LMFDB - Embedded newform 343.3.l.a.10.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,3,Mod(3,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(294))

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

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

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

chi := DirichletCharacter("343.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	343.l (of order $294$, degree $84$, 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:	$9.34607306756$
Analytic rank:	$0$
Dimension:	$5376$
Relative dimension:	$64$ over $\Q(\zeta_{294})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{294}]$

Embedding invariants

Embedding label			10.14
Character	$\chi$	$=$	343.10
Dual form			343.3.l.a.103.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.34266 - 1.19049i) q^{2} +(1.21559 - 1.15232i) q^{3} +(1.71273 + 2.34681i) q^{4} +(-8.23255 + 0.0879738i) q^{5} +(-4.21956 + 1.25234i) q^{6} +(5.60756 - 4.18991i) q^{7} +(0.459099 + 2.83969i) q^{8} +(-0.330804 + 6.18564i) q^{9} +(19.3908 + 9.59470i) q^{10} +(-0.332322 + 0.295388i) q^{11} +(4.78627 + 0.879150i) q^{12} +(18.7917 + 11.3917i) q^{13} +(-18.1247 + 3.13977i) q^{14} +(-9.90606 + 9.59349i) q^{15} +(5.84904 - 18.2668i) q^{16} +(-10.2330 + 1.20839i) q^{17} +(8.13893 - 14.0970i) q^{18} +(6.36972 - 3.67756i) q^{19} +(-14.3066 - 19.1696i) q^{20} +(1.98839 - 11.5549i) q^{21} +(1.13018 - 0.296367i) q^{22} +(-9.92423 - 28.8554i) q^{23} +(3.83031 + 2.92288i) q^{24} +(42.7728 - 0.914253i) q^{25} +(-30.4610 - 49.0582i) q^{26} +(16.4976 + 19.3790i) q^{27} +(19.4372 + 5.98368i) q^{28} +(27.4310 - 5.34218i) q^{29} +(34.6275 - 10.6812i) q^{30} +(-22.1006 + 8.67386i) q^{31} +(-27.3562 + 27.6501i) q^{32} +(-0.0635865 + 0.742015i) q^{33} +(25.4111 + 9.35152i) q^{34} +(-45.7959 + 34.9869i) q^{35} +(-15.0831 + 9.81802i) q^{36} +(-15.9767 - 6.86920i) q^{37} +(-19.3002 + 1.03216i) q^{38} +(35.9700 - 7.80650i) q^{39} +(-4.02937 - 23.3375i) q^{40} +(32.4782 - 22.6554i) q^{41} +(-18.4142 + 24.7021i) q^{42} +(1.27177 - 7.86637i) q^{43} +(-1.26240 - 0.273976i) q^{44} +(2.17919 - 50.9527i) q^{45} +(-11.1031 + 79.4132i) q^{46} +(39.1313 + 9.81576i) q^{47} +(-13.9392 - 28.9450i) q^{48} +(13.8893 - 46.9903i) q^{49} +(-101.291 - 48.7790i) q^{50} +(-11.0468 + 13.2607i) q^{51} +(5.45115 + 63.6115i) q^{52} +(-3.32775 + 12.1591i) q^{53} +(-15.5777 - 65.0387i) q^{54} +(2.70987 - 2.46103i) q^{55} +(14.4724 + 14.0001i) q^{56} +(3.50526 - 11.8104i) q^{57} +(-70.6213 - 20.1415i) q^{58} +(75.2222 - 35.2399i) q^{59} +(-39.4805 - 6.81658i) q^{60} +(-4.68149 - 109.460i) q^{61} +(62.1005 + 5.99076i) q^{62} +(24.0623 + 36.0724i) q^{63} +(24.1908 - 8.03189i) q^{64} +(-155.706 - 92.1292i) q^{65} +(1.03233 - 1.66259i) q^{66} +(96.0768 - 14.4812i) q^{67} +(-20.3623 - 21.9454i) q^{68} +(-45.3146 - 23.6406i) q^{69} +(148.936 - 27.4428i) q^{70} +(-15.8926 - 3.09509i) q^{71} +(-17.7172 + 1.90044i) q^{72} +(9.75699 - 2.44746i) q^{73} +(29.2503 + 35.1124i) q^{74} +(50.9409 - 50.3994i) q^{75} +(19.5402 + 8.64985i) q^{76} +(-0.625865 + 3.04881i) q^{77} +(-93.5591 - 24.5341i) q^{78} +(7.97479 + 106.416i) q^{79} +(-46.5455 + 150.897i) q^{80} +(-13.0471 - 1.39951i) q^{81} +(-103.056 + 14.4088i) q^{82} +(-65.3104 + 6.30041i) q^{83} +(30.5228 - 15.1242i) q^{84} +(84.1377 - 10.8483i) q^{85} +(-12.3442 + 16.9142i) q^{86} +(27.1890 - 38.1032i) q^{87} +(-0.991379 - 0.808079i) q^{88} +(145.941 - 60.9080i) q^{89} +(-65.7640 + 116.771i) q^{90} +(153.106 - 14.8563i) q^{91} +(50.7207 - 72.7120i) q^{92} +(-16.8703 + 36.0109i) q^{93} +(-79.9857 - 69.5806i) q^{94} +(-52.1155 + 30.8360i) q^{95} +(-1.39223 + 65.1346i) q^{96} +(53.1690 + 42.4009i) q^{97} +(-88.4797 + 93.5471i) q^{98} +(-1.71723 - 2.15334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) $ 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{223}{294}\right)$

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 $

$2$	−2.34266	−	1.19049i	−1.17133	−	0.595247i	−0.244104	−	0.969749i	$-0.578494\pi$
$2$	−2.34266	−	1.19049i	−1.17133	−	0.595247i	−0.927226	+	0.374502i	$0.877814\pi$
$3$	1.21559	−	1.15232i	0.405198	−	0.384107i	−0.458017	−	0.888943i	$-0.651440\pi$
$3$	1.21559	−	1.15232i	0.405198	−	0.384107i	0.863215	+	0.504836i	$0.168447\pi$
$4$	1.71273	+	2.34681i	0.428183	+	0.586703i
$5$	−8.23255	+	0.0879738i	−1.64651	+	0.0175948i	−0.829320	−	0.558774i	$-0.811272\pi$
$5$	−8.23255	+	0.0879738i	−1.64651	+	0.0175948i	−0.817190	+	0.576369i	$0.804469\pi$
$6$	−4.21956	+	1.25234i	−0.703260	+	0.208724i
$7$	5.60756	−	4.18991i	0.801079	−	0.598558i
$7$	5.60756	−	4.18991i	0.801079	−	0.598558i
$8$	0.459099	+	2.83969i	0.0573873	+	0.354961i
$9$	−0.330804	+	6.18564i	−0.0367560	+	0.687294i
$10$	19.3908	+	9.59470i	1.93908	+	0.959470i
$11$	−0.332322	+	0.295388i	−0.0302111	+	0.0268535i	−0.679322	−	0.733840i	$-0.737726\pi$
$11$	−0.332322	+	0.295388i	−0.0302111	+	0.0268535i	0.649111	+	0.760694i	$0.275141\pi$
$12$	4.78627	+	0.879150i	0.398856	+	0.0732625i
$13$	18.7917	+	11.3917i	1.44552	+	0.876282i	0.999821	−	0.0189022i	$-0.00601713\pi$
$13$	18.7917	+	11.3917i	1.44552	+	0.876282i	0.445697	+	0.895184i	$0.352956\pi$
$14$	−18.1247	+	3.13977i	−1.29462	+	0.224269i
$15$	−9.90606	+	9.59349i	−0.660404	+	0.639566i
$16$	5.84904	−	18.2668i	0.365565	−	1.14167i
$17$	−10.2330	+	1.20839i	−0.601943	+	0.0710816i	−0.412729	−	0.910854i	$-0.635424\pi$
$17$	−10.2330	+	1.20839i	−0.601943	+	0.0710816i	−0.189215	+	0.981936i	$0.560594\pi$
$18$	8.13893	−	14.0970i	0.452163	−	0.783169i
$19$	6.36972	−	3.67756i	0.335248	−	0.193556i	−0.322921	−	0.946426i	$-0.604665\pi$
$19$	6.36972	−	3.67756i	0.335248	−	0.193556i	0.658169	+	0.752870i	$0.271331\pi$
$20$	−14.3066	−	19.1696i	−0.715331	−	0.958478i
$21$	1.98839	−	11.5549i	0.0946852	−	0.550235i
$22$	1.13018	−	0.296367i	0.0513716	−	0.0134712i
$23$	−9.92423	−	28.8554i	−0.431488	−	1.25458i	−0.923366	−	0.383920i	$-0.874574\pi$
$23$	−9.92423	−	28.8554i	−0.431488	−	1.25458i	0.491878	−	0.870664i	$-0.336311\pi$
$24$	3.83031	+	2.92288i	0.159596	+	0.121787i
$25$	42.7728	−	0.914253i	1.71091	−	0.0365701i
$26$	−30.4610	−	49.0582i	−1.17158	−	1.88686i
$27$	16.4976	+	19.3790i	0.611022	+	0.717741i
$28$	19.4372	+	5.98368i	0.694184	+	0.213703i
$29$	27.4310	−	5.34218i	0.945895	−	0.184213i	0.305442	−	0.952211i	$-0.401196\pi$
$29$	27.4310	−	5.34218i	0.945895	−	0.184213i	0.640453	+	0.767998i	$0.278747\pi$
$30$	34.6275	−	10.6812i	1.15425	−	0.356039i
$31$	−22.1006	+	8.67386i	−0.712924	+	0.279802i	−0.693955	−	0.720018i	$-0.744133\pi$
$31$	−22.1006	+	8.67386i	−0.712924	+	0.279802i	−0.0189685	+	0.999820i	$0.506038\pi$
$32$	−27.3562	+	27.6501i	−0.854883	+	0.864067i
$33$	−0.0635865	+	0.742015i	−0.00192686	+	0.0224853i
$34$	25.4111	+	9.35152i	0.747386	+	0.275045i
$35$	−45.7959	+	34.9869i	−1.30845	+	0.999627i
$36$	−15.0831	+	9.81802i	−0.418975	+	0.272723i
$37$	−15.9767	−	6.86920i	−0.431803	−	0.185654i	0.168025	−	0.985783i	$-0.446261\pi$
$37$	−15.9767	−	6.86920i	−0.431803	−	0.185654i	−0.599828	+	0.800129i	$0.704764\pi$
$38$	−19.3002	+	1.03216i	−0.507900	+	0.0271622i
$39$	35.9700	−	7.80650i	0.922308	−	0.200167i
$40$	−4.02937	−	23.3375i	−0.100734	−	0.583437i
$41$	32.4782	−	22.6554i	0.792151	−	0.552570i	−0.104908	−	0.994482i	$-0.533455\pi$
$41$	32.4782	−	22.6554i	0.792151	−	0.552570i	0.897058	+	0.441912i	$0.145700\pi$
$42$	−18.4142	+	24.7021i	−0.438433	+	0.588146i
$43$	1.27177	−	7.86637i	0.0295761	−	0.182939i	−0.968147	−	0.250383i	$-0.919444\pi$
$43$	1.27177	−	7.86637i	0.0295761	−	0.182939i	0.997723	+	0.0674439i	$0.0214844\pi$
$44$	−1.26240	−	0.273976i	−0.0286909	−	0.00622673i
$45$	2.17919	−	50.9527i	0.0484264	−	1.13228i
$46$	−11.1031	+	79.4132i	−0.241372	+	1.72637i
$47$	39.1313	+	9.81576i	0.832580	+	0.208846i	0.636046	−	0.771651i	$-0.280569\pi$
$47$	39.1313	+	9.81576i	0.832580	+	0.208846i	0.196534	+	0.980497i	$0.437031\pi$
$48$	−13.9392	−	28.9450i	−0.290399	−	0.603020i
$49$	13.8893	−	46.9903i	0.283456	−	0.958985i
$50$	−101.291	−	48.7790i	−2.02581	−	0.975580i
$51$	−11.0468	+	13.2607i	−0.216603	+	0.260013i
$52$	5.45115	+	63.6115i	0.104830	+	1.22330i
$53$	−3.32775	+	12.1591i	−0.0627876	+	0.229417i	−0.989078	−	0.147394i	$-0.952911\pi$
$53$	−3.32775	+	12.1591i	−0.0627876	+	0.229417i	0.926290	+	0.376811i	$0.122979\pi$
$54$	−15.5777	−	65.0387i	−0.288475	−	1.20442i
$55$	2.70987	−	2.46103i	0.0492704	−	0.0447461i
$56$	14.4724	+	14.0001i	0.258437	+	0.250002i
$57$	3.50526	−	11.8104i	0.0614958	−	0.207200i
$58$	−70.6213	−	20.1415i	−1.21761	−	0.347267i
$59$	75.2222	−	35.2399i	1.27495	−	0.597287i	0.336172	−	0.941801i	$-0.390868\pi$
$59$	75.2222	−	35.2399i	1.27495	−	0.597287i	0.938781	+	0.344514i	$0.111956\pi$
$60$	−39.4805	−	6.81658i	−0.658009	−	0.113610i
$61$	−4.68149	−	109.460i	−0.0767458	−	1.79443i	−0.477891	−	0.878419i	$-0.658599\pi$
$61$	−4.68149	−	109.460i	−0.0767458	−	1.79443i	0.401145	−	0.916015i	$-0.368612\pi$
$62$	62.1005	+	5.99076i	1.00162	+	0.0966251i
$63$	24.0623	+	36.0724i	0.381941	+	0.572577i
$64$	24.1908	−	8.03189i	0.377981	−	0.125498i
$65$	−155.706	−	92.1292i	−2.39548	−	1.41737i
$66$	1.03233	−	1.66259i	0.0156413	−	0.0251908i
$67$	96.0768	−	14.4812i	1.43398	−	0.216138i	0.614352	−	0.789032i	$-0.289417\pi$
$67$	96.0768	−	14.4812i	1.43398	−	0.216138i	0.819630	+	0.572894i	$0.194179\pi$
$68$	−20.3623	−	21.9454i	−0.299446	−	0.322726i
$69$	−45.3146	−	23.6406i	−0.656733	−	0.342617i
$70$	148.936	−	27.4428i	2.12766	−	0.392040i
$71$	−15.8926	−	3.09509i	−0.223840	−	0.0435929i	0.0779919	−	0.996954i	$-0.475149\pi$
$71$	−15.8926	−	3.09509i	−0.223840	−	0.0435929i	−0.301832	+	0.953361i	$0.597598\pi$
$72$	−17.7172	+	1.90044i	−0.246072	+	0.0263950i
$73$	9.75699	−	2.44746i	0.133657	−	0.0335269i	−0.175897	−	0.984409i	$-0.556283\pi$
$73$	9.75699	−	2.44746i	0.133657	−	0.0335269i	0.309555	+	0.950882i	$0.399820\pi$
$74$	29.2503	+	35.1124i	0.395274	+	0.474492i
$75$	50.9409	−	50.3994i	0.679212	−	0.671992i
$76$	19.5402	+	8.64985i	0.257107	+	0.113814i
$77$	−0.625865	+	3.04881i	−0.00812812	+	0.0395949i
$78$	−93.5591	−	24.5341i	−1.19948	−	0.314540i
$79$	7.97479	+	106.416i	0.100947	+	1.34704i	0.785855	+	0.618411i	$0.212223\pi$
$79$	7.97479	+	106.416i	0.100947	+	1.34704i	−0.684908	+	0.728629i	$0.740158\pi$
$80$	−46.5455	+	150.897i	−0.581818	+	1.88621i
$81$	−13.0471	−	1.39951i	−0.161076	−	0.0172779i
$82$	−103.056	+	14.4088i	−1.25679	+	0.175717i
$83$	−65.3104	+	6.30041i	−0.786872	+	0.0759086i	−0.481640	−	0.876369i	$-0.659959\pi$
$83$	−65.3104	+	6.30041i	−0.786872	+	0.0759086i	−0.305232	+	0.952278i	$0.598734\pi$
$84$	30.5228	−	15.1242i	0.363367	−	0.180049i
$85$	84.1377	−	10.8483i	0.989855	−	0.127628i
$86$	−12.3442	+	16.9142i	−0.143537	+	0.196677i
$87$	27.1890	−	38.1032i	0.312517	−	0.437968i
$88$	−0.991379	−	0.808079i	−0.0112657	−	0.00918271i
$89$	145.941	−	60.9080i	1.63979	−	0.684360i	0.643107	−	0.765776i	$-0.277645\pi$
$89$	145.941	−	60.9080i	1.63979	−	0.684360i	0.996680	+	0.0814162i	$0.0259443\pi$
$90$	−65.7640	+	116.771i	−0.730711	+	1.29745i
$91$	153.106	−	14.8563i	1.68248	−	0.163256i
$92$	50.7207	−	72.7120i	0.551312	−	0.790347i
$93$	−16.8703	+	36.0109i	−0.181401	+	0.387214i
$94$	−79.9857	−	69.5806i	−0.850912	−	0.740219i
$95$	−52.1155	+	30.8360i	−0.548584	+	0.324590i
$96$	−1.39223	+	65.1346i	−0.0145024	+	0.678485i
$97$	53.1690	+	42.4009i	0.548134	+	0.437122i	0.857994	−	0.513660i	$-0.171711\pi$
$97$	53.1690	+	42.4009i	0.548134	+	0.437122i	−0.309860	+	0.950782i	$0.600282\pi$
$98$	−88.4797	+	93.5471i	−0.902854	+	0.954562i
$99$	−1.71723	−	2.15334i	−0.0173458	−	0.0217509i
$100$	75.4040	+	98.8138i	0.754040	+	0.988138i
$101$	46.2896	+	30.8404i	0.458313	+	0.305350i	0.762181	−	0.647364i	$-0.224129\pi$
$101$	46.2896	+	30.8404i	0.458313	+	0.305350i	−0.303868	+	0.952714i	$0.598278\pi$
$102$	41.6656	−	17.9141i	0.408486	−	0.175629i
$103$	47.6414	−	23.5733i	0.462538	−	0.228867i	−0.197200	−	0.980363i	$-0.563185\pi$
$103$	47.6414	−	23.5733i	0.462538	−	0.228867i	0.659737	+	0.751497i	$0.270668\pi$
$104$	−23.7215	+	58.5926i	−0.228091	+	0.563390i
$105$	−15.3530	+	95.3015i	−0.146219	+	0.907633i
$106$	22.2711	−	24.5229i	0.210105	−	0.231349i
$107$	−46.7879	+	85.1931i	−0.437270	+	0.796197i	−0.999527	−	0.0307657i	$-0.990205\pi$
$107$	−46.7879	+	85.1931i	−0.437270	+	0.796197i	0.562257	+	0.826963i	$0.309933\pi$
$108$	−17.2229	+	71.9078i	−0.159471	+	0.665813i
$109$	−15.7044	−	28.5952i	−0.144077	−	0.262341i	0.794603	−	0.607129i	$-0.207679\pi$
$109$	−15.7044	−	28.5952i	−0.144077	−	0.262341i	−0.938681	+	0.344788i	$0.887951\pi$
$110$	−9.27816	+	2.53928i	−0.0843469	+	0.0230844i
$111$	−27.3368	+	10.0602i	−0.246277	+	0.0906322i
$112$	−43.7373	−	126.939i	−0.390512	−	1.13338i
$113$	87.4191	+	11.2714i	0.773620	+	0.0997473i	0.504561	−	0.863376i	$-0.331655\pi$
$113$	87.4191	+	11.2714i	0.773620	+	0.0997473i	0.269060	+	0.963124i	$0.413287\pi$
$114$	−22.2718	+	23.4947i	−0.195367	+	0.206094i
$115$	84.2402	+	236.681i	0.732524	+	2.05809i
$116$	59.5190	+	55.2255i	0.513095	+	0.476082i
$117$	−76.6812	+	112.471i	−0.655394	+	0.961287i
$118$	−218.173	−	6.99639i	−1.84892	−	0.0592914i
$119$	−52.3193	+	49.6516i	−0.439658	+	0.417240i
$120$	−31.7904	−	23.7258i	−0.264920	−	0.197715i
$121$	−14.1667	+	119.969i	−0.117081	+	0.991477i
$122$	−119.345	+	262.002i	−0.978236	+	2.14756i
$123$	13.3740	−	64.9651i	0.108732	−	0.528171i
$124$	−58.2084	−	37.0100i	−0.469423	−	0.298468i
$125$	−146.329	+	4.69249i	−1.17063	+	0.0375399i
$126$	−13.4258	−	113.151i	−0.106554	−	0.898027i
$127$	−23.7822	−	20.2461i	−0.187261	−	0.159418i	0.549678	−	0.835376i	$-0.314750\pi$
$127$	−23.7822	−	20.2461i	−0.187261	−	0.159418i	−0.736940	+	0.675958i	$0.763730\pi$
$128$	87.6133	+	13.2056i	0.684479	+	0.103169i
$129$	−7.51863	−	11.0278i	−0.0582840	−	0.0854869i
$130$	255.087	+	401.195i	1.96221	+	3.08611i
$131$	64.5815	+	169.866i	0.492989	+	1.29669i	0.919814	+	0.392355i	$0.128339\pi$
$131$	64.5815	+	169.866i	0.492989	+	1.29669i	−0.426825	+	0.904334i	$0.640368\pi$
$132$	−1.85027	+	1.12165i	−0.0140172	+	0.00849733i
$133$	20.3099	−	47.3106i	0.152706	−	0.355719i
$134$	−242.315	−	80.4542i	−1.80832	−	0.600404i
$135$	−137.522	−	158.087i	−1.01868	−	1.17102i
$136$	−8.12942	−	28.5039i	−0.0597751	−	0.209587i
$137$	1.48370	−	138.844i	0.0108299	−	1.01346i	−0.856624	−	0.515941i	$-0.827442\pi$
$137$	1.48370	−	138.844i	0.0108299	−	1.01346i	0.867454	−	0.497517i	$-0.165755\pi$
$138$	78.0128	+	109.329i	0.565310	+	0.792237i
$139$	−6.58646	+	102.589i	−0.0473846	+	0.738053i	0.903516	+	0.428555i	$0.140977\pi$
$139$	−6.58646	+	102.589i	−0.0473846	+	0.738053i	−0.950900	+	0.309498i	$0.899839\pi$
$140$	−160.544	−	47.5510i	−1.14674	−	0.339650i
$141$	58.8787	−	33.1599i	0.417579	−	0.235176i
$142$	33.5464	+	26.1709i	0.236242	+	0.184302i
$143$	−9.60988	+	1.76516i	−0.0672019	+	0.0123438i
$144$	111.057	+	42.2228i	0.771229	+	0.293214i
$145$	−225.357	+	46.3929i	−1.55418	+	0.319951i
$146$	−25.7710	−	5.88206i	−0.176514	−	0.0402881i
$147$	−37.2641	−	73.1261i	−0.253497	−	0.497457i
$148$	−11.2432	−	49.2595i	−0.0759672	−	0.332834i
$149$	28.0760	−	12.7889i	0.188430	−	0.0858318i	−0.318089	−	0.948061i	$-0.603041\pi$
$149$	28.0760	−	12.7889i	0.188430	−	0.0858318i	0.506518	+	0.862229i	$0.330932\pi$
$150$	−179.337	+	57.4240i	−1.19558	+	0.382826i
$151$	148.668	+	79.5924i	0.984557	+	0.527102i	0.883828	−	0.467812i	$-0.154957\pi$
$151$	148.668	+	79.5924i	0.984557	+	0.527102i	0.100729	+	0.994914i	$0.467883\pi$
$152$	13.3674	+	16.3996i	0.0879437	+	0.107892i
$153$	−4.08953	−	63.6977i	−0.0267289	−	0.416325i
$154$	5.09577	−	6.39723i	0.0330894	−	0.0415404i
$155$	181.181	−	73.3522i	1.16891	−	0.473240i
$156$	79.9274	+	71.0443i	0.512355	+	0.455412i
$157$	−17.4204	−	22.3299i	−0.110958	−	0.142228i	0.729757	−	0.683707i	$-0.239633\pi$
$157$	−17.4204	−	22.3299i	−0.110958	−	0.142228i	−0.840714	+	0.541479i	$0.817865\pi$
$158$	108.006	−	258.791i	0.683580	−	1.63792i
$159$	9.96599	+	18.6151i	0.0626792	+	0.117076i
$160$	222.779	−	230.038i	1.39237	−	1.43774i
$161$	−176.552	−	120.227i	−1.09660	−	0.746751i
$162$	28.8989	+	18.8111i	0.178388	+	0.116118i
$163$	−131.191	−	196.910i	−0.804852	−	1.20804i	−0.974910	−	0.222601i	$-0.928545\pi$
$163$	−131.191	−	196.910i	−0.804852	−	1.20804i	0.170058	−	0.985434i	$-0.445605\pi$
$164$	108.794	+	37.4175i	0.663380	+	0.228156i
$165$	0.458201	−	6.11427i	0.00277697	−	0.0370562i
$166$	160.501	+	62.9919i	0.966871	+	0.379469i
$167$	202.091	−	89.4596i	1.21012	−	0.535686i	0.301567	−	0.953445i	$-0.402490\pi$
$167$	202.091	−	89.4596i	1.21012	−	0.535686i	0.908558	+	0.417759i	$0.137184\pi$
$168$	33.7253	+	0.341546i	0.200746	+	0.00203301i
$169$	145.190	+	278.303i	0.859115	+	1.64676i
$170$	−210.021	−	74.7514i	−1.23542	−	0.439714i
$171$	20.6409	+	40.6173i	0.120707	+	0.237528i
$172$	20.6391	−	10.4884i	0.119995	−	0.0609789i
$173$	62.6121	−	175.915i	0.361920	−	1.01685i	−0.612178	−	0.790720i	$-0.709706\pi$
$173$	62.6121	−	175.915i	0.361920	−	1.01685i	0.974098	−	0.226127i	$-0.0726065\pi$
$174$	−109.056	+	56.8946i	−0.626760	+	0.326980i
$175$	236.020	−	184.341i	1.34869	−	1.05338i
$176$	3.45203	+	7.79819i	0.0196138	+	0.0443079i
$177$	50.8320	−	129.518i	0.287186	−	0.731739i
$178$	−414.401	−	31.0551i	−2.32810	−	0.174467i
$179$	−45.5649	+	132.483i	−0.254552	+	0.740130i	0.742940	+	0.669358i	$0.233431\pi$
$179$	−45.5649	+	132.483i	−0.254552	+	0.740130i	−0.997493	+	0.0707720i	$0.977454\pi$
$180$	123.309	−	82.1542i	0.685049	−	0.456412i
$181$	113.358	−	174.149i	0.626288	−	0.962147i	−0.373121	−	0.927783i	$-0.621712\pi$
$181$	113.358	−	174.149i	0.626288	−	0.962147i	0.999409	−	0.0343643i	$-0.0109406\pi$
$182$	−376.361	−	147.468i	−2.06792	−	0.810265i
$183$	−131.825	−	127.665i	−0.720353	−	0.697623i
$184$	77.3842	−	41.4292i	0.420566	−	0.225159i
$185$	132.133	+	55.1455i	0.714235	+	0.298084i
$186$	82.3923	−	64.2774i	0.442969	−	0.345578i
$187$	3.04372	−	3.42429i	0.0162766	−	0.0183117i
$188$	43.9857	+	108.645i	0.233966	+	0.577902i
$189$	173.707	+	39.5455i	0.919087	+	0.209235i
$190$	158.799	−	10.1952i	0.835784	−	0.0536591i
$191$	−131.078	+	106.843i	−0.686274	+	0.559386i	−0.909665	−	0.415343i	$-0.863661\pi$
$191$	−131.078	+	106.843i	−0.686274	+	0.559386i	0.223391	+	0.974729i	$0.428287\pi$
$192$	20.1508	−	37.6391i	0.104952	−	0.196037i
$193$	−60.4153	−	188.680i	−0.313033	−	0.977614i	−0.973874	−	0.227089i	$-0.927079\pi$
$193$	−60.4153	−	188.680i	−0.313033	−	0.977614i	0.660841	−	0.750526i	$-0.270200\pi$
$194$	−74.0790	−	162.628i	−0.381850	−	0.838290i
$195$	−295.438	+	67.4318i	−1.51507	+	0.345804i
$196$	134.066	−	47.8861i	0.684010	−	0.244317i
$197$	−27.9953	+	122.655i	−0.142108	+	0.622617i	0.852835	+	0.522180i	$0.174881\pi$
$197$	−27.9953	+	122.655i	−0.142108	+	0.622617i	−0.994943	+	0.100437i	$0.967976\pi$
$198$	1.45935	+	7.08891i	0.00737048	+	0.0358026i
$199$	−81.0220	+	213.109i	−0.407146	+	1.07090i	0.562589	+	0.826737i	$0.309806\pi$
$199$	−81.0220	+	213.109i	−0.407146	+	1.07090i	−0.969734	+	0.244162i	$0.921487\pi$
$200$	22.2331	+	121.042i	0.111166	+	0.605208i
$201$	100.103	−	128.315i	0.498027	−	0.638382i
$202$	−71.7256	−	127.356i	−0.355077	−	0.630476i
$203$	131.437	−	144.890i	0.647475	−	0.713743i
$204$	−50.0404	−	3.21270i	−0.245296	−	0.0157485i
$205$	−265.385	+	189.369i	−1.29456	+	0.923749i
$206$	−139.671	−	1.49254i	−0.678017	−	0.00724535i
$207$	181.772	−	51.8423i	0.878128	−	0.250446i
$208$	318.003	−	276.634i	1.52886	−	1.32997i
$209$	−1.03049	+	3.10367i	−0.00493058	+	0.0148501i
$210$	149.423	−	204.982i	0.711537	−	0.976102i
$211$	−211.892	−	349.538i	−1.00423	−	1.65658i	−0.714729	−	0.699402i	$-0.753450\pi$
$211$	−211.892	−	349.538i	−1.00423	−	1.65658i	−0.289499	−	0.957178i	$-0.593489\pi$
$212$	−34.2346	+	13.0157i	−0.161484	+	0.0613947i
$213$	−22.8856	+	14.5511i	−0.107444	+	0.0683149i
$214$	211.030	−	143.878i	0.986122	−	0.672326i
$215$	−9.77790	+	64.8722i	−0.0454786	+	0.301731i
$216$	−47.4563	+	55.7449i	−0.219705	+	0.258078i
$217$	−87.5879	+	141.239i	−0.403631	+	0.650870i
$218$	2.74775	+	85.6848i	0.0126043	+	0.393050i
$219$	9.04028	−	14.2183i	0.0412798	−	0.0649238i
$220$	10.4169	+	2.14446i	0.0473494	+	0.00974756i
$221$	−206.062	−	93.8636i	−0.932408	−	0.424722i
$222$	76.0173	+	8.97665i	0.342420	+	0.0404354i
$223$	122.532	−	164.182i	0.549472	−	0.736243i	−0.437128	−	0.899399i	$-0.644004\pi$
$223$	122.532	−	164.182i	0.549472	−	0.736243i	0.986600	+	0.163156i	$0.0521675\pi$
$224$	−37.5501	+	269.670i	−0.167635	+	1.20388i
$225$	−8.49418	+	264.880i	−0.0377519	+	1.17724i
$226$	−191.375	−	130.477i	−0.846791	−	0.577332i
$227$	−289.828	+	312.360i	−1.27677	+	1.37603i	−0.385410	+	0.922746i	$0.625940\pi$
$227$	−289.828	+	312.360i	−1.27677	+	1.37603i	−0.891364	+	0.453289i	$0.850251\pi$
$228$	33.7203	−	12.0018i	0.147896	−	0.0526397i
$229$	168.926	+	160.133i	0.737668	+	0.699272i	0.961331	−	0.275394i	$-0.0888085\pi$
$229$	168.926	+	160.133i	0.737668	+	0.699272i	−0.223663	+	0.974666i	$0.571802\pi$
$230$	84.4207	−	654.750i	0.367046	−	2.84674i
$231$	2.75241	+	4.42731i	0.0119152	+	0.0191658i
$232$	27.7636	+	75.4427i	0.119671	+	0.325184i
$233$	−14.2329	−	52.0050i	−0.0610855	−	0.223197i	0.927509	−	0.373802i	$-0.121946\pi$
$233$	−14.2329	−	52.0050i	−0.0610855	−	0.223197i	−0.988594	+	0.150605i	$0.951878\pi$
$234$	313.533	−	172.192i	1.33989	−	0.735863i
$235$	−323.014	−	77.3662i	−1.37453	−	0.329218i
$236$	211.537	+	116.176i	0.896343	+	0.492270i
$237$	132.320	+	120.169i	0.558312	+	0.507044i
$238$	181.676	−	54.0310i	0.763346	−	0.227021i
$239$	−258.347	−	104.593i	−1.08095	−	0.437629i	−0.235606	−	0.971849i	$-0.575707\pi$
$239$	−258.347	−	104.593i	−1.08095	−	0.437629i	−0.845345	+	0.534220i	$0.820605\pi$
$240$	117.301	+	237.065i	0.488755	+	0.987769i
$241$	89.5552	+	208.292i	0.371598	+	0.864282i	0.996501	+	0.0835793i	$0.0266352\pi$
$241$	89.5552	+	208.292i	0.371598	+	0.864282i	−0.624903	+	0.780703i	$0.714861\pi$
$242$	176.010	−	264.181i	0.727314	−	1.09166i
$243$	−199.564	+	152.286i	−0.821251	+	0.626690i
$244$	248.865	−	198.463i	1.01994	−	0.813373i
$245$	−110.211	+	388.072i	−0.449840	+	1.58397i
$246$	−108.671	+	136.269i	−0.441753	+	0.553941i
$247$	161.592	+	3.45396i	0.654217	+	0.0139836i
$248$	−34.7774	−	58.7767i	−0.140232	−	0.237003i
$249$	−72.1308	+	82.9173i	−0.289682	+	0.333001i
$250$	348.386	+	163.211i	1.39354	+	0.652844i
$251$	56.9395	+	39.7186i	0.226851	+	0.158241i	0.680045	−	0.733171i	$-0.261960\pi$
$251$	56.9395	+	39.7186i	0.226851	+	0.158241i	−0.453194	+	0.891412i	$0.649715\pi$
$252$	−43.4428	+	118.252i	−0.172392	+	0.469254i
$253$	11.8216	+	6.65780i	0.0467257	+	0.0263154i
$254$	31.6108	+	75.7422i	0.124452	+	0.298198i
$255$	89.7765	−	110.141i	0.352065	−	0.431925i
$256$	−272.522	−	194.461i	−1.06454	−	0.759613i
$257$	−105.093	−	76.6981i	−0.408921	−	0.298436i	0.365855	−	0.930672i	$-0.380777\pi$
$257$	−105.093	−	76.6981i	−0.408921	−	0.298436i	−0.774776	+	0.632236i	$0.782137\pi$
$258$	4.48507	+	34.7853i	0.0173840	+	0.134827i
$259$	−118.372	+	28.4216i	−0.457034	+	0.109736i
$260$	−50.4730	−	523.205i	−0.194127	−	2.01233i
$261$	23.9705	+	171.445i	0.0918411	+	0.656879i
$262$	50.9321	−	474.823i	0.194397	−	1.81230i
$263$	−148.156	−	45.7001i	−0.563331	−	0.173765i	−6.05447e−6	−	1.00000i	$-0.500002\pi$
$263$	−148.156	−	45.7001i	−0.563331	−	0.173765i	−0.563325	+	0.826235i	$0.690478\pi$
$264$	−2.13628	+	0.160092i	−0.00809198	+	0.000606410i
$265$	26.3261	−	100.393i	0.0993439	−	0.378841i
$266$	−103.902	+	86.6539i	−0.390610	+	0.325767i
$267$	107.219	−	242.211i	0.401571	−	0.907156i
$268$	198.539	+	200.672i	0.740816	+	0.748775i
$269$	208.003	−	173.277i	0.773246	−	0.644151i	−0.166493	−	0.986043i	$-0.553244\pi$
$269$	208.003	−	173.277i	0.773246	−	0.644151i	0.939739	+	0.341892i	$0.111068\pi$
$270$	133.966	+	534.064i	0.496169	+	1.97801i
$271$	27.6358	+	257.639i	0.101977	+	0.950698i	0.924297	+	0.381673i	$0.124652\pi$
$271$	27.6358	+	257.639i	0.101977	+	0.950698i	−0.822320	+	0.569025i	$0.807321\pi$
$272$	−37.7800	+	193.993i	−0.138897	+	0.713208i
$273$	168.995	−	194.486i	0.619030	−	0.712404i
$274$	−168.769	+	323.498i	−0.615944	+	1.18065i
$275$	−13.9443	+	12.9384i	−0.0507065	+	0.0470488i
$276$	−22.1318	−	146.835i	−0.0801877	−	0.532010i
$277$	−352.680	−	218.984i	−1.27321	−	0.790555i	−0.287303	−	0.957840i	$-0.592759\pi$
$277$	−352.680	−	218.984i	−1.27321	−	0.790555i	−0.985909	+	0.167285i	$0.946500\pi$
$278$	137.562	−	232.491i	0.494827	−	0.836299i
$279$	−46.3424	−	139.576i	−0.166102	−	0.500272i
$280$	−120.377	−	113.983i	−0.429917	−	0.407084i
$281$	29.2619	−	303.331i	0.104135	−	1.07947i	−0.784274	−	0.620415i	$-0.786964\pi$
$281$	29.2619	−	303.331i	0.104135	−	1.07947i	0.888409	−	0.459053i	$-0.151811\pi$
$282$	−177.409	+	7.58759i	−0.629111	+	0.0269063i
$283$	17.8309	−	103.274i	0.0630066	−	0.364925i	−0.936877	−	0.349660i	$-0.886297\pi$
$283$	17.8309	−	103.274i	0.0630066	−	0.364925i	0.999883	−	0.0152650i	$-0.00485919\pi$
$284$	−19.9563	−	42.5981i	−0.0702685	−	0.149993i
$285$	−27.8182	+	97.5379i	−0.0976078	+	0.342238i
$286$	24.6141	+	7.30533i	0.0860633	+	0.0255431i
$287$	87.1993	−	263.122i	0.303830	−	0.916801i
$288$	−161.984	−	178.363i	−0.562446	−	0.619315i
$289$	−177.796	+	42.5846i	−0.615211	+	0.147352i
$290$	583.165	+	159.603i	2.01091	+	0.550355i
$291$	113.491	−	9.72557i	0.390005	−	0.0334212i
$292$	22.4548	+	18.7060i	0.0769001	+	0.0640615i
$293$	140.085	−	290.889i	0.478106	−	0.992797i	−0.512834	−	0.858488i	$-0.671404\pi$
$293$	140.085	−	290.889i	0.478106	−	0.992797i	0.990940	−	0.134309i	$-0.0428814\pi$
$294$	0.241009	+	215.672i	0.000819759	+	0.733580i
$295$	−616.170	+	296.732i	−2.08871	+	1.00587i
$296$	12.1715	−	48.5225i	0.0411199	−	0.163928i
$297$	−11.2068	−	1.56688i	−0.0377335	−	0.00527569i
$298$	−80.9977	−	3.46417i	−0.271804	−	0.0116247i
$299$	142.218	−	655.297i	0.475645	−	2.19163i
$300$	205.526	+	33.2279i	0.685087	+	0.110760i
$301$	−25.8278	−	49.4397i	−0.0858067	−	0.164252i
$302$	−253.525	−	363.447i	−0.839485	−	1.20347i
$303$	91.8075	−	15.8512i	0.302995	−	0.0523141i
$304$	−29.9204	−	137.864i	−0.0984225	−	0.453501i
$305$	48.1703	+	900.727i	0.157935	+	2.95320i
$306$	−66.2513	+	154.091i	−0.216508	+	0.503564i
$307$	−70.9730	−	109.034i	−0.231182	−	0.355158i	0.703468	−	0.710727i	$-0.251634\pi$
$307$	−70.9730	−	109.034i	−0.231182	−	0.355158i	−0.934650	+	0.355569i	$0.884287\pi$
$308$	−8.22691	+	3.75300i	−0.0267107	+	0.0121851i
$309$	30.7486	−	83.5538i	0.0995099	−	0.270401i
$310$	−511.772	−	43.8560i	−1.65088	−	0.141471i
$311$	232.351	+	229.882i	0.747110	+	0.739169i	0.971940	−	0.235229i	$-0.0755839\pi$
$311$	232.351	+	229.882i	0.747110	+	0.739169i	−0.224830	+	0.974398i	$0.572183\pi$
$312$	38.6818	+	98.5596i	0.123980	+	0.315896i
$313$	174.415	+	565.438i	0.557235	+	1.80651i	0.590464	+	0.807064i	$0.298945\pi$
$313$	174.415	+	565.438i	0.557235	+	1.80651i	−0.0332291	+	0.999448i	$0.510579\pi$
$314$	14.2265	+	73.0502i	0.0453074	+	0.232644i
$315$	−201.267	−	294.851i	−0.638944	−	0.936034i
$316$	−236.080	+	200.978i	−0.747088	+	0.636006i
$317$	117.120	−	72.7217i	0.369465	−	0.229406i	−0.330146	−	0.943930i	$-0.607098\pi$
$317$	117.120	−	72.7217i	0.369465	−	0.229406i	0.699611	+	0.714524i	$0.253357\pi$
$318$	−1.18572	−	55.4734i	−0.00372869	−	0.174445i
$319$	−7.53790	+	9.87811i	−0.0236298	+	0.0309659i
$320$	−198.445	+	68.2511i	−0.620141	+	0.213285i
$321$	41.2948	+	157.475i	0.128644	+	0.490576i
$322$	270.473	+	491.835i	0.839978	+	1.52744i
$323$	−60.7376	+	45.3297i	−0.188042	+	0.140340i
$324$	−19.0619	−	33.0161i	−0.0588330	−	0.101902i
$325$	814.190	+	470.073i	2.50520	+	1.44638i
$326$	72.9157	+	617.475i	0.223668	+	1.89409i
$327$	−52.0411	−	16.6636i	−0.159147	−	0.0509590i
$328$	79.2448	+	81.8268i	0.241600	+	0.249472i
$329$	260.558	−	108.914i	0.791969	−	0.331046i
$330$	−8.35240	+	13.7782i	−0.0253103	+	0.0417520i
$331$	−47.9675	+	261.145i	−0.144917	+	0.788956i	0.828513	+	0.559970i	$0.189187\pi$
$331$	−47.9675	+	261.145i	−0.144917	+	0.788956i	−0.973430	+	0.228986i	$0.926459\pi$
$332$	−126.645	−	142.480i	−0.381461	−	0.429157i
$333$	47.7756	−	96.5540i	0.143470	−	0.289952i
$334$	−579.931	−	31.0143i	−1.73632	−	0.0928573i
$335$	−789.683	+	127.670i	−2.35726	+	0.381104i
$336$	−199.441	−	103.907i	−0.593576	−	0.309246i
$337$	144.226	+	485.945i	0.427970	+	1.44197i	0.845825	+	0.533460i	$0.179109\pi$
$337$	144.226	+	485.945i	0.427970	+	1.44197i	−0.417855	+	0.908514i	$0.637218\pi$
$338$	−8.81408	−	824.818i	−0.0260772	−	2.44029i
$339$	119.254	−	87.0335i	0.351783	−	0.256736i
$340$	169.564	+	178.875i	0.498719	+	0.526103i
$341$	4.78237	−	9.41079i	0.0140246	−	0.0275976i
$342$		−	119.726i		−	0.350075i
$343$	−119.000	−	321.696i	−0.346938	−	0.937888i
$344$	22.9219			0.0666334
$345$	375.134	+	190.636i	1.08735	+	0.552568i
$346$	−356.104	+	337.569i	−1.02920	+	0.975632i
$347$	−136.380	−	186.870i	−0.393027	−	0.538531i	0.565045	−	0.825060i	$-0.308859\pi$
$347$	−136.380	−	186.870i	−0.393027	−	0.538531i	−0.958071	+	0.286529i	$0.907498\pi$
$348$	135.989	−	1.45319i	0.390772	−	0.00417582i
$349$	533.980	−	158.483i	1.53003	−	0.454105i	0.593542	−	0.804803i	$-0.297729\pi$
$349$	533.980	−	158.483i	1.53003	−	0.454105i	0.936488	+	0.350698i	$0.114056\pi$
$350$	−772.372	+	150.867i	−2.20678	+	0.431050i
$351$	89.2593	+	552.100i	0.254300	+	1.57293i
$352$	0.923560	−	17.2695i	0.00262375	−	0.0490610i
$353$	244.238	+	120.851i	0.691893	+	0.342354i	0.755066	−	0.655649i	$-0.227605\pi$
$353$	244.238	+	120.851i	0.691893	+	0.342354i	−0.0631727	+	0.998003i	$0.520122\pi$
$354$	−273.272	+	242.901i	−0.771955	+	0.686161i
$355$	131.109	+	24.0824i	0.369322	+	0.0678376i
$356$	392.898	+	238.177i	1.10365	+	0.669036i
$357$	−6.38441	+	120.645i	−0.0178835	+	0.337941i
$358$	264.463	−	256.119i	0.738725	−	0.715415i
$359$	48.0139	−	149.949i	0.133743	−	0.417686i	−0.862316	−	0.506370i	$-0.830987\pi$
$359$	48.0139	−	149.949i	0.133743	−	0.417686i	0.996060	+	0.0886835i	$0.0282660\pi$
$360$	145.690	−	17.2041i	0.404695	−	0.0477892i
$361$	−153.451	+	265.785i	−0.425072	+	0.736247i
$362$	−472.883	+	273.019i	−1.30631	+	0.754196i
$363$	121.022	+	162.158i	0.333393	+	0.446716i
$364$	297.094	+	333.865i	0.816192	+	0.917212i
$365$	−80.1095	+	21.0072i	−0.219478	+	0.0575540i
$366$	156.836	+	456.012i	0.428513	+	1.24593i
$367$	−401.776	−	306.592i	−1.09476	−	0.835400i	−0.107449	−	0.994211i	$-0.534268\pi$
$367$	−401.776	−	306.592i	−1.09476	−	0.835400i	−0.987309	+	0.158810i	$0.949234\pi$
$368$	−585.143	+	12.5072i	−1.59006	+	0.0339870i
$369$	129.394	+	208.393i	0.350662	+	0.564750i
$370$	−243.894	−	286.491i	−0.659172	−	0.774301i
$371$	32.2849	+	82.1257i	0.0870213	+	0.221363i
$372$	−113.405	+	22.0857i	−0.304853	+	0.0593701i
$373$	−26.8768	+	8.29039i	−0.0720558	+	0.0222263i	−0.330573	−	0.943780i	$-0.607242\pi$
$373$	−26.8768	+	8.29039i	−0.0720558	+	0.0222263i	0.258518	+	0.966007i	$0.416766\pi$
$374$	−11.2070	+	4.39843i	−0.0299653	+	0.0117605i
$375$	−172.470	+	174.322i	−0.459919	+	0.464860i
$376$	−9.90858	+	115.627i	−0.0263526	+	0.307519i
$377$	576.332	+	212.095i	1.52873	+	0.562587i
$378$	−359.859	−	299.439i	−0.952007	−	0.792167i
$379$	224.982	−	146.447i	0.593619	−	0.386403i	−0.213368	−	0.976972i	$-0.568443\pi$
$379$	224.982	−	146.447i	0.593619	−	0.386403i	0.806987	+	0.590569i	$0.201097\pi$
$380$	−161.626	−	69.4913i	−0.425332	−	0.182872i
$381$	−52.2395	+	2.79373i	−0.137112	+	0.00733263i
$382$	434.268	−	94.2482i	1.13683	−	0.246723i
$383$	−16.8621	−	97.6628i	−0.0440264	−	0.254994i	0.955124	−	0.296206i	$-0.0957216\pi$
$383$	−16.8621	−	97.6628i	−0.0440264	−	0.254994i	−0.999150	+	0.0412121i	$0.986878\pi$
$384$	121.719	−	84.9062i	0.316978	−	0.221110i
$385$	4.88425	−	25.1545i	0.0126864	−	0.0653364i
$386$	−83.0892	+	513.936i	−0.215257	+	1.33144i
$387$	48.2379	+	10.4690i	0.124646	+	0.0270516i
$388$	−8.44252	+	197.399i	−0.0217591	+	0.508760i
$389$	105.369	−	753.632i	0.270871	−	1.93736i	−0.0706893	−	0.997498i	$-0.522520\pi$
$389$	105.369	−	753.632i	0.270871	−	1.93736i	0.341560	−	0.939860i	$-0.389045\pi$
$390$	772.388	+	193.747i	1.98048	+	0.496788i
$391$	136.424	+	283.286i	0.348909	+	0.724518i
$392$	139.814	+	17.8682i	0.356669	+	0.0455822i
$393$	274.246	+	132.070i	0.697826	+	0.336055i
$394$	211.604	−	254.012i	0.537066	−	0.644700i
$395$	−75.0147	−	875.375i	−0.189911	−	2.21614i
$396$	2.11233	−	7.71812i	0.00533416	−	0.0194902i
$397$	−182.672	−	762.677i	−0.460130	−	1.92110i	−0.382012	−	0.924157i	$-0.624769\pi$
$397$	−182.672	−	762.677i	−0.460130	−	1.92110i	−0.0781179	−	0.996944i	$-0.524891\pi$
$398$	443.512	−	402.786i	1.11435	−	1.01202i
$399$	−29.8285	−	80.9141i	−0.0747581	−	0.202792i
$400$	233.479	−	786.669i	0.583698	−	1.96667i
$401$	−86.1008	−	24.5563i	−0.214715	−	0.0612377i	0.165195	−	0.986261i	$-0.447175\pi$
$401$	−86.1008	−	24.5563i	−0.214715	−	0.0612377i	−0.379911	+	0.925023i	$0.624045\pi$
$402$	−387.266	+	181.426i	−0.963349	+	0.451307i
$403$	−514.119	−	88.7661i	−1.27573	−	0.220263i
$404$	6.90521	+	161.454i	0.0170921	+	0.399640i
$405$	107.534	+	10.3737i	0.265517	+	0.0256141i
$406$	−480.404	+	182.952i	−1.18326	+	0.450621i
$407$	7.33850	−	2.43655i	0.0180307	−	0.00598661i
$408$	−42.7277	−	25.2814i	−0.104725	−	0.0619643i
$409$	−188.377	+	303.386i	−0.460579	+	0.741775i	−0.994610	−	0.103690i	$-0.966935\pi$
$409$	−188.377	+	303.386i	−0.460579	+	0.741775i	0.534031	+	0.845465i	$0.320677\pi$
$410$	847.149	−	127.687i	2.06622	−	0.311432i
$411$	−158.189	−	170.487i	−0.384889	−	0.414811i
$412$	136.919	+	71.4305i	0.332328	+	0.173375i
$413$	274.161	−	512.784i	0.663827	−	1.24161i
$414$	−487.549	−	94.9502i	−1.17765	−	0.229348i
$415$	537.116	−	57.6140i	1.29426	−	0.138829i
$416$	−829.052	+	207.961i	−1.99291	+	0.499906i
$417$	110.210	+	132.297i	0.264292	+	0.317259i
$418$	6.10899	−	6.04406i	0.0146148	−	0.0144595i
$419$	−3.71648	−	1.64517i	−0.00886987	−	0.00392643i	0.400344	−	0.916365i	$-0.368891\pi$
$419$	−3.71648	−	1.64517i	−0.00886987	−	0.00392643i	−0.409214	+	0.912439i	$0.634197\pi$
$420$	−249.950	+	127.195i	−0.595119	+	0.302846i
$421$	399.056	+	104.645i	0.947877	+	0.248562i	0.695060	−	0.718952i	$-0.255378\pi$
$421$	399.056	+	104.645i	0.947877	+	0.248562i	0.252817	+	0.967514i	$0.418643\pi$
$422$	80.2683	+	1071.11i	0.190209	+	2.53817i
$423$	−73.6616	+	238.805i	−0.174141	+	0.564551i
$424$	−36.0558	−	3.86754i	−0.0850372	−	0.00912155i
$425$	−436.591	+	61.0417i	−1.02727	+	0.143628i
$426$	70.9361	−	6.84312i	0.166517	−	0.0160637i
$427$	−484.881	−	594.191i	−1.13555	−	1.39155i
$428$	−280.067	+	36.1107i	−0.654363	+	0.0843707i
$429$	−9.64768	+	13.2194i	−0.0224888	+	0.0308144i
$430$	100.136	−	140.333i	0.232875	−	0.326356i
$431$	118.570	+	96.6471i	0.275104	+	0.224239i	0.759333	−	0.650702i	$-0.225525\pi$
$431$	118.570	+	96.6471i	0.275104	+	0.224239i	−0.484228	+	0.874942i	$0.660900\pi$
$432$	450.487	−	188.009i	1.04279	−	0.435207i
$433$	152.945	−	271.570i	0.353222	−	0.627182i	−0.636320	−	0.771425i	$-0.719544\pi$
$433$	152.945	−	271.570i	0.353222	−	0.627182i	0.989542	+	0.144243i	$0.0460748\pi$
$434$	373.333	−	226.602i	0.860213	−	0.522124i
$435$	−220.483	+	316.079i	−0.506857	+	0.726617i
$436$	40.2100	−	85.8312i	0.0922248	−	0.196861i
$437$	−169.332	−	147.304i	−0.387488	−	0.337080i
$438$	−38.1051	+	22.5463i	−0.0869980	+	0.0514756i
$439$	−9.43006	+	441.180i	−0.0214808	+	1.00497i	0.853583	+	0.520957i	$0.174425\pi$
$439$	−9.43006	+	441.180i	−0.0214808	+	1.00497i	−0.875063	+	0.484008i	$0.839180\pi$
$440$	8.23267	+	6.56533i	0.0187106	+	0.0149212i
$441$	286.070	+	101.459i	0.648686	+	0.230066i
$442$	370.990	+	465.206i	0.839343	+	1.05250i
$443$	155.085	+	203.232i	0.350079	+	0.458764i	0.936204	−	0.351456i	$-0.114313\pi$
$443$	155.085	+	203.232i	0.350079	+	0.458764i	−0.586125	+	0.810220i	$0.699347\pi$
$444$	−70.4299	−	46.9238i	−0.158626	−	0.105684i
$445$	−1196.11	+	514.267i	−2.68788	+	1.15566i
$446$	−482.510	+	238.749i	−1.08186	+	0.535312i
$447$	19.3921	−	47.8988i	0.0433827	−	0.107156i
$448$	101.998	−	146.396i	0.227675	−	0.326778i
$449$	−440.033	+	484.525i	−0.980028	+	1.07912i	0.0168255	+	0.999858i	$0.494644\pi$
$449$	−440.033	+	484.525i	−0.980028	+	1.07912i	−0.996854	+	0.0792617i	$0.974744\pi$
$450$	335.237	−	610.411i	0.744971	−	1.35647i
$451$	−4.10109	+	17.1226i	−0.00909332	+	0.0379658i
$452$	123.274	+	224.461i	0.272729	+	0.496595i
$453$	272.436	−	74.5614i	0.601404	−	0.164595i
$454$	1050.83	−	386.715i	2.31460	−	0.851796i
$455$	−1259.14	+	135.774i	−2.76735	+	0.298405i
$456$	35.1471	+	4.53171i	0.0770769	+	0.00993796i
$457$	−445.750	+	470.225i	−0.975382	+	1.02894i	0.0241906	+	0.999707i	$0.492299\pi$
$457$	−445.750	+	470.225i	−0.975382	+	1.02894i	−0.999573	+	0.0292313i	$0.990694\pi$
$458$	−205.098	−	576.243i	−0.447813	−	1.25817i
$459$	−192.238	−	178.371i	−0.418819	−	0.388607i
$460$	−411.164	+	603.067i	−0.893835	+	1.31101i
$461$	−667.625	−	21.4094i	−1.44821	−	0.0464413i	−0.702012	−	0.712165i	$-0.747715\pi$
$461$	−667.625	−	21.4094i	−1.44821	−	0.0464413i	−0.746198	+	0.665724i	$0.768123\pi$
$462$	−1.17727	−	13.6484i	−0.00254821	−	0.0295420i
$463$	−551.227	−	411.391i	−1.19055	−	0.888534i	−0.194824	−	0.980838i	$-0.562414\pi$
$463$	−551.227	−	411.391i	−1.19055	−	0.888534i	−0.995731	+	0.0923040i	$0.970577\pi$
$464$	62.8603	−	532.322i	0.135475	−	1.14725i
$465$	135.718	−	297.946i	0.291866	−	0.640744i
$466$	−28.5687	+	138.774i	−0.0613062	+	0.297799i
$467$	514.449	+	327.096i	1.10160	+	0.700421i	0.957295	−	0.289112i	$-0.0933600\pi$
$467$	514.449	+	327.096i	1.10160	+	0.700421i	0.144308	+	0.989533i	$0.453904\pi$
$468$	−395.282	+	12.6759i	−0.844619	+	0.0270853i
$469$	478.081	−	483.757i	1.01936	−	1.03147i
$470$	664.607	+	565.789i	1.41406	+	1.20381i
$471$	−46.9073	−	7.07014i	−0.0995909	−	0.0150109i
$472$	134.605	+	197.429i	0.285180	+	0.418282i
$473$	1.90100	+	2.98984i	0.00401902	+	0.00632101i
$474$	−166.920	−	439.042i	−0.352151	−	0.926249i
$475$	269.088	−	163.123i	0.566502	−	0.343417i
$476$	−206.132	−	37.7436i	−0.433050	−	0.0792932i
$477$	−74.1109	−	24.6065i	−0.155369	−	0.0515860i
$478$	480.703	+	552.587i	1.00565	+	1.15604i
$479$	−45.9593	−	161.145i	−0.0959484	−	0.336420i	0.898854	−	0.438249i	$-0.144401\pi$
$479$	−45.9593	−	161.145i	−0.0959484	−	0.336420i	−0.994802	+	0.101829i	$0.967530\pi$
$480$	5.73144	−	536.346i	0.0119405	−	1.11739i
$481$	−221.979	−	311.086i	−0.461495	−	0.646748i
$482$	38.1728	−	594.572i	0.0791967	−	1.23355i
$483$	−353.156	+	57.2980i	−0.731172	+	0.118629i
$484$	−305.808	+	172.228i	−0.631834	+	0.355842i
$485$	−441.446	−	344.390i	−0.910199	−	0.710082i
$486$	648.806	−	119.174i	1.33499	−	0.245213i
$487$	663.089	+	252.100i	1.36158	+	0.517660i	0.924300	−	0.381666i	$-0.124650\pi$
$487$	663.089	+	252.100i	1.36158	+	0.517660i	0.437279	+	0.899326i	$0.355942\pi$
$488$	308.684	−	63.5471i	0.632550	−	0.130219i
$489$	−386.378	−	88.1883i	−0.790140	−	0.180344i
$490$	720.183	−	777.915i	1.46976	−	1.58758i
$491$	153.113	+	670.832i	0.311839	+	1.36626i	0.851492	+	0.524368i	$0.175698\pi$
$491$	153.113	+	670.832i	0.311839	+	1.36626i	−0.539653	+	0.841888i	$0.681444\pi$
$492$	175.367	−	79.8815i	0.356437	−	0.162361i
$493$	−274.247	+	87.8139i	−0.556281	+	0.178122i
$494$	−374.442	−	200.465i	−0.757980	−	0.405800i
$495$	14.3266	+	17.5764i	0.0289427	+	0.0355079i
$496$	29.1761	+	454.441i	0.0588228	+	0.916212i
$497$	−102.087	+	49.2328i	−0.205407	+	0.0990600i
$498$	267.691	−	108.376i	0.537531	−	0.217622i
$499$	−619.657	−	550.789i	−1.24180	−	1.10379i	−0.990734	−	0.135814i	$-0.956635\pi$
$499$	−619.657	−	550.789i	−1.24180	−	1.10379i	−0.251063	−	0.967971i	$-0.580780\pi$
$500$	−261.635	−	335.370i	−0.523270	−	0.670739i
$501$	142.574	−	341.620i	0.284579	−	0.681877i
$502$	−86.1053	−	160.833i	−0.171525	−	0.320385i
$503$	−552.460	+	570.460i	−1.09833	+	1.13412i	−0.108176	+	0.994132i	$0.534501\pi$
$503$	−552.460	+	570.460i	−1.09833	+	1.13412i	−0.990154	+	0.139984i	$0.955295\pi$
$504$	−91.3873	+	84.8901i	−0.181324	+	0.168433i
$505$	−383.795	−	249.823i	−0.759990	−	0.494699i
$506$	−19.7679	−	29.6705i	−0.0390671	−	0.0586374i
$507$	497.187	+	170.997i	0.980646	+	0.337273i
$508$	6.78117	−	90.4884i	0.0133488	−	0.178127i
$509$	−398.717	−	156.485i	−0.783334	−	0.307436i	−0.0602382	−	0.998184i	$-0.519186\pi$
$509$	−398.717	−	156.485i	−0.783334	−	0.307436i	−0.723095	+	0.690748i	$0.757281\pi$
$510$	−341.438	+	151.144i	−0.669486	+	0.296362i
$511$	44.4582	−	54.6051i	0.0870024	−	0.106859i
$512$	242.992	+	465.770i	0.474594	+	0.909707i
$513$	176.352	+	62.7679i	0.343767	+	0.122355i
$514$	154.888	+	304.790i	0.301339	+	0.592976i
$515$	−390.136	+	198.259i	−0.757546	+	0.384970i
$516$	13.0028	−	36.5325i	0.0251992	−	0.0707994i
$517$	−15.9037	+	8.29693i	−0.0307614	+	0.0160482i
$518$	311.140	+	74.3386i	0.600657	+	0.143511i
$519$	−126.599	−	285.990i	−0.243929	−	0.551041i
$520$	190.134	−	484.453i	0.365642	−	0.931640i
$521$	107.540	+	8.05900i	0.206410	+	0.0154683i	0.177534	−	0.984115i	$-0.443188\pi$
$521$	107.540	+	8.05900i	0.206410	+	0.0154683i	0.0288764	+	0.999583i	$0.490807\pi$
$522$	147.950	−	430.175i	0.283429	−	0.824090i
$523$	165.398	−	110.196i	0.316249	−	0.210700i	−0.386234	−	0.922401i	$-0.626224\pi$
$523$	165.398	−	110.196i	0.316249	−	0.210700i	0.702483	+	0.711701i	$0.252075\pi$
$524$	−288.033	+	442.496i	−0.549681	+	0.844458i
$525$	74.4848	−	496.055i	0.141876	−	0.944867i
$526$	292.674	+	283.439i	0.556414	+	0.538857i
$527$	215.675	−	115.466i	0.409251	−	0.219101i
$528$	13.1823	+	5.50159i	0.0249665	+	0.0104197i
$529$	−317.057	+	247.348i	−0.599351	+	0.467577i
$530$	−181.190	+	203.846i	−0.341869	+	0.384614i
$531$	193.098	+	476.955i	0.363649	+	0.898221i
$532$	145.815	−	33.3669i	0.274087	−	0.0627198i
$533$	868.404	−	55.7534i	1.62928	−	0.104603i
$534$	−539.529	+	439.773i	−1.01035	+	0.823545i
$535$	377.689	−	705.472i	0.705960	−	1.31864i
$536$	85.2309	+	266.180i	0.159013	+	0.496604i
$537$	97.2750	+	213.551i	0.181145	+	0.397675i
$538$	−693.566	+	158.302i	−1.28916	+	0.294241i
$539$	9.26464	+	19.7187i	0.0171886	+	0.0365838i
$540$	135.462	−	593.499i	0.250856	−	1.09907i
$541$	95.3564	+	463.200i	0.176259	+	0.856191i	0.969082	+	0.246739i	$0.0793590\pi$
$541$	95.3564	+	463.200i	0.176259	+	0.856191i	−0.792823	+	0.609453i	$0.791389\pi$
$542$	241.976	−	636.461i	0.446451	−	1.17428i
$543$	−62.8777	−	342.319i	−0.115797	−	0.630422i
$544$	246.525	−	316.002i	0.453172	−	0.580886i
$545$	131.803	+	234.030i	0.241840	+	0.429412i
$546$	−627.433	+	254.428i	−1.14915	+	0.465985i
$547$	227.675	+	14.6172i	0.416224	+	0.0267225i	0.270774	−	0.962643i	$-0.412720\pi$
$547$	227.675	+	14.6172i	0.416224	+	0.0267225i	0.145451	+	0.989366i	$0.453537\pi$
$548$	328.381	−	234.320i	0.599236	−	0.427592i
$549$	678.632	+	7.25193i	1.23612	+	0.0132093i
$550$	48.0699	−	13.7097i	0.0873997	−	0.0249268i
$551$	155.081	−	134.907i	0.281454	−	0.244840i
$552$	46.3280	−	139.533i	0.0839276	−	0.252777i
$553$	490.593	+	563.321i	0.887148	+	1.01866i
$554$	565.510	+	932.868i	1.02078	+	1.68388i
$555$	224.166	−	85.2258i	0.403903	−	0.153560i
$556$	−252.039	+	160.251i	−0.453307	+	0.288221i
$557$	−119.614	+	81.5512i	−0.214746	+	0.146412i	−0.665916	−	0.746026i	$-0.731959\pi$
$557$	−119.614	+	81.5512i	−0.214746	+	0.146412i	0.451170	+	0.892438i	$0.351007\pi$
$558$	−57.5998	+	382.150i	−0.103225	+	0.684856i
$559$	113.510	−	133.335i	0.203059	−	0.238524i
$560$	371.237	+	1041.18i	0.662923	+	1.85925i
$561$	−0.245959	−	7.66990i	−0.000438429	−	0.0136718i
$562$	−429.664	+	675.765i	−0.764527	+	1.20243i
$563$	−235.489	−	48.4789i	−0.418276	−	0.0861082i	−0.0121520	−	0.999926i	$-0.503868\pi$
$563$	−235.489	−	48.4789i	−0.418276	−	0.0861082i	−0.406124	+	0.913818i	$0.633120\pi$
$564$	178.663	+	81.3832i	0.316779	+	0.144296i
$565$	−720.673	−	85.1021i	−1.27553	−	0.150623i
$566$	−164.718	+	220.708i	−0.291022	+	0.389943i
$567$	−79.0263	+	46.8185i	−0.139376	+	0.0825723i
$568$	1.49280	−	46.5511i	0.00262817	−	0.0819562i
$569$	585.711	+	399.331i	1.02937	+	0.701812i	0.955359	−	0.295446i	$-0.0954682\pi$
$569$	585.711	+	399.331i	1.02937	+	0.701812i	0.0740091	+	0.997258i	$0.476421\pi$
$570$	181.287	−	195.381i	0.318047	−	0.342773i
$571$	−83.4765	+	29.7113i	−0.146194	+	0.0520337i	−0.407403	−	0.913248i	$-0.633566\pi$
$571$	−83.4765	+	29.7113i	−0.146194	+	0.0520337i	0.261210	+	0.965282i	$0.415879\pi$
$572$	−20.6016	−	19.5293i	−0.0360169	−	0.0341422i
$573$	−36.2209	+	280.922i	−0.0632127	+	0.490265i
$574$	−517.523	+	512.595i	−0.901608	+	0.893022i
$575$	−450.868	−	1225.16i	−0.784119	−	2.13070i
$576$	41.6800	+	152.293i	0.0723611	+	0.264397i
$577$	−862.455	+	473.659i	−1.49472	+	0.820899i	−0.998871	−	0.0475081i	$-0.984872\pi$
$577$	−862.455	+	473.659i	−1.49472	+	0.820899i	−0.495852	+	0.868407i	$0.665144\pi$
$578$	467.213	+	111.904i	0.808326	+	0.193605i
$579$	−290.860	−	159.740i	−0.502349	−	0.275889i
$580$	−494.851	−	449.411i	−0.853192	−	0.774846i
$581$	−339.833	+	308.974i	−0.584911	+	0.531797i
$582$	−277.450	−	112.327i	−0.476718	−	0.193002i
$583$	−2.48577	−	5.02371i	−0.00426375	−	0.00861700i
$584$	11.4294	+	26.5832i	0.0195710	+	0.0455191i
$585$	621.387	−	932.665i	1.06220	−	1.59430i
$586$	−674.474	+	514.685i	−1.15098	+	0.878302i
$587$	−840.916	+	670.608i	−1.43257	+	1.14243i	−0.466381	+	0.884584i	$0.654442\pi$
$587$	−840.916	+	670.608i	−1.43257	+	1.14243i	−0.966185	+	0.257849i	$0.916986\pi$
$588$	107.790	−	212.697i	0.183316	−	0.361730i
$589$	−108.876	+	136.526i	−0.184849	+	0.231793i
$590$	1796.74	+	38.4046i	3.04532	+	0.0650925i
$591$	107.308	+	181.359i	0.181570	+	0.306868i
$592$	−218.927	+	251.665i	−0.369808	+	0.425110i
$593$	724.202	+	339.272i	1.22125	+	0.572129i	0.923898	−	0.382639i	$-0.124985\pi$
$593$	724.202	+	339.272i	1.22125	+	0.572129i	0.297353	+	0.954768i	$0.403896\pi$
$594$	24.3885	+	17.0123i	0.0410580	+	0.0286403i
$595$	426.353	−	413.362i	0.716560	−	0.694726i
$596$	78.0999	+	43.9850i	0.131040	+	0.0738004i
$597$	147.080	+	352.418i	0.246366	+	0.590314i
$598$	−1113.30	+	1365.83i	−1.86170	+	2.28400i
$599$	841.883	+	600.735i	1.40548	+	1.00290i	0.995885	+	0.0906299i	$0.0288880\pi$
$599$	841.883	+	600.735i	1.40548	+	1.00290i	0.409596	+	0.912267i	$0.365670\pi$
$600$	166.505	+	121.518i	0.277509	+	0.202530i
$601$	89.3772	+	693.192i	0.148714	+	1.15340i	0.881244	+	0.472662i	$0.156707\pi$
$601$	89.3772	+	693.192i	0.148714	+	1.15340i	−0.732529	+	0.680735i	$0.761660\pi$
$602$	1.64815	+	146.568i	0.00273779	+	0.243469i
$603$	57.7932	+	599.087i	0.0958428	+	0.993511i
$604$	67.8403	+	485.216i	0.112318	+	0.803338i
$605$	106.074	−	988.895i	0.175329	−	1.63454i
$606$	−233.945	−	72.1623i	−0.386047	−	0.119080i
$607$	138.213	−	10.3577i	0.227699	−	0.0170637i	0.0396080	−	0.999215i	$-0.487389\pi$
$607$	138.213	−	10.3577i	0.227699	−	0.0170637i	0.188091	+	0.982152i	$0.439770\pi$
$608$	−72.5665	+	276.728i	−0.119353	+	0.455144i
$609$	−7.18514	−	327.585i	−0.0117983	−	0.537907i
$610$	959.463	−	2167.44i	1.57289	−	3.55319i
$611$	623.527	+	630.226i	1.02050	+	1.03147i
$612$	142.482	−	118.694i	0.232814	−	0.193945i
$613$	−199.103	−	793.737i	−0.324800	−	1.29484i	−0.884653	−	0.466249i	$-0.845605\pi$
$613$	−199.103	−	793.737i	−0.324800	−	1.29484i	0.559853	−	0.828592i	$-0.310858\pi$
$614$	36.4618	+	339.922i	0.0593841	+	0.553618i
$615$	−104.387	+	536.005i	−0.169735	+	0.871552i
$616$	−8.94499	−	0.377560i	−0.0145211	−	0.000612921i
$617$	−151.418	+	290.239i	−0.245410	+	0.470404i	−0.977537	−	0.210763i	$-0.932405\pi$
$617$	−151.418	+	290.239i	−0.245410	+	0.470404i	0.732128	+	0.681168i	$0.238527\pi$
$618$	−171.504	+	159.132i	−0.277514	+	0.257495i
$619$	−100.991	−	670.034i	−0.163152	−	1.08245i	−0.909142	−	0.416487i	$-0.863261\pi$
$619$	−100.991	−	670.034i	−0.163152	−	1.08245i	0.745989	−	0.665958i	$-0.231977\pi$
$620$	482.459	+	299.566i	0.778160	+	0.483171i
$621$	395.464	−	668.367i	0.636818	−	1.07628i
$622$	−270.648	−	815.148i	−0.435125	−	1.31053i
$623$	563.174	−	953.025i	0.903970	−	1.52973i
$624$	67.7902	−	702.717i	0.108638	−	1.12615i
$625$	135.661	−	5.80204i	0.217057	−	0.00928326i
$626$	264.556	−	1532.27i	0.422614	−	2.44771i
$627$	2.32377	+	4.96027i	0.00370618	+	0.00791111i
$628$	22.5675	−	79.1275i	0.0359355	−	0.125999i
$629$	171.791	+	50.9867i	0.273118	+	0.0810599i
$630$	120.483	+	930.343i	0.191243	+	1.47673i
$631$	−266.314	−	293.242i	−0.422051	−	0.464726i	0.491839	−	0.870686i	$-0.336325\pi$
$631$	−266.314	−	293.242i	−0.422051	−	0.464726i	−0.913891	+	0.405961i	$0.866937\pi$
$632$	−298.527	+	71.5014i	−0.472354	+	0.113135i
$633$	−660.356	−	180.729i	−1.04322	−	0.285511i
$634$	−360.948	+	30.9312i	−0.569318	+	0.0487874i
$635$	197.569	+	164.585i	0.311132	+	0.259188i
$636$	−26.6171	+	55.2711i	−0.0418509	+	0.0869042i
$637$	796.302	−	724.806i	1.25008	−	1.13784i
$638$	29.4186	−	14.1672i	0.0461106	−	0.0222057i
$639$	24.4025	−	97.2824i	0.0381886	−	0.152242i
$640$	−722.443	−	101.008i	−1.12882	−	0.157825i
$641$	519.942	+	22.2373i	0.811142	+	0.0346916i	0.444622	−	0.895718i	$-0.353338\pi$
$641$	519.942	+	22.2373i	0.811142	+	0.0346916i	0.366521	+	0.930410i	$0.380549\pi$
$642$	90.7333	−	418.072i	0.141329	−	0.651202i
$643$	1059.20	+	171.243i	1.64728	+	0.266319i	0.911620	−	0.411035i	$-0.134832\pi$
$643$	1059.20	+	171.243i	1.64728	+	0.266319i	0.735658	+	0.677354i	$0.236873\pi$
$644$	−20.2372	−	620.251i	−0.0314242	−	0.963123i
$645$	62.8677	+	90.1255i	0.0974692	+	0.139729i
$646$	196.252	−	33.8843i	0.303796	−	0.0524524i
$647$	−105.657	−	486.837i	−0.163303	−	0.752453i	−0.983578	−	0.180483i	$-0.942234\pi$
$647$	−105.657	−	486.837i	−0.163303	−	0.752453i	0.820275	−	0.571970i	$-0.193821\pi$
$648$	−2.01576	−	37.6923i	−0.00311074	−	0.0581671i
$649$	−14.5886	+	33.9308i	−0.0224785	+	0.0522816i
$650$	−1347.75	−	2070.51i	−2.07347	−	3.18540i
$651$	56.2813	+	272.618i	0.0864536	+	0.418769i
$652$	237.415	−	645.134i	0.364134	−	0.989469i
$653$	−1251.27	−	107.227i	−1.91618	−	0.164206i	−0.934659	−	0.355546i	$-0.884295\pi$
$653$	−1251.27	−	107.227i	−1.91618	−	0.164206i	−0.981524	+	0.191340i	$0.938717\pi$
$654$	102.077	+	100.992i	0.156081	+	0.154422i
$655$	−546.614	−	1392.75i	−0.834525	−	2.12634i
$656$	−223.875	−	725.784i	−0.341272	−	1.10638i
$657$	11.9115	+	61.1629i	0.0181301	+	0.0930942i
$658$	−740.060	−	55.0441i	−1.12471	−	0.0836536i
$659$	−900.570	+	766.666i	−1.36657	+	1.16338i	−0.397212	+	0.917727i	$0.630022\pi$
$659$	−900.570	+	766.666i	−1.36657	+	1.16338i	−0.969358	+	0.245652i	$0.920998\pi$
$660$	15.1338	−	9.39679i	0.0229300	−	0.0142376i
$661$	14.5166	+	679.152i	0.0219616	+	1.02746i	0.868666	+	0.495398i	$0.164978\pi$
$661$	14.5166	+	679.152i	0.0219616	+	1.02746i	−0.846705	+	0.532063i	$0.821417\pi$
$662$	423.262	−	554.668i	0.639369	−	0.837867i
$663$	−358.649	+	123.350i	−0.540949	+	0.186048i
$664$	−47.8751	−	182.568i	−0.0721010	−	0.274953i
$665$	−163.040	+	391.274i	−0.245173	+	0.588382i
$666$	−226.869	+	169.317i	−0.340644	+	0.254229i
$667$	−426.382	−	738.515i	−0.639253	−	1.10722i
$668$	556.072	+	321.048i	0.832444	+	0.480611i
$669$	−40.2412	−	340.776i	−0.0601512	−	0.509381i
$670$	2001.95	+	641.026i	2.98798	+	0.956754i
$671$	33.8891	+	34.9933i	0.0505054	+	0.0521509i
$672$	265.101	+	371.079i	0.394495	+	0.552201i
$673$	−44.9273	+	74.1122i	−0.0667567	+	0.110122i	−0.886747	−	0.462256i	$-0.847040\pi$
$673$	−44.9273	+	74.1122i	−0.0667567	+	0.110122i	0.819990	+	0.572378i	$0.193979\pi$
$674$	240.642	−	1310.11i	0.357036	−	1.94378i
$675$	723.365	+	813.811i	1.07165	+	1.20565i
$676$	−404.452	+	817.393i	−0.598302	+	1.20916i
$677$	−255.607	−	13.6697i	−0.377558	−	0.0201916i	−0.136339	−	0.990662i	$-0.543534\pi$
$677$	−255.607	−	13.6697i	−0.377558	−	0.0201916i	−0.241219	+	0.970471i	$0.577547\pi$
$678$	−382.986	+	61.9181i	−0.564875	+	0.0913247i
$679$	475.804	+	14.9920i	0.700742	+	0.0220795i
$680$	69.4334	+	233.944i	0.102108	+	0.344036i
$681$	7.62643	+	713.678i	0.0111989	+	1.04798i
$682$	−22.4070	+	16.3529i	−0.0328548	+	0.0239778i
$683$	−154.192	−	162.658i	−0.225756	−	0.238152i	0.603029	−	0.797720i	$-0.293960\pi$
$683$	−154.192	−	162.658i	−0.225756	−	0.238152i	−0.828785	+	0.559567i	$0.810967\pi$
$684$	−59.9688	+	118.007i	−0.0876737	+	0.172525i
$685$			1143.17i			1.66886i
$686$	−104.201	+	895.292i	−0.151896	+	1.30509i
$687$	389.871			0.567497
$688$	−136.255	−	69.2419i	−0.198044	−	0.100642i
$689$	−201.046	+	190.582i	−0.291794	+	0.276606i
$690$	−651.862	−	893.190i	−0.944727	−	1.29448i
$691$	433.157	−	4.62875i	0.626855	−	0.00669863i	0.303280	−	0.952901i	$-0.401918\pi$
$691$	433.157	−	4.62875i	0.626855	−	0.00669863i	0.323574	+	0.946203i	$0.395115\pi$
$692$	520.076	−	154.356i	0.751555	−	0.223058i
$693$	−18.6518	−	4.87994i	−0.0269146	−	0.00704176i
$694$	97.0249	+	600.133i	0.139805	+	0.864746i
$695$	45.1982	−	845.152i	0.0650333	−	1.21605i
$696$	120.684	+	59.7151i	0.173396	+	0.0857976i
$697$	−304.974	+	271.079i	−0.437552	+	0.388923i
$698$	−1439.61	−	264.429i	−2.06248	−	0.378839i
$699$	−77.2280	−	46.8161i	−0.110484	−	0.0669758i
$700$	836.853	+	238.168i	1.19550	+	0.340240i
$701$	227.284	−	220.113i	0.324229	−	0.313998i	−0.515621	−	0.856817i	$-0.672439\pi$
$701$	227.284	−	220.113i	0.324229	−	0.313998i	0.839850	+	0.542819i	$0.182643\pi$
$702$	448.168	−	1399.65i	0.638415	−	1.99380i
$703$	−127.029	+	15.0005i	−0.180696	+	0.0213378i
$704$	−5.66661	+	9.81485i	−0.00804916	+	0.0139415i
$705$	−481.804	+	278.170i	−0.683410	+	0.394567i
$706$	−428.295	−	573.877i	−0.606651	−	0.812856i
$707$	388.790	−	21.0101i	0.549915	−	0.0297173i
$708$	391.015	−	102.536i	0.552281	−	0.144825i
$709$	−265.469	−	771.870i	−0.374427	−	1.08867i	−0.960468	−	0.278392i	$-0.910199\pi$
$709$	−265.469	−	771.870i	−0.374427	−	1.08867i	0.586041	−	0.810282i	$-0.300686\pi$
$710$	−278.475	−	212.502i	−0.392218	−	0.299298i
$711$	−660.891	+	14.1263i	−0.929523	+	0.0198682i
$712$	239.961	+	386.464i	0.337024	+	0.542787i
$713$	469.620	+	551.642i	0.658653	+	0.773692i
$714$	158.583	−	275.029i	0.222106	−	0.385195i
$715$	78.9585	−	15.3772i	0.110431	−	0.0215065i
$716$	−388.954	+	119.976i	−0.543231	+	0.167565i
$717$	−434.571	+	170.556i	−0.606096	+	0.237875i
$718$	−290.994	+	294.120i	−0.405284	+	0.409638i
$719$	−18.5874	+	216.903i	−0.0258517	+	0.301673i	0.971939	+	0.235234i	$0.0755856\pi$
$719$	−18.5874	+	216.903i	−0.0258517	+	0.301673i	−0.997790	+	0.0664392i	$0.978836\pi$
$720$	−917.996	−	337.831i	−1.27499	−	0.469210i
$721$	168.382	−	331.801i	0.233539	−	0.460196i
$722$	675.900	−	439.962i	0.936149	−	0.609366i
$723$	348.882	+	150.002i	0.482548	+	0.207472i
$724$	602.846	−	32.2398i	0.832660	−	0.0445301i
$725$	1168.41	−	253.579i	1.61161	−	0.349764i
$726$	−90.4646	−	523.957i	−0.124607	−	0.721703i
$727$	−806.222	+	562.386i	−1.10897	+	0.773570i	−0.976048	−	0.217556i	$-0.930192\pi$
$727$	−806.222	+	562.386i	−1.10897	+	0.773570i	−0.132923	+	0.991126i	$0.542436\pi$
$728$	112.478	+	427.952i	0.154502	+	0.587846i
$729$	−48.2585	+	298.496i	−0.0661982	+	0.409459i
$730$	212.678	+	46.1572i	0.291340	+	0.0632290i
$731$	−3.50848	+	82.0337i	−0.00479956	+	0.112221i
$732$	73.8253	−	528.023i	0.100854	−	0.721343i
$733$	26.2947	+	6.59580i	0.0358727	+	0.00899836i	0.261199	−	0.965285i	$-0.415882\pi$
$733$	26.2947	+	6.59580i	0.0358727	+	0.00899836i	−0.225326	+	0.974283i	$0.572345\pi$
$734$	576.230	+	1196.55i	0.785054	+	1.63018i
$735$	313.212	+	598.736i	0.426139	+	0.814607i
$736$	1069.35	+	514.970i	1.45292	+	0.699688i
$737$	−27.6509	+	33.1924i	−0.0375181	+	0.0450372i
$738$	−55.0361	−	642.237i	−0.0745746	−	0.870240i
$739$	−10.9232	+	39.9117i	−0.0147810	+	0.0540077i	−0.971542	−	0.236869i	$-0.923879\pi$
$739$	−10.9232	+	39.9117i	−0.0147810	+	0.0540077i	0.956761	+	0.290876i	$0.0939469\pi$
$740$	96.8933	+	404.542i	0.130937	+	0.546678i
$741$	200.410	−	182.007i	0.270459	−	0.245623i
$742$	22.1375	−	230.828i	0.0298349	−	0.311088i
$743$	158.686	−	534.667i	0.213575	−	0.719605i	−0.781799	−	0.623531i	$-0.785698\pi$
$743$	158.686	−	534.667i	0.213575	−	0.719605i	0.995374	−	0.0960749i	$-0.0306288\pi$
$744$	−110.005	−	31.3739i	−0.147856	−	0.0421692i
$745$	−230.012	+	107.755i	−0.308741	+	0.144638i
$746$	72.8329	+	12.5751i	0.0976312	+	0.0168567i
$747$	−17.3672	−	406.071i	−0.0232492	−	0.543602i
$748$	13.2493	+	1.27814i	0.0177129	+	0.00170874i
$749$	94.5855	+	673.762i	0.126282	+	0.899549i
$750$	611.567	−	203.054i	0.815423	−	0.270739i
$751$	−995.944	−	589.287i	−1.32616	−	0.784670i	−0.338450	−	0.940984i	$-0.609903\pi$
$751$	−995.944	−	589.287i	−1.32616	−	0.784670i	−0.987707	+	0.156314i	$0.950039\pi$
$752$	408.183	−	657.390i	0.542796	−	0.874188i
$753$	114.984	−	17.3310i	0.152701	−	0.0230160i
$754$	−1097.65	−	1182.99i	−1.45577	−	1.56895i
$755$	−1230.92	−	642.170i	−1.63036	−	0.850556i
$756$	204.709	+	475.389i	0.270779	+	0.628822i
$757$	−1453.62	−	283.092i	−1.92023	−	0.373965i	−0.920378	−	0.391031i	$-0.872119\pi$
$757$	−1453.62	−	283.092i	−1.92023	−	0.373965i	−0.999854	+	0.0170657i	$0.994568\pi$
$758$	−701.399	+	75.2359i	−0.925329	+	0.0992559i
$759$	22.0422	−	5.52911i	0.0290411	−	0.00728473i
$760$	−111.491	−	133.835i	−0.146698	−	0.176098i
$761$	472.625	−	467.602i	0.621058	−	0.614457i	−0.322138	−	0.946693i	$-0.604402\pi$
$761$	472.625	−	467.602i	0.621058	−	0.614457i	0.943196	+	0.332236i	$0.107803\pi$
$762$	125.705	+	55.6460i	0.164968	+	0.0730263i
$763$	−207.875	−	94.5490i	−0.272444	−	0.123917i
$764$	−475.242	−	124.623i	−0.622044	−	0.163119i
$765$	39.2709	+	524.034i	0.0513346	+	0.685012i
$766$	−76.7647	+	248.865i	−0.100215	+	0.324889i
$767$	1815.00	+	194.687i	2.36636	+	0.253829i
$768$	−555.357	+	77.6470i	−0.723122	+	0.101103i
$769$	496.106	−	47.8588i	0.645132	−	0.0622351i	0.231725	−	0.972781i	$-0.425563\pi$
$769$	496.106	−	47.8588i	0.645132	−	0.0622351i	0.413407	+	0.910546i	$0.364339\pi$
$770$	−41.3884	+	53.1138i	−0.0537512	+	0.0689789i
$771$	−216.131	+	27.8670i	−0.280326	+	0.0361440i
$772$	339.320	−	464.941i	0.439534	−	0.602255i
$773$	605.015	−	847.881i	0.782685	−	1.09687i	−0.210184	−	0.977662i	$-0.567406\pi$
$773$	605.015	−	847.881i	0.782685	−	1.09687i	0.992869	−	0.119209i	$-0.0380358\pi$
$774$	−100.542	−	81.9521i	−0.129899	−	0.105881i
$775$	−937.376	+	391.211i	−1.20952	+	0.504788i
$776$	−95.9953	+	170.449i	−0.123705	+	0.219651i
$777$	−111.141	+	170.951i	−0.143039	+	0.220015i
$778$	−1144.04	+	1640.06i	−1.47049	+	2.10805i
$779$	123.560	−	263.749i	0.158614	−	0.338573i
$780$	−664.256	−	577.844i	−0.851610	−	0.740826i
$781$	6.19573	−	3.66593i	0.00793308	−	0.00469390i
$782$	17.6566	−	826.056i	0.0225788	−	1.05634i
$783$	556.071	+	443.452i	0.710180	+	0.566349i
$784$	−777.122	−	528.562i	−0.991227	−	0.674186i
$785$	145.379	+	182.299i	0.185196	+	0.232228i
$786$	−485.236	−	635.882i	−0.617349	−	0.809010i
$787$	−1124.39	−	749.124i	−1.42871	−	0.951872i	−0.998799	−	0.0489991i	$-0.984397\pi$
$787$	−1124.39	−	749.124i	−1.42871	−	0.951872i	−0.429906	−	0.902873i	$-0.641453\pi$
$788$	−335.798	+	144.376i	−0.426139	+	0.183219i
$789$	−232.759	+	115.171i	−0.295005	+	0.145971i
$790$	−866.394	+	2140.01i	−1.09670	+	2.70887i
$791$	537.434	−	303.073i	0.679436	−	0.383151i
$792$	5.32644	−	5.86500i	0.00672530	−	0.00740531i
$793$	1158.96	−	2110.28i	1.46149	−	2.66114i
$794$	−480.025	+	2004.16i	−0.604565	+	2.52414i
$795$	−83.6832	−	152.373i	−0.105262	−	0.191665i
$796$	−638.896	+	174.855i	−0.802633	+	0.219668i
$797$	101.117	−	37.2120i	0.126872	−	0.0466901i	−0.281139	−	0.959667i	$-0.590712\pi$
$797$	101.117	−	37.2120i	0.126872	−	0.0466901i	0.408011	+	0.912977i	$0.366222\pi$
$798$	−26.4497	+	225.065i	−0.0331450	+	0.282036i
$799$	−412.293	−	53.1593i	−0.516011	−	0.0665323i
$800$	−1144.82	+	1207.68i	−1.43103	+	1.50961i
$801$	328.478	+	922.888i	0.410084	+	1.15217i
$802$	172.471	+	160.030i	0.215051	+	0.199538i
$803$	−2.51951	+	3.69545i	−0.00313762	+	0.00460205i
$804$	472.581	+	15.1547i	0.587787	+	0.0188492i
$805$	1464.05	+	974.241i	1.81870	+	1.21024i
$806$	1098.73	+	820.004i	1.36319	+	1.01738i
$807$	53.1770	−	450.321i	0.0658947	−	0.558018i
$808$	−66.3256	+	145.607i	−0.0820861	+	0.180207i
$809$	−55.7796	+	270.953i	−0.0689488	+	0.334923i	−0.999513	−	0.0312056i	$-0.990065\pi$
$809$	−55.7796	+	270.953i	−0.0689488	+	0.334923i	0.930564	+	0.366129i	$0.119317\pi$
$810$	−239.567	−	152.321i	−0.295761	−	0.188051i
$811$	−154.851	+	4.96577i	−0.190938	+	0.00612302i	−0.127374	−	0.991855i	$-0.540655\pi$
$811$	−154.851	+	4.96577i	−0.190938	+	0.00612302i	−0.0635641	+	0.997978i	$0.520247\pi$
$812$	565.146	+	60.3013i	0.695993	+	0.0742626i
$813$	330.477	+	281.339i	0.406491	+	0.346051i
$814$	−20.0923	−	3.02843i	−0.0246834	−	0.00372043i
$815$	1097.36	+	1609.53i	1.34645	+	1.97488i
$816$	177.617	+	279.351i	0.217668	+	0.342342i
$817$	−20.8282	−	54.7836i	−0.0254935	−	0.0670546i
$818$	802.482	−	486.469i	0.981030	−	0.594706i
$819$	41.2476	+	951.972i	0.0503634	+	1.16236i
$820$	−898.946	−	298.471i	−1.09628	−	0.363989i
$821$	944.927	+	1086.23i	1.15095	+	1.32306i	0.938256	+	0.345940i	$0.112440\pi$
$821$	944.927	+	1086.23i	1.15095	+	1.32306i	0.212690	+	0.977120i	$0.431778\pi$
$822$	167.620	+	587.718i	0.203917	+	0.714985i
$823$	11.3960	−	1066.43i	0.0138469	−	1.29579i	−0.754733	−	0.656032i	$-0.772234\pi$
$823$	11.3960	−	1066.43i	0.0138469	−	1.29579i	0.768580	−	0.639754i	$-0.220964\pi$
$824$	88.8128	+	124.464i	0.107783	+	0.151049i
$825$	−2.04138	+	31.7962i	−0.00247440	+	0.0385408i
$826$	−1252.73	+	874.893i	−1.51662	+	1.05919i
$827$	613.357	−	345.436i	0.741665	−	0.417698i	−0.0732238	−	0.997316i	$-0.523329\pi$
$827$	613.357	−	345.436i	0.741665	−	0.417698i	0.814888	+	0.579618i	$0.196798\pi$
$828$	432.992	+	337.794i	0.522937	+	0.407963i
$829$	338.174	−	62.1164i	0.407930	−	0.0749293i	0.0272333	−	0.999629i	$-0.491330\pi$
$829$	338.174	−	62.1164i	0.407930	−	0.0749293i	0.380697	+	0.924700i	$0.375684\pi$
$830$	−1326.87	−	504.464i	−1.59864	−	0.607787i
$831$	−681.055	+	140.205i	−0.819561	+	0.168719i
$832$	546.083	+	124.640i	0.656350	+	0.149808i
$833$	−85.3478	+	497.637i	−0.102458	+	0.597403i
$834$	−100.685	−	441.130i	−0.120726	−	0.528933i
$835$	−1655.85	+	754.259i	−1.98306	+	0.903304i
$836$	−9.04869	+	2.89740i	−0.0108238	+	0.00346579i
$837$	−532.698	−	285.191i	−0.636437	−	0.340729i
$838$	6.74787	+	8.27852i	0.00805235	+	0.00987891i
$839$	36.8225	+	573.540i	0.0438886	+	0.683600i	0.959530	+	0.281605i	$0.0908667\pi$
$839$	36.8225	+	573.540i	0.0438886	+	0.683600i	−0.915642	+	0.401995i	$0.868317\pi$
$840$	−277.675	+	0.155148i	−0.330565	+	0.000184700i
$841$	−55.6184	+	22.5174i	−0.0661337	+	0.0267746i
$842$	−810.274	−	720.221i	−0.962321	−	0.855369i
$843$	−313.964	−	402.446i	−0.372437	−	0.477398i
$844$	457.386	−	1095.94i	0.541926	−	1.29850i
$845$	−1219.77	−	2278.37i	−1.44352	−	2.69630i
$846$	456.860	−	471.746i	0.540024	−	0.557619i
$847$	423.217	+	732.089i	0.499666	+	0.864331i
$848$	202.643	+	131.906i	0.238966	+	0.155550i
$849$	−97.3294	−	146.086i	−0.114640	−	0.172068i
$850$	1095.45	+	376.759i	1.28877	+	0.443246i
$851$	−39.6571	+	529.187i	−0.0466006	+	0.621841i
$852$	−73.3455	−	28.7860i	−0.0860862	−	0.0337864i
$853$	725.841	−	321.308i	0.850927	−	0.376680i	0.0671653	−	0.997742i	$-0.478605\pi$
$853$	725.841	−	321.308i	0.850927	−	0.376680i	0.783762	+	0.621062i	$0.213298\pi$
$854$	428.531	+	1969.23i	0.501793	+	2.30590i
$855$	−173.501	−	332.568i	−0.202925	−	0.388969i
$856$	−263.402	−	93.7509i	−0.307713	−	0.109522i
$857$	26.3293	+	51.8110i	0.0307227	+	0.0604562i	0.906340	−	0.422550i	$-0.138865\pi$
$857$	26.3293	+	51.8110i	0.0307227	+	0.0604562i	−0.875617	+	0.483006i	$0.839545\pi$
$858$	38.3388	−	19.4830i	0.0446840	−	0.0227075i
$859$	−82.8189	+	232.687i	−0.0964132	+	0.270882i	−0.980525	−	0.196393i	$-0.937077\pi$
$859$	−82.8189	+	232.687i	−0.0964132	+	0.270882i	0.884112	+	0.467275i	$0.154764\pi$
$860$	−168.990	+	88.1618i	−0.196500	+	0.102514i
$861$	−197.202	−	420.331i	−0.229039	−	0.488189i
$862$	−162.712	−	367.568i	−0.188761	−	0.426413i
$863$	64.9937	−	165.601i	0.0753113	−	0.191890i	−0.888260	−	0.459340i	$-0.848086\pi$
$863$	64.9937	−	165.601i	0.0753113	−	0.191890i	0.963572	+	0.267450i	$0.0861811\pi$
$864$	−987.144	−	73.9762i	−1.14253	−	0.0856206i
$865$	−499.981	+	1453.73i	−0.578013	+	1.68062i
$866$	−681.601	+	454.116i	−0.787068	+	0.524383i
$867$	−167.057	+	256.644i	−0.192684	+	0.296014i
$868$	−481.475	+	36.3521i	−0.554695	+	0.0418803i
$869$	−34.0843	−	33.0088i	−0.0392224	−	0.0379848i
$870$	892.806	−	477.982i	1.02621	−	0.549404i
$871$	1970.42	+	822.347i	2.26224	+	0.944141i
$872$	73.9915	−	57.7237i	0.0848526	−	0.0661968i
$873$	−279.865	+	314.858i	−0.320579	+	0.360662i
$874$	221.323	+	546.672i	0.253230	+	0.625483i
$875$	−800.887	+	639.419i	−0.915300	+	0.730764i
$876$	48.8513	−	3.13636i	0.0557663	−	0.00358031i
$877$	354.603	−	289.039i	0.404336	−	0.329577i	−0.407772	−	0.913084i	$-0.633694\pi$
$877$	354.603	−	289.039i	0.404336	−	0.329577i	0.812108	+	0.583507i	$0.198320\pi$
$878$	547.313	−	1022.31i	0.623364	−	1.16436i
$879$	−164.912	−	515.027i	−0.187613	−	0.585923i
$880$	−29.1050	−	63.8953i	−0.0330739	−	0.0726083i
$881$	−371.994	+	84.9053i	−0.422241	+	0.0963737i	−0.428361	−	0.903608i	$-0.640909\pi$
$881$	−371.994	+	84.9053i	−0.422241	+	0.0963737i	0.00612041	+	0.999981i	$0.498052\pi$
$882$	−549.380	−	578.250i	−0.622879	−	0.655612i
$883$	−97.3507	+	426.521i	−0.110250	+	0.483037i	0.889414	+	0.457103i	$0.151113\pi$
$883$	−97.3507	+	426.521i	−0.110250	+	0.483037i	−0.999664	+	0.0259335i	$0.991744\pi$
$884$	−132.649	−	644.352i	−0.150056	−	0.728905i
$885$	−407.082	+	1070.73i	−0.459980	+	1.20987i
$886$	−121.364	−	660.732i	−0.136980	−	0.745748i
$887$	−385.272	+	493.850i	−0.434354	+	0.556765i	−0.954846	−	0.297102i	$-0.903980\pi$
$887$	−385.272	+	493.850i	−0.434354	+	0.556765i	0.520492	+	0.853867i	$0.325749\pi$
$888$	−41.1180	−	73.0092i	−0.0463041	−	0.0822176i
$889$	−218.189	−	13.8858i	−0.245432	−	0.0156196i
$890$	3414.31	+	219.206i	3.83630	+	0.246299i
$891$	4.74925	−	3.38888i	0.00533025	−	0.00380346i
$892$	595.170	+	6.36004i	0.667231	+	0.00713009i
$893$	285.353	−	81.3839i	0.319544	−	0.0911354i
$894$	−102.452	+	89.1244i	−0.114600	+	0.0996917i
$895$	363.460	−	1094.68i	0.406100	−	1.22311i
$896$	546.627	−	293.041i	0.610074	−	0.327054i
$897$	−582.234	−	960.457i	−0.649091	−	1.07074i
$898$	1607.67	−	611.221i	1.79028	−	0.680647i
$899$	−559.904	+	355.998i	−0.622808	+	0.395993i
$900$	−636.171	+	433.734i	−0.706857	+	0.481927i
$901$	19.3601	−	128.446i	0.0214873	−	0.142559i
$902$	29.9918	−	35.2300i	0.0332503	−	0.0390577i
$903$	−88.3667	−	30.3367i	−0.0978590	−	0.0335954i
$904$	8.12661	+	253.418i	0.00898961	+	0.280329i
$905$	−917.906	+	1443.66i	−1.01426	+	1.59520i
$906$	−726.991	−	149.662i	−0.802418	−	0.165189i
$907$	169.699	+	77.2999i	0.187100	+	0.0852260i	0.505885	−	0.862601i	$-0.331166\pi$
$907$	169.699	+	77.2999i	0.187100	+	0.0852260i	−0.318785	+	0.947827i	$0.603275\pi$
$908$	−1229.45	−	145.182i	−1.35402	−	0.159892i
$909$	−206.081	+	276.129i	−0.226711	+	0.303772i
$910$	3111.38	+	1180.93i	3.41910	+	1.29772i
$911$	19.0412	−	593.776i	0.0209015	−	0.651785i	−0.934413	−	0.356192i	$-0.884075\pi$
$911$	19.0412	−	593.776i	0.0209015	−	0.651785i	0.955314	−	0.295593i	$-0.0955171\pi$
$912$	−195.235	−	133.109i	−0.214074	−	0.145953i
$913$	19.8430	−	21.3857i	0.0217339	−	0.0234235i
$914$	1604.04	−	570.915i	1.75497	−	0.624634i
$915$	1096.48	+	1039.41i	1.19834	+	1.13597i
$916$	−86.4775	+	670.703i	−0.0944078	+	0.732208i
$917$	1073.87	+	681.944i	1.17107	+	0.743668i
$918$	237.999	+	646.720i	0.259258	+	0.704488i
$919$	−182.704	−	667.571i	−0.198807	−	0.726411i	−0.992935	−	0.118660i	$-0.962140\pi$
$919$	−182.704	−	667.571i	−0.198807	−	0.726411i	0.794128	−	0.607750i	$-0.207928\pi$
$920$	−633.425	+	347.876i	−0.688505	+	0.378126i
$921$	−211.916	−	50.7568i	−0.230094	−	0.0551106i
$922$	1538.53	+	844.959i	1.66869	+	0.916441i
$923$	−263.392	−	239.206i	−0.285365	−	0.259161i
$924$	−5.67592	+	14.0422i	−0.00614277	+	0.0151972i
$925$	−689.650	−	279.208i	−0.745567	−	0.301847i
$926$	801.579	+	1619.98i	0.865636	+	1.74944i
$927$	130.056	+	302.491i	0.140298	+	0.326311i
$928$	−602.696	+	904.612i	−0.649457	+	0.974797i
$929$	442.404	−	337.595i	0.476215	−	0.363396i	−0.340682	−	0.940178i	$-0.610658\pi$
$929$	442.404	−	337.595i	0.476215	−	0.363396i	0.816898	+	0.576783i	$0.195692\pi$
$930$	−672.643	+	536.415i	−0.723273	+	0.576791i
$931$	−84.3382	−	350.394i	−0.0905888	−	0.376363i
$932$	97.6687	−	122.473i	0.104795	−	0.131408i
$933$	547.343	+	11.6992i	0.586648	+	0.0125394i
$934$	−815.773	−	1378.72i	−0.873419	−	1.47615i
$935$	−24.7563	+	28.4584i	−0.0264774	+	0.0304368i
$936$	−354.586	−	166.115i	−0.378831	−	0.177474i
$937$	−792.128	−	552.555i	−0.845388	−	0.589706i	0.0675908	−	0.997713i	$-0.478469\pi$
$937$	−792.128	−	552.555i	−0.845388	−	0.589706i	−0.912979	+	0.408007i	$0.866224\pi$
$938$	−1695.89	+	564.127i	−1.80799	+	0.601415i
$939$	863.584	+	486.362i	0.919685	+	0.517957i
$940$	−371.672	−	890.560i	−0.395396	−	0.947404i
$941$	677.860	−	831.622i	0.720361	−	0.883764i	−0.276654	−	0.960970i	$-0.589226\pi$
$941$	677.860	−	831.622i	0.720361	−	0.883764i	0.997015	+	0.0772054i	$0.0245997\pi$
$942$	101.471	+	72.4058i	0.107719	+	0.0768639i
$943$	−976.051	−	712.335i	−1.03505	−	0.755392i
$944$	−203.743	−	1580.19i	−0.215829	−	1.67393i
$945$	−1433.53	−	310.278i	−1.51697	−	0.328337i
$946$	−0.894005	−	9.26730i	−0.000945037	−	0.00979630i
$947$	117.326	+	839.154i	0.123892	+	0.886118i	0.947680	+	0.319221i	$0.103421\pi$
$947$	117.326	+	839.154i	0.123892	+	0.886118i	−0.823788	+	0.566897i	$0.808144\pi$
$948$	−55.3863	+	516.348i	−0.0584243	+	0.544671i
$949$	211.231	+	65.1563i	0.222583	+	0.0686578i
$950$	−824.580	+	61.7937i	−0.867979	+	0.0650460i
$951$	58.5720	−	223.360i	0.0615899	−	0.234869i
$952$	−165.015	−	125.775i	−0.173335	−	0.132117i
$953$	−244.589	+	552.530i	−0.256651	+	0.579780i	−0.995571	−	0.0940139i	$-0.970030\pi$
$953$	−244.589	+	552.530i	−0.256651	+	0.579780i	0.738920	+	0.673794i	$0.235336\pi$
$954$	144.323	+	145.873i	0.151282	+	0.152907i
$955$	1069.71	−	891.119i	1.12011	−	0.933109i
$956$	−197.019	−	785.433i	−0.206087	−	0.821582i
$957$	2.21974	+	20.6939i	0.00231947	+	0.0216237i
$958$	−84.1754	+	432.223i	−0.0878657	+	0.451172i
$959$	−573.423	−	784.791i	−0.597938	−	0.818343i
$960$	−162.582	+	311.638i	−0.169356	+	0.324623i
$961$	−291.261	+	270.250i	−0.303081	+	0.281218i
$962$	149.676	+	993.033i	0.155588	+	1.03226i
$963$	−511.497	−	317.595i	−0.531149	−	0.329798i
$964$	−335.438	+	566.918i	−0.347964	+	0.588089i
$965$	513.971	+	1548.00i	0.532612	+	1.60414i
$966$	895.538	+	286.200i	0.927058	+	0.296274i
$967$	−115.393	+	1196.17i	−0.119331	+	1.23699i	0.720233	+	0.693733i	$0.244035\pi$
$967$	−115.393	+	1196.17i	−0.119331	+	1.23699i	−0.839564	+	0.543261i	$0.817189\pi$
$968$	−347.178	+	14.8484i	−0.358655	+	0.0153392i
$969$	−21.5979	+	125.092i	−0.0222889	+	0.129094i
$970$	624.166	+	1332.33i	0.643470	+	1.37353i
$971$	488.367	−	1712.34i	0.502952	−	1.76348i	−0.132334	−	0.991205i	$-0.542247\pi$
$971$	488.367	−	1712.34i	0.502952	−	1.76348i	0.635286	−	0.772277i	$-0.280882\pi$
$972$	−699.185	−	207.515i	−0.719327	−	0.213492i
$973$	392.906	+	602.872i	0.403809	+	0.619602i
$974$	−1253.27	−	1379.99i	−1.28672	−	1.41683i
$975$	1531.40	−	366.792i	1.57067	−	0.376196i
$976$	−2026.87	−	554.722i	−2.07671	−	0.568363i
$977$	−756.232	+	64.8048i	−0.774035	+	0.0663304i	−0.465694	−	0.884946i	$-0.654195\pi$
$977$	−756.232	+	64.8048i	−0.774035	+	0.0663304i	−0.308340	+	0.951276i	$0.599774\pi$
$978$	800.166	+	666.576i	0.818165	+	0.681571i
$979$	−30.5079	+	63.3504i	−0.0311623	+	0.0647093i
$980$	−1099.49	+	406.019i	−1.12193	+	0.414305i
$981$	182.075	−	87.6826i	0.185601	−	0.0893808i
$982$	439.929	−	1753.81i	0.447993	−	1.78596i
$983$	1400.39	+	195.794i	1.42460	+	0.199180i	0.808505	−	0.588489i	$-0.200277\pi$
$983$	1400.39	+	195.794i	1.42460	+	0.199180i	0.616098	+	0.787669i	$0.288712\pi$
$984$	190.620	+	8.15261i	0.193720	+	0.00828517i
$985$	219.682	−	1012.23i	0.223028	−	1.02764i
$986$	747.009	+	120.771i	0.757615	+	0.122485i
$987$	191.229	−	432.642i	0.193747	−	0.438340i
$988$	268.657	+	385.140i	0.271920	+	0.389818i
$989$	−239.609	+	41.3701i	−0.242274	+	0.0418302i
$990$	−12.6378	−	58.2314i	−0.0127655	−	0.0588196i
$991$	59.8354	+	1118.85i	0.0603788	+	1.12901i	0.853889	+	0.520455i	$0.174238\pi$
$991$	59.8354	+	1118.85i	0.0603788	+	1.12901i	−0.793510	+	0.608557i	$0.791749\pi$
$992$	364.757	−	848.370i	0.367699	−	0.855212i
$993$	242.614	+	372.720i	0.244324	+	0.375347i
$994$	297.767	+	6.19821i	0.299564	+	0.00623562i
$995$	648.270	−	1761.56i	0.651527	−	1.77041i
$996$	−318.132	−	27.2621i	−0.319410	−	0.0273716i
$997$	−958.753	−	948.562i	−0.961638	−	0.951416i	0.0372149	−	0.999307i	$-0.488151\pi$
$997$	−958.753	−	948.562i	−0.961638	−	0.951416i	−0.998853	+	0.0478908i	$0.984750\pi$
$998$	795.935	+	2028.01i	0.797530	+	2.03207i
$999$	−130.459	−	422.938i	−0.130590	−	0.423362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.3.l.a.10.14	✓	5376
343.103	odd	294	inner	343.3.l.a.103.14	yes	5376

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.3.l.a.10.14	✓	5376	1.1	even	1	trivial
343.3.l.a.103.14	yes	5376	343.103	odd	294	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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	343.l (of order \(294\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.34266 - 1.19049i) q^{2} +(1.21559 - 1.15232i) q^{3} +(1.71273 + 2.34681i) q^{4} +(-8.23255 + 0.0879738i) q^{5} +(-4.21956 + 1.25234i) q^{6} +(5.60756 - 4.18991i) q^{7} +(0.459099 + 2.83969i) q^{8} +(-0.330804 + 6.18564i) q^{9} +(19.3908 + 9.59470i) q^{10} +(-0.332322 + 0.295388i) q^{11} +(4.78627 + 0.879150i) q^{12} +(18.7917 + 11.3917i) q^{13} +(-18.1247 + 3.13977i) q^{14} +(-9.90606 + 9.59349i) q^{15} +(5.84904 - 18.2668i) q^{16} +(-10.2330 + 1.20839i) q^{17} +(8.13893 - 14.0970i) q^{18} +(6.36972 - 3.67756i) q^{19} +(-14.3066 - 19.1696i) q^{20} +(1.98839 - 11.5549i) q^{21} +(1.13018 - 0.296367i) q^{22} +(-9.92423 - 28.8554i) q^{23} +(3.83031 + 2.92288i) q^{24} +(42.7728 - 0.914253i) q^{25} +(-30.4610 - 49.0582i) q^{26} +(16.4976 + 19.3790i) q^{27} +(19.4372 + 5.98368i) q^{28} +(27.4310 - 5.34218i) q^{29} +(34.6275 - 10.6812i) q^{30} +(-22.1006 + 8.67386i) q^{31} +(-27.3562 + 27.6501i) q^{32} +(-0.0635865 + 0.742015i) q^{33} +(25.4111 + 9.35152i) q^{34} +(-45.7959 + 34.9869i) q^{35} +(-15.0831 + 9.81802i) q^{36} +(-15.9767 - 6.86920i) q^{37} +(-19.3002 + 1.03216i) q^{38} +(35.9700 - 7.80650i) q^{39} +(-4.02937 - 23.3375i) q^{40} +(32.4782 - 22.6554i) q^{41} +(-18.4142 + 24.7021i) q^{42} +(1.27177 - 7.86637i) q^{43} +(-1.26240 - 0.273976i) q^{44} +(2.17919 - 50.9527i) q^{45} +(-11.1031 + 79.4132i) q^{46} +(39.1313 + 9.81576i) q^{47} +(-13.9392 - 28.9450i) q^{48} +(13.8893 - 46.9903i) q^{49} +(-101.291 - 48.7790i) q^{50} +(-11.0468 + 13.2607i) q^{51} +(5.45115 + 63.6115i) q^{52} +(-3.32775 + 12.1591i) q^{53} +(-15.5777 - 65.0387i) q^{54} +(2.70987 - 2.46103i) q^{55} +(14.4724 + 14.0001i) q^{56} +(3.50526 - 11.8104i) q^{57} +(-70.6213 - 20.1415i) q^{58} +(75.2222 - 35.2399i) q^{59} +(-39.4805 - 6.81658i) q^{60} +(-4.68149 - 109.460i) q^{61} +(62.1005 + 5.99076i) q^{62} +(24.0623 + 36.0724i) q^{63} +(24.1908 - 8.03189i) q^{64} +(-155.706 - 92.1292i) q^{65} +(1.03233 - 1.66259i) q^{66} +(96.0768 - 14.4812i) q^{67} +(-20.3623 - 21.9454i) q^{68} +(-45.3146 - 23.6406i) q^{69} +(148.936 - 27.4428i) q^{70} +(-15.8926 - 3.09509i) q^{71} +(-17.7172 + 1.90044i) q^{72} +(9.75699 - 2.44746i) q^{73} +(29.2503 + 35.1124i) q^{74} +(50.9409 - 50.3994i) q^{75} +(19.5402 + 8.64985i) q^{76} +(-0.625865 + 3.04881i) q^{77} +(-93.5591 - 24.5341i) q^{78} +(7.97479 + 106.416i) q^{79} +(-46.5455 + 150.897i) q^{80} +(-13.0471 - 1.39951i) q^{81} +(-103.056 + 14.4088i) q^{82} +(-65.3104 + 6.30041i) q^{83} +(30.5228 - 15.1242i) q^{84} +(84.1377 - 10.8483i) q^{85} +(-12.3442 + 16.9142i) q^{86} +(27.1890 - 38.1032i) q^{87} +(-0.991379 - 0.808079i) q^{88} +(145.941 - 60.9080i) q^{89} +(-65.7640 + 116.771i) q^{90} +(153.106 - 14.8563i) q^{91} +(50.7207 - 72.7120i) q^{92} +(-16.8703 + 36.0109i) q^{93} +(-79.9857 - 69.5806i) q^{94} +(-52.1155 + 30.8360i) q^{95} +(-1.39223 + 65.1346i) q^{96} +(53.1690 + 42.4009i) q^{97} +(-88.4797 + 93.5471i) q^{98} +(-1.71723 - 2.15334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) \) 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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