# Properties

 Label 416.2.w.a.225.1 Level $416$ Weight $2$ Character 416.225 Analytic conductor $3.322$ Analytic rank $0$ Dimension $4$ 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: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 225.1 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 416.225 Dual form 416.2.w.a.257.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 1.50000i) q^{3} -3.46410i q^{5} +(-2.59808 + 1.50000i) q^{7} +O(q^{10})$$ $$q+(-0.866025 + 1.50000i) q^{3} -3.46410i q^{5} +(-2.59808 + 1.50000i) q^{7} +(4.33013 + 2.50000i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(5.19615 + 3.00000i) q^{15} +(3.50000 + 6.06218i) q^{17} +(4.33013 - 2.50000i) q^{19} -5.19615i q^{21} +(-2.59808 + 4.50000i) q^{23} -7.00000 q^{25} -5.19615 q^{27} +(2.50000 - 4.33013i) q^{29} +2.00000i q^{31} +(-7.50000 + 4.33013i) q^{33} +(5.19615 + 9.00000i) q^{35} +(4.50000 + 2.59808i) q^{37} +(-4.33013 - 4.50000i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(-2.59808 - 4.50000i) q^{43} +4.00000i q^{47} +(1.00000 - 1.73205i) q^{49} -12.1244 q^{51} +4.00000 q^{53} +(8.66025 - 15.0000i) q^{55} +8.66025i q^{57} +(-6.06218 + 3.50000i) q^{59} +(-1.50000 - 2.59808i) q^{61} +(12.0000 + 3.46410i) q^{65} +(2.59808 + 1.50000i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(6.06218 - 3.50000i) q^{71} -3.46410i q^{73} +(6.06218 - 10.5000i) q^{75} -15.0000 q^{77} +3.46410 q^{79} +(4.50000 - 7.79423i) q^{81} -14.0000i q^{83} +(21.0000 - 12.1244i) q^{85} +(4.33013 + 7.50000i) q^{87} +(1.50000 + 0.866025i) q^{89} +(-2.59808 - 10.5000i) q^{91} +(-3.00000 - 1.73205i) q^{93} +(-8.66025 - 15.0000i) q^{95} +(7.50000 - 4.33013i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q+O(q^{10})$$ 4 * q $$4 q - 4 q^{13} + 14 q^{17} - 28 q^{25} + 10 q^{29} - 30 q^{33} + 18 q^{37} - 6 q^{41} + 4 q^{49} + 16 q^{53} - 6 q^{61} + 48 q^{65} - 18 q^{69} - 60 q^{77} + 18 q^{81} + 84 q^{85} + 6 q^{89} - 12 q^{93} + 30 q^{97}+O(q^{100})$$ 4 * q - 4 * q^13 + 14 * q^17 - 28 * q^25 + 10 * q^29 - 30 * q^33 + 18 * q^37 - 6 * q^41 + 4 * q^49 + 16 * q^53 - 6 * q^61 + 48 * q^65 - 18 * q^69 - 60 * q^77 + 18 * q^81 + 84 * q^85 + 6 * q^89 - 12 * q^93 + 30 * 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
$$3$$ −0.866025 + 1.50000i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$4$$ 0 0
$$5$$ 3.46410i 1.54919i −0.632456 0.774597i $$-0.717953\pi$$
0.632456 0.774597i $$-0.282047\pi$$
$$6$$ 0 0
$$7$$ −2.59808 + 1.50000i −0.981981 + 0.566947i −0.902867 0.429919i $$-0.858542\pi$$
−0.0791130 + 0.996866i $$0.525209\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 4.33013 + 2.50000i 1.30558 + 0.753778i 0.981356 0.192201i $$-0.0615626\pi$$
0.324227 + 0.945979i $$0.394896\pi$$
$$12$$ 0 0
$$13$$ −1.00000 + 3.46410i −0.277350 + 0.960769i
$$14$$ 0 0
$$15$$ 5.19615 + 3.00000i 1.34164 + 0.774597i
$$16$$ 0 0
$$17$$ 3.50000 + 6.06218i 0.848875 + 1.47029i 0.882213 + 0.470850i $$0.156053\pi$$
−0.0333386 + 0.999444i $$0.510614\pi$$
$$18$$ 0 0
$$19$$ 4.33013 2.50000i 0.993399 0.573539i 0.0871106 0.996199i $$-0.472237\pi$$
0.906289 + 0.422659i $$0.138903\pi$$
$$20$$ 0 0
$$21$$ 5.19615i 1.13389i
$$22$$ 0 0
$$23$$ −2.59808 + 4.50000i −0.541736 + 0.938315i 0.457068 + 0.889432i $$0.348900\pi$$
−0.998805 + 0.0488832i $$0.984434\pi$$
$$24$$ 0 0
$$25$$ −7.00000 −1.40000
$$26$$ 0 0
$$27$$ −5.19615 −1.00000
$$28$$ 0 0
$$29$$ 2.50000 4.33013i 0.464238 0.804084i −0.534928 0.844897i $$-0.679661\pi$$
0.999167 + 0.0408130i $$0.0129948\pi$$
$$30$$ 0 0
$$31$$ 2.00000i 0.359211i 0.983739 + 0.179605i $$0.0574821\pi$$
−0.983739 + 0.179605i $$0.942518\pi$$
$$32$$ 0 0
$$33$$ −7.50000 + 4.33013i −1.30558 + 0.753778i
$$34$$ 0 0
$$35$$ 5.19615 + 9.00000i 0.878310 + 1.52128i
$$36$$ 0 0
$$37$$ 4.50000 + 2.59808i 0.739795 + 0.427121i 0.821995 0.569495i $$-0.192861\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 0 0
$$39$$ −4.33013 4.50000i −0.693375 0.720577i
$$40$$ 0 0
$$41$$ −1.50000 0.866025i −0.234261 0.135250i 0.378275 0.925693i $$-0.376517\pi$$
−0.612536 + 0.790443i $$0.709851\pi$$
$$42$$ 0 0
$$43$$ −2.59808 4.50000i −0.396203 0.686244i 0.597051 0.802203i $$-0.296339\pi$$
−0.993254 + 0.115960i $$0.963006\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 4.00000i 0.583460i 0.956501 + 0.291730i $$0.0942309\pi$$
−0.956501 + 0.291730i $$0.905769\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.73205i 0.142857 0.247436i
$$50$$ 0 0
$$51$$ −12.1244 −1.69775
$$52$$ 0 0
$$53$$ 4.00000 0.549442 0.274721 0.961524i $$-0.411414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 0 0
$$55$$ 8.66025 15.0000i 1.16775 2.02260i
$$56$$ 0 0
$$57$$ 8.66025i 1.14708i
$$58$$ 0 0
$$59$$ −6.06218 + 3.50000i −0.789228 + 0.455661i −0.839691 0.543065i $$-0.817264\pi$$
0.0504625 + 0.998726i $$0.483930\pi$$
$$60$$ 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
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 12.0000 + 3.46410i 1.48842 + 0.429669i
$$66$$ 0 0
$$67$$ 2.59808 + 1.50000i 0.317406 + 0.183254i 0.650236 0.759733i $$-0.274670\pi$$
−0.332830 + 0.942987i $$0.608004\pi$$
$$68$$ 0 0
$$69$$ −4.50000 7.79423i −0.541736 0.938315i
$$70$$ 0 0
$$71$$ 6.06218 3.50000i 0.719448 0.415374i −0.0951014 0.995468i $$-0.530318\pi$$
0.814550 + 0.580094i $$0.196984\pi$$
$$72$$ 0 0
$$73$$ 3.46410i 0.405442i −0.979236 0.202721i $$-0.935021\pi$$
0.979236 0.202721i $$-0.0649785\pi$$
$$74$$ 0 0
$$75$$ 6.06218 10.5000i 0.700000 1.21244i
$$76$$ 0 0
$$77$$ −15.0000 −1.70941
$$78$$ 0 0
$$79$$ 3.46410 0.389742 0.194871 0.980829i $$-0.437571\pi$$
0.194871 + 0.980829i $$0.437571\pi$$
$$80$$ 0 0
$$81$$ 4.50000 7.79423i 0.500000 0.866025i
$$82$$ 0 0
$$83$$ 14.0000i 1.53670i −0.640030 0.768350i $$-0.721078\pi$$
0.640030 0.768350i $$-0.278922\pi$$
$$84$$ 0 0
$$85$$ 21.0000 12.1244i 2.27777 1.31507i
$$86$$ 0 0
$$87$$ 4.33013 + 7.50000i 0.464238 + 0.804084i
$$88$$ 0 0
$$89$$ 1.50000 + 0.866025i 0.159000 + 0.0917985i 0.577389 0.816469i $$-0.304072\pi$$
−0.418389 + 0.908268i $$0.637405\pi$$
$$90$$ 0 0
$$91$$ −2.59808 10.5000i −0.272352 1.10070i
$$92$$ 0 0
$$93$$ −3.00000 1.73205i −0.311086 0.179605i
$$94$$ 0 0
$$95$$ −8.66025 15.0000i −0.888523 1.53897i
$$96$$ 0 0
$$97$$ 7.50000 4.33013i 0.761510 0.439658i −0.0683279 0.997663i $$-0.521766\pi$$
0.829837 + 0.558005i $$0.188433\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −8.50000 + 14.7224i −0.845782 + 1.46494i 0.0391591 + 0.999233i $$0.487532\pi$$
−0.884941 + 0.465704i $$0.845801\pi$$
$$102$$ 0 0
$$103$$ −6.92820 −0.682656 −0.341328 0.939944i $$-0.610877\pi$$
−0.341328 + 0.939944i $$0.610877\pi$$
$$104$$ 0 0
$$105$$ −18.0000 −1.75662
$$106$$ 0 0
$$107$$ −4.33013 + 7.50000i −0.418609 + 0.725052i −0.995800 0.0915571i $$-0.970816\pi$$
0.577191 + 0.816609i $$0.304149\pi$$
$$108$$ 0 0
$$109$$ 10.3923i 0.995402i 0.867349 + 0.497701i $$0.165822\pi$$
−0.867349 + 0.497701i $$0.834178\pi$$
$$110$$ 0 0
$$111$$ −7.79423 + 4.50000i −0.739795 + 0.427121i
$$112$$ 0 0
$$113$$ −2.50000 4.33013i −0.235180 0.407344i 0.724145 0.689648i $$-0.242235\pi$$
−0.959325 + 0.282304i $$0.908901\pi$$
$$114$$ 0 0
$$115$$ 15.5885 + 9.00000i 1.45363 + 0.839254i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −18.1865 10.5000i −1.66716 0.962533i
$$120$$ 0 0
$$121$$ 7.00000 + 12.1244i 0.636364 + 1.10221i
$$122$$ 0 0
$$123$$ 2.59808 1.50000i 0.234261 0.135250i
$$124$$ 0 0
$$125$$ 6.92820i 0.619677i
$$126$$ 0 0
$$127$$ 9.52628 16.5000i 0.845321 1.46414i −0.0400219 0.999199i $$-0.512743\pi$$
0.885342 0.464939i $$-0.153924\pi$$
$$128$$ 0 0
$$129$$ 9.00000 0.792406
$$130$$ 0 0
$$131$$ −13.8564 −1.21064 −0.605320 0.795982i $$-0.706955\pi$$
−0.605320 + 0.795982i $$0.706955\pi$$
$$132$$ 0 0
$$133$$ −7.50000 + 12.9904i −0.650332 + 1.12641i
$$134$$ 0 0
$$135$$ 18.0000i 1.54919i
$$136$$ 0 0
$$137$$ −4.50000 + 2.59808i −0.384461 + 0.221969i −0.679757 0.733437i $$-0.737915\pi$$
0.295296 + 0.955406i $$0.404582\pi$$
$$138$$ 0 0
$$139$$ −4.33013 7.50000i −0.367277 0.636142i 0.621862 0.783127i $$-0.286376\pi$$
−0.989139 + 0.146985i $$0.953043\pi$$
$$140$$ 0 0
$$141$$ −6.00000 3.46410i −0.505291 0.291730i
$$142$$ 0 0
$$143$$ −12.9904 + 12.5000i −1.08631 + 1.04530i
$$144$$ 0 0
$$145$$ −15.0000 8.66025i −1.24568 0.719195i
$$146$$ 0 0
$$147$$ 1.73205 + 3.00000i 0.142857 + 0.247436i
$$148$$ 0 0
$$149$$ 7.50000 4.33013i 0.614424 0.354738i −0.160271 0.987073i $$-0.551237\pi$$
0.774695 + 0.632335i $$0.217903\pi$$
$$150$$ 0 0
$$151$$ 2.00000i 0.162758i 0.996683 + 0.0813788i $$0.0259324\pi$$
−0.996683 + 0.0813788i $$0.974068\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.92820 0.556487
$$156$$ 0 0
$$157$$ −8.00000 −0.638470 −0.319235 0.947676i $$-0.603426\pi$$
−0.319235 + 0.947676i $$0.603426\pi$$
$$158$$ 0 0
$$159$$ −3.46410 + 6.00000i −0.274721 + 0.475831i
$$160$$ 0 0
$$161$$ 15.5885i 1.22854i
$$162$$ 0 0
$$163$$ 16.4545 9.50000i 1.28881 0.744097i 0.310372 0.950615i $$-0.399546\pi$$
0.978443 + 0.206518i $$0.0662131\pi$$
$$164$$ 0 0
$$165$$ 15.0000 + 25.9808i 1.16775 + 2.02260i
$$166$$ 0 0
$$167$$ 16.4545 + 9.50000i 1.27329 + 0.735132i 0.975605 0.219533i $$-0.0704535\pi$$
0.297681 + 0.954665i $$0.403787\pi$$
$$168$$ 0 0
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3.50000 6.06218i −0.266100 0.460899i 0.701751 0.712422i $$-0.252402\pi$$
−0.967851 + 0.251523i $$0.919068\pi$$
$$174$$ 0 0
$$175$$ 18.1865 10.5000i 1.37477 0.793725i
$$176$$ 0 0
$$177$$ 12.1244i 0.911322i
$$178$$ 0 0
$$179$$ 9.52628 16.5000i 0.712028 1.23327i −0.252067 0.967710i $$-0.581110\pi$$
0.964095 0.265558i $$-0.0855562\pi$$
$$180$$ 0 0
$$181$$ 12.0000 0.891953 0.445976 0.895045i $$-0.352856\pi$$
0.445976 + 0.895045i $$0.352856\pi$$
$$182$$ 0 0
$$183$$ 5.19615 0.384111
$$184$$ 0 0
$$185$$ 9.00000 15.5885i 0.661693 1.14609i
$$186$$ 0 0
$$187$$ 35.0000i 2.55945i
$$188$$ 0 0
$$189$$ 13.5000 7.79423i 0.981981 0.566947i
$$190$$ 0 0
$$191$$ 6.06218 + 10.5000i 0.438644 + 0.759753i 0.997585 0.0694538i $$-0.0221257\pi$$
−0.558941 + 0.829207i $$0.688792\pi$$
$$192$$ 0 0
$$193$$ 10.5000 + 6.06218i 0.755807 + 0.436365i 0.827788 0.561041i $$-0.189599\pi$$
−0.0719816 + 0.997406i $$0.522932\pi$$
$$194$$ 0 0
$$195$$ −15.5885 + 15.0000i −1.11631 + 1.07417i
$$196$$ 0 0
$$197$$ 1.50000 + 0.866025i 0.106871 + 0.0617018i 0.552483 0.833524i $$-0.313681\pi$$
−0.445612 + 0.895226i $$0.647014\pi$$
$$198$$ 0 0
$$199$$ 0.866025 + 1.50000i 0.0613909 + 0.106332i 0.895087 0.445891i $$-0.147113\pi$$
−0.833696 + 0.552223i $$0.813780\pi$$
$$200$$ 0 0
$$201$$ −4.50000 + 2.59808i −0.317406 + 0.183254i
$$202$$ 0 0
$$203$$ 15.0000i 1.05279i
$$204$$ 0 0
$$205$$ −3.00000 + 5.19615i −0.209529 + 0.362915i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 25.0000 1.72929
$$210$$ 0 0
$$211$$ 2.59808 4.50000i 0.178859 0.309793i −0.762631 0.646834i $$-0.776093\pi$$
0.941490 + 0.337041i $$0.109426\pi$$
$$212$$ 0 0
$$213$$ 12.1244i 0.830747i
$$214$$ 0 0
$$215$$ −15.5885 + 9.00000i −1.06312 + 0.613795i
$$216$$ 0 0
$$217$$ −3.00000 5.19615i −0.203653 0.352738i
$$218$$ 0 0
$$219$$ 5.19615 + 3.00000i 0.351123 + 0.202721i
$$220$$ 0 0
$$221$$ −24.5000 + 6.06218i −1.64805 + 0.407786i
$$222$$ 0 0
$$223$$ −11.2583 6.50000i −0.753914 0.435272i 0.0731927 0.997318i $$-0.476681\pi$$
−0.827106 + 0.562046i $$0.810015\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −19.9186 + 11.5000i −1.32204 + 0.763282i −0.984054 0.177868i $$-0.943080\pi$$
−0.337989 + 0.941150i $$0.609747\pi$$
$$228$$ 0 0
$$229$$ 24.2487i 1.60240i −0.598397 0.801200i $$-0.704195\pi$$
0.598397 0.801200i $$-0.295805\pi$$
$$230$$ 0 0
$$231$$ 12.9904 22.5000i 0.854704 1.48039i
$$232$$ 0 0
$$233$$ −8.00000 −0.524097 −0.262049 0.965055i $$-0.584398\pi$$
−0.262049 + 0.965055i $$0.584398\pi$$
$$234$$ 0 0
$$235$$ 13.8564 0.903892
$$236$$ 0 0
$$237$$ −3.00000 + 5.19615i −0.194871 + 0.337526i
$$238$$ 0 0
$$239$$ 2.00000i 0.129369i −0.997906 0.0646846i $$-0.979396\pi$$
0.997906 0.0646846i $$-0.0206041\pi$$
$$240$$ 0 0
$$241$$ −7.50000 + 4.33013i −0.483117 + 0.278928i −0.721715 0.692191i $$-0.756646\pi$$
0.238597 + 0.971119i $$0.423312\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −6.00000 3.46410i −0.383326 0.221313i
$$246$$ 0 0
$$247$$ 4.33013 + 17.5000i 0.275519 + 1.11350i
$$248$$ 0 0
$$249$$ 21.0000 + 12.1244i 1.33082 + 0.768350i
$$250$$ 0 0
$$251$$ 7.79423 + 13.5000i 0.491967 + 0.852112i 0.999957 0.00925060i $$-0.00294460\pi$$
−0.507990 + 0.861363i $$0.669611\pi$$
$$252$$ 0 0
$$253$$ −22.5000 + 12.9904i −1.41456 + 0.816698i
$$254$$ 0 0
$$255$$ 42.0000i 2.63014i
$$256$$ 0 0
$$257$$ 11.5000 19.9186i 0.717350 1.24249i −0.244696 0.969600i $$-0.578688\pi$$
0.962046 0.272887i $$-0.0879786\pi$$
$$258$$ 0 0
$$259$$ −15.5885 −0.968620
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0.866025 1.50000i 0.0534014 0.0924940i −0.838089 0.545534i $$-0.816327\pi$$
0.891490 + 0.453040i $$0.149660\pi$$
$$264$$ 0 0
$$265$$ 13.8564i 0.851192i
$$266$$ 0 0
$$267$$ −2.59808 + 1.50000i −0.159000 + 0.0917985i
$$268$$ 0 0
$$269$$ −0.500000 0.866025i −0.0304855 0.0528025i 0.850380 0.526169i $$-0.176372\pi$$
−0.880866 + 0.473366i $$0.843039\pi$$
$$270$$ 0 0
$$271$$ −7.79423 4.50000i −0.473466 0.273356i 0.244224 0.969719i $$-0.421467\pi$$
−0.717689 + 0.696363i $$0.754800\pi$$
$$272$$ 0 0
$$273$$ 18.0000 + 5.19615i 1.08941 + 0.314485i
$$274$$ 0 0
$$275$$ −30.3109 17.5000i −1.82782 1.05529i
$$276$$ 0 0
$$277$$ −4.50000 7.79423i −0.270379 0.468310i 0.698580 0.715532i $$-0.253816\pi$$
−0.968959 + 0.247222i $$0.920482\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 24.2487i 1.44656i 0.690557 + 0.723278i $$0.257366\pi$$
−0.690557 + 0.723278i $$0.742634\pi$$
$$282$$ 0 0
$$283$$ 16.4545 28.5000i 0.978117 1.69415i 0.308879 0.951101i $$-0.400046\pi$$
0.669238 0.743048i $$-0.266621\pi$$
$$284$$ 0 0
$$285$$ 30.0000 1.77705
$$286$$ 0 0
$$287$$ 5.19615 0.306719
$$288$$ 0 0
$$289$$ −16.0000 + 27.7128i −0.941176 + 1.63017i
$$290$$ 0 0
$$291$$ 15.0000i 0.879316i
$$292$$ 0 0
$$293$$ −22.5000 + 12.9904i −1.31446 + 0.758906i −0.982832 0.184503i $$-0.940933\pi$$
−0.331632 + 0.943409i $$0.607599\pi$$
$$294$$ 0 0
$$295$$ 12.1244 + 21.0000i 0.705907 + 1.22267i
$$296$$ 0 0
$$297$$ −22.5000 12.9904i −1.30558 0.753778i
$$298$$ 0 0
$$299$$ −12.9904 13.5000i −0.751253 0.780725i
$$300$$ 0 0
$$301$$ 13.5000 + 7.79423i 0.778127 + 0.449252i
$$302$$ 0 0
$$303$$ −14.7224 25.5000i −0.845782 1.46494i
$$304$$ 0 0
$$305$$ −9.00000 + 5.19615i −0.515339 + 0.297531i
$$306$$ 0 0
$$307$$ 6.00000i 0.342438i −0.985233 0.171219i $$-0.945229\pi$$
0.985233 0.171219i $$-0.0547706\pi$$
$$308$$ 0 0
$$309$$ 6.00000 10.3923i 0.341328 0.591198i
$$310$$ 0 0
$$311$$ 20.7846 1.17859 0.589294 0.807919i $$-0.299406\pi$$
0.589294 + 0.807919i $$0.299406\pi$$
$$312$$ 0 0
$$313$$ 12.0000 0.678280 0.339140 0.940736i $$-0.389864\pi$$
0.339140 + 0.940736i $$0.389864\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6.92820i 0.389127i 0.980890 + 0.194563i $$0.0623290\pi$$
−0.980890 + 0.194563i $$0.937671\pi$$
$$318$$ 0 0
$$319$$ 21.6506 12.5000i 1.21220 0.699866i
$$320$$ 0 0
$$321$$ −7.50000 12.9904i −0.418609 0.725052i
$$322$$ 0 0
$$323$$ 30.3109 + 17.5000i 1.68654 + 0.973726i
$$324$$ 0 0
$$325$$ 7.00000 24.2487i 0.388290 1.34508i
$$326$$ 0 0
$$327$$ −15.5885 9.00000i −0.862044 0.497701i
$$328$$ 0 0
$$329$$ −6.00000 10.3923i −0.330791 0.572946i
$$330$$ 0 0
$$331$$ 12.9904 7.50000i 0.714016 0.412237i −0.0985303 0.995134i $$-0.531414\pi$$
0.812546 + 0.582897i $$0.198081\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 5.19615 9.00000i 0.283896 0.491723i
$$336$$ 0 0
$$337$$ −28.0000 −1.52526 −0.762629 0.646837i $$-0.776092\pi$$
−0.762629 + 0.646837i $$0.776092\pi$$
$$338$$ 0 0
$$339$$ 8.66025 0.470360
$$340$$ 0 0
$$341$$ −5.00000 + 8.66025i −0.270765 + 0.468979i
$$342$$ 0 0
$$343$$ 15.0000i 0.809924i
$$344$$ 0 0
$$345$$ −27.0000 + 15.5885i −1.45363 + 0.839254i
$$346$$ 0 0
$$347$$ 7.79423 + 13.5000i 0.418416 + 0.724718i 0.995780 0.0917687i $$-0.0292521\pi$$
−0.577364 + 0.816487i $$0.695919\pi$$
$$348$$ 0 0
$$349$$ −13.5000 7.79423i −0.722638 0.417215i 0.0930846 0.995658i $$-0.470327\pi$$
−0.815723 + 0.578443i $$0.803661\pi$$
$$350$$ 0 0
$$351$$ 5.19615 18.0000i 0.277350 0.960769i
$$352$$ 0 0
$$353$$ 13.5000 + 7.79423i 0.718532 + 0.414845i 0.814212 0.580567i $$-0.197169\pi$$
−0.0956798 + 0.995412i $$0.530502\pi$$
$$354$$ 0 0
$$355$$ −12.1244 21.0000i −0.643494 1.11456i
$$356$$ 0 0
$$357$$ 31.5000 18.1865i 1.66716 0.962533i
$$358$$ 0 0
$$359$$ 22.0000i 1.16112i −0.814219 0.580558i $$-0.802835\pi$$
0.814219 0.580558i $$-0.197165\pi$$
$$360$$ 0 0
$$361$$ 3.00000 5.19615i 0.157895 0.273482i
$$362$$ 0 0
$$363$$ −24.2487 −1.27273
$$364$$ 0 0
$$365$$ −12.0000 −0.628109
$$366$$ 0 0
$$367$$ −6.06218 + 10.5000i −0.316443 + 0.548096i −0.979743 0.200258i $$-0.935822\pi$$
0.663300 + 0.748354i $$0.269155\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −10.3923 + 6.00000i −0.539542 + 0.311504i
$$372$$ 0 0
$$373$$ 1.50000 + 2.59808i 0.0776671 + 0.134523i 0.902243 0.431228i $$-0.141920\pi$$
−0.824576 + 0.565751i $$0.808586\pi$$
$$374$$ 0 0
$$375$$ −10.3923 6.00000i −0.536656 0.309839i
$$376$$ 0 0
$$377$$ 12.5000 + 12.9904i 0.643783 + 0.669039i
$$378$$ 0 0
$$379$$ −6.06218 3.50000i −0.311393 0.179783i 0.336157 0.941806i $$-0.390873\pi$$
−0.647550 + 0.762023i $$0.724206\pi$$
$$380$$ 0 0
$$381$$ 16.5000 + 28.5788i 0.845321 + 1.46414i
$$382$$ 0 0
$$383$$ −6.06218 + 3.50000i −0.309763 + 0.178842i −0.646820 0.762642i $$-0.723902\pi$$
0.337058 + 0.941484i $$0.390568\pi$$
$$384$$ 0 0
$$385$$ 51.9615i 2.64820i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 14.0000 0.709828 0.354914 0.934899i $$-0.384510\pi$$
0.354914 + 0.934899i $$0.384510\pi$$
$$390$$ 0 0
$$391$$ −36.3731 −1.83947
$$392$$ 0 0
$$393$$ 12.0000 20.7846i 0.605320 1.04844i
$$394$$ 0 0
$$395$$ 12.0000i 0.603786i
$$396$$ 0 0
$$397$$ 28.5000 16.4545i 1.43037 0.825827i 0.433225 0.901286i $$-0.357376\pi$$
0.997149 + 0.0754589i $$0.0240422\pi$$
$$398$$ 0 0
$$399$$ −12.9904 22.5000i −0.650332 1.12641i
$$400$$ 0 0
$$401$$ 28.5000 + 16.4545i 1.42322 + 0.821698i 0.996573 0.0827195i $$-0.0263606\pi$$
0.426649 + 0.904417i $$0.359694\pi$$
$$402$$ 0 0
$$403$$ −6.92820 2.00000i −0.345118 0.0996271i
$$404$$ 0 0
$$405$$ −27.0000 15.5885i −1.34164 0.774597i
$$406$$ 0 0
$$407$$ 12.9904 + 22.5000i 0.643909 + 1.11528i
$$408$$ 0 0
$$409$$ −13.5000 + 7.79423i −0.667532 + 0.385400i −0.795141 0.606425i $$-0.792603\pi$$
0.127609 + 0.991825i $$0.459270\pi$$
$$410$$ 0 0
$$411$$ 9.00000i 0.443937i
$$412$$ 0 0
$$413$$ 10.5000 18.1865i 0.516671 0.894901i
$$414$$ 0 0
$$415$$ −48.4974 −2.38064
$$416$$ 0 0
$$417$$ 15.0000 0.734553
$$418$$ 0 0
$$419$$ 14.7224 25.5000i 0.719238 1.24576i −0.242064 0.970260i $$-0.577824\pi$$
0.961302 0.275496i $$-0.0888422\pi$$
$$420$$ 0 0
$$421$$ 31.1769i 1.51947i −0.650233 0.759735i $$-0.725329\pi$$
0.650233 0.759735i $$-0.274671\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −24.5000 42.4352i −1.18842 2.05841i
$$426$$ 0 0
$$427$$ 7.79423 + 4.50000i 0.377189 + 0.217770i
$$428$$ 0 0
$$429$$ −7.50000 30.3109i −0.362103 1.46342i
$$430$$ 0 0
$$431$$ 32.0429 + 18.5000i 1.54345 + 0.891114i 0.998617 + 0.0525716i $$0.0167418\pi$$
0.544837 + 0.838542i $$0.316592\pi$$
$$432$$ 0 0
$$433$$ −16.5000 28.5788i −0.792939 1.37341i −0.924139 0.382055i $$-0.875216\pi$$
0.131200 0.991356i $$-0.458117\pi$$
$$434$$ 0 0
$$435$$ 25.9808 15.0000i 1.24568 0.719195i
$$436$$ 0 0
$$437$$ 25.9808i 1.24283i
$$438$$ 0 0
$$439$$ 2.59808 4.50000i 0.123999 0.214773i −0.797342 0.603528i $$-0.793761\pi$$
0.921341 + 0.388755i $$0.127095\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −13.8564 −0.658338 −0.329169 0.944271i $$-0.606769\pi$$
−0.329169 + 0.944271i $$0.606769\pi$$
$$444$$ 0 0
$$445$$ 3.00000 5.19615i 0.142214 0.246321i
$$446$$ 0 0
$$447$$ 15.0000i 0.709476i
$$448$$ 0 0
$$449$$ −7.50000 + 4.33013i −0.353947 + 0.204351i −0.666422 0.745575i $$-0.732175\pi$$
0.312475 + 0.949926i $$0.398842\pi$$
$$450$$ 0 0
$$451$$ −4.33013 7.50000i −0.203898 0.353161i
$$452$$ 0 0
$$453$$ −3.00000 1.73205i −0.140952 0.0813788i
$$454$$ 0 0
$$455$$ −36.3731 + 9.00000i −1.70520 + 0.421927i
$$456$$ 0 0
$$457$$ 31.5000 + 18.1865i 1.47351 + 0.850730i 0.999555 0.0298202i $$-0.00949348\pi$$
0.473953 + 0.880550i $$0.342827\pi$$
$$458$$ 0 0
$$459$$ −18.1865 31.5000i −0.848875 1.47029i
$$460$$ 0 0
$$461$$ 4.50000 2.59808i 0.209586 0.121004i −0.391533 0.920164i $$-0.628055\pi$$
0.601119 + 0.799160i $$0.294722\pi$$
$$462$$ 0 0
$$463$$ 18.0000i 0.836531i −0.908325 0.418265i $$-0.862638\pi$$
0.908325 0.418265i $$-0.137362\pi$$
$$464$$ 0 0
$$465$$ −6.00000 + 10.3923i −0.278243 + 0.481932i
$$466$$ 0 0
$$467$$ 38.1051 1.76329 0.881647 0.471909i $$-0.156435\pi$$
0.881647 + 0.471909i $$0.156435\pi$$
$$468$$ 0 0
$$469$$ −9.00000 −0.415581
$$470$$ 0 0
$$471$$ 6.92820 12.0000i 0.319235 0.552931i
$$472$$ 0 0
$$473$$ 25.9808i 1.19460i
$$474$$ 0 0
$$475$$ −30.3109 + 17.5000i −1.39076 + 0.802955i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 14.7224 + 8.50000i 0.672685 + 0.388375i 0.797093 0.603856i $$-0.206370\pi$$
−0.124408 + 0.992231i $$0.539703\pi$$
$$480$$ 0 0
$$481$$ −13.5000 + 12.9904i −0.615547 + 0.592310i
$$482$$ 0 0
$$483$$ 23.3827 + 13.5000i 1.06395 + 0.614271i
$$484$$ 0 0
$$485$$ −15.0000 25.9808i −0.681115 1.17973i
$$486$$ 0 0
$$487$$ 19.9186 11.5000i 0.902597 0.521115i 0.0245553 0.999698i $$-0.492183\pi$$
0.878042 + 0.478584i $$0.158850\pi$$
$$488$$ 0 0
$$489$$ 32.9090i 1.48819i
$$490$$ 0 0
$$491$$ −6.06218 + 10.5000i −0.273582 + 0.473858i −0.969776 0.243995i $$-0.921542\pi$$
0.696194 + 0.717853i $$0.254875\pi$$
$$492$$ 0 0
$$493$$ 35.0000 1.57632
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −10.5000 + 18.1865i −0.470989 + 0.815778i
$$498$$ 0 0
$$499$$ 6.00000i 0.268597i −0.990941 0.134298i $$-0.957122\pi$$
0.990941 0.134298i $$-0.0428781\pi$$
$$500$$ 0 0
$$501$$ −28.5000 + 16.4545i −1.27329 + 0.735132i
$$502$$ 0 0
$$503$$ −4.33013 7.50000i −0.193071 0.334408i 0.753196 0.657797i $$-0.228511\pi$$
−0.946266 + 0.323388i $$0.895178\pi$$
$$504$$ 0 0
$$505$$ 51.0000 + 29.4449i 2.26947 + 1.31028i
$$506$$ 0 0
$$507$$ 19.9186 10.5000i 0.884615 0.466321i
$$508$$ 0 0
$$509$$ −19.5000 11.2583i −0.864322 0.499017i 0.00113503 0.999999i $$-0.499639\pi$$
−0.865457 + 0.500983i $$0.832972\pi$$
$$510$$ 0 0
$$511$$ 5.19615 + 9.00000i 0.229864 + 0.398137i
$$512$$ 0 0
$$513$$ −22.5000 + 12.9904i −0.993399 + 0.573539i
$$514$$ 0 0
$$515$$ 24.0000i 1.05757i
$$516$$ 0 0
$$517$$ −10.0000 + 17.3205i −0.439799 + 0.761755i
$$518$$ 0 0
$$519$$ 12.1244 0.532200
$$520$$ 0 0
$$521$$ 4.00000 0.175243 0.0876216 0.996154i $$-0.472073\pi$$
0.0876216 + 0.996154i $$0.472073\pi$$
$$522$$ 0 0
$$523$$ −6.06218 + 10.5000i −0.265081 + 0.459133i −0.967585 0.252547i $$-0.918732\pi$$
0.702504 + 0.711680i $$0.252065\pi$$
$$524$$ 0 0
$$525$$ 36.3731i 1.58745i
$$526$$ 0 0
$$527$$ −12.1244 + 7.00000i −0.528145 + 0.304925i
$$528$$ 0 0
$$529$$ −2.00000 3.46410i −0.0869565 0.150613i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 4.50000 4.33013i 0.194917 0.187559i
$$534$$ 0 0
$$535$$ 25.9808 + 15.0000i 1.12325 + 0.648507i
$$536$$ 0 0
$$537$$ 16.5000 + 28.5788i 0.712028 + 1.23327i
$$538$$ 0 0
$$539$$ 8.66025 5.00000i 0.373024 0.215365i
$$540$$ 0 0
$$541$$ 20.7846i 0.893600i −0.894634 0.446800i $$-0.852564\pi$$
0.894634 0.446800i $$-0.147436\pi$$
$$542$$ 0 0
$$543$$ −10.3923 + 18.0000i −0.445976 + 0.772454i
$$544$$ 0 0
$$545$$ 36.0000 1.54207
$$546$$ 0 0
$$547$$ 6.92820 0.296229 0.148114 0.988970i $$-0.452680\pi$$
0.148114 + 0.988970i $$0.452680\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 25.0000i 1.06504i
$$552$$ 0 0
$$553$$ −9.00000 + 5.19615i −0.382719 + 0.220963i
$$554$$ 0 0
$$555$$ 15.5885 + 27.0000i 0.661693 + 1.14609i
$$556$$ 0 0
$$557$$ −34.5000 19.9186i −1.46181 0.843978i −0.462717 0.886506i $$-0.653125\pi$$
−0.999095 + 0.0425287i $$0.986459\pi$$
$$558$$ 0 0
$$559$$ 18.1865 4.50000i 0.769208 0.190330i
$$560$$ 0 0
$$561$$ −52.5000 30.3109i −2.21655 1.27973i
$$562$$ 0 0
$$563$$ −4.33013 7.50000i −0.182493 0.316087i 0.760236 0.649647i $$-0.225083\pi$$
−0.942729 + 0.333560i $$0.891750\pi$$
$$564$$ 0 0
$$565$$ −15.0000 + 8.66025i −0.631055 + 0.364340i
$$566$$ 0 0
$$567$$ 27.0000i 1.13389i
$$568$$ 0 0
$$569$$ −15.5000 + 26.8468i −0.649794 + 1.12548i 0.333378 + 0.942793i $$0.391811\pi$$
−0.983172 + 0.182683i $$0.941522\pi$$
$$570$$ 0 0
$$571$$ −27.7128 −1.15975 −0.579873 0.814707i $$-0.696898\pi$$
−0.579873 + 0.814707i $$0.696898\pi$$
$$572$$ 0 0
$$573$$ −21.0000 −0.877288
$$574$$ 0 0
$$575$$ 18.1865 31.5000i 0.758431 1.31364i
$$576$$ 0 0
$$577$$ 24.2487i 1.00949i −0.863269 0.504744i $$-0.831587\pi$$
0.863269 0.504744i $$-0.168413\pi$$
$$578$$ 0 0
$$579$$ −18.1865 + 10.5000i −0.755807 + 0.436365i
$$580$$ 0 0
$$581$$ 21.0000 + 36.3731i 0.871227 + 1.50901i
$$582$$ 0 0
$$583$$ 17.3205 + 10.0000i 0.717342 + 0.414158i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 16.4545 + 9.50000i 0.679149 + 0.392107i 0.799534 0.600620i $$-0.205080\pi$$
−0.120385 + 0.992727i $$0.538413\pi$$
$$588$$ 0 0
$$589$$ 5.00000 + 8.66025i 0.206021 + 0.356840i
$$590$$ 0 0
$$591$$ −2.59808 + 1.50000i −0.106871 + 0.0617018i
$$592$$ 0 0
$$593$$ 38.1051i 1.56479i −0.622783 0.782395i $$-0.713998\pi$$
0.622783 0.782395i $$-0.286002\pi$$
$$594$$ 0 0
$$595$$ −36.3731 + 63.0000i −1.49115 + 2.58275i
$$596$$ 0 0
$$597$$ −3.00000 −0.122782
$$598$$ 0 0
$$599$$ −17.3205 −0.707697 −0.353848 0.935303i $$-0.615127\pi$$
−0.353848 + 0.935303i $$0.615127\pi$$
$$600$$ 0 0
$$601$$ 19.5000 33.7750i 0.795422 1.37771i −0.127150 0.991884i $$-0.540583\pi$$
0.922571 0.385827i $$-0.126084\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 42.0000 24.2487i 1.70754 0.985850i
$$606$$ 0 0
$$607$$ 21.6506 + 37.5000i 0.878772 + 1.52208i 0.852689 + 0.522418i $$0.174970\pi$$
0.0260828 + 0.999660i $$0.491697\pi$$
$$608$$ 0 0
$$609$$ −22.5000 12.9904i −0.911746 0.526397i
$$610$$ 0 0
$$611$$ −13.8564 4.00000i −0.560570 0.161823i
$$612$$ 0 0
$$613$$ 34.5000 + 19.9186i 1.39344 + 0.804504i 0.993695 0.112121i $$-0.0357645\pi$$
0.399747 + 0.916625i $$0.369098\pi$$
$$614$$ 0 0
$$615$$ −5.19615 9.00000i −0.209529 0.362915i
$$616$$ 0 0
$$617$$ −4.50000 + 2.59808i −0.181163 + 0.104595i −0.587839 0.808978i $$-0.700021\pi$$
0.406676 + 0.913573i $$0.366688\pi$$
$$618$$ 0 0
$$619$$ 6.00000i 0.241160i −0.992704 0.120580i $$-0.961525\pi$$
0.992704 0.120580i $$-0.0384755\pi$$
$$620$$ 0 0
$$621$$ 13.5000 23.3827i 0.541736 0.938315i
$$622$$ 0 0
$$623$$ −5.19615 −0.208179
$$624$$ 0 0
$$625$$ −11.0000 −0.440000
$$626$$ 0 0
$$627$$ −21.6506 + 37.5000i −0.864643 + 1.49761i
$$628$$ 0 0
$$629$$ 36.3731i 1.45029i
$$630$$ 0 0
$$631$$ −4.33013 + 2.50000i −0.172380 + 0.0995234i −0.583707 0.811964i $$-0.698398\pi$$
0.411328 + 0.911487i $$0.365065\pi$$
$$632$$ 0 0
$$633$$ 4.50000 + 7.79423i 0.178859 + 0.309793i
$$634$$ 0 0
$$635$$ −57.1577 33.0000i −2.26823 1.30957i
$$636$$ 0 0
$$637$$ 5.00000 + 5.19615i 0.198107 + 0.205879i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −0.500000 0.866025i −0.0197488 0.0342059i 0.855982 0.517005i $$-0.172953\pi$$
−0.875731 + 0.482800i $$0.839620\pi$$
$$642$$ 0 0
$$643$$ −7.79423 + 4.50000i −0.307374 + 0.177463i −0.645751 0.763548i $$-0.723456\pi$$
0.338377 + 0.941011i $$0.390122\pi$$
$$644$$ 0 0
$$645$$ 31.1769i 1.22759i
$$646$$ 0 0
$$647$$ −7.79423 + 13.5000i −0.306423 + 0.530740i −0.977577 0.210578i $$-0.932465\pi$$
0.671154 + 0.741318i $$0.265799\pi$$
$$648$$ 0 0
$$649$$ −35.0000 −1.37387
$$650$$ 0 0
$$651$$ 10.3923 0.407307
$$652$$ 0 0
$$653$$ −2.50000 + 4.33013i −0.0978326 + 0.169451i −0.910787 0.412876i $$-0.864524\pi$$
0.812955 + 0.582327i $$0.197858\pi$$
$$654$$ 0 0
$$655$$ 48.0000i 1.87552i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 18.1865 + 31.5000i 0.708447 + 1.22707i 0.965433 + 0.260651i $$0.0839371\pi$$
−0.256986 + 0.966415i $$0.582730\pi$$
$$660$$ 0 0
$$661$$ −1.50000 0.866025i −0.0583432 0.0336845i 0.470545 0.882376i $$-0.344057\pi$$
−0.528888 + 0.848692i $$0.677391\pi$$
$$662$$ 0 0
$$663$$ 12.1244 42.0000i 0.470871 1.63114i
$$664$$ 0 0
$$665$$ 45.0000 + 25.9808i 1.74503 + 1.00749i
$$666$$ 0 0
$$667$$ 12.9904 + 22.5000i 0.502990 + 0.871203i
$$668$$ 0 0
$$669$$ 19.5000 11.2583i 0.753914 0.435272i
$$670$$ 0 0
$$671$$ 15.0000i 0.579069i
$$672$$ 0 0
$$673$$ 20.5000 35.5070i 0.790217 1.36870i −0.135615 0.990762i $$-0.543301\pi$$
0.925832 0.377934i $$-0.123365\pi$$
$$674$$ 0 0
$$675$$ 36.3731 1.40000
$$676$$ 0 0
$$677$$ −8.00000 −0.307465 −0.153732 0.988113i $$-0.549129\pi$$
−0.153732 + 0.988113i $$0.549129\pi$$
$$678$$ 0 0
$$679$$ −12.9904 + 22.5000i −0.498525 + 0.863471i
$$680$$ 0 0
$$681$$ 39.8372i 1.52656i
$$682$$ 0 0
$$683$$ 35.5070 20.5000i 1.35864 0.784411i 0.369199 0.929350i $$-0.379632\pi$$
0.989440 + 0.144940i $$0.0462988\pi$$
$$684$$ 0 0
$$685$$ 9.00000 + 15.5885i 0.343872 + 0.595604i
$$686$$ 0 0
$$687$$ 36.3731 + 21.0000i 1.38772 + 0.801200i
$$688$$ 0 0
$$689$$ −4.00000 + 13.8564i −0.152388 + 0.527887i
$$690$$ 0 0
$$691$$ −12.9904 7.50000i −0.494177 0.285313i 0.232128 0.972685i $$-0.425431\pi$$
−0.726306 + 0.687372i $$0.758764\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −25.9808 + 15.0000i −0.985506 + 0.568982i
$$696$$ 0 0
$$697$$ 12.1244i 0.459243i
$$698$$ 0 0
$$699$$ 6.92820 12.0000i 0.262049 0.453882i
$$700$$ 0 0
$$701$$ 8.00000 0.302156 0.151078 0.988522i $$-0.451726\pi$$
0.151078 + 0.988522i $$0.451726\pi$$
$$702$$ 0 0
$$703$$ 25.9808 0.979883
$$704$$ 0 0
$$705$$ −12.0000 + 20.7846i −0.451946 + 0.782794i
$$706$$ 0 0
$$707$$ 51.0000i 1.91805i
$$708$$ 0 0
$$709$$ −1.50000 + 0.866025i −0.0563337 + 0.0325243i −0.527902 0.849305i $$-0.677021\pi$$
0.471569 + 0.881829i $$0.343688\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −9.00000 5.19615i −0.337053 0.194597i
$$714$$ 0 0
$$715$$ 43.3013 + 45.0000i 1.61938 + 1.68290i
$$716$$ 0 0
$$717$$ 3.00000 + 1.73205i 0.112037 + 0.0646846i
$$718$$ 0 0
$$719$$ 6.06218 + 10.5000i 0.226081 + 0.391584i 0.956643 0.291262i $$-0.0940752\pi$$
−0.730562 + 0.682846i $$0.760742\pi$$
$$720$$ 0 0
$$721$$ 18.0000 10.3923i 0.670355 0.387030i
$$722$$ 0 0
$$723$$ 15.0000i 0.557856i
$$724$$ 0 0
$$725$$ −17.5000 + 30.3109i −0.649934 + 1.12572i
$$726$$ 0 0
$$727$$ −41.5692 −1.54172 −0.770859 0.637006i $$-0.780172\pi$$
−0.770859 + 0.637006i $$0.780172\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 18.1865 31.5000i 0.672653 1.16507i
$$732$$ 0 0
$$733$$ 48.4974i 1.79129i 0.444766 + 0.895647i $$0.353287\pi$$
−0.444766 + 0.895647i $$0.646713\pi$$
$$734$$ 0 0
$$735$$ 10.3923 6.00000i 0.383326 0.221313i
$$736$$ 0 0
$$737$$ 7.50000 + 12.9904i 0.276266 + 0.478507i
$$738$$ 0 0
$$739$$ −18.1865 10.5000i −0.669002 0.386249i 0.126696 0.991942i $$-0.459563\pi$$
−0.795699 + 0.605693i $$0.792896\pi$$
$$740$$ 0 0
$$741$$ −30.0000 8.66025i −1.10208 0.318142i
$$742$$ 0 0
$$743$$ 11.2583 + 6.50000i 0.413028 + 0.238462i 0.692090 0.721811i $$-0.256690\pi$$
−0.279062 + 0.960273i $$0.590023\pi$$
$$744$$ 0 0
$$745$$ −15.0000 25.9808i −0.549557 0.951861i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 25.9808i 0.949316i
$$750$$ 0 0
$$751$$ −6.06218 + 10.5000i −0.221212 + 0.383150i −0.955176 0.296038i $$-0.904335\pi$$
0.733964 + 0.679188i $$0.237668\pi$$
$$752$$ 0 0
$$753$$ −27.0000 −0.983935
$$754$$ 0 0
$$755$$ 6.92820 0.252143
$$756$$ 0 0
$$757$$ −26.5000 + 45.8993i −0.963159 + 1.66824i −0.248677 + 0.968587i $$0.579996\pi$$
−0.714482 + 0.699654i $$0.753338\pi$$
$$758$$ 0 0
$$759$$ 45.0000i 1.63340i
$$760$$ 0 0
$$761$$ 40.5000 23.3827i 1.46812 0.847622i 0.468761 0.883325i $$-0.344700\pi$$
0.999362 + 0.0357031i $$0.0113671\pi$$
$$762$$ 0 0
$$763$$ −15.5885 27.0000i −0.564340 0.977466i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −6.06218 24.5000i −0.218893 0.884644i
$$768$$ 0 0
$$769$$ −25.5000 14.7224i −0.919554 0.530904i −0.0360609 0.999350i $$-0.511481\pi$$
−0.883493 + 0.468445i $$0.844814\pi$$
$$770$$ 0 0
$$771$$ 19.9186 + 34.5000i 0.717350 + 1.24249i
$$772$$ 0 0
$$773$$ −1.50000 + 0.866025i −0.0539513 + 0.0311488i −0.526733 0.850031i $$-0.676583\pi$$
0.472782 + 0.881180i $$0.343250\pi$$
$$774$$ 0 0
$$775$$ 14.0000i 0.502895i
$$776$$ 0 0
$$777$$ 13.5000 23.3827i 0.484310 0.838849i
$$778$$ 0 0
$$779$$ −8.66025 −0.310286
$$780$$ 0 0
$$781$$ 35.0000 1.25240
$$782$$ 0 0
$$783$$ −12.9904 + 22.5000i −0.464238 + 0.804084i
$$784$$ 0 0
$$785$$ 27.7128i 0.989113i
$$786$$ 0 0
$$787$$ −7.79423 + 4.50000i −0.277834 + 0.160408i −0.632443 0.774607i $$-0.717948\pi$$
0.354608 + 0.935015i $$0.384614\pi$$
$$788$$ 0 0
$$789$$ 1.50000 + 2.59808i 0.0534014 + 0.0924940i
$$790$$ 0 0
$$791$$ 12.9904 + 7.50000i 0.461885 + 0.266669i