402i
$131$	6.69640	−	4.86522i	0.585068	−	0.425076i	−0.255480	−	0.966814i	$-0.582233\pi$
$131$	6.69640	−	4.86522i	0.585068	−	0.425076i	0.840547	+	0.541738i	$0.182233\pi$
$132$	6.61365			0.575644
$133$	28.1990	−	20.4877i	2.44516	−	1.77651i
$134$	−2.02099	−	6.21995i	−0.174587	−	0.537322i
$135$	−2.22675	+	0.203905i	−0.191648	+	0.0175494i
$136$	−0.433016	+	1.33268i	−0.0371308	+	0.114277i
$137$	4.89667	+	15.0704i	0.418351	+	1.28755i	0.909219	+	0.416318i	$0.136680\pi$
$137$	4.89667	+	15.0704i	0.418351	+	1.28755i	−0.490868	+	0.871234i	$0.663320\pi$
$138$	4.08524	+	12.5731i	0.347759	+	1.07029i
$139$	−0.400087	+	1.23134i	−0.0339350	+	0.104441i	−0.966589	−	0.256330i	$-0.917487\pi$
$139$	−0.400087	+	1.23134i	−0.0339350	+	0.104441i	0.932654	+	0.360771i	$0.117487\pi$
$140$	2.72496	−	12.0250i	0.230301	−	1.01630i
$141$	−2.80206	−	8.62385i	−0.235976	−	0.726259i
$142$	−4.95964	+	3.60339i	−0.416203	+	0.302390i
$143$	−5.24749			−0.438817
$144$	3.99025	−	2.89909i	0.332521	−	0.241591i
$145$	1.58581	−	6.99806i	0.131694	−	0.581157i
$146$	−9.32205	−	6.77287i	−0.771498	−	0.560526i
$147$	9.82253	+	7.13648i	0.810148	+	0.588607i
$148$	1.10844	−	3.41144i	0.0911135	−	0.280418i
$149$	0.559740			0.0458557			0.0229279	−	0.999737i	$-0.492701\pi$
$149$	0.559740			0.0458557			0.0229279	+	0.999737i	$0.492701\pi$
$150$	1.18404	−	8.95024i	0.0966761	−	0.730784i
$151$	−21.2906			−1.73261			−0.866303	−	0.499518i	$-0.833510\pi$
$151$	−21.2906			−1.73261			−0.866303	+	0.499518i	$0.833510\pi$
$152$	−3.28801	+	10.1194i	−0.266692	+	0.820795i
$153$	0.848825	+	0.616708i	0.0686234	+	0.0498579i
$154$	−33.5372	−	24.3662i	−2.70250	−	1.96348i
$155$	0.861920	+	0.513155i	0.0692310	+	0.0412176i
$156$	1.01964	−	0.740813i	0.0816366	−	0.0593125i
$157$	−14.3080			−1.14190			−0.570951	−	0.820984i	$-0.693425\pi$
$157$	−14.3080			−1.14190			−0.570951	+	0.820984i	$0.693425\pi$
$158$	18.7218	−	13.6022i	1.48943	−	1.08213i
$159$	−2.97034	−	9.14176i	−0.235563	−	0.724988i
$160$	5.49921	+	12.8108i	0.434751	+	1.01279i
$161$	9.89855	−	30.4646i	0.780115	−	2.40095i
$162$	−0.557974	−	1.71727i	−0.0438386	−	0.134921i
$163$	0.567972	+	1.74804i	0.0444870	+	0.136917i	0.970833	−	0.239757i	$-0.0770677\pi$
$163$	0.567972	+	1.74804i	0.0444870	+	0.136917i	−0.926346	+	0.376674i	$0.877068\pi$
$164$	3.37977	−	10.4019i	0.263915	−	0.812248i
$165$	−10.0822	−	6.00254i	−0.784895	−	0.467297i
$166$	5.31370	+	16.3539i	0.412423	+	1.26931i
$167$	5.59476	−	4.06483i	0.432936	−	0.314546i	−0.349886	−	0.936792i	$-0.613780\pi$
$167$	5.59476	−	4.06483i	0.432936	−	0.314546i	0.782822	+	0.622246i	$0.213780\pi$
$168$	−5.84314			−0.450808
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−3.18583	+	2.79213i	−0.244342	+	0.214146i
$171$	6.44536	+	4.68283i	0.492889	+	0.358105i
$172$	−0.284275	−	0.206538i	−0.0216757	−	0.0157483i
$173$	−1.55992	+	4.80094i	−0.118599	+	0.365009i	−0.992681	−	0.120770i	$-0.961464\pi$
$173$	−1.55992	+	4.80094i	−0.118599	+	0.365009i	0.874082	+	0.485778i	$0.161464\pi$
$174$	5.79426			0.439262
$175$	−15.0680	+	15.8584i	−1.13903	+	1.19878i
$176$	25.8818			1.95091
$177$	3.18943	−	9.81604i	0.239732	−	0.737819i
$178$	23.8228	+	17.3083i	1.78559	+	1.29731i
$179$	16.3150	+	11.8535i	1.21944	+	0.885974i	0.996053	−	0.0887564i	$-0.0282893\pi$
$179$	16.3150	+	11.8535i	1.21944	+	0.885974i	0.223385	+	0.974730i	$0.428289\pi$
$180$	2.80648	−	0.256991i	0.209182	−	0.0191550i
$181$	6.66983	−	4.84591i	0.495764	−	0.360194i	−0.311632	−	0.950203i	$-0.600876\pi$
$181$	6.66983	−	4.84591i	0.495764	−	0.360194i	0.807397	+	0.590009i	$0.200876\pi$
$182$	−7.89983			−0.585574
$183$	6.10302	−	4.43411i	0.451149	−	0.327779i
$184$	3.02167	+	9.29973i	0.222760	+	0.685585i
$185$	−4.78598	+	4.19454i	−0.351872	+	0.308389i
$186$	−0.250310	+	0.770375i	−0.0183536	+	0.0564867i
$187$	1.70135	+	5.23622i	0.124415	+	0.382911i
$188$	3.53156	+	10.8690i	0.257566	+	0.792706i
$189$	−1.35197	+	4.16095i	−0.0983416	+	0.302664i
$190$	−24.1909	+	21.2014i	−1.75499	+	1.53811i
$191$	−3.29398	−	10.1378i	−0.238344	−	0.733547i	−0.996660	−	0.0816603i	$-0.973978\pi$
$191$	−3.29398	−	10.1378i	−0.238344	−	0.733547i	0.758316	−	0.651887i	$-0.226022\pi$
$192$	−1.12716	+	0.818930i	−0.0813458	+	0.0591012i
$193$	8.66695			0.623861			0.311930	−	0.950105i	$-0.399024\pi$
$193$	8.66695			0.623861			0.311930	+	0.950105i	$0.399024\pi$
$194$	22.6783	−	16.4767i	1.62821	−	1.18296i
$195$	−2.22675	+	0.203905i	−0.159461	+	0.0146020i
$196$	−12.3798	−	8.99444i	−0.884270	−	0.642460i
$197$	−2.31136	−	1.67930i	−0.164678	−	0.119645i	0.502394	−	0.864639i	$-0.332453\pi$
$197$	−2.31136	−	1.67930i	−0.164678	−	0.119645i	−0.667072	+	0.744993i	$0.732453\pi$
$198$	2.92796	−	9.01134i	0.208081	−	0.640408i
$199$	10.5179			0.745595			0.372798	−	0.927913i	$-0.378399\pi$
$199$	10.5179			0.745595			0.372798	+	0.927913i	$0.378399\pi$
$200$	0.875777	−	6.62008i	0.0619268	−	0.468110i
$201$	−3.62200			−0.255477
$202$	−1.59192	+	4.89944i	−0.112007	+	0.344723i
$203$	−11.3582	−	8.25222i	−0.797190	−	0.579193i
$204$	−1.06981	−	0.777265i	−0.0749019	−	0.0544194i
$205$	−14.5930	+	12.7896i	−1.01922	+	0.893265i
$206$	−8.36243	+	6.07566i	−0.582638	+	0.423311i
$207$	7.32156			0.508883
$208$	3.99025	−	2.89909i	0.276674	−	0.201015i
$209$	12.9188	+	39.7601i	0.893614	+	2.75026i
$210$	−15.1782	−	9.03653i	−1.04740	−	0.623580i
$211$	−0.746444	+	2.29732i	−0.0513873	+	0.158154i	−0.973457	−	0.228870i	$-0.926497\pi$
$211$	−0.746444	+	2.29732i	−0.0513873	+	0.158154i	0.922070	+	0.387024i	$0.126497\pi$
$212$	3.74365	+	11.5218i	0.257115	+	0.791319i
$213$	1.04916	+	3.22899i	0.0718874	+	0.221247i
$214$	3.68710	−	11.3477i	0.252045	−	0.775715i
$215$	0.245909	+	0.572863i	0.0167708	+	0.0390689i
$216$	−0.412708	−	1.27018i	−0.0280812	−	0.0864251i
$217$	1.58784	−	1.15364i	0.107790	−	0.0783139i
$218$	−12.8938			−0.873281
$219$	−5.16273	+	3.75094i	−0.348865	+	0.253465i
$220$	12.7070	+	7.56528i	0.856707	+	0.510051i
$221$	0.848825	+	0.616708i	0.0570982	+	0.0414842i
$222$	−4.15749	−	3.02059i	−0.279032	−	0.202729i
$223$	−0.450041	+	1.38508i	−0.0301370	+	0.0927521i	−0.964994	−	0.262273i	$-0.915528\pi$
$223$	−0.450041	+	1.38508i	−0.0301370	+	0.0927521i	0.934857	+	0.355025i	$0.115528\pi$
$224$	27.2774			1.82255
$225$	−4.51157	−	2.15539i	−0.300772	−	0.143692i
$226$	−12.7616			−0.848888
$227$	1.53624	−	4.72806i	0.101964	−	0.313812i	−0.887042	−	0.461689i	$-0.847244\pi$
$227$	1.53624	−	4.72806i	0.101964	−	0.313812i	0.989006	+	0.147876i	$0.0472438\pi$
$228$	−8.12338	−	5.90198i	−0.537984	−	0.390868i
$229$	13.1213	+	9.53319i	0.867081	+	0.629971i	0.929802	−	0.368060i	$-0.119978\pi$
$229$	13.1213	+	9.53319i	0.867081	+	0.629971i	−0.0627211	+	0.998031i	$0.519978\pi$
$230$	−6.53310	+	28.8301i	−0.430780	+	1.90100i
$231$	−18.5735	+	13.4945i	−1.22205	+	0.887871i
$232$	4.28575			0.281373
$233$	−14.9086	+	10.8317i	−0.976696	+	0.709611i	−0.956968	−	0.290194i	$-0.906280\pi$
$233$	−14.9086	+	10.8317i	−0.976696	+	0.709611i	−0.0197280	+	0.999805i	$0.506280\pi$
$234$	−0.557974	−	1.71727i	−0.0364759	−	0.112261i
$235$	4.48104	−	19.7745i	0.292311	−	1.28995i
$236$	−4.01978	+	12.3716i	−0.261665	+	0.805323i
$237$	−3.96042	−	12.1889i	−0.257257	−	0.791754i
$238$	2.56130	+	7.88287i	0.166024	+	0.510971i
$239$	4.55407	−	14.0160i	0.294578	−	0.906619i	−0.688784	−	0.724966i	$-0.741855\pi$
$239$	4.55407	−	14.0160i	0.294578	−	0.906619i	0.983363	−	0.181653i	$-0.0581447\pi$
$240$	10.9828	−	1.00571i	0.708939	−	0.0649180i
$241$	−4.67983	−	14.4030i	−0.301455	−	0.927782i	−0.980976	−	0.194127i	$-0.937813\pi$
$241$	−4.67983	−	14.4030i	−0.301455	−	0.927782i	0.679522	−	0.733655i	$-0.262187\pi$
$242$	24.1559	−	17.5503i	1.55280	−	1.12817i
$243$	−1.00000			−0.0641500
$244$	−7.69192	+	5.58851i	−0.492425	+	0.357768i
$245$	10.7090	+	24.9474i	0.684173	+	1.59383i
$246$	−12.6766	−	9.21012i	−0.808233	−	0.587216i
$247$	6.44536	+	4.68283i	0.410108	+	0.297961i
$248$	−0.185143	+	0.569811i	−0.0117566	+	0.0361831i
$249$	9.52320			0.603508
$250$	12.5130	−	15.8420i	0.791392	−	1.00193i
$251$	29.7745			1.87935			0.939674	−	0.342073i	$-0.111129\pi$
$251$	29.7745			1.87935			0.939674	+	0.342073i	$0.111129\pi$
$252$	1.70395	−	5.24423i	0.107339	−	0.330356i
$253$	31.0822	+	22.5826i	1.95412	+	1.41975i
$254$	−26.5551	−	19.2934i	−1.66621	−	1.21058i
$255$	0.925430	+	2.15586i	0.0579527	+	0.135005i
$256$	−16.7947	+	12.2021i	−1.04967	+	0.762629i
$257$	−4.09301			−0.255315			−0.127658	−	0.991818i	$-0.540746\pi$
$257$	−4.09301			−0.255315			−0.127658	+	0.991818i	$0.540746\pi$
$258$	−0.407268	+	0.295897i	−0.0253554	+	0.0184218i
$259$	3.84777	+	11.8422i	0.239089	+	0.735840i
$260$	2.80648	−	0.256991i	0.174050	−	0.0159379i
$261$	0.991628	−	3.05192i	0.0613802	−	0.188909i
$262$	4.61847	+	14.2142i	0.285330	+	0.878156i
$263$	−3.28241	−	10.1022i	−0.202402	−	0.622929i	−0.999810	−	0.0194885i	$-0.993796\pi$
$263$	−3.28241	−	10.1022i	−0.202402	−	0.622929i	0.797408	−	0.603440i	$-0.206204\pi$
$264$	2.16568	−	6.66528i	0.133288	−	0.410219i
$265$	4.75015	−	20.9621i	0.291799	−	1.28769i
$266$	19.4487	+	59.8568i	1.19247	+	3.67006i
$267$	13.1935	−	9.58566i	0.807430	−	0.586633i
$268$	4.56498			0.278850
$269$	12.2750	−	8.91833i	0.748422	−	0.543760i	−0.146916	−	0.989149i	$-0.546935\pi$
$269$	12.2750	−	8.91833i	0.748422	−	0.543760i	0.895337	+	0.445389i	$0.146935\pi$
$270$	0.892310	−	3.93770i	0.0543043	−	0.239641i
$271$	19.2870	+	14.0128i	1.17160	+	0.851220i	0.991200	−	0.132373i	$-0.0422596\pi$
$271$	19.2870	+	14.0128i	1.17160	+	0.851220i	0.180404	+	0.983593i	$0.442260\pi$
$272$	−4.18659	−	3.04174i	−0.253849	−	0.184432i
$273$	−1.35197	+	4.16095i	−0.0818252	+	0.251832i
$274$	−28.6121			−1.72852
$275$	−12.5049	−	23.0658i	−0.754077	−	1.39092i
$276$	−9.22770			−0.555442
$277$	−2.29018	+	7.04846i	−0.137604	+	0.423501i	−0.995986	−	0.0895098i	$-0.971470\pi$
$277$	−2.29018	+	7.04846i	−0.137604	+	0.423501i	0.858382	+	0.513011i	$0.171470\pi$
$278$	−1.89131	−	1.37411i	−0.113433	−	0.0824139i
$279$	0.362929	+	0.263683i	0.0217280	+	0.0157863i
$280$	−11.2266	−	6.68390i	−0.670919	−	0.399440i
$281$	−10.4206	+	7.57100i	−0.621640	+	0.451648i	−0.853494	−	0.521103i	$-0.825521\pi$
$281$	−10.4206	+	7.57100i	−0.621640	+	0.451648i	0.231854	+	0.972751i	$0.425521\pi$
$282$	16.3729			0.974994
$283$	−2.41017	+	1.75109i	−0.143270	+	0.104091i	−0.657111	−	0.753794i	$-0.728222\pi$
$283$	−2.41017	+	1.75109i	−0.143270	+	0.104091i	0.513842	+	0.857885i	$0.328222\pi$
$284$	−1.32231	−	4.06964i	−0.0784645	−	0.241489i
$285$	7.02704	+	16.3700i	0.416246	+	0.969678i
$286$	2.92796	−	9.01134i	0.173134	−	0.532852i
$287$	11.7323	+	36.1083i	0.692535	+	2.13140i
$288$	1.92664	+	5.92958i	0.113528	+	0.349404i
$289$	−4.91311	+	15.1210i	−0.289007	+	0.889471i
$290$	11.1327	+	6.62800i	0.653735	+	0.389209i
$291$	−4.79737	−	14.7648i	−0.281227	−	0.865527i
$292$	6.50683	−	4.72749i	0.380783	−	0.276655i
$293$	28.5261			1.66651			0.833257	−	0.552886i	$-0.186474\pi$
$293$	28.5261			1.66651			0.833257	+	0.552886i	$0.186474\pi$
$294$	−17.7360	+	12.8859i	−1.03438	+	0.751523i
$295$	17.3564	−	15.2115i	1.01053	−	0.885649i
$296$	−3.07510	−	2.23419i	−0.178737	−	0.129860i
$297$	−4.24530	−	3.08439i	−0.246338	−	0.178975i
$298$	−0.312321	+	0.961224i	−0.0180923	+	0.0556822i
$299$	7.32156			0.423417
$300$	5.68614	+	2.71653i	0.328290	+	0.156839i
$301$	1.21977			0.0703061
$302$	11.8796	−	36.5617i	0.683595	−	2.10389i
$303$	2.30816	+	1.67698i	0.132600	+	0.0963398i
$304$	−31.7899	−	23.0967i	−1.82328	−	1.32469i
$305$	16.7981	−	1.53821i	0.961854	−	0.0880777i
$306$	−1.53267	+	1.11355i	−0.0876172	+	0.0636576i
$307$	11.2919			0.644465			0.322233	−	0.946660i	$-0.395567\pi$
$307$	11.2919			0.644465			0.322233	+	0.946660i	$0.395567\pi$
$308$	23.4091	−	17.0077i	1.33386	−	0.969103i
$309$	1.76899	+	5.44439i	0.100634	+	0.309721i
$310$	−1.36215	+	1.19382i	−0.0773651	+	0.0678044i
$311$	−9.44134	+	29.0575i	−0.535369	+	1.64770i	0.207480	+	0.978239i	$0.433474\pi$
$311$	−9.44134	+	29.0575i	−0.535369	+	1.64770i	−0.742850	+	0.669458i	$0.766526\pi$
$312$	−0.412708	−	1.27018i	−0.0233650	−	0.0719100i
$313$	5.52205	+	16.9951i	0.312125	+	0.960622i	0.976922	+	0.213597i	$0.0685181\pi$
$313$	5.52205	+	16.9951i	0.312125	+	0.960622i	−0.664797	+	0.747024i	$0.731482\pi$
$314$	7.98349	−	24.5707i	0.450534	−	1.38660i
$315$	−7.35725	+	6.44805i	−0.414534	+	0.363307i
$316$	4.99149	+	15.3622i	0.280793	+	0.864193i
$317$	−13.4987	+	9.80735i	−0.758160	+	0.550836i	−0.898346	−	0.439290i	$-0.855230\pi$
$317$	−13.4987	+	9.80735i	−0.758160	+	0.550836i	0.140185	+	0.990125i	$0.455230\pi$
$318$	17.3562			0.973288
$319$	13.6231	−	9.89775i	0.762746	−	0.554168i
$320$	−3.10241	+	0.284090i	−0.173430	+	0.0158811i
$321$	−5.34600	−	3.88409i	−0.298384	−	0.216789i
$322$	46.7928	+	33.9969i	2.60766	+	1.89458i
$323$	2.58305	−	7.94981i	0.143725	−	0.442339i
$324$	1.26035			0.0700192
$325$	−4.51157	−	2.15539i	−0.250257	−	0.119559i
$326$	−3.31877			−0.183809
$327$	−2.20665	+	6.79136i	−0.122028	+	0.375563i
$328$	−9.37633	−	6.81230i	−0.517721	−	0.376146i
$329$	−32.0951	−	23.3184i	−1.76946	−	1.28559i
$330$	15.9336	−	13.9645i	0.877114	−	0.768721i
$331$	13.3612	−	9.70747i	0.734397	−	0.533571i	−0.156554	−	0.987669i	$-0.550039\pi$
$331$	13.3612	−	9.70747i	0.734397	−	0.533571i	0.890951	+	0.454099i	$0.150039\pi$
$332$	−12.0025			−0.658724
$333$	−2.30250	+	1.67286i	−0.126176	+	0.0916722i
$334$	3.85868	+	11.8758i	0.211137	+	0.649814i
$335$	−6.95908	−	4.14317i	−0.380215	−	0.226366i
$336$	6.66823	−	20.5227i	0.363782	−	1.11961i
$337$	−8.59600	−	26.4558i	−0.468254	−	1.44114i	−0.854844	−	0.518886i	$-0.826347\pi$
$337$	−8.59600	−	26.4558i	−0.468254	−	1.44114i	0.386590	−	0.922252i	$-0.373653\pi$
$338$	−0.557974	−	1.71727i	−0.0303498	−	0.0934071i
$339$	−2.18401	+	6.72170i	−0.118619	+	0.365072i
$340$	−1.16636	−	2.71713i	−0.0632549	−	0.147357i
$341$	0.727441	+	2.23883i	0.0393931	+	0.121240i
$342$	−11.6380	+	8.45552i	−0.629312	+	0.457222i
$343$	22.4936			1.21454
$344$	−0.301237	+	0.218862i	−0.0162416	+	0.0118002i
$345$	14.0671	+	8.37505i	0.757350	+	0.450898i
$346$	−7.37411	−	5.35760i	−0.396434	−	0.288026i
$347$	15.3036	+	11.1187i	0.821539	+	0.596883i	0.917153	−	0.398536i	$-0.130481\pi$
$347$	15.3036	+	11.1187i	0.821539	+	0.596883i	−0.0956140	+	0.995418i	$0.530481\pi$
$348$	−1.24979	+	3.84647i	−0.0669960	+	0.206193i
$349$	8.31074			0.444864			0.222432	−	0.974948i	$-0.428600\pi$
$349$	8.31074			0.444864			0.222432	+	0.974948i	$0.428600\pi$
$350$	−18.8256	−	34.7243i	−1.00627	−	1.85609i
$351$	−1.00000			−0.0533761
$352$	−10.1100	+	31.1154i	−0.538864	+	1.65845i
$353$	−22.1740	−	16.1104i	−1.18020	−	0.857468i	−0.188008	−	0.982167i	$-0.560203\pi$
$353$	−22.1740	−	16.1104i	−1.18020	−	0.857468i	−0.992195	+	0.124700i	$0.960203\pi$
$354$	15.0772	+	10.9542i	0.801342	+	0.582209i
$355$	−1.67782	+	7.40409i	−0.0890493	+	0.392968i
$356$	−16.6284	+	12.0812i	−0.881304	+	0.640304i
$357$	4.59036			0.242947
$358$	−29.4590	+	21.4032i	−1.55696	+	1.13120i
$359$	2.68794	+	8.27264i	0.141864	+	0.436613i	0.996594	−	0.0824593i	$-0.0262774\pi$
$359$	2.68794	+	8.27264i	0.141864	+	0.436613i	−0.854730	+	0.519073i	$0.826277\pi$
$360$	0.660001	−	2.91254i	0.0347851	−	0.153504i
$361$	13.7425	−	42.2950i	0.723288	−	2.22605i
$362$	4.60014	+	14.1578i	0.241778	+	0.744116i
$363$	−5.10994	−	15.7268i	−0.268202	−	0.825441i
$364$	1.70395	−	5.24423i	0.0893115	−	0.274872i
$365$	−14.2100	+	1.30122i	−0.743785	+	0.0681089i
$366$	4.20922	+	12.9546i	0.220019	+	0.677150i
$367$	0.147014	−	0.106812i	0.00767406	−	0.00557553i	−0.583942	−	0.811796i	$-0.698490\pi$
$367$	0.147014	−	0.106812i	0.00767406	−	0.00557553i	0.591616	+	0.806220i	$0.298490\pi$
$368$	−36.1115			−1.88244
$369$	−7.02057	+	5.10074i	−0.365476	+	0.265534i
$370$	−4.53269	−	10.5593i	−0.235643	−	0.548950i
$371$	−34.0225	−	24.7188i	−1.76636	−	1.28334i
$372$	−0.457416	−	0.332332i	−0.0237159	−	0.0172306i
$373$	−2.58242	+	7.94788i	−0.133713	+	0.411526i	−0.995388	−	0.0959352i	$-0.969416\pi$
$373$	−2.58242	+	7.94788i	−0.133713	+	0.411526i	0.861675	+	0.507461i	$0.169416\pi$
$374$	−9.94131			−0.514053
$375$	−6.20271	−	9.30196i	−0.320307	−	0.480351i
$376$	12.1103			0.624542
$377$	0.991628	−	3.05192i	0.0510714	−	0.157182i
$378$	−6.39110	−	4.64340i	−0.328722	−	0.238831i
$379$	−1.19864	−	0.870864i	−0.0615701	−	0.0447333i	0.556575	−	0.830798i	$-0.312115\pi$
$379$	−1.19864	−	0.870864i	−0.0615701	−	0.0447333i	−0.618145	+	0.786064i	$0.712115\pi$
$380$	−8.85651	−	20.6319i	−0.454329	−	1.05840i
$381$	−14.7067	+	10.6851i	−0.753448	+	0.547412i
$382$	19.2473			0.984778
$383$	−19.2942	+	14.0181i	−0.985889	+	0.716290i	−0.959017	−	0.283349i	$-0.908555\pi$
$383$	−19.2942	+	14.0181i	−0.985889	+	0.716290i	−0.0268716	+	0.999639i	$0.508555\pi$
$384$	3.07588	+	9.46657i	0.156965	+	0.483089i
$385$	−51.1221	+	4.68129i	−2.60542	+	0.238580i
$386$	−4.83594	+	14.8835i	−0.246143	+	0.757549i
$387$	0.0861535	+	0.265153i	0.00437943	+	0.0134785i
$388$	6.04634	+	18.6087i	0.306957	+	0.944715i
$389$	3.07653	−	9.46859i	0.155986	−	0.480077i	−0.842273	−	0.539051i	$-0.818783\pi$
$389$	3.07653	−	9.46859i	0.155986	−	0.480077i	0.998260	+	0.0589743i	$0.0187830\pi$
$390$	0.892310	−	3.93770i	0.0451839	−	0.199393i
$391$	−2.37381	−	7.30584i	−0.120049	−	0.369472i
$392$	−13.1185	+	9.53114i	−0.662584	+	0.481395i
$393$	8.27721			0.417530
$394$	4.17349	−	3.03222i	0.210257	−	0.152761i
$395$	6.33348	−	27.9492i	0.318672	−	1.40628i
$396$	5.35055	+	3.88740i	0.268875	+	0.195349i
$397$	3.21611	+	2.33664i	0.161412	+	0.117273i	0.665559	−	0.746345i	$-0.268193\pi$
$397$	3.21611	+	2.33664i	0.161412	+	0.117273i	−0.504147	+	0.863618i	$0.668193\pi$
$398$	−5.86873	+	18.0621i	−0.294173	+	0.905370i
$399$	34.8558			1.74497
$400$	22.2521	+	10.6308i	1.11260	+	0.531542i
$401$	−15.2970			−0.763896			−0.381948	−	0.924184i	$-0.624747\pi$
$401$	−15.2970			−0.763896			−0.381948	+	0.924184i	$0.624747\pi$
$402$	2.02099	−	6.21995i	0.100798	−	0.310223i
$403$	0.362929	+	0.263683i	0.0180788	+	0.0131350i
$404$	−2.90908	−	2.11357i	−0.144732	−	0.105154i
$405$	−1.92133	−	1.14389i	−0.0954718	−	0.0568403i
$406$	20.5089	−	14.9006i	1.01784	−	0.739503i
$407$	−14.9346			−0.740279
$408$	−1.13365	+	0.823645i	−0.0561240	+	0.0407765i
$409$	−4.41580	−	13.5904i	−0.218347	−	0.672003i	−0.998899	−	0.0469123i	$-0.985062\pi$
$409$	−4.41580	−	13.5904i	−0.218347	−	0.672003i	0.780552	−	0.625091i	$-0.214938\pi$
$410$	−13.8207	−	32.1964i	−0.682555	−	1.59007i
$411$	−4.89667	+	15.0704i	−0.241535	+	0.743368i
$412$	−2.22954	−	6.86181i	−0.109841	−	0.338057i
$413$	−13.9540	−	42.9460i	−0.686631	−	2.11323i
$414$	−4.08524	+	12.5731i	−0.200779	+	0.617933i
$415$	18.2972	+	10.8935i	0.898176	+	0.534740i
$416$	1.92664	+	5.92958i	0.0944611	+	0.290721i
$417$	−1.04744	+	0.761011i	−0.0512935	+	0.0372669i
$418$	−75.4871			−3.69219
$419$	−9.95521	+	7.23288i	−0.486344	+	0.353349i	−0.803777	−	0.594931i	$-0.797179\pi$
$419$	−9.95521	+	7.23288i	−0.486344	+	0.353349i	0.317433	+	0.948281i	$0.397179\pi$
$420$	9.27268	−	8.12678i	0.452461	−	0.396546i
$421$	9.53649	+	6.92866i	0.464780	+	0.337682i	0.795403	−	0.606080i	$-0.207259\pi$
$421$	9.53649	+	6.92866i	0.464780	+	0.337682i	−0.330623	+	0.943763i	$0.607259\pi$
$422$	−3.52861	−	2.56369i	−0.171770	−	0.124798i
$423$	2.80206	−	8.62385i	0.136241	−	0.419306i
$424$	12.8376			0.623449
$425$	−0.688008	+	5.20072i	−0.0333733	+	0.252272i
$426$	−6.13045			−0.297021
$427$	10.1990	−	31.3892i	0.493562	−	1.51903i
$428$	6.73781	+	4.89530i	0.325684	+	0.236623i
$429$	−4.24530	−	3.08439i	−0.204965	−	0.148916i
$430$	−1.12097	+	0.102648i	−0.0540580	+	0.00495013i
$431$	−19.1903	+	13.9425i	−0.924363	+	0.671589i	−0.944606	−	0.328206i	$-0.893556\pi$
$431$	−19.1903	+	13.9425i	−0.924363	+	0.671589i	0.0202435	+	0.999795i	$0.493556\pi$
$432$	4.93222			0.237302
$433$	−9.90485	+	7.19629i	−0.475997	+	0.345832i	−0.799774	−	0.600302i	$-0.795047\pi$
$433$	−9.90485	+	7.19629i	−0.475997	+	0.345832i	0.323777	+	0.946133i	$0.395047\pi$
$434$	1.09513	+	3.37045i	0.0525678	+	0.161787i
$435$	5.39630	−	4.72944i	0.258733	−	0.226759i
$436$	2.78114	−	8.55947i	0.133192	−	0.409924i
$437$	−18.0250	−	55.4753i	−0.862253	−	2.65374i
$438$	−3.56071	−	10.9587i	−0.170137	−	0.523628i
$439$	−5.67422	+	17.4634i	−0.270816	+	0.833485i	0.719481	+	0.694512i	$0.244380\pi$
$439$	−5.67422	+	17.4634i	−0.270816	+	0.833485i	−0.990296	+	0.138972i	$0.955620\pi$
$440$	11.7853	−	10.3289i	0.561843	−	0.492412i
$441$	3.75187	+	11.5471i	0.178661	+	0.549861i
$442$	−1.53267	+	1.11355i	−0.0729019	+	0.0529663i
$443$	−8.79678			−0.417948			−0.208974	−	0.977921i	$-0.567012\pi$
$443$	−8.79678			−0.417948			−0.208974	+	0.977921i	$0.567012\pi$
$444$	2.90194	−	2.10838i	0.137720	−	0.100059i
$445$	36.3141	−	3.32530i	1.72145	−	0.157635i
$446$	−2.12745	−	1.54568i	−0.100738	−	0.0731902i
$447$	0.452839	+	0.329007i	0.0214186	+	0.0155615i
$448$	−1.88363	+	5.79722i	−0.0889933	+	0.273893i
$449$	30.7722			1.45223			0.726115	−	0.687573i	$-0.241324\pi$
$449$	30.7722			1.45223			0.726115	+	0.687573i	$0.241324\pi$
$450$	6.21872	−	6.54493i	0.293153	−	0.308531i
$451$	−45.5372			−2.14426
$452$	2.75261	−	8.47166i	0.129472	−	0.398473i
$453$	−17.2245	−	12.5143i	−0.809277	−	0.587974i
$454$	7.26216	+	5.27627i	0.340830	+	0.247628i
$455$	−7.35725	+	6.44805i	−0.344913	+	0.302289i
$456$	−8.60811	+	6.25416i	−0.403112	+	0.292878i
$457$	−37.9276			−1.77418			−0.887090	−	0.461596i	$-0.847277\pi$
$457$	−37.9276			−1.77418			−0.887090	+	0.461596i	$0.847277\pi$
$458$	−23.6924	+	17.2135i	−1.10707	+	0.804336i
$459$	0.324222	+	0.997854i	0.0151334	+	0.0465758i
$460$	−17.7295	−	10.5555i	−0.826641	−	0.492151i
$461$	8.37332	−	25.7704i	0.389984	−	1.20025i	−0.542815	−	0.839852i	$-0.682641\pi$
$461$	8.37332	−	25.7704i	0.389984	−	1.20025i	0.932799	−	0.360396i	$-0.117359\pi$
$462$	−12.8101	−	39.4253i	−0.595978	−	1.83423i
$463$	−0.0161854	−	0.0498136i	−0.000752200	−	0.00231503i	0.950680	−	0.310174i	$-0.100387\pi$
$463$	−0.0161854	−	0.0498136i	−0.000752200	−	0.00231503i	−0.951432	+	0.307859i	$0.900387\pi$
$464$	−4.89093	+	15.0527i	−0.227056	+	0.698805i
$465$	0.395683	+	0.921774i	0.0183494	+	0.0427463i
$466$	−10.2824	−	31.6459i	−0.476322	−	1.46597i
$467$	18.4409	−	13.3981i	0.853343	−	0.619990i	−0.0727229	−	0.997352i	$-0.523169\pi$
$467$	18.4409	−	13.3981i	0.853343	−	0.619990i	0.926066	+	0.377362i	$0.123169\pi$
$468$	1.26035			0.0582595
$469$	−12.8201	+	9.31437i	−0.591979	+	0.430098i
$470$	31.4579	+	18.7288i	1.45104	+	0.863896i
$471$	−11.5754	−	8.41003i	−0.533367	−	0.387513i
$472$	11.1519	+	8.10232i	0.513307	+	0.372939i
$473$	−0.452089	+	1.39139i	−0.0207871	+	0.0639761i
$474$	23.1414			1.06292
$475$	−5.22423	+	39.4905i	−0.239704	+	1.81195i
$476$	−5.78544			−0.265175
$477$	2.97034	−	9.14176i	0.136002	−	0.418572i
$478$	21.5282	+	15.6411i	0.984675	+	0.715408i
$479$	−9.09388	−	6.60709i	−0.415510	−	0.301886i	0.360319	−	0.932829i	$-0.382668\pi$
$479$	−9.09388	−	6.60709i	−0.415510	−	0.301886i	−0.775829	+	0.630944i	$0.782668\pi$
$480$	−3.08107	+	13.5965i	−0.140631	+	0.620594i
$481$	−2.30250	+	1.67286i	−0.104985	+	0.0762759i
$482$	27.3451			1.24554
$483$	25.9147	−	18.8282i	1.17916	−	0.856711i
$484$	6.44029	+	19.8212i	0.292740	+	0.900962i
$485$	7.67193	−	33.8557i	0.348365	−	1.53731i
$486$	0.557974	−	1.71727i	0.0253102	−	0.0778969i
$487$	8.75200	+	26.9359i	0.396591	+	1.22058i	0.927715	+	0.373288i	$0.121770\pi$
$487$	8.75200	+	26.9359i	0.396591	+	1.22058i	−0.531124	+	0.847294i	$0.678230\pi$
$488$	3.11337	+	9.58196i	0.140936	+	0.433755i
$489$	−0.567972	+	1.74804i	−0.0256846	+	0.0790491i
$490$	−48.8168	+	4.47019i	−2.20532	+	0.201942i
$491$	6.02201	+	18.5338i	0.271770	+	0.836421i	0.990056	+	0.140673i	$0.0449267\pi$
$491$	6.02201	+	18.5338i	0.271770	+	0.836421i	−0.718286	+	0.695747i	$0.755073\pi$
$492$	8.84834	−	6.42870i	0.398914	−	0.289828i
$493$	−3.36688			−0.151636
$494$	−11.6380	+	8.45552i	−0.523619	+	0.380432i
$495$	−4.62844	−	10.7823i	−0.208033	−	0.484629i
$496$	−1.79005	−	1.30055i	−0.0803755	−	0.0583962i
$497$	12.0172	+	8.73102i	0.539046	+	0.391640i
$498$	−5.31370	+	16.3539i	−0.238113	+	0.732835i
$499$	26.9207			1.20514			0.602568	−	0.798067i	$-0.294144\pi$
$499$	26.9207			1.20514			0.602568	+	0.798067i	$0.294144\pi$
$500$	7.81756	+	11.7237i	0.349612	+	0.524299i
$501$	6.91551			0.308962
$502$	−16.6134	+	51.1307i	−0.741492	+	2.28208i
$503$	−2.16521	−	1.57311i	−0.0965417	−	0.0701417i	0.538467	−	0.842646i	$-0.319004\pi$
$503$	−2.16521	−	1.57311i	−0.0965417	−	0.0701417i	−0.635009	+	0.772505i	$0.719004\pi$
$504$	−4.72720	−	3.43451i	−0.210566	−	0.152985i
$505$	2.51647	+	5.86231i	0.111981	+	0.260869i
$506$	−56.1234	+	40.7761i	−2.49499	+	1.81272i
$507$	−1.00000			−0.0444116
$508$	18.5355	−	13.4669i	0.822382	−	0.597496i
$509$	−6.30071	−	19.3916i	−0.279274	−	0.859517i	−0.988057	−	0.154090i	$-0.950755\pi$
$509$	−6.30071	−	19.3916i	−0.279274	−	0.859517i	0.708783	−	0.705427i	$-0.249245\pi$
$510$	−4.21856	+	0.386296i	−0.186801	+	0.0171055i
$511$	−8.62760	+	26.5530i	−0.381663	+	1.17464i
$512$	−5.43146	−	16.7163i	−0.240039	−	0.738764i
$513$	2.46191	+	7.57698i	0.108696	+	0.334532i
$514$	2.28380	−	7.02880i	0.100734	−	0.310027i
$515$	−2.82896	+	12.4840i	−0.124659	+	0.550111i
$516$	−0.108583	−	0.334185i	−0.00478011	−	0.0147117i
$517$	38.4949	−	27.9682i	1.69301	−	1.23004i
$518$	−22.4832			−0.987857
$519$	−4.08392	+	2.96714i	−0.179264	+	0.130243i
$520$	0.660001	−	2.91254i	0.0289430	−	0.127723i
$521$	−10.4292	−	7.57728i	−0.456913	−	0.331967i	0.335406	−	0.942074i	$-0.391127\pi$
$521$	−10.4292	−	7.57728i	−0.456913	−	0.331967i	−0.792319	+	0.610107i	$0.791127\pi$
$522$	4.68766	+	3.40578i	0.205173	+	0.149067i
$523$	9.97479	−	30.6992i	0.436167	−	1.34238i	−0.455719	−	0.890124i	$-0.650618\pi$
$523$	9.97479	−	30.6992i	0.436167	−	1.34238i	0.891886	−	0.452260i	$-0.149382\pi$
$524$	−10.4321			−0.455731
$525$	−21.5116	+	3.97297i	−0.938842	+	0.173395i
$526$	19.1797			0.836275
$527$	0.145448	−	0.447642i	0.00633581	−	0.0194996i
$528$	20.9388	+	15.2129i	0.911243	+	0.662057i
$529$	−24.7601	−	17.9893i	−1.07653	−	0.782143i
$530$	33.3471	+	19.8536i	1.44850	+	0.862385i
$531$	8.35002	−	6.06665i	0.362360	−	0.263270i
$532$	−43.9304			−1.90462
$533$	−7.02057	+	5.10074i	−0.304095	+	0.220938i
$534$	9.09950	+	28.0054i	0.393774	+	1.21191i
$535$	−5.82846	−	13.5779i	−0.251986	−	0.587022i
$536$	1.49483	−	4.60062i	0.0645668	−	0.198716i
$537$	6.23177	+	19.1794i	0.268921	+	0.827652i
$538$	8.46602	+	26.0557i	0.364996	+	1.12334i
$539$	−19.6879	+	60.5931i	−0.848017	+	2.60993i
$540$	2.42154	+	1.44170i	0.104207	+	0.0620407i
$541$	−5.89841	−	18.1535i	−0.253593	−	0.780478i	−0.994104	−	0.108434i	$-0.965417\pi$
$541$	−5.89841	−	18.1535i	−0.253593	−	0.780478i	0.740511	−	0.672044i	$-0.234583\pi$
$542$	−34.8255	+	25.3022i	−1.49588	+	1.08682i
$543$	8.24436			0.353799
$544$	5.29219	−	3.84500i	0.226901	−	0.164853i
$545$	−12.0083	+	10.5243i	−0.514378	+	0.450812i
$546$	−6.39110	−	4.64340i	−0.273514	−	0.198719i
$547$	−10.8756	−	7.90160i	−0.465008	−	0.337848i	0.330485	−	0.943811i	$-0.392788\pi$
$547$	−10.8756	−	7.90160i	−0.465008	−	0.337848i	−0.795492	+	0.605963i	$0.792788\pi$
$548$	6.17150	−	18.9939i	0.263633	−	0.811380i
$549$	7.54375			0.321960
$550$	46.5875	−	8.60425i	1.98650	−	0.366886i
$551$	−25.5656			−1.08913
$552$	−3.02167	+	9.29973i	−0.128611	+	0.395823i
$553$	−45.3630	−	32.9582i	−1.92903	−	1.40152i
$554$	−10.8262	−	7.86572i	−0.459963	−	0.334183i
$555$	−6.33743	+	0.580323i	−0.269009	+	0.0246333i
$556$	1.32014	−	0.959137i	0.0559864	−	0.0406765i
$557$	−31.9414			−1.35340			−0.676700	−	0.736259i	$-0.736591\pi$
$557$	−31.9414			−1.35340			−0.676700	+	0.736259i	$0.736591\pi$
$558$	−0.655320	+	0.476118i	−0.0277419	+	0.0201557i
$559$	0.0861535	+	0.265153i	0.00364390	+	0.0112148i
$560$	36.2876	−	31.8032i	1.53343	−	1.34393i
$561$	−1.70135	+	5.23622i	−0.0718311	+	0.221074i
$562$	−7.18701	−	22.1194i	−0.303166	−	0.933049i
$563$	−6.17591	−	19.0075i	−0.260283	−	0.801070i	−0.992743	−	0.120259i	$-0.961628\pi$
$563$	−6.17591	−	19.0075i	−0.260283	−	0.801070i	0.732459	−	0.680811i	$-0.238372\pi$
$564$	−3.53156	+	10.8690i	−0.148706	+	0.457669i
$565$	−11.8851	+	10.4163i	−0.500009	+	0.438219i
$566$	−1.66228	−	5.11597i	−0.0698708	−	0.215040i
$567$	−3.53951	+	2.57161i	−0.148646	+	0.107997i
$568$	−4.53441			−0.190260
$569$	−2.55166	+	1.85389i	−0.106971	+	0.0777192i	−0.639985	−	0.768387i	$-0.721059\pi$
$569$	−2.55166	+	1.85389i	−0.106971	+	0.0777192i	0.533014	+	0.846107i	$0.321059\pi$
$570$	−32.0327	+	2.93325i	−1.34170	+	0.122860i
$571$	32.1654	+	23.3695i	1.34608	+	0.977984i	0.999197	+	0.0400752i	$0.0127597\pi$
$571$	32.1654	+	23.3695i	1.34608	+	0.977984i	0.346883	+	0.937909i	$0.387240\pi$
$572$	5.35055	+	3.88740i	0.223718	+	0.162541i
$573$	3.29398	−	10.1378i	0.137608	−	0.423514i
$574$	−68.5539			−2.86139
$575$	17.4475	+	32.1825i	0.727613	+	1.34210i
$576$	−1.39325			−0.0580519
$577$	−4.03510	+	12.4188i	−0.167984	+	0.517000i	−0.999244	−	0.0388833i	$-0.987620\pi$
$577$	−4.03510	+	12.4188i	−0.167984	+	0.517000i	0.831260	+	0.555883i	$0.187620\pi$
$578$	−23.2254	−	16.8743i	−0.966051	−	0.701877i
$579$	7.01171	+	5.09431i	0.291397	+	0.211712i
$580$	−6.80121	+	5.96072i	−0.282405	+	0.247506i
$581$	33.7075	−	24.4899i	1.39842	−	1.01601i
$582$	28.0319			1.16196
$583$	40.8068	−	29.6479i	1.69004	−	1.22789i
$584$	−2.63369	−	8.10567i	−0.108983	−	0.335415i
$585$	−1.92133	−	1.14389i	−0.0794373	−	0.0472940i
$586$	−15.9168	+	48.9870i	−0.657519	+	2.02363i
$587$	−1.45075	−	4.46495i	−0.0598788	−	0.184288i	0.916643	−	0.399707i	$-0.130888\pi$
$587$	−1.45075	−	4.46495i	−0.0598788	−	0.184288i	−0.976522	+	0.215419i	$0.930888\pi$
$588$	−4.72866	−	14.5533i	−0.195006	−	0.600168i
$589$	1.10442	−	3.39907i	0.0455070	−	0.140056i
$590$	16.4378	+	38.2933i	0.676735	+	1.57651i
$591$	−0.882861	−	2.71717i	−0.0363161	−	0.111769i
$592$	11.3564	−	8.25092i	0.466746	−	0.339111i
$593$	42.1844			1.73231			0.866153	−	0.499778i	$-0.166585\pi$
$593$	42.1844			1.73231			0.866153	+	0.499778i	$0.166585\pi$
$594$	7.66550	−	5.56931i	0.314519	−	0.228512i
$595$	8.81960	+	5.25086i	0.361568	+	0.215264i
$596$	−0.570734	−	0.414663i	−0.0233782	−	0.0169852i
$597$	8.50917	+	6.18228i	0.348257	+	0.253024i
$598$	−4.08524	+	12.5731i	−0.167058	+	0.514151i
$599$	−19.0129			−0.776846			−0.388423	−	0.921481i	$-0.626980\pi$
$599$	−19.0129			−0.776846			−0.388423	+	0.921481i	$0.626980\pi$
$600$	4.59970	−	4.84099i	0.187782	−	0.197632i
$601$	0.434822			0.0177368			0.00886838	−	0.999961i	$-0.497177\pi$
$601$	0.434822			0.0177368			0.00886838	+	0.999961i	$0.497177\pi$
$602$	−0.680598	+	2.09466i	−0.0277391	+	0.0853722i
$603$	−2.93026	−	2.12896i	−0.119330	−	0.0866980i
$604$	21.7088	+	15.7724i	0.883319	+	0.641768i
$605$	8.17179	−	36.0615i	0.332231	−	1.46611i
$606$	−4.16771	+	3.02802i	−0.169302	+	0.123005i
$607$	−5.88444			−0.238842			−0.119421	−	0.992844i	$-0.538104\pi$
$607$	−5.88444			−0.238842			−0.119421	+	0.992844i	$0.538104\pi$
$608$	40.1851	−	29.1962i	1.62972	−	1.18406i
$609$	−4.33845	−	13.3524i	−0.175803	−	0.541066i
$610$	−6.73137	+	29.7051i	−0.272545	+	1.20272i
$611$	2.80206	−	8.62385i	0.113359	−	0.348884i
$612$	−0.408632	−	1.25764i	−0.0165180	−	0.0508371i
$613$	−11.7634	−	36.2039i	−0.475117	−	1.46226i	−0.845799	−	0.533501i	$-0.820876\pi$
$613$	−11.7634	−	36.2039i	−0.475117	−	1.46226i	0.370682	−	0.928760i	$-0.379124\pi$
$614$	−6.30062	+	19.3913i	−0.254272	+	0.782569i
$615$	−19.3235	+	1.76947i	−0.779200	+	0.0713519i
$616$	−9.47502	−	29.1611i	−0.381759	−	1.17493i
$617$	−15.1709	+	11.0223i	−0.610759	+	0.443742i	−0.849681	−	0.527296i	$-0.823206\pi$
$617$	−15.1709	+	11.0223i	−0.610759	+	0.443742i	0.238923	+	0.971039i	$0.423206\pi$
$618$	−10.3365			−0.415796
$619$	−7.29010	+	5.29657i	−0.293014	+	0.212887i	−0.724574	−	0.689197i	$-0.757963\pi$
$619$	−7.29010	+	5.29657i	−0.293014	+	0.212887i	0.431560	+	0.902084i	$0.357963\pi$
$620$	−0.498697	−	1.16175i	−0.0200282	−	0.0466572i
$621$	5.92327	+	4.30350i	0.237692	+	0.172694i
$622$	−44.6314	−	32.4266i	−1.78956	−	1.30019i
$623$	22.0481	−	67.8571i	0.883339	−	2.71864i
$624$	4.93222			0.197447
$625$	−1.27706	−	24.9674i	−0.0510826	−	0.998694i
$626$	−32.2664			−1.28962
$627$	−12.9188	+	39.7601i	−0.515928	+	1.58786i
$628$	14.5890	+	10.5995i	0.582165	+	0.422968i
$629$	2.41579	+	1.75518i	0.0963239	+	0.0699834i
$630$	−6.96788	−	16.2322i	−0.277607	−	0.646707i
$631$	−22.4701	+	16.3255i	−0.894522	+	0.649908i	−0.937053	−	0.349187i	$-0.886458\pi$
$631$	−22.4701	+	16.3255i	−0.894522	+	0.649908i	0.0425309	+	0.999095i	$0.486458\pi$
$632$	17.1167			0.680864
$633$	−1.95421	+	1.41982i	−0.0776731	+	0.0564328i
$634$	−9.30995	−	28.6531i	−0.369745	−	1.13796i
$635$	−40.4790	+	3.70669i	−1.60636	+	0.147096i
$636$	−3.74365	+	11.5218i	−0.148445	+	0.456868i
$637$	3.75187	+	11.5471i	0.148655	+	0.457512i
$638$	9.39576	+	28.9172i	0.371982	+	1.14484i
$639$	−1.04916	+	3.22899i	−0.0415042	+	0.127737i
$640$	−4.91893	+	21.7069i	−0.194438	+	0.858040i
$641$	6.14218	+	18.9037i	0.242601	+	0.746651i	0.996022	+	0.0891112i	$0.0284027\pi$
$641$	6.14218	+	18.9037i	0.242601	+	0.746651i	−0.753420	+	0.657539i	$0.771597\pi$
$642$	9.65296	−	7.01329i	0.380972	−	0.276792i
$643$	−15.2962			−0.603223			−0.301612	−	0.953431i	$-0.597525\pi$
$643$	−15.2962			−0.603223			−0.301612	+	0.953431i	$0.597525\pi$
$644$	−32.6615	+	23.7300i	−1.28705	+	0.935093i
$645$	−0.137776	+	0.607997i	−0.00542494	+	0.0239399i
$646$	12.2107	+	8.87157i	0.480423	+	0.349047i
$647$	−13.1601	−	9.56135i	−0.517376	−	0.375895i	0.298239	−	0.954491i	$-0.403601\pi$
$647$	−13.1601	−	9.56135i	−0.517376	−	0.375895i	−0.815614	+	0.578596i	$0.803601\pi$
$648$	0.412708	−	1.27018i	0.0162127	−	0.0498976i
$649$	54.1603			2.12598
$650$	6.21872	−	6.54493i	0.243918	−	0.256713i
$651$	1.96268			0.0769236
$652$	0.715842	−	2.20313i	0.0280345	−	0.0862814i
$653$	−31.7878	−	23.0952i	−1.24395	−	0.903783i	−0.246096	−	0.969245i	$-0.579148\pi$
$653$	−31.7878	−	23.0952i	−1.24395	−	0.903783i	−0.997855	+	0.0654619i	$0.979148\pi$
$654$	−10.4313	−	7.57881i	−0.407898	−	0.296355i
$655$	15.9033	+	9.46821i	0.621392	+	0.369954i
$656$	34.6270	−	25.1580i	1.35196	−	0.982254i
$657$	−6.38149			−0.248966
$658$	57.9522	−	42.1048i	2.25921	−	1.64141i
$659$	9.45711	+	29.1060i	0.368397	+	1.13381i	0.947826	+	0.318787i	$0.103275\pi$
$659$	9.45711	+	29.1060i	0.368397	+	1.13381i	−0.579430	+	0.815022i	$0.696725\pi$
$660$	5.83343	+	13.5894i	0.227066	+	0.528968i
$661$	5.52745	−	17.0117i	0.214993	−	0.661680i	−0.784161	−	0.620557i	$-0.786907\pi$
$661$	5.52745	−	17.0117i	0.214993	−	0.661680i	0.999154	−	0.0411228i	$-0.0130935\pi$
$662$	9.21513	+	28.3613i	0.358156	+	1.10229i
$663$	0.324222	+	0.997854i	0.0125918	+	0.0387534i
$664$	−3.93030	+	12.0962i	−0.152525	+	0.469424i
$665$	66.9696	+	39.8712i	2.59697	+	1.54614i
$666$	−1.58802	−	4.88742i	−0.0615345	−	0.189384i
$667$	−19.0076	+	13.8098i	−0.735978	+	0.534719i
$668$	−8.71593			−0.337230
$669$	−1.17822	+	0.856029i	−0.0455527	+	0.0330960i
$670$	10.9979	−	9.63882i	0.424887	−	0.372380i
$671$	32.0255	+	23.2679i	1.23633	+	0.898248i
$672$	22.0679	+	16.0333i	0.851287	+	0.618496i
$673$	−11.6353	+	35.8099i	−0.448510	+	1.38037i	0.430079	+	0.902791i	$0.358486\pi$
$673$	−11.6353	+	35.8099i	−0.448510	+	1.38037i	−0.878589	+	0.477579i	$0.841514\pi$
$674$	50.2280			1.93471
$675$	−2.38304	−	4.39558i	−0.0917231	−	0.169186i
$676$	1.26035			0.0484748
$677$	2.30640	−	7.09836i	0.0886420	−	0.272812i	−0.896903	−	0.442228i	$-0.854188\pi$
$677$	2.30640	−	7.09836i	0.0886420	−	0.272812i	0.985545	+	0.169416i	$0.0541882\pi$
$678$	−10.3243	−	7.50107i	−0.396504	−	0.288077i
$679$	−54.9496	−	39.9232i	−2.10877	−	1.53211i
$680$	−3.12028	+	0.285726i	−0.119657	+	0.0109571i
$681$	4.02193	−	2.92210i	0.154121	−	0.111975i
$682$	−4.25057			−0.162763
$683$	−28.7445	+	20.8841i	−1.09988	+	0.799107i	−0.981040	−	0.193807i	$-0.937916\pi$
$683$	−28.7445	+	20.8841i	−1.09988	+	0.799107i	−0.118836	+	0.992914i	$0.537916\pi$
$684$	−3.10286	−	9.54961i	−0.118641	−	0.365138i
$685$	−26.6470	+	23.3540i	−1.01813	+	0.892311i
$686$	−12.5509	+	38.6276i	−0.479195	+	1.47481i
$687$	5.01190	+	15.4250i	0.191216	+	0.588502i
$688$	−0.424928	−	1.30779i	−0.0162002	−	0.0498592i
$689$	2.97034	−	9.14176i	0.113161	−	0.348273i
$690$	−22.2313	+	19.4840i	−0.846332	+	0.741743i
$691$	9.13334	+	28.1095i	0.347448	+	1.06934i	0.960260	+	0.279107i	$0.0900385\pi$
$691$	9.13334	+	28.1095i	0.347448	+	1.06934i	−0.612811	+	0.790229i	$0.709961\pi$
$692$	5.14716	−	3.73963i	0.195665	−	0.142159i
$693$	−22.9582			−0.872108
$694$	−27.6328	+	20.0764i	−1.04893	+	0.762090i
$695$	−2.88300	+	0.263998i	−0.109358	+	0.0100140i
$696$	3.46725	+	2.51910i	0.131426	+	0.0954863i
$697$	7.36602	+	5.35173i	0.279008	+	0.202711i
$698$	−4.63718	+	14.2718i	−0.175520	+	0.540195i
$699$	−18.4281			−0.697013
$700$	27.1120	−	5.00732i	1.02474	−	0.189259i
$701$	−30.3236			−1.14531			−0.572653	−	0.819798i	$-0.694086\pi$
$701$	−30.3236			−1.14531			−0.572653	+	0.819798i	$0.694086\pi$
$702$	0.557974	−	1.71727i	0.0210594	−	0.0648141i
$703$	18.3438	+	13.3275i	0.691848	+	0.502657i
$704$	−5.91476	−	4.29732i	−0.222921	−	0.161961i
$705$	15.2484	−	13.3640i	0.574288	−	0.503319i
$706$	40.0383	−	29.0895i	1.50686	−	1.09480i
$707$	12.4823			0.469445
$708$	−10.5239	+	7.64607i	−0.395513	+	0.287357i
$709$	−2.86517	−	8.81808i	−0.107604	−	0.331170i	0.882729	−	0.469882i	$-0.155704\pi$
$709$	−2.86517	−	8.81808i	−0.107604	−	0.331170i	−0.990333	+	0.138712i	$0.955704\pi$
$710$	−11.7786	−	7.01255i	−0.442044	−	0.263176i
$711$	3.96042	−	12.1889i	0.148527	−	0.457120i
$712$	6.73048	+	20.7143i	0.252235	+	0.776301i
$713$	−1.01496	−	3.12373i	−0.0380107	−	0.116985i
$714$	−2.56130	+	7.88287i	−0.0958543	+	0.295009i
$715$	−4.62844	−	10.7823i	−0.173094	−	0.403235i
$716$	−7.85418	−	24.1727i	−0.293524	−	0.903375i
$717$	11.9227	−	8.66236i	0.445262	−	0.323502i
$718$	−15.7061			−0.586148
$719$	−12.1970	+	8.86168i	−0.454873	+	0.330485i	−0.791517	−	0.611147i	$-0.790708\pi$
$719$	−12.1970	+	8.86168i	−0.454873	+	0.330485i	0.336644	+	0.941632i	$0.390708\pi$
$720$	9.47643	+	5.64191i	0.353166	+	0.210262i
$721$	20.2622	+	14.7213i	0.754603	+	0.548251i
$722$	64.9639	+	47.1990i	2.41770	+	1.75657i
$723$	4.67983	−	14.4030i	0.174045	−	0.535655i
$724$	−10.3907			−0.386169
$725$	15.7780	−	2.91405i	0.585982	−	0.108225i
$726$	29.8583			1.10815
$727$	−12.4792	+	38.4070i	−0.462828	+	1.42444i	0.398866	+	0.917009i	$0.369404\pi$
$727$	−12.4792	+	38.4070i	−0.462828	+	1.42444i	−0.861694	+	0.507428i	$0.830596\pi$
$728$	−4.72720	−	3.43451i	−0.175202	−	0.127291i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	5.69427	−	25.1284i	0.210754	−	0.930044i
$731$	0.236651	−	0.171937i	0.00875286	−	0.00635933i
$732$	−9.50774			−0.351416
$733$	15.2025	−	11.0453i	0.561517	−	0.407966i	−0.270497	−	0.962721i	$-0.587188\pi$
$733$	15.2025	−	11.0453i	0.561517	−	0.407966i	0.832014	+	0.554755i	$0.187188\pi$
$734$	0.101395	+	0.312060i	0.00374254	+	0.0115184i
$735$	−5.99998	+	26.4775i	−0.221313	+	0.976637i
$736$	14.1060	−	43.4137i	0.519953	−	1.60025i
$737$	−5.87331	−	18.0762i	−0.216346	−	0.665845i
$738$	−4.84205	−	14.9023i	−0.178238	−	0.548561i
$739$	9.18049	−	28.2547i	0.337710	−	1.03936i	−0.627662	−	0.778486i	$-0.715988\pi$
$739$	9.18049	−	28.2547i	0.337710	−	1.03936i	0.965372	−	0.260878i	$-0.0840121\pi$
$740$	7.98735	−	0.731407i	0.293621	−	0.0268871i
$741$	2.46191	+	7.57698i	0.0904405	+	0.278347i
$742$	61.4326	−	44.6334i	2.25526	−	1.63854i
$743$	−7.02434			−0.257698			−0.128849	−	0.991664i	$-0.541128\pi$
$743$	−7.02434			−0.257698			−0.128849	+	0.991664i	$0.541128\pi$
$744$	−0.484711	+	0.352163i	−0.0177703	+	0.0129109i
$745$	0.493707	+	1.15013i	0.0180880	+	0.0421375i
$746$	−12.2077	−	8.86943i	−0.446956	−	0.324733i
$747$	7.70443	+	5.59760i	0.281890	+	0.204805i
$748$	2.14429	−	6.59945i	0.0784031	−	0.241300i
$749$	−28.9106			−1.05637
$750$	19.4349	−	5.46147i	0.709662	−	0.199425i
$751$	−17.3111			−0.631690			−0.315845	−	0.948811i	$-0.602288\pi$
$751$	−17.3111			−0.631690			−0.315845	+	0.948811i	$0.602288\pi$
$752$	−13.8204	+	42.5347i	−0.503977	+	1.55108i
$753$	24.0880	+	17.5010i	0.877817	+	0.637771i
$754$	4.68766	+	3.40578i	0.170714	+	0.124031i
$755$	−18.7790	−	43.7471i	−0.683436	−	1.59212i
$756$	4.46101	−	3.24111i	0.162245	−	0.117878i
$757$	28.3571			1.03066			0.515328	−	0.856993i	$-0.327670\pi$
$757$	28.3571			1.03066			0.515328	+	0.856993i	$0.327670\pi$
$758$	2.16432	−	1.57247i	0.0786116	−	0.0571147i
$759$	11.8724	+	36.5394i	0.430939	+	1.32630i
$760$	−23.6931	+	2.16959i	−0.859439	+	0.0786994i
$761$	5.23936	−	16.1251i	0.189927	−	0.584534i	−0.810072	−	0.586331i	$-0.800572\pi$
$761$	5.23936	−	16.1251i	0.189927	−	0.584534i	0.999998	+	0.00179655i	$0.000571859\pi$
$762$	−10.1431	−	31.2174i	−0.367447	−	1.13089i
$763$	9.65426	+	29.7127i	0.349508	+	1.07567i
$764$	−4.15155	+	12.7772i	−0.150198	+	0.462262i
$765$	−0.518495	+	2.28808i	−0.0187462	+	0.0827258i
$766$	−13.3071	−	40.9551i	−0.480805	−	1.47977i
$767$	8.35002	−	6.06665i	0.301502	−	0.219054i
$768$	−20.7594			−0.749090
$769$	18.0777	−	13.1342i	0.651899	−	0.473633i	−0.212018	−	0.977266i	$-0.568004\pi$
$769$	18.0777	−	13.1342i	0.651899	−	0.473633i	0.863918	+	0.503633i	$0.168004\pi$
$770$	20.4858	−	90.4024i	0.738257	−	3.25788i
$771$	−3.31132	−	2.40581i	−0.119254	−	0.0866432i
$772$	−8.83718	−	6.42059i	−0.318057	−	0.231082i
$773$	0.584469	−	1.79881i	0.0210219	−	0.0646987i	−0.939995	−	0.341188i	$-0.889171\pi$
$773$	0.584469	−	1.79881i	0.0210219	−	0.0646987i	0.961017	+	0.276489i	$0.0891709\pi$
$774$	−0.503411			−0.0180947
$775$	−0.294169	+	2.22365i	−0.0105669	+	0.0798759i
$776$	20.7339			0.744304
$777$	−3.84777	+	11.8422i	−0.138038	+	0.424838i
$778$	14.5435	+	10.5665i	0.521409	+	0.378826i
$779$	55.9322	+	40.6371i	2.00398	+	1.45598i
$780$	2.42154	+	1.44170i	0.0867052	+	0.0516210i
$781$	−14.4135	+	10.4720i	−0.515755	+	0.374718i
$782$	13.8706			0.496012
$783$	2.59612	−	1.88619i	0.0927776	−	0.0674069i
$784$	−18.5051	−	56.9527i	−0.660895	−	2.03403i
$785$	−12.6201	−	29.3994i	−0.450430	−	1.04931i
$786$	−4.61847	+	14.2142i	−0.164735	+	0.507003i
$787$	9.15279	+	28.1694i	0.326262	+	1.00413i	0.970868	+	0.239615i	$0.0770213\pi$
$787$	9.15279	+	28.1694i	0.326262	+	1.00413i	−0.644606	+	0.764515i	$0.722979\pi$
$788$	1.11271	+	3.42457i	0.0396387	+	0.121995i
$789$	3.28241	−	10.1022i	0.116857	−	0.359648i
$790$	44.4624	+	26.4712i	1.58190	+	0.941804i
$791$	9.55522	+	29.4079i	0.339745	+	1.04563i
$792$	5.66982	−	4.11937i	0.201468	−	0.146375i
$793$	7.54375			0.267887
$794$	−5.80715	+	4.21914i	−0.206088	+	0.149732i
$795$	16.1642	−	14.1666i	0.573284	−	0.502438i
$796$	−10.7245	−	7.79180i	−0.380120	−	0.276173i
$797$	1.75420	+	1.27450i	0.0621368	+	0.0451451i	0.618420	−	0.785848i	$-0.287773\pi$
$797$	1.75420	+	1.27450i	0.0621368	+	0.0451451i	−0.556283	+	0.830993i	$0.687773\pi$
$798$	−19.4487	+	59.8568i	−0.688475	+	2.11891i
$799$	−9.51383			−0.336575
$800$	−21.4727	+	22.5991i	−0.759174	+	0.798998i
$801$	16.3081			0.576218
$802$	8.53534	−	26.2691i	0.301393	−	0.927593i
$803$	−27.0914	−	19.6830i	−0.956033	−	0.694599i
$804$	3.69315	+	2.68323i	0.130247	+	0.0946301i
$805$	71.3282	−	6.53157i	2.51399	−	0.230208i
$806$	−0.655320	+	0.476118i	−0.0230827	+	0.0167705i
$807$	15.1728			0.534107
$808$	−3.08267	+	2.23969i	−0.108448	+	0.0787919i
$809$	−10.3955	−	31.9939i	−0.365485	−	1.12485i	−0.949677	−	0.313231i	$-0.898589\pi$
$809$	−10.3955	−	31.9939i	−0.365485	−	1.12485i	0.584192	−	0.811615i	$-0.301411\pi$
$810$	3.03642	−	2.66118i	0.106689	−	0.0935044i
$811$	−8.73098	+	26.8712i	−0.306586	+	0.943576i	0.672494	+	0.740102i	$0.265223\pi$
$811$	−8.73098	+	26.8712i	−0.306586	+	0.943576i	−0.979081	+	0.203473i	$0.934777\pi$
$812$	5.46795	+	16.8286i	0.191887	+	0.590569i
$813$	7.36699	+	22.6733i	0.258372	+	0.795186i
$814$	8.33310	−	25.6467i	0.292075	−	0.898915i
$815$	−3.09083	+	2.70887i	−0.108267	+	0.0948875i
$816$	−1.59914	−	4.92163i	−0.0559810	−	0.172292i
$817$	1.79696	−	1.30557i	0.0628676	−	0.0456760i
$818$	25.8023			0.902157
$819$	−3.53951	+	2.57161i	−0.123681	+	0.0898592i
$820$	24.3543	−	2.23014i	0.850490	−	0.0778800i
$821$	24.6665	+	17.9212i	0.860865	+	0.625455i	0.928120	−	0.372281i	$-0.121424\pi$
$821$	24.6665	+	17.9212i	0.860865	+	0.625455i	−0.0672549	+	0.997736i	$0.521424\pi$
$822$	−23.1477	−	16.8178i	−0.807369	−	0.586588i
$823$	7.36523	−	22.6678i	0.256736	−	0.790152i	−0.736747	−	0.676169i	$-0.763639\pi$
$823$	7.36523	−	22.6678i	0.256736	−	0.790152i	0.993483	−	0.113983i	$-0.0363609\pi$
$824$	−7.64546			−0.266342
$825$	3.44099	−	26.0108i	0.119800	−	0.905580i
$826$	81.5357			2.83699
$827$	−8.65431	+	26.6352i	−0.300940	+	0.926198i	0.680221	+	0.733007i	$0.261884\pi$
$827$	−8.65431	+	26.6352i	−0.300940	+	0.926198i	−0.981161	+	0.193191i	$0.938116\pi$
$828$	−7.46536	−	5.42390i	−0.259439	−	0.188494i
$829$	−22.1561	−	16.0973i	−0.769512	−	0.559083i	0.132301	−	0.991210i	$-0.457763\pi$
$829$	−22.1561	−	16.0973i	−0.769512	−	0.559083i	−0.901813	+	0.432126i	$0.857763\pi$
$830$	−28.9164	+	25.3430i	−1.00370	+	0.879667i
$831$	−5.99578	+	4.35619i	−0.207991	+	0.151115i
$832$	−1.39325			−0.0483021
$833$	10.3058	−	7.48764i	0.357077	−	0.259431i
$834$	−0.722415	−	2.22336i	−0.0250152	−	0.0769888i
$835$	13.2870	+	7.91057i	0.459815	+	0.273757i
$836$	16.2822	−	50.1114i	0.563131	−	1.73314i
$837$	0.138627	+	0.426649i	0.00479164	+	0.0147471i
$838$	−6.86605	−	21.1315i	−0.237184	−	0.729977i
$839$	−2.18105	+	6.71258i	−0.0752982	+	0.231744i	−0.981621	−	0.190843i	$-0.938878\pi$
$839$	−2.18105	+	6.71258i	−0.0752982	+	0.231744i	0.906322	+	0.422587i	$0.138878\pi$
$840$	−5.15382	−	12.0062i	−0.177824	−	0.414254i
$841$	−5.77938	−	17.7871i	−0.199289	−	0.613349i
$842$	−17.2195	+	12.5107i	−0.593423	+	0.431147i
$843$	−12.8805			−0.443630
$844$	2.46299	−	1.78946i	0.0847795	−	0.0615959i
$845$	−1.92133	−	1.14389i	−0.0660958	−	0.0393510i
$846$	13.2460	+	9.62377i	0.455406	+	0.330872i
$847$	−58.5297	−	42.5243i	−2.01111	−	1.46115i
$848$	−14.6504	+	45.0892i	−0.503095	+	1.54837i
$849$	−2.97913			−0.102244
$850$	−8.54714	−	4.08336i	−0.293164	−	0.140058i
$851$	20.8375			0.714299
$852$	1.32231	−	4.06964i	0.0453015	−	0.139424i
$853$	−11.8979	−	8.64431i	−0.407376	−	0.295976i	0.365163	−	0.930944i	$-0.381013\pi$
$853$	−11.8979	−	8.64431i	−0.407376	−	0.295976i	−0.772538	+	0.634968i	$0.781013\pi$
$854$	48.2129	+	35.0287i	1.64981	+	1.19866i
$855$	−3.93707	+	17.3740i	−0.134645	+	0.594180i
$856$	7.13985	−	5.18741i	0.244035	−	0.177302i
$857$	−47.0142			−1.60597			−0.802987	−	0.595997i	$-0.796757\pi$
$857$	−47.0142			−1.60597			−0.802987	+	0.595997i	$0.796757\pi$
$858$	7.66550	−	5.56931i	0.261696	−	0.190133i
$859$	1.19515	+	3.67829i	0.0407780	+	0.125502i	0.969373	−	0.245593i	$-0.0789826\pi$
$859$	1.19515	+	3.67829i	0.0407780	+	0.125502i	−0.928595	+	0.371094i	$0.878983\pi$
$860$	0.173646	−	0.766287i	0.00592127	−	0.0261302i
$861$	−11.7323	+	36.1083i	−0.399835	+	1.23057i
$862$	−13.2354	−	40.7344i	−0.450800	−	1.38742i
$863$	1.33916	+	4.12150i	0.0455854	+	0.140297i	0.971259	−	0.238027i	$-0.0765005\pi$
$863$	1.33916	+	4.12150i	0.0455854	+	0.140297i	−0.925673	+	0.378324i	$0.876501\pi$
$864$	−1.92664	+	5.92958i	−0.0655455	+	0.201728i
$865$	−11.2407	+	1.02931i	−0.382194	+	0.0349977i
$866$	−6.83132	−	21.0246i	−0.232138	−	0.714446i
$867$	−12.8627	+	9.34530i	−0.436840	+	0.317383i
$868$	−2.47366			−0.0839615
$869$	54.4086	−	39.5301i	1.84568	−	1.34097i
$870$	5.11071	+	11.9058i	0.173269	+	0.403645i
$871$	−2.93026	−	2.12896i	−0.0992882	−	0.0721371i
$872$	−7.71558	−	5.60570i	−0.261283	−	0.189833i
$873$	4.79737	−	14.7648i	0.162366	−	0.499712i
$874$	105.323			3.56262
$875$	−45.8755	−	16.9735i	−1.55088	−	0.573808i
$876$	8.04288			0.271744
$877$	−7.22984	+	22.2512i	−0.244134	+	0.751369i	0.751643	+	0.659570i	$0.229262\pi$
$877$	−7.22984	+	22.2512i	−0.244134	+	0.751369i	−0.995778	+	0.0917987i	$0.970738\pi$
$878$	−26.8233	−	19.4883i	−0.905244	−	0.657698i
$879$	23.0781	+	16.7672i	0.778405	+	0.565545i
$880$	22.8285	+	53.1807i	0.769547	+	1.79272i
$881$	−16.3398	+	11.8715i	−0.550501	+	0.399962i	−0.827970	−	0.560772i	$-0.810504\pi$
$881$	−16.3398	+	11.8715i	−0.550501	+	0.399962i	0.277469	+	0.960735i	$0.410504\pi$
$882$	−21.9229			−0.738181
$883$	−10.3618	+	7.52827i	−0.348701	+	0.253346i	−0.748324	−	0.663333i	$-0.769141\pi$
$883$	−10.3618	+	7.52827i	−0.348701	+	0.253346i	0.399623	+	0.916680i	$0.369141\pi$
$884$	−0.408632	−	1.25764i	−0.0137438	−	0.0422990i
$885$	22.9827	−	2.10455i	0.772556	−	0.0707435i
$886$	4.90838	−	15.1064i	0.164900	−	0.507510i
$887$	−9.98865	−	30.7419i	−0.335386	−	1.03221i	−0.966532	−	0.256548i	$-0.917415\pi$
$887$	−9.98865	−	30.7419i	−0.335386	−	1.03221i	0.631145	−	0.775665i	$-0.282585\pi$
$888$	−1.17458	−	3.61500i	−0.0394165	−	0.121311i
$889$	−24.5769	+	75.6398i	−0.824281	+	2.53688i
$890$	−14.5519	+	64.2164i	−0.487780	+	2.15254i
$891$	−1.62156	−	4.99066i	−0.0543244	−	0.167193i
$892$	1.48497	−	1.07889i	0.0497204	−	0.0361240i
$893$	−72.2411			−2.41746
$894$	−0.817666	+	0.594069i	−0.0273469	+	0.0198687i
$895$	−9.96582	+	43.9785i	−0.333120	+	1.47004i
$896$	35.2314	+	25.5971i	1.17700	+	0.855140i
$897$	5.92327	+	4.30350i	0.197772	+	0.143690i
$898$	−17.1701	+	52.8442i	−0.572974	+	1.76343i
$899$	−1.43956			−0.0480121
$900$	3.00345	+	5.53995i	0.100115	+	0.184665i
$901$	−10.0852			−0.335986
$902$	25.4086	−	78.1995i	0.846013	−	2.60376i
$903$	0.986811	+	0.716960i	0.0328390	+	0.0238589i
$904$	−7.63644	−	5.54820i	−0.253984	−	0.184530i
$905$	15.8402	+	9.43063i	0.526545	+	0.313485i
$906$	31.1013	−	22.5964i	1.03327	−	0.750715i
$907$	−2.19293			−0.0728151			−0.0364076	−	0.999337i	$-0.511591\pi$
$907$	−2.19293			−0.0728151			−0.0364076	+	0.999337i	$0.511591\pi$
$908$	−5.06902	+	3.68286i	−0.168221	+	0.122220i
$909$	0.881638	+	2.71340i	0.0292421	+	0.0899979i
$910$	−6.96788	−	16.2322i	−0.230983	−	0.538093i
$911$	−8.02363	+	24.6942i	−0.265835	+	0.818155i	0.725665	+	0.688048i	$0.241532\pi$
$911$	−8.02363	+	24.6942i	−0.265835	+	0.818155i	−0.991500	+	0.130107i	$0.958468\pi$
$912$	−12.1427	−	37.3713i	−0.402084	−	1.23749i
$913$	15.4425	+	47.5270i	0.511071	+	1.57291i
$914$	21.1626	−	65.1319i	0.699998	−	2.15437i
$915$	14.4941	+	8.62922i	0.479159	+	0.285273i
$916$	−6.31672	−	19.4409i	−0.208710	−	0.642345i
$917$	29.2973	−	21.2857i	0.967482	−	0.702917i
$918$	−1.89449			−0.0625275
$919$	1.42285	−	1.03376i	0.0469355	−	0.0341006i	−0.564070	−	0.825727i	$-0.690765\pi$
$919$	1.42285	−	1.03376i	0.0469355	−	0.0341006i	0.611006	+	0.791626i	$0.290765\pi$
$920$	−16.4435	+	14.4114i	−0.542126	+	0.475131i
$921$	9.13538	+	6.63724i	0.301021	+	0.218704i
$922$	39.5827	+	28.7585i	1.30359	+	0.947110i
$923$	−1.04916	+	3.22899i	−0.0345336	+	0.106284i
$924$	28.9352			0.951899
$925$	−12.8401	−	6.13432i	−0.422181	−	0.201695i
$926$	0.0945743			0.00310790
$927$	−1.76899	+	5.44439i	−0.0581012	+	0.178817i
$928$	−16.1861	−	11.7599i	−0.531334	−	0.386037i
$929$	−16.4775	−	11.9716i	−0.540608	−	0.392775i	0.283703	−	0.958912i	$-0.408437\pi$
$929$	−16.4775	−	11.9716i	−0.540608	−	0.392775i	−0.824311	+	0.566138i	$0.808437\pi$
$930$	−1.80371	+	0.165167i	−0.0591461	+	0.00541605i
$931$	78.2551	−	56.8557i	2.56471	−	1.86337i
$932$	23.2257			0.760784
$933$	−24.7178	+	17.9585i	−0.809223	+	0.587935i
$934$	12.7186	+	39.1438i	0.416165	+	1.28082i
$935$	−9.25852	+	8.11437i	−0.302786	+	0.265368i
$936$	0.412708	−	1.27018i	0.0134898	−	0.0415173i
$937$	−8.39591	−	25.8400i	−0.274282	−	0.844155i	−0.989408	−	0.145159i	$-0.953631\pi$
$937$	−8.39591	−	25.8400i	−0.274282	−	0.844155i	0.715126	−	0.698996i	$-0.246369\pi$
$938$	−8.84197	−	27.2128i	−0.288701	−	0.888529i
$939$	−5.52205	+	16.9951i	−0.180205	+	0.554615i
$940$	−19.2183	+	16.8433i	−0.626831	+	0.549368i
$941$	−10.5242	−	32.3903i	−0.343081	−	1.05589i	−0.962603	−	0.270915i	$-0.912674\pi$
$941$	−10.5242	−	32.3903i	−0.343081	−	1.05589i	0.619523	−	0.784979i	$-0.287326\pi$
$942$	20.9010	−	15.1855i	0.680993	−	0.494770i
$943$	63.5358			2.06901
$944$	−41.1842	+	29.9220i	−1.34043	+	0.973879i
$945$	−9.74221	+	0.892101i	−0.316914	+	0.0290200i
$946$	−2.13713	−	1.55272i	−0.0694841	−	0.0504832i
$947$	12.1936	+	8.85914i	0.396237	+	0.287883i	0.768007	−	0.640442i	$-0.221249\pi$
$947$	12.1936	+	8.85914i	0.396237	+	0.287883i	−0.371769	+	0.928325i	$0.621249\pi$
$948$	−4.99149	+	15.3622i	−0.162116	+	0.498942i
$949$	−6.38149			−0.207152
$950$	−64.9007	−	31.0061i	−2.10566	−	1.00597i
$951$	−16.6853			−0.541057
$952$	−1.89448	+	5.83060i	−0.0614004	+	0.188971i
$953$	−31.5623	−	22.9314i	−1.02240	−	0.742820i	−0.0556300	−	0.998451i	$-0.517717\pi$
$953$	−31.5623	−	22.9314i	−1.02240	−	0.742820i	−0.966774	+	0.255631i	$0.917717\pi$
$954$	14.0415	+	10.2017i	0.454610	+	0.330293i
$955$	17.9254	−	15.7102i	0.580051	−	0.508370i
$956$	−15.0267	+	10.9176i	−0.486000	+	0.353099i
$957$	16.8391			0.544329
$958$	16.4203	−	11.9300i	0.530516	−	0.385442i
$959$	21.4233	+	65.9342i	0.691795	+	2.12913i
$960$	−2.67689	−	1.59372i	−0.0863962	−	0.0514371i
$961$	−9.51734	+	29.2914i	−0.307011	+	0.944882i
$962$	−1.58802	−	4.88742i	−0.0511998	−	0.157577i
$963$	−2.04199	−	6.28460i	−0.0658022	−	0.202518i
$964$	−5.89821	+	18.1528i	−0.189969	+	0.584663i
$965$	7.64451	+	17.8085i	0.246085	+	0.573275i
$966$	17.8733	+	55.0082i	0.575062	+	1.76986i
$967$	23.3114	−	16.9367i	0.749644	−	0.544648i	−0.146073	−	0.989274i	$-0.546663\pi$
$967$	23.3114	−	16.9367i	0.749644	−	0.544648i	0.895716	+	0.444626i	$0.146663\pi$
$968$	22.0848			0.709833
$969$	6.76251	−	4.91325i	0.217243	−	0.157836i
$970$	53.8586	+	32.0654i	1.72930	+	1.02956i
$971$	−7.15869	−	5.20109i	−0.229733	−	0.166911i	0.466964	−	0.884276i	$-0.345348\pi$
$971$	−7.15869	−	5.20109i	−0.229733	−	0.166911i	−0.696697	+	0.717365i	$0.745348\pi$
$972$	1.01964	+	0.740813i	0.0327050	+	0.0237616i
$973$	−1.75041	+	5.38722i	−0.0561157	+	0.172706i
$974$	−51.1396			−1.63862
$975$	−2.38304	−	4.39558i	−0.0763182	−	0.140771i
$976$	−37.2075			−1.19098
$977$	−12.6981	+	39.0809i	−0.406249	+	1.25031i	0.513598	+	0.858031i	$0.328312\pi$
$977$	−12.6981	+	39.0809i	−0.406249	+	1.25031i	−0.919847	+	0.392276i	$0.871688\pi$
$978$	−2.68494	−	1.95072i	−0.0858549	−	0.0623772i
$979$	69.2328	+	50.3006i	2.21269	+	1.60761i
$980$	7.56205	−	33.3708i	0.241561	−	1.06599i
$981$	−5.77708	+	4.19729i	−0.184448	+	0.134009i
$982$	−35.1877			−1.12289
$983$	−10.7761	+	7.82932i	−0.343705	+	0.249717i	−0.746224	−	0.665695i	$-0.768135\pi$
$983$	−10.7761	+	7.82932i	−0.343705	+	0.249717i	0.402518	+	0.915412i	$0.368135\pi$
$984$	−3.58144	−	11.0225i	−0.114172	−	0.351386i
$985$	1.41187	−	6.23048i	0.0449859	−	0.198520i
$986$	1.87863	−	5.78183i	0.0598278	−	0.184131i
$987$	−12.2592	−	37.7300i	−0.390215	−	1.20096i
$988$	−3.10286	−	9.54961i	−0.0987150	−	0.303814i
$989$	0.630778	−	1.94133i	0.0200576	−	0.0617309i
$990$	21.0987	−	1.93202i	0.670559	−	0.0614036i
$991$	−12.9477	−	39.8490i	−0.411298	−	1.26585i	−0.915520	−	0.402272i	$-0.868221\pi$
$991$	−12.9477	−	39.8490i	−0.411298	−	1.26585i	0.504222	−	0.863574i	$-0.331779\pi$
$992$	2.26276	−	1.64399i	0.0718428	−	0.0521969i
$993$	16.5153			0.524098
$994$	−21.6988	+	15.7651i	−0.688244	+	0.500039i
$995$	9.27711	+	21.6118i	0.294104	+	0.685139i
$996$	−9.71025	−	7.05491i	−0.307681	−	0.223543i
$997$	−19.5456	−	14.2007i	−0.619014	−	0.449740i	0.233563	−	0.972342i	$-0.424962\pi$
$997$	−19.5456	−	14.2007i	−0.619014	−	0.449740i	−0.852577	+	0.522601i	$0.824962\pi$
$998$	−15.0211	+	46.2301i	−0.475484	+	1.46339i
$999$	−2.84604			−0.0900448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.v.c.196.5	✓	68
25.6	even	5	inner	975.2.v.c.781.5	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.v.c.196.5	✓	68	1.1	even	1	trivial
975.2.v.c.781.5	yes	68	25.6	even	5	inner

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.v (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557974 + 1.71727i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.01964 - 0.740813i) q^{4} +(0.882029 + 2.05476i) q^{5} +(-1.46080 + 1.06133i) q^{6} +4.37508 q^{7} +(-1.08048 + 0.785017i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.557974 + 1.71727i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.01964 - 0.740813i) q^{4} +(0.882029 + 2.05476i) q^{5} +(-1.46080 + 1.06133i) q^{6} +4.37508 q^{7} +(-1.08048 + 0.785017i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-4.02072 + 0.368180i) q^{10} +(-1.62156 + 4.99066i) q^{11} +(-0.389468 - 1.19866i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.44118 + 7.51318i) q^{14} +(-0.494179 + 2.18078i) q^{15} +(-1.52414 - 4.69082i) q^{16} +(0.848825 - 0.616708i) q^{17} -1.80564 q^{18} +(6.44536 - 4.68283i) q^{19} +(0.622836 - 2.74853i) q^{20} +(3.53951 + 2.57161i) q^{21} +(-7.66550 - 5.56931i) q^{22} +(2.26249 - 6.96322i) q^{23} -1.33555 q^{24} +(-3.44405 + 3.62471i) q^{25} -1.80564 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.46101 - 3.24111i) q^{28} +(-2.59612 - 1.88619i) q^{29} +(-3.46924 - 2.06545i) q^{30} +(0.362929 - 0.263683i) q^{31} +6.23473 q^{32} +(-4.24530 + 3.08439i) q^{33} +(0.585430 + 1.80177i) q^{34} +(3.85895 + 8.98972i) q^{35} +(0.389468 - 1.19866i) q^{36} +(0.879475 + 2.70675i) q^{37} +(4.44533 + 13.6813i) q^{38} +(-0.309017 + 0.951057i) q^{39} +(-2.56604 - 1.52772i) q^{40} +(2.68162 + 8.25317i) q^{41} +(-6.39110 + 4.64340i) q^{42} +0.278799 q^{43} +(5.35055 - 3.88740i) q^{44} +(-1.68163 + 1.47381i) q^{45} +(10.6953 + 7.77059i) q^{46} +(-7.33588 - 5.32983i) q^{47} +(1.52414 - 4.69082i) q^{48} +12.1413 q^{49} +(-4.30291 - 7.93685i) q^{50} +1.04921 q^{51} +(0.389468 - 1.19866i) q^{52} +(-7.77644 - 5.64992i) q^{53} +(-1.46080 - 1.06133i) q^{54} +(-11.6848 + 1.06999i) q^{55} +(-4.72720 + 3.43451i) q^{56} +7.96690 q^{57} +(4.68766 - 3.40578i) q^{58} +(-3.18943 - 9.81604i) q^{59} +(2.11943 - 1.85752i) q^{60} +(2.33115 - 7.17454i) q^{61} +(0.250310 + 0.770375i) q^{62} +(1.35197 + 4.16095i) q^{63} +(-0.430537 + 1.32506i) q^{64} +(-1.68163 + 1.47381i) q^{65} +(-2.92796 - 9.01134i) q^{66} +(-2.93026 + 2.12896i) q^{67} -1.32236 q^{68} +(5.92327 - 4.30350i) q^{69} +(-17.5910 + 1.61082i) q^{70} +(2.74674 + 1.99563i) q^{71} +(-1.08048 - 0.785017i) q^{72} +(-1.97199 + 6.06915i) q^{73} -5.13893 q^{74} +(-4.91685 + 0.908092i) q^{75} -10.0411 q^{76} +(-7.09446 + 21.8345i) q^{77} +(-1.46080 - 1.06133i) q^{78} +(-10.3685 - 7.53316i) q^{79} +(8.29416 - 7.26918i) q^{80} +(-0.809017 + 0.587785i) q^{81} -15.6692 q^{82} +(7.70443 - 5.59760i) q^{83} +(-1.70395 - 5.24423i) q^{84} +(2.01587 + 1.20017i) q^{85} +(-0.155562 + 0.478772i) q^{86} +(-0.991628 - 3.05192i) q^{87} +(-2.16568 - 6.66528i) q^{88} +(5.03948 - 15.5099i) q^{89} +(-1.59263 - 3.71016i) q^{90} +(1.35197 + 4.16095i) q^{91} +(-7.46536 + 5.42390i) q^{92} +0.448605 q^{93} +(13.2460 - 9.62377i) q^{94} +(15.3071 + 9.11325i) q^{95} +(5.04400 + 3.66468i) q^{96} +(-12.5597 - 9.12514i) q^{97} +(-6.77454 + 20.8499i) q^{98} -5.24749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9	\( 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 17 q^{13} - 26 q^{14} - q^{15} - 19 q^{16} - 7 q^{17} + 4 q^{18} - 8 q^{19} + 55 q^{20} - q^{21} - 26 q^{22} - 15 q^{23} - 18 q^{24} + 3 q^{25} + 4 q^{26} + 17 q^{27} + 9 q^{28} - 25 q^{29} - 28 q^{30} - 26 q^{31} + 180 q^{32} + 8 q^{33} + 26 q^{34} - 46 q^{35} - 19 q^{36} - 8 q^{37} + 8 q^{38} + 17 q^{39} + 82 q^{40} - 9 q^{41} - 4 q^{42} - 100 q^{43} - 5 q^{44} + 6 q^{45} + 32 q^{46} + 2 q^{47} + 19 q^{48} + 204 q^{49} - 29 q^{50} + 2 q^{51} - 19 q^{52} - 31 q^{53} + q^{54} - 37 q^{55} - 17 q^{56} + 8 q^{57} + 11 q^{58} - 13 q^{59} - 25 q^{60} + 14 q^{61} - 46 q^{62} + q^{63} - 56 q^{64} + 6 q^{65} - 39 q^{66} - 12 q^{67} + 26 q^{68} - 10 q^{69} + 117 q^{70} + 7 q^{71} - 12 q^{72} - 10 q^{73} + 76 q^{74} + 2 q^{75} + 6 q^{76} - 5 q^{77} + q^{78} - 46 q^{79} + 128 q^{80} - 17 q^{81} + 102 q^{82} + 28 q^{83} - 4 q^{84} - 40 q^{85} - 60 q^{86} + 64 q^{88} - 38 q^{89} - 17 q^{90} + q^{91} - 42 q^{92} - 64 q^{93} + 39 q^{94} - 49 q^{95} + 60 q^{96} - 34 q^{97} + 53 q^{98} + 12 q^{99}+O(q^{100}) \) 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 17 * q^13 - 26 * q^14 - q^15 - 19 * q^16 - 7 * q^17 + 4 * q^18 - 8 * q^19 + 55 * q^20 - q^21 - 26 * q^22 - 15 * q^23 - 18 * q^24 + 3 * q^25 + 4 * q^26 + 17 * q^27 + 9 * q^28 - 25 * q^29 - 28 * q^30 - 26 * q^31 + 180 * q^32 + 8 * q^33 + 26 * q^34 - 46 * q^35 - 19 * q^36 - 8 * q^37 + 8 * q^38 + 17 * q^39 + 82 * q^40 - 9 * q^41 - 4 * q^42 - 100 * q^43 - 5 * q^44 + 6 * q^45 + 32 * q^46 + 2 * q^47 + 19 * q^48 + 204 * q^49 - 29 * q^50 + 2 * q^51 - 19 * q^52 - 31 * q^53 + q^54 - 37 * q^55 - 17 * q^56 + 8 * q^57 + 11 * q^58 - 13 * q^59 - 25 * q^60 + 14 * q^61 - 46 * q^62 + q^63 - 56 * q^64 + 6 * q^65 - 39 * q^66 - 12 * q^67 + 26 * q^68 - 10 * q^69 + 117 * q^70 + 7 * q^71 - 12 * q^72 - 10 * q^73 + 76 * q^74 + 2 * q^75 + 6 * q^76 - 5 * q^77 + q^78 - 46 * q^79 + 128 * q^80 - 17 * q^81 + 102 * q^82 + 28 * q^83 - 4 * q^84 - 40 * q^85 - 60 * q^86 + 64 * q^88 - 38 * q^89 - 17 * q^90 + q^91 - 42 * q^92 - 64 * q^93 + 39 * q^94 - 49 * q^95 + 60 * q^96 - 34 * q^97 + 53 * q^98 + 12 * q^99

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