LMFDB - Embedded newform 195.2.k.a.148.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(112,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.112"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			148.1
Character	$\chi$	$=$	195.148
Dual form			195.2.k.a.112.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.48675i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.18390 q^{4} +(-2.00040 + 0.999208i) q^{5} +(-1.75839 + 1.75839i) q^{6} -0.242414 q^{7} +5.43081i q^{8} +1.00000i q^{9} +(2.48478 + 4.97448i) q^{10} +(-4.24054 - 4.24054i) q^{11} +(2.95847 + 2.95847i) q^{12} +(2.81694 + 2.25052i) q^{13} +0.602823i q^{14} +(2.12104 + 0.707947i) q^{15} +5.13724 q^{16} +(-1.37194 - 1.37194i) q^{17} +2.48675 q^{18} +(-3.91462 - 3.91462i) q^{19} +(8.36946 - 4.18059i) q^{20} +(0.171413 + 0.171413i) q^{21} +(-10.5451 + 10.5451i) q^{22} +(1.90471 - 1.90471i) q^{23} +(3.84016 - 3.84016i) q^{24} +(3.00317 - 3.99762i) q^{25} +(5.59648 - 7.00501i) q^{26} +(0.707107 - 0.707107i) q^{27} +1.01424 q^{28} -5.76992i q^{29} +(1.76048 - 5.27449i) q^{30} +(-5.69411 + 5.69411i) q^{31} -1.91338i q^{32} +5.99703i q^{33} +(-3.41167 + 3.41167i) q^{34} +(0.484925 - 0.242222i) q^{35} -4.18390i q^{36} +3.31881 q^{37} +(-9.73467 + 9.73467i) q^{38} +(-0.400516 - 3.58324i) q^{39} +(-5.42651 - 10.8638i) q^{40} +(-1.51472 + 1.51472i) q^{41} +(0.426260 - 0.426260i) q^{42} +(3.88596 - 3.88596i) q^{43} +(17.7420 + 17.7420i) q^{44} +(-0.999208 - 2.00040i) q^{45} +(-4.73652 - 4.73652i) q^{46} -1.68447 q^{47} +(-3.63258 - 3.63258i) q^{48} -6.94124 q^{49} +(-9.94107 - 7.46811i) q^{50} +1.94022i q^{51} +(-11.7858 - 9.41597i) q^{52} +(-2.22339 - 2.22339i) q^{53} +(-1.75839 - 1.75839i) q^{54} +(12.7199 + 4.24558i) q^{55} -1.31651i q^{56} +5.53612i q^{57} -14.3483 q^{58} +(5.27843 - 5.27843i) q^{59} +(-8.87423 - 2.96198i) q^{60} +10.2486 q^{61} +(14.1598 + 14.1598i) q^{62} -0.242414i q^{63} +5.51638 q^{64} +(-7.88373 - 1.68723i) q^{65} +14.9131 q^{66} -15.3086i q^{67} +(5.74007 + 5.74007i) q^{68} -2.69366 q^{69} +(-0.602346 - 1.20588i) q^{70} +(-0.0780456 + 0.0780456i) q^{71} -5.43081 q^{72} -1.45403i q^{73} -8.25304i q^{74} +(-4.95031 + 0.703187i) q^{75} +(16.3784 + 16.3784i) q^{76} +(1.02797 + 1.02797i) q^{77} +(-8.91060 + 0.995982i) q^{78} +7.60135i q^{79} +(-10.2765 + 5.13317i) q^{80} -1.00000 q^{81} +(3.76672 + 3.76672i) q^{82} +2.71964 q^{83} +(-0.717175 - 0.717175i) q^{84} +(4.11528 + 1.37357i) q^{85} +(-9.66338 - 9.66338i) q^{86} +(-4.07995 + 4.07995i) q^{87} +(23.0296 - 23.0296i) q^{88} +(0.887120 - 0.887120i) q^{89} +(-4.97448 + 2.48478i) q^{90} +(-0.682867 - 0.545559i) q^{91} +(-7.96910 + 7.96910i) q^{92} +8.05269 q^{93} +4.18886i q^{94} +(11.7423 + 3.91927i) q^{95} +(-1.35296 + 1.35296i) q^{96} +4.76021i q^{97} +17.2611i q^{98} +(4.24054 - 4.24054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 8 q^{5} - 8 q^{11} + 8 q^{12} - 12 q^{13} + 4 q^{15} + 28 q^{16} - 28 q^{17} - 4 q^{18} + 8 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} + 8 q^{39} - 48 q^{40}+ \cdots + 8 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 8 * q^5 - 8 * q^11 + 8 * q^12 - 12 * q^13 + 4 * q^15 + 28 * q^16 - 28 * q^17 - 4 * q^18 + 8 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 + 8 * q^39 - 48 * q^40 + 4 * q^41 + 40 * q^44 - 4 * q^45 - 16 * q^46 - 24 * q^47 - 16 * q^48 - 28 * q^49 - 32 * q^50 + 52 * q^52 + 20 * q^53 - 8 * q^55 - 8 * q^58 + 32 * q^59 - 12 * q^60 + 8 * q^61 + 72 * q^62 - 28 * q^64 - 8 * q^65 + 16 * q^66 + 60 * q^68 + 8 * q^69 + 64 * q^70 + 40 * q^71 + 12 * q^72 - 16 * q^75 - 40 * q^76 - 48 * q^77 + 8 * q^78 - 32 * q^80 - 28 * q^81 + 4 * q^82 - 104 * q^83 - 32 * q^84 - 4 * q^85 + 16 * q^86 - 24 * q^87 + 72 * q^88 - 36 * q^89 - 12 * q^90 - 56 * q^91 - 32 * q^92 + 56 * q^95 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	2.48675i		−	1.75839i	−0.476458	−	0.879197i	$-0.658080\pi$
$2$		−	2.48675i		−	1.75839i	0.476458	−	0.879197i	$-0.341920\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−4.18390			−2.09195
$5$	−2.00040	+	0.999208i	−0.894604	+	0.446859i
$5$	−2.00040	+	0.999208i	−0.894604	+	0.446859i
$6$	−1.75839	+	1.75839i	−0.717862	+	0.717862i
$7$	−0.242414			−0.0916240			−0.0458120	−	0.998950i	$-0.514588\pi$
$7$	−0.242414			−0.0916240			−0.0458120	+	0.998950i	$0.514588\pi$
$8$			5.43081i			1.92008i
$9$			1.00000i			0.333333i
$10$	2.48478	+	4.97448i	0.785755	+	1.57307i
$11$	−4.24054	−	4.24054i	−1.27857	−	1.27857i	−0.941467	−	0.337104i	$-0.890553\pi$
$11$	−4.24054	−	4.24054i	−1.27857	−	1.27857i	−0.337104	−	0.941467i	$-0.609447\pi$
$12$	2.95847	+	2.95847i	0.854036	+	0.854036i
$13$	2.81694	+	2.25052i	0.781278	+	0.624183i
$13$	2.81694	+	2.25052i	0.781278	+	0.624183i
$14$			0.602823i			0.161111i
$15$	2.12104	+	0.707947i	0.547650	+	0.182791i
$16$	5.13724			1.28431
$17$	−1.37194	−	1.37194i	−0.332745	−	0.332745i	0.520883	−	0.853628i	$-0.325603\pi$
$17$	−1.37194	−	1.37194i	−0.332745	−	0.332745i	−0.853628	+	0.520883i	$0.825603\pi$
$18$	2.48675			0.586132
$19$	−3.91462	−	3.91462i	−0.898076	−	0.898076i	0.0971894	−	0.995266i	$-0.469015\pi$
$19$	−3.91462	−	3.91462i	−0.898076	−	0.898076i	−0.995266	+	0.0971894i	$0.969015\pi$
$20$	8.36946	−	4.18059i	1.87147	−	0.934808i
$21$	0.171413	+	0.171413i	0.0374054	+	0.0374054i
$22$	−10.5451	+	10.5451i	−2.24823	+	2.24823i
$23$	1.90471	−	1.90471i	0.397159	−	0.397159i	−0.480071	−	0.877230i	$-0.659389\pi$
$23$	1.90471	−	1.90471i	0.397159	−	0.397159i	0.877230	+	0.480071i	$0.159389\pi$
$24$	3.84016	−	3.84016i	0.783870	−	0.783870i
$25$	3.00317	−	3.99762i	0.600633	−	0.799525i
$26$	5.59648	−	7.00501i	1.09756	−	1.37380i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.01424			0.191673
$29$		−	5.76992i		−	1.07145i	−0.844393	−	0.535724i	$-0.820039\pi$
$29$		−	5.76992i		−	1.07145i	0.844393	−	0.535724i	$-0.179961\pi$
$30$	1.76048	−	5.27449i	0.321419	−	0.962985i
$31$	−5.69411	+	5.69411i	−1.02269	+	1.02269i	−0.0229561	+	0.999736i	$0.507308\pi$
$31$	−5.69411	+	5.69411i	−1.02269	+	1.02269i	−0.999736	+	0.0229561i	$0.992692\pi$
$32$		−	1.91338i		−	0.338241i
$33$			5.99703i			1.04395i
$34$	−3.41167	+	3.41167i	−0.585096	+	0.585096i
$35$	0.484925	−	0.242222i	0.0819673	−	0.0409431i
$36$		−	4.18390i		−	0.697317i
$37$	3.31881			0.545609			0.272805	−	0.962069i	$-0.412049\pi$
$37$	3.31881			0.545609			0.272805	+	0.962069i	$0.412049\pi$
$38$	−9.73467	+	9.73467i	−1.57917	+	1.57917i
$39$	−0.400516	−	3.58324i	−0.0641339	−	0.573777i
$40$	−5.42651	−	10.8638i	−0.858007	−	1.71771i
$41$	−1.51472	+	1.51472i	−0.236559	+	0.236559i	−0.815424	−	0.578865i	$-0.803496\pi$
$41$	−1.51472	+	1.51472i	−0.236559	+	0.236559i	0.578865	+	0.815424i	$0.303496\pi$
$42$	0.426260	−	0.426260i	0.0657734	−	0.0657734i
$43$	3.88596	−	3.88596i	0.592603	−	0.592603i	−0.345731	−	0.938334i	$-0.612369\pi$
$43$	3.88596	−	3.88596i	0.592603	−	0.592603i	0.938334	+	0.345731i	$0.112369\pi$
$44$	17.7420	+	17.7420i	2.67471	+	2.67471i
$45$	−0.999208	−	2.00040i	−0.148953	−	0.298201i
$46$	−4.73652	−	4.73652i	−0.698362	−	0.698362i
$47$	−1.68447			−0.245706			−0.122853	−	0.992425i	$-0.539204\pi$
$47$	−1.68447			−0.245706			−0.122853	+	0.992425i	$0.539204\pi$
$48$	−3.63258	−	3.63258i	−0.524317	−	0.524317i
$49$	−6.94124			−0.991605
$50$	−9.94107	−	7.46811i	−1.40588	−	1.05615i
$51$			1.94022i			0.271685i
$52$	−11.7858	−	9.41597i	−1.63440	−	1.30576i
$53$	−2.22339	−	2.22339i	−0.305406	−	0.305406i	0.537718	−	0.843125i	$-0.319286\pi$
$53$	−2.22339	−	2.22339i	−0.305406	−	0.305406i	−0.843125	+	0.537718i	$0.819286\pi$
$54$	−1.75839	−	1.75839i	−0.239287	−	0.239287i
$55$	12.7199	+	4.24558i	1.71516	+	0.572474i
$56$		−	1.31651i		−	0.175926i
$57$			5.53612i			0.733276i
$58$	−14.3483			−1.88403
$59$	5.27843	−	5.27843i	0.687193	−	0.687193i	−0.274418	−	0.961611i	$-0.588485\pi$
$59$	5.27843	−	5.27843i	0.687193	−	0.687193i	0.961611	+	0.274418i	$0.0884852\pi$
$60$	−8.87423	−	2.96198i	−1.14566	−	0.382390i
$61$	10.2486			1.31220			0.656101	−	0.754673i	$-0.272204\pi$
$61$	10.2486			1.31220			0.656101	+	0.754673i	$0.272204\pi$
$62$	14.1598	+	14.1598i	1.79830	+	1.79830i
$63$		−	0.242414i		−	0.0305413i
$64$	5.51638			0.689548
$65$	−7.88373	−	1.68723i	−0.977857	−	0.209275i
$66$	14.9131			1.83567
$67$		−	15.3086i		−	1.87024i	−0.354328	−	0.935121i	$-0.615290\pi$
$67$		−	15.3086i		−	1.87024i	0.354328	−	0.935121i	$-0.384710\pi$
$68$	5.74007	+	5.74007i	0.696086	+	0.696086i
$69$	−2.69366			−0.324279
$70$	−0.602346	−	1.20588i	−0.0719941	−	0.144131i
$71$	−0.0780456	+	0.0780456i	−0.00926231	+	0.00926231i	−0.711723	−	0.702460i	$-0.752085\pi$
$71$	−0.0780456	+	0.0780456i	−0.00926231	+	0.00926231i	0.702460	+	0.711723i	$0.252085\pi$
$72$	−5.43081			−0.640027
$73$		−	1.45403i		−	0.170181i	−0.996373	−	0.0850905i	$-0.972882\pi$
$73$		−	1.45403i		−	0.170181i	0.996373	−	0.0850905i	$-0.0271179\pi$
$74$		−	8.25304i		−	0.959397i
$75$	−4.95031	+	0.703187i	−0.571612	+	0.0811971i
$76$	16.3784	+	16.3784i	1.87873	+	1.87873i
$77$	1.02797	+	1.02797i	0.117148	+	0.117148i
$78$	−8.91060	+	0.995982i	−1.00893	+	0.112773i
$79$			7.60135i			0.855219i	0.903964	+	0.427609i	$0.140644\pi$
$79$			7.60135i			0.855219i	−0.903964	+	0.427609i	$0.859356\pi$
$80$	−10.2765	+	5.13317i	−1.14895	+	0.573906i
$81$	−1.00000			−0.111111
$82$	3.76672	+	3.76672i	0.415964	+	0.415964i
$83$	2.71964			0.298520			0.149260	−	0.988798i	$-0.452311\pi$
$83$	2.71964			0.298520			0.149260	+	0.988798i	$0.452311\pi$
$84$	−0.717175	−	0.717175i	−0.0782502	−	0.0782502i
$85$	4.11528	+	1.37357i	0.446365	+	0.148985i
$86$	−9.66338	−	9.66338i	−1.04203	−	1.04203i
$87$	−4.07995	+	4.07995i	−0.437416	+	0.437416i
$88$	23.0296	−	23.0296i	2.45496	−	2.45496i
$89$	0.887120	−	0.887120i	0.0940345	−	0.0940345i	−0.658525	−	0.752559i	$-0.728819\pi$
$89$	0.887120	−	0.887120i	0.0940345	−	0.0940345i	0.752559	+	0.658525i	$0.228819\pi$
$90$	−4.97448	+	2.48478i	−0.524356	+	0.261918i
$91$	−0.682867	−	0.545559i	−0.0715839	−	0.0571902i
$92$	−7.96910	+	7.96910i	−0.830837	+	0.830837i
$93$	8.05269			0.835025
$94$			4.18886i			0.432048i
$95$	11.7423	+	3.91927i	1.20474	+	0.402109i
$96$	−1.35296	+	1.35296i	−0.138086	+	0.138086i
$97$			4.76021i			0.483326i	0.970360	+	0.241663i	$0.0776929\pi$
$97$			4.76021i			0.483326i	−0.970360	+	0.241663i	$0.922307\pi$
$98$			17.2611i			1.74363i
$99$	4.24054	−	4.24054i	0.426190	−	0.426190i
$100$	−12.5650	+	16.7257i	−1.25650	+	1.67257i
$101$			11.2837i			1.12277i	0.827553	+	0.561387i	$0.189732\pi$
$101$			11.2837i			1.12277i	−0.827553	+	0.561387i	$0.810268\pi$
$102$	4.82483			0.477729
$103$	9.85776	−	9.85776i	0.971314	−	0.971314i	−0.0282861	−	0.999600i	$-0.509005\pi$
$103$	9.85776	−	9.85776i	0.971314	−	0.971314i	0.999600	+	0.0282861i	$0.00900494\pi$
$104$	−12.2222	+	15.2983i	−1.19848	+	1.50012i
$105$	−0.514171	−	0.171616i	−0.0501779	−	0.0167481i
$106$	−5.52901	+	5.52901i	−0.537025	+	0.537025i
$107$	−4.00248	+	4.00248i	−0.386934	+	0.386934i	−0.873592	−	0.486658i	$-0.838216\pi$
$107$	−4.00248	+	4.00248i	−0.386934	+	0.386934i	0.486658	+	0.873592i	$0.338216\pi$
$108$	−2.95847	+	2.95847i	−0.284679	+	0.284679i
$109$	−4.59552	−	4.59552i	−0.440171	−	0.440171i	0.451899	−	0.892069i	$-0.350747\pi$
$109$	−4.59552	−	4.59552i	−0.440171	−	0.440171i	−0.892069	+	0.451899i	$0.850747\pi$
$110$	10.5577	−	31.6313i	1.00663	−	3.01592i
$111$	−2.34675	−	2.34675i	−0.222744	−	0.222744i
$112$	−1.24534			−0.117674
$113$	12.3277	+	12.3277i	1.15969	+	1.15969i	0.984542	+	0.175149i	$0.0560409\pi$
$113$	12.3277	+	12.3277i	1.15969	+	1.15969i	0.175149	+	0.984542i	$0.443959\pi$
$114$	13.7669			1.28939
$115$	−1.90697	+	5.71336i	−0.177826	+	0.532774i
$116$			24.1408i			2.24142i
$117$	−2.25052	+	2.81694i	−0.208061	+	0.260426i
$118$	−13.1261	−	13.1261i	−1.20836	−	1.20836i
$119$	0.332578	+	0.332578i	0.0304874	+	0.0304874i
$120$	−3.84472	+	11.5190i	−0.350974	+	1.05153i
$121$			24.9644i			2.26949i
$122$		−	25.4857i		−	2.30737i
$123$	2.14213			0.193150
$124$	23.8236	−	23.8236i	2.13942	−	2.13942i
$125$	−2.01306	+	10.9976i	−0.180054	+	0.983657i
$126$	−0.602823			−0.0537037
$127$	−3.83744	−	3.83744i	−0.340518	−	0.340518i	0.516044	−	0.856562i	$-0.327404\pi$
$127$	−3.83744	−	3.83744i	−0.340518	−	0.340518i	−0.856562	+	0.516044i	$0.827404\pi$
$128$		−	17.5446i		−	1.55074i
$129$	−5.49557			−0.483858
$130$	−4.19571	+	19.6048i	−0.367988	+	1.71946i
$131$	−5.03941			−0.440295			−0.220148	−	0.975467i	$-0.570654\pi$
$131$	−5.03941			−0.440295			−0.220148	+	0.975467i	$0.570654\pi$
$132$		−	25.0910i		−	2.18389i
$133$	0.948961	+	0.948961i	0.0822854	+	0.0822854i
$134$	−38.0686			−3.28862
$135$	−0.707947	+	2.12104i	−0.0609303	+	0.182550i
$136$	7.45075	−	7.45075i	0.638897	−	0.638897i
$137$	−13.3951			−1.14442			−0.572209	−	0.820108i	$-0.693913\pi$
$137$	−13.3951			−1.14442			−0.572209	+	0.820108i	$0.693913\pi$
$138$			6.69845i			0.570210i
$139$		−	6.03788i		−	0.512126i	−0.966660	−	0.256063i	$-0.917575\pi$
$139$		−	6.03788i		−	0.512126i	0.966660	−	0.256063i	$-0.0824255\pi$
$140$	−2.02888	+	1.01344i	−0.171472	+	0.0856509i
$141$	1.19110	+	1.19110i	0.100309	+	0.100309i
$142$	0.194080	+	0.194080i	0.0162868	+	0.0162868i
$143$	−2.40191	−	21.4888i	−0.200858	−	1.79698i
$144$			5.13724i			0.428103i
$145$	5.76535	+	11.5421i	0.478786	+	0.958521i
$146$	−3.61579			−0.299245
$147$	4.90819	+	4.90819i	0.404821	+	0.404821i
$148$	−13.8856			−1.14139
$149$	−14.7948	−	14.7948i	−1.21203	−	1.21203i	−0.970356	−	0.241678i	$-0.922302\pi$
$149$	−14.7948	−	14.7948i	−1.21203	−	1.21203i	−0.241678	−	0.970356i	$-0.577698\pi$
$150$	1.74865	+	12.3102i	0.142776	+	1.00512i
$151$	−14.6792	−	14.6792i	−1.19458	−	1.19458i	−0.975768	−	0.218808i	$-0.929783\pi$
$151$	−14.6792	−	14.6792i	−1.19458	−	1.19458i	−0.218808	−	0.975768i	$-0.570217\pi$
$152$	21.2596	−	21.2596i	1.72438	−	1.72438i
$153$	1.37194	−	1.37194i	0.110915	−	0.110915i
$154$	2.55630	−	2.55630i	0.205992	−	0.205992i
$155$	5.70087	−	17.0801i	0.457905	−	1.37190i
$156$	1.67572	+	14.9919i	0.134165	+	1.20031i
$157$	4.26691	−	4.26691i	0.340537	−	0.340537i	−0.516032	−	0.856569i	$-0.672592\pi$
$157$	4.26691	−	4.26691i	0.340537	−	0.340537i	0.856569	+	0.516032i	$0.172592\pi$
$158$	18.9026			1.50381
$159$			3.14435i			0.249363i
$160$	1.91187	+	3.82752i	0.151146	+	0.302592i
$161$	−0.461728	+	0.461728i	−0.0363893	+	0.0363893i
$162$			2.48675i			0.195377i
$163$			14.7233i			1.15322i	0.817019	+	0.576611i	$0.195625\pi$
$163$			14.7233i			1.15322i	−0.817019	+	0.576611i	$0.804375\pi$
$164$	6.33743	−	6.33743i	0.494870	−	0.494870i
$165$	−5.99228	−	11.9964i	−0.466499	−	0.933921i
$166$		−	6.76306i		−	0.524915i
$167$	6.08556			0.470915			0.235457	−	0.971885i	$-0.424341\pi$
$167$	6.08556			0.470915			0.235457	+	0.971885i	$0.424341\pi$
$168$	−0.930911	+	0.930911i	−0.0718213	+	0.0718213i
$169$	2.87029	+	12.6792i	0.220791	+	0.975321i
$170$	3.41572	−	10.2337i	0.261974	−	0.784886i
$171$	3.91462	−	3.91462i	0.299359	−	0.299359i
$172$	−16.2585	+	16.2585i	−1.23970	+	1.23970i
$173$	−11.3322	+	11.3322i	−0.861570	+	0.861570i	−0.991520	−	0.129951i	$-0.958518\pi$
$173$	−11.3322	+	11.3322i	−0.861570	+	0.861570i	0.129951	+	0.991520i	$0.458518\pi$
$174$	10.1458	+	10.1458i	0.769151	+	0.769151i
$175$	−0.728011	+	0.969082i	−0.0550324	+	0.0732557i
$176$	−21.7847	−	21.7847i	−1.64208	−	1.64208i
$177$	−7.46482			−0.561090
$178$	−2.20604	−	2.20604i	−0.165350	−	0.165350i
$179$	3.99730			0.298772			0.149386	−	0.988779i	$-0.452270\pi$
$179$	3.99730			0.298772			0.149386	+	0.988779i	$0.452270\pi$
$180$	4.18059	+	8.36946i	0.311603	+	0.623823i
$181$		−	16.5433i		−	1.22966i	−0.788661	−	0.614828i	$-0.789226\pi$
$181$		−	16.5433i		−	1.22966i	0.788661	−	0.614828i	$-0.210774\pi$
$182$	−1.35667	+	1.69812i	−0.100563	+	0.125873i
$183$	−7.24688	−	7.24688i	−0.535705	−	0.535705i
$184$	10.3441	+	10.3441i	0.762577	+	0.762577i
$185$	−6.63894	+	3.31618i	−0.488104	+	0.243811i
$186$		−	20.0250i		−	1.46830i
$187$			11.6355i			0.850876i
$188$	7.04768			0.514005
$189$	−0.171413	+	0.171413i	−0.0124685	+	0.0124685i
$190$	9.74624	−	29.2002i	0.707066	−	2.11840i
$191$	13.0425			0.943721			0.471860	−	0.881673i	$-0.343583\pi$
$191$	13.0425			0.943721			0.471860	+	0.881673i	$0.343583\pi$
$192$	−3.90067	−	3.90067i	−0.281507	−	0.281507i
$193$		−	9.28317i		−	0.668217i	−0.942535	−	0.334109i	$-0.891565\pi$
$193$		−	9.28317i		−	0.668217i	0.942535	−	0.334109i	$-0.108435\pi$
$194$	11.8374			0.849879
$195$	4.38159	+	6.76769i	0.313772	+	0.484645i
$196$	29.0415			2.07439
$197$			12.9124i			0.919967i	0.887927	+	0.459983i	$0.152145\pi$
$197$			12.9124i			0.919967i	−0.887927	+	0.459983i	$0.847855\pi$
$198$	−10.5451	−	10.5451i	−0.749411	−	0.749411i
$199$	2.35534			0.166966			0.0834830	−	0.996509i	$-0.473396\pi$
$199$	2.35534			0.166966			0.0834830	+	0.996509i	$0.473396\pi$
$200$	21.7103	+	16.3096i	1.53515	+	1.15326i
$201$	−10.8248	+	10.8248i	−0.763523	+	0.763523i
$202$	28.0598			1.97428
$203$			1.39871i			0.0981703i
$204$		−	8.11768i		−	0.568352i
$205$	1.51652	−	4.54355i	0.105918	−	0.317336i
$206$	−24.5137	−	24.5137i	−1.70795	−	1.70795i
$207$	1.90471	+	1.90471i	0.132386	+	0.132386i
$208$	14.4713	+	11.5615i	1.00340	+	0.801644i
$209$			33.2003i			2.29651i
$210$	−0.426766	+	1.27861i	−0.0294497	+	0.0882326i
$211$	−21.9810			−1.51323			−0.756617	−	0.653858i	$-0.773149\pi$
$211$	−21.9810			−1.51323			−0.756617	+	0.653858i	$0.773149\pi$
$212$	9.30245	+	9.30245i	0.638895	+	0.638895i
$213$	0.110373			0.00756264
$214$	9.95315	+	9.95315i	0.680383	+	0.680383i
$215$	−3.89057	+	11.6563i	−0.265335	+	0.794955i
$216$	3.84016	+	3.84016i	0.261290	+	0.261290i
$217$	1.38033	−	1.38033i	0.0937032	−	0.0937032i
$218$	−11.4279	+	11.4279i	−0.773993	+	0.773993i
$219$	−1.02815	+	1.02815i	−0.0694761	+	0.0694761i
$220$	−53.2190	−	17.7631i	−3.58802	−	1.19759i
$221$	−0.777089	−	6.95226i	−0.0522727	−	0.467660i
$222$	−5.83578	+	5.83578i	−0.391672	+	0.391672i
$223$	−8.72020			−0.583948			−0.291974	−	0.956426i	$-0.594312\pi$
$223$	−8.72020			−0.583948			−0.291974	+	0.956426i	$0.594312\pi$
$224$			0.463831i			0.0309910i
$225$	3.99762	+	3.00317i	0.266508	+	0.200211i
$226$	30.6558	−	30.6558i	2.03919	−	2.03919i
$227$			18.3913i			1.22068i	0.792141	+	0.610338i	$0.208966\pi$
$227$			18.3913i			1.22068i	−0.792141	+	0.610338i	$0.791034\pi$
$228$		−	23.1626i		−	1.53398i
$229$	16.7151	−	16.7151i	1.10456	−	1.10456i	0.110712	−	0.993852i	$-0.464687\pi$
$229$	16.7151	−	16.7151i	1.10456	−	1.10456i	0.993852	−	0.110712i	$-0.0353133\pi$
$230$	14.2077	+	4.74214i	0.936827	+	0.312688i
$231$		−	1.45377i		−	0.0956508i
$232$	31.3353			2.05727
$233$	0.600932	−	0.600932i	0.0393684	−	0.0393684i	−0.687149	−	0.726517i	$-0.741138\pi$
$233$	0.600932	−	0.600932i	0.0393684	−	0.0393684i	0.726517	+	0.687149i	$0.241138\pi$
$234$	7.00501	+	5.59648i	0.457932	+	0.365853i
$235$	3.36962	−	1.68314i	0.219809	−	0.109796i
$236$	−22.0844	+	22.0844i	−1.43757	+	1.43757i
$237$	5.37497	−	5.37497i	0.349141	−	0.349141i
$238$	0.827038	−	0.827038i	0.0536089	−	0.0536089i
$239$	−8.71291	−	8.71291i	−0.563591	−	0.563591i	0.366735	−	0.930326i	$-0.380476\pi$
$239$	−8.71291	−	8.71291i	−0.563591	−	0.563591i	−0.930326	+	0.366735i	$0.880476\pi$
$240$	10.8963	+	3.63689i	0.703352	+	0.234760i
$241$	−6.37606	−	6.37606i	−0.410718	−	0.410718i	0.471271	−	0.881989i	$-0.343796\pi$
$241$	−6.37606	−	6.37606i	−0.410718	−	0.410718i	−0.881989	+	0.471271i	$0.843796\pi$
$242$	62.0801			3.99066
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−42.8793			−2.74506
$245$	13.8852	−	6.93574i	0.887094	−	0.443108i
$246$		−	5.32694i		−	0.339633i
$247$	−2.21730	−	19.8372i	−0.141084	−	1.26221i
$248$	−30.9236	−	30.9236i	−1.96365	−	1.96365i
$249$	−1.92308	−	1.92308i	−0.121870	−	0.121870i
$250$	27.3483	+	5.00598i	1.72966	+	0.316606i
$251$		−	8.17534i		−	0.516023i	−0.966142	−	0.258011i	$-0.916933\pi$
$251$		−	8.17534i		−	0.516023i	0.966142	−	0.258011i	$-0.0830672\pi$
$252$			1.01424i			0.0638910i
$253$	−16.1540			−1.01559
$254$	−9.54274	+	9.54274i	−0.598765	+	0.598765i
$255$	−1.93868	−	3.88120i	−0.121405	−	0.243050i
$256$	−32.5962			−2.03726
$257$	−9.97233	−	9.97233i	−0.622057	−	0.622057i	0.324000	−	0.946057i	$-0.394972\pi$
$257$	−9.97233	−	9.97233i	−0.622057	−	0.622057i	−0.946057	+	0.324000i	$0.894972\pi$
$258$			13.6661i			0.850813i
$259$	−0.804528			−0.0499909
$260$	32.9848	+	7.05920i	2.04563	+	0.437793i
$261$	5.76992			0.357149
$262$			12.5317i			0.774212i
$263$	16.5535	+	16.5535i	1.02073	+	1.02073i	0.999780	+	0.0209533i	$0.00667013\pi$
$263$	16.5535	+	16.5535i	1.02073	+	1.02073i	0.0209533	+	0.999780i	$0.493330\pi$
$264$	−32.5687			−2.00447
$265$	6.66929	+	2.22603i	0.409691	+	0.136744i
$266$	2.35983	−	2.35983i	0.144690	−	0.144690i
$267$	−1.25458			−0.0767789
$268$			64.0497i			3.91246i
$269$			16.7169i			1.01925i	0.860397	+	0.509625i	$0.170216\pi$
$269$			16.7169i			1.01925i	−0.860397	+	0.509625i	$0.829784\pi$
$270$	5.27449	+	1.76048i	0.320995	+	0.107140i
$271$	12.5904	+	12.5904i	0.764814	+	0.764814i	0.977188	−	0.212374i	$-0.0681195\pi$
$271$	12.5904	+	12.5904i	0.764814	+	0.764814i	−0.212374	+	0.977188i	$0.568120\pi$
$272$	−7.04799	−	7.04799i	−0.427347	−	0.427347i
$273$	0.0970909	+	0.868628i	0.00587621	+	0.0525718i
$274$			33.3101i			2.01234i
$275$	−29.6871	+	4.21704i	−1.79020	+	0.254297i
$276$	11.2700			0.678375
$277$	−17.8939	−	17.8939i	−1.07514	−	1.07514i	−0.996937	−	0.0782056i	$-0.975081\pi$
$277$	−17.8939	−	17.8939i	−1.07514	−	1.07514i	−0.0782056	−	0.996937i	$-0.524919\pi$
$278$	−15.0147			−0.900520
$279$	−5.69411	−	5.69411i	−0.340898	−	0.340898i
$280$	1.31546	+	2.63353i	0.0786140	+	0.157384i
$281$	−2.64673	−	2.64673i	−0.157891	−	0.157891i	0.623741	−	0.781631i	$-0.285612\pi$
$281$	−2.64673	−	2.64673i	−0.157891	−	0.157891i	−0.781631	+	0.623741i	$0.785612\pi$
$282$	2.96197	−	2.96197i	0.176383	−	0.176383i
$283$	2.64156	−	2.64156i	0.157025	−	0.157025i	−0.624222	−	0.781247i	$-0.714584\pi$
$283$	2.64156	−	2.64156i	0.157025	−	0.157025i	0.781247	+	0.624222i	$0.214584\pi$
$284$	0.326535	−	0.326535i	0.0193763	−	0.0193763i
$285$	−5.53173	−	11.0744i	−0.327671	−	0.655992i
$286$	−53.4371	+	5.97293i	−3.15980	+	0.353187i
$287$	0.367189	−	0.367189i	0.0216745	−	0.0216745i
$288$	1.91338			0.112747
$289$		−	13.2356i		−	0.778562i
$290$	28.7023	−	14.3370i	1.68546	−	0.841895i
$291$	3.36598	−	3.36598i	0.197317	−	0.197317i
$292$			6.08351i			0.356010i
$293$		−	8.87232i		−	0.518327i	−0.965834	−	0.259163i	$-0.916553\pi$
$293$		−	8.87232i		−	0.518327i	0.965834	−	0.259163i	$-0.0834468\pi$
$294$	12.2054	−	12.2054i	0.711835	−	0.711835i
$295$	−5.28469	+	15.8332i	−0.307687	+	0.921844i
$296$			18.0238i			1.04761i
$297$	−5.99703			−0.347983
$298$	−36.7908	+	36.7908i	−2.13124	+	2.13124i
$299$	9.65203	−	1.07885i	0.558191	−	0.0623918i
$300$	20.7116	−	2.94207i	1.19578	−	0.169860i
$301$	−0.942012	+	0.942012i	−0.0542966	+	0.0542966i
$302$	−36.5034	+	36.5034i	−2.10054	+	2.10054i
$303$	7.97881	−	7.97881i	0.458370	−	0.458370i
$304$	−20.1104	−	20.1104i	−1.15341	−	1.15341i
$305$	−20.5013	+	10.2405i	−1.17390	+	0.586370i
$306$	−3.41167	−	3.41167i	−0.195032	−	0.195032i
$307$	25.1833			1.43729			0.718644	−	0.695378i	$-0.244763\pi$
$307$	25.1833			1.43729			0.718644	+	0.695378i	$0.244763\pi$
$308$	−4.30092	−	4.30092i	−0.245068	−	0.245068i
$309$	−13.9410			−0.793074
$310$	−42.4738	−	14.1766i	−2.41235	−	0.805178i
$311$		−	7.05837i		−	0.400243i	−0.979771	−	0.200122i	$-0.935866\pi$
$311$		−	7.05837i		−	0.400243i	0.979771	−	0.200122i	$-0.0641337\pi$
$312$	19.4599	−	2.17513i	1.10170	−	0.123142i
$313$	−3.85568	−	3.85568i	−0.217936	−	0.217936i	0.589692	−	0.807628i	$-0.299249\pi$
$313$	−3.85568	−	3.85568i	−0.217936	−	0.217936i	−0.807628	+	0.589692i	$0.799249\pi$
$314$	−10.6107	−	10.6107i	−0.598798	−	0.598798i
$315$	0.242222	+	0.484925i	0.0136477	+	0.0273224i
$316$		−	31.8033i		−	1.78908i
$317$		−	13.9177i		−	0.781695i	−0.920456	−	0.390847i	$-0.872182\pi$
$317$		−	13.9177i		−	0.781695i	0.920456	−	0.390847i	$-0.127818\pi$
$318$	7.81920			0.438479
$319$	−24.4676	+	24.4676i	−1.36992	+	1.36992i
$320$	−11.0350	+	5.51202i	−0.616873	+	0.308131i
$321$	5.66036			0.315931
$322$	1.14820	+	1.14820i	0.0639867	+	0.0639867i
$323$			10.7413i			0.597660i
$324$	4.18390			0.232439
$325$	17.4565	−	4.50236i	0.968311	−	0.249746i
$326$	36.6132			2.02782
$327$			6.49904i			0.359398i
$328$	−8.22614	−	8.22614i	−0.454213	−	0.454213i
$329$	0.408341			0.0225126
$330$	−29.8321	+	14.9013i	−1.64220	+	0.820288i
$331$	−6.88277	+	6.88277i	−0.378311	+	0.378311i	−0.870493	−	0.492181i	$-0.836200\pi$
$331$	−6.88277	+	6.88277i	−0.378311	+	0.378311i	0.492181	+	0.870493i	$0.336200\pi$
$332$	−11.3787			−0.624489
$333$			3.31881i			0.181870i
$334$		−	15.1332i		−	0.828054i
$335$	15.2965	+	30.6232i	0.835736	+	1.67313i
$336$	0.880589	+	0.880589i	0.0480400	+	0.0480400i
$337$	0.812119	+	0.812119i	0.0442389	+	0.0442389i	0.728880	−	0.684641i	$-0.240041\pi$
$337$	0.812119	+	0.812119i	0.0442389	+	0.0442389i	−0.684641	+	0.728880i	$0.740041\pi$
$338$	31.5299	−	7.13768i	1.71500	−	0.388238i
$339$		−	17.4340i		−	0.946884i
$340$	−17.2179	−	5.74689i	−0.933774	−	0.311669i
$341$	48.2922			2.61517
$342$	−9.73467	−	9.73467i	−0.526391	−	0.526391i
$343$	3.37956			0.182479
$344$	21.1039	+	21.1039i	1.13785	+	1.13785i
$345$	5.38839	−	2.69153i	0.290101	−	0.144907i
$346$	28.1803	+	28.1803i	1.51498	+	1.51498i
$347$	25.2146	−	25.2146i	1.35359	−	1.35359i	0.471983	−	0.881608i	$-0.343538\pi$
$347$	25.2146	−	25.2146i	1.35359	−	1.35359i	0.881608	−	0.471983i	$-0.156462\pi$
$348$	17.0701	−	17.0701i	0.915054	−	0.915054i
$349$	4.85536	−	4.85536i	0.259902	−	0.259902i	−0.565112	−	0.825014i	$-0.691167\pi$
$349$	4.85536	−	4.85536i	0.259902	−	0.259902i	0.825014	+	0.565112i	$0.191167\pi$
$350$	2.40986	+	1.81038i	0.128812	+	0.0967688i
$351$	3.58324	−	0.400516i	0.191259	−	0.0213780i
$352$	−8.11377	+	8.11377i	−0.432465	+	0.432465i
$353$	25.9459			1.38096			0.690480	−	0.723351i	$-0.257399\pi$
$353$	25.9459			1.38096			0.690480	+	0.723351i	$0.257399\pi$
$354$			18.5631i			0.986618i
$355$	0.0781383	−	0.234106i	0.00414715	−	0.0124250i
$356$	−3.71162	+	3.71162i	−0.196716	+	0.196716i
$357$		−	0.470337i		−	0.0248929i
$358$		−	9.94027i		−	0.525359i
$359$	−2.31461	+	2.31461i	−0.122160	+	0.122160i	−0.765544	−	0.643384i	$-0.777530\pi$
$359$	−2.31461	+	2.31461i	−0.122160	+	0.122160i	0.643384	+	0.765544i	$0.277530\pi$
$360$	10.8638	−	5.42651i	0.572571	−	0.286002i
$361$			11.6486i			0.613083i
$362$	−41.1390			−2.16222
$363$	17.6525	−	17.6525i	0.926515	−	0.926515i
$364$	2.85705	+	2.28257i	0.149750	+	0.119639i
$365$	1.45287	+	2.90863i	0.0760470	+	0.152245i
$366$	−18.0211	+	18.0211i	−0.941980	+	0.941980i
$367$	10.2557	−	10.2557i	0.535346	−	0.535346i	−0.386813	−	0.922158i	$-0.626424\pi$
$367$	10.2557	−	10.2557i	0.535346	−	0.535346i	0.922158	+	0.386813i	$0.126424\pi$
$368$	9.78493	−	9.78493i	0.510075	−	0.510075i
$369$	−1.51472	−	1.51472i	−0.0788531	−	0.0788531i
$370$	8.24651	+	16.5094i	0.428715	+	0.858280i
$371$	0.538982	+	0.538982i	0.0279826	+	0.0279826i
$372$	−33.6917			−1.74683
$373$	5.33438	+	5.33438i	0.276204	+	0.276204i	0.831592	−	0.555388i	$-0.187430\pi$
$373$	5.33438	+	5.33438i	0.276204	+	0.276204i	−0.555388	+	0.831592i	$0.687430\pi$
$374$	28.9346			1.49618
$375$	9.19994	−	6.35304i	0.475083	−	0.328069i
$376$		−	9.14806i		−	0.471775i
$377$	12.9853	−	16.2535i	0.668779	−	0.837098i
$378$	0.426260	+	0.426260i	0.0219245	+	0.0219245i
$379$	4.89160	+	4.89160i	0.251265	+	0.251265i	0.821489	−	0.570224i	$-0.193144\pi$
$379$	4.89160	+	4.89160i	0.251265	+	0.251265i	−0.570224	+	0.821489i	$0.693144\pi$
$380$	−49.1287	−	16.3979i	−2.52025	−	0.841193i
$381$			5.42696i			0.278032i
$382$		−	32.4333i		−	1.65943i
$383$	0.331496			0.0169386			0.00846932	−	0.999964i	$-0.497304\pi$
$383$	0.331496			0.0169386			0.00846932	+	0.999964i	$0.497304\pi$
$384$	−12.4059	+	12.4059i	−0.633086	+	0.633086i
$385$	−3.08350	−	1.02919i	−0.157150	−	0.0524523i
$386$	−23.0849			−1.17499
$387$	3.88596	+	3.88596i	0.197534	+	0.197534i
$388$		−	19.9163i		−	1.01110i
$389$	6.77907			0.343713			0.171856	−	0.985122i	$-0.445024\pi$
$389$	6.77907			0.343713			0.171856	+	0.985122i	$0.445024\pi$
$390$	16.8295	−	10.8959i	0.852196	−	0.551735i
$391$	−5.22629			−0.264305
$392$		−	37.6965i		−	1.90396i
$393$	3.56340	+	3.56340i	0.179750	+	0.179750i
$394$	32.1097			1.61766
$395$	−7.59533	−	15.2057i	−0.382162	−	0.765082i
$396$	−17.7420	+	17.7420i	−0.891570	+	0.891570i
$397$	25.7273			1.29121			0.645607	−	0.763670i	$-0.276604\pi$
$397$	25.7273			1.29121			0.645607	+	0.763670i	$0.276604\pi$
$398$		−	5.85714i		−	0.293592i
$399$		−	1.34203i		−	0.0671857i
$400$	15.4280	−	20.5367i	0.771399	−	1.02684i
$401$	7.72622	+	7.72622i	0.385829	+	0.385829i	0.873197	−	0.487368i	$-0.162043\pi$
$401$	7.72622	+	7.72622i	0.385829	+	0.385829i	−0.487368	+	0.873197i	$0.662043\pi$
$402$	26.9185	+	26.9185i	1.34258	+	1.34258i
$403$	−28.8547	+	3.22523i	−1.43735	+	0.160660i
$404$		−	47.2101i		−	2.34879i
$405$	2.00040	−	0.999208i	0.0994005	−	0.0496510i
$406$	3.47824			0.172622
$407$	−14.0736	−	14.0736i	−0.697601	−	0.697601i
$408$	−10.5370			−0.521657
$409$	7.15874	+	7.15874i	0.353977	+	0.353977i	0.861587	−	0.507610i	$-0.169471\pi$
$409$	7.15874	+	7.15874i	0.353977	+	0.353977i	−0.507610	+	0.861587i	$0.669471\pi$
$410$	−11.2987	−	3.77119i	−0.558001	−	0.186246i
$411$	9.47174	+	9.47174i	0.467207	+	0.467207i
$412$	−41.2439	+	41.2439i	−2.03194	+	2.03194i
$413$	−1.27957	+	1.27957i	−0.0629634	+	0.0629634i
$414$	4.73652	−	4.73652i	0.232787	−	0.232787i
$415$	−5.44036	+	2.71749i	−0.267057	+	0.133396i
$416$	4.30611	−	5.38988i	0.211124	−	0.264260i
$417$	−4.26942	+	4.26942i	−0.209075	+	0.209075i
$418$	82.5606			4.03817
$419$			23.1087i			1.12894i	0.825455	+	0.564468i	$0.190919\pi$
$419$			23.1087i			1.12894i	−0.825455	+	0.564468i	$0.809081\pi$
$420$	2.15124	+	0.718027i	0.104970	+	0.0350361i
$421$	−0.323390	+	0.323390i	−0.0157611	+	0.0157611i	−0.714943	−	0.699182i	$-0.753548\pi$
$421$	−0.323390	+	0.323390i	−0.0157611	+	0.0157611i	0.699182	+	0.714943i	$0.253548\pi$
$422$			54.6612i			2.66086i
$423$		−	1.68447i		−	0.0819019i
$424$	12.0748	−	12.0748i	0.586405	−	0.586405i
$425$	−9.60467	+	1.36434i	−0.465895	+	0.0661800i
$426$		−	0.274470i		−	0.0132981i
$427$	−2.48442			−0.120229
$428$	16.7460	−	16.7460i	0.809448	−	0.809448i
$429$	−13.4965	+	16.8933i	−0.651615	+	0.815615i
$430$	28.9863	+	9.67486i	1.39784	+	0.466563i
$431$	1.67187	−	1.67187i	0.0805312	−	0.0805312i	−0.665694	−	0.746225i	$-0.731864\pi$
$431$	1.67187	−	1.67187i	0.0805312	−	0.0805312i	0.746225	+	0.665694i	$0.231864\pi$
$432$	3.63258	−	3.63258i	0.174772	−	0.174772i
$433$	10.8483	−	10.8483i	0.521337	−	0.521337i	−0.396638	−	0.917975i	$-0.629823\pi$
$433$	10.8483	−	10.8483i	0.521337	−	0.521337i	0.917975	+	0.396638i	$0.129823\pi$
$434$	−3.43254	−	3.43254i	−0.164767	−	0.164767i
$435$	4.08479	−	12.2382i	0.195851	−	0.586778i
$436$	19.2272	+	19.2272i	0.920815	+	0.920815i
$437$	−14.9124			−0.713358
$438$	2.55675	+	2.55675i	0.122166	+	0.122166i
$439$	−20.2491			−0.966437			−0.483219	−	0.875500i	$-0.660532\pi$
$439$	−20.2491			−0.966437			−0.483219	+	0.875500i	$0.660532\pi$
$440$	−23.0569	+	69.0796i	−1.09920	+	3.29324i
$441$		−	6.94124i		−	0.330535i
$442$	−17.2885	+	1.93242i	−0.822330	+	0.0919159i
$443$	−13.2900	−	13.2900i	−0.631425	−	0.631425i	0.317000	−	0.948426i	$-0.397324\pi$
$443$	−13.2900	−	13.2900i	−0.631425	−	0.631425i	−0.948426	+	0.317000i	$0.897324\pi$
$444$	9.81859	+	9.81859i	0.465970	+	0.465970i
$445$	−0.888174	+	2.66101i	−0.0421035	+	0.126144i
$446$			21.6849i			1.02681i
$447$			20.9230i			0.989622i
$448$	−1.33725			−0.0631792
$449$	23.3059	−	23.3059i	1.09988	−	1.09988i	0.105451	−	0.994425i	$-0.466372\pi$
$449$	23.3059	−	23.3059i	1.09988	−	1.09988i	0.994425	−	0.105451i	$-0.0336285\pi$
$450$	7.46811	−	9.94107i	0.352050	−	0.468627i
$451$	12.8464			0.604916
$452$	−51.5778	−	51.5778i	−2.42602	−	2.42602i
$453$			20.7595i			0.975367i
$454$	45.7346			2.14643
$455$	1.91113	+	0.409009i	0.0895952	+	0.0191746i
$456$	−30.0656			−1.40795
$457$			15.5860i			0.729085i	0.931187	+	0.364542i	$0.118775\pi$
$457$			15.5860i			0.729085i	−0.931187	+	0.364542i	$0.881225\pi$
$458$	−41.5662	−	41.5662i	−1.94226	−	1.94226i
$459$	−1.94022			−0.0905616
$460$	7.97857	−	23.9042i	0.372003	−	1.11454i
$461$	20.8994	−	20.8994i	0.973381	−	0.973381i	−0.0262742	−	0.999655i	$-0.508364\pi$
$461$	20.8994	−	20.8994i	0.973381	−	0.973381i	0.999655	+	0.0262742i	$0.00836429\pi$
$462$	−3.61515			−0.168192
$463$		−	8.32123i		−	0.386720i	−0.981128	−	0.193360i	$-0.938061\pi$
$463$		−	8.32123i		−	0.386720i	0.981128	−	0.193360i	$-0.0619386\pi$
$464$		−	29.6414i		−	1.37607i
$465$	−16.1086	+	8.04631i	−0.747017	+	0.373139i
$466$	−1.49436	−	1.49436i	−0.0692251	−	0.0692251i
$467$	−21.9600	−	21.9600i	−1.01619	−	1.01619i	−0.999867	−	0.0163185i	$-0.994805\pi$
$467$	−21.9600	−	21.9600i	−1.01619	−	1.01619i	−0.0163185	−	0.999867i	$-0.505195\pi$
$468$	9.41597	−	11.7858i	0.435253	−	0.544799i
$469$			3.71102i			0.171359i
$470$	−4.18554	−	8.37937i	−0.193065	−	0.386512i
$471$	−6.03433			−0.278047
$472$	28.6661	+	28.6661i	1.31947	+	1.31947i
$473$	−32.9571			−1.51537
$474$	−13.3662	−	13.3662i	−0.613929	−	0.613929i
$475$	−27.4055	+	3.89293i	−1.25745	+	0.178620i
$476$	−1.39148	−	1.39148i	−0.0637782	−	0.0637782i
$477$	2.22339	−	2.22339i	0.101802	−	0.101802i
$478$	−21.6668	+	21.6668i	−0.991015	+	0.991015i
$479$	12.9813	−	12.9813i	0.593132	−	0.593132i	−0.345344	−	0.938476i	$-0.612238\pi$
$479$	12.9813	−	12.9813i	0.593132	−	0.593132i	0.938476	+	0.345344i	$0.112238\pi$
$480$	1.35457	−	4.05836i	0.0618274	−	0.185238i
$481$	9.34889	+	7.46907i	0.426273	+	0.340560i
$482$	−15.8556	+	15.8556i	−0.722204	+	0.722204i
$483$	0.652982			0.0297117
$484$		−	104.449i		−	4.74766i
$485$	−4.75644	−	9.52231i	−0.215979	−	0.432386i
$486$	1.75839	−	1.75839i	0.0797624	−	0.0797624i
$487$		−	12.6406i		−	0.572801i	−0.958110	−	0.286400i	$-0.907541\pi$
$487$		−	12.6406i		−	0.572801i	0.958110	−	0.286400i	$-0.0924587\pi$
$488$			55.6584i			2.51954i
$489$	10.4110	−	10.4110i	0.470801	−	0.470801i
$490$	−17.2474	−	34.5290i	−0.779159	−	1.55986i
$491$		−	27.8197i		−	1.25549i	−0.778421	−	0.627743i	$-0.783979\pi$
$491$		−	27.8197i		−	1.25549i	0.778421	−	0.627743i	$-0.216021\pi$
$492$	−8.96248			−0.404060
$493$	−7.91599	+	7.91599i	−0.356518	+	0.356518i
$494$	−49.3301	+	5.51387i	−2.21947	+	0.248081i
$495$	−4.24558	+	12.7199i	−0.190825	+	0.571719i
$496$	−29.2520	+	29.2520i	−1.31345	+	1.31345i
$497$	0.0189194	−	0.0189194i	0.000848650	−	0.000848650i
$498$	−4.78221	+	4.78221i	−0.214296	+	0.214296i
$499$	0.152074	+	0.152074i	0.00680776	+	0.00680776i	0.710502	−	0.703695i	$-0.248468\pi$
$499$	0.152074	+	0.152074i	0.00680776	+	0.00680776i	−0.703695	+	0.710502i	$0.748468\pi$
$500$	8.42246	−	46.0130i	0.376664	−	2.05776i
$501$	−4.30314	−	4.30314i	−0.192250	−	0.192250i
$502$	−20.3300			−0.907372
$503$	−4.59193	−	4.59193i	−0.204744	−	0.204744i	0.597285	−	0.802029i	$-0.296246\pi$
$503$	−4.59193	−	4.59193i	−0.204744	−	0.204744i	−0.802029	+	0.597285i	$0.796246\pi$
$504$	1.31651			0.0586419
$505$	−11.2748	−	22.5719i	−0.501722	−	1.00444i
$506$			40.1708i			1.78581i
$507$	6.93593	−	10.9951i	0.308035	−	0.488311i
$508$	16.0555	+	16.0555i	0.712347	+	0.712347i
$509$	−11.1303	−	11.1303i	−0.493341	−	0.493341i	0.416016	−	0.909357i	$-0.363426\pi$
$509$	−11.1303	−	11.1303i	−0.493341	−	0.493341i	−0.909357	+	0.416016i	$0.863426\pi$
$510$	−9.65157	+	4.82101i	−0.427379	+	0.213478i
$511$			0.352477i			0.0155927i
$512$			45.9692i			2.03157i
$513$	−5.53612			−0.244425
$514$	−24.7986	+	24.7986i	−1.09382	+	1.09382i
$515$	−9.86947	+	29.5694i	−0.434901	+	1.30298i
$516$	22.9929			1.01221
$517$	7.14308	+	7.14308i	0.314152	+	0.314152i
$518$			2.00066i			0.0879038i
$519$	16.0261			0.703469
$520$	9.16302	−	42.8151i	0.401825	−	1.87756i
$521$	−13.6076			−0.596161			−0.298080	−	0.954541i	$-0.596346\pi$
$521$	−13.6076			−0.596161			−0.298080	+	0.954541i	$0.596346\pi$
$522$		−	14.3483i		−	0.628009i
$523$	−12.9591	−	12.9591i	−0.566664	−	0.566664i	0.364528	−	0.931192i	$-0.381230\pi$
$523$	−12.9591	−	12.9591i	−0.566664	−	0.566664i	−0.931192	+	0.364528i	$0.881230\pi$
$524$	21.0844			0.921076
$525$	1.20003	−	0.170463i	0.0523734	−	0.00743960i
$526$	41.1644	−	41.1644i	1.79485	−	1.79485i
$527$	15.6240			0.680591
$528$			30.8082i			1.34075i
$529$			15.7442i			0.684530i
$530$	5.53558	−	16.5848i	0.240450	−	0.720399i
$531$	5.27843	+	5.27843i	0.229064	+	0.229064i
$532$	−3.97036	−	3.97036i	−0.172137	−	0.172137i
$533$	−7.67577	+	0.857959i	−0.332475	+	0.0371623i
$534$			3.11981i			0.135008i
$535$	4.00723	−	12.0059i	0.173248	−	0.519058i
$536$	83.1381			3.59102
$537$	−2.82652	−	2.82652i	−0.121973	−	0.121973i
$538$	41.5708			1.79224
$539$	29.4346	+	29.4346i	1.26784	+	1.26784i
$540$	2.96198	−	8.87423i	0.127463	−	0.381886i
$541$	−24.0220	−	24.0220i	−1.03279	−	1.03279i	−0.999444	−	0.0333420i	$-0.989385\pi$
$541$	−24.0220	−	24.0220i	−1.03279	−	1.03279i	−0.0333420	−	0.999444i	$-0.510615\pi$
$542$	31.3092	−	31.3092i	1.34485	−	1.34485i
$543$	−11.6979	+	11.6979i	−0.502005	+	0.502005i
$544$	−2.62505	+	2.62505i	−0.112548	+	0.112548i
$545$	13.7847	+	4.60097i	0.590473	+	0.197084i
$546$	2.16006	−	0.241440i	0.0924419	−	0.0103327i
$547$	−18.6456	+	18.6456i	−0.797229	+	0.797229i	−0.982658	−	0.185428i	$-0.940633\pi$
$547$	−18.6456	+	18.6456i	−0.797229	+	0.797229i	0.185428	+	0.982658i	$0.440633\pi$
$548$	56.0437			2.39407
$549$			10.2486i			0.437401i
$550$	10.4867	+	73.8244i	0.447154	+	3.14788i
$551$	−22.5871	+	22.5871i	−0.962241	+	0.962241i
$552$		−	14.6288i		−	0.622641i
$553$		−	1.84268i		−	0.0783586i
$554$	−44.4977	+	44.4977i	−1.89053	+	1.89053i
$555$	7.03933	+	2.34954i	0.298803	+	0.0997325i
$556$			25.2619i			1.07134i
$557$	−1.32872			−0.0562996			−0.0281498	−	0.999604i	$-0.508962\pi$
$557$	−1.32872			−0.0562996			−0.0281498	+	0.999604i	$0.508962\pi$
$558$	−14.1598	+	14.1598i	−0.599432	+	0.599432i
$559$	19.6919	−	2.20106i	0.832880	−	0.0930951i
$560$	2.49117	−	1.24435i	0.105271	−	0.0525836i
$561$	8.22758	−	8.22758i	0.347369	−	0.347369i
$562$	−6.58175	+	6.58175i	−0.277634	+	0.277634i
$563$	−15.2469	+	15.2469i	−0.642582	+	0.642582i	−0.951190	−	0.308607i	$-0.900137\pi$
$563$	−15.2469	+	15.2469i	−0.642582	+	0.642582i	0.308607	+	0.951190i	$0.400137\pi$
$564$	−4.98346	−	4.98346i	−0.209842	−	0.209842i
$565$	−36.9782	−	12.3423i	−1.55568	−	0.519246i
$566$	−6.56889	−	6.56889i	−0.276111	−	0.276111i
$567$	0.242414			0.0101804
$568$	−0.423851	−	0.423851i	−0.0177844	−	0.0177844i
$569$	31.7042			1.32911			0.664555	−	0.747239i	$-0.268621\pi$
$569$	31.7042			1.32911			0.664555	+	0.747239i	$0.268621\pi$
$570$	−27.5393	+	13.7560i	−1.15349	+	0.576176i
$571$		−	3.77184i		−	0.157847i	−0.996881	−	0.0789233i	$-0.974852\pi$
$571$		−	3.77184i		−	0.157847i	0.996881	−	0.0789233i	$-0.0251482\pi$
$572$	10.0493	+	89.9070i	0.420184	+	3.75920i
$573$	−9.22243	−	9.22243i	−0.385272	−	0.385272i
$574$	−0.913107	−	0.913107i	−0.0381123	−	0.0381123i
$575$	−1.89415	−	13.3344i	−0.0789914	−	0.556085i
$576$			5.51638i			0.229849i
$577$			38.7401i			1.61277i	0.591391	+	0.806385i	$0.298579\pi$
$577$			38.7401i			1.61277i	−0.591391	+	0.806385i	$0.701421\pi$
$578$	−32.9135			−1.36902
$579$	−6.56419	+	6.56419i	−0.272799	+	0.272799i
$580$	−24.1217	−	48.2911i	−1.00160	−	2.00518i
$581$	−0.659281			−0.0273516
$582$	−8.37033	−	8.37033i	−0.346962	−	0.346962i
$583$			18.8568i			0.780967i
$584$	7.89654			0.326761
$585$	1.68723	−	7.88373i	0.0697584	−	0.325952i
$586$	−22.0632			−0.911423
$587$		−	11.4947i		−	0.474438i	−0.971456	−	0.237219i	$-0.923764\pi$
$587$		−	11.4947i		−	0.474438i	0.971456	−	0.237219i	$-0.0762358\pi$
$588$	−20.5354	−	20.5354i	−0.846866	−	0.846866i
$589$	44.5806			1.83691
$590$	39.3731	+	13.1417i	1.62097	+	0.541035i
$591$	9.13041	−	9.13041i	0.375575	−	0.375575i
$592$	17.0495			0.700731
$593$		−	23.5194i		−	0.965824i	−0.875669	−	0.482912i	$-0.839579\pi$
$593$		−	23.5194i		−	0.965824i	0.875669	−	0.482912i	$-0.160421\pi$
$594$			14.9131i			0.611891i
$595$	−0.997603	−	0.332973i	−0.0408978	−	0.0136506i
$596$	61.8999	+	61.8999i	2.53552	+	2.53552i
$597$	−1.66548	−	1.66548i	−0.0681636	−	0.0681636i
$598$	−2.68284	−	24.0021i	−0.109709	−	0.981520i
$599$			15.0098i			0.613282i	0.951825	+	0.306641i	$0.0992051\pi$
$599$			15.0098i			0.613282i	−0.951825	+	0.306641i	$0.900795\pi$
$600$	−3.81888	−	26.8842i	−0.155905	−	1.09754i
$601$	−9.20174			−0.375347			−0.187673	−	0.982231i	$-0.560095\pi$
$601$	−9.20174			−0.375347			−0.187673	+	0.982231i	$0.560095\pi$
$602$	2.34254	+	2.34254i	0.0954749	+	0.0954749i
$603$	15.3086			0.623414
$604$	61.4163	+	61.4163i	2.49900	+	2.49900i
$605$	−24.9446	−	49.9386i	−1.01414	−	2.03029i
$606$	−19.8413	−	19.8413i	−0.805996	−	0.805996i
$607$	−1.90926	+	1.90926i	−0.0774945	+	0.0774945i	−0.744792	−	0.667297i	$-0.767451\pi$
$607$	−1.90926	+	1.90926i	−0.0774945	+	0.0774945i	0.667297	+	0.744792i	$0.267451\pi$
$608$	−7.49017	+	7.49017i	−0.303766	+	0.303766i
$609$	0.989038	−	0.989038i	0.0400779	−	0.0400779i
$610$	25.4656	+	50.9816i	1.03107	+	2.06418i
$611$	−4.74506	−	3.79095i	−0.191965	−	0.153365i
$612$	−5.74007	+	5.74007i	−0.232029	+	0.232029i
$613$	−8.40716			−0.339562			−0.169781	−	0.985482i	$-0.554306\pi$
$613$	−8.40716			−0.339562			−0.169781	+	0.985482i	$0.554306\pi$
$614$		−	62.6245i		−	2.52732i
$615$	−4.28512	+	2.14044i	−0.172793	+	0.0863108i
$616$	−5.58270	+	5.58270i	−0.224933	+	0.224933i
$617$			5.02106i			0.202140i	0.994879	+	0.101070i	$0.0322267\pi$
$617$			5.02106i			0.202140i	−0.994879	+	0.101070i	$0.967773\pi$
$618$			34.6677i			1.39454i
$619$	−28.7489	+	28.7489i	−1.15552	+	1.15552i	−0.170089	+	0.985429i	$0.554405\pi$
$619$	−28.7489	+	28.7489i	−1.15552	+	1.15552i	−0.985429	+	0.170089i	$0.945595\pi$
$620$	−23.8519	+	71.4614i	−0.957915	+	2.86996i
$621$		−	2.69366i		−	0.108093i
$622$	−17.5524			−0.703786
$623$	−0.215051	+	0.215051i	−0.00861582	+	0.00861582i
$624$	−2.05755	−	18.4079i	−0.0823678	−	0.736907i
$625$	−6.96198	−	24.0111i	−0.278479	−	0.960442i
$626$	−9.58810	+	9.58810i	−0.383218	+	0.383218i
$627$	23.4761	−	23.4761i	0.937546	−	0.937546i
$628$	−17.8524	+	17.8524i	−0.712386	+	0.712386i
$629$	−4.55322	−	4.55322i	−0.181549	−	0.181549i
$630$	1.20588	−	0.602346i	0.0480436	−	0.0239980i
$631$	21.7388	+	21.7388i	0.865407	+	0.865407i	0.991960	−	0.126553i	$-0.0403913\pi$
$631$	21.7388	+	21.7388i	0.865407	+	0.865407i	−0.126553	+	0.991960i	$0.540391\pi$
$632$	−41.2815			−1.64209
$633$	15.5429	+	15.5429i	0.617775	+	0.617775i
$634$	−34.6097			−1.37453
$635$	11.5108	+	3.84200i	0.456793	+	0.152465i
$636$		−	13.1557i		−	0.521656i
$637$	−19.5530	−	15.6214i	−0.774719	−	0.618943i
$638$	60.8446	+	60.8446i	2.40886	+	2.40886i
$639$	−0.0780456	−	0.0780456i	−0.00308744	−	0.00308744i
$640$	17.5307	+	35.0962i	0.692962	+	1.38730i
$641$			8.55187i			0.337779i	0.985635	+	0.168889i	$0.0540181\pi$
$641$			8.55187i			0.337779i	−0.985635	+	0.168889i	$0.945982\pi$
$642$		−	14.0759i		−	0.555531i
$643$	−3.11521			−0.122852			−0.0614259	−	0.998112i	$-0.519565\pi$
$643$	−3.11521			−0.122852			−0.0614259	+	0.998112i	$0.519565\pi$
$644$	1.93183	−	1.93183i	0.0761246	−	0.0761246i
$645$	10.9933	−	5.49122i	0.432861	−	0.216217i
$646$	26.7108			1.05092
$647$	26.4560	+	26.4560i	1.04009	+	1.04009i	0.999162	+	0.0409311i	$0.0130324\pi$
$647$	26.4560	+	26.4560i	1.04009	+	1.04009i	0.0409311	+	0.999162i	$0.486968\pi$
$648$		−	5.43081i		−	0.213342i
$649$	−44.7668			−1.75725
$650$	−11.1962	−	43.4098i	−0.439152	−	1.70267i
$651$	−1.95209			−0.0765084
$652$		−	61.6010i		−	2.41248i
$653$	−9.61272	−	9.61272i	−0.376175	−	0.376175i	0.493545	−	0.869720i	$-0.335701\pi$
$653$	−9.61272	−	9.61272i	−0.376175	−	0.376175i	−0.869720	+	0.493545i	$0.835701\pi$
$654$	16.1615			0.631963
$655$	10.0808	−	5.03542i	0.393890	−	0.196750i
$656$	−7.78146	+	7.78146i	−0.303815	+	0.303815i
$657$	1.45403			0.0567270
$658$		−	1.01544i		−	0.0395860i
$659$		−	15.1490i		−	0.590122i	−0.955478	−	0.295061i	$-0.904660\pi$
$659$		−	15.1490i		−	0.590122i	0.955478	−	0.295061i	$-0.0953400\pi$
$660$	25.0711	+	50.1919i	0.975892	+	1.95372i
$661$	18.9976	+	18.9976i	0.738920	+	0.738920i	0.972369	−	0.233449i	$-0.0750013\pi$
$661$	18.9976	+	18.9976i	0.738920	+	0.738920i	−0.233449	+	0.972369i	$0.575001\pi$
$662$	17.1157	+	17.1157i	0.665220	+	0.665220i
$663$	−4.36651	+	5.46548i	−0.169581	+	0.212262i
$664$			14.7699i			0.573182i
$665$	−2.84651	−	0.950089i	−0.110383	−	0.0368429i
$666$	8.25304			0.319799
$667$	−10.9900	−	10.9900i	−0.425534	−	0.425534i
$668$	−25.4614			−0.985131
$669$	6.16611	+	6.16611i	0.238396	+	0.238396i
$670$	76.1522	−	38.0384i	2.94202	−	1.46955i
$671$	−43.4597	−	43.4597i	−1.67774	−	1.67774i
$672$	0.327978	−	0.327978i	0.0126520	−	0.0126520i
$673$	26.4650	−	26.4650i	1.02015	−	1.02015i	0.0203584	−	0.999793i	$-0.493519\pi$
$673$	26.4650	−	26.4650i	1.02015	−	1.02015i	0.999793	−	0.0203584i	$-0.00648074\pi$
$674$	2.01953	−	2.01953i	0.0777895	−	0.0777895i
$675$	−0.703187	−	4.95031i	−0.0270657	−	0.190537i
$676$	−12.0090	−	53.0484i	−0.461885	−	2.04032i
$677$	−13.7029	+	13.7029i	−0.526645	+	0.526645i	−0.919570	−	0.392925i	$-0.871463\pi$
$677$	−13.7029	+	13.7029i	−0.526645	+	0.526645i	0.392925	+	0.919570i	$0.371463\pi$
$678$	−43.3539			−1.66500
$679$		−	1.15394i		−	0.0442843i
$680$	−7.45960	+	22.3493i	−0.286063	+	0.857057i
$681$	13.0046	−	13.0046i	0.498339	−	0.498339i
$682$		−	120.090i		−	4.59850i
$683$		−	14.6506i		−	0.560588i	−0.959914	−	0.280294i	$-0.909568\pi$
$683$		−	14.6506i		−	0.560588i	0.959914	−	0.280294i	$-0.0904320\pi$
$684$	−16.3784	+	16.3784i	−0.626244	+	0.626244i
$685$	26.7954	−	13.3845i	1.02380	−	0.511394i
$686$		−	8.40410i		−	0.320870i
$687$	−23.6387			−0.901873
$688$	19.9631	−	19.9631i	0.761085	−	0.761085i
$689$	−1.25936	−	11.2670i	−0.0479779	−	0.429237i
$690$	−6.69314	−	13.3995i	−0.254804	−	0.510112i
$691$	−34.7630	+	34.7630i	−1.32245	+	1.32245i	−0.410660	+	0.911789i	$0.634702\pi$
$691$	−34.7630	+	34.7630i	−1.32245	+	1.32245i	−0.911789	+	0.410660i	$0.865298\pi$
$692$	47.4128	−	47.4128i	1.80236	−	1.80236i
$693$	−1.02797	+	1.02797i	−0.0390493	+	0.0390493i
$694$	−62.7023	−	62.7023i	−2.38015	−	2.38015i
$695$	6.03310	+	12.0781i	0.228848	+	0.458150i
$696$	−22.1574	−	22.1574i	−0.839875	−	0.839875i
$697$	4.15621			0.157428
$698$	−12.0740	−	12.0740i	−0.457009	−	0.457009i
$699$	−0.849846			−0.0321441
$700$	3.04593	−	4.05454i	0.115125	−	0.153247i
$701$			13.7058i			0.517659i	0.965923	+	0.258830i	$0.0833369\pi$
$701$			13.7058i			0.517659i	−0.965923	+	0.258830i	$0.916663\pi$
$702$	−0.995982	−	8.91060i	−0.0375909	−	0.336309i
$703$	−12.9919	−	12.9919i	−0.489999	−	0.489999i
$704$	−23.3925	−	23.3925i	−0.881636	−	0.881636i
$705$	−3.57284	−	1.19252i	−0.134561	−	0.0449128i
$706$		−	64.5208i		−	2.42827i
$707$		−	2.73534i		−	0.102873i
$708$	31.2321			1.17377
$709$	−4.33781	+	4.33781i	−0.162910	+	0.162910i	−0.783854	−	0.620945i	$-0.786749\pi$
$709$	−4.33781	+	4.33781i	−0.162910	+	0.162910i	0.620945	+	0.783854i	$0.286749\pi$
$710$	−0.582162	−	0.194310i	−0.0218481	−	0.00729232i
$711$	−7.60135			−0.285073
$712$	4.81778	+	4.81778i	0.180554	+	0.180554i
$713$			21.6912i			0.812342i
$714$	−1.16961			−0.0437715
$715$	26.2765	+	40.5861i	0.982687	+	1.51783i
$716$	−16.7243			−0.625017
$717$			12.3219i			0.460170i
$718$	5.75584	+	5.75584i	0.214806	+	0.214806i
$719$	−27.4328			−1.02307			−0.511536	−	0.859262i	$-0.670923\pi$
$719$	−27.4328			−1.02307			−0.511536	+	0.859262i	$0.670923\pi$
$720$	−5.13317	−	10.2765i	−0.191302	−	0.382983i
$721$	−2.38966	+	2.38966i	−0.0889957	+	0.0889957i
$722$	28.9670			1.07804
$723$			9.01711i			0.335350i
$724$			69.2157i			2.57238i
$725$	−23.0660	−	17.3280i	−0.856648	−	0.643547i
$726$	−43.8972	−	43.8972i	−1.62918	−	1.62918i
$727$	27.8372	+	27.8372i	1.03243	+	1.03243i	0.999456	+	0.0329694i	$0.0104964\pi$
$727$	27.8372	+	27.8372i	1.03243	+	1.03243i	0.0329694	+	0.999456i	$0.489504\pi$
$728$	2.96283	−	3.70852i	0.109810	−	0.137447i
$729$		−	1.00000i		−	0.0370370i
$730$	7.23302	−	3.61293i	0.267706	−	0.133721i
$731$	−10.6626			−0.394371
$732$	30.3202	+	30.3202i	1.12067	+	1.12067i
$733$	16.0974			0.594571			0.297285	−	0.954789i	$-0.403919\pi$
$733$	16.0974			0.594571			0.297285	+	0.954789i	$0.403919\pi$
$734$	−25.5034	−	25.5034i	−0.941349	−	0.941349i
$735$	−14.7226	−	4.91402i	−0.543053	−	0.181256i
$736$	−3.64443	−	3.64443i	−0.134335	−	0.134335i
$737$	−64.9167	+	64.9167i	−2.39124	+	2.39124i
$738$	−3.76672	+	3.76672i	−0.138655	+	0.138655i
$739$	−9.67318	+	9.67318i	−0.355834	+	0.355834i	−0.862275	−	0.506441i	$-0.830961\pi$
$739$	−9.67318	+	9.67318i	−0.355834	+	0.355834i	0.506441	+	0.862275i	$0.330961\pi$
$740$	27.7767	−	13.8746i	1.02109	−	0.510040i
$741$	−12.4592	+	15.5949i	−0.457699	+	0.572893i
$742$	1.34031	−	1.34031i	0.0492044	−	0.0492044i
$743$	−0.660092			−0.0242164			−0.0121082	−	0.999927i	$-0.503854\pi$
$743$	−0.660092			−0.0242164			−0.0121082	+	0.999927i	$0.503854\pi$
$744$			43.7326i			1.60332i
$745$	44.3784	+	14.8123i	1.62590	+	0.542682i
$746$	13.2653	−	13.2653i	0.485675	−	0.485675i
$747$			2.71964i			0.0995066i
$748$		−	48.6820i		−	1.77999i
$749$	0.970259	−	0.970259i	0.0354525	−	0.0354525i
$750$	−15.7984	−	22.8779i	−0.576876	−	0.835383i
$751$		−	35.4818i		−	1.29475i	−0.762171	−	0.647375i	$-0.775867\pi$
$751$		−	35.4818i		−	1.29475i	0.762171	−	0.647375i	$-0.224133\pi$
$752$	−8.65354			−0.315562
$753$	−5.78084	+	5.78084i	−0.210665	+	0.210665i
$754$	−40.4183	−	32.2912i	−1.47195	−	1.17598i
$755$	44.0318	+	14.6966i	1.60248	+	0.534865i
$756$	0.717175	−	0.717175i	0.0260834	−	0.0260834i
$757$	10.5506	−	10.5506i	0.383469	−	0.383469i	−0.488881	−	0.872350i	$-0.662595\pi$
$757$	10.5506	−	10.5506i	0.383469	−	0.383469i	0.872350	+	0.488881i	$0.162595\pi$
$758$	12.1642	−	12.1642i	0.441823	−	0.441823i
$759$	11.4226	+	11.4226i	0.414613	+	0.414613i
$760$	−21.2848	+	63.7703i	−0.772082	+	2.31319i
$761$	22.4488	+	22.4488i	0.813767	+	0.813767i	0.985196	−	0.171429i	$-0.0548386\pi$
$761$	22.4488	+	22.4488i	0.813767	+	0.813767i	−0.171429	+	0.985196i	$0.554839\pi$
$762$	13.4955			0.488890
$763$	1.11402	+	1.11402i	0.0403302	+	0.0403302i
$764$	−54.5685			−1.97422
$765$	−1.37357	+	4.11528i	−0.0496616	+	0.148788i
$766$		−	0.824345i		−	0.0297848i
$767$	26.7482	−	2.98978i	0.965822	−	0.107955i
$768$	23.0490	+	23.0490i	0.831709	+	0.831709i
$769$	−3.44776	−	3.44776i	−0.124329	−	0.124329i	0.642204	−	0.766534i	$-0.278020\pi$
$769$	−3.44776	−	3.44776i	−0.124329	−	0.124329i	−0.766534	+	0.642204i	$0.778020\pi$
$770$	−2.55933	+	7.66787i	−0.0922319	+	0.276331i
$771$			14.1030i			0.507907i
$772$			38.8399i			1.39788i
$773$	25.5316			0.918307			0.459154	−	0.888357i	$-0.348153\pi$
$773$	25.5316			0.918307			0.459154	+	0.888357i	$0.348153\pi$
$774$	9.66338	−	9.66338i	0.347343	−	0.347343i
$775$	5.66255	+	39.8633i	0.203405	+	1.43193i
$776$	−25.8518			−0.928026
$777$	0.568887	+	0.568887i	0.0204087	+	0.0204087i
$778$		−	16.8578i		−	0.604383i
$779$	11.8591			0.424896
$780$	−18.3321	−	28.3154i	−0.656396	−	1.01385i
$781$	0.661911			0.0236850
$782$			12.9965i			0.464752i
$783$	−4.07995	−	4.07995i	−0.145805	−	0.145805i
$784$	−35.6588			−1.27353
$785$	−4.27198	+	12.7991i	−0.152474	+	0.456818i
$786$	8.86127	−	8.86127i	0.316071	−	0.316071i
$787$	−15.5693			−0.554986			−0.277493	−	0.960728i	$-0.589504\pi$
$787$	−15.5693			−0.554986			−0.277493	+	0.960728i	$0.589504\pi$
$788$		−	54.0240i		−	1.92453i
$789$		−	23.4102i		−	0.833426i
$790$	−37.8127	+	18.8876i	−1.34532	+	0.671992i
$791$	−2.98841	−	2.98841i	−0.106256	−	0.106256i
$792$	23.0296	+	23.0296i	0.818320	+	0.818320i
$793$	28.8698	+	23.0648i	1.02520	+	0.819055i
$794$		−	63.9772i		−	2.27046i
$795$	−3.14186	−	6.28995i	−0.111430	−	0.223081i
$796$	−9.85453			−0.349285
$797$	−7.35388	−	7.35388i	−0.260488	−	0.260488i	0.564764	−	0.825252i	$-0.308967\pi$
$797$	−7.35388	−	7.35388i	−0.260488	−	0.260488i	−0.825252	+	0.564764i	$0.808967\pi$
$798$	−3.33730			−0.118139
$799$	2.31100	+	2.31100i	0.0817573	+	0.0817573i
$800$	−7.64897	−	5.74620i	−0.270432	−	0.203159i
$801$	0.887120	+	0.887120i	0.0313448	+	0.0313448i
$802$	19.2132	−	19.2132i	0.678440	−	0.678440i
$803$	−6.16586	+	6.16586i	−0.217588	+	0.217588i
$804$	45.2900	−	45.2900i	1.59725	−	1.59725i
$805$	0.462277	−	1.38500i	0.0162931	−	0.0488149i
$806$	8.02033	+	71.7543i	0.282504	+	2.52744i
$807$	11.8207	−	11.8207i	0.416107	−	0.416107i
$808$	−61.2798			−2.15582
$809$			32.8074i			1.15345i	0.816939	+	0.576724i	$0.195669\pi$
$809$			32.8074i			1.15345i	−0.816939	+	0.576724i	$0.804331\pi$
$810$	−2.48478	−	4.97448i	−0.0873061	−	0.174785i
$811$	−23.4835	+	23.4835i	−0.824618	+	0.824618i	−0.986766	−	0.162149i	$-0.948158\pi$
$811$	−23.4835	+	23.4835i	−0.824618	+	0.824618i	0.162149	+	0.986766i	$0.448158\pi$
$812$		−	5.85207i		−	0.205368i
$813$		−	17.8056i		−	0.624468i
$814$	−34.9974	+	34.9974i	−1.22666	+	1.22666i
$815$	−14.7117	−	29.4525i	−0.515328	−	1.03168i
$816$			9.96736i			0.348927i
$817$	−30.4241			−1.06440
$818$	17.8020	−	17.8020i	0.622431	−	0.622431i
$819$	0.545559	−	0.682867i	0.0190634	−	0.0238613i
$820$	−6.34496	+	19.0098i	−0.221576	+	0.663850i
$821$	28.3481	−	28.3481i	0.989357	−	0.989357i	−0.0105868	−	0.999944i	$-0.503370\pi$
$821$	28.3481	−	28.3481i	0.989357	−	0.989357i	0.999944	+	0.0105868i	$0.00336993\pi$
$822$	23.5538	−	23.5538i	0.821534	−	0.821534i
$823$	−33.0457	+	33.0457i	−1.15190	+	1.15190i	−0.165729	+	0.986171i	$0.552998\pi$
$823$	−33.0457	+	33.0457i	−1.15190	+	1.15190i	−0.986171	+	0.165729i	$0.947002\pi$
$824$	53.5356	+	53.5356i	1.86500	+	1.86500i
$825$	23.9739	+	18.0101i	0.834663	+	0.627031i
$826$	3.18196	+	3.18196i	0.110714	+	0.110714i
$827$	50.1300			1.74319			0.871596	−	0.490225i	$-0.163085\pi$
$827$	50.1300			1.74319			0.871596	+	0.490225i	$0.163085\pi$
$828$	−7.96910	−	7.96910i	−0.276946	−	0.276946i
$829$	28.1449			0.977512			0.488756	−	0.872420i	$-0.337451\pi$
$829$	28.1449			0.977512			0.488756	+	0.872420i	$0.337451\pi$
$830$	6.75771	+	13.5288i	0.234563	+	0.469592i
$831$			25.3059i			0.877850i
$832$	15.5393	+	12.4148i	0.538729	+	0.430404i
$833$	9.52297	+	9.52297i	0.329951	+	0.329951i
$834$	10.6170	+	10.6170i	0.367636	+	0.367636i
$835$	−12.1735	+	6.08074i	−0.421282	+	0.210433i
$836$		−	138.907i		−	4.80419i
$837$			8.05269i			0.278342i
$838$	57.4655			1.98511
$839$	−25.8159	+	25.8159i	−0.891264	+	0.891264i	−0.994642	−	0.103378i	$-0.967035\pi$
$839$	−25.8159	+	25.8159i	−0.891264	+	0.891264i	0.103378	+	0.994642i	$0.467035\pi$
$840$	0.932016	−	2.79236i	0.0321576	−	0.0963457i
$841$	−4.29196			−0.147999
$842$	0.804189	+	0.804189i	0.0277142	+	0.0277142i
$843$			3.74304i			0.128917i
$844$	91.9664			3.16561
$845$	−18.4108	−	22.4953i	−0.633352	−	0.773864i
$846$	−4.18886			−0.144016
$847$		−	6.05173i		−	0.207940i
$848$	−11.4221	−	11.4221i	−0.392236	−	0.392236i
$849$	−3.73573			−0.128210
$850$	3.39276	+	23.8844i	0.116371	+	0.819227i
$851$	6.32136	−	6.32136i	0.216694	−	0.216694i
$852$	−0.461790			−0.0158207
$853$			6.25026i			0.214005i	0.994259	+	0.107002i	$0.0341253\pi$
$853$			6.25026i			0.214005i	−0.994259	+	0.107002i	$0.965875\pi$
$854$			6.17811i			0.211411i
$855$	−3.91927	+	11.7423i	−0.134036	+	0.401579i
$856$	−21.7367	−	21.7367i	−0.742945	−	0.742945i
$857$	−12.2252	−	12.2252i	−0.417607	−	0.417607i	0.466771	−	0.884378i	$-0.345417\pi$
$857$	−12.2252	−	12.2252i	−0.417607	−	0.417607i	−0.884378	+	0.466771i	$0.845417\pi$
$858$	42.0093	+	33.5623i	1.43417	+	1.14580i
$859$		−	25.0493i		−	0.854670i	−0.904093	−	0.427335i	$-0.859452\pi$
$859$		−	25.0493i		−	0.854670i	0.904093	−	0.427335i	$-0.140548\pi$
$860$	16.2778	−	48.7689i	0.555067	−	1.66301i
$861$	−0.519284			−0.0176972
$862$	−4.15752	−	4.15752i	−0.141606	−	0.141606i
$863$	−25.4480			−0.866261			−0.433130	−	0.901331i	$-0.642591\pi$
$863$	−25.4480			−0.866261			−0.433130	+	0.901331i	$0.642591\pi$
$864$	−1.35296	−	1.35296i	−0.0460288	−	0.0460288i
$865$	11.3456	−	33.9921i	0.385763	−	1.15576i
$866$	−26.9770	−	26.9770i	−0.916716	−	0.916716i
$867$	−9.35895	+	9.35895i	−0.317847	+	0.317847i
$868$	−5.77519	+	5.77519i	−0.196023	+	0.196023i
$869$	32.2338	−	32.2338i	1.09346	−	1.09346i
$870$	−30.4334	−	10.1578i	−1.03179	−	0.344383i
$871$	34.4524	−	43.1234i	1.16737	−	1.46118i
$872$	24.9574	−	24.9574i	0.845163	−	0.845163i
$873$	−4.76021			−0.161109
$874$			37.0834i			1.25436i
$875$	0.487996	−	2.66598i	0.0164973	−	0.0901266i
$876$	4.30169	−	4.30169i	0.145341	−	0.145341i
$877$			21.2930i			0.719015i	0.933142	+	0.359507i	$0.117055\pi$
$877$			21.2930i			0.719015i	−0.933142	+	0.359507i	$0.882945\pi$
$878$			50.3544i			1.69938i
$879$	−6.27368	+	6.27368i	−0.211606	+	0.211606i
$880$	65.3454	+	21.8105i	2.20279	+	0.735233i
$881$		−	10.5084i		−	0.354037i	−0.984208	−	0.177018i	$-0.943355\pi$
$881$		−	10.5084i		−	0.354037i	0.984208	−	0.177018i	$-0.0566452\pi$
$882$	−17.2611			−0.581211
$883$	9.86276	−	9.86276i	0.331908	−	0.331908i	−0.521403	−	0.853311i	$-0.674591\pi$
$883$	9.86276	−	9.86276i	0.331908	−	0.331908i	0.853311	+	0.521403i	$0.174591\pi$
$884$	3.25126	+	29.0876i	0.109352	+	0.978321i
$885$	14.9326	−	7.45891i	0.501954	−	0.250729i
$886$	−33.0488	+	33.0488i	−1.11030	+	1.11030i
$887$	21.5847	−	21.5847i	0.724745	−	0.724745i	−0.244823	−	0.969568i	$-0.578730\pi$
$887$	21.5847	−	21.5847i	0.724745	−	0.724745i	0.969568	+	0.244823i	$0.0787299\pi$
$888$	12.7448	−	12.7448i	0.427687	−	0.427687i
$889$	0.930252	+	0.930252i	0.0311996	+	0.0311996i
$890$	6.61725	+	2.20866i	0.221811	+	0.0740345i
$891$	4.24054	+	4.24054i	0.142063	+	0.142063i
$892$	36.4845			1.22159
$893$	6.59408	+	6.59408i	0.220663	+	0.220663i
$894$	52.0301			1.74015
$895$	−7.99618	+	3.99413i	−0.267283	+	0.133509i
$896$			4.25307i			0.142085i
$897$	−7.58788	−	6.06215i	−0.253352	−	0.202409i
$898$	−57.9559	−	57.9559i	−1.93401	−	1.93401i
$899$	32.8546	+	32.8546i	1.09576	+	1.09576i
$900$	−16.7257	−	12.5650i	−0.557522	−	0.418832i
$901$			6.10073i			0.203245i
$902$		−	31.9458i		−	1.06368i
$903$	1.33221			0.0443330
$904$	−66.9493	+	66.9493i	−2.22670	+	2.22670i
$905$	16.5302	+	33.0932i	0.549483	+	1.10005i
$906$	51.6236			1.71508
$907$	14.1974	+	14.1974i	0.471417	+	0.471417i	0.902373	−	0.430956i	$-0.141823\pi$
$907$	14.1974	+	14.1974i	0.471417	+	0.471417i	−0.430956	+	0.902373i	$0.641823\pi$
$908$		−	76.9475i		−	2.55359i
$909$	−11.2837			−0.374258
$910$	1.01710	−	4.75250i	0.0337166	−	0.157544i
$911$	−6.62609			−0.219532			−0.109766	−	0.993957i	$-0.535010\pi$
$911$	−6.62609			−0.219532			−0.109766	+	0.993957i	$0.535010\pi$
$912$			28.4403i			0.941754i
$913$	−11.5328	−	11.5328i	−0.381679	−	0.381679i
$914$	38.7585			1.28202
$915$	21.7378	+	7.25548i	0.718628	+	0.239859i
$916$	−69.9344	+	69.9344i	−2.31070	+	2.31070i
$917$	1.22162			0.0403416
$918$			4.82483i			0.159243i
$919$		−	56.0617i		−	1.84930i	−0.380813	−	0.924652i	$-0.624356\pi$
$919$		−	56.0617i		−	1.84930i	0.380813	−	0.924652i	$-0.375644\pi$
$920$	−31.0282	−	10.3564i	−1.02297	−	0.341440i
$921$	−17.8073	−	17.8073i	−0.586770	−	0.586770i
$922$	−51.9714	−	51.9714i	−1.71159	−	1.71159i
$923$	−0.395493	+	0.0442062i	−0.0130178	+	0.00145507i
$924$			6.08242i			0.200097i
$925$	9.96695	−	13.2674i	0.327711	−	0.436228i
$926$	−20.6928			−0.680007
$927$	9.85776	+	9.85776i	0.323771	+	0.323771i
$928$	−11.0400			−0.362407
$929$	−16.7396	−	16.7396i	−0.549210	−	0.549210i	0.377003	−	0.926212i	$-0.376955\pi$
$929$	−16.7396	−	16.7396i	−0.549210	−	0.549210i	−0.926212	+	0.377003i	$0.876955\pi$
$930$	20.0091	+	40.0579i	0.656125	+	1.31355i
$931$	27.1723	+	27.1723i	0.890537	+	0.890537i
$932$	−2.51424	+	2.51424i	−0.0823567	+	0.0823567i
$933$	−4.99102	+	4.99102i	−0.163399	+	0.163399i
$934$	−54.6088	+	54.6088i	−1.78685	+	1.78685i
$935$	−11.6263	−	23.2757i	−0.380222	−	0.761197i
$936$	−15.2983	−	12.2222i	−0.500039	−	0.399494i
$937$	12.3582	−	12.3582i	0.403724	−	0.403724i	−0.475819	−	0.879543i	$-0.657848\pi$
$937$	12.3582	−	12.3582i	0.403724	−	0.403724i	0.879543	+	0.475819i	$0.157848\pi$
$938$	9.22837			0.301317
$939$			5.45276i			0.177944i
$940$	−14.0981	+	7.04210i	−0.459831	+	0.229688i
$941$	18.8531	−	18.8531i	0.614594	−	0.614594i	−0.329545	−	0.944140i	$-0.606895\pi$
$941$	18.8531	−	18.8531i	0.614594	−	0.614594i	0.944140	+	0.329545i	$0.106895\pi$
$942$			15.0058i			0.488917i
$943$			5.77018i			0.187903i
$944$	27.1165	−	27.1165i	0.882568	−	0.882568i
$945$	0.171616	−	0.514171i	0.00558268	−	0.0167260i
$946$			81.9559i			2.66462i
$947$	13.5380			0.439926			0.219963	−	0.975508i	$-0.429406\pi$
$947$	13.5380			0.439926			0.219963	+	0.975508i	$0.429406\pi$
$948$	−22.4883	+	22.4883i	−0.730387	+	0.730387i
$949$	3.27232	−	4.09590i	0.106224	−	0.132959i
$950$	9.68071	+	68.1504i	0.314084	+	2.21109i
$951$	−9.84128	+	9.84128i	−0.319125	+	0.319125i
$952$	−1.80617	+	1.80617i	−0.0585383	+	0.0585383i
$953$	−10.8161	+	10.8161i	−0.350369	+	0.350369i	−0.860247	−	0.509878i	$-0.829691\pi$
$953$	−10.8161	+	10.8161i	−0.350369	+	0.350369i	0.509878	+	0.860247i	$0.329691\pi$
$954$	−5.52901	−	5.52901i	−0.179008	−	0.179008i
$955$	−26.0901	+	13.0322i	−0.844257	+	0.421711i
$956$	36.4540	+	36.4540i	1.17901	+	1.17901i
$957$	34.6024			1.11854
$958$	−32.2812	−	32.2812i	−1.04296	−	1.04296i
$959$	3.24716			0.104856
$960$	11.7005	+	3.90531i	0.377631	+	0.126043i
$961$		−	33.8458i		−	1.09180i
$962$	18.5737	−	23.2483i	0.598839	−	0.749556i
$963$	−4.00248	−	4.00248i	−0.128978	−	0.128978i
$964$	26.6768	+	26.6768i	0.859202	+	0.859202i
$965$	9.27582	+	18.5700i	0.298599	+	0.597790i
$966$		−	1.62380i		−	0.0522449i
$967$			16.5180i			0.531183i	0.964086	+	0.265591i	$0.0855672\pi$
$967$			16.5180i			0.531183i	−0.964086	+	0.265591i	$0.914433\pi$
$968$	−135.577			−4.35760
$969$	7.59523	−	7.59523i	0.243994	−	0.243994i
$970$	−23.6796	+	11.8281i	−0.760305	+	0.379776i
$971$	−40.8913			−1.31226			−0.656132	−	0.754646i	$-0.727809\pi$
$971$	−40.8913			−1.31226			−0.656132	+	0.754646i	$0.727809\pi$
$972$	−2.95847	−	2.95847i	−0.0948928	−	0.0948928i
$973$			1.46367i			0.0469231i
$974$	−31.4340			−1.00721
$975$	−15.5272	−	9.15994i	−0.497270	−	0.293353i
$976$	52.6497			1.68527
$977$			1.92441i			0.0615674i	0.999526	+	0.0307837i	$0.00980030\pi$
$977$			1.92441i			0.0615674i	−0.999526	+	0.0307837i	$0.990200\pi$
$978$	−25.8894	−	25.8894i	−0.827853	−	0.827853i
$979$	−7.52374			−0.240460
$980$	−58.0944	+	29.0185i	−1.85576	+	0.926961i
$981$	4.59552	−	4.59552i	0.146724	−	0.146724i
$982$	−69.1805			−2.20764
$983$			59.7525i			1.90581i	0.303273	+	0.952904i	$0.401921\pi$
$983$			59.7525i			1.90581i	−0.303273	+	0.952904i	$0.598079\pi$
$984$			11.6335i			0.370863i
$985$	−12.9021	−	25.8298i	−0.411096	−	0.823006i
$986$	19.6851	+	19.6851i	0.626900	+	0.626900i
$987$	−0.288741	−	0.288741i	−0.00919071	−	0.00919071i
$988$	9.27698	+	82.9970i	0.295140	+	2.64049i
$989$		−	14.8032i		−	0.470714i
$990$	31.6313	+	10.5577i	1.00531	+	0.335545i
$991$	29.3438			0.932136			0.466068	−	0.884749i	$-0.345670\pi$
$991$	29.3438			0.932136			0.466068	+	0.884749i	$0.345670\pi$
$992$	10.8950	+	10.8950i	0.345917	+	0.345917i
$993$	9.73371			0.308890
$994$	−0.0470477	−	0.0470477i	−0.00149226	−	0.00149226i
$995$	−4.71162	+	2.35348i	−0.149368	+	0.0746103i
$996$	8.04597	+	8.04597i	0.254946	+	0.254946i
$997$	−34.3919	+	34.3919i	−1.08920	+	1.08920i	−0.0935912	+	0.995611i	$0.529835\pi$
$997$	−34.3919	+	34.3919i	−1.08920	+	1.08920i	−0.995611	+	0.0935912i	$0.970165\pi$
$998$	0.378169	−	0.378169i	0.0119707	−	0.0119707i
$999$	2.34675	−	2.34675i	0.0742480	−	0.0742480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.k.a.148.1	yes	28
3.2	odd	2		585.2.n.g.343.14		28
5.2	odd	4		195.2.t.a.187.14	yes	28
5.3	odd	4		975.2.t.d.382.1		28
5.4	even	2		975.2.k.d.343.14		28
13.8	odd	4		195.2.t.a.73.14	yes	28
15.2	even	4		585.2.w.g.577.1		28
39.8	even	4		585.2.w.g.73.1		28
65.8	even	4		975.2.k.d.307.1		28
65.34	odd	4		975.2.t.d.268.1		28
65.47	even	4	inner	195.2.k.a.112.14	✓	28
195.47	odd	4		585.2.n.g.307.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.14	✓	28	65.47	even	4	inner
195.2.k.a.148.1	yes	28	1.1	even	1	trivial
195.2.t.a.73.14	yes	28	13.8	odd	4
195.2.t.a.187.14	yes	28	5.2	odd	4
585.2.n.g.307.1		28	195.47	odd	4
585.2.n.g.343.14		28	3.2	odd	2
585.2.w.g.73.1		28	39.8	even	4
585.2.w.g.577.1		28	15.2	even	4
975.2.k.d.307.1		28	65.8	even	4
975.2.k.d.343.14		28	5.4	even	2
975.2.t.d.268.1		28	65.34	odd	4
975.2.t.d.382.1		28	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.48675i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.18390 q^{4} +(-2.00040 + 0.999208i) q^{5} +(-1.75839 + 1.75839i) q^{6} -0.242414 q^{7} +5.43081i q^{8} +1.00000i q^{9} +(2.48478 + 4.97448i) q^{10} +(-4.24054 - 4.24054i) q^{11} +(2.95847 + 2.95847i) q^{12} +(2.81694 + 2.25052i) q^{13} +0.602823i q^{14} +(2.12104 + 0.707947i) q^{15} +5.13724 q^{16} +(-1.37194 - 1.37194i) q^{17} +2.48675 q^{18} +(-3.91462 - 3.91462i) q^{19} +(8.36946 - 4.18059i) q^{20} +(0.171413 + 0.171413i) q^{21} +(-10.5451 + 10.5451i) q^{22} +(1.90471 - 1.90471i) q^{23} +(3.84016 - 3.84016i) q^{24} +(3.00317 - 3.99762i) q^{25} +(5.59648 - 7.00501i) q^{26} +(0.707107 - 0.707107i) q^{27} +1.01424 q^{28} -5.76992i q^{29} +(1.76048 - 5.27449i) q^{30} +(-5.69411 + 5.69411i) q^{31} -1.91338i q^{32} +5.99703i q^{33} +(-3.41167 + 3.41167i) q^{34} +(0.484925 - 0.242222i) q^{35} -4.18390i q^{36} +3.31881 q^{37} +(-9.73467 + 9.73467i) q^{38} +(-0.400516 - 3.58324i) q^{39} +(-5.42651 - 10.8638i) q^{40} +(-1.51472 + 1.51472i) q^{41} +(0.426260 - 0.426260i) q^{42} +(3.88596 - 3.88596i) q^{43} +(17.7420 + 17.7420i) q^{44} +(-0.999208 - 2.00040i) q^{45} +(-4.73652 - 4.73652i) q^{46} -1.68447 q^{47} +(-3.63258 - 3.63258i) q^{48} -6.94124 q^{49} +(-9.94107 - 7.46811i) q^{50} +1.94022i q^{51} +(-11.7858 - 9.41597i) q^{52} +(-2.22339 - 2.22339i) q^{53} +(-1.75839 - 1.75839i) q^{54} +(12.7199 + 4.24558i) q^{55} -1.31651i q^{56} +5.53612i q^{57} -14.3483 q^{58} +(5.27843 - 5.27843i) q^{59} +(-8.87423 - 2.96198i) q^{60} +10.2486 q^{61} +(14.1598 + 14.1598i) q^{62} -0.242414i q^{63} +5.51638 q^{64} +(-7.88373 - 1.68723i) q^{65} +14.9131 q^{66} -15.3086i q^{67} +(5.74007 + 5.74007i) q^{68} -2.69366 q^{69} +(-0.602346 - 1.20588i) q^{70} +(-0.0780456 + 0.0780456i) q^{71} -5.43081 q^{72} -1.45403i q^{73} -8.25304i q^{74} +(-4.95031 + 0.703187i) q^{75} +(16.3784 + 16.3784i) q^{76} +(1.02797 + 1.02797i) q^{77} +(-8.91060 + 0.995982i) q^{78} +7.60135i q^{79} +(-10.2765 + 5.13317i) q^{80} -1.00000 q^{81} +(3.76672 + 3.76672i) q^{82} +2.71964 q^{83} +(-0.717175 - 0.717175i) q^{84} +(4.11528 + 1.37357i) q^{85} +(-9.66338 - 9.66338i) q^{86} +(-4.07995 + 4.07995i) q^{87} +(23.0296 - 23.0296i) q^{88} +(0.887120 - 0.887120i) q^{89} +(-4.97448 + 2.48478i) q^{90} +(-0.682867 - 0.545559i) q^{91} +(-7.96910 + 7.96910i) q^{92} +8.05269 q^{93} +4.18886i q^{94} +(11.7423 + 3.91927i) q^{95} +(-1.35296 + 1.35296i) q^{96} +4.76021i q^{97} +17.2611i q^{98} +(4.24054 - 4.24054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 8 q^{5} - 8 q^{11} + 8 q^{12} - 12 q^{13} + 4 q^{15} + 28 q^{16} - 28 q^{17} - 4 q^{18} + 8 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} + 8 q^{39} - 48 q^{40}+ \cdots + 8 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 8 * q^5 - 8 * q^11 + 8 * q^12 - 12 * q^13 + 4 * q^15 + 28 * q^16 - 28 * q^17 - 4 * q^18 + 8 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 + 8 * q^39 - 48 * q^40 + 4 * q^41 + 40 * q^44 - 4 * q^45 - 16 * q^46 - 24 * q^47 - 16 * q^48 - 28 * q^49 - 32 * q^50 + 52 * q^52 + 20 * q^53 - 8 * q^55 - 8 * q^58 + 32 * q^59 - 12 * q^60 + 8 * q^61 + 72 * q^62 - 28 * q^64 - 8 * q^65 + 16 * q^66 + 60 * q^68 + 8 * q^69 + 64 * q^70 + 40 * q^71 + 12 * q^72 - 16 * q^75 - 40 * q^76 - 48 * q^77 + 8 * q^78 - 32 * q^80 - 28 * q^81 + 4 * q^82 - 104 * q^83 - 32 * q^84 - 4 * q^85 + 16 * q^86 - 24 * q^87 + 72 * q^88 - 36 * q^89 - 12 * q^90 - 56 * q^91 - 32 * q^92 + 56 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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