LMFDB - Embedded newform 930.2.v.a.401.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.18
Character	$\chi$	$=$	930.401
Dual form			930.2.v.a.821.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.605307 + 1.62284i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.26721 + 1.96463i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.605307 + 1.62284i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.26721 + 1.96463i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.477187 - 1.46863i) q^{11} +(1.35636 - 1.07717i) q^{12} +(-0.190055 - 0.261588i) q^{13} +(1.79744 + 0.584024i) q^{14} +(-1.62284 + 0.605307i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.19339 + 3.67287i) q^{17} +(0.256788 + 2.98899i) q^{18} +(6.86216 + 4.98565i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-2.56344 + 2.03578i) q^{21} +(-1.46863 - 0.477187i) q^{22} +(0.144742 - 0.445469i) q^{23} +(-0.0741964 - 1.73046i) q^{24} -1.00000 q^{25} -0.323341 q^{26} +(-4.56063 - 2.49011i) q^{27} +(1.52899 - 1.11088i) q^{28} +(3.90941 + 2.84035i) q^{29} +(-0.464177 + 1.66869i) q^{30} +(-5.26827 + 1.80147i) q^{31} +1.00000i q^{32} +(2.09451 - 1.66337i) q^{33} +(2.26996 + 3.12433i) q^{34} +(-1.79744 + 0.584024i) q^{35} +(2.56908 + 1.54914i) q^{36} +5.75161i q^{37} +(8.06695 - 2.62111i) q^{38} +(0.309474 - 0.466769i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-5.28220 + 7.27033i) q^{41} +(0.140227 + 3.27047i) q^{42} +(-3.29598 + 4.53652i) q^{43} +(-1.24929 + 0.907664i) q^{44} +(-1.96463 - 2.26721i) q^{45} +(-0.275315 - 0.378938i) q^{46} +(-6.83937 - 9.41358i) q^{47} +(-1.44358 - 0.957113i) q^{48} +(2.77341 - 2.01500i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(-6.68284 + 0.286538i) q^{51} +(-0.190055 + 0.261588i) q^{52} +(3.59432 - 11.0622i) q^{53} +(-4.69521 + 2.22598i) q^{54} +(1.46863 - 0.477187i) q^{55} -1.88994i q^{56} +(-3.93719 + 14.1540i) q^{57} +(4.59578 - 1.49326i) q^{58} +(-0.437766 - 0.602534i) q^{59} +(1.07717 + 1.35636i) q^{60} -0.790467i q^{61} +(-1.63919 + 5.32100i) q^{62} +(-4.85541 - 2.92778i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.261588 - 0.190055i) q^{65} +(-0.114575 - 2.67220i) q^{66} +6.62011 q^{67} +3.86189 q^{68} +(0.810537 - 0.0347531i) q^{69} +(-0.584024 + 1.79744i) q^{70} +(9.48945 + 3.08331i) q^{71} +(2.76335 - 1.16787i) q^{72} +(4.30980 - 1.40034i) q^{73} +(4.65315 + 3.38071i) q^{74} +(-0.605307 - 1.62284i) q^{75} +(2.62111 - 8.06695i) q^{76} +(2.36109 - 1.71543i) q^{77} +(-0.195720 - 0.524730i) q^{78} +(8.90634 + 2.89384i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(1.28046 - 8.90845i) q^{81} +(2.77702 + 8.54678i) q^{82} +(5.70547 + 4.14527i) q^{83} +(2.72829 + 1.80889i) q^{84} +(-3.67287 - 1.19339i) q^{85} +(1.73280 + 5.33300i) q^{86} +(-2.24304 + 8.06362i) q^{87} +1.54421i q^{88} +(-0.263336 - 0.810465i) q^{89} +(-2.98899 + 0.256788i) q^{90} +(0.359192 - 0.494386i) q^{91} -0.468393 q^{92} +(-6.11242 - 7.45911i) q^{93} -11.6358 q^{94} +(-4.98565 + 6.86216i) q^{95} +(-1.62284 + 0.605307i) q^{96} +(-5.86265 - 18.0434i) q^{97} -3.42812i q^{98} +(3.96720 + 2.39220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.605307	+	1.62284i	0.349474	+	0.936946i
$3$	0.605307	+	1.62284i	0.349474	+	0.936946i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.66869	+	0.464177i	0.681241	+	0.189499i
$7$	0.584024	+	1.79744i	0.220740	+	0.679369i	0.998696	+	0.0510498i	$0.0162567\pi$
$7$	0.584024	+	1.79744i	0.220740	+	0.679369i	−0.777956	+	0.628319i	$0.783743\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−2.26721	+	1.96463i	−0.755736	+	0.654877i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	−0.477187	−	1.46863i	−0.143877	−	0.442809i	0.852988	−	0.521931i	$-0.174788\pi$
$11$	−0.477187	−	1.46863i	−0.143877	−	0.442809i	−0.996865	+	0.0791223i	$0.974788\pi$
$12$	1.35636	−	1.07717i	0.391548	−	0.310951i
$13$	−0.190055	−	0.261588i	−0.0527117	−	0.0725515i	0.781847	−	0.623470i	$-0.214278\pi$
$13$	−0.190055	−	0.261588i	−0.0527117	−	0.0725515i	−0.834559	+	0.550918i	$0.814278\pi$
$14$	1.79744	+	0.584024i	0.480386	+	0.156087i
$15$	−1.62284	+	0.605307i	−0.419015	+	0.156290i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.19339	+	3.67287i	−0.289439	+	0.890802i	0.695594	+	0.718435i	$0.255141\pi$
$17$	−1.19339	+	3.67287i	−0.289439	+	0.890802i	−0.985033	+	0.172367i	$0.944859\pi$
$18$	0.256788	+	2.98899i	0.0605255	+	0.704512i
$19$	6.86216	+	4.98565i	1.57429	+	1.14379i	0.922900	+	0.385041i	$0.125813\pi$
$19$	6.86216	+	4.98565i	1.57429	+	1.14379i	0.651387	+	0.758746i	$0.274187\pi$
$20$	0.951057	−	0.309017i	0.212663	−	0.0690983i
$21$	−2.56344	+	2.03578i	−0.559389	+	0.444243i
$22$	−1.46863	−	0.477187i	−0.313113	−	0.101737i
$23$	0.144742	−	0.445469i	0.0301807	−	0.0928866i	−0.934831	−	0.355092i	$-0.884450\pi$
$23$	0.144742	−	0.445469i	0.0301807	−	0.0928866i	0.965012	+	0.262205i	$0.0844497\pi$
$24$	−0.0741964	−	1.73046i	−0.0151453	−	0.353229i
$25$	−1.00000			−0.200000
$26$	−0.323341			−0.0634123
$27$	−4.56063	−	2.49011i	−0.877694	−	0.479221i
$28$	1.52899	−	1.11088i	0.288953	−	0.209936i
$29$	3.90941	+	2.84035i	0.725959	+	0.527440i	0.888282	−	0.459298i	$-0.151899\pi$
$29$	3.90941	+	2.84035i	0.725959	+	0.527440i	−0.162324	+	0.986738i	$0.551899\pi$
$30$	−0.464177	+	1.66869i	−0.0847467	+	0.304660i
$31$	−5.26827	+	1.80147i	−0.946210	+	0.323554i
$31$	−5.26827	+	1.80147i	−0.946210	+	0.323554i
$32$			1.00000i			0.176777i
$33$	2.09451	−	1.66337i	0.364607	−	0.289556i
$34$	2.26996	+	3.12433i	0.389295	+	0.535818i
$35$	−1.79744	+	0.584024i	−0.303823	+	0.0987181i
$36$	2.56908	+	1.54914i	0.428180	+	0.258190i
$37$			5.75161i			0.945559i	0.881181	+	0.472779i	$0.156749\pi$
$37$			5.75161i			0.945559i	−0.881181	+	0.472779i	$0.843251\pi$
$38$	8.06695	−	2.62111i	1.30863	−	0.425200i
$39$	0.309474	−	0.466769i	0.0495554	−	0.0747429i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−5.28220	+	7.27033i	−0.824942	+	1.13543i	0.163902	+	0.986477i	$0.447592\pi$
$41$	−5.28220	+	7.27033i	−0.824942	+	1.13543i	−0.988844	+	0.148958i	$0.952408\pi$
$42$	0.140227	+	3.27047i	0.0216375	+	0.504644i
$43$	−3.29598	+	4.53652i	−0.502632	+	0.691813i	−0.982655	−	0.185443i	$-0.940628\pi$
$43$	−3.29598	+	4.53652i	−0.502632	+	0.691813i	0.480024	+	0.877256i	$0.340628\pi$
$44$	−1.24929	+	0.907664i	−0.188338	+	0.136836i
$45$	−1.96463	−	2.26721i	−0.292870	−	0.337975i
$46$	−0.275315	−	0.378938i	−0.0405929	−	0.0558714i
$47$	−6.83937	−	9.41358i	−0.997624	−	1.37311i	−0.926772	−	0.375626i	$-0.877428\pi$
$47$	−6.83937	−	9.41358i	−0.997624	−	1.37311i	−0.0708529	−	0.997487i	$-0.522572\pi$
$48$	−1.44358	−	0.957113i	−0.208363	−	0.138147i
$49$	2.77341	−	2.01500i	0.396201	−	0.287857i
$50$	−0.587785	+	0.809017i	−0.0831254	+	0.114412i
$51$	−6.68284	+	0.286538i	−0.935785	+	0.0401234i
$52$	−0.190055	+	0.261588i	−0.0263559	+	0.0362757i
$53$	3.59432	−	11.0622i	0.493718	−	1.51951i	−0.325228	−	0.945636i	$-0.605441\pi$
$53$	3.59432	−	11.0622i	0.493718	−	1.51951i	0.818945	−	0.573871i	$-0.194559\pi$
$54$	−4.69521	+	2.22598i	−0.638937	+	0.302918i
$55$	1.46863	−	0.477187i	0.198030	−	0.0643439i
$56$		−	1.88994i		−	0.252554i
$57$	−3.93719	+	14.1540i	−0.521494	+	1.87475i
$58$	4.59578	−	1.49326i	0.603456	−	0.196075i
$59$	−0.437766	−	0.602534i	−0.0569923	−	0.0784432i	0.779570	−	0.626316i	$-0.215438\pi$
$59$	−0.437766	−	0.602534i	−0.0569923	−	0.0784432i	−0.836562	+	0.547872i	$0.815438\pi$
$60$	1.07717	+	1.35636i	0.139061	+	0.175105i
$61$		−	0.790467i		−	0.101209i	−0.998719	−	0.0506045i	$-0.983885\pi$
$61$		−	0.790467i		−	0.101209i	0.998719	−	0.0506045i	$-0.0161148\pi$
$62$	−1.63919	+	5.32100i	−0.208177	+	0.675768i
$63$	−4.85541	−	2.92778i	−0.611724	−	0.368866i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	0.261588	−	0.190055i	0.0324460	−	0.0235734i
$66$	−0.114575	−	2.67220i	−0.0141032	−	0.328925i
$67$	6.62011			0.808775			0.404387	−	0.914588i	$-0.367485\pi$
$67$	6.62011			0.808775			0.404387	+	0.914588i	$0.367485\pi$
$68$	3.86189			0.468322
$69$	0.810537	−	0.0347531i	0.0975771	−	0.00418378i
$70$	−0.584024	+	1.79744i	−0.0698042	+	0.214835i
$71$	9.48945	+	3.08331i	1.12619	+	0.365922i	0.812127	−	0.583480i	$-0.198310\pi$
$71$	9.48945	+	3.08331i	1.12619	+	0.365922i	0.314064	+	0.949402i	$0.398310\pi$
$72$	2.76335	−	1.16787i	0.325663	−	0.137635i
$73$	4.30980	−	1.40034i	0.504424	−	0.163897i	−0.0457407	−	0.998953i	$-0.514565\pi$
$73$	4.30980	−	1.40034i	0.504424	−	0.163897i	0.550165	+	0.835056i	$0.314565\pi$
$74$	4.65315	+	3.38071i	0.540918	+	0.393000i
$75$	−0.605307	−	1.62284i	−0.0698948	−	0.187389i
$76$	2.62111	−	8.06695i	0.300662	−	0.925342i
$77$	2.36109	−	1.71543i	0.269071	−	0.195492i
$78$	−0.195720	−	0.524730i	−0.0221610	−	0.0594139i
$79$	8.90634	+	2.89384i	1.00204	+	0.325583i	0.763681	−	0.645594i	$-0.223390\pi$
$79$	8.90634	+	2.89384i	1.00204	+	0.325583i	0.238360	+	0.971177i	$0.423390\pi$
$80$	−0.587785	−	0.809017i	−0.0657164	−	0.0904508i
$81$	1.28046	−	8.90845i	0.142273	−	0.989827i
$82$	2.77702	+	8.54678i	0.306670	+	0.943834i
$83$	5.70547	+	4.14527i	0.626257	+	0.455002i	0.855102	−	0.518461i	$-0.173495\pi$
$83$	5.70547	+	4.14527i	0.626257	+	0.455002i	−0.228844	+	0.973463i	$0.573495\pi$
$84$	2.72829	+	1.80889i	0.297681	+	0.197366i
$85$	−3.67287	−	1.19339i	−0.398379	−	0.129441i
$86$	1.73280	+	5.33300i	0.186852	+	0.575072i
$87$	−2.24304	+	8.06362i	−0.240479	+	0.864510i
$88$			1.54421i			0.164613i
$89$	−0.263336	−	0.810465i	−0.0279136	−	0.0859091i	0.936129	−	0.351656i	$-0.114381\pi$
$89$	−0.263336	−	0.810465i	−0.0279136	−	0.0859091i	−0.964043	+	0.265747i	$0.914381\pi$
$90$	−2.98899	+	0.256788i	−0.315067	+	0.0270678i
$91$	0.359192	−	0.494386i	0.0376536	−	0.0518257i
$92$	−0.468393			−0.0488334
$93$	−6.11242	−	7.45911i	−0.633828	−	0.773474i
$94$	−11.6358			−1.20014
$95$	−4.98565	+	6.86216i	−0.511517	+	0.704042i
$96$	−1.62284	+	0.605307i	−0.165630	+	0.0617789i
$97$	−5.86265	−	18.0434i	−0.595262	−	1.83203i	−0.553419	−	0.832903i	$-0.686677\pi$
$97$	−5.86265	−	18.0434i	−0.595262	−	1.83203i	−0.0418429	−	0.999124i	$-0.513323\pi$
$98$		−	3.42812i		−	0.346293i
$99$	3.96720	+	2.39220i	0.398719	+	0.240425i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	9.86879	+	3.20656i	0.981981	+	0.319065i	0.755643	−	0.654984i	$-0.227325\pi$
$101$	9.86879	+	3.20656i	0.981981	+	0.319065i	0.226338	+	0.974049i	$0.427325\pi$
$102$	−3.69626	+	5.57496i	−0.365984	+	0.552003i
$103$	−9.83640	−	7.14656i	−0.969209	−	0.704172i	−0.0139379	−	0.999903i	$-0.504437\pi$
$103$	−9.83640	−	7.14656i	−0.969209	−	0.704172i	−0.955271	+	0.295731i	$0.904437\pi$
$104$	0.0999178	+	0.307515i	0.00979774	+	0.0301544i
$105$	−2.03578	−	2.56344i	−0.198672	−	0.250166i
$106$	−6.83680	−	9.41005i	−0.664049	−	0.913985i
$107$	−5.82225	−	1.89176i	−0.562858	−	0.182884i	0.0137485	−	0.999905i	$-0.495624\pi$
$107$	−5.82225	−	1.89176i	−0.562858	−	0.182884i	−0.576607	+	0.817022i	$0.695624\pi$
$108$	−0.958919	+	5.10690i	−0.0922720	+	0.491412i
$109$	6.83939	−	4.96910i	0.655094	−	0.475954i	−0.209908	−	0.977721i	$-0.567317\pi$
$109$	6.83939	−	4.96910i	0.655094	−	0.475954i	0.865003	+	0.501767i	$0.167317\pi$
$110$	0.477187	−	1.46863i	0.0454980	−	0.140028i
$111$	−9.33393	+	3.48149i	−0.885937	+	0.330448i
$112$	−1.52899	−	1.11088i	−0.144476	−	0.104968i
$113$	9.49452	−	3.08496i	0.893169	−	0.290208i	0.173754	−	0.984789i	$-0.444410\pi$
$113$	9.49452	−	3.08496i	0.893169	−	0.290208i	0.719415	+	0.694581i	$0.244410\pi$
$114$	9.13662	+	11.5048i	0.855723	+	1.07752i
$115$	0.445469	+	0.144742i	0.0415402	+	0.0134972i
$116$	1.49326	−	4.59578i	0.138646	−	0.426708i
$117$	0.944818	+	0.219687i	0.0873484	+	0.0203101i
$118$	−0.744773			−0.0685619
$119$	−7.29874			−0.669074
$120$	1.73046	−	0.0741964i	0.157969	−	0.00677318i
$121$	6.97002	−	5.06401i	0.633638	−	0.460365i
$122$	−0.639501	−	0.464625i	−0.0578977	−	0.0420652i
$123$	−14.9959	−	4.17138i	−1.35214	−	0.376121i
$124$	3.34129	+	4.45374i	0.300057	+	0.399958i
$125$		−	1.00000i		−	0.0894427i
$126$	−5.22256	+	2.20720i	−0.465263	+	0.196633i
$127$	8.54336	+	11.7589i	0.758101	+	1.04344i	0.997370	+	0.0724829i	$0.0230923\pi$
$127$	8.54336	+	11.7589i	0.758101	+	1.04344i	−0.239269	+	0.970953i	$0.576908\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−9.35712	−	2.60285i	−0.823848	−	0.229168i
$130$		−	0.323341i		−	0.0283589i
$131$	1.77960	−	0.578228i	0.155485	−	0.0505201i	−0.230240	−	0.973134i	$-0.573951\pi$
$131$	1.77960	−	0.578228i	0.155485	−	0.0505201i	0.385725	+	0.922614i	$0.373951\pi$
$132$	−2.22920	−	1.47798i	−0.194027	−	0.128642i
$133$	−4.95374	+	15.2461i	−0.429544	+	1.32200i
$134$	3.89120	−	5.35578i	0.336149	−	0.462669i
$135$	2.49011	−	4.56063i	0.214314	−	0.392517i
$136$	2.26996	−	3.12433i	0.194647	−	0.267909i
$137$	−5.71804	+	4.15440i	−0.488525	+	0.354934i	−0.804617	−	0.593795i	$-0.797629\pi$
$137$	−5.71804	+	4.15440i	−0.488525	+	0.354934i	0.316092	+	0.948729i	$0.397629\pi$
$138$	0.448306	−	0.676165i	0.0381623	−	0.0575590i
$139$	−7.39836	−	10.1830i	−0.627521	−	0.863708i	0.370353	−	0.928891i	$-0.379237\pi$
$139$	−7.39836	−	10.1830i	−0.627521	−	0.863708i	−0.997873	+	0.0651833i	$0.979237\pi$
$140$	1.11088	+	1.52899i	0.0938864	+	0.129224i
$141$	11.1368	−	16.7973i	0.937888	−	1.41459i
$142$	8.07221	−	5.86480i	0.677405	−	0.492163i
$143$	−0.293485	+	0.403947i	−0.0245424	+	0.0337797i
$144$	0.679429	−	2.92205i	0.0566191	−	0.243504i
$145$	−2.84035	+	3.90941i	−0.235878	+	0.324659i
$146$	1.40034	−	4.30980i	0.115893	−	0.356682i
$147$	4.94878	+	3.28110i	0.408169	+	0.270621i
$148$	5.47010	−	1.77734i	0.449640	−	0.146097i
$149$			6.59311i			0.540129i	0.962842	+	0.270064i	$0.0870450\pi$
$149$			6.59311i			0.540129i	−0.962842	+	0.270064i	$0.912955\pi$
$150$	−1.66869	−	0.464177i	−0.136248	−	0.0378999i
$151$	3.03109	−	0.984862i	0.246667	−	0.0801469i	−0.183074	−	0.983099i	$-0.558605\pi$
$151$	3.03109	−	0.984862i	0.246667	−	0.0801469i	0.429741	+	0.902952i	$0.358605\pi$
$152$	−4.98565	−	6.86216i	−0.404389	−	0.556594i
$153$	−4.51018	−	10.6717i	−0.364626	−	0.862758i
$154$		−	2.91847i		−	0.235177i
$155$	−1.80147	−	5.26827i	−0.144698	−	0.423158i
$156$	−0.539557	−	0.150087i	−0.0431991	−	0.0120166i
$157$	5.52001	+	4.01052i	0.440545	+	0.320075i	0.785851	−	0.618415i	$-0.212225\pi$
$157$	5.52001	+	4.01052i	0.440545	+	0.320075i	−0.345306	+	0.938490i	$0.612225\pi$
$158$	7.57618	−	5.50442i	0.602729	−	0.437908i
$159$	20.1278	−	0.863013i	1.59624	−	0.0684414i
$160$	−1.00000			−0.0790569
$161$	0.885236			0.0697664
$162$	−6.45445	−	6.27217i	−0.507110	−	0.492788i
$163$	5.60453	−	17.2490i	0.438981	−	1.35104i	−0.449971	−	0.893043i	$-0.648566\pi$
$163$	5.60453	−	17.2490i	0.438981	−	1.35104i	0.888952	−	0.458001i	$-0.151434\pi$
$164$	8.54678	+	2.77702i	0.667392	+	0.216849i
$165$	1.66337	+	2.09451i	0.129493	+	0.163057i
$166$	6.70719	−	2.17930i	0.520579	−	0.169146i
$167$	−9.74357	−	7.07912i	−0.753980	−	0.547799i	0.143078	−	0.989711i	$-0.454300\pi$
$167$	−9.74357	−	7.07912i	−0.753980	−	0.547799i	−0.897058	+	0.441913i	$0.854300\pi$
$168$	3.06707	−	1.14399i	0.236629	−	0.0882611i
$169$	3.98491	−	12.2643i	0.306532	−	0.943408i
$170$	−3.12433	+	2.26996i	−0.239625	+	0.174098i
$171$	−25.3529	+	2.17810i	−1.93878	+	0.166563i
$172$	5.33300	+	1.73280i	0.406637	+	0.132125i
$173$	2.29744	+	3.16215i	0.174671	+	0.240414i	0.887372	−	0.461054i	$-0.152528\pi$
$173$	2.29744	+	3.16215i	0.174671	+	0.240414i	−0.712701	+	0.701468i	$0.752528\pi$
$174$	5.20518	+	6.55433i	0.394604	+	0.496883i
$175$	−0.584024	−	1.79744i	−0.0441481	−	0.135874i
$176$	1.24929	+	0.907664i	0.0941690	+	0.0684178i
$177$	0.712832	−	1.07514i	0.0535797	−	0.0808126i
$178$	−0.810465	−	0.263336i	−0.0607469	−	0.0197379i
$179$	4.77645	+	14.7004i	0.357009	+	1.09876i	0.954836	+	0.297135i	$0.0960311\pi$
$179$	4.77645	+	14.7004i	0.357009	+	1.09876i	−0.597827	+	0.801625i	$0.703969\pi$
$180$	−1.54914	+	2.56908i	−0.115466	+	0.191488i
$181$		−	20.0565i		−	1.49079i	−0.666623	−	0.745395i	$-0.732261\pi$
$181$		−	20.0565i		−	1.49079i	0.666623	−	0.745395i	$-0.267739\pi$
$182$	−0.188839	−	0.581186i	−0.0139977	−	0.0430803i
$183$	1.28280	−	0.478475i	0.0948273	−	0.0353699i
$184$	−0.275315	+	0.378938i	−0.0202965	+	0.0279357i
$185$	−5.75161			−0.422867
$186$	−9.62734	+	0.560696i	−0.705911	+	0.0411123i
$187$	5.96356			0.436099
$188$	−6.83937	+	9.41358i	−0.498812	+	0.686556i
$189$	1.81230	−	9.65175i	0.131825	−	0.702061i
$190$	2.62111	+	8.06695i	0.190155	+	0.585238i
$191$			1.75055i			0.126666i	0.997992	+	0.0633328i	$0.0201730\pi$
$191$			1.75055i			0.126666i	−0.997992	+	0.0633328i	$0.979827\pi$
$192$	−0.464177	+	1.66869i	−0.0334991	+	0.120428i
$193$	2.04695	+	6.29986i	0.147342	+	0.453474i	0.997305	−	0.0733700i	$-0.0233754\pi$
$193$	2.04695	+	6.29986i	0.147342	+	0.453474i	−0.849962	+	0.526843i	$0.823375\pi$
$194$	−18.0434	−	5.86265i	−1.29544	−	0.420914i
$195$	0.466769	+	0.309474i	0.0334260	+	0.0221619i
$196$	−2.77341	−	2.01500i	−0.198101	−	0.143929i
$197$	−3.87131	−	11.9147i	−0.275820	−	0.848886i	−0.989001	−	0.147906i	$-0.952747\pi$
$197$	−3.87131	−	11.9147i	−0.275820	−	0.848886i	0.713182	−	0.700979i	$-0.247253\pi$
$198$	4.26719	−	1.80343i	0.303256	−	0.128165i
$199$	−5.14171	−	7.07696i	−0.364486	−	0.501673i	0.586905	−	0.809656i	$-0.300346\pi$
$199$	−5.14171	−	7.07696i	−0.364486	−	0.501673i	−0.951392	+	0.307983i	$0.900346\pi$
$200$	0.951057	+	0.309017i	0.0672499	+	0.0218508i
$201$	4.00720	+	10.7434i	0.282646	+	0.757779i
$202$	8.39489	−	6.09925i	0.590663	−	0.429141i
$203$	−2.82217	+	8.68576i	−0.198078	+	0.609621i
$204$	2.33763	+	6.26722i	0.163667	+	0.438793i
$205$	−7.27033	−	5.28220i	−0.507782	−	0.368925i
$206$	−11.5634	+	3.75717i	−0.805659	+	0.261774i
$207$	0.547022	+	1.29433i	0.0380207	+	0.0899624i
$208$	0.307515	+	0.0999178i	0.0213223	+	0.00692805i
$209$	4.04755	−	12.4571i	0.279975	−	0.861673i
$210$	−3.27047	+	0.140227i	−0.225684	+	0.00967658i
$211$	8.00422			0.551033			0.275517	−	0.961296i	$-0.411151\pi$
$211$	8.00422			0.551033			0.275517	+	0.961296i	$0.411151\pi$
$212$	−11.6315			−0.798852
$213$	0.740317	+	17.2662i	0.0507257	+	1.18306i
$214$	−4.95270	+	3.59835i	−0.338560	+	0.245978i
$215$	−4.53652	−	3.29598i	−0.309388	−	0.224784i
$216$	3.56793	+	3.77754i	0.242767	+	0.257029i
$217$	−6.31484	−	8.41730i	−0.428679	−	0.571404i
$218$		−	8.45395i		−	0.572573i
$219$	4.88128	+	6.14648i	0.329846	+	0.415340i
$220$	−0.907664	−	1.24929i	−0.0611947	−	0.0842273i
$221$	1.18759	−	0.385871i	0.0798859	−	0.0259565i
$222$	−2.66976	+	9.59767i	−0.179183	+	0.644154i
$223$			4.86737i			0.325943i	0.986631	+	0.162972i	$0.0521079\pi$
$223$			4.86737i			0.325943i	−0.986631	+	0.162972i	$0.947892\pi$
$224$	−1.79744	+	0.584024i	−0.120097	+	0.0390217i
$225$	2.26721	−	1.96463i	0.151147	−	0.130975i
$226$	3.08496	−	9.49452i	0.205208	−	0.631566i
$227$	−16.7907	+	23.1104i	−1.11444	+	1.53389i	−0.299726	+	0.954025i	$0.596895\pi$
$227$	−16.7907	+	23.1104i	−1.11444	+	1.53389i	−0.814711	+	0.579867i	$0.803105\pi$
$228$	14.6779	−	0.629341i	0.972070	−	0.0416791i
$229$	13.4171	−	18.4670i	0.886624	−	1.22033i	−0.0879182	−	0.996128i	$-0.528021\pi$
$229$	13.4171	−	18.4670i	0.886624	−	1.22033i	0.974542	−	0.224205i	$-0.0719786\pi$
$230$	0.378938	−	0.275315i	0.0249864	−	0.0181537i
$231$	4.21305	+	2.79330i	0.277198	+	0.183786i
$232$	−2.84035	−	3.90941i	−0.186478	−	0.256665i
$233$	14.2494	+	19.6126i	0.933510	+	1.28487i	0.958475	+	0.285177i	$0.0920525\pi$
$233$	14.2494	+	19.6126i	0.933510	+	1.28487i	−0.0249653	+	0.999688i	$0.507948\pi$
$234$	0.733080	−	0.635245i	0.0479230	−	0.0415272i
$235$	9.41358	−	6.83937i	0.614074	−	0.446151i
$236$	−0.437766	+	0.602534i	−0.0284962	+	0.0392216i
$237$	0.694826	+	16.2052i	0.0451338	+	1.05264i
$238$	−4.29009	+	5.90480i	−0.278085	+	0.382751i
$239$	3.26277	−	10.0418i	0.211051	−	0.649549i	−0.788359	−	0.615215i	$-0.789069\pi$
$239$	3.26277	−	10.0418i	0.211051	−	0.649549i	0.999410	−	0.0343337i	$-0.0109309\pi$
$240$	0.957113	−	1.44358i	0.0617814	−	0.0931829i
$241$	1.18466	−	0.384920i	0.0763108	−	0.0247949i	−0.270613	−	0.962688i	$-0.587226\pi$
$241$	1.18466	−	0.384920i	0.0763108	−	0.0247949i	0.346924	+	0.937893i	$0.387226\pi$
$242$		−	8.61541i		−	0.553820i
$243$	15.2320	−	3.31437i	0.977136	−	0.212617i
$244$	−0.751779	+	0.244268i	−0.0481277	+	0.0156376i
$245$	2.01500	+	2.77341i	0.128734	+	0.177187i
$246$	−12.1891	+	9.68008i	−0.777149	+	0.617179i
$247$		−	2.74261i		−	0.174508i
$248$	5.56711	−	0.0853163i	0.353512	−	0.00541759i
$249$	−3.27354	+	11.7682i	−0.207452	+	0.745781i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−23.9500	+	17.4007i	−1.51171	+	1.09832i	−0.546304	+	0.837587i	$0.683966\pi$
$251$	−23.9500	+	17.4007i	−1.51171	+	1.09832i	−0.965410	+	0.260737i	$0.916034\pi$
$252$	−1.28408	+	5.52250i	−0.0808894	+	0.347885i
$253$	−0.723298			−0.0454734
$254$	14.5348			0.911997
$255$	−0.286538	−	6.68284i	−0.0179437	−	0.418496i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−12.3904	−	4.02590i	−0.772894	−	0.251129i	−0.104091	−	0.994568i	$-0.533193\pi$
$257$	−12.3904	−	4.02590i	−0.772894	−	0.251129i	−0.668803	+	0.743439i	$0.733193\pi$
$258$	−7.60572	+	6.04015i	−0.473512	+	0.376043i
$259$	−10.3382	+	3.35908i	−0.642383	+	0.208723i
$260$	−0.261588	−	0.190055i	−0.0162230	−	0.0117867i
$261$	−14.4437	+	1.24088i	−0.894041	+	0.0768082i
$262$	0.578228	−	1.77960i	0.0357231	−	0.109944i
$263$	−1.33593	+	0.970607i	−0.0823767	+	0.0598502i	−0.628211	−	0.778043i	$-0.716213\pi$
$263$	−1.33593	+	0.970607i	−0.0823767	+	0.0598502i	0.545835	+	0.837893i	$0.316213\pi$
$264$	−2.50600	+	0.934721i	−0.154234	+	0.0575281i
$265$	11.0622	+	3.59432i	0.679544	+	0.220797i
$266$	9.42258	+	12.9691i	0.577736	+	0.795185i
$267$	1.15585	−	0.917932i	0.0707372	−	0.0561765i
$268$	−2.04573	−	6.29610i	−0.124963	−	0.384595i
$269$	−10.9119	−	7.92798i	−0.665312	−	0.483377i	0.203141	−	0.979150i	$-0.434885\pi$
$269$	−10.9119	−	7.92798i	−0.665312	−	0.483377i	−0.868453	+	0.495772i	$0.834885\pi$
$270$	−2.22598	−	4.69521i	−0.135469	−	0.285741i
$271$	−14.6311	−	4.75394i	−0.888778	−	0.288781i	−0.171180	−	0.985240i	$-0.554758\pi$
$271$	−14.6311	−	4.75394i	−0.888778	−	0.288781i	−0.717597	+	0.696458i	$0.754758\pi$
$272$	−1.19339	−	3.67287i	−0.0723598	−	0.222701i
$273$	1.01973	+	0.283656i	0.0617169	+	0.0171676i
$274$			7.06788i			0.426986i
$275$	0.477187	+	1.46863i	0.0287755	+	0.0885618i
$276$	−0.283522	−	0.760127i	−0.0170660	−	0.0457543i
$277$	−9.33003	+	12.8417i	−0.560587	+	0.771582i	−0.991401	−	0.130859i	$-0.958227\pi$
$277$	−9.33003	+	12.8417i	−0.560587	+	0.771582i	0.430814	+	0.902441i	$0.358227\pi$
$278$	−12.5868			−0.754908
$279$	8.40504	−	14.4345i	0.503197	−	0.864172i
$280$	1.88994			0.112946
$281$	17.4881	−	24.0702i	1.04325	−	1.43591i	0.148733	−	0.988877i	$-0.452481\pi$
$281$	17.4881	−	24.0702i	1.04325	−	1.43591i	0.894517	−	0.447033i	$-0.147519\pi$
$282$	−7.04325	−	18.8831i	−0.419419	−	1.12447i
$283$	1.54557	+	4.75677i	0.0918744	+	0.282760i	0.986427	−	0.164203i	$-0.0525053\pi$
$283$	1.54557	+	4.75677i	0.0918744	+	0.282760i	−0.894552	+	0.446964i	$0.852505\pi$
$284$		−	9.97780i		−	0.592074i
$285$	−14.1540	−	3.93719i	−0.838412	−	0.233219i
$286$	0.154294	+	0.474868i	0.00912360	+	0.0280795i
$287$	−16.1529	−	5.24840i	−0.953477	−	0.309803i
$288$	−1.96463	−	2.26721i	−0.115767	−	0.133596i
$289$	1.68748	+	1.22603i	0.0992635	+	0.0721191i
$290$	1.49326	+	4.59578i	0.0876873	+	0.269874i
$291$	25.7328	−	20.4359i	1.50848	−	1.19797i
$292$	−2.66360	−	3.66614i	−0.155876	−	0.214544i
$293$	−6.62282	−	2.15189i	−0.386909	−	0.125715i	0.109102	−	0.994031i	$-0.465203\pi$
$293$	−6.62282	−	2.15189i	−0.386909	−	0.125715i	−0.496011	+	0.868316i	$0.665203\pi$
$294$	5.56329	−	2.07507i	0.324458	−	0.121020i
$295$	0.602534	−	0.437766i	0.0350809	−	0.0254878i
$296$	1.77734	−	5.47010i	0.103306	−	0.317943i
$297$	−1.48077	+	7.88613i	−0.0859231	+	0.457600i
$298$	5.33394	+	3.87533i	0.308987	+	0.224492i
$299$	−0.144038	+	0.0468008i	−0.00832994	+	0.00270656i
$300$	−1.35636	+	1.07717i	−0.0783095	+	0.0621902i
$301$	−10.0791	−	3.27488i	−0.580947	−	0.188761i
$302$	0.984862	−	3.03109i	0.0566724	−	0.174420i
$303$	0.769911	+	17.9564i	0.0442302	+	1.03157i
$304$	−8.48209			−0.486481
$305$	0.790467			0.0452620
$306$	−11.2846	−	2.62388i	−0.645099	−	0.149997i
$307$	−4.31014	+	3.13150i	−0.245993	+	0.178724i	−0.703949	−	0.710250i	$-0.748582\pi$
$307$	−4.31014	+	3.13150i	−0.245993	+	0.178724i	0.457956	+	0.888975i	$0.348582\pi$
$308$	−2.36109	−	1.71543i	−0.134536	−	0.0977458i
$309$	5.64367	−	20.2887i	0.321057	−	1.15419i
$310$	−5.32100	−	1.63919i	−0.302213	−	0.0930998i
$311$			21.5392i			1.22138i	0.791871	+	0.610688i	$0.209107\pi$
$311$			21.5392i			1.22138i	−0.791871	+	0.610688i	$0.790893\pi$
$312$	−0.438567	+	0.348291i	−0.0248289	+	0.0197181i
$313$	−4.80693	−	6.61618i	−0.271704	−	0.373968i	0.651260	−	0.758855i	$-0.274241\pi$
$313$	−4.80693	−	6.61618i	−0.271704	−	0.373968i	−0.922964	+	0.384886i	$0.874241\pi$
$314$	6.48916	−	2.10846i	0.366205	−	0.118987i
$315$	2.92778	−	4.85541i	0.164962	−	0.273571i
$316$		−	9.36468i		−	0.526804i
$317$	−1.47513	+	0.479298i	−0.0828514	+	0.0269201i	−0.350149	−	0.936694i	$-0.613869\pi$
$317$	−1.47513	+	0.479298i	−0.0828514	+	0.0269201i	0.267298	+	0.963614i	$0.413869\pi$
$318$	11.1326	−	16.7910i	0.624287	−	0.941592i
$319$	2.30591	−	7.09686i	0.129106	−	0.397348i
$320$	−0.587785	+	0.809017i	−0.0328582	+	0.0452254i
$321$	−0.454222	−	10.5937i	−0.0253522	−	0.591281i
$322$	0.520329	−	0.716171i	0.0289968	−	0.0399106i
$323$	−26.5009	+	19.2540i	−1.47455	+	1.07132i
$324$	−8.86812	+	1.53507i	−0.492673	+	0.0852819i
$325$	0.190055	+	0.261588i	0.0105423	+	0.0145103i
$326$	−10.6605	−	14.6729i	−0.590428	−	0.812655i
$327$	12.2040	+	8.09138i	0.674882	+	0.447455i
$328$	7.27033	−	5.28220i	0.401437	−	0.291661i
$329$	12.9260	−	17.7911i	0.712634	−	0.980856i
$330$	2.67220	−	0.114575i	0.147100	−	0.00630714i
$331$	−15.0955	+	20.7771i	−0.829722	+	1.14201i	0.158253	+	0.987399i	$0.449414\pi$
$331$	−15.0955	+	20.7771i	−0.829722	+	1.14201i	−0.987975	+	0.154616i	$0.950586\pi$
$332$	2.17930	−	6.70719i	0.119604	−	0.368105i
$333$	−11.2998	−	13.0401i	−0.619224	−	0.714592i
$334$	−11.4543	+	3.72171i	−0.626749	+	0.203643i
$335$			6.62011i			0.361695i
$336$	0.877267	−	3.15373i	0.0478588	−	0.172050i
$337$	−27.9759	+	9.08993i	−1.52395	+	0.495160i	−0.946894	−	0.321547i	$-0.895797\pi$
$337$	−27.9759	+	9.08993i	−1.52395	+	0.495160i	−0.577052	+	0.816707i	$0.695797\pi$
$338$	−7.57976	−	10.4326i	−0.412284	−	0.567461i
$339$	10.7535	+	13.5407i	0.584049	+	0.735431i
$340$			3.86189i			0.209440i
$341$	5.15965	+	6.87751i	0.279411	+	0.372438i
$342$	−13.1399	+	21.7912i	−0.710526	+	1.17833i
$343$	15.9445	+	11.5844i	0.860924	+	0.625498i
$344$	4.53652	−	3.29598i	0.244593	−	0.177707i
$345$	0.0347531	+	0.810537i	0.00187105	+	0.0436378i
$346$	3.90864			0.210130
$347$	5.24834			0.281746			0.140873	−	0.990028i	$-0.455009\pi$
$347$	5.24834			0.281746			0.140873	+	0.990028i	$0.455009\pi$
$348$	8.36209	−	0.358539i	0.448255	−	0.0192197i
$349$	2.16473	−	6.66235i	0.115875	−	0.356627i	−0.876253	−	0.481851i	$-0.839965\pi$
$349$	2.16473	−	6.66235i	0.115875	−	0.356627i	0.992129	+	0.125223i	$0.0399648\pi$
$350$	−1.79744	−	0.584024i	−0.0960772	−	0.0312174i
$351$	0.215388	+	1.66626i	0.0114966	+	0.0889386i
$352$	1.46863	−	0.477187i	0.0782783	−	0.0254342i
$353$	−10.1329	−	7.36199i	−0.539321	−	0.391839i	0.284512	−	0.958672i	$-0.408168\pi$
$353$	−10.1329	−	7.36199i	−0.539321	−	0.391839i	−0.823833	+	0.566833i	$0.808168\pi$
$354$	−0.450816	−	1.20865i	−0.0239606	−	0.0642388i
$355$	−3.08331	+	9.48945i	−0.163645	+	0.503648i
$356$	−0.689423	+	0.500895i	−0.0365393	+	0.0265474i
$357$	−4.41797	−	11.8447i	−0.233824	−	0.626886i
$358$	14.7004	+	4.77645i	0.776941	+	0.252443i
$359$	17.2240	+	23.7068i	0.909048	+	1.25120i	0.967491	+	0.252907i	$0.0813865\pi$
$359$	17.2240	+	23.7068i	0.909048	+	1.25120i	−0.0584427	+	0.998291i	$0.518613\pi$
$360$	1.16787	+	2.76335i	0.0615521	+	0.145641i
$361$	16.3612	+	50.3545i	0.861115	+	2.65024i
$362$	−16.2261	−	11.7889i	−0.852823	−	0.619612i
$363$	12.4371	+	8.24593i	0.652777	+	0.432799i
$364$	−0.581186	−	0.188839i	−0.0304624	−	0.00989784i
$365$	1.40034	+	4.30980i	0.0732971	+	0.225585i
$366$	0.366917	−	1.31905i	0.0191790	−	0.0689477i
$367$		−	11.6753i		−	0.609445i	−0.952441	−	0.304722i	$-0.901436\pi$
$367$		−	11.6753i		−	0.609445i	0.952441	−	0.304722i	$-0.0985637\pi$
$368$	0.144742	+	0.445469i	0.00754517	+	0.0232217i
$369$	−2.30766	−	26.8609i	−0.120132	−	1.39832i
$370$	−3.38071	+	4.65315i	−0.175755	+	0.241906i
$371$	21.9828			1.14129
$372$	−5.20519	+	8.11825i	−0.269877	+	0.420912i
$373$	0.348666			0.0180532			0.00902661	−	0.999959i	$-0.497127\pi$
$373$	0.348666			0.0180532			0.00902661	+	0.999959i	$0.497127\pi$
$374$	3.50529	−	4.82462i	0.181254	−	0.249475i
$375$	1.62284	−	0.605307i	0.0838030	−	0.0312579i
$376$	3.59567	+	11.0663i	0.185432	+	0.570702i
$377$		−	1.56248i		−	0.0804716i
$378$	−6.74318	−	7.13934i	−0.346832	−	0.367208i
$379$	−1.37904	−	4.24425i	−0.0708366	−	0.218013i	0.909371	−	0.415987i	$-0.136564\pi$
$379$	−1.37904	−	4.24425i	−0.0708366	−	0.218013i	−0.980207	+	0.197974i	$0.936564\pi$
$380$	8.06695	+	2.62111i	0.413826	+	0.134460i
$381$	−13.9115	+	20.9823i	−0.712707	+	1.07495i
$382$	1.41623	+	1.02895i	0.0724605	+	0.0526456i
$383$	4.11982	+	12.6795i	0.210513	+	0.647892i	0.999442	+	0.0334076i	$0.0106359\pi$
$383$	4.11982	+	12.6795i	0.210513	+	0.647892i	−0.788929	+	0.614484i	$0.789364\pi$
$384$	1.07717	+	1.35636i	0.0549689	+	0.0692165i
$385$	1.71543	+	2.36109i	0.0874265	+	0.120332i
$386$	6.29986	+	2.04695i	0.320654	+	0.104187i
$387$	−1.43993	−	16.7606i	−0.0731955	−	0.851990i
$388$	−15.3486	+	11.1514i	−0.779208	+	0.566128i
$389$	11.6643	−	35.8989i	0.591402	−	1.82015i	0.0195251	−	0.999809i	$-0.493785\pi$
$389$	11.6643	−	35.8989i	0.591402	−	1.82015i	0.571877	−	0.820339i	$-0.306215\pi$
$390$	0.524730	−	0.195720i	0.0265707	−	0.00991068i
$391$	1.46342	+	1.06323i	0.0740081	+	0.0537701i
$392$	−3.26034	+	1.05935i	−0.164672	+	0.0535052i
$393$	2.01558	+	2.53800i	0.101672	+	0.128025i
$394$	−11.9147	−	3.87131i	−0.600253	−	0.195034i
$395$	−2.89384	+	8.90634i	−0.145605	+	0.448127i
$396$	1.04918	−	4.51226i	0.0527233	−	0.226750i
$397$	−5.34692			−0.268354			−0.134177	−	0.990957i	$-0.542839\pi$
$397$	−5.34692			−0.268354			−0.134177	+	0.990957i	$0.542839\pi$
$398$	−8.74761			−0.438478
$399$	−27.7404	+	1.18942i	−1.38876	+	0.0595453i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	22.6135	+	16.4297i	1.12926	+	0.820458i	0.985587	−	0.169167i	$-0.0541076\pi$
$401$	22.6135	+	16.4297i	1.12926	+	0.820458i	0.143676	+	0.989625i	$0.454108\pi$
$402$	11.0469	+	3.07290i	0.550971	+	0.153262i
$403$	1.47250	+	1.03574i	0.0733507	+	0.0515938i
$404$		−	10.3767i		−	0.516258i
$405$	8.90845	+	1.28046i	0.442664	+	0.0636265i
$406$	5.36809	+	7.38855i	0.266414	+	0.366687i
$407$	8.44699	−	2.74459i	0.418702	−	0.136044i
$408$	6.44431	+	1.79260i	0.319041	+	0.0887468i
$409$		−	13.6060i		−	0.672775i	−0.941724	−	0.336388i	$-0.890795\pi$
$409$		−	13.6060i		−	0.672775i	0.941724	−	0.336388i	$-0.109205\pi$
$410$	−8.54678	+	2.77702i	−0.422096	+	0.137147i
$411$	−10.2031	−	6.76476i	−0.503281	−	0.333681i
$412$	−3.75717	+	11.5634i	−0.185102	+	0.569687i
$413$	0.827353	−	1.13875i	0.0407114	−	0.0560344i
$414$	1.36867	+	0.318240i	0.0672664	+	0.0156406i
$415$	−4.14527	+	5.70547i	−0.203483	+	0.280071i
$416$	0.261588	−	0.190055i	0.0128254	−	0.00931821i
$417$	12.0470	−	18.1702i	0.589946	−	0.889796i
$418$	−7.69889	−	10.5966i	−0.376565	−	0.518297i
$419$	9.03557	+	12.4364i	0.441417	+	0.607558i	0.970526	−	0.240996i	$-0.0774740\pi$
$419$	9.03557	+	12.4364i	0.441417	+	0.607558i	−0.529110	+	0.848554i	$0.677474\pi$
$420$	−1.80889	+	2.72829i	−0.0882647	+	0.133127i
$421$	23.6986	−	17.2181i	1.15500	−	0.839156i	0.165862	−	0.986149i	$-0.446959\pi$
$421$	23.6986	−	17.2181i	1.15500	−	0.839156i	0.989138	+	0.146993i	$0.0469593\pi$
$422$	4.70476	−	6.47555i	0.229024	−	0.315225i
$423$	34.0005	+	7.90572i	1.65316	+	0.384389i
$424$	−6.83680	+	9.41005i	−0.332024	+	0.456992i
$425$	1.19339	−	3.67287i	0.0578878	−	0.178160i
$426$	14.4038	+	9.54988i	0.697866	+	0.462693i
$427$	1.42082	−	0.461652i	0.0687582	−	0.0223409i
$428$			6.12188i			0.295912i
$429$	−0.833189	−	0.231766i	−0.0402267	−	0.0111898i
$430$	−5.33300	+	1.73280i	−0.257180	+	0.0835629i
$431$	20.2390	+	27.8566i	0.974878	+	1.34180i	0.939544	+	0.342429i	$0.111250\pi$
$431$	20.2390	+	27.8566i	0.974878	+	1.34180i	0.0353343	+	0.999376i	$0.488750\pi$
$432$	5.15328	−	0.666134i	0.247937	−	0.0320494i
$433$			33.0810i			1.58977i	0.606760	+	0.794885i	$0.292469\pi$
$433$			33.0810i			1.58977i	−0.606760	+	0.794885i	$0.707531\pi$
$434$	−10.5215	+	0.161243i	−0.505049	+	0.00773990i
$435$	−8.06362	−	2.24304i	−0.386621	−	0.107545i
$436$	−6.83939	−	4.96910i	−0.327547	−	0.237977i
$437$	3.21419	−	2.33525i	0.153756	−	0.111710i
$438$	7.84175	−	0.336228i	0.374693	−	0.0160656i
$439$	21.6381			1.03273			0.516366	−	0.856368i	$-0.327284\pi$
$439$	21.6381			1.03273			0.516366	+	0.856368i	$0.327284\pi$
$440$	−1.54421			−0.0736173
$441$	−2.32917	+	10.0171i	−0.110913	+	0.477007i
$442$	0.385871	−	1.18759i	0.0183540	−	0.0564878i
$443$	−20.6943	−	6.72398i	−0.983215	−	0.319466i	−0.227076	−	0.973877i	$-0.572917\pi$
$443$	−20.6943	−	6.72398i	−0.983215	−	0.319466i	−0.756139	+	0.654411i	$0.772917\pi$
$444$	6.19543	+	7.80126i	0.294022	+	0.370231i
$445$	0.810465	−	0.263336i	0.0384197	−	0.0124833i
$446$	3.93778	+	2.86097i	0.186459	+	0.135471i
$447$	−10.6996	+	3.99085i	−0.506071	+	0.188761i
$448$	−0.584024	+	1.79744i	−0.0275925	+	0.0849211i
$449$	−12.7587	+	9.26977i	−0.602122	+	0.437467i	−0.846632	−	0.532180i	$-0.821373\pi$
$449$	−12.7587	+	9.26977i	−0.602122	+	0.437467i	0.244509	+	0.969647i	$0.421373\pi$
$450$	−0.256788	−	2.98899i	−0.0121051	−	0.140902i
$451$	13.1980	+	4.28830i	0.621471	+	0.201928i
$452$	−5.86794	−	8.07652i	−0.276004	−	0.379888i
$453$	3.43301	+	4.32283i	0.161297	+	0.203104i
$454$	8.82739	+	27.1679i	0.414290	+	1.27505i
$455$	0.494386	+	0.359192i	0.0231772	+	0.0168392i
$456$	8.11832	−	12.2446i	0.380175	−	0.573406i
$457$	−22.5526	−	7.32777i	−1.05496	−	0.342779i	−0.270349	−	0.962762i	$-0.587139\pi$
$457$	−22.5526	−	7.32777i	−1.05496	−	0.342779i	−0.784615	+	0.619984i	$0.787139\pi$
$458$	−7.05376	−	21.7092i	−0.329601	−	1.01441i
$459$	14.5884	−	13.7790i	0.680930	−	0.643146i
$460$		−	0.468393i		−	0.0218390i
$461$	−6.13552	−	18.8832i	−0.285760	−	0.879478i	−0.986170	−	0.165737i	$-0.947000\pi$
$461$	−6.13552	−	18.8832i	−0.285760	−	0.879478i	0.700410	−	0.713740i	$-0.253000\pi$
$462$	4.73620	−	1.76657i	0.220348	−	0.0821882i
$463$	−8.76453	+	12.0633i	−0.407322	+	0.560631i	−0.962563	−	0.271059i	$-0.912626\pi$
$463$	−8.76453	+	12.0633i	−0.407322	+	0.560631i	0.555241	+	0.831690i	$0.312626\pi$
$464$	−4.83229			−0.224334
$465$	7.45911	−	6.11242i	0.345908	−	0.283457i
$466$	24.2425			1.12301
$467$	−1.84095	+	2.53385i	−0.0851888	+	0.117252i	−0.849484	−	0.527614i	$-0.823087\pi$
$467$	−1.84095	+	2.53385i	−0.0851888	+	0.117252i	0.764296	+	0.644866i	$0.223087\pi$
$468$	−0.0830300	−	0.966462i	−0.00383806	−	0.0446747i
$469$	3.86630	+	11.8993i	0.178529	+	0.549456i
$470$		−	11.6358i		−	0.536721i
$471$	−3.16713	+	11.3857i	−0.145934	+	0.524625i
$472$	0.230147	+	0.708321i	0.0105934	+	0.0326031i
$473$	8.23527	+	2.67580i	0.378658	+	0.123034i
$474$	13.5187	+	8.96306i	0.620934	+	0.411687i
$475$	−6.86216	−	4.98565i	−0.314857	−	0.228757i
$476$	2.25543	+	6.94151i	0.103378	+	0.318164i
$477$	13.5840	+	32.1418i	0.621970	+	1.47167i
$478$	−6.20616	−	8.54205i	−0.283863	−	0.390704i
$479$	5.98967	+	1.94616i	0.273675	+	0.0889225i	0.442639	−	0.896700i	$-0.354042\pi$
$479$	5.98967	+	1.94616i	0.273675	+	0.0889225i	−0.168964	+	0.985622i	$0.554042\pi$
$480$	−0.605307	−	1.62284i	−0.0276284	−	0.0740721i
$481$	1.50455	−	1.09312i	0.0686017	−	0.0498420i
$482$	0.384920	−	1.18466i	0.0175326	−	0.0539599i
$483$	0.535839	+	1.43659i	0.0243815	+	0.0653673i
$484$	−6.97002	−	5.06401i	−0.316819	−	0.230182i
$485$	18.0434	−	5.86265i	0.819308	−	0.266209i
$486$	6.27179	−	14.2711i	0.284494	−	0.647351i
$487$	37.5857	+	12.2123i	1.70317	+	0.553394i	0.989173	−	0.146754i	$-0.0468825\pi$
$487$	37.5857	+	12.2123i	1.70317	+	0.553394i	0.713998	+	0.700148i	$0.246883\pi$
$488$	−0.244268	+	0.751779i	−0.0110575	+	0.0340314i
$489$	31.3848	−	1.34568i	1.41927	−	0.0608535i
$490$	3.42812			0.154867
$491$	−17.5862			−0.793653			−0.396826	−	0.917894i	$-0.629888\pi$
$491$	−17.5862			−0.793653			−0.396826	+	0.917894i	$0.629888\pi$
$492$	0.666775	+	15.5510i	0.0300606	+	0.701093i
$493$	−15.0977	+	10.9691i	−0.679965	+	0.494024i
$494$	−2.21881	−	1.61206i	−0.0998292	−	0.0725301i
$495$	−2.39220	+	3.96720i	−0.107521	+	0.178312i
$496$	3.20324	−	4.55403i	0.143830	−	0.204482i
$497$			18.8575i			0.845872i
$498$	7.59655	+	9.56554i	0.340410	+	0.428642i
$499$	−6.78943	−	9.34484i	−0.303936	−	0.418333i	0.629542	−	0.776967i	$-0.283243\pi$
$499$	−6.78943	−	9.34484i	−0.303936	−	0.418333i	−0.933478	+	0.358634i	$0.883243\pi$
$500$	−0.951057	+	0.309017i	−0.0425325	+	0.0138197i
$501$	5.59042	−	20.0973i	0.249761	−	0.897880i
$502$			29.6039i			1.32129i
$503$	39.1614	−	12.7243i	1.74612	−	0.567348i	0.750502	−	0.660869i	$-0.229812\pi$
$503$	39.1614	−	12.7243i	1.74612	−	0.567348i	0.995617	+	0.0935201i	$0.0298120\pi$
$504$	3.71303	+	4.28489i	0.165392	+	0.190864i
$505$	−3.20656	+	9.86879i	−0.142690	+	0.439155i
$506$	−0.425144	+	0.585160i	−0.0189000	+	0.0260136i
$507$	22.3151	−	0.956797i	0.991047	−	0.0424928i
$508$	8.54336	−	11.7589i	0.379050	−	0.521718i
$509$	11.8004	−	8.57353i	0.523046	−	0.380015i	−0.294704	−	0.955588i	$-0.595221\pi$
$509$	11.8004	−	8.57353i	0.523046	−	0.380015i	0.817750	+	0.575574i	$0.195221\pi$
$510$	−5.57496	−	3.69626i	−0.246863	−	0.163673i
$511$	5.03406	+	6.92878i	0.222694	+	0.306511i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−18.8810	−	39.8252i	−0.833616	−	1.75833i
$514$	−10.5399	+	7.65771i	−0.464897	+	0.337767i
$515$	7.14656	−	9.83640i	0.314915	−	0.433443i
$516$	0.416053	+	9.70347i	0.0183157	+	0.427171i
$517$	−10.5614	+	14.5366i	−0.464491	+	0.639317i
$518$	−3.35908	+	10.3382i	−0.147589	+	0.454233i
$519$	−3.74101	+	5.64244i	−0.164212	+	0.247676i
$520$	−0.307515	+	0.0999178i	−0.0134854	+	0.00438168i
$521$		−	9.56309i		−	0.418967i	−0.977812	−	0.209483i	$-0.932822\pi$
$521$		−	9.56309i		−	0.418967i	0.977812	−	0.209483i	$-0.0671782\pi$
$522$	−7.48589	+	12.4145i	−0.327648	+	0.543370i
$523$	−7.42963	+	2.41403i	−0.324875	+	0.105558i	−0.466914	−	0.884303i	$-0.654634\pi$
$523$	−7.42963	+	2.41403i	−0.324875	+	0.105558i	0.142039	+	0.989861i	$0.454634\pi$
$524$	−1.09986	−	1.51382i	−0.0480474	−	0.0661316i
$525$	2.56344	−	2.03578i	0.111878	−	0.0888487i
$526$			1.65130i			0.0719999i
$527$	−0.329482	−	21.4995i	−0.0143525	−	0.936535i
$528$	−0.716787	+	2.57681i	−0.0311941	+	0.112141i
$529$	18.4299	+	13.3901i	0.801300	+	0.582178i
$530$	9.41005	−	6.83680i	0.408747	−	0.296972i
$531$	2.17626	+	0.506020i	0.0944418	+	0.0219594i
$532$	16.0307			0.695017
$533$	2.90574			0.125862
$534$	−0.0632283	−	1.47465i	−0.00273615	−	0.0638145i
$535$	1.89176	−	5.82225i	0.0817881	−	0.251718i
$536$	−6.29610	−	2.04573i	−0.271950	−	0.0883619i
$537$	−20.9652	+	16.6497i	−0.904714	+	0.718486i
$538$	−12.8277	+	4.16799i	−0.553043	+	0.179695i
$539$	−4.28273	−	3.11158i	−0.184470	−	0.134025i
$540$	−5.10690	−	0.958919i	−0.219766	−	0.0412653i
$541$	−7.83446	+	24.1120i	−0.336830	+	1.03666i	0.628984	+	0.777418i	$0.283471\pi$
$541$	−7.83446	+	24.1120i	−0.336830	+	1.03666i	−0.965814	+	0.259237i	$0.916529\pi$
$542$	−12.4460	+	9.04253i	−0.534601	+	0.388410i
$543$	32.5485	−	12.1403i	1.39679	−	0.520992i
$544$	−3.67287	−	1.19339i	−0.157473	−	0.0511661i
$545$	4.96910	+	6.83939i	0.212853	+	0.292967i
$546$	0.828865	−	0.658250i	0.0354721	−	0.0281705i
$547$	−1.74893	−	5.38265i	−0.0747788	−	0.230145i	0.906680	−	0.421819i	$-0.138608\pi$
$547$	−1.74893	−	5.38265i	−0.0747788	−	0.230145i	−0.981459	+	0.191674i	$0.938608\pi$
$548$	5.71804	+	4.15440i	0.244262	+	0.177467i
$549$	1.55298	+	1.79215i	0.0662794	+	0.0764872i
$550$	1.46863	+	0.477187i	0.0626226	+	0.0203473i
$551$	12.6660	+	38.9819i	0.539589	+	1.66068i
$552$	−0.781605	−	0.217417i	−0.0332673	−	0.00925390i
$553$			17.6987i			0.752625i
$554$	4.90509	+	15.0963i	0.208397	+	0.641381i
$555$	−3.48149	−	9.33393i	−0.147781	−	0.396203i
$556$	−7.39836	+	10.1830i	−0.313760	+	0.431854i
$557$	21.6520			0.917425			0.458712	−	0.888585i	$-0.348311\pi$
$557$	21.6520			0.917425			0.458712	+	0.888585i	$0.348311\pi$
$558$	−6.73741	−	15.2842i	−0.285217	−	0.647032i
$559$	1.81312			0.0766866
$560$	1.11088	−	1.52899i	0.0469432	−	0.0646118i
$561$	3.60979	+	9.67790i	0.152405	+	0.408601i
$562$	−9.19402	−	28.2963i	−0.387826	−	1.19361i
$563$		−	40.9406i		−	1.72544i	−0.505680	−	0.862721i	$-0.668758\pi$
$563$		−	40.9406i		−	1.72544i	0.505680	−	0.862721i	$-0.331242\pi$
$564$	−19.4166	−	5.40108i	−0.817588	−	0.227427i
$565$	3.08496	+	9.49452i	0.129785	+	0.399437i
$566$	4.75677	+	1.54557i	0.199942	+	0.0649650i
$567$	16.7602	−	2.90120i	0.703863	−	0.121839i
$568$	−8.07221	−	5.86480i	−0.338702	−	0.246082i
$569$	4.49020	+	13.8194i	0.188239	+	0.579340i	0.999989	−	0.00466481i	$-0.00148486\pi$
$569$	4.49020	+	13.8194i	0.188239	+	0.579340i	−0.811750	+	0.584005i	$0.801485\pi$
$570$	−11.5048	+	9.13662i	−0.481882	+	0.382691i
$571$	−20.5665	−	28.3073i	−0.860681	−	1.18463i	−0.981407	−	0.191939i	$-0.938522\pi$
$571$	−20.5665	−	28.3073i	−0.860681	−	1.18463i	0.120726	−	0.992686i	$-0.461478\pi$
$572$	0.474868	+	0.154294i	0.0198552	+	0.00645136i
$573$	−2.84086	+	1.05962i	−0.118679	+	0.0442663i
$574$	−13.7405	+	9.98305i	−0.573517	+	0.416685i
$575$	−0.144742	+	0.445469i	−0.00603614	+	0.0185773i
$576$	−2.98899	+	0.256788i	−0.124541	+	0.0106995i
$577$	−11.5838	−	8.41612i	−0.482240	−	0.350368i	0.319952	−	0.947434i	$-0.396333\pi$
$577$	−11.5838	−	8.41612i	−0.482240	−	0.350368i	−0.802192	+	0.597066i	$0.796333\pi$
$578$	1.98375	−	0.644559i	0.0825131	−	0.0268101i
$579$	−8.98461	+	7.13521i	−0.373388	+	0.296529i
$580$	4.59578	+	1.49326i	0.190829	+	0.0620043i
$581$	−4.11874	+	12.6762i	−0.170874	+	0.525897i
$582$	−1.40765	−	32.8302i	−0.0583490	−	1.36085i
$583$	−17.9614			−0.743886
$584$	−4.53160			−0.187519
$585$	−0.219687	+	0.944818i	−0.00908294	+	0.0390634i
$586$	−5.63371	+	4.09313i	−0.232726	+	0.169086i
$587$	−0.612674	−	0.445134i	−0.0252878	−	0.0183726i	0.575070	−	0.818105i	$-0.304975\pi$
$587$	−0.612674	−	0.445134i	−0.0252878	−	0.0183726i	−0.600357	+	0.799732i	$0.704975\pi$
$588$	1.59126	−	5.72049i	0.0656223	−	0.235909i
$589$	−45.1332	−	13.9038i	−1.85968	−	0.572895i
$590$		−	0.744773i		−	0.0306618i
$591$	16.9923	−	13.4946i	0.698968	−	0.555092i
$592$	−3.38071	−	4.65315i	−0.138946	−	0.191243i
$593$	23.8286	−	7.74237i	0.978521	−	0.317941i	0.224270	−	0.974527i	$-0.428000\pi$
$593$	23.8286	−	7.74237i	0.978521	−	0.317941i	0.754251	+	0.656586i	$0.228000\pi$
$594$	5.50964	+	5.83332i	0.226063	+	0.239344i
$595$		−	7.29874i		−	0.299219i
$596$	6.27042	−	2.03738i	0.256846	−	0.0834545i
$597$	8.37245	−	12.6279i	0.342662	−	0.516826i
$598$	−0.0468008	+	0.144038i	−0.00191383	+	0.00589016i
$599$	0.300012	−	0.412931i	0.0122582	−	0.0168719i	−0.802844	−	0.596189i	$-0.796681\pi$
$599$	0.300012	−	0.412931i	0.0122582	−	0.0168719i	0.815102	+	0.579317i	$0.196681\pi$
$600$	0.0741964	+	1.73046i	0.00302906	+	0.0706458i
$601$	2.18019	−	3.00078i	0.0889320	−	0.122404i	−0.762233	−	0.647303i	$-0.775897\pi$
$601$	2.18019	−	3.00078i	0.0889320	−	0.122404i	0.851165	+	0.524899i	$0.175897\pi$
$602$	−8.57376	+	6.22920i	−0.349440	+	0.253883i
$603$	−15.0092	+	13.0061i	−0.611220	+	0.529648i
$604$	−1.87332	−	2.57840i	−0.0762242	−	0.104914i
$605$	5.06401	+	6.97002i	0.205881	+	0.283371i
$606$	14.9796	+	9.93164i	0.608504	+	0.403445i
$607$	−2.29244	+	1.66555i	−0.0930472	+	0.0676028i	−0.633336	−	0.773877i	$-0.718315\pi$
$607$	−2.29244	+	1.66555i	−0.0930472	+	0.0676028i	0.540289	+	0.841480i	$0.318315\pi$
$608$	−4.98565	+	6.86216i	−0.202195	+	0.278297i
$609$	−15.8039	+	0.677617i	−0.640405	+	0.0274584i
$610$	0.464625	−	0.639501i	0.0188121	−	0.0258927i
$611$	−1.16263	+	3.57819i	−0.0470348	+	0.144758i
$612$	−8.75570	+	7.58718i	−0.353928	+	0.306693i
$613$	7.91276	−	2.57101i	0.319594	−	0.103842i	−0.144827	−	0.989457i	$-0.546263\pi$
$613$	7.91276	−	2.57101i	0.319594	−	0.103842i	0.464421	+	0.885615i	$0.346263\pi$
$614$			5.32763i			0.215006i
$615$	4.17138	−	14.9959i	0.168206	−	0.604694i
$616$	−2.77563	+	0.901856i	−0.111833	+	0.0363368i
$617$	−10.0329	−	13.8091i	−0.403908	−	0.555932i	0.557811	−	0.829968i	$-0.311641\pi$
$617$	−10.0329	−	13.8091i	−0.403908	−	0.555932i	−0.961720	+	0.274036i	$0.911641\pi$
$618$	−13.0967	−	16.4913i	−0.526825	−	0.663375i
$619$			22.0591i			0.886630i	0.896366	+	0.443315i	$0.146198\pi$
$619$			22.0591i			0.886630i	−0.896366	+	0.443315i	$0.853802\pi$
$620$	−4.45374	+	3.34129i	−0.178866	+	0.134189i
$621$	−1.76938	+	1.67120i	−0.0710027	+	0.0670628i
$622$	17.4256	+	12.6604i	0.698703	+	0.507637i
$623$	1.30297	−	0.946662i	0.0522023	−	0.0379272i
$624$	0.0239907	+	0.559528i	0.000960398	+	0.0223991i
$625$	1.00000			0.0400000
$626$	−8.17804			−0.326860
$627$	22.6658	−	0.971835i	0.905185	−	0.0388113i
$628$	2.10846	−	6.48916i	0.0841366	−	0.258946i
$629$	−21.1249	−	6.86390i	−0.842306	−	0.273682i
$630$	−2.20720	−	5.22256i	−0.0879371	−	0.208072i
$631$	−35.1921	+	11.4346i	−1.40097	+	0.455204i	−0.909506	−	0.415691i	$-0.863540\pi$
$631$	−35.1921	+	11.4346i	−1.40097	+	0.455204i	−0.491469	+	0.870895i	$0.663540\pi$
$632$	−7.57618	−	5.50442i	−0.301364	−	0.218954i
$633$	4.84501	+	12.9896i	0.192572	+	0.516288i
$634$	−0.479298	+	1.47513i	−0.0190354	+	0.0585848i
$635$	−11.7589	+	8.54336i	−0.466639	+	0.339033i
$636$	−7.04060	−	18.8760i	−0.279178	−	0.748481i
$637$	−1.05420	−	0.342530i	−0.0417689	−	0.0135715i
$638$	−4.38610	−	6.03695i	−0.173647	−	0.239005i
$639$	−27.5721	+	11.6528i	−1.09074	+	0.460976i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	13.1927	+	9.58503i	0.521079	+	0.378586i	0.817010	−	0.576623i	$-0.195630\pi$
$641$	13.1927	+	9.58503i	0.521079	+	0.378586i	−0.295931	+	0.955209i	$0.595630\pi$
$642$	−8.83745	−	5.85933i	−0.348786	−	0.231249i
$643$	−18.0584	−	5.86753i	−0.712153	−	0.231393i	−0.0695354	−	0.997579i	$-0.522152\pi$
$643$	−18.0584	−	5.86753i	−0.712153	−	0.231393i	−0.642618	+	0.766187i	$0.722152\pi$
$644$	−0.273553	−	0.841909i	−0.0107795	−	0.0331759i
$645$	2.60285	−	9.35712i	0.102487	−	0.368436i
$646$			32.7569i			1.28880i
$647$	3.18609	+	9.80577i	0.125258	+	0.385505i	0.993948	−	0.109852i	$-0.0350375\pi$
$647$	3.18609	+	9.80577i	0.125258	+	0.385505i	−0.868690	+	0.495356i	$0.835038\pi$
$648$	−3.97065	+	8.07675i	−0.155982	+	0.317285i
$649$	−0.676004	+	0.930439i	−0.0265355	+	0.0365229i
$650$	0.323341			0.0126825
$651$	9.83751	−	15.3430i	0.385562	−	0.601340i
$652$	−18.1367			−0.710286
$653$	−12.7114	+	17.4958i	−0.497437	+	0.684663i	−0.981738	−	0.190238i	$-0.939074\pi$
$653$	−12.7114	+	17.4958i	−0.497437	+	0.684663i	0.484301	+	0.874901i	$0.339074\pi$
$654$	13.7194	−	5.11723i	0.536470	−	0.200100i
$655$	0.578228	+	1.77960i	0.0225933	+	0.0695349i
$656$		−	8.98662i		−	0.350869i
$657$	−7.02007	+	11.6420i	−0.273879	+	0.454199i
$658$	−6.79560	−	20.9147i	−0.264920	−	0.815340i
$659$	−33.2261	−	10.7958i	−1.29430	−	0.420545i	−0.420707	−	0.907196i	$-0.638218\pi$
$659$	−33.2261	−	10.7958i	−1.29430	−	0.420545i	−0.873596	+	0.486652i	$0.838218\pi$
$660$	1.47798	−	2.22920i	0.0575305	−	0.0867714i
$661$	−8.54700	−	6.20976i	−0.332440	−	0.241532i	0.409025	−	0.912523i	$-0.365869\pi$
$661$	−8.54700	−	6.20976i	−0.332440	−	0.241532i	−0.741465	+	0.670991i	$0.765869\pi$
$662$	7.93616	+	24.4250i	0.308448	+	0.949304i
$663$	1.34506	+	1.69369i	0.0522379	+	0.0657776i
$664$	−4.14527	−	5.70547i	−0.160868	−	0.221415i
$665$	−15.2461	−	4.95374i	−0.591217	−	0.192098i
$666$	−17.1915	+	1.47694i	−0.666157	+	0.0572304i
$667$	1.83114	−	1.33040i	0.0709020	−	0.0515133i
$668$	−3.72171	+	11.4543i	−0.143997	+	0.443179i
$669$	−7.89895	+	2.94625i	−0.305391	+	0.113909i
$670$	5.35578	+	3.89120i	0.206912	+	0.150330i
$671$	−1.16090	+	0.377201i	−0.0448162	+	0.0145617i
$672$	−2.03578	−	2.56344i	−0.0785319	−	0.0988869i
$673$	38.2256	+	12.4203i	1.47349	+	0.478766i	0.932160	−	0.362046i	$-0.117922\pi$
$673$	38.2256	+	12.4203i	1.47349	+	0.478766i	0.541329	+	0.840811i	$0.317922\pi$
$674$	−9.08993	+	27.9759i	−0.350131	+	1.07759i
$675$	4.56063	+	2.49011i	0.175539	+	0.0958442i
$676$	−12.8955			−0.495979
$677$	−4.01787			−0.154419			−0.0772096	−	0.997015i	$-0.524601\pi$
$677$	−4.01787			−0.154419			−0.0772096	+	0.997015i	$0.524601\pi$
$678$	17.2754	−	0.740713i	0.663458	−	0.0284469i
$679$	29.0080	−	21.0755i	1.11322	−	0.808804i
$680$	3.12433	+	2.26996i	0.119813	+	0.0870490i
$681$	−47.6680	−	13.2597i	−1.82664	−	0.508113i
$682$	8.59679	−	0.131746i	0.329188	−	0.00504483i
$683$			38.2673i			1.46426i	0.681165	+	0.732130i	$0.261473\pi$
$683$			38.2673i			1.46426i	−0.681165	+	0.732130i	$0.738527\pi$
$684$	9.90597	+	23.4390i	0.378764	+	0.896211i
$685$	−4.15440	−	5.71804i	−0.158731	−	0.218475i
$686$	18.7439	−	6.09027i	0.715647	−	0.232528i
$687$	38.0904	+	10.5955i	1.45324	+	0.404244i
$688$		−	5.60745i		−	0.213782i
$689$	−3.57685	+	1.16219i	−0.136267	+	0.0442759i
$690$	0.676165	+	0.448306i	0.0257412	+	0.0170667i
$691$	−3.02771	+	9.31833i	−0.115179	+	0.354486i	−0.991984	−	0.126360i	$-0.959670\pi$
$691$	−3.02771	+	9.31833i	−0.115179	+	0.354486i	0.876805	+	0.480846i	$0.159670\pi$
$692$	2.29744	−	3.16215i	0.0873355	−	0.120207i
$693$	−1.98289	+	8.52790i	−0.0753238	+	0.323948i
$694$	3.08490	−	4.24600i	0.117101	−	0.161176i
$695$	10.1830	−	7.39836i	0.386262	−	0.280636i
$696$	4.62505	−	6.97582i	0.175312	−	0.264418i
$697$	−20.3993	−	28.0772i	−0.772677	−	1.06350i
$698$	−4.11756	−	5.66733i	−0.155852	−	0.214512i
$699$	−23.2028	+	34.9961i	−0.877612	+	1.32368i
$700$	−1.52899	+	1.11088i	−0.0577906	+	0.0419873i
$701$	23.8115	−	32.7738i	0.899350	−	1.23785i	−0.0713253	−	0.997453i	$-0.522723\pi$
$701$	23.8115	−	32.7738i	0.899350	−	1.23785i	0.970675	−	0.240396i	$-0.0772772\pi$
$702$	1.47464	+	0.805153i	0.0556566	+	0.0303885i
$703$	−28.6755	+	39.4684i	−1.08152	+	1.48858i
$704$	0.477187	−	1.46863i	0.0179847	−	0.0553511i
$705$	16.7973	+	11.1368i	0.632623	+	0.419436i
$706$	−11.9120	+	3.87043i	−0.448312	+	0.145665i
$707$			19.6113i			0.737558i
$708$	−1.24280	−	0.345706i	−0.0467072	−	0.0129924i
$709$	16.6776	−	5.41887i	0.626339	−	0.203510i	0.0213865	−	0.999771i	$-0.493192\pi$
$709$	16.6776	−	5.41887i	0.626339	−	0.203510i	0.604953	+	0.796261i	$0.293192\pi$
$710$	5.86480	+	8.07221i	0.220102	+	0.302945i
$711$	−25.8779	+	10.9367i	−0.970495	+	0.410159i
$712$			0.852174i			0.0319366i
$713$	0.0399616	+	2.60760i	0.00149657	+	0.0976553i
$714$	−12.1794	−	3.38790i	−0.455801	−	0.126789i
$715$	−0.403947	−	0.293485i	−0.0151068	−	0.0109757i
$716$	12.5049	−	9.08535i	0.467331	−	0.339536i
$717$	18.2712	−	0.783407i	0.682349	−	0.0292569i
$718$	29.3032			1.09359
$719$	−2.98024			−0.111144			−0.0555720	−	0.998455i	$-0.517698\pi$
$719$	−2.98024			−0.111144			−0.0555720	+	0.998455i	$0.517698\pi$
$720$	2.92205	+	0.679429i	0.108898	+	0.0253208i
$721$	7.10083	−	21.8541i	0.264449	−	0.813889i
$722$	50.3545	+	16.3612i	1.87400	+	0.608900i
$723$	1.34175	+	1.68952i	0.0499001	+	0.0628339i
$724$	−19.0749	+	6.19781i	−0.708912	+	0.230340i
$725$	−3.90941	−	2.84035i	−0.145192	−	0.105488i
$726$	13.9814	−	5.21497i	0.518899	−	0.193546i
$727$	10.5992	−	32.6210i	0.393103	−	1.20985i	−0.537326	−	0.843375i	$-0.680565\pi$
$727$	10.5992	−	32.6210i	0.393103	−	1.20985i	0.930429	−	0.366473i	$-0.119435\pi$
$728$	−0.494386	+	0.359192i	−0.0183232	+	0.0133126i
$729$	14.5987	+	22.7129i	0.540694	+	0.841219i
$730$	4.30980	+	1.40034i	0.159513	+	0.0518289i
$731$	−12.7287	−	17.5195i	−0.470787	−	0.647983i
$732$	−0.851464	−	1.07216i	−0.0314710	−	0.0396281i
$733$	−11.0678	−	34.0632i	−0.408799	−	1.25815i	−0.917681	−	0.397317i	$-0.869941\pi$
$733$	−11.0678	−	34.0632i	−0.408799	−	1.25815i	0.508883	−	0.860836i	$-0.330059\pi$
$734$	−9.44551	−	6.86256i	−0.348640	−	0.253302i
$735$	−3.28110	+	4.94878i	−0.121025	+	0.182539i
$736$	0.445469	+	0.144742i	0.0164202	+	0.00533524i
$737$	−3.15903	−	9.72250i	−0.116364	−	0.358133i
$738$	−23.0873	−	13.9215i	−0.849857	−	0.512458i
$739$			52.1476i			1.91828i	0.282932	+	0.959140i	$0.408693\pi$
$739$			52.1476i			1.91828i	−0.282932	+	0.959140i	$0.591307\pi$
$740$	1.77734	+	5.47010i	0.0653365	+	0.201085i
$741$	4.45080	−	1.66012i	0.163504	−	0.0609859i
$742$	12.9212	−	17.7844i	0.474350	−	0.652887i
$743$	−18.4558			−0.677076			−0.338538	−	0.940953i	$-0.609932\pi$
$743$	−18.4558			−0.677076			−0.338538	+	0.940953i	$0.609932\pi$
$744$	3.50826	+	8.98288i	0.128619	+	0.329328i
$745$	−6.59311			−0.241553
$746$	0.204940	−	0.282076i	0.00750340	−	0.0103275i
$747$	−21.0794	+	1.81096i	−0.771255	+	0.0662596i
$748$	−1.84284	−	5.67169i	−0.0673810	−	0.207377i
$749$		−	11.5700i		−	0.422758i
$750$	0.464177	−	1.66869i	0.0169493	−	0.0609321i
$751$	−12.4446	−	38.3006i	−0.454110	−	1.39761i	−0.872176	−	0.489192i	$-0.837292\pi$
$751$	−12.4446	−	38.3006i	−0.454110	−	1.39761i	0.418066	−	0.908417i	$-0.362708\pi$
$752$	11.0663	+	3.59567i	0.403548	+	0.131121i
$753$	−42.7357	−	28.3343i	−1.55738	−	1.03256i
$754$	−1.26407	−	0.918401i	−0.0460347	−	0.0334462i
$755$	0.984862	+	3.03109i	0.0358428	+	0.110313i
$756$	−9.73939	+	1.25895i	−0.354218	+	0.0457877i
$757$	−26.1746	−	36.0263i	−0.951333	−	1.30940i	−0.950933	−	0.309397i	$-0.899873\pi$
$757$	−26.1746	−	36.0263i	−0.951333	−	1.30940i	−0.000399929	−	1.00000i	$-0.500127\pi$
$758$	−4.24425	−	1.37904i	−0.154158	−	0.0500890i
$759$	−0.437817	−	1.17380i	−0.0158918	−	0.0426061i
$760$	6.86216	−	4.98565i	0.248917	−	0.180848i
$761$	−5.36770	+	16.5201i	−0.194579	+	0.598852i	0.805402	+	0.592728i	$0.201949\pi$
$761$	−5.36770	+	16.5201i	−0.194579	+	0.598852i	−0.999981	+	0.00612366i	$0.998051\pi$
$762$	8.79804	+	23.5877i	0.318719	+	0.854492i
$763$	12.9260	+	9.39131i	0.467954	+	0.339988i
$764$	1.66487	−	0.540951i	0.0602331	−	0.0195709i
$765$	10.6717	−	4.51018i	0.385837	−	0.163066i
$766$	12.6795	+	4.11982i	0.458129	+	0.148855i
$767$	−0.0744160	+	0.229029i	−0.00268701	+	0.00826976i
$768$	1.73046	−	0.0741964i	0.0624426	−	0.00267733i
$769$	−9.76398			−0.352098			−0.176049	−	0.984381i	$-0.556332\pi$
$769$	−9.76398			−0.352098			−0.176049	+	0.984381i	$0.556332\pi$
$770$	2.91847			0.105174
$771$	−0.966637	−	22.5446i	−0.0348126	−	0.811923i
$772$	5.35898	−	3.89352i	0.192874	−	0.140131i
$773$	−3.55069	−	2.57973i	−0.127709	−	0.0927863i	0.522097	−	0.852886i	$-0.325150\pi$
$773$	−3.55069	−	2.57973i	−0.127709	−	0.0927863i	−0.649806	+	0.760100i	$0.725150\pi$
$774$	−14.4060	−	8.68671i	−0.517812	−	0.312237i
$775$	5.26827	−	1.80147i	0.189242	−	0.0647108i
$776$			18.9719i			0.681053i
$777$	−11.7090	−	14.7439i	−0.420058	−	0.528935i
$778$	−22.1868	−	30.5375i	−0.795434	−	1.09482i
$779$	−72.4946	+	23.5549i	−2.59739	+	0.843943i
$780$	0.150087	−	0.539557i	0.00537399	−	0.0193192i
$781$		−	15.4078i		−	0.551335i
$782$	1.72035	−	0.558975i	0.0615196	−	0.0199889i
$783$	−10.7566	−	22.6886i	−0.384409	−	0.810826i
$784$	−1.05935	+	3.26034i	−0.0378339	+	0.116441i
$785$	−4.01052	+	5.52001i	−0.143142	+	0.197018i
$786$	3.23802	−	0.138835i	0.115496	−	0.00495209i
$787$	−8.19001	+	11.2726i	−0.291942	+	0.401824i	−0.929644	−	0.368460i	$-0.879885\pi$
$787$	−8.19001	+	11.2726i	−0.291942	+	0.401824i	0.637702	+	0.770284i	$0.279885\pi$
$788$	−10.1352	+	7.36368i	−0.361053	+	0.262320i
$789$	−2.38378	−	1.58048i	−0.0848649	−	0.0562665i
$790$	5.50442	+	7.57618i	0.195838	+	0.269549i
$791$	11.0901	+	15.2641i	0.394317	+	0.542731i
$792$	−3.03380	−	3.50104i	−0.107801	−	0.124404i
$793$	−0.206777	+	0.150232i	−0.00734286	+	0.00533490i
$794$	−3.14284	+	4.32575i	−0.111535	+	0.153515i
$795$	0.863013	+	20.1278i	0.0306079	+	0.713859i
$796$	−5.14171	+	7.07696i	−0.182243	+	0.250836i
$797$	16.8773	−	51.9430i	0.597825	−	1.83992i	0.0576942	−	0.998334i	$-0.481625\pi$
$797$	16.8773	−	51.9430i	0.597825	−	1.83992i	0.540131	−	0.841581i	$-0.318375\pi$
$798$	−15.3431	+	23.1416i	−0.543142	+	0.819203i
$799$	42.7369	−	13.8861i	1.51192	−	0.491254i
$800$		−	1.00000i		−	0.0353553i
$801$	2.18930	+	1.32013i	0.0773552	+	0.0466447i
$802$	26.5837	−	8.63758i	0.938705	−	0.305004i
$803$	−4.11317	−	5.66129i	−0.145150	−	0.199782i
$804$	8.97926	−	7.13095i	0.316674	−	0.251489i
$805$			0.885236i			0.0312005i
$806$	1.70345	−	0.582489i	0.0600014	−	0.0205173i
$807$	6.26076	−	22.5072i	0.220389	−	0.792289i
$808$	−8.39489	−	6.09925i	−0.295331	−	0.214571i
$809$	−19.3342	+	14.0471i	−0.679753	+	0.493869i	−0.873276	−	0.487227i	$-0.838009\pi$
$809$	−19.3342	+	14.0471i	−0.679753	+	0.493869i	0.193523	+	0.981096i	$0.438009\pi$
$810$	6.27217	−	6.45445i	0.220381	−	0.226786i
$811$	4.82580			0.169457			0.0847284	−	0.996404i	$-0.472998\pi$
$811$	4.82580			0.169457			0.0847284	+	0.996404i	$0.472998\pi$
$812$	9.13275			0.320497
$813$	−1.14144	−	26.6215i	−0.0400322	−	0.933658i
$814$	2.74459	−	8.44699i	0.0961980	−	0.296067i
$815$	17.2490	+	5.60453i	0.604205	+	0.196318i
$816$	5.23811	−	4.15989i	0.183371	−	0.145625i
$817$	−45.2350	+	14.6977i	−1.58257	+	0.514209i
$818$	−11.0075	−	7.99743i	−0.384869	−	0.279623i
$819$	0.156922	+	1.82656i	0.00548329	+	0.0638250i
$820$	−2.77702	+	8.54678i	−0.0969777	+	0.298467i
$821$	−5.17893	+	3.76271i	−0.180746	+	0.131320i	−0.674479	−	0.738294i	$-0.735632\pi$
$821$	−5.17893	+	3.76271i	−0.180746	+	0.131320i	0.493733	+	0.869613i	$0.335632\pi$
$822$	−11.4700	+	4.27824i	−0.400063	+	0.149221i
$823$	−2.28545	−	0.742588i	−0.0796658	−	0.0258850i	0.268913	−	0.963164i	$-0.413336\pi$
$823$	−2.28545	−	0.742588i	−0.0796658	−	0.0258850i	−0.348579	+	0.937279i	$0.613336\pi$
$824$	7.14656	+	9.83640i	0.248962	+	0.342667i
$825$	−2.09451	+	1.66337i	−0.0729213	+	0.0579111i
$826$	−0.434965	−	1.33868i	−0.0151344	−	0.0465788i
$827$	−42.3797	−	30.7907i	−1.47369	−	1.07070i	−0.979524	−	0.201327i	$-0.935475\pi$
$827$	−42.3797	−	30.7907i	−1.47369	−	1.07070i	−0.494163	−	0.869370i	$-0.664525\pi$
$828$	1.06195	−	0.920220i	0.0369051	−	0.0319799i
$829$	−8.96752	−	2.91372i	−0.311455	−	0.101198i	0.149119	−	0.988819i	$-0.452356\pi$
$829$	−8.96752	−	2.91372i	−0.311455	−	0.101198i	−0.460574	+	0.887622i	$0.652356\pi$
$830$	2.17930	+	6.70719i	0.0756445	+	0.232810i
$831$	−26.4875	−	7.36797i	−0.918842	−	0.255592i
$832$		−	0.323341i		−	0.0112098i
$833$	4.09108	+	12.5911i	0.141748	+	0.436254i
$834$	−7.61890	−	20.4264i	−0.263821	−	0.707308i
$835$	7.07912	−	9.74357i	0.244983	−	0.337190i
$836$	−13.0981			−0.453008
$837$	28.5125	+	4.90271i	0.985537	+	0.169462i
$838$	15.3722			0.531025
$839$	9.18216	−	12.6382i	0.317003	−	0.436317i	−0.620546	−	0.784170i	$-0.713089\pi$
$839$	9.18216	−	12.6382i	0.317003	−	0.436317i	0.937549	+	0.347853i	$0.113089\pi$
$840$	1.14399	+	3.06707i	0.0394715	+	0.105824i
$841$	−1.74562	−	5.37247i	−0.0601939	−	0.185258i
$842$		−	29.2931i		−	1.00951i
$843$	49.6478	+	13.8104i	1.70996	+	0.475656i
$844$	−2.47344	−	7.61247i	−0.0851393	−	0.262032i
$845$	12.2643	+	3.98491i	0.421905	+	0.137085i
$846$	26.3808	−	22.8601i	0.906992	−	0.785946i
$847$	13.1729	+	9.57069i	0.452627	+	0.328853i
$848$	3.59432	+	11.0622i	0.123429	+	0.379877i
$849$	−6.78392	+	5.38751i	−0.232824	+	0.184899i
$850$	−2.26996	−	3.12433i	−0.0778590	−	0.107164i
$851$	2.56216	+	0.832497i	0.0878298	+	0.0285376i
$852$	16.1924	−	6.03963i	0.554741	−	0.206914i
$853$	−27.4972	+	19.9779i	−0.941485	+	0.684029i	−0.948778	−	0.315944i	$-0.897679\pi$
$853$	−27.4972	+	19.9779i	−0.941485	+	0.684029i	0.00729250	+	0.999973i	$0.497679\pi$
$854$	0.461652	−	1.42082i	0.0157974	−	0.0486194i
$855$	−2.17810	−	25.3529i	−0.0744895	−	0.867050i
$856$	4.95270	+	3.59835i	0.169280	+	0.122989i
$857$	16.4181	−	5.33457i	0.560832	−	0.182225i	−0.0148634	−	0.999890i	$-0.504731\pi$
$857$	16.4181	−	5.33457i	0.560832	−	0.182225i	0.575696	+	0.817664i	$0.304731\pi$
$858$	−0.677239	+	0.537835i	−0.0231206	+	0.0183614i
$859$	35.9521	+	11.6815i	1.22667	+	0.398569i	0.849507	−	0.527578i	$-0.176900\pi$
$859$	35.9521	+	11.6815i	1.22667	+	0.398569i	0.377163	+	0.926147i	$0.376900\pi$
$860$	−1.73280	+	5.33300i	−0.0590879	+	0.181854i
$861$	−1.26017	−	29.3905i	−0.0429463	−	1.00162i
$862$	34.4326			1.17278
$863$	30.4706			1.03723			0.518615	−	0.855008i	$-0.326448\pi$
$863$	30.4706			1.03723			0.518615	+	0.855008i	$0.326448\pi$
$864$	2.49011	−	4.56063i	0.0847151	−	0.155156i
$865$	−3.16215	+	2.29744i	−0.107516	+	0.0781153i
$866$	26.7631	+	19.4445i	0.909446	+	0.660751i
$867$	−0.968198	+	3.48063i	−0.0328817	+	0.118208i
$868$	−6.05394	+	8.60686i	−0.205484	+	0.292136i
$869$		−	14.4610i		−	0.490557i
$870$	−6.55433	+	5.20518i	−0.222213	+	0.176472i
$871$	−1.25818	−	1.73174i	−0.0426319	−	0.0586778i
$872$	−8.04018	+	2.61241i	−0.272275	+	0.0884675i
$873$	48.7404	+	29.3901i	1.64961	+	0.994705i
$874$		−	3.97296i		−	0.134387i
$875$	1.79744	−	0.584024i	0.0607646	−	0.0197436i
$876$	4.33725	−	6.54174i	0.146542	−	0.221025i
$877$	−1.39984	+	4.30826i	−0.0472692	+	0.145480i	−0.971905	−	0.235372i	$-0.924369\pi$
$877$	−1.39984	+	4.30826i	−0.0472692	+	0.145480i	0.924636	+	0.380852i	$0.124369\pi$
$878$	12.7186	−	17.5056i	0.429231	−	0.590786i
$879$	−0.516678	−	12.0503i	−0.0174271	−	0.406447i
$880$	−0.907664	+	1.24929i	−0.0305973	+	0.0421136i
$881$	−41.6810	+	30.2830i	−1.40427	+	1.02026i	−0.410142	+	0.912022i	$0.634521\pi$
$881$	−41.6810	+	30.2830i	−1.40427	+	1.02026i	−0.994125	+	0.108238i	$0.965479\pi$
$882$	6.73499	+	7.77227i	0.226779	+	0.261706i
$883$	−2.68768	−	3.69927i	−0.0904476	−	0.124490i	0.761395	−	0.648288i	$-0.224515\pi$
$883$	−2.68768	−	3.69927i	−0.0904476	−	0.124490i	−0.851843	+	0.523798i	$0.824515\pi$
$884$	−0.733970	−	1.01022i	−0.0246861	−	0.0339775i
$885$	1.07514	+	0.712832i	0.0361405	+	0.0239616i
$886$	−17.6036	+	12.7898i	−0.591405	+	0.429681i
$887$	−14.7085	+	20.2445i	−0.493862	+	0.679743i	−0.981095	−	0.193529i	$-0.938007\pi$
$887$	−14.7085	+	20.2445i	−0.493862	+	0.679743i	0.487232	+	0.873273i	$0.338007\pi$
$888$	9.95293	−	0.426749i	0.333999	−	0.0143208i
$889$	−16.1464	+	22.2237i	−0.541535	+	0.745358i
$890$	0.263336	−	0.810465i	0.00882705	−	0.0271669i
$891$	−13.6942	+	2.37048i	−0.458774	+	0.0794140i
$892$	4.62914	−	1.50410i	0.154995	−	0.0503610i
$893$		−	98.6962i		−	3.30274i
$894$	−3.06037	+	11.0019i	−0.102354	+	0.367958i
$895$	−14.7004	+	4.77645i	−0.491380	+	0.159659i
$896$	1.11088	+	1.52899i	0.0371119	+	0.0510801i
$897$	−0.163137	−	0.205422i	−0.00544700	−	0.00685883i
$898$			15.7707i			0.526274i
$899$	−25.7126	−	7.92105i	−0.857564	−	0.264182i
$900$	−2.56908	−	1.54914i	−0.0856360	−	0.0516379i
$901$	36.3405	+	26.4030i	1.21068	+	0.879610i
$902$	11.2269	−	8.15683i	0.373815	−	0.271593i
$903$	−0.786315	−	18.3390i	−0.0261669	−	0.610283i
$904$	−9.98313			−0.332034
$905$	20.0565			0.666701
$906$	5.51512	−	0.236470i	0.183227	−	0.00785619i
$907$	−9.94088	+	30.5949i	−0.330081	+	1.01589i	0.639013	+	0.769196i	$0.279343\pi$
$907$	−9.94088	+	30.5949i	−0.330081	+	1.01589i	−0.969094	+	0.246690i	$0.920657\pi$
$908$	27.1679	+	8.82739i	0.901599	+	0.292947i
$909$	−28.6743	+	12.1186i	−0.951066	+	0.401948i
$910$	0.581186	−	0.188839i	0.0192661	−	0.00625994i
$911$	−6.05156	−	4.39672i	−0.200497	−	0.145670i	0.483007	−	0.875617i	$-0.339545\pi$
$911$	−6.05156	−	4.39672i	−0.200497	−	0.145670i	−0.683504	+	0.729947i	$0.739545\pi$
$912$	−5.13427	−	13.7651i	−0.170013	−	0.455807i
$913$	3.36529	−	10.3573i	0.111375	−	0.342777i
$914$	−19.1844	+	13.9382i	−0.634562	+	0.461036i
$915$	0.478475	+	1.28280i	0.0158179	+	0.0424081i
$916$	−21.7092	−	7.05376i	−0.717294	−	0.233063i
$917$	2.07866	+	2.86103i	0.0686435	+	0.0944797i
$918$	−2.57253	−	19.9014i	−0.0849063	−	0.656843i
$919$	−11.0955	−	34.1483i	−0.366006	−	1.12645i	−0.949349	−	0.314224i	$-0.898256\pi$
$919$	−11.0955	−	34.1483i	−0.366006	−	1.12645i	0.583343	−	0.812226i	$-0.301744\pi$
$920$	−0.378938	−	0.275315i	−0.0124932	−	0.00907686i
$921$	−7.69088	−	5.09915i	−0.253423	−	0.168023i
$922$	−18.8832	−	6.13552i	−0.621885	−	0.202063i
$923$	−0.996959	−	3.06833i	−0.0328153	−	0.100995i
$924$	1.35468	−	4.87003i	0.0445658	−	0.160212i
$925$		−	5.75161i		−	0.189112i
$926$	4.60779	+	14.1813i	0.151421	+	0.466027i
$927$	36.3415	−	3.12215i	1.19361	−	0.102545i
$928$	−2.84035	+	3.90941i	−0.0932391	+	0.128333i
$929$	20.5706			0.674898			0.337449	−	0.941344i	$-0.390436\pi$
$929$	20.5706			0.674898			0.337449	+	0.941344i	$0.390436\pi$
$930$	−0.560696	−	9.62734i	−0.0183860	−	0.315693i
$931$	29.0777			0.952982
$932$	14.2494	−	19.6126i	0.466755	−	0.642433i
$933$	−34.9547	+	13.0378i	−1.14436	+	0.426840i
$934$	0.967843	+	2.97871i	0.0316688	+	0.0974665i
$935$			5.96356i			0.195029i
$936$	−0.830688	−	0.500899i	−0.0271519	−	0.0163724i
$937$	9.52918	+	29.3278i	0.311305	+	0.958097i	0.977249	+	0.212096i	$0.0680288\pi$
$937$	9.52918	+	29.3278i	0.311305	+	0.958097i	−0.665944	+	0.746001i	$0.731971\pi$
$938$	11.8993	+	3.86630i	0.388524	+	0.126239i
$939$	7.82731	−	11.8057i	0.255435	−	0.385264i
$940$	−9.41358	−	6.83937i	−0.307037	−	0.223076i
$941$	1.16977	+	3.60018i	0.0381334	+	0.117362i	0.968311	−	0.249747i	$-0.0803474\pi$
$941$	1.16977	+	3.60018i	0.0381334	+	0.117362i	−0.930178	+	0.367109i	$0.880347\pi$
$942$	7.34962	+	9.25460i	0.239464	+	0.301531i
$943$	2.47415	+	3.40537i	0.0805694	+	0.110894i
$944$	0.708321	+	0.230147i	0.0230539	+	0.00749066i
$945$	9.65175	+	1.81230i	0.313971	+	0.0589541i
$946$	7.00534	−	5.08968i	0.227763	−	0.165480i
$947$	8.56130	−	26.3490i	0.278205	−	0.856226i	−0.710149	−	0.704052i	$-0.751372\pi$
$947$	8.56130	−	26.3490i	0.278205	−	0.856226i	0.988354	−	0.152175i	$-0.0486276\pi$
$948$	15.1974	−	5.66850i	0.493587	−	0.184104i
$949$	−1.18541	−	0.861252i	−0.0384801	−	0.0279574i
$950$	−8.06695	+	2.62111i	−0.261726	+	0.0850401i
$951$	−1.67073	−	2.10377i	−0.0541771	−	0.0682194i
$952$	6.94151	+	2.25543i	0.224976	+	0.0730990i
$953$	4.89676	−	15.0707i	0.158622	−	0.488187i	−0.839888	−	0.542760i	$-0.817379\pi$
$953$	4.89676	−	15.0707i	0.158622	−	0.488187i	0.998510	+	0.0545721i	$0.0173795\pi$
$954$	33.9877	+	7.90275i	1.10039	+	0.255861i
$955$	−1.75055			−0.0566466
$956$	−10.5586			−0.341488
$957$	12.9128	−	0.553659i	0.417412	−	0.0178973i
$958$	5.09512	−	3.70182i	0.164616	−	0.119600i
$959$	−10.8068	−	7.85156i	−0.348968	−	0.253540i
$960$	−1.66869	−	0.464177i	−0.0538569	−	0.0149812i
$961$	24.5094	−	18.9813i	0.790626	−	0.612300i
$962$		−	1.85973i		−	0.0599601i
$963$	16.9169	−	7.14955i	0.545139	−	0.230391i
$964$	−0.732162	−	1.00773i	−0.0235813	−	0.0324569i
$965$	−6.29986	+	2.04695i	−0.202800	+	0.0658936i
$966$	1.47719	+	0.410906i	0.0475277	+	0.0132207i
$967$		−	27.8186i		−	0.894586i	−0.894387	−	0.447293i	$-0.852388\pi$
$967$		−	27.8186i		−	0.894586i	0.894387	−	0.447293i	$-0.147612\pi$
$968$	−8.19375	+	2.66231i	−0.263357	+	0.0855699i
$969$	−47.2873	−	31.3520i	−1.51909	−	1.00717i
$970$	5.86265	−	18.0434i	0.188238	−	0.579338i
$971$	15.0980	−	20.7806i	0.484519	−	0.666883i	−0.494847	−	0.868980i	$-0.664776\pi$
$971$	15.0980	−	20.7806i	0.484519	−	0.666883i	0.979365	+	0.202098i	$0.0647758\pi$
$972$	−7.85911	−	13.4623i	−0.252081	−	0.431805i
$973$	13.9825	−	19.2452i	0.448257	−	0.616973i
$974$	31.9723	−	23.2292i	1.02446	−	0.744313i
$975$	−0.309474	+	0.466769i	−0.00991109	+	0.0149486i
$976$	0.464625	+	0.639501i	0.0148723	+	0.0204699i
$977$	7.73502	+	10.6463i	0.247465	+	0.340607i	0.914622	−	0.404311i	$-0.132489\pi$
$977$	7.73502	+	10.6463i	0.247465	+	0.340607i	−0.667156	+	0.744918i	$0.732489\pi$
$978$	17.3588	−	26.1818i	0.555074	−	0.837201i
$979$	−1.06461	+	0.773487i	−0.0340252	+	0.0247208i
$980$	2.01500	−	2.77341i	0.0643668	−	0.0885933i
$981$	−5.74385	+	24.7029i	−0.183387	+	0.788701i
$982$	−10.3369	+	14.2275i	−0.329863	+	0.454018i
$983$	−11.1777	+	34.4015i	−0.356514	+	1.09724i	0.598612	+	0.801039i	$0.295719\pi$
$983$	−11.1777	+	34.4015i	−0.356514	+	1.09724i	−0.955126	+	0.296199i	$0.904281\pi$
$984$	12.9729	+	8.60121i	0.413562	+	0.274197i
$985$	11.9147	−	3.87131i	0.379633	−	0.123350i
$986$			18.6618i			0.594312i
$987$	36.6963	+	10.2077i	1.16806	+	0.324916i
$988$	−2.60837	+	0.847512i	−0.0829834	+	0.0269629i
$989$	1.54381	+	2.12488i	0.0490904	+	0.0675672i
$990$	1.80343	+	4.26719i	0.0573169	+	0.135620i
$991$		−	13.7121i		−	0.435580i	−0.975996	−	0.217790i	$-0.930115\pi$
$991$		−	13.7121i		−	0.435580i	0.975996	−	0.217790i	$-0.0698849\pi$
$992$	−1.80147	−	5.26827i	−0.0571968	−	0.167268i
$993$	−42.8553	−	11.9210i	−1.35997	−	0.378300i
$994$	15.2560	+	11.0841i	0.483891	+	0.351567i
$995$	7.07696	−	5.14171i	0.224355	−	0.163003i
$996$	12.2038	−	0.523260i	0.386693	−	0.0165801i
$997$	18.9253			0.599370			0.299685	−	0.954038i	$-0.403118\pi$
$997$	18.9253			0.599370			0.299685	+	0.954038i	$0.403118\pi$
$998$	−11.5509			−0.365636
$999$	14.3221	−	26.2310i	0.453132	−	0.829911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.a.401.18	yes	80
3.2	odd	2	inner	930.2.v.a.401.8	✓	80
31.15	odd	10	inner	930.2.v.a.821.8	yes	80
93.77	even	10	inner	930.2.v.a.821.18	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.a.401.8	✓	80	3.2	odd	2	inner
930.2.v.a.401.18	yes	80	1.1	even	1	trivial
930.2.v.a.821.8	yes	80	31.15	odd	10	inner
930.2.v.a.821.18	yes	80	93.77	even	10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.605307 + 1.62284i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.26721 + 1.96463i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.605307 + 1.62284i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.26721 + 1.96463i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.477187 - 1.46863i) q^{11} +(1.35636 - 1.07717i) q^{12} +(-0.190055 - 0.261588i) q^{13} +(1.79744 + 0.584024i) q^{14} +(-1.62284 + 0.605307i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.19339 + 3.67287i) q^{17} +(0.256788 + 2.98899i) q^{18} +(6.86216 + 4.98565i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-2.56344 + 2.03578i) q^{21} +(-1.46863 - 0.477187i) q^{22} +(0.144742 - 0.445469i) q^{23} +(-0.0741964 - 1.73046i) q^{24} -1.00000 q^{25} -0.323341 q^{26} +(-4.56063 - 2.49011i) q^{27} +(1.52899 - 1.11088i) q^{28} +(3.90941 + 2.84035i) q^{29} +(-0.464177 + 1.66869i) q^{30} +(-5.26827 + 1.80147i) q^{31} +1.00000i q^{32} +(2.09451 - 1.66337i) q^{33} +(2.26996 + 3.12433i) q^{34} +(-1.79744 + 0.584024i) q^{35} +(2.56908 + 1.54914i) q^{36} +5.75161i q^{37} +(8.06695 - 2.62111i) q^{38} +(0.309474 - 0.466769i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-5.28220 + 7.27033i) q^{41} +(0.140227 + 3.27047i) q^{42} +(-3.29598 + 4.53652i) q^{43} +(-1.24929 + 0.907664i) q^{44} +(-1.96463 - 2.26721i) q^{45} +(-0.275315 - 0.378938i) q^{46} +(-6.83937 - 9.41358i) q^{47} +(-1.44358 - 0.957113i) q^{48} +(2.77341 - 2.01500i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(-6.68284 + 0.286538i) q^{51} +(-0.190055 + 0.261588i) q^{52} +(3.59432 - 11.0622i) q^{53} +(-4.69521 + 2.22598i) q^{54} +(1.46863 - 0.477187i) q^{55} -1.88994i q^{56} +(-3.93719 + 14.1540i) q^{57} +(4.59578 - 1.49326i) q^{58} +(-0.437766 - 0.602534i) q^{59} +(1.07717 + 1.35636i) q^{60} -0.790467i q^{61} +(-1.63919 + 5.32100i) q^{62} +(-4.85541 - 2.92778i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.261588 - 0.190055i) q^{65} +(-0.114575 - 2.67220i) q^{66} +6.62011 q^{67} +3.86189 q^{68} +(0.810537 - 0.0347531i) q^{69} +(-0.584024 + 1.79744i) q^{70} +(9.48945 + 3.08331i) q^{71} +(2.76335 - 1.16787i) q^{72} +(4.30980 - 1.40034i) q^{73} +(4.65315 + 3.38071i) q^{74} +(-0.605307 - 1.62284i) q^{75} +(2.62111 - 8.06695i) q^{76} +(2.36109 - 1.71543i) q^{77} +(-0.195720 - 0.524730i) q^{78} +(8.90634 + 2.89384i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(1.28046 - 8.90845i) q^{81} +(2.77702 + 8.54678i) q^{82} +(5.70547 + 4.14527i) q^{83} +(2.72829 + 1.80889i) q^{84} +(-3.67287 - 1.19339i) q^{85} +(1.73280 + 5.33300i) q^{86} +(-2.24304 + 8.06362i) q^{87} +1.54421i q^{88} +(-0.263336 - 0.810465i) q^{89} +(-2.98899 + 0.256788i) q^{90} +(0.359192 - 0.494386i) q^{91} -0.468393 q^{92} +(-6.11242 - 7.45911i) q^{93} -11.6358 q^{94} +(-4.98565 + 6.86216i) q^{95} +(-1.62284 + 0.605307i) q^{96} +(-5.86265 - 18.0434i) q^{97} -3.42812i q^{98} +(3.96720 + 2.39220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

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