LMFDB - Embedded newform 350.3.p.e.193.2

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			193.2
Root			$-0.707100 + 2.63893i$ of defining polynomial
Character	$\chi$	$=$	350.193
Dual form			350.3.p.e.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(-2.63893 + 0.707100i) q^{3} +(1.73205 + 1.00000i) q^{4} -3.86367 q^{6} +(-6.78261 - 1.73096i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.33025 + 0.768021i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(-2.63893 + 0.707100i) q^{3} +(1.73205 + 1.00000i) q^{4} -3.86367 q^{6} +(-6.78261 - 1.73096i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.33025 + 0.768021i) q^{9} +(10.0230 - 17.3604i) q^{11} +(-5.27787 - 1.41420i) q^{12} +(-2.21546 - 2.21546i) q^{13} +(-8.63164 - 4.84715i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-3.19722 - 11.9322i) q^{17} +(-2.09827 + 0.562230i) q^{18} +(-15.7940 + 9.11869i) q^{19} +(19.1228 - 0.228089i) q^{21} +(20.0461 - 20.0461i) q^{22} +(10.6451 - 39.7282i) q^{23} +(-6.69207 - 3.86367i) q^{24} +(-2.21546 - 3.83729i) q^{26} +(20.3539 - 20.3539i) q^{27} +(-10.0169 - 9.78072i) q^{28} -19.0242i q^{29} +(-3.14077 + 5.43998i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-14.1746 + 52.9003i) q^{33} -17.4700i q^{34} -3.07208 q^{36} +(-36.6587 - 9.82266i) q^{37} +(-24.9127 + 6.67534i) q^{38} +(7.41300 + 4.27990i) q^{39} -16.3689 q^{41} +(26.2057 + 6.68786i) q^{42} +(4.26669 + 4.26669i) q^{43} +(34.7208 - 20.0461i) q^{44} +(29.0830 - 50.3733i) q^{46} +(11.9322 + 3.19722i) q^{47} +(-7.72733 - 7.72733i) q^{48} +(43.0075 + 23.4809i) q^{49} +(16.8745 + 29.2275i) q^{51} +(-1.62183 - 6.05274i) q^{52} +(-51.7180 + 13.8578i) q^{53} +(35.2539 - 20.3539i) q^{54} +(-10.1033 - 17.0271i) q^{56} +(35.2316 - 35.2316i) q^{57} +(6.96333 - 25.9875i) q^{58} +(-82.3873 - 47.5663i) q^{59} +(-4.22958 - 7.32586i) q^{61} +(-6.28154 + 6.28154i) q^{62} +(10.3520 - 2.90657i) q^{63} +8.00000i q^{64} +(-38.7257 + 67.0749i) q^{66} +(-2.94188 - 10.9793i) q^{67} +(6.39445 - 23.8644i) q^{68} +112.367i q^{69} +94.8180 q^{71} +(-4.19654 - 1.12446i) q^{72} +(-7.87869 + 2.11109i) q^{73} +(-46.4813 - 26.8360i) q^{74} -36.4747 q^{76} +(-98.0326 + 100.399i) q^{77} +(8.55979 + 8.55979i) q^{78} +(15.1049 - 8.72081i) q^{79} +(-32.4081 + 56.1325i) q^{81} +(-22.3604 - 5.99144i) q^{82} +(63.0967 + 63.0967i) q^{83} +(33.3498 + 18.7278i) q^{84} +(4.26669 + 7.39012i) q^{86} +(13.4520 + 50.2035i) q^{87} +(54.7669 - 14.6748i) q^{88} +(-67.0808 + 38.7291i) q^{89} +(11.1917 + 18.8615i) q^{91} +(58.1661 - 58.1661i) q^{92} +(4.44168 - 16.5766i) q^{93} +(15.1294 + 8.73498i) q^{94} +(-7.72733 - 13.3841i) q^{96} +(-105.134 + 105.134i) q^{97} +(50.1548 + 47.8173i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	−2.63893	+	0.707100i	−0.879644	+	0.235700i	−0.670254	−	0.742132i	$-0.733815\pi$
$3$	−2.63893	+	0.707100i	−0.879644	+	0.235700i	−0.209391	+	0.977832i	$0.567148\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−3.86367			−0.643944
$7$	−6.78261	−	1.73096i	−0.968944	−	0.247280i
$7$	−6.78261	−	1.73096i	−0.968944	−	0.247280i
$8$	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	0.0987936	−	0.995108i	$-0.468502\pi$
$11$	10.0230	−	17.3604i	0.911186	−	1.57822i	0.812392	−	0.583112i	$-0.198165\pi$
$12$	−5.27787	−	1.41420i	−0.439822	−	0.117850i
$13$	−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
$17$	−3.19722	−	11.9322i	−0.188072	−	0.701894i	−0.993952	−	0.109815i	$-0.964974\pi$
$17$	−3.19722	−	11.9322i	−0.188072	−	0.701894i	0.805880	−	0.592079i	$-0.201693\pi$
$18$	−2.09827	+	0.562230i	−0.116571	+	0.0312350i
$19$	−15.7940	+	9.11869i	−0.831265	+	0.479931i	−0.854285	−	0.519804i	$-0.826005\pi$
$19$	−15.7940	+	9.11869i	−0.831265	+	0.479931i	0.0230208	+	0.999735i	$0.492672\pi$
$20$		0			0
$21$	19.1228	−	0.228089i	0.910610	−	0.0108614i
$22$	20.0461	−	20.0461i	0.911186	−	0.911186i
$23$	10.6451	−	39.7282i	0.462832	−	1.72731i	−0.201148	−	0.979561i	$-0.564467\pi$
$23$	10.6451	−	39.7282i	0.462832	−	1.72731i	0.663979	−	0.747751i	$-0.268866\pi$
$24$	−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
$28$	−10.0169	−	9.78072i	−0.357745	−	0.349312i
$29$		−	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	−0.912227	−	0.409686i	$-0.865638\pi$
$31$	−3.14077	+	5.43998i	−0.101315	+	0.175483i	0.810912	+	0.585169i	$0.198972\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−14.1746	+	52.9003i	−0.429533	+	1.60304i
$34$		−	17.4700i		−	0.513822i
$35$		0			0
$36$	−3.07208			−0.0853356
$37$	−36.6587	−	9.82266i	−0.990775	−	0.265477i	−0.273199	−	0.961958i	$-0.588082\pi$
$37$	−36.6587	−	9.82266i	−0.990775	−	0.265477i	−0.717576	+	0.696480i	$0.754748\pi$
$38$	−24.9127	+	6.67534i	−0.655598	+	0.175667i
$39$	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	$0.563971\pi$
$42$	26.2057	+	6.68786i	0.623946	+	0.159235i
$43$	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
$47$	11.9322	+	3.19722i	0.253877	+	0.0680260i	0.383513	−	0.923536i	$-0.374714\pi$
$47$	11.9322	+	3.19722i	0.253877	+	0.0680260i	−0.129636	+	0.991562i	$0.541381\pi$
$48$	−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
$52$	−1.62183	−	6.05274i	−0.0311890	−	0.116399i
$53$	−51.7180	+	13.8578i	−0.975811	+	0.261468i	−0.711279	−	0.702909i	$-0.751884\pi$
$53$	−51.7180	+	13.8578i	−0.975811	+	0.261468i	−0.264531	+	0.964377i	$0.585217\pi$
$54$	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
$58$	6.96333	−	25.9875i	0.120057	−	0.448060i
$59$	−82.3873	−	47.5663i	−1.39639	−	0.806209i	−0.402382	−	0.915472i	$-0.631817\pi$
$59$	−82.3873	−	47.5663i	−1.39639	−	0.806209i	−0.994013	+	0.109263i	$0.965151\pi$
$60$		0			0
$61$	−4.22958	−	7.32586i	−0.0693375	−	0.120096i	0.829272	−	0.558845i	$-0.188755\pi$
$61$	−4.22958	−	7.32586i	−0.0693375	−	0.120096i	−0.898610	+	0.438749i	$0.855422\pi$
$62$	−6.28154	+	6.28154i	−0.101315	+	0.101315i
$63$	10.3520	−	2.90657i	0.164317	−	0.0461360i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−38.7257	+	67.0749i	−0.586753	+	1.01629i
$67$	−2.94188	−	10.9793i	−0.0439087	−	0.163870i	0.940490	−	0.339821i	$-0.110366\pi$
$67$	−2.94188	−	10.9793i	−0.0439087	−	0.163870i	−0.984399	+	0.175951i	$0.943700\pi$
$68$	6.39445	−	23.8644i	0.0940360	−	0.350947i
$69$			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	$0.267265\pi$
$72$	−4.19654	−	1.12446i	−0.0582853	−	0.0156175i
$73$	−7.87869	+	2.11109i	−0.107927	+	0.0289190i	−0.312378	−	0.949958i	$-0.601126\pi$
$73$	−7.87869	+	2.11109i	−0.107927	+	0.0289190i	0.204451	+	0.978877i	$0.434459\pi$
$74$	−46.4813	−	26.8360i	−0.628126	−	0.362649i
$75$		0			0
$76$	−36.4747			−0.479931
$77$	−98.0326	+	100.399i	−1.27315	+	1.30389i
$78$	8.55979	+	8.55979i	0.109741	+	0.109741i
$79$	15.1049	−	8.72081i	0.191201	−	0.110390i	−0.401344	−	0.915928i	$-0.631457\pi$
$79$	15.1049	−	8.72081i	0.191201	−	0.110390i	0.592545	+	0.805538i	$0.298123\pi$
$80$		0			0
$81$	−32.4081	+	56.1325i	−0.400100	+	0.692994i
$82$	−22.3604	−	5.99144i	−0.272687	−	0.0730663i
$83$	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
$87$	13.4520	+	50.2035i	0.154621	+	0.577052i
$88$	54.7669	−	14.6748i	0.622351	−	0.166759i
$89$	−67.0808	+	38.7291i	−0.753717	+	0.435158i	−0.827035	−	0.562150i	$-0.809974\pi$
$89$	−67.0808	+	38.7291i	−0.753717	+	0.435158i	0.0733187	+	0.997309i	$0.476641\pi$
$90$		0			0
$91$	11.1917	+	18.8615i	0.122986	+	0.207269i
$92$	58.1661	−	58.1661i	0.632240	−	0.632240i
$93$	4.44168	−	16.5766i	0.0477600	−	0.178243i
$94$	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	$0.972047\pi$
$98$	50.1548	+	47.8173i	0.511784	+	0.487932i
$99$			30.7916i			0.311026i
$100$		0			0
$101$	−63.7196	+	110.366i	−0.630887	+	1.09273i	0.356483	+	0.934302i	$0.383976\pi$
$101$	−63.7196	+	110.366i	−0.630887	+	1.09273i	−0.987371	+	0.158427i	$0.949358\pi$
$102$	12.3530	+	46.1020i	0.121108	+	0.451981i
$103$	−1.94384	+	7.25451i	−0.0188722	+	0.0704321i	−0.974720	−	0.223431i	$-0.928274\pi$
$103$	−1.94384	+	7.25451i	−0.0188722	+	0.0704321i	0.955848	+	0.293863i	$0.0949410\pi$
$104$		−	8.86183i		−	0.0852099i
$105$		0			0
$106$	−75.7204			−0.714343
$107$	111.524	+	29.8828i	1.04228	+	0.279279i	0.739059	−	0.673641i	$-0.235270\pi$
$107$	111.524	+	29.8828i	1.04228	+	0.279279i	0.303224	+	0.952919i	$0.401937\pi$
$108$	55.6078	−	14.9001i	0.514887	−	0.137964i
$109$	36.9108	+	21.3104i	0.338631	+	0.195509i	0.659666	−	0.751559i	$-0.270698\pi$
$109$	36.9108	+	21.3104i	0.338631	+	0.195509i	−0.321036	+	0.947067i	$0.604031\pi$
$110$		0			0
$111$	103.685			0.934103
$112$	−7.56899	−	26.9576i	−0.0675802	−	0.240693i
$113$	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
$117$	4.64863	+	1.24560i	0.0397319	+	0.0106461i
$118$	−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
$122$	−3.09627	−	11.5554i	−0.0253793	−	0.0947167i
$123$	43.1965	−	11.5745i	0.351191	−	0.0941013i
$124$	−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	$0.294037\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	−14.2765	−	8.24252i	−0.110670	−	0.0638955i
$130$		0			0
$131$	−72.3622	−	125.335i	−0.552383	−	0.956756i	−0.998102	−	0.0615830i	$-0.980385\pi$
$131$	−72.3622	−	125.335i	−0.552383	−	0.956756i	0.445719	−	0.895173i	$-0.352948\pi$
$132$	−77.4514	+	77.4514i	−0.586753	+	0.586753i
$133$	122.909	−	34.5096i	0.924126	−	0.259471i
$134$		−	16.0748i		−	0.119961i
$135$		0			0
$136$	17.4700	−	30.2589i	0.128456	−	0.222492i
$137$	−12.2152	−	45.5877i	−0.0891619	−	0.332757i	0.906908	−	0.421329i	$-0.138436\pi$
$137$	−12.2152	−	45.5877i	−0.0891619	−	0.332757i	−0.996070	+	0.0885724i	$0.971770\pi$
$138$	−41.1292	+	153.496i	−0.298038	+	1.11229i
$139$		−	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
$142$	129.524	+	34.7058i	0.912140	+	0.244407i
$143$	−60.6669	+	16.2556i	−0.424244	+	0.113676i
$144$	−5.32100	−	3.07208i	−0.0369514	−	0.0213339i
$145$		0			0
$146$	−11.5352			−0.0790083
$147$	−130.097	−	31.5538i	−0.885016	−	0.214652i
$148$	−53.6720	−	53.6720i	−0.362649	−	0.362649i
$149$	117.569	−	67.8784i	0.789053	−	0.455560i	−0.0505763	−	0.998720i	$-0.516106\pi$
$149$	117.569	−	67.8784i	0.789053	−	0.455560i	0.839629	+	0.543160i	$0.182772\pi$
$150$		0			0
$151$	−41.3618	+	71.6408i	−0.273919	+	0.474442i	−0.969862	−	0.243655i	$-0.921653\pi$
$151$	−41.3618	+	71.6408i	−0.273919	+	0.474442i	0.695943	+	0.718097i	$0.254987\pi$
$152$	−49.8254	−	13.3507i	−0.327799	−	0.0878334i
$153$	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
$157$	10.1511	+	37.8843i	0.0646565	+	0.241301i	0.990689	−	0.136142i	$-0.0434702\pi$
$157$	10.1511	+	37.8843i	0.0646565	+	0.241301i	−0.926033	+	0.377443i	$0.876804\pi$
$158$	23.8257	−	6.38408i	0.150796	−	0.0404056i
$159$	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
$163$	31.9864	−	119.375i	0.196236	−	0.732361i	−0.795708	−	0.605680i	$-0.792901\pi$
$163$	31.9864	−	119.375i	0.196236	−	0.732361i	0.991944	−	0.126681i	$-0.0404324\pi$
$164$	−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	$-0.0123247\pi$
$168$	38.7018	+	37.7894i	0.230368	+	0.224937i
$169$		−	159.183i		−	0.941914i
$170$		0			0
$171$	14.0067	−	24.2603i	0.0819104	−	0.141873i
$172$	3.12343	+	11.6568i	0.0181595	+	0.0677721i
$173$	62.6900	−	233.962i	0.362370	−	1.35238i	−0.508582	−	0.861014i	$-0.669830\pi$
$173$	62.6900	−	233.962i	0.362370	−	1.35238i	0.870952	−	0.491369i	$-0.163503\pi$
$174$			73.5030i			0.422431i
$175$		0			0
$176$	80.1843			0.455593
$177$	251.049	+	67.2683i	1.41835	+	0.380047i
$178$	−105.810	+	28.3517i	−0.594438	+	0.159279i
$179$	150.152	+	86.6905i	0.838840	+	0.484304i	0.856870	−	0.515533i	$-0.172406\pi$
$179$	150.152	+	86.6905i	0.838840	+	0.484304i	−0.0180301	+	0.999837i	$0.505739\pi$
$180$		0			0
$181$	237.263			1.31085			0.655424	−	0.755262i	$-0.272490\pi$
$181$	237.263			1.31085			0.655424	+	0.755262i	$0.272490\pi$
$182$	8.38439	+	29.8617i	0.0460681	+	0.164075i
$183$	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
$187$	−239.194	−	64.0918i	−1.27911	−	0.342737i
$188$	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	0.837252	−	0.546818i	$-0.184161\pi$
$191$	−10.4921	−	18.1728i	−0.0549324	−	0.0951457i	−0.892184	+	0.451672i	$0.850828\pi$
$192$	−5.65680	−	21.1115i	−0.0294625	−	0.109956i
$193$	−48.3460	+	12.9543i	−0.250497	+	0.0671206i	−0.381883	−	0.924211i	$-0.624724\pi$
$193$	−48.3460	+	12.9543i	−0.250497	+	0.0671206i	0.131385	+	0.991331i	$0.458057\pi$
$194$	−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	$0.150596\pi$
$198$	−11.2705	+	42.0621i	−0.0569218	+	0.212435i
$199$	−266.269	−	153.731i	−1.33804	−	0.772515i	−0.351520	−	0.936180i	$-0.614335\pi$
$199$	−266.269	−	153.731i	−1.33804	−	0.772515i	−0.986516	+	0.163665i	$0.947668\pi$
$200$		0			0
$201$	15.5269	+	26.8933i	0.0772481	+	0.133798i
$202$	−127.439	+	127.439i	−0.630887	+	0.630887i
$203$	−32.9301	+	129.033i	−0.162217	+	0.635633i
$204$			67.4981i			0.330873i
$205$		0			0
$206$	−5.31067	+	9.19835i	−0.0257799	+	0.0446522i
$207$	16.3514	+	61.0241i	0.0789921	+	0.294803i
$208$	3.24366	−	12.1055i	0.0155945	−	0.0581995i
$209$			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	$0.589097\pi$
$212$	−103.436	−	27.7156i	−0.487905	−	0.130734i
$213$	−250.218	+	67.0458i	−1.17473	+	0.314769i
$214$	141.407	+	81.6414i	0.660781	+	0.381502i
$215$		0			0
$216$	81.4155			0.376924
$217$	30.7190	−	31.4607i	0.141562	−	0.144980i
$218$	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
$222$	141.637	+	37.9515i	0.638004	+	0.170953i
$223$	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
$227$	−87.2238	−	325.524i	−0.384246	−	1.43403i	−0.839352	−	0.543588i	$-0.817065\pi$
$227$	−87.2238	−	325.524i	−0.384246	−	1.43403i	0.455106	−	0.890437i	$-0.349601\pi$
$228$	96.2544	−	25.7913i	0.422168	−	0.113120i
$229$	330.729	−	190.946i	1.44423	−	0.833827i	0.446102	−	0.894982i	$-0.352812\pi$
$229$	330.729	−	190.946i	1.44423	−	0.833827i	0.998128	+	0.0611552i	$0.0194785\pi$
$230$		0			0
$231$	187.709	−	334.266i	0.812593	−	1.44704i
$232$	38.0483	−	38.0483i	0.164001	−	0.164001i
$233$	−86.3892	+	322.409i	−0.370769	+	1.38373i	0.488660	+	0.872474i	$0.337486\pi$
$233$	−86.3892	+	322.409i	−0.370769	+	1.38373i	−0.859429	+	0.511255i	$0.829181\pi$
$234$	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
$238$	−30.2398	+	118.492i	−0.127058	+	0.497865i
$239$		−	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	−0.861959	−	0.506977i	$-0.830763\pi$
$241$	1.94620	−	3.37093i	0.00807554	−	0.0139872i	0.870035	+	0.492990i	$0.164096\pi$
$242$	−102.797	−	383.642i	−0.424779	−	1.58530i
$243$	−21.2188	+	79.1896i	−0.0873201	+	0.325883i
$244$		−	16.9183i		−	0.0693375i
$245$		0			0
$246$	63.2440			0.257090
$247$	55.1931	+	14.7889i	0.223454	+	0.0598742i
$248$	−17.1615	+	4.59841i	−0.0691996	+	0.0185420i
$249$	−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	$0.237869\pi$
$252$	20.8367	+	5.31766i	0.0826855	+	0.0211018i
$253$	−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
$257$	255.790	+	68.5388i	0.995294	+	0.266688i	0.719473	−	0.694521i	$-0.244384\pi$
$257$	255.790	+	68.5388i	0.995294	+	0.266688i	0.275821	+	0.961209i	$0.411050\pi$
$258$	−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
$262$	−52.9728	−	197.697i	−0.202186	−	0.754570i
$263$	−265.172	+	71.0526i	−1.00826	+	0.270162i	−0.724902	−	0.688852i	$-0.758115\pi$
$263$	−265.172	+	71.0526i	−1.00826	+	0.270162i	−0.283357	+	0.959014i	$0.591448\pi$
$264$	−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
$268$	5.88377	−	21.9585i	0.0219544	−	0.0819348i
$269$	−120.599	−	69.6276i	−0.448322	−	0.258839i	0.258799	−	0.965931i	$-0.416673\pi$
$269$	−120.599	−	69.6276i	−0.448322	−	0.258839i	−0.707121	+	0.707092i	$0.750006\pi$
$270$		0			0
$271$	−31.0329	−	53.7505i	−0.114512	−	0.198341i	0.803072	−	0.595882i	$-0.203197\pi$
$271$	−31.0329	−	53.7505i	−0.114512	−	0.198341i	−0.917585	+	0.397540i	$0.869864\pi$
$272$	34.9399	−	34.9399i	0.128456	−	0.128456i
$273$	−42.8711	−	41.8605i	−0.157037	−	0.153335i
$274$		−	66.7450i		−	0.243595i
$275$		0			0
$276$	−112.367	+	194.626i	−0.407127	+	0.705165i
$277$	107.661	+	401.798i	0.388669	+	1.45053i	0.832301	+	0.554324i	$0.187023\pi$
$277$	107.661	+	401.798i	0.388669	+	1.45053i	−0.443632	+	0.896209i	$0.646310\pi$
$278$	44.4624	−	165.936i	0.159937	−	0.596891i
$279$		−	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	$0.729202\pi$
$282$	−46.1020	−	12.3530i	−0.163482	−	0.0438050i
$283$	466.250	−	124.931i	1.64753	−	0.441453i	0.688607	−	0.725135i	$-0.258222\pi$
$283$	466.250	−	124.931i	1.64753	−	0.441453i	0.958919	+	0.283681i	$0.0915558\pi$
$284$	164.230	+	94.8180i	0.578273	+	0.333866i
$285$		0			0
$286$	−88.8225			−0.310568
$287$	111.024	+	28.3340i	0.386843	+	0.0987247i
$288$	−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
$292$	−15.7574	−	4.22218i	−0.0539636	−	0.0144595i
$293$	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
$297$	−149.344	−	557.359i	−0.502842	−	1.87663i
$298$	185.447	−	49.6904i	0.622306	−	0.166746i
$299$	−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
$303$	90.1123	−	336.304i	0.297400	−	1.10991i
$304$	−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	$0.250152\pi$
$308$	−270.197	+	75.8643i	−0.877262	+	0.246313i
$309$		−	20.5187i		−	0.0664034i
$310$		0			0
$311$	−178.011	+	308.324i	−0.572382	+	0.991394i	0.423939	+	0.905691i	$0.360647\pi$
$311$	−178.011	+	308.324i	−0.572382	+	0.991394i	−0.996321	+	0.0857033i	$0.972686\pi$
$312$	6.26620	+	23.3858i	0.0200840	+	0.0749544i
$313$	67.4119	−	251.585i	0.215373	−	0.803784i	−0.770661	−	0.637245i	$-0.780074\pi$
$313$	67.4119	−	251.585i	0.215373	−	0.803784i	0.986035	−	0.166540i	$-0.0532593\pi$
$314$			55.4664i			0.176645i
$315$		0			0
$316$	34.8833			0.110390
$317$	−74.7155	−	20.0199i	−0.235695	−	0.0631544i	0.139038	−	0.990287i	$-0.455599\pi$
$317$	−74.7155	−	20.0199i	−0.235695	−	0.0631544i	−0.374733	+	0.927133i	$0.622266\pi$
$318$	199.821	−	53.5419i	0.628368	−	0.168371i
$319$	−330.267	−	190.680i	−1.03532	−	0.597743i
$320$		0			0
$321$	−315.435			−0.982664
$322$	−284.453	+	291.321i	−0.883395	+	0.904723i
$323$	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
$327$	−112.474	−	30.1372i	−0.343956	−	0.0921627i
$328$	−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	0.793470	−	0.608610i	$-0.208273\pi$
$331$	−43.1415	−	74.7232i	−0.130337	−	0.225750i	−0.923806	+	0.382860i	$0.874939\pi$
$332$	46.1900	+	172.383i	0.139126	+	0.519227i
$333$	56.3093	−	15.0880i	0.169097	−	0.0453094i
$334$	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	$0.312410\pi$
$338$	58.2652	−	217.449i	0.172382	−	0.643339i
$339$	−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
$343$	−251.059	−	233.706i	−0.731950	−	0.681359i
$344$			17.0667i			0.0496126i
$345$		0			0
$346$	171.272	−	296.652i	0.495006	−	0.857376i
$347$	103.674	+	386.918i	0.298773	+	1.11504i	0.938174	+	0.346164i	$0.112516\pi$
$347$	103.674	+	386.918i	0.298773	+	1.11504i	−0.639401	+	0.768874i	$0.720817\pi$
$348$	−26.9040	+	100.407i	−0.0773103	+	0.288526i
$349$			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
$352$	109.534	+	29.3495i	0.311176	+	0.0833793i
$353$	−318.934	+	85.4581i	−0.903496	+	0.242091i	−0.680517	−	0.732732i	$-0.738245\pi$
$353$	−318.934	+	85.4581i	−0.903496	+	0.242091i	−0.222979	+	0.974823i	$0.571578\pi$
$354$	318.317	+	183.780i	0.899200	+	0.519154i
$355$		0			0
$356$	−154.916			−0.435158
$357$	−63.8615	−	227.448i	−0.178884	−	0.637109i
$358$	173.381	+	173.381i	0.484304	+	0.484304i
$359$	−27.1220	+	15.6589i	−0.0755487	+	0.0436181i	−0.537298	−	0.843392i	$-0.680555\pi$
$359$	−27.1220	+	15.6589i	−0.0755487	+	0.0436181i	0.461750	+	0.887010i	$0.347222\pi$
$360$		0			0
$361$	−14.1991	+	24.5936i	−0.0393327	+	0.0681263i
$362$	324.108	+	86.8444i	0.895325	+	0.239902i
$363$	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
$367$	−45.4250	−	169.529i	−0.123774	−	0.461931i	0.876019	−	0.482276i	$-0.160190\pi$
$367$	−45.4250	−	169.529i	−0.123774	−	0.461931i	−0.999793	+	0.0203459i	$0.993523\pi$
$368$	158.913	−	42.5805i	0.431828	−	0.115708i
$369$	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
$373$	−27.9749	+	104.404i	−0.0749997	+	0.279903i	−0.993233	−	0.116137i	$-0.962949\pi$
$373$	−27.9749	+	104.404i	−0.0749997	+	0.279903i	0.918234	+	0.396039i	$0.129616\pi$
$374$	−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
$378$	−274.345	+	77.0291i	−0.725782	+	0.203781i
$379$			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
$382$	−7.68074	−	28.6649i	−0.0201066	−	0.0750390i
$383$	−0.910761	+	3.39901i	−0.00237797	+	0.00887469i	−0.967105	−	0.254379i	$-0.918129\pi$
$383$	−0.910761	+	3.39901i	−0.00237797	+	0.00887469i	0.964727	+	0.263254i	$0.0847956\pi$
$384$		−	30.9093i		−	0.0804930i
$385$		0			0
$386$	−70.7834			−0.183377
$387$	−8.95267	−	2.39886i	−0.0231335	−	0.00619860i
$388$	−287.230	+	76.9631i	−0.740284	+	0.198358i
$389$	628.167	+	362.672i	1.61482	+	0.932319i	0.988230	+	0.152973i	$0.0488847\pi$
$389$	628.167	+	362.672i	1.61482	+	0.932319i	0.626594	+	0.779346i	$0.284449\pi$
$390$		0			0
$391$	−508.079			−1.29944
$392$	39.0533	+	132.977i	0.0996258	+	0.339227i
$393$	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
$397$	−123.753	−	33.1595i	−0.311721	−	0.0835253i	0.0995671	−	0.995031i	$-0.468254\pi$
$397$	−123.753	−	33.1595i	−0.311721	−	0.0835253i	−0.411288	+	0.911506i	$0.634921\pi$
$398$	−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	0.857804	+	0.513976i	$0.171828\pi$
$401$	350.482	+	607.052i	0.874019	+	1.51384i	0.0162143	+	0.999869i	$0.494839\pi$
$402$	11.3665	+	42.4202i	0.0282748	+	0.105523i
$403$	19.0103	−	5.09379i	0.0471719	−	0.0126397i
$404$	−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
$408$	−24.7060	+	92.2041i	−0.0605540	+	0.225990i
$409$	391.838	+	226.228i	0.958039	+	0.553124i	0.895569	−	0.444923i	$-0.146769\pi$
$409$	391.838	+	226.228i	0.958039	+	0.553124i	0.0624701	+	0.998047i	$0.480102\pi$
$410$		0			0
$411$	64.4701	+	111.665i	0.156861	+	0.271692i
$412$	−10.6213	+	10.6213i	−0.0257799	+	0.0257799i
$413$	476.465	+	465.233i	1.15367	+	1.12647i
$414$			89.3455i			0.215810i
$415$		0			0
$416$	8.86183	−	15.3491i	0.0213025	−	0.0368970i
$417$	85.8939	+	320.560i	0.205981	+	0.768730i
$418$	−133.814	+	499.402i	−0.320130	+	1.19474i
$419$			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	$0.591608\pi$
$422$	−159.257	−	42.6729i	−0.377387	−	0.101121i
$423$	−18.3284	+	4.91107i	−0.0433295	+	0.0116101i
$424$	−131.152	−	75.7204i	−0.309320	−	0.178586i
$425$		0			0
$426$	−366.345			−0.859965
$427$	16.0068	+	57.0097i	0.0374867	+	0.133512i
$428$	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	−0.780167	−	0.625572i	$-0.784866\pi$
$431$	65.3730	−	113.229i	0.151677	−	0.262713i	0.931844	+	0.362858i	$0.118199\pi$
$432$	111.216	+	29.8001i	0.257444	+	0.0689818i
$433$	−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
$437$	194.139	+	724.537i	0.444255	+	1.65798i
$438$	30.4406	−	8.15654i	0.0694992	−	0.0186222i
$439$	187.891	−	108.479i	0.427998	−	0.247105i	−0.270495	−	0.962721i	$-0.587188\pi$
$439$	187.891	−	108.479i	0.427998	−	0.247105i	0.698493	+	0.715617i	$0.253854\pi$
$440$		0			0
$441$	−75.2446	+	1.79523i	−0.170623	+	0.00407081i
$442$	−38.7040	+	38.7040i	−0.0875655	+	0.0875655i
$443$	11.2087	−	41.8315i	0.0253018	−	0.0944277i	−0.952120	−	0.305724i	$-0.901102\pi$
$443$	11.2087	−	41.8315i	0.0253018	−	0.0944277i	0.977422	+	0.211296i	$0.0677683\pi$
$444$	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
$448$	13.8477	−	54.2609i	0.0309100	−	0.121118i
$449$			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
$452$	9.95586	+	37.1558i	0.0220262	+	0.0822030i
$453$	58.4939	−	218.302i	0.129126	−	0.481903i
$454$		−	476.600i		−	1.04978i
$455$		0			0
$456$	140.926			0.309049
$457$	−279.910	−	75.0016i	−0.612494	−	0.164117i	−0.0607809	−	0.998151i	$-0.519359\pi$
$457$	−279.910	−	75.0016i	−0.612494	−	0.164117i	−0.551713	+	0.834034i	$0.686026\pi$
$458$	521.675	−	139.782i	1.13903	−	0.305202i
$459$	−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	$0.376714\pi$
$462$	378.765	−	387.910i	0.819838	−	0.839631i
$463$	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
$467$	481.652	+	129.058i	1.03137	+	0.276356i	0.734535	−	0.678571i	$-0.237400\pi$
$467$	481.652	+	129.058i	1.03137	+	0.276356i	0.296840	+	0.954927i	$0.404067\pi$
$468$	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
$472$	−69.6419	−	259.907i	−0.147546	−	0.550651i
$473$	116.837	−	31.3063i	0.247012	−	0.0661866i
$474$	−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
$478$	160.015	−	597.184i	0.334759	−	1.24934i
$479$	−324.591	−	187.403i	−0.677643	−	0.391238i	0.121323	−	0.992613i	$-0.461286\pi$
$479$	−324.591	−	187.403i	−0.677643	−	0.391238i	−0.798967	+	0.601376i	$0.794620\pi$
$480$		0			0
$481$	59.4541	+	102.977i	0.123605	+	0.214090i
$482$	3.89241	−	3.89241i	0.00807554	−	0.00807554i
$483$	194.503	−	762.142i	0.402698	−	1.57793i
$484$		−	561.691i		−	1.16052i
$485$		0			0
$486$	−57.9708	+	100.408i	−0.119281	+	0.206602i
$487$	−101.575	−	379.084i	−0.208573	−	0.778406i	−0.988331	−	0.152324i	$-0.951324\pi$
$487$	−101.575	−	379.084i	−0.208573	−	0.778406i	0.779757	−	0.626082i	$-0.215342\pi$
$488$	6.19254	−	23.1109i	0.0126896	−	0.0473584i
$489$			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	$0.467382\pi$
$492$	86.3930	+	23.1489i	0.175595	+	0.0470507i
$493$	−227.000	+	60.8245i	−0.460447	+	0.123376i
$494$	69.9820	+	40.4041i	0.141664	+	0.0817897i
$495$		0			0
$496$	−25.1262			−0.0506576
$497$	−643.114	−	164.126i	−1.29399	−	0.330234i
$498$	−243.785	−	243.785i	−0.489527	−	0.489527i
$499$	−341.907	+	197.400i	−0.685184	+	0.395591i	−0.801805	−	0.597585i	$-0.796127\pi$
$499$	−341.907	+	197.400i	−0.685184	+	0.395591i	0.116621	+	0.993176i	$0.462794\pi$
$500$		0			0
$501$	−334.863	+	579.999i	−0.668388	+	1.15768i
$502$	503.018	+	134.783i	1.00203	+	0.268493i
$503$	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
$507$	112.559	+	420.075i	0.222009	+	0.828549i
$508$	−67.6682	+	18.1316i	−0.133205	+	0.0356922i
$509$	442.330	−	255.380i	0.869019	−	0.501728i	0.00199662	−	0.999998i	$-0.499364\pi$
$509$	442.330	−	255.380i	0.869019	−	0.501728i	0.867022	+	0.498270i	$0.166031\pi$
$510$		0			0
$511$	57.0923	−	0.680972i	0.111727	−	0.00133263i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−135.869	+	507.070i	−0.264852	+	0.988441i
$514$	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
$518$	268.813	+	262.476i	0.518943	+	0.506710i
$519$			661.738i			1.27503i
$520$		0			0
$521$	392.549	−	679.914i	0.753452	−	1.30502i	−0.192688	−	0.981260i	$-0.561720\pi$
$521$	392.549	−	679.914i	0.753452	−	1.30502i	0.946140	−	0.323758i	$-0.104946\pi$
$522$	10.6960	+	39.9179i	0.0204903	+	0.0764710i
$523$	79.2957	−	295.936i	0.151617	−	0.565843i	−0.847754	−	0.530389i	$-0.822046\pi$
$523$	79.2957	−	295.936i	0.151617	−	0.565843i	0.999371	−	0.0354535i	$-0.0112876\pi$
$524$		−	289.449i		−	0.552383i
$525$		0			0
$526$	−388.239			−0.738097
$527$	74.9526	+	20.0835i	0.142225	+	0.0381091i
$528$	−211.601	+	56.6983i	−0.400760	+	0.107383i
$529$	−1006.88	−	581.323i	−1.90337	−	1.09891i
$530$		0			0
$531$	146.128			0.275193
$532$	247.394	+	63.1364i	0.465026	+	0.118677i
$533$	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
$537$	−457.541	−	122.598i	−0.852031	−	0.228301i
$538$	−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	0.510453	−	0.859906i	$-0.329478\pi$
$541$	−264.805	−	458.656i	−0.489474	−	0.847793i	−0.999927	+	0.0121125i	$0.996144\pi$
$542$	−22.7176	−	84.7834i	−0.0419145	−	0.156427i
$543$	−626.122	+	167.769i	−1.15308	+	0.308967i
$544$	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	$0.103417\pi$
$548$	24.4303	−	91.1753i	0.0445809	−	0.166378i
$549$	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
$553$	−117.546	+	33.0039i	−0.212560	+	0.0596815i
$554$			588.273i			1.06186i
$555$		0			0
$556$	121.473	−	210.398i	0.218477	−	0.378414i
$557$	−96.2937	−	359.373i	−0.172879	−	0.645194i	−0.996903	−	0.0786389i	$-0.974943\pi$
$557$	−96.2937	−	359.373i	−0.172879	−	0.645194i	0.824024	−	0.566555i	$-0.191724\pi$
$558$	3.53167	−	13.1804i	0.00632916	−	0.0236208i
$559$		−	18.9053i		−	0.0338199i
$560$		0			0
$561$	676.536			1.20595
$562$	−506.247	−	135.649i	−0.900796	−	0.241368i
$563$	−927.276	+	248.463i	−1.64703	+	0.441319i	−0.958778	−	0.284156i	$-0.908287\pi$
$563$	−927.276	+	248.463i	−1.64703	+	0.441319i	−0.688248	+	0.725476i	$0.741620\pi$
$564$	−58.4551	−	33.7490i	−0.103644	−	0.0598387i
$565$		0			0
$566$	682.637			1.20607
$567$	316.975	−	324.627i	0.559038	−	0.572535i
$568$	189.636	+	189.636i	0.333866	+	0.333866i
$569$	−579.317	+	334.469i	−1.01813	+	0.587818i	−0.913562	−	0.406699i	$-0.866680\pi$
$569$	−579.317	+	334.469i	−1.01813	+	0.587818i	−0.104569	+	0.994518i	$0.533346\pi$
$570$		0			0
$571$	136.393	−	236.240i	0.238868	−	0.413731i	−0.721522	−	0.692391i	$-0.756557\pi$
$571$	136.393	−	236.240i	0.238868	−	0.413731i	0.960390	+	0.278661i	$0.0898905\pi$
$572$	−121.334	−	32.5113i	−0.212122	−	0.0568379i
$573$	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
$577$	−56.0052	−	209.014i	−0.0970627	−	0.362243i	0.900261	−	0.435350i	$-0.143375\pi$
$577$	−56.0052	−	209.014i	−0.0970627	−	0.362243i	−0.997324	+	0.0731068i	$0.976709\pi$
$578$	186.326	−	49.9260i	0.322364	−	0.0863771i
$579$	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
$583$	−277.794	+	1036.74i	−0.476491	+	1.77829i
$584$	−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	$0.175135\pi$
$588$	−193.781	−	184.750i	−0.329560	−	0.314201i
$589$		−	114.559i		−	0.194497i
$590$		0			0
$591$	−165.358	+	286.408i	−0.279793	+	0.484616i
$592$	−39.2907	−	146.635i	−0.0663694	−	0.247694i
$593$	37.6975	−	140.689i	0.0635708	−	0.237249i	−0.926829	−	0.375485i	$-0.877476\pi$
$593$	37.6975	−	140.689i	0.0635708	−	0.237249i	0.990399	+	0.138235i	$0.0441430\pi$
$594$		−	816.031i		−	1.37379i
$595$		0			0
$596$	271.514			0.455560
$597$	811.369	+	217.406i	1.35908	+	0.364164i
$598$	−176.032	+	47.1677i	−0.294368	+	0.0788757i
$599$	396.026	+	228.645i	0.661144	+	0.381712i	0.792713	−	0.609595i	$-0.208668\pi$
$599$	396.026	+	228.645i	0.661144	+	0.381712i	−0.131568	+	0.991307i	$0.542001\pi$
$600$		0			0
$601$	369.587			0.614953			0.307477	−	0.951556i	$-0.400515\pi$
$601$	369.587			0.614953			0.307477	+	0.951556i	$0.400515\pi$
$602$	−16.1472	−	57.5097i	−0.0268227	−	0.0955311i
$603$	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
$607$	−225.915	−	60.5336i	−0.372182	−	0.0997259i	0.0678794	−	0.997694i	$-0.478377\pi$
$607$	−225.915	−	60.5336i	−0.372182	−	0.0997259i	−0.440062	+	0.897968i	$0.645043\pi$
$608$	−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
$612$	9.82214	+	36.6567i	0.0160492	+	0.0598966i
$613$	927.194	−	248.441i	1.51255	−	0.405287i	0.595270	−	0.803526i	$-0.297045\pi$
$613$	927.194	−	248.441i	1.51255	−	0.405287i	0.917282	+	0.398239i	$0.130378\pi$
$614$	−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	$0.258262\pi$
$618$	7.51035	−	28.0290i	0.0121527	−	0.0453544i
$619$	−430.611	−	248.613i	−0.695655	−	0.401637i	0.110072	−	0.993924i	$-0.464892\pi$
$619$	−430.611	−	248.613i	−0.695655	−	0.401637i	−0.805727	+	0.592287i	$0.798225\pi$
$620$		0			0
$621$	−591.953	−	1025.29i	−0.953225	−	1.65103i
$622$	−356.021	+	356.021i	−0.572382	+	0.572382i
$623$	522.021	−	146.570i	0.837915	−	0.235265i
$624$			34.2392i			0.0548705i
$625$		0			0
$626$	184.173	−	318.996i	0.294205	−	0.509579i
$627$	−258.507	−	964.762i	−0.412292	−	1.53870i
$628$	−20.3021	+	75.7686i	−0.0323282	+	0.120651i
$629$			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	$0.222602\pi$
$632$	47.6514	+	12.7682i	0.0753978	+	0.0202028i
$633$	307.659	−	82.4369i	0.486033	−	0.130232i
$634$	−94.7354	−	54.6955i	−0.149425	−	0.0862705i
$635$		0			0
$636$	292.558			0.459997
$637$	−43.2605	−	147.302i	−0.0679129	−	0.231244i
$638$	−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	−0.163183	+	0.986596i	$0.552176\pi$
$641$	−599.981	+	1039.20i	−0.936008	+	1.62121i	−0.772826	+	0.634618i	$0.781157\pi$
$642$	−430.892	−	115.457i	−0.671172	−	0.179840i
$643$	−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
$647$	21.8446	+	81.5250i	0.0337628	+	0.126005i	0.980750	−	0.195266i	$-0.0625569\pi$
$647$	21.8446	+	81.5250i	0.0337628	+	0.126005i	−0.946988	+	0.321270i	$0.895890\pi$
$648$	−177.081	+	47.4488i	−0.273273	+	0.0732234i
$649$	−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
$653$	124.189	−	463.478i	0.190182	−	0.709767i	−0.803280	−	0.595601i	$-0.796914\pi$
$653$	124.189	−	463.478i	0.190182	−	0.709767i	0.993462	−	0.114166i	$-0.0364195\pi$
$654$	−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
$658$	−87.4971	−	85.4344i	−0.132974	−	0.129840i
$659$			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	−0.610291	−	0.792177i	$-0.708948\pi$
$661$	251.775	−	436.087i	0.380900	−	0.659738i	0.991191	+	0.132439i	$0.0422810\pi$
$662$	−31.5818	−	117.865i	−0.0477066	−	0.178043i
$663$	27.3676	−	102.137i	0.0412784	−	0.154053i
$664$			252.387i			0.380101i
$665$		0			0
$666$	82.4425			0.123788
$667$	−755.795	−	202.515i	−1.13313	−	0.303620i
$668$	473.572	−	126.893i	0.708940	−	0.189960i
$669$	−312.081	−	180.180i	−0.466489	−	0.269327i
$670$		0			0
$671$	−169.573			−0.252717
$672$	29.2440	+	104.155i	0.0435179	+	0.154993i
$673$	−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
$677$	117.369	+	31.4489i	0.173366	+	0.0464533i	0.344458	−	0.938802i	$-0.388063\pi$
$677$	117.369	+	31.4489i	0.173366	+	0.0464533i	−0.171092	+	0.985255i	$0.554729\pi$
$678$	−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
$682$	46.0900	+	172.010i	0.0675807	+	0.252215i
$683$	−783.543	+	209.950i	−1.14721	+	0.307393i	−0.781845	−	0.623472i	$-0.785721\pi$
$683$	−783.543	+	209.950i	−1.14721	+	0.307393i	−0.365362	+	0.930866i	$0.619055\pi$
$684$	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
$688$	−6.24686	+	23.3136i	−0.00907974	+	0.0338861i
$689$	145.280	+	83.8777i	0.210857	+	0.121738i
$690$		0			0
$691$	16.3168	+	28.2615i	0.0236133	+	0.0408994i	0.877591	−	0.479411i	$-0.159150\pi$
$691$	16.3168	+	28.2615i	0.0236133	+	0.0408994i	−0.853977	+	0.520310i	$0.825816\pi$
$692$	342.544	−	342.544i	0.495006	−	0.495006i
$693$	53.2991	−	208.847i	0.0769107	−	0.301367i
$694$			566.487i			0.816264i
$695$		0			0
$696$	−73.5030	+	127.311i	−0.105608	+	0.182918i
$697$	52.3351	+	195.317i	0.0750862	+	0.280226i
$698$	−74.0555	+	276.379i	−0.106097	+	0.395958i
$699$		−	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	$0.571341\pi$
$702$	−123.197	−	33.0105i	−0.175494	−	0.0470235i
$703$	668.558	−	179.140i	0.951007	−	0.254822i
$704$	138.883	+	80.1843i	0.197277	+	0.113898i
$705$		0			0
$706$	−466.952			−0.661405
$707$	623.224	−	638.270i	0.881505	−	0.902787i
$708$	367.561	+	367.561i	0.519154	+	0.519154i
$709$	622.782	−	359.564i	0.878396	−	0.507142i	0.00826649	−	0.999966i	$-0.497369\pi$
$709$	622.782	−	359.564i	0.878396	−	0.507142i	0.870129	+	0.492824i	$0.164035\pi$
$710$		0			0
$711$	−13.3955	+	23.2017i	−0.0188404	+	0.0326325i
$712$	−211.620	−	56.7033i	−0.297219	−	0.0796395i
$713$	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
$717$	309.122	+	1153.66i	0.431133	+	1.60901i
$718$	−42.7809	+	11.4631i	−0.0595834	+	0.0159653i
$719$	−278.808	+	160.970i	−0.387771	+	0.223880i	−0.681194	−	0.732103i	$-0.738539\pi$
$719$	−278.808	+	160.970i	−0.387771	+	0.223880i	0.293423	+	0.955983i	$0.405206\pi$
$720$		0			0
$721$	25.7416	−	45.8398i	0.0357026	−	0.0635780i
$722$	−28.3982	+	28.3982i	−0.0393327	+	0.0393327i
$723$	−2.75232	+	10.2718i	−0.00380681	+	0.0142072i
$724$	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	$-0.0927184\pi$
$728$	−15.3395	+	60.1063i	−0.0210707	+	0.0825636i
$729$		−	807.326i		−	1.10744i
$730$		0			0
$731$	37.2694	−	64.5525i	0.0509841	−	0.0883071i
$732$	11.9630	+	44.6464i	0.0163428	+	0.0609923i
$733$	−238.712	+	890.884i	−0.325664	+	1.21539i	0.587979	+	0.808876i	$0.299924\pi$
$733$	−238.712	+	890.884i	−0.325664	+	1.21539i	−0.913643	+	0.406518i	$0.866743\pi$
$734$		−	248.207i		−	0.338157i
$735$		0			0
$736$	232.664			0.316120
$737$	−220.091	−	58.9733i	−0.298631	−	0.0800180i
$738$	34.3464	−	9.20310i	0.0465399	−	0.0124703i
$739$	391.732	+	226.167i	0.530084	+	0.306044i	0.741051	−	0.671449i	$-0.234328\pi$
$739$	391.732	+	226.167i	0.530084	+	0.306044i	−0.210967	+	0.977493i	$0.567661\pi$
$740$		0			0
$741$	−156.108			−0.210672
$742$	513.582	+	131.069i	0.692158	+	0.176643i
$743$	−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
$747$	−132.394	−	35.4749i	−0.177234	−	0.0474898i
$748$	−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	0.931342	−	0.364145i	$-0.118639\pi$
$751$	112.885	+	195.522i	0.150312	+	0.260349i	−0.781030	+	0.624494i	$0.785305\pi$
$752$	12.7889	+	47.7288i	0.0170065	+	0.0634692i
$753$	−971.747	+	260.379i	−1.29050	+	0.345789i
$754$	−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	$0.113385\pi$
$758$	−135.572	+	505.960i	−0.178854	+	0.667494i
$759$	1950.74	+	1126.26i	2.57015	+	1.48387i
$760$		0			0
$761$	179.891	+	311.580i	0.236388	+	0.409436i	0.959675	−	0.281112i	$-0.0907031\pi$
$761$	179.891	+	311.580i	0.236388	+	0.409436i	−0.723287	+	0.690547i	$0.757370\pi$
$762$	95.6964	−	95.6964i	0.125586	−	0.125586i
$763$	−213.464	−	208.431i	−0.279769	−	0.273174i
$764$		−	41.9683i		−	0.0549324i
$765$		0			0
$766$	−2.48825	+	4.30977i	−0.00324836	+	0.00562633i
$767$	77.1444	+	287.907i	0.100579	+	0.375367i
$768$	11.3136	−	42.2229i	0.0147312	−	0.0549778i
$769$		−	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
$772$	−96.6920	−	25.9085i	−0.125249	−	0.0335603i
$773$	−12.4850	+	3.34535i	−0.0161514	+	0.00432775i	−0.266886	−	0.963728i	$-0.585995\pi$
$773$	−12.4850	+	3.34535i	−0.0161514	+	0.00432775i	0.250734	+	0.968056i	$0.419328\pi$
$774$	−11.3515	−	6.55381i	−0.0146661	−	0.00846745i
$775$		0			0
$776$	−420.534			−0.541925
$777$	−703.258	−	179.476i	−0.905093	−	0.230985i
$778$	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
$782$	−694.049	−	185.970i	−0.887531	−	0.237813i
$783$	−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
$787$	321.680	+	1200.53i	0.408742	+	1.52545i	0.797047	+	0.603917i	$0.206394\pi$
$787$	321.680	+	1200.53i	0.408742	+	1.52545i	−0.388305	+	0.921531i	$0.626939\pi$
$788$	233.853	−	62.6608i	0.296768	−	0.0795188i
$789$	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
$793$	−6.85966	+	25.6006i	−0.00865026	+	0.0322832i
$794$	−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	$0.0513489\pi$
$798$	−474.879	+	133.334i	−0.595086	+	0.167085i
$799$		−	152.600i		−	0.190988i
$800$		0			0
$801$	59.4895	−	103.039i	0.0742691	−	0.128638i
$802$	256.570	+	957.533i	0.319913	+	1.19393i
$803$	−42.3191	+	157.937i	−0.0527012	+	0.196684i
$804$			62.1075i			0.0772481i
$805$		0			0
$806$	27.8330			0.0345322
$807$	367.485	+	98.4674i	0.455372	+	0.122017i
$808$	−348.170	+	93.2920i	−0.430904	+	0.115460i
$809$	712.947	+	411.620i	0.881270	+	0.508802i	0.871077	−	0.491147i	$-0.163422\pi$
$809$	712.947	+	411.620i	0.881270	+	0.508802i	0.0101931	+	0.999948i	$0.496755\pi$
$810$		0			0
$811$	−1415.46			−1.74533			−0.872666	−	0.488318i	$-0.837610\pi$
$811$	−1415.46			−1.74533			−0.872666	+	0.488318i	$0.837610\pi$
$812$	−186.070	+	190.562i	−0.229150	+	0.234683i
$813$	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
$817$	−106.295	−	28.4816i	−0.130104	−	0.0348612i
$818$	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	0.847926	−	0.530115i	$-0.177851\pi$
$821$	−28.8421	−	49.9560i	−0.0351305	−	0.0608478i	−0.883056	+	0.469267i	$0.844518\pi$
$822$	47.1954	+	176.135i	0.0574153	+	0.214277i
$823$	373.416	−	100.057i	0.453725	−	0.121575i	−0.0247166	−	0.999694i	$-0.507868\pi$
$823$	373.416	−	100.057i	0.453725	−	0.121575i	0.478442	+	0.878119i	$0.341202\pi$
$824$	−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	$0.272884\pi$
$828$	−32.7027	+	122.048i	−0.0394961	+	0.147401i
$829$	880.574	+	508.399i	1.06221	+	0.613268i	0.926043	−	0.377417i	$-0.123188\pi$
$829$	880.574	+	508.399i	1.06221	+	0.613268i	0.136169	+	0.990686i	$0.456521\pi$
$830$		0			0
$831$	−568.222	−	984.190i	−0.683781	−	1.18434i
$832$	17.7237	−	17.7237i	0.0213025	−	0.0213025i
$833$	142.674	−	588.248i	0.171277	−	0.706180i
$834$			469.333i			0.562749i
$835$		0			0
$836$	−365.588	+	633.217i	−0.437306	+	0.757436i
$837$	46.7977	+	174.651i	0.0559112	+	0.208664i
$838$	−90.8382	+	339.013i	−0.108399	+	0.404550i
$839$		−	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
$842$	−326.469	−	87.4770i	−0.387730	−	0.103892i
$843$	977.985	−	262.050i	1.16013	−	0.310855i
$844$	−201.930	−	116.585i	−0.239254	−	0.138133i
$845$		0			0
$846$	−26.8346			−0.0317194
$847$	531.429	+	1892.73i	0.627425	+	2.23462i
$848$	−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
$852$	−500.437	−	134.092i	−0.587367	−	0.157385i
$853$	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
$857$	−262.477	−	979.577i	−0.306274	−	1.14303i	−0.931843	−	0.362861i	$-0.881800\pi$
$857$	−262.477	−	979.577i	−0.306274	−	1.14303i	0.625569	−	0.780169i	$-0.284867\pi$
$858$	234.397	−	62.8064i	0.273190	−	0.0732009i
$859$	−196.715	+	113.574i	−0.229005	+	0.132216i	−0.610113	−	0.792315i	$-0.708876\pi$
$859$	−196.715	+	113.574i	−0.229005	+	0.132216i	0.381108	+	0.924530i	$0.375543\pi$
$860$		0			0
$861$	−313.020	+	3.73356i	−0.363554	+	0.00433631i
$862$	130.746	−	130.746i	0.151677	−	0.151677i
$863$	126.070	−	470.501i	0.146084	−	0.545193i	−0.853621	−	0.520895i	$-0.825598\pi$
$863$	126.070	−	470.501i	0.146084	−	0.545193i	0.999705	−	0.0242979i	$-0.00773503\pi$
$864$	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
$868$	84.6676	−	23.7725i	0.0975433	−	0.0273876i
$869$		−	349.636i		−	0.402343i
$870$		0			0
$871$	−17.8065	+	30.8417i	−0.0204437	+	0.0354095i
$872$	31.2006	+	116.442i	0.0357806	+	0.133535i
$873$	59.1093	−	220.599i	0.0677082	−	0.252690i
$874$			1060.80i			1.21373i
$875$		0			0
$876$	44.5682			0.0508769
$877$	−137.801	−	36.9236i	−0.157127	−	0.0421022i	0.179398	−	0.983777i	$-0.442585\pi$
$877$	−137.801	−	36.9236i	−0.157127	−	0.0421022i	−0.336525	+	0.941674i	$0.609252\pi$
$878$	296.370	−	79.4121i	0.337551	−	0.0904466i
$879$	−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	$0.496080\pi$
$882$	−103.443	−	25.0891i	−0.117283	−	0.0284457i
$883$	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
$887$	−470.784	−	126.146i	−0.530759	−	0.142217i	−0.0165205	−	0.999864i	$-0.505259\pi$
$887$	−470.784	−	126.146i	−0.530759	−	0.142217i	−0.514239	+	0.857647i	$0.671926\pi$
$888$	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
$892$	68.2776	+	254.815i	0.0765444	+	0.285668i
$893$	−217.612	+	58.3090i	−0.243686	+	0.0652956i
$894$	−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
$898$	−17.6616	+	65.9140i	−0.0196677	+	0.0734009i
$899$	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
$903$	82.5642	+	80.6178i	0.0914332	+	0.0892778i
$904$			54.3998i			0.0601768i
$905$		0			0
$906$	159.808	−	276.796i	0.176389	−	0.305514i
$907$	−2.40540	−	8.97709i	−0.00265204	−	0.00989756i	0.964587	−	0.263764i	$-0.0849642\pi$
$907$	−2.40540	−	8.97709i	−0.00265204	−	0.00989756i	−0.967239	+	0.253867i	$0.918297\pi$
$908$	174.448	−	651.048i	0.192123	−	0.717013i
$909$		−	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	$0.700095\pi$
$912$	192.509	+	51.5826i	0.211084	+	0.0565599i
$913$	1727.81	−	462.964i	1.89245	−	0.507080i
$914$	−354.912	−	204.908i	−0.388306	−	0.224188i
$915$		0			0
$916$	763.785			0.833827
$917$	273.854	+	975.355i	0.298642	+	1.06364i
$918$	−355.581	−	355.581i	−0.387343	−	0.387343i
$919$	−1186.43	+	684.983i	−1.29100	+	0.745357i	−0.978831	−	0.204671i	$-0.934388\pi$
$919$	−1186.43	+	684.983i	−1.29100	+	0.745357i	−0.312165	+	0.950028i	$0.601054\pi$
$920$		0			0
$921$	0.400667	−	0.693975i	0.000435034	−	0.000753502i
$922$	475.708	+	127.466i	0.515952	+	0.138249i
$923$	−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
$927$	−2.98582	−	11.1432i	−0.00322095	−	0.0120207i
$928$	103.950	−	27.8533i	0.112015	−	0.0300143i
$929$	818.100	−	472.330i	0.880624	−	0.508429i	0.00976001	−	0.999952i	$-0.496893\pi$
$929$	818.100	−	472.330i	0.880624	−	0.508429i	0.870864	+	0.491524i	$0.163560\pi$
$930$		0			0
$931$	−893.377	+	21.3147i	−0.959589	+	0.0228944i
$932$	−472.039	+	472.039i	−0.506480	+	0.506480i
$933$	251.743	−	939.516i	0.269821	−	1.00698i
$934$	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	$0.413035\pi$
$938$	−27.8248	+	109.029i	−0.0296640	+	0.116235i
$939$			711.582i			0.757808i
$940$		0			0
$941$	18.0898	−	31.3324i	0.0192240	−	0.0332969i	−0.856253	−	0.516556i	$-0.827214\pi$
$941$	18.0898	−	31.3324i	0.0192240	−	0.0332969i	0.875477	+	0.483259i	$0.160547\pi$
$942$	−39.2203	−	146.372i	−0.0416352	−	0.155385i
$943$	−174.249	+	650.307i	−0.184782	+	0.689615i
$944$		−	380.530i		−	0.403104i
$945$		0			0
$946$	171.061			0.180825
$947$	−1460.44	−	391.323i	−1.54217	−	0.413223i	−0.615204	−	0.788368i	$-0.710926\pi$
$947$	−1460.44	−	391.323i	−1.54217	−	0.413223i	−0.926966	+	0.375144i	$0.877593\pi$
$948$	−92.0546	+	24.6659i	−0.0971040	+	0.0260189i
$949$	22.1319	+	12.7779i	0.0233213	+	0.0134646i
$950$		0			0
$951$	211.325			0.222214
$952$	−170.869	+	174.994i	−0.179484	+	0.183817i
$953$	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
$957$	1006.38	+	269.660i	1.05160	+	0.281776i
$958$	−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
$962$	43.5234	+	162.432i	0.0452426	+	0.168848i
$963$	−171.306	+	45.9013i	−0.177888	+	0.0476649i
$964$	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	$0.354301\pi$
$968$	205.593	−	767.284i	0.212390	−	0.792649i
$969$	−533.033	−	307.747i	−0.550086	−	0.317592i
$970$		0			0
$971$	−310.158	−	537.210i	−0.319421	−	0.553254i	0.660946	−	0.750433i	$-0.270155\pi$
$971$	−310.158	−	537.210i	−0.319421	−	0.553254i	−0.980367	+	0.197179i	$0.936822\pi$
$972$	−115.942	+	115.942i	−0.119281	+	0.119281i
$973$	−210.266	+	823.907i	−0.216101	+	0.846769i
$974$		−	555.017i		−	0.569832i
$975$		0			0
$976$	16.9183	−	29.3034i	0.0173344	−	0.0300240i
$977$	−27.6391	−	103.150i	−0.0282897	−	0.105579i	0.950337	−	0.311222i	$-0.100738\pi$
$977$	−27.6391	−	103.150i	−0.0282897	−	0.105579i	−0.978627	+	0.205643i	$0.934071\pi$
$978$	−123.585	+	461.225i	−0.126365	+	0.471600i
$979$			1552.73i			1.58604i
$980$		0			0
$981$	−65.4674			−0.0667354
$982$	137.219	+	36.7677i	0.139734	+	0.0374417i
$983$	−46.9821	+	12.5888i	−0.0477946	+	0.0128065i	−0.282637	−	0.959227i	$-0.591209\pi$
$983$	−46.9821	+	12.5888i	−0.0477946	+	0.0128065i	0.234843	+	0.972033i	$0.424543\pi$
$984$	109.542	+	63.2440i	0.111323	+	0.0642724i
$985$		0			0
$986$	−332.351			−0.337070
$987$	228.907	+	58.4183i	0.231921	+	0.0591878i
$988$	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	−0.989039	−	0.147651i	$-0.952829\pi$
$991$	−363.350	+	629.341i	−0.366650	+	0.635056i	0.622390	+	0.782708i	$0.286162\pi$
$992$	−34.3230	−	9.19682i	−0.0345998	−	0.00927098i
$993$	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
$997$	−352.926	−	1317.14i	−0.353987	−	1.32110i	−0.881754	−	0.471710i	$-0.843637\pi$
$997$	−352.926	−	1317.14i	−0.353987	−	1.32110i	0.527766	−	0.849390i	$-0.323030\pi$
$998$	−539.307	+	144.507i	−0.540388	+	0.144796i
$999$	−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.193.2		16
5.2	odd	4	inner	350.3.p.e.207.3		16
5.3	odd	4		70.3.l.c.67.2	yes	16
5.4	even	2		70.3.l.c.53.3	yes	16
7.2	even	3	inner	350.3.p.e.93.3		16
35.2	odd	12	inner	350.3.p.e.107.2		16
35.3	even	12		490.3.f.p.197.3		8
35.4	even	6		490.3.f.o.393.2		8
35.9	even	6		70.3.l.c.23.2	✓	16
35.18	odd	12		490.3.f.o.197.2		8
35.23	odd	12		70.3.l.c.37.3	yes	16
35.24	odd	6		490.3.f.p.393.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.2	✓	16	35.9	even	6
70.3.l.c.37.3	yes	16	35.23	odd	12
70.3.l.c.53.3	yes	16	5.4	even	2
70.3.l.c.67.2	yes	16	5.3	odd	4
350.3.p.e.93.3		16	7.2	even	3	inner
350.3.p.e.107.2		16	35.2	odd	12	inner
350.3.p.e.193.2		16	1.1	even	1	trivial
350.3.p.e.207.3		16	5.2	odd	4	inner
490.3.f.o.197.2		8	35.18	odd	12
490.3.f.o.393.2		8	35.4	even	6
490.3.f.p.197.3		8	35.3	even	12
490.3.f.p.393.3		8	35.24	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)

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