LMFDB - Embedded newform 350.3.p.e.93.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,3,Mod(93,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 4]))

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

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

chi := DirichletCharacter("350.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 8 x^{13} - 722 x^{12} + 1354 x^{11} - 1232 x^{10} + 9306 x^{9} + \cdots + 52200625 $ x^16 - 2x^15 + 2x^14 - 8x^13 - 722x^12 + 1354x^11 - 1232x^10 + 9306x^9 + 505731x^8 - 1157418x^7 + 1256080x^6 - 9824090x^5 + 5294974x^4 + 30978760x^3 + 12152450x^2 + 35619250*x + 52200625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			93.3
Root			$2.63893 - 0.707100i$ of defining polynomial
Character	$\chi$	$=$	350.93
Dual form			350.3.p.e.207.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(0.707100 - 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} -3.86367 q^{6} +(1.73096 + 6.78261i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(0.707100 - 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} -3.86367 q^{6} +(1.73096 + 6.78261i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +(10.0230 + 17.3604i) q^{11} +(1.41420 + 5.27787i) q^{12} +(-2.21546 - 2.21546i) q^{13} +(8.63164 - 4.84715i) q^{14} +(2.00000 - 3.46410i) q^{16} +(11.9322 + 3.19722i) q^{17} +(0.562230 - 2.09827i) q^{18} +(15.7940 + 9.11869i) q^{19} +(19.1228 + 0.228089i) q^{21} +(20.0461 - 20.0461i) q^{22} +(-39.7282 + 10.6451i) q^{23} +(6.69207 - 3.86367i) q^{24} +(-2.21546 + 3.83729i) q^{26} +(20.3539 - 20.3539i) q^{27} +(-9.78072 - 10.0169i) q^{28} -19.0242i q^{29} +(-3.14077 - 5.43998i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(52.9003 - 14.1746i) q^{33} -17.4700i q^{34} -3.07208 q^{36} +(9.82266 + 36.6587i) q^{37} +(6.67534 - 24.9127i) q^{38} +(-7.41300 + 4.27990i) q^{39} -16.3689 q^{41} +(-6.68786 - 26.2057i) q^{42} +(4.26669 + 4.26669i) q^{43} +(-34.7208 - 20.0461i) q^{44} +(29.0830 + 50.3733i) q^{46} +(-3.19722 - 11.9322i) q^{47} +(-7.72733 - 7.72733i) q^{48} +(-43.0075 + 23.4809i) q^{49} +(16.8745 - 29.2275i) q^{51} +(6.05274 + 1.62183i) q^{52} +(13.8578 - 51.7180i) q^{53} +(-35.2539 - 20.3539i) q^{54} +(-10.1033 + 17.0271i) q^{56} +(35.2316 - 35.2316i) q^{57} +(-25.9875 + 6.96333i) q^{58} +(82.3873 - 47.5663i) q^{59} +(-4.22958 + 7.32586i) q^{61} +(-6.28154 + 6.28154i) q^{62} +(-2.90657 + 10.3520i) q^{63} +8.00000i q^{64} +(-38.7257 - 67.0749i) q^{66} +(10.9793 + 2.94188i) q^{67} +(-23.8644 + 6.39445i) q^{68} +112.367i q^{69} +94.8180 q^{71} +(1.12446 + 4.19654i) q^{72} +(2.11109 - 7.87869i) q^{73} +(46.4813 - 26.8360i) q^{74} -36.4747 q^{76} +(-100.399 + 98.0326i) q^{77} +(8.55979 + 8.55979i) q^{78} +(-15.1049 - 8.72081i) q^{79} +(-32.4081 - 56.1325i) q^{81} +(5.99144 + 22.3604i) q^{82} +(63.0967 + 63.0967i) q^{83} +(-33.3498 + 18.7278i) q^{84} +(4.26669 - 7.39012i) q^{86} +(-50.2035 - 13.4520i) q^{87} +(-14.6748 + 54.7669i) q^{88} +(67.0808 + 38.7291i) q^{89} +(11.1917 - 18.8615i) q^{91} +(58.1661 - 58.1661i) q^{92} +(-16.5766 + 4.44168i) q^{93} +(-15.1294 + 8.73498i) q^{94} +(-7.72733 + 13.3841i) q^{96} +(-105.134 + 105.134i) q^{97} +(47.8173 + 50.1548i) q^{98} +30.7916i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	0.707100	−	2.63893i	0.235700	−	0.879644i	−0.742132	−	0.670254i	$-0.766185\pi$
$3$	0.707100	−	2.63893i	0.235700	−	0.879644i	0.977832	−	0.209391i	$-0.0671480\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−3.86367			−0.643944
$7$	1.73096	+	6.78261i	0.247280	+	0.968944i
$7$	1.73096	+	6.78261i	0.247280	+	0.968944i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	1.33025	+	0.768021i	0.147806	+	0.0853356i
$10$		0			0
$11$	10.0230	+	17.3604i	0.911186	+	1.57822i	0.812392	+	0.583112i	$0.198165\pi$
$11$	10.0230	+	17.3604i	0.911186	+	1.57822i	0.0987936	+	0.995108i	$0.468502\pi$
$12$	1.41420	+	5.27787i	0.117850	+	0.439822i
$13$	−2.21546	−	2.21546i	−0.170420	−	0.170420i	0.616744	−	0.787164i	$-0.288451\pi$
$13$	−2.21546	−	2.21546i	−0.170420	−	0.170420i	−0.787164	+	0.616744i	$0.788451\pi$
$14$	8.63164	−	4.84715i	0.616546	−	0.346225i
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	11.9322	+	3.19722i	0.701894	+	0.188072i	0.592079	−	0.805880i	$-0.298307\pi$
$17$	11.9322	+	3.19722i	0.701894	+	0.188072i	0.109815	+	0.993952i	$0.464974\pi$
$18$	0.562230	−	2.09827i	0.0312350	−	0.116571i
$19$	15.7940	+	9.11869i	0.831265	+	0.479931i	0.854285	−	0.519804i	$-0.173995\pi$
$19$	15.7940	+	9.11869i	0.831265	+	0.479931i	−0.0230208	+	0.999735i	$0.507328\pi$
$20$		0			0
$21$	19.1228	+	0.228089i	0.910610	+	0.0108614i
$22$	20.0461	−	20.0461i	0.911186	−	0.911186i
$23$	−39.7282	+	10.6451i	−1.72731	+	0.462832i	−0.979561	−	0.201148i	$-0.935533\pi$
$23$	−39.7282	+	10.6451i	−1.72731	+	0.462832i	−0.747751	+	0.663979i	$0.768866\pi$
$24$	6.69207	−	3.86367i	0.278836	−	0.160986i
$25$		0			0
$26$	−2.21546	+	3.83729i	−0.0852099	+	0.147588i
$27$	20.3539	−	20.3539i	0.753847	−	0.753847i
$28$	−9.78072	−	10.0169i	−0.349312	−	0.357745i
$29$		−	19.0242i		−	0.656006i	−0.944677	−	0.328003i	$-0.893624\pi$
$29$		−	19.0242i		−	0.656006i	0.944677	−	0.328003i	$-0.106376\pi$
$30$		0			0
$31$	−3.14077	−	5.43998i	−0.101315	−	0.175483i	0.810912	−	0.585169i	$-0.198972\pi$
$31$	−3.14077	−	5.43998i	−0.101315	−	0.175483i	−0.912227	+	0.409686i	$0.865638\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	52.9003	−	14.1746i	1.60304	−	0.429533i
$34$		−	17.4700i		−	0.513822i
$35$		0			0
$36$	−3.07208			−0.0853356
$37$	9.82266	+	36.6587i	0.265477	+	0.990775i	0.961958	+	0.273199i	$0.0880818\pi$
$37$	9.82266	+	36.6587i	0.265477	+	0.990775i	−0.696480	+	0.717576i	$0.745252\pi$
$38$	6.67534	−	24.9127i	0.175667	−	0.655598i
$39$	−7.41300	+	4.27990i	−0.190077	+	0.109741i
$40$		0			0
$41$	−16.3689			−0.399242			−0.199621	−	0.979873i	$-0.563971\pi$
$41$	−16.3689			−0.399242			−0.199621	+	0.979873i	$0.563971\pi$
$42$	−6.68786	−	26.2057i	−0.159235	−	0.623946i
$43$	4.26669	+	4.26669i	0.0992252	+	0.0992252i	0.754977	−	0.655752i	$-0.227648\pi$
$43$	4.26669	+	4.26669i	0.0992252	+	0.0992252i	−0.655752	+	0.754977i	$0.727648\pi$
$44$	−34.7208	−	20.0461i	−0.789110	−	0.455593i
$45$		0			0
$46$	29.0830	+	50.3733i	0.632240	+	1.09507i
$47$	−3.19722	−	11.9322i	−0.0680260	−	0.253877i	0.923536	−	0.383513i	$-0.125286\pi$
$47$	−3.19722	−	11.9322i	−0.0680260	−	0.253877i	−0.991562	+	0.129636i	$0.958619\pi$
$48$	−7.72733	−	7.72733i	−0.160986	−	0.160986i
$49$	−43.0075	+	23.4809i	−0.877705	+	0.479202i
$50$		0			0
$51$	16.8745	−	29.2275i	0.330873	−	0.573089i
$52$	6.05274	+	1.62183i	0.116399	+	0.0311890i
$53$	13.8578	−	51.7180i	0.261468	−	0.975811i	−0.702909	−	0.711279i	$-0.748116\pi$
$53$	13.8578	−	51.7180i	0.261468	−	0.975811i	0.964377	−	0.264531i	$-0.0852173\pi$
$54$	−35.2539	−	20.3539i	−0.652851	−	0.376924i
$55$		0			0
$56$	−10.1033	+	17.0271i	−0.180416	+	0.304056i
$57$	35.2316	−	35.2316i	0.618098	−	0.618098i
$58$	−25.9875	+	6.96333i	−0.448060	+	0.120057i
$59$	82.3873	−	47.5663i	1.39639	−	0.806209i	0.402382	−	0.915472i	$-0.368183\pi$
$59$	82.3873	−	47.5663i	1.39639	−	0.806209i	0.994013	+	0.109263i	$0.0348492\pi$
$60$		0			0
$61$	−4.22958	+	7.32586i	−0.0693375	+	0.120096i	−0.898610	−	0.438749i	$-0.855422\pi$
$61$	−4.22958	+	7.32586i	−0.0693375	+	0.120096i	0.829272	+	0.558845i	$0.188755\pi$
$62$	−6.28154	+	6.28154i	−0.101315	+	0.101315i
$63$	−2.90657	+	10.3520i	−0.0461360	+	0.164317i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−38.7257	−	67.0749i	−0.586753	−	1.01629i
$67$	10.9793	+	2.94188i	0.163870	+	0.0439087i	0.339821	−	0.940490i	$-0.389634\pi$
$67$	10.9793	+	2.94188i	0.163870	+	0.0439087i	−0.175951	+	0.984399i	$0.556300\pi$
$68$	−23.8644	+	6.39445i	−0.350947	+	0.0940360i
$69$			112.367i			1.62851i
$70$		0			0
$71$	94.8180			1.33547			0.667733	−	0.744401i	$-0.267265\pi$
$71$	94.8180			1.33547			0.667733	+	0.744401i	$0.267265\pi$
$72$	1.12446	+	4.19654i	0.0156175	+	0.0582853i
$73$	2.11109	−	7.87869i	0.0289190	−	0.107927i	−0.949958	−	0.312378i	$-0.898874\pi$
$73$	2.11109	−	7.87869i	0.0289190	−	0.107927i	0.978877	+	0.204451i	$0.0655410\pi$
$74$	46.4813	−	26.8360i	0.628126	−	0.362649i
$75$		0			0
$76$	−36.4747			−0.479931
$77$	−100.399	+	98.0326i	−1.30389	+	1.27315i
$78$	8.55979	+	8.55979i	0.109741	+	0.109741i
$79$	−15.1049	−	8.72081i	−0.191201	−	0.110390i	0.401344	−	0.915928i	$-0.368543\pi$
$79$	−15.1049	−	8.72081i	−0.191201	−	0.110390i	−0.592545	+	0.805538i	$0.701877\pi$
$80$		0			0
$81$	−32.4081	−	56.1325i	−0.400100	−	0.692994i
$82$	5.99144	+	22.3604i	0.0730663	+	0.272687i
$83$	63.0967	+	63.0967i	0.760201	+	0.760201i	0.976359	−	0.216157i	$-0.0693525\pi$
$83$	63.0967	+	63.0967i	0.760201	+	0.760201i	−0.216157	+	0.976359i	$0.569352\pi$
$84$	−33.3498	+	18.7278i	−0.397021	+	0.222949i
$85$		0			0
$86$	4.26669	−	7.39012i	0.0496126	−	0.0859316i
$87$	−50.2035	−	13.4520i	−0.577052	−	0.154621i
$88$	−14.6748	+	54.7669i	−0.166759	+	0.622351i
$89$	67.0808	+	38.7291i	0.753717	+	0.435158i	0.827035	−	0.562150i	$-0.190026\pi$
$89$	67.0808	+	38.7291i	0.753717	+	0.435158i	−0.0733187	+	0.997309i	$0.523359\pi$
$90$		0			0
$91$	11.1917	−	18.8615i	0.122986	−	0.207269i
$92$	58.1661	−	58.1661i	0.632240	−	0.632240i
$93$	−16.5766	+	4.44168i	−0.178243	+	0.0477600i
$94$	−15.1294	+	8.73498i	−0.160951	+	0.0929253i
$95$		0			0
$96$	−7.72733	+	13.3841i	−0.0804930	+	0.139418i
$97$	−105.134	+	105.134i	−1.08385	+	1.08385i	−0.0877043	+	0.996147i	$0.527953\pi$
$97$	−105.134	+	105.134i	−1.08385	+	1.08385i	−0.996147	+	0.0877043i	$0.972047\pi$
$98$	47.8173	+	50.1548i	0.487932	+	0.511784i
$99$			30.7916i			0.311026i
$100$		0			0
$101$	−63.7196	−	110.366i	−0.630887	−	1.09273i	−0.987371	−	0.158427i	$-0.949358\pi$
$101$	−63.7196	−	110.366i	−0.630887	−	1.09273i	0.356483	−	0.934302i	$-0.383976\pi$
$102$	−46.1020	−	12.3530i	−0.451981	−	0.121108i
$103$	7.25451	−	1.94384i	0.0704321	−	0.0188722i	−0.223431	−	0.974720i	$-0.571726\pi$
$103$	7.25451	−	1.94384i	0.0704321	−	0.0188722i	0.293863	+	0.955848i	$0.405059\pi$
$104$		−	8.86183i		−	0.0852099i
$105$		0			0
$106$	−75.7204			−0.714343
$107$	−29.8828	−	111.524i	−0.279279	−	1.04228i	−0.952919	−	0.303224i	$-0.901937\pi$
$107$	−29.8828	−	111.524i	−0.279279	−	1.04228i	0.673641	−	0.739059i	$-0.264730\pi$
$108$	−14.9001	+	55.6078i	−0.137964	+	0.514887i
$109$	−36.9108	+	21.3104i	−0.338631	+	0.195509i	−0.659666	−	0.751559i	$-0.729302\pi$
$109$	−36.9108	+	21.3104i	−0.338631	+	0.195509i	0.321036	+	0.947067i	$0.395969\pi$
$110$		0			0
$111$	103.685			0.934103
$112$	26.9576	+	7.56899i	0.240693	+	0.0675802i
$113$	13.6000	+	13.6000i	0.120354	+	0.120354i	0.764718	−	0.644365i	$-0.222878\pi$
$113$	13.6000	+	13.6000i	0.120354	+	0.120354i	−0.644365	+	0.764718i	$0.722878\pi$
$114$	−61.0229	−	35.2316i	−0.535288	−	0.309049i
$115$		0			0
$116$	19.0242	+	32.9508i	0.164001	+	0.284059i
$117$	−1.24560	−	4.64863i	−0.0106461	−	0.0397319i
$118$	−95.1326	−	95.1326i	−0.806209	−	0.806209i
$119$	−1.03133	+	86.4657i	−0.00866660	+	0.726603i
$120$		0			0
$121$	−140.423	+	243.219i	−1.16052	+	2.01008i
$122$	11.5554	+	3.09627i	0.0947167	+	0.0253793i
$123$	−11.5745	+	43.1965i	−0.0941013	+	0.351191i
$124$	10.8800	+	6.28154i	0.0877415	+	0.0506576i
$125$		0			0
$126$	15.2050	+	0.181358i	0.120674	+	0.00143935i
$127$	−24.7683	+	24.7683i	−0.195026	+	0.195026i	−0.797864	−	0.602838i	$-0.794037\pi$
$127$	−24.7683	+	24.7683i	−0.195026	+	0.195026i	0.602838	+	0.797864i	$0.294037\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$	14.2765	−	8.24252i	0.110670	−	0.0638955i
$130$		0			0
$131$	−72.3622	+	125.335i	−0.552383	+	0.956756i	0.445719	+	0.895173i	$0.352948\pi$
$131$	−72.3622	+	125.335i	−0.552383	+	0.956756i	−0.998102	+	0.0615830i	$0.980385\pi$
$132$	−77.4514	+	77.4514i	−0.586753	+	0.586753i
$133$	−34.5096	+	122.909i	−0.259471	+	0.924126i
$134$		−	16.0748i		−	0.119961i
$135$		0			0
$136$	17.4700	+	30.2589i	0.128456	+	0.222492i
$137$	45.5877	+	12.2152i	0.332757	+	0.0891619i	0.421329	−	0.906908i	$-0.361564\pi$
$137$	45.5877	+	12.2152i	0.332757	+	0.0891619i	−0.0885724	+	0.996070i	$0.528230\pi$
$138$	153.496	−	41.1292i	1.11229	−	0.298038i
$139$		−	121.473i		−	0.873910i	−0.899483	−	0.436955i	$-0.856057\pi$
$139$		−	121.473i		−	0.873910i	0.899483	−	0.436955i	$-0.143943\pi$
$140$		0			0
$141$	−33.7490			−0.239355
$142$	−34.7058	−	129.524i	−0.244407	−	0.912140i
$143$	16.2556	−	60.6669i	0.113676	−	0.424244i
$144$	5.32100	−	3.07208i	0.0369514	−	0.0213339i
$145$		0			0
$146$	−11.5352			−0.0790083
$147$	31.5538	+	130.097i	0.214652	+	0.885016i
$148$	−53.6720	−	53.6720i	−0.362649	−	0.362649i
$149$	−117.569	−	67.8784i	−0.789053	−	0.455560i	0.0505763	−	0.998720i	$-0.483894\pi$
$149$	−117.569	−	67.8784i	−0.789053	−	0.455560i	−0.839629	+	0.543160i	$0.817228\pi$
$150$		0			0
$151$	−41.3618	−	71.6408i	−0.273919	−	0.474442i	0.695943	−	0.718097i	$-0.254987\pi$
$151$	−41.3618	−	71.6408i	−0.273919	−	0.474442i	−0.969862	+	0.243655i	$0.921653\pi$
$152$	13.3507	+	49.8254i	0.0878334	+	0.327799i
$153$	13.4173	+	13.4173i	0.0876947	+	0.0876947i
$154$	170.664	+	101.266i	1.10821	+	0.657570i
$155$		0			0
$156$	8.55979	−	14.8260i	0.0548705	−	0.0950384i
$157$	−37.8843	−	10.1511i	−0.241301	−	0.0646565i	0.136142	−	0.990689i	$-0.456530\pi$
$157$	−37.8843	−	10.1511i	−0.241301	−	0.0646565i	−0.377443	+	0.926033i	$0.623196\pi$
$158$	−6.38408	+	23.8257i	−0.0404056	+	0.150796i
$159$	−126.681	−	73.1396i	−0.796739	−	0.459997i
$160$		0			0
$161$	−140.970	−	251.034i	−0.875588	−	1.55922i
$162$	−64.8162	+	64.8162i	−0.400100	+	0.400100i
$163$	−119.375	+	31.9864i	−0.732361	+	0.196236i	−0.605680	−	0.795708i	$-0.707099\pi$
$163$	−119.375	+	31.9864i	−0.732361	+	0.196236i	−0.126681	+	0.991944i	$0.540432\pi$
$164$	28.3518	−	16.3689i	0.172877	−	0.0998105i
$165$		0			0
$166$	63.0967	−	109.287i	0.380101	−	0.658353i
$167$	173.339	−	173.339i	1.03796	−	1.03796i	0.0387094	−	0.999251i	$-0.487675\pi$
$167$	173.339	−	173.339i	1.03796	−	1.03796i	0.999251	−	0.0387094i	$-0.0123247\pi$
$168$	37.7894	+	38.7018i	0.224937	+	0.230368i
$169$		−	159.183i		−	0.941914i
$170$		0			0
$171$	14.0067	+	24.2603i	0.0819104	+	0.141873i
$172$	−11.6568	−	3.12343i	−0.0677721	−	0.0181595i
$173$	−233.962	+	62.6900i	−1.35238	+	0.362370i	−0.861014	−	0.508582i	$-0.830170\pi$
$173$	−233.962	+	62.6900i	−1.35238	+	0.362370i	−0.491369	+	0.870952i	$0.663503\pi$
$174$			73.5030i			0.422431i
$175$		0			0
$176$	80.1843			0.455593
$177$	−67.2683	−	251.049i	−0.380047	−	1.41835i
$178$	28.3517	−	105.810i	0.159279	−	0.594438i
$179$	−150.152	+	86.6905i	−0.838840	+	0.484304i	−0.856870	−	0.515533i	$-0.827594\pi$
$179$	−150.152	+	86.6905i	−0.838840	+	0.484304i	0.0180301	+	0.999837i	$0.494261\pi$
$180$		0			0
$181$	237.263			1.31085			0.655424	−	0.755262i	$-0.272490\pi$
$181$	237.263			1.31085			0.655424	+	0.755262i	$0.272490\pi$
$182$	−29.8617	−	8.38439i	−0.164075	−	0.0460681i
$183$	16.3417	+	16.3417i	0.0892989	+	0.0892989i
$184$	−100.747	−	58.1661i	−0.547536	−	0.316120i
$185$		0			0
$186$	12.1349	+	21.0182i	0.0652414	+	0.113001i
$187$	64.0918	+	239.194i	0.342737	+	1.27911i
$188$	17.4700	+	17.4700i	0.0929253	+	0.0929253i
$189$	173.284	+	102.821i	0.916847	+	0.544024i
$190$		0			0
$191$	−10.4921	+	18.1728i	−0.0549324	+	0.0951457i	−0.892184	−	0.451672i	$-0.850828\pi$
$191$	−10.4921	+	18.1728i	−0.0549324	+	0.0951457i	0.837252	+	0.546818i	$0.184161\pi$
$192$	21.1115	+	5.65680i	0.109956	+	0.0294625i
$193$	12.9543	−	48.3460i	0.0671206	−	0.250497i	−0.924211	−	0.381883i	$-0.875276\pi$
$193$	12.9543	−	48.3460i	0.0671206	−	0.250497i	0.991331	+	0.131385i	$0.0419425\pi$
$194$	182.097	+	105.134i	0.938642	+	0.541925i
$195$		0			0
$196$	51.0104	−	83.6776i	0.260257	−	0.426927i
$197$	85.5963	−	85.5963i	0.434499	−	0.434499i	−0.455657	−	0.890156i	$-0.650596\pi$
$197$	85.5963	−	85.5963i	0.434499	−	0.434499i	0.890156	+	0.455657i	$0.150596\pi$
$198$	42.0621	−	11.2705i	0.212435	−	0.0569218i
$199$	266.269	−	153.731i	1.33804	−	0.772515i	0.351520	−	0.936180i	$-0.385665\pi$
$199$	266.269	−	153.731i	1.33804	−	0.772515i	0.986516	+	0.163665i	$0.0523316\pi$
$200$		0			0
$201$	15.5269	−	26.8933i	0.0772481	−	0.133798i
$202$	−127.439	+	127.439i	−0.630887	+	0.630887i
$203$	129.033	−	32.9301i	0.635633	−	0.162217i
$204$			67.4981i			0.330873i
$205$		0			0
$206$	−5.31067	−	9.19835i	−0.0257799	−	0.0446522i
$207$	−61.0241	−	16.3514i	−0.294803	−	0.0789921i
$208$	−12.1055	+	3.24366i	−0.0581995	+	0.0155945i
$209$			365.588i			1.74922i
$210$		0			0
$211$	−116.585			−0.552533			−0.276267	−	0.961081i	$-0.589097\pi$
$211$	−116.585			−0.552533			−0.276267	+	0.961081i	$0.589097\pi$
$212$	27.7156	+	103.436i	0.130734	+	0.487905i
$213$	67.0458	−	250.218i	0.314769	−	1.17473i
$214$	−141.407	+	81.6414i	−0.660781	+	0.381502i
$215$		0			0
$216$	81.4155			0.376924
$217$	31.4607	−	30.7190i	0.144980	−	0.141562i
$218$	42.6209	+	42.6209i	0.195509	+	0.195509i
$219$	−19.2986	−	11.1420i	−0.0881214	−	0.0508769i
$220$		0			0
$221$	−19.3520	−	33.5186i	−0.0875655	−	0.151668i
$222$	−37.9515	−	141.637i	−0.170953	−	0.638004i
$223$	93.2689	+	93.2689i	0.418246	+	0.418246i	0.884599	−	0.466353i	$-0.154432\pi$
$223$	93.2689	+	93.2689i	0.418246	+	0.418246i	−0.466353	+	0.884599i	$0.654432\pi$
$224$	0.472274	−	39.5952i	0.00210837	−	0.176764i
$225$		0			0
$226$	13.6000	−	23.5558i	0.0601768	−	0.104229i
$227$	325.524	+	87.2238i	1.43403	+	0.384246i	0.890437	−	0.455106i	$-0.150399\pi$
$227$	325.524	+	87.2238i	1.43403	+	0.384246i	0.543588	+	0.839352i	$0.317065\pi$
$228$	−25.7913	+	96.2544i	−0.113120	+	0.422168i
$229$	−330.729	−	190.946i	−1.44423	−	0.833827i	−0.446102	−	0.894982i	$-0.647188\pi$
$229$	−330.729	−	190.946i	−1.44423	−	0.833827i	−0.998128	+	0.0611552i	$0.980522\pi$
$230$		0			0
$231$	187.709	+	334.266i	0.812593	+	1.44704i
$232$	38.0483	−	38.0483i	0.164001	−	0.164001i
$233$	322.409	−	86.3892i	1.38373	−	0.370769i	0.511255	−	0.859429i	$-0.329181\pi$
$233$	322.409	−	86.3892i	1.38373	−	0.370769i	0.872474	+	0.488660i	$0.162514\pi$
$234$	−5.89423	+	3.40304i	−0.0251890	+	0.0145429i
$235$		0			0
$236$	−95.1326	+	164.775i	−0.403104	+	0.698197i
$237$	−33.6943	+	33.6943i	−0.142170	+	0.142170i
$238$	118.492	−	30.2398i	0.497865	−	0.127058i
$239$		−	437.169i		−	1.82916i	−0.404406	−	0.914579i	$-0.632522\pi$
$239$		−	437.169i		−	1.82916i	0.404406	−	0.914579i	$-0.367478\pi$
$240$		0			0
$241$	1.94620	+	3.37093i	0.00807554	+	0.0139872i	0.870035	−	0.492990i	$-0.164096\pi$
$241$	1.94620	+	3.37093i	0.00807554	+	0.0139872i	−0.861959	+	0.506977i	$0.830763\pi$
$242$	383.642	+	102.797i	1.58530	+	0.424779i
$243$	79.1896	−	21.2188i	0.325883	−	0.0873201i
$244$		−	16.9183i		−	0.0693375i
$245$		0			0
$246$	63.2440			0.257090
$247$	−14.7889	−	55.1931i	−0.0598742	−	0.223454i
$248$	4.59841	−	17.1615i	0.0185420	−	0.0691996i
$249$	211.124	−	121.892i	0.847886	−	0.489527i
$250$		0			0
$251$	368.235			1.46707			0.733535	−	0.679651i	$-0.237869\pi$
$251$	368.235			1.46707			0.733535	+	0.679651i	$0.237869\pi$
$252$	−5.31766	−	20.8367i	−0.0211018	−	0.0826855i
$253$	−583.001	−	583.001i	−2.30435	−	2.30435i
$254$	42.8999	+	24.7683i	0.168897	+	0.0975129i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−68.5388	−	255.790i	−0.266688	−	0.995294i	−0.961209	−	0.275821i	$-0.911050\pi$
$257$	−68.5388	−	255.790i	−0.266688	−	0.995294i	0.694521	−	0.719473i	$-0.255616\pi$
$258$	−16.4850	−	16.4850i	−0.0638955	−	0.0638955i
$259$	−231.639	+	130.078i	−0.894358	+	0.502232i
$260$		0			0
$261$	14.6110	−	25.3069i	0.0559807	−	0.0969614i
$262$	197.697	+	52.9728i	0.754570	+	0.202186i
$263$	71.0526	−	265.172i	0.270162	−	1.00826i	−0.688852	−	0.724902i	$-0.741885\pi$
$263$	71.0526	−	265.172i	0.270162	−	1.00826i	0.959014	−	0.283357i	$-0.0914482\pi$
$264$	134.150	+	77.4514i	0.508143	+	0.293376i
$265$		0			0
$266$	180.528	+	2.15326i	0.678676	+	0.00809496i
$267$	149.636	−	149.636i	0.560436	−	0.560436i
$268$	−21.9585	+	5.88377i	−0.0819348	+	0.0219544i
$269$	120.599	−	69.6276i	0.448322	−	0.258839i	−0.258799	−	0.965931i	$-0.583327\pi$
$269$	120.599	−	69.6276i	0.448322	−	0.258839i	0.707121	+	0.707092i	$0.249994\pi$
$270$		0			0
$271$	−31.0329	+	53.7505i	−0.114512	+	0.198341i	−0.917585	−	0.397540i	$-0.869864\pi$
$271$	−31.0329	+	53.7505i	−0.114512	+	0.198341i	0.803072	+	0.595882i	$0.203197\pi$
$272$	34.9399	−	34.9399i	0.128456	−	0.128456i
$273$	−41.8605	−	42.8711i	−0.153335	−	0.157037i
$274$		−	66.7450i		−	0.243595i
$275$		0			0
$276$	−112.367	−	194.626i	−0.407127	−	0.705165i
$277$	−401.798	−	107.661i	−1.45053	−	0.388669i	−0.554324	−	0.832301i	$-0.687023\pi$
$277$	−401.798	−	107.661i	−1.45053	−	0.388669i	−0.896209	+	0.443632i	$0.853690\pi$
$278$	−165.936	+	44.4624i	−0.596891	+	0.159937i
$279$		−	9.64871i		−	0.0345832i
$280$		0			0
$281$	−370.599			−1.31886			−0.659428	−	0.751767i	$-0.729202\pi$
$281$	−370.599			−1.31886			−0.659428	+	0.751767i	$0.729202\pi$
$282$	12.3530	+	46.1020i	0.0438050	+	0.163482i
$283$	−124.931	+	466.250i	−0.441453	+	1.64753i	0.283681	+	0.958919i	$0.408444\pi$
$283$	−124.931	+	466.250i	−0.441453	+	1.64753i	−0.725135	+	0.688607i	$0.758222\pi$
$284$	−164.230	+	94.8180i	−0.578273	+	0.333866i
$285$		0			0
$286$	−88.8225			−0.310568
$287$	−28.3340	−	111.024i	−0.0987247	−	0.386843i
$288$	−6.14417	−	6.14417i	−0.0213339	−	0.0213339i
$289$	−118.126	−	68.2002i	−0.408741	−	0.235987i
$290$		0			0
$291$	203.100	+	351.780i	0.697940	+	1.20887i
$292$	4.22218	+	15.7574i	0.0144595	+	0.0539636i
$293$	203.433	+	203.433i	0.694312	+	0.694312i	0.963178	−	0.268866i	$-0.0866489\pi$
$293$	203.433	+	203.433i	0.694312	+	0.694312i	−0.268866	+	0.963178i	$0.586649\pi$
$294$	166.167	−	90.7223i	0.565193	−	0.308579i
$295$		0			0
$296$	−53.6720	+	92.9627i	−0.181324	+	0.314063i
$297$	557.359	+	149.344i	1.87663	+	0.502842i
$298$	−49.6904	+	185.447i	−0.166746	+	0.622306i
$299$	111.600	+	64.4323i	0.373244	+	0.215492i
$300$		0			0
$301$	−21.5538	+	36.3247i	−0.0716073	+	0.120680i
$302$	−82.7236	+	82.7236i	−0.273919	+	0.273919i
$303$	−336.304	+	90.1123i	−1.10991	+	0.297400i
$304$	63.1761	−	36.4747i	0.207816	−	0.119983i
$305$		0			0
$306$	13.4173	−	23.2394i	0.0438474	−	0.0759458i
$307$	−0.207402	+	0.207402i	−0.000675578	+	0.000675578i	−0.707444	−	0.706769i	$-0.750152\pi$
$307$	−0.207402	+	0.207402i	−0.000675578	+	0.000675578i	0.706769	+	0.707444i	$0.250152\pi$
$308$	75.8643	−	270.197i	0.246313	−	0.877262i
$309$		−	20.5187i		−	0.0664034i
$310$		0			0
$311$	−178.011	−	308.324i	−0.572382	−	0.991394i	−0.996321	−	0.0857033i	$-0.972686\pi$
$311$	−178.011	−	308.324i	−0.572382	−	0.991394i	0.423939	−	0.905691i	$-0.360647\pi$
$312$	−23.3858	−	6.26620i	−0.0749544	−	0.0200840i
$313$	−251.585	+	67.4119i	−0.803784	+	0.215373i	−0.637245	−	0.770661i	$-0.719926\pi$
$313$	−251.585	+	67.4119i	−0.803784	+	0.215373i	−0.166540	+	0.986035i	$0.553259\pi$
$314$			55.4664i			0.176645i
$315$		0			0
$316$	34.8833			0.110390
$317$	20.0199	+	74.7155i	0.0631544	+	0.235695i	0.990287	−	0.139038i	$-0.0444010\pi$
$317$	20.0199	+	74.7155i	0.0631544	+	0.235695i	−0.927133	+	0.374733i	$0.877734\pi$
$318$	−53.5419	+	199.821i	−0.168371	+	0.628368i
$319$	330.267	−	190.680i	1.03532	−	0.597743i
$320$		0			0
$321$	−315.435			−0.982664
$322$	−291.321	+	284.453i	−0.904723	+	0.883395i
$323$	159.303	+	159.303i	0.493198	+	0.493198i
$324$	112.265	+	64.8162i	0.346497	+	0.200050i
$325$		0			0
$326$	87.3885	+	151.361i	0.268063	+	0.464298i
$327$	30.1372	+	112.474i	0.0921627	+	0.343956i
$328$	−32.7378	−	32.7378i	−0.0998105	−	0.0998105i
$329$	75.3972	−	42.3397i	0.229171	−	0.128692i
$330$		0			0
$331$	−43.1415	+	74.7232i	−0.130337	+	0.225750i	−0.923806	−	0.382860i	$-0.874939\pi$
$331$	−43.1415	+	74.7232i	−0.130337	+	0.225750i	0.793470	+	0.608610i	$0.208273\pi$
$332$	−172.383	−	46.1900i	−0.519227	−	0.139126i
$333$	−15.0880	+	56.3093i	−0.0453094	+	0.169097i
$334$	−300.232	−	173.339i	−0.898900	−	0.518980i
$335$		0			0
$336$	39.0357	−	65.7872i	0.116178	−	0.195795i
$337$	−92.8454	+	92.8454i	−0.275506	+	0.275506i	−0.831312	−	0.555806i	$-0.812410\pi$
$337$	−92.8454	+	92.8454i	−0.275506	+	0.275506i	0.555806	+	0.831312i	$0.312410\pi$
$338$	−217.449	+	58.2652i	−0.643339	+	0.172382i
$339$	45.5059	−	26.2728i	0.134236	−	0.0775010i
$340$		0			0
$341$	62.9602	−	109.050i	0.184634	−	0.319795i
$342$	28.0134	−	28.0134i	0.0819104	−	0.0819104i
$343$	−233.706	−	251.059i	−0.681359	−	0.731950i
$344$			17.0667i			0.0496126i
$345$		0			0
$346$	171.272	+	296.652i	0.495006	+	0.857376i
$347$	−386.918	−	103.674i	−1.11504	−	0.298773i	−0.346164	−	0.938174i	$-0.612516\pi$
$347$	−386.918	−	103.674i	−1.11504	−	0.298773i	−0.768874	+	0.639401i	$0.779183\pi$
$348$	100.407	−	26.9040i	0.288526	−	0.0773103i
$349$			202.323i			0.579723i	0.957069	+	0.289862i	$0.0936093\pi$
$349$			202.323i			0.579723i	−0.957069	+	0.289862i	$0.906391\pi$
$350$		0			0
$351$	−90.1863			−0.256941
$352$	−29.3495	−	109.534i	−0.0833793	−	0.311176i
$353$	85.4581	−	318.934i	0.242091	−	0.903496i	−0.732732	−	0.680517i	$-0.761755\pi$
$353$	85.4581	−	318.934i	0.242091	−	0.903496i	0.974823	−	0.222979i	$-0.0715781\pi$
$354$	−318.317	+	183.780i	−0.899200	+	0.519154i
$355$		0			0
$356$	−154.916			−0.435158
$357$	227.448	+	63.8615i	0.637109	+	0.178884i
$358$	173.381	+	173.381i	0.484304	+	0.484304i
$359$	27.1220	+	15.6589i	0.0755487	+	0.0436181i	0.537298	−	0.843392i	$-0.319445\pi$
$359$	27.1220	+	15.6589i	0.0755487	+	0.0436181i	−0.461750	+	0.887010i	$0.652778\pi$
$360$		0			0
$361$	−14.1991	−	24.5936i	−0.0393327	−	0.0681263i
$362$	−86.8444	−	324.108i	−0.239902	−	0.895325i
$363$	542.546	+	542.546i	1.49462	+	1.49462i
$364$	−0.523152	+	43.8607i	−0.00143723	+	0.120496i
$365$		0			0
$366$	16.3417	−	28.3047i	0.0446495	−	0.0773351i
$367$	169.529	+	45.4250i	0.461931	+	0.123774i	0.482276	−	0.876019i	$-0.339810\pi$
$367$	169.529	+	45.4250i	0.461931	+	0.123774i	−0.0203459	+	0.999793i	$0.506477\pi$
$368$	−42.5805	+	158.913i	−0.115708	+	0.431828i
$369$	−21.7748	−	12.5717i	−0.0590102	−	0.0340696i
$370$		0			0
$371$	374.770	+	4.47010i	1.01016	+	0.0120488i
$372$	24.2698	−	24.2698i	0.0652414	−	0.0652414i
$373$	104.404	−	27.9749i	0.279903	−	0.0749997i	−0.116137	−	0.993233i	$-0.537051\pi$
$373$	104.404	−	27.9749i	0.279903	−	0.0749997i	0.396039	+	0.918234i	$0.370384\pi$
$374$	303.286	−	175.102i	0.810924	−	0.468187i
$375$		0			0
$376$	17.4700	−	30.2589i	0.0464627	−	0.0804757i
$377$	−42.1472	+	42.1472i	−0.111796	+	0.111796i
$378$	77.0291	−	274.345i	0.203781	−	0.725782i
$379$			370.389i			0.977279i	0.872486	+	0.488639i	$0.162507\pi$
$379$			370.389i			0.977279i	−0.872486	+	0.488639i	$0.837493\pi$
$380$		0			0
$381$	47.8482	+	82.8755i	0.125586	+	0.217521i
$382$	28.6649	+	7.68074i	0.0750390	+	0.0201066i
$383$	3.39901	−	0.910761i	0.00887469	−	0.00237797i	−0.254379	−	0.967105i	$-0.581871\pi$
$383$	3.39901	−	0.910761i	0.00887469	−	0.00237797i	0.263254	+	0.964727i	$0.415204\pi$
$384$		−	30.9093i		−	0.0804930i
$385$		0			0
$386$	−70.7834			−0.183377
$387$	2.39886	+	8.95267i	0.00619860	+	0.0231335i
$388$	76.9631	−	287.230i	0.198358	−	0.740284i
$389$	−628.167	+	362.672i	−1.61482	+	0.932319i	−0.626594	+	0.779346i	$0.715551\pi$
$389$	−628.167	+	362.672i	−1.61482	+	0.932319i	−0.988230	+	0.152973i	$0.951115\pi$
$390$		0			0
$391$	−508.079			−1.29944
$392$	−132.977	−	39.0533i	−0.339227	−	0.0996258i
$393$	279.583	+	279.583i	0.711408	+	0.711408i
$394$	−148.257	−	85.5963i	−0.376287	−	0.217249i
$395$		0			0
$396$	−30.7916	−	53.3326i	−0.0777566	−	0.134678i
$397$	33.1595	+	123.753i	0.0835253	+	0.311721i	0.995031	−	0.0995671i	$-0.0317458\pi$
$397$	33.1595	+	123.753i	0.0835253	+	0.311721i	−0.911506	+	0.411288i	$0.865079\pi$
$398$	−307.461	−	307.461i	−0.772515	−	0.772515i
$399$	299.946	+	177.977i	0.751745	+	0.446059i
$400$		0			0
$401$	350.482	−	607.052i	0.874019	−	1.51384i	0.0162143	−	0.999869i	$-0.494839\pi$
$401$	350.482	−	607.052i	0.874019	−	1.51384i	0.857804	−	0.513976i	$-0.171828\pi$
$402$	−42.4202	−	11.3665i	−0.105523	−	0.0282748i
$403$	−5.09379	+	19.0103i	−0.0126397	+	0.0471719i
$404$	220.731	+	127.439i	0.546364	+	0.315444i
$405$		0			0
$406$	−92.2129	−	164.210i	−0.227125	−	0.404457i
$407$	−537.957	+	537.957i	−1.32176	+	1.32176i
$408$	92.2041	−	24.7060i	0.225990	−	0.0605540i
$409$	−391.838	+	226.228i	−0.958039	+	0.553124i	−0.895569	−	0.444923i	$-0.853231\pi$
$409$	−391.838	+	226.228i	−0.958039	+	0.553124i	−0.0624701	+	0.998047i	$0.519898\pi$
$410$		0			0
$411$	64.4701	−	111.665i	0.156861	−	0.271692i
$412$	−10.6213	+	10.6213i	−0.0257799	+	0.0257799i
$413$	465.233	+	476.465i	1.12647	+	1.15367i
$414$			89.3455i			0.215810i
$415$		0			0
$416$	8.86183	+	15.3491i	0.0213025	+	0.0368970i
$417$	−320.560	−	85.8939i	−0.768730	−	0.205981i
$418$	499.402	−	133.814i	1.19474	−	0.320130i
$419$			248.174i			0.592302i	0.955141	+	0.296151i	$0.0957031\pi$
$419$			248.174i			0.592302i	−0.955141	+	0.296151i	$0.904297\pi$
$420$		0			0
$421$	−238.992			−0.567676			−0.283838	−	0.958872i	$-0.591608\pi$
$421$	−238.992			−0.567676			−0.283838	+	0.958872i	$0.591608\pi$
$422$	42.6729	+	159.257i	0.101121	+	0.377387i
$423$	4.91107	−	18.3284i	0.0116101	−	0.0433295i
$424$	131.152	−	75.7204i	0.309320	−	0.178586i
$425$		0			0
$426$	−366.345			−0.859965
$427$	−57.0097	−	16.0068i	−0.133512	−	0.0374867i
$428$	163.283	+	163.283i	0.381502	+	0.381502i
$429$	−148.602	−	85.7951i	−0.346391	−	0.199989i
$430$		0			0
$431$	65.3730	+	113.229i	0.151677	+	0.262713i	0.931844	−	0.362858i	$-0.118199\pi$
$431$	65.3730	+	113.229i	0.151677	+	0.262713i	−0.780167	+	0.625572i	$0.784866\pi$
$432$	−29.8001	−	111.216i	−0.0689818	−	0.257444i
$433$	−456.850	−	456.850i	−1.05508	−	1.05508i	−0.998392	−	0.0566898i	$-0.981945\pi$
$433$	−456.850	−	456.850i	−1.05508	−	1.05508i	−0.0566898	−	0.998392i	$-0.518055\pi$
$434$	−53.4784	−	31.7321i	−0.123222	−	0.0731155i
$435$		0			0
$436$	42.6209	−	73.8215i	0.0977543	−	0.169315i
$437$	−724.537	−	194.139i	−1.65798	−	0.444255i
$438$	−8.15654	+	30.4406i	−0.0186222	+	0.0694992i
$439$	−187.891	−	108.479i	−0.427998	−	0.247105i	0.270495	−	0.962721i	$-0.412812\pi$
$439$	−187.891	−	108.479i	−0.427998	−	0.247105i	−0.698493	+	0.715617i	$0.746146\pi$
$440$		0			0
$441$	−75.2446	−	1.79523i	−0.170623	−	0.00407081i
$442$	−38.7040	+	38.7040i	−0.0875655	+	0.0875655i
$443$	−41.8315	+	11.2087i	−0.0944277	+	0.0253018i	−0.305724	−	0.952120i	$-0.598898\pi$
$443$	−41.8315	+	11.2087i	−0.0944277	+	0.0253018i	0.211296	+	0.977422i	$0.432232\pi$
$444$	−179.588	+	103.685i	−0.404478	+	0.233526i
$445$		0			0
$446$	93.2689	−	161.547i	0.209123	−	0.362212i
$447$	−262.259	+	262.259i	−0.586710	+	0.586710i
$448$	−54.2609	+	13.8477i	−0.121118	+	0.0309100i
$449$			48.2524i			0.107466i	0.998555	+	0.0537332i	$0.0171120\pi$
$449$			48.2524i			0.107466i	−0.998555	+	0.0537332i	$0.982888\pi$
$450$		0			0
$451$	−164.066	−	284.171i	−0.363783	−	0.630091i
$452$	−37.1558	−	9.95586i	−0.0822030	−	0.0220262i
$453$	−218.302	+	58.4939i	−0.481903	+	0.129126i
$454$		−	476.600i		−	1.04978i
$455$		0			0
$456$	140.926			0.309049
$457$	75.0016	+	279.910i	0.164117	+	0.612494i	0.998151	+	0.0607809i	$0.0193591\pi$
$457$	75.0016	+	279.910i	0.164117	+	0.612494i	−0.834034	+	0.551713i	$0.813974\pi$
$458$	−139.782	+	521.675i	−0.305202	+	1.13903i
$459$	307.942	−	177.791i	0.670899	−	0.387343i
$460$		0			0
$461$	348.242			0.755407			0.377703	−	0.925927i	$-0.376714\pi$
$461$	348.242			0.755407			0.377703	+	0.925927i	$0.376714\pi$
$462$	387.910	−	378.765i	0.839631	−	0.819838i
$463$	268.097	+	268.097i	0.579044	+	0.579044i	0.934640	−	0.355596i	$-0.115722\pi$
$463$	268.097	+	268.097i	0.579044	+	0.579044i	−0.355596	+	0.934640i	$0.615722\pi$
$464$	−65.9016	−	38.0483i	−0.142029	−	0.0820007i
$465$		0			0
$466$	−236.020	−	408.798i	−0.506480	−	0.877249i
$467$	−129.058	−	481.652i	−0.276356	−	1.03137i	−0.954927	−	0.296840i	$-0.904067\pi$
$467$	−129.058	−	481.652i	−0.276356	−	1.03137i	0.678571	−	0.734535i	$-0.262600\pi$
$468$	6.80607	+	6.80607i	0.0145429	+	0.0145429i
$469$	−0.948961	+	79.5603i	−0.00202337	+	0.169638i
$470$		0			0
$471$	−53.5760	+	92.7963i	−0.113749	+	0.197020i
$472$	259.907	+	69.6419i	0.550651	+	0.147546i
$473$	−31.3063	+	116.837i	−0.0661866	+	0.247012i
$474$	58.3603	+	33.6943i	0.123123	+	0.0710850i
$475$		0			0
$476$	−84.6794	−	150.794i	−0.177898	−	0.316795i
$477$	58.1548	−	58.1548i	0.121918	−	0.121918i
$478$	−597.184	+	160.015i	−1.24934	+	0.334759i
$479$	324.591	−	187.403i	0.677643	−	0.391238i	−0.121323	−	0.992613i	$-0.538714\pi$
$479$	324.591	−	187.403i	0.677643	−	0.391238i	0.798967	+	0.601376i	$0.205380\pi$
$480$		0			0
$481$	59.4541	−	102.977i	0.123605	−	0.214090i
$482$	3.89241	−	3.89241i	0.00807554	−	0.00807554i
$483$	−762.142	+	194.503i	−1.57793	+	0.402698i
$484$		−	561.691i		−	1.16052i
$485$		0			0
$486$	−57.9708	−	100.408i	−0.119281	−	0.206602i
$487$	379.084	+	101.575i	0.778406	+	0.208573i	0.626082	−	0.779757i	$-0.284658\pi$
$487$	379.084	+	101.575i	0.778406	+	0.208573i	0.152324	+	0.988331i	$0.451324\pi$
$488$	−23.1109	+	6.19254i	−0.0473584	+	0.0126896i
$489$			337.640i			0.690470i
$490$		0			0
$491$	100.451			0.204585			0.102293	−	0.994754i	$-0.467382\pi$
$491$	100.451			0.204585			0.102293	+	0.994754i	$0.467382\pi$
$492$	−23.1489	−	86.3930i	−0.0470507	−	0.175595i
$493$	60.8245	−	227.000i	0.123376	−	0.460447i
$494$	−69.9820	+	40.4041i	−0.141664	+	0.0817897i
$495$		0			0
$496$	−25.1262			−0.0506576
$497$	164.126	+	643.114i	0.330234	+	1.29399i
$498$	−243.785	−	243.785i	−0.489527	−	0.489527i
$499$	341.907	+	197.400i	0.685184	+	0.395591i	0.801805	−	0.597585i	$-0.203873\pi$
$499$	341.907	+	197.400i	0.685184	+	0.395591i	−0.116621	+	0.993176i	$0.537206\pi$
$500$		0			0
$501$	−334.863	−	579.999i	−0.668388	−	1.15768i
$502$	−134.783	−	503.018i	−0.268493	−	1.00203i
$503$	38.4894	+	38.4894i	0.0765197	+	0.0765197i	0.744331	−	0.667811i	$-0.232769\pi$
$503$	38.4894	+	38.4894i	0.0765197	+	0.0765197i	−0.667811	+	0.744331i	$0.732769\pi$
$504$	−26.5171	+	14.8908i	−0.0526133	+	0.0295453i
$505$		0			0
$506$	−583.001	+	1009.79i	−1.15218	+	1.99563i
$507$	−420.075	−	112.559i	−0.828549	−	0.222009i
$508$	18.1316	−	67.6682i	0.0356922	−	0.133205i
$509$	−442.330	−	255.380i	−0.869019	−	0.501728i	−0.00199662	−	0.999998i	$-0.500636\pi$
$509$	−442.330	−	255.380i	−0.869019	−	0.501728i	−0.867022	+	0.498270i	$0.833969\pi$
$510$		0			0
$511$	57.0923	+	0.680972i	0.111727	+	0.00133263i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	507.070	−	135.869i	0.988441	−	0.264852i
$514$	−324.329	+	187.252i	−0.630991	+	0.364303i
$515$		0			0
$516$	−16.4850	+	28.5529i	−0.0319478	+	0.0553352i
$517$	175.102	−	175.102i	0.338689	−	0.338689i
$518$	262.476	+	268.813i	0.506710	+	0.518943i
$519$			661.738i			1.27503i
$520$		0			0
$521$	392.549	+	679.914i	0.753452	+	1.30502i	0.946140	+	0.323758i	$0.104946\pi$
$521$	392.549	+	679.914i	0.753452	+	1.30502i	−0.192688	+	0.981260i	$0.561720\pi$
$522$	−39.9179	−	10.6960i	−0.0764710	−	0.0204903i
$523$	−295.936	+	79.2957i	−0.565843	+	0.151617i	−0.530389	−	0.847754i	$-0.677954\pi$
$523$	−295.936	+	79.2957i	−0.565843	+	0.151617i	−0.0354535	+	0.999371i	$0.511288\pi$
$524$		−	289.449i		−	0.552383i
$525$		0			0
$526$	−388.239			−0.738097
$527$	−20.0835	−	74.9526i	−0.0381091	−	0.142225i
$528$	56.6983	−	211.601i	0.107383	−	0.400760i
$529$	1006.88	−	581.323i	1.90337	−	1.09891i
$530$		0			0
$531$	146.128			0.275193
$532$	−63.1364	−	247.394i	−0.118677	−	0.465026i
$533$	36.2647	+	36.2647i	0.0680387	+	0.0680387i
$534$	−259.178	−	149.636i	−0.485352	−	0.280218i
$535$		0			0
$536$	16.0748	+	27.8423i	0.0299902	+	0.0519446i
$537$	122.598	+	457.541i	0.228301	+	0.852031i
$538$	−139.255	−	139.255i	−0.258839	−	0.258839i
$539$	−838.704	−	511.279i	−1.55604	−	0.948570i
$540$		0			0
$541$	−264.805	+	458.656i	−0.489474	+	0.847793i	−0.999927	−	0.0121125i	$-0.996144\pi$
$541$	−264.805	+	458.656i	−0.489474	+	0.847793i	0.510453	+	0.859906i	$0.329478\pi$
$542$	84.7834	+	22.7176i	0.156427	+	0.0419145i
$543$	167.769	−	626.122i	0.308967	−	1.15308i
$544$	−60.5177	−	34.9399i	−0.111246	−	0.0642278i
$545$		0			0
$546$	−43.2410	+	72.8744i	−0.0791960	+	0.133470i
$547$	343.777	−	343.777i	0.628477	−	0.628477i	−0.319207	−	0.947685i	$-0.603417\pi$
$547$	343.777	−	343.777i	0.628477	−	0.628477i	0.947685	+	0.319207i	$0.103417\pi$
$548$	−91.1753	+	24.4303i	−0.166378	+	0.0445809i
$549$	−11.2528	+	6.49682i	−0.0204969	+	0.0118339i
$550$		0			0
$551$	173.475	−	300.468i	0.314837	−	0.545314i
$552$	−224.734	+	224.734i	−0.407127	+	0.407127i
$553$	33.0039	−	117.546i	0.0596815	−	0.212560i
$554$			588.273i			1.06186i
$555$		0			0
$556$	121.473	+	210.398i	0.218477	+	0.378414i
$557$	359.373	+	96.2937i	0.645194	+	0.172879i	0.566555	−	0.824024i	$-0.308276\pi$
$557$	359.373	+	96.2937i	0.645194	+	0.172879i	0.0786389	+	0.996903i	$0.474943\pi$
$558$	−13.1804	+	3.53167i	−0.0236208	+	0.00632916i
$559$		−	18.9053i		−	0.0338199i
$560$		0			0
$561$	676.536			1.20595
$562$	135.649	+	506.247i	0.241368	+	0.900796i
$563$	248.463	−	927.276i	0.441319	−	1.64703i	−0.284156	−	0.958778i	$-0.591713\pi$
$563$	248.463	−	927.276i	0.441319	−	1.64703i	0.725476	−	0.688248i	$-0.241620\pi$
$564$	58.4551	−	33.7490i	0.103644	−	0.0598387i
$565$		0			0
$566$	682.637			1.20607
$567$	324.627	−	316.975i	0.572535	−	0.559038i
$568$	189.636	+	189.636i	0.333866	+	0.333866i
$569$	579.317	+	334.469i	1.01813	+	0.587818i	0.913562	−	0.406699i	$-0.133320\pi$
$569$	579.317	+	334.469i	1.01813	+	0.587818i	0.104569	+	0.994518i	$0.466654\pi$
$570$		0			0
$571$	136.393	+	236.240i	0.238868	+	0.413731i	0.960390	−	0.278661i	$-0.0898905\pi$
$571$	136.393	+	236.240i	0.238868	+	0.413731i	−0.721522	+	0.692391i	$0.756557\pi$
$572$	32.5113	+	121.334i	0.0568379	+	0.212122i
$573$	40.5379	+	40.5379i	0.0707468	+	0.0707468i
$574$	−141.291	+	79.3425i	−0.246151	+	0.138227i
$575$		0			0
$576$	−6.14417	+	10.6420i	−0.0106670	+	0.0184757i
$577$	209.014	+	56.0052i	0.362243	+	0.0970627i	0.435350	−	0.900261i	$-0.356625\pi$
$577$	209.014	+	56.0052i	0.362243	+	0.0970627i	−0.0731068	+	0.997324i	$0.523291\pi$
$578$	−49.9260	+	186.326i	−0.0863771	+	0.322364i
$579$	−118.422	−	68.3709i	−0.204528	−	0.118084i
$580$		0			0
$581$	−318.742	+	537.178i	−0.548609	+	0.924575i
$582$	406.201	−	406.201i	0.697940	−	0.697940i
$583$	1036.74	−	277.794i	1.77829	−	0.476491i
$584$	19.9796	−	11.5352i	0.0342116	−	0.0197521i
$585$		0			0
$586$	203.433	−	352.357i	0.347156	−	0.601292i
$587$	193.451	−	193.451i	0.329559	−	0.329559i	−0.522860	−	0.852419i	$-0.675135\pi$
$587$	193.451	−	193.451i	0.329559	−	0.329559i	0.852419	+	0.522860i	$0.175135\pi$
$588$	−184.750	−	193.781i	−0.314201	−	0.329560i
$589$		−	114.559i		−	0.194497i
$590$		0			0
$591$	−165.358	−	286.408i	−0.279793	−	0.484616i
$592$	146.635	+	39.2907i	0.247694	+	0.0663694i
$593$	−140.689	+	37.6975i	−0.237249	+	0.0635708i	−0.375485	−	0.926829i	$-0.622524\pi$
$593$	−140.689	+	37.6975i	−0.237249	+	0.0635708i	0.138235	+	0.990399i	$0.455857\pi$
$594$		−	816.031i		−	1.37379i
$595$		0			0
$596$	271.514			0.455560
$597$	−217.406	−	811.369i	−0.364164	−	1.35908i
$598$	47.1677	−	176.032i	0.0788757	−	0.294368i
$599$	−396.026	+	228.645i	−0.661144	+	0.381712i	−0.792713	−	0.609595i	$-0.791332\pi$
$599$	−396.026	+	228.645i	−0.661144	+	0.381712i	0.131568	+	0.991307i	$0.457999\pi$
$600$		0			0
$601$	369.587			0.614953			0.307477	−	0.951556i	$-0.400515\pi$
$601$	369.587			0.614953			0.307477	+	0.951556i	$0.400515\pi$
$602$	57.5097	+	16.1472i	0.0955311	+	0.0268227i
$603$	12.3457	+	12.3457i	0.0204739	+	0.0204739i
$604$	143.282	+	82.7236i	0.237221	+	0.136960i
$605$		0			0
$606$	246.191	+	426.416i	0.406256	+	0.703657i
$607$	60.5336	+	225.915i	0.0997259	+	0.372182i	0.997694	−	0.0678794i	$-0.0216233\pi$
$607$	60.5336	+	225.915i	0.0997259	+	0.372182i	−0.897968	+	0.440062i	$0.854957\pi$
$608$	−72.9495	−	72.9495i	−0.119983	−	0.119983i
$609$	4.33920	−	363.796i	0.00712512	−	0.597365i
$610$		0			0
$611$	−19.3520	+	33.5186i	−0.0316726	+	0.0548586i
$612$	−36.6567	−	9.82214i	−0.0598966	−	0.0160492i
$613$	−248.441	+	927.194i	−0.405287	+	1.51255i	0.398239	+	0.917282i	$0.369622\pi$
$613$	−248.441	+	927.194i	−0.405287	+	1.51255i	−0.803526	+	0.595270i	$0.797045\pi$
$614$	0.359231	+	0.207402i	0.000585067	+	0.000337789i
$615$		0			0
$616$	−396.864	−	4.73362i	−0.644260	−	0.00768445i
$617$	−22.6455	+	22.6455i	−0.0367026	+	0.0367026i	−0.725220	−	0.688517i	$-0.758262\pi$
$617$	−22.6455	+	22.6455i	−0.0367026	+	0.0367026i	0.688517	+	0.725220i	$0.258262\pi$
$618$	−28.0290	+	7.51035i	−0.0453544	+	0.0121527i
$619$	430.611	−	248.613i	0.695655	−	0.401637i	−0.110072	−	0.993924i	$-0.535108\pi$
$619$	430.611	−	248.613i	0.695655	−	0.401637i	0.805727	+	0.592287i	$0.201775\pi$
$620$		0			0
$621$	−591.953	+	1025.29i	−0.953225	+	1.65103i
$622$	−356.021	+	356.021i	−0.572382	+	0.572382i
$623$	−146.570	+	522.021i	−0.235265	+	0.837915i
$624$			34.2392i			0.0548705i
$625$		0			0
$626$	184.173	+	318.996i	0.294205	+	0.509579i
$627$	964.762	+	258.507i	1.53870	+	0.412292i
$628$	75.7686	−	20.3021i	0.120651	−	0.0323282i
$629$			468.824i			0.745348i
$630$		0			0
$631$	965.780			1.53056			0.765278	−	0.643700i	$-0.222602\pi$
$631$	965.780			1.53056			0.765278	+	0.643700i	$0.222602\pi$
$632$	−12.7682	−	47.6514i	−0.0202028	−	0.0753978i
$633$	−82.4369	+	307.659i	−0.130232	+	0.486033i
$634$	94.7354	−	54.6955i	0.149425	−	0.0862705i
$635$		0			0
$636$	292.558			0.459997
$637$	147.302	+	43.2605i	0.231244	+	0.0679129i
$638$	−381.360	−	381.360i	−0.597743	−	0.597743i
$639$	126.132	+	72.8222i	0.197389	+	0.113963i
$640$		0			0
$641$	−599.981	−	1039.20i	−0.936008	−	1.62121i	−0.772826	−	0.634618i	$-0.781157\pi$
$641$	−599.981	−	1039.20i	−0.936008	−	1.62121i	−0.163183	−	0.986596i	$-0.552176\pi$
$642$	115.457	+	430.892i	0.179840	+	0.671172i
$643$	−405.030	−	405.030i	−0.629906	−	0.629906i	0.318138	−	0.948044i	$-0.396942\pi$
$643$	−405.030	−	405.030i	−0.629906	−	0.629906i	−0.948044	+	0.318138i	$0.896942\pi$
$644$	495.201	+	293.834i	0.768946	+	0.456265i
$645$		0			0
$646$	159.303	−	275.921i	0.246599	−	0.427122i
$647$	−81.5250	−	21.8446i	−0.126005	−	0.0337628i	0.195266	−	0.980750i	$-0.437443\pi$
$647$	−81.5250	−	21.8446i	−0.126005	−	0.0337628i	−0.321270	+	0.946988i	$0.604110\pi$
$648$	47.4488	−	177.081i	0.0732234	−	0.273273i
$649$	1651.54	+	953.518i	2.54475	+	1.46921i
$650$		0			0
$651$	−58.8196	−	104.744i	−0.0903527	−	0.160897i
$652$	174.777	−	174.777i	0.268063	−	0.268063i
$653$	−463.478	+	124.189i	−0.709767	+	0.190182i	−0.595601	−	0.803280i	$-0.703086\pi$
$653$	−463.478	+	124.189i	−0.709767	+	0.190182i	−0.114166	+	0.993462i	$0.536420\pi$
$654$	142.611	−	82.3364i	0.218059	−	0.125897i
$655$		0			0
$656$	−32.7378	+	56.7036i	−0.0499052	+	0.0864384i
$657$	8.85928	−	8.85928i	0.0134844	−	0.0134844i
$658$	−85.4344	−	87.4971i	−0.129840	−	0.132974i
$659$			168.872i			0.256255i	0.991758	+	0.128127i	$0.0408966\pi$
$659$			168.872i			0.256255i	−0.991758	+	0.128127i	$0.959103\pi$
$660$		0			0
$661$	251.775	+	436.087i	0.380900	+	0.659738i	0.991191	−	0.132439i	$-0.0422810\pi$
$661$	251.775	+	436.087i	0.380900	+	0.659738i	−0.610291	+	0.792177i	$0.708948\pi$
$662$	117.865	+	31.5818i	0.178043	+	0.0477066i
$663$	−102.137	+	27.3676i	−0.154053	+	0.0412784i
$664$			252.387i			0.380101i
$665$		0			0
$666$	82.4425			0.123788
$667$	202.515	+	755.795i	0.303620	+	1.13313i
$668$	−126.893	+	473.572i	−0.189960	+	0.708940i
$669$	312.081	−	180.180i	0.466489	−	0.269327i
$670$		0			0
$671$	−169.573			−0.252717
$672$	−104.155	−	29.2440i	−0.154993	−	0.0435179i
$673$	−143.862	−	143.862i	−0.213763	−	0.213763i	0.592101	−	0.805864i	$-0.298299\pi$
$673$	−143.862	−	143.862i	−0.213763	−	0.213763i	−0.805864	+	0.592101i	$0.798299\pi$
$674$	160.813	+	92.8454i	0.238595	+	0.137753i
$675$		0			0
$676$	159.183	+	275.714i	0.235479	+	0.407861i
$677$	−31.4489	−	117.369i	−0.0464533	−	0.173366i	0.938802	−	0.344458i	$-0.111937\pi$
$677$	−31.4489	−	117.369i	−0.0464533	−	0.173366i	−0.985255	+	0.171092i	$0.945271\pi$
$678$	−52.5457	−	52.5457i	−0.0775010	−	0.0775010i
$679$	−895.062	−	531.097i	−1.31821	−	0.782176i
$680$		0			0
$681$	460.356	−	797.360i	0.676000	−	1.17087i
$682$	−172.010	−	46.0900i	−0.252215	−	0.0675807i
$683$	209.950	−	783.543i	0.307393	−	1.14721i	−0.623472	−	0.781845i	$-0.714279\pi$
$683$	209.950	−	783.543i	0.307393	−	1.14721i	0.930866	−	0.365362i	$-0.119055\pi$
$684$	−48.5206	−	28.0134i	−0.0709365	−	0.0409552i
$685$		0			0
$686$	−257.410	+	411.142i	−0.375234	+	0.599333i
$687$	−737.753	+	737.753i	−1.07388	+	1.07388i
$688$	23.3136	−	6.24686i	0.0338861	−	0.00907974i
$689$	−145.280	+	83.8777i	−0.210857	+	0.121738i
$690$		0			0
$691$	16.3168	−	28.2615i	0.0236133	−	0.0408994i	−0.853977	−	0.520310i	$-0.825816\pi$
$691$	16.3168	−	28.2615i	0.0236133	−	0.0408994i	0.877591	+	0.479411i	$0.159150\pi$
$692$	342.544	−	342.544i	0.495006	−	0.495006i
$693$	−208.847	+	53.2991i	−0.301367	+	0.0769107i
$694$			566.487i			0.816264i
$695$		0			0
$696$	−73.5030	−	127.311i	−0.105608	−	0.182918i
$697$	−195.317	−	52.3351i	−0.280226	−	0.0750862i
$698$	276.379	−	74.0555i	0.395958	−	0.106097i
$699$		−	911.901i		−	1.30458i
$700$		0			0
$701$	−311.596			−0.444503			−0.222251	−	0.974989i	$-0.571341\pi$
$701$	−311.596			−0.444503			−0.222251	+	0.974989i	$0.571341\pi$
$702$	33.0105	+	123.197i	0.0470235	+	0.175494i
$703$	−179.140	+	668.558i	−0.254822	+	0.951007i
$704$	−138.883	+	80.1843i	−0.197277	+	0.113898i
$705$		0			0
$706$	−466.952			−0.661405
$707$	638.270	−	623.224i	0.902787	−	0.881505i
$708$	367.561	+	367.561i	0.519154	+	0.519154i
$709$	−622.782	−	359.564i	−0.878396	−	0.507142i	−0.00826649	−	0.999966i	$-0.502631\pi$
$709$	−622.782	−	359.564i	−0.878396	−	0.507142i	−0.870129	+	0.492824i	$0.835965\pi$
$710$		0			0
$711$	−13.3955	−	23.2017i	−0.0188404	−	0.0326325i
$712$	56.7033	+	211.620i	0.0796395	+	0.297219i
$713$	182.686	+	182.686i	0.256222	+	0.256222i
$714$	3.98470	−	334.075i	0.00558081	−	0.467892i
$715$		0			0
$716$	173.381	−	300.305i	0.242152	−	0.419420i
$717$	−1153.66	−	309.122i	−1.60901	−	0.431133i
$718$	11.4631	−	42.7809i	0.0159653	−	0.0595834i
$719$	278.808	+	160.970i	0.387771	+	0.223880i	0.681194	−	0.732103i	$-0.261461\pi$
$719$	278.808	+	160.970i	0.387771	+	0.223880i	−0.293423	+	0.955983i	$0.594794\pi$
$720$		0			0
$721$	25.7416	+	45.8398i	0.0357026	+	0.0635780i
$722$	−28.3982	+	28.3982i	−0.0393327	+	0.0393327i
$723$	10.2718	−	2.75232i	0.0142072	−	0.00380681i
$724$	−410.952	+	237.263i	−0.567613	+	0.327712i
$725$		0			0
$726$	542.546	−	939.718i	0.747309	−	1.29438i
$727$	905.157	−	905.157i	1.24506	−	1.24506i	0.287182	−	0.957876i	$-0.407282\pi$
$727$	905.157	−	905.157i	1.24506	−	1.24506i	0.957876	−	0.287182i	$-0.0927184\pi$
$728$	60.1063	−	15.3395i	0.0825636	−	0.0210707i
$729$		−	807.326i		−	1.10744i
$730$		0			0
$731$	37.2694	+	64.5525i	0.0509841	+	0.0883071i
$732$	−44.6464	−	11.9630i	−0.0609923	−	0.0163428i
$733$	890.884	−	238.712i	1.21539	−	0.325664i	0.406518	−	0.913643i	$-0.366743\pi$
$733$	890.884	−	238.712i	1.21539	−	0.325664i	0.808876	+	0.587979i	$0.200076\pi$
$734$		−	248.207i		−	0.338157i
$735$		0			0
$736$	232.664			0.316120
$737$	58.9733	+	220.091i	0.0800180	+	0.298631i
$738$	−9.20310	+	34.3464i	−0.0124703	+	0.0465399i
$739$	−391.732	+	226.167i	−0.530084	+	0.306044i	−0.741051	−	0.671449i	$-0.765672\pi$
$739$	−391.732	+	226.167i	−0.530084	+	0.306044i	0.210967	+	0.977493i	$0.432339\pi$
$740$		0			0
$741$	−156.108			−0.210672
$742$	−131.069	−	513.582i	−0.176643	−	0.692158i
$743$	−664.894	−	664.894i	−0.894877	−	0.894877i	0.100100	−	0.994977i	$-0.468084\pi$
$743$	−664.894	−	664.894i	−0.894877	−	0.894877i	−0.994977	+	0.100100i	$0.968084\pi$
$744$	−42.0365	−	24.2698i	−0.0565007	−	0.0326207i
$745$		0			0
$746$	−76.4288	−	132.379i	−0.102452	−	0.177451i
$747$	35.4749	+	132.394i	0.0474898	+	0.177234i
$748$	−350.204	−	350.204i	−0.468187	−	0.468187i
$749$	704.699	−	395.728i	0.940853	−	0.528342i
$750$		0			0
$751$	112.885	−	195.522i	0.150312	−	0.260349i	−0.781030	−	0.624494i	$-0.785305\pi$
$751$	112.885	−	195.522i	0.150312	−	0.260349i	0.931342	+	0.364145i	$0.118639\pi$
$752$	−47.7288	−	12.7889i	−0.0634692	−	0.0170065i
$753$	260.379	−	971.747i	0.345789	−	1.29050i
$754$	73.0012	+	42.1472i	0.0968185	+	0.0558982i
$755$		0			0
$756$	−402.957	−	4.80630i	−0.533013	−	0.00635754i
$757$	445.497	−	445.497i	0.588503	−	0.588503i	−0.348723	−	0.937226i	$-0.613385\pi$
$757$	445.497	−	445.497i	0.588503	−	0.588503i	0.937226	+	0.348723i	$0.113385\pi$
$758$	505.960	−	135.572i	0.667494	−	0.178854i
$759$	−1950.74	+	1126.26i	−2.57015	+	1.48387i
$760$		0			0
$761$	179.891	−	311.580i	0.236388	−	0.409436i	−0.723287	−	0.690547i	$-0.757370\pi$
$761$	179.891	−	311.580i	0.236388	−	0.409436i	0.959675	+	0.281112i	$0.0907031\pi$
$762$	95.6964	−	95.6964i	0.125586	−	0.125586i
$763$	−208.431	−	213.464i	−0.273174	−	0.279769i
$764$		−	41.9683i		−	0.0549324i
$765$		0			0
$766$	−2.48825	−	4.30977i	−0.00324836	−	0.00562633i
$767$	−287.907	−	77.1444i	−0.375367	−	0.100579i
$768$	−42.2229	+	11.3136i	−0.0549778	+	0.0147312i
$769$		−	1100.57i		−	1.43117i	−0.698527	−	0.715584i	$-0.746161\pi$
$769$		−	1100.57i		−	1.43117i	0.698527	−	0.715584i	$-0.253839\pi$
$770$		0			0
$771$	−723.478			−0.938363
$772$	25.9085	+	96.6920i	0.0335603	+	0.125249i
$773$	3.34535	−	12.4850i	0.00432775	−	0.0161514i	−0.963728	−	0.266886i	$-0.914005\pi$
$773$	3.34535	−	12.4850i	0.00432775	−	0.0161514i	0.968056	+	0.250734i	$0.0806720\pi$
$774$	11.3515	−	6.55381i	0.0146661	−	0.00846745i
$775$		0			0
$776$	−420.534			−0.541925
$777$	179.476	+	703.258i	0.230985	+	0.905093i
$778$	725.344	+	725.344i	0.932319	+	0.932319i
$779$	−258.531	−	149.263i	−0.331876	−	0.191609i
$780$		0			0
$781$	950.365	+	1646.08i	1.21686	+	2.10766i
$782$	185.970	+	694.049i	0.237813	+	0.887531i
$783$	−387.216	−	387.216i	−0.494528	−	0.494528i
$784$	−4.67494	+	195.944i	−0.00596294	+	0.249929i
$785$		0			0
$786$	279.583	−	484.253i	0.355704	−	0.616098i
$787$	−1200.53	−	321.680i	−1.52545	−	0.408742i	−0.603917	−	0.797047i	$-0.706394\pi$
$787$	−1200.53	−	321.680i	−1.52545	−	0.408742i	−0.921531	+	0.388305i	$0.873061\pi$
$788$	−62.6608	+	233.853i	−0.0795188	+	0.296768i
$789$	−649.530	−	375.006i	−0.823232	−	0.475293i
$790$		0			0
$791$	−68.7021	+	115.784i	−0.0868548	+	0.146377i
$792$	−61.5832	+	61.5832i	−0.0777566	+	0.0777566i
$793$	25.6006	−	6.85966i	0.0322832	−	0.00865026i
$794$	156.913	−	90.5936i	0.197623	−	0.114098i
$795$		0			0
$796$	−307.461	+	532.538i	−0.386258	+	0.669018i
$797$	658.639	−	658.639i	0.826398	−	0.826398i	−0.160618	−	0.987017i	$-0.551349\pi$
$797$	658.639	−	658.639i	0.826398	−	0.826398i	0.987017	+	0.160618i	$0.0513489\pi$
$798$	133.334	−	474.879i	0.167085	−	0.595086i
$799$		−	152.600i		−	0.190988i
$800$		0			0
$801$	59.4895	+	103.039i	0.0742691	+	0.128638i
$802$	−957.533	−	256.570i	−1.19393	−	0.319913i
$803$	157.937	−	42.3191i	0.196684	−	0.0527012i
$804$			62.1075i			0.0772481i
$805$		0			0
$806$	27.8330			0.0345322
$807$	−98.4674	−	367.485i	−0.122017	−	0.455372i
$808$	93.2920	−	348.170i	0.115460	−	0.430904i
$809$	−712.947	+	411.620i	−0.881270	+	0.508802i	−0.871077	−	0.491147i	$-0.836578\pi$
$809$	−712.947	+	411.620i	−0.881270	+	0.508802i	−0.0101931	+	0.999948i	$0.503245\pi$
$810$		0			0
$811$	−1415.46			−1.74533			−0.872666	−	0.488318i	$-0.837610\pi$
$811$	−1415.46			−1.74533			−0.872666	+	0.488318i	$0.837610\pi$
$812$	−190.562	+	186.070i	−0.234683	+	0.229150i
$813$	119.901	+	119.901i	0.147479	+	0.147479i
$814$	931.769	+	537.957i	1.14468	+	0.660881i
$815$		0			0
$816$	−67.4981	−	116.910i	−0.0827182	−	0.143272i
$817$	28.4816	+	106.295i	0.0348612	+	0.130104i
$818$	452.456	+	452.456i	0.553124	+	0.553124i
$819$	29.3738	−	16.4950i	0.0358654	−	0.0201404i
$820$		0			0
$821$	−28.8421	+	49.9560i	−0.0351305	+	0.0608478i	−0.883056	−	0.469267i	$-0.844518\pi$
$821$	−28.8421	+	49.9560i	−0.0351305	+	0.0608478i	0.847926	+	0.530115i	$0.177851\pi$
$822$	−176.135	−	47.1954i	−0.214277	−	0.0574153i
$823$	−100.057	+	373.416i	−0.121575	+	0.453725i	−0.999694	−	0.0247166i	$-0.992132\pi$
$823$	−100.057	+	373.416i	−0.121575	+	0.453725i	0.878119	+	0.478442i	$0.158798\pi$
$824$	18.3967	+	10.6213i	0.0223261	+	0.0128900i
$825$		0			0
$826$	480.576	−	809.918i	0.581811	−	0.980531i
$827$	−84.0099	+	84.0099i	−0.101584	+	0.101584i	−0.756072	−	0.654488i	$-0.772884\pi$
$827$	−84.0099	+	84.0099i	−0.101584	+	0.101584i	0.654488	+	0.756072i	$0.272884\pi$
$828$	122.048	−	32.7027i	0.147401	−	0.0394961i
$829$	−880.574	+	508.399i	−1.06221	+	0.613268i	−0.926043	−	0.377417i	$-0.876812\pi$
$829$	−880.574	+	508.399i	−1.06221	+	0.613268i	−0.136169	+	0.990686i	$0.543479\pi$
$830$		0			0
$831$	−568.222	+	984.190i	−0.683781	+	1.18434i
$832$	17.7237	−	17.7237i	0.0213025	−	0.0213025i
$833$	−588.248	+	142.674i	−0.706180	+	0.171277i
$834$			469.333i			0.562749i
$835$		0			0
$836$	−365.588	−	633.217i	−0.437306	−	0.757436i
$837$	−174.651	−	46.7977i	−0.208664	−	0.0559112i
$838$	339.013	−	90.8382i	0.404550	−	0.108399i
$839$		−	538.853i		−	0.642256i	−0.947036	−	0.321128i	$-0.895938\pi$
$839$		−	538.853i		−	0.642256i	0.947036	−	0.321128i	$-0.104062\pi$
$840$		0			0
$841$	479.081			0.569656
$842$	87.4770	+	326.469i	0.103892	+	0.387730i
$843$	−262.050	+	977.985i	−0.310855	+	1.16013i
$844$	201.930	−	116.585i	0.239254	−	0.138133i
$845$		0			0
$846$	−26.8346			−0.0317194
$847$	−1892.73	−	531.429i	−2.23462	−	0.627425i
$848$	−151.441	−	151.441i	−0.178586	−	0.178586i
$849$	1142.06	+	659.370i	1.34519	+	0.776644i
$850$		0			0
$851$	−780.473	−	1351.82i	−0.917125	−	1.58851i
$852$	134.092	+	500.437i	0.157385	+	0.587367i
$853$	1067.08	+	1067.08i	1.25098	+	1.25098i	0.955283	+	0.295694i	$0.0955510\pi$
$853$	1067.08	+	1067.08i	1.25098	+	1.25098i	0.295694	+	0.955283i	$0.404449\pi$
$854$	−0.998762	+	83.7356i	−0.00116951	+	0.0980510i
$855$		0			0
$856$	163.283	−	282.814i	0.190751	−	0.330390i
$857$	979.577	+	262.477i	1.14303	+	0.306274i	0.780169	−	0.625569i	$-0.215133\pi$
$857$	979.577	+	262.477i	1.14303	+	0.306274i	0.362861	+	0.931843i	$0.381800\pi$
$858$	−62.8064	+	234.397i	−0.0732009	+	0.273190i
$859$	196.715	+	113.574i	0.229005	+	0.132216i	0.610113	−	0.792315i	$-0.291124\pi$
$859$	196.715	+	113.574i	0.229005	+	0.132216i	−0.381108	+	0.924530i	$0.624457\pi$
$860$		0			0
$861$	−313.020	−	3.73356i	−0.363554	−	0.00433631i
$862$	130.746	−	130.746i	0.151677	−	0.151677i
$863$	−470.501	+	126.070i	−0.545193	+	0.146084i	−0.520895	−	0.853621i	$-0.674402\pi$
$863$	−470.501	+	126.070i	−0.545193	+	0.146084i	−0.0242979	+	0.999705i	$0.507735\pi$
$864$	−141.016	+	81.4155i	−0.163213	+	0.0942309i
$865$		0			0
$866$	−456.850	+	791.288i	−0.527541	+	0.913727i
$867$	−263.503	+	263.503i	−0.303925	+	0.303925i
$868$	−23.7725	+	84.6676i	−0.0273876	+	0.0975433i
$869$		−	349.636i		−	0.402343i
$870$		0			0
$871$	−17.8065	−	30.8417i	−0.0204437	−	0.0354095i
$872$	−116.442	−	31.2006i	−0.133535	−	0.0357806i
$873$	−220.599	+	59.1093i	−0.252690	+	0.0677082i
$874$			1060.80i			1.21373i
$875$		0			0
$876$	44.5682			0.0508769
$877$	36.9236	+	137.801i	0.0421022	+	0.157127i	0.983777	−	0.179398i	$-0.0574149\pi$
$877$	36.9236	+	137.801i	0.0421022	+	0.157127i	−0.941674	+	0.336525i	$0.890748\pi$
$878$	−79.4121	+	296.370i	−0.0904466	+	0.337551i
$879$	680.695	−	392.999i	0.774397	−	0.447098i
$880$		0			0
$881$	21.6989			0.0246299			0.0123149	−	0.999924i	$-0.496080\pi$
$881$	21.6989			0.0246299			0.0123149	+	0.999924i	$0.496080\pi$
$882$	25.0891	+	103.443i	0.0284457	+	0.117283i
$883$	100.328	+	100.328i	0.113622	+	0.113622i	0.761632	−	0.648010i	$-0.224398\pi$
$883$	100.328	+	100.328i	0.113622	+	0.113622i	−0.648010	+	0.761632i	$0.724398\pi$
$884$	67.0372	+	38.7040i	0.0758340	+	0.0437828i
$885$		0			0
$886$	30.6228	+	53.0402i	0.0345629	+	0.0598647i
$887$	126.146	+	470.784i	0.142217	+	0.530759i	0.999864	+	0.0165205i	$0.00525888\pi$
$887$	126.146	+	470.784i	0.142217	+	0.530759i	−0.857647	+	0.514239i	$0.828074\pi$
$888$	207.371	+	207.371i	0.233526	+	0.233526i
$889$	−210.867	−	125.121i	−0.237195	−	0.140743i
$890$		0			0
$891$	649.655	−	1125.24i	0.729131	−	1.26289i
$892$	−254.815	−	68.2776i	−0.285668	−	0.0765444i
$893$	58.3090	−	217.612i	0.0652956	−	0.243686i
$894$	454.247	+	262.259i	0.508106	+	0.293355i
$895$		0			0
$896$	38.7772	+	69.0531i	0.0432781	+	0.0770682i
$897$	248.945	−	248.945i	0.277530	−	0.277530i
$898$	65.9140	−	17.6616i	0.0734009	−	0.0196677i
$899$	−103.491	+	59.7506i	−0.115118	+	0.0664634i
$900$		0			0
$901$	330.708	−	572.803i	0.367045	−	0.635741i
$902$	−328.133	+	328.133i	−0.363783	+	0.363783i
$903$	80.6178	+	82.5642i	0.0892778	+	0.0914332i
$904$			54.3998i			0.0601768i
$905$		0			0
$906$	159.808	+	276.796i	0.176389	+	0.305514i
$907$	8.97709	+	2.40540i	0.00989756	+	0.00265204i	0.263764	−	0.964587i	$-0.415036\pi$
$907$	8.97709	+	2.40540i	0.00989756	+	0.00265204i	−0.253867	+	0.967239i	$0.581703\pi$
$908$	−651.048	+	174.448i	−0.717013	+	0.192123i
$909$		−	195.752i		−	0.215349i
$910$		0			0
$911$	−1071.38			−1.17605			−0.588027	−	0.808841i	$-0.700095\pi$
$911$	−1071.38			−1.17605			−0.588027	+	0.808841i	$0.700095\pi$
$912$	−51.5826	−	192.509i	−0.0565599	−	0.211084i
$913$	−462.964	+	1727.81i	−0.507080	+	1.89245i
$914$	354.912	−	204.908i	0.388306	−	0.224188i
$915$		0			0
$916$	763.785			0.833827
$917$	−975.355	−	273.854i	−1.06364	−	0.298642i
$918$	−355.581	−	355.581i	−0.387343	−	0.387343i
$919$	1186.43	+	684.983i	1.29100	+	0.745357i	0.978831	−	0.204671i	$-0.0656125\pi$
$919$	1186.43	+	684.983i	1.29100	+	0.745357i	0.312165	+	0.950028i	$0.398946\pi$
$920$		0			0
$921$	0.400667	+	0.693975i	0.000435034	+	0.000753502i
$922$	−127.466	−	475.708i	−0.138249	−	0.515952i
$923$	−210.065	−	210.065i	−0.227590	−	0.227590i
$924$	−659.388	−	391.257i	−0.713623	−	0.423438i
$925$		0			0
$926$	268.097	−	464.358i	0.289522	−	0.501466i
$927$	11.1432	+	2.98582i	0.0120207	+	0.00322095i
$928$	−27.8533	+	103.950i	−0.0300143	+	0.112015i
$929$	−818.100	−	472.330i	−0.880624	−	0.508429i	−0.00976001	−	0.999952i	$-0.503107\pi$
$929$	−818.100	−	472.330i	−0.880624	−	0.508429i	−0.870864	+	0.491524i	$0.836440\pi$
$930$		0			0
$931$	−893.377	−	21.3147i	−0.959589	−	0.0228944i
$932$	−472.039	+	472.039i	−0.506480	+	0.506480i
$933$	−939.516	+	251.743i	−1.00698	+	0.269821i
$934$	−610.710	+	352.594i	−0.653865	+	0.377509i
$935$		0			0
$936$	6.80607	−	11.7885i	0.00727144	−	0.0125945i
$937$	−649.423	+	649.423i	−0.693087	+	0.693087i	−0.962910	−	0.269823i	$-0.913035\pi$
$937$	−649.423	+	649.423i	−0.693087	+	0.693087i	0.269823	+	0.962910i	$0.413035\pi$
$938$	109.029	−	27.8248i	0.116235	−	0.0296640i
$939$			711.582i			0.757808i
$940$		0			0
$941$	18.0898	+	31.3324i	0.0192240	+	0.0332969i	0.875477	−	0.483259i	$-0.160547\pi$
$941$	18.0898	+	31.3324i	0.0192240	+	0.0332969i	−0.856253	+	0.516556i	$0.827214\pi$
$942$	146.372	+	39.2203i	0.155385	+	0.0416352i
$943$	650.307	−	174.249i	0.689615	−	0.184782i
$944$		−	380.530i		−	0.403104i
$945$		0			0
$946$	171.061			0.180825
$947$	391.323	+	1460.44i	0.413223	+	1.54217i	0.788368	+	0.615204i	$0.210926\pi$
$947$	391.323	+	1460.44i	0.413223	+	1.54217i	−0.375144	+	0.926966i	$0.622407\pi$
$948$	24.6659	−	92.0546i	0.0260189	−	0.0971040i
$949$	−22.1319	+	12.7779i	−0.0233213	+	0.0134646i
$950$		0			0
$951$	211.325			0.222214
$952$	−174.994	+	170.869i	−0.183817	+	0.179484i
$953$	152.501	+	152.501i	0.160022	+	0.160022i	0.782576	−	0.622555i	$-0.213905\pi$
$953$	152.501	+	152.501i	0.160022	+	0.160022i	−0.622555	+	0.782576i	$0.713905\pi$
$954$	−100.727	−	58.1548i	−0.105584	−	0.0609589i
$955$		0			0
$956$	437.169	+	757.199i	0.457290	+	0.792049i
$957$	−269.660	−	1006.38i	−0.281776	−	1.05160i
$958$	−374.806	−	374.806i	−0.391238	−	0.391238i
$959$	−3.94024	+	330.347i	−0.00410869	+	0.344470i
$960$		0			0
$961$	460.771	−	798.079i	0.479470	−	0.830467i
$962$	−162.432	−	43.5234i	−0.168848	−	0.0452426i
$963$	45.9013	−	171.306i	0.0476649	−	0.177888i
$964$	−6.74185	−	3.89241i	−0.00699362	−	0.00403777i
$965$		0			0
$966$	544.660	+	969.913i	0.563830	+	1.00405i
$967$	−440.127	+	440.127i	−0.455147	+	0.455147i	−0.897059	−	0.441911i	$-0.854301\pi$
$967$	−440.127	+	440.127i	−0.455147	+	0.455147i	0.441911	+	0.897059i	$0.354301\pi$
$968$	−767.284	+	205.593i	−0.792649	+	0.212390i
$969$	533.033	−	307.747i	0.550086	−	0.317592i
$970$		0			0
$971$	−310.158	+	537.210i	−0.319421	+	0.553254i	−0.980367	−	0.197179i	$-0.936822\pi$
$971$	−310.158	+	537.210i	−0.319421	+	0.553254i	0.660946	+	0.750433i	$0.270155\pi$
$972$	−115.942	+	115.942i	−0.119281	+	0.119281i
$973$	823.907	−	210.266i	0.846769	−	0.216101i
$974$		−	555.017i		−	0.569832i
$975$		0			0
$976$	16.9183	+	29.3034i	0.0173344	+	0.0300240i
$977$	103.150	+	27.6391i	0.105579	+	0.0282897i	0.311222	−	0.950337i	$-0.399262\pi$
$977$	103.150	+	27.6391i	0.105579	+	0.0282897i	−0.205643	+	0.978627i	$0.565929\pi$
$978$	461.225	−	123.585i	0.471600	−	0.126365i
$979$			1552.73i			1.58604i
$980$		0			0
$981$	−65.4674			−0.0667354
$982$	−36.7677	−	137.219i	−0.0374417	−	0.139734i
$983$	12.5888	−	46.9821i	0.0128065	−	0.0477946i	−0.959227	−	0.282637i	$-0.908791\pi$
$983$	12.5888	−	46.9821i	0.0128065	−	0.0477946i	0.972033	+	0.234843i	$0.0754574\pi$
$984$	−109.542	+	63.2440i	−0.111323	+	0.0642724i
$985$		0			0
$986$	−332.351			−0.337070
$987$	−58.4183	−	228.907i	−0.0591878	−	0.231921i
$988$	80.8083	+	80.8083i	0.0817897	+	0.0817897i
$989$	−214.927	−	124.088i	−0.217318	−	0.125468i
$990$		0			0
$991$	−363.350	−	629.341i	−0.366650	−	0.635056i	0.622390	−	0.782708i	$-0.286162\pi$
$991$	−363.350	−	629.341i	−0.366650	−	0.635056i	−0.989039	+	0.147651i	$0.952829\pi$
$992$	9.19682	+	34.3230i	0.00927098	+	0.0345998i
$993$	166.684	+	166.684i	0.167859	+	0.167859i
$994$	818.435	−	459.597i	0.823375	−	0.462371i
$995$		0			0
$996$	−243.785	+	422.247i	−0.244764	+	0.423943i
$997$	1317.14	+	352.926i	1.32110	+	0.353987i	0.849390	−	0.527766i	$-0.176970\pi$
$997$	1317.14	+	352.926i	1.32110	+	0.353987i	0.471710	+	0.881754i	$0.343637\pi$
$998$	144.507	−	539.307i	0.144796	−	0.540388i
$999$	946.075	+	546.217i	0.947022	+	0.546764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.p.e.93.3		16
5.2	odd	4	inner	350.3.p.e.107.2		16
5.3	odd	4		70.3.l.c.37.3	yes	16
5.4	even	2		70.3.l.c.23.2	✓	16
7.4	even	3	inner	350.3.p.e.193.2		16
35.4	even	6		70.3.l.c.53.3	yes	16
35.9	even	6		490.3.f.o.393.2		8
35.18	odd	12		70.3.l.c.67.2	yes	16
35.19	odd	6		490.3.f.p.393.3		8
35.23	odd	12		490.3.f.o.197.2		8
35.32	odd	12	inner	350.3.p.e.207.3		16
35.33	even	12		490.3.f.p.197.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.2	✓	16	5.4	even	2
70.3.l.c.37.3	yes	16	5.3	odd	4
70.3.l.c.53.3	yes	16	35.4	even	6
70.3.l.c.67.2	yes	16	35.18	odd	12
350.3.p.e.93.3		16	1.1	even	1	trivial
350.3.p.e.107.2		16	5.2	odd	4	inner
350.3.p.e.193.2		16	7.4	even	3	inner
350.3.p.e.207.3		16	35.32	odd	12	inner
490.3.f.o.197.2		8	35.23	odd	12
490.3.f.o.393.2		8	35.9	even	6
490.3.f.p.197.3		8	35.33	even	12
490.3.f.p.393.3		8	35.19	odd	6

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.707100 - 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} -3.86367 q^{6} +(1.73096 + 6.78261i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.707100 - 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} -3.86367 q^{6} +(1.73096 + 6.78261i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +(10.0230 + 17.3604i) q^{11} +(1.41420 + 5.27787i) q^{12} +(-2.21546 - 2.21546i) q^{13} +(8.63164 - 4.84715i) q^{14} +(2.00000 - 3.46410i) q^{16} +(11.9322 + 3.19722i) q^{17} +(0.562230 - 2.09827i) q^{18} +(15.7940 + 9.11869i) q^{19} +(19.1228 + 0.228089i) q^{21} +(20.0461 - 20.0461i) q^{22} +(-39.7282 + 10.6451i) q^{23} +(6.69207 - 3.86367i) q^{24} +(-2.21546 + 3.83729i) q^{26} +(20.3539 - 20.3539i) q^{27} +(-9.78072 - 10.0169i) q^{28} -19.0242i q^{29} +(-3.14077 - 5.43998i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(52.9003 - 14.1746i) q^{33} -17.4700i q^{34} -3.07208 q^{36} +(9.82266 + 36.6587i) q^{37} +(6.67534 - 24.9127i) q^{38} +(-7.41300 + 4.27990i) q^{39} -16.3689 q^{41} +(-6.68786 - 26.2057i) q^{42} +(4.26669 + 4.26669i) q^{43} +(-34.7208 - 20.0461i) q^{44} +(29.0830 + 50.3733i) q^{46} +(-3.19722 - 11.9322i) q^{47} +(-7.72733 - 7.72733i) q^{48} +(-43.0075 + 23.4809i) q^{49} +(16.8745 - 29.2275i) q^{51} +(6.05274 + 1.62183i) q^{52} +(13.8578 - 51.7180i) q^{53} +(-35.2539 - 20.3539i) q^{54} +(-10.1033 + 17.0271i) q^{56} +(35.2316 - 35.2316i) q^{57} +(-25.9875 + 6.96333i) q^{58} +(82.3873 - 47.5663i) q^{59} +(-4.22958 + 7.32586i) q^{61} +(-6.28154 + 6.28154i) q^{62} +(-2.90657 + 10.3520i) q^{63} +8.00000i q^{64} +(-38.7257 - 67.0749i) q^{66} +(10.9793 + 2.94188i) q^{67} +(-23.8644 + 6.39445i) q^{68} +112.367i q^{69} +94.8180 q^{71} +(1.12446 + 4.19654i) q^{72} +(2.11109 - 7.87869i) q^{73} +(46.4813 - 26.8360i) q^{74} -36.4747 q^{76} +(-100.399 + 98.0326i) q^{77} +(8.55979 + 8.55979i) q^{78} +(-15.1049 - 8.72081i) q^{79} +(-32.4081 - 56.1325i) q^{81} +(5.99144 + 22.3604i) q^{82} +(63.0967 + 63.0967i) q^{83} +(-33.3498 + 18.7278i) q^{84} +(4.26669 - 7.39012i) q^{86} +(-50.2035 - 13.4520i) q^{87} +(-14.6748 + 54.7669i) q^{88} +(67.0808 + 38.7291i) q^{89} +(11.1917 - 18.8615i) q^{91} +(58.1661 - 58.1661i) q^{92} +(-16.5766 + 4.44168i) q^{93} +(-15.1294 + 8.73498i) q^{94} +(-7.72733 + 13.3841i) q^{96} +(-105.134 + 105.134i) q^{97} +(47.8173 + 50.1548i) q^{98} +30.7916i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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