LMFDB - Embedded newform 45.4.e.c.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.e (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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.6
Root			$2.13089 + 3.69081i$ of defining polynomial
Character	$\chi$	$=$	45.16
Dual form			45.4.e.c.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.13089 - 3.69081i) q^{2} +(4.39640 - 2.76977i) q^{3} +(-5.08138 - 8.80120i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-0.854448 - 22.1284i) q^{6} +(-15.3820 + 26.6423i) q^{7} -9.21718 q^{8} +(11.6567 - 24.3541i) q^{9} +O(q^{10})$	\(q+(2.13089 - 3.69081i) q^{2} +(4.39640 - 2.76977i) q^{3} +(-5.08138 - 8.80120i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-0.854448 - 22.1284i) q^{6} +(-15.3820 + 26.6423i) q^{7} -9.21718 q^{8} +(11.6567 - 24.3541i) q^{9} +21.3089 q^{10} +(-20.3573 + 35.2599i) q^{11} +(-46.7171 - 24.6194i) q^{12} +(-31.6089 - 54.7482i) q^{13} +(65.5545 + 113.544i) q^{14} +(22.9845 + 12.1126i) q^{15} +(21.0102 - 36.3908i) q^{16} -6.58990 q^{17} +(-65.0470 - 94.9186i) q^{18} +75.3803 q^{19} +(25.4069 - 44.0060i) q^{20} +(6.16789 + 159.735i) q^{21} +(86.7584 + 150.270i) q^{22} +(31.1814 + 54.0077i) q^{23} +(-40.5225 + 25.5295i) q^{24} +(-12.5000 + 21.6506i) q^{25} -269.420 q^{26} +(-16.2075 - 139.357i) q^{27} +312.646 q^{28} +(-24.8042 + 42.9621i) q^{29} +(93.6825 - 59.0208i) q^{30} +(-51.5021 - 89.2043i) q^{31} +(-126.410 - 218.948i) q^{32} +(8.16291 + 211.402i) q^{33} +(-14.0423 + 24.3221i) q^{34} -153.820 q^{35} +(-273.577 + 21.1590i) q^{36} -282.029 q^{37} +(160.627 - 278.214i) q^{38} +(-290.606 - 153.146i) q^{39} +(-23.0430 - 39.9116i) q^{40} +(78.7700 + 136.434i) q^{41} +(602.695 + 317.613i) q^{42} +(168.907 - 292.555i) q^{43} +413.773 q^{44} +(134.598 - 10.4101i) q^{45} +265.776 q^{46} +(-22.2579 + 38.5518i) q^{47} +(-8.42472 - 218.182i) q^{48} +(-301.710 - 522.577i) q^{49} +(53.2722 + 92.2702i) q^{50} +(-28.9719 + 18.2525i) q^{51} +(-321.234 + 556.393i) q^{52} +26.2752 q^{53} +(-548.876 - 237.135i) q^{54} -203.573 q^{55} +(141.778 - 245.567i) q^{56} +(331.402 - 208.786i) q^{57} +(105.710 + 183.095i) q^{58} +(212.963 + 368.863i) q^{59} +(-10.1877 - 263.840i) q^{60} +(-425.297 + 736.637i) q^{61} -438.981 q^{62} +(469.546 + 685.176i) q^{63} -741.296 q^{64} +(158.045 - 273.741i) q^{65} +(797.638 + 420.346i) q^{66} +(-48.1538 - 83.4048i) q^{67} +(33.4858 + 57.9990i) q^{68} +(286.675 + 151.075i) q^{69} +(-327.773 + 567.719i) q^{70} +952.164 q^{71} +(-107.442 + 224.476i) q^{72} -50.8558 q^{73} +(-600.973 + 1040.92i) q^{74} +(5.01227 + 129.807i) q^{75} +(-383.036 - 663.437i) q^{76} +(-626.271 - 1084.73i) q^{77} +(-1184.48 + 746.233i) q^{78} +(98.6395 - 170.849i) q^{79} +210.102 q^{80} +(-457.241 - 567.778i) q^{81} +671.400 q^{82} +(98.8693 - 171.247i) q^{83} +(1374.52 - 865.959i) q^{84} +(-16.4747 - 28.5351i) q^{85} +(-719.844 - 1246.81i) q^{86} +(9.94603 + 257.581i) q^{87} +(187.637 - 324.997i) q^{88} +1364.54 q^{89} +(248.392 - 518.958i) q^{90} +1944.83 q^{91} +(316.889 - 548.868i) q^{92} +(-473.499 - 249.529i) q^{93} +(94.8583 + 164.299i) q^{94} +(188.451 + 326.406i) q^{95} +(-1162.18 - 612.458i) q^{96} +(715.579 - 1239.42i) q^{97} -2571.64 q^{98} +(621.422 + 906.799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	2.13089	−	3.69081i	0.753383	−	1.30490i	−0.192791	−	0.981240i	$-0.561754\pi$
$2$	2.13089	−	3.69081i	0.753383	−	1.30490i	0.946174	−	0.323658i	$-0.104913\pi$
$3$	4.39640	−	2.76977i	0.846088	−	0.533043i
$3$	4.39640	−	2.76977i	0.846088	−	0.533043i
$4$	−5.08138	−	8.80120i	−0.635172	−	1.10015i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−0.854448	−	22.1284i	−0.0581378	−	1.50564i
$7$	−15.3820	+	26.6423i	−0.830548	+	1.43855i	0.0670561	+	0.997749i	$0.478639\pi$
$7$	−15.3820	+	26.6423i	−0.830548	+	1.43855i	−0.897604	+	0.440802i	$0.854694\pi$
$8$	−9.21718			−0.407346
$9$	11.6567	−	24.3541i	0.431731	−	0.902003i
$10$	21.3089			0.673846
$11$	−20.3573	+	35.2599i	−0.557996	+	0.966478i	0.439667	+	0.898161i	$0.355096\pi$
$11$	−20.3573	+	35.2599i	−0.557996	+	0.966478i	−0.997664	+	0.0683175i	$0.978237\pi$
$12$	−46.7171	−	24.6194i	−1.12384	−	0.592250i
$13$	−31.6089	−	54.7482i	−0.674364	−	1.16803i	−0.976654	−	0.214817i	$-0.931085\pi$
$13$	−31.6089	−	54.7482i	−0.674364	−	1.16803i	0.302290	−	0.953216i	$-0.402249\pi$
$14$	65.5545	+	113.544i	1.25144	+	2.16756i
$15$	22.9845	+	12.1126i	0.395638	+	0.208497i
$16$	21.0102	−	36.3908i	0.328285	−	0.568606i
$17$	−6.58990			−0.0940168			−0.0470084	−	0.998894i	$-0.514969\pi$
$17$	−6.58990			−0.0940168			−0.0470084	+	0.998894i	$0.514969\pi$
$18$	−65.0470	−	94.9186i	−0.851763	−	1.24292i
$19$	75.3803			0.910180			0.455090	−	0.890445i	$-0.349607\pi$
$19$	75.3803			0.910180			0.455090	+	0.890445i	$0.349607\pi$
$20$	25.4069	−	44.0060i	0.284058	−	0.492002i
$21$	6.16789	+	159.735i	0.0640926	+	1.65986i
$22$	86.7584	+	150.270i	0.840770	+	1.45626i
$23$	31.1814	+	54.0077i	0.282686	+	0.489626i	0.972045	−	0.234793i	$-0.0754414\pi$
$23$	31.1814	+	54.0077i	0.282686	+	0.489626i	−0.689360	+	0.724419i	$0.742108\pi$
$24$	−40.5225	+	25.5295i	−0.344651	+	0.217133i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−269.420			−2.03222
$27$	−16.2075	−	139.357i	−0.115524	−	0.993305i
$28$	312.646			2.11016
$29$	−24.8042	+	42.9621i	−0.158828	+	0.275099i	−0.934446	−	0.356104i	$-0.884105\pi$
$29$	−24.8042	+	42.9621i	−0.158828	+	0.275099i	0.775618	+	0.631202i	$0.217438\pi$
$30$	93.6825	−	59.0208i	0.570133	−	0.359189i
$31$	−51.5021	−	89.2043i	−0.298389	−	0.516824i	0.677379	−	0.735634i	$-0.263116\pi$
$31$	−51.5021	−	89.2043i	−0.298389	−	0.516824i	−0.975767	+	0.218810i	$0.929783\pi$
$32$	−126.410	−	218.948i	−0.698321	−	1.20953i
$33$	8.16291	+	211.402i	0.0430600	+	1.11516i
$34$	−14.0423	+	24.3221i	−0.0708306	+	0.122682i
$35$	−153.820			−0.742865
$36$	−273.577	+	21.1590i	−1.26656	+	0.0979582i
$37$	−282.029			−1.25312			−0.626559	−	0.779374i	$-0.715537\pi$
$37$	−282.029			−1.25312			−0.626559	+	0.779374i	$0.715537\pi$
$38$	160.627	−	278.214i	0.685714	−	1.18769i
$39$	−290.606	−	153.146i	−1.19318	−	0.628794i
$40$	−23.0430	−	39.9116i	−0.0910853	−	0.157764i
$41$	78.7700	+	136.434i	0.300044	+	0.519692i	0.976146	−	0.217117i	$-0.0696653\pi$
$41$	78.7700	+	136.434i	0.300044	+	0.519692i	−0.676102	+	0.736808i	$0.736332\pi$
$42$	602.695	+	317.613i	2.21423	+	1.16688i
$43$	168.907	−	292.555i	0.599025	−	1.03754i	−0.393940	−	0.919136i	$-0.628888\pi$
$43$	168.907	−	292.555i	0.599025	−	1.03754i	0.992965	−	0.118406i	$-0.0377783\pi$
$44$	413.773			1.41770
$45$	134.598	−	10.4101i	0.445882	−	0.0344853i
$46$	265.776			0.851882
$47$	−22.2579	+	38.5518i	−0.0690777	+	0.119646i	−0.898496	−	0.438983i	$-0.855339\pi$
$47$	−22.2579	+	38.5518i	−0.0690777	+	0.119646i	0.829418	+	0.558629i	$0.188672\pi$
$48$	−8.42472	−	218.182i	−0.0253334	−	0.656081i
$49$	−301.710	−	522.577i	−0.879620	−	1.52355i
$50$	53.2722	+	92.2702i	0.150677	+	0.260980i
$51$	−28.9719	+	18.2525i	−0.0795465	+	0.0501150i
$52$	−321.234	+	556.393i	−0.856675	+	1.48380i
$53$	26.2752			0.0680978			0.0340489	−	0.999420i	$-0.489160\pi$
$53$	26.2752			0.0680978			0.0340489	+	0.999420i	$0.489160\pi$
$54$	−548.876	−	237.135i	−1.38319	−	0.597592i
$55$	−203.573			−0.499087
$56$	141.778	−	245.567i	0.338320	−	0.585988i
$57$	331.402	−	208.786i	0.770093	−	0.485165i
$58$	105.710	+	183.095i	0.239317	+	0.414509i
$59$	212.963	+	368.863i	0.469923	+	0.813930i	0.999409	−	0.0343889i	$-0.0109485\pi$
$59$	212.963	+	368.863i	0.469923	+	0.813930i	−0.529486	+	0.848319i	$0.677615\pi$
$60$	−10.1877	−	263.840i	−0.0219204	−	0.567692i
$61$	−425.297	+	736.637i	−0.892684	+	1.54617i	−0.0560400	+	0.998429i	$0.517847\pi$
$61$	−425.297	+	736.637i	−0.892684	+	1.54617i	−0.836644	+	0.547746i	$0.815486\pi$
$62$	−438.981			−0.899204
$63$	469.546	+	685.176i	0.939004	+	1.37022i
$64$	−741.296			−1.44784
$65$	158.045	−	273.741i	0.301585	−	0.522360i
$66$	797.638	+	420.346i	1.48761	+	0.783955i
$67$	−48.1538	−	83.4048i	−0.0878048	−	0.152082i	0.818778	−	0.574110i	$-0.194652\pi$
$67$	−48.1538	−	83.4048i	−0.0878048	−	0.152082i	−0.906583	+	0.422028i	$0.861319\pi$
$68$	33.4858	+	57.9990i	0.0597168	+	0.103433i
$69$	286.675	+	151.075i	0.500169	+	0.263583i
$70$	−327.773	+	567.719i	−0.559662	+	0.969363i
$71$	952.164			1.59156			0.795782	−	0.605583i	$-0.207060\pi$
$71$	952.164			1.59156			0.795782	+	0.605583i	$0.207060\pi$
$72$	−107.442	+	224.476i	−0.175864	+	0.367427i
$73$	−50.8558			−0.0815373			−0.0407686	−	0.999169i	$-0.512981\pi$
$73$	−50.8558			−0.0815373			−0.0407686	+	0.999169i	$0.512981\pi$
$74$	−600.973	+	1040.92i	−0.944077	+	1.63519i
$75$	5.01227	+	129.807i	0.00771690	+	0.199851i
$76$	−383.036	−	663.437i	−0.578121	−	1.00134i
$77$	−626.271	−	1084.73i	−0.926886	−	1.60541i
$78$	−1184.48	+	746.233i	−1.71944	+	1.08326i
$79$	98.6395	−	170.849i	0.140479	−	0.243316i	−0.787198	−	0.616700i	$-0.788469\pi$
$79$	98.6395	−	170.849i	0.140479	−	0.243316i	0.927677	+	0.373384i	$0.121803\pi$
$80$	210.102			0.293627
$81$	−457.241	−	567.778i	−0.627217	−	0.778844i
$82$	671.400			0.904192
$83$	98.8693	−	171.247i	0.130751	−	0.226467i	−0.793215	−	0.608941i	$-0.791595\pi$
$83$	98.8693	−	171.247i	0.130751	−	0.226467i	0.923966	+	0.382474i	$0.124928\pi$
$84$	1374.52	−	865.959i	1.78539	−	1.12481i
$85$	−16.4747	−	28.5351i	−0.0210228	−	0.0364125i
$86$	−719.844	−	1246.81i	−0.902590	−	1.56333i
$87$	9.94603	+	257.581i	0.0122566	+	0.317420i
$88$	187.637	−	324.997i	0.227298	−	0.393691i
$89$	1364.54			1.62519			0.812593	−	0.582832i	$-0.198056\pi$
$89$	1364.54			1.62519			0.812593	+	0.582832i	$0.198056\pi$
$90$	248.392	−	518.958i	0.290920	−	0.607811i
$91$	1944.83			2.24037
$92$	316.889	−	548.868i	0.359108	−	0.621993i
$93$	−473.499	−	249.529i	−0.527953	−	0.278225i
$94$	94.8583	+	164.299i	0.104084	+	0.180279i
$95$	188.451	+	326.406i	0.203522	+	0.352511i
$96$	−1162.18	−	612.458i	−1.23557	−	0.651132i
$97$	715.579	−	1239.42i	0.749031	−	1.29736i	−0.199256	−	0.979947i	$-0.563853\pi$
$97$	715.579	−	1239.42i	0.749031	−	1.29736i	0.948288	−	0.317413i	$-0.102814\pi$
$98$	−2571.64			−2.65076
$99$	621.422	+	906.799i	0.630862	+	0.920573i
$100$	254.069			0.254069
$101$	−553.808	+	959.224i	−0.545604	+	0.945013i	0.452965	+	0.891528i	$0.350366\pi$
$101$	−553.808	+	959.224i	−0.545604	+	0.945013i	−0.998569	+	0.0534851i	$0.982967\pi$
$102$	5.63073	+	145.824i	0.00546593	+	0.141556i
$103$	−264.437	−	458.018i	−0.252969	−	0.438154i	0.711373	−	0.702814i	$-0.248074\pi$
$103$	−264.437	−	458.018i	−0.252969	−	0.438154i	−0.964342	+	0.264660i	$0.914740\pi$
$104$	291.345	+	504.624i	0.274699	+	0.475793i
$105$	−676.253	+	426.045i	−0.628529	+	0.395979i
$106$	55.9896	−	96.9769i	0.0513037	−	0.0888607i
$107$	490.910			0.443533			0.221766	−	0.975100i	$-0.428818\pi$
$107$	490.910			0.443533			0.221766	+	0.975100i	$0.428818\pi$
$108$	−1144.15	+	850.770i	−1.01941	+	0.758013i
$109$	−351.634			−0.308994			−0.154497	−	0.987993i	$-0.549376\pi$
$109$	−351.634			−0.308994			−0.154497	+	0.987993i	$0.549376\pi$
$110$	−433.792	+	751.349i	−0.376004	+	0.651258i
$111$	−1239.91	+	781.157i	−1.06025	+	0.667965i
$112$	646.357	+	1119.52i	0.545313	+	0.944509i
$113$	−881.226	−	1526.33i	−0.733618	−	1.27066i	−0.955327	−	0.295550i	$-0.904497\pi$
$113$	−881.226	−	1526.33i	−0.733618	−	1.27066i	0.221710	−	0.975113i	$-0.428836\pi$
$114$	−64.4085	−	1668.04i	−0.0529159	−	1.37041i
$115$	−155.907	+	270.039i	−0.126421	+	0.218967i
$116$	504.158			0.403533
$117$	−1701.80	+	131.620i	−1.34471	+	0.104002i
$118$	1815.20			1.41613
$119$	101.366	−	175.570i	0.0780854	−	0.135248i
$120$	−211.852	−	111.644i	−0.161161	−	0.0849302i
$121$	−163.340	−	282.914i	−0.122720	−	0.212557i
$122$	1812.52	+	3139.38i	1.34507	+	2.32972i
$123$	724.195	+	381.642i	0.530882	+	0.279769i
$124$	−523.403	+	906.561i	−0.379056	+	0.656545i
$125$	−125.000			−0.0894427
$126$	3529.40	−	272.971i	2.49543	−	0.193001i
$127$	−1506.12			−1.05234			−0.526169	−	0.850380i	$-0.676372\pi$
$127$	−1506.12			−1.05234			−0.526169	+	0.850380i	$0.676372\pi$
$128$	−568.343	+	984.399i	−0.392460	+	0.679761i
$129$	−67.7286	−	1754.03i	−0.0462262	−	1.19716i
$130$	−673.551	−	1166.62i	−0.454418	−	0.787075i
$131$	−637.562	−	1104.29i	−0.425222	−	0.736506i	0.571219	−	0.820798i	$-0.306471\pi$
$131$	−637.562	−	1104.29i	−0.425222	−	0.736506i	−0.996441	+	0.0842915i	$0.973137\pi$
$132$	1819.11	−	1146.06i	1.19950	−	0.755692i
$133$	−1159.50	+	2008.31i	−0.755948	+	1.30934i
$134$	−410.441			−0.264603
$135$	562.914	−	418.573i	0.358873	−	0.266852i
$136$	60.7403			0.0382973
$137$	−719.712	+	1246.58i	−0.448826	+	0.777389i	−0.998310	−	0.0581150i	$-0.981491\pi$
$137$	−719.712	+	1246.58i	−0.448826	+	0.777389i	0.549484	+	0.835504i	$0.314824\pi$
$138$	1168.46	−	736.140i	0.720768	−	0.454090i
$139$	1269.75	+	2199.27i	0.774811	+	1.34201i	0.934901	+	0.354909i	$0.115488\pi$
$139$	1269.75	+	2199.27i	0.774811	+	1.34201i	−0.160090	+	0.987102i	$0.551178\pi$
$140$	781.616	+	1353.80i	0.471847	+	0.817263i
$141$	8.92502	+	231.139i	0.00533065	+	0.138052i
$142$	2028.96	−	3514.25i	1.19906	−	2.07683i
$143$	2573.89			1.50517
$144$	−641.353	−	935.882i	−0.371153	−	0.541598i
$145$	−248.042			−0.142060
$146$	−108.368	+	187.699i	−0.0614288	+	0.106398i
$147$	−2773.86	−	1461.79i	−1.55635	−	0.820180i
$148$	1433.10	+	2482.20i	0.795945	+	1.37862i
$149$	−46.8796	−	81.1979i	−0.0257754	−	0.0446442i	0.852850	−	0.522156i	$-0.174872\pi$
$149$	−46.8796	−	81.1979i	−0.0257754	−	0.0446442i	−0.878625	+	0.477512i	$0.841539\pi$
$150$	489.774	+	258.105i	0.266599	+	0.140495i
$151$	534.065	−	925.027i	0.287825	−	0.498527i	−0.685465	−	0.728105i	$-0.740401\pi$
$151$	534.065	−	925.027i	0.287825	−	0.498527i	0.973290	+	0.229578i	$0.0737345\pi$
$152$	−694.794			−0.370758
$153$	−76.8166	+	160.491i	−0.0405899	+	0.0848034i
$154$	−5338.06			−2.79320
$155$	257.510	−	446.021i	0.133443	−	0.231131i
$156$	128.809	+	3335.87i	0.0661087	+	1.71207i
$157$	−90.8574	−	157.370i	−0.0461861	−	0.0799966i	0.842008	−	0.539465i	$-0.181373\pi$
$157$	−90.8574	−	157.370i	−0.0461861	−	0.0799966i	−0.888194	+	0.459468i	$0.848040\pi$
$158$	−420.380	−	728.119i	−0.211668	−	0.366621i
$159$	115.517	−	72.7764i	0.0576167	−	0.0362990i
$160$	632.048	−	1094.74i	0.312299	−	0.540917i
$161$	−1918.52			−0.939136
$162$	−3069.89	+	477.719i	−1.48885	+	0.231686i
$163$	−1103.07			−0.530056			−0.265028	−	0.964241i	$-0.585381\pi$
$163$	−1103.07			−0.530056			−0.265028	+	0.964241i	$0.585381\pi$
$164$	800.520	−	1386.54i	0.381159	−	0.660187i
$165$	−894.990	+	563.851i	−0.422272	+	0.266035i
$166$	−421.359	−	729.816i	−0.197011	−	0.341233i
$167$	2020.85	+	3500.22i	0.936396	+	1.62189i	0.772126	+	0.635470i	$0.219194\pi$
$167$	2020.85	+	3500.22i	0.936396	+	1.62189i	0.164270	+	0.986415i	$0.447473\pi$
$168$	−56.8506	−	1472.31i	−0.0261078	−	0.676137i
$169$	−899.745	+	1558.40i	−0.409534	+	0.709333i
$170$	−140.423			−0.0633529
$171$	878.687	−	1835.82i	0.392953	−	0.820985i
$172$	−3433.12			−1.52194
$173$	1373.88	−	2379.63i	0.603780	−	1.04578i	−0.388463	−	0.921465i	$-0.626994\pi$
$173$	1373.88	−	2379.63i	0.603780	−	1.04578i	0.992243	−	0.124314i	$-0.0396730\pi$
$174$	971.875	+	512.167i	0.423435	+	0.223145i
$175$	−384.549	−	666.059i	−0.166110	−	0.287710i
$176$	855.423	+	1481.64i	0.366363	+	0.634560i
$177$	1957.94	+	1031.81i	0.831456	+	0.438168i
$178$	2907.69	−	5036.27i	1.22439	−	2.12070i
$179$	−2838.32			−1.18517			−0.592587	−	0.805506i	$-0.701893\pi$
$179$	−2838.32			−1.18517			−0.592587	+	0.805506i	$0.701893\pi$
$180$	−775.564	−	1131.73i	−0.321151	−	0.468633i
$181$	3442.25			1.41359			0.706796	−	0.707417i	$-0.250140\pi$
$181$	3442.25			1.41359			0.706796	+	0.707417i	$0.250140\pi$
$182$	4144.21	−	7177.99i	1.68785	−	2.92345i
$183$	170.537	+	4416.53i	0.0688876	+	1.78404i
$184$	−287.405	−	497.799i	−0.115151	−	0.199447i
$185$	−705.073	−	1221.22i	−0.280206	−	0.485330i
$186$	−1929.94	+	1215.88i	−0.760806	+	0.479314i
$187$	134.153	−	232.359i	0.0524610	−	0.0908652i
$188$	452.403			0.175505
$189$	3962.10	+	1711.77i	1.52487	+	0.658801i
$190$	1606.27			0.613322
$191$	373.148	−	646.311i	0.141361	−	0.244845i	−0.786648	−	0.617402i	$-0.788185\pi$
$191$	373.148	−	646.311i	0.141361	−	0.244845i	0.928010	+	0.372557i	$0.121519\pi$
$192$	−3259.04	+	2053.22i	−1.22500	+	0.771763i
$193$	−53.9538	−	93.4506i	−0.0201227	−	0.0348535i	0.855789	−	0.517326i	$-0.173072\pi$
$193$	−53.9538	−	93.4506i	−0.0201227	−	0.0348535i	−0.875911	+	0.482472i	$0.839739\pi$
$194$	−3049.64	−	5282.13i	−1.12861	−	1.95482i
$195$	−63.3730	−	1641.22i	−0.0232730	−	0.602720i
$196$	−3066.20	+	5310.82i	−1.11742	+	1.93543i
$197$	−3361.02			−1.21555			−0.607774	−	0.794110i	$-0.707937\pi$
$197$	−3361.02			−1.21555			−0.607774	+	0.794110i	$0.707937\pi$
$198$	4671.00	−	361.264i	1.67653	−	0.129666i
$199$	1368.99			0.487663			0.243831	−	0.969818i	$-0.421596\pi$
$199$	1368.99			0.487663			0.243831	+	0.969818i	$0.421596\pi$
$200$	115.215	−	199.558i	0.0407346	−	0.0705544i
$201$	−442.716	−	233.306i	−0.155357	−	0.0818714i
$202$	2360.21	+	4088.00i	0.822097	+	1.42391i
$203$	−763.074	−	1321.68i	−0.263829	−	0.456965i
$204$	307.861	+	162.239i	0.105660	+	0.0556815i
$205$	−393.850	+	682.168i	−0.134184	+	0.232413i
$206$	−2253.94			−0.762329
$207$	1678.78	−	129.840i	0.563688	−	0.0435966i
$208$	−2656.44			−0.885534
$209$	−1534.54	+	2657.90i	−0.507877	+	0.879669i
$210$	131.431	+	3403.78i	0.0431885	+	1.11849i
$211$	−1251.27	−	2167.27i	−0.408252	−	0.707114i	0.586442	−	0.809991i	$-0.300528\pi$
$211$	−1251.27	−	2167.27i	−0.408252	−	0.707114i	−0.994694	+	0.102878i	$0.967195\pi$
$212$	−133.514	−	231.254i	−0.0432538	−	0.0749178i
$213$	4186.10	−	2637.28i	1.34660	−	0.848372i
$214$	1046.07	−	1811.85i	0.334150	−	0.578765i
$215$	1689.07			0.535784
$216$	149.388	+	1284.48i	0.0470581	+	0.404619i
$217$	3168.81			0.991305
$218$	−749.292	+	1297.81i	−0.232791	+	0.403206i
$219$	−223.583	+	140.859i	−0.0689877	+	0.0434629i
$220$	1034.43	+	1791.69i	0.317006	+	0.549071i
$221$	208.299	+	360.785i	0.0634015	+	0.109815i
$222$	240.979	+	6240.85i	0.0728535	+	1.88675i
$223$	−937.263	+	1623.39i	−0.281452	+	0.487489i	−0.971743	−	0.236043i	$-0.924149\pi$
$223$	−937.263	+	1623.39i	−0.281452	+	0.487489i	0.690291	+	0.723532i	$0.257483\pi$
$224$	7777.72			2.31996
$225$	381.572	+	556.801i	0.113058	+	0.164978i
$226$	−7511.18			−2.21078
$227$	−2539.37	+	4398.32i	−0.742484	+	1.28602i	0.208877	+	0.977942i	$0.433019\pi$
$227$	−2539.37	+	4398.32i	−0.742484	+	1.28602i	−0.951361	+	0.308078i	$0.900314\pi$
$228$	−3521.55	−	1855.82i	−1.02290	−	0.539055i
$229$	−432.933	−	749.861i	−0.124930	−	0.216385i	0.796776	−	0.604275i	$-0.206537\pi$
$229$	−432.933	−	749.861i	−0.124930	−	0.216385i	−0.921706	+	0.387890i	$0.873204\pi$
$230$	664.441	+	1150.85i	0.190487	+	0.329933i
$231$	−5757.80	−	3034.30i	−1.63998	−	0.864252i
$232$	228.625	−	395.990i	0.0646981	−	0.112060i
$233$	1142.10			0.321122			0.160561	−	0.987026i	$-0.448670\pi$
$233$	1142.10			0.321122			0.160561	+	0.987026i	$0.448670\pi$
$234$	−3140.56	+	6561.48i	−0.877371	+	1.83307i
$235$	−222.579			−0.0617849
$236$	2164.29	−	3748.66i	0.596964	−	1.03397i
$237$	−39.5527	−	1024.33i	−0.0108406	−	0.280748i
$238$	−431.998	−	748.242i	−0.117657	−	0.203787i
$239$	1574.68	+	2727.43i	0.426183	+	0.738171i	0.996530	−	0.0832330i	$-0.0265246\pi$
$239$	1574.68	+	2727.43i	0.426183	+	0.738171i	−0.570347	+	0.821404i	$0.693191\pi$
$240$	923.694	−	581.935i	0.248434	−	0.156516i
$241$	−2252.18	+	3900.90i	−0.601975	+	1.04265i	0.390547	+	0.920583i	$0.372286\pi$
$241$	−2252.18	+	3900.90i	−0.601975	+	1.04265i	−0.992522	+	0.122068i	$0.961047\pi$
$242$	−1392.24			−0.369821
$243$	−3582.83	−	1229.72i	−0.945839	−	0.324637i
$244$	8644.39			2.26803
$245$	1508.55	−	2612.88i	0.393378	−	0.681351i
$246$	2951.75	−	1859.63i	0.765027	−	0.481973i
$247$	−2382.69	−	4126.94i	−0.613793	−	1.06312i
$248$	474.704	+	822.212i	0.121547	+	0.210526i
$249$	−39.6448	−	1026.72i	−0.0100899	−	0.261307i
$250$	−266.361	+	461.351i	−0.0673846	+	0.116714i
$251$	886.861			0.223021			0.111510	−	0.993763i	$-0.464431\pi$
$251$	886.861			0.223021			0.111510	+	0.993763i	$0.464431\pi$
$252$	3644.43	−	7614.21i	0.911023	−	1.90337i
$253$	−2539.08			−0.630950
$254$	−3209.38	+	5558.81i	−0.792813	+	1.37319i
$255$	−151.465	−	79.8205i	−0.0371966	−	0.0196022i
$256$	−543.033	−	940.561i	−0.132576	−	0.229629i
$257$	−1131.02	−	1958.98i	−0.274517	−	0.475478i	0.695496	−	0.718530i	$-0.255185\pi$
$257$	−1131.02	−	1958.98i	−0.274517	−	0.475478i	−0.970013	+	0.243052i	$0.921851\pi$
$258$	−6618.09	−	3487.66i	−1.59699	−	0.841598i
$259$	4338.17	−	7513.92i	1.04077	−	1.80267i
$260$	−3212.34			−0.766233
$261$	757.166	+	1104.88i	0.179569	+	0.262032i
$262$	−5434.30			−1.28142
$263$	−3640.31	+	6305.20i	−0.853503	+	1.47831i	0.0245245	+	0.999699i	$0.492193\pi$
$263$	−3640.31	+	6305.20i	−0.853503	+	1.47831i	−0.878027	+	0.478611i	$0.841141\pi$
$264$	−75.2391	−	1948.53i	−0.0175403	−	0.454257i
$265$	65.6881	+	113.775i	0.0152271	+	0.0263742i
$266$	4941.52	+	8558.96i	1.13904	+	1.97287i
$267$	5999.09	−	3779.48i	1.37505	−	0.866293i
$268$	−489.375	+	847.622i	−0.111542	+	0.193197i
$269$	−106.781			−0.0242028			−0.0121014	−	0.999927i	$-0.503852\pi$
$269$	−106.781			−0.0242028			−0.0121014	+	0.999927i	$0.503852\pi$
$270$	−345.365	−	2969.54i	−0.0778452	−	0.669335i
$271$	5908.85			1.32449			0.662246	−	0.749287i	$-0.269603\pi$
$271$	5908.85			1.32449			0.662246	+	0.749287i	$0.269603\pi$
$272$	−138.455	+	239.811i	−0.0308643	+	0.0534585i
$273$	8550.25	−	5386.73i	1.89555	−	1.19421i
$274$	3067.25	+	5312.64i	0.676276	+	1.17134i
$275$	−508.933	−	881.498i	−0.111599	−	0.193296i
$276$	−127.067	−	3290.75i	−0.0277120	−	0.717681i
$277$	−1645.04	+	2849.30i	−0.356827	+	0.618042i	−0.987429	−	0.158064i	$-0.949475\pi$
$277$	−1645.04	+	2849.30i	−0.356827	+	0.618042i	0.630602	+	0.776106i	$0.282808\pi$
$278$	10822.8			2.33492
$279$	−2772.83	+	214.456i	−0.595000	+	0.0460184i
$280$	1417.78			0.302603
$281$	−169.861	+	294.209i	−0.0360608	+	0.0624591i	−0.883493	−	0.468445i	$-0.844814\pi$
$281$	−169.861	+	294.209i	−0.0360608	+	0.0624591i	0.847432	+	0.530904i	$0.178148\pi$
$282$	872.107	+	459.590i	0.184160	+	0.0970504i
$283$	−1299.83	−	2251.37i	−0.273028	−	0.472898i	0.696608	−	0.717452i	$-0.254692\pi$
$283$	−1299.83	−	2251.37i	−0.273028	−	0.472898i	−0.969636	+	0.244554i	$0.921358\pi$
$284$	−4838.30	−	8380.19i	−1.01092	−	1.75096i
$285$	1732.58	+	913.048i	0.360102	+	0.189769i
$286$	5484.67	−	9499.73i	1.13397	−	1.96409i
$287$	−4846.55			−0.996804
$288$	−6805.80	+	526.373i	−1.39248	+	0.107697i
$289$	−4869.57			−0.991161
$290$	−528.550	+	915.475i	−0.107026	+	0.185374i
$291$	−286.934	−	7430.98i	−0.0578020	−	1.49695i
$292$	258.418	+	447.592i	0.0517902	+	0.0897033i
$293$	−89.0427	−	154.227i	−0.0177540	−	0.0307509i	0.857012	−	0.515297i	$-0.172318\pi$
$293$	−89.0427	−	154.227i	−0.0177540	−	0.0307509i	−0.874766	+	0.484546i	$0.838985\pi$
$294$	−11306.0	+	7122.86i	−2.24278	+	1.41297i
$295$	−1064.82	+	1844.31i	−0.210156	+	0.364001i
$296$	2599.52			0.510452
$297$	5243.65	+	2265.45i	1.02447	+	0.442609i
$298$	−399.581			−0.0776749
$299$	1971.22	−	3414.25i	0.381266	−	0.660372i
$300$	1116.99	−	703.713i	0.214965	−	0.135430i
$301$	5196.24	+	9000.16i	0.995038	+	1.72346i
$302$	−2276.07	−	3942.26i	−0.433685	−	0.751164i
$303$	222.067	+	5751.06i	0.0421037	+	1.09039i
$304$	1583.76	−	2743.15i	0.298798	−	0.517534i
$305$	−4252.97			−0.798441
$306$	428.653	+	625.504i	0.0800800	+	0.116855i
$307$	1537.60			0.285848			0.142924	−	0.989734i	$-0.454349\pi$
$307$	1537.60			0.285848			0.142924	+	0.989734i	$0.454349\pi$
$308$	−6364.64	+	11023.9i	−1.17746	+	2.03943i
$309$	−2431.18	−	1281.20i	−0.447589	−	0.235874i
$310$	−1097.45	−	1900.84i	−0.201068	−	0.348260i
$311$	−472.662	−	818.674i	−0.0861807	−	0.149269i	0.819713	−	0.572774i	$-0.194133\pi$
$311$	−472.662	−	818.674i	−0.0861807	−	0.149269i	−0.905894	+	0.423505i	$0.860800\pi$
$312$	2678.57	+	1411.57i	0.486038	+	0.256137i
$313$	−992.767	+	1719.52i	−0.179280	+	0.310521i	−0.941634	−	0.336638i	$-0.890710\pi$
$313$	−992.767	+	1719.52i	−0.179280	+	0.310521i	0.762354	+	0.647160i	$0.224043\pi$
$314$	−774.428			−0.139183
$315$	−1793.03	+	3746.13i	−0.320718	+	0.670066i
$316$	−2004.90			−0.356913
$317$	2591.62	−	4488.81i	0.459179	−	0.795321i	−0.539739	−	0.841833i	$-0.681477\pi$
$317$	2591.62	−	4488.81i	0.459179	−	0.795321i	0.998918	+	0.0465112i	$0.0148103\pi$
$318$	−22.4508	−	581.428i	−0.00395906	−	0.102531i
$319$	−1009.89	−	1749.19i	−0.177251	−	0.307008i
$320$	−1853.24	−	3209.91i	−0.323748	−	0.560748i
$321$	2158.24	−	1359.71i	0.375268	−	0.236422i
$322$	−4088.16	+	7080.91i	−0.707529	+	1.22548i
$323$	−496.748			−0.0855722
$324$	−2673.71	+	6909.37i	−0.458455	+	1.18473i
$325$	1580.45			0.269746
$326$	−2350.52	+	4071.22i	−0.399336	+	0.691670i
$327$	−1545.92	+	973.945i	−0.261437	+	0.164707i
$328$	−726.037	−	1257.53i	−0.122222	−	0.211694i
$329$	−684.741	−	1186.01i	−0.114745	−	0.198744i
$330$	173.943	+	4504.74i	0.0290158	+	0.751448i
$331$	1086.68	−	1882.19i	0.180451	−	0.312551i	−0.761583	−	0.648067i	$-0.775578\pi$
$331$	1086.68	−	1882.19i	0.180451	−	0.312551i	0.942034	+	0.335517i	$0.108911\pi$
$332$	−2009.57			−0.332197
$333$	−3287.54	+	6868.56i	−0.541009	+	1.13032i
$334$	17224.8			2.82186
$335$	240.769	−	417.024i	0.0392675	−	0.0680133i
$336$	5942.47	+	3131.61i	0.964846	+	0.508463i
$337$	3925.16	+	6798.57i	0.634472	+	1.09894i	0.986627	+	0.162995i	$0.0521156\pi$
$337$	3925.16	+	6798.57i	0.634472	+	1.09894i	−0.352155	+	0.935942i	$0.614551\pi$
$338$	3834.52	+	6641.58i	0.617071	+	1.06880i
$339$	−8101.81	−	4269.56i	−1.29802	−	0.684043i
$340$	−167.429	+	289.995i	−0.0267062	+	0.0462565i
$341$	4193.78			0.665999
$342$	−4903.26	−	7154.99i	−0.775257	−	1.13128i
$343$	8011.53			1.26117
$344$	−1556.85	+	2696.54i	−0.244010	+	0.422638i
$345$	62.5159	+	1619.03i	0.00975577	+	0.252653i
$346$	−5855.16	−	10141.4i	−0.909756	−	1.57574i
$347$	4686.12	+	8116.60i	0.724969	+	1.25568i	0.958987	+	0.283451i	$0.0914792\pi$
$347$	4686.12	+	8116.60i	0.724969	+	1.25568i	−0.234018	+	0.972232i	$0.575187\pi$
$348$	2216.48	−	1396.40i	0.341425	−	0.215101i
$349$	588.952	−	1020.10i	0.0903321	−	0.156460i	−0.817319	−	0.576186i	$-0.804540\pi$
$349$	588.952	−	1020.10i	0.0903321	−	0.156460i	0.907651	+	0.419726i	$0.137874\pi$
$350$	−3277.73			−0.500577
$351$	−7117.23	+	5292.25i	−1.08231	+	0.804784i
$352$	10293.4			1.55864
$353$	3631.06	−	6289.19i	0.547484	−	0.948271i	−0.450962	−	0.892543i	$-0.648919\pi$
$353$	3631.06	−	6289.19i	0.547484	−	0.948271i	0.998446	−	0.0557274i	$-0.0177478\pi$
$354$	7980.37	−	5027.70i	1.19817	−	0.754856i
$355$	2380.41	+	4122.99i	0.355885	+	0.616410i
$356$	−6933.77	−	12009.6i	−1.03227	−	1.78795i
$357$	−40.6458	−	1052.64i	−0.00602578	−	0.156055i
$358$	−6048.15	+	10475.7i	−0.892890	+	1.54653i
$359$	−1939.95			−0.285199			−0.142600	−	0.989780i	$-0.545546\pi$
$359$	−1939.95			−0.285199			−0.142600	+	0.989780i	$0.545546\pi$
$360$	−1240.61	+	95.9514i	−0.181628	+	0.0140475i
$361$	−1176.81			−0.171572
$362$	7335.05	−	12704.7i	1.06498	−	1.84459i
$363$	−1501.72	−	791.388i	−0.217134	−	0.114427i
$364$	−9882.41	−	17116.8i	−1.42302	−	2.46474i
$365$	−127.139	−	220.212i	−0.0182323	−	0.0315792i
$366$	16664.0	+	8781.72i	2.37989	+	1.25417i
$367$	−3250.97	+	5630.85i	−0.462396	+	0.800893i	−0.999080	−	0.0428901i	$-0.986343\pi$
$367$	−3250.97	+	5630.85i	−0.462396	+	0.800893i	0.536684	+	0.843783i	$0.319677\pi$
$368$	2620.51			0.371205
$369$	4240.91	−	328.000i	0.598301	−	0.0462737i
$370$	−6009.73			−0.844409
$371$	−404.165	+	700.034i	−0.0565585	+	0.0979622i
$372$	209.875	+	5435.32i	0.0292514	+	0.757548i
$373$	−6659.02	−	11533.8i	−0.924372	−	1.60106i	−0.792568	−	0.609784i	$-0.791256\pi$
$373$	−6659.02	−	11533.8i	−0.924372	−	1.60106i	−0.131805	−	0.991276i	$-0.542077\pi$
$374$	−571.729	−	990.263i	−0.0790465	−	0.136913i
$375$	−549.550	+	346.221i	−0.0756764	+	0.0476768i
$376$	205.155	−	355.339i	0.0281385	−	0.0487373i
$377$	3136.13			0.428432
$378$	14760.6	−	10975.7i	2.00848	−	1.49347i
$379$	−3198.42			−0.433488			−0.216744	−	0.976228i	$-0.569544\pi$
$379$	−3198.42			−0.433488			−0.216744	+	0.976228i	$0.569544\pi$
$380$	1915.18	−	3317.19i	0.258544	−	0.447811i
$381$	−6621.53	+	4171.62i	−0.890370	+	0.560941i
$382$	−1590.27	−	2754.43i	−0.212999	−	0.368924i
$383$	1170.25	+	2026.93i	0.156128	+	0.270422i	0.933469	−	0.358658i	$-0.116765\pi$
$383$	1170.25	+	2026.93i	0.156128	+	0.270422i	−0.777341	+	0.629079i	$0.783432\pi$
$384$	227.895	+	5902.00i	0.0302858	+	0.784336i
$385$	3131.36	−	5423.67i	0.414516	−	0.717963i
$386$	−459.878			−0.0606403
$387$	−5156.01	−	7523.81i	−0.677248	−	0.988261i
$388$	−14544.5			−1.90305
$389$	−1995.97	+	3457.12i	−0.260153	+	0.450599i	−0.966282	−	0.257484i	$-0.917106\pi$
$389$	−1995.97	+	3457.12i	−0.260153	+	0.450599i	0.706129	+	0.708083i	$0.250440\pi$
$390$	−6192.48	−	3263.37i	−0.804022	−	0.423710i
$391$	−205.482	−	355.906i	−0.0265772	−	0.0460330i
$392$	2780.91	+	4816.69i	0.358310	+	0.620611i
$393$	−5861.61	−	3089.00i	−0.752365	−	0.396488i
$394$	−7161.96	+	12404.9i	−0.915773	+	1.58616i
$395$	986.395			0.125648
$396$	4823.24	−	10077.1i	0.612063	−	1.27876i
$397$	−4960.90			−0.627155			−0.313577	−	0.949563i	$-0.601528\pi$
$397$	−4960.90			−0.627155			−0.313577	+	0.949563i	$0.601528\pi$
$398$	2917.16	−	5052.66i	0.367397	−	0.636350i
$399$	464.937	+	12040.9i	0.0583358	+	1.51077i
$400$	525.256	+	909.769i	0.0656569	+	0.113721i
$401$	−413.811	−	716.742i	−0.0515330	−	0.0892578i	0.839108	−	0.543965i	$-0.183077\pi$
$401$	−413.811	−	716.742i	−0.0515330	−	0.0892578i	−0.890641	+	0.454707i	$0.849744\pi$
$402$	−1804.47	+	1136.83i	−0.223877	+	0.141044i
$403$	−3255.85	+	5639.30i	−0.402445	+	0.697056i
$404$	11256.4			1.38621
$405$	1315.45	−	3399.36i	0.161395	−	0.417075i
$406$	−6504.11			−0.795058
$407$	5741.36	−	9944.33i	0.699235	−	1.21111i
$408$	267.039	−	168.237i	0.0324029	−	0.0204141i
$409$	4183.82	+	7246.59i	0.505811	+	0.876090i	0.999977	+	0.00672263i	$0.00213989\pi$
$409$	4183.82	+	7246.59i	0.505811	+	0.876090i	−0.494167	+	0.869367i	$0.664527\pi$
$410$	1678.50	+	2907.25i	0.202184	+	0.350192i
$411$	288.592	+	7473.90i	0.0346354	+	0.896983i
$412$	−2687.41	+	4654.73i	−0.321357	+	0.556607i
$413$	−13103.2			−1.56117
$414$	3098.08	−	6472.74i	0.367784	−	0.768400i
$415$	988.693			0.116947
$416$	−7991.34	+	13841.4i	−0.941845	+	1.63132i
$417$	11673.8	+	6151.96i	1.37091	+	0.722453i
$418$	6539.87	+	11327.4i	0.765252	+	1.32546i
$419$	−2100.36	−	3637.93i	−0.244891	−	0.424163i	0.717210	−	0.696857i	$-0.245419\pi$
$419$	−2100.36	−	3637.93i	−0.244891	−	0.424163i	−0.962101	+	0.272694i	$0.912085\pi$
$420$	7186.01	+	3786.95i	0.834861	+	0.439962i
$421$	−3469.38	+	6009.14i	−0.401632	+	0.695648i	−0.993923	−	0.110077i	$-0.964890\pi$
$421$	−3469.38	+	6009.14i	−0.401632	+	0.695648i	0.592291	+	0.805724i	$0.298224\pi$
$422$	−10665.3			−1.23028
$423$	679.440	+	991.459i	0.0780981	+	0.113963i
$424$	−242.184			−0.0277394
$425$	82.3737	−	142.675i	0.00940168	−	0.0162842i
$426$	−813.575	−	21069.8i	−0.0925301	−	2.39633i
$427$	−13083.8	−	22661.8i	−1.48283	−	2.56835i
$428$	−2494.50	−	4320.60i	−0.281720	−	0.487953i
$429$	11315.9	−	7129.09i	1.27351	−	0.802321i
$430$	3599.22	−	6234.03i	0.403651	−	0.699144i
$431$	6827.09			0.762991			0.381496	−	0.924371i	$-0.375409\pi$
$431$	6827.09			0.762991			0.381496	+	0.924371i	$0.375409\pi$
$432$	−5411.83	−	2338.11i	−0.602724	−	0.260399i
$433$	−2199.59			−0.244124			−0.122062	−	0.992522i	$-0.538951\pi$
$433$	−2199.59			−0.244124			−0.122062	+	0.992522i	$0.538951\pi$
$434$	6752.39	−	11695.5i	0.746832	−	1.29355i
$435$	−1090.49	+	687.019i	−0.120196	+	0.0757243i
$436$	1786.78	+	3094.80i	0.196265	+	0.339940i
$437$	2350.46	+	4071.12i	0.257295	+	0.445648i
$438$	43.4536	+	1125.36i	0.00474040	+	0.122766i
$439$	−4162.16	+	7209.07i	−0.452504	+	0.783759i	−0.998541	−	0.0540018i	$-0.982802\pi$
$439$	−4162.16	+	7209.07i	−0.452504	+	0.783759i	0.546037	+	0.837761i	$0.316136\pi$
$440$	1876.37			0.203301
$441$	−16243.8	+	1256.33i	−1.75400	+	0.135658i
$442$	1775.45			0.191063
$443$	5433.41	−	9410.93i	0.582729	−	1.00932i	−0.412426	−	0.910991i	$-0.635318\pi$
$443$	5433.41	−	9410.93i	0.582729	−	1.00932i	0.995154	−	0.0983247i	$-0.0313484\pi$
$444$	13175.6	+	6943.39i	1.40830	+	0.742159i
$445$	3411.36	+	5908.65i	0.363402	+	0.629431i
$446$	3994.41	+	6918.51i	0.424082	+	0.734532i
$447$	−431.001	−	227.133i	−0.0456055	−	0.0240336i
$448$	11402.6	−	19749.9i	1.20250	−	2.08280i
$449$	−4947.73			−0.520040			−0.260020	−	0.965603i	$-0.583729\pi$
$449$	−4947.73			−0.520040			−0.260020	+	0.965603i	$0.583729\pi$
$450$	2868.13	−	221.827i	0.300456	−	0.0232378i
$451$	−6414.18			−0.669694
$452$	−8955.69	+	15511.7i	−0.931947	+	1.61418i
$453$	−214.150	−	5546.03i	−0.0222112	−	0.575221i
$454$	10822.2	+	18744.7i	1.11875	+	1.93773i
$455$	4862.07	+	8421.35i	0.500961	+	0.867690i
$456$	−3054.59	+	1924.42i	−0.313694	+	0.197630i
$457$	7098.85	−	12295.6i	0.726630	−	1.25856i	−0.231669	−	0.972795i	$-0.574419\pi$
$457$	7098.85	−	12295.6i	0.726630	−	1.25856i	0.958299	−	0.285766i	$-0.0922480\pi$
$458$	−3690.13			−0.376481
$459$	106.806	+	918.347i	0.0108612	+	0.0933873i
$460$	3168.89			0.321196
$461$	9114.02	−	15785.9i	0.920786	−	1.59485i	0.122584	−	0.992458i	$-0.460882\pi$
$461$	9114.02	−	15785.9i	0.920786	−	1.59485i	0.798202	−	0.602390i	$-0.205785\pi$
$462$	−23468.3	+	14785.2i	−2.36329	+	1.48890i
$463$	−2170.59	−	3759.58i	−0.217875	−	0.377370i	0.736283	−	0.676674i	$-0.236579\pi$
$463$	−2170.59	−	3759.58i	−0.217875	−	0.377370i	−0.954158	+	0.299303i	$0.903246\pi$
$464$	1042.28	+	1805.29i	0.104282	+	0.180621i
$465$	−103.257	−	2674.13i	−0.0102977	−	0.266688i
$466$	2433.69	−	4215.28i	0.241928	−	0.419032i
$467$	4919.63			0.487481			0.243740	−	0.969841i	$-0.421626\pi$
$467$	4919.63			0.487481			0.243740	+	0.969841i	$0.421626\pi$
$468$	9805.90	+	14309.1i	0.968542	+	1.41333i
$469$	2962.80			0.291704
$470$	−474.291	+	821.497i	−0.0465477	+	0.0806230i
$471$	−835.324	−	440.206i	−0.0817191	−	0.0430650i
$472$	−1962.92	−	3399.88i	−0.191421	−	0.331551i
$473$	6876.98	+	11911.3i	0.668508	+	1.15789i
$474$	−3864.88	−	2036.75i	−0.374515	−	0.197365i
$475$	−942.254	+	1632.03i	−0.0910180	+	0.157648i
$476$	−2060.31			−0.198391
$477$	306.283	−	639.909i	0.0293999	−	0.0614244i
$478$	13421.9			1.28432
$479$	−2286.41	+	3960.19i	−0.218098	+	0.377757i	−0.954226	−	0.299085i	$-0.903319\pi$
$479$	−2286.41	+	3960.19i	−0.218098	+	0.377757i	0.736128	+	0.676842i	$0.236652\pi$
$480$	−253.440	−	6563.55i	−0.0240998	−	0.624132i
$481$	8914.64	+	15440.6i	0.845057	+	1.46368i
$482$	9598.31	+	16624.8i	0.907035	+	1.57103i
$483$	−8434.61	+	5313.87i	−0.794592	+	0.500600i
$484$	−1659.99	+	2875.19i	−0.155897	+	0.270021i
$485$	7155.79			0.669954
$486$	−12173.3	+	10603.1i	−1.13620	+	0.989646i
$487$	15751.5			1.46564			0.732822	−	0.680421i	$-0.238203\pi$
$487$	15751.5			1.46564			0.732822	+	0.680421i	$0.238203\pi$
$488$	3920.04	−	6789.72i	0.363631	−	0.629828i
$489$	−4849.55	+	3055.26i	−0.448475	+	0.282543i
$490$	−6429.10	−	11135.5i	−0.592729	−	1.02664i
$491$	−7654.18	−	13257.4i	−0.703520	−	1.21853i	−0.967223	−	0.253928i	$-0.918277\pi$
$491$	−7654.18	−	13257.4i	−0.703520	−	1.21853i	0.263703	−	0.964604i	$-0.415056\pi$
$492$	−320.994	−	8313.05i	−0.0294137	−	0.761751i
$493$	163.457	−	283.116i	0.0149325	−	0.0258639i
$494$	−20309.0			−1.84968
$495$	−2373.00	+	4957.83i	−0.215471	+	0.450178i
$496$	−4328.28			−0.391826
$497$	−14646.2	+	25367.9i	−1.32187	+	2.28955i
$498$	−3873.89	−	2041.49i	−0.348580	−	0.183698i
$499$	−8866.05	−	15356.5i	−0.795389	−	1.37765i	−0.922592	−	0.385777i	$-0.873933\pi$
$499$	−8866.05	−	15356.5i	−0.795389	−	1.37765i	0.127203	−	0.991877i	$-0.459400\pi$
$500$	635.172	+	1100.15i	0.0568115	+	0.0984005i
$501$	18579.3	+	9791.07i	1.65681	+	0.873119i
$502$	1889.80	−	3273.23i	0.168020	−	0.291019i
$503$	−10511.5			−0.931775			−0.465887	−	0.884844i	$-0.654265\pi$
$503$	−10511.5			−0.931775			−0.465887	+	0.884844i	$0.654265\pi$
$504$	−4327.89	−	6315.39i	−0.382499	−	0.558155i
$505$	−5538.08			−0.488003
$506$	−5410.49	+	9371.25i	−0.475347	+	0.823326i
$507$	360.782	+	9343.47i	0.0316033	+	0.818457i
$508$	7653.18	+	13255.7i	0.668416	+	1.15773i
$509$	−9815.42	−	17000.8i	−0.854737	−	1.48045i	−0.876889	−	0.480693i	$-0.840385\pi$
$509$	−9815.42	−	17000.8i	−0.854737	−	1.48045i	0.0221524	−	0.999755i	$-0.492948\pi$
$510$	−617.358	+	388.941i	−0.0536021	+	0.0337698i
$511$	782.262	−	1354.92i	0.0677206	−	0.117296i
$512$	−13722.1			−1.18444
$513$	−1221.73	−	10504.8i	−0.105147	−	0.904086i
$514$	−9640.30			−0.827267
$515$	1322.19	−	2290.09i	0.113131	−	0.195949i
$516$	−15093.4	+	9508.96i	−1.28769	+	0.811257i
$517$	−906.223	−	1569.62i	−0.0770902	−	0.133524i
$518$	−18488.3	−	32022.7i	−1.56820	−	2.71621i
$519$	−550.900	−	14267.1i	−0.0465931	−	1.20666i
$520$	−1456.73	+	2523.12i	−0.122849	+	0.212781i
$521$	88.4336			0.00743636			0.00371818	−	0.999993i	$-0.498816\pi$
$521$	88.4336			0.00743636			0.00371818	+	0.999993i	$0.498816\pi$
$522$	5691.34	−	440.179i	0.477209	−	0.0369082i
$523$	21346.4			1.78473			0.892363	−	0.451317i	$-0.149046\pi$
$523$	21346.4			1.78473			0.892363	+	0.451317i	$0.149046\pi$
$524$	−6479.39	+	11222.6i	−0.540178	+	0.935616i
$525$	−3535.46	−	1863.15i	−0.293905	−	0.154885i
$526$	15514.2	+	26871.4i	1.28603	+	2.22747i
$527$	339.394	+	587.847i	0.0280535	+	0.0485902i
$528$	7864.58	+	4144.55i	0.648224	+	0.341606i
$529$	4138.94	−	7168.86i	0.340178	−	0.589205i
$530$	559.896			0.0458874
$531$	11465.8	−	886.783i	0.937047	−	0.0724729i
$532$	23567.4			1.92063
$533$	4979.67	−	8625.03i	0.404678	−	0.700923i
$534$	−1165.93	−	30195.1i	−0.0944847	−	2.44695i
$535$	1227.27	+	2125.70i	0.0991770	+	0.171780i
$536$	443.842	+	768.757i	0.0357669	+	0.0619501i
$537$	−12478.4	+	7861.51i	−1.00276	+	0.631749i
$538$	−227.538	+	394.108i	−0.0182340	+	0.0315821i
$539$	24568.0			1.96330
$540$	−6544.32	−	2827.39i	−0.521524	−	0.225318i
$541$	−14432.6			−1.14696			−0.573480	−	0.819220i	$-0.694407\pi$
$541$	−14432.6			−1.14696			−0.573480	+	0.819220i	$0.694407\pi$
$542$	12591.1	−	21808.4i	0.997850	−	1.72833i
$543$	15133.5	−	9534.24i	1.19602	−	0.753505i
$544$	833.027	+	1442.84i	0.0656539	+	0.113716i
$545$	−879.084	−	1522.62i	−0.0690933	−	0.119673i
$546$	−1661.75	−	43035.9i	−0.130250	−	3.37320i
$547$	8284.80	−	14349.7i	0.647592	−	1.12166i	−0.336105	−	0.941825i	$-0.609110\pi$
$547$	8284.80	−	14349.7i	0.647592	−	1.12166i	0.983696	−	0.179837i	$-0.0575571\pi$
$548$	14628.5			1.14033
$549$	12982.5	+	18944.5i	1.00925	+	1.47273i
$550$	−4337.92			−0.336308
$551$	−1869.75	+	3238.50i	−0.144562	+	0.250389i
$552$	−2642.34	−	1392.48i	−0.203742	−	0.107369i
$553$	3034.54	+	5255.98i	0.233349	+	0.404172i
$554$	7010.80	+	12143.1i	0.537654	+	0.931245i
$555$	−6482.30	−	3416.10i	−0.495780	−	0.261271i
$556$	12904.1	−	22350.6i	0.984277	−	1.70482i
$557$	11597.0			0.882191			0.441096	−	0.897460i	$-0.354590\pi$
$557$	11597.0			0.882191			0.441096	+	0.897460i	$0.354590\pi$
$558$	−5117.08	+	10691.0i	−0.388214	+	0.811084i
$559$	−21355.9			−1.61584
$560$	−3231.79	+	5597.62i	−0.243871	+	0.422397i
$561$	−53.7928	−	1393.12i	−0.00404836	−	0.104844i
$562$	723.912	+	1253.85i	0.0543352	+	0.0941113i
$563$	11524.6	+	19961.3i	0.862709	+	1.49426i	0.869304	+	0.494278i	$0.164568\pi$
$563$	11524.6	+	19961.3i	0.862709	+	1.49426i	−0.00659429	+	0.999978i	$0.502099\pi$
$564$	1988.95	−	1253.05i	0.148493	−	0.0935516i
$565$	4406.13	−	7631.64i	0.328084	−	0.568258i
$566$	−11079.2			−0.822778
$567$	22160.2	−	3448.45i	1.64134	−	0.255417i
$568$	−8776.27			−0.648317
$569$	−7366.96	+	12759.9i	−0.542775	+	0.940114i	0.455968	+	0.889996i	$0.349293\pi$
$569$	−7366.96	+	12759.9i	−0.542775	+	0.940114i	−0.998743	+	0.0501179i	$0.984040\pi$
$570$	7061.81	−	4449.00i	0.518924	−	0.326927i
$571$	−7555.94	−	13087.3i	−0.553776	−	0.959169i	−0.997998	−	0.0632515i	$-0.979853\pi$
$571$	−7555.94	−	13087.3i	−0.553776	−	0.959169i	0.444221	−	0.895917i	$-0.353480\pi$
$572$	−13078.9	−	22653.3i	−0.956043	−	1.65591i
$573$	−149.625	−	3874.98i	−0.0109087	−	0.282512i
$574$	−10327.5	+	17887.7i	−0.750975	+	1.30073i
$575$	−1559.07			−0.113074
$576$	−8641.09	+	18053.6i	−0.625079	+	1.30596i
$577$	−26150.5			−1.88676			−0.943380	−	0.331715i	$-0.892373\pi$
$577$	−26150.5			−1.88676			−0.943380	+	0.331715i	$0.892373\pi$
$578$	−10376.5	+	17972.7i	−0.746724	+	1.29336i
$579$	−496.039	−	261.407i	−0.0356040	−	0.0187629i
$580$	1260.39	+	2183.07i	0.0902328	+	0.156288i
$581$	3041.61	+	5268.22i	0.217190	+	0.376184i
$582$	−28037.7	−	14775.6i	−1.99691	−	1.05235i
$583$	−534.894	+	926.463i	−0.0379983	+	0.0658150i
$584$	468.747			0.0332139
$585$	−4824.43	−	7039.95i	−0.340967	−	0.497549i
$586$	−758.961			−0.0535023
$587$	−1045.77	+	1811.33i	−0.0735326	+	0.127362i	−0.900447	−	0.434965i	$-0.856761\pi$
$587$	−1045.77	+	1811.33i	−0.0735326	+	0.127362i	0.826915	+	0.562327i	$0.190094\pi$
$588$	1229.49	+	31841.2i	0.0862303	+	2.23318i
$589$	−3882.24	−	6724.24i	−0.271587	−	0.470403i
$590$	4538.01	+	7860.06i	0.316656	+	0.548464i
$591$	−14776.4	+	9309.26i	−1.02846	+	0.647939i
$592$	−5925.50	+	10263.3i	−0.411379	+	0.712530i
$593$	3260.34			0.225778			0.112889	−	0.993608i	$-0.463990\pi$
$593$	3260.34			0.225778			0.112889	+	0.993608i	$0.463990\pi$
$594$	19535.0	−	14525.9i	1.34938	−	1.00337i
$595$	1013.66			0.0698417
$596$	−476.426	+	825.194i	−0.0327436	+	0.0567135i
$597$	6018.61	−	3791.78i	0.412606	−	0.259945i
$598$	−8400.90	−	14550.8i	−0.574479	−	0.995026i
$599$	11499.6	+	19917.9i	0.784410	+	1.35864i	0.929351	+	0.369197i	$0.120367\pi$
$599$	11499.6	+	19917.9i	0.784410	+	1.35864i	−0.144941	+	0.989440i	$0.546299\pi$
$600$	−46.1991	−	1196.46i	−0.00314345	−	0.0814085i
$601$	7146.93	−	12378.9i	0.485074	−	0.840173i	−0.514779	−	0.857323i	$-0.672126\pi$
$601$	7146.93	−	12378.9i	0.485074	−	0.840173i	0.999853	+	0.0171500i	$0.00545928\pi$
$602$	44290.5			2.99858
$603$	−2592.56	+	200.513i	−0.175087	+	0.0135415i
$604$	−10855.1			−0.731274
$605$	816.702	−	1414.57i	0.0548821	−	0.0950586i
$606$	21699.3	+	11435.3i	1.45457	+	0.766544i
$607$	8217.04	+	14232.3i	0.549455	+	0.951685i	0.998312	+	0.0580809i	$0.0184981\pi$
$607$	8217.04	+	14232.3i	0.549455	+	0.951685i	−0.448856	+	0.893604i	$0.648169\pi$
$608$	−9528.80	−	16504.4i	−0.635598	−	1.10089i
$609$	−7015.54	−	3697.11i	−0.466805	−	0.246001i
$610$	−9062.62	+	15696.9i	−0.601532	+	1.04188i
$611$	2814.19			0.186334
$612$	1802.85	−	139.435i	0.119078	−	0.00920971i
$613$	3674.45			0.242104			0.121052	−	0.992646i	$-0.461373\pi$
$613$	3674.45			0.242104			0.121052	+	0.992646i	$0.461373\pi$
$614$	3276.45	−	5674.99i	0.215353	−	0.373003i
$615$	157.927	+	4089.96i	0.0103548	+	0.268168i
$616$	5772.46	+	9998.19i	0.377563	+	0.653958i
$617$	−4313.78	−	7471.69i	−0.281469	−	0.487519i	0.690278	−	0.723544i	$-0.257488\pi$
$617$	−4313.78	−	7471.69i	−0.281469	−	0.487519i	−0.971747	+	0.236026i	$0.924155\pi$
$618$	−9909.25	+	6242.91i	−0.644998	+	0.406354i
$619$	654.905	−	1134.33i	0.0425248	−	0.0736551i	−0.843980	−	0.536375i	$-0.819793\pi$
$619$	654.905	−	1134.33i	0.0425248	−	0.0736551i	0.886504	+	0.462720i	$0.153127\pi$
$620$	−5234.03			−0.339038
$621$	7020.97	−	5220.67i	0.453691	−	0.337356i
$622$	−4028.76			−0.259708
$623$	−20989.4	+	36354.7i	−1.34979	+	2.33791i
$624$	−11678.8	+	7357.73i	−0.749240	+	0.472027i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	4230.95	+	7328.23i	0.270132	+	0.467883i
$627$	615.323	+	15935.5i	0.0391924	+	1.01500i
$628$	−923.362	+	1599.31i	−0.0586722	+	0.101623i
$629$	1858.54			0.117814
$630$	10005.5	+	14600.3i	0.632744	+	0.923320i
$631$	14447.2			0.911463			0.455731	−	0.890117i	$-0.349378\pi$
$631$	14447.2			0.911463			0.455731	+	0.890117i	$0.349378\pi$
$632$	−909.179	+	1574.74i	−0.0572234	+	0.0991138i
$633$	−11503.9	−	6062.45i	−0.722339	−	0.380665i
$634$	−11044.9	−	19130.3i	−0.691875	−	1.19836i
$635$	−3765.31	−	6521.71i	−0.235310	−	0.407569i
$636$	−1227.50	−	646.881i	−0.0765310	−	0.0403309i
$637$	−19073.4	+	33036.2i	−1.18637	+	2.05485i
$638$	−8607.88			−0.534152
$639$	11099.1	−	23189.1i	0.687127	−	1.43560i
$640$	−5683.43			−0.351027
$641$	10036.6	−	17383.8i	0.618440	−	1.07117i	−0.371330	−	0.928501i	$-0.621098\pi$
$641$	10036.6	−	17383.8i	0.618440	−	1.07117i	0.989770	−	0.142669i	$-0.0455685\pi$
$642$	−419.457	−	10863.0i	−0.0257860	−	0.667803i
$643$	8867.96	+	15359.8i	0.543885	+	0.942037i	0.998676	+	0.0514386i	$0.0163807\pi$
$643$	8867.96	+	15359.8i	0.543885	+	0.942037i	−0.454791	+	0.890598i	$0.650286\pi$
$644$	9748.75	+	16885.3i	0.596513	+	1.03319i
$645$	7425.83	−	4678.34i	0.453321	−	0.285596i
$646$	−1058.52	+	1833.40i	−0.0644686	+	0.111663i
$647$	−11456.8			−0.696158			−0.348079	−	0.937465i	$-0.613166\pi$
$647$	−11456.8			−0.696158			−0.348079	+	0.937465i	$0.613166\pi$
$648$	4214.48	+	5233.31i	0.255494	+	0.317259i
$649$	−17341.4			−1.04886
$650$	3367.75	−	5833.12i	0.203222	−	0.351990i
$651$	13931.4	−	8776.89i	0.838731	−	0.528408i
$652$	5605.12	+	9708.36i	0.336677	+	0.583142i
$653$	−14536.0	−	25177.0i	−0.871113	−	1.50881i	−0.860847	−	0.508864i	$-0.830065\pi$
$653$	−14536.0	−	25177.0i	−0.871113	−	1.50881i	−0.0102660	−	0.999947i	$-0.503268\pi$
$654$	300.453	+	7781.08i	0.0179643	+	0.465236i
$655$	3187.81	−	5521.45i	0.190165	−	0.329376i
$656$	6619.90			0.393999
$657$	−592.812	+	1238.55i	−0.0352021	+	0.0735468i
$658$	−5836.43			−0.345787
$659$	2177.54	−	3771.62i	0.128718	−	0.222946i	−0.794462	−	0.607314i	$-0.792247\pi$
$659$	2177.54	−	3771.62i	0.128718	−	0.222946i	0.923180	+	0.384368i	$0.125581\pi$
$660$	9510.35	+	5011.85i	0.560894	+	0.295585i
$661$	−13647.7	−	23638.5i	−0.803075	−	1.39097i	−0.917583	−	0.397545i	$-0.869862\pi$
$661$	−13647.7	−	23638.5i	−0.803075	−	1.39097i	0.114508	−	0.993422i	$-0.463471\pi$
$662$	−4631.19	−	8021.46i	−0.271898	−	0.470941i
$663$	1915.06	+	1009.22i	0.112179	+	0.0591172i
$664$	−911.297	+	1578.41i	−0.0532608	+	0.0922504i
$665$	−11595.0			−0.676141
$666$	18345.2	+	26769.8i	1.06736	+	1.55752i
$667$	−3093.72			−0.179594
$668$	20537.4	−	35571.8i	1.18955	−	2.06035i
$669$	375.825	+	9733.06i	0.0217194	+	0.562484i
$670$	−1026.10	−	1777.26i	−0.0591669	−	0.102480i
$671$	−17315.8	−	29991.9i	−0.996230	−	1.72552i
$672$	34194.0	−	21542.5i	1.96289	−	1.23664i
$673$	8880.01	−	15380.6i	0.508617	−	0.880951i	−0.491333	−	0.870972i	$-0.663490\pi$
$673$	8880.01	−	15380.6i	0.508617	−	0.880951i	0.999950	−	0.00997909i	$-0.00317650\pi$
$674$	33456.3			1.91200
$675$	3219.76	+	1391.06i	0.183598	+	0.0793212i
$676$	18287.8			1.04050
$677$	−968.667	+	1677.78i	−0.0549910	+	0.0952472i	−0.892210	−	0.451620i	$-0.850846\pi$
$677$	−968.667	+	1677.78i	−0.0549910	+	0.0952472i	0.837219	+	0.546867i	$0.184180\pi$
$678$	−33022.2	+	20804.3i	−1.87052	+	1.17844i
$679$	22014.0	+	38129.4i	1.24421	+	2.15504i
$680$	151.851	+	263.013i	0.00856355	+	0.0148325i
$681$	1018.24	+	26370.3i	0.0572968	+	1.48386i
$682$	8936.48	−	15478.4i	0.501753	−	0.869061i
$683$	−2125.71			−0.119090			−0.0595448	−	0.998226i	$-0.518965\pi$
$683$	−2125.71			−0.119090			−0.0595448	+	0.998226i	$0.518965\pi$
$684$	−20622.3	+	1594.97i	−1.15280	+	0.0891596i
$685$	−7197.12			−0.401442
$686$	17071.7	−	29569.0i	0.950146	−	1.64570i
$687$	−3980.29	−	2097.57i	−0.221045	−	0.116488i
$688$	−7097.55	−	12293.3i	−0.393301	−	0.681218i
$689$	−830.532	−	1438.52i	−0.0459227	−	0.0795405i
$690$	6108.73	+	3219.23i	0.337037	+	0.177615i
$691$	−6913.13	+	11973.9i	−0.380590	+	0.659201i	−0.991147	−	0.132771i	$-0.957612\pi$
$691$	−6913.13	+	11973.9i	−0.380590	+	0.659201i	0.610557	+	0.791973i	$0.290946\pi$
$692$	−27924.8			−1.53402
$693$	−33717.9	+	2607.81i	−1.84825	+	0.142947i
$694$	39942.4			2.18472
$695$	−6348.74	+	10996.3i	−0.346506	+	0.600166i
$696$	−91.6744	−	2374.17i	−0.00499268	−	0.129300i
$697$	−519.086	−	899.084i	−0.0282092	−	0.0488597i
$698$	−2509.98	−	4347.42i	−0.136109	−	0.235748i
$699$	5021.14	−	3163.36i	0.271698	−	0.171172i
$700$	−3908.08	+	6768.99i	−0.211016	+	0.365491i
$701$	−24464.0			−1.31810			−0.659052	−	0.752097i	$-0.729042\pi$
$701$	−24464.0			−1.31810			−0.659052	+	0.752097i	$0.729042\pi$
$702$	4366.64	+	37545.5i	0.234769	+	2.01861i
$703$	−21259.5			−1.14056
$704$	15090.8	−	26138.0i	0.807892	−	1.39931i
$705$	−978.548	+	616.493i	−0.0522755	+	0.0329340i
$706$	−15474.8	−	26803.1i	−0.824931	−	1.42882i
$707$	−17037.3	−	29509.5i	−0.906300	−	1.56976i
$708$	−867.842	−	22475.2i	−0.0460671	−	1.19304i
$709$	14749.1	−	25546.2i	0.781263	−	1.35319i	−0.149944	−	0.988695i	$-0.547909\pi$
$709$	14749.1	−	25546.2i	0.781263	−	1.35319i	0.931206	−	0.364492i	$-0.118757\pi$
$710$	20289.6			1.07247
$711$	−3011.05	−	4393.81i	−0.158823	−	0.231759i
$712$	−12577.3			−0.662012
$713$	3211.81	−	5563.02i	0.168700	−	0.292198i
$714$	−3971.70	−	2093.04i	−0.208175	−	0.109706i
$715$	6434.72	+	11145.3i	0.336566	+	0.582950i
$716$	14422.6	+	24980.7i	0.752790	+	1.30387i
$717$	14477.3	+	7629.38i	0.754065	+	0.397384i
$718$	−4133.81	+	7159.98i	−0.214864	+	0.372156i
$719$	−3857.66			−0.200093			−0.100046	−	0.994983i	$-0.531899\pi$
$719$	−3857.66			−0.200093			−0.100046	+	0.994983i	$0.531899\pi$
$720$	2449.10	−	5116.84i	0.126768	−	0.264852i
$721$	16270.2			0.840410
$722$	−2507.66	+	4343.39i	−0.129260	+	0.223884i
$723$	903.085	+	23387.9i	0.0464538	+	1.20305i
$724$	−17491.4	−	30295.9i	−0.897874	−	1.55516i
$725$	−620.105	−	1074.05i	−0.0317657	−	0.0550197i
$726$	−6120.86	+	3856.19i	−0.312901	+	0.197130i
$727$	−4372.55	+	7573.48i	−0.223066	+	0.386361i	−0.955737	−	0.294221i	$-0.904940\pi$
$727$	−4372.55	+	7573.48i	−0.223066	+	0.386361i	0.732672	+	0.680582i	$0.238273\pi$
$728$	−17925.8			−0.912604
$729$	−19157.6	+	4517.26i	−0.973309	+	0.229501i
$730$	−1083.68			−0.0549436
$731$	−1113.08	+	1927.91i	−0.0563184	+	0.0975463i
$732$	38004.2	−	23943.0i	1.91896	−	1.20896i
$733$	4709.20	+	8156.58i	0.237296	+	0.411010i	0.959938	−	0.280214i	$-0.0904054\pi$
$733$	4709.20	+	8156.58i	0.237296	+	0.411010i	−0.722641	+	0.691223i	$0.757072\pi$
$734$	13854.9	+	23997.4i	0.696723	+	1.20676i
$735$	−604.901	−	15665.6i	−0.0303566	−	0.786171i
$736$	7883.26	−	13654.2i	0.394811	−	0.683832i
$737$	3921.13			0.195979
$738$	7826.33	−	16351.3i	0.390368	−	0.815584i
$739$	6219.42			0.309587			0.154794	−	0.987947i	$-0.450529\pi$
$739$	6219.42			0.309587			0.154794	+	0.987947i	$0.450529\pi$
$740$	−7165.49	+	12411.0i	−0.355958	+	0.616537i
$741$	−21905.9	−	11544.2i	−1.08601	−	0.572316i
$742$	1722.46	+	2983.39i	0.0852204	+	0.147606i
$743$	14693.7	+	25450.3i	0.725518	+	1.25663i	0.958760	+	0.284216i	$0.0917333\pi$
$743$	14693.7	+	25450.3i	0.725518	+	1.25663i	−0.233242	+	0.972419i	$0.574933\pi$
$744$	4364.33	+	2299.95i	0.215059	+	0.113334i
$745$	234.398	−	405.989i	0.0115271	−	0.0199655i
$746$	−56758.5			−2.78563
$747$	−3018.06	−	4404.05i	−0.147825	−	0.215710i
$748$	−2726.72			−0.133287
$749$	−7551.15	+	13079.0i	−0.368375	+	0.638045i
$750$	106.806	+	2766.04i	0.00520001	+	0.134669i
$751$	10823.6	+	18747.0i	0.525909	+	0.910901i	0.999544	+	0.0301801i	$0.00960808\pi$
$751$	10823.6	+	18747.0i	0.525909	+	0.910901i	−0.473636	+	0.880721i	$0.657059\pi$
$752$	935.287	+	1619.97i	0.0453543	+	0.0785559i
$753$	3899.00	−	2456.40i	0.188695	−	0.118880i
$754$	6682.75	−	11574.9i	0.322774	−	0.559061i
$755$	5340.65			0.257438
$756$	−5067.23	−	43569.4i	−0.243774	−	2.09604i
$757$	−13907.2			−0.667722			−0.333861	−	0.942622i	$-0.608352\pi$
$757$	−13907.2			−0.667722			−0.333861	+	0.942622i	$0.608352\pi$
$758$	−6815.48	+	11804.8i	−0.326582	+	0.565657i
$759$	−11162.8	+	7032.66i	−0.533840	+	0.336324i
$760$	−1736.98	−	3008.55i	−0.0829040	−	0.143594i
$761$	11953.0	+	20703.3i	0.569379	+	0.986193i	0.996628	+	0.0820585i	$0.0261494\pi$
$761$	11953.0	+	20703.3i	0.569379	+	0.986193i	−0.427249	+	0.904134i	$0.640517\pi$
$762$	1286.90	+	33328.0i	0.0611806	+	1.58445i
$763$	5408.82	−	9368.35i	0.256635	−	0.444504i
$764$	−7584.42			−0.359155
$765$	−886.987	+	68.6012i	−0.0419204	+	0.00324220i
$766$	9974.70			0.470497
$767$	13463.1	−	23318.7i	0.633798	−	1.09777i
$768$	−4992.53	−	2631.01i	−0.234573	−	0.123618i
$769$	12555.8	+	21747.3i	0.588783	+	1.01980i	0.994392	+	0.105755i	$0.0337261\pi$
$769$	12555.8	+	21747.3i	0.588783	+	1.01980i	−0.405609	+	0.914047i	$0.632941\pi$
$770$	−13345.1	−	23114.5i	−0.624579	−	1.08180i
$771$	−10398.3	−	5479.81i	−0.485716	−	0.255967i
$772$	−548.319	+	949.716i	−0.0255627	+	0.0442759i
$773$	14909.4			0.693729			0.346865	−	0.937915i	$-0.387246\pi$
$773$	14909.4			0.693729			0.346865	+	0.937915i	$0.387246\pi$
$774$	−38755.8	+	2997.45i	−1.79981	+	0.139200i
$775$	2575.10			0.119355
$776$	−6595.62	+	11424.0i	−0.305115	+	0.528474i
$777$	−1739.53	−	45050.0i	−0.0803155	−	2.08000i
$778$	8506.37	+	14733.5i	0.391990	+	0.678947i
$779$	5937.70	+	10284.4i	0.273094	+	0.473013i
$780$	−14122.7	+	8897.44i	−0.648301	+	0.408435i
$781$	−19383.5	+	33573.2i	−0.888087	+	1.53821i
$782$	−1751.44			−0.0800912
$783$	6389.08	+	2760.32i	0.291605	+	0.125984i
$784$	−25356.0			−1.15506
$785$	454.287	−	786.848i	0.0206550	−	0.0357756i
$786$	−23891.4	+	15051.8i	−1.08419	+	0.683052i
$787$	1329.38	+	2302.56i	0.0602128	+	0.104292i	0.894560	−	0.446947i	$-0.147489\pi$
$787$	1329.38	+	2302.56i	0.0602128	+	0.104292i	−0.834348	+	0.551239i	$0.814155\pi$
$788$	17078.6	+	29581.0i	0.772082	+	1.33728i
$789$	1459.70	+	37803.1i	0.0658640	+	1.70573i
$790$	2101.90	−	3640.60i	0.0946610	−	0.163958i
$791$	54220.0			2.43722
$792$	−5727.76	−	8358.13i	−0.256979	−	0.374991i
$793$	53772.7			2.40798
$794$	−10571.1	+	18309.7i	−0.472488	+	0.818373i
$795$	603.923	+	318.260i	0.0269421	+	0.0141982i
$796$	−6956.33	−	12048.7i	−0.309750	−	0.536502i
$797$	7086.11	+	12273.5i	0.314935	+	0.545483i	0.979424	−	0.201815i	$-0.0646840\pi$
$797$	7086.11	+	12273.5i	0.314935	+	0.545483i	−0.664489	+	0.747298i	$0.731351\pi$
$798$	45431.3	+	23941.8i	2.01535	+	1.06207i
$799$	146.677	−	254.053i	0.00649446	−	0.0112487i
$800$	6320.48			0.279329
$801$	15906.1	−	33232.2i	0.701642	−	1.46592i
$802$	−3527.14			−0.155296
$803$	1035.29	−	1793.17i	0.0454975	−	0.0788040i
$804$	196.231	+	5081.95i	0.00860761	+	0.222918i
$805$	−4796.31	−	8307.45i	−0.209997	−	0.363726i
$806$	13875.7	+	24033.4i	0.606391	+	1.05030i
$807$	−469.452	+	295.759i	−0.0204777	+	0.0129011i
$808$	5104.55	−	8841.34i	0.222249	−	0.384947i
$809$	−21077.7			−0.916012			−0.458006	−	0.888949i	$-0.651436\pi$
$809$	−21077.7			−0.916012			−0.458006	+	0.888949i	$0.651436\pi$
$810$	−9743.31	−	12098.7i	−0.422648	−	0.524821i
$811$	−11937.4			−0.516868			−0.258434	−	0.966029i	$-0.583206\pi$
$811$	−11937.4			−0.516868			−0.258434	+	0.966029i	$0.583206\pi$
$812$	−7754.94	+	13431.9i	−0.335154	+	0.580503i
$813$	25977.7	−	16366.2i	1.12064	−	0.706011i
$814$	−24468.4	−	42380.5i	−1.05358	−	1.82486i
$815$	−2757.68	−	4776.44i	−0.118524	−	0.205290i
$816$	55.5180	+	1437.80i	0.00238176	+	0.0616826i
$817$	12732.3	−	22052.9i	0.545221	−	0.944350i
$818$	35661.0			1.52428
$819$	22670.3	−	47364.5i	0.967235	−	2.02082i
$820$	8005.20			0.340919
$821$	−7400.25	+	12817.6i	−0.314580	+	0.544869i	−0.979348	−	0.202181i	$-0.935197\pi$
$821$	−7400.25	+	12817.6i	−0.314580	+	0.544869i	0.664768	+	0.747050i	$0.268530\pi$
$822$	28199.7	+	14860.9i	1.19657	+	0.630576i
$823$	−16588.3	−	28731.8i	−0.702591	−	1.21692i	−0.967554	−	0.252665i	$-0.918693\pi$
$823$	−16588.3	−	28731.8i	−0.702591	−	1.21692i	0.264963	−	0.964259i	$-0.414640\pi$
$824$	2437.37	+	4221.64i	0.103046	+	0.178480i
$825$	−4679.02	−	2465.79i	−0.197458	−	0.104058i
$826$	−27921.4	+	48361.3i	−1.17616	+	2.03717i
$827$	−29001.3			−1.21944			−0.609718	−	0.792619i	$-0.708717\pi$
$827$	−29001.3			−1.21944			−0.609718	+	0.792619i	$0.708717\pi$
$828$	−9673.27	−	14115.5i	−0.406002	−	0.592450i
$829$	13221.1			0.553904			0.276952	−	0.960884i	$-0.410676\pi$
$829$	13221.1			0.553904			0.276952	+	0.960884i	$0.410676\pi$
$830$	2106.80	−	3649.08i	0.0881060	−	0.152604i
$831$	659.632	+	17083.0i	0.0275360	+	0.713122i
$832$	23431.6	+	40584.7i	0.976374	+	1.69113i
$833$	1988.24	+	3443.73i	0.0826991	+	0.143239i
$834$	47581.3	−	29976.6i	1.97555	−	1.24461i
$835$	−10104.3	+	17501.1i	−0.418769	+	0.725329i
$836$	31190.3			1.29036
$837$	−11596.5	+	8622.95i	−0.478893	+	0.356096i
$838$	−17902.5			−0.737987
$839$	21062.0	−	36480.4i	0.866675	−	1.50112i	0.00129985	−	0.999999i	$-0.499586\pi$
$839$	21062.0	−	36480.4i	0.866675	−	1.50112i	0.865375	−	0.501125i	$-0.167080\pi$
$840$	6233.15	−	3926.94i	0.256029	−	0.161300i
$841$	10964.0	+	18990.2i	0.449547	+	0.778638i
$842$	14785.7	+	25609.6i	0.605166	+	1.04818i
$843$	68.1114	+	1763.94i	0.00278278	+	0.0720679i
$844$	−12716.4	+	22025.4i	−0.518621	+	0.898278i
$845$	−8997.45			−0.366298
$846$	5107.10	−	394.992i	0.207548	−	0.0160521i
$847$	10050.0			0.407700
$848$	552.049	−	956.177i	0.0223555	−	0.0387208i
$849$	−11950.4	−	6297.71i	−0.483081	−	0.254578i
$850$	−351.059	−	608.051i	−0.0141661	−	0.0245365i
$851$	−8794.07	−	15231.8i	−0.354238	−	0.613559i
$852$	−44482.4	−	23441.7i	−1.78866	−	0.942605i
$853$	−7215.84	+	12498.2i	−0.289643	+	0.501677i	−0.973725	−	0.227729i	$-0.926870\pi$
$853$	−7215.84	+	12498.2i	−0.289643	+	0.501677i	0.684081	+	0.729406i	$0.260203\pi$
$854$	−111521.			−4.46857
$855$	10146.0	−	784.713i	0.405833	−	0.0313879i
$856$	−4524.80			−0.180671
$857$	−8056.71	+	13954.6i	−0.321134	+	0.556220i	−0.980722	−	0.195407i	$-0.937397\pi$
$857$	−8056.71	+	13954.6i	−0.321134	+	0.556220i	0.659588	+	0.751627i	$0.270731\pi$
$858$	−2199.25	−	56956.0i	−0.0875074	−	2.26625i
$859$	11250.2	+	19485.9i	0.446858	+	0.773982i	0.998180	−	0.0603115i	$-0.0192094\pi$
$859$	11250.2	+	19485.9i	0.446858	+	0.773982i	−0.551321	+	0.834293i	$0.685876\pi$
$860$	−8582.80	−	14865.8i	−0.340315	−	0.589443i
$861$	−21307.4	+	13423.8i	−0.843384	+	0.531339i
$862$	14547.8	−	25197.5i	0.574825	−	0.995626i
$863$	−43396.8			−1.71175			−0.855877	−	0.517180i	$-0.826982\pi$
$863$	−43396.8			−1.71175			−0.855877	+	0.517180i	$0.826982\pi$
$864$	−28463.1	+	21164.6i	−1.12076	+	0.833375i
$865$	13738.8			0.540038
$866$	−4687.09	+	8118.28i	−0.183919	+	0.318557i
$867$	−21408.6	+	13487.6i	−0.838610	+	0.528331i
$868$	−16101.9	−	27889.4i	−0.629649	−	1.09058i
$869$	4016.07	+	6956.04i	0.156773	+	0.271539i
$870$	211.939	+	5488.76i	0.00825908	+	0.213892i
$871$	−3044.18	+	5272.67i	−0.118425	+	0.205118i
$872$	3241.07			0.125868
$873$	−21843.6	−	31874.8i	−0.846842	−	1.23574i
$874$	20034.3			0.775366
$875$	1922.75	−	3330.29i	0.0742865	−	0.128668i
$876$	2375.84	+	1252.04i	0.0916348	+	0.0482905i
$877$	1232.77	+	2135.21i	0.0474659	+	0.0822133i	0.888782	−	0.458330i	$-0.151552\pi$
$877$	1232.77	+	2135.21i	0.0474659	+	0.0822133i	−0.841316	+	0.540543i	$0.818219\pi$
$878$	17738.2	+	30723.5i	0.681817	+	1.18094i
$879$	−818.640	−	431.414i	−0.0314130	−	0.0165543i
$880$	−4277.12	+	7408.18i	−0.163843	+	0.283784i
$881$	24512.9			0.937412			0.468706	−	0.883354i	$-0.344720\pi$
$881$	24512.9			0.937412			0.468706	+	0.883354i	$0.344720\pi$
$882$	−29976.9	+	62629.9i	−1.14442	+	2.39100i
$883$	24236.1			0.923679			0.461840	−	0.886963i	$-0.347190\pi$
$883$	24236.1			0.923679			0.461840	+	0.886963i	$0.347190\pi$
$884$	2116.90	−	3666.57i	0.0805418	−	0.139502i
$885$	426.972	+	11057.6i	0.0162175	+	0.419999i
$886$	−23156.0	−	40107.3i	−0.878036	−	1.52080i
$887$	−12599.3	−	21822.7i	−0.476939	−	0.826082i	0.522712	−	0.852509i	$-0.324920\pi$
$887$	−12599.3	−	21822.7i	−0.476939	−	0.826082i	−0.999651	+	0.0264274i	$0.991587\pi$
$888$	11428.5	−	7200.07i	0.431888	−	0.272093i
$889$	23167.1	−	40126.7i	0.874017	−	1.51384i
$890$	29076.9			1.09512
$891$	29328.0	−	4563.86i	1.10272	−	0.171599i
$892$	19050.3			0.715081
$893$	−1677.81	+	2906.05i	−0.0628731	+	0.108899i
$894$	−1756.72	+	1106.75i	−0.0657198	+	0.0414040i
$895$	−7095.81	−	12290.3i	−0.265013	−	0.459016i
$896$	−17484.5	−	30284.0i	−0.651914	−	1.12915i
$897$	−790.423	−	20470.3i	−0.0294219	−	0.761964i
$898$	−10543.1	+	18261.1i	−0.391789	+	0.678599i
$899$	5109.87			0.189570
$900$	2961.61	−	6187.61i	0.109689	−	0.229171i
$901$	−173.151			−0.00640233
$902$	−13667.9	+	23673.5i	−0.504536	+	0.873882i
$903$	47773.2	+	25175.9i	1.76057	+	0.927798i
$904$	8122.42	+	14068.5i	0.298836	+	0.517599i
$905$	8605.62	+	14905.4i	0.316089	+	0.547482i
$906$	−20925.7	−	11027.6i	−0.767338	−	0.404379i
$907$	−13304.0	+	23043.3i	−0.487049	+	0.843594i	−0.999889	−	0.0148906i	$-0.995260\pi$
$907$	−13304.0	+	23043.3i	−0.487049	+	0.843594i	0.512840	+	0.858484i	$0.328593\pi$
$908$	51614.0			1.88642
$909$	16905.4	+	24668.9i	0.616851	+	0.900127i
$910$	41442.1			1.50966
$911$	−12416.1	+	21505.2i	−0.451550	+	0.782108i	−0.998483	−	0.0550686i	$-0.982462\pi$
$911$	−12416.1	+	21505.2i	−0.451550	+	0.782108i	0.546932	+	0.837177i	$0.315796\pi$
$912$	−635.058	−	16446.6i	−0.0230580	−	0.597151i
$913$	4025.43	+	6972.25i	0.145917	+	0.252736i
$914$	−30253.7	−	52401.0i	−1.09486	−	1.89636i
$915$	−18697.8	+	11779.8i	−0.675552	+	0.425603i
$916$	−4399.79	+	7620.66i	−0.158704	+	0.274884i
$917$	39227.8			1.41267
$918$	3617.03	+	1562.70i	0.130043	+	0.0561837i
$919$	−26107.2			−0.937102			−0.468551	−	0.883436i	$-0.655224\pi$
$919$	−26107.2			−0.937102			−0.468551	+	0.883436i	$0.655224\pi$
$920$	1437.02	−	2489.00i	0.0514970	−	0.0891954i
$921$	6759.91	−	4258.80i	0.241853	−	0.152369i
$922$	−38841.9	−	67276.2i	−1.38741	−	2.40306i
$923$	−30096.9	−	52129.3i	−1.07329	−	1.85900i
$924$	2552.11	+	66094.0i	0.0908637	+	2.35317i
$925$	3525.37	−	6106.11i	0.125312	−	0.217046i
$926$	−18501.2			−0.656573
$927$	−14237.1	+	1101.12i	−0.504431	+	0.0390136i
$928$	12542.0			0.443653
$929$	11680.8	−	20231.7i	0.412523	−	0.714511i	−0.582642	−	0.812729i	$-0.697981\pi$
$929$	11680.8	−	20231.7i	0.412523	−	0.714511i	0.995165	+	0.0982184i	$0.0313144\pi$
$930$	−10089.7	−	5317.18i	−0.355759	−	0.187481i
$931$	−22743.0	−	39392.0i	−0.800613	−	1.38670i
$932$	−5803.45	−	10051.9i	−0.203968	−	0.353283i
$933$	−4345.55	−	2290.06i	−0.152483	−	0.0803570i
$934$	10483.2	−	18157.4i	0.367260	−	0.636112i
$935$	1341.53			0.0469226
$936$	15685.8	−	1213.17i	0.547763	−	0.0423650i
$937$	10548.5			0.367775			0.183888	−	0.982947i	$-0.441132\pi$
$937$	10548.5			0.367775			0.183888	+	0.982947i	$0.441132\pi$
$938$	6313.40	−	10935.1i	0.219765	−	0.380644i
$939$	398.082	+	10309.5i	0.0138348	+	0.358292i
$940$	1131.01	+	1958.96i	0.0392441	+	0.0679727i
$941$	3245.07	+	5620.62i	0.112419	+	0.194715i	0.916745	−	0.399473i	$-0.130807\pi$
$941$	3245.07	+	5620.62i	0.112419	+	0.194715i	−0.804326	+	0.594188i	$0.797473\pi$
$942$	−3404.70	+	2144.99i	−0.117761	+	0.0741906i
$943$	−4912.32	+	8508.38i	−0.169636	+	0.293819i
$944$	17897.6			0.617074
$945$	2493.04	+	21435.8i	0.0858185	+	0.737891i
$946$	58616.4			2.01457
$947$	−11753.0	+	20356.8i	−0.403295	+	0.698528i	−0.994121	−	0.108271i	$-0.965469\pi$
$947$	−11753.0	+	20356.8i	−0.403295	+	0.698528i	0.590826	+	0.806799i	$0.298802\pi$
$948$	−8814.34	+	5553.11i	−0.301979	+	0.190250i
$949$	1607.50	+	2784.26i	0.0549858	+	0.0952382i
$950$	4015.68	+	6955.35i	0.137143	+	0.237538i
$951$	−1039.19	−	26912.8i	−0.0354344	−	0.917674i
$952$	−934.305	+	1618.26i	−0.0318078	+	0.0550927i
$953$	6740.26			0.229106			0.114553	−	0.993417i	$-0.463456\pi$
$953$	6740.26			0.229106			0.114553	+	0.993417i	$0.463456\pi$
$954$	−1709.13	−	2494.01i	−0.0580032	−	0.0846400i
$955$	3731.48			0.126437
$956$	16003.1	−	27718.2i	0.541399	−	0.937731i
$957$	−9284.74	−	4892.95i	−0.313619	−	0.165274i
$958$	9744.19	+	16877.4i	0.328623	+	0.569191i
$959$	−22141.2	−	38349.6i	−0.745543	−	1.29132i
$960$	−17038.3	−	8978.99i	−0.572822	−	0.301871i
$961$	9590.57	−	16611.4i	0.321928	−	0.557596i
$962$	75984.4			2.54661
$963$	5722.40	−	11955.6i	0.191487	−	0.400068i
$964$	45776.8			1.52943
$965$	269.769	−	467.253i	0.00899913	−	0.0155870i
$966$	1639.28	+	42453.8i	0.0545993	+	1.41400i
$967$	−8391.27	−	14534.1i	−0.279054	−	0.483336i	0.692096	−	0.721806i	$-0.256688\pi$
$967$	−8391.27	−	14534.1i	−0.279054	−	0.483336i	−0.971150	+	0.238470i	$0.923354\pi$
$968$	1505.54	+	2607.67i	0.0499895	+	0.0865844i
$969$	−2183.91	+	1375.88i	−0.0724016	+	0.0456136i
$970$	15248.2	−	26410.6i	0.504732	−	0.874221i
$971$	−46282.7			−1.52964			−0.764822	−	0.644242i	$-0.777173\pi$
$971$	−46282.7			−1.52964			−0.764822	+	0.644242i	$0.777173\pi$
$972$	7382.66	+	37781.9i	0.243620	+	1.24677i
$973$	−78124.9			−2.57407
$974$	33564.7	−	58135.8i	1.10419	−	1.91252i
$975$	6948.27	−	4377.47i	0.228229	−	0.143786i
$976$	17871.2	+	30953.8i	0.586109	+	1.01517i
$977$	−3383.98	−	5861.22i	−0.110812	−	0.191931i	0.805286	−	0.592886i	$-0.202012\pi$
$977$	−3383.98	−	5861.22i	−0.110812	−	0.191931i	−0.916098	+	0.400955i	$0.868678\pi$
$978$	942.517	+	24409.2i	0.0308163	+	0.798076i
$979$	−27778.5	+	48113.7i	−0.906848	+	1.57071i
$980$	−30662.0			−0.999452
$981$	−4098.90	+	8563.71i	−0.133402	+	0.278714i
$982$	−65240.8			−2.12008
$983$	25037.4	−	43366.1i	0.812381	−	1.40708i	−0.0988128	−	0.995106i	$-0.531504\pi$
$983$	25037.4	−	43366.1i	0.812381	−	1.40708i	0.911194	−	0.411979i	$-0.135162\pi$
$984$	−6675.04	−	3517.67i	−0.216252	−	0.113963i
$985$	−8402.55	−	14553.6i	−0.271805	−	0.470779i
$986$	−696.618	−	1206.58i	−0.0224998	−	0.0389708i
$987$	−6295.36	−	3317.58i	−0.203023	−	0.106991i
$988$	−24214.7	+	41941.0i	−0.779728	+	1.35053i
$989$	21067.0			0.677343
$990$	13241.8	+	19322.9i	0.425104	+	0.620324i
$991$	−2658.60			−0.0852200			−0.0426100	−	0.999092i	$-0.513567\pi$
$991$	−2658.60			−0.0852200			−0.0426100	+	0.999092i	$0.513567\pi$
$992$	−13020.7	+	22552.6i	−0.416742	+	0.721819i
$993$	−435.739	−	11284.7i	−0.0139252	−	0.360634i
$994$	62418.7	+	108112.i	1.99175	+	3.44981i
$995$	3422.46	+	5927.88i	0.109045	+	0.188871i
$996$	−8834.88	+	5566.05i	−0.281068	+	0.177075i
$997$	30310.0	−	52498.5i	0.962817	−	1.66765i	0.247449	−	0.968901i	$-0.420408\pi$
$997$	30310.0	−	52498.5i	0.962817	−	1.66765i	0.715368	−	0.698748i	$-0.246259\pi$
$998$	−75570.3			−2.39693
$999$	4571.00	+	39302.7i	0.144765	+	1.24473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.c.16.6	✓	14
3.2	odd	2		135.4.e.c.46.2		14
5.2	odd	4		225.4.k.d.124.12		28
5.3	odd	4		225.4.k.d.124.3		28
5.4	even	2		225.4.e.d.151.2		14
9.2	odd	6		405.4.a.n.1.6		7
9.4	even	3	inner	45.4.e.c.31.6	yes	14
9.5	odd	6		135.4.e.c.91.2		14
9.7	even	3		405.4.a.m.1.2		7
45.4	even	6		225.4.e.d.76.2		14
45.13	odd	12		225.4.k.d.49.12		28
45.22	odd	12		225.4.k.d.49.3		28
45.29	odd	6		2025.4.a.ba.1.2		7
45.34	even	6		2025.4.a.bb.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.6	✓	14	1.1	even	1	trivial
45.4.e.c.31.6	yes	14	9.4	even	3	inner
135.4.e.c.46.2		14	3.2	odd	2
135.4.e.c.91.2		14	9.5	odd	6
225.4.e.d.76.2		14	45.4	even	6
225.4.e.d.151.2		14	5.4	even	2
225.4.k.d.49.3		28	45.22	odd	12
225.4.k.d.49.12		28	45.13	odd	12
225.4.k.d.124.3		28	5.3	odd	4
225.4.k.d.124.12		28	5.2	odd	4
405.4.a.m.1.2		7	9.7	even	3
405.4.a.n.1.6		7	9.2	odd	6
2025.4.a.ba.1.2		7	45.29	odd	6
2025.4.a.bb.1.6		7	45.34	even	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13089 - 3.69081i) q^{2} +(4.39640 - 2.76977i) q^{3} +(-5.08138 - 8.80120i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-0.854448 - 22.1284i) q^{6} +(-15.3820 + 26.6423i) q^{7} -9.21718 q^{8} +(11.6567 - 24.3541i) q^{9} +O(q^{10})\)	\(q+(2.13089 - 3.69081i) q^{2} +(4.39640 - 2.76977i) q^{3} +(-5.08138 - 8.80120i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-0.854448 - 22.1284i) q^{6} +(-15.3820 + 26.6423i) q^{7} -9.21718 q^{8} +(11.6567 - 24.3541i) q^{9} +21.3089 q^{10} +(-20.3573 + 35.2599i) q^{11} +(-46.7171 - 24.6194i) q^{12} +(-31.6089 - 54.7482i) q^{13} +(65.5545 + 113.544i) q^{14} +(22.9845 + 12.1126i) q^{15} +(21.0102 - 36.3908i) q^{16} -6.58990 q^{17} +(-65.0470 - 94.9186i) q^{18} +75.3803 q^{19} +(25.4069 - 44.0060i) q^{20} +(6.16789 + 159.735i) q^{21} +(86.7584 + 150.270i) q^{22} +(31.1814 + 54.0077i) q^{23} +(-40.5225 + 25.5295i) q^{24} +(-12.5000 + 21.6506i) q^{25} -269.420 q^{26} +(-16.2075 - 139.357i) q^{27} +312.646 q^{28} +(-24.8042 + 42.9621i) q^{29} +(93.6825 - 59.0208i) q^{30} +(-51.5021 - 89.2043i) q^{31} +(-126.410 - 218.948i) q^{32} +(8.16291 + 211.402i) q^{33} +(-14.0423 + 24.3221i) q^{34} -153.820 q^{35} +(-273.577 + 21.1590i) q^{36} -282.029 q^{37} +(160.627 - 278.214i) q^{38} +(-290.606 - 153.146i) q^{39} +(-23.0430 - 39.9116i) q^{40} +(78.7700 + 136.434i) q^{41} +(602.695 + 317.613i) q^{42} +(168.907 - 292.555i) q^{43} +413.773 q^{44} +(134.598 - 10.4101i) q^{45} +265.776 q^{46} +(-22.2579 + 38.5518i) q^{47} +(-8.42472 - 218.182i) q^{48} +(-301.710 - 522.577i) q^{49} +(53.2722 + 92.2702i) q^{50} +(-28.9719 + 18.2525i) q^{51} +(-321.234 + 556.393i) q^{52} +26.2752 q^{53} +(-548.876 - 237.135i) q^{54} -203.573 q^{55} +(141.778 - 245.567i) q^{56} +(331.402 - 208.786i) q^{57} +(105.710 + 183.095i) q^{58} +(212.963 + 368.863i) q^{59} +(-10.1877 - 263.840i) q^{60} +(-425.297 + 736.637i) q^{61} -438.981 q^{62} +(469.546 + 685.176i) q^{63} -741.296 q^{64} +(158.045 - 273.741i) q^{65} +(797.638 + 420.346i) q^{66} +(-48.1538 - 83.4048i) q^{67} +(33.4858 + 57.9990i) q^{68} +(286.675 + 151.075i) q^{69} +(-327.773 + 567.719i) q^{70} +952.164 q^{71} +(-107.442 + 224.476i) q^{72} -50.8558 q^{73} +(-600.973 + 1040.92i) q^{74} +(5.01227 + 129.807i) q^{75} +(-383.036 - 663.437i) q^{76} +(-626.271 - 1084.73i) q^{77} +(-1184.48 + 746.233i) q^{78} +(98.6395 - 170.849i) q^{79} +210.102 q^{80} +(-457.241 - 567.778i) q^{81} +671.400 q^{82} +(98.8693 - 171.247i) q^{83} +(1374.52 - 865.959i) q^{84} +(-16.4747 - 28.5351i) q^{85} +(-719.844 - 1246.81i) q^{86} +(9.94603 + 257.581i) q^{87} +(187.637 - 324.997i) q^{88} +1364.54 q^{89} +(248.392 - 518.958i) q^{90} +1944.83 q^{91} +(316.889 - 548.868i) q^{92} +(-473.499 - 249.529i) q^{93} +(94.8583 + 164.299i) q^{94} +(188.451 + 326.406i) q^{95} +(-1162.18 - 612.458i) q^{96} +(715.579 - 1239.42i) q^{97} -2571.64 q^{98} +(621.422 + 906.799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Introduction

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