LMFDB - Embedded newform 17.4.d.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(2,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("17.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, 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:	$1.00303247010$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 $ x^12 + 54x^10 + 1085x^8 + 9836x^6 + 38276x^4 + 49664*x^2 + 16384
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			2.1
Root			$-3.86166i$ of defining polynomial
Character	$\chi$	$=$	17.2
Dual form			17.4.d.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.43772 - 3.43772i) q^{2} +(-4.67995 + 1.93850i) q^{3} +15.6358i q^{4} +(-7.10390 - 17.1503i) q^{5} +(22.7523 + 9.42432i) q^{6} +(5.36561 - 12.9537i) q^{7} +(26.2496 - 26.2496i) q^{8} +(-0.947753 + 0.947753i) q^{9} +O(q^{10})$	\(q+(-3.43772 - 3.43772i) q^{2} +(-4.67995 + 1.93850i) q^{3} +15.6358i q^{4} +(-7.10390 - 17.1503i) q^{5} +(22.7523 + 9.42432i) q^{6} +(5.36561 - 12.9537i) q^{7} +(26.2496 - 26.2496i) q^{8} +(-0.947753 + 0.947753i) q^{9} +(-34.5367 + 83.3791i) q^{10} +(17.9963 + 7.45431i) q^{11} +(-30.3099 - 73.1746i) q^{12} -29.9060i q^{13} +(-62.9767 + 26.0858i) q^{14} +(66.4917 + 66.4917i) q^{15} -55.3912 q^{16} +(-56.0566 - 42.0792i) q^{17} +6.51621 q^{18} +(-32.3771 - 32.3771i) q^{19} +(268.158 - 111.075i) q^{20} +71.0240i q^{21} +(-36.2404 - 87.4920i) q^{22} +(82.5263 + 34.1835i) q^{23} +(-71.9620 + 173.732i) q^{24} +(-155.280 + 155.280i) q^{25} +(-102.808 + 102.808i) q^{26} +(54.9376 - 132.631i) q^{27} +(202.542 + 83.8955i) q^{28} +(-22.1603 - 53.4998i) q^{29} -457.159i q^{30} +(149.621 - 61.9751i) q^{31} +(-19.5778 - 19.5778i) q^{32} -98.6719 q^{33} +(48.0504 + 337.363i) q^{34} -260.277 q^{35} +(-14.8188 - 14.8188i) q^{36} +(125.263 - 51.8855i) q^{37} +222.607i q^{38} +(57.9726 + 139.958i) q^{39} +(-636.664 - 263.715i) q^{40} +(-21.7716 + 52.5612i) q^{41} +(244.160 - 244.160i) q^{42} +(36.8715 - 36.8715i) q^{43} +(-116.554 + 281.386i) q^{44} +(22.9870 + 9.52153i) q^{45} +(-166.189 - 401.215i) q^{46} +482.699i q^{47} +(259.228 - 107.376i) q^{48} +(103.528 + 103.528i) q^{49} +1067.62 q^{50} +(343.912 + 88.2627i) q^{51} +467.603 q^{52} +(-374.747 - 374.747i) q^{53} +(-644.808 + 267.088i) q^{54} -361.597i q^{55} +(-199.185 - 480.875i) q^{56} +(214.286 + 88.7602i) q^{57} +(-107.736 + 260.098i) q^{58} +(198.031 - 198.031i) q^{59} +(-1039.65 + 1039.65i) q^{60} +(224.504 - 542.000i) q^{61} +(-727.408 - 301.302i) q^{62} +(7.19166 + 17.3622i) q^{63} +577.735i q^{64} +(-512.897 + 212.449i) q^{65} +(339.206 + 339.206i) q^{66} -367.471 q^{67} +(657.940 - 876.488i) q^{68} -452.484 q^{69} +(894.759 + 894.759i) q^{70} +(-55.9406 + 23.1713i) q^{71} +49.7563i q^{72} +(-140.861 - 340.067i) q^{73} +(-608.985 - 252.250i) q^{74} +(425.692 - 1027.71i) q^{75} +(506.241 - 506.241i) q^{76} +(193.122 - 193.122i) q^{77} +(281.843 - 680.430i) q^{78} +(201.148 + 83.3181i) q^{79} +(393.493 + 949.976i) q^{80} +691.015i q^{81} +(255.535 - 105.846i) q^{82} +(420.131 + 420.131i) q^{83} -1110.51 q^{84} +(-323.451 + 1260.31i) q^{85} -253.508 q^{86} +(207.418 + 207.418i) q^{87} +(668.069 - 276.723i) q^{88} -887.553i q^{89} +(-46.2905 - 111.755i) q^{90} +(-387.394 - 160.464i) q^{91} +(-534.486 + 1290.36i) q^{92} +(-580.081 + 580.081i) q^{93} +(1659.38 - 1659.38i) q^{94} +(-325.274 + 785.281i) q^{95} +(129.575 + 53.6716i) q^{96} +(338.553 + 817.340i) q^{97} -711.801i q^{98} +(-24.1209 + 9.99120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9} - 116 q^{10} + 40 q^{11} + 56 q^{12} - 132 q^{14} + 244 q^{15} + 184 q^{16} + 52 q^{17} - 12 q^{19} + 572 q^{20} - 620 q^{22} - 276 q^{23} - 184 q^{24} - 464 q^{25} - 708 q^{26} - 664 q^{27} + 452 q^{28} + 632 q^{29} + 188 q^{31} + 700 q^{32} + 1400 q^{33} + 764 q^{34} - 632 q^{35} + 524 q^{36} + 940 q^{37} - 1112 q^{39} - 1864 q^{40} + 176 q^{41} + 48 q^{42} - 1360 q^{43} - 1364 q^{44} - 32 q^{45} + 452 q^{46} - 540 q^{48} + 1044 q^{49} + 2856 q^{50} + 340 q^{51} + 792 q^{52} - 360 q^{53} - 244 q^{54} - 1788 q^{56} - 148 q^{57} - 360 q^{58} - 584 q^{59} - 1792 q^{60} - 1052 q^{61} - 380 q^{62} + 1752 q^{63} + 404 q^{65} + 1372 q^{66} + 1080 q^{67} + 2532 q^{68} - 344 q^{69} + 2072 q^{70} + 28 q^{71} + 824 q^{73} - 2292 q^{74} + 400 q^{75} + 1328 q^{76} - 1252 q^{77} + 1128 q^{78} - 196 q^{79} - 904 q^{80} - 1528 q^{82} - 1008 q^{83} - 4768 q^{84} - 2824 q^{85} - 1200 q^{86} - 2516 q^{87} - 56 q^{88} - 860 q^{90} + 2456 q^{91} + 396 q^{92} - 836 q^{93} + 6360 q^{94} + 2172 q^{95} + 1668 q^{96} - 904 q^{97} + 3280 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9 - 116 * q^10 + 40 * q^11 + 56 * q^12 - 132 * q^14 + 244 * q^15 + 184 * q^16 + 52 * q^17 - 12 * q^19 + 572 * q^20 - 620 * q^22 - 276 * q^23 - 184 * q^24 - 464 * q^25 - 708 * q^26 - 664 * q^27 + 452 * q^28 + 632 * q^29 + 188 * q^31 + 700 * q^32 + 1400 * q^33 + 764 * q^34 - 632 * q^35 + 524 * q^36 + 940 * q^37 - 1112 * q^39 - 1864 * q^40 + 176 * q^41 + 48 * q^42 - 1360 * q^43 - 1364 * q^44 - 32 * q^45 + 452 * q^46 - 540 * q^48 + 1044 * q^49 + 2856 * q^50 + 340 * q^51 + 792 * q^52 - 360 * q^53 - 244 * q^54 - 1788 * q^56 - 148 * q^57 - 360 * q^58 - 584 * q^59 - 1792 * q^60 - 1052 * q^61 - 380 * q^62 + 1752 * q^63 + 404 * q^65 + 1372 * q^66 + 1080 * q^67 + 2532 * q^68 - 344 * q^69 + 2072 * q^70 + 28 * q^71 + 824 * q^73 - 2292 * q^74 + 400 * q^75 + 1328 * q^76 - 1252 * q^77 + 1128 * q^78 - 196 * q^79 - 904 * q^80 - 1528 * q^82 - 1008 * q^83 - 4768 * q^84 - 2824 * q^85 - 1200 * q^86 - 2516 * q^87 - 56 * q^88 - 860 * q^90 + 2456 * q^91 + 396 * q^92 - 836 * q^93 + 6360 * q^94 + 2172 * q^95 + 1668 * q^96 - 904 * q^97 + 3280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−3.43772	−	3.43772i	−1.21542	−	1.21542i	−0.969220	−	0.246196i	$-0.920819\pi$
$2$	−3.43772	−	3.43772i	−1.21542	−	1.21542i	−0.246196	−	0.969220i	$-0.579181\pi$
$3$	−4.67995	+	1.93850i	−0.900656	+	0.373064i	−0.784472	−	0.620164i	$-0.787066\pi$
$3$	−4.67995	+	1.93850i	−0.900656	+	0.373064i	−0.116184	+	0.993228i	$0.537066\pi$
$4$			15.6358i			1.95447i
$5$	−7.10390	−	17.1503i	−0.635392	−	1.53397i	−0.832755	−	0.553641i	$-0.813238\pi$
$5$	−7.10390	−	17.1503i	−0.635392	−	1.53397i	0.197364	−	0.980330i	$-0.436762\pi$
$6$	22.7523	+	9.42432i	1.54810	+	0.641244i
$7$	5.36561	−	12.9537i	0.289716	−	0.699436i	−0.710274	−	0.703925i	$-0.751429\pi$
$7$	5.36561	−	12.9537i	0.289716	−	0.699436i	0.999990	+	0.00448945i	$0.00142904\pi$
$8$	26.2496	−	26.2496i	1.16008	−	1.16008i
$9$	−0.947753	+	0.947753i	−0.0351020	+	0.0351020i
$10$	−34.5367	+	83.3791i	−1.09215	+	2.63668i
$11$	17.9963	+	7.45431i	0.493281	+	0.204324i	0.615435	−	0.788187i	$-0.288980\pi$
$11$	17.9963	+	7.45431i	0.493281	+	0.204324i	−0.122154	+	0.992511i	$0.538980\pi$
$12$	−30.3099	−	73.1746i	−0.729143	−	1.76031i
$13$		−	29.9060i		−	0.638033i	−0.947749	−	0.319016i	$-0.896648\pi$
$13$		−	29.9060i		−	0.638033i	0.947749	−	0.319016i	$-0.103352\pi$
$14$	−62.9767	+	26.0858i	−1.20223	+	0.497980i
$15$	66.4917	+	66.4917i	1.14454	+	1.14454i
$16$	−55.3912			−0.865487
$17$	−56.0566	−	42.0792i	−0.799748	−	0.600335i
$17$	−56.0566	−	42.0792i	−0.799748	−	0.600335i
$18$	6.51621			0.0853269
$19$	−32.3771	−	32.3771i	−0.390938	−	0.390938i	0.484084	−	0.875022i	$-0.339153\pi$
$19$	−32.3771	−	32.3771i	−0.390938	−	0.390938i	−0.875022	+	0.484084i	$0.839153\pi$
$20$	268.158	−	111.075i	2.99810	−	1.24185i
$21$			71.0240i			0.738034i
$22$	−36.2404	−	87.4920i	−0.351203	−	0.847880i
$23$	82.5263	+	34.1835i	0.748171	+	0.309903i	0.723995	−	0.689805i	$-0.242304\pi$
$23$	82.5263	+	34.1835i	0.748171	+	0.309903i	0.0241759	+	0.999708i	$0.492304\pi$
$24$	−71.9620	+	173.732i	−0.612049	+	1.47762i
$25$	−155.280	+	155.280i	−1.24224	+	1.24224i
$26$	−102.808	+	102.808i	−0.775475	+	0.775475i
$27$	54.9376	−	132.631i	0.391584	−	0.945366i
$28$	202.542	+	83.8955i	1.36703	+	0.566241i
$29$	−22.1603	−	53.4998i	−0.141899	−	0.342574i	0.836913	−	0.547336i	$-0.184358\pi$
$29$	−22.1603	−	53.4998i	−0.141899	−	0.342574i	−0.978812	+	0.204762i	$0.934358\pi$
$30$		−	457.159i		−	2.78218i
$31$	149.621	−	61.9751i	0.866863	−	0.359067i	0.0954754	−	0.995432i	$-0.469563\pi$
$31$	149.621	−	61.9751i	0.866863	−	0.359067i	0.771388	+	0.636365i	$0.219563\pi$
$32$	−19.5778	−	19.5778i	−0.108153	−	0.108153i
$33$	−98.6719			−0.520502
$34$	48.0504	+	337.363i	0.242370	+	1.70168i
$35$	−260.277			−1.25700
$36$	−14.8188	−	14.8188i	−0.0686058	−	0.0686058i
$37$	125.263	−	51.8855i	0.556569	−	0.230538i	−0.0866259	−	0.996241i	$-0.527608\pi$
$37$	125.263	−	51.8855i	0.556569	−	0.230538i	0.643195	+	0.765702i	$0.277608\pi$
$38$			222.607i			0.950304i
$39$	57.9726	+	139.958i	0.238027	+	0.574648i
$40$	−636.664	−	263.715i	−2.51663	−	1.04242i
$41$	−21.7716	+	52.5612i	−0.0829304	+	0.200212i	−0.959905	−	0.280324i	$-0.909558\pi$
$41$	−21.7716	+	52.5612i	−0.0829304	+	0.200212i	0.876975	+	0.480536i	$0.159558\pi$
$42$	244.160	−	244.160i	0.897018	−	0.897018i
$43$	36.8715	−	36.8715i	0.130764	−	0.130764i	−0.638695	−	0.769460i	$-0.720526\pi$
$43$	36.8715	−	36.8715i	0.130764	−	0.130764i	0.769460	+	0.638695i	$0.220526\pi$
$44$	−116.554	+	281.386i	−0.399345	+	0.964104i
$45$	22.9870	+	9.52153i	0.0761489	+	0.0315419i
$46$	−166.189	−	401.215i	−0.532678	−	1.28600i
$47$			482.699i			1.49806i	0.662536	+	0.749030i	$0.269480\pi$
$47$			482.699i			1.49806i	−0.662536	+	0.749030i	$0.730520\pi$
$48$	259.228	−	107.376i	0.779506	−	0.322882i
$49$	103.528	+	103.528i	0.301832	+	0.301832i
$50$	1067.62			3.01967
$51$	343.912	+	88.2627i	0.944262	+	0.242338i
$52$	467.603			1.24702
$53$	−374.747	−	374.747i	−0.971234	−	0.971234i	0.0283638	−	0.999598i	$-0.490970\pi$
$53$	−374.747	−	374.747i	−0.971234	−	0.971234i	−0.999598	+	0.0283638i	$0.990970\pi$
$54$	−644.808	+	267.088i	−1.62495	+	0.673076i
$55$		−	361.597i		−	0.886504i
$56$	−199.185	−	480.875i	−0.475308	−	1.14749i
$57$	214.286	+	88.7602i	0.497945	+	0.206256i
$58$	−107.736	+	260.098i	−0.243904	+	0.588836i
$59$	198.031	−	198.031i	0.436973	−	0.436973i	−0.454019	−	0.890992i	$-0.650010\pi$
$59$	198.031	−	198.031i	0.436973	−	0.436973i	0.890992	+	0.454019i	$0.150010\pi$
$60$	−1039.65	+	1039.65i	−2.23697	+	2.23697i
$61$	224.504	−	542.000i	0.471226	−	1.13764i	−0.492397	−	0.870371i	$-0.663879\pi$
$61$	224.504	−	542.000i	0.471226	−	1.13764i	0.963622	−	0.267268i	$-0.0861209\pi$
$62$	−727.408	−	301.302i	−1.49001	−	0.617184i
$63$	7.19166	+	17.3622i	0.0143820	+	0.0347211i
$64$			577.735i			1.12839i
$65$	−512.897	+	212.449i	−0.978724	+	0.405401i
$66$	339.206	+	339.206i	0.632627	+	0.632627i
$67$	−367.471			−0.670056			−0.335028	−	0.942208i	$-0.608746\pi$
$67$	−367.471			−0.670056			−0.335028	+	0.942208i	$0.608746\pi$
$68$	657.940	−	876.488i	1.17334	−	1.56309i
$69$	−452.484			−0.789458
$70$	894.759	+	894.759i	1.52777	+	1.52777i
$71$	−55.9406	+	23.1713i	−0.0935060	+	0.0387314i	−0.428946	−	0.903330i	$-0.641115\pi$
$71$	−55.9406	+	23.1713i	−0.0935060	+	0.0387314i	0.335440	+	0.942062i	$0.391115\pi$
$72$			49.7563i			0.0814421i
$73$	−140.861	−	340.067i	−0.225842	−	0.545231i	0.769821	−	0.638259i	$-0.220345\pi$
$73$	−140.861	−	340.067i	−0.225842	−	0.545231i	−0.995663	+	0.0930283i	$0.970345\pi$
$74$	−608.985	−	252.250i	−0.956663	−	0.396263i
$75$	425.692	−	1027.71i	0.655395	−	1.58226i
$76$	506.241	−	506.241i	0.764077	−	0.764077i
$77$	193.122	−	193.122i	0.285823	−	0.285823i
$78$	281.843	−	680.430i	0.409134	−	0.987738i
$79$	201.148	+	83.3181i	0.286467	+	0.118659i	0.521290	−	0.853380i	$-0.325451\pi$
$79$	201.148	+	83.3181i	0.286467	+	0.118659i	−0.234823	+	0.972038i	$0.575451\pi$
$80$	393.493	+	949.976i	0.549923	+	1.32763i
$81$			691.015i			0.947894i
$82$	255.535	−	105.846i	0.344136	−	0.142546i
$83$	420.131	+	420.131i	0.555606	+	0.555606i	0.928053	−	0.372447i	$-0.121481\pi$
$83$	420.131	+	420.131i	0.555606	+	0.555606i	−0.372447	+	0.928053i	$0.621481\pi$
$84$	−1110.51			−1.44247
$85$	−323.451	+	1260.31i	−0.412743	+	1.60824i
$86$	−253.508			−0.317866
$87$	207.418	+	207.418i	0.255604	+	0.255604i
$88$	668.069	−	276.723i	0.809277	−	0.335213i
$89$		−	887.553i		−	1.05708i	−0.848907	−	0.528542i	$-0.822739\pi$
$89$		−	887.553i		−	1.05708i	0.848907	−	0.528542i	$-0.177261\pi$
$90$	−46.2905	−	111.755i	−0.0542160	−	0.130889i
$91$	−387.394	−	160.464i	−0.446263	−	0.184848i
$92$	−534.486	+	1290.36i	−0.605696	+	1.46228i
$93$	−580.081	+	580.081i	−0.646791	+	0.646791i
$94$	1659.38	−	1659.38i	1.82077	−	1.82077i
$95$	−325.274	+	785.281i	−0.351289	+	0.848086i
$96$	129.575	+	53.6716i	0.137757	+	0.0570607i
$97$	338.553	+	817.340i	0.354380	+	0.855549i	0.996069	+	0.0885841i	$0.0282342\pi$
$97$	338.553	+	817.340i	0.354380	+	0.855549i	−0.641688	+	0.766965i	$0.721766\pi$
$98$		−	711.801i		−	0.733702i
$99$	−24.1209	+	9.99120i	−0.0244873	+	0.0101430i
$100$	−2427.92	−	2427.92i	−2.42792	−	2.42792i
$101$	1845.31			1.81798			0.908988	−	0.416822i	$-0.136856\pi$
$101$	1845.31			1.81798			0.908988	+	0.416822i	$0.136856\pi$
$102$	−878.851	−	1485.69i	−0.853129	−	1.44221i
$103$	−1823.07			−1.74400			−0.872002	−	0.489502i	$-0.837178\pi$
$103$	−1823.07			−1.74400			−0.872002	+	0.489502i	$0.837178\pi$
$104$	−785.020	−	785.020i	−0.740169	−	0.740169i
$105$	1218.08	−	504.547i	1.13212	−	0.468940i
$106$			2576.54i			2.36091i
$107$	710.011	+	1714.12i	0.641490	+	1.54869i	0.824670	+	0.565613i	$0.191361\pi$
$107$	710.011	+	1714.12i	0.641490	+	1.54869i	−0.183181	+	0.983079i	$0.558639\pi$
$108$	2073.79	+	858.992i	1.84769	+	0.765339i
$109$	530.959	−	1281.85i	0.466575	−	1.12641i	−0.499073	−	0.866560i	$-0.666326\pi$
$109$	530.959	−	1281.85i	0.466575	−	1.12641i	0.965648	−	0.259852i	$-0.0836739\pi$
$110$	−1243.07	+	1243.07i	−1.07747	+	1.07747i
$111$	−485.643	+	485.643i	−0.415272	+	0.415272i
$112$	−297.207	+	717.522i	−0.250745	+	0.605352i
$113$	−566.444	−	234.629i	−0.471563	−	0.195328i	0.134230	−	0.990950i	$-0.457144\pi$
$113$	−566.444	−	234.629i	−0.471563	−	0.195328i	−0.605793	+	0.795623i	$0.707144\pi$
$114$	−431.522	−	1041.79i	−0.354524	−	0.855897i
$115$		−	1658.19i		−	1.34458i
$116$	836.510	−	346.494i	0.669552	−	0.277337i
$117$	28.3435	+	28.3435i	0.0223962	+	0.0223962i
$118$	−1361.55			−1.06221
$119$	−845.860	+	500.362i	−0.651596	+	0.385446i
$120$	3490.76			2.65551
$121$	−672.859	−	672.859i	−0.505529	−	0.505529i
$122$	−2635.02	+	1091.46i	−1.95544	+	0.809970i
$123$		−	288.188i		−	0.211260i
$124$	969.029	+	2339.44i	0.701785	+	1.69426i
$125$	1622.40	+	672.020i	1.16089	+	0.480858i
$126$	34.9634	−	84.4092i	0.0247206	−	0.0596807i
$127$	−78.9750	+	78.9750i	−0.0551803	+	0.0551803i	−0.734158	−	0.678978i	$-0.762423\pi$
$127$	−78.9750	+	78.9750i	−0.0551803	+	0.0551803i	0.678978	+	0.734158i	$0.262423\pi$
$128$	1829.47	−	1829.47i	1.26331	−	1.26331i
$129$	−101.081	+	244.032i	−0.0689901	+	0.166557i
$130$	2493.53	+	1032.85i	1.68229	+	0.696826i
$131$	−815.895	−	1969.75i	−0.544161	−	1.31372i	−0.921763	−	0.387753i	$-0.873251\pi$
$131$	−815.895	−	1969.75i	−0.544161	−	1.31372i	0.377602	−	0.925968i	$-0.376749\pi$
$132$		−	1542.81i		−	1.01731i
$133$	−593.127	+	245.681i	−0.386697	+	0.160175i
$134$	1263.26	+	1263.26i	0.814397	+	0.814397i
$135$	−2664.94			−1.69897
$136$	−2576.03	+	366.902i	−1.62421	+	0.231335i
$137$	3087.68			1.92554			0.962769	−	0.270327i	$-0.0871317\pi$
$137$	3087.68			1.92554			0.962769	+	0.270327i	$0.0871317\pi$
$138$	1555.51	+	1555.51i	0.959520	+	0.959520i
$139$	434.062	−	179.794i	0.264868	−	0.109712i	−0.246297	−	0.969194i	$-0.579214\pi$
$139$	434.062	−	179.794i	0.264868	−	0.109712i	0.511165	+	0.859482i	$0.329214\pi$
$140$		−	4069.64i		−	2.45677i
$141$	−935.710	−	2259.00i	−0.558872	−	1.34924i
$142$	271.964	+	112.651i	0.160723	+	0.0665738i
$143$	222.929	−	538.197i	0.130365	−	0.314729i
$144$	52.4971	−	52.4971i	0.0303803	−	0.0303803i
$145$	−760.113	+	760.113i	−0.435338	+	0.435338i
$146$	−684.816	+	1653.29i	−0.388190	+	0.937175i
$147$	−685.196	−	283.818i	−0.384449	−	0.159244i
$148$	811.270	+	1958.58i	0.450581	+	1.08780i
$149$			2209.36i			1.21475i	0.794416	+	0.607374i	$0.207777\pi$
$149$			2209.36i			1.21475i	−0.794416	+	0.607374i	$0.792223\pi$
$150$	−4996.38	+	2069.57i	−2.71969	+	1.12653i
$151$	532.003	+	532.003i	0.286714	+	0.286714i	0.835779	−	0.549065i	$-0.185016\pi$
$151$	532.003	+	532.003i	0.286714	+	0.286714i	−0.549065	+	0.835779i	$0.685016\pi$
$152$	−1699.77			−0.907038
$153$	93.0085	−	13.2471i	0.0491457	−	0.00699979i
$154$	−1327.80			−0.694787
$155$	−2125.79	−	2125.79i	−1.10160	−	1.10160i
$156$	−2188.36	+	906.447i	−1.12313	+	0.465217i
$157$			579.544i			0.294603i	0.989092	+	0.147301i	$0.0470587\pi$
$157$			579.544i			0.294603i	−0.989092	+	0.147301i	$0.952941\pi$
$158$	−405.065	−	977.913i	−0.203957	−	0.492396i
$159$	2480.24	+	1027.35i	1.23708	+	0.512415i
$160$	−196.687	+	474.844i	−0.0971842	+	0.234623i
$161$	885.609	−	885.609i	0.433514	−	0.433514i
$162$	2375.51	−	2375.51i	1.15209	−	1.15209i
$163$	680.311	−	1642.42i	0.326908	−	0.789227i	−0.671910	−	0.740633i	$-0.734526\pi$
$163$	680.311	−	1642.42i	0.326908	−	0.789227i	0.998819	−	0.0485941i	$-0.0154741\pi$
$164$	−821.835	−	340.415i	−0.391308	−	0.162085i
$165$	700.955	+	1692.26i	0.330723	+	0.798436i
$166$		−	2888.58i		−	1.35059i
$167$	2896.21	−	1199.65i	1.34201	−	0.555879i	0.407953	−	0.913003i	$-0.366243\pi$
$167$	2896.21	−	1199.65i	1.34201	−	0.555879i	0.934057	+	0.357124i	$0.116243\pi$
$168$	1864.35	+	1864.35i	0.856178	+	0.856178i
$169$	1302.63			0.592914
$170$	5444.54	−	3220.67i	2.45633	−	1.45302i
$171$	61.3710			0.0274454
$172$	576.515	+	576.515i	0.255575	+	0.255575i
$173$	−1080.32	+	447.482i	−0.474768	+	0.196656i	−0.607220	−	0.794534i	$-0.707715\pi$
$173$	−1080.32	+	447.482i	−0.474768	+	0.196656i	0.132451	+	0.991190i	$0.457715\pi$
$174$		−	1426.09i		−	0.621331i
$175$	1178.28	+	2844.62i	0.508970	+	1.22876i
$176$	−996.836	−	412.903i	−0.426928	−	0.176839i
$177$	−542.891	+	1310.65i	−0.230543	+	0.556581i
$178$	−3051.16	+	3051.16i	−1.28480	+	1.28480i
$179$	−1097.81	+	1097.81i	−0.458404	+	0.458404i	−0.898131	−	0.439727i	$-0.855075\pi$
$179$	−1097.81	+	1097.81i	−0.458404	+	0.458404i	0.439727	+	0.898131i	$0.355075\pi$
$180$	−148.876	+	359.419i	−0.0616477	+	0.148831i
$181$	−1382.05	−	572.462i	−0.567551	−	0.235087i	0.0804087	−	0.996762i	$-0.474377\pi$
$181$	−1382.05	−	572.462i	−0.567551	−	0.235087i	−0.647960	+	0.761675i	$0.724377\pi$
$182$	780.121	+	1883.38i	0.317728	+	0.767062i
$183$			2971.73i			1.20042i
$184$	3063.59	−	1268.98i	1.22745	−	0.508426i
$185$	−1779.71	−	1779.71i	−0.707279	−	0.707279i
$186$	3988.30			1.57224
$187$	−695.141	−	1175.13i	−0.271838	−	0.459542i
$188$	−7547.37			−2.92792
$189$	−1423.29	−	1423.29i	−0.547775	−	0.547775i
$190$	3817.77	−	1581.37i	1.45774	−	0.603815i
$191$			3008.79i			1.13983i	0.821702	+	0.569917i	$0.193025\pi$
$191$			3008.79i			1.13983i	−0.821702	+	0.569917i	$0.806975\pi$
$192$	−1119.94	−	2703.77i	−0.420961	−	1.01629i
$193$	−3597.18	−	1490.00i	−1.34161	−	0.555713i	−0.407666	−	0.913131i	$-0.633657\pi$
$193$	−3597.18	−	1490.00i	−1.34161	−	0.555713i	−0.933945	+	0.357418i	$0.883657\pi$
$194$	1645.93	−	3973.63i	0.609129	−	1.47057i
$195$	1988.50	−	1988.50i	0.730253	−	0.730253i
$196$	−1618.74	+	1618.74i	−0.589921	+	0.589921i
$197$	−362.277	+	874.614i	−0.131021	+	0.316313i	−0.975752	−	0.218878i	$-0.929760\pi$
$197$	−362.277	+	874.614i	−0.131021	+	0.316313i	0.844731	+	0.535191i	$0.179760\pi$
$198$	117.268	+	48.5739i	0.0420902	+	0.0174343i
$199$	675.758	+	1631.42i	0.240720	+	0.581149i	0.997355	−	0.0726889i	$-0.0231580\pi$
$199$	675.758	+	1631.42i	0.240720	+	0.581149i	−0.756635	+	0.653837i	$0.773158\pi$
$200$			8152.07i			2.88219i
$201$	1719.75	−	712.342i	0.603490	−	0.249974i
$202$	−6343.66	−	6343.66i	−2.20960	−	2.20960i
$203$	−811.925			−0.280719
$204$	−1380.06	+	5377.33i	−0.473643	+	1.84553i
$205$	1056.10			0.359812
$206$	6267.19	+	6267.19i	2.11969	+	2.11969i
$207$	−110.612	+	45.8170i	−0.0371404	+	0.0153841i
$208$			1656.53i			0.552209i
$209$	−341.319	−	824.018i	−0.112964	−	0.272720i
$210$	−5921.92	−	2452.94i	−1.94596	−	0.806042i
$211$	−142.128	+	343.127i	−0.0463720	+	0.111952i	−0.945368	−	0.326004i	$-0.894298\pi$
$211$	−142.128	+	343.127i	−0.0463720	+	0.111952i	0.898996	+	0.437956i	$0.144298\pi$
$212$	5859.45	−	5859.45i	1.89825	−	1.89825i
$213$	216.881	−	216.881i	0.0697674	−	0.0697674i
$214$	3451.84	−	8333.47i	1.10263	−	2.66198i
$215$	−894.290	−	370.427i	−0.283675	−	0.117502i
$216$	−2039.43	−	4923.61i	−0.642432	−	1.55097i
$217$		−	2270.69i		−	0.710342i
$218$	−6231.92	+	2581.35i	−1.93614	+	0.801976i
$219$	1318.44	+	1318.44i	0.406812	+	0.406812i
$220$	5653.85			1.73265
$221$	−1258.42	+	1676.43i	−0.383033	+	0.510266i
$222$	3339.00			1.00946
$223$	1820.02	+	1820.02i	0.546536	+	0.546536i	0.925437	−	0.378901i	$-0.123698\pi$
$223$	1820.02	+	1820.02i	0.546536	+	0.546536i	−0.378901	+	0.925437i	$0.623698\pi$
$224$	−358.653	+	148.559i	−0.106980	+	0.0443125i
$225$		−	294.334i		−	0.0872100i
$226$	1140.69	+	2753.86i	0.335740	+	0.810549i
$227$	−4808.47	−	1991.73i	−1.40594	−	0.582361i	−0.454657	−	0.890666i	$-0.650238\pi$
$227$	−4808.47	−	1991.73i	−1.40594	−	0.582361i	−0.951288	+	0.308305i	$0.900238\pi$
$228$	−1387.83	+	3350.53i	−0.403121	+	0.973220i
$229$	−2261.84	+	2261.84i	−0.652694	+	0.652694i	−0.953641	−	0.300947i	$-0.902697\pi$
$229$	−2261.84	+	2261.84i	−0.652694	+	0.652694i	0.300947	+	0.953641i	$0.402697\pi$
$230$	−5700.38	+	5700.38i	−1.63423	+	1.63423i
$231$	−529.435	+	1278.17i	−0.150798	+	0.364058i
$232$	−1986.05	−	822.648i	−0.562027	−	0.232799i
$233$	326.467	+	788.162i	0.0917923	+	0.221606i	0.963107	−	0.269118i	$-0.0867322\pi$
$233$	326.467	+	788.162i	0.0917923	+	0.221606i	−0.871315	+	0.490724i	$0.836732\pi$
$234$		−	194.873i		−	0.0544414i
$235$	8278.44	−	3429.04i	2.29798	−	0.951855i
$236$	3096.36	+	3096.36i	0.854051	+	0.854051i
$237$	−1102.87			−0.302276
$238$	4627.93	+	1187.73i	1.26044	+	0.323482i
$239$	1892.67			0.512246			0.256123	−	0.966644i	$-0.417555\pi$
$239$	1892.67			0.512246			0.256123	+	0.966644i	$0.417555\pi$
$240$	−3683.05	−	3683.05i	−0.990583	−	0.990583i
$241$	1708.64	−	707.742i	0.456694	−	0.189169i	−0.142464	−	0.989800i	$-0.545502\pi$
$241$	1708.64	−	707.742i	0.456694	−	0.189169i	0.599157	+	0.800631i	$0.295502\pi$
$242$			4626.19i			1.22886i
$243$	143.786	+	347.130i	0.0379584	+	0.0916396i
$244$	8474.59	+	3510.29i	2.22348	+	0.920997i
$245$	1040.09	−	2511.00i	0.271220	−	0.654783i
$246$	−990.708	+	990.708i	−0.256769	+	0.256769i
$247$	−968.269	+	968.269i	−0.249431	+	0.249431i
$248$	2300.67	−	5554.32i	0.589085	−	1.42218i
$249$	−2780.61	−	1151.77i	−0.707687	−	0.293134i
$250$	−3267.13	−	7887.56i	−0.826527	−	1.99541i
$251$		−	1026.39i		−	0.258109i	−0.991637	−	0.129055i	$-0.958806\pi$
$251$		−	1026.39i		−	0.258109i	0.991637	−	0.129055i	$-0.0411942\pi$
$252$	−271.471	+	112.447i	−0.0678615	+	0.0281091i
$253$	1230.35	+	1230.35i	0.305738	+	0.305738i
$254$	542.987			0.134134
$255$	−929.383	−	6525.22i	−0.228236	−	1.60245i
$256$	−7956.49			−1.94250
$257$	1849.68	+	1849.68i	0.448949	+	0.448949i	0.895005	−	0.446056i	$-0.147172\pi$
$257$	1849.68	+	1849.68i	0.448949	+	0.448949i	−0.446056	+	0.895005i	$0.647172\pi$
$258$	1186.40	−	491.424i	0.286288	−	0.118584i
$259$		−	1901.02i		−	0.456075i
$260$	−3321.80	−	8019.54i	−0.792344	−	1.91289i
$261$	71.7070	+	29.7020i	0.0170060	+	0.00704410i
$262$	−3966.61	+	9576.24i	−0.935335	+	2.25810i
$263$	3529.99	−	3529.99i	0.827637	−	0.827637i	−0.159553	−	0.987189i	$-0.551005\pi$
$263$	3529.99	−	3529.99i	0.827637	−	0.827637i	0.987189	+	0.159553i	$0.0510052\pi$
$264$	−2590.10	+	2590.10i	−0.603824	+	0.603824i
$265$	−3764.86	+	9089.18i	−0.872731	+	2.10696i
$266$	2883.59	+	1194.42i	0.664677	+	0.275318i
$267$	1720.52	+	4153.70i	0.394360	+	0.952069i
$268$		−	5745.70i		−	1.30961i
$269$	−3150.91	+	1305.15i	−0.714181	+	0.295823i	−0.710033	−	0.704168i	$-0.751320\pi$
$269$	−3150.91	+	1305.15i	−0.714181	+	0.295823i	−0.00414728	+	0.999991i	$0.501320\pi$
$270$	9161.30	+	9161.30i	2.06496	+	2.06496i
$271$	−75.0911			−0.0168319			−0.00841597	−	0.999965i	$-0.502679\pi$
$271$	−75.0911			−0.0168319			−0.00841597	+	0.999965i	$0.502679\pi$
$272$	3105.04	+	2330.81i	0.692172	+	0.519582i
$273$	2124.04			0.470889
$274$	−10614.6	−	10614.6i	−2.34033	−	2.34033i
$275$	−3951.97	+	1636.96i	−0.866591	+	0.358954i
$276$		−	7074.93i		−	1.54297i
$277$	−1317.15	−	3179.88i	−0.285704	−	0.689750i	0.714245	−	0.699896i	$-0.246770\pi$
$277$	−1317.15	−	3179.88i	−0.285704	−	0.689750i	−0.999949	+	0.0101463i	$0.996770\pi$
$278$	−2110.26	−	874.099i	−0.455270	−	0.188579i
$279$	−83.0668	+	200.541i	−0.0178247	+	0.0430325i
$280$	−6832.18	+	6832.18i	−1.45822	+	1.45822i
$281$	1183.03	−	1183.03i	0.251151	−	0.251151i	−0.570291	−	0.821443i	$-0.693170\pi$
$281$	1183.03	−	1183.03i	0.251151	−	0.251151i	0.821443	+	0.570291i	$0.193170\pi$
$282$	−4549.11	+	10982.5i	−0.960622	+	2.31915i
$283$	6275.19	+	2599.27i	1.31810	+	0.545973i	0.927236	−	0.374477i	$-0.122178\pi$
$283$	6275.19	+	2599.27i	1.31810	+	0.545973i	0.390860	+	0.920450i	$0.372178\pi$
$284$	−362.302	−	874.674i	−0.0756995	−	0.182755i
$285$		−	4305.62i		−	0.894887i
$286$	−2616.53	+	1083.80i	−0.540975	+	0.224079i
$287$	564.046	+	564.046i	0.116009	+	0.116009i
$288$	37.1098			0.00759277
$289$	1371.69	+	4717.63i	0.279195	+	0.960234i
$290$	5226.11			1.05823
$291$	−3168.82	−	3168.82i	−0.638349	−	0.638349i
$292$	5317.22	−	2202.46i	1.06564	−	0.441402i
$293$		−	6436.90i		−	1.28344i	−0.766939	−	0.641720i	$-0.778221\pi$
$293$		−	6436.90i		−	1.28344i	0.766939	−	0.641720i	$-0.221779\pi$
$294$	1379.83	+	3331.19i	0.273718	+	0.660813i
$295$	−4803.08	−	1989.50i	−0.947952	−	0.392655i
$296$	1926.12	−	4650.07i	0.378221	−	0.913107i
$297$	1977.35	−	1977.35i	0.386321	−	0.386321i
$298$	7595.14	−	7595.14i	1.47643	−	1.47643i
$299$	1022.29	−	2468.03i	0.197728	−	0.477357i
$300$	16069.0	+	6656.02i	3.09249	+	1.28095i
$301$	−279.786	−	675.462i	−0.0535767	−	0.129346i
$302$		−	3657.75i		−	0.696953i
$303$	−8635.97	+	3577.14i	−1.63737	+	0.678221i
$304$	1793.41	+	1793.41i	0.338352	+	0.338352i
$305$	−10890.3			−2.04452
$306$	−365.276	−	274.197i	−0.0682401	−	0.0512248i
$307$	5129.87			0.953672			0.476836	−	0.878992i	$-0.341784\pi$
$307$	5129.87			0.953672			0.476836	+	0.878992i	$0.341784\pi$
$308$	3019.62	+	3019.62i	0.558632	+	0.558632i
$309$	8531.87	−	3534.02i	1.57075	−	0.650625i
$310$			14615.7i			2.67779i
$311$	−1309.80	−	3162.14i	−0.238816	−	0.576554i	0.758344	−	0.651854i	$-0.226009\pi$
$311$	−1309.80	−	3162.14i	−0.238816	−	0.576554i	−0.997161	+	0.0753000i	$0.976009\pi$
$312$	5195.61	+	2152.09i	0.942768	+	0.390507i
$313$	−1639.23	+	3957.46i	−0.296022	+	0.714661i	0.703968	+	0.710232i	$0.251410\pi$
$313$	−1639.23	+	3957.46i	−0.296022	+	0.714661i	−0.999990	+	0.00442950i	$0.998590\pi$
$314$	1992.31	−	1992.31i	0.358065	−	0.358065i
$315$	246.679	−	246.679i	0.0441231	−	0.0441231i
$316$	−1302.74	+	3145.10i	−0.231915	+	0.559892i
$317$	360.637	+	149.381i	0.0638971	+	0.0264670i	0.414403	−	0.910093i	$-0.363990\pi$
$317$	360.637	+	149.381i	0.0638971	+	0.0264670i	−0.350506	+	0.936560i	$0.613990\pi$
$318$	−4994.62	−	12058.1i	−0.880769	−	2.12636i
$319$		−	1127.99i		−	0.197979i
$320$	9908.34	−	4104.17i	1.73092	−	0.716969i
$321$	−6645.63	−	6645.63i	−1.15552	−	1.15552i
$322$	−6088.94			−1.05380
$323$	452.549	+	3177.35i	0.0779582	+	0.547346i
$324$	−10804.5			−1.85263
$325$	4643.79	+	4643.79i	0.792589	+	0.792589i
$326$	−7984.87	+	3307.44i	−1.35657	+	0.561909i
$327$			7028.25i			1.18857i
$328$	808.216	+	1951.21i	0.136056	+	0.328467i
$329$	6252.75	+	2589.97i	1.04780	+	0.434012i
$330$	3407.81	−	8227.18i	0.568466	−	1.37240i
$331$	−2704.60	+	2704.60i	−0.449119	+	0.449119i	−0.895062	−	0.445942i	$-0.852869\pi$
$331$	−2704.60	+	2704.60i	−0.449119	+	0.449119i	0.445942	+	0.895062i	$0.352869\pi$
$332$	−6569.07	+	6569.07i	−1.08592	+	1.08592i
$333$	−69.5434	+	167.893i	−0.0114443	+	0.0276290i
$334$	−14080.4	−	5832.30i	−2.30672	−	0.955477i
$335$	2610.48	+	6302.25i	0.425748	+	1.02785i
$336$		−	3934.10i		−	0.638758i
$337$	2195.97	−	909.601i	0.354962	−	0.147030i	−0.198075	−	0.980187i	$-0.563469\pi$
$337$	2195.97	−	909.601i	0.354962	−	0.147030i	0.553037	+	0.833157i	$0.313469\pi$
$338$	−4478.08	−	4478.08i	−0.720638	−	0.720638i
$339$	3105.76			0.497586
$340$	−19706.0	−	5057.41i	−3.14326	−	0.806695i
$341$	3154.61			0.500973
$342$	−210.976	−	210.976i	−0.0333575	−	0.0333575i
$343$	6339.70	−	2625.99i	0.997993	−	0.413382i
$344$		−	1935.73i		−	0.303394i
$345$	3214.40	+	7760.24i	0.501615	+	1.21101i
$346$	5252.13	+	2175.51i	0.816059	+	0.338023i
$347$	−4562.82	+	11015.6i	−0.705893	+	1.70418i	0.00412480	+	0.999991i	$0.498687\pi$
$347$	−4562.82	+	11015.6i	−0.705893	+	1.70418i	−0.710017	+	0.704184i	$0.751313\pi$
$348$	−3243.14	+	3243.14i	−0.499571	+	0.499571i
$349$	−5225.48	+	5225.48i	−0.801471	+	0.801471i	−0.983326	−	0.181854i	$-0.941790\pi$
$349$	−5225.48	+	5225.48i	−0.801471	+	0.801471i	0.181854	+	0.983326i	$0.441790\pi$
$350$	5728.41	−	13829.6i	0.874847	−	2.11207i
$351$	−3966.46	−	1642.96i	−0.603174	−	0.249843i
$352$	−206.389	−	498.267i	−0.0312516	−	0.0754481i
$353$		−	2966.18i		−	0.447235i	−0.974677	−	0.223617i	$-0.928213\pi$
$353$		−	2966.18i		−	0.447235i	0.974677	−	0.223617i	$-0.0717866\pi$
$354$	6371.96	−	2639.35i	0.956684	−	0.396271i
$355$	794.792	+	794.792i	0.118826	+	0.118826i
$356$	13877.6			2.06604
$357$	2988.63	−	3981.36i	0.443068	−	0.590241i
$358$	7547.93			1.11430
$359$	−4614.81	−	4614.81i	−0.678441	−	0.678441i	0.281206	−	0.959647i	$-0.409265\pi$
$359$	−4614.81	−	4614.81i	−0.678441	−	0.678441i	−0.959647	+	0.281206i	$0.909265\pi$
$360$	853.336	−	353.463i	0.124930	−	0.0517476i
$361$		−	4762.44i		−	0.694335i
$362$	2783.12	+	6719.05i	0.404082	+	0.975539i
$363$	4453.28	+	1844.61i	0.643902	+	0.266713i
$364$	2508.97	−	6057.20i	0.361280	−	0.872208i
$365$	−4831.61	+	4831.61i	−0.692871	+	0.692871i
$366$	10216.0	−	10216.0i	1.45901	−	1.45901i
$367$	2256.50	−	5447.66i	0.320949	−	0.774838i	−0.678251	−	0.734831i	$-0.737262\pi$
$367$	2256.50	−	5447.66i	0.320949	−	0.774838i	0.999199	−	0.0400079i	$-0.0127383\pi$
$368$	−4571.23	−	1893.47i	−0.647532	−	0.268217i
$369$	−29.1810	−	70.4491i	−0.00411680	−	0.00993884i
$370$			12236.2i			1.71928i
$371$	−6865.11	+	2843.62i	−0.960697	+	0.397934i
$372$	−9070.01	−	9070.01i	−1.26413	−	1.26413i
$373$	9234.98			1.28195			0.640977	−	0.767560i	$-0.278529\pi$
$373$	9234.98			1.28195			0.640977	+	0.767560i	$0.278529\pi$
$374$	−1650.08	+	6429.47i	−0.228138	+	0.888930i
$375$	−8895.45			−1.22496
$376$	12670.6	+	12670.6i	1.73787	+	1.73787i
$377$	−1599.96	+	662.726i	−0.218574	+	0.0905361i
$378$			9785.77i			1.33155i
$379$	−554.759	−	1339.31i	−0.0751875	−	0.181519i	0.881817	−	0.471592i	$-0.156320\pi$
$379$	−554.759	−	1339.31i	−0.0751875	−	0.181519i	−0.957005	+	0.290073i	$0.906320\pi$
$380$	−12278.5	−	5085.91i	−1.65756	−	0.686584i
$381$	216.506	−	522.692i	0.0291127	−	0.0702843i
$382$	10343.4	−	10343.4i	1.38537	−	1.38537i
$383$	5769.34	−	5769.34i	0.769711	−	0.769711i	−0.208344	−	0.978056i	$-0.566808\pi$
$383$	5769.34	−	5769.34i	0.769711	−	0.769711i	0.978056	+	0.208344i	$0.0668075\pi$
$384$	−5015.39	+	12108.2i	−0.666512	+	1.60910i
$385$	−4684.03	−	1940.19i	−0.620053	−	0.256834i
$386$	7243.89	+	17488.3i	0.955192	+	2.30604i
$387$			69.8902i			0.00918015i
$388$	−12779.7	+	5293.54i	−1.67215	+	0.692626i
$389$	1037.93	+	1037.93i	0.135283	+	0.135283i	0.771506	−	0.636222i	$-0.219504\pi$
$389$	1037.93	+	1037.93i	0.135283	+	0.135283i	−0.636222	+	0.771506i	$0.719504\pi$
$390$	−13671.8			−1.77512
$391$	−3187.73	−	5388.85i	−0.412303	−	0.696998i
$392$	5435.15			0.700298
$393$	7636.69	+	7636.69i	0.980204	+	0.980204i
$394$	4252.08	−	1761.27i	0.543697	−	0.225207i
$395$		−	4041.63i		−	0.514827i
$396$	−156.220	−	377.149i	−0.0198241	−	0.0478597i
$397$	−5560.11	−	2303.07i	−0.702907	−	0.291154i	0.00245887	−	0.999997i	$-0.499217\pi$
$397$	−5560.11	−	2303.07i	−0.702907	−	0.291154i	−0.705366	+	0.708843i	$0.749217\pi$
$398$	3285.31	−	7931.43i	0.413763	−	0.998912i
$399$	2299.55	−	2299.55i	0.288525	−	0.288525i
$400$	8601.13	−	8601.13i	1.07514	−	1.07514i
$401$	2257.50	−	5450.08i	0.281132	−	0.678713i	−0.718730	−	0.695289i	$-0.755276\pi$
$401$	2257.50	−	5450.08i	0.281132	−	0.678713i	0.999863	+	0.0165756i	$0.00527641\pi$
$402$	−8360.83	−	3463.17i	−1.03731	−	0.429670i
$403$	−1853.43	−	4474.57i	−0.229096	−	0.553087i
$404$			28852.9i			3.55318i
$405$	11851.1	−	4908.90i	1.45404	−	0.602284i
$406$	2791.17	+	2791.17i	0.341190	+	0.341190i
$407$	2641.04			0.321649
$408$	11344.4	−	6710.70i	1.37655	−	0.814287i
$409$	−9261.09			−1.11964			−0.559818	−	0.828616i	$-0.689129\pi$
$409$	−9261.09			−1.11964			−0.559818	+	0.828616i	$0.689129\pi$
$410$	−3630.59	−	3630.59i	−0.437322	−	0.437322i
$411$	−14450.2	+	5985.47i	−1.73425	+	0.718349i
$412$		−	28505.1i		−	3.40861i
$413$	−1502.68	−	3627.79i	−0.179036	−	0.432232i
$414$	537.759	+	222.747i	0.0638391	+	0.0264430i
$415$	4220.81	−	10189.9i	0.499257	−	1.20531i
$416$	−585.493	+	585.493i	−0.0690052	+	0.0690052i
$417$	−1682.86	+	1682.86i	−0.197625	+	0.197625i
$418$	−1659.38	+	4006.10i	−0.194170	+	0.468767i
$419$	7888.15	+	3267.38i	0.919716	+	0.380959i	0.791768	−	0.610822i	$-0.209161\pi$
$419$	7888.15	+	3267.38i	0.919716	+	0.380959i	0.127948	+	0.991781i	$0.459161\pi$
$420$	7888.98	+	19045.7i	0.916531	+	2.21270i
$421$			1617.31i			0.187228i	0.995609	+	0.0936140i	$0.0298420\pi$
$421$			1617.31i			0.187228i	−0.995609	+	0.0936140i	$0.970158\pi$
$422$	1668.17	−	690.978i	0.192429	−	0.0797068i
$423$	−457.479	−	457.479i	−0.0525848	−	0.0525848i
$424$	−19673.9			−2.25342
$425$	15238.5	−	2170.41i	1.73924	−	0.247719i
$426$	−1491.15			−0.169593
$427$	−5816.32	−	5816.32i	−0.659184	−	0.659184i
$428$	−26801.6	+	11101.6i	−3.02688	+	1.25377i
$429$			2950.88i			0.332097i
$430$	1800.89	+	4347.74i	0.201969	+	0.487597i
$431$	2343.97	+	970.905i	0.261961	+	0.108508i	0.509799	−	0.860294i	$-0.329720\pi$
$431$	2343.97	+	970.905i	0.261961	+	0.108508i	−0.247838	+	0.968802i	$0.579720\pi$
$432$	−3043.06	+	7346.60i	−0.338910	+	0.818202i
$433$	−1296.36	+	1296.36i	−0.143878	+	0.143878i	−0.775377	−	0.631499i	$-0.782440\pi$
$433$	−1296.36	+	1296.36i	−0.143878	+	0.143878i	0.631499	+	0.775377i	$0.282440\pi$
$434$	−7805.98	+	7805.98i	−0.863361	+	0.863361i
$435$	2083.81	−	5030.77i	0.229681	−	0.554498i
$436$	20042.7	+	8301.96i	2.20154	+	0.911908i
$437$	−1565.20	−	3778.73i	−0.171336	−	0.413641i
$438$		−	9064.84i		−	0.988892i
$439$	−9607.00	+	3979.35i	−1.04446	+	0.432629i	−0.837911	−	0.545808i	$-0.816223\pi$
$439$	−9607.00	+	3979.35i	−1.04446	+	0.432629i	−0.206548	+	0.978436i	$0.566223\pi$
$440$	−9491.78	−	9491.78i	−1.02842	−	1.02842i
$441$	−196.238			−0.0211898
$442$	10089.2	−	1436.99i	1.08573	−	0.154640i
$443$	−3984.14			−0.427296			−0.213648	−	0.976911i	$-0.568535\pi$
$443$	−3984.14			−0.427296			−0.213648	+	0.976911i	$0.568535\pi$
$444$	−7593.40	−	7593.40i	−0.811637	−	0.811637i
$445$	−15221.8	+	6305.09i	−1.62154	+	0.671662i
$446$		−	12513.4i		−	1.32854i
$447$	−4282.83	−	10339.7i	−0.453179	−	1.09407i
$448$	7483.82	+	3099.90i	0.789235	+	0.326912i
$449$	5045.33	−	12180.5i	0.530298	−	1.28025i	−0.401027	−	0.916066i	$-0.631347\pi$
$449$	5045.33	−	12180.5i	0.530298	−	1.28025i	0.931326	−	0.364187i	$-0.118653\pi$
$450$	−1011.84	+	1011.84i	−0.105996	+	0.105996i
$451$	−783.616	+	783.616i	−0.0818160	+	0.0818160i
$452$	3668.60	−	8856.79i	0.381762	−	0.921656i
$453$	−3521.03	−	1458.46i	−0.365193	−	0.151268i
$454$	9683.14	+	23377.2i	1.00100	+	2.41662i
$455$			7783.85i			0.802005i
$456$	7954.85	−	3295.01i	0.816929	−	0.338383i
$457$	11484.8	+	11484.8i	1.17557	+	1.17557i	0.980862	+	0.194706i	$0.0623754\pi$
$457$	11484.8	+	11484.8i	1.17557	+	1.17557i	0.194706	+	0.980862i	$0.437625\pi$
$458$	15551.2			1.58659
$459$	−8660.63	+	5123.12i	−0.880705	+	0.520974i
$460$	25927.1			2.62795
$461$	7816.84	+	7816.84i	0.789732	+	0.789732i	0.981450	−	0.191718i	$-0.0614058\pi$
$461$	7816.84	+	7816.84i	0.789732	+	0.789732i	−0.191718	+	0.981450i	$0.561406\pi$
$462$	6214.03	−	2573.94i	0.625764	−	0.259200i
$463$			14185.7i			1.42390i	0.702228	+	0.711952i	$0.252189\pi$
$463$			14185.7i			1.42390i	−0.702228	+	0.711952i	$0.747811\pi$
$464$	1227.49	+	2963.41i	0.122812	+	0.296494i
$465$	14069.4	+	5827.74i	1.40312	+	0.581193i
$466$	1587.18	−	3831.78i	0.157778	−	0.380909i
$467$	−6851.43	+	6851.43i	−0.678900	+	0.678900i	−0.959751	−	0.280851i	$-0.909383\pi$
$467$	−6851.43	+	6851.43i	−0.678900	+	0.678900i	0.280851	+	0.959751i	$0.409383\pi$
$468$	−443.172	+	443.172i	−0.0437727	+	0.0437727i
$469$	−1971.71	+	4760.13i	−0.194126	+	0.468661i
$470$	−40247.0	−	16670.8i	−3.94990	−	1.63610i
$471$	−1123.44	−	2712.23i	−0.109906	−	0.265336i
$472$		−	10396.5i		−	1.01385i
$473$	938.404	−	388.699i	0.0912217	−	0.0377852i
$474$	3791.36	+	3791.36i	0.367390	+	0.367390i
$475$	10055.0			0.971276
$476$	−7823.54	−	13225.7i	−0.753343	−	1.27352i
$477$	710.334			0.0681844
$478$	−6506.47	−	6506.47i	−0.622592	−	0.622592i
$479$	12229.4	−	5065.58i	1.16655	−	0.483199i	0.286497	−	0.958081i	$-0.407509\pi$
$479$	12229.4	−	5065.58i	1.16655	−	0.483199i	0.880049	+	0.474882i	$0.157509\pi$
$480$		−	2603.52i		−	0.247571i
$481$	−1551.69	−	3746.10i	−0.147091	−	0.355109i
$482$	−8306.83	−	3440.80i	−0.784992	−	0.325154i
$483$	−2427.85	+	5861.35i	−0.228719	+	0.552175i
$484$	10520.7	−	10520.7i	0.988042	−	0.988042i
$485$	11612.6	−	11612.6i	1.08722	−	1.08722i
$486$	699.040	−	1687.63i	0.0652450	−	0.157515i
$487$	17831.1	+	7385.89i	1.65915	+	0.687242i	0.998012	−	0.0630247i	$-0.0200747\pi$
$487$	17831.1	+	7385.89i	1.65915	+	0.687242i	0.661136	+	0.750266i	$0.270075\pi$
$488$	−8334.15	−	20120.4i	−0.773093	−	1.86641i
$489$			9005.20i			0.832780i
$490$	−12207.6	+	5056.56i	−1.12548	+	0.466188i
$491$	51.1031	+	51.1031i	0.00469705	+	0.00469705i	0.709451	−	0.704754i	$-0.248943\pi$
$491$	51.1031	+	51.1031i	0.00469705	+	0.00469705i	−0.704754	+	0.709451i	$0.748943\pi$
$492$	4506.04			0.412902
$493$	−1008.99	+	3931.50i	−0.0921760	+	0.359160i
$494$	6657.27			0.606325
$495$	342.705	+	342.705i	0.0311180	+	0.0311180i
$496$	−8287.69	+	3432.87i	−0.750259	+	0.310767i
$497$			848.967i			0.0766225i
$498$	5599.50	+	13518.4i	0.503855	+	1.21641i
$499$	−13678.5	−	5665.84i	−1.22713	−	0.508292i	−0.327457	−	0.944866i	$-0.606192\pi$
$499$	−13678.5	−	5665.84i	−1.22713	−	0.508292i	−0.899668	+	0.436574i	$0.856192\pi$
$500$	−10507.5	+	25367.5i	−0.939824	+	2.26894i
$501$	−11228.6	+	11228.6i	−1.00131	+	1.00131i
$502$	−3528.45	+	3528.45i	−0.313710	+	0.313710i
$503$	2561.65	−	6184.36i	0.227074	−	0.548205i	−0.768745	−	0.639555i	$-0.779118\pi$
$503$	2561.65	−	6184.36i	0.227074	−	0.548205i	0.995819	+	0.0913508i	$0.0291184\pi$
$504$	644.529	+	266.973i	0.0569635	+	0.0235951i
$505$	−13108.9	−	31647.7i	−1.15513	−	2.78872i
$506$		−	8459.22i		−	0.743198i
$507$	−6096.25	+	2525.15i	−0.534012	+	0.221195i
$508$	−1234.84	−	1234.84i	−0.107848	−	0.107848i
$509$	−4414.17			−0.384390			−0.192195	−	0.981357i	$-0.561561\pi$
$509$	−4414.17			−0.384390			−0.192195	+	0.981357i	$0.561561\pi$
$510$	−19236.9	+	25626.8i	−1.67024	+	2.22505i
$511$	−5160.94			−0.446784
$512$	12716.4	+	12716.4i	1.09764	+	1.09764i
$513$	−6072.94	+	2515.49i	−0.522664	+	0.216495i
$514$		−	12717.4i		−	1.09132i
$515$	12950.9	+	31266.2i	1.10813	+	2.67525i
$516$	−3815.63	−	1580.49i	−0.325531	−	0.134839i
$517$	−3598.19	+	8686.79i	−0.306089	+	0.738965i
$518$	−6535.15	+	6535.15i	−0.554321	+	0.554321i
$519$	4188.38	−	4188.38i	0.354238	−	0.354238i
$520$	−7886.64	+	19040.0i	−0.665100	+	1.60569i
$521$	−1064.38	−	440.882i	−0.0895037	−	0.0370736i	0.337482	−	0.941332i	$-0.390425\pi$
$521$	−1064.38	−	440.882i	−0.0895037	−	0.0370736i	−0.426986	+	0.904258i	$0.640425\pi$
$522$	−144.401	−	348.615i	−0.0121078	−	0.0292308i
$523$		−	8548.79i		−	0.714747i	−0.933962	−	0.357373i	$-0.883672\pi$
$523$		−	8548.79i		−	0.714747i	0.933962	−	0.357373i	$-0.116328\pi$
$524$	30798.5	−	12757.2i	2.56763	−	1.06355i
$525$	−11028.6	−	11028.6i	−0.916814	−	0.916814i
$526$	−24270.2			−2.01185
$527$	−10995.1	−	2821.82i	−0.908833	−	0.233246i
$528$	5465.55			0.450488
$529$	−2961.28	−	2961.28i	−0.243387	−	0.243387i
$530$	44188.5	−	18303.5i	3.62156	−	1.50010i
$531$			375.368i			0.0306772i
$532$	−3841.42	−	9274.00i	−0.313058	−	0.755788i
$533$	1571.89	+	651.100i	0.127742	+	0.0529123i
$534$	8364.59	−	20193.9i	0.677849	−	1.63647i
$535$	24353.8	−	24353.8i	1.96805	−	1.96805i
$536$	−9645.98	+	9645.98i	−0.777319	+	0.777319i
$537$	3009.59	−	7265.80i	0.241850	−	0.583878i
$538$	15318.7	+	6345.20i	1.22757	+	0.508478i
$539$	1091.39	+	2634.86i	0.0872165	+	0.210559i
$540$		−	41668.4i		−	3.32060i
$541$	−1681.96	+	696.690i	−0.133666	+	0.0553661i	−0.448514	−	0.893776i	$-0.648046\pi$
$541$	−1681.96	+	696.690i	−0.133666	+	0.0553661i	0.314848	+	0.949142i	$0.398046\pi$
$542$	258.142	+	258.142i	0.0204578	+	0.0204578i
$543$	7577.62			0.598871
$544$	273.647	+	1921.28i	0.0215672	+	0.151423i
$545$	−25756.0			−2.02434
$546$	−7301.85	−	7301.85i	−0.572327	−	0.572327i
$547$	−76.4832	+	31.6804i	−0.00597840	+	0.00247633i	−0.385671	−	0.922637i	$-0.626030\pi$
$547$	−76.4832	+	31.6804i	−0.00597840	+	0.00247633i	0.379692	+	0.925113i	$0.376030\pi$
$548$			48278.3i			3.76341i
$549$	300.908	+	726.456i	0.0233924	+	0.0564743i
$550$	19213.1	+	7958.34i	1.48955	+	0.616991i
$551$	−1014.68	+	2449.65i	−0.0784516	+	0.189399i
$552$	−11877.5	+	11877.5i	−0.915835	+	0.915835i
$553$	2158.56	−	2158.56i	0.165988	−	0.165988i
$554$	−6403.54	+	15459.5i	−0.491084	+	1.18558i
$555$	11778.9	+	4878.97i	0.900875	+	0.373155i
$556$	2811.22	+	6786.89i	0.214429	+	0.517677i
$557$			12671.9i			0.963963i	0.876181	+	0.481981i	$0.160083\pi$
$557$			12671.9i			0.963963i	−0.876181	+	0.481981i	$0.839917\pi$
$558$	974.963	−	403.843i	0.0739668	−	0.0306380i
$559$	−1102.68	−	1102.68i	−0.0834318	−	0.0834318i
$560$	14417.1			1.08791
$561$	5531.21	+	4152.03i	0.416271	+	0.312476i
$562$	−8133.82			−0.610506
$563$	3329.39	+	3329.39i	0.249231	+	0.249231i	0.820655	−	0.571424i	$-0.193609\pi$
$563$	3329.39	+	3329.39i	0.249231	+	0.249231i	−0.571424	+	0.820655i	$0.693609\pi$
$564$	35321.3	−	14630.5i	2.63705	−	1.09230i
$565$			11381.5i			0.847473i
$566$	−12636.8	−	30507.9i	−0.938451	−	2.26562i
$567$	8951.22	+	3707.72i	0.662991	+	0.274620i
$568$	−860.179	+	2076.66i	−0.0635428	+	0.153406i
$569$	−6005.28	+	6005.28i	−0.442450	+	0.442450i	−0.892835	−	0.450384i	$-0.851287\pi$
$569$	−6005.28	+	6005.28i	−0.442450	+	0.442450i	0.450384	+	0.892835i	$0.351287\pi$
$570$	−14801.5	+	14801.5i	−1.08766	+	1.08766i
$571$	431.903	−	1042.71i	0.0316543	−	0.0764202i	−0.907262	−	0.420566i	$-0.861831\pi$
$571$	431.903	−	1042.71i	0.0316543	−	0.0764202i	0.938916	+	0.344146i	$0.111831\pi$
$572$	8415.13	+	3485.66i	0.615129	+	0.254795i
$573$	−5832.53	−	14081.0i	−0.425231	−	1.02660i
$574$		−	3878.06i		−	0.281998i
$575$	−18122.7	+	7506.66i	−1.31438	+	0.544434i
$576$	−547.550	−	547.550i	−0.0396087	−	0.0396087i
$577$	−18288.9			−1.31955			−0.659773	−	0.751465i	$-0.729348\pi$
$577$	−18288.9			−1.31955			−0.659773	+	0.751465i	$0.729348\pi$
$578$	11502.4	−	20933.3i	0.827746	−	1.50642i
$579$	19723.0			1.41565
$580$	−11885.0	−	11885.0i	−0.850855	−	0.850855i
$581$	7696.52	−	3188.00i	0.549579	−	0.227643i
$582$			21787.0i			1.55172i
$583$	−3950.58	−	9537.53i	−0.280645	−	0.677537i
$584$	−12624.2	−	5229.10i	−0.894506	−	0.370517i
$585$	284.750	−	687.448i	0.0201248	−	0.0485855i
$586$	−22128.2	+	22128.2i	−1.55991	+	1.55991i
$587$	7997.50	−	7997.50i	0.562338	−	0.562338i	−0.367633	−	0.929971i	$-0.619832\pi$
$587$	7997.50	−	7997.50i	0.562338	−	0.562338i	0.929971	+	0.367633i	$0.119832\pi$
$588$	4437.71	−	10713.6i	0.311238	−	0.751395i
$589$	−6850.88	−	2837.73i	−0.479262	−	0.198517i
$590$	9672.28	+	23350.9i	0.674918	+	1.62940i
$591$		−	4795.42i		−	0.333769i
$592$	−6938.44	+	2874.00i	−0.481703	+	0.199528i
$593$	−3735.98	−	3735.98i	−0.258715	−	0.258715i	0.565816	−	0.824532i	$-0.308561\pi$
$593$	−3735.98	−	3735.98i	−0.258715	−	0.258715i	−0.824532	+	0.565816i	$0.808561\pi$
$594$	−13595.1			−0.939082
$595$	14590.3	+	10952.3i	1.00528	+	0.754620i
$596$	−34545.0			−2.37419
$597$	−6325.02	−	6325.02i	−0.433611	−	0.433611i
$598$	−11998.7	+	4970.04i	−0.820509	+	0.339866i
$599$		−	22287.6i		−	1.52028i	−0.649762	−	0.760138i	$-0.725131\pi$
$599$		−	22287.6i		−	1.52028i	0.649762	−	0.760138i	$-0.274869\pi$
$600$	−15802.8	−	38151.2i	−1.07524	−	2.59586i
$601$	13901.4	+	5758.15i	0.943511	+	0.390815i	0.800788	−	0.598947i	$-0.204414\pi$
$601$	13901.4	+	5758.15i	0.943511	+	0.390815i	0.142723	+	0.989763i	$0.454414\pi$
$602$	−1360.22	+	3283.87i	−0.0920907	+	0.222326i
$603$	348.272	−	348.272i	0.0235203	−	0.0235203i
$604$	−8318.28	+	8318.28i	−0.560374	+	0.560374i
$605$	−6759.83	+	16319.7i	−0.454258	+	1.09668i
$606$	41985.2	+	17390.8i	2.81441	+	1.16577i
$607$	−4319.98	−	10429.4i	−0.288868	−	0.697388i	0.711116	−	0.703075i	$-0.248190\pi$
$607$	−4319.98	−	10429.4i	−0.288868	−	0.697388i	−0.999984	+	0.00568627i	$0.998190\pi$
$608$			1267.75i			0.0845623i
$609$	3799.77	−	1573.91i	0.252831	−	0.104726i
$610$	37437.8	+	37437.8i	2.48494	+	2.48494i
$611$	14435.6			0.955811
$612$	207.129	+	1454.26i	0.0136809	+	0.0960538i
$613$	14753.0			0.972054			0.486027	−	0.873944i	$-0.338446\pi$
$613$	14753.0			0.972054			0.486027	+	0.873944i	$0.338446\pi$
$614$	−17635.0	−	17635.0i	−1.15911	−	1.15911i
$615$	−4942.51	+	2047.26i	−0.324067	+	0.134233i
$616$		−	10138.8i		−	0.663154i
$617$	2561.52	+	6184.04i	0.167136	+	0.403501i	0.985150	−	0.171697i	$-0.0549250\pi$
$617$	2561.52	+	6184.04i	0.167136	+	0.403501i	−0.818014	+	0.575198i	$0.804925\pi$
$618$	−41479.1	−	17181.2i	−2.69989	−	1.11833i
$619$	491.884	−	1187.51i	0.0319394	−	0.0771085i	−0.907105	−	0.420904i	$-0.861713\pi$
$619$	491.884	−	1187.51i	0.0319394	−	0.0771085i	0.939044	+	0.343796i	$0.111713\pi$
$620$	33238.3	−	33238.3i	2.15304	−	2.15304i
$621$	9067.61	−	9067.61i	0.585943	−	0.585943i
$622$	−6367.81	+	15373.2i	−0.410492	+	0.991014i
$623$	−11497.1	−	4762.27i	−0.739362	−	0.306254i
$624$	−3211.17	−	7752.46i	−0.206009	−	0.497350i
$625$		−	5148.78i		−	0.329522i
$626$	19239.9	−	7969.41i	1.22840	−	0.508820i
$627$	3194.71	+	3194.71i	0.203484	+	0.203484i
$628$	−9061.61			−0.575792
$629$	−9205.10	−	2362.42i	−0.583516	−	0.149755i
$630$	−1696.02			−0.107256
$631$	19224.0	+	19224.0i	1.21283	+	1.21283i	0.970093	+	0.242734i	$0.0780442\pi$
$631$	19224.0	+	19224.0i	1.21283	+	1.21283i	0.242734	+	0.970093i	$0.421956\pi$
$632$	7467.12	−	3092.98i	0.469978	−	0.194671i
$633$		−	1881.33i		−	0.118130i
$634$	−726.238	−	1753.29i	−0.0454931	−	0.109830i
$635$	1915.48	+	793.417i	0.119706	+	0.0495839i
$636$	−16063.4	+	38780.5i	−1.00150	+	2.41784i
$637$	3096.11	−	3096.11i	0.192578	−	0.192578i
$638$	−3877.70	+	3877.70i	−0.240626	+	0.240626i
$639$	31.0571	−	74.9785i	0.00192269	−	0.00464179i
$640$	−44372.3	−	18379.6i	−2.74057	−	1.13518i
$641$	−4715.24	−	11383.6i	−0.290547	−	0.701442i	0.709448	−	0.704758i	$-0.248945\pi$
$641$	−4715.24	−	11383.6i	−0.290547	−	0.701442i	−0.999995	+	0.00331580i	$0.998945\pi$
$642$			45691.6i			2.80888i
$643$	−23630.2	+	9787.93i	−1.44927	+	0.600308i	−0.962026	−	0.272956i	$-0.911999\pi$
$643$	−23630.2	+	9787.93i	−1.44927	+	0.600308i	−0.487246	+	0.873265i	$0.661999\pi$
$644$	13847.2	+	13847.2i	0.847290	+	0.847290i
$645$	4903.30			0.299329
$646$	9367.10	−	12478.6i	0.570501	−	0.760004i
$647$	−28275.5			−1.71812			−0.859062	−	0.511872i	$-0.828952\pi$
$647$	−28275.5			−1.71812			−0.859062	+	0.511872i	$0.828952\pi$
$648$	18138.9	+	18138.9i	1.09963	+	1.09963i
$649$	5040.00	−	2087.64i	0.304834	−	0.126266i
$650$		−	31928.1i		−	1.92665i
$651$	4401.72	+	10626.7i	0.265003	+	0.639774i
$652$	25680.4	+	10637.2i	1.54252	+	0.638933i
$653$	900.910	−	2174.99i	0.0539898	−	0.130343i	−0.894583	−	0.446902i	$-0.852527\pi$
$653$	900.910	−	2174.99i	0.0539898	−	0.130343i	0.948573	+	0.316559i	$0.102527\pi$
$654$	24161.1	−	24161.1i	1.44461	−	1.44461i
$655$	−27985.7	+	27985.7i	−1.66945	+	1.66945i
$656$	1205.95	−	2911.43i	0.0717752	−	0.173281i
$657$	455.801	+	188.799i	0.0270662	+	0.0112112i
$658$	−12591.6	−	30398.8i	−0.746004	−	1.80101i
$659$		−	21272.6i		−	1.25745i	−0.777626	−	0.628727i	$-0.783576\pi$
$659$		−	21272.6i		−	1.25745i	0.777626	−	0.628727i	$-0.216424\pi$
$660$	−26459.7	+	10960.0i	−1.56052	+	0.646388i
$661$	11753.0	+	11753.0i	0.691587	+	0.691587i	0.962581	−	0.270994i	$-0.0873525\pi$
$661$	11753.0	+	11753.0i	0.691587	+	0.691587i	−0.270994	+	0.962581i	$0.587352\pi$
$662$	18595.3			1.09173
$663$	2639.58	−	10285.0i	0.154620	−	0.602470i
$664$	22056.5			1.28910
$665$	8427.03	+	8427.03i	0.491408	+	0.491408i
$666$	816.238	−	338.097i	0.0474903	−	0.0196711i
$667$		−	5172.66i		−	0.300279i
$668$	18757.5	+	45284.5i	1.08645	+	2.62292i
$669$	−12045.7	−	4989.49i	−0.696134	−	0.288348i
$670$	12691.3	−	30639.4i	0.731801	−	1.76672i
$671$	8080.48	−	8080.48i	0.464893	−	0.464893i
$672$	1390.49	−	1390.49i	0.0798206	−	0.0798206i
$673$	−87.5115	+	211.271i	−0.00501236	+	0.0121009i	−0.926366	−	0.376625i	$-0.877085\pi$
$673$	−87.5115	+	211.271i	−0.00501236	+	0.0121009i	0.921354	+	0.388726i	$0.127085\pi$
$674$	−10676.1	−	4422.17i	−0.610129	−	0.252724i
$675$	12064.2	+	29125.7i	0.687930	+	1.66081i
$676$			20367.7i			1.15883i
$677$	9216.32	−	3817.52i	0.523208	−	0.216720i	−0.105417	−	0.994428i	$-0.533618\pi$
$677$	9216.32	−	3817.52i	0.523208	−	0.216720i	0.628625	+	0.777708i	$0.283618\pi$
$678$	−10676.7	−	10676.7i	−0.604773	−	0.604773i
$679$	12404.1			0.701071
$680$	24592.3	+	41573.2i	1.38687	+	2.34450i
$681$	26364.4			1.48353
$682$	−10844.7	−	10844.7i	−0.608890	−	0.608890i
$683$	−28742.6	+	11905.6i	−1.61026	+	0.666990i	−0.992819	−	0.119630i	$-0.961829\pi$
$683$	−28742.6	+	11905.6i	−1.61026	+	0.666990i	−0.617437	+	0.786620i	$0.711829\pi$
$684$			959.583i			0.0536412i
$685$	−21934.6	−	52954.8i	−1.22347	−	2.95372i
$686$	−30821.5	−	12766.7i	−1.71541	−	0.710545i
$687$	6200.73	−	14969.9i	0.344356	−	0.831349i
$688$	−2042.36	+	2042.36i	−0.113175	+	0.113175i
$689$	−11207.2	+	11207.2i	−0.619679	+	0.619679i
$690$	15627.3	−	37727.7i	0.862205	−	2.08155i
$691$	−4720.02	−	1955.10i	−0.259852	−	0.107634i	0.248954	−	0.968515i	$-0.419913\pi$
$691$	−4720.02	−	1955.10i	−0.259852	−	0.107634i	−0.508807	+	0.860881i	$0.669913\pi$
$692$	−6996.72	−	16891.6i	−0.384358	−	0.927921i
$693$			366.064i			0.0200659i
$694$	53554.2	−	22182.9i	2.92924	−	1.21333i
$695$	−6167.06	−	6167.06i	−0.336590	−	0.336590i
$696$	10889.3			0.593043
$697$	3432.17	−	2030.27i	0.186518	−	0.110333i
$698$	35927.4			1.94824
$699$	−3055.70	−	3055.70i	−0.165347	−	0.165347i
$700$	−44477.9	+	18423.3i	−2.40158	+	0.994767i
$701$			11204.5i			0.603691i	0.953357	+	0.301846i	$0.0976027\pi$
$701$			11204.5i			0.603691i	−0.953357	+	0.301846i	$0.902397\pi$
$702$	7987.54	+	19283.6i	0.429445	+	1.03677i
$703$	−5735.55	−	2375.74i	−0.307710	−	0.127458i
$704$	−4306.62	+	10397.1i	−0.230557	+	0.556613i
$705$	−32095.5	+	32095.5i	−1.71459	+	1.71459i
$706$	−10196.9	+	10196.9i	−0.543576	+	0.543576i
$707$	9901.24	−	23903.7i	0.526696	−	1.27156i
$708$	−20493.1	−	8488.52i	−1.08782	−	0.450590i
$709$	12992.1	+	31365.7i	0.688193	+	1.66144i	0.748391	+	0.663258i	$0.230827\pi$
$709$	12992.1	+	31365.7i	0.688193	+	1.66144i	−0.0601983	+	0.998186i	$0.519173\pi$
$710$		−	5464.54i		−	0.288846i
$711$	−269.603	+	111.673i	−0.0142207	+	0.00589041i
$712$	−23297.9	−	23297.9i	−1.22630	−	1.22630i
$713$	14466.2			0.759838
$714$	−23960.9	+	3412.73i	−1.25590	+	0.178877i
$715$	−10813.9			−0.565619
$716$	−17165.1	−	17165.1i	−0.895937	−	0.895937i
$717$	−8857.61	+	3668.94i	−0.461358	+	0.191101i
$718$			31728.8i			1.64918i
$719$	2384.53	+	5756.76i	0.123683	+	0.298596i	0.973578	−	0.228355i	$-0.0733348\pi$
$719$	2384.53	+	5756.76i	0.123683	+	0.298596i	−0.849895	+	0.526952i	$0.823335\pi$
$720$	−1273.28	−	527.408i	−0.0659059	−	0.0272991i
$721$	−9781.88	+	23615.6i	−0.505265	+	1.21982i
$722$	−16371.9	+	16371.9i	−0.843906	+	0.843906i
$723$	−6624.39	+	6624.39i	−0.340752	+	0.340752i
$724$	8950.89	−	21609.4i	0.459471	−	1.10926i
$725$	11748.5	+	4866.38i	0.601831	+	0.249287i
$726$	−8967.87	−	21650.3i	−0.458442	−	1.10678i
$727$			5206.88i			0.265629i	0.991141	+	0.132815i	$0.0424015\pi$
$727$			5206.88i			0.265629i	−0.991141	+	0.132815i	$0.957598\pi$
$728$	−14381.0	+	5956.82i	−0.732139	+	0.303262i
$729$	−14538.6	−	14538.6i	−0.738637	−	0.738637i
$730$	33219.4			1.68425
$731$	−3618.42	+	515.369i	−0.183081	+	0.0260761i
$732$	−46465.3			−2.34618
$733$	2699.43	+	2699.43i	0.136024	+	0.136024i	0.771840	−	0.635816i	$-0.219336\pi$
$733$	2699.43	+	2699.43i	0.136024	+	0.136024i	−0.635816	+	0.771840i	$0.719336\pi$
$734$	−26484.7	+	10970.3i	−1.33184	+	0.551665i
$735$			13767.5i			0.690916i
$736$	−946.446	−	2284.92i	−0.0474001	−	0.114434i
$737$	−6613.13	−	2739.25i	−0.330526	−	0.136908i
$738$	−141.868	+	342.500i	−0.00707620	+	0.0170835i
$739$	6513.44	−	6513.44i	0.324223	−	0.324223i	−0.526162	−	0.850385i	$-0.676369\pi$
$739$	6513.44	−	6513.44i	0.324223	−	0.324223i	0.850385	+	0.526162i	$0.176369\pi$
$740$	27827.1	−	27827.1i	1.38236	−	1.38236i
$741$	2654.46	−	6408.43i	0.131598	−	0.317705i
$742$	33375.9	+	13824.7i	1.65130	+	0.683992i
$743$	8854.88	+	21377.6i	0.437219	+	1.05554i	0.976905	+	0.213674i	$0.0685431\pi$
$743$	8854.88	+	21377.6i	0.437219	+	1.05554i	−0.539686	+	0.841867i	$0.681457\pi$
$744$			30453.8i			1.50066i
$745$	37891.2	−	15695.0i	1.86339	−	0.771841i
$746$	−31747.2	−	31747.2i	−1.55811	−	1.55811i
$747$	−796.360			−0.0390057
$748$	18374.1	−	10869.1i	0.898161	−	0.531300i
$749$	26013.9			1.26906
$750$	30580.0	+	30580.0i	1.48883	+	1.48883i
$751$	28770.9	−	11917.3i	1.39796	−	0.579053i	0.448736	−	0.893664i	$-0.351874\pi$
$751$	28770.9	−	11917.3i	1.39796	−	0.579053i	0.949221	+	0.314612i	$0.101874\pi$
$752$		−	26737.2i		−	1.29655i
$753$	1989.66	+	4803.47i	0.0962912	+	0.232468i
$754$	7778.48	+	3221.95i	0.375697	+	0.155619i
$755$	5344.73	−	12903.3i	0.257635	−	0.621986i
$756$	22254.3	−	22254.3i	1.07061	−	1.07061i
$757$	21914.1	−	21914.1i	1.05216	−	1.05216i	0.0535946	−	0.998563i	$-0.482932\pi$
$757$	21914.1	−	21914.1i	1.05216	−	1.05216i	0.998563	−	0.0535946i	$-0.0170679\pi$
$758$	−2697.05	+	6511.26i	−0.129237	+	0.312005i
$759$	−8143.03	−	3372.96i	−0.389425	−	0.161305i
$760$	12075.0	+	29151.6i	0.576324	+	1.39137i
$761$			14150.5i			0.674053i	0.941495	+	0.337026i	$0.109421\pi$
$761$			14150.5i			0.674053i	−0.941495	+	0.337026i	$0.890579\pi$
$762$	−2541.15	+	1052.58i	−0.120809	+	0.0500406i
$763$	−13755.8	−	13755.8i	−0.652679	−	0.652679i
$764$	−47044.7			−2.22777
$765$	−887.915	−	1501.02i	−0.0419642	−	0.0709404i
$766$	−39666.7			−1.87104
$767$	−5922.30	−	5922.30i	−0.278803	−	0.278803i
$768$	37235.9	−	15423.6i	1.74953	−	0.724677i
$769$		−	619.823i		−	0.0290655i	−0.999894	−	0.0145328i	$-0.995374\pi$
$769$		−	619.823i		−	0.0290655i	0.999894	−	0.0145328i	$-0.00462608\pi$
$770$	9432.55	+	22772.2i	0.441462	+	1.06578i
$771$	−12242.0	−	5070.81i	−0.571836	−	0.236862i
$772$	23297.3	−	56244.7i	1.08613	−	2.62214i
$773$	−7209.95	+	7209.95i	−0.335477	+	0.335477i	−0.854662	−	0.519185i	$-0.826236\pi$
$773$	−7209.95	+	7209.95i	−0.335477	+	0.335477i	0.519185	+	0.854662i	$0.326236\pi$
$774$	240.263	−	240.263i	0.0111577	−	0.0111577i
$775$	−13609.7	+	32856.6i	−0.630805	+	1.52290i
$776$	30341.7	+	12568.0i	1.40361	+	0.581396i
$777$	3685.11	+	8896.65i	0.170145	+	0.410767i
$778$		−	7136.23i		−	0.328851i
$779$	2406.68	−	996.880i	0.110691	−	0.0458497i
$780$	31091.7	+	31091.7i	1.42726	+	1.42726i
$781$	−1179.45			−0.0540385
$782$	−7566.83	+	29483.9i	−0.346022	+	1.34826i
$783$	−8313.17			−0.379423
$784$	−5734.55	−	5734.55i	−0.261231	−	0.261231i
$785$	9939.36	−	4117.02i	0.451912	−	0.187188i
$786$		−	52505.5i		−	2.38271i
$787$	12707.6	+	30679.0i	0.575577	+	1.38956i	0.896747	+	0.442543i	$0.145924\pi$
$787$	12707.6	+	30679.0i	0.575577	+	1.38956i	−0.321171	+	0.947021i	$0.604076\pi$
$788$	−13675.3	−	5664.48i	−0.618225	−	0.256077i
$789$	−9677.29	+	23363.0i	−0.436655	+	1.05418i
$790$	−13894.0	+	13894.0i	−0.625729	+	0.625729i
$791$	−6078.64	+	6078.64i	−0.273238	+	0.273238i
$792$	−370.899	+	895.429i	−0.0166406	+	0.0401738i
$793$	−16209.0	−	6714.00i	−0.725851	−	0.300657i
$794$	11196.8	+	27031.4i	0.500452	+	1.20820i
$795$		−	49835.1i		−	2.22323i
$796$	−25508.6	+	10566.0i	−1.13584	+	0.470480i
$797$	3077.08	+	3077.08i	0.136757	+	0.136757i	0.772172	−	0.635414i	$-0.219171\pi$
$797$	3077.08	+	3077.08i	0.136757	+	0.136757i	−0.635414	+	0.772172i	$0.719171\pi$
$798$	−15810.4			−0.701356
$799$	20311.6	−	27058.4i	0.899338	−	1.19807i
$800$	6080.08			0.268704
$801$	841.181	+	841.181i	0.0371057	+	0.0371057i
$802$	−26496.5	+	10975.2i	−1.16661	+	0.483226i
$803$		−	7169.98i		−	0.315097i
$804$	11138.0	+	26889.6i	0.488567	+	1.17950i
$805$	−21479.7	−	8897.20i	−0.940449	−	0.389547i
$806$	−9010.73	+	21753.8i	−0.393784	+	0.950678i
$807$	12216.1	−	12216.1i	0.532870	−	0.532870i
$808$	48438.8	−	48438.8i	2.10900	−	2.10900i
$809$	−5172.06	+	12486.4i	−0.224771	+	0.542645i	−0.995526	−	0.0944862i	$-0.969879\pi$
$809$	−5172.06	+	12486.4i	−0.224771	+	0.542645i	0.770755	+	0.637132i	$0.219879\pi$
$810$	−57616.2	−	23865.4i	−2.49929	−	1.03524i
$811$	−2203.64	−	5320.06i	−0.0954135	−	0.230348i	0.868966	−	0.494872i	$-0.164785\pi$
$811$	−2203.64	−	5320.06i	−0.0954135	−	0.230348i	−0.964379	+	0.264524i	$0.914785\pi$
$812$		−	12695.1i		−	0.548657i
$813$	351.422	−	145.564i	0.0151598	−	0.00627939i
$814$	−9079.13	−	9079.13i	−0.390938	−	0.390938i
$815$	−33000.8			−1.41837
$816$	−19049.7	−	4888.97i	−0.817246	−	0.209741i
$817$	−2387.59			−0.102241
$818$	31837.0	+	31837.0i	1.36082	+	1.36082i
$819$	519.234	−	215.074i	0.0221532	−	0.00917616i
$820$			16513.0i			0.703243i
$821$	−10698.4	−	25828.3i	−0.454783	−	1.09794i	−0.970482	−	0.241174i	$-0.922468\pi$
$821$	−10698.4	−	25828.3i	−0.454783	−	1.09794i	0.515699	−	0.856770i	$-0.327532\pi$
$822$	70252.0	+	29099.3i	2.98092	+	1.23474i
$823$	−14557.5	+	35144.9i	−0.616576	+	1.48855i	0.239078	+	0.971000i	$0.423155\pi$
$823$	−14557.5	+	35144.9i	−0.616576	+	1.48855i	−0.855655	+	0.517547i	$0.826845\pi$
$824$	−47854.9	+	47854.9i	−2.02318	+	2.02318i
$825$	15321.8	−	15321.8i	0.646588	−	0.646588i
$826$	−7305.52	+	17637.1i	−0.307738	+	0.742946i
$827$	13366.2	+	5536.47i	0.562018	+	0.232795i	0.645561	−	0.763709i	$-0.276624\pi$
$827$	13366.2	+	5536.47i	0.562018	+	0.232795i	−0.0835432	+	0.996504i	$0.526624\pi$
$828$	−716.385	−	1729.51i	−0.0300677	−	0.0725899i
$829$			24519.4i			1.02726i	0.858013	+	0.513628i	$0.171699\pi$
$829$			24519.4i			1.02726i	−0.858013	+	0.513628i	$0.828301\pi$
$830$	−49540.1	+	20520.2i	−2.07176	+	0.858151i
$831$	12328.4	+	12328.4i	0.514642	+	0.514642i
$832$	17277.7			0.719949
$833$	−1447.06	−	10159.8i	−0.0601892	−	0.422590i
$834$	11570.4			0.480394
$835$	−41148.8	−	41148.8i	−1.70540	−	1.70540i
$836$	12884.2	−	5336.79i	0.533024	−	0.220786i
$837$		−	23249.2i		−	0.960108i
$838$	−15884.9	−	38349.5i	−0.654814	−	1.58086i
$839$	35168.5	+	14567.3i	1.44714	+	0.599426i	0.961518	−	0.274741i	$-0.0885921\pi$
$839$	35168.5	+	14567.3i	1.44714	+	0.599426i	0.485625	+	0.874167i	$0.338592\pi$
$840$	18730.1	−	45218.4i	0.769344	−	1.85736i
$841$	14874.5	−	14874.5i	0.609885	−	0.609885i
$842$	5559.86	−	5559.86i	0.227560	−	0.227560i
$843$	−3243.21	+	7829.80i	−0.132505	+	0.319896i
$844$	−5365.06	−	2222.28i	−0.218807	−	0.0906327i
$845$	−9253.77	−	22340.6i	−0.376733	−	0.909514i
$846$			3145.36i			0.127825i
$847$	−12326.3	+	5105.73i	−0.500045	+	0.207125i
$848$	20757.6	+	20757.6i	0.840590	+	0.840590i
$849$	−34406.2			−1.39083
$850$	−59846.9	−	44924.4i	−2.41498	−	1.81282i
$851$	12111.1			0.487853
$852$	3391.11	+	3391.11i	0.136358	+	0.136358i
$853$	34565.1	−	14317.3i	1.38744	−	0.574696i	0.440979	−	0.897517i	$-0.354631\pi$
$853$	34565.1	−	14317.3i	1.38744	−	0.574696i	0.946460	+	0.322821i	$0.104631\pi$
$854$			39989.7i			1.60237i
$855$	−435.973	−	1052.53i	−0.0174386	−	0.0421004i
$856$	63632.5	+	26357.4i	2.54079	+	1.05243i
$857$	11132.3	−	26875.7i	0.443723	−	1.07124i	−0.530908	−	0.847429i	$-0.678149\pi$
$857$	11132.3	−	26875.7i	0.443723	−	1.07124i	0.974632	−	0.223814i	$-0.0718508\pi$
$858$	10144.3	−	10144.3i	0.403637	−	0.403637i
$859$	−30775.9	+	30775.9i	−1.22242	+	1.22242i	−0.255651	+	0.966769i	$0.582290\pi$
$859$	−30775.9	+	30775.9i	−1.22242	+	1.22242i	−0.966769	+	0.255651i	$0.917710\pi$
$860$	5791.91	−	13982.9i	0.229654	−	0.554434i
$861$	−3733.11	−	1546.30i	−0.147763	−	0.0612054i
$862$	−4720.21	−	11395.6i	−0.186509	−	0.450274i
$863$		−	15659.4i		−	0.617672i	−0.951115	−	0.308836i	$-0.900061\pi$
$863$		−	15659.4i		−	0.617672i	0.951115	−	0.308836i	$-0.0999394\pi$
$864$	−3672.19	+	1521.07i	−0.144595	+	0.0598933i
$865$	15348.9	+	15348.9i	0.603328	+	0.603328i
$866$	8913.05			0.349743
$867$	−15564.5	−	19419.3i	−0.609688	−	0.760683i
$868$	35503.9			1.38834
$869$	2998.84	+	2998.84i	0.117064	+	0.117064i
$870$	−24457.9	+	10130.8i	−0.953104	+	0.394789i
$871$			10989.6i			0.427518i
$872$	−19710.6	−	47585.5i	−0.765463	−	1.84799i
$873$	−1095.50	−	453.771i	−0.0424709	−	0.0175920i
$874$	−7609.48	+	18370.9i	−0.294502	+	0.710990i
$875$	17410.3	−	17410.3i	0.672659	−	0.672659i
$876$	−20614.8	+	20614.8i	−0.795103	+	0.795103i
$877$	11056.4	−	26692.6i	0.425712	−	1.02776i	−0.554921	−	0.831903i	$-0.687252\pi$
$877$	11056.4	−	26692.6i	0.425712	−	1.02776i	0.980633	−	0.195856i	$-0.0627485\pi$
$878$	46706.0	+	19346.3i	1.79528	+	0.743627i
$879$	12477.9	+	30124.4i	0.478805	+	1.15594i
$880$			20029.3i			0.767258i
$881$	20413.0	−	8455.34i	0.780625	−	0.323346i	0.0434576	−	0.999055i	$-0.486163\pi$
$881$	20413.0	−	8455.34i	0.780625	−	0.323346i	0.737168	+	0.675710i	$0.236163\pi$
$882$	674.612	+	674.612i	0.0257544	+	0.0257544i
$883$	−40158.3			−1.53050			−0.765252	−	0.643731i	$-0.777385\pi$
$883$	−40158.3			−1.53050			−0.765252	+	0.643731i	$0.777385\pi$
$884$	−26212.2	−	19676.3i	−0.997299	−	0.748628i
$885$	26334.8			1.00026
$886$	13696.3	+	13696.3i	0.519343	+	0.519343i
$887$	−25685.4	+	10639.3i	−0.972303	+	0.402741i	−0.811569	−	0.584257i	$-0.801386\pi$
$887$	−25685.4	+	10639.3i	−0.972303	+	0.402741i	−0.160734	+	0.986998i	$0.551386\pi$
$888$			25495.9i			0.963497i
$889$	599.272	+	1446.77i	0.0226085	+	0.0545817i
$890$	74003.4	+	30653.2i	2.78719	+	1.15449i
$891$	−5151.04	+	12435.7i	−0.193677	+	0.467578i
$892$	−28457.4	+	28457.4i	−1.06819	+	1.06819i
$893$	15628.4	−	15628.4i	0.585648	−	0.585648i
$894$	−20821.7	+	50268.0i	−0.778950	+	1.88055i
$895$	26626.6	+	11029.1i	0.994444	+	0.411912i
$896$	−13882.2	−	33514.6i	−0.517603	−	1.24960i
$897$			13532.0i			0.503700i
$898$	−59217.5	+	24528.7i	−2.20057	+	0.911507i
$899$	−6631.31	−	6631.31i	−0.246014	−	0.246014i
$900$	4602.13			0.170449
$901$	5237.99	+	36776.0i	0.193677	+	1.35981i
$902$	5387.70			0.198881
$903$	2618.76	+	2618.76i	0.0965083	+	0.0965083i
$904$	−21027.8	+	8710.02i	−0.773646	+	0.320455i
$905$			27769.3i			1.01998i
$906$	7090.54	+	17118.1i	0.260008	+	0.627715i
$907$	−17011.7	−	7046.48i	−0.622783	−	0.257965i	0.0489002	−	0.998804i	$-0.484428\pi$
$907$	−17011.7	−	7046.48i	−0.622783	−	0.257965i	−0.671683	+	0.740839i	$0.734428\pi$
$908$	31142.3	−	75184.2i	1.13821	−	2.74788i
$909$	−1748.90	+	1748.90i	−0.0638145	+	0.0638145i
$910$	26758.6	−	26758.6i	0.974770	−	0.974770i
$911$	−12349.9	+	29815.2i	−0.449143	+	1.08433i	0.523501	+	0.852025i	$0.324626\pi$
$911$	−12349.9	+	29815.2i	−0.449143	+	1.08433i	−0.972644	+	0.232302i	$0.925374\pi$
$912$	−11869.6	−	4916.53i	−0.430965	−	0.178512i
$913$	4429.01	+	10692.6i	0.160547	+	0.387594i
$914$		−	78962.7i		−	2.85761i
$915$	50966.1	−	21110.9i	1.84141	−	0.762736i
$916$	−35365.7	−	35365.7i	−1.27567	−	1.27567i
$917$	−29893.3			−1.07652
$918$	47384.6	+	12160.9i	1.70362	+	0.437223i
$919$	19185.3			0.688643			0.344322	−	0.938852i	$-0.388109\pi$
$919$	19185.3			0.688643			0.344322	+	0.938852i	$0.388109\pi$
$920$	−43526.8	−	43526.8i	−1.55982	−	1.55982i
$921$	−24007.5	+	9944.24i	−0.858930	+	0.355781i
$922$		−	53744.2i		−	1.91971i
$923$	692.961	+	1672.96i	0.0247119	+	0.0596599i
$924$	−19985.2	−	8278.13i	−0.711541	−	0.294730i
$925$	−11394.0	+	27507.5i	−0.405008	+	0.977775i
$926$	48766.6	−	48766.6i	1.73064	−	1.73064i
$927$	1727.82	−	1727.82i	0.0612179	−	0.0612179i
$928$	−613.557	+	1481.26i	−0.0217037	+	0.0523973i
$929$	−19238.6	−	7968.89i	−0.679438	−	0.281433i	0.0161538	−	0.999870i	$-0.494858\pi$
$929$	−19238.6	−	7968.89i	−0.679438	−	0.281433i	−0.695592	+	0.718437i	$0.744858\pi$
$930$	−28332.5	−	68400.7i	−0.998988	−	2.41177i
$931$		−	6703.89i		−	0.235995i
$932$	−12323.5	+	5104.57i	−0.433123	+	0.179405i
$933$	12259.6	+	12259.6i	0.430183	+	0.430183i
$934$	47106.5			1.65029
$935$	−15215.7	+	20269.9i	−0.532200	+	0.708981i
$936$	1488.01			0.0519627
$937$	14900.1	+	14900.1i	0.519495	+	0.519495i	0.917418	−	0.397924i	$-0.130269\pi$
$937$	14900.1	+	14900.1i	0.519495	+	0.519495i	−0.397924	+	0.917418i	$0.630269\pi$
$938$	23142.1	−	9585.78i	0.805562	−	0.333675i
$939$		−	21698.4i		−	0.754100i
$940$	53615.7	+	129440.i	1.86037	+	4.49134i
$941$	−10307.2	−	4269.37i	−0.357071	−	0.147904i	0.196935	−	0.980417i	$-0.436901\pi$
$941$	−10307.2	−	4269.37i	−0.357071	−	0.147904i	−0.554006	+	0.832513i	$0.686901\pi$
$942$	−5461.81	+	13186.0i	−0.188912	+	0.456074i
$943$	−3593.46	+	3593.46i	−0.124092	+	0.124092i
$944$	−10969.1	+	10969.1i	−0.378194	+	0.378194i
$945$	−14299.0	+	34520.9i	−0.492219	+	1.18832i
$946$	−4562.20	−	1889.73i	−0.156797	−	0.0649475i
$947$	−1165.49	−	2813.74i	−0.0399929	−	0.0965514i	0.902621	−	0.430436i	$-0.141640\pi$
$947$	−1165.49	−	2813.74i	−0.0399929	−	0.0965514i	−0.942614	+	0.333885i	$0.891640\pi$
$948$		−	17244.3i		−	0.590789i
$949$	−10170.0	+	4212.57i	−0.347875	+	0.144095i
$950$	−34566.3	−	34566.3i	−1.18050	−	1.18050i
$951$	−1977.33			−0.0674232
$952$	−9069.20	+	35337.8i	−0.308755	+	1.20305i
$953$	6037.53			0.205220			0.102610	−	0.994722i	$-0.467281\pi$
$953$	6037.53			0.205220			0.102610	+	0.994722i	$0.467281\pi$
$954$	−2441.93	−	2441.93i	−0.0828724	−	0.0828724i
$955$	51601.7	−	21374.1i	1.74847	−	0.724241i
$956$			29593.4i			1.00117i
$957$	2186.60	+	5278.92i	0.0738587	+	0.178311i
$958$	−59455.2	−	24627.2i	−2.00513	−	0.830551i
$959$	16567.3	−	39997.0i	0.557858	−	1.34679i
$960$	−38414.6	+	38414.6i	−1.29149	+	1.29149i
$961$	−2519.83	+	2519.83i	−0.0845836	+	0.0845836i
$962$	−7543.77	+	18212.3i	−0.252829	+	0.610382i
$963$	−2297.48	−	951.646i	−0.0768797	−	0.0318446i
$964$	11066.1	+	26715.9i	0.369725	+	0.892595i
$965$			72277.6i			2.41109i
$966$	28495.9	−	11803.4i	0.949111	−	0.393135i
$967$	7884.94	+	7884.94i	0.262216	+	0.262216i	0.825954	−	0.563738i	$-0.190637\pi$
$967$	7884.94	+	7884.94i	0.262216	+	0.262216i	−0.563738	+	0.825954i	$0.690637\pi$
$968$	−35324.6			−1.17291
$969$	−8277.20	−	13992.6i	−0.274409	−	0.463887i
$970$	−79841.6			−2.64284
$971$	20542.5	+	20542.5i	0.678930	+	0.678930i	0.959758	−	0.280828i	$-0.0906091\pi$
$971$	20542.5	+	20542.5i	0.678930	+	0.678930i	−0.280828	+	0.959758i	$0.590609\pi$
$972$	−5427.65	+	2248.21i	−0.179107	+	0.0741885i
$973$		−	6587.43i		−	0.217043i
$974$	−35907.7	−	86688.9i	−1.18127	−	2.85184i
$975$	−30734.7	−	12730.7i	−1.00954	−	0.418164i
$976$	−12435.5	+	30022.0i	−0.407839	+	0.984612i
$977$	−1718.38	+	1718.38i	−0.0562700	+	0.0562700i	−0.734682	−	0.678412i	$-0.762669\pi$
$977$	−1718.38	+	1718.38i	−0.0562700	+	0.0562700i	0.678412	+	0.734682i	$0.262669\pi$
$978$	30957.3	−	30957.3i	1.01217	−	1.01217i
$979$	6616.10	−	15972.7i	0.215987	−	0.521439i
$980$	39261.4	+	16262.6i	1.27975	+	0.530091i
$981$	711.658	+	1718.09i	0.0231616	+	0.0559170i
$982$		−	351.356i		−	0.0114177i
$983$	−2002.34	+	829.397i	−0.0649693	+	0.0269112i	−0.414931	−	0.909853i	$-0.636194\pi$
$983$	−2002.34	+	829.397i	−0.0649693	+	0.0269112i	0.349962	+	0.936764i	$0.386194\pi$
$984$	−7564.82	−	7564.82i	−0.245079	−	0.245079i
$985$	17573.5			0.568465
$986$	16984.0	−	10046.8i	0.548561	−	0.324497i
$987$	−34283.2			−1.10562
$988$	−15139.6	−	15139.6i	−0.487506	−	0.487506i
$989$	4303.27	−	1782.47i	0.138358	−	0.0573098i
$990$		−	2356.24i		−	0.0756427i
$991$	7474.99	+	18046.2i	0.239607	+	0.578463i	0.997242	−	0.0742153i	$-0.0236452\pi$
$991$	7474.99	+	18046.2i	0.239607	+	0.578463i	−0.757635	+	0.652679i	$0.773645\pi$
$992$	−4142.59	−	1715.92i	−0.132588	−	0.0549198i
$993$	7414.54	−	17900.3i	0.236952	−	0.572052i
$994$	2918.51	−	2918.51i	0.0931282	−	0.0931282i
$995$	23178.9	−	23178.9i	0.738514	−	0.738514i
$996$	18008.8	−	43477.0i	0.572921	−	1.38315i
$997$	−8215.19	−	3402.84i	−0.260961	−	0.108093i	0.248367	−	0.968666i	$-0.420106\pi$
$997$	−8215.19	−	3402.84i	−0.260961	−	0.108093i	−0.509328	+	0.860572i	$0.670106\pi$
$998$	27545.4	+	66500.5i	0.873682	+	2.10925i
$999$		−	19464.2i		−	0.616437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.d.a.2.1	✓	12
3.2	odd	2		153.4.l.a.19.3		12
17.3	odd	16		289.4.a.g.1.1		12
17.5	odd	16		289.4.b.e.288.11		12
17.9	even	8	inner	17.4.d.a.9.1	yes	12
17.12	odd	16		289.4.b.e.288.12		12
17.14	odd	16		289.4.a.g.1.2		12
51.26	odd	8		153.4.l.a.145.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.1	✓	12	1.1	even	1	trivial
17.4.d.a.9.1	yes	12	17.9	even	8	inner
153.4.l.a.19.3		12	3.2	odd	2
153.4.l.a.145.3		12	51.26	odd	8
289.4.a.g.1.1		12	17.3	odd	16
289.4.a.g.1.2		12	17.14	odd	16
289.4.b.e.288.11		12	17.5	odd	16
289.4.b.e.288.12		12	17.12	odd	16

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.43772 - 3.43772i) q^{2} +(-4.67995 + 1.93850i) q^{3} +15.6358i q^{4} +(-7.10390 - 17.1503i) q^{5} +(22.7523 + 9.42432i) q^{6} +(5.36561 - 12.9537i) q^{7} +(26.2496 - 26.2496i) q^{8} +(-0.947753 + 0.947753i) q^{9} +O(q^{10})\)	\(q+(-3.43772 - 3.43772i) q^{2} +(-4.67995 + 1.93850i) q^{3} +15.6358i q^{4} +(-7.10390 - 17.1503i) q^{5} +(22.7523 + 9.42432i) q^{6} +(5.36561 - 12.9537i) q^{7} +(26.2496 - 26.2496i) q^{8} +(-0.947753 + 0.947753i) q^{9} +(-34.5367 + 83.3791i) q^{10} +(17.9963 + 7.45431i) q^{11} +(-30.3099 - 73.1746i) q^{12} -29.9060i q^{13} +(-62.9767 + 26.0858i) q^{14} +(66.4917 + 66.4917i) q^{15} -55.3912 q^{16} +(-56.0566 - 42.0792i) q^{17} +6.51621 q^{18} +(-32.3771 - 32.3771i) q^{19} +(268.158 - 111.075i) q^{20} +71.0240i q^{21} +(-36.2404 - 87.4920i) q^{22} +(82.5263 + 34.1835i) q^{23} +(-71.9620 + 173.732i) q^{24} +(-155.280 + 155.280i) q^{25} +(-102.808 + 102.808i) q^{26} +(54.9376 - 132.631i) q^{27} +(202.542 + 83.8955i) q^{28} +(-22.1603 - 53.4998i) q^{29} -457.159i q^{30} +(149.621 - 61.9751i) q^{31} +(-19.5778 - 19.5778i) q^{32} -98.6719 q^{33} +(48.0504 + 337.363i) q^{34} -260.277 q^{35} +(-14.8188 - 14.8188i) q^{36} +(125.263 - 51.8855i) q^{37} +222.607i q^{38} +(57.9726 + 139.958i) q^{39} +(-636.664 - 263.715i) q^{40} +(-21.7716 + 52.5612i) q^{41} +(244.160 - 244.160i) q^{42} +(36.8715 - 36.8715i) q^{43} +(-116.554 + 281.386i) q^{44} +(22.9870 + 9.52153i) q^{45} +(-166.189 - 401.215i) q^{46} +482.699i q^{47} +(259.228 - 107.376i) q^{48} +(103.528 + 103.528i) q^{49} +1067.62 q^{50} +(343.912 + 88.2627i) q^{51} +467.603 q^{52} +(-374.747 - 374.747i) q^{53} +(-644.808 + 267.088i) q^{54} -361.597i q^{55} +(-199.185 - 480.875i) q^{56} +(214.286 + 88.7602i) q^{57} +(-107.736 + 260.098i) q^{58} +(198.031 - 198.031i) q^{59} +(-1039.65 + 1039.65i) q^{60} +(224.504 - 542.000i) q^{61} +(-727.408 - 301.302i) q^{62} +(7.19166 + 17.3622i) q^{63} +577.735i q^{64} +(-512.897 + 212.449i) q^{65} +(339.206 + 339.206i) q^{66} -367.471 q^{67} +(657.940 - 876.488i) q^{68} -452.484 q^{69} +(894.759 + 894.759i) q^{70} +(-55.9406 + 23.1713i) q^{71} +49.7563i q^{72} +(-140.861 - 340.067i) q^{73} +(-608.985 - 252.250i) q^{74} +(425.692 - 1027.71i) q^{75} +(506.241 - 506.241i) q^{76} +(193.122 - 193.122i) q^{77} +(281.843 - 680.430i) q^{78} +(201.148 + 83.3181i) q^{79} +(393.493 + 949.976i) q^{80} +691.015i q^{81} +(255.535 - 105.846i) q^{82} +(420.131 + 420.131i) q^{83} -1110.51 q^{84} +(-323.451 + 1260.31i) q^{85} -253.508 q^{86} +(207.418 + 207.418i) q^{87} +(668.069 - 276.723i) q^{88} -887.553i q^{89} +(-46.2905 - 111.755i) q^{90} +(-387.394 - 160.464i) q^{91} +(-534.486 + 1290.36i) q^{92} +(-580.081 + 580.081i) q^{93} +(1659.38 - 1659.38i) q^{94} +(-325.274 + 785.281i) q^{95} +(129.575 + 53.6716i) q^{96} +(338.553 + 817.340i) q^{97} -711.801i q^{98} +(-24.1209 + 9.99120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9} - 116 q^{10} + 40 q^{11} + 56 q^{12} - 132 q^{14} + 244 q^{15} + 184 q^{16} + 52 q^{17} - 12 q^{19} + 572 q^{20} - 620 q^{22} - 276 q^{23} - 184 q^{24} - 464 q^{25} - 708 q^{26} - 664 q^{27} + 452 q^{28} + 632 q^{29} + 188 q^{31} + 700 q^{32} + 1400 q^{33} + 764 q^{34} - 632 q^{35} + 524 q^{36} + 940 q^{37} - 1112 q^{39} - 1864 q^{40} + 176 q^{41} + 48 q^{42} - 1360 q^{43} - 1364 q^{44} - 32 q^{45} + 452 q^{46} - 540 q^{48} + 1044 q^{49} + 2856 q^{50} + 340 q^{51} + 792 q^{52} - 360 q^{53} - 244 q^{54} - 1788 q^{56} - 148 q^{57} - 360 q^{58} - 584 q^{59} - 1792 q^{60} - 1052 q^{61} - 380 q^{62} + 1752 q^{63} + 404 q^{65} + 1372 q^{66} + 1080 q^{67} + 2532 q^{68} - 344 q^{69} + 2072 q^{70} + 28 q^{71} + 824 q^{73} - 2292 q^{74} + 400 q^{75} + 1328 q^{76} - 1252 q^{77} + 1128 q^{78} - 196 q^{79} - 904 q^{80} - 1528 q^{82} - 1008 q^{83} - 4768 q^{84} - 2824 q^{85} - 1200 q^{86} - 2516 q^{87} - 56 q^{88} - 860 q^{90} + 2456 q^{91} + 396 q^{92} - 836 q^{93} + 6360 q^{94} + 2172 q^{95} + 1668 q^{96} - 904 q^{97} + 3280 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9 - 116 * q^10 + 40 * q^11 + 56 * q^12 - 132 * q^14 + 244 * q^15 + 184 * q^16 + 52 * q^17 - 12 * q^19 + 572 * q^20 - 620 * q^22 - 276 * q^23 - 184 * q^24 - 464 * q^25 - 708 * q^26 - 664 * q^27 + 452 * q^28 + 632 * q^29 + 188 * q^31 + 700 * q^32 + 1400 * q^33 + 764 * q^34 - 632 * q^35 + 524 * q^36 + 940 * q^37 - 1112 * q^39 - 1864 * q^40 + 176 * q^41 + 48 * q^42 - 1360 * q^43 - 1364 * q^44 - 32 * q^45 + 452 * q^46 - 540 * q^48 + 1044 * q^49 + 2856 * q^50 + 340 * q^51 + 792 * q^52 - 360 * q^53 - 244 * q^54 - 1788 * q^56 - 148 * q^57 - 360 * q^58 - 584 * q^59 - 1792 * q^60 - 1052 * q^61 - 380 * q^62 + 1752 * q^63 + 404 * q^65 + 1372 * q^66 + 1080 * q^67 + 2532 * q^68 - 344 * q^69 + 2072 * q^70 + 28 * q^71 + 824 * q^73 - 2292 * q^74 + 400 * q^75 + 1328 * q^76 - 1252 * q^77 + 1128 * q^78 - 196 * q^79 - 904 * q^80 - 1528 * q^82 - 1008 * q^83 - 4768 * q^84 - 2824 * q^85 - 1200 * q^86 - 2516 * q^87 - 56 * q^88 - 860 * q^90 + 2456 * q^91 + 396 * q^92 - 836 * q^93 + 6360 * q^94 + 2172 * q^95 + 1668 * q^96 - 904 * q^97 + 3280 * q^99

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