LMFDB - Embedded newform 35.3.g.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.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:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 70 x^{8} - 248 x^{7} + 464 x^{6} + 432 x^{5} + 1129 x^{4} + \cdots + 100 $ x^12 - 4x^11 + 8x^10 + 8x^9 + 70x^8 - 248x^7 + 464x^6 + 432x^5 + 1129x^4 - 2708x^3 + 3528x^2 + 840*x + 100
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			8.1
Root			$2.47480 - 2.47480i$ of defining polynomial
Character	$\chi$	$=$	35.8
Dual form			35.3.g.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47480 + 2.47480i) q^{2} +(2.98009 + 2.98009i) q^{3} -8.24929i q^{4} +(-4.25027 + 2.63347i) q^{5} -14.7503 q^{6} +(1.87083 - 1.87083i) q^{7} +(10.5161 + 10.5161i) q^{8} +8.76185i q^{9} +O(q^{10})$	\(q+(-2.47480 + 2.47480i) q^{2} +(2.98009 + 2.98009i) q^{3} -8.24929i q^{4} +(-4.25027 + 2.63347i) q^{5} -14.7503 q^{6} +(1.87083 - 1.87083i) q^{7} +(10.5161 + 10.5161i) q^{8} +8.76185i q^{9} +(4.00127 - 17.0359i) q^{10} +11.1838 q^{11} +(24.5836 - 24.5836i) q^{12} +(7.26212 + 7.26212i) q^{13} +9.25986i q^{14} +(-20.5142 - 4.81822i) q^{15} -19.0536 q^{16} +(-2.00247 + 2.00247i) q^{17} +(-21.6838 - 21.6838i) q^{18} -5.59546i q^{19} +(21.7243 + 35.0617i) q^{20} +11.1505 q^{21} +(-27.6777 + 27.6777i) q^{22} +(-6.88848 - 6.88848i) q^{23} +62.6781i q^{24} +(11.1297 - 22.3859i) q^{25} -35.9446 q^{26} +(0.709702 - 0.709702i) q^{27} +(-15.4330 - 15.4330i) q^{28} -46.4655i q^{29} +(62.6926 - 38.8444i) q^{30} -23.7825 q^{31} +(5.08928 - 5.08928i) q^{32} +(33.3287 + 33.3287i) q^{33} -9.91145i q^{34} +(-3.02476 + 12.8783i) q^{35} +72.2790 q^{36} +(-14.8032 + 14.8032i) q^{37} +(13.8476 + 13.8476i) q^{38} +43.2835i q^{39} +(-72.3904 - 17.0025i) q^{40} +31.9337 q^{41} +(-27.5952 + 27.5952i) q^{42} +(-3.79278 - 3.79278i) q^{43} -92.2584i q^{44} +(-23.0741 - 37.2403i) q^{45} +34.0952 q^{46} +(-20.1256 + 20.1256i) q^{47} +(-56.7814 - 56.7814i) q^{48} -7.00000i q^{49} +(27.8570 + 82.9445i) q^{50} -11.9351 q^{51} +(59.9073 - 59.9073i) q^{52} +(-73.4024 - 73.4024i) q^{53} +3.51274i q^{54} +(-47.5342 + 29.4522i) q^{55} +39.3478 q^{56} +(16.6750 - 16.6750i) q^{57} +(114.993 + 114.993i) q^{58} +54.9205i q^{59} +(-39.7469 + 169.227i) q^{60} +96.1646 q^{61} +(58.8570 - 58.8570i) q^{62} +(16.3919 + 16.3919i) q^{63} -51.0244i q^{64} +(-49.9906 - 11.7414i) q^{65} -164.964 q^{66} +(-2.50990 + 2.50990i) q^{67} +(16.5190 + 16.5190i) q^{68} -41.0565i q^{69} +(-24.3856 - 39.3569i) q^{70} -104.612 q^{71} +(-92.1409 + 92.1409i) q^{72} +(20.1046 + 20.1046i) q^{73} -73.2698i q^{74} +(99.8795 - 33.5447i) q^{75} -46.1585 q^{76} +(20.9230 - 20.9230i) q^{77} +(-107.118 - 107.118i) q^{78} +100.405i q^{79} +(80.9830 - 50.1771i) q^{80} +83.0866 q^{81} +(-79.0297 + 79.0297i) q^{82} +(-8.15043 - 8.15043i) q^{83} -91.9834i q^{84} +(3.23761 - 13.7845i) q^{85} +18.7727 q^{86} +(138.471 - 138.471i) q^{87} +(117.610 + 117.610i) q^{88} +39.5406i q^{89} +(149.266 + 35.0585i) q^{90} +27.1724 q^{91} +(-56.8250 + 56.8250i) q^{92} +(-70.8740 - 70.8740i) q^{93} -99.6135i q^{94} +(14.7355 + 23.7822i) q^{95} +30.3330 q^{96} +(-52.3142 + 52.3142i) q^{97} +(17.3236 + 17.3236i) q^{98} +97.9908i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−2.47480	+	2.47480i	−1.23740	+	1.23740i	−0.276341	+	0.961060i	$0.589122\pi$
$2$	−2.47480	+	2.47480i	−1.23740	+	1.23740i	−0.961060	+	0.276341i	$0.910878\pi$
$3$	2.98009	+	2.98009i	0.993363	+	0.993363i	0.999978	−	0.00661536i	$-0.00210575\pi$
$3$	2.98009	+	2.98009i	0.993363	+	0.993363i	−0.00661536	+	0.999978i	$0.502106\pi$
$4$		−	8.24929i		−	2.06232i
$5$	−4.25027	+	2.63347i	−0.850055	+	0.526694i
$5$	−4.25027	+	2.63347i	−0.850055	+	0.526694i
$6$	−14.7503			−2.45838
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	10.5161	+	10.5161i	1.31452	+	1.31452i
$9$			8.76185i			0.973539i
$10$	4.00127	−	17.0359i	0.400127	−	1.70359i
$11$	11.1838			1.01671			0.508355	−	0.861148i	$-0.330254\pi$
$11$	11.1838			1.01671			0.508355	+	0.861148i	$0.330254\pi$
$12$	24.5836	−	24.5836i	2.04863	−	2.04863i
$13$	7.26212	+	7.26212i	0.558625	+	0.558625i	0.928916	−	0.370291i	$-0.120742\pi$
$13$	7.26212	+	7.26212i	0.558625	+	0.558625i	−0.370291	+	0.928916i	$0.620742\pi$
$14$			9.25986i			0.661419i
$15$	−20.5142	−	4.81822i	−1.36761	−	0.321215i
$16$	−19.0536			−1.19085
$17$	−2.00247	+	2.00247i	−0.117793	+	0.117793i	−0.763546	−	0.645753i	$-0.776543\pi$
$17$	−2.00247	+	2.00247i	−0.117793	+	0.117793i	0.645753	+	0.763546i	$0.276543\pi$
$18$	−21.6838	−	21.6838i	−1.20466	−	1.20466i
$19$		−	5.59546i		−	0.294498i	−0.989099	−	0.147249i	$-0.952958\pi$
$19$		−	5.59546i		−	0.294498i	0.989099	−	0.147249i	$-0.0470418\pi$
$20$	21.7243	+	35.0617i	1.08621	+	1.75309i
$21$	11.1505			0.530975
$22$	−27.6777	+	27.6777i	−1.25808	+	1.25808i
$23$	−6.88848	−	6.88848i	−0.299499	−	0.299499i	0.541319	−	0.840818i	$-0.317925\pi$
$23$	−6.88848	−	6.88848i	−0.299499	−	0.299499i	−0.840818	+	0.541319i	$0.817925\pi$
$24$			62.6781i			2.61159i
$25$	11.1297	−	22.3859i	0.445187	−	0.895438i
$26$	−35.9446			−1.38248
$27$	0.709702	−	0.709702i	0.0262852	−	0.0262852i
$28$	−15.4330	−	15.4330i	−0.551179	−	0.551179i
$29$		−	46.4655i		−	1.60226i	−0.598491	−	0.801130i	$-0.704233\pi$
$29$		−	46.4655i		−	1.60226i	0.598491	−	0.801130i	$-0.295767\pi$
$30$	62.6926	−	38.8444i	2.08975	−	1.29481i
$31$	−23.7825			−0.767178			−0.383589	−	0.923504i	$-0.625312\pi$
$31$	−23.7825			−0.767178			−0.383589	+	0.923504i	$0.625312\pi$
$32$	5.08928	−	5.08928i	0.159040	−	0.159040i
$33$	33.3287	+	33.3287i	1.00996	+	1.00996i
$34$		−	9.91145i		−	0.291513i
$35$	−3.02476	+	12.8783i	−0.0864218	+	0.367952i
$36$	72.2790			2.00775
$37$	−14.8032	+	14.8032i	−0.400085	+	0.400085i	−0.878263	−	0.478178i	$-0.841297\pi$
$37$	−14.8032	+	14.8032i	−0.400085	+	0.400085i	0.478178	+	0.878263i	$0.341297\pi$
$38$	13.8476	+	13.8476i	0.364412	+	0.364412i
$39$			43.2835i			1.10983i
$40$	−72.3904	−	17.0025i	−1.80976	−	0.425064i
$41$	31.9337			0.778872			0.389436	−	0.921054i	$-0.372670\pi$
$41$	31.9337			0.778872			0.389436	+	0.921054i	$0.372670\pi$
$42$	−27.5952	+	27.5952i	−0.657029	+	0.657029i
$43$	−3.79278	−	3.79278i	−0.0882041	−	0.0882041i	0.661628	−	0.749832i	$-0.269866\pi$
$43$	−3.79278	−	3.79278i	−0.0882041	−	0.0882041i	−0.749832	+	0.661628i	$0.769866\pi$
$44$		−	92.2584i		−	2.09678i
$45$	−23.0741	−	37.2403i	−0.512757	−	0.827562i
$46$	34.0952			0.741201
$47$	−20.1256	+	20.1256i	−0.428203	+	0.428203i	−0.888016	−	0.459813i	$-0.847917\pi$
$47$	−20.1256	+	20.1256i	−0.428203	+	0.428203i	0.459813	+	0.888016i	$0.347917\pi$
$48$	−56.7814	−	56.7814i	−1.18295	−	1.18295i
$49$		−	7.00000i		−	0.142857i
$50$	27.8570	+	82.9445i	0.557141	+	1.65889i
$51$	−11.9351			−0.234022
$52$	59.9073	−	59.9073i	1.15206	−	1.15206i
$53$	−73.4024	−	73.4024i	−1.38495	−	1.38495i	−0.835577	−	0.549374i	$-0.814866\pi$
$53$	−73.4024	−	73.4024i	−1.38495	−	1.38495i	−0.549374	−	0.835577i	$-0.685134\pi$
$54$			3.51274i			0.0650508i
$55$	−47.5342	+	29.4522i	−0.864259	+	0.535495i
$56$	39.3478			0.702639
$57$	16.6750	−	16.6750i	0.292543	−	0.292543i
$58$	114.993	+	114.993i	1.98264	+	1.98264i
$59$			54.9205i			0.930856i	0.885086	+	0.465428i	$0.154100\pi$
$59$			54.9205i			0.930856i	−0.885086	+	0.465428i	$0.845900\pi$
$60$	−39.7469	+	169.227i	−0.662448	+	2.82045i
$61$	96.1646			1.57647			0.788234	−	0.615375i	$-0.210995\pi$
$61$	96.1646			1.57647			0.788234	+	0.615375i	$0.210995\pi$
$62$	58.8570	−	58.8570i	0.949307	−	0.949307i
$63$	16.3919	+	16.3919i	0.260189	+	0.260189i
$64$		−	51.0244i		−	0.797257i
$65$	−49.9906	−	11.7414i	−0.769086	−	0.180637i
$66$	−164.964			−2.49945
$67$	−2.50990	+	2.50990i	−0.0374613	+	0.0374613i	−0.725589	−	0.688128i	$-0.758433\pi$
$67$	−2.50990	+	2.50990i	−0.0374613	+	0.0374613i	0.688128	+	0.725589i	$0.258433\pi$
$68$	16.5190	+	16.5190i	0.242926	+	0.242926i
$69$		−	41.0565i		−	0.595022i
$70$	−24.3856	−	39.3569i	−0.348365	−	0.562242i
$71$	−104.612			−1.47340			−0.736702	−	0.676218i	$-0.763618\pi$
$71$	−104.612			−1.47340			−0.736702	+	0.676218i	$0.763618\pi$
$72$	−92.1409	+	92.1409i	−1.27973	+	1.27973i
$73$	20.1046	+	20.1046i	0.275406	+	0.275406i	0.831272	−	0.555866i	$-0.187613\pi$
$73$	20.1046	+	20.1046i	0.275406	+	0.275406i	−0.555866	+	0.831272i	$0.687613\pi$
$74$		−	73.2698i		−	0.990132i
$75$	99.8795	−	33.5447i	1.33173	−	0.447262i
$76$	−46.1585			−0.607349
$77$	20.9230	−	20.9230i	0.271727	−	0.271727i
$78$	−107.118	−	107.118i	−1.37331	−	1.37331i
$79$			100.405i			1.27095i	0.772120	+	0.635477i	$0.219197\pi$
$79$			100.405i			1.27095i	−0.772120	+	0.635477i	$0.780803\pi$
$80$	80.9830	−	50.1771i	1.01229	−	0.627213i
$81$	83.0866			1.02576
$82$	−79.0297	+	79.0297i	−0.963776	+	0.963776i
$83$	−8.15043	−	8.15043i	−0.0981979	−	0.0981979i	0.656301	−	0.754499i	$-0.272120\pi$
$83$	−8.15043	−	8.15043i	−0.0981979	−	0.0981979i	−0.754499	+	0.656301i	$0.772120\pi$
$84$		−	91.9834i		−	1.09504i
$85$	3.23761	−	13.7845i	0.0380895	−	0.162171i
$86$	18.7727			0.218288
$87$	138.471	−	138.471i	1.59163	−	1.59163i
$88$	117.610	+	117.610i	1.33648	+	1.33648i
$89$			39.5406i			0.444277i	0.975015	+	0.222138i	$0.0713036\pi$
$89$			39.5406i			0.444277i	−0.975015	+	0.222138i	$0.928696\pi$
$90$	149.266	+	35.0585i	1.65851	+	0.389539i
$91$	27.1724			0.298597
$92$	−56.8250	+	56.8250i	−0.617663	+	0.617663i
$93$	−70.8740	−	70.8740i	−0.762086	−	0.762086i
$94$		−	99.6135i		−	1.05972i
$95$	14.7355	+	23.7822i	0.155110	+	0.250339i
$96$	30.3330			0.315969
$97$	−52.3142	+	52.3142i	−0.539322	+	0.539322i	−0.923330	−	0.384008i	$-0.874543\pi$
$97$	−52.3142	+	52.3142i	−0.539322	+	0.539322i	0.384008	+	0.923330i	$0.374543\pi$
$98$	17.3236	+	17.3236i	0.176772	+	0.176772i
$99$			97.9908i			0.989806i
$100$	−184.668	−	91.8118i	−1.84668	−	0.918118i
$101$	57.9878			0.574137			0.287068	−	0.957910i	$-0.407319\pi$
$101$	57.9878			0.574137			0.287068	+	0.957910i	$0.407319\pi$
$102$	29.5370	−	29.5370i	0.289578	−	0.289578i
$103$	−130.459	−	130.459i	−1.26660	−	1.26660i	−0.947835	−	0.318761i	$-0.896733\pi$
$103$	−130.459	−	130.459i	−1.26660	−	1.26660i	−0.318761	−	0.947835i	$-0.603267\pi$
$104$			152.739i			1.46864i
$105$	−47.3926	+	29.3644i	−0.451358	+	0.279661i
$106$	363.313			3.42748
$107$	54.8743	−	54.8743i	0.512844	−	0.512844i	−0.402553	−	0.915397i	$-0.631877\pi$
$107$	54.8743	−	54.8743i	0.512844	−	0.512844i	0.915397	+	0.402553i	$0.131877\pi$
$108$	−5.85453	−	5.85453i	−0.0542086	−	0.0542086i
$109$			92.2102i			0.845965i	0.906138	+	0.422982i	$0.139017\pi$
$109$			92.2102i			0.845965i	−0.906138	+	0.422982i	$0.860983\pi$
$110$	44.7494	−	190.526i	0.406813	−	1.73206i
$111$	−88.2294			−0.794860
$112$	−35.6460	+	35.6460i	−0.318268	+	0.318268i
$113$	75.6316	+	75.6316i	0.669306	+	0.669306i	0.957555	−	0.288250i	$-0.0930733\pi$
$113$	75.6316	+	75.6316i	0.669306	+	0.669306i	−0.288250	+	0.957555i	$0.593073\pi$
$114$			82.5344i			0.723986i
$115$	47.4185	+	11.1373i	0.412335	+	0.0968463i
$116$	−383.307			−3.30437
$117$	−63.6296	+	63.6296i	−0.543843	+	0.543843i
$118$	−135.917	−	135.917i	−1.15184	−	1.15184i
$119$			7.49257i			0.0629628i
$120$	−165.061	−	266.399i	−1.37551	−	2.21999i
$121$	4.07739			0.0336974
$122$	−237.988	+	237.988i	−1.95072	+	1.95072i
$123$	95.1653	+	95.1653i	0.773702	+	0.773702i
$124$			196.189i			1.58217i
$125$	11.6486	+	124.456i	0.0931885	+	0.995648i
$126$	−81.1335			−0.643917
$127$	−36.8683	+	36.8683i	−0.290301	+	0.290301i	−0.837199	−	0.546898i	$-0.815809\pi$
$127$	−36.8683	+	36.8683i	−0.290301	+	0.290301i	0.546898	+	0.837199i	$0.315809\pi$
$128$	146.632	+	146.632i	1.14557	+	1.14557i
$129$		−	22.6056i		−	0.175237i
$130$	152.774	−	94.6590i	1.17519	−	0.728147i
$131$	−139.325			−1.06355			−0.531775	−	0.846886i	$-0.678475\pi$
$131$	−139.325			−1.06355			−0.531775	+	0.846886i	$0.678475\pi$
$132$	274.938	−	274.938i	2.08286	−	2.08286i
$133$	−10.4681	−	10.4681i	−0.0787078	−	0.0787078i
$134$		−	12.4230i		−	0.0927092i
$135$	−1.14745	+	4.88541i	−0.00849962	+	0.0361882i
$136$	−42.1166			−0.309681
$137$	93.0650	−	93.0650i	0.679307	−	0.679307i	−0.280537	−	0.959843i	$-0.590512\pi$
$137$	93.0650	−	93.0650i	0.679307	−	0.679307i	0.959843	+	0.280537i	$0.0905124\pi$
$138$	101.607	+	101.607i	0.736281	+	0.736281i
$139$		−	109.594i		−	0.788449i	−0.919014	−	0.394225i	$-0.871013\pi$
$139$		−	109.594i		−	0.788449i	0.919014	−	0.394225i	$-0.128987\pi$
$140$	106.237	+	24.9521i	0.758835	+	0.178230i
$141$	−119.952			−0.850722
$142$	258.893	−	258.893i	1.82319	−	1.82319i
$143$	81.2181	+	81.2181i	0.567959	+	0.567959i
$144$		−	166.945i		−	1.15934i
$145$	122.366	+	197.491i	0.843901	+	1.36201i
$146$	−99.5100			−0.681576
$147$	20.8606	−	20.8606i	0.141909	−	0.141909i
$148$	122.116	+	122.116i	0.825105	+	0.825105i
$149$		−	108.363i		−	0.727268i	−0.931542	−	0.363634i	$-0.881536\pi$
$149$		−	108.363i		−	0.727268i	0.931542	−	0.363634i	$-0.118464\pi$
$150$	−164.165	+	330.198i	−1.09444	+	2.20132i
$151$	−45.6514			−0.302327			−0.151163	−	0.988509i	$-0.548302\pi$
$151$	−45.6514			−0.302327			−0.151163	+	0.988509i	$0.548302\pi$
$152$	58.8426	−	58.8426i	0.387122	−	0.387122i
$153$	−17.5454	−	17.5454i	−0.114676	−	0.114676i
$154$			103.560i			0.672470i
$155$	101.082	−	62.6306i	0.652144	−	0.404068i
$156$	357.058			2.28883
$157$	−90.6669	+	90.6669i	−0.577496	+	0.577496i	−0.934213	−	0.356717i	$-0.883896\pi$
$157$	−90.6669	+	90.6669i	−0.577496	+	0.577496i	0.356717	+	0.934213i	$0.383896\pi$
$158$	−248.483	−	248.483i	−1.57268	−	1.57268i
$159$		−	437.491i		−	2.75152i
$160$	−8.22837	+	35.0333i	−0.0514273	+	0.218958i
$161$	−25.7743			−0.160089
$162$	−205.623	+	205.623i	−1.26928	+	1.26928i
$163$	−178.839	−	178.839i	−1.09717	−	1.09717i	−0.994740	−	0.102433i	$-0.967337\pi$
$163$	−178.839	−	178.839i	−1.09717	−	1.09717i	−0.102433	−	0.994740i	$-0.532663\pi$
$164$		−	263.431i		−	1.60628i
$165$	−229.426	−	53.8860i	−1.39046	−	0.326582i
$166$	40.3414			0.243020
$167$	157.960	−	157.960i	0.945869	−	0.945869i	−0.0527393	−	0.998608i	$-0.516795\pi$
$167$	157.960	−	157.960i	0.945869	−	0.945869i	0.998608	+	0.0527393i	$0.0167952\pi$
$168$	117.260	+	117.260i	0.697976	+	0.697976i
$169$		−	63.5233i		−	0.375877i
$170$	26.1015	+	42.1264i	0.153538	+	0.247802i
$171$	49.0266			0.286705
$172$	−31.2877	+	31.2877i	−0.181905	+	0.181905i
$173$	65.1561	+	65.1561i	0.376625	+	0.376625i	0.869883	−	0.493258i	$-0.164194\pi$
$173$	65.1561	+	65.1561i	0.376625	+	0.376625i	−0.493258	+	0.869883i	$0.664194\pi$
$174$			685.378i			3.93896i
$175$	−21.0586	−	62.7020i	−0.120335	−	0.358297i
$176$	−213.092			−1.21075
$177$	−163.668	+	163.668i	−0.924678	+	0.924678i
$178$	−97.8552	−	97.8552i	−0.549748	−	0.549748i
$179$			35.7508i			0.199725i	0.995001	+	0.0998625i	$0.0318403\pi$
$179$			35.7508i			0.199725i	−0.995001	+	0.0998625i	$0.968160\pi$
$180$	−307.206	+	190.345i	−1.70670	+	1.05747i
$181$	−99.3391			−0.548835			−0.274417	−	0.961611i	$-0.588485\pi$
$181$	−99.3391			−0.548835			−0.274417	+	0.961611i	$0.588485\pi$
$182$	−67.2462	+	67.2462i	−0.369485	+	0.369485i
$183$	286.579	+	286.579i	1.56601	+	1.56601i
$184$		−	144.880i		−	0.787394i
$185$	23.9338	−	101.901i	0.129372	−	0.550817i
$186$	350.798			1.88601
$187$	−22.3953	+	22.3953i	−0.119761	+	0.119761i
$188$	166.021	+	166.021i	0.883093	+	0.883093i
$189$		−	2.65546i		−	0.0140501i
$190$	−95.3236	−	22.3889i	−0.501703	−	0.117836i
$191$	137.323			0.718969			0.359484	−	0.933151i	$-0.382953\pi$
$191$	137.323			0.718969			0.359484	+	0.933151i	$0.382953\pi$
$192$	152.057	−	152.057i	0.791965	−	0.791965i
$193$	16.6384	+	16.6384i	0.0862093	+	0.0862093i	0.748896	−	0.662687i	$-0.230584\pi$
$193$	16.6384	+	16.6384i	0.0862093	+	0.0862093i	−0.662687	+	0.748896i	$0.730584\pi$
$194$		−	258.935i		−	1.33471i
$195$	−113.986	−	183.967i	−0.584543	−	0.943419i
$196$	−57.7450			−0.294617
$197$	149.241	−	149.241i	0.757566	−	0.757566i	−0.218313	−	0.975879i	$-0.570055\pi$
$197$	149.241	−	149.241i	0.757566	−	0.757566i	0.975879	+	0.218313i	$0.0700552\pi$
$198$	−242.508	−	242.508i	−1.22479	−	1.22479i
$199$			357.480i			1.79638i	0.439604	+	0.898192i	$0.355119\pi$
$199$			357.480i			1.79638i	−0.439604	+	0.898192i	$0.644881\pi$
$200$	352.455	−	118.373i	1.76227	−	0.591863i
$201$	−14.9595			−0.0744252
$202$	−143.508	+	143.508i	−0.710437	+	0.710437i
$203$	−86.9290	−	86.9290i	−0.428222	−	0.428222i
$204$			98.4561i			0.482628i
$205$	−135.727	+	84.0965i	−0.662084	+	0.410227i
$206$	645.722			3.13457
$207$	60.3558	−	60.3558i	0.291574	−	0.291574i
$208$	−138.369	−	138.369i	−0.665238	−	0.665238i
$209$		−	62.5785i		−	0.299418i
$210$	44.6160	−	189.958i	0.212457	−	0.904563i
$211$	−41.6232			−0.197266			−0.0986331	−	0.995124i	$-0.531447\pi$
$211$	−41.6232			−0.197266			−0.0986331	+	0.995124i	$0.531447\pi$
$212$	−605.517	+	605.517i	−2.85621	+	2.85621i
$213$	−311.752	−	311.752i	−1.46362	−	1.46362i
$214$			271.606i			1.26919i
$215$	26.1085	+	6.13218i	0.121435	+	0.0285218i
$216$	14.9266			0.0691049
$217$	−44.4930	+	44.4930i	−0.205037	+	0.205037i
$218$	−228.202	−	228.202i	−1.04680	−	1.04680i
$219$			119.827i			0.547156i
$220$	242.960	+	392.123i	1.10436	+	1.78238i
$221$	−29.0844			−0.131604
$222$	218.350	−	218.350i	0.983560	−	0.983560i
$223$	87.8267	+	87.8267i	0.393842	+	0.393842i	0.876054	−	0.482213i	$-0.160167\pi$
$223$	87.8267	+	87.8267i	0.393842	+	0.393842i	−0.482213	+	0.876054i	$0.660167\pi$
$224$		−	19.0423i		−	0.0850105i
$225$	196.142	+	97.5165i	0.871744	+	0.433407i
$226$	−374.346			−1.65640
$227$	−305.149	+	305.149i	−1.34427	+	1.34427i	−0.452506	+	0.891762i	$0.649470\pi$
$227$	−305.149	+	305.149i	−1.34427	+	1.34427i	−0.891762	+	0.452506i	$0.850530\pi$
$228$	−137.556	−	137.556i	−0.603318	−	0.603318i
$229$		−	172.991i		−	0.755421i	−0.925924	−	0.377710i	$-0.876712\pi$
$229$		−	172.991i		−	0.755421i	0.925924	−	0.377710i	$-0.123288\pi$
$230$	−144.914	+	89.7888i	−0.630061	+	0.390386i
$231$	124.705			0.539847
$232$	488.638	−	488.638i	2.10620	−	2.10620i
$233$	121.883	+	121.883i	0.523103	+	0.523103i	0.918507	−	0.395404i	$-0.129395\pi$
$233$	121.883	+	121.883i	0.523103	+	0.523103i	−0.395404	+	0.918507i	$0.629395\pi$
$234$		−	314.941i		−	1.34590i
$235$	32.5391	−	138.539i	0.138464	−	0.589528i
$236$	453.055			1.91973
$237$	−299.217	+	299.217i	−1.26252	+	1.26252i
$238$	−18.5426	−	18.5426i	−0.0779102	−	0.0779102i
$239$			28.2098i			0.118033i	0.998257	+	0.0590164i	$0.0187964\pi$
$239$			28.2098i			0.118033i	−0.998257	+	0.0590164i	$0.981204\pi$
$240$	390.868	+	91.8044i	1.62862	+	0.382518i
$241$	271.712			1.12743			0.563717	−	0.825968i	$-0.309371\pi$
$241$	271.712			1.12743			0.563717	+	0.825968i	$0.309371\pi$
$242$	−10.0907	+	10.0907i	−0.0416972	+	0.0416972i
$243$	241.218	+	241.218i	0.992667	+	0.992667i
$244$		−	793.289i		−	3.25119i
$245$	18.4343	+	29.7519i	0.0752420	+	0.121436i
$246$	−471.031			−1.91476
$247$	40.6349	−	40.6349i	0.164514	−	0.164514i
$248$	−250.100	−	250.100i	−1.00847	−	1.00847i
$249$		−	48.5780i		−	0.195092i
$250$	−336.832	−	279.176i	−1.34733	−	1.11670i
$251$	171.914			0.684916			0.342458	−	0.939533i	$-0.388740\pi$
$251$	171.914			0.684916			0.342458	+	0.939533i	$0.388740\pi$
$252$	135.222	−	135.222i	0.536594	−	0.536594i
$253$	−77.0394	−	77.0394i	−0.304503	−	0.304503i
$254$		−	182.483i		−	0.718438i
$255$	50.7275	−	31.4307i	0.198931	−	0.123258i
$256$	−521.675			−2.03779
$257$	−222.767	+	222.767i	−0.866796	+	0.866796i	−0.992116	−	0.125320i	$-0.960004\pi$
$257$	−222.767	+	222.767i	−0.866796	+	0.866796i	0.125320	+	0.992116i	$0.460004\pi$
$258$	55.9444	+	55.9444i	0.216839	+	0.216839i
$259$			55.3884i			0.213855i
$260$	−96.8584	+	412.387i	−0.372532	+	1.58610i
$261$	407.124			1.55986
$262$	344.802	−	344.802i	1.31604	−	1.31604i
$263$	316.492	+	316.492i	1.20339	+	1.20339i	0.973128	+	0.230263i	$0.0739586\pi$
$263$	316.492	+	316.492i	1.20339	+	1.20339i	0.230263	+	0.973128i	$0.426041\pi$
$264$			700.979i			2.65522i
$265$	505.283	+	118.677i	1.90673	+	0.447839i
$266$	51.8131			0.194786
$267$	−117.835	+	117.835i	−0.441328	+	0.441328i
$268$	20.7049	+	20.7049i	0.0772572	+	0.0772572i
$269$		−	40.2370i		−	0.149580i	−0.997199	−	0.0747900i	$-0.976171\pi$
$269$		−	40.2370i		−	0.149580i	0.997199	−	0.0747900i	$-0.0238286\pi$
$270$	−9.25070	−	14.9301i	−0.0342619	−	0.0552967i
$271$	−257.857			−0.951502			−0.475751	−	0.879580i	$-0.657824\pi$
$271$	−257.857			−0.951502			−0.475751	+	0.879580i	$0.657824\pi$
$272$	38.1543	−	38.1543i	0.140273	−	0.140273i
$273$	80.9760	+	80.9760i	0.296615	+	0.296615i
$274$			460.635i			1.68115i
$275$	124.472	−	250.360i	0.452625	−	0.910400i
$276$	−338.687			−1.22713
$277$	138.225	−	138.225i	0.499008	−	0.499008i	−0.412121	−	0.911129i	$-0.635212\pi$
$277$	138.225	−	138.225i	0.499008	−	0.499008i	0.911129	+	0.412121i	$0.135212\pi$
$278$	271.224	+	271.224i	0.975628	+	0.975628i
$279$		−	208.379i		−	0.746878i
$280$	−167.239	+	103.621i	−0.597282	+	0.370076i
$281$	−262.860			−0.935444			−0.467722	−	0.883876i	$-0.654925\pi$
$281$	−262.860			−0.935444			−0.467722	+	0.883876i	$0.654925\pi$
$282$	296.857	−	296.857i	1.05268	−	1.05268i
$283$	−318.852	−	318.852i	−1.12669	−	1.12669i	−0.990713	−	0.135972i	$-0.956584\pi$
$283$	−318.852	−	318.852i	−1.12669	−	1.12669i	−0.135972	−	0.990713i	$-0.543416\pi$
$284$			862.972i			3.03863i
$285$	−26.9601	+	114.786i	−0.0945970	+	0.402758i
$286$	−401.997			−1.40558
$287$	59.7425	−	59.7425i	0.208162	−	0.208162i
$288$	44.5915	+	44.5915i	0.154832	+	0.154832i
$289$			280.980i			0.972250i
$290$	−791.582	−	185.921i	−2.72959	−	0.641107i
$291$	−311.802			−1.07148
$292$	165.849	−	165.849i	0.567976	−	0.567976i
$293$	−87.4554	−	87.4554i	−0.298483	−	0.298483i	0.541937	−	0.840419i	$-0.317691\pi$
$293$	−87.4554	−	87.4554i	−0.298483	−	0.298483i	−0.840419	+	0.541937i	$0.817691\pi$
$294$			103.252i			0.351197i
$295$	−144.632	−	233.427i	−0.490277	−	0.791279i
$296$	−311.344			−1.05184
$297$	7.93716	−	7.93716i	0.0267245	−	0.0267245i
$298$	268.177	+	268.177i	0.899922	+	0.899922i
$299$		−	100.050i		−	0.334615i
$300$	−276.720	−	823.935i	−0.922399	−	2.74645i
$301$	−14.1913			−0.0471471
$302$	112.978	−	112.978i	0.374100	−	0.374100i
$303$	172.809	+	172.809i	0.570326	+	0.570326i
$304$			106.614i			0.350702i
$305$	−408.726	+	253.247i	−1.34009	+	0.830317i
$306$	86.8427			0.283800
$307$	−89.7388	+	89.7388i	−0.292309	+	0.292309i	−0.837992	−	0.545683i	$-0.816270\pi$
$307$	−89.7388	+	89.7388i	−0.292309	+	0.292309i	0.545683	+	0.837992i	$0.316270\pi$
$308$	−172.600	−	172.600i	−0.560388	−	0.560388i
$309$		−	777.561i		−	2.51638i
$310$	−95.1603	+	405.157i	−0.306969	+	1.30696i
$311$	−206.628			−0.664400			−0.332200	−	0.943209i	$-0.607791\pi$
$311$	−206.628			−0.664400			−0.332200	+	0.943209i	$0.607791\pi$
$312$	−455.176	+	455.176i	−1.45890	+	1.45890i
$313$	−174.161	−	174.161i	−0.556425	−	0.556425i	0.371863	−	0.928288i	$-0.378719\pi$
$313$	−174.161	−	174.161i	−0.556425	−	0.556425i	−0.928288	+	0.371863i	$0.878719\pi$
$314$		−	448.765i		−	1.42919i
$315$	−112.838	−	26.5025i	−0.358215	−	0.0841350i
$316$	828.273			2.62112
$317$	393.047	−	393.047i	1.23990	−	1.23990i	0.279853	−	0.960043i	$-0.409714\pi$
$317$	393.047	−	393.047i	1.23990	−	1.23990i	0.960043	−	0.279853i	$-0.0902857\pi$
$318$	1082.70	+	1082.70i	3.40473	+	3.40473i
$319$		−	519.661i		−	1.62903i
$320$	134.371	+	216.868i	0.419910	+	0.677712i
$321$	327.061			1.01888
$322$	63.7863	−	63.7863i	0.198094	−	0.198094i
$323$	11.2048	+	11.2048i	0.0346896	+	0.0346896i
$324$		−	685.405i		−	2.11545i
$325$	243.394	−	81.7444i	0.748906	−	0.251521i
$326$	885.183			2.71529
$327$	−274.794	+	274.794i	−0.840350	+	0.840350i
$328$	335.820	+	335.820i	1.02384	+	1.02384i
$329$			75.3029i			0.228884i
$330$	701.142	−	434.428i	2.12467	−	1.31645i
$331$	−67.4895			−0.203896			−0.101948	−	0.994790i	$-0.532507\pi$
$331$	−67.4895			−0.203896			−0.101948	+	0.994790i	$0.532507\pi$
$332$	−67.2352	+	67.2352i	−0.202516	+	0.202516i
$333$	−129.703	−	129.703i	−0.389499	−	0.389499i
$334$			781.840i			2.34084i
$335$	4.05802	−	17.2775i	0.0121135	−	0.0515747i
$336$	−212.456			−0.632311
$337$	−114.802	+	114.802i	−0.340660	+	0.340660i	−0.856615	−	0.515956i	$-0.827437\pi$
$337$	−114.802	+	114.802i	−0.340660	+	0.340660i	0.515956	+	0.856615i	$0.327437\pi$
$338$	157.207	+	157.207i	0.465111	+	0.465111i
$339$			450.777i			1.32973i
$340$	−113.712	−	26.7080i	−0.334448	−	0.0785529i
$341$	−265.979			−0.779997
$342$	−121.331	+	121.331i	−0.354769	+	0.354769i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$		−	79.7707i		−	0.231892i
$345$	108.121	+	174.502i	0.313395	+	0.505802i
$346$	−322.497			−0.932071
$347$	14.5931	−	14.5931i	0.0420550	−	0.0420550i	−0.685767	−	0.727822i	$-0.740533\pi$
$347$	14.5931	−	14.5931i	0.0420550	−	0.0420550i	0.727822	+	0.685767i	$0.240533\pi$
$348$	−1142.29	−	1142.29i	−3.28244	−	3.28244i
$349$			462.318i			1.32469i	0.749198	+	0.662347i	$0.230439\pi$
$349$			462.318i			1.32469i	−0.749198	+	0.662347i	$0.769561\pi$
$350$	207.291	+	103.059i	0.592259	+	0.294455i
$351$	10.3079			0.0293672
$352$	56.9175	−	56.9175i	0.161697	−	0.161697i
$353$	−51.6991	−	51.6991i	−0.146456	−	0.146456i	0.630077	−	0.776533i	$-0.283023\pi$
$353$	−51.6991	−	51.6991i	−0.146456	−	0.146456i	−0.776533	+	0.630077i	$0.783023\pi$
$354$		−	810.092i		−	2.28840i
$355$	444.628	−	275.492i	1.25247	−	0.776033i
$356$	326.182			0.916241
$357$	−22.3285	+	22.3285i	−0.0625449	+	0.0625449i
$358$	−88.4761	−	88.4761i	−0.247140	−	0.247140i
$359$		−	196.132i		−	0.546329i	−0.961967	−	0.273164i	$-0.911930\pi$
$359$		−	196.132i		−	0.546329i	0.961967	−	0.273164i	$-0.0880703\pi$
$360$	148.974	−	634.274i	0.413816	−	1.76187i
$361$	329.691			0.913271
$362$	245.844	−	245.844i	0.679128	−	0.679128i
$363$	12.1510	+	12.1510i	0.0334738	+	0.0334738i
$364$		−	224.153i		−	0.615804i
$365$	−138.395	−	32.5053i	−0.379165	−	0.0890556i
$366$	−1418.45			−3.87555
$367$	144.016	−	144.016i	0.392415	−	0.392415i	−0.483133	−	0.875547i	$-0.660501\pi$
$367$	144.016	−	144.016i	0.392415	−	0.392415i	0.875547	+	0.483133i	$0.160501\pi$
$368$	131.250	+	131.250i	0.356658	+	0.356658i
$369$			279.799i			0.758262i
$370$	192.954	+	311.417i	0.521497	+	0.841667i
$371$	−274.647			−0.740287
$372$	−584.660	+	584.660i	−1.57167	+	1.57167i
$373$	−60.0380	−	60.0380i	−0.160960	−	0.160960i	0.622032	−	0.782992i	$-0.286307\pi$
$373$	−60.0380	−	60.0380i	−0.160960	−	0.160960i	−0.782992	+	0.622032i	$0.786307\pi$
$374$		−	110.848i		−	0.296384i
$375$	−336.176	+	405.604i	−0.896470	+	1.08161i
$376$	−423.286			−1.12576
$377$	337.438	−	337.438i	0.895061	−	0.895061i
$378$	6.57174	+	6.57174i	0.0173856	+	0.0173856i
$379$			516.516i			1.36284i	0.731893	+	0.681419i	$0.238637\pi$
$379$			516.516i			1.36284i	−0.731893	+	0.681419i	$0.761363\pi$
$380$	196.186	−	121.557i	0.516280	−	0.319887i
$381$	−219.741			−0.576749
$382$	−339.847	+	339.847i	−0.889653	+	0.889653i
$383$	202.403	+	202.403i	0.528468	+	0.528468i	0.920115	−	0.391648i	$-0.128095\pi$
$383$	202.403	+	202.403i	0.528468	+	0.528468i	−0.391648	+	0.920115i	$0.628095\pi$
$384$			873.955i			2.27593i
$385$	−33.8284	+	144.028i	−0.0878659	+	0.374100i
$386$	−82.3535			−0.213351
$387$	33.2317	−	33.2317i	0.0858701	−	0.0858701i
$388$	431.555	+	431.555i	1.11225	+	1.11225i
$389$			563.048i			1.44742i	0.690102	+	0.723712i	$0.257566\pi$
$389$			563.048i			1.44742i	−0.690102	+	0.723712i	$0.742434\pi$
$390$	737.374	+	173.189i	1.89070	+	0.444074i
$391$	27.5880			0.0705575
$392$	73.6130	−	73.6130i	0.187788	−	0.187788i
$393$	−415.201	−	415.201i	−1.05649	−	1.05649i
$394$			738.682i			1.87483i
$395$	−264.415	−	426.750i	−0.669404	−	1.08038i
$396$	808.354			2.04130
$397$	426.739	−	426.739i	1.07491	−	1.07491i	0.0779509	−	0.996957i	$-0.475162\pi$
$397$	426.739	−	426.739i	1.07491	−	1.07491i	0.996957	−	0.0779509i	$-0.0248378\pi$
$398$	−884.693	−	884.693i	−2.22285	−	2.22285i
$399$		−	62.3920i		−	0.156371i
$400$	−212.060	+	426.533i	−0.530150	+	1.06633i
$401$	15.9500			0.0397757			0.0198878	−	0.999802i	$-0.493669\pi$
$401$	15.9500			0.0397757			0.0198878	+	0.999802i	$0.493669\pi$
$402$	37.0217	−	37.0217i	0.0920938	−	0.0920938i
$403$	−172.712	−	172.712i	−0.428565	−	0.428565i
$404$		−	478.358i		−	1.18405i
$405$	−353.141	+	218.806i	−0.871953	+	0.540262i
$406$	430.264			1.05976
$407$	−165.556	+	165.556i	−0.406770	+	0.406770i
$408$	−125.511	−	125.511i	−0.307626	−	0.307626i
$409$		−	556.959i		−	1.36176i	−0.732395	−	0.680880i	$-0.761598\pi$
$409$		−	556.959i		−	1.36176i	0.732395	−	0.680880i	$-0.238402\pi$
$410$	127.776	−	544.020i	0.311648	−	1.32688i
$411$	554.684			1.34960
$412$	−1076.20	+	1076.20i	−2.61213	+	2.61213i
$413$	102.747	+	102.747i	0.248782	+	0.248782i
$414$			298.737i			0.721588i
$415$	56.1055	+	13.1777i	0.135194	+	0.0317534i
$416$	73.9179			0.177687
$417$	326.601	−	326.601i	0.783216	−	0.783216i
$418$	154.869	+	154.869i	0.370501	+	0.370501i
$419$			412.995i			0.985667i	0.870124	+	0.492834i	$0.164039\pi$
$419$			412.995i			0.985667i	−0.870124	+	0.492834i	$0.835961\pi$
$420$	242.236	+	390.955i	0.576751	+	0.930845i
$421$	295.939			0.702942			0.351471	−	0.936199i	$-0.385682\pi$
$421$	295.939			0.702942			0.351471	+	0.936199i	$0.385682\pi$
$422$	103.009	−	103.009i	0.244097	−	0.244097i
$423$	−176.337	−	176.337i	−0.416873	−	0.416873i
$424$		−	1543.82i		−	3.64108i
$425$	22.5404	+	67.1142i	0.0530362	+	0.157916i
$426$	1543.05			3.62218
$427$	179.907	−	179.907i	0.421329	−	0.421329i
$428$	−452.674	−	452.674i	−1.05765	−	1.05765i
$429$			484.074i			1.12838i
$430$	−79.7893	+	49.4374i	−0.185556	+	0.114971i
$431$	−667.943			−1.54975			−0.774876	−	0.632113i	$-0.782188\pi$
$431$	−667.943			−1.54975			−0.774876	+	0.632113i	$0.782188\pi$
$432$	−13.5224	+	13.5224i	−0.0313018	+	0.0313018i
$433$	374.119	+	374.119i	0.864016	+	0.864016i	0.991802	−	0.127786i	$-0.0407870\pi$
$433$	374.119	+	374.119i	0.864016	+	0.864016i	−0.127786	+	0.991802i	$0.540787\pi$
$434$		−	220.223i		−	0.507426i
$435$	−223.881	+	953.202i	−0.514669	+	2.19127i
$436$	760.668			1.74465
$437$	−38.5442	+	38.5442i	−0.0882018	+	0.0882018i
$438$	−296.549	−	296.549i	−0.677052	−	0.677052i
$439$			64.2323i			0.146315i	0.997320	+	0.0731575i	$0.0233076\pi$
$439$			64.2323i			0.146315i	−0.997320	+	0.0731575i	$0.976692\pi$
$440$	−809.600	−	190.153i	−1.84000	−	0.432166i
$441$	61.3330			0.139077
$442$	71.9782	−	71.9782i	0.162846	−	0.162846i
$443$	−50.2702	−	50.2702i	−0.113477	−	0.113477i	0.648088	−	0.761565i	$-0.275569\pi$
$443$	−50.2702	−	50.2702i	−0.113477	−	0.113477i	−0.761565	+	0.648088i	$0.775569\pi$
$444$			727.830i			1.63926i
$445$	−104.129	−	168.058i	−0.233998	−	0.377659i
$446$	−434.707			−0.974680
$447$	322.931	−	322.931i	0.722441	−	0.722441i
$448$	−95.4580	−	95.4580i	−0.213076	−	0.213076i
$449$		−	787.793i		−	1.75455i	−0.479989	−	0.877275i	$-0.659359\pi$
$449$		−	787.793i		−	1.75455i	0.479989	−	0.877275i	$-0.340641\pi$
$450$	−726.747	+	244.079i	−1.61499	+	0.542398i
$451$	357.140			0.791886
$452$	623.906	−	623.906i	1.38032	−	1.38032i
$453$	−136.045	−	136.045i	−0.300320	−	0.300320i
$454$		−	1510.36i		−	3.32679i
$455$	−115.490	+	71.5576i	−0.253824	+	0.157269i
$456$	350.712			0.769106
$457$	−55.5109	+	55.5109i	−0.121468	+	0.121468i	−0.765228	−	0.643760i	$-0.777374\pi$
$457$	−55.5109	+	55.5109i	−0.121468	+	0.121468i	0.643760	+	0.765228i	$0.277374\pi$
$458$	428.119	+	428.119i	0.934758	+	0.934758i
$459$			2.84232i			0.00619242i
$460$	91.8750	−	391.169i	0.199728	−	0.850367i
$461$	−703.204			−1.52539			−0.762694	−	0.646759i	$-0.776124\pi$
$461$	−703.204			−1.52539			−0.762694	+	0.646759i	$0.776124\pi$
$462$	−308.619	+	308.619i	−0.668007	+	0.668007i
$463$	334.966	+	334.966i	0.723468	+	0.723468i	0.969310	−	0.245842i	$-0.0790644\pi$
$463$	334.966	+	334.966i	0.723468	+	0.723468i	−0.245842	+	0.969310i	$0.579064\pi$
$464$			885.335i			1.90805i
$465$	487.879	+	114.589i	1.04920	+	0.246429i
$466$	−603.272			−1.29458
$467$	−137.940	+	137.940i	−0.295374	+	0.295374i	−0.839199	−	0.543825i	$-0.816976\pi$
$467$	−137.940	+	137.940i	−0.295374	+	0.295374i	0.543825	+	0.839199i	$0.316976\pi$
$468$	524.899	+	524.899i	1.12158	+	1.12158i
$469$			9.39120i			0.0200239i
$470$	262.329	+	423.385i	0.558147	+	0.900819i
$471$	−540.391			−1.14733
$472$	−577.552	+	577.552i	−1.22363	+	1.22363i
$473$	−42.4177	−	42.4177i	−0.0896779	−	0.0896779i
$474$		−	1481.00i		−	3.12448i
$475$	−125.260	−	62.2756i	−0.263704	−	0.131106i
$476$	61.8084			0.129850
$477$	643.141	−	643.141i	1.34830	−	1.34830i
$478$	−69.8137	−	69.8137i	−0.146054	−	0.146054i
$479$			542.255i			1.13206i	0.824386	+	0.566028i	$0.191521\pi$
$479$			542.255i			1.13206i	−0.824386	+	0.566028i	$0.808479\pi$
$480$	−128.924	+	79.8811i	−0.268591	+	0.166419i
$481$	−215.005			−0.446995
$482$	−672.432	+	672.432i	−1.39509	+	1.39509i
$483$	−76.8098	−	76.8098i	−0.159026	−	0.159026i
$484$		−	33.6356i		−	0.0694950i
$485$	84.5818	−	360.118i	0.174396	−	0.742511i
$486$	−1193.93			−2.45665
$487$	−389.386	+	389.386i	−0.799561	+	0.799561i	−0.983026	−	0.183465i	$-0.941269\pi$
$487$	−389.386	+	389.386i	−0.799561	+	0.799561i	0.183465	+	0.983026i	$0.441269\pi$
$488$	1011.28	+	1011.28i	2.07230	+	2.07230i
$489$		−	1065.91i		−	2.17978i
$490$	−119.251	−	28.0089i	−0.243370	−	0.0571610i
$491$	631.969			1.28711			0.643553	−	0.765402i	$-0.277460\pi$
$491$	631.969			1.28711			0.643553	+	0.765402i	$0.277460\pi$
$492$	785.046	−	785.046i	1.59562	−	1.59562i
$493$	93.0460	+	93.0460i	0.188734	+	0.188734i
$494$			201.126i			0.407139i
$495$	−258.056	−	416.488i	−0.521325	−	0.841390i
$496$	453.142			0.913594
$497$	−195.711	+	195.711i	−0.393784	+	0.393784i
$498$	120.221	+	120.221i	0.241407	+	0.241407i
$499$		−	61.5684i		−	0.123383i	−0.998095	−	0.0616917i	$-0.980350\pi$
$499$		−	61.5684i		−	0.123383i	0.998095	−	0.0616917i	$-0.0196496\pi$
$500$	1026.67	−	96.0923i	2.05335	−	0.192185i
$501$	941.470			1.87918
$502$	−425.453	+	425.453i	−0.847516	+	0.847516i
$503$	126.437	+	126.437i	0.251366	+	0.251366i	0.821530	−	0.570165i	$-0.193121\pi$
$503$	126.437	+	126.437i	0.251366	+	0.251366i	−0.570165	+	0.821530i	$0.693121\pi$
$504$			344.760i			0.684047i
$505$	−246.464	+	152.709i	−0.488048	+	0.302394i
$506$	381.314			0.753586
$507$	189.305	−	189.305i	0.373383	−	0.373383i
$508$	304.137	+	304.137i	0.598695	+	0.598695i
$509$			533.424i			1.04798i	0.851723	+	0.523992i	$0.175558\pi$
$509$			533.424i			1.04798i	−0.851723	+	0.523992i	$0.824442\pi$
$510$	−47.7556	+	203.325i	−0.0936384	+	0.398677i
$511$	75.2247			0.147211
$512$	704.512	−	704.512i	1.37600	−	1.37600i
$513$	−3.97110	−	3.97110i	−0.00774094	−	0.00774094i
$514$		−	1102.61i		−	2.14515i
$515$	898.049	+	210.927i	1.74378	+	0.409568i
$516$	−186.480			−0.361396
$517$	−225.080	+	225.080i	−0.435358	+	0.435358i
$518$	−137.075	−	137.075i	−0.264624	−	0.264624i
$519$			388.342i			0.748250i
$520$	−402.233	−	649.182i	−0.773526	−	1.24843i
$521$	−301.897			−0.579456			−0.289728	−	0.957109i	$-0.593565\pi$
$521$	−301.897			−0.579456			−0.289728	+	0.957109i	$0.593565\pi$
$522$	−1007.55	+	1007.55i	−1.93018	+	1.93018i
$523$	−122.377	−	122.377i	−0.233991	−	0.233991i	0.580365	−	0.814356i	$-0.302910\pi$
$523$	−122.377	−	122.377i	−0.233991	−	0.233991i	−0.814356	+	0.580365i	$0.802910\pi$
$524$			1149.33i			2.19338i
$525$	124.101	−	249.614i	0.236383	−	0.475455i
$526$	−1566.51			−2.97816
$527$	47.6239	−	47.6239i	0.0903679	−	0.0903679i
$528$	−635.032	−	635.032i	−1.20271	−	1.20271i
$529$		−	434.098i		−	0.820601i
$530$	−1544.18	+	956.773i	−2.91354	+	1.80523i
$531$	−481.206			−0.906225
$532$	−86.3547	+	86.3547i	−0.162321	+	0.162321i
$533$	231.907	+	231.907i	0.435097	+	0.435097i
$534$		−	583.234i		−	1.09220i
$535$	−88.7211	+	377.741i	−0.165834	+	0.706058i
$536$	−52.7890			−0.0984870
$537$	−106.540	+	106.540i	−0.198399	+	0.198399i
$538$	99.5787	+	99.5787i	0.185090	+	0.185090i
$539$		−	78.2866i		−	0.145244i
$540$	40.3011	+	9.46564i	0.0746317	+	0.0175290i
$541$	904.472			1.67185			0.835926	−	0.548843i	$-0.184931\pi$
$541$	904.472			1.67185			0.835926	+	0.548843i	$0.184931\pi$
$542$	638.145	−	638.145i	1.17739	−	1.17739i
$543$	−296.039	−	296.039i	−0.545192	−	0.545192i
$544$			20.3823i			0.0374675i
$545$	−242.833	−	391.918i	−0.445565	−	0.719116i
$546$	−400.799			−0.734065
$547$	52.3586	−	52.3586i	0.0957196	−	0.0957196i	−0.657625	−	0.753345i	$-0.728439\pi$
$547$	52.3586	−	52.3586i	0.0957196	−	0.0957196i	0.753345	+	0.657625i	$0.228439\pi$
$548$	−767.720	−	767.720i	−1.40095	−	1.40095i
$549$			842.580i			1.53475i
$550$	311.548	+	927.635i	0.566450	+	1.68661i
$551$	−259.996			−0.471862
$552$	431.756	−	431.756i	0.782167	−	0.782167i
$553$	187.841	+	187.841i	0.339677	+	0.339677i
$554$			684.160i			1.23495i
$555$	374.999	−	232.350i	0.675675	−	0.418648i
$556$	−904.076			−1.62604
$557$	−377.650	+	377.650i	−0.678007	+	0.678007i	−0.959549	−	0.281542i	$-0.909154\pi$
$557$	−377.650	+	377.650i	−0.678007	+	0.678007i	0.281542	+	0.959549i	$0.409154\pi$
$558$	515.697	+	515.697i	0.924188	+	0.924188i
$559$		−	55.0872i		−	0.0985459i
$560$	57.6326	−	245.378i	0.102915	−	0.438175i
$561$	−133.480			−0.237932
$562$	650.525	−	650.525i	1.15752	−	1.15752i
$563$	74.0280	+	74.0280i	0.131488	+	0.131488i	0.769788	−	0.638300i	$-0.220362\pi$
$563$	74.0280	+	74.0280i	0.131488	+	0.131488i	−0.638300	+	0.769788i	$0.720362\pi$
$564$			989.517i			1.75446i
$565$	−520.628	−	122.281i	−0.921466	−	0.216427i
$566$	1578.19			2.78832
$567$	155.441	−	155.441i	0.274146	−	0.274146i
$568$	−1100.11	−	1100.11i	−1.93682	−	1.93682i
$569$			789.496i			1.38752i	0.720209	+	0.693758i	$0.244046\pi$
$569$			789.496i			1.38752i	−0.720209	+	0.693758i	$0.755954\pi$
$570$	−217.352	−	350.794i	−0.381319	−	0.615428i
$571$	405.030			0.709334			0.354667	−	0.934993i	$-0.384594\pi$
$571$	405.030			0.709334			0.354667	+	0.934993i	$0.384594\pi$
$572$	669.991	−	669.991i	1.17131	−	1.17131i
$573$	409.235	+	409.235i	0.714197	+	0.714197i
$574$			295.702i			0.515160i
$575$	−230.872	+	77.5386i	−0.401516	+	0.134850i
$576$	447.069			0.776161
$577$	−683.949	+	683.949i	−1.18535	+	1.18535i	−0.207015	+	0.978338i	$0.566375\pi$
$577$	−683.949	+	683.949i	−1.18535	+	1.18535i	−0.978338	+	0.207015i	$0.933625\pi$
$578$	−695.370	−	695.370i	−1.20306	−	1.20306i
$579$			99.1678i			0.171274i
$580$	1629.16	−	1009.43i	2.80890	−	1.74039i
$581$	−30.4961			−0.0524890
$582$	771.648	−	771.648i	1.32586	−	1.32586i
$583$	−820.918	−	820.918i	−1.40809	−	1.40809i
$584$			422.847i			0.724053i
$585$	102.877	−	438.010i	0.175858	−	0.748735i
$586$	432.870			0.738685
$587$	527.161	−	527.161i	0.898060	−	0.898060i	−0.0972042	−	0.995264i	$-0.530990\pi$
$587$	527.161	−	527.161i	0.898060	−	0.898060i	0.995264	+	0.0972042i	$0.0309900\pi$
$588$	−172.085	−	172.085i	−0.292662	−	0.292662i
$589$			133.074i			0.225932i
$590$	935.621	+	219.752i	1.58580	+	0.372461i
$591$	889.500			1.50508
$592$	282.053	−	282.053i	0.476441	−	0.476441i
$593$	−444.296	−	444.296i	−0.749234	−	0.749234i	0.225101	−	0.974335i	$-0.427729\pi$
$593$	−444.296	−	444.296i	−0.749234	−	0.749234i	−0.974335	+	0.225101i	$0.927729\pi$
$594$			39.2858i			0.0661377i
$595$	−19.7315	−	31.8455i	−0.0331621	−	0.0535218i
$596$	−893.917			−1.49986
$597$	−1065.32	+	1065.32i	−1.78446	+	1.78446i
$598$	247.604	+	247.604i	0.414053	+	0.414053i
$599$			146.980i			0.245375i	0.992445	+	0.122688i	$0.0391513\pi$
$599$			146.980i			0.245375i	−0.992445	+	0.122688i	$0.960849\pi$
$600$	1403.11	+	697.586i	2.33851	+	1.16264i
$601$	−526.857			−0.876635			−0.438317	−	0.898820i	$-0.644425\pi$
$601$	−526.857			−0.876635			−0.438317	+	0.898820i	$0.644425\pi$
$602$	35.1206	−	35.1206i	0.0583398	−	0.0583398i
$603$	−21.9914	−	21.9914i	−0.0364700	−	0.0364700i
$604$			376.591i			0.623495i
$605$	−17.3300	+	10.7377i	−0.0286447	+	0.0177482i
$606$	−855.335			−1.41144
$607$	315.320	−	315.320i	0.519472	−	0.519472i	−0.397939	−	0.917412i	$-0.630275\pi$
$607$	315.320	−	315.320i	0.519472	−	0.519472i	0.917412	+	0.397939i	$0.130275\pi$
$608$	−28.4768	−	28.4768i	−0.0468369	−	0.0468369i
$609$		−	518.112i		−	0.850759i
$610$	384.781	−	1638.25i	0.630788	−	2.68566i
$611$	−292.308			−0.478410
$612$	−144.737	+	144.737i	−0.236498	+	0.236498i
$613$	287.540	+	287.540i	0.469069	+	0.469069i	0.901613	−	0.432544i	$-0.142384\pi$
$613$	287.540	+	287.540i	0.469069	+	0.469069i	−0.432544	+	0.901613i	$0.642384\pi$
$614$		−	444.172i		−	0.723406i
$615$	−655.094	−	153.864i	−1.06519	−	0.250185i
$616$	440.058			0.714380
$617$	−557.927	+	557.927i	−0.904258	+	0.904258i	−0.995801	−	0.0915432i	$-0.970820\pi$
$617$	−557.927	+	557.927i	−0.904258	+	0.904258i	0.0915432	+	0.995801i	$0.470820\pi$
$618$	1924.31	+	1924.31i	3.11377	+	3.11377i
$619$		−	545.474i		−	0.881218i	−0.897699	−	0.440609i	$-0.854763\pi$
$619$		−	545.474i		−	0.881218i	0.897699	−	0.440609i	$-0.145237\pi$
$620$	−516.658	−	833.857i	−0.833319	−	1.34493i
$621$	−9.77753			−0.0157448
$622$	511.364	−	511.364i	0.822129	−	0.822129i
$623$	73.9737	+	73.9737i	0.118738	+	0.118738i
$624$		−	824.706i		−	1.32164i
$625$	−377.261	−	498.296i	−0.603617	−	0.797274i
$626$	862.027			1.37704
$627$	186.489	−	186.489i	0.297431	−	0.297431i
$628$	747.937	+	747.937i	1.19098	+	1.19098i
$629$		−	59.2859i		−	0.0942542i
$630$	344.840	−	213.663i	0.547365	−	0.339147i
$631$	404.223			0.640608			0.320304	−	0.947315i	$-0.396215\pi$
$631$	404.223			0.640608			0.320304	+	0.947315i	$0.396215\pi$
$632$	−1055.88	+	1055.88i	−1.67069	+	1.67069i
$633$	−124.041	−	124.041i	−0.195957	−	0.195957i
$634$			1945.43i			3.06850i
$635$	59.6088	−	253.792i	0.0938721	−	0.399672i
$636$	−3608.99			−5.67451
$637$	50.8348	−	50.8348i	0.0798035	−	0.0798035i
$638$	1286.06	+	1286.06i	2.01577	+	2.01577i
$639$		−	916.592i		−	1.43442i
$640$	−1009.38	−	237.076i	−1.57716	−	0.370431i
$641$	259.464			0.404780			0.202390	−	0.979305i	$-0.435129\pi$
$641$	259.464			0.404780			0.202390	+	0.979305i	$0.435129\pi$
$642$	−809.410	+	809.410i	−1.26076	+	1.26076i
$643$	−655.423	−	655.423i	−1.01932	−	1.01932i	−0.999810	−	0.0195107i	$-0.993789\pi$
$643$	−655.423	−	655.423i	−1.01932	−	1.01932i	−0.0195107	−	0.999810i	$-0.506211\pi$
$644$			212.620i			0.330155i
$645$	59.5312	+	96.0801i	0.0922965	+	0.148961i
$646$	−55.4591			−0.0858500
$647$	45.7226	−	45.7226i	0.0706686	−	0.0706686i	−0.670889	−	0.741558i	$-0.734087\pi$
$647$	45.7226	−	45.7226i	0.0706686	−	0.0706686i	0.741558	+	0.670889i	$0.234087\pi$
$648$	873.751	+	873.751i	1.34838	+	1.34838i
$649$			614.220i			0.946410i
$650$	−400.052	+	804.654i	−0.615464	+	1.23793i
$651$	−265.186			−0.407352
$652$	−1475.30	+	1475.30i	−2.26272	+	2.26272i
$653$	−382.704	−	382.704i	−0.586070	−	0.586070i	0.350495	−	0.936565i	$-0.386013\pi$
$653$	−382.704	−	382.704i	−0.586070	−	0.586070i	−0.936565	+	0.350495i	$0.886013\pi$
$654$		−	1360.12i		−	2.07970i
$655$	592.169	−	366.908i	0.904076	−	0.560165i
$656$	−608.452			−0.927519
$657$	−176.154	+	176.154i	−0.268119	+	0.268119i
$658$	−186.360	−	186.360i	−0.283222	−	0.283222i
$659$		−	612.942i		−	0.930109i	−0.885282	−	0.465055i	$-0.846035\pi$
$659$		−	612.942i		−	0.930109i	0.885282	−	0.465055i	$-0.153965\pi$
$660$	−444.521	+	1892.60i	−0.673517	+	2.86758i
$661$	762.029			1.15284			0.576421	−	0.817153i	$-0.304449\pi$
$661$	762.029			1.15284			0.576421	+	0.817153i	$0.304449\pi$
$662$	167.023	−	167.023i	0.252301	−	0.252301i
$663$	−86.6741	−	86.6741i	−0.130730	−	0.130730i
$664$		−	171.422i		−	0.258166i
$665$	72.0600	+	16.9249i	0.108361	+	0.0254510i
$666$	641.979			0.963932
$667$	−320.077	+	320.077i	−0.479875	+	0.479875i
$668$	−1303.06	−	1303.06i	−1.95069	−	1.95069i
$669$			523.463i			0.782455i
$670$	32.7157	+	52.8013i	0.0488294	+	0.0788079i
$671$	1075.49			1.60281
$672$	56.7479	−	56.7479i	0.0844462	−	0.0844462i
$673$	324.549	+	324.549i	0.482242	+	0.482242i	0.905847	−	0.423605i	$-0.139236\pi$
$673$	324.549	+	324.549i	0.482242	+	0.482242i	−0.423605	+	0.905847i	$0.639236\pi$
$674$		−	568.226i		−	0.843065i
$675$	−7.98860	−	23.7861i	−0.0118350	−	0.0352387i
$676$	−524.022			−0.775180
$677$	761.375	−	761.375i	1.12463	−	1.12463i	0.133595	−	0.991036i	$-0.457348\pi$
$677$	761.375	−	761.375i	1.12463	−	1.12463i	0.991036	−	0.133595i	$-0.0426523\pi$
$678$	−1115.58	−	1115.58i	−1.64541	−	1.64541i
$679$			195.742i			0.288280i
$680$	179.007	−	110.913i	0.263246	−	0.163107i
$681$	−1818.74			−2.67069
$682$	658.245	−	658.245i	0.965169	−	0.965169i
$683$	316.532	+	316.532i	0.463444	+	0.463444i	0.899782	−	0.436339i	$-0.143725\pi$
$683$	316.532	+	316.532i	0.463444	+	0.463444i	−0.436339	+	0.899782i	$0.643725\pi$
$684$		−	404.434i		−	0.591278i
$685$	−150.468	+	640.636i	−0.219661	+	0.935235i
$686$	64.8190			0.0944884
$687$	515.529	−	515.529i	0.750407	−	0.750407i
$688$	72.2660	+	72.2660i	0.105038	+	0.105038i
$689$		−	1066.11i		−	1.54733i
$690$	−699.435	−	164.278i	−1.01367	−	0.238085i
$691$	688.066			0.995754			0.497877	−	0.867248i	$-0.334113\pi$
$691$	688.066			0.995754			0.497877	+	0.867248i	$0.334113\pi$
$692$	537.491	−	537.491i	0.776721	−	0.776721i
$693$	183.324	+	183.324i	0.264537	+	0.264537i
$694$			72.2299i			0.104078i
$695$	288.614	+	465.806i	0.415271	+	0.670225i
$696$	2912.37			4.18444
$697$	−63.9465	+	63.9465i	−0.0917453	+	0.0917453i
$698$	−1144.15	−	1144.15i	−1.63918	−	1.63918i
$699$			726.444i			1.03926i
$700$	−517.247	+	173.718i	−0.738924	+	0.248169i
$701$	707.438			1.00918			0.504592	−	0.863358i	$-0.331643\pi$
$701$	707.438			1.00918			0.504592	+	0.863358i	$0.331643\pi$
$702$	−25.5099	+	25.5099i	−0.0363390	+	0.0363390i
$703$	82.8304	+	82.8304i	0.117824	+	0.117824i
$704$		−	570.647i		−	0.810578i
$705$	509.828	−	315.890i	0.723161	−	0.448070i
$706$	255.890			0.362450
$707$	108.485	−	108.485i	0.153445	−	0.153445i
$708$	1350.14	+	1350.14i	1.90698	+	1.90698i
$709$		−	373.825i		−	0.527256i	−0.964624	−	0.263628i	$-0.915081\pi$
$709$		−	373.825i		−	0.527256i	0.964624	−	0.263628i	$-0.0849191\pi$
$710$	−418.580	+	1782.15i	−0.589549	+	2.51008i
$711$	−879.737			−1.23732
$712$	−415.815	+	415.815i	−0.584009	+	0.584009i
$713$	163.825	+	163.825i	0.229769	+	0.229769i
$714$		−	110.517i		−	0.154786i
$715$	−559.085	−	131.314i	−0.781936	−	0.183656i
$716$	294.918			0.411897
$717$	−84.0677	+	84.0677i	−0.117249	+	0.117249i
$718$	485.388	+	485.388i	0.676028	+	0.676028i
$719$		−	16.7074i		−	0.0232370i	−0.999933	−	0.0116185i	$-0.996302\pi$
$719$		−	16.7074i		−	0.0232370i	0.999933	−	0.0116185i	$-0.00369836\pi$
$720$	439.644	+	709.561i	0.610617	+	0.985501i
$721$	−488.134			−0.677024
$722$	−815.920	+	815.920i	−1.13008	+	1.13008i
$723$	809.724	+	809.724i	1.11995	+	1.11995i
$724$			819.476i			1.13187i
$725$	−1040.17	−	517.146i	−1.43472	−	0.713305i
$726$	−60.1426			−0.0828410
$727$	−158.158	+	158.158i	−0.217549	+	0.217549i	−0.807465	−	0.589916i	$-0.799161\pi$
$727$	−158.158	+	158.158i	−0.217549	+	0.217549i	0.589916	+	0.807465i	$0.299161\pi$
$728$	285.748	+	285.748i	0.392512	+	0.392512i
$729$			689.923i			0.946397i
$730$	422.945	−	262.057i	0.579377	−	0.358982i
$731$	15.1899			0.0207796
$732$	2364.07	−	2364.07i	3.22961	−	3.22961i
$733$	187.350	+	187.350i	0.255593	+	0.255593i	0.823259	−	0.567666i	$-0.192154\pi$
$733$	187.350	+	187.350i	0.255593	+	0.255593i	−0.567666	+	0.823259i	$0.692154\pi$
$734$			712.823i			0.971148i
$735$	−33.7275	+	143.599i	−0.0458878	+	0.195373i
$736$	−70.1148			−0.0952647
$737$	−28.0703	+	28.0703i	−0.0380872	+	0.0380872i
$738$	−692.446	−	692.446i	−0.938274	−	0.938274i
$739$		−	1160.58i		−	1.57048i	−0.619194	−	0.785238i	$-0.712540\pi$
$739$		−	1160.58i		−	1.57048i	0.619194	−	0.785238i	$-0.287460\pi$
$740$	−840.612	−	197.437i	−1.13596	−	0.266807i
$741$	242.191			0.326843
$742$	679.696	−	679.696i	0.916032	−	0.916032i
$743$	5.16032	+	5.16032i	0.00694524	+	0.00694524i	0.710571	−	0.703626i	$-0.248437\pi$
$743$	5.16032	+	5.16032i	0.00694524	+	0.00694524i	−0.703626	+	0.710571i	$0.748437\pi$
$744$		−	1490.64i		−	2.00355i
$745$	285.371	+	460.572i	0.383048	+	0.618218i
$746$	297.164			0.398344
$747$	71.4129	−	71.4129i	0.0955995	−	0.0955995i
$748$	184.745	+	184.745i	0.246985	+	0.246985i
$749$		−	205.321i		−	0.274127i
$750$	−171.819	−	1835.76i	−0.229092	−	2.44768i
$751$	−253.442			−0.337473			−0.168736	−	0.985661i	$-0.553969\pi$
$751$	−253.442			−0.337473			−0.168736	+	0.985661i	$0.553969\pi$
$752$	383.464	−	383.464i	0.509926	−	0.509926i
$753$	512.319	+	512.319i	0.680370	+	0.680370i
$754$			1670.19i			2.21510i
$755$	194.031	−	120.221i	0.256994	−	0.159234i
$756$	−21.9057			−0.0289757
$757$	29.5088	−	29.5088i	0.0389812	−	0.0389812i	−0.687348	−	0.726329i	$-0.741225\pi$
$757$	29.5088	−	29.5088i	0.0389812	−	0.0389812i	0.726329	+	0.687348i	$0.241225\pi$
$758$	−1278.27	−	1278.27i	−1.68638	−	1.68638i
$759$		−	459.168i		−	0.604965i
$760$	−95.1370	+	405.058i	−0.125180	+	0.532970i
$761$	584.622			0.768229			0.384114	−	0.923286i	$-0.374507\pi$
$761$	584.622			0.768229			0.384114	+	0.923286i	$0.374507\pi$
$762$	543.816	−	543.816i	0.713670	−	0.713670i
$763$	172.509	+	172.509i	0.226094	+	0.226094i
$764$		−	1132.82i		−	1.48274i
$765$	120.778	+	28.3675i	0.157880	+	0.0370816i
$766$	−1001.82			−1.30785
$767$	−398.839	+	398.839i	−0.519999	+	0.519999i
$768$	−1554.64	−	1554.64i	−2.02427	−	2.02427i
$769$			44.2333i			0.0575206i	0.999586	+	0.0287603i	$0.00915595\pi$
$769$			44.2333i			0.0575206i	−0.999586	+	0.0287603i	$0.990844\pi$
$770$	−272.723	−	440.160i	−0.354186	−	0.571637i
$771$	−1327.73			−1.72209
$772$	137.255	−	137.255i	0.177791	−	0.177791i
$773$	415.494	+	415.494i	0.537508	+	0.537508i	0.922796	−	0.385288i	$-0.125898\pi$
$773$	415.494	+	415.494i	0.537508	+	0.537508i	−0.385288	+	0.922796i	$0.625898\pi$
$774$			164.484i			0.212512i
$775$	−264.692	+	532.394i	−0.341538	+	0.686960i
$776$	−1100.29			−1.41790
$777$	−165.062	+	165.062i	−0.212435	+	0.212435i
$778$	−1393.43	−	1393.43i	−1.79104	−	1.79104i
$779$		−	178.684i		−	0.229376i
$780$	−1517.59	+	940.302i	−1.94563	+	1.20552i
$781$	−1169.96			−1.49802
$782$	−68.2748	+	68.2748i	−0.0873080	+	0.0873080i
$783$	−32.9767	−	32.9767i	−0.0421158	−	0.0421158i
$784$			133.375i			0.170121i
$785$	146.591	−	624.128i	0.186740	−	0.795067i
$786$	2055.08			2.61460
$787$	−871.881	+	871.881i	−1.10785	+	1.10785i	−0.114422	+	0.993432i	$0.536502\pi$
$787$	−871.881	+	871.881i	−1.10785	+	1.10785i	−0.993432	+	0.114422i	$0.963498\pi$
$788$	−1231.13	−	1231.13i	−1.56235	−	1.56235i
$789$			1886.35i			2.39081i
$790$	1710.50	+	401.749i	2.16519	+	0.508543i
$791$	282.987			0.357759
$792$	−1030.49	+	1030.49i	−1.30112	+	1.30112i
$793$	698.359	+	698.359i	0.880654	+	0.880654i
$794$			2112.19i			2.66018i
$795$	1152.12	+	1859.46i	1.44921	+	2.33894i
$796$	2948.96			3.70472
$797$	226.352	−	226.352i	0.284005	−	0.284005i	−0.550699	−	0.834704i	$-0.685639\pi$
$797$	226.352	−	226.352i	0.284005	−	0.284005i	0.834704	+	0.550699i	$0.185639\pi$
$798$	154.408	+	154.408i	0.193493	+	0.193493i
$799$		−	80.6018i		−	0.100878i
$800$	−57.2863	−	170.570i	−0.0716079	−	0.213213i
$801$	−346.449			−0.432521
$802$	−39.4732	+	39.4732i	−0.0492185	+	0.0492185i
$803$	224.846	+	224.846i	0.280008	+	0.280008i
$804$			123.405i			0.153489i
$805$	109.548	−	67.8759i	0.136084	−	0.0843179i
$806$	854.854			1.06061
$807$	119.910	−	119.910i	0.148587	−	0.148587i
$808$	609.808	+	609.808i	0.754713	+	0.754713i
$809$		−	839.195i		−	1.03732i	−0.854980	−	0.518662i	$-0.826430\pi$
$809$		−	839.195i		−	1.03732i	0.854980	−	0.518662i	$-0.173570\pi$
$810$	332.452	−	1415.46i	0.410435	−	1.74748i
$811$	−910.346			−1.12250			−0.561249	−	0.827647i	$-0.689679\pi$
$811$	−910.346			−1.12250			−0.561249	+	0.827647i	$0.689679\pi$
$812$	−717.103	+	717.103i	−0.883131	+	0.883131i
$813$	−768.437	−	768.437i	−0.945187	−	0.945187i
$814$		−	819.434i		−	1.00668i
$815$	1231.08	+	289.148i	1.51053	+	0.354783i
$816$	227.406			0.278684
$817$	−21.2223	+	21.2223i	−0.0259759	+	0.0259759i
$818$	1378.36	+	1378.36i	1.68504	+	1.68504i
$819$			238.080i			0.290696i
$820$	693.736	+	1119.65i	0.846020	+	1.36543i
$821$	621.807			0.757377			0.378689	−	0.925524i	$-0.376375\pi$
$821$	621.807			0.757377			0.378689	+	0.925524i	$0.376375\pi$
$822$	−1372.73	+	1372.73i	−1.66999	+	1.66999i
$823$	123.430	+	123.430i	0.149976	+	0.149976i	0.778107	−	0.628132i	$-0.216180\pi$
$823$	123.430	+	123.430i	0.149976	+	0.149976i	−0.628132	+	0.778107i	$0.716180\pi$
$824$		−	2743.86i		−	3.32993i
$825$	1117.03	−	375.157i	1.35398	−	0.454736i
$826$	−508.556			−0.615686
$827$	14.4127	−	14.4127i	0.0174277	−	0.0174277i	−0.698339	−	0.715767i	$-0.746077\pi$
$827$	14.4127	−	14.4127i	0.0174277	−	0.0174277i	0.715767	+	0.698339i	$0.246077\pi$
$828$	−497.892	−	497.892i	−0.601319	−	0.601319i
$829$		−	863.641i		−	1.04179i	−0.853622	−	0.520893i	$-0.825599\pi$
$829$		−	863.641i		−	1.04179i	0.853622	−	0.520893i	$-0.174401\pi$
$830$	−171.462	+	106.238i	−0.206581	+	0.127997i
$831$	823.847			0.991392
$832$	370.545	−	370.545i	0.445367	−	0.445367i
$833$	14.0173	+	14.0173i	0.0168275	+	0.0168275i
$834$			1616.55i			1.93830i
$835$	−255.391	+	1087.36i	−0.305857	+	1.30222i
$836$	−516.228			−0.617497
$837$	−16.8785	+	16.8785i	−0.0201655	+	0.0201655i
$838$	−1022.08	−	1022.08i	−1.21967	−	1.21967i
$839$			54.6235i			0.0651055i	0.999470	+	0.0325527i	$0.0103637\pi$
$839$			54.6235i			0.0651055i	−0.999470	+	0.0325527i	$0.989636\pi$
$840$	−807.187	−	189.586i	−0.960937	−	0.225698i
$841$	−1318.05			−1.56724
$842$	−732.390	+	732.390i	−0.869822	+	0.869822i
$843$	−783.345	−	783.345i	−0.929235	−	0.929235i
$844$			343.362i			0.406827i
$845$	167.287	+	269.991i	0.197972	+	0.319516i
$846$	872.799			1.03168
$847$	7.62810	−	7.62810i	0.00900602	−	0.00900602i
$848$	1398.58	+	1398.58i	1.64927	+	1.64927i
$849$		−	1900.41i		−	2.23841i
$850$	−221.877	−	110.311i	−0.261032	−	0.129778i
$851$	203.942			0.239650
$852$	−2571.73	+	2571.73i	−3.01846	+	3.01846i
$853$	196.771	+	196.771i	0.230681	+	0.230681i	0.812977	−	0.582296i	$-0.197845\pi$
$853$	196.771	+	196.771i	0.230681	+	0.230681i	−0.582296	+	0.812977i	$0.697845\pi$
$854$			890.471i			1.04271i
$855$	−208.376	+	129.110i	−0.243715	+	0.151006i
$856$	1154.13			1.34829
$857$	692.749	−	692.749i	0.808342	−	0.808342i	−0.176041	−	0.984383i	$-0.556329\pi$
$857$	692.749	−	692.749i	0.808342	−	0.808342i	0.984383	+	0.176041i	$0.0563291\pi$
$858$	−1197.99	−	1197.99i	−1.39626	−	1.39626i
$859$		−	1285.57i		−	1.49659i	−0.663368	−	0.748293i	$-0.730874\pi$
$859$		−	1285.57i		−	1.49659i	0.663368	−	0.748293i	$-0.269126\pi$
$860$	50.5861	−	215.377i	0.0588210	−	0.250438i
$861$	356.076			0.413561
$862$	1653.03	−	1653.03i	1.91766	−	1.91766i
$863$	99.1463	+	99.1463i	0.114886	+	0.114886i	0.762212	−	0.647327i	$-0.224113\pi$
$863$	99.1463	+	99.1463i	0.114886	+	0.114886i	−0.647327	+	0.762212i	$0.724113\pi$
$864$		−	7.22374i		−	0.00836081i
$865$	−448.518	−	105.345i	−0.518518	−	0.121786i
$866$	−1851.74			−2.13827
$867$	−837.346	+	837.346i	−0.965797	+	0.965797i
$868$	367.036	+	367.036i	0.422852	+	0.422852i
$869$			1122.91i			1.29219i
$870$	−1804.92	−	2913.05i	−2.07462	−	3.34833i
$871$	−36.4544			−0.0418535
$872$	−969.695	+	969.695i	−1.11204	+	1.11204i
$873$	−458.369	−	458.369i	−0.525051	−	0.525051i
$874$		−	190.778i		−	0.218282i
$875$	254.628	+	211.044i	0.291004	+	0.241193i
$876$	988.489			1.12841
$877$	912.432	−	912.432i	1.04040	−	1.04040i	0.0412528	−	0.999149i	$-0.486865\pi$
$877$	912.432	−	912.432i	1.04040	−	1.04040i	0.999149	−	0.0412528i	$-0.0131349\pi$
$878$	−158.962	−	158.962i	−0.181050	−	0.181050i
$879$		−	521.250i		−	0.593003i
$880$	905.698	−	561.170i	1.02920	−	0.637693i
$881$	−1348.43			−1.53057			−0.765283	−	0.643694i	$-0.777401\pi$
$881$	−1348.43			−1.53057			−0.765283	+	0.643694i	$0.777401\pi$
$882$	−151.787	+	151.787i	−0.172094	+	0.172094i
$883$	−545.199	−	545.199i	−0.617440	−	0.617440i	0.327434	−	0.944874i	$-0.393816\pi$
$883$	−545.199	−	545.199i	−0.617440	−	0.617440i	−0.944874	+	0.327434i	$0.893816\pi$
$884$			239.926i			0.271409i
$885$	264.619	−	1126.65i	0.299005	−	1.27305i
$886$	248.818			0.280833
$887$	−774.702	+	774.702i	−0.873395	+	0.873395i	−0.992841	−	0.119446i	$-0.961888\pi$
$887$	−774.702	+	774.702i	−0.873395	+	0.873395i	0.119446	+	0.992841i	$0.461888\pi$
$888$	−927.833	−	927.833i	−1.04486	−	1.04486i
$889$			137.948i			0.155173i
$890$	673.610	+	158.213i	0.756865	+	0.177767i
$891$	929.224			1.04290
$892$	724.507	−	724.507i	0.812228	−	0.812228i
$893$	112.612	+	112.612i	0.126105	+	0.126105i
$894$			1598.38i			1.78790i
$895$	−94.1486	−	151.951i	−0.105194	−	0.169777i
$896$	548.648			0.612331
$897$	298.157	−	298.157i	0.332394	−	0.332394i
$898$	1949.63	+	1949.63i	2.17108	+	2.17108i
$899$			1105.07i			1.22922i
$900$	804.442	−	1618.03i	0.893824	−	1.79782i
$901$	293.973			0.326274
$902$	−883.852	+	883.852i	−0.979880	+	0.979880i
$903$	−42.2912	−	42.2912i	−0.0468341	−	0.0468341i
$904$			1590.70i			1.75963i
$905$	422.218	−	261.606i	0.466540	−	0.289068i
$906$	673.369			0.743233
$907$	1015.38	−	1015.38i	1.11950	−	1.11950i	0.127680	−	0.991815i	$-0.459247\pi$
$907$	1015.38	−	1015.38i	1.11950	−	1.11950i	0.991815	−	0.127680i	$-0.0407531\pi$
$908$	2517.26	+	2517.26i	2.77231	+	2.77231i
$909$			508.081i			0.558945i
$910$	108.724	−	462.906i	0.119477	−	0.508688i
$911$	767.987			0.843016			0.421508	−	0.906825i	$-0.361501\pi$
$911$	767.987			0.843016			0.421508	+	0.906825i	$0.361501\pi$
$912$	−317.718	+	317.718i	−0.348375	+	0.348375i
$913$	−91.1528	−	91.1528i	−0.0998387	−	0.0998387i
$914$		−	274.757i		−	0.300609i
$915$	−1972.74	−	463.342i	−2.15600	−	0.506385i
$916$	−1427.06			−1.55792
$917$	−260.653	+	260.653i	−0.284246	+	0.284246i
$918$	−7.03418	−	7.03418i	−0.00766250	−	0.00766250i
$919$			1492.89i			1.62447i	0.583328	+	0.812237i	$0.301750\pi$
$919$			1492.89i			1.62447i	−0.583328	+	0.812237i	$0.698250\pi$
$920$	381.538	+	615.782i	0.414716	+	0.669328i
$921$	−534.859			−0.580737
$922$	1740.29	−	1740.29i	1.88752	−	1.88752i
$923$	−759.702	−	759.702i	−0.823080	−	0.823080i
$924$		−	1028.72i		−	1.11334i
$925$	166.628	+	496.137i	0.180139	+	0.536364i
$926$	−1657.95			−1.79044
$927$	1143.07	−	1143.07i	1.23308	−	1.23308i
$928$	−236.476	−	236.476i	−0.254823	−	0.254823i
$929$			339.342i			0.365277i	0.983180	+	0.182638i	$0.0584637\pi$
$929$			339.342i			0.365277i	−0.983180	+	0.182638i	$0.941536\pi$
$930$	−1490.99	+	923.817i	−1.60321	+	0.993352i
$931$	−39.1682			−0.0420711
$932$	1005.45	−	1005.45i	1.07881	−	1.07881i
$933$	−615.771	−	615.771i	−0.659990	−	0.659990i
$934$		−	682.746i		−	0.730992i
$935$	36.2088	−	154.163i	0.0387260	−	0.164881i
$936$	−1338.28			−1.42978
$937$	289.919	−	289.919i	0.309412	−	0.309412i	−0.535269	−	0.844682i	$-0.679790\pi$
$937$	289.919	−	289.919i	0.309412	−	0.309412i	0.844682	+	0.535269i	$0.179790\pi$
$938$	−23.2414	−	23.2414i	−0.0247776	−	0.0247776i
$939$		−	1038.03i		−	1.10546i
$940$	−1142.85	−	268.424i	−1.21580	−	0.285558i
$941$	−1412.22			−1.50076			−0.750382	−	0.661004i	$-0.770131\pi$
$941$	−1412.22			−1.50076			−0.750382	+	0.661004i	$0.770131\pi$
$942$	1337.36	−	1337.36i	1.41970	−	1.41970i
$943$	−219.975	−	219.975i	−0.233271	−	0.233271i
$944$		−	1046.43i		−	1.10851i
$945$	6.99308	+	11.2864i	0.00740008	+	0.0119433i
$946$	209.951			0.221935
$947$	−185.514	+	185.514i	−0.195897	+	0.195897i	−0.798238	−	0.602342i	$-0.794234\pi$
$947$	−185.514	+	185.514i	−0.195897	+	0.195897i	0.602342	+	0.798238i	$0.294234\pi$
$948$	2468.33	+	2468.33i	2.60372	+	2.60372i
$949$			292.005i			0.307697i
$950$	464.112	−	155.873i	0.488539	−	0.164077i
$951$	2342.63			2.46333
$952$	−78.7930	+	78.7930i	−0.0827657	+	0.0827657i
$953$	220.312	+	220.312i	0.231177	+	0.231177i	0.813184	−	0.582007i	$-0.197732\pi$
$953$	220.312	+	220.312i	0.231177	+	0.231177i	−0.582007	+	0.813184i	$0.697732\pi$
$954$			3183.29i			3.33678i
$955$	−583.661	+	361.636i	−0.611163	+	0.378677i
$956$	232.711			0.243421
$957$	1548.64	−	1548.64i	1.61822	−	1.61822i
$958$	−1341.97	−	1341.97i	−1.40081	−	1.40081i
$959$		−	348.217i		−	0.363105i
$960$	−245.847	+	1046.72i	−0.256091	+	1.09034i
$961$	−395.391			−0.411437
$962$	532.094	−	532.094i	0.553112	−	0.553112i
$963$	480.801	+	480.801i	0.499274	+	0.499274i
$964$		−	2241.43i		−	2.32513i
$965$	−114.534	−	26.9010i	−0.118689	−	0.0278767i
$966$	380.178			0.393559
$967$	−180.913	+	180.913i	−0.187087	+	0.187087i	−0.794436	−	0.607348i	$-0.792233\pi$
$967$	−180.913	+	180.913i	−0.187087	+	0.187087i	0.607348	+	0.794436i	$0.292233\pi$
$968$	42.8784	+	42.8784i	0.0442959	+	0.0442959i
$969$			66.7823i			0.0689188i
$970$	681.896	+	1100.54i	0.702986	+	1.13458i
$971$	−756.520			−0.779115			−0.389557	−	0.921002i	$-0.627372\pi$
$971$	−756.520			−0.779115			−0.389557	+	0.921002i	$0.627372\pi$
$972$	1989.88	−	1989.88i	2.04720	−	2.04720i
$973$	−205.032	−	205.032i	−0.210722	−	0.210722i
$974$		−	1927.31i		−	1.97876i
$975$	968.942	+	481.731i	0.993787	+	0.494083i
$976$	−1832.28			−1.87734
$977$	−33.2960	+	33.2960i	−0.0340799	+	0.0340799i	−0.723941	−	0.689861i	$-0.757671\pi$
$977$	−33.2960	+	33.2960i	−0.0340799	+	0.0340799i	0.689861	+	0.723941i	$0.257671\pi$
$978$	2637.92	+	2637.92i	2.69726	+	2.69726i
$979$			442.214i			0.451700i
$980$	245.432	−	152.070i	0.250441	−	0.155173i
$981$	−807.932			−0.823580
$982$	−1564.00	+	1564.00i	−1.59266	+	1.59266i
$983$	−758.261	−	758.261i	−0.771374	−	0.771374i	0.206972	−	0.978347i	$-0.433639\pi$
$983$	−758.261	−	758.261i	−0.771374	−	0.771374i	−0.978347	+	0.206972i	$0.933639\pi$
$984$			2001.54i			2.03409i
$985$	−241.293	+	1027.33i	−0.244967	+	1.04298i
$986$	−460.541			−0.467080
$987$	−224.409	+	224.409i	−0.227365	+	0.227365i
$988$	−335.209	−	335.209i	−0.339280	−	0.339280i
$989$			52.2529i			0.0528341i
$990$	1669.36	+	392.088i	1.68622	+	0.396048i
$991$	−1457.39			−1.47063			−0.735313	−	0.677728i	$-0.762965\pi$
$991$	−1457.39			−1.47063			−0.735313	+	0.677728i	$0.762965\pi$
$992$	−121.036	+	121.036i	−0.122012	+	0.122012i
$993$	−201.125	−	201.125i	−0.202542	−	0.202542i
$994$		−	968.689i		−	0.974537i
$995$	−941.414	−	1519.39i	−0.946145	−	1.52702i
$996$	−400.734			−0.402343
$997$	−441.177	+	441.177i	−0.442505	+	0.442505i	−0.892853	−	0.450348i	$-0.851300\pi$
$997$	−441.177	+	441.177i	−0.442505	+	0.442505i	0.450348	+	0.892853i	$0.351300\pi$
$998$	152.369	+	152.369i	0.152675	+	0.152675i
$999$			21.0117i			0.0210327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.g.a.8.1	✓	12
3.2	odd	2		315.3.o.a.253.6		12
4.3	odd	2		560.3.bh.e.113.1		12
5.2	odd	4	inner	35.3.g.a.22.1	yes	12
5.3	odd	4		175.3.g.b.57.6		12
5.4	even	2		175.3.g.b.43.6		12
7.2	even	3		245.3.m.d.18.6		24
7.3	odd	6		245.3.m.c.128.1		24
7.4	even	3		245.3.m.d.128.1		24
7.5	odd	6		245.3.m.c.18.6		24
7.6	odd	2		245.3.g.a.148.1		12
15.2	even	4		315.3.o.a.127.6		12
20.7	even	4		560.3.bh.e.337.1		12
35.2	odd	12		245.3.m.d.67.1		24
35.12	even	12		245.3.m.c.67.1		24
35.17	even	12		245.3.m.c.177.6		24
35.27	even	4		245.3.g.a.197.1		12
35.32	odd	12		245.3.m.d.177.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.g.a.8.1	✓	12	1.1	even	1	trivial
35.3.g.a.22.1	yes	12	5.2	odd	4	inner
175.3.g.b.43.6		12	5.4	even	2
175.3.g.b.57.6		12	5.3	odd	4
245.3.g.a.148.1		12	7.6	odd	2
245.3.g.a.197.1		12	35.27	even	4
245.3.m.c.18.6		24	7.5	odd	6
245.3.m.c.67.1		24	35.12	even	12
245.3.m.c.128.1		24	7.3	odd	6
245.3.m.c.177.6		24	35.17	even	12
245.3.m.d.18.6		24	7.2	even	3
245.3.m.d.67.1		24	35.2	odd	12
245.3.m.d.128.1		24	7.4	even	3
245.3.m.d.177.6		24	35.32	odd	12
315.3.o.a.127.6		12	15.2	even	4
315.3.o.a.253.6		12	3.2	odd	2
560.3.bh.e.113.1		12	4.3	odd	2
560.3.bh.e.337.1		12	20.7	even	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47480 + 2.47480i) q^{2} +(2.98009 + 2.98009i) q^{3} -8.24929i q^{4} +(-4.25027 + 2.63347i) q^{5} -14.7503 q^{6} +(1.87083 - 1.87083i) q^{7} +(10.5161 + 10.5161i) q^{8} +8.76185i q^{9} +O(q^{10})\)	\(q+(-2.47480 + 2.47480i) q^{2} +(2.98009 + 2.98009i) q^{3} -8.24929i q^{4} +(-4.25027 + 2.63347i) q^{5} -14.7503 q^{6} +(1.87083 - 1.87083i) q^{7} +(10.5161 + 10.5161i) q^{8} +8.76185i q^{9} +(4.00127 - 17.0359i) q^{10} +11.1838 q^{11} +(24.5836 - 24.5836i) q^{12} +(7.26212 + 7.26212i) q^{13} +9.25986i q^{14} +(-20.5142 - 4.81822i) q^{15} -19.0536 q^{16} +(-2.00247 + 2.00247i) q^{17} +(-21.6838 - 21.6838i) q^{18} -5.59546i q^{19} +(21.7243 + 35.0617i) q^{20} +11.1505 q^{21} +(-27.6777 + 27.6777i) q^{22} +(-6.88848 - 6.88848i) q^{23} +62.6781i q^{24} +(11.1297 - 22.3859i) q^{25} -35.9446 q^{26} +(0.709702 - 0.709702i) q^{27} +(-15.4330 - 15.4330i) q^{28} -46.4655i q^{29} +(62.6926 - 38.8444i) q^{30} -23.7825 q^{31} +(5.08928 - 5.08928i) q^{32} +(33.3287 + 33.3287i) q^{33} -9.91145i q^{34} +(-3.02476 + 12.8783i) q^{35} +72.2790 q^{36} +(-14.8032 + 14.8032i) q^{37} +(13.8476 + 13.8476i) q^{38} +43.2835i q^{39} +(-72.3904 - 17.0025i) q^{40} +31.9337 q^{41} +(-27.5952 + 27.5952i) q^{42} +(-3.79278 - 3.79278i) q^{43} -92.2584i q^{44} +(-23.0741 - 37.2403i) q^{45} +34.0952 q^{46} +(-20.1256 + 20.1256i) q^{47} +(-56.7814 - 56.7814i) q^{48} -7.00000i q^{49} +(27.8570 + 82.9445i) q^{50} -11.9351 q^{51} +(59.9073 - 59.9073i) q^{52} +(-73.4024 - 73.4024i) q^{53} +3.51274i q^{54} +(-47.5342 + 29.4522i) q^{55} +39.3478 q^{56} +(16.6750 - 16.6750i) q^{57} +(114.993 + 114.993i) q^{58} +54.9205i q^{59} +(-39.7469 + 169.227i) q^{60} +96.1646 q^{61} +(58.8570 - 58.8570i) q^{62} +(16.3919 + 16.3919i) q^{63} -51.0244i q^{64} +(-49.9906 - 11.7414i) q^{65} -164.964 q^{66} +(-2.50990 + 2.50990i) q^{67} +(16.5190 + 16.5190i) q^{68} -41.0565i q^{69} +(-24.3856 - 39.3569i) q^{70} -104.612 q^{71} +(-92.1409 + 92.1409i) q^{72} +(20.1046 + 20.1046i) q^{73} -73.2698i q^{74} +(99.8795 - 33.5447i) q^{75} -46.1585 q^{76} +(20.9230 - 20.9230i) q^{77} +(-107.118 - 107.118i) q^{78} +100.405i q^{79} +(80.9830 - 50.1771i) q^{80} +83.0866 q^{81} +(-79.0297 + 79.0297i) q^{82} +(-8.15043 - 8.15043i) q^{83} -91.9834i q^{84} +(3.23761 - 13.7845i) q^{85} +18.7727 q^{86} +(138.471 - 138.471i) q^{87} +(117.610 + 117.610i) q^{88} +39.5406i q^{89} +(149.266 + 35.0585i) q^{90} +27.1724 q^{91} +(-56.8250 + 56.8250i) q^{92} +(-70.8740 - 70.8740i) q^{93} -99.6135i q^{94} +(14.7355 + 23.7822i) q^{95} +30.3330 q^{96} +(-52.3142 + 52.3142i) q^{97} +(17.3236 + 17.3236i) q^{98} +97.9908i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

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