LMFDB - Embedded newform 63.4.f.c.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + \cdots + 387420489 $ x^18 - 3x^17 + 6x^16 - 23x^15 - 6x^14 + 255x^13 - 56x^12 - 81x^11 + 5832x^10 - 32373x^9 + 52488x^8 - 6561x^7 - 40824x^6 + 1673055x^5 - 354294x^4 - 12223143x^3 + 28697814x^2 - 129140163*x + 387420489
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.9
Root			$2.37763 - 1.82944i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.4.f.c.22.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.80688 - 4.86166i) q^{2} +(5.15079 + 0.685073i) q^{3} +(-11.7571 - 20.3640i) q^{4} +(5.31469 + 9.20530i) q^{5} +(17.7882 - 23.1185i) q^{6} +(-3.50000 + 6.06218i) q^{7} -87.0935 q^{8} +(26.0614 + 7.05734i) q^{9} +O(q^{10})$	\(q+(2.80688 - 4.86166i) q^{2} +(5.15079 + 0.685073i) q^{3} +(-11.7571 - 20.3640i) q^{4} +(5.31469 + 9.20530i) q^{5} +(17.7882 - 23.1185i) q^{6} +(-3.50000 + 6.06218i) q^{7} -87.0935 q^{8} +(26.0614 + 7.05734i) q^{9} +59.6707 q^{10} +(-6.90048 + 11.9520i) q^{11} +(-46.6078 - 112.945i) q^{12} +(6.55969 + 11.3617i) q^{13} +(19.6482 + 34.0316i) q^{14} +(21.0685 + 51.0556i) q^{15} +(-150.404 + 260.507i) q^{16} +23.0081 q^{17} +(107.461 - 106.892i) q^{18} -46.1335 q^{19} +(124.971 - 216.456i) q^{20} +(-22.1808 + 28.8273i) q^{21} +(38.7376 + 67.0955i) q^{22} +(-63.9637 - 110.788i) q^{23} +(-448.601 - 59.6654i) q^{24} +(6.00824 - 10.4066i) q^{25} +73.6491 q^{26} +(129.402 + 54.2048i) q^{27} +164.600 q^{28} +(54.4860 - 94.3726i) q^{29} +(307.352 + 40.8788i) q^{30} +(72.7157 + 125.947i) q^{31} +(495.957 + 859.022i) q^{32} +(-43.7309 + 56.8348i) q^{33} +(64.5809 - 111.857i) q^{34} -74.4056 q^{35} +(-162.692 - 613.687i) q^{36} -12.2214 q^{37} +(-129.491 + 224.286i) q^{38} +(26.0040 + 63.0158i) q^{39} +(-462.875 - 801.722i) q^{40} +(-155.766 - 269.795i) q^{41} +(77.8895 + 188.750i) q^{42} +(-78.5554 + 136.062i) q^{43} +324.520 q^{44} +(73.5429 + 277.410i) q^{45} -718.153 q^{46} +(-38.4253 + 66.5545i) q^{47} +(-953.165 + 1238.78i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-33.7288 - 58.4200i) q^{50} +(118.510 + 15.7622i) q^{51} +(154.247 - 267.163i) q^{52} -221.313 q^{53} +(626.741 - 476.961i) q^{54} -146.695 q^{55} +(304.827 - 527.976i) q^{56} +(-237.624 - 31.6048i) q^{57} +(-305.871 - 529.785i) q^{58} +(-243.121 - 421.097i) q^{59} +(791.988 - 1029.31i) q^{60} +(-465.583 + 806.414i) q^{61} +816.417 q^{62} +(-133.998 + 133.288i) q^{63} +3161.90 q^{64} +(-69.7254 + 120.768i) q^{65} +(153.564 + 372.133i) q^{66} +(111.333 + 192.834i) q^{67} +(-270.509 - 468.536i) q^{68} +(-253.566 - 614.468i) q^{69} +(-208.848 + 361.735i) q^{70} -336.134 q^{71} +(-2269.77 - 614.648i) q^{72} -119.012 q^{73} +(-34.3040 + 59.4163i) q^{74} +(38.0765 - 49.4861i) q^{75} +(542.399 + 939.462i) q^{76} +(-48.3033 - 83.6638i) q^{77} +(379.351 + 50.4550i) q^{78} +(-11.5440 + 19.9948i) q^{79} -3197.40 q^{80} +(629.388 + 367.848i) q^{81} -1748.87 q^{82} +(330.885 - 573.110i) q^{83} +(847.821 + 112.763i) q^{84} +(122.281 + 211.796i) q^{85} +(440.991 + 763.819i) q^{86} +(345.298 - 448.767i) q^{87} +(600.987 - 1040.94i) q^{88} +1029.81 q^{89} +(1555.10 + 421.116i) q^{90} -91.8357 q^{91} +(-1504.06 + 2605.11i) q^{92} +(288.260 + 698.544i) q^{93} +(215.710 + 373.621i) q^{94} +(-245.185 - 424.673i) q^{95} +(1966.08 + 4764.41i) q^{96} +(850.544 - 1473.19i) q^{97} -275.074 q^{98} +(-264.185 + 262.786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) $ 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.80688	−	4.86166i	0.992382	−	1.71886i	0.389496	−	0.921028i	$-0.372649\pi$
$2$	2.80688	−	4.86166i	0.992382	−	1.71886i	0.602886	−	0.797828i	$-0.294017\pi$
$3$	5.15079	+	0.685073i	0.991271	+	0.131842i
$3$	5.15079	+	0.685073i	0.991271	+	0.131842i
$4$	−11.7571	−	20.3640i	−1.46964	−	2.54550i
$5$	5.31469	+	9.20530i	0.475360	+	0.823347i	0.999602	−	0.0282220i	$-0.00898452\pi$
$5$	5.31469	+	9.20530i	0.475360	+	0.823347i	−0.524242	+	0.851569i	$0.675651\pi$
$6$	17.7882	−	23.1185i	1.21034	−	1.57301i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$	−87.0935			−3.84902
$9$	26.0614	+	7.05734i	0.965235	+	0.261383i
$10$	59.6707			1.88695
$11$	−6.90048	+	11.9520i	−0.189143	+	0.327605i	−0.944965	−	0.327172i	$-0.893904\pi$
$11$	−6.90048	+	11.9520i	−0.189143	+	0.327605i	0.755822	+	0.654777i	$0.227238\pi$
$12$	−46.6078	−	112.945i	−1.12121	−	2.71704i
$13$	6.55969	+	11.3617i	0.139949	+	0.242398i	0.927477	−	0.373880i	$-0.121973\pi$
$13$	6.55969	+	11.3617i	0.139949	+	0.242398i	−0.787528	+	0.616278i	$0.788640\pi$
$14$	19.6482	+	34.0316i	0.375085	+	0.649666i
$15$	21.0685	+	51.0556i	0.362658	+	0.878833i
$16$	−150.404	+	260.507i	−2.35006	+	4.07042i
$17$	23.0081			0.328252			0.164126	−	0.986439i	$-0.447520\pi$
$17$	23.0081			0.328252			0.164126	+	0.986439i	$0.447520\pi$
$18$	107.461	−	106.892i	1.40716	−	1.39971i
$19$	−46.1335			−0.557040			−0.278520	−	0.960430i	$-0.589844\pi$
$19$	−46.1335			−0.557040			−0.278520	+	0.960430i	$0.589844\pi$
$20$	124.971	−	216.456i	1.39722	−	2.42005i
$21$	−22.1808	+	28.8273i	−0.230488	+	0.299554i
$22$	38.7376	+	67.0955i	0.375404	+	0.650219i
$23$	−63.9637	−	110.788i	−0.579885	−	1.00439i	−0.995492	−	0.0948458i	$-0.969764\pi$
$23$	−63.9637	−	110.788i	−0.579885	−	1.00439i	0.415607	−	0.909544i	$-0.363569\pi$
$24$	−448.601	−	59.6654i	−3.81543	−	0.507464i
$25$	6.00824	−	10.4066i	0.0480659	−	0.0832526i
$26$	73.6491			0.555530
$27$	129.402	+	54.2048i	0.922348	+	0.386360i
$28$	164.600			1.11095
$29$	54.4860	−	94.3726i	0.348890	−	0.604295i	−0.637163	−	0.770729i	$-0.719892\pi$
$29$	54.4860	−	94.3726i	0.348890	−	0.604295i	0.986053	+	0.166435i	$0.0532254\pi$
$30$	307.352	+	40.8788i	1.87048	+	0.248780i
$31$	72.7157	+	125.947i	0.421294	+	0.729703i	0.996066	−	0.0886104i	$-0.0282426\pi$
$31$	72.7157	+	125.947i	0.421294	+	0.729703i	−0.574772	+	0.818314i	$0.694909\pi$
$32$	495.957	+	859.022i	2.73980	+	4.74547i
$33$	−43.7309	+	56.8348i	−0.230684	+	0.299808i
$34$	64.5809	−	111.857i	0.325751	−	0.564217i
$35$	−74.4056			−0.359338
$36$	−162.692	−	613.687i	−0.753202	−	2.84114i
$37$	−12.2214			−0.0543024			−0.0271512	−	0.999631i	$-0.508644\pi$
$37$	−12.2214			−0.0543024			−0.0271512	+	0.999631i	$0.508644\pi$
$38$	−129.491	+	224.286i	−0.552796	+	0.957472i
$39$	26.0040	+	63.0158i	0.106769	+	0.258733i
$40$	−462.875	−	801.722i	−1.82967	−	3.16909i
$41$	−155.766	−	269.795i	−0.593332	−	1.02768i	−0.993780	−	0.111362i	$-0.964479\pi$
$41$	−155.766	−	269.795i	−0.593332	−	1.02768i	0.400448	−	0.916320i	$-0.368855\pi$
$42$	77.8895	+	188.750i	0.286157	+	0.693447i
$43$	−78.5554	+	136.062i	−0.278595	+	0.482541i	−0.971036	−	0.238934i	$-0.923202\pi$
$43$	−78.5554	+	136.062i	−0.278595	+	0.482541i	0.692441	+	0.721475i	$0.256535\pi$
$44$	324.520			1.11189
$45$	73.5429	+	277.410i	0.243625	+	0.918975i
$46$	−718.153			−2.30187
$47$	−38.4253	+	66.5545i	−0.119253	+	0.206553i	−0.919472	−	0.393156i	$-0.871383\pi$
$47$	−38.4253	+	66.5545i	−0.119253	+	0.206553i	0.800219	+	0.599708i	$0.204717\pi$
$48$	−953.165	+	1238.78i	−2.86620	+	3.72505i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	−33.7288	−	58.4200i	−0.0953995	−	0.165237i
$51$	118.510	+	15.7622i	0.325386	+	0.0432775i
$52$	154.247	−	267.163i	0.411349	−	0.712477i
$53$	−221.313			−0.573578			−0.286789	−	0.957994i	$-0.592588\pi$
$53$	−221.313			−0.573578			−0.286789	+	0.957994i	$0.592588\pi$
$54$	626.741	−	476.961i	1.57942	−	1.20197i
$55$	−146.695			−0.359644
$56$	304.827	−	527.976i	0.727397	−	1.25989i
$57$	−237.624	−	31.6048i	−0.552178	−	0.0734415i
$58$	−305.871	−	529.785i	−0.692464	−	1.19938i
$59$	−243.121	−	421.097i	−0.536468	−	0.929190i	−0.999091	−	0.0426348i	$-0.986425\pi$
$59$	−243.121	−	421.097i	−0.536468	−	0.929190i	0.462623	−	0.886555i	$-0.346909\pi$
$60$	791.988	−	1029.31i	1.70409	−	2.21472i
$61$	−465.583	+	806.414i	−0.977243	+	1.69264i	−0.304920	+	0.952378i	$0.598630\pi$
$61$	−465.583	+	806.414i	−0.977243	+	1.69264i	−0.672324	+	0.740257i	$0.734704\pi$
$62$	816.417			1.67234
$63$	−133.998	+	133.288i	−0.267970	+	0.266551i
$64$	3161.90			6.17559
$65$	−69.7254	+	120.768i	−0.133052	+	0.230453i
$66$	153.564	+	372.133i	0.286401	+	0.694037i
$67$	111.333	+	192.834i	0.203007	+	0.351618i	0.949496	−	0.313780i	$-0.101595\pi$
$67$	111.333	+	192.834i	0.203007	+	0.351618i	−0.746489	+	0.665398i	$0.768262\pi$
$68$	−270.509	−	468.536i	−0.482413	−	0.835563i
$69$	−253.566	−	614.468i	−0.442402	−	1.07208i
$70$	−208.848	+	361.735i	−0.356601	+	0.617651i
$71$	−336.134			−0.561857			−0.280928	−	0.959729i	$-0.590642\pi$
$71$	−336.134			−0.561857			−0.280928	+	0.959729i	$0.590642\pi$
$72$	−2269.77	−	614.648i	−3.71521	−	1.00607i
$73$	−119.012			−0.190812			−0.0954061	−	0.995438i	$-0.530415\pi$
$73$	−119.012			−0.190812			−0.0954061	+	0.995438i	$0.530415\pi$
$74$	−34.3040	+	59.4163i	−0.0538887	+	0.0933379i
$75$	38.0765	−	49.4861i	0.0586226	−	0.0761888i
$76$	542.399	+	939.462i	0.818650	+	1.41794i
$77$	−48.3033	−	83.6638i	−0.0714893	−	0.123823i
$78$	379.351	+	50.4550i	0.550680	+	0.0732423i
$79$	−11.5440	+	19.9948i	−0.0164405	+	0.0284758i	−0.874129	−	0.485695i	$-0.838567\pi$
$79$	−11.5440	+	19.9948i	−0.0164405	+	0.0284758i	0.857688	+	0.514170i	$0.171900\pi$
$80$	−3197.40			−4.46850
$81$	629.388	+	367.848i	0.863358	+	0.504592i
$82$	−1748.87			−2.35525
$83$	330.885	−	573.110i	0.437582	−	0.757915i	−0.559920	−	0.828547i	$-0.689168\pi$
$83$	330.885	−	573.110i	0.437582	−	0.757915i	0.997502	+	0.0706317i	$0.0225015\pi$
$84$	847.821	+	112.763i	1.10125	+	0.146470i
$85$	122.281	+	211.796i	0.156038	+	0.270265i
$86$	440.991	+	763.819i	0.552945	+	0.957729i
$87$	345.298	−	448.767i	0.425516	−	0.553021i
$88$	600.987	−	1040.94i	0.728016	−	1.26096i
$89$	1029.81			1.22652			0.613258	−	0.789883i	$-0.289859\pi$
$89$	1029.81			1.22652			0.613258	+	0.789883i	$0.289859\pi$
$90$	1555.10	+	421.116i	1.82135	+	0.493217i
$91$	−91.8357			−0.105791
$92$	−1504.06	+	2605.11i	−1.70445	+	2.95219i
$93$	288.260	+	698.544i	0.321411	+	0.778878i
$94$	215.710	+	373.621i	0.236689	+	0.409958i
$95$	−245.185	−	424.673i	−0.264795	−	0.458638i
$96$	1966.08	+	4764.41i	2.09023	+	5.06527i
$97$	850.544	−	1473.19i	0.890306	−	1.54206i	0.0507973	−	0.998709i	$-0.483824\pi$
$97$	850.544	−	1473.19i	0.890306	−	1.54206i	0.839509	−	0.543346i	$-0.182843\pi$
$98$	−275.074			−0.283538
$99$	−264.185	+	262.786i	−0.268198	+	0.266777i
$100$	−282.559			−0.282559
$101$	732.521	−	1268.76i	0.721669	−	1.24997i	−0.238662	−	0.971103i	$-0.576709\pi$
$101$	732.521	−	1268.76i	0.721669	−	1.24997i	0.960331	−	0.278864i	$-0.0899579\pi$
$102$	409.273	−	531.912i	0.397295	−	0.516344i
$103$	625.912	+	1084.11i	0.598766	+	1.03709i	0.993004	+	0.118085i	$0.0376755\pi$
$103$	625.912	+	1084.11i	0.598766	+	1.03709i	−0.394237	+	0.919009i	$0.628991\pi$
$104$	−571.307	−	989.532i	−0.538666	−	0.932996i
$105$	−383.248	−	50.9733i	−0.356202	−	0.0473760i
$106$	−621.199	+	1075.95i	−0.569209	+	0.985899i
$107$	−1493.01			−1.34893			−0.674463	−	0.738308i	$-0.735625\pi$
$107$	−1493.01			−1.34893			−0.674463	+	0.738308i	$0.735625\pi$
$108$	−417.571	−	3272.43i	−0.372044	−	2.91565i
$109$	1181.10			1.03788			0.518941	−	0.854810i	$-0.326326\pi$
$109$	1181.10			1.03788			0.518941	+	0.854810i	$0.326326\pi$
$110$	−411.756	+	713.183i	−0.356904	+	0.618176i
$111$	−62.9500	−	8.37256i	−0.0538283	−	0.00715935i
$112$	−1052.83	−	1823.55i	−0.888239	−	1.53847i
$113$	541.384	+	937.704i	0.450700	+	0.780635i	0.998430	−	0.0560202i	$-0.0178411\pi$
$113$	541.384	+	937.704i	0.450700	+	0.780635i	−0.547730	+	0.836655i	$0.684508\pi$
$114$	−820.635	+	1066.54i	−0.674206	+	0.876231i
$115$	679.894	−	1177.61i	0.551308	−	0.954893i
$116$	−2562.40			−2.05097
$117$	90.7710	+	342.396i	0.0717246	+	0.270551i
$118$	−2729.64			−2.12953
$119$	−80.5283	+	139.479i	−0.0620337	+	0.107446i
$120$	−1834.93	−	4446.61i	−1.39588	−	3.38265i
$121$	570.267	+	987.731i	0.428450	+	0.742097i
$122$	2613.67	+	4527.01i	1.93960	+	3.35948i
$123$	−617.491	−	1496.37i	−0.452661	−	1.09694i
$124$	1709.86	−	2961.56i	1.23830	−	2.14481i
$125$	1456.40			1.04211
$126$	271.885	+	1025.57i	0.192234	+	0.725122i
$127$	−237.723			−0.166098			−0.0830492	−	0.996545i	$-0.526466\pi$
$127$	−237.723			−0.166098			−0.0830492	+	0.996545i	$0.526466\pi$
$128$	4907.42	−	8499.91i	3.38874	−	5.86947i
$129$	−497.835	+	647.011i	−0.339782	+	0.441598i
$130$	391.422	+	677.962i	0.264077	+	0.457394i
$131$	−418.414	−	724.715i	−0.279061	−	0.483348i	0.692090	−	0.721811i	$-0.256690\pi$
$131$	−418.414	−	724.715i	−0.279061	−	0.483348i	−0.971152	+	0.238462i	$0.923357\pi$
$132$	1671.53	+	222.320i	1.10218	+	0.146594i
$133$	161.467	−	279.670i	0.105271	−	0.182334i
$134$	1249.99			0.805841
$135$	188.758	+	1479.26i	0.120339	+	0.943073i
$136$	−2003.85			−1.26345
$137$	963.476	−	1668.79i	0.600842	−	1.04069i	−0.391852	−	0.920028i	$-0.628165\pi$
$137$	963.476	−	1668.79i	0.600842	−	1.04069i	0.992694	−	0.120660i	$-0.0385012\pi$
$138$	−3699.06	−	491.987i	−2.28177	−	0.303484i
$139$	−404.684	−	700.933i	−0.246941	−	0.427715i	0.715734	−	0.698373i	$-0.246092\pi$
$139$	−404.684	−	700.933i	−0.246941	−	0.427715i	−0.962676	+	0.270658i	$0.912759\pi$
$140$	874.797	+	1515.19i	0.528099	+	0.914694i
$141$	−243.515	+	316.484i	−0.145445	+	0.189027i
$142$	−943.489	+	1634.17i	−0.557576	+	0.965750i
$143$	−181.060			−0.105881
$144$	−5758.21	+	5727.71i	−3.33230	+	3.31465i
$145$	1158.30			0.663393
$146$	−334.052	+	578.595i	−0.189359	+	0.327979i
$147$	−97.1232	−	235.359i	−0.0544938	−	0.132055i
$148$	143.689	+	248.876i	0.0798051	+	0.138226i
$149$	−171.908	−	297.753i	−0.0945183	−	0.163710i	0.814889	−	0.579617i	$-0.196798\pi$
$149$	−171.908	−	297.753i	−0.0945183	−	0.163710i	−0.909407	+	0.415906i	$0.863464\pi$
$150$	−133.708	−	324.016i	−0.0727815	−	0.176372i
$151$	935.432	−	1620.22i	0.504135	−	0.873187i	−0.495854	−	0.868406i	$-0.665145\pi$
$151$	935.432	−	1620.22i	0.504135	−	0.873187i	0.999989	−	0.00478097i	$-0.00152184\pi$
$152$	4017.93			2.14406
$153$	599.621	+	162.376i	0.316840	+	0.0857994i
$154$	−542.327			−0.283779
$155$	−772.922	+	1338.74i	−0.400533	+	0.693743i
$156$	977.518	−	1270.43i	0.501693	−	0.652025i
$157$	−90.0098	−	155.902i	−0.0457552	−	0.0792503i	0.842241	−	0.539101i	$-0.181236\pi$
$157$	−90.0098	−	155.902i	−0.0457552	−	0.0792503i	−0.887996	+	0.459851i	$0.847903\pi$
$158$	64.8052	+	112.246i	0.0326305	+	0.0565178i
$159$	−1139.94	−	151.615i	−0.568572	−	0.0756219i
$160$	−5271.71	+	9130.86i	−2.60478	+	4.51161i
$161$	895.492			0.438352
$162$	3554.96	−	2027.37i	1.72410	−	0.983240i
$163$	−3034.93			−1.45837			−0.729184	−	0.684317i	$-0.760100\pi$
$163$	−3034.93			−1.45837			−0.729184	+	0.684317i	$0.760100\pi$
$164$	−3662.74	+	6344.05i	−1.74397	+	3.02065i
$165$	−755.598	−	100.497i	−0.356504	−	0.0474163i
$166$	−1857.51	−	3217.30i	−0.868498	−	1.50428i
$167$	1010.34	+	1749.97i	0.468160	+	0.810878i	0.999338	−	0.0363829i	$-0.0115836\pi$
$167$	1010.34	+	1749.97i	0.468160	+	0.810878i	−0.531177	+	0.847261i	$0.678250\pi$
$168$	1931.80	−	2510.67i	0.887154	−	1.15299i
$169$	1012.44	−	1753.60i	0.460829	−	0.798179i
$170$	1372.91			0.619396
$171$	−1202.30	−	325.580i	−0.537675	−	0.145601i
$172$	3694.35			1.63774
$173$	−1201.79	+	2081.56i	−0.528152	+	0.914786i	0.471309	+	0.881968i	$0.343782\pi$
$173$	−1201.79	+	2081.56i	−0.528152	+	0.914786i	−0.999461	+	0.0328181i	$0.989552\pi$
$174$	−1212.54	−	2938.36i	−0.528290	−	1.28021i
$175$	42.0577	+	72.8461i	0.0181672	+	0.0314665i
$176$	−2075.72	−	3595.24i	−0.888994	−	1.53978i
$177$	−963.782	−	2335.54i	−0.409279	−	0.991808i
$178$	2890.56	−	5006.60i	1.21717	−	2.10820i
$179$	−3067.07			−1.28069			−0.640345	−	0.768088i	$-0.721209\pi$
$179$	−3067.07			−1.28069			−0.640345	+	0.768088i	$0.721209\pi$
$180$	4784.52	−	4759.18i	1.98121	−	1.97071i
$181$	1400.80			0.575250			0.287625	−	0.957743i	$-0.407134\pi$
$181$	1400.80			0.575250			0.287625	+	0.957743i	$0.407134\pi$
$182$	−257.772	+	446.474i	−0.104985	+	0.181840i
$183$	−2950.58	+	3834.71i	−1.19187	+	1.54902i
$184$	5570.82	+	9648.95i	2.23199	+	3.86592i
$185$	−64.9530	−	112.502i	−0.0258132	−	0.0447097i
$186$	4205.19	+	559.305i	1.65774	+	0.220485i
$187$	−158.767	+	274.992i	−0.0620865	+	0.107537i
$188$	1807.09			0.701039
$189$	−781.506	+	594.740i	−0.300773	+	0.228894i
$190$	−2752.82			−1.05111
$191$	−1337.18	+	2316.06i	−0.506570	+	0.877406i	0.493401	+	0.869802i	$0.335754\pi$
$191$	−1337.18	+	2316.06i	−0.506570	+	0.877406i	−0.999971	+	0.00760356i	$0.997580\pi$
$192$	16286.3	+	2166.13i	6.12168	+	0.814204i
$193$	1537.71	+	2663.39i	0.573507	+	0.993343i	0.996202	+	0.0870711i	$0.0277507\pi$
$193$	1537.71	+	2663.39i	0.573507	+	0.993343i	−0.422695	+	0.906272i	$0.638916\pi$
$194$	−4774.75	−	8270.11i	−1.76705	−	3.06061i
$195$	−441.876	+	574.284i	−0.162274	+	0.210899i
$196$	−576.100	+	997.835i	−0.209949	+	0.363642i
$197$	−1265.39			−0.457641			−0.228820	−	0.973469i	$-0.573487\pi$
$197$	−1265.39			−0.457641			−0.228820	+	0.973469i	$0.573487\pi$
$198$	536.039	+	2021.98i	0.192397	+	0.725738i
$199$	−1644.24			−0.585714			−0.292857	−	0.956156i	$-0.594606\pi$
$199$	−1644.24			−0.585714			−0.292857	+	0.956156i	$0.594606\pi$
$200$	−523.279	+	906.345i	−0.185007	+	0.320441i
$201$	441.347	+	1069.52i	0.154877	+	0.375314i
$202$	−4112.20	−	7122.53i	−1.43234	−	2.48089i
$203$	381.402	+	660.608i	0.131868	+	0.228402i
$204$	−1072.36	−	2598.65i	−0.368039	−	0.891872i
$205$	1655.70	−	2867.75i	0.564093	−	0.977037i
$206$	7027.44			2.37682
$207$	−885.109	−	3338.71i	−0.297195	−	1.12104i
$208$	−3946.41			−1.31555
$209$	318.343	−	551.387i	0.105360	−	0.182489i
$210$	−1323.55	+	1720.14i	−0.434920	+	0.565244i
$211$	−139.672	−	241.918i	−0.0455705	−	0.0789305i	0.842340	−	0.538946i	$-0.181177\pi$
$211$	−139.672	−	241.918i	−0.0455705	−	0.0789305i	−0.887911	+	0.460015i	$0.847844\pi$
$212$	2602.01	+	4506.81i	0.842956	+	1.46004i
$213$	−1731.36	−	230.277i	−0.556952	−	0.0740765i
$214$	−4190.71	+	7258.53i	−1.33865	+	2.31861i
$215$	−1669.99			−0.529732
$216$	−11270.1	−	4720.89i	−3.55014	−	1.48711i
$217$	−1018.02			−0.318469
$218$	3315.21	−	5742.12i	1.02998	−	1.78397i
$219$	−613.006	−	81.5318i	−0.189147	−	0.0251571i
$220$	1724.72	+	2987.30i	0.528548	+	0.915472i
$221$	150.926	+	261.411i	0.0459383	+	0.0795676i
$222$	−217.397	+	282.540i	−0.0657242	+	0.0854183i
$223$	1610.82	−	2790.03i	0.483716	−	0.837820i	−0.516109	−	0.856523i	$-0.672620\pi$
$223$	1610.82	−	2790.03i	0.483716	−	0.837820i	0.999825	+	0.0187024i	$0.00595351\pi$
$224$	−6943.39			−2.07109
$225$	230.026	−	228.807i	0.0681557	−	0.0677948i
$226$	6078.39			1.78907
$227$	1153.60	−	1998.09i	0.337300	−	0.584221i	−0.646624	−	0.762809i	$-0.723820\pi$
$227$	1153.60	−	1998.09i	0.337300	−	0.584221i	0.983924	+	0.178588i	$0.0571529\pi$
$228$	2150.18	+	5210.56i	0.624559	+	1.51350i
$229$	2819.22	+	4883.04i	0.813535	+	1.40908i	0.910375	+	0.413784i	$0.135793\pi$
$229$	2819.22	+	4883.04i	0.813535	+	1.40908i	−0.0968396	+	0.995300i	$0.530873\pi$
$230$	−3816.76	−	6610.82i	−1.09422	−	1.89524i
$231$	−191.485	−	464.026i	−0.0545401	−	0.132168i
$232$	−4745.38	+	8219.24i	−1.34289	+	2.32595i
$233$	377.100			0.106028			0.0530142	−	0.998594i	$-0.483117\pi$
$233$	377.100			0.106028			0.0530142	+	0.998594i	$0.483117\pi$
$234$	1919.39	+	519.766i	0.536217	+	0.145206i
$235$	−816.873			−0.226753
$236$	−5716.81	+	9901.81i	−1.57683	+	2.73116i
$237$	−73.1586	+	95.0806i	−0.0200513	+	0.0260597i
$238$	452.066	+	783.002i	0.123122	+	0.213254i
$239$	2284.16	+	3956.27i	0.618200	+	1.07075i	0.989814	+	0.142366i	$0.0454710\pi$
$239$	2284.16	+	3956.27i	0.618200	+	1.07075i	−0.371614	+	0.928387i	$0.621196\pi$
$240$	−16469.1	−	2190.45i	−4.42949	−	0.589137i
$241$	−1769.81	+	3065.41i	−0.473044	+	0.819337i	−0.999524	−	0.0308510i	$-0.990178\pi$
$241$	−1769.81	+	3065.41i	−0.473044	+	0.819337i	0.526480	+	0.850188i	$0.323512\pi$
$242$	6402.68			1.70074
$243$	2989.85	+	2325.88i	0.789295	+	0.614014i
$244$	21895.7			5.74480
$245$	260.420	−	451.060i	0.0679086	−	0.117621i
$246$	−9008.07	−	1198.10i	−2.33469	−	0.310521i
$247$	−302.622	−	524.157i	−0.0779570	−	0.135025i
$248$	−6333.06	−	10969.2i	−1.62157	−	2.80865i
$249$	2096.94	−	2725.29i	0.533688	−	0.693607i
$250$	4087.94	−	7080.51i	1.03418	−	1.79124i
$251$	1971.96			0.495893			0.247946	−	0.968774i	$-0.420244\pi$
$251$	1971.96			0.495893			0.247946	+	0.968774i	$0.420244\pi$
$252$	4289.70	+	1161.64i	1.07232	+	0.290382i
$253$	1765.52			0.438724
$254$	−667.259	+	1155.73i	−0.164833	+	0.285499i
$255$	484.747	+	1174.69i	0.119043	+	0.288478i
$256$	−14901.5	−	25810.1i	−3.63806	−	6.30130i
$257$	720.799	+	1248.46i	0.174950	+	0.303023i	0.940144	−	0.340777i	$-0.110690\pi$
$257$	720.799	+	1248.46i	0.174950	+	0.303023i	−0.765194	+	0.643800i	$0.777357\pi$
$258$	1748.18	+	4236.38i	0.421849	+	1.02227i
$259$	42.7749	−	74.0884i	0.0102622	−	0.0177746i
$260$	3279.09			0.782155
$261$	2086.00	−	2074.95i	0.494713	−	0.492093i
$262$	−4697.75			−1.10774
$263$	146.066	−	252.994i	0.0342465	−	0.0593168i	−0.848394	−	0.529365i	$-0.822430\pi$
$263$	146.066	−	252.994i	0.0342465	−	0.0593168i	0.882641	+	0.470048i	$0.155764\pi$
$264$	3808.68	−	4949.94i	0.887909	−	1.15397i
$265$	−1176.21	−	2037.25i	−0.272656	−	0.472254i
$266$	−906.439	−	1570.00i	−0.208937	−	0.361890i
$267$	5304.35	+	705.497i	1.21581	+	0.161707i
$268$	2617.91	−	4534.35i	0.596695	−	1.03351i
$269$	862.029			0.195386			0.0976930	−	0.995217i	$-0.468854\pi$
$269$	862.029			0.195386			0.0976930	+	0.995217i	$0.468854\pi$
$270$	7721.50	+	3234.44i	1.74043	+	0.729044i
$271$	−2157.78			−0.483674			−0.241837	−	0.970317i	$-0.577750\pi$
$271$	−2157.78			−0.483674			−0.241837	+	0.970317i	$0.577750\pi$
$272$	−3460.50	+	5993.76i	−0.771411	+	1.33612i
$273$	−473.027	−	62.9141i	−0.104868	−	0.0139478i
$274$	−5408.72	−	9368.18i	−1.19253	−	2.06552i
$275$	82.9195	+	143.621i	0.0181827	+	0.0314933i
$276$	−9531.80	+	12388.0i	−2.07879	+	2.70170i
$277$	−3844.36	+	6658.63i	−0.833882	+	1.44433i	0.0610562	+	0.998134i	$0.480553\pi$
$277$	−3844.36	+	6658.63i	−0.833882	+	1.44433i	−0.894938	+	0.446191i	$0.852780\pi$
$278$	−4543.59			−0.980240
$279$	1006.22	+	3795.54i	0.215916	+	0.814454i
$280$	6480.24			1.38310
$281$	2511.43	−	4349.93i	0.533166	−	0.923470i	−0.466084	−	0.884740i	$-0.654336\pi$
$281$	2511.43	−	4349.93i	0.533166	−	0.923470i	0.999250	−	0.0387294i	$-0.0123310\pi$
$282$	855.121	+	2072.22i	0.180573	+	0.437585i
$283$	−1268.81	−	2197.65i	−0.266513	−	0.461614i	0.701446	−	0.712723i	$-0.252538\pi$
$283$	−1268.81	−	2197.65i	−0.266513	−	0.461614i	−0.967959	+	0.251109i	$0.919205\pi$
$284$	3951.98	+	6845.03i	0.825729	+	1.43020i
$285$	−971.967	−	2355.37i	−0.202015	−	0.489545i
$286$	−508.214	+	880.252i	−0.105074	+	0.181994i
$287$	2180.73			0.448517
$288$	6862.89	+	25887.4i	1.40417	+	5.29663i
$289$	−4383.63			−0.892251
$290$	3251.22	−	5631.28i	0.658339	−	1.14028i
$291$	5390.22	−	7005.39i	1.08584	−	1.41121i
$292$	1399.24	+	2423.56i	0.280426	+	0.485712i
$293$	2141.19	+	3708.66i	0.426928	+	0.739461i	0.996598	−	0.0824125i	$-0.0262625\pi$
$293$	2141.19	+	3708.66i	0.426928	+	0.739461i	−0.569670	+	0.821873i	$0.692929\pi$
$294$	−1416.85	−	188.446i	−0.281063	−	0.0373823i
$295$	2584.22	−	4476.00i	0.510031	−	0.883400i
$296$	1064.41			0.209011
$297$	−1540.79	+	1172.57i	−0.301029	+	0.229089i
$298$	−1930.10			−0.375193
$299$	839.164	−	1453.48i	0.162308	−	0.281126i
$300$	−1455.40	−	193.574i	−0.280093	−	0.0372532i
$301$	−549.888	−	952.433i	−0.105299	−	0.182383i
$302$	−5251.29	−	9095.50i	−1.00059	−	1.73307i
$303$	4642.26	−	6033.31i	0.880168	−	1.14391i
$304$	6938.66	−	12018.1i	1.30908	−	2.26739i
$305$	−9897.72			−1.85817
$306$	2472.48	−	2459.39i	0.461903	−	0.459457i
$307$	−6170.23			−1.14708			−0.573541	−	0.819177i	$-0.694430\pi$
$307$	−6170.23			−1.14708			−0.573541	+	0.819177i	$0.694430\pi$
$308$	−1135.82	+	1967.30i	−0.210128	+	0.363952i
$309$	2481.25	+	6012.83i	0.456807	+	1.10698i
$310$	4339.00	+	7515.37i	0.794963	+	1.37692i
$311$	3244.24	+	5619.19i	0.591525	+	1.02455i	0.994027	+	0.109132i	$0.0348070\pi$
$311$	3244.24	+	5619.19i	0.591525	+	1.02455i	−0.402503	+	0.915419i	$0.631860\pi$
$312$	−2264.78	−	5488.26i	−0.410955	−	0.995871i
$313$	−3636.59	+	6298.76i	−0.656716	+	1.13747i	0.324745	+	0.945802i	$0.394722\pi$
$313$	−3636.59	+	6298.76i	−0.656716	+	1.13747i	−0.981461	+	0.191664i	$0.938612\pi$
$314$	−1010.59			−0.181626
$315$	−1939.11	−	525.105i	−0.346846	−	0.0939249i
$316$	542.898			0.0966468
$317$	4223.12	−	7314.66i	0.748247	−	1.29600i	−0.200416	−	0.979711i	$-0.564229\pi$
$317$	4223.12	−	7314.66i	0.748247	−	1.29600i	0.948662	−	0.316290i	$-0.102437\pi$
$318$	−3936.77	+	5116.42i	−0.694223	+	0.902247i
$319$	751.959	+	1302.43i	0.131980	+	0.228596i
$320$	16804.5	+	29106.3i	2.93563	+	5.08466i
$321$	−7690.21	−	1022.82i	−1.33715	−	0.177846i
$322$	2513.54	−	4353.57i	0.435012	−	0.753463i
$323$	−1061.44			−0.182849
$324$	91.0311	−	17141.7i	0.0156089	−	2.93924i
$325$	157.649			0.0269070
$326$	−8518.69	+	14754.8i	−1.44726	+	2.50673i
$327$	6083.62	+	809.142i	1.02882	+	0.136837i
$328$	13566.2	+	23497.4i	2.28375	+	3.95557i
$329$	−268.977	−	465.882i	−0.0450735	−	0.0780695i
$330$	−2609.45	+	3391.38i	−0.435290	+	0.565724i
$331$	−1698.45	+	2941.80i	−0.282040	+	0.488507i	−0.971887	−	0.235448i	$-0.924344\pi$
$331$	−1698.45	+	2941.80i	−0.282040	+	0.488507i	0.689847	+	0.723955i	$0.257678\pi$
$332$	−15561.0			−2.57236
$333$	−318.506	−	86.2506i	−0.0524146	−	0.0141937i
$334$	11343.7			1.85838
$335$	−1183.40	+	2049.70i	−0.193003	+	0.334290i
$336$	−4173.63	−	10114.0i	−0.677649	−	1.64215i
$337$	−962.226	−	1666.62i	−0.155536	−	0.269397i	0.777718	−	0.628614i	$-0.216377\pi$
$337$	−962.226	−	1666.62i	−0.155536	−	0.269397i	−0.933254	+	0.359217i	$0.883044\pi$
$338$	−5683.60	−	9844.28i	−0.914636	−	1.58420i
$339$	2146.16	+	5200.81i	0.343845	+	0.833242i
$340$	2875.34	−	4980.24i	0.458639	−	0.794387i
$341$	−2007.09			−0.318739
$342$	−4957.58	+	4931.32i	−0.783845	+	0.779694i
$343$	343.000			0.0539949
$344$	6841.66	−	11850.1i	1.07232	−	1.85731i
$345$	4308.74	−	5599.85i	0.672391	−	0.873872i
$346$	6746.55	+	11685.4i	1.04826	+	1.81563i
$347$	−4715.73	−	8167.88i	−0.729549	−	1.26362i	−0.957074	−	0.289843i	$-0.906397\pi$
$347$	−4715.73	−	8167.88i	−0.729549	−	1.26362i	0.227525	−	0.973772i	$-0.426937\pi$
$348$	−13198.4	−	1755.43i	−2.03307	−	0.270405i
$349$	−5396.76	+	9347.47i	−0.827742	+	1.43369i	0.0720632	+	0.997400i	$0.477042\pi$
$349$	−5396.76	+	9347.47i	−0.827742	+	1.43369i	−0.899805	+	0.436291i	$0.856292\pi$
$350$	472.203			0.0721153
$351$	232.976	+	1825.79i	0.0354284	+	0.277646i
$352$	−13689.3			−2.07285
$353$	2415.70	−	4184.11i	0.364234	−	0.630871i	−0.624419	−	0.781090i	$-0.714664\pi$
$353$	2415.70	−	4184.11i	0.364234	−	0.630871i	0.988653	+	0.150218i	$0.0479976\pi$
$354$	−14059.8	−	1870.00i	−2.11094	−	0.280762i
$355$	−1786.45	−	3094.22i	−0.267084	−	0.462603i
$356$	−12107.7	−	20971.1i	−1.80254	−	3.12209i
$357$	−510.338	+	663.260i	−0.0756581	+	0.0983290i
$358$	−8608.89	+	14911.0i	−1.27093	+	2.20132i
$359$	−3882.67			−0.570806			−0.285403	−	0.958408i	$-0.592127\pi$
$359$	−3882.67			−0.570806			−0.285403	+	0.958408i	$0.592127\pi$
$360$	−6405.11	−	24160.6i	−0.937719	−	3.53716i
$361$	−4730.70			−0.689706
$362$	3931.87	−	6810.19i	0.570868	−	0.988772i
$363$	2260.66	+	5478.27i	0.326870	+	0.792107i
$364$	1079.73	+	1870.14i	0.155475	+	0.269291i
$365$	−632.511	−	1095.54i	−0.0907045	−	0.157105i
$366$	10361.2	+	25108.3i	1.47974	+	3.58588i
$367$	6176.84	−	10698.6i	0.878552	−	1.52170i	0.0256212	−	0.999672i	$-0.491844\pi$
$367$	6176.84	−	10698.6i	0.878552	−	1.52170i	0.852931	−	0.522024i	$-0.174823\pi$
$368$	38481.5			5.45105
$369$	−2155.45	−	8130.53i	−0.304087	−	1.14704i
$370$	−729.260			−0.102466
$371$	774.595	−	1341.64i	0.108396	−	0.187748i
$372$	10836.0	−	14083.0i	1.51027	−	1.96282i
$373$	334.533	+	579.428i	0.0464382	+	0.0804333i	0.888310	−	0.459244i	$-0.151880\pi$
$373$	334.533	+	579.428i	0.0464382	+	0.0804333i	−0.841872	+	0.539677i	$0.818546\pi$
$374$	891.278	+	1543.74i	0.123227	+	0.213435i
$375$	7501.61	+	997.739i	1.03302	+	0.137395i
$376$	3346.59	−	5796.46i	0.459009	−	0.795026i
$377$	1429.65			0.195306
$378$	697.831	+	5468.78i	0.0949538	+	0.744136i
$379$	−2686.32			−0.364082			−0.182041	−	0.983291i	$-0.558270\pi$
$379$	−2686.32			−0.364082			−0.182041	+	0.983291i	$0.558270\pi$
$380$	−5765.36	+	9985.89i	−0.778307	+	1.34807i
$381$	−1224.46	−	162.857i	−0.164648	−	0.0218988i
$382$	7506.61	+	13001.8i	1.00542	+	1.74144i
$383$	−115.067	−	199.301i	−0.0153515	−	0.0265896i	0.858248	−	0.513236i	$-0.171553\pi$
$383$	−115.067	−	199.301i	−0.0153515	−	0.0265896i	−0.873599	+	0.486646i	$0.838220\pi$
$384$	31100.2	−	40419.3i	4.13301	−	5.37146i
$385$	513.434	−	889.294i	0.0679663	−	0.117721i
$386$	17264.7			2.27655
$387$	−3007.49	+	2991.57i	−0.395038	+	0.392945i
$388$	−39999.9			−5.23373
$389$	−754.361	+	1306.59i	−0.0983230	+	0.170300i	−0.910991	−	0.412427i	$-0.864681\pi$
$389$	−754.361	+	1306.59i	−0.0983230	+	0.170300i	0.812668	+	0.582727i	$0.198014\pi$
$390$	1551.68	+	3760.20i	0.201467	+	0.488218i
$391$	−1471.68	−	2549.03i	−0.190348	−	0.329693i
$392$	2133.79	+	3695.83i	0.274930	+	0.476193i
$393$	−1658.68	−	4019.50i	−0.212900	−	0.515921i
$394$	−3551.79	+	6151.89i	−0.454154	+	0.786618i
$395$	−245.411			−0.0312607
$396$	8457.42	+	2290.24i	1.07324	+	0.290629i
$397$	11452.3			1.44780			0.723900	−	0.689905i	$-0.242348\pi$
$397$	11452.3			1.44780			0.723900	+	0.689905i	$0.242348\pi$
$398$	−4615.19	+	7993.74i	−0.581252	+	1.00676i
$399$	1023.28	−	1329.90i	0.128391	−	0.166863i
$400$	1807.32	+	3130.38i	0.225916	+	0.391297i
$401$	−4165.67	−	7215.15i	−0.518762	−	0.898522i	−0.999762	−	0.0218018i	$-0.993060\pi$
$401$	−4165.67	−	7215.15i	−0.518762	−	0.898522i	0.481000	−	0.876720i	$-0.340274\pi$
$402$	6438.44	+	856.335i	0.798807	+	0.106244i
$403$	−953.985	+	1652.35i	−0.117919	+	0.204242i
$404$	−34449.4			−4.24238
$405$	−41.1496	+	7748.70i	−0.00504874	+	0.950706i
$406$	4282.20			0.523453
$407$	84.3336	−	146.070i	0.0102709	−	0.0177897i
$408$	−10321.4	−	1372.79i	−1.25242	−	0.166576i
$409$	−4781.04	−	8281.01i	−0.578013	−	1.00115i	−0.995707	−	0.0925604i	$-0.970495\pi$
$409$	−4781.04	−	8281.01i	−0.578013	−	1.00115i	0.417694	−	0.908588i	$-0.362838\pi$
$410$	−9294.69	−	16098.9i	−1.11959	−	1.93919i
$411$	6105.91	−	7935.54i	0.732804	−	0.952388i
$412$	14717.9	−	25492.1i	1.75995	−	3.04832i
$413$	3403.69			0.405532
$414$	−18716.0	−	5068.25i	−2.22184	−	0.601669i
$415$	7034.20			0.832037
$416$	−6506.65	+	11269.8i	−0.766862	+	1.32824i
$417$	−1604.25	−	3887.60i	−0.188395	−	0.456538i
$418$	−1787.10	−	3095.35i	−0.209115	−	0.362198i
$419$	6668.33	+	11549.9i	0.777492	+	1.34666i	0.933383	+	0.358882i	$0.116842\pi$
$419$	6668.33	+	11549.9i	0.777492	+	1.34666i	−0.155891	+	0.987774i	$0.549825\pi$
$420$	3467.88	+	8403.75i	0.402894	+	0.976336i
$421$	−815.417	+	1412.34i	−0.0943967	+	0.163500i	−0.909357	−	0.416017i	$-0.863426\pi$
$421$	−815.417	+	1412.34i	−0.0943967	+	0.163500i	0.814960	+	0.579517i	$0.196759\pi$
$422$	−1568.16			−0.180894
$423$	−1471.11	+	1463.32i	−0.169097	+	0.168201i
$424$	19274.9			2.20772
$425$	138.238	−	239.435i	0.0157777	−	0.0273278i
$426$	−5979.24	+	7770.92i	−0.680036	+	0.883808i
$427$	−3259.08	−	5644.90i	−0.369363	−	0.639756i
$428$	17553.6	+	30403.7i	1.98244	+	3.43369i
$429$	−932.603	−	124.039i	−0.104957	−	0.0139596i
$430$	−4687.46	+	8118.91i	−0.525696	+	0.910532i
$431$	−12404.0			−1.38626			−0.693130	−	0.720813i	$-0.743769\pi$
$431$	−12404.0			−1.38626			−0.693130	+	0.720813i	$0.743769\pi$
$432$	−33583.3	+	25557.5i	−3.74022	+	2.84638i
$433$	−6278.82			−0.696861			−0.348430	−	0.937335i	$-0.613285\pi$
$433$	−6278.82			−0.696861			−0.348430	+	0.937335i	$0.613285\pi$
$434$	−2857.46	+	4949.26i	−0.316042	+	0.547401i
$435$	5966.19	+	793.523i	0.657602	+	0.0874632i
$436$	−13886.4	−	24052.0i	−1.52532	−	2.64193i
$437$	2950.87	+	5111.06i	0.323019	+	0.559485i
$438$	−2117.01	+	2751.37i	−0.230947	+	0.300150i
$439$	−7098.54	+	12295.0i	−0.771742	+	1.33670i	0.164865	+	0.986316i	$0.447281\pi$
$439$	−7098.54	+	12295.0i	−0.771742	+	1.33670i	−0.936607	+	0.350381i	$0.886052\pi$
$440$	12776.2			1.38428
$441$	−339.023	−	1278.82i	−0.0366076	−	0.138087i
$442$	1694.52			0.182354
$443$	−8308.71	+	14391.1i	−0.891104	+	1.54344i	−0.0525498	+	0.998618i	$0.516735\pi$
$443$	−8308.71	+	14391.1i	−0.891104	+	1.54344i	−0.838554	+	0.544819i	$0.816599\pi$
$444$	569.613	+	1380.35i	0.0608844	+	0.147542i
$445$	5473.13	+	9479.74i	0.583037	+	1.00985i
$446$	−9042.77	−	15662.5i	−0.960061	−	1.66288i
$447$	−681.479	−	1651.43i	−0.0721092	−	0.174743i
$448$	−11066.7	+	19168.0i	−1.16708	+	2.02144i
$449$	−424.376			−0.0446048			−0.0223024	−	0.999751i	$-0.507100\pi$
$449$	−424.376			−0.0446048			−0.0223024	+	0.999751i	$0.507100\pi$
$450$	−466.729	−	1760.54i	−0.0488929	−	0.184428i
$451$	4299.45			0.448898
$452$	12730.3	−	22049.4i	1.32474	−	2.29451i
$453$	5928.18	−	7704.55i	0.614857	−	0.799098i
$454$	−6476.03	−	11216.8i	−0.669461	−	1.15954i
$455$	−488.078	−	845.376i	−0.0502889	−	0.0871029i
$456$	20695.5	+	2752.58i	2.12535	+	0.282678i
$457$	3850.29	−	6668.89i	0.394111	−	0.682620i	−0.598876	−	0.800842i	$-0.704386\pi$
$457$	3850.29	−	6668.89i	0.394111	−	0.682620i	0.992987	+	0.118221i	$0.0377192\pi$
$458$	31652.9			3.22935
$459$	2977.29	+	1247.15i	0.302762	+	0.126823i
$460$	−31974.4			−3.24090
$461$	1846.30	−	3197.89i	0.186531	−	0.323082i	−0.757560	−	0.652765i	$-0.773609\pi$
$461$	1846.30	−	3197.89i	0.186531	−	0.323082i	0.944091	+	0.329684i	$0.106942\pi$
$462$	−2793.41	−	371.533i	−0.281302	−	0.0374140i
$463$	−7649.51	−	13249.3i	−0.767824	−	1.32991i	−0.938740	−	0.344625i	$-0.888006\pi$
$463$	−7649.51	−	13249.3i	−0.767824	−	1.32991i	0.170916	−	0.985286i	$-0.445327\pi$
$464$	16389.8	+	28388.0i	1.63982	+	2.84026i
$465$	−4898.30	+	6366.07i	−0.488501	+	0.634880i
$466$	1058.47	−	1833.33i	0.105221	−	0.182247i
$467$	14499.0			1.43669			0.718343	−	0.695689i	$-0.244901\pi$
$467$	14499.0			1.43669			0.718343	+	0.695689i	$0.244901\pi$
$468$	5905.33	−	5874.05i	0.583278	−	0.580189i
$469$	−1558.66			−0.153459
$470$	−2292.86	+	3971.36i	−0.225025	+	0.389755i
$471$	−356.818	−	864.680i	−0.0349072	−	0.0845910i
$472$	21174.2	+	36674.9i	2.06488	+	3.57648i
$473$	−1084.14	−	1877.78i	−0.105389	−	0.182538i
$474$	256.902	+	622.552i	0.0248943	+	0.0603265i
$475$	−277.181	+	480.092i	−0.0267747	+	0.0463751i
$476$	3787.13			0.364670
$477$	−5767.71	−	1561.88i	−0.553638	−	0.149924i
$478$	25645.4			2.45396
$479$	−5366.54	+	9295.13i	−0.511907	+	0.886650i	0.487997	+	0.872845i	$0.337728\pi$
$479$	−5366.54	+	9295.13i	−0.511907	+	0.886650i	−0.999905	+	0.0138046i	$0.995606\pi$
$480$	−33408.8	+	43419.7i	−3.17686	+	4.12881i
$481$	−80.1687	−	138.856i	−0.00759954	−	0.0131628i
$482$	9935.30	+	17208.5i	0.938881	+	1.62619i
$483$	4612.49	+	613.477i	0.434525	+	0.0577933i
$484$	13409.4	−	23225.8i	1.25934	−	2.18124i
$485$	18081.5			1.69286
$486$	19699.8	−	8007.13i	1.83868	−	0.747347i
$487$	16331.5			1.51961			0.759805	−	0.650151i	$-0.225295\pi$
$487$	16331.5			1.51961			0.759805	+	0.650151i	$0.225295\pi$
$488$	40549.3	−	70233.4i	3.76143	−	6.51500i
$489$	−15632.3	−	2079.15i	−1.44564	−	0.192275i
$490$	−1461.93	−	2532.14i	−0.134782	−	0.233450i
$491$	−2047.43	−	3546.25i	−0.188186	−	0.325947i	0.756460	−	0.654040i	$-0.226927\pi$
$491$	−2047.43	−	3546.25i	−0.188186	−	0.325947i	−0.944645	+	0.328093i	$0.893594\pi$
$492$	−23212.1	+	30167.6i	−2.12700	+	2.76435i
$493$	1253.62	−	2171.33i	0.114524	−	0.198361i
$494$	−3397.69			−0.309452
$495$	−3823.08	−	1035.28i	−0.347141	−	0.0940047i
$496$	−43746.9			−3.96027
$497$	1176.47	−	2037.71i	0.106181	−	0.183911i
$498$	−7363.56	−	17844.2i	−0.662588	−	1.60566i
$499$	6571.14	+	11381.5i	0.589508	+	1.02106i	0.994297	+	0.106648i	$0.0340118\pi$
$499$	6571.14	+	11381.5i	0.589508	+	1.02106i	−0.404789	+	0.914410i	$0.632655\pi$
$500$	−17123.1	−	29658.1i	−1.53154	−	2.65270i
$501$	4005.22	+	9705.88i	0.357166	+	0.865523i
$502$	5535.06	−	9587.00i	0.492115	−	0.852368i
$503$	855.175			0.0758059			0.0379030	−	0.999281i	$-0.487932\pi$
$503$	855.175			0.0758059			0.0379030	+	0.999281i	$0.487932\pi$
$504$	11670.3	−	11608.5i	1.03142	−	1.02596i
$505$	15572.5			1.37221
$506$	4955.60	−	8583.35i	0.435382	−	0.754104i
$507$	6416.22	−	8338.83i	0.562040	−	0.730455i
$508$	2794.94	+	4840.98i	0.244105	+	0.422803i
$509$	5523.35	+	9566.73i	0.480979	+	0.833080i	0.999762	−	0.0218259i	$-0.00694794\pi$
$509$	5523.35	+	9566.73i	0.480979	+	0.833080i	−0.518783	+	0.854906i	$0.673615\pi$
$510$	7071.57	+	940.542i	0.613989	+	0.0816626i
$511$	416.542	−	721.471i	0.0360601	−	0.0624580i
$512$	−88787.9			−7.66389
$513$	−5969.77	−	2500.66i	−0.513785	−	0.215218i
$514$	8092.79			0.694470
$515$	−6653.05	+	11523.4i	−0.569259	+	0.985985i
$516$	19028.8	+	2530.90i	1.62344	+	0.215924i
$517$	−530.305	−	918.515i	−0.0451118	−	0.0781359i
$518$	−240.128	−	415.914i	−0.0203680	−	0.0352784i
$519$	−7616.18	+	9898.37i	−0.644149	+	0.837168i
$520$	6072.63	−	10518.1i	0.512120	−	0.887018i
$521$	389.862			0.0327834			0.0163917	−	0.999866i	$-0.494782\pi$
$521$	389.862			0.0327834			0.0163917	+	0.999866i	$0.494782\pi$
$522$	−4232.55	−	15965.5i	−0.354892	−	1.33868i
$523$	6003.59			0.501948			0.250974	−	0.967994i	$-0.419249\pi$
$523$	6003.59			0.501948			0.250974	+	0.967994i	$0.419249\pi$
$524$	−9838.72	+	17041.2i	−0.820241	+	1.42070i
$525$	166.726	+	404.028i	0.0138600	+	0.0335871i
$526$	−819.982	−	1420.25i	−0.0679713	−	0.117730i
$527$	1673.05	+	2897.80i	0.138291	+	0.239526i
$528$	−8228.58	−	19940.4i	−0.678225	−	1.64355i
$529$	−2099.21	+	3635.93i	−0.172533	+	0.298836i
$530$	−13205.9			−1.08232
$531$	−3364.23	−	12690.2i	−0.274944	−	1.03711i
$532$	−7593.58			−0.618841
$533$	2043.56	−	3539.55i	0.166072	−	0.287645i
$534$	18318.6	−	23807.7i	1.48450	−	1.92933i
$535$	−7934.90	−	13743.7i	−0.641226	−	1.11064i
$536$	−9696.36	−	16794.6i	−0.781379	−	1.35339i
$537$	−15797.8	−	2101.17i	−1.26951	−	0.168849i
$538$	2419.61	−	4190.89i	0.193898	−	0.335840i
$539$	676.247			0.0540408
$540$	27904.5	−	21235.8i	2.22373	−	1.69230i
$541$	−4184.54			−0.332546			−0.166273	−	0.986080i	$-0.553173\pi$
$541$	−4184.54			−0.332546			−0.166273	+	0.986080i	$0.553173\pi$
$542$	−6056.62	+	10490.4i	−0.479989	+	0.831365i
$543$	7215.21	+	959.647i	0.570229	+	0.0758424i
$544$	11411.0	+	19764.4i	0.899344	+	1.55771i
$545$	6277.19	+	10872.4i	0.493368	+	0.854538i
$546$	−1633.60	+	2123.10i	−0.128043	+	0.166411i
$547$	−603.485	+	1045.27i	−0.0471722	+	0.0817046i	−0.888647	−	0.458591i	$-0.848354\pi$
$547$	−603.485	+	1045.27i	−0.0471722	+	0.0817046i	0.841475	+	0.540296i	$0.181688\pi$
$548$	−45310.9			−3.53209
$549$	−17824.9	+	17730.5i	−1.38570	+	1.37836i
$550$	930.980			0.0721766
$551$	−2513.63	+	4353.74i	−0.194346	+	0.336616i
$552$	22083.9	+	53516.1i	1.70282	+	4.12645i
$553$	−80.8080	−	139.964i	−0.00621393	−	0.0107628i
$554$	21581.3	+	37379.9i	1.65506	+	2.86664i
$555$	−257.487	−	623.971i	−0.0196932	−	0.0477227i
$556$	−9515.85	+	16481.9i	−0.725831	+	1.25718i
$557$	−11786.9			−0.896636			−0.448318	−	0.893874i	$-0.647977\pi$
$557$	−11786.9			−0.896636			−0.448318	+	0.893874i	$0.647977\pi$
$558$	21276.9	+	5761.73i	1.61420	+	0.437121i
$559$	−2061.20			−0.155956
$560$	11190.9	−	19383.2i	0.844466	−	1.46266i
$561$	−1006.16	+	1307.66i	−0.0757224	+	0.0984126i
$562$	−14098.6	−	24419.5i	−1.05821	−	1.83287i
$563$	−4019.11	−	6961.30i	−0.300862	−	0.521108i	0.675469	−	0.737388i	$-0.263941\pi$
$563$	−4019.11	−	6961.30i	−0.300862	−	0.521108i	−0.976331	+	0.216280i	$0.930608\pi$
$564$	9307.92	+	1237.99i	0.694919	+	0.0924266i
$565$	−5754.57	+	9967.20i	−0.428489	+	0.742165i
$566$	−14245.6			−1.05793
$567$	−4432.81	+	2528.00i	−0.328326	+	0.187241i
$568$	29275.1			2.16260
$569$	6427.13	−	11132.1i	0.473531	−	0.820180i	−0.526010	−	0.850479i	$-0.676312\pi$
$569$	6427.13	−	11132.1i	0.473531	−	0.820180i	0.999541	+	0.0302985i	$0.00964579\pi$
$570$	−14179.2	−	1885.88i	−1.04193	−	0.138581i
$571$	8707.64	+	15082.1i	0.638185	+	1.10537i	0.985831	+	0.167742i	$0.0536477\pi$
$571$	8707.64	+	15082.1i	0.638185	+	1.10537i	−0.347646	+	0.937626i	$0.613019\pi$
$572$	2128.75	+	3687.10i	0.155607	+	0.269520i
$573$	−8474.21	+	11013.5i	−0.617828	+	0.802959i
$574$	6121.05	−	10602.0i	0.445100	−	0.770936i
$575$	−1537.24			−0.111491
$576$	82403.4	+	22314.6i	5.96090	+	1.61419i
$577$	3508.04			0.253105			0.126553	−	0.991960i	$-0.459609\pi$
$577$	3508.04			0.253105			0.126553	+	0.991960i	$0.459609\pi$
$578$	−12304.3	+	21311.7i	−0.885454	+	1.53365i
$579$	6095.81	+	14772.0i	0.437536	+	1.06028i
$580$	−13618.4	−	23587.7i	−0.974951	−	1.68866i
$581$	2316.19	+	4011.77i	0.165391	+	0.286465i
$582$	−18928.1	−	45868.7i	−1.34810	−	3.26687i
$583$	1527.16	−	2645.13i	0.108488	−	0.187907i
$584$	10365.2			0.734441
$585$	−2669.44	+	2655.30i	−0.188663	+	0.187663i
$586$	24040.3			1.69470
$587$	12955.0	−	22438.8i	0.910923	−	1.57777i	0.0981600	−	0.995171i	$-0.468704\pi$
$587$	12955.0	−	22438.8i	0.910923	−	1.57777i	0.812763	−	0.582594i	$-0.197962\pi$
$588$	−3650.96	+	4744.97i	−0.256060	+	0.332788i
$589$	−3354.63	−	5810.39i	−0.234678	−	0.406474i
$590$	−14507.2	−	25127.2i	−1.01229	−	1.75334i
$591$	−6517.76	−	866.883i	−0.453646	−	0.0603364i
$592$	1838.15	−	3183.76i	0.127614	−	0.221034i
$593$	−14584.8			−1.00999			−0.504997	−	0.863121i	$-0.668506\pi$
$593$	−14584.8			−1.00999			−0.504997	+	0.863121i	$0.668506\pi$
$594$	1375.82	+	10782.0i	0.0950346	+	0.744769i
$595$	−1711.93			−0.117953
$596$	−4042.29	+	7001.45i	−0.277816	+	0.481192i
$597$	−8469.14	−	1126.42i	−0.580601	−	0.0772219i
$598$	−4710.87	−	8159.46i	−0.322143	−	0.557968i
$599$	1240.73	+	2149.00i	0.0846323	+	0.146587i	0.905234	−	0.424912i	$-0.139695\pi$
$599$	1240.73	+	2149.00i	0.0846323	+	0.146587i	−0.820602	+	0.571500i	$0.806362\pi$
$600$	−3316.21	+	4309.91i	−0.225640	+	0.293252i
$601$	−1911.16	+	3310.22i	−0.129713	+	0.224670i	−0.923566	−	0.383441i	$-0.874739\pi$
$601$	−1911.16	+	3310.22i	−0.129713	+	0.224670i	0.793852	+	0.608111i	$0.208072\pi$
$602$	−6173.87			−0.417987
$603$	1540.59	+	5811.23i	0.104042	+	0.392457i
$604$	−43992.0			−2.96359
$605$	−6061.58	+	10499.0i	−0.407336	+	0.705526i
$606$	−16301.6	−	39503.8i	−1.09275	−	2.64808i
$607$	−11045.1	−	19130.7i	−0.738563	−	1.27923i	−0.953143	−	0.302521i	$-0.902172\pi$
$607$	−11045.1	−	19130.7i	−0.738563	−	1.27923i	0.214580	−	0.976706i	$-0.431162\pi$
$608$	−22880.2	−	39629.7i	−1.52618	−	2.64342i
$609$	1511.96	+	3663.94i	0.100604	+	0.243794i
$610$	−27781.7	+	48119.3i	−1.84401	+	3.19393i
$611$	−1008.23			−0.0667573
$612$	−3743.22	−	14119.8i	−0.247240	−	0.932610i
$613$	−9356.85			−0.616509			−0.308254	−	0.951304i	$-0.599745\pi$
$613$	−9356.85			−0.616509			−0.308254	+	0.951304i	$0.599745\pi$
$614$	−17319.1	+	29997.6i	−1.13834	+	1.97167i
$615$	10492.8	−	13636.9i	0.687984	−	0.894137i
$616$	4206.91	+	7286.57i	0.275164	+	0.476598i
$617$	−6387.28	−	11063.1i	−0.416762	−	0.721853i	0.578849	−	0.815434i	$-0.303502\pi$
$617$	−6387.28	−	11063.1i	−0.416762	−	0.721853i	−0.995612	+	0.0935811i	$0.970169\pi$
$618$	36196.9	+	4814.31i	2.35607	+	0.313365i
$619$	6090.84	−	10549.6i	0.395495	−	0.685017i	−0.597669	−	0.801743i	$-0.703906\pi$
$619$	6090.84	−	10549.6i	0.395495	−	0.685017i	0.993164	+	0.116725i	$0.0372397\pi$
$620$	36349.4			2.35456
$621$	−2271.76	−	17803.4i	−0.146799	−	1.15044i
$622$	36424.8			2.34807
$623$	−3604.35	+	6242.91i	−0.231790	+	0.401472i
$624$	−20327.1	−	2703.58i	−1.30407	−	0.173445i
$625$	6989.27	+	12105.8i	0.447313	+	0.774770i
$626$	20414.9	+	35359.7i	1.30343	+	2.25760i
$627$	2017.46	−	2621.99i	0.128500	−	0.167005i
$628$	−2116.52	+	3665.91i	−0.134488	+	0.232939i
$629$	−281.191			−0.0178248
$630$	−7995.73	+	7953.38i	−0.505647	+	0.502969i
$631$	10990.8			0.693402			0.346701	−	0.937976i	$-0.387302\pi$
$631$	10990.8			0.693402			0.346701	+	0.937976i	$0.387302\pi$
$632$	1005.41	−	1741.42i	0.0632800	−	0.109604i
$633$	−553.688	−	1341.76i	−0.0347664	−	0.0842496i
$634$	−23707.6	−	41062.8i	−1.48509	−	2.57226i
$635$	−1263.42	−	2188.31i	−0.0789565	−	0.136757i
$636$	10314.9	+	24996.2i	0.643102	+	1.55843i
$637$	321.425	−	556.724i	0.0199927	−	0.0346283i
$638$	8442.63			0.523898
$639$	−8760.12	−	2372.21i	−0.542324	−	0.146860i
$640$	104326.			6.44349
$641$	6218.22	−	10770.3i	0.383159	−	0.663651i	−0.608353	−	0.793667i	$-0.708169\pi$
$641$	6218.22	−	10770.3i	0.383159	−	0.663651i	0.991512	+	0.130016i	$0.0415028\pi$
$642$	−26558.1	+	34516.2i	−1.63266	+	2.12188i
$643$	−5149.14	−	8918.58i	−0.315805	−	0.546990i	0.663804	−	0.747907i	$-0.268941\pi$
$643$	−5149.14	−	8918.58i	−0.315805	−	0.546990i	−0.979608	+	0.200917i	$0.935608\pi$
$644$	−10528.4	−	18235.8i	−0.644221	−	1.11582i
$645$	−8601.77	−	1144.06i	−0.525107	−	0.0698410i
$646$	−2979.35	+	5160.38i	−0.181456	+	0.314292i
$647$	5452.22			0.331297			0.165648	−	0.986185i	$-0.447028\pi$
$647$	5452.22			0.331297			0.165648	+	0.986185i	$0.447028\pi$
$648$	−54815.6	−	32037.1i	−3.32309	−	1.94219i
$649$	6710.60			0.405877
$650$	442.501	−	766.435i	0.0267021	−	0.0462493i
$651$	−5243.61	−	697.418i	−0.315689	−	0.0419876i
$652$	35682.1	+	61803.3i	2.14328	+	3.71227i
$653$	−630.874	−	1092.71i	−0.0378071	−	0.0654838i	0.846503	−	0.532384i	$-0.178704\pi$
$653$	−630.874	−	1092.71i	−0.0378071	−	0.0654838i	−0.884310	+	0.466901i	$0.845371\pi$
$654$	21009.8	−	27305.3i	1.25619	−	1.63260i
$655$	4447.48	−	7703.26i	0.265309	−	0.459529i
$656$	93711.4			5.57746
$657$	−3101.61	−	839.907i	−0.184179	−	0.0498750i
$658$	−3019.94			−0.178920
$659$	−10123.7	+	17534.8i	−0.598429	+	1.03651i	0.394624	+	0.918843i	$0.370875\pi$
$659$	−10123.7	+	17534.8i	−0.598429	+	1.03651i	−0.993053	+	0.117667i	$0.962458\pi$
$660$	6837.16	+	16568.5i	0.403236	+	0.977166i
$661$	5760.81	+	9978.01i	0.338986	+	0.587140i	0.984242	−	0.176826i	$-0.0565829\pi$
$661$	5760.81	+	9978.01i	0.338986	+	0.587140i	−0.645257	+	0.763966i	$0.723250\pi$
$662$	9534.68	+	16514.6i	0.559782	+	0.969572i
$663$	598.302	+	1449.87i	0.0350470	+	0.0849296i
$664$	−28817.9	+	49914.1i	−1.68427	+	2.91723i
$665$	3432.59			0.200166
$666$	−1313.33	+	1306.37i	−0.0764122	+	0.0760075i
$667$	−13940.5			−0.809263
$668$	23757.5	−	41149.3i	1.37606	−	2.38340i
$669$	10208.4	−	13267.3i	0.589953	−	0.766733i
$670$	6643.31	+	11506.5i	0.383065	+	0.663487i
$671$	−6425.49	−	11129.3i	−0.369677	−	0.640300i
$672$	−35764.0	−	4756.73i	−2.05301	−	0.273058i
$673$	11298.8	−	19570.1i	0.647156	−	1.12091i	−0.336643	−	0.941632i	$-0.609292\pi$
$673$	11298.8	−	19570.1i	0.647156	−	1.12091i	0.983799	−	0.179275i	$-0.0573751\pi$
$674$	−10803.4			−0.617406
$675$	1341.56	−	1020.95i	0.0764990	−	0.0582171i
$676$	−47613.7			−2.70902
$677$	4516.37	−	7822.59i	0.256393	−	0.444086i	−0.708880	−	0.705329i	$-0.750799\pi$
$677$	4516.37	−	7822.59i	0.256393	−	0.444086i	0.965273	+	0.261243i	$0.0841324\pi$
$678$	31308.6	+	4164.14i	1.77345	+	0.235875i
$679$	5953.81	+	10312.3i	0.336504	+	0.582842i
$680$	−10649.9	−	18446.1i	−0.600593	−	1.04026i
$681$	7310.80	−	9501.47i	0.411381	−	0.534651i
$682$	−5633.66	+	9757.79i	−0.316311	+	0.547867i
$683$	1017.77			0.0570187			0.0285094	−	0.999594i	$-0.490924\pi$
$683$	1017.77			0.0570187			0.0285094	+	0.999594i	$0.490924\pi$
$684$	7505.54	+	28311.5i	0.419564	+	1.58263i
$685$	20482.3			1.14246
$686$	962.760	−	1667.55i	0.0535836	−	0.0928095i
$687$	11176.0	+	27082.9i	0.620657	+	1.50404i
$688$	−23630.1	−	40928.5i	−1.30943	−	2.26800i
$689$	−1451.74	−	2514.50i	−0.0802715	−	0.139034i
$690$	−15130.4	−	36665.7i	−0.834792	−	2.02296i
$691$	−9299.51	+	16107.2i	−0.511968	+	0.886755i	0.487935	+	0.872880i	$0.337750\pi$
$691$	−9299.51	+	16107.2i	−0.511968	+	0.886755i	−0.999904	+	0.0138754i	$0.995583\pi$
$692$	56518.4			3.10478
$693$	−668.406	−	2521.29i	−0.0366387	−	0.138204i
$694$	−52945.9			−2.89596
$695$	4301.53	−	7450.47i	0.234772	−	0.406637i
$696$	−30073.2	+	39084.7i	−1.63782	+	2.12859i
$697$	−3583.89	−	6207.47i	−0.194762	−	0.337338i
$698$	30296.1	+	52474.4i	1.64287	+	2.84554i
$699$	1942.36	+	258.341i	0.105103	+	0.0139790i
$700$	988.957	−	1712.92i	0.0533986	−	0.0924892i
$701$	−9110.12			−0.490848			−0.245424	−	0.969416i	$-0.578927\pi$
$701$	−9110.12			−0.490848			−0.245424	+	0.969416i	$0.578927\pi$
$702$	9530.33	+	3992.13i	0.512392	+	0.214634i
$703$	563.817			0.0302486
$704$	−21818.6	+	37791.0i	−1.16807	+	2.02315i
$705$	−4207.54	−	559.617i	−0.224773	−	0.0298956i
$706$	−13561.1	−	23488.6i	−0.722918	−	1.25213i
$707$	5127.65	+	8881.34i	0.272765	+	0.472443i
$708$	−36229.6	+	47085.7i	−1.92315	+	2.49942i
$709$	−7772.00	+	13461.5i	−0.411683	+	0.713057i	−0.995074	−	0.0991351i	$-0.968392\pi$
$709$	−7772.00	+	13461.5i	−0.411683	+	0.713057i	0.583391	+	0.812192i	$0.301726\pi$
$710$	−20057.4			−1.06020
$711$	−441.962	+	439.621i	−0.0233121	+	0.0231886i
$712$	−89690.0			−4.72089
$713$	9302.33	−	16112.1i	0.488604	−	0.846288i
$714$	1792.09	+	4342.78i	0.0939316	+	0.227625i
$715$	−962.277	−	1666.71i	−0.0503316	−	0.0871770i
$716$	36060.0	+	62457.7i	1.88216	+	3.25999i
$717$	9054.88	+	21942.8i	0.471633	+	1.14291i
$718$	−10898.2	+	18876.2i	−0.566457	+	0.981133i
$719$	−16986.4			−0.881066			−0.440533	−	0.897736i	$-0.645211\pi$
$719$	−16986.4			−0.881066			−0.440533	+	0.897736i	$0.645211\pi$
$720$	−83328.4	−	22565.1i	−4.31315	−	1.16799i
$721$	−8762.77			−0.452625
$722$	−13278.5	+	22999.0i	−0.684452	+	1.18551i
$723$	−11216.0	+	14576.8i	−0.576938	+	0.749817i
$724$	−16469.4	−	28525.8i	−0.845413	−	1.46430i
$725$	−654.730	−	1134.03i	−0.0335394	−	0.0580920i
$726$	32978.9	+	4386.30i	1.68590	+	0.224230i
$727$	10774.1	−	18661.2i	0.549639	−	0.952003i	−0.448660	−	0.893703i	$-0.648098\pi$
$727$	10774.1	−	18661.2i	0.549639	−	0.952003i	0.998299	−	0.0583006i	$-0.0185682\pi$
$728$	7998.29			0.407193
$729$	13806.7	+	14028.4i	0.701452	+	0.712717i
$730$	−7101.53			−0.360054
$731$	−1807.41	+	3130.52i	−0.0914493	+	0.158395i
$732$	112780.	+	15000.2i	5.69465	+	0.757407i
$733$	−3935.30	−	6816.14i	−0.198300	−	0.343465i	0.749678	−	0.661803i	$-0.230209\pi$
$733$	−3935.30	−	6816.14i	−0.198300	−	0.343465i	−0.947977	+	0.318338i	$0.896875\pi$
$734$	−34675.3	−	60059.4i	−1.74372	−	3.02021i
$735$	1650.38	−	2144.91i	0.0828232	−	0.107641i
$736$	63446.4	−	109892.i	3.17754	−	5.50365i
$737$	−3073.00			−0.153589
$738$	−45577.9	−	12342.4i	−2.27337	−	0.615622i
$739$	11082.4			0.551656			0.275828	−	0.961207i	$-0.411048\pi$
$739$	11082.4			0.551656			0.275828	+	0.961207i	$0.411048\pi$
$740$	−1527.32	+	2645.40i	−0.0758723	+	0.131415i
$741$	−1199.66	−	2907.14i	−0.0594744	−	0.144125i
$742$	−4348.39	−	7531.63i	−0.215141	−	0.372635i
$743$	−16228.8	−	28109.1i	−0.801316	−	1.38792i	−0.918750	−	0.394839i	$-0.870800\pi$
$743$	−16228.8	−	28109.1i	−0.801316	−	1.38792i	0.117435	−	0.993081i	$-0.462533\pi$
$744$	−25105.6	−	60838.6i	−1.23712	−	2.99792i
$745$	1827.27	−	3164.93i	0.0898604	−	0.155643i
$746$	3755.97			0.184338
$747$	12667.9	−	12600.8i	0.620476	−	0.617190i
$748$	7466.57			0.364980
$749$	5225.55	−	9050.92i	0.254923	−	0.441540i
$750$	25906.8	−	33669.7i	1.26131	−	1.63926i
$751$	10309.9	+	17857.2i	0.500948	+	0.867667i	0.999999	+	0.00109477i	$0.000348475\pi$
$751$	10309.9	+	17857.2i	0.500948	+	0.867667i	−0.499052	+	0.866572i	$0.666318\pi$
$752$	−11558.6	−	20020.1i	−0.560504	−	0.970822i
$753$	10157.2	+	1350.94i	0.491564	+	0.0653797i
$754$	4012.85	−	6950.45i	0.193819	−	0.335704i
$755$	19886.1			0.958582
$756$	21299.5	+	8922.11i	1.02468	+	0.429225i
$757$	18444.6			0.885574			0.442787	−	0.896627i	$-0.353990\pi$
$757$	18444.6			0.885574			0.442787	+	0.896627i	$0.353990\pi$
$758$	−7540.18	+	13060.0i	−0.361308	+	0.625805i
$759$	9093.83	+	1209.51i	0.434895	+	0.0578424i
$760$	21354.0	+	36986.3i	1.01920	+	1.76531i
$761$	−15026.7	−	26027.1i	−0.715793	−	1.23979i	−0.962653	−	0.270739i	$-0.912732\pi$
$761$	−15026.7	−	26027.1i	−0.715793	−	1.23979i	0.246860	−	0.969051i	$-0.420601\pi$
$762$	−4228.67	+	5495.79i	−0.201035	+	0.261275i
$763$	−4133.86	+	7160.06i	−0.196141	+	0.339727i
$764$	62885.7			2.97791
$765$	1692.08	+	6382.67i	0.0799704	+	0.301655i
$766$	−1291.91			−0.0609383
$767$	3189.59	−	5524.54i	0.150156	−	0.260078i
$768$	−59072.7	−	143151.i	−2.77552	−	6.72595i
$769$	11397.9	+	19741.7i	0.534485	+	0.925755i	0.999188	+	0.0402883i	$0.0128276\pi$
$769$	11397.9	+	19741.7i	0.534485	+	0.925755i	−0.464703	+	0.885466i	$0.653839\pi$
$770$	−2882.29	−	4992.28i	−0.134897	−	0.233648i
$771$	2857.40	+	6924.36i	0.133472	+	0.323443i
$772$	36158.2	−	62627.8i	1.68570	−	2.91972i
$773$	−8130.82			−0.378325			−0.189163	−	0.981946i	$-0.560577\pi$
$773$	−8130.82			−0.378325			−0.189163	+	0.981946i	$0.560577\pi$
$774$	6102.29	+	23018.4i	0.283388	+	1.06896i
$775$	1747.57			0.0809996
$776$	−74076.9	+	128305.i	−3.42681	+	5.93541i
$777$	271.081	−	352.310i	0.0125160	−	0.0162665i
$778$	4234.80	+	7334.90i	0.195148	+	0.338006i
$779$	7186.06	+	12446.6i	0.330510	+	0.572460i
$780$	16889.9	+	2246.41i	0.775328	+	0.103121i
$781$	2319.49	−	4017.47i	0.106271	−	0.184067i
$782$	−16523.3			−0.755592
$783$	12166.0	−	9258.58i	0.555273	−	0.422573i
$784$	14739.6			0.671445
$785$	956.747	−	1657.13i	0.0435003	−	0.0753448i
$786$	−24197.2	−	3218.30i	−1.09807	−	0.146047i
$787$	9665.31	+	16740.8i	0.437778	+	0.758254i	0.997518	−	0.0704148i	$-0.0224323\pi$
$787$	9665.31	+	16740.8i	0.437778	+	0.758254i	−0.559740	+	0.828668i	$0.689099\pi$
$788$	14877.4	+	25768.3i	0.672568	+	1.16492i
$789$	925.678	−	1203.06i	0.0417681	−	0.0542838i
$790$	−688.839	+	1193.10i	−0.0310225	+	0.0537326i
$791$	−7579.37			−0.340697
$792$	23008.8	−	22886.9i	1.03230	−	1.02683i
$793$	−12216.3			−0.547055
$794$	32145.3	−	55677.4i	1.43677	−	2.48856i
$795$	−4662.74	−	11299.3i	−0.208013	−	0.504080i
$796$	19331.6	+	33483.3i	0.860791	+	1.49093i
$797$	6233.66	+	10797.0i	0.277048	+	0.479862i	0.970650	−	0.240497i	$-0.0773105\pi$
$797$	6233.66	+	10797.0i	0.277048	+	0.479862i	−0.693602	+	0.720359i	$0.743977\pi$
$798$	−3593.32	−	8707.72i	−0.159401	−	0.386278i
$799$	−884.091	+	1531.29i	−0.0391451	+	0.0678012i
$800$	11919.3			0.526764
$801$	26838.3	+	7267.74i	1.18388	+	0.320590i
$802$	−46770.1			−2.05924
$803$	821.239	−	1422.43i	0.0360908	−	0.0625110i
$804$	16590.7	−	21562.1i	0.727747	−	0.945815i
$805$	4759.26	+	8243.27i	0.208375	+	0.360916i
$806$	5355.44	+	9275.90i	0.234041	+	0.405372i
$807$	4440.13	+	590.553i	0.193680	+	0.0257602i
$808$	−63797.8	+	110501.i	−2.77772	+	4.81115i
$809$	25327.8			1.10071			0.550356	−	0.834930i	$-0.314492\pi$
$809$	25327.8			1.10071			0.550356	+	0.834930i	$0.314492\pi$
$810$	37556.0	+	21949.7i	1.62912	+	0.952142i
$811$	−279.496			−0.0121016			−0.00605081	−	0.999982i	$-0.501926\pi$
$811$	−279.496			−0.0121016			−0.00605081	+	0.999982i	$0.501926\pi$
$812$	8968.40	−	15533.7i	0.387598	−	0.671339i
$813$	−11114.3	−	1478.23i	−0.479452	−	0.0637687i
$814$	−473.428	−	820.002i	−0.0203853	−	0.0353084i
$815$	−16129.7	−	27937.5i	−0.693250	−	1.20074i
$816$	−21930.5	+	28501.9i	−0.940834	+	1.22275i
$817$	3624.04	−	6277.02i	0.155189	−	0.268795i
$818$	−53679.3			−2.29444
$819$	−2393.36	−	648.116i	−0.102113	−	0.0276520i
$820$	−77865.2			−3.31606
$821$	−5512.68	+	9548.23i	−0.234341	+	0.405890i	−0.959081	−	0.283132i	$-0.908626\pi$
$821$	−5512.68	+	9548.23i	−0.234341	+	0.405890i	0.724740	+	0.689022i	$0.241960\pi$
$822$	−21441.3	−	51958.9i	−0.909796	−	2.20472i
$823$	−1223.29	−	2118.81i	−0.0518120	−	0.0897411i	0.838956	−	0.544199i	$-0.183166\pi$
$823$	−1223.29	−	2118.81i	−0.0518120	−	0.0897411i	−0.890768	+	0.454458i	$0.849833\pi$
$824$	−54512.8	−	94419.0i	−2.30467	−	3.99180i
$825$	328.710	+	796.566i	0.0138718	+	0.0336156i
$826$	9553.75	−	16547.6i	0.402442	−	0.697051i
$827$	−11742.3			−0.493738			−0.246869	−	0.969049i	$-0.579402\pi$
$827$	−11742.3			−0.493738			−0.246869	+	0.969049i	$0.579402\pi$
$828$	−57583.0	+	57278.0i	−2.41684	+	2.40404i
$829$	4681.92			0.196152			0.0980759	−	0.995179i	$-0.468731\pi$
$829$	4681.92			0.196152			0.0980759	+	0.995179i	$0.468731\pi$
$830$	19744.1	−	34197.9i	0.825698	−	1.43015i
$831$	−24363.1	+	31663.5i	−1.01703	+	1.32178i
$832$	20741.1	+	35924.6i	0.864265	+	1.49695i
$833$	−563.698	−	976.353i	−0.0234465	−	0.0406106i
$834$	−23403.1	−	3112.69i	−0.971683	−	0.129237i
$835$	−10739.3	+	18601.1i	−0.445089	+	0.770918i
$836$	−14971.2			−0.619367
$837$	2582.60	+	20239.4i	0.106652	+	0.835812i
$838$	74868.8			3.08628
$839$	8672.67	−	15021.5i	0.356870	−	0.618117i	−0.630566	−	0.776136i	$-0.717177\pi$
$839$	8672.67	−	15021.5i	0.356870	−	0.618117i	0.987436	+	0.158018i	$0.0505106\pi$
$840$	33378.4	+	4439.44i	1.37103	+	0.182351i
$841$	6257.05	+	10837.5i	0.256552	+	0.444361i
$842$	4577.55	+	7928.56i	0.187355	+	0.324508i
$843$	15915.9	−	20685.1i	0.650264	−	0.845115i
$844$	−3284.28	+	5688.53i	−0.133945	+	0.231999i
$845$	21523.2			0.876238
$846$	2984.93	+	11259.4i	0.121305	+	0.457572i
$847$	−7983.74			−0.323878
$848$	33286.3	−	57653.5i	1.34794	−	2.33471i
$849$	−5029.85	−	12188.9i	−0.203326	−	0.492722i
$850$	−776.035	−	1344.13i	−0.0313150	−	0.0542392i
$851$	781.727	+	1353.99i	0.0314891	+	0.0545408i
$852$	15666.5	+	37964.8i	0.629959	+	1.52659i
$853$	−11230.4	+	19451.6i	−0.450786	+	0.780785i	−0.998435	−	0.0559236i	$-0.982190\pi$
$853$	−11230.4	+	19451.6i	−0.450786	+	0.780785i	0.547649	+	0.836708i	$0.315523\pi$
$854$	−36591.4			−1.46620
$855$	−3392.80	−	12797.9i	−0.135709	−	0.511906i
$856$	130032.			5.19205
$857$	13198.1	−	22859.8i	0.526066	−	0.911174i	−0.473472	−	0.880809i	$-0.657000\pi$
$857$	13198.1	−	22859.8i	0.526066	−	0.911174i	0.999539	−	0.0303652i	$-0.00966702\pi$
$858$	−3220.74	+	4185.83i	−0.128152	+	0.166552i
$859$	−16800.7	−	29099.6i	−0.667324	−	1.15584i	−0.978650	−	0.205536i	$-0.934106\pi$
$859$	−16800.7	−	29099.6i	−0.667324	−	1.15584i	0.311326	−	0.950303i	$-0.399227\pi$
$860$	19634.3	+	34007.6i	0.778516	+	1.34843i
$861$	11232.5	+	1493.96i	0.444602	+	0.0591335i
$862$	−34816.4	+	60303.8i	−1.37570	+	2.38278i
$863$	9012.26			0.355482			0.177741	−	0.984077i	$-0.443121\pi$
$863$	9012.26			0.355482			0.177741	+	0.984077i	$0.443121\pi$
$864$	17614.6	+	138042.i	0.693588	+	5.43553i
$865$	−25548.5			−1.00425
$866$	−17623.9	+	30525.5i	−0.691552	+	1.19780i
$867$	−22579.2	−	3003.10i	−0.884462	−	0.117636i
$868$	11969.0	+	20730.9i	0.468035	+	0.810661i
$869$	−159.318	−	275.947i	−0.00621922	−	0.0107720i
$870$	20604.2	−	26778.2i	0.802929	−	1.04353i
$871$	−1460.62	+	2529.86i	−0.0568211	+	0.0984170i
$872$	−102866.			−3.99484
$873$	32563.1	−	32390.6i	1.26242	−	1.25574i
$874$	33131.0			1.28223
$875$	−5097.40	+	8828.95i	−0.196941	+	0.341112i
$876$	5546.89	+	13441.8i	0.213941	+	0.518444i
$877$	8468.75	+	14668.3i	0.326077	+	0.564782i	0.981730	−	0.190281i	$-0.0609399\pi$
$877$	8468.75	+	14668.3i	0.326077	+	0.564782i	−0.655653	+	0.755062i	$0.727607\pi$
$878$	39849.5	+	69021.4i	1.53173	+	2.65303i
$879$	8488.15	+	20569.4i	0.325709	+	0.789293i
$880$	22063.5	−	38215.2i	0.845184	−	1.46390i
$881$	−34145.9			−1.30579			−0.652897	−	0.757447i	$-0.726446\pi$
$881$	−34145.9			−1.30579			−0.652897	+	0.757447i	$0.726446\pi$
$882$	−7168.80	−	1941.29i	−0.273681	−	0.0741119i
$883$	−27998.6			−1.06708			−0.533539	−	0.845776i	$-0.679138\pi$
$883$	−27998.6			−1.06708			−0.533539	+	0.845776i	$0.679138\pi$
$884$	3548.92	−	6146.90i	0.135026	−	0.233872i
$885$	16377.2	−	21284.6i	0.622048	−	0.808444i
$886$	46643.1	+	80788.3i	1.76863	+	3.06336i
$887$	−8529.46	−	14773.5i	−0.322876	−	0.559238i	0.658204	−	0.752840i	$-0.271316\pi$
$887$	−8529.46	−	14773.5i	−0.322876	−	0.559238i	−0.981080	+	0.193602i	$0.937983\pi$
$888$	5482.53	+	729.195i	0.207187	+	0.0275565i
$889$	832.030	−	1441.12i	0.0313896	−	0.0543685i
$890$	61449.7			2.31438
$891$	−8739.58	+	4984.11i	−0.328605	+	0.187401i
$892$	−75754.7			−2.84356
$893$	1772.69	−	3070.40i	0.0664288	−	0.115058i
$894$	−9941.53	−	1322.26i	−0.371918	−	0.0494663i
$895$	−16300.5	−	28233.3i	−0.608789	−	1.05445i
$896$	34352.0	+	59499.3i	1.28082	+	2.21845i
$897$	5318.10	−	6911.66i	0.197956	−	0.257273i
$898$	−1191.17	+	2063.17i	−0.0442650	+	0.0766692i
$899$	15848.0			0.587941
$900$	−7363.87	−	1994.11i	−0.272736	−	0.0738561i
$901$	−5091.98			−0.188278
$902$	12068.0	−	20902.5i	0.445479	−	0.771592i
$903$	−2179.87	−	5282.50i	−0.0803340	−	0.194674i
$904$	−47151.0	−	81667.9i	−1.73476	−	3.00468i
$905$	7444.79	+	12894.8i	0.273451	+	0.473631i
$906$	−20817.2	−	50446.5i	−0.763362	−	1.84986i
$907$	19372.2	−	33553.7i	0.709200	−	1.22837i	−0.255954	−	0.966689i	$-0.582390\pi$
$907$	19372.2	−	33553.7i	0.709200	−	1.22837i	0.965154	−	0.261682i	$-0.0842771\pi$
$908$	−54252.2			−1.98284
$909$	28044.6	−	27896.0i	1.02330	−	1.01788i
$910$	−5479.90			−0.199623
$911$	−15760.9	+	27298.7i	−0.573197	+	0.992806i	0.423038	+	0.906112i	$0.360964\pi$
$911$	−15760.9	+	27298.7i	−0.573197	+	0.992806i	−0.996235	+	0.0866940i	$0.972370\pi$
$912$	43972.9	−	57149.3i	1.59659	−	2.07500i
$913$	4566.53	+	7909.46i	0.165531	+	0.286708i
$914$	−21614.6	−	37437.5i	−0.782217	−	1.35484i
$915$	−50981.1	−	6780.66i	−1.84195	−	0.244985i
$916$	66292.1	−	114821.i	2.39121	−	4.14170i
$917$	5857.80			0.210951
$918$	14420.1	−	10974.0i	0.518447	−	0.394547i
$919$	−31567.2			−1.13309			−0.566543	−	0.824032i	$-0.691719\pi$
$919$	−31567.2			−1.13309			−0.566543	+	0.824032i	$0.691719\pi$
$920$	−59214.3	+	102562.i	−2.12200	+	3.67541i
$921$	−31781.6	−	4227.06i	−1.13707	−	0.151234i
$922$	−10364.7	−	17952.2i	−0.370221	−	0.641241i
$923$	−2204.94	−	3819.07i	−0.0786310	−	0.136193i
$924$	−7198.11	+	9355.02i	−0.256277	+	0.333071i
$925$	−73.4292	+	127.183i	−0.00261009	+	0.00452082i
$926$	−85885.0			−3.04790
$927$	8661.17	+	32670.7i	0.306872	+	1.15755i
$928$	108091.			3.82355
$929$	−3147.81	+	5452.17i	−0.111169	+	0.192551i	−0.916242	−	0.400625i	$-0.868793\pi$
$929$	−3147.81	+	5452.17i	−0.111169	+	0.192551i	0.805073	+	0.593176i	$0.202126\pi$
$930$	17200.7	+	41682.6i	0.606488	+	1.46971i
$931$	1130.27	+	1957.69i	0.0397886	+	0.0689158i
$932$	−4433.61	−	7679.25i	−0.155824	−	0.269895i
$933$	12860.9	+	31165.8i	0.451282	+	1.09359i
$934$	40696.9	−	70489.1i	1.42574	−	2.46946i
$935$	−3375.18			−0.118054
$936$	−7905.56	−	29820.4i	−0.276070	−	1.04136i
$937$	−44986.8			−1.56847			−0.784234	−	0.620465i	$-0.786944\pi$
$937$	−44986.8			−1.56847			−0.784234	+	0.620465i	$0.786944\pi$
$938$	−4374.97	+	7577.67i	−0.152290	+	0.263774i
$939$	−23046.4	+	29952.3i	−0.800949	+	1.04095i
$940$	9604.09	+	16634.8i	0.333246	+	0.577198i
$941$	−10341.7	−	17912.3i	−0.358267	−	0.620537i	0.629404	−	0.777078i	$-0.283299\pi$
$941$	−10341.7	−	17912.3i	−0.358267	−	0.620537i	−0.987671	+	0.156541i	$0.949966\pi$
$942$	−5205.32	−	692.325i	−0.180041	−	0.0239460i
$943$	−19926.8	+	34514.2i	−0.688129	+	1.19187i
$944$	146265.			5.04293
$945$	−9628.22	−	4033.14i	−0.331435	−	0.138834i
$946$	−12172.2			−0.418343
$947$	−13541.6	+	23454.7i	−0.464670	+	0.804833i	−0.999187	−	0.0403255i	$-0.987161\pi$
$947$	−13541.6	+	23454.7i	−0.464670	+	0.804833i	0.534516	+	0.845158i	$0.320494\pi$
$948$	2796.35	+	371.925i	0.0958031	+	0.0127421i
$949$	−780.682	−	1352.18i	−0.0267039	−	0.0462525i
$950$	1556.03	+	2695.12i	0.0531414	+	0.0920435i
$951$	26763.5	−	34783.2i	0.912583	−	1.18604i
$952$	7013.49	−	12147.7i	0.238769	−	0.413561i
$953$	−27673.1			−0.940631			−0.470315	−	0.882498i	$-0.655860\pi$
$953$	−27673.1			−0.940631			−0.470315	+	0.882498i	$0.655860\pi$
$954$	−23782.6	+	23656.6i	−0.807117	+	0.802843i
$955$	−28426.8			−0.963213
$956$	53710.3	−	93029.0i	1.81707	−	3.14725i
$957$	2980.93	+	7223.70i	0.100689	+	0.244001i
$958$	30126.5	+	52180.6i	1.01602	+	1.75979i
$959$	6744.33	+	11681.5i	0.227097	+	0.393343i
$960$	66616.7	+	161433.i	2.23963	+	5.42731i
$961$	4320.36	−	7483.08i	0.145022	−	0.251186i
$962$	−900.096			−0.0301666
$963$	−38910.0	−	10536.7i	−1.30203	−	0.352586i
$964$	83231.8			2.78083
$965$	−16344.9	+	28310.2i	−0.545244	+	0.944391i
$966$	15929.2	−	20702.4i	0.530553	−	0.689533i
$967$	−5471.72	−	9477.29i	−0.181963	−	0.315170i	0.760586	−	0.649238i	$-0.224912\pi$
$967$	−5471.72	−	9477.29i	−0.181963	−	0.315170i	−0.942549	+	0.334068i	$0.891579\pi$
$968$	−49666.5	−	86025.0i	−1.64911	−	2.85635i
$969$	−5467.28	−	727.167i	−0.181253	−	0.0241073i
$970$	50752.6	−	87906.1i	1.67997	−	2.90979i
$971$	44352.0			1.46583			0.732916	−	0.680320i	$-0.238159\pi$
$971$	44352.0			1.46583			0.732916	+	0.680320i	$0.238159\pi$
$972$	12212.2	−	88230.9i	0.402990	−	2.91153i
$973$	5665.57			0.186670
$974$	45840.5	−	79398.0i	1.50803	−	2.61199i
$975$	812.017	+	108.001i	0.0266722	+	0.00354749i
$976$	−140051.	−	242575.i	−4.59316	−	7.95559i
$977$	23175.0	+	40140.2i	0.758888	+	1.31443i	0.943418	+	0.331605i	$0.107590\pi$
$977$	23175.0	+	40140.2i	0.758888	+	1.31443i	−0.184530	+	0.982827i	$0.559076\pi$
$978$	−53986.1	+	70163.0i	−1.76512	+	2.29403i
$979$	−7106.20	+	12308.3i	−0.231987	+	0.401813i
$980$	−12247.2			−0.399205
$981$	30781.1	+	8335.44i	1.00180	+	0.271285i
$982$	−22987.6			−0.747009
$983$	−27296.7	+	47279.2i	−0.885685	+	1.53405i	−0.0407593	+	0.999169i	$0.512978\pi$
$983$	−27296.7	+	47279.2i	−0.885685	+	1.53405i	−0.844926	+	0.534883i	$0.820356\pi$
$984$	53779.5	+	130324.i	1.74230	+	4.22214i
$985$	−6725.14	−	11648.3i	−0.217544	−	0.376797i
$986$	−7037.51	−	12189.3i	−0.227302	−	0.393699i
$987$	−1066.28	−	2583.93i	−0.0343871	−	0.0833306i
$988$	−7115.94	+	12325.2i	−0.229138	+	0.396878i
$989$	20098.8			0.646212
$990$	−15764.1	+	15680.6i	−0.506077	+	0.503396i
$991$	−17104.6			−0.548279			−0.274139	−	0.961690i	$-0.588393\pi$
$991$	−17104.6			−0.548279			−0.274139	+	0.961690i	$0.588393\pi$
$992$	−72127.7	+	124929.i	−2.30852	+	3.99848i
$993$	−10763.7	+	13989.0i	−0.343984	+	0.447058i
$994$	−6604.42	−	11439.2i	−0.210744	−	0.365019i
$995$	−8738.62	−	15135.7i	−0.278425	−	0.482246i
$996$	−80151.8	−	10660.5i	−2.54991	−	0.339146i
$997$	−1809.32	+	3133.83i	−0.0574741	+	0.0995480i	−0.893331	−	0.449399i	$-0.851638\pi$
$997$	−1809.32	+	3133.83i	−0.0574741	+	0.0995480i	0.835857	+	0.548948i	$0.184971\pi$
$998$	73777.6			2.34007
$999$	−1581.47	−	662.459i	−0.0500857	−	0.0209803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.c.43.9	yes	18
3.2	odd	2		189.4.f.c.127.1		18
9.2	odd	6		567.4.a.k.1.9		9
9.4	even	3	inner	63.4.f.c.22.9	✓	18
9.5	odd	6		189.4.f.c.64.1		18
9.7	even	3		567.4.a.j.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.c.22.9	✓	18	9.4	even	3	inner
63.4.f.c.43.9	yes	18	1.1	even	1	trivial
189.4.f.c.64.1		18	9.5	odd	6
189.4.f.c.127.1		18	3.2	odd	2
567.4.a.j.1.1		9	9.7	even	3
567.4.a.k.1.9		9	9.2	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.80688 - 4.86166i) q^{2} +(5.15079 + 0.685073i) q^{3} +(-11.7571 - 20.3640i) q^{4} +(5.31469 + 9.20530i) q^{5} +(17.7882 - 23.1185i) q^{6} +(-3.50000 + 6.06218i) q^{7} -87.0935 q^{8} +(26.0614 + 7.05734i) q^{9} +O(q^{10})\)	\(q+(2.80688 - 4.86166i) q^{2} +(5.15079 + 0.685073i) q^{3} +(-11.7571 - 20.3640i) q^{4} +(5.31469 + 9.20530i) q^{5} +(17.7882 - 23.1185i) q^{6} +(-3.50000 + 6.06218i) q^{7} -87.0935 q^{8} +(26.0614 + 7.05734i) q^{9} +59.6707 q^{10} +(-6.90048 + 11.9520i) q^{11} +(-46.6078 - 112.945i) q^{12} +(6.55969 + 11.3617i) q^{13} +(19.6482 + 34.0316i) q^{14} +(21.0685 + 51.0556i) q^{15} +(-150.404 + 260.507i) q^{16} +23.0081 q^{17} +(107.461 - 106.892i) q^{18} -46.1335 q^{19} +(124.971 - 216.456i) q^{20} +(-22.1808 + 28.8273i) q^{21} +(38.7376 + 67.0955i) q^{22} +(-63.9637 - 110.788i) q^{23} +(-448.601 - 59.6654i) q^{24} +(6.00824 - 10.4066i) q^{25} +73.6491 q^{26} +(129.402 + 54.2048i) q^{27} +164.600 q^{28} +(54.4860 - 94.3726i) q^{29} +(307.352 + 40.8788i) q^{30} +(72.7157 + 125.947i) q^{31} +(495.957 + 859.022i) q^{32} +(-43.7309 + 56.8348i) q^{33} +(64.5809 - 111.857i) q^{34} -74.4056 q^{35} +(-162.692 - 613.687i) q^{36} -12.2214 q^{37} +(-129.491 + 224.286i) q^{38} +(26.0040 + 63.0158i) q^{39} +(-462.875 - 801.722i) q^{40} +(-155.766 - 269.795i) q^{41} +(77.8895 + 188.750i) q^{42} +(-78.5554 + 136.062i) q^{43} +324.520 q^{44} +(73.5429 + 277.410i) q^{45} -718.153 q^{46} +(-38.4253 + 66.5545i) q^{47} +(-953.165 + 1238.78i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-33.7288 - 58.4200i) q^{50} +(118.510 + 15.7622i) q^{51} +(154.247 - 267.163i) q^{52} -221.313 q^{53} +(626.741 - 476.961i) q^{54} -146.695 q^{55} +(304.827 - 527.976i) q^{56} +(-237.624 - 31.6048i) q^{57} +(-305.871 - 529.785i) q^{58} +(-243.121 - 421.097i) q^{59} +(791.988 - 1029.31i) q^{60} +(-465.583 + 806.414i) q^{61} +816.417 q^{62} +(-133.998 + 133.288i) q^{63} +3161.90 q^{64} +(-69.7254 + 120.768i) q^{65} +(153.564 + 372.133i) q^{66} +(111.333 + 192.834i) q^{67} +(-270.509 - 468.536i) q^{68} +(-253.566 - 614.468i) q^{69} +(-208.848 + 361.735i) q^{70} -336.134 q^{71} +(-2269.77 - 614.648i) q^{72} -119.012 q^{73} +(-34.3040 + 59.4163i) q^{74} +(38.0765 - 49.4861i) q^{75} +(542.399 + 939.462i) q^{76} +(-48.3033 - 83.6638i) q^{77} +(379.351 + 50.4550i) q^{78} +(-11.5440 + 19.9948i) q^{79} -3197.40 q^{80} +(629.388 + 367.848i) q^{81} -1748.87 q^{82} +(330.885 - 573.110i) q^{83} +(847.821 + 112.763i) q^{84} +(122.281 + 211.796i) q^{85} +(440.991 + 763.819i) q^{86} +(345.298 - 448.767i) q^{87} +(600.987 - 1040.94i) q^{88} +1029.81 q^{89} +(1555.10 + 421.116i) q^{90} -91.8357 q^{91} +(-1504.06 + 2605.11i) q^{92} +(288.260 + 698.544i) q^{93} +(215.710 + 373.621i) q^{94} +(-245.185 - 424.673i) q^{95} +(1966.08 + 4764.41i) q^{96} +(850.544 - 1473.19i) q^{97} -275.074 q^{98} +(-264.185 + 262.786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Introduction

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