LMFDB - Embedded newform 370.2.h.d.253.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 3x^{8} - 8x^{7} - 26x^{6} + 12x^{5} + 24x^{4} + 166x^{3} + 113x^{2} - 152x + 160 $ x^10 + 3x^8 - 8x^7 - 26x^6 + 12x^5 + 24x^4 + 166x^3 + 113x^2 - 152x + 160
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.4
Root			$2.03431 + 0.602710i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.d.117.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.78347 - 1.78347i) q^{3} +1.00000 q^{4} +(-2.22195 + 0.250846i) q^{5} +(1.78347 - 1.78347i) q^{6} +(0.501691 - 0.501691i) q^{7} +1.00000 q^{8} -3.36152i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.78347 - 1.78347i) q^{3} +1.00000 q^{4} +(-2.22195 + 0.250846i) q^{5} +(1.78347 - 1.78347i) q^{6} +(0.501691 - 0.501691i) q^{7} +1.00000 q^{8} -3.36152i q^{9} +(-2.22195 + 0.250846i) q^{10} -5.77574i q^{11} +(1.78347 - 1.78347i) q^{12} -0.334084 q^{13} +(0.501691 - 0.501691i) q^{14} +(-3.51541 + 4.41016i) q^{15} +1.00000 q^{16} +4.86321i q^{17} -3.36152i q^{18} +(5.60813 + 5.60813i) q^{19} +(-2.22195 + 0.250846i) q^{20} -1.78950i q^{21} -5.77574i q^{22} +1.33747 q^{23} +(1.78347 - 1.78347i) q^{24} +(4.87415 - 1.11473i) q^{25} -0.334084 q^{26} +(-0.644753 - 0.644753i) q^{27} +(0.501691 - 0.501691i) q^{28} +(-7.32635 + 7.32635i) q^{29} +(-3.51541 + 4.41016i) q^{30} +(-2.92991 - 2.92991i) q^{31} +1.00000 q^{32} +(-10.3008 - 10.3008i) q^{33} +4.86321i q^{34} +(-0.988888 + 1.24058i) q^{35} -3.36152i q^{36} +(-6.07201 + 0.361517i) q^{37} +(5.60813 + 5.60813i) q^{38} +(-0.595828 + 0.595828i) q^{39} +(-2.22195 + 0.250846i) q^{40} +7.31524i q^{41} -1.78950i q^{42} +1.15610 q^{43} -5.77574i q^{44} +(0.843222 + 7.46913i) q^{45} +1.33747 q^{46} +(4.83578 - 4.83578i) q^{47} +(1.78347 - 1.78347i) q^{48} +6.49661i q^{49} +(4.87415 - 1.11473i) q^{50} +(8.67338 + 8.67338i) q^{51} -0.334084 q^{52} +(-6.77574 - 6.77574i) q^{53} +(-0.644753 - 0.644753i) q^{54} +(1.44882 + 12.8334i) q^{55} +(0.501691 - 0.501691i) q^{56} +20.0038 q^{57} +(-7.32635 + 7.32635i) q^{58} +(-8.73793 - 8.73793i) q^{59} +(-3.51541 + 4.41016i) q^{60} +(0.472799 + 0.472799i) q^{61} +(-2.92991 - 2.92991i) q^{62} +(-1.68644 - 1.68644i) q^{63} +1.00000 q^{64} +(0.742319 - 0.0838036i) q^{65} +(-10.3008 - 10.3008i) q^{66} +(1.79312 + 1.79312i) q^{67} +4.86321i q^{68} +(2.38533 - 2.38533i) q^{69} +(-0.988888 + 1.24058i) q^{70} -3.33183 q^{71} -3.36152i q^{72} +(4.96073 - 4.96073i) q^{73} +(-6.07201 + 0.361517i) q^{74} +(6.70480 - 10.6810i) q^{75} +(5.60813 + 5.60813i) q^{76} +(-2.89764 - 2.89764i) q^{77} +(-0.595828 + 0.595828i) q^{78} +(5.53177 + 5.53177i) q^{79} +(-2.22195 + 0.250846i) q^{80} +7.78476 q^{81} +7.31524i q^{82} +(4.77799 + 4.77799i) q^{83} -1.78950i q^{84} +(-1.21991 - 10.8058i) q^{85} +1.15610 q^{86} +26.1326i q^{87} -5.77574i q^{88} +(3.08239 - 3.08239i) q^{89} +(0.843222 + 7.46913i) q^{90} +(-0.167607 + 0.167607i) q^{91} +1.33747 q^{92} -10.4508 q^{93} +(4.83578 - 4.83578i) q^{94} +(-13.8678 - 11.0542i) q^{95} +(1.78347 - 1.78347i) q^{96} +3.56694i q^{97} +6.49661i q^{98} -19.4152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8} + 2 q^{10} + 2 q^{12} - 12 q^{13} - 4 q^{14} - 14 q^{15} + 10 q^{16} + 8 q^{19} + 2 q^{20} + 4 q^{23} + 2 q^{24} + 28 q^{25} - 12 q^{26} - 28 q^{27} - 4 q^{28} - 32 q^{29} - 14 q^{30} - 26 q^{31} + 10 q^{32} - 24 q^{33} + 22 q^{35} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} + 12 q^{43} - 10 q^{45} + 4 q^{46} + 48 q^{47} + 2 q^{48} + 28 q^{50} + 16 q^{51} - 12 q^{52} - 2 q^{53} - 28 q^{54} + 12 q^{55} - 4 q^{56} + 76 q^{57} - 32 q^{58} - 20 q^{59} - 14 q^{60} - 24 q^{61} - 26 q^{62} + 20 q^{63} + 10 q^{64} + 28 q^{65} - 24 q^{66} - 10 q^{67} - 46 q^{69} + 22 q^{70} - 16 q^{71} + 4 q^{73} - 2 q^{74} - 48 q^{75} + 8 q^{76} - 24 q^{77} + 6 q^{78} - 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} - 10 q^{85} + 12 q^{86} - 2 q^{89} - 10 q^{90} + 16 q^{91} + 4 q^{92} - 60 q^{93} + 48 q^{94} - 28 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8 + 2 * q^10 + 2 * q^12 - 12 * q^13 - 4 * q^14 - 14 * q^15 + 10 * q^16 + 8 * q^19 + 2 * q^20 + 4 * q^23 + 2 * q^24 + 28 * q^25 - 12 * q^26 - 28 * q^27 - 4 * q^28 - 32 * q^29 - 14 * q^30 - 26 * q^31 + 10 * q^32 - 24 * q^33 + 22 * q^35 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 + 12 * q^43 - 10 * q^45 + 4 * q^46 + 48 * q^47 + 2 * q^48 + 28 * q^50 + 16 * q^51 - 12 * q^52 - 2 * q^53 - 28 * q^54 + 12 * q^55 - 4 * q^56 + 76 * q^57 - 32 * q^58 - 20 * q^59 - 14 * q^60 - 24 * q^61 - 26 * q^62 + 20 * q^63 + 10 * q^64 + 28 * q^65 - 24 * q^66 - 10 * q^67 - 46 * q^69 + 22 * q^70 - 16 * q^71 + 4 * q^73 - 2 * q^74 - 48 * q^75 + 8 * q^76 - 24 * q^77 + 6 * q^78 - 2 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 - 10 * q^85 + 12 * q^86 - 2 * q^89 - 10 * q^90 + 16 * q^91 + 4 * q^92 - 60 * q^93 + 48 * q^94 - 28 * q^95 + 2 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	1.78347	−	1.78347i	1.02969	−	1.02969i	0.0301401	−	0.999546i	$-0.490405\pi$
$3$	1.78347	−	1.78347i	1.02969	−	1.02969i	0.999546	−	0.0301401i	$-0.00959534\pi$
$4$	1.00000			0.500000
$5$	−2.22195	+	0.250846i	−0.993688	+	0.112182i
$5$	−2.22195	+	0.250846i	−0.993688	+	0.112182i
$6$	1.78347	−	1.78347i	0.728098	−	0.728098i
$7$	0.501691	−	0.501691i	0.189621	−	0.189621i	−0.605911	−	0.795532i	$-0.707191\pi$
$7$	0.501691	−	0.501691i	0.189621	−	0.189621i	0.795532	+	0.605911i	$0.207191\pi$
$8$	1.00000			0.353553
$9$		−	3.36152i		−	1.12051i
$10$	−2.22195	+	0.250846i	−0.702643	+	0.0793244i
$11$		−	5.77574i		−	1.74145i	−0.491770	−	0.870725i	$-0.663650\pi$
$11$		−	5.77574i		−	1.74145i	0.491770	−	0.870725i	$-0.336350\pi$
$12$	1.78347	−	1.78347i	0.514843	−	0.514843i
$13$	−0.334084			−0.0926583			−0.0463291	−	0.998926i	$-0.514752\pi$
$13$	−0.334084			−0.0926583			−0.0463291	+	0.998926i	$0.514752\pi$
$14$	0.501691	−	0.501691i	0.134083	−	0.134083i
$15$	−3.51541	+	4.41016i	−0.907674	+	1.13870i
$16$	1.00000			0.250000
$17$			4.86321i			1.17950i	0.807585	+	0.589751i	$0.200774\pi$
$17$			4.86321i			1.17950i	−0.807585	+	0.589751i	$0.799226\pi$
$18$		−	3.36152i		−	0.792317i
$19$	5.60813	+	5.60813i	1.28659	+	1.28659i	0.936843	+	0.349751i	$0.113734\pi$
$19$	5.60813	+	5.60813i	1.28659	+	1.28659i	0.349751	+	0.936843i	$0.386266\pi$
$20$	−2.22195	+	0.250846i	−0.496844	+	0.0560908i
$21$		−	1.78950i		−	0.390501i
$22$		−	5.77574i		−	1.23139i
$23$	1.33747			0.278881			0.139441	−	0.990230i	$-0.455470\pi$
$23$	1.33747			0.278881			0.139441	+	0.990230i	$0.455470\pi$
$24$	1.78347	−	1.78347i	0.364049	−	0.364049i
$25$	4.87415	−	1.11473i	0.974831	−	0.222947i
$26$	−0.334084			−0.0655193
$27$	−0.644753	−	0.644753i	−0.124083	−	0.124083i
$28$	0.501691	−	0.501691i	0.0948107	−	0.0948107i
$29$	−7.32635	+	7.32635i	−1.36047	+	1.36047i	−0.487153	+	0.873316i	$0.661965\pi$
$29$	−7.32635	+	7.32635i	−1.36047	+	1.36047i	−0.873316	+	0.487153i	$0.838035\pi$
$30$	−3.51541	+	4.41016i	−0.641823	+	0.805181i
$31$	−2.92991	−	2.92991i	−0.526228	−	0.526228i	0.393218	−	0.919445i	$-0.371362\pi$
$31$	−2.92991	−	2.92991i	−0.526228	−	0.526228i	−0.919445	+	0.393218i	$0.871362\pi$
$32$	1.00000			0.176777
$33$	−10.3008	−	10.3008i	−1.79315	−	1.79315i
$34$			4.86321i			0.834033i
$35$	−0.988888	+	1.24058i	−0.167153	+	0.209697i
$36$		−	3.36152i		−	0.560253i
$37$	−6.07201	+	0.361517i	−0.998232	+	0.0594330i
$37$	−6.07201	+	0.361517i	−0.998232	+	0.0594330i
$38$	5.60813	+	5.60813i	0.909759	+	0.909759i
$39$	−0.595828	+	0.595828i	−0.0954089	+	0.0954089i
$40$	−2.22195	+	0.250846i	−0.351322	+	0.0396622i
$41$			7.31524i			1.14245i	0.820794	+	0.571224i	$0.193531\pi$
$41$			7.31524i			1.14245i	−0.820794	+	0.571224i	$0.806469\pi$
$42$		−	1.78950i		−	0.276126i
$43$	1.15610			0.176303			0.0881516	−	0.996107i	$-0.471904\pi$
$43$	1.15610			0.176303			0.0881516	+	0.996107i	$0.471904\pi$
$44$		−	5.77574i		−	0.870725i
$45$	0.843222	+	7.46913i	0.125700	+	1.11343i
$46$	1.33747			0.197199
$47$	4.83578	−	4.83578i	0.705370	−	0.705370i	−0.260188	−	0.965558i	$-0.583784\pi$
$47$	4.83578	−	4.83578i	0.705370	−	0.705370i	0.965558	+	0.260188i	$0.0837844\pi$
$48$	1.78347	−	1.78347i	0.257421	−	0.257421i
$49$			6.49661i			0.928087i
$50$	4.87415	−	1.11473i	0.689309	−	0.157647i
$51$	8.67338	+	8.67338i	1.21452	+	1.21452i
$52$	−0.334084			−0.0463291
$53$	−6.77574	−	6.77574i	−0.930719	−	0.930719i	0.0670316	−	0.997751i	$-0.478647\pi$
$53$	−6.77574	−	6.77574i	−0.930719	−	0.930719i	−0.997751	+	0.0670316i	$0.978647\pi$
$54$	−0.644753	−	0.644753i	−0.0877398	−	0.0877398i
$55$	1.44882	+	12.8334i	0.195359	+	1.73046i
$56$	0.501691	−	0.501691i	0.0670413	−	0.0670413i
$57$	20.0038			2.64957
$58$	−7.32635	+	7.32635i	−0.961997	+	0.961997i
$59$	−8.73793	−	8.73793i	−1.13758	−	1.13758i	−0.988883	−	0.148698i	$-0.952492\pi$
$59$	−8.73793	−	8.73793i	−1.13758	−	1.13758i	−0.148698	−	0.988883i	$-0.547508\pi$
$60$	−3.51541	+	4.41016i	−0.453837	+	0.569349i
$61$	0.472799	+	0.472799i	0.0605357	+	0.0605357i	0.736727	−	0.676191i	$-0.236371\pi$
$61$	0.472799	+	0.472799i	0.0605357	+	0.0605357i	−0.676191	+	0.736727i	$0.736371\pi$
$62$	−2.92991	−	2.92991i	−0.372099	−	0.372099i
$63$	−1.68644	−	1.68644i	−0.212472	−	0.212472i
$64$	1.00000			0.125000
$65$	0.742319	−	0.0838036i	0.0920734	−	0.0103946i
$66$	−10.3008	−	10.3008i	−1.26795	−	1.26795i
$67$	1.79312	+	1.79312i	0.219065	+	0.219065i	0.808104	−	0.589040i	$-0.200494\pi$
$67$	1.79312	+	1.79312i	0.219065	+	0.219065i	−0.589040	+	0.808104i	$0.700494\pi$
$68$			4.86321i			0.589751i
$69$	2.38533	−	2.38533i	0.287160	−	0.287160i
$70$	−0.988888	+	1.24058i	−0.118195	+	0.148278i
$71$	−3.33183			−0.395416			−0.197708	−	0.980261i	$-0.563350\pi$
$71$	−3.33183			−0.395416			−0.197708	+	0.980261i	$0.563350\pi$
$72$		−	3.36152i		−	0.396159i
$73$	4.96073	−	4.96073i	0.580609	−	0.580609i	−0.354461	−	0.935071i	$-0.615336\pi$
$73$	4.96073	−	4.96073i	0.580609	−	0.580609i	0.935071	+	0.354461i	$0.115336\pi$
$74$	−6.07201	+	0.361517i	−0.705857	+	0.0420254i
$75$	6.70480	−	10.6810i	0.774204	−	1.23333i
$76$	5.60813	+	5.60813i	0.643297	+	0.643297i
$77$	−2.89764	−	2.89764i	−0.330216	−	0.330216i
$78$	−0.595828	+	0.595828i	−0.0674643	+	0.0674643i
$79$	5.53177	+	5.53177i	0.622373	+	0.622373i	0.946138	−	0.323765i	$-0.104949\pi$
$79$	5.53177	+	5.53177i	0.622373	+	0.622373i	−0.323765	+	0.946138i	$0.604949\pi$
$80$	−2.22195	+	0.250846i	−0.248422	+	0.0280454i
$81$	7.78476			0.864973
$82$			7.31524i			0.807833i
$83$	4.77799	+	4.77799i	0.524453	+	0.524453i	0.918913	−	0.394460i	$-0.129068\pi$
$83$	4.77799	+	4.77799i	0.524453	+	0.524453i	−0.394460	+	0.918913i	$0.629068\pi$
$84$		−	1.78950i		−	0.195251i
$85$	−1.21991	−	10.8058i	−0.132318	−	1.17206i
$86$	1.15610			0.124665
$87$			26.1326i			2.80171i
$88$		−	5.77574i		−	0.615696i
$89$	3.08239	−	3.08239i	0.326733	−	0.326733i	−0.524610	−	0.851343i	$-0.675789\pi$
$89$	3.08239	−	3.08239i	0.326733	−	0.326733i	0.851343	+	0.524610i	$0.175789\pi$
$90$	0.843222	+	7.46913i	0.0888834	+	0.787316i
$91$	−0.167607	+	0.167607i	−0.0175700	+	0.0175700i
$92$	1.33747			0.139441
$93$	−10.4508			−1.08370
$94$	4.83578	−	4.83578i	0.498772	−	0.498772i
$95$	−13.8678	−	11.0542i	−1.42280	−	1.13414i
$96$	1.78347	−	1.78347i	0.182024	−	0.182024i
$97$			3.56694i			0.362167i	0.983468	+	0.181084i	$0.0579605\pi$
$97$			3.56694i			0.362167i	−0.983468	+	0.181084i	$0.942039\pi$
$98$			6.49661i			0.656257i
$99$	−19.4152			−1.95131
$100$	4.87415	−	1.11473i	0.487415	−	0.111473i
$101$			0.222565i			0.0221460i	0.999939	+	0.0110730i	$0.00352472\pi$
$101$			0.222565i			0.0221460i	−0.999939	+	0.0110730i	$0.996475\pi$
$102$	8.67338	+	8.67338i	0.858792	+	0.858792i
$103$		−	5.38950i		−	0.531044i	−0.964105	−	0.265522i	$-0.914456\pi$
$103$		−	5.38950i		−	0.531044i	0.964105	−	0.265522i	$-0.0855442\pi$
$104$	−0.334084			−0.0327596
$105$	0.448889	+	3.97619i	0.0438070	+	0.388036i
$106$	−6.77574	−	6.77574i	−0.658118	−	0.658118i
$107$	2.00040	−	2.00040i	0.193386	−	0.193386i	−0.603772	−	0.797157i	$-0.706336\pi$
$107$	2.00040	−	2.00040i	0.193386	−	0.193386i	0.797157	+	0.603772i	$0.206336\pi$
$108$	−0.644753	−	0.644753i	−0.0620414	−	0.0620414i
$109$	0.389616	+	0.389616i	0.0373185	+	0.0373185i	0.725520	−	0.688201i	$-0.241599\pi$
$109$	0.389616	+	0.389616i	0.0373185	+	0.0373185i	−0.688201	+	0.725520i	$0.741599\pi$
$110$	1.44882	+	12.8334i	0.138139	+	1.22362i
$111$	−10.1845	+	11.4740i	−0.966668	+	1.08906i
$112$	0.501691	−	0.501691i	0.0474054	−	0.0474054i
$113$		−	5.48455i		−	0.515943i	−0.966153	−	0.257971i	$-0.916946\pi$
$113$		−	5.48455i		−	0.515943i	0.966153	−	0.257971i	$-0.0830540\pi$
$114$	20.0038			1.87353
$115$	−2.97179	+	0.335498i	−0.277121	+	0.0312853i
$116$	−7.32635	+	7.32635i	−0.680235	+	0.680235i
$117$			1.12303i			0.103824i
$118$	−8.73793	−	8.73793i	−0.804391	−	0.804391i
$119$	2.43983	+	2.43983i	0.223659	+	0.223659i
$120$	−3.51541	+	4.41016i	−0.320911	+	0.402590i
$121$	−22.3592			−2.03265
$122$	0.472799	+	0.472799i	0.0428052	+	0.0428052i
$123$	13.0465	+	13.0465i	1.17636	+	1.17636i
$124$	−2.92991	−	2.92991i	−0.263114	−	0.263114i
$125$	−10.5505	+	3.69955i	−0.943667	+	0.330898i
$126$	−1.68644	−	1.68644i	−0.150240	−	0.150240i
$127$	−7.39933	+	7.39933i	−0.656584	+	0.656584i	−0.954570	−	0.297986i	$-0.903685\pi$
$127$	−7.39933	+	7.39933i	−0.656584	+	0.656584i	0.297986	+	0.954570i	$0.403685\pi$
$128$	1.00000			0.0883883
$129$	2.06186	−	2.06186i	0.181537	−	0.181537i
$130$	0.742319	−	0.0838036i	0.0651057	−	0.00735006i
$131$	−8.93747	−	8.93747i	−0.780870	−	0.780870i	0.199107	−	0.979978i	$-0.436196\pi$
$131$	−8.93747	−	8.93747i	−0.780870	−	0.780870i	−0.979978	+	0.199107i	$0.936196\pi$
$132$	−10.3008	−	10.3008i	−0.896573	−	0.896573i
$133$	5.62710			0.487932
$134$	1.79312	+	1.79312i	0.154902	+	0.154902i
$135$	1.59435	+	1.27088i	0.137219	+	0.109380i
$136$			4.86321i			0.417017i
$137$	5.42935	−	5.42935i	0.463861	−	0.463861i	−0.436058	−	0.899919i	$-0.643626\pi$
$137$	5.42935	−	5.42935i	0.463861	−	0.463861i	0.899919	+	0.436058i	$0.143626\pi$
$138$	2.38533	−	2.38533i	0.203053	−	0.203053i
$139$	−13.4593			−1.14160			−0.570800	−	0.821089i	$-0.693367\pi$
$139$	−13.4593			−1.14160			−0.570800	+	0.821089i	$0.693367\pi$
$140$	−0.988888	+	1.24058i	−0.0835763	+	0.104848i
$141$		−	17.2489i		−	1.45262i
$142$	−3.33183			−0.279601
$143$			1.92958i			0.161360i
$144$		−	3.36152i		−	0.280126i
$145$	14.4410	−	18.1166i	1.19926	−	1.50450i
$146$	4.96073	−	4.96073i	0.410553	−	0.410553i
$147$	11.5865	+	11.5865i	0.955638	+	0.955638i
$148$	−6.07201	+	0.361517i	−0.499116	+	0.0297165i
$149$		−	13.8867i		−	1.13764i	−0.822461	−	0.568821i	$-0.807400\pi$
$149$		−	13.8867i		−	1.13764i	0.822461	−	0.568821i	$-0.192600\pi$
$150$	6.70480	−	10.6810i	0.547445	−	0.872099i
$151$			5.54233i			0.451028i	0.974240	+	0.225514i	$0.0724062\pi$
$151$			5.54233i			0.451028i	−0.974240	+	0.225514i	$0.927594\pi$
$152$	5.60813	+	5.60813i	0.454879	+	0.454879i
$153$	16.3478			1.32164
$154$	−2.89764	−	2.89764i	−0.233498	−	0.233498i
$155$	7.24508	+	5.77517i	0.581939	+	0.463873i
$156$	−0.595828	+	0.595828i	−0.0477045	+	0.0477045i
$157$	17.6224	−	17.6224i	1.40642	−	1.40642i	0.629062	−	0.777355i	$-0.283439\pi$
$157$	17.6224	−	17.6224i	1.40642	−	1.40642i	0.777355	−	0.629062i	$-0.216561\pi$
$158$	5.53177	+	5.53177i	0.440084	+	0.440084i
$159$	−24.1686			−1.91670
$160$	−2.22195	+	0.250846i	−0.175661	+	0.0198311i
$161$	0.670995	−	0.670995i	0.0528819	−	0.0528819i
$162$	7.78476			0.611628
$163$		−	13.5930i		−	1.06469i	−0.846529	−	0.532343i	$-0.821312\pi$
$163$		−	13.5930i		−	1.06469i	0.846529	−	0.532343i	$-0.178688\pi$
$164$			7.31524i			0.571224i
$165$	25.4719	+	20.3041i	1.98299	+	1.58067i
$166$	4.77799	+	4.77799i	0.370844	+	0.370844i
$167$		−	11.8884i		−	0.919951i	−0.887932	−	0.459976i	$-0.847858\pi$
$167$		−	11.8884i		−	0.919951i	0.887932	−	0.459976i	$-0.152142\pi$
$168$		−	1.78950i		−	0.138063i
$169$	−12.8884			−0.991414
$170$	−1.21991	−	10.8058i	−0.0935632	−	0.828769i
$171$	18.8518	−	18.8518i	1.44164	−	1.44164i
$172$	1.15610			0.0881516
$173$	1.19504	−	1.19504i	0.0908572	−	0.0908572i	−0.660217	−	0.751075i	$-0.729536\pi$
$173$	1.19504	−	1.19504i	0.0908572	−	0.0908572i	0.751075	+	0.660217i	$0.229536\pi$
$174$			26.1326i			1.98111i
$175$	1.88607	−	3.00457i	0.142573	−	0.227124i
$176$		−	5.77574i		−	0.435363i
$177$	−31.1676			−2.34270
$178$	3.08239	−	3.08239i	0.231035	−	0.231035i
$179$	−14.1150	+	14.1150i	−1.05501	+	1.05501i	−0.0566105	+	0.998396i	$0.518029\pi$
$179$	−14.1150	+	14.1150i	−1.05501	+	1.05501i	−0.998396	+	0.0566105i	$0.981971\pi$
$180$	0.843222	+	7.46913i	0.0628500	+	0.556716i
$181$	14.6126			1.08615			0.543075	−	0.839684i	$-0.317260\pi$
$181$	14.6126			1.08615			0.543075	+	0.839684i	$0.317260\pi$
$182$	−0.167607	+	0.167607i	−0.0124239	+	0.0124239i
$183$	1.68644			0.124666
$184$	1.33747			0.0985994
$185$	13.4010	−	2.32641i	0.985264	−	0.171041i
$186$	−10.4508			−0.766291
$187$	28.0886			2.05404
$188$	4.83578	−	4.83578i	0.352685	−	0.352685i
$189$	−0.646934			−0.0470575
$190$	−13.8678	−	11.0542i	−1.00607	−	0.801958i
$191$	−8.33714	+	8.33714i	−0.603254	+	0.603254i	−0.941175	−	0.337921i	$-0.890276\pi$
$191$	−8.33714	+	8.33714i	−0.603254	+	0.603254i	0.337921	+	0.941175i	$0.390276\pi$
$192$	1.78347	−	1.78347i	0.128711	−	0.128711i
$193$	19.5996			1.41081			0.705404	−	0.708805i	$-0.250766\pi$
$193$	19.5996			1.41081			0.705404	+	0.708805i	$0.250766\pi$
$194$			3.56694i			0.256091i
$195$	1.17444	−	1.47336i	0.0841035	−	0.105510i
$196$			6.49661i			0.464044i
$197$	−11.3654	+	11.3654i	−0.809749	+	0.809749i	−0.984596	−	0.174847i	$-0.944057\pi$
$197$	−11.3654	+	11.3654i	−0.809749	+	0.809749i	0.174847	+	0.984596i	$0.444057\pi$
$198$	−19.4152			−1.37978
$199$	4.39595	−	4.39595i	0.311620	−	0.311620i	−0.533917	−	0.845537i	$-0.679280\pi$
$199$	4.39595	−	4.39595i	0.311620	−	0.311620i	0.845537	+	0.533917i	$0.179280\pi$
$200$	4.87415	−	1.11473i	0.344655	−	0.0788236i
$201$	6.39595			0.451135
$202$			0.222565i			0.0156596i
$203$			7.35114i			0.515949i
$204$	8.67338	+	8.67338i	0.607258	+	0.607258i
$205$	−1.83500	−	16.2541i	−0.128162	−	1.13524i
$206$		−	5.38950i		−	0.375505i
$207$		−	4.49592i		−	0.312488i
$208$	−0.334084			−0.0231646
$209$	32.3911	−	32.3911i	2.24054	−	2.24054i
$210$	0.448889	+	3.97619i	0.0309762	+	0.274383i
$211$	−16.7875			−1.15570			−0.577849	−	0.816144i	$-0.696108\pi$
$211$	−16.7875			−1.15570			−0.577849	+	0.816144i	$0.696108\pi$
$212$	−6.77574	−	6.77574i	−0.465360	−	0.465360i
$213$	−5.94222	+	5.94222i	−0.407154	+	0.407154i
$214$	2.00040	−	2.00040i	0.136744	−	0.136744i
$215$	−2.56879	+	0.290002i	−0.175190	+	0.0197780i
$216$	−0.644753	−	0.644753i	−0.0438699	−	0.0438699i
$217$	−2.93982			−0.199568
$218$	0.389616	+	0.389616i	0.0263881	+	0.0263881i
$219$		−	17.6946i		−	1.19569i
$220$	1.44882	+	12.8334i	0.0976793	+	0.865229i
$221$		−	1.62472i		−	0.109291i
$222$	−10.1845	+	11.4740i	−0.683538	+	0.770084i
$223$	10.4136	+	10.4136i	0.697343	+	0.697343i	0.963837	−	0.266494i	$-0.0858651\pi$
$223$	10.4136	+	10.4136i	0.697343	+	0.697343i	−0.266494	+	0.963837i	$0.585865\pi$
$224$	0.501691	−	0.501691i	0.0335207	−	0.0335207i
$225$	−3.74720	−	16.3845i	−0.249813	−	1.09230i
$226$		−	5.48455i		−	0.364827i
$227$		−	6.88908i		−	0.457244i	−0.973515	−	0.228622i	$-0.926578\pi$
$227$		−	6.88908i		−	0.457244i	0.973515	−	0.228622i	$-0.0734221\pi$
$228$	20.0038			1.32479
$229$			13.4017i			0.885608i	0.896618	+	0.442804i	$0.146016\pi$
$229$			13.4017i			0.885608i	−0.896618	+	0.442804i	$0.853984\pi$
$230$	−2.97179	+	0.335498i	−0.195954	+	0.0221221i
$231$	−10.3357			−0.680038
$232$	−7.32635	+	7.32635i	−0.480999	+	0.480999i
$233$	−11.3590	+	11.3590i	−0.744152	+	0.744152i	−0.973374	−	0.229222i	$-0.926382\pi$
$233$	−11.3590	+	11.3590i	−0.744152	+	0.744152i	0.229222	+	0.973374i	$0.426382\pi$
$234$			1.12303i			0.0734147i
$235$	−9.53183	+	11.9579i	−0.621788	+	0.780047i
$236$	−8.73793	−	8.73793i	−0.568791	−	0.568791i
$237$	19.7315			1.28170
$238$	2.43983	+	2.43983i	0.158151	+	0.158151i
$239$	4.68385	+	4.68385i	0.302973	+	0.302973i	0.842176	−	0.539203i	$-0.181274\pi$
$239$	4.68385	+	4.68385i	0.302973	+	0.302973i	−0.539203	+	0.842176i	$0.681274\pi$
$240$	−3.51541	+	4.41016i	−0.226919	+	0.284674i
$241$	−8.74018	+	8.74018i	−0.563004	+	0.563004i	−0.930160	−	0.367155i	$-0.880332\pi$
$241$	−8.74018	+	8.74018i	−0.563004	+	0.563004i	0.367155	+	0.930160i	$0.380332\pi$
$242$	−22.3592			−1.43730
$243$	15.8181	−	15.8181i	1.01473	−	1.01473i
$244$	0.472799	+	0.472799i	0.0302679	+	0.0302679i
$245$	−1.62965	−	14.4352i	−0.104114	−	0.922229i
$246$	13.0465	+	13.0465i	0.831814	+	0.831814i
$247$	−1.87359	−	1.87359i	−0.119214	−	0.119214i
$248$	−2.92991	−	2.92991i	−0.186050	−	0.186050i
$249$	17.0428			1.08004
$250$	−10.5505	+	3.69955i	−0.667273	+	0.233980i
$251$	−12.8437	−	12.8437i	−0.810687	−	0.810687i	0.174050	−	0.984737i	$-0.444315\pi$
$251$	−12.8437	−	12.8437i	−0.810687	−	0.810687i	−0.984737	+	0.174050i	$0.944315\pi$
$252$	−1.68644	−	1.68644i	−0.106236	−	0.106236i
$253$		−	7.72486i		−	0.485658i
$254$	−7.39933	+	7.39933i	−0.464275	+	0.464275i
$255$	−21.4475	−	17.0962i	−1.34310	−	1.07060i
$256$	1.00000			0.0625000
$257$		−	2.20193i		−	0.137352i	−0.997639	−	0.0686762i	$-0.978122\pi$
$257$		−	2.20193i		−	0.137352i	0.997639	−	0.0686762i	$-0.0218775\pi$
$258$	2.06186	−	2.06186i	0.128366	−	0.128366i
$259$	−2.86490	+	3.22764i	−0.178017	+	0.200556i
$260$	0.742319	−	0.0838036i	0.0460367	−	0.00519728i
$261$	24.6277	+	24.6277i	1.52441	+	1.52441i
$262$	−8.93747	−	8.93747i	−0.552159	−	0.552159i
$263$	−11.0490	+	11.0490i	−0.681310	+	0.681310i	−0.960295	−	0.278985i	$-0.910002\pi$
$263$	−11.0490	+	11.0490i	−0.681310	+	0.681310i	0.278985	+	0.960295i	$0.410002\pi$
$264$	−10.3008	−	10.3008i	−0.633973	−	0.633973i
$265$	16.7550	+	13.3557i	1.02925	+	0.820435i
$266$	5.62710			0.345020
$267$		−	10.9947i		−	0.672864i
$268$	1.79312	+	1.79312i	0.109532	+	0.109532i
$269$			3.21918i			0.196277i	0.995173	+	0.0981385i	$0.0312888\pi$
$269$			3.21918i			0.196277i	−0.995173	+	0.0981385i	$0.968711\pi$
$270$	1.59435	+	1.27088i	0.0970288	+	0.0773432i
$271$	−8.39830			−0.510160			−0.255080	−	0.966920i	$-0.582102\pi$
$271$	−8.39830			−0.510160			−0.255080	+	0.966920i	$0.582102\pi$
$272$			4.86321i			0.294875i
$273$			0.597844i			0.0361832i
$274$	5.42935	−	5.42935i	0.327999	−	0.327999i
$275$	−6.43842	−	28.1518i	−0.388251	−	1.69762i
$276$	2.38533	−	2.38533i	0.143580	−	0.143580i
$277$	−5.30553			−0.318778			−0.159389	−	0.987216i	$-0.550952\pi$
$277$	−5.30553			−0.318778			−0.159389	+	0.987216i	$0.550952\pi$
$278$	−13.4593			−0.807233
$279$	−9.84895	+	9.84895i	−0.589641	+	0.589641i
$280$	−0.988888	+	1.24058i	−0.0590973	+	0.0741389i
$281$	1.81647	−	1.81647i	0.108362	−	0.108362i	−0.650847	−	0.759209i	$-0.725586\pi$
$281$	1.81647	−	1.81647i	0.108362	−	0.108362i	0.759209	+	0.650847i	$0.225586\pi$
$282$		−	17.2489i		−	1.02716i
$283$		−	10.9456i		−	0.650648i	−0.945603	−	0.325324i	$-0.894527\pi$
$283$		−	10.9456i		−	0.650648i	0.945603	−	0.325324i	$-0.105473\pi$
$284$	−3.33183			−0.197708
$285$	−44.4476	+	5.01788i	−2.63285	+	0.297233i
$286$			1.92958i			0.114099i
$287$	3.66999	+	3.66999i	0.216633	+	0.216633i
$288$		−	3.36152i		−	0.198079i
$289$	−6.65079			−0.391223
$290$	14.4410	−	18.1166i	0.848007	−	1.06384i
$291$	6.36152	+	6.36152i	0.372919	+	0.372919i
$292$	4.96073	−	4.96073i	0.290305	−	0.290305i
$293$	22.3110	+	22.3110i	1.30342	+	1.30342i	0.926071	+	0.377349i	$0.123164\pi$
$293$	22.3110	+	22.3110i	1.30342	+	1.30342i	0.377349	+	0.926071i	$0.376836\pi$
$294$	11.5865	+	11.5865i	0.675738	+	0.675738i
$295$	21.6071	+	17.2234i	1.25802	+	1.00278i
$296$	−6.07201	+	0.361517i	−0.352928	+	0.0210127i
$297$	−3.72393	+	3.72393i	−0.216084	+	0.216084i
$298$		−	13.8867i		−	0.804434i
$299$	−0.446826			−0.0258406
$300$	6.70480	−	10.6810i	0.387102	−	0.616667i
$301$	0.580004	−	0.580004i	0.0334309	−	0.0334309i
$302$			5.54233i			0.318925i
$303$	0.396937	+	0.396937i	0.0228034	+	0.0228034i
$304$	5.60813	+	5.60813i	0.321648	+	0.321648i
$305$	−1.16914	−	0.931938i	−0.0669446	−	0.0533626i
$306$	16.3478			0.934539
$307$	9.91801	+	9.91801i	0.566051	+	0.566051i	0.931020	−	0.364969i	$-0.118920\pi$
$307$	9.91801	+	9.91801i	0.566051	+	0.566051i	−0.364969	+	0.931020i	$0.618920\pi$
$308$	−2.89764	−	2.89764i	−0.165108	−	0.165108i
$309$	−9.61201	−	9.61201i	−0.546808	−	0.546808i
$310$	7.24508	+	5.77517i	0.411493	+	0.328008i
$311$	5.18143	+	5.18143i	0.293812	+	0.293812i	0.838584	−	0.544772i	$-0.183384\pi$
$311$	5.18143	+	5.18143i	0.293812	+	0.293812i	−0.544772	+	0.838584i	$0.683384\pi$
$312$	−0.595828	+	0.595828i	−0.0337321	+	0.0337321i
$313$	−24.2499			−1.37069			−0.685343	−	0.728221i	$-0.740348\pi$
$313$	−24.2499			−1.37069			−0.685343	+	0.728221i	$0.740348\pi$
$314$	17.6224	−	17.6224i	0.994487	−	0.994487i
$315$	4.17024	+	3.32416i	0.234966	+	0.187295i
$316$	5.53177	+	5.53177i	0.311187	+	0.311187i
$317$	−20.7768	−	20.7768i	−1.16694	−	1.16694i	−0.982923	−	0.184016i	$-0.941090\pi$
$317$	−20.7768	−	20.7768i	−1.16694	−	1.16694i	−0.184016	−	0.982923i	$-0.558910\pi$
$318$	−24.1686			−1.35531
$319$	42.3151	+	42.3151i	2.36919	+	2.36919i
$320$	−2.22195	+	0.250846i	−0.124211	+	0.0140227i
$321$		−	7.13529i		−	0.398253i
$322$	0.670995	−	0.670995i	0.0373931	−	0.0373931i
$323$	−27.2735	+	27.2735i	−1.51754	+	1.51754i
$324$	7.78476			0.432486
$325$	−1.62838	+	0.372415i	−0.0903261	+	0.0206579i
$326$		−	13.5930i		−	0.752847i
$327$	1.38974			0.0768526
$328$			7.31524i			0.403917i
$329$		−	4.85213i		−	0.267507i
$330$	25.4719	+	20.3041i	1.40218	+	1.11770i
$331$	16.8385	−	16.8385i	0.925527	−	0.925527i	−0.0718857	−	0.997413i	$-0.522902\pi$
$331$	16.8385	−	16.8385i	0.925527	−	0.925527i	0.997413	+	0.0718857i	$0.0229017\pi$
$332$	4.77799	+	4.77799i	0.262226	+	0.262226i
$333$	1.21524	+	20.4112i	0.0665950	+	1.11852i
$334$		−	11.8884i		−	0.650504i
$335$	−4.43403	−	3.53443i	−0.242257	−	0.193107i
$336$		−	1.78950i		−	0.0976253i
$337$	−17.1598	−	17.1598i	−0.934756	−	0.934756i	0.0632419	−	0.997998i	$-0.479856\pi$
$337$	−17.1598	−	17.1598i	−0.934756	−	0.934756i	−0.997998	+	0.0632419i	$0.979856\pi$
$338$	−12.8884			−0.701036
$339$	−9.78151	−	9.78151i	−0.531259	−	0.531259i
$340$	−1.21991	−	10.8058i	−0.0661592	−	0.586028i
$341$	−16.9224	+	16.9224i	−0.916400	+	0.916400i
$342$	18.8518	−	18.8518i	1.01939	−	1.01939i
$343$	6.77113	+	6.77113i	0.365607	+	0.365607i
$344$	1.15610			0.0623326
$345$	−4.70174	+	5.89844i	−0.253133	+	0.317561i
$346$	1.19504	−	1.19504i	0.0642457	−	0.0642457i
$347$	−19.3891			−1.04086			−0.520430	−	0.853904i	$-0.674228\pi$
$347$	−19.3891			−1.04086			−0.520430	+	0.853904i	$0.674228\pi$
$348$			26.1326i			1.40086i
$349$			11.5543i			0.618489i	0.950983	+	0.309245i	$0.100076\pi$
$349$			11.5543i			0.618489i	−0.950983	+	0.309245i	$0.899924\pi$
$350$	1.88607	−	3.00457i	0.100815	−	0.160601i
$351$	0.215402	+	0.215402i	0.0114973	+	0.0114973i
$352$		−	5.77574i		−	0.307848i
$353$		−	31.6556i		−	1.68486i	−0.538810	−	0.842428i	$-0.681126\pi$
$353$		−	31.6556i		−	1.68486i	0.538810	−	0.842428i	$-0.318874\pi$
$354$	−31.1676			−1.65654
$355$	7.40317	−	0.835775i	0.392920	−	0.0443584i
$356$	3.08239	−	3.08239i	0.163366	−	0.163366i
$357$	8.70271			0.460596
$358$	−14.1150	+	14.1150i	−0.746003	+	0.746003i
$359$			12.7254i			0.671622i	0.941929	+	0.335811i	$0.109010\pi$
$359$			12.7254i			0.671622i	−0.941929	+	0.335811i	$0.890990\pi$
$360$	0.843222	+	7.46913i	0.0444417	+	0.393658i
$361$			43.9023i			2.31065i
$362$	14.6126			0.768024
$363$	−39.8768	+	39.8768i	−2.09299	+	2.09299i
$364$	−0.167607	+	0.167607i	−0.00878500	+	0.00878500i
$365$	−9.77813	+	12.2669i	−0.511811	+	0.642078i
$366$	1.68644			0.0881518
$367$	7.49820	−	7.49820i	0.391403	−	0.391403i	−0.483784	−	0.875187i	$-0.660738\pi$
$367$	7.49820	−	7.49820i	0.391403	−	0.391403i	0.875187	+	0.483784i	$0.160738\pi$
$368$	1.33747			0.0697203
$369$	24.5903			1.28012
$370$	13.4010	−	2.32641i	0.696687	−	0.120944i
$371$	−6.79866			−0.352969
$372$	−10.4508			−0.541849
$373$	−0.0403047	+	0.0403047i	−0.00208690	+	0.00208690i	−0.708149	−	0.706063i	$-0.750470\pi$
$373$	−0.0403047	+	0.0403047i	−0.00208690	+	0.00208690i	0.706063	+	0.708149i	$0.250470\pi$
$374$	28.0886			1.45243
$375$	−12.2185	+	25.4145i	−0.630959	+	1.31240i
$376$	4.83578	−	4.83578i	0.249386	−	0.249386i
$377$	2.44762	−	2.44762i	0.126059	−	0.126059i
$378$	−0.646934			−0.0332747
$379$		−	2.29640i		−	0.117958i	−0.998259	−	0.0589791i	$-0.981215\pi$
$379$		−	2.29640i		−	0.117958i	0.998259	−	0.0589791i	$-0.0187845\pi$
$380$	−13.8678	−	11.0542i	−0.711402	−	0.567070i
$381$			26.3929i			1.35215i
$382$	−8.33714	+	8.33714i	−0.426565	+	0.426565i
$383$	23.9142			1.22196			0.610980	−	0.791646i	$-0.290776\pi$
$383$	23.9142			1.22196			0.610980	+	0.791646i	$0.290776\pi$
$384$	1.78347	−	1.78347i	0.0910122	−	0.0910122i
$385$	7.16528	+	5.71156i	0.365176	+	0.291088i
$386$	19.5996			0.997592
$387$		−	3.88624i		−	0.197549i
$388$			3.56694i			0.181084i
$389$	−14.5043	−	14.5043i	−0.735399	−	0.735399i	0.236285	−	0.971684i	$-0.424070\pi$
$389$	−14.5043	−	14.5043i	−0.735399	−	0.735399i	−0.971684	+	0.236285i	$0.924070\pi$
$390$	1.17444	−	1.47336i	0.0594702	−	0.0746067i
$391$			6.50438i			0.328941i
$392$			6.49661i			0.328128i
$393$	−31.8794			−1.60810
$394$	−11.3654	+	11.3654i	−0.572579	+	0.572579i
$395$	−13.6790	−	10.9037i	−0.688263	−	0.548626i
$396$	−19.4152			−0.975653
$397$	−12.5627	−	12.5627i	−0.630506	−	0.630506i	0.317689	−	0.948195i	$-0.397093\pi$
$397$	−12.5627	−	12.5627i	−0.630506	−	0.630506i	−0.948195	+	0.317689i	$0.897093\pi$
$398$	4.39595	−	4.39595i	0.220349	−	0.220349i
$399$	10.0358	−	10.0358i	0.502416	−	0.502416i
$400$	4.87415	−	1.11473i	0.243708	−	0.0557367i
$401$	10.0896	+	10.0896i	0.503851	+	0.503851i	0.912632	−	0.408781i	$-0.134046\pi$
$401$	10.0896	+	10.0896i	0.503851	+	0.503851i	−0.408781	+	0.912632i	$0.634046\pi$
$402$	6.39595			0.319001
$403$	0.978837	+	0.978837i	0.0487594	+	0.0487594i
$404$			0.222565i			0.0110730i
$405$	−17.2974	+	1.95277i	−0.859513	+	0.0970340i
$406$			7.35114i			0.364831i
$407$	2.08803	+	35.0703i	0.103500	+	1.73837i
$408$	8.67338	+	8.67338i	0.429396	+	0.429396i
$409$	−4.26841	+	4.26841i	−0.211059	+	0.211059i	−0.804717	−	0.593658i	$-0.797683\pi$
$409$	−4.26841	+	4.26841i	−0.211059	+	0.211059i	0.593658	+	0.804717i	$0.297683\pi$
$410$	−1.83500	−	16.2541i	−0.0906240	−	0.802734i
$411$		−	19.3661i		−	0.955262i
$412$		−	5.38950i		−	0.265522i
$413$	−8.76748			−0.431420
$414$		−	4.49592i		−	0.220962i
$415$	−11.8150	−	9.41793i	−0.579976	−	0.462308i
$416$	−0.334084			−0.0163798
$417$	−24.0042	+	24.0042i	−1.17549	+	1.17549i
$418$	32.3911	−	32.3911i	1.58430	−	1.58430i
$419$			3.25958i			0.159241i	0.996825	+	0.0796205i	$0.0253708\pi$
$419$			3.25958i			0.159241i	−0.996825	+	0.0796205i	$0.974629\pi$
$420$	0.448889	+	3.97619i	0.0219035	+	0.194018i
$421$	8.29816	+	8.29816i	0.404428	+	0.404428i	0.879790	−	0.475362i	$-0.157683\pi$
$421$	8.29816	+	8.29816i	0.404428	+	0.404428i	−0.475362	+	0.879790i	$0.657683\pi$
$422$	−16.7875			−0.817201
$423$	−16.2555	−	16.2555i	−0.790371	−	0.790371i
$424$	−6.77574	−	6.77574i	−0.329059	−	0.329059i
$425$	5.42119	+	23.7040i	0.262966	+	1.14981i
$426$	−5.94222	+	5.94222i	−0.287901	+	0.287901i
$427$	0.474398			0.0229577
$428$	2.00040	−	2.00040i	0.0966929	−	0.0966929i
$429$	3.44135	+	3.44135i	0.166150	+	0.166150i
$430$	−2.56879	+	0.290002i	−0.123878	+	0.0139851i
$431$	23.5256	+	23.5256i	1.13319	+	1.13319i	0.989644	+	0.143546i	$0.0458505\pi$
$431$	23.5256	+	23.5256i	1.13319	+	1.13319i	0.143546	+	0.989644i	$0.454149\pi$
$432$	−0.644753	−	0.644753i	−0.0310207	−	0.0310207i
$433$	1.12455	+	1.12455i	0.0540424	+	0.0540424i	0.733612	−	0.679569i	$-0.237833\pi$
$433$	1.12455	+	1.12455i	0.0540424	+	0.0540424i	−0.679569	+	0.733612i	$0.737833\pi$
$434$	−2.93982			−0.141116
$435$	−6.55526	−	58.0655i	−0.314301	−	2.78403i
$436$	0.389616	+	0.389616i	0.0186592	+	0.0186592i
$437$	7.50069	+	7.50069i	0.358807	+	0.358807i
$438$		−	17.6946i		−	0.845481i
$439$	16.8566	−	16.8566i	0.804523	−	0.804523i	−0.179276	−	0.983799i	$-0.557375\pi$
$439$	16.8566	−	16.8566i	0.804523	−	0.804523i	0.983799	+	0.179276i	$0.0573754\pi$
$440$	1.44882	+	12.8334i	0.0690697	+	0.611809i
$441$	21.8385			1.03993
$442$		−	1.62472i		−	0.0772801i
$443$	26.1307	−	26.1307i	1.24151	−	1.24151i	0.282132	−	0.959376i	$-0.408958\pi$
$443$	26.1307	−	26.1307i	1.24151	−	1.24151i	0.959376	−	0.282132i	$-0.0910417\pi$
$444$	−10.1845	+	11.4740i	−0.483334	+	0.544531i
$445$	−6.07572	+	7.62213i	−0.288017	+	0.361324i
$446$	10.4136	+	10.4136i	0.493096	+	0.493096i
$447$	−24.7665	−	24.7665i	−1.17141	−	1.17141i
$448$	0.501691	−	0.501691i	0.0237027	−	0.0237027i
$449$	5.69945	+	5.69945i	0.268973	+	0.268973i	0.828687	−	0.559713i	$-0.189089\pi$
$449$	5.69945	+	5.69945i	0.268973	+	0.268973i	−0.559713	+	0.828687i	$0.689089\pi$
$450$	−3.74720	−	16.3845i	−0.176645	−	0.772375i
$451$	42.2509			1.98952
$452$		−	5.48455i		−	0.257971i
$453$	9.88457	+	9.88457i	0.464418	+	0.464418i
$454$		−	6.88908i		−	0.323321i
$455$	0.330372	−	0.414459i	0.0154881	−	0.0194301i
$456$	20.0038			0.936766
$457$		−	2.23060i		−	0.104343i	−0.998638	−	0.0521715i	$-0.983386\pi$
$457$		−	2.23060i		−	0.104343i	0.998638	−	0.0521715i	$-0.0166143\pi$
$458$			13.4017i			0.626219i
$459$	3.13557	−	3.13557i	0.146356	−	0.146356i
$460$	−2.97179	+	0.335498i	−0.138560	+	0.0156427i
$461$	−13.6773	+	13.6773i	−0.637016	+	0.637016i	−0.949818	−	0.312802i	$-0.898732\pi$
$461$	−13.6773	+	13.6773i	−0.637016	+	0.637016i	0.312802	+	0.949818i	$0.398732\pi$
$462$	−10.3357			−0.480860
$463$	13.3262			0.619321			0.309660	−	0.950847i	$-0.399785\pi$
$463$	13.3262			0.619321			0.309660	+	0.950847i	$0.399785\pi$
$464$	−7.32635	+	7.32635i	−0.340117	+	0.340117i
$465$	23.2212	−	2.62154i	1.07686	−	0.121571i
$466$	−11.3590	+	11.3590i	−0.526195	+	0.526195i
$467$			30.6482i			1.41823i	0.705093	+	0.709115i	$0.250905\pi$
$467$			30.6482i			1.41823i	−0.705093	+	0.709115i	$0.749095\pi$
$468$			1.12303i			0.0519121i
$469$	1.79919			0.0830787
$470$	−9.53183	+	11.9579i	−0.439671	+	0.551577i
$471$		−	62.8578i		−	2.89634i
$472$	−8.73793	−	8.73793i	−0.402196	−	0.402196i
$473$		−	6.67731i		−	0.307023i
$474$	19.7315			0.906297
$475$	33.5865	+	21.0833i	1.54105	+	0.967369i
$476$	2.43983	+	2.43983i	0.111829	+	0.111829i
$477$	−22.7768	+	22.7768i	−1.04288	+	1.04288i
$478$	4.68385	+	4.68385i	0.214234	+	0.214234i
$479$	−22.7730	−	22.7730i	−1.04052	−	1.04052i	−0.999143	−	0.0413804i	$-0.986824\pi$
$479$	−22.7730	−	22.7730i	−1.04052	−	1.04052i	−0.0413804	−	0.999143i	$-0.513176\pi$
$480$	−3.51541	+	4.41016i	−0.160456	+	0.201295i
$481$	2.02856	−	0.120777i	0.0924945	−	0.00550696i
$482$	−8.74018	+	8.74018i	−0.398104	+	0.398104i
$483$		−	2.39340i		−	0.108903i
$484$	−22.3592			−1.01633
$485$	−0.894750	−	7.92557i	−0.0406285	−	0.359881i
$486$	15.8181	−	15.8181i	0.717525	−	0.717525i
$487$			1.55055i			0.0702622i	0.999383	+	0.0351311i	$0.0111849\pi$
$487$			1.55055i			0.0702622i	−0.999383	+	0.0351311i	$0.988815\pi$
$488$	0.472799	+	0.472799i	0.0214026	+	0.0214026i
$489$	−24.2427	−	24.2427i	−1.09629	−	1.09629i
$490$	−1.62965	−	14.4352i	−0.0736199	−	0.652114i
$491$	−13.6919			−0.617908			−0.308954	−	0.951077i	$-0.599979\pi$
$491$	−13.6919			−0.617908			−0.308954	+	0.951077i	$0.599979\pi$
$492$	13.0465	+	13.0465i	0.588182	+	0.588182i
$493$	−35.6296	−	35.6296i	−1.60468	−	1.60468i
$494$	−1.87359	−	1.87359i	−0.0842967	−	0.0842967i
$495$	43.1398	−	4.87023i	1.93899	−	0.218900i
$496$	−2.92991	−	2.92991i	−0.131557	−	0.131557i
$497$	−1.67155	+	1.67155i	−0.0749793	+	0.0749793i
$498$	17.0428			0.763706
$499$	−18.0930	+	18.0930i	−0.809954	+	0.809954i	−0.984627	−	0.174673i	$-0.944113\pi$
$499$	−18.0930	+	18.0930i	−0.809954	+	0.809954i	0.174673	+	0.984627i	$0.444113\pi$
$500$	−10.5505	+	3.69955i	−0.471833	+	0.165449i
$501$	−21.2026	−	21.2026i	−0.947261	−	0.947261i
$502$	−12.8437	−	12.8437i	−0.573242	−	0.573242i
$503$	0.456512			0.0203548			0.0101774	−	0.999948i	$-0.496760\pi$
$503$	0.456512			0.0203548			0.0101774	+	0.999948i	$0.496760\pi$
$504$	−1.68644	−	1.68644i	−0.0751202	−	0.0751202i
$505$	−0.0558294	−	0.494528i	−0.00248438	−	0.0220062i
$506$		−	7.72486i		−	0.343412i
$507$	−22.9860	+	22.9860i	−1.02085	+	1.02085i
$508$	−7.39933	+	7.39933i	−0.328292	+	0.328292i
$509$	30.1863			1.33798			0.668992	−	0.743270i	$-0.266726\pi$
$509$	30.1863			1.33798			0.668992	+	0.743270i	$0.266726\pi$
$510$	−21.4475	−	17.0962i	−0.949712	−	0.757031i
$511$		−	4.97751i		−	0.220192i
$512$	1.00000			0.0441942
$513$		−	7.23172i		−	0.319288i
$514$		−	2.20193i		−	0.0971228i
$515$	1.35193	+	11.9752i	0.0595733	+	0.527692i
$516$	2.06186	−	2.06186i	0.0907684	−	0.0907684i
$517$	−27.9302	−	27.9302i	−1.22837	−	1.22837i
$518$	−2.86490	+	3.22764i	−0.125877	+	0.141815i
$519$		−	4.26263i		−	0.187109i
$520$	0.742319	−	0.0838036i	0.0325529	−	0.00367503i
$521$		−	6.63499i		−	0.290684i	−0.989381	−	0.145342i	$-0.953572\pi$
$521$		−	6.63499i		−	0.290684i	0.989381	−	0.145342i	$-0.0464283\pi$
$522$	24.6277	+	24.6277i	1.07792	+	1.07792i
$523$	35.7281			1.56228			0.781141	−	0.624354i	$-0.214638\pi$
$523$	35.7281			1.56228			0.781141	+	0.624354i	$0.214638\pi$
$524$	−8.93747	−	8.93747i	−0.390435	−	0.390435i
$525$	−1.99482	−	8.72230i	−0.0870610	−	0.380672i
$526$	−11.0490	+	11.0490i	−0.481759	+	0.481759i
$527$	14.2488	−	14.2488i	0.620686	−	0.620686i
$528$	−10.3008	−	10.3008i	−0.448287	−	0.448287i
$529$	−21.2112			−0.922225
$530$	16.7550	+	13.3557i	0.727792	+	0.580135i
$531$	−29.3727	+	29.3727i	−1.27467	+	1.27467i
$532$	5.62710			0.243966
$533$		−	2.44391i		−	0.105857i
$534$		−	10.9947i		−	0.475787i
$535$	−3.94300	+	4.94658i	−0.170471	+	0.213859i
$536$	1.79312	+	1.79312i	0.0774510	+	0.0774510i
$537$			50.3474i			2.17265i
$538$			3.21918i			0.138789i
$539$	37.5227			1.61622
$540$	1.59435	+	1.27088i	0.0686097	+	0.0546899i
$541$	12.2996	−	12.2996i	0.528799	−	0.528799i	−0.391415	−	0.920214i	$-0.628014\pi$
$541$	12.2996	−	12.2996i	0.528799	−	0.528799i	0.920214	+	0.391415i	$0.128014\pi$
$542$	−8.39830			−0.360738
$543$	26.0612	−	26.0612i	1.11839	−	1.11839i
$544$			4.86321i			0.208508i
$545$	−0.963443	−	0.767976i	−0.0412694	−	0.0328965i
$546$			0.597844i			0.0255854i
$547$	−19.3374			−0.826807			−0.413403	−	0.910548i	$-0.635660\pi$
$547$	−19.3374			−0.826807			−0.413403	+	0.910548i	$0.635660\pi$
$548$	5.42935	−	5.42935i	0.231930	−	0.231930i
$549$	1.58932	−	1.58932i	0.0678306	−	0.0678306i
$550$	−6.43842	−	28.1518i	−0.274535	−	1.20040i
$551$	−82.1743			−3.50074
$552$	2.38533	−	2.38533i	0.101526	−	0.101526i
$553$	5.55049			0.236031
$554$	−5.30553			−0.225410
$555$	19.7512	−	28.0494i	0.838394	−	1.19063i
$556$	−13.4593			−0.570800
$557$	45.6308			1.93344			0.966720	−	0.255836i	$-0.0823506\pi$
$557$	45.6308			1.93344			0.966720	+	0.255836i	$0.0823506\pi$
$558$	−9.84895	+	9.84895i	−0.416939	+	0.416939i
$559$	−0.386234			−0.0163359
$560$	−0.988888	+	1.24058i	−0.0417881	+	0.0524241i
$561$	50.0951	−	50.0951i	2.11502	−	2.11502i
$562$	1.81647	−	1.81647i	0.0766232	−	0.0766232i
$563$	19.3770			0.816644			0.408322	−	0.912838i	$-0.366114\pi$
$563$	19.3770			0.816644			0.408322	+	0.912838i	$0.366114\pi$
$564$		−	17.2489i		−	0.726310i
$565$	1.37577	+	12.1864i	0.0578793	+	0.512686i
$566$		−	10.9456i		−	0.460078i
$567$	3.90554	−	3.90554i	0.164017	−	0.164017i
$568$	−3.33183			−0.139801
$569$	−14.4045	+	14.4045i	−0.603870	+	0.603870i	−0.941337	−	0.337468i	$-0.890430\pi$
$569$	−14.4045	+	14.4045i	−0.603870	+	0.603870i	0.337468	+	0.941337i	$0.390430\pi$
$570$	−44.4476	+	5.01788i	−1.86171	+	0.210176i
$571$	30.3965			1.27205			0.636027	−	0.771667i	$-0.280577\pi$
$571$	30.3965			1.27205			0.636027	+	0.771667i	$0.280577\pi$
$572$			1.92958i			0.0806799i
$573$			29.7380i			1.24232i
$574$	3.66999	+	3.66999i	0.153183	+	0.153183i
$575$	6.51902	−	1.49092i	0.271862	−	0.0621757i
$576$		−	3.36152i		−	0.140063i
$577$			43.4726i			1.80979i	0.425638	+	0.904894i	$0.360050\pi$
$577$			43.4726i			1.80979i	−0.425638	+	0.904894i	$0.639950\pi$
$578$	−6.65079			−0.276636
$579$	34.9552	−	34.9552i	1.45269	−	1.45269i
$580$	14.4410	−	18.1166i	0.599631	−	0.752251i
$581$	4.79415			0.198895
$582$	6.36152	+	6.36152i	0.263693	+	0.263693i
$583$	−39.1349	+	39.1349i	−1.62080	+	1.62080i
$584$	4.96073	−	4.96073i	0.205276	−	0.205276i
$585$	−0.281707	−	2.49532i	−0.0116472	−	0.103169i
$586$	22.3110	+	22.3110i	0.921657	+	0.921657i
$587$	26.6263			1.09898			0.549492	−	0.835499i	$-0.314821\pi$
$587$	26.6263			1.09898			0.549492	+	0.835499i	$0.314821\pi$
$588$	11.5865	+	11.5865i	0.477819	+	0.477819i
$589$		−	32.8627i		−	1.35408i
$590$	21.6071	+	17.2234i	0.889552	+	0.709076i
$591$			40.5395i			1.66757i
$592$	−6.07201	+	0.361517i	−0.249558	+	0.0148582i
$593$	2.88802	+	2.88802i	0.118597	+	0.118597i	0.763914	−	0.645318i	$-0.223275\pi$
$593$	2.88802	+	2.88802i	0.118597	+	0.118597i	−0.645318	+	0.763914i	$0.723275\pi$
$594$	−3.72393	+	3.72393i	−0.152795	+	0.152795i
$595$	−6.03321	−	4.80917i	−0.247337	−	0.197157i
$596$		−	13.8867i		−	0.568821i
$597$		−	15.6801i		−	0.641742i
$598$	−0.446826			−0.0182721
$599$		−	21.4346i		−	0.875796i	−0.899025	−	0.437898i	$-0.855723\pi$
$599$		−	21.4346i		−	0.875796i	0.899025	−	0.437898i	$-0.144277\pi$
$600$	6.70480	−	10.6810i	0.273722	−	0.436050i
$601$	30.4478			1.24199			0.620995	−	0.783815i	$-0.286729\pi$
$601$	30.4478			1.24199			0.620995	+	0.783815i	$0.286729\pi$
$602$	0.580004	−	0.580004i	0.0236392	−	0.0236392i
$603$	6.02760	−	6.02760i	0.245463	−	0.245463i
$604$			5.54233i			0.225514i
$605$	49.6810	−	5.60870i	2.01982	−	0.228026i
$606$	0.396937	+	0.396937i	0.0161245	+	0.0161245i
$607$	3.14401			0.127612			0.0638058	−	0.997962i	$-0.479676\pi$
$607$	3.14401			0.127612			0.0638058	+	0.997962i	$0.479676\pi$
$608$	5.60813	+	5.60813i	0.227440	+	0.227440i
$609$	13.1105	+	13.1105i	0.531265	+	0.531265i
$610$	−1.16914	−	0.931938i	−0.0473370	−	0.0377331i
$611$	−1.61556	+	1.61556i	−0.0653584	+	0.0653584i
$612$	16.3478			0.660819
$613$	19.3617	−	19.3617i	0.782013	−	0.782013i	−0.198157	−	0.980170i	$-0.563496\pi$
$613$	19.3617	−	19.3617i	0.782013	−	0.782013i	0.980170	+	0.198157i	$0.0634956\pi$
$614$	9.91801	+	9.91801i	0.400258	+	0.400258i
$615$	−32.2614	−	25.7161i	−1.30090	−	1.03697i
$616$	−2.89764	−	2.89764i	−0.116749	−	0.116749i
$617$	−10.3835	−	10.3835i	−0.418023	−	0.418023i	0.466499	−	0.884522i	$-0.345515\pi$
$617$	−10.3835	−	10.3835i	−0.418023	−	0.418023i	−0.884522	+	0.466499i	$0.845515\pi$
$618$	−9.61201	−	9.61201i	−0.386652	−	0.386652i
$619$	−6.04142			−0.242825			−0.121413	−	0.992602i	$-0.538742\pi$
$619$	−6.04142			−0.242825			−0.121413	+	0.992602i	$0.538742\pi$
$620$	7.24508	+	5.77517i	0.290970	+	0.231937i
$621$	−0.862336	−	0.862336i	−0.0346044	−	0.0346044i
$622$	5.18143	+	5.18143i	0.207757	+	0.207757i
$623$		−	3.09282i		−	0.123911i
$624$	−0.595828	+	0.595828i	−0.0238522	+	0.0238522i
$625$	22.5147	−	10.8668i	0.900589	−	0.434671i
$626$	−24.2499			−0.969221
$627$		−	115.537i		−	4.61410i
$628$	17.6224	−	17.6224i	0.703209	−	0.703209i
$629$	−1.75813	−	29.5294i	−0.0701012	−	1.17742i
$630$	4.17024	+	3.32416i	0.166146	+	0.132438i
$631$	−13.9853	−	13.9853i	−0.556745	−	0.556745i	0.371634	−	0.928379i	$-0.378798\pi$
$631$	−13.9853	−	13.9853i	−0.556745	−	0.556745i	−0.928379	+	0.371634i	$0.878798\pi$
$632$	5.53177	+	5.53177i	0.220042	+	0.220042i
$633$	−29.9399	+	29.9399i	−1.19000	+	1.19000i
$634$	−20.7768	−	20.7768i	−0.825150	−	0.825150i
$635$	14.5849	−	18.2971i	0.578783	−	0.726096i
$636$	−24.1686			−0.958348
$637$		−	2.17042i		−	0.0859950i
$638$	42.3151	+	42.3151i	1.67527	+	1.67527i
$639$			11.2000i			0.443065i
$640$	−2.22195	+	0.250846i	−0.0878304	+	0.00991555i
$641$	35.9486			1.41988			0.709942	−	0.704260i	$-0.248721\pi$
$641$	35.9486			1.41988			0.709942	+	0.704260i	$0.248721\pi$
$642$		−	7.13529i		−	0.281607i
$643$		−	13.2845i		−	0.523888i	−0.965083	−	0.261944i	$-0.915636\pi$
$643$		−	13.2845i		−	0.523888i	0.965083	−	0.261944i	$-0.0843636\pi$
$644$	0.670995	−	0.670995i	0.0264409	−	0.0264409i
$645$	−4.06415	+	5.09857i	−0.160026	+	0.200756i
$646$	−27.2735	+	27.2735i	−1.07306	+	1.07306i
$647$	−14.0753			−0.553357			−0.276678	−	0.960963i	$-0.589234\pi$
$647$	−14.0753			−0.553357			−0.276678	+	0.960963i	$0.589234\pi$
$648$	7.78476			0.305814
$649$	−50.4680	+	50.4680i	−1.98104	+	1.98104i
$650$	−1.62838	+	0.372415i	−0.0638702	+	0.0146073i
$651$	−5.24308	+	5.24308i	−0.205493	+	0.205493i
$652$		−	13.5930i		−	0.532343i
$653$			26.4506i			1.03509i	0.855656	+	0.517546i	$0.173154\pi$
$653$			26.4506i			1.03509i	−0.855656	+	0.517546i	$0.826846\pi$
$654$	1.38974			0.0543430
$655$	22.1006	+	17.6167i	0.863541	+	0.688342i
$656$			7.31524i			0.285612i
$657$	−16.6756	−	16.6756i	−0.650576	−	0.650576i
$658$		−	4.85213i		−	0.189156i
$659$	39.4936			1.53845			0.769225	−	0.638978i	$-0.220642\pi$
$659$	39.4936			1.53845			0.769225	+	0.638978i	$0.220642\pi$
$660$	25.4719	+	20.3041i	0.991493	+	0.790335i
$661$	−19.7441	−	19.7441i	−0.767956	−	0.767956i	0.209790	−	0.977746i	$-0.432722\pi$
$661$	−19.7441	−	19.7441i	−0.767956	−	0.767956i	−0.977746	+	0.209790i	$0.932722\pi$
$662$	16.8385	−	16.8385i	0.654447	−	0.654447i
$663$	−2.89764	−	2.89764i	−0.112535	−	0.112535i
$664$	4.77799	+	4.77799i	0.185422	+	0.185422i
$665$	−12.5032	+	1.41153i	−0.484852	+	0.0547369i
$666$	1.21524	+	20.4112i	0.0470897	+	0.790916i
$667$	−9.79876	+	9.79876i	−0.379409	+	0.379409i
$668$		−	11.8884i		−	0.459976i
$669$	37.1445			1.43609
$670$	−4.43403	−	3.53443i	−0.171301	−	0.136547i
$671$	2.73076	−	2.73076i	0.105420	−	0.105420i
$672$		−	1.78950i		−	0.0690315i
$673$	−14.9976	−	14.9976i	−0.578114	−	0.578114i	0.356269	−	0.934383i	$-0.384049\pi$
$673$	−14.9976	−	14.9976i	−0.578114	−	0.578114i	−0.934383	+	0.356269i	$0.884049\pi$
$674$	−17.1598	−	17.1598i	−0.660973	−	0.660973i
$675$	−3.86135	−	2.42390i	−0.148624	−	0.0932958i
$676$	−12.8884			−0.495707
$677$	−18.1131	−	18.1131i	−0.696143	−	0.696143i	0.267434	−	0.963576i	$-0.413824\pi$
$677$	−18.1131	−	18.1131i	−0.696143	−	0.696143i	−0.963576	+	0.267434i	$0.913824\pi$
$678$	−9.78151	−	9.78151i	−0.375657	−	0.375657i
$679$	1.78950	+	1.78950i	0.0686747	+	0.0686747i
$680$	−1.21991	−	10.8058i	−0.0467816	−	0.414384i
$681$	−12.2865	−	12.2865i	−0.470818	−	0.470818i
$682$	−16.9224	+	16.9224i	−0.647993	+	0.647993i
$683$	19.3794			0.741532			0.370766	−	0.928726i	$-0.379095\pi$
$683$	19.3794			0.741532			0.370766	+	0.928726i	$0.379095\pi$
$684$	18.8518	−	18.8518i	0.720818	−	0.720818i
$685$	−10.7018	+	13.4257i	−0.408896	+	0.512969i
$686$	6.77113	+	6.77113i	0.258523	+	0.258523i
$687$	23.9015	+	23.9015i	0.911898	+	0.911898i
$688$	1.15610			0.0440758
$689$	2.26367	+	2.26367i	0.0862388	+	0.0862388i
$690$	−4.70174	+	5.89844i	−0.178992	+	0.224550i
$691$			20.1237i			0.765543i	0.923843	+	0.382771i	$0.125030\pi$
$691$			20.1237i			0.765543i	−0.923843	+	0.382771i	$0.874970\pi$
$692$	1.19504	−	1.19504i	0.0454286	−	0.0454286i
$693$	−9.74046	+	9.74046i	−0.370009	+	0.370009i
$694$	−19.3891			−0.735999
$695$	29.9059	−	3.37620i	1.13439	−	0.128066i
$696$			26.1326i			0.990555i
$697$	−35.5755			−1.34752
$698$			11.5543i			0.437338i
$699$			40.5168i			1.53249i
$700$	1.88607	−	3.00457i	0.0712866	−	0.113562i
$701$	3.20394	−	3.20394i	0.121011	−	0.121011i	−0.644008	−	0.765019i	$-0.722730\pi$
$701$	3.20394	−	3.20394i	0.121011	−	0.121011i	0.765019	+	0.644008i	$0.222730\pi$
$702$	0.215402	+	0.215402i	0.00812982	+	0.00812982i
$703$	−36.0801	−	32.0252i	−1.36079	−	1.20785i
$704$		−	5.77574i		−	0.217681i
$705$	4.32681	+	38.3263i	0.162957	+	1.44345i
$706$		−	31.6556i		−	1.19137i
$707$	0.111659	+	0.111659i	0.00419936	+	0.00419936i
$708$	−31.1676			−1.17135
$709$	−24.4221	−	24.4221i	−0.917193	−	0.917193i	0.0796314	−	0.996824i	$-0.474626\pi$
$709$	−24.4221	−	24.4221i	−0.917193	−	0.917193i	−0.996824	+	0.0796314i	$0.974626\pi$
$710$	7.40317	−	0.835775i	0.277836	−	0.0313661i
$711$	18.5951	−	18.5951i	0.697373	−	0.697373i
$712$	3.08239	−	3.08239i	0.115517	−	0.115517i
$713$	−3.91866	−	3.91866i	−0.146755	−	0.146755i
$714$	8.70271			0.325691
$715$	−0.484027	−	4.28744i	−0.0181016	−	0.160341i
$716$	−14.1150	+	14.1150i	−0.527503	+	0.527503i
$717$	16.7070			0.623935
$718$			12.7254i			0.474908i
$719$			49.2033i			1.83497i	0.397766	+	0.917487i	$0.369786\pi$
$719$			49.2033i			1.83497i	−0.397766	+	0.917487i	$0.630214\pi$
$720$	0.843222	+	7.46913i	0.0314250	+	0.278358i
$721$	−2.70387	−	2.70387i	−0.100697	−	0.100697i
$722$			43.9023i			1.63387i
$723$			31.1757i			1.15944i
$724$	14.6126			0.543075
$725$	−27.5428	+	43.8767i	−1.02292	+	1.62954i
$726$	−39.8768	+	39.8768i	−1.47997	+	1.47997i
$727$	−17.2328			−0.639130			−0.319565	−	0.947564i	$-0.603537\pi$
$727$	−17.2328			−0.639130			−0.319565	+	0.947564i	$0.603537\pi$
$728$	−0.167607	+	0.167607i	−0.00621193	+	0.00621193i
$729$		−	33.0680i		−	1.22474i
$730$	−9.77813	+	12.2669i	−0.361905	+	0.454018i
$731$			5.62234i			0.207950i
$732$	1.68644			0.0623328
$733$	29.6069	−	29.6069i	1.09356	−	1.09356i	0.0984097	−	0.995146i	$-0.468624\pi$
$733$	29.6069	−	29.6069i	1.09356	−	1.09356i	0.995146	−	0.0984097i	$-0.0313756\pi$
$734$	7.49820	−	7.49820i	0.276763	−	0.276763i
$735$	−28.6511	−	22.8382i	−1.05681	−	0.842401i
$736$	1.33747			0.0492997
$737$	10.3566	−	10.3566i	0.381490	−	0.381490i
$738$	24.5903			0.905182
$739$	−44.1780			−1.62511			−0.812557	−	0.582881i	$-0.801925\pi$
$739$	−44.1780			−1.62511			−0.812557	+	0.582881i	$0.801925\pi$
$740$	13.4010	−	2.32641i	0.492632	−	0.0855205i
$741$	−6.68297			−0.245505
$742$	−6.79866			−0.249587
$743$	6.64187	−	6.64187i	0.243666	−	0.243666i	−0.574699	−	0.818365i	$-0.694881\pi$
$743$	6.64187	−	6.64187i	0.243666	−	0.243666i	0.818365	+	0.574699i	$0.194881\pi$
$744$	−10.4508			−0.383145
$745$	3.48342	+	30.8556i	0.127622	+	1.13046i
$746$	−0.0403047	+	0.0403047i	−0.00147566	+	0.00147566i
$747$	16.0613	−	16.0613i	0.587652	−	0.587652i
$748$	28.0886			1.02702
$749$		−	2.00716i		−	0.0733402i
$750$	−12.2185	+	25.4145i	−0.446156	+	0.928007i
$751$			19.6421i			0.716750i	0.933578	+	0.358375i	$0.116669\pi$
$751$			19.6421i			0.716750i	−0.933578	+	0.358375i	$0.883331\pi$
$752$	4.83578	−	4.83578i	0.176343	−	0.176343i
$753$	−45.8127			−1.66951
$754$	2.44762	−	2.44762i	0.0891370	−	0.0891370i
$755$	−1.39027	−	12.3148i	−0.0505971	−	0.448181i
$756$	−0.646934			−0.0235288
$757$			30.0218i			1.09116i	0.838059	+	0.545580i	$0.183691\pi$
$757$			30.0218i			1.09116i	−0.838059	+	0.545580i	$0.816309\pi$
$758$		−	2.29640i		−	0.0834090i
$759$	−13.7770	−	13.7770i	−0.500075	−	0.500075i
$760$	−13.8678	−	11.0542i	−0.503037	−	0.400979i
$761$			13.5486i			0.491135i	0.969379	+	0.245568i	$0.0789743\pi$
$761$			13.5486i			0.491135i	−0.969379	+	0.245568i	$0.921026\pi$
$762$			26.3929i			0.956115i
$763$	0.390934			0.0141528
$764$	−8.33714	+	8.33714i	−0.301627	+	0.301627i
$765$	−36.3239	+	4.10076i	−1.31330	+	0.148263i
$766$	23.9142			0.864056
$767$	2.91920	+	2.91920i	0.105406	+	0.105406i
$768$	1.78347	−	1.78347i	0.0643554	−	0.0643554i
$769$	−31.9437	+	31.9437i	−1.15192	+	1.15192i	−0.165752	+	0.986168i	$0.553005\pi$
$769$	−31.9437	+	31.9437i	−1.15192	+	1.15192i	−0.986168	+	0.165752i	$0.946995\pi$
$770$	7.16528	+	5.71156i	0.258219	+	0.205830i
$771$	−3.92706	−	3.92706i	−0.141430	−	0.141430i
$772$	19.5996			0.705404
$773$	26.6189	+	26.6189i	0.957414	+	0.957414i	0.999130	−	0.0417156i	$-0.0132823\pi$
$773$	26.6189	+	26.6189i	0.957414	+	0.957414i	−0.0417156	+	0.999130i	$0.513282\pi$
$774$		−	3.88624i		−	0.139688i
$775$	−17.5469	−	11.0148i	−0.630304	−	0.395662i
$776$			3.56694i			0.128046i
$777$	0.646934	+	10.8659i	0.0232086	+	0.389811i
$778$	−14.5043	−	14.5043i	−0.520006	−	0.520006i
$779$	−41.0248	+	41.0248i	−1.46987	+	1.46987i
$780$	1.17444	−	1.47336i	0.0420518	−	0.0527549i
$781$			19.2438i			0.688597i
$782$			6.50438i			0.232596i
$783$	9.44738			0.337622
$784$			6.49661i			0.232022i
$785$	−34.7356	+	43.5765i	−1.23977	+	1.55531i
$786$	−31.8794			−1.13710
$787$	35.6168	−	35.6168i	1.26960	−	1.26960i	0.323311	−	0.946293i	$-0.395204\pi$
$787$	35.6168	−	35.6168i	1.26960	−	1.26960i	0.946293	−	0.323311i	$-0.104796\pi$
$788$	−11.3654	+	11.3654i	−0.404874	+	0.404874i
$789$			39.4110i			1.40307i
$790$	−13.6790	−	10.9037i	−0.486676	−	0.387937i
$791$	−2.75155	−	2.75155i	−0.0978338	−	0.0978338i
$792$	−19.4152			−0.689891
$793$	−0.157955	−	0.157955i	−0.00560913	−	0.00560913i
$794$	−12.5627	−	12.5627i	−0.445835	−	0.445835i
$795$	53.7016	−	6.06259i	1.90460	−	0.215018i
$796$	4.39595	−	4.39595i	0.155810	−	0.155810i
$797$	11.4525			0.405668			0.202834	−	0.979213i	$-0.434985\pi$
$797$	11.4525			0.405668			0.202834	+	0.979213i	$0.434985\pi$
$798$	10.0358	−	10.0358i	0.355262	−	0.355262i
$799$	23.5174	+	23.5174i	0.831985	+	0.831985i
$800$	4.87415	−	1.11473i	0.172327	−	0.0394118i
$801$	−10.3615	−	10.3615i	−0.366106	−	0.366106i
$802$	10.0896	+	10.0896i	0.356277	+	0.356277i
$803$	−28.6519	−	28.6519i	−1.01110	−	1.01110i
$804$	6.39595			0.225568
$805$	−1.32260	+	1.65924i	−0.0466157	+	0.0584804i
$806$	0.978837	+	0.978837i	0.0344781	+	0.0344781i
$807$	5.74131	+	5.74131i	0.202104	+	0.202104i
$808$			0.222565i			0.00782980i
$809$	−13.3588	+	13.3588i	−0.469670	+	0.469670i	−0.901808	−	0.432137i	$-0.857760\pi$
$809$	−13.3588	+	13.3588i	−0.469670	+	0.469670i	0.432137	+	0.901808i	$0.357760\pi$
$810$	−17.2974	+	1.95277i	−0.607767	+	0.0686134i
$811$	−11.7051			−0.411022			−0.205511	−	0.978655i	$-0.565886\pi$
$811$	−11.7051			−0.411022			−0.205511	+	0.978655i	$0.565886\pi$
$812$			7.35114i			0.257974i
$813$	−14.9781	+	14.9781i	−0.525305	+	0.525305i
$814$	2.08803	+	35.0703i	0.0731852	+	1.22921i
$815$	3.40975	+	30.2030i	0.119438	+	1.05797i
$816$	8.67338	+	8.67338i	0.303629	+	0.303629i
$817$	6.48354	+	6.48354i	0.226830	+	0.226830i
$818$	−4.26841	+	4.26841i	−0.149242	+	0.149242i
$819$	0.563414	+	0.563414i	0.0196873	+	0.0196873i
$820$	−1.83500	−	16.2541i	−0.0640809	−	0.567619i
$821$	2.82473			0.0985837			0.0492918	−	0.998784i	$-0.484304\pi$
$821$	2.82473			0.0985837			0.0492918	+	0.998784i	$0.484304\pi$
$822$		−	19.3661i		−	0.675472i
$823$	−16.5874	−	16.5874i	−0.578199	−	0.578199i	0.356208	−	0.934407i	$-0.384070\pi$
$823$	−16.5874	−	16.5874i	−0.578199	−	0.578199i	−0.934407	+	0.356208i	$0.884070\pi$
$824$		−	5.38950i		−	0.187752i
$825$	−61.6906	−	38.7252i	−2.14779	−	1.34824i
$826$	−8.76748			−0.305060
$827$		−	19.6743i		−	0.684142i	−0.939674	−	0.342071i	$-0.888872\pi$
$827$		−	19.6743i		−	0.684142i	0.939674	−	0.342071i	$-0.111128\pi$
$828$		−	4.49592i		−	0.156244i
$829$	12.0827	−	12.0827i	0.419649	−	0.419649i	−0.465434	−	0.885083i	$-0.654102\pi$
$829$	12.0827	−	12.0827i	0.419649	−	0.419649i	0.885083	+	0.465434i	$0.154102\pi$
$830$	−11.8150	−	9.41793i	−0.410105	−	0.326901i
$831$	−9.46224	+	9.46224i	−0.328242	+	0.328242i
$832$	−0.334084			−0.0115823
$833$	−31.5944			−1.09468
$834$	−24.0042	+	24.0042i	−0.831196	+	0.831196i
$835$	2.98215	+	26.4154i	0.103202	+	0.914144i
$836$	32.3911	−	32.3911i	1.12027	−	1.12027i
$837$			3.77814i			0.130592i
$838$			3.25958i			0.112600i
$839$	39.9396			1.37887			0.689435	−	0.724348i	$-0.257859\pi$
$839$	39.9396			1.37887			0.689435	+	0.724348i	$0.257859\pi$
$840$	0.448889	+	3.97619i	0.0154881	+	0.137191i
$841$		−	78.3509i		−	2.70176i
$842$	8.29816	+	8.29816i	0.285974	+	0.285974i
$843$		−	6.47923i		−	0.223157i
$844$	−16.7875			−0.577849
$845$	28.6374	−	3.23300i	0.985156	−	0.111218i
$846$	−16.2555	−	16.2555i	−0.558877	−	0.558877i
$847$	−11.2174	+	11.2174i	−0.385434	+	0.385434i
$848$	−6.77574	−	6.77574i	−0.232680	−	0.232680i
$849$	−19.5211	−	19.5211i	−0.669963	−	0.669963i
$850$	5.42119	+	23.7040i	0.185945	+	0.813041i
$851$	−8.12111	+	0.483516i	−0.278388	+	0.0165747i
$852$	−5.94222	+	5.94222i	−0.203577	+	0.203577i
$853$			17.5843i			0.602077i	0.953612	+	0.301038i	$0.0973332\pi$
$853$			17.5843i			0.602077i	−0.953612	+	0.301038i	$0.902667\pi$
$854$	0.474398			0.0162336
$855$	−37.1590	+	46.6168i	−1.27081	+	1.59426i
$856$	2.00040	−	2.00040i	0.0683722	−	0.0683722i
$857$		−	11.7000i		−	0.399664i	−0.979830	−	0.199832i	$-0.935960\pi$
$857$		−	11.7000i		−	0.399664i	0.979830	−	0.199832i	$-0.0640397\pi$
$858$	3.44135	+	3.44135i	0.117486	+	0.117486i
$859$	−12.1759	−	12.1759i	−0.415435	−	0.415435i	0.468192	−	0.883627i	$-0.344906\pi$
$859$	−12.1759	−	12.1759i	−0.415435	−	0.415435i	−0.883627	+	0.468192i	$0.844906\pi$
$860$	−2.56879	+	0.290002i	−0.0875951	+	0.00988898i
$861$	13.0906			0.446128
$862$	23.5256	+	23.5256i	0.801286	+	0.801286i
$863$	5.03080	+	5.03080i	0.171250	+	0.171250i	0.787529	−	0.616278i	$-0.211360\pi$
$863$	5.03080	+	5.03080i	0.171250	+	0.171250i	−0.616278	+	0.787529i	$0.711360\pi$
$864$	−0.644753	−	0.644753i	−0.0219350	−	0.0219350i
$865$	−2.35555	+	2.95509i	−0.0800912	+	0.100476i
$866$	1.12455	+	1.12455i	0.0382138	+	0.0382138i
$867$	−11.8615	+	11.8615i	−0.402837	+	0.402837i
$868$	−2.93982			−0.0997841
$869$	31.9501	−	31.9501i	1.08383	−	1.08383i
$870$	−6.55526	−	58.0655i	−0.222244	−	1.96860i
$871$	−0.599053	−	0.599053i	−0.0202981	−	0.0202981i
$872$	0.389616	+	0.389616i	0.0131941	+	0.0131941i
$873$	11.9903			0.405811
$874$	7.50069	+	7.50069i	0.253715	+	0.253715i
$875$	−3.43707	+	7.14913i	−0.116194	+	0.241685i
$876$		−	17.6946i		−	0.597845i
$877$	12.8277	−	12.8277i	0.433162	−	0.433162i	−0.456540	−	0.889703i	$-0.650912\pi$
$877$	12.8277	−	12.8277i	0.433162	−	0.433162i	0.889703	+	0.456540i	$0.150912\pi$
$878$	16.8566	−	16.8566i	0.568884	−	0.568884i
$879$	79.5818			2.68423
$880$	1.44882	+	12.8334i	0.0488397	+	0.432615i
$881$			51.6791i			1.74111i	0.492067	+	0.870557i	$0.336241\pi$
$881$			51.6791i			1.74111i	−0.492067	+	0.870557i	$0.663759\pi$
$882$	21.8385			0.735339
$883$		−	3.88869i		−	0.130865i	−0.997857	−	0.0654323i	$-0.979157\pi$
$883$		−	3.88869i		−	0.130865i	0.997857	−	0.0654323i	$-0.0208427\pi$
$884$		−	1.62472i		−	0.0546453i
$885$	69.2530	−	7.81826i	2.32791	−	0.262808i
$886$	26.1307	−	26.1307i	0.877879	−	0.877879i
$887$	11.5256	+	11.5256i	0.386992	+	0.386992i	0.873613	−	0.486621i	$-0.161771\pi$
$887$	11.5256	+	11.5256i	0.386992	+	0.386992i	−0.486621	+	0.873613i	$0.661771\pi$
$888$	−10.1845	+	11.4740i	−0.341769	+	0.385042i
$889$			7.42436i			0.249005i
$890$	−6.07572	+	7.62213i	−0.203659	+	0.255494i
$891$		−	44.9627i		−	1.50631i
$892$	10.4136	+	10.4136i	0.348672	+	0.348672i
$893$	54.2393			1.81505
$894$	−24.7665	−	24.7665i	−0.828315	−	0.828315i
$895$	27.8222	−	34.9036i	0.929995	−	1.16670i
$896$	0.501691	−	0.501691i	0.0167603	−	0.0167603i
$897$	−0.796901	+	0.796901i	−0.0266077	+	0.0266077i
$898$	5.69945	+	5.69945i	0.190193	+	0.190193i
$899$	42.9312			1.43183
$900$	−3.74720	−	16.3845i	−0.124907	−	0.546152i
$901$	32.9518	−	32.9518i	1.09778	−	1.09778i
$902$	42.2509			1.40680
$903$		−	2.06884i		−	0.0688466i
$904$		−	5.48455i		−	0.182413i
$905$	−32.4686	+	3.66552i	−1.07929	+	0.121846i
$906$	9.88457	+	9.88457i	0.328393	+	0.328393i
$907$		−	8.00889i		−	0.265931i	−0.991121	−	0.132965i	$-0.957550\pi$
$907$		−	8.00889i		−	0.265931i	0.991121	−	0.132965i	$-0.0424499\pi$
$908$		−	6.88908i		−	0.228622i
$909$	0.748155			0.0248147
$910$	0.330372	−	0.414459i	0.0109517	−	0.0137392i
$911$	34.4483	−	34.4483i	1.14132	−	1.14132i	0.153116	−	0.988208i	$-0.451069\pi$
$911$	34.4483	−	34.4483i	1.14132	−	1.14132i	0.988208	−	0.153116i	$-0.0489309\pi$
$912$	20.0038			0.662394
$913$	27.5964	−	27.5964i	0.913308	−	0.913308i
$914$		−	2.23060i		−	0.0737817i
$915$	−3.74720	+	0.423037i	−0.123879	+	0.0139852i
$916$			13.4017i			0.442804i
$917$	−8.96770			−0.296140
$918$	3.13557	−	3.13557i	0.103489	−	0.103489i
$919$	18.8810	−	18.8810i	0.622827	−	0.622827i	−0.323426	−	0.946253i	$-0.604835\pi$
$919$	18.8810	−	18.8810i	0.622827	−	0.622827i	0.946253	+	0.323426i	$0.104835\pi$
$920$	−2.97179	+	0.335498i	−0.0979770	+	0.0110610i
$921$	35.3769			1.16571
$922$	−13.6773	+	13.6773i	−0.450438	+	0.450438i
$923$	1.11311			0.0366385
$924$	−10.3357			−0.340019
$925$	−29.1929	+	8.53077i	−0.959857	+	0.280490i
$926$	13.3262			0.437926
$927$	−18.1169			−0.595037
$928$	−7.32635	+	7.32635i	−0.240499	+	0.240499i
$929$	21.1823			0.694970			0.347485	−	0.937686i	$-0.387036\pi$
$929$	21.1823			0.694970			0.347485	+	0.937686i	$0.387036\pi$
$930$	23.2212	−	2.62154i	0.761454	−	0.0859637i
$931$	−36.4338	+	36.4338i	−1.19407	+	1.19407i
$932$	−11.3590	+	11.3590i	−0.372076	+	0.372076i
$933$	18.4818			0.605069
$934$			30.6482i			1.00284i
$935$	−62.4116	+	7.04591i	−2.04108	+	0.230426i
$936$			1.12303i			0.0367074i
$937$	29.5924	−	29.5924i	0.966741	−	0.966741i	−0.0327237	−	0.999464i	$-0.510418\pi$
$937$	29.5924	−	29.5924i	0.966741	−	0.966741i	0.999464	+	0.0327237i	$0.0104181\pi$
$938$	1.79919			0.0587455
$939$	−43.2489	+	43.2489i	−1.41138	+	1.41138i
$940$	−9.53183	+	11.9579i	−0.310894	+	0.390024i
$941$	−24.9980			−0.814911			−0.407456	−	0.913225i	$-0.633584\pi$
$941$	−24.9980			−0.814911			−0.407456	+	0.913225i	$0.633584\pi$
$942$		−	62.8578i		−	2.04802i
$943$			9.78389i			0.318607i
$944$	−8.73793	−	8.73793i	−0.284395	−	0.284395i
$945$	1.43746	−	0.162281i	0.0467605	−	0.00527899i
$946$		−	6.67731i		−	0.217098i
$947$			26.5685i			0.863361i	0.902027	+	0.431680i	$0.142079\pi$
$947$			26.5685i			0.863361i	−0.902027	+	0.431680i	$0.857921\pi$
$948$	19.7315			0.640849
$949$	−1.65730	+	1.65730i	−0.0537983	+	0.0537983i
$950$	33.5865	+	21.0833i	1.08969	+	0.684033i
$951$	−74.1094			−2.40316
$952$	2.43983	+	2.43983i	0.0790753	+	0.0790753i
$953$	−14.1106	+	14.1106i	−0.457088	+	0.457088i	−0.897698	−	0.440610i	$-0.854762\pi$
$953$	−14.1106	+	14.1106i	−0.457088	+	0.457088i	0.440610	+	0.897698i	$0.354762\pi$
$954$	−22.7768	+	22.7768i	−0.737425	+	0.737425i
$955$	16.4334	−	20.6161i	0.531772	−	0.667120i
$956$	4.68385	+	4.68385i	0.151487	+	0.151487i
$957$	150.935			4.87904
$958$	−22.7730	−	22.7730i	−0.735761	−	0.735761i
$959$		−	5.44772i		−	0.175916i
$960$	−3.51541	+	4.41016i	−0.113459	+	0.142337i
$961$		−	13.8312i		−	0.446169i
$962$	2.02856	−	0.120777i	0.0654035	−	0.00389401i
$963$	−6.72437	−	6.72437i	−0.216690	−	0.216690i
$964$	−8.74018	+	8.74018i	−0.281502	+	0.281502i
$965$	−43.5493	+	4.91647i	−1.40190	+	0.158267i
$966$		−	2.39340i		−	0.0770063i
$967$			5.25406i			0.168959i	0.996425	+	0.0844796i	$0.0269228\pi$
$967$			5.25406i			0.168959i	−0.996425	+	0.0844796i	$0.973077\pi$
$968$	−22.3592			−0.718650
$969$			97.2829i			3.12518i
$970$	−0.894750	−	7.92557i	−0.0287287	−	0.254475i
$971$	−15.5830			−0.500081			−0.250040	−	0.968235i	$-0.580444\pi$
$971$	−15.5830			−0.500081			−0.250040	+	0.968235i	$0.580444\pi$
$972$	15.8181	−	15.8181i	0.507367	−	0.507367i
$973$	−6.75239	+	6.75239i	−0.216472	+	0.216472i
$974$			1.55055i			0.0496829i
$975$	−2.23997	+	3.56835i	−0.0717364	+	0.114279i
$976$	0.472799	+	0.472799i	0.0151339	+	0.0151339i
$977$	35.6800			1.14150			0.570752	−	0.821123i	$-0.306652\pi$
$977$	35.6800			1.14150			0.570752	+	0.821123i	$0.306652\pi$
$978$	−24.2427	−	24.2427i	−0.775196	−	0.775196i
$979$	−17.8031	−	17.8031i	−0.568989	−	0.568989i
$980$	−1.62965	−	14.4352i	−0.0520572	−	0.461115i
$981$	1.30970	−	1.30970i	0.0418156	−	0.0418156i
$982$	−13.6919			−0.436927
$983$	−30.0050	+	30.0050i	−0.957009	+	0.957009i	−0.999113	−	0.0421038i	$-0.986594\pi$
$983$	−30.0050	+	30.0050i	−0.957009	+	0.957009i	0.0421038	+	0.999113i	$0.486594\pi$
$984$	13.0465	+	13.0465i	0.415907	+	0.415907i
$985$	22.4024	−	28.1043i	0.713798	−	0.895476i
$986$	−35.6296	−	35.6296i	−1.13468	−	1.13468i
$987$	−8.65362	−	8.65362i	−0.275448	−	0.275448i
$988$	−1.87359	−	1.87359i	−0.0596068	−	0.0596068i
$989$	1.54624			0.0491676
$990$	43.1398	−	4.87023i	1.37107	−	0.154786i
$991$	−24.2563	−	24.2563i	−0.770525	−	0.770525i	0.207673	−	0.978198i	$-0.433411\pi$
$991$	−24.2563	−	24.2563i	−0.770525	−	0.770525i	−0.978198	+	0.207673i	$0.933411\pi$
$992$	−2.92991	−	2.92991i	−0.0930248	−	0.0930248i
$993$		−	60.0618i		−	1.90600i
$994$	−1.67155	+	1.67155i	−0.0530184	+	0.0530184i
$995$	−8.66488	+	10.8703i	−0.274695	+	0.344611i
$996$	17.0428			0.540021
$997$			13.9792i			0.442727i	0.975191	+	0.221363i	$0.0710507\pi$
$997$			13.9792i			0.442727i	−0.975191	+	0.221363i	$0.928949\pi$
$998$	−18.0930	+	18.0930i	−0.572724	+	0.572724i
$999$	4.14804	+	3.68186i	0.131238	+	0.116489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.d.253.4	yes	10
5.2	odd	4		370.2.g.d.327.2	yes	10
37.6	odd	4		370.2.g.d.43.2	✓	10
185.117	even	4	inner	370.2.h.d.117.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.d.43.2	✓	10	37.6	odd	4
370.2.g.d.327.2	yes	10	5.2	odd	4
370.2.h.d.117.4	yes	10	185.117	even	4	inner
370.2.h.d.253.4	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.78347 - 1.78347i) q^{3} +1.00000 q^{4} +(-2.22195 + 0.250846i) q^{5} +(1.78347 - 1.78347i) q^{6} +(0.501691 - 0.501691i) q^{7} +1.00000 q^{8} -3.36152i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.78347 - 1.78347i) q^{3} +1.00000 q^{4} +(-2.22195 + 0.250846i) q^{5} +(1.78347 - 1.78347i) q^{6} +(0.501691 - 0.501691i) q^{7} +1.00000 q^{8} -3.36152i q^{9} +(-2.22195 + 0.250846i) q^{10} -5.77574i q^{11} +(1.78347 - 1.78347i) q^{12} -0.334084 q^{13} +(0.501691 - 0.501691i) q^{14} +(-3.51541 + 4.41016i) q^{15} +1.00000 q^{16} +4.86321i q^{17} -3.36152i q^{18} +(5.60813 + 5.60813i) q^{19} +(-2.22195 + 0.250846i) q^{20} -1.78950i q^{21} -5.77574i q^{22} +1.33747 q^{23} +(1.78347 - 1.78347i) q^{24} +(4.87415 - 1.11473i) q^{25} -0.334084 q^{26} +(-0.644753 - 0.644753i) q^{27} +(0.501691 - 0.501691i) q^{28} +(-7.32635 + 7.32635i) q^{29} +(-3.51541 + 4.41016i) q^{30} +(-2.92991 - 2.92991i) q^{31} +1.00000 q^{32} +(-10.3008 - 10.3008i) q^{33} +4.86321i q^{34} +(-0.988888 + 1.24058i) q^{35} -3.36152i q^{36} +(-6.07201 + 0.361517i) q^{37} +(5.60813 + 5.60813i) q^{38} +(-0.595828 + 0.595828i) q^{39} +(-2.22195 + 0.250846i) q^{40} +7.31524i q^{41} -1.78950i q^{42} +1.15610 q^{43} -5.77574i q^{44} +(0.843222 + 7.46913i) q^{45} +1.33747 q^{46} +(4.83578 - 4.83578i) q^{47} +(1.78347 - 1.78347i) q^{48} +6.49661i q^{49} +(4.87415 - 1.11473i) q^{50} +(8.67338 + 8.67338i) q^{51} -0.334084 q^{52} +(-6.77574 - 6.77574i) q^{53} +(-0.644753 - 0.644753i) q^{54} +(1.44882 + 12.8334i) q^{55} +(0.501691 - 0.501691i) q^{56} +20.0038 q^{57} +(-7.32635 + 7.32635i) q^{58} +(-8.73793 - 8.73793i) q^{59} +(-3.51541 + 4.41016i) q^{60} +(0.472799 + 0.472799i) q^{61} +(-2.92991 - 2.92991i) q^{62} +(-1.68644 - 1.68644i) q^{63} +1.00000 q^{64} +(0.742319 - 0.0838036i) q^{65} +(-10.3008 - 10.3008i) q^{66} +(1.79312 + 1.79312i) q^{67} +4.86321i q^{68} +(2.38533 - 2.38533i) q^{69} +(-0.988888 + 1.24058i) q^{70} -3.33183 q^{71} -3.36152i q^{72} +(4.96073 - 4.96073i) q^{73} +(-6.07201 + 0.361517i) q^{74} +(6.70480 - 10.6810i) q^{75} +(5.60813 + 5.60813i) q^{76} +(-2.89764 - 2.89764i) q^{77} +(-0.595828 + 0.595828i) q^{78} +(5.53177 + 5.53177i) q^{79} +(-2.22195 + 0.250846i) q^{80} +7.78476 q^{81} +7.31524i q^{82} +(4.77799 + 4.77799i) q^{83} -1.78950i q^{84} +(-1.21991 - 10.8058i) q^{85} +1.15610 q^{86} +26.1326i q^{87} -5.77574i q^{88} +(3.08239 - 3.08239i) q^{89} +(0.843222 + 7.46913i) q^{90} +(-0.167607 + 0.167607i) q^{91} +1.33747 q^{92} -10.4508 q^{93} +(4.83578 - 4.83578i) q^{94} +(-13.8678 - 11.0542i) q^{95} +(1.78347 - 1.78347i) q^{96} +3.56694i q^{97} +6.49661i q^{98} -19.4152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8} + 2 q^{10} + 2 q^{12} - 12 q^{13} - 4 q^{14} - 14 q^{15} + 10 q^{16} + 8 q^{19} + 2 q^{20} + 4 q^{23} + 2 q^{24} + 28 q^{25} - 12 q^{26} - 28 q^{27} - 4 q^{28} - 32 q^{29} - 14 q^{30} - 26 q^{31} + 10 q^{32} - 24 q^{33} + 22 q^{35} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} + 12 q^{43} - 10 q^{45} + 4 q^{46} + 48 q^{47} + 2 q^{48} + 28 q^{50} + 16 q^{51} - 12 q^{52} - 2 q^{53} - 28 q^{54} + 12 q^{55} - 4 q^{56} + 76 q^{57} - 32 q^{58} - 20 q^{59} - 14 q^{60} - 24 q^{61} - 26 q^{62} + 20 q^{63} + 10 q^{64} + 28 q^{65} - 24 q^{66} - 10 q^{67} - 46 q^{69} + 22 q^{70} - 16 q^{71} + 4 q^{73} - 2 q^{74} - 48 q^{75} + 8 q^{76} - 24 q^{77} + 6 q^{78} - 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} - 10 q^{85} + 12 q^{86} - 2 q^{89} - 10 q^{90} + 16 q^{91} + 4 q^{92} - 60 q^{93} + 48 q^{94} - 28 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8 + 2 * q^10 + 2 * q^12 - 12 * q^13 - 4 * q^14 - 14 * q^15 + 10 * q^16 + 8 * q^19 + 2 * q^20 + 4 * q^23 + 2 * q^24 + 28 * q^25 - 12 * q^26 - 28 * q^27 - 4 * q^28 - 32 * q^29 - 14 * q^30 - 26 * q^31 + 10 * q^32 - 24 * q^33 + 22 * q^35 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 + 12 * q^43 - 10 * q^45 + 4 * q^46 + 48 * q^47 + 2 * q^48 + 28 * q^50 + 16 * q^51 - 12 * q^52 - 2 * q^53 - 28 * q^54 + 12 * q^55 - 4 * q^56 + 76 * q^57 - 32 * q^58 - 20 * q^59 - 14 * q^60 - 24 * q^61 - 26 * q^62 + 20 * q^63 + 10 * q^64 + 28 * q^65 - 24 * q^66 - 10 * q^67 - 46 * q^69 + 22 * q^70 - 16 * q^71 + 4 * q^73 - 2 * q^74 - 48 * q^75 + 8 * q^76 - 24 * q^77 + 6 * q^78 - 2 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 - 10 * q^85 + 12 * q^86 - 2 * q^89 - 10 * q^90 + 16 * q^91 + 4 * q^92 - 60 * q^93 + 48 * q^94 - 28 * q^95 + 2 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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