LMFDB - Embedded newform 403.2.k.d.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.1
Character	$\chi$	$=$	403.157
Dual form			403.2.k.d.326.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95579 - 1.42096i) q^{2} +(-0.875508 + 0.636094i) q^{3} +(1.18794 + 3.65610i) q^{4} +2.12456 q^{5} +2.61618 q^{6} +(-0.805291 - 2.47843i) q^{7} +(1.37774 - 4.24024i) q^{8} +(-0.565152 + 1.73936i) q^{9} +O(q^{10})$	\(q+(-1.95579 - 1.42096i) q^{2} +(-0.875508 + 0.636094i) q^{3} +(1.18794 + 3.65610i) q^{4} +2.12456 q^{5} +2.61618 q^{6} +(-0.805291 - 2.47843i) q^{7} +(1.37774 - 4.24024i) q^{8} +(-0.565152 + 1.73936i) q^{9} +(-4.15519 - 3.01892i) q^{10} +(-0.213773 - 0.657924i) q^{11} +(-3.36567 - 2.44530i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-1.94678 + 5.99158i) q^{14} +(-1.86007 + 1.35142i) q^{15} +(-2.49967 + 1.81611i) q^{16} +(-1.73234 + 5.33160i) q^{17} +(3.57688 - 2.59876i) q^{18} +(5.93584 + 4.31264i) q^{19} +(2.52384 + 7.76759i) q^{20} +(2.28155 + 1.65765i) q^{21} +(-0.516793 + 1.59052i) q^{22} +(1.66993 - 5.13952i) q^{23} +(1.49097 + 4.58874i) q^{24} -0.486259 q^{25} -2.41749 q^{26} +(-1.61484 - 4.96998i) q^{27} +(8.10475 - 5.88845i) q^{28} +(4.44679 + 3.23078i) q^{29} +5.55821 q^{30} +(4.86941 + 2.69978i) q^{31} -1.44745 q^{32} +(0.605661 + 0.440039i) q^{33} +(10.9641 - 7.96589i) q^{34} +(-1.71089 - 5.26557i) q^{35} -7.03064 q^{36} +9.67353 q^{37} +(-5.48115 - 16.8692i) q^{38} +(-0.334414 + 1.02922i) q^{39} +(2.92708 - 9.00863i) q^{40} +(-7.09946 - 5.15806i) q^{41} +(-2.10678 - 6.48401i) q^{42} +(3.84067 + 2.79041i) q^{43} +(2.15149 - 1.56315i) q^{44} +(-1.20070 + 3.69537i) q^{45} +(-10.5691 + 7.67891i) q^{46} +(4.56063 - 3.31349i) q^{47} +(1.03326 - 3.18005i) q^{48} +(0.168991 - 0.122779i) q^{49} +(0.951019 + 0.690956i) q^{50} +(-1.87472 - 5.76979i) q^{51} +(3.11006 + 2.25959i) q^{52} +(-1.04604 + 3.21938i) q^{53} +(-3.90387 + 12.0149i) q^{54} +(-0.454172 - 1.39780i) q^{55} -11.6186 q^{56} -7.94012 q^{57} +(-4.10616 - 12.6375i) q^{58} +(8.16916 - 5.93524i) q^{59} +(-7.15056 - 5.19519i) q^{60} +7.73259 q^{61} +(-5.68724 - 12.1995i) q^{62} +4.76599 q^{63} +(7.83024 + 5.68900i) q^{64} +(1.71880 - 1.24878i) q^{65} +(-0.559267 - 1.72125i) q^{66} +7.23381 q^{67} -21.5508 q^{68} +(1.80718 + 5.56193i) q^{69} +(-4.13605 + 12.7294i) q^{70} +(-3.43986 + 10.5868i) q^{71} +(6.59667 + 4.79276i) q^{72} +(0.712468 + 2.19275i) q^{73} +(-18.9194 - 13.7457i) q^{74} +(0.425723 - 0.309306i) q^{75} +(-8.71603 + 26.8252i) q^{76} +(-1.45847 + 1.05964i) q^{77} +(2.11653 - 1.53775i) q^{78} +(0.964269 - 2.96771i) q^{79} +(-5.31069 + 3.85844i) q^{80} +(0.136418 + 0.0991135i) q^{81} +(6.55563 + 20.1762i) q^{82} +(-1.73269 - 1.25887i) q^{83} +(-3.35017 + 10.3108i) q^{84} +(-3.68046 + 11.3273i) q^{85} +(-3.54646 - 10.9149i) q^{86} -5.94828 q^{87} -3.08428 q^{88} +(0.892386 + 2.74648i) q^{89} +(7.59930 - 5.52121i) q^{90} +(-2.10828 - 1.53175i) q^{91} +20.7744 q^{92} +(-5.98052 + 0.733719i) q^{93} -13.6280 q^{94} +(12.6110 + 9.16245i) q^{95} +(1.26725 - 0.920714i) q^{96} +(0.610396 + 1.87861i) q^{97} -0.504977 q^{98} +1.26518 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.95579	−	1.42096i	−1.38295	−	1.00477i	−0.996597	−	0.0824229i	$-0.973734\pi$
$2$	−1.95579	−	1.42096i	−1.38295	−	1.00477i	−0.386354	−	0.922350i	$-0.626266\pi$
$3$	−0.875508	+	0.636094i	−0.505475	+	0.367249i	−0.811104	−	0.584902i	$-0.801133\pi$
$3$	−0.875508	+	0.636094i	−0.505475	+	0.367249i	0.305629	+	0.952151i	$0.401133\pi$
$4$	1.18794	+	3.65610i	0.593969	+	1.82805i
$5$	2.12456			0.950131			0.475065	−	0.879951i	$-0.342424\pi$
$5$	2.12456			0.950131			0.475065	+	0.879951i	$0.342424\pi$
$6$	2.61618			1.06805
$7$	−0.805291	−	2.47843i	−0.304371	−	0.936759i	−0.979911	−	0.199435i	$-0.936089\pi$
$7$	−0.805291	−	2.47843i	−0.304371	−	0.936759i	0.675540	−	0.737324i	$-0.263911\pi$
$8$	1.37774	−	4.24024i	0.487104	−	1.49915i
$9$	−0.565152	+	1.73936i	−0.188384	+	0.579786i
$10$	−4.15519	−	3.01892i	−1.31398	−	0.954666i
$11$	−0.213773	−	0.657924i	−0.0644549	−	0.198372i	0.913643	−	0.406518i	$-0.133257\pi$
$11$	−0.213773	−	0.657924i	−0.0644549	−	0.198372i	−0.978098	+	0.208146i	$0.933257\pi$
$12$	−3.36567	−	2.44530i	−0.971586	−	0.705898i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−1.94678	+	5.99158i	−0.520299	+	1.60132i
$15$	−1.86007	+	1.35142i	−0.480267	+	0.348934i
$16$	−2.49967	+	1.81611i	−0.624917	+	0.454029i
$17$	−1.73234	+	5.33160i	−0.420155	+	1.29310i	0.487404	+	0.873177i	$0.337944\pi$
$17$	−1.73234	+	5.33160i	−0.420155	+	1.29310i	−0.907558	+	0.419926i	$0.862056\pi$
$18$	3.57688	−	2.59876i	0.843080	−	0.612533i
$19$	5.93584	+	4.31264i	1.36178	+	0.989388i	0.998330	+	0.0577728i	$0.0183999\pi$
$19$	5.93584	+	4.31264i	1.36178	+	0.989388i	0.363446	+	0.931615i	$0.381600\pi$
$20$	2.52384	+	7.76759i	0.564348	+	1.73689i
$21$	2.28155	+	1.65765i	0.497876	+	0.361728i
$22$	−0.516793	+	1.59052i	−0.110181	+	0.339101i
$23$	1.66993	−	5.13952i	0.348205	−	1.07166i	−0.611641	−	0.791136i	$-0.709490\pi$
$23$	1.66993	−	5.13952i	0.348205	−	1.07166i	0.959846	−	0.280529i	$-0.0905098\pi$
$24$	1.49097	+	4.58874i	0.304343	+	0.936672i
$25$	−0.486259			−0.0972517
$26$	−2.41749			−0.474108
$27$	−1.61484	−	4.96998i	−0.310777	−	0.956472i
$28$	8.10475	−	5.88845i	1.53165	−	1.11281i
$29$	4.44679	+	3.23078i	0.825748	+	0.599941i	0.918353	−	0.395762i	$-0.129519\pi$
$29$	4.44679	+	3.23078i	0.825748	+	0.599941i	−0.0926050	+	0.995703i	$0.529519\pi$
$30$	5.55821			1.01479
$31$	4.86941	+	2.69978i	0.874572	+	0.484896i
$31$	4.86941	+	2.69978i	0.874572	+	0.484896i
$32$	−1.44745			−0.255875
$33$	0.605661	+	0.440039i	0.105432	+	0.0766009i
$34$	10.9641	−	7.96589i	1.88033	−	1.36614i
$35$	−1.71089	−	5.26557i	−0.289193	−	0.890043i
$36$	−7.03064			−1.17177
$37$	9.67353			1.59032			0.795159	−	0.606401i	$-0.207387\pi$
$37$	9.67353			1.59032			0.795159	+	0.606401i	$0.207387\pi$
$38$	−5.48115	−	16.8692i	−0.889160	−	2.73655i
$39$	−0.334414	+	1.02922i	−0.0535491	+	0.164807i
$40$	2.92708	−	9.00863i	0.462812	−	1.42439i
$41$	−7.09946	−	5.15806i	−1.10875	−	0.805553i	−0.126283	−	0.991994i	$-0.540305\pi$
$41$	−7.09946	−	5.15806i	−1.10875	−	0.805553i	−0.982466	+	0.186441i	$0.940305\pi$
$42$	−2.10678	−	6.48401i	−0.325084	−	1.00050i
$43$	3.84067	+	2.79041i	0.585696	+	0.425533i	0.840773	−	0.541388i	$-0.182101\pi$
$43$	3.84067	+	2.79041i	0.585696	+	0.425533i	−0.255077	+	0.966921i	$0.582101\pi$
$44$	2.15149	−	1.56315i	0.324349	−	0.235653i
$45$	−1.20070	+	3.69537i	−0.178989	+	0.550873i
$46$	−10.5691	+	7.67891i	−1.55833	+	1.13219i
$47$	4.56063	−	3.31349i	0.665236	−	0.483322i	−0.203191	−	0.979139i	$-0.565131\pi$
$47$	4.56063	−	3.31349i	0.665236	−	0.483322i	0.868427	+	0.495817i	$0.165131\pi$
$48$	1.03326	−	3.18005i	0.149138	−	0.459000i
$49$	0.168991	−	0.122779i	0.0241416	−	0.0175399i
$50$	0.951019	+	0.690956i	0.134494	+	0.0977159i
$51$	−1.87472	−	5.76979i	−0.262513	−	0.807932i
$52$	3.11006	+	2.25959i	0.431288	+	0.313349i
$53$	−1.04604	+	3.21938i	−0.143684	+	0.442215i	−0.996839	−	0.0794422i	$-0.974686\pi$
$53$	−1.04604	+	3.21938i	−0.143684	+	0.442215i	0.853155	+	0.521657i	$0.174686\pi$
$54$	−3.90387	+	12.0149i	−0.531249	+	1.63502i
$55$	−0.454172	−	1.39780i	−0.0612405	−	0.188479i
$56$	−11.6186			−1.55260
$57$	−7.94012			−1.05170
$58$	−4.10616	−	12.6375i	−0.539165	−	1.65938i
$59$	8.16916	−	5.93524i	1.06353	−	0.772703i	0.0887949	−	0.996050i	$-0.471698\pi$
$59$	8.16916	−	5.93524i	1.06353	−	0.772703i	0.974739	+	0.223347i	$0.0716984\pi$
$60$	−7.15056	−	5.19519i	−0.923133	−	0.670696i
$61$	7.73259			0.990057			0.495028	−	0.868877i	$-0.335158\pi$
$61$	7.73259			0.990057			0.495028	+	0.868877i	$0.335158\pi$
$62$	−5.68724	−	12.1995i	−0.722281	−	1.54933i
$63$	4.76599			0.600459
$64$	7.83024	+	5.68900i	0.978780	+	0.711125i
$65$	1.71880	−	1.24878i	0.213191	−	0.154892i
$66$	−0.559267	−	1.72125i	−0.0688410	−	0.211871i
$67$	7.23381			0.883751			0.441875	−	0.897076i	$-0.354313\pi$
$67$	7.23381			0.883751			0.441875	+	0.897076i	$0.354313\pi$
$68$	−21.5508			−2.61341
$69$	1.80718	+	5.56193i	0.217559	+	0.669577i
$70$	−4.13605	+	12.7294i	−0.494352	+	1.52146i
$71$	−3.43986	+	10.5868i	−0.408236	+	1.25642i	0.509927	+	0.860218i	$0.329672\pi$
$71$	−3.43986	+	10.5868i	−0.408236	+	1.25642i	−0.918163	+	0.396203i	$0.870328\pi$
$72$	6.59667	+	4.79276i	0.777425	+	0.564832i
$73$	0.712468	+	2.19275i	0.0833881	+	0.256642i	0.984054	−	0.177870i	$-0.0569207\pi$
$73$	0.712468	+	2.19275i	0.0833881	+	0.256642i	−0.900666	+	0.434512i	$0.856921\pi$
$74$	−18.9194	−	13.7457i	−2.19933	−	1.59791i
$75$	0.425723	−	0.309306i	0.0491583	−	0.0357156i
$76$	−8.71603	+	26.8252i	−0.999797	+	3.07706i
$77$	−1.45847	+	1.05964i	−0.166208	+	0.120757i
$78$	2.11653	−	1.53775i	0.239650	−	0.174116i
$79$	0.964269	−	2.96771i	0.108489	−	0.333894i	−0.882045	−	0.471166i	$-0.843833\pi$
$79$	0.964269	−	2.96771i	0.108489	−	0.333894i	0.990533	+	0.137272i	$0.0438334\pi$
$80$	−5.31069	+	3.85844i	−0.593753	+	0.431387i
$81$	0.136418	+	0.0991135i	0.0151576	+	0.0110126i
$82$	6.55563	+	20.1762i	0.723948	+	2.22808i
$83$	−1.73269	−	1.25887i	−0.190187	−	0.138179i	0.488617	−	0.872498i	$-0.337502\pi$
$83$	−1.73269	−	1.25887i	−0.190187	−	0.138179i	−0.678804	+	0.734319i	$0.737502\pi$
$84$	−3.35017	+	10.3108i	−0.365534	+	1.12500i
$85$	−3.68046	+	11.3273i	−0.399202	+	1.22862i
$86$	−3.54646	−	10.9149i	−0.382425	−	1.17698i
$87$	−5.94828			−0.637723
$88$	−3.08428			−0.328785
$89$	0.892386	+	2.74648i	0.0945927	+	0.291126i	0.987147	−	0.159813i	$-0.0510891\pi$
$89$	0.892386	+	2.74648i	0.0945927	+	0.291126i	−0.892555	+	0.450939i	$0.851089\pi$
$90$	7.59930	−	5.52121i	0.801036	−	0.581987i
$91$	−2.10828	−	1.53175i	−0.221008	−	0.160572i
$92$	20.7744			2.16588
$93$	−5.98052	+	0.733719i	−0.620152	+	0.0760831i
$94$	−13.6280			−1.40562
$95$	12.6110	+	9.16245i	1.29386	+	0.940048i
$96$	1.26725	−	0.920714i	0.129339	−	0.0939700i
$97$	0.610396	+	1.87861i	0.0619764	+	0.190744i	0.977251	−	0.212088i	$-0.0680262\pi$
$97$	0.610396	+	1.87861i	0.0619764	+	0.190744i	−0.915274	+	0.402831i	$0.868026\pi$
$98$	−0.504977			−0.0510103
$99$	1.26518			0.127155
$100$	−0.577645	−	1.77781i	−0.0577645	−	0.177781i
$101$	−5.46654	+	16.8243i	−0.543941	+	1.67408i	0.179554	+	0.983748i	$0.442535\pi$
$101$	−5.46654	+	16.8243i	−0.543941	+	1.67408i	−0.723495	+	0.690330i	$0.757465\pi$
$102$	−4.53211	+	13.9484i	−0.448746	+	1.38110i
$103$	−3.99702	−	2.90400i	−0.393838	−	0.286140i	0.373188	−	0.927756i	$-0.378264\pi$
$103$	−3.99702	−	2.90400i	−0.393838	−	0.286140i	−0.767026	+	0.641616i	$0.778264\pi$
$104$	−1.37774	−	4.24024i	−0.135098	−	0.415790i
$105$	4.84729	+	3.52176i	0.473047	+	0.343689i
$106$	6.62045	−	4.81004i	0.643035	−	0.467192i
$107$	1.93960	−	5.96948i	0.187508	−	0.577091i	−0.812474	−	0.582997i	$-0.801880\pi$
$107$	1.93960	−	5.96948i	0.187508	−	0.577091i	0.999983	+	0.00590583i	$0.00187990\pi$
$108$	16.2524	−	11.8081i	1.56389	−	1.13623i
$109$	−11.7028	+	8.50261i	−1.12093	+	0.814403i	−0.984350	−	0.176226i	$-0.943611\pi$
$109$	−11.7028	+	8.50261i	−1.12093	+	0.814403i	−0.136580	+	0.990629i	$0.543611\pi$
$110$	−1.09796	+	3.37916i	−0.104686	+	0.322190i
$111$	−8.46925	+	6.15327i	−0.803866	+	0.584043i
$112$	6.51408	+	4.73275i	0.615522	+	0.447203i
$113$	−0.670905	−	2.06483i	−0.0631134	−	0.194243i	0.914528	−	0.404523i	$-0.132562\pi$
$113$	−0.670905	−	2.06483i	−0.0631134	−	0.194243i	−0.977641	+	0.210280i	$0.932562\pi$
$114$	15.5292	+	11.2826i	1.45444	+	1.05672i
$115$	3.54787	−	10.9192i	0.330840	−	1.01822i
$116$	−6.52955	+	20.0959i	−0.606253	+	1.86586i
$117$	0.565152	+	1.73936i	0.0522483	+	0.160804i
$118$	−24.4109			−2.24721
$119$	14.6090			1.33921
$120$	3.16765	+	9.74903i	0.289166	+	0.889961i
$121$	8.51202	−	6.18435i	0.773820	−	0.562213i
$122$	−15.1233	−	10.9877i	−1.36920	−	0.994783i
$123$	9.49664			0.856283
$124$	−4.08612	+	21.0102i	−0.366944	+	1.88677i
$125$	−11.6559			−1.04253
$126$	−9.32128	−	6.77231i	−0.830406	−	0.603325i
$127$	−9.40717	+	6.83471i	−0.834751	+	0.606482i	−0.920900	−	0.389800i	$-0.872544\pi$
$127$	−9.40717	+	6.83471i	−0.834751	+	0.606482i	0.0861482	+	0.996282i	$0.472544\pi$
$128$	−6.33586	−	19.4998i	−0.560016	−	1.72355i
$129$	−5.13749			−0.452331
$130$	−5.13609			−0.450465
$131$	−4.06776	−	12.5193i	−0.355402	−	1.09382i	−0.955776	−	0.294096i	$-0.904981\pi$
$131$	−4.06776	−	12.5193i	−0.355402	−	1.09382i	0.600374	−	0.799720i	$-0.295019\pi$
$132$	−0.889337	+	2.73710i	−0.0774068	+	0.238234i
$133$	5.90851	−	18.1845i	0.512332	−	1.57680i
$134$	−14.1478	−	10.2790i	−1.22218	−	0.887969i
$135$	−3.43083	−	10.5590i	−0.295279	−	0.908774i
$136$	20.2206	+	14.6911i	1.73390	+	1.25975i
$137$	−2.82567	+	2.05297i	−0.241413	+	0.175397i	−0.701913	−	0.712263i	$-0.747670\pi$
$137$	−2.82567	+	2.05297i	−0.241413	+	0.175397i	0.460500	+	0.887660i	$0.347670\pi$
$138$	4.36884	−	13.4459i	0.371900	−	1.14459i
$139$	−8.02741	+	5.83226i	−0.680876	+	0.494685i	−0.873648	−	0.486558i	$-0.838252\pi$
$139$	−8.02741	+	5.83226i	−0.680876	+	0.494685i	0.192772	+	0.981244i	$0.438252\pi$
$140$	17.2190	−	12.5103i	1.45527	−	1.05732i
$141$	−1.88518	+	5.80197i	−0.158760	+	0.488614i
$142$	21.7711	−	15.8176i	1.82699	−	1.32739i
$143$	−0.559664	−	0.406620i	−0.0468014	−	0.0340032i
$144$	−1.74618	−	5.37420i	−0.145515	−	0.447850i
$145$	9.44746	+	6.86398i	0.784569	+	0.570023i
$146$	1.72238	−	5.30095i	0.142545	−	0.438710i
$147$	−0.0698541	+	0.214989i	−0.00576147	+	0.0177320i
$148$	11.4916	+	35.3674i	0.944600	+	2.90718i
$149$	−8.12388			−0.665534			−0.332767	−	0.943009i	$-0.607982\pi$
$149$	−8.12388			−0.665534			−0.332767	+	0.943009i	$0.607982\pi$
$150$	−1.27214			−0.103870
$151$	−4.88284	−	15.0278i	−0.397360	−	1.22295i	−0.927109	−	0.374793i	$-0.877714\pi$
$151$	−4.88284	−	15.0278i	−0.397360	−	1.22295i	0.529749	−	0.848155i	$-0.322286\pi$
$152$	26.4647	−	19.2277i	2.14657	−	1.55957i
$153$	−8.29453	−	6.02633i	−0.670573	−	0.487200i
$154$	4.35817			0.351192
$155$	10.3453	+	5.73585i	0.830958	+	0.460714i
$156$	−4.16020			−0.333083
$157$	−12.8561	−	9.34048i	−1.02603	−	0.745452i	−0.0585166	−	0.998286i	$-0.518637\pi$
$157$	−12.8561	−	9.34048i	−1.02603	−	0.745452i	−0.967509	+	0.252835i	$0.918637\pi$
$158$	−6.10292	+	4.43403i	−0.485522	+	0.352753i
$159$	−1.13201	−	3.48397i	−0.0897742	−	0.276297i
$160$	−3.07519			−0.243115
$161$	−14.0827			−1.10987
$162$	−0.125968	−	0.387690i	−0.00989700	−	0.0304598i
$163$	−3.54823	+	10.9203i	−0.277919	+	0.855346i	0.710513	+	0.703684i	$0.248463\pi$
$163$	−3.54823	+	10.9203i	−0.277919	+	0.855346i	−0.988432	+	0.151663i	$0.951537\pi$
$164$	10.4247	−	32.0838i	0.814029	−	2.50532i
$165$	1.28676	+	0.934887i	0.100174	+	0.0727809i
$166$	1.59996	+	4.92418i	0.124181	+	0.382190i
$167$	4.89622	+	3.55731i	0.378880	+	0.275273i	0.760884	−	0.648888i	$-0.224766\pi$
$167$	4.89622	+	3.55731i	0.378880	+	0.275273i	−0.382003	+	0.924161i	$0.624766\pi$
$168$	10.1722	−	7.39054i	0.784802	−	0.570192i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	23.2939	−	16.9240i	1.78656	−	1.29801i
$171$	−10.8559	+	7.88726i	−0.830170	+	0.603154i
$172$	−5.63953	+	17.3567i	−0.430010	+	1.32343i
$173$	7.04146	−	5.11592i	0.535353	−	0.388956i	−0.287004	−	0.957930i	$-0.592659\pi$
$173$	7.04146	−	5.11592i	0.535353	−	0.388956i	0.822356	+	0.568973i	$0.192659\pi$
$174$	11.6336	+	8.45229i	0.881940	+	0.640767i
$175$	0.391580	+	1.20516i	0.0296006	+	0.0911014i
$176$	1.72923	+	1.25636i	0.130345	+	0.0947015i
$177$	−3.37679	+	10.3927i	−0.253815	+	0.781163i
$178$	2.15733	−	6.63958i	0.161699	−	0.497658i
$179$	−1.34874	−	4.15101i	−0.100810	−	0.310261i	0.887914	−	0.460009i	$-0.152154\pi$
$179$	−1.34874	−	4.15101i	−0.100810	−	0.310261i	−0.988724	+	0.149748i	$0.952154\pi$
$180$	−14.9370			−1.11334
$181$	9.83454			0.730996			0.365498	−	0.930812i	$-0.380899\pi$
$181$	9.83454			0.730996			0.365498	+	0.930812i	$0.380899\pi$
$182$	1.94678	+	5.99158i	0.144305	+	0.444125i
$183$	−6.76994	+	4.91865i	−0.500449	+	0.363597i
$184$	−19.4921	−	14.1618i	−1.43698	−	1.04402i
$185$	20.5520			1.51101
$186$	12.7392	+	7.06311i	0.934086	+	0.517892i
$187$	3.87812			0.283596
$188$	17.5322	+	12.7379i	1.27867	+	0.929006i
$189$	−11.0173	+	8.00456i	−0.801393	+	0.582246i
$190$	−11.6450	−	35.8397i	−0.844818	−	2.60008i
$191$	−8.89892			−0.643903			−0.321952	−	0.946756i	$-0.604339\pi$
$191$	−8.89892			−0.643903			−0.321952	+	0.946756i	$0.604339\pi$
$192$	−10.4742			−0.755909
$193$	−3.14132	−	9.66799i	−0.226117	−	0.695918i	−0.998176	−	0.0603666i	$-0.980773\pi$
$193$	−3.14132	−	9.66799i	−0.226117	−	0.695918i	0.772059	−	0.635551i	$-0.219227\pi$
$194$	1.47563	−	4.54151i	0.105944	−	0.326061i
$195$	−0.710482	+	2.18664i	−0.0508787	+	0.156588i
$196$	0.649645	+	0.471995i	0.0464032	+	0.0337139i
$197$	1.35652	+	4.17493i	0.0966477	+	0.297451i	0.987680	−	0.156490i	$-0.0500178\pi$
$197$	1.35652	+	4.17493i	0.0966477	+	0.297451i	−0.891032	+	0.453941i	$0.850018\pi$
$198$	−2.47443	−	1.79778i	−0.175850	−	0.127762i
$199$	−11.3487	+	8.24529i	−0.804486	+	0.584493i	−0.912227	−	0.409686i	$-0.865638\pi$
$199$	−11.3487	+	8.24529i	−0.804486	+	0.584493i	0.107741	+	0.994179i	$0.465638\pi$
$200$	−0.669937	+	2.06185i	−0.0473717	+	0.145795i
$201$	−6.33326	+	4.60138i	−0.446714	+	0.324557i
$202$	34.5981	−	25.1370i	2.43431	−	1.76863i
$203$	4.42631	−	13.6228i	0.310666	−	0.956132i
$204$	18.8679	−	13.7083i	1.32102	−	0.959774i
$205$	−15.0832	−	10.9586i	−1.05346	−	0.765381i
$206$	3.69084	+	11.3592i	0.257153	+	0.791436i
$207$	7.99571	+	5.80922i	0.555740	+	0.403769i
$208$	−0.954788	+	2.93854i	−0.0662026	+	0.203751i
$209$	1.56847	−	4.82726i	0.108493	−	0.333909i
$210$	−4.47598	−	13.7756i	−0.308872	−	0.950610i
$211$	−3.22575			−0.222070			−0.111035	−	0.993817i	$-0.535417\pi$
$211$	−3.22575			−0.222070			−0.111035	+	0.993817i	$0.535417\pi$
$212$	−13.0130			−0.893735
$213$	−3.72257	−	11.4569i	−0.255066	−	0.785013i
$214$	−12.2759	+	8.91894i	−0.839161	+	0.609686i
$215$	8.15971	+	5.92838i	0.556488	+	0.404312i
$216$	−23.2987			−1.58528
$217$	2.76994	−	14.2426i	0.188036	−	0.966852i
$218$	34.9702			2.36848
$219$	−2.01857	−	1.46657i	−0.136402	−	0.0991019i
$220$	4.57096	−	3.32100i	0.308174	−	0.223901i
$221$	1.73234	+	5.33160i	0.116530	+	0.358642i
$222$	25.3077			1.69854
$223$	28.4111			1.90255			0.951273	−	0.308348i	$-0.0997763\pi$
$223$	28.4111			1.90255			0.951273	+	0.308348i	$0.0997763\pi$
$224$	1.16562	+	3.58740i	0.0778812	+	0.239694i
$225$	0.274810	−	0.845778i	0.0183207	−	0.0563852i
$226$	−1.62190	+	4.99171i	−0.107888	+	0.332044i
$227$	−2.58734	−	1.87981i	−0.171728	−	0.124768i	0.498601	−	0.866831i	$-0.333847\pi$
$227$	−2.58734	−	1.87981i	−0.171728	−	0.124768i	−0.670329	+	0.742064i	$0.733847\pi$
$228$	−9.43238	−	29.0299i	−0.624675	−	1.92255i
$229$	21.7007	+	15.7665i	1.43402	+	1.04188i	0.989250	+	0.146236i	$0.0467160\pi$
$229$	21.7007	+	15.7665i	1.43402	+	1.04188i	0.444774	+	0.895643i	$0.353284\pi$
$230$	−22.4547	+	16.3143i	−1.48062	+	1.07573i
$231$	0.602872	−	1.85545i	0.0396661	−	0.122080i
$232$	19.8258	−	14.4043i	1.30163	−	0.945688i
$233$	−22.9145	+	16.6483i	−1.50118	+	1.09067i	−0.531267	+	0.847205i	$0.678284\pi$
$233$	−22.9145	+	16.6483i	−1.50118	+	1.09067i	−0.969910	+	0.243464i	$0.921716\pi$
$234$	1.36625	−	4.20488i	0.0893145	−	0.274882i
$235$	9.68931	−	7.03970i	0.632061	−	0.459219i
$236$	31.4043	+	22.8166i	2.04425	+	1.48523i
$237$	1.04352	+	3.21162i	0.0677839	+	0.208617i
$238$	−28.5722	−	20.7589i	−1.85206	−	1.34560i
$239$	−7.09817	+	21.8459i	−0.459142	+	1.41310i	0.407060	+	0.913402i	$0.366554\pi$
$239$	−7.09817	+	21.8459i	−0.459142	+	1.41310i	−0.866202	+	0.499694i	$0.833446\pi$
$240$	2.19522	−	6.75619i	0.141701	−	0.436110i
$241$	−6.06804	−	18.6755i	−0.390877	−	1.20300i	−0.932126	−	0.362134i	$-0.882048\pi$
$241$	−6.06804	−	18.6755i	−0.390877	−	1.20300i	0.541249	−	0.840862i	$-0.317952\pi$
$242$	−25.4355			−1.63505
$243$	15.4947			0.993989
$244$	9.18584	+	28.2711i	0.588063	+	1.80987i
$245$	0.359032	−	0.260852i	0.0229377	−	0.0166652i
$246$	−18.5734	−	13.4944i	−1.18420	−	0.860371i
$247$	7.33711			0.466849
$248$	18.1565	−	16.9279i	1.15294	−	1.07492i
$249$	2.31774			0.146881
$250$	22.7964	+	16.5626i	1.44177	+	1.04751i
$251$	8.60344	−	6.25077i	0.543045	−	0.394545i	−0.282170	−	0.959364i	$-0.591054\pi$
$251$	8.60344	−	6.25077i	0.543045	−	0.394545i	0.825214	+	0.564820i	$0.191054\pi$
$252$	5.66171	+	17.4249i	0.356654	+	1.09767i
$253$	−3.73840			−0.235031
$254$	28.1103			1.76380
$255$	−3.98295	−	12.2582i	−0.249422	−	0.767641i
$256$	−9.33510	+	28.7305i	−0.583443	+	1.79565i
$257$	0.00919158	−	0.0282888i	0.000573355	−	0.00176460i	−0.950769	−	0.309899i	$-0.899705\pi$
$257$	0.00919158	−	0.0282888i	0.000573355	−	0.00176460i	0.951343	+	0.308135i	$0.0997047\pi$
$258$	10.0479	+	7.30019i	0.625552	+	0.454490i
$259$	−7.79001	−	23.9752i	−0.484048	−	1.48975i
$260$	6.60751	+	4.80063i	0.409780	+	0.297723i
$261$	−8.13260	+	5.90868i	−0.503395	+	0.365738i
$262$	−9.83377	+	30.2652i	−0.607533	+	1.86979i
$263$	8.33137	−	6.05309i	0.513734	−	0.373250i	−0.300504	−	0.953781i	$-0.597155\pi$
$263$	8.33137	−	6.05309i	0.513734	−	0.373250i	0.814238	+	0.580531i	$0.197155\pi$
$264$	2.70031	−	1.96189i	0.166193	−	0.120746i
$265$	−2.22237	+	6.83975i	−0.136519	+	0.420162i
$266$	−37.3953	+	27.1693i	−2.29285	+	1.66586i
$267$	−2.52831	−	1.83692i	−0.154730	−	0.112418i
$268$	8.59333	+	26.4475i	0.524921	+	1.61554i
$269$	7.48502	+	5.43819i	0.456370	+	0.331572i	0.792106	−	0.610384i	$-0.208985\pi$
$269$	7.48502	+	5.43819i	0.456370	+	0.331572i	−0.335736	+	0.941956i	$0.608985\pi$
$270$	−8.29398	+	25.5263i	−0.504756	+	1.55348i
$271$	6.29334	−	19.3689i	0.382293	−	1.17658i	−0.556132	−	0.831094i	$-0.687715\pi$
$271$	6.29334	−	19.3689i	0.382293	−	1.17658i	0.938425	−	0.345483i	$-0.112285\pi$
$272$	−5.35252	−	16.4734i	−0.324544	−	0.998844i
$273$	2.82016			0.170684
$274$	8.44360			0.510096
$275$	0.103949	+	0.319921i	0.00626835	+	0.0192920i
$276$	−18.1881	+	13.2145i	−1.09480	+	0.795417i
$277$	−12.8258	−	9.31848i	−0.770627	−	0.559893i	0.131524	−	0.991313i	$-0.458013\pi$
$277$	−12.8258	−	9.31848i	−0.770627	−	0.559893i	−0.902151	+	0.431420i	$0.858013\pi$
$278$	23.9874			1.43867
$279$	−7.44785	+	6.94387i	−0.445891	+	0.415718i
$280$	−24.6844			−1.47518
$281$	1.93233	+	1.40392i	0.115273	+	0.0837509i	0.643928	−	0.765086i	$-0.277303\pi$
$281$	1.93233	+	1.40392i	0.115273	+	0.0837509i	−0.528655	+	0.848837i	$0.677303\pi$
$282$	11.9314	−	8.66867i	0.710505	−	0.516212i
$283$	−1.24174	−	3.82169i	−0.0738139	−	0.227176i	0.907342	−	0.420393i	$-0.138108\pi$
$283$	−1.24174	−	3.82169i	−0.0738139	−	0.227176i	−0.981156	+	0.193217i	$0.938108\pi$
$284$	−42.7927			−2.53928
$285$	−16.8692			−0.999248
$286$	0.516793	+	1.59052i	0.0305586	+	0.0940497i
$287$	−7.06676	+	21.7493i	−0.417138	+	1.28382i
$288$	0.818029	−	2.51763i	0.0482028	−	0.148353i
$289$	−11.6717	−	8.47995i	−0.686568	−	0.498821i
$290$	−8.72377	−	26.8490i	−0.512277	−	1.57663i
$291$	−1.72938	−	1.25647i	−0.101378	−	0.0736553i
$292$	−7.17055	+	5.20971i	−0.419625	+	0.304875i
$293$	8.40927	−	25.8811i	0.491275	−	1.51199i	−0.331408	−	0.943488i	$-0.607524\pi$
$293$	8.40927	−	25.8811i	0.491275	−	1.51199i	0.822683	−	0.568501i	$-0.192476\pi$
$294$	0.442111	−	0.321213i	0.0257844	−	0.0187335i
$295$	17.3558	−	12.6098i	1.01050	−	0.734168i
$296$	13.3276	−	41.0181i	0.774650	−	2.38413i
$297$	−2.92466	+	2.12489i	−0.169706	+	0.123299i
$298$	15.8886	+	11.5437i	0.920402	+	0.668711i
$299$	−1.66993	−	5.13952i	−0.0965747	−	0.297226i
$300$	1.63659	+	1.18905i	0.0944884	+	0.0686498i
$301$	3.82298	−	11.7659i	0.220353	−	0.678176i
$302$	−11.8042	+	36.3296i	−0.679256	+	2.09053i
$303$	−5.91582	−	18.2070i	−0.339855	−	1.04597i
$304$	−22.6699			−1.30021
$305$	16.4283			0.940683
$306$	7.65915	+	23.5725i	0.437845	+	1.34755i
$307$	−7.40268	+	5.37836i	−0.422493	+	0.306959i	−0.778640	−	0.627471i	$-0.784090\pi$
$307$	−7.40268	+	5.37836i	−0.422493	+	0.306959i	0.356147	+	0.934430i	$0.384090\pi$
$308$	−5.60673	−	4.07353i	−0.319473	−	0.232111i
$309$	5.34664			0.304160
$310$	−12.0829	−	25.9185i	−0.686261	−	1.47207i
$311$	−19.2384			−1.09091			−0.545454	−	0.838141i	$-0.683643\pi$
$311$	−19.2384			−1.09091			−0.545454	+	0.838141i	$0.683643\pi$
$312$	3.90341	+	2.83599i	0.220987	+	0.160557i
$313$	−16.0565	+	11.6657i	−0.907566	+	0.659385i	−0.940398	−	0.340076i	$-0.889547\pi$
$313$	−16.0565	+	11.6657i	−0.907566	+	0.659385i	0.0328324	+	0.999461i	$0.489547\pi$
$314$	11.8713	+	36.5360i	0.669935	+	2.06185i
$315$	10.1256			0.570514
$316$	11.9957			0.674814
$317$	−0.526131	−	1.61926i	−0.0295504	−	0.0909469i	0.935194	−	0.354137i	$-0.115225\pi$
$317$	−0.526131	−	1.61926i	−0.0295504	−	0.0909469i	−0.964744	+	0.263190i	$0.915225\pi$
$318$	−2.73662	+	8.42245i	−0.153462	+	0.472308i
$319$	1.17501	−	3.61630i	0.0657878	−	0.202474i
$320$	16.6358	+	12.0866i	0.929969	+	0.675662i
$321$	2.09901	+	6.46009i	0.117155	+	0.360567i
$322$	27.5429	+	20.0111i	1.53490	+	1.11517i
$323$	−33.2762	+	24.1766i	−1.85154	+	1.34522i
$324$	−0.200313	+	0.616499i	−0.0111285	+	0.0342499i
$325$	−0.393391	+	0.285816i	−0.0218214	+	0.0158542i
$326$	22.4570	−	16.3160i	1.24378	−	0.903657i
$327$	4.83747	−	14.8882i	0.267513	−	0.823320i
$328$	−31.6526	+	22.9970i	−1.74772	+	1.26980i
$329$	−11.8849	−	8.63488i	−0.655235	−	0.476056i
$330$	−1.18819	−	3.65688i	−0.0654079	−	0.201305i
$331$	−24.4179	−	17.7406i	−1.34213	−	0.975114i	−0.999363	−	0.0356933i	$-0.988636\pi$
$331$	−24.4179	−	17.7406i	−1.34213	−	0.975114i	−0.342766	−	0.939421i	$-0.611364\pi$
$332$	2.54423	−	7.83034i	0.139633	−	0.429746i
$333$	−5.46702	+	16.8257i	−0.299591	+	0.922045i
$334$	−4.52116	−	13.9147i	−0.247387	−	0.761378i
$335$	15.3686			0.839679
$336$	−8.71360			−0.475366
$337$	8.05979	+	24.8055i	0.439045	+	1.35124i	0.888884	+	0.458132i	$0.151481\pi$
$337$	8.05979	+	24.8055i	0.439045	+	1.35124i	−0.449839	+	0.893109i	$0.648519\pi$
$338$	−1.95579	+	1.42096i	−0.106381	+	0.0772903i
$339$	1.90081	+	1.38102i	0.103238	+	0.0750067i
$340$	−45.7858			−2.48309
$341$	0.735308	−	3.78084i	0.0398191	−	0.204744i
$342$	32.4393			1.75412
$343$	−15.1983	−	11.0422i	−0.820633	−	0.596225i
$344$	17.1234	−	12.4409i	0.923233	−	0.670768i
$345$	3.83946	+	11.8166i	0.206709	+	0.636186i
$346$	−21.0412			−1.13118
$347$	−26.8373			−1.44070			−0.720351	−	0.693610i	$-0.756019\pi$
$347$	−26.8373			−1.44070			−0.720351	+	0.693610i	$0.756019\pi$
$348$	−7.06619	−	21.7475i	−0.378788	−	1.16579i
$349$	1.11092	−	3.41906i	0.0594662	−	0.183018i	−0.916911	−	0.399092i	$-0.869325\pi$
$349$	1.11092	−	3.41906i	0.0594662	−	0.183018i	0.976377	+	0.216074i	$0.0693253\pi$
$350$	0.946639	−	2.91346i	0.0506000	−	0.155731i
$351$	−4.22771	−	3.07161i	−0.225659	−	0.163951i
$352$	0.309425	+	0.952312i	0.0164924	+	0.0507584i
$353$	−2.74290	−	1.99283i	−0.145990	−	0.106068i	0.512393	−	0.858751i	$-0.328759\pi$
$353$	−2.74290	−	1.99283i	−0.145990	−	0.106068i	−0.658383	+	0.752683i	$0.728759\pi$
$354$	21.3720	−	15.5276i	1.13591	−	0.825284i
$355$	−7.30817	+	22.4922i	−0.387877	+	1.19376i
$356$	−8.98130	+	6.52530i	−0.476008	+	0.345840i
$357$	−12.7903	+	9.29272i	−0.676936	+	0.491823i
$358$	−3.26057	+	10.0350i	−0.172327	+	0.530367i
$359$	9.69693	−	7.04523i	0.511784	−	0.371833i	−0.301716	−	0.953398i	$-0.597559\pi$
$359$	9.69693	−	7.04523i	0.511784	−	0.371833i	0.813500	+	0.581565i	$0.197559\pi$
$360$	14.0150	+	10.1825i	0.738655	+	0.536665i
$361$	10.7640	+	33.1283i	0.566528	+	1.74359i
$362$	−19.2343	−	13.9745i	−1.01093	−	0.734485i
$363$	−3.51852	+	10.8289i	−0.184674	+	0.568369i
$364$	3.09574	−	9.52771i	0.162261	−	0.499388i
$365$	1.51368	+	4.65862i	0.0792296	+	0.243844i
$366$	20.2298			1.05743
$367$	−6.77861			−0.353840			−0.176920	−	0.984225i	$-0.556613\pi$
$367$	−6.77861			−0.353840			−0.176920	+	0.984225i	$0.556613\pi$
$368$	5.15969	+	15.8799i	0.268967	+	0.827796i
$369$	12.9840	−	9.43342i	0.675920	−	0.491084i
$370$	−40.1953	−	29.2036i	−2.08965	−	1.51822i
$371$	8.82137			0.457982
$372$	−9.78705	−	20.9938i	−0.507435	−	1.08848i
$373$	29.2334			1.51365			0.756823	−	0.653620i	$-0.226750\pi$
$373$	29.2334			1.51365			0.756823	+	0.653620i	$0.226750\pi$
$374$	−7.58478	−	5.51066i	−0.392200	−	0.284950i
$375$	10.2048	−	7.41423i	0.526974	−	0.382869i
$376$	−7.76665	−	23.9033i	−0.400534	−	1.23272i
$377$	5.49653			0.283086
$378$	32.9218			1.69331
$379$	−8.01399	−	24.6645i	−0.411651	−	1.26693i	−0.915212	−	0.402972i	$-0.867977\pi$
$379$	−8.01399	−	24.6645i	−0.411651	−	1.26693i	0.503562	−	0.863959i	$-0.332023\pi$
$380$	−18.5177	+	56.9916i	−0.949938	+	2.92361i
$381$	3.88854	−	11.9677i	0.199216	−	0.613123i
$382$	17.4044	+	12.6450i	0.890487	+	0.646977i
$383$	1.23190	+	3.79139i	0.0629470	+	0.193731i	0.977584	−	0.210545i	$-0.0675237\pi$
$383$	1.23190	+	3.79139i	0.0629470	+	0.193731i	−0.914637	+	0.404275i	$0.867524\pi$
$384$	17.9508	+	13.0420i	0.916047	+	0.665547i
$385$	−3.09860	+	2.25127i	−0.157920	+	0.114735i
$386$	−7.59411	+	23.3723i	−0.386530	+	1.18962i
$387$	−7.02408	+	5.10329i	−0.357054	+	0.259415i
$388$	−6.14326	+	4.46334i	−0.311877	+	0.226592i
$389$	1.66955	−	5.13835i	0.0846496	−	0.260525i	−0.899769	−	0.436367i	$-0.856265\pi$
$389$	1.66955	−	5.13835i	0.0846496	−	0.260525i	0.984418	+	0.175842i	$0.0562649\pi$
$390$	4.49669	−	3.26704i	0.227699	−	0.165433i
$391$	24.5090	+	17.8068i	1.23947	+	0.900529i
$392$	−0.287789	−	0.885722i	−0.0145355	−	0.0447357i
$393$	11.5248	+	8.37326i	0.581349	+	0.422375i
$394$	3.27936	−	10.0928i	0.165212	−	0.508470i
$395$	2.04864	−	6.30508i	0.103078	−	0.317243i
$396$	1.50296	+	4.62563i	0.0755264	+	0.232446i
$397$	−36.1867			−1.81616			−0.908080	−	0.418797i	$-0.862452\pi$
$397$	−36.1867			−1.81616			−0.908080	+	0.418797i	$0.862452\pi$
$398$	33.9119			1.69985
$399$	6.39411	+	19.6791i	0.320106	+	0.985185i
$400$	1.21548	−	0.883101i	0.0607742	−	0.0441551i
$401$	18.8525	+	13.6972i	0.941450	+	0.684003i	0.948769	−	0.315970i	$-0.102330\pi$
$401$	18.8525	+	13.6972i	0.941450	+	0.684003i	−0.00731946	+	0.999973i	$0.502330\pi$
$402$	18.9249			0.943889
$403$	5.52633	−	0.677996i	0.275286	−	0.0337734i
$404$	−68.0051			−3.38338
$405$	0.289828	+	0.210572i	0.0144017	+	0.0104634i
$406$	−28.0144	+	20.3537i	−1.39033	+	1.01014i
$407$	−2.06794	−	6.36445i	−0.102504	−	0.315474i
$408$	−27.0482			−1.33908
$409$	16.7293			0.827211			0.413606	−	0.910456i	$-0.364269\pi$
$409$	16.7293			0.827211			0.413606	+	0.910456i	$0.364269\pi$
$410$	13.9278	+	42.8654i	0.687845	+	2.11697i
$411$	1.16801	−	3.59478i	0.0576139	−	0.177317i
$412$	5.86911	−	18.0633i	0.289150	−	0.889914i
$413$	−21.2886	−	15.4671i	−1.04755	−	0.761086i
$414$	−7.38323	−	22.7232i	−0.362866	−	1.11679i
$415$	−3.68120	−	2.67455i	−0.180703	−	0.131288i
$416$	−1.17101	+	0.850790i	−0.0574136	+	0.0417134i
$417$	3.31820	−	10.2124i	0.162493	−	0.500102i
$418$	−9.92696	+	7.21236i	−0.485544	+	0.352768i
$419$	−7.10380	+	5.16121i	−0.347043	+	0.252142i	−0.747628	−	0.664118i	$-0.768807\pi$
$419$	−7.10380	+	5.16121i	−0.347043	+	0.252142i	0.400584	+	0.916260i	$0.368807\pi$
$420$	−7.11763	+	21.9058i	−0.347305	+	1.06889i
$421$	20.8807	−	15.1708i	1.01767	−	0.739377i	0.0518624	−	0.998654i	$-0.483484\pi$
$421$	20.8807	−	15.1708i	1.01767	−	0.739377i	0.965803	+	0.259277i	$0.0834843\pi$
$422$	6.30889	+	4.58368i	0.307112	+	0.223130i
$423$	3.18590	+	9.80519i	0.154904	+	0.476745i
$424$	12.2098	+	8.87091i	0.592958	+	0.430809i
$425$	0.842366	−	2.59254i	0.0408607	−	0.125756i
$426$	−8.99927	+	27.6969i	−0.436016	+	1.34192i
$427$	−6.22699	−	19.1647i	−0.301345	−	0.927445i
$428$	24.1291			1.16633
$429$	0.748638			0.0361446
$430$	−7.53466	−	23.1893i	−0.363354	−	1.11829i
$431$	10.9992	−	7.99142i	0.529815	−	0.384933i	−0.290474	−	0.956883i	$-0.593813\pi$
$431$	10.9992	−	7.99142i	0.529815	−	0.384933i	0.820288	+	0.571950i	$0.193813\pi$
$432$	13.0626	+	9.49055i	0.628476	+	0.456614i
$433$	−17.1946			−0.826319			−0.413160	−	0.910659i	$-0.635575\pi$
$433$	−17.1946			−0.826319			−0.413160	+	0.910659i	$0.635575\pi$
$434$	−25.6557	+	23.9196i	−1.23151	+	1.14818i
$435$	−12.6375			−0.605920
$436$	−44.9887	−	32.6862i	−2.15457	−	1.56538i
$437$	32.0774	−	23.3056i	1.53447	−	1.11486i
$438$	1.86394	+	5.73662i	0.0890626	+	0.274106i
$439$	−35.2297			−1.68142			−0.840711	−	0.541485i	$-0.817862\pi$
$439$	−35.2297			−1.68142			−0.840711	+	0.541485i	$0.817862\pi$
$440$	−6.55273			−0.312389
$441$	0.118052	+	0.363326i	0.00562151	+	0.0173012i
$442$	4.18792	−	12.8891i	0.199199	−	0.613071i
$443$	−0.909758	+	2.79995i	−0.0432239	+	0.133029i	−0.970340	−	0.241746i	$-0.922280\pi$
$443$	−0.909758	+	2.79995i	−0.0432239	+	0.133029i	0.927116	+	0.374775i	$0.122280\pi$
$444$	−32.5579	−	23.6547i	−1.54513	−	1.12260i
$445$	1.89592	+	5.83505i	0.0898754	+	0.276608i
$446$	−55.5661	−	40.3711i	−2.63113	−	1.91163i
$447$	7.11253	−	5.16755i	0.336411	−	0.244417i
$448$	7.79418	−	23.9880i	0.368240	−	1.13333i
$449$	27.2207	−	19.7770i	1.28462	−	0.933333i	0.284941	−	0.958545i	$-0.408026\pi$
$449$	27.2207	−	19.7770i	1.28462	−	0.933333i	0.999682	+	0.0252118i	$0.00802601\pi$
$450$	−1.73929	+	1.26367i	−0.0819910	+	0.0595699i
$451$	−1.87594	+	5.77356i	−0.0883347	+	0.271866i
$452$	6.75224	−	4.90579i	0.317599	−	0.230749i
$453$	13.8341	+	10.0510i	0.649981	+	0.472239i
$454$	2.38915	+	7.35304i	0.112128	+	0.345095i
$455$	−4.47916	−	3.25430i	−0.209986	−	0.152564i
$456$	−10.9394	+	33.6680i	−0.512285	+	1.57665i
$457$	−0.926889	+	2.85267i	−0.0433581	+	0.133442i	−0.970392	−	0.241534i	$-0.922349\pi$
$457$	−0.926889	+	2.85267i	−0.0433581	+	0.133442i	0.927034	+	0.374977i	$0.122349\pi$
$458$	−20.0384	−	61.6719i	−0.936333	−	2.88174i
$459$	29.2954			1.36739
$460$	44.1364			2.05787
$461$	7.48182	+	23.0267i	0.348463	+	1.07246i	0.959704	+	0.281014i	$0.0906708\pi$
$461$	7.48182	+	23.0267i	0.348463	+	1.07246i	−0.611241	+	0.791445i	$0.709329\pi$
$462$	−3.81562	+	2.77221i	−0.177519	+	0.128975i
$463$	24.3953	+	17.7242i	1.13375	+	0.823716i	0.986236	−	0.165345i	$-0.0528736\pi$
$463$	24.3953	+	17.7242i	1.13375	+	0.823716i	0.147512	+	0.989060i	$0.452874\pi$
$464$	−16.9830			−0.788415
$465$	−12.7060	+	1.55883i	−0.589225	+	0.0722889i
$466$	68.4725			3.17193
$467$	−16.5610	−	12.0323i	−0.766353	−	0.556788i	0.134499	−	0.990914i	$-0.457057\pi$
$467$	−16.5610	−	12.0323i	−0.766353	−	0.556788i	−0.900852	+	0.434126i	$0.857057\pi$
$468$	−5.68790	+	4.13250i	−0.262923	+	0.191025i
$469$	−5.82532	−	17.9285i	−0.268989	−	0.827862i
$470$	−28.9534			−1.33552
$471$	17.1970			0.792397
$472$	−13.9119	−	42.8164i	−0.640347	−	1.97078i
$473$	1.01485	−	3.12338i	0.0466627	−	0.143613i
$474$	2.52270	−	7.76406i	0.115871	−	0.356615i
$475$	−2.88635	−	2.09706i	−0.132435	−	0.0962197i
$476$	17.3546	+	53.4121i	0.795449	+	2.44814i
$477$	−5.00848	−	3.63887i	−0.229322	−	0.166613i
$478$	44.9248	−	32.6398i	2.05481	−	1.49291i
$479$	11.2161	−	34.5196i	0.512477	−	1.57724i	−0.275349	−	0.961344i	$-0.588793\pi$
$479$	11.2161	−	34.5196i	0.512477	−	1.57724i	0.787826	−	0.615898i	$-0.211207\pi$
$480$	2.69235	−	1.95611i	0.122889	−	0.0892837i
$481$	7.82605	−	5.68596i	0.356837	−	0.259257i
$482$	−14.6694	+	45.1479i	−0.668174	+	2.05643i
$483$	12.3295	−	8.95794i	0.561014	−	0.407600i
$484$	32.7223	+	23.7742i	1.48738	+	1.08064i
$485$	1.29682	+	3.99121i	0.0588856	+	0.181231i
$486$	−30.3045	−	22.0175i	−1.37464	−	0.998733i
$487$	2.51964	−	7.75465i	0.114176	−	0.351397i	−0.877599	−	0.479396i	$-0.840856\pi$
$487$	2.51964	−	7.75465i	0.114176	−	0.351397i	0.991774	+	0.128000i	$0.0408557\pi$
$488$	10.6535	−	32.7880i	0.482261	−	1.48425i
$489$	−3.83985	−	11.8178i	−0.173644	−	0.534421i
$490$	−1.07285			−0.0484665
$491$	−7.90619			−0.356801			−0.178401	−	0.983958i	$-0.557092\pi$
$491$	−7.90619			−0.356801			−0.178401	+	0.983958i	$0.557092\pi$
$492$	11.2814	+	34.7207i	0.508606	+	1.56533i
$493$	−24.9286	+	18.1117i	−1.12273	+	0.815709i
$494$	−14.3498	−	10.4258i	−0.645629	−	0.469077i
$495$	2.68795			0.120814
$496$	−17.0750	+	2.09485i	−0.766691	+	0.0940613i
$497$	29.0087			1.30122
$498$	−4.53302	−	3.29343i	−0.203129	−	0.147582i
$499$	27.7157	−	20.1367i	1.24073	−	0.901440i	0.243080	−	0.970006i	$-0.421842\pi$
$499$	27.7157	−	20.1367i	1.24073	−	0.901440i	0.997647	+	0.0685659i	$0.0218423\pi$
$500$	−13.8465	−	42.6150i	−0.619232	−	1.90580i
$501$	−6.54946			−0.292608
$502$	−25.7086			−1.14743
$503$	2.88331	+	8.87392i	0.128561	+	0.395669i	0.994533	−	0.104423i	$-0.0332996\pi$
$503$	2.88331	+	8.87392i	0.128561	+	0.395669i	−0.865972	+	0.500092i	$0.833300\pi$
$504$	6.56629	−	20.2090i	0.292486	−	0.900179i
$505$	−11.6140	+	35.7441i	−0.516815	+	1.59059i
$506$	7.31153	+	5.31214i	0.325037	+	0.236153i
$507$	0.334414	+	1.02922i	0.0148519	+	0.0457093i
$508$	−36.1635	−	26.2743i	−1.60450	−	1.16573i
$509$	14.1777	−	10.3007i	0.628415	−	0.456570i	−0.227436	−	0.973793i	$-0.573034\pi$
$509$	14.1777	−	10.3007i	0.628415	−	0.456570i	0.855851	+	0.517223i	$0.173034\pi$
$510$	−9.62872	+	29.6342i	−0.426367	+	1.31222i
$511$	4.86084	−	3.53161i	0.215031	−	0.156229i
$512$	25.9074	−	18.8229i	1.14496	−	0.831861i
$513$	11.8483	−	36.4652i	0.523114	−	1.60998i
$514$	−0.0581741	+	0.0422660i	−0.00256595	+	0.00186427i
$515$	−8.49189	−	6.16972i	−0.374198	−	0.271870i
$516$	−6.10303	−	18.7832i	−0.268671	−	0.826884i
$517$	−3.15496	−	2.29221i	−0.138755	−	0.100811i
$518$	−18.8323	+	57.9597i	−0.827442	+	2.54660i
$519$	−2.91065	+	8.95806i	−0.127763	+	0.393215i
$520$	−2.92708	−	9.00863i	−0.128361	−	0.395055i
$521$	22.5697			0.988795			0.494397	−	0.869236i	$-0.335389\pi$
$521$	22.5697			0.988795			0.494397	+	0.869236i	$0.335389\pi$
$522$	24.3017			1.06366
$523$	7.41025	+	22.8064i	0.324028	+	0.997254i	0.971878	+	0.235486i	$0.0756683\pi$
$523$	7.41025	+	22.8064i	0.324028	+	0.997254i	−0.647850	+	0.761768i	$0.724332\pi$
$524$	40.9395	−	29.7443i	1.78845	−	1.29939i
$525$	−1.10942	−	0.806044i	−0.0484193	−	0.0351787i
$526$	−24.8956			−1.08550
$527$	−22.8297	+	21.2848i	−0.994475	+	0.927180i
$528$	−2.31311			−0.100665
$529$	−5.01863	−	3.64625i	−0.218201	−	0.158532i
$530$	14.0655	−	10.2192i	0.610967	−	0.443893i
$531$	5.70670	+	17.5634i	0.247650	+	0.762187i
$532$	73.5033			3.18677
$533$	−8.77541			−0.380105
$534$	2.33464	+	7.18527i	0.101030	+	0.310937i
$535$	4.12079	−	12.6825i	0.178157	−	0.548312i
$536$	9.96630	−	30.6731i	0.430478	−	1.32488i
$537$	3.82126	+	2.77631i	0.164900	+	0.119807i
$538$	−6.91166	−	21.2719i	−0.297983	−	0.917096i
$539$	−0.116905	−	0.0849367i	−0.00503547	−	0.00365848i
$540$	34.5291	−	25.0869i	1.48590	−	1.07957i
$541$	0.0594623	−	0.183006i	0.00255648	−	0.00786805i	−0.949770	−	0.312948i	$-0.898683\pi$
$541$	0.0594623	−	0.183006i	0.00255648	−	0.00786805i	0.952327	+	0.305080i	$0.0986833\pi$
$542$	−39.8310	+	28.9389i	−1.71089	+	1.24303i
$543$	−8.61022	+	6.25569i	−0.369500	+	0.268457i
$544$	2.50748	−	7.71722i	0.107507	−	0.330873i
$545$	−24.8634	+	18.0643i	−1.06503	+	0.773789i
$546$	−5.51563	−	4.00734i	−0.236047	−	0.171498i
$547$	−11.5008	−	35.3959i	−0.491740	−	1.51342i	−0.821976	−	0.569522i	$-0.807128\pi$
$547$	−11.5008	−	35.3959i	−0.491740	−	1.51342i	0.330236	−	0.943898i	$-0.392872\pi$
$548$	−10.8626	−	7.89212i	−0.464026	−	0.337135i
$549$	−4.37009	+	13.4498i	−0.186511	+	0.574021i
$550$	0.251295	−	0.773406i	0.0107153	−	0.0329782i
$551$	12.4622	+	38.3548i	0.530909	+	1.63397i
$552$	26.0737			1.10977
$553$	−8.13179			−0.345799
$554$	11.8433	+	36.4500i	0.503174	+	1.54861i
$555$	−17.9934	+	13.0730i	−0.763778	+	0.554917i
$556$	−30.8594	−	22.4207i	−1.30873	−	0.950847i
$557$	−10.9144			−0.462456			−0.231228	−	0.972900i	$-0.574274\pi$
$557$	−10.9144			−0.462456			−0.231228	+	0.972900i	$0.574274\pi$
$558$	24.4334	−	2.99761i	1.03435	−	0.126899i
$559$	4.74732			0.200790
$560$	13.8395	+	10.0550i	0.584827	+	0.424901i
$561$	−3.39532	+	2.46685i	−0.143351	+	0.104150i
$562$	−1.78431	−	5.49155i	−0.0752667	−	0.231647i
$563$	24.3394			1.02578			0.512892	−	0.858453i	$-0.328574\pi$
$563$	24.3394			1.02578			0.512892	+	0.858453i	$0.328574\pi$
$564$	−23.4521			−0.987510
$565$	−1.42538	−	4.38686i	−0.0599660	−	0.184556i
$566$	−3.00190	+	9.23889i	−0.126179	+	0.388340i
$567$	0.135790	−	0.417918i	0.00570263	−	0.0175509i
$568$	40.1513	+	29.1716i	1.68471	+	1.22402i
$569$	10.1090	+	31.1122i	0.423790	+	1.30429i	0.904148	+	0.427219i	$0.140507\pi$
$569$	10.1090	+	31.1122i	0.423790	+	1.30429i	−0.480359	+	0.877072i	$0.659493\pi$
$570$	32.9927	+	23.9706i	1.38191	+	1.00402i
$571$	−17.9969	+	13.0755i	−0.753147	+	0.547193i	−0.896801	−	0.442435i	$-0.854115\pi$
$571$	−17.9969	+	13.0755i	−0.753147	+	0.547193i	0.143654	+	0.989628i	$0.454115\pi$
$572$	0.821795	−	2.52923i	0.0343610	−	0.105752i
$573$	7.79107	−	5.66055i	0.325477	−	0.236473i
$574$	44.7260	−	32.4954i	1.86683	−	1.35633i
$575$	−0.812019	+	2.49914i	−0.0338635	+	0.104221i
$576$	−14.3205	+	10.4045i	−0.596687	+	0.433519i
$577$	8.44384	+	6.13481i	0.351522	+	0.255395i	0.749507	−	0.661996i	$-0.230291\pi$
$577$	8.44384	+	6.13481i	0.351522	+	0.255395i	−0.397986	+	0.917392i	$0.630291\pi$
$578$	10.7776	+	33.1700i	0.448288	+	1.37969i
$579$	8.90000	+	6.46623i	0.369872	+	0.268727i
$580$	−13.8724	+	42.6948i	−0.576020	+	1.77281i
$581$	−1.72471	+	5.30811i	−0.0715530	+	0.220217i
$582$	1.59690	+	4.91477i	0.0661938	+	0.203724i
$583$	2.34172			0.0969841
$584$	10.2794			0.425364
$585$	1.20070	+	3.69537i	0.0496427	+	0.152785i
$586$	−53.2228	+	38.6687i	−2.19862	+	1.59739i
$587$	−22.4390	−	16.3029i	−0.926156	−	0.672892i	0.0188925	−	0.999822i	$-0.493986\pi$
$587$	−22.4390	−	16.3029i	−0.926156	−	0.672892i	−0.945049	+	0.326930i	$0.893986\pi$
$588$	−0.869002			−0.0358371
$589$	17.2609	+	37.0255i	0.711221	+	1.52561i
$590$	−51.8624			−2.13514
$591$	−3.84328	−	2.79231i	−0.158092	−	0.114860i
$592$	−24.1806	+	17.5682i	−0.993817	+	0.722050i
$593$	4.35755	+	13.4112i	0.178943	+	0.550731i	0.999792	−	0.0204155i	$-0.00649890\pi$
$593$	4.35755	+	13.4112i	0.178943	+	0.550731i	−0.820848	+	0.571146i	$0.806499\pi$
$594$	8.73941			0.358582
$595$	31.0377			1.27242
$596$	−9.65068	−	29.7017i	−0.395307	−	1.21663i
$597$	4.69107	−	14.4376i	0.191993	−	0.590893i
$598$	−4.03704	+	12.4247i	−0.165087	+	0.508085i
$599$	−3.07645	−	2.23517i	−0.125700	−	0.0913267i	0.523159	−	0.852235i	$-0.324754\pi$
$599$	−3.07645	−	2.23517i	−0.125700	−	0.0913267i	−0.648859	+	0.760909i	$0.724754\pi$
$600$	−0.724997	−	2.23131i	−0.0295979	−	0.0910929i
$601$	−18.4465	−	13.4021i	−0.752447	−	0.546685i	0.144137	−	0.989558i	$-0.453959\pi$
$601$	−18.4465	−	13.4021i	−0.752447	−	0.546685i	−0.896584	+	0.442873i	$0.853959\pi$
$602$	−24.1959	+	17.5793i	−0.986150	+	0.716480i
$603$	−4.08820	+	12.5822i	−0.166485	+	0.512387i
$604$	49.1427	−	35.7043i	1.99959	−	1.45279i
$605$	18.0843	−	13.1390i	0.735230	−	0.534176i
$606$	−14.3014	+	44.0153i	−0.580956	+	1.78800i
$607$	−33.5176	+	24.3519i	−1.36044	+	0.988415i	−0.362019	+	0.932171i	$0.617912\pi$
$607$	−33.5176	+	24.3519i	−1.36044	+	0.988415i	−0.998417	+	0.0562439i	$0.982088\pi$
$608$	−8.59183	−	6.24233i	−0.348445	−	0.253160i
$609$	4.79010	+	14.7424i	0.194105	+	0.597392i
$610$	−32.1303	−	23.3441i	−1.30092	−	0.945173i
$611$	1.74200	−	5.36134i	0.0704740	−	0.216897i
$612$	12.1795	−	37.4845i	0.492326	−	1.51522i
$613$	12.6674	+	38.9861i	0.511630	+	1.57463i	0.789332	+	0.613967i	$0.210427\pi$
$613$	12.6674	+	38.9861i	0.511630	+	1.57463i	−0.277702	+	0.960667i	$0.589573\pi$
$614$	22.1205			0.892712
$615$	20.1762			0.813581
$616$	2.48374	+	7.64418i	0.100073	+	0.307993i
$617$	9.27250	−	6.73686i	0.373297	−	0.271216i	−0.385280	−	0.922800i	$-0.625895\pi$
$617$	9.27250	−	6.73686i	0.373297	−	0.271216i	0.758577	+	0.651584i	$0.225895\pi$
$618$	−10.4569	−	7.59738i	−0.420638	−	0.305612i
$619$	3.93248			0.158060			0.0790298	−	0.996872i	$-0.474818\pi$
$619$	3.93248			0.158060			0.0790298	+	0.996872i	$0.474818\pi$
$620$	−8.68119	+	44.6374i	−0.348645	+	1.79268i
$621$	−28.2400			−1.13323
$622$	37.6262	+	27.3370i	1.50867	+	1.09611i
$623$	6.08833	−	4.42343i	0.243924	−	0.177221i
$624$	−1.03326	−	3.18005i	−0.0413635	−	0.127304i
$625$	−22.3323			−0.893290
$626$	47.9796			1.91765
$627$	1.69738	+	5.22400i	0.0677869	+	0.208626i
$628$	18.8775	−	58.0990i	0.753294	−	2.31840i
$629$	−16.7579	+	51.5754i	−0.668180	+	2.05645i
$630$	−19.8036	−	14.3881i	−0.788994	−	0.573238i
$631$	−6.82281	−	20.9984i	−0.271612	−	0.835935i	−0.990096	−	0.140392i	$-0.955164\pi$
$631$	−6.82281	−	20.9984i	−0.271612	−	0.835935i	0.718484	−	0.695543i	$-0.244836\pi$
$632$	−11.2553	−	8.17746i	−0.447712	−	0.325282i
$633$	2.82417	−	2.05188i	0.112251	−	0.0815549i
$634$	−1.27192	+	3.91455i	−0.0505142	+	0.155467i
$635$	−19.9861	+	14.5207i	−0.793123	+	0.576237i
$636$	11.3930	−	8.27748i	0.451761	−	0.328223i
$637$	0.0645490	−	0.198661i	0.00255752	−	0.00787125i
$638$	−7.43671	+	5.40308i	−0.294422	+	0.213910i
$639$	−16.4702	−	11.9663i	−0.651551	−	0.473379i
$640$	−13.4609	−	41.4284i	−0.532089	−	1.63760i
$641$	37.1039	+	26.9576i	1.46552	+	1.06476i	0.981883	+	0.189489i	$0.0606833\pi$
$641$	37.1039	+	26.9576i	1.46552	+	1.06476i	0.483634	+	0.875271i	$0.339317\pi$
$642$	5.07434	−	15.6172i	0.200268	−	0.616362i
$643$	−6.90326	+	21.2461i	−0.272238	+	0.837863i	0.717699	+	0.696354i	$0.245195\pi$
$643$	−6.90326	+	21.2461i	−0.272238	+	0.837863i	−0.989937	+	0.141509i	$0.954805\pi$
$644$	−16.7294	−	51.4879i	−0.659232	−	2.02891i
$645$	−10.9149			−0.429774
$646$	99.4352			3.91223
$647$	−14.9444	−	45.9942i	−0.587526	−	1.80822i	−0.588880	−	0.808220i	$-0.700431\pi$
$647$	−14.9444	−	45.9942i	−0.587526	−	1.80822i	0.00135386	−	0.999999i	$-0.499569\pi$
$648$	0.608213	−	0.441893i	0.0238929	−	0.0173592i
$649$	−5.65128	−	4.10590i	−0.221832	−	0.161171i
$650$	1.17552			0.0461079
$651$	6.63454	+	14.2315i	0.260028	+	0.557775i
$652$	−44.1409			−1.72869
$653$	−14.7608	−	10.7243i	−0.577634	−	0.419676i	0.260236	−	0.965545i	$-0.416200\pi$
$653$	−14.7608	−	10.7243i	−0.577634	−	0.419676i	−0.837870	+	0.545869i	$0.816200\pi$
$654$	−30.6167	+	22.2443i	−1.19721	+	0.869822i
$655$	−8.64220	−	26.5979i	−0.337679	−	1.03927i
$656$	27.1139			1.05862
$657$	−4.21663			−0.164507
$658$	10.9745	+	33.7760i	0.427830	+	1.31673i
$659$	10.8215	−	33.3050i	0.421544	−	1.29738i	−0.484721	−	0.874669i	$-0.661079\pi$
$659$	10.8215	−	33.3050i	0.421544	−	1.29738i	0.906265	−	0.422711i	$-0.138921\pi$
$660$	−1.88945	+	5.81512i	−0.0735466	+	0.226353i
$661$	−26.0792	−	18.9477i	−1.01436	−	0.736979i	−0.0492445	−	0.998787i	$-0.515681\pi$
$661$	−26.0792	−	18.9477i	−1.01436	−	0.736979i	−0.965120	+	0.261808i	$0.915681\pi$
$662$	22.5475	+	69.3939i	0.876332	+	2.69707i
$663$	−4.90808	−	3.56593i	−0.190614	−	0.138489i
$664$	−7.72511	+	5.61262i	−0.299792	+	0.217812i
$665$	12.5530	−	38.6340i	0.486783	−	1.49816i
$666$	34.6011	−	25.1392i	1.34077	−	0.974123i
$667$	24.0305	−	17.4592i	0.930465	−	0.676023i
$668$	−7.18947	+	22.1269i	−0.278169	+	0.856116i
$669$	−24.8741	+	18.0721i	−0.961690	+	0.698708i
$670$	−30.0578	−	21.8383i	−1.16124	−	0.843687i
$671$	−1.65302	−	5.08746i	−0.0638140	−	0.196399i
$672$	−3.30243	−	2.39936i	−0.127394	−	0.0925573i
$673$	−6.85194	+	21.0881i	−0.264123	+	0.812887i	0.727771	+	0.685820i	$0.240556\pi$
$673$	−6.85194	+	21.0881i	−0.264123	+	0.812887i	−0.991894	+	0.127067i	$0.959444\pi$
$674$	19.4845	−	59.9670i	0.750513	−	2.30984i
$675$	0.785231	+	2.41669i	0.0302236	+	0.0930186i
$676$	3.84425			0.147856
$677$	−47.8934			−1.84069			−0.920346	−	0.391104i	$-0.872093\pi$
$677$	−47.8934			−1.84069			−0.920346	+	0.391104i	$0.872093\pi$
$678$	−1.75521	−	5.40197i	−0.0674082	−	0.207461i
$679$	4.16445	−	3.02565i	0.159817	−	0.116114i
$680$	42.9597	+	31.2121i	1.64743	+	1.19693i
$681$	3.46098			0.132625
$682$	−6.81055	+	6.34969i	−0.260789	+	0.243142i
$683$	−20.6045			−0.788411			−0.394205	−	0.919022i	$-0.628980\pi$
$683$	−20.6045			−0.788411			−0.394205	+	0.919022i	$0.628980\pi$
$684$	−41.7327	−	30.3206i	−1.59569	−	1.15934i
$685$	−6.00329	+	4.36164i	−0.229374	+	0.166650i
$686$	14.0341	+	43.1926i	0.535825	+	1.64910i
$687$	−29.0281			−1.10749
$688$	−14.6681			−0.559216
$689$	1.04604	+	3.21938i	0.0398509	+	0.122648i
$690$	9.28184	−	28.5666i	0.353354	−	1.08751i
$691$	−8.51525	+	26.2073i	−0.323935	+	0.996971i	0.647983	+	0.761655i	$0.275613\pi$
$691$	−8.51525	+	26.2073i	−0.323935	+	0.996971i	−0.971919	+	0.235316i	$0.924387\pi$
$692$	27.0692	+	19.6669i	1.02901	+	0.747623i
$693$	−1.01884	−	3.13566i	−0.0387025	−	0.119114i
$694$	52.4881	+	38.1348i	1.99242	+	1.44758i
$695$	−17.0547	+	12.3910i	−0.646921	+	0.470016i
$696$	−8.19517	+	25.2221i	−0.310637	+	0.956043i
$697$	39.7994	−	28.9159i	1.50751	−	1.09527i
$698$	−7.03108	+	5.10838i	−0.266130	+	0.193355i
$699$	9.47190	−	29.1515i	0.358260	−	1.10261i
$700$	−3.94101	+	2.86331i	−0.148956	+	0.108223i
$701$	−5.03228	−	3.65617i	−0.190067	−	0.138092i	0.488683	−	0.872462i	$-0.337478\pi$
$701$	−5.03228	−	3.65617i	−0.190067	−	0.138092i	−0.678749	+	0.734370i	$0.737478\pi$
$702$	3.90387	+	12.0149i	0.147342	+	0.453472i
$703$	57.4206	+	41.7185i	2.16566	+	1.57344i
$704$	2.06904	−	6.36786i	0.0779800	−	0.239998i
$705$	−4.00516	+	12.3266i	−0.150843	+	0.464247i
$706$	2.53279	+	7.79512i	0.0953228	+	0.293373i
$707$	46.1000			1.73377
$708$	−42.0082			−1.57876
$709$	−14.7287	−	45.3304i	−0.553149	−	1.70242i	−0.700782	−	0.713376i	$-0.747165\pi$
$709$	−14.7287	−	45.3304i	−0.553149	−	1.70242i	0.147633	−	0.989042i	$-0.452835\pi$
$710$	46.2539	−	33.6054i	1.73588	−	1.26119i
$711$	4.61696	+	3.35442i	0.173150	+	0.125801i
$712$	12.8752			0.482519
$713$	22.0072	−	20.5180i	0.824176	−	0.768405i
$714$	38.2198			1.43034
$715$	−1.18904	−	0.863886i	−0.0444675	−	0.0323075i
$716$	13.5743	−	9.86228i	0.507294	−	0.368571i
$717$	−7.68155	−	23.6414i	−0.286873	−	0.882904i
$718$	−28.9762			−1.08138
$719$	−7.25606			−0.270605			−0.135303	−	0.990804i	$-0.543201\pi$
$719$	−7.25606			−0.270605			−0.135303	+	0.990804i	$0.543201\pi$
$720$	−3.70987	−	11.4178i	−0.138259	−	0.425516i
$721$	−3.97861	+	12.2449i	−0.148171	+	0.456024i
$722$	26.0219	−	80.0872i	0.968435	−	2.98054i
$723$	17.1920	+	12.4907i	0.639378	+	0.464535i
$724$	11.6828	+	35.9561i	0.434189	+	1.33630i
$725$	−2.16229	−	1.57100i	−0.0803054	−	0.0583453i
$726$	22.2689	−	16.1793i	0.826478	−	0.600471i
$727$	−0.999998	+	3.07768i	−0.0370879	+	0.114145i	−0.967886	−	0.251388i	$-0.919113\pi$
$727$	−0.999998	+	3.07768i	−0.0370879	+	0.114145i	0.930799	+	0.365532i	$0.119113\pi$
$728$	−9.39967	+	6.82926i	−0.348375	+	0.253109i
$729$	−13.9750	+	10.1535i	−0.517594	+	0.376054i
$730$	3.65930	−	11.2622i	0.135437	−	0.416832i
$731$	−21.5307	+	15.6430i	−0.796341	+	0.578575i
$732$	−26.0254	−	18.9085i	−0.961925	−	0.698879i
$733$	−8.43835	−	25.9706i	−0.311678	−	0.959245i	−0.977100	−	0.212779i	$-0.931749\pi$
$733$	−8.43835	−	25.9706i	−0.311678	−	0.959245i	0.665423	−	0.746467i	$-0.268251\pi$
$734$	13.2575	+	9.63215i	0.489344	+	0.355529i
$735$	−0.148409	+	0.456756i	−0.00547415	+	0.0168477i
$736$	−2.41714	+	7.43920i	−0.0890971	+	0.274213i
$737$	−1.54639	−	4.75930i	−0.0569620	−	0.175311i
$738$	−38.7985			−1.42819
$739$	15.0570			0.553881			0.276941	−	0.960887i	$-0.410679\pi$
$739$	15.0570			0.553881			0.276941	+	0.960887i	$0.410679\pi$
$740$	24.4145	+	75.1400i	0.897494	+	2.76220i
$741$	−6.42369	+	4.66709i	−0.235980	+	0.171450i
$742$	−17.2527	−	12.5348i	−0.633368	−	0.460169i
$743$	−26.8045			−0.983362			−0.491681	−	0.870775i	$-0.663617\pi$
$743$	−26.8045			−0.983362			−0.491681	+	0.870775i	$0.663617\pi$
$744$	−5.12845	+	26.3697i	−0.188018	+	0.966762i
$745$	−17.2597			−0.632345
$746$	−57.1743	−	41.5396i	−2.09330	−	1.52087i
$747$	3.16886	−	2.30231i	0.115943	−	0.0842373i
$748$	4.60696	+	14.1788i	0.168447	+	0.518427i
$749$	−16.3569			−0.597668
$750$	−30.4938			−1.11348
$751$	4.81537	+	14.8202i	0.175716	+	0.540797i	0.999665	−	0.0258659i	$-0.00823428\pi$
$751$	4.81537	+	14.8202i	0.175716	+	0.540797i	−0.823950	+	0.566663i	$0.808234\pi$
$752$	−5.38237	+	16.5652i	−0.196275	+	0.604072i
$753$	−3.55631	+	10.9452i	−0.129599	+	0.398865i
$754$	−10.7501	−	7.81038i	−0.391494	−	0.284437i
$755$	−10.3739	−	31.9275i	−0.377544	−	1.16196i
$756$	−42.3534	−	30.7715i	−1.54038	−	1.11915i
$757$	25.8272	−	18.7646i	0.938706	−	0.682010i	−0.00940307	−	0.999956i	$-0.502993\pi$
$757$	25.8272	−	18.7646i	0.938706	−	0.682010i	0.948109	+	0.317946i	$0.102993\pi$
$758$	−19.3737	+	59.6262i	−0.703685	+	2.16572i
$759$	3.27300	−	2.37797i	0.118802	−	0.0863150i
$760$	56.2257	−	40.8504i	2.03952	−	1.48180i
$761$	7.85601	−	24.1783i	0.284780	−	0.876463i	−0.701684	−	0.712488i	$-0.747568\pi$
$761$	7.85601	−	24.1783i	0.284780	−	0.876463i	0.986464	−	0.163975i	$-0.0524317\pi$
$762$	−24.6108	+	17.8808i	−0.891556	+	0.647753i
$763$	30.4973	+	22.1576i	1.10408	+	0.802160i
$764$	−10.5714	−	32.5353i	−0.382459	−	1.17709i
$765$	−17.6222	−	12.8033i	−0.637132	−	0.462903i
$766$	2.97810	−	9.16564i	0.107603	−	0.331168i
$767$	3.12034	−	9.60342i	0.112669	−	0.346759i
$768$	−10.1023	−	31.0918i	−0.364536	−	1.12193i
$769$	−17.0881			−0.616212			−0.308106	−	0.951352i	$-0.599695\pi$
$769$	−17.0881			−0.616212			−0.308106	+	0.951352i	$0.599695\pi$
$770$	9.25919			0.333678
$771$	0.00994701	+	0.0306137i	0.000358233	+	0.00110253i
$772$	31.6155	−	22.9700i	1.13786	−	0.826707i
$773$	39.8398	+	28.9453i	1.43294	+	1.04109i	0.989460	+	0.144804i	$0.0462551\pi$
$773$	39.8398	+	28.9453i	1.43294	+	1.04109i	0.443477	+	0.896286i	$0.353745\pi$
$774$	20.9892			0.754442
$775$	−2.36779	−	1.31279i	−0.0850536	−	0.0471569i
$776$	8.80671			0.316143
$777$	22.0707	+	16.0353i	0.791781	+	0.575263i
$778$	−10.5667	+	7.67716i	−0.378835	+	0.275240i
$779$	−19.8964	−	61.2349i	−0.712863	−	2.19397i
$780$	−8.83858			−0.316472
$781$	7.70066			0.275551
$782$	−22.6316	−	69.6528i	−0.809303	−	2.49078i
$783$	8.87604	−	27.3177i	0.317204	−	0.976253i
$784$	−0.199441	+	0.613816i	−0.00712288	+	0.0219220i
$785$	−27.3135	−	19.8444i	−0.974859	−	0.708276i
$786$	−10.6420	−	32.7527i	−0.379587	−	1.16825i
$787$	−35.0256	−	25.4476i	−1.24853	−	0.907110i	−0.250394	−	0.968144i	$-0.580560\pi$
$787$	−35.0256	−	25.4476i	−1.24853	−	0.907110i	−0.998136	+	0.0610346i	$0.980560\pi$
$788$	−13.6525	+	9.91911i	−0.486350	+	0.353354i
$789$	−3.44385	+	10.5991i	−0.122604	+	0.377337i
$790$	−12.9660	+	9.42035i	−0.461310	+	0.335161i
$791$	−4.57727	+	3.32558i	−0.162749	+	0.118244i
$792$	1.74309	−	5.36467i	0.0619379	−	0.190625i
$793$	6.25580	−	4.54510i	0.222150	−	0.161401i
$794$	70.7736	+	51.4200i	2.51166	+	1.82483i
$795$	−2.40502	−	7.40189i	−0.0852972	−	0.262518i
$796$	−43.6271	−	31.6970i	−1.54632	−	1.12347i
$797$	−3.48991	+	10.7408i	−0.123619	+	0.380460i	−0.993647	−	0.112543i	$-0.964101\pi$
$797$	−3.48991	+	10.7408i	−0.123619	+	0.380460i	0.870028	+	0.493002i	$0.164101\pi$
$798$	15.4577	−	47.5739i	0.547196	−	1.68410i
$799$	9.76563	+	30.0555i	0.345483	+	1.06329i
$800$	0.703835			0.0248843
$801$	−5.28145			−0.186611
$802$	−17.4084	−	53.5775i	−0.614711	−	1.89189i
$803$	1.29036	−	0.937500i	0.0455358	−	0.0330837i
$804$	−24.3466	−	17.6889i	−0.858640	−	0.623838i
$805$	−29.9196			−1.05453
$806$	−11.7717	−	6.52670i	−0.414642	−	0.229893i
$807$	−10.0124			−0.352453
$808$	63.8075	+	46.3589i	2.24474	+	1.63090i
$809$	−3.98832	+	2.89769i	−0.140222	+	0.101877i	−0.655685	−	0.755035i	$-0.727620\pi$
$809$	−3.98832	+	2.89769i	−0.140222	+	0.101877i	0.515463	+	0.856912i	$0.327620\pi$
$810$	−0.267627	−	0.823670i	−0.00940344	−	0.0289408i
$811$	−38.0970			−1.33777			−0.668883	−	0.743367i	$-0.733227\pi$
$811$	−38.0970			−1.33777			−0.668883	+	0.743367i	$0.733227\pi$
$812$	55.0644			1.93238
$813$	6.81057	+	20.9608i	0.238857	+	0.735127i
$814$	−4.99921	+	15.3860i	−0.175222	+	0.539279i
$815$	−7.53842	+	23.2009i	−0.264059	+	0.812691i
$816$	15.1648	+	11.0179i	0.530873	+	0.385702i
$817$	10.7636	+	33.1268i	0.376569	+	1.15896i
$818$	−32.7190	−	23.7718i	−1.14399	−	0.831160i
$819$	3.85577	−	2.80138i	0.134732	−	0.0978882i
$820$	22.1478	−	68.1638i	0.773434	−	2.38038i
$821$	−5.40370	+	3.92602i	−0.188591	+	0.137019i	−0.678074	−	0.734993i	$-0.737185\pi$
$821$	−5.40370	+	3.92602i	−0.188591	+	0.137019i	0.489484	+	0.872012i	$0.337185\pi$
$822$	−7.39244	+	5.37092i	−0.257841	+	0.187332i
$823$	7.76660	−	23.9031i	0.270727	−	0.833211i	−0.719592	−	0.694397i	$-0.755671\pi$
$823$	7.76660	−	23.9031i	0.270727	−	0.833211i	0.990319	−	0.138813i	$-0.0443288\pi$
$824$	−17.8205	+	12.9474i	−0.620807	+	0.451043i
$825$	−0.294508	−	0.213973i	−0.0102535	−	0.00744957i
$826$	19.6579	+	60.5008i	0.683986	+	2.10509i
$827$	36.4155	+	26.4574i	1.26629	+	0.920014i	0.999048	−	0.0436151i	$-0.0138875\pi$
$827$	36.4155	+	26.4574i	1.26629	+	0.920014i	0.267243	+	0.963629i	$0.413888\pi$
$828$	−11.7407	+	36.1341i	−0.408017	+	1.25575i
$829$	−0.398954	+	1.22785i	−0.0138562	+	0.0426451i	−0.957746	−	0.287617i	$-0.907137\pi$
$829$	−0.398954	+	1.22785i	−0.0138562	+	0.0426451i	0.943889	+	0.330262i	$0.107137\pi$
$830$	3.39921	+	10.4617i	0.117988	+	0.363131i
$831$	17.1565			0.595153
$832$	9.67871			0.335549
$833$	0.361860	+	1.11369i	0.0125377	+	0.0385871i
$834$	−21.0011	+	15.2582i	−0.727209	+	0.528348i
$835$	10.4023	+	7.55770i	0.359986	+	0.261545i
$836$	19.5122			0.674843
$837$	5.55453	−	28.5606i	0.191993	−	0.987198i
$838$	21.2274			0.733289
$839$	9.39071	+	6.82275i	0.324203	+	0.235548i	0.737967	−	0.674837i	$-0.235786\pi$
$839$	9.39071	+	6.82275i	0.324203	+	0.235548i	−0.413764	+	0.910384i	$0.635786\pi$
$840$	21.6114	−	15.7016i	0.745665	−	0.541757i
$841$	0.374496	+	1.15258i	0.0129137	+	0.0397442i
$842$	−62.3954			−2.15029
$843$	−2.58480			−0.0890252
$844$	−3.83199	−	11.7937i	−0.131903	−	0.405955i
$845$	0.656524	−	2.02057i	0.0225851	−	0.0695098i
$846$	7.70188	−	23.7039i	0.264796	−	0.814958i
$847$	−22.1821	−	16.1163i	−0.762187	−	0.553761i
$848$	−3.23201	−	9.94709i	−0.110988	−	0.341585i
$849$	3.51811	+	2.55606i	0.120741	+	0.0877236i
$850$	−5.33139	+	3.87348i	−0.182865	+	0.132859i
$851$	16.1541	−	49.7173i	0.553757	−	1.70429i
$852$	37.4654	−	27.2202i	1.28354	−	0.932548i
$853$	−31.9601	+	23.2203i	−1.09429	+	0.795049i	−0.980119	−	0.198412i	$-0.936422\pi$
$853$	−31.9601	+	23.2203i	−1.09429	+	0.795049i	−0.114173	+	0.993461i	$0.536422\pi$
$854$	−15.0537	+	46.3304i	−0.515126	+	1.58539i
$855$	−23.0639	+	16.7569i	−0.788770	+	0.573075i
$856$	−22.6398	−	16.4488i	−0.773811	−	0.562207i
$857$	−6.25189	−	19.2413i	−0.213560	−	0.657271i	−0.999253	−	0.0386538i	$-0.987693\pi$
$857$	−6.25189	−	19.2413i	−0.213560	−	0.657271i	0.785692	−	0.618618i	$-0.212307\pi$
$858$	−1.46418	−	1.06379i	−0.0499862	−	0.0363171i
$859$	2.49472	−	7.67797i	0.0851189	−	0.261969i	−0.899434	−	0.437057i	$-0.856021\pi$
$859$	2.49472	−	7.67797i	0.0851189	−	0.261969i	0.984553	+	0.175088i	$0.0560209\pi$
$860$	−11.9815	+	36.8753i	−0.408566	+	1.25744i
$861$	−7.64756	−	23.5368i	−0.260628	−	0.802131i
$862$	−32.8677			−1.11948
$863$	16.7356			0.569688			0.284844	−	0.958574i	$-0.408058\pi$
$863$	16.7356			0.569688			0.284844	+	0.958574i	$0.408058\pi$
$864$	2.33740	+	7.19379i	0.0795201	+	0.244738i
$865$	14.9600	−	10.8691i	0.508655	−	0.369559i
$866$	33.6290	+	24.4329i	1.14276	+	0.830264i
$867$	15.6127			0.530234
$868$	55.3629	−	6.79218i	1.87914	−	0.230542i
$869$	−2.15867			−0.0732277
$870$	24.7162	+	17.9574i	0.837958	+	0.608812i
$871$	5.85228	−	4.25193i	0.198297	−	0.144071i
$872$	19.9297	+	61.3373i	0.674904	+	2.07714i
$873$	−3.61254			−0.122266
$874$	−95.8530			−3.24228
$875$	9.38637	+	28.8883i	0.317317	+	0.976602i
$876$	2.96401	−	9.12228i	0.100145	−	0.308213i
$877$	−9.36977	+	28.8372i	−0.316395	+	0.973762i	0.658782	+	0.752334i	$0.271072\pi$
$877$	−9.36977	+	28.8372i	−0.316395	+	0.973762i	−0.975177	+	0.221429i	$0.928928\pi$
$878$	68.9018	+	50.0601i	2.32532	+	1.68945i
$879$	9.10041	+	28.0082i	0.306949	+	0.944692i
$880$	3.67384	+	2.66920i	0.123845	+	0.0899788i
$881$	37.7509	−	27.4276i	1.27186	−	0.924060i	0.272585	−	0.962132i	$-0.412122\pi$
$881$	37.7509	−	27.4276i	1.27186	−	0.924060i	0.999275	+	0.0380718i	$0.0121216\pi$
$882$	0.285389	−	0.878336i	0.00960953	−	0.0295751i
$883$	−5.85462	+	4.25363i	−0.197024	+	0.143146i	−0.681923	−	0.731424i	$-0.738856\pi$
$883$	−5.85462	+	4.25363i	−0.197024	+	0.143146i	0.484900	+	0.874570i	$0.338856\pi$
$884$	−17.4349	+	12.6672i	−0.586400	+	0.426045i
$885$	−7.17419	+	22.0799i	−0.241158	+	0.742207i
$886$	5.75792	−	4.18337i	0.193441	−	0.140543i
$887$	30.5638	+	22.2059i	1.02623	+	0.745601i	0.967551	−	0.252676i	$-0.0813107\pi$
$887$	30.5638	+	22.2059i	1.02623	+	0.745601i	0.0586803	+	0.998277i	$0.481311\pi$
$888$	14.4229	+	44.3893i	0.484002	+	1.48961i
$889$	24.5149	+	17.8111i	0.822202	+	0.597365i
$890$	4.58337	−	14.1062i	0.153635	−	0.472840i
$891$	0.0360468	−	0.110941i	0.00120761	−	0.00371665i
$892$	33.7506	+	103.874i	1.13005	+	3.47795i
$893$	41.3611			1.38410
$894$	−21.2535			−0.710824
$895$	−2.86548	−	8.81905i	−0.0957825	−	0.294788i
$896$	−43.2266	+	31.4060i	−1.44410	+	1.04920i
$897$	4.73126	+	3.43746i	0.157972	+	0.114773i
$898$	−81.3403			−2.71436
$899$	12.9308	+	27.7374i	0.431267	+	0.925093i
$900$	3.41871			0.113957
$901$	−15.3523	−	11.1541i	−0.511460	−	0.371597i
$902$	11.8730	−	8.62622i	0.395327	−	0.287222i
$903$	4.13718	+	12.7329i	0.137677	+	0.423725i
$904$	−9.67972			−0.321943
$905$	20.8940			0.694542
$906$	−12.7744	−	39.3154i	−0.424400	−	1.30617i
$907$	−15.0963	+	46.4616i	−0.501264	+	1.54273i	0.305698	+	0.952129i	$0.401110\pi$
$907$	−15.0963	+	46.4616i	−0.501264	+	1.54273i	−0.806962	+	0.590604i	$0.798890\pi$
$908$	3.79918	−	11.6927i	0.126080	−	0.388035i
$909$	−26.1740	−	19.0165i	−0.868138	−	0.630739i
$910$	4.13605	+	12.7294i	0.137109	+	0.421977i
$911$	7.29292	+	5.29862i	0.241625	+	0.175551i	0.702007	−	0.712170i	$-0.252287\pi$
$911$	7.29292	+	5.29862i	0.241625	+	0.175551i	−0.460382	+	0.887721i	$0.652287\pi$
$912$	19.8477	−	14.4202i	0.657222	−	0.477500i
$913$	−0.457841	+	1.40909i	−0.0151523	+	0.0466341i
$914$	5.86634	−	4.26215i	0.194041	−	0.140979i
$915$	−14.3831	+	10.4500i	−0.475492	+	0.345465i
$916$	−31.8647	+	98.0696i	−1.05284	+	3.24031i
$917$	−27.7525	+	20.1633i	−0.916467	+	0.665852i
$918$	−57.2956	−	41.6277i	−1.89104	−	1.37392i
$919$	−4.55361	−	14.0146i	−0.150210	−	0.462298i	0.847434	−	0.530900i	$-0.178146\pi$
$919$	−4.55361	−	14.0146i	−0.150210	−	0.462298i	−0.997644	+	0.0686021i	$0.978146\pi$
$920$	−41.4120	−	30.0876i	−1.36531	−	0.991959i
$921$	3.05996	−	9.41759i	0.100829	−	0.310320i
$922$	18.0872	−	55.6667i	0.595670	−	1.83329i
$923$	3.43986	+	10.5868i	0.113224	+	0.348469i
$924$	7.49988			0.246728
$925$	−4.70384			−0.154661
$926$	−22.5266	−	69.3298i	−0.740271	−	2.27832i
$927$	7.31003	−	5.31105i	0.240093	−	0.174438i
$928$	−6.43651	−	4.67639i	−0.211289	−	0.153510i
$929$	4.62058			0.151596			0.0757982	−	0.997123i	$-0.475850\pi$
$929$	4.62058			0.151596			0.0757982	+	0.997123i	$0.475850\pi$
$930$	27.0652	+	15.0060i	0.887504	+	0.492065i
$931$	1.53261			0.0502293
$932$	−88.0889	−	64.0004i	−2.88545	−	2.09640i
$933$	16.8433	−	12.2374i	0.551426	−	0.400635i
$934$	15.2924	+	47.0652i	0.500383	+	1.54002i
$935$	8.23928			0.269453
$936$	8.15393			0.266520
$937$	6.63868	+	20.4318i	0.216876	+	0.667477i	0.999015	+	0.0443724i	$0.0141288\pi$
$937$	6.63868	+	20.4318i	0.216876	+	0.667477i	−0.782139	+	0.623104i	$0.785871\pi$
$938$	−14.0827	+	43.3420i	−0.459815	+	1.41517i
$939$	6.63709	−	20.4268i	0.216593	−	0.666605i
$940$	37.2481	+	27.0624i	1.21490	+	0.882677i
$941$	8.35254	+	25.7065i	0.272285	+	0.838007i	0.989925	+	0.141593i	$0.0452223\pi$
$941$	8.35254	+	25.7065i	0.272285	+	0.838007i	−0.717640	+	0.696414i	$0.754778\pi$
$942$	−33.6337	−	24.4363i	−1.09585	−	0.796179i
$943$	−38.3656	+	27.8742i	−1.24935	+	0.907710i
$944$	−9.64110	+	29.6723i	−0.313791	+	0.965750i
$945$	−23.4069	+	17.0061i	−0.761428	+	0.553210i
$946$	−6.42304	+	4.66661i	−0.208831	+	0.151725i
$947$	0.981180	−	3.01976i	0.0318841	−	0.0981291i	−0.933848	−	0.357670i	$-0.883571\pi$
$947$	0.981180	−	3.01976i	0.0318841	−	0.0981291i	0.965732	+	0.259541i	$0.0835713\pi$
$948$	−10.5024	+	7.63042i	−0.341101	+	0.247825i
$949$	1.86527	+	1.35519i	0.0605491	+	0.0439915i
$950$	2.66526	+	8.20281i	0.0864723	+	0.266134i
$951$	1.49064	+	1.08301i	0.0483372	+	0.0351190i
$952$	20.1274	−	61.9459i	0.652334	−	2.00768i
$953$	15.1208	−	46.5372i	0.489812	−	1.50749i	−0.335076	−	0.942191i	$-0.608762\pi$
$953$	15.1208	−	46.5372i	0.489812	−	1.50749i	0.824888	−	0.565295i	$-0.191238\pi$
$954$	4.62482	+	14.2337i	0.149734	+	0.460834i
$955$	−18.9063			−0.611792
$956$	−88.3030			−2.85592
$957$	1.27158	+	3.91352i	0.0411043	+	0.126506i
$958$	−70.9875	+	51.5754i	−2.29350	+	1.66633i
$959$	7.36362	+	5.34998i	0.237784	+	0.172760i
$960$	−22.2530			−0.718212
$961$	16.4223	+	26.2927i	0.529752	+	0.848152i
$962$	−23.3856			−0.753984
$963$	9.28690	+	6.74733i	0.299266	+	0.217430i
$964$	61.0711	−	44.3707i	1.96697	−	1.42909i
$965$	−6.67392	−	20.5402i	−0.214841	−	0.661213i
$966$	−36.8429			−1.18540
$967$	−5.62031			−0.180737			−0.0903686	−	0.995908i	$-0.528804\pi$
$967$	−5.62031			−0.180737			−0.0903686	+	0.995908i	$0.528804\pi$
$968$	−14.4958	−	44.6134i	−0.465912	−	1.43393i
$969$	13.7550	−	42.3336i	0.441874	−	1.35995i
$970$	3.13505	−	9.64870i	0.100660	−	0.309801i
$971$	28.4794	+	20.6915i	0.913947	+	0.664021i	0.942010	−	0.335585i	$-0.108934\pi$
$971$	28.4794	+	20.6915i	0.913947	+	0.664021i	−0.0280631	+	0.999606i	$0.508934\pi$
$972$	18.4068	+	56.6503i	0.590399	+	1.81706i
$973$	20.9192	+	15.1987i	0.670640	+	0.487249i
$974$	−15.9470	+	11.5861i	−0.510973	+	0.371244i
$975$	0.162612	−	0.500468i	0.00520775	−	0.0160278i
$976$	−19.3289	+	14.0433i	−0.618703	+	0.449514i
$977$	−0.691767	+	0.502598i	−0.0221316	+	0.0160795i	−0.598796	−	0.800902i	$-0.704354\pi$
$977$	−0.691767	+	0.502598i	−0.0221316	+	0.0160795i	0.576664	+	0.816981i	$0.304354\pi$
$978$	−9.28280	+	28.5695i	−0.296831	+	0.913552i
$979$	1.61621	−	1.17424i	0.0516543	−	0.0375290i
$980$	1.38021	+	1.00278i	0.0440891	+	0.0320326i
$981$	−8.17521	−	25.1607i	−0.261014	−	0.803320i
$982$	15.4628	+	11.2344i	0.493439	+	0.358504i
$983$	6.85759	−	21.1055i	0.218723	−	0.673161i	−0.780145	−	0.625599i	$-0.784855\pi$
$983$	6.85759	−	21.1055i	0.218723	−	0.673161i	0.998868	−	0.0475622i	$-0.0151452\pi$
$984$	13.0839	−	40.2681i	0.417099	−	1.28370i
$985$	2.88199	+	8.86987i	0.0918280	+	0.282617i
$986$	74.4911			2.37228
$987$	15.8979			0.506036
$988$	8.71603	+	26.8252i	0.277294	+	0.853423i
$989$	20.7550	−	15.0794i	0.659971	−	0.479497i
$990$	−5.25706	−	3.81948i	−0.167080	−	0.121391i
$991$	20.4813			0.650611			0.325306	−	0.945609i	$-0.394533\pi$
$991$	20.4813			0.650611			0.325306	+	0.945609i	$0.394533\pi$
$992$	−7.04823	−	3.90780i	−0.223781	−	0.124073i
$993$	32.6628			1.03652
$994$	−56.7349	−	41.2204i	−1.79952	−	1.30743i
$995$	−24.1109	+	17.5176i	−0.764367	+	0.555345i
$996$	2.75334	+	8.47390i	0.0872428	+	0.268506i
$997$	−50.6912			−1.60541			−0.802703	−	0.596379i	$-0.796606\pi$
$997$	−50.6912			−1.60541			−0.802703	+	0.596379i	$0.796606\pi$
$998$	−82.8196			−2.62161
$999$	−15.6212	−	48.0772i	−0.494234	−	1.52110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.157.1	✓	48
31.16	even	5	inner	403.2.k.d.326.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.157.1	✓	48	1.1	even	1	trivial
403.2.k.d.326.1	yes	48	31.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95579 - 1.42096i) q^{2} +(-0.875508 + 0.636094i) q^{3} +(1.18794 + 3.65610i) q^{4} +2.12456 q^{5} +2.61618 q^{6} +(-0.805291 - 2.47843i) q^{7} +(1.37774 - 4.24024i) q^{8} +(-0.565152 + 1.73936i) q^{9} +O(q^{10})\)	\(q+(-1.95579 - 1.42096i) q^{2} +(-0.875508 + 0.636094i) q^{3} +(1.18794 + 3.65610i) q^{4} +2.12456 q^{5} +2.61618 q^{6} +(-0.805291 - 2.47843i) q^{7} +(1.37774 - 4.24024i) q^{8} +(-0.565152 + 1.73936i) q^{9} +(-4.15519 - 3.01892i) q^{10} +(-0.213773 - 0.657924i) q^{11} +(-3.36567 - 2.44530i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-1.94678 + 5.99158i) q^{14} +(-1.86007 + 1.35142i) q^{15} +(-2.49967 + 1.81611i) q^{16} +(-1.73234 + 5.33160i) q^{17} +(3.57688 - 2.59876i) q^{18} +(5.93584 + 4.31264i) q^{19} +(2.52384 + 7.76759i) q^{20} +(2.28155 + 1.65765i) q^{21} +(-0.516793 + 1.59052i) q^{22} +(1.66993 - 5.13952i) q^{23} +(1.49097 + 4.58874i) q^{24} -0.486259 q^{25} -2.41749 q^{26} +(-1.61484 - 4.96998i) q^{27} +(8.10475 - 5.88845i) q^{28} +(4.44679 + 3.23078i) q^{29} +5.55821 q^{30} +(4.86941 + 2.69978i) q^{31} -1.44745 q^{32} +(0.605661 + 0.440039i) q^{33} +(10.9641 - 7.96589i) q^{34} +(-1.71089 - 5.26557i) q^{35} -7.03064 q^{36} +9.67353 q^{37} +(-5.48115 - 16.8692i) q^{38} +(-0.334414 + 1.02922i) q^{39} +(2.92708 - 9.00863i) q^{40} +(-7.09946 - 5.15806i) q^{41} +(-2.10678 - 6.48401i) q^{42} +(3.84067 + 2.79041i) q^{43} +(2.15149 - 1.56315i) q^{44} +(-1.20070 + 3.69537i) q^{45} +(-10.5691 + 7.67891i) q^{46} +(4.56063 - 3.31349i) q^{47} +(1.03326 - 3.18005i) q^{48} +(0.168991 - 0.122779i) q^{49} +(0.951019 + 0.690956i) q^{50} +(-1.87472 - 5.76979i) q^{51} +(3.11006 + 2.25959i) q^{52} +(-1.04604 + 3.21938i) q^{53} +(-3.90387 + 12.0149i) q^{54} +(-0.454172 - 1.39780i) q^{55} -11.6186 q^{56} -7.94012 q^{57} +(-4.10616 - 12.6375i) q^{58} +(8.16916 - 5.93524i) q^{59} +(-7.15056 - 5.19519i) q^{60} +7.73259 q^{61} +(-5.68724 - 12.1995i) q^{62} +4.76599 q^{63} +(7.83024 + 5.68900i) q^{64} +(1.71880 - 1.24878i) q^{65} +(-0.559267 - 1.72125i) q^{66} +7.23381 q^{67} -21.5508 q^{68} +(1.80718 + 5.56193i) q^{69} +(-4.13605 + 12.7294i) q^{70} +(-3.43986 + 10.5868i) q^{71} +(6.59667 + 4.79276i) q^{72} +(0.712468 + 2.19275i) q^{73} +(-18.9194 - 13.7457i) q^{74} +(0.425723 - 0.309306i) q^{75} +(-8.71603 + 26.8252i) q^{76} +(-1.45847 + 1.05964i) q^{77} +(2.11653 - 1.53775i) q^{78} +(0.964269 - 2.96771i) q^{79} +(-5.31069 + 3.85844i) q^{80} +(0.136418 + 0.0991135i) q^{81} +(6.55563 + 20.1762i) q^{82} +(-1.73269 - 1.25887i) q^{83} +(-3.35017 + 10.3108i) q^{84} +(-3.68046 + 11.3273i) q^{85} +(-3.54646 - 10.9149i) q^{86} -5.94828 q^{87} -3.08428 q^{88} +(0.892386 + 2.74648i) q^{89} +(7.59930 - 5.52121i) q^{90} +(-2.10828 - 1.53175i) q^{91} +20.7744 q^{92} +(-5.98052 + 0.733719i) q^{93} -13.6280 q^{94} +(12.6110 + 9.16245i) q^{95} +(1.26725 - 0.920714i) q^{96} +(0.610396 + 1.87861i) q^{97} -0.504977 q^{98} +1.26518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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