LMFDB - Embedded newform 750.2.h.d.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(49,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("750.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.h (of order $10$, degree $4$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			199.4
Root			$2.17199 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.199
Dual form			750.2.h.d.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.714027 - 0.518771i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(-1.66061 + 2.28564i) q^{13} +(-3.88890 + 2.82545i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.57666 - 0.512289i) q^{17} +1.00000i q^{18} +(-1.66217 - 5.11563i) q^{19} +(-1.48543 + 4.57167i) q^{21} +(0.839389 + 0.272734i) q^{22} +(-3.44056 - 4.73553i) q^{23} -1.00000 q^{24} -2.82520 q^{26} +(0.587785 + 0.809017i) q^{27} +(-4.57167 - 1.48543i) q^{28} +(-1.10574 + 3.40313i) q^{29} +(3.22681 + 9.93109i) q^{31} -1.00000i q^{32} +(0.839389 - 0.272734i) q^{33} +(1.34119 + 0.974432i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(1.02631 - 1.41260i) q^{37} +(3.16163 - 4.35161i) q^{38} +(-2.28564 + 1.66061i) q^{39} +(1.40381 + 1.01993i) q^{41} +(-4.57167 + 1.48543i) q^{42} +2.27151i q^{43} +(0.272734 + 0.839389i) q^{44} +(1.80881 - 5.56695i) q^{46} +(8.29746 + 2.69601i) q^{47} +(-0.587785 - 0.809017i) q^{48} -16.1067 q^{49} +1.65780 q^{51} +(-1.66061 - 2.28564i) q^{52} +(3.37565 + 1.09681i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.48543 - 4.57167i) q^{56} -5.37889i q^{57} +(-3.40313 + 1.10574i) q^{58} +(8.37628 + 6.08572i) q^{59} +(0.0697810 - 0.0506988i) q^{61} +(-6.13775 + 8.44789i) q^{62} +(-2.82545 + 3.88890i) q^{63} +(0.809017 - 0.587785i) q^{64} +(0.714027 + 0.518771i) q^{66} +(11.3751 - 3.69601i) q^{67} +1.65780i q^{68} +(-1.80881 - 5.56695i) q^{69} +(-1.08390 + 3.33591i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-4.24851 - 5.84757i) q^{73} +1.74607 q^{74} +5.37889 q^{76} +(2.49370 + 3.43228i) q^{77} +(-2.68693 - 0.873035i) q^{78} +(3.88627 - 11.9607i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.73520i q^{82} +(12.6244 - 4.10192i) q^{83} +(-3.88890 - 2.82545i) q^{84} +(-1.83769 + 1.33516i) q^{86} +(-2.10325 + 2.89488i) q^{87} +(-0.518771 + 0.714027i) q^{88} +(15.1178 - 10.9837i) q^{89} +(-10.9869 - 7.98246i) q^{91} +(5.56695 - 1.80881i) q^{92} +10.4422i q^{93} +(2.69601 + 8.29746i) q^{94} +(0.309017 - 0.951057i) q^{96} +(-17.3764 - 5.64593i) q^{97} +(-9.46727 - 13.0306i) q^{98} +0.882586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9} + 2 q^{11} - 20 q^{13} + 2 q^{14} - 4 q^{16} + 30 q^{17} - 2 q^{21} + 20 q^{22} + 10 q^{23} - 16 q^{24} + 4 q^{26} - 10 q^{29} - 18 q^{31} + 20 q^{33} + 12 q^{34} - 4 q^{36} - 20 q^{37} - 10 q^{38} - 4 q^{39} + 22 q^{41} + 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} + 28 q^{51} - 20 q^{52} - 30 q^{53} + 4 q^{54} - 2 q^{56} + 30 q^{58} + 20 q^{59} + 12 q^{61} - 50 q^{62} - 10 q^{63} + 4 q^{64} + 2 q^{66} + 50 q^{67} + 6 q^{69} - 28 q^{71} - 20 q^{73} + 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{81} + 30 q^{83} + 2 q^{84} - 6 q^{86} - 10 q^{87} + 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} - 4 q^{96} + 10 q^{97} - 60 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 + 2 * q^11 - 20 * q^13 + 2 * q^14 - 4 * q^16 + 30 * q^17 - 2 * q^21 + 20 * q^22 + 10 * q^23 - 16 * q^24 + 4 * q^26 - 10 * q^29 - 18 * q^31 + 20 * q^33 + 12 * q^34 - 4 * q^36 - 20 * q^37 - 10 * q^38 - 4 * q^39 + 22 * q^41 + 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 + 28 * q^51 - 20 * q^52 - 30 * q^53 + 4 * q^54 - 2 * q^56 + 30 * q^58 + 20 * q^59 + 12 * q^61 - 50 * q^62 - 10 * q^63 + 4 * q^64 + 2 * q^66 + 50 * q^67 + 6 * q^69 - 28 * q^71 - 20 * q^73 + 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^81 + 30 * q^83 + 2 * q^84 - 6 * q^86 - 10 * q^87 + 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 - 4 * q^96 + 10 * q^97 - 60 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$			4.80694i			1.81685i	0.418045	+	0.908426i	$0.362716\pi$
$7$			4.80694i			1.81685i	−0.418045	+	0.908426i	$0.637284\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	0.714027	−	0.518771i	0.215287	−	0.156415i	−0.474915	−	0.880031i	$-0.657521\pi$
$11$	0.714027	−	0.518771i	0.215287	−	0.156415i	0.690203	+	0.723616i	$0.257521\pi$
$12$	−0.587785	+	0.809017i	−0.169679	+	0.233543i
$13$	−1.66061	+	2.28564i	−0.460571	+	0.633921i	−0.974627	−	0.223835i	$-0.928142\pi$
$13$	−1.66061	+	2.28564i	−0.460571	+	0.633921i	0.514056	+	0.857756i	$0.328142\pi$
$14$	−3.88890	+	2.82545i	−1.03935	+	0.755133i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.57666	−	0.512289i	0.382397	−	0.124248i	−0.111509	−	0.993763i	$-0.535568\pi$
$17$	1.57666	−	0.512289i	0.382397	−	0.124248i	0.493907	+	0.869515i	$0.335568\pi$
$18$			1.00000i			0.235702i
$19$	−1.66217	−	5.11563i	−0.381327	−	1.17361i	−0.939110	−	0.343618i	$-0.888348\pi$
$19$	−1.66217	−	5.11563i	−0.381327	−	1.17361i	0.557782	−	0.829987i	$-0.311652\pi$
$20$		0			0
$21$	−1.48543	+	4.57167i	−0.324147	+	0.997621i
$22$	0.839389	+	0.272734i	0.178958	+	0.0581471i
$23$	−3.44056	−	4.73553i	−0.717407	−	0.987426i	−0.999606	−	0.0280705i	$-0.991064\pi$
$23$	−3.44056	−	4.73553i	−0.717407	−	0.987426i	0.282199	−	0.959356i	$-0.408936\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	−2.82520			−0.554067
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−4.57167	−	1.48543i	−0.863965	−	0.280719i
$29$	−1.10574	+	3.40313i	−0.205332	+	0.631946i	0.794368	+	0.607437i	$0.207802\pi$
$29$	−1.10574	+	3.40313i	−0.205332	+	0.631946i	−0.999700	+	0.0245090i	$0.992198\pi$
$30$		0			0
$31$	3.22681	+	9.93109i	0.579551	+	1.78368i	0.620130	+	0.784499i	$0.287080\pi$
$31$	3.22681	+	9.93109i	0.579551	+	1.78368i	−0.0405785	+	0.999176i	$0.512920\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.839389	−	0.272734i	0.146119	−	0.0474769i
$34$	1.34119	+	0.974432i	0.230012	+	0.167114i
$35$		0			0
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	1.02631	−	1.41260i	0.168725	−	0.232230i	−0.716278	−	0.697815i	$-0.754156\pi$
$37$	1.02631	−	1.41260i	0.168725	−	0.232230i	0.885003	+	0.465585i	$0.154156\pi$
$38$	3.16163	−	4.35161i	0.512884	−	0.705925i
$39$	−2.28564	+	1.66061i	−0.365995	+	0.265911i
$40$		0			0
$41$	1.40381	+	1.01993i	0.219238	+	0.159286i	0.691984	−	0.721913i	$-0.256737\pi$
$41$	1.40381	+	1.01993i	0.219238	+	0.159286i	−0.472746	+	0.881199i	$0.656737\pi$
$42$	−4.57167	+	1.48543i	−0.705424	+	0.229206i
$43$			2.27151i			0.346403i	0.984886	+	0.173201i	$0.0554111\pi$
$43$			2.27151i			0.346403i	−0.984886	+	0.173201i	$0.944589\pi$
$44$	0.272734	+	0.839389i	0.0411162	+	0.126543i
$45$		0			0
$46$	1.80881	−	5.56695i	0.266695	−	0.820802i
$47$	8.29746	+	2.69601i	1.21031	+	0.393253i	0.843544	−	0.537060i	$-0.180465\pi$
$47$	8.29746	+	2.69601i	1.21031	+	0.393253i	0.366765	+	0.930314i	$0.380465\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	−16.1067			−2.30095
$50$		0			0
$51$	1.65780			0.232139
$52$	−1.66061	−	2.28564i	−0.230285	−	0.316961i
$53$	3.37565	+	1.09681i	0.463681	+	0.150659i	0.531535	−	0.847036i	$-0.321615\pi$
$53$	3.37565	+	1.09681i	0.463681	+	0.150659i	−0.0678545	+	0.997695i	$0.521615\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$		0			0
$56$	−1.48543	−	4.57167i	−0.198498	−	0.610915i
$57$		−	5.37889i		−	0.712451i
$58$	−3.40313	+	1.10574i	−0.446853	+	0.145191i
$59$	8.37628	+	6.08572i	1.09050	+	0.792293i	0.979483	−	0.201525i	$-0.0645898\pi$
$59$	8.37628	+	6.08572i	1.09050	+	0.792293i	0.111015	+	0.993819i	$0.464590\pi$
$60$		0			0
$61$	0.0697810	−	0.0506988i	0.00893454	−	0.00649132i	−0.583309	−	0.812250i	$-0.698242\pi$
$61$	0.0697810	−	0.0506988i	0.00893454	−	0.00649132i	0.592244	+	0.805759i	$0.298242\pi$
$62$	−6.13775	+	8.44789i	−0.779495	+	1.07288i
$63$	−2.82545	+	3.88890i	−0.355973	+	0.489955i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		0			0
$66$	0.714027	+	0.518771i	0.0878906	+	0.0638563i
$67$	11.3751	−	3.69601i	1.38969	−	0.451539i	0.483851	−	0.875150i	$-0.339238\pi$
$67$	11.3751	−	3.69601i	1.38969	−	0.451539i	0.905844	+	0.423611i	$0.139238\pi$
$68$			1.65780i			0.201038i
$69$	−1.80881	−	5.56695i	−0.217755	−	0.670182i
$70$		0			0
$71$	−1.08390	+	3.33591i	−0.128636	+	0.395900i	−0.994546	−	0.104300i	$-0.966740\pi$
$71$	−1.08390	+	3.33591i	−0.128636	+	0.395900i	0.865910	+	0.500199i	$0.166740\pi$
$72$	−0.951057	−	0.309017i	−0.112083	−	0.0364180i
$73$	−4.24851	−	5.84757i	−0.497251	−	0.684407i	0.484454	−	0.874817i	$-0.339018\pi$
$73$	−4.24851	−	5.84757i	−0.497251	−	0.684407i	−0.981705	+	0.190410i	$0.939018\pi$
$74$	1.74607			0.202977
$75$		0			0
$76$	5.37889			0.617001
$77$	2.49370	+	3.43228i	0.284184	+	0.391145i
$78$	−2.68693	−	0.873035i	−0.304234	−	0.0988518i
$79$	3.88627	−	11.9607i	0.437240	−	1.34569i	−0.453533	−	0.891239i	$-0.649837\pi$
$79$	3.88627	−	11.9607i	0.437240	−	1.34569i	0.890774	−	0.454447i	$-0.150163\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			1.73520i			0.191621i
$83$	12.6244	−	4.10192i	1.38571	−	0.450244i	0.481166	−	0.876629i	$-0.340213\pi$
$83$	12.6244	−	4.10192i	1.38571	−	0.450244i	0.904541	+	0.426386i	$0.140213\pi$
$84$	−3.88890	−	2.82545i	−0.424313	−	0.308282i
$85$		0			0
$86$	−1.83769	+	1.33516i	−0.198164	+	0.143974i
$87$	−2.10325	+	2.89488i	−0.225492	+	0.310363i
$88$	−0.518771	+	0.714027i	−0.0553011	+	0.0761155i
$89$	15.1178	−	10.9837i	1.60248	−	1.16427i	0.719939	−	0.694037i	$-0.244170\pi$
$89$	15.1178	−	10.9837i	1.60248	−	1.16427i	0.882542	−	0.470233i	$-0.155830\pi$
$90$		0			0
$91$	−10.9869	−	7.98246i	−1.15174	−	0.836789i
$92$	5.56695	−	1.80881i	0.580395	−	0.188582i
$93$			10.4422i			1.08280i
$94$	2.69601	+	8.29746i	0.278072	+	0.855818i
$95$		0			0
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−17.3764	−	5.64593i	−1.76430	−	0.573257i	−0.766672	−	0.642039i	$-0.778089\pi$
$97$	−17.3764	−	5.64593i	−1.76430	−	0.573257i	−0.997632	+	0.0687822i	$0.978089\pi$
$98$	−9.46727	−	13.0306i	−0.956339	−	1.31629i
$99$	0.882586			0.0887032
$100$		0			0
$101$	−5.46110			−0.543400			−0.271700	−	0.962382i	$-0.587586\pi$
$101$	−5.46110			−0.543400			−0.271700	+	0.962382i	$0.587586\pi$
$102$	0.974432	+	1.34119i	0.0964831	+	0.132798i
$103$	−6.31725	−	2.05260i	−0.622457	−	0.202248i	−0.0192260	−	0.999815i	$-0.506120\pi$
$103$	−6.31725	−	2.05260i	−0.622457	−	0.202248i	−0.603231	+	0.797567i	$0.706120\pi$
$104$	0.873035	−	2.68693i	0.0856081	−	0.263475i
$105$		0			0
$106$	1.09681	+	3.37565i	0.106532	+	0.327872i
$107$		−	14.5245i		−	1.40414i	−0.712108	−	0.702070i	$-0.752259\pi$
$107$		−	14.5245i		−	1.40414i	0.712108	−	0.702070i	$-0.247741\pi$
$108$	−0.951057	+	0.309017i	−0.0915155	+	0.0297352i
$109$	3.85954	+	2.80412i	0.369676	+	0.268586i	0.757077	−	0.653326i	$-0.226627\pi$
$109$	3.85954	+	2.80412i	0.369676	+	0.268586i	−0.387400	+	0.921912i	$0.626627\pi$
$110$		0			0
$111$	1.41260	−	1.02631i	0.134078	−	0.0974134i
$112$	2.82545	−	3.88890i	0.266980	−	0.367466i
$113$	−2.84228	+	3.91206i	−0.267379	+	0.368016i	−0.921503	−	0.388372i	$-0.873038\pi$
$113$	−2.84228	+	3.91206i	−0.267379	+	0.368016i	0.654124	+	0.756388i	$0.273038\pi$
$114$	4.35161	−	3.16163i	0.407566	−	0.296114i
$115$		0			0
$116$	−2.89488	−	2.10325i	−0.268783	−	0.195282i
$117$	−2.68693	+	0.873035i	−0.248406	+	0.0807121i
$118$			10.3536i			0.953131i
$119$	2.46254	+	7.57893i	0.225741	+	0.694759i
$120$		0			0
$121$	−3.15848	+	9.72079i	−0.287134	+	0.883708i
$122$	0.0820324	+	0.0266540i	0.00742687	+	0.00241314i
$123$	1.01993	+	1.40381i	0.0919637	+	0.126577i
$124$	−10.4422			−0.937734
$125$		0			0
$126$	−4.80694			−0.428236
$127$	−1.05908	−	1.45769i	−0.0939779	−	0.129349i	0.759439	−	0.650579i	$-0.225474\pi$
$127$	−1.05908	−	1.45769i	−0.0939779	−	0.129349i	−0.853417	+	0.521229i	$0.825474\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−0.701936	+	2.16034i	−0.0618021	+	0.190207i
$130$		0			0
$131$	−4.95400	−	15.2468i	−0.432833	−	1.33212i	−0.895291	−	0.445481i	$-0.853033\pi$
$131$	−4.95400	−	15.2468i	−0.432833	−	1.33212i	0.462459	−	0.886641i	$-0.346967\pi$
$132$			0.882586i			0.0768192i
$133$	24.5905	−	7.98994i	2.13227	−	0.692816i
$134$	9.67628	+	7.03023i	0.835903	+	0.607319i
$135$		0			0
$136$	−1.34119	+	0.974432i	−0.115006	+	0.0835569i
$137$	1.03872	−	1.42968i	0.0887443	−	0.122146i	−0.762336	−	0.647181i	$-0.775948\pi$
$137$	1.03872	−	1.42968i	0.0887443	−	0.122146i	0.851081	+	0.525035i	$0.175948\pi$
$138$	3.44056	−	4.73553i	0.292880	−	0.403115i
$139$	8.89636	−	6.46359i	0.754580	−	0.548234i	−0.142663	−	0.989771i	$-0.545567\pi$
$139$	8.89636	−	6.46359i	0.754580	−	0.548234i	0.897243	+	0.441537i	$0.145567\pi$
$140$		0			0
$141$	7.05824	+	5.12811i	0.594411	+	0.431865i
$142$	−3.33591	+	1.08390i	−0.279943	+	0.0909591i
$143$			2.49348i			0.208515i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$		0			0
$146$	2.23357	−	6.87424i	0.184852	−	0.568916i
$147$	−15.3184	−	4.97724i	−1.26344	−	0.410516i
$148$	1.02631	+	1.41260i	0.0843625	+	0.116115i
$149$	−2.90948			−0.238354			−0.119177	−	0.992873i	$-0.538026\pi$
$149$	−2.90948			−0.238354			−0.119177	+	0.992873i	$0.538026\pi$
$150$		0			0
$151$	−1.34184			−0.109197			−0.0545986	−	0.998508i	$-0.517388\pi$
$151$	−1.34184			−0.109197			−0.0545986	+	0.998508i	$0.517388\pi$
$152$	3.16163	+	4.35161i	0.256442	+	0.352962i
$153$	1.57666	+	0.512289i	0.127466	+	0.0414161i
$154$	−1.31102	+	4.03489i	−0.105645	+	0.325141i
$155$		0			0
$156$	−0.873035	−	2.68693i	−0.0698987	−	0.215126i
$157$			8.31169i			0.663345i	0.943395	+	0.331673i	$0.107613\pi$
$157$			8.31169i			0.663345i	−0.943395	+	0.331673i	$0.892387\pi$
$158$	11.9607	−	3.88627i	0.951544	−	0.309175i
$159$	2.87150	+	2.08626i	0.227724	+	0.165451i
$160$		0			0
$161$	22.7634	−	16.5386i	1.79401	−	1.30342i
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−3.66704	+	5.04724i	−0.287225	+	0.395331i	−0.928110	−	0.372306i	$-0.878567\pi$
$163$	−3.66704	+	5.04724i	−0.287225	+	0.395331i	0.640886	+	0.767636i	$0.278567\pi$
$164$	−1.40381	+	1.01993i	−0.109619	+	0.0796429i
$165$		0			0
$166$	10.7390	+	7.80231i	0.833505	+	0.605576i
$167$	14.1107	−	4.58483i	1.09192	−	0.354785i	0.292929	−	0.956134i	$-0.405370\pi$
$167$	14.1107	−	4.58483i	1.09192	−	0.354785i	0.798986	+	0.601349i	$0.205370\pi$
$168$		−	4.80694i		−	0.370864i
$169$	1.55072	+	4.77263i	0.119286	+	0.367125i
$170$		0			0
$171$	1.66217	−	5.11563i	0.127109	−	0.391202i
$172$	−2.16034	−	0.701936i	−0.164724	−	0.0535221i
$173$	9.42623	+	12.9741i	0.716663	+	0.986402i	0.999628	+	0.0272719i	$0.00868201\pi$
$173$	9.42623	+	12.9741i	0.716663	+	0.986402i	−0.282965	+	0.959130i	$0.591318\pi$
$174$	−3.57827			−0.271268
$175$		0			0
$176$	−0.882586			−0.0665274
$177$	6.08572	+	8.37628i	0.457431	+	0.629600i
$178$	17.7720	+	5.77448i	1.33207	+	0.432815i
$179$	−3.63061	+	11.1739i	−0.271365	+	0.835174i	0.718794	+	0.695223i	$0.244694\pi$
$179$	−3.63061	+	11.1739i	−0.271365	+	0.835174i	−0.990158	+	0.139951i	$0.955306\pi$
$180$		0			0
$181$	−1.24658	−	3.83658i	−0.0926577	−	0.285171i	0.893979	−	0.448110i	$-0.147903\pi$
$181$	−1.24658	−	3.83658i	−0.0926577	−	0.285171i	−0.986636	+	0.162939i	$0.947903\pi$
$182$		−	13.5806i		−	1.00666i
$183$	0.0820324	−	0.0266540i	0.00606401	−	0.00197032i
$184$	4.73553	+	3.44056i	0.349108	+	0.253642i
$185$		0			0
$186$	−8.44789	+	6.13775i	−0.619429	+	0.450042i
$187$	0.860020	−	1.18372i	0.0628909	−	0.0865618i
$188$	−5.12811	+	7.05824i	−0.374006	+	0.514775i
$189$	−3.88890	+	2.82545i	−0.282876	+	0.205521i
$190$		0			0
$191$	−9.64472	−	7.00730i	−0.697867	−	0.507030i	0.181370	−	0.983415i	$-0.441947\pi$
$191$	−9.64472	−	7.00730i	−0.697867	−	0.507030i	−0.879237	+	0.476385i	$0.841947\pi$
$192$	0.951057	−	0.309017i	0.0686366	−	0.0223014i
$193$			11.8088i			0.850019i	0.905189	+	0.425009i	$0.139729\pi$
$193$			11.8088i			0.850019i	−0.905189	+	0.425009i	$0.860271\pi$
$194$	−5.64593	−	17.3764i	−0.405354	−	1.24755i
$195$		0			0
$196$	4.97724	−	15.3184i	0.355517	−	1.09417i
$197$	6.92219	+	2.24916i	0.493186	+	0.160246i	0.545042	−	0.838409i	$-0.316514\pi$
$197$	6.92219	+	2.24916i	0.493186	+	0.160246i	−0.0518562	+	0.998655i	$0.516514\pi$
$198$	0.518771	+	0.714027i	0.0368674	+	0.0507437i
$199$	−2.27949			−0.161589			−0.0807944	−	0.996731i	$-0.525746\pi$
$199$	−2.27949			−0.161589			−0.0807944	+	0.996731i	$0.525746\pi$
$200$		0			0
$201$	11.9605			0.843631
$202$	−3.20996	−	4.41813i	−0.225852	−	0.310858i
$203$	−16.3587	−	5.31525i	−1.14815	−	0.373057i
$204$	−0.512289	+	1.57666i	−0.0358674	+	0.110389i
$205$		0			0
$206$	−2.05260	−	6.31725i	−0.143011	−	0.440143i
$207$		−	5.85344i		−	0.406842i
$208$	2.68693	−	0.873035i	0.186305	−	0.0605341i
$209$	−3.84067	−	2.79041i	−0.265665	−	0.193017i
$210$		0			0
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	−0.552455	−	0.833543i	$-0.686309\pi$
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	0.622029	+	0.782994i	$0.286309\pi$
$212$	−2.08626	+	2.87150i	−0.143285	+	0.197215i
$213$	−2.06170	+	2.83769i	−0.141266	+	0.194436i
$214$	11.7506	−	8.53731i	0.803255	−	0.583599i
$215$		0			0
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−47.7381	+	15.5111i	−3.24068	+	1.05296i
$218$			4.77065i			0.323109i
$219$	−2.23357	−	6.87424i	−0.150931	−	0.464518i
$220$		0			0
$221$	−1.44732	+	4.45439i	−0.0973573	+	0.299635i
$222$	1.66061	+	0.539565i	0.111453	+	0.0362133i
$223$	−5.19727	−	7.15343i	−0.348035	−	0.479029i	0.598732	−	0.800950i	$-0.295672\pi$
$223$	−5.19727	−	7.15343i	−0.348035	−	0.479029i	−0.946767	+	0.321921i	$0.895672\pi$
$224$	4.80694			0.321177
$225$		0			0
$226$	−4.83558			−0.321658
$227$	−10.4019	−	14.3170i	−0.690398	−	0.950251i	0.309602	−	0.950866i	$-0.399804\pi$
$227$	−10.4019	−	14.3170i	−0.690398	−	0.950251i	−1.00000		0.000615300i	$0.999804\pi$
$228$	5.11563	+	1.66217i	0.338791	+	0.110080i
$229$	2.75446	−	8.47737i	0.182020	−	0.560200i	−0.817864	−	0.575411i	$-0.804842\pi$
$229$	2.75446	−	8.47737i	0.182020	−	0.560200i	0.999884	+	0.0152110i	$0.00484200\pi$
$230$		0			0
$231$	1.31102	+	4.03489i	0.0862585	+	0.265476i
$232$		−	3.57827i		−	0.234925i
$233$	9.12123	−	2.96367i	0.597551	−	0.194156i	0.00540335	−	0.999985i	$-0.498280\pi$
$233$	9.12123	−	2.96367i	0.597551	−	0.194156i	0.592148	+	0.805829i	$0.298280\pi$
$234$	−2.28564	−	1.66061i	−0.149417	−	0.108558i
$235$		0			0
$236$	−8.37628	+	6.08572i	−0.545249	+	0.396147i
$237$	7.39213	−	10.1744i	0.480171	−	0.660898i
$238$	−4.68404	+	6.44702i	−0.303621	+	0.417898i
$239$	−7.41301	+	5.38587i	−0.479508	+	0.348383i	−0.801135	−	0.598483i	$-0.795770\pi$
$239$	−7.41301	+	5.38587i	−0.479508	+	0.348383i	0.321627	+	0.946866i	$0.395770\pi$
$240$		0			0
$241$	2.01891	+	1.46682i	0.130049	+	0.0944864i	0.650908	−	0.759156i	$-0.274388\pi$
$241$	2.01891	+	1.46682i	0.130049	+	0.0944864i	−0.520859	+	0.853643i	$0.674388\pi$
$242$	−9.72079	+	3.15848i	−0.624876	+	0.203035i
$243$			1.00000i			0.0641500i
$244$	0.0266540	+	0.0820324i	0.00170634	+	0.00525159i
$245$		0			0
$246$	−0.536207	+	1.65028i	−0.0341873	+	0.105218i
$247$	14.4527	+	4.69596i	0.919601	+	0.298797i
$248$	−6.13775	−	8.44789i	−0.389747	−	0.536441i
$249$	13.2741			0.841211
$250$		0			0
$251$	8.71262			0.549936			0.274968	−	0.961453i	$-0.411333\pi$
$251$	8.71262			0.549936			0.274968	+	0.961453i	$0.411333\pi$
$252$	−2.82545	−	3.88890i	−0.177987	−	0.244977i
$253$	−4.91331	−	1.59643i	−0.308897	−	0.100367i
$254$	0.556790	−	1.71362i	0.0349361	−	0.107522i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			19.7871i			1.23429i	0.786851	+	0.617143i	$0.211710\pi$
$257$			19.7871i			1.23429i	−0.786851	+	0.617143i	$0.788290\pi$
$258$	−2.16034	+	0.701936i	−0.134497	+	0.0437007i
$259$	6.79029	+	4.93343i	0.421928	+	0.306549i
$260$		0			0
$261$	−2.89488	+	2.10325i	−0.179188	+	0.130188i
$262$	9.42306	−	12.9697i	0.582159	−	0.801272i
$263$	15.0258	−	20.6813i	0.926532	−	1.27526i	−0.0346651	−	0.999399i	$-0.511036\pi$
$263$	15.0258	−	20.6813i	0.926532	−	1.27526i	0.961197	−	0.275863i	$-0.0889636\pi$
$264$	−0.714027	+	0.518771i	−0.0439453	+	0.0319281i
$265$		0			0
$266$	20.9179	+	15.1978i	1.28256	+	0.931835i
$267$	17.7720	−	5.77448i	1.08763	−	0.353392i
$268$			11.9605i			0.730606i
$269$	−7.54447	−	23.2195i	−0.459994	−	1.41572i	−0.865170	−	0.501478i	$-0.832790\pi$
$269$	−7.54447	−	23.2195i	−0.459994	−	1.41572i	0.405176	−	0.914239i	$-0.367210\pi$
$270$		0			0
$271$	0.848720	−	2.61209i	0.0515561	−	0.158673i	−0.921964	−	0.387277i	$-0.873416\pi$
$271$	0.848720	−	2.61209i	0.0515561	−	0.158673i	0.973520	+	0.228603i	$0.0734159\pi$
$272$	−1.57666	−	0.512289i	−0.0955993	−	0.0310621i
$273$	−7.98246	−	10.9869i	−0.483120	−	0.664958i
$274$	1.76718			0.106760
$275$		0			0
$276$	5.85344			0.352336
$277$	1.75206	+	2.41151i	0.105271	+	0.144893i	0.858402	−	0.512977i	$-0.171457\pi$
$277$	1.75206	+	2.41151i	0.105271	+	0.144893i	−0.753131	+	0.657870i	$0.771457\pi$
$278$	10.4583	+	3.39811i	0.627247	+	0.203805i
$279$	−3.22681	+	9.93109i	−0.193184	+	0.594559i
$280$		0			0
$281$	1.19334	+	3.67274i	0.0711890	+	0.219097i	0.980321	−	0.197412i	$-0.0632535\pi$
$281$	1.19334	+	3.67274i	0.0711890	+	0.219097i	−0.909132	+	0.416509i	$0.863254\pi$
$282$			8.72447i			0.519534i
$283$	15.8844	−	5.16117i	0.944232	−	0.306800i	0.203863	−	0.979000i	$-0.434650\pi$
$283$	15.8844	−	5.16117i	0.944232	−	0.306800i	0.740370	+	0.672200i	$0.234650\pi$
$284$	−2.83769	−	2.06170i	−0.168386	−	0.122340i
$285$		0			0
$286$	−2.01727	+	1.46563i	−0.119284	+	0.0866646i
$287$	−4.90273	+	6.74802i	−0.289399	+	0.398323i
$288$	0.587785	−	0.809017i	0.0346356	−	0.0476718i
$289$	−11.5299	+	8.37693i	−0.678227	+	0.492761i
$290$		0			0
$291$	−14.7812	−	10.7392i	−0.866491	−	0.629542i
$292$	6.87424	−	2.23357i	0.402284	−	0.130710i
$293$		−	0.503153i		−	0.0293945i	−0.999892	−	0.0146972i	$-0.995322\pi$
$293$		−	0.503153i		−	0.0293945i	0.999892	−	0.0146972i	$-0.00467845\pi$
$294$	−4.97724	−	15.3184i	−0.290278	−	0.893385i
$295$		0			0
$296$	−0.539565	+	1.66061i	−0.0313616	+	0.0965211i
$297$	0.839389	+	0.272734i	0.0487063	+	0.0158256i
$298$	−1.71015	−	2.35382i	−0.0990664	−	0.136353i
$299$	16.5371			0.956367
$300$		0			0
$301$	−10.9190			−0.629363
$302$	−0.788713	−	1.08557i	−0.0453853	−	0.0624675i
$303$	−5.19382	−	1.68757i	−0.298377	−	0.0969486i
$304$	−1.66217	+	5.11563i	−0.0953319	+	0.293401i
$305$		0			0
$306$	0.512289	+	1.57666i	0.0292856	+	0.0901319i
$307$			8.63375i			0.492754i	0.969174	+	0.246377i	$0.0792402\pi$
$307$			8.63375i			0.492754i	−0.969174	+	0.246377i	$0.920760\pi$
$308$	−4.03489	+	1.31102i	−0.229909	+	0.0747021i
$309$	−5.37377	−	3.90427i	−0.305703	−	0.222106i
$310$		0			0
$311$	−16.3967	+	11.9129i	−0.929771	+	0.675518i	−0.945937	−	0.324351i	$-0.894854\pi$
$311$	−16.3967	+	11.9129i	−0.929771	+	0.675518i	0.0161660	+	0.999869i	$0.494854\pi$
$312$	1.66061	−	2.28564i	0.0940136	−	0.129399i
$313$	−10.0101	+	13.7777i	−0.565805	+	0.778763i	−0.992050	−	0.125844i	$-0.959836\pi$
$313$	−10.0101	+	13.7777i	−0.565805	+	0.778763i	0.426245	+	0.904608i	$0.359836\pi$
$314$	−6.72430	+	4.88549i	−0.379474	+	0.275704i
$315$		0			0
$316$	10.1744	+	7.39213i	0.572355	+	0.415840i
$317$	−2.68347	+	0.871912i	−0.150719	+	0.0489715i	−0.383405	−	0.923580i	$-0.625249\pi$
$317$	−2.68347	+	0.871912i	−0.150719	+	0.0489715i	0.232686	+	0.972552i	$0.425249\pi$
$318$			3.54936i			0.199038i
$319$	0.975914	+	3.00356i	0.0546407	+	0.168167i
$320$		0			0
$321$	4.48833	−	13.8137i	0.250514	−	0.771003i
$322$	26.7600	+	8.69485i	1.49128	+	0.484545i
$323$	−5.24136	−	7.21411i	−0.291637	−	0.401404i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−6.23874			−0.345532
$327$	2.80412	+	3.85954i	0.155068	+	0.213433i
$328$	−1.65028	−	0.536207i	−0.0911212	−	0.0296071i
$329$	−12.9596	+	39.8854i	−0.714483	+	2.19895i
$330$		0			0
$331$	−1.25862	−	3.87364i	−0.0691802	−	0.212915i	0.910489	−	0.413532i	$-0.135705\pi$
$331$	−1.25862	−	3.87364i	−0.0691802	−	0.212915i	−0.979670	+	0.200618i	$0.935705\pi$
$332$			13.2741i			0.728510i
$333$	1.66061	−	0.539565i	0.0910009	−	0.0295680i
$334$	12.0032	+	8.72086i	0.656788	+	0.477184i
$335$		0			0
$336$	3.88890	−	2.82545i	0.212157	−	0.154141i
$337$	5.31818	−	7.31984i	0.289700	−	0.398737i	−0.639217	−	0.769026i	$-0.720741\pi$
$337$	5.31818	−	7.31984i	0.289700	−	0.398737i	0.928917	+	0.370289i	$0.120741\pi$
$338$	−2.94965	+	4.05984i	−0.160440	+	0.220826i
$339$	−3.91206	+	2.84228i	−0.212474	+	0.154371i
$340$		0			0
$341$	7.45598	+	5.41709i	0.403764	+	0.293352i
$342$	5.11563	−	1.66217i	0.276621	−	0.0898797i
$343$		−	43.7753i		−	2.36364i
$344$	−0.701936	−	2.16034i	−0.0378459	−	0.116478i
$345$		0			0
$346$	−4.95566	+	15.2520i	−0.266418	+	0.819951i
$347$	−8.26141	−	2.68429i	−0.443495	−	0.144100i	0.0787523	−	0.996894i	$-0.474906\pi$
$347$	−8.26141	−	2.68429i	−0.443495	−	0.144100i	−0.522248	+	0.852794i	$0.674906\pi$
$348$	−2.10325	−	2.89488i	−0.112746	−	0.155182i
$349$	−26.8305			−1.43620			−0.718101	−	0.695938i	$-0.754989\pi$
$349$	−26.8305			−1.43620			−0.718101	+	0.695938i	$0.754989\pi$
$350$		0			0
$351$	−2.82520			−0.150798
$352$	−0.518771	−	0.714027i	−0.0276506	−	0.0380577i
$353$	−26.9623	−	8.76060i	−1.43506	−	0.466279i	−0.514707	−	0.857366i	$-0.672099\pi$
$353$	−26.9623	−	8.76060i	−1.43506	−	0.466279i	−0.920354	+	0.391087i	$0.872099\pi$
$354$	−3.19945	+	9.84690i	−0.170049	+	0.523357i
$355$		0			0
$356$	5.77448	+	17.7720i	0.306047	+	0.941915i
$357$			7.96896i			0.421762i
$358$	−11.1739	+	3.63061i	−0.590557	+	0.191884i
$359$	7.02898	+	5.10686i	0.370976	+	0.269530i	0.757615	−	0.652701i	$-0.226364\pi$
$359$	7.02898	+	5.10686i	0.370976	+	0.269530i	−0.386640	+	0.922231i	$0.626364\pi$
$360$		0			0
$361$	−8.03551	+	5.83814i	−0.422921	+	0.307270i
$362$	2.37114	−	3.26359i	0.124624	−	0.171531i
$363$	−6.00778	+	8.26900i	−0.315327	+	0.434010i
$364$	10.9869	−	7.98246i	0.575871	−	0.418395i
$365$		0			0
$366$	0.0697810	+	0.0506988i	0.00364751	+	0.00265007i
$367$	−11.8609	+	3.85385i	−0.619136	+	0.201170i	−0.601757	−	0.798679i	$-0.705532\pi$
$367$	−11.8609	+	3.85385i	−0.619136	+	0.201170i	−0.0173794	+	0.999849i	$0.505532\pi$
$368$			5.85344i			0.305132i
$369$	0.536207	+	1.65028i	0.0279138	+	0.0859099i
$370$		0			0
$371$	−5.27232	+	16.2265i	−0.273725	+	0.842439i
$372$	−9.93109	−	3.22681i	−0.514903	−	0.167302i
$373$	7.64048	+	10.5162i	0.395609	+	0.544509i	0.959635	−	0.281248i	$-0.0907483\pi$
$373$	7.64048	+	10.5162i	0.395609	+	0.544509i	−0.564026	+	0.825757i	$0.690748\pi$
$374$	1.46315			0.0756578
$375$		0			0
$376$	−8.72447			−0.449930
$377$	−5.94211	−	8.17861i	−0.306034	−	0.421220i
$378$	−4.57167	−	1.48543i	−0.235141	−	0.0764021i
$379$	−0.541481	+	1.66651i	−0.0278140	+	0.0856027i	−0.964000	−	0.265903i	$-0.914330\pi$
$379$	−0.541481	+	1.66651i	−0.0278140	+	0.0856027i	0.936186	+	0.351505i	$0.114330\pi$
$380$		0			0
$381$	−0.556790	−	1.71362i	−0.0285252	−	0.0877915i
$382$		−	11.9215i		−	0.609958i
$383$	−32.4652	+	10.5486i	−1.65889	+	0.539007i	−0.980639	−	0.195822i	$-0.937262\pi$
$383$	−32.4652	+	10.5486i	−1.65889	+	0.539007i	−0.678252	+	0.734829i	$0.737262\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$		0			0
$386$	−9.55355	+	6.94106i	−0.486263	+	0.353291i
$387$	−1.33516	+	1.83769i	−0.0678701	+	0.0934152i
$388$	10.7392	−	14.7812i	0.545200	−	0.750403i
$389$	5.54704	−	4.03016i	0.281246	−	0.204337i	−0.438215	−	0.898870i	$-0.644389\pi$
$389$	5.54704	−	4.03016i	0.281246	−	0.204337i	0.719461	+	0.694533i	$0.244389\pi$
$390$		0			0
$391$	−7.85058	−	5.70378i	−0.397021	−	0.288452i
$392$	15.3184	−	4.97724i	0.773694	−	0.251388i
$393$		−	16.0315i		−	0.808680i
$394$	2.24916	+	6.92219i	0.113311	+	0.348735i
$395$		0			0
$396$	−0.272734	+	0.839389i	−0.0137054	+	0.0421809i
$397$	31.5358	+	10.2466i	1.58274	+	0.514262i	0.962760	−	0.270359i	$-0.0871424\pi$
$397$	31.5358	+	10.2466i	1.58274	+	0.514262i	0.619976	+	0.784621i	$0.287142\pi$
$398$	−1.33985	−	1.84415i	−0.0671607	−	0.0924387i
$399$	25.8560			1.29442
$400$		0			0
$401$	3.51432			0.175497			0.0877483	−	0.996143i	$-0.472033\pi$
$401$	3.51432			0.175497			0.0877483	+	0.996143i	$0.472033\pi$
$402$	7.03023	+	9.67628i	0.350636	+	0.482609i
$403$	−28.0573	−	9.11637i	−1.39763	−	0.454119i
$404$	1.68757	−	5.19382i	0.0839599	−	0.258402i
$405$		0			0
$406$	−5.31525	−	16.3587i	−0.263791	−	0.811866i
$407$		−	1.54106i		−	0.0763873i
$408$	−1.57666	+	0.512289i	−0.0780565	+	0.0253621i
$409$	−13.1746	−	9.57194i	−0.651444	−	0.473302i	0.212318	−	0.977201i	$-0.431899\pi$
$409$	−13.1746	−	9.57194i	−0.651444	−	0.473302i	−0.863763	+	0.503898i	$0.831899\pi$
$410$		0			0
$411$	1.42968	−	1.03872i	0.0705210	−	0.0512365i
$412$	3.90427	−	5.37377i	0.192350	−	0.264747i
$413$	−29.2537	+	40.2643i	−1.43948	+	1.98128i
$414$	4.73553	−	3.44056i	0.232739	−	0.169095i
$415$		0			0
$416$	2.28564	+	1.66061i	0.112062	+	0.0814182i
$417$	10.4583	−	3.39811i	0.512145	−	0.166406i
$418$		−	4.74733i		−	0.232199i
$419$	−8.18528	−	25.1917i	−0.399877	−	1.23070i	−0.925098	−	0.379730i	$-0.876017\pi$
$419$	−8.18528	−	25.1917i	−0.399877	−	1.23070i	0.525220	−	0.850966i	$-0.323983\pi$
$420$		0			0
$421$	−9.56476	+	29.4373i	−0.466158	+	1.43469i	0.391362	+	0.920237i	$0.372004\pi$
$421$	−9.56476	+	29.4373i	−0.466158	+	1.43469i	−0.857520	+	0.514450i	$0.827996\pi$
$422$	1.18806	+	0.386023i	0.0578337	+	0.0187913i
$423$	5.12811	+	7.05824i	0.249337	+	0.343183i
$424$	−3.54936			−0.172372
$425$		0			0
$426$	−3.50758			−0.169943
$427$	0.243706	+	0.335433i	0.0117938	+	0.0162327i
$428$	13.8137	+	4.48833i	0.667708	+	0.216952i
$429$	−0.770528	+	2.37144i	−0.0372014	+	0.114494i
$430$		0			0
$431$	−0.532381	−	1.63850i	−0.0256439	−	0.0789238i	0.937416	−	0.348213i	$-0.113211\pi$
$431$	−0.532381	−	1.63850i	−0.0256439	−	0.0789238i	−0.963059	+	0.269289i	$0.913211\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−22.9568	+	7.45911i	−1.10323	+	0.358462i	−0.803346	−	0.595513i	$-0.796949\pi$
$433$	−22.9568	+	7.45911i	−1.10323	+	0.358462i	−0.299886	+	0.953975i	$0.596949\pi$
$434$	−40.6085	−	29.5038i	−1.94927	−	1.41623i
$435$		0			0
$436$	−3.85954	+	2.80412i	−0.184838	+	0.134293i
$437$	−18.5064	+	25.4719i	−0.885282	+	1.21849i
$438$	4.24851	−	5.84757i	0.203002	−	0.279408i
$439$	6.66899	−	4.84531i	0.318294	−	0.231254i	−0.417153	−	0.908836i	$-0.636972\pi$
$439$	6.66899	−	4.84531i	0.318294	−	0.231254i	0.735447	+	0.677582i	$0.236972\pi$
$440$		0			0
$441$	−13.0306	−	9.46727i	−0.620504	−	0.450822i
$442$	−4.45439	+	1.44732i	−0.211874	+	0.0688420i
$443$			22.4652i			1.06735i	0.845689	+	0.533676i	$0.179190\pi$
$443$			22.4652i			1.06735i	−0.845689	+	0.533676i	$0.820810\pi$
$444$	0.539565	+	1.66061i	0.0256066	+	0.0788091i
$445$		0			0
$446$	2.73237	−	8.40936i	0.129381	−	0.398195i
$447$	−2.76708	−	0.899079i	−0.130878	−	0.0425250i
$448$	2.82545	+	3.88890i	0.133490	+	0.183733i
$449$	−30.4988			−1.43933			−0.719663	−	0.694323i	$-0.755704\pi$
$449$	−30.4988			−1.43933			−0.719663	+	0.694323i	$0.755704\pi$
$450$		0			0
$451$	1.53146			0.0721139
$452$	−2.84228	−	3.91206i	−0.133690	−	0.184008i
$453$	−1.27616	−	0.414651i	−0.0599594	−	0.0194820i
$454$	5.46860	−	16.8306i	0.256654	−	0.789900i
$455$		0			0
$456$	1.66217	+	5.11563i	0.0778381	+	0.239561i
$457$			6.65272i			0.311201i	0.987820	+	0.155601i	$0.0497313\pi$
$457$			6.65272i			0.311201i	−0.987820	+	0.155601i	$0.950269\pi$
$458$	8.47737	−	2.75446i	0.396121	−	0.128708i
$459$	1.34119	+	0.974432i	0.0626014	+	0.0454826i
$460$		0			0
$461$	19.1479	−	13.9118i	0.891808	−	0.647936i	−0.0445410	−	0.999008i	$-0.514183\pi$
$461$	19.1479	−	13.9118i	0.891808	−	0.647936i	0.936349	+	0.351071i	$0.114183\pi$
$462$	−2.49370	+	3.43228i	−0.116017	+	0.159684i
$463$	15.3328	−	21.1038i	0.712575	−	0.980775i	−0.287163	−	0.957882i	$-0.592712\pi$
$463$	15.3328	−	21.1038i	0.712575	−	0.980775i	0.999738	−	0.0228935i	$-0.00728787\pi$
$464$	2.89488	−	2.10325i	0.134391	−	0.0976410i
$465$		0			0
$466$	7.75898	+	5.63723i	0.359428	+	0.261140i
$467$	−1.40340	+	0.455993i	−0.0649417	+	0.0211008i	−0.341308	−	0.939952i	$-0.610870\pi$
$467$	−1.40340	+	0.455993i	−0.0649417	+	0.0211008i	0.276366	+	0.961052i	$0.410870\pi$
$468$		−	2.82520i		−	0.130595i
$469$	17.7665	+	54.6796i	0.820380	+	2.52487i
$470$		0			0
$471$	−2.56845	+	7.90489i	−0.118348	+	0.364238i
$472$	−9.84690	−	3.19945i	−0.453240	−	0.147267i
$473$	1.17839	+	1.62192i	0.0541827	+	0.0745760i
$474$	12.5762			0.577646
$475$		0			0
$476$	−7.96896			−0.365257
$477$	2.08626	+	2.87150i	0.0955235	+	0.131477i
$478$	−8.71452	−	2.83152i	−0.398593	−	0.129511i
$479$	4.14388	−	12.7536i	0.189339	−	0.582725i	−0.810657	−	0.585521i	$-0.800890\pi$
$479$	4.14388	−	12.7536i	0.189339	−	0.582725i	0.999996	+	0.00279598i	$0.000889988\pi$
$480$		0			0
$481$	1.52438	+	4.69156i	0.0695058	+	0.213917i
$482$			2.49551i			0.113667i
$483$	26.7600	−	8.69485i	1.21762	−	0.395629i
$484$	−8.26900	−	6.00778i	−0.375864	−	0.273081i
$485$		0			0
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	1.24615	−	1.71518i	0.0564686	−	0.0777224i	−0.779849	−	0.625968i	$-0.784704\pi$
$487$	1.24615	−	1.71518i	0.0564686	−	0.0777224i	0.836317	+	0.548246i	$0.184704\pi$
$488$	−0.0506988	+	0.0697810i	−0.00229503	+	0.00315884i
$489$	−5.04724	+	3.66704i	−0.228244	+	0.165829i
$490$		0			0
$491$	1.79947	+	1.30739i	0.0812091	+	0.0590019i	0.627649	−	0.778496i	$-0.284017\pi$
$491$	1.79947	+	1.30739i	0.0812091	+	0.0590019i	−0.546440	+	0.837498i	$0.684017\pi$
$492$	−1.65028	+	0.536207i	−0.0744002	+	0.0241741i
$493$			5.93206i			0.267166i
$494$	4.69596	+	14.4527i	0.211281	+	0.650256i
$495$		0			0
$496$	3.22681	−	9.93109i	0.144888	−	0.445919i
$497$	−16.0355	−	5.21025i	−0.719291	−	0.233712i
$498$	7.80231	+	10.7390i	0.349630	+	0.481224i
$499$	−14.5582			−0.651715			−0.325858	−	0.945419i	$-0.605653\pi$
$499$	−14.5582			−0.651715			−0.325858	+	0.945419i	$0.605653\pi$
$500$		0			0
$501$	14.8368			0.662860
$502$	5.12115	+	7.04866i	0.228568	+	0.314597i
$503$	22.6744	+	7.36734i	1.01100	+	0.328494i	0.767252	−	0.641345i	$-0.221623\pi$
$503$	22.6744	+	7.36734i	1.01100	+	0.328494i	0.243747	+	0.969839i	$0.421623\pi$
$504$	1.48543	−	4.57167i	0.0661662	−	0.203638i
$505$		0			0
$506$	−1.59643	−	4.91331i	−0.0709700	−	0.218423i
$507$			5.01824i			0.222868i
$508$	1.71362	−	0.556790i	0.0760297	−	0.0247035i
$509$	−28.1543	−	20.4553i	−1.24792	−	0.906664i	−0.249817	−	0.968293i	$-0.580370\pi$
$509$	−28.1543	−	20.4553i	−1.24792	−	0.906664i	−0.998099	+	0.0616289i	$0.980370\pi$
$510$		0			0
$511$	28.1089	−	20.4223i	1.24347	−	0.903431i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	3.16163	−	4.35161i	0.139589	−	0.192128i
$514$	−16.0081	+	11.6306i	−0.706088	+	0.513003i
$515$		0			0
$516$	−1.83769	−	1.33516i	−0.0808999	−	0.0587772i
$517$	7.32322	−	2.37946i	0.322075	−	0.104648i
$518$			8.39326i			0.368778i
$519$	4.95566	+	15.2520i	0.217529	+	0.669487i
$520$		0			0
$521$	−2.68575	+	8.26589i	−0.117665	+	0.362135i	−0.992494	−	0.122297i	$-0.960974\pi$
$521$	−2.68575	+	8.26589i	−0.117665	+	0.362135i	0.874829	+	0.484433i	$0.160974\pi$
$522$	−3.40313	−	1.10574i	−0.148951	−	0.0483971i
$523$	−19.0655	−	26.2414i	−0.833676	−	1.14746i	−0.987228	−	0.159317i	$-0.949071\pi$
$523$	−19.0655	−	26.2414i	−0.833676	−	1.14746i	0.153551	−	0.988141i	$-0.450929\pi$
$524$	16.0315			0.700338
$525$		0			0
$526$	25.5635			1.11462
$527$	10.1752	+	14.0049i	0.443238	+	0.610064i
$528$	−0.839389	−	0.272734i	−0.0365297	−	0.0118692i
$529$	−3.48038	+	10.7115i	−0.151321	+	0.465717i
$530$		0			0
$531$	3.19945	+	9.84690i	0.138844	+	0.427319i
$532$			25.8560i			1.12100i
$533$	−4.66236	+	1.51489i	−0.201949	+	0.0656173i
$534$	15.1178	+	10.9837i	0.654210	+	0.475312i
$535$		0			0
$536$	−9.67628	+	7.03023i	−0.417951	+	0.303659i
$537$	−6.90583	+	9.50506i	−0.298009	+	0.410174i
$538$	14.3504	−	19.7517i	0.618691	−	0.851555i
$539$	−11.5006	+	8.35567i	−0.495366	+	0.359904i
$540$		0			0
$541$	−25.0000	−	18.1636i	−1.07483	−	0.780913i	−0.0980596	−	0.995181i	$-0.531264\pi$
$541$	−25.0000	−	18.1636i	−1.07483	−	0.780913i	−0.976775	+	0.214268i	$0.931264\pi$
$542$	2.61209	−	0.848720i	0.112199	−	0.0364557i
$543$		−	4.03402i		−	0.173116i
$544$	−0.512289	−	1.57666i	−0.0219642	−	0.0675989i
$545$		0			0
$546$	4.19663	−	12.9159i	0.179599	−	0.552749i
$547$	29.7315	+	9.66035i	1.27123	+	0.413047i	0.865482	−	0.500940i	$-0.167012\pi$
$547$	29.7315	+	9.66035i	1.27123	+	0.413047i	0.405745	+	0.913986i	$0.367012\pi$
$548$	1.03872	+	1.42968i	0.0443721	+	0.0610730i
$549$	0.0862540			0.00368123
$550$		0			0
$551$	19.2471			0.819953
$552$	3.44056	+	4.73553i	0.146440	+	0.201558i
$553$	57.4945	+	18.6811i	2.44491	+	0.794401i
$554$	−0.921114	+	2.83490i	−0.0391344	+	0.120443i
$555$		0			0
$556$	3.39811	+	10.4583i	0.144112	+	0.443531i
$557$		−	34.8113i		−	1.47500i	−0.675347	−	0.737500i	$-0.736006\pi$
$557$		−	34.8113i		−	1.47500i	0.675347	−	0.737500i	$-0.263994\pi$
$558$	−9.93109	+	3.22681i	−0.420416	+	0.136602i
$559$	−5.19185	−	3.77210i	−0.219592	−	0.159543i
$560$		0			0
$561$	1.18372	−	0.860020i	0.0499765	−	0.0363101i
$562$	−2.26988	+	3.12422i	−0.0957490	+	0.131787i
$563$	2.87518	−	3.95734i	0.121174	−	0.166782i	−0.744121	−	0.668045i	$-0.767131\pi$
$563$	2.87518	−	3.95734i	0.121174	−	0.166782i	0.865295	+	0.501263i	$0.167131\pi$
$564$	−7.05824	+	5.12811i	−0.297206	+	0.215932i
$565$		0			0
$566$	13.5121	+	9.81713i	0.567957	+	0.412645i
$567$	−4.57167	+	1.48543i	−0.191992	+	0.0623820i
$568$		−	3.50758i		−	0.147175i
$569$	0.906980	+	2.79140i	0.0380226	+	0.117021i	0.968266	−	0.249921i	$-0.0804046\pi$
$569$	0.906980	+	2.79140i	0.0380226	+	0.117021i	−0.930244	+	0.366942i	$0.880405\pi$
$570$		0			0
$571$	9.85310	−	30.3247i	0.412339	−	1.26905i	−0.502270	−	0.864711i	$-0.667501\pi$
$571$	9.85310	−	30.3247i	0.412339	−	1.26905i	0.914609	−	0.404339i	$-0.132499\pi$
$572$	−2.37144	−	0.770528i	−0.0991550	−	0.0322174i
$573$	−7.00730	−	9.64472i	−0.292734	−	0.402914i
$574$	−8.34102			−0.348147
$575$		0			0
$576$	1.00000			0.0416667
$577$	−21.7254	−	29.9024i	−0.904439	−	1.24485i	−0.969030	−	0.246942i	$-0.920574\pi$
$577$	−21.7254	−	29.9024i	−0.904439	−	1.24485i	0.0645913	−	0.997912i	$-0.479426\pi$
$578$	−13.5542	−	4.40401i	−0.563779	−	0.183183i
$579$	−3.64913	+	11.2309i	−0.151653	+	0.466739i
$580$		0			0
$581$	19.7177	+	60.6847i	0.818027	+	2.51763i
$582$		−	18.2706i		−	0.757341i
$583$	2.97930	−	0.968032i	0.123390	−	0.0400918i
$584$	5.84757	+	4.24851i	0.241974	+	0.175805i
$585$		0			0
$586$	0.407059	−	0.295746i	0.0168155	−	0.0122171i
$587$	−16.4935	+	22.7014i	−0.680761	+	0.936988i	−0.999943	−	0.0107059i	$-0.996592\pi$
$587$	−16.4935	+	22.7014i	−0.680761	+	0.936988i	0.319181	+	0.947694i	$0.396592\pi$
$588$	9.46727	−	13.0306i	0.390424	−	0.537372i
$589$	45.4402	−	33.0143i	1.87233	−	1.36033i
$590$		0			0
$591$	5.88837	+	4.27815i	0.242215	+	0.175980i
$592$	−1.66061	+	0.539565i	−0.0682507	+	0.0221760i
$593$		−	40.6263i		−	1.66832i	−0.551521	−	0.834161i	$-0.685952\pi$
$593$		−	40.6263i		−	1.66832i	0.551521	−	0.834161i	$-0.314048\pi$
$594$	0.272734	+	0.839389i	0.0111904	+	0.0344405i
$595$		0			0
$596$	0.899079	−	2.76708i	0.0368277	−	0.113344i
$597$	−2.16792	−	0.704401i	−0.0887272	−	0.0288292i
$598$	9.72029	+	13.3788i	0.397492	+	0.547101i
$599$	22.6989			0.927451			0.463725	−	0.885979i	$-0.346512\pi$
$599$	22.6989			0.927451			0.463725	+	0.885979i	$0.346512\pi$
$600$		0			0
$601$	32.9640			1.34463			0.672316	−	0.740265i	$-0.265300\pi$
$601$	32.9640			1.34463			0.672316	+	0.740265i	$0.265300\pi$
$602$	−6.41805	−	8.83368i	−0.261580	−	0.360034i
$603$	11.3751	+	3.69601i	0.463232	+	0.150513i
$604$	0.414651	−	1.27616i	0.0168719	−	0.0519264i
$605$		0			0
$606$	−1.68757	−	5.19382i	−0.0685530	−	0.210984i
$607$		−	8.32854i		−	0.338045i	−0.985612	−	0.169023i	$-0.945939\pi$
$607$		−	8.32854i		−	0.338045i	0.985612	−	0.169023i	$-0.0540611\pi$
$608$	−5.11563	+	1.66217i	−0.207466	+	0.0674098i
$609$	−13.9155	−	10.1102i	−0.563885	−	0.409686i
$610$		0			0
$611$	−19.9409	+	14.4879i	−0.806724	+	0.586120i
$612$	−0.974432	+	1.34119i	−0.0393891	+	0.0542144i
$613$	−4.33351	+	5.96457i	−0.175029	+	0.240907i	−0.887514	−	0.460780i	$-0.847570\pi$
$613$	−4.33351	+	5.96457i	−0.175029	+	0.240907i	0.712485	+	0.701687i	$0.247570\pi$
$614$	−6.98485	+	5.07479i	−0.281886	+	0.204802i
$615$		0			0
$616$	−3.43228	−	2.49370i	−0.138291	−	0.100474i
$617$	−8.43210	+	2.73975i	−0.339463	+	0.110298i	−0.473788	−	0.880639i	$-0.657114\pi$
$617$	−8.43210	+	2.73975i	−0.339463	+	0.110298i	0.134324	+	0.990937i	$0.457114\pi$
$618$		−	6.64235i		−	0.267194i
$619$	0.139486	+	0.429292i	0.00560640	+	0.0172547i	0.953821	−	0.300377i	$-0.0971125\pi$
$619$	0.139486	+	0.429292i	0.00560640	+	0.0172547i	−0.948214	+	0.317632i	$0.897112\pi$
$620$		0			0
$621$	1.80881	−	5.56695i	0.0725851	−	0.223394i
$622$	−19.2755	−	6.26298i	−0.772875	−	0.251122i
$623$	52.7980	+	72.6703i	2.11531	+	2.91147i
$624$	2.82520			0.113099
$625$		0			0
$626$	−17.0302			−0.680664
$627$	−2.79041	−	3.84067i	−0.111438	−	0.153382i
$628$	−7.90489	−	2.56845i	−0.315439	−	0.102492i
$629$	0.894493	−	2.75297i	0.0356658	−	0.109768i
$630$		0			0
$631$	−9.74952	−	30.0059i	−0.388122	−	1.19452i	−0.934190	−	0.356776i	$-0.883876\pi$
$631$	−9.74952	−	30.0059i	−0.388122	−	1.19452i	0.546068	−	0.837741i	$-0.316124\pi$
$632$			12.5762i			0.500256i
$633$	1.18806	−	0.386023i	0.0472210	−	0.0153430i
$634$	−2.28270	−	1.65848i	−0.0906575	−	0.0658665i
$635$		0			0
$636$	−2.87150	+	2.08626i	−0.113862	+	0.0827257i
$637$	26.7469	−	36.8140i	1.05975	−	1.45862i
$638$	−1.85630	+	2.55498i	−0.0734916	+	0.101153i
$639$	−2.83769	+	2.06170i	−0.112257	+	0.0815598i
$640$		0			0
$641$	−15.1110	−	10.9788i	−0.596848	−	0.433635i	0.247911	−	0.968783i	$-0.420256\pi$
$641$	−15.1110	−	10.9788i	−0.596848	−	0.433635i	−0.844759	+	0.535147i	$0.820256\pi$
$642$	13.8137	−	4.48833i	0.545182	−	0.177140i
$643$			15.5969i			0.615083i	0.951535	+	0.307541i	$0.0995063\pi$
$643$			15.5969i			0.615083i	−0.951535	+	0.307541i	$0.900494\pi$
$644$	8.69485	+	26.7600i	0.342625	+	1.05449i
$645$		0			0
$646$	2.75555	−	8.48070i	0.108416	−	0.333669i
$647$	−25.0683	−	8.14520i	−0.985538	−	0.320221i	−0.228466	−	0.973552i	$-0.573371\pi$
$647$	−25.0683	−	8.14520i	−0.985538	−	0.320221i	−0.757072	+	0.653331i	$0.773371\pi$
$648$	−0.587785	−	0.809017i	−0.0230904	−	0.0317812i
$649$	9.13798			0.358697
$650$		0			0
$651$	−50.1948			−1.96729
$652$	−3.66704	−	5.04724i	−0.143612	−	0.197665i
$653$	18.6583	+	6.06245i	0.730156	+	0.237242i	0.650421	−	0.759574i	$-0.274593\pi$
$653$	18.6583	+	6.06245i	0.730156	+	0.237242i	0.0797351	+	0.996816i	$0.474593\pi$
$654$	−1.47421	+	4.53716i	−0.0576462	+	0.177417i
$655$		0			0
$656$	−0.536207	−	1.65028i	−0.0209354	−	0.0644324i
$657$		−	7.22800i		−	0.281991i
$658$	−39.8854	+	12.9596i	−1.55489	+	0.505216i
$659$	18.7179	+	13.5993i	0.729145	+	0.529755i	0.889293	−	0.457338i	$-0.151197\pi$
$659$	18.7179	+	13.5993i	0.729145	+	0.529755i	−0.160148	+	0.987093i	$0.551197\pi$
$660$		0			0
$661$	−14.1554	+	10.2845i	−0.550581	+	0.400021i	−0.828000	−	0.560729i	$-0.810521\pi$
$661$	−14.1554	+	10.2845i	−0.550581	+	0.400021i	0.277419	+	0.960749i	$0.410521\pi$
$662$	2.39404	−	3.29512i	0.0930472	−	0.128068i
$663$	−2.75297	+	3.78913i	−0.106916	+	0.147158i
$664$	−10.7390	+	7.80231i	−0.416752	+	0.302788i
$665$		0			0
$666$	1.41260	+	1.02631i	0.0547372	+	0.0397689i
$667$	19.9200	−	6.47241i	0.771306	−	0.250613i
$668$			14.8368i			0.574054i
$669$	−2.73237	−	8.40936i	−0.105639	−	0.325125i
$670$		0			0
$671$	0.0235244	−	0.0724006i	0.000908149	−	0.00279500i
$672$	4.57167	+	1.48543i	0.176356	+	0.0573016i
$673$	−0.608086	−	0.836959i	−0.0234400	−	0.0322624i	0.797136	−	0.603800i	$-0.206347\pi$
$673$	−0.608086	−	0.836959i	−0.0234400	−	0.0322624i	−0.820576	+	0.571537i	$0.806347\pi$
$674$	9.04782			0.348509
$675$		0			0
$676$	−5.01824			−0.193009
$677$	−5.53353	−	7.61625i	−0.212671	−	0.292716i	0.689333	−	0.724445i	$-0.257904\pi$
$677$	−5.53353	−	7.61625i	−0.212671	−	0.292716i	−0.902004	+	0.431729i	$0.857904\pi$
$678$	−4.59891	−	1.49428i	−0.176620	−	0.0573873i
$679$	27.1396	−	83.5272i	1.04152	−	3.20548i
$680$		0			0
$681$	−5.46860	−	16.8306i	−0.209557	−	0.644950i
$682$			9.21610i			0.352903i
$683$	−13.1823	+	4.28318i	−0.504405	+	0.163891i	−0.550156	−	0.835062i	$-0.685432\pi$
$683$	−13.1823	+	4.28318i	−0.504405	+	0.163891i	0.0457510	+	0.998953i	$0.485432\pi$
$684$	4.35161	+	3.16163i	0.166388	+	0.120888i
$685$		0			0
$686$	35.4149	−	25.7305i	1.35215	−	0.982394i
$687$	5.23930	−	7.21128i	0.199892	−	0.275128i
$688$	1.33516	−	1.83769i	0.0509026	−	0.0700614i
$689$	−8.11255	+	5.89411i	−0.309064	+	0.224548i
$690$		0			0
$691$	7.36726	+	5.35263i	0.280264	+	0.203624i	0.719032	−	0.694977i	$-0.244585\pi$
$691$	7.36726	+	5.35263i	0.280264	+	0.203624i	−0.438769	+	0.898600i	$0.644585\pi$
$692$	−15.2520	+	4.95566i	−0.579793	+	0.188386i
$693$			4.24254i			0.161161i
$694$	−2.68429	−	8.26141i	−0.101894	−	0.313599i
$695$		0			0
$696$	1.10574	−	3.40313i	0.0419131	−	0.128995i
$697$	2.73583	+	0.888926i	0.103627	+	0.0336705i
$698$	−15.7706	−	21.7063i	−0.596925	−	0.821596i
$699$	9.59063			0.362751
$700$		0			0
$701$	−22.6848			−0.856791			−0.428396	−	0.903591i	$-0.640921\pi$
$701$	−22.6848			−0.856791			−0.428396	+	0.903591i	$0.640921\pi$
$702$	−1.66061	−	2.28564i	−0.0626757	−	0.0862657i
$703$	−8.93224	−	2.90226i	−0.336886	−	0.109461i
$704$	0.272734	−	0.839389i	0.0102790	−	0.0316357i
$705$		0			0
$706$	−8.76060	−	26.9623i	−0.329709	−	1.01474i
$707$		−	26.2512i		−	0.987278i
$708$	−9.84690	+	3.19945i	−0.370069	+	0.120243i
$709$	18.1615	+	13.1951i	0.682069	+	0.495552i	0.874043	−	0.485848i	$-0.161489\pi$
$709$	18.1615	+	13.1951i	0.682069	+	0.495552i	−0.191974	+	0.981400i	$0.561489\pi$
$710$		0			0
$711$	10.1744	−	7.39213i	0.381570	−	0.277227i
$712$	−10.9837	+	15.1178i	−0.411632	+	0.566563i
$713$	35.9269	−	49.4492i	1.34547	−	1.85189i
$714$	−6.44702	+	4.68404i	−0.241274	+	0.175296i
$715$		0			0
$716$	−9.50506	−	6.90583i	−0.355221	−	0.258083i
$717$	−8.71452	+	2.83152i	−0.325450	+	0.105745i
$718$			8.68830i			0.324245i
$719$	−14.1238	−	43.4684i	−0.526727	−	1.62110i	−0.760875	−	0.648898i	$-0.775230\pi$
$719$	−14.1238	−	43.4684i	−0.526727	−	1.62110i	0.234148	−	0.972201i	$-0.424770\pi$
$720$		0			0
$721$	9.86672	−	30.3666i	0.367456	−	1.13091i
$722$	−9.44630	−	3.06929i	−0.351555	−	0.114227i
$723$	1.46682	+	2.01891i	0.0545517	+	0.0750840i
$724$	4.03402			0.149923
$725$		0			0
$726$	−10.2210			−0.379338
$727$	1.28973	+	1.77517i	0.0478336	+	0.0658373i	0.832264	−	0.554380i	$-0.187044\pi$
$727$	1.28973	+	1.77517i	0.0478336	+	0.0658373i	−0.784430	+	0.620217i	$0.787044\pi$
$728$	12.9159	+	4.19663i	0.478695	+	0.155537i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	1.16367	+	3.58141i	0.0430400	+	0.132463i
$732$			0.0862540i			0.00318804i
$733$	−8.72887	+	2.83618i	−0.322408	+	0.104757i	−0.465750	−	0.884917i	$-0.654215\pi$
$733$	−8.72887	+	2.83618i	−0.322408	+	0.104757i	0.143342	+	0.989673i	$0.454215\pi$
$734$	−10.0895	−	7.33046i	−0.372411	−	0.270572i
$735$		0			0
$736$	−4.73553	+	3.44056i	−0.174554	+	0.126821i
$737$	6.20478	−	8.54014i	0.228556	−	0.314580i
$738$	−1.01993	+	1.40381i	−0.0375440	+	0.0516749i
$739$	−35.2025	+	25.5761i	−1.29495	+	0.940833i	−0.999893	−	0.0146478i	$-0.995337\pi$
$739$	−35.2025	+	25.5761i	−1.29495	+	0.940833i	−0.295053	+	0.955481i	$0.595337\pi$
$740$		0			0
$741$	12.2942	+	8.93224i	0.451638	+	0.328134i
$742$	−16.2265	+	5.27232i	−0.595695	+	0.193553i
$743$		−	8.61668i		−	0.316115i	−0.987430	−	0.158058i	$-0.949477\pi$
$743$		−	8.61668i		−	0.316115i	0.987430	−	0.158058i	$-0.0505232\pi$
$744$	−3.22681	−	9.93109i	−0.118300	−	0.364091i
$745$		0			0
$746$	−4.01684	+	12.3626i	−0.147067	+	0.452625i
$747$	12.6244	+	4.10192i	0.461903	+	0.150081i
$748$	0.860020	+	1.18372i	0.0314454	+	0.0432809i
$749$	69.8186			2.55112
$750$		0			0
$751$	1.11603			0.0407245			0.0203623	−	0.999793i	$-0.493518\pi$
$751$	1.11603			0.0407245			0.0203623	+	0.999793i	$0.493518\pi$
$752$	−5.12811	−	7.05824i	−0.187003	−	0.257388i
$753$	8.28619	+	2.69235i	0.301966	+	0.0981146i
$754$	3.12395	−	9.61453i	0.113768	−	0.350141i
$755$		0			0
$756$	−1.48543	−	4.57167i	−0.0540244	−	0.166270i
$757$			37.2729i			1.35471i	0.735658	+	0.677354i	$0.236873\pi$
$757$			37.2729i			1.35471i	−0.735658	+	0.677354i	$0.763127\pi$
$758$	−1.66651	+	0.541481i	−0.0605302	+	0.0196675i
$759$	−4.17951	−	3.03659i	−0.151707	−	0.110221i
$760$		0			0
$761$	16.1999	−	11.7699i	0.587245	−	0.426659i	−0.254084	−	0.967182i	$-0.581774\pi$
$761$	16.1999	−	11.7699i	0.587245	−	0.426659i	0.841329	+	0.540524i	$0.181774\pi$
$762$	1.05908	−	1.45769i	0.0383663	−	0.0528067i
$763$	−13.4792	+	18.5526i	−0.487981	+	0.671648i
$764$	9.64472	−	7.00730i	0.348934	−	0.253515i
$765$		0			0
$766$	−27.6165	−	20.0646i	−0.997825	−	0.724962i
$767$	−27.8195	+	9.03910i	−1.00450	+	0.326383i
$768$			1.00000i			0.0360844i
$769$	4.78043	+	14.7126i	0.172387	+	0.530552i	0.999504	−	0.0314770i	$-0.0100211\pi$
$769$	4.78043	+	14.7126i	0.172387	+	0.530552i	−0.827118	+	0.562029i	$0.810021\pi$
$770$		0			0
$771$	−6.11455	+	18.8187i	−0.220210	+	0.677738i
$772$	−11.2309	−	3.64913i	−0.404208	−	0.131335i
$773$	14.1408	+	19.4632i	0.508610	+	0.700042i	0.983684	−	0.179904i	$-0.0575787\pi$
$773$	14.1408	+	19.4632i	0.508610	+	0.700042i	−0.475074	+	0.879946i	$0.657579\pi$
$774$	−2.27151			−0.0816479
$775$		0			0
$776$	18.2706			0.655876
$777$	4.93343	+	6.79029i	0.176986	+	0.243600i
$778$	6.52094	+	2.11878i	0.233787	+	0.0759620i
$779$	2.88420	−	8.87665i	0.103337	−	0.318039i
$780$		0			0
$781$	0.956637	+	2.94422i	0.0342311	+	0.105353i
$782$		−	9.70385i		−	0.347009i
$783$	−3.40313	+	1.10574i	−0.121618	+	0.0395161i
$784$	13.0306	+	9.46727i	0.465378	+	0.338117i
$785$		0			0
$786$	12.9697	−	9.42306i	0.462615	−	0.336109i
$787$	19.6062	−	26.9857i	0.698887	−	0.961935i	−0.301079	−	0.953599i	$-0.597347\pi$
$787$	19.6062	−	26.9857i	0.698887	−	0.961935i	0.999965	−	0.00833555i	$-0.00265332\pi$
$788$	−4.27815	+	5.88837i	−0.152403	+	0.209764i
$789$	20.6813	−	15.0258i	0.736273	−	0.534933i
$790$		0			0
$791$	−18.8051	−	13.6627i	−0.668631	−	0.485789i
$792$	−0.839389	+	0.272734i	−0.0298264	+	0.00969118i
$793$			0.243685i			0.00865350i
$794$	10.2466	+	31.5358i	0.363638	+	1.11916i
$795$		0			0
$796$	0.704401	−	2.16792i	0.0249668	−	0.0768400i
$797$	31.0587	+	10.0916i	1.10016	+	0.357462i	0.802162	−	0.597106i	$-0.203683\pi$
$797$	31.0587	+	10.0916i	1.10016	+	0.357462i	0.297993	+	0.954568i	$0.403683\pi$
$798$	15.1978	+	20.9179i	0.537995	+	0.740487i
$799$	14.4634			0.511680
$800$		0			0
$801$	18.6866			0.660259
$802$	2.06566	+	2.84314i	0.0729411	+	0.100395i
$803$	−6.06710	−	1.97132i	−0.214103	−	0.0695664i
$804$	−3.69601	+	11.3751i	−0.130348	+	0.401170i
$805$		0			0
$806$	−9.11637	−	28.0573i	−0.321111	−	0.988277i
$807$		−	24.4144i		−	0.859428i
$808$	5.19382	−	1.68757i	0.182718	−	0.0593686i
$809$	8.36995	+	6.08113i	0.294272	+	0.213801i	0.725118	−	0.688624i	$-0.241785\pi$
$809$	8.36995	+	6.08113i	0.294272	+	0.213801i	−0.430847	+	0.902425i	$0.641785\pi$
$810$		0			0
$811$	30.7731	−	22.3580i	1.08059	−	0.785094i	0.102804	−	0.994702i	$-0.467219\pi$
$811$	30.7731	−	22.3580i	1.08059	−	0.785094i	0.977786	+	0.209607i	$0.0672186\pi$
$812$	10.1102	−	13.9155i	0.354799	−	0.488338i
$813$	1.61436	−	2.22198i	0.0566181	−	0.0779282i
$814$	1.24674	−	0.905810i	0.0436982	−	0.0317486i
$815$		0			0
$816$	−1.34119	−	0.974432i	−0.0469511	−	0.0341119i
$817$	11.6202	−	3.77564i	0.406540	−	0.132093i
$818$		−	16.2848i		−	0.569383i
$819$	−4.19663	−	12.9159i	−0.146642	−	0.451318i
$820$		0			0
$821$	−6.18062	+	19.0220i	−0.215705	+	0.663872i	0.783398	+	0.621521i	$0.213485\pi$
$821$	−6.18062	+	19.0220i	−0.215705	+	0.663872i	−0.999103	+	0.0423510i	$0.986515\pi$
$822$	1.68069	+	0.546090i	0.0586209	+	0.0190471i
$823$	23.0591	+	31.7381i	0.803790	+	1.10632i	0.992252	+	0.124242i	$0.0396498\pi$
$823$	23.0591	+	31.7381i	0.803790	+	1.10632i	−0.188462	+	0.982080i	$0.560350\pi$
$824$	6.64235			0.231397
$825$		0			0
$826$	−49.7694			−1.73170
$827$	32.2736	+	44.4208i	1.12226	+	1.54466i	0.801991	+	0.597336i	$0.203774\pi$
$827$	32.2736	+	44.4208i	1.12226	+	1.54466i	0.320271	+	0.947326i	$0.396226\pi$
$828$	5.56695	+	1.80881i	0.193465	+	0.0628606i
$829$	2.01553	−	6.20315i	0.0700021	−	0.215444i	−0.909935	−	0.414751i	$-0.863869\pi$
$829$	2.01553	−	6.20315i	0.0700021	−	0.215444i	0.979937	+	0.199306i	$0.0638689\pi$
$830$		0			0
$831$	0.921114	+	2.83490i	0.0319531	+	0.0983415i
$832$			2.82520i			0.0979462i
$833$	−25.3948	+	8.25128i	−0.879879	+	0.285890i
$834$	8.89636	+	6.46359i	0.308056	+	0.223816i
$835$		0			0
$836$	3.84067	−	2.79041i	0.132832	−	0.0965083i
$837$	−6.13775	+	8.44789i	−0.212152	+	0.292002i
$838$	15.5693	−	21.4294i	0.537834	−	0.740265i
$839$	−35.1557	+	25.5421i	−1.21371	+	0.881811i	−0.995562	−	0.0941047i	$-0.970001\pi$
$839$	−35.1557	+	25.5421i	−1.21371	+	0.881811i	−0.218147	+	0.975916i	$0.570001\pi$
$840$		0			0
$841$	13.1029	+	9.51978i	0.451823	+	0.328268i
$842$	−29.4373	+	9.56476i	−1.01448	+	0.329624i
$843$			3.86174i			0.133006i
$844$	0.386023	+	1.18806i	0.0132875	+	0.0408946i
$845$		0			0
$846$	−2.69601	+	8.29746i	−0.0926907	+	0.285273i
$847$	−46.7273	−	15.1826i	−1.60557	−	0.521681i
$848$	−2.08626	−	2.87150i	−0.0716426	−	0.0986076i
$849$	16.7019			0.573208
$850$		0			0
$851$	−10.2205			−0.350355
$852$	−2.06170	−	2.83769i	−0.0706328	−	0.0972178i
$853$	19.8410	+	6.44673i	0.679343	+	0.220732i	0.628307	−	0.777965i	$-0.283748\pi$
$853$	19.8410	+	6.44673i	0.679343	+	0.220732i	0.0510350	+	0.998697i	$0.483748\pi$
$854$	−0.128124	+	0.394325i	−0.00438431	+	0.0134935i
$855$		0			0
$856$	4.48833	+	13.8137i	0.153408	+	0.472141i
$857$			10.2125i			0.348854i	0.984670	+	0.174427i	$0.0558073\pi$
$857$			10.2125i			0.348854i	−0.984670	+	0.174427i	$0.944193\pi$
$858$	−2.37144	+	0.770528i	−0.0809597	+	0.0263054i
$859$	2.14672	+	1.55969i	0.0732453	+	0.0532158i	0.623805	−	0.781580i	$-0.285586\pi$
$859$	2.14672	+	1.55969i	0.0732453	+	0.0532158i	−0.550560	+	0.834796i	$0.685586\pi$
$860$		0			0
$861$	−6.74802	+	4.90273i	−0.229972	+	0.167084i
$862$	1.01265	−	1.39379i	0.0344910	−	0.0474727i
$863$	1.31766	−	1.81361i	0.0448538	−	0.0617360i	−0.786001	−	0.618225i	$-0.787852\pi$
$863$	1.31766	−	1.81361i	0.0448538	−	0.0617360i	0.830855	+	0.556489i	$0.187852\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$		0			0
$866$	−19.5282	−	14.1881i	−0.663595	−	0.482130i
$867$	−13.5542	+	4.40401i	−0.460323	+	0.149568i
$868$		−	50.1948i		−	1.70372i
$869$	−3.42997	−	10.5564i	−0.116354	−	0.358100i
$870$		0			0
$871$	−10.4420	+	32.1371i	−0.353812	+	1.08892i
$872$	−4.53716	−	1.47421i	−0.153648	−	0.0499231i
$873$	−10.7392	−	14.7812i	−0.363467	−	0.500269i
$874$	−31.4850			−1.06500
$875$		0			0
$876$	7.22800			0.244211
$877$	−30.0466	−	41.3556i	−1.01460	−	1.39648i	−0.915921	−	0.401359i	$-0.868538\pi$
$877$	−30.0466	−	41.3556i	−1.01460	−	1.39648i	−0.0986803	−	0.995119i	$-0.531462\pi$
$878$	7.83987	+	2.54733i	0.264583	+	0.0859682i
$879$	0.155483	−	0.478527i	0.00524430	−	0.0161403i
$880$		0			0
$881$	−14.5343	−	44.7321i	−0.489674	−	1.50706i	−0.825096	−	0.564993i	$-0.808879\pi$
$881$	−14.5343	−	44.7321i	−0.489674	−	1.50706i	0.335422	−	0.942068i	$-0.391121\pi$
$882$		−	16.1067i		−	0.542340i
$883$	−25.2883	+	8.21666i	−0.851018	+	0.276513i	−0.701873	−	0.712303i	$-0.747652\pi$
$883$	−25.2883	+	8.21666i	−0.851018	+	0.276513i	−0.149146	+	0.988815i	$0.547652\pi$
$884$	−3.78913	−	2.75297i	−0.127442	−	0.0925923i
$885$		0			0
$886$	−18.1747	+	13.2047i	−0.610591	+	0.443621i
$887$	28.1751	−	38.7797i	0.946027	−	1.30209i	−0.00724276	−	0.999974i	$-0.502305\pi$
$887$	28.1751	−	38.7797i	0.946027	−	1.30209i	0.953270	−	0.302121i	$-0.0976945\pi$
$888$	−1.02631	+	1.41260i	−0.0344409	+	0.0474038i
$889$	7.00705	−	5.09092i	0.235009	−	0.170744i
$890$		0			0
$891$	0.714027	+	0.518771i	0.0239208	+	0.0173795i
$892$	8.40936	−	2.73237i	0.281566	−	0.0914864i
$893$		−	46.9279i		−	1.57038i
$894$	−0.899079	−	2.76708i	−0.0300697	−	0.0925451i
$895$		0			0
$896$	−1.48543	+	4.57167i	−0.0496246	+	0.152729i
$897$	15.7278	+	5.11026i	0.525134	+	0.170627i
$898$	−17.9267	−	24.6740i	−0.598223	−	0.823383i
$899$	−37.3648			−1.24619
$900$		0			0
$901$	5.88415			0.196029
$902$	0.900172	+	1.23898i	0.0299725	+	0.0412536i
$903$	−10.3846	−	3.37417i	−0.345578	−	0.112285i
$904$	1.49428	−	4.59891i	0.0496989	−	0.152957i
$905$		0			0
$906$	−0.414651	−	1.27616i	−0.0137759	−	0.0423977i
$907$		−	5.35392i		−	0.177774i	−0.996042	−	0.0888870i	$-0.971669\pi$
$907$		−	5.35392i		−	0.177774i	0.996042	−	0.0888870i	$-0.0283310\pi$
$908$	16.8306	−	5.46860i	0.558543	−	0.181482i
$909$	−4.41813	−	3.20996i	−0.146540	−	0.106468i
$910$		0			0
$911$	10.9464	−	7.95304i	0.362671	−	0.263496i	−0.391494	−	0.920181i	$-0.628042\pi$
$911$	10.9464	−	7.95304i	0.362671	−	0.263496i	0.754165	+	0.656685i	$0.228042\pi$
$912$	−3.16163	+	4.35161i	−0.104692	+	0.144096i
$913$	6.88620	−	9.47805i	0.227900	−	0.313678i
$914$	−5.38217	+	3.91037i	−0.178026	+	0.129344i
$915$		0			0
$916$	7.21128	+	5.23930i	0.238267	+	0.173111i
$917$	73.2906	−	23.8136i	2.42027	−	0.786393i
$918$			1.65780i			0.0547156i
$919$	17.2285	+	53.0240i	0.568317	+	1.74910i	0.657884	+	0.753119i	$0.271452\pi$
$919$	17.2285	+	53.0240i	0.568317	+	1.74910i	−0.0895666	+	0.995981i	$0.528548\pi$
$920$		0			0
$921$	−2.66798	+	8.21118i	−0.0879128	+	0.270568i
$922$	22.5097	+	7.31386i	0.741319	+	0.240869i
$923$	−5.82473	−	8.01705i	−0.191723	−	0.263885i
$924$	−4.24254			−0.139569
$925$		0			0
$926$	26.0857			0.857229
$927$	−3.90427	−	5.37377i	−0.128233	−	0.176498i
$928$	3.40313	+	1.10574i	0.111713	+	0.0362979i
$929$	16.0123	−	49.2807i	0.525346	−	1.61685i	−0.238284	−	0.971195i	$-0.576585\pi$
$929$	16.0123	−	49.2807i	0.525346	−	1.61685i	0.763631	−	0.645653i	$-0.223415\pi$
$930$		0			0
$931$	26.7720	+	82.3958i	0.877417	+	2.70041i
$932$			9.59063i			0.314151i
$933$	−19.2755	+	6.26298i	−0.631050	+	0.205041i
$934$	−1.19380	−	0.867350i	−0.0390625	−	0.0283805i
$935$		0			0
$936$	2.28564	−	1.66061i	0.0747083	−	0.0542788i
$937$	−23.4907	+	32.3322i	−0.767409	+	1.05625i	0.229152	+	0.973391i	$0.426405\pi$
$937$	−23.4907	+	32.3322i	−0.767409	+	1.05625i	−0.996561	+	0.0828575i	$0.973595\pi$
$938$	−33.7939	+	46.5133i	−1.10341	+	1.51871i
$939$	−13.7777	+	10.0101i	−0.449619	+	0.326667i
$940$		0			0
$941$	12.2262	+	8.88288i	0.398564	+	0.289574i	0.768956	−	0.639302i	$-0.220777\pi$
$941$	12.2262	+	8.88288i	0.398564	+	0.289574i	−0.370392	+	0.928876i	$0.620777\pi$
$942$	−7.90489	+	2.56845i	−0.257555	+	0.0836848i
$943$		−	10.1569i		−	0.330754i
$944$	−3.19945	−	9.84690i	−0.104133	−	0.320489i
$945$		0			0
$946$	−0.619519	+	1.90668i	−0.0201423	+	0.0619916i
$947$	−32.3992	−	10.5272i	−1.05283	−	0.342087i	−0.269054	−	0.963125i	$-0.586711\pi$
$947$	−32.3992	−	10.5272i	−1.05283	−	0.342087i	−0.783780	+	0.621039i	$0.786711\pi$
$948$	7.39213	+	10.1744i	0.240085	+	0.330449i
$949$	20.4205			0.662879
$950$		0			0
$951$	−2.82157			−0.0914956
$952$	−4.68404	−	6.44702i	−0.151811	−	0.208949i
$953$	−31.7376	−	10.3122i	−1.02808	−	0.334044i	−0.254050	−	0.967191i	$-0.581763\pi$
$953$	−31.7376	−	10.3122i	−1.02808	−	0.334044i	−0.774031	+	0.633147i	$0.781763\pi$
$954$	−1.09681	+	3.37565i	−0.0355107	+	0.109291i
$955$		0			0
$956$	−2.83152	−	8.71452i	−0.0915779	−	0.281848i
$957$			3.15813i			0.102088i
$958$	12.7536	−	4.14388i	0.412049	−	0.133883i
$959$	6.87240	+	4.99309i	0.221921	+	0.161235i
$960$		0			0
$961$	−63.1347	+	45.8700i	−2.03660	+	1.47968i
$962$	−2.89954	+	3.99088i	−0.0934850	+	0.128671i
$963$	8.53731	−	11.7506i	0.275111	−	0.378658i
$964$	−2.01891	+	1.46682i	−0.0650247	+	0.0472432i
$965$		0			0
$966$	22.7634	+	16.5386i	0.732401	+	0.532120i
$967$	25.1661	−	8.17697i	0.809288	−	0.262954i	0.124992	−	0.992158i	$-0.460110\pi$
$967$	25.1661	−	8.17697i	0.809288	−	0.262954i	0.684296	+	0.729204i	$0.260110\pi$
$968$		−	10.2210i		−	0.328517i
$969$	−2.75555	−	8.48070i	−0.0885209	−	0.272439i
$970$		0			0
$971$	9.76352	−	30.0490i	0.313326	−	0.964319i	−0.663112	−	0.748520i	$-0.730765\pi$
$971$	9.76352	−	30.0490i	0.313326	−	0.964319i	0.976438	−	0.215798i	$-0.0692354\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	31.0701	+	42.7643i	0.996061	+	1.37096i
$974$	2.12008			0.0679318
$975$		0			0
$976$	−0.0862540			−0.00276092
$977$	−2.72764	−	3.75428i	−0.0872650	−	0.120110i	0.763152	−	0.646219i	$-0.223651\pi$
$977$	−2.72764	−	3.75428i	−0.0872650	−	0.120110i	−0.850417	+	0.526109i	$0.823651\pi$
$978$	−5.93339	−	1.92788i	−0.189729	−	0.0616467i
$979$	5.09647	−	15.6853i	0.162884	−	0.501305i
$980$		0			0
$981$	1.47421	+	4.53716i	0.0470679	+	0.144860i
$982$			2.22427i			0.0709793i
$983$	−32.3253	+	10.5031i	−1.03102	+	0.334998i	−0.775192	−	0.631725i	$-0.782347\pi$
$983$	−32.3253	+	10.5031i	−1.03102	+	0.334998i	−0.255825	+	0.966723i	$0.582347\pi$
$984$	−1.40381	−	1.01993i	−0.0447518	−	0.0325141i
$985$		0			0
$986$	−4.79914	+	3.48678i	−0.152836	+	0.111042i
$987$	−24.6505	+	33.9285i	−0.784635	+	1.07996i
$988$	−8.93224	+	12.2942i	−0.284172	+	0.391130i
$989$	10.7568	−	7.81529i	0.342047	−	0.248512i
$990$		0			0
$991$	44.5440	+	32.3631i	1.41499	+	1.02805i	0.992574	+	0.121643i	$0.0388162\pi$
$991$	44.5440	+	32.3631i	1.41499	+	1.02805i	0.422411	+	0.906404i	$0.361184\pi$
$992$	9.93109	−	3.22681i	0.315312	−	0.102451i
$993$		−	4.07299i		−	0.129252i
$994$	−5.21025	−	16.0355i	−0.165259	−	0.508616i
$995$		0			0
$996$	−4.10192	+	12.6244i	−0.129974	+	0.400019i
$997$	0.695101	+	0.225852i	0.0220141	+	0.00715280i	0.320003	−	0.947416i	$-0.396316\pi$
$997$	0.695101	+	0.225852i	0.0220141	+	0.00715280i	−0.297989	+	0.954569i	$0.596316\pi$
$998$	−8.55710	−	11.7778i	−0.270870	−	0.372821i
$999$	1.74607			0.0552432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.h.d.199.4		16
5.2	odd	4		750.2.g.f.301.1		16
5.3	odd	4		750.2.g.g.301.4		16
5.4	even	2		150.2.h.b.139.2	yes	16
15.14	odd	2		450.2.l.c.289.3		16
25.3	odd	20		3750.2.a.u.1.8		8
25.4	even	10		3750.2.c.k.1249.9		16
25.9	even	10	inner	750.2.h.d.49.3		16
25.12	odd	20		750.2.g.f.451.1		16
25.13	odd	20		750.2.g.g.451.4		16
25.16	even	5		150.2.h.b.109.2	✓	16
25.21	even	5		3750.2.c.k.1249.8		16
25.22	odd	20		3750.2.a.v.1.1		8
75.41	odd	10		450.2.l.c.109.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.2	✓	16	25.16	even	5
150.2.h.b.139.2	yes	16	5.4	even	2
450.2.l.c.109.3		16	75.41	odd	10
450.2.l.c.289.3		16	15.14	odd	2
750.2.g.f.301.1		16	5.2	odd	4
750.2.g.f.451.1		16	25.12	odd	20
750.2.g.g.301.4		16	5.3	odd	4
750.2.g.g.451.4		16	25.13	odd	20
750.2.h.d.49.3		16	25.9	even	10	inner
750.2.h.d.199.4		16	1.1	even	1	trivial
3750.2.a.u.1.8		8	25.3	odd	20
3750.2.a.v.1.1		8	25.22	odd	20
3750.2.c.k.1249.8		16	25.21	even	5
3750.2.c.k.1249.9		16	25.4	even	10

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.714027 - 0.518771i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(-1.66061 + 2.28564i) q^{13} +(-3.88890 + 2.82545i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.57666 - 0.512289i) q^{17} +1.00000i q^{18} +(-1.66217 - 5.11563i) q^{19} +(-1.48543 + 4.57167i) q^{21} +(0.839389 + 0.272734i) q^{22} +(-3.44056 - 4.73553i) q^{23} -1.00000 q^{24} -2.82520 q^{26} +(0.587785 + 0.809017i) q^{27} +(-4.57167 - 1.48543i) q^{28} +(-1.10574 + 3.40313i) q^{29} +(3.22681 + 9.93109i) q^{31} -1.00000i q^{32} +(0.839389 - 0.272734i) q^{33} +(1.34119 + 0.974432i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(1.02631 - 1.41260i) q^{37} +(3.16163 - 4.35161i) q^{38} +(-2.28564 + 1.66061i) q^{39} +(1.40381 + 1.01993i) q^{41} +(-4.57167 + 1.48543i) q^{42} +2.27151i q^{43} +(0.272734 + 0.839389i) q^{44} +(1.80881 - 5.56695i) q^{46} +(8.29746 + 2.69601i) q^{47} +(-0.587785 - 0.809017i) q^{48} -16.1067 q^{49} +1.65780 q^{51} +(-1.66061 - 2.28564i) q^{52} +(3.37565 + 1.09681i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.48543 - 4.57167i) q^{56} -5.37889i q^{57} +(-3.40313 + 1.10574i) q^{58} +(8.37628 + 6.08572i) q^{59} +(0.0697810 - 0.0506988i) q^{61} +(-6.13775 + 8.44789i) q^{62} +(-2.82545 + 3.88890i) q^{63} +(0.809017 - 0.587785i) q^{64} +(0.714027 + 0.518771i) q^{66} +(11.3751 - 3.69601i) q^{67} +1.65780i q^{68} +(-1.80881 - 5.56695i) q^{69} +(-1.08390 + 3.33591i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-4.24851 - 5.84757i) q^{73} +1.74607 q^{74} +5.37889 q^{76} +(2.49370 + 3.43228i) q^{77} +(-2.68693 - 0.873035i) q^{78} +(3.88627 - 11.9607i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.73520i q^{82} +(12.6244 - 4.10192i) q^{83} +(-3.88890 - 2.82545i) q^{84} +(-1.83769 + 1.33516i) q^{86} +(-2.10325 + 2.89488i) q^{87} +(-0.518771 + 0.714027i) q^{88} +(15.1178 - 10.9837i) q^{89} +(-10.9869 - 7.98246i) q^{91} +(5.56695 - 1.80881i) q^{92} +10.4422i q^{93} +(2.69601 + 8.29746i) q^{94} +(0.309017 - 0.951057i) q^{96} +(-17.3764 - 5.64593i) q^{97} +(-9.46727 - 13.0306i) q^{98} +0.882586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9} + 2 q^{11} - 20 q^{13} + 2 q^{14} - 4 q^{16} + 30 q^{17} - 2 q^{21} + 20 q^{22} + 10 q^{23} - 16 q^{24} + 4 q^{26} - 10 q^{29} - 18 q^{31} + 20 q^{33} + 12 q^{34} - 4 q^{36} - 20 q^{37} - 10 q^{38} - 4 q^{39} + 22 q^{41} + 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} + 28 q^{51} - 20 q^{52} - 30 q^{53} + 4 q^{54} - 2 q^{56} + 30 q^{58} + 20 q^{59} + 12 q^{61} - 50 q^{62} - 10 q^{63} + 4 q^{64} + 2 q^{66} + 50 q^{67} + 6 q^{69} - 28 q^{71} - 20 q^{73} + 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{81} + 30 q^{83} + 2 q^{84} - 6 q^{86} - 10 q^{87} + 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} - 4 q^{96} + 10 q^{97} - 60 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 + 2 * q^11 - 20 * q^13 + 2 * q^14 - 4 * q^16 + 30 * q^17 - 2 * q^21 + 20 * q^22 + 10 * q^23 - 16 * q^24 + 4 * q^26 - 10 * q^29 - 18 * q^31 + 20 * q^33 + 12 * q^34 - 4 * q^36 - 20 * q^37 - 10 * q^38 - 4 * q^39 + 22 * q^41 + 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 + 28 * q^51 - 20 * q^52 - 30 * q^53 + 4 * q^54 - 2 * q^56 + 30 * q^58 + 20 * q^59 + 12 * q^61 - 50 * q^62 - 10 * q^63 + 4 * q^64 + 2 * q^66 + 50 * q^67 + 6 * q^69 - 28 * q^71 - 20 * q^73 + 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^81 + 30 * q^83 + 2 * q^84 - 6 * q^86 - 10 * q^87 + 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 - 4 * q^96 + 10 * q^97 - 60 * q^98 - 12 * q^99

Introduction

L-functions

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