# Properties

 Label 416.2.w.c.225.3 Level $416$ Weight $2$ Character 416.225 Analytic conductor $3.322$ Analytic rank $0$ Dimension $8$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(225,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("416.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$416 = 2^{5} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 416.w (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$3.32177672409$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.56070144.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13$$ x^8 - 4*x^7 + 16*x^6 - 34*x^5 + 63*x^4 - 74*x^3 + 70*x^2 - 38*x + 13 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 225.3 Root $$0.500000 + 2.19293i$$ of defining polynomial Character $$\chi$$ $$=$$ 416.225 Dual form 416.2.w.c.257.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.619657 - 1.07328i) q^{3} +2.00000i q^{5} +(-4.00552 + 2.31259i) q^{7} +(0.732051 + 1.26795i) q^{9} +O(q^{10})$$ $$q+(0.619657 - 1.07328i) q^{3} +2.00000i q^{5} +(-4.00552 + 2.31259i) q^{7} +(0.732051 + 1.26795i) q^{9} +(1.85897 + 1.07328i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(2.14655 + 1.23931i) q^{15} +(0.232051 + 0.401924i) q^{17} +(-4.00552 + 2.31259i) q^{19} +5.73205i q^{21} +(2.76621 - 4.79122i) q^{23} +1.00000 q^{25} +5.53242 q^{27} +(-1.50000 + 2.59808i) q^{29} -9.25036i q^{31} +(2.30385 - 1.33013i) q^{33} +(-4.62518 - 8.01105i) q^{35} +(6.69615 + 3.86603i) q^{37} +(3.09828 + 3.21983i) q^{39} +(-6.23205 - 3.59808i) q^{41} +(1.85897 + 3.21983i) q^{43} +(-2.53590 + 1.46410i) q^{45} +11.7290i q^{47} +(7.19615 - 12.4641i) q^{49} +0.575167 q^{51} +2.53590 q^{53} +(-2.14655 + 3.71794i) q^{55} +5.73205i q^{57} +(-8.29863 + 4.79122i) q^{59} +(-1.50000 - 2.59808i) q^{61} +(-5.86450 - 3.38587i) q^{63} +(-6.92820 - 2.00000i) q^{65} +(4.00552 + 2.31259i) q^{67} +(-3.42820 - 5.93782i) q^{69} +(5.57691 - 3.21983i) q^{71} -6.00000i q^{73} +(0.619657 - 1.07328i) q^{75} -9.92820 q^{77} -4.29311 q^{79} +(1.23205 - 2.13397i) q^{81} +4.29311i q^{83} +(-0.803848 + 0.464102i) q^{85} +(1.85897 + 3.21983i) q^{87} +(-1.03590 - 0.598076i) q^{89} +(-4.00552 - 16.1881i) q^{91} +(-9.92820 - 5.73205i) q^{93} +(-4.62518 - 8.01105i) q^{95} +(11.8923 - 6.86603i) q^{97} +3.14277i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 8 q^{9}+O(q^{10})$$ 8 * q - 8 * q^9 $$8 q - 8 q^{9} - 8 q^{13} - 12 q^{17} + 8 q^{25} - 12 q^{29} + 60 q^{33} + 12 q^{37} - 36 q^{41} - 48 q^{45} + 16 q^{49} + 48 q^{53} - 12 q^{61} + 28 q^{69} - 24 q^{77} - 4 q^{81} - 48 q^{85} - 36 q^{89} - 24 q^{93} + 12 q^{97}+O(q^{100})$$ 8 * q - 8 * q^9 - 8 * q^13 - 12 * q^17 + 8 * q^25 - 12 * q^29 + 60 * q^33 + 12 * q^37 - 36 * q^41 - 48 * q^45 + 16 * q^49 + 48 * q^53 - 12 * q^61 + 28 * q^69 - 24 * q^77 - 4 * q^81 - 48 * q^85 - 36 * q^89 - 24 * q^93 + 12 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$287$$ $$353$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.619657 1.07328i 0.357759 0.619657i −0.629827 0.776735i $$-0.716874\pi$$
0.987586 + 0.157079i $$0.0502076\pi$$
$$4$$ 0 0
$$5$$ 2.00000i 0.894427i 0.894427 + 0.447214i $$0.147584\pi$$
−0.894427 + 0.447214i $$0.852416\pi$$
$$6$$ 0 0
$$7$$ −4.00552 + 2.31259i −1.51395 + 0.874077i −0.514079 + 0.857743i $$0.671866\pi$$
−0.999867 + 0.0163346i $$0.994800\pi$$
$$8$$ 0 0
$$9$$ 0.732051 + 1.26795i 0.244017 + 0.422650i
$$10$$ 0 0
$$11$$ 1.85897 + 1.07328i 0.560501 + 0.323605i 0.753346 0.657624i $$-0.228438\pi$$
−0.192846 + 0.981229i $$0.561772\pi$$
$$12$$ 0 0
$$13$$ −1.00000 + 3.46410i −0.277350 + 0.960769i
$$14$$ 0 0
$$15$$ 2.14655 + 1.23931i 0.554238 + 0.319989i
$$16$$ 0 0
$$17$$ 0.232051 + 0.401924i 0.0562806 + 0.0974808i 0.892793 0.450467i $$-0.148743\pi$$
−0.836512 + 0.547948i $$0.815409\pi$$
$$18$$ 0 0
$$19$$ −4.00552 + 2.31259i −0.918930 + 0.530545i −0.883294 0.468820i $$-0.844679\pi$$
−0.0356367 + 0.999365i $$0.511346\pi$$
$$20$$ 0 0
$$21$$ 5.73205i 1.25084i
$$22$$ 0 0
$$23$$ 2.76621 4.79122i 0.576795 0.999038i −0.419049 0.907964i $$-0.637637\pi$$
0.995844 0.0910745i $$-0.0290301\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 5.53242 1.06472
$$28$$ 0 0
$$29$$ −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i $$-0.923185\pi$$
0.692480 + 0.721437i $$0.256518\pi$$
$$30$$ 0 0
$$31$$ 9.25036i 1.66141i −0.556710 0.830707i $$-0.687936\pi$$
0.556710 0.830707i $$-0.312064\pi$$
$$32$$ 0 0
$$33$$ 2.30385 1.33013i 0.401048 0.231545i
$$34$$ 0 0
$$35$$ −4.62518 8.01105i −0.781798 1.35411i
$$36$$ 0 0
$$37$$ 6.69615 + 3.86603i 1.10084 + 0.635571i 0.936442 0.350823i $$-0.114098\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 3.09828 + 3.21983i 0.496123 + 0.515586i
$$40$$ 0 0
$$41$$ −6.23205 3.59808i −0.973283 0.561925i −0.0730473 0.997328i $$-0.523272\pi$$
−0.900235 + 0.435403i $$0.856606\pi$$
$$42$$ 0 0
$$43$$ 1.85897 + 3.21983i 0.283490 + 0.491020i 0.972242 0.233978i $$-0.0751743\pi$$
−0.688752 + 0.724997i $$0.741841\pi$$
$$44$$ 0 0
$$45$$ −2.53590 + 1.46410i −0.378029 + 0.218255i
$$46$$ 0 0
$$47$$ 11.7290i 1.71085i 0.517927 + 0.855425i $$0.326704\pi$$
−0.517927 + 0.855425i $$0.673296\pi$$
$$48$$ 0 0
$$49$$ 7.19615 12.4641i 1.02802 1.78059i
$$50$$ 0 0
$$51$$ 0.575167 0.0805396
$$52$$ 0 0
$$53$$ 2.53590 0.348332 0.174166 0.984716i $$-0.444277\pi$$
0.174166 + 0.984716i $$0.444277\pi$$
$$54$$ 0 0
$$55$$ −2.14655 + 3.71794i −0.289441 + 0.501327i
$$56$$ 0 0
$$57$$ 5.73205i 0.759229i
$$58$$ 0 0
$$59$$ −8.29863 + 4.79122i −1.08039 + 0.623763i −0.931002 0.365015i $$-0.881064\pi$$
−0.149388 + 0.988779i $$0.547730\pi$$
$$60$$ 0 0
$$61$$ −1.50000 2.59808i −0.192055 0.332650i 0.753876 0.657017i $$-0.228182\pi$$
−0.945931 + 0.324367i $$0.894849\pi$$
$$62$$ 0 0
$$63$$ −5.86450 3.38587i −0.738857 0.426579i
$$64$$ 0 0
$$65$$ −6.92820 2.00000i −0.859338 0.248069i
$$66$$ 0 0
$$67$$ 4.00552 + 2.31259i 0.489353 + 0.282528i 0.724306 0.689479i $$-0.242160\pi$$
−0.234953 + 0.972007i $$0.575494\pi$$
$$68$$ 0 0
$$69$$ −3.42820 5.93782i −0.412707 0.714830i
$$70$$ 0 0
$$71$$ 5.57691 3.21983i 0.661858 0.382124i −0.131127 0.991366i $$-0.541859\pi$$
0.792984 + 0.609242i $$0.208526\pi$$
$$72$$ 0 0
$$73$$ 6.00000i 0.702247i −0.936329 0.351123i $$-0.885800\pi$$
0.936329 0.351123i $$-0.114200\pi$$
$$74$$ 0 0
$$75$$ 0.619657 1.07328i 0.0715518 0.123931i
$$76$$ 0 0
$$77$$ −9.92820 −1.13142
$$78$$ 0 0
$$79$$ −4.29311 −0.483012 −0.241506 0.970399i $$-0.577641\pi$$
−0.241506 + 0.970399i $$0.577641\pi$$
$$80$$ 0 0
$$81$$ 1.23205 2.13397i 0.136895 0.237108i
$$82$$ 0 0
$$83$$ 4.29311i 0.471230i 0.971846 + 0.235615i $$0.0757104\pi$$
−0.971846 + 0.235615i $$0.924290\pi$$
$$84$$ 0 0
$$85$$ −0.803848 + 0.464102i −0.0871895 + 0.0503389i
$$86$$ 0 0
$$87$$ 1.85897 + 3.21983i 0.199303 + 0.345202i
$$88$$ 0 0
$$89$$ −1.03590 0.598076i −0.109805 0.0633960i 0.444092 0.895981i $$-0.353526\pi$$
−0.553897 + 0.832585i $$0.686860\pi$$
$$90$$ 0 0
$$91$$ −4.00552 16.1881i −0.419893 1.69698i
$$92$$ 0 0
$$93$$ −9.92820 5.73205i −1.02951 0.594386i
$$94$$ 0 0
$$95$$ −4.62518 8.01105i −0.474534 0.821916i
$$96$$ 0 0
$$97$$ 11.8923 6.86603i 1.20748 0.697139i 0.245272 0.969454i $$-0.421123\pi$$
0.962208 + 0.272315i $$0.0877893\pi$$
$$98$$ 0 0
$$99$$ 3.14277i 0.315861i
$$100$$ 0 0
$$101$$ 9.69615 16.7942i 0.964803 1.67109i 0.254660 0.967031i $$-0.418036\pi$$
0.710143 0.704058i $$-0.248630\pi$$
$$102$$ 0 0
$$103$$ 8.58622 0.846025 0.423013 0.906124i $$-0.360973\pi$$
0.423013 + 0.906124i $$0.360973\pi$$
$$104$$ 0 0
$$105$$ −11.4641 −1.11878
$$106$$ 0 0
$$107$$ −1.85897 + 3.21983i −0.179713 + 0.311273i −0.941782 0.336223i $$-0.890850\pi$$
0.762069 + 0.647496i $$0.224184\pi$$
$$108$$ 0 0
$$109$$ 6.00000i 0.574696i −0.957826 0.287348i $$-0.907226\pi$$
0.957826 0.287348i $$-0.0927736\pi$$
$$110$$ 0 0
$$111$$ 8.29863 4.79122i 0.787671 0.454762i
$$112$$ 0 0
$$113$$ 6.23205 + 10.7942i 0.586262 + 1.01544i 0.994717 + 0.102657i $$0.0327344\pi$$
−0.408455 + 0.912779i $$0.633932\pi$$
$$114$$ 0 0
$$115$$ 9.58244 + 5.53242i 0.893567 + 0.515901i
$$116$$ 0 0
$$117$$ −5.12436 + 1.26795i −0.473747 + 0.117222i
$$118$$ 0 0
$$119$$ −1.85897 1.07328i −0.170412 0.0983872i
$$120$$ 0 0
$$121$$ −3.19615 5.53590i −0.290559 0.503263i
$$122$$ 0 0
$$123$$ −7.72347 + 4.45915i −0.696401 + 0.402068i
$$124$$ 0 0
$$125$$ 12.0000i 1.07331i
$$126$$ 0 0
$$127$$ −1.85897 + 3.21983i −0.164957 + 0.285714i −0.936640 0.350293i $$-0.886082\pi$$
0.771683 + 0.636007i $$0.219415\pi$$
$$128$$ 0 0
$$129$$ 4.60770 0.405685
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 10.6962 18.5263i 0.927474 1.60643i
$$134$$ 0 0
$$135$$ 11.0648i 0.952310i
$$136$$ 0 0
$$137$$ −11.4282 + 6.59808i −0.976377 + 0.563712i −0.901174 0.433457i $$-0.857294\pi$$
−0.0752028 + 0.997168i $$0.523960\pi$$
$$138$$ 0 0
$$139$$ 4.00552 + 6.93777i 0.339744 + 0.588454i 0.984384 0.176032i $$-0.0563262\pi$$
−0.644640 + 0.764486i $$0.722993\pi$$
$$140$$ 0 0
$$141$$ 12.5885 + 7.26795i 1.06014 + 0.612072i
$$142$$ 0 0
$$143$$ −5.57691 + 5.36639i −0.466365 + 0.448760i
$$144$$ 0 0
$$145$$ −5.19615 3.00000i −0.431517 0.249136i
$$146$$ 0 0
$$147$$ −8.91829 15.4469i −0.735568 1.27404i
$$148$$ 0 0
$$149$$ 10.0359 5.79423i 0.822173 0.474682i −0.0289923 0.999580i $$-0.509230\pi$$
0.851165 + 0.524898i $$0.175897\pi$$
$$150$$ 0 0
$$151$$ 9.25036i 0.752784i −0.926461 0.376392i $$-0.877165\pi$$
0.926461 0.376392i $$-0.122835\pi$$
$$152$$ 0 0
$$153$$ −0.339746 + 0.588457i −0.0274668 + 0.0475740i
$$154$$ 0 0
$$155$$ 18.5007 1.48601
$$156$$ 0 0
$$157$$ 4.39230 0.350544 0.175272 0.984520i $$-0.443920\pi$$
0.175272 + 0.984520i $$0.443920\pi$$
$$158$$ 0 0
$$159$$ 1.57139 2.72172i 0.124619 0.215847i
$$160$$ 0 0
$$161$$ 25.5885i 2.01665i
$$162$$ 0 0
$$163$$ 21.5990 12.4702i 1.69177 0.976741i 0.738671 0.674066i $$-0.235454\pi$$
0.953094 0.302675i $$-0.0978798\pi$$
$$164$$ 0 0
$$165$$ 2.66025 + 4.60770i 0.207100 + 0.358709i
$$166$$ 0 0
$$167$$ −19.4525 11.2309i −1.50528 0.869072i −0.999981 0.00612500i $$-0.998050\pi$$
−0.505295 0.862947i $$-0.668616\pi$$
$$168$$ 0 0
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ 0 0
$$171$$ −5.86450 3.38587i −0.448469 0.258924i
$$172$$ 0 0
$$173$$ −4.96410 8.59808i −0.377414 0.653700i 0.613271 0.789872i $$-0.289853\pi$$
−0.990685 + 0.136173i $$0.956520\pi$$
$$174$$ 0 0
$$175$$ −4.00552 + 2.31259i −0.302789 + 0.174815i
$$176$$ 0 0
$$177$$ 11.8756i 0.892628i
$$178$$ 0 0
$$179$$ −1.85897 + 3.21983i −0.138946 + 0.240661i −0.927098 0.374819i $$-0.877705\pi$$
0.788152 + 0.615481i $$0.211038\pi$$
$$180$$ 0 0
$$181$$ −16.3923 −1.21843 −0.609215 0.793005i $$-0.708515\pi$$
−0.609215 + 0.793005i $$0.708515\pi$$
$$182$$ 0 0
$$183$$ −3.71794 −0.274838
$$184$$ 0 0
$$185$$ −7.73205 + 13.3923i −0.568472 + 0.984622i
$$186$$ 0 0
$$187$$ 0.996219i 0.0728508i
$$188$$ 0 0
$$189$$ −22.1603 + 12.7942i −1.61192 + 0.930643i
$$190$$ 0 0
$$191$$ 6.48415 + 11.2309i 0.469177 + 0.812638i 0.999379 0.0352331i $$-0.0112174\pi$$
−0.530202 + 0.847871i $$0.677884\pi$$
$$192$$ 0 0
$$193$$ 17.0885 + 9.86603i 1.23005 + 0.710172i 0.967041 0.254620i $$-0.0819505\pi$$
0.263013 + 0.964792i $$0.415284\pi$$
$$194$$ 0 0
$$195$$ −6.43966 + 6.19657i −0.461154 + 0.443745i
$$196$$ 0 0
$$197$$ 20.4282 + 11.7942i 1.45545 + 0.840304i 0.998782 0.0493338i $$-0.0157098\pi$$
0.456667 + 0.889638i $$0.349043\pi$$
$$198$$ 0 0
$$199$$ 6.15208 + 10.6557i 0.436109 + 0.755363i 0.997385 0.0722651i $$-0.0230228\pi$$
−0.561276 + 0.827629i $$0.689689\pi$$
$$200$$ 0 0
$$201$$ 4.96410 2.86603i 0.350141 0.202154i
$$202$$ 0 0
$$203$$ 13.8755i 0.973872i
$$204$$ 0 0
$$205$$ 7.19615 12.4641i 0.502601 0.870531i
$$206$$ 0 0
$$207$$ 8.10003 0.562991
$$208$$ 0 0
$$209$$ −9.92820 −0.686748
$$210$$ 0 0
$$211$$ −13.5880 + 23.5350i −0.935434 + 1.62022i −0.161575 + 0.986860i $$0.551657\pi$$
−0.773859 + 0.633359i $$0.781676\pi$$
$$212$$ 0 0
$$213$$ 7.98076i 0.546833i
$$214$$ 0 0
$$215$$ −6.43966 + 3.71794i −0.439181 + 0.253561i
$$216$$ 0 0
$$217$$ 21.3923 + 37.0526i 1.45220 + 2.51529i
$$218$$ 0 0
$$219$$ −6.43966 3.71794i −0.435152 0.251235i
$$220$$ 0 0
$$221$$ −1.62436 + 0.401924i −0.109266 + 0.0270363i
$$222$$ 0 0
$$223$$ 4.00552 + 2.31259i 0.268230 + 0.154863i 0.628083 0.778146i $$-0.283840\pi$$
−0.359853 + 0.933009i $$0.617173\pi$$
$$224$$ 0 0
$$225$$ 0.732051 + 1.26795i 0.0488034 + 0.0845299i
$$226$$ 0 0
$$227$$ 12.0166 6.93777i 0.797568 0.460476i −0.0450520 0.998985i $$-0.514345\pi$$
0.842620 + 0.538509i $$0.181012\pi$$
$$228$$ 0 0
$$229$$ 0.928203i 0.0613374i 0.999530 + 0.0306687i $$0.00976368\pi$$
−0.999530 + 0.0306687i $$0.990236\pi$$
$$230$$ 0 0
$$231$$ −6.15208 + 10.6557i −0.404777 + 0.701094i
$$232$$ 0 0
$$233$$ −14.5359 −0.952278 −0.476139 0.879370i $$-0.657964\pi$$
−0.476139 + 0.879370i $$0.657964\pi$$
$$234$$ 0 0
$$235$$ −23.4580 −1.53023
$$236$$ 0 0
$$237$$ −2.66025 + 4.60770i −0.172802 + 0.299302i
$$238$$ 0 0
$$239$$ 4.29311i 0.277698i −0.990314 0.138849i $$-0.955660\pi$$
0.990314 0.138849i $$-0.0443403\pi$$
$$240$$ 0 0
$$241$$ 18.6962 10.7942i 1.20433 0.695317i 0.242811 0.970074i $$-0.421930\pi$$
0.961514 + 0.274756i $$0.0885971\pi$$
$$242$$ 0 0
$$243$$ 6.77174 + 11.7290i 0.434407 + 0.752415i
$$244$$ 0 0
$$245$$ 24.9282 + 14.3923i 1.59260 + 0.919491i
$$246$$ 0 0
$$247$$ −4.00552 16.1881i −0.254865 1.03003i
$$248$$ 0 0
$$249$$ 4.60770 + 2.66025i 0.292001 + 0.168587i
$$250$$ 0 0
$$251$$ 12.9238 + 22.3847i 0.815744 + 1.41291i 0.908792 + 0.417248i $$0.137005\pi$$
−0.0930485 + 0.995662i $$0.529661\pi$$
$$252$$ 0 0
$$253$$ 10.2846 5.93782i 0.646588 0.373308i
$$254$$ 0 0
$$255$$ 1.15033i 0.0720368i
$$256$$ 0 0
$$257$$ 0.232051 0.401924i 0.0144749 0.0250713i −0.858697 0.512483i $$-0.828726\pi$$
0.873172 + 0.487412i $$0.162059\pi$$
$$258$$ 0 0
$$259$$ −35.7621 −2.22215
$$260$$ 0 0
$$261$$ −4.39230 −0.271877
$$262$$ 0 0
$$263$$ 12.0166 20.8133i 0.740974 1.28340i −0.211079 0.977469i $$-0.567698\pi$$
0.952052 0.305935i $$-0.0989690\pi$$
$$264$$ 0 0
$$265$$ 5.07180i 0.311558i
$$266$$ 0 0
$$267$$ −1.28380 + 0.741204i −0.0785675 + 0.0453609i
$$268$$ 0 0
$$269$$ −2.30385 3.99038i −0.140468 0.243298i 0.787205 0.616692i $$-0.211527\pi$$
−0.927673 + 0.373394i $$0.878194\pi$$
$$270$$ 0 0
$$271$$ 20.0276 + 11.5630i 1.21659 + 0.702399i 0.964187 0.265222i $$-0.0854454\pi$$
0.252404 + 0.967622i $$0.418779\pi$$
$$272$$ 0 0
$$273$$ −19.8564 5.73205i −1.20176 0.346919i
$$274$$ 0 0
$$275$$ 1.85897 + 1.07328i 0.112100 + 0.0647210i
$$276$$ 0 0
$$277$$ 1.69615 + 2.93782i 0.101912 + 0.176517i 0.912472 0.409138i $$-0.134171\pi$$
−0.810560 + 0.585655i $$0.800837\pi$$
$$278$$ 0 0
$$279$$ 11.7290 6.77174i 0.702196 0.405413i
$$280$$ 0 0
$$281$$ 10.0000i 0.596550i 0.954480 + 0.298275i $$0.0964112\pi$$
−0.954480 + 0.298275i $$0.903589\pi$$
$$282$$ 0 0
$$283$$ 9.87002 17.0954i 0.586712 1.01621i −0.407948 0.913005i $$-0.633755\pi$$
0.994660 0.103209i $$-0.0329112\pi$$
$$284$$ 0 0
$$285$$ −11.4641 −0.679075
$$286$$ 0 0
$$287$$ 33.2835 1.96466
$$288$$ 0 0
$$289$$ 8.39230 14.5359i 0.493665 0.855053i
$$290$$ 0 0
$$291$$ 17.0183i 0.997631i
$$292$$ 0 0
$$293$$ −21.8205 + 12.5981i −1.27477 + 0.735987i −0.975881 0.218301i $$-0.929948\pi$$
−0.298886 + 0.954289i $$0.596615\pi$$
$$294$$ 0 0
$$295$$ −9.58244 16.5973i −0.557911 0.966330i
$$296$$ 0 0
$$297$$ 10.2846 + 5.93782i 0.596774 + 0.344547i
$$298$$ 0 0
$$299$$ 13.8311 + 14.3737i 0.799871 + 0.831250i
$$300$$ 0 0
$$301$$ −14.8923 8.59808i −0.858378 0.495585i
$$302$$ 0 0
$$303$$ −12.0166 20.8133i −0.690334 1.19569i
$$304$$ 0 0
$$305$$ 5.19615 3.00000i 0.297531 0.171780i
$$306$$ 0 0
$$307$$ 5.62140i 0.320830i −0.987050 0.160415i $$-0.948717\pi$$
0.987050 0.160415i $$-0.0512833\pi$$
$$308$$ 0 0
$$309$$ 5.32051 9.21539i 0.302673 0.524245i
$$310$$ 0 0
$$311$$ −18.5007 −1.04908 −0.524540 0.851386i $$-0.675763\pi$$
−0.524540 + 0.851386i $$0.675763\pi$$
$$312$$ 0 0
$$313$$ −8.39230 −0.474361 −0.237181 0.971466i $$-0.576223\pi$$
−0.237181 + 0.971466i $$0.576223\pi$$
$$314$$ 0 0
$$315$$ 6.77174 11.7290i 0.381544 0.660854i
$$316$$ 0 0
$$317$$ 4.00000i 0.224662i 0.993671 + 0.112331i $$0.0358318\pi$$
−0.993671 + 0.112331i $$0.964168\pi$$
$$318$$ 0 0
$$319$$ −5.57691 + 3.21983i −0.312247 + 0.180276i
$$320$$ 0 0
$$321$$ 2.30385 + 3.99038i 0.128588 + 0.222721i
$$322$$ 0 0
$$323$$ −1.85897 1.07328i −0.103436 0.0597187i
$$324$$ 0 0
$$325$$ −1.00000 + 3.46410i −0.0554700 + 0.192154i
$$326$$ 0 0
$$327$$ −6.43966 3.71794i −0.356114 0.205603i
$$328$$ 0 0
$$329$$ −27.1244 46.9808i −1.49541 2.59013i
$$330$$ 0 0
$$331$$ 2.43414 1.40535i 0.133792 0.0772450i −0.431610 0.902060i $$-0.642054\pi$$
0.565402 + 0.824815i $$0.308721\pi$$
$$332$$ 0 0
$$333$$ 11.3205i 0.620360i
$$334$$ 0 0
$$335$$ −4.62518 + 8.01105i −0.252701 + 0.437690i
$$336$$ 0 0
$$337$$ −0.392305 −0.0213702 −0.0106851 0.999943i $$-0.503401\pi$$
−0.0106851 + 0.999943i $$0.503401\pi$$
$$338$$ 0 0
$$339$$ 15.4469 0.838962
$$340$$ 0 0
$$341$$ 9.92820 17.1962i 0.537642 0.931224i
$$342$$ 0 0
$$343$$ 34.1908i 1.84613i
$$344$$ 0 0
$$345$$ 11.8756 6.85641i 0.639363 0.369137i
$$346$$ 0 0
$$347$$ −7.39139 12.8023i −0.396791 0.687262i 0.596537 0.802585i $$-0.296543\pi$$
−0.993328 + 0.115324i $$0.963209\pi$$
$$348$$ 0 0
$$349$$ 8.30385 + 4.79423i 0.444495 + 0.256629i 0.705502 0.708708i $$-0.250721\pi$$
−0.261008 + 0.965337i $$0.584055\pi$$
$$350$$ 0 0
$$351$$ −5.53242 + 19.1649i −0.295299 + 1.02295i
$$352$$ 0 0
$$353$$ −7.96410 4.59808i −0.423886 0.244731i 0.272852 0.962056i $$-0.412033\pi$$
−0.696739 + 0.717325i $$0.745366\pi$$
$$354$$ 0 0
$$355$$ 6.43966 + 11.1538i 0.341782 + 0.591983i
$$356$$ 0 0
$$357$$ −2.30385 + 1.33013i −0.121933 + 0.0703978i
$$358$$ 0 0
$$359$$ 4.29311i 0.226582i 0.993562 + 0.113291i $$0.0361392\pi$$
−0.993562 + 0.113291i $$0.963861\pi$$
$$360$$ 0 0
$$361$$ 1.19615 2.07180i 0.0629554 0.109042i
$$362$$ 0 0
$$363$$ −7.92207 −0.415801
$$364$$ 0 0
$$365$$ 12.0000 0.628109
$$366$$ 0 0
$$367$$ 0.287584 0.498110i 0.0150117 0.0260011i −0.858422 0.512944i $$-0.828555\pi$$
0.873434 + 0.486943i $$0.161888\pi$$
$$368$$ 0 0
$$369$$ 10.5359i 0.548477i
$$370$$ 0 0
$$371$$ −10.1576 + 5.86450i −0.527357 + 0.304469i
$$372$$ 0 0
$$373$$ −4.69615 8.13397i −0.243158 0.421161i 0.718454 0.695574i $$-0.244850\pi$$
−0.961612 + 0.274413i $$0.911517\pi$$
$$374$$ 0 0
$$375$$ 12.8793 + 7.43588i 0.665086 + 0.383987i
$$376$$ 0 0
$$377$$ −7.50000 7.79423i −0.386270 0.401423i
$$378$$ 0 0
$$379$$ −2.43414 1.40535i −0.125033 0.0721880i 0.436179 0.899860i $$-0.356331\pi$$
−0.561212 + 0.827672i $$0.689665\pi$$
$$380$$ 0 0
$$381$$ 2.30385 + 3.99038i 0.118030 + 0.204433i
$$382$$ 0 0
$$383$$ −23.1704 + 13.3774i −1.18395 + 0.683555i −0.956926 0.290334i $$-0.906234\pi$$
−0.227026 + 0.973889i $$0.572900\pi$$
$$384$$ 0 0
$$385$$ 19.8564i 1.01198i
$$386$$ 0 0
$$387$$ −2.72172 + 4.71416i −0.138353 + 0.239634i
$$388$$ 0 0
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 2.56761 0.129849
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 8.58622i 0.432019i
$$396$$ 0 0
$$397$$ −21.6962 + 12.5263i −1.08890 + 0.628676i −0.933283 0.359142i $$-0.883069\pi$$
−0.155616 + 0.987818i $$0.549736\pi$$
$$398$$ 0 0
$$399$$ −13.2559 22.9599i −0.663624 1.14943i
$$400$$ 0 0
$$401$$ −31.1603 17.9904i −1.55607 0.898397i −0.997627 0.0688532i $$-0.978066\pi$$
−0.558442 0.829544i $$-0.688601\pi$$
$$402$$ 0 0
$$403$$ 32.0442 + 9.25036i 1.59624 + 0.460793i
$$404$$ 0 0
$$405$$ 4.26795 + 2.46410i 0.212076 + 0.122442i
$$406$$ 0 0
$$407$$ 8.29863 + 14.3737i 0.411348 + 0.712476i
$$408$$ 0 0
$$409$$ 24.6962 14.2583i 1.22115 0.705029i 0.255984 0.966681i $$-0.417601\pi$$
0.965162 + 0.261652i $$0.0842673\pi$$
$$410$$ 0 0
$$411$$ 16.3542i 0.806692i
$$412$$ 0 0
$$413$$ 22.1603 38.3827i 1.09043 1.88869i
$$414$$ 0 0
$$415$$ −8.58622 −0.421481
$$416$$ 0 0
$$417$$ 9.92820 0.486186
$$418$$ 0 0
$$419$$ 12.0166 20.8133i 0.587048 1.01680i −0.407569 0.913175i $$-0.633623\pi$$
0.994617 0.103623i $$-0.0330434\pi$$
$$420$$ 0 0
$$421$$ 0.928203i 0.0452379i −0.999744 0.0226189i $$-0.992800\pi$$
0.999744 0.0226189i $$-0.00720044\pi$$
$$422$$ 0 0
$$423$$ −14.8718 + 8.58622i −0.723090 + 0.417476i
$$424$$ 0 0
$$425$$ 0.232051 + 0.401924i 0.0112561 + 0.0194962i
$$426$$ 0 0
$$427$$ 12.0166 + 6.93777i 0.581523 + 0.335742i
$$428$$ 0 0
$$429$$ 2.30385 + 9.31089i 0.111231 + 0.449534i
$$430$$ 0 0
$$431$$ −18.4562 10.6557i −0.889006 0.513268i −0.0153885 0.999882i $$-0.504899\pi$$
−0.873617 + 0.486614i $$0.838232\pi$$
$$432$$ 0 0
$$433$$ −6.69615 11.5981i −0.321797 0.557368i 0.659062 0.752088i $$-0.270953\pi$$
−0.980859 + 0.194720i $$0.937620\pi$$
$$434$$ 0 0
$$435$$ −6.43966 + 3.71794i −0.308758 + 0.178262i
$$436$$ 0 0
$$437$$ 25.5885i 1.22406i
$$438$$ 0 0
$$439$$ 9.87002 17.0954i 0.471070 0.815918i −0.528382 0.849007i $$-0.677201\pi$$
0.999452 + 0.0330889i $$0.0105345\pi$$
$$440$$ 0 0
$$441$$ 21.0718 1.00342
$$442$$ 0 0
$$443$$ −40.6304 −1.93041 −0.965205 0.261496i $$-0.915784\pi$$
−0.965205 + 0.261496i $$0.915784\pi$$
$$444$$ 0 0
$$445$$ 1.19615 2.07180i 0.0567031 0.0982126i
$$446$$ 0 0
$$447$$ 14.3617i 0.679287i
$$448$$ 0 0
$$449$$ 32.5526 18.7942i 1.53625 0.886954i 0.537197 0.843457i $$-0.319483\pi$$
0.999054 0.0434975i $$-0.0138501\pi$$
$$450$$ 0 0
$$451$$ −7.72347 13.3774i −0.363684 0.629919i
$$452$$ 0 0
$$453$$ −9.92820 5.73205i −0.466468 0.269315i
$$454$$ 0 0
$$455$$ 32.3763 8.01105i 1.51782 0.375564i
$$456$$ 0 0
$$457$$ −20.8923 12.0622i −0.977301 0.564245i −0.0758467 0.997119i $$-0.524166\pi$$
−0.901454 + 0.432875i $$0.857499\pi$$
$$458$$ 0 0
$$459$$ 1.28380 + 2.22361i 0.0599228 + 0.103789i
$$460$$ 0 0
$$461$$ −2.76795 + 1.59808i −0.128916 + 0.0744298i −0.563071 0.826408i $$-0.690380\pi$$
0.434155 + 0.900838i $$0.357047\pi$$
$$462$$ 0 0
$$463$$ 31.3801i 1.45835i −0.684325 0.729177i $$-0.739903\pi$$
0.684325 0.729177i $$-0.260097\pi$$
$$464$$ 0 0
$$465$$ 11.4641 19.8564i 0.531635 0.920819i
$$466$$ 0 0
$$467$$ −9.25036 −0.428056 −0.214028 0.976828i $$-0.568658\pi$$
−0.214028 + 0.976828i $$0.568658\pi$$
$$468$$ 0 0
$$469$$ −21.3923 −0.987805
$$470$$ 0 0
$$471$$ 2.72172 4.71416i 0.125410 0.217217i
$$472$$ 0 0
$$473$$ 7.98076i 0.366956i
$$474$$ 0 0
$$475$$ −4.00552 + 2.31259i −0.183786 + 0.106109i
$$476$$ 0 0
$$477$$ 1.85641 + 3.21539i 0.0849990 + 0.147223i
$$478$$ 0 0
$$479$$ 9.29485 + 5.36639i 0.424693 + 0.245196i 0.697083 0.716990i $$-0.254481\pi$$
−0.272390 + 0.962187i $$0.587814\pi$$
$$480$$ 0 0
$$481$$ −20.0885 + 19.3301i −0.915955 + 0.881378i
$$482$$ 0 0
$$483$$ 27.4635 + 15.8561i 1.24963 + 0.721476i
$$484$$ 0 0
$$485$$ 13.7321 + 23.7846i 0.623540 + 1.08000i
$$486$$ 0 0
$$487$$ 2.43414 1.40535i 0.110301 0.0636825i −0.443834 0.896109i $$-0.646382\pi$$
0.554136 + 0.832426i $$0.313049\pi$$
$$488$$ 0 0
$$489$$ 30.9090i 1.39775i
$$490$$ 0 0
$$491$$ −6.48415 + 11.2309i −0.292626 + 0.506843i −0.974430 0.224692i $$-0.927862\pi$$
0.681804 + 0.731535i $$0.261196\pi$$
$$492$$ 0 0
$$493$$ −1.39230 −0.0627063
$$494$$ 0 0
$$495$$ −6.28555 −0.282514
$$496$$ 0 0
$$497$$ −14.8923 + 25.7942i −0.668011 + 1.15703i
$$498$$ 0 0
$$499$$ 9.25036i 0.414103i −0.978330 0.207052i $$-0.933613\pi$$
0.978330 0.207052i $$-0.0663868\pi$$
$$500$$ 0 0
$$501$$ −24.1077 + 13.9186i −1.07705 + 0.621836i
$$502$$ 0 0
$$503$$ 15.7345 + 27.2530i 0.701567 + 1.21515i 0.967916 + 0.251274i $$0.0808494\pi$$
−0.266349 + 0.963877i $$0.585817\pi$$
$$504$$ 0 0
$$505$$ 33.5885 + 19.3923i 1.49467 + 0.862946i
$$506$$ 0 0
$$507$$ −14.2521 + 7.51294i −0.632958 + 0.333661i
$$508$$ 0 0
$$509$$ −23.5526 13.5981i −1.04395 0.602724i −0.123000 0.992407i $$-0.539251\pi$$
−0.920949 + 0.389683i $$0.872585\pi$$
$$510$$ 0 0
$$511$$ 13.8755 + 24.0331i 0.613818 + 1.06316i
$$512$$ 0 0
$$513$$ −22.1603 + 12.7942i −0.978399 + 0.564879i
$$514$$ 0 0
$$515$$ 17.1724i 0.756708i
$$516$$ 0 0
$$517$$ −12.5885 + 21.8038i −0.553640 + 0.958932i
$$518$$ 0 0
$$519$$ −12.3042 −0.540093
$$520$$ 0 0
$$521$$ 6.24871 0.273761 0.136881 0.990588i $$-0.456292\pi$$
0.136881 + 0.990588i $$0.456292\pi$$
$$522$$ 0 0
$$523$$ 3.43036 5.94155i 0.149999 0.259806i −0.781228 0.624246i $$-0.785406\pi$$
0.931227 + 0.364440i $$0.118740\pi$$
$$524$$ 0 0
$$525$$ 5.73205i 0.250167i
$$526$$ 0 0
$$527$$ 3.71794 2.14655i 0.161956 0.0935054i
$$528$$ 0 0
$$529$$ −3.80385 6.58846i −0.165385 0.286455i
$$530$$ 0 0
$$531$$ −12.1500 7.01483i −0.527267 0.304418i
$$532$$ 0 0
$$533$$ 18.6962 17.9904i 0.809820 0.779250i
$$534$$ 0 0
$$535$$ −6.43966 3.71794i −0.278411 0.160741i
$$536$$ 0 0
$$537$$ 2.30385 + 3.99038i 0.0994184 + 0.172198i
$$538$$ 0 0
$$539$$ 26.7549 15.4469i 1.15241 0.665346i
$$540$$ 0 0
$$541$$ 6.92820i 0.297867i 0.988847 + 0.148933i $$0.0475840\pi$$
−0.988847 + 0.148933i $$0.952416\pi$$
$$542$$ 0 0
$$543$$ −10.1576 + 17.5935i −0.435905 + 0.755009i
$$544$$ 0 0
$$545$$ 12.0000 0.514024
$$546$$ 0 0
$$547$$ 8.58622 0.367120 0.183560 0.983008i $$-0.441238\pi$$
0.183560 + 0.983008i $$0.441238\pi$$
$$548$$ 0 0
$$549$$ 2.19615 3.80385i 0.0937295 0.162344i
$$550$$ 0 0
$$551$$ 13.8755i 0.591118i
$$552$$ 0 0
$$553$$ 17.1962 9.92820i 0.731255 0.422190i
$$554$$ 0 0
$$555$$ 9.58244 + 16.5973i 0.406752 + 0.704515i
$$556$$ 0 0
$$557$$ 19.7487 + 11.4019i 0.836780 + 0.483115i 0.856168 0.516697i $$-0.172839\pi$$
−0.0193886 + 0.999812i $$0.506172\pi$$
$$558$$ 0 0
$$559$$ −13.0128 + 3.21983i −0.550383 + 0.136184i
$$560$$ 0 0
$$561$$ 1.06922 + 0.617314i 0.0451425 + 0.0260630i
$$562$$ 0 0
$$563$$ −19.4525 33.6926i −0.819823 1.41998i −0.905812 0.423679i $$-0.860738\pi$$
0.0859889 0.996296i $$-0.472595\pi$$
$$564$$ 0 0
$$565$$ −21.5885 + 12.4641i −0.908233 + 0.524369i
$$566$$ 0 0
$$567$$ 11.3969i 0.478626i
$$568$$ 0 0
$$569$$ −4.96410 + 8.59808i −0.208106 + 0.360450i −0.951118 0.308828i $$-0.900063\pi$$
0.743012 + 0.669278i $$0.233397\pi$$
$$570$$ 0 0
$$571$$ 23.4580 0.981686 0.490843 0.871248i $$-0.336689\pi$$
0.490843 + 0.871248i $$0.336689\pi$$
$$572$$ 0 0
$$573$$ 16.0718 0.671409
$$574$$ 0 0
$$575$$ 2.76621 4.79122i 0.115359 0.199808i
$$576$$ 0 0
$$577$$ 43.8564i 1.82577i 0.408221 + 0.912883i $$0.366149\pi$$
−0.408221 + 0.912883i $$0.633851\pi$$
$$578$$ 0 0
$$579$$ 21.1780 12.2271i 0.880126 0.508141i
$$580$$ 0 0
$$581$$ −9.92820 17.1962i −0.411891 0.713417i
$$582$$ 0 0
$$583$$ 4.71416 + 2.72172i 0.195241 + 0.112722i
$$584$$ 0 0
$$585$$ −2.53590 10.2487i −0.104846 0.423732i
$$586$$ 0 0
$$587$$ −19.4525 11.2309i −0.802889 0.463548i 0.0415915 0.999135i $$-0.486757\pi$$
−0.844480 + 0.535587i $$0.820091\pi$$
$$588$$ 0 0
$$589$$ 21.3923 + 37.0526i 0.881455 + 1.52672i
$$590$$ 0 0
$$591$$ 25.3170 14.6167i 1.04140 0.601253i
$$592$$ 0 0
$$593$$ 22.7846i 0.935652i 0.883821 + 0.467826i $$0.154963\pi$$
−0.883821 + 0.467826i $$0.845037\pi$$
$$594$$ 0 0
$$595$$ 2.14655 3.71794i 0.0880001 0.152421i
$$596$$ 0 0
$$597$$ 15.2487 0.624088
$$598$$ 0 0
$$599$$ −12.8793 −0.526235 −0.263117 0.964764i $$-0.584751\pi$$
−0.263117 + 0.964764i $$0.584751\pi$$
$$600$$ 0 0
$$601$$ −2.69615 + 4.66987i −0.109978 + 0.190488i −0.915761 0.401723i $$-0.868411\pi$$
0.805783 + 0.592211i $$0.201745\pi$$
$$602$$ 0 0
$$603$$ 6.77174i 0.275766i
$$604$$ 0 0
$$605$$ 11.0718 6.39230i 0.450133 0.259884i
$$606$$ 0 0
$$607$$ −2.43414 4.21605i −0.0987986 0.171124i 0.812389 0.583116i $$-0.198167\pi$$
−0.911188 + 0.411992i $$0.864833\pi$$
$$608$$ 0 0
$$609$$ −14.8923 8.59808i −0.603467 0.348412i
$$610$$ 0 0
$$611$$ −40.6304 11.7290i −1.64373 0.474504i
$$612$$ 0 0
$$613$$ 0.696152 + 0.401924i 0.0281173 + 0.0162335i 0.513993 0.857795i $$-0.328166\pi$$
−0.485875 + 0.874028i $$0.661499\pi$$
$$614$$ 0 0
$$615$$ −8.91829 15.4469i −0.359620 0.622880i
$$616$$ 0 0
$$617$$ 10.0359 5.79423i 0.404030 0.233267i −0.284191 0.958768i $$-0.591725\pi$$
0.688221 + 0.725501i $$0.258392\pi$$
$$618$$ 0 0
$$619$$ 9.25036i 0.371803i −0.982568 0.185902i $$-0.940479\pi$$
0.982568 0.185902i $$-0.0595206\pi$$
$$620$$ 0 0
$$621$$ 15.3038 26.5070i 0.614122 1.06369i
$$622$$ 0 0
$$623$$ 5.53242 0.221652
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ −6.15208 + 10.6557i −0.245690 + 0.425548i
$$628$$ 0 0
$$629$$ 3.58846i 0.143081i
$$630$$ 0 0
$$631$$ 24.7418 14.2847i 0.984955 0.568664i 0.0811925 0.996698i $$-0.474127\pi$$
0.903762 + 0.428034i $$0.140794\pi$$
$$632$$ 0 0
$$633$$ 16.8397 + 29.1673i 0.669320 + 1.15930i
$$634$$ 0 0
$$635$$ −6.43966 3.71794i −0.255550 0.147542i
$$636$$ 0 0
$$637$$ 35.9808 + 37.3923i 1.42561 + 1.48154i
$$638$$ 0 0
$$639$$ 8.16517 + 4.71416i 0.323009 + 0.186489i
$$640$$ 0 0
$$641$$ 9.69615 + 16.7942i 0.382975 + 0.663332i 0.991486 0.130213i $$-0.0415662\pi$$
−0.608511 + 0.793545i $$0.708233\pi$$
$$642$$ 0 0
$$643$$ −26.4673 + 15.2809i −1.04377 + 0.602620i −0.920898 0.389803i $$-0.872543\pi$$
−0.122870 + 0.992423i $$0.539210\pi$$
$$644$$ 0 0
$$645$$ 9.21539i 0.362856i
$$646$$ 0 0
$$647$$ 5.57691 9.65949i 0.219251 0.379754i −0.735328 0.677711i $$-0.762972\pi$$
0.954579 + 0.297957i $$0.0963053\pi$$
$$648$$ 0 0
$$649$$ −20.5692 −0.807412
$$650$$ 0 0
$$651$$ 53.0236 2.07816
$$652$$ 0 0
$$653$$ −7.62436 + 13.2058i −0.298364 + 0.516782i −0.975762 0.218835i $$-0.929774\pi$$
0.677398 + 0.735617i $$0.263108\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 7.60770 4.39230i 0.296804 0.171360i
$$658$$ 0 0
$$659$$ 3.67345 + 6.36260i 0.143097 + 0.247852i 0.928661 0.370928i $$-0.120960\pi$$
−0.785564 + 0.618780i $$0.787627\pi$$
$$660$$ 0 0
$$661$$ −11.3038 6.52628i −0.439669 0.253843i 0.263788 0.964581i $$-0.415028\pi$$
−0.703457 + 0.710738i $$0.748361\pi$$
$$662$$ 0 0
$$663$$ −0.575167 + 1.99244i −0.0223377 + 0.0773799i
$$664$$ 0 0
$$665$$ 37.0526 + 21.3923i 1.43684 + 0.829558i
$$666$$ 0 0
$$667$$ 8.29863 + 14.3737i 0.321324 + 0.556550i
$$668$$ 0 0
$$669$$ 4.96410 2.86603i 0.191923 0.110807i
$$670$$ 0 0
$$671$$ 6.43966i 0.248600i
$$672$$ 0 0
$$673$$ −11.8923 + 20.5981i −0.458415 + 0.793997i −0.998877 0.0473705i $$-0.984916\pi$$
0.540463 + 0.841368i $$0.318249\pi$$
$$674$$ 0 0
$$675$$ 5.53242 0.212943
$$676$$ 0 0
$$677$$ 9.46410 0.363735 0.181867 0.983323i $$-0.441786\pi$$
0.181867 + 0.983323i $$0.441786\pi$$
$$678$$ 0 0
$$679$$ −31.7566 + 55.0041i −1.21871 + 2.11086i
$$680$$ 0 0
$$681$$ 17.1962i 0.658958i
$$682$$ 0 0
$$683$$ −8.29863 + 4.79122i −0.317538 + 0.183331i −0.650295 0.759682i $$-0.725355\pi$$
0.332756 + 0.943013i $$0.392021\pi$$
$$684$$ 0 0
$$685$$ −13.1962 22.8564i −0.504199 0.873298i
$$686$$ 0 0
$$687$$ 0.996219 + 0.575167i 0.0380081 + 0.0219440i
$$688$$ 0 0
$$689$$ −2.53590 + 8.78461i −0.0966100 + 0.334667i
$$690$$ 0 0
$$691$$ −34.4783 19.9061i −1.31162 0.757263i −0.329254 0.944241i $$-0.606797\pi$$
−0.982364 + 0.186979i $$0.940130\pi$$
$$692$$ 0 0
$$693$$ −7.26795 12.5885i −0.276087 0.478196i
$$694$$ 0 0
$$695$$ −13.8755 + 8.01105i −0.526329 + 0.303876i
$$696$$ 0 0
$$697$$ 3.33975i 0.126502i
$$698$$ 0 0
$$699$$ −9.00727 + 15.6010i −0.340686 + 0.590086i
$$700$$ 0 0
$$701$$ 32.1051 1.21259 0.606297 0.795238i $$-0.292654\pi$$
0.606297 + 0.795238i $$0.292654\pi$$
$$702$$ 0 0
$$703$$ −35.7621 −1.34879
$$704$$ 0 0
$$705$$ −14.5359 + 25.1769i −0.547454 + 0.948217i
$$706$$ 0 0
$$707$$ 89.6929i 3.37325i
$$708$$ 0 0
$$709$$ −23.3038 + 13.4545i −0.875194 + 0.505294i −0.869071 0.494688i $$-0.835283\pi$$
−0.00612347 + 0.999981i $$0.501949\pi$$
$$710$$ 0 0
$$711$$ −3.14277 5.44344i −0.117863 0.204145i
$$712$$ 0 0
$$713$$ −44.3205 25.5885i −1.65982 0.958295i
$$714$$ 0 0
$$715$$ −10.7328 11.1538i −0.401383 0.417129i
$$716$$ 0 0
$$717$$ −4.60770 2.66025i −0.172078 0.0993490i
$$718$$ 0 0
$$719$$ 6.48415 + 11.2309i 0.241818 + 0.418841i 0.961232 0.275740i $$-0.0889229\pi$$
−0.719414 + 0.694581i $$0.755590\pi$$
$$720$$ 0 0
$$721$$ −34.3923 + 19.8564i −1.28084 + 0.739491i
$$722$$ 0 0
$$723$$ 26.7549i 0.995024i
$$724$$ 0 0
$$725$$ −1.50000 + 2.59808i −0.0557086 + 0.0964901i
$$726$$ 0 0
$$727$$ 17.1724 0.636890 0.318445 0.947941i $$-0.396839\pi$$
0.318445 + 0.947941i $$0.396839\pi$$
$$728$$ 0 0
$$729$$ 24.1769 0.895441
$$730$$ 0 0
$$731$$ −0.862751 + 1.49433i −0.0319100 + 0.0552698i
$$732$$ 0 0
$$733$$ 15.7128i 0.580366i −0.956971 0.290183i $$-0.906284\pi$$
0.956971 0.290183i $$-0.0937162\pi$$
$$734$$ 0 0
$$735$$ 30.8939 17.8366i 1.13954 0.657912i
$$736$$ 0 0
$$737$$ 4.96410 + 8.59808i 0.182855 + 0.316714i
$$738$$ 0 0
$$739$$ −31.1814 18.0026i −1.14703 0.662237i −0.198867 0.980027i $$-0.563726\pi$$
−0.948161 + 0.317790i $$0.897059\pi$$
$$740$$ 0 0
$$741$$ −19.8564 5.73205i −0.729443 0.210572i
$$742$$ 0 0
$$743$$ 37.0459 + 21.3885i 1.35908 + 0.784667i 0.989500 0.144530i $$-0.0461671\pi$$
0.369583 + 0.929198i $$0.379500\pi$$
$$744$$ 0 0
$$745$$ 11.5885 + 20.0718i 0.424568 + 0.735374i
$$746$$ 0 0
$$747$$ −5.44344 + 3.14277i −0.199165 + 0.114988i
$$748$$ 0 0
$$749$$ 17.1962i 0.628334i
$$750$$ 0 0
$$751$$ 0.287584 0.498110i 0.0104941 0.0181763i −0.860731 0.509061i $$-0.829993\pi$$
0.871225 + 0.490884i $$0.163326\pi$$
$$752$$ 0 0
$$753$$ 32.0333 1.16736
$$754$$ 0 0
$$755$$ 18.5007 0.673310
$$756$$ 0 0
$$757$$ 11.3038 19.5788i 0.410845 0.711605i −0.584137 0.811655i $$-0.698567\pi$$
0.994982 + 0.100050i $$0.0319003\pi$$
$$758$$ 0 0
$$759$$ 14.7176i 0.534217i
$$760$$ 0 0
$$761$$ −2.76795 + 1.59808i −0.100338 + 0.0579302i −0.549329 0.835606i $$-0.685117\pi$$
0.448991 + 0.893536i $$0.351783\pi$$
$$762$$ 0 0
$$763$$ 13.8755 + 24.0331i 0.502328 + 0.870058i
$$764$$ 0 0
$$765$$ −1.17691 0.679492i −0.0425514 0.0245671i
$$766$$ 0 0
$$767$$ −8.29863 33.5385i −0.299646 1.21101i
$$768$$ 0 0
$$769$$ −36.4808 21.0622i −1.31553 0.759522i −0.332524 0.943095i $$-0.607900\pi$$
−0.983006 + 0.183573i $$0.941234\pi$$
$$770$$ 0 0
$$771$$ −0.287584 0.498110i −0.0103571 0.0179390i
$$772$$ 0 0
$$773$$ 14.5526 8.40192i 0.523419 0.302196i −0.214913 0.976633i $$-0.568947\pi$$
0.738332 + 0.674437i $$0.235614\pi$$
$$774$$ 0 0
$$775$$ 9.25036i 0.332283i
$$776$$ 0 0
$$777$$ −22.1603 + 38.3827i −0.794995 + 1.37697i
$$778$$ 0 0
$$779$$ 33.2835 1.19251
$$780$$ 0 0
$$781$$ 13.8231 0.494629
$$782$$ 0 0
$$783$$ −8.29863 + 14.3737i −0.296569 + 0.513673i
$$784$$ 0 0
$$785$$ 8.78461i 0.313536i
$$786$$ 0 0
$$787$$ −23.3245 + 13.4664i −0.831429 + 0.480026i −0.854342 0.519712i $$-0.826039\pi$$
0.0229126 + 0.999737i $$0.492706\pi$$
$$788$$ 0 0
$$789$$ −14.8923 25.7942i −0.530180 0.918299i
$$790$$ 0