LMFDB - Embedded newform 425.2.k.c.86.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.19
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.08118 - 1.51206i) q^{2} +(0.601438 - 1.85103i) q^{3} +(1.42693 - 4.39163i) q^{4} +(-1.88021 + 1.21030i) q^{5} +(-1.54718 - 4.76174i) q^{6} -1.15333 q^{7} +(-2.08086 - 6.40424i) q^{8} +(-0.637551 - 0.463208i) q^{9} +(-2.08299 + 5.36184i) q^{10} +(1.04410 - 0.758583i) q^{11} +(-7.27086 - 5.28259i) q^{12} +(3.68650 + 2.67840i) q^{13} +(-2.40029 + 1.74392i) q^{14} +(1.10948 + 4.20825i) q^{15} +(-6.54276 - 4.75360i) q^{16} +(-0.309017 - 0.951057i) q^{17} -2.02726 q^{18} +(-0.626291 - 1.92753i) q^{19} +(2.63228 + 9.98419i) q^{20} +(-0.693659 + 2.13486i) q^{21} +(1.02593 - 3.15749i) q^{22} +(-4.19285 + 3.04629i) q^{23} -13.1060 q^{24} +(2.07034 - 4.55123i) q^{25} +11.7222 q^{26} +(3.48289 - 2.53047i) q^{27} +(-1.64573 + 5.06502i) q^{28} +(0.479222 - 1.47489i) q^{29} +(8.67217 + 7.08050i) q^{30} +(2.81376 + 8.65987i) q^{31} -7.33677 q^{32} +(-0.776202 - 2.38890i) q^{33} +(-2.08118 - 1.51206i) q^{34} +(2.16851 - 1.39588i) q^{35} +(-2.94398 + 2.13893i) q^{36} +(1.01958 + 0.740765i) q^{37} +(-4.21797 - 3.06453i) q^{38} +(7.17502 - 5.21295i) q^{39} +(11.6635 + 9.52281i) q^{40} +(-3.71915 - 2.70212i) q^{41} +(1.78442 + 5.49188i) q^{42} +10.2208 q^{43} +(-1.84156 - 5.66775i) q^{44} +(1.75935 + 0.0992977i) q^{45} +(-4.11989 + 12.6797i) q^{46} +(-0.512209 + 1.57642i) q^{47} +(-12.7341 + 9.25189i) q^{48} -5.66982 q^{49} +(-2.57299 - 12.6024i) q^{50} -1.94629 q^{51} +(17.0229 - 12.3679i) q^{52} +(-3.29255 + 10.1334i) q^{53} +(3.42228 - 10.5327i) q^{54} +(-1.04501 + 2.68997i) q^{55} +(2.39993 + 7.38622i) q^{56} -3.94459 q^{57} +(-1.23279 - 3.79413i) q^{58} +(-4.11783 - 2.99178i) q^{59} +(20.0642 + 1.13243i) q^{60} +(-8.79368 + 6.38898i) q^{61} +(18.9502 + 13.7681i) q^{62} +(0.735310 + 0.534234i) q^{63} +(-2.18360 + 1.58647i) q^{64} +(-10.1731 - 0.574167i) q^{65} +(-5.22759 - 3.79807i) q^{66} +(-1.57344 - 4.84256i) q^{67} -4.61764 q^{68} +(3.11704 + 9.59327i) q^{69} +(2.40238 - 6.18400i) q^{70} +(3.17325 - 9.76627i) q^{71} +(-1.63984 + 5.04690i) q^{72} +(-5.98525 + 4.34854i) q^{73} +3.24200 q^{74} +(-7.17930 - 6.56956i) q^{75} -9.35866 q^{76} +(-1.20420 + 0.874899i) q^{77} +(7.05016 - 21.6982i) q^{78} +(1.88322 - 5.79594i) q^{79} +(18.0550 + 1.01903i) q^{80} +(-3.31981 - 10.2173i) q^{81} -11.8260 q^{82} +(3.69279 + 11.3652i) q^{83} +(8.38573 + 6.09259i) q^{84} +(1.73208 + 1.41418i) q^{85} +(21.2713 - 15.4545i) q^{86} +(-2.44186 - 1.77411i) q^{87} +(-7.03077 - 5.10815i) q^{88} +(11.8911 - 8.63941i) q^{89} +(3.81166 - 2.45359i) q^{90} +(-4.25177 - 3.08909i) q^{91} +(7.39528 + 22.7603i) q^{92} +17.7220 q^{93} +(1.31765 + 4.05529i) q^{94} +(3.51044 + 2.86615i) q^{95} +(-4.41261 + 13.5806i) q^{96} +(-4.07114 + 12.5297i) q^{97} +(-11.7999 + 8.57313i) q^{98} -1.01705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	2.08118	−	1.51206i	1.47161	−	1.06919i	0.491473	−	0.870893i	$-0.336459\pi$
$2$	2.08118	−	1.51206i	1.47161	−	1.06919i	0.980142	−	0.198298i	$-0.0635413\pi$
$3$	0.601438	−	1.85103i	0.347240	−	1.06870i	−0.613133	−	0.789979i	$-0.710091\pi$
$3$	0.601438	−	1.85103i	0.347240	−	1.06870i	0.960374	−	0.278716i	$-0.0899088\pi$
$4$	1.42693	−	4.39163i	0.713464	−	2.19582i
$5$	−1.88021	+	1.21030i	−0.840853	+	0.541263i
$5$	−1.88021	+	1.21030i	−0.840853	+	0.541263i
$6$	−1.54718	−	4.76174i	−0.631635	−	1.94397i
$7$	−1.15333			−0.435919			−0.217960	−	0.975958i	$-0.569940\pi$
$7$	−1.15333			−0.435919			−0.217960	+	0.975958i	$0.569940\pi$
$8$	−2.08086	−	6.40424i	−0.735696	−	2.26424i
$9$	−0.637551	−	0.463208i	−0.212517	−	0.154403i
$10$	−2.08299	+	5.36184i	−0.658699	+	1.69556i
$11$	1.04410	−	0.758583i	0.314808	−	0.228721i	−0.419149	−	0.907917i	$-0.637671\pi$
$11$	1.04410	−	0.758583i	0.314808	−	0.228721i	0.733957	+	0.679196i	$0.237671\pi$
$12$	−7.27086	−	5.28259i	−2.09892	−	1.52495i
$13$	3.68650	+	2.67840i	1.02245	+	0.742855i	0.966784	−	0.255594i	$-0.0822712\pi$
$13$	3.68650	+	2.67840i	1.02245	+	0.742855i	0.0556680	+	0.998449i	$0.482271\pi$
$14$	−2.40029	+	1.74392i	−0.641505	+	0.466081i
$15$	1.10948	+	4.20825i	0.286467	+	1.08656i
$16$	−6.54276	−	4.75360i	−1.63569	−	1.18840i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−2.02726			−0.477829
$19$	−0.626291	−	1.92753i	−0.143681	−	0.442205i	0.853158	−	0.521653i	$-0.174684\pi$
$19$	−0.626291	−	1.92753i	−0.143681	−	0.442205i	−0.996839	+	0.0794478i	$0.974684\pi$
$20$	2.63228	+	9.98419i	0.588596	+	2.23253i
$21$	−0.693659	+	2.13486i	−0.151369	+	0.465865i
$22$	1.02593	−	3.15749i	0.218729	−	0.673179i
$23$	−4.19285	+	3.04629i	−0.874271	+	0.635195i	−0.931729	−	0.363153i	$-0.881700\pi$
$23$	−4.19285	+	3.04629i	−0.874271	+	0.635195i	0.0574589	+	0.998348i	$0.481700\pi$
$24$	−13.1060			−2.67525
$25$	2.07034	−	4.55123i	0.414069	−	0.910246i
$26$	11.7222			2.29891
$27$	3.48289	−	2.53047i	0.670283	−	0.486989i
$28$	−1.64573	+	5.06502i	−0.311013	+	0.957199i
$29$	0.479222	−	1.47489i	0.0889893	−	0.273881i	−0.896651	−	0.442737i	$-0.854007\pi$
$29$	0.479222	−	1.47489i	0.0889893	−	0.273881i	0.985641	+	0.168856i	$0.0540074\pi$
$30$	8.67217	+	7.08050i	1.58331	+	1.29272i
$31$	2.81376	+	8.65987i	0.505366	+	1.55536i	0.800154	+	0.599795i	$0.204751\pi$
$31$	2.81376	+	8.65987i	0.505366	+	1.55536i	−0.294787	+	0.955563i	$0.595249\pi$
$32$	−7.33677			−1.29697
$33$	−0.776202	−	2.38890i	−0.135119	−	0.415855i
$34$	−2.08118	−	1.51206i	−0.356919	−	0.259317i
$35$	2.16851	−	1.39588i	0.366544	−	0.235947i
$36$	−2.94398	+	2.13893i	−0.490664	+	0.356488i
$37$	1.01958	+	0.740765i	0.167617	+	0.121781i	0.668431	−	0.743774i	$-0.266966\pi$
$37$	1.01958	+	0.740765i	0.167617	+	0.121781i	−0.500814	+	0.865555i	$0.666966\pi$
$38$	−4.21797	−	3.06453i	−0.684245	−	0.497133i
$39$	7.17502	−	5.21295i	1.14892	−	0.834741i
$40$	11.6635	+	9.52281i	1.84416	+	1.50569i
$41$	−3.71915	−	2.70212i	−0.580834	−	0.422001i	0.258191	−	0.966094i	$-0.416874\pi$
$41$	−3.71915	−	2.70212i	−0.580834	−	0.422001i	−0.839025	+	0.544093i	$0.816874\pi$
$42$	1.78442	+	5.49188i	0.275342	+	0.847416i
$43$	10.2208			1.55866			0.779328	−	0.626617i	$-0.215561\pi$
$43$	10.2208			1.55866			0.779328	+	0.626617i	$0.215561\pi$
$44$	−1.84156	−	5.66775i	−0.277626	−	0.854445i
$45$	1.75935	+	0.0992977i	0.262268	+	0.0148024i
$46$	−4.11989	+	12.6797i	−0.607445	+	1.86952i
$47$	−0.512209	+	1.57642i	−0.0747133	+	0.229944i	−0.981438	−	0.191779i	$-0.938574\pi$
$47$	−0.512209	+	1.57642i	−0.0747133	+	0.229944i	0.906725	+	0.421723i	$0.138574\pi$
$48$	−12.7341	+	9.25189i	−1.83801	+	1.33540i
$49$	−5.66982			−0.809974
$50$	−2.57299	−	12.6024i	−0.363876	−	1.78225i
$51$	−1.94629			−0.272536
$52$	17.0229	−	12.3679i	2.36066	−	1.71512i
$53$	−3.29255	+	10.1334i	−0.452266	+	1.39193i	0.422048	+	0.906573i	$0.361311\pi$
$53$	−3.29255	+	10.1334i	−0.452266	+	1.39193i	−0.874315	+	0.485359i	$0.838689\pi$
$54$	3.42228	−	10.5327i	0.465714	−	1.43332i
$55$	−1.04501	+	2.68997i	−0.140909	+	0.362715i
$56$	2.39993	+	7.38622i	0.320704	+	0.987026i
$57$	−3.94459			−0.522474
$58$	−1.23279	−	3.79413i	−0.161873	−	0.498194i
$59$	−4.11783	−	2.99178i	−0.536096	−	0.389496i	0.286537	−	0.958069i	$-0.407496\pi$
$59$	−4.11783	−	2.99178i	−0.536096	−	0.389496i	−0.822633	+	0.568573i	$0.807496\pi$
$60$	20.0642	+	1.13243i	2.59028	+	0.146196i
$61$	−8.79368	+	6.38898i	−1.12592	+	0.818026i	−0.985095	−	0.172010i	$-0.944974\pi$
$61$	−8.79368	+	6.38898i	−1.12592	+	0.818026i	−0.140820	+	0.990035i	$0.544974\pi$
$62$	18.9502	+	13.7681i	2.40668	+	1.74855i
$63$	0.735310	+	0.534234i	0.0926403	+	0.0673072i
$64$	−2.18360	+	1.58647i	−0.272949	+	0.198309i
$65$	−10.1731	−	0.574167i	−1.26181	−	0.0712167i
$66$	−5.22759	−	3.79807i	−0.643472	−	0.467510i
$67$	−1.57344	−	4.84256i	−0.192227	−	0.591613i	−0.999998	−	0.00211670i	$-0.999326\pi$
$67$	−1.57344	−	4.84256i	−0.192227	−	0.591613i	0.807771	−	0.589496i	$-0.200674\pi$
$68$	−4.61764			−0.559971
$69$	3.11704	+	9.59327i	0.375248	+	1.15489i
$70$	2.40238	−	6.18400i	0.287140	−	0.739129i
$71$	3.17325	−	9.76627i	0.376596	−	1.15904i	−0.565800	−	0.824543i	$-0.691432\pi$
$71$	3.17325	−	9.76627i	0.376596	−	1.15904i	0.942396	−	0.334500i	$-0.108568\pi$
$72$	−1.63984	+	5.04690i	−0.193257	+	0.594783i
$73$	−5.98525	+	4.34854i	−0.700521	+	0.508958i	−0.880102	−	0.474785i	$-0.842526\pi$
$73$	−5.98525	+	4.34854i	−0.700521	+	0.508958i	0.179581	+	0.983743i	$0.442526\pi$
$74$	3.24200			0.376875
$75$	−7.17930	−	6.56956i	−0.828994	−	0.758587i
$76$	−9.35866			−1.07351
$77$	−1.20420	+	0.874899i	−0.137231	+	0.0997040i
$78$	7.05016	−	21.6982i	0.798274	−	2.45683i
$79$	1.88322	−	5.79594i	0.211878	−	0.652095i	−0.787482	−	0.616337i	$-0.788616\pi$
$79$	1.88322	−	5.79594i	0.211878	−	0.652095i	0.999361	−	0.0357571i	$-0.0113843\pi$
$80$	18.0550	+	1.01903i	2.01861	+	0.113931i
$81$	−3.31981	−	10.2173i	−0.368868	−	1.13526i
$82$	−11.8260			−1.30596
$83$	3.69279	+	11.3652i	0.405336	+	1.24750i	0.920614	+	0.390473i	$0.127688\pi$
$83$	3.69279	+	11.3652i	0.405336	+	1.24750i	−0.515279	+	0.857023i	$0.672312\pi$
$84$	8.38573	+	6.09259i	0.914958	+	0.664756i
$85$	1.73208	+	1.41418i	0.187870	+	0.153389i
$86$	21.2713	−	15.4545i	2.29374	−	1.66650i
$87$	−2.44186	−	1.77411i	−0.261795	−	0.190205i
$88$	−7.03077	−	5.10815i	−0.749482	−	0.544531i
$89$	11.8911	−	8.63941i	1.26046	−	0.915775i	0.261676	−	0.965156i	$-0.415725\pi$
$89$	11.8911	−	8.63941i	1.26046	−	0.915775i	0.998780	+	0.0493804i	$0.0157247\pi$
$90$	3.81166	−	2.45359i	0.401784	−	0.258631i
$91$	−4.25177	−	3.08909i	−0.445707	−	0.323825i
$92$	7.39528	+	22.7603i	0.771011	+	2.37293i
$93$	17.7220			1.83769
$94$	1.31765	+	4.05529i	0.135905	+	0.418272i
$95$	3.51044	+	2.86615i	0.360164	+	0.294060i
$96$	−4.41261	+	13.5806i	−0.450360	+	1.38607i
$97$	−4.07114	+	12.5297i	−0.413362	+	1.27220i	0.500346	+	0.865825i	$0.333206\pi$
$97$	−4.07114	+	12.5297i	−0.413362	+	1.27220i	−0.913708	+	0.406371i	$0.866794\pi$
$98$	−11.7999	+	8.57313i	−1.19197	+	0.866017i
$99$	−1.01705			−0.102217
$100$	−17.0331	−	15.5865i	−1.70331	−	1.55865i
$101$	−5.61829			−0.559041			−0.279521	−	0.960140i	$-0.590176\pi$
$101$	−5.61829			−0.559041			−0.279521	+	0.960140i	$0.590176\pi$
$102$	−4.05058	+	2.94292i	−0.401067	+	0.291392i
$103$	−4.55808	+	14.0283i	−0.449121	+	1.38225i	0.428781	+	0.903409i	$0.358943\pi$
$103$	−4.55808	+	14.0283i	−0.449121	+	1.38225i	−0.877901	+	0.478842i	$0.841057\pi$
$104$	9.48201	−	29.1826i	0.929787	−	2.86159i
$105$	−1.27960	−	4.85351i	−0.124877	−	0.473654i
$106$	8.47001	+	26.0680i	0.822680	+	2.53195i
$107$	−8.95476			−0.865689			−0.432845	−	0.901469i	$-0.642490\pi$
$107$	−8.95476			−0.865689			−0.432845	+	0.901469i	$0.642490\pi$
$108$	−6.14305	−	18.9064i	−0.591116	−	1.81927i
$109$	−11.5964	−	8.42529i	−1.11074	−	0.806996i	−0.127956	−	0.991780i	$-0.540842\pi$
$109$	−11.5964	−	8.42529i	−1.11074	−	0.806996i	−0.982779	+	0.184784i	$0.940842\pi$
$110$	1.89255	+	7.17841i	0.180448	+	0.684435i
$111$	1.98439	−	1.44175i	0.188350	−	0.136844i
$112$	7.54599	+	5.48249i	0.713029	+	0.518046i
$113$	−0.698627	−	0.507582i	−0.0657213	−	0.0477493i	0.554440	−	0.832224i	$-0.312933\pi$
$113$	−0.698627	−	0.507582i	−0.0657213	−	0.0477493i	−0.620161	+	0.784475i	$0.712933\pi$
$114$	−8.20940	+	5.96448i	−0.768881	+	0.558625i
$115$	4.19650	−	10.8023i	0.391326	−	1.00732i
$116$	−5.79338	−	4.20914i	−0.537902	−	0.390809i
$117$	−1.10968	−	3.41524i	−0.102590	−	0.315739i
$118$	−13.0937			−1.20537
$119$	0.356400	+	1.09689i	0.0326711	+	0.100551i
$120$	24.6419	−	15.8622i	2.24949	−	1.44801i
$121$	−2.88449	+	8.87755i	−0.262226	+	0.807050i
$122$	−8.64066	+	26.5932i	−0.782289	+	2.40764i
$123$	−7.23856	+	5.25912i	−0.652679	+	0.474199i
$124$	42.0460			3.77584
$125$	1.61568	+	11.0630i	0.144511	+	0.989503i
$126$	2.33811			0.208295
$127$	7.16465	−	5.20542i	0.635760	−	0.461907i	−0.222631	−	0.974903i	$-0.571465\pi$
$127$	7.16465	−	5.20542i	0.635760	−	0.461907i	0.858391	+	0.512996i	$0.171465\pi$
$128$	2.38878	−	7.35190i	0.211140	−	0.649822i
$129$	6.14717	−	18.9190i	0.541228	−	1.66573i
$130$	−22.0401	+	14.1874i	−1.93305	+	1.24431i
$131$	6.08338	+	18.7227i	0.531508	+	1.63581i	0.751076	+	0.660216i	$0.229535\pi$
$131$	6.08338	+	18.7227i	0.531508	+	1.63581i	−0.219568	+	0.975597i	$0.570465\pi$
$132$	−11.5988			−1.00954
$133$	0.722323	+	2.22308i	0.0626334	+	0.192766i
$134$	−10.5969	−	7.69908i	−0.915431	−	0.665099i
$135$	−3.48592	+	8.97314i	−0.300020	+	0.772285i
$136$	−5.44777	+	3.95804i	−0.467142	+	0.339399i
$137$	−4.48486	−	3.25844i	−0.383167	−	0.278387i	0.379483	−	0.925199i	$-0.376102\pi$
$137$	−4.48486	−	3.25844i	−0.383167	−	0.278387i	−0.762650	+	0.646812i	$0.776102\pi$
$138$	20.9928	+	15.2521i	1.78702	+	1.29835i
$139$	6.58877	−	4.78702i	0.558852	−	0.406030i	−0.272187	−	0.962244i	$-0.587747\pi$
$139$	6.58877	−	4.78702i	0.558852	−	0.406030i	0.831039	+	0.556215i	$0.187747\pi$
$140$	−3.03590	−	11.5151i	−0.256580	−	0.973204i
$141$	2.60994	+	1.89623i	0.219797	+	0.159692i
$142$	−8.16312	−	25.1235i	−0.685034	−	2.10832i
$143$	5.88086			0.491783
$144$	1.96944	+	6.06132i	0.164120	+	0.505110i
$145$	0.884029	+	3.35311i	0.0734146	+	0.278460i
$146$	−5.88110	+	18.1002i	−0.486724	+	1.49798i
$147$	−3.41004	+	10.4950i	−0.281256	+	0.865616i
$148$	4.70803	−	3.42058i	0.386998	−	0.281170i
$149$	−19.9356			−1.63318			−0.816592	−	0.577215i	$-0.804140\pi$
$149$	−19.9356			−1.63318			−0.816592	+	0.577215i	$0.804140\pi$
$150$	−24.8750	−	2.81686i	−2.03103	−	0.229996i
$151$	3.25247			0.264682			0.132341	−	0.991204i	$-0.457751\pi$
$151$	3.25247			0.264682			0.132341	+	0.991204i	$0.457751\pi$
$152$	−11.0411	+	8.02184i	−0.895552	+	0.650657i
$153$	−0.243523	+	0.749487i	−0.0196877	+	0.0605924i
$154$	−1.18324	+	3.64164i	−0.0953483	+	0.293452i
$155$	−15.7715	−	12.8768i	−1.26680	−	1.03429i
$156$	−12.6552	−	38.9486i	−1.01322	−	3.11838i
$157$	10.6509			0.850034			0.425017	−	0.905185i	$-0.360268\pi$
$157$	10.6509			0.850034			0.425017	+	0.905185i	$0.360268\pi$
$158$	−4.84453	−	14.9099i	−0.385410	−	1.18617i
$159$	16.7771	+	12.1892i	1.33051	+	0.966670i
$160$	13.7946	−	8.87970i	1.09056	−	0.702002i
$161$	4.83576	−	3.51339i	0.381111	−	0.276894i
$162$	−22.3584	−	16.2443i	−1.75664	−	1.27627i
$163$	13.6465	+	9.91474i	1.06887	+	0.776583i	0.975710	−	0.219068i	$-0.0703017\pi$
$163$	13.6465	+	9.91474i	1.06887	+	0.776583i	0.0931646	+	0.995651i	$0.470302\pi$
$164$	−17.1737	+	12.4774i	−1.34104	+	0.974323i
$165$	4.35071	+	3.55219i	0.338702	+	0.276538i
$166$	24.8703	+	18.0693i	1.93031	+	1.40245i
$167$	−2.60460	−	8.01614i	−0.201550	−	0.620308i	−0.999837	−	0.0180308i	$-0.994260\pi$
$167$	−2.60460	−	8.01614i	−0.201550	−	0.620308i	0.798287	−	0.602277i	$-0.205740\pi$
$168$	15.1156			1.16619
$169$	2.39925	+	7.38414i	0.184558	+	0.568011i
$170$	5.74309	+	0.324140i	0.440475	+	0.0248604i
$171$	−0.493553	+	1.51900i	−0.0377430	+	0.116161i
$172$	14.5843	−	44.8860i	1.11204	−	3.42252i
$173$	1.20040	−	0.872143i	0.0912648	−	0.0663078i	−0.541217	−	0.840883i	$-0.682036\pi$
$173$	1.20040	−	0.872143i	0.0912648	−	0.0663078i	0.632482	+	0.774575i	$0.282036\pi$
$174$	−7.76451			−0.588626
$175$	−2.38780	+	5.24909i	−0.180501	+	0.396794i
$176$	−10.4373			−0.786740
$177$	−8.01450	+	5.82288i	−0.602407	+	0.437674i
$178$	11.6842	−	35.9603i	0.875768	−	2.69534i
$179$	5.18260	−	15.9504i	0.387366	−	1.19219i	−0.547384	−	0.836882i	$-0.684376\pi$
$179$	5.18260	−	15.9504i	0.387366	−	1.19219i	0.934749	−	0.355308i	$-0.115624\pi$
$180$	2.94654	−	7.58473i	0.219622	−	0.565332i
$181$	−4.03256	−	12.4110i	−0.299738	−	0.922499i	−0.981589	−	0.191008i	$-0.938825\pi$
$181$	−4.03256	−	12.4110i	−0.299738	−	0.922499i	0.681850	−	0.731492i	$-0.261175\pi$
$182$	−13.5196			−1.00214
$183$	6.53738	+	20.1200i	0.483257	+	1.48731i
$184$	28.2339	+	20.5131i	2.08143	+	1.51225i
$185$	−2.81356	−	0.158797i	−0.206857	−	0.0116750i
$186$	36.8827	−	26.7968i	2.70437	−	1.96484i
$187$	−1.04410	−	0.758583i	−0.0763521	−	0.0554730i
$188$	6.19216	+	4.49887i	0.451610	+	0.328114i
$189$	−4.01694	+	2.91848i	−0.292189	+	0.212288i
$190$	11.6397	+	0.656942i	0.844429	+	0.0476596i
$191$	−10.7978	−	7.84509i	−0.781304	−	0.567651i	0.124066	−	0.992274i	$-0.460407\pi$
$191$	−10.7978	−	7.84509i	−0.781304	−	0.567651i	−0.905370	+	0.424623i	$0.860407\pi$
$192$	1.62332	+	4.99608i	0.117153	+	0.360561i
$193$	−6.97064			−0.501758			−0.250879	−	0.968019i	$-0.580720\pi$
$193$	−6.97064			−0.501758			−0.250879	+	0.968019i	$0.580720\pi$
$194$	10.4729	+	32.2323i	0.751912	+	2.31415i
$195$	−7.18126	+	18.4854i	−0.514261	+	1.32376i
$196$	−8.09043	+	24.8998i	−0.577888	+	1.77856i
$197$	2.59541	−	7.98785i	0.184915	−	0.569110i	−0.815032	−	0.579416i	$-0.803281\pi$
$197$	2.59541	−	7.98785i	0.184915	−	0.569110i	0.999947	+	0.0103059i	$0.00328053\pi$
$198$	−2.11666	+	1.53784i	−0.150424	+	0.109290i
$199$	4.56956			0.323928			0.161964	−	0.986797i	$-0.448217\pi$
$199$	4.56956			0.323928			0.161964	+	0.986797i	$0.448217\pi$
$200$	−33.4552	−	3.78850i	−2.36564	−	0.267887i
$201$	−9.91008			−0.699003
$202$	−11.6927	+	8.49522i	−0.822693	+	0.597722i
$203$	−0.552703	+	1.70105i	−0.0387922	+	0.119390i
$204$	−2.77722	+	8.54741i	−0.194444	+	0.598438i
$205$	10.2631	+	0.579252i	0.716809	+	0.0404567i
$206$	11.7255	+	36.0875i	0.816957	+	2.51434i
$207$	4.08423			0.283873
$208$	−11.3879	−	35.0483i	−0.789608	−	2.43016i
$209$	−2.11610	−	1.53744i	−0.146374	−	0.106347i
$210$	−10.0019	−	8.16618i	−0.690197	−	0.563520i
$211$	5.34846	−	3.88588i	0.368203	−	0.267515i	−0.388262	−	0.921549i	$-0.626925\pi$
$211$	5.34846	−	3.88588i	0.368203	−	0.267515i	0.756465	+	0.654034i	$0.226925\pi$
$212$	39.8041	+	28.9193i	2.73375	+	1.98619i
$213$	−16.1692	−	11.7476i	−1.10789	−	0.804933i
$214$	−18.6364	+	13.5402i	−1.27396	+	0.925587i
$215$	−19.2172	+	12.3702i	−1.31060	+	0.843642i
$216$	−23.4531	−	17.0397i	−1.59578	−	1.15940i
$217$	−3.24521	−	9.98772i	−0.220299	−	0.678011i
$218$	−36.8738			−2.49741
$219$	4.44954	+	13.6943i	0.300672	+	0.925374i
$220$	10.3222	+	8.42768i	0.695922	+	0.568194i
$221$	1.40812	−	4.33374i	0.0947203	−	0.291519i
$222$	1.94986	−	6.00105i	0.130866	−	0.402764i
$223$	9.19443	−	6.68015i	0.615705	−	0.447336i	−0.235714	−	0.971823i	$-0.575743\pi$
$223$	9.19443	−	6.68015i	0.615705	−	0.447336i	0.851419	+	0.524487i	$0.175743\pi$
$224$	8.46175			0.565374
$225$	−3.42812	+	1.94264i	−0.228541	+	0.129509i
$226$	−2.22146			−0.147770
$227$	−13.3291	+	9.68415i	−0.884683	+	0.642760i	−0.934486	−	0.355999i	$-0.884141\pi$
$227$	−13.3291	+	9.68415i	−0.884683	+	0.642760i	0.0498033	+	0.998759i	$0.484141\pi$
$228$	−5.62865	+	17.3232i	−0.372767	+	1.14726i
$229$	−3.56587	+	10.9746i	−0.235639	+	0.725223i	0.761397	+	0.648286i	$0.224514\pi$
$229$	−3.56587	+	10.9746i	−0.235639	+	0.725223i	−0.997036	+	0.0769366i	$0.975486\pi$
$230$	−7.60004	−	28.8268i	−0.501132	−	1.90078i
$231$	0.895220	+	2.75521i	0.0589012	+	0.181279i
$232$	−10.4428			−0.685601
$233$	−4.05315	−	12.4743i	−0.265531	−	0.817219i	−0.991571	−	0.129567i	$-0.958641\pi$
$233$	−4.05315	−	12.4743i	−0.265531	−	0.817219i	0.726040	−	0.687652i	$-0.241359\pi$
$234$	−7.47350	−	5.42981i	−0.488558	−	0.354958i
$235$	−0.944880	−	3.58391i	−0.0616372	−	0.233789i
$236$	−19.0146	+	13.8149i	−1.23775	+	0.899276i
$237$	−9.59585	−	6.97180i	−0.623318	−	0.452867i
$238$	2.40029	+	1.74392i	0.155588	+	0.113041i
$239$	−19.7541	+	14.3522i	−1.27779	+	0.928367i	−0.999484	−	0.0321263i	$-0.989772\pi$
$239$	−19.7541	+	14.3522i	−1.27779	+	0.928367i	−0.278304	+	0.960493i	$0.589772\pi$
$240$	12.7452	−	32.8076i	0.822701	−	2.11772i
$241$	23.1079	+	16.7889i	1.48851	+	1.08147i	0.974688	+	0.223570i	$0.0717711\pi$
$241$	23.1079	+	16.7889i	1.48851	+	1.08147i	0.513823	+	0.857896i	$0.328229\pi$
$242$	7.42029	+	22.8373i	0.476994	+	1.46804i
$243$	−7.99403			−0.512817
$244$	15.5101	+	47.7353i	0.992934	+	3.05594i
$245$	10.6604	−	6.86219i	0.681070	−	0.438409i
$246$	−7.11260	+	21.8903i	−0.453483	+	1.39568i
$247$	2.85387	−	8.78329i	0.181587	−	0.558868i
$248$	49.6048	−	36.0400i	3.14991	−	2.28854i
$249$	23.2584			1.47394
$250$	20.0905	+	20.5810i	1.27063	+	1.30166i
$251$	7.59565			0.479433			0.239716	−	0.970843i	$-0.422946\pi$
$251$	7.59565			0.479433			0.239716	+	0.970843i	$0.422946\pi$
$252$	3.39539	−	2.46690i	0.213890	−	0.155400i
$253$	−2.06690	+	6.36125i	−0.129945	+	0.399929i
$254$	7.03998	−	21.6668i	0.441727	−	1.35950i
$255$	3.65943	−	2.35560i	0.229162	−	0.147513i
$256$	−7.81319	−	24.0465i	−0.488324	−	1.50291i
$257$	−17.3189			−1.08032			−0.540162	−	0.841561i	$-0.681637\pi$
$257$	−17.3189			−1.08032			−0.540162	+	0.841561i	$0.681637\pi$
$258$	−15.8134	−	48.6688i	−0.984502	−	3.02999i
$259$	−1.17591	−	0.854349i	−0.0730675	−	0.0530867i
$260$	−17.0378	+	43.8570i	−1.05664	+	2.71990i
$261$	−0.988712	+	0.718341i	−0.0611997	+	0.0444642i
$262$	40.9706	+	29.7669i	2.53117	+	1.83900i
$263$	6.16267	+	4.47744i	0.380007	+	0.276091i	0.761348	−	0.648343i	$-0.224538\pi$
$263$	6.16267	+	4.47744i	0.380007	+	0.276091i	−0.381342	+	0.924434i	$0.624538\pi$
$264$	−13.6839	+	9.94196i	−0.842188	+	0.611885i
$265$	−6.07382	−	23.0379i	−0.373112	−	1.41521i
$266$	4.86473	+	3.53443i	0.298275	+	0.216710i
$267$	−8.84007	−	27.2069i	−0.541004	−	1.66504i
$268$	−23.5120			−1.43622
$269$	−6.82667	−	21.0103i	−0.416230	−	1.28102i	−0.911147	−	0.412083i	$-0.864802\pi$
$269$	−6.82667	−	21.0103i	−0.416230	−	1.28102i	0.494917	−	0.868940i	$-0.335198\pi$
$270$	6.31315	+	23.9456i	0.384206	+	1.45729i
$271$	5.85274	−	18.0129i	0.355528	−	1.09420i	−0.600174	−	0.799870i	$-0.704902\pi$
$271$	5.85274	−	18.0129i	0.355528	−	1.09420i	0.955702	−	0.294335i	$-0.0950980\pi$
$272$	−2.49911	+	7.69148i	−0.151531	+	0.466364i
$273$	−8.27519	+	6.01228i	−0.500837	+	0.363880i
$274$	−14.2608			−0.861524
$275$	−1.29084	−	6.32246i	−0.0778404	−	0.381259i
$276$	46.5779			2.80366
$277$	9.52365	−	6.91934i	0.572221	−	0.415743i	−0.263690	−	0.964607i	$-0.584940\pi$
$277$	9.52365	−	6.91934i	0.572221	−	0.415743i	0.835911	+	0.548865i	$0.184940\pi$
$278$	6.47411	−	19.9253i	0.388292	−	1.19504i
$279$	2.21740	−	6.82447i	0.132753	−	0.408570i
$280$	−13.4519	−	10.9830i	−0.803906	−	0.656359i
$281$	−6.21810	−	19.1374i	−0.370941	−	1.14164i	−0.946177	−	0.323651i	$-0.895090\pi$
$281$	−6.21810	−	19.1374i	−0.370941	−	1.14164i	0.575236	−	0.817988i	$-0.304910\pi$
$282$	8.29897			0.494197
$283$	−7.46939	−	22.9884i	−0.444009	−	1.36652i	−0.883567	−	0.468305i	$-0.844865\pi$
$283$	−7.46939	−	22.9884i	−0.444009	−	1.36652i	0.439558	−	0.898214i	$-0.355135\pi$
$284$	−38.3619	−	27.8715i	−2.27636	−	1.65387i
$285$	7.41665	−	4.77414i	0.439324	−	0.282796i
$286$	12.2391	−	8.89224i	0.723715	−	0.525809i
$287$	4.28943	+	3.11645i	0.253197	+	0.183958i
$288$	4.67757	+	3.39845i	0.275628	+	0.200256i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	6.90993	+	5.64170i	0.405765	+	0.331292i
$291$	20.7443	+	15.0716i	1.21606	+	0.883516i
$292$	10.5567	+	32.4901i	0.617783	+	1.90134i
$293$	−32.5404			−1.90103			−0.950516	−	0.310677i	$-0.899444\pi$
$293$	−32.5404			−1.90103			−0.950516	+	0.310677i	$0.899444\pi$
$294$	8.77226	+	26.9982i	0.511608	+	1.57457i
$295$	11.3633	+	0.641346i	0.661598	+	0.0373406i
$296$	2.62244	−	8.07103i	0.152426	−	0.469119i
$297$	1.71691	−	5.28412i	0.0996255	−	0.306616i
$298$	−41.4894	+	30.1438i	−2.40342	+	1.74619i
$299$	−23.6162			−1.36576
$300$	−39.0954	+	22.1546i	−2.25718	+	1.27909i
$301$	−11.7880			−0.679448
$302$	6.76896	−	4.91794i	0.389510	−	0.282995i
$303$	−3.37905	+	10.3997i	−0.194122	+	0.597445i
$304$	−5.06501	+	15.5885i	−0.290498	+	0.894061i
$305$	8.80134	−	22.6556i	0.503963	−	1.29726i
$306$	0.626457	+	1.92804i	0.0358122	+	0.110219i
$307$	−21.6805			−1.23737			−0.618685	−	0.785639i	$-0.712334\pi$
$307$	−21.6805			−1.23737			−0.618685	+	0.785639i	$0.712334\pi$
$308$	2.12394	+	6.53680i	0.121023	+	0.372469i
$309$	23.2255	+	16.8743i	1.32125	+	0.959946i
$310$	−52.2939	−	2.95147i	−2.97009	−	0.167632i
$311$	21.1044	−	15.3332i	1.19672	−	0.869467i	0.202761	−	0.979228i	$-0.435009\pi$
$311$	21.1044	−	15.3332i	1.19672	−	0.869467i	0.993958	+	0.109761i	$0.0350085\pi$
$312$	−48.3152	−	35.1031i	−2.73531	−	1.98732i
$313$	−11.5322	−	8.37861i	−0.651837	−	0.473587i	0.212060	−	0.977257i	$-0.431983\pi$
$313$	−11.5322	−	8.37861i	−0.651837	−	0.473587i	−0.863896	+	0.503670i	$0.831983\pi$
$314$	22.1664	−	16.1048i	1.25092	−	0.908849i
$315$	−2.02912	−	0.114523i	−0.114328	−	0.00645266i
$316$	−22.7664	−	16.5408i	−1.28071	−	0.930492i
$317$	−6.37342	−	19.6154i	−0.357967	−	1.10171i	−0.954269	−	0.298949i	$-0.903364\pi$
$317$	−6.37342	−	19.6154i	−0.357967	−	1.10171i	0.596302	−	0.802760i	$-0.296636\pi$
$318$	53.3469			2.99155
$319$	−0.618473	−	1.90347i	−0.0346279	−	0.106574i
$320$	2.18550	−	5.62571i	0.122173	−	0.314487i
$321$	−5.38573	+	16.5756i	−0.300602	+	0.925158i
$322$	4.75161	−	14.6240i	0.264797	−	0.814962i
$323$	−1.63965	+	1.19128i	−0.0912327	+	0.0662844i
$324$	−49.6079			−2.75600
$325$	19.8223	−	11.2329i	1.09955	−	0.623089i
$326$	43.3925			2.40329
$327$	−22.5700	+	16.3981i	−1.24813	+	0.906816i
$328$	−9.56598	+	29.4411i	−0.528193	+	1.62561i
$329$	0.590748	−	1.81813i	0.0325690	−	0.100237i
$330$	14.4257	+	0.814189i	0.794111	+	0.0448197i
$331$	−4.77553	−	14.6976i	−0.262487	−	0.807852i	−0.992262	−	0.124164i	$-0.960375\pi$
$331$	−4.77553	−	14.6976i	−0.262487	−	0.807852i	0.729775	−	0.683688i	$-0.239625\pi$
$332$	55.1813			3.02846
$333$	−0.306903	−	0.944551i	−0.0168182	−	0.0517611i
$334$	−17.5416	−	12.7447i	−0.959831	−	0.697358i
$335$	8.81935	+	7.20067i	0.481853	+	0.393415i
$336$	14.6867	−	10.6705i	0.801226	−	0.582125i
$337$	19.3418	+	14.0526i	1.05362	+	0.765496i	0.972897	−	0.231241i	$-0.0742785\pi$
$337$	19.3418	+	14.0526i	1.05362	+	0.765496i	0.0807186	+	0.996737i	$0.474278\pi$
$338$	16.1586	+	11.7399i	0.878910	+	0.638565i
$339$	−1.35973	+	0.987903i	−0.0738505	+	0.0536556i
$340$	8.68211	−	5.58873i	0.470853	−	0.303091i
$341$	9.50707	+	6.90729i	0.514837	+	0.374051i
$342$	1.26965	+	3.90759i	0.0686550	+	0.211299i
$343$	14.6125			0.789003
$344$	−21.2680	−	65.4563i	−1.14670	−	3.52917i
$345$	−17.4714	−	14.2648i	−0.940630	−	0.767989i
$346$	1.17951	−	3.63017i	0.0634110	−	0.195159i
$347$	−8.42275	+	25.9226i	−0.452157	+	1.39160i	0.422283	+	0.906464i	$0.361229\pi$
$347$	−8.42275	+	25.9226i	−0.452157	+	1.39160i	−0.874440	+	0.485133i	$0.838771\pi$
$348$	−11.2756	+	8.19221i	−0.604436	+	0.439149i
$349$	26.4796			1.41742			0.708711	−	0.705499i	$-0.249277\pi$
$349$	26.4796			1.41742			0.708711	+	0.705499i	$0.249277\pi$
$350$	2.96752	+	14.5348i	0.158621	+	0.776917i
$351$	19.6173			1.04709
$352$	−7.66032	+	5.56555i	−0.408296	+	0.296645i
$353$	1.48130	−	4.55896i	0.0788414	−	0.242649i	−0.903866	−	0.427817i	$-0.859283\pi$
$353$	1.48130	−	4.55896i	0.0788414	−	0.242649i	0.982707	+	0.185168i	$0.0592829\pi$
$354$	−7.87504	+	24.2369i	−0.418554	+	1.28818i
$355$	5.85376	+	22.2032i	0.310685	+	1.17842i
$356$	−20.9733	−	64.5493i	−1.11158	−	3.42110i
$357$	2.24473			0.118804
$358$	−13.3321	−	41.0321i	−0.704625	−	2.16861i
$359$	−9.44536	−	6.86246i	−0.498507	−	0.362187i	0.309939	−	0.950756i	$-0.399691\pi$
$359$	−9.44536	−	6.86246i	−0.498507	−	0.362187i	−0.808446	+	0.588570i	$0.799691\pi$
$360$	−3.02504	−	11.4739i	−0.159433	−	0.604728i
$361$	12.0482	−	8.75353i	0.634116	−	0.460712i
$362$	−27.1586	−	19.7319i	−1.42743	−	1.03709i
$363$	14.6978	+	10.6786i	0.771435	+	0.560480i
$364$	−19.6331	+	14.2643i	−1.02906	+	0.747653i
$365$	5.99046	−	15.4201i	0.313555	−	0.807125i
$366$	44.0282	+	31.9883i	2.30139	+	1.67206i
$367$	−3.21042	−	9.88067i	−0.167583	−	0.515767i	0.831635	−	0.555323i	$-0.187405\pi$
$367$	−3.21042	−	9.88067i	−0.167583	−	0.515767i	−0.999217	+	0.0395566i	$0.987405\pi$
$368$	41.9137			2.18490
$369$	1.11951	+	3.44548i	0.0582791	+	0.179365i
$370$	−6.09563	+	3.92379i	−0.316897	+	0.203988i
$371$	3.79741	−	11.6872i	0.197152	−	0.606770i
$372$	25.2880	−	77.8286i	1.31112	−	4.03523i
$373$	8.66721	−	6.29710i	0.448771	−	0.326051i	−0.340339	−	0.940303i	$-0.610542\pi$
$373$	8.66721	−	6.29710i	0.448771	−	0.326051i	0.789110	+	0.614251i	$0.210542\pi$
$374$	−3.31998			−0.171672
$375$	21.4497	+	3.66301i	1.10766	+	0.189157i
$376$	11.1616			0.575614
$377$	5.71701	−	4.15365i	0.294441	−	0.213924i
$378$	−3.94704	+	12.1477i	−0.203014	+	0.624812i
$379$	−9.09380	+	27.9878i	−0.467117	+	1.43764i	0.389183	+	0.921160i	$0.372757\pi$
$379$	−9.09380	+	27.9878i	−0.467117	+	1.43764i	−0.856300	+	0.516479i	$0.827243\pi$
$380$	17.5962	−	11.3268i	0.902667	−	0.581052i
$381$	−5.32633	−	16.3928i	−0.272876	−	0.839826i
$382$	−34.3345			−1.75671
$383$	11.5553	+	35.5636i	0.590450	+	1.81722i	0.576186	+	0.817319i	$0.304540\pi$
$383$	11.5553	+	35.5636i	0.590450	+	1.81722i	0.0142638	+	0.999898i	$0.495460\pi$
$384$	−12.1719	−	8.84341i	−0.621145	−	0.451289i
$385$	1.20524	−	3.10243i	0.0614249	−	0.158114i
$386$	−14.5071	+	10.5401i	−0.738394	+	0.536475i
$387$	−6.51628	−	4.73435i	−0.331241	−	0.240661i
$388$	49.2166	+	35.7579i	2.49859	+	1.81533i
$389$	12.9782	−	9.42919i	0.658019	−	0.478079i	−0.207974	−	0.978134i	$-0.566687\pi$
$389$	12.9782	−	9.42919i	0.658019	−	0.478079i	0.865993	+	0.500056i	$0.166687\pi$
$390$	13.0056	+	49.3298i	0.658562	+	2.49791i
$391$	4.19285	+	3.04629i	0.212042	+	0.154057i
$392$	11.7981	+	36.3109i	0.595895	+	1.83398i
$393$	38.3152			1.93275
$394$	−6.67663	−	20.5485i	−0.336364	−	1.03522i
$395$	3.47400	+	13.1768i	0.174796	+	0.662998i
$396$	−1.45126	+	4.46651i	−0.0729283	+	0.224450i
$397$	−0.637790	+	1.96292i	−0.0320098	+	0.0985159i	−0.965785	−	0.259344i	$-0.916494\pi$
$397$	−0.637790	+	1.96292i	−0.0320098	+	0.0985159i	0.933775	+	0.357860i	$0.116494\pi$
$398$	9.51007	−	6.90947i	0.476697	−	0.346341i
$399$	4.54944			0.227757
$400$	−35.1805	+	19.9360i	−1.75902	+	0.996801i
$401$	−11.3409			−0.566336			−0.283168	−	0.959070i	$-0.591385\pi$
$401$	−11.3409			−0.566336			−0.283168	+	0.959070i	$0.591385\pi$
$402$	−20.6246	+	14.9847i	−1.02866	+	0.747368i
$403$	−12.8217	+	39.4610i	−0.638692	+	1.96569i
$404$	−8.01690	+	24.6735i	−0.398856	+	1.22755i
$405$	18.6080	+	15.1927i	0.924637	+	0.754932i
$406$	1.42182	+	4.37590i	0.0705636	+	0.217172i
$407$	1.62647			0.0806211
$408$	4.04997	+	12.4645i	0.200503	+	0.617086i
$409$	−15.4946	−	11.2575i	−0.766159	−	0.556647i	0.134634	−	0.990895i	$-0.457014\pi$
$409$	−15.4946	−	11.2575i	−0.766159	−	0.556647i	−0.900793	+	0.434248i	$0.857014\pi$
$410$	22.2353	−	14.3130i	1.09812	−	0.706869i
$411$	−8.72885	+	6.34188i	−0.430562	+	0.312822i
$412$	55.1032	+	40.0348i	2.71474	+	1.97237i
$413$	4.74923	+	3.45052i	0.233694	+	0.169789i
$414$	8.50000	−	6.17561i	0.417752	−	0.303515i
$415$	−20.6985	−	16.8996i	−1.01605	−	0.829568i
$416$	−27.0470	−	19.6508i	−1.32609	−	0.963461i
$417$	−4.89821	−	15.0751i	−0.239866	−	0.738232i
$418$	−6.72868			−0.329110
$419$	0.833657	+	2.56573i	0.0407268	+	0.125344i	0.969353	−	0.245673i	$-0.0790090\pi$
$419$	0.833657	+	2.56573i	0.0407268	+	0.125344i	−0.928626	+	0.371017i	$0.879009\pi$
$420$	−23.1408	−	1.30607i	−1.12915	−	0.0637295i
$421$	−11.8314	+	36.4133i	−0.576626	+	1.77467i	0.0539469	+	0.998544i	$0.482820\pi$
$421$	−11.8314	+	36.4133i	−0.576626	+	1.77467i	−0.630573	+	0.776130i	$0.717180\pi$
$422$	5.25539	−	16.1744i	0.255828	−	0.787358i
$423$	1.05677	−	0.767787i	0.0513818	−	0.0373311i
$424$	71.7482			3.48440
$425$	−4.96825	−	0.562608i	−0.240995	−	0.0272905i
$426$	−51.4141			−2.49102
$427$	10.1421	−	7.36863i	0.490808	−	0.356593i
$428$	−12.7778	+	39.3260i	−0.617638	+	1.90090i
$429$	3.53697	−	10.8857i	0.170767	−	0.525566i
$430$	−21.2898	+	54.8022i	−1.02668	+	2.64280i
$431$	−0.361326	−	1.11205i	−0.0174044	−	0.0535654i	0.941977	−	0.335677i	$-0.108965\pi$
$431$	−0.361326	−	1.11205i	−0.0174044	−	0.0535654i	−0.959382	+	0.282112i	$0.908965\pi$
$432$	−34.8166			−1.67511
$433$	−2.25324	−	6.93477i	−0.108284	−	0.333264i	0.882203	−	0.470869i	$-0.156060\pi$
$433$	−2.25324	−	6.93477i	−0.108284	−	0.333264i	−0.990487	+	0.137605i	$0.956060\pi$
$434$	−21.8559	−	15.8793i	−1.04912	−	0.762229i
$435$	6.73841	+	0.380316i	0.323082	+	0.0182347i
$436$	−53.5480	+	38.9049i	−2.56449	+	1.86321i
$437$	8.49775	+	6.17398i	0.406502	+	0.295341i
$438$	29.9669	+	21.7723i	1.43188	+	1.04032i
$439$	29.2804	−	21.2734i	1.39748	−	1.01533i	0.402479	−	0.915429i	$-0.368149\pi$
$439$	29.2804	−	21.2734i	1.39748	−	1.01533i	0.994998	−	0.0998969i	$-0.0318513\pi$
$440$	19.4017	+	1.09503i	0.924939	+	0.0522036i
$441$	3.61480	+	2.62631i	0.172133	+	0.125062i
$442$	−3.62235	−	11.1485i	−0.172298	−	0.530278i
$443$	8.64555			0.410763			0.205381	−	0.978682i	$-0.434157\pi$
$443$	8.64555			0.410763			0.205381	+	0.978682i	$0.434157\pi$
$444$	−3.50003	−	10.7720i	−0.166104	−	0.511216i
$445$	−11.9015	+	30.6357i	−0.564184	+	1.45227i
$446$	9.03444	−	27.8051i	0.427793	−	1.31661i
$447$	−11.9900	+	36.9014i	−0.567107	+	1.74538i
$448$	2.51842	−	1.82974i	0.118984	−	0.0864469i
$449$	16.7261			0.789354			0.394677	−	0.918820i	$-0.370856\pi$
$449$	16.7261			0.789354			0.394677	+	0.918820i	$0.370856\pi$
$450$	−4.19712	+	9.22651i	−0.197854	+	0.434942i
$451$	−5.93295			−0.279372
$452$	−3.22601	+	2.34383i	−0.151739	+	0.110244i
$453$	1.95616	−	6.02043i	0.0919082	−	0.282864i
$454$	−13.0971	+	40.3089i	−0.614680	+	1.89179i
$455$	11.7329	+	0.662207i	0.550048	+	0.0310447i
$456$	8.20816	+	25.2621i	0.384382	+	1.18301i
$457$	9.90384			0.463282			0.231641	−	0.972801i	$-0.425591\pi$
$457$	9.90384			0.463282			0.231641	+	0.972801i	$0.425591\pi$
$458$	9.17311	+	28.2319i	0.428631	+	1.31919i
$459$	−3.48289	−	2.53047i	−0.162567	−	0.118112i
$460$	−41.4515	−	33.8436i	−1.93268	−	1.57796i
$461$	0.621694	−	0.451687i	0.0289552	−	0.0210372i	−0.573214	−	0.819406i	$-0.694303\pi$
$461$	0.621694	−	0.451687i	0.0289552	−	0.0210372i	0.602169	+	0.798369i	$0.294303\pi$
$462$	6.02916	+	4.38044i	0.280502	+	0.203797i
$463$	3.60085	+	2.61617i	0.167346	+	0.121584i	0.668306	−	0.743887i	$-0.267020\pi$
$463$	3.60085	+	2.61617i	0.167346	+	0.121584i	−0.500960	+	0.865470i	$0.667020\pi$
$464$	−10.1465	+	7.37186i	−0.471039	+	0.342230i
$465$	−33.3210	+	21.4490i	−1.54523	+	0.994672i
$466$	−27.2973	−	19.8326i	−1.26452	−	0.918729i
$467$	2.93365	+	9.02886i	0.135753	+	0.417806i	0.995706	−	0.0925673i	$-0.0295073\pi$
$467$	2.93365	+	9.02886i	0.135753	+	0.417806i	−0.859953	+	0.510373i	$0.829507\pi$
$468$	−16.5819			−0.766499
$469$	1.81471	+	5.58509i	0.0837954	+	0.257896i
$470$	−7.38557	−	6.03004i	−0.340671	−	0.278145i
$471$	6.40585	−	19.7152i	0.295166	−	0.908428i
$472$	−10.5914	+	32.5970i	−0.487509	+	1.50040i
$473$	10.6715	−	7.75331i	0.490677	−	0.356498i
$474$	−30.5125			−1.40148
$475$	−10.0693	−	1.14025i	−0.462009	−	0.0523183i
$476$	5.32568			0.244102
$477$	6.79305	−	4.93544i	0.311033	−	0.225978i
$478$	−19.4104	+	59.7390i	−0.887810	+	2.73240i
$479$	−3.45746	+	10.6410i	−0.157975	+	0.486198i	−0.998450	−	0.0556523i	$-0.982276\pi$
$479$	−3.45746	+	10.6410i	−0.157975	+	0.486198i	0.840475	+	0.541851i	$0.182276\pi$
$480$	−8.14002	−	30.8749i	−0.371539	−	1.40924i
$481$	1.77460	+	5.46166i	0.0809149	+	0.249030i
$482$	73.4775			3.34681
$483$	−3.59499	−	11.0642i	−0.163578	−	0.503441i
$484$	34.8710	+	25.3353i	1.58505	+	1.15160i
$485$	−7.51010	−	28.4857i	−0.341016	−	1.29347i
$486$	−16.6370	+	12.0875i	−0.754669	+	0.548299i
$487$	31.9531	+	23.2153i	1.44793	+	1.05198i	0.986309	+	0.164908i	$0.0527329\pi$
$487$	31.9531	+	23.2153i	1.44793	+	1.05198i	0.461623	+	0.887076i	$0.347267\pi$
$488$	59.2150	+	43.0222i	2.68054	+	1.94752i
$489$	26.5600	−	19.2970i	1.20109	−	0.872640i
$490$	11.8102	−	30.4007i	0.533529	−	1.37336i
$491$	−9.67946	−	7.03254i	−0.436828	−	0.317374i	0.347545	−	0.937663i	$-0.387015\pi$
$491$	−9.67946	−	7.03254i	−0.436828	−	0.317374i	−0.784373	+	0.620289i	$0.787015\pi$
$492$	12.7672	+	39.2935i	0.575591	+	1.77149i
$493$	−1.55080			−0.0698443
$494$	−7.34150	−	22.5948i	−0.330310	−	1.01659i
$495$	1.91226	−	1.23093i	0.0859497	−	0.0553264i
$496$	22.7557	−	70.0349i	1.02176	−	3.14466i
$497$	−3.65982	+	11.2638i	−0.164165	+	0.505249i
$498$	48.4049	−	35.1682i	2.16907	−	1.57592i
$499$	4.58893			0.205429			0.102714	−	0.994711i	$-0.467247\pi$
$499$	4.58893			0.205429			0.102714	+	0.994711i	$0.467247\pi$
$500$	50.8900	+	8.69061i	2.27587	+	0.388656i
$501$	−16.4047			−0.732906
$502$	15.8079	−	11.4851i	0.705541	−	0.512605i
$503$	10.7654	−	33.1325i	0.480006	−	1.47731i	−0.359079	−	0.933307i	$-0.616909\pi$
$503$	10.7654	−	33.1325i	0.480006	−	1.47731i	0.839085	−	0.544000i	$-0.183091\pi$
$504$	1.89128	−	5.82077i	0.0842444	−	0.259278i
$505$	10.5635	−	6.79982i	0.470072	−	0.302588i
$506$	5.31704	+	16.3642i	0.236371	+	0.727476i
$507$	15.1113			0.671116
$508$	−12.6369	−	38.8923i	−0.560670	−	1.72557i
$509$	27.2389	+	19.7902i	1.20734	+	0.877184i	0.994987	−	0.100008i	$-0.0318869\pi$
$509$	27.2389	+	19.7902i	1.20734	+	0.877184i	0.212354	+	0.977193i	$0.431887\pi$
$510$	4.05411	−	10.4357i	0.179519	−	0.462101i
$511$	6.90300	−	5.01532i	0.305371	−	0.221865i
$512$	−40.1127	−	29.1436i	−1.77275	−	1.28798i
$513$	−7.05885	−	5.12855i	−0.311656	−	0.226431i
$514$	−36.0437	+	26.1873i	−1.58982	+	1.15507i
$515$	−8.40836	−	31.8928i	−0.370517	−	1.40536i
$516$	−74.3139	−	53.9922i	−3.27149	−	2.37687i
$517$	0.661045	+	2.03449i	0.0290727	+	0.0894767i
$518$	−3.73911			−0.164287
$519$	−0.892400	−	2.74652i	−0.0391720	−	0.120559i
$520$	17.4916	+	66.3454i	0.767058	+	2.90944i
$521$	8.63871	−	26.5872i	0.378469	−	1.16481i	−0.562640	−	0.826702i	$-0.690214\pi$
$521$	8.63871	−	26.5872i	0.378469	−	1.16481i	0.941108	−	0.338105i	$-0.109786\pi$
$522$	−0.971507	+	2.98999i	−0.0425217	+	0.130868i
$523$	−2.45855	+	1.78624i	−0.107505	+	0.0781069i	−0.640239	−	0.768176i	$-0.721165\pi$
$523$	−2.45855	+	1.78624i	−0.107505	+	0.0781069i	0.532734	+	0.846283i	$0.321165\pi$
$524$	90.9040			3.97116
$525$	8.28013	+	7.57690i	0.361374	+	0.330683i
$526$	19.5958			0.854417
$527$	7.36652	−	5.35209i	0.320891	−	0.233141i
$528$	−6.27738	+	19.3198i	−0.273188	+	0.840786i
$529$	1.19277	−	3.67098i	0.0518597	−	0.159608i
$530$	−47.4755	−	38.7619i	−2.06220	−	1.68371i
$531$	1.23951	+	3.81482i	0.0537902	+	0.165549i
$532$	10.7937			0.467965
$533$	−6.47330	−	19.9228i	−0.280390	−	0.862951i
$534$	−59.5364	−	43.2557i	−2.57639	−	1.87186i
$535$	16.8368	−	10.8380i	0.727918	−	0.468566i
$536$	−27.7388	+	20.1534i	−1.19813	+	0.870495i
$537$	−26.4077	−	19.1864i	−1.13958	−	0.827952i
$538$	−45.9765	−	33.4039i	−1.98219	−	1.44014i
$539$	−5.91986	+	4.30103i	−0.254986	+	0.185258i
$540$	34.4326	+	28.1129i	1.48174	+	1.20979i
$541$	−2.84618	−	2.06787i	−0.122367	−	0.0889048i	0.524918	−	0.851153i	$-0.324096\pi$
$541$	−2.84618	−	2.06787i	−0.122367	−	0.0889048i	−0.647285	+	0.762248i	$0.724096\pi$
$542$	−15.0560	−	46.3377i	−0.646712	−	1.99037i
$543$	−25.3984			−1.08995
$544$	2.26719	+	6.97768i	0.0972048	+	0.299166i
$545$	32.0008	+	1.80612i	1.37076	+	0.0773659i
$546$	−8.13119	+	25.0252i	−0.347983	+	1.07098i
$547$	−3.48512	+	10.7261i	−0.149013	+	0.458615i	−0.997505	−	0.0705928i	$-0.977511\pi$
$547$	−3.48512	+	10.7261i	−0.149013	+	0.458615i	0.848492	+	0.529208i	$0.177511\pi$
$548$	−20.7094	+	15.0463i	−0.884664	+	0.642746i
$549$	8.56585			0.365582
$550$	−12.2464	−	11.2063i	−0.522189	−	0.477840i
$551$	−3.14303			−0.133898
$552$	54.9514	−	39.9246i	2.33889	−	1.69930i
$553$	−2.17198	+	6.68466i	−0.0923619	+	0.284261i
$554$	9.35793	−	28.8007i	0.397580	−	1.22363i
$555$	−1.98612	+	5.11249i	−0.0843061	+	0.217013i
$556$	−11.6211	−	35.7662i	−0.492846	−	1.51682i
$557$	16.3222			0.691595			0.345797	−	0.938309i	$-0.387608\pi$
$557$	16.3222			0.691595			0.345797	+	0.938309i	$0.387608\pi$
$558$	−5.70422	−	17.5558i	−0.241479	−	0.743196i
$559$	37.6790	+	27.3754i	1.59365	+	1.15785i
$560$	−20.8235	−	1.17528i	−0.879952	−	0.0496645i
$561$	−2.03212	+	1.47642i	−0.0857963	+	0.0623347i
$562$	−41.8779	−	30.4261i	−1.76651	−	1.28345i
$563$	−17.4095	−	12.6487i	−0.733721	−	0.533080i	0.157017	−	0.987596i	$-0.449812\pi$
$563$	−17.4095	−	12.6487i	−0.733721	−	0.533080i	−0.890739	+	0.454516i	$0.849812\pi$
$564$	12.0518	−	8.75611i	0.507470	−	0.368699i
$565$	1.92789	+	0.108810i	0.0811069	+	0.00457767i
$566$	−50.3051	−	36.5488i	−2.11448	−	1.53626i
$567$	3.82885	+	11.7840i	0.160797	+	0.494881i
$568$	−69.1486			−2.90141
$569$	8.35137	+	25.7029i	0.350108	+	1.07752i	0.958792	+	0.284108i	$0.0916975\pi$
$569$	8.35137	+	25.7029i	0.350108	+	1.07752i	−0.608685	+	0.793412i	$0.708303\pi$
$570$	8.21655	−	21.1503i	0.344153	−	0.885888i
$571$	3.55992	−	10.9563i	0.148978	−	0.458508i	−0.848523	−	0.529159i	$-0.822508\pi$
$571$	3.55992	−	10.9563i	0.148978	−	0.458508i	0.997501	+	0.0706510i	$0.0225077\pi$
$572$	8.39157	−	25.8266i	0.350869	−	1.07986i
$573$	−21.0158	+	15.2688i	−0.877946	+	0.637865i
$574$	13.6393			0.569295
$575$	5.18369	+	25.3895i	0.216175	+	1.05882i
$576$	2.12702			0.0886260
$577$	−5.34199	+	3.88118i	−0.222390	+	0.161576i	−0.693402	−	0.720551i	$-0.743889\pi$
$577$	−5.34199	+	3.88118i	−0.222390	+	0.161576i	0.471012	+	0.882127i	$0.343889\pi$
$578$	−0.794939	+	2.44657i	−0.0330651	+	0.101764i
$579$	−4.19240	+	12.9029i	−0.174230	+	0.536226i
$580$	15.9871	+	0.902310i	0.663827	+	0.0374664i
$581$	−4.25902	−	13.1079i	−0.176694	−	0.543807i
$582$	65.9620			2.73421
$583$	4.24929	+	13.0780i	0.175988	+	0.541634i
$584$	40.3036	+	29.2823i	1.66777	+	1.21171i
$585$	6.21989	+	5.07830i	0.257161	+	0.209962i
$586$	−67.7224	+	49.2032i	−2.79759	+	2.03256i
$587$	−12.4783	−	9.06602i	−0.515035	−	0.374195i	0.299695	−	0.954035i	$-0.403115\pi$
$587$	−12.4783	−	9.06602i	−0.515035	−	0.374195i	−0.814730	+	0.579840i	$0.803115\pi$
$588$	41.2245	+	29.9513i	1.70007	+	1.23517i
$589$	14.9299	−	10.8472i	0.615175	−	0.446951i
$590$	24.6188	−	15.8473i	1.01354	−	0.652423i
$591$	−13.2248	−	9.60838i	−0.543996	−	0.395236i
$592$	−3.14954	−	9.69330i	−0.129445	−	0.398392i
$593$	34.5946			1.42063			0.710315	−	0.703883i	$-0.248552\pi$
$593$	34.5946			1.42063			0.710315	+	0.703883i	$0.248552\pi$
$594$	−4.41672	−	13.5933i	−0.181220	−	0.557739i
$595$	−1.99767	−	1.63102i	−0.0818964	−	0.0668653i
$596$	−28.4466	+	87.5497i	−1.16522	+	3.58618i
$597$	2.74831	−	8.45842i	0.112481	−	0.346180i
$598$	−49.1494	+	35.7091i	−2.00987	+	1.46026i
$599$	−1.55092			−0.0633689			−0.0316845	−	0.999498i	$-0.510087\pi$
$599$	−1.55092			−0.0633689			−0.0316845	+	0.999498i	$0.510087\pi$
$600$	−27.1339	+	59.6483i	−1.10774	+	2.43513i
$601$	−24.5337			−1.00075			−0.500376	−	0.865808i	$-0.666805\pi$
$601$	−24.5337			−1.00075			−0.500376	+	0.865808i	$0.666805\pi$
$602$	−24.5329	+	17.8242i	−0.999886	+	0.726460i
$603$	−1.23996	+	3.81621i	−0.0504952	+	0.155408i
$604$	4.64104	−	14.2836i	0.188841	−	0.581193i
$605$	−5.32107	−	20.1827i	−0.216332	−	0.820544i
$606$	8.69254	+	26.7529i	0.353110	+	1.08676i
$607$	29.7564			1.20777			0.603887	−	0.797070i	$-0.293618\pi$
$607$	29.7564			1.20777			0.603887	+	0.797070i	$0.293618\pi$
$608$	4.59496	+	14.1418i	0.186350	+	0.573527i
$609$	2.81628	+	2.04615i	0.114121	+	0.0829140i
$610$	−15.9396	−	60.4585i	−0.645374	−	2.44789i
$611$	−6.11054	+	4.43956i	−0.247206	+	0.179606i
$612$	2.94398	+	2.13893i	0.119003	+	0.0864610i
$613$	23.5469	+	17.1078i	0.951052	+	0.690980i	0.951055	−	0.309020i	$-0.100001\pi$
$613$	23.5469	+	17.1078i	0.951052	+	0.690980i	−3.65744e−6		1.00000i	$0.500001\pi$
$614$	−45.1209	+	32.7823i	−1.82093	+	1.32299i
$615$	7.24486	−	18.6491i	0.292141	−	0.752003i
$616$	8.10883	+	5.89141i	0.326714	+	0.237372i
$617$	−3.97829	−	12.2439i	−0.160160	−	0.492922i	0.838487	−	0.544922i	$-0.183441\pi$
$617$	−3.97829	−	12.2439i	−0.160160	−	0.492922i	−0.998647	+	0.0519995i	$0.983441\pi$
$618$	73.8514			2.97074
$619$	−10.2646	−	31.5912i	−0.412570	−	1.26976i	−0.914407	−	0.404797i	$-0.867342\pi$
$619$	−10.2646	−	31.5912i	−0.412570	−	1.26976i	0.501837	−	0.864962i	$-0.332658\pi$
$620$	−79.0551	+	50.8883i	−3.17493	+	2.04372i
$621$	−6.89472	+	21.2198i	−0.276676	+	0.851520i
$622$	20.7371	−	63.8223i	0.831483	−	2.55904i
$623$	−13.7144	+	9.96412i	−0.549457	+	0.399204i
$624$	−71.7247			−2.87129
$625$	−16.4273	−	18.8452i	−0.657094	−	0.753809i
$626$	−36.6695			−1.46561
$627$	−4.11855	+	2.99230i	−0.164479	+	0.119501i
$628$	15.1981	−	46.7749i	0.606469	−	1.86652i
$629$	0.389443	−	1.19858i	0.0155281	−	0.0477906i
$630$	−4.39612	+	2.82981i	−0.175146	+	0.112742i
$631$	−1.88826	−	5.81148i	−0.0751706	−	0.231351i	0.906410	−	0.422398i	$-0.138812\pi$
$631$	−1.88826	−	5.81148i	−0.0751706	−	0.231351i	−0.981581	+	0.191047i	$0.938812\pi$
$632$	−41.0373			−1.63238
$633$	−3.97614	−	12.2373i	−0.158037	−	0.486389i
$634$	−42.9239	−	31.1860i	−1.70473	−	1.23856i
$635$	−7.17089	+	18.4586i	−0.284568	+	0.732509i
$636$	77.4704	−	56.2855i	3.07190	−	2.23187i
$637$	−20.9018	−	15.1861i	−0.828160	−	0.601693i
$638$	−4.16532	−	3.02628i	−0.164906	−	0.119812i
$639$	−6.54693	+	4.75662i	−0.258993	+	0.188169i
$640$	4.40662	+	16.7142i	0.174187	+	0.660687i
$641$	0.191831	+	0.139373i	0.00757685	+	0.00550490i	0.591567	−	0.806256i	$-0.298509\pi$
$641$	0.191831	+	0.139373i	0.00757685	+	0.00550490i	−0.583990	+	0.811761i	$0.698509\pi$
$642$	13.8547	+	42.6403i	0.546800	+	1.68288i
$643$	−3.09539			−0.122070			−0.0610352	−	0.998136i	$-0.519440\pi$
$643$	−3.09539			−0.122070			−0.0610352	+	0.998136i	$0.519440\pi$
$644$	−8.52922	−	26.2503i	−0.336099	−	1.03440i
$645$	11.3398	+	43.0116i	0.446503	+	1.69358i
$646$	−1.61112	+	4.95852i	−0.0633887	+	0.195090i
$647$	−12.0110	+	36.9659i	−0.472200	+	1.45328i	0.377498	+	0.926011i	$0.376785\pi$
$647$	−12.0110	+	36.9659i	−0.472200	+	1.45328i	−0.849697	+	0.527271i	$0.823215\pi$
$648$	−58.5261	+	42.5217i	−2.29912	+	1.67041i
$649$	−6.56893			−0.257853
$650$	24.2690	−	53.3503i	0.951907	−	2.09257i
$651$	−20.4394			−0.801084
$652$	63.0145	−	45.7827i	2.46784	−	1.79299i
$653$	1.11488	−	3.43124i	0.0436285	−	0.134275i	−0.926870	−	0.375383i	$-0.877511\pi$
$653$	1.11488	−	3.43124i	0.0436285	−	0.134275i	0.970498	+	0.241109i	$0.0775111\pi$
$654$	−22.1773	+	68.2546i	−0.867200	+	2.66897i
$655$	−34.0981	−	27.8399i	−1.33232	−	1.08779i
$656$	11.4887	+	35.3587i	0.448560	+	1.38053i
$657$	5.83019			0.227457
$658$	−1.51969	−	4.67711i	−0.0592435	−	0.182333i
$659$	−30.8633	−	22.4235i	−1.20226	−	0.873496i	−0.207758	−	0.978180i	$-0.566617\pi$
$659$	−30.8633	−	22.4235i	−1.20226	−	0.873496i	−0.994505	+	0.104685i	$0.966617\pi$
$660$	21.8081	−	14.0380i	0.848879	−	0.546429i
$661$	−21.8971	+	15.9092i	−0.851699	+	0.618795i	−0.925614	−	0.378469i	$-0.876451\pi$
$661$	−21.8971	+	15.9092i	−0.851699	+	0.618795i	0.0739152	+	0.997265i	$0.476451\pi$
$662$	−32.1624	−	23.3674i	−1.25003	−	0.908198i
$663$	−7.17502	−	5.21295i	−0.278655	−	0.202454i
$664$	65.1014	−	47.2989i	2.52642	−	1.83555i
$665$	−4.04871	−	3.30562i	−0.157002	−	0.128187i
$666$	−2.06694	−	1.50172i	−0.0800924	−	0.0581905i
$667$	2.48364	+	7.64387i	0.0961670	+	0.295972i
$668$	−38.9205			−1.50588
$669$	−6.83531	−	21.0369i	−0.264268	−	0.813334i
$670$	29.2425	+	1.65045i	1.12974	+	0.0637624i
$671$	−4.33491	+	13.3415i	−0.167347	+	0.515042i
$672$	5.08921	−	15.6630i	0.196321	−	0.604213i
$673$	29.8673	−	21.6998i	1.15130	−	0.836467i	0.162646	−	0.986685i	$-0.447997\pi$
$673$	29.8673	−	21.6998i	1.15130	−	0.836467i	0.988653	+	0.150217i	$0.0479973\pi$
$674$	61.5022			2.36898
$675$	−4.30595	−	21.0904i	−0.165736	−	0.811769i
$676$	35.8520			1.37892
$677$	−31.4571	+	22.8549i	−1.20899	+	0.878385i	−0.995139	−	0.0984809i	$-0.968602\pi$
$677$	−31.4571	+	22.8549i	−1.20899	+	0.878385i	−0.213854	+	0.976866i	$0.568602\pi$
$678$	−1.33607	+	4.11201i	−0.0513115	+	0.157921i
$679$	4.69539	−	14.4509i	0.180192	−	0.554575i
$680$	5.45251	−	14.0354i	0.209094	−	0.538231i
$681$	9.90908	+	30.4970i	0.379717	+	1.16865i
$682$	30.2302			1.15757
$683$	14.3607	+	44.1978i	0.549498	+	1.69118i	0.710048	+	0.704153i	$0.248673\pi$
$683$	14.3607	+	44.1978i	0.549498	+	1.69118i	−0.160550	+	0.987028i	$0.551327\pi$
$684$	5.96663	+	4.33501i	0.228140	+	0.165753i
$685$	12.3761	+	0.698510i	0.472868	+	0.0266887i
$686$	30.4113	−	22.0951i	1.16111	−	0.843595i
$687$	18.1697	+	13.2011i	0.693219	+	0.503653i
$688$	−66.8722	−	48.5855i	−2.54948	−	1.85230i
$689$	−39.2794	+	28.5381i	−1.49642	+	1.08722i
$690$	−57.9304	−	3.26959i	−2.20537	−	0.124471i
$691$	−23.9760	−	17.4196i	−0.912089	−	0.662671i	0.0294537	−	0.999566i	$-0.490623\pi$
$691$	−23.9760	−	17.4196i	−0.912089	−	0.662671i	−0.941542	+	0.336895i	$0.890623\pi$
$692$	−2.11724	−	6.51621i	−0.0804856	−	0.247709i
$693$	1.17300			0.0445585
$694$	21.6673	+	66.6852i	0.822481	+	2.53134i
$695$	−6.59450	+	16.9750i	−0.250144	+	0.643897i
$696$	−6.28067	+	19.3299i	−0.238068	+	0.732699i
$697$	−1.42059	+	4.37213i	−0.0538087	+	0.165606i
$698$	55.1088	−	40.0389i	2.08590	−	1.51549i
$699$	−25.5281			−0.965561
$700$	19.6448	+	17.9764i	0.742506	+	0.679445i
$701$	18.8340			0.711349			0.355674	−	0.934610i	$-0.384251\pi$
$701$	18.8340			0.711349			0.355674	+	0.934610i	$0.384251\pi$
$702$	40.8271	−	29.6626i	1.54092	−	1.11954i
$703$	0.789292	−	2.42919i	0.0297687	−	0.0916187i
$704$	−1.07642	+	3.31287i	−0.0405690	+	0.124859i
$705$	−7.20223	−	0.406494i	−0.271252	−	0.0153095i
$706$	−3.81060	−	11.7278i	−0.143414	−	0.441382i
$707$	6.47977			0.243697
$708$	14.1358	+	43.5056i	0.531257	+	1.63504i
$709$	−6.56566	−	4.77023i	−0.246579	−	0.179150i	0.457631	−	0.889142i	$-0.348698\pi$
$709$	−6.56566	−	4.77023i	−0.246579	−	0.179150i	−0.704209	+	0.709993i	$0.748698\pi$
$710$	45.7553	+	37.3575i	1.71717	+	1.40200i
$711$	−3.88538	+	2.82289i	−0.145713	+	0.105867i
$712$	−80.0726	−	58.1761i	−3.00085	−	2.18024i
$713$	−38.1781	−	27.7380i	−1.42978	−	1.03880i
$714$	4.67167	−	3.39417i	0.174833	−	0.127024i
$715$	−11.0572	+	7.11761i	−0.413517	+	0.266184i
$716$	−62.6532	−	45.5202i	−2.34146	−	1.70117i
$717$	14.6856	+	45.1975i	0.548442	+	1.68793i
$718$	−30.0339			−1.12086
$719$	−7.70184	−	23.7038i	−0.287230	−	0.884004i	−0.985721	−	0.168385i	$-0.946145\pi$
$719$	−7.70184	−	23.7038i	−0.287230	−	0.884004i	0.698491	−	0.715619i	$-0.253855\pi$
$720$	−11.0390	−	9.01292i	−0.411399	−	0.335892i
$721$	5.25698	−	16.1793i	0.195780	−	0.602550i
$722$	11.8386	−	36.4353i	0.440585	−	1.35598i
$723$	44.9747	−	32.6761i	1.67263	−	1.21524i
$724$	−60.2586			−2.23949
$725$	−5.72042	−	5.23459i	−0.212451	−	0.194408i
$726$	46.7355			1.73452
$727$	−3.38192	+	2.45711i	−0.125428	+	0.0911291i	−0.648731	−	0.761018i	$-0.724700\pi$
$727$	−3.38192	+	2.45711i	−0.125428	+	0.0911291i	0.523302	+	0.852147i	$0.324700\pi$
$728$	−10.9359	+	33.6573i	−0.405312	+	1.24742i
$729$	5.15153	−	15.8548i	0.190797	−	0.587214i
$730$	−10.8490	−	41.1500i	−0.401538	−	1.52303i
$731$	−3.15840	−	9.72055i	−0.116818	−	0.359527i
$732$	97.6880			3.61065
$733$	−0.653462	−	2.01115i	−0.0241362	−	0.0742835i	0.938263	−	0.345923i	$-0.112434\pi$
$733$	−0.653462	−	2.01115i	−0.0241362	−	0.0742835i	−0.962399	+	0.271640i	$0.912434\pi$
$734$	−21.6217	−	15.7091i	−0.798070	−	0.579832i
$735$	−6.29056	−	23.8600i	−0.232031	−	0.880089i
$736$	30.7620	−	22.3499i	1.13390	−	0.823829i
$737$	−5.31631	−	3.86253i	−0.195829	−	0.142278i
$738$	7.53968	+	5.47790i	0.277540	+	0.201644i
$739$	−18.7876	+	13.6500i	−0.691113	+	0.502123i	−0.877026	−	0.480443i	$-0.840476\pi$
$739$	−18.7876	+	13.6500i	−0.691113	+	0.502123i	0.185913	+	0.982566i	$0.440476\pi$
$740$	−4.71213	+	12.1295i	−0.173221	+	0.445890i
$741$	−14.5418	−	10.5652i	−0.534205	−	0.388123i
$742$	−9.76875	−	30.0651i	−0.358622	−	1.10373i
$743$	23.3964			0.858329			0.429165	−	0.903226i	$-0.358808\pi$
$743$	23.3964			0.858329			0.429165	+	0.903226i	$0.358808\pi$
$744$	−36.8771	−	113.496i	−1.35198	−	4.16096i
$745$	37.4829	−	24.1280i	1.37327	−	0.883982i
$746$	8.51639	−	26.2108i	0.311807	−	0.959644i
$747$	2.91013	−	8.95645i	0.106476	−	0.327699i
$748$	−4.82127	+	3.50286i	−0.176283	+	0.128077i
$749$	10.3278			0.377371
$750$	50.1793	−	24.8099i	1.83229	−	0.905931i
$751$	6.50187			0.237256			0.118628	−	0.992939i	$-0.462150\pi$
$751$	6.50187			0.237256			0.118628	+	0.992939i	$0.462150\pi$
$752$	10.8449	−	7.87929i	0.395473	−	0.287328i
$753$	4.56831	−	14.0598i	0.166478	−	0.512368i
$754$	5.61753	−	17.2890i	0.204578	−	0.629628i
$755$	−6.11530	+	3.93646i	−0.222559	+	0.143262i
$756$	7.08500	+	21.8054i	0.257679	+	0.793054i
$757$	−4.96007			−0.180277			−0.0901383	−	0.995929i	$-0.528731\pi$
$757$	−4.96007			−0.180277			−0.0901383	+	0.995929i	$0.528731\pi$
$758$	23.3936	+	71.9981i	0.849694	+	2.61509i
$759$	10.5318	+	7.65179i	0.382280	+	0.277743i
$760$	11.0507	−	28.4458i	0.400852	−	1.03184i
$761$	4.68915	−	3.40687i	0.169981	−	0.123499i	−0.499542	−	0.866290i	$-0.666498\pi$
$761$	4.68915	−	3.40687i	0.169981	−	0.123499i	0.669523	+	0.742791i	$0.266498\pi$
$762$	−35.8719	−	26.0625i	−1.29950	−	0.944144i
$763$	13.3745	+	9.71717i	0.484191	+	0.351785i
$764$	−49.8605	+	36.2258i	−1.80389	+	1.31060i
$765$	−0.449231	−	1.70393i	−0.0162420	−	0.0616055i
$766$	77.8232	+	56.5419i	2.81187	+	2.04294i
$767$	−7.16721	−	22.0584i	−0.258793	−	0.796483i
$768$	−49.2101			−1.77572
$769$	3.48760	+	10.7337i	0.125766	+	0.387068i	0.994040	−	0.109017i	$-0.0347704\pi$
$769$	3.48760	+	10.7337i	0.125766	+	0.387068i	−0.868274	+	0.496085i	$0.834770\pi$
$770$	−2.18274	−	8.27911i	−0.0786607	−	0.298358i
$771$	−10.4162	+	32.0579i	−0.375132	+	1.15454i
$772$	−9.94660	+	30.6125i	−0.357986	+	1.10177i
$773$	−28.7816	+	20.9111i	−1.03520	+	0.752118i	−0.969343	−	0.245711i	$-0.920979\pi$
$773$	−28.7816	+	20.9111i	−1.03520	+	0.752118i	−0.0658588	+	0.997829i	$0.520979\pi$
$774$	−20.7202			−0.744771
$775$	45.2385	+	5.12284i	1.62501	+	0.184018i
$776$	88.7145			3.18467
$777$	−2.28867	+	1.66281i	−0.0821055	+	0.0596531i
$778$	12.7523	−	39.2476i	0.457193	−	1.40710i
$779$	−2.87914	+	8.86108i	−0.103156	+	0.317481i
$780$	70.9338	+	57.9148i	2.53984	+	2.07368i
$781$	−4.09533	−	12.6041i	−0.146542	−	0.451011i
$782$	13.3323			0.476760
$783$	−2.06309	−	6.34955i	−0.0737290	−	0.226914i
$784$	37.0963	+	26.9520i	1.32487	+	0.962573i
$785$	−20.0259	+	12.8908i	−0.714754	+	0.460092i
$786$	79.7407	−	57.9350i	2.84426	−	2.06647i
$787$	18.7016	+	13.5875i	0.666640	+	0.484342i	0.868899	−	0.494990i	$-0.164828\pi$
$787$	18.7016	+	13.5875i	0.666640	+	0.484342i	−0.202259	+	0.979332i	$0.564828\pi$
$788$	−31.3762	−	22.7962i	−1.11773	−	0.812080i
$789$	11.9944	−	8.71441i	0.427011	−	0.310241i
$790$	27.1542	+	22.1704i	0.966103	+	0.788787i
$791$	0.805750	+	0.585412i	0.0286492	+	0.0208148i
$792$	2.11634	+	6.51342i	0.0752008	+	0.231444i
$793$	−49.5302			−1.75887
$794$	1.64070	+	5.04955i	0.0582263	+	0.179202i
$795$	−46.2970	−	2.61300i	−1.64198	−	0.0926736i
$796$	6.52044	−	20.0679i	0.231111	−	0.711286i
$797$	−13.1999	+	40.6252i	−0.467566	+	1.43902i	0.388161	+	0.921592i	$0.373111\pi$
$797$	−13.1999	+	40.6252i	−0.467566	+	1.43902i	−0.855727	+	0.517428i	$0.826889\pi$
$798$	9.46818	−	6.87904i	0.335170	−	0.243515i
$799$	1.65754			0.0586396
$800$	−15.1896	+	33.3913i	−0.537035	+	1.18056i
$801$	−11.5830			−0.409267
$802$	−23.6024	+	17.1481i	−0.833429	+	0.605521i
$803$	−2.95047	+	9.08062i	−0.104120	+	0.320448i
$804$	−14.1410	+	43.5214i	−0.498714	+	1.53488i
$805$	−4.83997	+	12.4586i	−0.170587	+	0.439109i
$806$	32.9834	+	101.513i	1.16179	+	3.57563i
$807$	−42.9967			−1.51355
$808$	11.6909	+	35.9809i	0.411284	+	1.26580i
$809$	28.1453	+	20.4488i	0.989537	+	0.718941i	0.959820	−	0.280617i	$-0.0905392\pi$
$809$	28.1453	+	20.4488i	0.989537	+	0.718941i	0.0297177	+	0.999558i	$0.490539\pi$
$810$	61.6988	+	3.48228i	2.16788	+	0.122355i
$811$	6.05120	−	4.39646i	0.212486	−	0.154380i	−0.476452	−	0.879201i	$-0.658077\pi$
$811$	6.05120	−	4.39646i	0.212486	−	0.154380i	0.688938	+	0.724820i	$0.258077\pi$
$812$	6.68170	+	4.85454i	0.234482	+	0.170361i
$813$	−29.8224	−	21.6672i	−1.04592	−	0.759903i
$814$	3.38497	−	2.45932i	0.118643	−	0.0861993i
$815$	−37.6580	−	2.12542i	−1.31910	−	0.0744501i
$816$	12.7341	+	9.25189i	0.445784	+	0.323881i
$817$	−6.40119	−	19.7008i	−0.223949	−	0.689245i
$818$	−49.2691			−1.72265
$819$	1.27983	+	3.93891i	0.0447209	+	0.137637i
$820$	17.1886	−	44.2454i	0.600254	−	1.54512i
$821$	−9.38053	+	28.8703i	−0.327383	+	1.00758i	0.642971	+	0.765890i	$0.277702\pi$
$821$	−9.38053	+	28.8703i	−0.327383	+	1.00758i	−0.970354	+	0.241690i	$0.922298\pi$
$822$	−8.57695	+	26.3972i	−0.299156	+	0.920706i
$823$	−2.56192	+	1.86134i	−0.0893028	+	0.0648823i	−0.631541	−	0.775343i	$-0.717577\pi$
$823$	−2.56192	+	1.86134i	−0.0893028	+	0.0648823i	0.542238	+	0.840225i	$0.317577\pi$
$824$	99.3254			3.46016
$825$	−12.4795	−	1.41318i	−0.434479	−	0.0492007i
$826$	15.1014			0.525445
$827$	0.930305	−	0.675906i	0.0323499	−	0.0235036i	−0.571493	−	0.820607i	$-0.693636\pi$
$827$	0.930305	−	0.675906i	0.0323499	−	0.0235036i	0.603843	+	0.797104i	$0.293636\pi$
$828$	5.82790	−	17.9364i	0.202533	−	0.623334i
$829$	−13.2234	+	40.6973i	−0.459266	+	1.41348i	0.406786	+	0.913523i	$0.366649\pi$
$829$	−13.2234	+	40.6973i	−0.459266	+	1.41348i	−0.866053	+	0.499953i	$0.833351\pi$
$830$	−68.6306	−	3.87351i	−2.38220	−	0.134452i
$831$	−7.08005	−	21.7902i	−0.245604	−	0.755892i
$832$	−12.2990			−0.426393
$833$	1.75207	+	5.39232i	0.0607057	+	0.186833i
$834$	−32.9886	−	23.9676i	−1.14230	−	0.829931i
$835$	14.5991	+	11.9196i	0.505224	+	0.412496i
$836$	−9.77138	+	7.09932i	−0.337950	+	0.245535i
$837$	31.7135	+	23.0412i	1.09618	+	0.796422i
$838$	5.61454	+	4.07920i	0.193951	+	0.140914i
$839$	32.4050	−	23.5436i	1.11875	−	0.812817i	0.134727	−	0.990883i	$-0.456984\pi$
$839$	32.4050	−	23.5436i	1.11875	−	0.812817i	0.984019	+	0.178066i	$0.0569841\pi$
$840$	−28.4204	+	18.2944i	−0.980596	+	0.631216i
$841$	21.5158	+	15.6322i	0.741925	+	0.539040i
$842$	30.4360	+	93.6723i	1.04889	+	3.22816i
$843$	−39.1637			−1.34887
$844$	−9.43351	−	29.0333i	−0.324715	−	0.999369i
$845$	−13.4481	−	10.9799i	−0.462629	−	0.377719i
$846$	1.03838	−	3.19580i	0.0357002	−	0.109874i
$847$	3.32678	−	10.2388i	0.114310	−	0.351809i
$848$	69.7126	−	50.6491i	2.39394	−	1.73930i
$849$	−47.0447			−1.61457
$850$	−11.1905	+	6.34142i	−0.383831	+	0.217509i
$851$	−6.53151			−0.223897
$852$	−74.6635	+	54.2462i	−2.55793	+	1.85844i
$853$	−2.14017	+	6.58676i	−0.0732780	+	0.225526i	−0.980987	−	0.194074i	$-0.937830\pi$
$853$	−2.14017	+	6.58676i	−0.0732780	+	0.225526i	0.907709	+	0.419600i	$0.137830\pi$
$854$	9.96557	−	30.6709i	0.341015	−	1.04954i
$855$	−0.910466	−	3.45338i	−0.0311373	−	0.118103i
$856$	18.6336	+	57.3484i	0.636884	+	1.96013i
$857$	−6.40445			−0.218772			−0.109386	−	0.993999i	$-0.534888\pi$
$857$	−6.40445			−0.218772			−0.109386	+	0.993999i	$0.534888\pi$
$858$	−9.09878	−	28.0032i	−0.310627	−	0.956013i
$859$	−30.1654	−	21.9164i	−1.02923	−	0.747779i	−0.0610752	−	0.998133i	$-0.519453\pi$
$859$	−30.1654	−	21.9164i	−1.02923	−	0.747779i	−0.968154	+	0.250354i	$0.919453\pi$
$860$	26.9040	+	102.046i	0.917418	+	3.47975i
$861$	8.34848	−	6.06553i	0.284515	−	0.206713i
$862$	−2.43347	−	1.76802i	−0.0828842	−	0.0602189i
$863$	−31.4044	−	22.8166i	−1.06902	−	0.776687i	−0.0932819	−	0.995640i	$-0.529736\pi$
$863$	−31.4044	−	22.8166i	−1.06902	−	0.776687i	−0.975735	+	0.218953i	$0.929736\pi$
$864$	−25.5532	+	18.5655i	−0.869337	+	0.631610i
$865$	−1.20145	+	3.09265i	−0.0408504	+	0.105153i
$866$	−15.1752	−	11.0254i	−0.515675	−	0.374660i
$867$	0.601438	+	1.85103i	0.0204259	+	0.0628644i
$868$	−48.4931			−1.64596
$869$	−2.43044	−	7.48011i	−0.0824469	−	0.253746i
$870$	14.5989	−	9.39740i	0.494948	−	0.318602i
$871$	7.16982	−	22.0664i	0.242940	−	0.747693i
$872$	−29.8270	+	91.7980i	−1.01007	+	3.10867i
$873$	8.39942	−	6.10253i	0.284277	−	0.206539i
$874$	27.0208			0.913991
$875$	−1.86342	−	12.7593i	−0.0629951	−	0.431344i
$876$	66.4895			2.24647
$877$	−36.8021	+	26.7383i	−1.24272	+	0.902888i	−0.997776	−	0.0666493i	$-0.978769\pi$
$877$	−36.8021	+	26.7383i	−1.24272	+	0.902888i	−0.244943	+	0.969538i	$0.578769\pi$
$878$	28.7709	−	88.5476i	0.970970	−	2.98834i
$879$	−19.5710	+	60.2334i	−0.660114	+	2.03162i
$880$	19.6242	−	12.6323i	0.661533	−	0.425833i
$881$	−6.84022	−	21.0520i	−0.230453	−	0.709261i	−0.997692	−	0.0679002i	$-0.978370\pi$
$881$	−6.84022	−	21.0520i	−0.230453	−	0.709261i	0.767239	−	0.641361i	$-0.221630\pi$
$882$	11.4942			0.387030
$883$	2.46787	+	7.59533i	0.0830505	+	0.255603i	0.983956	−	0.178413i	$-0.0570962\pi$
$883$	2.46787	+	7.59533i	0.0830505	+	0.255603i	−0.900905	+	0.434016i	$0.857096\pi$
$884$	−17.0229	−	12.3679i	−0.572543	−	0.415977i
$885$	8.02148	−	20.6482i	0.269639	−	0.694080i
$886$	17.9929	−	13.0726i	0.604484	−	0.439184i
$887$	−1.05114	−	0.763700i	−0.0352939	−	0.0256425i	0.569998	−	0.821646i	$-0.306944\pi$
$887$	−1.05114	−	0.763700i	−0.0352939	−	0.0256425i	−0.605292	+	0.796003i	$0.706944\pi$
$888$	−13.3625	−	9.70844i	−0.448417	−	0.325794i
$889$	−8.26324	+	6.00359i	−0.277140	+	0.201354i
$890$	21.5540	+	81.7541i	0.722493	+	2.74040i
$891$	−11.2169	−	8.14956i	−0.375780	−	0.273020i
$892$	−16.2170	−	49.9107i	−0.542984	−	1.67113i
$893$	3.35938			0.112417
$894$	30.8440	+	94.9280i	1.03158	+	3.17487i
$895$	9.56043	+	36.2625i	0.319570	+	1.21212i
$896$	−2.75506	+	8.47919i	−0.0920400	+	0.283270i
$897$	−14.2036	+	43.7143i	−0.474246	+	1.45958i
$898$	34.8100	−	25.2910i	1.16163	−	0.843970i
$899$	14.1208			0.470955
$900$	3.63969	+	17.8270i	0.121323	+	0.594235i
$901$	10.6549			0.354967
$902$	−12.3475	+	8.97100i	−0.411127	+	0.298701i
$903$	−7.08974	+	21.8200i	−0.235932	+	0.726123i
$904$	−1.79693	+	5.53038i	−0.0597650	+	0.183938i
$905$	22.6030	+	18.4545i	0.751350	+	0.613449i
$906$	−5.03216	−	15.4874i	−0.167182	−	0.514535i
$907$	46.9244			1.55810			0.779050	−	0.626962i	$-0.215702\pi$
$907$	46.9244			1.55810			0.779050	+	0.626962i	$0.215702\pi$
$908$	23.5096	+	72.3551i	0.780193	+	2.40119i
$909$	3.58195	+	2.60244i	0.118806	+	0.0863175i
$910$	25.4196	−	16.3628i	0.842652	−	0.542421i
$911$	5.75077	−	4.17818i	0.190531	−	0.138429i	−0.488430	−	0.872603i	$-0.662430\pi$
$911$	5.75077	−	4.17818i	0.190531	−	0.138429i	0.678962	+	0.734174i	$0.262430\pi$
$912$	25.8085	+	18.7510i	0.854606	+	0.620908i
$913$	12.4771	+	9.06514i	0.412932	+	0.300012i
$914$	20.6116	−	14.9752i	0.681773	−	0.495337i
$915$	−36.6428	−	29.9175i	−1.21138	−	0.989042i
$916$	43.1082	+	31.3200i	1.42434	+	1.03484i
$917$	−7.01618	−	21.5936i	−0.231695	−	0.713082i
$918$	−11.0747			−0.365521
$919$	−0.583979	−	1.79730i	−0.0192637	−	0.0592875i	0.940963	−	0.338511i	$-0.109923\pi$
$919$	−0.583979	−	1.79730i	−0.0192637	−	0.0592875i	−0.960226	+	0.279223i	$0.909923\pi$
$920$	−77.9126	−	4.39739i	−2.56870	−	0.144978i
$921$	−13.0395	+	40.1313i	−0.429665	+	1.32237i
$922$	0.610876	−	1.88008i	0.0201181	−	0.0619172i
$923$	37.8562	−	27.5041i	1.24605	−	0.905310i
$924$	13.3773			0.440080
$925$	5.48226	−	3.10668i	0.180256	−	0.102147i
$926$	11.4498			0.376265
$927$	9.40404	−	6.83243i	0.308869	−	0.224407i
$928$	−3.51594	+	10.8210i	−0.115417	+	0.355215i
$929$	−10.4417	+	32.1363i	−0.342582	+	1.05436i	0.620284	+	0.784378i	$0.287017\pi$
$929$	−10.4417	+	32.1363i	−0.342582	+	1.05436i	−0.962866	+	0.269981i	$0.912983\pi$
$930$	−36.9148	+	95.0226i	−1.21048	+	3.11591i
$931$	3.55096	+	10.9287i	0.116378	+	0.358175i
$932$	−60.5662			−1.98391
$933$	−15.6894	−	48.2869i	−0.513647	−	1.58084i
$934$	19.7577	+	14.3548i	0.646490	+	0.469703i
$935$	2.88123	+	0.162617i	0.0942264	+	0.00531814i
$936$	−19.5629	+	14.2133i	−0.639433	+	0.464576i
$937$	2.04054	+	1.48254i	0.0666617	+	0.0484325i	0.620617	−	0.784114i	$-0.286882\pi$
$937$	2.04054	+	1.48254i	0.0666617	+	0.0484325i	−0.553955	+	0.832546i	$0.686882\pi$
$938$	12.2217	+	8.87962i	0.399054	+	0.289930i
$939$	−22.4450	+	16.3072i	−0.732464	+	0.532166i
$940$	−17.0875	−	0.964420i	−0.557333	−	0.0314559i
$941$	−30.6083	−	22.2382i	−0.997801	−	0.724945i	−0.0361851	−	0.999345i	$-0.511521\pi$
$941$	−30.6083	−	22.2382i	−0.997801	−	0.724945i	−0.961615	+	0.274401i	$0.911521\pi$
$942$	−16.4789	−	50.7169i	−0.536912	−	1.65244i
$943$	23.8253			0.775859
$944$	12.7203	+	39.1490i	0.414010	+	1.27419i
$945$	4.02043	−	10.3490i	0.130785	−	0.336654i
$946$	10.4858	−	32.2720i	0.340923	−	1.04925i
$947$	9.88877	−	30.4345i	0.321342	−	0.988988i	−0.651723	−	0.758457i	$-0.725954\pi$
$947$	9.88877	−	30.4345i	0.321342	−	0.988988i	0.973065	−	0.230531i	$-0.0740464\pi$
$948$	−44.3102	+	32.1932i	−1.43913	+	1.04559i
$949$	−33.7118			−1.09433
$950$	−22.6800	+	12.8523i	−0.735837	+	0.416983i
$951$	−40.1419			−1.30169
$952$	6.28310	−	4.56494i	0.203636	−	0.147950i
$953$	12.2994	−	37.8536i	0.398416	−	1.22620i	−0.527853	−	0.849336i	$-0.677003\pi$
$953$	12.2994	−	37.8536i	0.398416	−	1.22620i	0.926269	−	0.376863i	$-0.122997\pi$
$954$	6.67485	−	20.5431i	0.216106	−	0.665106i
$955$	29.7971	+	1.68175i	0.964211	+	0.0544201i
$956$	34.8419	+	107.232i	1.12687	+	3.46814i
$957$	−3.89535			−0.125919
$958$	8.89424	+	27.3736i	0.287360	+	0.884402i
$959$	5.17254	+	3.75807i	0.167030	+	0.121354i
$960$	−9.09894	−	7.42894i	−0.293667	−	0.239768i
$961$	−41.9965	+	30.5122i	−1.35473	+	0.984266i
$962$	11.9516	+	8.68338i	0.385337	+	0.279963i
$963$	5.70912	+	4.14792i	0.183974	+	0.133665i
$964$	106.704	−	77.5249i	3.43670	−	2.49691i
$965$	13.1062	−	8.43657i	0.421905	−	0.271583i
$966$	−24.2117	−	17.5908i	−0.778998	−	0.565975i
$967$	12.7288	+	39.1751i	0.409329	+	1.25979i	0.917226	+	0.398367i	$0.130423\pi$
$967$	12.7288	+	39.1751i	0.409329	+	1.25979i	−0.507897	+	0.861418i	$0.669577\pi$
$968$	62.8562			2.02027
$969$	1.21895	+	3.75153i	0.0391582	+	0.120517i
$970$	−58.7020	−	47.9280i	−1.88481	−	1.53888i
$971$	−7.19100	+	22.1316i	−0.230770	+	0.710237i	0.766884	+	0.641785i	$0.221806\pi$
$971$	−7.19100	+	22.1316i	−0.230770	+	0.710237i	−0.997654	+	0.0684520i	$0.978194\pi$
$972$	−11.4069	+	35.1068i	−0.365877	+	1.12605i
$973$	−7.59905	+	5.52103i	−0.243614	+	0.176996i
$974$	101.603			3.25557
$975$	−8.87059	−	43.4477i	−0.284086	−	1.39144i
$976$	87.9056			2.81379
$977$	1.34597	−	0.977908i	0.0430615	−	0.0312860i	−0.566046	−	0.824373i	$-0.691528\pi$
$977$	1.34597	−	0.977908i	0.0430615	−	0.0312860i	0.609108	+	0.793087i	$0.291528\pi$
$978$	26.0979	−	80.3209i	0.834517	−	2.56838i
$979$	5.86181	−	18.0408i	0.187344	−	0.576586i
$980$	−14.9245	−	56.6085i	−0.476747	−	1.80829i
$981$	3.49065	+	10.7431i	0.111448	+	0.343001i
$982$	−30.7783			−0.982176
$983$	−2.02877	−	6.24391i	−0.0647077	−	0.199150i	0.913476	−	0.406894i	$-0.133388\pi$
$983$	−2.02877	−	6.24391i	−0.0647077	−	0.199150i	−0.978183	+	0.207744i	$0.933388\pi$
$984$	48.7431	+	35.4139i	1.55387	+	1.12896i
$985$	4.78779	+	18.1600i	0.152552	+	0.578626i
$986$	−3.22748	+	2.34490i	−0.102784	+	0.0746769i
$987$	−3.01013	−	2.18699i	−0.0958136	−	0.0696126i
$988$	−34.5008	−	25.0663i	−1.09762	−	0.797464i
$989$	−42.8543	+	31.1354i	−1.36269	+	0.990050i
$990$	2.11850	−	5.45325i	0.0673304	−	0.173316i
$991$	22.9285	+	16.6586i	0.728349	+	0.529176i	0.889041	−	0.457828i	$-0.151373\pi$
$991$	22.9285	+	16.6586i	0.728349	+	0.529176i	−0.160692	+	0.987005i	$0.551373\pi$
$992$	−20.6439	−	63.5355i	−0.655445	−	2.01725i
$993$	−30.0779			−0.954494
$994$	9.41481	+	28.9758i	0.298620	+	0.919057i
$995$	−8.59172	+	5.53055i	−0.272376	+	0.175330i
$996$	33.1881	−	102.142i	1.05160	−	3.23651i
$997$	3.77942	−	11.6318i	0.119695	−	0.368384i	−0.873202	−	0.487358i	$-0.837961\pi$
$997$	3.77942	−	11.6318i	0.119695	−	0.368384i	0.992897	+	0.118974i	$0.0379606\pi$
$998$	9.55038	−	6.93876i	0.302312	−	0.219642i
$999$	5.42555			0.171657

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.c.86.19	✓	80
25.16	even	5	inner	425.2.k.c.341.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.c.86.19	✓	80	1.1	even	1	trivial
425.2.k.c.341.19	yes	80	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.08118 - 1.51206i) q^{2} +(0.601438 - 1.85103i) q^{3} +(1.42693 - 4.39163i) q^{4} +(-1.88021 + 1.21030i) q^{5} +(-1.54718 - 4.76174i) q^{6} -1.15333 q^{7} +(-2.08086 - 6.40424i) q^{8} +(-0.637551 - 0.463208i) q^{9} +(-2.08299 + 5.36184i) q^{10} +(1.04410 - 0.758583i) q^{11} +(-7.27086 - 5.28259i) q^{12} +(3.68650 + 2.67840i) q^{13} +(-2.40029 + 1.74392i) q^{14} +(1.10948 + 4.20825i) q^{15} +(-6.54276 - 4.75360i) q^{16} +(-0.309017 - 0.951057i) q^{17} -2.02726 q^{18} +(-0.626291 - 1.92753i) q^{19} +(2.63228 + 9.98419i) q^{20} +(-0.693659 + 2.13486i) q^{21} +(1.02593 - 3.15749i) q^{22} +(-4.19285 + 3.04629i) q^{23} -13.1060 q^{24} +(2.07034 - 4.55123i) q^{25} +11.7222 q^{26} +(3.48289 - 2.53047i) q^{27} +(-1.64573 + 5.06502i) q^{28} +(0.479222 - 1.47489i) q^{29} +(8.67217 + 7.08050i) q^{30} +(2.81376 + 8.65987i) q^{31} -7.33677 q^{32} +(-0.776202 - 2.38890i) q^{33} +(-2.08118 - 1.51206i) q^{34} +(2.16851 - 1.39588i) q^{35} +(-2.94398 + 2.13893i) q^{36} +(1.01958 + 0.740765i) q^{37} +(-4.21797 - 3.06453i) q^{38} +(7.17502 - 5.21295i) q^{39} +(11.6635 + 9.52281i) q^{40} +(-3.71915 - 2.70212i) q^{41} +(1.78442 + 5.49188i) q^{42} +10.2208 q^{43} +(-1.84156 - 5.66775i) q^{44} +(1.75935 + 0.0992977i) q^{45} +(-4.11989 + 12.6797i) q^{46} +(-0.512209 + 1.57642i) q^{47} +(-12.7341 + 9.25189i) q^{48} -5.66982 q^{49} +(-2.57299 - 12.6024i) q^{50} -1.94629 q^{51} +(17.0229 - 12.3679i) q^{52} +(-3.29255 + 10.1334i) q^{53} +(3.42228 - 10.5327i) q^{54} +(-1.04501 + 2.68997i) q^{55} +(2.39993 + 7.38622i) q^{56} -3.94459 q^{57} +(-1.23279 - 3.79413i) q^{58} +(-4.11783 - 2.99178i) q^{59} +(20.0642 + 1.13243i) q^{60} +(-8.79368 + 6.38898i) q^{61} +(18.9502 + 13.7681i) q^{62} +(0.735310 + 0.534234i) q^{63} +(-2.18360 + 1.58647i) q^{64} +(-10.1731 - 0.574167i) q^{65} +(-5.22759 - 3.79807i) q^{66} +(-1.57344 - 4.84256i) q^{67} -4.61764 q^{68} +(3.11704 + 9.59327i) q^{69} +(2.40238 - 6.18400i) q^{70} +(3.17325 - 9.76627i) q^{71} +(-1.63984 + 5.04690i) q^{72} +(-5.98525 + 4.34854i) q^{73} +3.24200 q^{74} +(-7.17930 - 6.56956i) q^{75} -9.35866 q^{76} +(-1.20420 + 0.874899i) q^{77} +(7.05016 - 21.6982i) q^{78} +(1.88322 - 5.79594i) q^{79} +(18.0550 + 1.01903i) q^{80} +(-3.31981 - 10.2173i) q^{81} -11.8260 q^{82} +(3.69279 + 11.3652i) q^{83} +(8.38573 + 6.09259i) q^{84} +(1.73208 + 1.41418i) q^{85} +(21.2713 - 15.4545i) q^{86} +(-2.44186 - 1.77411i) q^{87} +(-7.03077 - 5.10815i) q^{88} +(11.8911 - 8.63941i) q^{89} +(3.81166 - 2.45359i) q^{90} +(-4.25177 - 3.08909i) q^{91} +(7.39528 + 22.7603i) q^{92} +17.7220 q^{93} +(1.31765 + 4.05529i) q^{94} +(3.51044 + 2.86615i) q^{95} +(-4.41261 + 13.5806i) q^{96} +(-4.07114 + 12.5297i) q^{97} +(-11.7999 + 8.57313i) q^{98} -1.01705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

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