LMFDB - Embedded newform 875.2.n.c.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(99,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("875.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.n (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			274.2
Character	$\chi$	$=$	875.274
Dual form			875.2.n.c.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11404 - 0.686892i) q^{2} +(-0.515049 + 0.708904i) q^{3} +(2.37929 + 1.72866i) q^{4} +(1.57577 - 1.14486i) q^{6} -1.00000i q^{7} +(-1.22941 - 1.69214i) q^{8} +(0.689782 + 2.12293i) q^{9} +O(q^{10})$	\(q+(-2.11404 - 0.686892i) q^{2} +(-0.515049 + 0.708904i) q^{3} +(2.37929 + 1.72866i) q^{4} +(1.57577 - 1.14486i) q^{6} -1.00000i q^{7} +(-1.22941 - 1.69214i) q^{8} +(0.689782 + 2.12293i) q^{9} +(-0.121412 + 0.373666i) q^{11} +(-2.45090 + 0.796346i) q^{12} +(2.20066 - 0.715037i) q^{13} +(-0.686892 + 2.11404i) q^{14} +(-0.380912 - 1.17233i) q^{16} +(1.50959 + 2.07778i) q^{17} -4.96175i q^{18} +(-2.59114 + 1.88257i) q^{19} +(0.708904 + 0.515049i) q^{21} +(0.513337 - 0.706547i) q^{22} +(2.83538 + 0.921271i) q^{23} +1.83277 q^{24} -5.14342 q^{26} +(-4.36032 - 1.41675i) q^{27} +(1.72866 - 2.37929i) q^{28} +(-1.59035 - 1.15546i) q^{29} +(7.28014 - 5.28933i) q^{31} +6.92319i q^{32} +(-0.202361 - 0.278525i) q^{33} +(-1.76412 - 5.42942i) q^{34} +(-2.02862 + 6.24346i) q^{36} +(-5.74156 + 1.86554i) q^{37} +(6.77088 - 2.19999i) q^{38} +(-0.626553 + 1.92833i) q^{39} +(1.76779 + 5.44071i) q^{41} +(-1.14486 - 1.57577i) q^{42} -9.34864i q^{43} +(-0.934814 + 0.679182i) q^{44} +(-5.36128 - 3.89520i) q^{46} +(-1.79851 + 2.47544i) q^{47} +(1.02726 + 0.333776i) q^{48} -1.00000 q^{49} -2.25046 q^{51} +(6.47205 + 2.10290i) q^{52} +(-6.06474 + 8.34740i) q^{53} +(8.24472 + 5.99014i) q^{54} +(-1.69214 + 1.22941i) q^{56} -2.80648i q^{57} +(2.56839 + 3.53508i) q^{58} +(-1.53233 - 4.71604i) q^{59} +(-3.30596 + 10.1747i) q^{61} +(-19.0237 + 6.18116i) q^{62} +(2.12293 - 0.689782i) q^{63} +(3.99366 - 12.2912i) q^{64} +(0.236481 + 0.727812i) q^{66} +(9.25908 + 12.7440i) q^{67} +7.55320i q^{68} +(-2.11345 + 1.53551i) q^{69} +(9.95930 + 7.23586i) q^{71} +(2.74427 - 3.77716i) q^{72} +(-1.27164 - 0.413179i) q^{73} +13.4193 q^{74} -9.41939 q^{76} +(0.373666 + 0.121412i) q^{77} +(2.64911 - 3.64619i) q^{78} +(0.855018 + 0.621207i) q^{79} +(-2.16750 + 1.57478i) q^{81} -12.7161i q^{82} +(8.36057 + 11.5073i) q^{83} +(0.796346 + 2.45090i) q^{84} +(-6.42150 + 19.7634i) q^{86} +(1.63822 - 0.532289i) q^{87} +(0.781561 - 0.253945i) q^{88} +(-4.34169 + 13.3623i) q^{89} +(-0.715037 - 2.20066i) q^{91} +(5.15363 + 7.09337i) q^{92} +7.88518i q^{93} +(5.50247 - 3.99778i) q^{94} +(-4.90787 - 3.56578i) q^{96} +(10.0074 - 13.7740i) q^{97} +(2.11404 + 0.686892i) q^{98} -0.877015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} + 6 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 + 6 * q^9	$ 56 q + 12 q^{4} + 6 q^{9} + 8 q^{11} + 40 q^{12} - 4 q^{14} - 32 q^{16} + 12 q^{19} + 4 q^{21} + 30 q^{22} - 10 q^{23} - 28 q^{24} + 12 q^{26} - 30 q^{27} - 2 q^{29} + 12 q^{31} - 20 q^{33} - 14 q^{36} + 70 q^{37} + 70 q^{38} - 4 q^{39} + 4 q^{41} - 50 q^{42} + 22 q^{44} - 4 q^{46} + 10 q^{47} - 30 q^{48} - 56 q^{49} - 44 q^{51} + 20 q^{53} + 54 q^{54} + 12 q^{56} - 10 q^{58} - 6 q^{59} - 4 q^{61} - 50 q^{62} - 20 q^{63} + 24 q^{64} - 74 q^{66} - 10 q^{67} - 78 q^{69} - 8 q^{71} - 140 q^{72} - 40 q^{73} + 60 q^{74} + 52 q^{76} + 20 q^{77} + 90 q^{78} - 72 q^{81} + 30 q^{83} - 12 q^{84} - 20 q^{86} - 30 q^{87} - 140 q^{88} + 38 q^{89} + 8 q^{91} - 80 q^{92} + 88 q^{94} - 28 q^{96} + 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 + 6 * q^9 + 8 * q^11 + 40 * q^12 - 4 * q^14 - 32 * q^16 + 12 * q^19 + 4 * q^21 + 30 * q^22 - 10 * q^23 - 28 * q^24 + 12 * q^26 - 30 * q^27 - 2 * q^29 + 12 * q^31 - 20 * q^33 - 14 * q^36 + 70 * q^37 + 70 * q^38 - 4 * q^39 + 4 * q^41 - 50 * q^42 + 22 * q^44 - 4 * q^46 + 10 * q^47 - 30 * q^48 - 56 * q^49 - 44 * q^51 + 20 * q^53 + 54 * q^54 + 12 * q^56 - 10 * q^58 - 6 * q^59 - 4 * q^61 - 50 * q^62 - 20 * q^63 + 24 * q^64 - 74 * q^66 - 10 * q^67 - 78 * q^69 - 8 * q^71 - 140 * q^72 - 40 * q^73 + 60 * q^74 + 52 * q^76 + 20 * q^77 + 90 * q^78 - 72 * q^81 + 30 * q^83 - 12 * q^84 - 20 * q^86 - 30 * q^87 - 140 * q^88 + 38 * q^89 + 8 * q^91 - 80 * q^92 + 88 * q^94 - 28 * q^96 + 30 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.11404	−	0.686892i	−1.49485	−	0.485706i	−0.556338	−	0.830956i	$-0.687794\pi$
$2$	−2.11404	−	0.686892i	−1.49485	−	0.485706i	−0.938511	+	0.345250i	$0.887794\pi$
$3$	−0.515049	+	0.708904i	−0.297363	+	0.409286i	−0.931388	−	0.364027i	$-0.881402\pi$
$3$	−0.515049	+	0.708904i	−0.297363	+	0.409286i	0.634025	+	0.773313i	$0.281402\pi$
$4$	2.37929	+	1.72866i	1.18964	+	0.864328i
$5$		0			0
$5$		0			0
$6$	1.57577	−	1.14486i	0.643306	−	0.467389i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.22941	−	1.69214i	−0.434663	−	0.598262i
$9$	0.689782	+	2.12293i	0.229927	+	0.707643i
$10$		0			0
$11$	−0.121412	+	0.373666i	−0.0366070	+	0.112665i	−0.967690	−	0.252142i	$-0.918865\pi$
$11$	−0.121412	+	0.373666i	−0.0366070	+	0.112665i	0.931083	+	0.364807i	$0.118865\pi$
$12$	−2.45090	+	0.796346i	−0.707514	+	0.229885i
$13$	2.20066	−	0.715037i	0.610352	−	0.198316i	0.0125002	−	0.999922i	$-0.496021\pi$
$13$	2.20066	−	0.715037i	0.610352	−	0.198316i	0.597852	+	0.801606i	$0.296021\pi$
$14$	−0.686892	+	2.11404i	−0.183580	+	0.565000i
$15$		0			0
$16$	−0.380912	−	1.17233i	−0.0952281	−	0.293082i
$17$	1.50959	+	2.07778i	0.366130	+	0.503935i	0.951844	−	0.306583i	$-0.0991858\pi$
$17$	1.50959	+	2.07778i	0.366130	+	0.503935i	−0.585714	+	0.810518i	$0.699186\pi$
$18$		−	4.96175i		−	1.16950i
$19$	−2.59114	+	1.88257i	−0.594448	+	0.431892i	−0.843904	−	0.536494i	$-0.819748\pi$
$19$	−2.59114	+	1.88257i	−0.594448	+	0.431892i	0.249456	+	0.968386i	$0.419748\pi$
$20$		0			0
$21$	0.708904	+	0.515049i	0.154695	+	0.112393i
$22$	0.513337	−	0.706547i	0.109444	−	0.150636i
$23$	2.83538	+	0.921271i	0.591218	+	0.192098i	0.589320	−	0.807900i	$-0.299396\pi$
$23$	2.83538	+	0.921271i	0.591218	+	0.192098i	0.00189810	+	0.999998i	$0.499396\pi$
$24$	1.83277			0.374113
$25$		0			0
$26$	−5.14342			−1.00871
$27$	−4.36032	−	1.41675i	−0.839144	−	0.272655i
$28$	1.72866	−	2.37929i	0.326685	−	0.449644i
$29$	−1.59035	−	1.15546i	−0.295321	−	0.214563i	0.430251	−	0.902709i	$-0.358425\pi$
$29$	−1.59035	−	1.15546i	−0.295321	−	0.214563i	−0.725572	+	0.688146i	$0.758425\pi$
$30$		0			0
$31$	7.28014	−	5.28933i	1.30755	−	0.949992i	0.307552	−	0.951531i	$-0.400490\pi$
$31$	7.28014	−	5.28933i	1.30755	−	0.949992i	0.999999	+	0.00153963i	$0.000490081\pi$
$32$			6.92319i			1.22386i
$33$	−0.202361	−	0.278525i	−0.0352265	−	0.0484850i
$34$	−1.76412	−	5.42942i	−0.302545	−	0.931137i
$35$		0			0
$36$	−2.02862	+	6.24346i	−0.338104	+	1.04058i
$37$	−5.74156	+	1.86554i	−0.943906	+	0.306694i	−0.740237	−	0.672346i	$-0.765287\pi$
$37$	−5.74156	+	1.86554i	−0.943906	+	0.306694i	−0.203669	+	0.979040i	$0.565287\pi$
$38$	6.77088	−	2.19999i	1.09838	−	0.356886i
$39$	−0.626553	+	1.92833i	−0.100329	+	0.308780i
$40$		0			0
$41$	1.76779	+	5.44071i	0.276083	+	0.849697i	0.988931	+	0.148378i	$0.0474051\pi$
$41$	1.76779	+	5.44071i	0.276083	+	0.849697i	−0.712848	+	0.701319i	$0.752595\pi$
$42$	−1.14486	−	1.57577i	−0.176656	−	0.243147i
$43$		−	9.34864i		−	1.42565i	−0.701340	−	0.712827i	$-0.747414\pi$
$43$		−	9.34864i		−	1.42565i	0.701340	−	0.712827i	$-0.252586\pi$
$44$	−0.934814	+	0.679182i	−0.140928	+	0.102391i
$45$		0			0
$46$	−5.36128	−	3.89520i	−0.790478	−	0.574316i
$47$	−1.79851	+	2.47544i	−0.262339	+	0.361079i	−0.919785	−	0.392423i	$-0.871637\pi$
$47$	−1.79851	+	2.47544i	−0.262339	+	0.361079i	0.657445	+	0.753502i	$0.271637\pi$
$48$	1.02726	+	0.333776i	0.148272	+	0.0481764i
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−2.25046			−0.315127
$52$	6.47205	+	2.10290i	0.897512	+	0.291619i
$53$	−6.06474	+	8.34740i	−0.833056	+	1.14660i	0.154290	+	0.988026i	$0.450691\pi$
$53$	−6.06474	+	8.34740i	−0.833056	+	1.14660i	−0.987346	+	0.158578i	$0.949309\pi$
$54$	8.24472	+	5.99014i	1.12196	+	0.815154i
$55$		0			0
$56$	−1.69214	+	1.22941i	−0.226122	+	0.164287i
$57$		−	2.80648i		−	0.371728i
$58$	2.56839	+	3.53508i	0.337246	+	0.464179i
$59$	−1.53233	−	4.71604i	−0.199493	−	0.613976i	−0.999895	−	0.0145120i	$-0.995381\pi$
$59$	−1.53233	−	4.71604i	−0.199493	−	0.613976i	0.800402	−	0.599464i	$-0.204619\pi$
$60$		0			0
$61$	−3.30596	+	10.1747i	−0.423285	+	1.30274i	0.481342	+	0.876533i	$0.340150\pi$
$61$	−3.30596	+	10.1747i	−0.423285	+	1.30274i	−0.904627	+	0.426205i	$0.859850\pi$
$62$	−19.0237	+	6.18116i	−2.41601	+	0.785008i
$63$	2.12293	−	0.689782i	0.267464	−	0.0869043i
$64$	3.99366	−	12.2912i	0.499207	−	1.53640i
$65$		0			0
$66$	0.236481	+	0.727812i	0.0291087	+	0.0895875i
$67$	9.25908	+	12.7440i	1.13118	+	1.55693i	0.785816	+	0.618460i	$0.212243\pi$
$67$	9.25908	+	12.7440i	1.13118	+	1.55693i	0.345360	+	0.938470i	$0.387757\pi$
$68$			7.55320i			0.915959i
$69$	−2.11345	+	1.53551i	−0.254430	+	0.184854i
$70$		0			0
$71$	9.95930	+	7.23586i	1.18195	+	0.858738i	0.992390	−	0.123130i	$-0.0392934\pi$
$71$	9.95930	+	7.23586i	1.18195	+	0.858738i	0.189562	+	0.981869i	$0.439293\pi$
$72$	2.74427	−	3.77716i	0.323415	−	0.445143i
$73$	−1.27164	−	0.413179i	−0.148834	−	0.0483590i	0.233653	−	0.972320i	$-0.424932\pi$
$73$	−1.27164	−	0.413179i	−0.148834	−	0.0483590i	−0.382486	+	0.923961i	$0.624932\pi$
$74$	13.4193			1.55996
$75$		0			0
$76$	−9.41939			−1.08048
$77$	0.373666	+	0.121412i	0.0425832	+	0.0138361i
$78$	2.64911	−	3.64619i	0.299953	−	0.412849i
$79$	0.855018	+	0.621207i	0.0961970	+	0.0698912i	0.634844	−	0.772640i	$-0.281064\pi$
$79$	0.855018	+	0.621207i	0.0961970	+	0.0698912i	−0.538647	+	0.842532i	$0.681064\pi$
$80$		0			0
$81$	−2.16750	+	1.57478i	−0.240833	+	0.174975i
$82$		−	12.7161i		−	1.40426i
$83$	8.36057	+	11.5073i	0.917692	+	1.26309i	0.964471	+	0.264189i	$0.0851042\pi$
$83$	8.36057	+	11.5073i	0.917692	+	1.26309i	−0.0467794	+	0.998905i	$0.514896\pi$
$84$	0.796346	+	2.45090i	0.0868884	+	0.267415i
$85$		0			0
$86$	−6.42150	+	19.7634i	−0.692448	+	2.13114i
$87$	1.63822	−	0.532289i	0.175635	−	0.0570674i
$88$	0.781561	−	0.253945i	0.0833147	−	0.0270706i
$89$	−4.34169	+	13.3623i	−0.460218	+	1.41640i	0.404681	+	0.914458i	$0.367383\pi$
$89$	−4.34169	+	13.3623i	−0.460218	+	1.41640i	−0.864898	+	0.501947i	$0.832617\pi$
$90$		0			0
$91$	−0.715037	−	2.20066i	−0.0749562	−	0.230692i
$92$	5.15363	+	7.09337i	0.537303	+	0.739535i
$93$			7.88518i			0.817655i
$94$	5.50247	−	3.99778i	0.567536	−	0.412339i
$95$		0			0
$96$	−4.90787	−	3.56578i	−0.500908	−	0.363931i
$97$	10.0074	−	13.7740i	1.01609	−	1.39853i	0.101188	−	0.994867i	$-0.467736\pi$
$97$	10.0074	−	13.7740i	1.01609	−	1.39853i	0.914906	−	0.403667i	$-0.132264\pi$
$98$	2.11404	+	0.686892i	0.213550	+	0.0693865i
$99$	−0.877015			−0.0881433
$100$		0			0
$101$	13.0194			1.29547			0.647737	−	0.761864i	$-0.275715\pi$
$101$	13.0194			1.29547			0.647737	+	0.761864i	$0.275715\pi$
$102$	4.75754	+	1.54582i	0.471067	+	0.153059i
$103$	−1.66360	+	2.28975i	−0.163920	+	0.225616i	−0.883073	−	0.469235i	$-0.844530\pi$
$103$	−1.66360	+	2.28975i	−0.163920	+	0.225616i	0.719154	+	0.694851i	$0.244530\pi$
$104$	−3.91546	−	2.84475i	−0.383942	−	0.278950i
$105$		0			0
$106$	18.5548	−	13.4809i	1.80220	−	1.30938i
$107$			7.07518i			0.683984i	0.939703	+	0.341992i	$0.111102\pi$
$107$			7.07518i			0.683984i	−0.939703	+	0.341992i	$0.888898\pi$
$108$	−7.92539	−	10.9084i	−0.762621	−	1.04966i
$109$	0.531071	+	1.63447i	0.0508674	+	0.156554i	0.973263	−	0.229692i	$-0.0737718\pi$
$109$	0.531071	+	1.63447i	0.0508674	+	0.156554i	−0.922396	+	0.386245i	$0.873772\pi$
$110$		0			0
$111$	1.63469	−	5.03105i	0.155158	−	0.477527i
$112$	−1.17233	+	0.380912i	−0.110775	+	0.0359928i
$113$	−1.16490	+	0.378498i	−0.109584	+	0.0356061i	−0.363296	−	0.931674i	$-0.618349\pi$
$113$	−1.16490	+	0.378498i	−0.109584	+	0.0356061i	0.253712	+	0.967280i	$0.418349\pi$
$114$	−1.92775	+	5.93301i	−0.180550	+	0.555677i
$115$		0			0
$116$	−1.78652	−	5.49835i	−0.165874	−	0.510509i
$117$	3.03595	+	4.17862i	0.280673	+	0.386314i
$118$			11.0224i			1.01470i
$119$	2.07778	−	1.50959i	0.190469	−	0.138384i
$120$		0			0
$121$	8.77430	+	6.37490i	0.797664	+	0.579537i
$122$	13.9778	−	19.2388i	1.26549	−	1.74180i
$123$	−4.76744	−	1.54904i	−0.429866	−	0.139672i
$124$	26.4650			2.37663
$125$		0			0
$126$	−4.96175			−0.442028
$127$	15.6844	+	5.09616i	1.39176	+	0.452211i	0.906518	−	0.422168i	$-0.138731\pi$
$127$	15.6844	+	5.09616i	1.39176	+	0.452211i	0.485244	+	0.874379i	$0.338731\pi$
$128$	−8.74676	+	12.0389i	−0.773112	+	1.06410i
$129$	6.62728	+	4.81500i	0.583500	+	0.423937i
$130$		0			0
$131$	−1.31477	+	0.955236i	−0.114872	+	0.0834594i	−0.643738	−	0.765246i	$-0.722617\pi$
$131$	−1.31477	+	0.955236i	−0.114872	+	0.0834594i	0.528866	+	0.848705i	$0.322617\pi$
$132$		−	1.01250i		−	0.0881272i
$133$	1.88257	+	2.59114i	0.163240	+	0.224680i
$134$	−10.8202	−	33.3013i	−0.934727	−	2.87679i
$135$		0			0
$136$	1.65998	−	5.10889i	0.142342	−	0.438083i
$137$	−11.0561	+	3.59235i	−0.944587	+	0.306915i	−0.740514	−	0.672041i	$-0.765418\pi$
$137$	−11.0561	+	3.59235i	−0.944587	+	0.306915i	−0.204073	+	0.978956i	$0.565418\pi$
$138$	5.52264	−	1.79441i	0.470118	−	0.152751i
$139$	−1.89409	+	5.82941i	−0.160655	+	0.494444i	−0.998690	−	0.0511720i	$-0.983704\pi$
$139$	−1.89409	+	5.82941i	−0.160655	+	0.494444i	0.838035	+	0.545616i	$0.183704\pi$
$140$		0			0
$141$	−0.828525	−	2.54994i	−0.0697744	−	0.214744i
$142$	−16.0841	−	22.1378i	−1.34975	−	1.85776i
$143$			0.909125i			0.0760249i
$144$	2.22602	−	1.61730i	0.185502	−	0.134775i
$145$		0			0
$146$	2.40447	+	1.74695i	0.198996	+	0.144579i
$147$	0.515049	−	0.708904i	0.0424805	−	0.0584694i
$148$	−16.8857	−	5.48650i	−1.38800	−	0.450987i
$149$	−15.0483			−1.23281			−0.616404	−	0.787430i	$-0.711411\pi$
$149$	−15.0483			−1.23281			−0.616404	+	0.787430i	$0.711411\pi$
$150$		0			0
$151$	−4.69108			−0.381755			−0.190878	−	0.981614i	$-0.561133\pi$
$151$	−4.69108			−0.381755			−0.190878	+	0.981614i	$0.561133\pi$
$152$	6.37116	+	2.07012i	0.516769	+	0.167909i
$153$	−3.36968	+	4.63797i	−0.272423	+	0.374958i
$154$	−0.706547	−	0.513337i	−0.0569352	−	0.0413658i
$155$		0			0
$156$	−4.82417	+	3.50497i	−0.386243	+	0.280622i
$157$		−	1.94047i		−	0.154867i	−0.996998	−	0.0774333i	$-0.975328\pi$
$157$		−	1.94047i		−	0.154867i	0.996998	−	0.0774333i	$-0.0246725\pi$
$158$	−1.38084	−	1.90056i	−0.109853	−	0.151200i
$159$	−2.79386	−	8.59863i	−0.221568	−	0.681916i
$160$		0			0
$161$	0.921271	−	2.83538i	0.0726063	−	0.223459i
$162$	5.66386	−	1.84030i	0.444995	−	0.144588i
$163$	−15.1542	+	4.92389i	−1.18697	+	0.385669i	−0.834950	−	0.550325i	$-0.814504\pi$
$163$	−15.1542	+	4.92389i	−1.18697	+	0.385669i	−0.352016	+	0.935994i	$0.614504\pi$
$164$	−5.19902	+	16.0009i	−0.405975	+	1.24946i
$165$		0			0
$166$	−9.77024	−	30.0697i	−0.758318	−	2.33386i
$167$	6.57134	+	9.04468i	0.508506	+	0.699898i	0.983666	−	0.180001i	$-0.0576101\pi$
$167$	6.57134	+	9.04468i	0.508506	+	0.699898i	−0.475161	+	0.879899i	$0.657610\pi$
$168$		−	1.83277i		−	0.141401i
$169$	−6.18561	+	4.49411i	−0.475816	+	0.345701i
$170$		0			0
$171$	−5.78389	−	4.20224i	−0.442305	−	0.321354i
$172$	16.1606	−	22.2431i	1.23223	−	1.69602i
$173$	15.3252	+	4.97945i	1.16515	+	0.378581i	0.826831	−	0.562450i	$-0.190141\pi$
$173$	15.3252	+	4.97945i	1.16515	+	0.378581i	0.338321	+	0.941031i	$0.390141\pi$
$174$	−3.82888			−0.290266
$175$		0			0
$176$	0.484307			0.0365060
$177$	4.13244	+	1.34271i	0.310613	+	0.100924i
$178$	18.3570	−	25.2662i	1.37591	−	1.89378i
$179$	−19.3867	−	14.0852i	−1.44903	−	1.05278i	−0.986058	−	0.166405i	$-0.946784\pi$
$179$	−19.3867	−	14.0852i	−1.44903	−	1.05278i	−0.462969	−	0.886375i	$-0.653216\pi$
$180$		0			0
$181$	−18.7843	+	13.6476i	−1.39623	+	1.01442i	−0.401076	+	0.916045i	$0.631364\pi$
$181$	−18.7843	+	13.6476i	−1.39623	+	1.01442i	−0.995150	+	0.0983725i	$0.968636\pi$
$182$			5.14342i			0.381256i
$183$	−5.51015	−	7.58408i	−0.407322	−	0.560631i
$184$	−1.92693	−	5.93049i	−0.142055	−	0.437201i
$185$		0			0
$186$	5.41626	−	16.6695i	0.397140	−	1.22227i
$187$	−0.959677	+	0.311818i	−0.0701785	+	0.0228024i
$188$	−8.55835	+	2.78078i	−0.624182	+	0.202809i
$189$	−1.41675	+	4.36032i	−0.103054	+	0.317167i
$190$		0			0
$191$	0.159524	+	0.490964i	0.0115427	+	0.0355249i	0.956662	−	0.291201i	$-0.0940547\pi$
$191$	0.159524	+	0.490964i	0.0115427	+	0.0355249i	−0.945119	+	0.326726i	$0.894055\pi$
$192$	6.65636	+	9.16169i	0.480381	+	0.661188i
$193$		−	24.3220i		−	1.75073i	−0.483460	−	0.875367i	$-0.660620\pi$
$193$		−	24.3220i		−	1.75073i	0.483460	−	0.875367i	$-0.339380\pi$
$194$	−30.6172	+	22.2447i	−2.19818	+	1.59707i
$195$		0			0
$196$	−2.37929	−	1.72866i	−0.169949	−	0.123475i
$197$	−6.70301	+	9.22590i	−0.477569	+	0.657318i	−0.978036	−	0.208438i	$-0.933162\pi$
$197$	−6.70301	+	9.22590i	−0.477569	+	0.657318i	0.500466	+	0.865756i	$0.333162\pi$
$198$	1.85404	+	0.602414i	0.131761	+	0.0428117i
$199$	0.916451			0.0649655			0.0324827	−	0.999472i	$-0.489659\pi$
$199$	0.916451			0.0649655			0.0324827	+	0.999472i	$0.489659\pi$
$200$		0			0
$201$	−13.8032			−0.973600
$202$	−27.5234	−	8.94289i	−1.93654	−	0.629219i
$203$	−1.15546	+	1.59035i	−0.0810973	+	0.111621i
$204$	−5.35449	−	3.89026i	−0.374889	−	0.272373i
$205$		0			0
$206$	5.08972	−	3.69790i	0.354618	−	0.257645i
$207$			6.65479i			0.462540i
$208$	−1.67651	−	2.30752i	−0.116245	−	0.159998i
$209$	−0.388860	−	1.19679i	−0.0268980	−	0.0827835i
$210$		0			0
$211$	6.87441	−	21.1573i	0.473254	−	1.45653i	−0.375044	−	0.927007i	$-0.622372\pi$
$211$	6.87441	−	21.1573i	0.473254	−	1.45653i	0.848298	−	0.529519i	$-0.177628\pi$
$212$	−28.8596	+	9.37704i	−1.98208	+	0.644018i
$213$	−10.2591	+	3.33337i	−0.702939	+	0.228399i
$214$	4.85988	−	14.9572i	0.332215	−	1.02245i
$215$		0			0
$216$	2.96329	+	9.12006i	0.201626	+	0.620541i
$217$	−5.28933	−	7.28014i	−0.359063	−	0.494208i
$218$		−	3.82011i		−	0.258731i
$219$	0.947858	−	0.688659i	0.0640503	−	0.0465353i
$220$		0			0
$221$	4.80778	+	3.49306i	0.323406	+	0.234968i
$222$	−6.91158	+	9.51297i	−0.463875	+	0.638469i
$223$	0.824913	+	0.268031i	0.0552403	+	0.0179487i	0.336507	−	0.941681i	$-0.390754\pi$
$223$	0.824913	+	0.268031i	0.0552403	+	0.0179487i	−0.281267	+	0.959630i	$0.590754\pi$
$224$	6.92319			0.462575
$225$		0			0
$226$	2.72262			0.181106
$227$	2.14652	+	0.697445i	0.142469	+	0.0462911i	0.379384	−	0.925239i	$-0.376136\pi$
$227$	2.14652	+	0.697445i	0.142469	+	0.0462911i	−0.236914	+	0.971531i	$0.576136\pi$
$228$	4.85145	−	6.67744i	0.321295	−	0.442224i
$229$	9.47871	+	6.88669i	0.626371	+	0.455085i	0.855141	−	0.518395i	$-0.173470\pi$
$229$	9.47871	+	6.88669i	0.626371	+	0.455085i	−0.228770	+	0.973480i	$0.573470\pi$
$230$		0			0
$231$	−0.278525	+	0.202361i	−0.0183256	+	0.0133143i
$232$			4.11164i			0.269942i
$233$	−3.02185	−	4.15922i	−0.197968	−	0.272480i	0.698479	−	0.715631i	$-0.253861\pi$
$233$	−3.02185	−	4.15922i	−0.197968	−	0.272480i	−0.896447	+	0.443151i	$0.853861\pi$
$234$	−3.54784	−	10.9191i	−0.231929	−	0.713805i
$235$		0			0
$236$	4.50654	−	13.8697i	0.293351	−	0.902840i
$237$	−0.880752	+	0.286174i	−0.0572110	+	0.0185890i
$238$	−5.42942	+	1.76412i	−0.351937	+	0.114351i
$239$	−2.39108	+	7.35899i	−0.154666	+	0.476013i	−0.998127	−	0.0611774i	$-0.980514\pi$
$239$	−2.39108	+	7.35899i	−0.154666	+	0.476013i	0.843461	+	0.537191i	$0.180514\pi$
$240$		0			0
$241$	−4.09536	−	12.6042i	−0.263805	−	0.811908i	−0.991966	−	0.126503i	$-0.959625\pi$
$241$	−4.09536	−	12.6042i	−0.263805	−	0.811908i	0.728161	−	0.685406i	$-0.240375\pi$
$242$	−14.1703	−	19.5038i	−0.910902	−	1.25375i
$243$		−	16.1018i		−	1.03293i
$244$	−25.4544	+	18.4937i	−1.62955	+	1.18394i
$245$		0			0
$246$	9.01452	+	6.54943i	0.574745	+	0.417576i
$247$	−4.35610	+	5.99566i	−0.277172	+	0.381495i
$248$	−17.9006	−	5.81625i	−1.13669	−	0.369332i
$249$	−12.4637			−0.789854
$250$		0			0
$251$	14.1607			0.893818			0.446909	−	0.894579i	$-0.352525\pi$
$251$	14.1607			0.893818			0.446909	+	0.894579i	$0.352525\pi$
$252$	6.24346	+	2.02862i	0.393301	+	0.127791i
$253$	−0.688496	+	0.947634i	−0.0432854	+	0.0595772i
$254$	−29.6568	−	21.5469i	−1.86083	−	1.35197i
$255$		0			0
$256$	5.84931	−	4.24977i	0.365582	−	0.265611i
$257$		−	12.2713i		−	0.765465i	−0.923859	−	0.382732i	$-0.874983\pi$
$257$		−	12.2713i		−	0.765465i	0.923859	−	0.382732i	$-0.125017\pi$
$258$	−10.7029	−	14.7313i	−0.666335	−	0.917131i
$259$	1.86554	+	5.74156i	0.115919	+	0.356763i
$260$		0			0
$261$	1.35596	−	4.17322i	0.0839320	−	0.258316i
$262$	3.43561	−	1.11630i	0.212253	−	0.0689651i
$263$	−4.01602	+	1.30488i	−0.247639	+	0.0804626i	−0.430206	−	0.902731i	$-0.641559\pi$
$263$	−4.01602	+	1.30488i	−0.247639	+	0.0804626i	0.182568	+	0.983193i	$0.441559\pi$
$264$	−0.222520	+	0.684845i	−0.0136951	+	0.0421493i
$265$		0			0
$266$	−2.19999	−	6.77088i	−0.134890	−	0.415150i
$267$	−7.23643	−	9.96009i	−0.442862	−	0.609548i
$268$			46.3275i			2.82990i
$269$	15.2520	−	11.0812i	0.929928	−	0.675633i	−0.0160469	−	0.999871i	$-0.505108\pi$
$269$	15.2520	−	11.0812i	0.929928	−	0.675633i	0.945975	+	0.324239i	$0.105108\pi$
$270$		0			0
$271$	17.3216	+	12.5849i	1.05221	+	0.764477i	0.972632	−	0.232351i	$-0.0746419\pi$
$271$	17.3216	+	12.5849i	1.05221	+	0.764477i	0.0795805	+	0.996828i	$0.474642\pi$
$272$	1.86081	−	2.56119i	0.112828	−	0.155295i
$273$	1.92833	+	0.626553i	0.116708	+	0.0379207i
$274$	25.8406			1.56109
$275$		0			0
$276$	−7.68289			−0.462455
$277$	6.46338	+	2.10008i	0.388347	+	0.126182i	0.496682	−	0.867933i	$-0.334552\pi$
$277$	6.46338	+	2.10008i	0.388347	+	0.126182i	−0.108334	+	0.994115i	$0.534552\pi$
$278$	8.00835	−	11.0225i	0.480309	−	0.661088i
$279$	16.2506	+	11.8067i	0.972897	+	0.706851i
$280$		0			0
$281$	−2.72814	+	1.98211i	−0.162747	+	0.118243i	−0.666178	−	0.745793i	$-0.732071\pi$
$281$	−2.72814	+	1.98211i	−0.162747	+	0.118243i	0.503431	+	0.864035i	$0.332071\pi$
$282$			5.95977i			0.354899i
$283$	−1.87527	−	2.58109i	−0.111473	−	0.153430i	0.749635	−	0.661851i	$-0.230229\pi$
$283$	−1.87527	−	2.58109i	−0.111473	−	0.153430i	−0.861108	+	0.508422i	$0.830229\pi$
$284$	11.1878	+	34.4324i	0.663872	+	2.04319i
$285$		0			0
$286$	0.624470	−	1.92192i	0.0369257	−	0.113646i
$287$	5.44071	−	1.76779i	0.321155	−	0.104350i
$288$	−14.6974	+	4.77549i	−0.866055	+	0.281398i
$289$	3.21501	−	9.89477i	0.189118	−	0.582045i
$290$		0			0
$291$	4.61013	+	14.1885i	0.270251	+	0.831746i
$292$	−2.31134	−	3.18129i	−0.135261	−	0.186171i
$293$		−	0.406826i		−	0.0237670i	−0.999929	−	0.0118835i	$-0.996217\pi$
$293$		−	0.406826i		−	0.0237670i	0.999929	−	0.0118835i	$-0.00378273\pi$
$294$	−1.57577	+	1.14486i	−0.0919008	+	0.0667698i
$295$		0			0
$296$	10.2155	+	7.42200i	0.593764	+	0.431395i
$297$	1.05879	−	1.45730i	0.0614371	−	0.0845608i
$298$	31.8127	+	10.3366i	1.84286	+	0.598782i
$299$	6.89844			0.398947
$300$		0			0
$301$	−9.34864			−0.538847
$302$	9.91712	+	3.22227i	0.570666	+	0.185421i
$303$	−6.70560	+	9.22947i	−0.385227	+	0.530219i
$304$	3.19399	+	2.32057i	0.183188	+	0.133094i
$305$		0			0
$306$	10.3094	−	7.49022i	0.589350	−	0.428188i
$307$		−	9.41718i		−	0.537467i	−0.963215	−	0.268733i	$-0.913395\pi$
$307$		−	9.41718i		−	0.537467i	0.963215	−	0.268733i	$-0.0866050\pi$
$308$	0.679182	+	0.934814i	0.0387000	+	0.0532659i
$309$	−0.766377	−	2.35867i	−0.0435977	−	0.134180i
$310$		0			0
$311$	2.62208	−	8.06992i	0.148684	−	0.457603i	−0.848782	−	0.528743i	$-0.822664\pi$
$311$	2.62208	−	8.06992i	0.148684	−	0.457603i	0.997466	+	0.0711396i	$0.0226636\pi$
$312$	4.03330	−	1.31050i	0.228341	−	0.0741924i
$313$	−3.51395	+	1.14175i	−0.198620	+	0.0645357i	−0.406638	−	0.913589i	$-0.633299\pi$
$313$	−3.51395	+	1.14175i	−0.198620	+	0.0645357i	0.208017	+	0.978125i	$0.433299\pi$
$314$	−1.33289	+	4.10223i	−0.0752196	+	0.231502i
$315$		0			0
$316$	0.960483	+	2.95606i	0.0540314	+	0.166292i
$317$	−18.3068	−	25.1971i	−1.02821	−	1.41521i	−0.906283	−	0.422671i	$-0.861093\pi$
$317$	−18.3068	−	25.1971i	−1.02821	−	1.41521i	−0.121927	−	0.992539i	$-0.538907\pi$
$318$			20.0969i			1.12698i
$319$	0.624844	−	0.453975i	0.0349845	−	0.0254177i
$320$		0			0
$321$	−5.01562	−	3.64406i	−0.279945	−	0.203392i
$322$	−3.89520	+	5.36128i	−0.217071	+	0.298773i
$323$	−7.82313	−	2.54189i	−0.435291	−	0.141434i
$324$	−7.87935			−0.437742
$325$		0			0
$326$	35.4186			1.96166
$327$	−1.43221	−	0.465353i	−0.0792013	−	0.0257341i
$328$	7.03311	−	9.68024i	0.388338	−	0.534502i
$329$	2.47544	+	1.79851i	0.136475	+	0.0991550i
$330$		0			0
$331$	3.43895	−	2.49854i	0.189022	−	0.137332i	−0.489250	−	0.872144i	$-0.662729\pi$
$331$	3.43895	−	2.49854i	0.189022	−	0.137332i	0.678271	+	0.734811i	$0.262729\pi$
$332$			41.8318i			2.29582i
$333$	−7.92084	−	10.9021i	−0.434059	−	0.597431i
$334$	−7.67934	−	23.6346i	−0.420195	−	1.29323i
$335$		0			0
$336$	0.333776	−	1.02726i	0.0182090	−	0.0560414i
$337$	6.80029	−	2.20955i	0.370435	−	0.120362i	−0.117883	−	0.993028i	$-0.537611\pi$
$337$	6.80029	−	2.20955i	0.370435	−	0.120362i	0.488318	+	0.872666i	$0.337611\pi$
$338$	16.1636	−	5.25186i	0.879182	−	0.285663i
$339$	0.331660	−	1.02075i	0.0180133	−	0.0554393i
$340$		0			0
$341$	1.09255	+	3.36253i	0.0591650	+	0.182091i
$342$	9.34086	+	12.8566i	0.505096	+	0.695205i
$343$			1.00000i			0.0539949i
$344$	−15.8192	+	11.4933i	−0.852915	+	0.619679i
$345$		0			0
$346$	−28.9776	−	21.0535i	−1.55785	−	1.13184i
$347$	18.2796	−	25.1597i	0.981300	−	1.35064i	0.0451739	−	0.998979i	$-0.485616\pi$
$347$	18.2796	−	25.1597i	0.981300	−	1.35064i	0.936126	−	0.351664i	$-0.114384\pi$
$348$	4.81794	+	1.56544i	0.258269	+	0.0839166i
$349$	21.2544			1.13772			0.568861	−	0.822433i	$-0.307384\pi$
$349$	21.2544			1.13772			0.568861	+	0.822433i	$0.307384\pi$
$350$		0			0
$351$	−10.6086			−0.566245
$352$	−2.58696	−	0.840555i	−0.137886	−	0.0448017i
$353$	−14.3710	+	19.7799i	−0.764889	+	1.05278i	0.231902	+	0.972739i	$0.425505\pi$
$353$	−14.3710	+	19.7799i	−0.764889	+	1.05278i	−0.996792	+	0.0800406i	$0.974495\pi$
$354$	−7.81383	−	5.67708i	−0.415300	−	0.301733i
$355$		0			0
$356$	−33.4290	+	24.2876i	−1.77173	+	1.28724i
$357$			2.25046i			0.119107i
$358$	31.3090	+	43.0932i	1.65473	+	2.27755i
$359$	−6.55245	−	20.1664i	−0.345825	−	1.06434i	−0.961141	−	0.276059i	$-0.910971\pi$
$359$	−6.55245	−	20.1664i	−0.345825	−	1.06434i	0.615315	−	0.788281i	$-0.289029\pi$
$360$		0			0
$361$	−2.70140	+	8.31405i	−0.142179	+	0.437582i
$362$	49.0851	−	15.9487i	2.57985	−	0.838245i
$363$	−9.03838	+	2.93675i	−0.474392	+	0.154139i
$364$	2.10290	−	6.47205i	0.110222	−	0.339228i
$365$		0			0
$366$	6.43922	+	19.8179i	0.336583	+	1.03590i
$367$	3.70891	+	5.10487i	0.193603	+	0.266472i	0.894772	−	0.446523i	$-0.147338\pi$
$367$	3.70891	+	5.10487i	0.193603	+	0.266472i	−0.701169	+	0.712996i	$0.747338\pi$
$368$		−	3.67492i		−	0.191568i
$369$	−10.3309	+	7.50581i	−0.537803	+	0.390737i
$370$		0			0
$371$	8.34740	+	6.06474i	0.433375	+	0.314866i
$372$	−13.6308	+	18.7611i	−0.706722	+	0.972719i
$373$	3.05017	+	0.991061i	0.157932	+	0.0513152i	0.386916	−	0.922115i	$-0.373540\pi$
$373$	3.05017	+	0.991061i	0.157932	+	0.0513152i	−0.228984	+	0.973430i	$0.573540\pi$
$374$	2.24298			0.115981
$375$		0			0
$376$	6.39989			0.330049
$377$	−4.32602	−	1.40561i	−0.222801	−	0.0723925i
$378$	5.99014	−	8.24472i	0.308099	−	0.424062i
$379$	22.2793	+	16.1869i	1.14441	+	0.831464i	0.987728	−	0.156185i	$-0.0499197\pi$
$379$	22.2793	+	16.1869i	1.14441	+	0.831464i	0.156684	+	0.987649i	$0.449920\pi$
$380$		0			0
$381$	−11.6909	+	8.49393i	−0.598942	+	0.435157i
$382$		−	1.14749i		−	0.0587108i
$383$	−0.399636	−	0.550052i	−0.0204205	−	0.0281063i	0.798685	−	0.601750i	$-0.205530\pi$
$383$	−0.399636	−	0.550052i	−0.0204205	−	0.0281063i	−0.819105	+	0.573643i	$0.805530\pi$
$384$	−4.02940	−	12.4012i	−0.205624	−	0.632847i
$385$		0			0
$386$	−16.7066	+	51.4175i	−0.850341	+	2.61708i
$387$	19.8465	−	6.44852i	1.00885	−	0.327797i
$388$	47.6209	−	15.4730i	2.41758	−	0.785520i
$389$	−5.81124	+	17.8852i	−0.294642	+	0.906814i	0.688700	+	0.725047i	$0.258182\pi$
$389$	−5.81124	+	17.8852i	−0.294642	+	0.906814i	−0.983342	+	0.181768i	$0.941818\pi$
$390$		0			0
$391$	2.36607	+	7.28203i	0.119658	+	0.368268i
$392$	1.22941	+	1.69214i	0.0620947	+	0.0854660i
$393$		−	1.42404i		−	0.0718332i
$394$	20.5076	−	14.8996i	1.03316	−	0.750633i
$395$		0			0
$396$	−2.08667	−	1.51606i	−0.104859	−	0.0761847i
$397$	−16.1166	+	22.1827i	−0.808871	+	1.11332i	0.182625	+	0.983183i	$0.441540\pi$
$397$	−16.1166	+	22.1827i	−0.808871	+	1.11332i	−0.991497	+	0.130133i	$0.958460\pi$
$398$	−1.93741	−	0.629502i	−0.0971135	−	0.0315541i
$399$	−2.80648			−0.140500
$400$		0			0
$401$	−20.7884			−1.03812			−0.519062	−	0.854737i	$-0.673719\pi$
$401$	−20.7884			−1.03812			−0.519062	+	0.854737i	$0.673719\pi$
$402$	29.1804	+	9.48127i	1.45538	+	0.472883i
$403$	12.2390	−	16.8456i	0.609669	−	0.839137i
$404$	30.9768	+	22.5060i	1.54115	+	1.11971i
$405$		0			0
$406$	3.53508	−	2.56839i	0.175443	−	0.127467i
$407$		−	2.37192i		−	0.117572i
$408$	2.76674	+	3.80809i	0.136974	+	0.188528i
$409$	10.3251	+	31.7774i	0.510543	+	1.57129i	0.791247	+	0.611496i	$0.209432\pi$
$409$	10.3251	+	31.7774i	0.510543	+	1.57129i	−0.280704	+	0.959794i	$0.590568\pi$
$410$		0			0
$411$	3.14781	−	9.68795i	0.155270	−	0.477871i
$412$	−7.91638	+	2.57219i	−0.390012	+	0.126723i
$413$	−4.71604	+	1.53233i	−0.232061	+	0.0754012i
$414$	4.57112	−	14.0685i	0.224658	−	0.691427i
$415$		0			0
$416$	4.95034	+	15.2356i	0.242710	+	0.746985i
$417$	−3.15694	−	4.34516i	−0.154596	−	0.212783i
$418$			2.79716i			0.136813i
$419$	13.2464	−	9.62404i	0.647127	−	0.470165i	−0.215164	−	0.976578i	$-0.569029\pi$
$419$	13.2464	−	9.62404i	0.647127	−	0.470165i	0.862291	+	0.506413i	$0.169029\pi$
$420$		0			0
$421$	−21.5760	−	15.6759i	−1.05155	−	0.763996i	−0.0790436	−	0.996871i	$-0.525187\pi$
$421$	−21.5760	−	15.6759i	−1.05155	−	0.763996i	−0.972507	+	0.232875i	$0.925187\pi$
$422$	−29.0655	+	40.0052i	−1.41489	+	1.94742i
$423$	−6.49575	−	2.11060i	−0.315834	−	0.102621i
$424$	21.5810			1.04807
$425$		0			0
$426$	23.9777			1.16172
$427$	10.1747	+	3.30596i	0.492389	+	0.159987i
$428$	−12.2306	+	16.8339i	−0.591186	+	0.813698i
$429$	−0.644482	−	0.468244i	−0.0311159	−	0.0226070i
$430$		0			0
$431$	−18.1907	+	13.2163i	−0.876215	+	0.636607i	−0.932247	−	0.361822i	$-0.882155\pi$
$431$	−18.1907	+	13.2163i	−0.876215	+	0.636607i	0.0560325	+	0.998429i	$0.482155\pi$
$432$			5.65139i			0.271902i
$433$	21.6486	+	29.7967i	1.04036	+	1.43194i	0.896875	+	0.442285i	$0.145832\pi$
$433$	21.6486	+	29.7967i	1.04036	+	1.43194i	0.143488	+	0.989652i	$0.454168\pi$
$434$	6.18116	+	19.0237i	0.296705	+	0.913165i
$435$		0			0
$436$	−1.56186	+	4.80691i	−0.0747996	+	0.230209i
$437$	−9.08123	+	2.95067i	−0.434414	+	0.141150i
$438$	−2.47684	+	0.804774i	−0.118348	+	0.0384536i
$439$	12.6434	−	38.9123i	0.603435	−	1.85718i	0.0962240	−	0.995360i	$-0.469323\pi$
$439$	12.6434	−	38.9123i	0.603435	−	1.85718i	0.507211	−	0.861822i	$-0.330677\pi$
$440$		0			0
$441$	−0.689782	−	2.12293i	−0.0328468	−	0.101092i
$442$	−7.76446	−	10.6869i	−0.369318	−	0.508322i
$443$		−	33.7257i		−	1.60236i	−0.598425	−	0.801178i	$-0.704207\pi$
$443$		−	33.7257i		−	1.60236i	0.598425	−	0.801178i	$-0.295793\pi$
$444$	12.5864	−	9.14452i	0.597322	−	0.433980i
$445$		0			0
$446$	−1.55979	−	1.13325i	−0.0738581	−	0.0536610i
$447$	7.75062	−	10.6678i	0.366592	−	0.504570i
$448$	−12.2912	−	3.99366i	−0.580705	−	0.188683i
$449$	10.2790			0.485094			0.242547	−	0.970140i	$-0.422017\pi$
$449$	10.2790			0.485094			0.242547	+	0.970140i	$0.422017\pi$
$450$		0			0
$451$	−2.24764			−0.105837
$452$	−3.42592	−	1.11315i	−0.161142	−	0.0523582i
$453$	2.41614	−	3.32553i	0.113520	−	0.156247i
$454$	−4.05874	−	2.94885i	−0.190486	−	0.138396i
$455$		0			0
$456$	−4.74897	+	3.45033i	−0.222391	+	0.161576i
$457$			1.65826i			0.0775703i	0.999248	+	0.0387851i	$0.0123488\pi$
$457$			1.65826i			0.0775703i	−0.999248	+	0.0387851i	$0.987651\pi$
$458$	−15.3079	−	21.0695i	−0.715292	−	0.984515i
$459$	−3.63861	−	11.1985i	−0.169836	−	0.522701i
$460$		0			0
$461$	2.33968	−	7.20080i	0.108970	−	0.335375i	−0.881672	−	0.471863i	$-0.843582\pi$
$461$	2.33968	−	7.20080i	0.108970	−	0.335375i	0.990642	+	0.136488i	$0.0435816\pi$
$462$	0.727812	−	0.236481i	0.0338609	−	0.0110021i
$463$	3.96383	−	1.28793i	0.184215	−	0.0598550i	−0.215457	−	0.976513i	$-0.569124\pi$
$463$	3.96383	−	1.28793i	0.184215	−	0.0598550i	0.399672	+	0.916658i	$0.369124\pi$
$464$	−0.748792	+	2.30454i	−0.0347618	+	0.106986i
$465$		0			0
$466$	3.53137	+	10.8684i	0.163587	+	0.503470i
$467$	7.92551	+	10.9085i	0.366749	+	0.504787i	0.952014	−	0.306056i	$-0.0990094\pi$
$467$	7.92551	+	10.9085i	0.366749	+	0.504787i	−0.585265	+	0.810842i	$0.699009\pi$
$468$			15.1903i			0.702170i
$469$	12.7440	−	9.25908i	0.588464	−	0.427544i
$470$		0			0
$471$	1.37561	+	0.999438i	0.0633847	+	0.0460517i
$472$	−6.09633	+	8.39088i	−0.280606	+	0.386222i
$473$	3.49327	+	1.13503i	0.160621	+	0.0521889i
$474$	2.05851			0.0945505
$475$		0			0
$476$	7.55320			0.346200
$477$	−21.9043	−	7.11714i	−1.00293	−	0.325871i
$478$	10.1097	−	13.9147i	0.462405	−	0.636446i
$479$	12.7796	+	9.28493i	0.583916	+	0.424239i	0.840134	−	0.542380i	$-0.182477\pi$
$479$	12.7796	+	9.28493i	0.583916	+	0.424239i	−0.256218	+	0.966619i	$0.582477\pi$
$480$		0			0
$481$	−11.3013	+	8.21085i	−0.515293	+	0.374382i
$482$			29.4588i			1.34181i
$483$	1.53551	+	2.11345i	0.0698682	+	0.0961654i
$484$	9.85660	+	30.3355i	0.448027	+	1.37889i
$485$		0			0
$486$	−11.0602	+	34.0397i	−0.501700	+	1.54407i
$487$	−7.68880	+	2.49824i	−0.348413	+	0.113206i	−0.477995	−	0.878363i	$-0.658636\pi$
$487$	−7.68880	+	2.49824i	−0.348413	+	0.113206i	0.129582	+	0.991569i	$0.458636\pi$
$488$	21.2814	−	6.91476i	0.963365	−	0.313016i
$489$	4.31457	−	13.2789i	0.195112	−	0.600492i
$490$		0			0
$491$	1.73455	+	5.33838i	0.0782790	+	0.240918i	0.982537	−	0.186069i	$-0.0595749\pi$
$491$	1.73455	+	5.33838i	0.0782790	+	0.240918i	−0.904258	+	0.426987i	$0.859575\pi$
$492$	−8.66538	−	11.9269i	−0.390665	−	0.537705i
$493$		−	5.04867i		−	0.227381i
$494$	13.3273	−	9.68286i	0.599624	−	0.435653i
$495$		0			0
$496$	−8.97392	−	6.51994i	−0.402941	−	0.292754i
$497$	7.23586	−	9.95930i	0.324573	−	0.446736i
$498$	26.3487	+	8.56120i	1.18071	+	0.383637i
$499$	−10.2308			−0.457994			−0.228997	−	0.973427i	$-0.573545\pi$
$499$	−10.2308			−0.457994			−0.228997	+	0.973427i	$0.573545\pi$
$500$		0			0
$501$	−9.79636			−0.437669
$502$	−29.9363	−	9.72689i	−1.33612	−	0.434132i
$503$	1.55097	−	2.13472i	0.0691542	−	0.0951827i	−0.773039	−	0.634359i	$-0.781264\pi$
$503$	1.55097	−	2.13472i	0.0691542	−	0.0951827i	0.842193	+	0.539176i	$0.181264\pi$
$504$	−3.77716	−	2.74427i	−0.168248	−	0.122240i
$505$		0			0
$506$	2.10643	−	1.53041i	0.0936421	−	0.0680350i
$507$		−	6.69968i		−	0.297543i
$508$	28.5081	+	39.2381i	1.26484	+	1.74091i
$509$	−13.7981	−	42.4661i	−0.611589	−	1.88228i	−0.442787	−	0.896627i	$-0.646010\pi$
$509$	−13.7981	−	42.4661i	−0.611589	−	1.88228i	−0.168802	−	0.985650i	$-0.553990\pi$
$510$		0			0
$511$	−0.413179	+	1.27164i	−0.0182780	+	0.0562538i
$512$	13.0203	−	4.23056i	0.575423	−	0.186966i
$513$	13.9653	−	4.53762i	0.616585	−	0.200341i
$514$	−8.42907	+	25.9420i	−0.371791	+	1.14425i
$515$		0			0
$516$	7.44475	+	22.9126i	0.327737	+	1.00867i
$517$	−0.706627	−	0.972589i	−0.0310774	−	0.0427744i
$518$		−	13.4193i		−	0.589609i
$519$	−11.4232	+	8.29942i	−0.501421	+	0.364304i
$520$		0			0
$521$	1.78965	+	1.30025i	0.0784058	+	0.0569651i	0.626298	−	0.779584i	$-0.284569\pi$
$521$	1.78965	+	1.30025i	0.0784058	+	0.0569651i	−0.547892	+	0.836549i	$0.684569\pi$
$522$	−5.73310	+	7.89094i	−0.250931	+	0.345377i
$523$	−15.8345	−	5.14494i	−0.692394	−	0.224973i	−0.0583807	−	0.998294i	$-0.518594\pi$
$523$	−15.8345	−	5.14494i	−0.692394	−	0.224973i	−0.634014	+	0.773322i	$0.718594\pi$
$524$	−4.77949			−0.208793
$525$		0			0
$526$	9.38633			0.409263
$527$	21.9801	+	7.14176i	0.957467	+	0.311100i
$528$	−0.249441	+	0.343327i	−0.0108555	+	0.0149414i
$529$	−11.4167	−	8.29475i	−0.496380	−	0.360641i
$530$		0			0
$531$	8.95484	−	6.50607i	0.388607	−	0.282340i
$532$			9.41939i			0.408382i
$533$	7.78062	+	10.7091i	0.337016	+	0.463863i
$534$	8.45656	+	26.0266i	0.365951	+	1.12628i
$535$		0			0
$536$	10.1815	−	31.3353i	0.439772	−	1.35348i
$537$	19.9701	−	6.48869i	0.861775	−	0.280008i
$538$	−39.8548	+	12.9496i	−1.71826	+	0.558297i
$539$	0.121412	−	0.373666i	0.00522957	−	0.0160949i
$540$		0			0
$541$	8.15227	+	25.0901i	0.350494	+	1.07871i	0.958577	+	0.284835i	$0.0919388\pi$
$541$	8.15227	+	25.0901i	0.350494	+	1.07871i	−0.608083	+	0.793874i	$0.708061\pi$
$542$	−27.9740	−	38.5029i	−1.20159	−	1.65384i
$543$		−	20.3454i		−	0.873106i
$544$	−14.3848	+	10.4512i	−0.616745	+	0.448091i
$545$		0			0
$546$	−3.64619	−	2.64911i	−0.156042	−	0.113371i
$547$	−21.2825	+	29.2929i	−0.909975	+	1.25247i	0.0572008	+	0.998363i	$0.481782\pi$
$547$	−21.2825	+	29.2929i	−0.909975	+	1.25247i	−0.967175	+	0.254110i	$0.918218\pi$
$548$	−32.5156	−	10.5650i	−1.38900	−	0.451313i
$549$	−23.8806			−1.01920
$550$		0			0
$551$	6.29606			0.268221
$552$	5.19661	+	1.68848i	0.221182	+	0.0718665i
$553$	0.621207	−	0.855018i	0.0264164	−	0.0363591i
$554$	−12.2213	−	8.87929i	−0.519233	−	0.377245i
$555$		0			0
$556$	−14.5836	+	10.5956i	−0.618484	+	0.449355i
$557$			43.3717i			1.83772i	0.394586	+	0.918859i	$0.370888\pi$
$557$			43.3717i			1.83772i	−0.394586	+	0.918859i	$0.629112\pi$
$558$	−26.2443	−	36.1222i	−1.11101	−	1.52918i
$559$	−6.68462	−	20.5731i	−0.282729	−	0.870151i
$560$		0			0
$561$	0.273231	−	0.840920i	0.0115358	−	0.0355037i
$562$	7.12887	−	2.31631i	0.300713	−	0.0977076i
$563$	36.5904	−	11.8889i	1.54210	−	0.501059i	0.590146	−	0.807297i	$-0.299070\pi$
$563$	36.5904	−	11.8889i	1.54210	−	0.501059i	0.951955	+	0.306237i	$0.0990702\pi$
$564$	2.43666	−	7.49928i	0.102602	−	0.315777i
$565$		0			0
$566$	2.19146	+	6.74461i	0.0921138	+	0.283497i
$567$	1.57478	+	2.16750i	0.0661345	+	0.0910263i
$568$		−	25.7484i		−	1.08038i
$569$	18.5065	−	13.4458i	0.775834	−	0.563677i	−0.127892	−	0.991788i	$-0.540821\pi$
$569$	18.5065	−	13.4458i	0.775834	−	0.563677i	0.903726	+	0.428111i	$0.140821\pi$
$570$		0			0
$571$	−28.9909	−	21.0631i	−1.21323	−	0.881463i	−0.217710	−	0.976014i	$-0.569859\pi$
$571$	−28.9909	−	21.0631i	−1.21323	−	0.881463i	−0.995520	+	0.0945506i	$0.969859\pi$
$572$	−1.57156	+	2.16307i	−0.0657104	+	0.0904426i
$573$	−0.430209	−	0.139783i	−0.0179722	−	0.00583953i
$574$	−12.7161			−0.530762
$575$		0			0
$576$	28.8481			1.20201
$577$	−28.6157	−	9.29780i	−1.19129	−	0.387072i	−0.354738	−	0.934966i	$-0.615430\pi$
$577$	−28.6157	−	9.29780i	−1.19129	−	0.387072i	−0.836548	+	0.547893i	$0.815430\pi$
$578$	−13.5933	+	18.7095i	−0.565406	+	0.778214i
$579$	17.2419	+	12.5270i	0.716550	+	0.520604i
$580$		0			0
$581$	11.5073	−	8.36057i	0.477405	−	0.346855i
$582$		−	33.1617i		−	1.37460i
$583$	−2.38281	−	3.27966i	−0.0986860	−	0.135830i
$584$	0.864206	+	2.65975i	0.0357611	+	0.110061i
$585$		0			0
$586$	−0.279446	+	0.860045i	−0.0115438	+	0.0355281i
$587$	13.5840	−	4.41371i	0.560671	−	0.182173i	−0.0149519	−	0.999888i	$-0.504760\pi$
$587$	13.5840	−	4.41371i	0.560671	−	0.182173i	0.575623	+	0.817715i	$0.304760\pi$
$588$	2.45090	−	0.796346i	0.101073	−	0.0328407i
$589$	−8.90630	+	27.4108i	−0.366978	+	1.12944i
$590$		0			0
$591$	−3.08790	−	9.50357i	−0.127019	−	0.390925i
$592$	4.37406	+	6.02037i	0.179773	+	0.247436i
$593$			3.32432i			0.136514i	0.997668	+	0.0682568i	$0.0217437\pi$
$593$			3.32432i			0.136514i	−0.997668	+	0.0682568i	$0.978256\pi$
$594$	−3.23932	+	2.35350i	−0.132911	+	0.0965653i
$595$		0			0
$596$	−35.8043	−	26.0134i	−1.46660	−	1.06555i
$597$	−0.472017	+	0.649675i	−0.0193184	+	0.0265894i
$598$	−14.5836	−	4.73848i	−0.596366	−	0.193771i
$599$	−6.84699			−0.279761			−0.139880	−	0.990168i	$-0.544672\pi$
$599$	−6.84699			−0.279761			−0.139880	+	0.990168i	$0.544672\pi$
$600$		0			0
$601$	46.2226			1.88546			0.942729	−	0.333561i	$-0.108250\pi$
$601$	46.2226			1.88546			0.942729	+	0.333561i	$0.108250\pi$
$602$	19.7634	+	6.42150i	0.805494	+	0.261721i
$603$	−20.6679	+	28.4470i	−0.841663	+	1.15845i
$604$	−11.1615	−	8.10927i	−0.454153	−	0.329961i
$605$		0			0
$606$	20.5155	−	14.9054i	0.833386	−	0.605491i
$607$		−	11.3032i		−	0.458782i	−0.973334	−	0.229391i	$-0.926327\pi$
$607$		−	11.3032i		−	0.458782i	0.973334	−	0.229391i	$-0.0736735\pi$
$608$	−13.0334	−	17.9390i	−0.528575	−	0.727521i
$609$	−0.532289	−	1.63822i	−0.0215695	−	0.0663840i
$610$		0			0
$611$	−2.18787	+	6.73358i	−0.0885119	+	0.272412i
$612$	−16.0349	+	5.21006i	−0.648173	+	0.210604i
$613$	−10.9140	+	3.54616i	−0.440811	+	0.143228i	−0.521010	−	0.853551i	$-0.674444\pi$
$613$	−10.9140	+	3.54616i	−0.440811	+	0.143228i	0.0801988	+	0.996779i	$0.474444\pi$
$614$	−6.46858	+	19.9082i	−0.261051	+	0.803431i
$615$		0			0
$616$	−0.253945	−	0.781561i	−0.0102317	−	0.0314900i
$617$	−22.4184	−	30.8562i	−0.902530	−	1.24223i	−0.969654	−	0.244481i	$-0.921382\pi$
$617$	−22.4184	−	30.8562i	−0.902530	−	1.24223i	0.0671242	−	0.997745i	$-0.478618\pi$
$618$			5.51272i			0.221754i
$619$	6.87598	−	4.99569i	0.276369	−	0.200794i	−0.440963	−	0.897525i	$-0.645363\pi$
$619$	6.87598	−	4.99569i	0.276369	−	0.200794i	0.717332	+	0.696731i	$0.245363\pi$
$620$		0			0
$621$	−11.0580	−	8.03408i	−0.443741	−	0.322396i
$622$	−11.0863	+	15.2590i	−0.444521	+	0.611831i
$623$	13.3623	+	4.34169i	0.535351	+	0.173946i
$624$	2.49930			0.100052
$625$		0			0
$626$	8.21288			0.328253
$627$	1.04869	+	0.340740i	0.0418806	+	0.0136078i
$628$	3.35441	−	4.61695i	0.133855	−	0.184236i
$629$	−12.5436	−	9.11345i	−0.500146	−	0.363377i
$630$		0			0
$631$	21.3561	−	15.5161i	0.850173	−	0.617687i	−0.0750210	−	0.997182i	$-0.523902\pi$
$631$	21.3561	−	15.5161i	0.850173	−	0.617687i	0.925194	+	0.379495i	$0.123902\pi$
$632$		−	2.21053i		−	0.0879302i
$633$	11.4578	+	15.7703i	0.455407	+	0.626814i
$634$	21.3935	+	65.8423i	0.849643	+	2.61493i
$635$		0			0
$636$	8.21666	−	25.2883i	0.325812	−	1.00275i
$637$	−2.20066	+	0.715037i	−0.0871932	+	0.0283308i
$638$	−1.63277	+	0.530520i	−0.0646421	+	0.0210035i
$639$	−8.49147	+	26.1341i	−0.335918	+	1.03385i
$640$		0			0
$641$	−4.60640	−	14.1770i	−0.181942	−	0.559959i	0.817941	−	0.575303i	$-0.195116\pi$
$641$	−4.60640	−	14.1770i	−0.181942	−	0.559959i	−0.999882	+	0.0153438i	$0.995116\pi$
$642$	8.10013	+	11.1489i	0.319686	+	0.440011i
$643$		−	23.5452i		−	0.928534i	−0.885695	−	0.464267i	$-0.846318\pi$
$643$		−	23.5452i		−	0.928534i	0.885695	−	0.464267i	$-0.153682\pi$
$644$	7.09337	−	5.15363i	0.279518	−	0.203082i
$645$		0			0
$646$	14.7924	+	10.7473i	0.581998	+	0.422846i
$647$	14.0204	−	19.2974i	0.551199	−	0.758660i	−0.438976	−	0.898499i	$-0.644659\pi$
$647$	14.0204	−	19.2974i	0.551199	−	0.758660i	0.990174	+	0.139839i	$0.0446585\pi$
$648$	5.32949	+	1.73166i	0.209362	+	0.0680259i
$649$	1.94827			0.0764762
$650$		0			0
$651$	7.88518			0.309044
$652$	−44.5679	−	14.4810i	−1.74541	−	0.567119i
$653$	−1.43317	+	1.97258i	−0.0560842	+	0.0771932i	−0.836138	−	0.548519i	$-0.815192\pi$
$653$	−1.43317	+	1.97258i	−0.0560842	+	0.0771932i	0.780054	+	0.625713i	$0.215192\pi$
$654$	2.70809	+	1.96754i	0.105895	+	0.0769370i
$655$		0			0
$656$	5.70492	−	4.14487i	0.222740	−	0.161830i
$657$		−	2.98460i		−	0.116440i
$658$	−3.99778	−	5.50247i	−0.155850	−	0.214508i
$659$	−1.21619	−	3.74306i	−0.0473761	−	0.145809i	0.924570	−	0.381012i	$-0.124424\pi$
$659$	−1.21619	−	3.74306i	−0.0473761	−	0.145809i	−0.971946	+	0.235203i	$0.924424\pi$
$660$		0			0
$661$	11.9984	−	36.9272i	0.466682	−	1.43630i	−0.390172	−	0.920742i	$-0.627584\pi$
$661$	11.9984	−	36.9272i	0.466682	−	1.43630i	0.856854	−	0.515559i	$-0.172416\pi$
$662$	−8.98628	+	2.91982i	−0.349262	+	0.113482i
$663$	−4.95248	+	1.60916i	−0.192338	+	0.0624945i
$664$	9.19345	−	28.2945i	0.356775	−	1.09804i
$665$		0			0
$666$	9.25637	+	28.4882i	0.358677	+	1.10389i
$667$	−3.44477	−	4.74131i	−0.133382	−	0.183584i
$668$			32.8795i			1.27215i
$669$	−0.614878	+	0.446735i	−0.0237726	+	0.0172718i
$670$		0			0
$671$	−3.40056	−	2.47065i	−0.131277	−	0.0953785i
$672$	−3.56578	+	4.90787i	−0.137553	+	0.189325i
$673$	36.8913	+	11.9867i	1.42205	+	0.462054i	0.916254	−	0.400597i	$-0.131197\pi$
$673$	36.8913	+	11.9867i	1.42205	+	0.462054i	0.505800	+	0.862650i	$0.331197\pi$
$674$	−15.8938			−0.612205
$675$		0			0
$676$	−22.4861			−0.864851
$677$	17.2975	+	5.62028i	0.664795	+	0.216005i	0.621926	−	0.783076i	$-0.286350\pi$
$677$	17.2975	+	5.62028i	0.664795	+	0.216005i	0.0428687	+	0.999081i	$0.486350\pi$
$678$	−1.40228	+	1.93008i	−0.0538544	+	0.0741242i
$679$	−13.7740	−	10.0074i	−0.528596	−	0.384048i
$680$		0			0
$681$	−1.59998	+	1.16245i	−0.0613114	+	0.0445453i
$682$		−	7.85897i		−	0.300935i
$683$	−6.57676	−	9.05213i	−0.251653	−	0.346370i	0.664437	−	0.747345i	$-0.268672\pi$
$683$	−6.57676	−	9.05213i	−0.251653	−	0.346370i	−0.916089	+	0.400974i	$0.868672\pi$
$684$	−6.49733	−	19.9967i	−0.248431	−	0.764593i
$685$		0			0
$686$	0.686892	−	2.11404i	0.0262256	−	0.0807142i
$687$	−9.76399	+	3.17251i	−0.372520	+	0.121039i
$688$	−10.9597	+	3.56101i	−0.417833	+	0.135762i
$689$	−7.37772	+	22.7063i	−0.281069	+	0.865040i
$690$		0			0
$691$	9.70842	+	29.8795i	0.369326	+	1.13667i	0.947228	+	0.320562i	$0.103872\pi$
$691$	9.70842	+	29.8795i	0.369326	+	1.13667i	−0.577902	+	0.816106i	$0.696128\pi$
$692$	27.8553	+	38.3395i	1.05890	+	1.45745i
$693$			0.877015i			0.0333150i
$694$	−55.9257	+	40.6324i	−2.12291	+	1.54238i
$695$		0			0
$696$	−2.91476	−	2.11769i	−0.110484	−	0.0802710i
$697$	−8.63593	+	11.8863i	−0.327109	+	0.450227i
$698$	−44.9326	−	14.5995i	−1.70072	−	0.552599i
$699$	4.50489			0.170390
$700$		0			0
$701$	−32.9719			−1.24533			−0.622665	−	0.782489i	$-0.713950\pi$
$701$	−32.9719			−1.24533			−0.622665	+	0.782489i	$0.713950\pi$
$702$	22.4270	+	7.28696i	0.846451	+	0.275029i
$703$	11.3651	−	15.6428i	0.428645	−	0.589979i
$704$	4.10794	+	2.98459i	0.154824	+	0.112486i
$705$		0			0
$706$	43.9674	−	31.9442i	1.65473	−	1.20224i
$707$		−	13.0194i		−	0.489643i
$708$	7.51119	+	10.3383i	0.282288	+	0.388536i
$709$	5.66249	+	17.4274i	0.212659	+	0.654498i	0.999311	+	0.0371016i	$0.0118125\pi$
$709$	5.66249	+	17.4274i	0.212659	+	0.654498i	−0.786652	+	0.617396i	$0.788187\pi$
$710$		0			0
$711$	−0.729003	+	2.24364i	−0.0273398	+	0.0841431i
$712$	27.9487	−	9.08108i	1.04742	−	0.340328i
$713$	25.5149	−	8.29028i	0.955539	−	0.310474i
$714$	1.54582	−	4.75754i	0.0578508	−	0.178047i
$715$		0			0
$716$	−21.7780	−	67.0257i	−0.813881	−	2.50487i
$717$	−3.98529	−	5.48528i	−0.148833	−	0.204852i
$718$			47.1332i			1.75900i
$719$	2.31422	−	1.68138i	0.0863058	−	0.0627048i	−0.543796	−	0.839218i	$-0.683013\pi$
$719$	2.31422	−	1.68138i	0.0863058	−	0.0627048i	0.630101	+	0.776513i	$0.283013\pi$
$720$		0			0
$721$	2.28975	+	1.66360i	0.0852748	+	0.0619558i
$722$	11.4217	−	15.7206i	0.425072	−	0.585061i
$723$	11.0445	+	3.58857i	0.410748	+	0.133460i
$724$	−68.2853			−2.53780
$725$		0			0
$726$	21.1247			0.784011
$727$	−24.0204	−	7.80469i	−0.890866	−	0.289460i	−0.172404	−	0.985026i	$-0.555154\pi$
$727$	−24.0204	−	7.80469i	−0.890866	−	0.289460i	−0.718462	+	0.695566i	$0.755154\pi$
$728$	−2.84475	+	3.91546i	−0.105433	+	0.145117i
$729$	4.91212	+	3.56886i	0.181930	+	0.132180i
$730$		0			0
$731$	19.4244	−	14.1126i	0.718436	−	0.521975i
$732$		−	27.5699i		−	1.01901i
$733$	−2.31886	−	3.19164i	−0.0856491	−	0.117886i	0.764042	−	0.645166i	$-0.223212\pi$
$733$	−2.31886	−	3.19164i	−0.0856491	−	0.117886i	−0.849691	+	0.527280i	$0.823212\pi$
$734$	−4.33427	−	13.3395i	−0.159981	−	0.492370i
$735$		0			0
$736$	−6.37814	+	19.6299i	−0.235101	+	0.723567i
$737$	−5.88617	+	1.91253i	−0.216820	+	0.0704491i
$738$	26.9955	−	8.77136i	0.993717	−	0.322878i
$739$	4.75260	−	14.6270i	0.174827	−	0.538063i	−0.824798	−	0.565427i	$-0.808711\pi$
$739$	4.75260	−	14.6270i	0.174827	−	0.538063i	0.999626	+	0.0273640i	$0.00871131\pi$
$740$		0			0
$741$	−2.00674	−	6.17611i	−0.0737194	−	0.226885i
$742$	−13.4809	−	18.5548i	−0.494898	−	0.681169i
$743$			2.93096i			0.107527i	0.998554	+	0.0537633i	$0.0171217\pi$
$743$			2.93096i			0.107527i	−0.998554	+	0.0537633i	$0.982878\pi$
$744$	13.3428	−	9.69413i	0.489172	−	0.355404i
$745$		0			0
$746$	−5.76742	−	4.19028i	−0.211160	−	0.153417i
$747$	−18.6623	+	25.6864i	−0.682818	+	0.939818i
$748$	−2.82237	−	0.917045i	−0.103196	−	0.0335305i
$749$	7.07518			0.258522
$750$		0			0
$751$	−14.1736			−0.517202			−0.258601	−	0.965984i	$-0.583262\pi$
$751$	−14.1736			−0.517202			−0.258601	+	0.965984i	$0.583262\pi$
$752$	3.58710	+	1.16552i	0.130808	+	0.0425021i
$753$	−7.29347	+	10.0386i	−0.265789	+	0.365827i
$754$	8.17985	+	5.94301i	0.297893	+	0.216432i
$755$		0			0
$756$	−10.9084	+	7.92539i	−0.396733	+	0.288244i
$757$		−	0.724796i		−	0.0263432i	−0.999913	−	0.0131716i	$-0.995807\pi$
$757$		−	0.724796i		−	0.0263432i	0.999913	−	0.0131716i	$-0.00419276\pi$
$758$	−35.9806	−	49.5231i	−1.30688	−	1.79876i
$759$	−0.317172	−	0.976155i	−0.0115126	−	0.0354322i
$760$		0			0
$761$	5.57065	−	17.1447i	0.201936	−	0.621495i	−0.797889	−	0.602804i	$-0.794050\pi$
$761$	5.57065	−	17.1447i	0.201936	−	0.621495i	0.999825	−	0.0186911i	$-0.00594991\pi$
$762$	30.5494	−	9.92609i	1.10669	−	0.359584i
$763$	1.63447	−	0.531071i	0.0591717	−	0.0192261i
$764$	−0.469154	+	1.44391i	−0.0169734	+	0.0522388i
$765$		0			0
$766$	0.467019	+	1.43734i	0.0168741	+	0.0519331i
$767$	−6.74428	−	9.28271i	−0.243522	−	0.335179i
$768$			6.33544i			0.228610i
$769$	−3.39252	+	2.46481i	−0.122337	+	0.0888832i	−0.647271	−	0.762260i	$-0.724090\pi$
$769$	−3.39252	+	2.46481i	−0.122337	+	0.0888832i	0.524934	+	0.851143i	$0.324090\pi$
$770$		0			0
$771$	8.69919	+	6.32033i	0.313294	+	0.227621i
$772$	42.0443	−	57.8690i	1.51321	−	2.08275i
$773$	9.01645	+	2.92962i	0.324299	+	0.105371i	0.466642	−	0.884446i	$-0.345464\pi$
$773$	9.01645	+	2.92962i	0.324299	+	0.105371i	−0.142343	+	0.989817i	$0.545464\pi$
$774$	−46.3856			−1.66730
$775$		0			0
$776$	−35.6107			−1.27835
$777$	−5.03105	−	1.63469i	−0.180488	−	0.0586441i
$778$	24.5703	−	33.8182i	0.880890	−	1.21244i
$779$	−14.8231	−	10.7696i	−0.531094	−	0.385863i
$780$		0			0
$781$	−3.91297	+	2.84294i	−0.140017	+	0.101728i
$782$		−	17.0197i		−	0.608623i
$783$	5.29745	+	7.29132i	0.189315	+	0.260570i
$784$	0.380912	+	1.17233i	0.0136040	+	0.0418688i
$785$		0			0
$786$	−0.978160	+	3.01047i	−0.0348898	+	0.107380i
$787$	−20.6190	+	6.69952i	−0.734988	+	0.238812i	−0.652509	−	0.757781i	$-0.726284\pi$
$787$	−20.6190	+	6.69952i	−0.734988	+	0.238812i	−0.0824786	+	0.996593i	$0.526284\pi$
$788$	−31.8968	+	10.3639i	−1.13628	+	0.369198i
$789$	1.14341	−	3.51905i	0.0407064	−	0.125282i
$790$		0			0
$791$	0.378498	+	1.16490i	0.0134579	+	0.0414190i
$792$	1.07821	+	1.48403i	0.0383126	+	0.0527328i
$793$			24.7549i			0.879073i
$794$	49.3082	−	35.8245i	1.74988	−	1.27136i
$795$		0			0
$796$	2.18050	+	1.58423i	0.0772858	+	0.0561515i
$797$	1.73319	−	2.38553i	0.0613926	−	0.0844996i	−0.777217	−	0.629233i	$-0.783369\pi$
$797$	1.73319	−	2.38553i	0.0613926	−	0.0844996i	0.838609	+	0.544733i	$0.183369\pi$
$798$	5.93301	+	1.92775i	0.210026	+	0.0682416i
$799$	−7.85841			−0.278011
$800$		0			0
$801$	−31.3621			−1.10813
$802$	43.9474	+	14.2794i	1.55184	+	0.504223i
$803$	0.308782	−	0.425003i	0.0108967	−	0.0149980i
$804$	−32.8417	−	23.8609i	−1.15824	−	0.841509i
$805$		0			0
$806$	−37.4448	+	27.2052i	−1.31894	+	0.958263i
$807$			16.5195i			0.581515i
$808$	−16.0062	−	22.0306i	−0.563095	−	0.775034i
$809$	12.0825	+	37.1862i	0.424799	+	1.30740i	0.903187	+	0.429247i	$0.141221\pi$
$809$	12.0825	+	37.1862i	0.424799	+	1.30740i	−0.478388	+	0.878148i	$0.658779\pi$
$810$		0			0
$811$	3.25685	−	10.0236i	0.114363	−	0.351975i	−0.877450	−	0.479668i	$-0.840757\pi$
$811$	3.25685	−	10.0236i	0.114363	−	0.351975i	0.991814	+	0.127693i	$0.0407572\pi$
$812$	−5.49835	+	1.78652i	−0.192954	+	0.0626946i
$813$	−17.8429	+	5.79752i	−0.625779	+	0.203328i
$814$	−1.62926	+	5.01433i	−0.0571054	+	0.175752i
$815$		0			0
$816$	0.857226	+	2.63827i	0.0300089	+	0.0923580i
$817$	17.5995	+	24.2236i	0.615728	+	0.847478i
$818$		−	74.2707i		−	2.59681i
$819$	4.17862	−	3.03595i	0.146013	−	0.106085i
$820$		0			0
$821$	16.3552	+	11.8827i	0.570799	+	0.414710i	0.835395	−	0.549649i	$-0.185239\pi$
$821$	16.3552	+	11.8827i	0.570799	+	0.414710i	−0.264596	+	0.964359i	$0.585239\pi$
$822$	−13.3091	+	18.3185i	−0.464210	+	0.638930i
$823$	−44.3253	−	14.4022i	−1.54508	−	0.502028i	−0.592310	−	0.805710i	$-0.701784\pi$
$823$	−44.3253	−	14.4022i	−1.54508	−	0.502028i	−0.952773	+	0.303682i	$0.901784\pi$
$824$	5.91984			0.206227
$825$		0			0
$826$	11.0224			0.383519
$827$	−42.4453	−	13.7913i	−1.47597	−	0.479571i	−0.543062	−	0.839693i	$-0.682735\pi$
$827$	−42.4453	−	13.7913i	−1.47597	−	0.479571i	−0.932905	+	0.360122i	$0.882735\pi$
$828$	−11.5038	+	15.8337i	−0.399786	+	0.550258i
$829$	−23.8942	−	17.3602i	−0.829880	−	0.602943i	0.0896454	−	0.995974i	$-0.471427\pi$
$829$	−23.8942	−	17.3602i	−0.829880	−	0.602943i	−0.919525	+	0.393031i	$0.871427\pi$
$830$		0			0
$831$	−4.81771	+	3.50027i	−0.167125	+	0.121423i
$832$		−	29.9043i		−	1.03675i
$833$	−1.50959	−	2.07778i	−0.0523043	−	0.0719907i
$834$	3.68923	+	11.3543i	0.127748	+	0.393167i
$835$		0			0
$836$	1.14362	−	3.51971i	0.0395530	−	0.121732i
$837$	−39.2374	+	12.7490i	−1.35624	+	0.440670i
$838$	−34.6139	+	11.2467i	−1.19572	+	0.388512i
$839$	7.63057	−	23.4845i	0.263436	−	0.810774i	−0.728613	−	0.684926i	$-0.759835\pi$
$839$	7.63057	−	23.4845i	0.263436	−	0.810774i	0.992049	−	0.125849i	$-0.0401653\pi$
$840$		0			0
$841$	−7.76736	−	23.9055i	−0.267840	−	0.824326i
$842$	34.8448	+	47.9597i	1.20083	+	1.65280i
$843$		−	2.95487i		−	0.101771i
$844$	52.9298	−	38.4558i	1.82192	−	1.32370i
$845$		0			0
$846$	12.2825	+	8.92376i	0.422281	+	0.306805i
$847$	6.37490	−	8.77430i	0.219044	−	0.301489i
$848$	12.0960	+	3.93024i	0.415379	+	0.134965i
$849$	2.79560			0.0959446
$850$		0			0
$851$	−17.9982			−0.616969
$852$	−30.1715	−	9.80332i	−1.03366	−	0.335856i
$853$	−15.2163	+	20.9435i	−0.520997	+	0.717091i	−0.985725	−	0.168362i	$-0.946152\pi$
$853$	−15.2163	+	20.9435i	−0.520997	+	0.717091i	0.464728	+	0.885454i	$0.346152\pi$
$854$	−19.2388	−	13.9778i	−0.658340	−	0.478312i
$855$		0			0
$856$	11.9722	−	8.69832i	0.409202	−	0.297302i
$857$		−	29.4598i		−	1.00633i	−0.864191	−	0.503164i	$-0.832169\pi$
$857$		−	29.4598i		−	1.00633i	0.864191	−	0.503164i	$-0.167831\pi$
$858$	1.04082	+	1.43257i	0.0355332	+	0.0489072i
$859$	−14.5480	−	44.7740i	−0.496370	−	1.52767i	−0.814811	−	0.579727i	$-0.803159\pi$
$859$	−14.5480	−	44.7740i	−0.496370	−	1.52767i	0.318441	−	0.947943i	$-0.396841\pi$
$860$		0			0
$861$	−1.54904	+	4.76744i	−0.0527910	+	0.162474i
$862$	47.5339	−	15.4447i	1.61901	−	0.526049i
$863$	12.2300	−	3.97378i	0.416315	−	0.135269i	−0.0933669	−	0.995632i	$-0.529763\pi$
$863$	12.2300	−	3.97378i	0.416315	−	0.135269i	0.509682	+	0.860363i	$0.329763\pi$
$864$	9.80846	−	30.1873i	0.333691	−	1.02699i
$865$		0			0
$866$	−25.2987	−	77.8614i	−0.859685	−	2.64584i
$867$	5.35856	+	7.37542i	0.181986	+	0.250482i
$868$		−	26.4650i		−	0.898280i
$869$	−0.335933	+	0.244070i	−0.0113958	+	0.00827950i
$870$		0			0
$871$	29.4885	+	21.4246i	0.999180	+	0.725946i
$872$	2.11285	−	2.90808i	0.0715500	−	0.0984801i
$873$	36.1441	+	11.7439i	1.22329	+	0.397471i
$874$	21.2248			0.717941
$875$		0			0
$876$	3.44568			0.116419
$877$	20.9771	+	6.81587i	0.708346	+	0.230156i	0.640963	−	0.767572i	$-0.278535\pi$
$877$	20.9771	+	6.81587i	0.708346	+	0.230156i	0.0673828	+	0.997727i	$0.478535\pi$
$878$	−53.4570	+	73.5773i	−1.80409	+	2.48311i
$879$	0.288401	+	0.209535i	0.00972751	+	0.00706745i
$880$		0			0
$881$	−1.95911	+	1.42338i	−0.0660042	+	0.0479549i	−0.620298	−	0.784366i	$-0.712988\pi$
$881$	−1.95911	+	1.42338i	−0.0660042	+	0.0479549i	0.554294	+	0.832321i	$0.312988\pi$
$882$			4.96175i			0.167071i
$883$	−6.35144	−	8.74201i	−0.213743	−	0.294192i	0.688661	−	0.725084i	$-0.258199\pi$
$883$	−6.35144	−	8.74201i	−0.213743	−	0.294192i	−0.902404	+	0.430892i	$0.858199\pi$
$884$	5.40081	+	16.6220i	0.181649	+	0.559058i
$885$		0			0
$886$	−23.1659	+	71.2973i	−0.778274	+	2.39528i
$887$	26.5749	−	8.63470i	0.892297	−	0.289925i	0.173243	−	0.984879i	$-0.444575\pi$
$887$	26.5749	−	8.63470i	0.892297	−	0.289925i	0.719054	+	0.694954i	$0.244575\pi$
$888$	−10.5230	+	3.41912i	−0.353127	+	0.114738i
$889$	5.09616	−	15.6844i	0.170920	−	0.526036i
$890$		0			0
$891$	−0.325283	−	1.00112i	−0.0108974	−	0.0335387i
$892$	1.49938	+	2.06371i	0.0502028	+	0.0690982i
$893$		−	9.80002i		−	0.327945i
$894$	−23.7127	+	17.2283i	−0.793072	+	0.576200i
$895$		0			0
$896$	12.0389	+	8.74676i	0.402191	+	0.292209i
$897$	−3.55303	+	4.89033i	−0.118632	+	0.163283i
$898$	−21.7301	−	7.06053i	−0.725142	−	0.235613i
$899$	−17.6896			−0.589981
$900$		0			0
$901$	−26.4993			−0.882820
$902$	4.75159	+	1.54389i	0.158211	+	0.0514058i
$903$	4.81500	−	6.62728i	0.160233	−	0.220542i
$904$	2.07261	+	1.50584i	0.0689341	+	0.0500835i
$905$		0			0
$906$	−7.39207	+	5.37066i	−0.245585	+	0.178428i
$907$			19.6907i			0.653818i	0.945056	+	0.326909i	$0.106007\pi$
$907$			19.6907i			0.653818i	−0.945056	+	0.326909i	$0.893993\pi$
$908$	3.90154	+	5.37001i	0.129477	+	0.178210i
$909$	8.98052	+	27.6392i	0.297865	+	0.916734i
$910$		0			0
$911$	8.32087	−	25.6090i	0.275683	−	0.848464i	−0.713355	−	0.700803i	$-0.752825\pi$
$911$	8.32087	−	25.6090i	0.275683	−	0.848464i	0.989038	−	0.147662i	$-0.0471746\pi$
$912$	−3.29012	+	1.06902i	−0.108947	+	0.0353989i
$913$	−5.31497	+	1.72694i	−0.175900	+	0.0571534i
$914$	1.13905	−	3.50563i	0.0376763	−	0.115956i
$915$		0			0
$916$	10.6479	+	32.7708i	0.351816	+	1.08278i
$917$	0.955236	+	1.31477i	0.0315447	+	0.0434175i
$918$			26.1733i			0.863849i
$919$	24.5160	−	17.8119i	0.808710	−	0.587562i	−0.104747	−	0.994499i	$-0.533403\pi$
$919$	24.5160	−	17.8119i	0.808710	−	0.587562i	0.913456	+	0.406937i	$0.133403\pi$
$920$		0			0
$921$	6.67587	+	4.85030i	0.219977	+	0.159823i
$922$	−9.89234	+	13.6156i	−0.325787	+	0.448407i
$923$	27.0909	+	8.80237i	0.891708	+	0.289734i
$924$	−1.01250			−0.0333089
$925$		0			0
$926$	−9.26434			−0.304445
$927$	−6.00851	−	1.95228i	−0.197345	−	0.0641213i
$928$	7.99946	−	11.0103i	0.262595	−	0.361431i
$929$	10.6834	+	7.76191i	0.350509	+	0.254660i	0.749083	−	0.662477i	$-0.230495\pi$
$929$	10.6834	+	7.76191i	0.350509	+	0.254660i	−0.398573	+	0.917136i	$0.630495\pi$
$930$		0			0
$931$	2.59114	−	1.88257i	0.0849212	−	0.0616988i
$932$		−	15.1197i		−	0.495263i
$933$	4.37030	+	6.01520i	0.143077	+	0.196929i
$934$	−9.26183	−	28.5050i	−0.303056	−	0.932712i
$935$		0			0
$936$	3.33839	−	10.2745i	0.109119	−	0.335832i
$937$	15.0738	−	4.89777i	0.492439	−	0.160003i	−0.0522621	−	0.998633i	$-0.516643\pi$
$937$	15.0738	−	4.89777i	0.492439	−	0.160003i	0.544701	+	0.838630i	$0.316643\pi$
$938$	−33.3013	+	10.8202i	−1.08733	+	0.353294i
$939$	1.00046	−	3.07911i	0.0326489	−	0.100483i
$940$		0			0
$941$	0.922511	+	2.83920i	0.0300730	+	0.0925552i	0.964966	−	0.262373i	$-0.0845052\pi$
$941$	0.922511	+	2.83920i	0.0300730	+	0.0925552i	−0.934893	+	0.354929i	$0.884505\pi$
$942$	−2.22158	−	3.05774i	−0.0723829	−	0.0996265i
$943$			17.0551i			0.555391i
$944$	−4.94506	+	3.59279i	−0.160948	+	0.116935i
$945$		0			0
$946$	−6.60525	−	4.79900i	−0.214755	−	0.156029i
$947$	4.62559	−	6.36657i	0.150311	−	0.206886i	−0.727221	−	0.686404i	$-0.759188\pi$
$947$	4.62559	−	6.36657i	0.150311	−	0.206886i	0.877532	+	0.479518i	$0.159188\pi$
$948$	−2.59026	−	0.841626i	−0.0841277	−	0.0273347i
$949$	−3.09387			−0.100431
$950$		0			0
$951$	27.2912			0.884977
$952$	−5.10889	−	1.65998i	−0.165580	−	0.0538002i
$953$	17.5180	−	24.1115i	0.567465	−	0.781048i	−0.424787	−	0.905293i	$-0.639651\pi$
$953$	17.5180	−	24.1115i	0.567465	−	0.781048i	0.992252	+	0.124245i	$0.0396510\pi$
$954$	41.4177	+	30.0917i	1.34095	+	0.974256i
$955$		0			0
$956$	−18.4102	+	13.3758i	−0.595429	+	0.432605i
$957$			0.676773i			0.0218770i
$958$	−20.6388	−	28.4069i	−0.666810	−	0.917785i
$959$	3.59235	+	11.0561i	0.116003	+	0.357020i
$960$		0			0
$961$	15.4439	−	47.5313i	0.498189	−	1.53327i
$962$	29.5312	−	9.59527i	0.952125	−	0.309364i
$963$	−15.0201	+	4.88033i	−0.484017	+	0.157267i
$964$	12.0443	−	37.0685i	0.387921	−	1.19390i
$965$		0			0
$966$	−1.79441	−	5.52264i	−0.0577344	−	0.177688i
$967$	32.4097	+	44.6081i	1.04222	+	1.43450i	0.895360	+	0.445342i	$0.146918\pi$
$967$	32.4097	+	44.6081i	1.04222	+	1.43450i	0.146864	+	0.989157i	$0.453082\pi$
$968$		−	22.6847i		−	0.729115i
$969$	5.83125	−	4.23665i	0.187327	−	0.136101i
$970$		0			0
$971$	31.4461	+	22.8469i	1.00915	+	0.733193i	0.964031	−	0.265788i	$-0.0856321\pi$
$971$	31.4461	+	22.8469i	1.00915	+	0.733193i	0.0451227	+	0.998981i	$0.485632\pi$
$972$	27.8344	−	38.3108i	0.892789	−	1.22882i
$973$	5.82941	+	1.89409i	0.186882	+	0.0607217i
$974$	17.9704			0.575809
$975$		0			0
$976$	13.1874			0.422117
$977$	−2.23004	−	0.724583i	−0.0713452	−	0.0231815i	0.273127	−	0.961978i	$-0.411942\pi$
$977$	−2.23004	−	0.724583i	−0.0713452	−	0.0231815i	−0.344472	+	0.938797i	$0.611942\pi$
$978$	−18.2423	+	25.1084i	−0.583325	+	0.802878i
$979$	−4.46592	−	3.24468i	−0.142732	−	0.103701i
$980$		0			0
$981$	−3.10354	+	2.25485i	−0.0990884	+	0.0719919i
$982$		−	12.4770i		−	0.398156i
$983$	24.4023	+	33.5869i	0.778314	+	1.07126i	0.995466	+	0.0951194i	$0.0303233\pi$
$983$	24.4023	+	33.5869i	0.778314	+	1.07126i	−0.217152	+	0.976138i	$0.569677\pi$
$984$	3.23996	+	9.97159i	0.103286	+	0.317883i
$985$		0			0
$986$	−3.46789	+	10.6731i	−0.110440	+	0.339900i
$987$	−2.54994	+	0.828525i	−0.0811654	+	0.0263723i
$988$	−20.7289	+	6.73521i	−0.659473	+	0.214276i
$989$	8.61263	−	26.5070i	0.273866	−	0.842872i
$990$		0			0
$991$	−4.89864	−	15.0765i	−0.155610	−	0.478920i	0.842612	−	0.538521i	$-0.181017\pi$
$991$	−4.89864	−	15.0765i	−0.155610	−	0.478920i	−0.998222	+	0.0596019i	$0.981017\pi$
$992$	36.6190	+	50.4018i	1.16266	+	1.60026i
$993$			3.72475i			0.118201i
$994$	−22.1378	+	16.0841i	−0.702169	+	0.510156i
$995$		0			0
$996$	−29.6547	−	21.5454i	−0.939646	−	0.682693i
$997$	6.95994	−	9.57954i	0.220424	−	0.303387i	−0.684456	−	0.729054i	$-0.739960\pi$
$997$	6.95994	−	9.57954i	0.220424	−	0.303387i	0.904880	+	0.425667i	$0.139960\pi$
$998$	21.6283	+	7.02745i	0.684631	+	0.222450i
$999$	27.6780			0.875695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.n.c.274.2		56
5.2	odd	4		875.2.h.e.351.14		56
5.3	odd	4		875.2.h.d.351.1		56
5.4	even	2		175.2.n.a.29.13	✓	56
25.6	even	5		175.2.n.a.169.13	yes	56
25.8	odd	20		875.2.h.d.526.1		56
25.12	odd	20		4375.2.a.o.1.26		28
25.13	odd	20		4375.2.a.p.1.3		28
25.17	odd	20		875.2.h.e.526.14		56
25.19	even	10	inner	875.2.n.c.99.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.13	✓	56	5.4	even	2
175.2.n.a.169.13	yes	56	25.6	even	5
875.2.h.d.351.1		56	5.3	odd	4
875.2.h.d.526.1		56	25.8	odd	20
875.2.h.e.351.14		56	5.2	odd	4
875.2.h.e.526.14		56	25.17	odd	20
875.2.n.c.99.2		56	25.19	even	10	inner
875.2.n.c.274.2		56	1.1	even	1	trivial
4375.2.a.o.1.26		28	25.12	odd	20
4375.2.a.p.1.3		28	25.13	odd	20

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.n (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.11404 - 0.686892i) q^{2} +(-0.515049 + 0.708904i) q^{3} +(2.37929 + 1.72866i) q^{4} +(1.57577 - 1.14486i) q^{6} -1.00000i q^{7} +(-1.22941 - 1.69214i) q^{8} +(0.689782 + 2.12293i) q^{9} +O(q^{10})\)	\(q+(-2.11404 - 0.686892i) q^{2} +(-0.515049 + 0.708904i) q^{3} +(2.37929 + 1.72866i) q^{4} +(1.57577 - 1.14486i) q^{6} -1.00000i q^{7} +(-1.22941 - 1.69214i) q^{8} +(0.689782 + 2.12293i) q^{9} +(-0.121412 + 0.373666i) q^{11} +(-2.45090 + 0.796346i) q^{12} +(2.20066 - 0.715037i) q^{13} +(-0.686892 + 2.11404i) q^{14} +(-0.380912 - 1.17233i) q^{16} +(1.50959 + 2.07778i) q^{17} -4.96175i q^{18} +(-2.59114 + 1.88257i) q^{19} +(0.708904 + 0.515049i) q^{21} +(0.513337 - 0.706547i) q^{22} +(2.83538 + 0.921271i) q^{23} +1.83277 q^{24} -5.14342 q^{26} +(-4.36032 - 1.41675i) q^{27} +(1.72866 - 2.37929i) q^{28} +(-1.59035 - 1.15546i) q^{29} +(7.28014 - 5.28933i) q^{31} +6.92319i q^{32} +(-0.202361 - 0.278525i) q^{33} +(-1.76412 - 5.42942i) q^{34} +(-2.02862 + 6.24346i) q^{36} +(-5.74156 + 1.86554i) q^{37} +(6.77088 - 2.19999i) q^{38} +(-0.626553 + 1.92833i) q^{39} +(1.76779 + 5.44071i) q^{41} +(-1.14486 - 1.57577i) q^{42} -9.34864i q^{43} +(-0.934814 + 0.679182i) q^{44} +(-5.36128 - 3.89520i) q^{46} +(-1.79851 + 2.47544i) q^{47} +(1.02726 + 0.333776i) q^{48} -1.00000 q^{49} -2.25046 q^{51} +(6.47205 + 2.10290i) q^{52} +(-6.06474 + 8.34740i) q^{53} +(8.24472 + 5.99014i) q^{54} +(-1.69214 + 1.22941i) q^{56} -2.80648i q^{57} +(2.56839 + 3.53508i) q^{58} +(-1.53233 - 4.71604i) q^{59} +(-3.30596 + 10.1747i) q^{61} +(-19.0237 + 6.18116i) q^{62} +(2.12293 - 0.689782i) q^{63} +(3.99366 - 12.2912i) q^{64} +(0.236481 + 0.727812i) q^{66} +(9.25908 + 12.7440i) q^{67} +7.55320i q^{68} +(-2.11345 + 1.53551i) q^{69} +(9.95930 + 7.23586i) q^{71} +(2.74427 - 3.77716i) q^{72} +(-1.27164 - 0.413179i) q^{73} +13.4193 q^{74} -9.41939 q^{76} +(0.373666 + 0.121412i) q^{77} +(2.64911 - 3.64619i) q^{78} +(0.855018 + 0.621207i) q^{79} +(-2.16750 + 1.57478i) q^{81} -12.7161i q^{82} +(8.36057 + 11.5073i) q^{83} +(0.796346 + 2.45090i) q^{84} +(-6.42150 + 19.7634i) q^{86} +(1.63822 - 0.532289i) q^{87} +(0.781561 - 0.253945i) q^{88} +(-4.34169 + 13.3623i) q^{89} +(-0.715037 - 2.20066i) q^{91} +(5.15363 + 7.09337i) q^{92} +7.88518i q^{93} +(5.50247 - 3.99778i) q^{94} +(-4.90787 - 3.56578i) q^{96} +(10.0074 - 13.7740i) q^{97} +(2.11404 + 0.686892i) q^{98} -0.877015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 + 6 * q^9	\( 56 q + 12 q^{4} + 6 q^{9} + 8 q^{11} + 40 q^{12} - 4 q^{14} - 32 q^{16} + 12 q^{19} + 4 q^{21} + 30 q^{22} - 10 q^{23} - 28 q^{24} + 12 q^{26} - 30 q^{27} - 2 q^{29} + 12 q^{31} - 20 q^{33} - 14 q^{36} + 70 q^{37} + 70 q^{38} - 4 q^{39} + 4 q^{41} - 50 q^{42} + 22 q^{44} - 4 q^{46} + 10 q^{47} - 30 q^{48} - 56 q^{49} - 44 q^{51} + 20 q^{53} + 54 q^{54} + 12 q^{56} - 10 q^{58} - 6 q^{59} - 4 q^{61} - 50 q^{62} - 20 q^{63} + 24 q^{64} - 74 q^{66} - 10 q^{67} - 78 q^{69} - 8 q^{71} - 140 q^{72} - 40 q^{73} + 60 q^{74} + 52 q^{76} + 20 q^{77} + 90 q^{78} - 72 q^{81} + 30 q^{83} - 12 q^{84} - 20 q^{86} - 30 q^{87} - 140 q^{88} + 38 q^{89} + 8 q^{91} - 80 q^{92} + 88 q^{94} - 28 q^{96} + 30 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 + 6 * q^9 + 8 * q^11 + 40 * q^12 - 4 * q^14 - 32 * q^16 + 12 * q^19 + 4 * q^21 + 30 * q^22 - 10 * q^23 - 28 * q^24 + 12 * q^26 - 30 * q^27 - 2 * q^29 + 12 * q^31 - 20 * q^33 - 14 * q^36 + 70 * q^37 + 70 * q^38 - 4 * q^39 + 4 * q^41 - 50 * q^42 + 22 * q^44 - 4 * q^46 + 10 * q^47 - 30 * q^48 - 56 * q^49 - 44 * q^51 + 20 * q^53 + 54 * q^54 + 12 * q^56 - 10 * q^58 - 6 * q^59 - 4 * q^61 - 50 * q^62 - 20 * q^63 + 24 * q^64 - 74 * q^66 - 10 * q^67 - 78 * q^69 - 8 * q^71 - 140 * q^72 - 40 * q^73 + 60 * q^74 + 52 * q^76 + 20 * q^77 + 90 * q^78 - 72 * q^81 + 30 * q^83 - 12 * q^84 - 20 * q^86 - 30 * q^87 - 140 * q^88 + 38 * q^89 + 8 * q^91 - 80 * q^92 + 88 * q^94 - 28 * q^96 + 30 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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