LMFDB - Embedded newform 1110.2.l.a.697.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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			697.10
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.a.43.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	1.87641	−	1.21617i	0.839158	−	0.543888i
$5$	1.87641	−	1.21617i	0.839158	−	0.543888i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−2.24767	−	2.24767i	−0.849539	−	0.849539i	0.140537	−	0.990075i	$-0.455117\pi$
$7$	−2.24767	−	2.24767i	−0.849539	−	0.849539i	−0.990075	+	0.140537i	$0.955117\pi$
$8$			1.00000i			0.353553i
$9$			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
$13$			4.81453i			1.33531i	0.744471	+	0.667655i	$0.232702\pi$
$13$			4.81453i			1.33531i	−0.744471	+	0.667655i	$0.767298\pi$
$14$	−2.24767	+	2.24767i	−0.600715	+	0.600715i
$15$	2.18679	+	0.466864i	0.564626	+	0.120544i
$16$	1.00000			0.250000
$17$	−7.58373			−1.83932			−0.919662	−	0.392710i	$-0.871537\pi$
$17$	−7.58373			−1.83932			−0.919662	+	0.392710i	$0.871537\pi$
$18$	1.00000			0.235702
$19$	−3.73408	−	3.73408i	−0.856657	−	0.856657i	0.134285	−	0.990943i	$-0.457126\pi$
$19$	−3.73408	−	3.73408i	−0.856657	−	0.856657i	−0.990943	+	0.134285i	$0.957126\pi$
$20$	−1.87641	+	1.21617i	−0.419579	+	0.271944i
$21$		−	3.17868i		−	0.693646i
$22$	−5.65930			−1.20657
$23$		−	4.23021i		−	0.882059i	−0.897493	−	0.441030i	$-0.854613\pi$
$23$		−	4.23021i		−	0.882059i	0.897493	−	0.441030i	$-0.145387\pi$
$24$	−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	−0.335684	−	0.941975i	$-0.608967\pi$
$29$	3.26498	−	3.26498i	0.606291	−	0.606291i	0.941975	+	0.335684i	$0.108967\pi$
$30$	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	$0.668751\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.00173	−	4.00173i	0.696611	−	0.696611i
$34$			7.58373i			1.30060i
$35$	−6.95110	−	1.48401i	−1.17495	−	0.250844i
$36$		−	1.00000i		−	0.166667i
$37$	−4.17208	+	4.42648i	−0.685886	+	0.727709i
$37$	−4.17208	+	4.42648i	−0.685886	+	0.727709i
$38$	−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	$0.939221\pi$
$42$	−3.17868			−0.490482
$43$			3.34656i			0.510346i	0.966895	+	0.255173i	$0.0821324\pi$
$43$			3.34656i			0.510346i	−0.966895	+	0.255173i	$0.917868\pi$
$44$			5.65930i			0.853171i
$45$	1.21617	+	1.87641i	0.181296	+	0.279719i
$46$	−4.23021			−0.623710
$47$	6.04560	+	6.04560i	0.881842	+	0.881842i	0.993722	−	0.111880i	$-0.0356873\pi$
$47$	6.04560	+	6.04560i	0.881842	+	0.881842i	−0.111880	+	0.993722i	$0.535687\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			3.10403i			0.443433i
$50$	−4.56408	−	2.04186i	−0.645458	−	0.288763i
$51$	−5.36251	−	5.36251i	−0.750901	−	0.750901i
$52$		−	4.81453i		−	0.667655i
$53$	8.02058	−	8.02058i	1.10171	−	1.10171i	0.107507	−	0.994204i	$-0.465713\pi$
$53$	8.02058	−	8.02058i	1.10171	−	1.10171i	0.994204	−	0.107507i	$-0.0342868\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−6.88266	−	10.6192i	−0.928058	−	1.43189i
$56$	2.24767	−	2.24767i	0.300357	−	0.300357i
$57$		−	5.28079i		−	0.699458i
$58$	−3.26498	−	3.26498i	−0.428712	−	0.428712i
$59$	−9.84721	−	9.84721i	−1.28200	−	1.28200i	−0.939530	−	0.342468i	$-0.888737\pi$
$59$	−9.84721	−	9.84721i	−1.28200	−	1.28200i	−0.342468	−	0.939530i	$-0.611263\pi$
$60$	−2.18679	−	0.466864i	−0.282313	−	0.0602718i
$61$	−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	$-0.546328\pi$
$67$	6.91167	−	6.91167i	0.844395	−	0.844395i	0.989427	+	0.145032i	$0.0463284\pi$
$68$	7.58373			0.919662
$69$	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	$0.618318\pi$
$72$	−1.00000			−0.117851
$73$	−2.58794	−	2.58794i	−0.302896	−	0.302896i	0.539250	−	0.842146i	$-0.318708\pi$
$73$	−2.58794	−	2.58794i	−0.302896	−	0.302896i	−0.842146	+	0.539250i	$0.818708\pi$
$74$	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	0.528146	−	0.849153i	$-0.322887\pi$
$79$	−2.85317	−	2.85317i	−0.321007	−	0.321007i	−0.849153	+	0.528146i	$0.822887\pi$
$80$	1.87641	−	1.21617i	0.209790	−	0.135972i
$81$	−1.00000			−0.111111
$82$	2.43043			0.268396
$83$	0.906248	−	0.906248i	0.0994737	−	0.0994737i	−0.655619	−	0.755092i	$-0.727592\pi$
$83$	0.906248	−	0.906248i	0.0994737	−	0.0994737i	0.755092	+	0.655619i	$0.227592\pi$
$84$			3.17868i			0.346823i
$85$	−14.2302	+	9.22310i	−1.54348	+	1.00039i
$86$	3.34656			0.360869
$87$	4.61737			0.495034
$88$	5.65930			0.603283
$89$	10.1878	−	10.1878i	1.07990	−	1.07990i	0.0833830	−	0.996518i	$-0.473428\pi$
$89$	10.1878	−	10.1878i	1.07990	−	1.07990i	0.996518	−	0.0833830i	$-0.0265725\pi$
$90$	1.87641	−	1.21617i	0.197791	−	0.128196i
$91$	10.8215	−	10.8215i	1.13440	−	1.13440i
$92$			4.23021i			0.441030i
$93$			2.81158i			0.291547i
$94$	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
$97$	−2.87834			−0.292251			−0.146125	−	0.989266i	$-0.546680\pi$
$97$	−2.87834			−0.292251			−0.146125	+	0.989266i	$0.546680\pi$
$98$	3.10403			0.313554
$99$	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
$103$	11.0997			1.09369			0.546845	−	0.837234i	$-0.315829\pi$
$103$	11.0997			1.09369			0.546845	+	0.837234i	$0.315829\pi$
$104$	−4.81453			−0.472103
$105$	−3.86582	−	5.96453i	−0.377265	−	0.582078i
$106$	−8.02058	−	8.02058i	−0.779028	−	0.779028i
$107$	8.64549	+	8.64549i	0.835791	+	0.835791i	0.988302	−	0.152511i	$-0.0487359\pi$
$107$	8.64549	+	8.64549i	0.835791	+	0.835791i	−0.152511	+	0.988302i	$0.548736\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−13.7592	−	13.7592i	−1.31790	−	1.31790i	−0.915438	−	0.402458i	$-0.868156\pi$
$109$	−13.7592	−	13.7592i	−1.31790	−	1.31790i	−0.402458	−	0.915438i	$-0.631844\pi$
$110$	−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
$113$	4.68689			0.440906			0.220453	−	0.975398i	$-0.429246\pi$
$113$	4.68689			0.440906			0.220453	+	0.975398i	$0.429246\pi$
$114$	−5.28079			−0.494591
$115$	−5.14465	−	7.93762i	−0.479741	−	0.740187i
$116$	−3.26498	+	3.26498i	−0.303145	+	0.303145i
$117$	−4.81453			−0.445103
$118$	−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
$125$	−1.71931	−	11.0474i	−0.153780	−	0.988105i
$126$	−2.24767	−	2.24767i	−0.200238	−	0.200238i
$127$	−14.6086	−	14.6086i	−1.29630	−	1.29630i	−0.930816	−	0.365488i	$-0.880902\pi$
$127$	−14.6086	−	14.6086i	−1.29630	−	1.29630i	−0.365488	−	0.930816i	$-0.619098\pi$
$128$			1.00000i			0.0883883i
$129$	−2.36638	+	2.36638i	−0.208348	+	0.208348i
$130$	9.03405	−	5.85528i	0.792339	−	0.513542i
$131$	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
$133$			16.7860i			1.45553i
$134$	−6.91167	−	6.91167i	−0.597078	−	0.597078i
$135$	−0.466864	+	2.18679i	−0.0401812	+	0.188209i
$136$		−	7.58373i		−	0.650299i
$137$	1.63948	+	1.63948i	0.140071	+	0.140071i	0.773665	−	0.633595i	$-0.218421\pi$
$137$	1.63948	+	1.63948i	0.140071	+	0.140071i	−0.633595	+	0.773665i	$0.718421\pi$
$138$	−2.99121	−	2.99121i	−0.254629	−	0.254629i
$139$	17.9432			1.52192			0.760959	−	0.648800i	$-0.224729\pi$
$139$	17.9432			1.52192			0.760959	+	0.648800i	$0.224729\pi$
$140$	6.95110	+	1.48401i	0.587476	+	0.125422i
$141$			8.54977i			0.720021i
$142$			6.12087i			0.513652i
$143$	27.2468			2.27850
$144$			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
$148$	4.17208	−	4.42648i	0.342943	−	0.363854i
$149$			9.20482i			0.754088i	0.926195	+	0.377044i	$0.123059\pi$
$149$			9.20482i			0.754088i	−0.926195	+	0.377044i	$0.876941\pi$
$150$	−1.78347	−	4.67110i	−0.145620	−	0.381394i
$151$		−	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
$153$		−	7.58373i		−	0.613108i
$154$	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	0.666132	−	0.745834i	$-0.267949\pi$
$157$	−0.998661	−	0.998661i	−0.0797019	−	0.0797019i	−0.745834	+	0.666132i	$0.767949\pi$
$158$	−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
$162$			1.00000i			0.0785674i
$163$	−7.74976			−0.607008			−0.303504	−	0.952830i	$-0.598157\pi$
$163$	−7.74976			−0.607008			−0.303504	+	0.952830i	$0.598157\pi$
$164$		−	2.43043i		−	0.189785i
$165$	2.64212	−	12.3757i	0.205689	−	0.963445i
$166$	−0.906248	−	0.906248i	−0.0703385	−	0.0703385i
$167$	19.2547			1.48997			0.744985	−	0.667081i	$-0.232457\pi$
$167$	19.2547			1.48997			0.744985	+	0.667081i	$0.232457\pi$
$168$	3.17868			0.245241
$169$	−10.1797			−0.783053
$170$	9.22310	+	14.2302i	0.707379	+	1.09141i
$171$	3.73408	−	3.73408i	0.285552	−	0.285552i
$172$		−	3.34656i		−	0.255173i
$173$	8.58579	+	8.58579i	0.652765	+	0.652765i	0.953658	−	0.300893i	$-0.0972846\pi$
$173$	8.58579	+	8.58579i	0.652765	+	0.652765i	−0.300893	+	0.953658i	$0.597285\pi$
$174$		−	4.61737i		−	0.350042i
$175$	−14.8480	+	5.66910i	−1.12240	+	0.428544i
$176$		−	5.65930i		−	0.426585i
$177$		−	13.9261i		−	1.04675i
$178$	−10.1878	−	10.1878i	−0.763605	−	0.763605i
$179$	−14.0961	+	14.0961i	−1.05359	+	1.05359i	−0.0551080	+	0.998480i	$0.517550\pi$
$179$	−14.0961	+	14.0961i	−1.05359	+	1.05359i	−0.998480	+	0.0551080i	$0.982450\pi$
$180$	−1.21617	−	1.87641i	−0.0906479	−	0.139860i
$181$	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
$183$		−	1.58187i		−	0.116935i
$184$	4.23021			0.311855
$185$	−2.44521	+	13.3799i	−0.179775	+	0.983708i
$186$	2.81158			0.206155
$187$			42.9186i			3.13852i
$188$	−6.04560	−	6.04560i	−0.440921	−	0.440921i
$189$	3.17868			0.231215
$190$	−2.46541	+	11.5480i	−0.178860	+	0.837777i
$191$	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
$193$			22.9897i			1.65484i	0.561585	+	0.827419i	$0.310192\pi$
$193$			22.9897i			1.65484i	−0.561585	+	0.827419i	$0.689808\pi$
$194$			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	0.644204	−	0.764854i	$-0.277189\pi$
$197$	−1.69341	−	1.69341i	−0.120650	−	0.120650i	−0.764854	+	0.644204i	$0.777189\pi$
$198$		−	5.65930i		−	0.402189i
$199$	7.33672	−	7.33672i	0.520087	−	0.520087i	−0.397511	−	0.917597i	$-0.630126\pi$
$199$	7.33672	−	7.33672i	0.520087	−	0.520087i	0.917597	+	0.397511i	$0.130126\pi$
$200$	4.56408	+	2.04186i	0.322729	+	0.144382i
$201$	9.77458			0.689446
$202$	16.0893			1.13204
$203$	−14.6772			−1.03014
$204$	5.36251	+	5.36251i	0.375451	+	0.375451i
$205$	2.95582	+	4.56050i	0.206443	+	0.318519i
$206$		−	11.0997i		−	0.773355i
$207$	4.23021			0.294020
$208$			4.81453i			0.333828i
$209$	−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
$217$		−	8.93712i		−	0.606691i
$218$	−13.7592	+	13.7592i	−0.931894	+	0.931894i
$219$		−	3.65991i		−	0.247314i
$220$	6.88266	+	10.6192i	0.464029	+	0.715945i
$221$		−	36.5121i		−	2.45607i
$222$	0.179886	+	6.08010i	0.0120732	+	0.408070i
$223$	11.0520	−	11.0520i	0.740100	−	0.740100i	−0.232497	−	0.972597i	$-0.574690\pi$
$223$	11.0520	−	11.0520i	0.740100	−	0.740100i	0.972597	+	0.232497i	$0.0746896\pi$
$224$	−2.24767	+	2.24767i	−0.150179	+	0.150179i
$225$	4.56408	+	2.04186i	0.304272	+	0.136124i
$226$		−	4.68689i		−	0.311768i
$227$	−6.40168			−0.424894			−0.212447	−	0.977173i	$-0.568143\pi$
$227$	−6.40168			−0.424894			−0.212447	+	0.977173i	$0.568143\pi$
$228$			5.28079i			0.349729i
$229$			16.3225i			1.07862i	0.842107	+	0.539310i	$0.181315\pi$
$229$			16.3225i			1.07862i	−0.842107	+	0.539310i	$0.818685\pi$
$230$	−7.93762	+	5.14465i	−0.523391	+	0.339228i
$231$	−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	$-0.239103\pi$
$233$	0.738837	+	0.738837i	0.0484028	+	0.0484028i	−0.682491	+	0.730894i	$0.739103\pi$
$234$			4.81453i			0.314736i
$235$	18.6965	+	3.99158i	1.21963	+	0.260382i
$236$	9.84721	+	9.84721i	0.640999	+	0.640999i
$237$		−	4.03499i		−	0.262101i
$238$	17.0457	−	17.0457i	1.10491	−	1.10491i
$239$	5.10981	+	5.10981i	0.330526	+	0.330526i	0.852786	−	0.522260i	$-0.174911\pi$
$239$	5.10981	+	5.10981i	0.330526	+	0.330526i	−0.522260	+	0.852786i	$0.674911\pi$
$240$	2.18679	+	0.466864i	0.141157	+	0.0301359i
$241$	−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	$0.372251\pi$
$242$			21.0276i			1.35171i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	1.11855	+	1.11855i	0.0716080	+	0.0716080i
$245$	3.77503	+	5.82445i	0.241178	+	0.372110i
$246$	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
$253$	−23.9400			−1.50509
$254$	−14.6086	+	14.6086i	−0.916626	+	0.916626i
$255$	−16.5840	−	3.54057i	−1.03853	−	0.221719i
$256$	1.00000			0.0625000
$257$	15.5767			0.971645			0.485823	−	0.874057i	$-0.338520\pi$
$257$	15.5767			0.971645			0.485823	+	0.874057i	$0.338520\pi$
$258$	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	0.998015	+	0.0629697i	$0.0200571\pi$
$263$	17.2063	+	17.2063i	1.06099	+	1.06099i	0.0629697	+	0.998015i	$0.479943\pi$
$264$	4.00173	+	4.00173i	0.246289	+	0.246289i
$265$	5.29555	−	24.8043i	0.325303	−	1.52372i
$266$	16.7860			1.02921
$267$	14.4077			0.881735
$268$	−6.91167	+	6.91167i	−0.422198	+	0.422198i
$269$		−	16.7896i		−	1.02368i	−0.859080	−	0.511841i	$-0.828964\pi$
$269$		−	16.7896i		−	1.02368i	0.859080	−	0.511841i	$-0.171036\pi$
$270$	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	$0.533616\pi$
$272$	−7.58373			−0.459831
$273$	15.3039			0.926232
$274$	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
$277$		−	5.08835i		−	0.305730i	−0.988247	−	0.152865i	$-0.951150\pi$
$277$		−	5.08835i		−	0.305730i	0.988247	−	0.152865i	$-0.0488499\pi$
$278$		−	17.9432i		−	1.07616i
$279$	−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	$-0.142141\pi$
$282$	8.54977			0.509131
$283$	−4.97011			−0.295442			−0.147721	−	0.989029i	$-0.547194\pi$
$283$	−4.97011			−0.295442			−0.147721	+	0.989029i	$0.547194\pi$
$284$	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
$288$	1.00000			0.0589256
$289$	40.5129			2.38311
$290$	−10.0972	−	2.15568i	−0.592929	−	0.126586i
$291$	−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	−0.808450	−	0.588564i	$-0.799693\pi$
$293$	−3.76385	+	3.76385i	−0.219886	+	0.219886i	0.588564	+	0.808450i	$0.299693\pi$
$294$	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
$298$	9.20482			0.533221
$299$	20.3665			1.17782
$300$	−4.67110	+	1.78347i	−0.269686	+	0.102969i
$301$	7.52196	−	7.52196i	0.433559	−	0.433559i
$302$	−5.59713			−0.322078
$303$	−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	$-0.887038\pi$
$307$	−10.3413	+	10.3413i	−0.590210	+	0.590210i	0.347478	+	0.937688i	$0.387038\pi$
$308$	12.7202	−	12.7202i	0.724802	−	0.724802i
$309$	7.84870	+	7.84870i	0.446497	+	0.446497i
$310$	1.31262	−	6.14832i	0.0745520	−	0.349201i
$311$	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
$313$			5.86237i			0.331361i	0.986179	+	0.165681i	$0.0529820\pi$
$313$			5.86237i			0.331361i	−0.986179	+	0.165681i	$0.947018\pi$
$314$	−0.998661	+	0.998661i	−0.0563577	+	0.0563577i
$315$	1.48401	−	6.95110i	0.0836146	−	0.391650i
$316$	2.85317	+	2.85317i	0.160503	+	0.160503i
$317$	−3.30695	+	3.30695i	−0.185737	+	0.185737i	−0.793850	−	0.608113i	$-0.791927\pi$
$317$	−3.30695	+	3.30695i	−0.185737	+	0.185737i	0.608113	+	0.793850i	$0.291927\pi$
$318$		−	11.3428i		−	0.636073i
$319$	−18.4775	−	18.4775i	−1.03454	−	1.03454i
$320$	−1.87641	+	1.21617i	−0.104895	+	0.0679859i
$321$			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
$325$	21.9739	+	9.83061i	1.21889	+	0.545304i
$326$			7.74976i			0.429220i
$327$		−	19.4585i		−	1.07606i
$328$	−2.43043			−0.134198
$329$		−	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
$333$	−4.42648	−	4.17208i	−0.242570	−	0.228629i
$334$		−	19.2547i		−	1.05357i
$335$	4.56340	−	21.3749i	0.249325	−	1.16784i
$336$		−	3.17868i		−	0.173411i
$337$	4.38679	−	4.38679i	0.238963	−	0.238963i	−0.577457	−	0.816421i	$-0.695955\pi$
$337$	4.38679	−	4.38679i	0.238963	−	0.238963i	0.816421	+	0.577457i	$0.195955\pi$
$338$			10.1797i			0.553702i
$339$	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
$347$			6.84918i			0.367683i	0.982956	+	0.183842i	$0.0588533\pi$
$347$			6.84918i			0.367683i	−0.982956	+	0.183842i	$0.941147\pi$
$348$	−4.61737			−0.247517
$349$		−	11.3003i		−	0.604891i	−0.953167	−	0.302445i	$-0.902197\pi$
$349$		−	11.3003i		−	0.604891i	0.953167	−	0.302445i	$-0.0978030\pi$
$350$	5.66910	+	14.8480i	0.303026	+	0.793657i
$351$	−3.40439	−	3.40439i	−0.181713	−	0.181713i
$352$	−5.65930			−0.301641
$353$	−21.3525			−1.13648			−0.568240	−	0.822863i	$-0.692375\pi$
$353$	−21.3525			−1.13648			−0.568240	+	0.822863i	$0.692375\pi$
$354$	−13.9261			−0.740162
$355$	−11.4853	+	7.44401i	−0.609576	+	0.395087i
$356$	−10.1878	+	10.1878i	−0.539950	+	0.539950i
$357$			24.1063i			1.27584i
$358$	14.0961	+	14.0961i	0.745000	+	0.745000i
$359$			5.23042i			0.276051i	0.990429	+	0.138025i	$0.0440756\pi$
$359$			5.23042i			0.276051i	−0.990429	+	0.138025i	$0.955924\pi$
$360$	−1.87641	+	1.21617i	−0.0988957	+	0.0640978i
$361$			8.88674i			0.467723i
$362$		−	13.7831i		−	0.724424i
$363$	−14.8688	−	14.8688i	−0.780408	−	0.780408i
$364$	−10.8215	+	10.8215i	−0.567199	+	0.567199i
$365$	−8.00344	−	1.70868i	−0.418919	−	0.0894362i
$366$	−1.58187			−0.0826858
$367$	−0.560713	−	0.560713i	−0.0292690	−	0.0292690i	0.692321	−	0.721590i	$-0.256588\pi$
$367$	−0.560713	−	0.560713i	−0.0292690	−	0.0292690i	−0.721590	+	0.692321i	$0.756588\pi$
$368$		−	4.23021i		−	0.220515i
$369$	−2.43043			−0.126523
$370$	13.3799	+	2.44521i	0.695586	+	0.127120i
$371$	−36.0552			−1.87189
$372$		−	2.81158i		−	0.145774i
$373$	3.16048	+	3.16048i	0.163643	+	0.163643i	0.784179	−	0.620535i	$-0.213085\pi$
$373$	3.16048	+	3.16048i	0.163643	+	0.163643i	−0.620535	+	0.784179i	$0.713085\pi$
$374$	42.9186			2.21927
$375$	6.59592	−	9.02739i	0.340612	−	0.466173i
$376$	−6.04560	+	6.04560i	−0.311778	+	0.311778i
$377$	15.7193	+	15.7193i	0.809586	+	0.809586i
$378$		−	3.17868i		−	0.163494i
$379$			1.59897i			0.0821335i	0.999156	+	0.0410667i	$0.0130756\pi$
$379$			1.59897i			0.0821335i	−0.999156	+	0.0410667i	$0.986924\pi$
$380$	11.5480	+	2.46541i	0.592398	+	0.126473i
$381$		−	20.6597i		−	1.05843i
$382$	−18.4453	−	18.4453i	−0.943746	−	0.943746i
$383$		−	1.83857i		−	0.0939464i	−0.998896	−	0.0469732i	$-0.985042\pi$
$383$		−	1.83857i		−	0.0939464i	0.998896	−	0.0469732i	$-0.0149575\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−8.39846	+	39.3384i	−0.428025	+	2.00487i
$386$	22.9897			1.17015
$387$	−3.34656			−0.170115
$388$	2.87834			0.146125
$389$	−21.9756	−	21.9756i	−1.11421	−	1.11421i	−0.992575	−	0.121630i	$-0.961188\pi$
$389$	−21.9756	−	21.9756i	−1.11421	−	1.11421i	−0.121630	−	0.992575i	$-0.538812\pi$
$390$	10.5284	+	2.24773i	0.533124	+	0.113818i
$391$			32.0807i			1.62239i
$392$	−3.10403			−0.156777
$393$			13.0987i			0.660743i
$394$	−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	$-0.920608\pi$
$397$	−14.3901	+	14.3901i	−0.722218	+	0.722218i	0.246838	+	0.969057i	$0.420608\pi$
$398$	−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	$0.767589\pi$
$402$		−	9.77458i		−	0.487512i
$403$	−9.57170	+	9.57170i	−0.476800	+	0.476800i
$404$		−	16.0893i		−	0.800474i
$405$	−1.87641	+	1.21617i	−0.0932398	+	0.0604320i
$406$			14.6772i			0.728416i
$407$	25.0508	+	23.6110i	1.24172	+	1.17036i
$408$	5.36251	−	5.36251i	0.265484	−	0.265484i
$409$	−6.64945	+	6.64945i	−0.328794	+	0.328794i	−0.852128	−	0.523334i	$-0.824688\pi$
$409$	−6.64945	+	6.64945i	−0.328794	+	0.328794i	0.523334	+	0.852128i	$0.324688\pi$
$410$	4.56050	−	2.95582i	0.225227	−	0.145978i
$411$			2.31858i			0.114367i
$412$	−11.0997			−0.546845
$413$			44.2665i			2.17821i
$414$		−	4.23021i		−	0.207903i
$415$	0.598346	−	2.80265i	0.0293716	−	0.137577i
$416$	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	$-0.816684\pi$
$419$		−	22.2951i		−	1.08919i	0.838701	−	0.544593i	$-0.183316\pi$
$420$	3.86582	+	5.96453i	0.188633	+	0.291039i
$421$	−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	$0.769152\pi$
$422$		−	11.9466i		−	0.581549i
$423$	−6.04560	+	6.04560i	−0.293947	+	0.293947i
$424$	8.02058	+	8.02058i	0.389514	+	0.389514i
$425$	−15.4849	+	34.6127i	−0.751130	+	1.67896i
$426$	−4.32811	+	4.32811i	−0.209697	+	0.209697i
$427$			5.02827i			0.243335i
$428$	−8.64549	−	8.64549i	−0.417896	−	0.417896i
$429$	19.2664	+	19.2664i	0.930192	+	0.930192i
$430$	6.27954	−	4.06999i	0.302826	−	0.196272i
$431$	−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	−0.889529	−	0.456879i	$-0.848967\pi$
$433$	−9.00285	+	9.00285i	−0.432649	+	0.432649i	0.456879	+	0.889529i	$0.348967\pi$
$434$	−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
$438$	−3.65991			−0.174877
$439$	−4.79636	+	4.79636i	−0.228918	+	0.228918i	−0.812240	−	0.583323i	$-0.801752\pi$
$439$	−4.79636	+	4.79636i	−0.228918	+	0.228918i	0.583323	+	0.812240i	$0.301752\pi$
$440$	10.6192	−	6.88266i	0.506250	−	0.328118i
$441$	−3.10403			−0.147811
$442$	−36.5121			−1.73670
$443$	7.85980	+	7.85980i	0.373430	+	0.373430i	0.868725	−	0.495295i	$-0.164940\pi$
$443$	7.85980	+	7.85980i	0.373430	+	0.373430i	−0.495295	+	0.868725i	$0.664940\pi$
$444$	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	0.979331	−	0.202265i	$-0.0648303\pi$
$449$	16.4657	+	16.4657i	0.777066	+	0.777066i	−0.202265	+	0.979331i	$0.564830\pi$
$450$	2.04186	−	4.56408i	0.0962543	−	0.215153i
$451$	13.7545			0.647676
$452$	−4.68689			−0.220453
$453$	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
$457$	−5.42876			−0.253947			−0.126973	−	0.991906i	$-0.540526\pi$
$457$	−5.42876			−0.253947			−0.126973	+	0.991906i	$0.540526\pi$
$458$	16.3225			0.762699
$459$	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	$0.110790\pi$
$462$			17.9891i			0.836929i
$463$		−	36.1282i		−	1.67902i	−0.543345	−	0.839509i	$-0.682843\pi$
$463$		−	36.1282i		−	1.67902i	0.543345	−	0.839509i	$-0.317157\pi$
$464$	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
$467$	4.96873			0.229925			0.114963	−	0.993370i	$-0.463325\pi$
$467$	4.96873			0.229925			0.114963	+	0.993370i	$0.463325\pi$
$468$	4.81453			0.222552
$469$	−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
$473$	18.9392			0.870825
$474$	−4.03499			−0.185333
$475$	−24.6671	+	9.41815i	−1.13181	+	0.432135i
$476$	−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	0.0358527	−	0.999357i	$-0.488585\pi$
$479$	−21.0873	−	21.0873i	−0.963504	−	0.963504i	−0.999357	+	0.0358527i	$0.988585\pi$
$480$	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
$483$	−13.4465			−0.611837
$484$	21.0276			0.955801
$485$	−5.40095	+	3.50054i	−0.245245	+	0.158952i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−10.6041			−0.480519			−0.240259	−	0.970709i	$-0.577233\pi$
$487$	−10.6041			−0.480519			−0.240259	+	0.970709i	$0.577233\pi$
$488$	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
$495$	10.6192	−	6.88266i	0.477297	−	0.309353i
$496$	1.98809	+	1.98809i	0.0892677	+	0.0892677i
$497$	13.7577	+	13.7577i	0.617116	+	0.617116i
$498$		−	1.28163i		−	0.0574312i
$499$	15.9396	−	15.9396i	0.713555	−	0.713555i	−0.253723	−	0.967277i	$-0.581655\pi$
$499$	15.9396	−	15.9396i	0.713555	−	0.713555i	0.967277	+	0.253723i	$0.0816550\pi$
$500$	1.71931	+	11.0474i	0.0768899	+	0.494053i
$501$	13.6151	+	13.6151i	0.608278	+	0.608278i
$502$	−10.0396	+	10.0396i	−0.448089	+	0.448089i
$503$		−	18.1285i		−	0.808309i	−0.914691	−	0.404155i	$-0.867566\pi$
$503$		−	18.1285i		−	0.808309i	0.914691	−	0.404155i	$-0.132434\pi$
$504$	2.24767	+	2.24767i	0.100119	+	0.100119i
$505$	19.5674	+	30.1903i	0.870736	+	1.34345i
$506$			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	$-0.605366\pi$
$509$	−14.6649			−0.650010			−0.325005	+	0.945712i	$0.605366\pi$
$510$	−3.54057	+	16.5840i	−0.156779	+	0.734352i
$511$			11.6337i			0.514644i
$512$		−	1.00000i		−	0.0441942i
$513$	5.28079			0.233153
$514$		−	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
$518$	−0.571801	−	19.3267i	−0.0251235	−	0.849167i
$519$			12.1421i			0.532981i
$520$	−9.03405	+	5.85528i	−0.396169	+	0.256771i
$521$			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
$523$		−	16.6140i		−	0.726479i	−0.931696	−	0.363239i	$-0.881671\pi$
$523$		−	16.6140i		−	0.726479i	0.931696	−	0.363239i	$-0.118329\pi$
$524$	−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
$532$		−	16.7860i		−	0.727764i
$533$	−11.7014			−0.506844
$534$		−	14.4077i		−	0.623481i
$535$	26.7369	+	5.70814i	1.15594	+	0.246784i
$536$	6.91167	+	6.91167i	0.298539	+	0.298539i
$537$	−19.9348			−0.860251
$538$	−16.7896			−0.723853
$539$	17.5666			0.756648
$540$	0.466864	−	2.18679i	0.0200906	−	0.0941043i
$541$	−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	$0.401046\pi$
$542$			3.47058i			0.149074i
$543$	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
$547$		−	1.60901i		−	0.0687964i	−0.999408	−	0.0343982i	$-0.989049\pi$
$547$		−	1.60901i		−	0.0687964i	0.999408	−	0.0343982i	$-0.0109514\pi$
$548$	−1.63948	−	1.63948i	−0.0700353	−	0.0700353i
$549$	1.11855	−	1.11855i	0.0477387	−	0.0477387i
$550$	−11.5555	+	25.8295i	−0.492728	+	1.10137i
$551$	−24.3834			−1.03877
$552$	2.99121	+	2.99121i	0.127314	+	0.127314i
$553$			12.8260i			0.545416i
$554$	−5.08835			−0.216183
$555$	−11.1900	+	7.73198i	−0.474990	+	0.328204i
$556$	−17.9432			−0.760959
$557$		−	13.8846i		−	0.588309i	−0.955758	−	0.294155i	$-0.904962\pi$
$557$		−	13.8846i		−	0.588309i	0.955758	−	0.294155i	$-0.0950381\pi$
$558$	1.98809	+	1.98809i	0.0841624	+	0.0841624i
$559$	−16.1121			−0.681470
$560$	−6.95110	−	1.48401i	−0.293738	−	0.0627109i
$561$	−30.3480	+	30.3480i	−1.28129	+	1.28129i
$562$	−22.3585	−	22.3585i	−0.943138	−	0.943138i
$563$			36.2994i			1.52984i	0.644126	+	0.764919i	$0.277221\pi$
$563$			36.2994i			1.52984i	−0.644126	+	0.764919i	$0.722779\pi$
$564$		−	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
$568$		−	6.12087i		−	0.256826i
$569$	−4.09043	+	4.09043i	−0.171480	+	0.171480i	−0.787629	−	0.616149i	$-0.788692\pi$
$569$	−4.09043	+	4.09043i	−0.171480	+	0.171480i	0.616149	+	0.787629i	$0.288692\pi$
$570$	−9.90895	+	6.42234i	−0.415040	+	0.269002i
$571$	9.17017			0.383760			0.191880	−	0.981418i	$-0.438542\pi$
$571$	9.17017			0.383760			0.191880	+	0.981418i	$0.438542\pi$
$572$	−27.2468			−1.13925
$573$	26.0857			1.08974
$574$	−5.46281	−	5.46281i	−0.228013	−	0.228013i
$575$	−19.3070	−	8.63750i	−0.805157	−	0.360209i
$576$		−	1.00000i		−	0.0416667i
$577$	−35.0406			−1.45876			−0.729381	−	0.684108i	$-0.760192\pi$
$577$	−35.0406			−1.45876			−0.729381	+	0.684108i	$0.760192\pi$
$578$		−	40.5129i		−	1.68512i
$579$	−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
$587$			33.5312i			1.38398i	0.721907	+	0.691990i	$0.243266\pi$
$587$			33.5312i			1.38398i	−0.721907	+	0.691990i	$0.756734\pi$
$588$	2.19488	−	2.19488i	0.0905153	−	0.0905153i
$589$		−	14.8474i		−	0.611775i
$590$	−6.50157	+	30.4533i	−0.267665	+	1.25374i
$591$		−	2.39484i		−	0.0985106i
$592$	−4.17208	+	4.42648i	−0.171472	+	0.181927i
$593$	1.10793	−	1.10793i	0.0454971	−	0.0454971i	−0.683992	−	0.729489i	$-0.739758\pi$
$593$	1.10793	−	1.10793i	0.0454971	−	0.0454971i	0.729489	+	0.683992i	$0.239758\pi$
$594$	4.00173	−	4.00173i	0.164193	−	0.164193i
$595$	52.7153	+	11.2543i	2.16112	+	0.461383i
$596$		−	9.20482i		−	0.377044i
$597$	10.3757			0.424649
$598$		−	20.3665i		−	0.832846i
$599$		−	0.823976i		−	0.0336668i	−0.999858	−	0.0168334i	$-0.994642\pi$
$599$		−	0.823976i		−	0.0336668i	0.999858	−	0.0168334i	$-0.00535848\pi$
$600$	1.78347	+	4.67110i	0.0728100	+	0.190697i
$601$	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
$605$	−39.4565	+	25.5732i	−1.60414	+	1.03970i
$606$	11.3769	+	11.3769i	0.462154	+	0.462154i
$607$			1.34105i			0.0544316i	0.999630	+	0.0272158i	$0.00866413\pi$
$607$			1.34105i			0.0544316i	−0.999630	+	0.0272158i	$0.991336\pi$
$608$	−3.73408	+	3.73408i	−0.151437	+	0.151437i
$609$	−10.3783	−	10.3783i	−0.420551	−	0.420551i
$610$	−0.738519	+	3.45922i	−0.0299018	+	0.140060i
$611$	−29.1067	+	29.1067i	−1.17753	+	1.17753i
$612$			7.58373i			0.306554i
$613$	3.50859	+	3.50859i	0.141711	+	0.141711i	0.774403	−	0.632693i	$-0.218050\pi$
$613$	3.50859	+	3.50859i	0.141711	+	0.141711i	−0.632693	+	0.774403i	$0.718050\pi$
$614$	10.3413	+	10.3413i	0.417342	+	0.417342i
$615$	−1.13468	+	5.31484i	−0.0457548	+	0.214315i
$616$	−12.7202	−	12.7202i	−0.512512	−	0.512512i
$617$	1.91217	−	1.91217i	0.0769810	−	0.0769810i	−0.667568	−	0.744549i	$-0.732665\pi$
$617$	1.91217	−	1.91217i	0.0769810	−	0.0769810i	0.744549	+	0.667568i	$0.232665\pi$
$618$	7.84870	−	7.84870i	0.315721	−	0.315721i
$619$	19.7786			0.794968			0.397484	−	0.917609i	$-0.369883\pi$
$619$	19.7786			0.794968			0.397484	+	0.917609i	$0.369883\pi$
$620$	−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
$623$	−45.7974			−1.83484
$624$	−3.40439	+	3.40439i	−0.136285	+	0.136285i
$625$	−16.6616	−	18.6384i	−0.666464	−	0.745538i
$626$	5.86237			0.234308
$627$	−29.8855			−1.19351
$628$	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
$635$	−45.1783	−	9.64526i	−1.79285	−	0.382760i
$636$	−11.3428			−0.449772
$637$	−14.9444			−0.592120
$638$	−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	$0.671087\pi$
$642$	12.2266			0.482544
$643$	−6.75346			−0.266331			−0.133165	−	0.991094i	$-0.542514\pi$
$643$	−6.75346			−0.266331			−0.133165	+	0.991094i	$0.542514\pi$
$644$	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
$647$			17.0199i			0.669122i	0.942374	+	0.334561i	$0.108588\pi$
$647$			17.0199i			0.669122i	−0.942374	+	0.334561i	$0.891412\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−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
$652$	7.74976			0.303504
$653$	2.21356			0.0866234			0.0433117	−	0.999062i	$-0.486209\pi$
$653$	2.21356			0.0866234			0.0433117	+	0.999062i	$0.486209\pi$
$654$	−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
$658$	−27.1770			−1.05947
$659$	−10.5454			−0.410790			−0.205395	−	0.978679i	$-0.565848\pi$
$659$	−10.5454			−0.410790			−0.205395	+	0.978679i	$0.565848\pi$
$660$	−2.64212	+	12.3757i	−0.102844	+	0.481722i
$661$	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
$668$	−19.2547			−0.744985
$669$	15.6300			0.604289
$670$	−21.3749	−	4.56340i	−0.825786	−	0.176299i
$671$	−6.33022	+	6.33022i	−0.244375	+	0.244375i
$672$	−3.17868			−0.122620
$673$	−18.5100	+	18.5100i	−0.713507	+	0.713507i	−0.967267	−	0.253760i	$-0.918333\pi$
$673$	−18.5100	+	18.5100i	−0.713507	+	0.713507i	0.253760	+	0.967267i	$0.418333\pi$
$674$	−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	$-0.572767\pi$
$677$	19.4458	−	19.4458i	0.747364	−	0.747364i	0.973983	+	0.226620i	$0.0727674\pi$
$678$	3.31414	−	3.31414i	0.127279	−	0.127279i
$679$	6.46955	+	6.46955i	0.248278	+	0.248278i
$680$	−9.22310	−	14.2302i	−0.353690	−	0.545704i
$681$	−4.52667	−	4.52667i	−0.173462	−	0.173462i
$682$	−11.2512	−	11.2512i	−0.430830	−	0.430830i
$683$		−	45.5661i		−	1.74354i	−0.489916	−	0.871770i	$-0.662972\pi$
$683$		−	45.5661i		−	1.74354i	0.489916	−	0.871770i	$-0.337028\pi$
$684$	−3.73408	+	3.73408i	−0.142776	+	0.142776i
$685$	5.07024	+	1.08246i	0.193724	+	0.0413587i
$686$	8.75685	+	8.75685i	0.334338	+	0.334338i
$687$	−11.5417	+	11.5417i	−0.440345	+	0.440345i
$688$			3.34656i			0.127587i
$689$	38.6153	+	38.6153i	1.47113	+	1.47113i
$690$	−9.25056	−	1.97493i	−0.352163	−	0.0751843i
$691$		−	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
$695$	33.6688	−	21.8219i	1.27713	−	0.827753i
$696$			4.61737i			0.175021i
$697$		−	18.4317i		−	0.698152i
$698$	−11.3003			−0.427722
$699$			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
$703$	32.1077	−	0.949941i	1.21097	−	0.0358277i
$704$			5.65930i			0.213293i
$705$	10.3980	+	16.0429i	0.391610	+	0.604211i
$706$			21.3525i			0.803612i
$707$	36.1635	−	36.1635i	1.36007	−	1.36007i
$708$			13.9261i			0.523373i
$709$	−1.20334	−	1.20334i	−0.0451926	−	0.0451926i	0.684149	−	0.729342i	$-0.260174\pi$
$709$	−1.20334	−	1.20334i	−0.0451926	−	0.0451926i	−0.729342	+	0.684149i	$0.760174\pi$
$710$	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
$717$			7.22636i			0.269873i
$718$	5.23042			0.195197
$719$			34.8068i			1.29807i	0.760757	+	0.649037i	$0.224828\pi$
$719$			34.8068i			1.29807i	−0.760757	+	0.649037i	$0.775172\pi$
$720$	1.21617	+	1.87641i	0.0453240	+	0.0699298i
$721$	−24.9485	−	24.9485i	−0.929131	−	0.929131i
$722$	8.88674			0.330730
$723$	−11.6335			−0.432655
$724$	−13.7831			−0.512245
$725$	−8.23497	−	21.5682i	−0.305839	−	0.801024i
$726$	−14.8688	+	14.8688i	−0.551832	+	0.551832i
$727$		−	29.0229i		−	1.07640i	−0.842817	−	0.538200i	$-0.819105\pi$
$727$		−	29.0229i		−	1.07640i	0.842817	−	0.538200i	$-0.180895\pi$
$728$	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
$732$			1.58187i			0.0584677i
$733$	−6.55654	−	6.55654i	−0.242171	−	0.242171i	0.575577	−	0.817748i	$-0.304778\pi$
$733$	−6.55654	−	6.55654i	−0.242171	−	0.242171i	−0.817748	+	0.575577i	$0.804778\pi$
$734$	−0.560713	+	0.560713i	−0.0206963	+	0.0206963i
$735$	−1.44916	+	6.78785i	−0.0534530	+	0.250374i
$736$	−4.23021			−0.155928
$737$	−39.1152	−	39.1152i	−1.44083	−	1.44083i
$738$			2.43043i			0.0894655i
$739$	−3.57785			−0.131613			−0.0658067	−	0.997832i	$-0.520962\pi$
$739$	−3.57785			−0.131613			−0.0658067	+	0.997832i	$0.520962\pi$
$740$	2.44521	−	13.3799i	0.0898876	−	0.491854i
$741$	25.4245			0.933993
$742$			36.0552i			1.32363i
$743$	−29.2655	−	29.2655i	−1.07365	−	1.07365i	−0.997063	−	0.0765832i	$-0.975599\pi$
$743$	−29.2655	−	29.2655i	−1.07365	−	1.07365i	−0.0765832	−	0.997063i	$-0.524401\pi$
$744$	−2.81158			−0.103077
$745$	11.1946	+	17.2720i	0.410139	+	0.632799i
$746$	3.16048	−	3.16048i	0.115713	−	0.115713i
$747$	0.906248	+	0.906248i	0.0331579	+	0.0331579i
$748$		−	42.9186i		−	1.56926i
$749$		−	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
$753$		−	14.1981i		−	0.517409i
$754$	15.7193	−	15.7193i	0.572464	−	0.572464i
$755$	−6.80705	−	10.5025i	−0.247734	−	0.382226i
$756$	−3.17868			−0.115608
$757$	−15.4393			−0.561153			−0.280576	−	0.959832i	$-0.590526\pi$
$757$	−15.4393			−0.561153			−0.280576	+	0.959832i	$0.590526\pi$
$758$	1.59897			0.0580771
$759$	−16.9281	−	16.9281i	−0.614452	−	0.614452i
$760$	2.46541	−	11.5480i	0.0894298	−	0.418889i
$761$			19.6274i			0.711492i	0.934583	+	0.355746i	$0.115773\pi$
$761$			19.6274i			0.711492i	−0.934583	+	0.355746i	$0.884227\pi$
$762$	−20.6597			−0.748422
$763$			61.8524i			2.23921i
$764$	−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	$-0.318024\pi$
$769$	38.3252	−	38.3252i	1.38204	−	1.38204i	0.840985	−	0.541058i	$-0.181976\pi$
$770$	39.3384	+	8.39846i	1.41766	+	0.302660i
$771$	11.0144	+	11.0144i	0.396672	+	0.396672i
$772$		−	22.9897i		−	0.827419i
$773$	13.6080	−	13.6080i	0.489445	−	0.489445i	−0.418686	−	0.908131i	$-0.637509\pi$
$773$	13.6080	−	13.6080i	0.489445	−	0.489445i	0.908131	+	0.418686i	$0.137509\pi$
$774$			3.34656i			0.120290i
$775$	13.1332	−	5.01438i	0.471758	−	0.180122i
$776$		−	2.87834i		−	0.103326i
$777$	14.0704	+	13.2617i	0.504772	+	0.475762i
$778$	−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
$782$	32.0807			1.14721
$783$			4.61737i			0.165011i
$784$			3.10403i			0.110858i
$785$	−3.08844	−	0.659361i	−0.110231	−	0.0235336i
$786$	13.0987			0.467216
$787$	0.848326	+	0.848326i	0.0302396	+	0.0302396i	0.722065	−	0.691825i	$-0.243193\pi$
$787$	0.848326	+	0.848326i	0.0302396	+	0.0302396i	−0.691825	+	0.722065i	$0.743193\pi$
$788$	1.69341	+	1.69341i	0.0603251	+	0.0603251i
$789$			24.3334i			0.866291i
$790$	−1.88379	+	8.82367i	−0.0670223	+	0.313932i
$791$	−10.5346	−	10.5346i	−0.374567	−	0.374567i
$792$			5.65930i			0.201094i
$793$	5.38530	−	5.38530i	0.191238	−	0.191238i
$794$	14.3901	+	14.3901i	0.510686	+	0.510686i
$795$	21.2838	−	13.7948i	0.754859	−	0.489251i
$796$	−7.33672	+	7.33672i	−0.260043	+	0.260043i
$797$		−	54.9817i		−	1.94755i	−0.227510	−	0.973776i	$-0.573058\pi$
$797$		−	54.9817i		−	1.94755i	0.227510	−	0.973776i	$-0.426942\pi$
$798$	11.8695	+	11.8695i	0.420175	+	0.420175i
$799$	−45.8482	−	45.8482i	−1.62199	−	1.62199i
$800$	−4.56408	−	2.04186i	−0.161364	−	0.0721908i
$801$	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
$808$	−16.0893			−0.566021
$809$	−4.86721	+	4.86721i	−0.171122	+	0.171122i	−0.787472	−	0.616350i	$-0.788611\pi$
$809$	−4.86721	+	4.86721i	−0.171122	+	0.171122i	0.616350	+	0.787472i	$0.288611\pi$
$810$	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	$0.575189\pi$
$812$	14.6772			0.515068
$813$	−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
$820$	−2.95582	−	4.56050i	−0.103222	−	0.159260i
$821$	43.5087			1.51846			0.759232	−	0.650820i	$-0.225575\pi$
$821$	43.5087			1.51846			0.759232	+	0.650820i	$0.225575\pi$
$822$	2.31858			0.0808698
$823$	−0.673165	+	0.673165i	−0.0234651	+	0.0234651i	−0.718742	−	0.695277i	$-0.755282\pi$
$823$	−0.673165	+	0.673165i	−0.0234651	+	0.0234651i	0.695277	+	0.718742i	$0.255282\pi$
$824$			11.0997i			0.386677i
$825$	−10.0932	−	26.4352i	−0.351400	−	0.920354i
$826$	44.2665			1.54023
$827$	33.1455			1.15258			0.576290	−	0.817245i	$-0.304500\pi$
$827$	33.1455			1.15258			0.576290	+	0.817245i	$0.304500\pi$
$828$	−4.23021			−0.147010
$829$	−17.7173	+	17.7173i	−0.615349	+	0.615349i	−0.944335	−	0.328986i	$-0.893293\pi$
$829$	−17.7173	+	17.7173i	−0.615349	+	0.615349i	0.328986	+	0.944335i	$0.393293\pi$
$830$	−2.80265	−	0.598346i	−0.0972814	−	0.0207689i
$831$	3.59801	−	3.59801i	0.124814	−	0.124814i
$832$		−	4.81453i		−	0.166914i
$833$		−	23.5401i		−	0.815617i
$834$	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
$837$	−2.81158			−0.0971824
$838$	−22.2951			−0.770170
$839$	−40.9132			−1.41248			−0.706240	−	0.707973i	$-0.749610\pi$
$839$	−40.9132			−1.41248			−0.706240	+	0.707973i	$0.749610\pi$
$840$	5.96453	−	3.86582i	0.205796	−	0.133383i
$841$			7.67986i			0.264823i
$842$	−1.74485	+	1.74485i	−0.0601315	+	0.0601315i
$843$	31.6197			1.08904
$844$	−11.9466			−0.411218
$845$	−19.1013	+	12.3802i	−0.657105	+	0.425893i
$846$	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
$853$	−42.0289			−1.43904			−0.719520	−	0.694471i	$-0.755638\pi$
$853$	−42.0289			−1.43904			−0.719520	+	0.694471i	$0.755638\pi$
$854$	5.02827			0.172064
$855$	2.46541	−	11.5480i	0.0843152	−	0.394932i
$856$	−8.64549	+	8.64549i	−0.295497	+	0.295497i
$857$	34.3759			1.17426			0.587129	−	0.809494i	$-0.300258\pi$
$857$	34.3759			1.17426			0.587129	+	0.809494i	$0.300258\pi$
$858$	19.2664	−	19.2664i	0.657745	−	0.657745i
$859$	29.2733	+	29.2733i	0.998794	+	0.998794i	0.999999	−	0.00120570i	$-0.000383786\pi$
$859$	29.2733	+	29.2733i	0.998794	+	0.998794i	−0.00120570	+	0.999999i	$0.500384\pi$
$860$	−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	−0.494251	−	0.869319i	$-0.664558\pi$
$863$	11.0183	−	11.0183i	0.375069	−	0.375069i	0.869319	+	0.494251i	$0.164558\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	26.5523	+	5.66872i	0.902804	+	0.192742i
$866$	9.00285	+	9.00285i	0.305929	+	0.305929i
$867$	28.6470	+	28.6470i	0.972902	+	0.972902i
$868$			8.93712i			0.303346i
$869$	−16.1469	+	16.1469i	−0.547747	+	0.547747i
$870$	−5.61551	−	8.66411i	−0.190384	−	0.293741i
$871$	33.2765	+	33.2765i	1.12753	+	1.12753i
$872$	13.7592	−	13.7592i	0.465947	−	0.465947i
$873$		−	2.87834i		−	0.0974169i
$874$	15.7959	+	15.7959i	0.534306	+	0.534306i
$875$	−20.9663	+	28.6952i	−0.708792	+	0.970076i
$876$			3.65991i			0.123657i
$877$	−5.02653	−	5.02653i	−0.169734	−	0.169734i	0.617129	−	0.786862i	$-0.288296\pi$
$877$	−5.02653	−	5.02653i	−0.169734	−	0.169734i	−0.786862	+	0.617129i	$0.788296\pi$
$878$	4.79636	+	4.79636i	0.161869	+	0.161869i
$879$	−5.32288			−0.179536
$880$	−6.88266	−	10.6192i	−0.232015	−	0.357973i
$881$			29.2467i			0.985345i	0.870215	+	0.492673i	$0.163980\pi$
$881$			29.2467i			0.985345i	−0.870215	+	0.492673i	$0.836020\pi$
$882$			3.10403i			0.104518i
$883$	−28.8964			−0.972441			−0.486220	−	0.873836i	$-0.661625\pi$
$883$	−28.8964			−0.972441			−0.486220	+	0.873836i	$0.661625\pi$
$884$			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	$-0.684699\pi$
$887$	8.58020	−	8.58020i	0.288095	−	0.288095i	0.836327	+	0.548232i	$0.184699\pi$
$888$	−0.179886	−	6.08010i	−0.00603658	−	0.204035i
$889$			65.6706i			2.20252i
$890$	−31.5065	−	6.72642i	−1.05610	−	0.225470i
$891$			5.65930i			0.189594i
$892$	−11.0520	+	11.0520i	−0.370050	+	0.370050i
$893$		−	45.1495i		−	1.51087i
$894$	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
$902$		−	13.7545i		−	0.457976i
$903$	10.6377			0.353999
$904$			4.68689i			0.155884i
$905$	25.8628	−	16.7626i	0.859709	−	0.557208i
$906$	−3.95777	−	3.95777i	−0.131488	−	0.131488i
$907$	0.367882			0.0122153			0.00610766	−	0.999981i	$-0.498056\pi$
$907$	0.367882			0.0122153			0.00610766	+	0.999981i	$0.498056\pi$
$908$	6.40168			0.212447
$909$	−16.0893			−0.533649
$910$	−33.4663	−	7.14482i	−1.10940	−	0.236848i
$911$	−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	$0.481245\pi$
$912$		−	5.28079i		−	0.174864i
$913$	−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
$917$		−	41.6367i		−	1.37496i
$918$	−5.36251	−	5.36251i	−0.176989	−	0.176989i
$919$	6.98899	−	6.98899i	0.230546	−	0.230546i	−0.582375	−	0.812920i	$-0.697876\pi$
$919$	6.98899	−	6.98899i	0.230546	−	0.230546i	0.812920	+	0.582375i	$0.197876\pi$
$920$	7.93762	−	5.14465i	0.261696	−	0.169614i
$921$	−14.6248			−0.481905
$922$	−12.8604	−	12.8604i	−0.423534	−	0.423534i
$923$		−	29.4691i		−	0.969987i
$924$	17.9891			0.591798
$925$	11.6840	+	28.0800i	0.384167	+	0.923264i
$926$	−36.1282			−1.18725
$927$			11.0997i			0.364563i
$928$	−3.26498	−	3.26498i	−0.107178	−	0.107178i
$929$	31.4501			1.03184			0.515922	−	0.856636i	$-0.327450\pi$
$929$	31.4501			1.03184			0.515922	+	0.856636i	$0.327450\pi$
$930$	5.27569	−	3.41936i	0.172997	−	0.112125i
$931$	11.5907	−	11.5907i	0.379870	−	0.379870i
$932$	−0.738837	−	0.738837i	−0.0242014	−	0.0242014i
$933$			2.94474i			0.0964064i
$934$		−	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	0.925837	−	0.377922i	$-0.123361\pi$
$937$	16.7719	+	16.7719i	0.547915	+	0.547915i	−0.377922	+	0.925837i	$0.623361\pi$
$938$			31.0703i			1.01448i
$939$	−4.14532	+	4.14532i	−0.135278	+	0.135278i
$940$	−18.6965	−	3.99158i	−0.609814	−	0.130191i
$941$	16.4771			0.537139			0.268570	−	0.963260i	$-0.413449\pi$
$941$	16.4771			0.537139			0.268570	+	0.963260i	$0.413449\pi$
$942$	−1.41232			−0.0460159
$943$	10.2812			0.334803
$944$	−9.84721	−	9.84721i	−0.320499	−	0.320499i
$945$	5.96453	−	3.86582i	0.194026	−	0.125755i
$946$		−	18.9392i		−	0.615766i
$947$	−56.8823			−1.84843			−0.924214	−	0.381876i	$-0.875278\pi$
$947$	−56.8823			−1.84843			−0.924214	+	0.381876i	$0.875278\pi$
$948$			4.03499i			0.131050i
$949$	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	$-0.226072\pi$
$953$	3.27877	+	3.27877i	0.106210	+	0.106210i	−0.652005	+	0.758215i	$0.726072\pi$
$954$	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
$957$		−	26.1311i		−	0.844698i
$958$	−21.0873	+	21.0873i	−0.681300	+	0.681300i
$959$		−	7.37004i		−	0.237991i
$960$	−2.18679	−	0.466864i	−0.0705783	−	0.0150680i
$961$		−	23.0950i		−	0.745001i
$962$	−20.0866	+	21.3114i	−0.647618	+	0.687108i
$963$	−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
$967$	−38.2625			−1.23044			−0.615219	−	0.788356i	$-0.710932\pi$
$967$	−38.2625			−1.23044			−0.615219	+	0.788356i	$0.710932\pi$
$968$		−	21.0276i		−	0.675853i
$969$			40.0481i			1.28653i
$970$	3.50054	+	5.40095i	0.112396	+	0.173414i
$971$	−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
$975$	8.58659	+	22.4892i	0.274991	+	0.720230i
$976$	−1.11855	−	1.11855i	−0.0358040	−	0.0358040i
$977$			23.6886i			0.757865i	0.925424	+	0.378932i	$0.123709\pi$
$977$			23.6886i			0.757865i	−0.925424	+	0.378932i	$0.876291\pi$
$978$	−5.47991	+	5.47991i	−0.175228	+	0.175228i
$979$	−57.6556	−	57.6556i	−1.84268	−	1.84268i
$980$	−3.77503	−	5.82445i	−0.120589	−	0.186055i
$981$	13.7592	−	13.7592i	0.439299	−	0.439299i
$982$		−	2.33716i		−	0.0745819i
$983$	29.2431	+	29.2431i	0.932711	+	0.932711i	0.997875	−	0.0651639i	$-0.0207570\pi$
$983$	29.2431	+	29.2431i	0.932711	+	0.932711i	−0.0651639	+	0.997875i	$0.520757\pi$
$984$	−1.71858	−	1.71858i	−0.0547862	−	0.0547862i
$985$	−5.23701	−	1.11806i	−0.166865	−	0.0356245i
$986$	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
$993$	2.88137			0.0914375
$994$	13.7577	−	13.7577i	0.436367	−	0.436367i
$995$	4.84403	−	22.6894i	0.153566	−	0.719303i
$996$	−1.28163			−0.0406100
$997$	14.2061			0.449913			0.224957	−	0.974369i	$-0.427776\pi$
$997$	14.2061			0.449913			0.224957	+	0.974369i	$0.427776\pi$
$998$	−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.l.a.697.10	yes	36
5.3	odd	4		1110.2.o.a.253.9	yes	36
37.6	odd	4		1110.2.o.a.487.9	yes	36
185.43	even	4	inner	1110.2.l.a.43.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.10	✓	36	185.43	even	4	inner
1110.2.l.a.697.10	yes	36	1.1	even	1	trivial
1110.2.o.a.253.9	yes	36	5.3	odd	4
1110.2.o.a.487.9	yes	36	37.6	odd	4

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.l (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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