LMFDB - Embedded newform 370.2.g.d.327.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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([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("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			327.2
Root			$2.03431 + 0.602710i$ of defining polynomial
Character	$\chi$	$=$	370.327
Dual form			370.2.g.d.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.78347	−	1.78347i	−1.02969	−	1.02969i	−0.999546	−	0.0301401i	$-0.990405\pi$
$3$	−1.78347	−	1.78347i	−1.02969	−	1.02969i	−0.0301401	−	0.999546i	$-0.509595\pi$
$4$	−1.00000			−0.500000
$5$	−0.250846	+	2.22195i	−0.112182	+	0.993688i
$5$	−0.250846	+	2.22195i	−0.112182	+	0.993688i
$6$	1.78347	−	1.78347i	0.728098	−	0.728098i
$7$	0.501691	+	0.501691i	0.189621	+	0.189621i	0.795532	−	0.605911i	$-0.207191\pi$
$7$	0.501691	+	0.501691i	0.189621	+	0.189621i	−0.605911	+	0.795532i	$0.707191\pi$
$8$		−	1.00000i		−	0.353553i
$9$			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
$13$			0.334084i			0.0926583i	0.998926	+	0.0463291i	$0.0147523\pi$
$13$			0.334084i			0.0926583i	−0.998926	+	0.0463291i	$0.985248\pi$
$14$	−0.501691	+	0.501691i	−0.134083	+	0.134083i
$15$	4.41016	−	3.51541i	1.13870	−	0.907674i
$16$	1.00000			0.250000
$17$	−4.86321			−1.17950			−0.589751	−	0.807585i	$-0.700774\pi$
$17$	−4.86321			−1.17950			−0.589751	+	0.807585i	$0.700774\pi$
$18$	−3.36152			−0.792317
$19$	−5.60813	−	5.60813i	−1.28659	−	1.28659i	−0.936843	−	0.349751i	$-0.886266\pi$
$19$	−5.60813	−	5.60813i	−1.28659	−	1.28659i	−0.349751	−	0.936843i	$-0.613734\pi$
$20$	0.250846	−	2.22195i	0.0560908	−	0.496844i
$21$		−	1.78950i		−	0.390501i
$22$	5.77574			1.23139
$23$		−	1.33747i		−	0.278881i	−0.990230	−	0.139441i	$-0.955470\pi$
$23$		−	1.33747i		−	0.278881i	0.990230	−	0.139441i	$-0.0445304\pi$
$24$	−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	$-0.338035\pi$
$29$	7.32635	−	7.32635i	1.36047	−	1.36047i	0.873316	−	0.487153i	$-0.161965\pi$
$30$	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	$0.871362\pi$
$32$			1.00000i			0.176777i
$33$	−10.3008	+	10.3008i	−1.79315	+	1.79315i
$34$		−	4.86321i		−	0.834033i
$35$	−1.24058	+	0.988888i	−0.209697	+	0.167153i
$36$		−	3.36152i		−	0.560253i
$37$	−0.361517	−	6.07201i	−0.0594330	−	0.998232i
$37$	−0.361517	−	6.07201i	−0.0594330	−	0.998232i
$38$	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	$0.806469\pi$
$42$	1.78950			0.276126
$43$		−	1.15610i		−	0.176303i	−0.996107	−	0.0881516i	$-0.971904\pi$
$43$		−	1.15610i		−	0.176303i	0.996107	−	0.0881516i	$-0.0280960\pi$
$44$			5.77574i			0.870725i
$45$	−7.46913	−	0.843222i	−1.11343	−	0.125700i
$46$	1.33747			0.197199
$47$	4.83578	+	4.83578i	0.705370	+	0.705370i	0.965558	−	0.260188i	$-0.0837844\pi$
$47$	4.83578	+	4.83578i	0.705370	+	0.705370i	−0.260188	+	0.965558i	$0.583784\pi$
$48$	−1.78347	−	1.78347i	−0.257421	−	0.257421i
$49$		−	6.49661i		−	0.928087i
$50$	1.11473	−	4.87415i	0.157647	−	0.689309i
$51$	8.67338	+	8.67338i	1.21452	+	1.21452i
$52$		−	0.334084i		−	0.0463291i
$53$	−6.77574	+	6.77574i	−0.930719	+	0.930719i	−0.997751	−	0.0670316i	$-0.978647\pi$
$53$	−6.77574	+	6.77574i	−0.930719	+	0.930719i	0.0670316	+	0.997751i	$0.478647\pi$
$54$	0.644753	+	0.644753i	0.0877398	+	0.0877398i
$55$	12.8334	+	1.44882i	1.73046	+	0.195359i
$56$	0.501691	−	0.501691i	0.0670413	−	0.0670413i
$57$			20.0038i			2.64957i
$58$	7.32635	+	7.32635i	0.961997	+	0.961997i
$59$	8.73793	+	8.73793i	1.13758	+	1.13758i	0.988883	+	0.148698i	$0.0475084\pi$
$59$	8.73793	+	8.73793i	1.13758	+	1.13758i	0.148698	+	0.988883i	$0.452492\pi$
$60$	−4.41016	+	3.51541i	−0.569349	+	0.453837i
$61$	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	$-0.799506\pi$
$67$	−1.79312	+	1.79312i	−0.219065	+	0.219065i	0.589040	+	0.808104i	$0.299506\pi$
$68$	4.86321			0.589751
$69$	−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	$0.563350\pi$
$72$	3.36152			0.396159
$73$	−4.96073	−	4.96073i	−0.580609	−	0.580609i	0.354461	−	0.935071i	$-0.384664\pi$
$73$	−4.96073	−	4.96073i	−0.580609	−	0.580609i	−0.935071	+	0.354461i	$0.884664\pi$
$74$	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	0.323765	−	0.946138i	$-0.395051\pi$
$79$	−5.53177	−	5.53177i	−0.622373	−	0.622373i	−0.946138	+	0.323765i	$0.895051\pi$
$80$	−0.250846	+	2.22195i	−0.0280454	+	0.248422i
$81$	7.78476			0.864973
$82$	−7.31524			−0.807833
$83$	4.77799	−	4.77799i	0.524453	−	0.524453i	−0.394460	−	0.918913i	$-0.629068\pi$
$83$	4.77799	−	4.77799i	0.524453	−	0.524453i	0.918913	+	0.394460i	$0.129068\pi$
$84$			1.78950i			0.195251i
$85$	1.21991	−	10.8058i	0.132318	−	1.17206i
$86$	1.15610			0.124665
$87$	−26.1326			−2.80171
$88$	−5.77574			−0.615696
$89$	−3.08239	+	3.08239i	−0.326733	+	0.326733i	−0.851343	−	0.524610i	$-0.824211\pi$
$89$	−3.08239	+	3.08239i	−0.326733	+	0.326733i	0.524610	+	0.851343i	$0.324211\pi$
$90$	0.843222	−	7.46913i	0.0888834	−	0.787316i
$91$	−0.167607	+	0.167607i	−0.0175700	+	0.0175700i
$92$			1.33747i			0.139441i
$93$			10.4508i			1.08370i
$94$	−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
$97$	−3.56694			−0.362167			−0.181084	−	0.983468i	$-0.557961\pi$
$97$	−3.56694			−0.362167			−0.181084	+	0.983468i	$0.557961\pi$
$98$	6.49661			0.656257
$99$	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
$103$	−5.38950			−0.531044			−0.265522	−	0.964105i	$-0.585544\pi$
$103$	−5.38950			−0.531044			−0.265522	+	0.964105i	$0.585544\pi$
$104$	0.334084			0.0327596
$105$	3.97619	+	0.448889i	0.388036	+	0.0438070i
$106$	−6.77574	−	6.77574i	−0.658118	−	0.658118i
$107$	2.00040	+	2.00040i	0.193386	+	0.193386i	0.797157	−	0.603772i	$-0.206336\pi$
$107$	2.00040	+	2.00040i	0.193386	+	0.193386i	−0.603772	+	0.797157i	$0.706336\pi$
$108$	−0.644753	+	0.644753i	−0.0620414	+	0.0620414i
$109$	−0.389616	−	0.389616i	−0.0373185	−	0.0373185i	0.688201	−	0.725520i	$-0.258401\pi$
$109$	−0.389616	−	0.389616i	−0.0373185	−	0.0373185i	−0.725520	+	0.688201i	$0.758401\pi$
$110$	−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
$113$	−5.48455			−0.515943			−0.257971	−	0.966153i	$-0.583054\pi$
$113$	−5.48455			−0.515943			−0.257971	+	0.966153i	$0.583054\pi$
$114$	−20.0038			−1.87353
$115$	2.97179	+	0.335498i	0.277121	+	0.0312853i
$116$	−7.32635	+	7.32635i	−0.680235	+	0.680235i
$117$	−1.12303			−0.103824
$118$	−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
$125$	3.69955	−	10.5505i	0.330898	−	0.943667i
$126$	−1.68644	−	1.68644i	−0.150240	−	0.150240i
$127$	−7.39933	−	7.39933i	−0.656584	−	0.656584i	0.297986	−	0.954570i	$-0.403685\pi$
$127$	−7.39933	−	7.39933i	−0.656584	−	0.656584i	−0.954570	+	0.297986i	$0.903685\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.06186	+	2.06186i	−0.181537	+	0.181537i
$130$	0.0838036	−	0.742319i	0.00735006	−	0.0651057i
$131$	−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
$133$		−	5.62710i		−	0.487932i
$134$	−1.79312	−	1.79312i	−0.154902	−	0.154902i
$135$	1.27088	+	1.59435i	0.109380	+	0.137219i
$136$			4.86321i			0.417017i
$137$	5.42935	+	5.42935i	0.463861	+	0.463861i	0.899919	−	0.436058i	$-0.143626\pi$
$137$	5.42935	+	5.42935i	0.463861	+	0.463861i	−0.436058	+	0.899919i	$0.643626\pi$
$138$	−2.38533	−	2.38533i	−0.203053	−	0.203053i
$139$	13.4593			1.14160			0.570800	−	0.821089i	$-0.306633\pi$
$139$	13.4593			1.14160			0.570800	+	0.821089i	$0.306633\pi$
$140$	1.24058	−	0.988888i	0.104848	−	0.0835763i
$141$		−	17.2489i		−	1.45262i
$142$		−	3.33183i		−	0.279601i
$143$	1.92958			0.161360
$144$			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
$148$	0.361517	+	6.07201i	0.0297165	+	0.499116i
$149$			13.8867i			1.13764i	0.822461	+	0.568821i	$0.192600\pi$
$149$			13.8867i			1.13764i	−0.822461	+	0.568821i	$0.807400\pi$
$150$	−10.6810	+	6.70480i	−0.872099	+	0.547445i
$151$			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
$153$		−	16.3478i		−	1.32164i
$154$	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	0.777355	+	0.629062i	$0.216561\pi$
$157$	17.6224	+	17.6224i	1.40642	+	1.40642i	0.629062	+	0.777355i	$0.283439\pi$
$158$	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
$162$			7.78476i			0.611628i
$163$	−13.5930			−1.06469			−0.532343	−	0.846529i	$-0.678688\pi$
$163$	−13.5930			−1.06469			−0.532343	+	0.846529i	$0.678688\pi$
$164$		−	7.31524i		−	0.571224i
$165$	−20.3041	−	25.4719i	−1.58067	−	1.98299i
$166$	4.77799	+	4.77799i	0.370844	+	0.370844i
$167$	11.8884			0.919951			0.459976	−	0.887932i	$-0.347858\pi$
$167$	11.8884			0.919951			0.459976	+	0.887932i	$0.347858\pi$
$168$	−1.78950			−0.138063
$169$	12.8884			0.991414
$170$	10.8058	+	1.21991i	0.828769	+	0.0935632i
$171$	18.8518	−	18.8518i	1.44164	−	1.44164i
$172$			1.15610i			0.0881516i
$173$	−1.19504	−	1.19504i	−0.0908572	−	0.0908572i	0.660217	−	0.751075i	$-0.270464\pi$
$173$	−1.19504	−	1.19504i	−0.0908572	−	0.0908572i	−0.751075	+	0.660217i	$0.770464\pi$
$174$		−	26.1326i		−	1.98111i
$175$	−1.88607	−	3.00457i	−0.142573	−	0.227124i
$176$		−	5.77574i		−	0.435363i
$177$		−	31.1676i		−	2.34270i
$178$	−3.08239	−	3.08239i	−0.231035	−	0.231035i
$179$	14.1150	−	14.1150i	1.05501	−	1.05501i	0.0566105	−	0.998396i	$-0.481971\pi$
$179$	14.1150	−	14.1150i	1.05501	−	1.05501i	0.998396	−	0.0566105i	$-0.0180293\pi$
$180$	7.46913	+	0.843222i	0.556716	+	0.0628500i
$181$	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
$183$		−	1.68644i		−	0.124666i
$184$	−1.33747			−0.0985994
$185$	13.5824	+	0.719864i	0.998598	+	0.0529255i
$186$	−10.4508			−0.766291
$187$			28.0886i			2.05404i
$188$	−4.83578	−	4.83578i	−0.352685	−	0.352685i
$189$	0.646934			0.0470575
$190$	11.0542	+	13.8678i	0.801958	+	1.00607i
$191$	−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
$193$		−	19.5996i		−	1.41081i	−0.708805	−	0.705404i	$-0.750766\pi$
$193$		−	19.5996i		−	1.41081i	0.708805	−	0.705404i	$-0.249234\pi$
$194$		−	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	0.174847	−	0.984596i	$-0.444057\pi$
$197$	−11.3654	−	11.3654i	−0.809749	−	0.809749i	−0.984596	+	0.174847i	$0.944057\pi$
$198$			19.4152i			1.37978i
$199$	−4.39595	+	4.39595i	−0.311620	+	0.311620i	−0.845537	−	0.533917i	$-0.820720\pi$
$199$	−4.39595	+	4.39595i	−0.311620	+	0.311620i	0.533917	+	0.845537i	$0.320720\pi$
$200$	−1.11473	+	4.87415i	−0.0788236	+	0.344655i
$201$	6.39595			0.451135
$202$	−0.222565			−0.0156596
$203$	7.35114			0.515949
$204$	−8.67338	−	8.67338i	−0.607258	−	0.607258i
$205$	−16.2541	−	1.83500i	−1.13524	−	0.128162i
$206$		−	5.38950i		−	0.375505i
$207$	4.49592			0.312488
$208$			0.334084i			0.0231646i
$209$	−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
$217$		−	2.93982i		−	0.199568i
$218$	0.389616	−	0.389616i	0.0263881	−	0.0263881i
$219$			17.6946i			1.19569i
$220$	−12.8334	−	1.44882i	−0.865229	−	0.0976793i
$221$		−	1.62472i		−	0.109291i
$222$	−11.4740	−	10.1845i	−0.770084	−	0.683538i
$223$	10.4136	−	10.4136i	0.697343	−	0.697343i	−0.266494	−	0.963837i	$-0.585865\pi$
$223$	10.4136	−	10.4136i	0.697343	−	0.697343i	0.963837	+	0.266494i	$0.0858651\pi$
$224$	−0.501691	+	0.501691i	−0.0335207	+	0.0335207i
$225$	3.74720	−	16.3845i	0.249813	−	1.09230i
$226$		−	5.48455i		−	0.364827i
$227$	6.88908			0.457244			0.228622	−	0.973515i	$-0.426578\pi$
$227$	6.88908			0.457244			0.228622	+	0.973515i	$0.426578\pi$
$228$		−	20.0038i		−	1.32479i
$229$		−	13.4017i		−	0.885608i	−0.896618	−	0.442804i	$-0.853984\pi$
$229$		−	13.4017i		−	0.885608i	0.896618	−	0.442804i	$-0.146016\pi$
$230$	−0.335498	+	2.97179i	−0.0221221	+	0.195954i
$231$	−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	$-0.0736181\pi$
$233$	11.3590	+	11.3590i	0.744152	+	0.744152i	−0.229222	+	0.973374i	$0.573618\pi$
$234$		−	1.12303i		−	0.0734147i
$235$	−11.9579	+	9.53183i	−0.780047	+	0.621788i
$236$	−8.73793	−	8.73793i	−0.568791	−	0.568791i
$237$			19.7315i			1.28170i
$238$	2.43983	−	2.43983i	0.158151	−	0.158151i
$239$	−4.68385	−	4.68385i	−0.302973	−	0.302973i	0.539203	−	0.842176i	$-0.318726\pi$
$239$	−4.68385	−	4.68385i	−0.302973	−	0.302973i	−0.842176	+	0.539203i	$0.818726\pi$
$240$	4.41016	−	3.51541i	0.284674	−	0.226919i
$241$	−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	$0.380332\pi$
$242$		−	22.3592i		−	1.43730i
$243$	−15.8181	−	15.8181i	−1.01473	−	1.01473i
$244$	−0.472799	−	0.472799i	−0.0302679	−	0.0302679i
$245$	14.4352	+	1.62965i	0.922229	+	0.104114i
$246$	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
$253$	−7.72486			−0.485658
$254$	7.39933	−	7.39933i	0.464275	−	0.464275i
$255$	−21.4475	+	17.0962i	−1.34310	+	1.07060i
$256$	1.00000			0.0625000
$257$	2.20193			0.137352			0.0686762	−	0.997639i	$-0.478122\pi$
$257$	2.20193			0.137352			0.0686762	+	0.997639i	$0.478122\pi$
$258$	−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	$-0.0899981\pi$
$263$	11.0490	+	11.0490i	0.681310	+	0.681310i	−0.278985	+	0.960295i	$0.589998\pi$
$264$	10.3008	+	10.3008i	0.633973	+	0.633973i
$265$	−13.3557	−	16.7550i	−0.820435	−	1.02925i
$266$	5.62710			0.345020
$267$	10.9947			0.672864
$268$	1.79312	−	1.79312i	0.109532	−	0.109532i
$269$		−	3.21918i		−	0.196277i	−0.995173	−	0.0981385i	$-0.968711\pi$
$269$		−	3.21918i		−	0.196277i	0.995173	−	0.0981385i	$-0.0312888\pi$
$270$	−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	$0.582102\pi$
$272$	−4.86321			−0.294875
$273$	0.597844			0.0361832
$274$	−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
$277$		−	5.30553i		−	0.318778i	−0.987216	−	0.159389i	$-0.949048\pi$
$277$		−	5.30553i		−	0.318778i	0.987216	−	0.159389i	$-0.0509525\pi$
$278$			13.4593i			0.807233i
$279$	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	$0.225586\pi$
$282$	17.2489			1.02716
$283$	−10.9456			−0.650648			−0.325324	−	0.945603i	$-0.605473\pi$
$283$	−10.9456			−0.650648			−0.325324	+	0.945603i	$0.605473\pi$
$284$	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
$288$	−3.36152			−0.198079
$289$	6.65079			0.391223
$290$	−18.1166	+	14.4410i	−1.06384	+	0.848007i
$291$	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	0.377349	−	0.926071i	$-0.376836\pi$
$293$	22.3110	−	22.3110i	1.30342	−	1.30342i	0.926071	−	0.377349i	$-0.123164\pi$
$294$	−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
$298$	−13.8867			−0.804434
$299$	0.446826			0.0258406
$300$	−6.70480	−	10.6810i	−0.387102	−	0.616667i
$301$	0.580004	−	0.580004i	0.0334309	−	0.0334309i
$302$	−5.54233			−0.318925
$303$	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	$-0.881080\pi$
$307$	−9.91801	+	9.91801i	−0.566051	+	0.566051i	0.364969	+	0.931020i	$0.381080\pi$
$308$	−2.89764	+	2.89764i	−0.165108	+	0.165108i
$309$	9.61201	+	9.61201i	0.546808	+	0.546808i
$310$	5.77517	+	7.24508i	0.328008	+	0.411493i
$311$	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
$313$			24.2499i			1.37069i	0.728221	+	0.685343i	$0.240348\pi$
$313$			24.2499i			1.37069i	−0.728221	+	0.685343i	$0.759652\pi$
$314$	−17.6224	+	17.6224i	−0.994487	+	0.994487i
$315$	−3.32416	−	4.17024i	−0.187295	−	0.234966i
$316$	5.53177	+	5.53177i	0.311187	+	0.311187i
$317$	20.7768	−	20.7768i	1.16694	−	1.16694i	0.184016	−	0.982923i	$-0.441090\pi$
$317$	20.7768	−	20.7768i	1.16694	−	1.16694i	0.982923	−	0.184016i	$-0.0589097\pi$
$318$			24.1686i			1.35531i
$319$	−42.3151	−	42.3151i	−2.36919	−	2.36919i
$320$	0.250846	−	2.22195i	0.0140227	−	0.124211i
$321$		−	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
$325$	0.372415	−	1.62838i	0.0206579	−	0.0903261i
$326$		−	13.5930i		−	0.752847i
$327$			1.38974i			0.0768526i
$328$	7.31524			0.403917
$329$			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
$333$	20.4112	−	1.21524i	1.11852	−	0.0665950i
$334$			11.8884i			0.650504i
$335$	−3.53443	−	4.43403i	−0.193107	−	0.242257i
$336$		−	1.78950i		−	0.0976253i
$337$	17.1598	−	17.1598i	0.934756	−	0.934756i	−0.0632419	−	0.997998i	$-0.520144\pi$
$337$	17.1598	−	17.1598i	0.934756	−	0.934756i	0.997998	+	0.0632419i	$0.0201440\pi$
$338$			12.8884i			0.701036i
$339$	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
$347$		−	19.3891i		−	1.04086i	−0.853904	−	0.520430i	$-0.825772\pi$
$347$		−	19.3891i		−	1.04086i	0.853904	−	0.520430i	$-0.174228\pi$
$348$	26.1326			1.40086
$349$		−	11.5543i		−	0.618489i	−0.950983	−	0.309245i	$-0.899924\pi$
$349$		−	11.5543i		−	0.618489i	0.950983	−	0.309245i	$-0.100076\pi$
$350$	3.00457	−	1.88607i	0.160601	−	0.100815i
$351$	0.215402	+	0.215402i	0.0114973	+	0.0114973i
$352$	5.77574			0.307848
$353$	−31.6556			−1.68486			−0.842428	−	0.538810i	$-0.818874\pi$
$353$	−31.6556			−1.68486			−0.842428	+	0.538810i	$0.818874\pi$
$354$	31.1676			1.65654
$355$	0.835775	−	7.40317i	0.0443584	−	0.392920i
$356$	3.08239	−	3.08239i	0.163366	−	0.163366i
$357$			8.70271i			0.460596i
$358$	14.1150	+	14.1150i	0.746003	+	0.746003i
$359$		−	12.7254i		−	0.671622i	−0.941929	−	0.335811i	$-0.890990\pi$
$359$		−	12.7254i		−	0.671622i	0.941929	−	0.335811i	$-0.109010\pi$
$360$	−0.843222	+	7.46913i	−0.0444417	+	0.393658i
$361$			43.9023i			2.31065i
$362$			14.6126i			0.768024i
$363$	39.8768	+	39.8768i	2.09299	+	2.09299i
$364$	0.167607	−	0.167607i	0.00878500	−	0.00878500i
$365$	12.2669	−	9.77813i	0.642078	−	0.511811i
$366$	1.68644			0.0881518
$367$	7.49820	+	7.49820i	0.391403	+	0.391403i	0.875187	−	0.483784i	$-0.160738\pi$
$367$	7.49820	+	7.49820i	0.391403	+	0.391403i	−0.483784	+	0.875187i	$0.660738\pi$
$368$		−	1.33747i		−	0.0697203i
$369$	−24.5903			−1.28012
$370$	−0.719864	+	13.5824i	−0.0374240	+	0.706116i
$371$	−6.79866			−0.352969
$372$		−	10.4508i		−	0.541849i
$373$	0.0403047	+	0.0403047i	0.00208690	+	0.00208690i	0.708149	−	0.706063i	$-0.249530\pi$
$373$	0.0403047	+	0.0403047i	0.00208690	+	0.00208690i	−0.706063	+	0.708149i	$0.749530\pi$
$374$	−28.0886			−1.45243
$375$	−25.4145	+	12.2185i	−1.31240	+	0.630959i
$376$	4.83578	−	4.83578i	0.249386	−	0.249386i
$377$	2.44762	+	2.44762i	0.126059	+	0.126059i
$378$			0.646934i			0.0332747i
$379$			2.29640i			0.117958i	0.998259	+	0.0589791i	$0.0187845\pi$
$379$			2.29640i			0.117958i	−0.998259	+	0.0589791i	$0.981215\pi$
$380$	−13.8678	+	11.0542i	−0.711402	+	0.567070i
$381$			26.3929i			1.35215i
$382$	−8.33714	−	8.33714i	−0.426565	−	0.426565i
$383$		−	23.9142i		−	1.22196i	−0.791646	−	0.610980i	$-0.790776\pi$
$383$		−	23.9142i		−	1.22196i	0.791646	−	0.610980i	$-0.209224\pi$
$384$	−1.78347	+	1.78347i	−0.0910122	+	0.0910122i
$385$	5.71156	+	7.16528i	0.291088	+	0.365176i
$386$	19.5996			0.997592
$387$	3.88624			0.197549
$388$	3.56694			0.181084
$389$	14.5043	+	14.5043i	0.735399	+	0.735399i	0.971684	−	0.236285i	$-0.0759298\pi$
$389$	14.5043	+	14.5043i	0.735399	+	0.735399i	−0.236285	+	0.971684i	$0.575930\pi$
$390$	−1.47336	+	1.17444i	−0.0746067	+	0.0594702i
$391$			6.50438i			0.328941i
$392$	−6.49661			−0.328128
$393$			31.8794i			1.60810i
$394$	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	$-0.602907\pi$
$397$	12.5627	−	12.5627i	0.630506	−	0.630506i	0.948195	+	0.317689i	$0.102907\pi$
$398$	−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	$0.634046\pi$
$402$			6.39595i			0.319001i
$403$	0.978837	−	0.978837i	0.0487594	−	0.0487594i
$404$		−	0.222565i		−	0.0110730i
$405$	−1.95277	+	17.2974i	−0.0970340	+	0.859513i
$406$			7.35114i			0.364831i
$407$	−35.0703	+	2.08803i	−1.73837	+	0.103500i
$408$	8.67338	−	8.67338i	0.429396	−	0.429396i
$409$	4.26841	−	4.26841i	0.211059	−	0.211059i	−0.593658	−	0.804717i	$-0.702317\pi$
$409$	4.26841	−	4.26841i	0.211059	−	0.211059i	0.804717	+	0.593658i	$0.202317\pi$
$410$	1.83500	−	16.2541i	0.0906240	−	0.802734i
$411$		−	19.3661i		−	0.955262i
$412$	5.38950			0.265522
$413$			8.76748i			0.431420i
$414$			4.49592i			0.220962i
$415$	9.41793	+	11.8150i	0.462308	+	0.579976i
$416$	−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	$-0.974629\pi$
$419$		−	3.25958i		−	0.159241i	0.996825	−	0.0796205i	$-0.0253708\pi$
$420$	−3.97619	−	0.448889i	−0.194018	−	0.0219035i
$421$	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	$0.657683\pi$
$422$		−	16.7875i		−	0.817201i
$423$	−16.2555	+	16.2555i	−0.790371	+	0.790371i
$424$	6.77574	+	6.77574i	0.329059	+	0.329059i
$425$	23.7040	+	5.42119i	1.14981	+	0.262966i
$426$	−5.94222	+	5.94222i	−0.287901	+	0.287901i
$427$			0.474398i			0.0229577i
$428$	−2.00040	−	2.00040i	−0.0966929	−	0.0966929i
$429$	−3.44135	−	3.44135i	−0.166150	−	0.166150i
$430$	−0.290002	+	2.56879i	−0.0139851	+	0.123878i
$431$	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	−0.679569	−	0.733612i	$-0.737833\pi$
$433$	1.12455	−	1.12455i	0.0540424	−	0.0540424i	0.733612	+	0.679569i	$0.237833\pi$
$434$	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
$438$	−17.6946			−0.845481
$439$	−16.8566	+	16.8566i	−0.804523	+	0.804523i	−0.983799	−	0.179276i	$-0.942625\pi$
$439$	−16.8566	+	16.8566i	−0.804523	+	0.804523i	0.179276	+	0.983799i	$0.442625\pi$
$440$	1.44882	−	12.8334i	0.0690697	−	0.611809i
$441$	21.8385			1.03993
$442$	1.62472			0.0772801
$443$	−26.1307	−	26.1307i	−1.24151	−	1.24151i	−0.959376	−	0.282132i	$-0.908958\pi$
$443$	−26.1307	−	26.1307i	−1.24151	−	1.24151i	−0.282132	−	0.959376i	$-0.591042\pi$
$444$	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	0.559713	−	0.828687i	$-0.310911\pi$
$449$	−5.69945	−	5.69945i	−0.268973	−	0.268973i	−0.828687	+	0.559713i	$0.810911\pi$
$450$	16.3845	+	3.74720i	0.772375	+	0.176645i
$451$	42.2509			1.98952
$452$	5.48455			0.257971
$453$	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
$457$	2.23060			0.104343			0.0521715	−	0.998638i	$-0.483386\pi$
$457$	2.23060			0.104343			0.0521715	+	0.998638i	$0.483386\pi$
$458$	13.4017			0.626219
$459$	−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	$0.398732\pi$
$462$		−	10.3357i		−	0.480860i
$463$		−	13.3262i		−	0.619321i	−0.950847	−	0.309660i	$-0.899785\pi$
$463$		−	13.3262i		−	0.619321i	0.950847	−	0.309660i	$-0.100215\pi$
$464$	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
$467$	−30.6482			−1.41823			−0.709115	−	0.705093i	$-0.750905\pi$
$467$	−30.6482			−1.41823			−0.709115	+	0.705093i	$0.750905\pi$
$468$	1.12303			0.0519121
$469$	−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
$473$	−6.67731			−0.307023
$474$	−19.7315			−0.906297
$475$	21.0833	+	33.5865i	0.967369	+	1.54105i
$476$	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	$0.0131755\pi$
$479$	22.7730	+	22.7730i	1.04052	+	1.04052i	0.0413804	+	0.999143i	$0.486824\pi$
$480$	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
$483$	−2.39340			−0.108903
$484$	22.3592			1.01633
$485$	0.894750	−	7.92557i	0.0406285	−	0.359881i
$486$	15.8181	−	15.8181i	0.717525	−	0.717525i
$487$	−1.55055			−0.0702622			−0.0351311	−	0.999383i	$-0.511185\pi$
$487$	−1.55055			−0.0702622			−0.0351311	+	0.999383i	$0.511185\pi$
$488$	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
$495$	−4.87023	+	43.1398i	−0.218900	+	1.93899i
$496$	−2.92991	−	2.92991i	−0.131557	−	0.131557i
$497$	−1.67155	−	1.67155i	−0.0749793	−	0.0749793i
$498$		−	17.0428i		−	0.763706i
$499$	18.0930	−	18.0930i	0.809954	−	0.809954i	−0.174673	−	0.984627i	$-0.555887\pi$
$499$	18.0930	−	18.0930i	0.809954	−	0.809954i	0.984627	+	0.174673i	$0.0558867\pi$
$500$	−3.69955	+	10.5505i	−0.165449	+	0.471833i
$501$	−21.2026	−	21.2026i	−0.947261	−	0.947261i
$502$	12.8437	−	12.8437i	0.573242	−	0.573242i
$503$		−	0.456512i		−	0.0203548i	−0.999948	−	0.0101774i	$-0.996760\pi$
$503$		−	0.456512i		−	0.0203548i	0.999948	−	0.0101774i	$-0.00323963\pi$
$504$	1.68644	+	1.68644i	0.0751202	+	0.0751202i
$505$	−0.494528	−	0.0558294i	−0.0220062	−	0.00248438i
$506$		−	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	$-0.733274\pi$
$509$	−30.1863			−1.33798			−0.668992	+	0.743270i	$0.733274\pi$
$510$	−17.0962	−	21.4475i	−0.757031	−	0.949712i
$511$		−	4.97751i		−	0.220192i
$512$			1.00000i			0.0441942i
$513$	−7.23172			−0.319288
$514$			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
$518$	3.22764	+	2.86490i	0.141815	+	0.125877i
$519$			4.26263i			0.187109i
$520$	−0.0838036	+	0.742319i	−0.00367503	+	0.0325529i
$521$		−	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
$523$		−	35.7281i		−	1.56228i	−0.624354	−	0.781141i	$-0.714638\pi$
$523$		−	35.7281i		−	1.56228i	0.624354	−	0.781141i	$-0.285362\pi$
$524$	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
$532$			5.62710i			0.243966i
$533$	−2.44391			−0.105857
$534$			10.9947i			0.475787i
$535$	−4.94658	+	3.94300i	−0.213859	+	0.170471i
$536$	1.79312	+	1.79312i	0.0774510	+	0.0774510i
$537$	−50.3474			−2.17265
$538$	3.21918			0.138789
$539$	−37.5227			−1.61622
$540$	−1.27088	−	1.59435i	−0.0546899	−	0.0686097i
$541$	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	$0.128014\pi$
$542$		−	8.39830i		−	0.360738i
$543$	−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
$547$		−	19.3374i		−	0.826807i	−0.910548	−	0.413403i	$-0.864340\pi$
$547$		−	19.3374i		−	0.826807i	0.910548	−	0.413403i	$-0.135660\pi$
$548$	−5.42935	−	5.42935i	−0.231930	−	0.231930i
$549$	−1.58932	+	1.58932i	−0.0678306	+	0.0678306i
$550$	−28.1518	−	6.43842i	−1.20040	−	0.274535i
$551$	−82.1743			−3.50074
$552$	2.38533	+	2.38533i	0.101526	+	0.101526i
$553$		−	5.55049i		−	0.236031i
$554$	5.30553			0.225410
$555$	−22.9399	−	25.5076i	−0.973746	−	1.08274i
$556$	−13.4593			−0.570800
$557$			45.6308i			1.93344i	0.255836	+	0.966720i	$0.417649\pi$
$557$			45.6308i			1.93344i	−0.255836	+	0.966720i	$0.582351\pi$
$558$	9.84895	+	9.84895i	0.416939	+	0.416939i
$559$	0.386234			0.0163359
$560$	−1.24058	+	0.988888i	−0.0524241	+	0.0417881i
$561$	50.0951	−	50.0951i	2.11502	−	2.11502i
$562$	1.81647	+	1.81647i	0.0766232	+	0.0766232i
$563$		−	19.3770i		−	0.816644i	−0.912838	−	0.408322i	$-0.866114\pi$
$563$		−	19.3770i		−	0.816644i	0.912838	−	0.408322i	$-0.133886\pi$
$564$			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
$568$			3.33183i			0.139801i
$569$	14.4045	−	14.4045i	0.603870	−	0.603870i	−0.337468	−	0.941337i	$-0.609570\pi$
$569$	14.4045	−	14.4045i	0.603870	−	0.603870i	0.941337	+	0.337468i	$0.109570\pi$
$570$	5.01788	−	44.4476i	0.210176	−	1.86171i
$571$	30.3965			1.27205			0.636027	−	0.771667i	$-0.280577\pi$
$571$	30.3965			1.27205			0.636027	+	0.771667i	$0.280577\pi$
$572$	−1.92958			−0.0806799
$573$	29.7380			1.24232
$574$	−3.66999	−	3.66999i	−0.153183	−	0.153183i
$575$	−1.49092	+	6.51902i	−0.0621757	+	0.271862i
$576$		−	3.36152i		−	0.140063i
$577$	−43.4726			−1.80979			−0.904894	−	0.425638i	$-0.860050\pi$
$577$	−43.4726			−1.80979			−0.904894	+	0.425638i	$0.860050\pi$
$578$			6.65079i			0.276636i
$579$	−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
$587$			26.6263i			1.09898i	0.835499	+	0.549492i	$0.185179\pi$
$587$			26.6263i			1.09898i	−0.835499	+	0.549492i	$0.814821\pi$
$588$	11.5865	−	11.5865i	0.477819	−	0.477819i
$589$			32.8627i			1.35408i
$590$	−17.2234	−	21.6071i	−0.709076	−	0.889552i
$591$			40.5395i			1.66757i
$592$	−0.361517	−	6.07201i	−0.0148582	−	0.249558i
$593$	2.88802	−	2.88802i	0.118597	−	0.118597i	−0.645318	−	0.763914i	$-0.723275\pi$
$593$	2.88802	−	2.88802i	0.118597	−	0.118597i	0.763914	+	0.645318i	$0.223275\pi$
$594$	3.72393	−	3.72393i	0.152795	−	0.152795i
$595$	6.03321	−	4.80917i	0.247337	−	0.197157i
$596$		−	13.8867i		−	0.568821i
$597$	15.6801			0.641742
$598$			0.446826i			0.0182721i
$599$			21.4346i			0.875796i	0.899025	+	0.437898i	$0.144277\pi$
$599$			21.4346i			0.875796i	−0.899025	+	0.437898i	$0.855723\pi$
$600$	10.6810	−	6.70480i	0.436050	−	0.273722i
$601$	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
$605$	5.60870	−	49.6810i	0.228026	−	2.01982i
$606$	0.396937	+	0.396937i	0.0161245	+	0.0161245i
$607$			3.14401i			0.127612i	0.997962	+	0.0638058i	$0.0203238\pi$
$607$			3.14401i			0.127612i	−0.997962	+	0.0638058i	$0.979676\pi$
$608$	5.60813	−	5.60813i	0.227440	−	0.227440i
$609$	−13.1105	−	13.1105i	−0.531265	−	0.531265i
$610$	−0.931938	−	1.16914i	−0.0377331	−	0.0473370i
$611$	−1.61556	+	1.61556i	−0.0653584	+	0.0653584i
$612$			16.3478i			0.660819i
$613$	−19.3617	−	19.3617i	−0.782013	−	0.782013i	0.198157	−	0.980170i	$-0.436504\pi$
$613$	−19.3617	−	19.3617i	−0.782013	−	0.782013i	−0.980170	+	0.198157i	$0.936504\pi$
$614$	−9.91801	−	9.91801i	−0.400258	−	0.400258i
$615$	25.7161	+	32.2614i	1.03697	+	1.30090i
$616$	−2.89764	−	2.89764i	−0.116749	−	0.116749i
$617$	10.3835	−	10.3835i	0.418023	−	0.418023i	−0.466499	−	0.884522i	$-0.654485\pi$
$617$	10.3835	−	10.3835i	0.418023	−	0.418023i	0.884522	+	0.466499i	$0.154485\pi$
$618$	−9.61201	+	9.61201i	−0.386652	+	0.386652i
$619$	6.04142			0.242825			0.121413	−	0.992602i	$-0.461258\pi$
$619$	6.04142			0.242825			0.121413	+	0.992602i	$0.461258\pi$
$620$	−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
$623$	−3.09282			−0.123911
$624$	0.595828	−	0.595828i	0.0238522	−	0.0238522i
$625$	22.5147	+	10.8668i	0.900589	+	0.434671i
$626$	−24.2499			−0.969221
$627$	115.537			4.61410
$628$	−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
$635$	18.2971	−	14.5849i	0.726096	−	0.578783i
$636$	−24.1686			−0.958348
$637$	2.17042			0.0859950
$638$	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	$0.248721\pi$
$642$	7.13529			0.281607
$643$	−13.2845			−0.523888			−0.261944	−	0.965083i	$-0.584364\pi$
$643$	−13.2845			−0.523888			−0.261944	+	0.965083i	$0.584364\pi$
$644$	−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
$647$		−	14.0753i		−	0.553357i	−0.960963	−	0.276678i	$-0.910766\pi$
$647$		−	14.0753i		−	0.553357i	0.960963	−	0.276678i	$-0.0892337\pi$
$648$		−	7.78476i		−	0.305814i
$649$	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
$652$	13.5930			0.532343
$653$	26.4506			1.03509			0.517546	−	0.855656i	$-0.326846\pi$
$653$	26.4506			1.03509			0.517546	+	0.855656i	$0.326846\pi$
$654$	−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
$658$	−4.85213			−0.189156
$659$	−39.4936			−1.53845			−0.769225	−	0.638978i	$-0.779358\pi$
$659$	−39.4936			−1.53845			−0.769225	+	0.638978i	$0.779358\pi$
$660$	20.3041	+	25.4719i	0.790335	+	0.991493i
$661$	−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
$668$	−11.8884			−0.459976
$669$	−37.1445			−1.43609
$670$	4.43403	−	3.53443i	0.171301	−	0.136547i
$671$	2.73076	−	2.73076i	0.105420	−	0.105420i
$672$	1.78950			0.0690315
$673$	−14.9976	+	14.9976i	−0.578114	+	0.578114i	−0.934383	−	0.356269i	$-0.884049\pi$
$673$	−14.9976	+	14.9976i	−0.578114	+	0.578114i	0.356269	+	0.934383i	$0.384049\pi$
$674$	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	$-0.586176\pi$
$677$	18.1131	−	18.1131i	0.696143	−	0.696143i	0.963576	+	0.267434i	$0.0861756\pi$
$678$	−9.78151	+	9.78151i	−0.375657	+	0.375657i
$679$	−1.78950	−	1.78950i	−0.0686747	−	0.0686747i
$680$	−10.8058	−	1.21991i	−0.414384	−	0.0467816i
$681$	−12.2865	−	12.2865i	−0.470818	−	0.470818i
$682$	−16.9224	−	16.9224i	−0.647993	−	0.647993i
$683$		−	19.3794i		−	0.741532i	−0.928726	−	0.370766i	$-0.879095\pi$
$683$		−	19.3794i		−	0.741532i	0.928726	−	0.370766i	$-0.120905\pi$
$684$	−18.8518	+	18.8518i	−0.720818	+	0.720818i
$685$	−13.4257	+	10.7018i	−0.512969	+	0.408896i
$686$	6.77113	+	6.77113i	0.258523	+	0.258523i
$687$	−23.9015	+	23.9015i	−0.911898	+	0.911898i
$688$		−	1.15610i		−	0.0440758i
$689$	−2.26367	−	2.26367i	−0.0862388	−	0.0862388i
$690$	5.89844	−	4.70174i	0.224550	−	0.178992i
$691$			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
$695$	−3.37620	+	29.9059i	−0.128066	+	1.13439i
$696$			26.1326i			0.990555i
$697$		−	35.5755i		−	1.34752i
$698$	11.5543			0.437338
$699$		−	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
$703$	−32.0252	+	36.0801i	−1.20785	+	1.36079i
$704$			5.77574i			0.217681i
$705$	38.3263	+	4.32681i	1.44345	+	0.162957i
$706$		−	31.6556i		−	1.19137i
$707$	−0.111659	+	0.111659i	−0.00419936	+	0.00419936i
$708$			31.1676i			1.17135i
$709$	24.4221	+	24.4221i	0.917193	+	0.917193i	0.996824	−	0.0796314i	$-0.0253743\pi$
$709$	24.4221	+	24.4221i	0.917193	+	0.917193i	−0.0796314	+	0.996824i	$0.525374\pi$
$710$	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
$717$			16.7070i			0.623935i
$718$	12.7254			0.474908
$719$		−	49.2033i		−	1.83497i	−0.397766	−	0.917487i	$-0.630214\pi$
$719$		−	49.2033i		−	1.83497i	0.397766	−	0.917487i	$-0.369786\pi$
$720$	−7.46913	−	0.843222i	−0.278358	−	0.0314250i
$721$	−2.70387	−	2.70387i	−0.100697	−	0.100697i
$722$	−43.9023			−1.63387
$723$	31.1757			1.15944
$724$	−14.6126			−0.543075
$725$	−43.8767	+	27.5428i	−1.62954	+	1.02292i
$726$	−39.8768	+	39.8768i	−1.47997	+	1.47997i
$727$		−	17.2328i		−	0.639130i	−0.947564	−	0.319565i	$-0.896463\pi$
$727$		−	17.2328i		−	0.639130i	0.947564	−	0.319565i	$-0.103537\pi$
$728$	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
$732$			1.68644i			0.0623328i
$733$	−29.6069	−	29.6069i	−1.09356	−	1.09356i	−0.995146	−	0.0984097i	$-0.968624\pi$
$733$	−29.6069	−	29.6069i	−1.09356	−	1.09356i	−0.0984097	−	0.995146i	$-0.531376\pi$
$734$	−7.49820	+	7.49820i	−0.276763	+	0.276763i
$735$	−22.8382	−	28.6511i	−0.842401	−	1.05681i
$736$	1.33747			0.0492997
$737$	10.3566	+	10.3566i	0.381490	+	0.381490i
$738$		−	24.5903i		−	0.905182i
$739$	44.1780			1.62511			0.812557	−	0.582881i	$-0.198075\pi$
$739$	44.1780			1.62511			0.812557	+	0.582881i	$0.198075\pi$
$740$	−13.5824	−	0.719864i	−0.499299	−	0.0264627i
$741$	−6.68297			−0.245505
$742$		−	6.79866i		−	0.249587i
$743$	−6.64187	−	6.64187i	−0.243666	−	0.243666i	0.574699	−	0.818365i	$-0.305119\pi$
$743$	−6.64187	−	6.64187i	−0.243666	−	0.243666i	−0.818365	+	0.574699i	$0.805119\pi$
$744$	10.4508			0.383145
$745$	−30.8556	−	3.48342i	−1.13046	−	0.127622i
$746$	−0.0403047	+	0.0403047i	−0.00147566	+	0.00147566i
$747$	16.0613	+	16.0613i	0.587652	+	0.587652i
$748$		−	28.0886i		−	1.02702i
$749$			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
$753$			45.8127i			1.66951i
$754$	−2.44762	+	2.44762i	−0.0891370	+	0.0891370i
$755$	−12.3148	−	1.39027i	−0.448181	−	0.0505971i
$756$	−0.646934			−0.0235288
$757$	−30.0218			−1.09116			−0.545580	−	0.838059i	$-0.683691\pi$
$757$	−30.0218			−1.09116			−0.545580	+	0.838059i	$0.683691\pi$
$758$	−2.29640			−0.0834090
$759$	13.7770	+	13.7770i	0.500075	+	0.500075i
$760$	−11.0542	−	13.8678i	−0.400979	−	0.503037i
$761$			13.5486i			0.491135i	0.969379	+	0.245568i	$0.0789743\pi$
$761$			13.5486i			0.491135i	−0.969379	+	0.245568i	$0.921026\pi$
$762$	−26.3929			−0.956115
$763$		−	0.390934i		−	0.0141528i
$764$	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	$-0.446995\pi$
$769$	31.9437	−	31.9437i	1.15192	−	1.15192i	0.986168	−	0.165752i	$-0.0530050\pi$
$770$	−7.16528	+	5.71156i	−0.258219	+	0.205830i
$771$	−3.92706	−	3.92706i	−0.141430	−	0.141430i
$772$			19.5996i			0.705404i
$773$	26.6189	−	26.6189i	0.957414	−	0.957414i	−0.0417156	−	0.999130i	$-0.513282\pi$
$773$	26.6189	−	26.6189i	0.957414	−	0.957414i	0.999130	+	0.0417156i	$0.0132823\pi$
$774$			3.88624i			0.139688i
$775$	11.0148	+	17.5469i	0.395662	+	0.630304i
$776$			3.56694i			0.128046i
$777$	−10.8659	+	0.646934i	−0.389811	+	0.0232086i
$778$	−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
$782$	−6.50438			−0.232596
$783$		−	9.44738i		−	0.337622i
$784$		−	6.49661i		−	0.232022i
$785$	−43.5765	+	34.7356i	−1.55531	+	1.23977i
$786$	−31.8794			−1.13710
$787$	35.6168	+	35.6168i	1.26960	+	1.26960i	0.946293	+	0.323311i	$0.104796\pi$
$787$	35.6168	+	35.6168i	1.26960	+	1.26960i	0.323311	+	0.946293i	$0.395204\pi$
$788$	11.3654	+	11.3654i	0.404874	+	0.404874i
$789$		−	39.4110i		−	1.40307i
$790$	10.9037	+	13.6790i	0.387937	+	0.486676i
$791$	−2.75155	−	2.75155i	−0.0978338	−	0.0978338i
$792$		−	19.4152i		−	0.689891i
$793$	−0.157955	+	0.157955i	−0.00560913	+	0.00560913i
$794$	12.5627	+	12.5627i	0.445835	+	0.445835i
$795$	−6.06259	+	53.7016i	−0.215018	+	1.90460i
$796$	4.39595	−	4.39595i	0.155810	−	0.155810i
$797$			11.4525i			0.405668i	0.979213	+	0.202834i	$0.0650152\pi$
$797$			11.4525i			0.405668i	−0.979213	+	0.202834i	$0.934985\pi$
$798$	−10.0358	−	10.0358i	−0.355262	−	0.355262i
$799$	−23.5174	−	23.5174i	−0.831985	−	0.831985i
$800$	1.11473	−	4.87415i	0.0394118	−	0.172327i
$801$	−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
$808$	0.222565			0.00782980
$809$	13.3588	−	13.3588i	0.469670	−	0.469670i	−0.432137	−	0.901808i	$-0.642240\pi$
$809$	13.3588	−	13.3588i	0.469670	−	0.469670i	0.901808	+	0.432137i	$0.142240\pi$
$810$	−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	$0.565886\pi$
$812$	−7.35114			−0.257974
$813$	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
$820$	16.2541	+	1.83500i	0.567619	+	0.0640809i
$821$	2.82473			0.0985837			0.0492918	−	0.998784i	$-0.484304\pi$
$821$	2.82473			0.0985837			0.0492918	+	0.998784i	$0.484304\pi$
$822$	19.3661			0.675472
$823$	−16.5874	+	16.5874i	−0.578199	+	0.578199i	−0.934407	−	0.356208i	$-0.884070\pi$
$823$	−16.5874	+	16.5874i	−0.578199	+	0.578199i	0.356208	+	0.934407i	$0.384070\pi$
$824$			5.38950i			0.187752i
$825$	61.6906	−	38.7252i	2.14779	−	1.34824i
$826$	−8.76748			−0.305060
$827$	19.6743			0.684142			0.342071	−	0.939674i	$-0.388872\pi$
$827$	19.6743			0.684142			0.342071	+	0.939674i	$0.388872\pi$
$828$	−4.49592			−0.156244
$829$	−12.0827	+	12.0827i	−0.419649	+	0.419649i	−0.885083	−	0.465434i	$-0.845898\pi$
$829$	−12.0827	+	12.0827i	−0.419649	+	0.419649i	0.465434	+	0.885083i	$0.345898\pi$
$830$	−11.8150	+	9.41793i	−0.410105	+	0.326901i
$831$	−9.46224	+	9.46224i	−0.328242	+	0.328242i
$832$		−	0.334084i		−	0.0115823i
$833$			31.5944i			1.09468i
$834$	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
$837$	−3.77814			−0.130592
$838$	3.25958			0.112600
$839$	−39.9396			−1.37887			−0.689435	−	0.724348i	$-0.742141\pi$
$839$	−39.9396			−1.37887			−0.689435	+	0.724348i	$0.742141\pi$
$840$	0.448889	−	3.97619i	0.0154881	−	0.137191i
$841$		−	78.3509i		−	2.70176i
$842$	−8.29816	+	8.29816i	−0.285974	+	0.285974i
$843$	−6.47923			−0.223157
$844$	16.7875			0.577849
$845$	−3.23300	+	28.6374i	−0.111218	+	0.985156i
$846$	−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
$853$	17.5843			0.602077			0.301038	−	0.953612i	$-0.402667\pi$
$853$	17.5843			0.602077			0.301038	+	0.953612i	$0.402667\pi$
$854$	−0.474398			−0.0162336
$855$	37.1590	+	46.6168i	1.27081	+	1.59426i
$856$	2.00040	−	2.00040i	0.0683722	−	0.0683722i
$857$	11.7000			0.399664			0.199832	−	0.979830i	$-0.435960\pi$
$857$	11.7000			0.399664			0.199832	+	0.979830i	$0.435960\pi$
$858$	3.44135	−	3.44135i	0.117486	−	0.117486i
$859$	12.1759	+	12.1759i	0.415435	+	0.415435i	0.883627	−	0.468192i	$-0.155094\pi$
$859$	12.1759	+	12.1759i	0.415435	+	0.415435i	−0.468192	+	0.883627i	$0.655094\pi$
$860$	−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	−0.616278	−	0.787529i	$-0.711360\pi$
$863$	5.03080	−	5.03080i	0.171250	−	0.171250i	0.787529	+	0.616278i	$0.211360\pi$
$864$	0.644753	+	0.644753i	0.0219350	+	0.0219350i
$865$	2.95509	−	2.35555i	0.100476	−	0.0800912i
$866$	1.12455	+	1.12455i	0.0382138	+	0.0382138i
$867$	−11.8615	−	11.8615i	−0.402837	−	0.402837i
$868$			2.93982i			0.0997841i
$869$	−31.9501	+	31.9501i	−1.08383	+	1.08383i
$870$	58.0655	+	6.55526i	1.96860	+	0.222244i
$871$	−0.599053	−	0.599053i	−0.0202981	−	0.0202981i
$872$	−0.389616	+	0.389616i	−0.0131941	+	0.0131941i
$873$		−	11.9903i		−	0.405811i
$874$	−7.50069	−	7.50069i	−0.253715	−	0.253715i
$875$	7.14913	−	3.43707i	0.241685	−	0.116194i
$876$		−	17.6946i		−	0.597845i
$877$	12.8277	+	12.8277i	0.433162	+	0.433162i	0.889703	−	0.456540i	$-0.150912\pi$
$877$	12.8277	+	12.8277i	0.433162	+	0.433162i	−0.456540	+	0.889703i	$0.650912\pi$
$878$	−16.8566	−	16.8566i	−0.568884	−	0.568884i
$879$	−79.5818			−2.68423
$880$	12.8334	+	1.44882i	0.432615	+	0.0488397i
$881$			51.6791i			1.74111i	0.492067	+	0.870557i	$0.336241\pi$
$881$			51.6791i			1.74111i	−0.492067	+	0.870557i	$0.663759\pi$
$882$			21.8385i			0.735339i
$883$	−3.88869			−0.130865			−0.0654323	−	0.997857i	$-0.520843\pi$
$883$	−3.88869			−0.130865			−0.0654323	+	0.997857i	$0.520843\pi$
$884$			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	$-0.838229\pi$
$887$	−11.5256	+	11.5256i	−0.386992	+	0.386992i	0.486621	+	0.873613i	$0.338229\pi$
$888$	11.4740	+	10.1845i	0.385042	+	0.341769i
$889$		−	7.42436i		−	0.249005i
$890$	7.62213	−	6.07572i	0.255494	−	0.203659i
$891$		−	44.9627i		−	1.50631i
$892$	−10.4136	+	10.4136i	−0.348672	+	0.348672i
$893$		−	54.2393i		−	1.81505i
$894$	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
$902$			42.2509i			1.40680i
$903$	−2.06884			−0.0688466
$904$			5.48455i			0.182413i
$905$	−3.66552	+	32.4686i	−0.121846	+	1.07929i
$906$	9.88457	+	9.88457i	0.328393	+	0.328393i
$907$	8.00889			0.265931			0.132965	−	0.991121i	$-0.457550\pi$
$907$	8.00889			0.265931			0.132965	+	0.991121i	$0.457550\pi$
$908$	−6.88908			−0.228622
$909$	−0.748155			−0.0248147
$910$	0.414459	−	0.330372i	0.0137392	−	0.0109517i
$911$	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	$-0.0489309\pi$
$912$			20.0038i			0.662394i
$913$	−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
$917$		−	8.96770i		−	0.296140i
$918$	−3.13557	−	3.13557i	−0.103489	−	0.103489i
$919$	−18.8810	+	18.8810i	−0.622827	+	0.622827i	−0.946253	−	0.323426i	$-0.895165\pi$
$919$	−18.8810	+	18.8810i	−0.622827	+	0.622827i	0.323426	+	0.946253i	$0.395165\pi$
$920$	0.335498	−	2.97179i	0.0110610	−	0.0979770i
$921$	35.3769			1.16571
$922$	−13.6773	−	13.6773i	−0.450438	−	0.450438i
$923$		−	1.11311i		−	0.0366385i
$924$	10.3357			0.340019
$925$	−5.00659	+	29.9989i	−0.164616	+	0.986358i
$926$	13.3262			0.437926
$927$		−	18.1169i		−	0.595037i
$928$	7.32635	+	7.32635i	0.240499	+	0.240499i
$929$	−21.1823			−0.694970			−0.347485	−	0.937686i	$-0.612964\pi$
$929$	−21.1823			−0.694970			−0.347485	+	0.937686i	$0.612964\pi$
$930$	2.62154	−	23.2212i	0.0859637	−	0.761454i
$931$	−36.4338	+	36.4338i	−1.19407	+	1.19407i
$932$	−11.3590	−	11.3590i	−0.372076	−	0.372076i
$933$		−	18.4818i		−	0.605069i
$934$		−	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	0.999464	−	0.0327237i	$-0.0104181\pi$
$937$	29.5924	+	29.5924i	0.966741	+	0.966741i	−0.0327237	+	0.999464i	$0.510418\pi$
$938$		−	1.79919i		−	0.0587455i
$939$	43.2489	−	43.2489i	1.41138	−	1.41138i
$940$	11.9579	−	9.53183i	0.390024	−	0.310894i
$941$	−24.9980			−0.814911			−0.407456	−	0.913225i	$-0.633584\pi$
$941$	−24.9980			−0.814911			−0.407456	+	0.913225i	$0.633584\pi$
$942$	62.8578			2.04802
$943$	9.78389			0.318607
$944$	8.73793	+	8.73793i	0.284395	+	0.284395i
$945$	−0.162281	+	1.43746i	−0.00527899	+	0.0467605i
$946$		−	6.67731i		−	0.217098i
$947$	−26.5685			−0.863361			−0.431680	−	0.902027i	$-0.642079\pi$
$947$	−26.5685			−0.863361			−0.431680	+	0.902027i	$0.642079\pi$
$948$		−	19.7315i		−	0.640849i
$949$	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	$-0.145238\pi$
$953$	14.1106	+	14.1106i	0.457088	+	0.457088i	−0.440610	+	0.897698i	$0.645238\pi$
$954$	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
$957$			150.935i			4.87904i
$958$	−22.7730	+	22.7730i	−0.735761	+	0.735761i
$959$			5.44772i			0.175916i
$960$	−4.41016	+	3.51541i	−0.142337	+	0.113459i
$961$		−	13.8312i		−	0.446169i
$962$	0.120777	+	2.02856i	0.00389401	+	0.0654035i
$963$	−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
$967$	−5.25406			−0.168959			−0.0844796	−	0.996425i	$-0.526923\pi$
$967$	−5.25406			−0.168959			−0.0844796	+	0.996425i	$0.526923\pi$
$968$			22.3592i			0.718650i
$969$		−	97.2829i		−	3.12518i
$970$	7.92557	+	0.894750i	0.254475	+	0.0287287i
$971$	−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
$975$	−3.56835	+	2.23997i	−0.114279	+	0.0717364i
$976$	0.472799	+	0.472799i	0.0151339	+	0.0151339i
$977$			35.6800i			1.14150i	0.821123	+	0.570752i	$0.193348\pi$
$977$			35.6800i			1.14150i	−0.821123	+	0.570752i	$0.806652\pi$
$978$	−24.2427	+	24.2427i	−0.775196	+	0.775196i
$979$	17.8031	+	17.8031i	0.568989	+	0.568989i
$980$	−14.4352	−	1.62965i	−0.461115	−	0.0520572i
$981$	1.30970	−	1.30970i	0.0418156	−	0.0418156i
$982$		−	13.6919i		−	0.436927i
$983$	30.0050	+	30.0050i	0.957009	+	0.957009i	0.999113	−	0.0421038i	$-0.0134060\pi$
$983$	30.0050	+	30.0050i	0.957009	+	0.957009i	−0.0421038	+	0.999113i	$0.513406\pi$
$984$	−13.0465	−	13.0465i	−0.415907	−	0.415907i
$985$	28.1043	−	22.4024i	0.895476	−	0.713798i
$986$	−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
$993$	−60.0618			−1.90600
$994$	1.67155	−	1.67155i	0.0530184	−	0.0530184i
$995$	−8.66488	−	10.8703i	−0.274695	−	0.344611i
$996$	17.0428			0.540021
$997$	−13.9792			−0.442727			−0.221363	−	0.975191i	$-0.571051\pi$
$997$	−13.9792			−0.442727			−0.221363	+	0.975191i	$0.571051\pi$
$998$	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.g.d.327.2	yes	10
5.3	odd	4		370.2.h.d.253.4	yes	10
37.6	odd	4		370.2.h.d.117.4	yes	10
185.43	even	4	inner	370.2.g.d.43.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.d.43.2	✓	10	185.43	even	4	inner
370.2.g.d.327.2	yes	10	1.1	even	1	trivial
370.2.h.d.117.4	yes	10	37.6	odd	4
370.2.h.d.253.4	yes	10	5.3	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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