# Properties

 Label 1911.2.c.d.883.1 Level $1911$ Weight $2$ Character 1911.883 Analytic conductor $15.259$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1911 = 3 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1911.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.2594118263$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 39) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 883.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1911.883 Dual form 1911.2.c.d.883.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.73205i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.73205i q^{6} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.73205i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.73205i q^{6} -1.73205i q^{8} +1.00000 q^{9} +3.46410i q^{11} -1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} -5.00000 q^{16} +6.00000 q^{17} -1.73205i q^{18} +3.46410i q^{19} +6.00000 q^{22} -1.73205i q^{24} +5.00000 q^{25} +(6.00000 - 1.73205i) q^{26} +1.00000 q^{27} +6.00000 q^{29} -3.46410i q^{31} +5.19615i q^{32} +3.46410i q^{33} -10.3923i q^{34} -1.00000 q^{36} -6.92820i q^{37} +6.00000 q^{38} +(1.00000 + 3.46410i) q^{39} -6.92820i q^{41} -4.00000 q^{43} -3.46410i q^{44} +3.46410i q^{47} -5.00000 q^{48} -8.66025i q^{50} +6.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} +6.00000 q^{53} -1.73205i q^{54} +3.46410i q^{57} -10.3923i q^{58} +10.3923i q^{59} +2.00000 q^{61} -6.00000 q^{62} -1.00000 q^{64} +6.00000 q^{66} +10.3923i q^{67} -6.00000 q^{68} -3.46410i q^{71} -1.73205i q^{72} -12.0000 q^{74} +5.00000 q^{75} -3.46410i q^{76} +(6.00000 - 1.73205i) q^{78} -8.00000 q^{79} +1.00000 q^{81} -12.0000 q^{82} -3.46410i q^{83} +6.92820i q^{86} +6.00000 q^{87} +6.00000 q^{88} -6.92820i q^{89} -3.46410i q^{93} +6.00000 q^{94} +5.19615i q^{96} -13.8564i q^{97} +3.46410i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10})$$ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 $$2 q + 2 q^{3} - 2 q^{4} + 2 q^{9} - 2 q^{12} + 2 q^{13} - 10 q^{16} + 12 q^{17} + 12 q^{22} + 10 q^{25} + 12 q^{26} + 2 q^{27} + 12 q^{29} - 2 q^{36} + 12 q^{38} + 2 q^{39} - 8 q^{43} - 10 q^{48} + 12 q^{51} - 2 q^{52} + 12 q^{53} + 4 q^{61} - 12 q^{62} - 2 q^{64} + 12 q^{66} - 12 q^{68} - 24 q^{74} + 10 q^{75} + 12 q^{78} - 16 q^{79} + 2 q^{81} - 24 q^{82} + 12 q^{87} + 12 q^{88} + 12 q^{94}+O(q^{100})$$ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 - 2 * q^12 + 2 * q^13 - 10 * q^16 + 12 * q^17 + 12 * q^22 + 10 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^29 - 2 * q^36 + 12 * q^38 + 2 * q^39 - 8 * q^43 - 10 * q^48 + 12 * q^51 - 2 * q^52 + 12 * q^53 + 4 * q^61 - 12 * q^62 - 2 * q^64 + 12 * q^66 - 12 * q^68 - 24 * q^74 + 10 * q^75 + 12 * q^78 - 16 * q^79 + 2 * q^81 - 24 * q^82 + 12 * q^87 + 12 * q^88 + 12 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times$$.

 $$n$$ $$638$$ $$1471$$ $$1522$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.73205i 1.22474i −0.790569 0.612372i $$-0.790215\pi$$
0.790569 0.612372i $$-0.209785\pi$$
$$3$$ 1.00000 0.577350
$$4$$ −1.00000 −0.500000
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 1.73205i 0.707107i
$$7$$ 0 0
$$8$$ 1.73205i 0.612372i
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 3.46410i 1.04447i 0.852803 + 0.522233i $$0.174901\pi$$
−0.852803 + 0.522233i $$0.825099\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 1.00000 + 3.46410i 0.277350 + 0.960769i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −5.00000 −1.25000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 1.73205i 0.408248i
$$19$$ 3.46410i 0.794719i 0.917663 + 0.397360i $$0.130073\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 6.00000 1.27920
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 1.73205i 0.353553i
$$25$$ 5.00000 1.00000
$$26$$ 6.00000 1.73205i 1.17670 0.339683i
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 3.46410i 0.622171i −0.950382 0.311086i $$-0.899307\pi$$
0.950382 0.311086i $$-0.100693\pi$$
$$32$$ 5.19615i 0.918559i
$$33$$ 3.46410i 0.603023i
$$34$$ 10.3923i 1.78227i
$$35$$ 0 0
$$36$$ −1.00000 −0.166667
$$37$$ 6.92820i 1.13899i −0.821995 0.569495i $$-0.807139\pi$$
0.821995 0.569495i $$-0.192861\pi$$
$$38$$ 6.00000 0.973329
$$39$$ 1.00000 + 3.46410i 0.160128 + 0.554700i
$$40$$ 0 0
$$41$$ 6.92820i 1.08200i −0.841021 0.541002i $$-0.818045\pi$$
0.841021 0.541002i $$-0.181955\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 3.46410i 0.522233i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.46410i 0.505291i 0.967559 + 0.252646i $$0.0813007\pi$$
−0.967559 + 0.252646i $$0.918699\pi$$
$$48$$ −5.00000 −0.721688
$$49$$ 0 0
$$50$$ 8.66025i 1.22474i
$$51$$ 6.00000 0.840168
$$52$$ −1.00000 3.46410i −0.138675 0.480384i
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 1.73205i 0.235702i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.46410i 0.458831i
$$58$$ 10.3923i 1.36458i
$$59$$ 10.3923i 1.35296i 0.736460 + 0.676481i $$0.236496\pi$$
−0.736460 + 0.676481i $$0.763504\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ −6.00000 −0.762001
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 6.00000 0.738549
$$67$$ 10.3923i 1.26962i 0.772667 + 0.634811i $$0.218922\pi$$
−0.772667 + 0.634811i $$0.781078\pi$$
$$68$$ −6.00000 −0.727607
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 3.46410i 0.411113i −0.978645 0.205557i $$-0.934100\pi$$
0.978645 0.205557i $$-0.0659005\pi$$
$$72$$ 1.73205i 0.204124i
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ −12.0000 −1.39497
$$75$$ 5.00000 0.577350
$$76$$ 3.46410i 0.397360i
$$77$$ 0 0
$$78$$ 6.00000 1.73205i 0.679366 0.196116i
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −12.0000 −1.32518
$$83$$ 3.46410i 0.380235i −0.981761 0.190117i $$-0.939113\pi$$
0.981761 0.190117i $$-0.0608868\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 6.92820i 0.747087i
$$87$$ 6.00000 0.643268
$$88$$ 6.00000 0.639602
$$89$$ 6.92820i 0.734388i −0.930144 0.367194i $$-0.880318\pi$$
0.930144 0.367194i $$-0.119682\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 3.46410i 0.359211i
$$94$$ 6.00000 0.618853
$$95$$ 0 0
$$96$$ 5.19615i 0.530330i
$$97$$ 13.8564i 1.40690i −0.710742 0.703452i $$-0.751641\pi$$
0.710742 0.703452i $$-0.248359\pi$$
$$98$$ 0 0
$$99$$ 3.46410i 0.348155i
$$100$$ −5.00000 −0.500000
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 10.3923i 1.02899i
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 6.00000 1.73205i 0.588348 0.169842i
$$105$$ 0 0
$$106$$ 10.3923i 1.00939i
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ 6.92820i 0.663602i −0.943349 0.331801i $$-0.892344\pi$$
0.943349 0.331801i $$-0.107656\pi$$
$$110$$ 0 0
$$111$$ 6.92820i 0.657596i
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 6.00000 0.561951
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ 1.00000 + 3.46410i 0.0924500 + 0.320256i
$$118$$ 18.0000 1.65703
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.00000 −0.0909091
$$122$$ 3.46410i 0.313625i
$$123$$ 6.92820i 0.624695i
$$124$$ 3.46410i 0.311086i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 12.1244i 1.07165i
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 3.46410i 0.301511i
$$133$$ 0 0
$$134$$ 18.0000 1.55496
$$135$$ 0 0
$$136$$ 10.3923i 0.891133i
$$137$$ 20.7846i 1.77575i 0.460086 + 0.887875i $$0.347819\pi$$
−0.460086 + 0.887875i $$0.652181\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 3.46410i 0.291730i
$$142$$ −6.00000 −0.503509
$$143$$ −12.0000 + 3.46410i −1.00349 + 0.289683i
$$144$$ −5.00000 −0.416667
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 6.92820i 0.569495i
$$149$$ 13.8564i 1.13516i −0.823318 0.567581i $$-0.807880\pi$$
0.823318 0.567581i $$-0.192120\pi$$
$$150$$ 8.66025i 0.707107i
$$151$$ 10.3923i 0.845714i −0.906196 0.422857i $$-0.861027\pi$$
0.906196 0.422857i $$-0.138973\pi$$
$$152$$ 6.00000 0.486664
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.00000 3.46410i −0.0800641 0.277350i
$$157$$ −14.0000 −1.11732 −0.558661 0.829396i $$-0.688685\pi$$
−0.558661 + 0.829396i $$0.688685\pi$$
$$158$$ 13.8564i 1.10236i
$$159$$ 6.00000 0.475831
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.73205i 0.136083i
$$163$$ 3.46410i 0.271329i −0.990755 0.135665i $$-0.956683\pi$$
0.990755 0.135665i $$-0.0433170\pi$$
$$164$$ 6.92820i 0.541002i
$$165$$ 0 0
$$166$$ −6.00000 −0.465690
$$167$$ 17.3205i 1.34030i 0.742225 + 0.670151i $$0.233770\pi$$
−0.742225 + 0.670151i $$0.766230\pi$$
$$168$$ 0 0
$$169$$ −11.0000 + 6.92820i −0.846154 + 0.532939i
$$170$$ 0 0
$$171$$ 3.46410i 0.264906i
$$172$$ 4.00000 0.304997
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 10.3923i 0.787839i
$$175$$ 0 0
$$176$$ 17.3205i 1.30558i
$$177$$ 10.3923i 0.781133i
$$178$$ −12.0000 −0.899438
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 0 0
$$185$$ 0 0
$$186$$ −6.00000 −0.439941
$$187$$ 20.7846i 1.51992i
$$188$$ 3.46410i 0.252646i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 24.0000 1.73658 0.868290 0.496058i $$-0.165220\pi$$
0.868290 + 0.496058i $$0.165220\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ −24.0000 −1.72310
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 6.00000 0.426401
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 8.66025i 0.612372i
$$201$$ 10.3923i 0.733017i
$$202$$ 10.3923i 0.731200i
$$203$$ 0 0
$$204$$ −6.00000 −0.420084
$$205$$ 0 0
$$206$$ 13.8564i 0.965422i
$$207$$ 0 0
$$208$$ −5.00000 17.3205i −0.346688 1.20096i
$$209$$ −12.0000 −0.830057
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 3.46410i 0.237356i
$$214$$ 20.7846i 1.42081i
$$215$$ 0 0
$$216$$ 1.73205i 0.117851i
$$217$$ 0 0
$$218$$ −12.0000 −0.812743
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.00000 + 20.7846i 0.403604 + 1.39812i
$$222$$ −12.0000 −0.805387
$$223$$ 3.46410i 0.231973i −0.993251 0.115987i $$-0.962997\pi$$
0.993251 0.115987i $$-0.0370030\pi$$
$$224$$ 0 0
$$225$$ 5.00000 0.333333
$$226$$ 10.3923i 0.691286i
$$227$$ 17.3205i 1.14960i −0.818293 0.574801i $$-0.805079\pi$$
0.818293 0.574801i $$-0.194921\pi$$
$$228$$ 3.46410i 0.229416i
$$229$$ 6.92820i 0.457829i −0.973447 0.228914i $$-0.926482\pi$$
0.973447 0.228914i $$-0.0735176\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 10.3923i 0.682288i
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 6.00000 1.73205i 0.392232 0.113228i
$$235$$ 0 0
$$236$$ 10.3923i 0.676481i
$$237$$ −8.00000 −0.519656
$$238$$ 0 0
$$239$$ 10.3923i 0.672222i 0.941822 + 0.336111i $$0.109112\pi$$
−0.941822 + 0.336111i $$0.890888\pi$$
$$240$$ 0 0
$$241$$ 13.8564i 0.892570i 0.894891 + 0.446285i $$0.147253\pi$$
−0.894891 + 0.446285i $$0.852747\pi$$
$$242$$ 1.73205i 0.111340i
$$243$$ 1.00000 0.0641500
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ −12.0000 −0.765092
$$247$$ −12.0000 + 3.46410i −0.763542 + 0.220416i
$$248$$ −6.00000 −0.381000
$$249$$ 3.46410i 0.219529i
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 13.8564i 0.869428i
$$255$$ 0 0
$$256$$ 19.0000 1.18750
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 6.92820i 0.431331i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 20.7846i 1.28408i
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ 6.00000 0.369274
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 6.92820i 0.423999i
$$268$$ 10.3923i 0.634811i
$$269$$ −6.00000 −0.365826 −0.182913 0.983129i $$-0.558553\pi$$
−0.182913 + 0.983129i $$0.558553\pi$$
$$270$$ 0 0
$$271$$ 10.3923i 0.631288i 0.948878 + 0.315644i $$0.102220\pi$$
−0.948878 + 0.315644i $$0.897780\pi$$
$$272$$ −30.0000 −1.81902
$$273$$ 0 0
$$274$$ 36.0000 2.17484
$$275$$ 17.3205i 1.04447i
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 6.92820i 0.415526i
$$279$$ 3.46410i 0.207390i
$$280$$ 0 0
$$281$$ 6.92820i 0.413302i −0.978415 0.206651i $$-0.933744\pi$$
0.978415 0.206651i $$-0.0662565\pi$$
$$282$$ 6.00000 0.357295
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 3.46410i 0.205557i
$$285$$ 0 0
$$286$$ 6.00000 + 20.7846i 0.354787 + 1.22902i
$$287$$ 0 0
$$288$$ 5.19615i 0.306186i
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 13.8564i 0.812277i
$$292$$ 0 0
$$293$$ 27.7128i 1.61900i 0.587120 + 0.809500i $$0.300262\pi$$
−0.587120 + 0.809500i $$0.699738\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −12.0000 −0.697486
$$297$$ 3.46410i 0.201008i
$$298$$ −24.0000 −1.39028
$$299$$ 0 0
$$300$$ −5.00000 −0.288675
$$301$$ 0 0
$$302$$ −18.0000 −1.03578
$$303$$ −6.00000 −0.344691
$$304$$ 17.3205i 0.993399i
$$305$$ 0 0
$$306$$ 10.3923i 0.594089i
$$307$$ 10.3923i 0.593120i −0.955014 0.296560i $$-0.904160\pi$$
0.955014 0.296560i $$-0.0958395\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 6.00000 1.73205i 0.339683 0.0980581i
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 24.2487i 1.36843i
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ 13.8564i 0.778253i −0.921184 0.389127i $$-0.872777\pi$$
0.921184 0.389127i $$-0.127223\pi$$
$$318$$ 10.3923i 0.582772i
$$319$$ 20.7846i 1.16371i
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 20.7846i 1.15649i
$$324$$ −1.00000 −0.0555556
$$325$$ 5.00000 + 17.3205i 0.277350 + 0.960769i
$$326$$ −6.00000 −0.332309
$$327$$ 6.92820i 0.383131i
$$328$$ −12.0000 −0.662589
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 3.46410i 0.190404i −0.995458 0.0952021i $$-0.969650\pi$$
0.995458 0.0952021i $$-0.0303497\pi$$
$$332$$ 3.46410i 0.190117i
$$333$$ 6.92820i 0.379663i
$$334$$ 30.0000 1.64153
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 12.0000 + 19.0526i 0.652714 + 1.03632i
$$339$$ −6.00000 −0.325875
$$340$$ 0 0
$$341$$ 12.0000 0.649836
$$342$$ 6.00000 0.324443
$$343$$ 0 0
$$344$$ 6.92820i 0.373544i
$$345$$ 0 0
$$346$$ 31.1769i 1.67608i
$$347$$ 36.0000 1.93258 0.966291 0.257454i $$-0.0828835\pi$$
0.966291 + 0.257454i $$0.0828835\pi$$
$$348$$ −6.00000 −0.321634
$$349$$ 6.92820i 0.370858i −0.982658 0.185429i $$-0.940632\pi$$
0.982658 0.185429i $$-0.0593675\pi$$
$$350$$ 0 0
$$351$$ 1.00000 + 3.46410i 0.0533761 + 0.184900i
$$352$$ −18.0000 −0.959403
$$353$$ 34.6410i 1.84376i 0.387481 + 0.921878i $$0.373345\pi$$
−0.387481 + 0.921878i $$0.626655\pi$$
$$354$$ 18.0000 0.956689
$$355$$ 0 0
$$356$$ 6.92820i 0.367194i
$$357$$ 0 0
$$358$$ 20.7846i 1.09850i
$$359$$ 17.3205i 0.914141i −0.889430 0.457071i $$-0.848899\pi$$
0.889430 0.457071i $$-0.151101\pi$$
$$360$$ 0 0
$$361$$ 7.00000 0.368421
$$362$$ 17.3205i 0.910346i
$$363$$ −1.00000 −0.0524864
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 3.46410i 0.181071i
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ 0 0
$$369$$ 6.92820i 0.360668i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 3.46410i 0.179605i
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ 36.0000 1.86152
$$375$$ 0 0
$$376$$ 6.00000 0.309426
$$377$$ 6.00000 + 20.7846i 0.309016 + 1.07046i
$$378$$ 0 0
$$379$$ 17.3205i 0.889695i −0.895606 0.444847i $$-0.853258\pi$$
0.895606 0.444847i $$-0.146742\pi$$
$$380$$ 0 0
$$381$$ −8.00000 −0.409852
$$382$$ 41.5692i 2.12687i
$$383$$ 3.46410i 0.177007i 0.996076 + 0.0885037i $$0.0282085\pi$$
−0.996076 + 0.0885037i $$0.971792\pi$$
$$384$$ 12.1244i 0.618718i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −4.00000 −0.203331
$$388$$ 13.8564i 0.703452i
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 12.0000 0.605320
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 3.46410i 0.174078i
$$397$$ 34.6410i 1.73858i −0.494300 0.869291i $$-0.664576\pi$$
0.494300 0.869291i $$-0.335424\pi$$
$$398$$ 27.7128i 1.38912i
$$399$$ 0 0
$$400$$ −25.0000 −1.25000
$$401$$ 6.92820i 0.345978i −0.984924 0.172989i $$-0.944657\pi$$
0.984924 0.172989i $$-0.0553425\pi$$
$$402$$ 18.0000 0.897758
$$403$$ 12.0000 3.46410i 0.597763 0.172559i
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 24.0000 1.18964
$$408$$ 10.3923i 0.514496i
$$409$$ 27.7128i 1.37031i 0.728397 + 0.685155i $$0.240266\pi$$
−0.728397 + 0.685155i $$0.759734\pi$$
$$410$$ 0 0
$$411$$ 20.7846i 1.02523i
$$412$$ 8.00000 0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −18.0000 + 5.19615i −0.882523 + 0.254762i
$$417$$ 4.00000 0.195881
$$418$$ 20.7846i 1.01661i
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 34.6410i 1.68830i 0.536107 + 0.844150i $$0.319894\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 34.6410i 1.68630i
$$423$$ 3.46410i 0.168430i
$$424$$ 10.3923i 0.504695i
$$425$$ 30.0000 1.45521
$$426$$ −6.00000 −0.290701
$$427$$ 0 0
$$428$$ −12.0000 −0.580042
$$429$$ −12.0000 + 3.46410i −0.579365 + 0.167248i
$$430$$ 0 0
$$431$$ 24.2487i 1.16802i 0.811747 + 0.584010i $$0.198517\pi$$
−0.811747 + 0.584010i $$0.801483\pi$$
$$432$$ −5.00000 −0.240563
$$433$$ −34.0000 −1.63394 −0.816968 0.576683i $$-0.804347\pi$$
−0.816968 + 0.576683i $$0.804347\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 6.92820i 0.331801i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −8.00000 −0.381819 −0.190910 0.981608i $$-0.561144\pi$$
−0.190910 + 0.981608i $$0.561144\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 36.0000 10.3923i 1.71235 0.494312i
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ 6.92820i 0.328798i
$$445$$ 0 0
$$446$$ −6.00000 −0.284108
$$447$$ 13.8564i 0.655386i
$$448$$ 0 0
$$449$$ 6.92820i 0.326962i −0.986546 0.163481i $$-0.947728\pi$$
0.986546 0.163481i $$-0.0522723\pi$$
$$450$$ 8.66025i 0.408248i
$$451$$ 24.0000 1.13012
$$452$$ 6.00000 0.282216
$$453$$ 10.3923i 0.488273i
$$454$$ −30.0000 −1.40797
$$455$$ 0 0
$$456$$ 6.00000 0.280976
$$457$$ 27.7128i 1.29635i 0.761491 + 0.648175i $$0.224468\pi$$
−0.761491 + 0.648175i $$0.775532\pi$$
$$458$$ −12.0000 −0.560723
$$459$$ 6.00000 0.280056
$$460$$ 0 0
$$461$$ 13.8564i 0.645357i −0.946509 0.322679i $$-0.895417\pi$$
0.946509 0.322679i $$-0.104583\pi$$
$$462$$ 0 0
$$463$$ 17.3205i 0.804952i 0.915430 + 0.402476i $$0.131850\pi$$
−0.915430 + 0.402476i $$0.868150\pi$$
$$464$$ −30.0000 −1.39272
$$465$$ 0 0
$$466$$ 10.3923i 0.481414i
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ −1.00000 3.46410i −0.0462250 0.160128i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −14.0000 −0.645086
$$472$$ 18.0000 0.828517
$$473$$ 13.8564i 0.637118i
$$474$$ 13.8564i 0.636446i
$$475$$ 17.3205i 0.794719i
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 18.0000 0.823301
$$479$$ 10.3923i 0.474837i −0.971408 0.237418i $$-0.923699\pi$$
0.971408 0.237418i $$-0.0763012\pi$$
$$480$$ 0 0
$$481$$ 24.0000 6.92820i 1.09431 0.315899i
$$482$$ 24.0000 1.09317
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 0 0
$$486$$ 1.73205i 0.0785674i
$$487$$ 38.1051i 1.72671i −0.504599 0.863354i $$-0.668360\pi$$
0.504599 0.863354i $$-0.331640\pi$$
$$488$$ 3.46410i 0.156813i
$$489$$ 3.46410i 0.156652i
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 6.92820i 0.312348i
$$493$$ 36.0000 1.62136
$$494$$ 6.00000 + 20.7846i 0.269953 + 0.935144i
$$495$$ 0 0
$$496$$ 17.3205i 0.777714i
$$497$$ 0 0
$$498$$ −6.00000 −0.268866
$$499$$ 10.3923i 0.465223i 0.972570 + 0.232612i $$0.0747271\pi$$
−0.972570 + 0.232612i $$0.925273\pi$$
$$500$$ 0 0
$$501$$ 17.3205i 0.773823i
$$502$$ 20.7846i 0.927663i
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −11.0000 + 6.92820i −0.488527 + 0.307692i
$$508$$ 8.00000 0.354943
$$509$$ 41.5692i 1.84252i −0.388943 0.921262i $$-0.627160\pi$$
0.388943 0.921262i $$-0.372840\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 8.66025i 0.382733i
$$513$$ 3.46410i 0.152944i
$$514$$ 31.1769i 1.37515i
$$515$$ 0 0
$$516$$ 4.00000 0.176090
$$517$$ −12.0000 −0.527759
$$518$$ 0 0
$$519$$ 18.0000 0.790112
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 10.3923i 0.454859i
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ 41.5692i 1.81250i
$$527$$ 20.7846i 0.905392i
$$528$$ 17.3205i 0.753778i
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ 10.3923i 0.450988i
$$532$$ 0 0
$$533$$ 24.0000 6.92820i 1.03956 0.300094i
$$534$$ −12.0000 −0.519291
$$535$$ 0 0
$$536$$ 18.0000 0.777482
$$537$$ −12.0000 −0.517838
$$538$$ 10.3923i 0.448044i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 6.92820i 0.297867i −0.988847 0.148933i $$-0.952416\pi$$
0.988847 0.148933i $$-0.0475840\pi$$
$$542$$ 18.0000 0.773166
$$543$$ 10.0000 0.429141
$$544$$ 31.1769i 1.33670i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 20.7846i 0.887875i
$$549$$ 2.00000 0.0853579
$$550$$ 30.0000 1.27920
$$551$$ 20.7846i 0.885454i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 17.3205i 0.735878i
$$555$$ 0 0
$$556$$ −4.00000 −0.169638
$$557$$ 13.8564i 0.587115i −0.955941 0.293557i $$-0.905161\pi$$
0.955941 0.293557i $$-0.0948392\pi$$
$$558$$ −6.00000 −0.254000
$$559$$ −4.00000 13.8564i −0.169182 0.586064i
$$560$$ 0 0
$$561$$ 20.7846i 0.877527i
$$562$$ −12.0000 −0.506189
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 3.46410i 0.145865i
$$565$$ 0 0
$$566$$ 6.92820i 0.291214i
$$567$$ 0 0
$$568$$ −6.00000 −0.251754
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 12.0000 3.46410i 0.501745 0.144841i
$$573$$ 24.0000 1.00261
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1.00000 −0.0416667
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 32.9090i 1.36883i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −24.0000 −0.994832
$$583$$ 20.7846i 0.860811i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 48.0000 1.98286
$$587$$ 10.3923i 0.428936i 0.976731 + 0.214468i $$0.0688018\pi$$
−0.976731 + 0.214468i $$0.931198\pi$$
$$588$$ 0 0
$$589$$ 12.0000 0.494451
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 34.6410i 1.42374i
$$593$$ 6.92820i 0.284507i 0.989830 + 0.142254i $$0.0454349\pi$$
−0.989830 + 0.142254i $$0.954565\pi$$
$$594$$ 6.00000 0.246183
$$595$$ 0 0
$$596$$ 13.8564i 0.567581i
$$597$$ −16.0000 −0.654836
$$598$$ 0 0
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 8.66025i 0.353553i
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ 10.3923i 0.423207i
$$604$$ 10.3923i 0.422857i
$$605$$ 0 0
$$606$$ 10.3923i 0.422159i
$$607$$ −32.0000 −1.29884 −0.649420 0.760430i $$-0.724988\pi$$
−0.649420 + 0.760430i $$0.724988\pi$$
$$608$$ −18.0000 −0.729996
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −12.0000 + 3.46410i −0.485468 + 0.140143i
$$612$$ −6.00000 −0.242536
$$613$$ 20.7846i 0.839482i 0.907644 + 0.419741i $$0.137879\pi$$
−0.907644 + 0.419741i $$0.862121\pi$$
$$614$$ −18.0000 −0.726421
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6.92820i 0.278919i 0.990228 + 0.139459i $$0.0445365\pi$$
−0.990228 + 0.139459i $$0.955464\pi$$
$$618$$ 13.8564i 0.557386i
$$619$$ 31.1769i 1.25311i 0.779379 + 0.626553i $$0.215535\pi$$
−0.779379 + 0.626553i $$0.784465\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −5.00000 17.3205i −0.200160 0.693375i
$$625$$ 25.0000 1.00000
$$626$$ 17.3205i 0.692267i
$$627$$ −12.0000 −0.479234
$$628$$ 14.0000 0.558661
$$629$$ 41.5692i 1.65747i
$$630$$ 0 0
$$631$$ 38.1051i 1.51694i −0.651707 0.758470i $$-0.725947\pi$$
0.651707 0.758470i $$-0.274053\pi$$
$$632$$ 13.8564i 0.551178i
$$633$$ −20.0000 −0.794929
$$634$$ −24.0000 −0.953162
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ 36.0000 1.42525
$$639$$ 3.46410i 0.137038i
$$640$$ 0 0
$$641$$ −6.00000 −0.236986 −0.118493 0.992955i $$-0.537806\pi$$
−0.118493 + 0.992955i $$0.537806\pi$$
$$642$$ 20.7846i 0.820303i
$$643$$ 10.3923i 0.409832i −0.978780 0.204916i $$-0.934308\pi$$
0.978780 0.204916i $$-0.0656922\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 36.0000 1.41640
$$647$$ 24.0000 0.943537 0.471769 0.881722i $$-0.343616\pi$$
0.471769 + 0.881722i $$0.343616\pi$$
$$648$$ 1.73205i 0.0680414i
$$649$$ −36.0000 −1.41312
$$650$$ 30.0000 8.66025i 1.17670 0.339683i
$$651$$ 0 0
$$652$$ 3.46410i 0.135665i
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ −12.0000 −0.469237
$$655$$ 0 0
$$656$$ 34.6410i 1.35250i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ 20.7846i 0.808428i −0.914665 0.404214i $$-0.867545\pi$$
0.914665 0.404214i $$-0.132455\pi$$
$$662$$ −6.00000 −0.233197
$$663$$ 6.00000 + 20.7846i 0.233021 + 0.807207i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ −12.0000 −0.464991
$$667$$ 0 0
$$668$$ 17.3205i 0.670151i
$$669$$ 3.46410i 0.133930i
$$670$$ 0 0
$$671$$ 6.92820i 0.267460i
$$672$$ 0 0
$$673$$ −46.0000 −1.77317 −0.886585 0.462566i $$-0.846929\pi$$
−0.886585 + 0.462566i $$0.846929\pi$$
$$674$$ 24.2487i 0.934025i
$$675$$ 5.00000 0.192450
$$676$$ 11.0000 6.92820i 0.423077 0.266469i
$$677$$ −6.00000 −0.230599 −0.115299 0.993331i $$-0.536783\pi$$
−0.115299 + 0.993331i $$0.536783\pi$$
$$678$$ 10.3923i 0.399114i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 17.3205i 0.663723i
$$682$$ 20.7846i 0.795884i
$$683$$ 31.1769i 1.19295i 0.802631 + 0.596476i $$0.203433\pi$$
−0.802631 + 0.596476i $$0.796567\pi$$
$$684$$ 3.46410i 0.132453i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 6.92820i 0.264327i
$$688$$ 20.0000 0.762493
$$689$$ 6.00000 + 20.7846i 0.228582 + 0.791831i
$$690$$ 0 0
$$691$$ 45.0333i 1.71315i 0.516024 + 0.856574i $$0.327412\pi$$
−0.516024 + 0.856574i $$0.672588\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ 62.3538i 2.36692i
$$695$$ 0 0
$$696$$ 10.3923i 0.393919i
$$697$$ 41.5692i 1.57455i
$$698$$ −12.0000 −0.454207
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ −42.0000 −1.58632 −0.793159 0.609015i $$-0.791565\pi$$
−0.793159 + 0.609015i $$0.791565\pi$$
$$702$$ 6.00000 1.73205i 0.226455 0.0653720i
$$703$$ 24.0000 0.905177
$$704$$ 3.46410i 0.130558i
$$705$$ 0 0
$$706$$ 60.0000 2.25813
$$707$$ 0 0
$$708$$ 10.3923i 0.390567i
$$709$$ 6.92820i 0.260194i 0.991501 + 0.130097i $$0.0415289\pi$$
−0.991501 + 0.130097i $$0.958471\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ −12.0000 −0.449719
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 10.3923i 0.388108i
$$718$$ −30.0000 −1.11959
$$719$$ −24.0000 −0.895049 −0.447524 0.894272i $$-0.647694\pi$$
−0.447524 + 0.894272i $$0.647694\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 12.1244i 0.451222i
$$723$$ 13.8564i 0.515325i
$$724$$ −10.0000 −0.371647
$$725$$ 30.0000 1.11417
$$726$$ 1.73205i 0.0642824i
$$727$$ −16.0000 −0.593407 −0.296704 0.954970i $$-0.595887\pi$$
−0.296704 + 0.954970i $$0.595887\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −24.0000 −0.887672
$$732$$ −2.00000 −0.0739221
$$733$$ 34.6410i 1.27950i 0.768585 + 0.639748i $$0.220961\pi$$
−0.768585 + 0.639748i $$0.779039\pi$$
$$734$$ 27.7128i 1.02290i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −36.0000 −1.32608
$$738$$ −12.0000 −0.441726
$$739$$ 38.1051i 1.40172i 0.713299 + 0.700860i $$0.247200\pi$$
−0.713299 + 0.700860i $$0.752800\pi$$
$$740$$ 0 0
$$741$$ −12.0000 + 3.46410i −0.440831 + 0.127257i
$$742$$ 0 0
$$743$$ 3.46410i 0.127086i −0.997979 0.0635428i $$-0.979760\pi$$
0.997979 0.0635428i $$-0.0202399\pi$$
$$744$$ −6.00000 −0.219971
$$745$$ 0 0
$$746$$ 38.1051i 1.39513i
$$747$$ 3.46410i 0.126745i
$$748$$ 20.7846i 0.759961i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 17.3205i 0.631614i
$$753$$ 12.0000 0.437304
$$754$$ 36.0000 10.3923i 1.31104 0.378465i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 22.0000 0.799604 0.399802 0.916602i $$-0.369079\pi$$
0.399802 + 0.916602i $$0.369079\pi$$
$$758$$ −30.0000 −1.08965
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 48.4974i 1.75803i −0.476794 0.879015i $$-0.658201\pi$$
0.476794 0.879015i $$-0.341799\pi$$
$$762$$ 13.8564i 0.501965i
$$763$$ 0 0
$$764$$ −24.0000 −0.868290
$$765$$ 0 0
$$766$$ 6.00000 0.216789
$$767$$ −36.0000 + 10.3923i −1.29988 + 0.375244i
$$768$$ 19.0000 0.685603
$$769$$ 27.7128i 0.999350i 0.866213 + 0.499675i $$0.166547\pi$$
−0.866213 + 0.499675i $$0.833453\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 0 0
$$773$$ 13.8564i 0.498380i −0.968455 0.249190i $$-0.919836\pi$$
0.968455 0.249190i $$-0.0801644\pi$$
$$774$$ 6.92820i 0.249029i
$$775$$ 17.3205i 0.622171i
$$776$$ −24.0000 −0.861550
$$777$$ 0 0
$$778$$ 31.1769i 1.11775i
$$779$$ 24.0000 0.859889
$$780$$ 0 0
$$781$$ 12.0000 0.429394
$$782$$ 0 0
$$783$$ 6.00000 0.214423
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 20.7846i 0.741362i
$$787$$ 10.3923i 0.370446i −0.982697 0.185223i $$-0.940699\pi$$
0.982697 0.185223i $$-0.0593007\pi$$
$$788$$ 0 0
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 6.00000 0.213201
$$793$$ 2.00000 + 6.92820i 0.0710221 + 0.246028i
$$794$$ −60.0000 −2.12932
$$795$$ 0 0
$$796$$ 16.0000 0.567105
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$