LMFDB - Embedded newform 1110.2.o.a.253.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.9
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.21617 - 1.87641i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.24767 + 2.24767i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.21617 - 1.87641i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.24767 + 2.24767i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-1.21617 + 1.87641i) q^{10} -5.65930i q^{11} +(-0.707107 + 0.707107i) q^{12} -4.81453 q^{13} +(2.24767 - 2.24767i) q^{14} +(0.466864 + 2.18679i) q^{15} +1.00000 q^{16} +7.58373i q^{17} +1.00000i q^{18} +(3.73408 + 3.73408i) q^{19} +(1.21617 - 1.87641i) q^{20} -3.17868i q^{21} +5.65930i q^{22} +4.23021 q^{23} +(0.707107 - 0.707107i) q^{24} +(-2.04186 - 4.56408i) q^{25} +4.81453 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.24767 + 2.24767i) q^{28} +(-3.26498 + 3.26498i) q^{29} +(-0.466864 - 2.18679i) q^{30} +(1.98809 + 1.98809i) q^{31} -1.00000 q^{32} +(4.00173 + 4.00173i) q^{33} -7.58373i q^{34} +(1.48401 + 6.95110i) q^{35} -1.00000i q^{36} +(4.42648 + 4.17208i) q^{37} +(-3.73408 - 3.73408i) q^{38} +(3.40439 - 3.40439i) q^{39} +(-1.21617 + 1.87641i) q^{40} +2.43043i q^{41} +3.17868i q^{42} -3.34656 q^{43} -5.65930i q^{44} +(-1.87641 - 1.21617i) q^{45} -4.23021 q^{46} +(6.04560 - 6.04560i) q^{47} +(-0.707107 + 0.707107i) q^{48} -3.10403i q^{49} +(2.04186 + 4.56408i) q^{50} +(-5.36251 - 5.36251i) q^{51} -4.81453 q^{52} +(8.02058 + 8.02058i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-10.6192 - 6.88266i) q^{55} +(2.24767 - 2.24767i) q^{56} -5.28079 q^{57} +(3.26498 - 3.26498i) q^{58} +(9.84721 + 9.84721i) q^{59} +(0.466864 + 2.18679i) q^{60} +(-1.11855 - 1.11855i) q^{61} +(-1.98809 - 1.98809i) q^{62} +(2.24767 + 2.24767i) q^{63} +1.00000 q^{64} +(-5.85528 + 9.03405i) q^{65} +(-4.00173 - 4.00173i) q^{66} +(-6.91167 - 6.91167i) q^{67} +7.58373i q^{68} +(-2.99121 + 2.99121i) q^{69} +(-1.48401 - 6.95110i) q^{70} -6.12087 q^{71} +1.00000i q^{72} +(2.58794 - 2.58794i) q^{73} +(-4.42648 - 4.17208i) q^{74} +(4.67110 + 1.78347i) q^{75} +(3.73408 + 3.73408i) q^{76} +(12.7202 + 12.7202i) q^{77} +(-3.40439 + 3.40439i) q^{78} +(2.85317 + 2.85317i) q^{79} +(1.21617 - 1.87641i) q^{80} -1.00000 q^{81} -2.43043i q^{82} +(0.906248 + 0.906248i) q^{83} -3.17868i q^{84} +(14.2302 + 9.22310i) q^{85} +3.34656 q^{86} -4.61737i q^{87} +5.65930i q^{88} +(-10.1878 + 10.1878i) q^{89} +(1.87641 + 1.21617i) q^{90} +(10.8215 - 10.8215i) q^{91} +4.23021 q^{92} -2.81158 q^{93} +(-6.04560 + 6.04560i) q^{94} +(11.5480 - 2.46541i) q^{95} +(0.707107 - 0.707107i) q^{96} +2.87834i q^{97} +3.10403i q^{98} -5.65930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	1.21617	−	1.87641i	0.543888	−	0.839158i
$5$	1.21617	−	1.87641i	0.543888	−	0.839158i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−2.24767	+	2.24767i	−0.849539	+	0.849539i	−0.990075	−	0.140537i	$-0.955117\pi$
$7$	−2.24767	+	2.24767i	−0.849539	+	0.849539i	0.140537	+	0.990075i	$0.455117\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−1.21617	+	1.87641i	−0.384587	+	0.593374i
$11$		−	5.65930i		−	1.70634i	−0.521632	−	0.853171i	$-0.674676\pi$
$11$		−	5.65930i		−	1.70634i	0.521632	−	0.853171i	$-0.325324\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−4.81453			−1.33531			−0.667655	−	0.744471i	$-0.732702\pi$
$13$	−4.81453			−1.33531			−0.667655	+	0.744471i	$0.732702\pi$
$14$	2.24767	−	2.24767i	0.600715	−	0.600715i
$15$	0.466864	+	2.18679i	0.120544	+	0.564626i
$16$	1.00000			0.250000
$17$			7.58373i			1.83932i	0.392710	+	0.919662i	$0.371537\pi$
$17$			7.58373i			1.83932i	−0.392710	+	0.919662i	$0.628463\pi$
$18$			1.00000i			0.235702i
$19$	3.73408	+	3.73408i	0.856657	+	0.856657i	0.990943	−	0.134285i	$-0.0428739\pi$
$19$	3.73408	+	3.73408i	0.856657	+	0.856657i	−0.134285	+	0.990943i	$0.542874\pi$
$20$	1.21617	−	1.87641i	0.271944	−	0.419579i
$21$		−	3.17868i		−	0.693646i
$22$			5.65930i			1.20657i
$23$	4.23021			0.882059			0.441030	−	0.897493i	$-0.354613\pi$
$23$	4.23021			0.882059			0.441030	+	0.897493i	$0.354613\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−2.04186	−	4.56408i	−0.408373	−	0.912815i
$26$	4.81453			0.944207
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.24767	+	2.24767i	−0.424769	+	0.424769i
$29$	−3.26498	+	3.26498i	−0.606291	+	0.606291i	−0.941975	−	0.335684i	$-0.891033\pi$
$29$	−3.26498	+	3.26498i	−0.606291	+	0.606291i	0.335684	+	0.941975i	$0.391033\pi$
$30$	−0.466864	−	2.18679i	−0.0852373	−	0.399251i
$31$	1.98809	+	1.98809i	0.357071	+	0.357071i	0.862732	−	0.505661i	$-0.168751\pi$
$31$	1.98809	+	1.98809i	0.357071	+	0.357071i	−0.505661	+	0.862732i	$0.668751\pi$
$32$	−1.00000			−0.176777
$33$	4.00173	+	4.00173i	0.696611	+	0.696611i
$34$		−	7.58373i		−	1.30060i
$35$	1.48401	+	6.95110i	0.250844	+	1.17495i
$36$		−	1.00000i		−	0.166667i
$37$	4.42648	+	4.17208i	0.727709	+	0.685886i
$37$	4.42648	+	4.17208i	0.727709	+	0.685886i
$38$	−3.73408	−	3.73408i	−0.605748	−	0.605748i
$39$	3.40439	−	3.40439i	0.545138	−	0.545138i
$40$	−1.21617	+	1.87641i	−0.192293	+	0.296687i
$41$			2.43043i			0.379570i	0.981826	+	0.189785i	$0.0607791\pi$
$41$			2.43043i			0.379570i	−0.981826	+	0.189785i	$0.939221\pi$
$42$			3.17868i			0.490482i
$43$	−3.34656			−0.510346			−0.255173	−	0.966895i	$-0.582132\pi$
$43$	−3.34656			−0.510346			−0.255173	+	0.966895i	$0.582132\pi$
$44$		−	5.65930i		−	0.853171i
$45$	−1.87641	−	1.21617i	−0.279719	−	0.181296i
$46$	−4.23021			−0.623710
$47$	6.04560	−	6.04560i	0.881842	−	0.881842i	−0.111880	−	0.993722i	$-0.535687\pi$
$47$	6.04560	−	6.04560i	0.881842	−	0.881842i	0.993722	+	0.111880i	$0.0356873\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	3.10403i		−	0.443433i
$50$	2.04186	+	4.56408i	0.288763	+	0.645458i
$51$	−5.36251	−	5.36251i	−0.750901	−	0.750901i
$52$	−4.81453			−0.667655
$53$	8.02058	+	8.02058i	1.10171	+	1.10171i	0.994204	+	0.107507i	$0.0342868\pi$
$53$	8.02058	+	8.02058i	1.10171	+	1.10171i	0.107507	+	0.994204i	$0.465713\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−10.6192	−	6.88266i	−1.43189	−	0.928058i
$56$	2.24767	−	2.24767i	0.300357	−	0.300357i
$57$	−5.28079			−0.699458
$58$	3.26498	−	3.26498i	0.428712	−	0.428712i
$59$	9.84721	+	9.84721i	1.28200	+	1.28200i	0.939530	+	0.342468i	$0.111263\pi$
$59$	9.84721	+	9.84721i	1.28200	+	1.28200i	0.342468	+	0.939530i	$0.388737\pi$
$60$	0.466864	+	2.18679i	0.0602718	+	0.282313i
$61$	−1.11855	−	1.11855i	−0.143216	−	0.143216i	0.631864	−	0.775080i	$-0.282290\pi$
$61$	−1.11855	−	1.11855i	−0.143216	−	0.143216i	−0.775080	+	0.631864i	$0.782290\pi$
$62$	−1.98809	−	1.98809i	−0.252487	−	0.252487i
$63$	2.24767	+	2.24767i	0.283180	+	0.283180i
$64$	1.00000			0.125000
$65$	−5.85528	+	9.03405i	−0.726259	+	1.12054i
$66$	−4.00173	−	4.00173i	−0.492578	−	0.492578i
$67$	−6.91167	−	6.91167i	−0.844395	−	0.844395i	0.145032	−	0.989427i	$-0.453672\pi$
$67$	−6.91167	−	6.91167i	−0.844395	−	0.844395i	−0.989427	+	0.145032i	$0.953672\pi$
$68$			7.58373i			0.919662i
$69$	−2.99121	+	2.99121i	−0.360099	+	0.360099i
$70$	−1.48401	−	6.95110i	−0.177373	−	0.830816i
$71$	−6.12087			−0.726413			−0.363207	−	0.931709i	$-0.618318\pi$
$71$	−6.12087			−0.726413			−0.363207	+	0.931709i	$0.618318\pi$
$72$			1.00000i			0.117851i
$73$	2.58794	−	2.58794i	0.302896	−	0.302896i	−0.539250	−	0.842146i	$-0.681292\pi$
$73$	2.58794	−	2.58794i	0.302896	−	0.302896i	0.842146	+	0.539250i	$0.181292\pi$
$74$	−4.42648	−	4.17208i	−0.514568	−	0.484995i
$75$	4.67110	+	1.78347i	0.539373	+	0.205938i
$76$	3.73408	+	3.73408i	0.428329	+	0.428329i
$77$	12.7202	+	12.7202i	1.44960	+	1.44960i
$78$	−3.40439	+	3.40439i	−0.385471	+	0.385471i
$79$	2.85317	+	2.85317i	0.321007	+	0.321007i	0.849153	−	0.528146i	$-0.177113\pi$
$79$	2.85317	+	2.85317i	0.321007	+	0.321007i	−0.528146	+	0.849153i	$0.677113\pi$
$80$	1.21617	−	1.87641i	0.135972	−	0.209790i
$81$	−1.00000			−0.111111
$82$		−	2.43043i		−	0.268396i
$83$	0.906248	+	0.906248i	0.0994737	+	0.0994737i	0.755092	−	0.655619i	$-0.227592\pi$
$83$	0.906248	+	0.906248i	0.0994737	+	0.0994737i	−0.655619	+	0.755092i	$0.727592\pi$
$84$		−	3.17868i		−	0.346823i
$85$	14.2302	+	9.22310i	1.54348	+	1.00039i
$86$	3.34656			0.360869
$87$		−	4.61737i		−	0.495034i
$88$			5.65930i			0.603283i
$89$	−10.1878	+	10.1878i	−1.07990	+	1.07990i	−0.0833830	+	0.996518i	$0.526572\pi$
$89$	−10.1878	+	10.1878i	−1.07990	+	1.07990i	−0.996518	+	0.0833830i	$0.973428\pi$
$90$	1.87641	+	1.21617i	0.197791	+	0.128196i
$91$	10.8215	−	10.8215i	1.13440	−	1.13440i
$92$	4.23021			0.441030
$93$	−2.81158			−0.291547
$94$	−6.04560	+	6.04560i	−0.623556	+	0.623556i
$95$	11.5480	−	2.46541i	1.18480	−	0.252946i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$			2.87834i			0.292251i	0.989266	+	0.146125i	$0.0466803\pi$
$97$			2.87834i			0.292251i	−0.989266	+	0.146125i	$0.953320\pi$
$98$			3.10403i			0.313554i
$99$	−5.65930			−0.568781
$100$	−2.04186	−	4.56408i	−0.204186	−	0.456408i
$101$			16.0893i			1.60095i	0.599367	+	0.800474i	$0.295419\pi$
$101$			16.0893i			1.60095i	−0.599367	+	0.800474i	$0.704581\pi$
$102$	5.36251	+	5.36251i	0.530967	+	0.530967i
$103$			11.0997i			1.09369i	0.837234	+	0.546845i	$0.184171\pi$
$103$			11.0997i			1.09369i	−0.837234	+	0.546845i	$0.815829\pi$
$104$	4.81453			0.472103
$105$	−5.96453	−	3.86582i	−0.582078	−	0.377265i
$106$	−8.02058	−	8.02058i	−0.779028	−	0.779028i
$107$	8.64549	−	8.64549i	0.835791	−	0.835791i	−0.152511	−	0.988302i	$-0.548736\pi$
$107$	8.64549	−	8.64549i	0.835791	−	0.835791i	0.988302	+	0.152511i	$0.0487359\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	13.7592	+	13.7592i	1.31790	+	1.31790i	0.915438	+	0.402458i	$0.131844\pi$
$109$	13.7592	+	13.7592i	1.31790	+	1.31790i	0.402458	+	0.915438i	$0.368156\pi$
$110$	10.6192	+	6.88266i	1.01250	+	0.656236i
$111$	−6.08010	+	0.179886i	−0.577098	+	0.0170740i
$112$	−2.24767	+	2.24767i	−0.212385	+	0.212385i
$113$			4.68689i			0.440906i	0.975398	+	0.220453i	$0.0707536\pi$
$113$			4.68689i			0.440906i	−0.975398	+	0.220453i	$0.929246\pi$
$114$	5.28079			0.494591
$115$	5.14465	−	7.93762i	0.479741	−	0.740187i
$116$	−3.26498	+	3.26498i	−0.303145	+	0.303145i
$117$			4.81453i			0.445103i
$118$	−9.84721	−	9.84721i	−0.906509	−	0.906509i
$119$	−17.0457	−	17.0457i	−1.56258	−	1.56258i
$120$	−0.466864	−	2.18679i	−0.0426186	−	0.199625i
$121$	−21.0276			−1.91160
$122$	1.11855	+	1.11855i	0.101269	+	0.101269i
$123$	−1.71858	−	1.71858i	−0.154959	−	0.154959i
$124$	1.98809	+	1.98809i	0.178535	+	0.178535i
$125$	−11.0474	−	1.71931i	−0.988105	−	0.153780i
$126$	−2.24767	−	2.24767i	−0.200238	−	0.200238i
$127$	−14.6086	+	14.6086i	−1.29630	+	1.29630i	−0.365488	+	0.930816i	$0.619098\pi$
$127$	−14.6086	+	14.6086i	−1.29630	+	1.29630i	−0.930816	+	0.365488i	$0.880902\pi$
$128$	−1.00000			−0.0883883
$129$	2.36638	−	2.36638i	0.208348	−	0.208348i
$130$	5.85528	−	9.03405i	0.513542	−	0.792339i
$131$	9.26219	+	9.26219i	0.809241	+	0.809241i	0.984519	−	0.175278i	$-0.0560824\pi$
$131$	9.26219	+	9.26219i	0.809241	+	0.809241i	−0.175278	+	0.984519i	$0.556082\pi$
$132$	4.00173	+	4.00173i	0.348306	+	0.348306i
$133$	−16.7860			−1.45553
$134$	6.91167	+	6.91167i	0.597078	+	0.597078i
$135$	2.18679	−	0.466864i	0.188209	−	0.0401812i
$136$		−	7.58373i		−	0.650299i
$137$	1.63948	−	1.63948i	0.140071	−	0.140071i	−0.633595	−	0.773665i	$-0.718421\pi$
$137$	1.63948	−	1.63948i	0.140071	−	0.140071i	0.773665	+	0.633595i	$0.218421\pi$
$138$	2.99121	−	2.99121i	0.254629	−	0.254629i
$139$	−17.9432			−1.52192			−0.760959	−	0.648800i	$-0.775271\pi$
$139$	−17.9432			−1.52192			−0.760959	+	0.648800i	$0.775271\pi$
$140$	1.48401	+	6.95110i	0.125422	+	0.587476i
$141$			8.54977i			0.720021i
$142$	6.12087			0.513652
$143$			27.2468i			2.27850i
$144$		−	1.00000i		−	0.0833333i
$145$	2.15568	+	10.0972i	0.179020	+	0.838528i
$146$	−2.58794	+	2.58794i	−0.214180	+	0.214180i
$147$	2.19488	+	2.19488i	0.181031	+	0.181031i
$148$	4.42648	+	4.17208i	0.363854	+	0.342943i
$149$		−	9.20482i		−	0.754088i	−0.926195	−	0.377044i	$-0.876941\pi$
$149$		−	9.20482i		−	0.754088i	0.926195	−	0.377044i	$-0.123059\pi$
$150$	−4.67110	−	1.78347i	−0.381394	−	0.145620i
$151$		−	5.59713i		−	0.455488i	−0.973721	−	0.227744i	$-0.926865\pi$
$151$		−	5.59713i		−	0.455488i	0.973721	−	0.227744i	$-0.0731349\pi$
$152$	−3.73408	−	3.73408i	−0.302874	−	0.302874i
$153$	7.58373			0.613108
$154$	−12.7202	−	12.7202i	−1.02502	−	1.02502i
$155$	6.14832	−	1.31262i	0.493845	−	0.105432i
$156$	3.40439	−	3.40439i	0.272569	−	0.272569i
$157$	−0.998661	+	0.998661i	−0.0797019	+	0.0797019i	−0.745834	−	0.666132i	$-0.767949\pi$
$157$	−0.998661	+	0.998661i	−0.0797019	+	0.0797019i	0.666132	+	0.745834i	$0.267949\pi$
$158$	−2.85317	−	2.85317i	−0.226986	−	0.226986i
$159$	−11.3428			−0.899543
$160$	−1.21617	+	1.87641i	−0.0961466	+	0.148344i
$161$	−9.50811	+	9.50811i	−0.749344	+	0.749344i
$162$	1.00000			0.0785674
$163$		−	7.74976i		−	0.607008i	−0.952830	−	0.303504i	$-0.901843\pi$
$163$		−	7.74976i		−	0.607008i	0.952830	−	0.303504i	$-0.0981566\pi$
$164$			2.43043i			0.189785i
$165$	12.3757	−	2.64212i	0.963445	−	0.205689i
$166$	−0.906248	−	0.906248i	−0.0703385	−	0.0703385i
$167$		−	19.2547i		−	1.48997i	−0.667081	−	0.744985i	$-0.732457\pi$
$167$		−	19.2547i		−	1.48997i	0.667081	−	0.744985i	$-0.267543\pi$
$168$			3.17868i			0.245241i
$169$	10.1797			0.783053
$170$	−14.2302	−	9.22310i	−1.09141	−	0.707379i
$171$	3.73408	−	3.73408i	0.285552	−	0.285552i
$172$	−3.34656			−0.255173
$173$	−8.58579	+	8.58579i	−0.652765	+	0.652765i	−0.953658	−	0.300893i	$-0.902715\pi$
$173$	−8.58579	+	8.58579i	−0.652765	+	0.652765i	0.300893	+	0.953658i	$0.402715\pi$
$174$			4.61737i			0.350042i
$175$	14.8480	+	5.66910i	1.12240	+	0.428544i
$176$		−	5.65930i		−	0.426585i
$177$	−13.9261			−1.04675
$178$	10.1878	−	10.1878i	0.763605	−	0.763605i
$179$	14.0961	−	14.0961i	1.05359	−	1.05359i	0.0551080	−	0.998480i	$-0.482450\pi$
$179$	14.0961	−	14.0961i	1.05359	−	1.05359i	0.998480	−	0.0551080i	$-0.0175503\pi$
$180$	−1.87641	−	1.21617i	−0.139860	−	0.0906479i
$181$	13.7831			1.02449			0.512245	−	0.858839i	$-0.328814\pi$
$181$	13.7831			1.02449			0.512245	+	0.858839i	$0.328814\pi$
$182$	−10.8215	+	10.8215i	−0.802140	+	0.802140i
$183$	1.58187			0.116935
$184$	−4.23021			−0.311855
$185$	13.2119	−	3.23195i	0.971359	−	0.237618i
$186$	2.81158			0.206155
$187$	42.9186			3.13852
$188$	6.04560	−	6.04560i	0.440921	−	0.440921i
$189$	−3.17868			−0.231215
$190$	−11.5480	+	2.46541i	−0.837777	+	0.178860i
$191$	18.4453	−	18.4453i	1.33466	−	1.33466i	0.433509	−	0.901149i	$-0.357275\pi$
$191$	18.4453	−	18.4453i	1.33466	−	1.33466i	0.901149	−	0.433509i	$-0.142725\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−22.9897			−1.65484			−0.827419	−	0.561585i	$-0.810192\pi$
$193$	−22.9897			−1.65484			−0.827419	+	0.561585i	$0.810192\pi$
$194$		−	2.87834i		−	0.206652i
$195$	−2.24773	−	10.5284i	−0.160963	−	0.753951i
$196$		−	3.10403i		−	0.221716i
$197$	−1.69341	+	1.69341i	−0.120650	+	0.120650i	−0.764854	−	0.644204i	$-0.777189\pi$
$197$	−1.69341	+	1.69341i	−0.120650	+	0.120650i	0.644204	+	0.764854i	$0.277189\pi$
$198$	5.65930			0.402189
$199$	−7.33672	+	7.33672i	−0.520087	+	0.520087i	−0.917597	−	0.397511i	$-0.869874\pi$
$199$	−7.33672	+	7.33672i	−0.520087	+	0.520087i	0.397511	+	0.917597i	$0.369874\pi$
$200$	2.04186	+	4.56408i	0.144382	+	0.322729i
$201$	9.77458			0.689446
$202$		−	16.0893i		−	1.13204i
$203$		−	14.6772i		−	1.03014i
$204$	−5.36251	−	5.36251i	−0.375451	−	0.375451i
$205$	4.56050	+	2.95582i	0.318519	+	0.206443i
$206$		−	11.0997i		−	0.773355i
$207$		−	4.23021i		−	0.294020i
$208$	−4.81453			−0.333828
$209$	21.1323	−	21.1323i	1.46175	−	1.46175i
$210$	5.96453	+	3.86582i	0.411592	+	0.266767i
$211$	11.9466			0.822435			0.411218	−	0.911537i	$-0.365104\pi$
$211$	11.9466			0.822435			0.411218	+	0.911537i	$0.365104\pi$
$212$	8.02058	+	8.02058i	0.550856	+	0.550856i
$213$	4.32811	−	4.32811i	0.296557	−	0.296557i
$214$	−8.64549	+	8.64549i	−0.590993	+	0.590993i
$215$	−4.06999	+	6.27954i	−0.277571	+	0.428261i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−8.93712			−0.606691
$218$	−13.7592	−	13.7592i	−0.931894	−	0.931894i
$219$			3.65991i			0.247314i
$220$	−10.6192	−	6.88266i	−0.715945	−	0.464029i
$221$		−	36.5121i		−	2.45607i
$222$	6.08010	−	0.179886i	0.408070	−	0.0120732i
$223$	11.0520	+	11.0520i	0.740100	+	0.740100i	0.972597	−	0.232497i	$-0.0746896\pi$
$223$	11.0520	+	11.0520i	0.740100	+	0.740100i	−0.232497	+	0.972597i	$0.574690\pi$
$224$	2.24767	−	2.24767i	0.150179	−	0.150179i
$225$	−4.56408	+	2.04186i	−0.304272	+	0.136124i
$226$		−	4.68689i		−	0.311768i
$227$			6.40168i			0.424894i	0.977173	+	0.212447i	$0.0681433\pi$
$227$			6.40168i			0.424894i	−0.977173	+	0.212447i	$0.931857\pi$
$228$	−5.28079			−0.349729
$229$		−	16.3225i		−	1.07862i	−0.842107	−	0.539310i	$-0.818685\pi$
$229$		−	16.3225i		−	1.07862i	0.842107	−	0.539310i	$-0.181315\pi$
$230$	−5.14465	+	7.93762i	−0.339228	+	0.523391i
$231$	−17.9891			−1.18360
$232$	3.26498	−	3.26498i	0.214356	−	0.214356i
$233$	−0.738837	+	0.738837i	−0.0484028	+	0.0484028i	−0.730894	−	0.682491i	$-0.760897\pi$
$233$	−0.738837	+	0.738837i	−0.0484028	+	0.0484028i	0.682491	+	0.730894i	$0.260897\pi$
$234$		−	4.81453i		−	0.314736i
$235$	−3.99158	−	18.6965i	−0.260382	−	1.21963i
$236$	9.84721	+	9.84721i	0.640999	+	0.640999i
$237$	−4.03499			−0.262101
$238$	17.0457	+	17.0457i	1.10491	+	1.10491i
$239$	−5.10981	−	5.10981i	−0.330526	−	0.330526i	0.522260	−	0.852786i	$-0.325089\pi$
$239$	−5.10981	−	5.10981i	−0.330526	−	0.330526i	−0.852786	+	0.522260i	$0.825089\pi$
$240$	0.466864	+	2.18679i	0.0301359	+	0.141157i
$241$	−8.22613	+	8.22613i	−0.529892	+	0.529892i	−0.920540	−	0.390648i	$-0.872251\pi$
$241$	−8.22613	+	8.22613i	−0.529892	+	0.529892i	0.390648	+	0.920540i	$0.372251\pi$
$242$	21.0276			1.35171
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−1.11855	−	1.11855i	−0.0716080	−	0.0716080i
$245$	−5.82445	−	3.77503i	−0.372110	−	0.241178i
$246$	1.71858	+	1.71858i	0.109572	+	0.109572i
$247$	−17.9778	−	17.9778i	−1.14390	−	1.14390i
$248$	−1.98809	−	1.98809i	−0.126244	−	0.126244i
$249$	−1.28163			−0.0812199
$250$	11.0474	+	1.71931i	0.698696	+	0.108739i
$251$	−10.0396	−	10.0396i	−0.633694	−	0.633694i	0.315299	−	0.948992i	$-0.397895\pi$
$251$	−10.0396	−	10.0396i	−0.633694	−	0.633694i	−0.948992	+	0.315299i	$0.897895\pi$
$252$	2.24767	+	2.24767i	0.141590	+	0.141590i
$253$		−	23.9400i		−	1.50509i
$254$	14.6086	−	14.6086i	0.916626	−	0.916626i
$255$	−16.5840	+	3.54057i	−1.03853	+	0.221719i
$256$	1.00000			0.0625000
$257$		−	15.5767i		−	0.971645i	−0.874057	−	0.485823i	$-0.838520\pi$
$257$		−	15.5767i		−	0.971645i	0.874057	−	0.485823i	$-0.161480\pi$
$258$	−2.36638	+	2.36638i	−0.147324	+	0.147324i
$259$	−19.3267	+	0.571801i	−1.20090	+	0.0355300i
$260$	−5.85528	+	9.03405i	−0.363129	+	0.560268i
$261$	3.26498	+	3.26498i	0.202097	+	0.202097i
$262$	−9.26219	−	9.26219i	−0.572220	−	0.572220i
$263$	−17.2063	+	17.2063i	−1.06099	+	1.06099i	−0.0629697	+	0.998015i	$0.520057\pi$
$263$	−17.2063	+	17.2063i	−1.06099	+	1.06099i	−0.998015	+	0.0629697i	$0.979943\pi$
$264$	−4.00173	−	4.00173i	−0.246289	−	0.246289i
$265$	24.8043	−	5.29555i	1.52372	−	0.325303i
$266$	16.7860			1.02921
$267$		−	14.4077i		−	0.881735i
$268$	−6.91167	−	6.91167i	−0.422198	−	0.422198i
$269$			16.7896i			1.02368i	0.859080	+	0.511841i	$0.171036\pi$
$269$			16.7896i			1.02368i	−0.859080	+	0.511841i	$0.828964\pi$
$270$	−2.18679	+	0.466864i	−0.133084	+	0.0284124i
$271$	−3.47058			−0.210823			−0.105411	−	0.994429i	$-0.533616\pi$
$271$	−3.47058			−0.210823			−0.105411	+	0.994429i	$0.533616\pi$
$272$			7.58373i			0.459831i
$273$			15.3039i			0.926232i
$274$	−1.63948	+	1.63948i	−0.0990449	+	0.0990449i
$275$	−25.8295	+	11.5555i	−1.55757	+	0.696823i
$276$	−2.99121	+	2.99121i	−0.180050	+	0.180050i
$277$	−5.08835			−0.305730			−0.152865	−	0.988247i	$-0.548850\pi$
$277$	−5.08835			−0.305730			−0.152865	+	0.988247i	$0.548850\pi$
$278$	17.9432			1.07616
$279$	1.98809	−	1.98809i	0.119024	−	0.119024i
$280$	−1.48401	−	6.95110i	−0.0886867	−	0.415408i
$281$	22.3585	−	22.3585i	1.33380	−	1.33380i	0.431856	−	0.901943i	$-0.357859\pi$
$281$	22.3585	−	22.3585i	1.33380	−	1.33380i	0.901943	−	0.431856i	$-0.142141\pi$
$282$		−	8.54977i		−	0.509131i
$283$		−	4.97011i		−	0.295442i	−0.989029	−	0.147721i	$-0.952806\pi$
$283$		−	4.97011i		−	0.295442i	0.989029	−	0.147721i	$-0.0471938\pi$
$284$	−6.12087			−0.363207
$285$	−6.42234	+	9.90895i	−0.380426	+	0.586956i
$286$		−	27.2468i		−	1.61114i
$287$	−5.46281	−	5.46281i	−0.322459	−	0.322459i
$288$			1.00000i			0.0589256i
$289$	−40.5129			−2.38311
$290$	−2.15568	−	10.0972i	−0.126586	−	0.592929i
$291$	−2.03529	−	2.03529i	−0.119311	−	0.119311i
$292$	2.58794	−	2.58794i	0.151448	−	0.151448i
$293$	−3.76385	−	3.76385i	−0.219886	−	0.219886i	0.588564	−	0.808450i	$-0.299693\pi$
$293$	−3.76385	−	3.76385i	−0.219886	−	0.219886i	−0.808450	+	0.588564i	$0.799693\pi$
$294$	−2.19488	−	2.19488i	−0.128008	−	0.128008i
$295$	30.4533	−	6.50157i	1.77306	−	0.378536i
$296$	−4.42648	−	4.17208i	−0.257284	−	0.242497i
$297$	4.00173	−	4.00173i	0.232204	−	0.232204i
$298$			9.20482i			0.533221i
$299$	−20.3665			−1.17782
$300$	4.67110	+	1.78347i	0.269686	+	0.102969i
$301$	7.52196	−	7.52196i	0.433559	−	0.433559i
$302$			5.59713i			0.322078i
$303$	−11.3769	−	11.3769i	−0.653584	−	0.653584i
$304$	3.73408	+	3.73408i	0.214164	+	0.214164i
$305$	−3.45922	+	0.738519i	−0.198074	+	0.0422875i
$306$	−7.58373			−0.433533
$307$	10.3413	+	10.3413i	0.590210	+	0.590210i	0.937688	−	0.347478i	$-0.112962\pi$
$307$	10.3413	+	10.3413i	0.590210	+	0.590210i	−0.347478	+	0.937688i	$0.612962\pi$
$308$	12.7202	+	12.7202i	0.724802	+	0.724802i
$309$	−7.84870	−	7.84870i	−0.446497	−	0.446497i
$310$	−6.14832	+	1.31262i	−0.349201	+	0.0745520i
$311$	2.08224	+	2.08224i	0.118073	+	0.118073i	0.763675	−	0.645601i	$-0.223393\pi$
$311$	2.08224	+	2.08224i	0.118073	+	0.118073i	−0.645601	+	0.763675i	$0.723393\pi$
$312$	−3.40439	+	3.40439i	−0.192735	+	0.192735i
$313$	−5.86237			−0.331361			−0.165681	−	0.986179i	$-0.552982\pi$
$313$	−5.86237			−0.331361			−0.165681	+	0.986179i	$0.552982\pi$
$314$	0.998661	−	0.998661i	0.0563577	−	0.0563577i
$315$	6.95110	−	1.48401i	0.391650	−	0.0836146i
$316$	2.85317	+	2.85317i	0.160503	+	0.160503i
$317$	3.30695	+	3.30695i	0.185737	+	0.185737i	0.793850	−	0.608113i	$-0.208073\pi$
$317$	3.30695	+	3.30695i	0.185737	+	0.185737i	−0.608113	+	0.793850i	$0.708073\pi$
$318$	11.3428			0.636073
$319$	18.4775	+	18.4775i	1.03454	+	1.03454i
$320$	1.21617	−	1.87641i	0.0679859	−	0.104895i
$321$			12.2266i			0.682421i
$322$	9.50811	−	9.50811i	0.529866	−	0.529866i
$323$	−28.3183	+	28.3183i	−1.57567	+	1.57567i
$324$	−1.00000			−0.0555556
$325$	9.83061	+	21.9739i	0.545304	+	1.21889i
$326$			7.74976i			0.429220i
$327$	−19.4585			−1.07606
$328$		−	2.43043i		−	0.134198i
$329$			27.1770i			1.49832i
$330$	−12.3757	+	2.64212i	−0.681258	+	0.145444i
$331$	2.03744	−	2.03744i	0.111988	−	0.111988i	−0.648892	−	0.760880i	$-0.724768\pi$
$331$	2.03744	−	2.03744i	0.111988	−	0.111988i	0.760880	+	0.648892i	$0.224768\pi$
$332$	0.906248	+	0.906248i	0.0497368	+	0.0497368i
$333$	4.17208	−	4.42648i	0.228629	−	0.242570i
$334$			19.2547i			1.05357i
$335$	−21.3749	+	4.56340i	−1.16784	+	0.249325i
$336$		−	3.17868i		−	0.173411i
$337$	−4.38679	−	4.38679i	−0.238963	−	0.238963i	0.577457	−	0.816421i	$-0.304045\pi$
$337$	−4.38679	−	4.38679i	−0.238963	−	0.238963i	−0.816421	+	0.577457i	$0.804045\pi$
$338$	−10.1797			−0.553702
$339$	−3.31414	−	3.31414i	−0.179999	−	0.179999i
$340$	14.2302	+	9.22310i	0.771742	+	0.500193i
$341$	11.2512	−	11.2512i	0.609285	−	0.609285i
$342$	−3.73408	+	3.73408i	−0.201916	+	0.201916i
$343$	−8.75685	−	8.75685i	−0.472826	−	0.472826i
$344$	3.34656			0.180435
$345$	1.97493	+	9.25056i	0.106327	+	0.498034i
$346$	8.58579	−	8.58579i	0.461575	−	0.461575i
$347$	6.84918			0.367683			0.183842	−	0.982956i	$-0.441147\pi$
$347$	6.84918			0.367683			0.183842	+	0.982956i	$0.441147\pi$
$348$		−	4.61737i		−	0.247517i
$349$			11.3003i			0.604891i	0.953167	+	0.302445i	$0.0978030\pi$
$349$			11.3003i			0.604891i	−0.953167	+	0.302445i	$0.902197\pi$
$350$	−14.8480	−	5.66910i	−0.793657	−	0.303026i
$351$	−3.40439	−	3.40439i	−0.181713	−	0.181713i
$352$			5.65930i			0.301641i
$353$		−	21.3525i		−	1.13648i	−0.822863	−	0.568240i	$-0.807625\pi$
$353$		−	21.3525i		−	1.13648i	0.822863	−	0.568240i	$-0.192375\pi$
$354$	13.9261			0.740162
$355$	−7.44401	+	11.4853i	−0.395087	+	0.609576i
$356$	−10.1878	+	10.1878i	−0.539950	+	0.539950i
$357$	24.1063			1.27584
$358$	−14.0961	+	14.0961i	−0.745000	+	0.745000i
$359$		−	5.23042i		−	0.276051i	−0.990429	−	0.138025i	$-0.955924\pi$
$359$		−	5.23042i		−	0.276051i	0.990429	−	0.138025i	$-0.0440756\pi$
$360$	1.87641	+	1.21617i	0.0988957	+	0.0640978i
$361$			8.88674i			0.467723i
$362$	−13.7831			−0.724424
$363$	14.8688	−	14.8688i	0.780408	−	0.780408i
$364$	10.8215	−	10.8215i	0.567199	−	0.567199i
$365$	−1.70868	−	8.00344i	−0.0894362	−	0.418919i
$366$	−1.58187			−0.0826858
$367$	−0.560713	+	0.560713i	−0.0292690	+	0.0292690i	−0.721590	−	0.692321i	$-0.756588\pi$
$367$	−0.560713	+	0.560713i	−0.0292690	+	0.0292690i	0.692321	+	0.721590i	$0.256588\pi$
$368$	4.23021			0.220515
$369$	2.43043			0.126523
$370$	−13.2119	+	3.23195i	−0.686854	+	0.168021i
$371$	−36.0552			−1.87189
$372$	−2.81158			−0.145774
$373$	−3.16048	+	3.16048i	−0.163643	+	0.163643i	−0.784179	−	0.620535i	$-0.786915\pi$
$373$	−3.16048	+	3.16048i	−0.163643	+	0.163643i	0.620535	+	0.784179i	$0.286915\pi$
$374$	−42.9186			−2.21927
$375$	9.02739	−	6.59592i	0.466173	−	0.340612i
$376$	−6.04560	+	6.04560i	−0.311778	+	0.311778i
$377$	15.7193	−	15.7193i	0.809586	−	0.809586i
$378$	3.17868			0.163494
$379$		−	1.59897i		−	0.0821335i	−0.999156	−	0.0410667i	$-0.986924\pi$
$379$		−	1.59897i		−	0.0821335i	0.999156	−	0.0410667i	$-0.0130756\pi$
$380$	11.5480	−	2.46541i	0.592398	−	0.126473i
$381$		−	20.6597i		−	1.05843i
$382$	−18.4453	+	18.4453i	−0.943746	+	0.943746i
$383$	1.83857			0.0939464			0.0469732	−	0.998896i	$-0.485042\pi$
$383$	1.83857			0.0939464			0.0469732	+	0.998896i	$0.485042\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	39.3384	−	8.39846i	2.00487	−	0.428025i
$386$	22.9897			1.17015
$387$			3.34656i			0.170115i
$388$			2.87834i			0.146125i
$389$	21.9756	+	21.9756i	1.11421	+	1.11421i	0.992575	+	0.121630i	$0.0388122\pi$
$389$	21.9756	+	21.9756i	1.11421	+	1.11421i	0.121630	+	0.992575i	$0.461188\pi$
$390$	2.24773	+	10.5284i	0.113818	+	0.533124i
$391$			32.0807i			1.62239i
$392$			3.10403i			0.156777i
$393$	−13.0987			−0.660743
$394$	1.69341	−	1.69341i	0.0853126	−	0.0853126i
$395$	8.82367	−	1.88379i	0.443967	−	0.0947838i
$396$	−5.65930			−0.284390
$397$	14.3901	+	14.3901i	0.722218	+	0.722218i	0.969057	−	0.246838i	$-0.0793916\pi$
$397$	14.3901	+	14.3901i	0.722218	+	0.722218i	−0.246838	+	0.969057i	$0.579392\pi$
$398$	7.33672	−	7.33672i	0.367757	−	0.367757i
$399$	11.8695	−	11.8695i	0.594217	−	0.594217i
$400$	−2.04186	−	4.56408i	−0.102093	−	0.228204i
$401$	−1.56403	−	1.56403i	−0.0781040	−	0.0781040i	0.666976	−	0.745080i	$-0.267589\pi$
$401$	−1.56403	−	1.56403i	−0.0781040	−	0.0781040i	−0.745080	+	0.666976i	$0.767589\pi$
$402$	−9.77458			−0.487512
$403$	−9.57170	−	9.57170i	−0.476800	−	0.476800i
$404$			16.0893i			0.800474i
$405$	−1.21617	+	1.87641i	−0.0604320	+	0.0932398i
$406$			14.6772i			0.728416i
$407$	23.6110	−	25.0508i	1.17036	−	1.24172i
$408$	5.36251	+	5.36251i	0.265484	+	0.265484i
$409$	6.64945	−	6.64945i	0.328794	−	0.328794i	−0.523334	−	0.852128i	$-0.675312\pi$
$409$	6.64945	−	6.64945i	0.328794	−	0.328794i	0.852128	+	0.523334i	$0.175312\pi$
$410$	−4.56050	−	2.95582i	−0.225227	−	0.145978i
$411$			2.31858i			0.114367i
$412$			11.0997i			0.546845i
$413$	−44.2665			−2.17821
$414$			4.23021i			0.207903i
$415$	2.80265	−	0.598346i	0.137577	−	0.0293716i
$416$	4.81453			0.236052
$417$	12.6877	−	12.6877i	0.621321	−	0.621321i
$418$	−21.1323	+	21.1323i	−1.03361	+	1.03361i
$419$			22.2951i			1.08919i	0.838701	+	0.544593i	$0.183316\pi$
$419$			22.2951i			1.08919i	−0.838701	+	0.544593i	$0.816684\pi$
$420$	−5.96453	−	3.86582i	−0.291039	−	0.188633i
$421$	−1.74485	−	1.74485i	−0.0850387	−	0.0850387i	0.663308	−	0.748347i	$-0.269152\pi$
$421$	−1.74485	−	1.74485i	−0.0850387	−	0.0850387i	−0.748347	+	0.663308i	$0.769152\pi$
$422$	−11.9466			−0.581549
$423$	−6.04560	−	6.04560i	−0.293947	−	0.293947i
$424$	−8.02058	−	8.02058i	−0.389514	−	0.389514i
$425$	34.6127	−	15.4849i	1.67896	−	0.751130i
$426$	−4.32811	+	4.32811i	−0.209697	+	0.209697i
$427$	5.02827			0.243335
$428$	8.64549	−	8.64549i	0.417896	−	0.417896i
$429$	−19.2664	−	19.2664i	−0.930192	−	0.930192i
$430$	4.06999	−	6.27954i	0.196272	−	0.302826i
$431$	−23.7856	−	23.7856i	−1.14571	−	1.14571i	−0.987387	−	0.158327i	$-0.949390\pi$
$431$	−23.7856	−	23.7856i	−1.14571	−	1.14571i	−0.158327	−	0.987387i	$-0.550610\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−9.00285	−	9.00285i	−0.432649	−	0.432649i	0.456879	−	0.889529i	$-0.348967\pi$
$433$	−9.00285	−	9.00285i	−0.432649	−	0.432649i	−0.889529	+	0.456879i	$0.848967\pi$
$434$	8.93712			0.428995
$435$	−8.66411	−	5.61551i	−0.415412	−	0.269243i
$436$	13.7592	+	13.7592i	0.658948	+	0.658948i
$437$	15.7959	+	15.7959i	0.755622	+	0.755622i
$438$		−	3.65991i		−	0.174877i
$439$	4.79636	−	4.79636i	0.228918	−	0.228918i	−0.583323	−	0.812240i	$-0.698248\pi$
$439$	4.79636	−	4.79636i	0.228918	−	0.228918i	0.812240	+	0.583323i	$0.198248\pi$
$440$	10.6192	+	6.88266i	0.506250	+	0.328118i
$441$	−3.10403			−0.147811
$442$			36.5121i			1.73670i
$443$	−7.85980	+	7.85980i	−0.373430	+	0.373430i	−0.868725	−	0.495295i	$-0.835060\pi$
$443$	−7.85980	+	7.85980i	−0.373430	+	0.373430i	0.495295	+	0.868725i	$0.335060\pi$
$444$	−6.08010	+	0.179886i	−0.288549	+	0.00853702i
$445$	6.72642	+	31.5065i	0.318863	+	1.49355i
$446$	−11.0520	−	11.0520i	−0.523330	−	0.523330i
$447$	6.50879	+	6.50879i	0.307855	+	0.307855i
$448$	−2.24767	+	2.24767i	−0.106192	+	0.106192i
$449$	−16.4657	−	16.4657i	−0.777066	−	0.777066i	0.202265	−	0.979331i	$-0.435170\pi$
$449$	−16.4657	−	16.4657i	−0.777066	−	0.777066i	−0.979331	+	0.202265i	$0.935170\pi$
$450$	4.56408	−	2.04186i	0.215153	−	0.0962543i
$451$	13.7545			0.647676
$452$			4.68689i			0.220453i
$453$	3.95777	+	3.95777i	0.185952	+	0.185952i
$454$		−	6.40168i		−	0.300446i
$455$	−7.14482	−	33.4663i	−0.334954	−	1.56892i
$456$	5.28079			0.247296
$457$			5.42876i			0.253947i	0.991906	+	0.126973i	$0.0405263\pi$
$457$			5.42876i			0.253947i	−0.991906	+	0.126973i	$0.959474\pi$
$458$			16.3225i			0.762699i
$459$	−5.36251	+	5.36251i	−0.250300	+	0.250300i
$460$	5.14465	−	7.93762i	0.239871	−	0.370094i
$461$	12.8604	−	12.8604i	0.598967	−	0.598967i	−0.341071	−	0.940038i	$-0.610790\pi$
$461$	12.8604	−	12.8604i	0.598967	−	0.598967i	0.940038	+	0.341071i	$0.110790\pi$
$462$	17.9891			0.836929
$463$	36.1282			1.67902			0.839509	−	0.543345i	$-0.182843\pi$
$463$	36.1282			1.67902			0.839509	+	0.543345i	$0.182843\pi$
$464$	−3.26498	+	3.26498i	−0.151573	+	0.151573i
$465$	−3.41936	+	5.27569i	−0.158569	+	0.244654i
$466$	0.738837	−	0.738837i	0.0342260	−	0.0342260i
$467$		−	4.96873i		−	0.229925i	−0.993370	−	0.114963i	$-0.963325\pi$
$467$		−	4.96873i		−	0.229925i	0.993370	−	0.114963i	$-0.0366748\pi$
$468$			4.81453i			0.222552i
$469$	31.0703			1.43469
$470$	3.99158	+	18.6965i	0.184118	+	0.862407i
$471$		−	1.41232i		−	0.0650763i
$472$	−9.84721	−	9.84721i	−0.453255	−	0.453255i
$473$			18.9392i			0.870825i
$474$	4.03499			0.185333
$475$	9.41815	−	24.6671i	0.432135	−	1.13181i
$476$	−17.0457	−	17.0457i	−0.781289	−	0.781289i
$477$	8.02058	−	8.02058i	0.367237	−	0.367237i
$478$	5.10981	+	5.10981i	0.233717	+	0.233717i
$479$	21.0873	+	21.0873i	0.963504	+	0.963504i	0.999357	−	0.0358527i	$-0.0114147\pi$
$479$	21.0873	+	21.0873i	0.963504	+	0.963504i	−0.0358527	+	0.999357i	$0.511415\pi$
$480$	−0.466864	−	2.18679i	−0.0213093	−	0.0998127i
$481$	−21.3114	−	20.0866i	−0.971717	−	0.915871i
$482$	8.22613	−	8.22613i	0.374690	−	0.374690i
$483$		−	13.4465i		−	0.611837i
$484$	−21.0276			−0.955801
$485$	5.40095	+	3.50054i	0.245245	+	0.158952i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$			10.6041i			0.480519i	0.970709	+	0.240259i	$0.0772325\pi$
$487$			10.6041i			0.480519i	−0.970709	+	0.240259i	$0.922767\pi$
$488$	1.11855	+	1.11855i	0.0506345	+	0.0506345i
$489$	5.47991	+	5.47991i	0.247810	+	0.247810i
$490$	5.82445	+	3.77503i	0.263122	+	0.170538i
$491$	2.33716			0.105475			0.0527373	−	0.998608i	$-0.483205\pi$
$491$	2.33716			0.105475			0.0527373	+	0.998608i	$0.483205\pi$
$492$	−1.71858	−	1.71858i	−0.0774794	−	0.0774794i
$493$	−24.7607	−	24.7607i	−1.11517	−	1.11517i
$494$	17.9778	+	17.9778i	0.808862	+	0.808862i
$495$	−6.88266	+	10.6192i	−0.309353	+	0.477297i
$496$	1.98809	+	1.98809i	0.0892677	+	0.0892677i
$497$	13.7577	−	13.7577i	0.617116	−	0.617116i
$498$	1.28163			0.0574312
$499$	−15.9396	+	15.9396i	−0.713555	+	0.713555i	−0.967277	−	0.253723i	$-0.918345\pi$
$499$	−15.9396	+	15.9396i	−0.713555	+	0.713555i	0.253723	+	0.967277i	$0.418345\pi$
$500$	−11.0474	−	1.71931i	−0.494053	−	0.0768899i
$501$	13.6151	+	13.6151i	0.608278	+	0.608278i
$502$	10.0396	+	10.0396i	0.448089	+	0.448089i
$503$	18.1285			0.808309			0.404155	−	0.914691i	$-0.367566\pi$
$503$	18.1285			0.808309			0.404155	+	0.914691i	$0.367566\pi$
$504$	−2.24767	−	2.24767i	−0.100119	−	0.100119i
$505$	30.1903	+	19.5674i	1.34345	+	0.870736i
$506$			23.9400i			1.06426i
$507$	−7.19813	+	7.19813i	−0.319680	+	0.319680i
$508$	−14.6086	+	14.6086i	−0.648152	+	0.648152i
$509$	14.6649			0.650010			0.325005	−	0.945712i	$-0.394634\pi$
$509$	14.6649			0.650010			0.325005	+	0.945712i	$0.394634\pi$
$510$	16.5840	−	3.54057i	0.734352	−	0.156779i
$511$			11.6337i			0.514644i
$512$	−1.00000			−0.0441942
$513$			5.28079i			0.233153i
$514$			15.5767i			0.687057i
$515$	20.8277	+	13.4992i	0.917778	+	0.594844i
$516$	2.36638	−	2.36638i	0.104174	−	0.104174i
$517$	−34.2138	−	34.2138i	−1.50472	−	1.50472i
$518$	19.3267	−	0.571801i	0.849167	−	0.0251235i
$519$		−	12.1421i		−	0.532981i
$520$	5.85528	−	9.03405i	0.256771	−	0.396169i
$521$			13.9917i			0.612988i	0.951873	+	0.306494i	$0.0991560\pi$
$521$			13.9917i			0.612988i	−0.951873	+	0.306494i	$0.900844\pi$
$522$	−3.26498	−	3.26498i	−0.142904	−	0.142904i
$523$	16.6140			0.726479			0.363239	−	0.931696i	$-0.381671\pi$
$523$	16.6140			0.726479			0.363239	+	0.931696i	$0.381671\pi$
$524$	9.26219	+	9.26219i	0.404621	+	0.404621i
$525$	−14.5078	+	6.49044i	−0.633170	+	0.283266i
$526$	17.2063	−	17.2063i	0.750230	−	0.750230i
$527$	−15.0771	+	15.0771i	−0.656769	+	0.656769i
$528$	4.00173	+	4.00173i	0.174153	+	0.174153i
$529$	−5.10534			−0.221971
$530$	−24.8043	+	5.29555i	−1.07743	+	0.230024i
$531$	9.84721	−	9.84721i	0.427332	−	0.427332i
$532$	−16.7860			−0.727764
$533$		−	11.7014i		−	0.506844i
$534$			14.4077i			0.623481i
$535$	−5.70814	−	26.7369i	−0.246784	−	1.15594i
$536$	6.91167	+	6.91167i	0.298539	+	0.298539i
$537$			19.9348i			0.860251i
$538$		−	16.7896i		−	0.723853i
$539$	−17.5666			−0.756648
$540$	2.18679	−	0.466864i	0.0941043	−	0.0200906i
$541$	−15.0297	+	15.0297i	−0.646177	+	0.646177i	−0.952067	−	0.305890i	$-0.901046\pi$
$541$	−15.0297	+	15.0297i	−0.646177	+	0.646177i	0.305890	+	0.952067i	$0.401046\pi$
$542$	3.47058			0.149074
$543$	−9.74613	+	9.74613i	−0.418246	+	0.418246i
$544$		−	7.58373i		−	0.325150i
$545$	42.5516	−	9.08447i	1.82271	−	0.389136i
$546$		−	15.3039i		−	0.654945i
$547$	−1.60901			−0.0687964			−0.0343982	−	0.999408i	$-0.510951\pi$
$547$	−1.60901			−0.0687964			−0.0343982	+	0.999408i	$0.510951\pi$
$548$	1.63948	−	1.63948i	0.0700353	−	0.0700353i
$549$	−1.11855	+	1.11855i	−0.0477387	+	0.0477387i
$550$	25.8295	−	11.5555i	1.10137	−	0.492728i
$551$	−24.3834			−1.03877
$552$	2.99121	−	2.99121i	0.127314	−	0.127314i
$553$	−12.8260			−0.545416
$554$	5.08835			0.216183
$555$	−7.05689	+	11.6276i	−0.299548	+	0.493563i
$556$	−17.9432			−0.760959
$557$	−13.8846			−0.588309			−0.294155	−	0.955758i	$-0.595038\pi$
$557$	−13.8846			−0.588309			−0.294155	+	0.955758i	$0.595038\pi$
$558$	−1.98809	+	1.98809i	−0.0841624	+	0.0841624i
$559$	16.1121			0.681470
$560$	1.48401	+	6.95110i	0.0627109	+	0.293738i
$561$	−30.3480	+	30.3480i	−1.28129	+	1.28129i
$562$	−22.3585	+	22.3585i	−0.943138	+	0.943138i
$563$	−36.2994			−1.52984			−0.764919	−	0.644126i	$-0.777221\pi$
$563$	−36.2994			−1.52984			−0.764919	+	0.644126i	$0.777221\pi$
$564$			8.54977i			0.360010i
$565$	8.79456	+	5.70006i	0.369990	+	0.239803i
$566$			4.97011i			0.208909i
$567$	2.24767	−	2.24767i	0.0943932	−	0.0943932i
$568$	6.12087			0.256826
$569$	4.09043	−	4.09043i	0.171480	−	0.171480i	−0.616149	−	0.787629i	$-0.711308\pi$
$569$	4.09043	−	4.09043i	0.171480	−	0.171480i	0.787629	+	0.616149i	$0.211308\pi$
$570$	6.42234	−	9.90895i	0.269002	−	0.415040i
$571$	9.17017			0.383760			0.191880	−	0.981418i	$-0.438542\pi$
$571$	9.17017			0.383760			0.191880	+	0.981418i	$0.438542\pi$
$572$			27.2468i			1.13925i
$573$			26.0857i			1.08974i
$574$	5.46281	+	5.46281i	0.228013	+	0.228013i
$575$	−8.63750	−	19.3070i	−0.360209	−	0.805157i
$576$		−	1.00000i		−	0.0416667i
$577$			35.0406i			1.45876i	0.684108	+	0.729381i	$0.260192\pi$
$577$			35.0406i			1.45876i	−0.684108	+	0.729381i	$0.739808\pi$
$578$	40.5129			1.68512
$579$	16.2562	−	16.2562i	0.675585	−	0.675585i
$580$	2.15568	+	10.0972i	0.0895099	+	0.419264i
$581$	−4.07389			−0.169014
$582$	2.03529	+	2.03529i	0.0843655	+	0.0843655i
$583$	45.3908	−	45.3908i	1.87990	−	1.87990i
$584$	−2.58794	+	2.58794i	−0.107090	+	0.107090i
$585$	9.03405	+	5.85528i	0.373512	+	0.242086i
$586$	3.76385	+	3.76385i	0.155483	+	0.155483i
$587$	33.5312			1.38398			0.691990	−	0.721907i	$-0.256734\pi$
$587$	33.5312			1.38398			0.691990	+	0.721907i	$0.256734\pi$
$588$	2.19488	+	2.19488i	0.0905153	+	0.0905153i
$589$			14.8474i			0.611775i
$590$	−30.4533	+	6.50157i	−1.25374	+	0.267665i
$591$		−	2.39484i		−	0.0985106i
$592$	4.42648	+	4.17208i	0.181927	+	0.171472i
$593$	1.10793	+	1.10793i	0.0454971	+	0.0454971i	0.729489	−	0.683992i	$-0.239758\pi$
$593$	1.10793	+	1.10793i	0.0454971	+	0.0454971i	−0.683992	+	0.729489i	$0.739758\pi$
$594$	−4.00173	+	4.00173i	−0.164193	+	0.164193i
$595$	−52.7153	+	11.2543i	−2.16112	+	0.461383i
$596$		−	9.20482i		−	0.377044i
$597$		−	10.3757i		−	0.424649i
$598$	20.3665			0.832846
$599$			0.823976i			0.0336668i	0.999858	+	0.0168334i	$0.00535848\pi$
$599$			0.823976i			0.0336668i	−0.999858	+	0.0168334i	$0.994642\pi$
$600$	−4.67110	−	1.78347i	−0.190697	−	0.0728100i
$601$	7.88760			0.321742			0.160871	−	0.986975i	$-0.448570\pi$
$601$	7.88760			0.321742			0.160871	+	0.986975i	$0.448570\pi$
$602$	−7.52196	+	7.52196i	−0.306572	+	0.306572i
$603$	−6.91167	+	6.91167i	−0.281465	+	0.281465i
$604$		−	5.59713i		−	0.227744i
$605$	−25.5732	+	39.4565i	−1.03970	+	1.60414i
$606$	11.3769	+	11.3769i	0.462154	+	0.462154i
$607$	1.34105			0.0544316			0.0272158	−	0.999630i	$-0.491336\pi$
$607$	1.34105			0.0544316			0.0272158	+	0.999630i	$0.491336\pi$
$608$	−3.73408	−	3.73408i	−0.151437	−	0.151437i
$609$	10.3783	+	10.3783i	0.420551	+	0.420551i
$610$	3.45922	−	0.738519i	0.140060	−	0.0299018i
$611$	−29.1067	+	29.1067i	−1.17753	+	1.17753i
$612$	7.58373			0.306554
$613$	−3.50859	+	3.50859i	−0.141711	+	0.141711i	−0.774403	−	0.632693i	$-0.781950\pi$
$613$	−3.50859	+	3.50859i	−0.141711	+	0.141711i	0.632693	+	0.774403i	$0.281950\pi$
$614$	−10.3413	−	10.3413i	−0.417342	−	0.417342i
$615$	−5.31484	+	1.13468i	−0.214315	+	0.0457548i
$616$	−12.7202	−	12.7202i	−0.512512	−	0.512512i
$617$	−1.91217	−	1.91217i	−0.0769810	−	0.0769810i	0.667568	−	0.744549i	$-0.267335\pi$
$617$	−1.91217	−	1.91217i	−0.0769810	−	0.0769810i	−0.744549	+	0.667568i	$0.767335\pi$
$618$	7.84870	+	7.84870i	0.315721	+	0.315721i
$619$	−19.7786			−0.794968			−0.397484	−	0.917609i	$-0.630117\pi$
$619$	−19.7786			−0.794968			−0.397484	+	0.917609i	$0.630117\pi$
$620$	6.14832	−	1.31262i	0.246923	−	0.0527162i
$621$	2.99121	+	2.99121i	0.120033	+	0.120033i
$622$	−2.08224	−	2.08224i	−0.0834904	−	0.0834904i
$623$		−	45.7974i		−	1.83484i
$624$	3.40439	−	3.40439i	0.136285	−	0.136285i
$625$	−16.6616	+	18.6384i	−0.666464	+	0.745538i
$626$	5.86237			0.234308
$627$			29.8855i			1.19351i
$628$	−0.998661	+	0.998661i	−0.0398509	+	0.0398509i
$629$	−31.6399	+	33.5692i	−1.26157	+	1.33849i
$630$	−6.95110	+	1.48401i	−0.276939	+	0.0591244i
$631$	−2.64808	−	2.64808i	−0.105418	−	0.105418i	0.652430	−	0.757849i	$-0.273749\pi$
$631$	−2.64808	−	2.64808i	−0.105418	−	0.105418i	−0.757849	+	0.652430i	$0.773749\pi$
$632$	−2.85317	−	2.85317i	−0.113493	−	0.113493i
$633$	−8.44749	+	8.44749i	−0.335758	+	0.335758i
$634$	−3.30695	−	3.30695i	−0.131336	−	0.131336i
$635$	9.64526	+	45.1783i	0.382760	+	1.79285i
$636$	−11.3428			−0.449772
$637$			14.9444i			0.592120i
$638$	−18.4775	−	18.4775i	−0.731530	−	0.731530i
$639$			6.12087i			0.242138i
$640$	−1.21617	+	1.87641i	−0.0480733	+	0.0741718i
$641$	−25.9245			−1.02395			−0.511977	−	0.858999i	$-0.671087\pi$
$641$	−25.9245			−1.02395			−0.511977	+	0.858999i	$0.671087\pi$
$642$		−	12.2266i		−	0.482544i
$643$		−	6.75346i		−	0.266331i	−0.991094	−	0.133165i	$-0.957486\pi$
$643$		−	6.75346i		−	0.266331i	0.991094	−	0.133165i	$-0.0425141\pi$
$644$	−9.50811	+	9.50811i	−0.374672	+	0.374672i
$645$	−1.56239	−	7.31822i	−0.0615190	−	0.288155i
$646$	28.3183	−	28.3183i	1.11417	−	1.11417i
$647$	17.0199			0.669122			0.334561	−	0.942374i	$-0.391412\pi$
$647$	17.0199			0.669122			0.334561	+	0.942374i	$0.391412\pi$
$648$	1.00000			0.0392837
$649$	55.7283	−	55.7283i	2.18753	−	2.18753i
$650$	−9.83061	−	21.9739i	−0.385588	−	0.861886i
$651$	6.31950	−	6.31950i	0.247681	−	0.247681i
$652$		−	7.74976i		−	0.303504i
$653$			2.21356i			0.0866234i	0.999062	+	0.0433117i	$0.0137909\pi$
$653$			2.21356i			0.0866234i	−0.999062	+	0.0433117i	$0.986209\pi$
$654$	19.4585			0.760888
$655$	28.6441	−	6.11531i	1.11922	−	0.238945i
$656$			2.43043i			0.0948925i
$657$	−2.58794	−	2.58794i	−0.100965	−	0.100965i
$658$		−	27.1770i		−	1.05947i
$659$	10.5454			0.410790			0.205395	−	0.978679i	$-0.434152\pi$
$659$	10.5454			0.410790			0.205395	+	0.978679i	$0.434152\pi$
$660$	12.3757	−	2.64212i	0.481722	−	0.102844i
$661$	26.5280	+	26.5280i	1.03182	+	1.03182i	0.999477	+	0.0323414i	$0.0102964\pi$
$661$	26.5280	+	26.5280i	1.03182	+	1.03182i	0.0323414	+	0.999477i	$0.489704\pi$
$662$	−2.03744	+	2.03744i	−0.0791872	+	0.0791872i
$663$	25.8179	+	25.8179i	1.00269	+	1.00269i
$664$	−0.906248	−	0.906248i	−0.0351693	−	0.0351693i
$665$	−20.4146	+	31.4974i	−0.791643	+	1.22142i
$666$	−4.17208	+	4.42648i	−0.161665	+	0.171523i
$667$	−13.8115	+	13.8115i	−0.534784	+	0.534784i
$668$		−	19.2547i		−	0.744985i
$669$	−15.6300			−0.604289
$670$	21.3749	−	4.56340i	0.825786	−	0.176299i
$671$	−6.33022	+	6.33022i	−0.244375	+	0.244375i
$672$			3.17868i			0.122620i
$673$	−18.5100	−	18.5100i	−0.713507	−	0.713507i	0.253760	−	0.967267i	$-0.418333\pi$
$673$	−18.5100	−	18.5100i	−0.713507	−	0.713507i	−0.967267	+	0.253760i	$0.918333\pi$
$674$	4.38679	+	4.38679i	0.168973	+	0.168973i
$675$	1.78347	−	4.67110i	0.0686460	−	0.179791i
$676$	10.1797			0.391527
$677$	−19.4458	−	19.4458i	−0.747364	−	0.747364i	0.226620	−	0.973983i	$-0.427233\pi$
$677$	−19.4458	−	19.4458i	−0.747364	−	0.747364i	−0.973983	+	0.226620i	$0.927233\pi$
$678$	3.31414	+	3.31414i	0.127279	+	0.127279i
$679$	−6.46955	−	6.46955i	−0.248278	−	0.248278i
$680$	−14.2302	−	9.22310i	−0.545704	−	0.353690i
$681$	−4.52667	−	4.52667i	−0.173462	−	0.173462i
$682$	−11.2512	+	11.2512i	−0.430830	+	0.430830i
$683$	45.5661			1.74354			0.871770	−	0.489916i	$-0.162972\pi$
$683$	45.5661			1.74354			0.871770	+	0.489916i	$0.162972\pi$
$684$	3.73408	−	3.73408i	0.142776	−	0.142776i
$685$	−1.08246	−	5.07024i	−0.0413587	−	0.193724i
$686$	8.75685	+	8.75685i	0.334338	+	0.334338i
$687$	11.5417	+	11.5417i	0.440345	+	0.440345i
$688$	−3.34656			−0.127587
$689$	−38.6153	−	38.6153i	−1.47113	−	1.47113i
$690$	−1.97493	−	9.25056i	−0.0751843	−	0.352163i
$691$		−	14.6674i		−	0.557973i	−0.960295	−	0.278986i	$-0.910002\pi$
$691$		−	14.6674i		−	0.557973i	0.960295	−	0.278986i	$-0.0899984\pi$
$692$	−8.58579	+	8.58579i	−0.326383	+	0.326383i
$693$	12.7202	−	12.7202i	0.483201	−	0.483201i
$694$	−6.84918			−0.259991
$695$	−21.8219	+	33.6688i	−0.827753	+	1.27713i
$696$			4.61737i			0.175021i
$697$	−18.4317			−0.698152
$698$		−	11.3003i		−	0.427722i
$699$		−	1.04487i		−	0.0395207i
$700$	14.8480	+	5.66910i	0.561200	+	0.214272i
$701$	−2.72887	+	2.72887i	−0.103068	+	0.103068i	−0.756760	−	0.653692i	$-0.773219\pi$
$701$	−2.72887	+	2.72887i	−0.103068	+	0.103068i	0.653692	+	0.756760i	$0.273219\pi$
$702$	3.40439	+	3.40439i	0.128490	+	0.128490i
$703$	0.949941	+	32.1077i	0.0358277	+	1.21097i
$704$		−	5.65930i		−	0.213293i
$705$	16.0429	+	10.3980i	0.604211	+	0.391610i
$706$			21.3525i			0.803612i
$707$	−36.1635	−	36.1635i	−1.36007	−	1.36007i
$708$	−13.9261			−0.523373
$709$	1.20334	+	1.20334i	0.0451926	+	0.0451926i	0.729342	−	0.684149i	$-0.239826\pi$
$709$	1.20334	+	1.20334i	0.0451926	+	0.0451926i	−0.684149	+	0.729342i	$0.739826\pi$
$710$	7.44401	−	11.4853i	0.279369	−	0.431035i
$711$	2.85317	−	2.85317i	0.107002	−	0.107002i
$712$	10.1878	−	10.1878i	0.381803	−	0.381803i
$713$	8.41002	+	8.41002i	0.314958	+	0.314958i
$714$	−24.1063			−0.902155
$715$	51.1264	+	33.1368i	1.91202	+	1.23925i
$716$	14.0961	−	14.0961i	0.526794	−	0.526794i
$717$	7.22636			0.269873
$718$			5.23042i			0.195197i
$719$		−	34.8068i		−	1.29807i	−0.760757	−	0.649037i	$-0.775172\pi$
$719$		−	34.8068i		−	1.29807i	0.760757	−	0.649037i	$-0.224828\pi$
$720$	−1.87641	−	1.21617i	−0.0699298	−	0.0453240i
$721$	−24.9485	−	24.9485i	−0.929131	−	0.929131i
$722$		−	8.88674i		−	0.330730i
$723$		−	11.6335i		−	0.432655i
$724$	13.7831			0.512245
$725$	21.5682	+	8.23497i	0.801024	+	0.305839i
$726$	−14.8688	+	14.8688i	−0.551832	+	0.551832i
$727$	−29.0229			−1.07640			−0.538200	−	0.842817i	$-0.680895\pi$
$727$	−29.0229			−1.07640			−0.538200	+	0.842817i	$0.680895\pi$
$728$	−10.8215	+	10.8215i	−0.401070	+	0.401070i
$729$			1.00000i			0.0370370i
$730$	1.70868	+	8.00344i	0.0632410	+	0.296220i
$731$		−	25.3794i		−	0.938692i
$732$	1.58187			0.0584677
$733$	6.55654	−	6.55654i	0.242171	−	0.242171i	−0.575577	−	0.817748i	$-0.695222\pi$
$733$	6.55654	−	6.55654i	0.242171	−	0.242171i	0.817748	+	0.575577i	$0.195222\pi$
$734$	0.560713	−	0.560713i	0.0206963	−	0.0206963i
$735$	6.78785	−	1.44916i	0.250374	−	0.0534530i
$736$	−4.23021			−0.155928
$737$	−39.1152	+	39.1152i	−1.44083	+	1.44083i
$738$	−2.43043			−0.0894655
$739$	3.57785			0.131613			0.0658067	−	0.997832i	$-0.479038\pi$
$739$	3.57785			0.131613			0.0658067	+	0.997832i	$0.479038\pi$
$740$	13.2119	−	3.23195i	0.485679	−	0.118809i
$741$	25.4245			0.933993
$742$	36.0552			1.32363
$743$	29.2655	−	29.2655i	1.07365	−	1.07365i	0.0765832	−	0.997063i	$-0.475599\pi$
$743$	29.2655	−	29.2655i	1.07365	−	1.07365i	0.997063	−	0.0765832i	$-0.0244011\pi$
$744$	2.81158			0.103077
$745$	−17.2720	−	11.1946i	−0.632799	−	0.410139i
$746$	3.16048	−	3.16048i	0.115713	−	0.115713i
$747$	0.906248	−	0.906248i	0.0331579	−	0.0331579i
$748$	42.9186			1.56926
$749$			38.8644i			1.42007i
$750$	−9.02739	+	6.59592i	−0.329634	+	0.240849i
$751$			17.5101i			0.638951i	0.947595	+	0.319476i	$0.103507\pi$
$751$			17.5101i			0.638951i	−0.947595	+	0.319476i	$0.896493\pi$
$752$	6.04560	−	6.04560i	0.220460	−	0.220460i
$753$	14.1981			0.517409
$754$	−15.7193	+	15.7193i	−0.572464	+	0.572464i
$755$	−10.5025	−	6.80705i	−0.382226	−	0.247734i
$756$	−3.17868			−0.115608
$757$			15.4393i			0.561153i	0.959832	+	0.280576i	$0.0905256\pi$
$757$			15.4393i			0.561153i	−0.959832	+	0.280576i	$0.909474\pi$
$758$			1.59897i			0.0580771i
$759$	16.9281	+	16.9281i	0.614452	+	0.614452i
$760$	−11.5480	+	2.46541i	−0.418889	+	0.0894298i
$761$			19.6274i			0.711492i	0.934583	+	0.355746i	$0.115773\pi$
$761$			19.6274i			0.711492i	−0.934583	+	0.355746i	$0.884227\pi$
$762$			20.6597i			0.748422i
$763$	−61.8524			−2.23921
$764$	18.4453	−	18.4453i	0.667329	−	0.667329i
$765$	9.22310	−	14.2302i	0.333462	−	0.514495i
$766$	−1.83857			−0.0664301
$767$	−47.4097	−	47.4097i	−1.71186	−	1.71186i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−38.3252	+	38.3252i	−1.38204	+	1.38204i	−0.541058	+	0.840985i	$0.681976\pi$
$769$	−38.3252	+	38.3252i	−1.38204	+	1.38204i	−0.840985	+	0.541058i	$0.818024\pi$
$770$	−39.3384	+	8.39846i	−1.41766	+	0.302660i
$771$	11.0144	+	11.0144i	0.396672	+	0.396672i
$772$	−22.9897			−0.827419
$773$	13.6080	+	13.6080i	0.489445	+	0.489445i	0.908131	−	0.418686i	$-0.137509\pi$
$773$	13.6080	+	13.6080i	0.489445	+	0.489445i	−0.418686	+	0.908131i	$0.637509\pi$
$774$		−	3.34656i		−	0.120290i
$775$	5.01438	−	13.1332i	0.180122	−	0.471758i
$776$		−	2.87834i		−	0.103326i
$777$	13.2617	−	14.0704i	0.475762	−	0.504772i
$778$	−21.9756	−	21.9756i	−0.787862	−	0.787862i
$779$	−9.07544	+	9.07544i	−0.325161	+	0.325161i
$780$	−2.24773	−	10.5284i	−0.0804816	−	0.376975i
$781$			34.6398i			1.23951i
$782$		−	32.0807i		−	1.14721i
$783$	−4.61737			−0.165011
$784$		−	3.10403i		−	0.110858i
$785$	0.659361	+	3.08844i	0.0235336	+	0.110231i
$786$	13.0987			0.467216
$787$	0.848326	−	0.848326i	0.0302396	−	0.0302396i	−0.691825	−	0.722065i	$-0.743193\pi$
$787$	0.848326	−	0.848326i	0.0302396	−	0.0302396i	0.722065	+	0.691825i	$0.243193\pi$
$788$	−1.69341	+	1.69341i	−0.0603251	+	0.0603251i
$789$		−	24.3334i		−	0.866291i
$790$	−8.82367	+	1.88379i	−0.313932	+	0.0670223i
$791$	−10.5346	−	10.5346i	−0.374567	−	0.374567i
$792$	5.65930			0.201094
$793$	5.38530	+	5.38530i	0.191238	+	0.191238i
$794$	−14.3901	−	14.3901i	−0.510686	−	0.510686i
$795$	−13.7948	+	21.2838i	−0.489251	+	0.754859i
$796$	−7.33672	+	7.33672i	−0.260043	+	0.260043i
$797$	−54.9817			−1.94755			−0.973776	−	0.227510i	$-0.926942\pi$
$797$	−54.9817			−1.94755			−0.973776	+	0.227510i	$0.926942\pi$
$798$	−11.8695	+	11.8695i	−0.420175	+	0.420175i
$799$	45.8482	+	45.8482i	1.62199	+	1.62199i
$800$	2.04186	+	4.56408i	0.0721908	+	0.161364i
$801$	10.1878	+	10.1878i	0.359967	+	0.359967i
$802$	1.56403	+	1.56403i	0.0552279	+	0.0552279i
$803$	−14.6459	−	14.6459i	−0.516844	−	0.516844i
$804$	9.77458			0.344723
$805$	6.27768	+	29.4046i	0.221259	+	1.03638i
$806$	9.57170	+	9.57170i	0.337149	+	0.337149i
$807$	−11.8721	−	11.8721i	−0.417916	−	0.417916i
$808$		−	16.0893i		−	0.566021i
$809$	4.86721	−	4.86721i	0.171122	−	0.171122i	−0.616350	−	0.787472i	$-0.711389\pi$
$809$	4.86721	−	4.86721i	0.171122	−	0.171122i	0.787472	+	0.616350i	$0.211389\pi$
$810$	1.21617	−	1.87641i	0.0427318	−	0.0659305i
$811$	−13.3290			−0.468044			−0.234022	−	0.972231i	$-0.575189\pi$
$811$	−13.3290			−0.468044			−0.234022	+	0.972231i	$0.575189\pi$
$812$		−	14.6772i		−	0.515068i
$813$	2.45407	−	2.45407i	0.0860680	−	0.0860680i
$814$	−23.6110	+	25.0508i	−0.827567	+	0.878029i
$815$	−14.5418	−	9.42503i	−0.509376	−	0.330144i
$816$	−5.36251	−	5.36251i	−0.187725	−	0.187725i
$817$	−12.4963	−	12.4963i	−0.437192	−	0.437192i
$818$	−6.64945	+	6.64945i	−0.232493	+	0.232493i
$819$	−10.8215	−	10.8215i	−0.378133	−	0.378133i
$820$	4.56050	+	2.95582i	0.159260	+	0.103222i
$821$	43.5087			1.51846			0.759232	−	0.650820i	$-0.225575\pi$
$821$	43.5087			1.51846			0.759232	+	0.650820i	$0.225575\pi$
$822$		−	2.31858i		−	0.0808698i
$823$	−0.673165	−	0.673165i	−0.0234651	−	0.0234651i	0.695277	−	0.718742i	$-0.255282\pi$
$823$	−0.673165	−	0.673165i	−0.0234651	−	0.0234651i	−0.718742	+	0.695277i	$0.755282\pi$
$824$		−	11.0997i		−	0.386677i
$825$	10.0932	−	26.4352i	0.351400	−	0.920354i
$826$	44.2665			1.54023
$827$		−	33.1455i		−	1.15258i	−0.817245	−	0.576290i	$-0.804500\pi$
$827$		−	33.1455i		−	1.15258i	0.817245	−	0.576290i	$-0.195500\pi$
$828$		−	4.23021i		−	0.147010i
$829$	17.7173	−	17.7173i	0.615349	−	0.615349i	−0.328986	−	0.944335i	$-0.606707\pi$
$829$	17.7173	−	17.7173i	0.615349	−	0.615349i	0.944335	+	0.328986i	$0.106707\pi$
$830$	−2.80265	+	0.598346i	−0.0972814	+	0.0207689i
$831$	3.59801	−	3.59801i	0.124814	−	0.124814i
$832$	−4.81453			−0.166914
$833$	23.5401			0.815617
$834$	−12.6877	+	12.6877i	−0.439340	+	0.439340i
$835$	−36.1297	−	23.4169i	−1.25032	−	0.810376i
$836$	21.1323	−	21.1323i	0.730875	−	0.730875i
$837$			2.81158i			0.0971824i
$838$		−	22.2951i		−	0.770170i
$839$	40.9132			1.41248			0.706240	−	0.707973i	$-0.250390\pi$
$839$	40.9132			1.41248			0.706240	+	0.707973i	$0.250390\pi$
$840$	5.96453	+	3.86582i	0.205796	+	0.133383i
$841$			7.67986i			0.264823i
$842$	1.74485	+	1.74485i	0.0601315	+	0.0601315i
$843$			31.6197i			1.08904i
$844$	11.9466			0.411218
$845$	12.3802	−	19.1013i	0.425893	−	0.657105i
$846$	6.04560	+	6.04560i	0.207852	+	0.207852i
$847$	47.2631	−	47.2631i	1.62398	−	1.62398i
$848$	8.02058	+	8.02058i	0.275428	+	0.275428i
$849$	3.51440	+	3.51440i	0.120614	+	0.120614i
$850$	−34.6127	+	15.4849i	−1.18721	+	0.531129i
$851$	18.7249	+	17.6488i	0.641882	+	0.604992i
$852$	4.32811	−	4.32811i	0.148279	−	0.148279i
$853$		−	42.0289i		−	1.43904i	−0.694471	−	0.719520i	$-0.744362\pi$
$853$		−	42.0289i		−	1.43904i	0.694471	−	0.719520i	$-0.255638\pi$
$854$	−5.02827			−0.172064
$855$	−2.46541	−	11.5480i	−0.0843152	−	0.394932i
$856$	−8.64549	+	8.64549i	−0.295497	+	0.295497i
$857$		−	34.3759i		−	1.17426i	−0.809494	−	0.587129i	$-0.800258\pi$
$857$		−	34.3759i		−	1.17426i	0.809494	−	0.587129i	$-0.199742\pi$
$858$	19.2664	+	19.2664i	0.657745	+	0.657745i
$859$	−29.2733	−	29.2733i	−0.998794	−	0.998794i	0.00120570	−	0.999999i	$-0.499616\pi$
$859$	−29.2733	−	29.2733i	−0.998794	−	0.998794i	−0.999999	+	0.00120570i	$0.999616\pi$
$860$	−4.06999	+	6.27954i	−0.138785	+	0.214130i
$861$	7.72558			0.263287
$862$	23.7856	+	23.7856i	0.810142	+	0.810142i
$863$	11.0183	+	11.0183i	0.375069	+	0.375069i	0.869319	−	0.494251i	$-0.164558\pi$
$863$	11.0183	+	11.0183i	0.375069	+	0.375069i	−0.494251	+	0.869319i	$0.664558\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	5.66872	+	26.5523i	0.192742	+	0.902804i
$866$	9.00285	+	9.00285i	0.305929	+	0.305929i
$867$	28.6470	−	28.6470i	0.972902	−	0.972902i
$868$	−8.93712			−0.303346
$869$	16.1469	−	16.1469i	0.547747	−	0.547747i
$870$	8.66411	+	5.61551i	0.293741	+	0.190384i
$871$	33.2765	+	33.2765i	1.12753	+	1.12753i
$872$	−13.7592	−	13.7592i	−0.465947	−	0.465947i
$873$	2.87834			0.0974169
$874$	−15.7959	−	15.7959i	−0.534306	−	0.534306i
$875$	28.6952	−	20.9663i	0.970076	−	0.708792i
$876$			3.65991i			0.123657i
$877$	−5.02653	+	5.02653i	−0.169734	+	0.169734i	−0.786862	−	0.617129i	$-0.788296\pi$
$877$	−5.02653	+	5.02653i	−0.169734	+	0.169734i	0.617129	+	0.786862i	$0.288296\pi$
$878$	−4.79636	+	4.79636i	−0.161869	+	0.161869i
$879$	5.32288			0.179536
$880$	−10.6192	−	6.88266i	−0.357973	−	0.232015i
$881$			29.2467i			0.985345i	0.870215	+	0.492673i	$0.163980\pi$
$881$			29.2467i			0.985345i	−0.870215	+	0.492673i	$0.836020\pi$
$882$	3.10403			0.104518
$883$		−	28.8964i		−	0.972441i	−0.873836	−	0.486220i	$-0.838375\pi$
$883$		−	28.8964i		−	0.972441i	0.873836	−	0.486220i	$-0.161625\pi$
$884$		−	36.5121i		−	1.22803i
$885$	−16.9364	+	26.1311i	−0.569312	+	0.878386i
$886$	7.85980	−	7.85980i	0.264055	−	0.264055i
$887$	−8.58020	−	8.58020i	−0.288095	−	0.288095i	0.548232	−	0.836327i	$-0.315301\pi$
$887$	−8.58020	−	8.58020i	−0.288095	−	0.288095i	−0.836327	+	0.548232i	$0.815301\pi$
$888$	6.08010	−	0.179886i	0.204035	−	0.00603658i
$889$		−	65.6706i		−	2.20252i
$890$	−6.72642	−	31.5065i	−0.225470	−	1.05610i
$891$			5.65930i			0.189594i
$892$	11.0520	+	11.0520i	0.370050	+	0.370050i
$893$	45.1495			1.51087
$894$	−6.50879	−	6.50879i	−0.217686	−	0.217686i
$895$	−9.30685	−	43.5932i	−0.311094	−	1.45716i
$896$	2.24767	−	2.24767i	0.0750893	−	0.0750893i
$897$	14.4013	−	14.4013i	0.480844	−	0.480844i
$898$	16.4657	+	16.4657i	0.549468	+	0.549468i
$899$	−12.9821			−0.432978
$900$	−4.56408	+	2.04186i	−0.152136	+	0.0680621i
$901$	−60.8259	+	60.8259i	−2.02640	+	2.02640i
$902$	−13.7545			−0.457976
$903$			10.6377i			0.353999i
$904$		−	4.68689i		−	0.155884i
$905$	16.7626	−	25.8628i	0.557208	−	0.859709i
$906$	−3.95777	−	3.95777i	−0.131488	−	0.131488i
$907$		−	0.367882i		−	0.0122153i	−0.999981	−	0.00610766i	$-0.998056\pi$
$907$		−	0.367882i		−	0.0122153i	0.999981	−	0.00610766i	$-0.00194414\pi$
$908$			6.40168i			0.212447i
$909$	16.0893			0.533649
$910$	7.14482	+	33.4663i	0.236848	+	1.10940i
$911$	−28.3530	+	28.3530i	−0.939377	+	0.939377i	−0.998265	−	0.0588872i	$-0.981245\pi$
$911$	−28.3530	+	28.3530i	−0.939377	+	0.939377i	0.0588872	+	0.998265i	$0.481245\pi$
$912$	−5.28079			−0.174864
$913$	5.12873	−	5.12873i	0.169736	−	0.169736i
$914$		−	5.42876i		−	0.179568i
$915$	1.92383	−	2.96825i	0.0635997	−	0.0981273i
$916$		−	16.3225i		−	0.539310i
$917$	−41.6367			−1.37496
$918$	5.36251	−	5.36251i	0.176989	−	0.176989i
$919$	−6.98899	+	6.98899i	−0.230546	+	0.230546i	−0.812920	−	0.582375i	$-0.802124\pi$
$919$	−6.98899	+	6.98899i	−0.230546	+	0.230546i	0.582375	+	0.812920i	$0.302124\pi$
$920$	−5.14465	+	7.93762i	−0.169614	+	0.261696i
$921$	−14.6248			−0.481905
$922$	−12.8604	+	12.8604i	−0.423534	+	0.423534i
$923$	29.4691			0.969987
$924$	−17.9891			−0.591798
$925$	10.0034	−	28.7216i	0.328911	−	0.944361i
$926$	−36.1282			−1.18725
$927$	11.0997			0.364563
$928$	3.26498	−	3.26498i	0.107178	−	0.107178i
$929$	−31.4501			−1.03184			−0.515922	−	0.856636i	$-0.672550\pi$
$929$	−31.4501			−1.03184			−0.515922	+	0.856636i	$0.672550\pi$
$930$	3.41936	−	5.27569i	0.112125	−	0.172997i
$931$	11.5907	−	11.5907i	0.379870	−	0.379870i
$932$	−0.738837	+	0.738837i	−0.0242014	+	0.0242014i
$933$	−2.94474			−0.0964064
$934$			4.96873i			0.162582i
$935$	52.1962	−	80.5330i	1.70700	−	2.63371i
$936$		−	4.81453i		−	0.157368i
$937$	16.7719	−	16.7719i	0.547915	−	0.547915i	−0.377922	−	0.925837i	$-0.623361\pi$
$937$	16.7719	−	16.7719i	0.547915	−	0.547915i	0.925837	+	0.377922i	$0.123361\pi$
$938$	−31.0703			−1.01448
$939$	4.14532	−	4.14532i	0.135278	−	0.135278i
$940$	−3.99158	−	18.6965i	−0.130191	−	0.609814i
$941$	16.4771			0.537139			0.268570	−	0.963260i	$-0.413449\pi$
$941$	16.4771			0.537139			0.268570	+	0.963260i	$0.413449\pi$
$942$			1.41232i			0.0460159i
$943$			10.2812i			0.334803i
$944$	9.84721	+	9.84721i	0.320499	+	0.320499i
$945$	−3.86582	+	5.96453i	−0.125755	+	0.194026i
$946$		−	18.9392i		−	0.615766i
$947$			56.8823i			1.84843i	0.381876	+	0.924214i	$0.375278\pi$
$947$			56.8823i			1.84843i	−0.381876	+	0.924214i	$0.624722\pi$
$948$	−4.03499			−0.131050
$949$	−12.4597	+	12.4597i	−0.404460	+	0.404460i
$950$	−9.41815	+	24.6671i	−0.305565	+	0.800307i
$951$	−4.67673			−0.151653
$952$	17.0457	+	17.0457i	0.552455	+	0.552455i
$953$	−3.27877	+	3.27877i	−0.106210	+	0.106210i	−0.758215	−	0.652005i	$-0.773928\pi$
$953$	−3.27877	+	3.27877i	−0.106210	+	0.106210i	0.652005	+	0.758215i	$0.273928\pi$
$954$	−8.02058	+	8.02058i	−0.259676	+	0.259676i
$955$	−12.1784	−	57.0438i	−0.394085	−	1.84589i
$956$	−5.10981	−	5.10981i	−0.165263	−	0.165263i
$957$	−26.1311			−0.844698
$958$	−21.0873	−	21.0873i	−0.681300	−	0.681300i
$959$			7.37004i			0.237991i
$960$	0.466864	+	2.18679i	0.0150680	+	0.0705783i
$961$		−	23.0950i		−	0.745001i
$962$	21.3114	+	20.0866i	0.687108	+	0.647618i
$963$	−8.64549	−	8.64549i	−0.278597	−	0.278597i
$964$	−8.22613	+	8.22613i	−0.264946	+	0.264946i
$965$	−27.9594	+	43.1383i	−0.900046	+	1.38867i
$966$			13.4465i			0.432634i
$967$			38.2625i			1.23044i	0.788356	+	0.615219i	$0.210932\pi$
$967$			38.2625i			1.23044i	−0.788356	+	0.615219i	$0.789068\pi$
$968$	21.0276			0.675853
$969$		−	40.0481i		−	1.28653i
$970$	−5.40095	−	3.50054i	−0.173414	−	0.112396i
$971$	−30.0272			−0.963620			−0.481810	−	0.876276i	$-0.660020\pi$
$971$	−30.0272			−0.963620			−0.481810	+	0.876276i	$0.660020\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	40.3303	−	40.3303i	1.29293	−	1.29293i
$974$		−	10.6041i		−	0.339778i
$975$	−22.4892	−	8.58659i	−0.720230	−	0.274991i
$976$	−1.11855	−	1.11855i	−0.0358040	−	0.0358040i
$977$	23.6886			0.757865			0.378932	−	0.925424i	$-0.376291\pi$
$977$	23.6886			0.757865			0.378932	+	0.925424i	$0.376291\pi$
$978$	−5.47991	−	5.47991i	−0.175228	−	0.175228i
$979$	57.6556	+	57.6556i	1.84268	+	1.84268i
$980$	−5.82445	−	3.77503i	−0.186055	−	0.120589i
$981$	13.7592	−	13.7592i	0.439299	−	0.439299i
$982$	−2.33716			−0.0745819
$983$	−29.2431	+	29.2431i	−0.932711	+	0.932711i	−0.997875	−	0.0651639i	$-0.979243\pi$
$983$	−29.2431	+	29.2431i	−0.932711	+	0.932711i	0.0651639	+	0.997875i	$0.479243\pi$
$984$	1.71858	+	1.71858i	0.0547862	+	0.0547862i
$985$	1.11806	+	5.23701i	0.0356245	+	0.166865i
$986$	24.7607	+	24.7607i	0.788541	+	0.788541i
$987$	−19.2171	−	19.2171i	−0.611686	−	0.611686i
$988$	−17.9778	−	17.9778i	−0.571952	−	0.571952i
$989$	−14.1567			−0.450155
$990$	6.88266	−	10.6192i	0.218745	−	0.337500i
$991$	6.15758	+	6.15758i	0.195602	+	0.195602i	0.798112	−	0.602510i	$-0.205833\pi$
$991$	6.15758	+	6.15758i	0.195602	+	0.195602i	−0.602510	+	0.798112i	$0.705833\pi$
$992$	−1.98809	−	1.98809i	−0.0631218	−	0.0631218i
$993$			2.88137i			0.0914375i
$994$	−13.7577	+	13.7577i	−0.436367	+	0.436367i
$995$	4.84403	+	22.6894i	0.153566	+	0.719303i
$996$	−1.28163			−0.0406100
$997$		−	14.2061i		−	0.449913i	−0.974369	−	0.224957i	$-0.927776\pi$
$997$		−	14.2061i		−	0.449913i	0.974369	−	0.224957i	$-0.0722240\pi$
$998$	15.9396	−	15.9396i	0.504559	−	0.504559i
$999$	0.179886	+	6.08010i	0.00569134	+	0.192366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.9	yes	36
5.2	odd	4		1110.2.l.a.697.10	yes	36
37.6	odd	4		1110.2.l.a.43.10	✓	36
185.117	even	4	inner	1110.2.o.a.487.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.10	✓	36	37.6	odd	4
1110.2.l.a.697.10	yes	36	5.2	odd	4
1110.2.o.a.253.9	yes	36	1.1	even	1	trivial
1110.2.o.a.487.9	yes	36	185.117	even	4	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.21617 - 1.87641i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.24767 + 2.24767i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.21617 - 1.87641i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.24767 + 2.24767i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-1.21617 + 1.87641i) q^{10} -5.65930i q^{11} +(-0.707107 + 0.707107i) q^{12} -4.81453 q^{13} +(2.24767 - 2.24767i) q^{14} +(0.466864 + 2.18679i) q^{15} +1.00000 q^{16} +7.58373i q^{17} +1.00000i q^{18} +(3.73408 + 3.73408i) q^{19} +(1.21617 - 1.87641i) q^{20} -3.17868i q^{21} +5.65930i q^{22} +4.23021 q^{23} +(0.707107 - 0.707107i) q^{24} +(-2.04186 - 4.56408i) q^{25} +4.81453 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.24767 + 2.24767i) q^{28} +(-3.26498 + 3.26498i) q^{29} +(-0.466864 - 2.18679i) q^{30} +(1.98809 + 1.98809i) q^{31} -1.00000 q^{32} +(4.00173 + 4.00173i) q^{33} -7.58373i q^{34} +(1.48401 + 6.95110i) q^{35} -1.00000i q^{36} +(4.42648 + 4.17208i) q^{37} +(-3.73408 - 3.73408i) q^{38} +(3.40439 - 3.40439i) q^{39} +(-1.21617 + 1.87641i) q^{40} +2.43043i q^{41} +3.17868i q^{42} -3.34656 q^{43} -5.65930i q^{44} +(-1.87641 - 1.21617i) q^{45} -4.23021 q^{46} +(6.04560 - 6.04560i) q^{47} +(-0.707107 + 0.707107i) q^{48} -3.10403i q^{49} +(2.04186 + 4.56408i) q^{50} +(-5.36251 - 5.36251i) q^{51} -4.81453 q^{52} +(8.02058 + 8.02058i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-10.6192 - 6.88266i) q^{55} +(2.24767 - 2.24767i) q^{56} -5.28079 q^{57} +(3.26498 - 3.26498i) q^{58} +(9.84721 + 9.84721i) q^{59} +(0.466864 + 2.18679i) q^{60} +(-1.11855 - 1.11855i) q^{61} +(-1.98809 - 1.98809i) q^{62} +(2.24767 + 2.24767i) q^{63} +1.00000 q^{64} +(-5.85528 + 9.03405i) q^{65} +(-4.00173 - 4.00173i) q^{66} +(-6.91167 - 6.91167i) q^{67} +7.58373i q^{68} +(-2.99121 + 2.99121i) q^{69} +(-1.48401 - 6.95110i) q^{70} -6.12087 q^{71} +1.00000i q^{72} +(2.58794 - 2.58794i) q^{73} +(-4.42648 - 4.17208i) q^{74} +(4.67110 + 1.78347i) q^{75} +(3.73408 + 3.73408i) q^{76} +(12.7202 + 12.7202i) q^{77} +(-3.40439 + 3.40439i) q^{78} +(2.85317 + 2.85317i) q^{79} +(1.21617 - 1.87641i) q^{80} -1.00000 q^{81} -2.43043i q^{82} +(0.906248 + 0.906248i) q^{83} -3.17868i q^{84} +(14.2302 + 9.22310i) q^{85} +3.34656 q^{86} -4.61737i q^{87} +5.65930i q^{88} +(-10.1878 + 10.1878i) q^{89} +(1.87641 + 1.21617i) q^{90} +(10.8215 - 10.8215i) q^{91} +4.23021 q^{92} -2.81158 q^{93} +(-6.04560 + 6.04560i) q^{94} +(11.5480 - 2.46541i) q^{95} +(0.707107 - 0.707107i) q^{96} +2.87834i q^{97} +3.10403i q^{98} -5.65930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more