LMFDB - Embedded newform 875.2.h.e.526.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(176,875)]

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([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("875.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.h (of order $5$, 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 $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			526.14
Character	$\chi$	$=$	875.526
Dual form			875.2.h.e.351.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.686892 + 2.11404i) q^{2} +(0.708904 - 0.515049i) q^{3} +(-2.37929 + 1.72866i) q^{4} +(1.57577 + 1.14486i) q^{6} +1.00000 q^{7} +(-1.69214 - 1.22941i) q^{8} +(-0.689782 + 2.12293i) q^{9} +O(q^{10})$	\(q+(0.686892 + 2.11404i) q^{2} +(0.708904 - 0.515049i) q^{3} +(-2.37929 + 1.72866i) q^{4} +(1.57577 + 1.14486i) q^{6} +1.00000 q^{7} +(-1.69214 - 1.22941i) q^{8} +(-0.689782 + 2.12293i) q^{9} +(-0.121412 - 0.373666i) q^{11} +(-0.796346 + 2.45090i) q^{12} +(-0.715037 + 2.20066i) q^{13} +(0.686892 + 2.11404i) q^{14} +(-0.380912 + 1.17233i) q^{16} +(-2.07778 - 1.50959i) q^{17} -4.96175 q^{18} +(2.59114 + 1.88257i) q^{19} +(0.708904 - 0.515049i) q^{21} +(0.706547 - 0.513337i) q^{22} +(0.921271 + 2.83538i) q^{23} -1.83277 q^{24} -5.14342 q^{26} +(1.41675 + 4.36032i) q^{27} +(-2.37929 + 1.72866i) q^{28} +(1.59035 - 1.15546i) q^{29} +(7.28014 + 5.28933i) q^{31} -6.92319 q^{32} +(-0.278525 - 0.202361i) q^{33} +(1.76412 - 5.42942i) q^{34} +(-2.02862 - 6.24346i) q^{36} +(-1.86554 + 5.74156i) q^{37} +(-2.19999 + 6.77088i) q^{38} +(0.626553 + 1.92833i) q^{39} +(1.76779 - 5.44071i) q^{41} +(1.57577 + 1.14486i) q^{42} -9.34864 q^{43} +(0.934814 + 0.679182i) q^{44} +(-5.36128 + 3.89520i) q^{46} +(-2.47544 + 1.79851i) q^{47} +(0.333776 + 1.02726i) q^{48} +1.00000 q^{49} -2.25046 q^{51} +(-2.10290 - 6.47205i) q^{52} +(8.34740 - 6.06474i) q^{53} +(-8.24472 + 5.99014i) q^{54} +(-1.69214 - 1.22941i) q^{56} +2.80648 q^{57} +(3.53508 + 2.56839i) q^{58} +(1.53233 - 4.71604i) q^{59} +(-3.30596 - 10.1747i) q^{61} +(-6.18116 + 19.0237i) q^{62} +(-0.689782 + 2.12293i) q^{63} +(-3.99366 - 12.2912i) q^{64} +(0.236481 - 0.727812i) q^{66} +(-12.7440 - 9.25908i) q^{67} +7.55320 q^{68} +(2.11345 + 1.53551i) q^{69} +(9.95930 - 7.23586i) q^{71} +(3.77716 - 2.74427i) q^{72} +(-0.413179 - 1.27164i) q^{73} -13.4193 q^{74} -9.41939 q^{76} +(-0.121412 - 0.373666i) q^{77} +(-3.64619 + 2.64911i) q^{78} +(-0.855018 + 0.621207i) q^{79} +(-2.16750 - 1.57478i) q^{81} +12.7161 q^{82} +(11.5073 + 8.36057i) q^{83} +(-0.796346 + 2.45090i) q^{84} +(-6.42150 - 19.7634i) q^{86} +(0.532289 - 1.63822i) q^{87} +(-0.253945 + 0.781561i) q^{88} +(4.34169 + 13.3623i) q^{89} +(-0.715037 + 2.20066i) q^{91} +(-7.09337 - 5.15363i) q^{92} +7.88518 q^{93} +(-5.50247 - 3.99778i) q^{94} +(-4.90787 + 3.56578i) q^{96} +(13.7740 - 10.0074i) q^{97} +(0.686892 + 2.11404i) q^{98} +0.877015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9}+O(q^{10}) $ 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9	$ 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9} + 8 q^{11} + 12 q^{12} + 8 q^{13} + 4 q^{14} - 32 q^{16} + 20 q^{17} - 48 q^{18} - 12 q^{19} + 4 q^{21} + 8 q^{22} + 16 q^{23} + 28 q^{24} + 12 q^{26} + 16 q^{27} - 12 q^{28} + 2 q^{29} + 12 q^{31} - 112 q^{32} + 14 q^{33} - 14 q^{36} + 16 q^{37} + 20 q^{38} + 4 q^{39} + 4 q^{41} - 32 q^{43} - 22 q^{44} - 4 q^{46} + 18 q^{47} + 48 q^{48} + 56 q^{49} - 44 q^{51} - 16 q^{52} + 20 q^{53} - 54 q^{54} + 12 q^{56} - 152 q^{57} - 32 q^{58} + 6 q^{59} - 4 q^{61} - 18 q^{62} - 6 q^{63} - 24 q^{64} - 74 q^{66} + 32 q^{67} - 124 q^{68} + 78 q^{69} - 8 q^{71} + 100 q^{72} + 48 q^{73} - 60 q^{74} + 52 q^{76} + 8 q^{77} - 124 q^{78} - 72 q^{81} - 44 q^{82} - 10 q^{83} + 12 q^{84} - 20 q^{86} - 26 q^{87} + 88 q^{88} - 38 q^{89} + 8 q^{91} + 96 q^{92} - 96 q^{93} - 88 q^{94} - 28 q^{96} + 90 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9 + 8 * q^11 + 12 * q^12 + 8 * q^13 + 4 * q^14 - 32 * q^16 + 20 * q^17 - 48 * q^18 - 12 * q^19 + 4 * q^21 + 8 * q^22 + 16 * q^23 + 28 * q^24 + 12 * q^26 + 16 * q^27 - 12 * q^28 + 2 * q^29 + 12 * q^31 - 112 * q^32 + 14 * q^33 - 14 * q^36 + 16 * q^37 + 20 * q^38 + 4 * q^39 + 4 * q^41 - 32 * q^43 - 22 * q^44 - 4 * q^46 + 18 * q^47 + 48 * q^48 + 56 * q^49 - 44 * q^51 - 16 * q^52 + 20 * q^53 - 54 * q^54 + 12 * q^56 - 152 * q^57 - 32 * q^58 + 6 * q^59 - 4 * q^61 - 18 * q^62 - 6 * q^63 - 24 * q^64 - 74 * q^66 + 32 * q^67 - 124 * q^68 + 78 * q^69 - 8 * q^71 + 100 * q^72 + 48 * q^73 - 60 * q^74 + 52 * q^76 + 8 * q^77 - 124 * q^78 - 72 * q^81 - 44 * q^82 - 10 * q^83 + 12 * q^84 - 20 * q^86 - 26 * q^87 + 88 * q^88 - 38 * q^89 + 8 * q^91 + 96 * q^92 - 96 * q^93 - 88 * q^94 - 28 * q^96 + 90 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.686892	+	2.11404i	0.485706	+	1.49485i	0.830956	+	0.556338i	$0.187794\pi$
$2$	0.686892	+	2.11404i	0.485706	+	1.49485i	−0.345250	+	0.938511i	$0.612206\pi$
$3$	0.708904	−	0.515049i	0.409286	−	0.297363i	−0.364027	−	0.931388i	$-0.618598\pi$
$3$	0.708904	−	0.515049i	0.409286	−	0.297363i	0.773313	+	0.634025i	$0.218598\pi$
$4$	−2.37929	+	1.72866i	−1.18964	+	0.864328i
$5$		0			0
$5$		0			0
$6$	1.57577	+	1.14486i	0.643306	+	0.467389i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.69214	−	1.22941i	−0.598262	−	0.434663i
$9$	−0.689782	+	2.12293i	−0.229927	+	0.707643i
$10$		0			0
$11$	−0.121412	−	0.373666i	−0.0366070	−	0.112665i	0.931083	−	0.364807i	$-0.118865\pi$
$11$	−0.121412	−	0.373666i	−0.0366070	−	0.112665i	−0.967690	+	0.252142i	$0.918865\pi$
$12$	−0.796346	+	2.45090i	−0.229885	+	0.707514i
$13$	−0.715037	+	2.20066i	−0.198316	+	0.610352i	0.801606	+	0.597852i	$0.203979\pi$
$13$	−0.715037	+	2.20066i	−0.198316	+	0.610352i	−0.999922	+	0.0125002i	$0.996021\pi$
$14$	0.686892	+	2.11404i	0.183580	+	0.565000i
$15$		0			0
$16$	−0.380912	+	1.17233i	−0.0952281	+	0.293082i
$17$	−2.07778	−	1.50959i	−0.503935	−	0.366130i	0.306583	−	0.951844i	$-0.400814\pi$
$17$	−2.07778	−	1.50959i	−0.503935	−	0.366130i	−0.810518	+	0.585714i	$0.800814\pi$
$18$	−4.96175			−1.16950
$19$	2.59114	+	1.88257i	0.594448	+	0.431892i	0.843904	−	0.536494i	$-0.180252\pi$
$19$	2.59114	+	1.88257i	0.594448	+	0.431892i	−0.249456	+	0.968386i	$0.580252\pi$
$20$		0			0
$21$	0.708904	−	0.515049i	0.154695	−	0.112393i
$22$	0.706547	−	0.513337i	0.150636	−	0.109444i
$23$	0.921271	+	2.83538i	0.192098	+	0.591218i	0.999998	+	0.00189810i	$0.000604183\pi$
$23$	0.921271	+	2.83538i	0.192098	+	0.591218i	−0.807900	+	0.589320i	$0.799396\pi$
$24$	−1.83277			−0.374113
$25$		0			0
$26$	−5.14342			−1.00871
$27$	1.41675	+	4.36032i	0.272655	+	0.839144i
$28$	−2.37929	+	1.72866i	−0.449644	+	0.326685i
$29$	1.59035	−	1.15546i	0.295321	−	0.214563i	−0.430251	−	0.902709i	$-0.641575\pi$
$29$	1.59035	−	1.15546i	0.295321	−	0.214563i	0.725572	+	0.688146i	$0.241575\pi$
$30$		0			0
$31$	7.28014	+	5.28933i	1.30755	+	0.949992i	0.999999	−	0.00153963i	$-0.000490081\pi$
$31$	7.28014	+	5.28933i	1.30755	+	0.949992i	0.307552	+	0.951531i	$0.400490\pi$
$32$	−6.92319			−1.22386
$33$	−0.278525	−	0.202361i	−0.0484850	−	0.0352265i
$34$	1.76412	−	5.42942i	0.302545	−	0.931137i
$35$		0			0
$36$	−2.02862	−	6.24346i	−0.338104	−	1.04058i
$37$	−1.86554	+	5.74156i	−0.306694	+	0.943906i	0.672346	+	0.740237i	$0.265287\pi$
$37$	−1.86554	+	5.74156i	−0.306694	+	0.943906i	−0.979040	+	0.203669i	$0.934713\pi$
$38$	−2.19999	+	6.77088i	−0.356886	+	1.09838i
$39$	0.626553	+	1.92833i	0.100329	+	0.308780i
$40$		0			0
$41$	1.76779	−	5.44071i	0.276083	−	0.849697i	−0.712848	−	0.701319i	$-0.752595\pi$
$41$	1.76779	−	5.44071i	0.276083	−	0.849697i	0.988931	−	0.148378i	$-0.0474051\pi$
$42$	1.57577	+	1.14486i	0.243147	+	0.176656i
$43$	−9.34864			−1.42565			−0.712827	−	0.701340i	$-0.752586\pi$
$43$	−9.34864			−1.42565			−0.712827	+	0.701340i	$0.752586\pi$
$44$	0.934814	+	0.679182i	0.140928	+	0.102391i
$45$		0			0
$46$	−5.36128	+	3.89520i	−0.790478	+	0.574316i
$47$	−2.47544	+	1.79851i	−0.361079	+	0.262339i	−0.753502	−	0.657445i	$-0.771637\pi$
$47$	−2.47544	+	1.79851i	−0.361079	+	0.262339i	0.392423	+	0.919785i	$0.371637\pi$
$48$	0.333776	+	1.02726i	0.0481764	+	0.148272i
$49$	1.00000			0.142857
$50$		0			0
$51$	−2.25046			−0.315127
$52$	−2.10290	−	6.47205i	−0.291619	−	0.897512i
$53$	8.34740	−	6.06474i	1.14660	−	0.833056i	0.158578	−	0.987346i	$-0.449309\pi$
$53$	8.34740	−	6.06474i	1.14660	−	0.833056i	0.988026	+	0.154290i	$0.0493091\pi$
$54$	−8.24472	+	5.99014i	−1.12196	+	0.815154i
$55$		0			0
$56$	−1.69214	−	1.22941i	−0.226122	−	0.164287i
$57$	2.80648			0.371728
$58$	3.53508	+	2.56839i	0.464179	+	0.337246i
$59$	1.53233	−	4.71604i	0.199493	−	0.613976i	−0.800402	−	0.599464i	$-0.795381\pi$
$59$	1.53233	−	4.71604i	0.199493	−	0.613976i	0.999895	−	0.0145120i	$-0.00461949\pi$
$60$		0			0
$61$	−3.30596	−	10.1747i	−0.423285	−	1.30274i	−0.904627	−	0.426205i	$-0.859850\pi$
$61$	−3.30596	−	10.1747i	−0.423285	−	1.30274i	0.481342	−	0.876533i	$-0.340150\pi$
$62$	−6.18116	+	19.0237i	−0.785008	+	2.41601i
$63$	−0.689782	+	2.12293i	−0.0869043	+	0.267464i
$64$	−3.99366	−	12.2912i	−0.499207	−	1.53640i
$65$		0			0
$66$	0.236481	−	0.727812i	0.0291087	−	0.0895875i
$67$	−12.7440	−	9.25908i	−1.55693	−	1.13118i	−0.938470	−	0.345360i	$-0.887757\pi$
$67$	−12.7440	−	9.25908i	−1.55693	−	1.13118i	−0.618460	−	0.785816i	$-0.712243\pi$
$68$	7.55320			0.915959
$69$	2.11345	+	1.53551i	0.254430	+	0.184854i
$70$		0			0
$71$	9.95930	−	7.23586i	1.18195	−	0.858738i	0.189562	−	0.981869i	$-0.439293\pi$
$71$	9.95930	−	7.23586i	1.18195	−	0.858738i	0.992390	+	0.123130i	$0.0392934\pi$
$72$	3.77716	−	2.74427i	0.445143	−	0.323415i
$73$	−0.413179	−	1.27164i	−0.0483590	−	0.148834i	0.923961	−	0.382486i	$-0.124932\pi$
$73$	−0.413179	−	1.27164i	−0.0483590	−	0.148834i	−0.972320	+	0.233653i	$0.924932\pi$
$74$	−13.4193			−1.55996
$75$		0			0
$76$	−9.41939			−1.08048
$77$	−0.121412	−	0.373666i	−0.0138361	−	0.0425832i
$78$	−3.64619	+	2.64911i	−0.412849	+	0.299953i
$79$	−0.855018	+	0.621207i	−0.0961970	+	0.0698912i	−0.634844	−	0.772640i	$-0.718936\pi$
$79$	−0.855018	+	0.621207i	−0.0961970	+	0.0698912i	0.538647	+	0.842532i	$0.318936\pi$
$80$		0			0
$81$	−2.16750	−	1.57478i	−0.240833	−	0.174975i
$82$	12.7161			1.40426
$83$	11.5073	+	8.36057i	1.26309	+	0.917692i	0.998905	−	0.0467794i	$-0.0148958\pi$
$83$	11.5073	+	8.36057i	1.26309	+	0.917692i	0.264189	+	0.964471i	$0.414896\pi$
$84$	−0.796346	+	2.45090i	−0.0868884	+	0.267415i
$85$		0			0
$86$	−6.42150	−	19.7634i	−0.692448	−	2.13114i
$87$	0.532289	−	1.63822i	0.0570674	−	0.175635i
$88$	−0.253945	+	0.781561i	−0.0270706	+	0.0833147i
$89$	4.34169	+	13.3623i	0.460218	+	1.41640i	0.864898	+	0.501947i	$0.167383\pi$
$89$	4.34169	+	13.3623i	0.460218	+	1.41640i	−0.404681	+	0.914458i	$0.632617\pi$
$90$		0			0
$91$	−0.715037	+	2.20066i	−0.0749562	+	0.230692i
$92$	−7.09337	−	5.15363i	−0.739535	−	0.537303i
$93$	7.88518			0.817655
$94$	−5.50247	−	3.99778i	−0.567536	−	0.412339i
$95$		0			0
$96$	−4.90787	+	3.56578i	−0.500908	+	0.363931i
$97$	13.7740	−	10.0074i	1.39853	−	1.01609i	0.403667	−	0.914906i	$-0.367736\pi$
$97$	13.7740	−	10.0074i	1.39853	−	1.01609i	0.994867	−	0.101188i	$-0.0322645\pi$
$98$	0.686892	+	2.11404i	0.0693865	+	0.213550i
$99$	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	$0.275715\pi$
$102$	−1.54582	−	4.75754i	−0.153059	−	0.471067i
$103$	2.28975	−	1.66360i	0.225616	−	0.163920i	−0.469235	−	0.883073i	$-0.655470\pi$
$103$	2.28975	−	1.66360i	0.225616	−	0.163920i	0.694851	+	0.719154i	$0.255470\pi$
$104$	3.91546	−	2.84475i	0.383942	−	0.278950i
$105$		0			0
$106$	18.5548	+	13.4809i	1.80220	+	1.30938i
$107$	−7.07518			−0.683984			−0.341992	−	0.939703i	$-0.611102\pi$
$107$	−7.07518			−0.683984			−0.341992	+	0.939703i	$0.611102\pi$
$108$	−10.9084	−	7.92539i	−1.04966	−	0.762621i
$109$	−0.531071	+	1.63447i	−0.0508674	+	0.156554i	−0.973263	−	0.229692i	$-0.926228\pi$
$109$	−0.531071	+	1.63447i	−0.0508674	+	0.156554i	0.922396	+	0.386245i	$0.126228\pi$
$110$		0			0
$111$	1.63469	+	5.03105i	0.155158	+	0.477527i
$112$	−0.380912	+	1.17233i	−0.0359928	+	0.110775i
$113$	0.378498	−	1.16490i	0.0356061	−	0.109584i	−0.931674	−	0.363296i	$-0.881651\pi$
$113$	0.378498	−	1.16490i	0.0356061	−	0.109584i	0.967280	+	0.253712i	$0.0816514\pi$
$114$	1.92775	+	5.93301i	0.180550	+	0.555677i
$115$		0			0
$116$	−1.78652	+	5.49835i	−0.165874	+	0.510509i
$117$	−4.17862	−	3.03595i	−0.386314	−	0.280673i
$118$	11.0224			1.01470
$119$	−2.07778	−	1.50959i	−0.190469	−	0.138384i
$120$		0			0
$121$	8.77430	−	6.37490i	0.797664	−	0.579537i
$122$	19.2388	−	13.9778i	1.74180	−	1.26549i
$123$	−1.54904	−	4.76744i	−0.139672	−	0.429866i
$124$	−26.4650			−2.37663
$125$		0			0
$126$	−4.96175			−0.442028
$127$	−5.09616	−	15.6844i	−0.452211	−	1.39176i	−0.874379	−	0.485244i	$-0.838731\pi$
$127$	−5.09616	−	15.6844i	−0.452211	−	1.39176i	0.422168	−	0.906518i	$-0.361269\pi$
$128$	12.0389	−	8.74676i	1.06410	−	0.773112i
$129$	−6.62728	+	4.81500i	−0.583500	+	0.423937i
$130$		0			0
$131$	−1.31477	−	0.955236i	−0.114872	−	0.0834594i	0.528866	−	0.848705i	$-0.322617\pi$
$131$	−1.31477	−	0.955236i	−0.114872	−	0.0834594i	−0.643738	+	0.765246i	$0.722617\pi$
$132$	1.01250			0.0881272
$133$	2.59114	+	1.88257i	0.224680	+	0.163240i
$134$	10.8202	−	33.3013i	0.934727	−	2.87679i
$135$		0			0
$136$	1.65998	+	5.10889i	0.142342	+	0.438083i
$137$	−3.59235	+	11.0561i	−0.306915	+	0.944587i	0.672041	+	0.740514i	$0.265418\pi$
$137$	−3.59235	+	11.0561i	−0.306915	+	0.944587i	−0.978956	+	0.204073i	$0.934582\pi$
$138$	−1.79441	+	5.52264i	−0.152751	+	0.470118i
$139$	1.89409	+	5.82941i	0.160655	+	0.494444i	0.998690	−	0.0511720i	$-0.0162957\pi$
$139$	1.89409	+	5.82941i	0.160655	+	0.494444i	−0.838035	+	0.545616i	$0.816296\pi$
$140$		0			0
$141$	−0.828525	+	2.54994i	−0.0697744	+	0.214744i
$142$	22.1378	+	16.0841i	1.85776	+	1.34975i
$143$	0.909125			0.0760249
$144$	−2.22602	−	1.61730i	−0.185502	−	0.134775i
$145$		0			0
$146$	2.40447	−	1.74695i	0.198996	−	0.144579i
$147$	0.708904	−	0.515049i	0.0584694	−	0.0424805i
$148$	−5.48650	−	16.8857i	−0.450987	−	1.38800i
$149$	15.0483			1.23281			0.616404	−	0.787430i	$-0.288589\pi$
$149$	15.0483			1.23281			0.616404	+	0.787430i	$0.288589\pi$
$150$		0			0
$151$	−4.69108			−0.381755			−0.190878	−	0.981614i	$-0.561133\pi$
$151$	−4.69108			−0.381755			−0.190878	+	0.981614i	$0.561133\pi$
$152$	−2.07012	−	6.37116i	−0.167909	−	0.516769i
$153$	4.63797	−	3.36968i	0.374958	−	0.272423i
$154$	0.706547	−	0.513337i	0.0569352	−	0.0413658i
$155$		0			0
$156$	−4.82417	−	3.50497i	−0.386243	−	0.280622i
$157$	1.94047			0.154867			0.0774333	−	0.996998i	$-0.475328\pi$
$157$	1.94047			0.154867			0.0774333	+	0.996998i	$0.475328\pi$
$158$	−1.90056	−	1.38084i	−0.151200	−	0.109853i
$159$	2.79386	−	8.59863i	0.221568	−	0.681916i
$160$		0			0
$161$	0.921271	+	2.83538i	0.0726063	+	0.223459i
$162$	1.84030	−	5.66386i	0.144588	−	0.444995i
$163$	4.92389	−	15.1542i	0.385669	−	1.18697i	−0.550325	−	0.834950i	$-0.685496\pi$
$163$	4.92389	−	15.1542i	0.385669	−	1.18697i	0.935994	−	0.352016i	$-0.114504\pi$
$164$	5.19902	+	16.0009i	0.405975	+	1.24946i
$165$		0			0
$166$	−9.77024	+	30.0697i	−0.758318	+	2.33386i
$167$	−9.04468	−	6.57134i	−0.699898	−	0.508506i	0.180001	−	0.983666i	$-0.442390\pi$
$167$	−9.04468	−	6.57134i	−0.699898	−	0.508506i	−0.879899	+	0.475161i	$0.842390\pi$
$168$	−1.83277			−0.141401
$169$	6.18561	+	4.49411i	0.475816	+	0.345701i
$170$		0			0
$171$	−5.78389	+	4.20224i	−0.442305	+	0.321354i
$172$	22.2431	−	16.1606i	1.69602	−	1.23223i
$173$	4.97945	+	15.3252i	0.378581	+	1.16515i	0.941031	+	0.338321i	$0.109859\pi$
$173$	4.97945	+	15.3252i	0.378581	+	1.16515i	−0.562450	+	0.826831i	$0.690141\pi$
$174$	3.82888			0.290266
$175$		0			0
$176$	0.484307			0.0365060
$177$	−1.34271	−	4.13244i	−0.100924	−	0.310613i
$178$	−25.2662	+	18.3570i	−1.89378	+	1.37591i
$179$	19.3867	−	14.0852i	1.44903	−	1.05278i	0.462969	−	0.886375i	$-0.346784\pi$
$179$	19.3867	−	14.0852i	1.44903	−	1.05278i	0.986058	−	0.166405i	$-0.0532158\pi$
$180$		0			0
$181$	−18.7843	−	13.6476i	−1.39623	−	1.01442i	−0.995150	−	0.0983725i	$-0.968636\pi$
$181$	−18.7843	−	13.6476i	−1.39623	−	1.01442i	−0.401076	−	0.916045i	$-0.631364\pi$
$182$	−5.14342			−0.381256
$183$	−7.58408	−	5.51015i	−0.560631	−	0.407322i
$184$	1.92693	−	5.93049i	0.142055	−	0.437201i
$185$		0			0
$186$	5.41626	+	16.6695i	0.397140	+	1.22227i
$187$	−0.311818	+	0.959677i	−0.0228024	+	0.0701785i
$188$	2.78078	−	8.55835i	0.202809	−	0.624182i
$189$	1.41675	+	4.36032i	0.103054	+	0.317167i
$190$		0			0
$191$	0.159524	−	0.490964i	0.0115427	−	0.0355249i	−0.945119	−	0.326726i	$-0.894055\pi$
$191$	0.159524	−	0.490964i	0.0115427	−	0.0355249i	0.956662	+	0.291201i	$0.0940547\pi$
$192$	−9.16169	−	6.65636i	−0.661188	−	0.480381i
$193$	−24.3220			−1.75073			−0.875367	−	0.483460i	$-0.839380\pi$
$193$	−24.3220			−1.75073			−0.875367	+	0.483460i	$0.839380\pi$
$194$	30.6172	+	22.2447i	2.19818	+	1.59707i
$195$		0			0
$196$	−2.37929	+	1.72866i	−0.169949	+	0.123475i
$197$	−9.22590	+	6.70301i	−0.657318	+	0.477569i	−0.865756	−	0.500466i	$-0.833162\pi$
$197$	−9.22590	+	6.70301i	−0.657318	+	0.477569i	0.208438	+	0.978036i	$0.433162\pi$
$198$	0.602414	+	1.85404i	0.0428117	+	0.131761i
$199$	−0.916451			−0.0649655			−0.0324827	−	0.999472i	$-0.510341\pi$
$199$	−0.916451			−0.0649655			−0.0324827	+	0.999472i	$0.510341\pi$
$200$		0			0
$201$	−13.8032			−0.973600
$202$	8.94289	+	27.5234i	0.629219	+	1.93654i
$203$	1.59035	−	1.15546i	0.111621	−	0.0810973i
$204$	5.35449	−	3.89026i	0.374889	−	0.272373i
$205$		0			0
$206$	5.08972	+	3.69790i	0.354618	+	0.257645i
$207$	−6.65479			−0.462540
$208$	−2.30752	−	1.67651i	−0.159998	−	0.116245i
$209$	0.388860	−	1.19679i	0.0268980	−	0.0827835i
$210$		0			0
$211$	6.87441	+	21.1573i	0.473254	+	1.45653i	0.848298	+	0.529519i	$0.177628\pi$
$211$	6.87441	+	21.1573i	0.473254	+	1.45653i	−0.375044	+	0.927007i	$0.622372\pi$
$212$	−9.37704	+	28.8596i	−0.644018	+	1.98208i
$213$	3.33337	−	10.2591i	0.228399	−	0.702939i
$214$	−4.85988	−	14.9572i	−0.332215	−	1.02245i
$215$		0			0
$216$	2.96329	−	9.12006i	0.201626	−	0.620541i
$217$	7.28014	+	5.28933i	0.494208	+	0.359063i
$218$	−3.82011			−0.258731
$219$	−0.947858	−	0.688659i	−0.0640503	−	0.0465353i
$220$		0			0
$221$	4.80778	−	3.49306i	0.323406	−	0.234968i
$222$	−9.51297	+	6.91158i	−0.638469	+	0.463875i
$223$	0.268031	+	0.824913i	0.0179487	+	0.0552403i	0.959630	−	0.281267i	$-0.0907545\pi$
$223$	0.268031	+	0.824913i	0.0179487	+	0.0552403i	−0.941681	+	0.336507i	$0.890754\pi$
$224$	−6.92319			−0.462575
$225$		0			0
$226$	2.72262			0.181106
$227$	−0.697445	−	2.14652i	−0.0462911	−	0.142469i	0.925239	−	0.379384i	$-0.123864\pi$
$227$	−0.697445	−	2.14652i	−0.0462911	−	0.142469i	−0.971531	+	0.236914i	$0.923864\pi$
$228$	−6.67744	+	4.85145i	−0.442224	+	0.321295i
$229$	−9.47871	+	6.88669i	−0.626371	+	0.455085i	−0.855141	−	0.518395i	$-0.826530\pi$
$229$	−9.47871	+	6.88669i	−0.626371	+	0.455085i	0.228770	+	0.973480i	$0.426530\pi$
$230$		0			0
$231$	−0.278525	−	0.202361i	−0.0183256	−	0.0133143i
$232$	−4.11164			−0.269942
$233$	−4.15922	−	3.02185i	−0.272480	−	0.197968i	0.443151	−	0.896447i	$-0.353861\pi$
$233$	−4.15922	−	3.02185i	−0.272480	−	0.197968i	−0.715631	+	0.698479i	$0.753861\pi$
$234$	3.54784	−	10.9191i	0.231929	−	0.713805i
$235$		0			0
$236$	4.50654	+	13.8697i	0.293351	+	0.902840i
$237$	−0.286174	+	0.880752i	−0.0185890	+	0.0572110i
$238$	1.76412	−	5.42942i	0.114351	−	0.351937i
$239$	2.39108	+	7.35899i	0.154666	+	0.476013i	0.998127	−	0.0611774i	$-0.0194855\pi$
$239$	2.39108	+	7.35899i	0.154666	+	0.476013i	−0.843461	+	0.537191i	$0.819486\pi$
$240$		0			0
$241$	−4.09536	+	12.6042i	−0.263805	+	0.811908i	0.728161	+	0.685406i	$0.240375\pi$
$241$	−4.09536	+	12.6042i	−0.263805	+	0.811908i	−0.991966	+	0.126503i	$0.959625\pi$
$242$	19.5038	+	14.1703i	1.25375	+	0.910902i
$243$	−16.1018			−1.03293
$244$	25.4544	+	18.4937i	1.62955	+	1.18394i
$245$		0			0
$246$	9.01452	−	6.54943i	0.574745	−	0.417576i
$247$	−5.99566	+	4.35610i	−0.381495	+	0.277172i
$248$	−5.81625	−	17.9006i	−0.369332	−	1.13669i
$249$	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	$0.352525\pi$
$252$	−2.02862	−	6.24346i	−0.127791	−	0.393301i
$253$	0.947634	−	0.688496i	0.0595772	−	0.0432854i
$254$	29.6568	−	21.5469i	1.86083	−	1.35197i
$255$		0			0
$256$	5.84931	+	4.24977i	0.365582	+	0.265611i
$257$	12.2713			0.765465			0.382732	−	0.923859i	$-0.374983\pi$
$257$	12.2713			0.765465			0.382732	+	0.923859i	$0.374983\pi$
$258$	−14.7313	−	10.7029i	−0.917131	−	0.666335i
$259$	−1.86554	+	5.74156i	−0.115919	+	0.356763i
$260$		0			0
$261$	1.35596	+	4.17322i	0.0839320	+	0.258316i
$262$	1.11630	−	3.43561i	0.0689651	−	0.212253i
$263$	1.30488	−	4.01602i	0.0804626	−	0.247639i	−0.902731	−	0.430206i	$-0.858441\pi$
$263$	1.30488	−	4.01602i	0.0804626	−	0.247639i	0.983193	+	0.182568i	$0.0584409\pi$
$264$	0.222520	+	0.684845i	0.0136951	+	0.0421493i
$265$		0			0
$266$	−2.19999	+	6.77088i	−0.134890	+	0.415150i
$267$	9.96009	+	7.23643i	0.609548	+	0.442862i
$268$	46.3275			2.82990
$269$	−15.2520	−	11.0812i	−0.929928	−	0.675633i	0.0160469	−	0.999871i	$-0.494892\pi$
$269$	−15.2520	−	11.0812i	−0.929928	−	0.675633i	−0.945975	+	0.324239i	$0.894892\pi$
$270$		0			0
$271$	17.3216	−	12.5849i	1.05221	−	0.764477i	0.0795805	−	0.996828i	$-0.474642\pi$
$271$	17.3216	−	12.5849i	1.05221	−	0.764477i	0.972632	+	0.232351i	$0.0746419\pi$
$272$	2.56119	−	1.86081i	0.155295	−	0.112828i
$273$	0.626553	+	1.92833i	0.0379207	+	0.116708i
$274$	−25.8406			−1.56109
$275$		0			0
$276$	−7.68289			−0.462455
$277$	−2.10008	−	6.46338i	−0.126182	−	0.388347i	0.867933	−	0.496682i	$-0.165448\pi$
$277$	−2.10008	−	6.46338i	−0.126182	−	0.388347i	−0.994115	+	0.108334i	$0.965448\pi$
$278$	−11.0225	+	8.00835i	−0.661088	+	0.480309i
$279$	−16.2506	+	11.8067i	−0.972897	+	0.706851i
$280$		0			0
$281$	−2.72814	−	1.98211i	−0.162747	−	0.118243i	0.503431	−	0.864035i	$-0.332071\pi$
$281$	−2.72814	−	1.98211i	−0.162747	−	0.118243i	−0.666178	+	0.745793i	$0.732071\pi$
$282$	−5.95977			−0.354899
$283$	−2.58109	−	1.87527i	−0.153430	−	0.111473i	0.508422	−	0.861108i	$-0.330229\pi$
$283$	−2.58109	−	1.87527i	−0.153430	−	0.111473i	−0.661851	+	0.749635i	$0.730229\pi$
$284$	−11.1878	+	34.4324i	−0.663872	+	2.04319i
$285$		0			0
$286$	0.624470	+	1.92192i	0.0369257	+	0.113646i
$287$	1.76779	−	5.44071i	0.104350	−	0.321155i
$288$	4.77549	−	14.6974i	0.281398	−	0.866055i
$289$	−3.21501	−	9.89477i	−0.189118	−	0.582045i
$290$		0			0
$291$	4.61013	−	14.1885i	0.270251	−	0.831746i
$292$	3.18129	+	2.31134i	0.186171	+	0.135261i
$293$	−0.406826			−0.0237670			−0.0118835	−	0.999929i	$-0.503783\pi$
$293$	−0.406826			−0.0237670			−0.0118835	+	0.999929i	$0.503783\pi$
$294$	1.57577	+	1.14486i	0.0919008	+	0.0667698i
$295$		0			0
$296$	10.2155	−	7.42200i	0.593764	−	0.431395i
$297$	1.45730	−	1.05879i	0.0845608	−	0.0614371i
$298$	10.3366	+	31.8127i	0.598782	+	1.84286i
$299$	−6.89844			−0.398947
$300$		0			0
$301$	−9.34864			−0.538847
$302$	−3.22227	−	9.91712i	−0.185421	−	0.570666i
$303$	9.22947	−	6.70560i	0.530219	−	0.385227i
$304$	−3.19399	+	2.32057i	−0.183188	+	0.133094i
$305$		0			0
$306$	10.3094	+	7.49022i	0.589350	+	0.428188i
$307$	9.41718			0.537467			0.268733	−	0.963215i	$-0.413395\pi$
$307$	9.41718			0.537467			0.268733	+	0.963215i	$0.413395\pi$
$308$	0.934814	+	0.679182i	0.0532659	+	0.0387000i
$309$	0.766377	−	2.35867i	0.0435977	−	0.134180i
$310$		0			0
$311$	2.62208	+	8.06992i	0.148684	+	0.457603i	0.997466	−	0.0711396i	$-0.0226636\pi$
$311$	2.62208	+	8.06992i	0.148684	+	0.457603i	−0.848782	+	0.528743i	$0.822664\pi$
$312$	1.31050	−	4.03330i	0.0741924	−	0.228341i
$313$	1.14175	−	3.51395i	0.0645357	−	0.198620i	−0.913589	−	0.406638i	$-0.866701\pi$
$313$	1.14175	−	3.51395i	0.0645357	−	0.198620i	0.978125	+	0.208017i	$0.0667011\pi$
$314$	1.33289	+	4.10223i	0.0752196	+	0.231502i
$315$		0			0
$316$	0.960483	−	2.95606i	0.0540314	−	0.166292i
$317$	25.1971	+	18.3068i	1.41521	+	1.02821i	0.992539	+	0.121927i	$0.0389074\pi$
$317$	25.1971	+	18.3068i	1.41521	+	1.02821i	0.422671	+	0.906283i	$0.361093\pi$
$318$	20.0969			1.12698
$319$	−0.624844	−	0.453975i	−0.0349845	−	0.0254177i
$320$		0			0
$321$	−5.01562	+	3.64406i	−0.279945	+	0.203392i
$322$	−5.36128	+	3.89520i	−0.298773	+	0.217071i
$323$	−2.54189	−	7.82313i	−0.141434	−	0.435291i
$324$	7.87935			0.437742
$325$		0			0
$326$	35.4186			1.96166
$327$	0.465353	+	1.43221i	0.0257341	+	0.0792013i
$328$	−9.68024	+	7.03311i	−0.534502	+	0.388338i
$329$	−2.47544	+	1.79851i	−0.136475	+	0.0991550i
$330$		0			0
$331$	3.43895	+	2.49854i	0.189022	+	0.137332i	0.678271	−	0.734811i	$-0.262729\pi$
$331$	3.43895	+	2.49854i	0.189022	+	0.137332i	−0.489250	+	0.872144i	$0.662729\pi$
$332$	−41.8318			−2.29582
$333$	−10.9021	−	7.92084i	−0.597431	−	0.434059i
$334$	7.67934	−	23.6346i	0.420195	−	1.29323i
$335$		0			0
$336$	0.333776	+	1.02726i	0.0182090	+	0.0560414i
$337$	2.20955	−	6.80029i	0.120362	−	0.370435i	−0.872666	−	0.488318i	$-0.837611\pi$
$337$	2.20955	−	6.80029i	0.120362	−	0.370435i	0.993028	+	0.117883i	$0.0376107\pi$
$338$	−5.25186	+	16.1636i	−0.285663	+	0.879182i
$339$	−0.331660	−	1.02075i	−0.0180133	−	0.0554393i
$340$		0			0
$341$	1.09255	−	3.36253i	0.0591650	−	0.182091i
$342$	−12.8566	−	9.34086i	−0.695205	−	0.505096i
$343$	1.00000			0.0539949
$344$	15.8192	+	11.4933i	0.852915	+	0.619679i
$345$		0			0
$346$	−28.9776	+	21.0535i	−1.55785	+	1.13184i
$347$	25.1597	−	18.2796i	1.35064	−	0.981300i	0.351664	−	0.936126i	$-0.385616\pi$
$347$	25.1597	−	18.2796i	1.35064	−	0.981300i	0.998979	−	0.0451739i	$-0.0143842\pi$
$348$	1.56544	+	4.81794i	0.0839166	+	0.258269i
$349$	−21.2544			−1.13772			−0.568861	−	0.822433i	$-0.692616\pi$
$349$	−21.2544			−1.13772			−0.568861	+	0.822433i	$0.692616\pi$
$350$		0			0
$351$	−10.6086			−0.566245
$352$	0.840555	+	2.58696i	0.0448017	+	0.137886i
$353$	19.7799	−	14.3710i	1.05278	−	0.764889i	0.0800406	−	0.996792i	$-0.474495\pi$
$353$	19.7799	−	14.3710i	1.05278	−	0.764889i	0.972739	+	0.231902i	$0.0744950\pi$
$354$	7.81383	−	5.67708i	0.415300	−	0.301733i
$355$		0			0
$356$	−33.4290	−	24.2876i	−1.77173	−	1.28724i
$357$	−2.25046			−0.119107
$358$	43.0932	+	31.3090i	2.27755	+	1.65473i
$359$	6.55245	−	20.1664i	0.345825	−	1.06434i	−0.615315	−	0.788281i	$-0.710971\pi$
$359$	6.55245	−	20.1664i	0.345825	−	1.06434i	0.961141	−	0.276059i	$-0.0890287\pi$
$360$		0			0
$361$	−2.70140	−	8.31405i	−0.142179	−	0.437582i
$362$	15.9487	−	49.0851i	0.838245	−	2.57985i
$363$	2.93675	−	9.03838i	0.154139	−	0.474392i
$364$	−2.10290	−	6.47205i	−0.110222	−	0.339228i
$365$		0			0
$366$	6.43922	−	19.8179i	0.336583	−	1.03590i
$367$	−5.10487	−	3.70891i	−0.266472	−	0.193603i	0.446523	−	0.894772i	$-0.352662\pi$
$367$	−5.10487	−	3.70891i	−0.266472	−	0.193603i	−0.712996	+	0.701169i	$0.752662\pi$
$368$	−3.67492			−0.191568
$369$	10.3309	+	7.50581i	0.537803	+	0.390737i
$370$		0			0
$371$	8.34740	−	6.06474i	0.433375	−	0.314866i
$372$	−18.7611	+	13.6308i	−0.972719	+	0.706722i
$373$	0.991061	+	3.05017i	0.0513152	+	0.157932i	0.973430	−	0.228984i	$-0.0735403\pi$
$373$	0.991061	+	3.05017i	0.0513152	+	0.157932i	−0.922115	+	0.386916i	$0.873540\pi$
$374$	−2.24298			−0.115981
$375$		0			0
$376$	6.39989			0.330049
$377$	1.40561	+	4.32602i	0.0723925	+	0.222801i
$378$	−8.24472	+	5.99014i	−0.424062	+	0.308099i
$379$	−22.2793	+	16.1869i	−1.14441	+	0.831464i	−0.987728	−	0.156185i	$-0.950080\pi$
$379$	−22.2793	+	16.1869i	−1.14441	+	0.831464i	−0.156684	+	0.987649i	$0.550080\pi$
$380$		0			0
$381$	−11.6909	−	8.49393i	−0.598942	−	0.435157i
$382$	1.14749			0.0587108
$383$	−0.550052	−	0.399636i	−0.0281063	−	0.0204205i	0.573643	−	0.819105i	$-0.305530\pi$
$383$	−0.550052	−	0.399636i	−0.0281063	−	0.0204205i	−0.601750	+	0.798685i	$0.705530\pi$
$384$	4.02940	−	12.4012i	0.205624	−	0.632847i
$385$		0			0
$386$	−16.7066	−	51.4175i	−0.850341	−	2.61708i
$387$	6.44852	−	19.8465i	0.327797	−	1.00885i
$388$	−15.4730	+	47.6209i	−0.785520	+	2.41758i
$389$	5.81124	+	17.8852i	0.294642	+	0.906814i	0.983342	+	0.181768i	$0.0581818\pi$
$389$	5.81124	+	17.8852i	0.294642	+	0.906814i	−0.688700	+	0.725047i	$0.741818\pi$
$390$		0			0
$391$	2.36607	−	7.28203i	0.119658	−	0.368268i
$392$	−1.69214	−	1.22941i	−0.0854660	−	0.0620947i
$393$	−1.42404			−0.0718332
$394$	−20.5076	−	14.8996i	−1.03316	−	0.750633i
$395$		0			0
$396$	−2.08667	+	1.51606i	−0.104859	+	0.0761847i
$397$	−22.1827	+	16.1166i	−1.11332	+	0.808871i	−0.983183	−	0.182625i	$-0.941540\pi$
$397$	−22.1827	+	16.1166i	−1.11332	+	0.808871i	−0.130133	+	0.991497i	$0.541540\pi$
$398$	−0.629502	−	1.93741i	−0.0315541	−	0.0971135i
$399$	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	$0.673719\pi$
$402$	−9.48127	−	29.1804i	−0.472883	−	1.45538i
$403$	−16.8456	+	12.2390i	−0.839137	+	0.609669i
$404$	−30.9768	+	22.5060i	−1.54115	+	1.11971i
$405$		0			0
$406$	3.53508	+	2.56839i	0.175443	+	0.127467i
$407$	2.37192			0.117572
$408$	3.80809	+	2.76674i	0.188528	+	0.136974i
$409$	−10.3251	+	31.7774i	−0.510543	+	1.57129i	0.280704	+	0.959794i	$0.409432\pi$
$409$	−10.3251	+	31.7774i	−0.510543	+	1.57129i	−0.791247	+	0.611496i	$0.790568\pi$
$410$		0			0
$411$	3.14781	+	9.68795i	0.155270	+	0.477871i
$412$	−2.57219	+	7.91638i	−0.126723	+	0.390012i
$413$	1.53233	−	4.71604i	0.0754012	−	0.232061i
$414$	−4.57112	−	14.0685i	−0.224658	−	0.691427i
$415$		0			0
$416$	4.95034	−	15.2356i	0.242710	−	0.746985i
$417$	4.34516	+	3.15694i	0.212783	+	0.154596i
$418$	2.79716			0.136813
$419$	−13.2464	−	9.62404i	−0.647127	−	0.470165i	0.215164	−	0.976578i	$-0.430971\pi$
$419$	−13.2464	−	9.62404i	−0.647127	−	0.470165i	−0.862291	+	0.506413i	$0.830971\pi$
$420$		0			0
$421$	−21.5760	+	15.6759i	−1.05155	+	0.763996i	−0.972507	−	0.232875i	$-0.925187\pi$
$421$	−21.5760	+	15.6759i	−1.05155	+	0.763996i	−0.0790436	+	0.996871i	$0.525187\pi$
$422$	−40.0052	+	29.0655i	−1.94742	+	1.41489i
$423$	−2.11060	−	6.49575i	−0.102621	−	0.315834i
$424$	−21.5810			−1.04807
$425$		0			0
$426$	23.9777			1.16172
$427$	−3.30596	−	10.1747i	−0.159987	−	0.492389i
$428$	16.8339	−	12.2306i	0.813698	−	0.591186i
$429$	0.644482	−	0.468244i	0.0311159	−	0.0226070i
$430$		0			0
$431$	−18.1907	−	13.2163i	−0.876215	−	0.636607i	0.0560325	−	0.998429i	$-0.482155\pi$
$431$	−18.1907	−	13.2163i	−0.876215	−	0.636607i	−0.932247	+	0.361822i	$0.882155\pi$
$432$	−5.65139			−0.271902
$433$	29.7967	+	21.6486i	1.43194	+	1.04036i	0.989652	+	0.143488i	$0.0458320\pi$
$433$	29.7967	+	21.6486i	1.43194	+	1.04036i	0.442285	+	0.896875i	$0.354168\pi$
$434$	−6.18116	+	19.0237i	−0.296705	+	0.913165i
$435$		0			0
$436$	−1.56186	−	4.80691i	−0.0747996	−	0.230209i
$437$	−2.95067	+	9.08123i	−0.141150	+	0.434414i
$438$	0.804774	−	2.47684i	0.0384536	−	0.118348i
$439$	−12.6434	−	38.9123i	−0.603435	−	1.85718i	−0.507211	−	0.861822i	$-0.669323\pi$
$439$	−12.6434	−	38.9123i	−0.603435	−	1.85718i	−0.0962240	−	0.995360i	$-0.530677\pi$
$440$		0			0
$441$	−0.689782	+	2.12293i	−0.0328468	+	0.101092i
$442$	10.6869	+	7.76446i	0.508322	+	0.369318i
$443$	−33.7257			−1.60236			−0.801178	−	0.598425i	$-0.795793\pi$
$443$	−33.7257			−1.60236			−0.801178	+	0.598425i	$0.795793\pi$
$444$	−12.5864	−	9.14452i	−0.597322	−	0.433980i
$445$		0			0
$446$	−1.55979	+	1.13325i	−0.0738581	+	0.0536610i
$447$	10.6678	−	7.75062i	0.504570	−	0.366592i
$448$	−3.99366	−	12.2912i	−0.188683	−	0.580705i
$449$	−10.2790			−0.485094			−0.242547	−	0.970140i	$-0.577983\pi$
$449$	−10.2790			−0.485094			−0.242547	+	0.970140i	$0.577983\pi$
$450$		0			0
$451$	−2.24764			−0.105837
$452$	1.11315	+	3.42592i	0.0523582	+	0.161142i
$453$	−3.32553	+	2.41614i	−0.156247	+	0.113520i
$454$	4.05874	−	2.94885i	0.190486	−	0.138396i
$455$		0			0
$456$	−4.74897	−	3.45033i	−0.222391	−	0.161576i
$457$	−1.65826			−0.0775703			−0.0387851	−	0.999248i	$-0.512349\pi$
$457$	−1.65826			−0.0775703			−0.0387851	+	0.999248i	$0.512349\pi$
$458$	−21.0695	−	15.3079i	−0.984515	−	0.715292i
$459$	3.63861	−	11.1985i	0.169836	−	0.522701i
$460$		0			0
$461$	2.33968	+	7.20080i	0.108970	+	0.335375i	0.990642	−	0.136488i	$-0.0435816\pi$
$461$	2.33968	+	7.20080i	0.108970	+	0.335375i	−0.881672	+	0.471863i	$0.843582\pi$
$462$	0.236481	−	0.727812i	0.0110021	−	0.0338609i
$463$	−1.28793	+	3.96383i	−0.0598550	+	0.184215i	−0.976513	−	0.215457i	$-0.930876\pi$
$463$	−1.28793	+	3.96383i	−0.0598550	+	0.184215i	0.916658	+	0.399672i	$0.130876\pi$
$464$	0.748792	+	2.30454i	0.0347618	+	0.106986i
$465$		0			0
$466$	3.53137	−	10.8684i	0.163587	−	0.503470i
$467$	−10.9085	−	7.92551i	−0.504787	−	0.366749i	0.306056	−	0.952014i	$-0.400991\pi$
$467$	−10.9085	−	7.92551i	−0.504787	−	0.366749i	−0.810842	+	0.585265i	$0.800991\pi$
$468$	15.1903			0.702170
$469$	−12.7440	−	9.25908i	−0.588464	−	0.427544i
$470$		0			0
$471$	1.37561	−	0.999438i	0.0633847	−	0.0460517i
$472$	−8.39088	+	6.09633i	−0.386222	+	0.280606i
$473$	1.13503	+	3.49327i	0.0521889	+	0.160621i
$474$	−2.05851			−0.0945505
$475$		0			0
$476$	7.55320			0.346200
$477$	7.11714	+	21.9043i	0.325871	+	1.00293i
$478$	−13.9147	+	10.1097i	−0.636446	+	0.462405i
$479$	−12.7796	+	9.28493i	−0.583916	+	0.424239i	−0.840134	−	0.542380i	$-0.817523\pi$
$479$	−12.7796	+	9.28493i	−0.583916	+	0.424239i	0.256218	+	0.966619i	$0.417523\pi$
$480$		0			0
$481$	−11.3013	−	8.21085i	−0.515293	−	0.374382i
$482$	−29.4588			−1.34181
$483$	2.11345	+	1.53551i	0.0961654	+	0.0698682i
$484$	−9.85660	+	30.3355i	−0.448027	+	1.37889i
$485$		0			0
$486$	−11.0602	−	34.0397i	−0.501700	−	1.54407i
$487$	−2.49824	+	7.68880i	−0.113206	+	0.348413i	−0.991569	−	0.129582i	$-0.958636\pi$
$487$	−2.49824	+	7.68880i	−0.113206	+	0.348413i	0.878363	+	0.477995i	$0.158636\pi$
$488$	−6.91476	+	21.2814i	−0.313016	+	0.963365i
$489$	−4.31457	−	13.2789i	−0.195112	−	0.600492i
$490$		0			0
$491$	1.73455	−	5.33838i	0.0782790	−	0.240918i	−0.904258	−	0.426987i	$-0.859575\pi$
$491$	1.73455	−	5.33838i	0.0782790	−	0.240918i	0.982537	+	0.186069i	$0.0595749\pi$
$492$	11.9269	+	8.66538i	0.537705	+	0.390665i
$493$	−5.04867			−0.227381
$494$	−13.3273	−	9.68286i	−0.599624	−	0.435653i
$495$		0			0
$496$	−8.97392	+	6.51994i	−0.402941	+	0.292754i
$497$	9.95930	−	7.23586i	0.446736	−	0.324573i
$498$	8.56120	+	26.3487i	0.383637	+	1.18071i
$499$	10.2308			0.457994			0.228997	−	0.973427i	$-0.426455\pi$
$499$	10.2308			0.457994			0.228997	+	0.973427i	$0.426455\pi$
$500$		0			0
$501$	−9.79636			−0.437669
$502$	9.72689	+	29.9363i	0.434132	+	1.33612i
$503$	−2.13472	+	1.55097i	−0.0951827	+	0.0691542i	−0.634359	−	0.773039i	$-0.718736\pi$
$503$	−2.13472	+	1.55097i	−0.0951827	+	0.0691542i	0.539176	+	0.842193i	$0.318736\pi$
$504$	3.77716	−	2.74427i	0.168248	−	0.122240i
$505$		0			0
$506$	2.10643	+	1.53041i	0.0936421	+	0.0680350i
$507$	6.69968			0.297543
$508$	39.2381	+	28.5081i	1.74091	+	1.26484i
$509$	13.7981	−	42.4661i	0.611589	−	1.88228i	0.168802	−	0.985650i	$-0.446010\pi$
$509$	13.7981	−	42.4661i	0.611589	−	1.88228i	0.442787	−	0.896627i	$-0.353990\pi$
$510$		0			0
$511$	−0.413179	−	1.27164i	−0.0182780	−	0.0562538i
$512$	4.23056	−	13.0203i	0.186966	−	0.575423i
$513$	−4.53762	+	13.9653i	−0.200341	+	0.616585i
$514$	8.42907	+	25.9420i	0.371791	+	1.14425i
$515$		0			0
$516$	7.44475	−	22.9126i	0.327737	−	1.00867i
$517$	0.972589	+	0.706627i	0.0427744	+	0.0310774i
$518$	−13.4193			−0.589609
$519$	11.4232	+	8.29942i	0.501421	+	0.364304i
$520$		0			0
$521$	1.78965	−	1.30025i	0.0784058	−	0.0569651i	−0.547892	−	0.836549i	$-0.684569\pi$
$521$	1.78965	−	1.30025i	0.0784058	−	0.0569651i	0.626298	+	0.779584i	$0.284569\pi$
$522$	−7.89094	+	5.73310i	−0.345377	+	0.250931i
$523$	−5.14494	−	15.8345i	−0.224973	−	0.692394i	−0.998294	−	0.0583807i	$-0.981406\pi$
$523$	−5.14494	−	15.8345i	−0.224973	−	0.692394i	0.773322	−	0.634014i	$-0.218594\pi$
$524$	4.77949			0.208793
$525$		0			0
$526$	9.38633			0.409263
$527$	−7.14176	−	21.9801i	−0.311100	−	0.957467i
$528$	0.343327	−	0.249441i	0.0149414	−	0.0108555i
$529$	11.4167	−	8.29475i	0.496380	−	0.360641i
$530$		0			0
$531$	8.95484	+	6.50607i	0.388607	+	0.282340i
$532$	−9.41939			−0.408382
$533$	10.7091	+	7.78062i	0.463863	+	0.337016i
$534$	−8.45656	+	26.0266i	−0.365951	+	1.12628i
$535$		0			0
$536$	10.1815	+	31.3353i	0.439772	+	1.35348i
$537$	6.48869	−	19.9701i	0.280008	−	0.861775i
$538$	12.9496	−	39.8548i	0.558297	−	1.71826i
$539$	−0.121412	−	0.373666i	−0.00522957	−	0.0160949i
$540$		0			0
$541$	8.15227	−	25.0901i	0.350494	−	1.07871i	−0.608083	−	0.793874i	$-0.708061\pi$
$541$	8.15227	−	25.0901i	0.350494	−	1.07871i	0.958577	−	0.284835i	$-0.0919388\pi$
$542$	38.5029	+	27.9740i	1.65384	+	1.20159i
$543$	−20.3454			−0.873106
$544$	14.3848	+	10.4512i	0.616745	+	0.448091i
$545$		0			0
$546$	−3.64619	+	2.64911i	−0.156042	+	0.113371i
$547$	−29.2929	+	21.2825i	−1.25247	+	0.909975i	−0.998363	−	0.0572008i	$-0.981782\pi$
$547$	−29.2929	+	21.2825i	−1.25247	+	0.909975i	−0.254110	+	0.967175i	$0.581782\pi$
$548$	−10.5650	−	32.5156i	−0.451313	−	1.38900i
$549$	23.8806			1.01920
$550$		0			0
$551$	6.29606			0.268221
$552$	−1.68848	−	5.19661i	−0.0718665	−	0.221182i
$553$	−0.855018	+	0.621207i	−0.0363591	+	0.0264164i
$554$	12.2213	−	8.87929i	0.519233	−	0.377245i
$555$		0			0
$556$	−14.5836	−	10.5956i	−0.618484	−	0.449355i
$557$	−43.3717			−1.83772			−0.918859	−	0.394586i	$-0.870888\pi$
$557$	−43.3717			−1.83772			−0.918859	+	0.394586i	$0.870888\pi$
$558$	−36.1222	−	26.2443i	−1.52918	−	1.11101i
$559$	6.68462	−	20.5731i	0.282729	−	0.870151i
$560$		0			0
$561$	0.273231	+	0.840920i	0.0115358	+	0.0355037i
$562$	2.31631	−	7.12887i	0.0977076	−	0.300713i
$563$	−11.8889	+	36.5904i	−0.501059	+	1.54210i	0.306237	+	0.951955i	$0.400930\pi$
$563$	−11.8889	+	36.5904i	−0.501059	+	1.54210i	−0.807297	+	0.590146i	$0.799070\pi$
$564$	−2.43666	−	7.49928i	−0.102602	−	0.315777i
$565$		0			0
$566$	2.19146	−	6.74461i	0.0921138	−	0.283497i
$567$	−2.16750	−	1.57478i	−0.0910263	−	0.0661345i
$568$	−25.7484			−1.08038
$569$	−18.5065	−	13.4458i	−0.775834	−	0.563677i	0.127892	−	0.991788i	$-0.459179\pi$
$569$	−18.5065	−	13.4458i	−0.775834	−	0.563677i	−0.903726	+	0.428111i	$0.859179\pi$
$570$		0			0
$571$	−28.9909	+	21.0631i	−1.21323	+	0.881463i	−0.995520	−	0.0945506i	$-0.969859\pi$
$571$	−28.9909	+	21.0631i	−1.21323	+	0.881463i	−0.217710	+	0.976014i	$0.569859\pi$
$572$	−2.16307	+	1.57156i	−0.0904426	+	0.0657104i
$573$	−0.139783	−	0.430209i	−0.00583953	−	0.0179722i
$574$	12.7161			0.530762
$575$		0			0
$576$	28.8481			1.20201
$577$	9.29780	+	28.6157i	0.387072	+	1.19129i	0.934966	+	0.354738i	$0.115430\pi$
$577$	9.29780	+	28.6157i	0.387072	+	1.19129i	−0.547893	+	0.836548i	$0.684570\pi$
$578$	18.7095	−	13.5933i	0.778214	−	0.565406i
$579$	−17.2419	+	12.5270i	−0.716550	+	0.520604i
$580$		0			0
$581$	11.5073	+	8.36057i	0.477405	+	0.346855i
$582$	33.1617			1.37460
$583$	−3.27966	−	2.38281i	−0.135830	−	0.0986860i
$584$	−0.864206	+	2.65975i	−0.0357611	+	0.110061i
$585$		0			0
$586$	−0.279446	−	0.860045i	−0.0115438	−	0.0355281i
$587$	4.41371	−	13.5840i	0.182173	−	0.560671i	−0.817715	−	0.575623i	$-0.804760\pi$
$587$	4.41371	−	13.5840i	0.182173	−	0.560671i	0.999888	+	0.0149519i	$0.00475952\pi$
$588$	−0.796346	+	2.45090i	−0.0328407	+	0.101073i
$589$	8.90630	+	27.4108i	0.366978	+	1.12944i
$590$		0			0
$591$	−3.08790	+	9.50357i	−0.127019	+	0.390925i
$592$	−6.02037	−	4.37406i	−0.247436	−	0.179773i
$593$	3.32432			0.136514			0.0682568	−	0.997668i	$-0.478256\pi$
$593$	3.32432			0.136514			0.0682568	+	0.997668i	$0.478256\pi$
$594$	3.23932	+	2.35350i	0.132911	+	0.0965653i
$595$		0			0
$596$	−35.8043	+	26.0134i	−1.46660	+	1.06555i
$597$	−0.649675	+	0.472017i	−0.0265894	+	0.0193184i
$598$	−4.73848	−	14.5836i	−0.193771	−	0.596366i
$599$	6.84699			0.279761			0.139880	−	0.990168i	$-0.455328\pi$
$599$	6.84699			0.279761			0.139880	+	0.990168i	$0.455328\pi$
$600$		0			0
$601$	46.2226			1.88546			0.942729	−	0.333561i	$-0.108250\pi$
$601$	46.2226			1.88546			0.942729	+	0.333561i	$0.108250\pi$
$602$	−6.42150	−	19.7634i	−0.261721	−	0.805494i
$603$	28.4470	−	20.6679i	1.15845	−	0.841663i
$604$	11.1615	−	8.10927i	0.454153	−	0.329961i
$605$		0			0
$606$	20.5155	+	14.9054i	0.833386	+	0.605491i
$607$	11.3032			0.458782			0.229391	−	0.973334i	$-0.426327\pi$
$607$	11.3032			0.458782			0.229391	+	0.973334i	$0.426327\pi$
$608$	−17.9390	−	13.0334i	−0.727521	−	0.528575i
$609$	0.532289	−	1.63822i	0.0215695	−	0.0663840i
$610$		0			0
$611$	−2.18787	−	6.73358i	−0.0885119	−	0.272412i
$612$	−5.21006	+	16.0349i	−0.210604	+	0.648173i
$613$	3.54616	−	10.9140i	0.143228	−	0.440811i	−0.853551	−	0.521010i	$-0.825556\pi$
$613$	3.54616	−	10.9140i	0.143228	−	0.440811i	0.996779	+	0.0801988i	$0.0255555\pi$
$614$	6.46858	+	19.9082i	0.261051	+	0.803431i
$615$		0			0
$616$	−0.253945	+	0.781561i	−0.0102317	+	0.0314900i
$617$	30.8562	+	22.4184i	1.24223	+	0.902530i	0.997745	−	0.0671242i	$-0.0213824\pi$
$617$	30.8562	+	22.4184i	1.24223	+	0.902530i	0.244481	+	0.969654i	$0.421382\pi$
$618$	5.51272			0.221754
$619$	−6.87598	−	4.99569i	−0.276369	−	0.200794i	0.440963	−	0.897525i	$-0.354637\pi$
$619$	−6.87598	−	4.99569i	−0.276369	−	0.200794i	−0.717332	+	0.696731i	$0.754637\pi$
$620$		0			0
$621$	−11.0580	+	8.03408i	−0.443741	+	0.322396i
$622$	−15.2590	+	11.0863i	−0.611831	+	0.444521i
$623$	4.34169	+	13.3623i	0.173946	+	0.535351i
$624$	−2.49930			−0.100052
$625$		0			0
$626$	8.21288			0.328253
$627$	−0.340740	−	1.04869i	−0.0136078	−	0.0418806i
$628$	−4.61695	+	3.35441i	−0.184236	+	0.133855i
$629$	12.5436	−	9.11345i	0.500146	−	0.363377i
$630$		0			0
$631$	21.3561	+	15.5161i	0.850173	+	0.617687i	0.925194	−	0.379495i	$-0.123902\pi$
$631$	21.3561	+	15.5161i	0.850173	+	0.617687i	−0.0750210	+	0.997182i	$0.523902\pi$
$632$	2.21053			0.0879302
$633$	15.7703	+	11.4578i	0.626814	+	0.455407i
$634$	−21.3935	+	65.8423i	−0.849643	+	2.61493i
$635$		0			0
$636$	8.21666	+	25.2883i	0.325812	+	1.00275i
$637$	−0.715037	+	2.20066i	−0.0283308	+	0.0871932i
$638$	0.530520	−	1.63277i	0.0210035	−	0.0646421i
$639$	8.49147	+	26.1341i	0.335918	+	1.03385i
$640$		0			0
$641$	−4.60640	+	14.1770i	−0.181942	+	0.559959i	−0.999882	−	0.0153438i	$-0.995116\pi$
$641$	−4.60640	+	14.1770i	−0.181942	+	0.559959i	0.817941	+	0.575303i	$0.195116\pi$
$642$	−11.1489	−	8.10013i	−0.440011	−	0.319686i
$643$	−23.5452			−0.928534			−0.464267	−	0.885695i	$-0.653682\pi$
$643$	−23.5452			−0.928534			−0.464267	+	0.885695i	$0.653682\pi$
$644$	−7.09337	−	5.15363i	−0.279518	−	0.203082i
$645$		0			0
$646$	14.7924	−	10.7473i	0.581998	−	0.422846i
$647$	19.2974	−	14.0204i	0.758660	−	0.551199i	−0.139839	−	0.990174i	$-0.544659\pi$
$647$	19.2974	−	14.0204i	0.758660	−	0.551199i	0.898499	+	0.438976i	$0.144659\pi$
$648$	1.73166	+	5.32949i	0.0680259	+	0.209362i
$649$	−1.94827			−0.0764762
$650$		0			0
$651$	7.88518			0.309044
$652$	14.4810	+	44.5679i	0.567119	+	1.74541i
$653$	1.97258	−	1.43317i	0.0771932	−	0.0560842i	−0.548519	−	0.836138i	$-0.684808\pi$
$653$	1.97258	−	1.43317i	0.0771932	−	0.0560842i	0.625713	+	0.780054i	$0.284808\pi$
$654$	−2.70809	+	1.96754i	−0.105895	+	0.0769370i
$655$		0			0
$656$	5.70492	+	4.14487i	0.222740	+	0.161830i
$657$	2.98460			0.116440
$658$	−5.50247	−	3.99778i	−0.214508	−	0.155850i
$659$	1.21619	−	3.74306i	0.0473761	−	0.145809i	−0.924570	−	0.381012i	$-0.875576\pi$
$659$	1.21619	−	3.74306i	0.0473761	−	0.145809i	0.971946	+	0.235203i	$0.0755756\pi$
$660$		0			0
$661$	11.9984	+	36.9272i	0.466682	+	1.43630i	0.856854	+	0.515559i	$0.172416\pi$
$661$	11.9984	+	36.9272i	0.466682	+	1.43630i	−0.390172	+	0.920742i	$0.627584\pi$
$662$	−2.91982	+	8.98628i	−0.113482	+	0.349262i
$663$	1.60916	−	4.95248i	0.0624945	−	0.192338i
$664$	−9.19345	−	28.2945i	−0.356775	−	1.09804i
$665$		0			0
$666$	9.25637	−	28.4882i	0.358677	−	1.10389i
$667$	4.74131	+	3.44477i	0.183584	+	0.133382i
$668$	32.8795			1.27215
$669$	0.614878	+	0.446735i	0.0237726	+	0.0172718i
$670$		0			0
$671$	−3.40056	+	2.47065i	−0.131277	+	0.0953785i
$672$	−4.90787	+	3.56578i	−0.189325	+	0.137553i
$673$	11.9867	+	36.8913i	0.462054	+	1.42205i	0.862650	+	0.505800i	$0.168803\pi$
$673$	11.9867	+	36.8913i	0.462054	+	1.42205i	−0.400597	+	0.916254i	$0.631197\pi$
$674$	15.8938			0.612205
$675$		0			0
$676$	−22.4861			−0.864851
$677$	−5.62028	−	17.2975i	−0.216005	−	0.664795i	−0.999081	−	0.0428687i	$-0.986350\pi$
$677$	−5.62028	−	17.2975i	−0.216005	−	0.664795i	0.783076	−	0.621926i	$-0.213650\pi$
$678$	1.93008	−	1.40228i	0.0741242	−	0.0538544i
$679$	13.7740	−	10.0074i	0.528596	−	0.384048i
$680$		0			0
$681$	−1.59998	−	1.16245i	−0.0613114	−	0.0445453i
$682$	7.85897			0.300935
$683$	−9.05213	−	6.57676i	−0.346370	−	0.251653i	0.400974	−	0.916089i	$-0.368672\pi$
$683$	−9.05213	−	6.57676i	−0.346370	−	0.251653i	−0.747345	+	0.664437i	$0.768672\pi$
$684$	6.49733	−	19.9967i	0.248431	−	0.764593i
$685$		0			0
$686$	0.686892	+	2.11404i	0.0262256	+	0.0807142i
$687$	−3.17251	+	9.76399i	−0.121039	+	0.372520i
$688$	3.56101	−	10.9597i	0.135762	−	0.417833i
$689$	7.37772	+	22.7063i	0.281069	+	0.865040i
$690$		0			0
$691$	9.70842	−	29.8795i	0.369326	−	1.13667i	−0.577902	−	0.816106i	$-0.696128\pi$
$691$	9.70842	−	29.8795i	0.369326	−	1.13667i	0.947228	−	0.320562i	$-0.103872\pi$
$692$	−38.3395	−	27.8553i	−1.45745	−	1.05890i
$693$	0.877015			0.0333150
$694$	55.9257	+	40.6324i	2.12291	+	1.54238i
$695$		0			0
$696$	−2.91476	+	2.11769i	−0.110484	+	0.0802710i
$697$	−11.8863	+	8.63593i	−0.450227	+	0.327109i
$698$	−14.5995	−	44.9326i	−0.552599	−	1.70072i
$699$	−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	$0.713950\pi$
$702$	−7.28696	−	22.4270i	−0.275029	−	0.846451i
$703$	−15.6428	+	11.3651i	−0.589979	+	0.428645i
$704$	−4.10794	+	2.98459i	−0.154824	+	0.112486i
$705$		0			0
$706$	43.9674	+	31.9442i	1.65473	+	1.20224i
$707$	13.0194			0.489643
$708$	10.3383	+	7.51119i	0.388536	+	0.282288i
$709$	−5.66249	+	17.4274i	−0.212659	+	0.654498i	0.786652	+	0.617396i	$0.211813\pi$
$709$	−5.66249	+	17.4274i	−0.212659	+	0.654498i	−0.999311	+	0.0371016i	$0.988187\pi$
$710$		0			0
$711$	−0.729003	−	2.24364i	−0.0273398	−	0.0841431i
$712$	9.08108	−	27.9487i	0.340328	−	1.04742i
$713$	−8.29028	+	25.5149i	−0.310474	+	0.955539i
$714$	−1.54582	−	4.75754i	−0.0578508	−	0.178047i
$715$		0			0
$716$	−21.7780	+	67.0257i	−0.813881	+	2.50487i
$717$	5.48528	+	3.98529i	0.204852	+	0.148833i
$718$	47.1332			1.75900
$719$	−2.31422	−	1.68138i	−0.0863058	−	0.0627048i	0.543796	−	0.839218i	$-0.316987\pi$
$719$	−2.31422	−	1.68138i	−0.0863058	−	0.0627048i	−0.630101	+	0.776513i	$0.716987\pi$
$720$		0			0
$721$	2.28975	−	1.66360i	0.0852748	−	0.0619558i
$722$	15.7206	−	11.4217i	0.585061	−	0.425072i
$723$	3.58857	+	11.0445i	0.133460	+	0.410748i
$724$	68.2853			2.53780
$725$		0			0
$726$	21.1247			0.784011
$727$	7.80469	+	24.0204i	0.289460	+	0.890866i	0.985026	+	0.172404i	$0.0551536\pi$
$727$	7.80469	+	24.0204i	0.289460	+	0.890866i	−0.695566	+	0.718462i	$0.744846\pi$
$728$	3.91546	−	2.84475i	0.145117	−	0.105433i
$729$	−4.91212	+	3.56886i	−0.181930	+	0.132180i
$730$		0			0
$731$	19.4244	+	14.1126i	0.718436	+	0.521975i
$732$	27.5699			1.01901
$733$	−3.19164	−	2.31886i	−0.117886	−	0.0856491i	0.527280	−	0.849691i	$-0.323212\pi$
$733$	−3.19164	−	2.31886i	−0.117886	−	0.0856491i	−0.645166	+	0.764042i	$0.723212\pi$
$734$	4.33427	−	13.3395i	0.159981	−	0.492370i
$735$		0			0
$736$	−6.37814	−	19.6299i	−0.235101	−	0.723567i
$737$	−1.91253	+	5.88617i	−0.0704491	+	0.216820i
$738$	−8.77136	+	26.9955i	−0.322878	+	0.993717i
$739$	−4.75260	−	14.6270i	−0.174827	−	0.538063i	0.824798	−	0.565427i	$-0.191289\pi$
$739$	−4.75260	−	14.6270i	−0.174827	−	0.538063i	−0.999626	+	0.0273640i	$0.991289\pi$
$740$		0			0
$741$	−2.00674	+	6.17611i	−0.0737194	+	0.226885i
$742$	18.5548	+	13.4809i	0.681169	+	0.494898i
$743$	2.93096			0.107527			0.0537633	−	0.998554i	$-0.482878\pi$
$743$	2.93096			0.107527			0.0537633	+	0.998554i	$0.482878\pi$
$744$	−13.3428	−	9.69413i	−0.489172	−	0.355404i
$745$		0			0
$746$	−5.76742	+	4.19028i	−0.211160	+	0.153417i
$747$	−25.6864	+	18.6623i	−0.939818	+	0.682818i
$748$	−0.917045	−	2.82237i	−0.0335305	−	0.103196i
$749$	−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	$0.583262\pi$
$752$	−1.16552	−	3.58710i	−0.0425021	−	0.130808i
$753$	10.0386	−	7.29347i	0.365827	−	0.265789i
$754$	−8.17985	+	5.94301i	−0.297893	+	0.216432i
$755$		0			0
$756$	−10.9084	−	7.92539i	−0.396733	−	0.288244i
$757$	0.724796			0.0263432			0.0131716	−	0.999913i	$-0.495807\pi$
$757$	0.724796			0.0263432			0.0131716	+	0.999913i	$0.495807\pi$
$758$	−49.5231	−	35.9806i	−1.79876	−	1.30688i
$759$	0.317172	−	0.976155i	0.0115126	−	0.0354322i
$760$		0			0
$761$	5.57065	+	17.1447i	0.201936	+	0.621495i	0.999825	+	0.0186911i	$0.00594991\pi$
$761$	5.57065	+	17.1447i	0.201936	+	0.621495i	−0.797889	+	0.602804i	$0.794050\pi$
$762$	9.92609	−	30.5494i	0.359584	−	1.10669i
$763$	−0.531071	+	1.63447i	−0.0192261	+	0.0591717i
$764$	0.469154	+	1.44391i	0.0169734	+	0.0522388i
$765$		0			0
$766$	0.467019	−	1.43734i	0.0168741	−	0.0519331i
$767$	9.28271	+	6.74428i	0.335179	+	0.243522i
$768$	6.33544			0.228610
$769$	3.39252	+	2.46481i	0.122337	+	0.0888832i	0.647271	−	0.762260i	$-0.275910\pi$
$769$	3.39252	+	2.46481i	0.122337	+	0.0888832i	−0.524934	+	0.851143i	$0.675910\pi$
$770$		0			0
$771$	8.69919	−	6.32033i	0.313294	−	0.227621i
$772$	57.8690	−	42.0443i	2.08275	−	1.51321i
$773$	2.92962	+	9.01645i	0.105371	+	0.324299i	0.989817	−	0.142343i	$-0.0454636\pi$
$773$	2.92962	+	9.01645i	0.105371	+	0.324299i	−0.884446	+	0.466642i	$0.845464\pi$
$774$	46.3856			1.66730
$775$		0			0
$776$	−35.6107			−1.27835
$777$	1.63469	+	5.03105i	0.0586441	+	0.180488i
$778$	−33.8182	+	24.5703i	−1.21244	+	0.880890i
$779$	14.8231	−	10.7696i	0.531094	−	0.385863i
$780$		0			0
$781$	−3.91297	−	2.84294i	−0.140017	−	0.101728i
$782$	17.0197			0.608623
$783$	7.29132	+	5.29745i	0.260570	+	0.189315i
$784$	−0.380912	+	1.17233i	−0.0136040	+	0.0418688i
$785$		0			0
$786$	−0.978160	−	3.01047i	−0.0348898	−	0.107380i
$787$	−6.69952	+	20.6190i	−0.238812	+	0.734988i	0.757781	+	0.652509i	$0.226284\pi$
$787$	−6.69952	+	20.6190i	−0.238812	+	0.734988i	−0.996593	+	0.0824786i	$0.973716\pi$
$788$	10.3639	−	31.8968i	0.369198	−	1.13628i
$789$	−1.14341	−	3.51905i	−0.0407064	−	0.125282i
$790$		0			0
$791$	0.378498	−	1.16490i	0.0134579	−	0.0414190i
$792$	−1.48403	−	1.07821i	−0.0527328	−	0.0383126i
$793$	24.7549			0.879073
$794$	−49.3082	−	35.8245i	−1.74988	−	1.27136i
$795$		0			0
$796$	2.18050	−	1.58423i	0.0772858	−	0.0561515i
$797$	2.38553	−	1.73319i	0.0844996	−	0.0613926i	−0.544733	−	0.838609i	$-0.683369\pi$
$797$	2.38553	−	1.73319i	0.0844996	−	0.0613926i	0.629233	+	0.777217i	$0.283369\pi$
$798$	1.92775	+	5.93301i	0.0682416	+	0.210026i
$799$	7.85841			0.278011
$800$		0			0
$801$	−31.3621			−1.10813
$802$	−14.2794	−	43.9474i	−0.504223	−	1.55184i
$803$	−0.425003	+	0.308782i	−0.0149980	+	0.0108967i
$804$	32.8417	−	23.8609i	1.15824	−	0.841509i
$805$		0			0
$806$	−37.4448	−	27.2052i	−1.31894	−	0.958263i
$807$	−16.5195			−0.581515
$808$	−22.0306	−	16.0062i	−0.775034	−	0.563095i
$809$	−12.0825	+	37.1862i	−0.424799	+	1.30740i	0.478388	+	0.878148i	$0.341221\pi$
$809$	−12.0825	+	37.1862i	−0.424799	+	1.30740i	−0.903187	+	0.429247i	$0.858779\pi$
$810$		0			0
$811$	3.25685	+	10.0236i	0.114363	+	0.351975i	0.991814	−	0.127693i	$-0.0407572\pi$
$811$	3.25685	+	10.0236i	0.114363	+	0.351975i	−0.877450	+	0.479668i	$0.840757\pi$
$812$	−1.78652	+	5.49835i	−0.0626946	+	0.192954i
$813$	5.79752	−	17.8429i	0.203328	−	0.625779i
$814$	1.62926	+	5.01433i	0.0571054	+	0.175752i
$815$		0			0
$816$	0.857226	−	2.63827i	0.0300089	−	0.0923580i
$817$	−24.2236	−	17.5995i	−0.847478	−	0.615728i
$818$	−74.2707			−2.59681
$819$	−4.17862	−	3.03595i	−0.146013	−	0.106085i
$820$		0			0
$821$	16.3552	−	11.8827i	0.570799	−	0.414710i	−0.264596	−	0.964359i	$-0.585239\pi$
$821$	16.3552	−	11.8827i	0.570799	−	0.414710i	0.835395	+	0.549649i	$0.185239\pi$
$822$	−18.3185	+	13.3091i	−0.638930	+	0.464210i
$823$	−14.4022	−	44.3253i	−0.502028	−	1.54508i	−0.805710	−	0.592310i	$-0.798216\pi$
$823$	−14.4022	−	44.3253i	−0.502028	−	1.54508i	0.303682	−	0.952773i	$-0.401784\pi$
$824$	−5.91984			−0.206227
$825$		0			0
$826$	11.0224			0.383519
$827$	13.7913	+	42.4453i	0.479571	+	1.47597i	0.839693	+	0.543062i	$0.182735\pi$
$827$	13.7913	+	42.4453i	0.479571	+	1.47597i	−0.360122	+	0.932905i	$0.617265\pi$
$828$	15.8337	−	11.5038i	0.550258	−	0.399786i
$829$	23.8942	−	17.3602i	0.829880	−	0.602943i	−0.0896454	−	0.995974i	$-0.528573\pi$
$829$	23.8942	−	17.3602i	0.829880	−	0.602943i	0.919525	+	0.393031i	$0.128573\pi$
$830$		0			0
$831$	−4.81771	−	3.50027i	−0.167125	−	0.121423i
$832$	29.9043			1.03675
$833$	−2.07778	−	1.50959i	−0.0719907	−	0.0523043i
$834$	−3.68923	+	11.3543i	−0.127748	+	0.393167i
$835$		0			0
$836$	1.14362	+	3.51971i	0.0395530	+	0.121732i
$837$	−12.7490	+	39.2374i	−0.440670	+	1.35624i
$838$	11.2467	−	34.6139i	0.388512	−	1.19572i
$839$	−7.63057	−	23.4845i	−0.263436	−	0.810774i	−0.992049	−	0.125849i	$-0.959835\pi$
$839$	−7.63057	−	23.4845i	−0.263436	−	0.810774i	0.728613	−	0.684926i	$-0.240165\pi$
$840$		0			0
$841$	−7.76736	+	23.9055i	−0.267840	+	0.824326i
$842$	−47.9597	−	34.8448i	−1.65280	−	1.20083i
$843$	−2.95487			−0.101771
$844$	−52.9298	−	38.4558i	−1.82192	−	1.32370i
$845$		0			0
$846$	12.2825	−	8.92376i	0.422281	−	0.306805i
$847$	8.77430	−	6.37490i	0.301489	−	0.219044i
$848$	3.93024	+	12.0960i	0.134965	+	0.415379i
$849$	−2.79560			−0.0959446
$850$		0			0
$851$	−17.9982			−0.616969
$852$	9.80332	+	30.1715i	0.335856	+	1.03366i
$853$	20.9435	−	15.2163i	0.717091	−	0.520997i	−0.168362	−	0.985725i	$-0.553848\pi$
$853$	20.9435	−	15.2163i	0.717091	−	0.520997i	0.885454	+	0.464728i	$0.153848\pi$
$854$	19.2388	−	13.9778i	0.658340	−	0.478312i
$855$		0			0
$856$	11.9722	+	8.69832i	0.409202	+	0.297302i
$857$	29.4598			1.00633			0.503164	−	0.864191i	$-0.332169\pi$
$857$	29.4598			1.00633			0.503164	+	0.864191i	$0.332169\pi$
$858$	1.43257	+	1.04082i	0.0489072	+	0.0355332i
$859$	14.5480	−	44.7740i	0.496370	−	1.52767i	−0.318441	−	0.947943i	$-0.603159\pi$
$859$	14.5480	−	44.7740i	0.496370	−	1.52767i	0.814811	−	0.579727i	$-0.196841\pi$
$860$		0			0
$861$	−1.54904	−	4.76744i	−0.0527910	−	0.162474i
$862$	15.4447	−	47.5339i	0.526049	−	1.61901i
$863$	−3.97378	+	12.2300i	−0.135269	+	0.416315i	−0.995632	−	0.0933669i	$-0.970237\pi$
$863$	−3.97378	+	12.2300i	−0.135269	+	0.416315i	0.860363	+	0.509682i	$0.170237\pi$
$864$	−9.80846	−	30.1873i	−0.333691	−	1.02699i
$865$		0			0
$866$	−25.2987	+	77.8614i	−0.859685	+	2.64584i
$867$	−7.37542	−	5.35856i	−0.250482	−	0.181986i
$868$	−26.4650			−0.898280
$869$	0.335933	+	0.244070i	0.0113958	+	0.00827950i
$870$		0			0
$871$	29.4885	−	21.4246i	0.999180	−	0.725946i
$872$	2.90808	−	2.11285i	0.0984801	−	0.0715500i
$873$	11.7439	+	36.1441i	0.397471	+	1.22329i
$874$	−21.2248			−0.717941
$875$		0			0
$876$	3.44568			0.116419
$877$	−6.81587	−	20.9771i	−0.230156	−	0.708346i	−0.997727	−	0.0673828i	$-0.978535\pi$
$877$	−6.81587	−	20.9771i	−0.230156	−	0.708346i	0.767572	−	0.640963i	$-0.221465\pi$
$878$	73.5773	−	53.4570i	2.48311	−	1.80409i
$879$	−0.288401	+	0.209535i	−0.00972751	+	0.00706745i
$880$		0			0
$881$	−1.95911	−	1.42338i	−0.0660042	−	0.0479549i	0.554294	−	0.832321i	$-0.312988\pi$
$881$	−1.95911	−	1.42338i	−0.0660042	−	0.0479549i	−0.620298	+	0.784366i	$0.712988\pi$
$882$	−4.96175			−0.167071
$883$	−8.74201	−	6.35144i	−0.294192	−	0.213743i	0.430892	−	0.902404i	$-0.358199\pi$
$883$	−8.74201	−	6.35144i	−0.294192	−	0.213743i	−0.725084	+	0.688661i	$0.758199\pi$
$884$	−5.40081	+	16.6220i	−0.181649	+	0.559058i
$885$		0			0
$886$	−23.1659	−	71.2973i	−0.778274	−	2.39528i
$887$	8.63470	−	26.5749i	0.289925	−	0.892297i	−0.694954	−	0.719054i	$-0.744575\pi$
$887$	8.63470	−	26.5749i	0.289925	−	0.892297i	0.984879	−	0.173243i	$-0.0554246\pi$
$888$	3.41912	−	10.5230i	0.114738	−	0.353127i
$889$	−5.09616	−	15.6844i	−0.170920	−	0.526036i
$890$		0			0
$891$	−0.325283	+	1.00112i	−0.0108974	+	0.0335387i
$892$	−2.06371	−	1.49938i	−0.0690982	−	0.0502028i
$893$	−9.80002			−0.327945
$894$	23.7127	+	17.2283i	0.793072	+	0.576200i
$895$		0			0
$896$	12.0389	−	8.74676i	0.402191	−	0.292209i
$897$	−4.89033	+	3.55303i	−0.163283	+	0.118632i
$898$	−7.06053	−	21.7301i	−0.235613	−	0.725142i
$899$	17.6896			0.589981
$900$		0			0
$901$	−26.4993			−0.882820
$902$	−1.54389	−	4.75159i	−0.0514058	−	0.158211i
$903$	−6.62728	+	4.81500i	−0.220542	+	0.160233i
$904$	−2.07261	+	1.50584i	−0.0689341	+	0.0500835i
$905$		0			0
$906$	−7.39207	−	5.37066i	−0.245585	−	0.178428i
$907$	−19.6907			−0.653818			−0.326909	−	0.945056i	$-0.606007\pi$
$907$	−19.6907			−0.653818			−0.326909	+	0.945056i	$0.606007\pi$
$908$	5.37001	+	3.90154i	0.178210	+	0.129477i
$909$	−8.98052	+	27.6392i	−0.297865	+	0.916734i
$910$		0			0
$911$	8.32087	+	25.6090i	0.275683	+	0.848464i	0.989038	+	0.147662i	$0.0471746\pi$
$911$	8.32087	+	25.6090i	0.275683	+	0.848464i	−0.713355	+	0.700803i	$0.752825\pi$
$912$	−1.06902	+	3.29012i	−0.0353989	+	0.108947i
$913$	1.72694	−	5.31497i	0.0571534	−	0.175900i
$914$	−1.13905	−	3.50563i	−0.0376763	−	0.115956i
$915$		0			0
$916$	10.6479	−	32.7708i	0.351816	−	1.08278i
$917$	−1.31477	−	0.955236i	−0.0434175	−	0.0315447i
$918$	26.1733			0.863849
$919$	−24.5160	−	17.8119i	−0.808710	−	0.587562i	0.104747	−	0.994499i	$-0.466597\pi$
$919$	−24.5160	−	17.8119i	−0.808710	−	0.587562i	−0.913456	+	0.406937i	$0.866597\pi$
$920$		0			0
$921$	6.67587	−	4.85030i	0.219977	−	0.159823i
$922$	−13.6156	+	9.89234i	−0.448407	+	0.325787i
$923$	8.80237	+	27.0909i	0.289734	+	0.891708i
$924$	1.01250			0.0333089
$925$		0			0
$926$	−9.26434			−0.304445
$927$	1.95228	+	6.00851i	0.0641213	+	0.197345i
$928$	−11.0103	+	7.99946i	−0.361431	+	0.262595i
$929$	−10.6834	+	7.76191i	−0.350509	+	0.254660i	−0.749083	−	0.662477i	$-0.769505\pi$
$929$	−10.6834	+	7.76191i	−0.350509	+	0.254660i	0.398573	+	0.917136i	$0.369505\pi$
$930$		0			0
$931$	2.59114	+	1.88257i	0.0849212	+	0.0616988i
$932$	15.1197			0.495263
$933$	6.01520	+	4.37030i	0.196929	+	0.143077i
$934$	9.26183	−	28.5050i	0.303056	−	0.932712i
$935$		0			0
$936$	3.33839	+	10.2745i	0.109119	+	0.335832i
$937$	4.89777	−	15.0738i	0.160003	−	0.492439i	−0.838630	−	0.544701i	$-0.816643\pi$
$937$	4.89777	−	15.0738i	0.160003	−	0.492439i	0.998633	+	0.0522621i	$0.0166431\pi$
$938$	10.8202	−	33.3013i	0.353294	−	1.08733i
$939$	−1.00046	−	3.07911i	−0.0326489	−	0.100483i
$940$		0			0
$941$	0.922511	−	2.83920i	0.0300730	−	0.0925552i	−0.934893	−	0.354929i	$-0.884505\pi$
$941$	0.922511	−	2.83920i	0.0300730	−	0.0925552i	0.964966	+	0.262373i	$0.0845052\pi$
$942$	3.05774	+	2.22158i	0.0996265	+	0.0723829i
$943$	17.0551			0.555391
$944$	4.94506	+	3.59279i	0.160948	+	0.116935i
$945$		0			0
$946$	−6.60525	+	4.79900i	−0.214755	+	0.156029i
$947$	6.36657	−	4.62559i	0.206886	−	0.150311i	−0.479518	−	0.877532i	$-0.659188\pi$
$947$	6.36657	−	4.62559i	0.206886	−	0.150311i	0.686404	+	0.727221i	$0.259188\pi$
$948$	−0.841626	−	2.59026i	−0.0273347	−	0.0841277i
$949$	3.09387			0.100431
$950$		0			0
$951$	27.2912			0.884977
$952$	1.65998	+	5.10889i	0.0538002	+	0.165580i
$953$	−24.1115	+	17.5180i	−0.781048	+	0.567465i	−0.905293	−	0.424787i	$-0.860349\pi$
$953$	−24.1115	+	17.5180i	−0.781048	+	0.567465i	0.124245	+	0.992252i	$0.460349\pi$
$954$	−41.4177	+	30.0917i	−1.34095	+	0.974256i
$955$		0			0
$956$	−18.4102	−	13.3758i	−0.595429	−	0.432605i
$957$	−0.676773			−0.0218770
$958$	−28.4069	−	20.6388i	−0.917785	−	0.666810i
$959$	−3.59235	+	11.0561i	−0.116003	+	0.357020i
$960$		0			0
$961$	15.4439	+	47.5313i	0.498189	+	1.53327i
$962$	9.59527	−	29.5312i	0.309364	−	0.952125i
$963$	4.88033	−	15.0201i	0.157267	−	0.484017i
$964$	−12.0443	−	37.0685i	−0.387921	−	1.19390i
$965$		0			0
$966$	−1.79441	+	5.52264i	−0.0577344	+	0.177688i
$967$	−44.6081	−	32.4097i	−1.43450	−	1.04222i	−0.989157	−	0.146864i	$-0.953082\pi$
$967$	−44.6081	−	32.4097i	−1.43450	−	1.04222i	−0.445342	−	0.895360i	$-0.646918\pi$
$968$	−22.6847			−0.729115
$969$	−5.83125	−	4.23665i	−0.187327	−	0.136101i
$970$		0			0
$971$	31.4461	−	22.8469i	1.00915	−	0.733193i	0.0451227	−	0.998981i	$-0.485632\pi$
$971$	31.4461	−	22.8469i	1.00915	−	0.733193i	0.964031	+	0.265788i	$0.0856321\pi$
$972$	38.3108	−	27.8344i	1.22882	−	0.892789i
$973$	1.89409	+	5.82941i	0.0607217	+	0.186882i
$974$	−17.9704			−0.575809
$975$		0			0
$976$	13.1874			0.422117
$977$	0.724583	+	2.23004i	0.0231815	+	0.0713452i	0.961978	−	0.273127i	$-0.0880579\pi$
$977$	0.724583	+	2.23004i	0.0231815	+	0.0713452i	−0.938797	+	0.344472i	$0.888058\pi$
$978$	25.1084	−	18.2423i	0.802878	−	0.583325i
$979$	4.46592	−	3.24468i	0.142732	−	0.103701i
$980$		0			0
$981$	−3.10354	−	2.25485i	−0.0990884	−	0.0719919i
$982$	12.4770			0.398156
$983$	33.5869	+	24.4023i	1.07126	+	0.778314i	0.976138	−	0.217152i	$-0.0696767\pi$
$983$	33.5869	+	24.4023i	1.07126	+	0.778314i	0.0951194	+	0.995466i	$0.469677\pi$
$984$	−3.23996	+	9.97159i	−0.103286	+	0.317883i
$985$		0			0
$986$	−3.46789	−	10.6731i	−0.110440	−	0.339900i
$987$	−0.828525	+	2.54994i	−0.0263723	+	0.0811654i
$988$	6.73521	−	20.7289i	0.214276	−	0.659473i
$989$	−8.61263	−	26.5070i	−0.273866	−	0.842872i
$990$		0			0
$991$	−4.89864	+	15.0765i	−0.155610	+	0.478920i	−0.998222	−	0.0596019i	$-0.981017\pi$
$991$	−4.89864	+	15.0765i	−0.155610	+	0.478920i	0.842612	+	0.538521i	$0.181017\pi$
$992$	−50.4018	−	36.6190i	−1.60026	−	1.16266i
$993$	3.72475			0.118201
$994$	22.1378	+	16.0841i	0.702169	+	0.510156i
$995$		0			0
$996$	−29.6547	+	21.5454i	−0.939646	+	0.682693i
$997$	9.57954	−	6.95994i	0.303387	−	0.220424i	−0.425667	−	0.904880i	$-0.639960\pi$
$997$	9.57954	−	6.95994i	0.303387	−	0.220424i	0.729054	+	0.684456i	$0.239960\pi$
$998$	7.02745	+	21.6283i	0.222450	+	0.684631i
$999$	−27.6780			−0.875695

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.13	✓	56	25.22	odd	20
175.2.n.a.169.13	yes	56	5.3	odd	4
875.2.h.d.351.1		56	25.4	even	10
875.2.h.d.526.1		56	5.4	even	2
875.2.h.e.351.14		56	25.21	even	5	inner
875.2.h.e.526.14		56	1.1	even	1	trivial
875.2.n.c.99.2		56	5.2	odd	4
875.2.n.c.274.2		56	25.3	odd	20
4375.2.a.o.1.26		28	25.11	even	5
4375.2.a.p.1.3		28	25.14	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.686892 + 2.11404i) q^{2} +(0.708904 - 0.515049i) q^{3} +(-2.37929 + 1.72866i) q^{4} +(1.57577 + 1.14486i) q^{6} +1.00000 q^{7} +(-1.69214 - 1.22941i) q^{8} +(-0.689782 + 2.12293i) q^{9} +O(q^{10})\)	\(q+(0.686892 + 2.11404i) q^{2} +(0.708904 - 0.515049i) q^{3} +(-2.37929 + 1.72866i) q^{4} +(1.57577 + 1.14486i) q^{6} +1.00000 q^{7} +(-1.69214 - 1.22941i) q^{8} +(-0.689782 + 2.12293i) q^{9} +(-0.121412 - 0.373666i) q^{11} +(-0.796346 + 2.45090i) q^{12} +(-0.715037 + 2.20066i) q^{13} +(0.686892 + 2.11404i) q^{14} +(-0.380912 + 1.17233i) q^{16} +(-2.07778 - 1.50959i) q^{17} -4.96175 q^{18} +(2.59114 + 1.88257i) q^{19} +(0.708904 - 0.515049i) q^{21} +(0.706547 - 0.513337i) q^{22} +(0.921271 + 2.83538i) q^{23} -1.83277 q^{24} -5.14342 q^{26} +(1.41675 + 4.36032i) q^{27} +(-2.37929 + 1.72866i) q^{28} +(1.59035 - 1.15546i) q^{29} +(7.28014 + 5.28933i) q^{31} -6.92319 q^{32} +(-0.278525 - 0.202361i) q^{33} +(1.76412 - 5.42942i) q^{34} +(-2.02862 - 6.24346i) q^{36} +(-1.86554 + 5.74156i) q^{37} +(-2.19999 + 6.77088i) q^{38} +(0.626553 + 1.92833i) q^{39} +(1.76779 - 5.44071i) q^{41} +(1.57577 + 1.14486i) q^{42} -9.34864 q^{43} +(0.934814 + 0.679182i) q^{44} +(-5.36128 + 3.89520i) q^{46} +(-2.47544 + 1.79851i) q^{47} +(0.333776 + 1.02726i) q^{48} +1.00000 q^{49} -2.25046 q^{51} +(-2.10290 - 6.47205i) q^{52} +(8.34740 - 6.06474i) q^{53} +(-8.24472 + 5.99014i) q^{54} +(-1.69214 - 1.22941i) q^{56} +2.80648 q^{57} +(3.53508 + 2.56839i) q^{58} +(1.53233 - 4.71604i) q^{59} +(-3.30596 - 10.1747i) q^{61} +(-6.18116 + 19.0237i) q^{62} +(-0.689782 + 2.12293i) q^{63} +(-3.99366 - 12.2912i) q^{64} +(0.236481 - 0.727812i) q^{66} +(-12.7440 - 9.25908i) q^{67} +7.55320 q^{68} +(2.11345 + 1.53551i) q^{69} +(9.95930 - 7.23586i) q^{71} +(3.77716 - 2.74427i) q^{72} +(-0.413179 - 1.27164i) q^{73} -13.4193 q^{74} -9.41939 q^{76} +(-0.121412 - 0.373666i) q^{77} +(-3.64619 + 2.64911i) q^{78} +(-0.855018 + 0.621207i) q^{79} +(-2.16750 - 1.57478i) q^{81} +12.7161 q^{82} +(11.5073 + 8.36057i) q^{83} +(-0.796346 + 2.45090i) q^{84} +(-6.42150 - 19.7634i) q^{86} +(0.532289 - 1.63822i) q^{87} +(-0.253945 + 0.781561i) q^{88} +(4.34169 + 13.3623i) q^{89} +(-0.715037 + 2.20066i) q^{91} +(-7.09337 - 5.15363i) q^{92} +7.88518 q^{93} +(-5.50247 - 3.99778i) q^{94} +(-4.90787 + 3.56578i) q^{96} +(13.7740 - 10.0074i) q^{97} +(0.686892 + 2.11404i) q^{98} +0.877015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9}+O(q^{10}) \) 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9	\( 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9} + 8 q^{11} + 12 q^{12} + 8 q^{13} + 4 q^{14} - 32 q^{16} + 20 q^{17} - 48 q^{18} - 12 q^{19} + 4 q^{21} + 8 q^{22} + 16 q^{23} + 28 q^{24} + 12 q^{26} + 16 q^{27} - 12 q^{28} + 2 q^{29} + 12 q^{31} - 112 q^{32} + 14 q^{33} - 14 q^{36} + 16 q^{37} + 20 q^{38} + 4 q^{39} + 4 q^{41} - 32 q^{43} - 22 q^{44} - 4 q^{46} + 18 q^{47} + 48 q^{48} + 56 q^{49} - 44 q^{51} - 16 q^{52} + 20 q^{53} - 54 q^{54} + 12 q^{56} - 152 q^{57} - 32 q^{58} + 6 q^{59} - 4 q^{61} - 18 q^{62} - 6 q^{63} - 24 q^{64} - 74 q^{66} + 32 q^{67} - 124 q^{68} + 78 q^{69} - 8 q^{71} + 100 q^{72} + 48 q^{73} - 60 q^{74} + 52 q^{76} + 8 q^{77} - 124 q^{78} - 72 q^{81} - 44 q^{82} - 10 q^{83} + 12 q^{84} - 20 q^{86} - 26 q^{87} + 88 q^{88} - 38 q^{89} + 8 q^{91} + 96 q^{92} - 96 q^{93} - 88 q^{94} - 28 q^{96} + 90 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9 + 8 * q^11 + 12 * q^12 + 8 * q^13 + 4 * q^14 - 32 * q^16 + 20 * q^17 - 48 * q^18 - 12 * q^19 + 4 * q^21 + 8 * q^22 + 16 * q^23 + 28 * q^24 + 12 * q^26 + 16 * q^27 - 12 * q^28 + 2 * q^29 + 12 * q^31 - 112 * q^32 + 14 * q^33 - 14 * q^36 + 16 * q^37 + 20 * q^38 + 4 * q^39 + 4 * q^41 - 32 * q^43 - 22 * q^44 - 4 * q^46 + 18 * q^47 + 48 * q^48 + 56 * q^49 - 44 * q^51 - 16 * q^52 + 20 * q^53 - 54 * q^54 + 12 * q^56 - 152 * q^57 - 32 * q^58 + 6 * q^59 - 4 * q^61 - 18 * q^62 - 6 * q^63 - 24 * q^64 - 74 * q^66 + 32 * q^67 - 124 * q^68 + 78 * q^69 - 8 * q^71 + 100 * q^72 + 48 * q^73 - 60 * q^74 + 52 * q^76 + 8 * q^77 - 124 * q^78 - 72 * q^81 - 44 * q^82 - 10 * q^83 + 12 * q^84 - 20 * q^86 - 26 * q^87 + 88 * q^88 - 38 * q^89 + 8 * q^91 + 96 * q^92 - 96 * q^93 - 88 * q^94 - 28 * q^96 + 90 * q^97 + 4 * q^98 - 60 * q^99

Introduction

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